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<?xml version="1.0"?>
<!DOCTYPE archimedes SYSTEM "../dtd/archimedes.dtd">
<archimedes xmlns:xlink="http://www.w3.org/1999/xlink">      <info>
        <author>Fabri, Honor&eacute;</author>
        <title>Tractatus physicus de motu locali</title>
        <date>1646</date>
        <place>Lyon</place>
        <translator/>
        <lang>la</lang>
        <cvs_file>fabri_tract_026_la_1646.xml</cvs_file>
        <cvs_version/>
        <locator>026.xml</locator>
</info>      <text>          <front>                    <section>       <pb xlink:href="026/01/001.jpg"/><p type="main">

<s><emph type="center"/>TRACTATVS <lb/>PHYSICVS <lb/>DE MOTV LOCALI, <lb/><emph type="italics"/>IN QVO<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>EFFECTVS OMNES, QVI AD IMPETVM, <lb/>Motum naturalem, violentum, &amp; mixtum pertinent, <lb/>explicantur, &amp; ex principiis Phy&longs;icis <lb/>demon&longs;trantur.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Auctore<emph.end type="italics"/> PETRO MOVSNERIO <emph type="italics"/>Doctore Medico:<emph.end type="italics"/><lb/>CVNCTA EXCERPTA<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Ex pr&aelig;lectionibus<emph.end type="italics"/> R. P. HONORATI FABRY, <lb/><emph type="italics"/>Societatis<emph.end type="italics"/> IESV.<emph.end type="center"/></s></p><figure id="id.026.01.001.1.jpg" xlink:href="026/01/001/1.jpg"/><p type="main">

<s><emph type="center"/><emph type="italics"/>LVGDVNI,<emph.end type="italics"/><lb/>Apud IOANNEM CHAMPION, <lb/>in foro Cambij.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>M. </s>

<s>D C. XLVI.<emph.end type="italics"/><lb/>Cum Priuilegio Regis, &amp; Approbatione Doctorum.<emph.end type="center"/></s></p><pb xlink:href="026/01/002.jpg"/><pb xlink:href="026/01/003.jpg"/><figure id="id.026.01.003.1.jpg" xlink:href="026/01/003/1.jpg"/><p type="main">

<s><emph type="center"/>AMPLISSIMO, <lb/>NOBILISSIMOQVE DOMINO,<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>D. PETRO DE SEVE, <lb/>DOMINO DE FLECHERES, <lb/>SANCTIORIS CONSILII REGIS <lb/>Con&longs;iliario, in Lugdunen&longs;i Curia Pr&aelig;tori prima&shy;<lb/>rio, &amp; &longs;ecund&ugrave;m Mercatorum Pr&aelig;po&longs;ito, &amp;c.<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/>PETRVS MOVSNERIVS,<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>TIBI alterum no&longs;tr&aelig; Philo&longs;o&shy;<lb/>phi&aelig; f&oelig;tum in&longs;cribo, cui iam <lb/>primum in&longs;crip&longs;i<emph.end type="italics"/> (PR&AElig;TOR <lb/>AMPLISSIME) <emph type="italics"/>nempe idem <lb/>e&longs;&longs;e debeo, quia tu &longs;emper idem <lb/>es: non muta&longs;ti merita, non mu&shy;<lb/>tabo officia: multos non expo&longs;cam Patronos, qui <lb/>iam omnium optimum, &amp; meriti&longs;simum habeo; neo <lb/>enim &longs;acra Philo&longs;ophi&aelig; anathemata rudi, &amp; ru&shy;<lb/>&longs;tico muro appendam, qu&aelig; ex &longs;acro tholo templi <lb/>Themidos am&oelig;niter pendent: Nec leuem toti rei li&shy;<lb/>terari&aelig; iniuriam inferrem, &longs;i alium illi, qu&agrave;m li-<emph.end type="italics"/><pb xlink:href="026/01/004.jpg"/><emph type="italics"/>teratum Mec&aelig;natem accer&longs;erem: &amp; ver&ograve; Tracta&shy;<lb/>tum hunc de Motu Locali, alteri qu&agrave;m tibi in&longs;cri&shy;<lb/>bere non debui, cuius imperia Ludgunen&longs;is orbis, po&shy;<lb/>ti&ugrave;s qu&agrave;m vrbis, componunt: Tu prudens Intelli&shy;<lb/>gentia, huic orbi &longs;emper a&longs;si&longs;tis; ita motibus in&shy;<lb/>uigilas, vt quieti public&aelig; con&longs;ulas, remque ita pu&shy;<lb/>blicam admini&longs;tras, vt &longs;ingulis commoda procures: <lb/>C&aelig;ter&ugrave;m dubitare non po&longs;&longs;um, quin hunc meu&mtail; <lb/>quantulumcumque conatum, fidemque meam ia&mtail; <lb/>tibi &longs;emel oppigneratam, &amp; nunc altero voto peni&shy;<lb/>tus ob&longs;trictam, &aelig;qui bonique &longs;is con&longs;ulturus, Val&etail;.<emph.end type="italics"/><!-- KEEP S--></s></p><pb xlink:href="026/01/005.jpg"/><figure id="id.026.01.005.1.jpg" xlink:href="026/01/005/1.jpg"/><p type="main">

<s><emph type="center"/>PR&AElig;FATIO.<emph.end type="center"/></s></p><p type="main">

<s>NIHIL habeo pr&aelig;fari (Beneuole Lector) <lb/>in gratiam huius tractatus de Motu Locali, <lb/>cuius am&oelig;nitatem &amp; vtilitatem, rerum co&shy;<lb/>piam &amp; &longs;yluam, tuo gu&longs;tui &amp; iudicio re&shy;<lb/>linquo: Multi &longs;an&egrave; hactenus in hac mate&shy;<lb/>ria feliciter de&longs;udarunt; &amp; quidem pr&aelig; c&aelig;teris magnus <lb/>ille Galileus, qui mirific&acirc;, &amp; fer&egrave; diuin&acirc; ingenij acie, <lb/>motum localem e&ograve; perduxit, qu&ograve; mortalium nemo per&shy;<lb/>duxerat; quia tamen multa omi&longs;it, qu&aelig; ad motum &longs;pe&shy;<lb/>ctant, vt nemo ne&longs;cit; nec ex principijs Phy&longs;icis mira&shy;<lb/>biles illos effectus demon&longs;trauit, &longs;ed tant&ugrave;m certis qui&shy;<lb/>bu&longs;dam proportionibus ex geometricis addixit; vt Phy&shy;<lb/>&longs;ic&aelig; con&longs;ulamus, aliam inimus viam: Geometriam qui&shy;<lb/>dem adhibemus, ad explicandas, exponenda&longs;que pr&aelig;&shy;<lb/>dictas illas proportiones, qu&aelig; motibus in&longs;unt; &longs;ed effe&shy;<lb/>ctus illos pr&aelig;dictis proportionibus affixos ad principia <lb/>Phy&longs;ica reducimus; id e&longs;t, c&ugrave;m &longs;upponamus qu&ograve;d &longs;int, <lb/>propter quid &longs;int demon&longs;tramus: in votis erat motus <lb/>omnes vno volumine complecti; id e&longs;t effectus omnes <lb/>cuiu&longs;uis potenti&aelig; motricis; tres enim agno&longs;cimus hu&shy;<lb/>iu&longs;modi potentias: primam naturalem voco, qu&aelig; e&longs;t <lb/>grauium: alteram animalem, qu&aelig; e&longs;t animantium: ter&shy;<lb/>tiam mediam, qu&aelig; ten&longs;orum e&longs;t vel compre&longs;&longs;orum: In <lb/>hoc tractatu t&ugrave;m &agrave; motu progre&longs;&longs;iuo animantium, t&ugrave;m <lb/>ab alijs motibus, qui in animato corpore, neruorum &amp; <pb xlink:href="026/01/006.jpg"/>mu&longs;culorum opera fiunt, penitus ab&longs;tinemus; c&ugrave;m &longs;ci&shy;<lb/>lic&egrave;t eas notiones &longs;upponant, qu&aelig; huius loci e&longs;&longs;e non <lb/>po&longs;&longs;unt, ab&longs;tinemus etiam &agrave; mirifica illa ten&longs;orum &amp; <lb/>compre&longs;&longs;orum vi, qu&aelig; medi&aelig; illius virtutis e&longs;t; neque <lb/>adhuc e&ograve; rem Phy&longs;icam adduximus; Sed h&icirc;c tant&ugrave;m na&shy;<lb/>turam impetus con&longs;ideramus, motus naturalis affectio&shy;<lb/>nes, violenti, mixti ex rectis, reflexi, circularis, mixti <lb/>ex circularibus, illius qui fit in planis inclinatis &longs;ur&longs;um <lb/>&amp; deor&longs;um, vibrationum funependuli, diuer&longs;arum im&shy;<lb/>pre&longs;&longs;ionum, centri percu&longs;&longs;ionis, &amp;c. </s>

<s>Fort&egrave; aliquis poten&shy;<lb/>tias mechanicas de&longs;ideraret, lineas, motus, &amp; c&aelig;le&longs;tes <lb/>&longs;piras; &longs;ed h&aelig; quidquid phy&longs;icum habent, &longs;ingulari tra&shy;<lb/>ctatui de corpore c&aelig;le&longs;ti, reliqua ver&ograve; A&longs;tronomi&aelig; con&shy;<lb/>cedunt: potenti&aelig; mechanic&aelig; ad Staticam pertinent, qua&shy;<lb/>re illarum tant&ugrave;m phy&longs;icum principium in hoc tractatu <lb/>explicamus, line&aelig; motus nihil phy&longs;icum habent. </s>

<s>Quare <lb/>ad vitandam confu&longs;ionem ad Mathe&longs;im illas remittimus, <lb/>cuius non modicam facient acce&longs;&longs;ionem; igitur &longs;ecun&shy;<lb/>dum Tomum de motu locali non expectabis, qui ne <lb/>cuncta quidem, qu&aelig; ad motum &longs;pectant comprehende&shy;<lb/>ret, &longs;ed huic &longs;tatim Metaphy&longs;icam demon&longs;tratiuam &longs;ub&shy;<lb/>necto. </s>

<s>C&aelig;ter&ugrave;m de &longs;ubtili&longs;&longs;imo i&longs;torum omnium inuen&shy;<lb/>torum auctore nihil dicam, qui cum &aelig;gr&egrave; tulerit paucula <lb/>illa qu&aelig; in prima tractatu pr&aelig;fatus &longs;um, os mihi peni&shy;<lb/>tus ob&longs;truxit: omitto etiam qu&aelig; in me quidam iniqu&egrave; <lb/>cert&egrave; rerum &aelig;&longs;timatores iactarunt: reponere po&longs;&longs;em cum <lb/>f&aelig;nore; &longs;ed nos talem con&longs;uetudinem non habemus; de&shy;<lb/>dici hactenus pati iniurias, non inferre; quod non mod&ograve; <lb/>moralis Philo&longs;ophia, &longs;ed pr&aelig;&longs;ertim Chri&longs;tiana Religio me <lb/>docet. </s></p><pb xlink:href="026/01/007.jpg"/><p type="main">

<s>Vnum e&longs;t, de quo te monitum velim (Amice Lector) <lb/>opu&longs;culum i&longs;tud non &longs;ine aliquot erratis edi potui&longs;&longs;e, <lb/>pr&aelig;&longs;ertim c&ugrave;m in a&longs;&longs;ignandis cuilibet figur&aelig; &longs;uis chara&shy;<lb/>cteribus &longs;&aelig;pi&ugrave;s peccatum &longs;it; operas excu&longs;abis in rebus <lb/>Geometricis minim&egrave; ver&longs;atos: auctor tibi &longs;um, vt errata, <lb/>qu&aelig; fideliter adnotaui ca&longs;tiges, vt deinde cum maiore <lb/>gu&longs;tu Librum hunc perlegere po&longs;&longs;is. <lb/><gap desc="hr tag"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>SYNOPSIS LIBRORVM<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>huius tractatus.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="table">

<s>TABELLE WAR HIER<!-- KEEP S--></s></p><pb xlink:href="026/01/008.jpg"/><figure id="id.026.01.008.1.jpg" xlink:href="026/01/008/1.jpg"/><p type="main">

<s><emph type="center"/><emph type="italics"/>SYNOPSIS AMPLIOR.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>BREVISSIMAM huius operis Epitomem h&icirc;c <lb/>habes (Amice Lector) quam ex The&longs;ibus no&longs;tri <lb/>Philo&longs;ophi huc traduxi, qu&aelig; tibi ampli&longs;&longs;imi <lb/>indicis loco erit. </s></p><figure id="id.026.01.008.2.jpg" xlink:href="026/01/008/2.jpg"/><p type="main">

<s><emph type="center"/><emph type="italics"/>De Impetu.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>1. IMPETVS e&longs;t qualitas exigens motum &longs;ui &longs;ubiecti: <lb/>datur impetus; quia non pote&longs;t e&longs;&longs;e alia cau&longs;a exi&shy;<lb/>gitiua motus: adde qu&ograve;d, potentia motrix e&longs;t acti&shy;<lb/>ua; igitur aliquid producit, &longs;ed non aliud qu&agrave;m <lb/>impetum, vt con&longs;tat ex dictis de motu: e&longs;t aliquid di&longs;tinctum &agrave; <lb/>&longs;ub&longs;tantia mobilis, qu&aelig; pote&longs;t e&longs;&longs;e &longs;ine impetu: non e&longs;t modus, <lb/>quia di&longs;tinguitur ab effectu &longs;uo formali &longs;ecundario: impetus non <lb/>producitur in eo mobili, quod moueri non pote&longs;t &agrave; potentia mo&shy;<lb/>trice applicata: &amp; produci tant&ugrave;m pote&longs;t, vel in omni parte, vel <lb/>in nulla; alioquin e&longs;&longs;et fru&longs;tr&agrave;; &amp; gratis ponitur ne&longs;cio quis impe&shy;<lb/>tus inefficax. </s></p><p type="main">

<s>2. Primo in&longs;tanti, quo e&longs;t impetus, non e&longs;t motus, ne &longs;imul im&shy;<lb/>petus &longs;it in duobus locis. </s>
<s>Impetus productus ad extra non produci&shy;<lb/>tur &agrave; quantitate, nec virtute re&longs;i&longs;titiua, nec ab alio, qu&agrave;m ab impe&shy;<lb/>tu, qui maxim&egrave; e&longs;t cau&longs;a connaturalis alterius impetus: agit tan&shy;<lb/>t&ugrave;m ad extra, vt tollat impedimentum: hinc, c&ugrave;m pro diuer&longs;a <lb/>applicatione &longs;it diuer&longs;um impedimentum, mod&ograve; pl&ugrave;s, mod&ograve; min&ugrave;s <lb/>agit; maxim&egrave; ver&ograve;, cum maximum e&longs;t impedimentum: hinc ictus <lb/>per lineam perpendicularem forti&longs;&longs;imus e&longs;t: port&ograve; omnes partes <lb/>impetus agunt ad extra actione communi. </s></p><p type="main">

<s>3. Impetus inten&longs;us producere pote&longs;t remi&longs;&longs;um, minoris mobi&shy;<lb/>lis in maiore; &amp; remi&longs;&longs;us inten&longs;um, maioris mobilis in minore, vt <lb/>patet; &aelig;qualis &aelig;qualem, &aelig;qualis mobilis in &aelig;quali, mod&ograve; &longs;it debi-<pb xlink:href="026/01/009.jpg"/>ta applicatio, cum maximo impedimento, quod reuer&acirc; tunc e&longs;t, <lb/>c&ugrave;m linea directionis connectit centra grauitatis vtriu&longs;que. </s>

<s>Datur <lb/>impetus alio impetu perfectior, &amp; imperfectior, &longs;ine quo non po&shy;<lb/>te&longs;t explicari natura vectis: itaque dato quocunque dari pote&longs;t per&shy;<lb/>fectior, &amp; imperfectior: quia dato quocunque motu pote&longs;t dari ve&shy;<lb/>locior, &amp; tardior. </s></p><p type="main">

<s>4. Propagatur impetus vniformiter tant&ugrave;m, c&ugrave;m omnes partes <lb/>corporis mouentur moctu recto &aelig;quali: ibi enim e&longs;t &aelig;qualis cau&longs;a, <lb/>vbi e&longs;t &aelig;qualis effectus: in motu circulari applicata potentia cen&shy;<lb/>tro vectis, producitur &aelig;qualis perfectionis vers&ugrave;s circunferentiam, <lb/>&amp; in&aelig;qualis numerus; applicata ver&ograve; potentia circunferenti&aelig;, pro&shy;<lb/>ducitur &aelig;qualis numerus, &longs;ed in&aelig;qualis perfectionis vers&ugrave;s cen&shy;<lb/>trum; quia potentia non pote&longs;t producere immediat&egrave; perfectiorem, <lb/>&amp; imperfectiorem in infinitum: eadem potentia nece&longs;&longs;aria &aelig;quali&shy;<lb/>bus temporibus, &amp; ii&longs;dem circun&longs;tantiis, producit &aelig;qualem impe&shy;<lb/>tum, &amp; in&aelig;qualibus in&aelig;qualem: e&longs;t enim h&aelig;c ratio cau&longs;&aelig; nece&longs;&shy;<lb/>&longs;ari&aelig;. </s></p><p type="main">

<s>5. Impetus innatus e&longs;t tant&ugrave;m determinatus ad lineam perpen&shy;<lb/>dicularem deor&longs;um; alioquin &longs;i ad aliam determinari po&longs;&longs;et, primo <lb/>e&longs;&longs;et &aelig;qualis motus per inclinatam, &amp; perpendicularem; corpus <lb/>graue mi&longs;&longs;um per lineam inclinatam ab eo non declinaret; im&ograve; im&shy;<lb/>petus &longs;emel productus (&longs;i liberum e&longs;&longs;et medium) non de&longs;trueretur: <lb/>qu&aelig; omnia phy&longs;icis hypothe&longs;ibus repugnant: omnis alius impetus, <lb/>etiam acqui&longs;itus motu naturali deor&longs;um, e&longs;t indifferens ad omnem <lb/>lineam, ad vitanda infinita fer&egrave; natur&aelig; incommoda. </s></p><p type="main">

<s>6. Impetus indifferens determinatur ad lineam multis modis: <lb/>prim&ograve;, &agrave; potentia motrice: &longs;ecund&ograve;, ab impetu: terti&ograve;, ab alio impe&shy;<lb/>tu concurrente; quart&ograve;, ab obice occurrente: quint&ograve;, ab ip&longs;o appli&shy;<lb/>cationis diuer&longs;o modo: qu&aelig; omnia clara &longs;unt: hinc duo impetus ad <lb/>motum mixtum &longs;&aelig;p&egrave; concurrunt, quod &longs;emper fit, ni&longs;i determina&shy;<lb/>tiones &longs;int oppo&longs;it&aelig; ex diametro. </s>

<s>Impetus e&longs;t capax inten&longs;ionis; <lb/>quia aliquando de&longs;truitur ex parte: eius exten&longs;io commen&longs;uratur <lb/>exten&longs;ioni mobilis; quod etiam c&aelig;teris qualitatibus commune e&longs;t: <lb/>impetus productus non con&longs;eruatur &agrave; cau&longs;a prim&ograve; productiua, &agrave; <lb/>qua etiam &longs;eparatus exi&longs;tit. </s></p><p type="main">

<s>7. Impetus non e&longs;t contrarius alteri ratione entitatis; quia qui&shy;<lb/>libet cum quolibet in eodem &longs;ubiecto co&euml;xi&longs;tere pote&longs;t: pugnat <lb/>tamen vnus cum alio ratione determinationis: hinc vnus impetus <lb/>pugnat cum alio ratione line&aelig; motus: hinc vnus videtur de&longs;trui ab <pb xlink:href="026/01/010.jpg"/>alio; quanquam impetus tant&ugrave;m de&longs;truitur, c&ugrave;m e&longs;t fru&longs;tr&agrave;: hinc, &longs;i <lb/>e&longs;&longs;et tant&ugrave;m vnicus in eodem mobili, &amp; liberum e&longs;&longs;et medium, <lb/>nunquam de&longs;trueretur nec vnquam dici po&longs;&longs;et functus &longs;uo mune&shy;<lb/>re; quod omnin&ograve; gratis dicitur. </s></p><p type="main">

<s>8. Hinc, &longs;i &longs;int tant&ugrave;m duo impetus in eodem mobili &aelig;quales <lb/>verbi gratia, vel ad eandem lineam determinantur, vel ad diver&longs;as; <lb/>&longs;i ad eandem, nihil impetus de&longs;truitur, &longs;ed e&longs;t dupl&ograve; velocior mo&shy;<lb/>tus; &longs;i ad diuer&longs;as, vel &longs;unt oppo&longs;it&aelig; ex diametro, vel concurrentes <lb/>faciunt angulum; &longs;i primum, vterque de&longs;truitur impetus; &longs;i &longs;e&shy;<lb/>cundum, de&longs;truitur aliquid illius, quod determinabimus in&shy;<lb/>fr&agrave;. </s>

<s>Impetus innatus nunquam de&longs;truitur: dici po&longs;&longs;et grauitas ab&shy;<lb/>&longs;oluta; &longs;altem nihil e&longs;t, quod di&longs;tingui ab illa probare po&longs;&longs;it. </s>

<s>Porr&ograve; <lb/>nunquam de&longs;truitur; quia nunquam e&longs;t fru&longs;tr&agrave;; quippe eius finis, <lb/>vel v&longs;us, non e&longs;t tant&ugrave;m motus deor&longs;um, &longs;ed grauitatio, &longs;eu ni&longs;us <lb/>quidam deor&longs;um. </s>

<s>Sed de grauitate ali&agrave;s. </s></p><figure id="id.026.01.010.1.jpg" xlink:href="026/01/010/1.jpg"/><p type="main">

<s><emph type="center"/><emph type="italics"/>De motu naturali deor&longs;um.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>1. DAtur motus naturalis grauium deor&longs;um ab intrin&longs;eco, <lb/>quippe non pote&longs;t e&longs;&longs;e, vel &agrave; vi tractrice terr&aelig; vel fila&shy;<lb/>mentis quibu&longs;dam, vel materia quadam tenui expultrice. </s>

<s>Eius finis <lb/>e&longs;t globi terre&longs;tris compactio, &amp;c. </s>

<s>E&longs;t autem motus naturalis ab <lb/>impetu: prim&ograve;, quia eius acceleratio &longs;ine impetu explicari non po&shy;<lb/>te&longs;t: &longs;ecund&ograve;, quia, c&ugrave;m graue deor&longs;um cadens imprimat impetum <lb/>in corpore occurrente, cert&egrave; debet habere impetum: nec alio ar&shy;<lb/>gumento mihi probabis, Solem e&longs;&longs;e lucidum, ignem calidum. </s></p><p type="main">

<s>2. Motus hic e&longs;t naturaliter acceleratus, &longs;cilicet, ab intrin&longs;eco; <lb/>patet experienti&acirc;. </s>

<s>Ratio e&longs;t: quia, c&ugrave;m in libero medio non impe&shy;<lb/>diatur motus, &amp; impetus productus primo in&longs;tanti non con&longs;erue&shy;<lb/>tur &longs;ecundo &agrave; cau&longs;a prim&ograve; productiua, &longs;ed ab alia, &longs;itque ip&longs;a mo&shy;<lb/>bilis &longs;ub&longs;tantia cau&longs;a nece&longs;&longs;aria; cert&egrave; &longs;ecundo in&longs;tanti producit <lb/>nouum impetum: idem dica de tertio, quarto, &amp;c. </s>

<s>igitur cre&longs;cit <lb/>cau&longs;a motus; igitur &amp; motus: qu&aelig; ratio clari&longs;&longs;ima e&longs;t: hinc &aelig;quali&shy;<lb/>bus temporibus &aelig;qualia acquiruntur velocitatis momenta; quia <lb/>cau&longs;a nece&longs;&longs;aria &aelig;qualibus temporibus, &aelig;qualem effectum produ&shy;<lb/>cit: quid clarius? </s></p><p type="main">

<s>3. Hinc non pote&longs;t cre&longs;cere hic impetus &longs;ecund&ugrave;m porportio-<pb xlink:href="026/01/011.jpg"/>nem duplicatam temporum, c&ugrave;m cre&longs;cat &longs;ecund&ugrave;m proportionem <lb/>temporum, et&iuml;am ex mente Galilei: cre&longs;cit autem velocitas, vt im&shy;<lb/>petus; effectus, &longs;cilicet, vt cau&longs;a: idem dico de motu, ratione velo&shy;<lb/>citatis; quippe motus ip&longs;e e&longs;t &longs;ua velocitas: at ver&ograve; ip&longs;a &longs;patia, <lb/>qu&aelig; decurruntur illo motu, &longs;i con&longs;ideretur crementum in in&longs;tan&shy;<lb/>tibus, cre&longs;cunt iuxta progre&longs;&longs;ionem arithmeticam &longs;implicem, <lb/>id e&longs;t, &longs;i primo in&longs;tanti, acquiritur vnum &longs;patium, &longs;ecundo acquiri&shy;<lb/>tur vnum &longs;patium, &longs;ecundo acquiruntur duo, tertio 3. quarto 4. at&shy;<lb/>que ita deinceps. </s></p><p type="main">

<s>4. Hoc autem facil&egrave; pote&longs;t <expan abbr="dem&otilde;&longs;trari">demon&longs;trari</expan>: quia, c&ugrave;m velocitas cre&longs;&shy;<lb/>cat iuxta proportionem temporum, &longs;i primo in&longs;tanti &longs;it vnus gradus <lb/>velocitatis, &longs;ecundo erunt duo, tertio tres, at que ita deinceps: igitur, <lb/>&longs;i mobile cum vno gradu velocitatis acquirit vnum &longs;patium, cert&egrave; <lb/>cum duobus acquiret duo &longs;patia, cum tribus tria, atque ita dein&shy;<lb/>ceps: debet autem vera progre&longs;&longs;io crementorum a&longs;&longs;umi in &longs;ingulis <lb/>in&longs;tantibus, quia reuer&agrave; &longs;ingulis in&longs;tantibus phy&longs;icis (nam de iis <lb/>loquor) noua fit huius crementi acce&longs;&longs;io. </s></p><p type="main">

<s>5. Quia tamen in&longs;tantia non &longs;unt &longs;en&longs;ibilia, vt Phy&longs;ic&aelig; con&longs;u&shy;<lb/>latur, qu&aelig; res &longs;en&longs;ibiles con&longs;iderat, a&longs;&longs;umi debent partes temporis <lb/>&longs;en&longs;ibiles, in quibus reuer&acirc; progre&longs;&longs;io &longs;patiorum non e&longs;t arithmeti&shy;<lb/>ca &longs;implex; &longs;ed tam prop&egrave; accedit ad hanc numerorum imparium, <lb/>1. 3. 5. 7. &amp;c. </s>

<s>quam Galileus excogitauit, vt &longs;ine &longs;crupulo h&aelig;c a&longs;&shy;<lb/>&longs;umi po&longs;&longs;it: hinc &longs;patia &longs;unt fer&egrave; vt temporum quadrata: dixi, fer&egrave;: <lb/>nam e&longs;t paul&ograve; minor proportio, c&ugrave;m tant&ugrave;m finita &longs;int in&longs;tantia <lb/>phy&longs;ica, qu&aelig; reuer&agrave; &longs;i infinita e&longs;&longs;ent in qualibet temporis &longs;en&longs;ibilis <lb/>parte, haud dubi&egrave; &longs;patia e&longs;&longs;ent omnin&ograve; in ratione duplicata tem&shy;<lb/>porum: &longs;ed, quia parum pro nihilo computatur, hanc progre&longs;&longs;io&shy;<lb/>nem Galilei deinceps v&longs;urpabimus in Phy&longs;ica. <!-- KEEP S--></s></p><p type="main">

<s>6. Hinc ratio euidens maioris ictus inflicti &agrave; corpore graui, <lb/>c&ugrave;m ex maiori altitudine cadit. </s>

<s>Sunt autem ictus, vt impetus; <lb/>impetus, vt tempora; h&aelig;c demum, vt radices &longs;patiorum &longs;en&longs;ibi&shy;<lb/>liter qu&aelig; omnia con&longs;tant ex dictis. </s>

<s>Impetus acqui&longs;itus in de&longs;cen&longs;u <lb/>e&longs;t &longs;emper imperfectior, &longs;i a&longs;&longs;umantur &longs;ingula in&longs;tantia, qu&aelig; reuer&acirc; <lb/>&longs;unt &longs;emper minora; quia motus fit &longs;emper velocior: c&ugrave;m graue <lb/>de&longs;cendit in medio, quod re&longs;i&longs;tit, min&ugrave;s accurat&egrave; &longs;eruantur pr&aelig;di&shy;<lb/>ct&aelig; proportiones, qu&aelig; in vacuo modico accurati&longs;&longs;im&egrave; &longs;eruaren&shy;<lb/>tur. </s></p><p type="main">

<s>7. Re&longs;i&longs;tentia medij non e&longs;t propter vllam formam improportio&shy;<lb/>natam, qua&longs;i ver&ograve; impetus &longs;it forma improportionata a&euml;ri: &longs;ed in <pb xlink:href="026/01/012.jpg"/>duobus pr&aelig;&longs;ertim con&longs;i&longs;tit; prim&ograve;, e&ograve; qu&ograve;d medium detrahat ali&shy;<lb/>quid grauitationis corporis grauis; &longs;ecund&ograve;, e&ograve; qu&ograve;d partes medij <lb/>aliquam implicationem habeant, qu&aelig; &longs;olui non pote&longs;t &longs;ine aliqua <lb/>compre&longs;&longs;ione, vel ten&longs;ione; vtraque autem re&longs;i&longs;tit impetui: quod <lb/>&longs;pectat ad primum, &longs;i medium &longs;it &aelig;qualis grauitatis cum ip&longs;o cor&shy;<lb/>pore, detrahitur tota grauitatio, &longs;i &longs;ubdupl&aelig; &longs;ubduplum, &amp;c. </s>

<s>de quo <lb/>ali&agrave;s. </s></p><p type="main">

<s>8. Hinc corpus graue per medium rarius, c&aelig;teris paribus, fa&shy;<lb/>cil&egrave; de&longs;cendit; non tamen ex re&longs;i&longs;tentia medij cognita, pote&longs;t co&shy;<lb/>gno&longs;ci proportio grauitatis vtriu&longs;que, propter &longs;ecundum caput, ex <lb/>quo etiam petitur re&longs;i&longs;tentia. </s>

<s>Idem corpus cum eodem medio <lb/>comparatum, habet tres coniugationes: nam, vel e&longs;t grauius, vel&shy;<lb/>e&longs;t grauius, vel &aelig;qu&egrave; graue, vel min&ugrave;s. </s>

<s>Sunt etiam tres ali&aelig; con&shy;<lb/>iugationes, &longs;cilicet, eiu&longs;dem mobilis cum diuer&longs;is mediis, duorum <lb/>mobilium cum eodem medio, duorum mobilium cum duobus <lb/>mediis. </s></p><p type="main">

<s>9. Figura corporis grauis deor&longs;um cadentis motum vel retardat <lb/>vel accelerat; retardat quidem, &longs;i plures partes medij amouend&aelig; <lb/>&longs;unt vel pauciores velociori motu; accelerat &egrave; contrario: hinc idem <lb/>corpus <expan abbr="paralleliped&utilde;">parallelipedum</expan> iuxta tres diuer&longs;os &longs;itus, triplici motu diuer&shy;<lb/>&longs;o de&longs;cendere pote&longs;t: hinc ratio, cur acuminata tam facil&egrave; de&longs;cen&shy;<lb/>dant. </s>

<s>Cubus, qui de&longs;cendit, imprimit a&euml;ri velociorem motum, <lb/>qu&agrave;m ip&longs;e habeat; &amp; qu&ograve; maior e&longs;t eius &longs;uperficies, e&ograve; velociorem. </s></p><p type="main">

<s>10. Duo globi, vel cubi eiu&longs;dem materi&aelig; &aelig;qu&egrave; velociter de&longs;&shy;<lb/>cendunt: ratio e&longs;t, quia, lic&egrave;t maioris vires habeant maiorem pro&shy;<lb/>portionem ad molem a&euml;ris re&longs;i&longs;tentis, qu&agrave;m vires minoris ad alte&shy;<lb/>ram a&euml;ris molem, qu&aelig; proprium illius motum retardat, c&ugrave;m tamen <lb/>a&euml;r, qui re&longs;i&longs;tit maiori cubo, debeat amoueri velociori motu, qu&agrave;m <lb/>a&euml;r, qui re&longs;i&longs;tit minori, &longs;itque eadem proportio re&longs;i&longs;tenti&aelig; ratione <lb/>motus, minoris ad maiorem, qu&aelig; e&longs;t ratione molis, maioris ad mi&shy;<lb/>norem; cert&egrave; ratio compo&longs;ita vtriu&longs;que erit eadem in vtroque cu&shy;<lb/>bo: igitur &aelig;qualiter de&longs;cendet vterque. </s></p><p type="main">

<s>11. Si tamen &longs;int diuer&longs;&aelig; materi&aelig;, haud dubi&egrave;, qui con&longs;tat leuio&shy;<lb/>ri materia, tardi&ugrave;s de&longs;cendet; quia eius vires habent minorem <lb/>proportionem ad re&longs;i&longs;tentiam. </s>

<s>Corpu&longs;cula etiam ex graui&longs;&longs;ima ma&shy;<lb/>teria tardi&longs;&longs;im&egrave; de&longs;cendunt: tum, quia &agrave; filamentis illis, quibus par&shy;<lb/>tes a&euml;ris implicantur, facil&egrave; detinentur; analogiam habes in lapil&shy;<lb/>lo, qui ab arane&aelig; tela intercipitur: tum, quia, c&ugrave;m lati&longs;&longs;imam ali&shy;<lb/>quando habeant &longs;uperficiem pro modica mole, minimam habent <pb xlink:href="026/01/013.jpg"/><expan abbr="proportion&etilde;">proportionem</expan> virium ad <expan abbr="re&longs;i&longs;tenti&atilde;">re&longs;i&longs;tentiam</expan>: t&ugrave;m denique, quia, c&ugrave;m modico <lb/>impetu agitari po&longs;&longs;int ab a&euml;re mobili, vnus motus alium impedit. </s></p><p type="main">

<s>12. Singulis in&longs;tantibus motus naturaliter accelerati cre&longs;cit <lb/>re&longs;i&longs;tentia; quia, c&ugrave;m motus cre&longs;cat, &aelig;qualibus temporibus, plures <lb/>partes medij occurrunt; cre&longs;cunt tamen vires in eadem proportio&shy;<lb/>ne, &longs;cilicet, impetus: igitur non mutatur progre&longs;&longs;io motus. </s>

<s>Hinc <lb/>colligo, contra Galil&aelig;um, motum rectum ex naturaliter accelerato <lb/>nunquam fieri &aelig;quabilem: dixi motum rectum; quia motus corpo&shy;<lb/>rum c&oelig;le&longs;tium ex accelerato factus e&longs;t &aelig;qualis. </s></p><figure id="id.026.01.013.1.jpg" xlink:href="026/01/013/1.jpg"/><p type="main">

<s><emph type="center"/><emph type="italics"/>De motu violento &longs;ur&longs;um.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>1. MOtus violentus &longs;ur&longs;um vulg&ograve; dicitur e&longs;&longs;e &agrave; principio ex&shy;<lb/>trin&longs;eco. </s>

<s>Triplici modo accidere pote&longs;t: prim&ograve;, &longs;i reuer&agrave; <lb/>imprimatur impetus ab extrin&longs;eco, vt, c&ugrave;m mitto lapidem &longs;ur&longs;um: <lb/>&longs;ecund&ograve;, &longs;i corpus deor&longs;um cadens deinde reflectatur &longs;ur&longs;um; tunc <lb/>autem nihil e&longs;t ab extrin&longs;eco, ni&longs;i determinatio noua, qu&aelig; e&longs;t &agrave; cor&shy;<lb/>pore reflectente: terti&ograve;, &longs;i terra vtrinque e&longs;&longs;et peruia; nam lapis haud <lb/>dubi&egrave; non &longs;i&longs;teret in centro, &longs;altem po&longs;t primum de&longs;cen&longs;um; igitur <lb/>a&longs;cenderet per eandem lineam; nullum tamen e&longs;t principium ex&shy;<lb/>trin&longs;ecum; igitur motus violentus dicit tant&ugrave;m motum &longs;ur&longs;um <lb/>corporis grauis. </s></p><p type="main">

<s>2. Dari autem motum violentum, dubium e&longs;&longs;e non pote&longs;t, qui <lb/>&longs;upponit impetum, vel impre&longs;&longs;um ab extrin&longs;eco, vel in de&longs;cen&longs;u <lb/>acqui&longs;itum, qui reuer&acirc; ine&longs;t ip&longs;i mobili, c&ugrave;m ip&longs;um medium hunc <lb/>motum poti&ugrave;s impediat, qu&agrave;m iuuet: hinc, &longs;i nullus e&longs;&longs;et impetus <lb/>extrin&longs;ecus, vel acqui&longs;itus, nullus e&longs;&longs;et motus violentus; quia im&shy;<lb/>petus innatus illius cau&longs;a e&longs;&longs;e non pote&longs;t. </s>

<s>Port&ograve; hic motus non e&longs;t <lb/>acceleratus, nec &aelig;qualis, alioquin <expan abbr="nunqu&atilde;">nunquam</expan> rediret deor&longs;um mobile. </s></p><p type="main">

<s>3. Hinc nece&longs;&longs;ari&ograve; e&longs;t retardatus: igitur de&longs;truitur impetus, non <lb/>quidem ab ip&longs;a medij re&longs;i&longs;tentia; quippe idem medium non magis <lb/>re&longs;i&longs;tit motui &longs;ur&longs;um, qu&agrave;m motui deor&longs;um, vt patet: igitur de&longs;trui&shy;<lb/>tur ille impetus motus violenti ab impetu innato aliquo modo; non <lb/>quidem vt &agrave; contrario ratione entitatis, &longs;ed ratione determinatio&shy;<lb/>nis: c&ugrave;m enim impetus innatus exigat motum deor&longs;um, &amp; alius &longs;ur&shy;<lb/>&longs;um: hic quidem pr&aelig;ualet, attamen fru&longs;tr&agrave; e&longs;t, ratione gradus <lb/>&aelig;qualis impetui innato: igitur de&longs;truitur ille gradus illo in&longs;tanti. </s></p><pb xlink:href="026/01/014.jpg"/><p type="main">

<s>4. Hinc &longs;ingulis temporibus &aelig;qualibus de&longs;truitur gradus impe&shy;<lb/>tui innato; e&longs;t enim eadem ratio pro omnibus: igitur temporibus <lb/>&aelig;qualibus de&longs;truitur &aelig;qualis impetus: igitur amittit ille motus <lb/>&aelig;qualia velocitatis momenta: igitur e&longs;t naturaliter retardatus: igi&shy;<lb/>tur iuxta eam proportionem decre&longs;cit motus violentus, iuxtaquam <lb/>cre&longs;cit naturalis: igitur dici debent de hac progre&longs;&longs;ione retardatio&shy;<lb/>nis, qu&aelig; dicta &longs;unt de illa progre&longs;&longs;ione accelerationis. </s></p><p type="main">

<s>5. Hinc impetus imperfectior initio de&longs;truitur: quia, c&ugrave;m motus <lb/>ille &longs;it velocior initio, in&longs;tantia &longs;unt minora: atqui minori tempore <lb/>min&ugrave;s retardatur: igitur inperfectior impetus de&longs;truitur; c&ugrave;m &egrave; <lb/>contrario in motu acceleratio initio acquiratur imperfectior, quia <lb/>in&longs;tantia &longs;unt maiora: vnde vides, gradus impetus e&longs;&longs;e heteroge&shy;<lb/>neos, &amp; principium illud etiam in impetu valere, &longs;cilicet, &longs;ubiectum <lb/>ita compleri ab vna forma, vt alterius homogene&aelig; non &longs;it ampli&ugrave;s <lb/>capax, &longs;altem naturaliter. </s></p><p type="main">

<s>6. Hinc vltimus gradus impetus violenti e&longs;t omnium perfecti&longs;&shy;<lb/>&longs;imus, vt con&longs;tat. </s>

<s>Quie&longs;ceret vno in&longs;tanti mobile iactum &longs;ur&longs;um, &longs;i <lb/>gradus vltimus violenti e&longs;&longs;et &aelig;qualis perfectionis, cum impetu in&shy;<lb/>nato: vbi enim ventum e&longs;&longs;et ad in&longs;tans &aelig;qualitatis, neutrum pr&aelig;&shy;<lb/>ualere po&longs;&longs;et: igitur in&longs;tanti &longs;equenti e&longs;&longs;et quies: c&ugrave;m tamen &longs;int <lb/>diuer&longs;&aelig; perfectionis, perfectior pr&aelig;ualet: vter autem &longs;it perfectior, <lb/>dicemus infr&agrave;. </s></p><p type="main">

<s>7. Cum mobile &longs;ur&longs;um reflectitur, vel terra perforata &longs;uam lineam <lb/>motus &longs;ur&longs;um versus oppo&longs;itam c&oelig;li plagam promouet, vel aliud <lb/>&aelig;qualis ponderis, vel maioris, &longs;ur&longs;um mouet, tunc certum e&longs;t, inna&shy;<lb/>tum e&longs;&longs;e perfectiorem: &longs;i ver&ograve; imprimitur ab alia potentia motrice, <lb/>tunc etiam imperfectior e&longs;t impetu innato; nam in&aelig;qualis e&longs;t; alio&shy;<lb/>quin, &longs;i e&longs;&longs;et &aelig;qualis, &longs;imul e&longs;&longs;ent in eodem &longs;ubiecto duo gradus <lb/>homogenei: pr&aelig;&longs;tat autem e&longs;&longs;e imperfectiorem, qu&agrave;m perfectio&shy;<lb/>rem, vt plura impetus puncta &agrave; potentia imprimantur; qu&ograve;d mul&shy;<lb/>tum facit ad mouenda maiora pondera: hinc nullo in&longs;tanti quie&longs;&shy;<lb/>cunt proiecta &longs;ur&longs;um. </s></p><p type="main">

<s>8. Tandiu durat &longs;en&longs;ibiliter de&longs;cen&longs;us globi proiecti &longs;ur&longs;um, <lb/>quandiu durauit a&longs;cen&longs;us; e&longs;t enim eadem ratio: &longs;agitt&aelig; ver&ograve; mi&shy;<lb/>n&ugrave;s durat a&longs;cen&longs;us, qu&agrave;m de&longs;cen&longs;us propter mixtionem materi&aelig;. </s>

<s><lb/>Si motus violentus e&longs;&longs;et &aelig;quabilis, percurreret proiectum &longs;patium <lb/>fer&egrave; duplum eo tempore, quo retardato percurrit &longs;ubduplum: hinc <lb/>&longs;onus tam cit&ograve; auditur; quia propagatur cum particulis a&euml;ris &aelig;qua&shy;<lb/>bili fer&egrave; motu: e&longs;&longs;e autem &longs;patium fer&egrave; duplum, probatur ex eo, <pb xlink:href="026/01/015.jpg"/>qu&ograve;d &longs;patium motu &aelig;quabili decur&longs;um re&longs;pondet rectangulo; de&shy;<lb/>cur&longs;um ver&ograve; motu retardato, re&longs;pondet triangulo, &longs;ubduplo rectan&shy;<lb/>guli: a&longs;&longs;umpto &longs;cilicet, &aelig;quali tempore. </s></p><p type="main">

<s>9. Vites potenti&aelig; proiicientis toto ni&longs;u re&longs;pondent velocitati <lb/>acqui&longs;it&aelig; in toto de&longs;cen&longs;u corporis proiecti; <expan abbr="tant&utilde;dem">tantundem</expan> enim <lb/>impetus in de&longs;cen&longs;u acquiritur, quant&ugrave;m in a&longs;cen&longs;u deperditur. </s>

<s><lb/>Impetus primo in&longs;tanti, quo e&longs;t, agit, &longs;i e&longs;t aliquod impedimen&shy;<lb/>tum; e&longs;t enim cau&longs;a nece&longs;&longs;aria: primo in&longs;tanti motus aliquid im&shy;<lb/>petus de&longs;truitur: &longs;iue pr&aelig;ce&longs;&longs;erit motus violentus, &longs;iue non pr&aelig;ce&longs;&shy;<lb/>&longs;erit, corpus graue &aelig;quali motu deor&longs;um cadit: re&longs;i&longs;tentia a&euml;ris e&longs;t <lb/>quidem maior initio; &longs;ed etiam &longs;unt maiores vires. </s></p><figure id="id.026.01.015.1.jpg" xlink:href="026/01/015/1.jpg"/><p type="main">

<s><emph type="center"/><emph type="italics"/>De motu in planis inclinatis.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>1. PLanum inclinatum e&longs;t &longs;ur&longs;um, vel deor&longs;um: in hoc de&longs;cen&shy;<lb/>dit corpus graue, ni&longs;i fort&egrave; retineatur ab a&longs;peritate, vel pro&shy;<lb/>pria, vel ip&longs;ius plani: impeditur autem motus naturalis in plano <lb/>pr&aelig;dicto, quia impeditur eius linea: ide&ograve; e&longs;t tardior hic motus in <lb/>plano inclinato, qu&agrave;m in perpendiculari: in ea porr&ograve; proportione <lb/>e&longs;t tardior, in qua perpendiculum e&longs;t minus linea inclinata, eiu&longs;dem <lb/>&longs;cilicet, altitudinis; quippe e&ograve; tardior e&longs;t, qu&ograve; magis impeditur, &amp; <lb/>magis impeditur, qu&ograve; maius &longs;patium decurrendum e&longs;t, ad acqui&shy;<lb/>rendam eandem altitudinem: igitur eadem e&longs;t proportio impe&shy;<lb/>dimenti, qu&aelig; &longs;patij, &amp;c. </s></p><p type="main">

<s>2. Hinc motus &longs;unt vt line&aelig; permutando: hinc mobile de&longs;cendit <lb/>per &longs;e in pr&aelig;dicto plano: licet enim motus impediatur, non tamen <lb/><expan abbr="tous">totus</expan>, impetus, qui acquiritur in eodem plano e&longs;t imperfectior ac&shy;<lb/>qui&longs;ito in perpendiculari in eadem proportione; nam impetus &longs;unt <lb/>vt motus: hinc pote&longs;t perfectio impetus imminui in infinitum, c&ugrave;m <lb/>po&longs;&longs;it e&longs;&longs;e in infinitum linea magis, ac magis inclinata: igitur mo&shy;<lb/>tum imminui po&longs;&longs;e in infinitum, non tant&ugrave;m ex vecte, &longs;ed etiam <lb/>ex planis inclinatis haberi pote&longs;t. </s></p><p type="main">

<s>3. Hinc producit impetum imperfectiorem impetus acqui&longs;itus <lb/>in hoc eodem plano, qu&agrave;m acqui&longs;itus in perpendiculari, &aelig;qualibus <lb/>&longs;cilicet temporibus, quia cau&longs;a imperfectior imperfectiorem pro&shy;<lb/>ducit effectum: motus in plano inclinato deor&longs;um e&longs;t acceleratus <lb/>iuxta eandem proportionem, iuxta quam acceleratur in perpendi-<pb xlink:href="026/01/016.jpg"/>culo: tempora, quibus percurruntur perpendiculum, &amp; linea plani <lb/>inclinati, &longs;unt vt line&aelig;; &longs;patia autem, qu&aelig; in pr&aelig;dictis lineis acqui&shy;<lb/>runtur &aelig;qualibus temporibus, &longs;unt vt motus, id e&longs;t, vt line&aelig; per&shy;<lb/>mutando, vt patet ex dictis. </s></p><p type="main">

<s>4. Ex his concludo, nece&longs;&longs;ari&ograve; per plana omnia eiu&longs;dem altitu&shy;<lb/>dinis acquiri eandem velocitatem, quantumuis a&longs;&longs;umantur longi&longs;&shy;<lb/>&longs;ima, mod&ograve; &longs;cilicet perpendicula &longs;int &longs;emper parallela. </s>

<s>Hinc habes <lb/>apud Galileum, per omnes chordas circuli erecti de&longs;cen&longs;um fieri <lb/>&aelig;qualibus temporibus. </s>

<s>Vires, qu&aelig; &longs;u&longs;tinent pondus in plano in&shy;<lb/>clinato per lineam plano <expan abbr="parallel&atilde;">parallelam</expan>, &longs;unt ad eas, qu&aelig; &longs;u&longs;tinent in per&shy;<lb/>pendiculo, vt line&aelig; permutando; quia debent ad&aelig;quare impetum, <lb/>qui producitur, t&ugrave;m in plano inclinato, t&ugrave;m in perpendiculo. </s></p><p type="main">

<s>5. Porr&ograve; min&ugrave;s grauitat in ip&longs;um planum inclinatum corpus gra&shy;<lb/>ue, qu&agrave;m in planum horizontale: e&longs;t autem grauitatio in horizonta&shy;<lb/>li, &longs;eu Tangente, ad grauitationem in inclinata, &longs;eu &longs;ecante, vt ip&longs;&aelig; <lb/>line&aelig; permutando: quod facil&egrave; demon&longs;tramus. </s>

<s>Proiicitur mobile <lb/>facili&ugrave;s per inclinatum planum &longs;ur&longs;um, qu&agrave;m per ip&longs;am perpendi&shy;<lb/>cularem: patet experientia: cuius ratio e&longs;t, quia min&ugrave;s re&longs;i&longs;tit im&shy;<lb/>petus innatus, cuius minor e&longs;t ni&longs;us per inclinatam, vt con&longs;tat ex <lb/>dictis. </s></p><p type="main">

<s>6. Ill&aelig; vires, qu&aelig; &longs;ufficiunt ad eum motum &longs;ur&longs;um in perpendi&shy;<lb/>culo, &longs;ufficiunt ad motum &longs;ur&longs;um in plano inclinato eiu&longs;dem alti&shy;<lb/>tudinis: quia ill&aelig; vires &longs;ufficiunt ad a&longs;cen&longs;um, qu&aelig; acquiruntur in <lb/>toto de&longs;cen&longs;u: &longs;ed in de&longs;cen&longs;u inclinat&aelig;, &amp; perpendiculi acquirun&shy;<lb/>tur vires &aelig;quales, id e&longs;t, velocitas &aelig;qualis, vt dictum e&longs;t &longs;upr&agrave;. </s>

<s>Om&shy;<lb/>nia puncta plani inclinati rectilinei, im&ograve; &amp; horizontalis, &longs;unt di&shy;<lb/>uer&longs;&aelig; inclinationis: in iis tamen planis inclinatis qu&aelig; vulg&ograve; a&longs;&longs;u&shy;<lb/>muntur, non mutatur &longs;en&longs;ibiliter inclinatio. </s></p><p type="main">

<s>7. Hinc min&ugrave;s de&longs;truitur impetus in plano inclinato &longs;ur&longs;um, <lb/>qu&agrave;m in perpendiculo; quia diuti&ugrave;s durat: c&ugrave;m enim min&ugrave;s ac&shy;<lb/>quiratur in de&longs;cen&longs;u, vt dictum e&longs;t, min&ugrave;s etiam de&longs;truitur in a&longs;&shy;<lb/>cen&longs;u: hinc accedit propri&ugrave;s hic motus ad &aelig;quabilem: in eodem <lb/>plano rectilineo pote&longs;t e&longs;&longs;e a&longs;cen&longs;us, &amp; de&longs;cen&longs;us, vers&ugrave;s eandem <lb/>partem: tale e&longs;&longs;et planum horizontale, in cuius vnico tant&ugrave;m pun&shy;<lb/>cto nulla e&longs;t inclinatio: in quolibet puncto huius plani e&longs;t &longs;ingu&shy;<lb/>laris inclinatio, vt patet, qu&aelig; e&longs;t ad perpendiculum, vt Tangens ad <lb/>&longs;ecantem &eacute;&longs;tque eadem proportio motuum. </s></p><p type="main">

<s>8. Corpus graue in &longs;uperficie quadrantis caua, deor&longs;um cadit <lb/>motu naturaliter accelerato; quia &longs;ingulis in&longs;tantibus accedit nouus <pb xlink:href="026/01/017.jpg"/>impetus; non tamen &aelig;qualibus temporibus, acquiruntur &aelig;qualia <lb/>velocitatis momenta; quia in &longs;ingulis punctis quadrantis, e&longs;t diuer&shy;<lb/>&longs;a tangens; igitur mutatur progre&longs;&longs;io accelerationis, qu&aelig; cert&egrave; ma&shy;<lb/>jor e&longs;t initio, &amp; &longs;ub finem minor; quia initio tangentes acce&shy;<lb/>dunt propri&ugrave;s ad perpendiculum, &amp; &longs;ub finem ad horizonta<lb/>lem. </s></p><p type="main">

<s>9. De&longs;cendit etiam in &longs;uperficie conuexa globi erecti motu ac&shy;<lb/>celerato; initio quidem, in minore proportione; &longs;ub finem, in maio&shy;<lb/>re; vnde e&longs;t inuer&longs;a prioris: pote&longs;t etiam de&longs;cendere corpus graue <lb/>v&longs;que ad centrum terr&aelig; motu accelerato, in &longs;uperficie conuexa &longs;e&shy;<lb/>micirculi: &longs;i &longs;uperficies terr&aelig; e&longs;&longs;et l&aelig;uigati&longs;&longs;ima, corpus proje&shy;<lb/>ctum moueretur in ea motu &aelig;quabili, nec de&longs;trueretur impetus im&shy;<lb/>pre&longs;&longs;us, vt con&longs;tat; pote&longs;t quoque de&longs;cendere per &longs;piralem: &longs;unt in&shy;<lb/>finita plana curua, in quibus facili&ugrave;s moueri pote&longs;t, quam in ho&shy;<lb/>rizontali recta. </s></p><figure id="id.026.01.017.1.jpg" xlink:href="026/01/017/1.jpg"/><p type="main">

<s><emph type="center"/><emph type="italics"/>De motu mixto ex rectis.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>1. DAri motum mixtum ille non dubitat, qui di&longs;cum proiicit. </s>

<s><lb/>Mixtus ex duobus rectis &aelig;quabilibus e&longs;t rectus, e&longs;t que <lb/>diagonalis vtriu&longs;que: hinc de&longs;truitur aliquid impetus, iuxta pro&shy;<lb/>portionem differenti&aelig; diagonalis, &amp; vtriu&longs;que lateris &longs;imul &longs;ump&shy;<lb/>ti; quia, &longs;cilicet, e&longs;t fru&longs;tr&agrave;: qu&ograve; maior e&longs;t angulus, quem faciunt li&shy;<lb/>ne&aelig; determinationum, minor e&longs;t diagonalis; igitur pl&ugrave;s impetus <lb/>de&longs;truitur, donec tandem concurrant in oppo&longs;itas lineas, tunc enim <lb/>totius impetus de&longs;truitur. </s></p><p type="main">

<s>2. <expan abbr="Qu&utilde;">Quum</expan> minor e&longs;t, vel acutior pr&aelig;dictus angulus, min&ugrave;s impetus <lb/>de&longs;truitur; quia diagonalis maior e&longs;t; donec tandem conueniant in <lb/>eandem lineam, tunc enim nihil de&longs;truitur: datur de facto hic mo&shy;<lb/>tus in rerum natura; talis e&longs;t motus nauis &agrave; duobus ventis impre&longs;&shy;<lb/>&longs;us; vel eiu&longs;dem partis a&euml;ris; im&ograve; &amp; ip&longs;ius venti: motus mixtus ex <lb/>duobus retardatis iuxta eandem progre&longs;&longs;ionem e&longs;t rectus; quia fit <lb/>per hypothenu&longs;im triangulorum proportionalium: idem dico de <lb/>duobus acceleratis. </s></p><p type="main">

<s>3. Si mixtus &longs;it ex &aelig;quali, &amp; accelerato, vel ex duobus accelera&shy;<lb/>tis in diuer&longs;a progre&longs;&longs;ione, vel ex duobus retardatis &longs;imiliter, fit per <lb/>lineam curuam, vt patet: dum proiicitur corpus graue per horizon-<pb xlink:href="026/01/018.jpg"/>talem in medio libero e&longs;t motus mixtus ex accelerato naturali, &amp; <lb/>retardato violento: e&longs;t enim acceleratus naturalis, c&ugrave;m deor&longs;um <lb/>deor&longs;um tendat qua&longs;i per gradus, &longs;eu diuer&longs;a plana inclinata. </s></p><p type="main">

<s>4. Non tamen impetus acqui&longs;itus in eo motu e&longs;t eiu&longs;dem perfe&shy;<lb/>ctionis cum illo, qui acquireretur in perpendiculari eiu&longs;dem longi&shy;<lb/>tudinis; &longs;ed tant&ugrave;m eiu&longs;dem altitudinis: nam perinde cre&longs;cit ille <lb/>impetus, atque cre&longs;ceret in diuer&longs;is planis inclinaris: impetus ver&ograve; <lb/>violentus in hoc motu retardatur; t&ugrave;m, quia, &longs;i maneret idem, maior <lb/>e&longs;&longs;et ictus &longs;ub finem iactus, quod e&longs;t ridiculum; nec e&longs;t, qu&ograve;d aliqui <lb/>dicant, ab a&euml;re de&longs;trui, qui non min&ugrave;s re&longs;i&longs;tit naturali, qu&agrave;m vio&shy;<lb/>lento. </s></p><p type="main">

<s>5. Adde, qu&ograve;d e&longs;t duplex determinatio: igitur aliquid de&longs;trui de&shy;<lb/>bet, non acqui&longs;iti; igitur impre&longs;&longs;i: de&longs;trui autem non dicitur acqui&shy;<lb/>&longs;itus, qu&ograve;d, &longs;cilicet, pl&ugrave;s de nouo accedat, qu&agrave;m pereat; e&longs;t enim ac&shy;<lb/>celeratus: adde, qu&ograve;d non infligitur tantus ictus &longs;ub finem; igitur <lb/>de&longs;truitur aliquid impetus, non acqui&longs;iti, eo modo, quo diximus; <lb/>igitur impre&longs;&longs;i: ita tamen &longs;en&longs;im de&longs;truitur, vt pro &aelig;quabili per ali&shy;<lb/>quod &longs;patium qua&longs;i haberi po&longs;&longs;it. </s></p><p type="main">

<s>6. Hinc mobile proiectum per horizontalem, ne primo quidem <lb/>in&longs;tanti per horizontalem mouetur, alioqui non e&longs;&longs;et motus mix&shy;<lb/>tus: tardi&ugrave;s cadit mobile ita proiectum in plan&ugrave;m horizontale &longs;ub&shy;<lb/>iectum, qu&agrave;m cum &longs;ua &longs;ponte, ex eadem altitudine de&longs;cendit: cuius <lb/>rei clari&longs;&longs;ima e&longs;t experientia: ratio e&longs;t; quia impetus acqui&longs;itus in <lb/>hoc iactu non e&longs;t eiu&longs;dem perfectionis, c&ugrave;m acqui&longs;ito in perpendi&shy;<lb/>culo: c&ugrave;m proiicitur mobile per inclinatam &longs;ur&longs;um, mouetur motu <lb/>mixto ex naturali &aelig;quabili, &amp; violento retardato: patet prima pars; <lb/>quia acceleratur tant&ugrave;m naturalis deor&longs;um, &longs;altem in inclinata: &longs;e&shy;<lb/>cunda pars etiam patet; quia &longs;ub finem minor e&longs;t ictus. </s></p><p type="main">

<s>7. Hinc linea motus e&longs;t curua: iuxta diuer&longs;am progre&longs;&longs;ionem de&shy;<lb/>&longs;truitur hic impetus impre&longs;&longs;us: t&ugrave;m pro diuer&longs;a inclinatione plani, <lb/>cuius etiam h&icirc;c habetur ratio; nam &longs;ingulis in&longs;tantibus mutatur: <lb/>t&ugrave;m, quia mod&ograve; pl&ugrave;s impetus e&longs;t fru&longs;tr&agrave;, mod&ograve; min&ugrave;s; pl&ugrave;s <lb/>cert&egrave;, c&ugrave;m linea determinationis impetus impre&longs;&longs;i facit obtu&shy;<lb/>&longs;iorem: atqui initio e&longs;t obtu&longs;ior; &longs;ub finem ver&ograve; a&longs;cen&longs;us acu&shy;<lb/>tior. </s></p><p type="main">

<s>8. A&longs;cen&longs;us proiecti per inclinatam diuti&ugrave;s durat, qu&agrave;m de&longs;&shy;<lb/>cen&longs;us, ratione eiu&longs;dem plani horizontalis; quia, &longs;cilicet, a&longs;&shy;<lb/>cen&longs;us longior e&longs;t, qu&agrave;m de&longs;cen&longs;us: e&longs;t autem longior; quia, vt <lb/>e&longs;&longs;et &aelig;qualis, nihil impetus impre&longs;&longs;i deberet de&longs;trui in a&longs;cen&longs;u <pb xlink:href="026/01/019.jpg"/>porr&ograve; in de&longs;cen&longs;u e&longs;t motus mixtus ex accelerato naturali, <lb/>&amp; retardato violento, vt con&longs;tat ex dictis: iactus per incli&shy;<lb/>natam ad angulum 45. e&longs;t omnium maximus, ratione eiu&longs;dem <lb/>plani horizontalis: clara e&longs;t experientia. </s>

<s>Ratio e&longs;t: quia per verti&shy;<lb/>calem &longs;ur&longs;um, nihil acquiritur in plano horizontali, ex quo fit ia&shy;<lb/>ctus; nihil etiam per ip&longs;am horizontalem; igitur pl&ugrave;s acquiritur per <lb/>illam, qu&aelig; maxim&egrave; ab vtraque &longs;imul recedit. </s></p><p type="main">

<s>9. H&aelig;c ratio e&longs;t ver&egrave; phy&longs;ica, geometrica nulla e&longs;t: hinc illi <lb/>iactus &aelig;quale &longs;patium acquirunt in pr&aelig;dicto plano horizontali, <lb/>qui fiunt per inclinatas &aelig;qualiter &agrave; pr&aelig;dicta inclinata ad ang. 45. <lb/>di&longs;tantes. </s>

<s>C&ugrave;m emittitur mobile per inclinatum deor&longs;um, in libero <lb/>medio, mouetur motu mixto ex naturali accelerato, &amp; impre&longs;&shy;<lb/>&longs;o retardato, vt con&longs;tat ex dictis; ille autem primus accelera&shy;<lb/>tur per acce&longs;&longs;ionem impetus perfectionis qu&agrave;m in iactu per ho&shy;<lb/>rizontalem; &longs;ed imperfectionis, qu&agrave;m in perpendiculo: retarda&shy;<lb/>tur ver&ograve; impetus min&ugrave;s, qu&agrave;m in iactu per horizontalem; pl&ugrave;s ve&shy;<lb/>r&ograve;, qu&agrave;m in iactu per ip&longs;um perpendiculum, in quo nihil impetus <lb/>de&longs;truitur. </s></p><p type="main">

<s>10. C&ugrave;m &egrave; naui mobili &longs;ur&longs;um mittitur corpus graue, e&longs;t motus <lb/>mixtus ex tribus, in a&longs;cen&longs;u, &longs;cilicet, ex naturali &aelig;quabili, ex verti&shy;<lb/>cali retardato, &amp; horizontali &aelig;quabili: mouetur &longs;ur&longs;um per cur&shy;<lb/>uam, &longs;emp&eacute;rque capiti iaculatoris imminet; quippe tant&ugrave;m acqui&shy;<lb/>rit in horizontali, quant&ugrave;m nauis: in de&longs;cen&longs;u ver&ograve; e&longs;t motus <expan abbr="mix&shy;">mixtus</expan> <lb/>ex horizontali retardato, &amp; naturali accelerato: quia tamen bre&shy;<lb/>ui&longs;&longs;imo illo tempore, retardatio illa horizontalis non e&longs;t &longs;en&longs;ibilis, <lb/>fer&egrave; in ip&longs;ius iaculatoris caput de&longs;cendit; quod cert&egrave; ph&aelig;nomenon <lb/>ex no&longs;tris principiis euincitur. </s></p><p type="main">

<s>11. Parum caut&egrave; Vfanus vniuer&longs;im a&longs;&longs;erit, iaculationem pil&aelig; ex&shy;<lb/>tormento, maiorem e&longs;&longs;e ex naui in continentem, &amp; minorem vi&shy;<lb/>ci&longs;&longs;im, c&ugrave;m vtriu&longs;que differentia peti po&longs;&longs;it, vel &agrave; puluere tormen&shy;<lb/>tario, vel ab eius compre&longs;&longs;ione, vel humiditate, vel tormenti fabri&shy;<lb/>ca, vel ip&longs;ius demum nauigij motu, qui pil&aelig; motum, vel accelerat, &longs;i <lb/>vers&ugrave;s eandem partem e&longs;t, vel retardat &egrave; contrario: in plano ho&shy;<lb/>rizontali duro pote&longs;t e&longs;&longs;e motus mixtus ex duobus, tribus, qua&shy;<lb/>tuor, &amp; pluribus aliis. </s></p><p type="main">

<s>12. C&ugrave;m &egrave; naui mobili emittitur &longs;agitta per horizontalem, qu&aelig; fa&shy;<lb/>cit angelum rectum cum linea directionis nauis, fertur qua&longs;i per dia&shy;<lb/>gonalem vtriu&longs;que, &longs;altem per aliquod &longs;patium: c&ugrave;m ver&ograve; emitti-<pb xlink:href="026/01/020.jpg"/>tur per horizontalem, qu&aelig; conueniat cum eadem linea directionis, <lb/>iactus e&longs;t longior toto illo &longs;patio, quod nauis decurrit, dum iactus <lb/>durat; breuior tamen, &longs;i in partem oppo&longs;itam fiat iactus in hoc ca&shy;<lb/>&longs;u, &longs;i nauis &aelig;qualem impetum imprimeret, deor&longs;um rect&agrave; ferretur <lb/>mobile motu naturali; im&ograve; &longs;agitta po&longs;&longs;et retorqueri in iaculatorem: <lb/>&longs;i terra e&longs;&longs;et vtrimque peruia, lapis demi&longs;&longs;us per multa annorum <lb/>millia libraretur; non tamen e&longs;&longs;et motuus perpetuus. </s></p><figure id="id.026.01.020.1.jpg" xlink:href="026/01/020/1.jpg"/><p type="main">

<s><emph type="center"/><emph type="italics"/>De motu reflexo.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>1. MOtus reflexi vera cau&longs;a e&longs;t impetus prior, ad nouam li&shy;<lb/>neam determinatus ab occurrente obice; planum refle&shy;<lb/>ctens e&longs;t cau&longs;a nou&aelig; determinationis &longs;uo modo; cau&longs;am enim di&shy;<lb/>co eam, ex qua aliquid &longs;equitur: ex gemina determinatione, noua, <lb/>&longs;cilicet, per ip&longs;am perpendicularem erectam in puncto contactus, <lb/>&amp; priore per lineam incidenti&aelig;, ab eodem puncto contactus pro&shy;<lb/>pagatam, fit determinatio mixta per lineam reflexionis; qu&aelig; omnia <lb/>patent ex terminis: hinc nullus impetus producitur &agrave; plano refle&shy;<lb/>ctente; quippe prior pote&longs;t determinari ad nouam lineam: adde, <lb/>qu&ograve;d planum, quod caret impetu, impetum producere non pote&longs;t. </s></p><p type="main">

<s>2. Im&ograve; nihil impetus de&longs;truitur in reflexione pura per &longs;e; quia ni&shy;<lb/>hil impetus e&longs;t fru&longs;tr&agrave; per &longs;e in pura reflexione; multus tamen im&shy;<lb/>petus de&longs;truitur per accidens, t&ugrave;m ab ip&longs;o attritu t&ugrave;m mollitie <lb/>&amp; ce&longs;&longs;ione, t&ugrave;m pre&longs;&longs;ione: hinc &longs;uppo&longs;ito eodem iactu, perpendi&shy;<lb/>cularis reflexa e&longs;t omnium reflexarum minima; quia per eam li&shy;<lb/>neam maximus ictus infligitur; igitur maxima e&longs;t partium colli&longs;io, <lb/>&amp; pre&longs;&longs;io: hinc etiam corpora duriora longi&ugrave;s reflectuntur, per ip&longs;am <lb/>quoque <expan abbr="perpendicular&etilde;">perpendicularem</expan>, dum planum reflectens &longs;it &aelig;qu&egrave; durum. </s></p><p type="main">

<s>3. Determinatio noua dupla e&longs;t prioris, po&longs;ita linea incidenti&aelig; <lb/>perpendiculari, &amp; po&longs;ito etiam plano reflectente immobili; quia <lb/>alioquin anguli reflexionis non e&longs;&longs;ent &aelig;quales angulis incidenti&aelig;: <lb/>&longs;i globus reflectens &longs;it &aelig;qualis impacto, &aelig;qualis e&longs;t ce&longs;&longs;io re&longs;i&longs;tenci&aelig; <lb/>c&ugrave;m &longs;it &aelig;quale agens re&longs;i&longs;tenti, perid enim reflectens re&longs;i&longs;tit, per <lb/>quod e&longs;t: igitur, &longs;i &aelig;qualis re&longs;i&longs;tit, &amp; cedit, cert&egrave; &aelig;qualiter ce&shy;<lb/>dit, &amp; re&longs;i&longs;tit: hinc noua determinatio &aelig;qualis e&longs;t priori: hinc glo&shy;<lb/>bus impactis &longs;i&longs;tit immobilis; quia ex duabus determinationibus <lb/>oppo&longs;itis neutra pr&aelig;ualet. </s></p><pb xlink:href="026/01/021.jpg"/><p type="main">

<s>4. Tantum e&longs;t ab &aelig;qualitate pr&aelig;dicta ce&longs;&longs;ionis, &amp; re&longs;i&longs;tenti&aelig;, ad <lb/>nullam ce&longs;&longs;ionem, &amp; notam re&longs;i&longs;tentiam, quantum e&longs;t ad nullam <lb/><expan abbr="re&longs;i&longs;t&etilde;tiam">re&longs;i&longs;tentiam</expan>, &amp; totam ce&longs;&longs;ionem: hinc, c&ugrave;m &agrave; tota ce&longs;&longs;ione ad &aelig;qua&shy;<lb/>litatem pr&aelig;dictam acquiratur tant&ugrave;m noua determinato &aelig;qualis <lb/>priori; igitur ab eadem &aelig;qualitate ad nullam ce&longs;&longs;ionem tantun&shy;<lb/>dem acquiritur; igitur dupla prioris, vt iam &longs;upr&agrave; dictum e&longs;t; nulla <lb/>e&longs;&longs;et re&longs;i&longs;tentia in vacuo; nulla e&longs;t ce&longs;&longs;io, c&ugrave;m ip&longs;um corpus refle&shy;<lb/>ctens nullo modo mouetur ab ictu. </s></p><p type="main">

<s>5. Determinatio noua per lineam obliquam, e&longs;t ad nouam per <lb/>lineam perpendicularem, vt &longs;inus rectus anguli incidenti&aelig;, ad &longs;i&shy;<lb/>num totum, in qualibet hypothe&longs;i; quia &longs;unt h&aelig;, vt ictus, per vtran&shy;<lb/>que lineam; ictus ver&ograve; vt grauitationes in horizontale planum, &amp; <lb/>in planum inclinatum, &longs;ub angulo complementi anguli incidenti&aelig;: <lb/>hinc noua determinatio per lineam obliquam, e&longs;t vt dupla &longs;inus re&shy;<lb/>cti anguli incidenti&aelig;, ad &longs;inum totum: hinc &longs;upra angulum inci&shy;<lb/>denti&aelig; 30, noua e&longs;t maior priore, infr&agrave; minor; in ip&longs;o angulo 30. <lb/>&aelig;qualis, &longs;uppo&longs;ita hypothe&longs;i plani reflectentis immobilis. </s></p><p type="main">

<s>6. Ex hoc po&longs;itiuo principio demon&longs;tratur accurati&longs;&longs;im&egrave; &aelig;qua&shy;<lb/>litas anguli reflexionis, &amp; incidenti&aelig;, quod cert&egrave; demon&longs;tratum <lb/>non fuit ab Ari&longs;t.
in problematis, &longs;ect. 17. problem. 4. &amp; 13. quibus <lb/>in locis fus&egrave; &longs;atis explicatur hoc Theorema, ducta comparatione, <lb/>t&ugrave;m &agrave; grauibus, qu&aelig; cadunt, t&ugrave;m ab orbibus, qu&aelig; rotantur, r&ugrave;m &agrave; <lb/>&longs;peculis: &longs;ed minim&egrave; demon&longs;tratur ex certis principiis &longs;ine petitio&shy;<lb/>ne principij. </s>

<s>In puncto reflexionis, po&longs;ita hypothe&longs;i plani immo&shy;<lb/>bilis reflectentis, nulla datur quies; quia vnum tant&ugrave;m e&longs;t conta&shy;<lb/>ctus in&longs;tans; &longs;ed eo in&longs;tanti e&longs;t motus, quo primo acquiritur locus. </s></p><p type="main">

<s>7. Omnes line&aelig; reflex&aelig; per &longs;e &longs;unt &aelig;qualis longitudinis, &amp; ab <lb/>eodem puncto contactus, ad communem peripheriam terminan&shy;<lb/>tur: &longs;i globus impactus &longs;it &aelig;qualis reflectenti, &longs;itque linea inciden&shy;<lb/>ti&aelig; obliqua qu&aelig;libet terminata ad idem punctum contactus, re&shy;<lb/>flectitur pr&aelig;dictus globus per lineam tangentem globum refle&shy;<lb/>ctentem in eodem puncto; quia h&aelig;c tangens e&longs;t diagonalis com&shy;<lb/>munis, &amp; determinatio mixta communis omnibus lineis inciden&shy;<lb/>ti&aelig;: e&longs;t tamen mod&ograve; longior, mod&ograve; breuior linea reflexa, &eacute;&longs;tque vt <lb/>vt &longs;inus complementi anguli incidenti&aelig;, ad &longs;inum totum, qui &longs;it <lb/>determinatio prior, vt facil&egrave; demon&longs;tramus. </s></p><p type="main">

<s>8. Si globus impactus &longs;it minor corpore reflectente, reflectitur <lb/>etiam per ip&longs;am perpendicularem, &amp; determinatio noua e&longs;t dupla&shy;<lb/>prioris, min&ugrave;s ratione globorum v. g. &longs;i globus impactus &longs;it &longs;ubdu-<pb xlink:href="026/01/022.jpg"/>plus, determinatio noua e&longs;t dupla prioris, min&ugrave;s vna quarta, <lb/>&amp;c. </s>

<s>ratio e&longs;t, quia in ea proportione globus reflectens cedit, in <lb/>qua mouetur, igitur tant&ugrave;m detrahitur determinationis impacto <lb/>globo, quant&ugrave;m additur motus reflectenti: at ver&ograve; noua determina&shy;<lb/>tio per lineam incidenti&aelig; obliquam, e&longs;t ad nouam per ip&longs;am per&shy;<lb/>pendicularem, vt &longs;inus rectus anguli incidenti&aelig; ad &longs;inum totum. </s></p><p type="main">

<s>9. In hac hypothe&longs;i line&aelig; reflex&aelig; omnes &longs;unt &longs;upra pr&aelig;dictam <lb/>tangentem, &longs;eu &longs;ectionem plani, maiores, vel minores, pro diuer&longs;a <lb/>men&longs;ura diagonalis: in &longs;uperiori ver&ograve; hypothe&longs;i &aelig;qualium globo&shy;<lb/>rum, &longs;unt omnes in ip&longs;a &longs;ectione plani: &longs;i denique globus impactus <lb/>&longs;it maior alio, omnes &longs;unt infra pr&aelig;dictam &longs;ectionem. </s>

<s>Porr&ograve; in hac <lb/>hypothe&longs;i vltima, determinatio noua per ip&longs;am perpendicularem <lb/>e&longs;t minor priore: hinc non mod&ograve; nulla fit reflexio in perpendicula&shy;<lb/>ri, &longs;ed linea directa vlteri&ugrave;s propagatur; quia prior determinatio <lb/>pr&aelig;ualet. </s></p><p type="main">

<s>10. Detrahitur priori portio &aelig;qualis rationi globorum; v. g. glo&shy;<lb/>bus reflectens e&longs;t &longs;ubduplus impacto de trahitur priori determina&shy;<lb/>tioni vna &longs;ecunda; e&longs;t &longs;ubquadruplus, vna quarta; atque ita dein&shy;<lb/>ceps: ratio patet ex dictis: in linea ver&ograve; incidenti&aelig; obliqua, deter&shy;<lb/>minatio e&longs;t ad determinationem in perpendiculari, vt &longs;inus rectus <lb/>anguli incidenti&aelig; ad &longs;inum totum: linea demum reflexa e&longs;t mod&ograve; <lb/>maior, mod&ograve; minor pro diuer&longs;a diagonali. </s>



</p><p type="main">

<s>11. Si duo globi &aelig;quales in &longs;e inuicem impingantur &aelig;quali mo&shy;<lb/>tu, per lineam connectentem centra, vterque &aelig;quali motu priori re&shy;<lb/>troagitur; quia &aelig;qualis in &aelig;qualis &aelig;qualem impetum imprimit: non <lb/>e&longs;t tamen motus reflexus; quia totus prior impetus de&longs;truitur, vt <lb/>patet ex dictis: &longs;i autem in&aelig;quali motu concurrant, retroaguntur <lb/>ii&longs;dem motibus, permutando; quod etiam clarum e&longs;t: hinc egre&shy;<lb/>gium paradoxum, &longs;i quod aliud con&longs;equitur, &longs;cilicet, globum A, v. <lb/>g. &aelig;qualem motum imprimere globo B, &longs;iue hic moueatur, &longs;iue <lb/>quie&longs;cat. </s>



</p><p type="main">

<s>12. Si ver&ograve; linea incidenti&aelig; &longs;it obliqua, vterque globus reflecte&shy;<lb/>tur pror&longs;us vt &agrave; plano immobili: hinc reflexio &longs;it ad angulos &aelig;qua&shy;<lb/>les, &amp; line&aelig; omnes reflexionis &longs;unt &aelig;quales: ratio e&longs;t; quia, quant&ugrave;m <lb/>detrahit globus reflectens re&longs;i&longs;tendo, tant&ugrave;m addit in partem op&shy;<lb/>po&longs;itam repellendo, po&longs;itiuo ni&longs;u, vel impetu: qu&ograve;d &longs;i alter globus <lb/>maiore, vel minore motu moueatur, vel &longs;i globi &longs;int in&aelig;quales, <lb/>cum &aelig;quali motu, vel in&aelig;quali, res etiam determinari pote&longs;t ex <lb/>pr&aelig;mi&longs;&longs;is. </s></p><pb xlink:href="026/01/023.jpg"/><p type="main">

<s>13. Cum duo globi in &longs;e&longs;e inuicem impinguntur &aelig;quali motu, <lb/>minor retroagitur velociore motu, qu&agrave;m ante moueretur, vt clarum <lb/>e&longs;t: maior ver&ograve;, &longs;i duplus e&longs;t alterius, &longs;i&longs;tit immobilis in puncto <lb/>contactus; &longs;i maior duplo &longs;uum iter pro&longs;equitur, &longs;ed tardiore mo&shy;<lb/>tu; &longs;i minor duplo, retroagitur: qu&aelig; omnia facil&egrave; ex dictis demon&shy;<lb/>&longs;trantur. </s>

<s>Pote&longs;t impetus e&longs;&longs;e &aelig;qualis alteri, &amp; pr&aelig;ualere; pote&longs;t <lb/>&aelig;qualem impetum producere hoc in&longs;tanti, &amp; &longs;tatim in&longs;tanti, quod <lb/>&longs;equitur, totus de&longs;trui. </s></p><p type="main">

<s>14. Pote&longs;t globus retroagi in plano horizontali, lic&egrave;t in aliud cor&shy;<lb/>pus non incidat, ita vt initio tendat in ortum, verbi gratia: t&ugrave;m <lb/>deinde, lic&egrave;t nihil pror&longs;us addatur, vers&ugrave;s occa&longs;um; quod accidit, <lb/>cum globus vtroque motu, centri, &longs;cilicet, &amp; orbis, mouetur, &longs;ed <lb/>contrario; prim&ugrave;m enim motus centri pr&aelig;ualet, &longs;ed facil&egrave; cedit <lb/>propter attritum maiorem partium. </s>

<s>Nullus datur propri&egrave; motus <lb/>refractus: lic&egrave;t enim incuruetur linea motus, dum per aquam &longs;u&shy;<lb/>bit mobile; h&aelig;c tamen e&longs;t reflexionis &longs;pecies. </s></p><p type="main">

<s>15. Globus reflectens, qui ab ictu alterius mouetur, non mouetur <lb/>in&longs;tanti contactus; quia impetus primo in&longs;tanti, quo e&longs;t, non mo&shy;<lb/>uetur; producitur enim impetus primo in&longs;tanti contactus: &longs;i impe&shy;<lb/>tus e&longs;&longs;et tant&ugrave;m determinatus ad vnam lineam, nulla fieri po&longs;&longs;et <lb/>reflexio, &longs;ed tant&ugrave;m repercu&longs;&longs;io; quia veri&longs;&longs;ima cau&longs;a reflexionis <lb/>con&longs;i&longs;tit in noua determinatione: per reflexionem po&longs;&longs;unt colligi <lb/>plures partes a&euml;ris &longs;onori ad Echometriam: &longs;agitta emi&longs;&longs;a per ho&shy;<lb/>rizontalem &longs;urs&ugrave;m, tantill&ugrave;m a&longs;cendit per arcum; quia tantill&ugrave;m <lb/>reflectitur ab a&euml;re. </s></p><figure id="id.026.01.023.1.jpg" xlink:href="026/01/023/1.jpg"/><p type="main">

<s><emph type="center"/><emph type="italics"/>De motu circulari.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>1. DAri motum circularem, probatur infinitis fer&egrave; experimen&shy;<lb/>tis: cuius ratio &agrave; priori e&longs;t, qu&ograve;d po&longs;&longs;int extremitates eiu&longs;&shy;<lb/>dem cylindri in partes oppo&longs;itas pelli; vnde &longs;equitur nece&longs;&longs;ari&ograve; <lb/>motus circularis; quem ij negare coguntur, qui ex punctis mathe&shy;<lb/>maticis quantitatem componunt. </s>

<s>Motus circularis in &longs;ublunaribus <lb/>oritur ex recto impedito; quia, &longs;cilicet, determinatur tant&ugrave;m im&shy;<lb/>petus ad lineam rectam: hinc quidam motus circularis e&longs;t mer&egrave; <lb/>per accidens, vt c&ugrave;m retinetur extremitas funependuli, &longs;eu <pb xlink:href="026/01/024.jpg"/>fund&aelig;, qu&aelig; &longs;i demittatur, &longs;equitur motus rectus: quidam tamen <lb/>non e&longs;t mer&egrave; peraccidens, vt c&ugrave;m pellitur extremitas cylindri in <lb/>plano horizontali; e&longs;t enim, iuxta in&longs;titutionem natur&aelig;, ad facili&shy;<lb/>tatem motus. </s></p><p type="main">

<s>2. Quippe tale e&longs;t natur&aelig; in&longs;titutum, vt eo motu corpora mo&shy;<lb/>ueantur, quo facili&ugrave;s moueri po&longs;&longs;unt: atqui c&ugrave;m pellitur altera cy&shy;<lb/>lindri extremitas, in plano horizontali put&agrave; innatantis, facili&ugrave;s <lb/>mouetur, qu&agrave;m recto, &amp; qua&longs;i minore &longs;umptu, c&ugrave;m min&ugrave;s &longs;patij <lb/>acquirat: &aelig;quali tempore: pote&longs;t dari motus circularis mixtus ex <lb/>duobus rectis, quorum vnus &longs;it, vt &longs;inus recti, alius vt ver&longs;i; vix <lb/>tamen hoc accidit vnqu&agrave;m, &longs;ed tant&ugrave;m oritur hic motus ex <lb/>determinatione per tangentem impedita, ratione alicuius puncti <lb/>immobilis. </s></p><p type="main">

<s>3. Hinc, &longs;i tollatur impedimentum, &longs;tatim per tangentem or&shy;<lb/>bis fit motus, vt patet in funda: in&aelig;qualiter partes radij pr&aelig;dicti <lb/>orbis mouentur, iuxta proportionem di&longs;tanti&aelig; maioris, &amp; minoris <lb/>&agrave; centro: hinc propagatio impetus in&aelig;qualis, de qua iam &longs;upr&agrave;, <lb/>&longs;ingulis in&longs;tantibus &amp; punctis e&longs;t noua determinatio; quia, &longs;cilicet, <lb/>&longs;ingulis punctis &longs;ua tangens re&longs;pondet: hinc, &longs;i imponatur rot&aelig; <lb/>aliud corpus, &longs;tatim abigitur, &longs;ine &longs;it in &longs;itu verticali, &longs;iue in &longs;itu ho&shy;<lb/>rizontali; hinc dum turbo rotatur, &longs;i vel aqu&aelig; guttula eius &longs;uper&shy;<lb/>ficies a&longs;pergitur, &amp; &longs;tatim di&longs;pergitur. </s></p><p type="main">

<s>4 Dari impetum in motu circulari certi&longs;&longs;imum e&longs;t: punctum phy&shy;<lb/>&longs;icum e&longs;t capax huius motus; cuius finis multiplex e&longs;t; corpus mo&shy;<lb/>uetur motu circulari circa centrum immobile cum motus centri <lb/>impeditur non tamen motus orbis, ad quem impetus facil&egrave; deter&shy;<lb/>minatur, c&ugrave;m &longs;it ad omnes lineas indifferens: adde v&longs;um vectis, <lb/>trochle&aelig;, alior&uacute;mque organorum, qui &longs;ine motu circulari e&longs;&longs;e non <lb/>pote&longs;t: omitto motum progre&longs;&longs;iuum, ips&uacute;mque brachiorum, &amp; ti&shy;<lb/>biarum v&longs;um, qui motu circulari carere non pote&longs;t. </s></p><p type="main">

<s>5. Motus circularis rot&aelig; in plano verticali e&longs;t &aelig;quabilis per &longs;e; <lb/>quia nihil e&longs;t, quod impetum &longs;emel impre&longs;&longs;um de&longs;truat: lic&egrave;t enim <lb/>&longs;ingulis in&longs;tantibus &longs;it noua determinatio, nullus tamen impetus <lb/>e&longs;t fru&longs;tr&agrave;; quippe illud &longs;patium acquiritur in linea curua, quod in <lb/>recta, &longs;i nullum e&longs;&longs;et impedimentum, percurreret: quemadmodum <lb/>enim in reflexione, qu&aelig; fit &agrave; plano immobili, nullus de&longs;truitur im&shy;<lb/>petus; ita nullus h&icirc;c de&longs;truitur; tam enim centrum illud immobile <lb/>ad &longs;e qua&longs;i trahit mobile, qu&agrave;m planum immobile &agrave; &longs;e repellit; in <lb/>quo e&longs;t perfect&egrave; analogia. </s></p><pb xlink:href="026/01/025.jpg"/><p type="main">

<s>6. Hinc per &longs;e motus circularis integri orbis e&longs;t perpetuus; de&shy;<lb/>&longs;truitur tamen per accidens, &longs;cilicet, propter attritum axis: hinc <lb/>tam diu durat hic motus: clari&longs;&longs;imum experimentum habes in tur&shy;<lb/>bine, cuius cu&longs;pis l&aelig;uigati&longs;&longs;ima in plano l&aelig;uigati&longs;&longs;imo rotatur; nec <lb/>vnquam ce&longs;&longs;aret hic motus &longs;ine pr&aelig;dicto attritu, &amp; partium a&longs;peri&shy;<lb/>tate: nec quidquam ob&longs;tat, qu&ograve;d aliqu&aelig; partes rot&aelig;, qu&aelig; in circu&shy;<lb/>lo verticali voluitur, a&longs;cendant; quia etiam aliqu&aelig; de&longs;cendunt: qua&shy;<lb/>re &longs;emper remanet perfectum &aelig;quilibrium, &amp; harum de&longs;cen&longs;us, il&shy;<lb/>larum a&longs;cen&longs;um compen&longs;at. </s>

<s>Qu&ograve; diuti&ugrave;s potentia motrix manet <lb/>applicata manubrio axis rot&aelig;, ita vt nouum &longs;emper producat im&shy;<lb/>petum, rot&aelig; motus velocior e&longs;t, atque diuti&ugrave;s durat: idem pror&longs;us <lb/>dico de rota circulo horizontali parallela. </s></p><p type="main">

<s>7. C&ugrave;m mouetur &aelig;quali ni&longs;u acus circa immobile centrum, t&ugrave;m <lb/>in plano <expan abbr="horiz&otilde;tali">horizontali</expan>, t&ugrave;m in verticali, &longs;iue &longs;it <expan abbr="l&otilde;gior">longior</expan> vna, &longs;iue breuior <lb/>alia, per &longs;e plures gyros non de&longs;cribit vna, qu&agrave;m alia; quia per &longs;e <lb/>mouetur motu &aelig;quabili: per accidens tamen &longs;ecus accidit; quippe <lb/>maior e&longs;t maioris attritus: dixi, c&ugrave;m mouetur &aelig;quali ni&longs;u; nam &longs;&aelig;p&egrave; <lb/>contingit, maiore ni&longs;u potentiam motricem agere circa maiorem; <lb/>&aelig;quali tamen tempore numerus circuitionum minoris, e&longs;t ad nu&shy;<lb/>merum circuitionum maioris per &longs;e vt acuum quadrata permu&shy;<lb/>tando; &longs;unt enim motus vt &longs;patia, &longs;pacia vt quadrata. </s></p><p type="main">

<s>8. Verbi gratia, &longs;it acus maior 2. minor 1. cert&egrave; c&ugrave;m tota area or&shy;<lb/>bis maioris &longs;it quadrupla minoris, &longs;itque area maioris, &longs;patium ma&shy;<lb/>ioris, &amp; area minoris &longs;patium minoris, haud dubi&egrave; de&longs;cribet minor <lb/>quatuor circuitiones, eo tempore, quo maior decurret vnicam: li&shy;<lb/>c&egrave;t enim extremitas minoris, qu&aelig; impellitur, habeat tant&ugrave;m du&shy;<lb/>plum impetum extremitatis maioris, &longs;itque impetus inten&longs;io in <lb/>minore, dupla inten&longs;ionis impetus in maiore; e&longs;t tamen quadrupla <lb/>illius, qu&aelig; e&longs;t in &longs;egmento maioris vers&ugrave;s centrum &aelig;quali minori <lb/>acui: porr&ograve; motus circulares &aelig;quabiles in vtraque cum eodem <lb/>impetu, &longs;unt vt motus recti. </s></p><p type="main">

<s>9. Rota in plano verticali facili&ugrave;s mouetur, qu&agrave;m in horizonta&shy;<lb/>li; quia in illo mouetur per minimam impetus, vel potenti&aelig; acce&longs;&shy;<lb/>&longs;ionem; &longs;ec&ugrave;s in i&longs;to; quippe per minimam acce&longs;&longs;ionem tollitur <lb/>&aelig;quilibrium; im&ograve; moueri pote&longs;t in plano verticali, lic&egrave;t nullus im&shy;<lb/>primatur impetus rot&aelig;, v. <!-- REMOVE S-->g. <!-- REMOVE S-->per additionem minimi ponderis, vel <lb/>momenti, vt patet; c&ugrave;m tamen in plano horizontali moueri non <lb/>po&longs;&longs;it, ni&longs;i impetus imprimatur. </s>



</p><p type="main">

<s>10. Si cylindrus in plano horizontali l&aelig;uigato in altera extremi&shy;<lb/>tate per tangentem impellatur, mouebitur motu circulati, &longs;cilicet, <pb xlink:href="026/01/026.jpg"/>faciliori, circa centrum, quod di&longs;tet ab altera extremitate vna <lb/>quarta totius cylindri: ratio e&longs;t: quia facili&ugrave;s mouetur circa illud <lb/>centrum, qu&agrave;m circa alia puncta, qu&ograve;d, &longs;cilicet, min&ugrave;s &longs;patij decur&shy;<lb/>ratur, po&longs;ito eodem &longs;emper motu alterius extremitatis, cui appli&shy;<lb/>catur immediat&egrave; potentia motrix. </s></p><p type="main">

<s>11. C&ugrave;m rota mouetur in verticali, atque pr&aelig;ponderat alter &longs;emi&shy;<lb/>circulus, haud dubi&egrave; hic pr&aelig;ponderans producit impetum in alio <lb/>&longs;emicirculo: hinc fort&egrave; e&longs;t, qu&ograve;d mirere, impetus determinatus <lb/>deor&longs;um producit alium &longs;ur&longs;um: hinc impetus vnius partis mobi&shy;<lb/>lis pote&longs;t producere &longs;imilem in alia parte continua; quod tant&ugrave;m in <lb/>hoc ca&longs;u locum habet: quando corpus incumbit plano, quod mo&shy;<lb/>uetur motu recto &aelig;quabili, ab eo non &longs;eparatur; &longs;ec&ugrave;s ver&ograve;, &longs;i in&shy;<lb/>cumbat plano, quod mouetur motu circulari. </s></p><figure id="id.026.01.026.1.jpg" xlink:href="026/01/026/1.jpg"/><p type="main">

<s><emph type="center"/><emph type="italics"/>De motu funependuli.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>1. FVnependulum de&longs;cendit per arcum motu naturaliter acce&shy;<lb/>lerato: experientia clari&longs;&longs;ima e&longs;t: c&ugrave;m enim ex maiori &longs;ubli&shy;<lb/>mitate de&longs;cendit, maiorem ictum infligit. </s>

<s>Ratio &agrave; priori e&longs;t quia <lb/>priori impetui acqui&longs;ito nouus accedit: non acceleratur in eadem <lb/>proportione, in qua &longs;upr&agrave; dictum e&longs;t accelerari in linea recta; quia <lb/>in hac acceleratur vniformiter, id e&longs;t, &aelig;qualibus temporibus, <lb/>&aelig;qualia acquiruntur velocitatis momenta; quia vel e&longs;t &longs;emper ea&shy;<lb/>dem inclinatio plani, vel idem perpendiculum: at ver&ograve; in fune&shy;<lb/>pendulo in &longs;ingulis punctis e&longs;t noua tangens; igitur noua inclina&shy;<lb/>tio plani; igitur noua ratio motus. </s></p><p type="main">

<s>2. Initio acceleratur motus per maiora crementa, &longs;ub finem per mi&shy;<lb/>nora; v.g. <!-- REMOVE S-->&longs;i dato tempore acqui&longs;iuit vnum gradum impetus initio, <lb/>&aelig;quali deinde tempore acquiret min&ugrave;s: ratio clara e&longs;t: quia, vt ac&shy;<lb/>quireret &aelig;qualem, deberet e&longs;&longs;e eadem plani inclinatio; &longs;ed &longs;emper <lb/>cre&longs;cit Inclinatio; igitur &longs;emper imminuitur impetus &aelig;quali <expan abbr="t&etilde;pore">tempore</expan> <lb/>acqui&longs;itus: acquiritur tamen &aelig;qualis velocitas in arcu, &amp; in chor&shy;<lb/>da, &longs;eu plano inclinato, eiu&longs;dem altitudinis; igitur &longs;emper cre&longs;cit <lb/>motus funependuli in de&longs;cen&longs;u, &longs;ed minoribus incrementis. </s>

</p><p type="main">

<s>3. Hinc breuiore tempore de&longs;cendit per radium perpendicula&shy;<lb/>rem, qu&agrave;m per quadrantis arcum eiu&longs;dem radij; t&ugrave;m quia breuior <lb/>e&longs;t linea; t&ugrave;m, quia in perpendiculari acceleratur motus per maiora <lb/>crementa. </s>

<s>Vibratio maior eiu&longs;dem funependuli &aelig;quali fer&egrave; tem-<pb xlink:href="026/01/027.jpg"/>pore cum minore perficitur: ratio e&longs;t: quia, c&ugrave;m fer&egrave; decurrantur <lb/>arcus iuxta &longs;ubten&longs;arum proportionem, cert&egrave; c&ugrave;m &longs;ubten&longs;&aelig; om&shy;<lb/>nes &aelig;quali tempore decurrantur, idem fer&egrave; fit in ip&longs;is arcubus: dixi <lb/>fer&egrave;: nam reuer&agrave; minor vibratio citi&ugrave;s, maior tardi&ugrave;s perficitur, vt <lb/><expan abbr="c&otilde;&longs;tat">con&longs;tat</expan> <expan abbr="experi&etilde;tia">experientia</expan>: neque dee&longs;t ratio, quam in <expan abbr="analyticc&atilde;">analyticam</expan> remittimus. </s></p><p type="main">

<s>4. Non a&longs;cendit funependulum ad eam altitudinem, ex qua pri&ugrave;s <lb/>de&longs;cenderat: clara e&longs;t experientia: neque ratio tant&ugrave;m petitur ab <lb/>a&euml;ris re&longs;i&longs;tentia; tam enim re&longs;i&longs;tit de&longs;cen&longs;ui, qu&agrave;m a&longs;cen&longs;ui; &longs;ed ex <lb/>eo, qu&ograve;d &longs;ingulis in&longs;tantibus &longs;it qu&aelig;dam pugna, inter impetum in&shy;<lb/>natum, &amp; alium determinatum ad arcum &longs;ur&longs;um: quippe impetus <lb/>innatus ad totum de&longs;cen&longs;um, &longs;ed nullo modo ad a&longs;cen&longs;um con&shy;<lb/>currit: hinc in maiori vibratione imminuitur motus, &amp; &longs;patium in <lb/>maiori proportione, qu&agrave;m in minori; quia in hac line&aelig; &longs;ingul&aelig; a&longs;&shy;<lb/>cen&longs;us qua&longs;i <expan abbr="totid&etilde;">totidem</expan> inclinat&aelig; &longs;unt inclinatiores; in illa ver&ograve; min&ugrave;s. </s></p><p type="main">

<s>5. Hinc diu vibratur funependulum per minores arcus, quippe <lb/>facilis e&longs;t a&longs;cen&longs;us per planum proxim&egrave; ad horizontale accedens: <lb/>hinc etiam in funependulo maiori diuti&ugrave;s durant huiu&longs;modi vi&shy;<lb/>brationes, idque in arcubus paul&ograve; maioribus; quia &longs;ubten&longs;&aelig; his <lb/>arcubus &longs;unt inclinatiores: hinc refutabis eos, qui dicunt, vibra&shy;<lb/>tiones funependuli in vacuo fore perpetuas: arcus vibratio&shy;<lb/>nis a&longs;cen&longs;us fit motu naturaliter retardato, &longs;ed per imminu&shy;<lb/>tiones in&aelig;quales; quia pro diuer&longs;a inclinatione plani diuer&longs;imod&egrave; <lb/>retardatur. </s></p><p type="main">

<s>6. Vltimum punctum impetus acqui&longs;itus acqui&longs;itum in de&longs;cen&longs;u, <lb/>nullo modo ad de&longs;cen&longs;um concurrit, &longs;ed ad a&longs;cen&longs;um, vnico tan&shy;<lb/>t&ugrave;m in&longs;tanti; quippe e&longs;t omnium imperfecti&longs;&longs;imum; quod reuer&agrave; &longs;i <lb/>e&longs;&longs;et eiu&longs;dem perfectionis cum innato, a&longs;cen&longs;us &aelig;qualis e&longs;t de&longs;cen&shy;<lb/>&longs;ui: &longs;i &longs;int funependula in&aelig;qualia, vibrationes non &longs;unt &aelig;qu&egrave; diu&shy;<lb/>turn&aelig;: ratio e&longs;t: quia, &longs;i a&longs;&longs;umantur, v.g. duo quadrantes in&aelig;quales, <lb/>&longs;unt eju&longs;dem inclinationis; igitur minor citi&ugrave;s percurritur. </s></p><p type="main">

<s>7. Porr&ograve; tempora vibrationum &longs;unt in ratione &longs;ubduplicata ar&shy;<lb/>cuum &longs;imilium, vel chordarum &longs;imilium, vel radiorum; id e&longs;t, vt <lb/>radices &longs;patiorum &longs;imilium: verbi gratia, &longs;it quadruplus alterius, <lb/>tempus vibrationis maioris e&longs;t duplum temporis vibrationis mino&shy;<lb/>ris; quod ita intelligendum e&longs;t, vt h&aelig;c proportio con&longs;ideretur in <lb/>partibus temporis &longs;en&longs;ibilibus, vt iam dictum e&longs;t de motu natura&shy;<lb/>liter accelerato deor&longs;um in perpendiculo, &amp; in planis inclinatis; <lb/>nam progre&longs;&longs;io arithmetica; a&longs;&longs;umpta in &longs;ingulis in&longs;tantibus, tran&shy;<lb/>&longs;it in hanc, &longs;i a&longs;&longs;umantur partes temporis &longs;en&longs;ibiles, quarum &longs;ingu&shy;<lb/>l&aelig; infinitis fer&egrave; con&longs;tent in&longs;tantibus. </s></p><pb xlink:href="026/01/028.jpg"/><p type="main">

<s>8. In maiori quadrante, circa &longs;upremam extremitatem, e&longs;t minor <lb/>inclinatio, qu&agrave;m in minore; hic enim &longs;tatim detorquetur &agrave; perpen&shy;<lb/>diculo, cum quo facit angulum maiorem: at ver&ograve; circa infirmam <lb/>extremitatem, e&longs;t maior inclinatio in maiore, qu&agrave;m in minore: hinc, <lb/>&longs;i comparetur vibratio maioris, cum vibratione minoris in modico <lb/>arcu, tempus illius e&longs;t paul&ograve; maius duplo, temporis huius; in maxi&shy;<lb/>mo arcu paul&ograve; min&ugrave;s duplo, dum, &longs;cilicet, longitudinum ratio <lb/>&longs;it quadrupla. </s></p><p type="main">

<s>9. In de&longs;cen&longs;u funependuli velocitas acqui&longs;ita e&longs;t eadem cum ea, <lb/>qu&aelig; in &longs;ubten&longs;a eiu&longs;dem arcus acquiritur: hinc &longs;unt ijdem ictus: <lb/>numerus, vibrationum non e&longs;t infinitus, lic&egrave;t in vacuo vibraretur <lb/>funependulum; quia, c&ugrave;m &longs;ingul&aelig; imminuantur, &amp; infinitis pun&shy;<lb/>ctis non con&longs;tent; tandem ad vltimam peruenitur: illa autem e&longs;t vl&shy;<lb/>tima, in cuius de&longs;cen&longs;u acquiritur tant&ugrave;m vnum punctum impetus <lb/>&longs;upra innatum; in ea tamen &longs;ententia, qu&aelig; vel infinitas partes actu, <lb/>vel infinita puncta cogno&longs;cit, cert&egrave; nunquam quie&longs;ceret funepen&shy;<lb/>dulum in vacuo vibratum. </s></p><p type="main">

<s>10. Funependulum in fine a&longs;cen&longs;us non quie&longs;cit vno in&longs;tanti; <lb/>quia impetui innato <expan abbr="n&utilde;quam">nunquam</expan> redditur &aelig;qualis acqui&longs;itus; po&longs;ita ta&shy;<lb/>men illa &aelig;qualitate, in&longs;tanti &longs;equenti e&longs;&longs;et quies: funependulum <lb/>grauius citi&ugrave;s de&longs;cendit; e&longs;t enim eadem ratio, qu&aelig; fuit pro mo&shy;<lb/>tu naturali; corpus oblongum &longs;olidum circa punctum immobile <lb/>in circulo verticali rotatum vibratur adin&longs;tat funependuli; de&longs;&shy;<lb/>cendit tamen citi&ugrave;s, qu&agrave;m funependulum eiu&longs;dem longitudinis. </s></p><p type="main">

<s>11. Ratio facilis e&longs;t; quia partes &longs;olid&aelig;, qu&aelig; accedunt propi&ugrave;s <lb/>ad extremitatem immobilem, accelerant motum aliarum, qu&aelig; <lb/>ad mobilem extremitatem accedunt; faciunt enim arcum mino&shy;<lb/>rem: hinc a&longs;cen&longs;us non peruenit ad tantam &longs;ublimitatem; quia, vt <lb/>pr&aelig;dict&aelig; partes accelerant motum aliarum in de&longs;cen&longs;u, ita retar&shy;<lb/>dant in de&longs;cen&longs;u: hinc citi&ugrave;s quie&longs;cit hoc penduli genus, qu&agrave;m <lb/>aliud: ex hoc colligo paradoxon, &longs;cilicet, corpus moueri po&longs;&longs;e &longs;ua <lb/>&longs;ponte veloci&ugrave;s in arcu deor&longs;um, qu&agrave;m in perpendiculo; v.g. <!-- REMOVE S-->&longs;i iuxta <lb/>extremitatem immobilem &longs;it nodus plumbeus, cuius vi, altera ex&shy;<lb/>tremitas longi&ugrave;s di&longs;tans deor&longs;um rapiatur. </s>

</p><figure id="id.026.01.028.1.jpg" xlink:href="026/01/028/1.jpg"/><p type="main">

<s><emph type="center"/><emph type="italics"/>De motu mixto ex circulari.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>1. ROta, qu&aelig; mouetur in &longs;uperficie plana, mouetur motu mixto <lb/>ex recto centri, &amp; circulari orbis: axis tant&ugrave;m rot&aelig; mouetur <lb/>motu recto: punctum contactus rot&aelig; mouetur motu tardi&longs;&longs;imo, <pb xlink:href="026/01/029.jpg"/>quando motus centri, &amp; &longs;uprema rot&aelig; pars in eandem partem &longs;e&shy;<lb/>runtur; punctum ver&ograve; oppo&longs;itum veloci&longs;&longs;imo, quia in motu huius <lb/>rotus motus orbis additur motui centri; in motu ver&ograve; illius, to&shy;<lb/>tus motus orbis, motui centri detrahitur: quod autem detrahit mo&shy;<lb/>tus orbis, nunquam &aelig;quale e&longs;t toti motui centri. </s></p><p type="main">

<s>2. Hinc omnia puncta eiu&longs;dem circuli rot&aelig; mobilis in plano <lb/>hoc motu mixto mouentur in &aelig;quali motu: hoc etiam motu mo&shy;<lb/>uetur globus de&longs;cendens in plano inclinato, in quo reuer&acirc; motu <lb/>h&aelig;c habes: prim&ograve;, non mod&ograve; accelerari <expan abbr="mot&utilde;">motum</expan> centri, ver&ugrave;m etiam <lb/>motum orbis; <expan abbr="&longs;ec&utilde;d&ograve;">&longs;ecund&ograve;</expan>, ita <expan abbr="impet&utilde;">impetum</expan> propagari ab intrin&longs;eco, vt &longs;ingu&shy;<lb/>lis partibus eiu&longs;dem circuli, &amp; plani in &aelig;qualiter di&longs;tribuatur, terti&ograve; <lb/>hoc motu motum rectum non impediri &agrave; circulari, &amp; &longs;ed iuuari. </s></p><p type="main">

<s>3. C&ugrave;m rota voluitur in &longs;uperficie connexa, mouetur motu mix&shy;<lb/>to ex duobus circularibus: &longs;imilis e&longs;t hic motus motui epicycli. </s>

<s>Ca&shy;<lb/>lamus volatilis, cuius mi&longs;&longs;io frequens, &amp; repercu&longs;&longs;io, ludi non in&shy;<lb/>grati copiam facit: mouetur motu mixto ex recto, &amp; circulari: in <lb/>hoc porr&ograve; motu pr&aelig;it calami caput, &amp; &longs;equuntur penn&aelig;; quia a&euml;r <lb/>forti&ugrave;s re&longs;i&longs;tit pennis, qu&agrave;m thec&aelig;: hinc pennarum motum theca <lb/>grauior accelerat, cuius motum penn&aelig; retardant. </s></p><p type="main">

<s>4. Hinc, &longs;i quando accidat, penas educi ex theca in libero medio; <lb/>&longs;tatim theca velociori motu mouetur, c&ugrave;m tamen penn&aelig; ip&longs;&aelig; &longs;i&shy;<lb/>&longs;tant: ex hac in&aelig;qualitate, ne impetus &longs;it fru&longs;tr&agrave;, propter detortas <lb/>in alteram partem pennas ab a&euml;re re&longs;i&longs;tente totum iaculum defle&shy;<lb/>ctitur, agit&uacute;r que in orbem; hinc motus orbis traducitur ex theca in <lb/>pennas, non contr&agrave;, vt aliquis fort&egrave; exi&longs;timaret, lic&egrave;t pennarum tar&shy;<lb/>ditas, &amp; obliqua deflexio, ratione cuius ab a&euml;re re&longs;tante, in alteram <lb/>partem qua&longs;i reflectentur, &longs;int nece&longs;&longs;aria conditio huius traductio&shy;<lb/>nis. </s></p><p type="main">

<s>5. Hinc motu recto pr&aelig;dictum iaculum in vacuo tant&ugrave;m mo&shy;<lb/>ueretur, vt patet: hinc: c&ugrave;m penn&aelig; &longs;unt explicatiores, tardi&ugrave;s; c&ugrave;m <lb/>ver&ograve; contractiores, veloci&ugrave;s mouetur, etiam motu orbis; cui non <lb/>min&ugrave;s a&euml;r re&longs;i&longs;tit, in pennis, &longs;cilicet, qu&agrave;m motui axis: hinc, &longs;i theca <lb/>&longs;it grauior, veloci&ugrave;s; &longs;i leuior, tardi&ugrave;s iaculum fertur; etiam tenera <lb/>plumarum lanugo tarditatem conciliat: porr&ograve;, &longs;i axis mouetur mo&shy;<lb/>tu recto, quod reuer&agrave; fit, c&ugrave;m iaculum deor&longs;um demittitur in per&shy;<lb/>pendiculo, hic motus e&longs;t &longs;piralis cylindricus: ex his infinita fer&egrave; <lb/>ph&aelig;nomena explicari po&longs;&longs;unt. </s></p><p type="main">

