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version 1.21, 2007/02/02 17:59:17

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<?xml version="1.0"?>

<?xml version="1.0" encoding="UTF-8"?>

<!DOCTYPE archimedes SYSTEM "../dtd/archimedes.dtd">

<info>

<author>Fabri, Honoré</author>

<title>Tractatus physicus de motu locali</title>

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<cvs_file>fabri_tract_026_la_1646.xml</cvs_file>

<cvs_version/>

</info> <text> <front> <section> <pb xlink:href="026/01/001.jpg"/>

</info>

<text>

<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>

<front>

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

<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>

<s id="N1001D"><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>

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

<s id="N10030"><emph type="center"/>EFFECTVS OMNES, QVI AD IMPETVM, <lb/>Motum naturalem, violentum, & mixtum pertinent, <lb/>explicantur, & ex principiis Phy&longs;icis <lb/>demon&longs;trantur.<emph.end type="center"/></s>

<s><emph type="center"/><emph type="italics"/>LVGDVNI,<emph.end type="italics"/><lb/>Apud IOANNEM CHAMPION, <lb/>in foro Cambij.<emph.end type="center"/></s>

<s id="N1003F"><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>

<s>D C. XLVI.<emph.end type="italics"/><lb/>Cum Priuilegio Regis, & Approbatione Doctorum.<emph.end type="center"/></s><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"/>

<s id="N10054"><emph type="center"/><emph type="italics"/>Ex prælectionibus<emph.end type="italics"/> R. P. HONORATI FABRY, <lb/><emph type="italics"/>Societatis<emph.end type="italics"/> IESV.<emph.end type="center"/></s>

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

<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 Prætori prima<lb/>rio, & &longs;ecundùm Mercatorum Præpo&longs;ito, &c.<emph.end type="center"/></s>

<s id="N1006E"><emph type="center"/><emph type="italics"/>LVGDVNI,<emph.end type="italics"/><lb/>Apud IOANNEM CHAMPION, <lb/>in foro Cambij.<emph.end type="center"/></s>

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

<s><emph type="italics"/>TIBI alterum no&longs;træ Philo&longs;o<lb/>phiæ f&oelig;tum in&longs;cribo, cui iam <lb/>primum in&longs;crip&longs;i<emph.end type="italics"/> (PRÆTOR <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<lb/>tabo officia: multos non expo&longs;cam Patronos, qui <lb/>iam omnium optimum, & meriti&longs;simum habeo; neo <lb/>enim &longs;acra Philo&longs;ophiæ anathemata rudi, & ru<lb/>&longs;tico muro appendam, quæ ex &longs;acro tholo templi <lb/>Themidos am&oelig;niter pendent: Nec leuem toti rei li<lb/>terariæ iniuriam inferrem, &longs;i alium illi, quàm li-<emph.end type="italics"/><pb xlink:href="026/01/004.jpg"/><emph type="italics"/>teratum Mecænatem accer&longs;erem: & verò Tracta<lb/>tum hunc de Motu Locali, alteri quàm tibi in&longs;cri<lb/>bere non debui, cuius imperia Ludgunen&longs;is orbis, po<lb/>tiùs quàm vrbis, componunt: Tu prudens Intelli<lb/>gentia, huic orbi &longs;emper a&longs;si&longs;tis; ita motibus in<lb/>uigilas, vt quieti publicæ con&longs;ulas, remque ita pu<lb/>blicam admini&longs;tras, vt &longs;ingulis commoda procures: <lb/>Cæterùm dubitare non po&longs;&longs;um, quin hunc meu&mtail; <lb/>quantulumcumque conatum, fidemque meam ia&mtail; <lb/>tibi &longs;emel oppigneratam, & nunc altero voto peni<lb/>tus ob&longs;trictam, æqui bonique &longs;is con&longs;ulturus, Val&etail;.<emph.end type="italics"/></s><pb xlink:href="026/01/005.jpg"/><figure id="id.026.01.005.1.jpg" xlink:href="026/01/005/1.jpg"/>

<s id="N10087">D C. XLVI.<emph.end type="italics"/><lb/>Cum Priuilegio Regis, & Approbatione Doctorum.<emph.end type="center"/></s>

<s><emph type="center"/>PRÆFATIO.<emph.end type="center"/></s>

<s>NIHIL habeo præfari (Beneuole Lector) <lb/>in gratiam huius tractatus de Motu Locali, <lb/>cuius am&oelig;nitatem & vtilitatem, rerum co<lb/>piam & &longs;yluam, tuo gu&longs;tui & iudicio re<lb/>linquo: Multi &longs;anè hactenus in hac mate<lb/>ria feliciter de&longs;udarunt; & quidem præ cæteris magnus <lb/>ille Galileus, qui mirificâ, & ferè diuinâ ingenij acie, <lb/>motum localem eò perduxit, quò mortalium nemo per<lb/>duxerat; quia tamen multa omi&longs;it, quæ ad motum &longs;pe<lb/>ctant, vt nemo ne&longs;cit; nec ex principijs Phy&longs;icis mira<lb/>biles illos effectus demon&longs;trauit, &longs;ed tantùm certis qui<lb/>bu&longs;dam proportionibus ex geometricis addixit; vt Phy<lb/>&longs;icæ con&longs;ulamus, aliam inimus viam: Geometriam qui<lb/>dem adhibemus, ad explicandas, exponenda&longs;que præ<lb/>dictas illas proportiones, quæ motibus in&longs;unt; &longs;ed effe<lb/>ctus illos prædictis proportionibus affixos ad principia <lb/>Phy&longs;ica reducimus; id e&longs;t, cùm &longs;upponamus quòd &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 potentiæ motricis; tres enim agno&longs;cimus hu<lb/>iu&longs;modi potentias: primam naturalem voco, quæ e&longs;t <lb/>grauium: alteram animalem, quæ e&longs;t animantium: ter<lb/>tiam mediam, quæ ten&longs;orum e&longs;t vel compre&longs;&longs;orum: In <lb/>hoc tractatu tùm à motu progre&longs;&longs;iuo animantium, tùm <lb/>ab alijs motibus, qui in animato corpore, neruorum & <pb xlink:href="026/01/006.jpg"/>mu&longs;culorum opera fiunt, penitus ab&longs;tinemus; cùm &longs;ci<lb/>licèt eas notiones &longs;upponant, quæ huius loci e&longs;&longs;e non <lb/>po&longs;&longs;unt, ab&longs;tinemus etiam à mirifica illa ten&longs;orum & <lb/>compre&longs;&longs;orum vi, quæ mediæ illius virtutis e&longs;t; neque <lb/>adhuc eò rem Phy&longs;icam adduximus; Sed hîc tantùm na<lb/>turam impetus con&longs;ideramus, motus naturalis affectio<lb/>nes, violenti, mixti ex rectis, reflexi, circularis, mixti <lb/>ex circularibus, illius qui fit in planis inclinatis &longs;ur&longs;um <lb/>& deor&longs;um, vibrationum funependuli, diuer&longs;arum im<lb/>pre&longs;&longs;ionum, centri percu&longs;&longs;ionis, &c. </s>

</section>

<s>Fortè aliquis poten<lb/>tias mechanicas de&longs;ideraret, lineas, motus, & cæle&longs;tes <lb/>&longs;piras; &longs;ed hæ quidquid phy&longs;icum habent, &longs;ingulari tra<lb/>ctatui de corpore cæle&longs;ti, reliqua verò A&longs;tronomiæ con<lb/>cedunt: potentiæ mechanicæ ad Staticam pertinent, qua<lb/>re illarum tantùm phy&longs;icum principium in hoc tractatu <lb/>explicamus, lineæ 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<lb/>dum Tomum de motu locali non expectabis, qui ne <lb/>cuncta quidem, quæ ad motum &longs;pectant comprehende<lb/>ret, &longs;ed huic &longs;tatim Metaphy&longs;icam demon&longs;tratiuam &longs;ub<lb/>necto. </s>

<s id="N1009E"><emph type="center"/>AMPLISSIMO, <lb/>NOBILISSIMOQVE DOMINO,<emph.end type="center"/></s>

<s>Cæterùm de &longs;ubtili&longs;&longs;imo i&longs;torum omnium inuen<lb/>torum auctore nihil dicam, qui cum ægrè tulerit paucula <lb/>illa quæ in prima tractatu præfatus &longs;um, os mihi peni<lb/>tus ob&longs;truxit: omitto etiam quæ in me quidam iniquè <lb/>certè rerum æ&longs;timatores iactarunt: reponere po&longs;&longs;em cum <lb/>fænore; &longs;ed nos talem con&longs;uetudinem non habemus; de<lb/>dici hactenus pati iniurias, non inferre; quod non modò <lb/>moralis Philo&longs;ophia, &longs;ed præ&longs;ertim Chri&longs;tiana Religio me <lb/>docet. </s><pb xlink:href="026/01/007.jpg"/>

<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/>præ&longs;ertim cùm in a&longs;&longs;ignandis cuilibet figuræ &longs;uis chara<lb/>cteribus &longs;æpiùs peccatum &longs;it; operas excu&longs;abis in rebus <lb/>Geometricis minimè ver&longs;atos: auctor tibi &longs;um, vt errata, <lb/>quæ 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>

<s id="N100A9"><emph type="center"/>D. PETRO DE SEVE, <lb/>DOMINO DE FLECHERES, <lb/>SANCTIORIS CONSILII REGIS <lb/>Con&longs;iliario, in Lugdunen&longs;i Curia Prætori prima<lb/>rio, & &longs;ecundùm Mercatorum Præpo&longs;ito, &c.<emph.end type="center"/></s>

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

<s id="N100BA"><emph type="center"/>PETRVS MOVSNERIVS,<emph.end type="center"/></s>

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

<s>TABELLE WAR HIER</s><pb xlink:href="026/01/008.jpg"/><figure id="id.026.01.008.1.jpg" xlink:href="026/01/008/1.jpg"/>

<s id="N100C3"><emph type="italics"/>TIBI alterum no&longs;træ Philo&longs;o<lb/>phiæ f&oelig;tum in&longs;cribo, cui iam <lb/>primum in&longs;crip&longs;i<emph.end type="italics"/> (PRÆTOR <lb/>AMPLISSIME) <emph type="italics"/>nempe idem <lb/>e&longs;&longs;e debeo, quia tu &longs;emper idem <lb/>es: </s>

<s id="N100D9">non muta&longs;ti merita, non mu<lb/>tabo officia: </s>

<s><emph type="center"/><emph type="italics"/>SYNOPSIS AMPLIOR.<emph.end type="italics"/><emph.end type="center"/></s>

<s id="N100DF">multos non expo&longs;cam Patronos, qui <lb/>iam omnium optimum, & meriti&longs;simum habeo; </s>

<s id="N100E5">neo <lb/>enim &longs;acra Philo&longs;ophiæ anathemata rudi, & ru<lb/>&longs;tico muro appendam, quæ ex &longs;acro tholo templi <lb/>Themidos am&oelig;niter pendent: </s>

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

<s id="N100EF">Nec leuem toti rei li<lb/>terariæ iniuriam inferrem, &longs;i alium illi, quàm li-<emph.end type="italics"/><pb xlink:href="026/01/004.jpg"/><emph type="italics"/>teratum Mecænatem accer&longs;erem: </s>

<s id="N100FD">& verò Tracta<lb/>tum hunc de Motu Locali, alteri quàm tibi in&longs;cri<lb/>bere non debui, cuius imperia Ludgunen&longs;is orbis, po<lb/>tiùs quàm vrbis, componunt: </s>

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

<s id="N10107">Tu prudens Intelli<lb/>gentia, huic orbi &longs;emper a&longs;si&longs;tis; </s>

<s id="N1010D">ita motibus in<lb/>uigilas, vt quieti publicæ con&longs;ulas, remque ita pu<lb/>blicam admini&longs;tras, vt &longs;ingulis commoda procures: <lb/>Cæterùm dubitare non po&longs;&longs;um, quin hunc meu&mtail; <lb/>quantulumcumque conatum, fidemque meam ia&mtail; <lb/>tibi &longs;emel oppigneratam, & nunc altero voto peni<lb/>tus ob&longs;trictam, æqui bonique &longs;is con&longs;ulturus, Val&etail;.<emph.end type="italics"/></s>

<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<lb/>gitiua motus: adde quòd, potentia motrix e&longs;t acti<lb/>ua; igitur aliquid producit, &longs;ed non aliud quàm <lb/>impetum, vt con&longs;tat ex dictis de motu: e&longs;t aliquid di&longs;tinctum à <lb/>&longs;ub&longs;tantia mobilis, quæ 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 à potentia mo<lb/>trice applicata: & produci tantùm pote&longs;t, vel in omni parte, vel <lb/>in nulla; alioquin e&longs;&longs;et fru&longs;trà; & gratis ponitur ne&longs;cio quis impe<lb/>tus inefficax. </s>

</section>

<s>2. Primo in&longs;tanti, quo e&longs;t impetus, non e&longs;t motus, ne &longs;imul im<lb/>petus &longs;it in duobus locis. </s>

<s>Impetus productus ad extra non produci<lb/>tur à quantitate, nec virtute re&longs;i&longs;titiua, nec ab alio, quàm ab impe<lb/>tu, qui maximè e&longs;t cau&longs;a connaturalis alterius impetus: agit tan<lb/>tùm ad extra, vt tollat impedimentum: hinc, cùm pro diuer&longs;a <lb/>applicatione &longs;it diuer&longs;um impedimentum, modò plùs, modò minùs <lb/>agit; maximè verò, cum maximum e&longs;t impedimentum: hinc ictus <lb/>per lineam perpendicularem forti&longs;&longs;imus e&longs;t: portò omnes partes <lb/>impetus agunt ad extra actione communi. </s>

<s>3. Impetus inten&longs;us producere pote&longs;t remi&longs;&longs;um, minoris mobi<lb/>lis in maiore; & remi&longs;&longs;us inten&longs;um, maioris mobilis in minore, vt <lb/>patet; æqualis æqualem, æqualis mobilis in æquali, modò &longs;it debi-<pb xlink:href="026/01/009.jpg"/>ta applicatio, cum maximo impedimento, quod reuerâ tunc e&longs;t, <lb/>cùm linea directionis connectit centra grauitatis vtriu&longs;que. </s>

<s id="N1012B"><emph type="center"/>PRÆFATIO.<emph.end type="center"/></s>

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

<s>4. Propagatur impetus vniformiter tantùm, cùm omnes partes <lb/>corporis mouentur moctu recto æquali: ibi enim e&longs;t æqualis cau&longs;a, <lb/>vbi e&longs;t æqualis effectus: in motu circulari applicata potentia cen<lb/>tro vectis, producitur æqualis perfectionis versùs circunferentiam, <lb/>& inæqualis numerus; applicata verò potentia circunferentiæ, pro<lb/>ducitur æqualis numerus, &longs;ed inæqualis perfectionis versùs cen<lb/>trum; quia potentia non pote&longs;t producere immediatè perfectiorem, <lb/>& imperfectiorem in infinitum: eadem potentia nece&longs;&longs;aria æquali<lb/>bus temporibus, & ii&longs;dem circun&longs;tantiis, producit æqualem impe<lb/>tum, & inæqualibus inæqualem: e&longs;t enim hæc ratio cau&longs;æ nece&longs;<lb/>&longs;ariæ. </s>

<s id="N10134">NIHIL habeo præfari (Beneuole Lector) <lb/>in gratiam huius tractatus de Motu Locali, <lb/>cuius am&oelig;nitatem & vtilitatem, rerum co<lb/>piam & &longs;yluam, tuo gu&longs;tui & iudicio re<lb/>linquo: </s>

<s id="N10140">Multi &longs;anè hactenus in hac mate<lb/>ria feliciter de&longs;udarunt; </s>

<s>5. Impetus innatus e&longs;t tantùm determinatus ad lineam perpen<lb/>dicularem deor&longs;um; alioquin &longs;i ad aliam determinari po&longs;&longs;et, primo <lb/>e&longs;&longs;et æqualis motus per inclinatam, & perpendicularem; corpus <lb/>graue mi&longs;&longs;um per lineam inclinatam ab eo non declinaret; imò im<lb/>petus &longs;emel productus (&longs;i liberum e&longs;&longs;et medium) non de&longs;trueretur: <lb/>quæ 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 ferè naturæ incommoda. </s>

<s id="N10146">& quidem præ cæteris magnus <lb/>ille Galileus, qui mirificâ, & ferè diuinâ ingenij acie, <lb/>motum localem eò perduxit, quò mortalium nemo per<lb/>duxerat; </s>

<s id="N10150">quia tamen multa omi&longs;it, quæ ad motum &longs;pe<lb/>ctant, vt nemo ne&longs;cit; </s>

<s>6. Impetus indifferens determinatur ad lineam multis modis: <lb/>primò, à potentia motrice: &longs;ecundò, ab impetu: tertiò, ab alio impe<lb/>tu concurrente; quartò, ab obice occurrente: quintò, ab ip&longs;o appli<lb/>cationis diuer&longs;o modo: quæ omnia clara &longs;unt: hinc duo impetus ad <lb/>motum mixtum &longs;æpè concurrunt, quod &longs;emper fit, ni&longs;i determina<lb/>tiones &longs;int oppo&longs;itæ ex diametro. </s>

<s id="N10156">nec ex principijs Phy&longs;icis mira<lb/>biles illos effectus demon&longs;trauit, &longs;ed tantùm certis qui<lb/>bu&longs;dam proportionibus ex geometricis addixit; </s>

<s id="N1015E">vt Phy<lb/>&longs;icæ con&longs;ulamus, aliam inimus viam: </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 cæteris qualitatibus commune e&longs;t: <lb/>impetus productus non con&longs;eruatur à cau&longs;a primò productiua, à <lb/>qua etiam &longs;eparatus exi&longs;tit. </s>

<s id="N10164">Geometriam qui<lb/>dem adhibemus, ad explicandas, exponenda&longs;que præ<lb/>dictas illas proportiones, quæ motibus in&longs;unt; </s>

<s id="N1016C">&longs;ed effe<lb/>ctus illos prædictis proportionibus affixos ad principia <lb/>Phy&longs;ica reducimus; </s>

<s>7. Impetus non e&longs;t contrarius alteri ratione entitatis; quia qui<lb/>libet cum quolibet in eodem &longs;ubiecto coëxi&longs;tere pote&longs;t: pugnat <lb/>tamen vnus cum alio ratione determinationis: hinc vnus impetus <lb/>pugnat cum alio ratione lineæ motus: hinc vnus videtur de&longs;trui ab <pb xlink:href="026/01/010.jpg"/>alio; quanquam impetus tantùm de&longs;truitur, cùm e&longs;t fru&longs;trà: hinc, &longs;i <lb/>e&longs;&longs;et tantùm vnicus in eodem mobili, & liberum e&longs;&longs;et medium, <lb/>nunquam de&longs;trueretur nec vnquam dici po&longs;&longs;et functus &longs;uo mune<lb/>re; quod omninò gratis dicitur. </s>

<s id="N10174">id e&longs;t, cùm &longs;upponamus quòd &longs;int, <lb/>propter quid &longs;int demon&longs;tramus: </s>

<s id="N1017A">in votis erat motus <lb/>omnes vno volumine complecti; </s>

<s>8. Hinc, &longs;i &longs;int tantùm duo impetus in eodem mobili æquales <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 duplò velocior mo<lb/>tus; &longs;i ad diuer&longs;as, vel &longs;unt oppo&longs;itæ ex diametro, vel concurrentes <lb/>faciunt angulum; &longs;i primum, vterque de&longs;truitur impetus; &longs;i &longs;e<lb/>cundum, de&longs;truitur aliquid illius, quod determinabimus in<lb/>frà. </s>

<s id="N10180">id e&longs;t effectus omnes <lb/>cuiu&longs;uis potentiæ motricis; </s>

<s id="N10186">tres enim agno&longs;cimus hu<lb/>iu&longs;modi potentias: </s>

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

<s id="N1018C">primam naturalem voco, quæ e&longs;t <lb/>grauium: </s>

<s id="N10192">alteram animalem, quæ e&longs;t animantium: </s>

<s>Porrò <lb/>nunquam de&longs;truitur; quia nunquam e&longs;t fru&longs;trà; quippe eius finis, <lb/>vel v&longs;us, non e&longs;t tantùm motus deor&longs;um, &longs;ed grauitatio, &longs;eu ni&longs;us <lb/>quidam deor&longs;um. </s>

<s id="N10196">ter<lb/>tiam mediam, quæ ten&longs;orum e&longs;t vel compre&longs;&longs;orum: </s>

<s id="N1019C">In <lb/>hoc tractatu tùm à motu progre&longs;&longs;iuo animantium, tùm <lb/>ab alijs motibus, qui in animato corpore, neruorum & <pb xlink:href="026/01/006.jpg"/>mu&longs;culorum opera fiunt, penitus ab&longs;tinemus; </s>

<s>Sed de grauitate aliàs. </s><figure id="id.026.01.010.1.jpg" xlink:href="026/01/010/1.jpg"/>

<s id="N101A8">cùm &longs;ci<lb/>licèt eas notiones &longs;upponant, quæ huius loci e&longs;&longs;e non <lb/>po&longs;&longs;unt, ab&longs;tinemus etiam à mirifica illa ten&longs;orum & <lb/>compre&longs;&longs;orum vi, quæ mediæ illius virtutis e&longs;t; </s>

<s id="N101B2">neque <lb/>adhuc eò rem Phy&longs;icam adduximus; Sed hîc tantùm na<lb/>turam impetus con&longs;ideramus, motus naturalis affectio<lb/>nes, violenti, mixti ex rectis, reflexi, circularis, mixti <lb/>ex circularibus, illius qui fit in planis inclinatis &longs;ur&longs;um <lb/>& deor&longs;um, vibrationum funependuli, diuer&longs;arum im<lb/>pre&longs;&longs;ionum, centri percu&longs;&longs;ionis, &c. </s>

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

<s id="N101C2">Fortè aliquis poten<lb/>tias mechanicas de&longs;ideraret, lineas, motus, & cæle&longs;tes <lb/>&longs;piras; </s>

<s id="N101CA">&longs;ed hæ quidquid phy&longs;icum habent, &longs;ingulari tra<lb/>ctatui de corpore cæle&longs;ti, reliqua verò A&longs;tronomiæ con<lb/>cedunt: potentiæ mechanicæ ad Staticam pertinent, qua<lb/>re illarum tantùm phy&longs;icum principium in hoc tractatu <lb/>explicamus, lineæ motus nihil phy&longs;icum habent. </s>

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

<s id="N101D6">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<lb/>dum Tomum de motu locali non expectabis, qui ne <lb/>cuncta quidem, quæ ad motum &longs;pectant comprehende<lb/>ret, &longs;ed huic &longs;tatim Metaphy&longs;icam demon&longs;tratiuam &longs;ub<lb/>necto. </s>

<s id="N101E6">Cæterùm de &longs;ubtili&longs;&longs;imo i&longs;torum omnium inuen<lb/>torum auctore nihil dicam, qui cum ægrè tulerit paucula <lb/>illa quæ in prima tractatu præfatus &longs;um, os mihi peni<lb/>tus ob&longs;truxit: </s>

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

<s id="N101F0">omitto etiam quæ in me quidam iniquè <lb/>certè rerum æ&longs;timatores iactarunt: </s>

<s id="N101F6">reponere po&longs;&longs;em cum <lb/>fænore; </s>

<s>E&longs;t autem motus naturalis ab <lb/>impetu: primò, quia eius acceleratio &longs;ine impetu explicari non po<lb/>te&longs;t: &longs;ecundò, quia, cùm graue deor&longs;um cadens imprimat impetum <lb/>in corpore occurrente, certè debet habere impetum: nec alio ar<lb/>gumento mihi probabis, Solem e&longs;&longs;e lucidum, ignem calidum. </s>

<s id="N101FC">&longs;ed nos talem con&longs;uetudinem non habemus; </s>

<s id="N10200">de<lb/>dici hactenus pati iniurias, non inferre; quod non modò <lb/>moralis Philo&longs;ophia, &longs;ed præ&longs;ertim Chri&longs;tiana Religio me <lb/>docet. </s>

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

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

<s id="N1020F">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/>præ&longs;ertim cùm in a&longs;&longs;ignandis cuilibet figuræ &longs;uis chara<lb/>cteribus &longs;æpiùs peccatum &longs;it; </s>

<s>igitur cre&longs;cit <lb/>cau&longs;a motus; igitur & motus: quæ ratio clari&longs;&longs;ima e&longs;t: hinc æquali<lb/>bus temporibus æqualia acquiruntur velocitatis momenta; quia <lb/>cau&longs;a nece&longs;&longs;aria æqualibus temporibus, æqualem effectum produ<lb/>cit: quid clarius? </s>

<s id="N10219">operas excu&longs;abis in rebus <lb/>Geometricis minimè ver&longs;atos: auctor tibi &longs;um, vt errata, <lb/>quæ 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>

<s>3. Hinc non pote&longs;t cre&longs;cere hic impetus &longs;ecundùm porportio-<pb xlink:href="026/01/011.jpg"/>nem duplicatam temporum, cùm cre&longs;cat &longs;ecundùm proportionem <lb/>temporum, etïam ex mente Galilei: cre&longs;cit autem velocitas, vt im<lb/>petus; effectus, &longs;cilicet, vt cau&longs;a: idem dico de motu, ratione velo<lb/>citatis; quippe motus ip&longs;e e&longs;t &longs;ua velocitas: at verò ip&longs;a &longs;patia, <lb/>quæ decurruntur illo motu, &longs;i con&longs;ideretur crementum in in&longs;tan<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<lb/>tur vnum &longs;patium, &longs;ecundo acquiruntur duo, tertio 3. quarto 4. at<lb/>que ita deinceps. </s>

<s id="N10228"><emph type="center"/><emph type="italics"/>SYNOPSIS LIBRORVM<emph.end type="italics"/><emph.end type="center"/></s>

<s>4. Hoc autem facilè pote&longs;t <expan abbr="demõ&longs;trari">demon&longs;trari</expan>: quia, cùm velocitas cre&longs;<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, certè <lb/>cum duobus acquiret duo &longs;patia, cum tribus tria, atque ita dein<lb/>ceps: debet autem vera progre&longs;&longs;io crementorum a&longs;&longs;umi in &longs;ingulis <lb/>in&longs;tantibus, quia reuerà &longs;ingulis in&longs;tantibus phy&longs;icis (nam de iis <lb/>loquor) noua fit huius crementi acce&longs;&longs;io. </s>

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

<s id="N10235"><emph type="center"/><emph type="italics"/>huius tractatus.<emph.end type="italics"/><emph.end type="center"/></s>

<s>quam Galileus excogitauit, vt &longs;ine &longs;crupulo hæc a&longs;<lb/>&longs;umi po&longs;&longs;it: hinc &longs;patia &longs;unt ferè vt temporum quadrata: dixi, ferè: <lb/>nam e&longs;t paulò minor proportio, cùm tantùm finita &longs;int in&longs;tantia <lb/>phy&longs;ica, quæ reuerà &longs;i infinita e&longs;&longs;ent in qualibet temporis &longs;en&longs;ibilis <lb/>parte, haud dubiè &longs;patia e&longs;&longs;ent omninò in ratione duplicata tem<lb/>porum: &longs;ed, quia parum pro nihilo computatur, hanc progre&longs;&longs;io<lb/>nem Galilei deinceps v&longs;urpabimus in Phy&longs;ica. </s>

<s id="N10242">TABELLE WAR HIER</s>

<s>6. Hinc ratio euidens maioris ictus inflicti à corpore graui, <lb/>cùm ex maiori altitudine cadit. </s>

</section>

<s>Sunt autem ictus, vt impetus; <lb/>impetus, vt tempora; hæc demum, vt radices &longs;patiorum &longs;en&longs;ibi<lb/>liter quæ 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, quæ reuerâ <lb/>&longs;unt &longs;emper minora; quia motus fit &longs;emper velocior: cùm graue <lb/>de&longs;cendit in medio, quod re&longs;i&longs;tit, minùs accuratè &longs;eruantur prædi<lb/>ctæ proportiones, quæ in vacuo modico accurati&longs;&longs;imè &longs;eruaren<lb/>tur. </s>

<s>7. Re&longs;i&longs;tentia medij non e&longs;t propter vllam formam improportio<lb/>natam, qua&longs;i verò impetus &longs;it forma improportionata aëri: &longs;ed in <pb xlink:href="026/01/012.jpg"/>duobus præ&longs;ertim con&longs;i&longs;tit; primò, eò quòd medium detrahat ali<lb/>quid grauitationis corporis grauis; &longs;ecundò, eò quòd partes medij <lb/>aliquam implicationem habeant, quæ &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 æqualis grauitatis cum ip&longs;o cor<lb/>pore, detrahitur tota grauitatio, &longs;i &longs;ubduplæ &longs;ubduplum, &c. </s>

<s id="N10251"><emph type="center"/><emph type="italics"/>SYNOPSIS AMPLIOR.<emph.end type="italics"/><emph.end type="center"/></s>

<s>de quo <lb/>aliàs. </s>

<s id="N1025F">BREVISSIMAM huius operis Epitomem hîc <lb/>habes (Amice Lector) quam ex The&longs;ibus no&longs;tri <lb/>Philo&longs;ophi huc traduxi, quæ tibi ampli&longs;&longs;imi <lb/>indicis loco erit. </s>

<s>8. Hinc corpus graue per medium rarius, cæteris paribus, fa<lb/>cilè de&longs;cendit; non tamen ex re&longs;i&longs;tentia medij cognita, pote&longs;t co<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<lb/>e&longs;t grauius, vel æquè graue, vel minùs. </s>

<s id="N1026F"><emph type="center"/><emph type="italics"/>De Impetu.<emph.end type="italics"/><emph.end type="center"/></s>

<s>Sunt etiam tres aliæ con<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>

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

<s id="N1027C">1. IMPETVS e&longs;t qualitas exigens motum &longs;ui &longs;ubiecti: </s>

<s id="N10280"><lb/>datur impetus; </s>

<s>Cubus, qui de&longs;cendit, imprimit aëri velociorem motum, <lb/>quàm ip&longs;e habeat; & quò maior e&longs;t eius &longs;uperficies, eò velociorem. </s>

<s id="N10285">quia non pote&longs;t e&longs;&longs;e alia cau&longs;a exi<lb/>gitiua motus: </s>

<s id="N1028B">adde quòd, potentia motrix e&longs;t acti<lb/>ua; </s>

<s>10. Duo globi, vel cubi eiu&longs;dem materiæ æquè velociter de&longs;<lb/>cendunt: ratio e&longs;t, quia, licèt maioris vires habeant maiorem pro<lb/>portionem ad molem aëris re&longs;i&longs;tentis, quàm vires minoris ad alte<lb/>ram aëris molem, quæ proprium illius motum retardat, cùm tamen <lb/>aër, qui re&longs;i&longs;tit maiori cubo, debeat amoueri velociori motu, quàm <lb/>aër, qui re&longs;i&longs;tit minori, &longs;itque eadem proportio re&longs;i&longs;tentiæ ratione <lb/>motus, minoris ad maiorem, quæ e&longs;t ratione molis, maioris ad mi<lb/>norem; certè ratio compo&longs;ita vtriu&longs;que erit eadem in vtroque cu<lb/>bo: igitur æqualiter de&longs;cendet vterque. </s>

<s id="N10291">igitur aliquid producit, &longs;ed non aliud quàm <lb/>impetum, vt con&longs;tat ex dictis de motu: </s>

<s id="N10297">e&longs;t aliquid di&longs;tinctum à <lb/>&longs;ub&longs;tantia mobilis, quæ pote&longs;t e&longs;&longs;e &longs;ine impetu: </s>

<s>11. Si tamen &longs;int diuer&longs;æ materiæ, haud dubiè, qui con&longs;tat leuio<lb/>ri materia, tardiùs de&longs;cendet; quia eius vires habent minorem <lb/>proportionem ad re&longs;i&longs;tentiam. </s>

<s id="N1029D">non e&longs;t modus, <lb/>quia di&longs;tinguitur ab effectu &longs;uo formali &longs;ecundario: </s>

<s id="N102A3">impetus non <lb/>producitur in eo mobili, quod moueri non pote&longs;t à potentia mo<lb/>trice applicata: </s>

<s>Corpu&longs;cula etiam ex graui&longs;&longs;ima ma<lb/>teria tardi&longs;&longs;imè de&longs;cendunt: tum, quia à filamentis illis, quibus par<lb/>tes aëris implicantur, facilè detinentur; analogiam habes in lapil<lb/>lo, qui ab araneæ tela intercipitur: tum, quia, cùm lati&longs;&longs;imam ali<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;tentiã">re&longs;i&longs;tentiam</expan>: tùm denique, quia, cùm modico <lb/>impetu agitari po&longs;&longs;int ab aëre mobili, vnus motus alium impedit. </s>

<s id="N102AB">& produci tantùm pote&longs;t, vel in omni parte, vel <lb/>in nulla; </s>

<s id="N102B1">alioquin e&longs;&longs;et fru&longs;trà; & gratis ponitur ne&longs;cio quis impe<lb/>tus inefficax. </s>

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

<s>Hinc <lb/>colligo, contra Galilæum, motum rectum ex naturaliter accelerato <lb/>nunquam fieri æquabilem: dixi motum rectum; quia motus corpo<lb/>rum c&oelig;le&longs;tium ex accelerato factus e&longs;t æqualis. </s><figure id="id.026.01.013.1.jpg" xlink:href="026/01/013/1.jpg"/>

<s id="N102B9">2. Primo in&longs;tanti, quo e&longs;t impetus, non e&longs;t motus, ne &longs;imul im<lb/>petus &longs;it in duobus locis. </s>

<s id="N102BE">Impetus productus ad extra non produci<lb/>tur à quantitate, nec virtute re&longs;i&longs;titiua, nec ab alio, quàm ab impe<lb/>tu, qui maximè e&longs;t cau&longs;a connaturalis alterius impetus: </s>

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

<s id="N102C6">agit tan<lb/>tùm ad extra, vt tollat impedimentum: </s>

<s id="N102CC">hinc, cùm pro diuer&longs;a <lb/>applicatione &longs;it diuer&longs;um impedimentum, modò plùs, modò minùs <lb/>agit; </s>

<s>1. MOtus violentus &longs;ur&longs;um vulgò dicitur e&longs;&longs;e à principio ex<lb/>trin&longs;eco. </s>

<s id="N102D4">maximè verò, cum maximum e&longs;t impedimentum: </s>

<s id="N102D8">hinc ictus <lb/>per lineam perpendicularem forti&longs;&longs;imus e&longs;t: portò omnes partes <lb/>impetus agunt ad extra actione communi. </s>

<s>Triplici modo accidere pote&longs;t: primò, &longs;i reuerà <lb/>imprimatur impetus ab extrin&longs;eco, vt, cùm mitto lapidem &longs;ur&longs;um: <lb/>&longs;ecundò, &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, quæ e&longs;t à cor<lb/>pore reflectente: tertiò, &longs;i terra vtrinque e&longs;&longs;et peruia; nam lapis haud <lb/>dubiè 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<lb/>trin&longs;ecum; igitur motus violentus dicit tantùm motum &longs;ur&longs;um <lb/>corporis grauis. </s>

<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 reuerâ ine&longs;t ip&longs;i mobili, cùm ip&longs;um medium hunc <lb/>motum potiùs impediat, quàm 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<lb/>petus innatus illius cau&longs;a e&longs;&longs;e non pote&longs;t. </s>

<s id="N102E2">3. Impetus inten&longs;us producere pote&longs;t remi&longs;&longs;um, minoris mobi<lb/>lis in maiore; </s>

<s id="N102E8">& remi&longs;&longs;us inten&longs;um, maioris mobilis in minore, vt <lb/>patet; æqualis æqualem, æqualis mobilis in æquali, modò &longs;it debi-<pb xlink:href="026/01/009.jpg"/>ta applicatio, cum maximo impedimento, quod reuerâ tunc e&longs;t, <lb/>cùm linea directionis connectit centra grauitatis vtriu&longs;que. </s>

<s>Portò hic motus non e&longs;t <lb/>acceleratus, nec æqualis, alioquin <expan abbr="nunquã">nunquam</expan> rediret deor&longs;um mobile. </s>

<s id="N102F4">Datur <lb/>impetus alio impetu perfectior, & imperfectior, &longs;ine quo non po<lb/>te&longs;t explicari natura vectis: </s>

<s id="N102FC">itaque dato quocunque dari pote&longs;t per<lb/>fectior, & imperfectior: quia dato quocunque motu pote&longs;t dari ve<lb/>locior, & tardior. </s>

<s>3. Hinc nece&longs;&longs;ariò 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, quàm motui deor&longs;um, vt patet: igitur de&longs;trui<lb/>tur ille impetus motus violenti ab impetu innato aliquo modo; non <lb/>quidem vt à contrario ratione entitatis, &longs;ed ratione determinatio<lb/>nis: cùm enim impetus innatus exigat motum deor&longs;um, & alius &longs;ur<lb/>&longs;um: hic quidem præualet, attamen fru&longs;trà e&longs;t, ratione gradus <lb/>æqualis impetui innato: igitur de&longs;truitur ille gradus illo in&longs;tanti. </s><pb xlink:href="026/01/014.jpg"/>

<s>4. Hinc &longs;ingulis temporibus æqualibus de&longs;truitur gradus impe<lb/>tui innato; e&longs;t enim eadem ratio pro omnibus: igitur temporibus <lb/>æqualibus de&longs;truitur æqualis impetus: igitur amittit ille motus <lb/>æqualia velocitatis momenta: igitur e&longs;t naturaliter retardatus: igi<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<lb/>nis, quæ dicta &longs;unt de illa progre&longs;&longs;ione accelerationis. </s>

<s id="N10306">4. Propagatur impetus vniformiter tantùm, cùm omnes partes <lb/>corporis mouentur moctu recto æquali: </s>

<s id="N1030C">ibi enim e&longs;t æqualis cau&longs;a, <lb/>vbi e&longs;t æqualis effectus: </s>

<s>5. Hinc impetus imperfectior initio de&longs;truitur: quia, cùm motus <lb/>ille &longs;it velocior initio, in&longs;tantia &longs;unt minora: atqui minori tempore <lb/>minùs retardatur: igitur inperfectior impetus de&longs;truitur; cùm è <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<lb/>neos, & principium illud etiam in impetu valere, &longs;cilicet, &longs;ubiectum <lb/>ita compleri ab vna forma, vt alterius homogeneæ non &longs;it ampliùs <lb/>capax, &longs;altem naturaliter. </s>

<s id="N10312">in motu circulari applicata potentia cen<lb/>tro vectis, producitur æqualis perfectionis versùs circunferentiam, <lb/>& inæqualis numerus; </s>

<s id="N1031A">applicata verò potentia circunferentiæ, pro<lb/>ducitur æqualis numerus, &longs;ed inæqualis perfectionis versùs cen<lb/>trum; </s>

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

<s id="N10322">quia potentia non pote&longs;t producere immediatè perfectiorem, <lb/>& imperfectiorem in infinitum: </s>

<s id="N10328">eadem potentia nece&longs;&longs;aria æquali<lb/>bus temporibus, & ii&longs;dem circun&longs;tantiis, producit æqualem impe<lb/>tum, & inæqualibus inæqualem: e&longs;t enim hæc ratio cau&longs;æ nece&longs;<lb/>&longs;ariæ. </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 æqualis perfectionis, cum impetu in<lb/>nato: vbi enim ventum e&longs;&longs;et ad in&longs;tans æqualitatis, neutrum præ<lb/>ualere po&longs;&longs;et: igitur in&longs;tanti &longs;equenti e&longs;&longs;et quies: cùm tamen &longs;int <lb/>diuer&longs;æ perfectionis, perfectior præualet: vter autem &longs;it perfectior, <lb/>dicemus infrà. </s>

<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/>æqualis ponderis, vel maioris, &longs;ur&longs;um mouet, tunc certum e&longs;t, inna<lb/>tum e&longs;&longs;e perfectiorem: &longs;i verò imprimitur ab alia potentia motrice, <lb/>tunc etiam imperfectior e&longs;t impetu innato; nam inæqualis e&longs;t; alio<lb/>quin, &longs;i e&longs;&longs;et æqualis, &longs;imul e&longs;&longs;ent in eodem &longs;ubiecto duo gradus <lb/>homogenei: præ&longs;tat autem e&longs;&longs;e imperfectiorem, quàm perfectio<lb/>rem, vt plura impetus puncta à potentia imprimantur; quòd mul<lb/>tum facit ad mouenda maiora pondera: hinc nullo in&longs;tanti quie&longs;<lb/>cunt proiecta &longs;ur&longs;um. </s>

<s id="N10334">5. Impetus innatus e&longs;t tantùm determinatus ad lineam perpen<lb/>dicularem deor&longs;um; </s>

<s id="N1033A">alioquin &longs;i ad aliam determinari po&longs;&longs;et, primo <lb/>e&longs;&longs;et æqualis motus per inclinatam, & perpendicularem; </s>

<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;agittæ verò mi<lb/>nùs durat a&longs;cen&longs;us, quàm de&longs;cen&longs;us propter mixtionem materiæ. </s>

<s id="N10340">corpus <lb/>graue mi&longs;&longs;um per lineam inclinatam ab eo non declinaret; </s>

<s id="N10346">imò im<lb/>petus &longs;emel productus (&longs;i liberum e&longs;&longs;et medium) non de&longs;trueretur: </s>

<s><lb/>Si motus violentus e&longs;&longs;et æquabilis, percurreret proiectum &longs;patium <lb/>ferè duplum eo tempore, quo retardato percurrit &longs;ubduplum: hinc <lb/>&longs;onus tam citò auditur; quia propagatur cum particulis aëris æqua<lb/>bili ferè motu: e&longs;&longs;e autem &longs;patium ferè duplum, probatur ex eo, <pb xlink:href="026/01/015.jpg"/>quòd &longs;patium motu æquabili decur&longs;um re&longs;pondet rectangulo; de<lb/>cur&longs;um verò motu retardato, re&longs;pondet triangulo, &longs;ubduplo rectan<lb/>guli: a&longs;&longs;umpto &longs;cilicet, æquali tempore. </s>

<s id="N1034C"><lb/>quæ 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 ferè naturæ incommoda. </s>

<s>9. Vites potentiæ proiicientis toto ni&longs;u re&longs;pondent velocitati <lb/>acqui&longs;itæ in toto de&longs;cen&longs;u corporis proiecti; tantumdem enim <lb/>impetus in de&longs;cen&longs;u acquiritur, quantùm in a&longs;cen&longs;u deperditur. </s>

<s id="N10357">6. Impetus indifferens determinatur ad lineam multis modis: <lb/>primò, à potentia motrice: </s>

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

<s id="N1035D">&longs;ecundò, ab impetu: </s>

<s id="N10361">tertiò, ab alio impe<lb/>tu concurrente; quartò, ab obice occurrente: </s>

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

<s id="N10367">quintò, ab ip&longs;o appli<lb/>cationis diuer&longs;o modo: quæ omnia clara &longs;unt: hinc duo impetus ad <lb/>motum mixtum &longs;æpè concurrunt, quod &longs;emper fit, ni&longs;i determina<lb/>tiones &longs;int oppo&longs;itæ ex diametro. </s>

<s id="N10371">Impetus e&longs;t capax inten&longs;ionis; </s>

<s>1. PLanum inclinatum e&longs;t &longs;ur&longs;um, vel deor&longs;um: in hoc de&longs;cen<lb/>dit corpus graue, ni&longs;i fortè retineatur ab a&longs;peritate, vel pro<lb/>pria, vel ip&longs;ius plani: impeditur autem motus naturalis in plano <lb/>prædicto, quia impeditur eius linea: ideò e&longs;t tardior hic motus in <lb/>plano inclinato, quàm in perpendiculari: in ea porrò proportione <lb/>e&longs;t tardior, in qua perpendiculum e&longs;t minus linea inclinata, eiu&longs;dem <lb/>&longs;cilicet, altitudinis; quippe eò tardior e&longs;t, quò magis impeditur, & <lb/>magis impeditur, quò maius &longs;patium decurrendum e&longs;t, ad acqui<lb/>rendam eandem altitudinem: igitur eadem e&longs;t proportio impe<lb/>dimenti, quæ &longs;patij, &c. </s>

<s id="N10375"><lb/>quia aliquando de&longs;truitur ex parte: </s>

<s id="N1037A">eius exten&longs;io commen&longs;uratur <lb/>exten&longs;ioni mobilis; </s>

<s>2. Hinc motus &longs;unt vt lineæ permutando: hinc mobile de&longs;cendit <lb/>per &longs;e in prædicto plano: licet enim motus impediatur, non tamen <lb/><expan abbr="tous">totus</expan>, impetus, qui acquiritur in eodem plano e&longs;t imperfectior ac<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, cùm <lb/>po&longs;&longs;it e&longs;&longs;e in infinitum linea magis, ac magis inclinata: igitur mo<lb/>tum imminui po&longs;&longs;e in infinitum, non tantùm ex vecte, &longs;ed etiam <lb/>ex planis inclinatis haberi pote&longs;t. </s>

