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<?xml version="1.0" encoding="UTF-8"?> <!DOCTYPE archimedes SYSTEM "../dtd/archimedes.dtd"> <archimedes xmlns:xlink="http://www.w3.org/1999/xlink"> <info> <author>Fabri, Honoré</author> <title>Tractatus physicus de motu locali</title> <date>1646</date> <place>Lyon</place> <translator/> <lang>la</lang> <cvs_file>fabri_tract_026_la_1646.xml</cvs_file> <cvs_version/> <locator>026.xml</locator> </info> <text> <front> <section> <pb xlink:href="026/01/001.jpg"/> <p id="N1001B" type="head"> <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> </p> <p id="N1002E" type="main"> <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> </p> <p id="N1003D" type="main"> <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> </p> <p id="N10052" type="main"> <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> </p> <figure id="id.026.01.001.1.jpg" xlink:href="026/01/001/1.jpg"/> <p id="N1006C" type="main"> <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"/><!-- KEEP S--></s> </p> <p id="N1007E" type="main"> <s id="N10080"><emph type="center"/><emph type="italics"/>M. </s> <s id="N10087">D C. XLVI.<emph.end type="italics"/><lb/>Cum Priuilegio Regis, & Approbatione Doctorum.<emph.end type="center"/></s> </p> <pb xlink:href="026/01/002.jpg"/> </section> <section> <pb xlink:href="026/01/003.jpg"/> <figure id="id.026.01.003.1.jpg" xlink:href="026/01/003/1.jpg"/> <p id="N1009C" type="head"> <s id="N1009E"><emph type="center"/>AMPLISSIMO, <lb/>NOBILISSIMOQVE DOMINO,<emph.end type="center"/></s> </p> <p id="N100A7" type="main"> <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> </p> <p id="N100B8" type="main"> <s id="N100BA"><emph type="center"/>PETRVS MOVSNERIVS,<emph.end type="center"/></s> </p> <p id="N100C1" type="main"> <s id="N100C3"><!-- NEW --><emph type="italics"/>TIBI alterum no&longs;træ Philo&longs;o­<lb/>phiæ fœtum 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"><!-- NEW -->non muta&longs;ti merita, non mu­<lb/>tabo officia: </s> <s id="N100DF"><!-- NEW -->multos non expo&longs;cam Patronos, qui <lb/>iam omnium optimum, & meriti&longs;simum habeo; </s> <s id="N100E5"><!-- NEW -->neo <lb/>enim &longs;acra Philo&longs;ophiæ anathemata rudi, & ru­<lb/>&longs;tico muro appendam, quæ ex &longs;acro tholo templi <lb/>Themidos amœniter pendent: </s> <s id="N100EF"><!-- NEW -->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"><!-- NEW -->& 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 id="N10107"><!-- NEW -->Tu prudens Intelli­<lb/>gentia, huic orbi &longs;emper a&longs;si&longs;tis; </s> <s id="N1010D"><!-- NEW -->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"/><!-- KEEP S--></s> </p> </section> <section> <pb xlink:href="026/01/005.jpg"/> <figure id="id.026.01.005.1.jpg" xlink:href="026/01/005/1.jpg"/> <p id="N10129" type="head"> <s id="N1012B"><emph type="center"/>PRÆFATIO.<emph.end type="center"/></s> </p> <p id="N10132" type="main"> <s id="N10134"><!-- NEW -->NIHIL habeo præfari (Beneuole Lector) <lb/>in gratiam huius tractatus de Motu Locali, <lb/>cuius amœnitatem & vtilitatem, rerum co­<lb/>piam & &longs;yluam, tuo gu&longs;tui & iudicio re­<lb/>linquo: </s> <s id="N10140"><!-- NEW -->Multi &longs;anè hactenus in hac mate­<lb/>ria feliciter de&longs;udarunt; </s> <s id="N10146"><!-- NEW -->& 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"><!-- NEW -->quia tamen multa omi&longs;it, quæ ad motum &longs;pe­<lb/>ctant, vt nemo ne&longs;cit; </s> <s id="N10156"><!-- NEW -->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"><!-- NEW -->vt Phy­<lb/>&longs;icæ con&longs;ulamus, aliam inimus viam: </s> <s id="N10164"><!-- NEW -->Geometriam qui­<lb/>dem adhibemus, ad explicandas, exponenda&longs;que præ­<lb/>dictas illas proportiones, quæ motibus in&longs;unt; </s> <s id="N1016C"><!-- NEW -->&longs;ed effe­<lb/>ctus illos prædictis proportionibus affixos ad principia <lb/>Phy&longs;ica reducimus; </s> <s id="N10174"><!-- NEW -->id e&longs;t, cùm &longs;upponamus quòd &longs;int, <lb/>propter quid &longs;int demon&longs;tramus: </s> <s id="N1017A"><!-- NEW -->in votis erat motus <lb/>omnes vno volumine complecti; </s> <s id="N10180"><!-- NEW -->id e&longs;t effectus omnes <lb/>cuiu&longs;uis potentiæ motricis; </s> <s id="N10186"><!-- NEW -->tres enim agno&longs;cimus hu­<lb/>iu&longs;modi potentias: </s> <s id="N1018C"><!-- NEW -->primam naturalem voco, quæ e&longs;t <lb/>grauium: </s> <s id="N10192"><!-- NEW -->alteram animalem, quæ e&longs;t animantium: </s> <s id="N10196"><!-- NEW -->ter­<lb/>tiam mediam, quæ ten&longs;orum e&longs;t vel compre&longs;&longs;orum: </s> <s id="N1019C"><!-- NEW -->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 id="N101A8"><!-- NEW -->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"><!-- NEW -->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 id="N101C2"><!-- NEW -->Fortè aliquis poten­<lb/>tias mechanicas de&longs;ideraret, lineas, motus, & cæle&longs;tes <lb/>&longs;piras; </s> <s id="N101CA"><!-- NEW -->&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 id="N101D6"><!-- NEW -->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"><!-- NEW -->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 id="N101F0"><!-- NEW -->omitto etiam quæ in me quidam iniquè <lb/>certè rerum æ&longs;timatores iactarunt: </s> <s id="N101F6"><!-- NEW -->reponere po&longs;&longs;em cum <lb/>fænore; </s> <s id="N101FC"><!-- NEW -->&longs;ed nos talem con&longs;uetudinem non habemus; </s> <s id="N10200"><!-- NEW -->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> </p> <pb xlink:href="026/01/007.jpg"/> <p id="N1020D" type="main"> <s id="N1020F"><!-- NEW -->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 id="N10219"><!-- NEW -->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> </p> <p id="N10226" type="main"> <s id="N10228"><emph type="center"/><emph type="italics"/>SYNOPSIS LIBRORVM<emph.end type="italics"/><emph.end type="center"/></s> </p> <p id="N10233" type="main"> <s id="N10235"><emph type="center"/><emph type="italics"/>huius tractatus.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p id="N10240" type="table"> <s id="N10242">TABELLE WAR HIER<!-- KEEP S--></s> </p> </section> <section> <pb xlink:href="026/01/008.jpg"/> <figure id="id.026.01.008.1.jpg" xlink:href="026/01/008/1.jpg"/> <p id="N1024F" type="head"> <s id="N10251"><emph type="center"/><emph type="italics"/>SYNOPSIS AMPLIOR.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N1025D" type="main"> <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> </p> <figure id="id.026.01.008.2.jpg" xlink:href="026/01/008/2.jpg"/> <p id="N1026D" type="main"> <s id="N1026F"><emph type="center"/><emph type="italics"/>De Impetu.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p id="N1027A" type="main"> <s id="N1027C"><!-- NEW -->1. IMPETVS e&longs;t qualitas exigens motum &longs;ui &longs;ubiecti: </s> <s id="N10280"><!-- NEW --><lb/>datur impetus; </s> <s id="N10285"><!-- NEW -->quia non pote&longs;t e&longs;&longs;e alia cau&longs;a exi­<lb/>gitiua motus: </s> <s id="N1028B"><!-- NEW -->adde quòd, potentia motrix e&longs;t acti­<lb/>ua; </s> <s id="N10291"><!-- NEW -->igitur aliquid producit, &longs;ed non aliud quàm <lb/>impetum, vt con&longs;tat ex dictis de motu: </s> <s id="N10297"><!-- NEW -->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 id="N1029D"><!-- NEW -->non e&longs;t modus, <lb/>quia di&longs;tinguitur ab effectu &longs;uo formali &longs;ecundario: </s> <s id="N102A3"><!-- NEW -->impetus non <lb/>producitur in eo mobili, quod moueri non pote&longs;t à potentia mo­<lb/>trice applicata: </s> <s id="N102AB"><!-- NEW -->& produci tantùm pote&longs;t, vel in omni parte, vel <lb/>in nulla; </s> <s id="N102B1"><!-- NEW -->alioquin e&longs;&longs;et fru&longs;trà; & gratis ponitur ne&longs;cio quis impe­<lb/>tus inefficax. </s> </p> <p id="N102B7" type="main"> <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"><!-- NEW -->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 id="N102C6"><!-- NEW -->agit tan­<lb/>tùm ad extra, vt tollat impedimentum: </s> <s id="N102CC"><!-- NEW -->hinc, cùm pro diuer&longs;a <lb/>applicatione &longs;it diuer&longs;um impedimentum, modò plùs, modò minùs <lb/>agit; </s> <s id="N102D4"><!-- NEW -->maximè verò, cum maximum e&longs;t impedimentum: </s> <s id="N102D8"><!-- NEW -->hinc ictus <lb/>per lineam perpendicularem forti&longs;&longs;imus e&longs;t: portò omnes partes <lb/>impetus agunt ad extra actione communi. </s> </p> <p id="N102E0" type="main"> <s id="N102E2"><!-- NEW -->3. Impetus inten&longs;us producere pote&longs;t remi&longs;&longs;um, minoris mobi­<lb/>lis in maiore; </s> <s id="N102E8"><!-- NEW -->& 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="N102F4"><!-- NEW -->Datur <lb/>impetus alio impetu perfectior, & imperfectior, &longs;ine quo non po­<lb/>te&longs;t explicari natura vectis: </s> <s id="N102FC"><!-- NEW -->itaque dato quocunque dari pote&longs;t per­<lb/>fectior, & imperfectior: quia dato quocunque motu pote&longs;t dari ve­<lb/>locior, & tardior. </s> </p> <p id="N10304" type="main"> <s id="N10306"><!-- NEW -->4. Propagatur impetus vniformiter tantùm, cùm omnes partes <lb/>corporis mouentur moctu recto æquali: </s> <s id="N1030C"><!-- NEW -->ibi enim e&longs;t æqualis cau&longs;a, <lb/>vbi e&longs;t æqualis effectus: </s> <s id="N10312"><!-- NEW -->in motu circulari applicata potentia cen­<lb/>tro vectis, producitur æqualis perfectionis versùs circunferentiam, <lb/>& inæqualis numerus; </s> <s id="N1031A"><!-- NEW -->applicata verò potentia circunferentiæ, pro­<lb/>ducitur æqualis numerus, &longs;ed inæqualis perfectionis versùs cen­<lb/>trum; </s> <s id="N10322"><!-- NEW -->quia potentia non pote&longs;t producere immediatè perfectiorem, <lb/>& imperfectiorem in infinitum: </s> <s id="N10328"><!-- NEW -->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> </p> <p id="N10332" type="main"> <s id="N10334"><!-- NEW -->5. Impetus innatus e&longs;t tantùm determinatus ad lineam perpen­<lb/>dicularem deor&longs;um; </s> <s id="N1033A"><!-- NEW -->alioquin &longs;i ad aliam determinari po&longs;&longs;et, primo <lb/>e&longs;&longs;et æqualis motus per inclinatam, & perpendicularem; </s> <s id="N10340"><!-- NEW -->corpus <lb/>graue mi&longs;&longs;um per lineam inclinatam ab eo non declinaret; </s> <s id="N10346"><!-- NEW -->imò im­<lb/>petus &longs;emel productus (&longs;i liberum e&longs;&longs;et medium) non de&longs;trueretur: </s> <s id="N1034C"><!-- NEW --><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> </p> <p id="N10355" type="main"> <s id="N10357"><!-- NEW -->6. Impetus indifferens determinatur ad lineam multis modis: <lb/>primò, à potentia motrice: </s> <s id="N1035D"><!-- NEW -->&longs;ecundò, ab impetu: </s> <s id="N10361"><!-- NEW -->tertiò, ab alio impe­<lb/>tu concurrente; quartò, ab obice occurrente: </s> <s id="N10367"><!-- NEW -->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"><!-- NEW -->Impetus e&longs;t capax inten&longs;ionis; </s> <s id="N10375"><!-- NEW --><lb/>quia aliquando de&longs;truitur ex parte: </s> <s id="N1037A"><!-- NEW -->eius exten&longs;io commen&longs;uratur <lb/>exten&longs;ioni mobilis; </s> <s id="N10380"><!-- NEW -->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> </p> <p id="N10388" type="main"> <s id="N1038A"><!-- NEW -->7. Impetus non e&longs;t contrarius alteri ratione entitatis; </s> <s id="N1038E"><!-- NEW -->quia qui­<lb/>libet cum quolibet in eodem &longs;ubiecto coëxi&longs;tere pote&longs;t: </s> <s id="N10394"><!-- NEW -->pugnat <lb/>tamen vnus cum alio ratione determinationis: </s> <s id="N1039A"><!-- NEW -->hinc vnus impetus <lb/>pugnat cum alio ratione lineæ motus: </s> <s id="N103A0"><!-- NEW -->hinc vnus videtur de&longs;trui ab <pb xlink:href="026/01/010.jpg"/>alio; </s> <s id="N103A8"><!-- NEW -->quanquam impetus tantùm de&longs;truitur, cùm e&longs;t fru&longs;trà: </s> <s id="N103AC"><!-- NEW -->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> </p> <p id="N103B6" type="main"> <s id="N103B8"><!-- NEW -->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"><!-- NEW --><lb/>&longs;i ad eandem, nihil impetus de&longs;truitur, &longs;ed e&longs;t duplò velocior mo­<lb/>tus; </s> <s id="N103C5"><!-- NEW -->&longs;i ad diuer&longs;as, vel &longs;unt oppo&longs;itæ ex diametro, vel concurrentes <lb/>faciunt angulum; </s> <s id="N103CB"><!-- NEW -->&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="N103D3"><!-- NEW -->Impetus innatus nunquam de&longs;truitur: </s> <s id="N103D7"><!-- NEW -->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="N103DD">Porrò <lb/>nunquam de&longs;truitur; </s> <s id="N103E2"><!-- NEW -->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="N103EA">Sed de grauitate aliàs. </s> </p> <figure id="id.026.01.010.1.jpg" xlink:href="026/01/010/1.jpg"/> <p id="N103F2" type="main"> <s id="N103F4"><emph type="center"/><emph type="italics"/>De motu naturali deor&longs;um.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p id="N103FF" type="main"> <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 id="N10408">Eius finis <lb/>e&longs;t globi terre&longs;tris compactio, &c. </s> <s id="N1040D"><!-- NEW -->E&longs;t autem motus naturalis ab <lb/>impetu: </s> <s id="N10413"><!-- NEW -->primò, quia eius acceleratio &longs;ine impetu explicari non po­<lb/>te&longs;t: </s> <s id="N10419"><!-- NEW -->&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> </p> <p id="N10421" type="main"> <s id="N10423"><!-- NEW -->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 id="N1042C"><!-- NEW -->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"><!-- NEW -->certè &longs;ecundo in&longs;tanti producit <lb/>nouum impetum: idem dica de tertio, quarto, &c. </s> <s id="N1043C"><!-- NEW -->igitur cre&longs;cit <lb/>cau&longs;a motus; </s> <s id="N10442"><!-- NEW -->igitur & motus: quæ ratio clari&longs;&longs;ima e&longs;t: </s> <s id="N10446"><!-- NEW -->hinc æquali­<lb/>bus temporibus æqualia acquiruntur velocitatis momenta; </s> <s id="N1044C"><!-- NEW -->quia <lb/>cau&longs;a nece&longs;&longs;aria æqualibus temporibus, æqualem effectum produ­<lb/>cit: quid clarius? </s> </p> <p id="N10454" type="main"> <s id="N10456"><!-- NEW -->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"><!-- NEW -->cre&longs;cit autem velocitas, vt im­<lb/>petus; </s> <s id="N10466"><!-- NEW -->effectus, &longs;cilicet, vt cau&longs;a: </s> <s id="N1046A"><!-- NEW -->idem dico de motu, ratione velo­<lb/>citatis; </s> <s id="N10470"><!-- NEW -->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> </p> <p id="N1047E" type="main"> <s id="N10480"><!-- NEW -->4. Hoc autem facilè pote&longs;t <expan abbr="demõ&longs;trari">demon&longs;trari</expan>: </s> <s id="N10488"><!-- NEW -->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"><!-- NEW -->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> </p> <p id="N1049E" type="main"> <s id="N104A0"><!-- NEW -->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"><!-- NEW -->quam Galileus excogitauit, vt &longs;ine &longs;crupulo hæc a&longs;­<lb/>&longs;umi po&longs;&longs;it: </s> <s id="N104B2"><!-- NEW -->hinc &longs;patia &longs;unt ferè vt temporum quadrata: dixi, ferè: </s> <s id="N104B6"><!-- NEW --><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. <!-- KEEP S--></s> </p> <p id="N104C4" type="main"> <s id="N104C6">6. Hinc ratio euidens maioris ictus inflicti à corpore graui, <lb/>cùm ex maiori altitudine cadit. </s> <s id="N104CB"><!-- NEW -->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 id="N104D3"><!-- NEW -->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"><!-- NEW -->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> </p> <p id="N104E5" type="main"> <s id="N104E7"><!-- NEW -->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> <s id="N104ED"><!-- NEW -->&longs;ed in <pb xlink:href="026/01/012.jpg"/>duobus præ&longs;ertim con&longs;i&longs;tit; </s> <s id="N104F5"><!-- NEW -->primò, eò quòd medium detrahat ali­<lb/>quid grauitationis corporis grauis; </s> <s id="N104FB"><!-- NEW -->&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"><!-- NEW -->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="N1050B">de quo <lb/>aliàs. </s> </p> <p id="N10510" type="main"> <s id="N10512"><!-- NEW -->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 id="N1051C"><!-- NEW -->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> </p> <p id="N1052D" type="main"> <s id="N1052F"><!-- NEW -->9. Figura corporis grauis deor&longs;um cadentis motum vel retardat <lb/>vel accelerat; </s> <s id="N10535"><!-- NEW -->retardat quidem, &longs;i plures partes medij amouendæ <lb/>&longs;unt vel pauciores velociori motu; accelerat è contrario: </s> <s id="N1053B"><!-- NEW -->hinc idem <lb/>corpus <expan abbr="parallelipedũ">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"><!-- NEW -->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> </p> <p id="N1054F" type="main"> <s id="N10551"><!-- NEW -->10. Duo globi, vel cubi eiu&longs;dem materiæ æquè velociter de&longs;­<lb/>cendunt: </s> <s id="N10557"><!-- NEW -->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 id="N10567"><!-- NEW -->certè ratio compo&longs;ita vtriu&longs;que erit eadem in vtroque cu­<lb/>bo: igitur æqualiter de&longs;cendet vterque. </s> </p> <p id="N1056D" type="main"> <s id="N1056F"><!-- NEW -->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"><!-- NEW -->Corpu&longs;cula etiam ex graui&longs;&longs;ima ma­<lb/>teria tardi&longs;&longs;imè de&longs;cendunt: </s> <s id="N1057D"><!-- NEW -->tum, quia à filamentis illis, quibus par­<lb/>tes aëris implicantur, facilè detinentur; </s> <s id="N10583"><!-- NEW -->analogiam habes in lapil­<lb/>lo, qui ab araneæ tela intercipitur: </s> <s id="N10589"><!-- NEW -->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> </p> <p id="N1059C" type="main"> <s id="N1059E"><!-- NEW -->12. Singulis in&longs;tantibus motus naturaliter accelerati cre&longs;cit <lb/>re&longs;i&longs;tentia; </s> <s id="N105A4"><!-- NEW -->quia, cùm motus cre&longs;cat, æqualibus temporibus, plures <lb/>partes medij occurrunt; </s> <s id="N105AA"><!-- NEW -->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"><!-- NEW -->Hinc <lb/>colligo, contra Galilæum, motum rectum ex naturaliter accelerato <lb/>nunquam fieri æquabilem: dixi motum rectum; quia motus corpo­<lb/>rum cœle&longs;tium ex accelerato factus e&longs;t æqualis. </s> </p> <figure id="id.026.01.013.1.jpg" xlink:href="026/01/013/1.jpg"/> <p id="N105BF" type="main"> <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> </p> <p id="N105CC" type="main"> <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"><!-- NEW -->Triplici modo accidere pote&longs;t: </s> <s id="N105D7"><!-- NEW -->primò, &longs;i reuerà <lb/>imprimatur impetus ab extrin&longs;eco, vt, cùm mitto lapidem &longs;ur&longs;um: </s> <s id="N105DD"><!-- NEW --><lb/>&longs;ecundò, &longs;i corpus deor&longs;um cadens deinde reflectatur &longs;ur&longs;um; </s> <s id="N105E2"><!-- NEW -->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"><!-- NEW -->tertiò, &longs;i terra vtrinque e&longs;&longs;et peruia; </s> <s id="N105EE"><!-- NEW -->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"><!-- NEW -->igitur <lb/>a&longs;cenderet per eandem lineam; </s> <s id="N105FA"><!-- NEW -->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> </p> <p id="N10602" type="main"> <s id="N10604"><!-- NEW -->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 id="N1060E"><!-- NEW -->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> </p> <p id="N1061F" type="main"> <s id="N10621"><!-- NEW -->3. Hinc nece&longs;&longs;ariò e&longs;t retardatus: </s> <s id="N10625"><!-- NEW -->igitur de&longs;truitur impetus, non <lb/>quidem ab ip&longs;a medij re&longs;i&longs;tentia; </s> <s id="N1062B"><!-- NEW -->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"><!-- NEW -->igitur de&longs;trui­<lb/>tur ille impetus motus violenti ab impetu innato aliquo modo; </s> <s id="N10637"><!-- NEW -->non <lb/>quidem vt à contrario ratione entitatis, &longs;ed ratione determinatio­<lb/>nis: </s> <s id="N1063F"><!-- NEW -->cùm enim impetus innatus exigat motum deor&longs;um, & alius &longs;ur­<lb/>&longs;um: </s> <s id="N10645"><!-- NEW -->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> </p> <pb xlink:href="026/01/014.jpg"/> <p id="N1064E" type="main"> <s id="N10650"><!-- NEW -->4. Hinc &longs;ingulis temporibus æqualibus de&longs;truitur gradus impe­<lb/>tui innato; </s> <s id="N10656"><!-- NEW -->e&longs;t enim eadem ratio pro omnibus: </s> <s id="N1065A"><!-- NEW -->igitur temporibus <lb/>æqualibus de&longs;truitur æqualis impetus: </s> <s id="N10660"><!-- NEW -->igitur amittit ille motus <lb/>æqualia velocitatis momenta: </s> <s id="N10666"><!-- NEW -->igitur e&longs;t naturaliter retardatus: </s> <s id="N1066A"><!-- NEW -->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> </p> <p id="N10674" type="main"> <s id="N10676"><!-- NEW -->5. Hinc impetus imperfectior initio de&longs;truitur: </s> <s id="N1067A"><!-- NEW -->quia, cùm motus <lb/>ille &longs;it velocior initio, in&longs;tantia &longs;unt minora: </s> <s id="N10680"><!-- NEW -->atqui minori tempore <lb/>minùs retardatur: </s> <s id="N10686"><!-- NEW -->igitur inperfectior impetus de&longs;truitur; </s> <s id="N1068A"><!-- NEW -->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> </p> <p id="N10698" type="main"> <s id="N1069A">6. Hinc vltimus gradus impetus violenti e&longs;t omnium perfecti&longs;­<lb/>&longs;imus, vt con&longs;tat. </s> <s id="N1069F"><!-- NEW -->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"><!-- NEW -->vbi enim ventum e&longs;&longs;et ad in&longs;tans æqualitatis, neutrum præ­<lb/>ualere po&longs;&longs;et: </s> <s id="N106AD"><!-- NEW -->igitur in&longs;tanti &longs;equenti e&longs;&longs;et quies: </s> <s id="N106B1"><!-- NEW -->cùm tamen &longs;int <lb/>diuer&longs;æ perfectionis, perfectior præualet: vter autem &longs;it perfectior, <lb/>dicemus infrà. </s> </p> <p id="N106B9" type="main"> <s id="N106BB"><!-- NEW -->7. Cum mobile &longs;ur&longs;um reflectitur, vel terra perforata &longs;uam lineam <lb/>motus &longs;ur&longs;um versus oppo&longs;itam cœli 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"><!-- NEW -->&longs;i verò imprimitur ab alia potentia motrice, <lb/>tunc etiam imperfectior e&longs;t impetu innato; </s> <s id="N106CB"><!-- NEW -->nam inæqualis e&longs;t; </s> <s id="N106CF"><!-- NEW -->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 id="N106D7"><!-- NEW -->præ&longs;tat autem e&longs;&longs;e imperfectiorem, quàm perfectio­<lb/>rem, vt plura impetus puncta à potentia imprimantur; </s> <s id="N106DD"><!-- NEW -->quòd mul­<lb/>tum facit ad mouenda maiora pondera: hinc nullo in&longs;tanti quie&longs;­<lb/>cunt proiecta &longs;ur&longs;um. </s> </p> <p id="N106E5" type="main"> <s id="N106E7"><!-- NEW -->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"><!-- NEW -->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="N106F3"><!-- NEW --><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"><!-- NEW -->hinc <lb/>&longs;onus tam citò auditur; </s> <s id="N10700"><!-- NEW -->quia propagatur cum particulis aëris æqua­<lb/>bili ferè motu: </s> <s id="N10706"><!-- NEW -->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 id="N1070E"><!-- NEW -->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> </p> <p id="N10716" type="main"> <s id="N10718"><!-- NEW -->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="tantũdem">tantundem</expan> enim <lb/>impetus in de&longs;cen&longs;u acquiritur, quantùm in a&longs;cen&longs;u deperditur. </s> <s id="N10724"><!-- NEW --><lb/>Impetus primo in&longs;tanti, quo e&longs;t, agit, &longs;i e&longs;t aliquod impedimen­<lb/>tum; </s> <s id="N1072B"><!-- NEW -->e&longs;t enim cau&longs;a nece&longs;&longs;aria: </s> <s id="N1072F"><!-- NEW -->primo in&longs;tanti motus aliquid im­<lb/>petus de&longs;truitur: </s> <s id="N10735"><!-- NEW -->&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 id="N1073B"><!-- NEW -->re&longs;i&longs;tentia aëris e&longs;t <lb/>quidem maior initio; &longs;ed etiam &longs;unt maiores vires. </s> </p> <figure id="id.026.01.015.1.jpg" xlink:href="026/01/015/1.jpg"/> <p id="N10746" type="main"> <s id="N10748"><emph type="center"/><emph type="italics"/>De motu in planis inclinatis.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p id="N10753" type="main"> <s id="N10755"><!-- NEW -->1. PLanum inclinatum e&longs;t &longs;ur&longs;um, vel deor&longs;um: </s> <s id="N10759"><!-- NEW -->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"><!-- NEW -->impeditur autem motus naturalis in plano <lb/>prædicto, quia impeditur eius linea: </s> <s id="N10767"><!-- NEW -->ideò e&longs;t tardior hic motus in <lb/>plano inclinato, quàm in perpendiculari: </s> <s id="N1076D"><!-- NEW -->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 id="N10775"><!-- NEW -->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> </p> <p id="N1077F" type="main"> <s id="N10781"><!-- NEW -->2. Hinc motus &longs;unt vt lineæ permutando: </s> <s id="N10785"><!-- NEW -->hinc mobile de&longs;cendit <lb/>per &longs;e in prædicto plano: </s> <s id="N1078B"><!-- NEW -->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 id="N10796"><!-- NEW -->nam impetus &longs;unt <lb/>vt motus: </s> <s id="N1079C"><!-- NEW -->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> </p> <p id="N107A6" type="main"> <s id="N107A8"><!-- NEW -->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"><!-- NEW -->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 id="N107BC"><!-- NEW -->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> </p> <p id="N107C6" type="main"> <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 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"><!-- NEW -->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> </p> <p id="N107E4" type="main"> <s id="N107E6"><!-- NEW -->5. Porrò minùs grauitat in ip&longs;um planum inclinatum corpus gra­<lb/>ue, quàm in planum horizontale: </s> <s id="N107EC"><!-- NEW -->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 id="N107F4"><!-- NEW -->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> </p> <p id="N10800" type="main"> <s id="N10802"><!-- NEW -->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"><!-- NEW -->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"><!-- NEW -->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> </p> <p id="N1081C" type="main"> <s id="N1081E"><!-- NEW -->7. Hinc minùs de&longs;truitur impetus in plano inclinato &longs;ur&longs;um, <lb/>quàm in perpendiculo; </s> <s id="N10824"><!-- NEW -->quia diutiùs durat: </s> <s id="N10828"><!-- NEW -->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"><!-- NEW -->hinc accedit propriùs hic motus ad æquabilem: </s> <s id="N10834"><!-- NEW -->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"><!-- NEW -->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> </p> <p id="N10846" type="main"> <s id="N10848"><!-- NEW -->8. Corpus graue in &longs;uperficie quadrantis caua, deor&longs;um cadit <lb/>motu naturaliter accelerato; </s> <s id="N1084E"><!-- NEW -->quia &longs;ingulis in&longs;tantibus accedit nouus <pb xlink:href="026/01/017.jpg"/>impetus; </s> <s id="N10856"><!-- NEW -->non tamen æqualibus temporibus, acquiruntur æqualia <lb/>velocitatis momenta; </s> <s id="N1085C"><!-- NEW -->quia in &longs;ingulis punctis quadrantis, e&longs;t diuer­<lb/>&longs;a tangens; </s> <s id="N10862"><!-- NEW -->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> </p> <p id="N1086C" type="main"> <s id="N1086E"><!-- NEW -->9. De&longs;cendit etiam in &longs;uperficie conuexa globi erecti motu ac­<lb/>celerato; </s> <s id="N10874"><!-- NEW -->initio quidem, in minore proportione; </s> <s id="N10878"><!-- NEW -->&longs;ub finem, in maio­<lb/>re; </s> <s id="N1087E"><!-- NEW -->vnde e&longs;t inuer&longs;a prioris: </s> <s id="N10882"><!-- NEW -->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"><!-- NEW -->&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"><!-- NEW -->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> </p> <figure id="id.026.01.017.1.jpg" xlink:href="026/01/017/1.jpg"/> <p id="N1089F" type="main"> <s id="N108A1"><emph type="center"/><emph type="italics"/>De motu mixto ex rectis.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p id="N108AC" type="main"> <s id="N108AE">1. DAri motum mixtum ille non dubitat, qui di&longs;cum proiicit. </s> <s id="N108B1"><!-- NEW --><lb/>Mixtus ex duobus rectis æquabilibus e&longs;t rectus, e&longs;t que <lb/>diagonalis vtriu&longs;que: </s> <s id="N108B8"><!-- NEW -->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"><!-- NEW -->quia, &longs;cilicet, e&longs;t fru&longs;trà: </s> <s id="N108C4"><!-- NEW -->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> </p> <p id="N108CE" type="main"> <s id="N108D0"><!-- NEW -->2. <expan abbr="Quũ">Quum</expan> minor e&longs;t, vel acutior prædictus angulus, minùs impetus <lb/>de&longs;truitur; </s> <s id="N108DA"><!-- NEW -->quia diagonalis maior e&longs;t; </s> <s id="N108DE"><!-- NEW -->donec tandem conueniant in <lb/>eandem lineam, tunc enim nihil de&longs;truitur: </s> <s id="N108E4"><!-- NEW -->datur de facto hic mo­<lb/>tus in rerum natura; </s> <s id="N108EA"><!-- NEW -->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"><!-- NEW -->motus mixtus ex <lb/>duobus retardatis iuxta eandem progre&longs;&longs;ionem e&longs;t rectus; </s> <s id="N108F6"><!-- NEW -->quia fit <lb/>per hypothenu&longs;im triangulorum proportionalium: idem dico de <lb/>duobus acceleratis. </s> </p> <p id="N108FE" type="main"> <s id="N10900"><!-- NEW -->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"><!-- NEW -->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> </p> <p id="N10914" type="main"> <s id="N10916"><!-- NEW -->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"><!-- NEW -->&longs;ed tantùm eiu&longs;dem altitudinis: </s> <s id="N10922"><!-- NEW -->nam perinde cre&longs;cit ille <lb/>impetus, atque cre&longs;ceret in diuer&longs;is planis inclinaris: </s> <s id="N10928"><!-- NEW -->impetus verò <lb/>violentus in hoc motu retardatur; </s> <s id="N1092E"><!-- NEW -->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> </p> <p id="N10938" type="main"> <s id="N1093A"><!-- NEW -->5. Adde, quòd e&longs;t duplex determinatio: </s> <s id="N1093E"><!-- NEW -->igitur aliquid de&longs;trui de­<lb/>bet, non acqui&longs;iti; igitur impre&longs;&longs;i: </s> <s id="N10944"><!-- NEW -->de&longs;trui autem non dicitur acqui­<lb/>&longs;itus, quòd, &longs;cilicet, plùs de nouo accedat, quàm pereat; </s> <s id="N1094A"><!-- NEW -->e&longs;t enim ac­<lb/>celeratus: </s> <s id="N10950"><!-- NEW -->adde, quòd non infligitur tantus ictus &longs;ub finem; </s> <s id="N10954"><!-- NEW -->igitur <lb/>de&longs;truitur aliquid impetus, non acqui&longs;iti, eo modo, quo diximus; </s> <s id="N1095A"><!-- NEW --><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> </p> <p id="N10961" type="main"> <s id="N10963"><!-- NEW -->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"><!-- NEW -->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"><!-- NEW -->cuius <lb/>rei clari&longs;&longs;ima e&longs;t experientia: ratio e&longs;t; </s> <s id="N10977"><!-- NEW -->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"><!-- NEW -->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"><!-- NEW --><lb/>quia acceleratur tantùm naturalis deor&longs;um, &longs;altem in inclinata: </s> <s id="N1098A"><!-- NEW -->&longs;e­<lb/>cunda pars etiam patet; quia &longs;ub finem minor e&longs;t ictus. </s> </p> <p id="N10990" type="main"> <s id="N10992"><!-- NEW -->7. Hinc linea motus e&longs;t curua: </s> <s id="N10996"><!-- NEW -->iuxta diuer&longs;am progre&longs;&longs;ionem de­<lb/>&longs;truitur hic impetus impre&longs;&longs;us: </s> <s id="N1099C"><!-- NEW -->tùm pro diuer&longs;a inclinatione plani, <lb/>cuius etiam hîc habetur ratio; </s> <s id="N109A2"><!-- NEW -->nam &longs;ingulis in&longs;tantibus mutatur: </s> <s id="N109A6"><!-- NEW --><lb/>tùm, quia modò plùs impetus e&longs;t fru&longs;trà, modò minùs; </s> <s id="N109AB"><!-- NEW -->plùs <lb/>certè, cùm linea determinationis impetus impre&longs;&longs;i facit obtu­<lb/>&longs;iorem: </s> <s id="N109B3"><!-- NEW -->atqui initio e&longs;t obtu&longs;ior; &longs;ub finem verò a&longs;cen&longs;us acu­<lb/>tior. </s> </p> <p id="N109B9" type="main"> <s id="N109BB"><!-- NEW -->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"><!-- NEW -->quia, &longs;cilicet, a&longs;­<lb/>cen&longs;us longior e&longs;t, quàm de&longs;cen&longs;us: </s> <s id="N109C7"><!-- NEW -->e&longs;t autem longior; </s> <s id="N109CB"><!-- NEW -->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"><!-- NEW -->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"><!-- NEW -->quia per verti­<lb/>calem &longs;ur&longs;um, nihil acquiritur in plano horizontali, ex quo fit ia­<lb/>ctus; </s> <s id="N109EA"><!-- NEW -->nihil etiam per ip&longs;am horizontalem; igitur plùs acquiritur per <lb/>illam, quæ maximè ab vtraque &longs;imul recedit. </s> </p> <p id="N109F0" type="main"> <s id="N109F2"><!