<s>6. Sunt infiniti propemodum motus mixti; v. <!-- REMOVE S-->g. <!-- REMOVE S-->cylindri ab alte&shy;<lb/>ra extremitate rotata emi&longs;&longs;i; longioris ha&longs;t&aelig;, qu&aelig; &longs;ur&longs;um facta cir&shy;<lb/>cuitione emittitur; brachij, gladij, &amp;c.  &longs;ed poti&longs;&longs;im&ugrave;m turbinis, qui <pb xlink:href="026/01/030.jpg"/>vel &longs;cutica, vel funiculo in torto circumagitur, in quo clari&longs;&longs;i&shy;<lb/>m&egrave; apparet motus centri, &amp; orbis: ratio motus orbis e&longs;t impe&shy;<lb/>tus impre&longs;&longs;us vtrique extremitati diametri va&longs;is in partes contra&shy;<lb/>rias; ratio ver&ograve; motus centri e&longs;t, quia adducitur funiculo vel ex&shy;<lb/>ploditur, &longs;eu expellitur &longs;cutica: huius motus ph&aelig;nomena &longs;unt fer&egrave; <lb/>infinita: &longs;ingula ex no&longs;tris principiis facil&egrave; explicantur. </s></p><figure id="id.026.01.030.1.jpg" xlink:href="026/01/030/1.jpg"/><p type="main">

<s><emph type="center"/><emph type="italics"/>De diuer&longs;is impre&longs;&longs;ionibus motus.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>1. CVm &longs;u&longs;tinetur manus, &longs;eu brachium, in &longs;itu horizontali im&shy;<lb/>mobile, producitur nece&longs;&longs;ari&ograve; impetus &aelig;qualis impetui gra&shy;<lb/>uitationis; alioquin, &longs;i maior e&longs;&longs;et, &longs;ur&longs;um ferretur brachium; &longs;i ver&ograve; <lb/>minor, deor&longs;um: quia pr&aelig;ualeret grauitatio, porr&ograve; hic impetus pro&shy;<lb/>ducitur tant&ugrave;m &agrave; potentia motrice animantis, in &longs;ingulari organo; <lb/>non ver&ograve; in aliis partibus, etiam animatis, ni&longs;i quando mouentur; <lb/>nec in ip&longs;o pondere, &longs;i aliquod &longs;u&longs;tinetur: &longs;ic men&longs;a in pondere &longs;u&shy;<lb/>per po&longs;ito impetum nullum producit. </s>

<s>Si anima immediat&egrave; in toto <lb/>corpore po&longs;&longs;et producere impetum, homo facil&egrave; volare po&longs;&longs;et. </s></p><p type="main">

<s>2. C&ugrave;m &longs;u&longs;tinetur funependulum, nullus impetus producitur &agrave; <lb/>&longs;u&longs;tinente in ip&longs;o globo, ne &longs;cilicet, &longs;it fru&longs;tr&agrave;; &longs;ec&ugrave;s ver&ograve;, &longs;i attolla&shy;<lb/>tur: &longs;ic per quamlibet lineam corpus retineri pote&longs;t &longs;ine impetu in <lb/>eo corpore producto per &longs;e: hinc, c&ugrave;m duo &longs;e&longs;e inuicem trahunt ad&shy;<lb/>uer&longs;o ni&longs;u, neuter in altero producit impetum per &longs;e; &longs;ed per acci&shy;<lb/>dens, propter mollitiem, &amp; ten&longs;ionem partium: c&ugrave;m ver&ograve; defertur <lb/>aliquid coniunctum, producitur haud dubi&egrave; &aelig;qualis impetus; hinc <lb/>&longs;eparari non pote&longs;t; quia &aelig;qualis e&longs;t motus latoris, &amp; delati: exem&shy;<lb/>plum habes in naui. </s></p><p type="main">

<s>3. Si ver&ograve; nauis illic&ograve; &longs;i&longs;tat, vel tardi&ugrave;s moueri pergat, tunc fit &longs;e&shy;<lb/>paratio: hinc liquida effunduntur, &longs;i dum feruntur, breuior quietis <lb/>in va&longs;e intercedat morula. </s>

<s>Vt feratur cylindrus humeris <expan abbr="c&otilde;modi&ugrave;s">commodi&ugrave;s</expan> <lb/>debet &longs;u&longs;tineri in <expan abbr="c&etilde;tro">centro</expan> grauitatis, ad eleuationem anguli 49. quia <lb/><expan abbr="t&utilde;c">tunc</expan> manui, &amp; humero &aelig;qualiter <expan abbr="p&otilde;dus">pondus</expan> di&longs;tribuitur: ide&ograve; in circulo <lb/>voluitur &longs;cyphus aqua plenus &longs;ine effu&longs;ione; quia impetus determi&shy;<lb/>natus per tangentem circuli aquam ip&longs;am &agrave; centro circuli remouet. </s></p><p type="main">

<s>4. C&ugrave;m trahitur aliquod corpus impetus impre&longs;&longs;us in vna parte <lb/>non producit impetum in alia, alioquin daretur proce&longs;&longs;us in infi&shy;<lb/>nitum; &longs;i chorda vtrinque trahatur, rumpetur in medio: &longs;i affixa <lb/>extremitati immobili, trahatur &agrave; potentia applicata alteri extremi-<pb xlink:href="026/01/031.jpg"/>tati, rumpetur iuxta primam illam extremitatem: &longs;i denique pon&shy;<lb/>ticulo &longs;uppo&longs;ito tendatur, vel pondere deprimente, in eo puncto <lb/>rumpetur. </s>

<s>Ratio communis i&longs;torum omnium e&longs;t: quia inter illas <lb/>duas partes fieri debet diui&longs;io per &longs;e, quarum vna mouetur, &longs;ec&ugrave;s <lb/>alia; vel quarum vtraque in partes oppo&longs;itas mouetur. </s></p><p type="main">

<s>5. Vt quodlibet pondus facili&ugrave;s trahatur, &longs;inguli equi trahere <lb/>debent fune communi, poti&ugrave;s qu&agrave;m bigati; quia tunc nihil fer&egrave; pe&shy;<lb/>rit impetus: c&ugrave;m plures idem pondus trahunt, agunt actione com&shy;<lb/>muni, alioqui &longs;inguli in toto pondere &longs;uum impetum producerent; <lb/>igitur &longs;inguli &longs;eor&longs;um trahere? </s>

<s>e&longs;&longs;ent, quod fal&longs;um e&longs;t: ide&ograve; currus <lb/>paul&ograve; po&longs;t initium motus facili&ugrave;s mouetur; quia aliquid impetus <lb/>pri&ugrave;s producti remanet: hinc etiam rupto fune, quo trahitur currus, <lb/>currus ip&longs;e modicum tempus adhuc mouetur. </s></p><p type="main">

<s>6. Si, dum quis trahit toto ni&longs;u magnum aliquod pondus, funis <lb/>rumpatur, pron&ugrave;s corruit: quia maiorem impetum in &longs;e producit, <lb/>totum, &longs;cilicet, illum, quem in toto pondere produxi&longs;&longs;et eo in&longs;tan&shy;<lb/>ti, quo rumpitur finis, qui reuer&agrave; maior e&longs;t, propter impedimen&shy;<lb/>tum, ex pr&aelig;mi&longs;&longs;is principiis, maiorique applicatione potenti&aelig;, ner&shy;<lb/>uorum ten&longs;ione, &amp;c. </s>

<s>dum trahitur vnco an nullus immobilis ver&shy;<lb/>s&ugrave;s nauim, nauis fertur vers&ugrave;s littus; dum pellitur aduers&ugrave;m littus, <lb/>recedit &agrave; littore, quia pede, vel genu, imprimitur naui impetus in <lb/>contrariam pattem. </s></p><p type="main">

<s>7. C&ugrave;m trahitur cylindrus vtrinque &aelig;qualiter, qui neque flecti, <lb/>neque tendi pote&longs;t, nullum impetum accipit; im&ograve; in tractione nul&shy;<lb/>lus impetus e&longs;t inutilis: brachium infligit maiorem ictum, c&ugrave;m ma&shy;<lb/>iorem <expan abbr="arc&utilde;">arcum</expan> de&longs;cribit &longs;uo motu; quia, &longs;cilicet, mouetur motu natu&shy;<lb/>raliter accelerato: hinc auer&longs;a manu validior impingitur colaphus, <lb/>qu&agrave;m aduer&longs;a; quia illa maiorem arcum de&longs;cribit: hinc longius bra&shy;<lb/>chium c&aelig;teris paribus graui&ugrave;s ferit: hinc diu qua&longs;i rotatur bra&shy;<lb/>chium, vt longi&ugrave;s mittatur lapis. </s></p><p type="main">

<s>8. Maiore fu&longs;te maior ictus infligitur; quia potentia toto ni&longs;u <lb/>agens, diuti&ugrave;s manet applicata maiori, qu&agrave;m minori; &longs;untque ictus <lb/>in ratione &longs;ubduplicata vtriu&longs;que fu&longs;tis; v. <!-- REMOVE S-->g. <!-- REMOVE S-->fu&longs;tis pendens vnam <lb/>libram per maximum arcum impactus, infligit &longs;ubduplum ictum <lb/>alterius, quem infligit fu&longs;tis quatuor pendens libras per eundem <lb/>arcum impactus: idem dicatur de mi&longs;&longs;o lapide: principium huius <lb/>veritatis pendet ex iis, qu&aelig; diximus lib. 2. de motu naturali&shy;<lb/>ter accelerate, iuxta progre&longs;&longs;ionem numerorum imparium, <lb/>1. 3. 5. &amp;c. </s>



</p><p type="main">

<s>9. Fu&longs;tis circa centrum immobile vibratus, maximum ictum in-<pb xlink:href="026/01/032.jpg"/>fligit, non quidem in centro grauitatis, id e&longs;t, in medio, &longs;i &longs;it cy&shy;<lb/>lindrus, vel parallelipedum; nec in extremitate mobili; &longs;ed in eo <lb/>puncto, in quo e&longs;t centrum impetus impre&longs;&longs;i, id e&longs;t, quod &aelig;qualem <lb/>vtrinque dirimit impetum: ratio e&longs;t; quia tunc totus impetus agit, <lb/>quant&ugrave;m pote&longs;t; illud autem punctum Geometria demon&longs;trat e&longs;&longs;e <lb/>terminum medi&aelig; proportionalis, inter totum cylindrum, &amp; &longs;ub&shy;<lb/>duplum; mod&ograve; nulla ratio vectis habeatur alioquin centrum pro&shy;<lb/>cu&longs;&longs;ionis di&longs;tat 2/3 ab extremitate immobili. </s></p><p type="main">

<s>10. C&ugrave;m fu&longs;tis inflectitur, reditque ad pri&longs;tinum &longs;tatum, vt <lb/>videre e&longs;t in tudicula maiore, maior ictus imprimitur: quia non <lb/>tant&ugrave;m agit impetus extrin&longs;ec&ugrave;s adueniens; ver&ugrave;m etiam potentia <lb/>qu&aelig;dam media, qu&aelig; corpora compre&longs;&longs;a, vel ten&longs;a, ad pri&longs;tinum <lb/>&longs;tatum reducit: hinc maximus e&longs;t ictus tudicul&aelig;, c&ugrave;m eo in&longs;tanti, <lb/>quo reductum e&longs;t omnin&ograve; manubrium priori rectitudini, infligitur <lb/>ictus, quia tunc vis potenti&aelig; medi&aelig; e&longs;t maxima. </s></p><p type="main">

<s>11. Rotato flagello ide&ograve; maxima vis ine&longs;t, quia diuti&ugrave;s potentia <lb/>manet applicata: hinc vides hoc principium e&longs;&longs;e vniuer&longs;ali&longs;&longs;imum, <lb/>quod iactis, pul&longs;is, &amp; impactis competit; de malleorum ictu idem <lb/>pror&longs;us dicendum e&longs;t, quod de fu&longs;te; &longs;i autem mallei cadant <lb/>ex eadem altitudine, motu naturali accelerato, ictus &longs;unt vt <lb/>mallei, quia duplus malleus, v. <!-- REMOVE S-->g. <!-- REMOVE S-->duplum impetum acquirit: nam <lb/>&longs;ingul&aelig; partes &longs;eor&longs;im &aelig;qualem impetum acquirunt. </s>



</p><p type="main">

<s>12. Si ver&ograve; ex diuer&longs;a altitudine cadant, vel &longs;unt &aelig;quales, vel <lb/>in&aelig;quales: &longs;i primum, ictus &longs;unt vt tempora, quibus cadunt: &longs;i <lb/>&longs;ecundum, ictus &longs;unt in ratione compo&longs;ita temporum, &amp; mal&shy;<lb/>leorum: &longs;i &longs;unt infinit&aelig;, partes actu, nulla e&longs;t proportio percu&longs;&longs;ionis <lb/>granuli cadentis, &amp; rupis ingentis grauitantis; &longs;ed hoc vltimum fal&shy;<lb/>&longs;um e&longs;&longs;e con&longs;tat; non pote&longs;t tamen determinari proportio vitium <lb/>grauitationis, &amp; percu&longs;&longs;ionis, ni&longs;i numerus in&longs;tantium: quibus durat <lb/>motus deor&longs;um cogno&longs;catur. </s></p>
<p type="main"><s>13. Leui&longs;&longs;imi lapides vix emittuntur ad modicam di&longs;tantiam; <lb/>quia &longs;tatim &longs;eparantur &agrave; potentia: parallelipedum cadens de or&shy;<lb/>&longs;um in &longs;itu horizontali maximum ictum infligit in centro grauita&shy;<lb/>tis, id e&longs;t, in medio; quia tunc totus impetus agit, totus enim impe&shy;<lb/>ditur: in aliis punctis minor e&longs;t ictus, iuxta proportionem maioris <lb/>di&longs;tanti&aelig; &agrave; pr&aelig;dicto centro: &longs;i ver&ograve; percutiatur cylindrus innatans, <lb/>maxima erit vis, vel effectus ictus in centro grauitatis propter ean&shy;<lb/>dem rationem. </s></p>
</section>
</front>          
<body>
<chap>

<pb xlink:href="026/01/033.jpg" pagenum="1"/><figure id="id.026.01.033.1.jpg" xlink:href="026/01/033/1.jpg"/><p type="main">

<s><emph type="center"/>LIBER PRIMVS,<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>DE IMPETV.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>TRACTATVM hunc de motu locali <lb/>ab ip&longs;o impetu au&longs;picamur, ex cuius <lb/>profect&ograve; cognitione tota res i&longs;ta de&shy;<lb/>pendet; cum enim impetus &longs;it cau&longs;a <lb/>immediata motus, vt fus&egrave; demon&longs;tra&shy;<lb/>bimus infr&agrave;; &amp; cum propter quid &longs;it res cogno&longs;ci <lb/>non po&longs;&longs;it, ni&longs;i eius cau&longs;a cogno&longs;catur; dubium e&longs;&longs;e <lb/>non pote&longs;t, quin pr&aelig;mittenda &longs;it tractatio illa, qu&aelig; <lb/>e&longs;t de impetu, vt deinde affectiones ip&longs;ius motus <lb/>per cau&longs;am eiu&longs;dem demon&longs;trentur; imm&ograve; au&longs;im <lb/>dicere ex vnius impetus cognitione, non mod&ograve; mo&shy;<lb/>tum ip&longs;um, ver&ugrave;m etiam totam rem Phy&longs;icam pen&shy;<lb/>dere. <lb/><gap desc="hr tag"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>DEFINITIO I.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>MOTVS <emph type="italics"/>localis e&longs;t tran&longs;itus mobilis &egrave; loco in locum continuo fluxu.<emph.end type="italics"/><lb/>Huius definitionis explicationem habebis in Metaphy&longs;ic&acirc;, <lb/>qu&aelig; &longs;an&egrave; explicatio ad rem pr&aelig;&longs;entem non facit. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Definitio II.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s><emph type="italics"/>Motus velox e&longs;t quo percurritur maius &longs;patium &aelig;quali tempore, vel <lb/>&aelig;quale &longs;patium minori tempore; contr&agrave; ver&ograve; motus tardus.<emph.end type="italics"/></s></p><pb xlink:href="026/01/034.jpg" pagenum="2"/><p type="main">

<s><emph type="center"/><emph type="italics"/>Definitio III.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s><emph type="italics"/>Impetus e&longs;t qualitas exigens motum, &longs;eu fluxum localem &longs;ui &longs;ubiecti, vel <lb/>qua est cau&longs;a proxima motus illius mobilis, cui ine&longs;t, eo &longs;cilicet modo, quo <lb/>pote&longs;t e&longs;&longs;e cau&longs;a motus.<emph.end type="italics"/></s></p><p type="main">

<s>Dico e&longs;&longs;e qualitatem &longs;iue di&longs;tincta &longs;it, &longs;iue non di&longs;tincta; quod h&icirc;c <lb/>cert&egrave; non di&longs;cutio; nec enim affirmo in hac definitione dari impetum; <lb/>&longs;ed definio tant&ugrave;m quid &longs;it impetus; qui reuera aliud non e&longs;t, &longs;i e&longs;t: <lb/>quippe id tant&ugrave;m concipio, cum impetum appello; &longs;iue &longs;it, &longs;iue non &longs;it, <lb/>ne quis fort&egrave; initio &longs;tatim mihi litem intendat; quemadmodum definit <lb/>circulum Geometra; lic&egrave;t non a&longs;&longs;erat dari perfectum circulum; ita Phy&shy;<lb/>&longs;icus definit impetum, quamuis non affirmet dari impetum; quod tamen <lb/>in &longs;exto Theoremate demon&longs;trabimus; itaque &longs;i e&longs;t impetus, haud dubi&egrave; <lb/>nihil omnin&ograve; pr&aelig;&longs;tat in &longs;uo &longs;ubiecto ni&longs;i motum; quod quomod&ograve; fiat, <lb/>explicabimus intr&agrave; in Theorematis. <!-- KEEP S--></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Hypothe&longs;is I.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s><emph type="italics"/>Datur motus localis<emph.end type="italics"/>; quis enim non videt volantem auem, natantem <lb/>pi&longs;cem; currentem equum, rotatum globum; denique vnum corpus mi&shy;<lb/>grans &egrave; loco in locum? </s>

<s>&longs;ed hoc e&longs;t moueri per Def. <!-- REMOVE S-->1. igitur infinitis fe&shy;<lb/>r&egrave; experimentis nititur h&aelig;c hypothe&longs;is, quam veram e&longs;&longs;e nece&longs;&longs;e e&longs;t, &longs;i <lb/>illa vera &longs;unt; &longs;ed illa certa &longs;unt phy&longs;ic&egrave;, neque citra miraculum fallere <lb/>po&longs;&longs;unt. </s>

</p><p type="main">

<s>Diceret fort&egrave; aliquis etiam motum &longs;ube&longs;&longs;e oculorum fallaci&aelig;; c&ugrave;m &egrave; <lb/>naui mobili littus ip&longs;um moueri, ip&longs;umque nauigium non moueri iudi&shy;<lb/>cemus. </s>

<s>Quis enim oculos in Solem intendens, primo intuitu Solem &longs;ta&shy;<lb/>re non iudicet? </s>

<s>cum tamen deinde pernici&longs;&longs;imo cur&longs;u rotari demon&longs;tre&shy;<lb/>mus; adde alias oculorum fallacias circa motum; &longs;ic rotata &longs;cintilla, vel <lb/>carbo accen&longs;us immotum orbem de&longs;cribere videtur; &longs;ic nota inu&longs;ta <lb/>trocho, dum celerrim&egrave; rotatur, orbem etiam immobilem de&longs;cribere iu&shy;<lb/>dicatur; &longs;ic &longs;tella cadens, vel exhalatio continenti &longs;ucce&longs;&longs;ione accen&longs;a <lb/>moueri videtur; licet minim&egrave; moueatur; idem dicendum de puluere <lb/>tormentario, vel alia qualibet materia; qu&aelig; continuata con&longs;ecutione <lb/>accenditur; imm&ograve; trochus ip&longs;e in orbem celerrim&egrave; agitatus, quie&longs;cere <lb/>videtur; &longs;ic qui vertigine laborant, ea moueri exi&longs;timant, qu&aelig; quie&longs;cunt; <lb/>idem exemplum habemus in ebrio&longs;is, iracundis, in iis qui ex graui febris <lb/>ardore delirant, &amp; in pueris qui diu in gyros eunt, vbi verti de&longs;ierint; <lb/>&longs;ic eorum qu&aelig; motu &aelig;quali feruntur, remotiora tardi&ugrave;s moueri viden&shy;<lb/>tur; imm&ograve; &longs;i per eandem lineam oculus, &amp; mobile pari velocitate ince&shy;<lb/>dant, ip&longs;um mobile quie&longs;cere videtur, plura leges apud Opticos, de <lb/>quibus agemus &longs;uo loco: Igitur ex his omnibus con&longs;tat minim&egrave; con&longs;ta&shy;<lb/>re dari motum, ex eo qu&ograve;d oculis aliquid moueri videatur. </s></p><p type="main">

<s>Re&longs;pondeo equidem fateri me, vi&longs;um ip&longs;um plurimis &longs;ube&longs;&longs;e fraudi&shy;<lb/>bus; attamen &longs;i rect&egrave; oculus admoueatur, iu&longs;ta di&longs;tanti&agrave;, nec vllum &longs;it <lb/>impedimentum exterius nec interius; fieri non pote&longs;t, quin oculus mo&shy;<lb/>tum ob&longs;eruet; an fort&egrave; currentis calami motus oculum meum fallere po-<pb xlink:href="026/01/035.jpg" pagenum="3"/>te&longs;t? </s>

<s>quidquid &longs;it, fateor vltr&ograve; hanc hypothe&longs;im in eo tant&ugrave;m certitudi&shy;<lb/>nis gradu e&longs;&longs;e reponendam, in quo reponitur h&aelig;c cognitio, qu&acirc; modo <lb/>cogno&longs;co me &longs;cribere, manu&longs;que, &amp; calami motum ob&longs;eruo; &longs;iue id tan&shy;<lb/>t&ugrave;m oculis fiat, &longs;iue intellectu ex oculis; quod ali&agrave;s di&longs;cutiemus; &longs;i quis <lb/>fort&egrave; in Phy&longs;ica maiorem certitudinem po&longs;tularet, cum eo cert&egrave; conue&shy;<lb/>nire non po&longs;&longs;um. </s></p><p type="main">

<s>Porr&ograve; quod &longs;pectat ad fallacias illas qu&aelig; &longs;upra adduct&aelig; &longs;unt; certum <lb/>e&longs;t vel obiectum e&longs;&longs;e remotius, quam par &longs;it; vel moueri celeri&ugrave;s, vel <lb/>e&longs;&longs;e aliquod impedimentum interius; pr&aelig;&longs;ertim in iis, qui &longs;eu vertigine, <lb/>vel alio capitis morbo laborant; &longs;ed ne h&icirc;c opticum agere videar, harum <lb/>fallaciarum certi&longs;&longs;imas cau&longs;as in &longs;uum locum remittimus. </s></p><p type="main">

<s>C&aelig;ter&ugrave;m lic&egrave;t ad &longs;tatuendam, firmandamque hanc hypote&longs;im, Phy&shy;<lb/>&longs;ica experimenta rect&egrave; applicato &longs;en&longs;u comprobata &longs;ufficere po&longs;&longs;int; <lb/>non de&longs;unt tamen rationes mult&aelig; &agrave; priori, vt vulg&ograve; aiunt, quibus euin&shy;<lb/>citur, non mod&ograve; quid &longs;it motus, ver&ugrave;m etiam propter quid &longs;it. </s></p><p type="main">

<s>Prima duci pote&longs;t &agrave; fine motus; cum enim res creat&aelig; vbique &longs;imul <lb/>e&longs;&longs;e non po&longs;&longs;int, cert&egrave;, vt illo bono gaudeant, quo fort&egrave; carent, &amp; vt <lb/>coniungantur &longs;uo fini, motu locali opus e&longs;t; &longs;itit equus, abe&longs;t aqua, <lb/>cert&egrave;, ni&longs;i vel h&aelig;c propinetur, vel ille accedat, &longs;itim leuare non pote&shy;<lb/>rit; at neutrum &longs;ine motu haberi pote&longs;t: Lapis remouetur &agrave; &longs;uo centro, <lb/>&agrave; &longs;uo globo, &agrave; &longs;uo fine, vt &longs;e&longs;e illi re&longs;tituat, deor&longs;um cadat nece&longs;&longs;e e&longs;t. </s>

<s><lb/>Itaque ad cum finem res omnes creat&aelig; in&longs;titut&aelig; &longs;unt, quem &longs;ine motu <lb/>a&longs;&longs;equi non po&longs;&longs;unt; igitur dari motum nece&longs;&longs;e e&longs;t, vt res creat&aelig; cum lo&shy;<lb/>cum acquirant, in quo &longs;uo bono, &longs;uo fini, &longs;u&aelig; perfectioni coniungan&shy;<lb/>tur; vel &longs;altem id muneris obeant, cui ab ips&acirc; natur&acirc; de&longs;tinantur. </s></p><p type="main">

<s>Secunda ratio ducitur &agrave; cau&longs;a efficiente; ni&longs;i enim daretur motus, <lb/>fru&longs;tr&agrave; daretur potentia motrix, t&ugrave;m in animantibus, t&ugrave;m in grauibus, <lb/>de qu&acirc; ali&agrave;s. </s></p><p type="main">

<s>Tertia petitur &agrave; cau&longs;a formali; cum enim detur impetus, vt demon&shy;<lb/>&longs;trabimus infr&agrave;, nece&longs;&longs;e e&longs;t dari motum. </s></p><p type="main">

<s>Quarta petitur &agrave; termino motus; cum enim globus proiectus &longs;it in <lb/>nouo loco in quo ante non erat; cert&egrave; nouus locus qui &longs;uccedit alteri <lb/>relicto, e&longs;t terminus motus citra miraculum; igitur &longs;i e&longs;t nouus locus, <lb/>e&longs;t quoque motus. </s></p><p type="main">

<s>Quinta ab v&longs;u; nec enim &longs;ine motu flueret aqua, caderet lapis, gyros <lb/>agerent a&longs;tra, flaret ventus, volarent nubes, &amp;c. </s></p><p type="main">

<s>Sexta ab ip&longs;a Mechanica, qu&aelig; organa motui mini&longs;trat: quis enim ne&shy;<lb/>garet maius momentum e&longs;&longs;e cum maiori di&longs;tanti&acirc; coniunctum; &longs;i ver&ograve; <lb/>maius momentum e&longs;t, nunquid pr&aelig;ualebit; igitur deor&longs;um cadet, imm&ograve; <lb/>&longs;euerior Geometria, vt omittam A&longs;tronomiam, motum &longs;upponit, cum ex <lb/>fluxu &longs;eu motu puncti infinitas fere lineas de&longs;cribat. </s>

<s>Igitur certum e&longs;t <lb/>dari motum localem. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Hypothe&longs;is II.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s><emph type="italics"/>Datur quies, id e&longs;t priuatio motus.<emph.end type="italics"/> H&aelig;c hypothe&longs;is etiam certa e&longs;t, <pb xlink:href="026/01/036.jpg" pagenum="4"/>Quis enim neget &longs;edentem humi, vel decumbentem in lecto quie&longs;ceret <lb/>con&longs;ule &longs;en&longs;us rect&egrave; applicatos; tam enim certus &longs;um me iam in cathe&shy;<lb/>dra quie&longs;cere, quam &longs;um certus Solem lucere; igitur ex certis experi&shy;<lb/>mentis certa hypothe&longs;is con&longs;equitur. </s>

<s>Non de&longs;unt rationes &agrave; priori; nam <lb/>prim&ograve; res aliqua &longs;uo bono, &longs;eu fini coniuncta ab eo &longs;eparari non po&longs;tu&shy;<lb/>lat, igitur nec moueri. </s>

<s>Secund&ograve; maximum incommodum e&longs;&longs;et, &longs;i res &longs;e&shy;<lb/>mel mota perpetu&ograve; moueretur. </s>

<s>Terti&ograve;, finis, &longs;eu terminus motus recti, <lb/>e&longs;t quies; nam ideo lapis deor&longs;um cadit, vt in &longs;uo centro &longs;eu globo <lb/>quie&longs;cat, id e&longs;t vt cum aliis partibus totum illud, &longs;eu globum componat, <lb/>vt dicemus ali&agrave;s. </s></p><p type="main">

<s>Diceret fort&egrave; aliquis &longs;ententias pr&aelig;dictas non valere in &longs;ententi&acirc; <lb/>Copernici, qu&aelig; terr&aelig; motum ad&longs;truit; pr&aelig;terea non mod&ograve; falli &longs;en&longs;us <lb/>circa motum, ver&ugrave;m etiam circa quietem. </s></p><p type="main">

<s>Re&longs;pondeo prim&ograve; illam Copernici &longs;ententiam e&longs;&longs;e fal&longs;i&longs;&longs;imam, vt &longs;uo <lb/>loco o&longs;tendemus: &longs;ecund&ograve;, lic&egrave;t terra moueretur &longs;ecundum Coperni&shy;<lb/>cum, Sol, &amp; &longs;tell&aelig; quie&longs;cerent. </s></p><p type="main">

<s>Dices iuxta hypothe&longs;im Heraclidis Pontici, terra ip&longs;a, Sol etiam, &amp; <lb/>&longs;tell&aelig; mouentur. </s>

<s>Re&longs;pondeo prim&ograve; hypothe&longs;im illam e&longs;&longs;e fal&longs;am, vt &longs;uo <lb/>loco videbimus; &longs;ecund&ograve; etiam data illa hypothe&longs;i po&longs;&longs;et dari quies; &longs;i <lb/>enim globus eodem ver&longs;us occa&longs;um impetu proiiceretur, qu&ograve; ver&longs;us or&shy;<lb/>tum &agrave; terra ip&longs;a rapitur, ha&ugrave;d dubi&egrave; quie&longs;ceret: pr&aelig;terea iuxta hanc hy&shy;<lb/>pothe&longs;im, quietem appellarem vnius partis cum alia connexionem in ip&shy;<lb/>&longs;o toto &longs;eu globo, &amp; quie&longs;cere dicerem lapidem, qui tant&ugrave;m totius glo&shy;<lb/>bi motu mouetur, ex quo profect&ograve; tota &longs;oluitur difficultas. </s></p><p type="main">

<s>Quod ver&ograve; &longs;pectat ad fallacias oculi circa quietem; codem pror&longs;us <lb/>modo &longs;oluend&aelig; &longs;unt, quo iam &longs;upra &longs;olut&aelig; &longs;unt ali&aelig; circa motum: <lb/>vtr&ugrave;m ver&ograve; motus, &amp; quies dicant aliquid di&longs;tinctum &agrave; mobili, dice&shy;<lb/>mus infr&agrave;. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Hypothe&longs;is III.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s><emph type="italics"/>Aliquid mouetur quod inc&oelig;pit moueri.<emph.end type="italics"/></s><s> Video lapidem quie&longs;centem, <lb/>qui deinde proiectus mouetur; igitur ante non mouebatur, igitur cum <lb/>deinde mouetur, c&oelig;pit moueri; mille aliis experimentis h&aelig;c hypothe&shy;<lb/>&longs;is confirmari pote&longs;t. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Hypothe&longs;is IV.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s><emph type="italics"/>Aliquid mouetur quod tandem de&longs;init moueri, vel incipit quie&longs;cere.<emph.end type="italics"/></s><s> Vi&shy;<lb/>deo rotatam pilam, qu&aelig; tandem quie&longs;cit, cadentem lapidem, qui tan&shy;<lb/>dem &longs;i&longs;tit, &amp;c. </s>

<s>igitur certa e&longs;t h&aelig;c hypothe&longs;is. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Hypothe&longs;is V.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s><emph type="italics"/>Idem mouetur mod&ograve; tardi&ugrave;s, mod&ograve; veloci&ugrave;s.<emph.end type="italics"/></s><s> Video rotatum globum, <lb/>qui &longs;en&longs;im quie&longs;cit: &longs;entio ab codem globo mod&ograve; maiorem, mod&ograve; mi&shy;<lb/>norem ictum infligi, &amp;c. </s>

<s>igitur e&longs;t certa hypothe&longs;is. </s></p><pb xlink:href="026/01/037.jpg" pagenum="5"/><p type="main">

<s><emph type="center"/><emph type="italics"/>Hypothe&longs;is VI.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s><emph type="italics"/>Corpus proiectum etiam &agrave; potenti&acirc; motrice &longs;eiunctum adhuc mouetur.<emph.end type="italics"/><lb/>Oculos omnium te&longs;tes appello. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Hypothe&longs;is VII.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s><emph type="italics"/>Corpus proiectum, &amp; in aliud impactum illud ip&longs;um impellit, &amp; mouet.<emph.end type="italics"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Hypothe&longs;is VIII.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s><emph type="italics"/>Ignis applicatus &longs;ubiectum aptum, cui rect&egrave; applicatur nece&longs;&longs;ari&ograve; calefa&shy;<lb/>cit, nix frigefacit, Sol illuminat, corpus in aliud impactum illud ip&longs;um im&shy;<lb/>pellit.<emph.end type="italics"/></s><s> Pr&aelig;dict&aelig; omnes Hypothe&longs;es certi&longs;&longs;imis nix&aelig; experimentis certi&shy;<lb/>tudinem phy&longs;icam habent, &amp; citra miraculum fallere non po&longs;&longs;unt. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Axioma I.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s><emph type="italics"/>Contradictoria &longs;imul e&longs;&longs;e non po&longs;&longs;unt, vel non e&longs;&longs;e.<emph.end type="italics"/></s><s> Hoc ip&longs;um iam pr&aelig;&shy;<lb/>mi&longs;imus Logic&aelig; no&longs;tr&aelig; demon&longs;tratiu&aelig;, complectiturque prima illa <lb/>principia Metaphy&longs;ic&aelig;. </s></p><p type="main">

<s>1. <emph type="italics"/>Impo&longs;&longs;ibile est idem &longs;imul e&longs;&longs;e, &amp; non e&longs;&longs;e.<emph.end type="italics"/></s></p><p type="main">

<s>2. <emph type="italics"/>Quodlibet e&longs;t, vel non est.<emph.end type="italics"/></s></p><p type="main">

<s>3. <emph type="italics"/>De eodem alterum contradictoriorum ver&egrave; affirmatur, &amp; alterum ver&egrave; <lb/>negatur, non &longs;imul vtrumque.<emph.end type="italics"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Axioma II.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s><emph type="italics"/>Maximum &longs;ignum di&longs;tinctionis realis in phy&longs;icis est &longs;eparabilitas, vel op&shy;<lb/>po&longs;itio.<emph.end type="italics"/></s><s> Nihil enim a &longs;e ip&longs;o &longs;eparari po&longs;t; quippe, vbi e&longs;t &longs;eparatio, &longs;eu <lb/>diui&longs;io, e&longs;t pluralitas; cur enim nummus A &amp; nummus B eiu&longs;dem ma&shy;<lb/>teri&aelig;, form&aelig;, ponderis, realiter di&longs;tinguuntur? </s>

<s>quia &longs;cilicet vnus <lb/>non e&longs;t alius inquies; &amp; quare vnus non e&longs;t alius? </s>

<s>quia vnus e&longs;t hic &amp; <lb/>alius non e&longs;t hic, vnum tango, &amp; alium non tango, vnus e&longs;t meus, &amp; <lb/>alius non e&longs;t meus, &amp;c. </s>

<s>vides pr&aelig;dicata contradictoria, qu&aelig; cum eidem <lb/>&longs;imul ine&longs;&longs;e non po&longs;&longs;int per Ax. 1. diuer&longs;is, &amp; di&longs;tinctis ine&longs;&longs;e nece&longs;&longs;e <lb/>e&longs;t. </s></p><p type="main">

<s>Diceret fort&egrave; aliquis hominem reproductum in duobus locis e&longs;&longs;e po&longs;&shy;<lb/>&longs;e, &amp; dum Rom&aelig; e&longs;t &agrave; &longs;e ip&longs;o Lugduni exi&longs;tente &longs;eiunctum e&longs;&longs;e; hoc <lb/>ip&longs;um ali&agrave;s examinabimus, dum con&longs;tet mod&ograve; id totum, &longs;i fiat, mira&shy;<lb/>culo tribuendum e&longs;&longs;e, cum tamen res phy&longs;icas citra miraculum con&longs;ide&shy;<lb/>remus. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Axioma III.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s><emph type="italics"/>Vt dicatur aliquid exi&longs;tere, vel debet &longs;en&longs;u percipi, vel aliqua ratione <lb/>probari.<emph.end type="italics"/></s><s> Qui enim a&longs;&longs;erit rem aliquam po&longs;itiuam exi&longs;tere, cert&egrave; po&longs;i&shy;<lb/>tiuo argumento demon&longs;trare debet quod &longs;it; illud porr&ograve; argumentum <lb/>duci pote&longs;t vel ab experimento certo; &longs;ic probo exi&longs;tere rem aliquam, <lb/>quam video; vel ab aliqua ratione; &longs;ic ex eo qu&ograve;d cau&longs;a &longs;it nece&longs;&longs;aria <lb/>applicata &longs;ubiecto apto, probo effectum ip&longs;um produci; vel eo qu&ograve;d &longs;it <lb/>effectus probo cau&longs;am e&longs;&longs;e vel ex nece&longs;&longs;itate, qu&acirc; aliquid e&longs;t nece&longs;&longs;a&shy;<lb/>rium ad aliquem finem &agrave; natura in&longs;titutum, quo natura ip&longs;a &longs;ine ab&longs;ur-<pb xlink:href="026/01/038.jpg" pagenum="6"/>do, vel graui&longs;&longs;imo incommodo carere non pote&longs;t, probo illud ip&longs;um <lb/>e&longs;&longs;e; vel dem&ugrave;m ex aliqua reuelatione certa in rebus fidei; igitur hoc <lb/>Axioma certum e&longs;t phy&longs;ic&egrave;; quod ni&longs;i recipiatur &agrave; Philo&longs;ophis; cuique <lb/>licebit impun&egrave; mentiri; &longs;i enim dicam extra mundi huius fines e&longs;&longs;e <lb/>alios orbes, intra tuum mu&longs;&aelig;um, in quo &longs;olus fort&egrave; degis, e&longs;&longs;e quin&shy;<lb/>quaginta homines, e&longs;&longs;e mille Soles, &amp; totidem Lunas in c&oelig;lo, &amp;c. </s>

<s><lb/>numquid &longs;tatim oppones Axioma i&longs;tud, <emph type="italics"/>qua ratio, qua experientia, qua <lb/>nece&longs;&longs;itas, qua reuelatio?<emph.end type="italics"/> Qu&aelig;&longs;tio facti e&longs;t, producendi &longs;unt te&longs;tes: huc <lb/>reuoca principium illud commune. </s></p><p type="main">

<s>1. <emph type="italics"/>Non &longs;unt multiplicanda entia &longs;ine nece&longs;&longs;itate, quod cert&egrave; non valet ni&longs;i <lb/>addas, vel &longs;ine ratione, vel &longs;ine experientia.<emph.end type="italics"/></s></p><p type="main">

<s>2. <emph type="italics"/>Qui a&longs;&longs;erit aliquid po&longs;itiu&egrave;, debet argumento po&longs;itiuo probare.<emph.end type="italics"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Axioma IV.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s><emph type="italics"/>Quidquid exi&longs;tit phy&longs;ic&egrave; extra &longs;uas cau&longs;as ab omni alio &longs;eparatum, de&shy;<lb/>terminatum e&longs;t.<emph.end type="italics"/></s></p><p type="main">

<s>Hoc Axioma explicatione modic&acirc; indiget: Determinatum illud <lb/>apello, quod illud ip&longs;um e&longs;t, quod e&longs;t, &amp; nihil aliud; quod e&longs;t hoc, id <lb/>e&longs;t ab omni alio di&longs;tinctum; atqui quidquid productum e&longs;t, &longs;ingulare <lb/>e&longs;t, id e&longs;t, e&longs;t hoc; &longs;i enim producitur, alicubi producitur, &amp; ali&shy;<lb/>quando, ergo dici pote&longs;t, e&longs;t h&icirc;c, e&longs;t nunc; igitur determinatum e&longs;t. </s>

<s><lb/>Aliquis fort&egrave; &longs;tatim opponet mihi partes indeterminatas quantitatis: &longs;ed <lb/>pro&longs;ect&ograve; nulla pars actu e&longs;t qu&aelig; non &longs;it h&aelig;c, &amp; non alia; igitur qu&aelig; <lb/>non &longs;it determinata, de quo ali&agrave;s; quidquid &longs;it, &longs;altem partes ill&aelig; fa&shy;<lb/>ciunt aliquod totum quod e&longs;t determinatum, quod mihi &longs;atis e&longs;t mod&ograve; <lb/>ad veritatem huius Axiomatis. <!-- KEEP S--></s>

<s>Dices aliquid po&longs;&longs;e e&longs;&longs;e nullibi; has <lb/>nugas refutabimus in Metaphy&longs;ica, qu&aelig; in mentem &longs;apientis viri ca&shy;<lb/>dere non po&longs;&longs;unt; nunc &longs;altem con&longs;tat id naturali modo fieri non <lb/>po&longs;&longs;e. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Axioma V.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s><emph type="italics"/>Quod vnum e&longs;t, determinatum e&longs;t.<emph.end type="italics"/></s><s> Quia quod vnum e&longs;t, e&longs;t hoc, &amp; <lb/>nihil aliud; nihil enim aliud e&longs;t vnum, ni&longs;i indiui&longs;um in &longs;e, &amp; diui&shy;<lb/>&longs;um &agrave; quolibet alio: quipp&egrave; indifferentia, vel indeterminatio ibi tan&shy;<lb/>tum e&longs;t, vbi &longs;unt plura; &longs;i enim tantum vnum e&longs;t, cert&egrave; non datur op&shy;<lb/>tio, &longs;i aliqua cau&longs;a e&longs;t indifferens ad effectum A &amp; B, id e&longs;t &longs;i non e&longs;t, <lb/>cur vnum potius qu&agrave;m alium producat? </s>

<s>plures e&longs;&longs;e nece&longs;&longs;e e&longs;t; &longs;i enim <lb/>tant&ugrave;m vnus e&longs;t, cert&egrave; indifferens non e&longs;t. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Axioma VI.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s><emph type="italics"/>Quidquid e&longs;t, fru&longs;tr&agrave; non e&longs;t.<emph.end type="italics"/></s><s> Quidquid e&longs;t, id e&longs;t exi&longs;tit naturaliter <lb/>&longs;cilicet, &amp; citra miraculum, fru&longs;tr&agrave; non e&longs;t, id e&longs;t propter aliquem fi&shy;<lb/>nem e&longs;t ab ip&longs;a natura in&longs;titutum; finem autem rei ex ip&longs;o v&longs;u cogno&shy;<lb/>&longs;cimus; v&longs;um ver&ograve; ip&longs;o fer&egrave; &longs;en&longs;u: quod vt breui inductione confirme&shy;<lb/>mus, quidquid exi&longs;tit vel e&longs;t &longs;ub&longs;tantia, vel accidens; &longs;i &longs;ub&longs;tantia, vel <lb/>incorporea, vel corporea; &longs;i incorporea, vel e&longs;t Deus, vel Angelus, vel <pb xlink:href="026/01/039.jpg" pagenum="7"/>Anima rationalis; atqui nihil horum fru&longs;tr&agrave; e&longs;t, vt con&longs;tat; &longs;i corporea, <lb/>vel e&longs;t corpus, vel forma; &longs;i corpus, vel elementum, vel mixtum; <lb/>vtrumque &longs;uum finem habet, &amp; con&longs;tantem v&longs;um; &longs;i forma quamdiu <lb/>e&longs;t principium actionum compo&longs;iti fru&longs;tr&agrave; non e&longs;t; quippe ad cum finem <lb/>e&longs;t in&longs;tituta; hinc optima ratio ducitur, cur forma materialis &longs;eparata <lb/>exi&longs;tere non po&longs;&longs;it citra miraculum, quia &longs;cilicet fru&longs;tr&agrave; e&longs;&longs;et; cum enim <lb/>non po&longs;&longs;it agere ni&longs;i in &longs;ubiecto, &longs;i &longs;ubiectum non e&longs;t, fru&longs;tr&agrave; e&longs;t; at ver&ograve; <lb/>anima rationalis, qu&aelig; aliquas actiones in organicas habet, fru&longs;tr&agrave; non <lb/>e&longs;t etiam &longs;eparata, igitur immortalis e&longs;t: vtramque rationem &longs;uo loco fu&shy;<lb/>s&egrave; demon&longs;trabimus; &longs;i ver&ograve; accidens e&longs;t, haud dubi&egrave; alteri ine&longs;&longs;e debet <lb/>propter &longs;uum finem intrin&longs;ecum, quem alibi effectum formalem &longs;ecun&shy;<lb/>darium appellamus; quem &longs;cilicet pr&aelig;&longs;tat in &longs;uo &longs;ubiecto, cui cert&egrave; &longs;i ni&shy;<lb/>hil pr&aelig;&longs;taret, in eo fru&longs;tr&agrave; e&longs;&longs;et; &longs;ic caloris effectus &longs;ecundarius e&longs;t rare&shy;<lb/>factio, vel re&longs;olutio partium &longs;ui &longs;ubiecti, vel aliquid aliud; impetus, <lb/>motus &amp;c. </s>

<s>Igitur tunc effet fru&longs;tr&agrave; accidens, cum &longs;uo illo effectu careret; <lb/>hinc rationem contrarietatis aliquando petemus, certi&longs;&longs;imam quidem, <lb/>licet nouam, &amp; inde clari&longs;&longs;im&egrave; con&longs;tabit, cur, &amp; quomodo vnum contra&shy;<lb/>rium ab alio de&longs;trui dicatur; &longs;ed non e&longs;t huius loci: c&ugrave;m ver&ograve; audis fi&shy;<lb/>nem: ne qu&aelig;&longs;o cogites aliquid morale, nec enim illum finem intelligo, ad <lb/>quem ab agente rationabili de&longs;tinatur: &longs;ed eum dumtaxat, ad quem na&shy;<lb/>tura ip&longs;a, vel e&longs;&longs;entia rei &longs;pectat, &longs;ed de his &longs;atis. </s></p><p type="main">

<s>Huc reuoca Principium illud, <emph type="italics"/>Deus &amp; Natura nihil faciunt fru&longs;tr&agrave;,<emph.end type="italics"/><lb/>id e&longs;t quod &longs;uo fine careat intrin&longs;eco. </s></p><p type="main">

<s>Dices fort&egrave;, multa videri e&longs;&longs;e fru&longs;tr&agrave;, qu&aelig; tamen exi&longs;tunt; ad quid <lb/>enim vel tanta aquarum copia, vel tantus &longs;tellarum numerus, vel tot are&shy;<lb/>n&aelig; puncta? </s>

<s>tot fluitantes atomi? </s>

<s>tot in&longs;ecta? </s>

<s>&amp; vermiculi: Re&longs;pondeo <lb/>quamlibet &longs;tellam, quodlibet in&longs;ectum, &longs;eu vermiculum &longs;uis pollere pro&shy;<lb/>prietatibus; igitur fru&longs;tr&agrave; non e&longs;t, &amp; quodlibet punctum, quamlibet ato&shy;<lb/>mum, &amp; quamlibet guttulam aqu&aelig; e&longs;&longs;e partem huius vniuer&longs;itatis: quod <lb/>enim dices de vna, dicam de omnibus; equidem pauciores e&longs;&longs;e po&longs;&longs;ent; <lb/>attamen nulla e&longs;t fru&longs;tr&agrave;, cum qu&aelig;libet &longs;imul cum aliis totum hoc com&shy;<lb/>ponat. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Axioma VII.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s><emph type="italics"/>Tunc ponenda e&longs;t forma distincta &longs;ub&longs;tantialis vel accidentalis, dum e&longs;t ali&shy;<lb/>qua proprietas &longs;en&longs;ibilis, qu&aelig; non pote&longs;t tribui ip&longs;i materi&aelig;,<emph.end type="italics"/> h&icirc;c res tant&ugrave;m <lb/>naturales con&longs;idero, nec &longs;uper naturales attingo, qu&aelig; &longs;uas regulas diui&shy;<lb/>n&aelig; fidei debent, non &longs;en&longs;ibus. </s></p><p type="main">

<s>Hoc Axioma omnin&ograve; certum e&longs;t, &amp; per Ax. 3. confirmatur, vt enim <lb/>dicas aliquid di&longs;tinctum ab omni alio exi&longs;tere, vel debet id &longs;en&longs;u percipi, <lb/>vel aliqua ratione probari quod &longs;it; atqui formam &longs;ub&longs;tantialem &longs;en&longs;u <lb/>non percipis immediat&egrave;; igitur aliquem eius effectum &longs;en&longs;ibilem vel me&shy;<lb/>diat&egrave;, vel immediat&egrave;; qui cert&egrave; &longs;i tribui po&longs;&longs;it materi&aelig;, haud dubi&egrave; per il&shy;<lb/>lum formam non probabis, ni&longs;i form&aelig; ip&longs;ius e&longs;&longs;e ant&egrave; demon&longs;tres; &longs;i ve&shy;<lb/>to e&longs;t forma accidentalis, quam &longs;en&longs;u percipis; cert&egrave; id tant&ugrave;m accidit ex <pb xlink:href="026/01/040.jpg" pagenum="8"/>aliqua affectione, qu&acirc; &longs;en&longs;um ip&longs;um afficit h&aelig;c forma, igitur ex effectu il&shy;<lb/>lo illam percipis, quod clarum e&longs;t. </s></p><p type="main">

<s>Huc reuoca vulgare illud principium, <emph type="italics"/>Frustr&agrave; fit per plura, quod po&shy;<lb/>test fieri per pauciora,<emph.end type="italics"/> quod ad Tertium etiam reuocatur; quod ita in&shy;<lb/>telligi non debet, vt &longs;ine gutta aqu&aelig; Oceanus, &longs;ine &longs;tella c&oelig;lum, &longs;ine gra&shy;<lb/>nulo aren&aelig; terra, &longs;ine altero oculorum homo &longs;tare non po&longs;&longs;int; qu&aelig; <lb/>omnia fal&longs;i&longs;&longs;ima e&longs;&longs;e con&longs;tat; &longs;ed tant&ugrave;m quod illud dicatur exi&longs;tere &longs;iue <lb/>&longs;it &longs;ub&longs;tantia, &longs;iue accidens, quod vel experientia certa euincit, vel nece&longs;&shy;<lb/>&longs;itas, vel ratio, vel diuina fides (imm&ograve; &amp; humana in rebus humanis, non <lb/>tamen in &longs;cientiis.) </s></p><p type="main">

<s>Igitur nunquam claudicat hic equus Okami, vt vulg&ograve; dicitur, &longs;i hoc <lb/>fr&aelig;no regatur, &amp; pr&aelig;&longs;cripto ambulet pa&longs;&longs;u. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Ob&longs;eruabis &longs;eptem pr&aelig;mi&longs;&longs;a Axiomata, licet metaphy&longs;ica &longs;altem ali&shy;<lb/>qua ex parte e&longs;&longs;e videantur, ita pertinere ad Phy&longs;icam, vt plurim&aelig; phy&shy;<lb/>&longs;ic&aelig; affectiones &longs;ine illis explicari, &amp; demon&longs;trari non po&longs;&longs;int. </s></p><p type="main">

<s>Primum certum e&longs;t etiam certitudine metaphy&longs;ica, &longs;eu geometrica. </s>

<s><lb/>Secundum, Quartum, &amp; Quintum per Primum demon&longs;trari po&longs;&longs;unt. </s>

<s><lb/>Tertium e&longs;t veluti communis po&longs;itio, &longs;eu commune po&longs;tulatum, in quo <lb/>docti omnes conunciunt; quippe nihil &longs;ine ratione dici debet &agrave; philo&longs;o&shy;<lb/>pho; Sextum &amp; Septimum probari po&longs;&longs;unt per Tertium; &longs;ed iam ad <lb/>alia, qu&aelig; propi&ugrave;s ad phy&longs;icam accedunt, veniamus. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Axioma VIII.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s><emph type="italics"/>Quidquid prim&ograve; e&longs;t, &amp; ant&egrave; non erat, habet cau&longs;am di&longs;tinctam.<emph.end type="italics"/></s><s> Id e&longs;t quid&shy;<lb/>quid incipit e&longs;&longs;e ab alio e&longs;t; quippe &agrave; &longs;e e&longs;&longs;e non pote&longs;t; nihil enim &agrave; &longs;e <lb/>ip&longs;o dependere pote&longs;t &longs;eu produci; quia quod &agrave; &longs;e e&longs;t, nece&longs;&longs;ari&ograve; e&longs;t, <lb/>quod ver&ograve; nece&longs;&longs;ari&ograve; e&longs;t, non e&longs;&longs;e non pote&longs;t, alioquin pri&ugrave;s e&longs;&longs;et, &amp; <lb/>po&longs;terius, pri&ugrave;s vt cau&longs;a, po&longs;teri&ugrave;s vt effectus: pr&aelig;terea quidquid produci&shy;<lb/>tur aliquando producitur, &amp; alicubi, vt certi&longs;&longs;imum e&longs;t; &longs;ed quia hoc ali&shy;<lb/>qui negant, contendo tant&ugrave;m in hoc rerum ordine, &amp; naturaliter lo&shy;<lb/>quendo, quidquid producitur alicubi produci, &amp; aliquando, quod nemo <lb/>negabit; Igitur &longs;i aliquid &longs;e producit; cur h&icirc;c poti&ugrave;s quam ill&icirc;c? </s>

<s>cur <lb/>nunc potius quam ant&egrave;? </s>

<s>cum enim ant&egrave; nullibi e&longs;&longs;et, cur de&longs;init non <lb/>e&longs;&longs;e h&icirc;c &amp; non ill&icirc;c, nunc &amp; non ant&egrave;? </s>

<s>hinc quod &agrave; &longs;e e&longs;t, vbique, &amp; <lb/>&longs;emper e&longs;t, &longs;ed ne quis mihi litem intendat, licet hoc Axioma certitudi&shy;<lb/>nem geometricam habeat; &longs;ufficit mod&ograve; habere phy&longs;icam, quod ex om&shy;<lb/>nibus hypothe&longs;ibus demon&longs;tratur; &longs;i enim aliquid de nouo produci&shy;<lb/>tur, quod certum e&longs;t, ab alio produci video: calor ab igne mediat&egrave; <lb/>vel immediat&egrave;, impetus &agrave; potentia motrice, vel ab alio impetu: cuncta <lb/>h&aelig;c &longs;i reuera producuntur de quo alibi, ab alio produci con&longs;tat; in Me&shy;<lb/>taphy&longs;ica hoc ip&longs;um geometric&egrave; demon&longs;trabimus; cum enim agere &longs;up&shy;<lb/>ponat e&longs;&longs;e; quippe omnis actio alicuius agentis e&longs;t; &amp; cum agere termi&shy;<lb/>netur ad effectum, nam fieri e&longs;t alicuius fieri; cert&egrave; agens, &amp; terminus, <lb/>cau&longs;a, &amp; effectus di&longs;tinguuntur, igitur. <emph type="italics"/>Quidquid primo e&longs;t, &amp;c.<emph.end type="italics"/></s></p><pb xlink:href="026/01/041.jpg" pagenum="9"/><p type="main">

<s><emph type="center"/><emph type="italics"/>Axioma IX.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s><emph type="italics"/>Cau&longs;a debet exi&longs;tere vt immediat&egrave; agat.<emph.end type="italics"/></s><s> Hoc certum e&longs;t; quia agere <lb/>&longs;upponit e&longs;&longs;e; quippe agere e&longs;t perfectio realis actu exi&longs;tens; igitur ali&shy;<lb/>cuius actu exi&longs;tentis; igitur certum e&longs;t etiam Geometric&egrave;, de quo in <lb/>Metaph. <!-- KEEP S--></s>

<s>Iam vero &longs;ufficiat certum e&longs;&longs;e phi&longs;ic&egrave;, vt con&longs;tat ex omnibus <lb/>hypoth. </s>

<s>phy&longs;icis; nihil enim videmus agere, ni&longs;i quod e&longs;t; &longs;i enim age&shy;<lb/>ret quod non e&longs;t; cur potius h&icirc;c, &amp; nunc quam alibi, &amp; ali&agrave;s? </s>

<s>cur in <lb/>hoc &longs;ubiecto potius qu&agrave;m in alio? </s></p><p type="main">

<s>Dices, finis qui non e&longs;t influit; igitur agit; Re&longs;pondeo finem non <lb/>agere, nec influere ni&longs;i obiectiu&egrave;; atqui quod non exi&longs;tit actu, id e&longs;t in <lb/>&longs;tatu entatiuo, &amp; reali, pote&longs;t e&longs;&longs;e in &longs;tatu obiectiuo; id e&longs;t quod non <lb/>habet actum rei, pote&longs;t habere actum obiecti, id e&longs;t e&longs;&longs;e cognitum, &amp; <lb/>volitum, de quo ali&agrave;s; porr&ograve; h&icirc;c tant&ugrave;m intelligimus cau&longs;am efficien&shy;<lb/>tem, &amp;c. </s></p><p type="main">

<s>Dices, cau&longs;a principalis pulli exclu&longs;i pote&longs;t non e&longs;&longs;e; h&aelig;c omnia di&shy;<lb/>&longs;cutiemus &longs;uo loco cum de generatione animalium; &longs;ufficiat dixi&longs;&longs;e non <lb/>e&longs;&longs;e cau&longs;am immediatam, de qua h&icirc;c tantum loquimur; idem re&longs;pon&longs;um <lb/>e&longs;to de rana vaga. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Axioma X.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s><emph type="italics"/>Cau&longs;a debet e&longs;&longs;e applicata vt immediat&egrave; agat.<emph.end type="italics"/></s><s> Cur enim poti&ugrave;s h&icirc;c <lb/>quam ill&icirc;c; in hoc &longs;ubiecto poti&ugrave;s, quam in alio, in hac di&longs;tantia poti&ugrave;s, <lb/>quam in alia? </s>

<s>quidquid &longs;it, certum e&longs;t phy&longs;ic&egrave;; nec enim ignis, qui e&longs;t <lb/>Rom&aelig;, calefacit Lugduni. </s></p><p type="main">

<s>Dices dari fort&egrave; actionem in di&longs;tans; Re&longs;pondeo negando, quod de&shy;<lb/>mon&longs;trabimus in Metaph. 

pr&aelig;terea, licet daretur in productione quali&shy;<lb/>tatum occultarum, &amp; &longs;impathicorum quorundam effectuum, quos exa&shy;<lb/>minabimus &longs;uo loco; nemo tamen dubitat quin productio caloris, lu&shy;<lb/>minis, impetus; de quibus hic tant&ugrave;m agimus, debeat e&longs;&longs;e ab applicata <lb/>cau&longs;a. </s></p><p type="main">

<s>Dices impetum produci in extremitate pertic&aelig;, qu&aelig; non e&longs;t applica&shy;<lb/>ta, vel in globo tudiculario etiam non applicato; calorem &amp; lucem <lb/>produci &agrave; Sole in terra non applicata. </s>

<s>Re&longs;pondeo, e&longs;&longs;e applicationem <lb/>mediatam; nam &longs;i reuera h&aelig; qualitates producuntur continuata propa&shy;<lb/>gatione, diffunduntur per medium, in quo non e&longs;t difficultas. </s></p><p type="main">

<s>Dices etiam partes interiores cau&longs;&aelig; v. <!-- REMOVE S-->g. <!-- REMOVE S-->Solis agunt, &longs;ed non agunt <lb/>per totum medium; alioquin agerent in alias partes Solis, &agrave; quibus <lb/>obteguntur. </s>





<s>Re&longs;pondeo, diffu&longs;ionem vel propagationem actionis in&shy;<lb/>choari tantum ab ips&acirc; &longs;uperficie Solis; quippe omnes partes agunt <lb/>actione communi, de quo infr&agrave;; atqui actio communis &agrave; communi me&shy;<lb/>dio incipit. </s></p><p type="main">

<s>Dices ignem produci in parte medij remota interrupta propagatio&shy;<lb/>ne, vt con&longs;tat, &longs;i vitro per refractionem, vel &longs;peculo per reflectionem <lb/>radios Solares colligas. </s></p><p type="main">

<s>Re&longs;pondeo, ignem quidem accendi in data di&longs;tantia; at non &longs;ine <pb xlink:href="026/01/042.jpg" pagenum="10"/>aliqua applicatione, &longs;altem virtutis, in quo non e&longs;t difficultas; quomo&shy;<lb/>do vero ignis accendatur, &amp; quid &longs;it ignem accendi, explicabimus &longs;uo <lb/>loco; quidquid &longs;it, certum e&longs;t ad productionem impetus requiri ali&shy;<lb/>quam applicationem, vt patet etiam in magnte. </s>

<s>e </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Axioma XI.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s><emph type="italics"/>Si cau&longs;a vniuoca applicata, &amp; non impedita est &longs;ufficiens ad productionem <lb/>effectus, non e&longs;t ponenda alia &longs;cilicet &aelig;quiuoca.<emph.end type="italics"/></s><s> Non dico omnem cau&longs;am <lb/>e&longs;&longs;e vniuocam, &longs;ed tant&ugrave;m vniuocam &longs;ufficientem, &amp; applicatam e&longs;&longs;e <lb/>cau&longs;am, v. <!-- REMOVE S-->g. <!-- REMOVE S-->calor e&longs;t cau&longs;a &longs;ufficiens caloris, vt con&longs;tat in aqua calida; <lb/>igitur &longs;i calor e&longs;t applicatus &longs;ubiecto, in quo producitur calor non &longs;upe&shy;<lb/>rans vires caloris applicati; dicendum e&longs;t calorem illum ab hoc produ&shy;<lb/>ci; cum calor &longs;it cau&longs;a nece&longs;&longs;aria; igitur &longs;i &longs;it applicatus &longs;ubjecto apto, <lb/>nece&longs;&longs;ari&ograve; agit; igitur quantum pote&longs;t; igitur effectus non e&longs;t tribuen&shy;<lb/>dus alteri cau&longs;&aelig;, quam &longs;ufficientem e&longs;&longs;e ignoramus. </s>



</p><p type="main">

<s>Ad hoc Axioma aliud reuoca. <emph type="italics"/>Si ex applicatione alicuius &longs;equitur &longs;em&shy;<lb/>per effectus aliquis, illud ip&longs;um cau&longs;a dici debet huius effectus; licet aliud &longs;it <lb/>coniunctum, ex quo &longs;eor&longs;im &longs;umpto applicato non &longs;equitur effectus<emph.end type="italics"/>; v. <!-- REMOVE S-->g. <!-- REMOVE S-->ex <lb/>applicatione aqu&aelig; calid&aelig; &longs;equitur productio caloris; ex applicatione &longs;o&shy;<lb/>lius aqu&aelig; non &longs;equitur; igitur dicendum e&longs;t calorem hunc produci ab <lb/>ip&longs;o calore, qui aqu&aelig; ine&longs;t, non ver&ograve; ab ip&longs;a aqu&aelig; &longs;ub&longs;tantia; idem dico <lb/>de ferro frigido, &amp;c. </s>



</p><p type="main">

<s>Dices non e&longs;&longs;e certum calorem produci; Re&longs;pondeo, negando; &longs;ed, <lb/>quidquid &longs;it, loquor tant&ugrave;m hypothetic&egrave;; dixi enim &longs;i producatur, &agrave; <lb/>calore aqu&aelig; inh&aelig;rente producitur. </s></p><p type="main">

<s>Dices produci po&longs;&longs;e ab aliqua cau&longs;a ignota po&longs;ita dumtaxat tali, vel <lb/>tali conditione. </s>

<s>Re&longs;pondeo, hoc reuera geometric&egrave; non probari, &longs;ed <lb/>tant&ugrave;m phy&longs;ic&egrave;; quidquid &longs;it, voco cau&longs;am id, ex cuius applicatione <lb/>&longs;equitur &longs;emper effectus, &amp; nunquam ali&agrave;s; nam phy&longs;ic&egrave; loquendo, &longs;iue <lb/>&longs;it alia cau&longs;a, &longs;iue non, codem modo &longs;e habet, ac &longs;i e&longs;&longs;et cau&longs;a; quippe <lb/>certum e&longs;t phy&longs;ic&egrave; ignem calefacere, Solem illuminare, quod &longs;atis e&longs;t. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Axioma XII.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s><emph type="italics"/>Cau&longs;a nece&longs;&longs;aria &longs;ubiecto apto applicata, &amp; non impedita &longs;emper agit, &amp; <lb/>quantum pote&longs;t.<emph.end type="italics"/></s><s> Hoc Axioma duas partes habet; prima certa e&longs;t per hy&shy;<lb/>poth. 8. &amp; per definitionem cau&longs;&aelig; nece&longs;&longs;ari&aelig;, qu&aelig; in hoc differt &agrave; libe&shy;<lb/>r&acirc;: Secunda pars probatur; quia &longs;i partem effectus omitteret, quam ta&shy;<lb/>men ponere po&longs;&longs;et; haud dubi&egrave; non e&longs;&longs;et cau&longs;a nece&longs;&longs;aria contra hypoth. </s>

<s><lb/>nam &longs;i vnam partem effectus omittat; cur vnam poti&ugrave;s quam aliam? </s>

<s><lb/>cur non duas? </s>

<s>cur non omnes? </s>

<s>denique video cau&longs;am eandem eidem <lb/>&longs;ubiecto codem modo applicatam, eundem &longs;emper effectum producere <lb/>per Hyp. <!-- REMOVE S-->8. </s>

</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Axioma XIII<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s><emph type="italics"/>Exten&longs;io cau&longs;a non intendit effectum ad intra.<emph.end type="italics"/></s><s> Qu&aelig;libet pars maioris <lb/>ignis non habet calorem inten&longs;iorem, qu&agrave;m qu&aelig;libet pars minoris; idem <pb xlink:href="026/01/043.jpg" pagenum="11"/>dico de grauitate plumbi, &amp;c. </s>

<s>nec enim libra plumbi coniuncta cum <lb/>alia habet diuer&longs;am grauitatem ab e&acirc;, quam habet &longs;eparata. </s></p><p type="main">

<s>Dixi ad intra; quia ad extra multum iuuat exten&longs;io; &longs;ic maior ignis <lb/>longi&ugrave;s diffundit &longs;uum calorem; corpus graui&ugrave;s cadens majorem ictum <lb/>infligit; Ad hoc Axioma reuocatur i&longs;tud. </s></p><p type="main">

<s>1. <emph type="italics"/>Omnes partes eiu&longs;dem cau&longs;&aelig; agunt ad extra actione communi,<emph.end type="italics"/> iuxta <lb/>eum modum quo illam explicabimus in Metaph. 

nec punctum Solis &longs;e&shy;<lb/>paratum ad eandem di&longs;tantiam &longs;uam lucem, caloremque &longs;uum diffunde&shy;<lb/>ret; ad quam diffundit coniunctum cum aliis; idem dico de igne maiori, <lb/>&amp; minori; de quibus omnibus &longs;uo loco. </s>

<s>Huc etiam reuoca dicta illa <lb/>communia. </s></p><p type="main">

<s>2. <emph type="italics"/>Plures partes cau&longs;a plures partes effectus producunt, &amp; vici&longs;&longs;im.<emph.end type="italics"/></s></p><p type="main">

<s>3. <emph type="italics"/>Maior, &amp; perfectior cau&longs;a maiorem effectum producit, &amp; perfectiorem, <lb/>&amp; vici&longs;&longs;im.<emph.end type="italics"/></s></p><p type="main">

<s>4. <emph type="italics"/>Perfectior effectus, vel imperfectior arguit cau&longs;am perfectiorem, vel im&shy;<lb/>perfectiorem, &longs;uppo&longs;it&acirc; e&acirc;dem applicatione; &longs;i enim maior e&longs;t applicatio &longs;ine <lb/>ratione loci, &longs;iue ratione temporis; haud dubi&egrave; maior erit effectus, vt con&longs;tat.<emph.end type="italics"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Axioma XIV.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s><emph type="italics"/>Quidquid de&longs;truitur non e&longs;t &agrave; &longs;e.<emph.end type="italics"/></s><s> Hoc Axioma geometricum e&longs;t; Quod <lb/>enim e&longs;t &agrave; &longs;e, nece&longs;&longs;ari&ograve; e&longs;t; c&ugrave;m &agrave; libertate &longs;eu voluntate alterius non <lb/>pendeat; cum enim primo in&longs;tanti quo res e&longs;t, non &longs;it &agrave; &longs;e per Axiom. <!-- REMOVE S-->8. <lb/>de &longs;ecundo idem dici debet, quod de primo, vt patet: quippe id eo <lb/>primo in&longs;tanti non e&longs;t nece&longs;&longs;ari&ograve;, quia ita e&longs;t illo in&longs;tanti, vt po&longs;&longs;it non <lb/>e&longs;&longs;e; &longs;ed etiam &longs;ecundo in&longs;tanti ita e&longs;t vt po&longs;&longs;it non e&longs;&longs;e; igitur non e&longs;t <lb/>nece&longs;&longs;ari&ograve;, igitur pendet ab alio, quod pote&longs;t facere vt non &longs;it. </s>

</p><p type="main">

<s>Dices po&longs;&longs;e de&longs;trui &longs;ecundo in&longs;tanti ab aliquo contrario, &agrave; quo tamen <lb/>non pendet per po&longs;itiuum influxum. </s>

<s>Re&longs;pondeo, non videri quomo&shy;<lb/>do de&longs;trui po&longs;&longs;it, quod influxu po&longs;itiuo non indiget, vt &longs;it; quid enim <lb/>faceret contrarium, quod tant&ugrave;m exigere pote&longs;t contrarij de&longs;tructio&shy;<lb/>nem, quid e&longs;t porro de&longs;trui, ni&longs;i de&longs;inere con&longs;eruari? </s>

<s>qu&aelig; omnia fus&egrave; <lb/>in Metaphy&longs;ica demon&longs;trabimus; quidquid enim e&longs;t aliquo in&longs;tanti vel <lb/>e&longs;t &agrave; &longs;e, vel non &agrave; &longs;e; &longs;i prim&ugrave;m Deus e&longs;t; &longs;i &longs;ecundum ab alio e&longs;t: <lb/>quidquid &longs;it, hoc Axioma certum e&longs;t phy&longs;ic&egrave;. </s></p><p type="main">

<s>Huc reuoca Axiomata &longs;equentia, qu&aelig; ex hoc vno deducuntur. </s></p><p type="main">

<s>1. <emph type="italics"/>Quidquid e&longs;t, &amp; non e&longs;t &agrave; &longs;e, e&longs;t, &longs;eu pendet, &longs;eu con&longs;eruatur ab alio.<emph.end type="italics"/><lb/>H&aelig;c enim &longs;unt idem, vt con&longs;tat. </s></p><p type="main">

<s>2. <emph type="italics"/>Quidquid destruitur, ad exigentiam alicuius de&longs;truitur, &longs;altem totius <lb/>natura, ne aliquid &longs;it fru&longs;tr&agrave;.<emph.end type="italics"/></s><s> Hoc etiam ex hypothe&longs;ibus &longs;equitur; cum <lb/>enim de&longs;trui &longs;it idem ac de&longs;inere con&longs;eruari; cert&egrave; qui de&longs;init con&longs;er&shy;<lb/>uare in&longs;tanti A poti&ugrave;s quam in&longs;tanti B, hoc facere non pote&longs;t ni&longs;i ali&shy;<lb/>quid hoc exigat; &longs;cilicet iuxta leges natur&aelig;. </s></p><p type="main">

<s>3. <emph type="italics"/>Tandiu aliquid con&longs;eruatur, quandiu nihil exigit eius de&longs;tructionem.<emph.end type="italics"/><lb/>Hoc &longs;equitur ex priori, id e&longs;t quandiu e&longs;t eadem ratio, cur &longs;it, &amp; con&shy;<lb/>&longs;eruetur, qu&aelig; erat ant&egrave;. </s></p><pb xlink:href="026/01/044.jpg" pagenum="12"/><p type="main">

<s><emph type="center"/><emph type="italics"/>Axioma XV.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s><emph type="italics"/>Contraria pugnant pro rata.<emph.end type="italics"/></s><s> Nec enim alia regula e&longs;&longs;e pote&longs;t; &longs;ic minor <lb/>calor min&ugrave;s de&longs;truit frigoris; minor impetus min&ugrave;s de&longs;truit impetus <lb/>contrarij (&longs;i contrarium habet) qu&aelig; omnia con&longs;tant ex hypothe&longs;ibus. </s>

<s><lb/>Ratio e&longs;t, quia pl&ugrave;s vel min&ugrave;s contrarij de&longs;truere, multam habet ex&shy;<lb/>ten&longs;ionem. </s>

<s>v.g. <!-- REMOVE S-->&longs;int duo contraria A &amp; B, &longs;it A vt 20. &longs;it B vt 5. cert&egrave; &longs;i <lb/>B de&longs;truat A &longs;upra ratam, vel &longs;upra id, quod &longs;ibi ex &aelig;quo re&longs;pondet, id <lb/>e&longs;t &longs;upra 5. cur potius 6. quam 7. 8. &amp;c. </s>



<s>Si infra, cur potius 4. quam 3. <lb/>2. &amp;c. </s>

<s>Igitur cum plures &longs;int termini t&ugrave;m infra, t&ugrave;m &longs;upra 5. cur potius <lb/>vnus qu&agrave;m alius? </s>

<s>atqui vnus tant&ugrave;m ex &aelig;quo re&longs;pondet, &longs;cilicet 5. &longs;ed <lb/>quod vnum e&longs;t determinatum e&longs;t, per Axioma 5. igitur pugnant pro <lb/>rata. </s>

<s>Nec dicas A totum de&longs;trui &agrave; B, qu&ograve;d e&longs;t contra hypothe&longs;im, nam <lb/>modicum caloris non de&longs;truit totum frigus: in impetu res e&longs;t clari&longs;&longs;ima; <lb/>adde quod minor cau&longs;a min&ugrave;s agit per Ax. 13. num. </s>

<s>3. igitur min&ugrave;s exi&shy;<lb/>git; porr&ograve; cum dico vnum ab alio de&longs;trui, intelligo tant&ugrave;m ex applica&shy;<lb/>tione vnius &longs;equi de&longs;tructionem alterius &longs;altem ex parte. </s></p><p type="main">

<s>Ob&longs;eruabis h&aelig;c Axiomata &longs;altem maiori ex parte e&longs;&longs;e metaph. </s>

<s>qu&aelig; <lb/>nos fus&egrave; in Theorematis metaph. </s>

<s>explicabimus, &amp; demon&longs;trabimus; &longs;ed <lb/>nobis hoc loco &longs;atis e&longs;t, &longs;i parem cum phy&longs;icis &longs;upponas habere cer&shy;<lb/>titudinem, quod nemo negabit; con&longs;t&aacute;tque ex hypothe&longs;ibus, lic&egrave;t ma&shy;<lb/>iorem etiam habeant, de qua &longs;uo loco. </s></p><p type="main">

<s>Ob&longs;eruabis pr&aelig;tere&agrave; nos diuti&ugrave;s h&aelig;&longs;i&longs;&longs;e in pr&aelig;mittendis huic libro <lb/>Axiomatis, quod tamen in aliis libris non faciemus. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Postulatum,<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s><emph type="italics"/>Liceat datum corpus impellere, proiicere, deor&longs;um cadens excipere, motus <lb/>durationem &longs;en&longs;ibilem, &longs;patiumque &longs;en&longs;ibile, metiri, comparare, &amp;c.<emph.end type="italics"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 1.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s><emph type="italics"/>Motus e&longs;t aliquid realiter di&longs;tinctum &agrave; mobili.<emph.end type="italics"/></s><s> Demon&longs;tratur; Motus <lb/>e&longs;t in mobili, in quo ant&egrave; non erat per hypoth. </s>

<s>3. &amp; de&longs;init e&longs;&longs;e in mobili, <lb/>in quo ant&egrave; erat per hypoth.4. igitur mobile e&longs;t, &amp; non e&longs;t motus; igi&shy;<lb/>tur &agrave; motu &longs;eparatum; igitur realiter di&longs;tinctum per Ax. 2. pr&aelig;terea <lb/>moueri, &amp; non moueri &longs;unt pr&aelig;dicata contradictoria, vt con&longs;tat; igi&shy;<lb/>tur eidem &longs;imul ine&longs;&longs;e non po&longs;&longs;unt per Ax. 1. igitur cum eo non &longs;unt <lb/>idem; alioquin &longs;imul e&longs;&longs;ent; igitur alterum illorum e&longs;t di&longs;tinctum &agrave; <lb/>mobili; non quies, vt con&longs;tat, qu&aelig; e&longs;t tant&ugrave;m negatio motus, &longs;eu per&shy;<lb/>&longs;euerantia in eodem loco; igitur nullam dicit mutationem; at ver&ograve; <lb/>motus mutationem dicit, per Def. <!-- REMOVE S-->1. hoc Theorema fus&egrave; demon&longs;trabo <lb/>in Metaph. <!-- KEEP S--></s>

</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 2.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s><emph type="italics"/>Motus non pote&longs;t dici propri&egrave; productus immediat&egrave;, vel effectus immedia&shy;<lb/>tus cau&longs;&aelig; efficientis.<emph.end type="italics"/></s><s> Demon&longs;t. </s>

<s>Motus e&longs;t mutatio, &longs;eu tran&longs;itus ex loco <lb/>in locum per Def. <!-- REMOVE S-->1. &longs;ed mutatio propri&egrave; non producitur; quipp&egrave; pro&shy;<lb/>ductio tant&ugrave;m terminatur ad ens; nihil enim ni&longs;i ens produci pote&longs;t; <pb xlink:href="026/01/045.jpg" pagenum="13"/>atqui nulla mutatio dicit tant&ugrave;m ens; pr&aelig;&longs;ertim h&aelig;c, qu&aelig; tant&ugrave;m dicit <lb/>terminum &agrave; quo, ide&longs;t locum relictum; &amp; terminum ad quem, id e&longs;t lo&shy;<lb/>cum immediatum acqui&longs;itum; nam &longs;eparato quocunque alio ab ip&longs;o <lb/>mobili; modo &longs;imul, id e&longs;t eodem in&longs;tanti relinquat primum locum, &amp; <lb/>nouum acquirat, omnin&ograve; mouetur, &longs;ed concretum illud ex loco relicto, <lb/>&amp; acqui&longs;ito produci non pote&longs;t; illud autem e&longs;t motus, qui cert&egrave; non <lb/>dicit tant&ugrave;m locum relictum &longs;ine acqui&longs;ito; alioqui &longs;i mobile de&longs;true&shy;<lb/>retur, diceretur moueri; nec etiam locum acqui&longs;itum &longs;ine priori relicto: <lb/>alioqui &longs;i mobile prim&ograve; produceretur, diceretur moueri localiter; igitur <lb/>motus neutrum dicit &longs;eor&longs;im; &longs;i primum, diceretur de&longs;tructus; &longs;i &longs;ecun&shy;<lb/>dum, diceretur aliquo modo productus, vel poti&ugrave;s acqui&longs;itus; at vtrum&shy;<lb/>que coniunctim, &longs;imulque e&longs;&longs;entialiter dicit motus; nec enim conci&shy;<lb/>pio aliud, dum concipio motum: porr&ograve; vtrumque &longs;imul &longs;umptum indi&shy;<lb/>ui&longs;ibiliter non pote&longs;t dici, vel de&longs;tructum propri&egrave;, vel productum; Di<gap/><lb/>xi propri&egrave;; nam impropri&egrave; dici pote&longs;t motus productus. </s>

</p><p type="main">

<s>Dices Motus e&longs;t ens, non &agrave; &longs;e; igitur ab alio; igitur motus e&longs;t pro&shy;<lb/>ductus. </s>

<s>Re&longs;pondeo Motum non e&longs;&longs;e ens ab&longs;olutum, &longs;ed e&longs;&longs;e mutatio&shy;<lb/>nem entis, qu&aelig; mutatio e&longs;t concretum quoddam ex ente &amp; non ente; <lb/>qu&ograve;d cert&egrave; non pote&longs;t dici propri&egrave; productum, &longs;ed re&longs;ultans, vt relatio; <lb/>nam producatur, &longs;i fieri pote&longs;t; cert&egrave; e&longs;t aliquid, quod tam facil&egrave; de&shy;<lb/>&longs;trui pote&longs;t, quam produci; igitur de&longs;truatur, &amp; remaneat tant&ugrave;m en&shy;<lb/>titas mobilis, qu&aelig;, quo in&longs;tanti priorem locum relinquit, nouum acqui&shy;<lb/>rat; cert&egrave; dicitur adhuc moueri, &amp; tamen non erit motus ex &longs;uppo&longs;itio&shy;<lb/>ne, quod ab&longs;urdum e&longs;t. </s></p><p type="main">

<s>Dices potentia motrix e&longs;t actiua; igitur agit; igitur producit, &longs;ed ni&shy;<lb/>hil ni&longs;i motum. </s>

<s>Re&longs;p. potentiam motricem e&longs;&longs;e actiuam vt dicemus, <lb/>&amp; ab e&acirc; produci impetum, qui deinde exigit motum, vt dicemus <lb/>infr&agrave;. </s></p><p type="main">

<s>Nec e&longs;t quod aliqui ita mirentur h&aelig;c &agrave; me dici; cum certum &longs;it effe&shy;<lb/>ctus formales &longs;ecundarios principum fer&egrave; qualitatum tales e&longs;&longs;e, vt mini&shy;<lb/>m&egrave; producantur; &longs;ed qua&longs;i re&longs;ultent ab exigentia; v. <!-- REMOVE S-->g. <!-- REMOVE S-->effectus calo&shy;<lb/>ris in &longs;uo &longs;ubiecto e&longs;t eiu&longs;dem &longs;ubiecti rarefactio, qu&aelig; reuer&acirc; non <lb/>producitur, vt con&longs;tat. </s>



</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 3.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s><emph type="italics"/>Motus e&longs;t ab alio di&longs;tincto in aliquo genere cau&longs;&aelig;.<emph.end type="italics"/></s><s> Demon&longs;tratur, quia <lb/>motus, qui non erat, incipit e&longs;&longs;e per hypothe&longs;im tertiam; &longs;ed quod <lb/>huiu&longs;modi e&longs;t, habet cau&longs;am di&longs;tinctam per Ax.8. <!-- KEEP S--></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Ob&longs;eruabis motum localem e&longs;&longs;e duplicis generis; primum genus mo&shy;<lb/>tus e&longs;t actio potenti&aelig; motricis, qu&aelig; reuer&agrave; mouet, &amp; cuius exercitium <lb/>dicitur motus, &longs;eu latio, &longs;eu motio, &longs;eu actio, qua reuer&acirc; agit, produ&shy;<lb/>citque impetum, non motum; cum etiam &longs;ine motu defatigetur, vt cum <lb/>quis alium pellit, &agrave; quo pellitur &aelig;quali ni&longs;u; patet etiam in manu &longs;u&shy;<lb/>&longs;tinente aliquod pondus, qu&aelig; non mouetur; licet reuer&acirc; etiam &longs;ummo <pb xlink:href="026/01/046.jpg" pagenum="14"/>conatu agat: imm&ograve; &longs;i potentia motrix produceret motum primum, non <lb/>impetum in corpore proiecto; nulla deinde e&longs;&longs;et cau&longs;a applicata ad pro&shy;<lb/>ducendum impetum: Itaque hic motus primi generis, &longs;i comparetur <lb/>cum potentia motrice, e&longs;t ver&egrave; influxus, vel actio; &longs;i cum termino, e&longs;t <lb/>eius fieri, &longs;eu dependentia; &longs;i cum &longs;ubiecto, &longs;eu mobili e&longs;t pa&longs;&longs;io; nec <lb/>propri&egrave; dicitur produci, ni&longs;i vt quo (vt vulg&ograve; loquuntur) nec enim <lb/>actio e&longs;t terminus, vel effectus, in quo &longs;i&longs;tat cau&longs;a; &longs;ed e&longs;t via, qua ten&shy;<lb/>dit ad terminum. </s>

<s>Motus &longs;ecundi generis e&longs;t mutatio, &longs;eu tran&longs;itus ex <lb/>vno loco in alium; hoc e&longs;t finis, vel effectus formalis &longs;ecundarius, <lb/>quem exigit impetus; &amp; fru&longs;tr&agrave; ponitur alia entitas, qu&aelig; tant&ugrave;m e&longs;&longs;et <lb/>in&longs;tituta ad exigendam i&longs;tam loci mutationem; Igitur &longs;i &longs;ufficienter <lb/>exigatur ab ip&longs;o impetu, de quo infr&agrave;, cert&egrave; fru&longs;tra ponitur quodcun&shy;<lb/>que aliud per Ax.3. &amp; 7. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 4.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s><emph type="italics"/>Cau&longs;a illa immediata motus, qu&aelig; non est efficiens, potest tant&ugrave;m e&longs;&longs;e exi&shy;<lb/>gens, qu&aelig; reducitur ad formalem, qu&aelig; &longs;uum effectum formalem &longs;ecundarium, <lb/>id est &longs;uum finem intrin&longs;ecum exigit.<emph.end type="italics"/></s><s> Sic calor exigit rarefactionem, vel <lb/>re&longs;olutionem, impetus motum; cum enim non &longs;it cau&longs;a efficiens per Th. <!-- REMOVE S--><lb/>2. &longs;it tamen cau&longs;a per Th.3. nec &longs;it materialis, nec finalis, vt con&longs;tat, de&shy;<lb/>bet e&longs;&longs;e formalis, vel exigens, &longs;eu exigitiua; vt patet ex ip&longs;a cau&longs;arum <lb/>enumeratione; non e&longs;t materialis, quia non recipit motum, ni&longs;i ab alio; <lb/>nec finalis, qu&aelig; &longs;upponit alias; cum ip&longs;a non &longs;it dum ponitur <lb/>effectus. </s>

</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 5.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s><emph type="italics"/>Entitas &longs;eu &longs;ubstantia mobilis non e&longs;t cau&longs;a immediata motus,<emph.end type="italics"/> Sit enim <lb/>lapis proiectus per Po&longs;tul. <!-- REMOVE S-->haud dubi&egrave; &longs;ub&longs;tantia lapidis non e&longs;t cau&longs;a <lb/>huius motus; quia lapis tandem &longs;i&longs;tit per hypoth.4. igitur non e&longs;t cau&longs;a <lb/>motus, quia e&longs;&longs;et cau&longs;a nece&longs;&longs;aria; igitur &longs;emper cau&longs;aret per Ax.12. pr&aelig;&shy;<lb/>terea potentia motrix proiicientis ver&egrave; agit, cum etiam defatigetur; igi&shy;<lb/>tur aliquid producit, non motum immediat&egrave;, qui produci non pote&longs;t pro<lb/>pri&egrave;per Th. 2. Adde quod motus &longs;ecundi generis habet tant&ugrave;m cau&longs;am <lb/>immediatam exigentem, &longs;ed potentia motrix non exigit; quia prim&ograve; <lb/>non defatigaretur exigendo; &longs;ecund&ograve; quia lapis &longs;eparatus &agrave; manu etiam <lb/>mouetur, &longs;ed non ad exigentiam potenti&aelig; motricis, vt patet; quia &longs;tatim <lb/>po&longs;t &longs;eparationem pote&longs;t illa potentia de&longs;trui, lic&egrave;t lapis longo p&ograve;&longs;t <lb/>tempore moueatur; &longs;ed quod non e&longs;t, nihil exigit. </s>

</p><p type="main">

<s>Aliquis fort&egrave; diceret potentiam motricem exigere primam partem <lb/>motus, qu&aelig; deinde &longs;ecundam exigit, &amp; &longs;ecunda tertiam, tertia quar&shy;<lb/>tam, &amp;c. </s>

<s>Sed contra; qu&aelig;ro quid &longs;it prima illa pars motus; nec enim <lb/>aliud agno&longs;co ni&longs;i primam mutationem loci, qu&aelig; mutatio non pote&longs;t <lb/>exigere ni&longs;i quando e&longs;t; atqui quando e&longs;t, nihil reale e&longs;t actu ni&longs;i mo&shy;<lb/>bile, &amp; nouus locus acqui&longs;itus, mobile ip&longs;um non exigit, vt demon&longs;tra&shy;<lb/>tum e&longs;t, &amp; conce&longs;&longs;um, nec etiam locus de nouo acqui&longs;itus, in quo <lb/>&longs;cilicet mobile &longs;i&longs;tere pote&longs;t: quidquid pones aliud, impetum appellabo. </s></p><pb xlink:href="026/01/047.jpg" pagenum="15"/><p type="main">

<s>Dices cum graue aliquod mouetur deor&longs;um, vel leue &longs;ur&longs;um, vel <lb/>corpus animatum &longs;e ip&longs;um mouet, dici pote&longs;t &longs;ub&longs;tantia corporis cau&longs;a <lb/>immediata motus. </s>

<s>Re&longs;p. negando, t&ugrave;m quia omnis potentia motrix <lb/>agit; igitur producit aliquid aliud, quod e&longs;t cau&longs;a motus: pr&aelig;terea po&shy;<lb/>tentia motrix corporis animati, agit v&longs;que ad defatigationem, &longs;udorem, <lb/>lic&egrave;t non &longs;it motus, igitur aliud producit, de corpore graui probabi&shy;<lb/>mus infr&agrave;. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 6.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s><emph type="italics"/>Datur impetus.<emph.end type="italics"/></s><s> Demon&longs;tro, Sub&longs;tantia mobilis non e&longs;t cau&longs;a imme&shy;<lb/>diata motus, per Th.5. ergo aliquid aliud; igitur impetus, nam quod di&shy;<lb/>&longs;tinctum e&longs;t &agrave; &longs;ub&longs;tantia mobilis, &amp; exigit motum, e&longs;t impetus per <lb/>Def.3. &longs;ed quia hoc Theorema e&longs;t veluti princeps huius tractatus cardo, <lb/>in eo paul&ograve; diutius h&aelig;rendum e&longs;t, igitur. </s></p><p type="main">

<s>Demon&longs;tro prim&ograve; dari impetum: Quidquid e&longs;t, &amp; ant&egrave; non erat, non <lb/>e&longs;t &agrave; &longs;e, &longs;ed habet cau&longs;am per Ax.8. Motus de nouo e&longs;t per hypothe&longs;im <lb/>tertiam; igitur habet cau&longs;am, &longs;ed non aliam, quam impetum, quod pro&shy;<lb/>bo: Lapis cadens, vel impactus in alium lapidem mouet illum per hy&shy;<lb/>poth.7. &longs;ed &longs;ub&longs;tantia lapidis in alium impacti non e&longs;t cau&longs;a huius mo&shy;<lb/>tus, quia e&longs;&longs;et cau&longs;a nece&longs;&longs;aria vt patet; igitur applicata eundem effe&shy;<lb/>ctum produceret per Ax.12. &longs;ed etiam applicata immediata non agit, vt <lb/>con&longs;tat experientia; igitur per idem Axioma non e&longs;t cau&longs;a. </s></p><p type="main">

<s>Scio e&longs;&longs;e aliquas re&longs;pon&longs;iones, quas infr&agrave; refellemus; nunc &longs;ufficiat <lb/>dixi&longs;&longs;e lapidem impactum non producere motum, qui propri&egrave; non pro&shy;<lb/>ducitur per Th.2. nec exigere, vt con&longs;tat ex &longs;ecunda probatione Th. 5. <lb/>igitur &longs;i aliquid exigit, vel producit, voco impetum. </s></p><p type="main">

<s>Secund&ograve; probatur; potentia motrix e&longs;t actiua, quia defatigatur, quis <lb/>hoc neget? </s>

<s>igitur aliquid producit; non motum, qui propri&egrave; non pro&shy;<lb/>ducitur per Th.2. igitur aliquid aliud; voco impetum; adde quod etiam <lb/>&longs;ine motu agit, &amp; defatigatur vt iam dictum e&longs;t; igitur habet alium effe&shy;<lb/>ctum immediatum; denique mouere, pellere, trahere, proiicere, percu&shy;<lb/>tere, nihil ni&longs;i actionem &longs;onant. </s></p><p type="main">

<s>Terti&ograve; probatur; pila di&longs;iuncta &agrave; manu proiicientis diu adhuc mo&shy;<lb/>uetur per hypoth.6. igitur hic motus habet cau&longs;am per Ax. 8. qu&aelig;libet <lb/>enim pars motus de nouo e&longs;t, neque du&aelig; illius partes &longs;imul e&longs;&longs;e po&longs;&longs;unt. </s>

<s><lb/>atqui potentia motrix non e&longs;t cau&longs;a per Ax.10. imm&ograve; pote&longs;t e&longs;&longs;e de&longs;tru&shy;<lb/>cta; igitur non e&longs;t cau&longs;a per Ax. 9. <!--neuer Satz-->Non e&longs;t etiam cau&longs;a &longs;ub&longs;tantia pil&aelig; <lb/>mobilis per Th.5.5. nec priores pattes motus per re&longs;p. </s>

<s>ad primam in&shy;<lb/>&longs;tantiam Th 5. igitur aliquid aliud; voco impetum. </s></p><p type="main">

<s>Quart&ograve; probatur; pila proiecta &longs;en&longs;im &longs;ine &longs;en&longs;u tardiore motu <lb/>mouetur; donec tandem moueri omnino de&longs;inat per hypoth. </s>

<s>5. igitur <lb/>non e&longs;t &longs;emper &aelig;qualis, &amp; eadem cau&longs;a huius motus per Ax. 12. &amp; 13. <lb/>num.3. igitur cau&longs;a huius motus eodem modo debilitatur, &longs;eu remitti&shy;<lb/>tur, quo ip&longs;e motus; &longs;ed decre&longs;cit &longs;ub&longs;tantia mobilis, nec potentia mo-<pb xlink:href="026/01/048.jpg" pagenum="16"/>trix, vel corpus prius impactum; ergo e&longs;t alia cau&longs;a pr&aelig;&longs;ens, qu&aelig; mi&shy;<lb/>nuitur; voco impetum. </s></p><p type="main">

<s>Quint&ograve; corpus graue deor&longs;um cadens accelerat &longs;uum motum, vt patet <lb/>experientia; qu&aelig; maxim&egrave; clara e&longs;t in funependulis, de qua in &longs;equen&shy;<lb/>tibus libris; igitur debet e&longs;&longs;e cau&longs;a huius motus velocioris; non e&longs;t au&shy;<lb/>tem &longs;ub&longs;tantia lapidis, nec grauitas per Ax. 12. nec aliud quidpiam ex&shy;<lb/>trin&longs;ecum, vt videbimus &longs;uo loco; igitur aliquid aliquid intrin&longs;ecum, <lb/>voco impetum. </s>

<s>Igitur certum e&longs;t dari impetum; qui cert&egrave; tribui non <lb/>pote&longs;t, vel vlli connotationi, vel alteri exigenti&aelig;, vt con&longs;tat ex <lb/>dictis. </s></p><p type="main">

<s>Diceret fort&egrave; alius h&aelig;c omnia e&longs;&longs;e dubia; nam fieri pote&longs;t vt Deus <lb/>tant&ugrave;m moueat; quod &longs;ine impetu fieri po&longs;&longs;e certum e&longs;t; Re&longs;p. equi&shy;<lb/>dem per miraculum hoc fieri po&longs;&longs;e; &longs;ed quemadmadum certum e&longs;t phy&shy;<lb/>&longs;ic&egrave; ignem applicatum calefacere, niuem frigefacere, &amp; mod&ograve; calamum <lb/>&agrave; me h&aelig;c &longs;cribente moueri, ita certum o&longs;t phy&longs;ic&egrave; &longs;agittam &agrave; &longs;agittario <lb/>emitti, &amp; pilam &agrave; proiiciente, &amp;c. </s>

<s>adde quod Deus, vt auctor natur&aelig; <lb/>e&longs;t, agit tant&ugrave;m; vel de&longs;init agere iuxta exigentiam cau&longs;arum &longs;ecunda&shy;<lb/>rum; denique cau&longs;am phy&longs;ic&egrave; appello, ex cuius applicatione nunquam <lb/>non &longs;equitur effectus per Ax.11. num.1. </s></p><p type="main">

<s>Dicerent alij hoc totum prouenire &agrave; corpu&longs;culis; vel atomis, vel fila&shy;<lb/>mentis &longs;ine vlla actione; equidem non reiicio corpu&longs;cula, &amp; perennia <lb/>corporum effluuia: Dico tamen prim&ograve; globum quie&longs;centem humi ha&shy;<lb/>bere &longs;altem aliquas partes quie&longs;centes, vel immobiles; quis hoc neget? </s>

<s><lb/>imm&ograve; maximam &longs;uarum partium partem; igitur cum deinde proiicitur <lb/>idem globus, ill&aelig; partes mouentur; dari igitur debet cau&longs;a huius motus <lb/>per Ax.8, igitur impetus: nec dicas moueri illas partes &agrave; corpu&longs;culis; quia <lb/>ant&egrave; erant eadem, imm&ograve; plura corpu&longs;cula; &amp; tamen non mouebant: igi&shy;<lb/>tur non &longs;unt cau&longs;a huius motus per Ax.12. Dices excitari; &longs;ed quid hoc <lb/>e&longs;t excitari? </s>

<s>vel enim mutantur, vel non mutantur; &longs;ecundum dici <lb/>non pote&longs;t; quia vt excitentur, ex non excitatis mutari debent; igitur <lb/>per aliquid: deinde quid e&longs;t illa excitatio, ni&longs;i impul&longs;io; igitur &longs;i mouen&shy;<lb/>tur illa corpu&longs;cula, &amp; excitantur &agrave; potentia motrice, etiam partes prius <lb/>immobiles mouebuntur, &amp; excitabuntur per Ax.12. quia &longs;unt applicat&aelig; <lb/>cau&longs;&aelig; nece&longs;&longs;ari&aelig;. </s></p><p type="main">

<s>Dico &longs;ecund&ograve; minimum ex his corpu&longs;culis non &longs;emper moueri; po&shy;<lb/>te&longs;t enim &longs;i&longs;tere; quis hoc neget? </s>

<s>igitur &longs;i mod&ograve; mouetur, mod&ograve; quie&longs;&shy;<lb/>cit, motus ab eo di&longs;tinguitur per Th.1. igitur mouetur per impetum, de <lb/>quo infr&agrave;. </s></p><p type="main">

<s>Igitur datur nece&longs;&longs;ari&ograve; impetus, &longs;ine quo non po&longs;&longs;unt explicari pr&aelig;di&shy;<lb/>ct&aelig; omnes hypothe&longs;es, contra quem &longs;unt quidem graui&longs;&longs;im&aelig; difficultates, <lb/>quas &longs;en&longs;im in &longs;equentibus Theorematis, in quibus explicantur pro&shy;<lb/>prietates huius impetus, di&longs;cutiemus. </s></p><p type="main">

<s>Diceret aliquis lapidem impul&longs;um ab a&euml;re deinde propelli; &longs;ed a&euml;r po&shy;<lb/>tius re&longs;i&longs;tit motui; vt con&longs;tat experienti&acirc;; &longs;ed hoc &longs;oluemus infr&agrave;. </s></p><pb xlink:href="026/01/049.jpg" pagenum="17"/><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 7.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Impetus est aliquid distinctum &agrave; &longs;ubstanti&acirc; mobilis.<emph.end type="italics"/></s><s> Demon&longs;tratur. </s>

<s><lb/>Quia &longs;ub&longs;tantia mobilis non e&longs;t cau&longs;a exigens motum per Th. 5. Impe&shy;<lb/>tus e&longs;t cau&longs;a exigens per Def. <!-- REMOVE S-->3. &amp; Th. 6. de codem contradictoria dici <lb/>non po&longs;&longs;unt per Ax. 1. n. </s>

<s>3. Igitur impetus non e&longs;t idem cum &longs;ub&longs;tanti&agrave; <lb/>mobilis; igitur di&longs;tinctus; deinde &longs;eparari pote&longs;t &agrave; &longs;ub&longs;tantia mobilis <lb/>per Hypoth. <!-- KEEP S--></s>

<s>4. igitur e&longs;t di&longs;tinctus per Ax. 2. <!-- KEEP S--></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 8.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Impetus est accidens<emph.end type="italics"/>; Quippe non e&longs;t corpus, nec forma &longs;ub&longs;tantia&shy;<lb/>lis; quia omne corpus, &amp; omnis forma &longs;ub&longs;tantialis moueri pote&longs;t, &amp; <lb/>non moueri, vt con&longs;tat ex po&longs;t. </s>

<s>&amp; ex Hypoth. <!-- KEEP S--></s>

<s>3. &amp; 4. igitur di&longs;tingui&shy;<lb/>tur &agrave; motu; igitur &amp; ab impetu per Ax. 2. igitur impetus non e&longs;t &longs;ub&shy;<lb/>&longs;tantia; igitur accidens. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 9.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Impetus non e&longs;t modus.<emph.end type="italics"/></s><s> Modus duplicis generis e&longs;&longs;e pote&longs;t: Modus <lb/>primi generis e&longs;t entitas qu&aelig;dam diminuta, vt vulg&ograve; loquuntur, di&longs;tin&shy;<lb/>cta quidem modaliter, vt aiunt, &agrave; re, cui adh&aelig;ret; ac proinde ab ca &longs;e&shy;<lb/>parari pote&longs;t, non tamen exi&longs;tere &longs;eparata. </s>

<s>Modus &longs;ecundi generis non <lb/>e&longs;t entitas quidem di&longs;tincta; e&longs;t tamen &longs;tatus quidam corporis; &longs;ic &longs;e&longs;&longs;io <lb/>e&longs;t modus, conden&longs;atio, compre&longs;&longs;io, &amp;c. </s>

<s>His po&longs;itis Impetus non e&longs;t mo&shy;<lb/>dus primi generis; nihil enim probat impetum e&longs;&longs;e modum, quod etiam <lb/>non probet calorem, &amp; lucem e&longs;&longs;e modos; dicere autem omnia acci&shy;<lb/>dentia e&longs;&longs;e modos non debemus, de quo &longs;uo loco; modus enim ita &agrave; na&shy;<lb/>tur&acirc; comparatus e&longs;t, vt &longs;ine &longs;ubiecto actuali &longs;eu fulcro non exi&longs;tere mo&shy;<lb/>d&ograve;, &longs;ed ne concipi quidem po&longs;&longs;it; v. <!-- REMOVE S-->g. <!-- REMOVE S-->actio non pote&longs;t concipi ni&longs;i &longs;it <lb/>alicuius actio; nec fieri &longs;ine facto; nec via &longs;ine termino; nec dependen&shy;<lb/>tia &longs;ine dependente; at ver&ograve; po&longs;&longs;um concipere calorem, &amp; impetum <lb/>&longs;ine alio, quod &longs;it actu; lic&egrave;t enim calor exigat re&longs;olutionem partium <lb/>&longs;ui &longs;ubiecti, &longs;eu rarefactionem, &amp; impetus motum; nihil tamen impe&shy;<lb/>dit, quin per miraculum calor, &amp; impetus con&longs;eruari po&longs;&longs;int &longs;ine eo. </s>

<s><lb/>quod exigunt, hoc e&longs;t &longs;ine &longs;uo &longs;ine; igitur &longs;ine &longs;ubiecto; non e&longs;t etiam <lb/>modus &longs;ecundi generis vt patet, &longs;ed de modis in Metaphy&longs;ica; vix enim <lb/>hoc Theorema ad rem Phy&longs;icam quicquam facit. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 10.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Impetus e&longs;t qualitas Phy&longs;ica.<emph.end type="italics"/><!-- KEEP S--></s><s> Sequitur ex dictis; cum nec &longs;it motus. </s>

<s><lb/>nec &longs;ub&longs;tantia, nec modus, nec quidquam negatiuum, alioquin exige&shy;<lb/>ret; igitur e&longs;t aliud accidens; vocetur qualitas. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 11.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Impetus est qualitas Phy&longs;ica.<emph.end type="italics"/><!-- KEEP S--></s><s> Quia impetus e&longs;t di&longs;tinctus realiter &agrave; &longs;ue <lb/>&longs;ubiecto per Th. 7. E&longs;t enim &longs;eparabilis per Hypoth. <!-- KEEP S--></s>

<s>3. &amp; 4. igitur di&shy;<lb/>&longs;tinctus per Ax. 2. &longs;ed qualitatem realiter di&longs;tinctam apello Phy&longs;icam; <lb/>pr&aelig;&longs;ertim cum nec moralis &longs;it, nec Logica, &amp;c. </s></p><pb xlink:href="026/01/050.jpg" pagenum="18"/><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 12.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Impetus est qualitas permanens.<emph.end type="italics"/></s><s> Quia lapis proiectus etiam &longs;eparatus <lb/>mouetur aliquandiu per Hyp. <!-- REMOVE S-->6. igitur durat eius cau&longs;a, &longs;cilicet impe&shy;<lb/>tus; igitur e&longs;t qualitas permanens. </s>

</p><p type="main">

<s>Diceret fort&egrave; aliquis lapidem proiectum pelli ab a&euml;re &agrave; tergo in&longs;tan&shy;<lb/>te, vt voluit Ari&longs;toteles pluribus in locis; &longs;ed pr&aelig;&longs;ertim 8. Ph.c.vlt.&amp; 7. <lb/>cap.2. 3.de C&oelig;lo, cap. 

3. Re&longs;pondeo hoc dici non po&longs;&longs;e; Prim&ograve; quia non <lb/>mod&ograve; non iuuat a&euml;r; &longs;ed etiam impedit motum proiecti, quod de omni <lb/>medio nece&longs;&longs;ari&ograve; dicendum e&longs;t, vt patet experienti&acirc;; vnde quo cra&longs;&longs;ius, <lb/>&longs;eu den&longs;ius e&longs;t <expan abbr="medi&utilde;">medium</expan>, motum potenti&ugrave;s retardat, vt videmus in proiectis <lb/>per aquam; rationem &agrave; priori afferemus infr&agrave;, cum de re&longs;i&longs;tentia medij: </s>

<s><lb/>Secund&ograve;, quis dicat pilam rotatam in &longs;olo moueri a&euml;ris appul&longs;u? cum <lb/>alia corpora, qu&aelig; pila rotata pr&aelig;terlambendo qua&longs;i allambit, nullo mo&shy;<lb/>do moueantur; pr&aelig;&longs;ertim granula pulueris. </s>

<s>Terti&ograve;, an fort&egrave; a&euml;r id pr&aelig;&shy;<lb/>&longs;tare pote&longs;t &longs;ine vi impre&longs;&longs;a; igitur non minus ip&longs;i pil&aelig; proiect&aelig;, quam <lb/>a&euml;ri ambienti imprimi poterit: </s>

<s>Quart&ograve;, nullus a&euml;r &agrave; tergo pellitur; &longs;ed <lb/>potius ip&longs;a pila aduer&longs;us a&euml;ra pellit, dum emittitur manu; igitur &longs;i a&euml;r <lb/>&longs;uccedit &agrave; tergo, id totum accidit, vel metu vacui, vel ne a&euml;r compri&shy;<lb/>matur, vt videbimus infr&agrave;. </s>

<s>Quint&ograve; denique, cum diu moueatur eadem <lb/>pars a&euml;ris, haud dubi&egrave; in ca manet vis impre&longs;&longs;a; igitur impetus erit ad&shy;<lb/>huc qualitas permanens. </s></p><p type="main">

<s>Ad id quod obiicitur ex Ari&longs;totele; aliqui putant inclina&longs;&longs;e in cam &longs;en&shy;<lb/>tentiam; c&ugrave;m tam en no&longs;tram teneant illu&longs;tres Peripatetici, quorum no&shy;<lb/>minibus parco, ne tot citationes paginas impleant; vide apud Conim&shy;<lb/>bric. </s>

<s>l. <!-- REMOVE S-->7. Phy&longs;. cap. 