<s id="N10380">quod etiam cæteris qualitatibus commune e&longs;t: <lb/>impetus productus non con&longs;eruatur à cau&longs;a primò productiua, à <lb/>qua etiam &longs;eparatus exi&longs;tit. </s>

<s>3. Hinc producit impetum imperfectiorem impetus acqui&longs;itus <lb/>in hoc eodem plano, quàm acqui&longs;itus in perpendiculari, æqualibus <lb/>&longs;cilicet temporibus, quia cau&longs;a imperfectior imperfectiorem pro<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, & linea plani <lb/>inclinati, &longs;unt vt lineæ; &longs;patia autem, quæ in prædictis lineis acqui<lb/>runtur æqualibus temporibus, &longs;unt vt motus, id e&longs;t, vt lineæ per<lb/>mutando, vt patet ex dictis. </s>

<s id="N1038A">7. Impetus non e&longs;t contrarius alteri ratione entitatis; </s>

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

<s id="N1038E">quia qui<lb/>libet cum quolibet in eodem &longs;ubiecto coëxi&longs;tere pote&longs;t: </s>

<s id="N10394">pugnat <lb/>tamen vnus cum alio ratione determinationis: </s>

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

<s id="N1039A">hinc vnus impetus <lb/>pugnat cum alio ratione lineæ motus: </s>

<s id="N103A0">hinc vnus videtur de&longs;trui ab <pb xlink:href="026/01/010.jpg"/>alio; </s>

<s>Vires, quæ &longs;u&longs;tinent pondus in plano in<lb/>clinato per lineam plano <expan abbr="parallelã">parallelam</expan>, &longs;unt ad eas, quæ &longs;u&longs;tinent in per<lb/>pendiculo, vt lineæ permutando; quia debent adæquare impetum, <lb/>qui producitur, tùm in plano inclinato, tùm in perpendiculo. </s>

<s id="N103A8">quanquam impetus tantùm de&longs;truitur, cùm e&longs;t fru&longs;trà: </s>

<s id="N103AC">hinc, &longs;i <lb/>e&longs;&longs;et tantùm vnicus in eodem mobili, & liberum e&longs;&longs;et medium, <lb/>nunquam de&longs;trueretur nec vnquam dici po&longs;&longs;et functus &longs;uo mune<lb/>re; quod omninò gratis dicitur. </s>

<s>5. Porrò minùs grauitat in ip&longs;um planum inclinatum corpus gra<lb/>ue, quàm in planum horizontale: e&longs;t autem grauitatio in horizonta<lb/>li, &longs;eu Tangente, ad grauitationem in inclinata, &longs;eu &longs;ecante, vt ip&longs;æ <lb/>lineæ permutando: quod facilè demon&longs;tramus. </s>

<s>Proiicitur mobile <lb/>faciliùs per inclinatum planum &longs;ur&longs;um, quàm per ip&longs;am perpendi<lb/>cularem: patet experientia: cuius ratio e&longs;t, quia minùs re&longs;i&longs;tit im<lb/>petus innatus, cuius minor e&longs;t ni&longs;us per inclinatam, vt con&longs;tat ex <lb/>dictis. </s>

<s id="N103B8">8. Hinc, &longs;i &longs;int tantùm duo impetus in eodem mobili æquales <lb/>verbi gratia, vel ad eandem lineam determinantur, vel ad diver&longs;as; </s>

<s id="N103BE"><lb/>&longs;i ad eandem, nihil impetus de&longs;truitur, &longs;ed e&longs;t duplò velocior mo<lb/>tus; </s>

<s>6. Illæ vires, quæ &longs;ufficiunt ad eum motum &longs;ur&longs;um in perpendi<lb/>culo, &longs;ufficiunt ad motum &longs;ur&longs;um in plano inclinato eiu&longs;dem alti<lb/>tudinis: quia illæ vires &longs;ufficiunt ad a&longs;cen&longs;um, quæ acquiruntur in <lb/>toto de&longs;cen&longs;u: &longs;ed in de&longs;cen&longs;u inclinatæ, & perpendiculi acquirun<lb/>tur vires æquales, id e&longs;t, velocitas æqualis, vt dictum e&longs;t &longs;uprà. </s>

<s id="N103C5">&longs;i ad diuer&longs;as, vel &longs;unt oppo&longs;itæ ex diametro, vel concurrentes <lb/>faciunt angulum; </s>

<s id="N103CB">&longs;i primum, vterque de&longs;truitur impetus; &longs;i &longs;e<lb/>cundum, de&longs;truitur aliquid illius, quod determinabimus in<lb/>frà. </s>

<s>Om<lb/>nia puncta plani inclinati rectilinei, imò & horizontalis, &longs;unt di<lb/>uer&longs;æ inclinationis: in iis tamen planis inclinatis quæ vulgò a&longs;&longs;u<lb/>muntur, non mutatur &longs;en&longs;ibiliter inclinatio. </s>

<s id="N103D3">Impetus innatus nunquam de&longs;truitur: </s>

<s id="N103D7">dici po&longs;&longs;et grauitas ab<lb/>&longs;oluta; &longs;altem nihil e&longs;t, quod di&longs;tingui ab illa probare po&longs;&longs;it. </s>

<s>7. Hinc minùs de&longs;truitur impetus in plano inclinato &longs;ur&longs;um, <lb/>quàm in perpendiculo; quia diutiùs durat: cùm enim minùs ac<lb/>quiratur in de&longs;cen&longs;u, vt dictum e&longs;t, minùs etiam de&longs;truitur in a&longs;<lb/>cen&longs;u: hinc accedit propriùs hic motus ad æquabilem: in eodem <lb/>plano rectilineo pote&longs;t e&longs;&longs;e a&longs;cen&longs;us, & de&longs;cen&longs;us, versùs eandem <lb/>partem: tale e&longs;&longs;et planum horizontale, in cuius vnico tantùm pun<lb/>cto nulla e&longs;t inclinatio: in quolibet puncto huius plani e&longs;t &longs;ingu<lb/>laris inclinatio, vt patet, quæ e&longs;t ad perpendiculum, vt Tangens ad <lb/>&longs;ecantem é&longs;tque eadem proportio motuum. </s>

<s id="N103DD">Porrò <lb/>nunquam de&longs;truitur; </s>

<s id="N103E2">quia nunquam e&longs;t fru&longs;trà; quippe eius finis, <lb/>vel v&longs;us, non e&longs;t tantùm motus deor&longs;um, &longs;ed grauitatio, &longs;eu ni&longs;us <lb/>quidam deor&longs;um. </s>

<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 æqualibus temporibus, acquiruntur æqualia <lb/>velocitatis momenta; quia in &longs;ingulis punctis quadrantis, e&longs;t diuer<lb/>&longs;a tangens; igitur mutatur progre&longs;&longs;io accelerationis, quæ certè ma<lb/>jor e&longs;t initio, & &longs;ub finem minor; quia initio tangentes acce<lb/>dunt propriùs ad perpendiculum, & &longs;ub finem ad horizonta<lb/>lem. </s>

<s id="N103EA">Sed de grauitate aliàs. </s>

<s>9. De&longs;cendit etiam in &longs;uperficie conuexa globi erecti motu ac<lb/>celerato; initio quidem, in minore proportione; &longs;ub finem, in maio<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 terræ motu accelerato, in &longs;uperficie conuexa &longs;e<lb/>micirculi: &longs;i &longs;uperficies terræ e&longs;&longs;et læuigati&longs;&longs;ima, corpus proje<lb/>ctum moueretur in ea motu æquabili, nec de&longs;trueretur impetus im<lb/>pre&longs;&longs;us, vt con&longs;tat; pote&longs;t quoque de&longs;cendere per &longs;piralem: &longs;unt in<lb/>finita plana curua, in quibus faciliùs moueri pote&longs;t, quam in ho<lb/>rizontali recta. </s><figure id="id.026.01.017.1.jpg" xlink:href="026/01/017/1.jpg"/>

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

<s id="N103F4"><emph type="center"/><emph type="italics"/>De motu naturali deor&longs;um.<emph.end type="italics"/><emph.end type="center"/></s>

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

<s id="N10401">1. DAtur motus naturalis grauium deor&longs;um ab intrin&longs;eco, <lb/>quippe non pote&longs;t e&longs;&longs;e, vel à vi tractrice terræ vel fila<lb/>mentis quibu&longs;dam, vel materia quadam tenui expultrice. </s>

<s><lb/>Mixtus ex duobus rectis æquabilibus e&longs;t rectus, e&longs;t que <lb/>diagonalis vtriu&longs;que: hinc de&longs;truitur aliquid impetus, iuxta pro<lb/>portionem differentiæ diagonalis, & vtriu&longs;que lateris &longs;imul &longs;ump<lb/>ti; quia, &longs;cilicet, e&longs;t fru&longs;trà: quò maior e&longs;t angulus, quem faciunt li<lb/>neæ determinationum, minor e&longs;t diagonalis; igitur plùs impetus <lb/>de&longs;truitur, donec tandem concurrant in oppo&longs;itas lineas, tunc enim <lb/>totius impetus de&longs;truitur. </s>

<s id="N10408">Eius finis <lb/>e&longs;t globi terre&longs;tris compactio, &c. </s>

<s id="N1040D">E&longs;t autem motus naturalis ab <lb/>impetu: </s>

<s>2. <expan abbr="Qu&utilde;">Quum</expan> minor e&longs;t, vel acutior prædictus angulus, minùs 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<lb/>tus in rerum natura; talis e&longs;t motus nauis à duobus ventis impre&longs;<lb/>&longs;us; vel eiu&longs;dem partis aëris; imò & 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>

<s id="N10413">primò, quia eius acceleratio &longs;ine impetu explicari non po<lb/>te&longs;t: </s>

<s id="N10419">&longs;ecundò, quia, cùm graue deor&longs;um cadens imprimat impetum <lb/>in corpore occurrente, certè debet habere impetum: nec alio ar<lb/>gumento mihi probabis, Solem e&longs;&longs;e lucidum, ignem calidum. </s>

<s>3. Si mixtus &longs;it ex æquali, & accelerato, vel ex duobus accelera<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, & <lb/>retardato violento: e&longs;t enim acceleratus naturalis, cùm deor&longs;um <lb/>deor&longs;um tendat qua&longs;i per gradus, &longs;eu diuer&longs;a plana inclinata. </s>

<s>4. Non tamen impetus acqui&longs;itus in eo motu e&longs;t eiu&longs;dem perfe<lb/>ctionis cum illo, qui acquireretur in perpendiculari eiu&longs;dem longi<lb/>tudinis; &longs;ed tantùm eiu&longs;dem altitudinis: nam perinde cre&longs;cit ille <lb/>impetus, atque cre&longs;ceret in diuer&longs;is planis inclinaris: impetus verò <lb/>violentus in hoc motu retardatur; tùm, 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, quòd aliqui <lb/>dicant, ab aëre de&longs;trui, qui non minùs re&longs;i&longs;tit naturali, quàm vio<lb/>lento. </s>

<s id="N10423">2. Motus hic e&longs;t naturaliter acceleratus, &longs;cilicet, ab intrin&longs;eco; <lb/>patet experientiâ. </s>

<s id="N10429">Ratio e&longs;t: </s>

<s>5. Adde, quòd e&longs;t duplex determinatio: igitur aliquid de&longs;trui de<lb/>bet, non acqui&longs;iti; igitur impre&longs;&longs;i: de&longs;trui autem non dicitur acqui<lb/>&longs;itus, quòd, &longs;cilicet, plùs de nouo accedat, quàm pereat; e&longs;t enim ac<lb/>celeratus: adde, quòd 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 æquabili per ali<lb/>quod &longs;patium qua&longs;i haberi po&longs;&longs;it. </s>

<s id="N1042C">quia, cùm in libero medio non impe<lb/>diatur motus, & impetus productus primo in&longs;tanti non con&longs;erue<lb/>tur &longs;ecundo à cau&longs;a primò productiua, &longs;ed ab alia, &longs;itque ip&longs;a mo<lb/>bilis &longs;ub&longs;tantia cau&longs;a nece&longs;&longs;aria; </s>

<s id="N10436">certè &longs;ecundo in&longs;tanti producit <lb/>nouum impetum: idem dica de tertio, quarto, &c. </s>

<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<lb/>tus: tardiùs cadit mobile ita proiectum in planùm horizontale &longs;ub<lb/>iectum, quàm 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, cùm acqui&longs;ito in perpendi<lb/>culo: cùm proiicitur mobile per inclinatam &longs;ur&longs;um, mouetur motu <lb/>mixto ex naturali æquabili, & violento retardato: patet prima pars; <lb/>quia acceleratur tantùm naturalis deor&longs;um, &longs;altem in inclinata: &longs;e<lb/>cunda pars etiam patet; quia &longs;ub finem minor e&longs;t ictus. </s>

<s id="N1043C">igitur cre&longs;cit <lb/>cau&longs;a motus; </s>

<s id="N10442">igitur & motus: quæ ratio clari&longs;&longs;ima e&longs;t: </s>

<s>7. Hinc linea motus e&longs;t curua: iuxta diuer&longs;am progre&longs;&longs;ionem de<lb/>&longs;truitur hic impetus impre&longs;&longs;us: tùm pro diuer&longs;a inclinatione plani, <lb/>cuius etiam hîc habetur ratio; nam &longs;ingulis in&longs;tantibus mutatur: <lb/>tùm, quia modò plùs impetus e&longs;t fru&longs;trà, modò minùs; plùs <lb/>certè, cùm linea determinationis impetus impre&longs;&longs;i facit obtu<lb/>&longs;iorem: atqui initio e&longs;t obtu&longs;ior; &longs;ub finem verò a&longs;cen&longs;us acu<lb/>tior. </s>

<s id="N10446">hinc æquali<lb/>bus temporibus æqualia acquiruntur velocitatis momenta; </s>

<s id="N1044C">quia <lb/>cau&longs;a nece&longs;&longs;aria æqualibus temporibus, æqualem effectum produ<lb/>cit: quid clarius? </s>

<s>8. A&longs;cen&longs;us proiecti per inclinatam diutiùs durat, quàm de&longs;<lb/>cen&longs;us, ratione eiu&longs;dem plani horizontalis; quia, &longs;cilicet, a&longs;<lb/>cen&longs;us longior e&longs;t, quàm de&longs;cen&longs;us: e&longs;t autem longior; quia, vt <lb/>e&longs;&longs;et æqualis, nihil impetus impre&longs;&longs;i deberet de&longs;trui in a&longs;cen&longs;u <pb xlink:href="026/01/019.jpg"/>porrò in de&longs;cen&longs;u e&longs;t motus mixtus ex accelerato naturali, <lb/>& retardato violento, vt con&longs;tat ex dictis: iactus per incli<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<lb/>calem &longs;ur&longs;um, nihil acquiritur in plano horizontali, ex quo fit ia<lb/>ctus; nihil etiam per ip&longs;am horizontalem; igitur plùs acquiritur per <lb/>illam, quæ maximè ab vtraque &longs;imul recedit. </s>

<s id="N10456">3. Hinc non pote&longs;t cre&longs;cere hic impetus &longs;ecundùm porportio-<pb xlink:href="026/01/011.jpg"/>nem duplicatam temporum, cùm cre&longs;cat &longs;ecundùm proportionem <lb/>temporum, etïam ex mente Galilei: </s>

<s id="N10460">cre&longs;cit autem velocitas, vt im<lb/>petus; </s>

<s>9. Hæc ratio e&longs;t verè phy&longs;ica, geometrica nulla e&longs;t: hinc illi <lb/>iactus æquale &longs;patium acquirunt in prædicto plano horizontali, <lb/>qui fiunt per inclinatas æqualiter à prædicta inclinata ad ang. 45. <lb/>di&longs;tantes. </s>

<s id="N10466">effectus, &longs;cilicet, vt cau&longs;a: </s>

<s id="N1046A">idem dico de motu, ratione velo<lb/>citatis; </s>

<s>Cùm emittitur mobile per inclinatum deor&longs;um, in libero <lb/>medio, mouetur motu mixto ex naturali accelerato, & impre&longs;<lb/>&longs;o retardato, vt con&longs;tat ex dictis; ille autem primus accelera<lb/>tur per acce&longs;&longs;ionem impetus perfectionis quàm in iactu per ho<lb/>rizontalem; &longs;ed imperfectionis, quàm in perpendiculo: retarda<lb/>tur verò impetus minùs, quàm in iactu per horizontalem; plùs ve<lb/>rò, quàm in iactu per ip&longs;um perpendiculum, in quo nihil impetus <lb/>de&longs;truitur. </s>

<s id="N10470">quippe motus ip&longs;e e&longs;t &longs;ua velocitas: at verò ip&longs;a &longs;patia, <lb/>quæ decurruntur illo motu, &longs;i con&longs;ideretur crementum in in&longs;tan<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<lb/>tur vnum &longs;patium, &longs;ecundo acquiruntur duo, tertio 3. quarto 4. at<lb/>que ita deinceps. </s>

<s>10. Cùm è 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 æquabili, ex verti<lb/>cali retardato, & horizontali æquabili: mouetur &longs;ur&longs;um per cur<lb/>uam, &longs;empérque capiti iaculatoris imminet; quippe tantùm acqui<lb/>rit in horizontali, quantùm nauis: in de&longs;cen&longs;u verò e&longs;t motus <expan abbr="mix">mixtus</expan> <lb/>ex horizontali retardato, & naturali accelerato: quia tamen bre<lb/>ui&longs;&longs;imo illo tempore, retardatio illa horizontalis non e&longs;t &longs;en&longs;ibilis, <lb/>ferè in ip&longs;ius iaculatoris caput de&longs;cendit; quod certè phænomenon <lb/>ex no&longs;tris principiis euincitur. </s>

<s id="N10480">4. Hoc autem facilè pote&longs;t <expan abbr="demõ&longs;trari">demon&longs;trari</expan>: </s>

<s>11. Parum cautè Vfanus vniuer&longs;im a&longs;&longs;erit, iaculationem pilæ ex<lb/>tormento, maiorem e&longs;&longs;e ex naui in continentem, & minorem vi<lb/>ci&longs;&longs;im, cùm vtriu&longs;que differentia peti po&longs;&longs;it, vel à puluere tormen<lb/>tario, vel ab eius compre&longs;&longs;ione, vel humiditate, vel tormenti fabri<lb/>ca, vel ip&longs;ius demum nauigij motu, qui pilæ motum, vel accelerat, &longs;i <lb/>versùs eandem partem e&longs;t, vel retardat è contrario: in plano ho<lb/>rizontali duro pote&longs;t e&longs;&longs;e motus mixtus ex duobus, tribus, qua<lb/>tuor, & pluribus aliis. </s>

<s id="N10488">quia, cùm velocitas cre&longs;<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: </s>

<s id="N10490">igitur, <lb/>&longs;i mobile cum vno gradu velocitatis acquirit vnum &longs;patium, certè <lb/>cum duobus acquiret duo &longs;patia, cum tribus tria, atque ita dein<lb/>ceps: debet autem vera progre&longs;&longs;io crementorum a&longs;&longs;umi in &longs;ingulis <lb/>in&longs;tantibus, quia reuerà &longs;ingulis in&longs;tantibus phy&longs;icis (nam de iis <lb/>loquor) noua fit huius crementi acce&longs;&longs;io. </s>

<s>12. Cùm è naui mobili emittitur &longs;agitta per horizontalem, quæ fa<lb/>cit angelum rectum cum linea directionis nauis, fertur qua&longs;i per dia<lb/>gonalem vtriu&longs;que, &longs;altem per aliquod &longs;patium: cùm verò emitti-<pb xlink:href="026/01/020.jpg"/>tur per horizontalem, quæ 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<lb/>&longs;u, &longs;i nauis æqualem impetum imprimeret, deor&longs;um rectà ferretur <lb/>mobile motu naturali; imò &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><figure id="id.026.01.020.1.jpg" xlink:href="026/01/020/1.jpg"/>

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

<s id="N104A0">5. Quia tamen in&longs;tantia non &longs;unt &longs;en&longs;ibilia, vt Phy&longs;icæ con&longs;u<lb/>latur, quæ res &longs;en&longs;ibiles con&longs;iderat, a&longs;&longs;umi debent partes temporis <lb/>&longs;en&longs;ibiles, in quibus reuerâ progre&longs;&longs;io &longs;patiorum non e&longs;t arithmeti<lb/>ca &longs;implex; &longs;ed tam propè accedit ad hanc numerorum imparium, <lb/>1. 3. 5. 7. &c. </s>

<s id="N104AC">quam Galileus excogitauit, vt &longs;ine &longs;crupulo hæc a&longs;<lb/>&longs;umi po&longs;&longs;it: </s>

<s>1. MOtus reflexi vera cau&longs;a e&longs;t impetus prior, ad nouam li<lb/>neam determinatus ab occurrente obice; planum refle<lb/>ctens e&longs;t cau&longs;a nouæ determinationis &longs;uo modo; cau&longs;am enim di<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/>& priore per lineam incidentiæ, ab eodem puncto contactus pro<lb/>pagatam, fit determinatio mixta per lineam reflexionis; quæ omnia <lb/>patent ex terminis: hinc nullus impetus producitur à plano refle<lb/>ctente; quippe prior pote&longs;t determinari ad nouam lineam: adde, <lb/>quòd planum, quod caret impetu, impetum producere non pote&longs;t. </s>

<s id="N104B2">hinc &longs;patia &longs;unt ferè vt temporum quadrata: dixi, ferè: </s>

<s id="N104B6"><lb/>nam e&longs;t paulò minor proportio, cùm tantùm finita &longs;int in&longs;tantia <lb/>phy&longs;ica, quæ reuerà &longs;i infinita e&longs;&longs;ent in qualibet temporis &longs;en&longs;ibilis <lb/>parte, haud dubiè &longs;patia e&longs;&longs;ent omninò in ratione duplicata tem<lb/>porum: &longs;ed, quia parum pro nihilo computatur, hanc progre&longs;&longs;io<lb/>nem Galilei deinceps v&longs;urpabimus in Phy&longs;ica. </s>

<s>2. Imò nihil impetus de&longs;truitur in reflexione pura per &longs;e; quia ni<lb/>hil impetus e&longs;t fru&longs;trà per &longs;e in pura reflexione; multus tamen im<lb/>petus de&longs;truitur per accidens, tùm ab ip&longs;o attritu tùm mollitie <lb/>& ce&longs;&longs;ione, tùm pre&longs;&longs;ione: hinc &longs;uppo&longs;ito eodem iactu, perpendi<lb/>cularis reflexa e&longs;t omnium reflexarum minima; quia per eam li<lb/>neam maximus ictus infligitur; igitur maxima e&longs;t partium colli&longs;io, <lb/>& pre&longs;&longs;io: hinc etiam corpora duriora longiùs reflectuntur, per ip&longs;am <lb/>quoque <expan abbr="perpendicular&etilde;">perpendicularem</expan>, dum planum reflectens &longs;it æquè durum. </s>

<s>3. Determinatio noua dupla e&longs;t prioris, po&longs;ita linea incidentiæ <lb/>perpendiculari, & po&longs;ito etiam plano reflectente immobili; quia <lb/>alioquin anguli reflexionis non e&longs;&longs;ent æquales angulis incidentiæ: <lb/>&longs;i globus reflectens &longs;it æqualis impacto, æqualis e&longs;t ce&longs;&longs;io re&longs;i&longs;tenciæ <lb/>cùm &longs;it æquale agens re&longs;i&longs;tenti, perid enim reflectens re&longs;i&longs;tit, per <lb/>quod e&longs;t: igitur, &longs;i æqualis re&longs;i&longs;tit, & cedit, certè æqualiter ce<lb/>dit, & re&longs;i&longs;tit: hinc noua determinatio æqualis e&longs;t priori: hinc glo<lb/>bus impactis &longs;i&longs;tit immobilis; quia ex duabus determinationibus <lb/>oppo&longs;itis neutra præualet. </s><pb xlink:href="026/01/021.jpg"/>

<s id="N104C6">6. Hinc ratio euidens maioris ictus inflicti à corpore graui, <lb/>cùm ex maiori altitudine cadit. </s>

<s id="N104CB">Sunt autem ictus, vt impetus; <lb/>impetus, vt tempora; hæc demum, vt radices &longs;patiorum &longs;en&longs;ibi<lb/>liter quæ omnia con&longs;tant ex dictis. </s>

<s>4. Tantum e&longs;t ab æqualitate prædicta ce&longs;&longs;ionis, & re&longs;i&longs;tentiæ, ad <lb/>nullam ce&longs;&longs;ionem, & 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>, & totam ce&longs;&longs;ionem: hinc, cùm à tota ce&longs;&longs;ione ad æqua<lb/>litatem prædictam acquiratur tantùm noua determinato æqualis <lb/>priori; igitur ab eadem æqualitate ad nullam ce&longs;&longs;ionem tantun<lb/>dem acquiritur; igitur dupla prioris, vt iam &longs;uprà 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, cùm ip&longs;um corpus refle<lb/>ctens nullo modo mouetur ab ictu. </s>

<s id="N104D3">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, quæ reuerâ <lb/>&longs;unt &longs;emper minora; </s>

<s id="N104DB">quia motus fit &longs;emper velocior: cùm graue <lb/>de&longs;cendit in medio, quod re&longs;i&longs;tit, minùs accuratè &longs;eruantur prædi<lb/>ctæ proportiones, quæ in vacuo modico accurati&longs;&longs;imè &longs;eruaren<lb/>tur. </s>

<s>5. Determinatio noua per lineam obliquam, e&longs;t ad nouam per <lb/>lineam perpendicularem, vt &longs;inus rectus anguli incidentiæ, ad &longs;i<lb/>num totum, in qualibet hypothe&longs;i; quia &longs;unt hæ, vt ictus, per vtran<lb/>que lineam; ictus verò vt grauitationes in horizontale planum, & <lb/>in planum inclinatum, &longs;ub angulo complementi anguli incidentiæ: <lb/>hinc noua determinatio per lineam obliquam, e&longs;t vt dupla &longs;inus re<lb/>cti anguli incidentiæ, ad &longs;inum totum: hinc &longs;upra angulum inci<lb/>dentiæ 30, noua e&longs;t maior priore, infrà minor; in ip&longs;o angulo 30. <lb/>æqualis, &longs;uppo&longs;ita hypothe&longs;i plani reflectentis immobilis. </s>

<s>6. Ex hoc po&longs;itiuo principio demon&longs;tratur accurati&longs;&longs;imè æqua<lb/>litas anguli reflexionis, & incidentiæ, quod certè demon&longs;tratum <lb/>non fuit ab Ari&longs;t.

<s id="N104E7">7. Re&longs;i&longs;tentia medij non e&longs;t propter vllam formam improportio<lb/>natam, qua&longs;i verò impetus &longs;it forma improportionata aëri: </s>

in problematis, &longs;ect. 17. problem. 4. & 13. quibus <lb/>in locis fusè &longs;atis explicatur hoc Theorema, ducta comparatione, <lb/>tùm à grauibus, quæ cadunt, tùm ab orbibus, quæ rotantur, rùm à <lb/>&longs;peculis: &longs;ed minimè demon&longs;tratur ex certis principiis &longs;ine petitio<lb/>ne principij. </s>

<s id="N104ED">&longs;ed in <pb xlink:href="026/01/012.jpg"/>duobus præ&longs;ertim con&longs;i&longs;tit; </s>

<s id="N104F5">primò, eò quòd medium detrahat ali<lb/>quid grauitationis corporis grauis; </s>

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

<s id="N104FB">&longs;ecundò, eò quòd partes medij <lb/>aliquam implicationem habeant, quæ &longs;olui non pote&longs;t &longs;ine aliqua <lb/>compre&longs;&longs;ione, vel ten&longs;ione; </s>

<s id="N10503">vtraque autem re&longs;i&longs;tit impetui: quod <lb/>&longs;pectat ad primum, &longs;i medium &longs;it æqualis grauitatis cum ip&longs;o cor<lb/>pore, detrahitur tota grauitatio, &longs;i &longs;ubduplæ &longs;ubduplum, &c. </s>

<s>7. Omnes lineæ reflexæ per &longs;e &longs;unt æqualis longitudinis, & ab <lb/>eodem puncto contactus, ad communem peripheriam terminan<lb/>tur: &longs;i globus impactus &longs;it æqualis reflectenti, &longs;itque linea inciden<lb/>tiæ obliqua quælibet terminata ad idem punctum contactus, re<lb/>flectitur prædictus globus per lineam tangentem globum refle<lb/>ctentem in eodem puncto; quia hæc tangens e&longs;t diagonalis com<lb/>munis, & determinatio mixta communis omnibus lineis inciden<lb/>tiæ: e&longs;t tamen modò longior, modò breuior linea reflexa, é&longs;tque vt <lb/>vt &longs;inus complementi anguli incidentiæ, ad &longs;inum totum, qui &longs;it <lb/>determinatio prior, vt facilè demon&longs;tramus. </s>

<s id="N1050B">de quo <lb/>aliàs. </s>

<s>8. Si globus impactus &longs;it minor corpore reflectente, reflectitur <lb/>etiam per ip&longs;am perpendicularem, & determinatio noua e&longs;t dupla<lb/>prioris, minùs 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, minùs vna quarta, <lb/>&c. </s>

<s id="N10512">8. Hinc corpus graue per medium rarius, cæteris paribus, fa<lb/>cilè de&longs;cendit; non tamen ex re&longs;i&longs;tentia medij cognita, pote&longs;t co<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>ratio e&longs;t, quia in ea proportione globus reflectens cedit, in <lb/>qua mouetur, igitur tantùm detrahitur determinationis impacto <lb/>globo, quantùm additur motus reflectenti: at verò noua determina<lb/>tio per lineam incidentiæ obliquam, e&longs;t ad nouam per ip&longs;am per<lb/>pendicularem, vt &longs;inus rectus anguli incidentiæ ad &longs;inum totum. </s>

<s id="N1051C">Idem corpus cum eodem medio <lb/>comparatum, habet tres coniugationes: nam, vel e&longs;t grauius, vel<lb/>e&longs;t grauius, vel æquè graue, vel minùs. </s>

<s id="N10524">Sunt etiam tres aliæ con<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>

<s>9. In hac hypothe&longs;i lineæ reflexæ omnes &longs;unt &longs;upra prædictam <lb/>tangentem, &longs;eu &longs;ectionem plani, maiores, vel minores, pro diuer&longs;a <lb/>men&longs;ura diagonalis: in &longs;uperiori verò hypothe&longs;i æqualium globo<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 prædictam &longs;ectionem. </s>

<s>Porrò in hac <lb/>hypothe&longs;i vltima, determinatio noua per ip&longs;am perpendicularem <lb/>e&longs;t minor priore: hinc non modò nulla fit reflexio in perpendicula<lb/>ri, &longs;ed linea directa vlteriùs propagatur; quia prior determinatio <lb/>præualet. </s>

<s id="N1052F">9. Figura corporis grauis deor&longs;um cadentis motum vel retardat <lb/>vel accelerat; </s>

<s id="N10535">retardat quidem, &longs;i plures partes medij amouendæ <lb/>&longs;unt vel pauciores velociori motu; accelerat è contrario: </s>

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

<s id="N1053B">hinc idem <lb/>corpus <expan abbr="paralleliped&utilde;">parallelipedum</expan> iuxta tres diuer&longs;os &longs;itus, triplici motu diuer<lb/>&longs;o de&longs;cendere pote&longs;t: hinc ratio, cur acuminata tam facilè de&longs;cen<lb/>dant. </s>

<s id="N10549">Cubus, qui de&longs;cendit, imprimit aëri velociorem motum, <lb/>quàm ip&longs;e habeat; & quò maior e&longs;t eius &longs;uperficies, eò velociorem. </s>

<s id="N10551">10. Duo globi, vel cubi eiu&longs;dem materiæ æquè velociter de&longs;<lb/>cendunt: </s>

<s id="N10557">ratio e&longs;t, quia, licèt maioris vires habeant maiorem pro<lb/>portionem ad molem aëris re&longs;i&longs;tentis, quàm vires minoris ad alte<lb/>ram aëris molem, quæ proprium illius motum retardat, cùm tamen <lb/>aër, qui re&longs;i&longs;tit maiori cubo, debeat amoueri velociori motu, quàm <lb/>aër, qui re&longs;i&longs;tit minori, &longs;itque eadem proportio re&longs;i&longs;tentiæ ratione <lb/>motus, minoris ad maiorem, quæ e&longs;t ratione molis, maioris ad mi<lb/>norem; </s>

<s>11. Si duo globi æquales in &longs;e inuicem impingantur æquali mo<lb/>tu, per lineam connectentem centra, vterque æquali motu priori re<lb/>troagitur; quia æqualis in æqualis æqualem 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 inæquali motu concurrant, retroaguntur <lb/>ii&longs;dem motibus, permutando; quod etiam clarum e&longs;t: hinc egre<lb/>gium paradoxum, &longs;i quod aliud con&longs;equitur, &longs;cilicet, globum A, v. <lb/>g. æqualem motum imprimere globo B, &longs;iue hic moueatur, &longs;iue <lb/>quie&longs;cat. </s>

<s id="N10567">certè ratio compo&longs;ita vtriu&longs;que erit eadem in vtroque cu<lb/>bo: igitur æqualiter de&longs;cendet vterque. </s>

<s id="N1056F">11. Si tamen &longs;int diuer&longs;æ materiæ, haud dubiè, qui con&longs;tat leuio<lb/>ri materia, tardiùs de&longs;cendet; quia eius vires habent minorem <lb/>proportionem ad re&longs;i&longs;tentiam. </s>

<s id="N10577">Corpu&longs;cula etiam ex graui&longs;&longs;ima ma<lb/>teria tardi&longs;&longs;imè de&longs;cendunt: </s>

<s id="N1057D">tum, quia à filamentis illis, quibus par<lb/>tes aëris implicantur, facilè detinentur; </s>

<s>12. Si verò linea incidentiæ &longs;it obliqua, vterque globus reflecte<lb/>tur pror&longs;us vt à plano immobili: hinc reflexio &longs;it ad angulos æqua<lb/>les, & lineæ omnes reflexionis &longs;unt æquales: ratio e&longs;t; quia, quantùm <lb/>detrahit globus reflectens re&longs;i&longs;tendo, tantùm addit in partem op<lb/>po&longs;itam repellendo, po&longs;itiuo ni&longs;u, vel impetu: quòd &longs;i alter globus <lb/>maiore, vel minore motu moueatur, vel &longs;i globi &longs;int inæquales, <lb/>cum æquali motu, vel inæquali, res etiam determinari pote&longs;t ex <lb/>præmi&longs;&longs;is. </s><pb xlink:href="026/01/023.jpg"/>

<s id="N10583">analogiam habes in lapil<lb/>lo, qui ab araneæ tela intercipitur: </s>

<s id="N10589">tum, quia, cùm lati&longs;&longs;imam ali<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;tentiã">re&longs;i&longs;tentiam</expan>: tùm denique, quia, cùm modico <lb/>impetu agitari po&longs;&longs;int ab aëre mobili, vnus motus alium impedit. </s>

<s>13. Cum duo globi in &longs;e&longs;e inuicem impinguntur æquali motu, <lb/>minor retroagitur velociore motu, quàm ante moueretur, vt clarum <lb/>e&longs;t: maior verò, &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<lb/>tu; &longs;i minor duplo, retroagitur: quæ omnia facilè ex dictis demon<lb/>&longs;trantur. </s>

<s>Pote&longs;t impetus e&longs;&longs;e æqualis alteri, & præualere; pote&longs;t <lb/>æqualem impetum producere hoc in&longs;tanti, & &longs;tatim in&longs;tanti, quod <lb/>&longs;equitur, totus de&longs;trui. </s>

<s id="N1059E">12. Singulis in&longs;tantibus motus naturaliter accelerati cre&longs;cit <lb/>re&longs;i&longs;tentia; </s>

<s id="N105A4">quia, cùm motus cre&longs;cat, æqualibus temporibus, plures <lb/>partes medij occurrunt; </s>

<s>14. Pote&longs;t globus retroagi in plano horizontali, licèt in aliud cor<lb/>pus non incidat, ita vt initio tendat in ortum, verbi gratia: tùm <lb/>deinde, licèt nihil pror&longs;us addatur, versùs occa&longs;um; quod accidit, <lb/>cum globus vtroque motu, centri, &longs;cilicet, & orbis, mouetur, &longs;ed <lb/>contrario; primùm enim motus centri præualet, &longs;ed facilè cedit <lb/>propter attritum maiorem partium. </s>

<s id="N105AA">cre&longs;cunt tamen vires in eadem proportio<lb/>ne, &longs;cilicet, impetus: igitur non mutatur progre&longs;&longs;io motus. </s>

<s id="N105B0">Hinc <lb/>colligo, contra Galilæum, motum rectum ex naturaliter accelerato <lb/>nunquam fieri æquabilem: dixi motum rectum; quia motus corpo<lb/>rum c&oelig;le&longs;tium ex accelerato factus e&longs;t æqualis. </s>

<s>Nullus datur propriè motus <lb/>refractus: licèt enim incuruetur linea motus, dum per aquam &longs;u<lb/>bit mobile; hæc tamen e&longs;t reflexionis &longs;pecies. </s>

<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<lb/>uetur; producitur enim impetus primo in&longs;tanti contactus: &longs;i impe<lb/>tus e&longs;&longs;et tantùm determinatus ad vnam lineam, nulla fieri po&longs;&longs;et <lb/>reflexio, &longs;ed tantùm 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 aëris &longs;onori ad Echometriam: &longs;agitta emi&longs;&longs;a per ho<lb/>rizontalem &longs;ursùm, tantillùm a&longs;cendit per arcum; quia tantillùm <lb/>reflectitur ab aëre. </s><figure id="id.026.01.023.1.jpg" xlink:href="026/01/023/1.jpg"/>

<s id="N105C1"><emph type="center"/><emph type="italics"/>De motu violento &longs;ur&longs;um.<emph.end type="italics"/><emph.end type="center"/></s>

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

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

<s id="N105CE">1. MOtus violentus &longs;ur&longs;um vulgò dicitur e&longs;&longs;e à principio ex<lb/>trin&longs;eco. </s>

<s id="N105D3">Triplici modo accidere pote&longs;t: </s>

<s>Motus circularis in &longs;ublunaribus <lb/>oritur ex recto impedito; quia, &longs;cilicet, determinatur tantùm im<lb/>petus ad lineam rectam: hinc quidam motus circularis e&longs;t merè <lb/>per accidens, vt cùm retinetur extremitas funependuli, &longs;eu <pb xlink:href="026/01/024.jpg"/>fundæ, quæ &longs;i demittatur, &longs;equitur motus rectus: quidam tamen <lb/>non e&longs;t merè peraccidens, vt cùm pellitur extremitas cylindri in <lb/>plano horizontali; e&longs;t enim, iuxta in&longs;titutionem naturæ, ad facili<lb/>tatem motus. </s>

<s id="N105D7">primò, &longs;i reuerà <lb/>imprimatur impetus ab extrin&longs;eco, vt, cùm mitto lapidem &longs;ur&longs;um: </s>

<s id="N105DD"><lb/>&longs;ecundò, &longs;i corpus deor&longs;um cadens deinde reflectatur &longs;ur&longs;um; </s>

<s>2. Quippe tale e&longs;t naturæ in&longs;titutum, vt eo motu corpora mo<lb/>ueantur, quo faciliùs moueri po&longs;&longs;unt: atqui cùm pellitur altera cy<lb/>lindri extremitas, in plano horizontali putà innatantis, faciliùs <lb/>mouetur, quàm recto, & qua&longs;i minore &longs;umptu, cùm minùs &longs;patij <lb/>acquirat: æquali 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 vnquàm, &longs;ed tantùm oritur hic motus ex <lb/>determinatione per tangentem impedita, ratione alicuius puncti <lb/>immobilis. </s>

<s id="N105E2">tunc <lb/>autem nihil e&longs;t ab extrin&longs;eco, ni&longs;i determinatio noua, quæ e&longs;t à cor<lb/>pore reflectente: </s>

<s id="N105EA">tertiò, &longs;i terra vtrinque e&longs;&longs;et peruia; </s>

<s>3. Hinc, &longs;i tollatur impedimentum, &longs;tatim per tangentem or<lb/>bis fit motus, vt patet in funda: inæqualiter partes radij prædicti <lb/>orbis mouentur, iuxta proportionem di&longs;tantiæ maioris, & minoris <lb/>à centro: hinc propagatio impetus inæqualis, de qua iam &longs;uprà, <lb/>&longs;ingulis in&longs;tantibus & punctis e&longs;t noua determinatio; quia, &longs;cilicet, <lb/>&longs;ingulis punctis &longs;ua tangens re&longs;pondet: hinc, &longs;i imponatur rotæ <lb/>aliud corpus, &longs;tatim abigitur, &longs;ine &longs;it in &longs;itu verticali, &longs;iue in &longs;itu ho<lb/>rizontali; hinc dum turbo rotatur, &longs;i vel aquæ guttula eius &longs;uper<lb/>ficies a&longs;pergitur, & &longs;tatim di&longs;pergitur. </s>

<s id="N105EE">nam lapis haud <lb/>dubiè non &longs;i&longs;teret in centro, &longs;altem po&longs;t primum de&longs;cen&longs;um; </s>

<s id="N105F4">igitur <lb/>a&longs;cenderet per eandem lineam; </s>

<s>4 Dari impetum in motu circulari certi&longs;&longs;imum e&longs;t: punctum phy<lb/>&longs;icum e&longs;t capax huius motus; cuius finis multiplex e&longs;t; corpus mo<lb/>uetur motu circulari circa centrum immobile cum motus centri <lb/>impeditur non tamen motus orbis, ad quem impetus facilè deter<lb/>minatur, cùm &longs;it ad omnes lineas indifferens: adde v&longs;um vectis, <lb/>trochleæ, aliorúmque organorum, qui &longs;ine motu circulari e&longs;&longs;e non <lb/>pote&longs;t: omitto motum progre&longs;&longs;iuum, ipsúmque brachiorum, & ti<lb/>biarum v&longs;um, qui motu circulari carere non pote&longs;t. </s>

<s id="N105FA">nullum tamen e&longs;t principium ex<lb/>trin&longs;ecum; igitur motus violentus dicit tantùm motum &longs;ur&longs;um <lb/>corporis grauis. </s>

<s>5. Motus circularis rotæ in plano verticali e&longs;t æquabilis per &longs;e; <lb/>quia nihil e&longs;t, quod impetum &longs;emel impre&longs;&longs;um de&longs;truat: licèt enim <lb/>&longs;ingulis in&longs;tantibus &longs;it noua determinatio, nullus tamen impetus <lb/>e&longs;t fru&longs;trà; 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, quæ fit à plano immobili, nullus de&longs;truitur im<lb/>petus; ita nullus hîc de&longs;truitur; tam enim centrum illud immobile <lb/>ad &longs;e qua&longs;i trahit mobile, quàm planum immobile à &longs;e repellit; in <lb/>quo e&longs;t perfectè analogia. </s><pb xlink:href="026/01/025.jpg"/>

<s id="N10604">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 reuerâ ine&longs;t ip&longs;i mobili, cùm ip&longs;um medium hunc <lb/>motum potiùs impediat, quàm iuuet: </s>

<s>6. Hinc per &longs;e motus circularis integri orbis e&longs;t perpetuus; de<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<lb/>bine, cuius cu&longs;pis læuigati&longs;&longs;ima in plano læuigati&longs;&longs;imo rotatur; nec <lb/>vnquam ce&longs;&longs;aret hic motus &longs;ine prædicto attritu, & partium a&longs;peri<lb/>tate: nec quidquam ob&longs;tat, quòd aliquæ partes rotæ, quæ in circu<lb/>lo verticali voluitur, a&longs;cendant; quia etiam aliquæ de&longs;cendunt: qua<lb/>re &longs;emper remanet perfectum æquilibrium, & harum de&longs;cen&longs;us, il<lb/>larum a&longs;cen&longs;um compen&longs;at. </s>

<s id="N1060E">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<lb/>petus innatus illius cau&longs;a e&longs;&longs;e non pote&longs;t. </s>

<s id="N10616">Portò hic motus non e&longs;t <lb/>acceleratus, nec æqualis, alioquin <expan abbr="nunquã">nunquam</expan> rediret deor&longs;um mobile. </s>

<s>Quò diutiùs potentia motrix manet <lb/>applicata manubrio axis rotæ, ita vt nouum &longs;emper producat im<lb/>petum, rotæ motus velocior e&longs;t, atque diutiùs durat: idem pror&longs;us <lb/>dico de rota circulo horizontali parallela. </s>