-- NEW -->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"><!-- NEW -->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"><!-- NEW -->ille autem primus accelera­<lb/>tur per acce&longs;&longs;ionem impetus perfectionis quàm in iactu per ho­<lb/>rizontalem; </s> <s id="N10A0C"><!-- NEW -->&longs;ed imperfectionis, quàm in perpendiculo: </s> <s id="N10A10"><!-- NEW -->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> </p> <p id="N10A1A" type="main"> <s id="N10A1C"><!-- NEW -->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"><!-- NEW -->mouetur &longs;ur&longs;um per cur­<lb/>uam, &longs;empérque capiti iaculatoris imminet; </s> <s id="N10A2A"><!-- NEW -->quippe tantùm acqui­<lb/>rit in horizontali, quantùm nauis: </s> <s id="N10A30"><!-- NEW -->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"><!-- NEW -->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> </p> <p id="N10A44" type="main"> <s id="N10A46"><!-- NEW -->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> </p> <p id="N10A58" type="main"> <s id="N10A5A"><!-- NEW -->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"><!-- NEW -->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"><!-- NEW -->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"><!-- NEW -->imò &longs;agitta po&longs;&longs;et retorqueri in iaculatorem: </s> <s id="N10A7A"><!-- NEW --><lb/>&longs;i terra e&longs;&longs;et vtrimque peruia, lapis demi&longs;&longs;us per multa annorum <lb/>millia libraretur; non tamen e&longs;&longs;et motuus perpetuus. </s> </p> <figure id="id.026.01.020.1.jpg" xlink:href="026/01/020/1.jpg"/> <p id="N10A86" type="main"> <s id="N10A88"><emph type="center"/><emph type="italics"/>De motu reflexo.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p id="N10A93" type="main"> <s id="N10A95"><!-- NEW -->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"><!-- NEW -->planum refle­<lb/>ctens e&longs;t cau&longs;a nouæ determinationis &longs;uo modo; </s> <s id="N10AA1"><!-- NEW -->cau&longs;am enim di­<lb/>co eam, ex qua aliquid &longs;equitur: </s> <s id="N10AA7"><!-- NEW -->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"><!-- NEW -->quæ omnia <lb/>patent ex terminis: </s> <s id="N10AB7"><!-- NEW -->hinc nullus impetus producitur à plano refle­<lb/>ctente; </s> <s id="N10ABD"><!-- NEW -->quippe prior pote&longs;t determinari ad nouam lineam: adde, <lb/>quòd planum, quod caret impetu, impetum producere non pote&longs;t. </s> </p> <p id="N10AC3" type="main"> <s id="N10AC5"><!-- NEW -->2. Imò nihil impetus de&longs;truitur in reflexione pura per &longs;e; </s> <s id="N10AC9"><!-- NEW -->quia ni­<lb/>hil impetus e&longs;t fru&longs;trà per &longs;e in pura reflexione; </s> <s id="N10ACF"><!-- NEW -->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"><!-- NEW -->hinc &longs;uppo&longs;ito eodem iactu, perpendi­<lb/>cularis reflexa e&longs;t omnium reflexarum minima; </s> <s id="N10ADD"><!-- NEW -->quia per eam li­<lb/>neam maximus ictus infligitur; </s> <s id="N10AE3"><!-- NEW -->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> </p> <p id="N10AEF" type="main"> <s id="N10AF1"><!-- NEW -->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"><!-- NEW -->quia <lb/>alioquin anguli reflexionis non e&longs;&longs;ent æquales angulis incidentiæ: </s> <s id="N10AFD"><!-- NEW --><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"><!-- NEW -->igitur, &longs;i æqualis re&longs;i&longs;tit, & cedit, certè æqualiter ce­<lb/>dit, & re&longs;i&longs;tit: </s> <s id="N10B0C"><!-- NEW -->hinc noua determinatio æqualis e&longs;t priori: </s> <s id="N10B10"><!-- NEW -->hinc glo­<lb/>bus impactis &longs;i&longs;tit immobilis; quia ex duabus determinationibus <lb/>oppo&longs;itis neutra præualet. </s> </p> <pb xlink:href="026/01/021.jpg"/> <p id="N10B1B" type="main"> <s id="N10B1D"><!-- NEW -->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"><!-- NEW -->hinc, cùm à tota ce&longs;&longs;ione ad æqua­<lb/>litatem prædictam acquiratur tantùm noua determinato æqualis <lb/>priori; </s> <s id="N10B30"><!-- NEW -->igitur ab eadem æqualitate ad nullam ce&longs;&longs;ionem tantun­<lb/>dem acquiritur; </s> <s id="N10B36"><!-- NEW -->igitur dupla prioris, vt iam &longs;uprà dictum e&longs;t; </s> <s id="N10B3A"><!-- NEW -->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> </p> <p id="N10B42" type="main"> <s id="N10B44"><!-- NEW -->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"><!-- NEW -->quia &longs;unt hæ, vt ictus, per vtran­<lb/>que lineam; </s> <s id="N10B52"><!-- NEW -->ictus verò vt grauitationes in horizontale planum, & <lb/>in planum inclinatum, &longs;ub angulo complementi anguli incidentiæ: </s> <s id="N10B58"><!-- NEW --><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"><!-- NEW -->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> </p> <p id="N10B67" type="main"> <s id="N10B69"><!-- NEW -->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"><!-- NEW -->In puncto reflexionis, po&longs;ita hypothe&longs;i plani immo­<lb/>bilis reflectentis, nulla datur quies; </s> <s id="N10B7F"><!-- NEW -->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> </p> <p id="N10B85" type="main"> <s id="N10B87"><!-- NEW -->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"><!-- NEW -->&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"><!-- NEW -->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> </p> <p id="N10BA5" type="main"> <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"><!-- NEW -->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> </p> <p id="N10BC0" type="main"> <s id="N10BC2"><!-- NEW -->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"><!-- NEW -->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"><!-- NEW -->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"><!-- NEW -->hinc non modò nulla fit reflexio in perpendicula­<lb/>ri, &longs;ed linea directa vlteriùs propagatur; quia prior determinatio <lb/>præualet. </s> </p> <p id="N10BE2" type="main"> <s id="N10BE4"><!-- NEW -->10. Detrahitur priori portio æqualis rationi globorum; </s> <s id="N10BE8"><!-- NEW -->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"><!-- NEW -->e&longs;t &longs;ubquadruplus, vna quarta; atque ita dein­<lb/>ceps: </s> <s id="N10BF6"><!-- NEW -->ratio patet ex dictis: </s> <s id="N10BFA"><!-- NEW -->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> </p> <p id="N10C04" type="main"> <s id="N10C06"><!-- NEW -->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"><!-- NEW -->quia æqualis in æqualis æqualem impetum imprimit: </s> <s id="N10C12"><!-- NEW -->non <lb/>e&longs;t tamen motus reflexus; </s> <s id="N10C18"><!-- NEW -->quia totus prior impetus de&longs;truitur, vt <lb/>patet ex dictis: </s> <s id="N10C1E"><!-- NEW -->&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> </p> <p id="N10C2A" type="main"> <s id="N10C2C"><!-- NEW -->12. Si verò linea incidentiæ &longs;it obliqua, vterque globus reflecte­<lb/>tur pror&longs;us vt à plano immobili: </s> <s id="N10C32"><!-- NEW -->hinc reflexio &longs;it ad angulos æqua­<lb/>les, & lineæ omnes reflexionis &longs;unt æquales: ratio e&longs;t; </s> <s id="N10C38"><!-- NEW -->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> </p> <pb xlink:href="026/01/023.jpg"/> <p id="N10C49" type="main"> <s id="N10C4B"><!-- NEW -->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"><!-- NEW -->maior verò, &longs;i duplus e&longs;t alterius, &longs;i&longs;tit immobilis in puncto <lb/>contactus; </s> <s id="N10C59"><!-- NEW -->&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"><!-- NEW -->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> </p> <p id="N10C69" type="main"> <s id="N10C6B"><!-- NEW -->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"><!-- NEW -->tùm <lb/>deinde, licèt nihil pror&longs;us addatur, versùs occa&longs;um; </s> <s id="N10C77"><!-- NEW -->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"><!-- NEW -->Nullus datur propriè motus <lb/>refractus: </s> <s id="N10C87"><!-- NEW -->licèt enim incuruetur linea motus, dum per aquam &longs;u­<lb/>bit mobile; hæc tamen e&longs;t reflexionis &longs;pecies. </s> </p> <p id="N10C8D" type="main"> <s id="N10C8F"><!-- NEW -->15. Globus reflectens, qui ab ictu alterius mouetur, non mouetur <lb/>in&longs;tanti contactus; </s> <s id="N10C95"><!-- NEW -->quia impetus primo in&longs;tanti, quo e&longs;t, non mo­<lb/>uetur; </s> <s id="N10C9B"><!-- NEW -->producitur enim impetus primo in&longs;tanti contactus: </s> <s id="N10C9F"><!-- NEW -->&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"><!-- NEW -->quia veri&longs;&longs;ima cau&longs;a reflexionis <lb/>con&longs;i&longs;tit in noua determinatione: </s> <s id="N10CAD"><!-- NEW -->per reflexionem po&longs;&longs;unt colligi <lb/>plures partes aëris &longs;onori ad Echometriam: </s> <s id="N10CB3"><!-- NEW -->&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> </p> <figure id="id.026.01.023.1.jpg" xlink:href="026/01/023/1.jpg"/> <p id="N10CC0" type="main"> <s id="N10CC2"><emph type="center"/><emph type="italics"/>De motu circulari.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p id="N10CCD" type="main"> <s id="N10CCF"><!-- NEW -->1. DAri motum circularem, probatur infinitis ferè experimen­<lb/>tis: </s> <s id="N10CD5"><!-- NEW -->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"><!-- NEW -->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"><!-- NEW -->Motus circularis in &longs;ublunaribus <lb/>oritur ex recto impedito; </s> <s id="N10CE9"><!-- NEW -->quia, &longs;cilicet, determinatur tantùm im­<lb/>petus ad lineam rectam: </s> <s id="N10CEF"><!-- NEW -->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"><!-- NEW -->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> </p> <p id="N10D03" type="main"> <s id="N10D05"><!-- NEW -->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"><!-- NEW -->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"><!-- NEW -->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> </p> <p id="N10D21" type="main"> <s id="N10D23"><!-- NEW -->3. Hinc, &longs;i tollatur impedimentum, &longs;tatim per tangentem or­<lb/>bis fit motus, vt patet in funda: </s> <s id="N10D29"><!-- NEW -->inæqualiter partes radij prædicti <lb/>orbis mouentur, iuxta proportionem di&longs;tantiæ maioris, & minoris <lb/>à centro: </s> <s id="N10D31"><!-- NEW -->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"><!-- NEW -->quia, &longs;cilicet, <lb/>&longs;ingulis punctis &longs;ua tangens re&longs;pondet: </s> <s id="N10D3D"><!-- NEW -->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> </p> <p id="N10D47" type="main"> <s id="N10D49"><!-- NEW -->4 Dari impetum in motu circulari certi&longs;&longs;imum e&longs;t: </s> <s id="N10D4D"><!-- NEW -->punctum phy­<lb/>&longs;icum e&longs;t capax huius motus; cuius finis multiplex e&longs;t; </s> <s id="N10D53"><!-- NEW -->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"><!-- NEW -->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> </p> <p id="N10D67" type="main"> <s id="N10D69"><!-- NEW -->5. Motus circularis rotæ in plano verticali e&longs;t æquabilis per &longs;e; </s> <s id="N10D6D"><!-- NEW --><lb/>quia nihil e&longs;t, quod impetum &longs;emel impre&longs;&longs;um de&longs;truat: </s> <s id="N10D72"><!-- NEW -->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"><!-- NEW -->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"><!-- NEW -->quemadmodum <lb/>enim in reflexione, quæ fit à plano immobili, nullus de&longs;truitur im­<lb/>petus; </s> <s id="N10D88"><!-- NEW -->ita nullus hîc de&longs;truitur; </s> <s id="N10D8C"><!-- NEW -->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> </p> <pb xlink:href="026/01/025.jpg"/> <p id="N10D97" type="main"> <s id="N10D99"><!-- NEW -->6. Hinc per &longs;e motus circularis integri orbis e&longs;t perpetuus; </s> <s id="N10D9D"><!-- NEW -->de­<lb/>&longs;truitur tamen per accidens, &longs;cilicet, propter attritum axis: </s> <s id="N10DA3"><!-- NEW -->hinc <lb/>tam diu durat hic motus: </s> <s id="N10DA9"><!-- NEW -->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"><!-- NEW -->nec <lb/>vnquam ce&longs;&longs;aret hic motus &longs;ine prædicto attritu, & partium a&longs;peri­<lb/>tate: </s> <s id="N10DB7"><!-- NEW -->nec quidquam ob&longs;tat, quòd aliquæ partes rotæ, quæ in circu­<lb/>lo verticali voluitur, a&longs;cendant; </s> <s id="N10DBD"><!-- NEW -->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"><!-- NEW -->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> </p> <p id="N10DCF" type="main"> <s id="N10DD1"><!-- NEW -->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"><!-- NEW -->quia per &longs;e <lb/>mouetur motu æquabili: </s> <s id="N10DE7"><!-- NEW -->per accidens tamen &longs;ecus accidit; </s> <s id="N10DEB"><!-- NEW -->quippe <lb/>maior e&longs;t maioris attritus: </s> <s id="N10DF1"><!-- NEW -->dixi, cùm mouetur æquali ni&longs;u; </s> <s id="N10DF5"><!-- NEW -->nam &longs;æpè <lb/>contingit, maiore ni&longs;u potentiam motricem agere circa maiorem; </s> <s id="N10DFB"><!-- NEW --><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> </p> <p id="N10E04" type="main"> <s id="N10E06"><!-- NEW -->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"><!-- NEW -->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"><!-- NEW -->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> </p> <p id="N10E24" type="main"> <s id="N10E26"><!-- NEW -->9. Rota in plano verticali faciliùs mouetur, quàm in horizonta­<lb/>li; </s> <s id="N10E2C"><!-- NEW -->quia in illo mouetur per minimam impetus, vel potentiæ acce&longs;­<lb/>&longs;ionem; </s> <s id="N10E32"><!-- NEW -->&longs;ecùs in i&longs;to; </s> <s id="N10E36"><!-- NEW -->quippe per minimam acce&longs;&longs;ionem tollitur <lb/>æquilibrium; </s> <s id="N10E3C"><!-- NEW -->imò moueri pote&longs;t in plano verticali, licèt nullus im­<lb/>primatur impetus rotæ, v. <!-- REMOVE S-->g. <!-- REMOVE S-->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> </p> <p id="N10E4A" type="main"> <s id="N10E4C"><!-- NEW -->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> </p> <p id="N10E5E" type="main"> <s id="N10E60"><!-- NEW -->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"><!-- NEW -->hinc fortè e&longs;t, quòd mirere, impetus determinatus <lb/>deor&longs;um producit alium &longs;ur&longs;um: </s> <s id="N10E6E"><!-- NEW -->hinc impetus vnius partis mobi­<lb/>lis pote&longs;t producere &longs;imilem in alia parte continua; </s> <s id="N10E74"><!-- NEW -->quod tantùm in <lb/>hoc ca&longs;u locum habet: </s> <s id="N10E7A"><!-- NEW -->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> </p> <figure id="id.026.01.026.1.jpg" xlink:href="026/01/026/1.jpg"/> <p id="N10E87" type="main"> <s id="N10E89"><emph type="center"/><emph type="italics"/>De motu funependuli.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p id="N10E94" type="main"> <s id="N10E96"><!-- NEW -->1. FVnependulum de&longs;cendit per arcum motu naturaliter acce­<lb/>lerato: </s> <s id="N10E9C"><!-- NEW -->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"><!-- NEW -->Ratio à priori e&longs;t quia <lb/>priori impetui acqui&longs;ito nouus accedit: </s> <s id="N10EA8"><!-- NEW -->non acceleratur in eadem <lb/>proportione, in qua &longs;uprà dictum e&longs;t accelerari in linea recta; </s> <s id="N10EAE"><!-- NEW -->quia <lb/>in hac acceleratur vniformiter, id e&longs;t, æqualibus temporibus, <lb/>æqualia acquiruntur velocitatis momenta; </s> <s id="N10EB6"><!-- NEW -->quia vel e&longs;t &longs;emper ea­<lb/>dem inclinatio plani, vel idem perpendiculum: </s> <s id="N10EBC"><!-- NEW -->at verò in fune­<lb/>pendulo in &longs;ingulis punctis e&longs;t noua tangens; </s> <s id="N10EC2"><!-- NEW -->igitur noua inclina­<lb/>tio plani; igitur noua ratio motus. </s> </p> <p id="N10EC8" type="main"> <s id="N10ECA"><!-- NEW -->2. Initio acceleratur motus per maiora crementa, &longs;ub finem per mi­<lb/>nora; </s> <s id="N10ED0"><!-- NEW -->v.g. <!-- REMOVE S-->&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"><!-- NEW -->quia, vt ac­<lb/>quireret æqualem, deberet e&longs;&longs;e eadem plani inclinatio; </s> <s id="N10EDE"><!-- NEW -->&longs;ed &longs;emper <lb/>cre&longs;cit Inclinatio; </s> <s id="N10EE4"><!-- NEW -->igitur &longs;emper imminuitur impetus æquali <expan abbr="t&etilde;pore">tempore</expan> <lb/>acqui&longs;itus: </s> <s id="N10EEE"><!-- NEW -->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> </p> <p id="N10EF6" type="main"> <s id="N10EF8"><!-- NEW -->3. Hinc breuiore tempore de&longs;cendit per radium perpendicula­<lb/>rem, quàm per quadrantis arcum eiu&longs;dem radij; </s> <s id="N10EFE"><!-- NEW -->tùm quia breuior <lb/>e&longs;t linea; tùm, quia in perpendiculari acceleratur motus per maiora <lb/>crementa. </s> <s id="N10F06"><!-- NEW -->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"><!-- NEW -->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="N10F16"><!-- NEW -->dixi <lb/>ferè: </s> <s id="N10F1C"><!-- NEW -->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> </p> <p id="N10F2D" type="main"> <s id="N10F2F"><!-- NEW -->4. Non a&longs;cendit funependulum ad eam altitudinem, ex qua priùs <lb/>de&longs;cenderat: </s> <s id="N10F35"><!-- NEW -->clara e&longs;t experientia: </s> <s id="N10F39"><!-- NEW -->neque ratio tantùm petitur ab <lb/>aëris re&longs;i&longs;tentia; </s> <s id="N10F3F"><!-- NEW -->tam enim re&longs;i&longs;tit de&longs;cen&longs;ui, quàm a&longs;cen&longs;ui; </s> <s id="N10F43"><!-- NEW -->&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"><!-- NEW -->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"><!-- NEW -->hinc in maiori vibratione imminuitur motus, & &longs;patium in <lb/>maiori proportione, quàm in minori; </s> <s id="N10F59"><!-- NEW -->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> </p> <p id="N10F63" type="main"> <s id="N10F65"><!-- NEW -->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"><!-- NEW --><lb/>hinc etiam in funependulo maiori diutiùs durant huiu&longs;modi vi­<lb/>brationes, idque in arcubus paulò maioribus; </s> <s id="N10F72"><!-- NEW -->quia &longs;ubten&longs;æ his <lb/>arcubus &longs;unt inclinatiores: </s> <s id="N10F78"><!-- NEW -->hinc refutabis eos, qui dicunt, vibra­<lb/>tiones funependuli in vacuo fore perpetuas: </s> <s id="N10F7E"><!-- NEW -->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> </p> <p id="N10F88" type="main"> <s id="N10F8A"><!-- NEW -->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"><!-- NEW -->quippe e&longs;t omnium imperfecti&longs;&longs;imum; </s> <s id="N10F96"><!-- NEW -->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"><!-- NEW -->&longs;i &longs;int funependula inæqualia, vibrationes non &longs;unt æquè diu­<lb/>turnæ: ratio e&longs;t: </s> <s id="N10FA4"><!-- NEW -->quia, &longs;i a&longs;&longs;umantur, v.g. duo quadrantes inæquales, <lb/>&longs;unt eju&longs;dem inclinationis; igitur minor citiùs percurritur. </s> </p> <p id="N10FAA" type="main"> <s id="N10FAC"><!-- NEW -->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"><!-- NEW -->id e&longs;t, vt <lb/>radices &longs;patiorum &longs;imilium: </s> <s id="N10FB8"><!-- NEW -->verbi gratia, &longs;it quadruplus alterius, <lb/>tempus vibrationis maioris e&longs;t duplum temporis vibrationis mino­<lb/>ris; </s> <s id="N10FC0"><!-- NEW -->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> </p> <pb xlink:href="026/01/028.jpg"/> <p id="N10FD1" type="main"> <s id="N10FD3"><!-- NEW -->8. In maiori quadrante, circa &longs;upremam extremitatem, e&longs;t minor <lb/>inclinatio, quàm in minore; </s> <s id="N10FD9"><!-- NEW -->hic enim &longs;tatim detorquetur à perpen­<lb/>diculo, cum quo facit angulum maiorem: </s> <s id="N10FDF"><!-- NEW -->at verò circa infirmam <lb/>extremitatem, e&longs;t maior inclinatio in maiore, quàm in minore: </s> <s id="N10FE5"><!-- NEW -->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> </p> <p id="N10FF1" type="main"> <s id="N10FF3"><!-- NEW -->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"><!-- NEW -->hinc &longs;unt ijdem ictus: </s> <s id="N10FFD"><!-- NEW --><lb/>numerus, vibrationum non e&longs;t infinitus, licèt in vacuo vibraretur <lb/>funependulum; </s> <s id="N11004"><!-- NEW -->quia, cùm &longs;ingulæ imminuantur, & infinitis pun­<lb/>ctis non con&longs;tent; </s> <s id="N1100A"><!-- NEW -->tandem ad vltimam peruenitur: </s> <s id="N1100E"><!-- NEW -->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> </p> <p id="N1101A" type="main"> <s id="N1101C"><!-- NEW -->10. Funependulum in fine a&longs;cen&longs;us non quie&longs;cit vno in&longs;tanti; </s> <s id="N11020"><!-- NEW --><lb/>quia impetui innato <expan abbr="nũquam">nunquam</expan> redditur æqualis acqui&longs;itus; </s> <s id="N11029"><!-- NEW -->po&longs;ita ta­<lb/>men illa æqualitate, in&longs;tanti &longs;equenti e&longs;&longs;et quies: </s> <s id="N1102F"><!-- NEW -->funependulum <lb/>grauius citiùs de&longs;cendit; </s> <s id="N11035"><!-- NEW -->e&longs;t enim eadem ratio, quæ fuit pro mo­<lb/>tu naturali; </s> <s id="N1103B"><!-- NEW -->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> </p> <p id="N11043" type="main"> <s id="N11045">11. Ratio facilis e&longs;t; </s> <s id="N11048"><!-- NEW -->quia partes &longs;olidæ, quæ accedunt propiùs <lb/>ad extremitatem immobilem, accelerant motum aliarum, quæ <lb/>ad mobilem extremitatem accedunt; </s> <s id="N11050"><!-- NEW -->faciunt enim arcum mino­<lb/>rem: </s> <s id="N11056"><!-- NEW -->hinc a&longs;cen&longs;us non peruenit ad tantam &longs;ublimitatem; </s> <s id="N1105A"><!-- NEW -->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"><!-- NEW -->hinc citiùs quie&longs;cit hoc penduli genus, quàm <lb/>aliud: </s> <s id="N11068"><!-- NEW -->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. <!-- REMOVE S-->&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> </p> <figure id="id.026.01.028.1.jpg" xlink:href="026/01/028/1.jpg"/> <p id="N11079" type="main"> <s id="N1107B"><emph type="center"/><emph type="italics"/>De motu mixto ex circulari.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p id="N11086" type="main"> <s id="N11088"><!-- NEW -->1. ROta, quæ mouetur in &longs;uperficie plana, mouetur motu mixto <lb/>ex recto centri, & circulari orbis: </s> <s id="N1108E"><!-- NEW -->axis tantùm rotæ mouetur <lb/>motu recto: </s> <s id="N11094"><!-- NEW -->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"><!-- NEW -->punctum verò oppo&longs;itum veloci&longs;&longs;imo, quia in motu huius <lb/>rotus motus orbis additur motui centri; </s> <s id="N110A4"><!-- NEW -->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> </p> <p id="N110AC" type="main"> <s id="N110AE"><!-- NEW -->2. Hinc omnia puncta eiu&longs;dem circuli rotæ mobilis in plano <lb/>hoc motu mixto mouentur in æquali motu: </s> <s id="N110B4"><!-- NEW -->hoc etiam motu mo­<lb/>uetur globus de&longs;cendens in plano inclinato, in quo reuerâ motu <lb/>hæc habes: </s> <s id="N110BC"><!-- NEW -->primò, non modò accelerari <expan abbr="motũ">motum</expan> centri, verùm etiam <lb/>motum orbis; <expan abbr="&longs;ecũdò">&longs;ecundò</expan>, ita <expan abbr="impetũ">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> </p> <p id="N110D2" type="main"> <s id="N110D4"><!-- NEW -->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"><!-- NEW -->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"><!-- NEW -->mouetur motu mixto ex recto, & circulari: </s> <s id="N110E6"><!-- NEW -->in <lb/>hoc porrò motu præit calami caput, & &longs;equuntur pennæ; </s> <s id="N110EC"><!-- NEW -->quia aër <lb/>fortiùs re&longs;i&longs;tit pennis, quàm thecæ: hinc pennarum motum theca <lb/>grauior accelerat, cuius motum pennæ retardant. </s> </p> <p id="N110F4" type="main"> <s id="N110F6"><!-- NEW -->4. Hinc, &longs;i quando accidat, penas educi ex theca in libero medio; </s> <s id="N110FA"><!-- NEW --><lb/>&longs;tatim theca velociori motu mouetur, cùm tamen pennæ ip&longs;æ &longs;i­<lb/>&longs;tant: </s> <s id="N11101"><!-- NEW -->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> </p> <p id="N11111" type="main"> <s id="N11113"><!-- NEW -->5. Hinc motu recto prædictum iaculum in vacuo tantùm mo­<lb/>ueretur, vt patet: hinc: </s> <s id="N11119"><!-- NEW -->cùm pennæ &longs;unt explicatiores, tardiùs; </s> <s id="N1111D"><!-- NEW -->cùm <lb/>verò contractiores, velociùs mouetur, etiam motu orbis; </s> <s id="N11123"><!-- NEW -->cui non <lb/>minùs aër re&longs;i&longs;tit, in pennis, &longs;cilicet, quàm motui axis: </s> <s id="N11129"><!-- NEW -->hinc, &longs;i theca <lb/>&longs;it grauior, velociùs; </s> <s id="N1112F"><!-- NEW -->&longs;i leuior, tardiùs iaculum fertur; </s> <s id="N11133"><!-- NEW -->etiam tenera <lb/>plumarum lanugo tarditatem conciliat: </s> <s id="N11139"><!-- NEW -->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> </p> <p id="N11143" type="main"> <s id="N11145"><!-- NEW -->6. Sunt infiniti propemodum motus mixti; </s> <s id="N11149"><!-- NEW -->v. <!-- REMOVE S-->g. <!-- REMOVE S-->cylindri ab alte­<lb/>ra extremitate rotata emi&longs;&longs;i; </s> <s id="N11153"><!-- NEW -->longioris ha&longs;tæ, quæ &longs;ur&longs;um facta cir­<lb/>cuitione emittitur; </s> <s id="N11159"><!-- NEW -->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"><!-- NEW -->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"><!-- NEW -->ratio verò motus centri e&longs;t, quia adducitur funiculo vel ex­<lb/>ploditur, &longs;eu expellitur &longs;cutica: </s> <s id="N11171"><!-- NEW -->huius motus phænomena &longs;unt ferè <lb/>infinita: &longs;ingula ex no&longs;tris principiis facilè explicantur. </s> </p> <figure id="id.026.01.030.1.jpg" xlink:href="026/01/030/1.jpg"/> <p id="N1117C" type="main"> <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> </p> <p id="N11189" type="main"> <s id="N1118B"><!-- NEW -->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"><!-- NEW -->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"><!-- NEW -->quia præualeret grauitatio, porrò hic impetus pro­<lb/>ducitur tantùm à potentia motrice animantis, in &longs;ingulari organo; </s> <s id="N1119F"><!-- NEW --><lb/>non verò in aliis partibus, etiam animatis, ni&longs;i quando mouentur; </s> <s id="N111A4"><!-- NEW --><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> </p> <p id="N111B0" type="main"> <s id="N111B2"><!-- NEW -->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"><!-- NEW -->&longs;ecùs verò, &longs;i attolla­<lb/>tur: </s> <s id="N111BE"><!-- NEW -->&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"><!-- NEW -->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"><!-- NEW -->&longs;ed per acci­<lb/>dens, propter mollitiem, & ten&longs;ionem partium: </s> <s id="N111D0"><!-- NEW -->cùm verò defertur <lb/>aliquid coniunctum, producitur haud dubiè æqualis impetus; </s> <s id="N111D6"><!-- NEW -->hinc <lb/>&longs;eparari non pote&longs;t; </s> <s id="N111DC"><!-- NEW -->quia æqualis e&longs;t motus latoris, & delati: exem­<lb/>plum habes in naui. </s> </p> <p id="N111E2" type="main"> <s id="N111E4"><!-- NEW -->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"><!-- NEW -->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="tũc">tunc</expan> manui, & humero æqualiter <expan abbr="põdus">pondus</expan> di&longs;tribuitur: </s> <s id="N11203"><!-- NEW -->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> </p> <p id="N1120B" type="main"> <s id="N1120D"><!-- NEW -->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"><!-- NEW -->&longs;i chorda vtrinque trahatur, rumpetur in medio: </s> <s id="N11219"><!-- NEW -->&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"><!-- NEW -->Ratio communis i&longs;torum omnium e&longs;t: </s> <s id="N1122B"><!-- NEW -->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> </p> <p id="N11233" type="main"> <s id="N11235"><!-- NEW -->5. Vt quodlibet pondus faciliùs trahatur, &longs;inguli equi trahere <lb/>debent fune communi, potiùs quàm bigati; </s> <s id="N1123B"><!-- NEW -->quia tunc nihil ferè pe­<lb/>rit impetus: </s> <s id="N11241"><!-- NEW -->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"><!-- NEW -->e&longs;&longs;ent, quod fal&longs;um e&longs;t: </s> <s id="N1124D"><!-- NEW -->ideò currus <lb/>paulò po&longs;t initium motus faciliùs mouetur; </s> <s id="N11253"><!-- NEW -->quia aliquid impetus <lb/>priùs producti remanet: hinc etiam rupto fune, quo trahitur currus, <lb/>currus ip&longs;e modicum tempus adhuc mouetur. </s> </p> <p id="N1125B" type="main"> <s id="N1125D"><!-- NEW -->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"><!-- NEW -->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> </p> <p id="N11275" type="main"> <s id="N11277"><!-- NEW -->7. Cùm trahitur cylindrus vtrinque æqualiter, qui neque flecti, <lb/>neque tendi pote&longs;t, nullum impetum accipit; </s> <s id="N1127D"><!-- NEW -->imò in tractione nul­<lb/>lus impetus e&longs;t inutilis: </s> <s id="N11283"><!-- NEW -->brachium infligit maiorem ictum, cùm ma­<lb/>iorem <expan abbr="arcũ">arcum</expan> de&longs;cribit &longs;uo motu; </s> <s id="N1128D"><!-- NEW -->quia, &longs;cilicet, mouetur motu natu­<lb/>raliter accelerato: </s> <s id="N11293"><!-- NEW -->hinc auer&longs;a manu validior impingitur colaphus, <lb/>quàm aduer&longs;a; </s> <s id="N11299"><!-- NEW -->quia illa maiorem arcum de&longs;cribit: </s> <s id="N1129D"><!-- NEW -->hinc longius bra­<lb/>chium cæteris paribus grauiùs ferit: hinc diu qua&longs;i rotatur bra­<lb/>chium, vt longiùs mittatur lapis. </s> </p> <p id="N112A5" type="main"> <s id="N112A7"><!-- NEW -->8. Maiore fu&longs;te maior ictus infligitur; </s> <s id="N112AB"><!-- NEW -->quia potentia toto ni&longs;u <lb/>agens, diutiùs manet applicata maiori, quàm minori; </s> <s id="N112B1"><!-- NEW -->&longs;untque ictus <lb/>in ratione &longs;ubduplicata vtriu&longs;que fu&longs;tis; </s> <s id="N112B7"><!-- NEW -->v. <!-- REMOVE S-->g. <!-- REMOVE S-->fu&longs;tis pendens vnam <lb/>libram per maximum arcum impactus, infligit &longs;ubduplum ictum <lb/>alterius, quem infligit fu&longs;tis quatuor pendens libras per eundem <lb/>arcum impactus: </s> <s id="N112C5"><!-- NEW -->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> </p> <p id="N112CF" type="main"> <s id="N112D1"><!-- NEW -->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"><!-- NEW -->nec in extremitate mobili; </s> <s id="N112DF"><!-- NEW -->&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"><!-- NEW -->quia tunc totus impetus agit, <lb/>quantùm pote&longs;t; </s> <s id="N112ED"><!-- NEW -->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> </p> <p id="N112F7" type="main"> <s id="N112F9"><!-- NEW -->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"><!-- NEW -->quia non <lb/>tantùm agit impetus extrin&longs;ecùs adueniens; </s> <s id="N11305"><!-- NEW -->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> </p> <p id="N11311" type="main"> <s id="N11313"><!-- NEW -->11. Rotato flagello ideò maxima vis ine&longs;t, quia diutiùs potentia <lb/>manet applicata: </s> <s id="N11319"><!-- NEW -->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"><!-- NEW -->de malleorum ictu idem <lb/>pror&longs;us dicendum e&longs;t, quod de fu&longs;te; </s> <s id="N11325"><!-- NEW -->&longs;i autem mallei cadant <lb/>ex eadem altitudine, motu naturali accelerato, ictus &longs;unt vt <lb/>mallei, quia duplus malleus, v. <!-- REMOVE S-->g. <!-- REMOVE S-->duplum impetum acquirit: nam <lb/>&longs;ingulæ partes &longs;eor&longs;im æqualem impetum acquirunt. </s> </p> <p id="N11333" type="main"> <s id="N11335"><!-- NEW -->12. Si verò ex diuer&longs;a altitudine cadant, vel &longs;unt æquales, vel <lb/>inæquales: </s> <s id="N1133B"><!-- NEW -->&longs;i primum, ictus &longs;unt vt tempora, quibus cadunt: </s> <s id="N1133F"><!-- NEW -->&longs;i <lb/>&longs;ecundum, ictus &longs;unt in ratione compo&longs;ita temporum, & mal­<lb/>leorum: </s> <s id="N11347"><!-- NEW -->&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"><!-- NEW -->&longs;ed hoc vltimum fal­<lb/>&longs;um e&longs;&longs;e con&longs;tat; </s> <s id="N11353"><!-- NEW -->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> </p> <p id="N1135B" type="main"> <s id="N1135D"><!-- NEW -->13. Leui&longs;&longs;imi lapides vix emittuntur ad modicam di&longs;tantiam; </s> <s id="N11361"><!-- NEW --><lb/>quia &longs;tatim &longs;eparantur à potentia: </s> <s id="N11366"><!-- NEW -->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"><!-- NEW -->quia tunc totus impetus agit, totus enim impe­<lb/>ditur: </s> <s id="N11374"><!-- NEW -->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> </p> </section> </front> <body> <chap id="N1137F"> <pb pagenum="1" xlink:href="026/01/033.jpg"/> <figure id="id.026.01.033.1.jpg" xlink:href="026/01/033/1.jpg"/> <p id="N11389" type="head"> <s id="N1138B"><emph type="center"/>LIBER PRIMVS, <lb/><emph type="italics"/>DE IMPETV.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p id="N11398" type="main"> <s id="N1139A"><!-- NEW -->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 id="N113A4"><!