2. Aliqui excu&longs;ant ip&longs;um Ari&longs;torelem, putantque <lb/>non e&longs;&longs;e locutum ex propri&acirc; &longs;ententi&acirc;: Alij dicunt Ari&longs;totelem quidem <lb/>tribui&longs;&longs;e aliquam vim extrin&longs;ecam a&euml;ri; non tamen nega&longs;&longs;e intrin&longs;ecam <lb/>impetus; quidquid &longs;it, ip&longs;a verba Ari&longs;totelis demon&longs;trant ip&longs;um agno&shy;<lb/>ui&longs;&longs;e vim motricem impre&longs;&longs;am a&euml;ri, hoc e&longs;t impetum (<emph type="italics"/>potentia enim<emph.end type="italics"/> (in&shy;<lb/>quit) &longs;cilicet motrix, <emph type="italics"/>qu&acirc; pollet proijciens qua&longs;i vim impre&longs;&longs;am tradit vtrique<emph.end type="italics"/>) <lb/>id e&longs;t a&euml;ri &longs;ur&longs;um, &amp; deor&longs;um; quid porr&ograve; e&longs;t illa vis motrix, ni&longs;i impetus. </s>

</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 13.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Impetus non producit motum.<emph.end type="italics"/></s><s> Probatur, quia motus non dicitur pro&shy;<lb/>ductus per Th. 2. Adde &longs;i vis rationem metaphy&longs;icam; quia nihil cogit <lb/>dicere accidens aliquod, ex iis &longs;cilicet, qu&aelig; &longs;en&longs;u percipimus, agere ad <lb/>intra; quod videtur e&longs;&longs;e proprium &longs;ub&longs;tanti&aelig;, &longs;altem naturaliter; vt <lb/>demon&longs;trabimus in Metaph. <!-- KEEP S--></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 14.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Impetus exigit motum, id est fluxum mobilis in loco<emph.end type="italics"/>; quia cau&longs;a imme&shy;<lb/>diata motus e&longs;t tantum exigens, per Th. 4. &longs;ed impetus e&longs;t cau&longs;a motus <lb/>immediata per Th. 5. &amp; 6. igitur e&longs;t cau&longs;a exigens, adde quod id tant&ugrave;m <lb/>accidens &longs;en&longs;ibile pr&aelig;&longs;tare pote&longs;t in &longs;uo &longs;ubiecto, vt aliquam illius mu&shy;<lb/>tationem pr&aelig;&longs;tet, vel exigat; qu&aelig; vel e&longs;t localis, hoc e&longs;t fluxus quidam: <pb xlink:href="026/01/051.jpg" pagenum="19"/>per &longs;patium loci; vel alteratiua, vt vulg&ograve; vocatur; qu&agrave; &longs;cilicet vel re&shy;<lb/>&longs;oluuntur partes, vel rarefiunt, vel lique&longs;cunt, vel concre&longs;cunt &amp;c. </s>

<s>vel <lb/>dem&ugrave;m mutant &longs;en&longs;ibilem &longs;tatum; vel e&longs;t perfectiua aliquo modo, qua&shy;<lb/>tenus &longs;ubiectum nouam aliquam habitudinem acquirit ad &longs;en&longs;us; &longs;ic <lb/>lumen illuminando obiectum reddit illud vi&longs;ibile. </s>

<s>&amp;c. </s>

<s>de quibus ali&agrave;s. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 15.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Motus e&longs;t effectus formalis &longs;ecundarius impetus.<emph.end type="italics"/></s><s> Cum enim &longs;it cau&longs;a <lb/>exigens per Th. 121. Voco effectum formalem &longs;ecundarium, quem in <lb/>mobili exigit impetus; quippe, vt iam dictum e&longs;t, cau&longs;a exigens redu&shy;<lb/>citur ad formalem; nec enim cau&longs;at aliquid producendo, quod &longs;pectat ad <lb/>efficientem; nec mouendo, quod &longs;pectat ad finalem; nec determinando, <lb/>quod &longs;pectat ad obiectiuam; nec recipiendo, quod &longs;pectat ad materia&shy;<lb/>lem; nec dirigendo, quod &longs;pectat ad id&aelig;alem, vel exemplarem; &longs;ed <lb/>exigendo; quatenus &longs;cilicet ad id &agrave; natura e&longs;t in&longs;tituta, vt ex eius in <lb/>&longs;ubiecto pr&aelig;&longs;entia talis affectio, vel mutatio con&longs;equatur; vocatur au&shy;<lb/>tem effectus formalis &longs;ecundarius; non ver&ograve; primarius, qui e&longs;t tant&ugrave;m <lb/>concretum ex ip&longs;a form&acirc;, &amp; &longs;ubiecto. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 16.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Motus e&longs;t finis intrin&longs;ecus impetus.<emph.end type="italics"/></s><s> Dum finem audis intrin&longs;ecum, <lb/>cogita qu&aelig;&longs;o aliquid phy&longs;icum; e&longs;t enim id, propter quod talis, vel ta&shy;<lb/>lis forma in&longs;tituta e&longs;t: quid enim aliud e&longs;&longs;e pote&longs;t; finem enim rerum <lb/>naturalium ex ip&longs;o v&longs;u cogno&longs;cimus; imm&ograve; idem e&longs;t finis cum ip&longs;o v&longs;u; <lb/>cum igitur impetus illum tant&ugrave;m v&longs;um habeat, quem in ip&longs;o mobili <lb/>pr&aelig;&longs;tare cernimus, &longs;cilicet motum; dicendum e&longs;t motum e&longs;&longs;e finem in&shy;<lb/>trin&longs;ecum impetus; adde quod cum fru&longs;tr&agrave; &longs;it impetus ille, qui non pr&aelig;&shy;<lb/>&longs;tat motum mediat&egrave; &longs;altem in &longs;uo &longs;ubiecto; quid enim aliud in &longs;uo &longs;ub&shy;<lb/>iecto pr&aelig;&longs;taret, quem effectum, quam mutationem? </s>

<s>cert&egrave; &longs;i fru&longs;tr&agrave; e&longs;t, non <lb/>e&longs;t, per Ax.6.igitur vt &longs;it, debet habere id, &longs;ine quo e&longs;&longs;e non pote&longs;t; igitur <lb/>maximum eius bonum e&longs;t, igitur finis, quem natiu&acirc; vel innat&acirc; velut <lb/>appetenti&acirc; concupi&longs;cit, vel exigit. </s>

<s>Dixi mediat&egrave;, vel immediat&egrave;; num <lb/>reuera datur fort&egrave; aliquis impetus, vt dicemus infr&agrave;; &longs;cilicet primus na&shy;<lb/>turalis, qui &longs;cilicet duos fines habet di&longs;iunctiu&egrave;; quorum alter e&longs;t gra&shy;<lb/>uitatio, alter motus deor&longs;um. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 17.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Ni&longs;i e&longs;&longs;et motus non e&longs;&longs;et impetus.<emph.end type="italics"/></s><s> Probatur quia motus e&longs;t finis intrin&shy;<lb/>&longs;ecus impetus per Th. 16. igitur &longs;i nullus motus e&longs;&longs;e po&longs;&longs;et, &longs;uo fine ca&shy;<lb/>reret impetus; igitur non e&longs;&longs;et, vt patet, igitur non e&longs;&longs;et; quia quod <lb/>fru&longs;tr&agrave; e&longs;t, non e&longs;t per Ax. 6. nec ob&longs;tat quod &longs;upr&agrave; indicatum e&longs;t de im <lb/>petu naturali primo vel innato (&longs;ic enim deinceps appellabimus vt recti <lb/>di&longs;tinguamus ab acqui&longs;ito quem vocabimus impetum accelerationis) <lb/>qui &longs;ine motu con&longs;eruatur in corpore grauitante; quia ni&longs;i po&longs;&longs;ibilis e&longs;&shy;<lb/>&longs;et motus deor&longs;um nulla e&longs;&longs;et grauitatio; quippe grauitare e&longs;t dcor&shy;<lb/>&longs;um inclinari, motumque inclinationis impediri; hinc dicemus <pb xlink:href="026/01/052.jpg" pagenum="20"/>in &longs;ecundo libro impetum innatum &longs;&aelig;pi&ugrave;s e&longs;&longs;e &longs;ine motu; cum &longs;cilicet <lb/>impeditur &agrave; corpore &longs;u&longs;tinente? </s>

<s>imm&ograve; dicemus infr&agrave; primo in&longs;tanti, <lb/>quo e&longs;t impetus, nondum e&longs;&longs;e motum. </s></p><p type="main">

<s>Ob&longs;eruabis autem certi&longs;&longs;imam regulam; &longs;cilicet ex impo&longs;&longs;ibilitate <lb/>effectus formalis, &longs;equi impo&longs;&longs;ibilitatem cau&longs;&aelig; formalis, huiu&longs;que po&longs;&longs;i&shy;<lb/>bilitatem ex illius po&longs;&longs;ibilitate. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 18.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Ni&longs;i e&longs;&longs;et impetus, non e&longs;&longs;et naturaliter motus.<emph.end type="italics"/></s><s> Quia ni&longs;i e&longs;&longs;et cau&longs;a, non <lb/>e&longs;&longs;et naturaliter effectus per Ax. 8. Impetus enim e&longs;t cau&longs;a motus per <lb/>Th.15. Deinde omnis motus e&longs;t ab aliqua potentia motrice, vt patet ex <lb/>omni hypothe&longs;i; &longs;iue &longs;it naturalis in grauibus, &amp; leuibus, &longs;iue &longs;it vitalis <lb/>in viuentibus; &longs;iue &longs;it media in compre&longs;&longs;is, &amp; dilatatis; &longs;iue alia qu&aelig;li&shy;<lb/>bet: &longs;ed omnis potentia motrix e&longs;t actiua, quia mouet; ergo agit, &longs;ed <lb/>motum non producit per Th. 2. Igitur impetum, qui deinde exigit mo&shy;<lb/>tum per Th. 14. Dixi naturaliter; quia non e&longs;t dubium, quin Deus &longs;ine <lb/>impetu aliquo modo mouere po&longs;&longs;it; ide&longs;t, facere &longs;ine impetu, vt corpus <lb/>mutet locum: nec dicas Deum non po&longs;&longs;e &longs;upplere vices cau&longs;&aelig; formalis; <lb/>nam concedo id quidem pro effectu formali primario; nec enim Deus <lb/>pote&longs;t facere, vt aliquid &longs;it calidum &longs;ine calore; cum e&longs;&longs;e calidum &longs;it <lb/>idem, ac e&longs;&longs;e habens calorem; id tamen nego pro effectu &longs;ecundario, <lb/>quem &longs;cilicet cau&longs;a formalis exigit: Etenim &longs;icut pote&longs;t &longs;ummo iure non <lb/>&longs;atisfacere exigenti&aelig;; ita pote&longs;t id <expan abbr="c&otilde;ferre">conferre</expan> &longs;ine exigenti&acirc;, qu&ograve;d cum exi&shy;<lb/>gentia conferre pote&longs;t; &longs;ic pote&longs;t corpus re&longs;oluere &longs;ine calore, mouere <lb/>fine impetu &amp;c. </s>

<s>quanquam vt verum fatear non e&longs;&longs;et propri&egrave; motus, &longs;ed <lb/>qua&longs;i continu&aelig; reproductionis modus; nam motus dicit aliquam pa&longs;&shy;<lb/>&longs;ionem; &longs;cilicet actum entis in potenti&acirc;, vt aiunt. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 19.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Si e&longs;&longs;et motus naturaliter &longs;ine impetu, corpus per &longs;e ip&longs;um moueretur,<emph.end type="italics"/> id e&longs;t, <lb/>exigeret motum per &longs;uam entitatem; quia nullus impetus exigeret; ergo <lb/>aliquid aliud, nihil di&longs;tinctum, alioquin e&longs;&longs;et impetus; ergo ip&longs;a corpo&shy;<lb/>ris entitas; quanquam non e&longs;&longs;et motus, vt iam dictum e&longs;t, quia non e&longs;&shy;<lb/>&longs;et pa&longs;&longs;io. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 20.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Corpus illud &aelig;quali &longs;emper motu ferretur per &longs;e<emph.end type="italics"/>; Quia e&longs;&longs;et &longs;emper ea&shy;<lb/>dem cau&longs;a nece&longs;&longs;aria motus, id e&longs;t, ip&longs;a entitas corporis; igitur idem <lb/>effectus per Axioma 12. igitur idem, vel &aelig;qualis motus: dixi per &longs;e pro&shy;<lb/>pter diuer&longs;um medium. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 21.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Si e&longs;&longs;et aliquod corpus e&longs;&longs;entialiter mobile, impetu non indigeret.<emph.end type="italics"/></s><s> Probatur; <lb/>quia in tantum indiget mobile impetu vt impetus exigat motum; &longs;ed <lb/>corpus illud per &longs;uam e&longs;&longs;entiam exigeret motum; igitur non indigeret <lb/>impetu; po&longs;&longs;et tamen impediri eius motus, vt patet; imm&ograve; e&longs;&longs;et capax <lb/>recipiendi impetus., &longs;iue quem in ip&longs;o produceret, &longs;iue quem ab alia <pb xlink:href="026/01/053.jpg" pagenum="21"/>cau&longs;a extrin&longs;eca acciperet. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 22.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Si e&longs;&longs;et aliquod corpus e&longs;&longs;entialiter immobile, e&longs;&longs;et incapax impetus.<emph.end type="italics"/></s><s> Pro&shy;<lb/>batur; quia, ni&longs;i e&longs;&longs;et motus, non e&longs;&longs;et impetus per Th. 17. igitur &longs;ubie&shy;<lb/>ctum incapax motus e&longs;t incapax impetus. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 23.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Si e&longs;&longs;et aliquod &longs;ubiectum incapax impetus, e&longs;&longs;et incapax motus.<emph.end type="italics"/></s><s> Quia <lb/>vbi non pote&longs;t e&longs;&longs;e cau&longs;a formalis, ibi non pote&longs;t e&longs;&longs;e effectus forma&shy;<lb/>lis, quod certum e&longs;t. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 24.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Omne corpus, quod e&longs;t capax motus, e&longs;t capax impetus, &amp; vici&longs;&longs;im.<emph.end type="italics"/><lb/>Probatur 1. pars; quia impetus in eo non e&longs;&longs;et fru&longs;tr&agrave;; haberet enim <lb/>&longs;uum effectum formalem, &amp; finem intrin&longs;ecum. </s>

<s>Probatur 2.pars; quia in <lb/>eo impetus non e&longs;&longs;et fru&longs;tr&agrave; per Ax. 6. igitur haberet &longs;uum effectum; <lb/>igitur motum. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 25.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Omne corpus finitum e&longs;t capax motus, &amp; impetus.<emph.end type="italics"/></s><s> Probatur 1. pars; <lb/>quia non e&longs;t vbique, igitur pote&longs;t transferri &egrave; loco in locum; cur enim <lb/>non po&longs;&longs;et? </s>

<s>Dices fort&egrave; quia affixum e&longs;&longs;et e&longs;&longs;entialiter tali, vel tali lo&shy;<lb/>co, &longs;ed contra; quia de&longs;truantur omnia, pr&aelig;ter ip&longs;um corpus; cert&egrave; <lb/>nulli affixum manet. </s>

<s>Dices &longs;patio imaginario; apage i&longs;tas nugas: <lb/>de i&longs;to &longs;patio plura demon&longs;trabimus in Metaphy. <!-- KEEP S--></s>

<s>Probatur 2. pars; quia <lb/>&longs;i e&longs;t capax motus, e&longs;t capax impetus per Th. 24. Quod dixi de corpo&shy;<lb/>re; dicendum e&longs;t de omni re creata finita permanente. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 26.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Quod durat tant&ugrave;m vno in&longs;tanti, e&longs;t incapax motus, &amp; impetus.<emph.end type="italics"/></s><s> Pro&shy;<lb/>batur, quia non e&longs;t moueri, ni&longs;i relinquat locum, &amp; acquirat alium; &longs;ed <lb/>1. acquirere locum, e&longs;t 1. e&longs;&longs;e in illo loco; &amp; relinquere locum e&longs;t, <lb/>1. non e&longs;&longs;e in eo loco; nec &longs;imul e&longs;t in vtroque, quia in duobus locis <lb/>idem &longs;imul e&longs;&longs;e non pote&longs;t; vt demon&longs;tramus in Metaphy&longs;ica; &amp; phy&shy;<lb/>&longs;ic&egrave; certum e&longs;t ex omni hypothe&longs;i; igitur moueri nunc, id e&longs;t, hoc in&shy;<lb/>&longs;tanti, id e&longs;t, 1. acquirere nouum locum, &amp; 1. relinquere priorem, <lb/>&longs;upponit nece&longs;&longs;ari&ograve; ant&egrave; fui&longs;&longs;e in loco nunc relicto; &longs;ed quod durat <lb/>tant&ugrave;m in in&longs;tanti, non habet ant&egrave;, neque po&longs;t; igitur quod durat tan&shy;<lb/>t&ugrave;m vno in&longs;tanti, moueri non pote&longs;t; igitur e&longs;t incapax motus; igitur <lb/>&amp; impetus. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 27.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Deus e&longs;t incapax motus, &amp; impetus<emph.end type="italics"/>: Tum quia vbique, e&longs;t igitur <lb/>nouum locum acquirere non pote&longs;t; igitur nec moueri per Definitio&shy;<lb/>nem 1. t&ugrave;m quia &aelig;ternitas Dei tota &longs;imul e&longs;t; igitur nec fuit ant&egrave;, ne&shy;<lb/>que po&longs;t in ca; igitur non pote&longs;t dici ant&egrave; habui&longs;&longs;e locum, quo nunc <lb/>caret: &amp; nunc non habere illum quo caret; t&ugrave;m quia immutabilitas <pb xlink:href="026/01/054.jpg" pagenum="22"/>Dei hoc prohibet; nam moueri, e&longs;t affici intrin&longs;ec&egrave;; quia etiam de&shy;<lb/>&longs;tructis omnibus extrin&longs;ecis creatis moueri po&longs;&longs;em, &amp; fru&longs;tr&agrave; recurres <lb/>ad partes virtuales immen&longs;itatis Dei, quas fer&egrave; animus abhorret; apa&shy;<lb/>ge partes in Deo: quis hoc ferre po&longs;&longs;it? </s>

<s>pr&aelig;terea &longs;i &longs;unt, &longs;unt e&longs;&longs;entia&shy;<lb/>liter immobiles; igitur valet &longs;emper ratio allata; igitur Deus e&longs;t inca&shy;<lb/>pax motus; igitur &amp; impetus. </s></p><p type="main">

<s>Diceret aliquis Deum quantumuis Immen&longs;um in orbem conuolui <lb/>po&longs;&longs;e; igitur 1. ratio non probat de omni motu. </s>

<s>Re&longs;pondeo adhuc va&shy;<lb/>lere, quia etiam in orbem conuolui non pote&longs;t, ni&longs;i mutetur intrin&longs;e&shy;<lb/>c&egrave;; atqui &longs;i e&longs;t immen&longs;us, non pote&longs;t mutari intrin&longs;ec&egrave; per motum; <lb/>quia nullum locum de nouo acquireret; &longs;ed de hoc motu ali&agrave;s, cum de <lb/>infinito; vel de puncto phy&longs;ico mobili; quidquid &longs;it. </s>

<s>valet &longs;altem <lb/>1. ratio pro motu recto, &amp; ali&aelig; du&aelig; pro omni motu. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 28.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Motus ip&longs;e moueri non pote&longs;t.<emph.end type="italics"/></s><s> Quia cum tant&ugrave;m dicat mutationem <lb/>loci; cert&egrave; mutatio non e&longs;t in loco; dicit enim tant&ugrave;m locum relictum <lb/>eo in&longs;tanti, quo nouus acquiritur. </s>

<s>Pr&aelig;terea quod e&longs;t in loco dicit tan&shy;<lb/>t&ugrave;m ens phy&longs;icum; &longs;ed mutatio dicit etiam non ens; <emph type="italics"/>Hinc egregium pa&shy;<lb/>radoxum; illud non mouetur per quod cuncta mouentur, qu&aelig; mouentur.<emph.end type="italics"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 29.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Duratio moueri non pote&longs;t.<emph.end type="italics"/></s><s> Cum enim &longs;it &longs;ucce&longs;&longs;iua, fluit per partes, <lb/>igitur qu&aelig;libet illius pars, &longs;eu quod durat vna in&longs;tanti tant&ugrave;m e&longs;t inca&shy;<lb/>pax motus, per Th. 26. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 30.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc actio moueri non pote&longs;t<emph.end type="italics"/>; cum enim actio per quam res con&longs;erua&shy;<lb/>tur, &longs;it eius duratio; vt con&longs;tabit ex iis, qu&aelig; demon&longs;trabimus in Me&shy;<lb/>taphy&longs;ica, &amp; cum duratio moueri non po&longs;&longs;it, per Th. 29. cert&egrave; neque <lb/>actio moueri pote&longs;t. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 1.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Hinc in tanta rerum creatarum multitudine &longs;unt tant&ugrave;m du&aelig;, qu&aelig; <lb/>&longs;unt e&longs;&longs;entialiter immobiles; &longs;cilicet motus, &amp; actio; quorum ille cum <lb/>&longs;it mutatio non e&longs;t ad&aelig;quat&egrave; aliquid po&longs;itiuum; &longs;ecus actio. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 2.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Hinc &longs;unt tant&ugrave;m duo ad&aelig;quat&egrave; po&longs;itiua, qu&aelig; moueri non po&longs;&longs;unt; <lb/>&longs;cilicet Deus, &amp; actio; Deus, qui &longs;emper e&longs;t; actio, qu&aelig; tant&ugrave;m vno <lb/>in&longs;tanti e&longs;t; Deus vbique e&longs;&longs;entialiter; actio hic tantum e&longs;&longs;entialiter; <lb/>Deus primum ens; actio infinitum ens; e&longs;t enim modus; Deus primum <lb/>mouens; actio ip&longs;e motus; &longs;cilicet primi generis, de quo in &longs;ect. </s>

<s>Th.3. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 3.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Hinc &longs;i res aliqua creata per actionem tant&aelig; perfectionis, qu&aelig; mille <lb/>annis e&longs;&longs;entialiter re&longs;ponderet, con&longs;eruaretur; cert&egrave; per totum illud <lb/>tempus moueri non po&longs;&longs;et; e&longs;&longs;et enim vnicum in&longs;tans, hoc e&longs;t duratio <pb xlink:href="026/01/055.jpg" pagenum="23"/>tota &longs;imul; &longs;ed codem in&longs;tanti in pluribus locis e&longs;&longs;e non pote&longs;t; igitur <lb/>nec moueri; adde quod per cam actionem &longs;um in loco, per quam &longs;um <lb/>in tempore; igitur &longs;i h&aelig;c e&longs;t &longs;emper eadem, illam eandem e&longs;&longs;e nece&longs;&longs;e <lb/>e&longs;t; &longs;ed h&aelig;c &longs;unt metaphy&longs;ica, qu&aelig; obiter tant&ugrave;m attingo, ali&agrave;s fus&egrave; <lb/>de mon&longs;trabo. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Scolium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Ob&longs;eruabis prim&ograve; ex dictis pr&aelig;clarum natur&aelig; in&longs;titutum; cum enim <lb/>corpus moueri &longs;emper non debeat, (quippe hoc e&longs;&longs;et maxim&egrave; incom&shy;<lb/>modum) cert&egrave; per &longs;uam entitatem moueri non exigit; alioquin &longs;emper <lb/>moueretur; igitur per aliud ab entitate di&longs;tinctum, id e&longs;t per impetum; <lb/>itaque licet per &longs;uam entitatem exigat fluxum in tempore, id e&longs;t con&longs;er&shy;<lb/>uari, &amp; durare; id e&longs;t nouam &longs;emper actionem con&longs;eruatiuam; quia <lb/>maximum eius bonum e&longs;t durare vel exi&longs;tere; Igitur per &longs;e ip&longs;um illud <lb/>exigit; quia &longs;emper exigit, non tamen per &longs;e ip&longs;um exigit fluxum in <lb/>loco, id e&longs;t motum; quia moueri non &longs;emper e&longs;t bonum. </s></p><p type="main">

<s>Ob&longs;eruabis &longs;ecund&ograve;, cum idem corpus aliquando veloci&ugrave;s, tardi&ugrave;s <lb/>aliquando moueri exigat; &longs;i per &longs;uam entitatem moueri exigeret, eo&shy;<lb/>dem &longs;emper ferretur motu; quia eadem &longs;emper e&longs;&longs;et exigentia; igitur <lb/>debet e&longs;&longs;e aliquid aliud; illud autem e&longs;t impetus, qui aliquando maior <lb/>&longs;eu perfectior, aliquando ver&ograve; minor e&longs;t; igitur maiorem &longs;eu <expan abbr="velcio&shy;rem">velocio&shy;<lb/>rem</expan> motum aliquando exigit, aliquando minorem, &longs;eu tardiorem; <lb/>cum enim motus &longs;it eius finis intrin&longs;ecus, vt re&longs;olutio e&longs;t finis caloris <lb/>vel rarefactio; quemadmodum maior calor maiorem exigit, &longs;eu pr&aelig;&shy;<lb/>&longs;tat re&longs;olutionem; ita &amp; maior, &longs;eu perfectior impetus maiorem, &longs;eu <lb/>velociorem motum exigit. </s></p><p type="main">

<s>Ob&longs;eruabis terti&ograve; aliud natur&aelig; in&longs;titutum, quo &longs;cilicet in eo tan&shy;<lb/>t&ugrave;m &longs;ubiecto recipi pote&longs;t cau&longs;a formalis, in quo recipi pote&longs;t eius effe&shy;<lb/>ctus formalis &longs;ecundarius: nec alia regula, pr&aelig;ter eam excogitari pote&longs;t; <lb/>cum enim aliqua forma ad talem, vel talem finem &agrave; natura in&longs;tituta e&longs;t; <lb/>cert&egrave; propter illum finem e&longs;t, igitur in eo non e&longs;t, in quo &longs;uum finem <lb/>con&longs;equi non pote&longs;t; alioquin fru&longs;tr&agrave; e&longs;&longs;et; &amp; contra in eo e&longs;&longs;e pote&longs;t, <lb/>in quo fru&longs;tr&agrave; non e&longs;t; cum &longs;cilicet in eo &longs;uum finem con&longs;equatur; ad&shy;<lb/>de quod finis ille intrin&longs;ecus phy&longs;icus &longs;cilicet, non moralis, aliquis no&shy;<lb/>uus effectus e&longs;t; atqui nouus effectus &longs;ine &longs;ua cau&longs;a e&longs;&longs;e non pote&longs;t, neque <lb/>cau&longs;a nece&longs;&longs;aria &longs;ine effectu; igitur ibi, &longs;cilicet in hoc &longs;ubiecto, in quo <lb/>e&longs;t, vel e&longs;&longs;e pote&longs;t effectus formalis, cau&longs;a formalis e&longs;t, vel e&longs;&longs;e pote&longs;t, <lb/>e&longs;t inquam citra miraculum. </s></p><p type="main">

<s>Ob&longs;eruabis quart&ograve; egregiam rationem; propter quam res eadem in <lb/>pluribus locis naturaliter e&longs;&longs;e non pote&longs;t; quippe cum res fuerit primo <lb/>producta in aliquo loco, illa cert&egrave; nouum locum acquirere non pote&longs;t <lb/>naturaliter; ni&longs;i per motum, atqui motus dicit nece&longs;&longs;ario priorem lo&shy;<lb/>tum relictum, &amp; nouum acqui&longs;itum; igitur cum tot acquirantur loca <lb/>per motum, quot relinquuntur; &longs;i ante motum vnus tant&ugrave;m erat eiu&longs;&shy;<lb/>dem rei locus, po&longs;t motum etiam vnus e&longs;t: quod autem producatur tan-<pb xlink:href="026/01/056.jpg" pagenum="24"/>t&ugrave;m res in vno loco patet; vel enim &agrave; cau&longs;a prima vel ab aliqua 2. pro&shy;<lb/>ducitur; &longs;i &agrave; 2. ergo ab aliqua aplicata; igitur ex &longs;uppo&longs;itione qu&ograve;d il&shy;<lb/>la cau&longs;a 2. in vno tant&ugrave;m loco producta &longs;it, vni tantum applicari po&shy;<lb/>te&longs;t; quod autem cau&longs;a 1. in pluribus locis naturaliter eundem effectum <lb/>non producat, certum e&longs;t, &amp; demon&longs;trabimus in Metaphy&longs;. quia &longs;in&shy;<lb/>gulis effectibus &longs;ingul&aelig; &longs;ufficiunt actiones; &longs;ingulis terminis &longs;ingul&aelig; <lb/>vi&aelig;; imm&ograve; hoc requiri videtur, &longs;eu &longs;pectare ad huius vniuer&longs;itatis or&shy;<lb/>dinem; quippe &longs;i res eadem in pluribus locis e&longs;&longs;et; cur potius in duo&shy;<lb/>bus quam in tribus? </s>

<s>deinde multiplex iure po&longs;&longs;et exi&longs;timari; denique <lb/>quod vnum e&longs;t in entitate creata, &longs;eu dependente ab eadem cau&longs;a, vnum <lb/>e&longs;t etiam in dependentia; qu&aelig; e&longs;t actio, per quam dependet; &longs;ed de his <lb/>ali&agrave;s. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 31.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Impetus non producitur in eo mobili, quod moueri non pote&longs;t &agrave; potentia <lb/>motrice applicata, lic&egrave;t &agrave; fortiori moueri po&longs;&longs;it.<emph.end type="italics"/></s><s> Probatur, quia impetus <lb/>e&longs;t tant&ugrave;m propter motum, qui eius effectus e&longs;t, &amp; finis, per Th. 15. <lb/>&amp; 16. Igitur vbi non e&longs;t motus, fru&longs;tr&agrave; e&longs;t impetus; &longs;ed quod fru&longs;tr&agrave; <lb/>e&longs;t, non e&longs;t; id e&longs;t non e&longs;t, quod fru&longs;tr&agrave; e&longs;&longs;et, &longs;i e&longs;&longs;et per Ax. 6. Exci&shy;<lb/>pio tamen impetum naturalem innatum, qui nunquam e&longs;t fru&longs;tr&agrave;, vt <lb/>dictum e&longs;t &longs;upr&agrave; in Theorem. <!-- KEEP S--></s>

<s>17. adde quod non pote&longs;t cogno&longs;ci <lb/>impetus, ni&longs;i vel ex motu, vel ex ictu, vel ex contrario ni&longs;u, vel <lb/>impul&longs;u; &longs;ed nihil horum cernitur in rupe quam ferio; Igitur non <lb/>e&longs;t dicendum in ea produci impetum, cuius rationem afferemus infr&agrave;; <lb/>nunc &longs;atis e&longs;t Ax. 3. id manife&longs;t&egrave; probari; nam qui diceret in rupe im&shy;<lb/>mobili impetum imprimi; cert&egrave; po&longs;itiuo argumento probare tenere&shy;<lb/>tur, quod tant&ugrave;m duci pote&longs;t, vel ab experimento; atqui h&icirc;c nullum e&longs;t; <lb/>vel &agrave; nece&longs;&longs;itate, qu&aelig; nulla e&longs;t; vel ex alio quocumque capite, quod <lb/>nullum excogitari pote&longs;t; &longs;ed maiorem lucem huic Th. 3. ex proxim&egrave; <lb/>&longs;equentibus accer&longs;emus; nec e&longs;t qu&ograve;d aliqui dicant produci impetum <lb/>inefficacem; qui cum fru&longs;tr&agrave; &longs;it, &longs;i e&longs;t, ex nullo capite probari pote&longs;t: ad&shy;<lb/>de qu&ograve;d de&longs;truitur impetus, ne &longs;it fru&longs;tr&agrave;; Igitur non producitur, ne &longs;it <lb/>fru&longs;tr&agrave;; nam con&longs;eruatio e&longs;t vera actio, vt dicemus &longs;uo loco; Igitur &longs;i <lb/>h&aelig;c non ponitur, ne aliquid &longs;it fru&longs;tr&agrave;; etiam 1. productio poni non <lb/>debet; vnde commentum illud impetus inefficacis pror&longs;us inefficax e&longs;t. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 32.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Ideo potentia motrix non producit impetum in pr&aelig;dicta rupe.<emph.end type="italics"/> v.g. <emph type="italics"/>quia de&shy;<lb/>bilior e&longs;t.<emph.end type="italics"/></s><s> Probatur, &amp; explicatur; quippe debilior potentia minorem ef&shy;<lb/>fectum producit per. </s>

<s>Ax. 13. <emph type="italics"/>num.<emph.end type="italics"/> 2. igitur pauciores partes impetus <lb/>&aelig;quales vni cert&aelig; per idem <emph type="italics"/>num.<emph.end type="italics"/> 1. igitur &longs;i &longs;int plures partes &longs;ubiecti <lb/>mobilis, &longs;eu rupis, qu&agrave;m impetus; cum vna pars impetus duobus parti&shy;<lb/>bus &longs;ubiecti ine&longs;&longs;e non po&longs;&longs;it; licet plures vni &longs;imul in e&longs;&longs;e po&longs;&longs;int; <lb/>non e&longs;t mirum &longs;i nullus impetus producatur; cum non po&longs;&longs;int tot partes <lb/>illius produci, quot e&longs;&longs;ent nece&longs;&longs;ari&aelig;; vt &longs;altem &longs;ingul&aelig; &longs;ingulis &longs;ubie&shy;<lb/>cti, &longs;eu rupis partibus di&longs;tribuerentur. </s></p><pb xlink:href="026/01/057.jpg" pagenum="25"/><p type="main">

<s>Ob&longs;eruabis autem nouum quoddam gen&uacute;s re&longs;i&longs;tenti&aelig;; nam &longs;ingul&aelig; <lb/>partes rupis ab applicata potenti&acirc; apt&aelig; &longs;unt loco moueri per impre&longs;&shy;<lb/>&longs;um impetum, &amp; maior potentia &longs;imul omnes loco moueret; at ver&ograve; <lb/>omnes &longs;imul, &amp; coniunctim con&longs;iderat&aelig;; quatenus &longs;cilicet vna pars <lb/>non pote&longs;t moueri &longs;ine alia, &amp; comparat&aelig; cum illa potentia debili di&shy;<lb/>cuntur habere pr&aelig;dictam re&longs;i&longs;tentiam, qu&aelig; &longs;uperat potenti&aelig; vires; <lb/>qu&ograve;d &longs;cilicet &agrave; maiori moueri tant&ugrave;m po&longs;&longs;int; quia plures partes im&shy;<lb/>petus po&longs;tulantur, quam &longs;int e&aelig;, qu&aelig; &agrave; pr&aelig;dict&acirc; potenti&acirc; po&longs;&longs;unt pro&shy;<lb/>duci. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 33.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Vel producitur impetus in omnibus &longs;ubiecti partibus vnitis, vel in nulla; <lb/>mod&ograve; nulla fiat &longs;eparatio, neque compre&longs;&longs;io<emph.end type="italics"/>: Certum e&longs;t enim in ijs omni&shy;<lb/>bus partibus, qu&aelig; auolant ab ictu, produci impetum. </s>

<s>Probatur igitur <lb/>1. quia &longs;i non producatur in omnibus partibus, &amp; nulla &longs;eparetur ab <lb/>alijs; cert&egrave; nulla mouetur, vt certum e&longs;t; igitur nulla habet impetum; <lb/>quia ibi non e&longs;t cau&longs;a formalis, vbi non e&longs;t effectus formalis; alioquin <lb/>e&longs;&longs;et fru&longs;tr&agrave;, contra Ax. 6.2. </s>
<s>Tu dicis produci impetum in aliquot parti&shy;<lb/>bus; hoc dicis, hoc proba? </s>

<s>an potes digno&longs;cere impetum ni&longs;i ex motu? </s>

<s><lb/>vel con&longs;eruaretur h&icirc;c impetus &longs;equentibus in&longs;tantibus, vel &longs;tatim &longs;ecun&shy;<lb/>do in&longs;tanti de&longs;trucretur. </s>

<s>Primum dicere ab&longs;urdume&longs;t; quia &longs;i hoc e&longs;&longs;et <lb/>multisictibus repetitis tandem moueretur totum mobile; &longs;i ver&ograve; de&shy;<lb/>ftrui dicatur. </s>

<s>Secundo in&longs;tanti; eadem ratio probat non produci. </s>

<s>Pri&shy;<lb/>mo in&longs;tanti, qu&aelig; probat de&longs;trui. </s>

<s>Secundo nam ideo de&longs;truitur. </s>

<s>Secun&shy;<lb/>do quia e&longs;t fru&longs;tr&agrave;, &longs;ed non minus e&longs;t fru&longs;tr&agrave;. </s>

<s>Primo igitur non produ&shy;<lb/>citur. </s>

<s>Primo 4. probatur; quia cum non &longs;ufficiant partes impetus, quas <lb/>dixi produci, vt omnibus partibus &longs;ubiecti di&longs;tribuantur; cert&egrave; non e&longs;t <lb/>vlla ratio, cur poti&ugrave;s his qu&agrave;m illis di&longs;tribui dicantur; cum vna &longs;it tan&shy;<lb/>t&ugrave;m immediat&egrave; applicata. </s>

<s>Igitur certum e&longs;t vel produci in omnibus, vel <lb/>in nulla, ni&longs;i forte aliqu&aelig; auolent, &longs;ed tunc &longs;eparantur. </s></p><p type="main">

<s>Obiiciet aliquis 1. e&longs;&longs;e cau&longs;am nece&longs;&longs;ariam applicatam &longs;ubiecto ap&shy;<lb/>to: igitur agit per Ax. 12. Re&longs;pondeo e&longs;&longs;e impeditam; nam re&longs;i&longs;tentia <lb/>&longs;ubiecti &longs;uperat vires potenti&aelig; vt dictum e&longs;t; imm&ograve; in ip&longs;o motu re&shy;<lb/>torqueo argumentum; lic&egrave;t enim &longs;it applicata cau&longs;a nece&longs;&longs;aria mouens, <lb/>non tamen mouet. </s></p><p type="main">

<s>Obiiciet 2. Ignis applicatus agit in nonnullas partes fubiecti, lic&egrave;t <lb/>non agat in omnes; igitur &amp; potentia motrix. </s>

<s>Re&longs;pondeo non e&longs;&longs;e pa&shy;<lb/>ritatem; quia vna pars pote&longs;t calefieri, &amp; re&longs;olui &longs;ine alia, vt con&longs;tat <lb/>non tamen vna moueri &longs;ine alia, cui coniuncta e&longs;t, ni&longs;i &longs;eparetur; igi&shy;<lb/>tur nec recipere impetum &longs;ine alia. </s></p><p type="main">

<s>Obiiciet. </s>

<s>3. &longs;int duo trahentes idem mobile; ita vt &longs;eor&longs;im neuter <lb/>trahere po&longs;&longs;it, coniunctim ver&ograve; vterque po&longs;&longs;it; cert&egrave; &longs;i alter non pro&shy;<lb/>ducit impetum &longs;eor&longs;im, nec etiam coniunctim producet; nec enim au&shy;<lb/>gentur eius vires ab altero: Re&longs;pondeo vtrunque agere actione com&shy;<lb/>muni; igitur non e&longs;t mirum &longs;i effectus maior e&longs;t, quem tamen neuter <pb xlink:href="026/01/058.jpg" pagenum="26"/>&longs;eor&longs;im producere pote&longs;t. </s></p><p type="main">

<s>Dices &longs;i vterque coniunctim producit effectum: &longs;int v. <!-- REMOVE S-->g. <!-- REMOVE S-->100. par&shy;<lb/>tes impetus; Igitur &longs;inguli producunt tant&ugrave;m 50. Igitur cur poti&ugrave;s in <lb/>in his partibus &longs;ubiecti, qu&agrave;m in alijs, cum vtriu&longs;que potentia eidem <lb/>&longs;ubiecti parti po&longs;&longs;et e&longs;&longs;e applicata? </s>





<s>Re&longs;pondeo &longs;ingulos producere 100. <lb/>actione &longs;cilicet communi indiui&longs;ibiliter; &longs;int enim duo trahentes A. &amp; <lb/>B. A. producit 100. &longs;ed non &longs;olus; B. producit ea&longs;dem 100. &longs;ed non &longs;o&shy;<lb/>lus; &longs;ed explicabimus hunc modum actionis communis in Metaphys. <!-- REMOVE S--><lb/>quod autem agant actione communi patet per Ax. 13. </s>

</p><p type="main">

<s>Obiicies 4. producitur &longs;onus &longs;i ferias rupem; igitur &amp; impetus; Re&longs;&shy;<lb/>pondeo ad &longs;onum &longs;olam a&euml;ris colli&longs;ionem &longs;ufficere, quam fieri certum <lb/>e&longs;t &agrave; pr&aelig;dicto ictu; deinde mallej motus impacti in rupem facit &longs;onum; <lb/>quidquid tandem &longs;it &longs;onus, de quo h&icirc;c non di&longs;puto: adde quod in ru&shy;<lb/>pe &longs;unt &longs;emper aliqu&aelig; partes tremul&aelig;, qu&aelig; modico tant&ugrave;m, eoque flexi&shy;<lb/>bili nexu cum alijs partibus copulantur; adde aliquam compre&longs;&longs;ionem, <lb/>ex qua modic&aelig; vibrationes &longs;equuntur. </s></p><p type="main">

<s>Obiicies 5. Quando aliqu&aelig; partes auolant ab ictu, haud dubi&egrave; auo&shy;<lb/>lant propter impetum impre&longs;&longs;um: Igitur prius e&longs;t imprimi impetum, <lb/>qu&agrave;m auolare; igitur productus e&longs;t impetus in nonnullis partibus, &amp; <lb/>non in aliis, cum quibus ill&aelig; &longs;unt coniunct&aelig;. </s>

<s>Re&longs;pondeo equidem im&shy;<lb/>petum produci in illis partibus antequam auolent; &longs;ed ideo produci vt <lb/>deinde auolent nam tota ratio cur non producatur, e&longs;t ne &longs;it fru&longs;tr&agrave;; &longs;ed <lb/>&longs;i auolent aliqu&aelig; partes: cert&egrave; in ijs non e&longs;t fru&longs;tr&agrave;, in quibus habet <lb/>&longs;uum effectum, id e&longs;t, motum. </s></p><p type="main">

<s>Dices; igitur primo in&longs;tanti impetus ille e&longs;t fru&longs;tr&agrave;; in quo non <lb/>habet &longs;uum effectum; Re&longs;pondeo nunquam primo in&longs;tanti e&longs;&longs;e fru&longs;tr&agrave;, <lb/>mod&ograve; &longs;it motus &longs;ecundo cum etiam primo in&longs;tanti, quo e&longs;t impetus, <lb/>non po&longs;&longs;it e&longs;&longs;e motus, vt demon&longs;trabo infr&agrave;; imm&ograve; ideo ponitur im&shy;<lb/>petus primo vt &longs;it motus &longs;ecundo exigendo pro in&longs;tant &longs;equenti, de <lb/>cum impetus ponat tant&ugrave;m motum quo ali&agrave;s. </s></p><p type="main">

<s>Dices; &longs;ed potentia motrix ne&longs;cit an po&longs;&longs;it pars aliqua mobilis &longs;epa&shy;<lb/>rari; igitur non e&longs;t qu&ograve;d aliquando producat impetum, aliquando <lb/>non producat. </s>

<s>Re&longs;pondeo non &longs;tare per cau&longs;am nece&longs;&longs;ariam, quin &longs;em&shy;<lb/>per agat; &longs;ed per &longs;ubiectum, quod &longs;i aptum e&longs;t, &amp; capax effectus; haud <lb/>dubi&egrave; eo ip&longs;o cau&longs;a nece&longs;&longs;aria applicata in ip&longs;um aget; &longs;i ver&ograve; ineptum. </s>

<s><lb/>haud dubi&egrave; non aget; nam ad hoc vt producatur effectus in &longs;ubiecto; <lb/>non &longs;atis e&longs;t cau&longs;am po&longs;&longs;e producere, ni&longs;i etiam &longs;ubiectum po&longs;&longs;it recipe&shy;<lb/>re; igitur cum &longs;it talis ordo &agrave; natura in&longs;titutus, ne aliquid &longs;it fru&longs;tr&agrave;; <lb/>cert&egrave; &longs;i impetus producibilis &longs;it futurus fru&longs;tr&agrave;, hauddubi&egrave; non produ&shy;<lb/>cetur; &longs;ecus ver&ograve; &longs;i fru&longs;tr&agrave; non &longs;it futurus, in quo non e&longs;t difficultas. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Ob&longs;eruabis 1. vix fieri po&longs;&longs;e quin &longs;emper aliqu&aelig; partes &longs;eparentur, <lb/>comprimantur, vel dilatentur, vt patet experienti&acirc;. </s></p><p type="main">

<s>Ob&longs;eruabis 2. etiam maximam corporis molem &agrave; debili potentia mi-<pb xlink:href="026/01/059.jpg" pagenum="27"/>nimo etiam ictu moueri; quod etiam ob&longs;eruauit Galileus in &longs;uis dialo&shy;<lb/>gis de motu; quem cert&egrave; motum ob&longs;eruabis etiam in&longs;en&longs;ibilem, t&ugrave;m <lb/>oper&acirc; radij luminis repercu&longs;&longs;i, &amp; ad aliquod interuallum proiecti; t&ugrave;m <lb/>oper&acirc; &longs;eu pi&longs;orum in tympani membran&acirc; tremulo qua&longs;i motu &longs;ub&longs;ul&shy;<lb/>tantium; qu&acirc; etiam arte deprehenditur in arce ob&longs;e&longs;&longs;a, &longs;ub quam muri <lb/>partem cuniculi agantur. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 1.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Hinc egregia ratio erui pote&longs;t, cur ingens corporis moles &agrave; debili po&shy;<lb/>tentia loco moueri non po&longs;&longs;it; cum enim tot &longs;altem requirantur partes <lb/>impetus, quot &longs;unt partes &longs;ubiecti: quia vel in omnibus, vel in nulla <lb/>producitur; cert&egrave; cum &longs;int plures partes &longs;ubiecti, qu&agrave;m vt in &longs;ingulis <lb/>ab ea dumtaxat potenti&acirc; impetus produci po&longs;&longs;it; quid mirum e&longs;t, &longs;i mo&shy;<lb/>ueri non po&longs;&longs;it. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Collorarium<emph.end type="italics"/> 2.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Hinc certa ratio alterius vulgaris effectus potenti&aelig; motricis, qu&aelig; lapi&shy;<lb/>dem 40. librarum tardo tant&ugrave;m motu impellit, etiam cum &longs;ummo ni&longs;u, <lb/>cum tamen &longs;axo vnius libr&aelig; velociorem motum imprimat; quia &longs;cilicet <lb/>partes impetus producti di&longs;tribuuntur pluribus partibus &longs;ubiecti in ma&shy;<lb/>iori lapide, &amp; paucioribus in minori; igitur &longs;ingul&aelig; partes minoris <lb/>habent plures partes impetus, vt manife&longs;t&egrave; con&longs;tat; ergo ille impetus <lb/>inten&longs;ior e&longs;t; igitur maiorem exigit &longs;eu perfectiorem motum per Ax. <!-- REMOVE S--><lb/>13. num.2. </s>

</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Collorarium<emph.end type="italics"/> 3.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Hinc &longs;ublata ratione diuer&longs;&aelig; re&longs;i&longs;tenti&aelig; medij, dato pondere <lb/>mobilis vtriu&longs;que, datoque ni&longs;u communi potenti&aelig;, pote&longs;t de&shy;<lb/>terminari certus velocitatis gradus vtriu&longs;que; nam ratio velocitatum <lb/>e&longs;t inuer&longs;a ponderum v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;it pond&ugrave;s 4. librarum; fit etiam 2. librarum <lb/>&longs;it impetus impre&longs;&longs;us vtrique &longs;uppo&longs;ito communi, &amp; &aelig;quali ni&longs;u <lb/>potenti&aelig;, &amp; &aelig;quali tempore; haud dubi&egrave; velocitas mobilis 2. libra&shy;<lb/>rum erit dupla velocitatis mobilis 4. librarum; quia cum &longs;int duplo <lb/>plures partes &longs;ubiecti in hoc mobili qu&agrave;m in illo (accipio enim vtrum&shy;<lb/>que eiu&longs;dem materi&aelig;, vt omnes lites fugiam) igitur in minori e&longs;t duplo <lb/>inten&longs;ior impetus: Igitur duplo velocior motus; dixi, &longs;i fiat &aelig;quali <lb/>ni&longs;u, &amp; &aelig;quali tempore; quia reuer&acirc; non fit in tempore &aelig;quali, &longs;ed <lb/>in&aelig;quali, &longs;i &longs;upponatur idem arcus brachij v. <!-- REMOVE S-->g. <!-- REMOVE S-->iacientis; nam tempo&shy;<lb/>ra &longs;unt in ratione &longs;ubduplicata ponderum; vt demon&longs;trabimus lib. 

10. <lb/>&amp; velocitates &longs;unt vt tempora permutando. </s>


</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Collorarium<emph.end type="italics"/> 4.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Hinc facil&egrave; determinari pote&longs;t proportio impetus impre&longs;&longs;i cognit&acirc; <lb/>grauitate mobilium; v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;it mobile graue vt4. &amp; aliud graue vt 2. haud <lb/>dubi&egrave; vt moueatur  &aelig;quali gradu velocitatis, debet produci duplo <lb/>maior impetus in maiori mobili, hoc e&longs;t, iuxta rationem maioris ad mi&shy;<lb/>nus, quod clari&longs;&longs;im&egrave; &longs;equitur ex dictis; vt enim tot&longs;int gradus impetus <pb xlink:href="026/01/060.jpg" pagenum="28"/>in qualibet parte minoris, quot &longs;unt in qualibet parte minoris; haud <lb/>dubi&egrave; impetus maioris habet eandem rationem ad impetum minoris; <lb/>quam habet maius ad minus. </s>



</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Collorarium<emph.end type="italics"/> 5.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Hinc quoque ducitur manife&longs;ta ratio &longs;eu re&longs;pon&longs;io ad illud pr&aelig;cla&shy;<lb/>rum cert&egrave; quorundam philo&longs;ophorum <expan abbr="comm&etilde;tum">commentum</expan>, qui volunt ex mini&shy;<lb/>ma ponderis acce&longs;&longs;ione totam terr&aelig; molem inclinari, vt in nouo &aelig;qui&shy;<lb/>librio &longs;tatuatur; quod omnin&ograve; fal&longs;um e&longs;t; nam ex &longs;uppotione qu&ograve;d <lb/>terra non grauitet (vt vulg&ograve; dicitur, &amp; ali&agrave;s &agrave; nobis <expan abbr="dem&otilde;&longs;trabitur">demon&longs;trabitur</expan>) illa <lb/>cert&egrave; moueri non pote&longs;t ni&longs;i producantur tot partes impetus quot &longs;unt <lb/>partes &longs;ubiecti in tota terra; qu&aelig; cert&egrave; maximas <expan abbr="pot&etilde;ti&aelig;">potenti&aelig;</expan> vires po&longs;tulant. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 34.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Primo in&longs;tanti, quo est impetus, non est ille motus, cuius hic impetus e&longs;t <lb/>cau&longs;a.<emph.end type="italics"/></s><s> Probatur; quia non pote&longs;t e&longs;&longs;e motus, ni&longs;i &longs;it locus prior reli&shy;<lb/>ctus, &amp; nouus acqui&longs;itus, igitur &longs;i eodem in&longs;tanti, quo e&longs;t impetus, <lb/>haberet motum, codem in&longs;tanti e&longs;&longs;et in duobus locis, quod dici non <lb/>pote&longs;t; &amp; iam diximus in Th. 26. igitur impetus primo in&longs;tanti quo <lb/>e&longs;t non habet &longs;uum motum. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 35.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Imm&ograve; nihil e&longs;t, quod primo in&longs;tanti, quo e&longs;t, moueri po&longs;&longs;it.<emph.end type="italics"/></s><s> Quia non pote&longs;t <lb/>moueri, ni&longs;i acquirat nouum locum, &amp; priorem relinquat; igitur, vel &longs;i&shy;<lb/>mul in vtroque e&longs;t, quod dici non pote&longs;t; vel in relicto ant&egrave; fuit; igitur <lb/>non e&longs;t primum in&longs;tans, contra &longs;uppo&longs;itionem. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 36.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Potest impetus aliquo in&longs;tanti non moueri quo mouetur ip&longs;um mobile, in <lb/>quo est.<emph.end type="italics"/></s><s> Nam moueatur mobile quodlibet; &amp; dum mouetur, impella&shy;<lb/>tur, fact&acirc; &longs;cilicet acce&longs;&longs;ione noui impetus; haud dubi&egrave; hoc primo in&shy;<lb/>&longs;tanti, quo producitur impetus in dato mobili non mouetur per Th. <!-- REMOVE S--><lb/>35. quo tamen in&longs;tanti mouetur pr&aelig;dictum mobile. </s>

</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Collorarium<emph.end type="italics"/> 1.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Hinc egregium paradoxon; <emph type="italics"/>Pote&longs;t alique in&longs;tanti moueri &longs;ubiectum, lic&egrave;t <lb/>non moueantur illa omnia, que eidem &longs;ubiecto reuer&acirc; in&longs;unt.<emph.end type="italics"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 2.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Hinc etiam aliud paradoxon; <emph type="italics"/>Impetus primo in&longs;tanti, quo e&longs;t, non habet <lb/>&longs;uum finem, nec habere pote&longs;t<emph.end type="italics"/>; patet, quia primo in&longs;tanti non habet <expan abbr="mot&utilde;">motum</expan>. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 3.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Hinc pote&longs;t aliquid dato in&longs;tanti carere &longs;uo fine; lic&egrave;t non &longs;it fru&longs;tr&agrave;; <lb/>fru&longs;tr&acirc; enim tant&ugrave;m dicitur ille impetus, qui pro in&longs;tanti &longs;equenti <lb/>non pote&longs;t habere motum. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 37.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Impetus pars recepta in parte &longs;ubiecti non exigit motum aliarum partium<emph.end type="italics"/><pb xlink:href="026/01/061.jpg" pagenum="29"/><emph type="italics"/>eiu&longs;dem &longs;ubiecti, lic&egrave;t coniunctarum.<emph.end type="italics"/></s><s> Probatur 1. quia alioquin vna pars <lb/>impetus &longs;ufficeret ad mouendam ingentem rupem; quod ab&longs;urdum e&longs;t. </s>

<s><lb/>2. &longs;icut vna pars caloris non re&longs;oluit alias partes &longs;ubiecti; ita nec im&shy;<lb/>petus. </s>

<s>3. Ratio &agrave; priori e&longs;t; quia impetus non e&longs;t cau&longs;a efficiens motus <lb/>per Th. 13. &longs;ed tant&ugrave;m cau&longs;a formalis per Th. 15. Igitur pr&aelig;&longs;tat tant&ugrave;m <lb/>&longs;uum effectum formalem in eo &longs;ubiecto, in quo e&longs;t. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 1.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Hinc partes impetus non cau&longs;ant motum in &longs;uo &longs;ubiecto actione, vel <lb/>exigentia communi; quia qu&aelig;libet pars impetus exigit tant&ugrave;m motum <lb/>&longs;ui &longs;ubiecti; id e&longs;t illius partis, qu&agrave;m afficit; quod etiam probatur per <lb/>Ax. 13. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 2.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Hinc corpus grauius per&longs;e, &longs;altem eiu&longs;dem materi&aelig;, non cadit velo&shy;<lb/>ci&ugrave;s, qu&agrave;m leuius, vti globus plumbeus 100. librarum, qu&agrave;m globus <lb/>vnius libr&aelig; plumbeus; quia &longs;cilicet impetus vnius partis non iuuat mo&shy;<lb/>tum alterius: pr&aelig;terea tam facil&egrave; 2, partes impetus in 2. partibus &longs;ubie&shy;<lb/>cti recept&aelig; ea&longs;dem mouent, qu&agrave;m 100. alias 100. dixi per &longs;e; nam di&shy;<lb/>uer&longs;a e&longs;&longs;e pote&longs;t medij re&longs;i&longs;tentia; &longs;ed de his fu&longs;e in 2. lib. <!-- REMOVE S--><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 38.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Impetus recipitur tant&ugrave;m in ip&longs;a &longs;ub&longs;tantia &longs;ubiecti naturaliter.<emph.end type="italics"/> v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;i <lb/>mobile &longs;it ferrum calidum, recipitur in ip&longs;a &longs;ub&longs;tantia ferri; non ver&ograve; <lb/>in ip&longs;o calore (ex &longs;uppo&longs;itione quod calor &longs;it accidens, vt ali&agrave;s demon&shy;<lb/>&longs;trabimus; nec in alijs accidentibus, &longs;i qu&aelig; &longs;unt, in eodem &longs;ubiecto; pro&shy;<lb/>batur 1. quia &longs;i produceretur etiam impetus in accidentibus, quo plu&shy;<lb/>ra e&longs;&longs;ent accidentia in aliquo &longs;ubiecto; plures quoque partes impetus <lb/>producend&aelig; e&longs;&longs;ent; igitur maiori potenti&acirc; opus e&longs;&longs;et per Ax. 13. n. </s>





<s>4. <lb/>Igitur difficili&ugrave;s mouerentur, quod e&longs;t ab&longs;urdum. </s>

<s>Diceret fort&egrave; ali&shy;<lb/>quis eundem impetum recipi &longs;imul in &longs;ub&longs;tantia &amp; in ip&longs;is accidenti&shy;<lb/>bus; &longs;ed contra, nam reuera, &longs;i hoc e&longs;&longs;et, dum proijcitur ferrum cali&shy;<lb/>dum, &amp; &longs;tatim frigefit, de&longs;trueretur totus impetus, de&longs;tructo &longs;cilicet <lb/>eius &longs;ubiecto: 2. qui hoc diceret, deberet probare; nam codem modo <lb/>mouetur corpus &longs;iue afficiatur pluribus accidentibus, &longs;iue paucioribus; <lb/>igitur non euincit experientia recipi in illis impetum, nec etiam ratio, <lb/>vt dicam paul&ograve; po&longs;t. </s>

<s>Ratio &agrave; priori e&longs;&longs;e pote&longs;t; quia accidens cum &longs;uo <lb/>&longs;ubiecto coniunctum exigit &longs;emper e&longs;&longs;e pr&aelig;&longs;ens &longs;ubiecto, cum natura&shy;<lb/>liter extra &longs;ubiectum exi&longs;tere non po&longs;&longs;it; igitur cum exigat con&longs;erua&shy;<lb/>ri, &amp; exi&longs;tere; eo tant&ugrave;m modo, quo pote&longs;t naturaliter con&longs;eruari &amp; <lb/>exi&longs;tere; cert&egrave; exigit con&longs;eruari, &amp; ine&longs;&longs;e &longs;ubiecto; igitur exi&longs;tere in <lb/>eo loco, in quo exi&longs;tit &longs;ubiectum, vt patet; igitur, &longs;i &longs;ubiectum mutet <lb/>locum etiam accidens cum eo coniunctum mutare debet. </s></p><p type="main">

<s>Dices, igitur &longs;imiliter dici pote&longs;t non recipi impetum in omni&shy;<lb/>bus partibus &longs;ubiecti mobilis, &longs;ed in vn&acirc; dumtaxat; cui cum <lb/>ali&aelig; &longs;int vnit&aelig;, exigunt moueri &longs;ine impetu ad illius motum? </s>

<s>cum <lb/>hoc ip&longs;um ad omnem vnionem &longs;pectare videatur; Re&longs;pondeo vnam <pb xlink:href="026/01/062.jpg" pagenum="30"/>partem plumbi ita coniungi cum alia, vt etiam &longs;eparata naturaliter <lb/>exi&longs;tere po&longs;&longs;it; igitur non e&longs;t par ratio; pr&aelig;terea vna pars plumbi non <lb/>e&longs;t in loco alterius; nec enim inuicem penetrantur cum &longs;it compene&shy;<lb/>tratio accidentium cum &longs;ubiecto; deinde, qu&ograve; plures &longs;unt partes vnit&aelig;, <lb/>maior e&longs;t re&longs;i&longs;tentia, qu&aelig; ip&longs;o etiam &longs;en&longs;u percipitur; denique non vide&shy;<lb/>tur cur potius produceretur in vna parte, quam in alia; qu&aelig; omnia <lb/>iam &longs;upr&agrave; Th. 33. demon&longs;trauimus. </s></p><p type="main">

<s>Adde quod &longs;i impetus produceretur in ip&longs;is accidentibus, etiam in <lb/>ip&longs;o impetu prius producto alius impetus produceretur; cum &longs;cilicet <lb/>noua fit impetus acce&longs;&longs;io; quod &longs;atis ridiculum e&longs;t; qua&longs;i ver&ograve; impetus <lb/>indigeat impetu &amp;c. </s>

<s>h&icirc;c loquor tant&ugrave;m de accidentibus in &longs;ubiecto; <lb/>non ver&ograve; de Euchari&longs;ticis, qu&aelig; &agrave; &longs;ubiecto per miraculum &longs;eparata etiam <lb/>moueri po&longs;&longs;unt per impre&longs;&longs;um impetum. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 1.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Hinc manife&longs;t&egrave; patet, quid dicendum &longs;it de anima bruti, qu&aelig; moue&shy;<lb/>tur etiam &longs;ine impetu; quia exigit &longs;emper e&longs;&longs;e coniuncta corpori, &agrave; <lb/>quo di&longs;iuncta naturaliter exi&longs;tere non pote&longs;t, vt &longs;uo loco dicemus; igi&shy;<lb/>tur ad motum corporis, &longs;eu &longs;ubiecti moueri deber. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 2.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Idem quoque de Anima rationali dicendum e&longs;&longs;e videtur; lic&egrave;t <lb/>enim &agrave; corpore &longs;eparata naturaliter exi&longs;tere po&longs;&longs;it; tandi&ugrave; tamen cum <lb/>corpore manet coniuncta, quandiu agere pote&longs;t in organis corporeis; <lb/>ac proinde exigit con&longs;eruari in corpore ip&longs;o, quandiu &longs;uas operatio&shy;<lb/>nes organicas in eo exercere pote&longs;t. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 3.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Hinc patet ratio manife&longs;ta ad qu&aelig;&longs;itum illud; quomodo &longs;cilicet po&shy;<lb/>tentia motrix materialis v.g. <!-- REMOVE S-->Taurus &longs;uo cornu hominem ventilare po&longs;&shy;<lb/>&longs;it; nec vlla &longs;upere&longs;t difficultas, dum dicas impetum non produci in <lb/>anima. </s>

</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Scolium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Ob&longs;eruabis prim&ograve; In hoc Theoremate dictum e&longs;&longs;e naturaliter; quia <lb/>per miraculum accidens &longs;eparatum ab omni &longs;ub&longs;tantia, dum &longs;it impe&shy;<lb/>netrabile, per impetum &longs;ibi impre&longs;&longs;um moueri pote&longs;t. </s></p><p type="main">

<s>Ob&longs;eruabis &longs;ecund&ograve; de anima bruti per miraculum &longs;eparat&acirc;, idem <lb/>pror&longs;us dicendum e&longs;&longs;e. </s></p><p type="main">

<s>Ob&longs;eruabis terti&ograve; etiam Animam rationalem &longs;eparatam, mod&ograve; &longs;it <lb/>cum impenetrabilitate coniuncta, capacem e&longs;&longs;e impetus; quem etiam <lb/>&agrave; potentia motrice corporea recipere pote&longs;t; idem dictum e&longs;to de An&shy;<lb/>gelo; &longs;ed de vtroque ali&agrave;s. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 39.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Quando corpus pellitur ab alio corpore per impetum impre&longs;&longs;um; haud du&shy;<lb/>bi&egrave; impetus ille impre&longs;&longs;us ab aliqua cau&longs;a efficiente producitur<emph.end type="italics"/>; patet <lb/>per Ax. 8. </s></p><pb xlink:href="026/01/063.jpg" pagenum="31"/><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 40.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Ille impetus non producitur &agrave; &longs;ub&longs;tantia corporis in aliud impacti.<emph.end type="italics"/></s><s> Proba&shy;<lb/>tur; quia &longs;i produceretur, e&longs;&longs;et cau&longs;a nece&longs;&longs;aria vt <expan abbr="clar&utilde;">clarum</expan> e&longs;t; igitur appli&shy;<lb/>cata, &amp; non impedita ageret per Ax. 32. quod e&longs;t contra experientiam. </s>

<s><lb/>Dicunt aliqui requiri <expan abbr="mot&utilde;">motum</expan> pr&aelig;uium, vt agat; &longs;ed contra; nam motus <lb/>pr&aelig;uius non requiritur vt cau&longs;a, vt patet; quia cau&longs;a vt agat debet exi&shy;<lb/>&longs;tere per Ax. 9. Igitur requiritur, vt conditio, quod dici non pote&longs;t; <lb/>quia primo etiam conditio debet e&longs;&longs;e pr&aelig;&longs;ens; &longs;ed motus pr&aelig;uius de <lb/>nihil pre&longs;enti e&longs;t &longs;ecundo quia non pote&longs;t excogitari aliud munus con&shy;<lb/>ditionis; ni&longs;i vel vt tollat impedimentum, vel vt applicet cau&longs;am &longs;ubie&shy;<lb/>cto apto; pr&aelig;terea motus pr&aelig;uius non e&longs;t; igitur codem modo &longs;e <lb/>habet, ac &longs;i nunquam extiti&longs;&longs;et; &amp; &longs;i eo in&longs;tanti quo corpus impa&shy;<lb/>ctum primo tangit, amitteret totum impetum, ita vt expr&aelig;terito motu <lb/>nihil reliquum e&longs;&longs;et, haud dubi&egrave; corpus aliud non pelleret. </s></p><p type="main">

<s>Diceret alius impetum e&longs;&longs;e tant&ugrave;m conditionem, qu&aelig; &longs;emper e&longs;t <lb/>de pr&aelig;&longs;enti: ad hanc in&longs;tantiam non valet &longs;uperior re&longs;pon&longs;io; &amp; cert&egrave; <lb/>&longs;i eo ip&longs;o in&longs;tanti contactus noua fieret impetus acce&longs;&longs;io; haud dubi&egrave; <lb/>maior e&longs;&longs;et ictus; lic&egrave;t cum codem motu pr&aelig;uio, &amp; tamen idem e&longs;&longs;et <lb/>corpus <expan abbr="impact&utilde;">impactum</expan>, Igitur ad hanc <expan abbr="in&longs;tanti&atilde;">in&longs;tantiam</expan> alio modo re&longs;pondeo, ex appli&shy;<lb/>catione impetus &longs;emper &longs;equitur productio alterius impetus; dum &longs;cili&shy;<lb/>cet &longs;ubiectum, cui applicatur &longs;it capax motus; ex applicatione corporis <lb/>&longs;eu &longs;ubiecti ip&longs;ius non &longs;emper &longs;equitur; igitur dicendum e&longs;t impetum <lb/>ip&longs;um e&longs;&longs;e cau&longs;am alterius per Ax. 11. n. </s>

<s>1. voco enim illud cau&longs;am, <lb/>ex cuius applicatione &longs;emper &longs;equitur &longs;imilis effectus; alioquin &longs;i hoc <lb/>neges; proba mihi aliter ignem accendi ab alio igne; dicam enim tibi <lb/>ignem applicatum e&longs;&longs;e tant&ugrave;m conditionem, &amp; produci &agrave; c&oelig;lo; proba <lb/>mihi aliter calorem produci &agrave; calore? </s>

<s>quo enim medio, vel argu&shy;<lb/>mento id euinces? </s>

<s>quo etiam non euincam impetum produci ab im&shy;<lb/>petu: Deinde affer rationem &agrave; priori, propter quam &longs;ub&longs;tantia <lb/>corporis producat impetum &longs;ur&longs;um? </s>

<s>v. <!-- REMOVE S-->g. <!-- REMOVE S-->cum non exigat &agrave; &longs;e ip&longs;a mo&shy;<lb/>tum &longs;urs&ugrave;m, qui violentus e&longs;t corpori graui; numquid certum e&longs;t, vt <lb/>dicemus infr&agrave; impetum produci ad extra, vt tollatur impedimentum <lb/>motus? </s>





<s>igitur illius e&longs;t tollere impedimentum, cuius e&longs;t exigere motum, <lb/>corpus ip&longs;um graue non exigit motum &longs;ur&longs;um, &longs;ed impetus; igitur im&shy;<lb/>petus e&longs;t tollere impedimentum &longs;ui effectus; igitur producere impetum, <lb/>quo vno tolli tant&ugrave;m pote&longs;t: En tibi rationem &agrave; priori, cutum nullam <lb/>habeas: Pr&aelig;terea, cur negas impetum e&longs;&longs;e cau&longs;am &longs;ufficientem alterius <lb/>impetus, cum ex eius applicatione ip&longs;o &longs;en&longs;u percipiamus produci alium <lb/>impetum? </s>

<s>qu&aelig; ratio? </s>

<s>quid inde ab&longs;urdi, quid incommodi: Igitur t&agrave;m <lb/>certum e&longs;t, imm&ograve; certius impetum produci ab alio impetu, qu&agrave;m calo&shy;<lb/>rem &agrave; calore. </s>

<s>Dices impetum iam habere alium effectum &longs;cilicet mo&shy;<lb/>tum; bella profecto ratio! &longs;ed numquid motus e&longs;t effectus formalis im&shy;<lb/>petus? </s>

<s>pr&aelig;tere&agrave; e&longs;t-ne effectus ad extra? </s>

<s>deinde idem dico de calore; <pb xlink:href="026/01/064.jpg" pagenum="32"/>qui reuera habet effectum formalem &longs;ecundarium ad intra, &longs;cilicet rare&shy;<lb/>factionem, qu&aelig; e&longs;t mutatio exten&longs;ionis; quemadmodum motus e&longs;t mu&shy;<lb/>tatio loci, vel vbicationis; igitur cum hoc &verbar; non ob&longs;tante, calor pro&shy;<lb/>ducat calorem ad extra; cur impetus non producit impetum? </s>

<s>cuius pro&shy;<lb/>ductionem concedis virtuti corporum re&longs;i&longs;titiu&aelig;, id e&longs;t vnioni, impe&shy;<lb/>netrabilitati, &amp; c&aelig;teris huiu&longs;modi modorum &longs;uperfluorum qui&longs;quiliis; <lb/>de quibus plurimi tecum contendunt. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Ob&longs;eruabis nonnullas e&longs;&longs;e difficultates, qu&aelig; communes &longs;unt etiam <lb/>illi &longs;ententi&aelig;, quam &longs;equuntur ij, qui exi&longs;timant impetum ad extra <lb/>produci &agrave; corpore impacto; quas tamen facil&egrave; &longs;oluemus infr&agrave; in conti&shy;<lb/>nuata no&longs;trorum Theorematum &longs;erie. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 41.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Aliquis impetus non producitur ab alio impetu.<emph.end type="italics"/></s><s> Probatur, quia aliquis <lb/>impetus producitur ad intra &agrave; potentia motrice, vt patet. </s>

<s>2. cum non <lb/>detur progre&longs;&longs;us in infinitum, nec impetus idem producatur &agrave; &longs;e ip&longs;o, ad <lb/>aliquem tandem vltimum &longs;eu primum deueniendum e&longs;t, qui ab alio im&shy;<lb/>petu non producatur. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 42.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Impetus producitur &longs;emper ad extra ab alio impetu.<emph.end type="italics"/></s><s> Quia cum &longs;emper <lb/>ad illius productionem requiratur applicatio alterius impetus; cert&egrave; <lb/>non e&longs;t ponenda alia cau&longs;a per Ax. 11. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 43.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc impetus habet duplex munus cau&longs;&aelig;; &longs;cilicet cau&longs;&aelig; exigentis ad intra <lb/>&amp; efficientis ad extra<emph.end type="italics"/>; vtrumque patet ex dictis. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 44.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Impetus agit tant&ugrave;m ad extra, vt tollat impedimentum motus<emph.end type="italics"/>; cum enim <lb/>motus &longs;it finis intrin&longs;ecus impetus; cert&egrave; &longs;i nihil impediret motum, <lb/>haud dubi&egrave; gauderet impetus &longs;uo fine; igitur fru&longs;tr&agrave; quidquam aliud <lb/>de&longs;ideraret; pr&aelig;terea lic&egrave;t applicetur &agrave; tergo aliud mobile; non tamen <lb/>propterea in eo producit, vt con&longs;tat experienti&acirc;; denique cum tan&shy;<lb/>t&ugrave;m impetum cogno&longs;camus per motum; cum nequidem e&longs;&longs;et impetus, <lb/>&longs;i non e&longs;&longs;et motus, per Th. 17. cert&egrave; totus e&longs;t impetus propter motum <lb/>qui e&longs;t eius finis; igitur non agit ni&longs;i propter motum: &longs;ed non pote&longs;t <lb/>excogitari, quid faciat propter motum, dum agit, ni&longs;i dicamus ideo <lb/>tant&ugrave;m agere, vt tollatur impedimentum; cum certum &longs;it corpus im&shy;<lb/>mobile, in quod impingitur aliud mobile, impedire eius motum. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 45.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc non &longs;imul agit impetus in orbem &longs;ed tant&ugrave;m per lineam <lb/>&longs;ui motus; cui &longs;i nullum corpus occurrit reuer&agrave; non agit,<emph.end type="italics"/> Ratio e&longs;t; quia li&shy;<lb/>c&egrave;t aliud corpus mobili admoueatur in alia linea; cum non impediat <lb/>eius motum, vt &longs;uppono; cum agat tant&ugrave;m impetus ad extra, vt tollat, <pb xlink:href="026/01/065.jpg" pagenum="33"/>impedimentum motu &longs;ui &longs;ubiecti, in eo non agit, quod non impedit; &amp; <lb/>cum impediatur tant&ugrave;m in vna linea, in ca tant&ugrave;m agit; igitur non <lb/>agit in orbem. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Ob&longs;eruabis prim&ograve;, hanc primam e&longs;&longs;e difficultatem; cum in hoc im&shy;<lb/>petus maxim&egrave; differat ab alijs qualitatibus &longs;i qu&aelig; &longs;unt, qu&aelig; agunt in or&shy;<lb/>bem, vt dicemus &longs;uo loco. </s></p><p type="main">

<s>Ob&longs;eruabis &longs;ecund&ograve;, hanc etiam e&longs;&longs;e communem illorum &longs;ententiam, <lb/>qui dicunt impetum ad extr&agrave; produci ab ip&longs;o mobili, &longs;ed ita vt ab illis <lb/>vix &longs;olui po&longs;&longs;it; cum tamen &agrave; nobis facil&egrave; &longs;oluatur. </s></p><p type="main">

<s>Ob&longs;eruabis terti&ograve;, impetum in vtroque munere cau&longs;&aelig; &longs;ube&longs;&longs;e tant&ugrave;m <lb/>vni line&aelig;; &longs;cilicet exigit motum per vnam lineam; cum per plures &longs;i&shy;<lb/>mul motus e&longs;&longs;e non po&longs;&longs;it; ne idem mobile &longs;imul e&longs;&longs;et in pluribus lo&shy;<lb/>cis; &amp; producit impetum per vnam lineam; cum producat tant&ugrave;m pro&shy;<lb/>pter motum. </s></p><p type="main">

<s>Ob&longs;eruabis quart&ograve;, alias qualitates, &longs;i qu&aelig; &longs;unt, non agere ad extra, <lb/>vt tollant impedimentum &longs;ui effectus ad intra; qui &longs;cilicet ab impedi&shy;<lb/>mento extrin&longs;eco impediri non pote&longs;t; vt accidit in ip&longs;o impetu; etenim <lb/>corpus non pote&longs;t moueri ni&longs;i nouum locum acquirat: neque nouum <lb/>locum acquirere ab alio corpore occupatum, ni&longs;i corpus hoc loco ce&shy;<lb/>dat, neque hoc loco cedere pote&longs;t &longs;ine motu, vel moueri &longs;ine impetu, <lb/>igitur cum impediat motum amoueri debet, accepto dumtaxat impetu <lb/>ab alio mobili. </s></p><p type="main">

<s>Ob&longs;eruabis quint&ograve; nonnullos e&longs;&longs;e, qui volunt motum vnius corporis <lb/>transferri in aliud corpus; &longs;ed mera e&longs;t metaphora; nihil cnim pror&longs;us <lb/>e&longs;t quod ab vno in aliud tran&longs;eat, &longs;eu transferatur; nec aliud dici po&shy;<lb/>te&longs;t, ni&longs;i quod dictum e&longs;t, impetum &longs;cilicet nouum produci. </s></p><p type="main">

<s>Hinc etiam reiicies commentum illorum, qui dicunt ideo vnum <lb/>corpus ab alio moueri, quia ab vno in aliud deriuantur corpu&longs;cula illa, <lb/>qu&aelig; faciunt lumen, &amp; calorem; quia lumen, &amp; calor &longs;unt ver&aelig; qualita&shy;<lb/>tes, non corpu&longs;cula, vt demon&longs;trabimus in 5. tractatu: Adde quod li&shy;<lb/>cet ferrum candens aliud frigidum impellat, etiam veloci&longs;&longs;im&egrave;; hoc ip&shy;<lb/>&longs;um &aelig;qu&egrave; frigidum manet; denique in cra&longs;&longs;is tenebris nix &longs;eu glacies <lb/>frigidi&longs;&longs;ima pernici&longs;&longs;im&egrave; moueri pote&longs;t: &longs;ed apage i&longs;ta commenta. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 46.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Omnes partes impetus mobilis agunt ad extra actione communi.<emph.end type="italics"/></s><s> Probatur <lb/>per Ax. 13. n. </s>

<s>1. ni&longs;i enim agerent actione communi &longs;ed qu&aelig;libet &longs;uam <lb/>produceret; cur potius in hac parte &longs;ubiecti, quam in alia, deinde ap&shy;<lb/>plicatur tant&ugrave;m vna immediat&egrave;; Igitur agunt omnes actione commu&shy;<lb/>ni; omnes inquam ill&aelig;, qu&aelig; impediuntur; cum enim impetus agat <lb/>tant&ugrave;m ad extr&agrave; vt tollat impedimentum &longs;ui motus; ille pro&longs;ect&ograve; age&shy;<lb/>re non debet, cuius motus vel effectus non impeditur. </s></p><pb xlink:href="026/01/066.jpg" pagenum="34"/><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 47.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc maiora corpora put&agrave; onerari&aelig; naues, lic&egrave;t tardi&longs;&longs;imo motu ferantur, <lb/>cum in aliud corpus impinguntur maxima vi illud impellunt.<emph.end type="italics"/></s><s> Ratio e&longs;t; <lb/>quia cum &longs;int plures partes impetus in pluribus partibus &longs;ubiecti, &amp; <lb/>omnes agant actione communi, non mirum e&longs;t &longs;i maiorem effectum <lb/>producant, per Ax. 13. n. </s>

<s>2. <!-- KEEP S--></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Vides prim&ograve; in hoc ca&longs;u compen&longs;ari inten&longs;ionem ab exten&longs;ione; <lb/>quippe quod pr&aelig;&longs;tarent plures partes impetus in minore corporis mole <lb/>inten&longs;&aelig;; hoc idem pr&aelig;&longs;tare po&longs;&longs;unt exten&longs;&aelig; in maiore mole. </s></p><p type="main">

<s>Secund&ograve; &longs;icut maior moles aptior e&longs;t ad motum imprimendum, &amp; mi&shy;<lb/>n&ugrave;s apta ad recipiendum ita minor contr&agrave; aptior e&longs;t ad recipiendum, &amp; <lb/>min&ugrave;s apta ad imprimendum. </s></p><p type="main">

<s>Terti&ograve;, Hinc corpora illa, quorum partes vel nullo vel modico nexu <lb/>copulantur, minimo fer&egrave; impul&longs;u commouentur; &longs;ic a&euml;r &amp; aqua mini&shy;<lb/>mo flante vento agitantur, nubes pelluntur; hinc tot procell&aelig; tempe&shy;<lb/>&longs;tate&longs;que cientur; nec vlla e&longs;t alia ratio, cur minima fer&egrave; venti vis, cui <lb/>modicum &longs;axum re&longs;i&longs;tit, tantam aqu&aelig;, vel a&euml;ris molem commoueat, ni&shy;<lb/>&longs;i quia cum partes illorum corporum nullo fer&egrave; nexu coniunct&aelig; &longs;int vna <lb/>&longs;ine alia moueri pote&longs;t, quod in aqua gelu concreta minim&egrave; accidit. </s></p><p type="main">

<s>Quart&ograve;, Hinc &longs;i maxima rupes ita comminueretur vt tota in pulue&shy;<lb/>rem &longs;eu &longs;abulum abiret, minima vis impre&longs;&longs;a particulas illas moueret. </s></p><p type="main">

<s>Quint&ograve;, Hinc diuino pen&egrave; con&longs;ilio factum e&longs;t, vt partes terre&longs;tris <lb/>globi arctiore fibula copulentur; ne, &longs;i di&longs;iunct&aelig; e&longs;&longs;ent, minimo flatu <lb/>di&longs;pergerentur: vt videre e&longs;t in puluere etiam graui&longs;&longs;imo, qui ab aura <lb/>flant e di&longs;pergitur. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 48.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Impetus, cuius motus non impeditur, non agit ad extr&agrave;.<emph.end type="italics"/></s><s> Probatur per <lb/>Th. 44. hinc &longs;i aliud corpus affigas mobili &agrave; tergo, nullum impetum in <lb/>eo producet, cuius effectus, qui cert&egrave; impetui &longs;ingularis e&longs;t, alia ratio <lb/>e&longs;&longs;e non pote&longs;t; tam enim corpus e&longs;t applicatum &agrave; tergo, quam in <lb/>ip&longs;a fronte; &amp; nihil e&longs;t in vno, quod non &longs;it in alio, ni&longs;i quod in fronte <lb/>impedit motum, &agrave; tergo ver&ograve; non impedit. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 1.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Hinc egregium paradoxon erui pote&longs;t; quod &longs;cilicet cau&longs;a nece&longs;&longs;aria <lb/>etiam immediat&egrave; applicata, &amp; non impedita in &longs;ubiecto apto non agit; <lb/>quod videtur e&longs;&longs;e contra Ax. 12. vnde vt agat cau&longs;a nece&longs;&longs;aria, debet <lb/>applicari debito modo; &longs;i agat in orbem, omnis applicatio &longs;ufficiens <lb/>e&longs;t: &longs;i ver&ograve; agat tant&ugrave;m per vnam lineam; cert&egrave; applicari debet in ca <lb/>linea; alioquin non aget defectu debit&aelig; applicationis. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 2.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Hinc etiam aliud paradoxon non minus iucundum; cau&longs;a nece&longs;&longs;aria <pb xlink:href="026/01/067.jpg" pagenum="35"/>appllcata, &amp; non impedita non agit; at ver&ograve; agit impedita; &longs;cilicet <lb/>impetus qui tant&ugrave;m agit, vt tollat impedimentum; igitur, &longs;i non <lb/>impediatur non agit. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 49.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Quo min&ugrave;s impeditur impetus, min&ugrave;s agit ad extra, &amp; contr&agrave;; quo pl&ugrave;s <lb/>impeditur, pl&ugrave;s agit.<emph.end type="italics"/></s><s> Cum enim ide&ograve; agat ad extra, vt tollat impedi&shy;<lb/>mentum; cert&egrave; &longs;i nullum e&longs;t, nihil agit, &longs;i min&ugrave;s, min&ugrave;s agit; igitur <lb/>agit pro rata, id e&longs;t, pro diuer&longs;a impedimenti ratione. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 50.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Si linea motus, quam directionis appellant, ducatur per centrum vtriu&longs;que <lb/>corporis, maximum est impedimentum,<emph.end type="italics"/> vt patet. </s>

<s>&longs;int enim duo globi, <lb/>A mobilis, &amp; B. occurrens ip&longs;i A, &longs;itque linea directionis DE ducta <lb/>per centrum vtriu&longs;que AB, &amp; punctum contactus &longs;it C; cert&egrave; glo&shy;<lb/>bus B maximum ponit impedimentum, quod ab eo poni po&longs;&longs;it; Igitur <lb/>impetus globi A agit quant&ugrave;m pote&longs;t in globum B; vt &longs;cilicet maxi&shy;<lb/>mum impedimentum remoueat. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 51.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Si linea motus vel ip&longs;ius parallela cadat perpendiculariter in extremam <lb/>diametrum globi immobilis: haud dubi&egrave; nihil impedit<emph.end type="italics"/>; &longs;it enim globus <lb/>mobilis A, Immobilis B, linea directionis &longs;it GA, ip&longs;i parallela FC; <lb/>cert&egrave; globus B. non impedit motum globi A. cum nihil loci globi B <lb/>occupari debeat &agrave; globo A; Igitur impetus A non agit in globum B per <lb/>Th. 48. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 52.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Si linea motus &longs;it inter vtramque; est minus impedimentum.<emph.end type="italics"/> &longs;it globus <lb/>immobilis BA; &longs;it linea motus GC cum impedimento, de qua in Th. 50. <lb/>&longs;it alia KB cum nullo impedimento, de qua in Th. 51. &longs;int ali&aelig; HD, <lb/>IE; cert&egrave; minus e&longs;t impedimentum in contactu D, qu&agrave;m in C; quia ca&shy;<lb/>dit obliqu&egrave; in D, perinde atque &longs;i caderet in tangentem NO; Igitur <lb/>minus impeditur; in qua vero proportione, dicemus ali&agrave;s, cum de re&shy;<lb/>flexione, &amp; de motu mixto. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 53.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc producitur in contactu<emph.end type="italics"/> C, <emph type="italics"/>totus impetus; in contactu<emph.end type="italics"/> D, <emph type="italics"/>min&ugrave;s; in <lb/>contactu<emph.end type="italics"/> E <emph type="italics"/>adhuc min&ugrave;s; in<emph.end type="italics"/> B <emph type="italics"/>nihil<emph.end type="italics"/>; quia in ea proportione producitur <lb/>pl&ugrave;s vel min&ugrave;s impetus, quo pl&ugrave;s e&longs;t, vel min&ugrave;s impedimenti per <lb/>Th. 49. &longs;ed min&ugrave;s e&longs;t impedimentum in E, qu&agrave;m in C; &amp; in E, qu&agrave;m <lb/>in D, per Th. 52; Igitur in D producitur min&ugrave;s impetus, qu&agrave;m in C, <lb/>&amp; min&ugrave;s in E, qu&agrave;m in D. <!-- KEEP S--></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 54.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc eadem cau&longs;a nece&longs;&longs;aria etiam immediate applicata diuer&longs;um impe<emph.end type="italics"/><pb xlink:href="026/01/068.jpg" pagenum="36"/><emph type="italics"/>tum producit; vt patet in impetu, non tamen est eodem modo applicata, <lb/>id e&longs;t in eadem linea.<emph.end type="italics"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 55.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc ratio multorum effectuum phy&longs;icorum e. </s>

<s>ui potest<emph.end type="italics"/>; cur &longs;cilicet cor&shy;<lb/>pus incidens in aliud perpendiculariter maximum ictum infligat; quia <lb/>&longs;cilicet maximum impetum producit, qui po&longs;&longs;it ab eo produci; cur <lb/>idem corpus obliqu&egrave; incidens in aliud minorem ictum infligat; cuius <lb/>rei alia ratio e&longs;&longs;e non pote&longs;t. </s>

<s>Huc etiam reuoca tormenta bellica, qu&aelig; <lb/>vel directo, vel obliquo ictu muros verberant; hinc perpendicularis <lb/>forti&longs;&longs;ima e&longs;t; lic&egrave;t eadem ratio pro motu corporum non valeat, qu&aelig; <lb/>valet pro diffu&longs;ione, &longs;eu propagatione qualitatum. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 56.<emph.end type="center"/></s></p><p type="main">

<s>Hinc pote&longs;t determinari quota pars impetus producatur, &amp; quantus <lb/>&longs;it ictus; cognito &longs;cilicet &amp; &longs;uppo&longs;ito eo impetus gradu, qui producitur, <lb/>cum totus producitur, vt fit in perpendiculari; quippe tota men&longs;ura <lb/>impetus continetur in arcu CB; quam proportionem nos infr&agrave; demon&shy;<lb/>&longs;trabimus. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 57.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Si linea directionis ducatur per centrum vtriu&longs;que globi, mobilis &longs;cilicet <lb/>&amp; immobilis, impetus producit totum impetum quem pote&longs;t producere &longs;iue in <lb/>maiori globo, &longs;iue in minori, &longs;iue in &aelig;quali<emph.end type="italics"/>; patet experientia; cuius ratio <lb/>e&longs;t; quia impetus e&longs;t cau&longs;a nece&longs;&longs;aria; Igitur idem impetus codem mo&shy;<lb/>do applicatus &aelig;quali tempore, &aelig;qualem &longs;emper effectum producit, per <lb/>Ax. 12. igitur cum impetus agat tant&ugrave;m, vt tollat impedimentum per <lb/>Th. 44. &amp; cum in pr&aelig;dicta linea agat quantum pote&longs;t per Th. 50. cer&shy;<lb/>t&egrave; &aelig;qualem effectum producat nece&longs;&longs;e e&longs;t; &longs;iue in maiori &longs;iue in mino&shy;<lb/>ri, &longs;iue in &aelig;quali globo immobili. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 58.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc impetus remi&longs;&longs;us potest producere inten&longs;um; &amp; h&aelig;c e&longs;t altera difficul&shy;<lb/>tas; cum &longs;cilicet maior globus in minorem impingitur<emph.end type="italics"/>; cum enim omnes <lb/>partes impetus maioris globi agant actione communi per Th. 46. &amp; <lb/>cum agant quant&ugrave;m maxim&egrave; po&longs;&longs;unt; in minore globo, tot partes pro&shy;<lb/>ducunt impetus, quot in maiore, vt patet; igitur in minore globo pau&shy;<lb/>cioribus partibus &longs;ubiecti di&longs;tribuuntur plures partes impetus; crgo in <lb/>qualibet parte &longs;ubiecti &longs;unt plures; &longs;ed hoc e&longs;t e&longs;&longs;e inten&longs;um, vt con&longs;tat, <lb/>igitur impetus remi&longs;&longs;us producit inten&longs;um; quod e&longs;t paradoxon egre&shy;<lb/>gium. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 59.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc etiam impetus inten&longs;us producit remi&longs;&longs;um, cum &longs;cilicet minor globus <lb/>in maiorem incidit<emph.end type="italics"/>; quia &longs;cilicet pauciores partes impetus di&longs;tribuun&shy;<lb/>tur pluribus partibus &longs;ubiecti; igitur qu&aelig;libet &longs;ubiecti pauciores impe&shy;<lb/>tus habet; qu&aelig; omnia con&longs;tant ex dictis. </s></p><pb xlink:href="026/01/069.jpg" pagenum="37"/><p type="main">

<s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Ob&longs;eruabis prim&ograve;, &longs;ingularem impetus proprietatem, qu&aelig; alijs qua&shy;<lb/>litatibus minim&egrave; competit; nam ali&aelig; qualitates v. <!-- REMOVE S-->g. <!-- REMOVE S-->calor; lumen in <lb/>eadem di&longs;tantia effectum &longs;emper &aelig;qu&egrave; inten&longs;um producunt; &longs;ecus ver&ograve; <lb/>impetus, qui pro maiori vel minori obice maiorem, vel minorem, hoc <lb/>e&longs;t inten&longs;iorem, vel remi&longs;&longs;iorem impetum in eadem di&longs;tantia producit; <lb/>cuius ratio ex eo capite petitur; qu&ograve;d impetus agat tant&ugrave;m ad extra <lb/>propter &longs;uum effectum ad intra, vt &longs;cilicet tollat impedimentum; igi&shy;<lb/>tur in totum, quod impedit, agit; igitur non habet certam, &amp; deter&shy;<lb/>minatam &longs;ph&aelig;ram; cum tant&ugrave;m agat in obicem, &longs;iue &longs;it maior, &longs;iue <lb/>minor: Quia ver&ograve; e&longs;t cau&longs;a nece&longs;&longs;aria, &aelig;qualem effectum producit, id <lb/>e&longs;t tot partes impetus in maiore, quot in minore, ergo, cum in mino&shy;<lb/>re &longs;int pauciores partes &longs;ubiecti, &amp; plures in maiore; haud dubi&egrave; qu&aelig;li&shy;<lb/>bet pars minoris habebit plures partes effectus, &amp; qu&aelig;libet pars maio&shy;<lb/>ris pauciores; igitur effectus erit inten&longs;ior in minore, &amp; remi&longs;&longs;ior in <lb/>maiore. </s>



</p><p type="main">

<s>Pr&aelig;tere&agrave;, cum dixi omnes partes mobilis actione communi agere ad <lb/>extra; ita prim&ograve; intelligi debet, vt omnes ill&aelig; partes moueantur: &longs;ecun&shy;<lb/>d&ograve;, vt linea motus, &longs;eu directionis per centra grauitatis vtriu&longs;que glo&shy;<lb/>bi v, g. <!-- REMOVE S-->ducatur; alioquin, vel omnes actione communi non agunt, vel <lb/>minus agunt, de quo infr&agrave;; &longs;ufficit ver&ograve; iuxta pr&aelig;&longs;ens in&longs;titutum, vt <lb/>globus ita impellat alium vel &aelig;qualem, vel in&aelig;qualem, vt linea dire&shy;<lb/>ctionis ducatur per centrum grauitatis alterius; vide figuram. </s>



<s>in qua <lb/>linea directionis e&longs;t DE. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 60.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Impetus globi impacti in alium globum eo modo, quo diximus, id est, linea <lb/>directionis ducta per centra grauitatis vtriu&longs;que producit in eo &aelig;qualem<emph.end type="italics"/>; Pro&shy;<lb/>batur, quia impetus e&longs;t cau&longs;a nece&longs;&longs;aria, qu&aelig; tunc agit quantum pote&longs;t <lb/>per Th. 57. &longs;ed &aelig;qualis pote&longs;t producere &aelig;qualem: </s>

<s>Probatur prim&ograve;, <lb/>exemplo aliarum qualitatum; &longs;ecund&ograve;, quia ideo agit vt tollat impedi&shy;<lb/>mentum, hoc e&longs;t vt corpus illud amoueat loco; igitur &aelig;quali motu per <lb/>&longs;e; alioquin ni&longs;i &aelig;quali motu amoueret, non tolleret impedimentum, <lb/>vt pater; terti&ograve; &longs;int 30. partes impetus, cert&egrave;vel producent plures vel <lb/>pauciores, vel totidem, non plures; cur enim potius 31. quam 32. <lb/>nec etiam pauciores; cur enim potius 20. quam 18, &amp;c. </s>

<s>Igitur totidem; <lb/>quia cum &longs;int plures numeri plurium partium &longs;upra 30. &amp; pauciorum <lb/>infra vt patet; &longs;itque tant&ugrave;m vnicus numerus &aelig;qualium; cert&egrave; quod <lb/>vnum e&longs;t, determinatum e&longs;t, per Ax. 5. h&aelig;c ratio lic&egrave;t videatur negati&shy;<lb/>ua e&longs;t tamen potenti&longs;&longs;ima: quart&ograve;, quia actus &longs;ecundus, re&longs;pondet actui <lb/>primo, id e&longs;t, effectus productus virtuti cau&longs;&aelig; producentis; itaque cum <lb/>virtus agendi impetus &longs;it eius entitas, vt patet, cert&egrave; impetus productus <lb/>e&longs;t per &longs;e &aelig;qualis impetui producenti per &longs;e; id e&longs;t remoto omni <lb/>impedimento, &amp; facto eo contactu iuxta modum pr&aelig;dictum, ea quo-<pb xlink:href="026/01/070.jpg" pagenum="38"/>que lege, vt impetus agat quantum pote&longs;t, &amp; omnes partes mobilis <lb/>moueantur &aelig;quali motu. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 1.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Hinc reijcis illos, qui volunt &agrave; globo &aelig;quali produci in &aelig;quali &longs;ub&shy;<lb/>duplum impetum; in &longs;ubduplo &longs;ubtriplum; in &longs;ubquadruplo &longs;ubquin&shy;<lb/>tuplum; ratio illorum e&longs;t; quia duo globi &aelig;quales in&longs;tanti contactus <lb/>perinde &longs;e habent, atque &longs;i conflarent vnum corpus; &longs;ed &longs;i conflarent <lb/>vnum corpus quilibet &longs;ubduplum impetum haberet; &longs;i ver&ograve; globus cum <lb/>alio &longs;ubduplo faceret vnum mobile; haud dubi&egrave; minor, id e&longs;t, &longs;ubduplus <lb/>haberet tant&ugrave;m &longs;ubtriplum impetum; atque ita deinceps; hoc totum <lb/>fal&longs;i&longs;&longs;imum e&longs;t; nam prim&ograve; &longs;i globus &aelig;qualis acciperet tant&ugrave;m &longs;ubdu&shy;<lb/>plum impetum ab alio, &longs;ubduplo tant&ugrave;m motu ferretur; igitur &longs;ubdu&shy;<lb/>plum &longs;patium decurreret, quod e&longs;t contra experientiam, &amp; Th. 47. Se&shy;<lb/>cund&ograve;, ratio propo&longs;ita nulla e&longs;t; quia quando globus impactus impellit <lb/>alium, e&longs;t veluti potenti&acirc;, qu&aelig; cum tota&longs;ua vi, &amp; cum impetu agit, <lb/>cuius nulla pars transfertur in alium globum; nec enim migrat de <lb/>de &longs;ubiecto in &longs;ubiectum, &longs;ed producit &longs;ibi &aelig;qualem: equidem &longs;i duo <lb/>globi &aelig;quales e&longs;&longs;ent vel coniuncti, vel contigui in linea directionis, <lb/>quilibet pro rata acciperet impetus producti partem &agrave; potentia applica&shy;<lb/>ta; &longs;i e&longs;&longs;ent &aelig;quales, qui&longs;que &longs;ubduplum: &longs;i alter &longs;ubduplus &longs;ubtri&shy;<lb/>plum, &amp;c. </s>

<s>&longs;ed h&aelig;c &longs;unt &longs;atis facilia. </s></p><p type="main">

<s>Obijci fort&egrave; po&longs;&longs;et ab aliquo prim&ograve; experientia; videmus enim &longs;&aelig;p&egrave; <lb/>globum impul&longs;um in ludo Tudiculario moueri tardi&ugrave;s globo impellen&shy;<lb/>te; re&longs;pondeo id &longs;&aelig;p&egrave; accidere; t&ugrave;m quia linea directionis non connec&shy;<lb/>tit centra vtriu&longs;que globi; igitur minor e&longs;t ictus per Th 52. t&ugrave;m quia <lb/>globus impellens, vel impul&longs;us deficiunt &agrave; perfecta &longs;ph&aelig;ra; t&ugrave;m quia <lb/>non e&longs;t perfecta &aelig;qualitas globorum; adde quod qu&ograve; accurati&ugrave;s pr&aelig;di&shy;<lb/>ct&aelig; leges ob&longs;eruantur, ip&longs;i motus ad &aelig;qualitatem propi&ugrave;s accedunt, vt <lb/>con&longs;tat experientia. </s></p><p type="main">

<s>Obiici po&longs;&longs;et &longs;ecund&ograve; de&longs;trui aliquid impetus globi impellentis ab ip&longs;o <lb/>ictu, vt con&longs;tat experientia; igitur illa pars impetus, qu&aelig; de&longs;truitur, non <lb/>producit nouum impetum in globo impul&longs;o; </s><s>Re&longs;pondeo de&longs;truiquidem <lb/>aliquid impetus in globo impacto, vt videbimus infr&agrave;; cum tamen de&shy;<lb/>&longs;truatur tant&ugrave;m &longs;equenti po&longs;t ictum in&longs;tanti; cert&egrave; cum exi&longs;tat adhuc <lb/>ip&longs;o in&longs;tanti contactus, nece&longs;&longs;ari&ograve; agit, quippe aliquid vltimo in&longs;tanti <lb/>pote&longs;t agere; adde quod illud ip&longs;um repugnat manife&longs;t&aelig; experienti&aelig;; <lb/>lic&egrave;t enim aliquando de&longs;truatur totus impetus in globo impacto, quod <lb/>&longs;&aelig;p&egrave; accidit in ludo Tudiculario, nam illic&ograve; &longs;i&longs;tit pila eburnea; alius <lb/>tamen globus velociter mouetur, cuius effectus rationem infr&agrave; addu&shy;<lb/>cemus. </s></p><p type="main">

<s>Obijci po&longs;&longs;et terti&ograve; inde &longs;equi progre&longs;&longs;um in infinitum, nam globus <lb/>A impactus in globum B impellet cum &aelig;quali motu, &amp; B in C etiam <lb/>&aelig;quali, C in D, atque ita deinceps; mod&ograve; illi globi ita &longs;tatuantur, vt <lb/>linea directionis per omnium centra rect&agrave; ducatur; Re&longs;pondco, vel il-<pb xlink:href="026/01/071.jpg" pagenum="39"/>los omnes globos ita e&longs;&longs;e contiguos, vt mutuo contactu &longs;e inuicem tan&shy;<lb/>gant; vel aliquod &longs;patium inter &longs;ingulos intercipi; &longs;i primum, produci&shy;<lb/>tur impetus &agrave; potentia motrice in omnibus, &longs;i &longs;ufficiens e&longs;t; non ver&ograve; <lb/>vnus globus in alio, vt con&longs;tat; &longs;icut duo pondera &longs;imul attollo, quorum <lb/>vnum alteri incumbit: &longs;i ver&ograve; non &longs;e tangant, dico antequam A im&shy;<lb/>pingatur in B, dum &longs;patium illud interiectum percurrit, amittere aliquid <lb/>impetus: idem dico de B, &amp; C, vnde &longs;i nihil impetus in eo primo motu <lb/>periret &amp; linea directionis omnium centra perfect&egrave; connecteret; ita vt <lb/>omnium ictus illi omnino &longs;ine vlla deflexione re&longs;ponderent; haud du&shy;<lb/>bi&egrave; non po&longs;&longs;ent e&longs;&longs;e tot globi, quin po&longs;&longs;et alius addi, qui ab vltimo <lb/>pelleretur; &longs;ed vix illa omnia de quibus &longs;upr&agrave; po&longs;&longs;unt ob&longs;eruari; Hinc <lb/>tamen facil&egrave; vna pars a&euml;ris aliam pellit, quod di&longs;tinct&egrave; videmus in <lb/>aqua; &longs;ed de his ali&agrave;s, &longs;ufficiat mod&ograve; propo&longs;itam obiectionem inde <lb/>manere &longs;olutam. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 61.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Globus maior impactus in minorem imprimit illi inten&longs;iorem impetum, &amp; <lb/>velociorem motum per Th.<emph.end type="italics"/> 48. <emph type="italics"/>&amp;<emph.end type="italics"/> 47. Nec e&longs;t quod aliqui opponant Prin&shy;<lb/>cipium illud mechanicum; id e&longs;t, nullum corpus po&longs;&longs;e maiorem veloci&shy;<lb/>tatis gradum alteri corpori imprimere; eo &longs;cilicet gradu, quem ip&longs;um <lb/>habet; nec enim inuenio Principium illud apud eos Mechanicos, qui <lb/>mechanica momenta &longs;uarum demon&longs;trationum momentis confirmant; <lb/>qu&icirc; porro fieri pote&longs;t, vt principium illud admittatur, quod manife&longs;t&aelig; <lb/>experienti&aelig; repugnat? </s>

<s>Quis enim non vidit vel maius &longs;axum in aliud <lb/>etiam tardo motu impactum maiorem motum, &amp; impetum imprimere? </s>

<s><lb/>quis non vidit maiores illas onerarias naues etiam pigro, &amp; tardo motu <lb/>labentes maximum impetum minori occurrenti cymb&aelig; etiam impri&shy;<lb/>mere? </s>

<s>Rationem habes in Th. 47. &longs;ed dices; igitur aliquis velocitatis <lb/>gradus nullam habet cau&longs;am; igitur e&longs;t &agrave; nihilo, quod dici non pote&longs;t. </s>

<s><lb/>Re&longs;pondeo, plures partes impetus non produci in minore globo, qu&agrave;m <lb/>&longs;int in maiore; igitur nulla pars e&longs;t impetus minoris globi, qu&aelig; &longs;ui <lb/>cau&longs;am &longs;ufficientem non habeat; &longs;ed cum partes impetus maioris globi <lb/>di&longs;tribuantur pluribus partibus &longs;ubiecti, faciunt remi&longs;&longs;um impetum, igi&shy;<lb/>tur &amp; tardum; cum &longs;cilicet impetus vnius partis non iuuet motum alte&shy;<lb/>rius per Th. 37. at ver&ograve; cum partes impetus producti in minore globo <lb/>di&longs;tribuantur paucioribus partibus &longs;ubiecti, faciunt inten&longs;iorem im&shy;<lb/>petum; igitur velociorem motum, quippe omnes producuntur ab <lb/>omnibus illis actione communi per Ax. 17. num. </s>

<s>1. quid clarius. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 62.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Globus minor imprimit maiori remi&longs;&longs;iorem impetum &amp; tardiorem motum <lb/>&amp; &aelig;qualis, aqitali &aelig;qualem<emph.end type="italics"/>; h&aelig;c omnia probantur per Th. 60. &amp; pr&aelig;-, <lb/>cedentia. </s></p><pb xlink:href="026/01/072.jpg" pagenum="40"/><p type="main">

<s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Ob&longs;eruabis prim&ograve;, vtrumque globum e&longs;&longs;e eiu&longs;dem materi&aelig;; &longs;i enim <lb/>&longs;int diuer&longs;&aelig; materi&aelig;, &longs;ec&ugrave;s accidit, qu&agrave;m diximus; &longs;i v. <!-- REMOVE S-->g. <!-- REMOVE S-->&aelig;neus mi&shy;<lb/>nor pellatur ab eburneo maiore, maiorem motum hic illi non impri&shy;<lb/>met; lic&egrave;t enim &longs;it maior exten&longs;io eburnei; e&longs;t tamen minus pondus; <lb/>igitur pauciores partes. </s>



</p><p type="main">

<s>Secund&ograve;, eos globos accipiendos e&longs;&longs;e, quorum partes, vel non auo&shy;<lb/>lent ab ictu, vel non comprimantur; comprimuntur in plumbeis, <lb/>&aelig;neis, &amp; auolant in vitreis; cum enim &longs;it compre&longs;&longs;io, vel partium di&shy;<lb/>ui&longs;io, de&longs;truitur mult&ugrave;m impetus. </s></p><p type="main">

<s>Terti&ograve; reiice commentum illorum, qui dicunt corpus illud e&longs;&longs;e ma&shy;<lb/>joris velocitatis capax, quod plures habet partes materi&aelig; &longs;ub eadem <lb/>quantitate; nam &longs;uppo&longs;ita eadem re&longs;i&longs;tenti&aelig; ratione, omne corpus e&longs;t <lb/>capax illius velocitatis, cuius aliud e&longs;t capax; cum nullus &longs;it motus, quo <lb/>non po&longs;&longs;it dari velocior, &amp; tardior, vt dicemus infr&agrave;; imm&ograve; &longs;it glo&shy;<lb/>bus plumbeus 12. librarum, &longs;it eburneus eiu&longs;dem diametri 2. librarum, <lb/>v. <!-- REMOVE S-->g. <!-- REMOVE S-->haud dubi&egrave; eadem potentia producet inten&longs;iorem impetum in <lb/>eburneo, vt patet experientia, &amp; ratio con&longs;tat ex dictis; qua&longs;i ver&ograve; &longs;it <lb/>aliqua materi&aelig; inertia, qu&aelig; motum re&longs;puat; lic&egrave;t fort&egrave; maior &longs;it pro&shy;<lb/>portio re&longs;i&longs;tenti&aelig; medij comparat&aelig; cum globo eburneo, qu&agrave;m compa&shy;<lb/>rat&aelig; cum plumbeo; &longs;ed de re&longs;i&longs;tentia de percu&longs;&longs;ione, &amp; de &longs;patio age&shy;<lb/>mus infra. </s>



</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 63.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Omnis globus, qui in alium, qui mouetur impingitur, dum hic mouetur, ve&shy;<lb/>loci&ugrave;s mouetur eo &amp;c. </s>

<s>in quem impingitur <emph.end type="italics"/> patet; alioquin numquam a&longs;&longs;equi <lb/>po&longs;&longs;et, quod ex ip&longs;is terminis con&longs;tat. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 64.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Ex hac hypothe&longs;i globus impactus producit in alie nouas partes impetus<emph.end type="italics"/>; <lb/>quia impeditur eius motus, igitur vt tollat impedimentum, agit ad <lb/>extra per Th. 44. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 65.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hic impetus nouus productus minor e&longs;t eo qui produceretur in eodem globo <lb/>immobili<emph.end type="italics"/>: ratio e&longs;t; quia &longs;i &longs;i&longs;teret, maius e&longs;&longs;et impedimentum, quia <lb/>totum motum impediret, cuius tant&ugrave;m partem impedit, dum mouetur , <lb/>lic&egrave;t paul&ograve; tardius; igitur minus agit ad extra per Th. 49. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 66.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Mobile adh&aelig;rens alteri mobili &agrave; tergo; dum vtrumque &aelig;que velociter <lb/>feratur nullum producit in eo impetum.<emph.end type="italics"/></s><s> Probatur, quia mobile quod pr&aelig;it, <lb/>non impedit motum &longs;ub&longs;equentis; igitur nullum impetum ab eo acci<lb/>pit per Th. 48. </s></p><pb xlink:href="026/01/073.jpg" pagenum="41"/><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 67.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc paradoxon egregium &longs;i quod aliud; globus percu&longs;&longs;us ab alio eadem <lb/>&longs;emper velocitate mouetur, &longs;iue moueretur in&longs;tanti percu&longs;&longs;ionis, &longs;iue &longs;i&shy;<lb/>&longs;teret.<emph.end type="italics"/> v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;it globus A quie&longs;cens, cui imprimantur ab alio B 40. gra&shy;<lb/>dus velocitatis: id e&longs;t &aelig;qualis impetus impetui percutientis, iam ver&ograve; <lb/>moueatur A, cum 20. grad. <!-- REMOVE S-->velocitatis, &amp; B, qui mouetur cum 40. <lb/>impingatur, cert&egrave; cum impediatur tant&ugrave;m &longs;ubduplum motus, produce&shy;<lb/>tur tant&ugrave;m &longs;ubduplum impetus, id e&longs;t 20. qui &longs;i addantur 20. grad. <!-- REMOVE S-->erunt <lb/>40. qu&aelig; omnia con&longs;tant per Th.49.48.&amp;c. </s>







</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 1.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Hinc &aelig;quale &longs;emper &longs;patium percu&longs;&longs;us globus conficit, &longs;iue ante per&shy;<lb/>cu&longs;&longs;ionem moueretur, &longs;iue quie&longs;ceret. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 2.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Hinc &longs;i &longs;ecund&ograve; percutiatur idem globus, &longs;patium totum, quod per&shy;<lb/>currit t&ugrave;m &agrave; prim&ograve;, t&ugrave;m &agrave; &longs;ecundo ictu e&longs;t maius eo, quod &agrave; primo ictu <lb/>confeci&longs;&longs;et, &longs;i non fui&longs;&longs;et &longs;ecund&ograve; percu&longs;&longs;us; maius inquam &longs;egmento &longs;pa&shy;<lb/>tij interiecto inter primum &amp; &longs;ecundum ictum. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 3.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Hinc reiicies aliquos, quorum &longs;ententiam habes apud Doctum Mer&shy;<lb/>&longs;emium, <emph type="italics"/>in prop.<emph.end type="italics"/> 20. <emph type="italics"/>ph&aelig;n. mech. quorum &longs;unt h&aelig;c verba; &longs;i malleus pilam <lb/>currentem eodem, ac ante&agrave; modo percutiat, nonam &longs;ui motus partem; &longs;i ver&ograve; <lb/>currentem tertia vice percutiat, vnam vige&longs;imam &longs;eptimam &longs;ui motus par&shy;<lb/>tem ei tribuet, atque ita deinceps.<emph.end type="italics"/></s><s> Supponit prim&ograve; h&aelig;c &longs;ententia mal&shy;<lb/>leum e&longs;&longs;e duplum pil&aelig; percu&longs;&longs;&aelig;. </s>

<s>Secund&ograve;, malleum imprimere pil&aelig; &longs;ub&shy;<lb/>dupl&aelig; &longs;ubtriplum motum; quod fal&longs;um e&longs;t, vt con&longs;tat ex Th 6. &amp; Co&shy;<lb/>roll. </s>

<s>1. Pr&aelig;terea, lic&egrave;tin prim&agrave; percu&longs;&longs;ione imprimeret tant&ugrave;m pr&aelig;di&shy;<lb/>ct&aelig; pil&aelig; &longs;ubtriplum impetum, in &longs;ecunda percu&longs;&longs;ione maiorem impri&shy;<lb/>meret po&longs;t longiorem motum, vbi iam ad quietem propi&ugrave;s accedit; mi&shy;<lb/>norem ver&ograve; paul&ograve; po&longs;t initium motus, vt con&longs;tat ex dictis, &amp; ex ip&longs;a ex&shy;<lb/>perientia; pote&longs;t quidem in aliquo puncto &longs;ui motus &longs;ecunda vice per&shy;<lb/>cuti, in quo &longs;ubtriplum tant&ugrave;m motum imprimet; hoc e&longs;t eo in&longs;tanti&shy;<lb/>quo tant&ugrave;m ami&longs;it tertiam fui impetus partem; tum deinde in tertia <lb/>percu&longs;&longs;ione pote&longs;t tant&ugrave;m (1/27) motus partem illi tribuere; eo &longs;cilicet in&shy;<lb/>&longs;tanti, quo tant&ugrave;m ami&longs;it (1/27) &longs;ui impetus partem; &longs;ed in alijs temporis <lb/>punctis long&egrave; alia erit impetus producti ratio; Igitur tota h&aelig;c progre&longs;&shy;<lb/>&longs;io gratis omnin&ograve; fuit excogitata. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 4.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Hinc etiam po&longs;t &longs;ecundam percu&longs;&longs;ionem &aelig;quale &longs;patium conficiet al&shy;<lb/>teri, quod iam confecit po&longs;t primam &aelig;qualibus temporibus; igitur &aelig;qua&shy;<lb/>lis e&longs;t velocitas vtriu&longs;que motus; quia &longs;cilicet, &longs;i e&longs;t &aelig;qualis impetus, e&longs;t <lb/>qualis motus: Ex his maximam carum dubitationum partem &longs;oluere po&shy;<lb/>teris qu&aelig; in eadem Mer&longs;enni propo&longs;itione courinentur reliquas vero ex <lb/>dicendis infr&agrave;. </s></p><pb xlink:href="026/01/074.jpg" pagenum="42"/><p type="main">

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 5.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Ex dictis etiam colliges diuer&longs;as percu&longs;&longs;ionum rationes &longs;uppo&longs;ita di&shy;<lb/>uer&longs;a ratione ponderum globi percutientis, &amp; percu&longs;&longs;i; cum enim impe&shy;<lb/>tus productus &longs;it &aelig;qualis per &longs;e impetui producenti, per Th.60. mod&ograve; <lb/>debita fiat applicatio, de qua in Th.50. &longs;i percutiens &longs;it duplus percu&longs;&longs;i, <lb/>&longs;uppo&longs;ita eadem materia, motus percu&longs;&longs;i erit dupl&ograve; velocior; quia im&shy;<lb/>petus erit dupl&ograve; inten&longs;ior, vt con&longs;tat ex Th. 61. &longs;i ver&ograve; &longs;it quadruplus, <lb/>quadruplo, &amp;c. </s>

<s>Igitur velocitates motuum &longs;unt in rati&ograve;ne ponderum <lb/>permutando. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 68.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Si corpus percu&longs;&longs;um &longs;it oblongum, &amp; percu&longs;&longs;io fiat in centro grauitatis eiu&longs;&shy;<lb/>dem corporis; producitur impetus in percu&longs;&longs;io &aelig;qualis impetui percutientis<emph.end type="italics"/>; &longs;ed <lb/>opus e&longs;t aliqua figura: Sit corpus AD, parallelipedum; diuidatur &aelig;qua&shy;<lb/>liter in E ita vt E &longs;it centrum grauitatis; &longs;i percu&longs;&longs;io fiatin E per lineam <lb/>perpendicularem HE, producetur impetus in corpore AD &aelig;qualis im&shy;<lb/>petui corporis percutientis; quia &longs;cilicet &agrave; corpore AD non pote&longs;t maius <lb/>e&longs;&longs;e impedimentum; igitur agit quant&ugrave;m pote&longs;t impetus corporis per&shy;<lb/>cutientis per Th.50. igitur producit &aelig;qualem per Th.69. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 69.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Si percu&longs;&longs;io fiat in<emph.end type="italics"/> F <emph type="italics"/>per lineam perpendicularem<emph.end type="italics"/> IF, <emph type="italics"/>minus erit impedi&shy;<lb/>mentum, qu&agrave;m per<emph.end type="italics"/> HE, Quia &longs;i per HE, moueri tant&ugrave;m pote&longs;t motu <lb/>recto, &longs;i per IF, etiam motu circulari circa aliquod centrum; &longs;ed hic <lb/>motus e&longs;t facilior quam ille; igitur minus e&longs;t impedimentum; (&longs;uppono <lb/>autem cylindrum BC vtroque modo moueri po&longs;&longs;e ab applicata potentia) <lb/>igitur min&ugrave;s impetus producitur, &longs;i percu&longs;&longs;io fiat per IF, qu&agrave;m &longs;i fiat <lb/>per LK: In qua ver&ograve; proportione &longs;it minus impedimentum, &amp; minori <lb/>opus impetu, po&longs;ito eodem potenti&aelig; ni&longs;u, determinabimus facil&egrave; ali&agrave;s; <lb/>vt etiam demon&longs;trabimus circa quod centrum hic circularis motus fieri <lb/>debeat. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Ex duobus capitibus minus e&longs;&longs;e pote&longs;t impedimentum; primum e&longs;t, <lb/>quod petitur &agrave; puncto contactus, &longs;ecundum &agrave; linea incidenti&aelig;; v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;i <lb/>accipiatur punctum E, in quo e&longs;t centrum grauitatis corporis AD, &amp; in <lb/>eo fiat percu&longs;&longs;io; maximum e&longs;t impedimentum ratione puncti conta&shy;<lb/>ctus, in quo fit percu&longs;&longs;io; &longs;i ver&ograve; percu&longs;&longs;io fiat per lineam perpendicu&shy;<lb/>larem HE, maximum e&longs;t impedimentum, ratione line&aelig;; &longs;i autem ex <lb/>vtroque capite &longs;imul accidat impedimentum, maximum e&longs;t omnium; <lb/>iam ver&ograve; &longs;i accipiatur punctum E, &amp; linea percu&longs;sionis ME; minor e&longs;t <lb/>percu&longs;sio ratione line&aelig; non puncti; accipiatur punctum N, &amp; linea <lb/>percu&longs;sionis MN, minor e&longs;t percu&longs;sio ratione puncti non line&aelig;, acci&shy;<lb/>piatur punctum N, &amp; linea IN, minor e&longs;t percu&longs;sio ratione vtriu&longs;que; <lb/>&longs;i demum accipiatur punctum E, &amp; linea ME, minor e&longs;t percu&longs;sio ra&shy;<pb xlink:href="026/01/075.jpg" pagenum="43"/>tione line&aelig; non puncti; accipiatur punctum N linea percu&longs;&longs;ionis MN, <lb/>minor e&longs;t percu&longs;&longs;io ratione puncti non line&aelig;; &longs;i accipiatur punctum N, <lb/>&amp; linea IN, minor e&longs;t percu&longs;&longs;io ratione vtriu&longs;que: &longs;i demum accipia&shy;<lb/>tur punctum E &amp; linea HE, maior e&longs;t percu&longs;&longs;io ratione vtriu&longs;que; igi&shy;<lb/>tur &longs;unt quatuor coniugationes; &longs;eu quatuor cla&longs;&longs;es diuer&longs;arum percu&longs;&shy;<lb/>&longs;ionum. </s>



</p><p type="main">

<s>Hinc compen&longs;ari pote&longs;t ratione vnius quod dee&longs;t ratione alterius, <lb/>v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;i fiat percu&longs;&longs;io in puncto E per lineam ME, pote&longs;t &longs;ciri punctum <lb/>inter ED, in quo percu&longs;&longs;io per lineam perpendicularem &longs;it &aelig;qualis <lb/>percu&longs;&longs;ioni per lineam ME; &longs;ed de his infr&agrave; in lib. 