<s>7. Cùm mouetur æquali ni&longs;u acus circa immobile centrum, tùm <lb/>in plano <expan abbr="horizõtali">horizontali</expan>, tùm in verticali, &longs;iue &longs;it <expan abbr="lõgior">longior</expan> vna, &longs;iue breuior <lb/>alia, per &longs;e plures gyros non de&longs;cribit vna, quàm alia; quia per &longs;e <lb/>mouetur motu æquabili: per accidens tamen &longs;ecus accidit; quippe <lb/>maior e&longs;t maioris attritus: dixi, cùm mouetur æquali ni&longs;u; nam &longs;æpè <lb/>contingit, maiore ni&longs;u potentiam motricem agere circa maiorem; <lb/>æquali tamen tempore numerus circuitionum minoris, e&longs;t ad nu<lb/>merum circuitionum maioris per &longs;e vt acuum quadrata permu<lb/>tando; &longs;unt enim motus vt &longs;patia, &longs;pacia vt quadrata. </s>

<s id="N10621">3. Hinc nece&longs;&longs;ariò e&longs;t retardatus: </s>

<s id="N10625">igitur de&longs;truitur impetus, non <lb/>quidem ab ip&longs;a medij re&longs;i&longs;tentia; </s>

<s>8. Verbi gratia, &longs;it acus maior 2. minor 1. certè cùm tota area or<lb/>bis maioris &longs;it quadrupla minoris, &longs;itque area maioris, &longs;patium ma<lb/>ioris, & area minoris &longs;patium minoris, haud dubiè de&longs;cribet minor <lb/>quatuor circuitiones, eo tempore, quo maior decurret vnicam: li<lb/>cèt enim extremitas minoris, quæ impellitur, habeat tantùm du<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, quæ e&longs;t in &longs;egmento maioris versùs centrum æquali minori <lb/>acui: porrò motus circulares æquabiles in vtraque cum eodem <lb/>impetu, &longs;unt vt motus recti. </s>

<s id="N1062B">quippe idem medium non magis <lb/>re&longs;i&longs;tit motui &longs;ur&longs;um, quàm motui deor&longs;um, vt patet: </s>

<s id="N10631">igitur de&longs;trui<lb/>tur ille impetus motus violenti ab impetu innato aliquo modo; </s>

<s>9. Rota in plano verticali faciliùs mouetur, quàm in horizonta<lb/>li; quia in illo mouetur per minimam impetus, vel potentiæ acce&longs;<lb/>&longs;ionem; &longs;ecùs in i&longs;to; quippe per minimam acce&longs;&longs;ionem tollitur <lb/>æquilibrium; imò moueri pote&longs;t in plano verticali, licèt nullus im<lb/>primatur impetus rotæ, v. g. per additionem minimi ponderis, vel <lb/>momenti, vt patet; cùm tamen in plano horizontali moueri non <lb/>po&longs;&longs;it, ni&longs;i impetus imprimatur. </s>

<s id="N10637">non <lb/>quidem vt à contrario ratione entitatis, &longs;ed ratione determinatio<lb/>nis: </s>

<s id="N1063F">cùm enim impetus innatus exigat motum deor&longs;um, & alius &longs;ur<lb/>&longs;um: </s>

<s id="N10645">hic quidem præualet, attamen fru&longs;trà e&longs;t, ratione gradus <lb/>æqualis impetui innato: igitur de&longs;truitur ille gradus illo in&longs;tanti. </s>

<s>10. Si cylindrus in plano horizontali læuigato in altera extremi<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 faciliùs mouetur circa illud <lb/>centrum, quàm circa alia puncta, quòd, &longs;cilicet, minùs &longs;patij decur<lb/>ratur, po&longs;ito eodem &longs;emper motu alterius extremitatis, cui appli<lb/>catur immediatè potentia motrix. </s>

<s id="N10650">4. Hinc &longs;ingulis temporibus æqualibus de&longs;truitur gradus impe<lb/>tui innato; </s>

<s id="N10656">e&longs;t enim eadem ratio pro omnibus: </s>

<s>11. Cùm rota mouetur in verticali, atque præponderat alter &longs;emi<lb/>circulus, haud dubiè hic præponderans producit impetum in alio <lb/>&longs;emicirculo: hinc fortè e&longs;t, quòd mirere, impetus determinatus <lb/>deor&longs;um producit alium &longs;ur&longs;um: hinc impetus vnius partis mobi<lb/>lis pote&longs;t producere &longs;imilem in alia parte continua; quod tantùm in <lb/>hoc ca&longs;u locum habet: quando corpus incumbit plano, quod mo<lb/>uetur motu recto æquabili, ab eo non &longs;eparatur; &longs;ecùs verò, &longs;i in<lb/>cumbat plano, quod mouetur motu circulari. </s><figure id="id.026.01.026.1.jpg" xlink:href="026/01/026/1.jpg"/>

<s id="N1065A">igitur temporibus <lb/>æqualibus de&longs;truitur æqualis impetus: </s>

<s id="N10660">igitur amittit ille motus <lb/>æqualia velocitatis momenta: </s>

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

<s id="N10666">igitur e&longs;t naturaliter retardatus: </s>

<s id="N1066A">igi<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<lb/>nis, quæ dicta &longs;unt de illa progre&longs;&longs;ione accelerationis. </s>

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

<s>Ratio à priori e&longs;t quia <lb/>priori impetui acqui&longs;ito nouus accedit: non acceleratur in eadem <lb/>proportione, in qua &longs;uprà dictum e&longs;t accelerari in linea recta; quia <lb/>in hac acceleratur vniformiter, id e&longs;t, æqualibus temporibus, <lb/>æqualia acquiruntur velocitatis momenta; quia vel e&longs;t &longs;emper ea<lb/>dem inclinatio plani, vel idem perpendiculum: at verò in fune<lb/>pendulo in &longs;ingulis punctis e&longs;t noua tangens; igitur noua inclina<lb/>tio plani; igitur noua ratio motus. </s>

<s id="N10676">5. Hinc impetus imperfectior initio de&longs;truitur: </s>

<s id="N1067A">quia, cùm motus <lb/>ille &longs;it velocior initio, in&longs;tantia &longs;unt minora: </s>

<s>2. Initio acceleratur motus per maiora crementa, &longs;ub finem per mi<lb/>nora; v.g. &longs;i dato tempore acqui&longs;iuit vnum gradum impetus initio, <lb/>æquali deinde tempore acquiret minùs: ratio clara e&longs;t: quia, vt ac<lb/>quireret æqualem, deberet e&longs;&longs;e eadem plani inclinatio; &longs;ed &longs;emper <lb/>cre&longs;cit Inclinatio; igitur &longs;emper imminuitur impetus æquali <expan abbr="t&etilde;pore">tempore</expan> <lb/>acqui&longs;itus: acquiritur tamen æqualis velocitas in arcu, & in chor<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>

<s id="N10680">atqui minori tempore <lb/>minùs retardatur: </s>

<s id="N10686">igitur inperfectior impetus de&longs;truitur; </s>

<s id="N1068A">cùm è <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<lb/>neos, & principium illud etiam in impetu valere, &longs;cilicet, &longs;ubiectum <lb/>ita compleri ab vna forma, vt alterius homogeneæ non &longs;it ampliùs <lb/>capax, &longs;altem naturaliter. </s>

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

<s id="N1069A">6. Hinc vltimus gradus impetus violenti e&longs;t omnium perfecti&longs;<lb/>&longs;imus, vt con&longs;tat. </s>

<s>Vibratio maior eiu&longs;dem funependuli æquali ferè tem-<pb xlink:href="026/01/027.jpg"/>pore cum minore perficitur: ratio e&longs;t: quia, cùm ferè decurrantur <lb/>arcus iuxta &longs;ubten&longs;arum proportionem, certè cùm &longs;ubten&longs;æ om<lb/>nes æquali tempore decurrantur, idem ferè fit in ip&longs;is arcubus: dixi <lb/>ferè: nam reuerà minor vibratio citiùs, maior tardiùs perficitur, vt <lb/><expan abbr="cõ&longs;tat">con&longs;tat</expan> <expan abbr="experi&etilde;tia">experientia</expan>: neque dee&longs;t ratio, quam in <expan abbr="analyticcã">analyticam</expan> remittimus. </s>

<s id="N1069F">Quie&longs;ceret vno in&longs;tanti mobile iactum &longs;ur&longs;um, &longs;i <lb/>gradus vltimus violenti e&longs;&longs;et æqualis perfectionis, cum impetu in<lb/>nato: </s>

<s id="N106A7">vbi enim ventum e&longs;&longs;et ad in&longs;tans æqualitatis, neutrum præ<lb/>ualere po&longs;&longs;et: </s>

<s>4. Non a&longs;cendit funependulum ad eam altitudinem, ex qua priùs <lb/>de&longs;cenderat: clara e&longs;t experientia: neque ratio tantùm petitur ab <lb/>aëris re&longs;i&longs;tentia; tam enim re&longs;i&longs;tit de&longs;cen&longs;ui, quàm a&longs;cen&longs;ui; &longs;ed ex <lb/>eo, quòd &longs;ingulis in&longs;tantibus &longs;it quædam pugna, inter impetum in<lb/>natum, & 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<lb/>currit: hinc in maiori vibratione imminuitur motus, & &longs;patium in <lb/>maiori proportione, quàm in minori; quia in hac lineæ &longs;ingulæ a&longs;<lb/>cen&longs;us qua&longs;i <expan abbr="totid&etilde;">totidem</expan> inclinatæ &longs;unt inclinatiores; in illa verò minùs. </s>

<s id="N106AD">igitur in&longs;tanti &longs;equenti e&longs;&longs;et quies: </s>

<s id="N106B1">cùm tamen &longs;int <lb/>diuer&longs;æ perfectionis, perfectior præualet: vter autem &longs;it perfectior, <lb/>dicemus infrà. </s>

<s>5. Hinc diu vibratur funependulum per minores arcus, quippe <lb/>facilis e&longs;t a&longs;cen&longs;us per planum proximè ad horizontale accedens: <lb/>hinc etiam in funependulo maiori diutiùs durant huiu&longs;modi vi<lb/>brationes, idque in arcubus paulò maioribus; quia &longs;ubten&longs;æ his <lb/>arcubus &longs;unt inclinatiores: hinc refutabis eos, qui dicunt, vibra<lb/>tiones funependuli in vacuo fore perpetuas: arcus vibratio<lb/>nis a&longs;cen&longs;us fit motu naturaliter retardato, &longs;ed per imminu<lb/>tiones inæquales; quia pro diuer&longs;a inclinatione plani diuer&longs;imodè <lb/>retardatur. </s>

<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<lb/>tùm in&longs;tanti; quippe e&longs;t omnium imperfecti&longs;&longs;imum; quod reuerà &longs;i <lb/>e&longs;&longs;et eiu&longs;dem perfectionis cum innato, a&longs;cen&longs;us æqualis e&longs;t de&longs;cen<lb/>&longs;ui: &longs;i &longs;int funependula inæqualia, vibrationes non &longs;unt æquè diu<lb/>turnæ: ratio e&longs;t: quia, &longs;i a&longs;&longs;umantur, v.g. duo quadrantes inæquales, <lb/>&longs;unt eju&longs;dem inclinationis; igitur minor citiùs percurritur. </s>

<s id="N106BB">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/>æqualis ponderis, vel maioris, &longs;ur&longs;um mouet, tunc certum e&longs;t, inna<lb/>tum e&longs;&longs;e perfectiorem: </s>

<s id="N106C5">&longs;i verò imprimitur ab alia potentia motrice, <lb/>tunc etiam imperfectior e&longs;t impetu innato; </s>

<s>7. Porrò tempora vibrationum &longs;unt in ratione &longs;ubduplicata ar<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<lb/>ris; quod ita intelligendum e&longs;t, vt hæc proportio con&longs;ideretur in <lb/>partibus temporis &longs;en&longs;ibilibus, vt iam dictum e&longs;t de motu natura<lb/>liter accelerato deor&longs;um in perpendiculo, & in planis inclinatis; <lb/>nam progre&longs;&longs;io arithmetica; a&longs;&longs;umpta in &longs;ingulis in&longs;tantibus, tran<lb/>&longs;it in hanc, &longs;i a&longs;&longs;umantur partes temporis &longs;en&longs;ibiles, quarum &longs;ingu<lb/>læ infinitis ferè con&longs;tent in&longs;tantibus. </s><pb xlink:href="026/01/028.jpg"/>

<s id="N106CB">nam inæqualis e&longs;t; </s>

<s id="N106CF">alio<lb/>quin, &longs;i e&longs;&longs;et æqualis, &longs;imul e&longs;&longs;ent in eodem &longs;ubiecto duo gradus <lb/>homogenei: </s>

<s>8. In maiori quadrante, circa &longs;upremam extremitatem, e&longs;t minor <lb/>inclinatio, quàm in minore; hic enim &longs;tatim detorquetur à perpen<lb/>diculo, cum quo facit angulum maiorem: at verò circa infirmam <lb/>extremitatem, e&longs;t maior inclinatio in maiore, quàm in minore: hinc, <lb/>&longs;i comparetur vibratio maioris, cum vibratione minoris in modico <lb/>arcu, tempus illius e&longs;t paulò maius duplo, temporis huius; in maxi<lb/>mo arcu paulò minùs duplo, dum, &longs;cilicet, longitudinum ratio <lb/>&longs;it quadrupla. </s>

<s id="N106D7">præ&longs;tat autem e&longs;&longs;e imperfectiorem, quàm perfectio<lb/>rem, vt plura impetus puncta à potentia imprimantur; </s>

<s id="N106DD">quòd mul<lb/>tum facit ad mouenda maiora pondera: hinc nullo in&longs;tanti quie&longs;<lb/>cunt proiecta &longs;ur&longs;um. </s>

<s>9. In de&longs;cen&longs;u funependuli velocitas acqui&longs;ita e&longs;t eadem cum ea, <lb/>quæ in &longs;ubten&longs;a eiu&longs;dem arcus acquiritur: hinc &longs;unt ijdem ictus: <lb/>numerus, vibrationum non e&longs;t infinitus, licèt in vacuo vibraretur <lb/>funependulum; quia, cùm &longs;ingulæ imminuantur, & infinitis pun<lb/>ctis non con&longs;tent; tandem ad vltimam peruenitur: illa autem e&longs;t vl<lb/>tima, in cuius de&longs;cen&longs;u acquiritur tantùm vnum punctum impetus <lb/>&longs;upra innatum; in ea tamen &longs;ententia, quæ vel infinitas partes actu, <lb/>vel infinita puncta cogno&longs;cit, certè nunquam quie&longs;ceret funepen<lb/>dulum in vacuo vibratum. </s>

<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 æqualis acqui&longs;itus; po&longs;ita ta<lb/>men illa æqualitate, in&longs;tanti &longs;equenti e&longs;&longs;et quies: funependulum <lb/>grauius citiùs de&longs;cendit; e&longs;t enim eadem ratio, quæ fuit pro mo<lb/>tu naturali; corpus oblongum &longs;olidum circa punctum immobile <lb/>in circulo verticali rotatum vibratur adin&longs;tat funependuli; de&longs;<lb/>cendit tamen citiùs, quàm funependulum eiu&longs;dem longitudinis. </s>

<s id="N106E7">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; </s>

<s id="N106ED">e&longs;t enim eadem ratio: &longs;agittæ verò mi<lb/>nùs durat a&longs;cen&longs;us, quàm de&longs;cen&longs;us propter mixtionem materiæ. </s>

<s>11. Ratio facilis e&longs;t; quia partes &longs;olidæ, quæ accedunt propiùs <lb/>ad extremitatem immobilem, accelerant motum aliarum, quæ <lb/>ad mobilem extremitatem accedunt; faciunt enim arcum mino<lb/>rem: hinc a&longs;cen&longs;us non peruenit ad tantam &longs;ublimitatem; quia, vt <lb/>prædictæ partes accelerant motum aliarum in de&longs;cen&longs;u, ita retar<lb/>dant in de&longs;cen&longs;u: hinc citiùs quie&longs;cit hoc penduli genus, quàm <lb/>aliud: ex hoc colligo paradoxon, &longs;cilicet, corpus moueri po&longs;&longs;e &longs;ua <lb/>&longs;ponte velociùs in arcu deor&longs;um, quàm in perpendiculo; v.g. &longs;i iuxta <lb/>extremitatem immobilem &longs;it nodus plumbeus, cuius vi, altera ex<lb/>tremitas longiùs di&longs;tans deor&longs;um rapiatur. </s>

<s id="N106F3"><lb/>Si motus violentus e&longs;&longs;et æquabilis, percurreret proiectum &longs;patium <lb/>ferè duplum eo tempore, quo retardato percurrit &longs;ubduplum: </s>

<s id="N106FA">hinc <lb/>&longs;onus tam citò auditur; </s>

<s id="N10700">quia propagatur cum particulis aëris æqua<lb/>bili ferè motu: </s>

<s id="N10706">e&longs;&longs;e autem &longs;patium ferè duplum, probatur ex eo, <pb xlink:href="026/01/015.jpg"/>quòd &longs;patium motu æquabili decur&longs;um re&longs;pondet rectangulo; </s>

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

<s id="N1070E">de<lb/>cur&longs;um verò motu retardato, re&longs;pondet triangulo, &longs;ubduplo rectan<lb/>guli: a&longs;&longs;umpto &longs;cilicet, æquali tempore. </s>

<s>1. ROta, quæ mouetur in &longs;uperficie plana, mouetur motu mixto <lb/>ex recto centri, & circulari orbis: axis tantùm rotæ mouetur <lb/>motu recto: punctum contactus rotæ mouetur motu tardi&longs;&longs;imo, <pb xlink:href="026/01/029.jpg"/>quando motus centri, & &longs;uprema rotæ pars in eandem partem &longs;e<lb/>runtur; punctum verò oppo&longs;itum veloci&longs;&longs;imo, quia in motu huius <lb/>rotus motus orbis additur motui centri; in motu verò illius, to<lb/>tus motus orbis, motui centri detrahitur: quod autem detrahit mo<lb/>tus orbis, nunquam æquale e&longs;t toti motui centri. </s>

<s id="N10718">9. Vites potentiæ proiicientis toto ni&longs;u re&longs;pondent velocitati <lb/>acqui&longs;itæ 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, quantùm in a&longs;cen&longs;u deperditur. </s>

<s>2. Hinc omnia puncta eiu&longs;dem circuli rotæ mobilis in plano <lb/>hoc motu mixto mouentur in æquali motu: hoc etiam motu mo<lb/>uetur globus de&longs;cendens in plano inclinato, in quo reuerâ motu <lb/>hæc habes: primò, non modò accelerari <expan abbr="mot&utilde;">motum</expan> centri, verùm etiam <lb/>motum orbis; <expan abbr="&longs;ec&utilde;dò">&longs;ecundò</expan>, ita <expan abbr="impet&utilde;">impetum</expan> propagari ab intrin&longs;eco, vt &longs;ingu<lb/>lis partibus eiu&longs;dem circuli, & plani in æqualiter di&longs;tribuatur, tertiò <lb/>hoc motu motum rectum non impediri à circulari, & &longs;ed iuuari. </s>

<s id="N10724"><lb/>Impetus primo in&longs;tanti, quo e&longs;t, agit, &longs;i e&longs;t aliquod impedimen<lb/>tum; </s>

<s id="N1072B">e&longs;t enim cau&longs;a nece&longs;&longs;aria: </s>

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

<s id="N1072F">primo in&longs;tanti motus aliquid im<lb/>petus de&longs;truitur: </s>

<s id="N10735">&longs;iue præce&longs;&longs;erit motus violentus, &longs;iue non præce&longs;<lb/>&longs;erit, corpus graue æquali motu deor&longs;um cadit: </s>

<s>Ca<lb/>lamus volatilis, cuius mi&longs;&longs;io frequens, & repercu&longs;&longs;io, ludi non in<lb/>grati copiam facit: mouetur motu mixto ex recto, & circulari: in <lb/>hoc porrò motu præit calami caput, & &longs;equuntur pennæ; quia aër <lb/>fortiùs re&longs;i&longs;tit pennis, quàm thecæ: hinc pennarum motum theca <lb/>grauior accelerat, cuius motum pennæ retardant. </s>

<s id="N1073B">re&longs;i&longs;tentia aëris e&longs;t <lb/>quidem maior initio; &longs;ed etiam &longs;unt maiores vires. </s>

<s>4. Hinc, &longs;i quando accidat, penas educi ex theca in libero medio; <lb/>&longs;tatim theca velociori motu mouetur, cùm tamen pennæ ip&longs;æ &longs;i<lb/>&longs;tant: ex hac inæqualitate, ne impetus &longs;it fru&longs;trà, propter detortas <lb/>in alteram partem pennas ab aëre re&longs;i&longs;tente totum iaculum defle<lb/>ctitur, agitúr que in orbem; hinc motus orbis traducitur ex theca in <lb/>pennas, non contrà, vt aliquis fortè exi&longs;timaret, licèt pennarum tar<lb/>ditas, & obliqua deflexio, ratione cuius ab aëre re&longs;tante, in alteram <lb/>partem qua&longs;i reflectentur, &longs;int nece&longs;&longs;aria conditio huius traductio<lb/>nis. </s>

<s>5. Hinc motu recto prædictum iaculum in vacuo tantùm mo<lb/>ueretur, vt patet: hinc: cùm pennæ &longs;unt explicatiores, tardiùs; cùm <lb/>verò contractiores, velociùs mouetur, etiam motu orbis; cui non <lb/>minùs aër re&longs;i&longs;tit, in pennis, &longs;cilicet, quàm motui axis: hinc, &longs;i theca <lb/>&longs;it grauior, velociùs; &longs;i leuior, tardiùs iaculum fertur; etiam tenera <lb/>plumarum lanugo tarditatem conciliat: porrò, &longs;i axis mouetur mo<lb/>tu recto, quod reuerà fit, cùm iaculum deor&longs;um demittitur in per<lb/>pendiculo, hic motus e&longs;t &longs;piralis cylindricus: ex his infinita ferè <lb/>phænomena explicari po&longs;&longs;unt. </s>

<s id="N10748"><emph type="center"/><emph type="italics"/>De motu in planis inclinatis.<emph.end type="italics"/><emph.end type="center"/></s>

<s>6. Sunt infiniti propemodum motus mixti; v. g. cylindri ab alte<lb/>ra extremitate rotata emi&longs;&longs;i; longioris ha&longs;tæ, quæ &longs;ur&longs;um facta cir<lb/>cuitione emittitur; brachij, gladij, &c. &longs;ed poti&longs;&longs;imùm turbinis, qui <pb xlink:href="026/01/030.jpg"/>vel &longs;cutica, vel funiculo in torto circumagitur, in quo clari&longs;&longs;i<lb/>mè apparet motus centri, & orbis: ratio motus orbis e&longs;t impe<lb/>tus impre&longs;&longs;us vtrique extremitati diametri va&longs;is in partes contra<lb/>rias; ratio verò motus centri e&longs;t, quia adducitur funiculo vel ex<lb/>ploditur, &longs;eu expellitur &longs;cutica: huius motus phænomena &longs;unt ferè <lb/>infinita: &longs;ingula ex no&longs;tris principiis facilè explicantur. </s><figure id="id.026.01.030.1.jpg" xlink:href="026/01/030/1.jpg"/>

<s id="N10755">1. PLanum inclinatum e&longs;t &longs;ur&longs;um, vel deor&longs;um: </s>

<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>

<s id="N10759">in hoc de&longs;cen<lb/>dit corpus graue, ni&longs;i fortè retineatur ab a&longs;peritate, vel pro<lb/>pria, vel ip&longs;ius plani: </s>

<s id="N10761">impeditur autem motus naturalis in plano <lb/>prædicto, quia impeditur eius linea: </s>

<s>1. CVm &longs;u&longs;tinetur manus, &longs;eu brachium, in &longs;itu horizontali im<lb/>mobile, producitur nece&longs;&longs;ariò impetus æqualis impetui gra<lb/>uitationis; alioquin, &longs;i maior e&longs;&longs;et, &longs;ur&longs;um ferretur brachium; &longs;i verò <lb/>minor, deor&longs;um: quia præualeret grauitatio, porrò hic impetus pro<lb/>ducitur tantùm à potentia motrice animantis, in &longs;ingulari organo; <lb/>non verò 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<lb/>per po&longs;ito impetum nullum producit. </s>

<s id="N10767">ideò e&longs;t tardior hic motus in <lb/>plano inclinato, quàm in perpendiculari: </s>

<s id="N1076D">in ea porrò proportione <lb/>e&longs;t tardior, in qua perpendiculum e&longs;t minus linea inclinata, eiu&longs;dem <lb/>&longs;cilicet, altitudinis; </s>

<s>Si anima immediatè in toto <lb/>corpore po&longs;&longs;et producere impetum, homo facilè volare po&longs;&longs;et. </s>

<s id="N10775">quippe eò tardior e&longs;t, quò magis impeditur, & <lb/>magis impeditur, quò maius &longs;patium decurrendum e&longs;t, ad acqui<lb/>rendam eandem altitudinem: igitur eadem e&longs;t proportio impe<lb/>dimenti, quæ &longs;patij, &c. </s>

<s>2. Cùm &longs;u&longs;tinetur funependulum, nullus impetus producitur à <lb/>&longs;u&longs;tinente in ip&longs;o globo, ne &longs;cilicet, &longs;it fru&longs;trà; &longs;ecùs verò, &longs;i attolla<lb/>tur: &longs;ic per quamlibet lineam corpus retineri pote&longs;t &longs;ine impetu in <lb/>eo corpore producto per &longs;e: hinc, cùm duo &longs;e&longs;e inuicem trahunt ad<lb/>uer&longs;o ni&longs;u, neuter in altero producit impetum per &longs;e; &longs;ed per acci<lb/>dens, propter mollitiem, & ten&longs;ionem partium: cùm verò defertur <lb/>aliquid coniunctum, producitur haud dubiè æqualis impetus; hinc <lb/>&longs;eparari non pote&longs;t; quia æqualis e&longs;t motus latoris, & delati: exem<lb/>plum habes in naui. </s>

<s id="N10781">2. Hinc motus &longs;unt vt lineæ permutando: </s>

<s>3. Si verò nauis illicò &longs;i&longs;tat, vel tardiùs moueri pergat, tunc fit &longs;e<lb/>paratio: hinc liquida effunduntur, &longs;i dum feruntur, breuior quietis <lb/>in va&longs;e intercedat morula. </s>

<s id="N10785">hinc mobile de&longs;cendit <lb/>per &longs;e in prædicto plano: </s>

<s id="N1078B">licet enim motus impediatur, non tamen <lb/><expan abbr="tous">totus</expan>, impetus, qui acquiritur in eodem plano e&longs;t imperfectior ac<lb/>qui&longs;ito in perpendiculari in eadem proportione; </s>

<s>Vt feratur cylindrus humeris <expan abbr="cõmodiùs">commodiùs</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, & humero æqualiter <expan abbr="põdus">pondus</expan> di&longs;tribuitur: ideò in circulo <lb/>voluitur &longs;cyphus aqua plenus &longs;ine effu&longs;ione; quia impetus determi<lb/>natus per tangentem circuli aquam ip&longs;am à centro circuli remouet. </s>

<s id="N10796">nam impetus &longs;unt <lb/>vt motus: </s>

<s id="N1079C">hinc pote&longs;t perfectio impetus imminui in infinitum, cùm <lb/>po&longs;&longs;it e&longs;&longs;e in infinitum linea magis, ac magis inclinata: igitur mo<lb/>tum imminui po&longs;&longs;e in infinitum, non tantùm ex vecte, &longs;ed etiam <lb/>ex planis inclinatis haberi pote&longs;t. </s>

<s>4. Cùm 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<lb/>nitum; &longs;i chorda vtrinque trahatur, rumpetur in medio: &longs;i affixa <lb/>extremitati immobili, trahatur à potentia applicata alteri extremi-<pb xlink:href="026/01/031.jpg"/>tati, rumpetur iuxta primam illam extremitatem: &longs;i denique pon<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;ecùs <lb/>alia; vel quarum vtraque in partes oppo&longs;itas mouetur. </s>

<s id="N107A8">3. Hinc producit impetum imperfectiorem impetus acqui&longs;itus <lb/>in hoc eodem plano, quàm acqui&longs;itus in perpendiculari, æqualibus <lb/>&longs;cilicet temporibus, quia cau&longs;a imperfectior imperfectiorem pro<lb/>ducit effectum: </s>

<s id="N107B2">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: </s>

<s>5. Vt quodlibet pondus faciliùs trahatur, &longs;inguli equi trahere <lb/>debent fune communi, potiùs quàm bigati; quia tunc nihil ferè pe<lb/>rit impetus: cùm plures idem pondus trahunt, agunt actione com<lb/>muni, alioqui &longs;inguli in toto pondere &longs;uum impetum producerent; <lb/>igitur &longs;inguli &longs;eor&longs;um trahere? </s>

<s id="N107BC">tempora, quibus percurruntur perpendiculum, & linea plani <lb/>inclinati, &longs;unt vt lineæ; &longs;patia autem, quæ in prædictis lineis acqui<lb/>runtur æqualibus temporibus, &longs;unt vt motus, id e&longs;t, vt lineæ per<lb/>mutando, vt patet ex dictis. </s>

<s>e&longs;&longs;ent, quod fal&longs;um e&longs;t: ideò currus <lb/>paulò po&longs;t initium motus faciliùs mouetur; quia aliquid impetus <lb/>priùs producti remanet: hinc etiam rupto fune, quo trahitur currus, <lb/>currus ip&longs;e modicum tempus adhuc mouetur. </s>

<s id="N107C8">4. Ex his concludo, nece&longs;&longs;ariò per plana omnia eiu&longs;dem altitu<lb/>dinis acquiri eandem velocitatem, quantumuis a&longs;&longs;umantur longi&longs;<lb/>&longs;ima, modò &longs;cilicet perpendicula &longs;int &longs;emper parallela. </s>

<s>6. Si, dum quis trahit toto ni&longs;u magnum aliquod pondus, funis <lb/>rumpatur, pronùs 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<lb/>ti, quo rumpitur finis, qui reuerà maior e&longs;t, propter impedimen<lb/>tum, ex præmi&longs;&longs;is principiis, maiorique applicatione potentiæ, ner<lb/>uorum ten&longs;ione, &c. </s>

<s id="N107CF">Hinc habes <lb/>apud Galileum, per omnes chordas circuli erecti de&longs;cen&longs;um fieri <lb/>æqualibus temporibus. </s>

<s id="N107D6">Vires, quæ &longs;u&longs;tinent pondus in plano in<lb/>clinato per lineam plano <expan abbr="parallelã">parallelam</expan>, &longs;unt ad eas, quæ &longs;u&longs;tinent in per<lb/>pendiculo, vt lineæ permutando; quia debent adæquare impetum, <lb/>qui producitur, tùm in plano inclinato, tùm in perpendiculo. </s>

<s>dum trahitur vnco an nullus immobilis ver<lb/>sùs nauim, nauis fertur versùs littus; dum pellitur aduersùm littus, <lb/>recedit à littore, quia pede, vel genu, imprimitur naui impetus in <lb/>contrariam pattem. </s>

<s>7. Cùm trahitur cylindrus vtrinque æqualiter, qui neque flecti, <lb/>neque tendi pote&longs;t, nullum impetum accipit; imò in tractione nul<lb/>lus impetus e&longs;t inutilis: brachium infligit maiorem ictum, cùm ma<lb/>iorem <expan abbr="arc&utilde;">arcum</expan> de&longs;cribit &longs;uo motu; quia, &longs;cilicet, mouetur motu natu<lb/>raliter accelerato: hinc auer&longs;a manu validior impingitur colaphus, <lb/>quàm aduer&longs;a; quia illa maiorem arcum de&longs;cribit: hinc longius bra<lb/>chium cæteris paribus grauiùs ferit: hinc diu qua&longs;i rotatur bra<lb/>chium, vt longiùs mittatur lapis. </s>

<s id="N107E6">5. Porrò minùs grauitat in ip&longs;um planum inclinatum corpus gra<lb/>ue, quàm in planum horizontale: </s>

<s id="N107EC">e&longs;t autem grauitatio in horizonta<lb/>li, &longs;eu Tangente, ad grauitationem in inclinata, &longs;eu &longs;ecante, vt ip&longs;æ <lb/>lineæ permutando: quod facilè demon&longs;tramus. </s>

<s>8. Maiore fu&longs;te maior ictus infligitur; quia potentia toto ni&longs;u <lb/>agens, diutiùs manet applicata maiori, quàm minori; &longs;untque ictus <lb/>in ratione &longs;ubduplicata vtriu&longs;que fu&longs;tis; v. g. 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, quæ diximus lib. 2. de motu naturali<lb/>ter accelerate, iuxta progre&longs;&longs;ionem numerorum imparium, <lb/>1. 3. 5. &c. </s>

<s id="N107F4">Proiicitur mobile <lb/>faciliùs per inclinatum planum &longs;ur&longs;um, quàm per ip&longs;am perpendi<lb/>cularem: patet experientia: cuius ratio e&longs;t, quia minùs re&longs;i&longs;tit im<lb/>petus innatus, cuius minor e&longs;t ni&longs;us per inclinatam, vt con&longs;tat ex <lb/>dictis. </s>

<s id="N10802">6. Illæ vires, quæ &longs;ufficiunt ad eum motum &longs;ur&longs;um in perpendi<lb/>culo, &longs;ufficiunt ad motum &longs;ur&longs;um in plano inclinato eiu&longs;dem alti<lb/>tudinis: </s>

<s id="N1080A">quia illæ vires &longs;ufficiunt ad a&longs;cen&longs;um, quæ acquiruntur in <lb/>toto de&longs;cen&longs;u: &longs;ed in de&longs;cen&longs;u inclinatæ, & perpendiculi acquirun<lb/>tur vires æquales, id e&longs;t, velocitas æqualis, vt dictum e&longs;t &longs;uprà. </s>

<s id="N10812">Om<lb/>nia puncta plani inclinati rectilinei, imò & horizontalis, &longs;unt di<lb/>uer&longs;æ inclinationis: in iis tamen planis inclinatis quæ vulgò a&longs;&longs;u<lb/>muntur, non mutatur &longs;en&longs;ibiliter inclinatio. </s>

<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<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 æqualem <lb/>vtrinque dirimit impetum: ratio e&longs;t; quia tunc totus impetus agit, <lb/>quantùm pote&longs;t; illud autem punctum Geometria demon&longs;trat e&longs;&longs;e <lb/>terminum mediæ proportionalis, inter totum cylindrum, & &longs;ub<lb/>duplum; modò nulla ratio vectis habeatur alioquin centrum pro<lb/>cu&longs;&longs;ionis di&longs;tat 2/3 ab extremitate immobili. </s>

<s>10. Cùm 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/>tantùm agit impetus extrin&longs;ecùs adueniens; verùm etiam potentia <lb/>quædam media, quæ corpora compre&longs;&longs;a, vel ten&longs;a, ad pri&longs;tinum <lb/>&longs;tatum reducit: hinc maximus e&longs;t ictus tudiculæ, cùm eo in&longs;tanti, <lb/>quo reductum e&longs;t omninò manubrium priori rectitudini, infligitur <lb/>ictus, quia tunc vis potentiæ mediæ e&longs;t maxima. </s>

<s id="N1081E">7. Hinc minùs de&longs;truitur impetus in plano inclinato &longs;ur&longs;um, <lb/>quàm in perpendiculo; </s>

<s id="N10824">quia diutiùs durat: </s>

<s>11. Rotato flagello ideò maxima vis ine&longs;t, quia diutiùs potentia <lb/>manet applicata: hinc vides hoc principium e&longs;&longs;e vniuer&longs;ali&longs;&longs;imum, <lb/>quod iactis, pul&longs;is, & 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. g. duplum impetum acquirit: nam <lb/>&longs;ingulæ partes &longs;eor&longs;im æqualem impetum acquirunt. </s>

<s id="N10828">cùm enim minùs ac<lb/>quiratur in de&longs;cen&longs;u, vt dictum e&longs;t, minùs etiam de&longs;truitur in a&longs;<lb/>cen&longs;u: </s>

<s id="N10830">hinc accedit propriùs hic motus ad æquabilem: </s>

<s id="N10834">in eodem <lb/>plano rectilineo pote&longs;t e&longs;&longs;e a&longs;cen&longs;us, & de&longs;cen&longs;us, versùs eandem <lb/>partem: </s>

<s id="N1083C">tale e&longs;&longs;et planum horizontale, in cuius vnico tantùm pun<lb/>cto nulla e&longs;t inclinatio: in quolibet puncto huius plani e&longs;t &longs;ingu<lb/>laris inclinatio, vt patet, quæ e&longs;t ad perpendiculum, vt Tangens ad <lb/>&longs;ecantem é&longs;tque eadem proportio motuum. </s>

<s>12. Si verò ex diuer&longs;a altitudine cadant, vel &longs;unt æquales, vel <lb/>inæquales: &longs;i primum, ictus &longs;unt vt tempora, quibus cadunt: &longs;i <lb/>&longs;ecundum, ictus &longs;unt in ratione compo&longs;ita temporum, & mal<lb/>leorum: &longs;i &longs;unt infinitæ, partes actu, nulla e&longs;t proportio percu&longs;&longs;ionis <lb/>granuli cadentis, & rupis ingentis grauitantis; &longs;ed hoc vltimum fal<lb/>&longs;um e&longs;&longs;e con&longs;tat; non pote&longs;t tamen determinari proportio vitium <lb/>grauitationis, & percu&longs;&longs;ionis, ni&longs;i numerus in&longs;tantium: quibus durat <lb/>motus deor&longs;um cogno&longs;catur. </s>

<s id="N10848">8. Corpus graue in &longs;uperficie quadrantis caua, deor&longs;um cadit <lb/>motu naturaliter accelerato; </s>

<s>13. Leui&longs;&longs;imi lapides vix emittuntur ad modicam di&longs;tantiam; <lb/>quia &longs;tatim &longs;eparantur à potentia: parallelipedum cadens de or<lb/>&longs;um in &longs;itu horizontali maximum ictum infligit in centro grauita<lb/>tis, id e&longs;t, in medio; quia tunc totus impetus agit, totus enim impe<lb/>ditur: in aliis punctis minor e&longs;t ictus, iuxta proportionem maioris <lb/>di&longs;tantiæ à prædicto centro: &longs;i verò percutiatur cylindrus innatans, <lb/>maxima erit vis, vel effectus ictus in centro grauitatis propter ean<lb/>dem rationem. </s>

<s id="N1084E">quia &longs;ingulis in&longs;tantibus accedit nouus <pb xlink:href="026/01/017.jpg"/>impetus; </s>

<s id="N10856">non tamen æqualibus temporibus, acquiruntur æqualia <lb/>velocitatis momenta; </s>

<s id="N1085C">quia in &longs;ingulis punctis quadrantis, e&longs;t diuer<lb/>&longs;a tangens; </s>

<s id="N10862">igitur mutatur progre&longs;&longs;io accelerationis, quæ certè ma<lb/>jor e&longs;t initio, & &longs;ub finem minor; quia initio tangentes acce<lb/>dunt propriùs ad perpendiculum, & &longs;ub finem ad horizonta<lb/>lem. </s>

<s id="N1086E">9. De&longs;cendit etiam in &longs;uperficie conuexa globi erecti motu ac<lb/>celerato; </s>

<s id="N10874">initio quidem, in minore proportione; </s>

<s id="N10878">&longs;ub finem, in maio<lb/>re; </s>

<s id="N1087E">vnde e&longs;t inuer&longs;a prioris: </s>

<s id="N10882">pote&longs;t etiam de&longs;cendere corpus graue <lb/>v&longs;que ad centrum terræ motu accelerato, in &longs;uperficie conuexa &longs;e<lb/>micirculi: </s>

<s id="N1088A">&longs;i &longs;uperficies terræ e&longs;&longs;et læuigati&longs;&longs;ima, corpus proje<lb/>ctum moueretur in ea motu æquabili, nec de&longs;trueretur impetus im<lb/>pre&longs;&longs;us, vt con&longs;tat; </s>

<s id="N10892">pote&longs;t quoque de&longs;cendere per &longs;piralem: &longs;unt in<lb/>finita plana curua, in quibus faciliùs moueri pote&longs;t, quam in ho<lb/>rizontali recta. </s>

<s id="N108A1"><emph type="center"/><emph type="italics"/>De motu mixto ex rectis.<emph.end type="italics"/><emph.end type="center"/></s>

<s id="N108AE">1. DAri motum mixtum ille non dubitat, qui di&longs;cum proiicit. </s>

<s id="N108B1"><lb/>Mixtus ex duobus rectis æquabilibus e&longs;t rectus, e&longs;t que <lb/>diagonalis vtriu&longs;que: </s>

<s id="N108B8">hinc de&longs;truitur aliquid impetus, iuxta pro<lb/>portionem differentiæ diagonalis, & vtriu&longs;que lateris &longs;imul &longs;ump<lb/>ti; </s>

<s id="N108C0">quia, &longs;cilicet, e&longs;t fru&longs;trà: </s>

<s id="N108C4">quò maior e&longs;t angulus, quem faciunt li<lb/>neæ determinationum, minor e&longs;t diagonalis; igitur plùs impetus <lb/>de&longs;truitur, donec tandem concurrant in oppo&longs;itas lineas, tunc enim <lb/>totius impetus de&longs;truitur. </s>

<s id="N108D0">2. <expan abbr="Qu&utilde;">Quum</expan> minor e&longs;t, vel acutior prædictus angulus, minùs impetus <lb/>de&longs;truitur; </s>

<s id="N108DA">quia diagonalis maior e&longs;t; </s>

<s id="N108DE">donec tandem conueniant in <lb/>eandem lineam, tunc enim nihil de&longs;truitur: </s>

<s id="N108E4">datur de facto hic mo<lb/>tus in rerum natura; </s>

<s id="N108EA">talis e&longs;t motus nauis à duobus ventis impre&longs;<lb/>&longs;us; vel eiu&longs;dem partis aëris; imò & ip&longs;ius venti: </s>

<s id="N108F0">motus mixtus ex <lb/>duobus retardatis iuxta eandem progre&longs;&longs;ionem e&longs;t rectus; </s>

<s id="N108F6">quia fit <lb/>per hypothenu&longs;im triangulorum proportionalium: idem dico de <lb/>duobus acceleratis. </s>

<s id="N10900">3. Si mixtus &longs;it ex æquali, & accelerato, vel ex duobus accelera<lb/>tis in diuer&longs;a progre&longs;&longs;ione, vel ex duobus retardatis &longs;imiliter, fit per <lb/>lineam curuam, vt patet: </s>

<s id="N10908">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, & <lb/>retardato violento: e&longs;t enim acceleratus naturalis, cùm deor&longs;um <lb/>deor&longs;um tendat qua&longs;i per gradus, &longs;eu diuer&longs;a plana inclinata. </s>

<s id="N10916">4. Non tamen impetus acqui&longs;itus in eo motu e&longs;t eiu&longs;dem perfe<lb/>ctionis cum illo, qui acquireretur in perpendiculari eiu&longs;dem longi<lb/>tudinis; </s>

<s id="N1091E">&longs;ed tantùm eiu&longs;dem altitudinis: </s>

<s id="N10922">nam perinde cre&longs;cit ille <lb/>impetus, atque cre&longs;ceret in diuer&longs;is planis inclinaris: </s>

<s id="N10928">impetus verò <lb/>violentus in hoc motu retardatur; </s>

<s id="N1092E">tùm, 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, quòd aliqui <lb/>dicant, ab aëre de&longs;trui, qui non minùs re&longs;i&longs;tit naturali, quàm vio<lb/>lento. </s>

<s id="N1093A">5. Adde, quòd e&longs;t duplex determinatio: </s>

<s id="N1093E">igitur aliquid de&longs;trui de<lb/>bet, non acqui&longs;iti; igitur impre&longs;&longs;i: </s>

<s id="N10944">de&longs;trui autem non dicitur acqui<lb/>&longs;itus, quòd, &longs;cilicet, plùs de nouo accedat, quàm pereat; </s>

<s id="N1094A">e&longs;t enim ac<lb/>celeratus: </s>

<s id="N10950">adde, quòd non infligitur tantus ictus &longs;ub finem; </s>

<s id="N10954">igitur <lb/>de&longs;truitur aliquid impetus, non acqui&longs;iti, eo modo, quo diximus; </s>

<s id="N1095A"><lb/>igitur impre&longs;&longs;i: ita tamen &longs;en&longs;im de&longs;truitur, vt pro æquabili per ali<lb/>quod &longs;patium qua&longs;i haberi po&longs;&longs;it. </s>