-- NEW -->cum enim impetus &longs;it cau&longs;a <lb/>immediata motus, vt fusè demon&longs;tra­<lb/>bimus infrà; </s> <s id="N113AC"><!-- NEW -->& 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 id="N113B2"><!-- NEW -->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> </p> <p id="N113C5" type="main"> <s id="N113C7"><emph type="center"/><emph type="italics"/>DEFINITIO I.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N113D3" type="main"> <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> </p> <p id="N113E1" type="main"> <s id="N113E3"><emph type="center"/><emph type="italics"/>Definitio II.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N113EF" type="main"> <s id="N113F1"><!-- NEW --><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> </p> <pb pagenum="2" xlink:href="026/01/034.jpg"/> <p id="N113FF" type="main"> <s id="N11401"><emph type="center"/><emph type="italics"/>Definitio III.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N1140D" type="main"> <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> </p> <p id="N1141A" type="main"> <s id="N1141C"><!-- NEW -->Dico e&longs;&longs;e qualitatem &longs;iue di&longs;tincta &longs;it, &longs;iue non di&longs;tincta; </s> <s id="N11420"><!-- NEW -->quod hîc <lb/>certè non di&longs;cutio; </s> <s id="N11426"><!-- NEW -->nec enim affirmo in hac definitione dari impetum; </s> <s id="N1142A"><!-- NEW --><lb/>&longs;ed definio tantùm quid &longs;it impetus; </s> <s id="N1142F"><!-- NEW -->qui reuera aliud non e&longs;t, &longs;i e&longs;t: </s> <s id="N11433"><!-- NEW --><lb/>quippe id tantùm concipio, cum impetum appello; </s> <s id="N11438"><!-- NEW -->&longs;iue &longs;it, &longs;iue non &longs;it, <lb/>ne quis fortè initio &longs;tatim mihi litem intendat; </s> <s id="N1143E"><!-- NEW -->quemadmodum definit <lb/>circulum Geometra; </s> <s id="N11444"><!-- NEW -->licèt non a&longs;&longs;erat dari perfectum circulum; </s> <s id="N11448"><!-- NEW -->ita Phy­<lb/>&longs;icus definit impetum, quamuis non affirmet dari impetum; </s> <s id="N1144E"><!-- NEW -->quod tamen <lb/>in &longs;exto Theoremate demon&longs;trabimus; </s> <s id="N11454"><!-- NEW -->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. <!-- KEEP S--></s> </p> <p id="N1145D" type="main"> <s id="N1145F"><emph type="center"/><emph type="italics"/>Hypothe&longs;is I.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N1146B" type="main"> <s id="N1146D"><!-- NEW --><emph type="italics"/>Datur motus localis<emph.end type="italics"/>; </s> <s id="N11476"><!-- NEW -->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"><!-- NEW -->&longs;ed hoc e&longs;t moueri per Def. <!-- REMOVE S-->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> </p> <p id="N1148A" type="main"> <s id="N1148C"><!-- NEW -->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 id="N11499"><!-- NEW -->cum tamen deinde pernici&longs;&longs;imo cur&longs;u rotari demon&longs;tre­<lb/>mus; </s> <s id="N1149F"><!-- NEW -->adde alias oculorum fallacias circa motum; </s> <s id="N114A3"><!-- NEW -->&longs;ic rotata &longs;cintilla, vel <lb/>carbo accen&longs;us immotum orbem de&longs;cribere videtur; </s> <s id="N114A9"><!-- NEW -->&longs;ic nota inu&longs;ta <lb/>trocho, dum celerrimè rotatur, orbem etiam immobilem de&longs;cribere iu­<lb/>dicatur; </s> <s id="N114B1"><!-- NEW -->&longs;ic &longs;tella cadens, vel exhalatio continenti &longs;ucce&longs;&longs;ione accen&longs;a <lb/>moueri videtur; </s> <s id="N114B7"><!-- NEW -->licet minimè moueatur; </s> <s id="N114BB"><!-- NEW -->idem dicendum de puluere <lb/>tormentario, vel alia qualibet materia; quæ continuata con&longs;ecutione <lb/>accenditur; </s> <s id="N114C3"><!-- NEW -->immò trochus ip&longs;e in orbem celerrimè agitatus, quie&longs;cere <lb/>videtur; </s> <s id="N114C9"><!-- NEW -->&longs;ic qui vertigine laborant, ea moueri exi&longs;timant, quæ quie&longs;cunt; </s> <s id="N114CD"><!-- NEW --><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 id="N114D4"><!-- NEW --><lb/>&longs;ic eorum quæ motu æquali feruntur, remotiora tardiùs moueri viden­<lb/>tur; </s> <s id="N114DB"><!-- NEW -->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> </p> <p id="N114E5" type="main"> <s id="N114E7"><!-- NEW -->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"><!-- NEW -->attamen &longs;i rectè oculus admoueatur, iu&longs;ta di&longs;tantià, nec vllum &longs;it <lb/>impedimentum exterius nec interius; </s> <s id="N114F3"><!-- NEW -->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"><!-- NEW -->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 id="N11506"><!-- NEW -->&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> </p> <p id="N11510" type="main"> <s id="N11512"><!-- NEW -->Porrò quod &longs;pectat ad fallacias illas quæ &longs;upra adductæ &longs;unt; </s> <s id="N11516"><!-- NEW -->certum <lb/>e&longs;t vel obiectum e&longs;&longs;e remotius, quam par &longs;it; </s> <s id="N1151C"><!-- NEW -->vel moueri celeriùs, vel <lb/>e&longs;&longs;e aliquod impedimentum interius; </s> <s id="N11522"><!-- NEW -->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> </p> <p id="N1152A" type="main"> <s id="N1152C"><!-- NEW -->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> </p> <p id="N11536" type="main"> <s id="N11538"><!-- NEW -->Prima duci pote&longs;t à fine motus; </s> <s id="N1153C"><!-- NEW -->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 id="N11544"><!-- NEW -->&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"><!-- NEW -->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="N11552"><!-- NEW --><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"><!-- NEW -->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> </p> <p id="N11561" type="main"> <s id="N11563"><!-- NEW -->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> </p> <p id="N1156B" type="main"> <s id="N1156D"><!-- NEW -->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> </p> <p id="N11573" type="main"> <s id="N11575"><!-- NEW -->Quarta petitur à termino motus; </s> <s id="N11579"><!-- NEW -->cum enim globus proiectus &longs;it in <lb/>nouo loco in quo ante non erat; </s> <s id="N1157F"><!-- NEW -->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> </p> <p id="N11587" type="main"> <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> </p> <p id="N1158E" type="main"> <s id="N11590"><!-- NEW -->Sexta ab ip&longs;a Mechanica, quæ organa motui mini&longs;trat: </s> <s id="N11594"><!-- NEW -->quis enim ne­<lb/>garet maius momentum e&longs;&longs;e cum maiori di&longs;tantiâ coniunctum; </s> <s id="N1159A"><!-- NEW -->&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> </p> <p id="N115A9" type="main"> <s id="N115AB"><emph type="center"/><emph type="italics"/>Hypothe&longs;is II.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N115B7" type="main"> <s id="N115B9"><!-- NEW --><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 id="N115C9"><!-- NEW -->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"><!-- NEW -->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="N115D9">Secundò maximum incommodum e&longs;&longs;et, &longs;i res &longs;e­<lb/>mel mota perpetuò moueretur. </s> <s id="N115DE"><!-- NEW -->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> </p> <p id="N115E8" type="main"> <s id="N115EA"><!-- NEW -->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> </p> <p id="N115F2" type="main"> <s id="N115F4"><!-- NEW -->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> </p> <p id="N115FC" type="main"> <s id="N115FE">Dices iuxta hypothe&longs;im Heraclidis Pontici, terra ip&longs;a, Sol etiam, & <lb/>&longs;tellæ mouentur. </s> <s id="N11603"><!-- NEW -->Re&longs;pondeo primò hypothe&longs;im illam e&longs;&longs;e fal&longs;am, vt &longs;uo <lb/>loco videbimus; </s> <s id="N11609"><!-- NEW -->&longs;ecundò etiam data illa hypothe&longs;i po&longs;&longs;et dari quies; </s> <s id="N1160D"><!-- NEW -->&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> </p> <p id="N1161B" type="main"> <s id="N1161D"><!-- NEW -->Quod verò &longs;pectat ad fallacias oculi circa quietem; </s> <s id="N11621"><!-- NEW -->eodem 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> </p> <p id="N1162B" type="main"> <s id="N1162D"><emph type="center"/><emph type="italics"/>Hypothe&longs;is III.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N11639" type="main"> <s id="N1163B"><emph type="italics"/>Aliquid mouetur quod incœpit moueri.<emph.end type="italics"/></s> <s id="N11642"><!-- NEW --> Video lapidem quie&longs;centem, <lb/>qui deinde proiectus mouetur; </s> <s id="N11648"><!-- NEW -->igitur ante non mouebatur, igitur cum <lb/>deinde mouetur, cœpit moueri; mille aliis experimentis hæc hypothe­<lb/>&longs;is confirmari pote&longs;t. </s> </p> <p id="N11650" type="main"> <s id="N11652"><emph type="center"/><emph type="italics"/>Hypothe&longs;is IV.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N1165E" type="main"> <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 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> </p> <p id="N11671" type="main"> <s id="N11673"><emph type="center"/><emph type="italics"/>Hypothe&longs;is V.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N1167F" type="main"> <s id="N11681"><emph type="italics"/>Idem mouetur modò tardiùs, modò velociùs.<emph.end type="italics"/></s> <s id="N11688"><!-- NEW --> Video rotatum globum, <lb/>qui &longs;en&longs;im quie&longs;cit: &longs;entio ab eodem globo modò maiorem, modò mi­<lb/>norem ictum infligi, &c. </s> <s id="N11690">igitur e&longs;t certa hypothe&longs;is. </s> </p> <pb pagenum="5" xlink:href="026/01/037.jpg"/> <p id="N11697" type="main"> <s id="N11699"><emph type="center"/><emph type="italics"/>Hypothe&longs;is VI.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N116A5" type="main"> <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> </p> <p id="N116B0" type="main"> <s id="N116B2"><emph type="center"/><emph type="italics"/>Hypothe&longs;is VII.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N116BE" type="main"> <s id="N116C0"><emph type="italics"/>Corpus proiectum, & in aliud impactum illud ip&longs;um impellit, & mouet.<emph.end type="italics"/></s> </p> <p id="N116C7" type="main"> <s id="N116C9"><emph type="center"/><emph type="italics"/>Hypothe&longs;is VIII.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N116D5" type="main"> <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> </p> <p id="N116E7" type="main"> <s id="N116E9"><emph type="center"/><emph type="italics"/>Axioma I.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N116F5" type="main"> <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 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> </p> <p id="N11705" type="main"> <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> </p> <p id="N1170F" type="main"> <s id="N11711">2. <emph type="italics"/>Quodlibet e&longs;t, vel non est.<emph.end type="italics"/></s> </p> <p id="N11719" type="main"> <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> </p> <p id="N11725" type="main"> <s id="N11727"><emph type="center"/><emph type="italics"/>Axioma II.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N11733" type="main"> <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 id="N1173E"><!-- NEW --> Nihil enim a &longs;e ip&longs;o &longs;eparari po&longs;t; </s> <s id="N11742"><!-- NEW -->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 id="N1174A"><!-- NEW -->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 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> </p> <p id="N1175E" type="main"> <s id="N11760"><!-- NEW -->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> </p> <p id="N1176C" type="main"> <s id="N1176E"><emph type="center"/><emph type="italics"/>Axioma III.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N1177A" type="main"> <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 id="N11785"><!-- NEW --> 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"><!-- NEW -->illud porrò argumentum <lb/>duci pote&longs;t vel ab experimento certo; </s> <s id="N11791"><!-- NEW -->&longs;ic probo exi&longs;tere rem aliquam, <lb/>quam video; vel ab aliqua ratione; </s> <s id="N11797"><!-- NEW -->&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 id="N1179D"><!-- NEW -->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"><!-- NEW -->vel demùm ex aliqua reuelatione certa in rebus fidei; </s> <s id="N117B0"><!-- NEW -->igitur hoc <lb/>Axioma certum e&longs;t phy&longs;icè; </s> <s id="N117B6"><!-- NEW -->quod ni&longs;i recipiatur à Philo&longs;ophis; </s> <s id="N117BA"><!-- NEW -->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 cœlo, &c. </s> <s id="N117C4"><!-- NEW --><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> </p> <p id="N117D3" type="main"> <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> </p> <p id="N117DF" type="main"> <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> </p> <p id="N117E9" type="main"> <s id="N117EB"><emph type="center"/><emph type="italics"/>Axioma IV.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N117F7" type="main"> <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> </p> <p id="N11802" type="main"> <s id="N11804"><!-- NEW -->Hoc Axioma explicatione modicâ indiget: </s> <s id="N11808"><!-- NEW -->Determinatum illud <lb/>apello, quod illud ip&longs;um e&longs;t, quod e&longs;t, & nihil aliud; </s> <s id="N1180E"><!-- NEW -->quod e&longs;t hoc, id <lb/>e&longs;t ab omni alio di&longs;tinctum; </s> <s id="N11814"><!-- NEW -->atqui quidquid productum e&longs;t, &longs;ingulare <lb/>e&longs;t, id e&longs;t, e&longs;t hoc; </s> <s id="N1181A"><!-- NEW -->&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"><!-- NEW --><lb/>Aliquis fortè &longs;tatim opponet mihi partes indeterminatas quantitatis: </s> <s id="N11825"><!-- NEW -->&longs;ed <lb/>pro&longs;ectò nulla pars actu e&longs;t quæ non &longs;it hæc, & non alia; </s> <s id="N1182B"><!-- NEW -->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. <!-- KEEP S--></s> <s id="N11836"><!-- NEW -->Dices aliquid po&longs;&longs;e e&longs;&longs;e nullibi; </s> <s id="N1183A"><!-- NEW -->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> </p> <p id="N11844" type="main"> <s id="N11846"><emph type="center"/><emph type="italics"/>Axioma V.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N11852" type="main"> <s id="N11854"><emph type="italics"/>Quod vnum e&longs;t, determinatum e&longs;t.<emph.end type="italics"/></s> <s id="N1185B"><!-- NEW --> Quia quod vnum e&longs;t, e&longs;t hoc, & <lb/>nihil aliud; </s> <s id="N11861"><!-- NEW -->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 id="N11867"><!-- NEW -->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"><!-- NEW -->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> </p> <p id="N11877" type="main"> <s id="N11879"><emph type="center"/><emph type="italics"/>Axioma VI.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N11885" type="main"> <s id="N11887"><emph type="italics"/>Quidquid e&longs;t, fru&longs;trà non e&longs;t.<emph.end type="italics"/></s> <s id="N1188E"><!-- NEW --> 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"><!-- NEW -->finem autem rei ex ip&longs;o v&longs;u cogno­<lb/>&longs;cimus; </s> <s id="N1189C"><!-- NEW -->v&longs;um verò ip&longs;o ferè &longs;en&longs;u: </s> <s id="N118A0"><!-- NEW -->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"><!-- NEW -->&longs;i &longs;ub&longs;tantia, vel <lb/>incorporea, vel corporea; </s> <s id="N118AC"><!-- NEW -->&longs;i incorporea, vel e&longs;t Deus, vel Angelus, vel <pb pagenum="7" xlink:href="026/01/039.jpg"/>Anima rationalis; </s> <s id="N118B5"><!-- NEW -->atqui nihil horum fru&longs;trà e&longs;t, vt con&longs;tat; </s> <s id="N118B9"><!-- NEW -->&longs;i corporea, <lb/>vel e&longs;t corpus, vel forma; </s> <s id="N118BF"><!-- NEW -->&longs;i corpus, vel elementum, vel mixtum; </s> <s id="N118C3"><!-- NEW --><lb/>vtrumque &longs;uum finem habet, & con&longs;tantem v&longs;um; </s> <s id="N118C8"><!-- NEW -->&longs;i forma quamdiu <lb/>e&longs;t principium actionum compo&longs;iti fru&longs;trà non e&longs;t; </s> <s id="N118CE"><!-- NEW -->quippe ad cum finem <lb/>e&longs;t in&longs;tituta; </s> <s id="N118D4"><!-- NEW -->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"><!-- NEW -->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 id="N118E0"><!-- NEW -->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"><!-- NEW -->vtramque rationem &longs;uo loco fu­<lb/>sè demon&longs;trabimus; </s> <s id="N118EE"><!-- NEW -->&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"><!-- NEW -->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 id="N118FC"><!-- NEW -->&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"><!-- NEW -->Igitur tunc effet fru&longs;trà accidens, cum &longs;uo illo effectu careret; </s> <s id="N11908"><!-- NEW --><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"><!-- NEW -->&longs;ed non e&longs;t huius loci: cùm verò audis fi­<lb/>nem: </s> <s id="N11917"><!-- NEW -->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> </p> <p id="N1191F" type="main"> <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> </p> <p id="N1192B" type="main"> <s id="N1192D"><!-- NEW -->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 id="N11938">tot in&longs;ecta? </s> <s id="N1193B">& vermiculi: </s> <s id="N1193E"><!-- NEW -->Re&longs;pondeo <lb/>quamlibet &longs;tellam, quodlibet in&longs;ectum, &longs;eu vermiculum &longs;uis pollere pro­<lb/>prietatibus; </s> <s id="N11946"><!-- NEW -->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 id="N1194C"><!-- NEW -->quod <lb/>enim dices de vna, dicam de omnibus; </s> <s id="N11952"><!-- NEW -->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> </p> <p id="N1195A" type="main"> <s id="N1195C"><emph type="center"/><emph type="italics"/>Axioma VII.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N11968" type="main"> <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> </p> <p id="N11978" type="main"> <s id="N1197A"><!-- NEW -->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"><!-- NEW -->atqui formam &longs;ub&longs;tantialem &longs;en&longs;u <lb/>non percipis immediatè; </s> <s id="N11988"><!-- NEW -->igitur aliquem eius effectum &longs;en&longs;ibilem vel me­<lb/>diatè, vel immediatè; </s> <s id="N1198E"><!-- NEW -->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 id="N11994"><!-- NEW -->&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> </p> <p id="N119A1" type="main"> <s id="N119A3"><!-- NEW -->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 id="N119AF"><!-- NEW -->quod ita in­<lb/>telligi non debet, vt &longs;ine gutta aquæ Oceanus, &longs;ine &longs;tella cœlum, &longs;ine gra­<lb/>nulo arenæ terra, &longs;ine altero oculorum homo &longs;tare non po&longs;&longs;int; </s> <s id="N119B7"><!-- NEW -->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> </p> <p id="N119C3" type="main"> <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> </p> <p id="N119CA" type="main"> <s id="N119CC"><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N119D8" type="main"> <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> </p> <p id="N119E1" type="main"> <s id="N119E3">Primum certum e&longs;t etiam certitudine metaphy&longs;ica, &longs;eu geometrica. </s> <s id="N119E6"><lb/>Secundum, Quartum, & Quintum per Primum demon&longs;trari po&longs;&longs;unt. </s> <s id="N119EA"><!-- NEW --><lb/>Tertium e&longs;t veluti communis po&longs;itio, &longs;eu commune po&longs;tulatum, in quo <lb/>docti omnes conunciunt; </s> <s id="N119F1"><!-- NEW -->quippe nihil &longs;ine ratione dici debet à philo&longs;o­<lb/>pho; </s> <s id="N119F7"><!-- NEW -->Sextum & Septimum probari po&longs;&longs;unt per Tertium; &longs;ed iam ad <lb/>alia, quæ propiùs ad phy&longs;icam accedunt, veniamus. </s> </p> <p id="N119FD" type="main"> <s id="N119FF"><emph type="center"/><emph type="italics"/>Axioma VIII.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N11A0B" type="main"> <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 id="N11A14"><!-- NEW --> Id e&longs;t quid­<lb/>quid incipit e&longs;&longs;e ab alio e&longs;t; </s> <s id="N11A1A"><!-- NEW -->quippe à &longs;e e&longs;&longs;e non pote&longs;t; </s> <s id="N11A1E"><!-- NEW -->nihil enim à &longs;e <lb/>ip&longs;o dependere pote&longs;t &longs;eu produci; </s> <s id="N11A24"><!-- NEW -->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 id="N11A2C"><!-- NEW -->præterea quidquid produci­<lb/>tur aliquando producitur, & alicubi, vt certi&longs;&longs;imum e&longs;t; </s> <s id="N11A32"><!-- NEW -->&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 id="N11A3C"><!-- NEW -->Igitur &longs;i aliquid &longs;e producit; cur hîc potiùs quam illîc? </s> <s id="N11A40">cur <lb/>nunc potius quam antè? </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"><!-- NEW -->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 id="N11A52"><!-- NEW -->&longs;ufficit modò habere phy&longs;icam, quod ex om­<lb/>nibus hypothe&longs;ibus demon&longs;tratur; </s> <s id="N11A58"><!-- NEW -->&longs;i enim aliquid de nouo produci­<lb/>tur, quod certum e&longs;t, ab alio produci video: </s> <s id="N11A5E"><!-- NEW -->calor ab igne mediatè <lb/>vel immediatè, impetus à potentia motrice, vel ab alio impetu: </s> <s id="N11A64"><!-- NEW -->cuncta <lb/>hæc &longs;i reuera producuntur de quo alibi, ab alio produci con&longs;tat; </s> <s id="N11A6A"><!-- NEW -->in Me­<lb/>taphy&longs;ica hoc ip&longs;um geometricè demon&longs;trabimus; </s> <s id="N11A70"><!-- NEW -->cum enim agere &longs;up­<lb/>ponat e&longs;&longs;e; </s> <s id="N11A76"><!-- NEW -->quippe omnis actio alicuius agentis e&longs;t; </s> <s id="N11A7A"><!-- NEW -->& 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> </p> <pb pagenum="9" xlink:href="026/01/041.jpg"/> <p id="N11A8B" type="main"> <s id="N11A8D"><emph type="center"/><emph type="italics"/>Axioma IX.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N11A99" type="main"> <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 id="N11AA5"><!-- NEW -->quia agere <lb/>&longs;upponit e&longs;&longs;e; </s> <s id="N11AAB"><!-- NEW -->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. <!-- KEEP S--></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 id="N11ABC"><!-- NEW -->nihil enim videmus agere, ni&longs;i quod e&longs;t; </s> <s id="N11AC0"><!-- NEW -->&longs;i enim age­<lb/>ret quod non e&longs;t; cur potius hîc, & nunc quam alibi, & aliàs? </s> <s id="N11AC6">cur in <lb/>hoc &longs;ubiecto potius quàm in alio? </s> </p> <p id="N11ACB" type="main"> <s id="N11ACD"><!-- NEW -->Dices, finis qui non e&longs;t influit; </s> <s id="N11AD1"><!-- NEW -->igitur agit; </s> <s id="N11AD5"><!-- NEW -->Re&longs;pondeo finem non <lb/>agere, nec influere ni&longs;i obiectiuè; </s> <s id="N11ADB"><!-- NEW -->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"><!-- NEW -->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> </p> <p id="N11AEB" type="main"> <s id="N11AED"><!-- NEW -->Dices, cau&longs;a principalis pulli exclu&longs;i pote&longs;t non e&longs;&longs;e; </s> <s id="N11AF1"><!-- NEW -->hæc omnia di­<lb/>&longs;cutiemus &longs;uo loco cum de generatione animalium; </s> <s id="N11AF7"><!-- NEW -->&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> </p> <p id="N11AFF" type="main"> <s id="N11B01"><emph type="center"/><emph type="italics"/>Axioma X.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N11B0D" type="main"> <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"><!-- NEW --> 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"><!-- NEW -->quidquid &longs;it, certum e&longs;t phy&longs;icè; nec enim ignis, qui e&longs;t <lb/>Romæ, calefacit Lugduni. </s> </p> <p id="N11B24" type="main"> <s id="N11B26"><!-- NEW -->Dices dari fortè actionem in di&longs;tans; </s> <s id="N11B2A"><!-- NEW -->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"><!-- NEW -->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> </p> <p id="N11B3C" type="main"> <s id="N11B3E"><!-- NEW -->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"><!-- NEW -->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> </p> <p id="N11B4E" type="main"> <s id="N11B50"><!-- NEW -->Dices etiam partes interiores cau&longs;æ v. <!-- REMOVE S-->g. <!-- REMOVE S-->Solis agunt, &longs;ed non agunt <lb/>per totum medium; alioquin agerent in alias partes Solis, à quibus <lb/>obteguntur. </s> <s id="N11B5C"><!-- NEW -->Re&longs;pondeo, diffu&longs;ionem vel propagationem actionis in­<lb/>choari tantum ab ipsâ &longs;uperficie Solis; </s> <s id="N11B62"><!-- NEW -->quippe omnes partes agunt <lb/>actione communi, de quo infrà; atqui actio communis à communi me­<lb/>dio incipit. </s> </p> <p id="N11B6A" type="main"> <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> </p> <p id="N11B73" type="main"> <s id="N11B75"><!-- NEW -->Re&longs;pondeo, ignem quidem accendi in data di&longs;tantia; </s> <s id="N11B79"><!-- NEW -->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 id="N11B82"><!-- NEW -->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="N11B8C">e </s> </p> <p id="N11B8F" type="main"> <s id="N11B91"><emph type="center"/><emph type="italics"/>Axioma XI.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N11B9D" type="main"> <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 id="N11BA8"><!-- NEW --> 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. <!-- REMOVE S-->g. <!-- REMOVE S-->calor e&longs;t cau&longs;a &longs;ufficiens caloris, vt con&longs;tat in aqua calida; </s> <s id="N11BB4"><!-- NEW --><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 id="N11BBB"><!-- NEW -->dicendum e&longs;t calorem illum ab hoc produ­<lb/>ci; </s> <s id="N11BC1"><!-- NEW -->cum calor &longs;it cau&longs;a nece&longs;&longs;aria; </s> <s id="N11BC5"><!-- NEW -->igitur &longs;i &longs;it applicatus &longs;ubjecto apto, <lb/>nece&longs;&longs;ariò agit; </s> <s id="N11BCB"><!-- NEW -->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> </p> <p id="N11BD1" type="main"> <s id="N11BD3"><!-- NEW -->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"><!-- NEW -->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 id="N11BE5"><!-- NEW -->v. <!-- REMOVE S-->g. <!-- REMOVE S-->ex <lb/>applicatione aquæ calidæ &longs;equitur productio caloris; </s> <s id="N11BEF"><!-- NEW -->ex applicatione &longs;o­<lb/>lius aquæ non &longs;equitur; </s> <s id="N11BF5"><!-- NEW -->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> </p> <p id="N11BFD" type="main"> <s id="N11BFF"><!-- NEW -->Dices non e&longs;&longs;e certum calorem produci; Re&longs;pondeo, negando; </s> <s id="N11C03"><!-- NEW -->&longs;ed, <lb/>quidquid &longs;it, loquor tantùm hypotheticè; dixi enim &longs;i producatur, à <lb/>calore aquæ inhærente producitur. </s> </p> <p id="N11C0B" type="main"> <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 id="N11C12"><!-- NEW -->Re&longs;pondeo, hoc reuera geometricè non probari, &longs;ed <lb/>tantùm phy&longs;icè; </s> <s id="N11C18"><!-- NEW -->quidquid &longs;it, voco cau&longs;am id, ex cuius applicatione <lb/>&longs;equitur &longs;emper effectus, & nunquam aliàs; </s> <s id="N11C1E"><!-- NEW -->nam phy&longs;icè loquendo, &longs;iue <lb/>&longs;it alia cau&longs;a, &longs;iue non, eodem 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> </p> <p id="N11C26" type="main"> <s id="N11C28"><emph type="center"/><emph type="italics"/>Axioma XII.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N11C34" type="main"> <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"><!-- NEW --> Hoc Axioma duas partes habet; </s> <s id="N11C43"><!-- NEW -->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"><!-- NEW -->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="N11C51"><!-- NEW --><lb/>nam &longs;i vnam partem effectus omittat; cur vnam potiùs quam aliam? </s> <s id="N11C56"><lb/>cur non duas? </s> <s id="N11C5A">cur non omnes? </s> <s id="N11C5D">denique video cau&longs;am eandem eidem <lb/>&longs;ubiecto eodem modo applicatam, eundem &longs;emper effectum producere <lb/>per Hyp. <!-- REMOVE S-->8. </s> </p> <p id="N11C66" type="main"> <s id="N11C68"><emph type="center"/><emph type="italics"/>Axioma XIII<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N11C74" type="main"> <s id="N11C76"><emph type="italics"/>Exten&longs;io cau&longs;a non intendit effectum ad intra.<emph.end type="italics"/></s> <s id="N11C7D"><!-- NEW --> 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> </p> <p id="N11C8D" type="main"> <s id="N11C8F">Dixi ad intra; </s> <s id="N11C92"><!-- NEW -->quia ad extra multum iuuat exten&longs;io; </s> <s id="N11C96"><!-- NEW -->&longs;ic maior ignis <lb/>longiùs diffundit &longs;uum calorem; </s> <s id="N11C9C"><!-- NEW -->corpus grauiùs cadens majorem ictum <lb/>infligit; Ad hoc Axioma reuocatur i&longs;tud. </s> </p> <p id="N11CA2" type="main"> <s id="N11CA4"><!-- NEW -->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"><!-- NEW -->ad quam diffundit coniunctum cum aliis; </s> <s id="N11CB8"><!-- NEW -->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> </p> <p id="N11CC3" type="main"> <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> </p> <p id="N11CCD" type="main"> <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> </p> <p id="N11CD9" type="main"> <s id="N11CDB"><!-- NEW -->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"><!-- NEW -->&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> </p> <p id="N11CEC" type="main"> <s id="N11CEE"><emph type="center"/><emph type="italics"/>Axioma XIV.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N11CFA" type="main"> <s id="N11CFC"><emph type="italics"/>Quidquid de&longs;truitur non e&longs;t à &longs;e.<emph.end type="italics"/></s> <s id="N11D03"><!-- NEW --> Hoc Axioma geometricum e&longs;t; </s> <s id="N11D07"><!-- NEW -->Quod <lb/>enim e&longs;t à &longs;e, nece&longs;&longs;ariò e&longs;t; </s> <s id="N11D0D"><!-- NEW -->cùm à libertate &longs;eu voluntate alterius non <lb/>pendeat; </s> <s id="N11D13"><!-- NEW -->cum enim primo in&longs;tanti quo res e&longs;t, non &longs;it à &longs;e per Axiom. <!-- REMOVE S-->8. <lb/>de &longs;ecundo idem dici debet, quod de primo, vt patet: </s> <s id="N11D1B"><!-- NEW -->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"><!-- NEW -->&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> </p> <p id="N11D29" type="main"> <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"><!-- NEW -->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="N11D3A"><!-- NEW -->quæ omnia fusè <lb/>in Metaphy&longs;ica demon&longs;trabimus; </s> <s id="N11D40"><!-- NEW -->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 id="N11D46"><!-- NEW -->&longs;i &longs;ecundum ab alio e&longs;t: <lb/>quidquid &longs;it, hoc Axioma certum e&longs;t phy&longs;icè. </s> </p> <p id="N11D4C" type="main"> <s id="N11D4E">Huc reuoca Axiomata &longs;equentia, quæ ex hoc vno deducuntur. </s> </p> <p id="N11D51" type="main"> <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> </p> <p id="N11D5D" type="main"> <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"><!-- NEW --> Hoc etiam ex hypothe&longs;ibus &longs;equitur; </s> <s id="N11D6D"><!-- NEW -->cum <lb/>enim de&longs;trui &longs;it idem ac de&longs;inere con&longs;eruari; </s> <s id="N11D73"><!-- NEW -->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> </p> <p id="N11D7B" type="main"> <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> </p> <pb pagenum="12" xlink:href="026/01/044.jpg"/> <p id="N11D8D" type="main"> <s id="N11D8F"><emph type="center"/><emph type="italics"/>Axioma XV.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N11D9B" type="main"> <s id="N11D9D"><emph type="italics"/>Contraria pugnant pro rata.<emph.end type="italics"/></s> <s id="N11DA4"><!-- NEW --> Nec enim alia regula e&longs;&longs;e pote&longs;t; </s> <s id="N11DA8"><!-- NEW -->&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 id="N11DB6">v.g. <!-- REMOVE S-->&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 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 id="N11DD0"><!-- NEW -->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"><!-- NEW -->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="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> </p> <p id="N11DE3" type="main"> <s id="N11DE5">Ob&longs;eruabis hæc Axiomata &longs;altem maiori ex parte e&longs;&longs;e metaph. </s> <s id="N11DE8">quæ <lb/>nos fusè in Theorematis metaph. </s> <s id="N11DED"><!-- NEW -->explicabimus, & demon&longs;trabimus; </s> <s id="N11DF1"><!-- NEW -->&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> </p> <p id="N11DFB" type="main"> <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> </p> <p id="N11E02" type="main"> <s id="N11E04"><emph type="center"/><emph type="italics"/>Postulatum,<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N11E10" type="main"> <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> </p> <p id="N11E1B" type="main"> <s id="N11E1D"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 1.<emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N11E2A" type="main"> <s id="N11E2C"><emph type="italics"/>Motus e&longs;t aliquid realiter di&longs;tinctum à mobili.<emph.end type="italics"/></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"><!-- NEW -->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 id="N11E3E"><!-- NEW -->igi­<lb/>tur à motu &longs;eparatum; </s> <s id="N11E44"><!-- NEW -->igitur realiter di&longs;tinctum per Ax. 2. præterea <lb/>moueri, & non moueri &longs;unt prædicata contradictoria, vt con&longs;tat; </s> <s id="N11E4A"><!-- NEW -->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"><!-- NEW -->alioquin &longs;imul e&longs;&longs;ent; </s> <s id="N11E56"><!-- NEW -->igitur alterum illorum e&longs;t di&longs;tinctum à <lb/>mobili; </s> <s id="N11E5C"><!-- NEW -->non quies, vt con&longs;tat, quæ e&longs;t tantùm negatio motus, &longs;eu per­<lb/>&longs;euerantia in eodem loco; </s> <s id="N11E62"><!-- NEW -->igitur nullam dicit mutationem; at verò <lb/>motus mutationem dicit, per Def. <!-- REMOVE S-->1. hoc Theorema fusè demon&longs;trabo <lb/>in Metaph. <!-- KEEP S--></s> </p> <p id="N11E6D" type="main"> <s id="N11E6F"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 2.<emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N11E7C" type="main"> <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 id="N11E8A"><!-- NEW -->Motus e&longs;t mutatio, &longs;eu tran&longs;itus ex loco <lb/>in locum per Def. <!-- REMOVE S-->1. &longs;ed mutatio propriè non producitur; </s> <s id="N11E92"><!-- NEW -->quippè pro­<lb/>ductio tantùm terminatur ad ens; </s> <s id="N11E98"><!-- NEW -->nihil enim ni&longs;i ens produci pote&longs;t; </s> <s id="N11E9C"><!-- NEW --><pb pagenum="13" xlink:href="026/01/045.jpg"/>atqui nulla mutatio dicit tantùm ens; </s> <s id="N11EA4"><!-- NEW -->præ&longs;ertim hæc, quæ tantùm dicit <lb/>terminum à quo, ide&longs;t locum relictum; </s> <s id="N11EAA"><!-- NEW -->& terminum ad quem, id e&longs;t lo­<lb/>cum immediatum acqui&longs;itum; </s> <s id="N11EB0"><!-- NEW -->nam &longs;eparato quocunque alio ab ip&longs;o <lb/>mobili; </s> <s id="N11EB6"><!-- NEW -->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 id="N11EBE"><!-- NEW -->illud autem e&longs;t motus, qui certè non <lb/>dicit tantùm locum relictum &longs;ine acqui&longs;ito; </s> <s id="N11EC4"><!-- NEW -->alioqui &longs;i mobile de&longs;true­<lb/>retur, diceretur moueri; </s> <s id="N11ECA"><!-- NEW -->nec etiam locum acqui&longs;itum &longs;ine priori relicto: </s> <s id="N11ECE"><!-- NEW --><lb/>alioqui &longs;i mobile primò produceretur, diceretur moueri localiter; </s> <s id="N11ED3"><!-- NEW -->igitur <lb/>motus neutrum dicit &longs;eor&longs;im; &longs;i primum, diceretur de&longs;tructus; </s> <s id="N11ED9"><!-- NEW -->&longs;i &longs;ecun­<lb/>dum, diceretur aliquo modo productus, vel potiùs acqui&longs;itus; </s> <s id="N11EDF"><!-- NEW -->at vtrum­<lb/>que coniunctim, &longs;imulque e&longs;&longs;entialiter dicit motus; </s> <s id="N11EE5"><!-- NEW -->nec enim conci­<lb/>pio aliud, dum concipio motum: </s> <s id="N11EEB"><!-- NEW -->porrò vtrumque &longs;imul &longs;umptum indi­<lb/>ui&longs;ibiliter non pote&longs;t dici, vel de&longs;tructum propriè, vel productum; Di­<lb/>xi propriè; nam impropriè dici pote&longs;t motus productus. </s> </p> <p id="N11EF4" type="main"> <s id="N11EF6"><!-- NEW -->Dices Motus e&longs;t ens, non à &longs;e; igitur ab alio; igitur motus e&longs;t pro­<lb/>ductus. </s> <s id="N11EFC"><!-- NEW -->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"><!-- NEW --><lb/>quòd certè non pote&longs;t dici propriè productum, &longs;ed re&longs;ultans, vt relatio; </s> <s id="N11F07"><!-- NEW --><lb/>nam producatur, &longs;i fieri pote&longs;t; </s> <s id="N11F0C"><!-- NEW -->certè e&longs;t aliquid, quod tam facilè de­<lb/>&longs;trui pote&longs;t, quam produci; </s> <s id="N11F12"><!-- NEW -->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> </p> <p id="N11F1C" type="main"> <s id="N11F1E"><!-- NEW -->Dices potentia motrix e&longs;t actiua; </s> <s id="N11F22"><!-- NEW -->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> </p> <p id="N11F2F" type="main"> <s id="N11F31"><!-- NEW -->Nec e&longs;t quod aliqui ita mirentur hæc à me dici; </s> <s id="N11F35"><!-- NEW -->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 id="N11F3D"><!-- NEW -->&longs;ed qua&longs;i re&longs;ultent ab exigentia; v. <!-- REMOVE S-->g. <!-- REMOVE S-->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> </p> <p id="N11F49" type="main"> <s id="N11F4B"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 3.<emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N11F58" type="main"> <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"><!-- NEW --> Demon&longs;tratur, quia <lb/>motus, qui non erat, incipit e&longs;&longs;e per hypothe&longs;im tertiam; &longs;ed quod <lb/>huiu&longs;modi e&longs;t, habet cau&longs;am di&longs;tinctam per Ax.8. <!-- KEEP S--></s> </p> <p id="N11F6A" type="main"> <s id="N11F6C"><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N11F78" type="main"> <s id="N11F7A"><!-- NEW -->Ob&longs;eruabis motum localem e&longs;&longs;e duplicis generis; </s> <s id="N11F7E"><!-- NEW -->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"><!-- NEW -->cum etiam &longs;ine motu defatigetur, vt cum <lb/>quis alium pellit, à quo pellitur æquali ni&longs;u; </s> <s id="N11F8E"><!-- NEW -->patet etiam in manu &longs;u­<lb/>&longs;tinente aliquod pondus, quæ non mouetur; </s> <s id="N11F94"><!-- NEW -->licet reuerâ etiam &longs;ummo <pb pagenum="14" xlink:href="026/01/046.jpg"/>conatu agat: </s> <s id="N11F9D"><!-- NEW -->immò &longs;i potentia motrix produceret motum primum, non <lb/>impetum in corpore proiecto; </s> <s id="N11FA3"><!-- NEW -->nulla deinde e&longs;&longs;et cau&longs;a applicata ad pro­<lb/>ducendum impetum: </s> <s id="N11FA9"><!-- NEW -->Itaque hic motus primi generis, &longs;i comparetur <lb/>cum potentia motrice, e&longs;t verè influxus, vel actio; </s> <s id="N11FAF"><!-- NEW -->&longs;i cum termino, e&longs;t <lb/>eius fieri, &longs;eu dependentia; </s> <s id="N11FB5"><!-- NEW -->&longs;i cum &longs;ubiecto, &longs;eu mobili e&longs;t pa&longs;&longs;io; </s> <s id="N11FB9"><!-- NEW -->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="N11FC3"><!-- NEW -->Motus &longs;ecundi generis e&longs;t mutatio, &longs;eu tran&longs;itus ex <lb/>vno loco in alium; </s> <s id="N11FC9"><!-- NEW -->hoc e&longs;t finis, vel effectus formalis &longs;ecundarius, <lb/>quem exigit impetus; </s> <s id="N11FCF"><!-- NEW -->& 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> </p> <p id="N11FD9" type="main"> <s id="N11FDB"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 4.<emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N11FE8" type="main"> <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"><!-- NEW --> Sic calor exigit rarefactionem, vel <lb/>re&longs;olutionem, impetus motum; </s> <s id="N11FFB"><!-- NEW -->cum enim non &longs;it cau&longs;a efficiens per Th. <!-- REMOVE S--><lb/>2. &longs;it tamen cau&longs;a per Th.3. nec &longs;it materialis, nec finalis, vt con&longs;tat, de­<lb/>bet e&longs;&longs;e formalis, vel exigens, &longs;eu exigitiua; </s> <s id="N12004"><!-- NEW -->vt patet ex ip&longs;a cau&longs;arum <lb/>enumeratione; </s> <s id="N1200A"><!-- NEW -->non e&longs;t materialis, quia non recipit motum, ni&longs;i ab alio; </s> <s id="N1200E"><!-- NEW --><lb/>nec finalis, quæ &longs;upponit alias; cum ip&longs;a non &longs;it dum ponitur <lb/>effectus. </s> </p> <p id="N12015" type="main"> <s id="N12017"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 5.<emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N12024" type="main"> <s id="N12026"><!-- NEW --><emph type="italics"/>Entitas &longs;eu &longs;ubstantia mobilis non e&longs;t cau&longs;a immediata motus,<emph.end type="italics"/> Sit enim <lb/>lapis proiectus per Po&longs;tul. <!-- REMOVE S-->haud dubiè &longs;ub&longs;tantia lapidis non e&longs;t cau&longs;a <lb/>huius motus; </s> <s id="N12035"><!-- NEW -->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"><!-- NEW -->igitur &longs;emper cau&longs;aret per Ax.12. præ­<lb/>terea potentia motrix proiicientis verè agit, cum etiam defatigetur; </s> <s id="N12041"><!-- NEW -->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"><!-- NEW -->quia primò <lb/>non defatigaretur exigendo; </s> <s id="N12051"><!-- NEW -->&longs;ecundò quia lapis &longs;eparatus à manu etiam <lb/>mouetur, &longs;ed non ad exigentiam potentiæ motricis, vt patet; </s> <s id="N12057"><!-- NEW -->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> </p> <p id="N1205F" type="main"> <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 id="N1206B"><!-- NEW -->quæro quid &longs;it prima illa pars motus; </s> <s id="N1206F"><!-- NEW -->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 id="N12077"><!-- NEW -->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> </p> <pb pagenum="15" xlink:href="026/01/047.jpg"/> <p id="N12085" type="main"> <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"><!-- NEW -->Re&longs;p. negando, tùm quia omnis potentia motrix <lb/>agit; </s> <s id="N12094"><!-- NEW -->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> </p> <p id="N1209E" type="main"> <s id="N120A0"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 6.<emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N120AD" type="main"> <s id="N120AF"><emph type="italics"/>Datur impetus.<emph.end type="italics"/></s> <s id="N120B6"><!-- NEW --> 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> </p> <p id="N120C2" type="main"> <s id="N120C4"><!-- NEW -->Demon&longs;tro primò dari impetum: </s> <s id="N120C8"><!-- NEW -->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 id="N120D0"><!-- NEW -->igitur habet cau&longs;am, &longs;ed non aliam, quam impetum, quod pro­<lb/>bo: </s> <s id="N120D6"><!-- NEW -->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 id="N120DE"><!-- NEW -->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> </p> <p id="N120E6" type="main"> <s id="N120E8"><!-- NEW -->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> </p> <p id="N120F2" type="main"> <s id="N120F4">Secundò probatur; potentia motrix e&longs;t actiua, quia defatigatur, quis <lb/>hoc neget? </s> <s id="N120F9"><!-- NEW -->igitur aliquid producit; </s> <s id="N120FD"><!-- NEW -->non motum, qui propriè non pro­<lb/>ducitur per Th.2. igitur aliquid aliud; voco impetum; </s> <s id="N12103"><!-- NEW -->adde quod etiam <lb/>&longs;ine motu agit, & defatigatur vt iam dictum e&longs;t; </s> <s id="N12109"><!-- NEW -->igitur habet alium effe­<lb/>ctum immediatum; denique mouere, pellere, trahere, proiicere, percu­<lb/>tere, nihil ni&longs;i actionem &longs;onant. </s> </p> <p id="N12111" type="main"> <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 id="N1211A"><!-- NEW --><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. <!--neuer Satz-->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"><!-- NEW -->ad primam in­<lb/>&longs;tantiam Th 5. igitur aliquid aliud; voco impetum. </s> </p> <p id="N1212B" type="main"> <s id="N1212D">Quartò probatur; </s> <s id="N12130"><!-- NEW -->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="N12136"><!-- NEW -->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"><!-- NEW -->&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"><!-- NEW -->ergo e&longs;t alia cau&longs;a præ&longs;ens, quæ mi­<lb/>nuitur; voco impetum. </s> </p> <p id="N1214F" type="main"> <s id="N12151"><!-- NEW -->Quintò corpus graue deor&longs;um cadens accelerat &longs;uum motum, vt patet <lb/>experientia; </s> <s id="N12157"><!-- NEW -->quæ maximè clara e&longs;t in funependulis, de qua in &longs;equen­<lb/>tibus libris; </s> <s id="N1215D"><!-- NEW -->igitur debet e&longs;&longs;e cau&longs;a huius motus velocioris; </s> <s id="N12161"><!-- NEW -->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"><!-- NEW -->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> </p> <p id="N12173" type="main"> <s id="N12175"><!-- NEW -->Diceret fortè alius hæc omnia e&longs;&longs;e dubia; </s> <s id="N12179"><!-- NEW -->nam fieri pote&longs;t vt Deus <lb/>tantùm moueat; </s> <s id="N1217F"><!-- NEW -->quod &longs;ine impetu fieri po&longs;&longs;e certum e&longs;t; </s> <s id="N12183"><!-- NEW -->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="N1218F"><!-- NEW -->adde quod Deus, vt auctor naturæ <lb/>e&longs;t, agit tantùm; </s> <s id="N12195"><!-- NEW -->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> </p> <p id="N1219D" type="main"> <s id="N1219F"><!-- NEW -->Dicerent alij hoc totum prouenire à corpu&longs;culis; </s> <s id="N121A3"><!-- NEW -->vel atomis, vel fila­<lb/>mentis &longs;ine vlla actione; </s> <s id="N121A9"><!-- NEW -->equidem non reiicio corpu&longs;cula, & perennia <lb/>corporum effluuia: </s> <s id="N121AF"><!-- NEW -->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="N121B5"><!-- NEW --><lb/>immò maximam &longs;uarum partium partem; </s> <s id="N121BA"><!-- NEW -->igitur cum deinde proiicitur <lb/>idem globus, illæ partes mouentur; </s> <s id="N121C0"><!-- NEW -->dari igitur debet cau&longs;a huius motus <lb/>per Ax.8, igitur impetus: </s> <s id="N121C6"><!-- NEW -->nec dicas moueri illas partes à corpu&longs;culis; </s> <s id="N121CA"><!-- NEW -->quia <lb/>antè erant eadem, immò plura corpu&longs;cula; </s> <s id="N121D0"><!-- NEW -->& tamen non mouebant: </s> <s id="N121D4"><!-- NEW -->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"><!-- NEW -->vel enim mutantur, vel non mutantur; </s> <s id="N121E0"><!-- NEW -->&longs;ecundum dici <lb/>non pote&longs;t; </s> <s id="N121E6"><!-- NEW -->quia vt excitentur, ex non excitatis mutari debent; igitur <lb/>per aliquid: </s> <s id="N121EC"><!-- NEW -->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> </p> <p id="N121F6" type="main"> <s id="N121F8"><!-- NEW -->Dico &longs;ecundò minimum ex his corpu&longs;culis non &longs;emper moueri; </s> <s id="N121FC"><!-- NEW -->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> </p> <p id="N12209" type="main"> <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> </p> <p id="N12214" type="main"> <s id="N12216"><!-- NEW -->Diceret aliquis lapidem impul&longs;um ab aëre deinde propelli; </s> <s id="N1221A"><!-- NEW -->&longs;ed aër po­<lb/>tius re&longs;i&longs;tit motui; vt con&longs;tat experientiâ; &longs;ed hoc &longs;oluemus infrà. </s> </p> <pb pagenum="17" xlink:href="026/01/049.jpg"/> <p id="N12224" type="main"> <s id="N12226"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 7.<emph.end type="center"/></s> </p> <p id="N12232" type="main"> <s id="N12234"><emph type="italics"/>Impetus est aliquid distinctum à &longs;ubstantiâ mobilis.<emph.end type="italics"/></s> <s id="N1223B"> Demon&longs;tratur. </s> <s id="N1223E"><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. <!-- REMOVE S-->3. & Th. 6. de eodem contradictoria dici <lb/>non po&longs;&longs;unt per Ax. 1. n. </s> <s id="N12248"><!-- NEW -->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. <!-- KEEP S--></s> <s id="N12251">4. igitur e&longs;t di&longs;tinctus per Ax. 2. <!-- KEEP S--></s> </p> <p id="N12255" type="main"> <s id="N12257"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 8.<emph.end type="center"/></s> </p> <p id="N12263" type="main"> <s id="N12265"><!-- NEW --><emph type="italics"/>Impetus est accidens<emph.end type="italics"/>; </s> <s id="N1226E"><!-- NEW -->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="N12276">& ex Hypoth. <!-- KEEP S--></s> <s id="N1227A"><!-- NEW -->3. & 4. igitur di&longs;tingui­<lb/>tur à motu; </s> <s id="N12280"><!-- NEW -->igitur & ab impetu per Ax. 2. igitur impetus non e&longs;t &longs;ub­<lb/>&longs;tantia; igitur accidens. </s> </p> <p id="N12286" type="main"> <s id="N12288"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 9.<emph.end type="center"/></s> </p> <p id="N12294" type="main"> <s id="N12296"><emph type="italics"/>Impetus non e&longs;t modus.<emph.end type="italics"/></s> <s id="N1229D"><!-- NEW --> Modus duplicis generis e&longs;&longs;e pote&longs;t: </s> <s id="N122A1"><!-- NEW -->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 id="N122AB"><!-- NEW -->Modus &longs;ecundi generis non <lb/>e&longs;t entitas quidem di&longs;tincta; </s> <s id="N122B1"><!-- NEW -->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="N122B7"><!-- NEW -->His po&longs;itis Impetus non e&longs;t mo­<lb/>dus primi generis; </s> <s id="N122BD"><!-- NEW -->nihil enim probat impetum e&longs;&longs;e modum, quod etiam <lb/>non probet calorem, & lucem e&longs;&longs;e modos; </s> <s id="N122C3"><!-- NEW -->dicere autem omnia acci­<lb/>dentia e&longs;&longs;e modos non debemus, de quo &longs;uo loco; </s> <s id="N122C9"><!-- NEW -->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; </s> <s id="N122D1"><!-- NEW -->v. <!-- REMOVE S-->g. <!-- REMOVE S-->actio non pote&longs;t concipi ni&longs;i &longs;it <lb/>alicuius actio; </s> <s id="N122DB"><!-- NEW -->nec fieri &longs;ine facto; </s> <s id="N122DF"><!-- NEW -->nec via &longs;ine termino; </s> <s id="N122E3"><!-- NEW -->nec dependen­<lb/>tia &longs;ine dependente; </s> <s id="N122E9"><!-- NEW -->at verò po&longs;&longs;um concipere calorem, & impetum <lb/>&longs;ine alio, quod &longs;it actu; </s> <s id="N122EF"><!-- NEW -->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="N122F7"><!-- NEW --><lb/>quod exigunt, hoc e&longs;t &longs;ine &longs;uo &longs;ine; </s> <s id="N122FC"><!-- NEW -->igitur &longs;ine &longs;ubiecto; </s> <s id="N12300"><!-- NEW -->non e&longs;t etiam <lb/>modus &longs;ecundi generis vt patet, &longs;ed de modis in Metaphy&longs;ica; vix enim <lb/>hoc Theorema ad rem Phy&longs;icam quicquam facit. </s> </p> <p id="N12308" type="main"> <s id="N1230A"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 10.<emph.end type="center"/></s> </p> <p id="N12316" type="main"> <s id="N12318"><emph type="italics"/>Impetus e&longs;t qualitas Phy&longs;ica.<emph.end type="italics"/><!-- KEEP S--></s> <s id="N12320"> Sequitur ex dictis; cum nec &longs;it motus. </s> <s id="N12323"><!-- NEW --><lb/>nec &longs;ub&longs;tantia, nec modus, nec quidquam negatiuum, alioquin exige­<lb/>ret; </s> <s id="N1232A"><!-- NEW -->igitur e&longs;t aliud accidens; vocetur qualitas. </s> </p> <p id="N1232E" type="main"> <s id="N12330"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 11.<emph.end type="center"/></s> </p> <p id="N1233C" type="main"> <s id="N1233E"><emph type="italics"/>Impetus est qualitas Phy&longs;ica.<emph.end type="italics"/><!-- KEEP S--></s> <s id="N12346"> 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. <!-- KEEP S--></s> <s id="N1234C"><!-- NEW -->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> </p> <pb pagenum="18" xlink:href="026/01/050.jpg"/> <p id="N12358" type="main"> <s id="N1235A"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 12.<emph.end type="center"/></s> </p> <p id="N12366" type="main"> <s id="N12368"><emph type="italics"/>Impetus est qualitas permanens.<emph.end type="italics"/></s> <s id="N1236F"><!-- NEW --> Quia lapis proiectus etiam &longs;eparatus <lb/>mouetur aliquandiu per Hyp. <!-- REMOVE S-->6. igitur durat eius cau&longs;a, &longs;cilicet impe­<lb/>tus; igitur e&longs;t qualitas permanens. </s> </p> <p id="N12379" type="main"> <s id="N1237B"><!-- NEW -->Diceret fortè aliquis lapidem proiectum pelli ab aëre à tergo in&longs;tan­<lb/>te, vt voluit Ari&longs;toteles pluribus in locis; </s> <s id="N12381"><!-- NEW -->&longs;ed præ&longs;ertim 8. Ph.c.vlt.& 7. <lb/>cap.2. 3.de Cœlo, cap. 3. Re&longs;pondeo hoc dici non po&longs;&longs;e; </s> <s id="N12387"><!-- NEW -->Primò quia non <lb/>modò non iuuat aër; </s> <s id="N1238D"><!-- NEW -->&longs;ed etiam impedit motum proiecti, quod de omni <lb/>medio nece&longs;&longs;ariò dicendum e&longs;t, vt patet experientiâ; </s> <s id="N12393"><!-- NEW -->vnde quo cra&longs;&longs;ius, <lb/>&longs;eu den&longs;ius e&longs;t <expan abbr="mediũ">medium</expan>, motum potentiùs retardat, vt videmus in proiectis <lb/>per aquam; </s> <s id="N1239F"><!-- NEW -->rationem à priori afferemus infrà, cum de re&longs;i&longs;tentia medij: </s> <s id="N123A3"><!-- NEW --><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="N123AC"><!-- NEW -->Tertiò, an fortè aër id præ­<lb/>&longs;tare pote&longs;t &longs;ine vi impre&longs;&longs;a; </s> <s id="N123B2"><!-- NEW -->igitur non minus ip&longs;i pilæ proiectæ, quam <lb/>aëri ambienti imprimi poterit: </s> <s id="N123B8"><!-- NEW -->Quartò, nullus aër à tergo pellitur; </s> <s id="N123BC"><!-- NEW -->&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="N123C6"><!-- NEW -->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> </p> <p id="N123CE" type="main"> <s id="N123D0"><!-- NEW -->Ad id quod obiicitur ex Ari&longs;totele; </s> <s id="N123D4"><!-- NEW -->aliqui putant inclina&longs;&longs;e in cam &longs;en­<lb/>tentiam; </s> <s id="N123DA"><!-- NEW -->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 id="N123E2"><!-- NEW -->l. <!-- REMOVE S-->7. Phy&longs;. cap. 2. Aliqui excu&longs;ant ip&longs;um Ari&longs;torelem, putantque <lb/>non e&longs;&longs;e locutum ex propriâ &longs;ententiâ: </s> <s id="N123EA"><!-- NEW -->Alij dicunt Ari&longs;totelem quidem <lb/>tribui&longs;&longs;e aliquam vim extrin&longs;ecam aëri; </s> <s id="N123F0"><!-- NEW -->non tamen nega&longs;&longs;e intrin&longs;ecam <lb/>impetus; </s> <s id="N123F6"><!-- NEW -->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> </p> <p id="N1240C" type="main"> <s id="N1240E"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 13.<emph.end type="center"/></s> </p> <p id="N1241A" type="main"> <s id="N1241C"><emph type="italics"/>Impetus non producit motum.<emph.end type="italics"/></s> <s id="N12423"><!-- NEW --> Probatur, quia motus non dicitur pro­<lb/>ductus per Th. 2. Adde &longs;i vis rationem metaphy&longs;icam; </s> <s id="N12429"><!-- NEW -->quia nihil cogit <lb/>dicere accidens aliquod, ex iis &longs;cilicet, quæ &longs;en&longs;u percipimus, agere ad <lb/>intra; </s> <s id="N12431"><!-- NEW -->quod videtur e&longs;&longs;e proprium &longs;ub&longs;tantiæ, &longs;altem naturaliter; vt <lb/>demon&longs;trabimus in Metaph. <!-- KEEP S--></s> </p> <p id="N12438" type="main"> <s id="N1243A"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 14.<emph.end type="center"/></s> </p> <p id="N12446" type="main"> <s id="N12448"><!-- NEW --><emph type="italics"/>Impetus exigit motum, id est fluxum mobilis in loco<emph.end type="italics"/>; </s> <s id="N12451"><!-- NEW -->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; </s> <s id="N1245D"><!-- NEW -->quæ vel e&longs;t localis, hoc e&longs;t fluxus quidam: </s> <s id="N12461"><!-- NEW --><pb pagenum="19" xlink:href="026/01/051.jpg"/>per &longs;patium loci; </s> <s id="N12469"><!-- NEW -->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="N1246F"><!-- NEW -->vel <lb/>demùm mutant &longs;en&longs;ibilem &longs;tatum; </s> <s id="N12475"><!-- NEW -->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="N1247D">&c. </s> <s id="N12480">de quibus aliàs. </s> </p> <p id="N12483" type="main"> <s id="N12485"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 15.<emph.end type="center"/></s> </p> <p id="N12491" type="main"> <s id="N12493"><emph type="italics"/>Motus e&longs;t effectus formalis &longs;ecundarius impetus.<emph.end type="italics"/></s> <s id="N1249A"><!-- NEW --> Cum enim &longs;it cau&longs;a <lb/>exigens per Th. 121. Voco effectum formalem &longs;ecundarium, quem in <lb/>mobili exigit impetus; </s> <s id="N124A2"><!-- NEW -->quippe, vt iam dictum e&longs;t, cau&longs;a exigens redu­<lb/>citur ad formalem; </s> <s id="N124A8"><!-- NEW -->nec enim cau&longs;at aliquid producendo, quod &longs;pectat ad <lb/>efficientem; </s> <s id="N124AE"><!-- NEW -->nec mouendo, quod &longs;pectat ad finalem; </s> <s id="N124B2"><!-- NEW -->nec determinando, <lb/>quod &longs;pectat ad obiectiuam; </s> <s id="N124B8"><!-- NEW -->nec recipiendo, quod &longs;pectat ad materia­<lb/>lem; </s> <s id="N124BE"><!-- NEW -->nec dirigendo, quod &longs;pectat ad idæalem, vel exemplarem; &longs;ed <lb/>exigendo; </s> <s id="N124C4"><!-- NEW -->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; </s> <s id="N124CA"><!-- NEW -->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> </p> <p id="N124D2" type="main"> <s id="N124D4"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 16.<emph.end type="center"/></s> </p> <p id="N124E0" type="main"> <s id="N124E2"><emph type="italics"/>Motus e&longs;t finis intrin&longs;ecus impetus.<emph.end type="italics"/></s> <s id="N124E9"><!-- NEW --> Dum finem audis intrin&longs;ecum, <lb/>cogita quæ&longs;o aliquid phy&longs;icum; </s> <s id="N124EF"><!-- NEW -->e&longs;t enim id, propter quod talis, vel ta­<lb/>lis forma in&longs;tituta e&longs;t: </s> <s id="N124F5"><!-- NEW -->quid enim aliud e&longs;&longs;e pote&longs;t; </s> <s id="N124F9"><!-- NEW -->finem enim rerum <lb/>naturalium ex ip&longs;o v&longs;u cogno&longs;cimus; </s> <s id="N124FF"><!-- NEW -->immò idem e&longs;t finis cum ip&longs;o v&longs;u; </s> <s id="N12503"><!-- NEW --><lb/>cum igitur impetus illum tantùm v&longs;um habeat, quem in ip&longs;o mobili <lb/>præ&longs;tare cernimus, &longs;cilicet motum; </s> <s id="N1250A"><!-- NEW -->dicendum e&longs;t motum e&longs;&longs;e finem in­<lb/>trin&longs;ecum impetus; </s> <s id="N12510"><!-- NEW -->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="N12518"><!-- NEW -->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="N12522">Dixi mediatè, vel immediatè; </s> <s id="N12525"><!-- NEW -->num <lb/>reuera datur fortè aliquis impetus, vt dicemus infrà; </s> <s id="N1252B"><!-- NEW -->&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> </p> <p id="N12533" type="main"> <s id="N12535"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 17.<emph.end type="center"/></s> </p> <p id="N12541" type="main"> <s id="N12543"><emph type="italics"/>Ni&longs;i e&longs;&longs;et motus non e&longs;&longs;et impetus.<emph.end type="italics"/></s> <s id="N1254A"><!-- NEW --> 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; </s> <s id="N12552"><!-- NEW -->igitur non e&longs;&longs;et, vt patet, igitur non e&longs;&longs;et; </s> <s id="N12556"><!-- NEW -->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; </s> <s id="N12562"><!-- NEW -->quia ni&longs;i po&longs;&longs;ibilis e&longs;­<lb/>&longs;et motus deor&longs;um nulla e&longs;&longs;et grauitatio; </s> <s id="N12568"><!-- NEW -->quippe grauitare e&longs;t dcor­<lb/>&longs;um inclinari, motumque inclinationis impediri; </s> <s id="N1256E"><!-- NEW -->hinc dicemus <pb pagenum="20" xlink:href="026/01/052.jpg"/>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="N12579">immò dicemus infrà primo in&longs;tanti, <lb/>quo e&longs;t impetus, nondum e&longs;&longs;e motum. </s> </p> <p id="N1257E" type="main"> <s id="N12580"><!-- NEW -->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> </p> <p id="N12588" type="main"> <s id="N1258A"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 18.<emph.end type="center"/></s> </p> <p id="N12596" type="main"> <s id="N12598"><emph type="italics"/>Ni&longs;i e&longs;&longs;et impetus, non e&longs;&longs;et naturaliter motus.<emph.end type="italics"/></s> <s id="N1259F"><!-- NEW --> 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; </s> <s id="N125A9"><!-- NEW -->&longs;iue &longs;it naturalis in grauibus, & leuibus, &longs;iue &longs;it vitalis <lb/>in viuentibus; </s> <s id="N125AF"><!-- NEW -->&longs;iue &longs;it media in compre&longs;&longs;is, & dilatatis; &longs;iue alia quæli­<lb/>bet: </s> <s id="N125B5"><!-- NEW -->&longs;ed omnis potentia motrix e&longs;t actiua, quia mouet; </s> <s id="N125B9"><!-- NEW -->ergo agit, &longs;ed <lb/>motum non producit per Th. 2. Igitur impetum, qui deinde exigit mo­<lb/>tum per Th. 14. Dixi naturaliter; </s> <s id="N125C1"><!-- NEW -->quia non e&longs;t dubium, quin Deus &longs;ine <lb/>impetu aliquo modo mouere po&longs;&longs;it; </s> <s id="N125C7"><!-- NEW -->ide&longs;t, facere &longs;ine impetu, vt corpus <lb/>mutet locum: </s> <s id="N125CD"><!-- NEW -->nec dicas Deum non po&longs;&longs;e &longs;upplere vices cau&longs;æ formalis; </s> <s id="N125D1"><!-- NEW --><lb/>nam concedo id quidem pro effectu formali primario; </s> <s id="N125D6"><!-- NEW -->nec enim Deus <lb/>pote&longs;t facere, vt aliquid &longs;it calidum &longs;ine calore; </s> <s id="N125DC"><!-- NEW -->cum e&longs;&longs;e calidum &longs;it <lb/>idem, ac e&longs;&longs;e habens calorem; </s> <s id="N125E2"><!-- NEW -->id tamen nego pro effectu &longs;ecundario, <lb/>quem &longs;cilicet cau&longs;a formalis exigit: </s> <s id="N125E8"><!-- NEW -->Etenim &longs;icut pote&longs;t &longs;ummo iure non <lb/>&longs;atisfacere exigentiæ; </s> <s id="N125EE"><!-- NEW -->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 id="N125FA"><!-- NEW -->quanquam vt verum fatear non e&longs;&longs;et propriè motus, &longs;ed <lb/>qua&longs;i continuæ reproductionis modus; </s> <s id="N12600"><!-- NEW -->nam motus dicit aliquam pa&longs;­<lb/>&longs;ionem; &longs;cilicet actum entis in potentiâ, vt aiunt. </s> </p> <p id="N12606" type="main"> <s id="N12608"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 19.<emph.end type="center"/></s> </p> <p id="N12614" type="main"> <s id="N12616"><!-- NEW --><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; </s> <s id="N12621"><!-- NEW -->quia nullus impetus exigeret; </s> <s id="N12625"><!-- NEW -->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> </p> <p id="N1262F" type="main"> <s id="N12631"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 20.<emph.end type="center"/></s> </p> <p id="N1263D" type="main"> <s id="N1263F"><!-- NEW --><emph type="italics"/>Corpus illud æquali &longs;emper motu ferretur per &longs;e<emph.end type="italics"/>; </s> <s id="N12648"><!-- NEW -->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; </s> <s id="N1264E"><!-- NEW -->igitur idem <lb/>effectus per Axioma 12. igitur idem, vel æqualis motus: dixi per &longs;e pro­<lb/>pter diuer&longs;um medium. </s> </p> <p id="N12656" type="main"> <s id="N12658"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 21.<emph.end type="center"/></s> </p> <p id="N12664" type="main"> <s id="N12666"><emph type="italics"/>Si e&longs;&longs;et aliquod corpus e&longs;&longs;entialiter mobile, impetu non indigeret.<emph.end type="italics"/></s> <s id="N1266D"> Probatur; </s> <s id="N12670"><!-- NEW --><lb/>quia in tantum indiget mobile impetu vt impetus exigat motum; </s> <s id="N12675"><!-- NEW -->&longs;ed <lb/>corpus illud per &longs;uam e&longs;&longs;entiam exigeret motum; </s> <s id="N1267B"><!-- NEW -->igitur non indigeret <lb/>impetu; </s> <s id="N12681"><!-- NEW -->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 pagenum="21" xlink:href="026/01/053.jpg"/>cau&longs;a extrin&longs;eca acciperet. </s> </p> <p id="N1268C" type="main"> <s id="N1268E"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 22.<emph.end type="center"/></s> </p> <p id="N1269A" type="main"> <s id="N1269C"><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 id="N126A3"> 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> </p> <p id="N126AA" type="main"> <s id="N126AC"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 23.<emph.end type="center"/></s> </p> <p id="N126B8" type="main"> <s id="N126BA"><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 id="N126C1"> 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> </p> <p id="N126C8" type="main"> <s id="N126CA"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 24.<emph.end type="center"/></s> </p> <p id="N126D6" type="main"> <s id="N126D8"><!-- NEW --><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; </s> <s id="N126E2"><!-- NEW -->quia impetus in eo non e&longs;&longs;et fru&longs;trà; haberet enim <lb/>&longs;uum effectum formalem, & finem intrin&longs;ecum. </s> <s id="N126E8">Probatur 2.pars; </s> <s id="N126EB"><!-- NEW -->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> </p> <p id="N126F3" type="main"> <s id="N126F5"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 25.<emph.end type="center"/></s> </p> <p id="N12701" type="main"> <s id="N12703"><emph type="italics"/>Omne corpus finitum e&longs;t capax motus, & impetus.<emph.end type="italics"/></s> <s id="N1270A"> Probatur 1. pars; </s> <s id="N1270D"><!-- NEW --><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="N12714"><!-- NEW -->Dices fortè quia affixum e&longs;&longs;et e&longs;&longs;entialiter tali, vel tali lo­<lb/>co, &longs;ed contra; </s> <s id="N1271A"><!-- NEW -->quia de&longs;truantur omnia, præter ip&longs;um corpus; certè <lb/>nulli affixum manet. </s> <s id="N12720">Dices &longs;patio imaginario; apage i&longs;tas nugas: <lb/>de i&longs;to &longs;patio plura demon&longs;trabimus in Metaphy. <!-- KEEP S--></s> <s id="N12726">Probatur 2. pars; </s> <s id="N12729"><!-- NEW -->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> </p> <p id="N12731" type="main"> <s id="N12733"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 26.