10. cum de percu&longs;&shy;<lb/>&longs;ione, determinabimus enim vnde proportiones i&longs;t&aelig; petend&aelig; &longs;<gap/>, &amp; <lb/>demon&longs;trabimus totam i&longs;tam rem, qu&aelig; mult&ugrave;m curio&longs;itatis habet, &amp; <lb/>vtilitatis. </s>



</p><p type="main">

<s>Determinabimus etiam dato puncto percu&longs;&longs;ionis F v.g. <!-- REMOVE S-->cum &longs;equatur <lb/>motus vectis, quodnam &longs;it centrum vectis &longs;eu huius motus. </s>

</p><p type="main">

<s>Hinc demum &longs;equitur, ne hoc omittam, data minim&acirc; percu&longs;&longs;ione per <lb/>lineam MN dari po&longs;&longs;e adhuc minorem per lineam IN, &amp; alias incli&shy;<lb/>natas; &amp; data percu&longs;&longs;ione per lineam quantumuis inclinatam, po&longs;&longs;e da&shy;<lb/>ri &aelig;qualem per lineam perpendicularem; &amp; data per lineam perpendi&shy;<lb/>cularem extra centrum grauitatis E, po&longs;&longs;e dari &aelig;qualem; &amp; in qualibet <lb/>data ratione per aliquam inclinatam, qu&aelig; cadat in E, &longs;ed de his fus&egrave; <lb/>&longs;uo loco. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 70.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Corpus oblongum parallelipedum percutiens aliud corpus, put&agrave; globu&mtail;, <lb/>motu recto per lineam directionis, qu&aelig; producta &agrave; puncto contactus ducitur per <lb/>centrum globi, dum fiat contactus in centro grauitatis parallelipedi, maximum <lb/>ictum infligit, &longs;eu agit quant&ugrave;m pote&longs;t.<emph.end type="italics"/> v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;it parallelipedum EB; quod <lb/>moueatur motu recto parallelo, lineis CD, HG, &amp;c. </s>


<s>&longs;itque globus in <lb/>D; haud dubi&egrave; agit quant&ugrave;m pote&longs;t, quia &longs;cilicet e&longs;t maximum impedi&shy;<lb/>mentum per Th.68. Tam enim globus in D impedit motum paralleli&shy;<lb/>pedi, qu&agrave;m parallelipedum motum globi impacti per lineam ID; impedit <lb/>inquam ratione oppo&longs;itionis; quia centra grauitatis vtriu&longs;que con&shy;<lb/>currunt in eadem linea; igitur &longs;i maximum e&longs;t impedimentum, agit <lb/>quant&ugrave;m pote&longs;t Th. 50. hinc producitur impetus &aelig;qualis per Th.60. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 71.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Si percu&longs;&longs;io fiat in G, id e&longs;t &longs;i globus e&longs;&longs;et in G, producetur minor impetus, <lb/>&amp; in<emph.end type="italics"/> M <emph type="italics"/>adhuc minor<emph.end type="italics"/>; vt con&longs;tat ex dictis in &longs;uperioribus Theorematis; <lb/>in qua vero proportione determinabimus ali&agrave;s. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 72.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Si corpus percutiens non &longs;it parallelipedum, &longs;ed alterius figur&aelig; v.g.<emph.end type="italics"/> <emph type="italics"/>trigo&shy;<lb/>non,<emph.end type="italics"/> ADE, &longs;itque maioris facilitatis gratia Orthonium; eiu&longs;que motus <lb/>&longs;it parallelus lineis ED, BC: &longs;it autem DA dupla DE; &longs;itque diui&longs;a to&shy;<lb/>ta DA &aelig;qualiter in C, in C non erit maximus ictus; quia in C non <pb xlink:href="026/01/076.jpg" pagenum="44"/>e&longs;t centrum grauitatis, vt patet; vt autem habeatur centrum impre&longs;&longs;io&shy;<lb/>nis; a&longs;&longs;umatur AN media proportionalis inter totam AD, &amp; &longs;ubdu&shy;<lb/>plum AC; cert&egrave; cum triangulum ANO &longs;it &longs;ubduplum totius ADE, <lb/>vt con&longs;tat ex Geometria, &amp; &aelig;quale trapezo ND EO; erit impetus in <lb/>vtroque &aelig;qualis; igitur in N erit centrum impre&longs;&longs;ionis, vel impetus; vt <lb/>autem habeatur centrum percu&longs;&longs;ionis; in quo &longs;cilicet maximus ictus in&shy;<lb/>fligitur, inueniatur centrum grauitatis H, ducaturque KHI parallela <lb/>DE, centrum percu&longs;&longs;ionis erit in I; quippe in I totus impeditur impetus <lb/>grauitatis vtrimque, cum &longs;it in &aelig;quilibrio; quomodo ver&ograve; inueniatur <lb/>punctum H facil&egrave; habetur ex Archimede, ductis &longs;cilicet AF, DB, qu&aelig; <lb/>diuidant bifariam &aelig;qualiter DE, EA; vel a&longs;&longs;umpta AI dupla ID, quod <lb/>demon&longs;trabimus in Mechan. <!-- KEEP S--></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 37.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Si circa centrum immobile rotetur corpus parallelipedum<emph.end type="italics"/> CA, <emph type="italics"/>diuer&longs;a e&longs;t <lb/>ratio percu&longs;&longs;ionum ab ea, qu&agrave;m &longs;upr&agrave; propo&longs;uimus<emph.end type="italics"/>; moueatur  enim circa <lb/>centrum C, fitque CA diui&longs;a bifariam in B, haud dubi&egrave; punctum A <lb/>faciet arcum AE eo tempore, qu&ograve; punctum B faciet BD &longs;ubduplum <lb/>AE; igitur punctum A dupl&ograve; veloci&ugrave;s mouetur qu&agrave;m B, vt con&longs;tat; igi&shy;<lb/>tur habet dupl&ograve; maiorem impetum; cum effectum habeat dupl&ograve; maio&shy;<lb/>rem per Ax. 13. n. </s>

<s>4. igitur cum totus motus &longs;egmenti AB &longs;it ad to&shy;<lb/>tum motum &longs;egmenti BC, vt &longs;patia acqui&longs;ita; cert&egrave; &longs;patia acqui&longs;ita <lb/>&longs;unt vt arcus; igitur &amp; trapezus BAED, continet 3/4 totius CAE, vt <lb/>con&longs;tat; &longs;unt enim &longs;ectores &longs;imilis in ratione duplicata radiorum; igi&shy;<lb/>tur totus motus &longs;egmenti BC &longs;ubquadruplus motus totius CA; igitur <lb/>&amp; impetus; vt autem habeatur centrum impre&longs;&longs;ionis, vel impetus; &longs;it &longs;e&shy;<lb/>ctor CHI, &longs;ubduplus totius CAE quod quomodo fiat, patet ex Geo&shy;<lb/>metria; accipiatur tant&ugrave;m &longs;ubdupla diagonalis quadrati lateris CA, igi&shy;<lb/>tur in puncto H e&longs;t centrum impre&longs;&longs;ionis, &longs;eu media proportionalis in&shy;<lb/>ter totam CA, &amp; &longs;ubduplam CB: vt autem habeatur percu&longs;&longs;ionis, a&longs;&shy;<lb/>&longs;umatur CY dupla YA; </s>
<s>Dico punctum Y e&longs;&longs;e centrum percu&longs;&longs;ionis; <lb/>quia perinde &longs;e habet, atque &longs;i e&longs;&longs;et trianguli cadentis ictus, vt demon&shy;<lb/>&longs;trabimus ali&agrave;s nunc tant&ugrave;m indica&longs;&longs;e &longs;ufficiat. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 1.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Hinc etiam &longs;oluetur, quod proponunt aliqui; &longs;eu poti&ugrave;s qu&aelig;runt; <lb/>in qu&agrave; &longs;cilicet parte maiorem ictum infligat en&longs;is; &longs;i enim &longs;it eiu&longs;dem <lb/>cra&longs;&longs;itiei in omnibus &longs;uis partibus, idem dicendum e&longs;t quod de cylin&shy;<lb/>dro CA; &longs;i ver&ograve; in mucronem de&longs;inat, inueniemus etiam centrum <lb/>percu&longs;&longs;ionis. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 2.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Huc etiam reuoca clauarum ictus, vel aliorum corporum, qu&aelig; ad in&shy;<lb/>&longs;tar &longs;eu conorum, &longs;eu pyramidum ver&longs;us mucronem maiora &longs;unt, vel <lb/>den&longs;iora; quippe ex iacto &longs;upr&agrave; principio i&longs;torum omnium effectuum <lb/>rationes demon&longs;trabimus. </s></p><pb xlink:href="026/01/077.jpg" pagenum="45"/><p type="main">

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 1.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Colligemus etiam quid dicendum &longs;it de malleorum ictu; &longs;it enim <lb/>malleus F &aelig;qualis malleo G (in his vna fere manubrij longitudinis ha&shy;<lb/>betur ratio) ducatur arcus NM, itemque OG; ictus mallei G e&longs;t fer&egrave; <lb/>&longs;ubduplus alterius, dum vterque malleus &longs;it &aelig;qualis; dixi fer&egrave;, quia <lb/>motus totius mallei G non e&longs;t omnin&ograve; &longs;ubduplus motus mallci F, quia <lb/>&longs;cilicet trapezus OD e&longs;t minor &longs;ubduplo alterius NE; quot&acirc; vero parte <lb/>&longs;it minor facil&egrave; pote&longs;t &longs;ciri opera Geometri&aelig;: &longs;ed h&aelig;c omnia determi&shy;<lb/>nabimus. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 74.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Si daretur potentia motrix, qu&aelig; &longs;emper agere po&longs;&longs;et, impetus po&longs;&longs;et intendi <lb/>in infinitum<emph.end type="italics"/>; pater, quia quocumque dato motu pote&longs;t dari velocior in <lb/>infinitum; igitur pote&longs;t dari impetus inten&longs;ior, &amp; inten&longs;ior in infinitum. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>H&icirc;c ob&longs;erua nouum di&longs;crimen, quod intercedit inter impetum, &amp; <lb/>alias qualitates; qu&aelig; fort&egrave; non po&longs;&longs;unt intendi in infinitum, ratio di&longs;&shy;<lb/>criminis e&longs;t, quia totus calor exten&longs;us in maiore &longs;ubiecto non pote&longs;t <lb/>produci in minore, in quo eadem cau&longs;a eumdem &longs;emper effectum pro&shy;<lb/>ducit; quia &longs;cilicet agit vniformiter difformiter; at ver&ograve; impetus exten&shy;<lb/>&longs;us in magno <expan abbr="den&longs;o&qacute;ue">den&longs;oque</expan> malleo pote&longs;t producere &aelig;qualem in maxim&acirc; <lb/>fer&egrave; pil&acirc;. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 75.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Impetus &longs;imilis, id e&longs;t, ad <expan abbr="e&atilde;dem">eandem</expan> lineam determinatus, &amp; &aelig;qualis in in&shy;<lb/>ten&longs;ione, non pote&longs;t intendere alium &longs;imilem<emph.end type="italics"/>; Probatur, quia agit tant&ugrave;m ad <lb/>extra, vt tollat impedimentum per Th. 44. &longs;ed eorum mobilium, qu&aelig; <lb/>ver&longs;us <expan abbr="e&atilde;dem">eandem</expan> partem pari velocitate mouentur, neutrum impedit al&shy;<lb/>terius motum, vt con&longs;tat; igitur impetus &longs;imilis, &amp;c. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Ob&longs;erua de impetu &longs;imili id tant&ugrave;m dici; &longs;imili inquam id e&longs;t non <lb/>mod&ograve; eiu&longs;dem inten&longs;ionis; &longs;ed etiam eiu&longs;dem line&aelig;: &longs;i enim alterum <lb/>de&longs;it, haud dubi&egrave; &longs;imilis impetus non e&longs;t; &longs;ic impetus quatuor grad. <!-- REMOVE S-->in&shy;<lb/>tendere pote&longs;t impetum duorum graduum; lic&egrave;t vterque ad <expan abbr="e&atilde;dem">eandem</expan> li&shy;<lb/>neam &longs;it determinatus; &longs;i ver&ograve; ad diuer&longs;as lineas determinentur; etiam <lb/>impetus vt duo pote&longs;t intendere impetum vt quatuor. </s>

</p><p type="main">

<s>Ob&longs;eruabis pr&aelig;terea hoc Theorema ita e&longs;&longs;e intelligendum, vt impe&shy;<lb/>tus mobilis pr&aelig;euntis nullo modo impediatur; alioquin mobile &longs;ucce&shy;<lb/>dens omnin&ograve; aliud vrgeret, vt con&longs;tat. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Corollarium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Hinc &longs;imile pote&longs;t in aliquo ca&longs;u agere in &longs;imile; vnde rect&egrave; colligo <lb/>id tant&ugrave;m dictum e&longs;&longs;e ab Ari&longs;totele de qualitatibus alteratiuis; quid <lb/>ver&ograve; accidat, cum mobile graue mobili alteri &longs;uperponitur; dicemus <lb/>infr&agrave;. </s></p><pb xlink:href="026/01/078.jpg" pagenum="46"/><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 76.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Exten&longs;io impetus respondet extentioni &longs;ui &longs;ubiecti, &longs;cilicet mobilis<emph.end type="italics"/>; cum <lb/>enim extra &longs;ubjectum e&longs;&longs;e non po&longs;&longs;it, cum &longs;it qualitas; cert&egrave; ibi e&longs;t, vbi <lb/>&longs;ubjectum e&longs;t; nam penetratur accidens cum ip&longs;o <expan abbr="&longs;ujecto">&longs;ubjecto</expan>. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Scolium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Ob&longs;eruabis qualitatem omnem ita &longs;uo &longs;ubjecto co&euml;xtendi, vt &aelig;qua&shy;<lb/>lem omnino quodlibet eius punctum, &longs;eu pars extentionem habeat ex&shy;<lb/>tentioni puncti, &longs;eu partis &longs;ui &longs;ubjecti; nec enim alliud e&longs;t, vnde po&longs;&longs;it <lb/>determinari extentio qualitatum, pr&aelig;ter ip&longs;am exten&longs;ionem &longs;ubjecti; <lb/>quod maxim&egrave; in impetu videre e&longs;t, cuius partes in mobili den&longs;o minori <lb/>extentioni &longs;ubjacent, qu&agrave;m in mobili raro; cum ex maiore ictu &longs;eu per&shy;<lb/>cu&longs;&longs;ione in mobili den&longs;o plures impetus agentis partes e&longs;&longs;e con&longs;tet; quia <lb/>&longs;cilicet &longs;unt plures partes &longs;ubiecti. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 77.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Datur impetus altero impetu perfectior &longs;ecundum entitatem<emph.end type="italics"/>; dixi &longs;ecun&shy;<lb/>dum entitatem; quia iam dictum e&longs;t &longs;upr&agrave; dari perfectiorem &longs;ecundum <lb/>inten&longs;ionem; huius Theorematis veritas mihi maxim&egrave; demon&longs;tranda <lb/>e&longs;t, ex quo t&agrave;m multa infr&agrave; deducemus; &longs;ic autem probamus; Quotie&longs;&shy;<lb/>cunque mouetur corpus, producuntur &longs;altem tot partes impetus quot <lb/>&longs;unt partes mobilis per Th. 33. Quotie&longs;cunque producuntur in mobili <lb/>tot partes impetus quot &longs;unt in mobili partes &longs;ubjecti, mouetur mobile, <lb/>mod&oacute; non impediatur; quia po&longs;ita cau&longs;a nece&longs;&longs;aria, &amp; non impedita per <lb/>Ax. 11. ponitur effectus, quod de omni cau&longs;a, &longs;ed de formali poti&longs;&longs;imum <lb/>dici debet; pr&aelig;terea datur aliquod pondus, quod data potentia &longs;ine me&shy;<lb/>chanico organo mouere non pote&longs;t, lic&egrave;t cum organo facil&egrave; moueat; h&aelig;c <lb/>hypothe&longs;is certa e&longs;t; igitur cum mouet, producit tot partes impetus quot <lb/>&longs;unt nece&longs;&longs;ari&aelig;, vt omnibus partibus mobilis di&longs;tribuantur per idem Th. <!-- REMOVE S--><lb/>33. cum ver&ograve; non mouet, non producit tot partes impetus vt con&longs;tat ex <lb/>dictis; igitur producit plures cum organo in mobili, qu&agrave;m &longs;ine organo; <lb/>igitur imperfectiores, quod demon&longs;tro: &longs;it enim vectis BF, cuius cen&shy;<lb/>trum &longs;eu fulcrum &longs;it in A, potentia in B, pondus G, quod attollitur in F; <lb/>plures partes impetus produci po&longs;&longs;unt in F, vel in E, qu&agrave;m in B, &longs;cilicet <lb/>in ip&longs;o pondere; quia pondus quod non pote&longs;t attolli in B, attollitur in <lb/>E, vel in F, vt patet ex dictis; pr&aelig;terea punctum F mouetur tardius, qu&agrave;m <lb/>B; quia motus &longs;unt vt arcus, arcus vt &longs;emidiametri, h&aelig; demum vt AF, <lb/>ad AB; igitur motus puncti F, e&longs;t tardior, vel imperfectior; igitur im&shy;<lb/>petus puncti F, e&longs;t imperfectior impetu puncti B, per Ax. 13 num.4. atqui <lb/>non e&longs;t imperfectior ratione numeri partium, igitur ratione entitatis, <lb/>qu&aelig; imperfectior e&longs;t; igitur datur impetus altero impetu imperfectior. </s>

</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Ob&longs;eruabis prim&ograve; multa h&icirc;c &longs;upponi &longs;eu de&longs;iderari, qu&aelig; pertinent <lb/>ad propagationem impetus, de quibus infr&agrave;; Secund&ograve; hoc Theorema <pb xlink:href="026/01/079.jpg" pagenum="47"/>per Axioma illud Metaph. 

probari, <emph type="italics"/>Data quacumque creatura dari potest <lb/>perfectior, vel imperfectior.<emph.end type="italics"/></s></p><p type="main">

<s>Terti&ograve;, &longs;i dato quocunque motu pote&longs;t dari tardior: igitur dato quo&shy;<lb/>cunque impetu pote&longs;t dari imperfectior. </s></p><p type="main">

<s>Quart&ograve;, &longs;i daretur punctum impetus in inten&longs;ione: non po&longs;&longs;et dari <lb/>motus tardior in infinitum &longs;ine diuer&longs;is gradibus perfectionis. </s></p><p type="main">

<s>Quint&ograve;, &longs;ine hac diuer&longs;a impetus perfectione non po&longs;&longs;et explicari <lb/>productio continua impetus, qu&aelig; &longs;it temporibus in&aelig;qualibus, neque de&shy;<lb/>&longs;tructio eiu&longs;dem impetus; nec motus in diuer&longs;is planis inclinatis, vel in&shy;<lb/>diuer&longs;is lineis citra perpendicularem, &longs;ed de his omnibus &longs;uo loco. </s></p><p type="main">

<s>Sext&ograve;, Denique ratio propo&longs;ita rem i&longs;tam euincit; cum enim in motu <lb/>vectis plures partes producantur ver&longs;us centrum, &longs;cilicet, in maiori pon&shy;<lb/>dere, quod attollitur; &amp; cum h&aelig; habeant motum tardiorem, &longs;equitur ne&shy;<lb/>ce&longs;&longs;ari&ograve; e&longs;&longs;e imperfectiores. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 78.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Dato quocumque impetu dari pote&longs;t imperfectior, &amp; imperfectior,<emph.end type="italics"/> quia da&shy;<lb/>to quocumque motu dari pote&longs;t tardior, ergo dato quocumque impetu <lb/>imperfectior. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 79.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Non pote&longs;t explicari tarditas motus &longs;ine diuer&longs;a perfectione impetus, per <lb/>pauciores &longs;cilicet eiu&longs;dem impetus partes.<emph.end type="italics"/></s><s> Prim&ograve;, quia cum retardari po&longs;&longs;it <lb/>hic motus, &amp; de&longs;trui &longs;ucce&longs;&longs;in&egrave; hic impetus; cumque in&longs;tantia motus <lb/>velocioris &longs;int breuiora; cert&egrave; initio motus, breuiori &longs;cilicet tempore <lb/>imperfectior impetus de&longs;trui tant&ugrave;m pote&longs;t; cum enim &aelig;qualis &aelig;quali&shy;<lb/>bus temporibus; cert&egrave; in&aelig;qualis in&aelig;qualibus. </s>

<s>Secund&ograve; quia vix explica&shy;<lb/>ri pore&longs;t quomodo du&aelig; form&aelig; homogene&aelig; in eodem &longs;ubiecti puncto <lb/>exi&longs;tere po&longs;&longs;int, quod etiam in commune e&longs;t calori, lumini, &amp;c. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 80.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Cum applicatur potentia centro vectis, non producitur &aelig;qualis impetus ver&shy;<lb/>&longs;us circumferentiam in omnibus partibus, &longs;ed maior ver&longs;us eandem circumfe&shy;<lb/>rentiam,<emph.end type="italics"/> quia e&longs;t maior motus. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 1.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Hinc difficili&ugrave;s attollitur pertica CA ex puncto C motu circulari, <lb/>qu&agrave;m ex puncto B motu recto; quia &longs;cilicet, cum motu recto ex puncto B <lb/>attollitur, omnes partes mouentur motu &aelig;quali; igitur impetus &aelig;qualiter <lb/>omnibus di&longs;tribuitur; igitur mod&ograve; producantur tot partes impetus, quot <lb/>&longs;unt partes in mobili; haud dubi&egrave; attolletur: at ver&ograve;, cum motu circulari <lb/>ex puncto C attollitur, omnes partes in&aelig;quali motu attolluntur; igitur <lb/>plures &longs;unt nece&longs;&longs;ari&aelig;, vt attollatur motu circulari; igitur difficili&ugrave;s iuxta <lb/>experimentum; adde quod cum applicatur potentia in C, punctum A, <lb/>maius momentum habet, de quo a&ugrave;&agrave;s. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 2.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Hinc ratio euidens illius experimenti, quo manife&longs;t&egrave; con&longs;tat perti-<pb xlink:href="026/01/080.jpg" pagenum="48"/>cam CA, ex A, facilius attolli motu recto, qu&agrave;m circulari; cum &longs;ci&shy;<lb/>licet cuiu&longs;dam qua&longs;i reflexionis opera eodem tempore vtraque extremi&shy;<lb/>tas &aelig;quali motu attollitur. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 81.<emph.end type="center"/></s></p><p type="main">

<s><arrow.to.target n="note1"/></s></p><p type="margin">

<s><margin.target id="note1"/><emph type="italics"/>Fig.<emph.end type="italics"/>7. <lb/><emph type="italics"/>Tab.<emph.end type="italics"/>1.<!-- KEEP S--></s></p><p type="main">

<s><emph type="italics"/>Si ver&ograve; applicetur potentia extra centrum vectis v. <!-- REMOVE S-->g. <!-- REMOVE S-->in<emph.end type="italics"/> F, <emph type="italics"/>po&longs;ito centro in<emph.end type="italics"/><lb/>A, <emph type="italics"/>producitur impetus minor ab<emph.end type="italics"/> F, <emph type="italics"/>ver&longs;us<emph.end type="italics"/> A; <emph type="italics"/>ab ver&ograve; ver&longs;us<emph.end type="italics"/> E, <emph type="italics"/>producitur <lb/>eiu&longs;dem perfectionis proportionaliter, cuius e&longs;t ab<emph.end type="italics"/> F, <emph type="italics"/>ver&longs;us<emph.end type="italics"/> A; denique ab E, <lb/>ver&longs;us B, producitur quidem vnum punctum, vel vnus gradus impetus <lb/>eiu&longs;dem perfectionis cum eo, qui productus e&longs;t in F, &amp; in E (&longs;upponi&shy;<lb/>tur enim ex. gr. <!-- REMOVE S-->vnus tant&ugrave;m gradus in F, &amp; in E, productus) at ver&ograve; <lb/>producuntur alij imperfectiones. </s>



<s>v.g. <!-- REMOVE S-->in D, pr&aelig;ter &aelig;qu&egrave; perfectum pro&shy;<lb/>ducuntur 3. alij ad&aelig;quantes perfectionem prioris; in C ver&ograve;, pr&aelig;ter 4. <lb/>&longs;imiles ijs, qui &longs;unt in D, producuntur 5. alij ad&aelig;quantes prioris perfe&shy;<lb/>ctionem in B7; atque ita deinceps per numeros impares, &amp; quadrata, <lb/>nullus tamen producitur perfectioris entitatis. </s>

</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 82.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Determinatur h&aelig;c diuer&longs;a perfectio impetus &agrave; diuer&longs;a perfectione motus, <lb/>quatenus fit tali modo<emph.end type="italics"/>; qu&aelig; non pote&longs;t explicari per impetum remi&longs;&longs;io&shy;<lb/>rem, vel inten&longs;iorem; nam cum &longs;it tant&ugrave;m impetus in&longs;titutus propter <lb/>motum; cert&egrave; ille tant&ugrave;m impetus produci pote&longs;t, ex quo pote&longs;t &longs;equi <lb/>motus; igitur &longs;i tali tant&ugrave;m motu data pars mobilis moueri pote&longs;t; haud <lb/>dubi&egrave; talis tant&ugrave;m impetus, ex quo &longs;equitur talis motus, in ea produ&shy;<lb/>cetur, &amp; tali modo. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 83.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Perfectio impetus non petitur tant&ugrave;m &agrave; perfectione motus &longs;i con&longs;ideretur <lb/>&longs;eor&longs;im entitas eiu&longs;dem impetus; &longs;ed debet comparari tota collectio omniu&mtail; <lb/>partium impetus, qu&aelig; in&longs;unt dat&aelig; parti &longs;ubiecti, cum tota collectione partium <lb/>qu&aelig; alteri porti mobilis in&longs;unt<emph.end type="italics"/>; quippe plures partes impetus po&longs;&longs;unt ha&shy;<lb/>bere eum motum, vel potius eam motus perfectionem, quam pauciores <lb/>haberent; igitur perfectio illarum e&longs;t ab ip&longs;o motu, quatenus cum ip&longs;o <lb/>partium numero comparatur. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 84.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Impetus perfectus producere pote&longs;t imperfectum<emph.end type="italics"/>; patet in vecte; nam po&shy;<lb/>tentia, &longs;en pondus extremitati appen&longs;um producit in &longs;e impetum, &agrave; quo <lb/>deinde impetus in toto vecte producitur per Th.42. &longs;ed impetus pon&shy;<lb/>deris appen&longs;i e&longs;t eiu&longs;dem perfectionis cum impetu producto in ip&longs;a ve&shy;<lb/>ctis extremitate, ex qua pendet; cum &longs;it vtriu&longs;que &aelig;qualis motus; &longs;ed <lb/>ver&longs;us centrum eiu&longs;dem vectis producitur impetus imperfectior per <lb/>Th.82. igitur imperfectus &agrave; perfecto producitur. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 85.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Impetus perfectus nunquam producitur ab imperfecto, per Ax.<emph.end type="italics"/> 3. <emph type="italics"/>num.<emph.end type="italics"/> 2. <lb/>adde quod nunquam effectus perfectio &longs;uperat perfectionem cau&longs;&aelig;; dixi <lb/>perfectum ab imperfecto; &longs;cilicet &longs;i con&longs;ideretur perfectio ratione en-<pb xlink:href="026/01/081.jpg" pagenum="49"/>titatis; cum reuer&acirc;, vt dictum e&longs;t &longs;upr&agrave;, remi&longs;&longs;us producat inten&longs;um, <lb/>quod in vecte clari&longs;&longs;imum e&longs;t; quippe momentum applicatum in F, quod <lb/>tardi&ugrave;s mouetur deor&longs;um, qu&agrave;m B, &longs;ur&longs;um, vt patet, habet impetum re&shy;<lb/>mi&longs;&longs;iorem, qui tamen producit in B, inten&longs;iorem: Pro quo, ob&longs;eruabis <lb/>impetum imperfectum cum alio perfecto actione communi agentem <lb/>po&longs;&longs;e concurrere ad producendum perfectum, vt patet; non tamen in <lb/>ratione cau&longs;&aelig; totalis: &longs;imiliter plures imperfecti &longs;imul concurrentes <lb/>po&longs;&longs;unt producere perfectum; quia plures imperfecti conjunctim ad&aelig;&shy;<lb/>quant perfectionem alterius perfectioris &longs;inguli &longs;eor&longs;im. </s></p><p type="main">

<s>Ob&longs;eruabis &longs;ecund&ograve; pr&aelig;clarum natur&aelig; in&longs;titutum, quo factum e&longs;t; <lb/>vt cum vires hominum maiora pondera leuare non po&longs;&longs;int, &longs;i &longs;eor&longs;un <lb/>con&longs;iderentur; cum organis tamen mechanicis conjunct&aelig; nullum pon&shy;<lb/>dus quantumuis immane leuare non po&longs;&longs;int; quod cert&egrave; nullo modo ac&shy;<lb/>cideret, ni&longs;i plures partes impetus producerent neque plures producere <lb/>po&longs;&longs;ent, ni&longs;i minoris perfectionis e&longs;&longs;ent; quia facili&ugrave;s producitur effe&shy;<lb/>ctus imperfectus, quam perfectus per Ax. 13.num.4. </s></p><p type="main">

<s>Terti&ograve; hinc optim&egrave; &agrave; natura proui&longs;um e&longs;t, vt motus tardior in infi&shy;<lb/>nitum e&longs;&longs;e po&longs;&longs;it; quod reuer&acirc; fieri non po&longs;&longs;et, ni&longs;i dari po&longs;&longs;et impetus <lb/>alio imperfectior. </s></p><p type="main">

<s>Quart&ograve;, hinc quoque ben&egrave; explicatur diuer&longs;itas impetus, qu&aelig; oritur <lb/>tum &agrave; diuer&longs;o medio, t&ugrave;m &agrave; plano inclinato, t&ugrave;m ab aliis impedimentis, <lb/>t&ugrave;m &agrave; diuer&longs;o ni&longs;u eiu&longs;dem potenti&aelig;, t&ugrave;m maxim&egrave; &agrave; diuer&longs;o applicatio&shy;<lb/>nis modo; de quibus ali&agrave;s. </s></p><p type="main">

<s>Quint&ograve;, &longs;i potentia applicata mobili immediat&egrave; illud moueat motu <lb/>recto, vel in &longs;ingulis punctis mobilis producitur vnum punctum impe&shy;<lb/>tus, vel plura; &longs;i primum, erit primus tant&ugrave;m gradus maxim&aelig; perfectio&shy;<lb/>nis; ita vt perfectiorem producere non po&longs;&longs;it, ad quem e&longs;t determinata <lb/>potentia; imperfectiorem tamen impetu innato, de quo infr&agrave;; &longs;i ver&ograve; <lb/>&longs;ecundum, producet in &longs;ingulis partibus <expan abbr="e&utilde;dem">eundem</expan> gradum perfecti&longs;&longs;i&shy;<lb/>mum cum aliis pluribus, vel paucioribus heterogeneis, &amp; imperfectio&shy;<lb/>ribus. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 86.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Potentia naturalis grauium producit tant&ugrave;m vno in&longs;tanti ad intra vnicum <lb/>punctum impetus in quolibet puncto &longs;ubiecti; &longs;i tamen impetum producit, quod <lb/>definiam lib.<emph.end type="italics"/> 20. <emph type="italics"/>&amp; &longs;i dentur puncta &longs;ubiecti, quod ad pr&aelig;&longs;ens in&longs;titutum non <lb/>pertinet<emph.end type="italics"/>; Probatur, quia fru&longs;tr&agrave; e&longs;&longs;ent plura puncta impetus; nec enim <lb/>&longs;unt multiplicand&aelig; form&aelig; &longs;ine nece&longs;&longs;itate, ratione &amp;c. </s>

<s>per Ax. 7. &amp; 3. <lb/>n. </s>

<s>1. Pr&aelig;terea non e&longs;t, cur potius produceret 2. qu&agrave;m 3. 4. &amp;c. </s>

<s>atqui <lb/>quod vnum e&longs;t, determinatum e&longs;t per Ax. 5. <!-- KEEP S--></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 87.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Potentia motrix animantium etiam vno in&longs;tanti plura puncta, &longs;en partes <lb/>impetus in eadem parte &longs;ubiecti producere potest<emph.end type="italics"/>; Probatur in proiectis, <lb/>quorum impetus aliquando pl&ugrave;s, aliquando min&ugrave;s durat lic&egrave;t &longs;en&longs;im <lb/>&longs;ingulis in&longs;tantibus aliquid illius de&longs;truatur; determinatur autem <pb xlink:href="026/01/082.jpg" pagenum="50"/>numerus punctorum, &longs;eu partium ab ea potentia, cui &longs;ube&longs;t potentia <lb/>motrix; quia mod&ograve; maior e&longs;t ni&longs;us, mod&ograve; minor. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 88.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Eadem potentia in&aelig;qualibus temporibus impetum in&aelig;qualem in perfectio&shy;<lb/>ne producit<emph.end type="italics"/>; accipiatur enim totum illud tempus, quo vnicum tant&ugrave;m <lb/>punctum impetus producit (vocetur in&longs;tans) de quo in Th. 86; cert&egrave; <lb/>&longs;i in minori tempore agat, min&ugrave;s aget, per Ax. 13. num. </s>

<s>4. &longs;ed non <lb/>pote&longs;t min&ugrave;s agere ratione numeri, vt patet; igitur ratione perfectio&shy;<lb/>nis. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Ob&longs;eruabis &longs;ine hoc Theoremate explicari non po&longs;&longs;e accelerationem <lb/>motus naturalis, vel augmentum impetus, vt videbimus. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 89.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Impetus violenti, qui &longs;en&longs;im de&longs;truitur in proiectis, po&longs;itis ij&longs;dem circum&shy;<lb/>&longs;tantiis medij, &amp; re&longs;i&longs;tenti&aelig;, minori tempore min&ugrave;s de&longs;truitur; plus ver&ograve; ma&shy;<lb/>jori:<emph.end type="italics"/> Quia h&aelig;c de&longs;tructio habet cau&longs;am; nam quidquid de&longs;truitur, ad <lb/>exigentiam alicuius de&longs;truitur, per Ax. 14. num. </s>

<s>2. igitur minori <lb/>tempore min&ugrave;s de&longs;truitur per Ax. <!-- REMOVE S-->13. 4. alioquin totus &longs;imul debe&shy;<lb/>ret de&longs;trui. </s>

</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Ob&longs;eruabis etiam &longs;ine hoc Theoremate non po&longs;&longs;e explicari de&longs;tru&shy;<lb/>ctionem impetus violenti, vt videbimus infr&agrave;. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 1.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Hinc, qu&ograve; potentia diuti&ugrave;s manet applicata (put&agrave; malleo) percu&longs;&longs;io ma&shy;<lb/>ior e&longs;t. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 2.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Hinc, qu&ograve; impedimentum diuti&ugrave;s manet applicatum, illa de&longs;tructio <lb/>e&longs;t maior. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 3.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Hinc pr&aelig;clara eruitur ratio, cur maior lapis, qu&agrave;m minor impactus <lb/>maiorem ictum infligat; lic&egrave;t tot partes impetus eodem in&longs;tanti produ&shy;<lb/>cantur in vno, quot in alio: quia &longs;cilicet diuti&ugrave;s manet applicatus po&shy;<lb/>tenti&aelig;; &longs;ed hanc rationem explicabimus fus&egrave; lib. 

10. cum de percu&longs;&shy;<lb/>&longs;ione. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 90.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Impetus propagatur nece&longs;&longs;ari&ograve; per totum corpus impul&longs;um, &longs;eu proiectum.<emph.end type="italics"/></s></p><p type="main">

<s>Probatur; quia cum omnes eius partes moueantur, nec vlla &longs;ine im&shy;<lb/>petu moueri po&longs;&longs;it per Th. 18. &amp; 33. cum etiam potentia motrix non <lb/>&longs;it omnibus immediat&egrave; applicata, vt con&longs;tat; cert&egrave; &longs;ine propagatione, <lb/>vel diffu&longs;ione non pote&longs;t explicari productio huius motus. </s></p><pb xlink:href="026/01/083.jpg" pagenum="51"/><p type="main">

<s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Ob&longs;eruabis propagationem impetus, vel alterius qualitatis e&longs;&longs;e tan&shy;<lb/>t&ugrave;m continuatam eiu&longs;dem productionem, qu&aelig; incipit ab ea parte, cui <lb/>potentia e&longs;t immediat&egrave; applicata, &amp; propagatur, &longs;eu diffunditur per <lb/>omnes alias donec ad vltimam perueniat eo modo, quo iam definio. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 92.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Illa progatio non fit per motum localem, ita vt pars impetus producta in <lb/>prima parte &longs;ubiecti tran&longs;eat ad &longs;ecundam,<emph.end type="italics"/> patet; quia cum impetus &longs;it ac&shy;<lb/>cidens per Th. 8. de &longs;ubiecto in &longs;ubiectum tran&longs;ire non pote&longs;t per deff. </s>

<s><lb/>accidentis; de qua in Metaphy&longs;ic&acirc;; nec e&longs;t quod aliqui dicant &longs;e <expan abbr="n&otilde;">non</expan> po&longs;&longs;e <lb/>concipere, quomodo id fiat &longs;ine motu locali; cum ip&longs;is etiam oculis <lb/>qua&longs;i cernatur; cum enim percutis corpus oblongum AE, &amp; cadit ictus <lb/>in extremitatem A, corpus ip&longs;um totum &longs;imul moues; igitur pars impe&shy;<lb/>tus, qu&aelig; recipitur in A, non migrat in E, &longs;ed h&aelig;c producitur in A, &amp; <lb/>alia in B, alia in C, atque ita deinceps. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Ob&longs;eruabis ex hac propagatione impetus per analogiam rect&egrave; om&shy;<lb/>nin&ograve; explicari propagationem luminis, &amp; aliarum qualitatum, de qui&shy;<lb/>bus &longs;uo loco. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 92.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>In propagatione impetus prima pars<emph.end type="italics"/> A v. <!-- REMOVE S-->g. <emph type="italics"/>non producit partem<emph.end type="italics"/> B, <emph type="italics"/>&amp; <lb/>h&aelig;c<emph.end type="italics"/> C; <emph type="italics"/>h&aelig;c ver&ograve;<emph.end type="italics"/> D, <emph type="italics"/>atque ita deinceps<emph.end type="italics"/>; Probatur. <!-- KEEP S--></s>



<s>Prim&ograve;, quia &longs;i hoc e&longs;&longs;et, <lb/>omne corpus po&longs;&longs;et moueri &agrave; qualibet potentia; nam mod&ograve; po&longs;&longs;et pro&shy;<lb/>duci vnum punctum impetus, hoc etiam aliud produceret, &amp; hoc aliud, <lb/>atque ita deinceps. </s>

<s>Secund&ograve;, Minimum granum &longs;uperpo&longs;itum rupi, to&shy;<lb/>tam ip&longs;am rupem mouere po&longs;&longs;et. </s>

<s>Tertio, Quia vel in omnibus, vel in <lb/>nulla parte impetus producitur per Th.33. Quart&ograve;, quia impetus mobi&shy;<lb/>lis projecti intenderetur; nam impetus vnius partis impetum alterius <lb/>intenderet. </s>

<s>Quint&ograve;, quia impetus partis B, t&agrave;m ageret in A, trahendo, <lb/>qu&agrave;m in C pellendo; cum impetus vtroque modo propagetur. </s>

<s>Sext&ograve;, &longs;i <lb/>applicaretur potentia in C, non video, cur impetus partis C, ageret po&shy;<lb/>tius vers&ugrave;s E, qu&agrave;m vers&ugrave;s A? alioquin eadem pars impetus plures pro&shy;<lb/>ducere po&longs;&longs;et; igitur impetus potenti&aelig; motricis &longs;ufficiens erit cau&longs;a ad <lb/>producendum totum alium. </s>

<s>Septim&ograve;, tractionis impetus explicari non <lb/>pote&longs;t, &longs;i impetus vnius partis producat in alia impetum; alioquin dare&shy;<lb/>tur mutua actio infinities repetita, vt con&longs;ideranti patebit. </s>

<s>Octau&ograve;, &longs;i <lb/>impetus vnius partis producit in alia; &longs;int duo globi contigui; igitur il&shy;<lb/>le, qui impellit alium, reflecti po&longs;&longs;et, quod nunquam accidit quando <lb/>&longs;unt contigui. </s></p><p type="main">

<s>Ob&longs;eruabis illud quidem verum e&longs;&longs;e in motu recto, &longs;ecus in circulari; <lb/>nam cum cylindrus circa alteram extremitatem vibratus deor&longs;um cadit; <lb/>partes, qu&aelig; propi&ugrave;s ad extremitatem immobilem accedunt iuuant mo&shy;<lb/>tum aliarum, qu&aelig; longi&ugrave;s ab eadem recedunt. </s></p><pb xlink:href="026/01/084.jpg" pagenum="52"/><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 93.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Impetus propagatur eodem in&longs;tanti, id e&longs;t, &longs;ine temporis &longs;ucce&longs;&longs;ione.<emph.end type="italics"/></s><s> Proba&shy;<lb/>tur; &longs;it enim applicata potentia in A, dico &longs;imul produci impetum in <lb/>BCDE; quia &longs;i primo in&longs;tanti produceretur in A, &amp; &longs;ecundo in B, vel <lb/>A moueretur ante B, vel impetus in A e&longs;&longs;et fru&longs;tr&agrave;; vtrumque e&longs;t ab&longs;ur&shy;<lb/>dum; nam totum AE, &longs;imul mouetur. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 94.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Tribus tant&ugrave;m modis propagari pote&longs;t impetus ratione inten&longs;ionis.<emph.end type="italics"/></s><s> Prim&ograve; <lb/>&longs;i &aelig;qualiter omnibus partibus &longs;ubjecti di&longs;tribuatur; id e&longs;t vniformiter. </s>

<s><lb/>Secund&ograve;, &longs;i pl&ugrave;s partibus propioribus, &amp; min&ugrave;s remotioribus. </s>

<s>Terti&ograve;, &egrave; <lb/>contra, &longs;i pl&ugrave;s remotioribus, &amp; min&ugrave;s propioribus; tribus etiam ratione <lb/>perfectionis eo modo, quo diximus de inten&longs;ione; at ver&ograve; nouem mo&shy;<lb/>dis propagari pote&longs;t ratione vtriu&longs;que; patet ex regula combinationum; <lb/>&longs;i enim 3. ducantur in 3. habebis 9. Iam &longs;upere&longs;t, vt videamus, an reue&shy;<lb/>r&agrave; omnibus i&longs;tis modis impetus re ip&longs;a propagetur; quod lic&egrave;t difficile <lb/>&longs;it, &amp; vix hactenus explicatum: Audeo tamen polliceri meum &longs;uper hac <lb/>re conatum non pror&longs;us inutilem fore. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 95.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Impetus propagatur vniformiter in mobili, cuius omnes partes mouentur <lb/>&aelig;quali motu<emph.end type="italics"/>; probatur, quia impetus non cogno&longs;citur ni&longs;i per motum; <lb/>igitur vbi e&longs;t &aelig;qualis motus, debet e&longs;&longs;e &aelig;qualis impetus in omnibus par&shy;<lb/>tibus, id e&longs;t &aelig;qualis graduum heterogeneorum collectio, in quo non <lb/>e&longs;t difficultas. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Ob&longs;eruabis illud mobile moueri motu &aelig;quali &longs;ecundum omnes &longs;ui <lb/>partes, quod mouetur motu recto; quippe fieri non pote&longs;t, quin omnes <lb/>partes, qu&aelig; mouentur motu recto &longs;implici, motu etiam &aelig;quali mouean&shy;<lb/>tur. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 96.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Cum duo corpora &longs;e&longs;e mutu&ograve; tangunt, impetus in vtroque propagatur<emph.end type="italics"/> &longs;int <lb/>v. <!-- REMOVE S-->g. <!-- REMOVE S-->globi A &amp; B, &aelig;quales &longs;ibi inuicem contigui in C, &longs;it applicata po&shy;<lb/>tentia in D, non mod&ograve; producet impetum in globo A, &longs;ed etiam in B: <lb/>probatur prim&ograve;, quia &longs;e habent per modum vnius, vt patet ex re&longs;i&longs;ten&shy;<lb/>tia, nec enim A moueri pote&longs;t &longs;ine B per lineam DE, quod cert&egrave; cla&shy;<lb/>ri&longs;&longs;imum e&longs;t; probatur &longs;ecund&ograve; quia &longs;i A produceret impetum in B, duo <lb/>globi, vel 3. vel 5. vel infiniti tant&ugrave;m re&longs;i&longs;terent, quant&ugrave;m vnicus glo&shy;<lb/>bus, quod fal&longs;um &amp; ab&longs;urdum e&longs;t. </s>





<s>Terti&ograve;, Ratio &agrave; priori e&longs;t; quia ideo <lb/>producitur, &amp; propagatur impetus in toto A; quia vna pars non pote&longs;t <lb/>moueri &longs;ine alia per Th. 33. &longs;ed non pote&longs;t A moueri ni&longs;i moueatur  B; <lb/>igitur in vtroque &longs;imul, &amp; &aelig;qualiter propagatur impetus. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 1.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Hinc ratio manife&longs;ta cur maior &longs;it re&longs;i&longs;tentia duorum qu&agrave;m vnius. </s></p><pb xlink:href="026/01/085.jpg" pagenum="53"/><p type="main">

<s><emph type="center"/><emph type="italics"/>Corollarium.<emph.end type="italics"/> 2.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Hinc eadem vis requiritur ad &longs;u&longs;tinenda duo pondera; &longs;iue vtrum&shy;<lb/>que &longs;eor&longs;im humeris incubet, &longs;iue alterum alteri &longs;uperponatur. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 3.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Hinc percu&longs;&longs;io vel ictus globi B, cui alter A &agrave; tergo immediat&egrave; in&shy;<lb/>&longs;i&longs;tit maior e&longs;t. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 4.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Hinc pondus alteri &longs;uperpo&longs;itum actione communi cum alio graui&shy;<lb/>tat in &longs;uppo&longs;itam manum. </s>

<s>v. <!-- REMOVE S-->g. <!-- REMOVE S--><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 5.<emph.end type="center"/><!-- KEEP S--></s>

</p><p type="main">

<s>Hinc potentia applicata in D, min&ugrave;s impetus &longs;ingulis imprimit. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 6.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Hinc demum lic&egrave;t impetus ratione inten&longs;ionis &longs;it &aelig;qualis in vtroque <lb/>globo; attamen, &longs;i accipiatur numerus partium vtriu&longs;que impetus, im&shy;<lb/>petus &longs;unt vt globi v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;i B e&longs;t &aelig;qualis A impetus productus in B e&longs;t <lb/>&aelig;qualis producto in A, &longs;i B &longs;it &longs;ubduplus, vel &longs;ubtriplus, impetus e&longs;t <lb/>&longs;ubtriplus, vel &longs;ubduplus; quorum omnium rationes patent ex Th.96. </s>



</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 7.<emph.end type="center"/></s></p><p type="main">

<s>Hinc etiam colligi pote&longs;t manife&longs;tum di&longs;crimen, quod intercedit inter <lb/>propagationem impetus, &amp; aliarum qualitatum, qu&aelig; (vt vulg&ograve; dicitur) <lb/>vniformiter difformiter propagantur, id e&longs;t, &aelig;qualiter in &aelig;quali <lb/>di&longs;tantia, &amp; in&aelig;qualiter in&aelig;quali. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 8.<emph.end type="center"/></s></p><p type="main">

<s>Hinc demum colligi pote&longs;t non mod&ograve; impetum produci in globo B <lb/>v. <!-- REMOVE S-->g. <!-- REMOVE S-->ver&ugrave;m etiam in a&euml;re ambiente, cui &longs;cilicet globus contiguus e&longs;t; <lb/>qui reuera a&euml;r facil&egrave; amouetur; t&ugrave;m quia propter raritatem pauci&longs;&longs;im&aelig; <lb/>partes mouend&aelig; &longs;unt; t&ugrave;m quia facil&egrave; diuiduntur, de quibus alias; t&ugrave;m <lb/>quia, ne detur va&ccedil;uum, &longs;patium &agrave; tergo relictum occupare debet, quod <lb/>reuer&agrave; pr&aelig;&longs;tat breui peracto circuitu, vt videre e&longs;t in aqua; nec enim <lb/>totus a&euml;r agitari debet; quis enim id con&longs;equi po&longs;&longs;et; tum denique, quia <lb/>a&euml;r non grauitat in a&euml;re, igitur cum non re&longs;i&longs;tat vlla grauitatio, facil&egrave; <lb/>moueri pote&longs;t. </s>



</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 97.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Cum applicatur potentia centro motus circularis, ita propagatur impetus, vt <lb/>plures partes impetus continu&ograve; producantur ver&longs;us <expan abbr="circumferenti&atilde;">circumferentiam</expan><emph.end type="italics"/>; &longs;it enim <lb/>cylindrus CA, fig. </s>

<s>Th. 73. &longs;it centrum motus C; haud dubi&egrave; plures <lb/>partes impetus producuntur in B, qu&agrave;m in C, &amp; plures in A, quam in B; <lb/>quia, cum pars B moueatur veloci&ugrave;s, qu&agrave;m C, &amp; A qu&agrave;m B; cert&egrave;, vbi e&longs;t <lb/>maior motus, vel effectus, ibi debet e&longs;&longs;e maior impetus, vel cau&longs;a per <lb/>Ax. 13. n. </s>

<s>4. quod autem &longs;it maior motus, con&longs;tat ex maioribus &longs;patiis, <lb/>vel arcubus &aelig;quali tempore confectis; quod ver&ograve; &longs;it impetus inten&longs;ior <pb xlink:href="026/01/086.jpg" pagenum="54"/>vers&ugrave;s circumferentiam, non perfectior, patet per Th. 8. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 98.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Inten&longs;io impetus propagati iuxta hunc modum &longs;e habet, vt distantia &agrave; cen&shy;<lb/>tro motus<emph.end type="italics"/>; &longs;int enim punctum B, &amp; punctum A: ita &longs;e habet inten&longs;io <lb/>impetus puncti A ad inten&longs;ionem impetus puncti B, vt di&longs;tantia AC <lb/>ad BC. Probatur, quia cum impetus &longs;int vt motus, motus vt &longs;patia, &longs;patia <lb/>ver&ograve; &longs;int arcus AE. BD; arcus &longs;unt, vt &longs;emidiametri AC, BC; igitur vt <lb/>di&longs;tanti&aelig; qu&ograve;d erat demon&longs;trandum. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 1.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Hinc &longs;i di&longs;tantia CA e&longs;t dupla di&longs;tanti&aelig; CB, impetus in A e&longs;t du&shy;<lb/>plus impetus in B: at ver&ograve; impetus &longs;egmenti e&longs;t ad impetum alterius, <lb/>vt diximus in Th. 73. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 2.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Hinc h&aelig;c propagatio fit iuxta progre&longs;&longs;ionem arithmeticam id e&longs;t, &longs;i <lb/>in prim&acirc; parte ver&longs;us centrum producitur impetus vt 1. in &longs;ecunda pro&shy;<lb/>ducitur vt duo, in terti&acirc; vt tria, atque ita deinceps; quia proportio <lb/>arithmetica e&longs;t laterum, &longs;eu linearum. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 3.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Hinc h&aelig;c propagatio e&longs;t omnin&ograve; inuer&longs;a illius, qu&aelig; aliis qualitatibus <lb/>competit, vt patet. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 4.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Hinc etiam manife&longs;ta ratio &longs;equitur illius experimenti, quod propo&shy;<lb/>&longs;uimus corol. </s>

<s>2. Th. 80. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 5.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Hinc &longs;i tant&ugrave;m habeatur ratio impetus, facil&egrave; pote&longs;t determinari in <lb/>qua proportione cylindrus facili&ugrave;s moueatur motu recto, qu&agrave;m motu <lb/>circulari; po&longs;ito &longs;cilicet centro motus in altera extremitate, cui applica&shy;<lb/>tur potentia; quippe impetus propagatus in motu circulari e&longs;t &longs;umma <lb/>terminorum; propagatus ver&ograve; in motu recto e&longs;t vltimus terminorum, <lb/>v.g. <!-- REMOVE S-->&longs;int &longs;ex puncta &longs;ubiecti; in quolibet producatur impetus vt vnum; <lb/>haud dubi&egrave; erit motus rectus; vt ver&ograve; &longs;it motus circularis in primo <lb/>puncto; producatur vt 1. in &longs;ecundo vt 2. in tertio, vt 3. atque ita dein&shy;<lb/>ceps; &longs;umma erit 21. cum tamen in motu recto e&longs;&longs;ent tant&ugrave;m 6. igitur <lb/>vt &longs;e habent 21. ad 6. ita &longs;e habet facilitas motus recti ad facilitatem <lb/>motus circularis. </s>

</p><p type="main">

<s>Dixi, &longs;i tant&ugrave;m habeatur ratio impetus; quia &longs;i addatur ratio graui&shy;<lb/>tationis, &longs;eu momenti; haud dubi&egrave; maior erit adhuc difficultas, de <lb/>quo infr&agrave; in Schol. <!-- REMOVE S--><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 6.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Hinc qu&ograve; longior e&longs;t cylindrus, v. <!-- REMOVE S-->g. <!-- REMOVE S-->cre&longs;cit proportio maioris illius <lb/>facilitatis, vt patet inductione; nam &longs;i &longs;int tant&ugrave;m 2. puncta, proportio <lb/>erit 3. ad 2.; &longs;it tria 6. ad 3.; &longs;i 4. 10. ad 4. &longs;i 5. 15. ad 5.; &longs;i 6. 21. ad 6. <pb xlink:href="026/01/087.jpg" pagenum="55"/>&longs;i 7. 28. ad 7; &longs;i 8. 36. ad 8; &longs;i 9. 45. ad 9; atque ita deinceps; ex quibus prim&ograve; <lb/>vides cre&longs;cere &longs;emper proportionem. </s>





<s>Secund&ograve; inter duplam, &amp; triplam <lb/>rationem, &longs;cilicet 6. ad 3. &amp; 15. ad 5. intercedere 2 1/2; inter triplam &amp; <lb/>quadruplam intercedere 3. 1/2; inter quadruplam &amp; quintuplam inter&shy;<lb/>cedere 4 1/2; atque ita deinceps. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 7.<emph.end type="center"/></s></p><p type="main">

<s>Colligo denique po&longs;&longs;e in motu recto cum maiore ni&longs;u produci inten&shy;<lb/>&longs;iorem impetum in data ratione; &longs;it enim cylindrus AB, qui moueatur <lb/>circa centrum A, percurr&aacute;tque B, arcum BD; qui accipiatur vt recta, <lb/>qu&aelig; &agrave; minimis arcubus &longs;en&longs;u di&longs;tingui non pote&longs;t; haud dubi&egrave; &longs;i eo <lb/>tempore, vel &aelig;quali, quo AB tran&longs;it in AD; eadem AB, vel &aelig;qualis <lb/>motu recto tran&longs;eat in FD, Dico impetum huius motus e&longs;&longs;e dupl&ograve; in&shy;<lb/>ten&longs;iorem impetu illius; quia impetus &longs;unt vt motus; motus ver&ograve; vt <lb/>&longs;patia, qu&aelig; percurruntur &aelig;qualibus temporibus; &longs;ed &longs;patium rectanguli <lb/>AD, e&longs;t duplum trianguli ADB; igitur &amp; motus; igitur &amp; impetus; &longs;i <lb/>ver&ograve; AB tran&longs;eat in EL, ita vt AF, &longs;it dupla AE; impetus erunt <lb/>&aelig;quales; quia rectangulum AC, e&longs;t &aelig;quale triangulo ABD. </s></p><p type="main">

<s>Dixi arcum BD, accipi vt lineam rectam; Si enim accipiatur vt ar&shy;<lb/>cus; haud dubi&egrave; motus cylindri AB, dum transfertur in FD, e&longs;t ad mo&shy;<lb/>tum eiu&longs;dem AB, dum transfertur in AD, vt rectangulum AD, ad &longs;e&shy;<lb/>ctorem, cuius arcus &longs;it &aelig;qualis rect&aelig; BD, &amp; radius ip&longs;i AB. <!-- KEEP S--></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Ob&longs;eruabis prim&ograve;, id quod &longs;upr&agrave; dictum e&longs;t ita e&longs;&longs;e intelligendum, <lb/>vt momentum grauitationis nullo modo con&longs;ideretur, &amp; pr&aelig;dictus <lb/>cylindrus cen&longs;eatur poti&ugrave;s moueri in plano horizontali, &agrave; quo &longs;u&longs;tinea&shy;<lb/>tur, qu&agrave;m in circulo verticali, in quo libera &longs;it eius libratio, &longs;eu gra&shy;<lb/>uitatio. </s></p><p type="main">

<s>Secund&ograve;, non po&longs;&longs;e &longs;u&longs;tineri cylindrum horizonti parallelum, ni&longs;i <lb/>aliqua eius portio &longs;eu manu, &longs;eu forcipe, vel alio quouis modo accipia&shy;<lb/>tur, v.g. <!-- REMOVE S-->&longs;it cylindrus AG horizonti parallelus; vt in hoc &longs;itu reti&shy;<lb/>neatur, debet aliqua eius portio put&agrave; AB, manu teneri, alioqui ne &agrave; po&shy;<lb/>tenti&acirc; quidem infinita &longs;u&longs;tineri po&longs;&longs;et. </s>

</p><p type="main">

<s>Terti&ograve;, &longs;i &longs;upponatur fulcitus in B; vt retineatur in &aelig;quilibrio, debet <lb/>addi momentum in A; &longs;eu debet retineri ab ip&longs;a potenti&acirc; applicata <lb/>in A. <!-- KEEP S--></s></p><p type="main">

<s>Quart&ograve;, pondus in G &longs;e habet ad idem pondus in A, &longs;tatuto centro in <lb/>B, vt &longs;egmentum GB, ad BA, id e&longs;t, vt 5. ad 1. <!-- KEEP S--></s></p><p type="main">

<s>Quint&ograve;, &longs;i proprio pondere frangeretur BG, haud dubi&egrave; in B frange&shy;<lb/>retur; e&longs;t autem momentum ponderis BG, vt &longs;ubduplum eiu&longs;dem BG <lb/>po&longs;itum in G, vt demon&longs;trat Galileus prop.1.de re&longs;i&longs;tentia corp.&longs;it enim <lb/>BG, duarum librarum, &longs;itque BG, diui&longs;a bifariam in H; haud dubi&egrave; <lb/>pondus in H, facit momentum &longs;ubduplum eiu&longs;dem in G, vt patet; &longs;unt <lb/>enim vt di&longs;tanti&aelig;; igitur cum &longs;egmentum HG tant&ugrave;m addat momenti <lb/>&longs;upra H, quant&ugrave;m detrahit HB; cert&egrave; momentum totius ponderis BG, <pb xlink:href="026/01/088.jpg" pagenum="56"/>e&longs;t tant&ugrave;m &longs;ubduplum eiu&longs;dem po&longs;iti in G; itaque &longs;it BG, 10. librarum, <lb/>&aelig;quiualet 5. libris &longs;tatutis in G, &amp; AB, vni libr&aelig; po&longs;it&aelig; in A; &longs;ed h&aelig;c <lb/>libra in A, habet tant&ugrave;m &longs;ubquintuplum momentum eiu&longs;dem in G, igi&shy;<lb/>tur 5. libr&aelig; in A, &aelig;quiualent vni in G; igitur vt &longs;tatuatur &aelig;quilibrium, <lb/>debent e&longs;&longs;e 24. libr&aelig; in A, &longs;eu vires &aelig;quiualentes; quibus adde pondus <lb/>ab&longs;olutum 12. librarum; erunt 36. igitur re&longs;i&longs;tentia ad motum circula&shy;<lb/>rem verticalem ex triplici capite oritur. </s>

<s>Prim&ograve; ex ip&longs;o pondere ab&longs;olut&egrave; <lb/>&longs;umpto, qu&aelig; communis e&longs;t motui propagationis. </s>

<s>Secund&ograve;, ex momento <lb/>eiu&longs;dem ponderis; Terti&ograve;, ex tali genere propagationis, de quo &longs;upr&agrave;; <lb/>qu&aelig; omnia &longs;unt apprim&egrave; tenenda, ne quis error &longs;ubrepat. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 99.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Cum applicatur potentia circumferenti&aelig; motus circularis; ita propagatur <lb/>impetus, vt plures partes ver&longs;us centrum motus producantur in pondere, quod <lb/>attollitur<emph.end type="italics"/>; &longs;it enim idem cylindrus CA; &longs;itque applicata potentia in <lb/>A, dico ver&longs;us C, plures partes produci in pondere, Probatur, quia attol&shy;<lb/>litur pondus in C, quod moueri non pote&longs;tin A, oper&acirc; vectis AC, vt con&shy;<lb/>&longs;tat ex certa hypothe&longs;i; igitur plures partes impetus producuntur per <lb/>rationem 6. &amp; 7. Th.77, </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Scio quidem hoc ip&longs;um &agrave; nemine hactenus, quod &longs;ciam, explicatum <lb/>e&longs;&longs;e; atque fore vt &agrave; multis tanquam nouum, &amp; in&longs;olens min&ugrave;s fort&egrave; <lb/>probetur: quamquam illa hypothe&longs;is hoc ip&longs;um euincit, vulgaris cert&egrave;, <lb/>&amp; nemini qua&longs;i non nota; qua nemp&egrave; dicimus in omnibus partibus mo&shy;<lb/>bilis, quod actu mouetur, impetum produci; &amp; &longs;i quando accidat corpo&shy;<lb/>ris ingentem molem ab applicata potentia non po&longs;&longs;e moueri, illud e&longs;&longs;e <lb/>tant&ugrave;m, qu&ograve;d non po&longs;&longs;int produci tot partes impetus, quot &longs;unt nece&longs;&longs;a&shy;<lb/>ri&aelig;, vt omnibus partibus &longs;ubjecti di&longs;tribuantur; igitur ex hac hypothe&shy;<lb/>&longs;i, qu&aelig; ex manife&longs;tis ducitur experimentis, nece&longs;&longs;ari&ograve; dicendum e&longs;t plu&shy;<lb/>res partes impetus vers&ugrave;s centrum vectis produci in pondere, quod at&shy;<lb/>tollitur, cuius propagationis proportionem infr&agrave; demon&longs;trabimus. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 100.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Impetus, qui producitur ver&longs;us centrum vectis in pondere, lic&egrave;t cre&longs;cat nu&shy;<lb/>mero, decre&longs;cit tamen in perfectione.<emph.end type="italics"/></s><s> Probatur per Th.81. ex motu imper&shy;<lb/>fectiore, cui re&longs;pondet impetus imperfectior per Ax. 17.num.4. non ratio&shy;<lb/>ne numeri, qui maior e&longs;t per Th.99. igitur ratione entitatis, &longs;eu perfe&shy;<lb/>ctionis entitatiu&aelig;. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 101.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Tota collectio impetus, qu&aelig; in pondere ex dato puncto vectis producitur, e&longs;t <lb/>ad aliam collectionem alterius puncti in perfectione, vt distantia illius puncti <lb/>&agrave; centro, ad di&longs;tantiam huius<emph.end type="italics"/>: probatur, quia perfectio vnius collectionis <lb/>e&longs;t ad perfectionem alterius, vt motus ad motum; motus ver&ograve; &longs;unt vt <lb/>&longs;patia, &longs;patia vt arcus, arcus vt &longs;emediametri, h&aelig; demum, vt di&longs;tanti&aelig;. </s></p><pb xlink:href="026/01/089.jpg" pagenum="57"/><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 102.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Impetus in ip&longs;o vecte &longs;ine pondere addito ita propagatur, vt &longs;it imperfectior <lb/>ver&longs;us centrum vectis<emph.end type="italics"/>; probatur, quia pondus ver&longs;us centrum mouetur <lb/>minore motu, vt con&longs;tat; igitur ab imperfectiore impetu; &longs;ed non e&longs;t <lb/>imperfectior tant&ugrave;m ratione numeri, id e&longs;t, pauciorum partium impe&shy;<lb/>tus; quia &longs;i hoc e&longs;&longs;et, &longs;it vectis AC, motus B, e&longs;t &longs;ubduplus motus <lb/>A; igitur &longs;i e&longs;t impetus eiu&longs;dem perfectionis entitatiu&aelig;, vt &longs;ic loquar; <lb/>ita &longs;e habet numerus partium impetus in B, ad numerum partium in A, <lb/>vt motus B, ad motum A; &amp; hic vt arcus BD, ad arcum AE; &amp; hic vt <lb/>BC, ad AC; igitur e&longs;t &longs;ubduplus; igitur &aelig;qualis omnin&ograve; producitur <lb/>impetus ab eadem potentia in vecte AC, &longs;iue applicetur centro C, &longs;iue <lb/>circumferenti&aelig; A; igitur &aelig;qu&egrave; facil&egrave;; quod e&longs;t contra experientiam; <lb/>probatur &longs;ecund&ograve;, quia &longs;i hoc e&longs;&longs;et, pondus idem t&agrave;m facil&egrave; attolleretur <lb/>in A, qu&agrave;m in B; quia idem impetus produceretur, quod e&longs;t contra ex&shy;<lb/>perientiam. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 103.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Ex hoc facil&egrave; intelligitur, cur impetus propagetur facili&ugrave;s &agrave; circumferen&shy;<lb/>tia ad centrum, qu&agrave;m &agrave; centro ad circumferentiam, &amp; cur longior vectis ab <lb/>eadem potentia moueri po&longs;&longs;it primo modo, non &longs;ecundo, quod clarum est.<emph.end type="italics"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 104.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Decre&longs;cit impetus ver&longs;us centrum iuxta rationem distantiarum<emph.end type="italics"/>; probatur <lb/>quia decre&longs;cit iuxta rationem motuum; &amp; h&aelig;c iuxta rationem di&longs;tan&shy;<lb/>tiarum. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 105.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Non decre&longs;cit numerus partium impetus &agrave; circumferentia ad centrum<emph.end type="italics"/>; <lb/>probatur, quia cum &agrave; circumferentia ad centrum ita propagetur impe&shy;<lb/>tus, vt vnicum tant&ugrave;m punctum producatur in ip&longs;a extremitate mobilis; <lb/>cert&egrave; non pote&longs;t min&ugrave;s impetus produci ver&longs;us centrum ratione nume&shy;<lb/>ri; igitur non decre&longs;cit numerus; hinc producitur nece&longs;&longs;ari&ograve; imperfe&shy;<lb/>ctior ver&longs;us centrum. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 106.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Non producuntur plures partes impetus in vecte ver&longs;us centrum, id est, non <lb/>&longs;unt plures in puncto vectis propi&ugrave;s ad centrum accedente, qu&agrave;m in co; quod <lb/>longi&ugrave;s distat:<emph.end type="italics"/> Probatur prim&ograve;, quia fru&longs;tr&agrave; e&longs;&longs;ent plures. </s>

<s>Secund&ograve;, cur <lb/>poti&ugrave;s in vna proportione, qu&agrave;m in alia? </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 107.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Ex his constat produci impetum &aelig;qualem numero in omnibus punctis vectis <lb/>a circumferentia ad centrum, cum &longs;cilicet applicatur potentia circumferenti&aelig;<emph.end type="italics"/>; <lb/>probatur, quia non producitur numerus minor per Th.105. neque maior <lb/>per Th. 106. igitur &aelig;qualis; adde quod res explicari non pote&longs;t per ma&shy;<lb/>iorem, neque per minorem; ita vt &longs;cilicet pondera, qu&aelig; &agrave; data potentia <lb/>leuantur, &longs;int vt di&longs;tanti&aelig;, de quo &longs;upr&agrave;. </s></p><pb xlink:href="026/01/090.jpg" pagenum="58"/><p type="main">

<s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Ob&longs;eruabis, quod aliquando in mentem venerat; &longs;cilicet, ver&longs;us cen&shy;<lb/>trum produci maiorem numerum in ratione di&longs;tantiarum permutando; <lb/>&amp; imperfectiorem in ratione duplicata earumdem di&longs;tantiarum, etiam <lb/>permutando, v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;it idem vectis AC &longs;ectus bifariam in B; in puncto <lb/>B producitur numerus duplus producti in A; at ver&ograve; perfectio impetus <lb/>in B e&longs;t ad perfectionem impetus in A, vt quadratum BC ad quadra&shy;<lb/>tum AC; vel in ratione &longs;ubquadrupla, lic&egrave;t tota collectio impetus B <lb/>&longs;it tant&ugrave;m &longs;ubdupla perfectione collectionis impetus A; &longs;ed hoc profe&shy;<lb/>ct&ograve; dici non pote&longs;t; nam &longs;int in A 4. partes impetus; igitur in B erunt <lb/>8. applicetur autem pondus in B. </s>





<s>Prim&ograve; producentur in eo partes 8. <lb/>impetus perfectionis &longs;ubquadrupl&aelig;; &longs;i comparentur cum partibus A, <lb/>tum producentur 16. qu&aelig; &aelig;quiualent 4 A; igitur 24. at ver&ograve; in A pro&shy;<lb/>ducentur prim&ograve; 4. tum deinde 2. qu&aelig; &aelig;quiualent 8. productis in B; igitur <lb/>6. igitur pondus, quod leuari pote&longs;t in B, e&longs;t ad pondus, quod leuari pote&longs;t <lb/>in A, vt 24. ad 6.id e&longs;t, in ratione quadrupla quod omnin&ograve; fal&longs;um e&longs;t. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 108.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Iam facil&egrave; explicatur ex dictis, quomodo, &amp; cuius rationis pondera attol&shy;<lb/>lantur ex diuer&longs;is punctis vectis<emph.end type="italics"/>; &longs;it enim idem vectis AC, &amp; producan&shy;<lb/>tur.v.g. </s>

<s>in &longs;ingulis punctis vectis &longs;ingula puncta impetus, &longs;ed diuer&longs;&aelig; <lb/>perfectionis; haud dubi&egrave; plures partes impetus imperfecti po&longs;&longs;unt face&shy;<lb/>re impetum &aelig;qualem in perfectione alteri, qui con&longs;tat paucioribus, &longs;ed <lb/>perfectioribus; igitur cum impetus B &longs;it imperfectior dupl&ograve; qu&agrave;m im&shy;<lb/>petus in A, dupl&ograve; plures partes impetus producentur in B, qu&agrave;m in A, er&shy;<lb/>go dupl&ograve; maius pondus mouebitur; atque ita deinceps; eum enim ap&shy;<lb/>ponitur pondus in B, producuntur in eo partes impetus omnes eiu&longs;dem <lb/>perfectionis; qu&aelig; &longs;cilicet re&longs;pondet B, id e&longs;t, qu&aelig; e&longs;t &longs;ubdupla perfectio&shy;<lb/>nis impetus A; igitur plures partes producuntur, qu&agrave;m &longs;i e&longs;&longs;ent perfe&shy;<lb/>ctionis A; &longs;ed pauciores qu&agrave;m &longs;i e&longs;&longs;ent perfectionis O, qu&aelig; minor e&longs;t; <lb/>quippe eadem potentia, &longs;eu cau&longs;a, qu&aelig; agit quantum pote&longs;t (quod &longs;up&shy;<lb/>pono mod&ograve;) producit &aelig;qualem effectum in perfectione, per Ax. 13. n. </s>

<s><lb/>4. &longs;ed &aelig;qualis perfectio pote&longs;t con&longs;tare pluribus, vel paucioribus parti&shy;<lb/>bus perfectionis, nam 4. pattes perfectionis vt 4. faciunt &aelig;qualem effe&shy;<lb/>ctum alteri qui con&longs;tat 8. partibus perfectionis vt 2. quod certum e&longs;t; &longs;ed <lb/>de his plura ali&agrave;s. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 109.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Perfectio decre&longs;cit ver&longs;us centrum iuxta diuer&longs;am rationem longitudinum <lb/>vectis, &longs;eu distantiarum.<emph.end type="italics"/> v.g.&longs;it idem vectis AC, ita decre&longs;cit ab A ver&longs;us <lb/>centrum C; vt impetus puncti B &longs;it &longs;ubduplus in perfectione, puncti R <lb/>&longs;ubtriplus: iam ver&ograve; &longs;it vectis &longs;ubduplus prioris BC, &longs;ectus bifariam in <lb/>Z; &longs;i impetus productus in B, qu&ecedil; e&longs;t extremitas minoris vectis B &longs;it &aelig;qua&shy;<lb/>lis perfectionis cum impetu producto in A (&amp; reuera &longs;unt &aelig;quales) &longs;i <lb/>&aelig;quali tempore percurrant arcus &aelig;quales, &longs;cilicet AV, &amp; BD) cert&egrave; im-<pb xlink:href="026/01/091.jpg" pagenum="59"/>petus productus in Z e&longs;t &aelig;qualis producto in B, cum B pertinet ad ma&shy;<lb/>iorem vectem; quia vt AC totus maior vectis e&longs;t ad BC ita BC ad <lb/>ZC: igitur decre&longs;cit perfectio vers&ugrave;s centrum iuxta rationem longi&shy;<lb/>tudinum. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 110.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Minima potentia est illa, qu&aelig; in extremitate vectis, qu&aelig; procul recedit &agrave; <lb/>centro, vnam tant&ugrave;m partem, vel vnum punctum impetus producit<emph.end type="italics"/>; nihil <lb/>enim min&ugrave;s produci pote&longs;t, po&longs;ito quod potentia applicata ad talem gra&shy;<lb/>dum perfectionis &longs;it determinata, id e&longs;t ad producendum impetum talis <lb/>perfectionis in ea parte &longs;ubjecti, cui applicatur immediat&egrave;, vt &longs;upr&agrave; di&shy;<lb/>ctum e&longs;t. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 111.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Si &longs;int tantum duo puncta vel du&aelig; partes vectis, illa potentia ad illum mo&shy;<lb/>uendum &longs;ufficiens motu circulari est ad aliam &longs;ufficientem ad illum mouen&shy;<lb/>dum motu recto, vt<emph.end type="italics"/> 1/2 <emph type="italics"/>ad<emph.end type="italics"/> 2. &longs;i &longs;int tria puncta vt 2. ad 3. &longs;i 4. vt 2. 1/2 ad 4. <lb/>&longs;i 5. vt 3. ad 5. &longs;i 6. vt 3. 1/2 ad 6. atque ita deinceps iuxta hanc propor&shy;<lb/>tionem in quo non e&longs;t difficultas, cum hoc totum &longs;equatur ex Th. 109. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Ob&longs;erua tamen quacumque data potentia po&longs;&longs;e dari minorem; quia <lb/>quocumque dato motu, etiam recto, pote&longs;t dari tardior; igitur quocum&shy;<lb/>que impetu imperfectior; igitur quando appellaui potentiam minimam; <lb/>intellige illam qu&aelig; comparatur cum vnico puncto impetus talis perfe&shy;<lb/>ctionis; h&aelig;c enim reuera minima e&longs;t illarum omnium, qu&aelig; po&longs;&longs;unt pro&shy;<lb/>ducere impetum talis perfectionis, &longs;i ver&ograve; comparetur cum impetu im&shy;<lb/>perfectiore, haud dubi&egrave; minima non e&longs;t. </s></p><p type="main">

<s>Ob&longs;erua pr&aelig;terea &longs;uppo&longs;itum e&longs;&longs;e hactenus in extremitate vectis &longs;iue <lb/>maioris, &longs;iue minoris, produci impetum eiu&longs;dem perfectionis, eiu&longs;que <lb/>vnicum punctum, &longs;eu partem, vnde potentia qu&aelig; applicatur maiori vecti <lb/>conuenit quidem cum ea, qu&aelig; applicatur minori in eo, qu&ograve;d vtraque in <lb/>extremitate &longs;ui vectis producat vnum punctum impetus eiu&longs;dem perfe&shy;<lb/>ctionis; differt tamen in eo, qu&ograve;d illa, qu&aelig; applicatur maiori vecti, &longs;it <lb/>maior iuxta rationes pr&aelig;dictas in Theoremate. <!-- KEEP S--></s>

<s>v. <!-- REMOVE S-->g. <!-- REMOVE S-->illa, qu&aelig; applicatur <lb/>vecti. </s>





<s>2. punctorum e&longs;t ad eam, qu&aelig; applicatur vecti trium punctorum, <lb/>&longs;cu partium, vt 1. 1/2 ad 2. &amp; &longs;i vectis &longs;it 4. punctorum ad 2. 1/2; &longs;i 5. ad 3. <lb/>&longs;i 6. ad 3. 1/2; &longs;i 7. ad 4. &longs;i 8. ad 4. 1/2. Vides egregiam progre&longs;&longs;ionem; &longs;it <lb/>enim vectis 2. punctorum AB, in puncto A, quod e&longs;t extremitas, produ&shy;<lb/>catur punctum impetus dat&aelig; perfectionis, in B producetur aliud, cuius <lb/>perfectio e&longs;t &longs;ubdupla prioris per Th. 109. igitur caracter, &longs;eu momen&shy;<lb/>tum totius impetus e&longs;t 1. 1/2. &longs;it porr&ograve; vectis 4. punctorum CDEF, in <lb/>C, quod e&longs;t extremitas; producatur vnum punctum impetus eiu&longs;dem <lb/>perfectionis cum eo, quod productum e&longs;t in A; cert&egrave; in D producetur <lb/>aliud cuius perfectio erit ad priorem vt 3.ad 4. per idem Th. &longs;ic autem <lb/>notetur 1/4, in E 2/4, in F 3/4, in C vero 4/4; perfectiones enim &longs;unt vt lon-<pb xlink:href="026/01/092.jpg" pagenum="60"/>gitudines; qu&aelig; &longs;i colligantur, habebis characterem totius impetus, 2 1/2: <lb/>igitur totus impetus productus in minore vecte, qui con&longs;tat 2. punctis, <lb/>e&longs;t ad impetum, qui producitur in maiore con&longs;tante 4.punctis, vt 1. 1/2 ad <lb/>2. 1/2; igitur vectis maior maiorem potentiam ad mouendum ip&longs;um ve&shy;<lb/>ctem requirit; non cert&egrave; in de&longs;cen&longs;u; quippe &longs;uo pondere de&longs;cendit, &longs;ed <lb/>in plano horizontali; ni&longs;i enim potentia po&longs;&longs;it mouere vectem; haud <lb/>dubi&egrave; nullum pondus vecte mouebit. </s></p><p type="main">

<s>At ver&ograve; &longs;i potentia &longs;it tant&ugrave;m dupla minim&aelig;, qu&aelig; datum vectem mo&shy;<lb/>uere po&longs;&longs;it; haud dubi&egrave; dato illo vecte datum fer&egrave; quodcumque pondus <lb/>mouere poterit; cum ip&longs;e vectis con&longs;tet fer&egrave; infinitis punctis in longi&shy;<lb/>tudine, vt patet ex dictis, &amp; con&longs;ideranti patebit. </s></p><p type="main">

<s>Ob&longs;eruabis demum in mechanicis nullam fer&egrave; haberi rationem pon&shy;<lb/>deris ip&longs;ius vectis; parum enim pro nihilo computatur: Ex his tamen <lb/>erui po&longs;&longs;unt veri&longs;&longs;im&aelig; rationes Phy&longs;ic&aelig; proportionum vectis AH; &longs;ia&shy;<lb/>que A extremitas, H centrum; &longs;itque BH 1/2. CH 1/4, DH 1/2, EH (1/16), <lb/>FH (1/32), GH (1/64) pondus I applicetur in A, &amp; moueatur; cert&egrave; in B moue&shy;<lb/>bitur pondus K duplum I; quia, cum impetus productus in B, &longs;it &longs;ubdu&shy;<lb/>plus in perfectione illius, qui producitur in A; vt &aelig;qualis producatur in <lb/>B, &amp; in A, debent produci in B dupl&ograve; plures partes impetus; igitur du&shy;<lb/>pl&ograve; maius pondus mouebit; at ver&ograve; in C mouebitur pondus L quadru&shy;<lb/>plum I, in D octuplum, atque ita deinceps; donec tandem in G mouea&shy;<lb/>tur pondus, quod &longs;it ad I vt 64. ad 1. &amp; cum adhuc po&longs;&longs;int accipi inter <lb/>GH, partes aliquot&aelig; minores, &amp; minores fer&egrave; in infinitum, non mirum <lb/>e&longs;t &longs;i pondus maius po&longs;&longs;it adhuc moueri. </s></p><p type="main">

<s>Ob&longs;eruabis etiam in omni vecte ab&longs;trahendo ab eius pondere, &amp; ap&shy;<lb/>plicata eadem potentia, hoc e&longs;&longs;e commune; vt po&longs;&longs;it quodcumque pon&shy;<lb/>dus attolli, lic&egrave;t difficili&ugrave;s in minore; quia hic non pote&longs;t in tam mul&shy;<lb/>tas partes aliquotas &longs;en&longs;ibiliter diuidi, in medio tamen vecte duplum <lb/>&longs;emper pondus mouetur; &longs;iue ip&longs;e vectis &longs;it maior, &longs;iue minor. </s></p><p type="main">

<s>Ob&longs;eruabis deinde, &longs;i centrum vectis non &longs;it in altera extremitate, <lb/>&longs;ed. </s>

<s>v.g. <!-- REMOVE S-->in C; haud dubi&egrave; producitur in H, &amp; in B impetus &aelig;qualis; quia <lb/>&aelig;qualiter di&longs;tat vtrumque punctum &agrave; centro C; igitur &aelig;quale pondus <lb/>mouebitur in B, &amp; in H; propagatur tamen nouo modo &agrave; C ver&longs;us H, de <lb/>quo iam &longs;upr&agrave; dictum e&longs;t. </s>

</p><p type="main">

<s>Ob&longs;eruabis denique triplicem propagationem impetus e&longs;&longs;e legiti&shy;<lb/>mam. </s>

<s>Prima e&longs;t in motu recto, cum propagatur per partes &aelig;quales, t&ugrave;m <lb/>in perfectione, t&ugrave;m in numero in &longs;ingulis partibus &longs;ubjecti per gradus, <lb/>&longs;cilicet heterogencos. </s>

<s>Secunda e&longs;t in motu circulari, applicata &longs;cilicet <lb/>potentia centro; cum propagatur per partes &aelig;quales in perfectione, &amp; <lb/>in&aelig;quales in numero. </s>

<s>Tertia e&longs;t in vecte, cum propagatur per partes <lb/>&aelig;quales in numero, &amp; in&aelig;quales in perfectione. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 112.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Impetus debet determinari ad aliquam lineam motus<emph.end type="italics"/>; probatur, quia <lb/>non pote&longs;t e&longs;&longs;e impetus, ni&longs;i exigat motum per Th.14. nec exigere mo-<pb xlink:href="026/01/093.jpg" pagenum="61"/>tum, ni&longs;i per aliquam lineam, vt patet; &longs;ed hoc e&longs;t impetum e&longs;&longs;e de&shy;<lb/>terminatum ad aliquam lineam motus; pr&aelig;terea &longs;i non e&longs;t determina&shy;<lb/>tus ad aliquam lineam; igitur indeterminatus, &amp; indifferens per Ax.1. <lb/>&longs;ed indifferens manere non pote&longs;t; cur enim potius haberet motum <lb/>per vnam lineam, qu&agrave;m per aliam? </s>

<s>igitur debet determinari. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 113.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Impetus ad plures lineas &longs;eor&longs;im indifferens e&longs;t:<emph.end type="italics"/> Probatur, quia idem im&shy;<lb/>petus pil&aelig; in aliam impact&aelig; producit in ea impetum, qui pro diuer&longs;o <lb/>contactu ad diuer&longs;am lineam determinari pote&longs;t; pr&aelig;terea corpus graue <lb/>in diuer&longs;is planis inclinatis de&longs;cendit; igitur per diuer&longs;as lineas; deinde <lb/>pila reflectitur propter impetum priorem, qui tant&ugrave;m mutat lineam, vt <lb/>dicemus infr&agrave;; adde quod funependuli vibrati impetus &longs;ine reflexione <lb/>mutat lineam motus; igitur idem impetus ad plures lineas &longs;eor&longs;im e&longs;t <lb/>indifferens. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 114.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc idem impetus ad plures lineas potest determinari &longs;eor&longs;im<emph.end type="italics"/>; quia ad <lb/>eas pote&longs;t determinari, ad quas e&longs;t indifferens, vt patet; &longs;ed ad multas <lb/>e&longs;t indifferens per Theorema 113. igitur ad multas pote&longs;t determi&shy;<lb/>nari. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Ob&longs;eruabis prim&ograve; determinationem hanc nihil e&longs;&longs;e aliud, ni&longs;i ip&longs;um <lb/>impetum cum tali linea comparatum, &longs;eu coniunctum; vnam ver&ograve; li&shy;<lb/>neam differre ab alia ratione terminorum v. <!-- REMOVE S-->g. <!-- REMOVE S-->illa qu&aelig; tendit ver&longs;us <lb/>ortum differt ab ea, qu&aelig; tendit ver&longs;us au&longs;trum, vel occa&longs;um, &longs;cilicet <lb/>ratione terminorum, &longs;unt enim duo termini, nemp&egrave; &agrave; quo, &amp; ad quem; <lb/>4. autem modis differunt termini line&aelig;, vel enim neuter communis e&longs;t <lb/>vt AB. DC, vel terminus &agrave; quo vtrique line&aelig; communis e&longs;t, vt BA. <lb/>BE, vel terminus ad quem vt AB, EB; vel denique vici&longs;&longs;im commu&shy;<lb/>tantur termini, vt BE, EB, &amp; h&aelig;c terminorum coniugatio facit oppo&shy;<lb/>&longs;itionem maximam, id e&longs;t diametralem. </s>



</p><p type="main">

<s>Secund&ograve; ob&longs;eruabis aliquando videri e&longs;&longs;e vtrumque terminum com&shy;<lb/>munem lic&egrave;t differant line&aelig;; &longs;it linea recta BE, habet communes ter&shy;<lb/>minos cum curua BFE, lic&egrave;t omnin&ograve; differat ab illa; at profect&ograve; lic&egrave;t <lb/>BE videatur e&longs;&longs;e vnica &longs;implex linea duobus terminis clau&longs;a; con&longs;tat <lb/>ramen ex pluribus aliis continuata, rect&aacute;que &longs;erie iunctis; vnde, vt <lb/>linea dicatur eadem e&longs;&longs;e cum alia, debet vna cum ali&acirc; conuenire; ita vt <lb/>alteri &longs;uperpo&longs;ita nec excedat, nec deficiat. </s></p><p type="main">

<s>Terti&ograve; linea motus non differt ab ip&longs;o motu continuo tractu, &longs;eu <lb/>fluxu qua&longs;i labenti: Porr&ograve; vnus motus differt ab alio, vel ratione velo&shy;<lb/>citatis, vel ratione terminorum; &longs;ed h&aelig;c parum difficultatis habent. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 115.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Impetus aliquis ad vnam tant&ugrave;m lineam pote&longs;t e&longs;&longs;e determinatus<emph.end type="italics"/>; v. <!-- REMOVE S-->g. <lb/><emph type="italics"/>impetus naturalis innatus, de quo in Th.<emph.end type="italics"/> 17. <emph type="italics"/>nam de acqui&longs;ito certum e&longs;t ad<emph.end type="italics"/><pb xlink:href="026/01/094.jpg" pagenum="62"/><emph type="italics"/>plures determinari po&longs;&longs;e, vt videbimus cum de motu reflexo<emph.end type="italics"/>; probatur quia <lb/>motus deor&longs;um e&longs;t finis huius impetus; quia ideo corpus graue produ&shy;<lb/>cit in &longs;e impetum (&longs;i tamen producit) vt tendat deor&longs;um, vt certum e&longs;t; <lb/>t&agrave;m enim omne graue non impeditum tendit deor&longs;um, qu&agrave;m omnis <lb/>ignis e&longs;t calidus; igitur &longs;i e&longs;t proprietas omnis ignis e&longs;&longs;e calidum, quia <lb/>omni competit; ita omni graui competit tendere infr&agrave; leuius, mod&ograve; <lb/>non impediatur; igitur e&longs;t eius proprietas; igitur ille impetus e&longs;t de&shy;<lb/>terminatus ad lineam qu&aelig; tendit deor&longs;um; &longs;ed de hoc impetu naturali <lb/>innato fus&egrave; agemus infr&agrave; in &longs;ecund&ograve; libro; nunc &longs;ufficiat dixi&longs;&longs;e po&longs;&longs;e <lb/>dari aliquem impetum ita determinatum ad certam lineam, vt ad aliam <lb/>determinari non po&longs;&longs;it naturaliter, nulla e&longs;t enim repugnantia. </s>

</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 116.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Impetus determinatur aliquando ad lineam motus &agrave; potentia motrice<emph.end type="italics"/>; pro&shy;<lb/>batur, quia primus impetus ab ip&longs;a potentia productus &longs;ine impedimen&shy;<lb/>to ab alio determinari non pote&longs;t; potentia porr&ograve; motrix vel e&longs;t gra&shy;<lb/>uium, vel leuium, vel animantium, vel proiectorum, vel compre&longs;&longs;o&shy;<lb/>rum, &amp;c. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 117.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Potentia ver&ograve; motrix determinatur vel &agrave; &longs;uo fine intrin&longs;eco, vel potius ab <lb/>ip&longs;a &longs;ua natura<emph.end type="italics"/>; &longs;ic grauitas &longs;eu potentia motrix grauium determinata <lb/>e&longs;t ad motum deor&longs;um perpendicularem, dum in medio libero corpus <lb/>graue mouetur; vel &agrave; plano inclinato; pro cuius diuer&longs;a inclinatione <lb/>diuer&longs;a e&longs;t linea motus deor&longs;um; vel ab ip&longs;a via, &longs;eu exitu patefacto; <lb/>&longs;ic potentia motrix compre&longs;&longs;orum &longs;uas vires exerit, &amp; mobile ip&longs;um <lb/>agit, qu&acirc; patet vi&acirc;, &longs;ur&longs;um, deor&longs;um &amp;c. </s>

<s>vel ab appetitu &longs;eu libero, &longs;eu <lb/>&longs;en&longs;itiuo; &longs;ic potentia progre&longs;&longs;iua animantium c&ograve; corpus agit, qu&ograve; iu&shy;<lb/>bet appetitus, vel ab aliqua affectione intrin&longs;eca intrin&longs;ec&ugrave;s vel extrin&shy;<lb/>&longs;ec&ugrave;s adueniente; &longs;ic dilatatur pupilla, vel contrahitur pro diuer&longs;a lu&shy;<lb/>minis appul&longs;i vi, vel obiecti di&longs;tantia: Huc reuoca motus illos natura&shy;<lb/>les, qui animalibus competunt v. <!-- REMOVE S-->g. <!-- REMOVE S-->tu&longs;&longs;is, &longs;ingultus, &longs;ternutationis, &amp;c. </s>





<s><lb/>de quibus fus&egrave; &longs;uo loco. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 118.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Impetus determinatur aliquando ad lineam ab alio impetu producente<emph.end type="italics"/>; <lb/>&longs;ic impetus corporis proiecti determinatur ab impetu vel organi vel <lb/>manus proiicientis; quia nihil e&longs;t aliud &agrave; quo determinari po&longs;&longs;it, vt <lb/>patet; adde figuram organi, di&longs;po&longs;itionem &longs;eu &longs;itum mobilis, quod ma&shy;<lb/>nu tenetur; impedimenti etiam habetur ratio v. <!-- REMOVE S-->g. <!-- REMOVE S-->corpus oblongum <lb/>proiici pote&longs;t, vel motu recto ad in&longs;tar teli, vel motu mixto ex recto <lb/>&amp; circulari; cum &longs;cilicet diuer&longs;imod&egrave; vibratur: &longs;i enim altera extremi&shy;<lb/>tas adhuc h&aelig;reat in manu, dum altera mouetur, vt cum quis baculo <lb/>ferit; tunc cert&egrave; e&longs;t aliqu&ograve;d impedimenti genus, ex quo oritur talis li&shy;<lb/>nea motus; illud autem impedimentum emergit ex diuer&longs;a applicatione <lb/>diuer&longs;aque brachij vibratione, qu&aelig; omnia &longs;unt &longs;atis clara. </s>



</p><pb xlink:href="026/01/095.jpg" pagenum="63"/><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 119.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Impetus determinatus ad vnam lineam pote&longs;t ad aliam in &longs;uo fluxu deter&shy;<lb/>minatu<emph.end type="italics"/>; vt patet in corpore reflexo; nec enim dici pote&longs;t totum prio&shy;<lb/>rem impetum in ip&longs;o reflexionis puncto de&longs;trui, vt demon&longs;trabimus <lb/>ali&agrave;s. </s>

<s>Probatur etiam ex impetu proiectorum, qu&aelig; mutant lineam mo&shy;<lb/>tus manente adhuc priore impetu &longs;altem ex parte. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 120.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Corpus proiectum in aliud ita illud impellit, vt determinet lineam motus <lb/>ratione puncti contactus<emph.end type="italics"/>; Sit enim, ne multiplicemus figuras, globus, <lb/>cuius linea directionis &longs;it DC, punctum contactus C, ita globus A im&shy;<lb/>pellet globum B, vt linea motus, ad quam determinatur, &longs;it CB, id e&longs;t <lb/>ducta &agrave; puncto contactus ad centrum globi impul&longs;i; &longs;it etiam globus <lb/>P impactus in globum A punctum contactus &longs;it D, linea motus, ad <lb/>quam determinatur, e&longs;t DA, qu&aelig; &longs;cilicet &agrave; puncto contactus ducitur <lb/>per centrum grauitatis corporis impul&longs;i: experientia huius rei certa <lb/>e&longs;t, nec ignorant qui in ludo minoris tudicul&aelig; ver&longs;ati &longs;unt; ratio au&shy;<lb/>tem inde tant&ugrave;m duci pote&longs;t, quod &longs;cilicet ab ip&longs;o puncto contactus ita <lb/>diffunditur impetus, vt hinc inde &aelig;qualiter in vtroque hemi&longs;ph&aelig;rio <lb/>diffundatur; coniungitur autem vtrumque hemi&longs;ph&aelig;rium circulo A, <lb/>vel B, in priore figura, e&longs;tque vtriu&longs;que communis &longs;ectio; cum autem <lb/>vtrimque &longs;it &aelig;qualis impetus, nulla e&longs;t ratio, cur linea directionis in&shy;<lb/>clinet poti&ugrave;s in vnum hemi&longs;ph&aelig;rium, qu&agrave;m in aliud: pr&aelig;terea cum <lb/>motus orbis globi determinetur &agrave; motu centri; cum &longs;cilicet globus in <lb/>globum impingitur; haud dubi&egrave; non pote&longs;t e&longs;&longs;e alius motus centri, ni&longs;i <lb/>qui determinatur &agrave; puncto contactus, &agrave; quo vnica tant&ugrave;m linea ad cen&shy;<lb/>trum duci pote&longs;t, vt con&longs;tat; &amp; h&aelig;c ratio veri&longs;&longs;ima e&longs;t, &amp; totam rem <lb/>ip&longs;am euincit. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 121.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc lic&egrave;t diuer&longs;&aelig; &longs;int linea motus globi impellentis, &longs;i tamen &longs;it idem pun&shy;<lb/>ctum contactus ad <expan abbr="e&atilde;dem">eandem</expan> lineam globus impul&longs;us determinabitur,<emph.end type="italics"/> v. <!-- REMOVE S-->g. <!-- REMOVE S-->li&shy;<lb/>cet globus P. eiu&longs;dem figur&aelig; tangat globum A in D per lineam PD &longs;iue <lb/>per lineam HD &longs;iue per quamlibet aliam, globus A mouebitur &longs;emper <lb/>per lineam directionis DA propter rationem propo&longs;itam, quod etiam <lb/>mille experimentis conuincitur. </s>



</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 122.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Determinatur impetus corporis proiecti impacti in corpus reflectens ad no&shy;<lb/>uam lineam<emph.end type="italics"/>; patet experienti&acirc; in pil&acirc; reflex&acirc;; reflexionis autem ratio&shy;<lb/>nem afferemus in lib. 

de motu reflexo. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 123.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Non determinatur tant&ugrave;m ratione puncti contactus.<emph.end type="italics"/></s><s> Probatur, quia cum <lb/>eodem puncto contactus pote&longs;t e&longs;&longs;e determinatio ad diuer&longs;am lineam, <lb/>vt manife&longs;tum e&longs;t; &longs;it enim reflexio per angulum &aelig;qualem incidenti&aelig;, <lb/>&longs;ed diuer&longs;i anguli po&longs;&longs;unt in idem punctum coire, vt patet. </s></p><pb xlink:href="026/01/096.jpg" pagenum="64"/><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 124.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Non determinatur noua linea in motu reflexo &acirc; priore tant&ugrave;m linea <lb/>incidenti&aelig;<emph.end type="italics"/>; probatur, quia pote&longs;t e&longs;&longs;e eadem linea incidenti&aelig; cum di&shy;<lb/>uer&longs;is lineis motus reflexi, vt patet. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 125.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Non determinatur noua linea motus reflexi ratione tant&ugrave;m plani reflecten&shy;<lb/>tis<emph.end type="italics"/>: Probatur, quia cum eodem plano reflectente diuer&longs;&aelig; line&aelig; motus <lb/>reflexi e&longs;&longs;e po&longs;&longs;unt, vt con&longs;tat. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 126.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Determinatur noua linea motus reflexi ratione line&aelig; prioris incidenti&aelig; com&shy;<lb/>parat&aelig; cum plano reflectente,<emph.end type="italics"/> e&longs;t enim angulus reflexionis &aelig;qualis angu&shy;<lb/>lo incidenti&aelig;, cuius effectus rationem ali&agrave;s afferemus, cum de motu <lb/>reflexo; &amp; ver&ograve; multa h&icirc;c cur&longs;im tant&ugrave;m per&longs;tringimus, qu&aelig; in libro <lb/>de motu reflexo accurati&longs;&longs;im&egrave; demon&longs;trabimus; H&igrave;c tant&ugrave;m dixi&longs;&longs;e &longs;uf&shy;<lb/>ficiat determinari mobile in reflexionis puncto ad nouam lineam motus, <lb/>quod nemo in dubium reuocare pote&longs;t, &amp; propter quid fiat loco citato <lb/>demon&longs;trabimus. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 127.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Quando globus in globum &aelig;qualem ita impingitur, vt linea directionis per <lb/>centra vtriu&longs;que ducatur, determinatio noua e&longs;t &aelig;qualis priori<emph.end type="italics"/>; Patet ex&shy;<lb/>perientia in pilis illis eburneis, quas de&longs;iderat ludus minoris tudicul&aelig;; <lb/>nec e&longs;t vlla ratio, cur determinatio &longs;it maior poti&ugrave;s, qu&agrave;m minor, cum <lb/>vtraque pila &longs;it &aelig;qualis; &longs;i enim maior e&longs;&longs;et, vel minor; cur poti&ugrave;s vno <lb/>gradu, qu&agrave;m duobus? </s>

<s>qu&agrave;m tribus? </s>

<s>Pr&aelig;terea, cum re&longs;i&longs;tens, vel im&shy;<lb/>pediens e&longs;t &aelig;quale agenti; certe &longs;icut agens refundit in pa&longs;&longs;um totum <lb/>id, quod habet, id e&longs;t &aelig;qualem impetum in inten&longs;ione, &amp; &aelig;qu&egrave; velo&shy;<lb/>cem motum per Th. 60. <!--neuer Satz-->Ita re&longs;i&longs;tens, vel impediens refundit &aelig;quale <lb/>impedimentum, quod tant&ugrave;m &longs;umi pote&longs;t ex &aelig;qualitate mobilium; &longs;ed <lb/>ex &aelig;quali impedimento duci tant&ugrave;m pote&longs;t &aelig;qualis determinatio priori; <lb/>denique pote&longs;t dari determinatio noua &aelig;qualis priori, vt con&longs;tat, &longs;ed <lb/>aliunde duci non pote&longs;t qu&agrave;m ex ip&longs;a mobilium &aelig;qualitate, mod&ograve; fiat <lb/>contactus per lineam connectentem centra. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 128.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc ratio manife&longs;ta illius mirifici effectus, &longs;cilicet quietis pil&aelig; impact&aelig;<emph.end type="italics"/>; <lb/>quippe h&aelig;c quie&longs;cet illic&ograve; ab ictu; quia &longs;cilicet, cum noua determina&shy;<lb/>tio &longs;it &aelig;qualis priori, non e&longs;t vlla ratio, cur alterutra pr&aelig;ualeat; nec <lb/>etiam pote&longs;t e&longs;&longs;e determinatio communis, &longs;eu mixta; cur enim potius <lb/>dextror&longs;um quam &longs;ini&longs;tror&longs;um? </s>

<s>de quo infr&agrave;. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 129.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Quando linea directionis globi impacti non connectit centra vtriu&longs;qu&etail; <lb/>globi, determinatur noua linea motus t&ugrave;m &agrave; priore linea incidenti&aelig;, t&ugrave;m &agrave; <lb/>connectente centra, qu&aelig; &longs;cilicet per punctum contactus &agrave; centro impacti globi<emph.end type="italics"/><pb xlink:href="026/01/097.jpg" pagenum="65"/><emph type="italics"/>ad centrum alterius ducitur<emph.end type="italics"/>; quippe nihil e&longs;t aliud &agrave; quo determinari. </s>

<s><lb/>po&longs;&longs;it, vt patet; non determinatur etiam ab alterutra &longs;eor&longs;im, vt con&shy;<lb/>&longs;tat, igitur ab vtraque conjunctim; in qua ver&ograve; proportione dicemus, <lb/>&amp; demon&longs;trabimus in libro de motu reflexo; &longs;unt enim mirific&aelig; qu&aelig;&shy;<lb/>dam reflexionum proportiones, quas ibidem explicabimus. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 130.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc globus &longs;ic impactus nunquam quie&longs;cit<emph.end type="italics"/>; ratio e&longs;t, quia vtraque linea <lb/>determinationis cum angulum faciat, in communem lineam abit; nam <lb/>ex duabus lineis motus minim&egrave; oppo&longs;itis ex diametro, fit alia tertia me&shy;<lb/>dia pro rata; h&icirc;c etiam latent my&longs;teria, de quibus loco citato. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 131.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Si globus minor in maiorem impingatur per quamcumque lineam directio&shy;<lb/>nis, determinatur ad nouam lineam motus reflexi<emph.end type="italics"/>; experientia clara e&longs;t; ra&shy;<lb/>tio e&longs;t, quia maior globus maius e&longs;t impedimentum, hinc nunquam <lb/>quie&longs;cit minor globus impactus. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 132.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Si globus major in minorem impingatur per lineam directionis, qu&aelig; conne&shy;<lb/>ctat centra, &longs;eruat <expan abbr="e&atilde;dem">eandem</expan> lineam<emph.end type="italics"/>; patet etiam experienti&acirc;, cuius ratio e&longs;t <lb/>minor re&longs;i&longs;tentia minoris globi; &longs;i ver&ograve; &longs;it alia linea directionis, omni&shy;<lb/>n&ograve; reflectitur &longs;uo modo; id e&longs;t mutat lineam; &longs;ed de his omnibus fus&egrave; <lb/>ali&agrave;s; h&icirc;c tant&ugrave;m &longs;ufficiat indica&longs;&longs;e; (&longs;uppo&longs;ita linea directionis cen&shy;<lb/>trali &longs;eu connectente centra, &longs;ic enim deinceps eam appellabimus, in <lb/>quo ca&longs;u duplex determinatio tertiam mediam conflare non pote&longs;t) in&shy;<lb/>dica&longs;&longs;e inquam &longs;ufficiat nouam determinationem, vel e&longs;&longs;e &aelig;qualem prio&shy;<lb/>ri, vel maiorem, vel minorem; &longs;i &aelig;qualis e&longs;t, globus impactus &longs;i&longs;tit; &longs;i <lb/>maior, reflectitur; &longs;i minor, <expan abbr="e&atilde;dem">eandem</expan> lineam, &longs;ed lenti&ugrave;s pro rata pro&shy;<lb/>&longs;equitur. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 133.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Si &longs;it duplex impetus &aelig;qualis ad diuer&longs;as lineas determinatus in eodem mo&shy;<lb/>bili, &longs;ique ill&aelig; &longs;int ex diametro oppo&longs;it&aelig; &longs;i&longs;tere debet mobile<emph.end type="italics"/>; patet; &longs;it enim <lb/>globus vtrimque gemino malleo percu&longs;&longs;us &aelig;quali ictu; haud dubi&egrave; &longs;i&longs;tit; <lb/>cur enim poti&ugrave;s in vnam partem quam in aliam? </s>