<s id="N10963">6. Hinc mobile proiectum per horizontalem, ne primo quidem <lb/>in&longs;tanti per horizontalem mouetur, alioqui non e&longs;&longs;et motus mix<lb/>tus: </s>

<s id="N1096B">tardiùs cadit mobile ita proiectum in planùm horizontale &longs;ub<lb/>iectum, quàm cum &longs;ua &longs;ponte, ex eadem altitudine de&longs;cendit: </s>

<s id="N10971">cuius <lb/>rei clari&longs;&longs;ima e&longs;t experientia: ratio e&longs;t; </s>

<s id="N10977">quia impetus acqui&longs;itus in <lb/>hoc iactu non e&longs;t eiu&longs;dem perfectionis, cùm acqui&longs;ito in perpendi<lb/>culo: </s>

<s id="N1097F">cùm proiicitur mobile per inclinatam &longs;ur&longs;um, mouetur motu <lb/>mixto ex naturali æquabili, & violento retardato: patet prima pars; </s>

<s id="N10985"><lb/>quia acceleratur tantùm naturalis deor&longs;um, &longs;altem in inclinata: </s>

<s id="N1098A">&longs;e<lb/>cunda pars etiam patet; quia &longs;ub finem minor e&longs;t ictus. </s>

<s id="N10992">7. Hinc linea motus e&longs;t curua: </s>

<s id="N10996">iuxta diuer&longs;am progre&longs;&longs;ionem de<lb/>&longs;truitur hic impetus impre&longs;&longs;us: </s>

<s id="N1099C">tùm pro diuer&longs;a inclinatione plani, <lb/>cuius etiam hîc habetur ratio; </s>

<s id="N109A2">nam &longs;ingulis in&longs;tantibus mutatur: </s>

<s id="N109A6"><lb/>tùm, quia modò plùs impetus e&longs;t fru&longs;trà, modò minùs; </s>

<s id="N109AB">plùs <lb/>certè, cùm linea determinationis impetus impre&longs;&longs;i facit obtu<lb/>&longs;iorem: </s>

<s id="N109B3">atqui initio e&longs;t obtu&longs;ior; &longs;ub finem verò a&longs;cen&longs;us acu<lb/>tior. </s>

<s id="N109BB">8. A&longs;cen&longs;us proiecti per inclinatam diutiùs durat, quàm de&longs;<lb/>cen&longs;us, ratione eiu&longs;dem plani horizontalis; </s>

<s id="N109C1">quia, &longs;cilicet, a&longs;<lb/>cen&longs;us longior e&longs;t, quàm de&longs;cen&longs;us: </s>

<s id="N109C7">e&longs;t autem longior; </s>

<s id="N109CB">quia, vt <lb/>e&longs;&longs;et æqualis, nihil impetus impre&longs;&longs;i deberet de&longs;trui in a&longs;cen&longs;u <pb xlink:href="026/01/019.jpg"/>porrò in de&longs;cen&longs;u e&longs;t motus mixtus ex accelerato naturali, <lb/>& retardato violento, vt con&longs;tat ex dictis: </s>

<s id="N109D7">iactus per incli<lb/>natam ad angulum 45. e&longs;t omnium maximus, ratione eiu&longs;dem <lb/>plani horizontalis: clara e&longs;t experientia. </s>

<s id="N109DF">Ratio e&longs;t: </s>

<s id="N109E2">quia per verti<lb/>calem &longs;ur&longs;um, nihil acquiritur in plano horizontali, ex quo fit ia<lb/>ctus; </s>

<s id="N109EA">nihil etiam per ip&longs;am horizontalem; igitur plùs acquiritur per <lb/>illam, quæ maximè ab vtraque &longs;imul recedit. </s>

<s id="N109F2">9. Hæc ratio e&longs;t verè phy&longs;ica, geometrica nulla e&longs;t: hinc illi <lb/>iactus æquale &longs;patium acquirunt in prædicto plano horizontali, <lb/>qui fiunt per inclinatas æqualiter à prædicta inclinata ad ang. 45. <lb/>di&longs;tantes. </s>

<s id="N109FC">Cùm emittitur mobile per inclinatum deor&longs;um, in libero <lb/>medio, mouetur motu mixto ex naturali accelerato, & impre&longs;<lb/>&longs;o retardato, vt con&longs;tat ex dictis; </s>

<s id="N10A04">ille autem primus accelera<lb/>tur per acce&longs;&longs;ionem impetus perfectionis quàm in iactu per ho<lb/>rizontalem; </s>

<s id="N10A0C">&longs;ed imperfectionis, quàm in perpendiculo: </s>

<s id="N10A10">retarda<lb/>tur verò impetus minùs, quàm in iactu per horizontalem; plùs ve<lb/>rò, quàm in iactu per ip&longs;um perpendiculum, in quo nihil impetus <lb/>de&longs;truitur. </s>

<s id="N10A1C">10. Cùm è 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 æquabili, ex verti<lb/>cali retardato, & horizontali æquabili: </s>

<s id="N10A24">mouetur &longs;ur&longs;um per cur<lb/>uam, &longs;empérque capiti iaculatoris imminet; </s>

<s id="N10A2A">quippe tantùm acqui<lb/>rit in horizontali, quantùm nauis: </s>

<s id="N10A30">in de&longs;cen&longs;u verò e&longs;t motus <expan abbr="mix">mixtus</expan> <lb/>ex horizontali retardato, & naturali accelerato: </s>

<s id="N10A3A">quia tamen bre<lb/>ui&longs;&longs;imo illo tempore, retardatio illa horizontalis non e&longs;t &longs;en&longs;ibilis, <lb/>ferè in ip&longs;ius iaculatoris caput de&longs;cendit; quod certè phænomenon <lb/>ex no&longs;tris principiis euincitur. </s>

<s id="N10A46">11. Parum cautè Vfanus vniuer&longs;im a&longs;&longs;erit, iaculationem pilæ ex<lb/>tormento, maiorem e&longs;&longs;e ex naui in continentem, & minorem vi<lb/>ci&longs;&longs;im, cùm vtriu&longs;que differentia peti po&longs;&longs;it, vel à puluere tormen<lb/>tario, vel ab eius compre&longs;&longs;ione, vel humiditate, vel tormenti fabri<lb/>ca, vel ip&longs;ius demum nauigij motu, qui pilæ motum, vel accelerat, &longs;i <lb/>versùs eandem partem e&longs;t, vel retardat è contrario: in plano ho<lb/>rizontali duro pote&longs;t e&longs;&longs;e motus mixtus ex duobus, tribus, qua<lb/>tuor, & pluribus aliis. </s>

<s id="N10A5A">12. Cùm è naui mobili emittitur &longs;agitta per horizontalem, quæ fa<lb/>cit angelum rectum cum linea directionis nauis, fertur qua&longs;i per dia<lb/>gonalem vtriu&longs;que, &longs;altem per aliquod &longs;patium: </s>

<s id="N10A62">cùm verò emitti-<pb xlink:href="026/01/020.jpg"/>tur per horizontalem, quæ conueniat cum eadem linea directionis, <lb/>iactus e&longs;t longior toto illo &longs;patio, quod nauis decurrit, dum iactus <lb/>durat; </s>

<s id="N10A6E">breuior tamen, &longs;i in partem oppo&longs;itam fiat iactus in hoc ca<lb/>&longs;u, &longs;i nauis æqualem impetum imprimeret, deor&longs;um rectà ferretur <lb/>mobile motu naturali; </s>

<s id="N10A76">imò &longs;agitta po&longs;&longs;et retorqueri in iaculatorem: </s>

<s id="N10A7A"><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>

<s id="N10A88"><emph type="center"/><emph type="italics"/>De motu reflexo.<emph.end type="italics"/><emph.end type="center"/></s>

<s id="N10A95">1. MOtus reflexi vera cau&longs;a e&longs;t impetus prior, ad nouam li<lb/>neam determinatus ab occurrente obice; </s>

<s id="N10A9B">planum refle<lb/>ctens e&longs;t cau&longs;a nouæ determinationis &longs;uo modo; </s>

<s id="N10AA1">cau&longs;am enim di<lb/>co eam, ex qua aliquid &longs;equitur: </s>

<s id="N10AA7">ex gemina determinatione, noua, <lb/>&longs;cilicet, per ip&longs;am perpendicularem erectam in puncto contactus, <lb/>& priore per lineam incidentiæ, ab eodem puncto contactus pro<lb/>pagatam, fit determinatio mixta per lineam reflexionis; </s>

<s id="N10AB1">quæ omnia <lb/>patent ex terminis: </s>

<s id="N10AB7">hinc nullus impetus producitur à plano refle<lb/>ctente; </s>

<s id="N10ABD">quippe prior pote&longs;t determinari ad nouam lineam: adde, <lb/>quòd planum, quod caret impetu, impetum producere non pote&longs;t. </s>

<s id="N10AC5">2. Imò nihil impetus de&longs;truitur in reflexione pura per &longs;e; </s>

<s id="N10AC9">quia ni<lb/>hil impetus e&longs;t fru&longs;trà per &longs;e in pura reflexione; </s>

<s id="N10ACF">multus tamen im<lb/>petus de&longs;truitur per accidens, tùm ab ip&longs;o attritu tùm mollitie <lb/>& ce&longs;&longs;ione, tùm pre&longs;&longs;ione: </s>

<s id="N10AD7">hinc &longs;uppo&longs;ito eodem iactu, perpendi<lb/>cularis reflexa e&longs;t omnium reflexarum minima; </s>

<s id="N10ADD">quia per eam li<lb/>neam maximus ictus infligitur; </s>

<s id="N10AE3">igitur maxima e&longs;t partium colli&longs;io, <lb/>& pre&longs;&longs;io: hinc etiam corpora duriora longiùs reflectuntur, per ip&longs;am <lb/>quoque <expan abbr="perpendicular&etilde;">perpendicularem</expan>, dum planum reflectens &longs;it æquè durum. </s>

<s id="N10AF1">3. Determinatio noua dupla e&longs;t prioris, po&longs;ita linea incidentiæ <lb/>perpendiculari, & po&longs;ito etiam plano reflectente immobili; </s>

<s id="N10AF7">quia <lb/>alioquin anguli reflexionis non e&longs;&longs;ent æquales angulis incidentiæ: </s>

<s id="N10AFD"><lb/>&longs;i globus reflectens &longs;it æqualis impacto, æqualis e&longs;t ce&longs;&longs;io re&longs;i&longs;tenciæ <lb/>cùm &longs;it æquale agens re&longs;i&longs;tenti, perid enim reflectens re&longs;i&longs;tit, per <lb/>quod e&longs;t: </s>

<s id="N10B06">igitur, &longs;i æqualis re&longs;i&longs;tit, & cedit, certè æqualiter ce<lb/>dit, & re&longs;i&longs;tit: </s>

<s id="N10B0C">hinc noua determinatio æqualis e&longs;t priori: </s>

<s id="N10B10">hinc glo<lb/>bus impactis &longs;i&longs;tit immobilis; quia ex duabus determinationibus <lb/>oppo&longs;itis neutra præualet. </s>

<s id="N10B1D">4. Tantum e&longs;t ab æqualitate prædicta ce&longs;&longs;ionis, & re&longs;i&longs;tentiæ, ad <lb/>nullam ce&longs;&longs;ionem, & 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>, & totam ce&longs;&longs;ionem: </s>

<s id="N10B28">hinc, cùm à tota ce&longs;&longs;ione ad æqua<lb/>litatem prædictam acquiratur tantùm noua determinato æqualis <lb/>priori; </s>

<s id="N10B30">igitur ab eadem æqualitate ad nullam ce&longs;&longs;ionem tantun<lb/>dem acquiritur; </s>

<s id="N10B36">igitur dupla prioris, vt iam &longs;uprà dictum e&longs;t; </s>

<s id="N10B3A">nulla <lb/>e&longs;&longs;et re&longs;i&longs;tentia in vacuo; nulla e&longs;t ce&longs;&longs;io, cùm ip&longs;um corpus refle<lb/>ctens nullo modo mouetur ab ictu. </s>

<s id="N10B44">5. Determinatio noua per lineam obliquam, e&longs;t ad nouam per <lb/>lineam perpendicularem, vt &longs;inus rectus anguli incidentiæ, ad &longs;i<lb/>num totum, in qualibet hypothe&longs;i; </s>

<s id="N10B4C">quia &longs;unt hæ, vt ictus, per vtran<lb/>que lineam; </s>

<s id="N10B52">ictus verò vt grauitationes in horizontale planum, & <lb/>in planum inclinatum, &longs;ub angulo complementi anguli incidentiæ: </s>

<s id="N10B58"><lb/>hinc noua determinatio per lineam obliquam, e&longs;t vt dupla &longs;inus re<lb/>cti anguli incidentiæ, ad &longs;inum totum: </s>

<s id="N10B5F">hinc &longs;upra angulum inci<lb/>dentiæ 30, noua e&longs;t maior priore, infrà minor; in ip&longs;o angulo 30. <lb/>æqualis, &longs;uppo&longs;ita hypothe&longs;i plani reflectentis immobilis. </s>

<s id="N10B69">6. Ex hoc po&longs;itiuo principio demon&longs;tratur accurati&longs;&longs;imè æqua<lb/>litas anguli reflexionis, & incidentiæ, quod certè demon&longs;tratum <lb/>non fuit ab Ari&longs;t. in problematis, &longs;ect. 17. problem. 4. & 13. quibus <lb/>in locis fusè &longs;atis explicatur hoc Theorema, ducta comparatione, <lb/>tùm à grauibus, quæ cadunt, tùm ab orbibus, quæ rotantur, rùm à <lb/>&longs;peculis: &longs;ed minimè demon&longs;tratur ex certis principiis &longs;ine petitio<lb/>ne principij. </s>

<s id="N10B79">In puncto reflexionis, po&longs;ita hypothe&longs;i plani immo<lb/>bilis reflectentis, nulla datur quies; </s>

<s id="N10B7F">quia vnum tantùm e&longs;t conta<lb/>ctus in&longs;tans; &longs;ed eo in&longs;tanti e&longs;t motus, quo primo acquiritur locus. </s>

<s id="N10B87">7. Omnes lineæ reflexæ per &longs;e &longs;unt æqualis longitudinis, & ab <lb/>eodem puncto contactus, ad communem peripheriam terminan<lb/>tur: </s>

<s id="N10B8F">&longs;i globus impactus &longs;it æqualis reflectenti, &longs;itque linea inciden<lb/>tiæ obliqua quælibet terminata ad idem punctum contactus, re<lb/>flectitur prædictus globus per lineam tangentem globum refle<lb/>ctentem in eodem puncto; </s>

<s id="N10B99">quia hæc tangens e&longs;t diagonalis com<lb/>munis, & determinatio mixta communis omnibus lineis inciden<lb/>tiæ: e&longs;t tamen modò longior, modò breuior linea reflexa, é&longs;tque vt <lb/>vt &longs;inus complementi anguli incidentiæ, ad &longs;inum totum, qui &longs;it <lb/>determinatio prior, vt facilè demon&longs;tramus. </s>

<s id="N10BA7">8. Si globus impactus &longs;it minor corpore reflectente, reflectitur <lb/>etiam per ip&longs;am perpendicularem, & determinatio noua e&longs;t dupla<lb/>prioris, minùs 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, minùs vna quarta, <lb/>&c. </s>

<s id="N10BB4">ratio e&longs;t, quia in ea proportione globus reflectens cedit, in <lb/>qua mouetur, igitur tantùm detrahitur determinationis impacto <lb/>globo, quantùm additur motus reflectenti: at verò noua determina<lb/>tio per lineam incidentiæ obliquam, e&longs;t ad nouam per ip&longs;am per<lb/>pendicularem, vt &longs;inus rectus anguli incidentiæ ad &longs;inum totum. </s>

<s id="N10BC2">9. In hac hypothe&longs;i lineæ reflexæ omnes &longs;unt &longs;upra prædictam <lb/>tangentem, &longs;eu &longs;ectionem plani, maiores, vel minores, pro diuer&longs;a <lb/>men&longs;ura diagonalis: </s>

<s id="N10BCA">in &longs;uperiori verò hypothe&longs;i æqualium globo<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 prædictam &longs;ectionem. </s>

<s id="N10BD2">Porrò in hac <lb/>hypothe&longs;i vltima, determinatio noua per ip&longs;am perpendicularem <lb/>e&longs;t minor priore: </s>

<s id="N10BDA">hinc non modò nulla fit reflexio in perpendicula<lb/>ri, &longs;ed linea directa vlteriùs propagatur; quia prior determinatio <lb/>præualet. </s>

<s id="N10BE4">10. Detrahitur priori portio æqualis rationi globorum; </s>

<s id="N10BE8">v. g. glo<lb/>bus reflectens e&longs;t &longs;ubduplus impacto de trahitur priori determina<lb/>tioni vna &longs;ecunda; </s>

<s id="N10BF0">e&longs;t &longs;ubquadruplus, vna quarta; atque ita dein<lb/>ceps: </s>

<s id="N10BF6">ratio patet ex dictis: </s>

<s id="N10BFA">in linea verò incidentiæ obliqua, deter<lb/>minatio e&longs;t ad determinationem in perpendiculari, vt &longs;inus rectus <lb/>anguli incidentiæ ad &longs;inum totum: linea demum reflexa e&longs;t modò <lb/>maior, modò minor pro diuer&longs;a diagonali. </s>

<s id="N10C06">11. Si duo globi æquales in &longs;e inuicem impingantur æquali mo<lb/>tu, per lineam connectentem centra, vterque æquali motu priori re<lb/>troagitur; </s>

<s id="N10C0E">quia æqualis in æqualis æqualem impetum imprimit: </s>

<s id="N10C12">non <lb/>e&longs;t tamen motus reflexus; </s>

<s id="N10C18">quia totus prior impetus de&longs;truitur, vt <lb/>patet ex dictis: </s>

<s id="N10C1E">&longs;i autem inæquali motu concurrant, retroaguntur <lb/>ii&longs;dem motibus, permutando; quod etiam clarum e&longs;t: hinc egre<lb/>gium paradoxum, &longs;i quod aliud con&longs;equitur, &longs;cilicet, globum A, v. <lb/>g. æqualem motum imprimere globo B, &longs;iue hic moueatur, &longs;iue <lb/>quie&longs;cat. </s>

<s id="N10C2C">12. Si verò linea incidentiæ &longs;it obliqua, vterque globus reflecte<lb/>tur pror&longs;us vt à plano immobili: </s>

<s id="N10C32">hinc reflexio &longs;it ad angulos æqua<lb/>les, & lineæ omnes reflexionis &longs;unt æquales: ratio e&longs;t; </s>

<s id="N10C38">quia, quantùm <lb/>detrahit globus reflectens re&longs;i&longs;tendo, tantùm addit in partem op<lb/>po&longs;itam repellendo, po&longs;itiuo ni&longs;u, vel impetu: quòd &longs;i alter globus <lb/>maiore, vel minore motu moueatur, vel &longs;i globi &longs;int inæquales, <lb/>cum æquali motu, vel inæquali, res etiam determinari pote&longs;t ex <lb/>præmi&longs;&longs;is. </s>

<s id="N10C4B">13. Cum duo globi in &longs;e&longs;e inuicem impinguntur æquali motu, <lb/>minor retroagitur velociore motu, quàm ante moueretur, vt clarum <lb/>e&longs;t: </s>

<s id="N10C53">maior verò, &longs;i duplus e&longs;t alterius, &longs;i&longs;tit immobilis in puncto <lb/>contactus; </s>

<s id="N10C59">&longs;i maior duplo &longs;uum iter pro&longs;equitur, &longs;ed tardiore mo<lb/>tu; &longs;i minor duplo, retroagitur: quæ omnia facilè ex dictis demon<lb/>&longs;trantur. </s>

<s id="N10C61">Pote&longs;t impetus e&longs;&longs;e æqualis alteri, & præualere; pote&longs;t <lb/>æqualem impetum producere hoc in&longs;tanti, & &longs;tatim in&longs;tanti, quod <lb/>&longs;equitur, totus de&longs;trui. </s>

<s id="N10C6B">14. Pote&longs;t globus retroagi in plano horizontali, licèt in aliud cor<lb/>pus non incidat, ita vt initio tendat in ortum, verbi gratia: </s>

<s id="N10C71">tùm <lb/>deinde, licèt nihil pror&longs;us addatur, versùs occa&longs;um; </s>

<s id="N10C77">quod accidit, <lb/>cum globus vtroque motu, centri, &longs;cilicet, & orbis, mouetur, &longs;ed <lb/>contrario; primùm enim motus centri præualet, &longs;ed facilè cedit <lb/>propter attritum maiorem partium. </s>

<s id="N10C81">Nullus datur propriè motus <lb/>refractus: </s>

<s id="N10C87">licèt enim incuruetur linea motus, dum per aquam &longs;u<lb/>bit mobile; hæc tamen e&longs;t reflexionis &longs;pecies. </s>

<s id="N10C8F">15. Globus reflectens, qui ab ictu alterius mouetur, non mouetur <lb/>in&longs;tanti contactus; </s>

<s id="N10C95">quia impetus primo in&longs;tanti, quo e&longs;t, non mo<lb/>uetur; </s>

<s id="N10C9B">producitur enim impetus primo in&longs;tanti contactus: </s>

<s id="N10C9F">&longs;i impe<lb/>tus e&longs;&longs;et tantùm determinatus ad vnam lineam, nulla fieri po&longs;&longs;et <lb/>reflexio, &longs;ed tantùm repercu&longs;&longs;io; </s>

<s id="N10CA7">quia veri&longs;&longs;ima cau&longs;a reflexionis <lb/>con&longs;i&longs;tit in noua determinatione: </s>

<s id="N10CAD">per reflexionem po&longs;&longs;unt colligi <lb/>plures partes aëris &longs;onori ad Echometriam: </s>

<s id="N10CB3">&longs;agitta emi&longs;&longs;a per ho<lb/>rizontalem &longs;ursùm, tantillùm a&longs;cendit per arcum; quia tantillùm <lb/>reflectitur ab aëre. </s>

<s id="N10CC2"><emph type="center"/><emph type="italics"/>De motu circulari.<emph.end type="italics"/><emph.end type="center"/></s>

<s id="N10CCF">1. DAri motum circularem, probatur infinitis ferè experimen<lb/>tis: </s>

<s id="N10CD5">cuius ratio à priori e&longs;t, quòd po&longs;&longs;int extremitates eiu&longs;<lb/>dem cylindri in partes oppo&longs;itas pelli; </s>

<s id="N10CDB">vnde &longs;equitur nece&longs;&longs;ariò <lb/>motus circularis; quem ij negare coguntur, qui ex punctis mathe<lb/>maticis quantitatem componunt. </s>

<s id="N10CE3">Motus circularis in &longs;ublunaribus <lb/>oritur ex recto impedito; </s>

<s id="N10CE9">quia, &longs;cilicet, determinatur tantùm im<lb/>petus ad lineam rectam: </s>

<s id="N10CEF">hinc quidam motus circularis e&longs;t merè <lb/>per accidens, vt cùm retinetur extremitas funependuli, &longs;eu <pb xlink:href="026/01/024.jpg"/>fundæ, quæ &longs;i demittatur, &longs;equitur motus rectus: </s>

<s id="N10CF9">quidam tamen <lb/>non e&longs;t merè peraccidens, vt cùm pellitur extremitas cylindri in <lb/>plano horizontali; e&longs;t enim, iuxta in&longs;titutionem naturæ, ad facili<lb/>tatem motus. </s>

<s id="N10D05">2. Quippe tale e&longs;t naturæ in&longs;titutum, vt eo motu corpora mo<lb/>ueantur, quo faciliùs moueri po&longs;&longs;unt: </s>

<s id="N10D0B">atqui cùm pellitur altera cy<lb/>lindri extremitas, in plano horizontali putà innatantis, faciliùs <lb/>mouetur, quàm recto, & qua&longs;i minore &longs;umptu, cùm minùs &longs;patij <lb/>acquirat: æquali tempore: </s>

<s id="N10D15">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 vnquàm, &longs;ed tantùm oritur hic motus ex <lb/>determinatione per tangentem impedita, ratione alicuius puncti <lb/>immobilis. </s>

<s id="N10D23">3. Hinc, &longs;i tollatur impedimentum, &longs;tatim per tangentem or<lb/>bis fit motus, vt patet in funda: </s>

<s id="N10D29">inæqualiter partes radij prædicti <lb/>orbis mouentur, iuxta proportionem di&longs;tantiæ maioris, & minoris <lb/>à centro: </s>

<s id="N10D31">hinc propagatio impetus inæqualis, de qua iam &longs;uprà, <lb/>&longs;ingulis in&longs;tantibus & punctis e&longs;t noua determinatio; </s>

<s id="N10D37">quia, &longs;cilicet, <lb/>&longs;ingulis punctis &longs;ua tangens re&longs;pondet: </s>

<s id="N10D3D">hinc, &longs;i imponatur rotæ <lb/>aliud corpus, &longs;tatim abigitur, &longs;ine &longs;it in &longs;itu verticali, &longs;iue in &longs;itu ho<lb/>rizontali; hinc dum turbo rotatur, &longs;i vel aquæ guttula eius &longs;uper<lb/>ficies a&longs;pergitur, & &longs;tatim di&longs;pergitur. </s>

<s id="N10D49">4 Dari impetum in motu circulari certi&longs;&longs;imum e&longs;t: </s>

<s id="N10D4D">punctum phy<lb/>&longs;icum e&longs;t capax huius motus; cuius finis multiplex e&longs;t; </s>

<s id="N10D53">corpus mo<lb/>uetur motu circulari circa centrum immobile cum motus centri <lb/>impeditur non tamen motus orbis, ad quem impetus facilè deter<lb/>minatur, cùm &longs;it ad omnes lineas indifferens: </s>

<s id="N10D5D">adde v&longs;um vectis, <lb/>trochleæ, aliorúmque organorum, qui &longs;ine motu circulari e&longs;&longs;e non <lb/>pote&longs;t: omitto motum progre&longs;&longs;iuum, ipsúmque brachiorum, & ti<lb/>biarum v&longs;um, qui motu circulari carere non pote&longs;t. </s>

<s id="N10D69">5. Motus circularis rotæ in plano verticali e&longs;t æquabilis per &longs;e; </s>

<s id="N10D6D"><lb/>quia nihil e&longs;t, quod impetum &longs;emel impre&longs;&longs;um de&longs;truat: </s>

<s id="N10D72">licèt enim <lb/>&longs;ingulis in&longs;tantibus &longs;it noua determinatio, nullus tamen impetus <lb/>e&longs;t fru&longs;trà; </s>

<s id="N10D7A">quippe illud &longs;patium acquiritur in linea curua, quod in <lb/>recta, &longs;i nullum e&longs;&longs;et impedimentum, percurreret: </s>

<s id="N10D80">quemadmodum <lb/>enim in reflexione, quæ fit à plano immobili, nullus de&longs;truitur im<lb/>petus; </s>

<s id="N10D88">ita nullus hîc de&longs;truitur; </s>

<s id="N10D8C">tam enim centrum illud immobile <lb/>ad &longs;e qua&longs;i trahit mobile, quàm planum immobile à &longs;e repellit; in <lb/>quo e&longs;t perfectè analogia. </s>

<s id="N10D99">6. Hinc per &longs;e motus circularis integri orbis e&longs;t perpetuus; </s>

<s id="N10D9D">de<lb/>&longs;truitur tamen per accidens, &longs;cilicet, propter attritum axis: </s>

<s id="N10DA3">hinc <lb/>tam diu durat hic motus: </s>

<s id="N10DA9">clari&longs;&longs;imum experimentum habes in tur<lb/>bine, cuius cu&longs;pis læuigati&longs;&longs;ima in plano læuigati&longs;&longs;imo rotatur; </s>

<s id="N10DAF">nec <lb/>vnquam ce&longs;&longs;aret hic motus &longs;ine prædicto attritu, & partium a&longs;peri<lb/>tate: </s>

<s id="N10DB7">nec quidquam ob&longs;tat, quòd aliquæ partes rotæ, quæ in circu<lb/>lo verticali voluitur, a&longs;cendant; </s>

<s id="N10DBD">quia etiam aliquæ de&longs;cendunt: qua<lb/>re &longs;emper remanet perfectum æquilibrium, & harum de&longs;cen&longs;us, il<lb/>larum a&longs;cen&longs;um compen&longs;at. </s>

<s id="N10DC5">Quò diutiùs potentia motrix manet <lb/>applicata manubrio axis rotæ, ita vt nouum &longs;emper producat im<lb/>petum, rotæ motus velocior e&longs;t, atque diutiùs durat: idem pror&longs;us <lb/>dico de rota circulo horizontali parallela. </s>

<s id="N10DD1">7. Cùm mouetur æquali ni&longs;u acus circa immobile centrum, tùm <lb/>in plano <expan abbr="horizõtali">horizontali</expan>, tùm in verticali, &longs;iue &longs;it <expan abbr="lõgior">longior</expan> vna, &longs;iue breuior <lb/>alia, per &longs;e plures gyros non de&longs;cribit vna, quàm alia; </s>

<s id="N10DE1">quia per &longs;e <lb/>mouetur motu æquabili: </s>

<s id="N10DE7">per accidens tamen &longs;ecus accidit; </s>

<s id="N10DEB">quippe <lb/>maior e&longs;t maioris attritus: </s>

<s id="N10DF1">dixi, cùm mouetur æquali ni&longs;u; </s>

<s id="N10DF5">nam &longs;æpè <lb/>contingit, maiore ni&longs;u potentiam motricem agere circa maiorem; </s>

<s id="N10DFB"><lb/>æquali tamen tempore numerus circuitionum minoris, e&longs;t ad nu<lb/>merum circuitionum maioris per &longs;e vt acuum quadrata permu<lb/>tando; &longs;unt enim motus vt &longs;patia, &longs;pacia vt quadrata. </s>

<s id="N10E06">8. Verbi gratia, &longs;it acus maior 2. minor 1. certè cùm tota area or<lb/>bis maioris &longs;it quadrupla minoris, &longs;itque area maioris, &longs;patium ma<lb/>ioris, & area minoris &longs;patium minoris, haud dubiè de&longs;cribet minor <lb/>quatuor circuitiones, eo tempore, quo maior decurret vnicam: </s>

<s id="N10E10">li<lb/>cèt enim extremitas minoris, quæ impellitur, habeat tantùm du<lb/>plum impetum extremitatis maioris, &longs;itque impetus inten&longs;io in <lb/>minore, dupla inten&longs;ionis impetus in maiore; </s>

<s id="N10E1A">e&longs;t tamen quadrupla <lb/>illius, quæ e&longs;t in &longs;egmento maioris versùs centrum æquali minori <lb/>acui: porrò motus circulares æquabiles in vtraque cum eodem <lb/>impetu, &longs;unt vt motus recti. </s>

<s id="N10E26">9. Rota in plano verticali faciliùs mouetur, quàm in horizonta<lb/>li; </s>

<s id="N10E2C">quia in illo mouetur per minimam impetus, vel potentiæ acce&longs;<lb/>&longs;ionem; </s>

<s id="N10E32">&longs;ecùs in i&longs;to; </s>

<s id="N10E36">quippe per minimam acce&longs;&longs;ionem tollitur <lb/>æquilibrium; </s>

<s id="N10E3C">imò moueri pote&longs;t in plano verticali, licèt nullus im<lb/>primatur impetus rotæ, v. g. per additionem minimi ponderis, vel <lb/>momenti, vt patet; cùm tamen in plano horizontali moueri non <lb/>po&longs;&longs;it, ni&longs;i impetus imprimatur. </s>

<s id="N10E4C">10. Si cylindrus in plano horizontali læuigato in altera extremi<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 faciliùs mouetur circa illud <lb/>centrum, quàm circa alia puncta, quòd, &longs;cilicet, minùs &longs;patij decur<lb/>ratur, po&longs;ito eodem &longs;emper motu alterius extremitatis, cui appli<lb/>catur immediatè potentia motrix. </s>

<s id="N10E60">11. Cùm rota mouetur in verticali, atque præponderat alter &longs;emi<lb/>circulus, haud dubiè hic præponderans producit impetum in alio <lb/>&longs;emicirculo: </s>

<s id="N10E68">hinc fortè e&longs;t, quòd mirere, impetus determinatus <lb/>deor&longs;um producit alium &longs;ur&longs;um: </s>

<s id="N10E6E">hinc impetus vnius partis mobi<lb/>lis pote&longs;t producere &longs;imilem in alia parte continua; </s>

<s id="N10E74">quod tantùm in <lb/>hoc ca&longs;u locum habet: </s>

<s id="N10E7A">quando corpus incumbit plano, quod mo<lb/>uetur motu recto æquabili, ab eo non &longs;eparatur; &longs;ecùs verò, &longs;i in<lb/>cumbat plano, quod mouetur motu circulari. </s>

<s id="N10E89"><emph type="center"/><emph type="italics"/>De motu funependuli.<emph.end type="italics"/><emph.end type="center"/></s>

<s id="N10E96">1. FVnependulum de&longs;cendit per arcum motu naturaliter acce<lb/>lerato: </s>

<s id="N10E9C">experientia clari&longs;&longs;ima e&longs;t: cùm enim ex maiori &longs;ubli<lb/>mitate de&longs;cendit, maiorem ictum infligit. </s>

<s id="N10EA2">Ratio à priori e&longs;t quia <lb/>priori impetui acqui&longs;ito nouus accedit: </s>

<s id="N10EA8">non acceleratur in eadem <lb/>proportione, in qua &longs;uprà dictum e&longs;t accelerari in linea recta; </s>

<s id="N10EAE">quia <lb/>in hac acceleratur vniformiter, id e&longs;t, æqualibus temporibus, <lb/>æqualia acquiruntur velocitatis momenta; </s>

<s id="N10EB6">quia vel e&longs;t &longs;emper ea<lb/>dem inclinatio plani, vel idem perpendiculum: </s>

<s id="N10EBC">at verò in fune<lb/>pendulo in &longs;ingulis punctis e&longs;t noua tangens; </s>

<s id="N10EC2">igitur noua inclina<lb/>tio plani; igitur noua ratio motus. </s>

<s id="N10ECA">2. Initio acceleratur motus per maiora crementa, &longs;ub finem per mi<lb/>nora; </s>

<s id="N10ED0">v.g. &longs;i dato tempore acqui&longs;iuit vnum gradum impetus initio, <lb/>æquali deinde tempore acquiret minùs: ratio clara e&longs;t: </s>

<s id="N10ED8">quia, vt ac<lb/>quireret æqualem, deberet e&longs;&longs;e eadem plani inclinatio; </s>

<s id="N10EDE">&longs;ed &longs;emper <lb/>cre&longs;cit Inclinatio; </s>

<s id="N10EE4">igitur &longs;emper imminuitur impetus æquali <expan abbr="t&etilde;pore">tempore</expan> <lb/>acqui&longs;itus: </s>

<s id="N10EEE">acquiritur tamen æqualis velocitas in arcu, & in chor<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>

<s id="N10EF8">3. Hinc breuiore tempore de&longs;cendit per radium perpendicula<lb/>rem, quàm per quadrantis arcum eiu&longs;dem radij; </s>

<s id="N10EFE">tùm quia breuior <lb/>e&longs;t linea; tùm, quia in perpendiculari acceleratur motus per maiora <lb/>crementa. </s>

<s id="N10F06">Vibratio maior eiu&longs;dem funependuli æquali ferè tem-<pb xlink:href="026/01/027.jpg"/>pore cum minore perficitur: ratio e&longs;t: </s>

<s id="N10F0E">quia, cùm ferè decurrantur <lb/>arcus iuxta &longs;ubten&longs;arum proportionem, certè cùm &longs;ubten&longs;æ om<lb/>nes æquali tempore decurrantur, idem ferè fit in ip&longs;is arcubus: </s>

<s id="N10F1C">nam reuerà minor vibratio citiùs, maior tardiùs perficitur, vt <lb/><expan abbr="cõ&longs;tat">con&longs;tat</expan> <expan abbr="experi&etilde;tia">experientia</expan>: neque dee&longs;t ratio, quam in <expan abbr="analyticcã">analyticam</expan> remittimus. </s>

<s id="N10F2F">4. Non a&longs;cendit funependulum ad eam altitudinem, ex qua priùs <lb/>de&longs;cenderat: </s>

<s id="N10F35">clara e&longs;t experientia: </s>

<s id="N10F39">neque ratio tantùm petitur ab <lb/>aëris re&longs;i&longs;tentia; </s>

<s id="N10F3F">tam enim re&longs;i&longs;tit de&longs;cen&longs;ui, quàm a&longs;cen&longs;ui; </s>

<s id="N10F43">&longs;ed ex <lb/>eo, quòd &longs;ingulis in&longs;tantibus &longs;it quædam pugna, inter impetum in<lb/>natum, & alium determinatum ad arcum &longs;ur&longs;um: </s>

<s id="N10F4B">quippe impetus <lb/>innatus ad totum de&longs;cen&longs;um, &longs;ed nullo modo ad a&longs;cen&longs;um con<lb/>currit: </s>

<s id="N10F53">hinc in maiori vibratione imminuitur motus, & &longs;patium in <lb/>maiori proportione, quàm in minori; </s>

<s id="N10F59">quia in hac lineæ &longs;ingulæ a&longs;<lb/>cen&longs;us qua&longs;i <expan abbr="totid&etilde;">totidem</expan> inclinatæ &longs;unt inclinatiores; in illa verò minùs. </s>

<s id="N10F65">5. Hinc diu vibratur funependulum per minores arcus, quippe <lb/>facilis e&longs;t a&longs;cen&longs;us per planum proximè ad horizontale accedens: </s>

<s id="N10F6B"><lb/>hinc etiam in funependulo maiori diutiùs durant huiu&longs;modi vi<lb/>brationes, idque in arcubus paulò maioribus; </s>

<s id="N10F72">quia &longs;ubten&longs;æ his <lb/>arcubus &longs;unt inclinatiores: </s>

<s id="N10F78">hinc refutabis eos, qui dicunt, vibra<lb/>tiones funependuli in vacuo fore perpetuas: </s>

<s id="N10F7E">arcus vibratio<lb/>nis a&longs;cen&longs;us fit motu naturaliter retardato, &longs;ed per imminu<lb/>tiones inæquales; quia pro diuer&longs;a inclinatione plani diuer&longs;imodè <lb/>retardatur. </s>

<s id="N10F8A">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<lb/>tùm in&longs;tanti; </s>

<s id="N10F92">quippe e&longs;t omnium imperfecti&longs;&longs;imum; </s>

<s id="N10F96">quod reuerà &longs;i <lb/>e&longs;&longs;et eiu&longs;dem perfectionis cum innato, a&longs;cen&longs;us æqualis e&longs;t de&longs;cen<lb/>&longs;ui: </s>

<s id="N10F9E">&longs;i &longs;int funependula inæqualia, vibrationes non &longs;unt æquè diu<lb/>turnæ: ratio e&longs;t: </s>

<s id="N10FA4">quia, &longs;i a&longs;&longs;umantur, v.g. duo quadrantes inæquales, <lb/>&longs;unt eju&longs;dem inclinationis; igitur minor citiùs percurritur. </s>

<s id="N10FAC">7. Porrò tempora vibrationum &longs;unt in ratione &longs;ubduplicata ar<lb/>cuum &longs;imilium, vel chordarum &longs;imilium, vel radiorum; </s>

<s id="N10FB2">id e&longs;t, vt <lb/>radices &longs;patiorum &longs;imilium: </s>

<s id="N10FB8">verbi gratia, &longs;it quadruplus alterius, <lb/>tempus vibrationis maioris e&longs;t duplum temporis vibrationis mino<lb/>ris; </s>

<s id="N10FC0">quod ita intelligendum e&longs;t, vt hæc proportio con&longs;ideretur in <lb/>partibus temporis &longs;en&longs;ibilibus, vt iam dictum e&longs;t de motu natura<lb/>liter accelerato deor&longs;um in perpendiculo, & in planis inclinatis; <lb/>nam progre&longs;&longs;io arithmetica; a&longs;&longs;umpta in &longs;ingulis in&longs;tantibus, tran<lb/>&longs;it in hanc, &longs;i a&longs;&longs;umantur partes temporis &longs;en&longs;ibiles, quarum &longs;ingu<lb/>læ infinitis ferè con&longs;tent in&longs;tantibus. </s>

<s id="N10FD3">8. In maiori quadrante, circa &longs;upremam extremitatem, e&longs;t minor <lb/>inclinatio, quàm in minore; </s>

<s id="N10FD9">hic enim &longs;tatim detorquetur à perpen<lb/>diculo, cum quo facit angulum maiorem: </s>

<s id="N10FDF">at verò circa infirmam <lb/>extremitatem, e&longs;t maior inclinatio in maiore, quàm in minore: </s>

<s id="N10FE5">hinc, <lb/>&longs;i comparetur vibratio maioris, cum vibratione minoris in modico <lb/>arcu, tempus illius e&longs;t paulò maius duplo, temporis huius; in maxi<lb/>mo arcu paulò minùs duplo, dum, &longs;cilicet, longitudinum ratio <lb/>&longs;it quadrupla. </s>

<s id="N10FF3">9. In de&longs;cen&longs;u funependuli velocitas acqui&longs;ita e&longs;t eadem cum ea, <lb/>quæ in &longs;ubten&longs;a eiu&longs;dem arcus acquiritur: </s>

<s id="N10FF9">hinc &longs;unt ijdem ictus: </s>

<s id="N10FFD"><lb/>numerus, vibrationum non e&longs;t infinitus, licèt in vacuo vibraretur <lb/>funependulum; </s>

<s id="N11004">quia, cùm &longs;ingulæ imminuantur, & infinitis pun<lb/>ctis non con&longs;tent; </s>

<s id="N1100A">tandem ad vltimam peruenitur: </s>

<s id="N1100E">illa autem e&longs;t vl<lb/>tima, in cuius de&longs;cen&longs;u acquiritur tantùm vnum punctum impetus <lb/>&longs;upra innatum; in ea tamen &longs;ententia, quæ vel infinitas partes actu, <lb/>vel infinita puncta cogno&longs;cit, certè nunquam quie&longs;ceret funepen<lb/>dulum in vacuo vibratum. </s>

<s id="N1101C">10. Funependulum in fine a&longs;cen&longs;us non quie&longs;cit vno in&longs;tanti; </s>

<s id="N11020"><lb/>quia impetui innato <expan abbr="n&utilde;quam">nunquam</expan> redditur æqualis acqui&longs;itus; </s>

<s id="N11029">po&longs;ita ta<lb/>men illa æqualitate, in&longs;tanti &longs;equenti e&longs;&longs;et quies: </s>

<s id="N1102F">funependulum <lb/>grauius citiùs de&longs;cendit; </s>

<s id="N11035">e&longs;t enim eadem ratio, quæ fuit pro mo<lb/>tu naturali; </s>

<s id="N1103B">corpus oblongum &longs;olidum circa punctum immobile <lb/>in circulo verticali rotatum vibratur adin&longs;tat funependuli; de&longs;<lb/>cendit tamen citiùs, quàm funependulum eiu&longs;dem longitudinis. </s>

<s id="N11045">11. Ratio facilis e&longs;t; </s>

<s id="N11048">quia partes &longs;olidæ, quæ accedunt propiùs <lb/>ad extremitatem immobilem, accelerant motum aliarum, quæ <lb/>ad mobilem extremitatem accedunt; </s>

<s id="N11050">faciunt enim arcum mino<lb/>rem: </s>

<s id="N11056">hinc a&longs;cen&longs;us non peruenit ad tantam &longs;ublimitatem; </s>

<s id="N1105A">quia, vt <lb/>prædictæ partes accelerant motum aliarum in de&longs;cen&longs;u, ita retar<lb/>dant in de&longs;cen&longs;u: </s>

<s id="N11062">hinc citiùs quie&longs;cit hoc penduli genus, quàm <lb/>aliud: </s>

<s id="N11068">ex hoc colligo paradoxon, &longs;cilicet, corpus moueri po&longs;&longs;e &longs;ua <lb/>&longs;ponte velociùs in arcu deor&longs;um, quàm in perpendiculo; v.g. &longs;i iuxta <lb/>extremitatem immobilem &longs;it nodus plumbeus, cuius vi, altera ex<lb/>tremitas longiùs di&longs;tans deor&longs;um rapiatur. </s>

<s id="N1107B"><emph type="center"/><emph type="italics"/>De motu mixto ex circulari.<emph.end type="italics"/><emph.end type="center"/></s>

<s id="N11088">1. ROta, quæ mouetur in &longs;uperficie plana, mouetur motu mixto <lb/>ex recto centri, & circulari orbis: </s>

<s id="N1108E">axis tantùm rotæ mouetur <lb/>motu recto: </s>

<s id="N11094">punctum contactus rotæ mouetur motu tardi&longs;&longs;imo, <pb xlink:href="026/01/029.jpg"/>quando motus centri, & &longs;uprema rotæ pars in eandem partem &longs;e<lb/>runtur; </s>