<emph.end type="center"/></s> </p> <p id="N1273F" type="main"> <s id="N12741"><emph type="italics"/>Quod durat tantùm vno in&longs;tanti, e&longs;t incapax motus, & impetus.<emph.end type="italics"/></s> <s id="N12748"><!-- NEW --> Pro­<lb/>batur, quia non e&longs;t moueri, ni&longs;i relinquat locum, & acquirat alium; </s> <s id="N1274E"><!-- NEW -->&longs;ed <lb/>1. acquirere locum, e&longs;t 1. e&longs;&longs;e in illo loco; </s> <s id="N12754"><!-- NEW -->& relinquere locum e&longs;t, <lb/>1. non e&longs;&longs;e in eo loco; </s> <s id="N1275A"><!-- NEW -->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; </s> <s id="N12760"><!-- NEW -->& phy­<lb/>&longs;icè certum e&longs;t ex omni hypothe&longs;i; </s> <s id="N12766"><!-- NEW -->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; </s> <s id="N1276E"><!-- NEW -->&longs;ed quod durat <lb/>tantùm in in&longs;tanti, non habet antè, neque po&longs;t; </s> <s id="N12774"><!-- NEW -->igitur quod durat tan­<lb/>tùm vno in&longs;tanti, moueri non pote&longs;t; </s> <s id="N1277A"><!-- NEW -->igitur e&longs;t incapax motus; igitur <lb/>& impetus. </s> </p> <p id="N12780" type="main"> <s id="N12782"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 27.<emph.end type="center"/></s> </p> <p id="N1278E" type="main"> <s id="N12790"><!-- NEW --><emph type="italics"/>Deus e&longs;t incapax motus, & impetus<emph.end type="italics"/>: </s> <s id="N12799"><!-- NEW -->Tum quia vbique, e&longs;t igitur <lb/>nouum locum acquirere non pote&longs;t; </s> <s id="N1279F"><!-- NEW -->igitur nec moueri per Definitio­<lb/>nem 1. tùm quia æternitas Dei tota &longs;imul e&longs;t; </s> <s id="N127A5"><!-- NEW -->igitur nec fuit antè, ne­<lb/>que po&longs;t in ca; </s> <s id="N127AB"><!-- NEW -->igitur non pote&longs;t dici antè habui&longs;&longs;e locum, quo nunc <lb/>caret: </s> <s id="N127B1"><!-- NEW -->& nunc non habere illum quo caret; </s> <s id="N127B5"><!-- NEW -->tùm quia immutabilitas <pb pagenum="22" xlink:href="026/01/054.jpg"/>Dei hoc prohibet; </s> <s id="N127BE"><!-- NEW -->nam moueri, e&longs;t affici intrin&longs;ecè; </s> <s id="N127C2"><!-- NEW -->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="N127CC"><!-- NEW -->præterea &longs;i &longs;unt, &longs;unt e&longs;&longs;entia­<lb/>liter immobiles; </s> <s id="N127D2"><!-- NEW -->igitur valet &longs;emper ratio allata; </s> <s id="N127D6"><!-- NEW -->igitur Deus e&longs;t inca­<lb/>pax motus; igitur & impetus. </s> </p> <p id="N127DC" type="main"> <s id="N127DE"><!-- NEW -->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="N127E4"><!-- NEW -->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; </s> <s id="N127EC"><!-- NEW -->atqui &longs;i e&longs;t immen&longs;us, non pote&longs;t mutari intrin&longs;ecè per motum; </s> <s id="N127F0"><!-- NEW --><lb/>quia nullum locum de nouo acquireret; </s> <s id="N127F5"><!-- NEW -->&longs;ed de hoc motu aliàs, cum de <lb/>infinito; </s> <s id="N127FB"><!-- NEW -->vel de puncto phy&longs;ico mobili; quidquid &longs;it. </s> <s id="N127FF">valet &longs;altem <lb/>1. ratio pro motu recto, & aliæ duæ pro omni motu. </s> </p> <p id="N12804" type="main"> <s id="N12806"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 28.<emph.end type="center"/></s> </p> <p id="N12812" type="main"> <s id="N12814"><emph type="italics"/>Motus ip&longs;e moueri non pote&longs;t.<emph.end type="italics"/></s> <s id="N1281B"><!-- NEW --> Quia cum tantùm dicat mutationem <lb/>loci; </s> <s id="N12821"><!-- NEW -->certè mutatio non e&longs;t in loco; dicit enim tantùm locum relictum <lb/>eo in&longs;tanti, quo nouus acquiritur. </s> <s id="N12827"><!-- NEW -->Præterea quod e&longs;t in loco dicit tan­<lb/>tùm ens phy&longs;icum; </s> <s id="N1282D"><!-- NEW -->&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> </p> <p id="N12838" type="main"> <s id="N1283A"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 29.<emph.end type="center"/></s> </p> <p id="N12846" type="main"> <s id="N12848"><emph type="italics"/>Duratio moueri non pote&longs;t.<emph.end type="italics"/></s> <s id="N1284F"> 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> </p> <p id="N12856" type="main"> <s id="N12858"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 30.<emph.end type="center"/></s> </p> <p id="N12864" type="main"> <s id="N12866"><!-- NEW --><emph type="italics"/>Hinc actio moueri non pote&longs;t<emph.end type="italics"/>; </s> <s id="N1286F"><!-- NEW -->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> </p> <p id="N12879" type="main"> <s id="N1287B"><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 1.<emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N12888" type="main"> <s id="N1288A"><!-- NEW -->Hinc in tanta rerum creatarum multitudine &longs;unt tantùm duæ, quæ <lb/>&longs;unt e&longs;&longs;entialiter immobiles; &longs;cilicet motus, & actio; </s> <s id="N12890"><!-- NEW -->quorum ille cum <lb/>&longs;it mutatio non e&longs;t adæquatè aliquid po&longs;itiuum; &longs;ecus actio. </s> </p> <p id="N12896" type="main"> <s id="N12898"><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 2.<emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N128A5" type="main"> <s id="N128A7"><!-- NEW -->Hinc &longs;unt tantùm duo adæquatè po&longs;itiua, quæ moueri non po&longs;&longs;unt; </s> <s id="N128AB"><!-- NEW --><lb/>&longs;cilicet Deus, & actio; Deus, qui &longs;emper e&longs;t; </s> <s id="N128B0"><!-- NEW -->actio, quæ tantùm vno <lb/>in&longs;tanti e&longs;t; Deus vbique e&longs;&longs;entialiter; actio hic tantum e&longs;&longs;entialiter; </s> <s id="N128B6"><!-- NEW --><lb/>Deus primum ens; actio infinitum ens; </s> <s id="N128BB"><!-- NEW -->e&longs;t enim modus; </s> <s id="N128BF"><!-- NEW -->Deus primum <lb/>mouens; actio ip&longs;e motus; &longs;cilicet primi generis, de quo in &longs;ect. </s> <s id="N128C5">Th.3. </s> </p> <p id="N128C8" type="main"> <s id="N128CA"><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 3.<emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N128D7" type="main"> <s id="N128D9"><!-- NEW -->Hinc &longs;i res aliqua creata per actionem tantæ perfectionis, quæ mille <lb/>annis e&longs;&longs;entialiter re&longs;ponderet, con&longs;eruaretur; </s> <s id="N128DF"><!-- NEW -->certè per totum illud <lb/>tempus moueri non po&longs;&longs;et; </s> <s id="N128E5"><!-- NEW -->e&longs;&longs;et enim vnicum in&longs;tans, hoc e&longs;t duratio <pb pagenum="23" xlink:href="026/01/055.jpg"/>tota &longs;imul; </s> <s id="N128EE"><!-- NEW -->&longs;ed eodem in&longs;tanti in pluribus locis e&longs;&longs;e non pote&longs;t; igitur <lb/>nec moueri; </s> <s id="N128F4"><!-- NEW -->adde quod per cam actionem &longs;um in loco, per quam &longs;um <lb/>in tempore; </s> <s id="N128FA"><!-- NEW -->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> </p> <p id="N12902" type="main"> <s id="N12904"><emph type="center"/><emph type="italics"/>Scolium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N12910" type="main"> <s id="N12912"><!-- NEW -->Ob&longs;eruabis primò ex dictis præclarum naturæ in&longs;titutum; </s> <s id="N12916"><!-- NEW -->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; </s> <s id="N1291E"><!-- NEW -->alioquin &longs;emper <lb/>moueretur; </s> <s id="N12924"><!-- NEW -->igitur per aliud ab entitate di&longs;tinctum, id e&longs;t per impetum; </s> <s id="N12928"><!-- NEW --><lb/>itaque licet per &longs;uam entitatem exigat fluxum in tempore, id e&longs;t con&longs;er­<lb/>uari, & durare; </s> <s id="N1292F"><!-- NEW -->id e&longs;t nouam &longs;emper actionem con&longs;eruatiuam; </s> <s id="N12933"><!-- NEW -->quia <lb/>maximum eius bonum e&longs;t durare vel exi&longs;tere; </s> <s id="N12939"><!-- NEW -->Igitur per &longs;e ip&longs;um illud <lb/>exigit; </s> <s id="N1293F"><!-- NEW -->quia &longs;emper exigit, non tamen per &longs;e ip&longs;um exigit fluxum in <lb/>loco, id e&longs;t motum; quia moueri non &longs;emper e&longs;t bonum. </s> </p> <p id="N12945" type="main"> <s id="N12947"><!-- NEW -->Ob&longs;eruabis &longs;ecundò, cum idem corpus aliquando velociùs, tardiùs <lb/>aliquando moueri exigat; </s> <s id="N1294D"><!-- NEW -->&longs;i per &longs;uam entitatem moueri exigeret, eo­<lb/>dem &longs;emper ferretur motu; </s> <s id="N12953"><!-- NEW -->quia eadem &longs;emper e&longs;&longs;et exigentia; </s> <s id="N12957"><!-- NEW -->igitur <lb/>debet e&longs;&longs;e aliquid aliud; </s> <s id="N1295D"><!-- NEW -->illud autem e&longs;t impetus, qui aliquando maior <lb/>&longs;eu perfectior, aliquando verò minor e&longs;t; </s> <s id="N12963"><!-- NEW -->igitur maiorem &longs;eu <expan abbr="velcio­rem">velocio­<lb/>rem</expan> motum aliquando exigit, aliquando minorem, &longs;eu tardiorem; </s> <s id="N1296D"><!-- NEW --><lb/>cum enim motus &longs;it eius finis intrin&longs;ecus, vt re&longs;olutio e&longs;t finis caloris <lb/>vel rarefactio; </s> <s id="N12974"><!-- NEW -->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> </p> <p id="N1297C" type="main"> <s id="N1297E"><!-- NEW -->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: </s> <s id="N12986"><!-- NEW -->nec alia regula, præter eam excogitari pote&longs;t; </s> <s id="N1298A"><!-- NEW --><lb/>cum enim aliqua forma ad talem, vel talem finem à natura in&longs;tituta e&longs;t; </s> <s id="N1298F"><!-- NEW --><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; </s> <s id="N12996"><!-- NEW -->alioquin fru&longs;trà e&longs;&longs;et; </s> <s id="N1299A"><!-- NEW -->& contra in eo e&longs;&longs;e pote&longs;t, <lb/>in quo fru&longs;trà non e&longs;t; </s> <s id="N129A0"><!-- NEW -->cum &longs;cilicet in eo &longs;uum finem con&longs;equatur; </s> <s id="N129A4"><!-- NEW -->ad­<lb/>de quod finis ille intrin&longs;ecus phy&longs;icus &longs;cilicet, non moralis, aliquis no­<lb/>uus effectus e&longs;t; </s> <s id="N129AC"><!-- NEW -->atqui nouus effectus &longs;ine &longs;ua cau&longs;a e&longs;&longs;e non pote&longs;t, neque <lb/>cau&longs;a nece&longs;&longs;aria &longs;ine effectu; igitur ibi, &longs;cilicet in hoc &longs;ubiecto, in quo <lb/>e&longs;t, vel e&longs;&longs;e pote&longs;t effectus formalis, cau&longs;a formalis e&longs;t, vel e&longs;&longs;e pote&longs;t, <lb/>e&longs;t inquam citra miraculum. </s> </p> <p id="N129B6" type="main"> <s id="N129B8">Ob&longs;eruabis quartò egregiam rationem; </s> <s id="N129BB"><!-- NEW -->propter quam res eadem in <lb/>pluribus locis naturaliter e&longs;&longs;e non pote&longs;t; </s> <s id="N129C1"><!-- NEW -->quippe cum res fuerit primo <lb/>producta in aliquo loco, illa certè nouum locum acquirere non pote&longs;t <lb/>naturaliter; </s> <s id="N129C9"><!-- NEW -->ni&longs;i per motum, atqui motus dicit nece&longs;&longs;ario priorem lo­<lb/>tum relictum, & nouum acqui&longs;itum; </s> <s id="N129CF"><!-- NEW -->igitur cum tot acquirantur loca <lb/>per motum, quot relinquuntur; </s> <s id="N129D5"><!-- NEW -->&longs;i ante motum vnus tantùm erat eiu&longs;­<lb/>dem rei locus, po&longs;t motum etiam vnus e&longs;t: </s> <s id="N129DB"><!-- NEW -->quod autem producatur tan-<pb pagenum="24" xlink:href="026/01/056.jpg"/>tùm res in vno loco patet; </s> <s id="N129E4"><!-- NEW -->vel enim à cau&longs;a prima vel ab aliqua 2. pro­<lb/>ducitur; </s> <s id="N129EA"><!-- NEW -->&longs;i à 2. ergo ab aliqua aplicata; </s> <s id="N129EE"><!-- NEW -->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; </s> <s id="N129F6"><!-- NEW -->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; </s> <s id="N129FE"><!-- NEW -->&longs;ingulis terminis &longs;ingulæ <lb/>viæ; </s> <s id="N12A04"><!-- NEW -->immò hoc requiri videtur, &longs;eu &longs;pectare ad huius vniuer&longs;itatis or­<lb/>dinem; </s> <s id="N12A0A"><!-- NEW -->quippe &longs;i res eadem in pluribus locis e&longs;&longs;et; cur potius in duo­<lb/>bus quam in tribus? </s> <s id="N12A10"><!-- NEW -->deinde multiplex iure po&longs;&longs;et exi&longs;timari; </s> <s id="N12A14"><!-- NEW -->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; </s> <s id="N12A1C"><!-- NEW -->quæ e&longs;t actio, per quam dependet; &longs;ed de his <lb/>aliàs. </s> </p> <p id="N12A22" type="main"> <s id="N12A24"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 31.<emph.end type="center"/></s> </p> <p id="N12A30" type="main"> <s id="N12A32"><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 id="N12A3B"><!-- NEW --> 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; </s> <s id="N12A43"><!-- NEW -->&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. <!-- KEEP S--></s> <s id="N12A4E"><!-- NEW -->17. adde quod non pote&longs;t cogno&longs;ci <lb/>impetus, ni&longs;i vel ex motu, vel ex ictu, vel ex contrario ni&longs;u, vel <lb/>impul&longs;u; </s> <s id="N12A56"><!-- NEW -->&longs;ed nihil horum cernitur in rupe quam ferio; </s> <s id="N12A5A"><!-- NEW -->Igitur non <lb/>e&longs;t dicendum in ea produci impetum, cuius rationem afferemus infrà; </s> <s id="N12A60"><!-- NEW --><lb/>nunc &longs;atis e&longs;t Ax. 3. id manife&longs;tè probari; </s> <s id="N12A65"><!-- NEW -->nam qui diceret in rupe im­<lb/>mobili impetum imprimi; </s> <s id="N12A6B"><!-- NEW -->certè po&longs;itiuo argumento probare tenere­<lb/>tur, quod tantùm duci pote&longs;t, vel ab experimento; </s> <s id="N12A71"><!-- NEW -->atqui hîc nullum e&longs;t; </s> <s id="N12A75"><!-- NEW --><lb/>vel à nece&longs;&longs;itate, quæ nulla e&longs;t; </s> <s id="N12A7A"><!-- NEW -->vel ex alio quocumque capite, quod <lb/>nullum excogitari pote&longs;t; </s> <s id="N12A80"><!-- NEW -->&longs;ed maiorem lucem huic Th. 3. ex proximè <lb/>&longs;equentibus accer&longs;emus; </s> <s id="N12A86"><!-- NEW -->nec e&longs;t quòd aliqui dicant produci impetum <lb/>inefficacem; </s> <s id="N12A8C"><!-- NEW -->qui cum fru&longs;trà &longs;it, &longs;i e&longs;t, ex nullo capite probari pote&longs;t: </s> <s id="N12A90"><!-- NEW -->ad­<lb/>de quòd de&longs;truitur impetus, ne &longs;it fru&longs;trà; </s> <s id="N12A96"><!-- NEW -->Igitur non producitur, ne &longs;it <lb/>fru&longs;trà; </s> <s id="N12A9C"><!-- NEW -->nam con&longs;eruatio e&longs;t vera actio, vt dicemus &longs;uo loco; </s> <s id="N12AA0"><!-- NEW -->Igitur &longs;i <lb/>hæc non ponitur, ne aliquid &longs;it fru&longs;trà; </s> <s id="N12AA6"><!-- NEW -->etiam 1. productio poni non <lb/>debet; vnde commentum illud impetus inefficacis pror&longs;us inefficax e&longs;t. </s> </p> <p id="N12AAC" type="main"> <s id="N12AAE"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 32.<emph.end type="center"/></s> </p> <p id="N12ABA" type="main"> <s id="N12ABC"><emph type="italics"/>Ideo potentia motrix non producit impetum in prædicta rupe.<emph.end type="italics"/> v.g. <emph type="italics"/>quia de­<lb/>bilior e&longs;t.<emph.end type="italics"/></s> <s id="N12ACB"> Probatur, & explicatur; quippe debilior potentia minorem ef­<lb/>fectum producit per. </s> <s id="N12AD0"><!-- NEW -->Ax. 13. <emph type="italics"/>num.<emph.end type="italics"/> 2. igitur pauciores partes impetus <lb/>æquales vni certæ per idem <emph type="italics"/>num.<emph.end type="italics"/> 1. igitur &longs;i &longs;int plures partes &longs;ubiecti <lb/>mobilis, &longs;eu rupis, quàm impetus; </s> <s id="N12AE4"><!-- NEW -->cum vna pars impetus duobus parti­<lb/>bus &longs;ubiecti ine&longs;&longs;e non po&longs;&longs;it; </s> <s id="N12AEA"><!-- NEW -->licet plures vni &longs;imul in e&longs;&longs;e po&longs;&longs;int; </s> <s id="N12AEE"><!-- NEW --><lb/>non e&longs;t mirum &longs;i nullus impetus producatur; </s> <s id="N12AF3"><!-- NEW -->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> </p> <pb pagenum="25" xlink:href="026/01/057.jpg"/> <p id="N12AFF" type="main"> <s id="N12B01"><!-- NEW -->Ob&longs;eruabis autem nouum quoddam genús re&longs;i&longs;tentiæ; </s> <s id="N12B05"><!-- NEW -->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; </s> <s id="N12B0D"><!-- NEW -->at verò <lb/>omnes &longs;imul, & coniunctim con&longs;ideratæ; </s> <s id="N12B13"><!-- NEW -->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; </s> <s id="N12B1B"><!-- NEW --><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> </p> <p id="N12B24" type="main"> <s id="N12B26"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 33.<emph.end type="center"/></s> </p> <p id="N12B32" type="main"> <s id="N12B34"><!-- NEW --><emph type="italics"/>Vel producitur impetus in omnibus &longs;ubiecti partibus vnitis, vel in nulla; </s> <s id="N12B3A"><!-- NEW --><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="N12B44"><!-- NEW -->Probatur igitur <lb/>1. quia &longs;i non producatur in omnibus partibus, & nulla &longs;eparetur ab <lb/>alijs; </s> <s id="N12B4C"><!-- NEW -->certè nulla mouetur, vt certum e&longs;t; </s> <s id="N12B50"><!-- NEW -->igitur nulla habet impetum; </s> <s id="N12B54"><!-- NEW --><lb/>quia ibi non e&longs;t cau&longs;a formalis, vbi non e&longs;t effectus formalis; alioquin <lb/>e&longs;&longs;et fru&longs;trà, contra Ax. 6.2. </s> <s id="N12B5B"><!-- NEW -->Tu dicis produci impetum in aliquot parti­<lb/>bus; hoc dicis, hoc proba? </s> <s id="N12B61">an potes digno&longs;cere impetum ni&longs;i ex motu? </s> <s id="N12B64"><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="N12B6A">Primum dicere ab&longs;urdume&longs;t; </s> <s id="N12B6D"><!-- NEW -->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="N12B75">Secundo in&longs;tanti; eadem ratio probat non produci. </s> <s id="N12B78">Pri­<lb/>mo in&longs;tanti, quæ probat de&longs;trui. </s> <s id="N12B7D">Secundo nam ideo de&longs;truitur. </s> <s id="N12B80">Secun­<lb/>do quia e&longs;t fru&longs;trà, &longs;ed non minus e&longs;t fru&longs;trà. </s> <s id="N12B85">Primo igitur non produ­<lb/>citur. </s> <s id="N12B8A">Primo 4. probatur; </s> <s id="N12B8D"><!-- NEW -->quia cum non &longs;ufficiant partes impetus, quas <lb/>dixi produci, vt omnibus partibus &longs;ubiecti di&longs;tribuantur; </s> <s id="N12B93"><!-- NEW -->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="N12B9B">Igitur certum e&longs;t vel produci in omnibus, vel <lb/>in nulla, ni&longs;i forte aliquæ auolent, &longs;ed tunc &longs;eparantur. </s> </p> <p id="N12BA0" type="main"> <s id="N12BA2"><!-- NEW -->Obiiciet aliquis 1. e&longs;&longs;e cau&longs;am nece&longs;&longs;ariam applicatam &longs;ubiecto ap­<lb/>to: </s> <s id="N12BA8"><!-- NEW -->igitur agit per Ax. 12. Re&longs;pondeo e&longs;&longs;e impeditam; </s> <s id="N12BAC"><!-- NEW -->nam re&longs;i&longs;tentia <lb/>&longs;ubiecti &longs;uperat vires potentiæ vt dictum e&longs;t; </s> <s id="N12BB2"><!-- NEW -->immò in ip&longs;o motu re­<lb/>torqueo argumentum; licèt enim &longs;it applicata cau&longs;a nece&longs;&longs;aria mouens, <lb/>non tamen mouet. </s> </p> <p id="N12BBA" type="main"> <s id="N12BBC"><!-- NEW -->Obiiciet 2. Ignis applicatus agit in nonnullas partes fubiecti, licèt <lb/>non agat in omnes; igitur & potentia motrix. </s> <s id="N12BC2"><!-- NEW -->Re&longs;pondeo non e&longs;&longs;e pa­<lb/>ritatem; </s> <s id="N12BC8"><!-- NEW -->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> </p> <p id="N12BD0" type="main"> <s id="N12BD2">Obiiciet. </s> <s id="N12BD5"><!-- NEW -->3. &longs;int duo trahentes idem mobile; </s> <s id="N12BD9"><!-- NEW -->ita vt &longs;eor&longs;im neuter <lb/>trahere po&longs;&longs;it, coniunctim verò vterque po&longs;&longs;it; </s> <s id="N12BDF"><!-- NEW -->certè &longs;i alter non pro­<lb/>ducit impetum &longs;eor&longs;im, nec etiam coniunctim producet; </s> <s id="N12BE5"><!-- NEW -->nec enim au­<lb/>gentur eius vires ab altero: </s> <s id="N12BEB"><!-- NEW -->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 pagenum="26" xlink:href="026/01/058.jpg"/>&longs;eor&longs;im producere pote&longs;t. </s> </p> <p id="N12BF6" type="main"> <s id="N12BF8"><!-- NEW -->Dices &longs;i vterque coniunctim producit effectum: </s> <s id="N12BFC"><!-- NEW -->&longs;int v. <!-- REMOVE S-->g. <!-- REMOVE S-->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="N12C0A"><!-- NEW -->Re&longs;pondeo &longs;ingulos producere 100. <lb/>actione &longs;cilicet communi indiui&longs;ibiliter; </s> <s id="N12C10"><!-- NEW -->&longs;int enim duo trahentes A. & <lb/>B. A. producit 100. &longs;ed non &longs;olus; </s> <s id="N12C16"><!-- NEW -->B. producit ea&longs;dem 100. &longs;ed non &longs;o­<lb/>lus; &longs;ed explicabimus hunc modum actionis communis in Metaphys. <!-- REMOVE S--><lb/>quod autem agant actione communi patet per Ax. 13. </s> </p> <p id="N12C1F" type="main"> <s id="N12C21"><!-- NEW -->Obiicies 4. producitur &longs;onus &longs;i ferias rupem; </s> <s id="N12C25"><!-- NEW -->igitur & impetus; </s> <s id="N12C29"><!-- NEW -->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; </s> <s id="N12C31"><!-- NEW -->deinde mallej motus impacti in rupem facit &longs;onum; </s> <s id="N12C35"><!-- NEW --><lb/>quidquid tandem &longs;it &longs;onus, de quo hîc non di&longs;puto: </s> <s id="N12C3A"><!-- NEW -->adde quod in ru­<lb/>pe &longs;unt &longs;emper aliquæ partes tremulæ, quæ modico tantùm, eoque flexi­<lb/>bili nexu cum alijs partibus copulantur; adde aliquam compre&longs;&longs;ionem, <lb/>ex qua modicæ vibrationes &longs;equuntur. </s> </p> <p id="N12C44" type="main"> <s id="N12C46"><!-- NEW -->Obiicies 5. Quando aliquæ partes auolant ab ictu, haud dubiè auo­<lb/>lant propter impetum impre&longs;&longs;um: </s> <s id="N12C4C"><!-- NEW -->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="N12C54"><!-- NEW -->Re&longs;pondeo equidem im­<lb/>petum produci in illis partibus antequam auolent; </s> <s id="N12C5A"><!-- NEW -->&longs;ed ideo produci vt <lb/>deinde auolent nam tota ratio cur non producatur, e&longs;t ne &longs;it fru&longs;trà; </s> <s id="N12C60"><!-- NEW -->&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> </p> <p id="N12C68" type="main"> <s id="N12C6A">Dices; </s> <s id="N12C6D"><!-- NEW -->igitur primo in&longs;tanti impetus ille e&longs;t fru&longs;trà; </s> <s id="N12C71"><!-- NEW -->in quo non <lb/>habet &longs;uum effectum; </s> <s id="N12C77"><!-- NEW -->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 in&longs;tant &longs;equenti, de <lb/>cum impetus ponat tantùm motum quo aliàs. </s> </p> <p id="N12C83" type="main"> <s id="N12C85">Dices; </s> <s id="N12C88"><!-- NEW -->&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="N12C90"><!-- NEW -->Re&longs;pondeo non &longs;tare per cau&longs;am nece&longs;&longs;ariam, quin &longs;em­<lb/>per agat; </s> <s id="N12C96"><!-- NEW -->&longs;ed per &longs;ubiectum, quod &longs;i aptum e&longs;t, & capax effectus; </s> <s id="N12C9A"><!-- NEW -->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="N12CA0"><lb/>haud dubiè non aget; </s> <s id="N12CA4"><!-- NEW -->nam ad hoc vt producatur effectus in &longs;ubiecto; </s> <s id="N12CA8"><!-- NEW --><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; </s> <s id="N12CAF"><!-- NEW -->igitur cum &longs;it talis ordo à natura in&longs;titutus, ne aliquid &longs;it fru&longs;trà; </s> <s id="N12CB3"><!-- NEW --><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> </p> <p id="N12CBA" type="main"> <s id="N12CBC"><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N12CC8" type="main"> <s id="N12CCA">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> </p> <p id="N12CCF" type="main"> <s id="N12CD1"><!-- NEW -->Ob&longs;eruabis 2. etiam maximam corporis molem à debili potentia mi-<pb pagenum="27" xlink:href="026/01/059.jpg"/>nimo etiam ictu moueri; </s> <s id="N12CDA"><!-- NEW -->quod etiam ob&longs;eruauit Galileus in &longs;uis dialo­<lb/>gis de motu; </s> <s id="N12CE0"><!-- NEW -->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; </s> <s id="N12CE6"><!-- NEW -->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> </p> <p id="N12CF0" type="main"> <s id="N12CF2"><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 1.<emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N12CFF" type="main"> <s id="N12D01"><!-- NEW -->Hinc egregia ratio erui pote&longs;t, cur ingens corporis moles à debili po­<lb/>tentia loco moueri non po&longs;&longs;it; </s> <s id="N12D07"><!-- NEW -->cum enim tot &longs;altem requirantur partes <lb/>impetus, quot &longs;unt partes &longs;ubiecti: </s> <s id="N12D0D"><!-- NEW -->quia vel in omnibus, vel in nulla <lb/>producitur; </s> <s id="N12D13"><!-- NEW -->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> </p> <p id="N12D1B" type="main"> <s id="N12D1D"><emph type="center"/><emph type="italics"/>Collorarium<emph.end type="italics"/> 2.<emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N12D2A" type="main"> <s id="N12D2C"><!-- NEW -->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 velociorem motum imprimat; </s> <s id="N12D34"><!-- NEW -->quia &longs;cilicet <lb/>partes impetus producti di&longs;tribuuntur pluribus partibus &longs;ubiecti in ma­<lb/>iori lapide, & paucioribus in minori; </s> <s id="N12D3C"><!-- NEW -->igitur &longs;ingulæ partes minoris <lb/>habent plures partes impetus, vt manife&longs;tè con&longs;tat; </s> <s id="N12D42"><!-- NEW -->ergo ille impetus <lb/>inten&longs;ior e&longs;t; igitur maiorem exigit &longs;eu perfectiorem motum per Ax. <!-- REMOVE S--><lb/>13. num.2. </s> </p> <p id="N12D4B" type="main"> <s id="N12D4D"><emph type="center"/><emph type="italics"/>Collorarium<emph.end type="italics"/> 3.<emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N12D5A" type="main"> <s id="N12D5C"><!-- NEW -->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; </s> <s id="N12D64"><!-- NEW -->nam ratio velocitatum <lb/>e&longs;t inuer&longs;a ponderum v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;it pondùs 4. librarum; </s> <s id="N12D6E"><!-- NEW -->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; </s> <s id="N12D76"><!-- NEW -->haud dubiè velocitas mobilis 2. libra­<lb/>rum erit dupla velocitatis mobilis 4. librarum; </s> <s id="N12D7C"><!-- NEW -->quia cum &longs;int duplo <lb/>plures partes &longs;ubiecti in hoc mobili quàm in illo (accipio enim vtrum­<lb/>que eiu&longs;dem materiæ, vt omnes lites fugiam) igitur in minori e&longs;t duplo <lb/>inten&longs;ior impetus: Igitur duplo velocior motus; </s> <s id="N12D86"><!-- NEW -->dixi, &longs;i fiat æquali <lb/>ni&longs;u, & æquali tempore; </s> <s id="N12D8C"><!-- NEW -->quia reuerâ non fit in tempore æquali, &longs;ed <lb/>inæquali, &longs;i &longs;upponatur idem arcus brachij v. <!-- REMOVE S-->g. <!-- REMOVE S-->iacientis; </s> <s id="N12D96"><!-- NEW -->nam tempo­<lb/>ra &longs;unt in ratione &longs;ubduplicata ponderum; vt demon&longs;trabimus lib. 10. <lb/>& velocitates &longs;unt vt tempora permutando. </s> </p> <p id="N12D9E" type="main"> <s id="N12DA0"><emph type="center"/><emph type="italics"/>Collorarium<emph.end type="italics"/> 4.<emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N12DAD" type="main"> <s id="N12DAF"><!-- NEW -->Hinc facilè determinari pote&longs;t proportio impetus impre&longs;&longs;i cognitâ <lb/>grauitate mobilium; </s> <s id="N12DB5"><!-- NEW -->v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;it mobile graue vt4. & aliud graue vt 2. haud <lb/>dubiè vt moueatur æquali gradu velocitatis, debet produci duplo <lb/>maior impetus in maiori mobili, hoc e&longs;t, iuxta rationem maioris ad mi­<lb/>nus, quod clari&longs;&longs;imè &longs;equitur ex dictis; </s> <s id="N12DC3"><!-- NEW -->vt enim tot&longs;int gradus impetus <pb pagenum="28" xlink:href="026/01/060.jpg"/>in qualibet parte minoris, quot &longs;unt in qualibet parte minoris; </s> <s id="N12DCC"><!-- NEW -->haud <lb/>dubiè impetus maioris habet eandem rationem ad impetum minoris; <lb/>quam habet maius ad minus. </s> </p> <p id="N12DD4" type="main"> <s id="N12DD6"><emph type="center"/><emph type="italics"/>Collorarium<emph.end type="italics"/> 5.<emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N12DE3" type="main"> <s id="N12DE5"><!-- NEW -->Hinc quoque ducitur manife&longs;ta ratio &longs;eu re&longs;pon&longs;io ad illud præcla­<lb/>rum certè quorundam philo&longs;ophorum <expan abbr="comm&etilde;tum">commentum</expan>, qui volunt ex mini­<lb/>ma ponderis acce&longs;&longs;ione totam terræ molem inclinari, vt in nouo æqui­<lb/>librio &longs;tatuatur; quod omninò fal&longs;um e&longs;t; </s> <s id="N12DF3"><!-- NEW -->nam ex &longs;uppotione quòd <lb/>terra non grauitet (vt vulgò dicitur, & aliàs à nobis <expan abbr="demõ&longs;trabitur">demon&longs;trabitur</expan>) illa <lb/>certè moueri non pote&longs;t ni&longs;i producantur tot partes impetus quot &longs;unt <lb/>partes &longs;ubiecti in tota terra; quæ certè maximas <expan abbr="pot&etilde;tiæ">potentiæ</expan> vires po&longs;tulant. </s> </p> <p id="N12E05" type="main"> <s id="N12E07"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 34.<emph.end type="center"/></s> </p> <p id="N12E13" type="main"> <s id="N12E15"><emph type="italics"/>Primo in&longs;tanti, quo est impetus, non est ille motus, cuius hic impetus e&longs;t <lb/>cau&longs;a.<emph.end type="italics"/></s> <s id="N12E1E"> Probatur; </s> <s id="N12E21"><!-- NEW -->quia non pote&longs;t e&longs;&longs;e motus, ni&longs;i &longs;it locus prior reli­<lb/>ctus, & nouus acqui&longs;itus, igitur &longs;i eodem in&longs;tanti, quo e&longs;t impetus, <lb/>haberet motum, eodem in&longs;tanti e&longs;&longs;et in duobus locis, quod dici non <lb/>pote&longs;t; & iam diximus in Th. 26. igitur impetus primo in&longs;tanti quo <lb/>e&longs;t non habet &longs;uum motum. </s> </p> <p id="N12E2D" type="main"> <s id="N12E2F"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 35.<emph.end type="center"/></s> </p> <p id="N12E3B" type="main"> <s id="N12E3D"><emph type="italics"/>Immò nihil e&longs;t, quod primo in&longs;tanti, quo e&longs;t, moueri po&longs;&longs;it.<emph.end type="italics"/></s> <s id="N12E44"><!-- NEW --> Quia non pote&longs;t <lb/>moueri, ni&longs;i acquirat nouum locum, & priorem relinquat; </s> <s id="N12E4A"><!-- NEW -->igitur, vel &longs;i­<lb/>mul in vtroque e&longs;t, quod dici non pote&longs;t; </s> <s id="N12E50"><!-- NEW -->vel in relicto antè fuit; igitur <lb/>non e&longs;t primum in&longs;tans, contra &longs;uppo&longs;itionem. </s> </p> <p id="N12E56" type="main"> <s id="N12E58"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 36.<emph.end type="center"/></s> </p> <p id="N12E64" type="main"> <s id="N12E66"><emph type="italics"/>Potest impetus aliquo in&longs;tanti non moueri quo mouetur ip&longs;um mobile, in <lb/>quo est.<emph.end type="italics"/></s> <s id="N12E6F"><!-- NEW --> Nam moueatur mobile quodlibet; </s> <s id="N12E73"><!-- NEW -->& dum mouetur, impella­<lb/>tur, factâ &longs;cilicet acce&longs;&longs;ione noui impetus; haud dubiè hoc primo in­<lb/>&longs;tanti, quo producitur impetus in dato mobili non mouetur per Th. <!-- REMOVE S--><lb/>35. quo tamen in&longs;tanti mouetur prædictum mobile. </s> </p> <p id="N12E7E" type="main"> <s id="N12E80"><emph type="center"/><emph type="italics"/>Collorarium<emph.end type="italics"/> 1.<emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N12E8D" type="main"> <s id="N12E8F"><!-- NEW -->Hinc egregium paradoxon; <emph type="italics"/>Pote&longs;t alique in&longs;tanti moueri &longs;ubiectum, licèt <lb/>non moueantur illa omnia, que eidem &longs;ubiecto reuerâ in&longs;unt.<emph.end type="italics"/></s> </p> <p id="N12E9A" type="main"> <s id="N12E9C"><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 2.<emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N12EA9" type="main"> <s id="N12EAB"><!-- NEW -->Hinc etiam aliud paradoxon; </s> <s id="N12EAF"><!-- NEW --><emph type="italics"/>Impetus primo in&longs;tanti, quo e&longs;t, non habet <lb/>&longs;uum finem, nec habere pote&longs;t<emph.end type="italics"/>; patet, quia primo in&longs;tanti non habet <expan abbr="motũ">motum</expan>. </s> </p> <p id="N12EBE" type="main"> <s id="N12EC0"><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 3.<emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N12ECD" type="main"> <s id="N12ECF"><!-- NEW -->Hinc pote&longs;t aliquid dato in&longs;tanti carere &longs;uo fine; </s> <s id="N12ED3"><!-- NEW -->licèt non &longs;it fru&longs;trà; <lb/>fru&longs;trâ enim tantùm dicitur ille impetus, qui pro in&longs;tanti &longs;equenti <lb/>non pote&longs;t habere motum. </s> </p> <p id="N12EDB" type="main"> <s id="N12EDD"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 37.<emph.end type="center"/></s> </p> <p id="N12EE9" type="main"> <s id="N12EEB"><emph type="italics"/>Impetus pars recepta in parte &longs;ubiecti non exigit motum aliarum partium<emph.end type="italics"/><pb pagenum="29" xlink:href="026/01/061.jpg"/><emph type="italics"/>eiu&longs;dem &longs;ubiecti, licèt coniunctarum.<emph.end type="italics"/></s> <s id="N12EFB"><!-- NEW --> Probatur 1. quia alioquin vna pars <lb/>impetus &longs;ufficeret ad mouendam ingentem rupem; quod ab&longs;urdum e&longs;t. </s> <s id="N12F01"><!-- NEW --><lb/>2. &longs;icut vna pars caloris non re&longs;oluit alias partes &longs;ubiecti; ita nec im­<lb/>petus. </s> <s id="N12F08"><!-- NEW -->3. Ratio à priori e&longs;t; quia impetus non e&longs;t cau&longs;a efficiens motus <lb/>per Th. 13. &longs;ed tantùm cau&longs;a formalis per Th. 15. Igitur præ&longs;tat tantùm <lb/>&longs;uum effectum formalem in eo &longs;ubiecto, in quo e&longs;t. </s> </p> <p id="N12F10" type="main"> <s id="N12F12"><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 1.<emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N12F1F" type="main"> <s id="N12F21"><!-- NEW -->Hinc partes impetus non cau&longs;ant motum in &longs;uo &longs;ubiecto actione, vel <lb/>exigentia communi; </s> <s id="N12F27"><!-- NEW -->quia quælibet pars impetus exigit tantùm motum <lb/>&longs;ui &longs;ubiecti; </s> <s id="N12F2D"><!-- NEW -->id e&longs;t illius partis, quàm afficit; quod etiam probatur per <lb/>Ax. 13. </s> </p> <p id="N12F33" type="main"> <s id="N12F35"><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 2.<emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N12F42" type="main"> <s id="N12F44"><!-- NEW -->Hinc corpus grauius per&longs;e, &longs;altem eiu&longs;dem materiæ, non cadit velo­<lb/>ciùs, quàm leuius, vti globus plumbeus 100. librarum, quàm globus <lb/>vnius libræ plumbeus; </s> <s id="N12F4C"><!-- NEW -->quia &longs;cilicet impetus vnius partis non iuuat mo­<lb/>tum alterius: </s> <s id="N12F52"><!-- NEW -->præterea tam facilè 2, partes impetus in 2. partibus &longs;ubie­<lb/>cti receptæ ea&longs;dem mouent, quàm 100. alias 100. dixi per &longs;e; </s> <s id="N12F58"><!-- NEW -->nam di­<lb/>uer&longs;a e&longs;&longs;e pote&longs;t medij re&longs;i&longs;tentia; &longs;ed de his fu&longs;e in 2. lib. <!-- REMOVE S--><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 38.<emph.end type="center"/></s> </p> <p id="N12F69" type="main"> <s id="N12F6B"><!-- NEW --><emph type="italics"/>Impetus recipitur tantùm in ip&longs;a &longs;ub&longs;tantia &longs;ubiecti naturaliter.<emph.end type="italics"/> v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;i <lb/>mobile &longs;it ferrum calidum, recipitur in ip&longs;a &longs;ub&longs;tantia ferri; </s> <s id="N12F7A"><!-- NEW -->non verò <lb/>in ip&longs;o calore (ex &longs;uppo&longs;itione quod calor &longs;it accidens, vt aliàs demon­<lb/>&longs;trabimus; </s> <s id="N12F82"><!-- NEW -->nec in alijs accidentibus, &longs;i quæ &longs;unt, in eodem &longs;ubiecto; </s> <s id="N12F86"><!-- NEW -->pro­<lb/>batur 1. quia &longs;i produceretur etiam impetus in accidentibus, quo plu­<lb/>ra e&longs;&longs;ent accidentia in aliquo &longs;ubiecto; </s> <s id="N12F8E"><!-- NEW -->plures quoque partes impetus <lb/>producendæ e&longs;&longs;ent; igitur maiori potentiâ opus e&longs;&longs;et per Ax. 13. n. </s> <s id="N12F94">4. <lb/>Igitur difficiliùs mouerentur, quod e&longs;t ab&longs;urdum. </s> <s id="N12F99"><!-- NEW -->Diceret fortè ali­<lb/>quis eundem impetum recipi &longs;imul in &longs;ub&longs;tantia & in ip&longs;is accidenti­<lb/>bus; </s> <s id="N12FA1"><!-- NEW -->&longs;ed contra, nam reuera, &longs;i hoc e&longs;&longs;et, dum proijcitur ferrum cali­<lb/>dum, & &longs;tatim frigefit, de&longs;trueretur totus impetus, de&longs;tructo &longs;cilicet <lb/>eius &longs;ubiecto: </s> <s id="N12FA9"><!-- NEW -->2. qui hoc diceret, deberet probare; </s> <s id="N12FAD"><!-- NEW -->nam eodem modo <lb/>mouetur corpus &longs;iue afficiatur pluribus accidentibus, &longs;iue paucioribus; <lb/>igitur non euincit experientia recipi in illis impetum, nec etiam ratio, <lb/>vt dicam paulò po&longs;t. </s> <s id="N12FB7"><!-- NEW -->Ratio à priori e&longs;&longs;e pote&longs;t; </s> <s id="N12FBB"><!-- NEW -->quia accidens cum &longs;uo <lb/>&longs;ubiecto coniunctum exigit &longs;emper e&longs;&longs;e præ&longs;ens &longs;ubiecto, cum natura­<lb/>liter extra &longs;ubiectum exi&longs;tere non po&longs;&longs;it; </s> <s id="N12FC3"><!-- NEW -->igitur cum exigat con&longs;erua­<lb/>ri, & exi&longs;tere; </s> <s id="N12FC9"><!-- NEW -->eo tantùm modo, quo pote&longs;t naturaliter con&longs;eruari & <lb/>exi&longs;tere; </s> <s id="N12FCF"><!-- NEW -->certè exigit con&longs;eruari, & ine&longs;&longs;e &longs;ubiecto; </s> <s id="N12FD3"><!-- NEW -->igitur exi&longs;tere in <lb/>eo loco, in quo exi&longs;tit &longs;ubiectum, vt patet; igitur, &longs;i &longs;ubiectum mutet <lb/>locum etiam accidens cum eo coniunctum mutare debet. </s> </p> <p id="N12FDB" type="main"> <s id="N12FDD"><!-- NEW -->Dices, igitur &longs;imiliter dici pote&longs;t non recipi impetum in omni­<lb/>bus partibus &longs;ubiecti mobilis, &longs;ed in vnâ dumtaxat; cui cum <lb/>aliæ &longs;int vnitæ, exigunt moueri &longs;ine impetu ad illius motum? </s> <s id="N12FE5"><!-- NEW -->cum <lb/>hoc ip&longs;um ad omnem vnionem &longs;pectare videatur; </s> <s id="N12FEB"><!-- NEW -->Re&longs;pondeo vnam <pb pagenum="30" xlink:href="026/01/062.jpg"/>partem plumbi ita coniungi cum alia, vt etiam &longs;eparata naturaliter <lb/>exi&longs;tere po&longs;&longs;it; </s> <s id="N12FF6"><!-- NEW -->igitur non e&longs;t par ratio; </s> <s id="N12FFA"><!-- NEW -->præterea vna pars plumbi non <lb/>e&longs;t in loco alterius; </s> <s id="N13000"><!-- NEW -->nec enim inuicem penetrantur cum &longs;it compene­<lb/>tratio accidentium cum &longs;ubiecto; </s> <s id="N13006"><!-- NEW -->deinde, quò plures &longs;unt partes vnitæ, <lb/>maior e&longs;t re&longs;i&longs;tentia, quæ ip&longs;o etiam &longs;en&longs;u percipitur; </s> <s id="N1300C"><!-- NEW -->denique non vide­<lb/>tur cur potius produceretur in vna parte, quam in alia; quæ omnia <lb/>iam &longs;uprà Th. 33. demon&longs;trauimus. </s> </p> <p id="N13014" type="main"> <s id="N13016"><!-- NEW -->Adde quod &longs;i impetus produceretur in ip&longs;is accidentibus, etiam in <lb/>ip&longs;o impetu prius producto alius impetus produceretur; </s> <s id="N1301C"><!-- NEW -->cum &longs;cilicet <lb/>noua fit impetus acce&longs;&longs;io; quod &longs;atis ridiculum e&longs;t; qua&longs;i verò impetus <lb/>indigeat impetu &c. </s> <s id="N13024"><!-- NEW -->hîc loquor tantùm de accidentibus in &longs;ubiecto; <lb/>non verò de Euchari&longs;ticis, quæ à &longs;ubiecto per miraculum &longs;eparata etiam <lb/>moueri po&longs;&longs;unt per impre&longs;&longs;um impetum. </s> </p> <p id="N1302C" type="main"> <s id="N1302E"><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 1.<emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N1303B" type="main"> <s id="N1303D"><!-- NEW -->Hinc manife&longs;tè patet, quid dicendum &longs;it de anima bruti, quæ moue­<lb/>tur etiam &longs;ine impetu; </s> <s id="N13043"><!-- NEW -->quia exigit &longs;emper e&longs;&longs;e coniuncta corpori, à <lb/>quo di&longs;iuncta naturaliter exi&longs;tere non pote&longs;t, vt &longs;uo loco dicemus; igi­<lb/>tur ad motum corporis, &longs;eu &longs;ubiecti moueri deber. </s> </p> <p id="N1304B" type="main"> <s id="N1304D"><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 2.<emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N1305A" type="main"> <s id="N1305C"><!-- NEW -->Idem quoque de Anima rationali dicendum e&longs;&longs;e videtur; </s> <s id="N13060"><!-- NEW -->licèt <lb/>enim à corpore &longs;eparata naturaliter exi&longs;tere po&longs;&longs;it; </s> <s id="N13066"><!-- NEW -->tandiù tamen cum <lb/>corpore manet coniuncta, quandiu agere pote&longs;t in organis corporeis; <lb/>ac proinde exigit con&longs;eruari in corpore ip&longs;o, quandiu &longs;uas operatio­<lb/>nes organicas in eo exercere pote&longs;t. </s> </p> <p id="N13070" type="main"> <s id="N13072"><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 3.<emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N1307F" type="main"> <s id="N13081"><!-- NEW -->Hinc patet ratio manife&longs;ta ad quæ&longs;itum illud; </s> <s id="N13085"><!-- NEW -->quomodo &longs;cilicet po­<lb/>tentia motrix materialis v.g. <!-- REMOVE S-->Taurus &longs;uo cornu hominem ventilare po&longs;­<lb/>&longs;it; nec vlla &longs;upere&longs;t difficultas, dum dicas impetum non produci in <lb/>anima. </s> </p> <p id="N13091" type="main"> <s id="N13093"><emph type="center"/><emph type="italics"/>Scolium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N1309F" type="main"> <s id="N130A1"><!-- NEW -->Ob&longs;eruabis primò In hoc Theoremate dictum e&longs;&longs;e naturaliter; quia <lb/>per miraculum accidens &longs;eparatum ab omni &longs;ub&longs;tantia, dum &longs;it impe­<lb/>netrabile, per impetum &longs;ibi impre&longs;&longs;um moueri pote&longs;t. </s> </p> <p id="N130A9" type="main"> <s id="N130AB">Ob&longs;eruabis &longs;ecundò de anima bruti per miraculum &longs;eparatâ, idem <lb/>pror&longs;us dicendum e&longs;&longs;e. </s> </p> <p id="N130B0" type="main"> <s id="N130B2"><!-- NEW -->Ob&longs;eruabis tertiò etiam Animam rationalem &longs;eparatam, modò &longs;it <lb/>cum impenetrabilitate coniuncta, capacem e&longs;&longs;e impetus; </s> <s id="N130B8"><!-- NEW -->quem etiam <lb/>à potentia motrice corporea recipere pote&longs;t; </s> <s id="N130BE"><!-- NEW -->idem dictum e&longs;to de An­<lb/>gelo; &longs;ed de vtroque aliàs. </s> </p> <p id="N130C4" type="main"> <s id="N130C6"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 39.<emph.end type="center"/></s> </p> <p id="N130D2" type="main"> <s id="N130D4"><!-- NEW --><emph type="italics"/>Quando corpus pellitur ab alio corpore per impetum impre&longs;&longs;um; </s> <s id="N130DA"><!-- NEW -->haud du­<lb/>biè impetus ille impre&longs;&longs;us ab aliqua cau&longs;a efficiente producitur<emph.end type="italics"/>; patet <lb/>per Ax. 8. </s> </p> <pb pagenum="31" xlink:href="026/01/063.jpg"/> <p id="N130E9" type="main"> <s id="N130EB"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 40.<emph.end type="center"/></s> </p> <p id="N130F7" type="main"> <s id="N130F9"><emph type="italics"/>Ille impetus non producitur à &longs;ub&longs;tantia corporis in aliud impacti.<emph.end type="italics"/></s> <s id="N13100"> Proba­<lb/>tur; </s> <s id="N13105"><!-- NEW -->quia &longs;i produceretur, e&longs;&longs;et cau&longs;a nece&longs;&longs;aria vt <expan abbr="clarũ">clarum</expan> e&longs;t; igitur appli­<lb/>cata, & non impedita ageret per Ax. 32. quod e&longs;t contra experientiam. </s> <s id="N1310F"><!-- NEW --><lb/>Dicunt aliqui requiri <expan abbr="motũ">motum</expan> præuium, vt agat; &longs;ed contra; </s> <s id="N13118"><!-- NEW -->nam motus <lb/>præuius non requiritur vt cau&longs;a, vt patet; </s> <s id="N1311E"><!-- NEW -->quia cau&longs;a vt agat debet exi­<lb/>&longs;tere per Ax. 9. Igitur requiritur, vt conditio, quod dici non pote&longs;t; </s> <s id="N13124"><!-- NEW --><lb/>quia primo etiam conditio debet e&longs;&longs;e præ&longs;ens; </s> <s id="N13129"><!-- NEW -->&longs;ed motus præuius de <lb/>nihil pre&longs;enti e&longs;t &longs;ecundo quia non pote&longs;t excogitari aliud munus con­<lb/>ditionis; </s> <s id="N13131"><!-- NEW -->ni&longs;i vel vt tollat impedimentum, vel vt applicet cau&longs;am &longs;ubie­<lb/>cto apto; </s> <s id="N13137"><!-- NEW -->præterea motus præuius non e&longs;t; </s> <s id="N1313B"><!-- NEW -->igitur eodem modo &longs;e <lb/>habet, ac &longs;i nunquam extiti&longs;&longs;et; & &longs;i eo in&longs;tanti quo corpus impa­<lb/>ctum primo tangit, amitteret totum impetum, ita vt expræterito motu <lb/>nihil reliquum e&longs;&longs;et, haud dubiè corpus aliud non pelleret. </s> </p> <p id="N13145" type="main"> <s id="N13147"><!-- NEW -->Diceret alius impetum e&longs;&longs;e tantùm conditionem, quæ &longs;emper e&longs;t <lb/>de præ&longs;enti: </s> <s id="N1314D"><!-- NEW -->ad hanc in&longs;tantiam non valet &longs;uperior re&longs;pon&longs;io; </s> <s id="N13151"><!-- NEW -->& certè <lb/>&longs;i eo ip&longs;o in&longs;tanti contactus noua fieret impetus acce&longs;&longs;io; </s> <s id="N13157"><!-- NEW -->haud dubiè <lb/>maior e&longs;&longs;et ictus; </s> <s id="N1315D"><!-- NEW -->licèt cum eodem motu præuio, & tamen idem e&longs;&longs;et <lb/>corpus <expan abbr="impactũ">impactum</expan>, Igitur ad hanc <expan abbr="in&longs;tantiã">in&longs;tantiam</expan> alio modo re&longs;pondeo, ex appli­<lb/>catione impetus &longs;emper &longs;equitur productio alterius impetus; </s> <s id="N1316D"><!-- NEW -->dum &longs;cili­<lb/>cet &longs;ubiectum, cui applicatur &longs;it capax motus; </s> <s id="N13173"><!-- NEW -->ex applicatione corporis <lb/>&longs;eu &longs;ubiecti ip&longs;ius non &longs;emper &longs;equitur; igitur dicendum e&longs;t impetum <lb/>ip&longs;um e&longs;&longs;e cau&longs;am alterius per Ax. 11. n. </s> <s id="N1317B"><!-- NEW -->1. voco enim illud cau&longs;am, <lb/>ex cuius applicatione &longs;emper &longs;equitur &longs;imilis effectus; alioquin &longs;i hoc <lb/>neges; </s> <s id="N13183"><!-- NEW -->proba mihi aliter ignem accendi ab alio igne; </s> <s id="N13187"><!-- NEW -->dicam enim tibi <lb/>ignem applicatum e&longs;&longs;e tantùm conditionem, & produci à cœlo; proba <lb/>mihi aliter calorem produci à calore? </s> <s id="N1318F">quo enim medio, vel argu­<lb/>mento id euinces? </s> <s id="N13194"><!-- NEW -->quo etiam non euincam impetum produci ab im­<lb/>petu: Deinde affer rationem à priori, propter quam &longs;ub&longs;tantia <lb/>corporis producat impetum &longs;ur&longs;um? </s> <s id="N1319C"><!-- NEW -->v. <!-- REMOVE S-->g. <!-- REMOVE S-->cum non exigat à &longs;e ip&longs;a mo­<lb/>tum &longs;ursùm, qui violentus e&longs;t corpori graui; numquid certum e&longs;t, vt <lb/>dicemus infrà impetum produci ad extra, vt tollatur impedimentum <lb/>motus? </s> <s id="N131AA"><!-- NEW -->igitur illius e&longs;t tollere impedimentum, cuius e&longs;t exigere motum, <lb/>corpus ip&longs;um graue non exigit motum &longs;ur&longs;um, &longs;ed impetus; </s> <s id="N131B0"><!-- NEW -->igitur im­<lb/>petus e&longs;t tollere impedimentum &longs;ui effectus; </s> <s id="N131B6"><!-- NEW -->igitur producere impetum, <lb/>quo vno tolli tantùm pote&longs;t: </s> <s id="N131BC"><!-- NEW -->En tibi rationem à priori, cutum nullam <lb/>habeas: Præterea, cur negas impetum e&longs;&longs;e cau&longs;am &longs;ufficientem alterius <lb/>impetus, cum ex eius applicatione ip&longs;o &longs;en&longs;u percipiamus produci alium <lb/>impetum? </s> <s id="N131C6">quæ ratio? </s> <s id="N131C9"><!-- NEW -->quid inde ab&longs;urdi, quid incommodi: Igitur tàm <lb/>certum e&longs;t, immò certius impetum produci ab alio impetu, quàm calo­<lb/>rem à calore. </s> <s id="N131D1"><!-- NEW -->Dices impetum iam habere alium effectum &longs;cilicet mo­<lb/>tum; bella profecto ratio! &longs;ed numquid motus e&longs;t effectus formalis im­<lb/>petus? </s> <s id="N131D9">prætereà e&longs;t-ne effectus ad extra? </s> <s id="N131DC"><!-- NEW -->deinde idem dico de calore; </s> <s id="N131E0"><!-- NEW --><pb pagenum="32" xlink:href="026/01/064.jpg"/>qui reuera habet effectum formalem &longs;ecundarium ad intra, &longs;cilicet rare­<lb/>factionem, quæ e&longs;t mutatio exten&longs;ionis; </s> <s id="N131EA"><!-- NEW -->quemadmodum motus e&longs;t mu­<lb/>tatio loci, vel vbicationis; </s> <s id="N131F0"><!-- NEW -->igitur cum hoc | non ob&longs;tante, calor pro­<lb/>ducat calorem ad extra; cur impetus non producit impetum? </s> <s id="N131F6"><!-- NEW -->cuius pro­<lb/>ductionem concedis virtuti corporum re&longs;i&longs;titiuæ, id e&longs;t vnioni, impe­<lb/>netrabilitati, & cæteris huiu&longs;modi modorum &longs;uperfluorum qui&longs;quiliis; <lb/>de quibus plurimi tecum contendunt. </s> </p> <p id="N13200" type="main"> <s id="N13202"><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N1320E" type="main"> <s id="N13210"><!-- NEW -->Ob&longs;eruabis nonnullas e&longs;&longs;e difficultates, quæ communes &longs;unt etiam <lb/>illi &longs;ententiæ, quam &longs;equuntur ij, qui exi&longs;timant impetum ad extra <lb/>produci à corpore impacto; quas tamen facilè &longs;oluemus infrà in conti­<lb/>nuata no&longs;trorum Theorematum &longs;erie. </s> </p> <p id="N1321A" type="main"> <s id="N1321C"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 41.<emph.end type="center"/></s> </p> <p id="N13228" type="main"> <s id="N1322A"><emph type="italics"/>Aliquis impetus non producitur ab alio impetu.<emph.end type="italics"/></s> <s id="N13231"> Probatur, quia aliquis <lb/>impetus producitur ad intra à potentia motrice, vt patet. </s> <s id="N13236">2. cum non <lb/>detur progre&longs;&longs;us in infinitum, nec impetus idem producatur à &longs;e ip&longs;o, ad <lb/>aliquem tandem vltimum &longs;eu primum deueniendum e&longs;t, qui ab alio im­<lb/>petu non producatur. </s> </p> <p id="N1323F" type="main"> <s id="N13241"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 42.<emph.end type="center"/></s> </p> <p id="N1324D" type="main"> <s id="N1324F"><emph type="italics"/>Impetus producitur &longs;emper ad extra ab alio impetu.<emph.end type="italics"/></s> <s id="N13256"><!-- NEW --> Quia cum &longs;emper <lb/>ad illius productionem requiratur applicatio alterius impetus; certè <lb/>non e&longs;t ponenda alia cau&longs;a per Ax. 11. </s> </p> <p id="N1325E" type="main"> <s id="N13260"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 43.<emph.end type="center"/></s> </p> <p id="N1326C" type="main"> <s id="N1326E"><!-- NEW --><emph type="italics"/>Hinc impetus habet duplex munus cau&longs;æ; </s> <s id="N13274"><!-- NEW -->&longs;cilicet cau&longs;æ exigentis ad intra <lb/>& efficientis ad extra<emph.end type="italics"/>; vtrumque patet ex dictis. </s> </p> <p id="N1327D" type="main"> <s id="N1327F"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 44.<emph.end type="center"/></s> </p> <p id="N1328B" type="main"> <s id="N1328D"><!-- NEW --><emph type="italics"/>Impetus agit tantùm ad extra, vt tollat impedimentum motus<emph.end type="italics"/>; </s> <s id="N13296"><!-- NEW -->cum enim <lb/>motus &longs;it finis intrin&longs;ecus impetus; </s> <s id="N1329C"><!-- NEW -->certè &longs;i nihil impediret motum, <lb/>haud dubiè gauderet impetus &longs;uo fine; </s> <s id="N132A2"><!-- NEW -->igitur fru&longs;trà quidquam aliud <lb/>de&longs;ideraret; </s> <s id="N132A8"><!-- NEW -->præterea licèt applicetur à tergo aliud mobile; </s> <s id="N132AC"><!-- NEW -->non tamen <lb/>propterea in eo producit, vt con&longs;tat experientiâ; </s> <s id="N132B2"><!-- NEW -->denique cum tan­<lb/>tùm impetum cogno&longs;camus per motum; </s> <s id="N132B8"><!-- NEW -->cum nequidem e&longs;&longs;et impetus, <lb/>&longs;i non e&longs;&longs;et motus, per Th. 17. certè totus e&longs;t impetus propter motum <lb/>qui e&longs;t eius finis; </s> <s id="N132C0"><!-- NEW -->igitur non agit ni&longs;i propter motum: </s> <s id="N132C4"><!-- NEW -->&longs;ed non pote&longs;t <lb/>excogitari, quid faciat propter motum, dum agit, ni&longs;i dicamus ideo <lb/>tantùm agere, vt tollatur impedimentum; cum certum &longs;it corpus im­<lb/>mobile, in quod impingitur aliud mobile, impedire eius motum. </s> </p> <p id="N132CE" type="main"> <s id="N132D0"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 45.<emph.end type="center"/></s> </p> <p id="N132DC" type="main"> <s id="N132DE"><!-- NEW --><emph type="italics"/>Hinc non &longs;imul agit impetus in orbem &longs;ed tantùm per lineam <lb/>&longs;ui motus; </s> <s id="N132E6"><!-- NEW -->cui &longs;i nullum corpus occurrit reuerà non agit,<emph.end type="italics"/> Ratio e&longs;t; </s> <s id="N132ED"><!-- NEW -->quia li­<lb/>cèt aliud corpus mobili admoueatur in alia linea; </s> <s id="N132F3"><!-- NEW -->cum non impediat <lb/>eius motum, vt &longs;uppono; </s> <s id="N132F9"><!-- NEW -->cum agat tantùm impetus ad extra, vt tollat, <pb pagenum="33" xlink:href="026/01/065.jpg"/>impedimentum motu &longs;ui &longs;ubiecti, in eo non agit, quod non impedit; </s> <s id="N13302"><!-- NEW -->& <lb/>cum impediatur tantùm in vna linea, in ca tantùm agit; igitur non <lb/>agit in orbem. </s> </p> <p id="N1330A" type="main"> <s id="N1330C"><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N13318" type="main"> <s id="N1331A"><!-- NEW -->Ob&longs;eruabis primò, hanc primam e&longs;&longs;e difficultatem; cum in hoc im­<lb/>petus maximè differat ab alijs qualitatibus &longs;i quæ &longs;unt, quæ agunt in or­<lb/>bem, vt dicemus &longs;uo loco. </s> </p> <p id="N13322" type="main"> <s id="N13324"><!-- NEW -->Ob&longs;eruabis &longs;ecundò, hanc etiam e&longs;&longs;e communem illorum &longs;ententiam, <lb/>qui dicunt impetum ad extrà produci ab ip&longs;o mobili, &longs;ed ita vt ab illis <lb/>vix &longs;olui po&longs;&longs;it; cum tamen à nobis facilè &longs;oluatur. </s> </p> <p id="N1332C" type="main"> <s id="N1332E"><!-- NEW -->Ob&longs;eruabis tertiò, impetum in vtroque munere cau&longs;æ &longs;ube&longs;&longs;e tantùm <lb/>vni lineæ; </s> <s id="N13334"><!-- NEW -->&longs;cilicet exigit motum per vnam lineam; </s> <s id="N13338"><!-- NEW -->cum per plures &longs;i­<lb/>mul motus e&longs;&longs;e non po&longs;&longs;it; </s> <s id="N1333E"><!-- NEW -->ne idem mobile &longs;imul e&longs;&longs;et in pluribus lo­<lb/>cis; </s> <s id="N13344"><!-- NEW -->& producit impetum per vnam lineam; cum producat tantùm pro­<lb/>pter motum. </s> </p> <p id="N1334A" type="main"> <s id="N1334C"><!-- NEW -->Ob&longs;eruabis quartò, alias qualitates, &longs;i quæ &longs;unt, non agere ad extra, <lb/>vt tollant impedimentum &longs;ui effectus ad intra; </s> <s id="N13352"><!-- NEW -->qui &longs;cilicet ab impedi­<lb/>mento extrin&longs;eco impediri non pote&longs;t; </s> <s id="N13358"><!-- NEW -->vt accidit in ip&longs;o impetu; </s> <s id="N1335C"><!-- NEW -->etenim <lb/>corpus non pote&longs;t moueri ni&longs;i nouum locum acquirat: neque nouum <lb/>locum acquirere ab alio corpore occupatum, ni&longs;i corpus hoc loco ce­<lb/>dat, neque hoc loco cedere pote&longs;t &longs;ine motu, vel moueri &longs;ine impetu, <lb/>igitur cum impediat motum amoueri debet, accepto dumtaxat impetu <lb/>ab alio mobili. </s> </p> <p id="N1336A" type="main"> <s id="N1336C"><!-- NEW -->Ob&longs;eruabis quintò nonnullos e&longs;&longs;e, qui volunt motum vnius corporis <lb/>transferri in aliud corpus; </s> <s id="N13372"><!-- NEW -->&longs;ed mera e&longs;t metaphora; </s> <s id="N13376"><!-- NEW -->nihil cnim pror&longs;us <lb/>e&longs;t quod ab vno in aliud tran&longs;eat, &longs;eu transferatur; nec aliud dici po­<lb/>te&longs;t, ni&longs;i quod dictum e&longs;t, impetum &longs;cilicet nouum produci. </s> </p> <p id="N1337E" type="main"> <s id="N13380"><!-- NEW -->Hinc etiam reiicies commentum illorum, qui dicunt ideo vnum <lb/>corpus ab alio moueri, quia ab vno in aliud deriuantur corpu&longs;cula illa, <lb/>quæ faciunt lumen, & calorem; </s> <s id="N13388"><!-- NEW -->quia lumen, & calor &longs;unt veræ qualita­<lb/>tes, non corpu&longs;cula, vt demon&longs;trabimus in 5. tractatu: </s> <s id="N1338E"><!-- NEW -->Adde quod li­<lb/>cet ferrum candens aliud frigidum impellat, etiam veloci&longs;&longs;imè; </s> <s id="N13394"><!-- NEW -->hoc ip­<lb/>&longs;um æquè frigidum manet; </s> <s id="N1339A"><!-- NEW -->denique in cra&longs;&longs;is tenebris nix &longs;eu glacies <lb/>frigidi&longs;&longs;ima pernici&longs;&longs;imè moueri pote&longs;t: &longs;ed apage i&longs;ta commenta. </s> </p> <p id="N133A0" type="main"> <s id="N133A2"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 46.<emph.end type="center"/></s> </p> <p id="N133AE" type="main"> <s id="N133B0"><emph type="italics"/>Omnes partes impetus mobilis agunt ad extra actione communi.<emph.end type="italics"/></s> <s id="N133B7"> Probatur <lb/>per Ax. 13. n. </s> <s id="N133BC"><!-- NEW -->1. ni&longs;i enim agerent actione communi &longs;ed quælibet &longs;uam <lb/>produceret; </s> <s id="N133C2"><!-- NEW -->cur potius in hac parte &longs;ubiecti, quam in alia, deinde ap­<lb/>plicatur tantùm vna immediatè; </s> <s id="N133C8"><!-- NEW -->Igitur agunt omnes actione commu­<lb/>ni; </s> <s id="N133CE"><!-- NEW -->omnes inquam illæ, quæ impediuntur; </s> <s id="N133D2"><!-- NEW -->cum enim impetus agat <lb/>tantùm ad extrà vt tollat impedimentum &longs;ui motus; ille pro&longs;ectò age­<lb/>re non debet, cuius motus vel effectus non impeditur. </s> </p> <pb pagenum="34" xlink:href="026/01/066.jpg"/> <p id="N133DE" type="main"> <s id="N133E0"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 47.<emph.end type="center"/></s> </p> <p id="N133EC" type="main"> <s id="N133EE"><emph type="italics"/>Hinc maiora corpora putà onerariæ naues, licèt tardi&longs;&longs;imo motu ferantur, <lb/>cum in aliud corpus impinguntur maxima vi illud impellunt.<emph.end type="italics"/></s> <s id="N133F7"> Ratio e&longs;t; <lb/>quia cum &longs;int plures partes impetus in pluribus partibus &longs;ubiecti, & <lb/>omnes agant actione communi, non mirum e&longs;t &longs;i maiorem effectum <lb/>producant, per Ax. 13. n. </s> <s id="N13400">2. <!-- KEEP S--></s> </p> <p id="N13404" type="main"> <s id="N13406"><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N13412" type="main"> <s id="N13414"><!-- NEW -->Vides primò in hoc ca&longs;u compen&longs;ari inten&longs;ionem ab exten&longs;ione; </s> <s id="N13418"><!-- NEW --><lb/>quippe quod præ&longs;tarent plures partes impetus in minore corporis mole <lb/>inten&longs;æ; hoc idem præ&longs;tare po&longs;&longs;unt exten&longs;æ in maiore mole. </s> </p> <p id="N1341F" type="main"> <s id="N13421">Secundò &longs;icut maior moles aptior e&longs;t ad motum imprimendum, & mi­<lb/>nùs apta ad recipiendum ita minor contrà aptior e&longs;t ad recipiendum, & <lb/>minùs apta ad imprimendum. </s> </p> <p id="N13428" type="main"> <s id="N1342A"><!-- NEW -->Tertiò, Hinc corpora illa, quorum partes vel nullo vel modico nexu <lb/>copulantur, minimo ferè impul&longs;u commouentur; </s> <s id="N13430"><!-- NEW -->&longs;ic aër & aqua mini­<lb/>mo flante vento agitantur, nubes pelluntur; </s> <s id="N13436"><!-- NEW -->hinc tot procellæ tempe­<lb/>&longs;tate&longs;que cientur; nec vlla e&longs;t alia ratio, cur minima ferè venti vis, cui <lb/>modicum &longs;axum re&longs;i&longs;tit, tantam aquæ, vel aëris molem commoueat, ni­<lb/>&longs;i quia cum partes illorum corporum nullo ferè nexu coniunctæ &longs;int vna <lb/>&longs;ine alia moueri pote&longs;t, quod in aqua gelu concreta minimè accidit. </s> </p> <p id="N13442" type="main"> <s id="N13444">Quartò, Hinc &longs;i maxima rupes ita comminueretur vt tota in pulue­<lb/>rem &longs;eu &longs;abulum abiret, minima vis impre&longs;&longs;a particulas illas moueret. </s> </p> <p id="N13449" type="main"> <s id="N1344B"><!-- NEW -->Quintò, Hinc diuino penè con&longs;ilio factum e&longs;t, vt partes terre&longs;tris <lb/>globi arctiore fibula copulentur; </s> <s id="N13451"><!-- NEW -->ne, &longs;i di&longs;iunctæ e&longs;&longs;ent, minimo flatu <lb/>di&longs;pergerentur: vt videre e&longs;t in puluere etiam graui&longs;&longs;imo, qui ab aura <lb/>flant e di&longs;pergitur. </s> </p> <p id="N13459" type="main"> <s id="N1345B"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 48.<emph.end type="center"/></s> </p> <p id="N13467" type="main"> <s id="N13469"><emph type="italics"/>Impetus, cuius motus non impeditur, non agit ad extrà.<emph.end type="italics"/></s> <s id="N13470"><!-- NEW --> Probatur per <lb/>Th. 44. hinc &longs;i aliud corpus affigas mobili à tergo, nullum impetum in <lb/>eo producet, cuius effectus, qui certè impetui &longs;ingularis e&longs;t, alia ratio <lb/>e&longs;&longs;e non pote&longs;t; </s> <s id="N1347A"><!-- NEW -->tam enim corpus e&longs;t applicatum à tergo, quam in <lb/>ip&longs;a fronte; & nihil e&longs;t in vno, quod non &longs;it in alio, ni&longs;i quod in fronte <lb/>impedit motum, à tergo verò non impedit. </s> </p> <p id="N13482" type="main"> <s id="N13484"><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 1.<emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N13491" type="main"> <s id="N13493"><!-- NEW -->Hinc egregium paradoxon erui pote&longs;t; </s> <s id="N13497"><!-- NEW -->quod &longs;cilicet cau&longs;a nece&longs;&longs;aria <lb/>etiam immediatè applicata, & non impedita in &longs;ubiecto apto non agit; </s> <s id="N1349D"><!-- NEW --><lb/>quod videtur e&longs;&longs;e contra Ax. 12. vnde vt agat cau&longs;a nece&longs;&longs;aria, debet <lb/>applicari debito modo; </s> <s id="N134A4"><!-- NEW -->&longs;i agat in orbem, omnis applicatio &longs;ufficiens <lb/>e&longs;t: </s> <s id="N134AA"><!-- NEW -->&longs;i verò agat tantùm per vnam lineam; </s> <s id="N134AE"><!-- NEW -->certè applicari debet in ca <lb/>linea; alioquin non aget defectu debitæ applicationis. </s> </p> <p id="N134B4" type="main"> <s id="N134B6"><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 2.<emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N134C3" type="main"> <s id="N134C5"><!-- NEW -->Hinc etiam aliud paradoxon non minus iucundum; </s> <s id="N134C9"><!-- NEW -->cau&longs;a nece&longs;&longs;aria <pb pagenum="35" xlink:href="026/01/067.jpg"/>appllcata, & non impedita non agit; </s> <s id="N134D2"><!-- NEW -->at verò agit impedita; </s> <s id="N134D6"><!-- NEW -->&longs;cilicet <lb/>impetus qui tantùm agit, vt tollat impedimentum; igitur, &longs;i non <lb/>impediatur non agit. </s> </p> <p id="N134DE" type="main"> <s id="N134E0"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 49.<emph.end type="center"/></s> </p> <p id="N134EC" type="main"> <s id="N134EE"><!-- NEW --><emph type="italics"/>Quo minùs impeditur impetus, minùs agit ad extra, & contrà; quo plùs <lb/>impeditur, plùs agit.<emph.end type="italics"/></s> <s id="N134F8"><!-- NEW --> Cum enim ideò agat ad extra, vt tollat impedi­<lb/>mentum; </s> <s id="N134FE"><!-- NEW -->certè &longs;i nullum e&longs;t, nihil agit, &longs;i minùs, minùs agit; igitur <lb/>agit pro rata, id e&longs;t, pro diuer&longs;a impedimenti ratione. </s> </p> <p id="N13504" type="main"> <s id="N13506"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 50.<emph.end type="center"/></s> </p> <p id="N13512" type="main"> <s id="N13514"><emph type="italics"/>Si linea motus, quam directionis appellant, ducatur per centrum vtriu&longs;que <lb/>corporis, maximum est impedimentum,<emph.end type="italics"/> vt patet. </s> <s id="N1351E"><!-- NEW -->&longs;int enim duo globi, <lb/>A mobilis, & B. occurrens ip&longs;i A, &longs;itque linea directionis DE ducta <lb/>per centrum vtriu&longs;que AB, & punctum contactus &longs;it C; </s> <s id="N13526"><!-- NEW -->certè glo­<lb/>bus B maximum ponit impedimentum, quod ab eo poni po&longs;&longs;it; </s> <s id="N1352C"><!-- NEW -->Igitur <lb/>impetus globi A agit quantùm pote&longs;t in globum B; vt &longs;cilicet maxi­<lb/>mum impedimentum remoueat. </s> </p> <p id="N13534" type="main"> <s id="N13536"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 51.<emph.end type="center"/></s> </p> <p id="N13542" type="main"> <s id="N13544"><!-- NEW --><emph type="italics"/>Si linea motus vel ip&longs;ius parallela cadat perpendiculariter in extremam <lb/>diametrum globi immobilis: </s> <s id="N1354C"><!-- NEW -->haud dubiè nihil impedit<emph.end type="italics"/>; </s> <s id="N13553"><!-- NEW -->&longs;it enim globus <lb/>mobilis A, Immobilis B, linea directionis &longs;it GA, ip&longs;i parallela FC; </s> <s id="N13559"><!-- NEW --><lb/>certè globus B. non impedit motum globi A. cum nihil loci globi B <lb/>occupari debeat à globo A; Igitur impetus A non agit in globum B per <lb/>Th. 48. </s> </p> <p id="N13562" type="main"> <s id="N13564"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 52.<emph.end type="center"/></s> </p> <p id="N13570" type="main"> <s id="N13572"><!-- NEW --><emph type="italics"/>Si linea motus &longs;it inter vtramque; </s> <s id="N13578"><!-- NEW -->est minus impedimentum.<emph.end type="italics"/> &longs;it globus <lb/>immobilis BA; </s> <s id="N13581"><!-- NEW -->&longs;it linea motus GC cum impedimento, de qua in Th. 50. <lb/>&longs;it alia KB cum nullo impedimento, de qua in Th. 51. &longs;int aliæ HD, <lb/>IE; </s> <s id="N13589"><!-- NEW -->certè minus e&longs;t impedimentum in contactu D, quàm in C; </s> <s id="N1358D"><!-- NEW -->quia ca­<lb/>dit obliquè in D, perinde atque &longs;i caderet in tangentem NO; Igitur <lb/>minus impeditur; in qua vero proportione, dicemus aliàs, cum de re­<lb/>flexione, & de motu mixto. </s> </p> <p id="N13597" type="main"> <s id="N13599"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 53.<emph.end type="center"/></s> </p> <p id="N135A5" type="main"> <s id="N135A7"><!-- NEW --><emph type="italics"/>Hinc producitur in contactu<emph.end type="italics"/> C, <emph type="italics"/>totus impetus; </s> <s id="N135B3"><!-- NEW -->in contactu<emph.end type="italics"/> D, <emph type="italics"/>minùs; </s> <s id="N135BD"><!-- NEW -->in <lb/>contactu<emph.end type="italics"/> E <emph type="italics"/>adhuc minùs; </s> <s id="N135C9"><!-- NEW -->in<emph.end type="italics"/> B <emph type="italics"/>nihil<emph.end type="italics"/>; </s> <s id="N135D6"><!-- NEW -->quia in ea proportione producitur <lb/>plùs vel minùs impetus, quo plùs e&longs;t, vel minùs impedimenti per <lb/>Th. 49. &longs;ed minùs e&longs;t impedimentum in E, quàm in C; </s> <s id="N135DE"><!-- NEW -->& in E, quàm <lb/>in D, per Th. 52; Igitur in D producitur minùs impetus, quàm in C, <lb/>& minùs in E, quàm in D. <!-- KEEP S--></s> </p> <p id="N135E7" type="main"> <s id="N135E9"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 54.<emph.end type="center"/></s> </p> <p id="N135F5" type="main"> <s id="N135F7"><!