<s>cum &longs;imul in vtramque <lb/>moueri non po&longs;&longs;it. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 134.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Si ver&ograve; alter impetus &longs;it inten&longs;ior, po&longs;ito eodem ca&longs;u, haud dubi&egrave; eius de&shy;<lb/>terminatio pr&aelig;ualebit pro rata<emph.end type="italics"/>; patet etiam experienti&agrave;; ratio e&longs;t, quia im&shy;<lb/>petus fortior debiliorem vincit; pugnant enim pro rata per Ax. 15. <lb/>hinc &longs;i &longs;it dupl&ograve; inten&longs;ior, &longs;ubduplum &longs;u&aelig; velocitatis amittet, &longs;i tripl&egrave; <lb/>&longs;ubtriplum, &amp;c. </s>

<s>de quo ali&agrave;s. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 135.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Si duo globi projecti &longs;ibi inuicem occurrant in line&aelig; directionis connectente <lb/>centra, reflectitur vterque &aelig;quali motu, quo ant&egrave;.<emph.end type="italics"/></s><s> Probatur; &longs;unt enim globi <pb xlink:href="026/01/098.jpg" pagenum="66"/>A &amp; B, &amp; A feratur per lineam DE, &amp; B per lineam ED, punctum con&shy;<lb/>tactus &longs;it C, haud dubi&egrave; globus A impactus in B amittit totum &longs;uum im&shy;<lb/>petum per Th.127. &amp; 128. B, item impactus in A amittit totum &longs;uum per <lb/>eandem rationem; globus A producit impetum in B &aelig;qualem &longs;uo per <lb/>Th.60. item B producit in A &aelig;qualem per idem Th. igitur tant&ugrave;m perit <lb/>impetus quant&ugrave;m accedit; igitur in vtroque globo remanet &aelig;qualis im&shy;<lb/>petus priori; igitur &aelig;quali motu vterque mouetur, quod erat dem. </s>

<s>&amp; h&aelig;c <lb/>e&longs;t ratio veri&longs;&longs;ima toties probat&aelig; experienti&aelig;. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 136.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc &aelig;quale &longs;patium conficiet regrediendo po&longs;t reflexionem, quem confeci&longs;&shy;<lb/>&longs;et motu directo, &longs;i propagatus fui&longs;&longs;et &longs;ine obice<emph.end type="italics"/>; nam &aelig;quali motu &aelig;quali <lb/>tempore in eodem plano &longs;eu medio idem &longs;patium decurritur; quid ver&ograve; <lb/>accidat in aliis punctis contactus dicemus infr&agrave;, cum de reflexione. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 137.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Si in eodem mobili duplex impetus producatur, quorum vterque &longs;eor&longs;im <lb/>ad duas lineas &longs;it determinatus qu&aelig; conjunct&aelig; faciant angulum, determinatur <lb/>vterque ad tertiam lineam mediam<emph.end type="italics"/>; &longs;it enim mobile in A. v. <!-- REMOVE S-->g. <!-- REMOVE S-->globus, <lb/>cui &longs;imul imprimatur impetus determinatus ad lineam AD, in plano <lb/>horizontali AF; &longs;i vterque &longs;it &aelig;qualis, ad nouam lineam determinabi&shy;<lb/>tur AE; quippe tant&ugrave;m debet acquirere in horizontali AB, vel in eius <lb/>parallela DE, quantum acquirit in alia horizontali AD, vel in eius pa&shy;<lb/>rallela BE; igitur debet ferri in E; igitur per diagonalem AE; clara e&longs;t <lb/>omnin&ograve; experientia; cuius ratio &agrave; priori h&aelig;c e&longs;t, qu&ograve;d &longs;cilicet impetus <lb/>po&longs;&longs;it determinari ad quamlibet lineam ab alio impetu per Th.118.119. <lb/>igitur in eodem mobili pro rata quilibet alium determinat; igitur &longs;i <lb/>vterque &aelig;qualis e&longs;t, vterque &aelig;qualiter; igitur debet tantum &longs;patij acqui&shy;<lb/>ri in linea vnius, quantum in linea alterius. </s>



</p><p type="main">

<s>Si ver&ograve; impetus per AC &longs;it duplus impetus per AD; accipiatur AC <lb/>dupla AD, ducatur DF &aelig;qualis &amp; parallela AC; linea motus noua <lb/>erit diagonalis AF, quia vtraque determinatio concurrit ad nouam pro <lb/>rata; igitur debet &longs;patium acqui&longs;itum in AC e&longs;&longs;e duplum acqui&longs;iti <lb/>in AD. <!-- KEEP S--></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 138.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Si &longs;it duplex impetus in eodem mobili ad <expan abbr="e&atilde;dem">eandem</expan> lineam determinatus, non <lb/>mutabitur linea; &longs;ed cre&longs;cet motus &amp; &longs;patium<emph.end type="italics"/> Imprimatur impetus in A, <lb/>per AB, quo dato tempore percurratur &longs;patium AB; deinde produca&shy;<lb/>tur &longs;imul alius impetus &aelig;qualis priori in eodem mobili per lineam AB; <lb/>Dico quod eodem tempore percurretur tota AE, dupla &longs;cilicet AB; <lb/>quia &longs;cilicet dupla cau&longs;a non impedita duplum effectum habet per Ax. <!-- REMOVE S--><lb/>13. num.1. duplus impetus duplum motum; igitur duplum &longs;patium; &longs;i <lb/>ver&ograve; &longs;it triplus impetus, triplum erit &longs;patium, &amp;c. </s>

</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 139.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Si line&aelig; duplicis impetus, faciunt angulum acutiorem, longius erit &longs;patium<emph.end type="italics"/><pb xlink:href="026/01/099.jpg" pagenum="67"/><emph type="italics"/>acqui&longs;itum<emph.end type="italics"/>: &longs;int du&aelig; line&aelig; IK IL, mobili &longs;cilicet &longs;tatuto in I; <lb/>haud dubi&egrave; noua linea erit IM; &amp; quo angulus KIL, erit acutior (&longs;up&shy;<lb/>po&longs;itis &aelig;qualibus &longs;emper lateribus IK IL) Diagonalis IM, erit ma&shy;<lb/>ior; donec tandem IL &amp; IK coeant in eandem lineam; tunc enim li&shy;<lb/>nea erit dupla IK per Th. &longs;uperius: quandiu ver&ograve; e&longs;t aliquis angulus in <lb/>I quantumuis acutus, linea motus erit minor dupla IK, ad quam tamen <lb/>propi&ugrave;s &longs;emper accedit; qu&aelig; omnia con&longs;tant ex elementis. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 140.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Si line&aelig; duplicis impetus faciunt angulum obtu&longs;um, &longs;patium acqui&longs;itum erit <lb/>breuius, &amp; e&ograve; breuius qu&ograve; angulus e&longs;t obtu&longs;ior<emph.end type="italics"/>; &longs;int enim <emph type="sup"/>c<emph.end type="sup"/> du&aelig; line&aelig; AD <lb/>AB mobili &longs;tatuto in A, noua linea erit AC per Th. 137. &amp; &longs;i accipia&shy;<lb/>tur angulus obtu&longs;ior HEF; noua linea erit EG, eo rect&egrave; breuior, <lb/>qu&ograve; angulus e&longs;t obtu&longs;ior, non tamen iuxta rationem angulorum; donec <lb/>tandem de&longs;inat angulus, &amp; ED EF co&euml;ant in vnam lineam; tunc enim <lb/>nullum erit &longs;patium, quia &longs;i&longs;ter omnin&ograve; mobile per Th.133.qu&aelig; omnia <lb/>ip&longs;a luce clariora e&longs;&longs;e con&longs;tat; quippe qu&aelig; cum certis experimentis, &amp; <lb/>clari&longs;&longs;imis principiis con&longs;entiant; &longs;ed de his plura infr&agrave;. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 141.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Ex his nece&longs;&longs;aria ducitur ratio, cur impetus duplus ad diuer&longs;as lineas de&shy;<lb/>terminatus non habeat motum duplum, &amp; con&longs;equenter &longs;patium duplum<emph.end type="italics"/>; nec <lb/>enim AE e&longs;t dupla AB, vt con&longs;tat; nam &longs;i line&aelig; &longs;int oppo&longs;it&aelig; ex <lb/>diametro vt BA BE totus de&longs;truitur impetus, per Th.133. &longs;i ver&ograve; vna <lb/>in <expan abbr="e&atilde;dem">eandem</expan> lineam co&euml;at cum ali&acirc;, nihil impetus de&longs;truitur, nec impedi&shy;<lb/>tur per Th.138. igitur qu&agrave; proportione propi&ugrave;s accedet ad oppo&longs;itas; <lb/>pl&ugrave;s de&longs;truetur, &amp; minus erit &longs;patium; &amp; qu&acirc; proportione accedent <lb/>propi&ugrave;s ad co&euml;untes, min&ugrave;s de&longs;truetur, &amp; maius erit &longs;patium, vt con&longs;tat <lb/>ex dictis. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 142.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc impetus ad diuer&longs;as lineas determinati it a pugnant pro rata, vt mi&shy;<lb/>n&ugrave;s pugnent, quorum line&aelig; propi&ugrave;s accedunt ad co&euml;untes; pl&ugrave;s ver&ograve;, quorum <lb/>line&aelig; propi&ugrave;s accedunt ad oppo&longs;itas, idque iuxta proportiones Diagonalium,<emph.end type="italics"/><lb/>quod totum &longs;equitur ex dictis. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Ob&longs;eruabis vt facili&ugrave;s concipias duos impetus ad duas lineas deter&shy;<lb/>minatos; finge tibi nauim &agrave; diuer&longs;is ventis impul&longs;am, &longs;eu lapidem pro&shy;<lb/>jectum &egrave; naui mobili; &longs;ed de his plura in lib.4. cum de motu mixto. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 143.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Impetus &longs;emel productus, quamdiu durat motus, con&longs;eruatur.<emph.end type="italics"/></s><s> Probatur, <lb/>quia non pote&longs;t e&longs;&longs;e effectus, ni&longs;i &longs;it eius cau&longs;a per Ax. 8. igitur &longs;i e&longs;t mo&shy;<lb/>tus, e&longs;t impetus. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 144.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Impetus non con&longs;eruatur &agrave; cau&longs;a prim&ograve; productiua.<emph.end type="italics"/></s><s> Probatur; quia proii-<pb xlink:href="026/01/100.jpg" pagenum="68"/>ciatur mobile per Po&longs;tulatum, etiam mouetur &longs;eparatum &agrave; potentia mo&shy;<lb/>trice per hypoth. </s>

<s>6. igitur non con&longs;eruatur &agrave; potentia motrice per Ax. <!-- REMOVE S--><lb/>10. igitur nec &agrave; caus&acirc; prim&ograve; productiua. </s>

</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 145.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc ab alia caus&acirc; con&longs;eruari nece&longs;&longs;e e&longs;t impetum<emph.end type="italics"/>: Probatur, quia impe&shy;<lb/>tus non e&longs;t &agrave; &longs;e, quia de&longs;truitur aliquando per Ax. 14. igitur con&longs;eruatur <lb/>ab alio per Ax.14. num. </s>

<s>1. non &agrave; cau&longs;a prim&ograve; productiua per Th.144.igi&shy;<lb/>tur ab alia, eaque applicata per Ax. <!-- REMOVE S-->10. qu&aelig;cumque tandem illa &longs;it, ali&shy;<lb/>quando cau&longs;am primam e&longs;&longs;e demon&longs;trabimus; nunc ver&ograve; &longs;ufficiat dixi&longs;&shy;<lb/>&longs;e dari aliquam cau&longs;am reuer&acirc; applicatam, qu&aelig; ip&longs;um con&longs;eruat impe&shy;<lb/>tum; imm&ograve; ex hac ip&longs;a rerum con&longs;eruatione argumentum aliquando <lb/>ducemus, quo Deum ip&longs;um exi&longs;tere demon&longs;trabimus. </s>

</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 146.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Si impetus con&longs;eruaretur &agrave; cau&longs;a prim&ograve; productiua, nunquam de&longs;truere&shy;<lb/>tur, quamdiu e&longs;&longs;et applicata.<emph.end type="italics"/></s><s> Demon&longs;tratur, quia e&longs;&longs;et cau&longs;a nece&longs;&longs;aria <lb/>(nam de hac ip&longs;a loquor) igitur &longs;emper ageret, igitur &longs;emper con&shy;<lb/>&longs;eruaret, quod e&longs;t contra experientiam; nam reuer&acirc; impetus pro&shy;<lb/>ductus deor&longs;um &agrave; corpore graui motu naturaliter accelerato de&longs;truitur, <lb/>vt patet; pr&aelig;terea &longs;i corpus graue con&longs;eruaret impetum prim&ograve; produ&shy;<lb/>ctum, non produceret nouum contra experientiam; quippe cau&longs;a ne&shy;<lb/>ce&longs;&longs;aria non pl&ugrave;s agit vno in&longs;tanti qu&agrave;m alio, per Ax.12. adde quod im&shy;<lb/>petus de&longs;truitur ad exigentiam alterius, quidquid tandem illud &longs;it per <lb/>Ax.14. num.2. &amp; 3. &longs;ed cau&longs;a prim&ograve; productiua impetus non nouit rerum <lb/>exigentiam; igitur illi facere &longs;atis non pote&longs;t; ex hoc etiam capite cau&shy;<lb/>&longs;&aelig; prim&aelig; exi&longs;tentiam &longs;uo loco demon&longs;trabimus. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Ob&longs;eruabis prim&ograve; rem quamlibet ideo de&longs;trui, quia ce&longs;&longs;at cau&longs;a con&shy;<lb/>&longs;eruans illam con&longs;eruare; quippe quod de&longs;truitur eo in&longs;tanti dicitur de&shy;<lb/>&longs;trui, quo prim&ograve; non e&longs;t, &longs;eu quo incipit prim&ograve; non e&longs;&longs;e; atqui incipit <lb/>prim&ograve; non e&longs;&longs;e &longs;eu de&longs;init e&longs;&longs;e, cum de&longs;init con&longs;eruari. </s></p><p type="main">

<s>Secund&ograve; ob&longs;eruabis pr&aelig;clarum natur&aelig; in&longs;titutum, quod etiam ex ip&longs;is <lb/>hypothe&longs;ibus con&longs;tat, quo fit vt qualitates qu&aelig; carent contrario &agrave; cau&longs;a <lb/>prim&ograve; productiua con&longs;eruentur, vt lumen; ne &longs;i ab alia con&longs;eruarentur, <lb/>de&longs;truerentur vmquam; cum earum de&longs;tructionem nihil exigeret per <lb/>Ax.14.n.2. &amp; 3. at ver&ograve; qualitates, qu&aelig; contrarias habent: &longs;i qu&aelig; &longs;unt, <lb/>&agrave; cau&longs;a prim&ograve; productiua minim&egrave; con&longs;eruantur; cum enim ideo con&shy;<lb/>trarium dicatur de&longs;truere contrarium, quia exigit eius de&longs;tructionem, id <lb/>e&longs;t, ne con&longs;eruetur amplius; cert&egrave; vt cau&longs;a con&longs;eruans ce&longs;&longs;et con&longs;eruare, <lb/>debet no&longs;&longs;e illam exigentiam; atqui nulla cognitione pollent cau&longs;&aelig; ill&aelig; <lb/>motrices naturales, de quibus e&longs;t qu&aelig;&longs;tio. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 147.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Tamdiu con&longs;eruatur impetus, quamdiu nihil exigit eius destructionem<emph.end type="italics"/>; quia <lb/>de&longs;truitur tant&ugrave;m ad exigentiam alicuius, quidquid tandem illud &longs;it, de <pb xlink:href="026/01/101.jpg" pagenum="69"/>quo infr&agrave;, per Ax.14.num.2. cert&egrave; tamdiu non de&longs;truitur, quamdiu nihil <lb/>e&longs;t, quod exigat eius de&longs;tructionem; igitur tamdiu con&longs;eruatur per Ax. <!-- REMOVE S--><lb/>14.num.3. </s>

</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 1.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Inde certa ducitur ratio, cur mobile etiam &longs;eparatum &agrave; manu mouea&shy;<lb/>tur; quia &longs;cilicet ip&longs;i adhuc ine&longs;t impetus, qui e&longs;t cau&longs;a motus; quippe <lb/>&longs;uppo&longs;ui iam ant&egrave; de hac hypothe&longs;i quod &longs;it, non tamen propter quid &longs;it; <lb/>igitur h&aelig;c e&longs;t germana illius ratio &amp; cau&longs;a. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Corollarium.<emph.end type="italics"/> 2.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Hinc etiam rationem ducemus &aelig;qu&egrave; pr&aelig;claram in lib.2. motus natu&shy;<lb/>raliter accelerati. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 148.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Impetus productus aliquando de&longs;truitur<emph.end type="italics"/>; Probatur, quia mobile, quod <lb/>ant&egrave; mouebatur, de&longs;init tandem moueri per hyp. </s>

<s>4. igitur de&longs;truitur <lb/>impetus; alioqui &longs;i remaneret, e&longs;&longs;et cau&longs;a nece&longs;&longs;aria &longs;ine effectu contra <lb/>Ax.12. ideo porr&ograve; de&longs;truitur, quia aliquid exigit eius de&longs;tructionem, <lb/>quippe h&aelig;c e&longs;t vnica de&longs;tructionis ratio per Ax.14. num.2. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 149.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>In lineis oppo&longs;itis impetus de&longs;truitur ab impetu &longs;uo modo<emph.end type="italics"/>; &longs;it enim globus <lb/>proiectus ver&longs;us au&longs;trum; cui deinde imprimatur nouus impetus ver&shy;<lb/>&longs;us Boream; de&longs;truitur prior vt con&longs;tat, igitur ad exigentiam alicuius, <lb/>&longs;ed nihil e&longs;t quod po&longs;&longs;it exigere, ni&longs;i nouus impetus, &longs;cilicet mediat&egrave;; <lb/>nihil enim aliud e&longs;t applicatum, igitur nihil aliud exigit per Ax. 10. <lb/>h&aelig;c porr&ograve; exigentia non e&longs;t immediata, &longs;ed mediata, vt dixi. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 150.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Impetus naturalis innatus exigit de&longs;tructionem alterius, qui ab extrin&longs;eco <lb/>ad diuer&longs;am lineam corpori graui impre&longs;&longs;us e&longs;t &longs;cilicet mediat&egrave;,<emph.end type="italics"/> experientia <lb/>certa e&longs;t in proiectis, qu&aelig; tandem quie&longs;cunt; igitur ad exigentiam ali&shy;<lb/>cuius, &longs;ed illud tant&ugrave;m e&longs;t impetus innatus; nec enim e&longs;t &longs;ub&longs;tantia <lb/>corporis; t&ugrave;m quia qualitas &longs;ub&longs;tanti&aelig; non opponitur; t&ugrave;m quia nulla <lb/>e&longs;&longs;et ratio, cur &longs;ub&longs;tantia de&longs;trueret poti&ugrave;s vno in&longs;tanti vnum gradum, <lb/>qu&agrave;m duos, qu&agrave;m tres; adde quod ex duobus violentis oppo&longs;itis alte&shy;<lb/>rum de&longs;truit; igitur impetus e&longs;t cau&longs;a &longs;ufficiens de&longs;tructiua impetus, <lb/>igitur non e&longs;t ponenda alia, eo &longs;cilicet modo, quo diximus. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 151.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>In reflexione de&longs;truitur aliquid impotus &longs;altem per accidens<emph.end type="italics"/>; patet expe&shy;<lb/>rientia, &longs;iue propter nouam determinationem, &longs;iue propter attritum, <lb/>vel pre&longs;&longs;ionem partium, de quo infr&agrave;. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 152.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc &longs;i excipias tant&ugrave;m impetum naturalem innatum, qui per &longs;uam de&shy;<lb/>terminationem nece&longs;&longs;ariam, &amp; quam nunquam mutat, pugnat cum omni<emph.end type="italics"/><pb xlink:href="026/01/102.jpg" pagenum="70"/><emph type="italics"/>extrin&longs;eco ad aliam lineam determinato, &amp; cum ip&longs;o acqui&longs;ito, quando mu&shy;<lb/>tat lineam perpendicularem deor&longs;um, de quo infr&agrave;; &longs;i hunc igitur excipias, <lb/>omnes aly pugnant tant&ugrave;m ratione diuer&longs;&aelig; line&aelig;, &longs;eu determinationis, in eodem <lb/>mobili:<emph.end type="italics"/> Vnde ille idem, qui modo pugnat prob&egrave; conueniet, &longs;i ad ean&shy;<lb/>dem lineam determinetur. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Ob&longs;eruabis prim&ograve;, pr&aelig;clarum natur&aelig; in&longs;titutum, quo fit, vt impe&shy;<lb/>tus perennis non &longs;it; vnde cert&egrave; infinita propemodum emergerent ab&shy;<lb/>&longs;urda, &amp; incommoda. </s></p><p type="main">

<s>Secund&ograve;, faciliorem modum de&longs;tructionis impetus in&longs;titui non po&shy;<lb/>tui&longs;&longs;e, imm&ograve; nec excogitari po&longs;&longs;e; qu&agrave;m enim facil&egrave;, vel impetus op&shy;<lb/>po&longs;itus in mobili producitur, vel corpus durum opponitur &amp;c. </s></p><p type="main">

<s>Terti&ograve;, pr&aelig;cipuam rationem huius de&longs;tructionis ducendam e&longs;&longs;e ex <lb/>Ax.6. in quo dicimus nihil e&longs;&longs;e fru&longs;tr&agrave;, cumque ordinem &agrave; natura e&longs;&longs;e <lb/>in&longs;titutum, vt poti&ugrave;s aliquid de&longs;truatur, &amp; de&longs;inat e&longs;&longs;e, qu&agrave;m fru&longs;tr&agrave; &longs;it, <lb/>&amp; dicimus de&longs;trui ad exigentiam totius natur&aelig;. </s></p><p type="main">

<s>Quart&ograve;, cum impetus &longs;uo fine caret, fru&longs;tr&agrave; e&longs;t; finis impetus e&longs;t mo&shy;<lb/>tus, vt &longs;&aelig;p&egrave; diximus, &longs;ic cum globus impactus in alium &aelig;qualem &longs;tatim <lb/>ab ictu &longs;i&longs;tit immobilis; certe ne fru&longs;tr&agrave; &longs;it impetus, de&longs;truitur per Ax.6. <lb/>&amp; per Ax. 14. num.2. cum ver&ograve; determinatio altera maior e&longs;t, cert&egrave; pr&aelig;&shy;<lb/>ualet tant&ugrave;m pro rata; igitur minor e&longs;t motus; igitur, ne aliqui gradus <lb/>impetus &longs;int fru&longs;tr&agrave;, de&longs;truuntur, cum ver&ograve; &longs;unt duo impetus in eodem <lb/>mobili, vt in naui mobili ad lineas oppo&longs;itas determinati; haud dubi&egrave; <lb/>maior impetus pr&aelig;ualet pro rata per Ax. 15. Igitur non mod&ograve; totus <lb/>impetus minor perit, ne &longs;it fru&longs;tr&agrave;; &longs;ed etiam aliquot gradus maioris, ne <lb/>&longs;int etiam fru&longs;tr&agrave;; nec enim in communem lineam co&iuml;re po&longs;&longs;unt. </s></p><p type="main">

<s>Denique quando &longs;unt duo impetus ad lineas diuer&longs;as determinati, <lb/>&longs;ed non oppo&longs;itas ex diametro, pugnant pro diuer&longs;o oppo&longs;itionis gradu, <lb/>vt &longs;upr&agrave; fus&egrave; dictum e&longs;t. </s>

<s>Igitur cum totus impetus non habeat totum <lb/>motum, quod duplex illa determinatio impedit, ne aliqui gradus <lb/>&longs;int fru&longs;tr&agrave;, de&longs;truuntur; igitur vides impetum impre&longs;&longs;um ab ex&shy;<lb/>trin&longs;eco de&longs;trui tant&ugrave;m ne &longs;it fru&longs;tr&agrave;; faceret enim vt e&longs;&longs;et fru&longs;tr&agrave; vel <lb/>nouus impetus, vel determinato noua, &amp; in hoc &longs;en&longs;u dicitur impetus <lb/>de&longs;trui ab impetu. </s></p><p type="main">

<s>Quint&ograve;, &longs;i de&longs;trueretur mobile, etiam de&longs;trueretur impetus per idem <lb/>Ax. 6. quia e&longs;&longs;et fru&longs;tr&agrave; &longs;eparatum; imm&ograve; ex hoc vno principio demon&shy;<lb/>&longs;tramus accidentia &amp; formas &longs;ub&longs;tantiales materiales non po&longs;&longs;e natura&shy;<lb/>liter con&longs;eruari extra &longs;uum &longs;ubiectum, quia &longs;cilicet e&longs;&longs;ent fru&longs;tr&agrave;; quip&shy;<lb/>pe finem &longs;uum habent in &longs;ubiecto. </s></p><p type="main">

<s>Sext&ograve;, Impetus naturalis innatus nunquam de&longs;truitur; quia nunquam <lb/>e&longs;t fru&longs;tr&agrave;; quippe &longs;emper habet alterum &longs;uorum effectuum formalium, <lb/>id e&longs;t vel motum deor&longs;um, vel grauitationem, adde quod fru&longs;tr&agrave; de&shy;<lb/>&longs;trueretur, cum &longs;it &longs;emper applicata potentia, id e&longs;t ip&longs;a grauitas, &longs;ed de <lb/>his infr&acirc; fus&egrave;. </s></p><pb xlink:href="026/01/103.jpg" pagenum="71"/><p type="main">

<s>Septim&ograve;, Impetus &longs;ur&longs;um de&longs;truitur etiam, quia e&longs;t fru&longs;tr&agrave;; quippe <lb/>naturalis detrahit aliquid &longs;patij pro rata; igitur ne aliquid impetus &longs;it <lb/>fru&longs;tr&agrave;, de&longs;truitur; idem dico de impetu per inclinatam &longs;ur&longs;um, lic&egrave;t <lb/>min&ugrave;s de&longs;truatur qu&agrave;m in perpendiculari &longs;ur&longs;um; idem de impetu per <lb/>inclinatam deor&longs;um, &longs;ed min&ugrave;s adhuc, &longs;ed h&aelig;c acuratiori meditationi <lb/>&longs;unt relinquenda; quod reuer&acirc; pr&aelig;&longs;tabimus in lib.4. de motu mixto; <lb/>quidquid &longs;it, con&longs;tat ex dictis per idem Principium probari po&longs;&longs;e de&shy;<lb/>&longs;tructionem impetus, &longs;cilicet ne &longs;it fru&longs;tr&agrave;; &longs;ed de his ali&agrave;s fus&egrave;. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 153.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Impetus productus ab extrin&longs;eco e&longs;t tant&ugrave;m contrarius ratione diuer&longs;&aelig; de&shy;<lb/>terminationis, &longs;eu diuer&longs;&aelig; line&aelig;<emph.end type="italics"/>; Probatur prim&ograve;, quia vterque ad omnem <lb/>lineam e&longs;t indifferens per Th.113. igitur vnus non e&longs;t alteri contrarius <lb/>ratione entitatis; c&ugrave;m vterque &longs;imilem motum, imm&ograve; <expan abbr="e&utilde;dem">eundem</expan> habere <lb/>po&longs;&longs;it, vt patet ex dictis: </s>
<s>Igitur ratione tant&ugrave;m line&aelig; vnus alteri e&longs;t <lb/>contrarius; hinc min&ugrave;s e&longs;t contrarietatis, quo min&ugrave;s e&longs;t oppo&longs;itionis <lb/>inter lineas &amp; contr&agrave;. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 154.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Impetus naturalis acqui&longs;itus e&longs;t tant&ugrave;m contrarius alteri extrin&longs;eco ratio&shy;<lb/>ne line&aelig;.<emph.end type="italics"/></s><s> Probatur eodem modo; quia determinari pote&longs;t ad omnem li&shy;<lb/>neam, vt patet ex reflexione grauis cadentis. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 155.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Impetus naturalis innatus non e&longs;t tant&ugrave;m contrarius ratione line&aelig;<emph.end type="italics"/>; quia <lb/>&longs;cilicet non pote&longs;t determinari ad omnem lineam, patet, alioquin cor&shy;<lb/>pus graue, quod &longs;ur&longs;um po&longs;t ca&longs;um reflectitur non de&longs;cenderet amplius, <lb/>de quo ali&agrave;s, h&aelig;c enim cur&longs;im tant&ugrave;m per&longs;tringo, ne quid aliis libris <lb/>detrahatur. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 156.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Impetus ex naturali acqui&longs;ito pote&longs;t fieri violentus<emph.end type="italics"/>; vt patet in motu re&shy;<lb/>flexo grauium; ratio e&longs;t. </s>

<s>quia mutatur linea. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 157.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Impetus ex non contrario eidem fit contrarius<emph.end type="italics"/>; vt patet in eodem ca&longs;u; <lb/>nam impetus naturalis innatus, qui in de&longs;cen&longs;u non erat contrarius <lb/>acqui&longs;ito, in motu &longs;ur&longs;um reflexo fit contrarius. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 158.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Impetus deor&longs;um ab extrin&longs;eco non e&longs;t contrarius naturali innato ratione <lb/>line&aelig;,<emph.end type="italics"/> quia &longs;cilicet e&longs;t determinatus ad eandem lineam, &longs;i tamen e&longs;t con&shy;<lb/>trarius, id tant&ugrave;m e&longs;t ratione propagationis impetus acqui&longs;iti, vel ac <lb/>celerationis motus; quod reuer&agrave; multa, &amp; ben&egrave; long&acirc; explicatione indi&shy;<lb/>get, quam con&longs;ule in lib.4. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Ob&longs;eruabis cogno&longs;ci tant&ugrave;m contrarietatem qualitatum ex mutua de&shy;<lb/>&longs;tructione; cur ver&ograve; vna qualitas dicatur de&longs;truere aliam, &amp; cur illam <pb xlink:href="026/01/104.jpg" pagenum="72"/>de&longs;tructionem exigat; maximum my&longs;terium e&longs;t, quod alibi enucleabi&shy;<lb/>mus; qu&agrave;m multa enim &longs;uper hac re tacuere Philo&longs;ophi! <!-- KEEP S--></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 159.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Impetus &longs;ibi ip&longs;i pote&longs;t reddi contrarius,<emph.end type="italics"/> vt reuer&acirc; accidit in reflexione, <lb/>in qua de&longs;truitur impetus ex parte propter diuer&longs;as determinationes; <lb/>cum &longs;cilicet corpus reflectens mouetur; igitur impetus prout determina&shy;<lb/>tus ad lineam incidenti&aelig; e&longs;t aliquo modo &longs;ibi ip&longs;i contrarius, prout e&longs;t <lb/>determinatus ad lineam reflexionis. </s></p><p type="main">

<s>Iam fer&egrave; tumultuatim, &longs;i qu&aelig; &longs;unt reliqua, Theoremata congeremus. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 160.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Impetus violentus intendi pote&longs;t &agrave; naturali, &amp; vici&longs;&longs;im<emph.end type="italics"/>; patet in projectis <lb/>deor&longs;um. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 161.<emph.end type="center"/></s></p><p type="main">

<s>Idem impetus pote&longs;t <expan abbr="e&utilde;dem">eundem</expan> alium aliquando pl&ugrave;s, aliquando min&ugrave;s <lb/>intendere. </s>

<s>v. <!-- REMOVE S-->g. <!-- REMOVE S-->4. gradus impetus additi aliis 4. per <expan abbr="e&atilde;dem">eandem</expan> lineam <lb/>iidem ei&longs;dem, min&ugrave;s intendunt, vt iam &longs;upr&agrave; &longs;atis fus&egrave; dictum e&longs;t. </s>



</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 162.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Impetus dici pote&longs;t propri&egrave; de&longs;trui ad exigentiam totius natur&aelig;<emph.end type="italics"/> per Ax.14. <lb/>num.2. vt con&longs;tat ex multis Theorematis &longs;uperioribus. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 163.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Omnis dici debet incipere, &amp; de&longs;inere intrin&longs;ec&egrave;, &amp; extrin&longs;ec&egrave;<emph.end type="italics"/>; quod enim <lb/>hoc in&longs;tanti primo e&longs;t, immediat&egrave; antecedenti vltimo non fuit, &amp; quod <lb/>primo non e&longs;t hoc in&longs;tanti, immediat&egrave; ant&egrave; vltimo fuit, nec pote&longs;t e&longs;&longs;e <lb/>immediat&egrave; p&ograve;&longs;t, ni&longs;i &longs;it immediat&egrave; ant&egrave;, &amp; vici&longs;&longs;im. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 164.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Ideo producitur hic impetus numero poti&ugrave;s, qu&agrave;m alius omnin&ograve; &longs;imilis<emph.end type="italics"/>; quia <lb/>potentia motrix e&longs;t determinata ad tale indiuiduum &longs;iue &agrave; &longs;e, &longs;iue ab <lb/>alio; idem enim de illa dicendum e&longs;t, quod de aliis cau&longs;is naturalibus; <lb/>porr&ograve; idem dici debet de de&longs;tructione, quod de productione. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Ob&longs;eruabis breuiter aliqua, qu&aelig; fort&egrave; in no&longs;tris Theorematis fuere <lb/>omi&longs;&longs;a. </s></p><p type="main">

<s>Prim&ograve; qualitates, qu&aelig; &agrave; cau&longs;a prim&ograve; productiua con&longs;eruantur, ab ea <lb/>intendi non po&longs;&longs;e; quia &longs;ingulis in&longs;tantibus nouum effectum non pro&shy;<lb/>ducit; exemplum habes in luce; &longs;ecus vero de iis dicendum e&longs;t, qu&aelig; &agrave; <lb/>cau&longs;a prim&ograve; productiua non con&longs;eruantur. </s></p><p type="main">

<s>Secund&ograve; qualitates, qu&aelig; contrarias habent, etiam de&longs;trui po&longs;&longs;e ab <lb/>alio, quam ab iis, &longs;cilicet ad exigentiam totius natur&aelig;; ne &longs;cilicet &longs;int <lb/>fru&longs;tr&agrave;. </s></p><p type="main">

<s>Terti&ograve; aliqua carere contrario, non tamen con&longs;eruari &agrave; cau&longs;a prim&ograve; <lb/>productiua. </s>

<s>v.g. <!-- REMOVE S-->anima bruti, qu&aelig; de&longs;truitur ad exigentiam totius natu&shy;<lb/>r&aelig;, n&ccedil; &longs;it fru&longs;tr&agrave;. </s>

</p><pb xlink:href="026/01/105.jpg" pagenum="73"/><p type="main">

<s>Quart&ograve;, impetum inten&longs;iorem in projectis diuti&ugrave;s durare; quia cum <lb/>&longs;en&longs;im de&longs;truatur; cert&egrave; plures partes maiori tempore de&longs;truuntur, qu&agrave;m <lb/>pauciores. </s></p><p type="main">

<s>Quint&ograve;, &longs;i totus impetus de&longs;trueretur vno in&longs;tanti, minima re&longs;i&longs;tentia <lb/>&longs;ufficeret ad motum impediendum: adde quod contraria pugnant pro <lb/>rata per Ax.15. </s></p><p type="main">

<s>Sext&ograve;, ob&longs;eruabis plurima in hoc libro qua&longs;i obiter e&longs;&longs;e indicata, qu&aelig; <lb/>in aliis fus&egrave; explicata maiorem lucem accipient. </s></p><p type="main">

<s>Septim&ograve;, denique totam rem i&longs;tam, qu&aelig; pertinet ad impetum paul&ograve; <lb/>fu&longs;ius pertractatam in hoc primo libro; qu&ograve;d &longs;cilicet ab ea reliqua fer&egrave; <lb/>omnia pendeant, qu&aelig; in hoc tractatu habentur; &longs;ed de his &longs;atis. <lb/><figure id="id.026.01.105.1.jpg" xlink:href="026/01/105/1.jpg"/></s></p><pb xlink:href="026/01/106.jpg" pagenum="74"/><figure id="id.026.01.106.1.jpg" xlink:href="026/01/106/1.jpg"/><p type="main">

<s><emph type="center"/>LIBER SECVNDVS, <lb/><emph type="italics"/>DE MOTV NATVRALI.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>MOtus localis naturalis lat&egrave; &longs;umptus e&longs;t, <lb/>qui ab aliqua caus&acirc; naturali ponitur; <lb/>&longs;trict&egrave; ver&ograve; &longs;umitur pro motu grauium <lb/>deor&longs;um, &agrave; principio intrin&longs;eco &longs;altem <lb/>&longs;en&longs;ibiliter; In hoc vltimo &longs;en&longs;u mo&shy;<lb/>tum naturalem v&longs;urpabo; &longs;it ergo. <lb/><gap desc="hr tag"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>DEFINITIO 1.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s><emph type="italics"/>MOtus localis naturalis e&longs;t, qui e&longs;t &agrave; grauitate deor&longs;um.<emph.end type="italics"/> h&aelig;c defini&shy;<lb/>tio vix aliqua explicatione indiget; dicitur e&longs;&longs;e &agrave; grauitate, <lb/>quidquid &longs;it grauitas, &longs;iue qualitas di&longs;tincta, &longs;iue non. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Definitio<emph.end type="italics"/> 2.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s><emph type="italics"/>Motus &aelig;quabilis e&longs;t, quo &aelig;qualibus quibu&longs;cumque temporibus &aelig;qualia per&shy;<lb/>curruntur &longs;patia ab eodem mobili.<emph.end type="italics"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Definitio<emph.end type="italics"/> 3.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s><emph type="italics"/>Motus naturaliter acceleratus e&longs;t, quo &longs;ecundo tempore &aelig;quali primo ma&shy;<lb/>ius &longs;patium acquiritur, &amp; tertio, qu&agrave;m &longs;ecundo, &amp; quarto qu&agrave;m tertio, atque <lb/>ita deinceps; nulla &longs;cilicet addita vi ab extrin&longs;eco &longs;altem &longs;en&longs;ibiliter.<emph.end type="italics"/></s></p><p type="main">

<s>Definit aliter hunc motum Galileus; dicit enim eum e&longs;&longs;e, qui &aelig;quali&shy;<lb/>bus temporibus &aelig;qualia acquirit velocitatis momenta; &longs;ed profect&ograve; non <lb/>conuenit h&aelig;c definitio omni motui naturaliter accelerato, v. <!-- REMOVE S-->g. <!-- REMOVE S-->motui <lb/>de&longs;cen&longs;us funependuli, vel in orbe cauo, vel etiam in plano decliui ma&shy;<lb/>xim&aelig; longitudinis; definitio no&longs;tra clarior e&longs;t. </s>



</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Hypothe&longs;is<emph.end type="italics"/> 1.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s><emph type="italics"/>Corpus graue cadit deor&longs;um, &amp; cadens ex maiori altitudine maiorem ictum <lb/>infligit quam &longs;i caderet ex minore<emph.end type="italics"/>; &longs;i quis hoc neget hoc probet, patet ma&shy;<lb/>nife&longs;ta experientia. </s></p><pb xlink:href="026/01/107.jpg" pagenum="75"/><p type="main">

<s><emph type="center"/><emph type="italics"/>Hypothe&longs;is<emph.end type="italics"/> 2.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s><emph type="italics"/>Arcus maior &amp; minor eiu&longs;dem funependuli &aelig;qualibus fer&egrave; temporibus, <lb/>percurruntur<emph.end type="italics"/>; h&aelig;c etiam &longs;&aelig;pi&ugrave;s probata e&longs;t, &amp; &longs;i quis fidem detrectat, <lb/>probare conetur. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Hypothe&longs;is<emph.end type="italics"/> 3.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Globus per planum inclinatum l&aelig;uigatum de&longs;cendens &longs;ecundum &longs;pa&shy;<lb/>tium citi&ugrave;s percurrit, qu&agrave;m primum; quod etiam &longs;en&longs;u percipi pote&longs;t, <lb/>&amp; tam &longs;&aelig;p&egrave; probatum e&longs;t, vt nemo iam negare audeat motus naturalis <lb/>accelerationem. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Hypothe&longs;is<emph.end type="italics"/> 4.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s><emph type="italics"/>Omne tempus &longs;en&longs;ibile non e&longs;t; idem dico de &longs;patio,<emph.end type="italics"/> quod nemo etiam <lb/>negare au&longs;it; alioquin &longs;i quis negaret, dicat mihi qu&aelig;&longs;o quot &longs;int in mi&shy;<lb/>nuto hor&aelig; in&longs;tantia? </s>

<s>quot in apice acus puncta? </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Axioma<emph.end type="italics"/> 1.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s><emph type="italics"/>Impetus additus alteri, &amp; determinatus ad <expan abbr="e&atilde;dem">eandem</expan> lineam, facit maiorem <lb/>&amp; inten&longs;iorem impetum<emph.end type="italics"/>; patet, &amp; vici&longs;&longs;im, &amp; detractus alteri minorem <lb/>facit, &amp; vici&longs;&longs;im. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Axioma<emph.end type="italics"/> 2.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s><emph type="italics"/>Qu&acirc; proportione cre&longs;cit cau&longs;a, e&acirc;dem cre&longs;cit effectus, &amp; vici&longs;&longs;im, &longs;i eodem <lb/>modo eidemque &longs;ubjecto &longs;it applicata,<emph.end type="italics"/> probatur per Ax.12. l. <!-- REMOVE S-->1. &amp; qu&acirc; pro&shy;<lb/>portione illa decre&longs;cit, hic decre&longs;cit, &amp; vici&longs;&longs;im. </s>

</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Axioma<emph.end type="italics"/> 3.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s><emph type="italics"/>Eadem cau&longs;a nece&longs;&longs;aria non impedita &longs;ubjecto apte applicata &aelig;qualibus <lb/>temporibus &aelig;qualem effectum producit, &amp; contr&agrave;.<emph.end type="italics"/></s><s> Probatur per Ax.12.l. </s>

<s>1. &amp; <lb/>vici&longs;&longs;im &aelig;qualis effectus &longs;upponit &aelig;qualem cau&longs;am. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Axioma<emph.end type="italics"/> 4.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s><emph type="italics"/>Ille effectus, qui non producitur &agrave; caus&acirc; prim&acirc;, &amp; ad cuius productionem <lb/>nulla cau&longs;a extrin&longs;eca e&longs;t applicata, producitur ab intrin&longs;eco<emph.end type="italics"/>; probatur, quia <lb/>habere debet aliquam cau&longs;am per Ax.8. <!-- KEEP S--></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Axioma<emph.end type="italics"/> 5.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s><emph type="italics"/>Illa cau&longs;a plus agit proportionaliter qu&aelig; habet minorem re&longs;istentiam; min&ugrave;s <lb/>ver&ograve;, qu&aelig; maiorem, qu&aelig; demum &aelig;qualem, &aelig;quali proportione agit.<emph.end type="italics"/> v.g. <!-- REMOVE S-->cau&longs;a, <lb/>cuius virtus, vel actiuitas e&longs;t vt 20. &amp; re&longs;i&longs;tentia vt 10. agit in maiori <lb/>proportione, qu&agrave;m illa cuius actiuitas e&longs;t 30. &amp; re&longs;i&longs;tentia 20. in minori <lb/>ver&ograve; qu&agrave;m ea, cuius actiuitas e&longs;t vt 3. &amp; re&longs;i&longs;tentia vt 1. in &aelig;quali de&shy;<lb/>nique cum illa, cuius actiuitas e&longs;t vt 4. &amp; re&longs;i&longs;tentia vt 2. <!-- KEEP S--></s>

</p><p type="main">

<s>Hoc Axioma certi&longs;&longs;imum e&longs;t; quippe 20. facili&ugrave;s &longs;uperabunt 10. qu&agrave;m <lb/>30. 20. &amp; difficili&ugrave;s quam 3. 1. &amp; &aelig;qu&egrave; facil&egrave;, ac 4. 2. In motu locali <lb/>res e&longs;t clari&longs;&longs;ima; quippe vires vt 12. tam facil&egrave; mouebunt 12. libras, <lb/>qu&agrave;m vires vt 4. 4.libras; &longs;ed facili&ugrave;s, qu&agrave;m vires vt 20. 30.libras, &amp; dif&shy;<lb/>ficili&ugrave;s qu&agrave;m vires vt 4. 3. libras; quid clarius? </s>

<s>Igitur illa cau&longs;a facili&ugrave;s <pb xlink:href="026/01/108.jpg" pagenum="76"/>&longs;uperat re&longs;i&longs;tentiam impedimenti, qu&aelig; habet maiorem proportionem <lb/>virium cum re&longs;i&longs;tentia, qu&agrave;m qu&aelig; minorem. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Si quando appellandum erit aliquod Axioma vel Theorema lib. 

1.ci&shy;<lb/>tabitur Liber. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 1.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s><emph type="italics"/>Datur motus localis naturalis, i&longs;que ab intrin&longs;eco.<emph.end type="italics"/></s><s> Probatur; corpus gra&shy;<lb/>ue mouetur localiter deor&longs;um per hypoth. </s>

<s>hic motus e&longs;t ab intrin&longs;eco, <lb/>quod probatur; non e&longs;t ab vll&acirc; caus&acirc; extrin&longs;ec&acirc;; igitur e&longs;t ab intrin&longs;eca <lb/>per Ax.4. antecedens probatur inductione fact&acirc; omnium extrin&longs;ecorum. </s>

<s><lb/>Prim&ograve; non e&longs;t &agrave; cau&longs;a prima, vt aliquis fort&egrave; min&ugrave;s prudenter, &amp; magis <lb/>pi&egrave;, qu&agrave;m par &longs;it, diceret; quia ille effectus tribui tant&ugrave;m debet cau&longs;&aelig; <lb/>prim&aelig;, qui nullam habere pote&longs;t cau&longs;am &longs;ecundam applicatam, vt patet; <lb/>&longs;ed hic effectus pote&longs;t habere cau&longs;am &longs;ecundam applicatam, quam a&longs;&longs;i&shy;<lb/>gnabimus infr&agrave;; deinde cau&longs;a prima agit tant&ugrave;m naturaliter iuxta exi&shy;<lb/>gentiam cau&longs;arum &longs;ecundarum; igitur ideo moueret corpus graue deor&shy;<lb/>&longs;um; quia tunc motum corpus graue exigeret; &longs;ed hoc mihi &longs;ufficit, vt <lb/>dicatur hic motus e&longs;&longs;e ab intrin&longs;eco; pr&aelig;terea, &longs;i dicatur Deus mouere <lb/>corpus graue deor&longs;um iuxta illius exigentiam, dicetur etiam t&ugrave;m cale&shy;<lb/>facere, t&ugrave;m illuminare, ad exigentiam ignis; quippe t&agrave;m mihi &longs;en&longs;ibile <lb/>e&longs;t corpus graue de&longs;cendere &longs;ine vi impre&longs;&longs;a ab extrin&longs;eco, qu&agrave;m ignem <lb/>calefacere, &amp; &longs;olem lucere &longs;ine vi extrin&longs;eca; adde quod illud &longs;olenne <lb/>e&longs;t natur&aelig; in&longs;titutum, vt id, quod exigit res aliqua ad finem &longs;uum con&longs;e&shy;<lb/>quendum, per virtutem intrin&longs;ecam po&longs;&longs;it ponere, &longs;i dumtaxat excipias <lb/>concur&longs;um diuinum, &amp; ip&longs;am con&longs;eruationem; &longs;ic animal exigit vide&shy;<lb/>re, audire, &longs;entire, moueri; igitur habet virtutem intrin&longs;ecam, per quam <lb/>videat, audiat, &amp; moueatur; &longs;ic ignis exigit calefacere, lucere; a&euml;r, vel aqua <lb/>frigefacere, quidquid tandem &longs;int i&longs;t&aelig; qualitates, de quibus alibi; &longs;ic <lb/>demum corpus graue exigit moueri deor&longs;um; quis enim neget corpori <lb/>graui t&agrave;m natiuum e&longs;&longs;e tendere deor&longs;um, cum &longs;cilicet corpus leuius &longs;ub&shy;<lb/>e&longs;t, qu&agrave;m &longs;it animali progredi, vrere igni, lucere, &amp;c. </s></p><p type="main">

<s>Denique &longs;atis e&longs;t mihi, vt dicatur aliquid cau&longs;a, Phy&longs;ic&egrave; loquendo, &longs;i <lb/>ex illius applicatione &longs;emper &longs;equatur effectus; nam non nego po&longs;&longs;e fie&shy;<lb/>ri effectus omnes, qui no&longs;tris &longs;en&longs;ibus &longs;ubiiciuntur, &longs;altem extrin&longs;ecos, <lb/>e&longs;&longs;e &agrave; cau&longs;a prima, quippe &longs;i &longs;emper ex ignis applicatione Deus diffun&shy;<lb/>deret lucem, &amp; calorem, quem &longs;olus ip&longs;e produceret, igne ip&longs;o inerte re&shy;<lb/>licto, nullam pror&longs;us mutationem perciperemus; &amp; nemo e&longs;&longs;et, qui non <lb/>exi&longs;timaret lucem hanc &amp; calorem hunc e&longs;&longs;e ab igne; igitur Phy&longs;ic&egrave; lo&shy;<lb/>quendo cau&longs;am appellamus id, ex cuius applicatione &longs;emper &longs;equitur <lb/>effectus, vt iam diximus in Ax. 11.l.1. n.1. Igitur cum ex corpore graui <lb/>po&longs;ito in a&euml;re libero &longs;equatur motus deor&longs;um; dicendum e&longs;t, Phy&longs;ic&egrave; lo&shy;<lb/>quend&ograve;, e&longs;&longs;e huius motus cau&longs;am, id e&longs;t in ordine ad Phy&longs;icam, perinde <lb/>omnin&ograve; &longs;e habere, atque &longs;i e&longs;&longs;et cau&longs;a, lic&egrave;t cau&longs;a non e&longs;&longs;et. </s></p><pb xlink:href="026/01/109.jpg" pagenum="77"/><p type="main">

<s>Secund&ograve; hic motus non e&longs;t ab a&euml;re ambiente; probatur, ruderet a&euml;r <lb/>deor&longs;um corpus graue, quia leuior e&longs;t, id e&longs;t ne &longs;upr&agrave; &longs;e corpus grauius <lb/>haberet; &longs;ed e&acirc;dem ratione corpus graue debet remouere &longs;ur&longs;um a&euml;ra, <lb/>id e&longs;t corpus leue, ne infr&agrave; &longs;e habeat corpus leuius; e&longs;t enim par omni&shy;<lb/>n&ograve; ratio: Pr&aelig;terea &longs;i a&euml;r trudit deor&longs;inn corpus graue, quia ip&longs;i loco <lb/>cedit; cert&egrave; ip&longs;e a&euml;r mouetur, igitur ab intrin&longs;eco; &longs;i enim vna pars a&euml;&shy;<lb/>ris pellit aliam, &amp; h&aelig;c aliam, tandem ad aliquam peruenitur, qu&aelig; &longs;e ip&shy;<lb/>&longs;am mouet; igitur motus illius e&longs;t ab intrin&longs;eco; igitur motus natura&shy;<lb/>lis; deinde non mod&ograve; lapis de&longs;cendit per a&euml;ra, &longs;ed per mediam aquam; <lb/>igitur &longs;i ab a&euml;re truditur deor&longs;um, idem dicendum e&longs;t de aqu&acirc;, a qui <lb/>haud dubi&egrave; maiore vi truderetur; nam corpus den&longs;um maiore vi pellit, <lb/>qu&agrave;m rarum, vt con&longs;tat exprienti&acirc;; cum tamen corpus graue per me&shy;<lb/>dium den&longs;ius difficili&ugrave;s decendat; igitur medium ip&longs;um re&longs;i&longs;tit motui, <lb/>quis hoc neget? </s>

<s>igitur non e&longs;t cau&longs;a motus, quem impedit. </s></p><p type="main">

<s>Denique &longs;i corpus graue non tendit, fertur que deor&longs;um &longs;u&aacute; &longs;ponte, <lb/>&longs;ed ab a&euml;re extru&longs;um; igitur dum vix &longs;u&longs;tineo manu; o. </s>

<s>libras ferri, &longs;eu <lb/>plumbi; h&aelig;c vis illata manui, quam prob&egrave; &longs;entio, e&longs;t ab a&euml;re impel&shy;<lb/>lente plumbum, quod e&longs;t ridiculum, cum eadem quantitas a&euml;ris incu&shy;<lb/>ber, &amp; &longs;ub&longs;it manui, &longs;iue &longs;u&longs;tineat plumbum, &longs;iue &longs;it vacua; ex hoc, ni <lb/>fallor, euincitur pondus ip&longs;um &longs;ui &longs;ponte deor&longs;um tendere. </s></p><p type="main">

<s>Terti&ograve; non de&longs;unt, qui dicant corpus graue trahi ab ip&longs;a vi quadam <lb/>magnetic&acirc;, quod triplici modo fieri pote&longs;t; Prim&ograve; per qualitatem <lb/>quamdam diffu&longs;am, quod dici non pote&longs;t; quia capillus traheretur faci&shy;<lb/>li&ugrave;s, qu&agrave;m ingens &longs;axum, qu&agrave;m ma&longs;&longs;a, &longs;eu lamina; &amp; facili&ugrave;s eadem po&shy;<lb/>tentia motrix minus pondus moueret qu&agrave;m maius, c&aelig;teris paribus; pr&aelig;&shy;<lb/>terea manum meam &aelig;qualiter traheret, &longs;iue &longs;it cum aliquo pondere con&shy;<lb/>iuncta, &longs;iuc &longs;it nuda &longs;ine pondere; deinde illa virtus tractrix ita diffun&shy;<lb/>ditur, vt in maiori di&longs;tantia &longs;it infirmior, fortior in minori; alioqui <lb/>diffunderetur in infinitum, quod dici non pote&longs;t; igitur &longs;i idem lapis <lb/>demittatur ex maiore altitudine, tum ex minore; haud dubi&egrave; morus ille <lb/>primus initio e&longs;&longs;et tardior i&longs;to contra experientiam; deinde in &longs;pecu al&shy;<lb/>ti&longs;&longs;ima &longs;ubterranea trahi po&longs;&longs;et corpus vndequaque, &longs;icut in magnete; <lb/>qu&aelig; omnia intelligi non po&longs;&longs;unt; denique virtutes illas &longs;eu qualitates <lb/>tractrices refellemus &longs;uo loco. </s></p><p type="main">

<s>Secund&ograve;, aliqui dicunt hoc totum fieri per vim quamdam &longs;ympathi&shy;<lb/>cam, quod etiam fal&longs;i&longs;&longs;imum e&longs;t; t&ugrave;m quia h&aelig;c &longs;ympathia explicari <lb/>non pote&longs;t; t&ugrave;m quia vel terra ip&longs;a producit aliquid in corpore graui, <lb/>quod in a&euml;re libratur; vel corpus in &longs;e ip&longs;o; &longs;i primum; refellitur ii&longs;&shy;<lb/>dem omnin&ograve; rationibus, quibus ip&longs;am vim terr&aelig; tractricem &longs;upr&agrave; expu&shy;<lb/>gnauimus; &longs;i ver&ograve; &longs;ecundum, hoc ip&longs;um e&longs;t, quod &longs;upr&agrave; diximus. </s></p><p type="main">

<s>Terti&ograve;, Dixere aliqui &longs;ubtili&ugrave;s profect&ograve; qu&agrave;m veri&ugrave;s, corpus graue <lb/>trahi deor&longs;um, non vi quadam occult&acirc;, vt &longs;upr&agrave; dictum e&longs;t; &longs;ed filamen&shy;<lb/>tis quibu&longs;dam, &longs;eu ductili terr&aelig; profluuio, quod illius capillitium vo&shy;<lb/>cant; idque tant&ugrave;m fieri probant ducta ab electro analogi&acirc;, quod pa&shy;<lb/>leam &amp; minutiora corpu&longs;cula hac e&acirc;dem arte trahit; &longs;ed profect&ograve; gra-<pb xlink:href="026/01/110.jpg" pagenum="78"/>uiores &longs;unt difficultates, quam vt illis fieri &longs;atis queat; nam prim&ograve; cor&shy;<lb/>pus leuius ab his filamentis abripi facili&ugrave;s po&longs;&longs;et, vt con&longs;tat in electro; <lb/>igitur citi&ugrave;s de&longs;cenderet. </s></p><p type="main">

<s>Secund&ograve;, corpus vicinius etiam facili&ugrave;s abriperetur. </s></p><p type="main">

<s>Terti&ograve;, numquid flante vento, vel imbre cadente di&longs;&longs;ipantur h&aelig;c fi&shy;<lb/>lamenta? </s>

<s>quod etiam videmus in electro. </s></p><p type="main">

<s>Quart&ograve;, manum meam &aelig;qu&egrave; facil&egrave; traheret terra his funiculis &longs;eu <lb/>pondere grauatam, &longs;eu vacuam. </s></p><p type="main">

<s>Quint&ograve;, quemadmodum electrum ex omni parte trahit, ita terra ip&longs;a <lb/>per omnem lineam traheret; imm&ograve; etiam &longs;ur&longs;um in &longs;ubterranea &longs;pecu, <lb/>quod e&longs;t ab&longs;urdum. </s></p><p type="main">

<s>Sext&ograve;, h&aelig;c filamenta, qu&aelig; deinde reducuntur, debent habere cau&shy;<lb/>&longs;am huius reductionis non extrin&longs;ecam; igitur intrin&longs;ecam; igitur datur <lb/>motus naturalis. </s></p><p type="main">

<s>Septim&ograve;, h&aelig;c filamenta per mediam flammam non traherent, quod <lb/>etiam fieri videmus in electro. </s></p><p type="main">

<s>Quart&ograve;, motus naturalis non e&longs;t &agrave; virtute quadam pellente, quam <lb/>c&aelig;lo quidam affingunt; nam vel ab omni parte c&aelig;li deor&longs;um trudere&shy;<lb/>tur, vel ab vn&acirc;; &longs;i ab vna; igitur in omni c&aelig;li plaga corpus non fertur <lb/>deor&longs;um; &longs;i ab omni, ergo cum pellatur corpus per plures lineas etiam <lb/>oppo&longs;itas moueri non pote&longs;t: Pr&aelig;terea debilior e&longs;&longs;et h&aelig;c vis in maiori <lb/>di&longs;tanti&acirc;; denique vapores, &amp; alia minutiora corpu&longs;cula in a&euml;re fluitan&shy;<lb/>tia facili&ugrave;s deor&longs;um truderentur, contra experientiam. </s></p><p type="main">

<s>Sed non e&longs;t omittendum, quod aliqui putant ex illis filamentis con&shy;<lb/>texi po&longs;&longs;e legitimam rationem, cur atomi etiam plumbe&aelig; materi&aelig; non <lb/>ita facil&egrave; de&longs;cendant; qu&ograve;d &longs;cilicet propter &longs;uam tenuitatem ab illis fi&shy;<lb/>lamentis non ita intercipi vel implicari po&longs;&longs;int; &longs;ed qua&longs;i pi&longs;ces per fo&shy;<lb/>ramina retium euadant; &longs;ed profect&ograve; long&egrave; alia ratio e&longs;t, qu&agrave;m &longs;uo loco <lb/>afferemus, nam etiam plum&aelig;, fe&longs;tuc&aelig;, pale&aelig;, &amp; alia corpu&longs;cula longio&shy;<lb/>ra, &longs;ed leui&longs;&longs;ima iis filamentis implicarentur, vt videre e&longs;t in electro. </s></p><p type="main">

<s>Quint&ograve;, aliqui recentiores exi&longs;timant corpora deor&longs;um trudi ab <lb/>ip&longs;a luce, qu&aelig; nihil e&longs;t aliud, quam motio &aelig;there&aelig; cuiu&longs;dam &longs;ub&longs;tan&shy;<lb/>ti&aelig; per poros a&euml;ris traduct&aelig;, vt ip&longs;i volunt; &longs;ed neque hoc probari po&shy;<lb/>te&longs;t. </s>

<s>Prim&ograve; quia de nocte corpora &aelig;quali motu deor&longs;um feruntur; pe&shy;<lb/>rinde atque de die, nec min&ugrave;s in ob&longs;curi&longs;&longs;imo conclaui, qu&agrave;m &longs;ub dio, <lb/>vel aperto c&aelig;lo. </s>

<s>Secund&ograve;, in &longs;ubterraneis locis etiam grauia &aelig;qu&egrave; veloci&shy;<lb/>ter de&longs;cendunt; lic&egrave;t e&ograve; lumen non penetret; quod &longs;i aliquis ob&longs;tinat&egrave;, <lb/>id a&longs;&longs;ereret; haud dubi&egrave; per medium a&euml;ra maior huius materi&aelig; copia <lb/>diffunditur, qu&agrave;m per medias rupes, quis hoc neget; igitur pauci&longs;&longs;imi <lb/>radij v&longs;que ad interius &amp; inferius antrum perueniunt. </s>

<s>Terti&ograve;, manum <lb/>meam &longs;iue ponderi coniunctam &longs;iue ab eo <expan abbr="&longs;eparat&atilde;">&longs;eparatam</expan> &aelig;qualis portio illius <lb/>materi&aelig; deor&longs;um pelleret, vt patet; igitur &aelig;quali motus vi. </s>

<s>Quart&ograve;, cor&shy;<lb/>pus diaphanum, per cuius poros facil&egrave; traiicitur h&aelig;c materia, e&longs;&longs;et leuius <lb/>alio quod tamen fal&longs;um e&longs;t, vt videre e&longs;t in vitro, cry&longs;tallo, adamante, <lb/>glacie. </s>

<s>Quint&ograve; maxima huius materi&aelig; copia collecta &longs;eu &longs;peculi opera <pb xlink:href="026/01/111.jpg" pagenum="79"/>&longs;eu vitri, maiore vi corpora deor&longs;um truderet; quia maior cau&longs;a maio&shy;<lb/>rem effectum producit per Ax.2. Sext&ograve; po&longs;t refractionem lineam mutat <lb/>radius luminis; igitur deor&longs;um rect&agrave; non pelleret. </s>

<s>Septim&ograve; radij traie&shy;<lb/>cti per vitrum maiore vi deor&longs;um pellerent qu&agrave;m per lignum, vel &longs;pon&shy;<lb/>giam; quipp&egrave; per h&aelig;c corpora traiecti &longs;ecundum authores huius &longs;enten&shy;<lb/>ti&aelig; di&longs;trahuntur propter obliquitatem pororum. </s>

<s>Octau&ograve; denique radij <lb/>profecti &agrave; Sole iuxta ortum, vel occa&longs;um &longs;unt vald&egrave; obliqui; igitur non <lb/>truderent deor&longs;um rect&agrave;. </s></p><p type="main">

<s>Nec e&longs;t quod pr&aelig;dicti &agrave;uthores confugiant ad experientiam, qua <lb/>&longs;cilicet videmus tripudiantes atomos in radio &longs;olari immer&longs;as; igitur <lb/>agitantur ab ip&longs;o radio, quod maxim&egrave; accidit in linea v&longs;toria, cuius <lb/>effectus veri&longs;&longs;imam rationem &longs;uo loco afferemus, cum de lumine. </s></p><p type="main">

<s>Sext&ograve;, &longs;unt denique multi, <expan abbr="ii&qacute;ue">iique</expan> ex &longs;euerioribus Peripateticis, qui <lb/>exi&longs;timant grauia moueri deor&longs;um &agrave; generante, quod expre&longs;&longs;is verbis <lb/>traditum e&longs;t ab <emph type="italics"/>Ari&longs;totele l.<emph.end type="italics"/>8. <emph type="italics"/>phy&longs;. cap.<emph.end type="italics"/>4. <emph type="italics"/>iuxta<emph.end type="italics"/> principium illud vniuer&shy;<lb/>&longs;ali&longs;&longs;imum; <emph type="italics"/>Quidquid mouetur; ab alio mouetur<emph.end type="italics"/>; &longs;ed profect&ograve; ij ip&longs;i, qui <lb/>motum grauium generanti tribuunt, tanquam principi cau&longs;&aelig;, non ne&shy;<lb/>gant ine&longs;&longs;e grauibus grauitatem, qu&aelig; &longs;it principium actiuum minus <lb/>principale motus; ad quem etiam, vt ip&longs;i exi&longs;timant, forma &longs;ub&longs;tantialis <lb/>concurrit; In hoc quippe conueniunt omnes t&ugrave;m &longs;ectarum Principes, <lb/>t&ugrave;m recentiores: quidquid &longs;it etiam ex iis ip&longs;is datur motus naturalis, <lb/>qui e&longs;t &agrave; virtute proxima intrin&longs;eca; hoc ip&longs;um etiam &longs;en&longs;it Ari&longs;toteles <lb/>lib.4. de c&aelig;lo cap. 

3. t. </s>

<s>25. vbi ait grauibus &amp; leuibus ine&longs;&longs;e principium <lb/>actiuum &longs;uorum motuum; imm&ograve; &longs;i totum cap.4. l.8. phy&longs;. attent&egrave; lega&shy;<lb/>tur, vbi dicit moueri &agrave; generante, haud dubi&egrave; intelligetur nihil aliud in&shy;<lb/>tendi&longs;&longs;e Ari&longs;totelem qu&agrave;m grauia &agrave; generante, in&longs;tanti, quo generan&shy;<lb/>tur, accipere actum primum huius motus; id e&longs;t virtutem, &agrave; qua po&longs;&shy;<lb/>&longs;int reduci ad actum &longs;ecundum, id e&longs;t ad ip&longs;um motum, de cuius rei ve&shy;<lb/>ritate iam mihi non e&longs;t laborandum. </s></p><p type="main">

<s>Igitur non mouetur corpus graue &agrave; cau&longs;a prim&acirc;, lic&egrave;t h&aelig;c concurrat <lb/>cum ali&acirc; ad eius motum, nec ab a&euml;re, nec &agrave; virtute magnetica, qu&aelig; in&shy;<lb/>&longs;it terr&aelig;, nec adductis, reducti&longs;que filamentis, nec &agrave; c&aelig;lo pellente, nec <lb/>&agrave; vi &longs;ympathic&acirc;, nec &agrave; generante proxim&egrave; &amp; immediat&egrave;; quia fort&egrave; iam <lb/>interiit, nec ab vllo alio extrin&longs;eco, vt con&longs;tat inductione; igitur ab ali&shy;<lb/>qu&acirc; vi intrin&longs;ec&acirc;, quidquid &longs;it, de qua alibi: h&aelig;c omnia paul&ograve; fu&longs;i&ugrave;s <lb/>tractauimus, quia in hoc vno Theoremate totam motus naturalis rem <lb/>verti iudicamus. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 2.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s><emph type="italics"/>Motus naturalis est aliquid distinctum realiter &agrave; mobili:<emph.end type="italics"/> Probatur; <lb/>mobile ip&longs;um aliquando quie&longs;cit per hypoth.4.lib.1. igitur e&longs;t &longs;ine mo&shy;<lb/>tu; igitur &longs;eparatum &agrave; motu; igitur realiter di&longs;tinctum per Ax.2. lib.1. <lb/>hoc etiam probatus per Th. 1.lib. 

1. Et cert&egrave; mirari &longs;atis non po&longs;&longs;um <lb/>aliquos recentiores non po&longs;&longs;e concipere, vt ip&longs;i aiunt, motum e&longs;&longs;e ali&shy;<lb/>quid ab ip&longs;o mobili di&longs;tinctum; nam quotie&longs;cunque duo pr&aelig;dicata, vel <pb xlink:href="026/01/112.jpg" pagenum="80"/>attributa contradictoria, quorum &longs;cilicet vnum negat aliud, eidem &longs;ub&shy;<lb/>jecto diuer&longs;is temporibus ine&longs;&longs;e dicuntur, haud dubi&egrave; alterum &longs;altem ab <lb/>eo di&longs;tingui realiter nece&longs;&longs;e e&longs;t; alioqui &longs;i vtrumque idem e&longs;&longs;e cum vno <lb/>tertio vere dicitur; <emph type="italics"/>mouetur, non monetur,<emph.end type="italics"/> qu&aelig; &longs;unt pr&aelig;dicata contradi&shy;<lb/>ctoria; igitur vel moueri, vel non moueri dicit di&longs;tinctum realiter &agrave; mo&shy;<lb/>bili; Secundum e&longs;t mera negatio; nam eo ip&longs;o, quod mobile e&longs;t &longs;ine vllo <lb/>addito, non mouetur; igitur &longs;upr&agrave; ip&longs;um mobile dicit puram putam ne&shy;<lb/>gationem motus; igitur moueri, dicit aliquid di&longs;tinctum. </s></p><p type="main">

<s>Pr&aelig;terea quotie&longs;cunque pr&aelig;dicatum aliquod tribuitur in propo&longs;i&shy;<lb/>tione affirmatiua fals&acirc;; cert&egrave; pr&aelig;dicatum illud non ine&longs;t &longs;ubiecto; alio&shy;<lb/>quin e&longs;&longs;et vera, vt patet; igitur di&longs;tinguitur &agrave; &longs;ubiecto realiter; &longs;ed h&aelig;c <lb/>propo&longs;itio, <emph type="italics"/>lapis mouetur,<emph.end type="italics"/> dum ip&longs;e quie&longs;cit, e&longs;t fal&longs;a; igitur motus non <lb/>ine&longs;t mobili, igitur ab eo di&longs;tinguitur realiter, &longs;eu modaliter, qu&aelig; e&longs;t <lb/>di&longs;tinctio realis minor. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 3.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s><emph type="italics"/>Metus naturalis non e&longs;t immediat&egrave; ab entitate mobilis, ita vt nihil &longs;it aliud <lb/>vnde &longs;it hic motus:<emph.end type="italics"/> Probatur; lapis cadens ex maiore altitudine maiorem <lb/>ictum infligit perhypoth. </s>

<s>1. maior e&longs;t effectus, igitur maior cau&longs;a, id e&longs;t <lb/>motus; igitur cau&longs;a motus per Ax.2. &longs;ed e&longs;t eadem entitas mobilis, vt <lb/>patet; igitur non e&longs;t cau&longs;a immediata motus; Pr&aelig;terea globus per pla&shy;<lb/>num inclinatum deuolutus &longs;uum motum accelerat per hypotl. </s>

<s>3. &amp; fune&shy;<lb/>pendulum &longs;uam vibrationem per hypoth. </s>

<s>2. igitur debet e&longs;&longs;e cau&longs;a huius <lb/>maioris, &longs;eu velocioris motus per Ax.8. lib. 

1. h&aelig;c porr&ograve; non e&longs;t &longs;ub&shy;<lb/>&longs;tantia ip&longs;ius corporis, qu&aelig; &longs;emper eadem e&longs;t, t&ugrave;m initio, t&ugrave;m in fine <lb/>motus per Ax.2. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 4.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s><emph type="italics"/>Motus naturalis non e&longs;t immediat&egrave; ab ip&longs;a grauitate.<emph.end type="italics"/></s><s> Probatur, &longs;int <lb/>enim e&aelig;dem hypoth.1.2.3. igitur maior ictus in fine motus, &amp; velocior <lb/>motus debent habere cau&longs;am; &longs;ed h&aelig;c grauitas non e&longs;t, qu&aelig; &longs;emper ea&shy;<lb/>dem e&longs;t, vt patet, vtrum ver&ograve; di&longs;tinguatur grauitas ab ip&longs;a corporis <lb/>&longs;ub&longs;tantia di&longs;cutiemus in tractatu &longs;equenti. </s>

<s>Fuit aliquis non infim&aelig; no&shy;<lb/>t&aelig; Philo&longs;ophus, qui diceret maiorem illum ictum e&longs;&longs;e ab ips&acirc; corporis <lb/>&longs;ub&longs;tanti&acirc;; &longs;ed hoc iam refellimus Theoremate 4. lib.1. Adde quod im&shy;<lb/>petu, ad extra producitur ab alio impetu per Th.42.lib.1. Dicebat etiam <lb/>velociorem motum e&longs;&longs;e ab ips&acirc; grauitate connotante pr&aelig;uium motum, <lb/>quod etiam refellemus infr&agrave;. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 5.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s><emph type="italics"/>Hinc motus naturalis e&longs;t ab impetu.<emph.end type="italics"/></s><s> Probatur; e&longs;t ab aliqua cau&longs;a per <lb/>Ax.8. lib.1. ab aliqua intrin&longs;eca per Th. 1. non &agrave; &longs;ub&longs;tantia corporis <lb/>grauis per Th. 3. non &agrave; grauitate per Th. 4. igitur ab impetu, quia <lb/>nihil aliud e&longs;&longs;e pote&longs;t intrin&longs;ecum, &agrave; quo &longs;it motus per definitionem <lb/>3. lib. 

1. <!-- KEEP S--></s></p><pb xlink:href="026/01/113.jpg" pagenum="81"/><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 6.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s><emph type="italics"/>Ille impetus ab aliqua cau&longs;a producitur.<emph.end type="italics"/></s><s> Probatur, quia quidquid de no&shy;<lb/>uo e&longs;t, habet cau&longs;am per Ax.8. lib. 

1. <!-- KEEP S--></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 7.<emph.end type="center"/></s></p><p type="main">

<s>Producitur ab aliqua cau&longs;a intrin&longs;eca, quia non producitur ab aliqua <lb/>extrin&longs;eca; alioquin motus naturalis e&longs;&longs;et ab extrin&longs;eco contra definitio&shy;<lb/>nem primam, &amp; Th.1. <!-- KEEP S--></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 8.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc produci tant&ugrave;m pote&longs;t ab ip&longs;a &longs;ubstantia corporis grauis; nam graui&shy;<lb/>tas e&longs;t ip&longs;e impetus innatus, de qua infr&agrave;:<emph.end type="italics"/> probatur; quia nihil e&longs;t aliud in&shy;<lb/>trin&longs;ecum, &agrave; quo produci po&longs;&longs;it; qu&ograve;d autem non producatur ab alio im&shy;<lb/>petu ad intra, patet per Th.41. lib. 

1. <!-- KEEP S--></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 9.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Impetus productus primo instanti durat proxim&egrave; &longs;equenti.<emph.end type="italics"/></s><s> Probatur pri&shy;<lb/>m&ograve;; quia &longs;emper habet &longs;uum effectum formalem; vel grauitationis, &longs;i <lb/>impeditur; vel motus in medio libero; igitur non e&longs;t fru&longs;tr&agrave;; igitur <lb/>non de&longs;truitur per Th.162.lib.1. nihil enim exigit de&longs;tructionem; non <lb/>tota natura, quia non e&longs;t fru&longs;tr&agrave; per Ax. 6. non &agrave; contrario impetu, qui <lb/>&longs;&aelig;p&egrave; abe&longs;t, vt cum liber&egrave; mouetur corpus graue in a&euml;re, vel &longs;u&longs;tinetur, <lb/>v.g. <!-- REMOVE S-->glans plumbea ab ingenti rupe: adde quod, lic&egrave;t producatur in cor&shy;<lb/>pore graui impetus violentus &longs;ur&longs;um, non de&longs;truitur, tamen innatus; alio&shy;<lb/>quin nihil e&longs;&longs;et, quod de&longs;trueret violentum per Th.150. &amp; Schol. <!-- REMOVE S-->Th. <!-- REMOVE S--><lb/>152.num.6.lib.1. <!-- KEEP S--></s>





</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 10.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Impetus ille innatus, qui durat &longs;ecundo instanti, con&longs;eruatur ab aliqua cau&shy;<lb/>&longs;a<emph.end type="italics"/>; e&longs;t certum per Ax. 14.lib.1.num.1. <!-- KEEP S--></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 11.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Non con&longs;eruatur &agrave; cau&longs;a prim&ograve; productiua.<emph.end type="italics"/></s><s> Probatur per Th.144. lib.1. <lb/>alioquin non po&longs;&longs;et intendi ab eadem cau&longs;a per Th. 146. lib 1. quipp&egrave; <lb/>con&longs;eruatio nihil e&longs;t aliud, qu&agrave;m repetita productio, vt con&longs;tat; nam <lb/>cau&longs;a con&longs;eruans ver&egrave; influit; igitur &longs;i e&longs;t cau&longs;a nece&longs;&longs;aria primo, &amp; &longs;e&shy;<lb/>cundo in&longs;tanti &aelig;quali ni&longs;u influit; influit enim quantum pote&longs;t per Ax. <!-- REMOVE S--><lb/>12.lib.1.qu&ograve;d autem impetus intendatur, demon&longs;trabimus infr&agrave;; con&longs;ule <lb/>Schol.Th.146.lib.1.in quo habes rationem pr&aelig;clari natura in&longs;tituti; quo <lb/>&longs;cilicet factum e&longs;t, vt qualitates, qu&aelig; contrario carent &agrave; caus&acirc; prim&ograve; pro&shy;<lb/>ductiua; ali&aelig; ver&ograve;, qu&aelig; contrarium habent, ab alia caus&agrave; con&longs;er&shy;<lb/>uentur. </s>

</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Corollarium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Hinc ab ali&acirc; caus&acirc; con&longs;eruari nece&longs;&longs;e e&longs;t, vt patet, e&aacute;que aplicat&acirc; per <lb/>Ax.10.lib.1. qu&aelig;cumque tandem illa &longs;it; nos aliquando cau&longs;am primam <lb/>e&longs;&longs;e dicemus. </s></p><pb xlink:href="026/01/114.jpg" pagenum="82"/><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 12.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Quando graue e&longs;t in medio libero, per quod &longs;cilicet de&longs;cendere pote&longs;t, &longs;ecun&shy;<lb/>do instanti producitur nouus impetus, itemque tertio, quarto, quinto. </s>

<s>&amp;c.<emph.end type="italics"/></s><s> Pro&shy;<lb/>batur prim&ograve;; quia &longs;ecundo in&longs;tanti e&longs;t eadem cau&longs;a qu&aelig; primo non ma&shy;<lb/>gis impedita, e&aacute;que nece&longs;&longs;aria; igitur nece&longs;&longs;ari&ograve; agit per Ax. 12. lib.1. <lb/>igitur aliquem effectum producit; &longs;ed hic effectus non e&longs;t impetus pro&shy;<lb/>ductus primo in&longs;tanti, quia non con&longs;eruatur &agrave; cau&longs;a prim&ograve; productiua <lb/>per Th.11. igitur e&longs;t nouus. </s>

<s>Probatur &longs;ecund&ograve;; cre&longs;cit motus grauium in <lb/>libero medio per hypoth. </s>

<s>1.2.3. igitur cre&longs;cit impetus; quia cum motus <lb/>naturalis &longs;it ab impetu per Th.5. qu&acirc; proportione cre&longs;cit effectus, &longs;cilicet <lb/>formalis, &amp; exigenti&aelig;; &longs;ic enim motus e&longs;t effectus impetus per Th. 15. <lb/>lib.1.e&agrave;dem cre&longs;cit cau&longs;a per Ax.2. Probatur terti&ograve;, quia corpus graue ex <lb/>maiore altitudine cadens maiorem quoque ictum infligit per hypoth.1. <lb/>igitur maior impetus imprimitur in corpore percu&longs;&longs;o; &longs;ed impetus ad ex&shy;<lb/>tra producitur ab alio impetu per Th.42.lib.1. igitur &longs;i cre&longs;cit productus <lb/>inpetus, cre&longs;cit impetus producens. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Corollarium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Hinc reiicies quorumdam placitum, qui volunt cau&longs;am velocioris <lb/>motus e&longs;&longs;e grauitatem ip&longs;am, quatenus connotat motum pr&aelig;uium; quia <lb/>&longs;cilicet grauitas non producit illum maiorem impetum ad extra, vt con&shy;<lb/>&longs;tat; nec &longs;ub&longs;tantia ip&longs;ius corporis grauis per Th.40.lib.1.igitur ip&longs;e im&shy;<lb/>petus: pr&aelig;terea &longs;i hoc e&longs;&longs;et, fru&longs;tr&agrave; requireretur impetus contra Th. 5. <lb/>Denique motus pr&aelig;uius nihil e&longs;t amplius, cum alius &longs;uccedit: Vide Th. <!-- REMOVE S--><lb/>40.lib.1. vbi h&aelig;c fus&egrave; di&longs;cu&longs;&longs;imus. </s>

</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 13.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Impetus productus &longs;ecundo instanti in medio libero con&longs;eruatur tertio, &amp; <lb/>productus tertio con&longs;eruatur, quarto, atque ita deinceps<emph.end type="italics"/>; quia &longs;cilicet nec con&shy;<lb/>&longs;eruantur &agrave; cau&longs;a primo productiua per Th.144.libri: nec aliquid exigit <lb/>de&longs;tructionem; non contrarius impetus, quia nullus e&longs;t applicatus, vt <lb/>con&longs;tat; non re&longs;i&longs;tentia medij, qu&aelig; quidem alicuius momenti e&longs;t; &longs;ed <lb/>non tanti, vt impedire po&longs;&longs;it motum omnin&ograve;, vt con&longs;tat; nam &longs;uppono <lb/>liberum medium, igitur nec de&longs;truere impetum; cum tamdiu duret cau&shy;<lb/>&longs;a quamdiu durat effectus, vt patet; igitur nihil e&longs;t quod exigat impe&shy;<lb/>tus huius de&longs;tructionem; igitur non de&longs;truitur per Ax. 14. lib.1. <lb/><expan abbr="q&umacr;anta">quanta</expan> ver&ograve; &longs;it, &amp; quid &longs;it cuiu&longs;libet medij re&longs;i&longs;tentia, dicemus <lb/>infr&agrave;. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 14.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Si impetus innatus impeditur, ita vt moueri non po&longs;&longs;it corpus graue, &longs;e&shy;<lb/>cundo instanti non producitur nouus impetus.<emph.end type="italics"/></s><s> Probatur prim&ograve;, non cre&longs;cit <lb/>corporis grauis &longs;eu grauitas, &longs;eu grauitatio, vt con&longs;tat experienti&acirc;; igitur <lb/>non cre&longs;cit impetus; alioquin &longs;i cre&longs;ceret cau&longs;a, cre&longs;ceret effectus per <lb/>Ax.2. igitur de re, qu&ograve;d &longs;it, certum e&longs;t, atque cuidens; iam demon&longs;tratur <lb/>propter quid &longs;it; impetus &longs;ecundo in&longs;tanti productus e&longs;&longs;et fru&longs;tr&agrave;; careret <pb xlink:href="026/01/115.jpg" pagenum="83"/>enim &longs;uo fine, vel effectu formali, id e&longs;t motu; igitur e&longs;&longs;et fru&longs;tr&agrave;, &longs;ed <lb/>quod fru&longs;tr&agrave; e&longs;t, non e&longs;t per Ax.6.l.1. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Ob&longs;erua qu&aelig;&longs;o, quod iam &longs;upr&agrave; indicatum e&longs;t, e&longs;&longs;e tres veluti &longs;pecies <lb/>impetus. </s>

<s>Prima e&longs;t impetus naturalis innati. </s>

<s>Secunda naturalis acqui&longs;iti. </s>

<s><lb/>Tertia violenti; innatus e&longs;t qui vel &agrave; generante &longs;imul cum corpore <lb/>graui productus e&longs;t; qui&longs;quis tandem &longs;it generans, de quo ali&agrave;s; vel ab <lb/>ip&longs;o graui qua&longs;i profunditur, id e&longs;t, producitur in &longs;e ip&longs;o &longs;tatim initio, <lb/>quo e&longs;t; porr&ograve; cum in corpore graui duplex qua&longs;i proprietas &longs;en&longs;ibilis <lb/>e&longs;&longs;e videatur, &longs;cilicet grauitas, &longs;eu pondus &amp; motus deor&longs;um; cert&egrave; de&shy;<lb/>bet e&longs;&longs;e in eo aliquid per quod t&ugrave;m cogno&longs;ci po&longs;&longs;it eius pondus, t&ugrave;m in&shy;<lb/>cipiat moueri deor&longs;um; quippe maxim&egrave; corpora ex pondere cogno&longs;ci&shy;<lb/>mus, vnumque ab alio di&longs;tinguimus; igitur debet e&longs;&longs;e aliquid, quod &longs;en&shy;<lb/>&longs;um afficiat, vt cogno&longs;ci po&longs;&longs;it; atqui illud ip&longs;um non e&longs;t &longs;ub&longs;tantia cor&shy;<lb/>poris; nam corpus graue me&aelig; manui &longs;u&longs;tinenti impetum imprimit; <lb/>imm&ograve; vim alterius impetus infringit; igitur oper&acirc; alterius per Th. 40. <lb/>&amp; 42.lib.1. Pr&aelig;terea illud ip&longs;um, quod agit, &longs;eu deor&longs;um pellit &longs;u&longs;tinen&shy;<lb/>tem manum, e&longs;t illud ip&longs;um quod inclinat corpus graue deor&longs;um imme&shy;<lb/>diat&egrave;, &longs;eu quod exigit motum naturalem deor&longs;um; illud autem quod <lb/>immediat&egrave; pr&aelig;&longs;tat hunc motum, nec e&longs;t &longs;ub&longs;tantia corporis grauis per <lb/>Th.3. igitur ip&longs;e impetus per Th.5. adde quod primo in&longs;tanti, quo e&longs;t im&shy;<lb/>petus, non e&longs;t motus ille, quem exigit per Th.34. lib.1. igitur pr&aelig;exi&longs;tit <lb/>&longs;emper impetus, qui ne &longs;it fru&longs;tr&agrave;, habet primum effectum &longs;uum forma&shy;<lb/>lem, id e&longs;t grauitationem: Ex his dicendum e&longs;t hunc impetum natiuum <lb/>nunquam de&longs;trui, quia nunquam e&longs;t fru&longs;tr&agrave;, habet enim &longs;emper aliquem <lb/>effectum, primum quidem &longs;i caret &longs;ecundo; &longs;ecundum ver&ograve; &longs;i caret pri&shy;<lb/>mo; quippe vtrumque &longs;imul habere non pote&longs;t; nam corporis pondus <lb/>cogno&longs;ci non pote&longs;t, dum fertur deor&longs;um accelerato motu, quot ver&ograve;, <lb/>&amp; quanta commoda ex cognitione ponderis cuiu&longs;libet materi&aelig; proce&shy;<lb/>dant, vix explicari pote&longs;t. </s></p><p type="main">

<s>Ex his ver&ograve; concludendum &longs;upere&longs;t impetum innatum e&longs;&longs;e proprie&shy;<lb/>tatem quarto modo, vt vulg&ograve; aiunt, corporis grauis; ac proinde ab illo <lb/>in&longs;eparabilem; quid ver&ograve; fiat de illo, cum corpus graue fit leue; &longs;i tamen <lb/>hoc aliquando accidit, dicemus cum de grauitate, &amp; grauitatione, iam <lb/>ver&ograve; &longs;atis e&longs;t ad pr&aelig;&longs;ens in&longs;titutum impetum innatum ab ip&longs;o corpori <lb/>graui nunquam &longs;eparari, quandiu remanet graue. </s></p><p type="main">

<s>Impetus naturalis acqui&longs;itus producitur ab codem principio intrin&shy;<lb/>&longs;eco; hinc dicitur naturalis: dicitur ver&ograve; acqui&longs;itus, quia non e&longs;t inna&shy;<lb/>tus; &longs;ed &longs;eparatur &agrave; corpore graui; quod &longs;emper eo caret, quandiu <lb/>quie&longs;cit: &longs;ed innato tant&ugrave;m accedit ad motus accelerationem, &amp; ad alia <lb/>quamplurima, qu&aelig; ex ea &longs;equuntur; put&agrave; maiorem percu&longs;&longs;ionem, re&longs;i&shy;<lb/>&longs;tentiam, vim, &amp; ad tollendum totius natur&aelig; langudiorem; quo cert&egrave; af&shy;<lb/>ficeretur, &longs;i corpus graue tardi&longs;&longs;imo motu deor&longs;um ferretur, de quo in&shy;<lb/>fr&agrave;; Porr&ograve; impetus acqui&longs;itus in multis differt ab innato; prim&ograve; quia <pb xlink:href="026/01/116.jpg" pagenum="84"/>de&longs;truitur &agrave; corpore re&longs;i&longs;tente eo modo, quo diximus, &amp; dicemus infr&agrave;. </s>

<s><lb/>Secund&ograve;, quia determinari pote&longs;t ad omnem lineam. </s></p><p type="main">

<s>Impetus violentus e&longs;t, qui e&longs;t ab extrin&longs;eco, de quo agemus infr&agrave;, &amp; <lb/>iam &longs;upr&agrave; in lib.1. multa &longs;unt de eo demon&longs;trata. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 15.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Impetus naturalis corporis grauis intenditur dum hoc ip&longs;um de&longs;cendit in <lb/>medio libero<emph.end type="italics"/>; demon&longs;tratur, Impetus nouus producitur in &longs;ecundo, ter&shy;<lb/>tio, quarto, &amp;c. </s>

<s>in&longs;tantibus per Th.12. &longs;ed productus in primo con&longs;er&shy;<lb/>uatur &longs;ecundo, per Th.9. productus &longs;ecundo con&longs;eruatur tertio, produ&shy;<lb/>ctus tertio con&longs;eruatur quarto per Th.13. igitur &longs;ecundus additur tertio, <lb/>tertius primo, &longs;ecundo, quartus primo, &longs;ecundo, &amp; tertio, &amp;c.&longs;ed impetus <lb/>additus alteri facit inten&longs;iorem impetum per Ax.1. igitur impetus natu&shy;<lb/>ralis intenditur, quod crat demon&longs;trandum. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 16.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc motus naturalis deor&longs;um acceleratur<emph.end type="italics"/>; hoc ip&longs;um &longs;uppo&longs;ui &longs;upr&agrave; <lb/>Quod e&longs;&longs;et in hyp.1.2.3. iam ver&ograve; demon&longs;tro propter quid e&longs;t; &longs;ie enim <lb/>hypothe&longs;is in Theorema conuerti pote&longs;t, vt 6longs;&aelig;p&egrave; monuimus in metho&shy;<lb/>do; igitur probatur hoc Theorema facil&egrave;; cre&longs;cit impetus in corpore gra&shy;<lb/>ui, quod tendit deor&longs;um in libero medio per T. 15. igitur cre&longs;cit cau&longs;a <lb/>motus; nam impetus e&longs;t cau&longs;a immediata motus naturalis per Th. 51. <lb/>&longs;ed qu&acirc; proportione cre&longs;cit cau&longs;a, debet cre&longs;cere effectus per Ax.2. igi&shy;<lb/>tur motus naturalis deor&longs;um cre&longs;cit, id e&longs;t acceleratur, id e&longs;t fit velo&shy;<lb/>cior, quod erat dem: nec e&longs;t quod aliquis exi&longs;timet hic &agrave; me committi <lb/>vitio&longs;um argumentationis circulum; quippe probaui &longs;upr&agrave; cre&longs;cere im&shy;<lb/>petum, quia cre&longs;cit motus; iam ver&ograve; probo cre&longs;cere motum, quia cre&longs;&shy;<lb/>cit impetus; nam prim&ograve; probaui produci nouum impetum in Th.12. eo <lb/>quod &longs;ecundo in&longs;tanti. </s>

<s>v.g. <!-- REMOVE S-->&longs;it eadem cau&longs;a nece&longs;&longs;aria applicata non im&shy;<lb/>pedita, igitur t&agrave;m debet agere &longs;ecundo qu&agrave;m primo in&longs;tanti, h&aelig;c fuit <lb/>mea probatio &agrave; priori; &longs;ecund&ograve; ver&ograve; probaui ex hypothe&longs;i certa; quia <lb/>&longs;cilicet cre&longs;cit motus, cuius veritatem cogno&longs;co &longs;en&longs;ibiliter in &longs;e, vnde <lb/>&longs;uppono tant&ugrave;m de illa quod &longs;it; igitur nullus committitur circulus; nam <lb/>diuer&longs;a e&longs;t omnin&ograve; cognitio. </s>



<s>Prima &longs;cilicet qua cogno&longs;co de motu na&shy;<lb/>turaliter accelerato quod &longs;it, qu&aelig; mihi, &amp; ru&longs;tico communis e&longs;t. </s>

<s>Secun&shy;<lb/>da ver&ograve; qua non mod&ograve; cogno&longs;co de motu illo quod &longs;it acceleratus, ve&shy;<lb/>r&ugrave;m propter quid &longs;it acceleratus, id e&longs;t cau&longs;am huius accelerationis, id <lb/>e&longs;t propter quam attributum hoc ine&longs;t &longs;ubiecto, &amp; h&aelig;c e&longs;t vera demon&shy;<lb/>&longs;tratio &agrave; priori; porr&ograve; in Phy&longs;ica de effectu &longs;en&longs;ibili &longs;upponi debet quod <lb/>&longs;it, hoc enim percipitur &longs;en&longs;u. </s>

<s>v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;upponam in Phy&longs;ica quod &longs;it motus <lb/>acceleratus, quod ignis &longs;it calidus, Sol lucidus, nix candida, vinum ru&shy;<lb/>brum, &amp;c. </s>





<s>at ver&ograve; demon&longs;trabo propter quid h&aelig;c &longs;int, &longs;ed de his <lb/>&longs;atis. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Ob&longs;eruabis etiam aliud natur&aelig; in&longs;titutum, quo &longs;cilicet factum e&longs;t, vt <pb xlink:href="026/01/117.jpg" pagenum="85"/>corpora grauia motu naturali accelerato deor&longs;um ferantur; &longs;i enim motu <lb/>ferrentur &aelig;quabili, vel e&longs;&longs;et &aelig;qualis illi quem initio &longs;ui de&longs;cen&longs;us ha&shy;<lb/>bent, qui e&longs;t tardi&longs;&longs;imus, vt con&longs;tat ex ip&longs;a ictuum differentia; atque <lb/>ita infinitum fer&egrave; tempus ponerent grauia in minimo etiam de&longs;cen&longs;u, <lb/>quod e&longs;&longs;et maxim&egrave; incommodum; &longs;i ver&ograve; motus ille e&longs;&longs;et &aelig;qualis mo&shy;<lb/>tui v.g. <!-- REMOVE S-->quem acqui&longs;iuit in &longs;patio 3. vel 4. perticarum, pondera corpo&shy;<lb/>rum cre&longs;cerent in immen&longs;um, ide&longs;t in ea proportione, qua ictus, qui in&shy;<lb/>fligitur &agrave; corpore graui confecto 4. perticarum &longs;patio maior e&longs;t ictu, qui <lb/>infligitur po&longs;t decur&longs;um minimum omnium &longs;patiorum, quod vald&egrave; in&shy;<lb/>commodum e&longs;&longs;et. </s>

</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 17.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>&AElig;qualibus temporibus &aelig;qualis impetus producitur, &longs;i &longs;it eadem applica&shy;<lb/>tio, idemque impedimentum<emph.end type="italics"/>; probatur, quia cau&longs;a huius impetus e&longs;t ne&shy;<lb/>ce&longs;&longs;aria; &longs;ed eadem cau&longs;a nece&longs;&longs;aria &aelig;qualibus temporibus &aelig;qualem <lb/>impetum producit per Ax.3. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 18.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Qua proportione cre&longs;cit impetus acceleratur motus<emph.end type="italics"/>; quia qu&aelig; proportio&shy;<lb/>ne cre&longs;cit cau&longs;a, etiam cre&longs;cit effectus per Ax.2. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 19.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc &aelig;qualibus temporibus in de&longs;cen&longs;u corpus graue acquirit aqualia ve&shy;<lb/>locitatis, vel accelerationis momenta<emph.end type="italics"/>; hoc ip&longs;um e&longs;t quod definitionis lo&shy;<lb/>co Galileus in dialogo tertio de motu naturali a&longs;&longs;umit; quod tamen <lb/>meo iudicio fuit ant&egrave; demon&longs;trandum qu&agrave;m &longs;upponendum; quare &longs;ic <lb/>demon&longs;tramus, qu&acirc; proportione cre&longs;cit impetus, cre&longs;cit motus per Th. <!-- REMOVE S--><lb/>18. &longs;ed temporibus &aelig;qualibus acquiruntur &aelig;quales impetus gradus per <lb/>Th.17. igitur &aelig;qualia velocitatis momenta, vel incrementa. </s>

</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 20.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Spatia que per curruntur motu &aelig;quabili &aelig;qualibus temporibus &longs;unt &aelig;qualia<emph.end type="italics"/>; <lb/>Probatur per Def.2. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 21.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Duo motus &aelig;quabiles, qui durant &aelig;qualibus temporibus, &longs;unt vt &longs;patia<emph.end type="italics"/>; <lb/>patet; c&ugrave;m enim impetus &longs;int vt motus per Ax. 2. motus &longs;unt vt &longs;patia; <lb/>quippe vt ex impetu &longs;equitur motus, ita ex motu confectum &longs;pa&shy;<lb/>tium. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 22.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Duo motus &aelig;quabiles, quibus percurruntur &longs;patia &aelig;qualia &longs;unt vt tempora <lb/>permutande<emph.end type="italics"/>;, patet, quia velocior e&longs;t, qu&ograve; percurritur &longs;patium &aelig;quale <lb/>minori tempore per Def.2. l. <!-- REMOVE S-->1. Igitur e&ograve; velocior, qu&ograve; minori tem&shy;<lb/>pore. </s>

</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 23.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Spatium, quod percurritur maiori tempore motu &aelig;quabili, est maius eo, <lb/>quod percurritur minori &aelig;qu&egrave; veloci motu in ea ratione, qua vnum tempus<emph.end type="italics"/><pb xlink:href="026/01/118.jpg" pagenum="86"/><emph type="italics"/>est maius alio<emph.end type="italics"/>; patet, quia &aelig;qualia &longs;unt &aelig;qualibus temporibus per Th. <!-- REMOVE S--><lb/>20. igitur in&aelig;qualibus in&aelig;qualia iuxta rationem temporum; item &longs;pa&shy;<lb/>tium, quod idem percurritur minori tempore minus e&longs;t. </s>

</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 24.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Tempus quo maius &longs;patium percurritur eodem motu &aelig;quabili, e&longs;t maius e&ograve; <lb/>qu&ograve; minus conficitur iuxta rationem &longs;patiorum:<emph.end type="italics"/> Si enim &longs;patia &longs;unt vt tem&shy;<lb/>pora, igitur tempora &longs;unt vt &longs;patia; item tempus, quo minus &longs;patium <lb/>percurritur e&longs;t minus co, quo maius. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 25.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Spatium, quod conficitur motu velociore, e&longs;t maius eo, quod percur&shy;<lb/>ritur &aelig;quali cert&egrave; tempore, &longs;ed tardiore motu,<emph.end type="italics"/> vt con&longs;tat per def. </s>

<s>2. l. <!-- REMOVE S-->1. <lb/>im&ograve; e&longs;t maius iuxta rationem velocitatis maioris, item e&longs;t minus iuxta <lb/>rationem tarditatis maioris. </s>

</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 26.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Tempus, quo conficitur &longs;patium &aelig;quale &longs;ed uelociore motu, est minus eo <lb/>quo conficitur tardiore<emph.end type="italics"/>; Probatur per def.2. &amp; per Th.22. idque in ratio&shy;<lb/>ne velocitatum permutando; item tempus quo conficitur &longs;patium &aelig;qua&shy;<lb/>le tardiore motu e&longs;t maius eo, quo conficitur velociore, patet. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 27.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Si datum mobile eodem motu &aelig;quabili duo percurrat &longs;patia, tempora mo&shy;<lb/>tuum erunt vt &longs;patia, &amp; vici&longs;&longs;im &longs;patia vt tempora.<emph.end type="italics"/></s><s> Probatur per Th. <!-- REMOVE S--><lb/>24. &amp; 23. </s>

</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 28.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Si idem mobile temporibus &aelig;qualibus percurrat duo &longs;patia motu &aelig;quabili, <lb/>&longs;ed in&aelig;quali velocitate; &longs;patia erunt vt velocitates, &amp; h&aelig; vt illa; im&ograve; &longs;i <lb/>&longs;patia &longs;unt vt velocitates, tempora erunt &aelig;qualia<emph.end type="italics"/>; pater etiam per <lb/>Th.25. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 29.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Si percurrantnr &agrave; mobili &aelig;qualia &longs;patia, &longs;ed in&aelig;quali velocitate, ip&longs;&aelig; ve&shy;<lb/>locitates erunt in ratione permutata temporum, ide&longs;t maior velocitas re&longs;pon&shy;<lb/>debit minori tempori, &amp; minor maiori<emph.end type="italics"/>; Probatur per Th.23. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 30.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Si duo mobilia mouentur motu &aelig;quabili, &longs;ed in&aelig;quali velocitate, &amp; in&aelig;qua&shy;<lb/>libus temporibus, &longs;patia &longs;unt in ratione compo&longs;ita ex ratione temporum, &amp; ex <lb/>ratione velocitatum,<emph.end type="italics"/> &longs;i enim &aelig;qualia &longs;int tempora, &longs;patia erunt vt velo&shy;<lb/>citates per Th.25. &longs;i &aelig;quales &longs;int velocitates, &longs;patia erunt vt tempora, per <lb/>Th.29. igitur &longs;i nec &aelig;quales velocitates, nec &aelig;qualia tempora, erit ratio <lb/>&longs;patiorum compo&longs;ita ex ratione temporum, &amp; ex ratione velocitatum; <lb/>&longs;it ratio temporum 3/2 ratio velocitatum 2/3 compo&longs;ita ex vtraque erit 6/2 <lb/>&longs;eu 3. vt con&longs;tat ex ip&longs;is elementis. </s></p><pb xlink:href="026/01/119.jpg" pagenum="87"/><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 31.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Si duo mobilia ferantur motu &aelig;quabili per diuer&longs;a &longs;patia, &amp; diuer&longs;a velo&shy;<lb/>citate, tempora erunt in ratione compo&longs;ita ex ratione &longs;patiorum &amp; ratione <lb/>velocitatum permutata<emph.end type="italics"/>; probatur eodem modo quo &longs;uperius Th. 30. &longs;it <lb/>ratio &longs;patiorum 4/1, velocitatum 4/2; permutetur h&aelig;c 1/4; componetur ex <lb/>vtraque 4/1, ide&longs;t 1/2, qu&aelig; e&longs;t ratio temporum. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 32.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Si duo mobilia &aelig;quabili motu ferantur per diuer&longs;a &longs;patia, &amp; in&aelig;qualibus <lb/>temporibus; ratio velocitatum erit compo&longs;ita ex ratione &longs;patiorum, &amp; ex ra&shy;<lb/>tione temporum permutata<emph.end type="italics"/>; Probatur eodem modo; &longs;it ratio &longs;patiorum <lb/>4/2 temporum 1/2, permutetur 2/1, compo&longs;ita ex vtraque erit 2/2, ide&longs;t 4. <lb/>qu&aelig; e&longs;t ratio velocitatum. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Ob&longs;eruabis h&aelig;c omnia &agrave; vige&longs;imo Theoremate maiori ex parte tradi <lb/>&agrave; Galileo &longs;uo modo, optimo quidem, &longs;ed fort&egrave; longiore qu&agrave;m par &longs;it, <lb/>nulla habita ratione cau&longs;arum phy&longs;icarum. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 33.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>In motu naturaliter accelerato impetus nouus acquiritur &longs;ingulis in&longs;tanti&shy;<lb/>bus<emph.end type="italics"/>; Probatur quia &longs;ingulis in&longs;tantibus e&longs;t eadem cau&longs;a nece&longs;&longs;aria, igi&shy;<lb/>tur &longs;ingulis in&longs;tantibus aliquem effectum producit, per Ax. 12. l.1. &longs;ed <lb/>priorem non con&longs;eruat, vt dictum e&longs;t &longs;upr&agrave;, igitur nouum producit. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 34.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc &longs;ingulis in&longs;tantibus &aelig;qualibus nouus impetus &aelig;qualis acquiritur,<emph.end type="italics"/> quip&shy;<lb/>pe e&longs;t &aelig;qualis, im&ograve; eadem cau&longs;a, igitur &aelig;qualem effectum producit per <lb/>Ax.12. l.1. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 35.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc &longs;ingulis in&longs;tantibus intenditur impetus in hoc motu<emph.end type="italics"/>; cum &longs;ingulis <lb/>in&longs;tantibus producatur nouus, &amp; prior con&longs;eruetur, cui cum addatur, <lb/>intenditur per Ax. 1. <!-- KEEP S--></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 36.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc &longs;ingulis in&longs;tantibus &aelig;qualiter cre&longs;cit &amp; intenditur impetus<emph.end type="italics"/> per Th. <!-- REMOVE S--><lb/>34. igitur &aelig;qualiter etiam &longs;ingulis in&longs;tantibus cre&longs;cit velocitas motus <lb/>per Ax.2. </s>

</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Scholium<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>Ob&longs;eruabis <expan abbr="dict&umacr;">dictum</expan> e&longs;&longs;e &longs;upr&agrave; <emph type="italics"/>instantibus &aelig;qualibus,<emph.end type="italics"/> quia temporis natura <lb/>aliter explicari non pote&longs;t, qu&agrave;m per in&longs;tantia finita, vt demon&longs;trabimus <lb/>in Metaphy&longs;ica; quid quid &longs;it, voco in&longs;tans totum illud tempus, quo res <lb/>aliqua &longs;imul producitur, &longs;iue &longs;it maius, &longs;iue minus, &longs;iue &longs;it pars maior, <lb/>vel minor, quod ad rem no&longs;tram nihil facit penitus; nam dato quocun&shy;<lb/>que tempore finito pote&longs;t dari maius &amp; minus, quod certum e&longs;t; igitur <lb/>totum illud tempus, quo producitur primus impetus acqui&longs;itus, vo-<pb xlink:href="026/01/120.jpg" pagenum="88"/>co in&longs;tans primum motus; cui &aelig;qualia deinde &longs;uccedunt tem&shy;<lb/>pora. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 37.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc cre&longs;cit impetus iuxta progre&longs;&longs;ionem arithmeticam; cum &longs;ingula in&shy;<lb/>&longs;tantia &aelig;qualem impetum addant<emph.end type="italics"/>; &longs;i primo in&longs;tanti &longs;it vnus gradus, erunt <lb/>duo; productus &longs;cilicet alteri additus qui con&longs;eruatur, tertio erunt;. </s>

<s><lb/>quarto 4. quinto 5. &amp;c. </s>

<s>igitur cre&longs;cit &longs;ecundum progre&longs;&longs;ionem arith&shy;<lb/>meticam. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 38.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Eodem modo cre&longs;cit velocitas, quia &longs;ingulis in&longs;tantibus &aelig;qualia acquirun&shy;<lb/>tur velocitatis momenta<emph.end type="italics"/> per Ax.2. &amp; per Th.36. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 39.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Maius &longs;patium acquiritur &longs;ecundo in&longs;tanti, qu&agrave;m primo, quia &longs;ecundo<emph.end type="italics"/><lb/>in&longs;tanti motus e&longs;t velocior per Th.36. igitur maius conficitur &longs;patium, <lb/>tempore &longs;cilicet &aelig;quali per Def. <!-- REMOVE S-->2. l. <!-- REMOVE S-->1. idem dico de tertio, quar&shy;<lb/>to, &amp;c. </s>



</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 40.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Spatium quod acquiritur &longs;ecund&ograve; instanti e&longs;t ad &longs;patium quod acquiritur <lb/>primo vt velocitas, qu&aelig; e&longs;t &longs;ecundo ad velocitatem, qu&aelig; e&longs;t primo.<emph.end type="italics"/></s><s> Patet per <lb/>Th.28. quia cum tempora illa &longs;int &aelig;qualia, &longs;patia &longs;unt nece&longs;&longs;ari&ograve; vt ve&shy;<lb/>locitates; quippe &aelig;quali velocitati &aelig;quale &longs;patium re&longs;pondet tempore <lb/>&aelig;quali, igitur in&aelig;quale in&aelig;quali, igitur maius maiori, idem dico de <lb/>aliis in&longs;tantibus. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 41.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc &longs;patium qucd acquiritur &longs;ecundo in&longs;tanti e&longs;t duplum illius, quod ac&shy;<lb/>quiritur primo.<emph.end type="italics"/></s><s> Probatur, quia velocitas e&longs;t dupla per Th 38. igitur &longs;pa&shy;<lb/>tium duplum, &amp; triplum tertio, quadruplum quarto, &amp;c. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 42.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc quodlibet &longs;patium cre&longs;cit &aelig;qualiter &longs;ingulis in&longs;tantibus &aelig;qualibus<emph.end type="italics"/>; <lb/>quia &longs;patia cre&longs;cunt vt motus, &longs;eu vt velocitates; h&aelig; cre&longs;cunt &aelig;qualiter <lb/>&longs;ingulis in&longs;tantibus &aelig;qualibus per Th.36. igitur &aelig;qualiter cre&longs;cunt &longs;in&shy;<lb/>gula &longs;patia per Th.40. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 43.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc &longs;patia cre&longs;cunt &longs;ingulis in&longs;tantibus &aelig;qualibus &longs;ecund&ugrave;m progre&longs;&longs;io&shy;<lb/>nem arithmeticam<emph.end type="italics"/>; quia cre&longs;cit vt velocitas per Th.40. h&aelig;c vt impetus <lb/>per Th.38. hic demum iuxta progre&longs;&longs;ionem arithmeticam per Th. 37. <lb/>igitur &longs;i &longs;patium acqui&longs;itum primo in&longs;tanti &longs;it 1. acqui&longs;itum &longs;ecundo erit <lb/>2. tertio 3. quarto 4. &amp;c. </s>

<s>hinc &longs;patia acqui&longs;ita &longs;ingulis in&longs;tantibus &longs;unt <lb/>vt &longs;eries numerorum, qui componunt progre&longs;&longs;ionem &longs;implicem, &longs;cilicet <lb/>1.2.3.4.5.6. &amp;c. </s>