<s id="N1109E">punctum verò oppo&longs;itum veloci&longs;&longs;imo, quia in motu huius <lb/>rotus motus orbis additur motui centri; </s>

<s id="N110A4">in motu verò illius, to<lb/>tus motus orbis, motui centri detrahitur: quod autem detrahit mo<lb/>tus orbis, nunquam æquale e&longs;t toti motui centri. </s>

<s id="N110AE">2. Hinc omnia puncta eiu&longs;dem circuli rotæ mobilis in plano <lb/>hoc motu mixto mouentur in æquali motu: </s>

<s id="N110B4">hoc etiam motu mo<lb/>uetur globus de&longs;cendens in plano inclinato, in quo reuerâ motu <lb/>hæc habes: </s>

<s id="N110BC">primò, non modò accelerari <expan abbr="mot&utilde;">motum</expan> centri, verùm etiam <lb/>motum orbis; <expan abbr="&longs;ec&utilde;dò">&longs;ecundò</expan>, ita <expan abbr="impet&utilde;">impetum</expan> propagari ab intrin&longs;eco, vt &longs;ingu<lb/>lis partibus eiu&longs;dem circuli, & plani in æqualiter di&longs;tribuatur, tertiò <lb/>hoc motu motum rectum non impediri à circulari, & &longs;ed iuuari. </s>

<s id="N110D4">3. Cùm rota voluitur in &longs;uperficie connexa, mouetur motu mix<lb/>to ex duobus circularibus: &longs;imilis e&longs;t hic motus motui epicycli. </s>

<s id="N110DA">Ca<lb/>lamus volatilis, cuius mi&longs;&longs;io frequens, & repercu&longs;&longs;io, ludi non in<lb/>grati copiam facit: </s>

<s id="N110E2">mouetur motu mixto ex recto, & circulari: </s>

<s id="N110E6">in <lb/>hoc porrò motu præit calami caput, & &longs;equuntur pennæ; </s>

<s id="N110EC">quia aër <lb/>fortiùs re&longs;i&longs;tit pennis, quàm thecæ: hinc pennarum motum theca <lb/>grauior accelerat, cuius motum pennæ retardant. </s>

<s id="N110F6">4. Hinc, &longs;i quando accidat, penas educi ex theca in libero medio; </s>

<s id="N110FA"><lb/>&longs;tatim theca velociori motu mouetur, cùm tamen pennæ ip&longs;æ &longs;i<lb/>&longs;tant: </s>

<s id="N11101">ex hac inæqualitate, ne impetus &longs;it fru&longs;trà, propter detortas <lb/>in alteram partem pennas ab aëre re&longs;i&longs;tente totum iaculum defle<lb/>ctitur, agitúr que in orbem; hinc motus orbis traducitur ex theca in <lb/>pennas, non contrà, vt aliquis fortè exi&longs;timaret, licèt pennarum tar<lb/>ditas, & obliqua deflexio, ratione cuius ab aëre re&longs;tante, in alteram <lb/>partem qua&longs;i reflectentur, &longs;int nece&longs;&longs;aria conditio huius traductio<lb/>nis. </s>

<s id="N11113">5. Hinc motu recto prædictum iaculum in vacuo tantùm mo<lb/>ueretur, vt patet: hinc: </s>

<s id="N11119">cùm pennæ &longs;unt explicatiores, tardiùs; </s>

<s id="N1111D">cùm <lb/>verò contractiores, velociùs mouetur, etiam motu orbis; </s>

<s id="N11123">cui non <lb/>minùs aër re&longs;i&longs;tit, in pennis, &longs;cilicet, quàm motui axis: </s>

<s id="N11129">hinc, &longs;i theca <lb/>&longs;it grauior, velociùs; </s>

<s id="N1112F">&longs;i leuior, tardiùs iaculum fertur; </s>

<s id="N11133">etiam tenera <lb/>plumarum lanugo tarditatem conciliat: </s>

<s id="N11139">porrò, &longs;i axis mouetur mo<lb/>tu recto, quod reuerà fit, cùm iaculum deor&longs;um demittitur in per<lb/>pendiculo, hic motus e&longs;t &longs;piralis cylindricus: ex his infinita ferè <lb/>phænomena explicari po&longs;&longs;unt. </s>

<s id="N11145">6. Sunt infiniti propemodum motus mixti; </s>

<s id="N11149">v. g. cylindri ab alte<lb/>ra extremitate rotata emi&longs;&longs;i; </s>

<s id="N11153">longioris ha&longs;tæ, quæ &longs;ur&longs;um facta cir<lb/>cuitione emittitur; </s>

<s id="N11159">brachij, gladij, &c. &longs;ed poti&longs;&longs;imùm turbinis, qui <pb xlink:href="026/01/030.jpg"/>vel &longs;cutica, vel funiculo in torto circumagitur, in quo clari&longs;&longs;i<lb/>mè apparet motus centri, & orbis: </s>

<s id="N11163">ratio motus orbis e&longs;t impe<lb/>tus impre&longs;&longs;us vtrique extremitati diametri va&longs;is in partes contra<lb/>rias; </s>

<s id="N1116B">ratio verò motus centri e&longs;t, quia adducitur funiculo vel ex<lb/>ploditur, &longs;eu expellitur &longs;cutica: </s>

<s id="N11171">huius motus phænomena &longs;unt ferè <lb/>infinita: &longs;ingula ex no&longs;tris principiis facilè explicantur. </s>

<s id="N1117E"><emph type="center"/><emph type="italics"/>De diuer&longs;is impre&longs;&longs;ionibus motus.<emph.end type="italics"/><emph.end type="center"/></s>

<s id="N1118B">1. CVm &longs;u&longs;tinetur manus, &longs;eu brachium, in &longs;itu horizontali im<lb/>mobile, producitur nece&longs;&longs;ariò impetus æqualis impetui gra<lb/>uitationis; </s>

<s id="N11193">alioquin, &longs;i maior e&longs;&longs;et, &longs;ur&longs;um ferretur brachium; &longs;i verò <lb/>minor, deor&longs;um: </s>

<s id="N11199">quia præualeret grauitatio, porrò hic impetus pro<lb/>ducitur tantùm à potentia motrice animantis, in &longs;ingulari organo; </s>

<s id="N1119F"><lb/>non verò in aliis partibus, etiam animatis, ni&longs;i quando mouentur; </s>

<s id="N111A4"><lb/>nec in ip&longs;o pondere, &longs;i aliquod &longs;u&longs;tinetur: &longs;ic men&longs;a in pondere &longs;u<lb/>per po&longs;ito impetum nullum producit. </s>

<s id="N111AB">Si anima immediatè in toto <lb/>corpore po&longs;&longs;et producere impetum, homo facilè volare po&longs;&longs;et. </s>

<s id="N111B2">2. Cùm &longs;u&longs;tinetur funependulum, nullus impetus producitur à <lb/>&longs;u&longs;tinente in ip&longs;o globo, ne &longs;cilicet, &longs;it fru&longs;trà; </s>

<s id="N111B8">&longs;ecùs verò, &longs;i attolla<lb/>tur: </s>

<s id="N111BE">&longs;ic per quamlibet lineam corpus retineri pote&longs;t &longs;ine impetu in <lb/>eo corpore producto per &longs;e: </s>

<s id="N111C4">hinc, cùm duo &longs;e&longs;e inuicem trahunt ad<lb/>uer&longs;o ni&longs;u, neuter in altero producit impetum per &longs;e; </s>

<s id="N111CA">&longs;ed per acci<lb/>dens, propter mollitiem, & ten&longs;ionem partium: </s>

<s id="N111D0">cùm verò defertur <lb/>aliquid coniunctum, producitur haud dubiè æqualis impetus; </s>

<s id="N111D6">hinc <lb/>&longs;eparari non pote&longs;t; </s>

<s id="N111DC">quia æqualis e&longs;t motus latoris, & delati: exem<lb/>plum habes in naui. </s>

<s id="N111E4">3. Si verò nauis illicò &longs;i&longs;tat, vel tardiùs moueri pergat, tunc fit &longs;e<lb/>paratio: hinc liquida effunduntur, &longs;i dum feruntur, breuior quietis <lb/>in va&longs;e intercedat morula. </s>

<s id="N111EC">Vt feratur cylindrus humeris <expan abbr="cõmodiùs">commodiùs</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, & humero æqualiter <expan abbr="põdus">pondus</expan> di&longs;tribuitur: </s>

<s id="N11203">ideò in circulo <lb/>voluitur &longs;cyphus aqua plenus &longs;ine effu&longs;ione; quia impetus determi<lb/>natus per tangentem circuli aquam ip&longs;am à centro circuli remouet. </s>

<s id="N1120D">4. Cùm 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<lb/>nitum; </s>

<s id="N11215">&longs;i chorda vtrinque trahatur, rumpetur in medio: </s>

<s id="N11219">&longs;i affixa <lb/>extremitati immobili, trahatur à potentia applicata alteri extremi-<pb xlink:href="026/01/031.jpg"/>tati, rumpetur iuxta primam illam extremitatem: &longs;i denique pon<lb/>ticulo &longs;uppo&longs;ito tendatur, vel pondere deprimente, in eo puncto <lb/>rumpetur. </s>

<s id="N11227">Ratio communis i&longs;torum omnium e&longs;t: </s>

<s id="N1122B">quia inter illas <lb/>duas partes fieri debet diui&longs;io per &longs;e, quarum vna mouetur, &longs;ecùs <lb/>alia; vel quarum vtraque in partes oppo&longs;itas mouetur. </s>

<s id="N11235">5. Vt quodlibet pondus faciliùs trahatur, &longs;inguli equi trahere <lb/>debent fune communi, potiùs quàm bigati; </s>

<s id="N1123B">quia tunc nihil ferè pe<lb/>rit impetus: </s>

<s id="N11241">cùm plures idem pondus trahunt, agunt actione com<lb/>muni, alioqui &longs;inguli in toto pondere &longs;uum impetum producerent; <lb/>igitur &longs;inguli &longs;eor&longs;um trahere? </s>

<s id="N11249">e&longs;&longs;ent, quod fal&longs;um e&longs;t: </s>

<s id="N1124D">ideò currus <lb/>paulò po&longs;t initium motus faciliùs mouetur; </s>

<s id="N11253">quia aliquid impetus <lb/>priùs producti remanet: hinc etiam rupto fune, quo trahitur currus, <lb/>currus ip&longs;e modicum tempus adhuc mouetur. </s>

<s id="N1125D">6. Si, dum quis trahit toto ni&longs;u magnum aliquod pondus, funis <lb/>rumpatur, pronùs 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<lb/>ti, quo rumpitur finis, qui reuerà maior e&longs;t, propter impedimen<lb/>tum, ex præmi&longs;&longs;is principiis, maiorique applicatione potentiæ, ner<lb/>uorum ten&longs;ione, &c. </s>

<s id="N1126B">dum trahitur vnco an nullus immobilis ver<lb/>sùs nauim, nauis fertur versùs littus; dum pellitur aduersùm littus, <lb/>recedit à littore, quia pede, vel genu, imprimitur naui impetus in <lb/>contrariam pattem. </s>

<s id="N11277">7. Cùm trahitur cylindrus vtrinque æqualiter, qui neque flecti, <lb/>neque tendi pote&longs;t, nullum impetum accipit; </s>

<s id="N1127D">imò in tractione nul<lb/>lus impetus e&longs;t inutilis: </s>

<s id="N11283">brachium infligit maiorem ictum, cùm ma<lb/>iorem <expan abbr="arc&utilde;">arcum</expan> de&longs;cribit &longs;uo motu; </s>

<s id="N1128D">quia, &longs;cilicet, mouetur motu natu<lb/>raliter accelerato: </s>

<s id="N11293">hinc auer&longs;a manu validior impingitur colaphus, <lb/>quàm aduer&longs;a; </s>

<s id="N11299">quia illa maiorem arcum de&longs;cribit: </s>

<s id="N1129D">hinc longius bra<lb/>chium cæteris paribus grauiùs ferit: hinc diu qua&longs;i rotatur bra<lb/>chium, vt longiùs mittatur lapis. </s>

<s id="N112A7">8. Maiore fu&longs;te maior ictus infligitur; </s>

<s id="N112AB">quia potentia toto ni&longs;u <lb/>agens, diutiùs manet applicata maiori, quàm minori; </s>

<s id="N112B1">&longs;untque ictus <lb/>in ratione &longs;ubduplicata vtriu&longs;que fu&longs;tis; </s>

<s id="N112B7">v. g. 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: </s>

<s id="N112C5">idem dicatur de mi&longs;&longs;o lapide: principium huius <lb/>veritatis pendet ex iis, quæ diximus lib. 2. de motu naturali<lb/>ter accelerate, iuxta progre&longs;&longs;ionem numerorum imparium, <lb/>1. 3. 5. &c. </s>

<s id="N112D1">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<lb/>lindrus, vel parallelipedum; </s>

<s id="N112DB">nec in extremitate mobili; </s>

<s id="N112DF">&longs;ed in eo <lb/>puncto, in quo e&longs;t centrum impetus impre&longs;&longs;i, id e&longs;t, quod æqualem <lb/>vtrinque dirimit impetum: ratio e&longs;t; </s>

<s id="N112E7">quia tunc totus impetus agit, <lb/>quantùm pote&longs;t; </s>

<s id="N112ED">illud autem punctum Geometria demon&longs;trat e&longs;&longs;e <lb/>terminum mediæ proportionalis, inter totum cylindrum, & &longs;ub<lb/>duplum; modò nulla ratio vectis habeatur alioquin centrum pro<lb/>cu&longs;&longs;ionis di&longs;tat 2/3 ab extremitate immobili. </s>

<s id="N112F9">10. Cùm fu&longs;tis inflectitur, reditque ad pri&longs;tinum &longs;tatum, vt <lb/>videre e&longs;t in tudicula maiore, maior ictus imprimitur: </s>

<s id="N112FF">quia non <lb/>tantùm agit impetus extrin&longs;ecùs adueniens; </s>

<s id="N11305">verùm etiam potentia <lb/>quædam media, quæ corpora compre&longs;&longs;a, vel ten&longs;a, ad pri&longs;tinum <lb/>&longs;tatum reducit: hinc maximus e&longs;t ictus tudiculæ, cùm eo in&longs;tanti, <lb/>quo reductum e&longs;t omninò manubrium priori rectitudini, infligitur <lb/>ictus, quia tunc vis potentiæ mediæ e&longs;t maxima. </s>

<s id="N11313">11. Rotato flagello ideò maxima vis ine&longs;t, quia diutiùs potentia <lb/>manet applicata: </s>

<s id="N11319">hinc vides hoc principium e&longs;&longs;e vniuer&longs;ali&longs;&longs;imum, <lb/>quod iactis, pul&longs;is, & impactis competit; </s>

<s id="N1131F">de malleorum ictu idem <lb/>pror&longs;us dicendum e&longs;t, quod de fu&longs;te; </s>

<s id="N11325">&longs;i autem mallei cadant <lb/>ex eadem altitudine, motu naturali accelerato, ictus &longs;unt vt <lb/>mallei, quia duplus malleus, v. g. duplum impetum acquirit: nam <lb/>&longs;ingulæ partes &longs;eor&longs;im æqualem impetum acquirunt. </s>

<s id="N11335">12. Si verò ex diuer&longs;a altitudine cadant, vel &longs;unt æquales, vel <lb/>inæquales: </s>

<s id="N1133B">&longs;i primum, ictus &longs;unt vt tempora, quibus cadunt: </s>

<s id="N1133F">&longs;i <lb/>&longs;ecundum, ictus &longs;unt in ratione compo&longs;ita temporum, & mal<lb/>leorum: </s>

<s id="N11347">&longs;i &longs;unt infinitæ, partes actu, nulla e&longs;t proportio percu&longs;&longs;ionis <lb/>granuli cadentis, & rupis ingentis grauitantis; </s>

<s id="N1134D">&longs;ed hoc vltimum fal<lb/>&longs;um e&longs;&longs;e con&longs;tat; </s>

<s id="N11353">non pote&longs;t tamen determinari proportio vitium <lb/>grauitationis, & percu&longs;&longs;ionis, ni&longs;i numerus in&longs;tantium: quibus durat <lb/>motus deor&longs;um cogno&longs;catur. </s>

<s id="N1135D">13. Leui&longs;&longs;imi lapides vix emittuntur ad modicam di&longs;tantiam; </s>

<s id="N11361"><lb/>quia &longs;tatim &longs;eparantur à potentia: </s>

<s id="N11366">parallelipedum cadens de or<lb/>&longs;um in &longs;itu horizontali maximum ictum infligit in centro grauita<lb/>tis, id e&longs;t, in medio; </s>

<s id="N1136E">quia tunc totus impetus agit, totus enim impe<lb/>ditur: </s>

<s id="N11374">in aliis punctis minor e&longs;t ictus, iuxta proportionem maioris <lb/>di&longs;tantiæ à prædicto centro: &longs;i verò percutiatur cylindrus innatans, <lb/>maxima erit vis, vel effectus ictus in centro grauitatis propter ean<lb/>dem rationem. </s>

</section>

</front>

<body>

<chap>

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

<s id="N1138B"><emph type="center"/>LIBER PRIMVS, <lb/><emph type="italics"/>DE IMPETV.<emph.end type="italics"/><emph.end type="center"/></s>

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

<s id="N1139A">TRACTATVM hunc de motu locali <lb/>ab ip&longs;o impetu au&longs;picamur, ex cuius <lb/>profectò cognitione tota res i&longs;ta de<lb/>pendet; </s>

<s>TRACTATVM hunc de motu locali <lb/>ab ip&longs;o impetu au&longs;picamur, ex cuius <lb/>profectò cognitione tota res i&longs;ta de<lb/>pendet; cum enim impetus &longs;it cau&longs;a <lb/>immediata motus, vt fusè demon&longs;tra<lb/>bimus infrà; & 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 præmittenda &longs;it tractatio illa, quæ <lb/>e&longs;t de impetu, vt deinde affectiones ip&longs;ius motus <lb/>per cau&longs;am eiu&longs;dem demon&longs;trentur; immò au&longs;im <lb/>dicere ex vnius impetus cognitione, non modò mo<lb/>tum ip&longs;um, verùm etiam totam rem Phy&longs;icam pen<lb/>dere. <lb/><gap desc="hr tag"/></s>

<s id="N113A4">cum enim impetus &longs;it cau&longs;a <lb/>immediata motus, vt fusè demon&longs;tra<lb/>bimus infrà; </s>

<s id="N113AC">& 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; </s>

<s><emph type="center"/><emph type="italics"/>DEFINITIO I.<emph.end type="italics"/><emph.end type="center"/></s>

<s id="N113B2">dubium e&longs;&longs;e <lb/>non pote&longs;t, quin præmittenda &longs;it tractatio illa, quæ <lb/>e&longs;t de impetu, vt deinde affectiones ip&longs;ius motus <lb/>per cau&longs;am eiu&longs;dem demon&longs;trentur; immò au&longs;im <lb/>dicere ex vnius impetus cognitione, non modò mo<lb/>tum ip&longs;um, verùm etiam totam rem Phy&longs;icam pen<lb/>dere. <lb/><gap desc="hr tag"/></s>

<s>MOTVS <emph type="italics"/>localis e&longs;t tran&longs;itus mobilis è loco in locum continuo fluxu.<emph.end type="italics"/><lb/>Huius definitionis explicationem habebis in Metaphy&longs;icâ, <lb/>quæ &longs;anè explicatio ad rem præ&longs;entem non facit. </s>

<s id="N113C7"><emph type="center"/><emph type="italics"/>DEFINITIO I.<emph.end type="italics"/><emph.end type="center"/></s>

<s><emph type="center"/><emph type="italics"/>Definitio II.<emph.end type="italics"/><emph.end type="center"/></s>

<s><emph type="italics"/>Motus velox e&longs;t quo percurritur maius &longs;patium æquali tempore, vel <lb/>æquale &longs;patium minori tempore; contrà verò motus tardus.<emph.end type="italics"/></s><pb xlink:href="026/01/034.jpg" pagenum="2"/>

<s id="N113D5">MOTVS <emph type="italics"/>localis e&longs;t tran&longs;itus mobilis è loco in locum continuo fluxu.<emph.end type="italics"/><lb/>Huius definitionis explicationem habebis in Metaphy&longs;icâ, <lb/>quæ &longs;anè explicatio ad rem præ&longs;entem non facit. </s>

<s><emph type="center"/><emph type="italics"/>Definitio III.<emph.end type="italics"/><emph.end type="center"/></s>

<s id="N113E3"><emph type="center"/><emph type="italics"/>Definitio II.<emph.end type="italics"/><emph.end type="center"/></s>

<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>

<s>Dico e&longs;&longs;e qualitatem &longs;iue di&longs;tincta &longs;it, &longs;iue non di&longs;tincta; quod hîc <lb/>certè non di&longs;cutio; nec enim affirmo in hac definitione dari impetum; <lb/>&longs;ed definio tantùm quid &longs;it impetus; qui reuera aliud non e&longs;t, &longs;i e&longs;t: <lb/>quippe id tantùm concipio, cum impetum appello; &longs;iue &longs;it, &longs;iue non &longs;it, <lb/>ne quis fortè initio &longs;tatim mihi litem intendat; quemadmodum definit <lb/>circulum Geometra; licèt non a&longs;&longs;erat dari perfectum circulum; ita Phy<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 dubiè <lb/>nihil omninò præ&longs;tat in &longs;uo &longs;ubiecto ni&longs;i motum; quod quomodò fiat, <lb/>explicabimus intrà in Theorematis. </s>

<s id="N113F1"><emph type="italics"/>Motus velox e&longs;t quo percurritur maius &longs;patium æquali tempore, vel <lb/>æquale &longs;patium minori tempore; contrà verò motus tardus.<emph.end type="italics"/></s>

<s><emph type="center"/><emph type="italics"/>Hypothe&longs;is I.<emph.end type="italics"/><emph.end type="center"/></s>

<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<lb/>grans è loco in locum? </s>

<s id="N11401"><emph type="center"/><emph type="italics"/>Definitio III.<emph.end type="italics"/><emph.end type="center"/></s>

<s>&longs;ed hoc e&longs;t moueri per Def. 1. igitur infinitis fe<lb/>rè experimentis nititur hæc 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;icè, neque citra miraculum fallere <lb/>po&longs;&longs;unt. </s>

<s id="N1140F"><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>

<s>Diceret fortè aliquis etiam motum &longs;ube&longs;&longs;e oculorum fallaciæ; cùm è <lb/>naui mobili littus ip&longs;um moueri, ip&longs;umque nauigium non moueri iudi<lb/>cemus. </s>

<s id="N1141C">Dico e&longs;&longs;e qualitatem &longs;iue di&longs;tincta &longs;it, &longs;iue non di&longs;tincta; </s>

<s id="N11420">quod hîc <lb/>certè non di&longs;cutio; </s>

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

<s id="N11426">nec enim affirmo in hac definitione dari impetum; </s>

<s id="N1142A"><lb/>&longs;ed definio tantùm quid &longs;it impetus; </s>

<s>cum tamen deinde pernici&longs;&longs;imo cur&longs;u rotari demon&longs;tre<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 celerrimè rotatur, orbem etiam immobilem de&longs;cribere iu<lb/>dicatur; &longs;ic &longs;tella cadens, vel exhalatio continenti &longs;ucce&longs;&longs;ione accen&longs;a <lb/>moueri videtur; licet minimè moueatur; idem dicendum de puluere <lb/>tormentario, vel alia qualibet materia; quæ continuata con&longs;ecutione <lb/>accenditur; immò trochus ip&longs;e in orbem celerrimè agitatus, quie&longs;cere <lb/>videtur; &longs;ic qui vertigine laborant, ea moueri exi&longs;timant, quæ quie&longs;cunt; <lb/>idem exemplum habemus in ebrio&longs;is, iracundis, in iis qui ex graui febris <lb/>ardore delirant, & in pueris qui diu in gyros eunt, vbi verti de&longs;ierint; <lb/>&longs;ic eorum quæ motu æquali feruntur, remotiora tardiùs moueri viden<lb/>tur; immò &longs;i per eandem lineam oculus, & mobile pari velocitate ince<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 minimè con&longs;ta<lb/>re dari motum, ex eo quòd oculis aliquid moueri videatur. </s>

<s id="N1142F">qui reuera aliud non e&longs;t, &longs;i e&longs;t: </s>

<s id="N11433"><lb/>quippe id tantùm concipio, cum impetum appello; </s>

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

<s id="N11438">&longs;iue &longs;it, &longs;iue non &longs;it, <lb/>ne quis fortè initio &longs;tatim mihi litem intendat; </s>

<s id="N1143E">quemadmodum definit <lb/>circulum Geometra; </s>

<s>quidquid &longs;it, fateor vltrò hanc hypothe&longs;im in eo tantùm certitudi<lb/>nis gradu e&longs;&longs;e reponendam, in quo reponitur hæc cognitio, quâ modo <lb/>cogno&longs;co me &longs;cribere, manu&longs;que, & calami motum ob&longs;eruo; &longs;iue id tan<lb/>tùm oculis fiat, &longs;iue intellectu ex oculis; quod aliàs di&longs;cutiemus; &longs;i quis <lb/>fortè in Phy&longs;ica maiorem certitudinem po&longs;tularet, cum eo certè conue<lb/>nire non po&longs;&longs;um. </s>

<s id="N11444">licèt non a&longs;&longs;erat dari perfectum circulum; </s>

<s id="N11448">ita Phy<lb/>&longs;icus definit impetum, quamuis non affirmet dari impetum; </s>

<s>Porrò quod &longs;pectat ad fallacias illas quæ &longs;upra adductæ &longs;unt; certum <lb/>e&longs;t vel obiectum e&longs;&longs;e remotius, quam par &longs;it; vel moueri celeriùs, vel <lb/>e&longs;&longs;e aliquod impedimentum interius; præ&longs;ertim in iis, qui &longs;eu vertigine, <lb/>vel alio capitis morbo laborant; &longs;ed ne hîc opticum agere videar, harum <lb/>fallaciarum certi&longs;&longs;imas cau&longs;as in &longs;uum locum remittimus. </s>

<s id="N1144E">quod tamen <lb/>in &longs;exto Theoremate demon&longs;trabimus; </s>

<s id="N11454">itaque &longs;i e&longs;t impetus, haud dubiè <lb/>nihil omninò præ&longs;tat in &longs;uo &longs;ubiecto ni&longs;i motum; quod quomodò fiat, <lb/>explicabimus intrà in Theorematis. </s>

<s>Cæterùm licèt ad &longs;tatuendam, firmandamque hanc hypote&longs;im, Phy<lb/>&longs;ica experimenta rectè applicato &longs;en&longs;u comprobata &longs;ufficere po&longs;&longs;int; <lb/>non de&longs;unt tamen rationes multæ à priori, vt vulgò aiunt, quibus euin<lb/>citur, non modò quid &longs;it motus, verùm etiam propter quid &longs;it. </s>

<s>Prima duci pote&longs;t à fine motus; cum enim res creatæ vbique &longs;imul <lb/>e&longs;&longs;e non po&longs;&longs;int, certè, vt illo bono gaudeant, quo fortè carent, & vt <lb/>coniungantur &longs;uo fini, motu locali opus e&longs;t; &longs;itit equus, abe&longs;t aqua, <lb/>certè, ni&longs;i vel hæc propinetur, vel ille accedat, &longs;itim leuare non pote<lb/>rit; at neutrum &longs;ine motu haberi pote&longs;t: Lapis remouetur à &longs;uo centro, <lb/>à &longs;uo globo, à &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 id="N1145F"><emph type="center"/><emph type="italics"/>Hypothe&longs;is I.<emph.end type="italics"/><emph.end type="center"/></s>

<s><lb/>Itaque ad cum finem res omnes creatæ in&longs;titutæ &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 creatæ cum lo<lb/>cum acquirant, in quo &longs;uo bono, &longs;uo fini, &longs;uæ perfectioni coniungan<lb/>tur; vel &longs;altem id muneris obeant, cui ab ipsâ naturâ de&longs;tinantur. </s>

<s id="N1146D"><emph type="italics"/>Datur motus localis<emph.end type="italics"/>; </s>

<s>Secunda ratio ducitur à cau&longs;a efficiente; ni&longs;i enim daretur motus, <lb/>fru&longs;trà daretur potentia motrix, tùm in animantibus, tùm in grauibus, <lb/>de quâ aliàs. </s>

<s id="N11476">quis enim non videt volantem auem, natantem <lb/>pi&longs;cem; currentem equum, rotatum globum; denique vnum corpus mi<lb/>grans è loco in locum? </s>

<s id="N1147E">&longs;ed hoc e&longs;t moueri per Def. 1. igitur infinitis fe<lb/>rè experimentis nititur hæc 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;icè, neque citra miraculum fallere <lb/>po&longs;&longs;unt. </s>

<s>Tertia petitur à cau&longs;a formali; cum enim detur impetus, vt demon<lb/>&longs;trabimus infrà, nece&longs;&longs;e e&longs;t dari motum. </s>

<s>Quarta petitur à termino motus; cum enim globus proiectus &longs;it in <lb/>nouo loco in quo ante non erat; certè 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>

<s id="N1148C">Diceret fortè aliquis etiam motum &longs;ube&longs;&longs;e oculorum fallaciæ; cùm è <lb/>naui mobili littus ip&longs;um moueri, ip&longs;umque nauigium non moueri iudi<lb/>cemus. </s>

<s id="N11494">Quis enim oculos in Solem intendens, primo intuitu Solem &longs;ta<lb/>re non iudicet? </s>

<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, &c. </s>

<s id="N11499">cum tamen deinde pernici&longs;&longs;imo cur&longs;u rotari demon&longs;tre<lb/>mus; </s>

<s id="N1149F">adde alias oculorum fallacias circa motum; </s>

<s>Sexta ab ip&longs;a Mechanica, quæ organa motui mini&longs;trat: quis enim ne<lb/>garet maius momentum e&longs;&longs;e cum maiori di&longs;tantiâ coniunctum; &longs;i verò <lb/>maius momentum e&longs;t, nunquid præualebit; igitur deor&longs;um cadet, immò <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 id="N114A3">&longs;ic rotata &longs;cintilla, vel <lb/>carbo accen&longs;us immotum orbem de&longs;cribere videtur; </s>

<s id="N114A9">&longs;ic nota inu&longs;ta <lb/>trocho, dum celerrimè rotatur, orbem etiam immobilem de&longs;cribere iu<lb/>dicatur; </s>

<s>Igitur certum e&longs;t <lb/>dari motum localem. </s>

<s id="N114B1">&longs;ic &longs;tella cadens, vel exhalatio continenti &longs;ucce&longs;&longs;ione accen&longs;a <lb/>moueri videtur; </s>

<s id="N114B7">licet minimè moueatur; </s>

<s><emph type="center"/><emph type="italics"/>Hypothe&longs;is II.<emph.end type="italics"/><emph.end type="center"/></s>

<s id="N114BB">idem dicendum de puluere <lb/>tormentario, vel alia qualibet materia; quæ continuata con&longs;ecutione <lb/>accenditur; </s>

<s id="N114C3">immò trochus ip&longs;e in orbem celerrimè agitatus, quie&longs;cere <lb/>videtur; </s>

<s><emph type="italics"/>Datur quies, id e&longs;t priuatio motus.<emph.end type="italics"/> Hæc 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 rectè applicatos; tam enim certus &longs;um me iam in cathe<lb/>dra quie&longs;cere, quam &longs;um certus Solem lucere; igitur ex certis experi<lb/>mentis certa hypothe&longs;is con&longs;equitur. </s>

<s id="N114C9">&longs;ic qui vertigine laborant, ea moueri exi&longs;timant, quæ quie&longs;cunt; </s>

<s id="N114CD"><lb/>idem exemplum habemus in ebrio&longs;is, iracundis, in iis qui ex graui febris <lb/>ardore delirant, & in pueris qui diu in gyros eunt, vbi verti de&longs;ierint; </s>

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

<s id="N114D4"><lb/>&longs;ic eorum quæ motu æquali feruntur, remotiora tardiùs moueri viden<lb/>tur; </s>

<s id="N114DB">immò &longs;i per eandem lineam oculus, & mobile pari velocitate ince<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 minimè con&longs;ta<lb/>re dari motum, ex eo quòd oculis aliquid moueri videatur. </s>

<s>Secundò maximum incommodum e&longs;&longs;et, &longs;i res &longs;e<lb/>mel mota perpetuò moueretur. </s>

<s>Tertiò, 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 aliàs. </s>

<s id="N114E7">Re&longs;pondeo equidem fateri me, vi&longs;um ip&longs;um plurimis &longs;ube&longs;&longs;e fraudi<lb/>bus; </s>

<s id="N114ED">attamen &longs;i rectè oculus admoueatur, iu&longs;ta di&longs;tantià, nec vllum &longs;it <lb/>impedimentum exterius nec interius; </s>

<s>Diceret fortè aliquis &longs;ententias prædictas non valere in &longs;ententiâ <lb/>Copernici, quæ terræ motum ad&longs;truit; præterea non modò falli &longs;en&longs;us <lb/>circa motum, verùm etiam circa quietem. </s>

<s id="N114F3">fieri non pote&longs;t, quin oculus mo<lb/>tum ob&longs;eruet; an fortè currentis calami motus oculum meum fallere po-<pb pagenum="3" xlink:href="026/01/035.jpg"/>te&longs;t? </s>

<s id="N114FE">quidquid &longs;it, fateor vltrò hanc hypothe&longs;im in eo tantùm certitudi<lb/>nis gradu e&longs;&longs;e reponendam, in quo reponitur hæc cognitio, quâ modo <lb/>cogno&longs;co me &longs;cribere, manu&longs;que, & calami motum ob&longs;eruo; </s>

<s>Re&longs;pondeo primò illam Copernici &longs;ententiam e&longs;&longs;e fal&longs;i&longs;&longs;imam, vt &longs;uo <lb/>loco o&longs;tendemus: &longs;ecundò, licèt terra moueretur &longs;ecundum Coperni<lb/>cum, Sol, & &longs;tellæ quie&longs;cerent. </s>

<s id="N11506">&longs;iue id tan<lb/>tùm oculis fiat, &longs;iue intellectu ex oculis; quod aliàs di&longs;cutiemus; &longs;i quis <lb/>fortè in Phy&longs;ica maiorem certitudinem po&longs;tularet, cum eo certè conue<lb/>nire non po&longs;&longs;um. </s>

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

<s id="N11512">Porrò quod &longs;pectat ad fallacias illas quæ &longs;upra adductæ &longs;unt; </s>

<s>Re&longs;pondeo primò hypothe&longs;im illam e&longs;&longs;e fal&longs;am, vt &longs;uo <lb/>loco videbimus; &longs;ecundò 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, quò ver&longs;us or<lb/>tum à terra ip&longs;a rapitur, haùd dubiè quie&longs;ceret: præterea iuxta hanc hy<lb/>pothe&longs;im, quietem appellarem vnius partis cum alia connexionem in ip<lb/>&longs;o toto &longs;eu globo, & quie&longs;cere dicerem lapidem, qui tantùm totius glo<lb/>bi motu mouetur, ex quo profectò tota &longs;oluitur difficultas. </s>

<s id="N11516">certum <lb/>e&longs;t vel obiectum e&longs;&longs;e remotius, quam par &longs;it; </s>

<s id="N1151C">vel moueri celeriùs, vel <lb/>e&longs;&longs;e aliquod impedimentum interius; </s>

<s>Quod verò &longs;pectat ad fallacias oculi circa quietem; codem pror&longs;us <lb/>modo &longs;oluendæ &longs;unt, quo iam &longs;upra &longs;olutæ &longs;unt aliæ circa motum: <lb/>vtrùm verò motus, & quies dicant aliquid di&longs;tinctum à mobili, dice<lb/>mus infrà. </s>

<s id="N11522">præ&longs;ertim in iis, qui &longs;eu vertigine, <lb/>vel alio capitis morbo laborant; &longs;ed ne hîc opticum agere videar, harum <lb/>fallaciarum certi&longs;&longs;imas cau&longs;as in &longs;uum locum remittimus. </s>

<s><emph type="center"/><emph type="italics"/>Hypothe&longs;is III.<emph.end type="italics"/><emph.end type="center"/></s>

<s id="N1152C">Cæterùm licèt ad &longs;tatuendam, firmandamque hanc hypote&longs;im, Phy<lb/>&longs;ica experimenta rectè applicato &longs;en&longs;u comprobata &longs;ufficere po&longs;&longs;int; <lb/>non de&longs;unt tamen rationes multæ à priori, vt vulgò aiunt, quibus euin<lb/>citur, non modò quid &longs;it motus, verùm etiam propter quid &longs;it. </s>

<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 hæc hypothe<lb/>&longs;is confirmari pote&longs;t. </s>

<s><emph type="center"/><emph type="italics"/>Hypothe&longs;is IV.<emph.end type="italics"/><emph.end type="center"/></s>

<s id="N11538">Prima duci pote&longs;t à fine motus; </s>

<s id="N1153C">cum enim res creatæ vbique &longs;imul <lb/>e&longs;&longs;e non po&longs;&longs;int, certè, vt illo bono gaudeant, quo fortè carent, & vt <lb/>coniungantur &longs;uo fini, motu locali opus e&longs;t; </s>

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

<s id="N11544">&longs;itit equus, abe&longs;t aqua, <lb/>certè, ni&longs;i vel hæc propinetur, vel ille accedat, &longs;itim leuare non pote<lb/>rit; </s>

<s id="N1154C">at neutrum &longs;ine motu haberi pote&longs;t: Lapis remouetur à &longs;uo centro, <lb/>à &longs;uo globo, à &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>igitur certa e&longs;t hæc hypothe&longs;is. </s>

<s id="N11552"><lb/>Itaque ad cum finem res omnes creatæ in&longs;titutæ &longs;unt, quem &longs;ine motu <lb/>a&longs;&longs;equi non po&longs;&longs;unt; </s>

<s id="N11559">igitur dari motum nece&longs;&longs;e e&longs;t, vt res creatæ cum lo<lb/>cum acquirant, in quo &longs;uo bono, &longs;uo fini, &longs;uæ perfectioni coniungan<lb/>tur; vel &longs;altem id muneris obeant, cui ab ipsâ naturâ de&longs;tinantur. </s>

<s><emph type="center"/><emph type="italics"/>Hypothe&longs;is V.<emph.end type="italics"/><emph.end type="center"/></s>

<s><emph type="italics"/>Idem mouetur modò tardiùs, modò velociùs.<emph.end type="italics"/></s><s> Video rotatum globum, <lb/>qui &longs;en&longs;im quie&longs;cit: &longs;entio ab codem globo modò maiorem, modò mi<lb/>norem ictum infligi, &c. </s>

<s id="N11563">Secunda ratio ducitur à cau&longs;a efficiente; ni&longs;i enim daretur motus, <lb/>fru&longs;trà daretur potentia motrix, tùm in animantibus, tùm in grauibus, <lb/>de quâ aliàs. </s>

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

<s id="N1156D">Tertia petitur à cau&longs;a formali; cum enim detur impetus, vt demon<lb/>&longs;trabimus infrà, nece&longs;&longs;e e&longs;t dari motum. </s>

<s><emph type="center"/><emph type="italics"/>Hypothe&longs;is VI.<emph.end type="italics"/><emph.end type="center"/></s>

<s><emph type="italics"/>Corpus proiectum etiam à potentiâ motrice &longs;eiunctum adhuc mouetur.<emph.end type="italics"/><lb/>Oculos omnium te&longs;tes appello. </s>

<s id="N11575">Quarta petitur à termino motus; </s>

<s id="N11579">cum enim globus proiectus &longs;it in <lb/>nouo loco in quo ante non erat; </s>

<s><emph type="center"/><emph type="italics"/>Hypothe&longs;is VII.<emph.end type="italics"/><emph.end type="center"/></s>

<s id="N1157F">certè 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>

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

<s id="N11589">Quinta ab v&longs;u; nec enim &longs;ine motu flueret aqua, caderet lapis, gyros <lb/>agerent a&longs;tra, flaret ventus, volarent nubes, &c. </s>

<s><emph type="center"/><emph type="italics"/>Hypothe&longs;is VIII.<emph.end type="italics"/><emph.end type="center"/></s>

<s><emph type="italics"/>Ignis applicatus &longs;ubiectum aptum, cui rectè applicatur nece&longs;&longs;ariò calefa<lb/>cit, nix frigefacit, Sol illuminat, corpus in aliud impactum illud ip&longs;um im<lb/>pellit.<emph.end type="italics"/></s><s> Prædictæ omnes Hypothe&longs;es certi&longs;&longs;imis nixæ experimentis certi<lb/>tudinem phy&longs;icam habent, & citra miraculum fallere non po&longs;&longs;unt. </s>

<s id="N11590">Sexta ab ip&longs;a Mechanica, quæ organa motui mini&longs;trat: </s>

<s id="N11594">quis enim ne<lb/>garet maius momentum e&longs;&longs;e cum maiori di&longs;tantiâ coniunctum; </s>

<s><emph type="center"/><emph type="italics"/>Axioma I.<emph.end type="italics"/><emph.end type="center"/></s>

<s id="N1159A">&longs;i verò <lb/>maius momentum e&longs;t, nunquid præualebit; igitur deor&longs;um cadet, immò <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 id="N115A4">Igitur certum e&longs;t <lb/>dari motum localem. </s>

<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 præ<lb/>mi&longs;imus Logicæ no&longs;træ demon&longs;tratiuæ, complectiturque prima illa <lb/>principia Metaphy&longs;icæ. </s>

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

<s id="N115AB"><emph type="center"/><emph type="italics"/>Hypothe&longs;is II.<emph.end type="italics"/><emph.end type="center"/></s>

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

<s id="N115B9"><emph type="italics"/>Datur quies, id e&longs;t priuatio motus.<emph.end type="italics"/> Hæc hypothe&longs;is etiam certa e&longs;t, <pb pagenum="4" xlink:href="026/01/036.jpg"/>Quis enim neget &longs;edentem humi, vel decumbentem in lecto quie&longs;ceret <lb/>con&longs;ule &longs;en&longs;us rectè applicatos; </s>

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

<s id="N115C9">tam enim certus &longs;um me iam in cathe<lb/>dra quie&longs;cere, quam &longs;um certus Solem lucere; igitur ex certis experi<lb/>mentis certa hypothe&longs;is con&longs;equitur. </s>

<s id="N115D1">Non de&longs;unt rationes à priori; nam <lb/>primò res aliqua &longs;uo bono, &longs;eu fini coniuncta ab eo &longs;eparari non po&longs;tu<lb/>lat, igitur nec moueri. </s>

<s><emph type="center"/><emph type="italics"/>Axioma II.<emph.end type="italics"/><emph.end type="center"/></s>

<s id="N115D9">Secundò maximum incommodum e&longs;&longs;et, &longs;i res &longs;e<lb/>mel mota perpetuò moueretur. </s>

<s id="N115DE">Tertiò, 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 aliàs. </s>

<s><emph type="italics"/>Maximum &longs;ignum di&longs;tinctionis realis in phy&longs;icis est &longs;eparabilitas, vel op<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 & nummus B eiu&longs;dem ma<lb/>teriæ, formæ, ponderis, realiter di&longs;tinguuntur? </s>

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

<s id="N115EA">Diceret fortè aliquis &longs;ententias prædictas non valere in &longs;ententiâ <lb/>Copernici, quæ terræ motum ad&longs;truit; præterea non modò falli &longs;en&longs;us <lb/>circa motum, verùm etiam circa quietem. </s>

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

<s id="N115F4">Re&longs;pondeo primò illam Copernici &longs;ententiam e&longs;&longs;e fal&longs;i&longs;&longs;imam, vt &longs;uo <lb/>loco o&longs;tendemus: &longs;ecundò, licèt terra moueretur &longs;ecundum Coperni<lb/>cum, Sol, & &longs;tellæ quie&longs;cerent. </s>

<s>vides prædicata contradictoria, quæ cum eidem <lb/>&longs;imul ine&longs;&longs;e non po&longs;&longs;int per Ax. 1. diuer&longs;is, & di&longs;tinctis ine&longs;&longs;e nece&longs;&longs;e <lb/>e&longs;t. </s>

<s>Diceret fortè aliquis hominem reproductum in duobus locis e&longs;&longs;e po&longs;<lb/>&longs;e, & dum Romæ e&longs;t à &longs;e ip&longs;o Lugduni exi&longs;tente &longs;eiunctum e&longs;&longs;e; hoc <lb/>ip&longs;um aliàs examinabimus, dum con&longs;tet modò id totum, &longs;i fiat, mira<lb/>culo tribuendum e&longs;&longs;e, cum tamen res phy&longs;icas citra miraculum con&longs;ide<lb/>remus. </s>