-- NEW --><emph type="italics"/>Hinc eadem cau&longs;a nece&longs;&longs;aria etiam immediate applicata diuer&longs;um impe<emph.end type="italics"/><pb pagenum="36" xlink:href="026/01/068.jpg"/><emph type="italics"/>tum producit; vt patet in impetu, non tamen est eodem modo applicata, <lb/>id e&longs;t in eadem linea.<emph.end type="italics"/></s> </p> <p id="N1360A" type="main"> <s id="N1360C"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 55.<emph.end type="center"/></s> </p> <p id="N13618" type="main"> <s id="N1361A"><emph type="italics"/>Hinc ratio multorum effectuum phy&longs;icorum e. </s> <s id="N1361F">ui potest<emph.end type="italics"/>; </s> <s id="N13625"><!-- NEW -->cur &longs;cilicet cor­<lb/>pus incidens in aliud perpendiculariter maximum ictum infligat; </s> <s id="N1362B"><!-- NEW -->quia <lb/>&longs;cilicet maximum impetum producit, qui po&longs;&longs;it ab eo produci; </s> <s id="N13631"><!-- NEW -->cur <lb/>idem corpus obliquè incidens in aliud minorem ictum infligat; cuius <lb/>rei alia ratio e&longs;&longs;e non pote&longs;t. </s> <s id="N13639"><!-- NEW -->Huc etiam reuoca tormenta bellica, quæ <lb/>vel directo, vel obliquo ictu muros verberant; </s> <s id="N1363F"><!-- NEW -->hinc perpendicularis <lb/>forti&longs;&longs;ima e&longs;t; licèt eadem ratio pro motu corporum non valeat, quæ <lb/>valet pro diffu&longs;ione, &longs;eu propagatione qualitatum. </s> </p> <p id="N13647" type="main"> <s id="N13649"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 56.<emph.end type="center"/></s> </p> <p id="N13655" type="main"> <s id="N13657"><!-- NEW -->Hinc pote&longs;t determinari quota pars impetus producatur, & quantus <lb/>&longs;it ictus; </s> <s id="N1365D"><!-- NEW -->cognito &longs;cilicet & &longs;uppo&longs;ito eo impetus gradu, qui producitur, <lb/>cum totus producitur, vt fit in perpendiculari; </s> <s id="N13663"><!-- NEW -->quippe tota men&longs;ura <lb/>impetus continetur in arcu CB; quam proportionem nos infrà demon­<lb/>&longs;trabimus. </s> </p> <p id="N1366B" type="main"> <s id="N1366D"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 57.<emph.end type="center"/></s> </p> <p id="N13679" type="main"> <s id="N1367B"><!-- NEW --><emph type="italics"/>Si linea directionis ducatur per centrum vtriu&longs;que globi, mobilis &longs;cilicet <lb/>& immobilis, impetus producit totum impetum quem pote&longs;t producere &longs;iue in <lb/>maiori globo, &longs;iue in minori, &longs;iue in æquali<emph.end type="italics"/>; patet experientia; cuius ratio <lb/>e&longs;t; </s> <s id="N1368A"><!-- NEW -->quia impetus e&longs;t cau&longs;a nece&longs;&longs;aria; </s> <s id="N1368E"><!-- NEW -->Igitur idem impetus eodem mo­<lb/>do applicatus æquali tempore, æqualem &longs;emper effectum producit, per <lb/>Ax. 12. igitur cum impetus agat tantùm, vt tollat impedimentum per <lb/>Th. 44. & cum in prædicta linea agat quantum pote&longs;t per Th. 50. cer­<lb/>tè æqualem effectum producat nece&longs;&longs;e e&longs;t; &longs;iue in maiori &longs;iue in mino­<lb/>ri, &longs;iue in æquali globo immobili. </s> </p> <p id="N1369C" type="main"> <s id="N1369E"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 58.<emph.end type="center"/></s> </p> <p id="N136AA" type="main"> <s id="N136AC"><!-- NEW --><emph type="italics"/>Hinc impetus remi&longs;&longs;us potest producere inten&longs;um; </s> <s id="N136B2"><!-- NEW -->& hæc e&longs;t altera difficul­<lb/>tas; </s> <s id="N136B8"><!-- NEW -->cum &longs;cilicet maior globus in minorem impingitur<emph.end type="italics"/>; </s> <s id="N136BF"><!-- NEW -->cum enim omnes <lb/>partes impetus maioris globi agant actione communi per Th. 46. & <lb/>cum agant quantùm maximè po&longs;&longs;unt; </s> <s id="N136C7"><!-- NEW -->in minore globo, tot partes pro­<lb/>ducunt impetus, quot in maiore, vt patet; </s> <s id="N136CD"><!-- NEW -->igitur in minore globo pau­<lb/>cioribus partibus &longs;ubiecti di&longs;tribuuntur plures partes impetus; </s> <s id="N136D3"><!-- NEW -->crgo in <lb/>qualibet parte &longs;ubiecti &longs;unt plures; </s> <s id="N136D9"><!-- NEW -->&longs;ed hoc e&longs;t e&longs;&longs;e inten&longs;um, vt con&longs;tat, <lb/>igitur impetus remi&longs;&longs;us producit inten&longs;um; quod e&longs;t paradoxon egre­<lb/>gium. </s> </p> <p id="N136E1" type="main"> <s id="N136E3"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 59.<emph.end type="center"/></s> </p> <p id="N136EF" type="main"> <s id="N136F1"><!-- NEW --><emph type="italics"/>Hinc etiam impetus inten&longs;us producit remi&longs;&longs;um, cum &longs;cilicet minor globus <lb/>in maiorem incidit<emph.end type="italics"/>; </s> <s id="N136FC"><!-- NEW -->quia &longs;cilicet pauciores partes impetus di&longs;tribuun­<lb/>tur pluribus partibus &longs;ubiecti; </s> <s id="N13702"><!-- NEW -->igitur quælibet &longs;ubiecti pauciores impe­<lb/>tus habet; quæ omnia con&longs;tant ex dictis. </s> </p> <pb pagenum="37" xlink:href="026/01/069.jpg"/> <p id="N1370C" type="main"> <s id="N1370E"><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N1371A" type="main"> <s id="N1371C"><!-- NEW -->Ob&longs;eruabis primò, &longs;ingularem impetus proprietatem, quæ alijs qua­<lb/>litatibus minimè competit; </s> <s id="N13722"><!-- NEW -->nam aliæ qualitates v. <!-- REMOVE S-->g. <!-- REMOVE S-->calor; </s> <s id="N1372A"><!-- NEW -->lumen in <lb/>eadem di&longs;tantia effectum &longs;emper æquè inten&longs;um producunt; </s> <s id="N13730"><!-- NEW -->&longs;ecus verò <lb/>impetus, qui pro maiori vel minori obice maiorem, vel minorem, hoc <lb/>e&longs;t inten&longs;iorem, vel remi&longs;&longs;iorem impetum in eadem di&longs;tantia producit; </s> <s id="N13738"><!-- NEW --><lb/>cuius ratio ex eo capite petitur; </s> <s id="N1373D"><!-- NEW -->quòd impetus agat tantùm ad extra <lb/>propter &longs;uum effectum ad intra, vt &longs;cilicet tollat impedimentum; </s> <s id="N13743"><!-- NEW -->igi­<lb/>tur in totum, quod impedit, agit; </s> <s id="N13749"><!-- NEW -->igitur non habet certam, & deter­<lb/>minatam &longs;phæram; </s> <s id="N1374F"><!-- NEW -->cum tantùm agat in obicem, &longs;iue &longs;it maior, &longs;iue <lb/>minor: </s> <s id="N13755"><!-- NEW -->Quia verò e&longs;t cau&longs;a nece&longs;&longs;aria, æqualem effectum producit, id <lb/>e&longs;t tot partes impetus in maiore, quot in minore, ergo, cum in mino­<lb/>re &longs;int pauciores partes &longs;ubiecti, & plures in maiore; </s> <s id="N1375D"><!-- NEW -->haud dubiè quæli­<lb/>bet pars minoris habebit plures partes effectus, & quælibet pars maio­<lb/>ris pauciores; igitur effectus erit inten&longs;ior in minore, & remi&longs;&longs;ior in <lb/>maiore. </s> </p> <p id="N13767" type="main"> <s id="N13769"><!-- NEW -->Prætereà, cum dixi omnes partes mobilis actione communi agere ad <lb/>extra; </s> <s id="N1376F"><!-- NEW -->ita primò intelligi debet, vt omnes illæ partes moueantur: </s> <s id="N13773"><!-- NEW -->&longs;ecun­<lb/>dò, vt linea motus, &longs;eu directionis per centra grauitatis vtriu&longs;que glo­<lb/>bi v, g. <!-- REMOVE S-->ducatur; </s> <s id="N1377D"><!-- NEW -->alioquin, vel omnes actione communi non agunt, vel <lb/>minus agunt, de quo infrà; </s> <s id="N13783"><!-- NEW -->&longs;ufficit verò iuxta præ&longs;ens in&longs;titutum, vt <lb/>globus ita impellat alium vel æqualem, vel inæqualem, vt linea dire­<lb/>ctionis ducatur per centrum grauitatis alterius; vide figuram. </s> <s id="N1378B">in qua <lb/>linea directionis e&longs;t DE. </s> </p> <p id="N13790" type="main"> <s id="N13792"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 60.<emph.end type="center"/></s> </p> <p id="N1379E" type="main"> <s id="N137A0"><!-- NEW --><emph type="italics"/>Impetus globi impacti in alium globum eo modo, quo diximus, id est, linea <lb/>directionis ducta per centra grauitatis vtriu&longs;que producit in eo æqualem<emph.end type="italics"/>; </s> <s id="N137AB"><!-- NEW -->Pro­<lb/>batur, quia impetus e&longs;t cau&longs;a nece&longs;&longs;aria, quæ tunc agit quantum pote&longs;t <lb/>per Th. 57. &longs;ed æqualis pote&longs;t producere æqualem: </s> <s id="N137B3"><!-- NEW -->Probatur primò, <lb/>exemplo aliarum qualitatum; </s> <s id="N137B9"><!-- NEW -->&longs;ecundò, quia ideo agit vt tollat impedi­<lb/>mentum, hoc e&longs;t vt corpus illud amoueat loco; </s> <s id="N137BF"><!-- NEW -->igitur æquali motu per <lb/>&longs;e; </s> <s id="N137C5"><!-- NEW -->alioquin ni&longs;i æquali motu amoueret, non tolleret impedimentum, <lb/>vt pater; </s> <s id="N137CB"><!-- NEW -->tertiò &longs;int 30. partes impetus, certèvel producent plures vel <lb/>pauciores, vel totidem, non plures; </s> <s id="N137D1"><!-- NEW -->cur enim potius 31. quam 32. <lb/>nec etiam pauciores; cur enim potius 20. quam 18, &c. </s> <s id="N137D7"><!-- NEW -->Igitur totidem; </s> <s id="N137DB"><!-- NEW --><lb/>quia cum &longs;int plures numeri plurium partium &longs;upra 30. & pauciorum <lb/>infra vt patet; </s> <s id="N137E2"><!-- NEW -->&longs;itque tantùm vnicus numerus æqualium; </s> <s id="N137E6"><!-- NEW -->certè quod <lb/>vnum e&longs;t, determinatum e&longs;t, per Ax. 5. hæc ratio licèt videatur negati­<lb/>ua e&longs;t tamen potenti&longs;&longs;ima: </s> <s id="N137EE"><!-- NEW -->quartò, quia actus &longs;ecundus, re&longs;pondet actui <lb/>primo, id e&longs;t, effectus productus virtuti cau&longs;æ producentis; </s> <s id="N137F4"><!-- NEW -->itaque cum <lb/>virtus agendi impetus &longs;it eius entitas, vt patet, certè impetus productus <lb/>e&longs;t per &longs;e æqualis impetui producenti per &longs;e; id e&longs;t remoto omni <lb/>impedimento, & facto eo contactu iuxta modum prædictum, ea quo-<pb pagenum="38" xlink:href="026/01/070.jpg"/>que lege, vt impetus agat quantum pote&longs;t, & omnes partes mobilis <lb/>moueantur æquali motu. </s> </p> <p id="N13805" type="main"> <s id="N13807"><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 1.<emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N13814" type="main"> <s id="N13816"><!-- NEW -->Hinc reijcis illos, qui volunt à globo æquali produci in æquali &longs;ub­<lb/>duplum impetum; in &longs;ubduplo &longs;ubtriplum; in &longs;ubquadruplo &longs;ubquin­<lb/>tuplum; ratio illorum e&longs;t; </s> <s id="N1381E"><!-- NEW -->quia duo globi æquales in&longs;tanti contactus <lb/>perinde &longs;e habent, atque &longs;i conflarent vnum corpus; </s> <s id="N13824"><!-- NEW -->&longs;ed &longs;i conflarent <lb/>vnum corpus quilibet &longs;ubduplum impetum haberet; </s> <s id="N1382A"><!-- NEW -->&longs;i verò globus cum <lb/>alio &longs;ubduplo faceret vnum mobile; </s> <s id="N13830"><!-- NEW -->haud dubiè minor, id e&longs;t, &longs;ubduplus <lb/>haberet tantùm &longs;ubtriplum impetum; atque ita deinceps; </s> <s id="N13836"><!-- NEW -->hoc totum <lb/>fal&longs;i&longs;&longs;imum e&longs;t; </s> <s id="N1383C"><!-- NEW -->nam primò &longs;i globus æqualis acciperet tantùm &longs;ubdu­<lb/>plum impetum ab alio, &longs;ubduplo tantùm motu ferretur; </s> <s id="N13842"><!-- NEW -->igitur &longs;ubdu­<lb/>plum &longs;patium decurreret, quod e&longs;t contra experientiam, & Th. 47. Se­<lb/>cundò, ratio propo&longs;ita nulla e&longs;t; </s> <s id="N1384A"><!-- NEW -->quia quando globus impactus impellit <lb/>alium, e&longs;t veluti potentiâ, quæ cum tota&longs;ua vi, & cum impetu agit, <lb/>cuius nulla pars transfertur in alium globum; </s> <s id="N13852"><!-- NEW -->nec enim migrat de <lb/>de &longs;ubiecto in &longs;ubiectum, &longs;ed producit &longs;ibi æqualem: </s> <s id="N13858"><!-- NEW -->equidem &longs;i duo <lb/>globi æquales e&longs;&longs;ent vel coniuncti, vel contigui in linea directionis, <lb/>quilibet pro rata acciperet impetus producti partem à potentia applica­<lb/>ta; </s> <s id="N13862"><!-- NEW -->&longs;i e&longs;&longs;ent æquales, qui&longs;que &longs;ubduplum: &longs;i alter &longs;ubduplus &longs;ubtri­<lb/>plum, &c. </s> <s id="N13868">&longs;ed hæc &longs;unt &longs;atis facilia. </s> </p> <p id="N1386B" type="main"> <s id="N1386D"><!-- NEW -->Obijci fortè po&longs;&longs;et ab aliquo primò experientia; </s> <s id="N13871"><!-- NEW -->videmus enim &longs;æpè <lb/>globum impul&longs;um in ludo Tudiculario moueri tardiùs globo impellen­<lb/>te; </s> <s id="N13879"><!-- NEW -->re&longs;pondeo id &longs;æpè accidere; </s> <s id="N1387D"><!-- NEW -->tùm quia linea directionis non connec­<lb/>tit centra vtriu&longs;que globi; </s> <s id="N13883"><!-- NEW -->igitur minor e&longs;t ictus per Th 52. tùm quia <lb/>globus impellens, vel impul&longs;us deficiunt à perfecta &longs;phæra; </s> <s id="N13889"><!-- NEW -->tùm quia <lb/>non e&longs;t perfecta æqualitas globorum; adde quod quò accuratiùs prædi­<lb/>ctæ leges ob&longs;eruantur, ip&longs;i motus ad æqualitatem propiùs accedunt, vt <lb/>con&longs;tat experientia. </s> </p> <p id="N13893" type="main"> <s id="N13895"><!-- NEW -->Obiici po&longs;&longs;et &longs;ecundò de&longs;trui aliquid impetus globi impellentis ab ip&longs;o <lb/>ictu, vt con&longs;tat experientia; </s> <s id="N1389B"><!-- NEW -->igitur illa pars impetus, quæ de&longs;truitur, non <lb/>producit nouum impetum in globo impul&longs;o; </s> <s id="N138A1"><!-- NEW -->Re&longs;pondeo de&longs;truiquidem <lb/>aliquid impetus in globo impacto, vt videbimus infrà; </s> <s id="N138A7"><!-- NEW -->cum tamen de­<lb/>&longs;truatur tantùm &longs;equenti po&longs;t ictum in&longs;tanti; </s> <s id="N138AD"><!-- NEW -->certè cum exi&longs;tat adhuc <lb/>ip&longs;o in&longs;tanti contactus, nece&longs;&longs;ariò agit, quippe aliquid vltimo in&longs;tanti <lb/>pote&longs;t agere; </s> <s id="N138B5"><!-- NEW -->adde quod illud ip&longs;um repugnat manife&longs;tæ experientiæ; </s> <s id="N138B9"><!-- NEW --><lb/>licèt enim aliquando de&longs;truatur totus impetus in globo impacto, quod <lb/>&longs;æpè accidit in ludo Tudiculario, nam illicò &longs;i&longs;tit pila eburnea; alius <lb/>tamen globus velociter mouetur, cuius effectus rationem infrà addu­<lb/>cemus. </s> </p> <p id="N138C4" type="main"> <s id="N138C6"><!-- NEW -->Obijci po&longs;&longs;et tertiò inde &longs;equi progre&longs;&longs;um in infinitum, nam globus <lb/>A impactus in globum B impellet cum æquali motu, & B in C etiam <lb/>æquali, C in D, atque ita deinceps; </s> <s id="N138CE"><!-- NEW -->modò illi globi ita &longs;tatuantur, vt <lb/>linea directionis per omnium centra rectà ducatur; </s> <s id="N138D4"><!-- NEW -->Re&longs;pondco, vel il-<pb pagenum="39" xlink:href="026/01/071.jpg"/>los omnes globos ita e&longs;&longs;e contiguos, vt mutuo contactu &longs;e inuicem tan­<lb/>gant; </s> <s id="N138DF"><!-- NEW -->vel aliquod &longs;patium inter &longs;ingulos intercipi; </s> <s id="N138E3"><!-- NEW -->&longs;i primum, produci­<lb/>tur impetus à potentia motrice in omnibus, &longs;i &longs;ufficiens e&longs;t; </s> <s id="N138E9"><!-- NEW -->non verò <lb/>vnus globus in alio, vt con&longs;tat; </s> <s id="N138EF"><!-- NEW -->&longs;icut duo pondera &longs;imul attollo, quorum <lb/>vnum alteri incumbit: </s> <s id="N138F5"><!-- NEW -->&longs;i verò non &longs;e tangant, dico antequam A im­<lb/>pingatur in B, dum &longs;patium illud interiectum percurrit, amittere aliquid <lb/>impetus: </s> <s id="N138FD"><!-- NEW -->idem dico de B, & C, vnde &longs;i nihil impetus in eo primo motu <lb/>periret & linea directionis omnium centra perfectè connecteret; </s> <s id="N13903"><!-- NEW -->ita vt <lb/>omnium ictus illi omnino &longs;ine vlla deflexione re&longs;ponderent; </s> <s id="N13909"><!-- NEW -->haud du­<lb/>biè non po&longs;&longs;ent e&longs;&longs;e tot globi, quin po&longs;&longs;et alius addi, qui ab vltimo <lb/>pelleretur; </s> <s id="N13911"><!-- NEW -->&longs;ed vix illa omnia de quibus &longs;uprà po&longs;&longs;unt ob&longs;eruari; </s> <s id="N13915"><!-- NEW -->Hinc <lb/>tamen facilè vna pars aëris aliam pellit, quod di&longs;tinctè videmus in <lb/>aqua; &longs;ed de his aliàs, &longs;ufficiat modò propo&longs;itam obiectionem inde <lb/>manere &longs;olutam. </s> </p> <p id="N1391F" type="main"> <s id="N13921"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 61.<emph.end type="center"/></s> </p> <p id="N1392D" type="main"> <s id="N1392F"><!-- NEW --><emph type="italics"/>Globus maior impactus in minorem imprimit illi inten&longs;iorem impetum, & <lb/>velociorem motum per Th.<emph.end type="italics"/> 48. <emph type="italics"/>&<emph.end type="italics"/> 47. Nec e&longs;t quod aliqui opponant Prin­<lb/>cipium illud mechanicum; </s> <s id="N13942"><!-- NEW -->id e&longs;t, nullum corpus po&longs;&longs;e maiorem veloci­<lb/>tatis gradum alteri corpori imprimere; </s> <s id="N13948"><!-- NEW -->eo &longs;cilicet gradu, quem ip&longs;um <lb/>habet; </s> <s id="N1394E"><!-- NEW -->nec enim inuenio Principium illud apud eos Mechanicos, qui <lb/>mechanica momenta &longs;uarum demon&longs;trationum momentis confirmant; <lb/>quî porro fieri pote&longs;t, vt principium illud admittatur, quod manife&longs;tæ <lb/>experientiæ repugnat? </s> <s id="N13958">Quis enim non vidit vel maius &longs;axum in aliud <lb/>etiam tardo motu impactum maiorem motum, & impetum imprimere? </s> <s id="N1395D"><lb/>quis non vidit maiores illas onerarias naues etiam pigro, & tardo motu <lb/>labentes maximum impetum minori occurrenti cymbæ etiam impri­<lb/>mere? </s> <s id="N13965"><!-- NEW -->Rationem habes in Th. 47. &longs;ed dices; </s> <s id="N13969"><!-- NEW -->igitur aliquis velocitatis <lb/>gradus nullam habet cau&longs;am; igitur e&longs;t à nihilo, quod dici non pote&longs;t. </s> <s id="N1396F"><!-- NEW --><lb/>Re&longs;pondeo, plures partes impetus non produci in minore globo, quàm <lb/>&longs;int in maiore; </s> <s id="N13976"><!-- NEW -->igitur nulla pars e&longs;t impetus minoris globi, quæ &longs;ui <lb/>cau&longs;am &longs;ufficientem non habeat; </s> <s id="N1397C"><!-- NEW -->&longs;ed cum partes impetus maioris globi <lb/>di&longs;tribuantur pluribus partibus &longs;ubiecti, faciunt remi&longs;&longs;um impetum, igi­<lb/>tur & tardum; </s> <s id="N13984"><!-- NEW -->cum &longs;cilicet impetus vnius partis non iuuet motum alte­<lb/>rius per Th. 37. at verò cum partes impetus producti in minore globo <lb/>di&longs;tribuantur paucioribus partibus &longs;ubiecti, faciunt inten&longs;iorem im­<lb/>petum; igitur velociorem motum, quippe omnes producuntur ab <lb/>omnibus illis actione communi per Ax. 17. num. </s> <s id="N13990">1. quid clarius. </s> </p> <p id="N13993" type="main"> <s id="N13995"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 62.<emph.end type="center"/></s> </p> <p id="N139A1" type="main"> <s id="N139A3"><!-- NEW --><emph type="italics"/>Globus minor imprimit maiori remi&longs;&longs;iorem impetum & tardiorem motum <lb/>& æqualis, aqitali æqualem<emph.end type="italics"/>; hæc omnia probantur per Th. 60. & præ-, <lb/>cedentia. </s> </p> <pb pagenum="40" xlink:href="026/01/072.jpg"/> <p id="N139B4" type="main"> <s id="N139B6"><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N139C2" type="main"> <s id="N139C4"><!-- NEW -->Ob&longs;eruabis primò, vtrumque globum e&longs;&longs;e eiu&longs;dem materiæ; </s> <s id="N139C8"><!-- NEW -->&longs;i enim <lb/>&longs;int diuer&longs;æ materiæ, &longs;ecùs accidit, quàm diximus; </s> <s id="N139CE"><!-- NEW -->&longs;i v. <!-- REMOVE S-->g. <!-- REMOVE S-->æneus mi­<lb/>nor pellatur ab eburneo maiore, maiorem motum hic illi non impri­<lb/>met; </s> <s id="N139DA"><!-- NEW -->licèt enim &longs;it maior exten&longs;io eburnei; </s> <s id="N139DE"><!-- NEW -->e&longs;t tamen minus pondus; <lb/>igitur pauciores partes. </s> </p> <p id="N139E4" type="main"> <s id="N139E6"><!-- NEW -->Secundò, eos globos accipiendos e&longs;&longs;e, quorum partes, vel non auo­<lb/>lent ab ictu, vel non comprimantur; </s> <s id="N139EC"><!-- NEW -->comprimuntur in plumbeis, <lb/>æneis, & auolant in vitreis; cum enim &longs;it compre&longs;&longs;io, vel partium di­<lb/>ui&longs;io, de&longs;truitur multùm impetus. </s> </p> <p id="N139F4" type="main"> <s id="N139F6"><!-- NEW -->Tertiò reiice commentum illorum, qui dicunt corpus illud e&longs;&longs;e ma­<lb/>joris velocitatis capax, quod plures habet partes materiæ &longs;ub eadem <lb/>quantitate; </s> <s id="N139FE"><!-- NEW -->nam &longs;uppo&longs;ita eadem re&longs;i&longs;tentiæ ratione, omne corpus e&longs;t <lb/>capax illius velocitatis, cuius aliud e&longs;t capax; </s> <s id="N13A04"><!-- NEW -->cum nullus &longs;it motus, quo <lb/>non po&longs;&longs;it dari velocior, & tardior, vt dicemus infrà; </s> <s id="N13A0A"><!-- NEW -->immò &longs;it glo­<lb/>bus plumbeus 12. librarum, &longs;it eburneus eiu&longs;dem diametri 2. librarum, <lb/>v. <!-- REMOVE S-->g. <!-- REMOVE S-->haud dubiè eadem potentia producet inten&longs;iorem impetum in <lb/>eburneo, vt patet experientia, & ratio con&longs;tat ex dictis; </s> <s id="N13A18"><!-- NEW -->qua&longs;i verò &longs;it <lb/>aliqua materiæ inertia, quæ motum re&longs;puat; </s> <s id="N13A1E"><!-- NEW -->licèt fortè maior &longs;it pro­<lb/>portio re&longs;i&longs;tentiæ medij comparatæ cum globo eburneo, quàm compa­<lb/>ratæ cum plumbeo; &longs;ed de re&longs;i&longs;tentia de percu&longs;&longs;ione, & de &longs;patio age­<lb/>mus infra. </s> </p> <p id="N13A28" type="main"> <s id="N13A2A"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 63.<emph.end type="center"/></s> </p> <p id="N13A36" type="main"> <s id="N13A38"><emph type="italics"/>Omnis globus, qui in alium, qui mouetur impingitur, dum hic mouetur, ve­<lb/>lociùs mouetur eo &c. </s> <s id="N13A3F"><!-- NEW -->in quem impingitur <emph.end type="italics"/> patet; alioquin numquam a&longs;&longs;equi <lb/>po&longs;&longs;et, quod ex ip&longs;is terminis con&longs;tat. </s> </p> <p id="N13A48" type="main"> <s id="N13A4A"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 64.<emph.end type="center"/></s> </p> <p id="N13A56" type="main"> <s id="N13A58"><!-- NEW --><emph type="italics"/>Ex hac hypothe&longs;i globus impactus producit in alie nouas partes impetus<emph.end type="italics"/>; <lb/>quia impeditur eius motus, igitur vt tollat impedimentum, agit ad <lb/>extra per Th. 44. </s> </p> <p id="N13A65" type="main"> <s id="N13A67"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 65.<emph.end type="center"/></s> </p> <p id="N13A73" type="main"> <s id="N13A75"><!-- NEW --><emph type="italics"/>Hic impetus nouus productus minor e&longs;t eo qui produceretur in eodem globo <lb/>immobili<emph.end type="italics"/>: ratio e&longs;t; </s> <s id="N13A80"><!-- NEW -->quia &longs;i &longs;i&longs;teret, maius e&longs;&longs;et impedimentum, quia <lb/>totum motum impediret, cuius tantùm partem impedit, dum mouetur , <lb/>licèt paulò tardius; igitur minus agit ad extra per Th. 49. </s> </p> <p id="N13A88" type="main"> <s id="N13A8A"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 66.<emph.end type="center"/></s> </p> <p id="N13A96" type="main"> <s id="N13A98"><!-- NEW --><emph type="italics"/>Mobile adhærens alteri mobili à tergo; dum vtrumque æque velociter <lb/>feratur nullum producit in eo impetum.<emph.end type="italics"/></s> <s id="N13AA2"><!-- NEW --> Probatur, quia mobile quod præit, <lb/>non impedit motum &longs;ub&longs;equentis; igitur nullum impetum ab eo acci<lb/>pit per Th. 48. </s> </p> <pb pagenum="41" xlink:href="026/01/073.jpg"/> <p id="N13AAE" type="main"> <s id="N13AB0"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 67.<emph.end type="center"/></s> </p> <p id="N13ABC" type="main"> <s id="N13ABE"><!-- NEW --><emph type="italics"/>Hinc paradoxon egregium &longs;i quod aliud; </s> <s id="N13AC4"><!-- NEW -->globus percu&longs;&longs;us ab alio eadem <lb/>&longs;emper velocitate mouetur, &longs;iue moueretur in&longs;tanti percu&longs;&longs;ionis, &longs;iue &longs;i­<lb/>&longs;teret.<emph.end type="italics"/> v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;it globus A quie&longs;cens, cui imprimantur ab alio B 40. gra­<lb/>dus velocitatis: id e&longs;t æqualis impetus impetui percutientis, iam verò <lb/>moueatur A, cum 20. grad. <!-- REMOVE S-->velocitatis, & B, qui mouetur cum 40. <lb/>impingatur, certè cum impediatur tantùm &longs;ubduplum motus, produce­<lb/>tur tantùm &longs;ubduplum impetus, id e&longs;t 20. qui &longs;i addantur 20. grad. <!-- REMOVE S-->erunt <lb/>40. quæ omnia con&longs;tant per Th.49.48.&c. </s> </p> <p id="N13AE1" type="main"> <s id="N13AE3"><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 1.<emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N13AF0" type="main"> <s id="N13AF2">Hinc æquale &longs;emper &longs;patium percu&longs;&longs;us globus conficit, &longs;iue ante per­<lb/>cu&longs;&longs;ionem moueretur, &longs;iue quie&longs;ceret. </s> </p> <p id="N13AF7" type="main"> <s id="N13AF9"><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 2.<emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N13B06" type="main"> <s id="N13B08"><!-- NEW -->Hinc &longs;i &longs;ecundò percutiatur idem globus, &longs;patium totum, quod per­<lb/>currit tùm à primò, tùm à &longs;ecundo ictu e&longs;t maius eo, quod à primo ictu <lb/>confeci&longs;&longs;et, &longs;i non fui&longs;&longs;et &longs;ecundò percu&longs;&longs;us; maius inquam &longs;egmento &longs;pa­<lb/>tij interiecto inter primum & &longs;ecundum ictum. </s> </p> <p id="N13B12" type="main"> <s id="N13B14"><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 3.<emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N13B21" type="main"> <s id="N13B23"><!-- NEW -->Hinc reiicies aliquos, quorum &longs;ententiam habes apud Doctum Mer­<lb/>&longs;emium, <emph type="italics"/>in prop.<emph.end type="italics"/> 20. <emph type="italics"/>phæn. mech. quorum &longs;unt hæc verba; </s> <s id="N13B32"><!-- NEW -->&longs;i malleus pilam <lb/>currentem eodem, ac anteà modo percutiat, nonam &longs;ui motus partem; &longs;i verò <lb/>currentem tertia vice percutiat, vnam vige&longs;imam &longs;eptimam &longs;ui motus par­<lb/>tem ei tribuet, atque ita deinceps.<emph.end type="italics"/></s> <s id="N13B3E"> Supponit primò hæc &longs;ententia mal­<lb/>leum e&longs;&longs;e duplum pilæ percu&longs;&longs;æ. </s> <s id="N13B43"><!-- NEW -->Secundò, malleum imprimere pilæ &longs;ub­<lb/>duplæ &longs;ubtriplum motum; quod fal&longs;um e&longs;t, vt con&longs;tat ex Th 6. & Co­<lb/>roll. </s> <s id="N13B4B"><!-- NEW -->1. Præterea, licètin primà percu&longs;&longs;ione imprimeret tantùm prædi­<lb/>ctæ pilæ &longs;ubtriplum impetum, in &longs;ecunda percu&longs;&longs;ione maiorem impri­<lb/>meret po&longs;t longiorem motum, vbi iam ad quietem propiùs accedit; </s> <s id="N13B53"><!-- NEW -->mi­<lb/>norem verò paulò po&longs;t initium motus, vt con&longs;tat ex dictis, & ex ip&longs;a ex­<lb/>perientia; </s> <s id="N13B5B"><!-- NEW -->pote&longs;t quidem in aliquo puncto &longs;ui motus &longs;ecunda vice per­<lb/>cuti, in quo &longs;ubtriplum tantùm motum imprimet; </s> <s id="N13B61"><!-- NEW -->hoc e&longs;t eo in&longs;tanti­<lb/>quo tantùm ami&longs;it tertiam fui impetus partem; </s> <s id="N13B67"><!-- NEW -->tum deinde in tertia <lb/>percu&longs;&longs;ione pote&longs;t tantùm (1/27) motus partem illi tribuere; </s> <s id="N13B6D"><!-- NEW -->eo &longs;cilicet in­<lb/>&longs;tanti, quo tantùm ami&longs;it (1/27) &longs;ui impetus partem; </s> <s id="N13B73"><!-- NEW -->&longs;ed in alijs temporis <lb/>punctis longè alia erit impetus producti ratio; Igitur tota hæc progre&longs;­<lb/>&longs;io gratis omninò fuit excogitata. </s> </p> <p id="N13B7B" type="main"> <s id="N13B7D"><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 4.<emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N13B8A" type="main"> <s id="N13B8C"><!-- NEW -->Hinc etiam po&longs;t &longs;ecundam percu&longs;&longs;ionem æquale &longs;patium conficiet al­<lb/>teri, quod iam confecit po&longs;t primam æqualibus temporibus; </s> <s id="N13B92"><!-- NEW -->igitur æqua­<lb/>lis e&longs;t velocitas vtriu&longs;que motus; </s> <s id="N13B98"><!-- NEW -->quia &longs;cilicet, &longs;i e&longs;t æqualis impetus, e&longs;t <lb/>qualis motus: Ex his maximam carum dubitationum partem &longs;oluere po­<lb/>teris quæ in eadem Mer&longs;enni propo&longs;itione courinentur reliquas vero ex <lb/>dicendis infrà. </s> </p> <pb pagenum="42" xlink:href="026/01/074.jpg"/> <p id="N13BA6" type="main"> <s id="N13BA8"><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 5.<emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N13BB5" type="main"> <s id="N13BB7"><!-- NEW -->Ex dictis etiam colliges diuer&longs;as percu&longs;&longs;ionum rationes &longs;uppo&longs;ita di­<lb/>uer&longs;a ratione ponderum globi percutientis, & percu&longs;&longs;i; </s> <s id="N13BBD"><!-- NEW -->cum enim impe­<lb/>tus productus &longs;it æqualis per &longs;e impetui producenti, per Th.60. modò <lb/>debita fiat applicatio, de qua in Th.50. &longs;i percutiens &longs;it duplus percu&longs;&longs;i, <lb/>&longs;uppo&longs;ita eadem materia, motus percu&longs;&longs;i erit duplò velocior; quia im­<lb/>petus erit duplò inten&longs;ior, vt con&longs;tat ex Th. 61. &longs;i verò &longs;it quadruplus, <lb/>quadruplo, &c. </s> <s id="N13BCB">Igitur velocitates motuum &longs;unt in ratiòne ponderum <lb/>permutando. </s> </p> <p id="N13BD0" type="main"> <s id="N13BD2"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 68.<emph.end type="center"/></s> </p> <p id="N13BDE" type="main"> <s id="N13BE0"><!-- NEW --><emph type="italics"/>Si corpus percu&longs;&longs;um &longs;it oblongum, & percu&longs;&longs;io fiat in centro grauitatis eiu&longs;­<lb/>dem corporis; </s> <s id="N13BE8"><!-- NEW -->producitur impetus in percu&longs;&longs;io æqualis impetui percutientis<emph.end type="italics"/>; </s> <s id="N13BEF"><!-- NEW -->&longs;ed <lb/>opus e&longs;t aliqua figura: </s> <s id="N13BF5"><!-- NEW -->Sit corpus AD, parallelipedum; </s> <s id="N13BF9"><!-- NEW -->diuidatur æqua­<lb/>liter in E ita vt E &longs;it centrum grauitatis; </s> <s id="N13BFF"><!-- NEW -->&longs;i percu&longs;&longs;io fiatin E per lineam <lb/>perpendicularem HE, producetur impetus in corpore AD æqualis im­<lb/>petui corporis percutientis; </s> <s id="N13C07"><!-- NEW -->quia &longs;cilicet à corpore AD non pote&longs;t maius <lb/>e&longs;&longs;e impedimentum; igitur agit quantùm pote&longs;t impetus corporis per­<lb/>cutientis per Th.50. igitur producit æqualem per Th.69. </s> </p> <p id="N13C0F" type="main"> <s id="N13C11"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 69.<emph.end type="center"/></s> </p> <p id="N13C1D" type="main"> <s id="N13C1F"><!-- NEW --><emph type="italics"/>Si percu&longs;&longs;io fiat in<emph.end type="italics"/> F <emph type="italics"/>per lineam perpendicularem<emph.end type="italics"/> IF, <emph type="italics"/>minus erit impedi­<lb/>mentum, quàm per<emph.end type="italics"/> HE, Quia &longs;i per HE, moueri tantùm pote&longs;t motu <lb/>recto, &longs;i per IF, etiam motu circulari circa aliquod centrum; </s> <s id="N13C38"><!-- NEW -->&longs;ed hic <lb/>motus e&longs;t facilior quam ille; </s> <s id="N13C3E"><!-- NEW -->igitur minus e&longs;t impedimentum; </s> <s id="N13C42"><!-- NEW -->(&longs;uppono <lb/>autem cylindrum BC vtroque modo moueri po&longs;&longs;e ab applicata potentia) <lb/>igitur minùs impetus producitur, &longs;i percu&longs;&longs;io fiat per IF, quàm &longs;i fiat <lb/>per LK: </s> <s id="N13C4C"><!-- NEW -->In qua verò proportione &longs;it minus impedimentum, & minori <lb/>opus impetu, po&longs;ito eodem potentiæ ni&longs;u, determinabimus facilè aliàs; <lb/>vt etiam demon&longs;trabimus circa quod centrum hic circularis motus fieri <lb/>debeat. </s> </p> <p id="N13C56" type="main"> <s id="N13C58"><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N13C64" type="main"> <s id="N13C66"><!-- NEW -->Ex duobus capitibus minus e&longs;&longs;e pote&longs;t impedimentum; </s> <s id="N13C6A"><!-- NEW -->primum e&longs;t, <lb/>quod petitur à puncto contactus, &longs;ecundum à linea incidentiæ; </s> <s id="N13C70"><!-- NEW -->v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;i <lb/>accipiatur punctum E, in quo e&longs;t centrum grauitatis corporis AD, & in <lb/>eo fiat percu&longs;&longs;io; </s> <s id="N13C7C"><!-- NEW -->maximum e&longs;t impedimentum ratione puncti conta­<lb/>ctus, in quo fit percu&longs;&longs;io; </s> <s id="N13C82"><!-- NEW -->&longs;i verò percu&longs;&longs;io fiat per lineam perpendicu­<lb/>larem HE, maximum e&longs;t impedimentum, ratione lineæ; </s> <s id="N13C88"><!-- NEW -->&longs;i autem ex <lb/>vtroque capite &longs;imul accidat impedimentum, maximum e&longs;t omnium; </s> <s id="N13C8E"><!-- NEW --><lb/>iam verò &longs;i accipiatur punctum E, & linea percu&longs;sionis ME; </s> <s id="N13C93"><!-- NEW -->minor e&longs;t <lb/>percu&longs;sio ratione lineæ non puncti; </s> <s id="N13C99"><!-- NEW -->accipiatur punctum N, & linea <lb/>percu&longs;sionis MN, minor e&longs;t percu&longs;sio ratione puncti non lineæ, acci­<lb/>piatur punctum N, & linea IN, minor e&longs;t percu&longs;sio ratione vtriu&longs;que; </s> <s id="N13CA1"><!-- NEW --><lb/>&longs;i demum accipiatur punctum E, & linea ME, minor e&longs;t percu&longs;sio ra­<pb pagenum="43" xlink:href="026/01/075.jpg"/>tione lineæ non puncti; </s> <s id="N13CAB"><!