<s>dixi &longs;ingulis in&longs;tantibus &aelig;qualibus, quod e&longs;t apprim&egrave; <lb/>tenendum; &longs;i enim a&longs;&longs;umantur partes temporis maiores, perturbatur <lb/>h&aelig;c progre&longs;&longs;io, de quo infr&agrave;. </s></p><pb xlink:href="026/01/121.jpg" pagenum="89"/><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 44.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc pete&longs;t dici cre&longs;cere velocitatem quolibet in&longs;tanti iuxta rationem &longs;patij <lb/>quod illo in&longs;tanti decurritur<emph.end type="italics"/>; quod cert&egrave; verum e&longs;t, dum intelligatur legi&shy;<lb/>timus horum verborum &longs;en&longs;us; quidquid reclamet Saluiatus apud <lb/>Galil. <!-- REMOVE S-->dialogo 3. mod&ograve; a&longs;&longs;umatur progre&longs;&longs;io incrementi in &longs;ingulis in&shy;<lb/>&longs;tantibus, in quibus reuer&agrave; fit; cur enim poti&ugrave;s in vno qu&agrave;m in alio? </s>



<s><lb/>quippe &longs;i comparetur velocitas vnius in&longs;tantis cum velocitate alterius; <lb/>haud dubi&egrave; erit eadem vtriu&longs;que ratio, qu&aelig; &longs;patiorum; &longs;i enim vno in&shy;<lb/>&longs;tanti percurritur vnum &longs;patium cum vno velocitatis gradu; cert&egrave; in&shy;<lb/>&longs;tanti &aelig;quali acquiritur duplum &longs;patium cum duobus velocitatis gradi&shy;<lb/>bus, nec obe&longs;t, quod obiicit Galileus tunc motus e&longs;&longs;e &aelig;quabiles; quia <lb/>motus qui fit in in&longs;tanti debet con&longs;iderari vt &aelig;quabilis; appello enim <lb/>in&longs;tans totum illud tempus, quo &longs;imul acquiritur aliquid impetus, ali&shy;<lb/>quid enim &longs;imul acquiri nece&longs;&longs;e e&longs;t; nec demum ob&longs;tat quod dicit, dari <lb/>non po&longs;&longs;e motum in&longs;tantaneum, quod multi haud dubi&egrave; negabunt; ego <lb/>in Metaphy&longs;ica explicabo quonam pacto dari po&longs;&longs;it motus in&longs;tanta&shy;<lb/>neus, qui reuer&agrave; datur actu, non potenti&acirc;; quia quacunque duratione <lb/>data pote&longs;t dari minor; igitur quocunque dato motu pote&longs;t dari minor. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Ob&longs;eruabis prim&ograve; hanc &longs;patiorum rationem, qu&aelig; e&longs;t eadem cum ra&shy;<lb/>tione velocitatum a&longs;&longs;umendam tant&ugrave;m e&longs;&longs;e in iis &longs;patiis, qu&aelig; acquirun&shy;<lb/>tur &longs;ingulis in&longs;tantibus; &longs;i enim accipiantur partes temporis maiores, qu&aelig; <lb/>conflentur ex multis in&longs;tantibus; haud dubi&egrave; maior erit ratio &longs;patio&shy;<lb/>rum, qu&agrave;m velocitatum.v.g.&longs;i primo in&longs;tanti acquiratur primo &longs;patium, <lb/>&longs;ecundo, 2.tertio, 3.quarto 4.igitur &longs;i <expan abbr="c&otilde;paretur">comparetur</expan> velocitas primi in&longs;tantis <lb/>cum velocitate quarti &aelig;qualis erit, vt ratio &longs;patiorum, id e&longs;t, vt 1. ad 4. <lb/>At ver&ograve; &longs;i accipiatur pars temporis con&longs;tans duobus in&longs;tantibus, h&aelig;c 4. <lb/>in&longs;tantia conflabunt tant&ugrave;m 2. partes temporis &aelig;quales; in prima ac&shy;<lb/>quirentur 3.&longs;patia, in &longs;ecunda 7.vt patet: &longs;ed quia velocitas prim&aelig; par&shy;<lb/>tis temporis non e&longs;t &aelig;quabilis, nec etiam velocitas &longs;ecund&aelig;; addantur <lb/>velocitates primi &amp; &longs;ecundi in&longs;tantis, itemque &longs;eor&longs;im velocitates tertij, <lb/>&amp; quarti; cert&egrave; ratio collectorum erit vt ratio &longs;patiorum; &longs;i enim velo&shy;<lb/>citas &longs;ecundi in&longs;tantis comparetur cum velocitate quarti e&longs;t tant&ugrave;m <lb/>1/2 cum tamen primum &longs;patium &longs;it ad &longs;ecundum in ratione 3/7. </s></p><p type="main">

<s>Secund&ograve;, &longs;i comparentur &longs;patia cum temporibus e&longs;t alia ratio v.g.&longs;pa&shy;<lb/>tium acqui&longs;itum vno in&longs;tanti &longs;e habet ad &longs;patium acqui&longs;itum in duobus <lb/>in&longs;tantibus, vt 1, ad 3.in tribus vt 1.ad 6.in 4. vt 1. ad 10. </s></p><p type="main">

<s>Terti&ograve; ob&longs;eruabis, non po&longs;&longs;e &longs;en&longs;u percipi in&longs;tans, im&ograve; neque tempo&shy;<lb/>ris partem ex mille in&longs;tantibus conflatam; nec etiam &longs;patium quod ac&shy;<lb/>quiritur primo in&longs;tanti; adhibenda &longs;unt tamen in&longs;tantia nece&longs;&longs;ari&ograve; ad <lb/>explicandam proportionem huius accelerationis, qu&aelig; fit in &longs;ingulis in&shy;<lb/>&longs;tantibus; vt ver&ograve; rem i&longs;tam reuocemus ad &longs;en&longs;ibilem praxim, a&longs;&longs;ume&shy;<lb/>mus proportionem aliam &longs;en&longs;ibilem, qu&aelig; proxim&egrave; ad veram accedit, nec <lb/>fer&egrave; &longs;en&longs;ibiliter fallere pote&longs;t, de qua infr&agrave;. </s></p><pb xlink:href="026/01/122.jpg" pagenum="90"/><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 40.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Collectio &longs;patiorum e&longs;t &longs;umma terminorum huius progre&longs;&longs;ionis arithmetic&aelig;<emph.end type="italics"/>; <lb/></s>

<s>C&ugrave;m enim ratio &longs;patiorum &longs;it vt ratio velocitatum; dum &longs;cilicet h&aelig;c <lb/>progre&longs;&longs;io accipitur in in&longs;tantibus, &amp; ratio velocitatum vt ratio incre&shy;<lb/>menti impetuum; vt con&longs;tat ex dictis, &amp; h&aelig;c &longs;equatur &longs;implicem <lb/>progre&longs;&longs;ionem 1. 2. 3. 4. &amp;c. </s>

<s>cert&egrave; collectio &longs;patiorum e&longs;t &longs;umma ter&shy;<lb/>minorum. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 41.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc cognito primo termino, &amp; vltimo, id e&longs;t &longs;patio quod per curritur primo <lb/>in&longs;tanti &amp; &longs;patio quod percurritur vltimo instanti, cogno&longs;citur &longs;umma, id e&longs;t <lb/>collectio &longs;patiorum, id e&longs;t, totum &longs;patium confectum.<emph.end type="italics"/> v.g.&longs;i primus terminus, <lb/>&longs;ecundus S.igitur &longs;umma e&longs;t 36. quippe vltimus terminus indicat nume&shy;<lb/>rum terminorum, quia primus e&longs;t &longs;emper vnitas, &amp; progre&longs;&longs;iuus etiam <lb/>vnitas. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 42.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc cognita &longs;umma &amp; vltimo termino cogno&longs;citur etiam numerus in&longs;tan&shy;<lb/>tium &aelig;qualium, qui &longs;emper est idem cum numero terminorum, cogno&longs;citur <lb/>etiam primus terminus, id e&longs;t &longs;patium quod primo instanti percurritur, cogno&shy;<lb/>&longs;cuntur etiam gradus velocitatis<emph.end type="italics"/>; quippe h&aelig;c omnia &longs;unt in eadem ratio&shy;<lb/>ne; qu&aelig; omnia con&longs;tant ex regulis arithmeticis pr&aelig;ter alia multa data, <lb/>qu&aelig; lubens omitto; t&ugrave;m quia Phy&longs;icam non &longs;apiunt, t&ugrave;m quia hypothe&shy;<lb/>&longs;is illa e&longs;t impo&longs;&longs;ibilis phy&longs;ic&egrave;; quis enim &longs;en&longs;u percipere po&longs;&longs;it &amp; di&shy;<lb/>&longs;tinguere vnum temporis in&longs;tans, vel &longs;patij punctum? </s>

<s>lic&egrave;t recen&longs;enda <lb/>fuerit h&aelig;c accelerati motus proportio in in&longs;tantibus, vt ad &longs;ua phy&longs;ica <lb/>principia reduceretur. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 43.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Data &longs;umma progre&longs;&longs;ionis huius &longs;implicis, inuenietur numerus terminorum, <lb/>&longs;i inueniatur numerus, per quem diuidatur, qui &longs;uperet tant&ugrave;m vnitate du&shy;<lb/>plum quotientis<emph.end type="italics"/>; quippe habebis in duplo quotientis numerum termino&shy;<lb/>rum v.g. <!-- REMOVE S-->&longs;it &longs;umma 10. diui&longs;or &longs;it 5. quotiens 2. duplus 4. hic e&longs;t nume&shy;<lb/>rus terminorum dat&aelig; &longs;umm&aelig;; &longs;it alia &longs;umma 21. diui&longs;or &longs;it 7.quotiens 3. <lb/>numerus terminorum 6. &longs;it alia &longs;umma 36. dini&longs;or &longs;it 9. quotiens 4. nu&shy;<lb/>merus terminorum 8. &longs;it alia &longs;umma 45. partitor &longs;it 10. quotiens 4 1/2, <lb/>numerus terminorum 9. quomodo ver&ograve; hic partitor inueniri po&longs;&longs;it, vi&shy;<lb/>derint Arithmetici; nec enim e&longs;t huius loci, quamquam dat&acirc; &longs;umm&acirc; <lb/>huius progre&longs;&longs;ionis &longs;implicis facil&egrave; cogno&longs;ci pote&longs;t numerus termino&shy;<lb/>rum; duplicetur enim, &amp; radix 9. neglecto re&longs;iduo dabit numerum ter&shy;<lb/>minorum v.g. <!-- REMOVE S-->&longs;it &longs;umma 21. duplicetur, erit 42. rad. </s>





<s>9. 6. dat numerum <lb/>terminorum; &longs;it &longs;umma 36. duplicetur, erit 72.rad.9.8. dabit numerum <lb/>terminorum. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 44.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Semper decre&longs;cit proportio incrementi velocitatis, id est maior est proportio <lb/>velocitatis &longs;ecundi in&longs;tantis ad primum qu&agrave;m tertij ad &longs;ecundum, &amp; maior<emph.end type="italics"/><pb xlink:href="026/01/123.jpg" pagenum="91"/><emph type="italics"/>tertij ad &longs;ecundum qu&agrave;m quarti ad tertium, atque ita deinceps<emph.end type="italics"/>; &longs;it enim <lb/>primo in&longs;tanti velocitas vt 1.&longs;ecundo erit, vt 2.tertio, vt 3.quarto, vt 4. <lb/>&longs;ed maior e&longs;t proportio 2.ad 1.qu&agrave;m 3.ad 2. &amp; h&aelig;c maior qu&agrave;m 4. ad 3. <lb/>atque ita deinceps; &longs;imiliter maior e&longs;t proportio &longs;patij quod percurritur <lb/>&longs;ecundo in&longs;tanti ad &longs;patium, quod percurritur primo, qu&agrave;m &longs;patij, quod <lb/>percurritur &longs;ecundo in&longs;tanti ad &longs;patium, quod percurritur primo qu&agrave;m <lb/>&longs;patij quod percurritur tertio ad &longs;patium, quod percurritur &longs;ecundo, at&shy;<lb/>que ita deinceps; e&longs;t enim eadem ratio &longs;patiorum qu&aelig; &longs;ingulis in&longs;tanti&shy;<lb/>bus re&longs;pondent, qu&aelig; velocitatum, vt demon&longs;tratum e&longs;t &longs;upr&agrave;. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 45.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Minor e&longs;t proportio totius &longs;patij, quod acquiritur duobus instantibus ad to<lb/>tum &longs;patium, quod acquiritur vno, qu&agrave;m &longs;it illius, quod acquiritur quatuor in&shy;<lb/>&longs;tantibus ad aliud, quod acquiritur duobus<emph.end type="italics"/>; patet ex dictis; &longs;i enim primo <lb/>in&longs;tanti acquiritur vnum &longs;patium, &longs;ecundo acquiruntur 2.igitur duobus <lb/>&longs;imul acquirantur 3. igitur proportio e&longs;t vt 3.ad 1.Sed &longs;i duobus acqui&shy;<lb/>runtur 3. &longs;patia; cert&egrave; 4.in&longs;tantibus acquiruntur 10. igitur proportio e&longs;t <lb/>vt 10.ad 3. &longs;ed proportio 10/3 e&longs;t maior 3/1, erit adhuc maior proportio &longs;pa&shy;<lb/>tij quod acquiretur 6. in&longs;tantibus ad illud quod acquiritur tribus; e&longs;t <lb/>enim (21/6) vt patet. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 46.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Si componatur &aelig;quabilis motus ex &longs;ubdupla velocitate maxima, &amp; mini&shy;<lb/>ma, &aelig;quali tempore, idem &longs;patium percurretur hoc motu naturaliter aceclera&shy;<lb/>to<emph.end type="italics"/>; &longs;it enim maxima velocitas vt 6. minima vt 1. motu naturaliter acce&shy;<lb/>lerato percurrentur &longs;patia 21. cuius &longs;umm&aelig; termini &longs;unt 6.igitur 6. in&shy;<lb/>&longs;tantibus con&longs;tat hic motus; accipiatur &longs;ubduplum maxim&aelig;, &amp; minim&aelig; <lb/>velocitatis, &longs;cilicet 3 1/2. s&iacute;tque velocitas motus &aelig;quabilis in&longs;tantium 6. <lb/>haud dubi&egrave; &longs;i ducantur 3 1/2 in 6 erunt 21.ratio ex eo petitur quod &longs;cili&shy;<lb/>cet, vt habeatur &longs;umma progre&longs;&longs;ionis arithmetic&aelig;, debet addi primus <lb/>terminus maximo, &amp; a&longs;&longs;umi &longs;ubduplum totius; illudque ducere in nu&shy;<lb/>merum terminorum per regulam arithmeticam; atqui eadem e&longs;t ratio <lb/>velocitatum, qu&aelig; &longs;patiorum; vt dictum e&longs;t &longs;upr&agrave;; &longs;cilice, in &longs;ingulis <lb/>in&longs;tantibus. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 47.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Si a&longs;&longs;umantur partes temporis majores; qu&aelig; &longs;cilicet pluribus in&longs;tantibus <lb/>constent, &longs;erueturque eadem accelerationis progre&longs;&longs;io arithmetica, &longs;patium <lb/>quod ex &longs;umma huius progre&longs;&longs;ionis re&longs;ultabit, erit minus vero,<emph.end type="italics"/> &longs;int enim 6.in&shy;<lb/>&longs;tantia, &amp; cuilibet iuxta progre&longs;&longs;ionem pr&aelig;dictam &longs;uum &longs;patium re&longs;pon&shy;<lb/>deat, haud dubi&egrave; &longs;patium &longs;ecundi erit duplum &longs;patij primi, &amp; tertium <lb/>triplum, &amp;c. </s>

<s>vt con&longs;tat ex dictis; igitur erunt &longs;patia 21. iam ver&ograve; a&longs;&longs;u&shy;<lb/>mantur 3. partes temporis, quarum qu&aelig;libet ex 2. con&longs;tet in&longs;tantibus; <lb/>prim&aelig; parti tria ex pr&aelig;dictis &longs;patiis re&longs;pondeant; cert&egrave; &longs;i &longs;eruetur pro&shy;<lb/>gre&longs;&longs;io arithmetica, &longs;ecund&aelig; re&longs;pondebunt 6. &amp; terti&aelig; 9. igitur totum <lb/>&longs;patium erit 18. minus vero quod erat 21. &longs;i ver&ograve; a&longs;&longs;umantur tant&ugrave;m 2. <lb/>partes, quarum qu&aelig;libet tribus in&longs;tantibus con&longs;tet; prim&aelig; parti re&longs;pon-<pb xlink:href="026/01/124.jpg" pagenum="92"/>debunt 6. &longs;ecund&aelig; 12. igitur &longs;umma erit 18. minor vero &longs;patio &longs;cilicet <lb/>21.hinc vides &longs;uppo&longs;ito eodem in&longs;tantium numero &longs;patium e&longs;&longs;e &longs;emper <lb/>&aelig;quale, &longs;iue a&longs;&longs;umantur partes maiores temporis, &longs;iuc minores, v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;up&shy;<lb/>po&longs;itis 6.in&longs;tantibus, ex quibus totum &longs;patium 21.con&longs;equitur, &longs;iue a&longs;&longs;u&shy;<lb/>mantur tres partes, quarum qu&aelig;libet con&longs;tet 2. in&longs;tantibus, &longs;iue du&aelig;, <lb/>quarum qu&aelig;libet con&longs;tet tribus, &longs;patium quod ex illis re&longs;ultat, e&longs;t &longs;em&shy;<lb/>per idem &longs;cilicet 18. a&longs;&longs;umptis ver&ograve; 8. in&longs;tantibus, &amp; totali &longs;patio, quod <lb/>illis re&longs;pondet 36. &longs;patium quod ex partibus re&longs;ultabit erit 30. &longs;iue &longs;int <lb/>du&aelig; partes, quarum qu&aelig;libet con&longs;tet 4. in&longs;tantibus, &longs;iue &longs;int 4. quarum <lb/>qu&aelig;libet con&longs;tet duobus: hinc rur&longs;us vides a&longs;&longs;umpto maiori in&longs;tantium <lb/>numero &longs;patium verum habere maiorem rationem ad non verum, qu&agrave;m <lb/>a&longs;&longs;umpto minori in&longs;tantium numero, v.g.a&longs;&longs;umantur 4.in&longs;tantia, &longs;umma <lb/>&longs;patiorum erit 10. &longs;i ver&ograve; a&longs;&longs;umantur 2.partes temporis, quarum qu&aelig;li&shy;<lb/>bet duobus in&longs;tantibus re&longs;pondeat; &longs;umma &longs;patij erit 9.igitur ratio ve&shy;<lb/>ri &longs;patij ad non verum e&longs;t (10/9). a&longs;&longs;umantur 6. in&longs;tantia &longs;patij veri, &longs;umma <lb/>erit 21.non veri 18. igitur ratio (21/18) &longs;eu 7/6 qu&aelig; maior e&longs;t priori: denique <lb/>a&longs;&longs;umantur 8. in&longs;tantia &longs;patij veri, &longs;umma erit 36. non veri 30 igitur ra&shy;<lb/>tio (36/30) &longs;eu 6/3 qu&aelig; maior e&longs;t prioribus, atque ita deinceps. </s>



</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 48.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Datis duabus partibus temporis, &amp; cognito &longs;patio quod percurritur in prima, <lb/>matius &longs;patium re&longs;pondebit &longs;ecund&aelig; quo vtraque in plures partes minores diui&shy;<lb/>detur, &longs;uppo&longs;ita &longs;emper eadem progre&longs;&longs;ione arithmetica in ip&longs;o incremento<emph.end type="italics"/>; <lb/>&longs;int enim du&aelig; partes temporis &longs;en&longs;ibiles &aelig;quales AG. GH. &amp; &longs;pa&shy;<lb/>tium quod percurritur prima parte temporis AG &longs;it HI; in &longs;ecunda <lb/>percurretur IO, id e&longs;t, duplum HI; at ver&ograve; diuidatur pars temporis <lb/>AG in duas &aelig;quales AF, FG, &amp; con&longs;equenter totum tempus AH in 4. <lb/>&aelig;quales; haud dubi&egrave; in prima AF percurretur NP &longs;ubtripla HI, &amp; in <lb/>&longs;ecunda FG percurretur PK dupla NP; igitur in 4. partibus temporis <lb/>AH percurretur &longs;patium decuplum PN, &longs;ed HO e&longs;t tant&ugrave;m nonecupla <lb/>NP; igitur re&longs;ultabit maius &longs;patium in 4.partibus temporis, quam in dua&shy;<lb/>bus; lic&egrave;t du&aelig; &aelig;quiualeant 4. iuxta progre&longs;&longs;ionem arithmeticam. </s></p><p type="main">

<s>Similiter AF diuidatur bifariam in E. &amp; tota AH in 8. &aelig;quales AE; <lb/>cert&egrave; primis 4.percurretur idem &longs;patium ML &aelig;quale NK &amp; HI; igitur <lb/>in prima AE percurretur MR. cuius ML &longs;it decupla; nam 4. terminis <lb/>re&longs;pondet &longs;umma 10. &longs;ed 8. terminis id e&longs;t 8.partibus temporis re&longs;pon&shy;<lb/>det &longs;umma; 6. &aelig;qualium RM; &longs;ed HO tripla ML e&longs;t tantum 30. <lb/>&aelig;qualium MR; igitur in 8.partibus re&longs;ultabit maius &longs;patium, qu&agrave;m in <lb/>4.qu&aelig; &aelig;quiualent 8. </s></p><p type="main">

<s>Ex quibus etiam con&longs;tat quo plures accipientur partes temporis ma&shy;<lb/>ius &longs;patium re&longs;ultare, donec tandem perueniatur ad vltima in&longs;tantia, ex <lb/>quibus re&longs;ultat maximum; &amp; &longs;i accipias AG partes temporis AG. GH. <lb/>habebitur HO; &longs;i ver&ograve; 4.&aelig;quales AF, cre&longs;cet &longs;patium &longs;eu &longs;umma 1/9 HO; <lb/>&longs;i autem 8. &aelig;quales AE cre&longs;cet 1/5 HO; &longs;i porr&ograve; 16. &aelig;quales AD cre&longs;&shy;<lb/>cet (22/108) &longs;i 32. &aelig;quales AC cre&longs;cet (120/408); &longs;i 64. &aelig;quales AB cre&longs;cet (496/1584). </s></p><pb xlink:href="026/01/125.jpg" pagenum="93"/><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 49.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>In progre&longs;&longs;ione arithmetica &longs;i diuidatur numerus terminorum bifariam &aelig;&shy;<lb/>qualiter nunquam &longs;umma po&longs;terioris &longs;egmenti e&longs;t tripla prioris<emph.end type="italics"/>; &longs;ed &longs;i acci&shy;<lb/>piantur duo termini e&longs;t tant&ugrave;m 2/1, &longs;i 4. e&longs;t 7/3 &longs;i 6. e&longs;t (15/6), &longs;i 8. e&longs;t (26/10), &longs;i 10&shy;<lb/>(40/25), &longs;i 12. (57/21), &longs;i 14. (77/28), atque ita deinceps. </s></p><p type="main">

<s>Ex quo ob&longs;erua mirabilem con&longs;equutionem; quippe &longs;i a&longs;&longs;umantur <lb/>tant&ugrave;m duo termini, &amp; diuidantur bifariam, &longs;umma po&longs;terioris medie&shy;<lb/>tatis e&longs;t tripla prim&aelig; min&ugrave;s vnitate; &longs;i accipiantur 4. e&longs;t tripla min&ugrave;s <lb/>2. &longs;i 6. min&ugrave;s 3. &longs;i 8. min&ugrave;s 4. &longs;i 10. min&ugrave;s 5. &longs;i 12. min&ugrave;s 6. &longs;i 14. mi&shy;<lb/>n&ugrave;s 7. atque ita deinceps; vnde &longs;umma po&longs;terioris medietatis e&longs;t &longs;emper <lb/>tripla min&ugrave;s numero &longs;uorum terminorum, vel quod clarum e&longs;t min&ugrave;s <lb/>&longs;ubduplo vltimi, &longs;eu maximi termini, vel numeri terminorum totius <lb/>progre&longs;&longs;ionis, quod prob&egrave; omnin&ograve; tenendum e&longs;t, vt omnes experienti&aelig; <lb/>explica ri po&longs;&longs;int, quod infr&agrave; faciemus. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 50.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Ex dictis hactenus facil&egrave; redditur ratio maioris ictus eiu&longs;dem corporis im&shy;<lb/>pacti quod cadit ex maiori altitudine<emph.end type="italics"/>; fuit hyp. </s>

<s>1. &longs;ed ide&ograve; e&longs;t maior ictus, <lb/>quia maior imprimitur impetus, vt patet, at ide&ograve; maior impetus impri&shy;<lb/>mitur, quia maior e&longs;t imprimens per Ax. 2. cre&longs;cit enim impetus, vt <lb/>con&longs;tat ex dictis. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 51.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc quoque ratio maxim&aelig; percu&longs;&longs;ionis ex &longs;olo pondere cadentis illius arie&shy;<lb/>tis inflict&aelig;<emph.end type="italics"/>; qu&acirc; &longs;cilicet alt&egrave; infiguntur lignei pali, quibus in mediis <lb/>aquis tanquam iacto fundamini &longs;uper&aelig;dificatur ingens &longs;&aelig;p&egrave; &aelig;dificij <lb/>moles. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 52.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc ex minima altitudine cadens corpus graue minimum fer&egrave; ictum in&shy;<lb/>fligit<emph.end type="italics"/>; quia primus impetus vald&egrave; debilis e&longs;t, qui tamen deinde facta <lb/>acce&longs;&longs;ione maximus fer&egrave; euadit. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 53.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc ratio, cur tanta &longs;it differentia impetus grauitationis, &amp; percu&longs;&longs;ionis <lb/>ab eodem mobili<emph.end type="italics"/>; quia &longs;cilicet quantumuis tempore breui&longs;&longs;imo mouea&shy;<lb/>tur, plurimis tamen eius motus durat in&longs;tantibus; atqui quolibet in&longs;tan&shy;<lb/>ti motus acquiritur impetus &aelig;qualis primo impetui grauitationis, vt <lb/>con&longs;tat ex dictis. </s>

<s>v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;it mobile quod moueatur per mille in&longs;tantia <lb/>(modicum cert&egrave; tempus &amp; minim&egrave; &longs;en&longs;ibile) po&longs;t hunc motum impetus <lb/>erit millecuplus; igitur effectus etiam millecuplus; qu&aelig; omnia con&longs;tant <lb/>ex dictis. </s>



</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 54.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc percu&longs;&longs;io qu&aelig; fit in primo in&longs;tanti contactus cre&longs;cit vt tempus<emph.end type="italics"/>; quia <lb/>c&ugrave;m &longs;ingulis in&longs;tantibus cre&longs;cat impetus per partes &aelig;quales, &amp; c&ugrave;m per&shy;<lb/>cu&longs;&longs;io &longs;it vt impetus; etiam erit vt tempus; igitur percu&longs;&longs;io, qu&aelig; fit po&longs;t <lb/>duo in&longs;tantia motus eiu&longs;dem corporis grauis deor&longs;um cadentis e&longs;t du-<pb xlink:href="026/01/126.jpg" pagenum="94"/>pla illius, qu&aelig; &longs;it po&longs;t vnum in&longs;tans motus, &amp; qu&aelig; fit po&longs;t tria tripla, po&longs;t <lb/>4. quadrupla, atque ita deinceps; c&ugrave;m enim &aelig;qualibus temporibus &aelig;qua&shy;<lb/>lia acquirantur velocitatis momenta, id e&longs;t &aelig;quales impetus, impetus <lb/>erunt vt tempora, percu&longs;&longs;iones vt impetus, igitur percu&longs;&longs;iones vt tem&shy;<lb/>pora. </s></p><p type="main">

<s>Dixi in primo in&longs;tanti contactus; nam reuer&acirc; &longs;ecund&ograve; in&longs;tanti con&shy;<lb/>tactus, ni&longs;i fiat reflexio, augetur vis ictus, quia cau&longs;a nece&longs;&longs;aria e&longs;t ap&shy;<lb/>plicata. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 55.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc po&longs;&longs;unt comparari du&aelig; percu&longs;&longs;iones duorum grauium in&aelig;qualium <lb/>dum cadunt deor&longs;um<emph.end type="italics"/>; &longs;i enim cadunt &aelig;qualibus temporibus, percu&longs;&longs;io&shy;<lb/>nes erunt vt corpora &longs;eu grauitates, vt patet v.g. <!-- REMOVE S-->corpus 2. librarum po&longs;t <lb/>2. in&longs;tantia motus infligit duplam percu&longs;&longs;ionem illius, quam infligit cor&shy;<lb/>pus vnius libr&aelig; po&longs;t 2. in&longs;tantia motus; &longs;i ver&ograve; tempora motus &longs;unt in&aelig;&shy;<lb/>qualia, &amp; grauitates &aelig;quales, percu&longs;&longs;iones erunt vt tempora; &longs;i demum <lb/>grauitates in&aelig;quales, &amp; tempora motus in&aelig;qualia, percu&longs;&longs;iones erunt <lb/>in ratione compo&longs;ita ex ratione grauitatum &amp; temporum, qu&aelig; omnia <lb/>patent ex dictis in Th. &longs;uperioribus, v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;it corpus duarum librarum, <lb/>&amp; alterum trium librarum; primum moueatur per 5. in&longs;tantia, &amp; &longs;ecun&shy;<lb/>dum 2.per 5. ratio grauitatum e&longs;t 3/2; ratio temporum e&longs;t 7/5; compo&longs;ita <lb/>ex vtraque erit (21/10); &amp; h&aelig;c e&longs;t ratio percu&longs;&longs;ionum. </s>





</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 56.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc pote&longs;t &longs;ciri ratio percu&longs;&longs;ionis. </s>

<s>&amp; grauitationis eiu&longs;dem mobilis in pri&shy;<lb/>mo in&longs;tanti vtriu&longs;que, &longs;i cogno&longs;catur numerus in&longs;tantium motus<emph.end type="italics"/>; cum enim <lb/>&longs;ingulis in&longs;tantibus &aelig;qualis impetus accedat, vt &longs;&aelig;p&egrave; dictum e&longs;t; cert&egrave; <lb/>erit percu&longs;&longs;io ad grauitationem, vt numerus in&longs;tantium motus ad vnita&shy;<lb/>tem, v.g. <!-- REMOVE S-->grauitatio &longs;it vt 4.&longs;it&qacute;ue motus eiu&longs;dem corporis per 8. in&longs;tan&shy;<lb/>tia; percu&longs;&longs;io erit ad grauitationem, vt 32. ad 4.vel vt 8.ad 1.qu&aelig; om&shy;<lb/>nia con&longs;tant ex dictis. </s>

</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 57.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc data percu&longs;&longs;ione, &longs;i cogno&longs;ceretur prob&egrave; numerus in&longs;tantium motus, <lb/>dari po&longs;&longs;et grauitatio ip&longs;i &aelig;qualis<emph.end type="italics"/>; v.g. <!-- REMOVE S-->&longs;it percu&longs;&longs;io dati corporis cadentis <lb/>per 8.in&longs;tantia, eius percu&longs;&longs;io e&longs;t octupla grauitationis eiu&longs;dem per Th. <!-- REMOVE S--><lb/>56. igitur &longs;i detur grauitatio octupla huius, erit &aelig;qualis dat&aelig; percu&longs;&shy;<lb/>&longs;ioni; dabitur autem grauitatio octupla, &longs;i detur corpus eiu&longs;dem mate&shy;<lb/>ri&aelig; octupl&ograve; grauius, vt con&longs;tat. </s>



</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 38.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc primo in&longs;tanti grauitationis nullum fer&egrave; &longs;entitur pondus,<emph.end type="italics"/> quia mini&shy;<lb/>ma vis e&longs;t, qu&aelig; con&longs;equentibus in&longs;tantibus augetur, hinc lic&egrave;t corpus <lb/>breui tempore quis &longs;u&longs;tineat, paul&ograve; po&longs;t tamen ponderi cedit, ratio e&longs;t <lb/>clara ex dictis. </s></p><pb xlink:href="026/01/127.jpg" pagenum="95"/><p type="main">

<s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Ob&longs;eruabis prim&ograve; numerum in&longs;tantium non po&longs;&longs;e &agrave; quoquam &longs;en&longs;u <lb/>percipi, nec in calculos vocari, vt patet; vnde Theoremata non po&longs;&longs;unt <lb/>ad praxim reduci defectu huius cognitionis; quam &longs;upra adhibui hypo&shy;<lb/>the&longs;eos loco. </s></p><p type="main">

<s>Secund&ograve; non pote&longs;t ad amu&longs;&longs;im tempus cum tempore componi ad <lb/>&aelig;qualitatem, vel aliam datam rationem; lic&egrave;t enim vnum tempus &longs;en&longs;i&shy;<lb/>bile haberet mille in&longs;tantia &longs;upra aliud; illa tamen in&aelig;qualitas &longs;en&longs;u <lb/>minim&egrave; perciperetur; idem dico de aliis rationibus, in quo, ni fallor, <lb/>maxim&egrave; peccant, qui temporum &aelig;qualitatem perfectam ob&longs;eruari po&longs;&longs;e <lb/>contendunt. </s></p><p type="main">

<s>Terti&ograve;, idem dico de percu&longs;&longs;ionum ratione; quippe non pote&longs;t &longs;en&longs;u <lb/>percipi in&aelig;qualitas duarum percu&longs;&longs;ionum, lic&egrave;t vires vnius pr&aelig;ualeant <lb/>mille punctis &longs;eu gradibus in&longs;en&longs;ibilibus; quippe non pote&longs;t di&longs;tingui <lb/>ab alia ni&longs;i vel ex &longs;patio; atqui di&longs;cerni non pote&longs;t, an vnum &longs;patium <lb/>&longs;uperet aliud mille punctis; vel ex &longs;ono; atqui &longs;onus pote&longs;t diuidi in in&shy;<lb/>finitos fer&egrave; gradus &longs;en&longs;u minim&egrave; perceptibiles; igitur nulla hypothe&longs;is <lb/>in his experimentis &longs;tatui pote&longs;t, quibus &aelig;qualitas vel temporum, vel <lb/>&longs;patiorum cogno&longs;ci dicatur; nec dicas aliquot in&longs;tantia par&ugrave;m di&longs;eri&shy;<lb/>minis importare, nam c&ugrave;m &longs;ingulis in&longs;tantibus fiat &aelig;qualis impetus ac&shy;<lb/>ce&longs;&longs;io, mille in&longs;tantia reddunt percu&longs;&longs;ionem millecuplam grauitationis; <lb/>hinc certum e&longs;t ex numero in&longs;tantium cognito cogno&longs;ci tant&ugrave;m po&longs;&longs;e <lb/>numerum punctorum, &amp; vici&longs;&longs;im; at cert&egrave; neuter &longs;en&longs;u percipi pote&longs;t; ne&shy;<lb/>que tanti e&longs;t hoc &longs;cire. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 59.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc &longs;i corpus graue de&longs;cenderet motu &aelig;quabili eoque &aelig;quali motui primi <lb/>in&longs;tantis; cert&egrave; vix modicum &longs;patium post multos annos decurreret<emph.end type="italics"/>; &longs;uppo&shy;<lb/>namus enim quod plures habent, lic&egrave;t accurat&egrave; experimento &longs;ubii&shy;<lb/>ci non po&longs;&longs;it, &longs;cilicet vno &longs;ecundo minuto temporis decurri &agrave; corpore <lb/>graui deor&longs;um 12. pedes &longs;patij; in &longs;ecundo minuto &longs;upponamus e&longs;&longs;e <lb/>mille in&longs;tantia, quamuis infinita pen&egrave; contineat; &longs;itque in primo in&shy;<lb/>&longs;tanti motus vnus gradus impetus; &longs;ic enim vocetur illa pars impetus, que <lb/>producitur primo in&longs;tanti; cert&egrave; po&longs;t mille in&longs;tantia motus, erunt mille <lb/>gradus impetus; iam vcr&ograve; &longs;i accipiatur &longs;ubduplum maxim&aelig; &amp; minim&aelig; <lb/>velocitatis; id e&longs;t vnius gradus, &amp; mille graduum, &longs;cilicet 500. 1/2 tri&shy;<lb/>buaturque motui &aelig;quabili; haud dubi&egrave; vno fecundo minuto percur&shy;<lb/>rentur 12. pedes &longs;patij per Th. 46. Igitur &longs;i cum velocitate vt 500, 1/2 <lb/>percurrentur 12. pedes 1.minuto, cum velocitate vt 1. percurrentur <lb/>12. pedes 500.&longs;ecundis minutis, &amp;; 30. tertiis; &longs;i ver&ograve; accipiantur plura <lb/>in&longs;tantia, v.g. <!-- REMOVE S-->1000000.in&longs;tantia, percurrentur 12. pedes 500000. &longs;e&shy;<lb/>cundis minutis; &longs;i ver&ograve; 1000000000000. percurremur 500000000000. <lb/>&longs;ecundis, id e&longs;t 8333333333. minutis, id e&longs;t 138888888. horis <pb xlink:href="026/01/128.jpg" pagenum="96"/>id e&longs;t 5787037. diebus id e&longs;t 89031. annis, omitto minutias; atqui lon&shy;<lb/>g&egrave; adhuc plura in vno minuto continentur in&longs;tantia. </s>

</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 60.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Si corpus graue de&longs;cenderet motu &aelig;quabili, eoque &aelig;quali motui vltimi in&shy;<lb/>stantis, duplum fer&egrave; &longs;patium &aelig;quali tempore conficeret illius quod conficit <lb/>motu accelerato, duplum inquam fer&egrave; &longs;cilicet paul&ograve; min&ugrave;s<emph.end type="italics"/>; quia conficit <lb/>idem motu &aelig;quabili; cuius velocitas e&longs;t &longs;ubdupla maxim&aelig; &amp; minim&aelig;; <lb/>&longs;ed minima velocitas primi in&longs;tantis pro nihilo reputatur; igitur acci&shy;<lb/>piatur tant&ugrave;m &longs;ubduplum maxim&aelig;, igitur cum velocitate &aelig;quali maxi&shy;<lb/>m&aelig;, eodem tempore duplum &longs;patium percurretur; igitur in vno minuto <lb/>&longs;ecundo, v.g. <!-- REMOVE S-->24. pedes; igitur in vno minuto primo codem motu &aelig;qua&shy;<lb/>bili 1440. pedes percurrentur; igitur in vna hora 86400. pedes; hinc <lb/>non e&longs;t quod aliqui adeo mirentur, &longs;eu poti&ugrave;s reiiciant hanc motus <lb/>accelerationem quod ex ea t&ugrave;m tardi&longs;&longs;imus motus, t&ugrave;m veloci&longs;&longs;imus <lb/>con&longs;equatur. </s>

</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 61.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Motus naturaliter acceleratus non propagatur per omnes tarditatis gra&shy;<lb/>dus<emph.end type="italics"/>; quia tot &longs;unt huius propagationis gradus, quot &longs;unt in&longs;tantia, <lb/>quibus durat hic motus, cum &longs;ingulis in&longs;tantibus noua fiat impetus ac&shy;<lb/>ce&longs;&longs;io, &longs;ed non &longs;unt infinita in&longs;tantia, vt demon&longs;trabimus in Metaphy&shy;<lb/>&longs;ica; pr&aelig;tere&agrave; lic&egrave;t e&longs;&longs;ent infinita in&longs;tantia, non fieret adhuc per omnes <lb/>tarditatis gradus h&aelig;c propagatio; quia daretur aliquis gradus tarditatis, <lb/>quem non comprehenderet h&aelig;c graduum &longs;eries; nam incipit moueri <lb/>tardi&ugrave;s in plano inclinato qu&agrave;m in libero medio rect&agrave; deor&longs;um, vt con&shy;<lb/>&longs;tat, &amp; in medio den&longs;o qu&agrave;m in raro v.g. <!-- REMOVE S-->in aqua qu&agrave;m in a&euml;re; igitur <lb/>hic tarditatis gradus, quo incipit moueri in plano tantill&ugrave;m inclinato, <lb/>non continetur inter illos, quibus mouetur rect&agrave; deor&longs;um. </s>

</p><p type="main">

<s>Hinc duplici nomine reiice Galil&aelig;um qui hoc a&longs;&longs;erit. </s>

<s>Prim&ograve;, quia <lb/>fru&longs;tr&agrave; ponit infinita in&longs;tantia &longs;ine nece&longs;&longs;itate; &longs;ecund&ograve;, quia ratio, quam <lb/>habet, non conuincit; vocat enim quietem tarditatem infinitam; &agrave; qua <lb/>dum recedit mobile, haud dubi&egrave; per omnes tarditatis gradus propagari <lb/>pote&longs;t eius motus; &longs;ed contr&agrave; prim&ograve;, nam reuer&agrave; quies non e&longs;t tarditas, <lb/>qu&aelig; motui tant&ugrave;m ine&longs;&longs;e pote&longs;t. </s>

<s>Secund&ograve;, quia t&agrave;m ex quiete &longs;equi po&shy;<lb/>te&longs;t immediat&egrave; velox motus, qu&agrave;m tardus, vt patet in proiectis. </s>

<s>Terti&ograve;, <lb/>quia motus incipit; igitur per aliquid &longs;ui, igitur ille primus motus &agrave; <lb/>quiete infinit&egrave; non di&longs;tat; denique rationes &longs;upr&agrave; propo&longs;it&aelig; rem i&longs;tam <lb/>euincunt. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Ob&longs;eruabis con&longs;ideratum e&longs;&longs;e hactenus hunc motum nulla habita <lb/>ratione re&longs;i&longs;tenti&aelig; medij, qu&aelig; haud dubi&egrave; hanc propo&longs;itionem motus <lb/>accelerati tantill&ugrave;m impedit, &longs;ed de re&longs;i&longs;tenti&agrave; medij agemus infr&agrave;. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 1.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Ex dictis facil&egrave; reiicies prim&ograve; &longs;ententiam illorum, qui negant mo-<pb xlink:href="026/01/129.jpg" pagenum="97"/>tum naturalem accelerari, quos non ratio mod&ograve; euidenti&longs;&longs;ima, &longs;ed ade&ograve; <lb/>&longs;en&longs;ibile experimentum omnin&ograve; conuincere pote&longs;t. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Corollarium.<emph.end type="italics"/> 2.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Secund&ograve; reiicies illos, qui volunt accelerationem motus e&longs;&longs;e, vel &agrave; vi <lb/>magnetica, qu&acirc; terra trahit ad &longs;e omnia grauia; vel ab alia vi occulta, <lb/>qu&acirc; c&oelig;lum pellit deor&longs;um; vel &agrave; c&oelig;le&longs;ti illa, im&ograve; poti&ugrave;s fabulos&acirc; mate&shy;<lb/>ri&acirc;; vel demum ab ip&longs;a vi &longs;ympathic&acirc;, qu&acirc; corpus &longs;uo centro propi&ugrave;s <lb/>factum totas &longs;uas vires exerit, vt ei &longs;e conjungat; qu&aelig; omnia gratis di&shy;<lb/>cuntur, &amp; ex dictis plu&longs;quam efficaciter refelli po&longs;&longs;unt, ne fru&longs;tr&agrave; tempus <lb/>in iis iterum refellendis teramus. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 3.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Terti&ograve; reiicies, qui volunt motum accelerari ex a&euml;ris &agrave; tergo impel&shy;<lb/>lentis appul&longs;u, quod ridiculum e&longs;t: lic&egrave;t enim Ari&longs;toteles videatur illud <lb/>&longs;en&longs;i&longs;&longs;e de projectis, quod examinabimus &longs;uo loco; nunquam tamen hoc <lb/>dixit de motu naturali; quin poti&ugrave;s antiquorum fuit omnium hic &longs;en&shy;<lb/>&longs;us, fieri <expan abbr="acce&longs;&longs;ion&etilde;">acce&longs;&longs;ionem</expan> mobili alicuius, vnde reddatur motus velocior; hinc <lb/>dictum illud vulgare, <emph type="italics"/>vire&longs;que acquirit eundo<emph.end type="italics"/>; nihil porr&ograve; intelligi pote&longs;t <lb/>nomine virium, ni&longs;i id, ex quo maior ictus, &longs;eu percu&longs;&longs;io &longs;equitur; illud <lb/>autem e&longs;&longs;e impetum con&longs;tat. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Corollarium.<emph.end type="italics"/> 4.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Quart&ograve; ex his &longs;ententia Ari&longs;totelica de motu accelerato optim&egrave; vin&shy;<lb/>dicatur; qu&ograve;d &longs;cilicet grauia &longs;ub finem &longs;ui motus veloci&ugrave;s &longs;erantur ver&shy;<lb/>s&ugrave;s centrum; quod ex dictis, &amp; &longs;implici&longs;&longs;imis, certi&longs;&longs;imi&longs;que principiis <lb/>demon&longs;tratum fuit. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Corollarium.<emph.end type="italics"/> 5.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Quint&ograve; reiicies etiam illorum &longs;ententiam, qui hanc accelerationem <lb/>tribuunt vel medio min&ugrave;s re&longs;i&longs;tenti, vel grauitatis augmento, vel impe&shy;<lb/>tui violento pri&ugrave;s impre&longs;&longs;o dum corpus graue attollitur, quod meo iudi&shy;<lb/>cio ridiculum e&longs;t; qua&longs;i ver&ograve; fru&longs;tum rupis deci&longs;um, deor&longs;umque ruens <lb/>impetum violentum aliquando habuerit. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 6.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Sext&ograve; reiicies illorum &longs;ententiam, qui volunt accelerationem motus <lb/>naturalis ita fieri, vt &longs;patia temporibus &aelig;qualibus acqui&longs;ita &longs;equantur &longs;e&shy;<lb/>riem numerorum imparium 1.3.5.7.9.11.13. &amp;c. </s>

<s>&amp; &longs;patia &longs;int vt <lb/>quadrata temporum v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;i primo in&longs;tanti acquiritur 1.&longs;patium: &longs;ecundo <lb/>acquiruntur 3. tertio 5. quarto 7. &amp;c. </s>





<s>fique vno in&longs;tanti acquiritur 1. <lb/>&longs;patium, duobus acquiruntur 4. tribus 9. quatuor 16. atque ita deinceps <lb/>per quadrata, qu&aelig; omnia ex dictis fal&longs;a e&longs;&longs;e con&longs;tat; quippe &longs;i &aelig;qualibus <lb/>temporibus acquiruntur &aelig;qualia velocitatis momenta; igitur &longs;i primo <lb/>in&longs;tanti e&longs;t 1.gradus, &longs;ecundo erunt 2. igitur &longs;ecundo tempore cum duo&shy;<lb/>bus gradibus velocitatis vel impetus percurrentur duo tant&ugrave;m &longs;patia, &longs;i <lb/>prim&ograve; in&longs;tanti &aelig;quali cum vno gradu percurritur vnus, &longs;ed de his fus&egrave; <lb/>infr&agrave;. </s></p><pb xlink:href="026/01/130.jpg" pagenum="98"/><p type="main">

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 7.<emph.end type="center"/></s></p><p type="main">

<s>Septim&ograve; reiicies etiam aliquos recentiores, qui volunt fieri hanc pro&shy;<lb/>gre&longs;&longs;ionem &longs;patiorum &aelig;qualibus temporibus re&longs;pondentium &longs;ecund&ugrave;m <lb/>progre&longs;&longs;ionem Geometricam, duplam, &longs;cilicet iuxta hos numeros 1. 2. 4. <lb/>8. 16. 32. &amp;c. </s>

<s>quod etiam ex eadem ratione facil&egrave; confutatur: reiicies <lb/>etiam alium recentiorem, qui vult hanc progre&longs;&longs;ionem &longs;umi ex linea <lb/>proportionaliter &longs;ect&acirc;, id e&longs;t in mediam &amp; extremam rationem; &longs;ed de <lb/>his omnibus in di&longs;&longs;ertatione &longs;equenti fus&egrave; di&longs;putamus; quippe rem hanc <lb/>tanti e&longs;&longs;e putamus, vt nihil omittendum &longs;it, quod ad eius pleni&longs;&longs;imam <lb/>confirmationem pertineat. <lb/><gap desc="hr tag"/></s></p><p type="main">

<s><emph type="center"/>DISSERTATIO<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>De Motu naturaliter accelerato.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>DV&aelig; &longs;unt poti&longs;&longs;im&ugrave;m in hac materia celebres &longs;ententi&aelig;; Prima e&longs;t <lb/>Galilei, &amp; fer&egrave; omnium recentiorum, qui po&longs;t Galileum de motu <lb/>&longs;crip&longs;erunt; inter quos, ne omittam Genuen&longs;em Patricium, Balianum; <lb/>Doctus Mer&longs;ennus, &amp; eruditus Ga&longs;&longs;endus primum locum obtinent; <lb/>quorum ille hanc &longs;ententiam multis in locis, &longs;cilicet in &longs;uis qu&aelig;&longs;tioni&shy;<lb/>bus Phy&longs;icis, in &longs;ua Galilei ver&longs;ione, in harmonia vniuer&longs;ali, &amp; demum <lb/>in &longs;ua Bali&longs;tica pa&longs;&longs;im, t&ugrave;m fus&egrave; proponit, &amp; explicat, t&ugrave;m etiam &longs;uis ra&shy;<lb/>tionibus confirmat; Galileus ver&ograve; illam habet t&ugrave;m in gemino &longs;y&longs;tema&shy;<lb/>te, t&ugrave;m in dialogo tertio de motu locali. </s></p><p type="main">

<s>Secunda &longs;ententia no&longs;tra e&longs;t, de qua non &longs;emel di&longs;putandum fuit &agrave; <lb/>Magi&longs;tro, t&ugrave;m verbis t&ugrave;m etiam litteris &longs;criptis; &amp; ne quid fort&egrave; di&longs;&longs;imu&shy;<lb/>lem, illa e&longs;t &longs;ententia quam anonimo Philo&longs;ophe (quem non &longs;ine laude <lb/>appellat idem Mer&longs;ennus) tribuit. </s>

<s>prop.18.&longs;u&aelig; Bali&longs;tic&aelig; &longs;ub finem; illa <lb/>e&longs;t inquam &longs;ententia, quam hactenus meo iudicio &longs;atis luculenter de&shy;<lb/>mon&longs;trauimus. </s></p><p type="main">

<s>Sunt tres ali&aelig; &longs;ententi&aelig;, qu&aelig; ab eodem Mer&longs;enno referuntur; prima <lb/>e&longs;t qu&aelig; progre&longs;&longs;ionem &longs;patiorum <expan abbr="e&atilde;dem">eandem</expan> e&longs;&longs;e vult cum e&acirc;, qu&aelig; e&longs;t &longs;i&shy;<lb/>nuum ver&longs;orum, centro quadrantis po&longs;ito in centro terr&aelig;, &amp; altero ex&shy;<lb/>tremo &longs;inus totius in eo punct&ograve;, in quo incipit motus. </s>

<s>Secunda e&longs;t quo&shy;<lb/>rumdam, qui volunt progre&longs;&longs;ionem &longs;patiorum, qu&aelig; &longs;ingulis temporibus <lb/>re&longs;pondent, e&longs;&longs;e in progre&longs;&longs;ione geometrica dupla iuxta hos numeros, <lb/>1.2.4.8.32. Tertia e&longs;t alicuius, qui voluit e&longs;&longs;e iuxta proportionem line&aelig; <lb/>&longs;ect&aelig; in mediam, &amp; extremam rationem. </s></p><p type="main">

<s>Tres vltim&aelig; &longs;ententi&aelig; nullo pror&longs;us nituntur fundamento; igitur vel <lb/>inde maxim&egrave; confutantur, qu&ograve;d gratis &longs;ine vllo pror&longs;us vel rationis vel <lb/>experimenti momento excogitat&aelig; &longs;int. </s>

<s>Igitur in hac di&longs;&longs;ertatione du&aelig; <lb/>tant&ugrave;m prim&aelig; di&longs;cutiend&aelig; &longs;unt Sententi&aelig; Galilei &longs;chema hic habes <lb/>in linea AF, in qua a&longs;&longs;umitur AB, &longs;patium &longs;cilicet, quod dato tempore <pb xlink:href="026/01/131.jpg" pagenum="99"/>corpus graue &longs;uo motu percurrit; &amp; &longs;ecundo tempore &aelig;quali BC, qu&aelig; <lb/>tripla e&longs;t AB, tertio CD quintupla quarto DE &longs;eptupla, quinto EF <lb/>nonecupla; vides prim&ograve; &longs;eriem numerorum imparium 1. 3. 5. 7. 9.atque <lb/>ita deinceps. </s>

<s>Secund&ograve; vides &longs;patia e&longs;&longs;e in ratione duplicata temporum, <lb/>hoc e&longs;t vt temporum quadrata. </s>

<s>v.g. <!-- REMOVE S-->&longs;i accipiatur &longs;patium AB primo tem&shy;<lb/>pore peractum, &amp; &longs;patium AC duobus temporibus confectum: ratio hu&shy;<lb/>ius ad illud e&longs;t vt 4.ad 1.id e&longs;t vt quadratum 2.ad quadratum 1. &longs;imiliter, <lb/>&longs;i accipiatur &longs;patium AD confectum tribus temporibus, erit 9.id e&longs;t qua&shy;<lb/>dratum 3, &longs;patium AE confectum 4.temporibus erit 16.id e&longs;t quadratum <lb/>4. &amp; AF 25. quadratum 5. <!-- KEEP S--></s>

</p><p type="main">

<s>H&aelig;c &longs;ententia ingenios&egrave; &agrave; Galileo excogitata ex duplici capite &agrave; &longs;uis <lb/>auctoribus confirmatur; prim&ograve; experienti&acirc;, &longs;ecund&ograve; ratione. </s>

<s>Experien&shy;<lb/>tia tribus poti&longs;&longs;imum experimentis fulcitur; primum e&longs;t in motu deor&shy;<lb/>&longs;um per lineam perpendicularem. </s>

<s>v. <!-- REMOVE S-->g. <!-- REMOVE S-->in linea AF; nam reuer&agrave; multi <lb/>&longs;unt, iique graui&longs;&longs;imi auctores in rebus t&ugrave;m philo&longs;ophicis, t&ugrave;m mathe&shy;<lb/>maticis ver&longs;ati&longs;&longs;imi, qui &longs;&aelig;pi&ugrave;s &longs;en&longs;u ip&longs;o probarunt, repetitis v&longs;que ad <lb/>nau&longs;eam experimentis, tempore vnius &longs;ecundi minuti corpus graue in <lb/>libero a&euml;re 12. pedes &longs;patij motu naturali deor&longs;um percurrere; in 2.ve&shy;<lb/>r&ograve; &longs;ecundis 48. in 3.&longs;ecundis 108.&longs;ed &longs;patia i&longs;ta &longs;unt vt temporum qua&shy;<lb/>drata, vt con&longs;tat. </s>



</p><p type="main">

<s>Secundum experimentum e&longs;t in plano inclinato, in quo corpus graue <lb/>de&longs;cendit iuxta pr&aelig;dictam progre&longs;&longs;ionem, quod expre&longs;&longs;is verbis te&longs;tatur <lb/>Galileus &agrave; &longs;e fui&longs;&longs;e probatum &longs;&aelig;pi&ugrave;s, nec vnquam &agrave; vero ne tantill&ugrave;m <lb/>quidem aberra&longs;&longs;e. </s>

<s>&longs;ed in perpendiculari deor&longs;um eadem proportione <lb/>cre&longs;cit motus, qu&acirc; in plano inclinato; lic&egrave;t in plano inclinato tardior &longs;it <lb/>motus, vt demon&longs;trabimus ali&agrave;s. </s></p><p type="main">

<s>Tertium experimentum petitur ex funependulis; in quibus &longs;&aelig;pi&ugrave;s <lb/>ob&longs;eruatum e&longs;t longitudinem funis, &amp; con&longs;equenter arcum quadrantis <lb/>longioris funependuli e&longs;&longs;e ad longitudinem, &longs;eu quadrantem alterius <lb/>breuioris, vt quadratum temporis, quo perficitur vibratio maioris ad <lb/>quadratum temporis, quo perficitur vibratio minoris.v.g.&longs;it longitudo <lb/>funependuli maioris, CG minoris ver&ograve; &longs;ubquadrupla CF; eleuetur vter&shy;<lb/>que funis, cui pondus &aelig;quale &longs;it appen&longs;um v&longs;que ad horizontalem <lb/>CDE &amp; alterum ex D; alterum ver&ograve; ex E demi&longs;&longs;um cadat deor&longs;um; haud <lb/>dubi&egrave; funependulum CE duplum temporis collocabit in decurrendo <lb/>quadrante EG, &amp; funependulum ED &longs;ubduplum. </s>

<s>v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;i CD conficit <lb/>&longs;uam vibrationem DF vno &longs;ecundo, EG conficiet &longs;uam EG duobus, vt <lb/>centies ob&longs;eruatum e&longs;t; &longs;ed EG e&longs;t quadruplus DF, vt patet; igitur EG <lb/>&amp; DF &longs;unt vt quadrata temporum, quibus percurritur EG &amp; DF &longs;ed vt <lb/>de&longs;cendit graue per DF &amp; EG, ita de&longs;cendit per CF &amp; CG, quippe <lb/>DF &amp; EG habent rationem plani inclinati deor&longs;um. </s>



</p><p type="main">

<s>Adde quod, vt &longs;e habet tempus, quo de&longs;cendit per totum quadrantem <lb/>DF, ad tempus, quo de&longs;cendit per totum quadrantem EG. &longs;ic &longs;e habet <lb/>tempus, quo de&longs;cendit per arcum DL &longs;ubduplum DF ad tempus, quo <lb/>de&longs;cendit per arcum EI &longs;ubduplum EG; item tempus, quo de&longs;cendit <pb xlink:href="026/01/132.jpg" pagenum="100"/>per arcum DM &longs;ubquadruplum DF.ad tempus, quo de&longs;cendit per arcum <lb/>EK &longs;ubquadruplum EG; denique vt tempus, quo per minimum ar&shy;<lb/>cum quadrantis DF, ad tempus, quo de&longs;cendit per alium proportiona&shy;<lb/>lem, &longs;cilicet quadruplum in quadrante EG; atqui tam parui arcus po&longs;&shy;<lb/>&longs;unt a&longs;&longs;umi, vt &longs;int ad in&longs;tar line&aelig; rect&aelig; deor&longs;um tangentis &longs;cilicet in D <lb/>&amp; in E; igitur in his rectis de&longs;cendunt grauia iuxta progre&longs;&longs;ionem pr&aelig;&shy;<lb/>dictam; id e&longs;t, cum arcus minimus a&longs;&longs;umptus ab E, qui &aelig;quiualet rect&aelig;, <lb/>&longs;it quadruplus arcus minimi a&longs;&longs;umpti &agrave; puncto D, tempus, quo percurri&shy;<lb/>tur ille primus, e&longs;t ad tempus, quo percurritur hic &longs;ubquadruplus, vt tem&shy;<lb/>pus, quo percurritur EG ad tempus, quo percurritur DF vt dictum e&longs;t; <lb/>&longs;ed tempus, quo percurritur EG e&longs;t duplum illius, quo percurritur DF; <lb/>igitur tempus, quo percurritur minimus arcus a&longs;&longs;umptus ab E, &amp; qui e&longs;t <lb/>ad in&longs;tar rect&aelig;, e&longs;t duplum temporis quo percurritur minimus arcus a&longs;&shy;<lb/>&longs;umptus &agrave; puncto D &longs;ubquadruplus prioris, &amp; qui e&longs;t etiam ad in&longs;tar re&shy;<lb/>ct&aelig;; igitur &longs;patia &longs;unt vt temporum quadrata. </s></p><p type="main">

<s>Quod autem tempus, quo percurritur EG &longs;it duplum illius, quo per&shy;<lb/>curritur DF, patet experienti&acirc;; nam &longs;i numerentur ducent&aelig; vibrationes <lb/>funependuli CD; eodem tempore numerabuntur centum vibrationes <lb/>maioris CE; igitur vibrationum minoris numerus e&longs;t duplus numeri vi&shy;<lb/>brationum maioris, dum &longs;imul vibrantur; igitur eo tempore, quo fiunt <lb/>100.maioris, fient 200. minoris; nam omnes vibrationes eiu&longs;dem fune&shy;<lb/>penduli &longs;unt &aelig;qu&ograve; diuturn&aelig;, lic&egrave;t fiant per arcus in&aelig;quales eiu&longs;dem. </s>

<s><lb/>quadrantis, vt &longs;&aelig;p&egrave; ob&longs;eruatum e&longs;t. </s>

<s>In his tribus poti&longs;&longs;imum experimen&shy;<lb/>tis fundatur h&aelig;c hypothe&longs;is Galilei, qu&aelig; nec clari&ugrave;s meo. </s>

<s>iudicio, nec <lb/>&longs;inceri&ugrave;s exponi po&longs;&longs;unt. </s></p><p type="main">

<s>Antequam rationes, qu&aelig; pro hac &longs;ententia facere videntur, propona&shy;<lb/>mus, refellamu&longs;que; o&longs;tendo prim&ograve; quomodo cum his experimentis <lb/>&longs;tare po&longs;&longs;it no&longs;tra hypothe&longs;is; igitur ex iis hypothe&longs;is Galilei rect&egrave; de&shy;<lb/>duci non pote&longs;t: quippe h&aelig;c e&longs;t certi&longs;&longs;ima regula, quam nemo Philo&longs;o&shy;<lb/>phus negare au&longs;it: Quotie&longs;cumque aliquod experimentum tale e&longs;t, vt <lb/>cum eo &longs;tare po&longs;&longs;int contrari&aelig; hypothe&longs;es; ex eo cert&egrave; neutra deduci po&shy;<lb/>te&longs;t; igitur ex propo&longs;itis experimentis &longs;uam hypothe&longs;im Galileus non <lb/>legitim&egrave; deducit, quod vt clari&longs;&longs;im&egrave; o&longs;tendam. </s></p><p type="main">

<s>Suppono, quando dicitur &longs;ecundum &longs;patium e&longs;&longs;e triplum primi &longs;up&shy;<lb/>po&longs;itis &aelig;qualibus temporibus, non ita Geometric&egrave;, certaque, &amp; acurat&acirc; <lb/>a&longs;&longs;ertione hoc dici; quin vel aliqua puncta in &longs;patiis, vel in&longs;tantia in <lb/>temporibus de&longs;int, vel &longs;uper&longs;int; &longs;i enim quis diceret &longs;patium e&longs;&longs;e tri&shy;<lb/>plum primi minus 100000. punctis, vel &longs;ecundum tempus e&longs;&longs;e maius <lb/>primo 100000. in&longs;tantibus; quis hanc, vel &longs;patij, vel temporis differen&shy;<lb/>tiam &longs;en&longs;u percipiat? </s>

<s>cum tamen experimentum omne phy&longs;icum &longs;en&longs;ui <lb/>&longs;ube&longs;&longs;e po&longs;&longs;it; nec e&longs;t quod aliquis dicat hoc idem toties ob&longs;eruatum <lb/>e&longs;&longs;e, tam multis locis temporibus, totque ac tantis etiam te&longs;tibus, vt mi&shy;<lb/>nim&egrave; fraus aliqua, vel error &longs;ubrepere potuerit; nam cum parua &longs;it, &amp; <lb/>in&longs;en&longs;ibilis t&ugrave;m &longs;patiorum, t&ugrave;m temporum differentia, maius vel minus <lb/>&aelig;quali tempus, pro &aelig;quali, maius.vel minus tripl&ograve; &longs;patium pro triplo <pb xlink:href="026/01/133.jpg" pagenum="101"/>facil&egrave; accipi pote&longs;t, cum nullum di&longs;erimen &longs;en&longs;ibile e&longs;t. </s></p><p type="main">

<s>Adde quod non de&longs;unt viri graui&longs;&longs;imi qui dicant &longs;e vix ob&longs;eruare po&shy;<lb/>tui&longs;&longs;e hanc &longs;patiorum progre&longs;&longs;ionem; plures appellare po&longs;&longs;em; vnus <lb/>Ga&longs;&longs;endus e&longs;t in&longs;tar omnium; qui &longs;an&egrave; in ob&longs;eruando fuit acurati&longs;&longs;imus, <lb/>qui literis &longs;criptis, quas ego vidi, expre&longs;&longs;is verbis a&longs;&longs;erit progre&longs;&longs;ionem <lb/>hanc non e&longs;&longs;e omnin&ograve; iuxta hos numeros 1.3.5.7. &longs;ed &longs;ingulis addendas <lb/>e&longs;&longs;e &longs;uas minutias, quas ip&longs;e habet; &longs;ed ego omitto, quia etiam &longs;ua incer&shy;<lb/>titudine laborant; igitur nullo experimento ad amu&longs;&longs;im concludes, <lb/>vel <expan abbr="&aelig;qualitat&etilde;">&aelig;qualitatem</expan> vel aliam accuratam t&ugrave;m temporum t&ugrave;m &longs;patiorum pro&shy;<lb/>portionem: Equidem &longs;en&longs;u percipio practicam hanc e&longs;&longs;e maiorem pede; <lb/>at tot lineis vel <expan abbr="p&utilde;ctis">punctis</expan> &longs;uperare ne Argus quidem cert&ograve;, ac di&longs;tinct&egrave; cer&shy;<lb/>neret: Sed efficaciter, meo iudicio, hanc Galilei hypothe&longs;im refello; &longs;int <lb/> 2.partes temporis &aelig;quales AE, EF, e&aelig;que &longs;en&longs;ibiles; nec enim ali&aelig; a&longs;&shy;<lb/>&longs;umi po&longs;&longs;unt; &longs;intque minim&aelig; omnium &longs;en&longs;ibilium; haud dubi&egrave; con&longs;tant <lb/>&longs;ingul&aelig; infinitis fer&egrave; aliis in&longs;en&longs;ibilibus, vt patet; igitur &longs;ic ratiocinatur <lb/>Galileus; in prima parte temporis AE corpus graue percurrit &longs;patium <lb/>GH, &amp; in &longs;ecunda &aelig;quali EF percurrit &longs;patium HL triplum prioris; <lb/>igitur &longs;patia &longs;unt vt quadrata temporum, rect&egrave;; &longs;ed antequam vlterius <lb/>progrediar;</s><s> Qu&aelig;ro vel &agrave; Galileo, vel &agrave; quolibet alto, vtrum &longs;patium <lb/>HL &longs;it omnino triplum? </s>

<s>&amp; &longs;i aliquis contenderet dee&longs;&longs;e (1/1000000) GH <lb/>vtrum experimento pr&aelig;&longs;enti conuinci po&longs;&longs;it? </s>

<s>nemo, vt puto, id a&longs;&longs;erere <lb/>au&longs;it; hoc po&longs;ito, a&longs;&longs;umptaque progre&longs;&longs;ione arithmetica <expan abbr="qu&atilde;">quam</expan> no&longs;tra &longs;en&shy;<lb/>tentia in &longs;patiis ad&longs;truit; &longs;i prima parte temporis AE percurratur &longs;pa&shy;<lb/>tium GH, &longs;ecunda EF. percurretur tant&ugrave;m HK duplum GH; igitur <lb/>minus e&longs;t hoc &longs;patium vero &longs;patio 1/4. &longs;cilicet tota KL; res pror&longs;us de&shy;<lb/>mon&longs;trata e&longs;&longs;et, &longs;i termini proportionis vnius e&longs;&longs;ent tant&ugrave;m 2. id e&longs;t, &longs;i <lb/>progre&longs;&longs;io fieret in partibus temporis &longs;en&longs;ibilibus; at po&longs;ito quod &longs;int <lb/>plures termini, vt reuer&acirc; &longs;unt; nam in totidem terminis fit progre&longs;&longs;io, in <lb/>quibus fit augmentum impetus, vel accelerationis acce&longs;&longs;io; atqui h&aelig;c <lb/>fit in &longs;ingulis in&longs;tantibus, lic&egrave;t finitis, igitur &amp; progre&longs;&longs;io; Quare du&aelig; <lb/>partes temporis AE, EF diuidantur in 4. &aelig;quales AD; cert&egrave; in duabus <lb/>primis percurretur &longs;patium. </s>

<s>VQ &aelig;quale GH; igitur duabus vltimis per&shy;<lb/>curretur QK, qu&aelig; &longs;it ad QV vt 7. ad 3. nam prima parte percurritur 1. <lb/>&longs;patium. </s>

<s>&longs;ecunda 2. igitur QV continet tria &longs;patia; tertia ver&ograve; 3. quarta <lb/>4.ergo h&aelig; du&aelig; vltim&aelig; 7. &longs;ed QM e&longs;t dupla QV; igitur continet 6. igi&shy;<lb/>tur MK e&longs;t 1/3 VQ, vel KL; igitur KM e&longs;t (1/12) GL; igitur 12. L (1/10), vel <lb/>1/6, igitur VK e&longs;t ad GL vt 10.ad 12. igitur totum &longs;patium VK e&longs;t mi&shy;<lb/>nus vero 1/6. Pr&aelig;terea 2. partes temporis AE EF diuidantur in 8. partes <lb/>&aelig;quales AE; haud dubi&egrave; 4. primis percurretur &longs;patium XT &aelig;quale <lb/>GH, quod debet diuidi in 10. &longs;patia; nam 4. terminis, &longs;eu temporibus <lb/>re&longs;pondent &longs;patia 10. quibus &aelig;qualia &longs;unt 40. in teta GL, cuius XT e&longs;t <lb/>(1/14), &longs;ed &longs;i in 4.primis acquiruntur 10. 4. vltimis EF acquiruntur 26.&longs;cili&shy;<lb/>cet T 5; igitur tota X 5. e&longs;t 6. igitur e&longs;t ad GL vt 36. ad 40. &longs;eu 9. ad <lb/>10. igitur X 5. e&longs;t &longs;patium minus vero (1/10). </s></p><p type="main">

<s>Pr&aelig;terea diuidatur tempus AF in 16. partes &aelig;quales AB; haud dubi&egrave; <pb xlink:href="026/01/134.jpg" pagenum="102"/>8 primis acquiritur &longs;patium YS &aelig;quale GH; quod debet diuidi in &longs;pa&shy;<lb/>tiola 36, qu&aelig; re&longs;pondent 8. temporibus, &longs;eu terminis huius progre&longs;&longs;io&shy;<lb/>nis, quibus &aelig;qualia &longs;unt 144. in GL, cuius YS e&longs;t 1/4, &longs;ed &longs;i in 8. primis <lb/>acquiruntur 36. in 8. vltimis acquirentur 100. igitur S 6. e&longs;t 100. igitur <lb/>Y6. e&longs;t 136. igitur e&longs;t ad GL vt 136. ad 144.&longs;eu 17.ad 18.igitur Y6.e&longs;t <lb/>&longs;patium totale minus vero (1/18). </s></p><p type="main">

<s>Deinde diuidatur adhuc tempus AF in partes 32. &aelig;quales, 16. pri&shy;<lb/>mis acquiritur ZR &aelig;quale GH, quod debet diuidi in &longs;patiola 136.qu&aelig; <lb/>re&longs;pondent 16. temporibus quibus &aelig;qualia &longs;unt 544. in tota GL, cuius <lb/>ZR e&longs;t 1/4 &longs;ed &longs;i in 16. primis temporibus acquiruntur 136. in vltimis <lb/>16. acquiruntur 392. igitur R 7. e&longs;t 392. &amp; ZR 136. igitur Z 7.528. <lb/>igitur Z 7. e&longs;t ad GL, vt 528. ad 544. &longs;eu vt 33. ad 34. igitur Z 7 e&longs;t <lb/>&longs;patium minus ver&ograve; (1/34) </s></p><p type="main">

<s>Denique &longs;i diuidatur tempus AF in partes 64.&longs;patium acqui&longs;itum erit <lb/>minus vero, a&longs;&longs;umpto &longs;cilicet tota HL (1/66), &longs;i diuidatur in 128. partes, erit <lb/>minus (1/130) &longs;i diuidatur in 256. partes, erit minus (1/258) &longs;ed temporis par&shy;<lb/>tes 2.AE. EF minim&egrave; &longs;en&longs;ibilium diuidi po&longs;&longs;unt in infinita fer&egrave; in&longs;tan&shy;<lb/>tia; &longs;int tant&ugrave;m ex.g. </s>

<s>1000000. igitur &longs;patium tunc acqui&longs;itum erit mi&shy;<lb/>nus &longs;uppo&longs;ito vero HL (1/1000002), qu&aelig; &longs;i de&longs;it tant&ugrave;m &longs;patio KL vt &longs;it 1/4 <lb/>totius GL, quis hoc di&longs;cernat? </s>

<s>igitur etiam &longs;uppo&longs;ita progre&longs;&longs;ione arith&shy;<lb/>metica, qu&aelig; fiat in finitis in&longs;tantibus; &longs;i ob&longs;eruetur acurati&longs;&longs;im&egrave; &longs;patium, <lb/>quod percurritur in vna parte temporis &longs;en&longs;ibili v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;patium GH in <lb/>parte temporis AE; &longs;patium, quod acquiretur in tempore &longs;ecundo &aelig;qua&shy;<lb/>li t&agrave;m prop&egrave; accedet ad &longs;patium HL, id e&longs;t ad triplum prioris GH, vt <lb/>nullus mortalium di&longs;cernere po&longs;&longs;it; igitur cum hoc experimento t&agrave;m <lb/>pote&longs;t &longs;tare no&longs;tra hypothe&longs;is, qu&agrave;m alia Galilei, igitur neutra ex eo tan&shy;<lb/>t&ugrave;m euinci pote&longs;t. </s>



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<s>Hinc obiter ob&longs;erua progre&longs;&longs;ionem differentiarum; quippe &longs;i &longs;int <lb/>tant&ugrave;m 2. partes temporis, differentia e&longs;t 1/4; &longs;i 4.1/6 &longs;i 8. (1/10); &longs;i 16.(1/18); &longs;i 32. <lb/>(1/34); &longs;i 64.(1/66) nam prim&ograve; denominator fractionis &longs;uperat tant&ugrave;m binario <lb/>numerum partium temporis; &longs;ecund&ograve; differenti&aelig; denominatorum &longs;unt <lb/>in progre&longs;&longs;ione geometrica dupla numerorum 2. 4. 8. 16. 32. 64. <lb/>128. &amp;c. </s></p><p type="main">

<s>Eodem modo &longs;oluendum e&longs;t &longs;ecundum experimentum rotati globi in <lb/>plano decliui; pr&aelig;&longs;ertim cum globus ab incur&longs;u a&longs;periorum partium <lb/>t&ugrave;m globi, t&ugrave;m plani &longs;altuatim de&longs;cendat; quod dubium e&longs;&longs;e non pote&longs;t, <lb/>&amp; qu&ograve; decliuius erit, facili&ugrave;s re&longs;iliet a plano, vt patet; &longs;ed de motu in <lb/>planis inclinatis fus&egrave; agemus infr&agrave; libro integro. </s></p><p type="main">

<s>Quod &longs;pectat ad tertium experimentum; multa in eo &longs;upponuntur <lb/>vel fal&longs;a, vel &longs;altem dubia: vel ea qu&aelig; cum no&longs;tra hypothe&longs;i optim&egrave; con&shy;<lb/>ueniant. </s>

<s>Primum e&longs;t, quando dicuntur omnes vibrationes eiu&longs;dem fune&shy;<lb/>penduli, &longs;iue maiores, &longs;iue minores e&longs;&longs;e &aelig;quediuturn&aelig;, quod manife&longs;tis <lb/>experimentis repugnat; quippe vibratio maior pl&ugrave;s temporis; minor ve&shy;<lb/>r&ograve; min&ugrave;s in &longs;uo de&longs;cen&longs;u ponit; dimittantur enim duo funependula &aelig;&shy;<lb/>qualia; alterum quidem ex altitudine 90.graduum, alterum ex altitudine <pb xlink:href="026/01/135.jpg" pagenum="103"/>10. vel 15.graduum; ita vt &longs;imul vibrationes &longs;uas incipiant; numerentur <lb/>vibrationes vtriu&longs;que, vbi 100. &egrave; minoribus numerat&ccedil; fuerint, numera&shy;<lb/>buntur circiter 97. &egrave; maioribus, quod &longs;&aelig;pi&ugrave;s ob&longs;eruaui te&longs;tibus etiam <lb/>adhibitis; hoc ip&longs;um etiam ob&longs;eruarunt alij; atque adeo ip&longs;e P.Mer&longs;en&shy;<lb/>nus, qui L. 2. &longs;u&aelig; ver&longs;ionis, Ar.17. Galileum arguit par&ugrave;m acurati &longs;tu&shy;<lb/>dij in his ob&longs;eruationibus adhibiti: rationem huius effectus in libro de <lb/>funependulis explicabimus; imm&ograve; &longs;i omnes vibrat&igrave;ones maiores prim&aelig; <lb/>vibrationi 90. grad. <!-- REMOVE S-->e&longs;&longs;ent &aelig;quales, &amp; ali&aelig; minores alterius funependu&shy;<lb/>li &longs;en&longs;un, vt &longs;it, minuerentur; vix 90. maiores numerare po&longs;&longs;es, iam enu&shy;<lb/>meratis 100. ex minoribus; &longs;ed de his omnibus &longs;uo loco; in vna tamen <lb/>vel altera vibratione vix aliquod di&longs;crimen ob&longs;eruatur; quod tamen ob&shy;<lb/>&longs;eruari facil&egrave; po&longs;&longs;et in maioribus funependulis. </s>

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<s>Secundum, quod &longs;upponitur, e&longs;t quod longitudines funependulorum <lb/>&longs;int pror&longs;us, vt quadrata temporum, quibus vibrationes &longs;ingulorum <lb/>fiunt, v.g. <!-- REMOVE S-->funependulum longitudinis 4. pedum facere vnam vibratio&shy;<lb/>nem eo tempore, quo funependulum longitudinis vnius pedis facit duas; <lb/>quod prim&ograve; in multis vibrationibus non t&agrave;m accurat&egrave; ob&longs;eruatur; <expan abbr="&longs;ec&umacr;-d&ograve;">&longs;ecun&shy;<lb/>d&ograve;</expan> lic&egrave;t ob&longs;eruaretur &longs;en&longs;ibiliter, id emre&longs;ponderi debet, quod &longs;upr&agrave; in <lb/>&longs;ingulis vibrationibus e&longs;&longs;e tant&ugrave;m di&longs;crimen; uod etiam in multis &longs;en&longs;i&shy;<lb/>bile non e&longs;t; &longs;i enim di&longs;crimen primarum vibrationem v.g.&longs;it (1/100000000) <lb/>cert&egrave; vltimarum adhuc in&longs;en&longs;ibile erit. </s>

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<s>Tertium &longs;uppo&longs;itum fuit, minimum arcum minoris quadrantis a&longs;&longs;um&shy;<lb/>ptum, &amp; alium minoris quadrantis e&longs;&longs;e ad in&longs;tar perpendicularium; c&ugrave;m <lb/>tamen diuer&longs;a &longs;it inclinatio minoris, &amp; maioris quadrantis: quippe <lb/>principium maioris accedit propi&ugrave;s ad perpendicularem; facit enim <lb/>angulum contingenti&aelig; minorem; alia ver&ograve; extremitas accedit propi&ugrave;s <lb/>ad horizontalem propter rationem pr&aelig;dictam; hinc illa extremitas ma&shy;<lb/>ioris, vnde e&longs;t initium motus, planum decliuius facit; altera ver&ograve; min&ugrave;s <lb/>decliue; &longs;ed h&aelig;c fus&egrave; pro&longs;equar &longs;uo loco. </s></p><p type="main">

<s>Quartum, quod &longs;upponitur e&longs;t, accelerationem motus fieri in qua&shy;<lb/>drante in ea ratione, in qua fit per plana chordarum inclinata, quod <lb/>etiam fai&longs;um e&longs;t; quia in eodem plano inclinato &longs;upponitur eadem <lb/>inclinatio; &longs;ecus in quadrante, cuius &longs;ingula puncta nouam faciunt in&shy;<lb/>clinationem: adde quod quarta pars quadrantis maioris EK non facit <lb/>eandem inclinationem, quam totus quadrans minor DF ip&longs;i EK &aelig;qua&shy;<lb/>lis; quamquam hoc ip&longs;i vltr&ograve; concedent aduer&longs;arij. </s></p><p type="main">

<s>Pr&aelig;terea, &longs;it ita vt &longs;upponitur; ita vt &longs;en&longs;ibiliter differentia huius <lb/>progre&longs;&longs;ionis percipi non po&longs;&longs;it, &longs;intque numerat&aelig; omnes vibrationes <lb/>&longs;en&longs;ibiles dati funependuli ex altitudine 90, grad. <!-- REMOVE S-->demi&longs;&longs;i; qu&aelig; vix e&longs;&longs;e <lb/>po&longs;&longs;unt 1800; &longs;int autem plures &longs;cilicet 2000. dicis confectas e&longs;&longs;e 2000 <lb/>minoris funependuli eo tempore, quo 1000. tant&ugrave;m in quadruplo fune&shy;<lb/>pendulo nnmerantur; annuo quidem, &longs;i res tant&ugrave;m &longs;en&longs;ibiliter con&longs;ide&shy;<lb/>retur; &longs;in ver&ograve; &longs;ec&ugrave;s, id pernego; &longs;ed dico dee&longs;&longs;e v. <!-- REMOVE S-->g. <!-- REMOVE S-->1000000. puncta <lb/>&longs;patij, qu&aelig; di&longs;cerni non po&longs;&longs;unt, ita vt prim&aelig; vibrationi 1000. pun&shy;<lb/>cta &longs;ecund&aelig;, 2000. terti&aelig; 3000. &amp;c. </s>







<s>vltim&aelig; ver&ograve;, &longs;eu mille&longs;im&aelig; <pb xlink:href="026/01/136.jpg" pagenum="104"/>1000000. qu&aelig; omnia &longs;unt in&longs;en&longs;ibilia, neque maiorem habent diffi&shy;<lb/>cultatem, qu&agrave;m in motu perpendiculari, de quo &longs;upr&agrave;; etiam conce&longs;&longs;is <lb/>vltr&ograve; omnibus experim&eacute;tis propo&longs;itis. </s>

<s>Igitur &longs;uppo&longs;it&acirc; progre&longs;&longs;ione &longs;pa&shy;<lb/>tiorum arithinetica in in&longs;tantibus, t&agrave;m prop&egrave; accedit ad aliam, qu&agrave;m <lb/>Galileus ponit, &longs;iue in perpendiculari deor&longs;um, &longs;iue in quadrante fune&shy;<lb/>penduli; a&longs;&longs;umptis &longs;cilicet partibus temporis &longs;en&longs;ibilibus, vt differentia <lb/>di&longs;cernit non po&longs;&longs;it; imm&ograve; nec duplum diffetenti&aelig;, nec centuplum, nec <lb/>millecuplum; &longs;ed de his &longs;atis qu&aelig; ex dictis &longs;upr&agrave; facil&egrave; intelligi po&longs;&longs;unt: <lb/>quare veniemus iam ad rationes. </s></p><p type="main">

<s>Prima ratio, quam affert Galileus e&longs;t; quia cum natura in &longs;uis opera&shy;<lb/>tionibus adhibeat &longs;implici&longs;&longs;ima media; &amp; cum acceleratio motus natu&shy;<lb/>ralis non po&longs;&longs;it fieri iuxta faciliorem, vel &longs;impliciorem progre&longs;&longs;ionem, <lb/>qu&agrave;m &longs;it-ea qu&aelig; fit per quadrata; non e&longs;t dubium, quin iuxta illam pro&shy;<lb/>gre&longs;&longs;io motus naturaliter accelerati fieri debeat; pr&aelig;&longs;ertim c&ugrave;m omni&shy;<lb/>bus experimentis con&longs;entiat, &amp; in ea omnia ph&aelig;nomena explicari <lb/>po&longs;&longs;int. </s></p><p type="main">

<s>Re&longs;p. Prim&ograve; progre&longs;&longs;ionem arithmeticam &longs;implicem iuxta hos nu&shy;<lb/>meros 1.2.3.4. long&egrave; &longs;impliciorem e&longs;&longs;e alia qu&aelig; fit iuxta illos 1.3.5.7.vt <lb/>nemo non iudicabit. </s>

<s>Secund&ograve; <expan abbr="c&utilde;">cum</expan> accidit duas hypothe&longs;es conuenire cum <lb/>omnibus experimentis &longs;eu ph&aelig;nomonis, debet e&longs;&longs;e aliqua ratio, cur ad&shy;<lb/>hibeatur vna poti&ugrave;s qu&agrave;m alia; &longs;ed nulla e&longs;t ratio, cur Galileus adhibeat <lb/>&longs;uam, vti videbimus; nos ver&ograve; ratione demon&longs;tratiu&acirc; probamus no&longs;tram; <lb/>igitur no&longs;tra e&longs;t pr&aelig;ferenda pro theorica rei veritate; quia ver&ograve; alia in <lb/>temporibus &longs;en&longs;ibilibus proxim&egrave; ad verum accedit eam adhibendam e&longs;&longs;e <lb/>decernemus infr&agrave; ad praxim, &amp; communem i&longs;torum motuum men&shy;<lb/>&longs;uram. </s></p><p type="main">

<s>Secunda ratio e&longs;t; quia, &longs;i accipiatur &longs;ubduplum maxim&aelig;, &amp; minim&aelig; <lb/>velocitatis; &longs;itque ex his qua&longs;i conflata velocitas motus &aelig;quabilis, hoc <lb/>motu &aelig;quabili &aelig;quali tempore p&egrave;rcurretur &longs;patium idem, quod ant&egrave; <lb/>motu naturaliter accelerato v.g. <!-- REMOVE S-->&longs;int numeri dat&aelig; progre&longs;&longs;ionis 1.3.5.7. <lb/>9.11. cert&egrave; &longs;umma terminorum &longs;eu totum &longs;patium erit 36. accipiatur <lb/>&longs;ubduplum primi 1/2 &amp; &longs;exti 5. 1/2 habebitur velocitas vt 6. igitur cum <lb/>velocitate vt 6. &aelig;quali tempore percurretur &longs;patium 36. quod rect&egrave; de&shy;<lb/>mon&longs;trauit Galileus. <!-- KEEP S--></s>

</p><p type="main">

<s>Re&longs;pondeo non min&ugrave;s no&longs;tram hypothe&longs;im cum hoc ip&longs;o &longs;tare, qu&agrave;m <lb/>&longs;tet hypothe&longs;is Galilei: &longs;int enim 6. in&longs;tantia, &amp; &longs;ingulis &longs;ua tribuantur <lb/>&longs;patiola more dicto 1 2 3 4 5 6. &longs;umma &longs;patiorum e&longs;t 21. a&longs;&longs;umatur &longs;ub&shy;<lb/>duplum velocitatis primi in&longs;tantis 1/2, &amp; &longs;ubduplum &longs;exti in&longs;tantis, &longs;cili&shy;<lb/>cet 3. conflatum ex vtroque 3 1/3; ducatur in 6.id e&longs;t in numerum termi&shy;<lb/>norum, vel in&longs;tantium; &longs;umma erit 21. igitur quod tribuit Galileus &longs;u&aelig; <lb/>progre&longs;&longs;ioni, etiam no&longs;tr&aelig; competit. </s></p><p type="main">

<s>Tertia ratio petitur ex mathe&longs;i &longs;it enim linea AE diui&longs;a in qautuor <lb/>partes &aelig;quales, qu&aelig; nobis repre&longs;entent 4. partes temporis &aelig;quales; <lb/>haud dubi&egrave;, c&ugrave;m acquirantur temporibus &aelig;qualibus &aelig;qualia velocitatis <lb/>momenta; haud dubi&egrave;, inquam, his 4. temporibus AB, BC, CD, DE, ac-<pb xlink:href="026/01/137.jpg" pagenum="105"/>quirentur &aelig;quales velocitatis gradus; &longs;it autem BI, men&longs;ura velocitatis, <lb/>quam acquirit mobile cadens ex &longs;ua quiete in fine prim&aelig; partis tempo&shy;<lb/>ris AB; cert&egrave; in fine &longs;ecund&aelig; partis temporis BC acquiret velocitatem, <lb/>qu&aelig; coniuncta cum priore BI faciet duplam CH, &amp; in fine terti&aelig; par&shy;<lb/>ti&aelig; CD triplam DG; denique in fine quart&aelig; DE quadruplam EF; quip&shy;<lb/>pe cum in parte BC remaneat tota velocitas B, &amp; acquiratur &aelig;qualis; <lb/>cert&egrave; in fine BC e&longs;t velocitas CH dupla illius qu&aelig; commen&longs;uratur BI. <lb/>&longs;uniliter in parte CD remanebit vtraque, &amp; accedet altera; igitur e&longs;t ve&shy;<lb/>locitas DG tripla BI, &amp; EF e&longs;t quadrupla: Similiter ita &longs;e ratio habet <lb/>cuiu&longs;libet alterius partis inter AB ad aliam alterius partis inter BC, vt <lb/>line&aelig; duct&aelig; parallel&aelig; BICH, &amp;c. </s>

<s>igitur cum &longs;patium acqui&longs;itum re&longs;&shy;<lb/>pondeat exercitio huius velocitatis; &longs;itque in&longs;tanti B vt BI, &amp; in&longs;tanti <lb/>C vt CH; cert&egrave; tempore AB e&longs;t vt triangulum AIB; nam &longs;patium AIB <lb/>e&longs;t collectio omnium linearum, qu&aelig; duci po&longs;&longs;unt parallel&aelig; in tempote <lb/>AB; idem dico de trapezo CBIH, qui e&longs;t triplus trianguli IBA; &amp; de <lb/>trapezo GDCH, qui e&longs;t quintuplus; igitur triangulum HCA e&longs;t qua&shy;<lb/>druplum IBA; quia h&aelig;c triangula &longs;unt vt quadrata laterum; igitur &longs;pa&shy;<lb/>tium acqui&longs;itum temporibus AB, BC, e&longs;t ad &longs;patium acqui&longs;itum tempo&shy;<lb/>re AB, vt triangulum HCB ad triangulum IBA; igitur vt quadratum <lb/>AB ad quadratum AC; igitur vt quadratum temporis AB ad quadra&shy;<lb/>tum temporis AC; igitur &longs;patia diuer&longs;is temporibus decur&longs;a &longs;unt vt qua&shy;<lb/>drata temporum, quibus &longs;ingula decurruntur. </s></p><p type="main">

<s>H&aelig;c ratio ad &longs;peciem videtur e&longs;&longs;e demon&longs;tratiua, deficit tamen &agrave; ve&shy;<lb/>ra demon&longs;tratione; primo, quia &longs;upponit in&longs;tantia infinita, qu&aelig; multi <lb/>pa&longs;&longs;im negabunt in tempore; imm&ograve; aliquis vltr&ograve; demon&longs;trare tentaret <lb/>non e&longs;&longs;e infinita; itaque ex &longs;uppo&longs;itione quod &longs;int tant&ugrave;m finita in&longs;tan&shy;<lb/>tia a&longs;&longs;umantur 4. &aelig;qualia AC, CD, DE, EF, cert&egrave; cum in&longs;tans &longs;it to&shy;<lb/>rum &longs;imul, velocitatem habet &aelig;quabilem &longs;ibi toti re&longs;pondentem; igitur <lb/>in&longs;tanti AC re&longs;pondeat velocitas, cuius men&longs;ura &longs;it ABCG; haud du&shy;<lb/>bi&egrave; in&longs;tanti CD re&longs;pondebit velocitas CH, &longs;cilicet dupla AB; nam re&shy;<lb/>manet primus velocitatis gradus acqui&longs;itus primo in&longs;tanti: &longs;ed alter &aelig;&shy;<lb/>qualis acquiritur; igitur e&longs;t duplus prioris; igitur re&longs;pondet line&aelig; DK. <lb/>qu&aelig; tripla e&longs;t AB, &amp; quarto line&aelig; FN, qu&aelig; e&longs;t quadrupla AB; igitur <lb/>cre&longs;cit &longs;patium, vt rectangula CB, DH, EK, FM; &longs;ed h&aelig;c cre&longs;cunt iuxta <lb/>progre&longs;&longs;ionem numerorum 1.2.3.4. nec aliter res e&longs;&longs;e pote&longs;t ex &longs;uppo&longs;i&shy;<lb/>tione quod &longs;int in&longs;tantia finita; quod alibi ex profe&longs;&longs;o tractamus: quippe <lb/>illa qu&aelig;&longs;tio pertinet ad Metaphy&longs;icam, non ver&ograve; ad phy&longs;icun; nam vel <lb/>&longs;ingula aliquid addunt, vel nihil: aliquid addunt haud dubi&egrave;; igitur con&shy;<lb/>&longs;iderantur tant&ugrave;m 4. in&longs;tantia prima AC, CD, DE, EF, in &longs;ua &longs;crie; cert&egrave; <lb/>non po&longs;&longs;unt aliam progre&longs;&longs;ionem facere qu&agrave;m eam, qu&aelig; e&longs;t iuxta hos <lb/>numeros 1.2.3.4.vnde non fit per triangula &longs;ed per rectangula minima; <lb/>igitur linea AF pr&aelig;cedentis figur&aelig; non e&longs;t recta, &longs;ed denticulata, qualis <lb/>e&longs;&longs;et ABGHIKLMN, &longs;ed long&egrave; minoribus gradibus, &longs;eu denticulis. </s>

<s><lb/>Hinc qu&ograve; rectangula CB, DH, &amp;c. </s>

<s>fient maiora in partibus &longs;cilicet tem&shy;<lb/>poris &longs;en&longs;ibilibus, &longs;eruata &longs;cilicet in illis progre&longs;&longs;ione numerorum 1.2.3. <pb xlink:href="026/01/138.jpg" pagenum="106"/>4.progre&longs;&longs;io longi&ugrave;s di&longs;cedet &agrave; vera; vt &longs;upr&agrave; iam totius repetitum fuit: <lb/>quippe h&aelig;c progre&longs;&longs;io in puris in&longs;tantibus fieri tant&ugrave;m pote&longs;t, cum &longs;in&shy;<lb/>gulis in&longs;tantibus noua fiat acce&longs;&longs;io velocitatis, in hoc enim e&longs;t error, <lb/>qu&ograve;d in tota parte temporis AC ponatur &aelig;quabilis velocitas, eiu&longs;que <lb/>principium A, &longs;it &aelig;quale fini C; nam AB, &amp; GH &longs;unt &aelig;quales; c&ugrave;m ta&shy;<lb/>men &longs;it minor velocitas in A, qu&agrave;m in C, ni&longs;i AC &longs;it tant&ugrave;m <expan abbr="in&longs;t&atilde;s">in&longs;tans</expan>; vnde <lb/>tota velocitas in hypothe&longs;i Galilci acqui&longs;ita in 4.partibus temporis a&longs;&shy;<lb/>&longs;umptis e&longs;t, vt triangulum AFN; acqui&longs;ita ver&ograve; in no&longs;tra hypothe&longs;i e&longs;t vt <lb/>&longs;umma rectangulorum CB, CI, EK, EN, qu&aelig; &longs;umma e&longs;t ad triangulum <lb/>AFN, vt 10, ad 8. vel vt 5.ad 4. igitur maior 1/4; nam prima pars tempo&shy;<lb/>ris addit triangulum ABG, &longs;ecunda GHI. &amp;c. </s></p><p type="main">

<s>Si tamen diuidantur i&longs;t&aelig; partes temporis in minores v. <!-- REMOVE S-->g. <!-- REMOVE S-->in 8. tunc <lb/>&longs;umma rectangulorum erit tant&ugrave;m maior 1/8; &longs;i in 16. (1/16) &longs;i in 32. (1/32); &longs;i in <lb/>64.(11/64), cuius &longs;eliema h&icirc;c habes; &longs;int enim 3.partes temporis &longs;en&longs;ibiles A <lb/>CDFE, &amp; &longs;patium vt triangulum AFN, &longs;patia ver&ograve; acqui&longs;ita in &longs;ingulis <lb/>partibus, vt portiones trianguli pr&aelig;dicti, qu&aelig; ip&longs;is re&longs;pondent v. <!-- REMOVE S-->g. <!-- REMOVE S-->ac&shy;<lb/>qui&longs;itum in prima parte ad acqui&longs;itum in &longs;ecunda tant&ugrave;m, vt triangu&shy;<lb/>lum ACG ad trapezum GCDI &amp;c. </s>









<s>denique acqui&longs;itum in temporibus <lb/>in&aelig;qualibus, vt quadrata temporum v. <!-- REMOVE S-->g. <!-- REMOVE S-->acqui&longs;itum in prima parte ad <lb/>acqui&longs;itum in duabus, vt triangulum ACG ad triangulum ADI; id e&longs;t <lb/>quadratum CA ad quadratum DA; in no&longs;tra ver&ograve; hypothe&longs;i, &longs;i velocitas <lb/>in tota prima parte AC ponatur vt CG &aelig;quabiliter; haud dubi&egrave; &longs;patium <lb/>acqui&longs;itum in pr&aelig;dictis 4. temporibus erit, vt &longs;umma rectangulorum C <lb/>B, CI, EK, EN, qu&aelig; maior e&longs;t toto triangulo, AFN, 4. triangulis ABG, <lb/>GHI, IKL, LMN, ie e&longs;t 1/4 totius trianguli AFN; atque ita &longs;umma re&shy;<lb/>ctangulorum continet 10. quadrata &aelig;qualia quadrato CB, &amp; triangu&shy;<lb/>lum AFN, continet. </s>





<s>tant&ugrave;m 8. </s></p><p type="main">

<s>Iam ver&ograve; diuidantur 4. partes temporis AF, in 8. &aelig;quales; in &longs;enten&shy;<lb/>tia Galilei totum &longs;patium erit &longs;emper triangulum AFN, id e&longs;t vt &longs;ubdu&shy;<lb/>plum quadrati &longs;ub AF; qu&aelig; c&ugrave;m &longs;it 8. quadratum erit 64.&amp; &longs;ubduplum <lb/>quadrati 32. at ver&ograve; &longs;umma rectangulorum e&longs;t 36. id e&longs;t continet 36. <lb/>quadrata &aelig;qualia quadrato XA; c&ugrave;m tamen triangulum AFN, conti&shy;<lb/>neat tant&ugrave;m 32. igitur &longs;umma pr&aelig;dicta e&longs;t ad triangulum AFN, vt 36. <lb/>ad 32. id e&longs;t vt 9.ad 8. igitur &longs;umma e&longs;t maior triangulo 1/8, qu&aelig; omnia <lb/>con&longs;tant. </s></p><p type="main">

<s>Pr&aelig;terea diuidatur vlteri&ugrave;s tempus AF in 16. &aelig;quales partes; qua&shy;<lb/>dratum 16. cum &longs;it 256. accipiatur &longs;ubduplum id e&longs;t 128. &amp; erit trian&shy;<lb/>gulum AFN, cui &longs;emper re&longs;pondet totum &longs;patium acqui&longs;itum in &longs;enten&shy;<lb/>tia Galilei; at ver&ograve; &longs;umma rectangulorum erit 136. igitur &longs;umma e&longs;t ad <lb/>&longs;ummam vt 136.ad 128.id e&longs;t vt 17.ad 16. igitur e&longs;t maior &longs;umma trian&shy;<lb/>gulo (1/16) atque ita deinceps; &longs;i vlteri&ugrave;s diuidas pr&aelig;dictum tempus in par&shy;<lb/>tes minores: quot porr&ograve; erunt, antequam fiat tota re&longs;olutio in in&longs;tan&shy;<lb/>tia, &longs;int enim v. <!-- REMOVE S-->g. <!-- REMOVE S-->in tempore AF in&longs;tantia 1000000. &longs;umma qu&aelig; re&longs;&shy;<lb/>pondet no&longs;tr&aelig; progre&longs;&longs;ioni, erit maior altera, qu&aelig; re&longs;pondet progre&longs;&longs;io&shy;<lb/>ni Galilei (1/1000000)quis hoc percipiat? </s>



</p><pb xlink:href="026/01/139.jpg" pagenum="107"/><p type="main">

<s>Si ver&ograve; in no&longs;tra hypothe&longs;i &longs;patium, quod re&longs;pondet prim&aelig; parti tem&shy;<lb/>poris AC &longs;it idem cum illo, quod re&longs;pondet eidem parti in &longs;ententia <lb/>Galilei, id e&longs;t &aelig;quale triangulo CAG, &longs;umma &longs;patiorum erit minor in <lb/>no&longs;tra hypothe&longs;i triangulo AFN &longs;ex triangulis &aelig;qualibus triangulo <lb/>ACG; igitur erit vt 10.ad 16. igitur minor 1/8. </s>

<s>&longs;i ver&ograve; diuidantur in 8. <lb/>temporis partes, triangulum AFN continebit 64. triangula &aelig;qualia <lb/>AXQ: at ver&ograve; &longs;umma qu&aelig; re&longs;pondet no&longs;tr&aelig; hypothe&longs;i 36.igitur minor <lb/>(7/16). denique &longs;i diuidantur in 16. partes, triangulum AFN continebit <lb/>256. triangula &aelig;qualia AYZ; at ver&ograve; &longs;umma no&longs;tra 136. igitur minor <lb/>(15/52) &longs;ed nunquam erit minor 1/2. </s></p><p type="main">

<s>Ob&longs;eruabis obiter dictum e&longs;&longs;e &longs;upr&agrave; &longs;ummam rectangulorum CB CI <lb/>EK EN e&longs;&longs;e maiorem triangulo AFN, 2.quadratis &aelig;qualibus CB; &longs;i <lb/>ver&ograve; diuidatur tempus in 8. partes, &longs;umma rectangulorum e&longs;t minor pr&aelig;&shy;<lb/>cedenti &longs;umm&acirc;, toto quadrato &aelig;quali CB, id e&longs;t 4.quadratis &aelig;qualibus <lb/>XB, id e&longs;t 1/2 prim&aelig; differenti&aelig;, qu&aelig; e&longs;t &longs;umma duorum quadratorum <lb/>&aelig;qualium CB; at &longs;i diuidatur in 16. partes, tempus AF, &longs;umma rectan&shy;<lb/>gulorum e&longs;t minor pr&aelig;cedente 8. quadratis &aelig;qualibus QZ, vel &longs;ubdu&shy;<lb/>plo quadrati CB, id e&longs;t 1/4 prim&aelig; differenti&aelig; qu&aelig; e&longs;t &longs;umma duorum <lb/>quadratorum &aelig;qualium CB; &longs;i 4. partes temporis diuidantur in 8. de&shy;<lb/>trahitur 1/2 differenti&aelig;, qu&aelig; e&longs;t inter &longs;ummam primam rectangulorum, <lb/>&amp; triangulum AFN; &longs;i diuidantur in 16. detrahitur 1/4 eiu&longs;dem diffe&shy;<lb/>renti&aelig;; &longs;i diuidantur in 32. detrahitur 1/8, &longs;i in 64. (1/16); atque ita deinceps, <lb/>&amp; nunquam h&aelig; minuti&aelig; &longs;ubtract&aelig; in infinitum totam differentiam ex&shy;<lb/>haurient; hinc minuti&aelig; i&longs;t&aelig; 1/2 1/4 1/8 (1/16) (1/32) (1/64) &amp;c. </s>

<s>in infinitum non fa&shy;<lb/>ciunt vnum integrum; &longs;ed h&aelig;c &longs;unt facilia. </s></p><p type="main">

<s>Quarta ratio, quam afferunt aliqui, e&longs;t; quia &longs;i cum eadem velocita&shy;<lb/>te acqui&longs;ita in fine temporis dati &longs;ine augmento nouo moueatur mobi&shy;<lb/>le; haud dubi&egrave; acquiret duplum &longs;patium tempore &aelig;quali tempori dato; <lb/>v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;it triangulum AFE; &longs;itque velocitas acqui&longs;ita EF in 4. parti&shy;<lb/>bus temporis AE, vt iam &longs;upr&agrave; dictum e&longs;t, ne cogar repetere: cert&egrave; &longs;i du&shy;<lb/>catur velocitas EF in tempus AE, vel EL &aelig;quale; habebitur rectan&shy;<lb/>gulum EK duplum trianguli AFE: &longs;ed triangulum AFE e&longs;t &longs;umma <lb/>&longs;patiorum motus accelerati tempore AE, &amp; rectangulum EK e&longs;t &longs;um&shy;<lb/>ma &longs;patiorum motus &aelig;quabilis cum velocitate EF; igitur duplum e&longs;t <lb/>&longs;patium motus quabilis, quod erat demon&longs;trandum. </s>





<s>Pr&aelig;terea &longs;i diai&shy;<lb/>datur velocitas EF, &amp; eius &longs;ubdupla ducatur in tempus AE; habebitur <lb/>rectangulum &aelig;quale triangulo AFE, vt con&longs;tat. </s>

<s>Re&longs;pondeo facil&egrave; ex di&shy;<lb/>ctis, hoc ip&longs;um etiam ex no&longs;tra hypothe&longs;i proxime &longs;equi; &longs;int enim duo <lb/>in&longs;tantia; haud dubie &longs;i non cre&longs;cit velocitas, &longs;ecundo in&longs;tanti &aelig;quale <lb/>&longs;patium percurretur; &longs;i vero &longs;ecundo in&longs;tanti cre&longs;cat, percurrentur illo <lb/>motu 3.&longs;patia; &amp; c&ugrave;m velocitas <expan abbr="&longs;ec&utilde;di">&longs;ecundi</expan> <expan abbr="in&longs;t&atilde;tis">in&longs;tantis</expan> &longs;it dupla velocitatis primi <lb/>in&longs;tantis, primo in&longs;tanti &longs;it 1.gradus v.g. <!-- REMOVE S-->&longs;ecundo erunt 2. gradus; igi&shy;<lb/>tur moueatur per duo in&longs;tantia motu &aelig;quabili veloci vt 2. percurrentur <lb/>4. &longs;patia; igitur totum &longs;patium, quod percurritur motu veloci vt 2. per <lb/>2.in&longs;tantia e&longs;t ad totum &longs;patium, quod percurritur &aelig;quali tempore mo-<pb xlink:href="026/01/140.jpg" pagenum="108"/>tu naturaliter accelerato vt 4. ad 3. igitur continet illud 1. (11/3); &longs;i ver&ograve; <lb/>&longs;int 3. in&longs;tantis continet illud, 1/2; &longs;i 4. continet 1. 3/5, &longs;i 5. continet 1.2/3 <lb/>&longs;i 5. continet 1 2/3. &longs;i 6. continet 1 5/7. &longs;i 7. continet 1 3/4. &longs;i 8. continet <lb/>1 7/9. &longs;i 9. continet 1 (4/11). &longs;i 10. continet 1 9/5 &longs;ic quo plura erunt in&longs;tantia <lb/>accedet propi&ugrave;s ad rationem duplam, nunquam tamen ad illam perue&shy;<lb/>niet. </s>



<s>Ex dictis multa tumultuatim Corollaria congeri po&longs;&longs;unt; </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 1.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Etiam&longs;i non &longs;int partes infinit&aelig; temporis; in ordine tamen ad praxim <lb/>eodem modo &longs;e habent, ac &longs;i e&longs;&longs;ent infinit&aelig;; quia lic&egrave;t finit&aelig; &longs;int, nume&shy;<lb/>rari tamen non po&longs;&longs;unt. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 2.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Etiam &longs;i non &longs;int infiniti tarditatis gradus, vt con&longs;tat ex dictis, &longs;ed fi&shy;<lb/>niti; in ordine tamen ad praxim eodem modo &longs;e habent, ac &longs;i e&longs;&longs;ent in&shy;<lb/>finiti; quia non pote&longs;t di&longs;tingui primus, &amp; minimus ab omnibus <lb/>aliis. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 3.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Lic&egrave;t hypothe&longs;is Galilei &longs;it fal&longs;a in hypothe&longs;i in&longs;tantium finitorum; <lb/>nam &longs;ingulis in&longs;tantibus noua fit velocitatis acce&longs;&longs;io; phy&longs;ic&egrave; tamen lo&shy;<lb/>quendo eodem modo &longs;e habet, ac &longs;i e&longs;&longs;et vera; quia cum non po&longs;&longs;it pro&shy;<lb/>bari, ni&longs;i in partibus temporis &longs;en&longs;ibilibus; cert&agrave;, c&ugrave;m qu&aelig;libet pars <lb/>&longs;en&longs;ibilis innumera fer&egrave; in&longs;tantia contineat, in quibus fit progre&longs;&longs;io; <lb/>differentia vtriu&longs;que &longs;en&longs;ibilis e&longs;&longs;e non pote&longs;t; igitur linea denticulata <lb/> eodem modo &longs;e habet phy&longs;ic&egrave;, hoc e&longs;t &longs;en&longs;ibiliter, ac &longs;i e&longs;&longs;et recta; &longs;ic&shy;<lb/>que progre&longs;&longs;io arithmetica in multis terminis reducitur &longs;en&longs;ibiliter ad <lb/>Geometriam in paucioribus terminis; imm&ograve; in communi illa &longs;ententia. </s>

<s><lb/>in qua dicitur tempus con&longs;tare ex partibus actu infinitis, progre&longs;&longs;io Ga&shy;<lb/>lilei tant&ugrave;m locum habere pete&longs;t; igitur h&aelig;c e&longs;to clauis huius difficul&shy;<lb/>tatis; progre&longs;&longs;io &longs;implex principium phy&longs;icum habet, non experimen&shy;<lb/>tum; progre&longs;&longs;io numerorum imparium experimentum non principium; <lb/>vtramque cum principio &amp; experimento componimus; prima enim &longs;i. </s>

<s><lb/>a&longs;&longs;umantur partes temporis &longs;en&longs;ibiles tran&longs;it in &longs;ecundam, &longs;ecunda in <lb/>primam, &longs;i vltima a&longs;&longs;umantur in&longs;tantia. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 4.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Cognito &longs;patio quod percurritur in data parte temporis &longs;en&longs;ibili, co&shy;<lb/>gno&longs;ci pote&longs;t &longs;patium quod in duabus &aelig;qualibus vel 3.vel 4.&amp;c.percurri <lb/>pote&longs;t.v.g. </s>

<s>multi probarunt &longs;&aelig;pi&ugrave;s primo &longs;ecundo minuto corpus graue <lb/>percurrere 12. pedes; igitur duobus percurreret 48. accipe enim 9. 2. <lb/>id e&longs;t 4. &amp; in 4. duces 12. vt habeas 48. 4. ver&ograve; minutis percurret 192. <lb/>nam accipe 9. 4. id e&longs;t 16. &amp; in 16. duces 12.vt habeat 192. res omnin&ograve; <lb/>facilis. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 5.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Similiter cognito &longs;patio quod percurrit 4. &longs;ecundis minutis, cogno&shy;<lb/>&longs;ces &longs;patium, quod percurret 2. vel 1. v.g. <!-- REMOVE S-->percurrit 4. &longs;ecundis 192. pe-<pb xlink:href="026/01/141.jpg" pagenum="109"/>des; accipe 9.4. id e&longs;t 16. &amp; per 16. diuide 192. quot&iacute;ens dabit 12. pro <lb/>primo &longs;ecundo: accipe 9.2. id e&longs;t, 4. &amp; diuide 192. per 4.quotiens dabit <lb/>48. pro duobus minutis, atque ita deinceps. </s>