<s id="N115FE">Dices iuxta hypothe&longs;im Heraclidis Pontici, terra ip&longs;a, Sol etiam, & <lb/>&longs;tellæ mouentur. </s>

<s id="N11603">Re&longs;pondeo primò hypothe&longs;im illam e&longs;&longs;e fal&longs;am, vt &longs;uo <lb/>loco videbimus; </s>

<s><emph type="center"/><emph type="italics"/>Axioma III.<emph.end type="italics"/><emph.end type="center"/></s>

<s id="N11609">&longs;ecundò etiam data illa hypothe&longs;i po&longs;&longs;et dari quies; </s>

<s id="N1160D">&longs;i <lb/>enim globus eodem ver&longs;us occa&longs;um impetu proiiceretur, quò ver&longs;us or<lb/>tum à terra ip&longs;a rapitur, haùd dubiè quie&longs;ceret: præterea iuxta hanc hy<lb/>pothe&longs;im, quietem appellarem vnius partis cum alia connexionem in ip<lb/>&longs;o toto &longs;eu globo, & quie&longs;cere dicerem lapidem, qui tantùm totius glo<lb/>bi motu mouetur, ex quo profectò tota &longs;oluitur difficultas. </s>

<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, certè po&longs;i<lb/>tiuo argumento demon&longs;trare debet quod &longs;it; illud porrò 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 quòd cau&longs;a &longs;it nece&longs;&longs;aria <lb/>applicata &longs;ubiecto apto, probo effectum ip&longs;um produci; vel eo quòd &longs;it <lb/>effectus probo cau&longs;am e&longs;&longs;e vel ex nece&longs;&longs;itate, quâ aliquid e&longs;t nece&longs;&longs;a<lb/>rium ad aliquem finem à 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 demùm ex aliqua reuelatione certa in rebus fidei; igitur hoc <lb/>Axioma certum e&longs;t phy&longs;icè; quod ni&longs;i recipiatur à Philo&longs;ophis; cuique <lb/>licebit impunè mentiri; &longs;i enim dicam extra mundi huius fines e&longs;&longs;e <lb/>alios orbes, intra tuum mu&longs;æum, in quo &longs;olus fortè degis, e&longs;&longs;e quin<lb/>quaginta homines, e&longs;&longs;e mille Soles, & totidem Lunas in c&oelig;lo, &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"/> Quæ&longs;tio facti e&longs;t, producendi &longs;unt te&longs;tes: huc <lb/>reuoca principium illud commune. </s>

<s id="N1161D">Quod verò &longs;pectat ad fallacias oculi circa quietem; </s>

<s id="N11621">codem pror&longs;us <lb/>modo &longs;oluendæ &longs;unt, quo iam &longs;upra &longs;olutæ &longs;unt aliæ circa motum: <lb/>vtrùm verò motus, & quies dicant aliquid di&longs;tinctum à mobili, dice<lb/>mus infrà. </s>

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

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

<s id="N1162D"><emph type="center"/><emph type="italics"/>Hypothe&longs;is III.<emph.end type="italics"/><emph.end type="center"/></s>

<s><emph type="center"/><emph type="italics"/>Axioma IV.<emph.end type="italics"/><emph.end type="center"/></s>

<s id="N1163B"><emph type="italics"/>Aliquid mouetur quod inc&oelig;pit moueri.<emph.end type="italics"/></s>

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

<s id="N11642"> Video lapidem quie&longs;centem, <lb/>qui deinde proiectus mouetur; </s>

<s id="N11648">igitur ante non mouebatur, igitur cum <lb/>deinde mouetur, c&oelig;pit moueri; mille aliis experimentis hæc hypothe<lb/>&longs;is confirmari pote&longs;t. </s>

<s>Hoc Axioma explicatione modicâ indiget: Determinatum illud <lb/>apello, quod illud ip&longs;um e&longs;t, quod e&longs;t, & 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, & ali<lb/>quando, ergo dici pote&longs;t, e&longs;t hîc, e&longs;t nunc; igitur determinatum e&longs;t. </s>

<s><lb/>Aliquis fortè &longs;tatim opponet mihi partes indeterminatas quantitatis: &longs;ed <lb/>pro&longs;ectò nulla pars actu e&longs;t quæ non &longs;it hæc, & non alia; igitur quæ <lb/>non &longs;it determinata, de quo aliàs; quidquid &longs;it, &longs;altem partes illæ fa<lb/>ciunt aliquod totum quod e&longs;t determinatum, quod mihi &longs;atis e&longs;t modò <lb/>ad veritatem huius Axiomatis. </s>

<s id="N11652"><emph type="center"/><emph type="italics"/>Hypothe&longs;is IV.<emph.end type="italics"/><emph.end type="center"/></s>

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

<s id="N11660"><emph type="italics"/>Aliquid mouetur quod tandem de&longs;init moueri, vel incipit quie&longs;cere.<emph.end type="italics"/></s>

<s><emph type="center"/><emph type="italics"/>Axioma V.<emph.end type="italics"/><emph.end type="center"/></s>

<s id="N11667"> Vi<lb/>deo rotatam pilam, quæ tandem quie&longs;cit, cadentem lapidem, qui tan<lb/>dem &longs;i&longs;tit, &c. </s>

<s id="N1166E">igitur certa e&longs;t hæc hypothe&longs;is. </s>

<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, & <lb/>nihil aliud; nihil enim aliud e&longs;t vnum, ni&longs;i indiui&longs;um in &longs;e, & diui<lb/>&longs;um à quolibet alio: quippè indifferentia, vel indeterminatio ibi tan<lb/>tum e&longs;t, vbi &longs;unt plura; &longs;i enim tantum vnum e&longs;t, certè non datur op<lb/>tio, &longs;i aliqua cau&longs;a e&longs;t indifferens ad effectum A & B, id e&longs;t &longs;i non e&longs;t, <lb/>cur vnum potius quàm alium producat? </s>

<s>plures e&longs;&longs;e nece&longs;&longs;e e&longs;t; &longs;i enim <lb/>tantùm vnus e&longs;t, certè indifferens non e&longs;t. </s>

<s id="N11673"><emph type="center"/><emph type="italics"/>Hypothe&longs;is V.<emph.end type="italics"/><emph.end type="center"/></s>

<s><emph type="center"/><emph type="italics"/>Axioma VI.<emph.end type="italics"/><emph.end type="center"/></s>

<s id="N11681"><emph type="italics"/>Idem mouetur modò tardiùs, modò velociùs.<emph.end type="italics"/></s>

<s><emph type="italics"/>Quidquid e&longs;t, fru&longs;trà 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, & citra miraculum, fru&longs;trà non e&longs;t, id e&longs;t propter aliquem fi<lb/>nem e&longs;t ab ip&longs;a natura in&longs;titutum; finem autem rei ex ip&longs;o v&longs;u cogno<lb/>&longs;cimus; v&longs;um verò ip&longs;o ferè &longs;en&longs;u: quod vt breui inductione confirme<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;trà 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, & con&longs;tantem v&longs;um; &longs;i forma quamdiu <lb/>e&longs;t principium actionum compo&longs;iti fru&longs;trà 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;trà 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;trà e&longs;t; at verò <lb/>anima rationalis, quæ aliquas actiones in organicas habet, fru&longs;trà non <lb/>e&longs;t etiam &longs;eparata, igitur immortalis e&longs;t: vtramque rationem &longs;uo loco fu<lb/>sè demon&longs;trabimus; &longs;i verò accidens e&longs;t, haud dubiè alteri ine&longs;&longs;e debet <lb/>propter &longs;uum finem intrin&longs;ecum, quem alibi effectum formalem &longs;ecun<lb/>darium appellamus; quem &longs;cilicet præ&longs;tat in &longs;uo &longs;ubiecto, cui certè &longs;i ni<lb/>hil præ&longs;taret, in eo fru&longs;trà e&longs;&longs;et; &longs;ic caloris effectus &longs;ecundarius e&longs;t rare<lb/>factio, vel re&longs;olutio partium &longs;ui &longs;ubiecti, vel aliquid aliud; impetus, <lb/>motus &c. </s>

<s id="N11688"> Video rotatum globum, <lb/>qui &longs;en&longs;im quie&longs;cit: &longs;entio ab codem globo modò maiorem, modò mi<lb/>norem ictum infligi, &c. </s>

<s id="N11690">igitur e&longs;t certa hypothe&longs;is. </s>

<s>Igitur tunc effet fru&longs;trà accidens, cum &longs;uo illo effectu careret; <lb/>hinc rationem contrarietatis aliquando petemus, certi&longs;&longs;imam quidem, <lb/>licet nouam, & inde clari&longs;&longs;imè con&longs;tabit, cur, & quomodo vnum contra<lb/>rium ab alio de&longs;trui dicatur; &longs;ed non e&longs;t huius loci: cùm verò audis fi<lb/>nem: ne quæ&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<lb/>tura ip&longs;a, vel e&longs;&longs;entia rei &longs;pectat, &longs;ed de his &longs;atis. </s>

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

<s id="N11699"><emph type="center"/><emph type="italics"/>Hypothe&longs;is VI.<emph.end type="italics"/><emph.end type="center"/></s>

<s>Dices fortè, multa videri e&longs;&longs;e fru&longs;trà, quæ tamen exi&longs;tunt; ad quid <lb/>enim vel tanta aquarum copia, vel tantus &longs;tellarum numerus, vel tot are<lb/>næ puncta? </s>

<s>tot fluitantes atomi? </s>

<s id="N116A7"><emph type="italics"/>Corpus proiectum etiam à potentiâ motrice &longs;eiunctum adhuc mouetur.<emph.end type="italics"/><lb/>Oculos omnium te&longs;tes appello. </s>

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

<s id="N116B2"><emph type="center"/><emph type="italics"/>Hypothe&longs;is VII.<emph.end type="italics"/><emph.end type="center"/></s>

<s>& vermiculi: Re&longs;pondeo <lb/>quamlibet &longs;tellam, quodlibet in&longs;ectum, &longs;eu vermiculum &longs;uis pollere pro<lb/>prietatibus; igitur fru&longs;trà non e&longs;t, & quodlibet punctum, quamlibet ato<lb/>mum, & quamlibet guttulam aquæ 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;trà, cum quælibet &longs;imul cum aliis totum hoc com<lb/>ponat. </s>

<s><emph type="center"/><emph type="italics"/>Axioma VII.<emph.end type="italics"/><emph.end type="center"/></s>

<s id="N116C0"><emph type="italics"/>Corpus proiectum, & in aliud impactum illud ip&longs;um impellit, & mouet.<emph.end type="italics"/></s>

<s><emph type="italics"/>Tunc ponenda e&longs;t forma distincta &longs;ub&longs;tantialis vel accidentalis, dum e&longs;t ali<lb/>qua proprietas &longs;en&longs;ibilis, quæ non pote&longs;t tribui ip&longs;i materiæ,<emph.end type="italics"/> hîc res tantùm <lb/>naturales con&longs;idero, nec &longs;uper naturales attingo, quæ &longs;uas regulas diui<lb/>næ fidei debent, non &longs;en&longs;ibus. </s>

<s id="N116C9"><emph type="center"/><emph type="italics"/>Hypothe&longs;is VIII.<emph.end type="italics"/><emph.end type="center"/></s>

<s>Hoc Axioma omninò certum e&longs;t, & 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 immediatè; igitur aliquem eius effectum &longs;en&longs;ibilem vel me<lb/>diatè, vel immediatè; qui certè &longs;i tribui po&longs;&longs;it materiæ, haud dubiè per il<lb/>lum formam non probabis, ni&longs;i formæ ip&longs;ius e&longs;&longs;e antè demon&longs;tres; &longs;i ve<lb/>to e&longs;t forma accidentalis, quam &longs;en&longs;u percipis; certè id tantùm accidit ex <pb xlink:href="026/01/040.jpg" pagenum="8"/>aliqua affectione, quâ &longs;en&longs;um ip&longs;um afficit hæc forma, igitur ex effectu il<lb/>lo illam percipis, quod clarum e&longs;t. </s>

<s>Huc reuoca vulgare illud principium, <emph type="italics"/>Frustrà fit per plura, quod po<lb/>test fieri per pauciora,<emph.end type="italics"/> quod ad Tertium etiam reuocatur; quod ita in<lb/>telligi non debet, vt &longs;ine gutta aquæ Oceanus, &longs;ine &longs;tella c&oelig;lum, &longs;ine gra<lb/>nulo arenæ terra, &longs;ine altero oculorum homo &longs;tare non po&longs;&longs;int; quæ <lb/>omnia fal&longs;i&longs;&longs;ima e&longs;&longs;e con&longs;tat; &longs;ed tantùm 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;<lb/>&longs;itas, vel ratio, vel diuina fides (immò & humana in rebus humanis, non <lb/>tamen in &longs;cientiis.) </s>

<s id="N116D7"><emph type="italics"/>Ignis applicatus &longs;ubiectum aptum, cui rectè applicatur nece&longs;&longs;ariò calefa<lb/>cit, nix frigefacit, Sol illuminat, corpus in aliud impactum illud ip&longs;um im<lb/>pellit.<emph.end type="italics"/></s>

<s id="N116E2"> Prædictæ omnes Hypothe&longs;es certi&longs;&longs;imis nixæ experimentis certi<lb/>tudinem phy&longs;icam habent, & citra miraculum fallere non po&longs;&longs;unt. </s>

<s>Igitur nunquam claudicat hic equus Okami, vt vulgò dicitur, &longs;i hoc <lb/>fræno regatur, & præ&longs;cripto ambulet pa&longs;&longs;u. </s>

<s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/></s>

<s id="N116E9"><emph type="center"/><emph type="italics"/>Axioma I.<emph.end type="italics"/><emph.end type="center"/></s>

<s>Ob&longs;eruabis &longs;eptem præmi&longs;&longs;a Axiomata, licet metaphy&longs;ica &longs;altem ali<lb/>qua ex parte e&longs;&longs;e videantur, ita pertinere ad Phy&longs;icam, vt plurimæ phy<lb/>&longs;icæ affectiones &longs;ine illis explicari, & demon&longs;trari non po&longs;&longs;int. </s>

<s id="N116F7"><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>Primum certum e&longs;t etiam certitudine metaphy&longs;ica, &longs;eu geometrica. </s>

<s id="N116FE"> Hoc ip&longs;um iam præ<lb/>mi&longs;imus Logicæ no&longs;træ demon&longs;tratiuæ, complectiturque prima illa <lb/>principia Metaphy&longs;icæ. </s>

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

<s id="N11707">1. <emph type="italics"/>Impo&longs;&longs;ibile est idem &longs;imul e&longs;&longs;e, & non e&longs;&longs;e.<emph.end type="italics"/></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 à philo&longs;o<lb/>pho; Sextum & Septimum probari po&longs;&longs;unt per Tertium; &longs;ed iam ad <lb/>alia, quæ propiùs ad phy&longs;icam accedunt, veniamus. </s>

<s><emph type="center"/><emph type="italics"/>Axioma VIII.<emph.end type="italics"/><emph.end type="center"/></s>

<s id="N11711">2. <emph type="italics"/>Quodlibet e&longs;t, vel non est.<emph.end type="italics"/></s>

<s><emph type="italics"/>Quidquid primò e&longs;t, & antè non erat, habet cau&longs;am di&longs;tinctam.<emph.end type="italics"/></s><s> Id e&longs;t quid<lb/>quid incipit e&longs;&longs;e ab alio e&longs;t; quippe à &longs;e e&longs;&longs;e non pote&longs;t; nihil enim à &longs;e <lb/>ip&longs;o dependere pote&longs;t &longs;eu produci; quia quod à &longs;e e&longs;t, nece&longs;&longs;ariò e&longs;t, <lb/>quod verò nece&longs;&longs;ariò e&longs;t, non e&longs;&longs;e non pote&longs;t, alioquin priùs e&longs;&longs;et, & <lb/>po&longs;terius, priùs vt cau&longs;a, po&longs;teriùs vt effectus: præterea quidquid produci<lb/>tur aliquando producitur, & alicubi, vt certi&longs;&longs;imum e&longs;t; &longs;ed quia hoc ali<lb/>qui negant, contendo tantùm in hoc rerum ordine, & naturaliter lo<lb/>quendo, quidquid producitur alicubi produci, & aliquando, quod nemo <lb/>negabit; Igitur &longs;i aliquid &longs;e producit; cur hîc potiùs quam illîc? </s>

<s id="N1171B">3. <emph type="italics"/>De eodem alterum contradictoriorum verè affirmatur, & alterum verè <lb/>negatur, non &longs;imul vtrumque.<emph.end type="italics"/></s>

<s>cur <lb/>nunc potius quam antè? </s>

<s>cum enim antè nullibi e&longs;&longs;et, cur de&longs;init non <lb/>e&longs;&longs;e hîc & non illîc, nunc & non antè? </s>

<s id="N11727"><emph type="center"/><emph type="italics"/>Axioma II.<emph.end type="italics"/><emph.end type="center"/></s>

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

<s id="N11735"><emph type="italics"/>Maximum &longs;ignum di&longs;tinctionis realis in phy&longs;icis est &longs;eparabilitas, vel op<lb/>po&longs;itio.<emph.end type="italics"/></s>

<s><emph type="center"/><emph type="italics"/>Axioma IX.<emph.end type="italics"/><emph.end type="center"/></s>

<s id="N1173E"> Nihil enim a &longs;e ip&longs;o &longs;eparari po&longs;t; </s>

<s id="N11742">quippe, vbi e&longs;t &longs;eparatio, &longs;eu <lb/>diui&longs;io, e&longs;t pluralitas; cur enim nummus A & nummus B eiu&longs;dem ma<lb/>teriæ, formæ, ponderis, realiter di&longs;tinguuntur? </s>

<s><emph type="italics"/>Cau&longs;a debet exi&longs;tere vt immediatè 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<lb/>cuius actu exi&longs;tentis; igitur certum e&longs;t etiam Geometricè, de quo in <lb/>Metaph. </s>

<s id="N1174A">quia &longs;cilicet vnus <lb/>non e&longs;t alius inquies; & quare vnus non e&longs;t alius? </s>

<s id="N11750">quia vnus e&longs;t hic & <lb/>alius non e&longs;t hic, vnum tango, & alium non tango, vnus e&longs;t meus, & <lb/>alius non e&longs;t meus, &c. </s>

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

<s id="N11757">vides prædicata contradictoria, quæ cum eidem <lb/>&longs;imul ine&longs;&longs;e non po&longs;&longs;int per Ax. 1. diuer&longs;is, & di&longs;tinctis ine&longs;&longs;e nece&longs;&longs;e <lb/>e&longs;t. </s>

<s>phy&longs;icis; nihil enim videmus agere, ni&longs;i quod e&longs;t; &longs;i enim age<lb/>ret quod non e&longs;t; cur potius hîc, & nunc quam alibi, & aliàs? </s>

<s id="N11760">Diceret fortè aliquis hominem reproductum in duobus locis e&longs;&longs;e po&longs;<lb/>&longs;e, & dum Romæ e&longs;t à &longs;e ip&longs;o Lugduni exi&longs;tente &longs;eiunctum e&longs;&longs;e; hoc <lb/>ip&longs;um aliàs examinabimus, dum con&longs;tet modò id totum, &longs;i fiat, mira<lb/>culo tribuendum e&longs;&longs;e, cum tamen res phy&longs;icas citra miraculum con&longs;ide<lb/>remus. </s>

<s>cur in <lb/>hoc &longs;ubiecto potius quàm in alio? </s>

<s>Dices, finis qui non e&longs;t influit; igitur agit; Re&longs;pondeo finem non <lb/>agere, nec influere ni&longs;i obiectiuè; atqui quod non exi&longs;tit actu, id e&longs;t in <lb/>&longs;tatu entatiuo, & 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, & <lb/>volitum, de quo aliàs; porrò hîc tantùm intelligimus cau&longs;am efficien<lb/>tem, &c. </s>

<s id="N1176E"><emph type="center"/><emph type="italics"/>Axioma III.<emph.end type="italics"/><emph.end type="center"/></s>

<s>Dices, cau&longs;a principalis pulli exclu&longs;i pote&longs;t non e&longs;&longs;e; hæc omnia di<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 hîc tantum loquimur; idem re&longs;pon&longs;um <lb/>e&longs;to de rana vaga. </s>

<s id="N1177C"><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><emph type="center"/><emph type="italics"/>Axioma X.<emph.end type="italics"/><emph.end type="center"/></s>

<s id="N11785"> Qui enim a&longs;&longs;erit rem aliquam po&longs;itiuam exi&longs;tere, certè po&longs;i<lb/>tiuo argumento demon&longs;trare debet quod &longs;it; </s>

<s id="N1178B">illud porrò argumentum <lb/>duci pote&longs;t vel ab experimento certo; </s>

<s><emph type="italics"/>Cau&longs;a debet e&longs;&longs;e applicata vt immediatè agat.<emph.end type="italics"/></s><s> Cur enim potiùs hîc <lb/>quam illîc; in hoc &longs;ubiecto potiùs, quam in alio, in hac di&longs;tantia potiùs, <lb/>quam in alia? </s>

<s id="N11791">&longs;ic probo exi&longs;tere rem aliquam, <lb/>quam video; vel ab aliqua ratione; </s>

<s id="N11797">&longs;ic ex eo quòd cau&longs;a &longs;it nece&longs;&longs;aria <lb/>applicata &longs;ubiecto apto, probo effectum ip&longs;um produci; </s>

<s>quidquid &longs;it, certum e&longs;t phy&longs;icè; nec enim ignis, qui e&longs;t <lb/>Romæ, calefacit Lugduni. </s>

<s id="N1179D">vel eo quòd &longs;it <lb/>effectus probo cau&longs;am e&longs;&longs;e vel ex nece&longs;&longs;itate, quâ aliquid e&longs;t nece&longs;&longs;a<lb/>rium ad aliquem finem à natura in&longs;titutum, quo natura ip&longs;a &longs;ine ab&longs;ur-<pb pagenum="6" xlink:href="026/01/038.jpg"/>do, vel graui&longs;&longs;imo incommodo carere non pote&longs;t, probo illud ip&longs;um <lb/>e&longs;&longs;e; </s>

<s id="N117AC">vel demùm ex aliqua reuelatione certa in rebus fidei; </s>

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

<s id="N117B0">igitur hoc <lb/>Axioma certum e&longs;t phy&longs;icè; </s>

<s id="N117B6">quod ni&longs;i recipiatur à Philo&longs;ophis; </s>

præterea, licet daretur in productione quali<lb/>tatum occultarum, & &longs;impathicorum quorundam effectuum, quos exa<lb/>minabimus &longs;uo loco; nemo tamen dubitat quin productio caloris, lu<lb/>minis, impetus; de quibus hic tantùm agimus, debeat e&longs;&longs;e ab applicata <lb/>cau&longs;a. </s>

<s id="N117BA">cuique <lb/>licebit impunè mentiri; &longs;i enim dicam extra mundi huius fines e&longs;&longs;e <lb/>alios orbes, intra tuum mu&longs;æum, in quo &longs;olus fortè degis, e&longs;&longs;e quin<lb/>quaginta homines, e&longs;&longs;e mille Soles, & totidem Lunas in c&oelig;lo, &c. </s>

<s id="N117C4"><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"/> Quæ&longs;tio facti e&longs;t, producendi &longs;unt te&longs;tes: huc <lb/>reuoca principium illud commune. </s>

<s>Dices impetum produci in extremitate perticæ, quæ non e&longs;t applica<lb/>ta, vel in globo tudiculario etiam non applicato; calorem & lucem <lb/>produci à Sole in terra non applicata. </s>

<s>Re&longs;pondeo, e&longs;&longs;e applicationem <lb/>mediatam; nam &longs;i reuera hæ qualitates producuntur continuata propa<lb/>gatione, diffunduntur per medium, in quo non e&longs;t difficultas. </s>

<s id="N117D5">1. <emph type="italics"/>Non &longs;unt multiplicanda entia &longs;ine nece&longs;&longs;itate, quod certè non valet ni&longs;i <lb/>addas, vel &longs;ine ratione, vel &longs;ine experientia.<emph.end type="italics"/></s>

<s>Dices etiam partes interiores cau&longs;æ v. g. Solis agunt, &longs;ed non agunt <lb/>per totum medium; alioquin agerent in alias partes Solis, à quibus <lb/>obteguntur. </s>

<s id="N117E1">2. <emph type="italics"/>Qui a&longs;&longs;erit aliquid po&longs;itiuè, debet argumento po&longs;itiuo probare.<emph.end type="italics"/></s>

<s id="N117EB"><emph type="center"/><emph type="italics"/>Axioma IV.<emph.end type="italics"/><emph.end type="center"/></s>

<s>Re&longs;pondeo, diffu&longs;ionem vel propagationem actionis in<lb/>choari tantum ab ipsâ &longs;uperficie Solis; quippe omnes partes agunt <lb/>actione communi, de quo infrà; atqui actio communis à communi me<lb/>dio incipit. </s>

<s id="N117F9"><emph type="italics"/>Quidquid exi&longs;tit phy&longs;icè extra &longs;uas cau&longs;as ab omni alio &longs;eparatum, de<lb/>terminatum e&longs;t.<emph.end type="italics"/></s>

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

<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<lb/>do vero ignis accendatur, & quid &longs;it ignem accendi, explicabimus &longs;uo <lb/>loco; quidquid &longs;it, certum e&longs;t ad productionem impetus requiri ali<lb/>quam applicationem, vt patet etiam in magnte. </s>

<s id="N11804">Hoc Axioma explicatione modicâ indiget: </s>

<s id="N11808">Determinatum illud <lb/>apello, quod illud ip&longs;um e&longs;t, quod e&longs;t, & nihil aliud; </s>

<s id="N1180E">quod e&longs;t hoc, id <lb/>e&longs;t ab omni alio di&longs;tinctum; </s>

<s id="N11814">atqui quidquid productum e&longs;t, &longs;ingulare <lb/>e&longs;t, id e&longs;t, e&longs;t hoc; </s>

<s><emph type="center"/><emph type="italics"/>Axioma XI.<emph.end type="italics"/><emph.end type="center"/></s>

<s id="N1181A">&longs;i enim producitur, alicubi producitur, & ali<lb/>quando, ergo dici pote&longs;t, e&longs;t hîc, e&longs;t nunc; igitur determinatum e&longs;t. </s>

<s id="N11820"><lb/>Aliquis fortè &longs;tatim opponet mihi partes indeterminatas quantitatis: </s>

<s><emph type="italics"/>Si cau&longs;a vniuoca applicata, & non impedita est &longs;ufficiens ad productionem <lb/>effectus, non e&longs;t ponenda alia &longs;cilicet æquiuoca.<emph.end type="italics"/></s><s> Non dico omnem cau&longs;am <lb/>e&longs;&longs;e vniuocam, &longs;ed tantùm vniuocam &longs;ufficientem, & applicatam e&longs;&longs;e <lb/>cau&longs;am, v. g. 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<lb/>rans vires caloris applicati; dicendum e&longs;t calorem illum ab hoc produ<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;ariò agit; igitur quantum pote&longs;t; igitur effectus non e&longs;t tribuen<lb/>dus alteri cau&longs;æ, quam &longs;ufficientem e&longs;&longs;e ignoramus. </s>

<s id="N11825">&longs;ed <lb/>pro&longs;ectò nulla pars actu e&longs;t quæ non &longs;it hæc, & non alia; </s>

<s id="N1182B">igitur quæ <lb/>non &longs;it determinata, de quo aliàs; quidquid &longs;it, &longs;altem partes illæ fa<lb/>ciunt aliquod totum quod e&longs;t determinatum, quod mihi &longs;atis e&longs;t modò <lb/>ad veritatem huius Axiomatis. </s>

<s id="N11836">Dices aliquid po&longs;&longs;e e&longs;&longs;e nullibi; </s>

<s id="N1183A">has <lb/>nugas refutabimus in Metaphy&longs;ica, quæ in mentem &longs;apientis viri ca<lb/>dere non po&longs;&longs;unt; nunc &longs;altem con&longs;tat id naturali modo fieri non <lb/>po&longs;&longs;e. </s>

<s>Ad hoc Axioma aliud reuoca. <emph type="italics"/>Si ex applicatione alicuius &longs;equitur &longs;em<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. g. ex <lb/>applicatione aquæ calidæ &longs;equitur productio caloris; ex applicatione &longs;o<lb/>lius aquæ non &longs;equitur; igitur dicendum e&longs;t calorem hunc produci ab <lb/>ip&longs;o calore, qui aquæ ine&longs;t, non verò ab ip&longs;a aquæ &longs;ub&longs;tantia; idem dico <lb/>de ferro frigido, &c. </s>

<s id="N11846"><emph type="center"/><emph type="italics"/>Axioma V.<emph.end type="italics"/><emph.end type="center"/></s>

<s id="N11854"><emph type="italics"/>Quod vnum e&longs;t, determinatum e&longs;t.<emph.end type="italics"/></s>

<s id="N1185B"> Quia quod vnum e&longs;t, e&longs;t hoc, & <lb/>nihil aliud; </s>

<s id="N11861">nihil enim aliud e&longs;t vnum, ni&longs;i indiui&longs;um in &longs;e, & diui<lb/>&longs;um à quolibet alio: </s>

<s>Dices non e&longs;&longs;e certum calorem produci; Re&longs;pondeo, negando; &longs;ed, <lb/>quidquid &longs;it, loquor tantùm hypotheticè; dixi enim &longs;i producatur, à <lb/>calore aquæ inhærente producitur. </s>

<s id="N11867">quippè indifferentia, vel indeterminatio ibi tan<lb/>tum e&longs;t, vbi &longs;unt plura; &longs;i enim tantum vnum e&longs;t, certè non datur op<lb/>tio, &longs;i aliqua cau&longs;a e&longs;t indifferens ad effectum A & B, id e&longs;t &longs;i non e&longs;t, <lb/>cur vnum potius quàm alium producat? </s>

<s id="N11871">plures e&longs;&longs;e nece&longs;&longs;e e&longs;t; &longs;i enim <lb/>tantùm vnus e&longs;t, certè indifferens non e&longs;t. </s>

<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 geometricè non probari, &longs;ed <lb/>tantùm phy&longs;icè; quidquid &longs;it, voco cau&longs;am id, ex cuius applicatione <lb/>&longs;equitur &longs;emper effectus, & nunquam aliàs; nam phy&longs;icè 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;icè ignem calefacere, Solem illuminare, quod &longs;atis e&longs;t. </s>

<s id="N11879"><emph type="center"/><emph type="italics"/>Axioma VI.<emph.end type="italics"/><emph.end type="center"/></s>

<s><emph type="center"/><emph type="italics"/>Axioma XII.<emph.end type="italics"/><emph.end type="center"/></s>

<s id="N11887"><emph type="italics"/>Quidquid e&longs;t, fru&longs;trà non e&longs;t.<emph.end type="italics"/></s>

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

<s id="N1188E"> Quidquid e&longs;t, id e&longs;t exi&longs;tit naturaliter <lb/>&longs;cilicet, & citra miraculum, fru&longs;trà non e&longs;t, id e&longs;t propter aliquem fi<lb/>nem e&longs;t ab ip&longs;a natura in&longs;titutum; </s>

<s id="N11896">finem autem rei ex ip&longs;o v&longs;u cogno<lb/>&longs;cimus; </s>

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

<s id="N1189C">v&longs;um verò ip&longs;o ferè &longs;en&longs;u: </s>

<s id="N118A0">quod vt breui inductione confirme<lb/>mus, quidquid exi&longs;tit vel e&longs;t &longs;ub&longs;tantia, vel accidens; </s>

<s id="N118A6">&longs;i &longs;ub&longs;tantia, vel <lb/>incorporea, vel corporea; </s>

<s id="N118AC">&longs;i incorporea, vel e&longs;t Deus, vel Angelus, vel <pb pagenum="7" xlink:href="026/01/039.jpg"/>Anima rationalis; </s>

<s>cur non omnes? </s>

<s id="N118B5">atqui nihil horum fru&longs;trà e&longs;t, vt con&longs;tat; </s>

<s id="N118B9">&longs;i corporea, <lb/>vel e&longs;t corpus, vel forma; </s>

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

<s id="N118BF">&longs;i corpus, vel elementum, vel mixtum; </s>

<s id="N118C3"><lb/>vtrumque &longs;uum finem habet, & con&longs;tantem v&longs;um; </s>

<s id="N118C8">&longs;i forma quamdiu <lb/>e&longs;t principium actionum compo&longs;iti fru&longs;trà non e&longs;t; </s>

<s id="N118CE">quippe ad cum finem <lb/>e&longs;t in&longs;tituta; </s>

<s><emph type="center"/><emph type="italics"/>Axioma XIII<emph.end type="italics"/><emph.end type="center"/></s>

<s id="N118D4">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;trà e&longs;&longs;et; </s>

<s id="N118DA">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;trà e&longs;t; </s>

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

<s id="N118E0">at verò <lb/>anima rationalis, quæ aliquas actiones in organicas habet, fru&longs;trà non <lb/>e&longs;t etiam &longs;eparata, igitur immortalis e&longs;t: </s>

<s id="N118E8">vtramque rationem &longs;uo loco fu<lb/>sè demon&longs;trabimus; </s>

<s>nec enim libra plumbi coniuncta cum <lb/>alia habet diuer&longs;am grauitatem ab eâ, quam habet &longs;eparata. </s>

<s id="N118EE">&longs;i verò accidens e&longs;t, haud dubiè alteri ine&longs;&longs;e debet <lb/>propter &longs;uum finem intrin&longs;ecum, quem alibi effectum formalem &longs;ecun<lb/>darium appellamus; </s>

<s id="N118F6">quem &longs;cilicet præ&longs;tat in &longs;uo &longs;ubiecto, cui certè &longs;i ni<lb/>hil præ&longs;taret, in eo fru&longs;trà e&longs;&longs;et; </s>

<s>Dixi ad intra; quia ad extra multum iuuat exten&longs;io; &longs;ic maior ignis <lb/>longiùs diffundit &longs;uum calorem; corpus grauiùs cadens majorem ictum <lb/>infligit; Ad hoc Axioma reuocatur i&longs;tud. </s>

<s id="N118FC">&longs;ic caloris effectus &longs;ecundarius e&longs;t rare<lb/>factio, vel re&longs;olutio partium &longs;ui &longs;ubiecti, vel aliquid aliud; impetus, <lb/>motus &c. </s>

<s id="N11904">Igitur tunc effet fru&longs;trà accidens, cum &longs;uo illo effectu careret; </s>

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

<s id="N11908"><lb/>hinc rationem contrarietatis aliquando petemus, certi&longs;&longs;imam quidem, <lb/>licet nouam, & inde clari&longs;&longs;imè con&longs;tabit, cur, & quomodo vnum contra<lb/>rium ab alio de&longs;trui dicatur; </s>

<s id="N11911">&longs;ed non e&longs;t huius loci: cùm verò audis fi<lb/>nem: </s>

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

<s id="N11917">ne quæ&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<lb/>tura ip&longs;a, vel e&longs;&longs;entia rei &longs;pectat, &longs;ed de his &longs;atis. </s>

<s>Huc etiam reuoca dicta illa <lb/>communia. </s>

<s id="N11921">Huc reuoca Principium illud, <emph type="italics"/>Deus & Natura nihil faciunt fru&longs;trà,<emph.end type="italics"/><lb/>id e&longs;t quod &longs;uo fine careat intrin&longs;eco. </s>

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

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

<s id="N1192D">Dices fortè, multa videri e&longs;&longs;e fru&longs;trà, quæ tamen exi&longs;tunt; ad quid <lb/>enim vel tanta aquarum copia, vel tantus &longs;tellarum numerus, vel tot are<lb/>næ puncta? </s>

<s id="N11935">tot fluitantes atomi? </s>

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

<s id="N11938">tot in&longs;ecta? </s>

<s id="N1193B">& vermiculi: </s>

<s><emph type="center"/><emph type="italics"/>Axioma XIV.<emph.end type="italics"/><emph.end type="center"/></s>

<s id="N1193E">Re&longs;pondeo <lb/>quamlibet &longs;tellam, quodlibet in&longs;ectum, &longs;eu vermiculum &longs;uis pollere pro<lb/>prietatibus; </s>

<s id="N11946">igitur fru&longs;trà non e&longs;t, & quodlibet punctum, quamlibet ato<lb/>mum, & quamlibet guttulam aquæ e&longs;&longs;e partem huius vniuer&longs;itatis: </s>

<s><emph type="italics"/>Quidquid de&longs;truitur non e&longs;t à &longs;e.<emph.end type="italics"/></s><s> Hoc Axioma geometricum e&longs;t; Quod <lb/>enim e&longs;t à &longs;e, nece&longs;&longs;ariò e&longs;t; cùm à libertate &longs;eu voluntate alterius non <lb/>pendeat; cum enim primo in&longs;tanti quo res e&longs;t, non &longs;it à &longs;e per Axiom. 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;ariò, 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;ariò, igitur pendet ab alio, quod pote&longs;t facere vt non &longs;it. </s>

<s id="N1194C">quod <lb/>enim dices de vna, dicam de omnibus; </s>

<s id="N11952">equidem pauciores e&longs;&longs;e po&longs;&longs;ent; <lb/>attamen nulla e&longs;t fru&longs;trà, cum quælibet &longs;imul cum aliis totum hoc com<lb/>ponat. </s>

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

<s id="N1195C"><emph type="center"/><emph type="italics"/>Axioma VII.<emph.end type="italics"/><emph.end type="center"/></s>

<s>Re&longs;pondeo, non videri quomo<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 tantùm exigere pote&longs;t contrarij de&longs;tructio<lb/>nem, quid e&longs;t porro de&longs;trui, ni&longs;i de&longs;inere con&longs;eruari? </s>

<s id="N1196A"><emph type="italics"/>Tunc ponenda e&longs;t forma distincta &longs;ub&longs;tantialis vel accidentalis, dum e&longs;t ali<lb/>qua proprietas &longs;en&longs;ibilis, quæ non pote&longs;t tribui ip&longs;i materiæ,<emph.end type="italics"/> hîc res tantùm <lb/>naturales con&longs;idero, nec &longs;uper naturales attingo, quæ &longs;uas regulas diui<lb/>næ fidei debent, non &longs;en&longs;ibus. </s>

<s>quæ omnia fusè <lb/>in Metaphy&longs;ica demon&longs;trabimus; quidquid enim e&longs;t aliquo in&longs;tanti vel <lb/>e&longs;t à &longs;e, vel non à &longs;e; &longs;i primùm 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;icè. </s>

<s>Huc reuoca Axiomata &longs;equentia, quæ ex hoc vno deducuntur. </s>

<s id="N1197A">Hoc Axioma omninò certum e&longs;t, & 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; </s>

<s id="N11982">atqui formam &longs;ub&longs;tantialem &longs;en&longs;u <lb/>non percipis immediatè; </s>

<s>1. <emph type="italics"/>Quidquid e&longs;t, & non e&longs;t à &longs;e, e&longs;t, &longs;eu pendet, &longs;eu con&longs;eruatur ab alio.<emph.end type="italics"/><lb/>Hæc enim &longs;unt idem, vt con&longs;tat. </s>

<s id="N11988">igitur aliquem eius effectum &longs;en&longs;ibilem vel me<lb/>diatè, vel immediatè; </s>

<s id="N1198E">qui certè &longs;i tribui po&longs;&longs;it materiæ, haud dubiè per il<lb/>lum formam non probabis, ni&longs;i formæ ip&longs;ius e&longs;&longs;e antè demon&longs;tres; </s>

<s>2. <emph type="italics"/>Quidquid destruitur, ad exigentiam alicuius de&longs;truitur, &longs;altem totius <lb/>natura, ne aliquid &longs;it fru&longs;trà.<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; certè qui de&longs;init con&longs;er<lb/>uare in&longs;tanti A potiùs quam in&longs;tanti B, hoc facere non pote&longs;t ni&longs;i ali<lb/>quid hoc exigat; &longs;cilicet iuxta leges naturæ. </s>

<s id="N11994">&longs;i ve<lb/>to e&longs;t forma accidentalis, quam &longs;en&longs;u percipis; certè id tantùm accidit ex <pb pagenum="8" xlink:href="026/01/040.jpg"/>aliqua affectione, quâ &longs;en&longs;um ip&longs;um afficit hæc forma, igitur ex effectu il<lb/>lo illam percipis, quod clarum e&longs;t. </s>

<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, & con<lb/>&longs;eruetur, quæ erat antè. </s><pb xlink:href="026/01/044.jpg" pagenum="12"/>

<s id="N119A3">Huc reuoca vulgare illud principium, <emph type="italics"/>Frustrà fit per plura, quod po<lb/>test fieri per pauciora,<emph.end type="italics"/> quod ad Tertium etiam reuocatur; </s>

<s><emph type="center"/><emph type="italics"/>Axioma XV.<emph.end type="italics"/><emph.end type="center"/></s>

<s id="N119AF">quod ita in<lb/>telligi non debet, vt &longs;ine gutta aquæ Oceanus, &longs;ine &longs;tella c&oelig;lum, &longs;ine gra<lb/>nulo arenæ terra, &longs;ine altero oculorum homo &longs;tare non po&longs;&longs;int; </s>

<s id="N119B7">quæ <lb/>omnia fal&longs;i&longs;&longs;ima e&longs;&longs;e con&longs;tat; &longs;ed tantùm 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;<lb/>&longs;itas, vel ratio, vel diuina fides (immò & humana in rebus humanis, non <lb/>tamen in &longs;cientiis.) </s>

<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 minùs de&longs;truit frigoris; minor impetus minùs de&longs;truit impetus <lb/>contrarij (&longs;i contrarium habet) quæ omnia con&longs;tant ex hypothe&longs;ibus. </s>

<s><lb/>Ratio e&longs;t, quia plùs vel minùs contrarij de&longs;truere, multam habet ex<lb/>ten&longs;ionem. </s>

<s id="N119C5">Igitur nunquam claudicat hic equus Okami, vt vulgò dicitur, &longs;i hoc <lb/>fræno regatur, & præ&longs;cripto ambulet pa&longs;&longs;u. </s>

<s>v.g. &longs;int duo contraria A & B, &longs;it A vt 20. &longs;it B vt 5. certè &longs;i <lb/>B de&longs;truat A &longs;upra ratam, vel &longs;upra id, quod &longs;ibi ex æquo re&longs;pondet, id <lb/>e&longs;t &longs;upra 5. cur potius 6. quam 7. 8. &c. </s>

<s id="N119CC"><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/></s>

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

<s id="N119DA">Ob&longs;eruabis &longs;eptem præmi&longs;&longs;a Axiomata, licet metaphy&longs;ica &longs;altem ali<lb/>qua ex parte e&longs;&longs;e videantur, ita pertinere ad Phy&longs;icam, vt plurimæ phy<lb/>&longs;icæ affectiones &longs;ine illis explicari, & demon&longs;trari non po&longs;&longs;int. </s>

<s>Igitur cum plures &longs;int termini tùm infra, tùm &longs;upra 5. cur potius <lb/>vnus quàm alius? </s>

<s id="N119E3">Primum certum e&longs;t etiam certitudine metaphy&longs;ica, &longs;eu geometrica. </s>

<s>atqui vnus tantùm ex æquo 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 id="N119E6"><lb/>Secundum, Quartum, & Quintum per Primum demon&longs;trari po&longs;&longs;unt. </s>

<s id="N119EA"><lb/>Tertium e&longs;t veluti communis po&longs;itio, &longs;eu commune po&longs;tulatum, in quo <lb/>docti omnes conunciunt; </s>

<s>Nec dicas A totum de&longs;trui à B, quòd 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 minùs agit per Ax. 13. num. </s>

<s id="N119F1">quippe nihil &longs;ine ratione dici debet à philo&longs;o<lb/>pho; </s>

<s id="N119F7">Sextum & Septimum probari po&longs;&longs;unt per Tertium; &longs;ed iam ad <lb/>alia, quæ propiùs ad phy&longs;icam accedunt, veniamus. </s>

<s>3. igitur minùs exi<lb/>git; porrò cum dico vnum ab alio de&longs;trui, intelligo tantùm ex applica<lb/>tione vnius &longs;equi de&longs;tructionem alterius &longs;altem ex parte. </s>

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

<s id="N119FF"><emph type="center"/><emph type="italics"/>Axioma VIII.<emph.end type="italics"/><emph.end type="center"/></s>

<s>quæ <lb/>nos fusè in Theorematis metaph. </s>

<s id="N11A0D"><emph type="italics"/>Quidquid primò e&longs;t, & antè non erat, habet cau&longs;am di&longs;tinctam.<emph.end type="italics"/></s>

<s>explicabimus, & 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<lb/>titudinem, quod nemo negabit; con&longs;tátque ex hypothe&longs;ibus, licèt ma<lb/>iorem etiam habeant, de qua &longs;uo loco. </s>