</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 6.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Similiter cognito tempore cogno&longs;ci pote&longs;t &longs;patium decur&longs;um; quia <lb/>&longs;patia &longs;unt vt quadrata temporum; vel cognito &longs;patio cogno&longs;ci pote&longs;t <lb/>tempus; quia tempora &longs;unt, vt radices &longs;patiorum, h&aelig;c elementa &longs;altem <lb/>Arithmetices de&longs;iderant. </s></p><p type="main">

<s>Sed iam re&longs;tat, vt &longs;oluamus objectiones aliquas, qu&aelig; contra motus ac&shy;<lb/>celerationem pugnare videntur. </s></p><p type="main">

<s>Prima objectio e&longs;t; &longs;i motus acceleratio fieret in in&longs;tantibus, &longs;ecundo <lb/>in&longs;tanti idem corpus e&longs;&longs;et in duobus locis ad&aelig;quatis quod &longs;ic o&longs;tendo: <lb/> &longs;it &longs;patium AB quod percurrit corpus graue primo in&longs;tanti; haud du&shy;<lb/>bi&egrave; AB, e&longs;t eius locus ad&aelig;quatus; &longs;ecundo in&longs;tanti percurrit BC duplum <lb/>AB; igitur eodem in&longs;tanti re&longs;pondet loco BD, &amp; DC, quorum vterque <lb/>e&longs;t &aelig;qualis AB; igitur &longs;ecundo in&longs;tanti e&longs;t in duobus locis, &longs;cilicet BD <lb/>&amp; DC, quod dici non pote&longs;t. </s></p><p type="main">

<s>H&aelig;c objectio impugnat omnem velocitatem; hoc e&longs;t, non mod&ograve; eam, <lb/>qu&aelig; motui naturaliter accelerato competit; ver&ugrave;m etiam illam, qu&aelig; <lb/>ine&longs;t motui violento; igitur vt re&longs;pondeam facili&ugrave;s; &longs;uppono punctum <lb/>phy&longs;icum, mobile &longs;cilicet A; aut &longs;i mauis Angelum co&euml;xten&longs;um quadra&shy;<lb/>to A; qui &longs;cilicet moueatur motu accelerato, &amp; primo in&longs;tanti acquirat <lb/>locum immediatum &aelig;qualem priori, &longs;cilicet AB; lic&egrave;t enim po&longs;&longs;et ac&shy;<lb/>quirere vibrationem participantem de priori; quia tamen acquireret <lb/>tandem non participantem, id e&longs;t, qu&aelig; tota &longs;it extra illam, cui e&longs;t imme&shy;<lb/>diata, qualis e&longs;t AB. &longs;uppono h&icirc;c acquiri vibrationem non participan&shy;<lb/>tem de priori, id e&longs;t &longs;patium AB, &aelig;quale priori, in quo erat A, &amp; pror&shy;<lb/>&longs;us extra illud po&longs;itum lic&egrave;t immediatum; hoc po&longs;ito, primo in&longs;tanti pun&shy;<lb/>ctum A acquirit AB tanquam locum ad&aelig;quatum, vt certum e&longs;t: certum <lb/>e&longs;t etiam loca BC, CD, e&longs;&longs;e ad&aelig;quata: igitur &longs;imul, id e&longs;t eodem in&shy;<lb/>&longs;tanti in vtroque e&longs;&longs;e non pote&longs;t; nam in&longs;tans &longs;imul totum e&longs;t; igitur <lb/>&longs;ecundo in&longs;tanti non percurrit BC, &longs;ed &longs;ecundo tempore &aelig;quali primo; <lb/>hoc enim &longs;ecundum tempus con&longs;tat duobus in&longs;tantibus, quod &longs;imul <lb/>vtrumque re&longs;pondet primo: quippe dari po&longs;&longs;unt in&longs;tantia phy&longs;ica; igitur <lb/>primum in&longs;tans quo percurritur AB e&longs;t &aelig;quale duobus aliis, quibus <lb/>percurruntur BD, &amp; CD; vnde quando dixi primo in&longs;tanti acquiri &longs;pa&shy;<lb/>tium duplum primi, idem e&longs;t, ac &longs;i dixi&longs;&longs;em &longs;ecundo tempore &aelig;quali pri&shy;<lb/>mo, quod reuer&agrave; tempus con&longs;tat 2. in&longs;tantibus, quorum alterum re&longs;pon&shy;<lb/>det &longs;patio BC, &amp; alterum &longs;patio DC. <!-- KEEP S--></s></p><p type="main">

<s>Secunda objectio; Sed inquiet aliquis, igitur non e&longs;t continua acce&shy;<lb/>leratio motus; nam in&longs;tans quo percurritur &longs;ecundum &longs;patium BD, c&ugrave;m <lb/>&longs;it &aelig;quale in&longs;tanti quo percurritur tertium &longs;patium DC, in vtroque &longs;pa&shy;<lb/>tio e&longs;t &aelig;quabilis motus. </s>

<s>Re&longs;pondeo in&longs;tans quo percurritur &longs;ecundum <lb/>&longs;patium BD, e&longs;&longs;e maius in&longs;tanti, quo percurritur tertium &longs;patium DC; <lb/>t&agrave; tamen lege, vt vtrumque &longs;imul &longs;umptum &longs;it onmin&ograve; equale in&longs;tanti, <pb xlink:href="026/01/142.jpg" pagenum="110"/>quo percurritur primum &longs;pat&iacute;um AB; &longs;imiliter totum &longs;patium CG ita <lb/>percurritur tertio tempore, vt &longs;ingula &longs;patia CE. EI. FG. &longs;ingulis in&shy;<lb/>&longs;tantibus percurrantur; &longs;ed h&aelig;c tria in&longs;tantia &longs;imul &longs;umpta &longs;unt &aelig;qualia <lb/>primo in&longs;tanti, quo percurritur &longs;patium; lic&egrave;t primum quo percurritur <lb/>CE &longs;it maius &longs;ecundo, quo percurritur EF, &amp; hoc maius tertio, quo per&shy;<lb/>curritur FG, atque ita deinceps. </s></p><p type="main">

<s>Ob&longs;eruabis po&longs;&longs;e velocitatem motus explicari duobus modis. </s>

<s>Prim&ograve;, <lb/>&longs;i a&longs;&longs;umantur tempora &aelig;qualia, &amp; &longs;patia in&aelig;qualia in ea progre&longs;&longs;ione, <lb/>quam hactenus explicuimus. </s>

<s>Secund&ograve; &longs;i accipiantur &longs;patia &aelig;qualia &amp; <lb/>tempora in&aelig;qualia, quod duobus modis fieri tant&ugrave;m pote&longs;t. </s>

<s>Prim&ograve; &longs;i ac&shy;<lb/>cipiantur &longs;patia &aelig;qualia primo &longs;patio, quod percurritur primo in&longs;tanti. </s>

<s><lb/>Secund&ograve; &longs;i accipiantur &longs;patia &aelig;qualia alteri &longs;patio, quod in parte tempo&shy;<lb/>ris &longs;en&longs;ibili percurritur; in qua ver&ograve; proportione tempora fiant &longs;emper <lb/>minora, 'dicemus infr&agrave;; nec dicas durum e&longs;&longs;e dicere in&longs;tans e&longs;&longs;e po&longs;&longs;e <lb/>minus in&longs;tanti; nam equidem fateor in&longs;tanti mathematico nihil e&longs;&longs;e <lb/>po&longs;&longs;e minus; &longs;ecus ver&ograve; in&longs;tanti phy&longs;ico, quod e&longs;t diui&longs;ibile potenti&acirc;, vt <lb/>dicemus ali&agrave;s; nomine in&longs;tantis phy&longs;ici intelligo durationem indiui&longs;i&shy;<lb/>bilem, hoc e&longs;t, cuius entitas tota &longs;imul e&longs;t. </s></p><p type="main">

<s>Tertia objectio. </s>

<s>Sed inquies, igitur &longs;ecundo tempore &aelig;quali primo <lb/>acquiruntur 2.gradus velocitatis, vel impetus; igitur tria &longs;patia &longs;ecun&shy;<lb/>do tempore percurruntur, quod e&longs;t contra hypothe&longs;im; quippe duo gra&shy;<lb/>dus impetus accedunt primo, &longs;imiliter tertio tempore producentur tres <lb/>gradus impetus; qui &longs;i iungantur tribus pr&aelig;cedentibus, erunt 6. Igitur <lb/>percurrentur tertio tempore 6. &longs;patia, &amp; quarto 10.quinto 15. quia &longs;in&shy;<lb/>gulis in&longs;tantibus debet produci impetus; e&longs;t enim cau&longs;a nece&longs;&longs;aria ap&shy;<lb/>plicata. </s></p><p type="main">

<s>Re&longs;pond&ecedil;o, equidem eo in&longs;tanti, quo percurritur &longs;patium BD, pro&shy;<lb/>duci aliquid impetus, &amp; aliquid eo in&longs;tanti, quo percurritur &longs;patium <lb/>DC; ita vt tamen totus ille impetus, qui producitur his duobus in&longs;tan&shy;<lb/>tibus, &longs;it &aelig;qualis illi, qui producitur primo in&longs;tanti, quo &longs;cilicet percurri&shy;<lb/>tur &longs;patium AB; quia duo illa in&longs;tantia &longs;imul &longs;umpta faciunt tempus <lb/>&aelig;quale primo in&longs;tanti; atqui temporibus &aelig;qualibus eadem cau&longs;a nece&longs;&shy;<lb/>&longs;aria non impedita &aelig;qualem effectum producit per Ax.3.hinc vides &longs;in&shy;<lb/>gulis in&longs;tantibus eadem proportione decre&longs;cere impetum in perfectio&shy;<lb/>ne, qua tempus e&longs;t breuius, &longs;eu velocior motus; &longs;ed de hoc infr&agrave;. </s></p><p type="main">

<s>Quarta objectio; &longs;i impetus &longs;ingulis in&longs;titutibus cre&longs;ceret, vel intende&shy;<lb/>retur, augeretur grauitatio: quippe &longs;i grauitas primo in&longs;tanti producat <lb/>vnum gradum impetus; &longs;ecundo &aelig;qualem producet, &amp; tertio, atque ita <lb/>deinceps, quod e&longs;&longs;et ab&longs;urdum; alioqui minima atomus quodlibet cor&shy;<lb/>pus graue ad&aelig;quaret, quod e&longs;t ab&longs;urdum. </s></p><p type="main">

<s>Re&longs;pondeo nunquam impetum intendi, ni&longs;i &longs;it motus, qui e&longs;t illius fi&shy;<lb/>nis; alioquin fru&longs;tra e&longs;&longs;et per plura in&longs;tantia; igitur de&longs;trui deberet; nec <lb/>dicas impetum naturalem etiam fru&longs;tr&agrave; e&longs;&longs;e &longs;ine motu; quia cum mo&shy;<lb/>tus non &longs;it eius finis ad&aelig;quatus; non mirum e&longs;t &longs;i po&longs;&longs;it e&longs;&longs;e &longs;ine motu; <lb/>atqui iam diximus &longs;upr&agrave; habere duos fines, quorum alterum &longs;emper ha-<pb xlink:href="026/01/143.jpg" pagenum="111"/>bet; primus e&longs;t grauitatio, &longs;eu ni&longs;us ver&longs;us centrum; &longs;ecundus motus <lb/>deor&longs;um; c&ugrave;m tamen impetus additivius motum tant&ugrave;m pro fine habeat; <lb/>igitur &longs;i impeditur totus motus, non producitur hic impetus. </s></p><p type="main">

<s>Quinta objectio; &longs;i impetum &longs;uum intendit corpus graue; &longs;imiliter <lb/>Ignis diceretur intendere calorem; Sol lucem, &amp;c. </s>

<s>Re&longs;pondeo prim&ograve; de <lb/>luce &longs;ingularem e&longs;&longs;e rationem; quia &longs;cilicet con&longs;eruatur &agrave; cau&longs;a &longs;ua pri&shy;<lb/>mo productiua; quidquid &longs;it; &longs;i viderem effectum caloris, vel frigoris <lb/>perpetu&ograve; cre&longs;cere; haud dubi&egrave; dicerem etiam cau&longs;as ip&longs;as intendi; atqui <lb/>hoc ip&longs;um video in motu naturali, qui effectus impetus e&longs;t; adde quod <lb/>argumentum &agrave; pari debile e&longs;t; cum enim &longs;int diuer&longs;i natur&aelig; fines, diuer&shy;<lb/>&longs;&aelig; &longs;unt vi&aelig; quibus &longs;uos fines con&longs;equ&iacute;tur; denique contrarietas caloris, <lb/>&amp; frigoris impedit fort&egrave;, ne vlterius vtraque qualitas intendatur, de qua <lb/>fus&egrave; &longs;uo loco; porr&ograve; dicemus Tomo &longs;exto calorem con&longs;eruari &agrave; cau&longs;a &longs;ua <lb/>primo productiua; quo po&longs;ito ce&longs;&longs;at difficultas; quod lic&egrave;t alicui durum <lb/>videri po&longs;&longs;it, demon&longs;trabo tamen. </s></p><p type="main">

<s>Sexta objectio; igitur &longs;i ex infinita di&longs;tantia lapis de&longs;cenderet, inten&shy;<lb/>deret etiam &longs;uum motum. </s>

<s>Re&longs;pondeo prim&ograve;, non po&longs;&longs;e dari infinitam il&shy;<lb/>lam di&longs;tantiam. </s>

<s>Secund&ograve; etiam&longs;i daretur lapis, ex ea non caderet; fru&longs;tr&agrave; <lb/>enim e&longs;&longs;et ille motus: Terti&ograve;, &longs;i daretur motus infinitus, haud dubi&egrave; e&longs;&longs;et <lb/>&aelig;quabilis; qualis e&longs;t motus circularis corporum c&oelig;le&longs;tium; at ver&ograve; <lb/>motus naturalis deor&longs;um corporum grauium debet e&longs;&longs;e acceleratus ne <lb/>vel de&longs;cenderent tardi&ugrave;s, &longs;i cum primo tant&ugrave;m velocitatis gradu de&longs;cen&shy;<lb/>derent; vel &longs;u&longs;tineri vix po&longs;&longs;ent, &longs;i impetum innatum intentiorem habe&shy;<lb/>rent; vtrum ver&ograve; &longs;emper intendatur, &amp; ex quacumque altitudine cadat <lb/>corpus graue, videbimus infr&agrave;. </s></p><p type="main">

<s>Ex dictis hactenus facil&egrave; refelluntur ali&aelig; &longs;ententi&aelig; de proportione <lb/>motus naturaliter accelerati. </s></p><p type="main">

<s>Et prim&ograve; quidem illa, qu&aelig; vult fieri &longs;ecundum rationem &longs;inuum <lb/>ver&longs;orum, lic&egrave;t initio t&agrave;m prop&egrave; accedat ad proportionem Galilei, vt <lb/>di&longs;cerni &longs;en&longs;ibiliter ab ea non po&longs;&longs;it; quare tut&ograve; &longs;atis a&longs;&longs;umi po&shy;<lb/>terit, &longs;i quando &longs;it opus illius loco, quod nos in explicandis motibus c&oelig;&shy;<lb/>le&longs;tibus pr&aelig;&longs;tabimus; interim quia facili&ugrave;s explicatur in motu recto per <lb/>rationem quadratorum qu&agrave;m &longs;inuum, illam retinebimus; pr&aelig;&longs;ertim c&ugrave;m <lb/>vtraque ad no&longs;tram reducatur; mod&ograve; progre&longs;&longs;io fiat in in&longs;tantibus. </s>

<s><lb/>Secund&ograve; reiicitur &longs;ententia illorum qui volunt hanc progre&longs;&longs;ionem fie&shy;<lb/>ri iuxta proportionem geometricam, quam vides in his numeris 1.2.4.8. <lb/>16. qu&aelig; lic&egrave;t initio min&ugrave;s recedat &agrave; vera, in progre&longs;&longs;u tamen mult&ugrave;m <lb/>aberrat, nec e&longs;t vlla ratio qu&aelig; pro illa faciat: Et ver&ograve; nulla in mentem <lb/>venire pote&longs;t; ni&longs;i fort&egrave; dicatur, c&ugrave;m &longs;ecundo in&longs;tanti &longs;it dupla velocitas, <lb/>tertio <expan abbr="pon&etilde;dam">ponendam</expan> e&longs;&longs;e quadruplam, &amp; 4&deg;. </s>

<s>octuplam; quia vt velocitas pri&shy;<lb/>mi in&longs;tantis e&longs;t ad velocitatem &longs;ecundi, ita velocitas huius ad velocita&shy;<lb/>tem tertij, &amp; velocitas huius ad velocitatem quarti; igitur &longs;equitur pro&shy;<lb/>gre&longs;&longs;ionem rationis geometric&aelig; dupl&aelig;; cur enim e&longs;&longs;et maior ratio pri&shy;<lb/>mi in&longs;tantis ad &longs;ecundum qu&agrave;m &longs;ecundi ad tertium tertij ad quartum? <lb/></s>

<s>&amp;c. </s>

<s>&longs;ed profect&ograve; vix vlla apparet rationis &longs;pecies, c&ugrave;m nulla &longs;it cau&longs;a, <pb xlink:href="026/01/144.jpg" pagenum="112"/>qu&aelig; 3&deg;in&longs;tanti, &amp; 4&deg;pl&ugrave;s agat <expan abbr="qu&atilde;">quam</expan> primo, &amp; &longs;ecundo; igitur e&longs;t peculiaris <lb/>cau&longs;a huius in&aelig;qualitatis rationum; qu&ograve;d &longs;cilicet &aelig;qualibus temporibus <lb/>&aelig;qualia acquirantur velocitatis momenta; vt &longs;upr&agrave; demon&longs;trauimus; <lb/>quippe id pr&aelig;&longs;tari debet in explicandis in&aelig;qualitatibus motuum recto&shy;<lb/>rum naturalium, quod pr&aelig;&longs;tant A&longs;tronomi in explicanda in&aelig;qualitate <lb/>motuum c&aelig;le&longs;tium; qui &longs;emper &aelig;qualitatem aliquam &longs;upponunt, nec e&longs;t <lb/>qu&ograve;d hanc &longs;ententiam nonnullis experimentis ictuum qui&longs;quam con&shy;<lb/>firmet, in quibus multa fraus &longs;ube&longs;&longs;e pote&longs;t. </s></p><p type="main">

<s>Terti&ograve; reiicitur illa quoque &longs;ententia, qu&aelig; proportionem line&aelig; &longs;ect&aelig; <lb/>in mediam, &amp; extremam rationem huic line&aelig; tribuit, quam fer&egrave; in his <lb/>numeris vides 1.2.3.5.8, 13. 21. 34. 55. qu&aelig; &longs;ub finem etiam longi&longs;&longs;im&egrave; <lb/>aberrat, vt videre e&longs;t, quare ii&longs;dem rationibus impugnatur, quibus iam <lb/>aliam impugnauimus. </s></p><p type="main">

<s>Scio e&longs;&longs;e alias multas rationes, quibus aliqui recentiores motus natu&shy;<lb/>ralis accelerationem explicare nituntur, &longs;ed iam &longs;upr&agrave; &longs;atis &longs;uperque re&shy;<lb/>iect&aelig; fuerunt, vel profect&ograve; e&aelig; &longs;unt, qu&aelig; ne quidem inter fabulo&longs;a po&euml;&shy;<lb/>tarum commenta locum aliquem habere po&longs;&longs;int: Et ver&ograve; ni&longs;i me ani&shy;<lb/>mus fallit in re clari&longs;&longs;ima, rationem huius effectus ex communibus <lb/>principiis deductam cum ip&longs;is etiam experimentis con&longs;entire hactenus <lb/>ita demon&longs;trauimus, vt iam vix vllus dubitationi locus relinquatur; &longs;ed <lb/>interruptam Theorematum &longs;eriem tandem repetimus. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 62.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Si accipiantur &longs;patia &aelig;qualia primo &longs;patio, quod vno in&longs;tanti percurritur, <lb/>in&longs;tantia &longs;unt in&aelig;qualia in motu natur aliter accelerato<emph.end type="italics"/>; probatur, quia &longs;e&shy;<lb/>cundum &longs;patium &aelig;quale primo percurritur motu velociore, qu&agrave;m pri&shy;<lb/>mo, &amp; tertium quam &longs;ecundo: ergo minori tempore per Def.2.l.1. &longs;ed <lb/>primum &longs;patium conficitur vno in&longs;tanti; igitur &longs;ecundum vno in&longs;tanti, <lb/>&longs;ed minore; idem dico de tertio. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 63.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>In ea proportione decre&longs;cunt h&aelig;c instantia,<emph.end type="italics"/> vt primum &longs;it maius &longs;ecundo, <lb/>&longs;ecundum tertio, tertium quarto, quartum quinto, quintum &longs;exto, <lb/>atque ita deinceps; ita vt &longs;ecundum &amp; tertium &longs;imul &longs;umpta, item quar&shy;<lb/>tum, quintum, &longs;extum, &longs;eptimum, item octauum, nonum, decimum, &longs;imul <lb/>&longs;umpta ad&aelig;quent primum, hoc e&longs;t vt vnum, duo, tria, quatuor, quinque, <lb/>&longs;ex, &amp;c. </s>

<s>faciant &longs;emper tempora &aelig;qualia, quia temporibus &aelig;qualibus &aelig;&shy;<lb/>qualia acquiruntur velocitatis momenta? </s>

<s>igitur &longs;i primo in&longs;tanti per&shy;<lb/>curritur vnum &longs;patium; &longs;ecundo tempore &aelig;quali percurruntur duo &longs;pa&shy;<lb/>tia &aelig;qualia primo, &amp; tertio, tria; atque deinceps; &longs;ed vt &longs;upr&agrave; dictum e&longs;t <lb/>in re&longs;pon&longs;. ad obiect. primam, vno, &amp; <expan abbr="eod&etilde;">eodem</expan> in&longs;tanti non pote&longs;t idem cor&shy;<lb/>pus percurrere duo &longs;patia, ne &longs;imul e&longs;&longs;et in duobus locis; igitur &longs;ingula <lb/>&longs;patia re&longs;pondent &longs;ingulis in&longs;tantibus lic&egrave;t minoribus; &longs;ed &longs;ecundo tem&shy;<lb/>pore &aelig;quali primo in&longs;tanti percurruntur duo &longs;patia &aelig;qualia primo &longs;pa&shy;<lb/>tio; igitur &longs;ecundum, &amp; tertium in&longs;tans debent &longs;imul &longs;umpta ad&aelig;quare <pb xlink:href="026/01/145.jpg" pagenum="113"/>primum, &longs;ed non &longs;unt &aelig;qualia, vt con&longs;tat; alioquin duobus illis in&longs;tanti <lb/>bus motus e&longs;&longs;et &aelig;quabilis; igitur &longs;ecundum e&longs;t maius tertio, ita vt tamen <lb/>ex vtroque tempus fiat &aelig;quale primo in&longs;tanti. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 64.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Non decre&longs;cunt illa in&longs;tantia &longs;ecundum lineam &longs;extam in extremam &amp; <lb/>mediam rationem propagatam; ita vt primum &longs;it ad &longs;ecundum, vt &longs;ecundum <lb/>ad tertium, tertium ad quartum, quartum ad quintum at que ita deinceps<emph.end type="italics"/>; <lb/>&longs;it enim aliqua &longs;eries numerorum, qui aliquo modo accedant ad pr&aelig;di&shy;<lb/>ctam proportionem 1.2.3.5.8.13.21.34.55. &longs;itque primum in&longs;tans vlti&shy;<lb/>mus numerus 55. &longs;ecundum 34.tertium 21. atque ita deinceps: Equidem <lb/>&longs;ecundum, &amp; tertium ad&aelig;quant primum; at ver&ograve; quartum, quintum, <lb/>&longs;extum nullo modo ad&aelig;quant; imm&ograve; ne quidem eius &longs;ubduplum, &amp; <lb/>mult&ograve; minus 3. alij addito primo: imm&ograve; &longs;i linea data duodecies propor&shy;<lb/>tionaliter diuidatur, vltimum &longs;egmentum vix e&longs;&longs;et &longs;ubcentuplum primi, <lb/>vt con&longs;tat; igitur reiici debet h&aelig;c propo&longs;itio. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 65.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>In&longs;tans primum non e&longs;t ad &longs;ecundum vt numerus ad numerum; nec ad <lb/>tertium, quartum, quintum, &longs;extum, &amp;c.<emph.end type="italics"/> probatur, quia nullus numerus <lb/>excogitari pote&longs;t quo de&longs;ignari po&longs;&longs;it quantitas, &longs;eu perfectio, &longs;eu va&shy;<lb/>lor i&longs;torum in&longs;tantium; &longs;it enim primum in&longs;tans &longs;ecundum &longs;it 3/5. tertium <lb/>2/5 quartum 4/9 quintum 2/9 &longs;extum 2/9. <!--neuer Satz-->Equidem &longs;ecundum, &amp; tertium ad&ecedil;&shy;<lb/>quant primum; adde quod non pote&longs;t amplius &longs;eries propagari per nu&shy;<lb/>meros rationales; &longs;it autem &longs;ecundum (6/11) 3. (5/11) cum tribus aliis 4/9 1/9 7/9; <lb/>equidem &longs;i reducantur h&aelig; 5. minuti&aelig;, re&longs;pondebunt his (54/99) (45/99) (44/99) (12/99) (26/99): <lb/>igitur &longs;ecunda erit maior quarta; at prima &longs;uperat &longs;ecundam (9/999) &longs;ecunda <lb/>tertiam (1/99) tertia quartam (11/99) quarta quintam (12/99). Cur porr&ograve; h&aelig;c in&aelig;qua&shy;<lb/>litas, igitur numeri po&longs;&longs;unt a&longs;&longs;ignari; non po&longs;&longs;unt etiam poni in &longs;erie <lb/>geometrica &longs;ubdupla 1. 1/2 1/4 1/8 &amp;c. </s>

<s>quia &longs;ecunda. </s>

<s>&amp; tertia non ad&aelig;quant <lb/>primam idem dicendum e&longs;t potiori iure de tribus aliis; nec etiam in &longs;e&shy;<lb/>rie arithmetica &longs;implici 1. 1/2 1/3 1/4 2/5 1/6; quia &longs;ecunda, &amp; tertia &longs;unt mi&shy;<lb/>nores prima 1/6, vt quarta, quinta, &longs;exta &longs;unt minores prima (26/74). </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 66.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Datur aliquis &longs;eries numerorum irrationabilium, &longs;eu &longs;urdorum minorum, &amp; <lb/>minorum<emph.end type="italics"/>; quorum primus ita &longs;uperet &longs;ecundum, &longs;ecundus tertium, <lb/>tertius quartum, &amp;c. </s>

<s>vt &longs;ecundus, &amp; tertius ad&aelig;quent primum, item <lb/>quartus, quintus, &longs;extus. </s>

<s>item 4. alij, qui &longs;equuntur, item 5. item 6. &amp;c. </s>

<s><lb/>v. <!-- REMOVE S-->g. <!-- REMOVE S-->pote&longs;t dari linea AG con&longs;tans tribus partibus &aelig;qualibus, &longs;cilicet <lb/>AB, BC, CG, &amp; &longs;ecunda BC duabus BD maiore, &amp; DC minore, &amp; ter&shy;<lb/>tia tribus prima CE minore ED, &longs;ed maiore EF, &longs;ecunda EF maiore F <lb/>G, atque ita deinceps; addi pote&longs;t quartum &longs;egmentum &aelig;quale AB; quod <lb/>&longs;ubdiuidetur in 4. partes, quarum prima &longs;it maior &longs;ecunda, &amp; <expan abbr="h&ecedil;c">haec</expan> tertia <lb/>&amp; h&aelig;c quarta, &amp; omnes minores FG; ita autem &longs;uperant prim&aelig; &longs;equen&shy;<lb/>tes, vt differentia prim&aelig;, &amp; &longs;ecund&aelig; &longs;it maior differentia &longs;ecund&aelig;, &amp; <pb xlink:href="026/01/146.jpg" pagenum="114"/>terti&aelig;, &amp; h&aelig;c maior differentia terti&aelig;, &amp; quart&aelig;; atque ita deinceps, nec <lb/>aliter res e&longs;&longs;e pote&longs;t. </s>



</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 67.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc partes, quo fiunt minores, accedunt propi&ugrave;s ad &aelig;qualitatem,<emph.end type="italics"/> v.g. <!-- REMOVE S-->BD, <lb/>&amp; DC accedunt propi&ugrave;s ad &aelig;qualitatem qu&agrave;m AB, BD, &amp; DC, CE, pro&shy;<lb/>pi&ugrave;s qu&agrave;m CD, DB, &amp; CE, EF, qu&agrave;m EC, CD, atque ita deinceps, vt patet; <lb/>hinc po&longs;t aliquot in&longs;tantia motus, &aelig;qualia fer&egrave; redduntur in&longs;tantia, vt <lb/>con&longs;tat. </s>

</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 68.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc qua proportione decre&longs;cunt instantia, decre&longs;cit etiam perfectio <lb/>impetus<emph.end type="italics"/>; quia temporibus &aelig;qualibus eadem cau&longs;a nece&longs;&longs;aria &aelig;qualem ef&shy;<lb/>fectum producit per Ax. tertium igitur in&aelig;qualem in&aelig;qualibus, per Ax. <!-- REMOVE S--><lb/>13. num.4. igitur minorem minore tempore; igitur minorem in eadem <lb/>proportione, in qua tempus e&longs;t; igitur qua proportione, &amp;c. </s>

</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 69.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc vides qu&acirc;m &longs;it nece&longs;&longs;aria illa diuer&longs;a perfectio impetus, quam indi&shy;<lb/>cauimus lib.<emph.end type="italics"/>1. hinc impetus productus &longs;ecundo, &amp; tertio in&longs;tanti ad&aelig;&shy;<lb/>quat impetum productum primo, quem etiam ad&aelig;quat productus quar&shy;<lb/>to, quinto, &longs;exto, item productus &longs;eptimo, octauo, nono; decimo, atque ita <lb/>deinceps; hinc e&longs;t eadem differentia impetuum, qu&aelig; <expan abbr="in&longs;t&atilde;tium">in&longs;tantium</expan>; hinc &longs;in&shy;<lb/>gulis &longs;patiis &aelig;qualibus primo &longs;patio, quod percurritur primo in&longs;tanti; <lb/>re&longs;pondent &longs;ingula in&longs;tantia, &amp; &longs;ingulis in&longs;tantibus &longs;inguli, &amp; &longs;ingulares <lb/>impetus; hinc non e&longs;t quod primo in&longs;tanti dicantur produci plura pun&shy;<lb/>cta impetus in eodem puncto corporis grauis; &longs;ed vnicum tant&ugrave;m pun&shy;<lb/>ctum talis perfectionis &longs;cilicet phy&longs;icum; cur enim potius duo puncta, <lb/>quam tria? </s>

<s>&longs;ed quod vnum e&longs;t determinatum e&longs;t per Ax. 5. lib. 

1. hinc <lb/>optima ratio cur potius tali in&longs;tanti producatur impetus talis perfectio&shy;<lb/>nis qu&agrave;m alterius? </s>

<s>quippe perfectio impetus &longs;equitur perfectionem in&shy;<lb/>&longs;tantis quo producitur; hinc dicendum videtur omnia puncta impetus <lb/>e&longs;&longs;e diuer&longs;&aelig; perfectionis, vel heterogenea; vt vulg&ograve; aiunt Philo&longs;ophi; <lb/>cuius rationem demon&longs;tratiuam afferemus lib. 

&longs;equenti cum de motu <lb/>violento; hinc vides duplicem progre&longs;&longs;ionem; primam &longs;cilicet, qua ex <lb/>&longs;uppo&longs;itis temporibus &aelig;qualibus acquiruntur &longs;patia in&aelig;qualia, de qua <lb/>fus&egrave; &longs;upr&agrave;; in hac enim velocitas eadem proportione cum impetu cre&longs;&shy;<lb/>cit, &amp; cum ip&longs;o tempore; hoc e&longs;t tempore triplo e&longs;t tripla, quadruplo <lb/>quadrupla; item impetus in duplo tempore e&longs;t duplus, in triplo triplus; <lb/>mod&ograve; progre&longs;&longs;io fiat in temporibus primo in&longs;tanti &aelig;qualibus; &longs;ecunda <lb/>progre&longs;&longs;io e&longs;t qua ex &longs;uppo&longs;itis &longs;patiis &aelig;qualibus tempora fluunt in&aelig;&shy;<lb/>qualia, hoc e&longs;t minora &amp; minora; quibus etiam re&longs;pondet impetus im&shy;<lb/>perfectior in eadem proportione temporum; prima fit per differentias <lb/>&aelig;quales, &amp; proportiones in&aelig;quales, &longs;ecunda ver&ograve; per differentias in&aelig;&shy;<lb/>quales, &amp; proportiones in&aelig;quales. </s></p><pb xlink:href="026/01/147.jpg" pagenum="115"/><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 70.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Si a&longs;&longs;umantur &longs;patia &longs;en&longs;ibilia &aelig;qualia, tempora &longs;unt fer&egrave; in ratione &longs;ubdu&shy;<lb/>plicata &longs;patiorum<emph.end type="italics"/>; crun enim &longs;patia &longs;int vt quadrata <expan abbr="t&etilde;porum">temporum</expan> &longs;en&longs;ibiliter; <lb/>cert&egrave; tempora &longs;unt, vt radices i&longs;torum quadratorum, &longs;cilicet &longs;patiorum; <lb/>&longs;int enim qu&aelig;cunque &longs;patia &aelig;qualia in linea AF; &longs;intque &longs;patia AC 4. <lb/>AE 16. radix quadr.4. e&longs;t 2.16. ver&ograve; 4. igitur tempora &longs;unt vt 4.2.&longs;i ve&shy;<lb/>r&ograve; accipiatur primum &longs;patium, quod vno tempore percurritur; tempus <lb/>quo percurruntur duo &longs;patia &aelig;qualia primum e&longs;t v.2.quo percurruntur <lb/>tria v.3.quo percurruntur 4.&longs;patia, 2. atque ita deinceps; igitur in praxi <lb/>qu&aelig; tant&ugrave;m fit in &longs;patiis &longs;en&longs;ibilibus h&aelig;c progre&longs;&longs;io adhibenda e&longs;t, il&shy;<lb/>lamque deinceps, &longs;i quando opus e&longs;t, adhibebimus. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 71.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>In vacuo &longs;i corpus graue de&longs;cenderet, pr&aelig;dict&aelig; proportiones accurati&longs;&longs;im&egrave; <lb/>&longs;eruarentur<emph.end type="italics"/>; quia &longs;cilicet nullum e&longs;&longs;e impedimentum; at ver&ograve; &longs;i aliquod <lb/>intercedit impedimentum; haud dubi&egrave; non &longs;eruantur accurat&egrave;; e&longs;t autem <lb/>aliquod impedimentum in medio, quantumuis liberum e&longs;&longs;e videatur, <lb/>qu&aelig; omnia con&longs;tant. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 72.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Impetus naturalis addititius de&longs;truitur<emph.end type="italics"/>; patet experienti&acirc;; quippe pila <lb/>deor&longs;um cadens tandem quie&longs;cit, lic&egrave;t &agrave; terra reflectatur ratione impe&shy;<lb/>dimenti, ex quo re&longs;ultat duplex determinatio, ratione cuius idem im&shy;<lb/>petus &longs;ibi aliquo modo redditur <expan abbr="c&otilde;trarius">contrarius</expan>; &longs;ed de his fus&egrave; in primo libro <lb/>&agrave; Th.148. ad finem v&longs;que libri: nam reuer&acirc; du&aelig; determinationes op&shy;<lb/>po&longs;it&aelig; pugnant pro rata per Ax. 15.l.1. &amp; quotie&longs;cunque idem impetus <lb/>e&longs;t ad lineas oppo&longs;itas determinatus eodem modo &longs;e habet, ac &longs;i duplex <lb/>e&longs;&longs;et, &amp; quilibet &longs;u&aelig; &longs;ube&longs;&longs;et determinationi; atqui &longs;i duplex e&longs;&longs;et oppo&shy;<lb/>&longs;itus, pugnarent pro rata; igitur t&agrave;m pugnant du&aelig; determinationes op&shy;<lb/>po&longs;it&aelig; in codem impetu, qu&agrave;m duo impetus ad oppo&longs;itas lineas deter&shy;<lb/>minati; igitur impetus naturalis aduentitius de&longs;truitur, &amp;c. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 73.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Impetus naturalis innatus nunquam de&longs;truitur<emph.end type="italics"/>; Probatur, quia nihil e&longs;te <lb/>quod exigat eius de&longs;tructionem, quia &longs;cilicet nunquam e&longs;t fru&longs;tr&agrave;; nam <lb/>vel habet motum deor&longs;um, vel grauitationis effectum, vel de&longs;truit impe&shy;<lb/>tum extrin&longs;ecum in motu violento; igitur nunquam e&longs;t fru&longs;tr&agrave;, cum &longs;em&shy;<lb/>per habeat aliquem effectum. </s></p><p type="main">

<s>Dices lignum vi extrin&longs;eca in aqua immer&longs;um &longs;ua &longs;ponte a&longs;cendit; <lb/>igitur ille gradus impetus grauitationis de&longs;truitur, &amp; alius producitur; <lb/>h&aelig;c qu&aelig;&longs;tio ad pr&aelig;&longs;ens in&longs;titutum non pertinet, &longs;ed ad librum de gra&shy;<lb/>uitate, &amp; leuitate. </s>

<s>Igitur breuiter re&longs;pondeo illum impetum nunquam <lb/>de&longs;trui, quandiu mobile grauitat, vel grauitatione &longs;ingulari, (&longs;ic corpus <lb/>grauitat in manum &longs;u&longs;tinentis,) vel grauitatione communi, (&longs;ic lignum <lb/>humori innatans grauitat, non quidem in aquam, at &longs;imul cum aqua;) <lb/>&longs;ed de grauitate, &amp; grauitatione in Tomo de &longs;tatibus corporum &longs;en&longs;ibi-<pb xlink:href="026/01/148.jpg" pagenum="116"/>libus, in quo o&longs;tendemus ideo lignum &longs;ur&longs;um emergere, quia ab aqua <lb/>extenditur, &amp; idco corpora &longs;ur&longs;um ire, quia alia deor&longs;um eunt. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 74.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Quando lapis de&longs;cendit per medium a&euml;ra, impeditur aliquantulum eius <lb/>motus<emph.end type="italics"/>: Probatur prim&ograve; experienti&acirc;, qu&aelig; certa e&longs;t; t&agrave;m enim a&euml;r impe&shy;<lb/>dit motum deor&longs;um, qu&agrave;m &longs;ur&longs;um, vt videre e&longs;t in mobili leuiore &longs;eu ra&shy;<lb/>riore, quod etiam flante vento ob&longs;eruare omnes po&longs;&longs;unt; quomodo ve&shy;<lb/>r&ograve; impediat, dicemus ali&agrave;s; &longs;ecund&ograve; corpus immobile, in quod mobile <lb/>impingitur, motum illius impedit; &longs;ed in diuer&longs;as partes a&euml;ris corpus <lb/>graue impingitur in de&longs;cen&longs;u; igitur aliquantulum impeditur eius <lb/>motus. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 75.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc motus naturalis deor&longs;um aliquantulum retardatur,<emph.end type="italics"/> quia nihil aliud <lb/>pr&aelig;&longs;tare pote&longs;t huiu&longs;modi impedimentum, ni&longs;i aliquam retardationem; <lb/>igitur motus inde redditur tardior. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 76.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc etiam impetus producitur imperfectior<emph.end type="italics"/>; quia ex imperfectione ef&shy;<lb/>fectus requiritur imperfectio cau&longs;&aelig; per Ax. 13.l. </s>

<s>1. &amp; qu&acirc; proportione <lb/>e&longs;t tardior motus e&acirc;dem impetus e&longs;t imperfectior, per Ax. <!-- REMOVE S-->5. excipe ta&shy;<lb/>men impetum innatum, qui &longs;emper habet eundem effectum grauitatio&shy;<lb/>nis, vel &longs;ingularis, qu&acirc; grauitas cum ip&longs;o medio, &longs;i reuer&acirc; medium gra&shy;<lb/>uitat, de quo ali&agrave;s. </s>

</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 77.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Quo medium den&longs;ius e&longs;t plus impedit motum deor&longs;um<emph.end type="italics"/>; Probatur, quia &longs;i <lb/>motum impedit; cert&egrave; non totum; quis enim hoc dicat; &longs;ed e&aelig; dumta&shy;<lb/>xat partes, quibus incubat corpus graue; igitur qu&ograve; &longs;unt plures huiu&longs;&shy;<lb/>modi partes, maius e&longs;t impedimentum; &longs;ed in medio den&longs;iori plures &longs;unt <lb/>cum minore exten&longs;ione; hoc enim e&longs;t, quod voco den&longs;ius; igitur me&shy;<lb/>dium den&longs;ius pl&ugrave;s impedit. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 78.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc tardi&ugrave;s de&longs;cendit mobile per mediam aquam, qu&agrave;m per medium <lb/>a&euml;ra,<emph.end type="italics"/> quia aqua e&longs;t den&longs;ior a&euml;re. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Ob&longs;erua e&longs;&longs;e aliqua corpora minus den&longs;a, qu&aelig; motum omnin&ograve; im&shy;<lb/>pediunt; quippe certum e&longs;t aquam e&longs;&longs;e den&longs;iorem ligno; atqui li&shy;<lb/>gnum de&longs;cen&longs;um lapidis impedit, non ver&ograve; aqua; quia &longs;cilicet lignum <lb/>non e&longs;t medium, vt aqua; vt enim aliquod corpus &longs;it medium, debet e&longs;&longs;e <lb/>liquidum, vt, aqua &amp; alij liquores; vel &longs;pirabile vt a&euml;r, vapor, &amp;c. </s>

<s>ratio <lb/>e&longs;t, quia partes ligni, vel alterius corporis durioris, ita &longs;unt inter &longs;e con&shy;<lb/>junct&aelig;, vel implicat&aelig;, vt omnem tran&longs;itum intercludant, ni&longs;i corpus ip&shy;<lb/>&longs;um graue valido ictu vel impetu &longs;ibi viam aperiat; igitur vt corpus ali&shy;<lb/>quod vice medij defungatur, debet in eo &longs;tatu e&longs;&longs;e, in quo eius partes <pb xlink:href="026/01/149.jpg" pagenum="117"/>modico fer&egrave; ni&longs;u &longs;eiungantur, &amp; loco cedant; &longs;ed de his &longs;tatibus cor&shy;<lb/>porum fus&egrave; agemus Tomo 5. adde quod ad medium &longs;ufficit vacuum &longs;i <lb/>motus in vacuo e&longs;&longs;e pote&longs;t, de quo alibi; quod cert&egrave; e&longs;t omnium me&shy;<lb/>diorum optimum, cum nullo modo re&longs;i&longs;tar mobili. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 79.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc producitur impetus imperfectior in medio den&longs;iore:<emph.end type="italics"/> quia in eo tar&shy;<lb/>dior e&longs;t motus, ex cuius tarditate arguitur imperfectio impetus per Ax. <!-- REMOVE S--><lb/>13.num.4. </s>

</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Ob&longs;erua den&longs;itatem medij cogno&longs;ci ex eius grauitate; illud enim <lb/>den&longs;ius e&longs;t, quod e&longs;t grauius &amp; vici&longs;&longs;im; quod fus&egrave; explicabimus &longs;uo lo&shy;<lb/>co; e&longs;t enim grauitas qu&aelig;dam <emph type="italics"/>den&longs;itas, vt ait<emph.end type="italics"/> Philo&longs;ophus <emph type="italics"/>t&ugrave;m l.<emph.end type="italics"/>4.<emph type="italics"/>pb.c.<emph.end type="italics"/><lb/>9.<emph type="italics"/>t.<emph.end type="italics"/>85. &amp; 86. <emph type="italics"/>den&longs;um &amp; rarum,<emph.end type="italics"/> inquit, <emph type="italics"/>&longs;unt lationis efficientia,<emph.end type="italics"/> &amp; paul&ograve; &longs;u&shy;<lb/>peri&ugrave;s; <emph type="italics"/>e&longs;t autem den&longs;um graue, rarum ver&ograve; leue, &amp; l.<emph.end type="italics"/>8.<emph type="italics"/>c.<emph.end type="italics"/>7.<emph type="italics"/>t.<emph.end type="italics"/>55. <emph type="italics"/>h&aelig;c habet, <lb/>graue &amp; leue; molle &amp; durum den&longs;itates qu&aelig;dam e&longs;&longs;e, &amp; raritates videntur,<emph.end type="italics"/><lb/>qu&aelig; adnotare volui, vt vel inde con&longs;tet doctrinam hanc cum Peripate&shy;<lb/>tica optim&egrave; con&longs;entire. </s></p><p type="main">

<s>Ob&longs;eruabis etiam h&icirc;c &agrave; me non di&longs;cuti, in quo con&longs;i&longs;tat den&longs;itas, vel <lb/>raritas, grauitas, vel leuitas; &longs;uppono tant&ugrave;m graue illud e&longs;&longs;e, quod ten&shy;<lb/>dit deor&longs;um; leue illud, quod tendit &longs;ur&longs;um &longs;iue pellatur &agrave; grauiori, &longs;iue <lb/>non, den&longs;um ver&ograve; e&longs;&longs;e id quod mult&ugrave;m materia habet &longs;ub parua exten&shy;<lb/>&longs;ione, rarum &egrave; contrario; quorum omnium cau&longs;as, &amp; rationes &longs;uo loco <lb/>explicabimus. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 80.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Sub medium leuius corpus graue de&longs;cendit<emph.end type="italics"/>; certa e&longs;t hypothe&longs;is, ni&longs;i for&shy;<lb/>t&egrave; aliquando per accidens &longs;ecus accidat; ratio porr&ograve; petitur ex ip&longs;a <lb/>grauitatis natura, qu&acirc; corpus graue tendit deor&longs;um; nihil enim aliud <lb/>grauitas e&longs;t, quidquid tandem illa &longs;it; quippe corpus graue de&longs;cendit, <lb/>quando medium liberum habet, idemque leuius, per quod de&longs;cendat; <lb/>quod cert&egrave; &longs;i grauius e&longs;&longs;et, haud dubi&egrave; non de&longs;cenderet; &longs;ic ferrum, &amp; <lb/>&longs;axum plumbo liquato innatant; cum tamen per mediam aquam de&shy;<lb/>&longs;cendant; fic lignum aqu&aelig; &longs;upernatat, quod per liberum a&euml;ra de&longs;cendit; <lb/>ratio e&longs;t, quia grauius de&longs;cendit &longs;ub medium leuius; cur autem id fiat <lb/>fus&egrave; alibi explicabo; id tant&ugrave;m obiter indico. </s>

<s>Omnis motus, qui fit &agrave; <lb/>principio intrin&longs;eco per lineam rectam propter locum e&longs;t, vt patet; quis <lb/>enim neget corpus graue ideo de&longs;cendere &longs;ub leuius, vt occupet aliquem <lb/>locum quo prius carebat, qui tamen illi connaturalis e&longs;t in hoc rerum <lb/>ordine? </s>

<s>cum &agrave; natura acceperit vim illam intrin&longs;ecam, qu&acirc; in eum lo&shy;<lb/>cum &longs;e&longs;e recipere pote&longs;t; quam cert&egrave; vim intrin&longs;ecam nunquam &agrave; na&shy;<lb/>tura rebus creatis in&longs;itam e&longs;&longs;e con&longs;tat, ni&longs;i ad eum finem con&longs;equendum, <lb/>cui &agrave; natura de&longs;tinantur; cur ver&ograve; locus connaturalis corporis grauio&shy;<lb/>ris &longs;it ille, in quo leuiori &longs;ube&longs;t, non diu h&aelig;rebit animus, quin &longs;tatim ra&shy;<lb/>tio affulgeat; cum enim corpus, quod e&longs;t &longs;upr&agrave;, &longs;u&longs;tineatur ab eo quod e&longs;t <lb/>infr&agrave;; illud cert&egrave; infra e&longs;&longs;e connaturalius e&longs;t, quod aptius e&longs;t ad &longs;u&longs;tinen-<pb xlink:href="026/01/150.jpg" pagenum="118"/>dum; atqui den&longs;um aptius e&longs;t ad id munus, quia plures partes &longs;u&longs;tinentis <lb/>pauciores &longs;u&longs;tinent alterius leuioris, &longs;eu rarioris, vt con&longs;tat; v.g. <!-- REMOVE S-->certum <lb/>e&longs;t <expan abbr="c&atilde;dem">eandem</expan> a&euml;ris partem pluribus aqu&aelig; partibus re&longs;pondere; &longs;ed de hoc <lb/>alias fus&egrave;; h&aelig;c interim &longs;ufficiat indica&longs;&longs;e, vt vel aliqua ratio affulgeat; <lb/>cur &longs;cilicet corpus graue &longs;ub medium leuius &longs;ua &longs;ponte de&longs;cendat; adde <lb/>quod cum omne corpus graue tendat deor&longs;um, tunc vnum infra aliud de&shy;<lb/>&longs;cendit, cum &longs;unt plures partes pellentis, qu&agrave;m pul&longs;i; denique per va&shy;<lb/>cuum modicum &longs;ine vlla re&longs;i&longs;tentia de&longs;cenderet. </s>

</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 81.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Sub medium grauius corpus leuius minim&egrave; de&longs;cendit, &longs;ed huic inna&shy;<lb/>tat<emph.end type="italics"/>; v.g. <!-- REMOVE S-->lignum aqu&aelig;, ferrum plumbo liquato; certa e&longs;t hypothe&longs;is: ratio <lb/>e&longs;t, quia ideo de&longs;cendit graue &longs;ub medium, quia grauius &longs;eu den&longs;ius e&longs;t <lb/>medio; igitur, &longs;i den&longs;ius e&longs;t ip&longs;um medium, non de&longs;cendet; clarum e&longs;t; <lb/>cur ver&ograve; a&longs;cendat &longs;upra medium. </s>



<s>v.g. <!-- REMOVE S-->cur lignum aqu&aelig; immer&longs;um tan&shy;<lb/>dem emergat h&icirc;c non di&longs;cutio, &longs;ed tant&ugrave;m indico ab ip&longs;a aqua &longs;ur&longs;um <lb/>extendi; quanta ver&ograve; parte lignum emergat, dicemus ali&agrave;s, cum de in&shy;<lb/>natantibus humido. </s>

</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 82.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Sub medium &aelig;qu&egrave; graue corpus non de&longs;cendit, nec etiam &longs;upra a&longs;cendit<emph.end type="italics"/>; ra&shy;<lb/>tio e&longs;t, quia ideo de&longs;cendit &longs;ub medium, quia medium leuius e&longs;t, ideo <lb/>a&longs;cendit &longs;upra, quia medium grauius e&longs;t; igitur &longs;i nec &longs;it grauius nec <lb/>leuius, non e&longs;t quod a&longs;cendat vel de&longs;cendat; nihil tamen illius &longs;upra <lb/>primam medij &longs;uperficiem extare poterit; alioqui e&longs;&longs;et leuius medio, <lb/>contra &longs;uppo&longs;itionem. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 83.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>A&euml;r &longs;uam grauitatem habet<emph.end type="italics"/>; quod iam &agrave; nullo in dubium reuocari po&shy;<lb/>te&longs;t; nam &longs;i comprimatur intra vas &aelig;neum v.g. <!-- REMOVE S-->etiam minim&aelig; cra&longs;&longs;itu&shy;<lb/>dinis; &longs;i deinde ponderetur, maius e&longs;t haud dubi&egrave; pondus, quo maior <lb/>e&longs;t a&euml;ris copia intru&longs;a; atqui non modo triplum totius a&euml;ris, qui ante <lb/>compre&longs;&longs;ionem totam va&longs;is capacitatem occupabat intrudi pote&longs;t, vel <lb/>decuplum; ver&ugrave;m etiam vigecuplum; imm&ograve; centuplum, &amp; millecuplum <lb/>adhibita cochle&acirc;, vel alio mechanico organo, &amp; aucta va&longs;is cra&longs;&longs;itudine, <lb/>de quo ali&agrave;s: quanta ver&ograve; &longs;it grauitas a&euml;ris comparata cum grauitate <lb/>aqu&aelig;, cen&longs;et Galileus e&longs;&longs;e fer&egrave; vt 1. ad 400. Mer&longs;ennus ver&ograve; vt 1. ad <lb/>1356. vel &longs;altem vt 1.ad 1300. Nos maiorem ill&agrave;; h&acirc;c vero minorem <lb/>e&longs;&longs;e ob&longs;eruauimus, de quo ali&agrave;s; nec enim e&longs;t pr&aelig;&longs;entis in&longs;tituti, pro <lb/>quo &longs;ufficiat mod&ograve;, a&euml;ri aliquam ine&longs;&longs;e grauitatem; nec dicas a&euml;ra le&shy;<lb/>uem e&longs;&longs;e; nam reuer&acirc; leuis e&longs;t, &longs;i comparetur cum aqua; grauis autem &longs;i <lb/>comparetur cum a&longs;cendente halitu, vel fort&egrave; cum vacuo; nec e&longs;t quod <lb/>aliquis fort&egrave; metuat, ne &longs;i a&euml;r &longs;it grauis, ab eo tandem opprimatur, nam <lb/>etiam&longs;i aqua &longs;it grauis non tamen opprimit vrinatores, cuius rei veri&longs;&longs;i&shy;<lb/>mam rationem &longs;uo loco afferemus; denique non e&longs;t quod aliqui &longs;atis <lb/>incaut&egrave; re&longs;pondeant, ip&longs;um a&euml;ra non e&longs;&longs;e grauem, &longs;ed tant&ugrave;m &longs;entiri ali&shy;<lb/>quod pondus cra&longs;&longs;ioris vaporis immixti; nam de alio a&euml;re non affirmo <pb xlink:href="026/01/151.jpg" pagenum="119"/>grauem e&longs;&longs;e, ni&longs;i tant&ugrave;m de illo, quem &longs;piramus, in quo ambulamus, qui <lb/>nos ambit: adde quod Ari&longs;toteles l.4. <emph type="italics"/>de C&oelig;lo, c.<emph.end type="italics"/>5.<emph type="italics"/>t.<emph.end type="italics"/>36. tribuit a&euml;ri gra&shy;<lb/>uitatem his verbis; <emph type="italics"/>quapropter<emph.end type="italics"/> inquit, <emph type="italics"/>a&euml;r, &amp; aqua habent &amp; leuitatem, &amp; <lb/>grauitatem.<emph.end type="italics"/></s>

</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 84.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Medium eiu&longs;dem grauitatis cum dato corpore graui detrahit totam eius <lb/>grauitationem &longs;ingularem; hoc e&longs;t corpus graue in medium &aelig;qu&egrave; graue non <lb/>grauitat<emph.end type="italics"/>; quia &longs;i grauitaret de&longs;cenderet; &longs;ic pars aqu&aelig; in aliam partem <lb/>aqu&aelig; non grauitat, &amp; &longs;i aqua ponderetur in aqua, nullius ponderis e&longs;t; <lb/>cum enim nulla &longs;it ratio cur vna &longs;it infr&agrave; poti&ugrave;s, qu&agrave;m alia, vna cert&egrave; al&shy;<lb/>terius locum non ambit; igitur caret grauitatione &longs;ingulari. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 85.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Medium graue detrahit aliquid de &longs;ingulari grauitatione corporis grauio&shy;<lb/>ris<emph.end type="italics"/>; certa e&longs;t hypothe&longs;is; nec enim plumbum e&longs;t eius ponderis &longs;ingula&shy;<lb/>ris in aqua, cuius e&longs;t in a&euml;re; dixi &longs;ingularis; nam &longs;i plumbum &amp; ip&longs;a <lb/>aqua &longs;imul appendantur, haud dubi&egrave; totum habebis pondus plumbi, &amp; <lb/>totum pondus aqu&aelig;; ratio ver&ograve; huius effectus non e&longs;t huius loci; quid&shy;<lb/>quid &longs;it, &longs;i &aelig;qualis grauitas medij tollit totam &aelig;qualem alterius corpo&shy;<lb/>ris; cert&egrave; maiorem alterius corporis totam non tollit per Th. 80. &longs;ed <lb/>tant&ugrave;m aliquid illius, quod quomodo fiat, dicemus Tomo quinto cum de <lb/>graui, &amp; leui. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 86.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Medium graue detrahit eam partem grauit ationis corporis grauioris, qu&aelig; <lb/>e&longs;t &aelig;qualis &longs;u&aelig; grauitationi.<emph.end type="italics"/> v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;i medij grauitas e&longs;t &longs;ubdupla, detrahit <lb/>&longs;ubduplum grauitationis; &longs;i &longs;ubdecupla, &longs;ubdecuplum, atque ita dein&shy;<lb/>ceps; hoc iam olim &longs;uppo&longs;uit magnus Archim. <!-- KEEP S--></s>





<s>&longs;upponunt etiam reliqui <lb/>omnes, pr&aelig;&longs;ertim recentior Galileus; &longs;i enim &aelig;qualis &longs;uperat &aelig;qualem, <lb/>ergo in&aelig;qualis pro rata; &longs;cilicet &longs;ubdupla &longs;ubduplum &longs;ubtripla, &amp;c. </s>

<s>Pr&aelig;&shy;<lb/>terea, cum detrahat aliquam partem grauitationis maioris per Th.85.nec <lb/>detrahat in&aelig;qualem maiorem, per Th.80.nec in&aelig;qualem minorem; cur <lb/>enim potius vnam minorem quam aliam? </s>

<s>cert&egrave; &aelig;qualem tant&ugrave;m <lb/>detrahere pote&longs;t, quod &longs;uo loco per Principium po&longs;itiuum demon&longs;tra&shy;<lb/>bimus. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 87.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc ratio cur grauia de&longs;cendant tardius in aqua, qu&agrave;m in a&euml;re, &amp; in <lb/>a&euml;re, qu&agrave;m in vacuo<emph.end type="italics"/>; hinc etiam maioris &longs;unt ponderis in a&euml;re quam in <lb/>aqua; hinc &longs;i grauitas alicuius corporis &longs;it ad grauitatem a&euml;ris vt 100. <lb/>ad 1. haud dubi&egrave; decre&longs;cet eius pondus in a&euml;re (1/100); id e&longs;t, &longs;i penderet 100. <lb/>libras in vacuo, in a&euml;re penderet 99. &amp; eo tempore quo in vacuo decur&shy;<lb/>reret 100. pa&longs;&longs;us, in a&euml;re decurreret 99. &longs;i nulla &longs;it aliunde re&longs;i&longs;tentia, <lb/>qualis reuer&acirc; e&longs;t, vt dicam infr&agrave;; &longs;imiliter &longs;i grauitas alicuius corporis <lb/>&longs;it ad grauitatem aqu&aelig;, vt 10. ad 1. decre&longs;cet eius pondus in aqua (1/<gap/>), &amp; <lb/>co tempore quo decurreret in vacuo 10. palmos &longs;patij, in aqua decurre <pb xlink:href="026/01/152.jpg" pagenum="120"/>ret tant&ugrave;m 9. po&longs;ito quod non &longs;it aliud quod re&longs;i&longs;tat; quanta ver&ograve; &longs;it <lb/>grauitas omnium corporum t&ugrave;m duriorum, qualia &longs;unt metalla, t&ugrave;m li&shy;<lb/>quidorum, t&ugrave;m &longs;pirabilium, dicemus &longs;uo loco; illorum tabulas habes <lb/>apud Gethaldum, &amp; Mer&longs;ennum. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 88.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc, &longs;i nihil aliud de&longs;cen&longs;um corporum grauium impediret, cognito pen&shy;<lb/>dere vtriu&longs;que, medij &amp; corporis grauis, &longs;patio, quod in vno illorum conficit, <lb/>cogno&longs;ci po&longs;&longs;et &longs;patium, quod in alio conficeret &aelig;quali tempore<emph.end type="italics"/>, v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;uppona&shy;<lb/>mus grauitatem aqu&aelig; e&longs;&longs;e ad grauitatem a&euml;ris vt 400. ad 1. &longs;itque corpus, <lb/>cuius grauitas &longs;it dupla grauitatis aqu&aelig;; haud dubi&egrave; eo tempore, quo <lb/>conficit in a&euml;re 799. &longs;patia, in aqua conf;iciet tant&ugrave;m 400. quia in vacuo <lb/>conficeret 800. a&euml;r autem detrahit (1/800), &amp; aqua 1/2, vt con&longs;tat ex dictis; &longs;i&shy;<lb/>militer cognitis &longs;patiis in vtroque medio confectis, &amp; grauitate vtriu&longs;que <lb/>medij cogno&longs;ceretur grauitas corporis de&longs;cendentis; quia tamen e&longs;t alia <lb/>re&longs;i&longs;tenti&aelig; ratio, h&icirc;c non h&aelig;reo. </s>



</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Ob&longs;eruabis dictum e&longs;&longs;e hactenus; &longs;i nihil aliud de&longs;cen&longs;um corporis <lb/>grauis impedit; nam cert&egrave; aliud e&longs;t, de quo infr&agrave;, ex cuius ignoratione <lb/>plures haud dubi&egrave; in inue&longs;tigandis grauitatum medij rationibus hallu&shy;<lb/>cinarentur; cum enim ob&longs;eruatum &longs;it globum plumbeum, cuius graui&shy;<lb/>tas e&longs;t fer&egrave; dodecupla grauitatis aqu&aelig;, conficere in libero a&euml;re 48. pedes <lb/>&longs;patij tempore duorum &longs;ecundorum, in aqua ver&ograve; 12. pedes codem tem&shy;<lb/>pore; cert&egrave; in vacuo ip&longs;o moueretur tardi&ugrave;s qu&agrave;m in a&euml;re; quia eo tem&shy;<lb/>pore, quo conficit in aqua 12.pedes in vacuo conficeret (13 1/21), &longs;i tant&ugrave;m <lb/>detrahitur (1/12) grauitationis, &amp; de&longs;cen&longs;us; atqui in a&euml;re codem tempore <lb/>conficit 48. pedes; igitur veloci&ugrave;s moueretur in a&euml;re qu&agrave;m in vacuo; <lb/>igitur e&longs;t aliquid aliud quod impedit motum; vt enim optim&egrave; monet <lb/>Mer&longs;ennus, &longs;i grauitas aqu&aelig; &longs;it ad grauitatem a&euml;ris vt 400 ad 1.&amp; graui&shy;<lb/>tas plumbi ad grauitatem aqu&aelig; vt 12. ad 1.eadem grauitas plumbi e&longs;t ad <lb/>grauitatem a&euml;ris vt 4800. igitur &longs;i &longs;patium, quod decurrit plumbum in <lb/>vacuo diuidatur in 4800. partes, decurret in a&euml;re 4799. partes; in aqua <lb/>ver&ograve; 4400. quod e&longs;t contra experientiam; nam &longs;patium, quod decurrit <lb/>in a&euml;re e&longs;t maius &longs;patio, quod decurrit in aqua 3/4; quippe conficit 12. <lb/>pedes in aqua eodem tempore, quo in a&euml;re conficit 48; igitur in aqua <lb/>amittit 3/4 &longs;u&aelig; grauitationis, &amp; &longs;ui motus; igitur 3600. partes; igitur <lb/>plumbi grauitas e&longs;&longs;et ad grauitatem aqu&aelig; vt 4.ad 3.&amp; ad grauitatem a&euml;&shy;<lb/>ris vt 3600. ad 1. atqui vtrumque fal&longs;um e&longs;&longs;e con&longs;tat; igitur e&longs;t aliquid <lb/>aliud, quod etiam impedit motum; nec ex motu diuer&longs;o per diuer&longs;a me&shy;<lb/>dia cogno&longs;ci pote&longs;t eorum grauitas. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 89.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc potiori iure reiicies illorum &longs;ententiam, qui volunt impediri motum <lb/>corporis de&longs;cendentis per diuer&longs;a media pro diuer&longs;a ratione grauitatum vtriu&longs;&shy;<lb/>que medy<emph.end type="italics"/>; quod cert&egrave; fal&longs;um e&longs;t; nam aqua &longs;it ad grauitatem a&euml;ris vt <lb/>400. ad 1. deberet omne corpus de&longs;cendere veloci&ugrave;s in a&euml;re quadrin-<pb xlink:href="026/01/153.jpg" pagenum="121"/>gente&longs;ies, qu&agrave;m in aqua, quod fal&longs;um e&longs;t; cum aliquod corpus nullo mo&shy;<lb/>do de&longs;cendat in aqua, quod de&longs;cendit in a&euml;re, vt lignum. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 90.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Non pote&longs;t corpus graue per medium corporeum de&longs;cendere, ni&longs;i vel totum <lb/>medium loco cedat, vel aliqu&aelig; partes eiu&longs;dem medij,<emph.end type="italics"/> patet; quia vnum cor&shy;<lb/>pus non pote&longs;t penetrari cum alio. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 91.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Totum medium loco non cedit in de&longs;cen&longs;u grauium<emph.end type="italics"/>; patet etiam, t&ugrave;m <lb/>quia ad mouendum totum medium exigua vis corporis grauis non &longs;uffi&shy;<lb/>cit; t&ugrave;m quia t&agrave;m facil&egrave; per medium durum eiu&longs;dem grauitatis de&longs;cen&shy;<lb/>deret; denique patet manife&longs;t&acirc; experienti&acirc;. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 92.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc aliqua tant&ugrave;m partes medij loco cedunt<emph.end type="italics"/>; probatur, quia vel totum <lb/>medium, vel aliqu&aelig; eius partes, per Th.90.non primum per Th.91. igitur <lb/>&longs;ecundum, in his cert&egrave; non e&longs;t vlla difficultas. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 93.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Non po&longs;&longs;unt ill&aelig; partes loco cedere &longs;ine motu; nec moueri &longs;ine impetu, nec <lb/>habere impetum, ni&longs;i producatur in illis &agrave; cau&longs;a aliqua applicata; qu&aelig; cert&egrave; <lb/>alia none&longs;t qu&agrave;m impetus corporis de&longs;cendentis,<emph.end type="italics"/> vt con&longs;tat ex iis, qu&aelig; dixi&shy;<lb/>mus primo lib. <!-- REMOVE S--><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 94.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Ill&aelig; partes, qu&aelig; loco cedunt de&longs;cendenti corpori graui, nece&longs;&longs;ari&ograve; ab aliis <lb/>&longs;eparantur, &amp; &longs;uo appul&longs;u, vel impul&longs;u alias multas impellunt, ac &longs;eparant,<emph.end type="italics"/><lb/>atqui &longs;eparari non po&longs;&longs;unt ab aliis, ni&longs;i &longs;oluatur vnio, &longs;eu nexus, <lb/>quo cum aliis deuinciuntur; quidquid tandem &longs;it illa vnio, de qua <lb/>ali&agrave;s. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 95.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc qu&ograve; arctior e&longs;t ille nexus, difficilius &longs;oluitur<emph.end type="italics"/>; igitur maiore vi, vel <lb/>impetu opus e&longs;t, vt &longs;olui po&longs;&longs;it, vt con&longs;tat. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 96.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc corpus grauius &longs;ustinetur &agrave; leuiore.<emph.end type="italics"/> v.g. <!-- REMOVE S-->plumbum &agrave; ligno propter <lb/>arctiorem nexum partium ligni, qui ab impetu plumbi quantumuis gra&shy;<lb/>ui&longs;&longs;imi &longs;uperari non pote&longs;t; hinc corpus illud, medium tant&ugrave;m appello <lb/>in quo po&longs;&longs;int corpora moueri, cuius nexus &longs;uperari pote&longs;t &agrave; corpore <lb/>grauiori in aliqua &longs;altem figura, vel &longs;itu; hinc corpora dura non po&longs;&longs;unt <lb/>e&longs;&longs;e medium; imm&ograve; neque mollia, vt cera, argilla; &longs;ed vel liquida, vel <lb/>&longs;pirabilia. </s>

</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 97.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc ducitur euidens ratio, cur medium impediat motum &longs;i dumtaxat ha&shy;<lb/>beat arctiorum partium implicationem &amp; nexum<emph.end type="italics"/>; quia non modo partes <pb xlink:href="026/01/154.jpg" pagenum="122"/>medij amouend&aelig; &longs;unt &egrave; &longs;uo loco; ver&ugrave;m etiam nexus ille partium &longs;ol&shy;<lb/>uendus; igitur ex vtroque capite impeditur motus. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 98.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Quo &longs;ubtiliores &longs;unt partes difficilius inter &longs;e implicari po&longs;&longs;unt &longs;eu ligari <lb/>quibu&longs;dam filamentis<emph.end type="italics"/>, con&longs;tat; igitur cum a&euml;ris partes &longs;int magis lubric&aelig;, <lb/>qu&agrave;m partes aqu&aelig;, &amp; facili&ugrave;s per obuia qu&aelig;que foramina irrepere po&longs;&shy;<lb/>&longs;int, non po&longs;&longs;unt ita contineri; &longs;ic videmus mult&ugrave;m aqu&aelig; hauriri, dum <lb/>arctioribus retibus attollitur; imm&ograve; dum aquam manu &longs;tringimus, ali&shy;<lb/>quam re&longs;i&longs;tentiam &longs;en&longs;u percipimus; qu&aelig; cert&egrave; nulla e&longs;t, dum a&euml;ra &longs;trin&shy;<lb/>gimus. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Ob&longs;eruabis vnionem continuatiuam corporum aliquando po&longs;itam <lb/>e&longs;&longs;e in plexu, vel implicatione partium, vt videmus in fune, ligno, carne, <lb/>o&longs;&longs;ibus, &amp;c. </s>

<s>aliquando in vacui metu; &longs;ic aqua, vt &longs;uo va&longs;i adh&aelig;reat, <lb/>a&longs;cendit, vel &longs;ur&longs;um attollitur, ne detur vacuum; aliquando in coitione <lb/>quadam magnetica; porr&ograve; hic plexus con&longs;tat ex infinitis fer&egrave; tenui&longs;&longs;i&shy;<lb/>morum filamentorum voluminibus, vel aduncis &longs;iue hamatis partibus, <lb/>&longs;eu corpu&longs;culis: Vtrum ver&ograve; pr&aelig;ter h&aelig;c requiratur alius vnionis mo&shy;<lb/>dus, di&longs;cutiemus fus&egrave; Tomo 5. quidquid &longs;it; certum e&longs;t medium illud, <lb/>cuius partes arctiori maiorique nexu copulantur, long&egrave; difficili&ugrave;s per&shy;<lb/>curri po&longs;&longs;e, &longs;eu perrumpi. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 99.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc non mod&ograve; aqua detrahit plumbo<emph.end type="italics"/> (1/22) <emph type="italics"/>&longs;ui motus, quod &longs;cilicet plumbi gra&shy;<lb/>uitas &longs;it dedecupla grauitatis aqu&aelig;, ver&ugrave;m etiam propter re&longs;istentiam petitam <lb/>ex alio capite aliquid adhuc detrahere pote&longs;t<emph.end type="italics"/>; &longs;cilicet quia partes aqu&aelig; non <lb/>po&longs;&longs;unt amoueri, ni&longs;i ab aliis &longs;eparentur; atqui maiore vi opus e&longs;t ad&shy;<lb/>&longs;oluendum &longs;trictiorem nexum; imm&ograve; lic&egrave;t partes aqu&aelig; nullo penitus <lb/>nexu vniantur, &longs;ed tant&ugrave;m vel vacui metu, vel alio modo, quod alibi ex&shy;<lb/>plicabimus; omnin&ograve; detraherent adhuc plumbo (1/12) motus; igitur, &longs;i <lb/>pr&aelig;ter illud impedimentum, quod petitur &agrave; comparatione grauitatis <lb/>corporis mobilis cum grauitate medij, addatur aliud long&egrave; robu&longs;tius; <lb/>non mirum e&longs;t, &longs;i maior inde &longs;equatur effectus, id e&longs;t maior imminutio <lb/>motus, qui qua&longs;i frangitur ab impedimento. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 100.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc petitur ratio illius experimenti, &longs;i verum e&longs;t, duobus &longs;ecundis per&shy;<lb/>currere plumbeam pilam in a&euml;re<emph.end type="italics"/> 48. <emph type="italics"/>&longs;patij pedes, in aqua ver&ograve;<emph.end type="italics"/> 12. <emph type="italics"/>pedes<emph.end type="italics"/>; hinc <lb/>tenui nexu partes a&euml;ris copulantur; partes ver&ograve; aqu&aelig; firmiori; hinc a&euml;r <lb/>min&ugrave;s re&longs;i&longs;tit etiam motibus violentis; hinc vix pote&longs;t qui&longs;piam in aqua <lb/>currere propter maiorem aqu&aelig; re&longs;i&longs;tentiam; hinc pote&longs;t dici quota parte <lb/>firmior &longs;it nexus vnius corporis qu&agrave;m alterius; hinc non tant&ugrave;m copu&shy;<lb/>lantur partes metu vacui; alioquin &aelig;qu&egrave; re&longs;i&longs;terent partes a&euml;ris, ac par&shy;<lb/>tes aqu&aelig; ratione nexus; hinc videntur guttul&aelig; ill&aelig; &longs;pheric&aelig; inuolui te&shy;<lb/>nui qua&longs;i membranula, &longs;eu &longs;uperficie, cuius analogiam videmus in aqua<gap/><pb xlink:href="026/01/155.jpg" pagenum="123"/>feruente; in bullis, qu&aelig; ex guttis pluui&aelig; re&longs;ilientibus na&longs;ci videntur; in <lb/>bullis etiam illis &longs;aponariis, quas leui calamo pueri inter ludendum in&shy;<lb/>flant; hinc ex minimo fer&egrave; contactu guttula &longs;pargitur, ni&longs;i fort&egrave; cum <lb/>multo a&longs;per&longs;a puluere cru&longs;tam quamdam induit &longs;olidiorem; &longs;ic bull&aelig; il&shy;<lb/>l&aelig; ad minimum etiam contactum di&longs;&longs;ipantur; hinc ip&longs;a &longs;uperficies <lb/>aqu&aelig; plus videtur re&longs;i&longs;tere quod multis experimentis comprobatur; &longs;ed <lb/>illo maxim&egrave;, quo videmus findi &agrave; remo cum quodam qua&longs;i &longs;tridulo cre&shy;<lb/>pitu re&longs;i&longs;tenti&aelig; maioris te&longs;te; imm&ograve; cum ab ip&longs;a naui qua&longs;i &longs;ulcatur, <lb/>idem &longs;tridor auditur, maxim&egrave; in iis tractibus; in quibus nullis fluctibus <lb/>agitata l&aelig;uigati&longs;&longs;imam faciem pr&aelig;fert; habes analogiam in illa cru&longs;ta, <lb/>qu&aelig; concre&longs;cit in &longs;uperficie liquorum, &longs;ed pr&aelig;&longs;ertim o&longs;&longs;arum: adde quod <lb/>a&euml;r paul&ograve; compre&longs;&longs;ior vndique guttulam premens &aelig;quali ni&longs;u eam miri&shy;<lb/>fic&egrave; tornat: h&aelig;c tant&ugrave;m tumultuatim conge&longs;ta alibi fus&egrave; pertractabi&shy;<lb/>mus, &amp; ex &longs;implici&longs;&longs;imis principiis demon&longs;trabimus; plura h&icirc;c de graui&shy;<lb/>tate crant dicenda, &amp; de grauitatione, qu&aelig; tant&ugrave;m indica&longs;&longs;e &longs;ufficiat, vt <lb/>deinde Tomo quinto fus&egrave; explicentur. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 101.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Non re&longs;istit medium propter compre&longs;&longs;ionem partium inferiorum, quas nullo <lb/>modo comprimi nece&longs;&longs;e e&longs;t, vel in&longs;en&longs;ibiliter<emph.end type="italics"/>; cum enim tantus relinquatur <lb/>locus retr&ograve;, quantus acquiritur ant&egrave;, nulla opus e&longs;t compre&longs;&longs;ione; &longs;ed <lb/>partes &agrave; fronte pul&longs;&aelig; fact&acirc; circuitione retror&longs;um eunt, non cert&egrave; tramite <lb/>recto; &longs;i enim frons ip&longs;ius lata &longs;it, haud dubi&egrave; partes pul&longs;&aelig; alias pellunt, <lb/>&amp; h&aelig; vici&longs;&longs;im alias longo circuitu, vt patet experientia; nulla tamen, vel <lb/>modica fieri videtur compre&longs;&longs;io. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 102.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc quo &longs;unt plures partes diuidend&aelig;, qu&aelig; ant&egrave; uniebantur, maior e&longs;t re&longs;i&shy;<lb/>&longs;tentia<emph.end type="italics"/>; igitur maiore vi opus e&longs;t, igitur maiore grauitate; &longs;ed in medio <lb/>den&longs;iore ab codem mobili plures &longs;eparantur qu&agrave;m in rariore; quia &longs;ci&shy;<lb/>licet corpus den&longs;um plures habet &longs;ub minori exten&longs;ione, &amp; rarum &egrave; con&shy;<lb/>trario, vt videbimus &longs;uo loco; igitur in medio den&longs;iore idem mobile ma&shy;<lb/>jorem re&longs;i&longs;tentiam inuenit, qu&agrave;m in rariore; lic&egrave;t vtriu&longs;que partes <lb/>&aelig;quali nexu &longs;eu fibula copulentur; quia &longs;cilicet plures &longs;unt diuidend&aelig; <lb/>in den&longs;iore; quia plures &longs;cilicet in &aelig;quali &longs;patio occurrunt, qu&agrave;m in ra&shy;<lb/>riore; igitur maiore vi grauitatis opus e&longs;t. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 103.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc medium pote&longs;t comparari cum alio in<emph.end type="italics"/> 2. <emph type="italics"/>capitibus<emph.end type="italics"/>; Primum e&longs;t in <lb/>grauitate, vel den&longs;itate, nam reuer&acirc; ex maiori den&longs;itate maiorem gra&shy;<lb/>uitatem reducimus; Secundum e&longs;t in maiori, vel minori partium nexu, <lb/>ex quo 4. &longs;equuntur combinationes 2.mediorum; nam vel &longs;unt eiu&longs;dem <lb/>grauitatis, &amp; mollitiei; vel eiu&longs;dem grauitatis &amp; diuer&longs;&aelig; mollitiei; vel <lb/>eiu&longs;dem mollitiei, &amp; diuer&longs;&aelig; grauitatis; vel diuer&longs;&aelig; grauitatis, &amp; eiu&longs;&shy;<lb/>dem mollitiei; mollius autem illud appello, cuius partes laxiori nexu <lb/>copulantur; porr&ograve; 4. i&longs;t&aelig; combinationes &longs;upponunt <expan abbr="id&etilde;">idem</expan> mobile <expan abbr="invtroq;">in vtroque</expan> <lb/>medio; &longs;i &longs;it prima combinatio, motus e&longs;t &aelig;qualis in vtroque; &longs;i &longs;ecunda <pb xlink:href="026/01/156.jpg" pagenum="124"/>maior e&longs;t in molliori; &longs;i tertia maior in grauiori; &longs;i ver&ograve; quarta &longs;ubdi&shy;<lb/>uidi pote&longs;t in duas; nam vel grauius e&longs;t conjunctum cum maiori molli&shy;<lb/>tie, vel leuius; &longs;i leuius, haud dubi&egrave; maior e&longs;t motus in leuiore; &longs;i gra&shy;<lb/>uius &amp; mollities compen&longs;et grauitatem, id e&longs;t, &longs;i vt &longs;e habet grauitas gra&shy;<lb/>uioris ad leuitatem leuioris; ita &longs;e habet mollities illius ad mollitiem <lb/>huius, &aelig;qualis e&longs;t in vtroque; &longs;i &longs;ecus, pro rata; hinc pote&longs;t e&longs;&longs;e &aelig;qualis <lb/>motus in grauiore &amp; leuiore medio, &amp; in &aelig;qu&egrave; graui pote&longs;t e&longs;&longs;e maior <lb/>in grauiore; &amp; minor; maior quidem, &longs;i maior &longs;it ratio mollitiei gra&shy;<lb/>uioris ad mollitiem leuioris, qu&agrave;m grauitatis ad grauitatem; minor ve&shy;<lb/>r&ograve;, &longs;i maior &longs;itratio grauitatis ad grauitatem, qu&agrave;m mollitiei ad molli&shy;<lb/>tiem; &aelig;qualis denique &longs;i &aelig;qualis ratio; &amp; his regulis cuncta facil&egrave; ex&shy;<lb/>plicari po&longs;&longs;unt; h&icirc;c porr&ograve; &longs;uppono idem mobile, quod per vtrumque me&shy;<lb/>dium de&longs;cendere po&longs;&longs;it, id e&longs;t, quod &longs;it vtroque grauius, medium autem <lb/>appello illud, per quod mobile grauius per &longs;e de&longs;cendit; dixi per &longs;e quia <lb/>nonnunquam accidit, vt vel ratione figur&aelig;, vel alterius impedimenti non <lb/>de&longs;cendat. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 104.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Sunt tres combinationes mobilis cum medio<emph.end type="italics"/>; prima, &longs;i &longs;it idem mobile <lb/>cum diuer&longs;is mediis; &longs;ecunda, &longs;i idem medium cum diuer&longs;is mobilibus; <lb/>tertia &longs;i diuer&longs;a mob&iuml;lia cum diuer&longs;is mediis; de prim&acirc; actum e&longs;t iam <lb/>&longs;upr&agrave;; &longs;ecunda &longs;ube&longs;t 4. combinationibus. </s>

<s>Prima &longs;i mobilia &longs;int eiu&longs;&shy;<lb/>dem materi&aelig;, &longs;ed diuer&longs;&aelig; figur&aelig;; Secunda eiu&longs;dem figur&aelig; &amp; diuer&longs;&aelig; <lb/>materi&aelig;. </s>

<s>Quarta diuer&longs;&aelig; materi&aelig; &amp; figur&aelig;; &longs;i prima &amp; &longs;ecunda, vel &longs;unt <lb/>figur&aelig; &aelig;quales, vel in&aelig;quales; &longs;i primum &longs;unt eiu&longs;dem grauitatis; &longs;i &longs;e&shy;<lb/>cundum diuer&longs;&aelig;; quippe figur&aelig; &longs;imiles po&longs;&longs;unt e&longs;&longs;e &aelig;quales, vel in&aelig;&shy;<lb/>quales; &amp; figur&aelig; &aelig;quales po&longs;&longs;unt e&longs;&longs;e &longs;imiles, vel di&longs;&longs;imiles; &longs;i &longs;it tertia <lb/>combinatio, in qua &longs;int eiu&longs;dem figur&aelig;, &amp; diuer&longs;&aelig; materi&aelig;, diuer&longs;&aelig; in&shy;<lb/>quam in grauitate; &longs;i figur&aelig; &longs;unt &aelig;quales, &longs;emper e&longs;t diuer&longs;a grauitas; &longs;i <lb/>in&aelig;quales pote&longs;t e&longs;&longs;e vel eadem, vel tertia; in quarta combinatione di&shy;<lb/>uer&longs;a compen&longs;atio fieri pote&longs;t; idem dicendum e&longs;t de tertia combinatio&shy;<lb/>ne diuer&longs;orum mobilium, &amp; mediorum, de quibus omnibus &longs;eor&longs;im iam <lb/>dicemus. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 105.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Si mobilia duo eiu&longs;dem materi&aelig;, figur&aelig;, &amp; grauitatis in eodem medio de&shy;<lb/>&longs;cendant, &aelig;quali motu feruntur<emph.end type="italics"/> dem. </s>

<s>vbi e&longs;t eadem proportio cau&longs;&aelig; &amp; re&longs;i&shy;<lb/>&longs;tenti&aelig; ibi e&longs;t idem effectus, per Ax. 5. &longs;ed in hoc ca&longs;u eadem e&longs;t illa pro&shy;<lb/>portio; nam e&longs;t &aelig;qualis cau&longs;a, &longs;cilicet grauitas; idem medium &aelig;qualiter <lb/>vtrique re&longs;i&longs;tens, cum non plures medij partes re&longs;i&longs;tant vni, quam alteri; <lb/>igitur &aelig;qualis proportio. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 106.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Maior e&longs;t re&longs;istentia eiu&longs;dem medij ratione &longs;cilicet partium, cum plures <lb/>eius partes re&longs;istunt qu&agrave;m cum pauciores<emph.end type="italics"/>; patet, quia maior effectus re&shy;<lb/>&longs;pondet pluribus partibus cau&longs;&aelig; per Ax.13.l.1. num.2. </s></p><pb xlink:href="026/01/157.jpg" pagenum="125"/><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 107.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Plures partes re&longs;istunt, quando plures pelluntur &agrave; mobili deor&longs;um<emph.end type="italics"/>; quip&shy;<lb/>pe in tantum re&longs;i&longs;tunt, in quantum ab aliis &longs;eparantur; atqui in tantum <lb/>&longs;eparantur, in quantum amouentur &egrave; &longs;uo loco; &longs;ed ideo amouentur &egrave; <lb/>&longs;uo loco, in quantum pelluntur; igitur cum plures pelluntur tunc plures <lb/>re&longs;i&longs;tunt; igitur tunc maior e&longs;t re&longs;i&longs;tentia. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 108.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Plures pelluntur &agrave; maiori &longs;uperficie, qu&agrave;m &agrave; minori, qu&aelig; tendit deor&longs;um <lb/>parallela horizonti.<emph.end type="italics"/> v.g. <!-- REMOVE S-->&agrave; &longs;uperficie cubi maioris, qu&agrave;m minoris; quippe <lb/>tot pelluntur quot re&longs;pondent prim&aelig; faciei, &longs;eu primo plano, quod e&longs;t in <lb/>fronte. </s>

</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 109.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Si diuidatur cubus in cubos minores, ratio &longs;uperficierum erit duplicat a la&shy;<lb/>terum, &amp; ratio &longs;olidorum triplicata,<emph.end type="italics"/> con&longs;tat ex Geometria, &longs;it enim cubus </s></p><p type="main">

<s><arrow.to.target n="note2"/><lb/>GK, nam in gratiam eorum qui Geometriam ignorant hoc ip&longs;um ocu&shy;<lb/>lis &longs;ubiiciendum e&longs;&longs;e videtur; diuidantur 6. eius facies in 4. quadrata <lb/>&aelig;qualia v. <!-- REMOVE S-->g. <!-- REMOVE S-->facies AI in quad. </s>





<s>AE. EC. EG. EI. idem fiat in aliis <lb/>5. faciebus, quarum du&aelig; h&icirc;c tantum apparent; &longs;cilicet AK. KL; &longs;ed <lb/>tribus aliis parallelis; his tribus c&aelig;dem diui&longs;iones re&longs;pondent; haud <lb/>dubi&egrave; erunt cubi minores, quorum latus &longs;it &aelig;quale AB, &amp; qu&aelig;libet fa&shy;<lb/>cies &aelig;qualis quadrato AE, &longs;ed facies maior AI, e&longs;t quadrupla minoris <lb/>AE, ergo AI e&longs;t ad AE vt quadratum lateris AG ad quadratum lateris <lb/>AD; &longs;ed h&aelig;c e&longs;t ratio duplicata laterum 1. 2. 4. &longs;imiliter cubus maior <lb/>GK e&longs;t octuplum minoris DN, igitur vt cubus lateris AG ad cubum <lb/>lateris AD. &longs;ed h&aelig;c e&longs;t ratio triplicata. </s>

<s>1.2.4.8. </s></p><p type="margin">

<s><margin.target id="note2"/>a <emph type="italics"/>Fig.<emph.end type="italics"/>26 <lb/><emph type="italics"/>Tab.<emph.end type="italics"/>1.<!-- KEEP S--></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 110.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc pl&ugrave;s minuitur &longs;olidum in diuer&longs;ione cubi quam facies, &amp; pl&ugrave;s facies <lb/>qu&agrave;m latus<emph.end type="italics"/>; patet ex dictis, nam latus minoris cubi e&longs;t tant&ugrave;m &longs;ubdu&shy;<lb/>plum lateris maioris, &amp; facies &longs;ubquadrupla; &longs;olidum ver&ograve; &longs;ub&shy;<lb/>octuplum. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 111.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc pl&ugrave;s minuitur grauitas, qu&agrave;m re&longs;i&longs;tentia minoris cubi<emph.end type="italics"/>; quia grauitas <lb/>re&longs;pondet &longs;olido, &amp; re&longs;i&longs;tentia prim&ecedil; faciei; re&longs;i&longs;tentia <expan abbr="inqu&amacr;">inquam</expan> ratione par&shy;<lb/>tium medij; &longs;ed &longs;olidum plus miuuitur qu&agrave;m facies, vt dictum e&longs;t; igitur <lb/>plus minuitur grauitas, qu&aelig; e&longs;t cau&longs;a virium qu&agrave;m h&aelig;c re&longs;i&longs;tentia; ergo <lb/>decre&longs;cunt vires in maiore proportione qu&agrave;m h&aelig;c re&longs;i&longs;tentia, quod be&shy;<lb/>n&egrave; ob&longs;eruauit Galileus in d&igrave;alogis. </s></p><p type="main">

<s>Hinc concludit Galileus duos cubos eiu&longs;dem materi&aelig;, &longs;ed in&aelig;quales <lb/>de&longs;cendere in&aelig;quali motu; maiorem &longs;cilicet veloci&ugrave;s minori; demon&shy;<lb/>&longs;trare videtur, quia maior habet maiorem proportionem virium ad re&shy;<lb/>&longs;i&longs;tentiam, qu&agrave;m minor; igitur maiorem habet effectum per Ax. 5. igi&shy;<lb/>tur maiorem, &amp; velociorem motum. </s></p><p type="main">

<s>Scio non dee&longs;&longs;e multos viros doctos qui acriter in hanc &longs;ententiam <pb xlink:href="026/01/158.jpg" pagenum="126"/>in&longs;urgant: Obiicient fort&egrave; prim&ograve;, experientiam e&longs;&longs;e contrariam; &longs;i enim <lb/>accipiantur duo cubi maior, &amp; minor eiu&longs;dem materi&aelig;, &amp; dimittantur <lb/>ex eadem altitudine codem pror&longs;us momento terram ferient; Re&longs;ponde&shy;<lb/>ri pote&longs;t momentum illud &longs;en&longs;u percipi non po&longs;&longs;e; &longs;i enim dicam ma&shy;<lb/>iorem tangere terram 1000. in&longs;tantibus ante minorem, an fort&egrave; &longs;en&longs;u <lb/>hoc percipies, vi&longs;u &longs;cilicet vel auditu? </s>

<s>igitur in maxima altitudine h&aelig;c <lb/>&longs;patiorum in&aelig;qualitas, &amp; temporum &longs;en&longs;u percipi po&longs;&longs;et, qu&aelig; in minori <lb/>&longs;ub &longs;en&longs;um non cadit: pr&aelig;terea accipe pulueris granulum eiu&longs;dem ma&shy;<lb/>teri&aelig;, tuncque etiam &longs;en&longs;ibilem motuum differentiam videb&icirc;s, atqui <lb/>e&longs;t eadem ratio de omni minore. </s></p><p type="main">

<s>Secund&ograve; obiicient, &longs;i &longs;uperponatur cubus minor maiori in &longs;uo motu <lb/>nunquam &longs;eparantur; igitur &aelig;quali motu de&longs;cendunt. </s>

<s>Re&longs;p. videri po&shy;<lb/>te&longs;t equidem &aelig;quali motu de&longs;cendere quia &longs;unt veluti partes eiu&longs;dem <lb/>corporis, &amp; grauitant grauitatione communi, neque minor habet &longs;ingu&shy;<lb/>larem re&longs;i&longs;tentiam &longs;uperandam; imm&ograve; &longs;i &longs;uperponatur minor maiori, <lb/>vel maior minori, motus e&longs;t velocior qu&agrave;m e&longs;&longs;et &longs;olius maioris; quia <lb/>cum non &longs;it maior re&longs;i&longs;tentia, maiores illi vires opponuntur; igitur fa&shy;<lb/>cili&ugrave;s &longs;uperatur. </s></p><p type="main">

<s>Terti&ograve; obiicient; e&longs;t eadem &longs;pecie grauitas; igitur eadem grauitatio, <lb/>idemque motus deor&longs;um; Re&longs;ponderi po&longs;&longs;et concedendo antecedens, <lb/>vnde in vacuo omnia grauia &aelig;qu&egrave; velociter de&longs;cenderent, &longs;i in eo mo&shy;<lb/>tus e&longs;&longs;et; at ver&ograve; altera duarum cau&longs;arum eiu&longs;dem &longs;peciei, qu&aelig; habet mi&shy;<lb/>norem proportionem actiuitatis ad re&longs;i&longs;tentiam, profect&ograve; min&ugrave;s agit, <lb/>quod certum e&longs;t. </s></p><p type="main">

<s>Quart&ograve; obij:igitur motus po&longs;&longs;et e&longs;&longs;e velocior, &amp; velocior in infini&shy;<lb/>tum; &longs;i enim maior cubus de&longs;cenderet veloci&ugrave;s; igitur &longs;i detur maior ad&shy;<lb/>huc veloci&ugrave;s, atque ita deinceps: Re&longs;p. inanem pror&longs;us e&longs;&longs;e difficulta&shy;<lb/>tem; quia cubus ille quantumuis maximus in vacuo de&longs;cendit veloci&ugrave;s <lb/>qu&agrave;m in aliquo medio v.g.in a&euml;re, igitur nunquam augmentum veloci&shy;<lb/>tatis infinitum e&longs;t; quippe inter duos gradus velocitatis infiniti &longs;unt <lb/>po&longs;&longs;ibiles. </s>

<s>v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;it velocitas, quam habet in vacuo vt 2. illa ver&ograve; qu&agrave;m <lb/>habet in a&euml;re vt 1. &longs;i cre&longs;cat velocitas iuxta has minutias &longs;ingulis in&longs;tan&shy;<lb/>tibus 1/2 1/4 1/8 (1/16) (1/32), atque ita deinceps; qu&agrave;m porr&ograve; mult&aelig; &longs;unt huiu&longs;modi <lb/>progre&longs;&longs;iones 1/3 1/6 (1/12) (1/24) &amp;c. </s>





<s>igitur obiectiones ill&aelig; non euertunt Gali&shy;<lb/>lei &longs;ententiam. </s></p><p type="main">

<s>Inde idem Galileus o&longs;tendere videtur cur atomi materi&aelig; etiam gra&shy;<lb/>ui&longs;&longs;im&aelig;, &longs;eu granula pulueris motu tardi&longs;&longs;imo de&longs;cendant in a&euml;re vel in <lb/>aqua; quia &longs;cilicet per illam diui&longs;ionem ita imminut&aelig; &longs;unt vires graui&shy;<lb/>tatis, vt iam re&longs;i&longs;tentiam medij &longs;uperare non po&longs;&longs;int. </s></p><p type="main">

<s>Sed videtur e&longs;&longs;e graui&longs;&longs;ima difficultas, &longs;int enim duo cubi, maior B <lb/>F, minor GM, &amp; vterque innatet medio liquido duplo grauiori; cert&egrave; ex&shy;<lb/>tabit maior toto rectangulo CA &aelig;quali CF, &amp; minor toto rectangulo <lb/>KH &aelig;quali KM; igitur e&longs;t eadem proportio grauitatis maioris ad re&longs;i&shy;<lb/>&longs;tentiam medij in grauitatione, qu&aelig; e&longs;t minoris; igitur &amp; in motu. </s></p><p type="main">

<s>Re&longs;ponderi pote&longs;t e&longs;&longs;e maximam di&longs;paritatem inter grauitationem, &amp; <pb xlink:href="026/01/159.jpg" pagenum="127"/>motum; &longs;it enim cubus BD qui de&longs;cendat per totam AH; haud dubi&egrave; <lb/>cum &longs;patium DI, contineat 3. cubos medij &aelig;quales DB, eos debet remo&shy;<lb/>uere in &longs;uo de&longs;cen&longs;u; &longs;it autem cubus BG; haud dubi&egrave;, cum &longs;it eadem pro&shy;<lb/>portio cubi AE ad cubum medij DM, qu&aelig; e&longs;t cubi BG ad cubum me&shy;<lb/>dij FL, eodem tempore vterque cubum medij &longs;uppo&longs;iti &egrave; &longs;uo loco extru&shy;<lb/>det; igitur eo tempore, quo AE expellet 3. DI, FL extrudet 3. EO, ergo <lb/>&aelig;quabili tempore in&aelig;quale &longs;patium percurrunt. </s></p><p type="main">

<s>Dices ergo &longs;patia &longs;unt vt latera: Re&longs;ponderi pote&longs;t hoc reuer&acirc; per &longs;e <lb/>e&longs;&longs;e debere; &longs;ed quia cubus DM vt extrudatur, maiorem debet facere cir&shy;<lb/>cuitionem, vt &agrave; fronte retr&ograve; eat, velociori motu extrudi debet; igitur vi&shy;<lb/>res &longs;uas in eo con&longs;umit maiori ex parte cubus AE; hinc compen&longs;atio e&longs;&longs;e <lb/>videtur. </s></p><p type="main">

<s>Vt &longs;olui po&longs;&longs;it pr&aelig;&longs;ens difficultas, qu&aelig; cett&egrave; maxima e&longs;t, totam rem <lb/>i&longs;tam paul&ograve; fu&longs;i&ugrave;s e&longs;&longs;e explicandam iudico. </s>

<s>Prim&ograve; itaque certum e&longs;t <lb/>partes medij, qu&aelig; prius in fronte erant, retroire; hoc ip&longs;um videmus in <lb/>naui qu&aelig; &longs;ulcat aquas, hoc ip&longs;um accidit in omni corpore natante etiam <lb/>immobili, quippe partes aqu&aelig; retinentur ab illa membranula, de qua &longs;u&shy;<lb/>pr&agrave;; &longs;ic enim &longs;&aelig;p&egrave; a&longs;&longs;urgunt, &amp; intume&longs;cunt &longs;upra labra va&longs;is; cur ver&ograve; <lb/>continui pen&egrave; circulares limbi dilatentur: Re&longs;p. nullo flante vento <lb/>vix aliquem circulum huiu&longs;modi in &longs;uperficie aqu&aelig; apparere &agrave; fronte, <lb/>&longs;ed tant&ugrave;m &agrave; tergo, &amp; lateribus, qua&longs;i ad in&longs;tar pyramidis; &longs;ed de his ali&agrave;s <lb/>fus&egrave;. </s></p><p type="main">

<s>Secund&ograve; certum e&longs;t numerum partium, quas impellit maior cubus A <lb/>E; e&longs;&longs;e quadruplum numeri partium, quas impellit cubus BG: &longs;int autem <lb/>v.g.8. partes re&longs;i&longs;tentes cubo maiori, &longs;unt du&aelig; re&longs;i&longs;tentes cubo minoris; <lb/>&longs;ed vires cubi maioris &longs;unt ad vires cubi minoris vt 8. ad 1. igitur vires <lb/>vt 8. &longs;uperabunt facili&ugrave;s re&longs;i&longs;tentiam vt 8. quam vires vt 1. re&longs;i&longs;tentiam <lb/>vt 2.vnde dupl&ograve; veloci&ugrave;s moueretur, ni&longs;i a&euml;r dupl&ograve; velociori motu amo&shy;<lb/>uendus e&longs;&longs;et, quod vt clarius explicetur;</s></p><p type="main">

<s>Sit cubus maior AF octuplus cubi GI, vt iam dictum e&longs;t; haud <lb/>dubi&egrave; a&euml;r qui &longs;ub&longs;tat cubo AF e&longs;t quadruplus a&euml;ris, qui &longs;ub&longs;tat cubo GI, <lb/>vnde &longs;i vires cubi AF e&longs;&longs;ent quadrupl&aelig; virium cubi GI, e&longs;&longs;et &aelig;qualis <lb/>proportio in vtroque virium, &amp; re&longs;i&longs;tenti&aelig;; &longs;ed &longs;unt octupl&aelig;; igitur faci&shy;<lb/>li&ugrave;s vincetur re&longs;i&longs;tentia; igitur amouebitur a&euml;r facili&ugrave;s; &longs;it autem a&euml;r <lb/>expre&longs;&longs;us in globulis EFB, &amp;c. </s>

<s>cuius &longs;uperficies cum relinquatur retr&ograve; <lb/>ver&longs;us AB, &amp; occupetur illa qu&aelig; e&longs;t in fronte EF; haud dubi&egrave; partes <lb/>hinc inde diuiduntur in D, &amp; &longs;egmentum NB tran&longs;it in locum relicti <lb/>loci BC, FN tran&longs;it in NB, &amp; DF, in FN; idem dico de &longs;egmentis oppo&shy;<lb/>&longs;itis; idem pror&longs;us dico de minori globo; nam MH tran&longs;it in HQ, &amp; H <lb/>Q in QG, &amp; QG in GL, idem dico de &longs;egmentis oppo&longs;itis; igitur h&aelig;c <lb/>e&longs;t circuitio partium medij, qu&agrave;m &longs;upr&agrave; indicauimus; hinc a&euml;r, qui amo&shy;<lb/>uetur &agrave; corpore graui de&longs;cendente moueri debet nece&longs;&longs;ari&ograve; veloci&ugrave;s <lb/>qu&agrave;m ip&longs;um corpus graue, quod de&longs;cendit. </s></p><p type="main">

<s>In hoc porr&ograve; ob&longs;erua &longs;egmentum MH moueri tardi&ugrave;s qu&agrave;m DF; quia <lb/>conficit &longs;ubduplum &longs;patium, eo tempore, quo DF conficit duplum; <pb xlink:href="026/01/160.jpg" pagenum="128"/>nam DF &amp; FN &longs;unt dupl&aelig; MH &amp; &amp; HQ igitur dupla vi motrice opus <lb/>e&longs;t; &longs;ed vires cubi AF &longs;unt ad vires cubi GI, vt 8. ad 1. partes ver&ograve; a&euml;ris, <lb/>quas impellit AF, &longs;unt ad partes a&euml;ris, quas impellit GI, vt 4.ad 1. igitur <lb/>&longs;i partes a&euml;ris mouerentur &aelig;quali motu cum ip&longs;is cubis, &agrave; quibus mo&shy;<lb/>uentur; cert&egrave; maior moueretur motu velociori; vt autem moueantur par&shy;<lb/>tes DF dupl&ograve; velociore motu, qu&agrave;m partes MH; debent vires, qu&aelig; mo&shy;<lb/>nent DF, e&longs;&longs;e in ratione dupla ad illas, qu&aelig; mouent MH, id e&longs;t eo tem&shy;<lb/>pore, quo vires vt 8.mouebunt mobile vt 4. motu vt 2. vires vt 1.moue&shy;<lb/>bunt mobile vt 1. motu vt 1. lic&egrave;t enim &longs;uperficies a&euml;ris EF moueatur <lb/>deor&longs;um; attamen ab alio a&euml;ere inferiore ita repertitur, vt &longs;ur&longs;um ver&longs;us <lb/>FN repellatur. </s></p><p type="main">

<s>Equidem tota &longs;uperficies a&euml;ris DF, cum pluribus partibus con&longs;tet, <lb/>non pote&longs;t &longs;imul tran&longs;ire in FN; quia pars D antequam perueniat ad F <lb/>tran&longs;it per medium DF; igitur &longs;ucce&longs;&longs;iu&egrave; per mea ad illud &longs;patium DF, <lb/>quo tempore quie&longs;ceret globus AF, quod ridiculum e&longs;t. </s></p><p type="main">

<s>Quare fit nece&longs;&longs;ari&ograve; aliqua circuitio, &amp; partium a&euml;ris commixtio, <lb/>&longs;eu conflictus; ita vt retroeant pul&longs;&aelig; prius &amp; repercu&longs;&longs;&aelig;; non quidem <lb/>tramite recto, &longs;ed cum aliqua circuitione; quod cert&egrave; facil&egrave; concipi po&shy;<lb/>te&longs;t, qu&aelig; circuitio e&ograve; maior e&longs;t, quo latera cuborum &longs;unt maiora; ita&shy;<lb/>que cum h&aelig;c &longs;atis fus&egrave; videantur e&longs;&longs;e explicata, &longs;it. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 112.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Duo cubi eiu&longs;de<emph.end type="italics"/>m <emph type="italics"/>materi&aelig;, &amp; diuer&longs;&aelig; grauitatis &aelig;quali motu per &longs;e de&longs;&shy;<lb/>cendunt<emph.end type="italics"/>; probatur, quia lic&egrave;t &longs;it maior proportio actiuitatis minus ad <lb/>&longs;uam re&longs;i&longs;tentiam, qu&agrave;m alterius; illud tamen compen&longs;atur; e&oacute;que par&shy;<lb/>tes a&euml;ris veloci&ugrave;s moueri debeant iuxta rationem laterum, vt patet ex <lb/>dictis; vnde nece&longs;&longs;ari&ograve; &longs;equitur motus &aelig;qualis in vtroque cubo; igitur <lb/>lic&egrave;t maioris cubi vires habeant maiorem proportionem ad molem, <lb/>qu&aelig; pr&aelig;cipuum illius motus retardat; tum tamen a&euml;r, qui re&longs;i&longs;tit maiori <lb/>cubo debeat amoueri, vt dictum e&longs;t velociore motu quam a&euml;r, qui re&longs;i&shy;<lb/>&longs;tit minori, &longs;itque eadem proportio re&longs;i&longs;tenti&aelig; ratione motus minoris <lb/>ad maiorem, qu&aelig; e&longs;t ratione molis maioris ad minorem; cert&egrave; ratio <lb/>compo&longs;ita vtriu&longs;qu&egrave; erit eadem in vtroque cubo; igitur &aelig;qu&egrave; velociter <lb/>vterque de&longs;cendet: hinc &longs;at&iacute;s facil&egrave; &longs;oluitur ratio Galilei, quam multi <lb/>parum cauti pro demon&longs;tratione venditarunt, ad aliam ver&ograve; rationem, <lb/>quam ex minuto puluere ducere videtur, etiam facil&egrave; re&longs;ponderi pote&longs;t; <lb/>ideo corpu&longs;cula illa diu fluitare in a&euml;re, t&ugrave;m qu&ograve;d minimo fer&egrave; tenuis <lb/>aur&aelig; flatu agitentur; &longs;ic pulueris nubes medius ventus agit; quis enim <lb/>ne&longs;cit a&euml;ris partes agitari perpetu&ograve;; imm&ograve; &amp; aqu&aelig; inter &longs;e mi&longs;ceri; igi&shy;<lb/>tur ab agitationis veluti impre&longs;&longs;ione fluitant illa corpu&longs;cula, cum mini&shy;<lb/>mus fer&egrave; impetus extrin&longs;ecus illa commouere po&longs;&longs;it; t&ugrave;m etiam qu&ograve;d &agrave; <lb/>filamentis illis, quibus partes a&euml;ris implicantur facil&egrave; detineantur; ana&shy;<lb/>logiam habes in lapillo, qui ab arane&aelig; tela intercipitur. </s></p><pb xlink:href="026/01/161.jpg" pagenum="129"/><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 113.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Duo globi eiu&longs;dem materi&aelig;, &amp; diuer&longs;&aelig; diametri de&longs;cendunt etiam &aelig;quali <lb/>motu propter <expan abbr="e&atilde;dem">eandem</expan> rationem<emph.end type="italics"/>; imm&ograve; e&longs;t perfectior &aelig;qualitas in globis, <lb/>qu&agrave;m in cubis; quia perfectior fit circuitio, vt con&longs;ideranti patebit; <lb/>hinc globus eiu&longs;dem materi&aelig;, &amp; grauitatis cum cubo de&longs;cendit veloci&ugrave;s <lb/>quia &longs;cilicet a&euml;r in de&longs;cen&longs;u globi facili&ugrave;s agitur retr&ograve;, vt con&longs;tat. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 114.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Corpus vtrimque in mucronem de&longs;inens facili&ugrave;s adhuc de&longs;cendit, <lb/>qu&acirc;m globus eiu&longs;dem materi&aelig;<emph.end type="italics"/>; ratio e&longs;t; quia breuiore circuitu partes re&shy;<lb/>troeunt; quippe tunc maxima e&longs;t facilitas in pellendo a&euml;re, qui e&longs;t &agrave; fron&shy;<lb/>te mobilis, cum veloci&ugrave;s moueri non debet ip&longs;o mobili; atqui hoc ip&shy;<lb/>&longs;um e&longs;t quod accidit mobili vtrimque aucto; nam linea curua DBA, <lb/>quam percurrit de&longs;criptum mobile, non e&longs;t mult&ograve; longior; at ver&ograve; in <lb/>quadrato &longs;uperiori AF maiori e&longs;t dupl&ograve;; in circulo quidem minor dia&shy;<lb/>meter &longs;emiperipheri&aelig;, &longs;ed non dupl&ograve;. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 115.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Idem corpus diuer&longs;o motu de&longs;cendere pote&longs;t,<emph.end type="italics"/> v. <!-- REMOVE S-->g. <!-- REMOVE S-->parallipedum A, &longs;i re&shy;<lb/>ctangulum BF &longs;it in fronte tardi&ugrave;s de&longs;cendet, qu&agrave;m &longs;i in fronte &longs;it re&shy;<lb/>ctangulum CE, vel rectangulum FH; hinc tribus motibus diuer&longs;is de&longs;&shy;<lb/>cendere pote&longs;t idem parallipedum, mod&ograve; habeat &longs;emper alteram facie&shy;<lb/>rum horizonti parallelam; hinc cylindrus eiu&longs;dem grauitatis de&longs;cendet <lb/>veloci&ugrave;s qu&agrave;m parallelipedum, vt patet ex dictis; ex quibus facil&egrave; intel&shy;<lb/>ligi pote&longs;t, qu&aelig;nam corpora facili&ugrave;s qu&agrave;m alia de&longs;cendant; quippe illa <lb/>regula e&longs;t certi&longs;&longs;ima qu&agrave;m &longs;upr&agrave; attulimus. </s>





<s>Porr&ograve; ob&longs;eruabis omne <lb/>corpus difficili&ugrave;s pelli per lineam perpendicularem qu&agrave;m per obliquam; <lb/>hinc globus pellit tant&ugrave;m vnicum punctum perpendiculariter; idem di&shy;<lb/>co de cono; cylindrus ver&ograve; vnam lineam, cubus integrum planum. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 116.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc duo corpora eiu&longs;dem grauitatis, &longs;ed quorum alterum<emph.end type="italics"/> f<emph type="italics"/>aciem, qu&aelig; e&longs;t <lb/>in fronte, habet maiorem, in&aelig;quali motu de&longs;cendunt<emph.end type="italics"/>; patet ex dictis; quia in <lb/>vtroque &longs;unt &aelig;quales vires, &longs;ed diuer&longs;a re&longs;i&longs;tentia. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 117.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc tenues ill&aelig; &longs;uperficies corporum etiam materi&aelig; graui&longs;&longs;im&aelig;, vel in <lb/>a&euml;re fluitant, vel aquis innatant<emph.end type="italics"/>; ratio e&longs;t, quia re&longs;i&longs;tentia &longs;uperat <lb/>vires. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Ob&longs;eruabis primam &longs;uperficiem aqu&aelig; habere maiorem quamdam re&shy;<lb/>&longs;i&longs;tentiam propter illam, qua&longs;i membranulam, de qua &longs;upr&agrave;; vnde a&longs;&longs;ur&shy;<lb/>git quiddam lymbus in margine bracte&aelig; ferri, vel auri innatantis; vel <lb/>etiam globuli paul&ograve; grauioris aqu&acirc;, igitur vt immergatur corpus debet <lb/>e&longs;&longs;e grauius tot&acirc; ill&acirc; aqu&acirc;, qu&aelig; capacitatem illam non cauam occu&shy;<lb/>paret. </s></p><pb xlink:href="026/01/162.jpg" pagenum="130"/><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 118.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Globi &aelig;quales diuer&longs;&aelig; materi&aelig; in&aelig;qualiter de&longs;cendunt<emph.end type="italics"/>; quia &longs;cilicet alte&shy;<lb/>rum e&longs;t grauius, quod &longs;uppono; igitur &aelig;qualis e&longs;t re&longs;i&longs;tentia, &amp; vires <lb/>in&aelig;quales; igitur non e&longs;t eadem proportio actiuitatis: &amp; re&longs;i&longs;tenti&aelig;; igi&shy;<lb/>tur non e&longs;t &aelig;qualis motus per Ax.5. <!-- KEEP S--></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 119.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Globi otiam in&aelig;quales diuer&longs;&aelig; materi&aelig; in&aelig;qualiter de&longs;cendunt<emph.end type="italics"/>; quod de&shy;<lb/>mon&longs;tro; quia globi eiu&longs;dem materi&aelig; in&aelig;qualiter de&longs;cendunt per Th. <!-- REMOVE S--><lb/>113. &longs;ed duo globi &aelig;quales diuer&longs;&aelig; materi&aelig; de&longs;cendunt in&aelig;qualiter per <lb/>Th.118. igitur, &amp; in&aelig;quales; quod dico de globis', dicatur de cubis, &amp; <lb/>aliis figuris &longs;imilibus. </s>

</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 120.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Globus materi&aelig; leuioris pote&longs;t de&longs;cendere velociori motu quam parallelipe&shy;<lb/>dum grauioris<emph.end type="italics"/>; con&longs;tat experientia; ratio e&longs;t, quia cum globus ferreus de&longs;&shy;<lb/>cendat veloci&ugrave;s, qu&agrave;m ligneus per Th. 118. in data ratione, put&agrave; (1/100) <lb/>haud dubi&egrave; bractea ferri non modo (1/100) tardi&ugrave;s de&longs;cendet, ver&ugrave;m etiam <lb/>(20/100) in quo non e&longs;t difficultas. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 121.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc &longs;i mutetur figura po&longs;&longs;unt grauia diuer&longs;&aelig; materi&aelig; ita de&longs;cendere, vn <lb/>vel grauius, vel leuius, vel grauioris materi&aelig;, vel leuioris veloci&ugrave;s de&longs;cendat<emph.end type="italics"/>; <lb/>vt con&longs;tat ex regulis pr&aelig;&longs;criptis. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 122.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Globi &aelig;quales diuer&longs;&aelig; materi&aelig;,<emph.end type="italics"/> v. <!-- REMOVE S-->g. <!-- REMOVE S-->ligneus, &amp; plumbeus de&longs;cendunt <lb/>in&aelig;qualiter iuxta proportionem grauitatis, &amp; re&longs;i&longs;tenti&aelig; medij compa&shy;<lb/>rat&aelig; cum vtroque, v.g. <!-- REMOVE S-->plumbo detrahitur (1/4800); ligno ver&ograve; (8/300) v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;i <lb/>grauitas ligni &longs;it ad grauitatem a&euml;ris vt 300.ad 1. &amp; plumbi vt 4800. ad <lb/>1. &longs;it enim altitudo 33. pedum 4. digit. </s>











<s>reducantur in digitos erunt 400. <lb/>in lineas 4800. igitur detrahetur vna linea &longs;patij plumbeo globo; ligneo <lb/>ver&ograve; vnus digitus cum 4. lineis; &longs;ed quis hoc ob&longs;eruet? </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 123.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Corpus graue &longs;pongio&longs;um long&egrave; tardi&ugrave;s de&longs;cendit<emph.end type="italics"/>; quia a&euml;r in perexigua <lb/>illa foramina inten&longs;us frangitur, re&longs;ilit, ac proinde motum impedit; talis <lb/>e&longs;t medulla &longs;ambuci, &longs;pongia, &longs;tupa, &amp;c. </s>

<s>imm&ograve; a&longs;perum corpus tardi&ugrave;s <lb/>de&longs;cendit, qu&ograve;d &longs;cilicet a&euml;r ab a&longs;perioribus illis &longs;alebris re&longs;iliens mo&shy;<lb/>tum retardet, hinc &longs;ibilus ille auditur &amp;c. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Ex his con&longs;tat quid dicendum &longs;it de motu corporum grauium in <lb/>medio, &longs;iue &longs;int eiu&longs;dem materi&aelig;, &amp; &longs;imilis figur&aelig;, maioris vel minoris, <lb/>vel &aelig;qualis; tunc enim de&longs;cendunt &aelig;qualiter contra Galileum, &longs;iue <lb/>&longs;int diuer&longs;&aelig; materi&aelig;, &amp; &longs;imilis figur&aelig;, &aelig;qualis, vel in&aelig;qualis, <pb xlink:href="026/01/163.jpg" pagenum="131"/>tunc enim de&longs;cendunt in&aelig;qualiter, &longs;iue diuer&longs;&aelig; materi&aelig; &amp; diuer&longs;&aelig; fi&shy;<lb/>gur&aelig;; tunc enim de&longs;cendunt mod&ograve; &aelig;qualiter, mod&ograve; in&aelig;qualiter; &aelig;quali&shy;<lb/>ter cert&egrave;, cum figura compen&longs;at materiam; cum ver&ograve; non compen&longs;at, <lb/>in&aelig;qualiter pro rata; denique &longs;i comparentur duo corpora cum diuer&longs;is <lb/>mediis; primo inuenienda e&longs;t proportio motuum vtriu&longs;que in eodem <lb/>t&ugrave;m &longs;ingulorum in diuer&longs;is mediis, vt &longs;upr&agrave; dictum e&longs;t. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 124.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>In modico vacuo omnia &aelig;qu&egrave; velociter de&longs;cenderent<emph.end type="italics"/>: Probatur, quia tota <lb/>diuer&longs;itas vel in&aelig;qualitas mediorum petitur &agrave; diuer&longs;a proportione acti&shy;<lb/>uitatis cum re&longs;i&longs;tentia medij per Ax. 5. &longs;ed in vacuo nulla e&longs;t re&longs;i&longs;ten&shy;<lb/>tia; igitur nulla proportio; igitur nulla ratio motus in&aelig;qualis. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 125.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>In motu natur aliter accelerato deor&longs;um cre&longs;cit re&longs;istentia medij &longs;ingulis in&shy;<lb/>&longs;tantibus<emph.end type="italics"/>: probatur, quia &longs;ingulis in&longs;tantibus plures partes medij &longs;unt <lb/>&longs;uperand&aelig;; cre&longs;cunt enim &longs;patia, vt con&longs;tat ex dictis; igitur cre&longs;cit re&longs;i&shy;<lb/>&longs;tentia &longs;ingulis in&longs;tantibus. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 126.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Cre&longs;cit re&longs;istentia iuxta rationem &longs;patiorum,<emph.end type="italics"/> probatur; quia cre&longs;cit iux&shy;<lb/>ta rationem plurium partium medij, qu&aelig; temporibus &aelig;qualibus percur&shy;<lb/>runtur; &longs;ed e&aelig; cre&longs;cunt iuxta rationem &longs;patiorum, vt con&longs;tat. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 127.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc cre&longs;cit re&longs;i&longs;tentia iuxta rationem velocitatum &longs;ingulis instantibus<emph.end type="italics"/>; <lb/>qu&aelig; ratio &longs;equitur progre&longs;&longs;ionem arithmeticam &longs;implicem numerorum <lb/>1.2.3.4.5.6. ex &longs;uppo&longs;itione qu&ograve;d tempus con&longs;tet ex partibus finitis actu; <lb/>nam codem modo cre&longs;cit velocitas, quo cre&longs;cunt numeri pr&aelig;dicti; &longs;ed <lb/>eodem modo cre&longs;cunt &longs;patia, &longs;i dumtaxat accipiantur in &longs;ingulis in&longs;tan&shy;<lb/>tibus; re&longs;i&longs;tentia cre&longs;cit iuxta rationem &longs;patiorum; igitur iuxta ratio&shy;<lb/>nem velocitatum. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Ob&longs;eruabis, &longs;i tempus con&longs;tet ex infinitis actu partibus, ita vt &longs;ingu&shy;<lb/>l&aelig; partes motus &longs;ingulis partibus temporis &amp; infinit&aelig; infinitis re&longs;pon&shy;<lb/>deant; non pote&longs;t e&longs;&longs;e alia progre&longs;&longs;io, in qua fiat acceleratio motus na&shy;<lb/>turalis, qu&agrave;m illa Galilei iuxta hos numeros 1. 3. 5. 7. vt con&longs;tat ex dictis <lb/>per illud Principium; <emph type="italics"/>&aelig;qualibus temporibus &aelig;qualia acquiruntur velocita&shy;<lb/>tis momenta<emph.end type="italics"/>; &longs;i ver&ograve; tempus con&longs;tat ex finitis in&longs;tantibus &aelig;qualibus, nul&shy;<lb/>la datur progre&longs;&longs;io motus naturaliter accelerati; quia motus accelerari <lb/>non pote&longs;t; ne &longs;cilicet eodem in&longs;tanti mobile &longs;it in pluribus locis ad&aelig;&shy;<lb/>quatis; denique &longs;i tempus con&longs;tat ex finitis in&longs;tantibus actu, &amp; infinitis <lb/>potenti&acirc;, non pote&longs;t e&longs;&longs;e alia progre&longs;&longs;io huius accelerationis, quam h&aelig;c <lb/>no&longs;tra iuxta numeros toties repetitos 1.2.3.4.5. attamen quia illa finita <lb/>in&longs;tantia &longs;unt fer&egrave; innumera in qualibet parte &longs;en&longs;ibili temporis, in <lb/>praxi &longs;ine &longs;en&longs;ibili errore in partibus temporis &longs;en&longs;ibilibus po&longs;&longs;umus <pb xlink:href="026/01/164.jpg" pagenum="132"/>adhibere priorem progre&longs;&longs;ionem Galilei, &amp; in hoc cardine tota verri&shy;<lb/>tur, meo iudicio, propo&longs;it&aelig; qu&aelig;&longs;tionis difficultas. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 128.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc cre&longs;cit re&longs;istentia iuxta rationem crementi impetus<emph.end type="italics"/>; cum enim cre&shy;<lb/>&longs;cant impetus in ratione velocitatum, vt con&longs;tat, &amp; cre&longs;cat re&longs;i&longs;tentia <lb/>medij in eadem ratione per Theor. <!-- REMOVE S-->127. cre&longs;cit etiam in ratione im&shy;<lb/>petuum. </s>

</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 129.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc cre&longs;cit re&longs;istentia medij in eadem ratione, in qua cre&longs;cunt vires mobi&shy;<lb/>lis<emph.end type="italics"/>; demon&longs;tr. </s>

<s>quia cre&longs;cunt vires, vt cre&longs;cit impetus; nam impetus e&longs;t <lb/>vis illa, qu&acirc; mobile &longs;uperat re&longs;i&longs;tentiam medij vt con&longs;tat, &longs;ed re&longs;i&longs;ten&shy;<lb/>tia cre&longs;cit vt impetus per Th. 128. igitur cre&longs;cit in ratione virium. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 130.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Si cre&longs;cit re&longs;i&longs;tentia in eadem ratione in qua cre&longs;cunt vires, non mutatur <lb/>progre&longs;&longs;io effectuum.<emph.end type="italics"/> v.g. <!-- REMOVE S-->primo in&longs;tanti impetus &longs;it vt 1.&longs;itque 1.&longs;patium, <lb/>in quo e&longs;t re&longs;i&longs;tentia, vt 1. Secundo in&longs;tanti &longs;it impetus vt 2. re&longs;i&longs;tentia in <lb/>2. &longs;patiis vt 2. haud dubi&egrave; &longs;i vno in&longs;tanti vnus gradus impetus &longs;uperat <lb/>re&longs;i&longs;tentiam vt 1. dum percurrit 1.&longs;patium; cert&egrave; 2. gradus impetus vno <lb/>in&longs;tanti &longs;uperabunt re&longs;i&longs;tentiam vt 2. dum conficit mobile 2. &longs;patia; at&shy;<lb/>que ita deinceps. </s>

</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 132.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc cert&egrave; concludo contra Galileum, &amp; alios quo&longs;dam motum grauium <lb/>po&longs;t aliquod &longs;patium decur&longs;um ex naturaliter accelerato non fieri &aelig;quabilem,<emph.end type="italics"/><lb/>quia in tantum fieret &aelig;quabilis in quantum tanta e&longs;&longs;et re&longs;i&longs;tentia, vt no&shy;<lb/>uam accelerationem impediret; &longs;ed h&aelig;c ratio nulla e&longs;t; quia in eadem <lb/>ratione cre&longs;cit re&longs;i&longs;tentia, in qua cre&longs;cunt vires per Th. 129. igitur non <lb/>mutatur progre&longs;&longs;io motuum per Th. 130. igitur nec acceleratio; igitur <lb/>motus naturalis ex accelerato non fit &aelig;quabilis: Equidem, vt iam &longs;upr&agrave; <lb/>dictum e&longs;t, in minori &longs;emper ratione cre&longs;cit velocitas, it&eacute;mque ip&longs;a re&longs;i&shy;<lb/>&longs;tentia quod in omni progre&longs;&longs;ione arithmetica iuxta numeros 1.2.3.4.5. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Ob&longs;eruabis remitti &agrave; nobis motum leuium &longs;ur&longs;um in 5. Tomum, in cu&shy;<lb/>ius tertio libro agemus de graui, &amp; leui; quia ideo corpus a&longs;cendit, quia <lb/>ab alio de&longs;cendente truditur &longs;ur&longs;um. </s></p><pb xlink:href="026/01/165.jpg" pagenum="133"/><figure id="id.026.01.165.1.jpg" xlink:href="026/01/165/1.jpg"/><p type="main">

<s><emph type="center"/>LIBER TERTIVS,<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>DE MOTV VIOLENTO <lb/>&longs;ur&longs;um Perpendiculariter.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>OMnis cert&egrave; motus, qui e&longs;t &agrave; principio ex&shy;<lb/>trin&longs;eco, violentus appellari pote&longs;t, attamen <lb/>h&icirc;c non ago de omni violento, &longs;ed dumta&shy;<lb/>xat de illo, qui fit &longs;urs&ugrave;m per lineam verticalem; quia <lb/>&longs;cilicet ex diametro opponitur motui naturali, qui <lb/>fit deors&ugrave;m perpendiculariter; igitur cum de hoc <lb/>ip&longs;o in &longs;ecundo Libro egerimus, de illo in hoc non <lb/>agemus. <lb/><gap desc="hr tag"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>DEFINITIO 1.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s><emph type="italics"/>MOtus violentus e&longs;t, quo corpus graue mouetur &longs;urs&ugrave;m per li&shy;<lb/>neam verticalem &agrave; principio extrin&longs;eco mediat&egrave;, vel immediat&egrave; vt <lb/>plurim&ugrave;m.<emph.end type="italics"/></s></p><p type="main">

<s>Dixi &agrave; principio extrin&longs;eco, &longs;iue cunjuncto, vt cum manu attollo &longs;ur&shy;<lb/>&longs;um corpus graue, &longs;iue non conjuncto, vt cum quis proiicit lapidem &longs;ur&shy;<lb/>s&ugrave;m, &longs;iue &longs;it verum principium effectiuum, vt cum impetus, quem poten&shy;<lb/>tia motrix producit in manu, producit alium in mobili; &longs;iue non &longs;it <lb/>principium effectiuum, &longs;ed tant&ugrave;m determinans, vt cum mobile quod <lb/>cadit deor&longs;um, &longs;ur&longs;um deinde repercutitur; nec enim corpus repercu&shy;<lb/>tiens producit impetum nouum, vt dicemus cum de motu reflexo; quin <lb/>poti&ugrave;s producti partem de&longs;truit per accidens, &amp; quidquid illius &longs;upere&longs;t, <lb/>ad nouam lineam determinat; quod quomodo fiat fus&egrave; &longs;uo loco expli&shy;<lb/>cabimus, igitur lic&egrave;t corpus reflectens &longs;it tant&ugrave;m principium nou&aelig; de&shy;<lb/>terminationis, non ver&ograve; alicuius impetus producti, dici pote&longs;t princi&shy;<lb/>pium huius motus violenti. </s></p><p type="main">

<s>Dixi vt plurim&ugrave;m, nam &longs;i terra ducto per centrum foramine e&longs;&longs;et <lb/>peruia, haud dubi&egrave; lapis demi&longs;&longs;us vers&ugrave;s centrum iret motu naturaliter <pb xlink:href="026/01/166.jpg" pagenum="134"/>accelerato, t&ugrave;m deinde propter impetus acqui&longs;iti vim, &agrave; centro vers&ugrave;s <lb/>oppo&longs;itum circumferenti&aelig; punctum iret, motu cert&egrave; violento, qui ta&shy;<lb/>men ab extrin&longs;eco non e&longs;&longs;et. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Hypothe&longs;is<emph.end type="italics"/> 1.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s><emph type="italics"/>Corpus graue projectum &longs;ur&longs;um tandem redit<emph.end type="italics"/>; H&aelig;c hypothe&longs;is certa e&longs;t, <lb/>&amp; nemo e&longs;t qui eam in dubium vocet. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Axioma<emph.end type="italics"/> 1.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s><emph type="italics"/>Quidquid erat, &amp; de&longs;init e&longs;&longs;e de&longs;truitur<emph.end type="italics"/>; Hoc Axioma certum e&longs;t, quip&shy;<lb/>pe de&longs;trui hoc tant&ugrave;m dicitur, quod de&longs;init e&longs;&longs;e. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Axioma<emph.end type="italics"/> 2.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s><emph type="italics"/>Quidquid destruitur, ad exigentiam alicuius destruitur, &longs;altem totius na&shy;<lb/>tur&aelig;.<emph.end type="italics"/></s><s> Hoc Axioma idem e&longs;t cum Axiom. <!-- REMOVE S-->14. l. <!-- REMOVE S-->1. n. </s>





<s>2. vnde alia expli&shy;<lb/>catione minim&egrave; indiget; hoc ip&longs;um etiam demon&longs;traui in Th.147.149. <lb/>150,&amp;c. </s>

<s>l. <!-- REMOVE S-->1. <!-- KEEP S--></s>

</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 1.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s><emph type="italics"/>Datur motus violentus<emph.end type="italics"/>; demon&longs;tro; corpus proiicitur per lineam ver&shy;<lb/>ticalem per hyp. </s>

<s>1. &longs;ed hic motus e&longs;t &agrave; principio extrin&longs;eco, igitur e&longs;t <lb/>violentus per def.1. probatur minor; Prim&ograve;, quia illud e&longs;t principium, <lb/>&longs;eu cau&longs;a motus, ex cuius applicatione &longs;emper &longs;equitur motus per Ax.11. <lb/>l. <!-- REMOVE S-->1.n. </s>



<s>1. &longs;ed ex applicatione potenti&aelig; extrin&longs;ec&aelig; v. <!-- REMOVE S-->g. <!-- REMOVE S-->arcus, manus, &amp;c. </s>





<s><lb/>ad lineam &longs;ur&longs;um &longs;emper &longs;equitur motus &longs;ur&longs;um; igitur e&longs;t illius cau&longs;a. </s>

<s><lb/>Secund&ograve; probatur, quia mobile projectum &longs;urs&ugrave;m mouetur adhuc &longs;epa&shy;<lb/>ratum &agrave; potentia motrice per hyp. </s>

<s>6.l.1. igitur potentia motrix impre&longs;&shy;<lb/>&longs;it aliquid mobili, vi cuius deinde mouetur, igitur hic motus e&longs;t &agrave; prin&shy;<lb/>cipio extrin&longs;eco. </s></p><p type="main">

<s>Diceret fort&egrave; aliquis produci hunc motum ab ip&longs;o mobili; &longs;ed con&shy;<lb/>tr&agrave;; igitur &longs;emper produceret, quod ab&longs;urdum e&longs;t: dicet, ad hoc vt pro&shy;<lb/>ducat determinari debere ab aliquo, &longs;ed contr&agrave;; illud &agrave; quo determina&shy;<lb/>tur vel e&longs;t extrin&longs;ecum, vel intrin&longs;ecum, &longs;i primum, ergo hic motus e&longs;t <lb/>&longs;emper &agrave; principio extrin&longs;eco, quod &longs;atis e&longs;t e&longs;&longs;e determinans per def.1. <lb/>&longs;i ver&ograve; e&longs;t intrin&longs;ecum; igitur &longs;emper e&longs;&longs;et hic motus, quamdiu e&longs;&longs;et <lb/>ip&longs;um mobile, quod e&longs;t contra hyp. </s>

<s>1. nam reuera non &longs;emper mo&shy;<lb/>uetur. </s></p><p type="main">

<s>Diceret fort&egrave; alius excitari qu&aelig;dam corpu&longs;cula, &agrave; quibus mouetur <lb/>corpus graue &longs;urs&ugrave;m; &longs;ed contr&agrave;; nam vel &longs;unt in ip&longs;o mobili illa cor&shy;<lb/>pu&longs;cula, vel extra mobile; &longs;i primum; igitur hic motus &longs;emper erit ab <lb/>extrin&longs;eco mediat&egrave;, cum ab extrin&longs;eco excitentur; &longs;ed hoc &longs;ufficit ad <lb/>hoc; vt motus dicatur violentus per def. </s>

<s>1. &longs;i ver&ograve; &longs;unt extra mobile; <lb/>igitur motus ille e&longs;t &longs;emper ab extrin&longs;eco, idque duplici nomine. </s></p><p type="main">

<s>Denique diceret alius ex &longs;uppo&longs;itione, quod terra moueatur non po&longs;&shy;<lb/>&longs;e corpus graue proiici &longs;urs&ugrave;m per lineam verticalem, ni&longs;i tant&ugrave;m ad <lb/>&longs;peciem; vt &longs;i quis &egrave; naui mobili &longs;ur&longs;um proiiceret pilam rect&agrave; omni&shy;<lb/>n&ograve;, quoad eius fieri po&longs;&longs;it; videbitur enim iis, qui vehuntur eadem naui <pb xlink:href="026/01/167.jpg" pagenum="135"/>&longs;ur&longs;um ferri per lineam verticalem, aliis ver&ograve; in&longs;tantibus videbitur cla&shy;<lb/>ri&longs;&longs;im&egrave; ferri per lineam nouam inclinatam. </s></p><p type="main">

<s>Re&longs;pondeo etiam admi&longs;&longs;a &longs;uppo&longs;itione dici &agrave; me motum illum &longs;ur&shy;<lb/>&longs;um e&longs;&longs;e per lineam verticalem, quando eadem linea recta connectit <lb/>&longs;emper h&aelig;c tria puncta; &longs;cilicet centrum terr&aelig;, idem punctum &longs;uperfi&shy;<lb/>ciei terr&aelig;, &amp; ip&longs;am pilam; ad illud ver&ograve; quod dicitur de naui, non diffi&shy;<lb/>teor verum e&longs;&longs;e; &longs;ed dico non e&longs;&longs;e propri&egrave; motum violentum, de quo h&icirc;c <lb/>tant&ugrave;m e&longs;t qu&aelig;&longs;tio, &longs;ed e&longs;&longs;e motum mixtum, de quo fus&egrave; &longs;uo loco. </s>

<s>Ob&longs;er&shy;<lb/>uabis autem h&icirc;c me ab&longs;tinere &agrave; refellendis ab&longs;urdis illis &longs;uppo&longs;itioni&shy;<lb/>bus, quibus pr&aelig;mi&longs;&longs;&aelig; objectiones innituntur; nam, cui qu&aelig;&longs;o in men&shy;<lb/>tem venire pote&longs;t ab ip&longs;a entitate corporis grauis produci motum in &longs;e? </s>

<s><lb/>quis credat produci frigus ab igne? </s>

<s>calorem &agrave; niue? </s>

<s>lucem &agrave; tenebris? </s>

<s><lb/>qu&aelig; porr&ograve; fabul&aelig;, qu&aelig; commenta, qu&aelig; &longs;omnia excogitari po&longs;&longs;unt, qu&aelig; <lb/>non vile&longs;cant &longs;i cum his comparentur. </s></p><p type="main">

<s>Illa quoque corpu&longs;cula excitata leuiora &longs;unt, qu&agrave;m vt aliquod pr&aelig;fe&shy;<lb/>rant rationis momentum; cum mera &longs;int philo&longs;ophi&aelig; ludibria. </s></p><p type="main">

<s>Denique illa hypothe&longs;is de terr&aelig; motu nullis demon&longs;trationibus fir&shy;<lb/>mata e&longs;t, vt videbimus &longs;uo loco. </s></p><p type="main">

<s>Vnum fort&egrave; e&longs;t, quod difficilius obiici pote&longs;t; &longs;it enim linea vertica&shy;<lb/>lis AC, &longs;itque globus in A &aelig;qualiter impul&longs;us per lineas AD &amp; AB; <lb/>haud dubi&egrave; &longs;i anguli DAC, BAC &longs;int &aelig;quales: cert&egrave; mobile feretur <lb/>per lineam verticalem AC, vt con&longs;tat ex dictis. </s>

<s>Re&longs;pondeo motum illum <lb/>e&longs;&longs;e violentum; e&longs;t enim &agrave; principio extrin&longs;eco, coque gemino, &longs;eu mix&shy;<lb/>to, in quo non e&longs;t difficultas. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 2.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s><emph type="italics"/>Motus violentus habet cau&longs;am<emph.end type="italics"/>; quia de nouo e&longs;t, &amp; tandem de&longs;init per <lb/>hypoth. </s>

<s>1. igitur habet cau&longs;am per Ax.8.l.1. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 3.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s><emph type="italics"/>I&longs;te motus &longs;upponit impetum<emph.end type="italics"/>; quia ni&longs;i e&longs;&longs;et impetus non e&longs;&longs;et natura&shy;<lb/>liter motus per Th.18.l.1. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 4.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s><emph type="italics"/>I&longs;te impetus debet e&longs;&longs;e in mobili projecto &longs;ur&longs;um<emph.end type="italics"/>; quia ibi e&longs;t cau&longs;a, vbi <lb/>e&longs;t effectus formalis, &longs;ed motus e&longs;t effectus formalis &longs;ecundarius impe&shy;<lb/>tus per Th.15.l.1. igitur cum motus &longs;it in projecto &longs;ur&longs;um, in eo e&longs;t etiam <lb/>impetus: pr&aelig;terea &longs;ecunda pars motus non ponitur &agrave; potentia motrice; <lb/>quia illa non e&longs;t applicata mobili cum ponitur noua pars motus, igitur <lb/>ab alia cau&longs;a applicata, &longs;ed nulla e&longs;t extrin&longs;eca, vt patet, nulla intrin&longs;eca <lb/>pr&aelig;ter impetum. </s></p><p type="main">

<s>Diceret aliquis ab a&euml;re extrin&longs;ec&ugrave;s ambiente mobile ip&longs;um propelli; <lb/>&longs;ed contra, nam a&euml;r, &amp; omne aliud medium re&longs;i&longs;tit poti&ugrave;s qu&agrave;m iuuet, vt <lb/>demon&longs;trauimus l. <!-- REMOVE S-->&longs;ecundo Th. 1. Nec dicas fui&longs;&longs;e mentem Ari&longs;totelis, <lb/>cum nobiles Peripatetici contr&acirc; &longs;entiant; Albertus Magnus, Toletus, <lb/>Scaliger, Suarius, &amp; recentiores; neque hoc negauit vnquam Ari&longs;tote-<pb xlink:href="026/01/168.jpg" pagenum="136"/>les, &longs;ed in hoc non mult&ugrave;m laboramus; nec dicas hinc &longs;equi motum <lb/>violentum e&longs;&longs;e &agrave; principio intrin&longs;eco contra def. </s>



<s>1. nam e&longs;t quidem &agrave; <lb/>principio intrin&longs;eco formali, non tamen &agrave; principio intrin&longs;eco mouen&shy;<lb/>te vel agente; nec enim impetus e&longs;t cau&longs;a efficiens motus &longs;ui &longs;ubjecti; <lb/>&longs;ed cau&longs;a formalis vt &longs;&aelig;p&egrave; explicuimus. </s></p><p type="main">

<s>Diceret fort&egrave; alius primam partem motus produci &agrave; potenti&acirc; motri&shy;<lb/>ce, &longs;ecundam ver&ograve; ab entitate ip&longs;ius corporis; &longs;ed contr&agrave;; igitur corpus <lb/>e&longs;&longs;et cau&longs;a nece&longs;&longs;aria; igitur &longs;emper produceret. </s>

<s>Dices &longs;emper producere <lb/>&longs;i determinetur, &longs;ed contr&agrave;; &agrave; quo determinatur ad producendam &longs;ecun&shy;<lb/>dam partem? </s>

<s>nihil e&longs;t enim applicatum, &agrave; quo determinari po&longs;&longs;it; Dices <lb/>accepi&longs;&longs;e determinationem; &longs;ed contr&agrave;; quid e&longs;t illa determinatio? </s>

<s><lb/>Dices e&longs;&longs;e modum; igitur permanentem; igitur e&longs;t cau&longs;a motus per Ax. <!-- REMOVE S--><lb/>1. l. <!-- REMOVE S-->1. n. </s>





<s>1. igitur e&longs;t impetus per def. </s>

<s>3. l. <!-- REMOVE S-->1. Dices determinari &agrave; priori <lb/>parte motus; &longs;ed contr&agrave; prim&ograve;, nam reuer&acirc; non e&longs;t illa pars cum deter&shy;<lb/>minatur corpus. </s>



<s>Secund&ograve;, quid e&longs;t illa prima pars motus, ni&longs;i migratio &egrave; <lb/>loco in locum, qu&aelig; reuer&acirc; &agrave; potentia motrice produci propri&egrave; non po&shy;<lb/>te&longs;t per Th.2. l. <!-- REMOVE S-->1. &longs;ed de his iam fus&egrave; actum e&longs;t in toto fer&egrave; libro primo, <lb/>&longs;ed pr&aelig;&longs;ertim in Th.6. </s>

</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 5.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s><emph type="italics"/>Ille impetus e&longs;t vera qualitas Phy&longs;ica ab&longs;oluta<emph.end type="italics"/>; hoc iam &longs;upr&agrave; demon&shy;<lb/>&longs;tratum e&longs;t, &longs;cilicet phy&longs;ic&egrave;; imm&ograve; ex motu violento maxim&egrave; probatur <lb/>dari impetum, &amp; vix quidquam e&longs;t in rerum natur&acirc;, quod clari&ugrave;s euin&shy;<lb/>cat aliquid de nouo produci. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 6.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s><emph type="italics"/>I&longs;te impetus producitur ab aliqua cau&longs;a<emph.end type="italics"/>; Probatur, quia e&longs;t de nouo; igi&shy;<lb/>tur non e&longs;t &agrave; &longs;e per Ax. 8. l. <!-- REMOVE S-->1. igitur e&longs;t ab alio; igitur ab aliqua <lb/>cau&longs;a. </s>

</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 7.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Producitur ab aliqua cau&longs;a extrin&longs;eca<emph.end type="italics"/>; Probatur prim&ograve;, quia aliquis <lb/>motus violentus e&longs;t &agrave; cau&longs;a extrin&longs;eca per def.1. Secund&ograve;, e&longs;t ab aliqua <lb/>cau&longs;a applicata, &longs;ed e&longs;t tant&ugrave;m applicata potentia motrix; igitur e&longs;t cau&shy;<lb/>&longs;a, per Ax. 11. l. <!-- REMOVE S-->1. nec enim producitur hic impetus ab entitate corpo&shy;<lb/>ris projecti, quod plu&longs;qu&agrave;m certum e&longs;t ex dictis; h&icirc;c enim tant&ugrave;m <lb/>e&longs;t qu&aelig;&longs;tio de illo motu, qui extrin&longs;ec&ugrave;s aduenit, non vero de reflexo <lb/>&longs;urs&ugrave;m, &amp;c. </s>

</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 8.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Producitur ab alio impetu<emph.end type="italics"/>; quia potentia motrix non agit ad extra ni&longs;i <lb/>per impetum productum in organo, vt patet; pr&aelig;terea &longs;i e&longs;t cau&longs;a vni&shy;<lb/>uoca &longs;ufficiens applicata, non e&longs;t ponenda &aelig;quiuoca per Ax.11.l.1. adde <lb/>quod impetus producitur &longs;emper ad extra ab alio impetu per Th. 42. <lb/>l.1.nec in his hactenus propo&longs;itis vlla e&longs;t difficultas. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 9.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Impetus impre&longs;&longs;us mobili &longs;ur&longs;um con&longs;eruatur per aliquod tempus<emph.end type="italics"/>; Probatur, <pb xlink:href="026/01/169.jpg" pagenum="137"/>quia mobile &longs;eparatum &agrave; potentia motrice adhuc mouetur per hyp.6.l.1, <lb/>igitur ille motus habet cau&longs;am, vt &longs;&aelig;p&egrave; dictum e&longs;t; non aliam, qu&agrave;m im&shy;<lb/>petum per Th.4. non productum de nouo, quippe nulla e&longs;t cau&longs;a mobili <lb/>applicata per Th. 7. &amp; 8. igitur iam ant&egrave; productam; igitur con&longs;er&shy;<lb/>uatur. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 10.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Con&longs;eruatur ab aliqua cau&longs;a extrin&longs;eca applicata<emph.end type="italics"/>; vt patet ex dictis, non <lb/>ab a&euml;re; igitur &agrave; nullo corpore; igitur ab alia caus&acirc; in&longs;en&longs;ibili; igitur <lb/>illam e&longs;&longs;e oportet, &amp; no&longs;&longs;e rerum omnium exigentias, &amp; po&longs;&longs;e cuncta <lb/>producere; quippe con&longs;eruatio e&longs;t repetita productio; imm&ograve; con&longs;erua&shy;<lb/>re per actionem, per quam &longs;it res in tali loco, &amp; tali tempore; illa porr&ograve; <lb/>cau&longs;a in&longs;en&longs;ibilis incorporea, qu&aelig; vbique e&longs;t, &amp; &longs;emper, Deus e&longs;t: Nec <lb/>puta po&longs;&longs;e exi&longs;tentiam cau&longs;&aelig; prim&aelig; probari &longs;en&longs;ibiliori, vt &longs;ic loquar, <lb/>argumento, qu&agrave;m eo, quod petitur ex motu projectorum, quorum motus <lb/>durat etiam&longs;i &agrave; potentia motrice mobile ip&longs;um &longs;it &longs;eparatum. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 11.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc multa colligi po&longs;&longs;unt.<emph.end type="italics"/></s><s> Prim&ograve;, &longs;i nullus e&longs;&longs;et impetus extrin&longs;ecus, <lb/>vel acqui&longs;itus, nullus e&longs;&longs;et motus violentus, ni&longs;i tant&ugrave;m motus reflexus <lb/>cadentium deors&ugrave;m. </s>

<s>Secund&ograve;, &longs;i nullus e&longs;&longs;et Deus, nullus e&longs;&longs;et motus <lb/>violentus; imm&ograve; nec vllus naturaliter acceleratus. </s>

<s>Terti&ograve;, &longs;i impetus e&longs;&shy;<lb/>&longs;et fluens vt motus, nullus e&longs;&longs;et motus violentus. </s>

<s>Quart&ograve;, &longs;i &longs;ingul&aelig; par&shy;<lb/>tes motus produci debent ab aliqu&acirc; caus&acirc; efficiente, nullus etiam e&longs;&longs;et <lb/>motus violentus. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 12.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Vt &longs;it motus violentus debent produci plures partes impetus violenti <lb/>qu&agrave;m &longs;int partes impetus naturalis<emph.end type="italics"/>; Probatur, quia &longs;i e&longs;&longs;ent plures natura&shy;<lb/>lis deors&ugrave;m, qu&agrave;m &longs;int violenti &longs;ur&longs;um, corpus tenderet deor&longs;um; &longs;ed <lb/>tardi&ugrave;s per Th.134.l.1. &amp; &longs;i tot e&longs;&longs;ent vnius, quot alterius, mobile ip&longs;um <lb/>non moueretur per Th.133.l.1. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 13.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Motus violentus non e&longs;t acceleratus<emph.end type="italics"/>; probatur prim&ograve; experienti&acirc;, qu&aelig; <lb/>certa e&longs;t. </s>

<s>Secund&ograve;, quia &longs;i &longs;emper cre&longs;ceret, numquam rediret mobile <lb/>contra hyp.1. nec enim ab vllo reflectitur; &longs;i enim reflecteretur ab a&euml;re <lb/>inten&longs;us, mult&ograve; magis remi&longs;&longs;us. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 14.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc impetus in mobili &longs;ur&longs;um projecto non intenditur,<emph.end type="italics"/> quia non inten&shy;<lb/>ditur effectus per Th.13. igitur nec cau&longs;a per Ax.2.l.2. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 15.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Motus violentus non e&longs;t &aelig;quabilis<emph.end type="italics"/>; quia mobile tandem redit per hyp.1. <lb/>&longs;ed numquam rediret, &longs;i e&longs;&longs;et &aelig;quabilis; cur enim poti&ugrave;s hoc in&longs;tanti <lb/>qu&agrave;m alio? </s>

<s>cur ab hoc puncto &longs;patij poti&ugrave;s, qu&agrave;m ab alio? </s></p><pb xlink:href="026/01/170.jpg" pagenum="138"/><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 16.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc non con&longs;eruatur intactus impetus<emph.end type="italics"/>; quia &longs;i e&longs;&longs;et intactus, e&longs;&longs;et &longs;em&shy;<lb/>per &aelig;qualis; igitur haberet &longs;emper &aelig;qualem motum per Ax.3.l.2. igitur <lb/>motus e&longs;&longs;et &aelig;quabilis, contra Th.15. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 17.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc nece&longs;&longs;e e&longs;t aliquid impetus destrui<emph.end type="italics"/>; cum enim non remaneat inta&shy;<lb/>ctus, &amp; &aelig;qualis; nec fiat maior per Th.14. cert&egrave; fit minor, igitur detra&shy;<lb/>ctione aliqua per Ax.1.l.2. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 18.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Singulis in&longs;tantibus aliquid de&longs;truitur impetus impre&longs;&longs;i<emph.end type="italics"/>; probatur quia <lb/>cur poti&ugrave;s vno quam alio? </s>

<s>quippe illa ratio, qu&aelig; probat de vno probat <lb/>de &longs;ingulis. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 19.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc nece&longs;&longs;ari&egrave; eadem vel aqualis cau&longs;a de&longs;tructionis debet e&longs;&longs;e applicata<emph.end type="italics"/>; <lb/>probatur, quia &aelig;qualis effectus &aelig;qualem cau&longs;am &longs;upponit, per Ax. <!-- REMOVE S--><lb/>3. l. <!-- REMOVE S-->2. <!-- KEEP S--></s>



</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 20.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Illa cau&longs;a non e&longs;t tant&ugrave;m a&euml;r ambiens vt volunt aliqui<emph.end type="italics"/>; quia lic&egrave;t re&longs;i&shy;<lb/>&longs;tat motui, &longs;eu potius mobili, non tamen e&longs;t ea re&longs;i&longs;tentia, qu&aelig; po&longs;&longs;it <lb/>impetum tam cit&ograve; de&longs;truere; probatur prim&ograve;, quia &longs;i hoc e&longs;&longs;et, de&longs;true&shy;<lb/>retur &aelig;quali tempore per omnem lineam &longs;ur&longs;um, quod e&longs;t contra expe&shy;<lb/>rientiam, vt dicemus infr&agrave;; e&longs;&longs;et enim eadem cau&longs;a applicata; igitur idem <lb/>&amp; &aelig;qualis effectus; probatur &longs;ecund&ograve;, quia non de&longs;truit a&euml;r primum il&shy;<lb/>lum gradum impetus naturalis acqui&longs;iti, vt con&longs;tat in motu deor&longs;um, qui <lb/>tamen e&longs;t imperfecti&longs;&longs;imus; igitur non e&longs;t &longs;ufficiens ad de&longs;truendum im&shy;<lb/>petum violentum, ni&longs;i longo tempore. </s>

<s>Terti&ograve;, globus &longs;urs&ugrave;m projectus <lb/>a&longs;cendit, &amp; deinde de&longs;cendit &aelig;quali tempore; igitur &longs;altem &longs;ingulis in&shy;<lb/>&longs;tantibus de&longs;truitur vnus gradus impetus violenti &aelig;qualis primo gradui <lb/>innato; atqui a&euml;r non pote&longs;t vno in&longs;tanti de&longs;truere impetum &aelig;qualem <lb/>primo innato; alioqui non intenderetur motus naturalis. </s>

<s>Quart&ograve;, &amp; h&aelig;c <lb/>e&longs;t ratio &agrave; priori, quotie&longs;cumque &longs;unt in eodem mobili duo impetus ad <lb/>oppo&longs;itas lineas determinati, pugnant pro rata, vt demon&longs;trauimus l.1. <lb/>Th. 149. 150. 152. &amp; in toto Schol. <!-- REMOVE S-->&amp; multis aliis pa&longs;&longs;im; atqui con&longs;er&shy;<lb/>uatur &longs;emper impetus naturalis innatus per Sch. <!-- REMOVE S-->Th.152.n.6.l.1.per Th. <!-- REMOVE S--><lb/>9. &amp; Schol.Th.14. &amp; Th.73.l.2. </s>





</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 21.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Illa cau&longs;a non e&longs;t entitas corporis mobilis, vel ip&longs;a grauitas, di&longs;tincta &longs;cili&shy;<lb/>cet ab impetu muato&longs;i qu&aelig; e&longs;t de qu&aelig; alias,<emph.end type="italics"/> probatur, quia non e&longs;&longs;et potior <lb/>ratiocur vno in&longs;tanti de&longs;truerentur duo gradus impetus, qu&agrave;m 3. 4. 5. <lb/>quippe grauitas exigeret de&longs;tructionem omnium: pr&aelig;terea omnis impe&shy;<lb/>tus de&longs;truitur ne &longs;it fru&longs;tr&agrave; per Schol, Th.152. &amp; Th.162.l.1. denique &longs;i <pb xlink:href="026/01/171.jpg" pagenum="139"/>ade&longs;t contrarius impetus de&longs;tructiuus eo modo, quo explicuimus l. <!-- REMOVE S-->1. non <lb/>e&longs;t ponenda alia cau&longs;a de&longs;tructiua. </s>

</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 22.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc nece&longs;&longs;e e&longs;t impetum violentum de&longs;trui ab impetu naturali innato<emph.end type="italics"/>; pro&shy;<lb/>batur, quia nulla e&longs;t cau&longs;a extrin&longs;eca de&longs;tructiua &longs;altem ad&aelig;quat&egrave; per hT. <lb/>20.igitur e&longs;t intrin&longs;eca per Ax.4. l.2. &longs;ed intrin&longs;eca vel e&longs;t mobilis enti&shy;<lb/>tas, vel grauitas, vel impetus innatus; &longs;ed mobilis entitas non e&longs;t cau&longs;a <lb/>de&longs;tructiua; nec etiam ip&longs;a grauitas per Th.21. igitur impetus naturalis <lb/>innatus. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 23.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc vera ratio cur &longs;ingulis in&longs;tantibus aliquid de&longs;truatur,<emph.end type="italics"/> quia &longs;ingulis <lb/>in&longs;tantibus e&longs;t cau&longs;a de&longs;tructiua applicata, igitur &longs;ingulis in&longs;tantibus de&shy;<lb/>&longs;truit per Ax. 12. l. <!-- REMOVE S-->1. <!-- KEEP S--></s>

</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 24.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc etiam ratio cur &longs;ingulis instantibus, &longs;eu &aelig;qualibus temporibus &aelig;qua&shy;<lb/>liter de&longs;truatur<emph.end type="italics"/>; quia &longs;ingulis in&longs;tantibus e&longs;t eadem cau&longs;a de&longs;tructiua ap&shy;<lb/>plicata; igitur &longs;ingulis in&longs;tantibus &aelig;qualiter de&longs;truit per Ax.3.l.2.porr&ograve; <lb/>in tantum de&longs;truit in quantum efficit, vt aliquid &longs;it fru&longs;tr&agrave;, vt fus&egrave; di&shy;<lb/>ctum e&longs;t lib.1.vel in quantum exigit eius <expan abbr="de&longs;truction&etilde;">de&longs;tructionem</expan>, nam perinde e&longs;t. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 25.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc etiam petitur ratio, propter quam talis portio impetus violenti de&shy;<lb/>&longs;truatur vne in&longs;tanti<emph.end type="italics"/>; quia &longs;cilicet contraria pugnant prorata per Ax.15. <lb/>&amp; per Th.134.l.1. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 26.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc illa inuer&longs;a communis dicti, &aelig;qualibus temporibus &aelig;qualia de&longs;truun&shy;<lb/>tur velocitatis momenta in motu violento<emph.end type="italics"/>; quippe eadem cau&longs;a eidem &longs;ub&shy;<lb/>jecto applicata &aelig;qualibus temporibus &aelig;qualem effectum producit per <lb/>Ax.3.l.2. &longs;ed impetus innatus e&longs;t cau&longs;a de&longs;tructiua impetus violenti per <lb/>Th. 22. igitur &aelig;qualibus temporibus, &amp;c. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 27.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>In eadem proportione retardatur motus violentus, in qua naturaiis accele&shy;<lb/>ratur<emph.end type="italics"/>: probatur quia &longs;ingulis in&longs;tantibus &aelig;qualibus acquiritur &aelig;qualis <lb/>gradus impetus, vt &longs;&aelig;p&egrave; dictum e&longs;t &longs;upr&agrave;; atqui &longs;ingulis in&longs;tantibus de&shy;<lb/>&longs;truitur vnus gradus impetus violenti per Th.24. &longs;ed ille gradus re&longs;pon&shy;<lb/>det impetui innato per Th. 25. igitur &aelig;qualibus temporibus tant&ugrave;m de&shy;<lb/>&longs;truitur violenti, quant&ugrave;m acquiritur naturalis; cum enim primo in&shy;<lb/>&longs;tanti &longs;it impetus naturalis, &amp; &longs;ecundo tempore &aelig;quali acquiratur &aelig;qua&shy;<lb/>lis, item tertio, quarto, &amp;c. </s>

<s>cert&egrave; cum impetus innatus pugnet cum vio&shy;<lb/>lento pro rata; nec &longs;it potior ratio cur maiorem portionem qu&agrave;m mino&shy;<lb/>rem de&longs;truat, &aelig;qualem cert&egrave; de&longs;truit, itemque &longs;ecundo in&longs;tanti &aelig;qua&shy;<lb/>lem, item tertio, quarto; igitur in eadem proportione decre&longs;cit violentus, <lb/>&longs;eu retardatur, in qua naturalis acceleratur. </s></p><pb xlink:href="026/01/172.jpg" pagenum="140"/><p type="main">

<s>Hinc inuertenda e&longs;t progre&longs;&longs;ionis linea; quippe linea AE repr&aelig;&longs;en&shy;<lb/>tat nobis progre&longs;&longs;ionem motus accelerati, qu&aelig; fit in in&longs;tantibus, &amp; li&shy;<lb/>nea FK progre&longs;&longs;ionem motus, qu&aelig; fit in partibus temporis &longs;en&longs;ibilibus; <lb/>in illa primo in&longs;tanti decurritur primum &longs;patium AB, &longs;ecundo tempore <lb/>&aelig;quali BC, tertio CD, quarto DE: in hac vero prima parte acquiritur <lb/>&longs;patium FG &longs;ecunda &aelig;quali prim&aelig; GH, tertia HI, quarta IK; igitur &longs;i ac&shy;<lb/>cipiatur linea AE, progrediendo ab A ver&longs;us E, vel linea FK progre&shy;<lb/>diendo ab F ver&longs;us K habebitur progre&longs;&longs;io motus naturaliter accelerati; <lb/>&longs;i ver&ograve; accipiatur EA, vel KF, progrediendo &longs;cilicet ab E ver&longs;us A, vel &agrave; <lb/>K ver&longs;us F, erit progre&longs;&longs;io motus violenti naturaliter retardati; vt con&shy;<lb/>&longs;tat ex pr&aelig;ced&egrave;ntibus Theorematis; &amp; quemadmodum progre&longs;&longs;io acce&shy;<lb/>lerationis in in&longs;tantibus finitis fit iuxta &longs;eriem i&longs;torum numerorum 1.2. <lb/>3.4. in partibus ver&ograve; temporis &longs;en&longs;ibilibus iuxta &longs;eriem i&longs;torum 1.3.5.7. <lb/>ita fit omnin&ograve; progre&longs;&longs;io retardationis in in&longs;tantibus iuxta hos nume&shy;<lb/>ros 4.3.2.1. in partibus temporis &longs;en&longs;ibilibus iuxta hos 7.5. 3. 1. <!-- KEEP S--></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 28.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Motus violentus durat tot in&longs;tantibus &longs;cilicet &aelig;quiualentibus quot &longs;unt ij <lb/>gradus impetus quibus violentus &longs;uperat innatum,<emph.end type="italics"/> v.g. <!-- REMOVE S-->&longs;it vnus gradus im&shy;<lb/>petus innati; producantur 5. gradus violenti, quorum &longs;inguli &longs;int &aelig;qua&shy;<lb/>les innato etiam <expan abbr="&aelig;quiual&etilde;ter">&aelig;quiualenter</expan>, motus durabit 4. in&longs;tantibus etiam &aelig;qui&shy;<lb/>ualenter id e&longs;t 4. temporibus, quorum &longs;ingula erunr &aelig;qualia primo in&shy;<lb/>&longs;tanti motus naturalis, probatur, cum &longs;ingulis in&longs;tantibus &aelig;qualibus de&shy;<lb/>&longs;truatur vnus gradus; cert&egrave; 4. in&longs;tantibus durat motus. </s>

</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 29.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Si accipiantur &longs;patia &aelig;qualia in hac progre&longs;&longs;ione retardationis, e&longs;t inuer&longs;a <lb/>illius, qu&agrave;m tribuimus &longs;upr&agrave; accelerationi, a&longs;&longs;umptis &longs;cilicet &longs;patiis &aelig;qualibus; <lb/>tum &longs;i accipiantur &longs;patia &aelig;qualia prime &longs;patie quod decurritur prime in&longs;tan&shy;<lb/>ti metus naturalis, tum &longs;i accipiantur &longs;patia &aelig;qualia date &longs;patie quod in par&shy;<lb/>te temporis &longs;en&longs;ibili percurritur<emph.end type="italics"/>; quippe quemadmodum in progre&longs;&longs;ione <lb/>accelerationis decre&longs;cunt tempora; &longs;ic in progre&longs;&longs;ione retardationis <lb/>cre&longs;cunt, a&longs;&longs;umptis &longs;cilicet &longs;patiis &aelig;qualibus; quare ne iam dicta hic re&shy;<lb/>petam, con&longs;ule qu&aelig; diximus lib.2. de hac progre&longs;&longs;ione. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 30.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc instantia initio huius metus &longs;unt minora &longs;icut initio motus naturalis <lb/>&longs;unt maiora; &amp; &longs;ub finem in motu violente &longs;unt maiora, in naturali &longs;unt mi&shy;<lb/>nora<emph.end type="italics"/>; quia &longs;cilicet hic acceleratur, ille retardatur: igitur velo&shy;<lb/>citas accelerati cre&longs;cit; igitur &longs;i accipiantur &longs;patia &aelig;qualia, decre&longs;cit tem&shy;<lb/>pus; at ver&ograve; velocitas retardati decre&longs;cit, igitur a&longs;&longs;umptis &longs;patiis &aelig;quali&shy;<lb/>bus, cre&longs;cit tempus; igitur &longs;i accipiatur &longs;patium, quod percurritur primo <lb/>in&longs;tanti huius motus, &amp; deinde alia huic &aelig;qualia; haud dubi&egrave;, cum &longs;e&shy;<lb/>cundo in&longs;tanti motus &longs;it tardior, &longs;itque a&longs;&longs;umptum &aelig;quale &longs;patium; haud <lb/>dubi&egrave; inquam in&longs;tans &longs;ecundum erit maius primo, &amp; tertium &longs;ecundo, <lb/>atque ita deinceps. </s></p><pb xlink:href="026/01/173.jpg" pagenum="141"/><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 31.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc primo in&longs;tanti motus violenti de&longs;truitur minor gradus impetus qu&agrave;m <lb/>&longs;ecundo,<emph.end type="italics"/> quod demon&longs;tro; quia eadem cau&longs;a breuiore tempore min&ugrave;s agit <lb/>per Ax.3.l.2. &amp; Ax. 13.l.1. num.4. igitur min&ugrave;s impetus de&longs;truitur pri&shy;<lb/>mo, qu&agrave;m &longs;ecundo, &amp; min&ugrave;s &longs;ecundo qu&agrave;m tertio, atque ita deinceps; <lb/>idem enim dici debet de cau&longs;a de&longs;tructiua, quod de productiua. </s></p><p type="main">

<s>Dices, igitur idem impetus de&longs;truitur primo in&longs;tanti, quo e&longs;t, &longs;i de&longs;trui&shy;<lb/>tur primo in&longs;tanti motus. </s>

<s>Re&longs;pondeo negando; quia primo in&longs;tanti, quo <lb/>e&longs;t impetus, non e&longs;t motus per Th.34.l.1. <!-- KEEP S--></s></p><p type="main">

<s>Dices, igitur impetus ille e&longs;t fru&longs;tr&agrave;, quia nullus effectus, &longs;eu motus <lb/>ex eo &longs;equitur; Re&longs;pondeo negando; nam omnes gradus impetus qui ei&shy;<lb/>dem parti mobilis in&longs;unt, communi qua&longs;i actione, vel exigentia indi&shy;<lb/>ui&longs;ibiliter exigunt motum. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 32.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc gradus omnes producti in eadem parte &longs;ubiecti &longs;unt in&aelig;quales in&shy;<lb/>perfectione<emph.end type="italics"/>; cum enim &longs;inguli &longs;ingulis in&longs;tantibus de&longs;truantur, vt dictum <lb/>e&longs;t; quippe e&longs;t tant&ugrave;m vnus gradus impetus innati, &amp; cum &longs;ingula in&shy;<lb/>&longs;tantia &longs;int in&aelig;qualia, etiam &longs;inguli gradus illius impetus &longs;unt in&aelig;quales <lb/>in perfectione. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 33.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc redditur optima ratio, cur tot producantur poti&ugrave;s qu&agrave;m plures, qu&aelig; <lb/>alioquin minim&egrave; afferri pote&longs;t<emph.end type="italics"/>; imm&ograve;, ni&longs;i hoc e&longs;&longs;et, nulla e&longs;&longs;et huiu&longs;modi <lb/>naturalis retardatio; nam producantur, &longs;i fieri pote&longs;t, omnes &aelig;quales, &longs;int&shy;<lb/>que v.g.20. nunquid po&longs;&longs;unt e&longs;&longs;e 40. perfectionis &longs;ubdupl&aelig;, vel 10. du&shy;<lb/>pl&aelig;, vel 5. quadrupl&aelig; &amp;c. </s>

<s>cur autem poti&ugrave;s vnum dices qu&agrave;m aliud? </s>

<s>at <lb/>ver&ograve; optimam inde reddo rationem qu&ograve;d cum &longs;int omnes in&aelig;quales, c&ograve; <lb/>plures &longs;unt, qu&ograve; maior e&longs;t ni&longs;us; pauciores ver&ograve;, qu&ograve; minor. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 34.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc &longs;unt in&aelig;quales in e&acirc;dem proportione, in qu&aelig; in&longs;tantia &longs;unt in&aelig;qualia<emph.end type="italics"/><lb/>v. </s>

<s>g. <!-- REMOVE S-->qu&agrave; proportione primum in&longs;tans e&longs;t minus &longs;ecundo, &amp; &longs;ecundum <lb/>tertio, ita ille gradus impetus, qui de&longs;truitur primo in&longs;tanti, e&longs;t minor <lb/>vel imperfectior co, qui de&longs;truitur &longs;ecundo, &amp; qui de&longs;truitur &longs;ecundo <lb/>imperfectior co, qui de&longs;truitur tertio, atque ita deinceps. </s>

</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 35.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc perfecti&longs;&longs;imus omnium graduum ille e&longs;t qui de&longs;truitur vltimo in&longs;tan&shy;<lb/>ti, de quo infr&aacute;<emph.end type="italics"/>; quod &longs;equitur ex dictis nece&longs;&longs;ari&ograve;: vtr&ugrave;m ver&ograve; ille &longs;it &aelig;&shy;<lb/>qualis omnin&ograve; in perfectione impetui naturali innato, dicemus <lb/>infr&agrave;. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Hic ob&longs;eruabis mirabilem &longs;an&aelig; natur&aelig; prouidentiam, qu&aelig; motus <lb/>omnes cum ip&longs;o naturali ita compo&longs;uit, vt &longs;it veluti regula omnium mo&shy;<lb/>tuum, &longs;itque vnum qua&longs;i principium perfectionis totius impetus; t&ugrave;m in <pb xlink:href="026/01/174.jpg" pagenum="142"/>motu naturali, in cuius progre&longs;&longs;ione producitur &longs;emper imperfectior, <lb/>t&ugrave;m in violento, in cuius progre&longs;&longs;ione de&longs;truitur &longs;emper perfectior; <lb/>producitur imperfectior ab eadem cau&longs;a in minoribus temporibus, &amp; <lb/>de&longs;truitur perfectior ab eadem cau&longs;a in maioribus temporibus; &amp; cum <lb/>impetus innatus &longs;it cau&longs;a de&longs;tructiua impetus violenti, habet in&aelig;qualem <lb/>proportionem cum &longs;uo effectu pro temporibus in&aelig;qualibus; &amp; cum <lb/>idem impetus innatus &longs;it qua&longs;i principium crementi, vel accelerationis, <lb/>&longs;icut e&longs;t principium retardationis; cert&egrave; pro in&aelig;qualitate temporum e&longs;t <lb/>diuer&longs;a proportio crementorum; quo nihil clarius in hac materia meo <lb/>iudicio dici pote&longs;t. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 36.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc finis motus naturalis omnin&ograve; conuenit cum principio motus violenti; <lb/>&amp; finis huius cum principio illius<emph.end type="italics"/>; qu&aelig;cumque tandem progre&longs;&longs;io accipia&shy;<lb/>tur; &longs;iue temporum &aelig;qualium in &longs;patiis in&aelig;qualibus; &longs;iue &longs;patio&shy;<lb/>rum &aelig;qualium in temporibus in&aelig;qualibus, &longs;iue a&longs;&longs;umantur in&longs;tan&shy;<lb/>tia in progre&longs;&longs;ione arithmetica &longs;implici iuxta hos numeros 1.2.3.4. &longs;iue <lb/>a&longs;&longs;umantur temporis partes &longs;en&longs;ibiles in progre&longs;&longs;ione Galilei iuxta hos <lb/>numeros 1.3.5.7. qu&aelig; omnia ex dictis nece&longs;&longs;ari&ograve; con&longs;equuntur. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 37.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Nec mod&ograve; conuenit principium vnius cum alterius fine, &amp; vici&longs;&longs;im, &longs;ed <lb/>etiam ali&aelig; partes motus in di&longs;tantiis &aelig;qualibus<emph.end type="italics"/> &longs;it enim linea AG, quam <lb/>percurrit mobile demi&longs;&longs;um ex puncto A deor&longs;um motu naturaliter ac&shy;<lb/>celerato, &amp; moueatur per 6. in&longs;tantia, &longs;eu 6. tempora &aelig;qualia: Primo <lb/>in&longs;tanti, quo percurrit &longs;patium AB; haud dubi&egrave;, quando peruenit ad pun&shy;<lb/>ctum G, habet 7. gradus impetus &aelig;quales, quia ante motum AB habebat <lb/>innatum; &longs;ed in motu illo fluunt 6. tempora &aelig;qualia, vt dictum e&longs;t; igitur <lb/>6. acquirit gradus impetus, quorum quidem vltim&ograve; acqui&longs;itus nullum <lb/>adhuc habuit motum; &longs;ed haud dubi&egrave; haberet, &longs;i vlteri&ugrave;s hic motus pro&shy;<lb/>pagaretur: his po&longs;itis imprimantur mobili in O 7.gradus impetus &aelig;qua&shy;<lb/>les prioribus &longs;urs&ugrave;m motu violento, per lineam OH; cert&egrave; primo in&longs;tan&shy;<lb/>ti motus, &longs;eu tempore &aelig;quali prioribus percurret ON, id e&longs;t 6. &longs;patiola; <lb/>quia lic&egrave;t &longs;int 7.gradus; attamen impetus innatus corporis grauis detra&shy;<lb/>hit vnum &longs;patium, &longs;imulque de&longs;truit vnum gradum, &longs;ecundo tempore <lb/>percurret NM 5. tertio ML 4. quarto LK 3. quinto KI 2. &longs;exto IH 1. <lb/>igitur primum violenti ON re&longs;pondet vltimo naturali FG &longs;eu &longs;ecun&shy;<lb/>dum illius quinto huius, tertium illius quarto huius, quartum tertio, <lb/>quintum &longs;ecundo &longs;extum primo, &amp; vici&longs;&longs;im; idem pror&longs;us in progre&longs;&longs;ione <lb/>Galilei accidit, a&longs;&longs;umptis &longs;cilicet partibus temporis &longs;en&longs;ibilibus. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 38.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc ad eam altitudinem a&longs;cendit motu violento cum iis gradibus impe&shy;<lb/>tus, quos habuit ab eadem altitudine decidens motu naturali<emph.end type="italics"/>; con&longs;tat ex <lb/>dictis. </s></p><pb xlink:href="026/01/175.jpg" pagenum="143"/><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 39.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc &longs;i motus violentus, &amp; naturalis durent &aelig;qualibus temporibus, &longs;patia <lb/>vtriu&longs;que erunt &aelig;qualia<emph.end type="italics"/>; con&longs;tat etiam ex dictis v.g. <!-- REMOVE S-->corpus graue, motu <lb/>naturali in libero a&euml;re tempore duorum &longs;ecundorum percurrit 48. pe&shy;<lb/>des, igitur &longs;i moueatur &longs;ur&longs;um &aelig;quali tempore percurret 48. pedes per <lb/>&longs;e, dico per &longs;e; quippe ratione figur&aelig; corporis &longs;ecus accidere pote&longs;t, vt <lb/>plurim&ugrave;m etiam accedit ratione motus mixti ex motu centri recto, &amp; <lb/>motu orbis circulari, de quo infr&agrave;. </s>

</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 40.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc, vt &longs;patia vtroque motu diuer&longs;a &longs;unt &aelig;qualia, ita tempora quibus de&shy;<lb/>curruntur &longs;unt &aelig;qualia,<emph.end type="italics"/> &amp; impetus acqui&longs;itus in fine naturalis cum in&shy;<lb/>nato e&longs;t &aelig;qualis impetui producta in principio violenti. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 41.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc tandiu durat de&longs;cen&longs;us mobilis proiecti &longs;urs&ugrave;m motu violento, quan&shy;<lb/>diu durat eiu&longs;dem a&longs;cen&longs;us, &amp; tot habet gradus impetus in fine de&longs;cen&longs;us, <lb/>quot habet in principio a&longs;cen&longs;us<emph.end type="italics"/>; e&longs;t enim &aelig;quale &longs;patium; igitur &aelig;quale <lb/>tempus; igitur &aelig;qualis vtrobique impetus. </s>

<s>Sed h&icirc;c duo obiici po&longs;&longs;unt, <lb/>prim&ograve; &longs;agittam per lineam verticalem vibratam po&longs;ui&longs;&longs;e tant&ugrave;m in a&longs;&shy;<lb/>cen&longs;u 3. &longs;ecunda, in de&longs;cen&longs;u ver&ograve; 5. vt &longs;&aelig;pi&ugrave;s ob&longs;eruatum e&longs;t, te&longs;te Mer&shy;<lb/>&longs;enno; &longs;ecund&ograve;, &longs;i eodem tempore corpus graue &longs;urs&ugrave;m proiectum motu <lb/>violento a&longs;cenderet, quo deinde de&longs;cendit, in fine de&longs;cen&longs;us &aelig;qualis <lb/>e&longs;&longs;et ictus, &longs;eu percu&longs;&longs;io vtriu&longs;que; cum tamen illa &longs;it maior, qu&aelig; infli&shy;<lb/>gitur motu violento, vt con&longs;tat multis experimentis. </s></p><p type="main">

<s>Re&longs;pondeo ad primum etiam te&longs;te Mer&longs;enno globum ferreum trium <lb/>aut 4. librarum &longs;ur&longs;um explo&longs;um &egrave; breuiore tormento &longs;ed latiore, &aelig;qua&shy;<lb/>le tempus in a&longs;cen&longs;u, &amp; in de&longs;cen&longs;u in&longs;ump&longs;i&longs;&longs;e; quod reuer&acirc; &longs;ec&ugrave;s acci&shy;<lb/>dit &longs;agitt&aelig;, cuius differentia a&longs;cen&longs;us, &amp; de&longs;cen&longs;us &longs;en&longs;u etiam percipi <lb/>pote&longs;t; t&ugrave;m quia lignea materia mult&ograve; leuior e&longs;t ferro, t&ugrave;m quia leui&longs;&longs;i&shy;<lb/>m&aelig; ill&aelig; penn&aelig;, quibus in&longs;truitur, motum retardant in de&longs;cen&longs;u; quod <lb/>maxim&egrave; confirmatur ex eo quod pluma facil&egrave; anhelitu &longs;ur&longs;um pellatur <lb/>&longs;atis veloci motu, qu&aelig; deinde tardi&longs;&longs;imo &longs;ua &longs;ponte de&longs;cendit: pr&aelig;terea <lb/>mucro ferreus, quo &longs;agitta armatur, &longs;emper pr&aelig;ire debet, cuius rei ratio&shy;<lb/>nem afferemus infr&agrave;; igitur cum in a&longs;cen&longs;u pr&aelig;eat, vt pr&aelig;eat in de&longs;cen&shy;<lb/>&longs;u, altera extremitas &longs;emicirculum &longs;uo motu facere debet, qui cert&egrave; ad <lb/>naturalem motum pertinet, altera tamen extremitas, qu&aelig; mouetur mo&shy;<lb/>tu contrario alterius motum retardat; ad &longs;ecundam obiectionem <lb/>re&longs;pondebo Th.44. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 42.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Si motus violentus e&longs;&longs;et &aelig;quabilis, &longs;patium e&longs;&longs;et fer&egrave; duplum illius, quod <lb/>percurritur motu naturaliter retardato, a&longs;&longs;umptis &longs;cilicet <expan abbr="t&etilde;poribus">temporibus</expan> &aelig;qualibus<emph.end type="italics"/>; <lb/>cum enim motu &aelig;quabili compo&longs;ito ex &longs;ubdupla velocitate maxim&aelig;, &amp; <lb/>minim&aelig; motus accelerati &aelig;quali tempore percurratur &aelig;quale &longs;patium, <lb/>&longs;ubduplum minim&aelig; pro nihilo fer&egrave; habetur; igitur pote&longs;t tant&ugrave;m a&longs;&longs;u-<pb xlink:href="026/01/176.jpg" pagenum="144"/>mi &longs;ubduplum maxim&aelig;; igitur velocitas motus &longs;it &aelig;qualis maxim&aelig;, haud <lb/>dubi&egrave; &longs;patium duplum percurretur. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 43.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc ben&egrave; &agrave; natur&acirc; in&longs;titutum fuit impetum naturalem innatum &longs;emper <lb/>con&longs;eruari<emph.end type="italics"/>; alioqui violentus e&longs;&longs;et &aelig;quabilis, igitur nunquam de&longs;ineret: <lb/>quantum ab&longs;urdum! quale incommodum &amp;c. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 44.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Eadem e&longs;t ratio &longs;eu proportio ictuum, &amp; percu&longs;&longs;ionum, qu&aelig; integrorum <lb/>&longs;patiorum qu&aelig; &longs;cilicet toto motu percurruntur in a&longs;cen&longs;u &amp; de&longs;cen&longs;u,<emph.end type="italics"/> v. <!-- REMOVE S-->g. <lb/><!-- REMOVE S-->corpus graue cadens ex data altitudine 48 pedum &aelig;qualem ictum infli&shy;<lb/>git in fine de&longs;cen&longs;us, &amp; in principio a&longs;cen&longs;us, quo &longs;cilicet ad <expan abbr="e&atilde;dem">eandem</expan> <lb/>altitudinem a&longs;cenderet; probatur, quia &aelig;qualis acquiritur impetus in <lb/>de&longs;cen&longs;u alteri, qui de&longs;truitur in a&longs;cen&longs;u, a&longs;&longs;umptis dumtaxat &longs;patiis illis <lb/>&aelig;qualibus; igitur &aelig;qualis e&longs;t in fine de&longs;cen&longs;us, in quo e&longs;t totus acqui&longs;i&shy;<lb/>tus, atque in principio a&longs;cen&longs;us, in quo nullus e&longs;t de&longs;tructus: ad id ver&ograve;, <lb/>quod dicebatur &longs;upr&agrave; de &longs;agitta, cuius ictus maior e&longs;t initio a&longs;cen&longs;us, <lb/>qu&agrave;m in fine de&longs;cen&longs;us non diffiteor; quia materia &longs;agitt&aelig;, t&ugrave;m lignea <lb/>t&ugrave;m plumea motum &longs;atis &longs;uperque retardat, vt differentia ictuum &longs;en&longs;u <lb/>ip&longs;o percipi po&longs;&longs;it; qu&aelig; tamen nulla perciperetur in a&longs;cen&longs;u de&longs;cen&longs;u&shy;<lb/>que globi ferrei. </s>



</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 45.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc reiicies Galileum, &amp; alios eius &longs;ectatores qui volunt impetum corpori <lb/>impre&longs;&longs;um de&longs;trui tant&ugrave;m ab a&euml;re<emph.end type="italics"/>; quod plu&longs;qu&agrave;m fal&longs;um e&longs;&longs;e comper&shy;<lb/>tum e&longs;t, vt demon&longs;trauimus &longs;upr&agrave; Th. 20. qua&longs;i ver&ograve; non ad&longs;it aliqua <lb/>cau&longs;a nece&longs;&longs;aria de&longs;tructiua, &longs;cilicet impetus innatus; hinc etiam eum&shy;<lb/>dem reiicies, qui vult numquam fieri po&longs;&longs;e, vt motu naturaliter accelera&shy;<lb/>to tanta acquiratur velocitas, quanta imprimitur in motu violento; vult <lb/>enim motum acceleratum tran&longs;ire in &aelig;quabilem, cuius contrarium de&shy;<lb/>mon&longs;trauimus &longs;upr&agrave; Th. 131, l. <!-- REMOVE S-->2. igitur cum cre&longs;cat &longs;emper velocitas, <lb/>nullus e&longs;t finitus gradus, quem tandem non a&longs;&longs;equatur; imm&ograve; vt dictum <lb/>e&longs;t in pr&aelig;cedenti Th. a&longs;&longs;umptis &aelig;qualibus &longs;patiis, impetus, qui e&longs;t in <lb/>principio a&longs;cen&longs;us, &aelig;qualis e&longs;t cum eo, qui e&longs;t in fine de&longs;cen&longs;us. </s>

</p><p type="main">

<s>Diceret fort&egrave; aliquis cadentem globum ex alti&longs;&longs;im&aelig; turris apice de&shy;<lb/>clinare &agrave; perpendiculari antequam terram feriat, vt con&longs;tat ex multis <lb/>experimentis; igitur pr&aelig;ualet tandem re&longs;i&longs;tentia a&euml;ris: &longs;ed re&longs;pondeo id <lb/>tant&ugrave;m accidere propter currentem illac a&euml;ris tractum; alioquin non <lb/>e&longs;&longs;et poti&ugrave;s ratio, cur in vnam partem declinaret, qu&agrave;m in aliam. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theoroma<emph.end type="italics"/> 46.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Non e&longs;t eadem ratio ictuum, &longs;eu percu&longs;&longs;ionum, qu&aelig; e&longs;t &longs;egmentorum in&shy;<lb/>tegri &longs;patij<emph.end type="italics"/>; v.g. <!-- REMOVE S-->in &longs;ubduplo &longs;patij &longs;egmento non e&longs;t &longs;ubduplus ictus, &longs;it <lb/> enim &longs;patium integrum motus v&icirc;olenti OH, &amp; principium motus &longs;it <lb/>in O, finis in H; accipiatur &longs;egmentum OM, quod e&longs;t qua&longs;i &longs;ubduplum O <lb/>H, ictus in M non e&longs;t profect&ograve; &longs;ubduplus ictus in O, &longs;ed tant&ugrave;m in L, vt <pb xlink:href="026/01/177.jpg" pagenum="145"/>con&longs;tat ex dictis; igitur rationes ictuum non &longs;unt, vt rationes &longs;egmen&shy;<lb/>torum integri &longs;patij. </s>

</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 47.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Vt in praxi determinentur rationes ictuum<emph.end type="italics"/>; a&longs;&longs;umatur progre&longs;&longs;io Gali&shy;<lb/>lei in AF, ita vt &longs;i prima parte temporis &longs;en&longs;ibili percurratur &longs;patium <lb/>FE 9 partium &aelig;qualium; &longs;ecunda percurratur ED. 7. partium, tertia <lb/>DC 5. quarta CB 3; quinta BA 1. hoc po&longs;ito facil&egrave; erit determinare <lb/>rationes ictuum; nam in de&longs;cen&longs;u ictus &longs;unt vt velocitates, &amp; h&aelig; vt tem&shy;<lb/>pora; igitur &longs;i AB percurritur in dato tempore, &amp; AC in duobus prio&shy;<lb/>ri &aelig;qualibus; cert&egrave; ictus in de&longs;cen&longs;u AC e&longs;t duplus ictus in de&longs;cen&longs;u <lb/>AB; in AD triplus, &amp;c. </s>

<s>Igitur in a&longs;cen&longs;u ictus in F erit quintuplus, <lb/>ictus in E quadruplus in D triplus, &amp;c. </s>

<s>igitur ictus &longs;unt in ratione dupli&shy;<lb/>cata &longs;patiorum facto &longs;patij initio &agrave; &longs;ummo puncto A. <!-- KEEP S--></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 48.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc cognitis viribus, quibus corpus graue proijcitur ad datam altitudi&shy;<lb/>nem, cogno&longs;ci po&longs;&longs;unt vires, quibus ad aliam quamcumque proijciatur<emph.end type="italics"/>; v. <!-- REMOVE S-->g. <lb/><!-- REMOVE S-->proiiciatur corpus graue ad altitudinem 48. pedum; vires &longs;unt iis &aelig;qua&shy;<lb/>les, quas acquirit in de&longs;cen&longs;u eiu&longs;dem altitudinis 48. pedum; &longs;it alia di&shy;<lb/>&longs;tantia 100. pedum; haud dubi&egrave; vires nece&longs;&longs;ari&aelig; ad motum hunc violen&shy;<lb/>tum &longs;unt &aelig;quales iis, quas acquireret in de&longs;cen&longs;u 100. pedum per Th. <!-- REMOVE S--><lb/>40. atqui ita &longs;e habent vires acqui&longs;it&aelig; in de&longs;cen&longs;u 48. pedum ad vires <lb/>acqui&longs;itas in de&longs;cen&longs;u 100. vt v.g. <!-- REMOVE S-->48. ad v.g. <!-- REMOVE S-->100. id e&longs;t fer&egrave; vt 7. <lb/>ad 10. </s>









</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 49.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Cognitis etiam &longs;patiis cogno&longs;cetur tempus<emph.end type="italics"/>; &longs;it enim decur&longs;um idem &longs;pa&shy;<lb/>tium 48. pedum motu violento &longs;ur&longs;um; idque v. <!-- REMOVE S-->g. <!-- REMOVE S-->tempore 2. &longs;ecundo&shy;<lb/>rum, quod fer&egrave; cum experientia con&longs;entit; &longs;it aliud &longs;patium 100. tempus <lb/>primi motus e&longs;t ad tempus &longs;ecundi vt v. <!-- REMOVE S-->g. <!-- REMOVE S-->48. ad v. <!-- REMOVE S-->g. <!-- REMOVE S-->100. quia &longs;patia <lb/>&longs;unt vt quadrata temporum; igitur tempora vt radices 4. hinc vires &longs;unt <lb/>in ratione temporum; quia vt temporibus &aelig;qualibus acquiruntur &aelig;qua&shy;<lb/>lia velocitatis momenta in motu naturali, ita &amp; de&longs;truuntur &aelig;qualia in <lb/>motu violento, qu&aelig; omnia con&longs;tant; igitur ictus &longs;unt vt vires, vires vt <lb/>tempora, tempora denique, vt radices <expan abbr="q.">que</expan> &longs;patiorum. </s>











</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 150.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>In vltimo contactu motus violenti nullus e&longs;t ictus, v. <!-- REMOVE S-->g. <!-- REMOVE S-->mobile projectum <lb/>&longs;ur&longs;um<emph.end type="italics"/> <emph type="italics"/>per lineam<emph.end type="italics"/> FA <emph type="italics"/>nullam percu&longs;&longs;ionem infligeret in<emph.end type="italics"/> A; probatur <lb/>quia non tendit vlteri&ugrave;s; igitur non impeditur eius motus &agrave; &longs;uperficie <lb/>corporis terminati ad punctum A; igitur nullum impetum in eo produ&shy;<lb/>cit, qui tant&ugrave;m producitur ad tollendum impedimentum per Th.44.l.1. <lb/>igitur nullum ictum infligit, qui tant&ugrave;m infligitur per impetum, vt <lb/>con&longs;tat. </s>



</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 51.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Ex his &longs;atis facil&egrave; comparari po&longs;&longs;unt rationes percu&longs;&longs;ionis,<emph.end type="italics"/> qu&aelig; infliguntur <pb xlink:href="026/01/178.jpg" pagenum="146"/>t&ugrave;m ex ca&longs;u corporis grauis cadentis, t&ugrave;m ex vi mallei impacti, t&ugrave;m ex <lb/>impetu corporis projecti, t&ugrave;m ex grauitatione corporis grauis incum&shy;<lb/>bentis, qu&aelig; omnia h&icirc;c fu&longs;i&ugrave;s e&longs;&longs;ent tractanda, ni&longs;i locum proprium infr&agrave; <lb/>&longs;ibi vendicarent. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 52.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Ad motum violentum non concurrit impetus innatus,<emph.end type="italics"/> probatur, quia im&shy;<lb/>petus ad lineas oppo&longs;itas ex diametro determinati ad communem li&shy;<lb/>neam determinari non po&longs;&longs;unt, cur enim poti&ugrave;s dextror&longs;um quam &longs;ini&shy;<lb/>stror&longs;um? </s>

<s>igitur non concurrunt ad communem motum, ni&longs;i dicatur <lb/>impetus innatus valeo nomine concurrere ad violentum, quod eius li&shy;<lb/>neam &longs;ingulis temporibus qua&longs;i ca&longs;tiget, vltr&oacute;que, vel vlteri&ugrave;s currentem <lb/>contineat. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 53.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc ad motum violentum impetus ab exteriore potentia mobili impre&longs;&longs;us <lb/>tant&ugrave;m concurrit<emph.end type="italics"/>; patet, cum enim in mobili projecto &longs;ur&longs;um &longs;it tant&ugrave;m <lb/>ille impetus pr&aelig;ter innatum, nec innatus concurrat per Th. 52. illum <lb/>tant&ugrave;m concurrere nece&longs;&longs;e e&longs;t: excipe &longs;emper impetum acqui&longs;itum, de <lb/>quo iam &longs;upr&agrave;. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 54.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Primo instanti quo producitur impetus ille &agrave; potentia motrice in mobili, me&shy;<lb/>diante &longs;cilicet impetu producto in organo proprio, non e&longs;t motus<emph.end type="italics"/>; probatur, <lb/>quia primo in&longs;tanti, quo e&longs;t impetus, non e&longs;t motus, per Th.34.l.1. <!-- KEEP S--></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 55.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Impetus productus in manu producit impetum in organo vel in mobili pri&shy;<lb/>mo in&longs;tanti, quo e&longs;t<emph.end type="italics"/>; probatur, quia &longs;ecundo in&longs;tanti exigit motum &longs;ui &longs;ub&shy;<lb/>jecti; igitur tolli etiam impedimentum; igitur per motum medij; igitur <lb/>priori in&longs;tanti in eodem mobili debet e&longs;&longs;e impetus; igitur produci ab <lb/>impetu organi; igitur &amp; in organo ab impetu manus. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 56.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Primo in&longs;tanti, quo producitur impetus in motu violento, nullus eius gra&shy;<lb/>dus de&longs;truitur<emph.end type="italics"/>; probatur, quia alioquin &longs;imul eodem in&longs;tanti, quo e&longs;&longs;e in&shy;<lb/>ciperet, e&longs;&longs;e de&longs;ineret, quod dici non pote&longs;t. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 57.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Impetus innatus impedit ne producatur tantus impetus in motu violento,<emph.end type="italics"/><lb/>probatur, quia cert&egrave; t&agrave;m impedit primam productionem, qu&agrave;m con&longs;er&shy;<lb/>uationem, vt patet; e&longs;t enim par vtrobique ratio; pr&aelig;terea agit in ip&longs;am <lb/>manum. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 58.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Impetus violentus producitur minor, qu&agrave;m produceretur vno dumtaxat gra&shy;<lb/>du aquali ip&longs;i impetui innato<emph.end type="italics"/>; quippe &longs;icut de&longs;truit &longs;ingulis in&longs;tantibus <lb/>&aelig;qualibus vnum gradum; quia pugnat pro rata; ita pror&longs;us impedit, ne <pb xlink:href="026/01/179.jpg" pagenum="147"/>producatur vnus gradus &longs;ibi &aelig;qualis primo in&longs;tanti; cur enim duo po&shy;<lb/>ti&ugrave;s, qu&agrave;m tres? </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 59.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Secundo &longs;tatim in&longs;tanti de&longs;truit alterum gradum<emph.end type="italics"/>: quippe e&longs;t cau&longs;a ne&shy;<lb/>ce&longs;&longs;aria; igitur &longs;tatim primo in&longs;tanti exigit de&longs;tructionem; non cert&egrave; <lb/>pro primo in&longs;tanti per Th.56.igitur pro &longs;ecundo, atque ita pro aliis dein&shy;<lb/>ceps; de&longs;truitur autem, ne &longs;it fru&longs;tr&agrave; eo modo, quo diximus &longs;upr&agrave;. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 60.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc optima ratio illius instituti natur&aelig;, quo factum e&longs;t, vt impetus innatus <lb/>numquam destruatur<emph.end type="italics"/>; ne &longs;i aliquando de&longs;trueretur, nulla e&longs;&longs;et cau&longs;a de&shy;<lb/>&longs;tructiua impetus violenti; ac proinde &aelig;quabilis e&longs;&longs;et, &longs;emperque dura&shy;<lb/>ret, de&longs;tructiua inquam &longs;uo modo. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 61.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc corpus quod non grauitat, facil&egrave; proijcitur, vel impellitur<emph.end type="italics"/>: &longs;ic na&shy;<lb/>uis aquis innatans, nubes in a&euml;re liberat&aelig;; halitus, atque adeo ip&longs;&aelig; partes <lb/>aqu&aelig;, quas perexiguus lapillus in orbes pen&egrave; innumeros agit, ne quid <lb/>dicam de partibus a&euml;ris, qu&aelig; tam cit&ograve; &amp; procul mouentur, vt con&longs;tat in <lb/>&longs;ono, motu &longs;cilicet fer&egrave; &aelig;quabili. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 62.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc etiam &egrave; contrario corpus grauius difficili&ugrave;s &longs;ur&longs;um proijcitur<emph.end type="italics"/>: t&ugrave;m <lb/>quia plures partes impetus &longs;unt producend&aelig; in &longs;ubjecto grauiore quod <lb/>pluribus partibus con&longs;tat, t&ugrave;m impetus innatus maior e&longs;t, non quidem in <lb/>inten&longs;ione &longs;ed in exten&longs;ione, ac proinde impedit ne plures gradus pro&shy;<lb/>ducantur; quippe maius impedimentum plus impedit, quis hoc neget? </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 63.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Omnes partes impetus product&aelig; in mobili primo instanti concurrunt ad <lb/>motum &longs;ecundi instantis<emph.end type="italics"/>; probatur, quia alioqui aliqua e&longs;&longs;et fru&longs;tr&agrave;, quod <lb/>dici non debet. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 64.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Concurrunt omnes ill&aelig;, qu&aelig; in&longs;unt eidem parti &longs;eu puncto mobilis <expan abbr="commun">communes</expan> <lb/>qua&longs;i actione vel exigentia<emph.end type="italics"/>; patet ex dictis de impetu, quia concurrunt ad <lb/>velocitatem, qu&aelig; e&longs;t indiui&longs;ibilis actu. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 65.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Non ponitur tamen totus motus &longs;ecundo instanti, quem exigunt primo; <emph.end type="italics"/><lb/>quia impetus innatus aliquid detrahit, cum exigat motum deor&longs;um per <lb/>lineam oppo&longs;itam, igitur imminuitur motus pro rata. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 66.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc ille gradus motus qui non ponitur &longs;ecundo instanti respondet gradus <lb/>impetus qui destruitur<emph.end type="italics"/>; cum vterque habeat <expan abbr="e&atilde;dem">eandem</expan> men&longs;uram, &longs;cilicet <lb/>impetum innatum. </s></p><pb xlink:href="026/01/180.jpg" pagenum="148"/><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 67.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc effectus pete&longs;t e&longs;&longs;e eo instanti quo non existit eius cau&longs;a partialis<emph.end type="italics"/>; v.g. <!-- REMOVE S--><lb/>motus qui ponitur &longs;ecundo in&longs;tanti non min&ugrave;s exigitur ab eo gradu im&shy;<lb/>petus qui de&longs;truitur &longs;ecund&ograve; in&longs;tanti, qu&agrave;m ab aliis, non exigitur qui&shy;<lb/>dem &longs;ecundo &longs;ed primo pro &longs;ecundo; vnde dixi cau&longs;am partialem, quia <lb/>etiam exigitur ab aliis gradibus impetus, qui non de&longs;truuntur exigenti&acirc; <lb/>communi; quippe impetus non exigit ni&longs;i pro &longs;ecundo in&longs;tanti; nec vl&shy;<lb/>lum ab&longs;urdum e&longs;t eo in&longs;tanti cau&longs;am exigenti&aelig; non exi&longs;tere cum poni&shy;<lb/>tur eius effectus, &longs;cilicet id quod exigebat priori in&longs;tanti quo erat; nul&shy;<lb/>lus e&longs;t enim influxus huius cau&longs;&aelig;; pr&aelig;&longs;ertim cum non &longs;it cau&longs;a <lb/>totalis. </s>

</p><p type="main">

<s>Vnde cum effectus qui ponitur &longs;ecundo in&longs;tanti non re&longs;pondeat per&shy;<lb/>fectioni cau&longs;&aelig; totius propter impedimentum, aliquis gradus cau&longs;&aelig; e&longs;&longs;et <lb/>fru&longs;tr&agrave;; igitur eodem in&longs;tanti &longs;ecundo de&longs;trui debet, alioqui ni&longs;i de&longs;true&shy;<lb/>retur &longs;ingulis in&longs;tantibus poneretur effectus non re&longs;pondens perfectioni <lb/>cau&longs;&aelig;; imm&ograve; numquam de&longs;trueretur totus motus violentus, vt con&longs;tat; <lb/>itaque primo in&longs;tanti omnes gradus impetus qui &longs;unt exigunt motum <lb/>pro &longs;ecundo ne aliquis eo in&longs;tanti &longs;it fru&longs;tr&agrave; &longs;i non exigeret, &amp; &longs;ecundo <lb/>in&longs;tanti aliquis gradus impetus de&longs;truitur, ne &longs;it fru&longs;tr&agrave; codem in&longs;tanti <lb/>&longs;ecundo, cum &longs;cilicet non &longs;int tot gradus motus, quot &longs;unt gradus impe&shy;<lb/>tus; atque ita deinceps tertio in&longs;tanti de&longs;truitur vnus gradus, vt iam &longs;u&shy;<lb/>pr&agrave; dictum e&longs;t. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 68.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Ideo de&longs;truitur poti&ugrave;s vnus gradus impetus qu&agrave;m alius &longs;ecundo in&longs;tanti, <lb/>tertioque, &amp;c. </s>

<s>quia talis e&longs;t perfectionis<emph.end type="italics"/>; hoc iam &longs;upr&agrave; explicatum e&longs;t; quia <lb/>cum motus initio &longs;it velocior, in&longs;tantia &longs;unt minora, igitur min&ugrave;s im&shy;<lb/>petus in &longs;ingulis de&longs;truitur, pater ex dictis. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 69.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Ille gradus impetus qui de&longs;truitur &longs;ecundo in&longs;tanti non concurrit ad motum <lb/>tertij in&longs;tantis<emph.end type="italics"/>; quia non pote&longs;t concurrere ad motum ni&longs;i exigendo; at&shy;<lb/>qui exigere tant&ugrave;m pote&longs;t, quando e&longs;t; quod enim non e&longs;t non exigit, <lb/>&longs;ed motus tertij in&longs;tantis exigitur &longs;ecundo; &longs;ic enim tota res motus pro&shy;<lb/>cedit vt impetus primo in&longs;tanti exigat motum pro &longs;ecundo; &amp; &longs;ecundo <lb/>pro tertio; &amp; tertio pro quarto, atque ita deinceps; igitur impetus ille <lb/>qui de&longs;truitur; &longs;ecundo in&longs;tanti non exigit motum pro tertio, &amp; qui de&shy;<lb/>&longs;truitur tertio non exigit pro quarto, atque ita deinceps. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 70.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc impetus innatus non concurrit ad motum violentum,<emph.end type="italics"/> vt dictum e&longs;t, <lb/>&longs;ed tant&ugrave;m impedit, immediat&egrave; quidem, quia cum exigat motum deor&shy;<lb/>s&ugrave;m, facit vt non &longs;it tantus motus &longs;ur&longs;um; mediat&egrave; ver&ograve;, quia cum non <lb/>&longs;it tantus motus &longs;urs&ugrave;m, quantus e&longs;&longs;et, haud dubi&egrave; non re&longs;pondet ad&aelig;&shy;<lb/>quat&egrave; cau&longs;&aelig;; igitur aliquid cau&longs;&aelig; fru&longs;tr&agrave; e&longs;t; igitur de&longs;trui debet; hinc <pb xlink:href="026/01/181.jpg" pagenum="149"/>de&longs;truitur etiam hic impetus per principium commune, ne aliquid &longs;it <lb/>fru&longs;tr&agrave;. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 71.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Linea motus &longs;ur&longs;um determinatur &agrave; potentia motrice<emph.end type="italics"/>; probatur, quia h&aelig;c <lb/>determinat impetum productum in manu vel in organo; hic ver&ograve; im&shy;<lb/>petum, quem producit in mobili &longs;urs&ugrave;m projecto; patet, quia nulla e&longs;t <lb/>alia cau&longs;a applicata. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 72.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Tandem duo impetus violentus, &longs;cilicet, &amp; innatus ad &aelig;qualitatem perue&shy;<lb/>nirent, &longs;i vel vnus gradus violenti e&longs;&longs;et &aelig;qualis perfectionis cum innato<emph.end type="italics"/>; cum <lb/>enim detrahatur &longs;emper pars aliquota alicuius totius, tandem perueni&shy;<lb/>tur ad vltimam; igitur &longs;int 100. gradus impetus violenti, quorum quili&shy;<lb/>bet &longs;it &aelig;qualis impetui innato; cert&egrave; cum temporibus &aelig;qualibus &aelig;qua&shy;<lb/>lis gradus impetus de&longs;truatur; accipiatur illud tempus, in quo de&longs;trui&shy;<lb/>tur vnus, haud dubi&egrave; 100. &aelig;qualibus temporibus de&longs;truentur omnes 100. <lb/>igitur 99. in&longs;tantibus de&longs;truentur 99. gradus; igitur &longs;upere&longs;t vnus; igitur <lb/>duo illi impetus perueniunt tandem ad &aelig;qualitatem. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 73.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Vbi vterque perueni&longs;&longs;et ad &aelig;qualitatem, non e&longs;&longs;et potior ratio cur mobile mo&shy;<lb/>ueretur &longs;urs&ugrave;m qu&agrave;m deor&longs;um in&longs;tanti &longs;equenti<emph.end type="italics"/>; probatur, quia t&agrave;m gra&shy;<lb/>dus impetus innati exigit motum deor&longs;um qu&agrave;m gradus impetus vio&shy;<lb/>lenti &longs;urs&ugrave;m; igitur neuter habebit motum per Th.133.l. </s>

<s>1. <!-- KEEP S--></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 74.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc ip&longs;o in&longs;tanti, quo e&longs;&longs;et &aelig;qualitas, e&longs;&longs;et adhuc motus<emph.end type="italics"/>; quia in&longs;tanti <lb/>immediat&egrave; antecedenti erant duo gradus impetus violenti, &amp; vnus in&shy;<lb/>nati; igitur duo illi pr&aelig;ualent pro in&longs;tanti &longs;equenti, in quo e&longs;t &aelig;qua&shy;<lb/>litas. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 75.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Itaque quie&longs;ceret mobile ip&longs;o &longs;tatim in&longs;tanti, quod in&longs;tanti &aelig;qualitatis &longs;uc&shy;<lb/>cedit<emph.end type="italics"/>; patet, quia neuter impetus pro illo in&longs;tanti pr&aelig;ualere po&longs;&longs;et per <lb/>Th. 73. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 76.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Igitur in&longs;tanti quietis nullus e&longs;&longs;et ampli&ugrave;s impetus violentus<emph.end type="italics"/>; cum enim <lb/>&longs;ingulis in&longs;tantibus de&longs;truatur vnus gradus, v. <!-- REMOVE S-->g in&longs;tanti illo, quod &longs;e&shy;<lb/>quitur po&longs;t in&longs;tans &aelig;qualitatis, de&longs;truitur ille gradus, qui &longs;upere&longs;t; nec <lb/>pote&longs;t vel pl&ugrave;s, vel min&ugrave;s de&longs;trui; pugnant enim pro rata; quod cert&egrave; <lb/>cuiquam fort&egrave; paradoxor videbitur, &longs;cilicet nullum tune e&longs;&longs;e motum <lb/>propter pugnam, cum tamen nulla e&longs;t amplius pugna. </s>

</p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 77.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Quies illa duraret tant&ugrave;m vno in&longs;tanti,<emph.end type="italics"/> probatur, quia cum in&longs;tanti quie&shy;<lb/>tis &longs;it tant&ugrave;m impetus innatus per Th. 76. cert&egrave; non impeditur quomi&shy;<lb/>nus habeat motum pro in&longs;tanti &longs;equenti, quem reuer&agrave; exigit; igitur pro <pb xlink:href="026/01/182.jpg" pagenum="150"/>in&longs;tanti &longs;equenti moueritur; &longs;ed pro alio antecedente mouebatur; igi&shy;<lb/>tur quies illa durat tant&ugrave;m vno in&longs;tanti. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 78.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Quies illa non fit propter aliquam reflexionem, vt aliqui dicunt<emph.end type="italics"/>; quia nul&shy;<lb/>la pror&longs;us e&longs;t reflexio, vbi nullum e&longs;t reflectens; atqui nullum e&longs;t refle&shy;<lb/>ctens, vt patet, quia nullum e&longs;t corpus impediens motus propagationem; <lb/>lic&egrave;t enim medium impediat, non tamen per modum reflectentis pro&shy;<lb/>pri&egrave;; immo vt dicemus infr&agrave; in puncto reflexionis nulla datur quies; &longs;ed <lb/>motus reflexus &longs;ibi vendicat librum &longs;ingularem. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 79.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc &longs;iue pr&aelig;ce&longs;&longs;erit motus violentus, &longs;iue non, corpus graue eodem vel &aelig;&shy;<lb/>quali motu deor&longs;um cadit,<emph.end type="italics"/> quia nullus amplius remanet impetus violen&shy;<lb/>tus in fine motus violenti, per Th.76. igitur &longs;olus impetus naturalis li&shy;<lb/>bero motu deors&ugrave;m fertur. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 80.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc reiicies aliquos apud Galileum, qui volunt ideo motum naturalem <lb/>accelerari, quia &longs;en&longs;im de&longs;truitur impetus violentus ant&egrave; impre&longs;&longs;us,<emph.end type="italics"/> quod pe&shy;<lb/>nitus ridiculum e&longs;t; quia lapis deci&longs;us &egrave; rupe etiam motu naturaliter <lb/>accelerato deor&longs;um cadit, lic&egrave;t e&ograve; nunquam motu violento euectus <lb/>fuerit. </s></p><p type="main">

<s>Ob&longs;eruabis hanc hypothe&longs;im gradus impetus violenti &aelig;qualis perfe&shy;<lb/>ctionis cum innato e&longs;&longs;e fal&longs;am. </s>

<s>Prim&ograve;, quia commodius e&longs;t potenti&aelig; <lb/>motrici producere imperfectiorem impetum, &longs;ic enim plures illius gra&shy;<lb/>dus producere pote&longs;t. </s>

<s>Secund&ograve;, quia in reflexo &longs;ur&longs;um vltimus gradus <lb/>qui de&longs;truitur e&longs;t imperfectior innato, e&longs;t enim acqui&longs;itus; igitur in omni <lb/>alio motu &longs;urs&ugrave;m. </s>

<s>Terti&ograve;, quia violentus e&longs;t cum innato in eadem &longs;ubie&shy;<lb/>cti parte; &longs;ed idem &longs;ubiectum formas homogeneas non patitur, de qu&ograve; <lb/>ali&agrave;s, hinc dicendum &longs;upere&longs;t non quie&longs;cere mobile in fine motus </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 81.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Corpus quod non grauitat proiicitur &longs;ur&longs;um motu &aelig;quabili per &longs;e<emph.end type="italics"/>; patet, quia <lb/>nihil e&longs;t quod de&longs;truat ip&longs;um impetum; igitur &longs;emper moueretur, ni&longs;i <lb/>per accidens ab ip&longs;o medio eius motus retardaretur; vnde dixi <emph type="italics"/>per &longs;e,<emph.end type="italics"/><lb/>cum ratione medij retardetur; imm&ograve; qu&ograve; leuius e&longs;t, facili&ugrave;s &agrave; medio re&shy;<lb/>tinetur, vide Th.61. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 82.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Non cre&longs;cit impetus naturalis in motu violento &longs;ur&longs;um<emph.end type="italics"/>; probatur prim&ograve;, <lb/>quia impetus naturalis aduentitius &longs;upponit motum deor&longs;um, ad cuius <lb/>inten&longs;ionem &agrave; natura fuit in&longs;titutus per re&longs;p. </s>

<s>ad quartam obiect. </s>

<s>in di&longs;&shy;<lb/>&longs;ert.l.2. adde quod tardi&ugrave;s a&longs;cenderet, qu&agrave;m de&longs;cenderet; deinde velo&shy;<lb/>ci&ugrave;s de&longs;cenderet po&longs;tmotum violentum corpus graue, qu&agrave;m &longs;i nullo mo&shy;<lb/>tu violento pr&aelig;uio demitteretur deor&longs;um, qu&aelig; omnia experimentis <pb xlink:href="026/01/183.jpg" pagenum="151"/><expan abbr="eti&atilde;">etiam</expan> vulgaribus repugnant; imm&ograve; &amp; cunctis fer&egrave; pr&aelig;mi&longs;&longs;is Theorematis. <!-- KEEP S--></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 83.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Motus violentus non tendit ad quietem per omnes tarditatis gradus, vt <lb/>pa&longs;&longs;im a&longs;&longs;erit Galileus<emph.end type="italics"/>; Prim&ograve;, quia non &longs;unt infinita in&longs;tantia, &longs;ed retarda&shy;<lb/>tur tant&ugrave;m &longs;ingulis in&longs;tantibus; Secund&ograve; in medio den&longs;iore min&ugrave;s du&shy;<lb/>rat; igitur non tran&longs;it per tot gradus tarditatis; pr&aelig;terea in plano incli&shy;<lb/>nato &longs;ur&longs;um &icirc;n minore proportione retardatur motus, quod etiam in <lb/>plano horizontali certi&longs;&longs;imum e&longs;t; quorum omnium rationes &longs;uo loco <lb/>videbimus. </s></p><p type="main">

<s>Nec e&longs;t quod aliqui dicant infinito tribui non po&longs;&longs;e h&aelig;c pr&aelig;dicata <lb/>&aelig;qualitatis vel in&aelig;qualitatis, quod fal&longs;um e&longs;t, loquamur de infinito actu; <lb/>&longs;i enim e&longs;&longs;et numerus infinitus hominum, nunquid verum e&longs;&longs;et dicere <lb/>numerum oculorum e&longs;&longs;e maiorem numero hominum; nec e&longs;t quod ali&shy;<lb/>qui confugiant ad di&longs;iunctiones; nos rem i&longs;tam &longs;uo loco fus&egrave; tractabi&shy;<lb/>mus &amp; demon&longs;trabimus, ni fallor, cum Ari&longs;totele, fieri non p&ograve;&longs;&longs;e vt &longs;it <lb/>aliquod creatum infinitum actu; lic&egrave;t vltr&ograve; concedamus plura e&longs;&longs;e infi&shy;<lb/>nita potenti&acirc;; &amp; ver&ograve; certum e&longs;t infinito potenti&acirc; non ine&longs;&longs;e huiu&longs;modi <lb/>pr&aelig;dicata &aelig;qualitatis, vel in&aelig;qualitatis. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 84.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Imm&ograve; &longs;i tran&longs;iret mobile &longs;urs&ugrave;m proiectum per omnes tarditatis gradus, <lb/>nunquam profect&ograve; de&longs;cenderat<emph.end type="italics"/>; quia cum &longs;ingulis in&longs;tantibus &longs;inguli gra&shy;<lb/>dus re&longs;pondeant, &amp; duo in&longs;tantia &longs;imul e&longs;&longs;e non po&longs;&longs;int; nunquam cert&egrave; <lb/>verum e&longs;&longs;et dicere fluxi&longs;&longs;e infinita; igitur nec mobile per infinitos tar&shy;<lb/>ditatis gradus ad quietem perueni&longs;&longs;e; hoc Theorema &longs;upponit e&longs;&longs;e tan&shy;<lb/>t&ugrave;m finita in&longs;tantia. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 85.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Re&longs;i&longs;tentia a&euml;ris est maior initio, qu&agrave;m in fine motus violenti,<emph.end type="italics"/> vt con&longs;tat ex <lb/>dictis, quia initio motus e&longs;t velocior, igitur plures partes a&euml;ris &aelig;quali <lb/>tempore re&longs;i&longs;tunt; in fine ver&ograve; &egrave; contrario. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 86.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Hinc oppo&longs;ita e&longs;t omnin&ograve; ratio re&longs;istentia, qu&aelig; &longs;equitur ex motu violento illi, <lb/>qu&aelig; cum naturali e&longs;t coniuncta,<emph.end type="italics"/> h&aelig;c enim initio minor, in fine maior, illa <lb/>ver&ograve; initio maior, &amp; in fine minor; hinc prima cre&longs;cit cam &longs;uo motu, <lb/>&longs;ecunda cum &longs;uo decre&longs;cit. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 87.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Decre&longs;cit igitur impetus eadem proportione, qua decre&longs;cit re&longs;i&longs;tentia<emph.end type="italics"/>; vt pa&shy;<lb/>tet ex dictis; igitur in toto motu eadem e&longs;t re&longs;i&longs;tenti&aelig; proportio. </s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 88.<emph.end type="center"/></s></p><p type="main">

<s><emph type="italics"/>Vari&aelig; &longs;unt potenti&aelig; motrices, &agrave; quibus mobile &longs;ur&longs;um proiici potest motu <lb/>violento,<emph.end type="italics"/> v.g. <!-- REMOVE S-->potentia motrix animantium, potentia motrix grauium mo&shy;<lb/>bili &longs;cilicet &longs;ur&longs;um repercu&longs;&longs;o; potentia motrix, qu&aelig; &longs;equitur ex com&shy;<lb/>pre&longs;&longs;ione &amp; rarefactione corporum, &longs;ed de his omnibus ali&agrave;s. </s>

</p><pb xlink:href="026/01/184.jpg" pagenum="152"/><p type="main">

<s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main">

<s>Ob&longs;eruabis prim&ograve; &longs;i aliquando accidat, vt aliqui volunt ictum, qui <lb/>&longs;tatim initio motus violenti infligitur, non e&longs;&longs;e maximum, &longs;ed minorem <lb/>eo, qui po&longs;t aliquod confectum &longs;patium infligitur; quod probant in pila <lb/>ex fi&longs;tula &aelig;nea &longs;ur&longs;um emi&longs;&longs;a, qu&aelig; <expan abbr="moior&etilde;">maiorem</expan> ictum infligit in data di&longs;tantia, <lb/>quod &longs;an&egrave; &longs;i verum e&longs;t, h&aelig;c vnica e&longs;t, &longs;eu ratio, &longs;eu cau&longs;a, qu&ograve;d &longs;cilicet &longs;ur&shy;<lb/>&longs;um pila pellatur ab igne, qui ab ore fi&longs;tul&aelig; erumpens per aliquod &longs;pa&shy;<lb/>tium &agrave; tergo vrget; igni enim innatum e&longs;t &longs;ur&longs;um euolare. </s></p><p type="main">

<s>Ob&longs;eruabis &longs;ecund&ograve;, vix po&longs;&longs;e manu mobile &longs;ur&longs;um rect&agrave; proiici, quia <lb/>&longs;cilicet manus extremitas motu mixto mouetur ex duobus vel pluribus <lb/>circularibus, de quo infr&agrave;. </s></p><p type="main">

<s>Ob&longs;erua terti&ograve;, non tant&ugrave;m propter grauitationem con&longs;eruari impe&shy;<lb/>tum naturalem innatum, &longs;ed etiam vt motui violento re&longs;i&longs;tat; at ver&ograve; <lb/>non re&longs;i&longs;teret, ni&longs;i grauitaret. </s></p><p type="main">

<s>Ob&longs;erua quart&ograve;, reciprocas rationes motus naturalis &amp; violenti; in <lb/>quibus mirabile pror&longs;us fuit natur&aelig; in&longs;titutum, cum idem in vtroque il&shy;<lb/>larum &longs;it principium. </s></p><p type="main">

<s>Ob&longs;erua quint&ograve;, finem motus violenti e&longs;&longs;e multiplicem, nullum ta&shy;<lb/>men &agrave; natura in&longs;titutum; quippe potentia motrix, qu&aelig; agit ex appetitu <lb/>elicito, (vt vulg&ograve; aiunt,) &longs;eu cum cognitione, finem &longs;ibi proponit ad libi&shy;<lb/>t&ugrave;m; illa ver&ograve; qu&aelig; vi compre&longs;&longs;ionis excitatur per accidens &longs;ur&longs;um agit <lb/>mobile poti&ugrave;s, qu&agrave;m per aliam lineam; repercu&longs;&longs;a &longs;urs&ugrave;m videntur e&longs;&longs;e <lb/>magis iuxta in&longs;titutum natur&aelig;. <lb/><figure id="id.026.01.184.1.jpg" xlink:href="026/01/184/1.jpg"/></s></p><pb xlink:href="026/01/185.jpg" pagenum="153"/><figure id="id.026.01.185.1.jpg" xlink:href="026/01/185/1.jpg"/><p type="main">

<s><emph type="center"/>LIBER QVARTVS,<emph.end type="center"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>DE MOTV MIXTO EX <lb/>duobus, vel pluribus rectis.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main">

<s>MOTVM mixtum eum e&longs;&longs;e non dico, qui <lb/>ex pluribus aliis motibus componatur; <lb/>&longs;eu mi&longs;ceatur; nec enim plures motus <lb/>&longs;imul e&longs;&longs;e po&longs;&longs;unt in eodem mobili; c&ugrave;m <lb/>tant&ugrave;m e&longs;&longs;e po&longs;&longs;it vno dumtaxat in&longs;tan&shy;<lb/>ti vnica migratio ex loco in locum; nec plura loca <lb/>naturali virtute &longs;imul acquiri po&longs;&longs;unt; Igitur nec &longs;i&shy;<lb/>mul e&longs;&longs;e duo motus; Itaque motus mixtus &longs;implex <lb/>e&longs;t, &longs;i con&longs;ideretur ratio, &amp; linea motus; mixtus ver&ograve; <lb/>dicitur, quod ex pluribus re&longs;ultet, qui reuer&acirc; non <lb/>&longs;unt, &longs;ed c&ugrave;m e&longs;&longs;e po&longs;&longs;int, qua&longs;i confluunt in tertium <lb/>motum communi &longs;umptu qua&longs;i de vtroque partici&shy;<lb/>pantem, quod totum fit propter diuer&longs;os impetus, <lb/>vel <expan abbr="e&utilde;dem">eundem</expan> ad diuer&longs;as lineas determinatum, vt fus&egrave; <lb/>explicabimus infr&agrave;: Porr&ograve; in hoc Libro explicamus <lb/>tant&ugrave;m motum mixtum, qui re&longs;ultat ex pluribus re&shy;<lb/>ctis, vt titulus ip&longs;e pr&aelig;fert. <lb/><gap desc="hr tag"/></s></p><p type="main">

<s><emph type="center"/><emph type="italics"/>DEFINITIO 1.<emph.end type="italics"/><emph.end type="center"/><!-- K