<s id="N11A14"> Id e&longs;t quid<lb/>quid incipit e&longs;&longs;e ab alio e&longs;t; </s>

<s id="N11A1A">quippe à &longs;e e&longs;&longs;e non pote&longs;t; </s>

<s>Ob&longs;eruabis prætereà nos diutiùs hæ&longs;i&longs;&longs;e in præmittendis huic libro <lb/>Axiomatis, quod tamen in aliis libris non faciemus. </s>

<s id="N11A1E">nihil enim à &longs;e <lb/>ip&longs;o dependere pote&longs;t &longs;eu produci; </s>

<s id="N11A24">quia quod à &longs;e e&longs;t, nece&longs;&longs;ariò e&longs;t, <lb/>quod verò nece&longs;&longs;ariò e&longs;t, non e&longs;&longs;e non pote&longs;t, alioquin priùs e&longs;&longs;et, & <lb/>po&longs;terius, priùs vt cau&longs;a, po&longs;teriùs vt effectus: </s>

<s><emph type="center"/><emph type="italics"/>Postulatum,<emph.end type="italics"/><emph.end type="center"/></s>

<s id="N11A2C">præterea quidquid produci<lb/>tur aliquando producitur, & alicubi, vt certi&longs;&longs;imum e&longs;t; </s>

<s id="N11A32">&longs;ed quia hoc ali<lb/>qui negant, contendo tantùm in hoc rerum ordine, & naturaliter lo<lb/>quendo, quidquid producitur alicubi produci, & aliquando, quod nemo <lb/>negabit; </s>

<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, &c.<emph.end type="italics"/></s>

<s id="N11A3C">Igitur &longs;i aliquid &longs;e producit; cur hîc potiùs quam illîc? </s>

<s id="N11A40">cur <lb/>nunc potius quam antè? </s>

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 1.<emph.end type="center"/></s>

<s id="N11A45">cum enim antè nullibi e&longs;&longs;et, cur de&longs;init non <lb/>e&longs;&longs;e hîc & non illîc, nunc & non antè? </s>

<s id="N11A4A">hinc quod à &longs;e e&longs;t, vbique, & <lb/>&longs;emper e&longs;t, &longs;ed ne quis mihi litem intendat, licet hoc Axioma certitudi<lb/>nem geometricam habeat; </s>

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

<s id="N11A52">&longs;ufficit modò habere phy&longs;icam, quod ex om<lb/>nibus hypothe&longs;ibus demon&longs;tratur; </s>

<s id="N11A58">&longs;i enim aliquid de nouo produci<lb/>tur, quod certum e&longs;t, ab alio produci video: </s>

<s>3. & de&longs;init e&longs;&longs;e in mobili, <lb/>in quo antè erat per hypoth.4. igitur mobile e&longs;t, & non e&longs;t motus; igi<lb/>tur à motu &longs;eparatum; igitur realiter di&longs;tinctum per Ax. 2. præterea <lb/>moueri, & non moueri &longs;unt prædicata contradictoria, vt con&longs;tat; igi<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 à <lb/>mobili; non quies, vt con&longs;tat, quæ e&longs;t tantùm negatio motus, &longs;eu per<lb/>&longs;euerantia in eodem loco; igitur nullam dicit mutationem; at verò <lb/>motus mutationem dicit, per Def. 1. hoc Theorema fusè demon&longs;trabo <lb/>in Metaph. </s>

<s id="N11A5E">calor ab igne mediatè <lb/>vel immediatè, impetus à potentia motrice, vel ab alio impetu: </s>

<s id="N11A64">cuncta <lb/>hæc &longs;i reuera producuntur de quo alibi, ab alio produci con&longs;tat; </s>

<s id="N11A6A">in Me<lb/>taphy&longs;ica hoc ip&longs;um geometricè demon&longs;trabimus; </s>

<s id="N11A70">cum enim agere &longs;up<lb/>ponat e&longs;&longs;e; </s>

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 2.<emph.end type="center"/></s>

<s id="N11A76">quippe omnis actio alicuius agentis e&longs;t; </s>

<s id="N11A7A">& cum agere termi<lb/>netur ad effectum, nam fieri e&longs;t alicuius fieri; certè agens, & terminus, <lb/>cau&longs;a, & effectus di&longs;tinguuntur, igitur. <emph type="italics"/>Quidquid primo e&longs;t, &c.<emph.end type="italics"/></s>

<s><emph type="italics"/>Motus non pote&longs;t dici propriè productus immediatè, vel effectus immedia<lb/>tus cau&longs;æ 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. 1. &longs;ed mutatio propriè non producitur; quippè pro<lb/>ductio tantùm 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 tantùm ens; præ&longs;ertim hæc, quæ tantùm dicit <lb/>terminum à quo, ide&longs;t locum relictum; & terminum ad quem, id e&longs;t lo<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, & <lb/>nouum acquirat, omninò mouetur, &longs;ed concretum illud ex loco relicto, <lb/>& acqui&longs;ito produci non pote&longs;t; illud autem e&longs;t motus, qui certè non <lb/>dicit tantùm locum relictum &longs;ine acqui&longs;ito; alioqui &longs;i mobile de&longs;true<lb/>retur, diceretur moueri; nec etiam locum acqui&longs;itum &longs;ine priori relicto: <lb/>alioqui &longs;i mobile primò produceretur, diceretur moueri localiter; igitur <lb/>motus neutrum dicit &longs;eor&longs;im; &longs;i primum, diceretur de&longs;tructus; &longs;i &longs;ecun<lb/>dum, diceretur aliquo modo productus, vel potiùs acqui&longs;itus; at vtrum<lb/>que coniunctim, &longs;imulque e&longs;&longs;entialiter dicit motus; nec enim conci<lb/>pio aliud, dum concipio motum: porrò vtrumque &longs;imul &longs;umptum indi<lb/>ui&longs;ibiliter non pote&longs;t dici, vel de&longs;tructum propriè, vel productum; Di<gap/><lb/>xi propriè; nam impropriè dici pote&longs;t motus productus. </s>

<s id="N11A8D"><emph type="center"/><emph type="italics"/>Axioma IX.<emph.end type="italics"/><emph.end type="center"/></s>

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

<s id="N11A9B"><emph type="italics"/>Cau&longs;a debet exi&longs;tere vt immediatè agat.<emph.end type="italics"/></s>

<s id="N11AA2"> Hoc certum e&longs;t; </s>

<s>Re&longs;pondeo Motum non e&longs;&longs;e ens ab&longs;olutum, &longs;ed e&longs;&longs;e mutatio<lb/>nem entis, quæ mutatio e&longs;t concretum quoddam ex ente & non ente; <lb/>quòd certè non pote&longs;t dici propriè productum, &longs;ed re&longs;ultans, vt relatio; <lb/>nam producatur, &longs;i fieri pote&longs;t; certè e&longs;t aliquid, quod tam facilè de<lb/>&longs;trui pote&longs;t, quam produci; igitur de&longs;truatur, & remaneat tantùm en<lb/>titas mobilis, quæ, quo in&longs;tanti priorem locum relinquit, nouum acqui<lb/>rat; certè dicitur adhuc moueri, & tamen non erit motus ex &longs;uppo&longs;itio<lb/>ne, quod ab&longs;urdum e&longs;t. </s>

<s id="N11AA5">quia agere <lb/>&longs;upponit e&longs;&longs;e; </s>

<s id="N11AAB">quippe agere e&longs;t perfectio realis actu exi&longs;tens; igitur ali<lb/>cuius actu exi&longs;tentis; igitur certum e&longs;t etiam Geometricè, de quo in <lb/>Metaph. </s>

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

<s id="N11AB4">Iam vero &longs;ufficiat certum e&longs;&longs;e phi&longs;icè, vt con&longs;tat ex omnibus <lb/>hypoth. </s>

<s id="N11AB9">phy&longs;icis; </s>

<s>Re&longs;p. potentiam motricem e&longs;&longs;e actiuam vt dicemus, <lb/>& ab eâ produci impetum, qui deinde exigit motum, vt dicemus <lb/>infrà. </s>

<s id="N11ABC">nihil enim videmus agere, ni&longs;i quod e&longs;t; </s>

<s id="N11AC0">&longs;i enim age<lb/>ret quod non e&longs;t; cur potius hîc, & nunc quam alibi, & aliàs? </s>

<s>Nec e&longs;t quod aliqui ita mirentur hæc à me dici; cum certum &longs;it effe<lb/>ctus formales &longs;ecundarios principum ferè qualitatum tales e&longs;&longs;e, vt mini<lb/>mè producantur; &longs;ed qua&longs;i re&longs;ultent ab exigentia; v. g. effectus calo<lb/>ris in &longs;uo &longs;ubiecto e&longs;t eiu&longs;dem &longs;ubiecti rarefactio, quæ reuerâ non <lb/>producitur, vt con&longs;tat. </s>

<s id="N11AC6">cur in <lb/>hoc &longs;ubiecto potius quàm in alio? </s>

<s id="N11ACD">Dices, finis qui non e&longs;t influit; </s>

<s id="N11AD1">igitur agit; </s>

<s id="N11AD5">Re&longs;pondeo finem non <lb/>agere, nec influere ni&longs;i obiectiuè; </s>

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 3.<emph.end type="center"/></s>

<s id="N11ADB">atqui quod non exi&longs;tit actu, id e&longs;t in <lb/>&longs;tatu entatiuo, & reali, pote&longs;t e&longs;&longs;e in &longs;tatu obiectiuo; </s>

<s id="N11AE1">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, & <lb/>volitum, de quo aliàs; porrò hîc tantùm intelligimus cau&longs;am efficien<lb/>tem, &c. </s>

<s><emph type="italics"/>Motus e&longs;t ab alio di&longs;tincto in aliquo genere cau&longs;æ.<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. </s>

<s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/></s>

<s id="N11AED">Dices, cau&longs;a principalis pulli exclu&longs;i pote&longs;t non e&longs;&longs;e; </s>

<s id="N11AF1">hæc omnia di<lb/>&longs;cutiemus &longs;uo loco cum de generatione animalium; </s>

<s>Ob&longs;eruabis motum localem e&longs;&longs;e duplicis generis; primum genus mo<lb/>tus e&longs;t actio potentiæ motricis, quæ reuerà mouet, & cuius exercitium <lb/>dicitur motus, &longs;eu latio, &longs;eu motio, &longs;eu actio, qua reuerâ agit, produ<lb/>citque impetum, non motum; cum etiam &longs;ine motu defatigetur, vt cum <lb/>quis alium pellit, à quo pellitur æquali ni&longs;u; patet etiam in manu &longs;u<lb/>&longs;tinente aliquod pondus, quæ non mouetur; licet reuerâ etiam &longs;ummo <pb xlink:href="026/01/046.jpg" pagenum="14"/>conatu agat: immò &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<lb/>ducendum impetum: Itaque hic motus primi generis, &longs;i comparetur <lb/>cum potentia motrice, e&longs;t verè 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/>propriè dicitur produci, ni&longs;i vt quo (vt vulgò 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<lb/>dit ad terminum. </s>

<s id="N11AF7">&longs;ufficiat dixi&longs;&longs;e non <lb/>e&longs;&longs;e cau&longs;am immediatam, de qua hîc tantum loquimur; idem re&longs;pon&longs;um <lb/>e&longs;to de rana vaga. </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; & fru&longs;trà ponitur alia entitas, quæ tantùm 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 infrà, certè fru&longs;tra ponitur quodcun<lb/>que aliud per Ax.3. & 7. </s>

<s id="N11B01"><emph type="center"/><emph type="italics"/>Axioma X.<emph.end type="italics"/><emph.end type="center"/></s>

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 4.<emph.end type="center"/></s>

<s><emph type="italics"/>Cau&longs;a illa immediata motus, quæ non est efficiens, potest tantùm e&longs;&longs;e exi<lb/>gens, quæ reducitur ad formalem, quæ &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. <lb/>2. &longs;it tamen cau&longs;a per Th.3. nec &longs;it materialis, nec finalis, vt con&longs;tat, de<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, quæ &longs;upponit alias; cum ip&longs;a non &longs;it dum ponitur <lb/>effectus. </s>

<s id="N11B0F"><emph type="italics"/>Cau&longs;a debet e&longs;&longs;e applicata vt immediatè agat.<emph.end type="italics"/></s>

<s id="N11B16"> Cur enim potiùs hîc <lb/>quam illîc; in hoc &longs;ubiecto potiùs, quam in alio, in hac di&longs;tantia potiùs, <lb/>quam in alia? </s>

<s id="N11B1E">quidquid &longs;it, certum e&longs;t phy&longs;icè; nec enim ignis, qui e&longs;t <lb/>Romæ, calefacit Lugduni. </s>

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 5.<emph.end type="center"/></s>

<s id="N11B26">Dices dari fortè actionem in di&longs;tans; </s>

<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. haud dubiè &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. præ<lb/>terea potentia motrix proiicientis verè agit, cum etiam defatigetur; igi<lb/>tur aliquid producit, non motum immediatè, qui produci non pote&longs;t pro<lb/>prièper Th. 2. Adde quod motus &longs;ecundi generis habet tantùm cau&longs;am <lb/>immediatam exigentem, &longs;ed potentia motrix non exigit; quia primò <lb/>non defatigaretur exigendo; &longs;ecundò quia lapis &longs;eparatus à manu etiam <lb/>mouetur, &longs;ed non ad exigentiam potentiæ motricis, vt patet; quia &longs;tatim <lb/>po&longs;t &longs;eparationem pote&longs;t illa potentia de&longs;trui, licèt lapis longo pò&longs;t <lb/>tempore moueatur; &longs;ed quod non e&longs;t, nihil exigit. </s>

<s id="N11B2A">Re&longs;pondeo negando, quod de<lb/>mon&longs;trabimus in Metaph. præterea, licet daretur in productione quali<lb/>tatum occultarum, & &longs;impathicorum quorundam effectuum, quos exa<lb/>minabimus &longs;uo loco; </s>

<s id="N11B34">nemo tamen dubitat quin productio caloris, lu<lb/>minis, impetus; de quibus hic tantùm agimus, debeat e&longs;&longs;e ab applicata <lb/>cau&longs;a. </s>

<s>Aliquis fortè diceret potentiam motricem exigere primam partem <lb/>motus, quæ deinde &longs;ecundam exigit, & &longs;ecunda tertiam, tertia quar<lb/>tam, &c. </s>

<s id="N11B3E">Dices impetum produci in extremitate perticæ, quæ non e&longs;t applica<lb/>ta, vel in globo tudiculario etiam non applicato; calorem & lucem <lb/>produci à Sole in terra non applicata. </s>

<s id="N11B46">Re&longs;pondeo, e&longs;&longs;e applicationem <lb/>mediatam; nam &longs;i reuera hæ qualitates producuntur continuata propa<lb/>gatione, diffunduntur per medium, in quo non e&longs;t difficultas. </s>

<s>Sed contra; quæro quid &longs;it prima illa pars motus; nec enim <lb/>aliud agno&longs;co ni&longs;i primam mutationem loci, quæ 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<lb/>bile, & nouus locus acqui&longs;itus, mobile ip&longs;um non exigit, vt demon&longs;tra<lb/>tum e&longs;t, & 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><pb xlink:href="026/01/047.jpg" pagenum="15"/>

<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 id="N11B50">Dices etiam partes interiores cau&longs;æ v. g. Solis agunt, &longs;ed non agunt <lb/>per totum medium; alioquin agerent in alias partes Solis, à quibus <lb/>obteguntur. </s>

<s id="N11B5C">Re&longs;pondeo, diffu&longs;ionem vel propagationem actionis in<lb/>choari tantum ab ipsâ &longs;uperficie Solis; </s>

<s>Re&longs;p. negando, tùm quia omnis potentia motrix <lb/>agit; igitur producit aliquid aliud, quod e&longs;t cau&longs;a motus: præterea po<lb/>tentia motrix corporis animati, agit v&longs;que ad defatigationem, &longs;udorem, <lb/>licèt non &longs;it motus, igitur aliud producit, de corpore graui probabi<lb/>mus infrà. </s>

<s id="N11B62">quippe omnes partes agunt <lb/>actione communi, de quo infrà; atqui actio communis à communi me<lb/>dio incipit. </s>

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 6.<emph.end type="center"/></s>

<s id="N11B6C">Dices ignem produci in parte medij remota interrupta propagatio<lb/>ne, vt con&longs;tat, &longs;i vitro per refractionem, vel &longs;peculo per reflectionem <lb/>radios Solares colligas. </s>

<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<lb/>diata motus, per Th.5. ergo aliquid aliud; igitur impetus, nam quod di<lb/>&longs;tinctum e&longs;t à &longs;ub&longs;tantia mobilis, & 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 paulò diutius hærendum e&longs;t, igitur. </s>

<s>Demon&longs;tro primò dari impetum: Quidquid e&longs;t, & antè non erat, non <lb/>e&longs;t à &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<lb/>bo: Lapis cadens, vel impactus in alium lapidem mouet illum per hy<lb/>poth.7. &longs;ed &longs;ub&longs;tantia lapidis in alium impacti non e&longs;t cau&longs;a huius mo<lb/>tus, quia e&longs;&longs;et cau&longs;a nece&longs;&longs;aria vt patet; igitur applicata eundem effe<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>

<s id="N11B75">Re&longs;pondeo, ignem quidem accendi in data di&longs;tantia; </s>

<s id="N11B79">at non &longs;ine <pb pagenum="10" xlink:href="026/01/042.jpg"/>aliqua applicatione, &longs;altem virtutis, in quo non e&longs;t difficultas; </s>

<s>Scio e&longs;&longs;e aliquas re&longs;pon&longs;iones, quas infrà refellemus; nunc &longs;ufficiat <lb/>dixi&longs;&longs;e lapidem impactum non producere motum, qui propriè non pro<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>

<s id="N11B82">quomo<lb/>do vero ignis accendatur, & quid &longs;it ignem accendi, explicabimus &longs;uo <lb/>loco; quidquid &longs;it, certum e&longs;t ad productionem impetus requiri ali<lb/>quam applicationem, vt patet etiam in magnte. </s>

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

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

<s id="N11B91"><emph type="center"/><emph type="italics"/>Axioma XI.<emph.end type="italics"/><emph.end type="center"/></s>

<s>Tertiò probatur; pila di&longs;iuncta à manu proiicientis diu adhuc mo<lb/>uetur per hypoth.6. igitur hic motus habet cau&longs;am per Ax. 8. quælibet <lb/>enim pars motus de nouo e&longs;t, neque duæ illius partes &longs;imul e&longs;&longs;e po&longs;&longs;unt. </s>

<s id="N11B9F"><emph type="italics"/>Si cau&longs;a vniuoca applicata, & non impedita est &longs;ufficiens ad productionem <lb/>effectus, non e&longs;t ponenda alia &longs;cilicet æquiuoca.<emph.end type="italics"/></s>

<s><lb/>atqui potentia motrix non e&longs;t cau&longs;a per Ax.10. immò pote&longs;t e&longs;&longs;e de&longs;tru<lb/>cta; igitur non e&longs;t cau&longs;a per Ax. 9. Non e&longs;t etiam cau&longs;a &longs;ub&longs;tantia pilæ <lb/>mobilis per Th.5.5. nec priores pattes motus per re&longs;p. </s>

<s id="N11BA8"> Non dico omnem cau&longs;am <lb/>e&longs;&longs;e vniuocam, &longs;ed tantùm vniuocam &longs;ufficientem, & applicatam e&longs;&longs;e <lb/>cau&longs;am, v. g. calor e&longs;t cau&longs;a &longs;ufficiens caloris, vt con&longs;tat in aqua calida; </s>

<s id="N11BB4"><lb/>igitur &longs;i calor e&longs;t applicatus &longs;ubiecto, in quo producitur calor non &longs;upe<lb/>rans vires caloris applicati; </s>

<s>ad primam in<lb/>&longs;tantiam Th 5. igitur aliquid aliud; voco impetum. </s>

<s id="N11BBB">dicendum e&longs;t calorem illum ab hoc produ<lb/>ci; </s>

<s id="N11BC1">cum calor &longs;it cau&longs;a nece&longs;&longs;aria; </s>

<s>Quartò 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 id="N11BC5">igitur &longs;i &longs;it applicatus &longs;ubjecto apto, <lb/>nece&longs;&longs;ariò agit; </s>

<s id="N11BCB">igitur quantum pote&longs;t; igitur effectus non e&longs;t tribuen<lb/>dus alteri cau&longs;æ, quam &longs;ufficientem e&longs;&longs;e ignoramus. </s>

<s>5. igitur <lb/>non e&longs;t &longs;emper æqualis, & eadem cau&longs;a huius motus per Ax. 12. & 13. <lb/>num.3. igitur cau&longs;a huius motus eodem modo debilitatur, &longs;eu remitti<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 præ&longs;ens, quæ mi<lb/>nuitur; voco impetum. </s>

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

<s id="N11BD3">Ad hoc Axioma aliud reuoca. <emph type="italics"/>Si ex applicatione alicuius &longs;equitur &longs;em<lb/>per effectus aliquis, illud ip&longs;um cau&longs;a dici debet huius effectus; </s>

<s id="N11BDC">licet aliud &longs;it <lb/>coniunctum, ex quo &longs;eor&longs;im &longs;umpto applicato non &longs;equitur effectus<emph.end type="italics"/>; </s>

<s>Igitur certum e&longs;t dari impetum; qui certè tribui non <lb/>pote&longs;t, vel vlli connotationi, vel alteri exigentiæ, vt con&longs;tat ex <lb/>dictis. </s>

<s id="N11BE5">v. g. ex <lb/>applicatione aquæ calidæ &longs;equitur productio caloris; </s>

<s id="N11BEF">ex applicatione &longs;o<lb/>lius aquæ non &longs;equitur; </s>

<s>Diceret fortè alius hæc omnia e&longs;&longs;e dubia; nam fieri pote&longs;t vt Deus <lb/>tantùm moueat; quod &longs;ine impetu fieri po&longs;&longs;e certum e&longs;t; Re&longs;p. equi<lb/>dem per miraculum hoc fieri po&longs;&longs;e; &longs;ed quemadmadum certum e&longs;t phy<lb/>&longs;icè ignem applicatum calefacere, niuem frigefacere, & modò calamum <lb/>à me hæc &longs;cribente moueri, ita certum o&longs;t phy&longs;icè &longs;agittam à &longs;agittario <lb/>emitti, & pilam à proiiciente, &c. </s>

<s id="N11BF5">igitur dicendum e&longs;t calorem hunc produci ab <lb/>ip&longs;o calore, qui aquæ ine&longs;t, non verò ab ip&longs;a aquæ &longs;ub&longs;tantia; idem dico <lb/>de ferro frigido, &c. </s>

<s>adde quod Deus, vt auctor naturæ <lb/>e&longs;t, agit tantùm; vel de&longs;init agere iuxta exigentiam cau&longs;arum &longs;ecunda<lb/>rum; denique cau&longs;am phy&longs;icè appello, ex cuius applicatione nunquam <lb/>non &longs;equitur effectus per Ax.11. num.1. </s>

<s id="N11BFF">Dices non e&longs;&longs;e certum calorem produci; Re&longs;pondeo, negando; </s>

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

<s id="N11C03">&longs;ed, <lb/>quidquid &longs;it, loquor tantùm hypotheticè; dixi enim &longs;i producatur, à <lb/>calore aquæ inhærente producitur. </s>

<s><lb/>immò maximam &longs;uarum partium partem; igitur cum deinde proiicitur <lb/>idem globus, illæ partes mouentur; dari igitur debet cau&longs;a huius motus <lb/>per Ax.8, igitur impetus: nec dicas moueri illas partes à corpu&longs;culis; quia <lb/>antè erant eadem, immò plura corpu&longs;cula; & tamen non mouebant: igi<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 id="N11C0D">Dices produci po&longs;&longs;e ab aliqua cau&longs;a ignota po&longs;ita dumtaxat tali, vel <lb/>tali conditione. </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<lb/>tur illa corpu&longs;cula, & excitantur à potentia motrice, etiam partes prius <lb/>immobiles mouebuntur, & excitabuntur per Ax.12. quia &longs;unt applicatæ <lb/>cau&longs;æ nece&longs;&longs;ariæ. </s>

<s id="N11C12">Re&longs;pondeo, hoc reuera geometricè non probari, &longs;ed <lb/>tantùm phy&longs;icè; </s>

<s id="N11C18">quidquid &longs;it, voco cau&longs;am id, ex cuius applicatione <lb/>&longs;equitur &longs;emper effectus, & nunquam aliàs; </s>

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

<s id="N11C1E">nam phy&longs;icè 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;icè ignem calefacere, Solem illuminare, quod &longs;atis e&longs;t. </s>

<s>igitur &longs;i modò mouetur, modò quie&longs;<lb/>cit, motus ab eo di&longs;tinguitur per Th.1. igitur mouetur per impetum, de <lb/>quo infrà. </s>

<s id="N11C28"><emph type="center"/><emph type="italics"/>Axioma XII.<emph.end type="italics"/><emph.end type="center"/></s>

<s>Igitur datur nece&longs;&longs;ariò impetus, &longs;ine quo non po&longs;&longs;unt explicari prædi<lb/>ctæ omnes hypothe&longs;es, contra quem &longs;unt quidem graui&longs;&longs;imæ difficultates, <lb/>quas &longs;en&longs;im in &longs;equentibus Theorematis, in quibus explicantur pro<lb/>prietates huius impetus, di&longs;cutiemus. </s>

<s>Diceret aliquis lapidem impul&longs;um ab aëre deinde propelli; &longs;ed aër po<lb/>tius re&longs;i&longs;tit motui; vt con&longs;tat experientiâ; &longs;ed hoc &longs;oluemus infrà. </s><pb xlink:href="026/01/049.jpg" pagenum="17"/>

<s id="N11C36"><emph type="italics"/>Cau&longs;a nece&longs;&longs;aria &longs;ubiecto apto applicata, & non impedita &longs;emper agit, & <lb/>quantum pote&longs;t.<emph.end type="italics"/></s>

<s id="N11C3F"> Hoc Axioma duas partes habet; </s>

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

<s id="N11C43">prima certa e&longs;t per hy<lb/>poth. 8. & per definitionem cau&longs;æ nece&longs;&longs;ariæ, quæ in hoc differt à libe<lb/>râ: Secunda pars probatur; </s>

<s id="N11C4B">quia &longs;i partem effectus omitteret, quam ta<lb/>men ponere po&longs;&longs;et; haud dubiè non e&longs;&longs;et cau&longs;a nece&longs;&longs;aria contra hypoth. </s>

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

<s id="N11C51"><lb/>nam &longs;i vnam partem effectus omittat; cur vnam potiùs quam aliam? </s>

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

<s id="N11C5A">cur non omnes? </s>

<s id="N11C5D">denique video cau&longs;am eandem eidem <lb/>&longs;ubiecto codem modo applicatam, eundem &longs;emper effectum producere <lb/>per Hyp. 8. </s>

<s>3. Igitur impetus non e&longs;t idem cum &longs;ub&longs;tantià <lb/>mobilis; igitur di&longs;tinctus; deinde &longs;eparari pote&longs;t à &longs;ub&longs;tantia mobilis <lb/>per Hypoth. </s>

<s>4. igitur e&longs;t di&longs;tinctus per Ax. 2. </s>

<s id="N11C68"><emph type="center"/><emph type="italics"/>Axioma XIII<emph.end type="italics"/><emph.end type="center"/></s>

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

<s id="N11C76"><emph type="italics"/>Exten&longs;io cau&longs;a non intendit effectum ad intra.<emph.end type="italics"/></s>

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

<s id="N11C7D"> Quælibet pars maioris <lb/>ignis non habet calorem inten&longs;iorem, quàm quælibet pars minoris; idem <pb pagenum="11" xlink:href="026/01/043.jpg"/>dico de grauitate plumbi, &c. </s>

<s id="N11C88">nec enim libra plumbi coniuncta cum <lb/>alia habet diuer&longs;am grauitatem ab eâ, quam habet &longs;eparata. </s>

<s>& ex Hypoth. </s>

<s>3. & 4. igitur di&longs;tingui<lb/>tur à motu; igitur & ab impetu per Ax. 2. igitur impetus non e&longs;t &longs;ub<lb/>&longs;tantia; igitur accidens. </s>

<s id="N11C8F">Dixi ad intra; </s>

<s id="N11C92">quia ad extra multum iuuat exten&longs;io; </s>

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

<s id="N11C96">&longs;ic maior ignis <lb/>longiùs diffundit &longs;uum calorem; </s>

<s id="N11C9C">corpus grauiùs cadens majorem ictum <lb/>infligit; Ad hoc Axioma reuocatur i&longs;tud. </s>

<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 quædam diminuta, vt vulgò loquuntur, di&longs;tin<lb/>cta quidem modaliter, vt aiunt, à re, cui adhæret; ac proinde ab ca &longs;e<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, &c. </s>

<s id="N11CA4">1. <emph type="italics"/>Omnes partes eiu&longs;dem cau&longs;æ agunt ad extra actione communi,<emph.end type="italics"/> iuxta <lb/>eum modum quo illam explicabimus in Metaph. nec punctum Solis &longs;e<lb/>paratum ad eandem di&longs;tantiam &longs;uam lucem, caloremque &longs;uum diffunde<lb/>ret; </s>

<s id="N11CB4">ad quam diffundit coniunctum cum aliis; </s>

<s>His po&longs;itis Impetus non e&longs;t mo<lb/>dus primi generis; nihil enim probat impetum e&longs;&longs;e modum, quod etiam <lb/>non probet calorem, & lucem e&longs;&longs;e modos; dicere autem omnia acci<lb/>dentia e&longs;&longs;e modos non debemus, de quo &longs;uo loco; modus enim ita à na<lb/>turâ comparatus e&longs;t, vt &longs;ine &longs;ubiecto actuali &longs;eu fulcro non exi&longs;tere mo<lb/>dò, &longs;ed ne concipi quidem po&longs;&longs;it; v. g. 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<lb/>tia &longs;ine dependente; at verò po&longs;&longs;um concipere calorem, & impetum <lb/>&longs;ine alio, quod &longs;it actu; licèt enim calor exigat re&longs;olutionem partium <lb/>&longs;ui &longs;ubiecti, &longs;eu rarefactionem, & impetus motum; nihil tamen impe<lb/>dit, quin per miraculum calor, & impetus con&longs;eruari po&longs;&longs;int &longs;ine eo. </s>

<s id="N11CB8">idem dico de igne maiori, <lb/>& minori; de quibus omnibus &longs;uo loco. </s>

<s id="N11CBE">Huc etiam reuoca dicta illa <lb/>communia. </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>

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

<s id="N11CC5">2. <emph type="italics"/>Plures partes cau&longs;a plures partes effectus producunt, & vici&longs;&longs;im.<emph.end type="italics"/></s>

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

<s id="N11CCF">3. <emph type="italics"/>Maior, & perfectior cau&longs;a maiorem effectum producit, & perfectiorem, <lb/>& vici&longs;&longs;im.<emph.end type="italics"/></s>

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

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

<s id="N11CDB">4. <emph type="italics"/>Perfectior effectus, vel imperfectior arguit cau&longs;am perfectiorem, vel im<lb/>perfectiorem, &longs;uppo&longs;itâ eâdem applicatione; </s>

<s id="N11CE4">&longs;i enim maior e&longs;t applicatio &longs;ine <lb/>ratione loci, &longs;iue ratione temporis; haud dubiè maior erit effectus, vt con&longs;tat.<emph.end type="italics"/></s>

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

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

<s id="N11CEE"><emph type="center"/><emph type="italics"/>Axioma XIV.<emph.end type="italics"/><emph.end type="center"/></s>

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

<s id="N11CFC"><emph type="italics"/>Quidquid de&longs;truitur non e&longs;t à &longs;e.<emph.end type="italics"/></s>

<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. 6. igitur durat eius cau&longs;a, &longs;cilicet impe<lb/>tus; igitur e&longs;t qualitas permanens. </s>

<s id="N11D03"> Hoc Axioma geometricum e&longs;t; </s>

<s id="N11D07">Quod <lb/>enim e&longs;t à &longs;e, nece&longs;&longs;ariò e&longs;t; </s>

<s id="N11D0D">cùm à libertate &longs;eu voluntate alterius non <lb/>pendeat; </s>

<s id="N11D13">cum enim primo in&longs;tanti quo res e&longs;t, non &longs;it à &longs;e per Axiom. 8. <lb/>de &longs;ecundo idem dici debet, quod de primo, vt patet: </s>

<s>Diceret fortè aliquis lapidem proiectum pelli ab aëre à tergo in&longs;tan<lb/>te, vt voluit Ari&longs;toteles pluribus in locis; &longs;ed præ&longs;ertim 8. Ph.c.vlt.& 7. <lb/>cap.2. 3.de C&oelig;lo, cap.

<s id="N11D1B">quippe id eo <lb/>primo in&longs;tanti non e&longs;t nece&longs;&longs;ariò, quia ita e&longs;t illo in&longs;tanti, vt po&longs;&longs;it non <lb/>e&longs;&longs;e; </s>

<s id="N11D23">&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;ariò, igitur pendet ab alio, quod pote&longs;t facere vt non &longs;it. </s>

3. Re&longs;pondeo hoc dici non po&longs;&longs;e; Primò quia non <lb/>modò non iuuat aër; &longs;ed etiam impedit motum proiecti, quod de omni <lb/>medio nece&longs;&longs;ariò dicendum e&longs;t, vt patet experientiâ; vnde quo cra&longs;&longs;ius, <lb/>&longs;eu den&longs;ius e&longs;t <expan abbr="medi&utilde;">medium</expan>, motum potentiùs retardat, vt videmus in proiectis <lb/>per aquam; rationem à priori afferemus infrà, cum de re&longs;i&longs;tentia medij: </s>

<s><lb/>Secundò, quis dicat pilam rotatam in &longs;olo moueri aëris appul&longs;u? cum <lb/>alia corpora, quæ pila rotata præterlambendo qua&longs;i allambit, nullo mo<lb/>do moueantur; præ&longs;ertim granula pulueris. </s>

<s id="N11D2B">Dices po&longs;&longs;e de&longs;trui &longs;ecundo in&longs;tanti ab aliquo contrario, à quo tamen <lb/>non pendet per po&longs;itiuum influxum. </s>

<s id="N11D30">Re&longs;pondeo, non videri quomo<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 tantùm exigere pote&longs;t contrarij de&longs;tructio<lb/>nem, quid e&longs;t porro de&longs;trui, ni&longs;i de&longs;inere con&longs;eruari? </s>

<s>Tertiò, an fortè aër id præ<lb/>&longs;tare pote&longs;t &longs;ine vi impre&longs;&longs;a; igitur non minus ip&longs;i pilæ proiectæ, quam <lb/>aëri ambienti imprimi poterit: </s>

<s id="N11D3A">quæ omnia fusè <lb/>in Metaphy&longs;ica demon&longs;trabimus; </s>

<s id="N11D40">quidquid enim e&longs;t aliquo in&longs;tanti vel <lb/>e&longs;t à &longs;e, vel non à &longs;e; &longs;i primùm Deus e&longs;t; </s>

<s>Quartò, nullus aër à tergo pellitur; &longs;ed <lb/>potius ip&longs;a pila aduer&longs;us aëra pellit, dum emittitur manu; igitur &longs;i aër <lb/>&longs;uccedit à tergo, id totum accidit, vel metu vacui, vel ne aër compri<lb/>matur, vt videbimus infrà. </s>

<s id="N11D46">&longs;i &longs;ecundum ab alio e&longs;t: <lb/>quidquid &longs;it, hoc Axioma certum e&longs;t phy&longs;icè. </s>

<s>Quintò denique, cum diu moueatur eadem <lb/>pars aëris, haud dubiè in ca manet vis impre&longs;&longs;a; igitur impetus erit ad<lb/>huc qualitas permanens. </s>

<s id="N11D4E">Huc reuoca Axiomata &longs;equentia, quæ ex hoc vno deducuntur. </s>

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

<s>l. 7. Phy&longs;. cap.

<s id="N11D53">1. <emph type="italics"/>Quidquid e&longs;t, & non e&longs;t à &longs;e, e&longs;t, &longs;eu pendet, &longs;eu con&longs;eruatur ab alio.<emph.end type="italics"/><lb/>Hæc enim &longs;unt idem, vt con&longs;tat. </s>

2. Aliqui excu&longs;ant ip&longs;um Ari&longs;torelem, putantque <lb/>non e&longs;&longs;e locutum ex propriâ &longs;ententiâ: Alij dicunt Ari&longs;totelem quidem <lb/>tribui&longs;&longs;e aliquam vim extrin&longs;ecam aëri; 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<lb/>ui&longs;&longs;e vim motricem impre&longs;&longs;am aëri, hoc e&longs;t impetum (<emph type="italics"/>potentia enim<emph.end type="italics"/> (in<lb/>quit) &longs;cilicet motrix, <emph type="italics"/>quâ pollet proijciens qua&longs;i vim impre&longs;&longs;am tradit vtrique<emph.end type="italics"/>) <lb/>id e&longs;t aëri &longs;ur&longs;um, & deor&longs;um; quid porrò e&longs;t illa vis motrix, ni&longs;i impetus. </s>

<s id="N11D5F">2. <emph type="italics"/>Quidquid destruitur, ad exigentiam alicuius de&longs;truitur, &longs;altem totius <lb/>natura, ne aliquid &longs;it fru&longs;trà.<emph.end type="italics"/></s>

<s id="N11D69"> Hoc etiam ex hypothe&longs;ibus &longs;equitur; </s>

<s id="N11D6D">cum <lb/>enim de&longs;trui &longs;it idem ac de&longs;inere con&longs;eruari; </s>

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

<s id="N11D73">certè qui de&longs;init con&longs;er<lb/>uare in&longs;tanti A potiùs quam in&longs;tanti B, hoc facere non pote&longs;t ni&longs;i ali<lb/>quid hoc exigat; &longs;cilicet iuxta leges naturæ. </s>

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

<s id="N11D7D">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, & con<lb/>&longs;eruetur, quæ erat antè. </s>

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

<s><emph type="italics"/>Impetus exigit motum, id est fluxum mobilis in loco<emph.end type="italics"/>; quia cau&longs;a imme<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. & 6. igitur e&longs;t cau&longs;a exigens, adde quod id tantùm <lb/>accidens &longs;en&longs;ibile præ&longs;tare pote&longs;t in &longs;uo &longs;ubiecto, vt aliquam illius mu<lb/>tationem præ&longs;tet, vel exigat; quæ 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 vulgò vocatur; quà &longs;cilicet vel re<lb/>&longs;oluuntur partes, vel rarefiunt, vel lique&longs;cunt, vel concre&longs;cunt &c. </s>

<s id="N11D8F"><emph type="center"/><emph type="italics"/>Axioma XV.<emph.end type="italics"/><emph.end type="center"/></s>

<s>vel <lb/>demùm mutant &longs;en&longs;ibilem &longs;tatum; vel e&longs;t perfectiua aliquo modo, qua<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 id="N11D9D"><emph type="italics"/>Contraria pugnant pro rata.<emph.end type="italics"/></s>

<s id="N11DA4"> Nec enim alia regula e&longs;&longs;e pote&longs;t; </s>

<s>de quibus aliàs. </s>

<s id="N11DA8">&longs;ic minor <lb/>calor minùs de&longs;truit frigoris; minor impetus minùs de&longs;truit impetus <lb/>contrarij (&longs;i contrarium habet) quæ omnia con&longs;tant ex hypothe&longs;ibus. </s>

<s id="N11DB0"><lb/>Ratio e&longs;t, quia plùs vel minùs contrarij de&longs;truere, multam habet ex<lb/>ten&longs;ionem. </s>

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

<s id="N11DB6">v.g. &longs;int duo contraria A & B, &longs;it A vt 20. &longs;it B vt 5. certè &longs;i <lb/>B de&longs;truat A &longs;upra ratam, vel &longs;upra id, quod &longs;ibi ex æquo re&longs;pondet, id <lb/>e&longs;t &longs;upra 5. cur potius 6. quam 7. 8. &c. </s>

<s id="N11DBF">Si infra, cur potius 4. quam 3. <lb/>2. &c. </s>

<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<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<lb/>lem; nec dirigendo, quod &longs;pectat ad idæalem, vel exemplarem; &longs;ed <lb/>exigendo; quatenus &longs;cilicet ad id à natura e&longs;t in&longs;tituta, vt ex eius in <lb/>&longs;ubiecto præ&longs;entia talis affectio, vel mutatio con&longs;equatur; vocatur au<lb/>tem effectus formalis &longs;ecundarius; non verò primarius, qui e&longs;t tantùm <lb/>concretum ex ip&longs;a formâ, & &longs;ubiecto. </s>

<s id="N11DC4">Igitur cum plures &longs;int termini tùm infra, tùm &longs;upra 5. cur potius <lb/>vnus quàm alius? </s>

<s id="N11DC9">atqui vnus tantùm ex æquo 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><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 16.<emph.end type="center"/></s>

<s id="N11DD0">Nec dicas A totum de&longs;trui à B, quòd e&longs;t contra hypothe&longs;im, nam <lb/>modicum caloris non de&longs;truit totum frigus: </s>

<s id="N11DD6">in impetu res e&longs;t clari&longs;&longs;ima; <lb/>adde quod minor cau&longs;a minùs agit per Ax. 13. num. </s>

<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 quæ&longs;o aliquid phy&longs;icum; e&longs;t enim id, propter quod talis, vel ta<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; immò idem e&longs;t finis cum ip&longs;o v&longs;u; <lb/>cum igitur impetus illum tantùm v&longs;um habeat, quem in ip&longs;o mobili <lb/>præ&longs;tare cernimus, &longs;cilicet motum; dicendum e&longs;t motum e&longs;&longs;e finem in<lb/>trin&longs;ecum impetus; adde quod cum fru&longs;trà &longs;it impetus ille, qui non præ<lb/>&longs;tat motum mediatè &longs;altem in &longs;uo &longs;ubiecto; quid enim aliud in &longs;uo &longs;ub<lb/>iecto præ&longs;taret, quem effectum, quam mutationem? </s>

<s id="N11DDC">3. igitur minùs exi<lb/>git; porrò cum dico vnum ab alio de&longs;trui, intelligo tantùm ex applica<lb/>tione vnius &longs;equi de&longs;tructionem alterius &longs;altem ex parte. </s>

<s>certè &longs;i fru&longs;trà 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 natiuâ vel innatâ velut <lb/>appetentiâ concupi&longs;cit, vel exigit. </s>

<s id="N11DE5">Ob&longs;eruabis hæc Axiomata &longs;altem maiori ex parte e&longs;&longs;e metaph. </s>

<s>Dixi mediatè, vel immediatè; num <lb/>reuera datur fortè aliquis impetus, vt dicemus infrà; &longs;cilicet primus na<lb/>turalis, qui &longs;cilicet duos fines habet di&longs;iunctiuè; quorum alter e&longs;t gra<lb/>uitatio, alter motus deor&longs;um. </s>

<s id="N11DE8">quæ <lb/>nos fusè in Theorematis metaph. </s>

<s id="N11DED">explicabimus, & demon&longs;trabimus; </s>

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

<s id="N11DF1">&longs;ed <lb/>nobis hoc loco &longs;atis e&longs;t, &longs;i parem cum phy&longs;icis &longs;upponas habere cer<lb/>titudinem, quod nemo negabit; con&longs;tátque ex hypothe&longs;ibus, licèt ma<lb/>iorem etiam habeant, de qua &longs;uo loco. </s>

<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<lb/>&longs;ecus impetus per Th. 16. igitur &longs;i nullus motus e&longs;&longs;e po&longs;&longs;et, &longs;uo fine ca<lb/>reret impetus; igitur non e&longs;&longs;et, vt patet, igitur non e&longs;&longs;et; quia quod <lb/>fru&longs;trà e&longs;t, non e&longs;t per Ax. 6. nec ob&longs;tat quod &longs;uprà 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;<lb/>&longs;et motus deor&longs;um nulla e&longs;&longs;et grauitatio; quippe grauitare e&longs;t dcor<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;æpiùs e&longs;&longs;e &longs;ine motu; cum &longs;cilicet <lb/>impeditur à corpore &longs;u&longs;tinente? </s>

<s id="N11DFD">Ob&longs;eruabis prætereà nos diutiùs hæ&longs;i&longs;&longs;e in præmittendis huic libro <lb/>Axiomatis, quod tamen in aliis libris non faciemus. </s>

<s>immò dicemus infrà primo in&longs;tanti, <lb/>quo e&longs;t impetus, nondum e&longs;&longs;e motum. </s>

<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;æ formalis, huiu&longs;que po&longs;&longs;i<lb/>bilitatem ex illius po&longs;&longs;ibilitate. </s>

<s id="N11E04"><emph type="center"/><emph type="italics"/>Postulatum,<emph.end type="italics"/><emph.end type="center"/></s>

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

<s id="N11E12"><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, &c.<emph.end type="italics"/></s>

<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, & leuibus, &longs;iue &longs;it vitalis <lb/>in viuentibus; &longs;iue &longs;it media in compre&longs;&longs;is, & dilatatis; &longs;iue alia quæli<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<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;æ 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 exigentiæ; ita pote&longs;t id <expan abbr="cõferre">conferre</expan> &longs;ine exigentiâ, quòd cum exi<lb/>gentia conferre pote&longs;t; &longs;ic pote&longs;t corpus re&longs;oluere &longs;ine calore, mouere <lb/>fine impetu &c. </s>

<s>quanquam vt verum fatear non e&longs;&longs;et propriè motus, &longs;ed <lb/>qua&longs;i continuæ reproductionis modus; nam motus dicit aliquam pa&longs;<lb/>&longs;ionem; &longs;cilicet actum entis in potentiâ, vt aiunt. </s>

<s id="N11E1D"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 1.<emph.end type="center"/></s>

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

<s id="N11E2C"><emph type="italics"/>Motus e&longs;t aliquid realiter di&longs;tinctum à mobili.<emph.end type="italics"/></s>

<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<lb/>ris entitas; quanquam non e&longs;&longs;et motus, vt iam dictum e&longs;t, quia non e&longs;<lb/>&longs;et pa&longs;&longs;io. </s>

<s id="N11E33"> Demon&longs;tratur; Motus <lb/>e&longs;t in mobili, in quo antè non erat per hypoth. </s>

<s id="N11E38">3. & de&longs;init e&longs;&longs;e in mobili, <lb/>in quo antè erat per hypoth.4. igitur mobile e&longs;t, & non e&longs;t motus; </s>

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

<s id="N11E3E">igi<lb/>tur à motu &longs;eparatum; </s>

<s id="N11E44">igitur realiter di&longs;tinctum per Ax. 2. præterea <lb/>moueri, & non moueri &longs;unt prædicata contradictoria, vt con&longs;tat; </s>

<s><emph type="italics"/>Corpus illud æquali &longs;emper motu ferretur per &longs;e<emph.end type="italics"/>; Quia e&longs;&longs;et &longs;emper ea<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 æqualis motus: dixi per &longs;e pro<lb/>pter diuer&longs;um medium. </s>

<s id="N11E4A">igi<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; </s>

<s id="N11E52">alioquin &longs;imul e&longs;&longs;ent; </s>

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

<s id="N11E56">igitur alterum illorum e&longs;t di&longs;tinctum à <lb/>mobili; </s>

<s id="N11E5C">non quies, vt con&longs;tat, quæ e&longs;t tantùm negatio motus, &longs;eu per<lb/>&longs;euerantia in eodem loco; </s>

<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; immò 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>

<s id="N11E62">igitur nullam dicit mutationem; at verò <lb/>motus mutationem dicit, per Def. 1. hoc Theorema fusè demon&longs;trabo <lb/>in Metaph. </s>

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

<s id="N11E6F"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 2.<emph.end type="center"/></s>

<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<lb/>batur; quia, ni&longs;i e&longs;&longs;et motus, non e&longs;&longs;et impetus per Th. 17. igitur &longs;ubie<lb/>ctum incapax motus e&longs;t incapax impetus. </s>

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

<s id="N11E7E"><emph type="italics"/>Motus non pote&longs;t dici propriè productus immediatè, vel effectus immedia<lb/>tus cau&longs;æ efficientis.<emph.end type="italics"/></s>

<s id="N11E87"> Demon&longs;t. </s>

<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<lb/>lis, quod certum e&longs;t. </s>

<s id="N11E8A">Motus e&longs;t mutatio, &longs;eu tran&longs;itus ex loco <lb/>in locum per Def. 1. &longs;ed mutatio propriè non producitur; </s>

<s id="N11E92">quippè pro<lb/>ductio tantùm terminatur ad ens; </s>

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

<s id="N11E98">nihil enim ni&longs;i ens produci pote&longs;t; </s>

<s id="N11E9C"><pb pagenum="13" xlink:href="026/01/045.jpg"/>atqui nulla mutatio dicit tantùm ens; </s>

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

<s id="N11EA4">præ&longs;ertim hæc, quæ tantùm dicit <lb/>terminum à quo, ide&longs;t locum relictum; </s>

<s id="N11EAA">& terminum ad quem, id e&longs;t lo<lb/>cum immediatum acqui&longs;itum; </s>

<s>Probatur 2.pars; quia in <lb/>eo impetus non e&longs;&longs;et fru&longs;trà per Ax. 6. igitur haberet &longs;uum effectum; <lb/>igitur motum. </s>

<s id="N11EB0">nam &longs;eparato quocunque alio ab ip&longs;o <lb/>mobili; </s>

<s id="N11EB6">modo &longs;imul, id e&longs;t eodem in&longs;tanti relinquat primum locum, & <lb/>nouum acquirat, omninò mouetur, &longs;ed concretum illud ex loco relicto, <lb/>& acqui&longs;ito produci non pote&longs;t; </s>

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

<s id="N11EBE">illud autem e&longs;t motus, qui certè non <lb/>dicit tantùm locum relictum &longs;ine acqui&longs;ito; </s>

<s id="N11EC4">alioqui &longs;i mobile de&longs;true<lb/>retur, diceretur moueri; </s>

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

<s id="N11ECA">nec etiam locum acqui&longs;itum &longs;ine priori relicto: </s>

<s id="N11ECE"><lb/>alioqui &longs;i mobile primò produceretur, diceretur moueri localiter; </s>

<s>Dices fortè quia affixum e&longs;&longs;et e&longs;&longs;entialiter tali, vel tali lo<lb/>co, &longs;ed contra; quia de&longs;truantur omnia, præter ip&longs;um corpus; certè <lb/>nulli affixum manet. </s>

<s id="N11ED3">igitur <lb/>motus neutrum dicit &longs;eor&longs;im; &longs;i primum, diceretur de&longs;tructus; </s>

<s id="N11ED9">&longs;i &longs;ecun<lb/>dum, diceretur aliquo modo productus, vel potiùs acqui&longs;itus; </s>

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

<s id="N11EDF">at vtrum<lb/>que coniunctim, &longs;imulque e&longs;&longs;entialiter dicit motus; </s>

<s id="N11EE5">nec enim conci<lb/>pio aliud, dum concipio motum: </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<lb/>re; dicendum e&longs;t de omni re creata finita permanente. </s>

<s id="N11EEB">porrò vtrumque &longs;imul &longs;umptum indi<lb/>ui&longs;ibiliter non pote&longs;t dici, vel de&longs;tructum propriè, vel productum; Di<gap/><lb/>xi propriè; nam impropriè dici pote&longs;t motus productus. </s>

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

<s id="N11EF6">Dices Motus e&longs;t ens, non à &longs;e; igitur ab alio; igitur motus e&longs;t pro<lb/>ductus. </s>

<s><emph type="italics"/>Quod durat tantùm vno in&longs;tanti, e&longs;t incapax motus, & impetus.<emph.end type="italics"/></s><s> Pro<lb/>batur, quia non e&longs;t moueri, ni&longs;i relinquat locum, & acquirat alium; &longs;ed <lb/>1. acquirere locum, e&longs;t 1. e&longs;&longs;e in illo loco; & 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; & phy<lb/>&longs;icè certum e&longs;t ex omni hypothe&longs;i; igitur moueri nunc, id e&longs;t, hoc in<lb/>&longs;tanti, id e&longs;t, 1. acquirere nouum locum, & 1. relinquere priorem, <lb/>&longs;upponit nece&longs;&longs;ariò antè fui&longs;&longs;e in loco nunc relicto; &longs;ed quod durat <lb/>tantùm in in&longs;tanti, non habet antè, neque po&longs;t; igitur quod durat tan<lb/>tùm vno in&longs;tanti, moueri non pote&longs;t; igitur e&longs;t incapax motus; igitur <lb/>& impetus. </s>

<s id="N11EFC">Re&longs;pondeo Motum non e&longs;&longs;e ens ab&longs;olutum, &longs;ed e&longs;&longs;e mutatio<lb/>nem entis, quæ mutatio e&longs;t concretum quoddam ex ente & non ente; </s>

<s id="N11F02"><lb/>quòd certè non pote&longs;t dici propriè productum, &longs;ed re&longs;ultans, vt relatio; </s>

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

<s id="N11F07"><lb/>nam producatur, &longs;i fieri pote&longs;t; </s>

<s id="N11F0C">certè e&longs;t aliquid, quod tam facilè de<lb/>&longs;trui pote&longs;t, quam produci; </s>

<s><emph type="italics"/>Deus e&longs;t incapax motus, & 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<lb/>nem 1. tùm quia æternitas Dei tota &longs;imul e&longs;t; igitur nec fuit antè, ne<lb/>que po&longs;t in ca; igitur non pote&longs;t dici antè habui&longs;&longs;e locum, quo nunc <lb/>caret: & nunc non habere illum quo caret; tùm quia immutabilitas <pb xlink:href="026/01/054.jpg" pagenum="22"/>Dei hoc prohibet; nam moueri, e&longs;t affici intrin&longs;ecè; quia etiam de<lb/>&longs;tructis omnibus extrin&longs;ecis creatis moueri po&longs;&longs;em, & fru&longs;trà recurres <lb/>ad partes virtuales immen&longs;itatis Dei, quas ferè animus abhorret; apa<lb/>ge partes in Deo: quis hoc ferre po&longs;&longs;it? </s>

<s id="N11F12">igitur de&longs;truatur, & remaneat tantùm en<lb/>titas mobilis, quæ, quo in&longs;tanti priorem locum relinquit, nouum acqui<lb/>rat; certè dicitur adhuc moueri, & tamen non erit motus ex &longs;uppo&longs;itio<lb/>ne, quod ab&longs;urdum e&longs;t. </s>

<s>præterea &longs;i &longs;unt, &longs;unt e&longs;&longs;entia<lb/>liter immobiles; igitur valet &longs;emper ratio allata; igitur Deus e&longs;t inca<lb/>pax motus; igitur & impetus. </s>

<s id="N11F1E">Dices potentia motrix e&longs;t actiua; </s>

<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 id="N11F22">igitur agit; igitur producit, &longs;ed ni<lb/>hil ni&longs;i motum. </s>

<s id="N11F28">Re&longs;p. potentiam motricem e&longs;&longs;e actiuam vt dicemus, <lb/>& ab eâ produci impetum, qui deinde exigit motum, vt dicemus <lb/>infrà. </s>

<s>Re&longs;pondeo adhuc va<lb/>lere, quia etiam in orbem conuolui non pote&longs;t, ni&longs;i mutetur intrin&longs;e<lb/>cè; atqui &longs;i e&longs;t immen&longs;us, non pote&longs;t mutari intrin&longs;ecè per motum; <lb/>quia nullum locum de nouo acquireret; &longs;ed de hoc motu aliàs, 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, & aliæ duæ pro omni motu. </s>

<s id="N11F31">Nec e&longs;t quod aliqui ita mirentur hæc à me dici; </s>

<s id="N11F35">cum certum &longs;it effe<lb/>ctus formales &longs;ecundarios principum ferè qualitatum tales e&longs;&longs;e, vt mini<lb/>mè producantur; </s>

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

<s id="N11F3D">&longs;ed qua&longs;i re&longs;ultent ab exigentia; v. g. effectus calo<lb/>ris in &longs;uo &longs;ubiecto e&longs;t eiu&longs;dem &longs;ubiecti rarefactio, quæ reuerâ non <lb/>producitur, vt con&longs;tat. </s>

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

<s id="N11F4B"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 3.<emph.end type="center"/></s>

<s>Præterea quod e&longs;t in loco dicit tan<lb/>tùm ens phy&longs;icum; &longs;ed mutatio dicit etiam non ens; <emph type="italics"/>Hinc egregium pa<lb/>radoxum; illud non mouetur per quod cuncta mouentur, quæ mouentur.<emph.end type="italics"/></s>

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

<s id="N11F5A"><emph type="italics"/>Motus e&longs;t ab alio di&longs;tincto in aliquo genere cau&longs;æ.<emph.end type="italics"/></s>

<s id="N11F61"> 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. </s>

<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 quælibet illius pars, &longs;eu quod durat vna in&longs;tanti tantùm e&longs;t inca<lb/>pax motus, per Th. 26. </s>

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

<s id="N11F6C"><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/></s>

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

<s id="N11F7A">Ob&longs;eruabis motum localem e&longs;&longs;e duplicis generis; </s>

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 1.<emph.end type="center"/></s>

<s id="N11F7E">primum genus mo<lb/>tus e&longs;t actio potentiæ motricis, quæ reuerà mouet, & cuius exercitium <lb/>dicitur motus, &longs;eu latio, &longs;eu motio, &longs;eu actio, qua reuerâ agit, produ<lb/>citque impetum, non motum; </s>

<s id="N11F88">cum etiam &longs;ine motu defatigetur, vt cum <lb/>quis alium pellit, à quo pellitur æquali ni&longs;u; </s>

<s>Hinc in tanta rerum creatarum multitudine &longs;unt tantùm duæ, quæ <lb/>&longs;unt e&longs;&longs;entialiter immobiles; &longs;cilicet motus, & actio; quorum ille cum <lb/>&longs;it mutatio non e&longs;t adæquatè aliquid po&longs;itiuum; &longs;ecus actio. </s>

<s id="N11F8E">patet etiam in manu &longs;u<lb/>&longs;tinente aliquod pondus, quæ non mouetur; </s>

<s id="N11F94">licet reuerâ etiam &longs;ummo <pb pagenum="14" xlink:href="026/01/046.jpg"/>conatu agat: </s>

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 2.<emph.end type="center"/></s>

<s id="N11F9D">immò &longs;i potentia motrix produceret motum primum, non <lb/>impetum in corpore proiecto; </s>

<s id="N11FA3">nulla deinde e&longs;&longs;et cau&longs;a applicata ad pro<lb/>ducendum impetum: </s>

<s>Hinc &longs;unt tantùm duo adæquatè po&longs;itiua, quæ moueri non po&longs;&longs;unt; <lb/>&longs;cilicet Deus, & actio; Deus, qui &longs;emper e&longs;t; actio, quæ tantùm 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 id="N11FA9">Itaque hic motus primi generis, &longs;i comparetur <lb/>cum potentia motrice, e&longs;t verè influxus, vel actio; </s>

<s id="N11FAF">&longs;i cum termino, e&longs;t <lb/>eius fieri, &longs;eu dependentia; </s>

<s id="N11FB5">&longs;i cum &longs;ubiecto, &longs;eu mobili e&longs;t pa&longs;&longs;io; </s>

<s id="N11FB9">nec <lb/>propriè dicitur produci, ni&longs;i vt quo (vt vulgò 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<lb/>dit ad terminum. </s>

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 3.<emph.end type="center"/></s>

<s id="N11FC3">Motus &longs;ecundi generis e&longs;t mutatio, &longs;eu tran&longs;itus ex <lb/>vno loco in alium; </s>

<s id="N11FC9">hoc e&longs;t finis, vel effectus formalis &longs;ecundarius, <lb/>quem exigit impetus; </s>

<s>Hinc &longs;i res aliqua creata per actionem tantæ perfectionis, quæ mille <lb/>annis e&longs;&longs;entialiter re&longs;ponderet, con&longs;eruaretur; certè 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 hæc e&longs;t &longs;emper eadem, illam eandem e&longs;&longs;e nece&longs;&longs;e <lb/>e&longs;t; &longs;ed hæc &longs;unt metaphy&longs;ica, quæ obiter tantùm attingo, aliàs fusè <lb/>de mon&longs;trabo. </s>

<s id="N11FCF">& fru&longs;trà ponitur alia entitas, quæ tantùm 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 infrà, certè fru&longs;tra ponitur quodcun<lb/>que aliud per Ax.3. & 7. </s>

<s><emph type="center"/><emph type="italics"/>Scolium.<emph.end type="italics"/><emph.end type="center"/></s>

<s id="N11FDB"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 4.<emph.end type="center"/></s>

<s>Ob&longs;eruabis primò ex dictis præclarum naturæ in&longs;titutum; cum enim <lb/>corpus moueri &longs;emper non debeat, (quippe hoc e&longs;&longs;et maximè incom<lb/>modum) certè 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<lb/>nari, & 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>

<s>Ob&longs;eruabis &longs;ecundò, cum idem corpus aliquando velociùs, tardiùs <lb/>aliquando moueri exigat; &longs;i per &longs;uam entitatem moueri exigeret, eo<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 verò minor e&longs;t; igitur maiorem &longs;eu velcio<lb/>rem 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 præ<lb/>&longs;tat re&longs;olutionem; ita & maior, &longs;eu perfectior impetus maiorem, &longs;eu <lb/>velociorem motum exigit. </s>

<s id="N11FEA"><emph type="italics"/>Cau&longs;a illa immediata motus, quæ non est efficiens, potest tantùm e&longs;&longs;e exi<lb/>gens, quæ reducitur ad formalem, quæ &longs;uum effectum formalem &longs;ecundarium, <lb/>id est &longs;uum finem intrin&longs;ecum exigit.<emph.end type="italics"/></s>

<s id="N11FF5"> Sic calor exigit rarefactionem, vel <lb/>re&longs;olutionem, impetus motum; </s>

<s>Ob&longs;eruabis tertiò aliud naturæ in&longs;titutum, quo &longs;cilicet in eo tan<lb/>tùm &longs;ubiecto recipi pote&longs;t cau&longs;a formalis, in quo recipi pote&longs;t eius effe<lb/>ctus formalis &longs;ecundarius: nec alia regula, præter eam excogitari pote&longs;t; <lb/>cum enim aliqua forma ad talem, vel talem finem à natura in&longs;tituta e&longs;t; <lb/>certè 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;trà e&longs;&longs;et; & contra in eo e&longs;&longs;e pote&longs;t, <lb/>in quo fru&longs;trà non e&longs;t; cum &longs;cilicet in eo &longs;uum finem con&longs;equatur; ad<lb/>de quod finis ille intrin&longs;ecus phy&longs;icus &longs;cilicet, non moralis, aliquis no<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 e&longs;&longs;ectu; 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>

<s id="N11FFB">cum enim non &longs;it cau&longs;a efficiens per Th. <lb/>2. &longs;it tamen cau&longs;a per Th.3. nec &longs;it materialis, nec finalis, vt con&longs;tat, de<lb/>bet e&longs;&longs;e formalis, vel exigens, &longs;eu exigitiua; </s>

<s id="N12004">vt patet ex ip&longs;a cau&longs;arum <lb/>enumeratione; </s>

<s>Ob&longs;eruabis quartò 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 certè nouum locum acquirere non pote&longs;t <lb/>naturaliter; ni&longs;i per motum, atqui motus dicit nece&longs;&longs;ario priorem lo<lb/>tum relictum, & nouum acqui&longs;itum; igitur cum tot acquirantur loca <lb/>per motum, quot relinquuntur; &longs;i ante motum vnus tantùm erat eiu&longs;<lb/>dem rci locus, po&longs;t motum etiam vnus e&longs;t: quod autem producatur tan-<pb xlink:href="026/01/056.jpg" pagenum="24"/>tùm res in vno loco patet; vel enim à cau&longs;a prima vel ab aliqua 2. pro<lb/>ducitur; &longs;i à 2. ergo ab aliqua aplicata; igitur ex &longs;uppo&longs;itione quòd il<lb/>la cau&longs;a 2. in vno tantùm loco producta &longs;it, vni tantum applicari po<lb/>te&longs;t; quod autem cau&longs;a 1. in pluribus locis naturaliter eundem effectum <lb/>non producat, certum e&longs;t, & demon&longs;trabimus in Metaphy&longs;. quia &longs;in<lb/>gulis effectibus &longs;ingulæ &longs;ufficiunt actiones; &longs;ingulis terminis &longs;ingulæ <lb/>viæ; immò hoc requiri videtur, &longs;eu &longs;pectare ad huius vniuer&longs;itatis or<lb/>dinem; quippe &longs;i res eadem in pluribus locis e&longs;&longs;et; cur potius in duo<lb/>bus quam in tribus? </s>

<s id="N1200A">non e&longs;t materialis, quia non recipit motum, ni&longs;i ab alio; </s>

<s id="N1200E"><lb/>nec finalis, quæ &longs;upponit alias; cum ip&longs;a non &longs;it dum ponitur <lb/>effectus. </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; quæ e&longs;t actio, per quam dependet; &longs;ed de his <lb/>aliàs. </s>

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

<s id="N12017"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 5.<emph.end type="center"/></s>

<s><emph type="italics"/>Impetus non producitur in eo mobili, quod moueri non pote&longs;t à potentia <lb/>motrice applicata, licèt à fortiori moueri po&longs;&longs;it.<emph.end type="italics"/></s><s> Probatur, quia impetus <lb/>e&longs;t tantùm propter motum, qui eius effectus e&longs;t, & finis, per Th. 15. <lb/>& 16. Igitur vbi non e&longs;t motus, fru&longs;trà e&longs;t impetus; &longs;ed quod fru&longs;trà <lb/>e&longs;t, non e&longs;t; id e&longs;t non e&longs;t, quod fru&longs;trà e&longs;&longs;et, &longs;i e&longs;&longs;et per Ax. 6. Exci<lb/>pio tamen impetum naturalem innatum, qui nunquam e&longs;t fru&longs;trà, vt <lb/>dictum e&longs;t &longs;uprà in Theorem. </s>

<s id="N12026"><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. haud dubiè &longs;ub&longs;tantia lapidis non e&longs;t cau&longs;a <lb/>huius motus; </s>

<s>17. adde quod non pote&longs;t cogno&longs;oi <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 infrà; <lb/>nunc&longs;atis e&longs;t Ax. 3. id manife&longs;tè probari; nam qui diceret in rupe im<lb/>mobili impetum imprimi; certè po&longs;itiuo argumento probare tenere<lb/>tur, quod tantùm duci pote&longs;t, vel ab experimento; atqui hîc nullum e&longs;t; <lb/>vel à nece&longs;&longs;itate, quæ nulla e&longs;t; vel ex alio quocumque capite, quod <lb/>nullum excogitari pote&longs;t; &longs;ed maiorem lucem huic Th. 3. ex proximè <lb/>&longs;equentibus accer&longs;emus; nec e&longs;t quòd aliqui dicant produci impetum <lb/>inefficacem; qui cum fru&longs;trà &longs;it, &longs;i e&longs;t, ex nullo capite probari pote&longs;t: ad<lb/>de quòd de&longs;truitur impetus, ne &longs;it fru&longs;trà; Igitur non producitur, ne &longs;it <lb/>fru&longs;trà; nam con&longs;eruatio e&longs;t vera actio, vt dicemus &longs;uo loco; Igitur &longs;i <lb/>hæc non ponitur, ne aliquid &longs;it fru&longs;trà; etiam 1. productio poni non <lb/>debet; vnde commentum illud impetus inefficacis pror&longs;us inefficax e&longs;t. </s>

<s id="N12035">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; </s>

<s id="N1203B">igitur &longs;emper cau&longs;aret per Ax.12. præ<lb/>terea potentia motrix proiicientis verè agit, cum etiam defatigetur; </s>

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

<s id="N12041">igi<lb/>tur aliquid producit, non motum immediatè, qui produci non pote&longs;t pro<lb/>prièper Th. 2. Adde quod motus &longs;ecundi generis habet tantùm cau&longs;am <lb/>immediatam exigentem, &longs;ed potentia motrix non exigit; </s>

<s id="N1204B">quia primò <lb/>non defatigaretur exigendo; </s>

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

<s id="N12051">&longs;ecundò quia lapis &longs;eparatus à manu etiam <lb/>mouetur, &longs;ed non ad exigentiam potentiæ motricis, vt patet; </s>

<s id="N12057">quia &longs;tatim <lb/>po&longs;t &longs;eparationem pote&longs;t illa potentia de&longs;trui, licèt lapis longo pò&longs;t <lb/>tempore moueatur; &longs;ed quod non e&longs;t, nihil exigit. </s>

<s>Ax. 13. <emph type="italics"/>num.<emph.end type="italics"/> 2. igitur pauciores partes impetus <lb/>æquales vni certæper idem <emph type="italics"/>num.<emph.end type="italics"/> 1. igitur &longs;i &longs;int plures partes &longs;ubiecti <lb/>mobilis, &longs;eu rupis, quàm impetus; cum vna pars impetus duobus parti<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;ariæ; vt &longs;altem &longs;ingulæ &longs;ingulis &longs;ubie<lb/>cti, &longs;eu rupis partibus di&longs;tribuerentur. </s><pb xlink:href="026/01/057.jpg" pagenum="25"/>

<s>Ob&longs;eruabis autem nouum quoddam genús re&longs;i&longs;tentiæ; nam &longs;ingulæ <lb/>partes rupis ab applicata potentiâ aptæ &longs;unt loco moueri per impre&longs;<lb/>&longs;um impetum, & maior potentia &longs;imul omnes loco moueret; at verò <lb/>omnes &longs;imul, & coniunctim con&longs;ideratæ; quatenus &longs;cilicet vna pars <lb/>non pote&longs;t moueri &longs;ine alia, & comparatæ cum illa potentia debili di<lb/>cuntur habere prædictam re&longs;i&longs;tentiam, quæ &longs;uperat potentiæ vires; <lb/>quòd &longs;cilicet à maiori moueri tantùm po&longs;&longs;int; quia plures partes im<lb/>petus po&longs;tulantur, quam &longs;int eæ, quæ à prædictâ potentiâ po&longs;&longs;unt pro<lb/>duci. </s>

<s id="N12061">Aliquis fortè diceret potentiam motricem exigere primam partem <lb/>motus, quæ deinde &longs;ecundam exigit, & &longs;ecunda tertiam, tertia quar<lb/>tam, &c. </s>

<s id="N12068">Sed contra; </s>

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

<s id="N1206B">quæro quid &longs;it prima illa pars motus; </s>

<s id="N1206F">nec enim <lb/>aliud agno&longs;co ni&longs;i primam mutationem loci, quæ mutatio non pote&longs;t <lb/>exigere ni&longs;i quando e&longs;t; </s>

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

<s id="N12077">atqui quando e&longs;t, nihil reale e&longs;t actu ni&longs;i mo<lb/>bile, & nouus locus acqui&longs;itus, mobile ip&longs;um non exigit, vt demon&longs;tra<lb/>tum e&longs;t, & 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>

<s>Probatur igitur <lb/>1. quia &longs;i non producatur in omnibus partibus, & nulla &longs;eparetur ab <lb/>alijs; certè 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; alicquin <lb/>e&longs;&longs;et fru&longs;trà, contra Ax. 6.2. Tu dicis produci impetum in aliquot parti<lb/>hus; hoc dicis, hoc proba? </s>

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

<s id="N12087">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 id="N1208E">Re&longs;p. negando, tùm quia omnis potentia motrix <lb/>agit; </s>

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

<s id="N12094">igitur producit aliquid aliud, quod e&longs;t cau&longs;a motus: præterea po<lb/>tentia motrix corporis animati, agit v&longs;que ad defatigationem, &longs;udorem, <lb/>licèt non &longs;it motus, igitur aliud producit, de corpore graui probabi<lb/>mus infrà. </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 verò de<lb/>ftrui dicatur. </s>

<s id="N120A0"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 6.<emph.end type="center"/></s>

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

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

<s id="N120AF"><emph type="italics"/>Datur impetus.<emph.end type="italics"/></s>

<s id="N120B6"> Demon&longs;tro, Sub&longs;tantia mobilis non e&longs;t cau&longs;a imme<lb/>diata motus, per Th.5. ergo aliquid aliud; igitur impetus, nam quod di<lb/>&longs;tinctum e&longs;t à &longs;ub&longs;tantia mobilis, & 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 paulò diutius hærendum e&longs;t, igitur. </s>

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

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

<s id="N120C4">Demon&longs;tro primò dari impetum: </s>

<s id="N120C8">Quidquid e&longs;t, & antè non erat, non <lb/>e&longs;t à &longs;e, &longs;ed habet cau&longs;am per Ax.8. Motus de nouo e&longs;t per hypothe&longs;im <lb/>tertiam; </s>

<s>Primo igitur non produ<lb/>citur. </s>

<s id="N120D0">igitur habet cau&longs;am, &longs;ed non aliam, quam impetum, quod pro<lb/>bo: </s>

<s id="N120D6">Lapis cadens, vel impactus in alium lapidem mouet illum per hy<lb/>poth.7. &longs;ed &longs;ub&longs;tantia lapidis in alium impacti non e&longs;t cau&longs;a huius mo<lb/>tus, quia e&longs;&longs;et cau&longs;a nece&longs;&longs;aria vt patet; </s>

<s>Primo 4. probatur; quia cum non &longs;ufficiant partes impetus, quas <lb/>dixi produci, vt omnibus partibus &longs;ubiecti di&longs;tribuantur; certè non e&longs;t <lb/>vlla ratio, cur potiùs his quàm illis di&longs;tribui dicantur; cum vna &longs;it tan<lb/>tùm immediatè applicata. </s>

<s id="N120DE">igitur applicata eundem effe<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>

<s>Igitur certum e&longs;tvel produci in omnibus, vel <lb/>in nulla, ni&longs;i forte aliquæ auolent, &longs;ed tunc &longs;eparantur. </s>

<s id="N120E8">Scio e&longs;&longs;e aliquas re&longs;pon&longs;iones, quas infrà refellemus; nunc &longs;ufficiat <lb/>dixi&longs;&longs;e lapidem impactum non producere motum, qui propriè non pro<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>

<s>Obiiciet aliquis 1. e&longs;&longs;e cau&longs;am nece&longs;&longs;ariam applicatam &longs;ubiecto ap<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 potentiæ vt dictum e&longs;t; immò in ip&longs;o motu re<lb/>torqueo argumentum; licèt enim &longs;it applicata cau&longs;a nec&longs;&longs;aria mouens, <lb/>non tamen mouet. </s>

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

<s id="N120F4">Secundò probatur; potentia motrix e&longs;t actiua, quia defatigatur, quis <lb/>hoc neget? </s>

<s id="N120F9">igitur aliquid producit; </s>

<s>Re&longs;pondeo non e&longs;&longs;e pa<lb/>ritatem; quia vna pars pote&longs;t calefieri, & 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<lb/>tur nec recipere impetum &longs;ine alia. </s>

<s id="N120FD">non motum, qui propriè non pro<lb/>ducitur per Th.2. igitur aliquid aliud; voco impetum; </s>

<s id="N12103">adde quod etiam <lb/>&longs;ine motu agit, & defatigatur vt iam dictum e&longs;t; </s>

<s>Obiiciet. </s>

<s id="N12109">igitur habet alium effe<lb/>ctum immediatum; denique mouere, pellere, trahere, proiicere, percu<lb/>tere, nihil ni&longs;i actionem &longs;onant. </s>

<s>3. &longs;int duo trahentes idem mobile; ita vt &longs;eor&longs;im neuter <lb/>trahere po&longs;&longs;it, coniunctim verò vterque po&longs;&longs;it; certè &longs;i alter non pro<lb/>ducit impetum &longs;cor&longs;un, nec etiam coniunctim producet; nec enim au<lb/>gentur eius vires ab altero: Re&longs;pondeo vtrunque agere actione com<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>

<s id="N12113">Tertiò probatur; pila di&longs;iuncta à manu proiicientis diu adhuc mo<lb/>uetur per hypoth.6. igitur hic motus habet cau&longs;am per Ax. 8. quælibet <lb/>enim pars motus de nouo e&longs;t, neque duæ illius partes &longs;imul e&longs;&longs;e po&longs;&longs;unt. </s>

<s>Dices &longs;i vterque coniunctim producit effectum: &longs;int v. g. 100. par<lb/>tes impetus; Igitur &longs;inguli producunt tantùm 50. Igitur cur potiùs in <lb/>in his partibus &longs;ubiecti, quàm in alijs, cum vtriu&longs;que potentia eidem <lb/>&longs;ubiecti parti po&longs;&longs;et e&longs;&longs;e applicata? </s>

<s id="N1211A"><lb/>atqui potentia motrix non e&longs;t cau&longs;a per Ax.10. immò pote&longs;t e&longs;&longs;e de&longs;tru<lb/>cta; igitur non e&longs;t cau&longs;a per Ax. 9. Non e&longs;t etiam cau&longs;a &longs;ub&longs;tantia pilæ <lb/>mobilis per Th.5.5. nec priores pattes motus per re&longs;p. </s>

<s id="N12125">ad primam in<lb/>&longs;tantiam Th 5. igitur aliquid aliud; voco impetum. </s>

<s id="N1212D">Quartò probatur; </s>

<s id="N12130">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>Re&longs;pondeo &longs;ingulos producere 100. <lb/>actione &longs;cilicet communi indiui&longs;ibiliter; &longs;int enim duo trahentes A. & <lb/>B. A. producit 100. &longs;ed non &longs;olus; B. producit ea&longs;dem 100. &longs;ed non &longs;o<lb/>lus; &longs;ed explicabimus hunc modum actionis communis in Metaphys. <lb/>quod autem agant actione communi patet per Ax. 13. </s>

<s id="N12136">5. igitur <lb/>non e&longs;t &longs;emper æqualis, & eadem cau&longs;a huius motus per Ax. 12. & 13. <lb/>num.3. igitur cau&longs;a huius motus eodem modo debilitatur, &longs;eu remitti<lb/>tur, quo ip&longs;e motus; </s>

<s id="N12140">&longs;ed decre&longs;cit &longs;ub&longs;tantia mobilis, nec potentia mo-<pb pagenum="16" xlink:href="026/01/048.jpg"/>trix, vel corpus prius impactum; </s>

<s id="N12149">ergo e&longs;t alia cau&longs;a præ&longs;ens, quæ mi<lb/>nuitur; voco impetum. </s>

<s>Obiicies 4. producitur &longs;onus &longs;i ferias rupem; igitur & impetus; Re&longs;<lb/>pondeo ad &longs;onum &longs;olam aëris colli&longs;ionem &longs;ufficere, quam fieri certum <lb/>e&longs;t à prædicto ictu; deinde mallej motus impacti in rupem facit &longs;onum; <lb/>quidquid tandem &longs;it &longs;onus, de quo hîc non di&longs;puto: adde qnod in ru<lb/>pe &longs;unt &longs;emper aliquæ partes trem ulæ, quæ modico tantùm, coque flexi<lb/>bili nexu cum alijs partibus copu lantur; adde aliquam compre&longs;&longs;ionem, <lb/>ex qua modicæ vibrationes &longs;equuntur. </s>

<s id="N12151">Quintò corpus graue deor&longs;um cadens accelerat &longs;uum motum, vt patet <lb/>experientia; </s>

<s>Obiicies 5. Quando aliquæ partes auolant ab ictu, haud dubiè auo<lb/>lant propter impetum impre&longs;&longs;um: Igitur prius e&longs;t imprimi impetum, <lb/>quàm auolare; igitur productus e&longs;t impetus in nonnullis partibus, & <lb/>non in aliis, cum quibus illæ &longs;unt coniunctæ. </s>

<s id="N12157">quæ maximè clara e&longs;t in funependulis, de qua in &longs;equen<lb/>tibus libris; </s>

<s id="N1215D">igitur debet e&longs;&longs;e cau&longs;a huius motus velocioris; </s>

<s>Re&longs;pondeo equidem im<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;trà; &longs;ed <lb/>&longs;i auolent aliquæ partes: certè in ijs non e&longs;t fru&longs;trà, in quibus habet <lb/>&longs;uum effectum, id e&longs;t, motum. </s>

<s id="N12161">non e&longs;t au<lb/>tem &longs;ub&longs;tantia lapidis, nec grauitas per Ax. 12. nec aliud quidpiam ex<lb/>trin&longs;ecum, vt videbimus &longs;uo loco; igitur aliquid aliquid intrin&longs;ecum, <lb/>voco impetum. </s>

<s id="N1216B">Igitur certum e&longs;t dari impetum; qui certè tribui non <lb/>pote&longs;t, vel vlli connotationi, vel alteri exigentiæ, vt con&longs;tat ex <lb/>dictis. </s>

<s>Dices; igitur primo in&longs;tanti impetus ille e&longs;t fru&longs;trà; in quo non <lb/>habet &longs;uum effectum; Re&longs;pondeo nunquam primo in&longs;tanti e&longs;&longs;e fru&longs;trà, <lb/>modò &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 infrà; immò ideo ponitur im<lb/>petus primo vt &longs;it motus &longs;ecundo exigendo pro i n&longs;tant i &longs;equenti, de <lb/>cum impetus ponat tantùm motum quo aliàs. </s>

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

<s id="N12175">Diceret fortè alius hæc omnia e&longs;&longs;e dubia; </s>

<s id="N12179">nam fieri pote&longs;t vt Deus <lb/>tantùm moueat; </s>

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

<s id="N1217F">quod &longs;ine impetu fieri po&longs;&longs;e certum e&longs;t; </s>

<s id="N12183">Re&longs;p. equi<lb/>dem per miraculum hoc fieri po&longs;&longs;e; &longs;ed quemadmadum certum e&longs;t phy<lb/>&longs;icè ignem applicatum calefacere, niuem frigefacere, & modò calamum <lb/>à me hæc &longs;cribente moueri, ita certum o&longs;t phy&longs;icè &longs;agittam à &longs;agittario <lb/>emitti, & pilam à proiiciente, &c. </s>

<s><lb/>haud dubiè 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<lb/>re; igitur cum &longs;it talis ordo à natura in&longs;titutus, ne aliquid &longs;it fru&longs;trà; <lb/>certè &longs;i impetus producibilis &longs;it futurus fru&longs;trà, hauddubiè non produ<lb/>cetur; &longs;ecus verò &longs;i fru&longs;trà non &longs;it futurus, in quo non e&longs;t difficultas. </s>

<s id="N1218F">adde quod Deus, vt auctor naturæ <lb/>e&longs;t, agit tantùm; </s>

<s id="N12195">vel de&longs;init agere iuxta exigentiam cau&longs;arum &longs;ecunda<lb/>rum; denique cau&longs;am phy&longs;icè appello, ex cuius applicatione nunquam <lb/>non &longs;equitur effectus per Ax.11. num.1. </s>

<s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/></s>

<s>Ob&longs;eruabis 1. vix fieri po&longs;&longs;e quin &longs;emper aliquæ partes &longs;eparentur, <lb/>comprimantur, vel dilatentur, vt patet experientiâ. </s>

<s id="N1219F">Dicerent alij hoc totum prouenire à corpu&longs;culis; </s>

<s id="N121A3">vel atomis, vel fila<lb/>mentis &longs;ine vlla actione; </s>

<s>Ob&longs;eruabis 2. etiam maximam corporis molem à 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<lb/>gis de motu; quem certè motum ob&longs;eruabis etiam in&longs;en&longs;ibilem, tùm <lb/>operâ radij luminis repercu&longs;&longs;i, & ad aliquod interuallum proiecti; tùm <lb/>operâ &longs;eu pi&longs;orum in tympani membranâ tremulo qua&longs;i motu &longs;ub&longs;ul<lb/>tantium; quâ etiam arte deprehenditur in arce ob&longs;e&longs;&longs;a, &longs;ub quam muri <lb/>partem cuniculi agantur. </s>

<s id="N121A9">equidem non reiicio corpu&longs;cula, & perennia <lb/>corporum effluuia: </s>

<s id="N121AF">Dico tamen primò globum quie&longs;centem humi ha<lb/>bere &longs;altem aliquas partes quie&longs;centes, vel immobiles; quis hoc neget? </s>

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 1.<emph.end type="center"/></s>

<s id="N121B5"><lb/>immò maximam &longs;uarum partium partem; </s>

<s id="N121BA">igitur cum deinde proiicitur <lb/>idem globus, illæ partes mouentur; </s>

<s>Hinc egregia ratio erui pote&longs;t, cur ingens corporis moles à debili po<lb/>tenria 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; certè cum &longs;int plures partes &longs;ubiecti, quàm vt in &longs;ingulis <lb/>ab ea dumtaxat potentiâ impetus produci po&longs;&longs;it; quid mirum e&longs;t, &longs;i mo<lb/>ueri non po&longs;&longs;it. </s>

<s id="N121C0">dari igitur debet cau&longs;a huius motus <lb/>per Ax.8, igitur impetus: </s>

<s id="N121C6">nec dicas moueri illas partes à corpu&longs;culis; </s>

<s><emph type="center"/><emph type="italics"/>Collorarium<emph.end type="italics"/> 2.<emph.end type="center"/></s>

<s id="N121CA">quia <lb/>antè erant eadem, immò plura corpu&longs;cula; </s>

<s id="N121D0">& tamen non mouebant: </s>

<s>Hinc certa ratio alterius vulgaris effectus potentiæ motricis, quæ lapi<lb/>dem 40. librarum tardo tantùm motu impellit, etiam cum &longs;ummo ni&longs;u, <lb/>cum tamen &longs;axo vnius libræ velocioremmotum imprimat; quia &longs;cilicet <lb/>partes impetus producti di&longs;tribuuntur pluribus partibus &longs;ubiecti in ma<lb/>iori lapide, & paucioribus in minori; igitur &longs;ingulæ partes minoris <lb/>habent plures partes impetus, vt manife&longs;tè coa&longs;tat; ergo ille impetus <lb/>inten&longs;ior e&longs;t; igitur maiorem exigit &longs;eu perfectiorem motum per Ax. <lb/>13. num.2. </s>

<s id="N121D4">igi<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 id="N121DC">vel enim mutantur, vel non mutantur; </s>

<s id="N121E0">&longs;ecundum dici <lb/>non pote&longs;t; </s>

<s id="N121E6">quia vt excitentur, ex non excitatis mutari debent; igitur <lb/>per aliquid: </s>

<s><emph type="center"/><emph type="italics"/>Collorarium<emph.end type="italics"/> 3.<emph.end type="center"/></s>

<s id="N121EC">deinde quid e&longs;t illa excitatio, ni&longs;i impul&longs;io; igitur &longs;i mouen<lb/>tur illa corpu&longs;cula, & excitantur à potentia motrice, etiam partes prius <lb/>immobiles mouebuntur, & excitabuntur per Ax.12. quia &longs;unt applicatæ <lb/>cau&longs;æ nece&longs;&longs;ariæ. </s>

<s>Hinc &longs;ublata ratione diuer&longs;æ re&longs;i&longs;tentiæ medij, dato pondere <lb/>mobilis vtriu&longs;que, datoque ni&longs;u communi potentiæ, pote&longs;t de<lb/>terminari certus velocitatis gradus vtriu&longs;que; nam ratio velocitatum <lb/>e&longs;t inuer&longs;a ponderum v. g. &longs;it pondùs 4. librarum; fit etiam 2. librarum <lb/>&longs;it impetus impre&longs;&longs;us vtrique &longs;uppo&longs;ito communi, & æquali ni&longs;u <lb/>potentiæ, & æquali tempore; haud dubiè velocitas mobilis 2. libra<lb/>rum erit dupla velocitatis mobilis 4. librarum; quia cum &longs;int duplo <lb/>plures partes &longs;ubiecti in hoc mobili quàm in illo (accipio enim vtrum<lb/>que eiu&longs;dem mareriæ, vt omnes lites fugiam) igitur in minori e&longs;t duplo <lb/>inten&longs;ior impetus: Igitur duplo velocior motus; dixi, &longs;i fiat æquali <lb/>ni&longs;u, & æquali tempore; quia reuerâ non fit in tempore æquali, &longs;ed <lb/>inæquali, &longs;i &longs;upponatur idem arcus brachij v. g. iacientis; nam tempo<lb/>ra &longs;unt in ratione &longs;ubduplicata ponderum; vt demon&longs;trabimus lib.

<s id="N121F8">Dico &longs;ecundò minimum ex his corpu&longs;culis non &longs;emper moueri; </s>

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

<s id="N121FC">po<lb/>te&longs;t enim &longs;i&longs;tere; quis hoc neget? </s>

<s id="N12202">igitur &longs;i modò mouetur, modò quie&longs;<lb/>cit, motus ab eo di&longs;tinguitur per Th.1. igitur mouetur per impetum, de <lb/>quo infrà. </s>

<s id="N1220B">Igitur datur nece&longs;&longs;ariò impetus, &longs;ine quo non po&longs;&longs;unt explicari prædi<lb/>ctæ omnes hypothe&longs;es, contra quem &longs;unt quidem graui&longs;&longs;imæ difficultates, <lb/>quas &longs;en&longs;im in &longs;equentibus Theorematis, in quibus explicantur pro<lb/>prietates huius impetus, di&longs;cutiemus. </s>

<s id="N12216">Diceret aliquis lapidem impul&longs;um ab aëre deinde propelli; </s>

<s id="N1221A">&longs;ed aër po<lb/>tius re&longs;