-- NEW -->accipiatur punctum N linea percu&longs;&longs;ionis MN, <lb/>minor e&longs;t percu&longs;&longs;io ratione puncti non lineæ; </s> <s id="N13CB1"><!-- NEW -->&longs;i accipiatur punctum N, <lb/>& linea IN, minor e&longs;t percu&longs;&longs;io ratione vtriu&longs;que: </s> <s id="N13CB7"><!-- NEW -->&longs;i demum accipia­<lb/>tur punctum E & linea HE, maior e&longs;t percu&longs;&longs;io ratione vtriu&longs;que; </s> <s id="N13CBD"><!-- NEW -->igi­<lb/>tur &longs;unt quatuor coniugationes; &longs;eu quatuor cla&longs;&longs;es diuer&longs;arum percu&longs;­<lb/>&longs;ionum. </s> </p> <p id="N13CC5" type="main"> <s id="N13CC7"><!-- NEW -->Hinc compen&longs;ari pote&longs;t ratione vnius quod dee&longs;t ratione alterius, <lb/>v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;i fiat percu&longs;&longs;io in puncto E per lineam ME, pote&longs;t &longs;ciri punctum <lb/>inter ED, in quo percu&longs;&longs;io per lineam perpendicularem &longs;it æqualis <lb/>percu&longs;&longs;ioni per lineam ME; &longs;ed de his infrà in lib. 10. cum de percu&longs;­<lb/>&longs;ione, determinabimus enim vnde proportiones i&longs;tæ petendæ &longs;int, & <lb/>demon&longs;trabimus totam i&longs;tam rem, quæ multùm curio&longs;itatis habet, & <lb/>vtilitatis. </s> </p> <p id="N13CDD" type="main"> <s id="N13CDF">Determinabimus etiam dato puncto percu&longs;&longs;ionis F v.g. <!-- REMOVE S-->cum &longs;equatur <lb/>motus vectis, quodnam &longs;it centrum vectis &longs;eu huius motus. </s> </p> <p id="N13CE6" type="main"> <s id="N13CE8"><!-- NEW -->Hinc demum &longs;equitur, ne hoc omittam, data minimâ percu&longs;&longs;ione per <lb/>lineam MN dari po&longs;&longs;e adhuc minorem per lineam IN, & alias incli­<lb/>natas; </s> <s id="N13CF0"><!-- NEW -->& data percu&longs;&longs;ione per lineam quantumuis inclinatam, po&longs;&longs;e da­<lb/>ri æqualem per lineam perpendicularem; </s> <s id="N13CF6"><!-- NEW -->& data per lineam perpendi­<lb/>cularem extra centrum grauitatis E, po&longs;&longs;e dari æqualem; & in qualibet <lb/>data ratione per aliquam inclinatam, quæ cadat in E, &longs;ed de his fusè <lb/>&longs;uo loco. </s> </p> <p id="N13D00" type="main"> <s id="N13D02"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 70.<emph.end type="center"/></s> </p> <p id="N13D0E" type="main"> <s id="N13D10"><!-- NEW --><emph type="italics"/>Corpus oblongum parallelipedum percutiens aliud corpus, putà globu&mtail;, <lb/>motu recto per lineam directionis, quæ producta à puncto contactus ducitur per <lb/>centrum globi, dum fiat contactus in centro grauitatis parallelipedi, maximum <lb/>ictum infligit, &longs;eu agit quantùm pote&longs;t.<emph.end type="italics"/> v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;it parallelipedum EB; quod <lb/>moueatur motu recto parallelo, lineis CD, HG, &c. </s> <s id="N13D25"><!-- NEW -->&longs;itque globus in <lb/>D; </s> <s id="N13D2B"><!-- NEW -->haud dubiè agit quantùm pote&longs;t, quia &longs;cilicet e&longs;t maximum impedi­<lb/>mentum per Th.68. Tam enim globus in D impedit motum paralleli­<lb/>pedi, quàm parallelipedum motum globi impacti per lineam ID; </s> <s id="N13D33"><!-- NEW -->impedit <lb/>inquam ratione oppo&longs;itionis; </s> <s id="N13D39"><!-- NEW -->quia centra grauitatis vtriu&longs;que con­<lb/>currunt in eadem linea; igitur &longs;i maximum e&longs;t impedimentum, agit <lb/>quantùm pote&longs;t Th. 50. hinc producitur impetus æqualis per Th.60. </s> </p> <p id="N13D41" type="main"> <s id="N13D43"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 71.<emph.end type="center"/></s> </p> <p id="N13D4F" type="main"> <s id="N13D51"><!-- NEW --><emph type="italics"/>Si percu&longs;&longs;io fiat in G, id e&longs;t &longs;i globus e&longs;&longs;et in G, producetur minor impetus, <lb/>& in<emph.end type="italics"/> M <emph type="italics"/>adhuc minor<emph.end type="italics"/>; </s> <s id="N13D62"><!-- NEW -->vt con&longs;tat ex dictis in &longs;uperioribus Theorematis; <lb/>in qua vero proportione determinabimus aliàs. </s> </p> <p id="N13D68" type="main"> <s id="N13D6A"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 72.<emph.end type="center"/></s> </p> <p id="N13D76" type="main"> <s id="N13D78"><!-- NEW --><emph type="italics"/>Si corpus percutiens non &longs;it parallelipedum, &longs;ed alterius figuræ v.g.<emph.end type="italics"/> <emph type="italics"/>trigo­<lb/>non,<emph.end type="italics"/> ADE, &longs;itque maioris facilitatis gratia Orthonium; </s> <s id="N13D89"><!-- NEW -->eiu&longs;que motus <lb/>&longs;it parallelus lineis ED, BC: </s> <s id="N13D8F"><!-- NEW -->&longs;it autem DA dupla DE; </s> <s id="N13D93"><!-- NEW -->&longs;itque diui&longs;a to­<lb/>ta DA æqualiter in C, in C non erit maximus ictus; </s> <s id="N13D99"><!-- NEW -->quia in C non <pb pagenum="44" xlink:href="026/01/076.jpg"/>e&longs;t centrum grauitatis, vt patet; </s> <s id="N13DA2"><!-- NEW -->vt autem habeatur centrum impre&longs;&longs;io­<lb/>nis; </s> <s id="N13DA8"><!-- NEW -->a&longs;&longs;umatur AN media proportionalis inter totam AD, & &longs;ubdu­<lb/>plum AC; </s> <s id="N13DAE"><!-- NEW -->certè cum triangulum ANO &longs;it &longs;ubduplum totius ADE, <lb/>vt con&longs;tat ex Geometria, & æquale trapezo ND EO; </s> <s id="N13DB4"><!-- NEW -->erit impetus in <lb/>vtroque æqualis; </s> <s id="N13DBA"><!-- NEW -->igitur in N erit centrum impre&longs;&longs;ionis, vel impetus; </s> <s id="N13DBE"><!-- NEW -->vt <lb/>autem habeatur centrum percu&longs;&longs;ionis; </s> <s id="N13DC4"><!-- NEW -->in quo &longs;cilicet maximus ictus in­<lb/>fligitur, inueniatur centrum grauitatis H, ducaturque KHI parallela <lb/>DE, centrum percu&longs;&longs;ionis erit in I; </s> <s id="N13DCC"><!-- NEW -->quippe in I totus impeditur impetus <lb/>grauitatis vtrimque, cum &longs;it in æquilibrio; </s> <s id="N13DD2"><!-- NEW -->quomodo verò inueniatur <lb/>punctum H facilè habetur ex Archimede, ductis &longs;cilicet AF, DB, quæ <lb/>diuidant bifariam æqualiter DE, EA; vel a&longs;&longs;umpta AI dupla ID, quod <lb/>demon&longs;trabimus in Mechan. <!-- KEEP S--></s> </p> <p id="N13DDD" type="main"> <s id="N13DDF"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 37.<emph.end type="center"/></s> </p> <p id="N13DEB" type="main"> <s id="N13DED"><!-- NEW --><emph type="italics"/>Si circa centrum immobile rotetur corpus parallelipedum<emph.end type="italics"/> CA, <emph type="italics"/>diuer&longs;a e&longs;t <lb/>ratio percu&longs;&longs;ionum ab ea, quàm &longs;uprà propo&longs;uimus<emph.end type="italics"/>; </s> <s id="N13DFE"><!-- NEW -->moueatur enim circa <lb/>centrum C, fitque CA diui&longs;a bifariam in B, haud dubiè punctum A <lb/>faciet arcum AE eo tempore, quò punctum B faciet BD &longs;ubduplum <lb/>AE; </s> <s id="N13E08"><!-- NEW -->igitur punctum A duplò velociùs mouetur quàm B, vt con&longs;tat; </s> <s id="N13E0C"><!-- NEW -->igi­<lb/>tur habet duplò maiorem impetum; cum effectum habeat duplò maio­<lb/>rem per Ax. 13. n. </s> <s id="N13E14"><!-- NEW -->4. igitur cum totus motus &longs;egmenti AB &longs;it ad to­<lb/>tum motum &longs;egmenti BC, vt &longs;patia acqui&longs;ita; </s> <s id="N13E1A"><!-- NEW -->certè &longs;patia acqui&longs;ita <lb/>&longs;unt vt arcus; </s> <s id="N13E20"><!-- NEW -->igitur & trapezus BAED, continet 3/4 totius CAE, vt <lb/>con&longs;tat; </s> <s id="N13E26"><!-- NEW -->&longs;unt enim &longs;ectores &longs;imilis in ratione duplicata radiorum; </s> <s id="N13E2A"><!-- NEW -->igi­<lb/>tur totus motus &longs;egmenti BC &longs;ubquadruplus motus totius CA; igitur <lb/>& impetus; </s> <s id="N13E32"><!-- NEW -->vt autem habeatur centrum impre&longs;&longs;ionis, vel impetus; </s> <s id="N13E36"><!-- NEW -->&longs;it &longs;e­<lb/>ctor CHI, &longs;ubduplus totius CAE quod quomodo fiat, patet ex Geo­<lb/>metria; </s> <s id="N13E3E"><!-- NEW -->accipiatur tantùm &longs;ubdupla diagonalis quadrati lateris CA, igi­<lb/>tur in puncto H e&longs;t centrum impre&longs;&longs;ionis, &longs;eu media proportionalis in­<lb/>ter totam CA, & &longs;ubduplam CB: </s> <s id="N13E46"><!-- NEW -->vt autem habeatur percu&longs;&longs;ionis, a&longs;­<lb/>&longs;umatur CY dupla YA; </s> <s id="N13E4C"><!-- NEW -->Dico punctum Y e&longs;&longs;e centrum percu&longs;&longs;ionis; <lb/>quia perinde &longs;e habet, atque &longs;i e&longs;&longs;et trianguli cadentis ictus, vt demon­<lb/>&longs;trabimus aliàs nunc tantùm indica&longs;&longs;e &longs;ufficiat. </s> </p> <p id="N13E54" type="main"> <s id="N13E56"><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 1.<emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N13E63" type="main"> <s id="N13E65"><!-- NEW -->Hinc etiam &longs;oluetur, quod proponunt aliqui; &longs;eu potiùs quærunt; </s> <s id="N13E69"><!-- NEW --><lb/>in quà &longs;cilicet parte maiorem ictum infligat en&longs;is; </s> <s id="N13E6E"><!-- NEW -->&longs;i enim &longs;it eiu&longs;dem <lb/>cra&longs;&longs;itiei in omnibus &longs;uis partibus, idem dicendum e&longs;t quod de cylin­<lb/>dro CA; &longs;i verò in mucronem de&longs;inat, inueniemus etiam centrum <lb/>percu&longs;&longs;ionis. </s> </p> <p id="N13E78" type="main"> <s id="N13E7A"><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 2.<emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N13E87" type="main"> <s id="N13E89"><!-- NEW -->Huc etiam reuoca clauarum ictus, vel aliorum corporum, quæ ad in­<lb/>&longs;tar &longs;eu conorum, &longs;eu pyramidum ver&longs;us mucronem maiora &longs;unt, vel <lb/>den&longs;iora; quippe ex iacto &longs;uprà principio i&longs;torum omnium effectuum <lb/>rationes demon&longs;trabimus. </s> </p> <pb pagenum="45" xlink:href="026/01/077.jpg"/> <p id="N13E97" type="main"> <s id="N13E99"><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 1.<emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N13EA6" type="main"> <s id="N13EA8"><!-- NEW -->Colligemus etiam quid dicendum &longs;it de malleorum ictu; </s> <s id="N13EAC"><!-- NEW -->&longs;it enim <lb/>malleus F æqualis malleo G (in his vna fere manubrij longitudinis ha­<lb/>betur ratio) ducatur arcus NM, itemque OG; </s> <s id="N13EB4"><!-- NEW -->ictus mallei G e&longs;t ferè <lb/>&longs;ubduplus alterius, dum vterque malleus &longs;it æqualis; </s> <s id="N13EBA"><!-- NEW -->dixi ferè, quia <lb/>motus totius mallei G non e&longs;t omninò &longs;ubduplus motus mallci F, quia <lb/>&longs;cilicet trapezus OD e&longs;t minor &longs;ubduplo alterius NE; </s> <s id="N13EC2"><!-- NEW -->quotâ vero parte <lb/>&longs;it minor facilè pote&longs;t &longs;ciri opera Geometriæ: &longs;ed hæc omnia determi­<lb/>nabimus. </s> </p> <p id="N13ECA" type="main"> <s id="N13ECC"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 74.<emph.end type="center"/></s> </p> <p id="N13ED8" type="main"> <s id="N13EDA"><!-- NEW --><emph type="italics"/>Si daretur potentia motrix, quæ &longs;emper agere po&longs;&longs;et, impetus po&longs;&longs;et intendi <lb/>in infinitum<emph.end type="italics"/>; </s> <s id="N13EE5"><!-- NEW -->pater, quia quocumque dato motu pote&longs;t dari velocior in <lb/>infinitum; igitur pote&longs;t dari impetus inten&longs;ior, & inten&longs;ior in infinitum. </s> </p> <p id="N13EEB" type="main"> <s id="N13EED"><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N13EF9" type="main"> <s id="N13EFB"><!-- NEW -->Hîc ob&longs;erua nouum di&longs;crimen, quod intercedit inter impetum, & <lb/>alias qualitates; </s> <s id="N13F01"><!-- NEW -->quæ fortè non po&longs;&longs;unt intendi in infinitum, ratio di&longs;­<lb/>criminis e&longs;t, quia totus calor exten&longs;us in maiore &longs;ubiecto non pote&longs;t <lb/>produci in minore, in quo eadem cau&longs;a eumdem &longs;emper effectum pro­<lb/>ducit; </s> <s id="N13F0B"><!-- NEW -->quia &longs;cilicet agit vniformiter difformiter; at verò impetus exten­<lb/>&longs;us in magno <expan abbr="den&longs;o&qacute;ue">den&longs;oque</expan> malleo pote&longs;t producere æqualem in maximâ <lb/>ferè pilâ. </s> </p> <p id="N13F17" type="main"> <s id="N13F19"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 75.<emph.end type="center"/></s> </p> <p id="N13F25" type="main"> <s id="N13F27"><!-- NEW --><emph type="italics"/>Impetus &longs;imilis, id e&longs;t, ad <expan abbr="eãdem">eandem</expan> lineam determinatus, & æqualis in in­<lb/>ten&longs;ione, non pote&longs;t intendere alium &longs;imilem<emph.end type="italics"/>; </s> <s id="N13F36"><!-- NEW -->Probatur, quia agit tantùm ad <lb/>extra, vt tollat impedimentum per Th. 44. &longs;ed eorum mobilium, quæ <lb/>ver&longs;us <expan abbr="eãdem">eandem</expan> partem pari velocitate mouentur, neutrum impedit al­<lb/>terius motum, vt con&longs;tat; igitur impetus &longs;imilis, &c. </s> </p> <p id="N13F44" type="main"> <s id="N13F46"><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N13F52" type="main"> <s id="N13F54"><!-- NEW -->Ob&longs;erua de impetu &longs;imili id tantùm dici; </s> <s id="N13F58"><!-- NEW -->&longs;imili inquam id e&longs;t non <lb/>modò eiu&longs;dem inten&longs;ionis; </s> <s id="N13F5E"><!-- NEW -->&longs;ed etiam eiu&longs;dem lineæ: </s> <s id="N13F62"><!-- NEW -->&longs;i enim alterum <lb/>de&longs;it, haud dubiè &longs;imilis impetus non e&longs;t; </s> <s id="N13F68"><!-- NEW -->&longs;ic impetus quatuor grad. <!-- REMOVE S-->in­<lb/>tendere pote&longs;t impetum duorum graduum; </s> <s id="N13F70"><!-- NEW -->licèt vterque ad <expan abbr="eãdem">eandem</expan> li­<lb/>neam &longs;it determinatus; </s> <s id="N13F7A"><!-- NEW -->&longs;i verò ad diuer&longs;as lineas determinentur; etiam <lb/>impetus vt duo pote&longs;t intendere impetum vt quatuor. </s> </p> <p id="N13F80" type="main"> <s id="N13F82"><!-- NEW -->Ob&longs;eruabis præterea hoc Theorema ita e&longs;&longs;e intelligendum, vt impe­<lb/>tus mobilis præeuntis nullo modo impediatur; alioquin mobile &longs;ucce­<lb/>dens omninò aliud vrgeret, vt con&longs;tat. </s> </p> <p id="N13F8A" type="main"> <s id="N13F8C"><emph type="center"/><emph type="italics"/>Corollarium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N13F98" type="main"> <s id="N13F9A"><!-- NEW -->Hinc &longs;imile pote&longs;t in aliquo ca&longs;u agere in &longs;imile; </s> <s id="N13F9E"><!-- NEW -->vnde rectè colligo <lb/>id tantùm dictum e&longs;&longs;e ab Ari&longs;totele de qualitatibus alteratiuis; </s> <s id="N13FA4"><!-- NEW -->quid <lb/>verò accidat, cum mobile graue mobili alteri &longs;uperponitur; dicemus <lb/>infrà. </s> </p> <pb pagenum="46" xlink:href="026/01/078.jpg"/> <p id="N13FB0" type="main"> <s id="N13FB2"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 76.<emph.end type="center"/></s> </p> <p id="N13FBE" type="main"> <s id="N13FC0"><!-- NEW --><emph type="italics"/>Exten&longs;io impetus respondet extentioni &longs;ui &longs;ubiecti, &longs;cilicet mobilis<emph.end type="italics"/>; </s> <s id="N13FC9"><!-- NEW -->cum <lb/>enim extra &longs;ubjectum e&longs;&longs;e non po&longs;&longs;it, cum &longs;it qualitas; </s> <s id="N13FCF"><!-- NEW -->certè ibi e&longs;t, vbi <lb/>&longs;ubjectum e&longs;t; nam penetratur accidens cum ip&longs;o <expan abbr="&longs;ujecto">&longs;ubjecto</expan>. </s> </p> <p id="N13FD9" type="main"> <s id="N13FDB"><emph type="center"/><emph type="italics"/>Scolium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N13FE7" type="main"> <s id="N13FE9"><!-- NEW -->Ob&longs;eruabis qualitatem omnem ita &longs;uo &longs;ubjecto coëxtendi, vt æqua­<lb/>lem omnino quodlibet eius punctum, &longs;eu pars extentionem habeat ex­<lb/>tentioni puncti, &longs;eu partis &longs;ui &longs;ubjecti; </s> <s id="N13FF1"><!-- NEW -->nec enim alliud e&longs;t, vnde po&longs;&longs;it <lb/>determinari extentio qualitatum, præter ip&longs;am exten&longs;ionem &longs;ubjecti; </s> <s id="N13FF7"><!-- NEW --><lb/>quod maximè in impetu videre e&longs;t, cuius partes in mobili den&longs;o minori <lb/>extentioni &longs;ubjacent, quàm in mobili raro; </s> <s id="N13FFE"><!-- NEW -->cum ex maiore ictu &longs;eu per­<lb/>cu&longs;&longs;ione in mobili den&longs;o plures impetus agentis partes e&longs;&longs;e con&longs;tet; quia <lb/>&longs;cilicet &longs;unt plures partes &longs;ubiecti. </s> </p> <p id="N14006" type="main"> <s id="N14008"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 77.<emph.end type="center"/></s> </p> <p id="N14014" type="main"> <s id="N14016"><!-- NEW --><emph type="italics"/>Datur impetus altero impetu perfectior &longs;ecundum entitatem<emph.end type="italics"/>; dixi &longs;ecun­<lb/>dum entitatem; </s> <s id="N14021"><!-- NEW -->quia iam dictum e&longs;t &longs;uprà dari perfectiorem &longs;ecundum <lb/>inten&longs;ionem; </s> <s id="N14027"><!-- NEW -->huius Theorematis veritas mihi maximè demon&longs;tranda <lb/>e&longs;t, ex quo tàm multa infrà deducemus; </s> <s id="N1402D"><!-- NEW -->&longs;ic autem probamus; </s> <s id="N14031"><!-- NEW -->Quotie&longs;­<lb/>cunque mouetur corpus, producuntur &longs;altem tot partes impetus quot <lb/>&longs;unt partes mobilis per Th. 33. Quotie&longs;cunque producuntur in mobili <lb/>tot partes impetus quot &longs;unt in mobili partes &longs;ubjecti, mouetur mobile, <lb/>modó non impediatur; </s> <s id="N1403D"><!-- NEW -->quia po&longs;ita cau&longs;a nece&longs;&longs;aria, & non impedita per <lb/>Ax. 11. ponitur effectus, quod de omni cau&longs;a, &longs;ed de formali poti&longs;&longs;imum <lb/>dici debet; </s> <s id="N14045"><!-- NEW -->præterea datur aliquod pondus, quod data potentia &longs;ine me­<lb/>chanico organo mouere non pote&longs;t, licèt cum organo facilè moueat; </s> <s id="N1404B"><!-- NEW -->hæc <lb/>hypothe&longs;is certa e&longs;t; </s> <s id="N14051"><!-- NEW -->igitur cum mouet, producit tot partes impetus quot <lb/>&longs;unt nece&longs;&longs;ariæ, vt omnibus partibus mobilis di&longs;tribuantur per idem Th. <!-- REMOVE S--><lb/>33. cum verò non mouet, non producit tot partes impetus vt con&longs;tat ex <lb/>dictis; </s> <s id="N1405C"><!-- NEW -->igitur producit plures cum organo in mobili, quàm &longs;ine organo; <lb/>igitur imperfectiores, quod demon&longs;tro: </s> <s id="N14062"><!-- NEW -->&longs;it enim vectis BF, cuius cen­<lb/>trum &longs;eu fulcrum &longs;it in A, potentia in B, pondus G, quod attollitur in F; </s> <s id="N14068"><!-- NEW --><lb/>plures partes impetus produci po&longs;&longs;unt in F, vel in E, quàm in B, &longs;cilicet <lb/>in ip&longs;o pondere; </s> <s id="N1406F"><!-- NEW -->quia pondus quod non pote&longs;t attolli in B, attollitur in <lb/>E, vel in F, vt patet ex dictis; </s> <s id="N14075"><!-- NEW -->præterea punctum F mouetur tardius, quàm <lb/>B; </s> <s id="N1407B"><!-- NEW -->quia motus &longs;unt vt arcus, arcus vt &longs;emidiametri, hæ demum vt AF, <lb/>ad AB; </s> <s id="N14081"><!-- NEW -->igitur motus puncti F, e&longs;t tardior, vel imperfectior; </s> <s id="N14085"><!-- NEW -->igitur im­<lb/>petus puncti F, e&longs;t imperfectior impetu puncti B, per Ax. 13 num.4. atqui <lb/>non e&longs;t imperfectior ratione numeri partium, igitur ratione entitatis, <lb/>quæ imperfectior e&longs;t; igitur datur impetus altero impetu imperfectior. </s> </p> <p id="N1408F" type="main"> <s id="N14091"><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N1409D" type="main"> <s id="N1409F"><!-- NEW -->Ob&longs;eruabis primò multa hîc &longs;upponi &longs;eu de&longs;iderari, quæ pertinent <lb/>ad propagationem impetus, de quibus infrà; Secundò hoc Theorema <pb pagenum="47" xlink:href="026/01/079.jpg"/>per Axioma illud Metaph. probari, <emph type="italics"/>Data quacumque creatura dari potest <lb/>perfectior, vel imperfectior.<emph.end type="italics"/></s> </p> <p id="N140B1" type="main"> <s id="N140B3"><!-- NEW -->Tertiò, &longs;i dato quocunque motu pote&longs;t dari tardior: igitur dato quo­<lb/>cunque impetu pote&longs;t dari imperfectior. </s> </p> <p id="N140B9" type="main"> <s id="N140BB"><!-- NEW -->Quartò, &longs;i daretur punctum impetus in inten&longs;ione: non po&longs;&longs;et dari <lb/>motus tardior in infinitum &longs;ine diuer&longs;is gradibus perfectionis. </s> </p> <p id="N140C1" type="main"> <s id="N140C3"><!-- NEW -->Quintò, &longs;ine hac diuer&longs;a impetus perfectione non po&longs;&longs;et explicari <lb/>productio continua impetus, quæ &longs;it temporibus inæqualibus, neque de­<lb/>&longs;tructio eiu&longs;dem impetus; nec motus in diuer&longs;is planis inclinatis, vel in­<lb/>diuer&longs;is lineis citra perpendicularem, &longs;ed de his omnibus &longs;uo loco. </s> </p> <p id="N140CD" type="main"> <s id="N140CF"><!-- NEW -->Sextò, Denique ratio propo&longs;ita rem i&longs;tam euincit; </s> <s id="N140D3"><!-- NEW -->cum enim in motu <lb/>vectis plures partes producantur ver&longs;us centrum, &longs;cilicet, in maiori pon­<lb/>dere, quod attollitur; & cum hæ habeant motum tardiorem, &longs;equitur ne­<lb/>ce&longs;&longs;ariò e&longs;&longs;e imperfectiores. </s> </p> <p id="N140DD" type="main"> <s id="N140DF"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 78.<emph.end type="center"/></s> </p> <p id="N140EB" type="main"> <s id="N140ED"><emph type="italics"/>Dato quocumque impetu dari pote&longs;t imperfectior, & imperfectior,<emph.end type="italics"/> quia da­<lb/>to quocumque motu dari pote&longs;t tardior, ergo dato quocumque impetu <lb/>imperfectior. </s> </p> <p id="N140F9" type="main"> <s id="N140FB"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 79.<emph.end type="center"/></s> </p> <p id="N14107" type="main"> <s id="N14109"><emph type="italics"/>Non pote&longs;t explicari tarditas motus &longs;ine diuer&longs;a perfectione impetus, per <lb/>pauciores &longs;cilicet eiu&longs;dem impetus partes.<emph.end type="italics"/></s> <s id="N14112"><!-- NEW --> Primò, quia cum retardari po&longs;&longs;it <lb/>hic motus, & de&longs;trui &longs;ucce&longs;&longs;inè hic impetus; </s> <s id="N14118"><!-- NEW -->cumque in&longs;tantia motus <lb/>velocioris &longs;int breuiora; </s> <s id="N1411E"><!-- NEW -->certè initio motus, breuiori &longs;cilicet tempore <lb/>imperfectior impetus de&longs;trui tantùm pote&longs;t; </s> <s id="N14124"><!-- NEW -->cum enim æqualis æquali­<lb/>bus temporibus; certè inæqualis inæqualibus. </s> <s id="N1412A">Secundò quia vix explica­<lb/>ri pore&longs;t quomodo duæ formæ homogeneæ in eodem &longs;ubiecti puncto <lb/>exi&longs;tere po&longs;&longs;int, quod etiam in commune e&longs;t calori, lumini, &c. </s> </p> <p id="N14131" type="main"> <s id="N14133"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 80.<emph.end type="center"/></s> </p> <p id="N1413F" type="main"> <s id="N14141"><emph type="italics"/>Cum applicatur potentia centro vectis, non producitur æqualis impetus ver­<lb/>&longs;us circumferentiam in omnibus partibus, &longs;ed maior ver&longs;us eandem circumfe­<lb/>rentiam,<emph.end type="italics"/> quia e&longs;t maior motus. </s> </p> <p id="N1414D" type="main"> <s id="N1414F"><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 1.<emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N1415C" type="main"> <s id="N1415E"><!-- NEW -->Hinc difficiliùs attollitur pertica CA ex puncto C motu circulari, <lb/>quàm ex puncto B motu recto; </s> <s id="N14164"><!-- NEW -->quia &longs;cilicet, cum motu recto ex puncto B <lb/>attollitur, omnes partes mouentur motu æquali; </s> <s id="N1416A"><!-- NEW -->igitur impetus æqualiter <lb/>omnibus di&longs;tribuitur; </s> <s id="N14170"><!-- NEW -->igitur modò producantur tot partes impetus, quot <lb/>&longs;unt partes in mobili; </s> <s id="N14176"><!-- NEW -->haud dubiè attolletur: </s> <s id="N1417A"><!-- NEW -->at verò, cum motu circulari <lb/>ex puncto C attollitur, omnes partes inæquali motu attolluntur; </s> <s id="N14180"><!-- NEW -->igitur <lb/>plures &longs;unt nece&longs;&longs;ariæ, vt attollatur motu circulari; </s> <s id="N14186"><!-- NEW -->igitur difficiliùs iuxta <lb/>experimentum; adde quod cum applicatur potentia in C, punctum A, <lb/>maius momentum habet, de quo aùàs. </s> </p> <p id="N1418E" type="main"> <s id="N14190"><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 2.<emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N1419D" type="main"> <s id="N1419F"><!-- NEW -->Hinc ratio euidens illius experimenti, quo manife&longs;tè con&longs;tat perti-<pb pagenum="48" xlink:href="026/01/080.jpg"/>cam CA, ex A, facilius attolli motu recto, quàm circulari; cum &longs;ci­<lb/>licet cuiu&longs;dam qua&longs;i reflexionis opera eodem tempore vtraque extremi­<lb/>tas æquali motu attollitur. </s> </p> <p id="N141AC" type="main"> <s id="N141AE"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 81.<emph.end type="center"/></s> </p> <p id="N141BA" type="main"> <s id="N141BC"><arrow.to.target n="note1"/></s> </p> <p id="N141C1" type="margin"> <s id="N141C3"><margin.target id="note1"/><emph type="italics"/>Fig.<emph.end type="italics"/>7. <lb/><emph type="italics"/>Tab.<emph.end type="italics"/>1.<!-- KEEP S--></s> </p> <p id="N141D5" type="main"> <s id="N141D7"><!-- NEW --><emph type="italics"/>Si verò applicetur potentia extra centrum vectis v. <!-- REMOVE S-->g. <!-- REMOVE S-->in<emph.end type="italics"/> F, <emph type="italics"/>po&longs;ito centro in<emph.end type="italics"/><lb/>A, <emph type="italics"/>producitur impetus minor ab<emph.end type="italics"/> F, <emph type="italics"/>ver&longs;us<emph.end type="italics"/> A; </s> <s id="N141F7"><!-- NEW --><emph type="italics"/>ab verò ver&longs;us<emph.end type="italics"/> E, <emph type="italics"/>producitur <lb/>eiu&longs;dem perfectionis proportionaliter, cuius e&longs;t ab<emph.end type="italics"/> F, <emph type="italics"/>ver&longs;us<emph.end type="italics"/> A; denique ab E, <lb/>ver&longs;us B, producitur quidem vnum punctum, vel vnus gradus impetus <lb/>eiu&longs;dem perfectionis cum eo, qui productus e&longs;t in F, & in E (&longs;upponi­<lb/>tur enim ex. gr. <!-- REMOVE S-->vnus tantùm gradus in F, & in E, productus) at verò <lb/>producuntur alij imperfectiones. </s> <s id="N14218"><!-- NEW -->v.g. <!-- REMOVE S-->in D, præter æquè perfectum pro­<lb/>ducuntur 3. alij adæquantes perfectionem prioris; </s> <s id="N14220"><!-- NEW -->in C verò, præter 4. <lb/>&longs;imiles ijs, qui &longs;unt in D, producuntur 5. alij adæquantes prioris perfe­<lb/>ctionem in B7; atque ita deinceps per numeros impares, & quadrata, <lb/>nullus tamen producitur perfectioris entitatis. </s> </p> <p id="N1422A" type="main"> <s id="N1422C"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 82.<emph.end type="center"/></s> </p> <p id="N14238" type="main"> <s id="N1423A"><!-- NEW --><emph type="italics"/>Determinatur hæc diuer&longs;a perfectio impetus à diuer&longs;a perfectione motus, <lb/>quatenus fit tali modo<emph.end type="italics"/>; </s> <s id="N14245"><!-- NEW -->quæ non pote&longs;t explicari per impetum remi&longs;&longs;io­<lb/>rem, vel inten&longs;iorem; </s> <s id="N1424B"><!-- NEW -->nam cum &longs;it tantùm impetus in&longs;titutus propter <lb/>motum; </s> <s id="N14251"><!-- NEW -->certè ille tantùm impetus produci pote&longs;t, ex quo pote&longs;t &longs;equi <lb/>motus; </s> <s id="N14257"><!-- NEW -->igitur &longs;i tali tantùm motu data pars mobilis moueri pote&longs;t; haud <lb/>dubiè talis tantùm impetus, ex quo &longs;equitur talis motus, in ea produ­<lb/>cetur, & tali modo. </s> </p> <p id="N1425F" type="main"> <s id="N14261"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 83.<emph.end type="center"/></s> </p> <p id="N1426D" type="main"> <s id="N1426F"><!-- NEW --><emph type="italics"/>Perfectio impetus non petitur tantùm à perfectione motus &longs;i con&longs;ideretur <lb/>&longs;eor&longs;im entitas eiu&longs;dem impetus; </s> <s id="N14277"><!-- NEW -->&longs;ed debet comparari tota collectio omniu&mtail; <lb/>partium impetus, quæ in&longs;unt datæ parti &longs;ubiecti, cum tota collectione partium <lb/>quæ alteri porti mobilis in&longs;unt<emph.end type="italics"/>; </s> <s id="N14282"><!-- NEW -->quippe plures partes impetus po&longs;&longs;unt ha­<lb/>bere eum motum, vel potius eam motus perfectionem, quam pauciores <lb/>haberent; igitur perfectio illarum e&longs;t ab ip&longs;o motu, quatenus cum ip&longs;o <lb/>partium numero comparatur. </s> </p> <p id="N1428C" type="main"> <s id="N1428E"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 84.<emph.end type="center"/></s> </p> <p id="N1429A" type="main"> <s id="N1429C"><!-- NEW --><emph type="italics"/>Impetus perfectus producere pote&longs;t imperfectum<emph.end type="italics"/>; patet in vecte; </s> <s id="N142A5"><!-- NEW -->nam po­<lb/>tentia, &longs;en pondus extremitati appen&longs;um producit in &longs;e impetum, à quo <lb/>deinde impetus in toto vecte producitur per Th.42. &longs;ed impetus pon­<lb/>deris appen&longs;i e&longs;t eiu&longs;dem perfectionis cum impetu producto in ip&longs;a ve­<lb/>ctis extremitate, ex qua pendet; </s> <s id="N142B1"><!-- NEW -->cum &longs;it vtriu&longs;que æqualis motus; &longs;ed <lb/>ver&longs;us centrum eiu&longs;dem vectis producitur impetus imperfectior per <lb/>Th.82. igitur imperfectus à perfecto producitur. </s> </p> <p id="N142B9" type="main"> <s id="N142BB"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 85.<emph.end type="center"/></s> </p> <p id="N142C7" type="main"> <s id="N142C9"><!-- NEW --><emph type="italics"/>Impetus perfectus nunquam producitur ab imperfecto, per Ax.<emph.end type="italics"/> 3. <emph type="italics"/>num.<emph.end type="italics"/> 2. <lb/>adde quod nunquam effectus perfectio &longs;uperat perfectionem cau&longs;æ; </s> <s id="N142DA"><!-- NEW -->dixi <lb/>perfectum ab imperfecto; </s> <s id="N142E0"><!-- NEW -->&longs;cilicet &longs;i con&longs;ideretur perfectio ratione en-<pb pagenum="49" xlink:href="026/01/081.jpg"/>titatis; </s> <s id="N142E9"><!-- NEW -->cum reuerâ, vt dictum e&longs;t &longs;uprà, remi&longs;&longs;us producat inten&longs;um, <lb/>quod in vecte clari&longs;&longs;imum e&longs;t; </s> <s id="N142EF"><!-- NEW -->quippe momentum applicatum in F, quod <lb/>tardiùs mouetur deor&longs;um, quàm B, &longs;ur&longs;um, vt patet, habet impetum re­<lb/>mi&longs;&longs;iorem, qui tamen producit in B, inten&longs;iorem: </s> <s id="N142F7"><!-- NEW -->Pro quo, ob&longs;eruabis <lb/>impetum imperfectum cum alio perfecto actione communi agentem <lb/>po&longs;&longs;e concurrere ad producendum perfectum, vt patet; </s> <s id="N142FF"><!-- NEW -->non tamen in <lb/>ratione cau&longs;æ totalis: </s> <s id="N14305"><!-- NEW -->&longs;imiliter plures imperfecti &longs;imul concurrentes <lb/>po&longs;&longs;unt producere perfectum; quia plures imperfecti conjunctim adæ­<lb/>quant perfectionem alterius perfectioris &longs;inguli &longs;eor&longs;im. </s> </p> <p id="N1430D" type="main"> <s id="N1430F"><!-- NEW -->Ob&longs;eruabis &longs;ecundò præclarum naturæ in&longs;titutum, quo factum e&longs;t; </s> <s id="N14313"><!-- NEW --><lb/>vt cum vires hominum maiora pondera leuare non po&longs;&longs;int, &longs;i &longs;eor&longs;un <lb/>con&longs;iderentur; </s> <s id="N1431A"><!-- NEW -->cum organis tamen mechanicis conjunctæ nullum pon­<lb/>dus quantumuis immane leuare non po&longs;&longs;int; </s> <s id="N14320"><!-- NEW -->quod certè nullo modo ac­<lb/>cideret, ni&longs;i plures partes impetus producerent neque plures producere <lb/>po&longs;&longs;ent, ni&longs;i minoris perfectionis e&longs;&longs;ent; quia faciliùs producitur effe­<lb/>ctus imperfectus, quam perfectus per Ax. 13.num.4. </s> </p> <p id="N1432A" type="main"> <s id="N1432C"><!-- NEW -->Tertiò hinc optimè à natura proui&longs;um e&longs;t, vt motus tardior in infi­<lb/>nitum e&longs;&longs;e po&longs;&longs;it; quod reuerâ fieri non po&longs;&longs;et, ni&longs;i dari po&longs;&longs;et impetus <lb/>alio imperfectior. </s> </p> <p id="N14334" type="main"> <s id="N14336"><!-- NEW -->Quartò, hinc quoque benè explicatur diuer&longs;itas impetus, quæ oritur <lb/>tum à diuer&longs;o medio, tùm à plano inclinato, tùm ab aliis impedimentis, <lb/>tùm à diuer&longs;o ni&longs;u eiu&longs;dem potentiæ, tùm maximè à diuer&longs;o applicatio­<lb/>nis modo; de quibus aliàs. </s> </p> <p id="N14340" type="main"> <s id="N14342"><!-- NEW -->Quintò, &longs;i potentia applicata mobili immediatè illud moueat motu <lb/>recto, vel in &longs;ingulis punctis mobilis producitur vnum punctum impe­<lb/>tus, vel plura; </s> <s id="N1434A"><!-- NEW -->&longs;i primum, erit primus tantùm gradus maximæ perfectio­<lb/>nis; </s> <s id="N14350"><!-- NEW -->ita vt perfectiorem producere non po&longs;&longs;it, ad quem e&longs;t determinata <lb/>potentia; </s> <s id="N14356"><!-- NEW -->imperfectiorem tamen impetu innato, de quo infrà; &longs;i verò <lb/>&longs;ecundum, producet in &longs;ingulis partibus <expan abbr="eũdem">eundem</expan> gradum perfecti&longs;&longs;i­<lb/>mum cum aliis pluribus, vel paucioribus heterogeneis, & imperfectio­<lb/>ribus. </s> </p> <p id="N14364" type="main"> <s id="N14366"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 86.<emph.end type="center"/></s> </p> <p id="N14372" type="main"> <s id="N14374"><!-- NEW --><emph type="italics"/>Potentia naturalis grauium producit tantùm vno in&longs;tanti ad intra vnicum <lb/>punctum impetus in quolibet puncto &longs;ubiecti; </s> <s id="N1437C"><!-- NEW -->&longs;i tamen impetum producit, quod <lb/>definiam lib.<emph.end type="italics"/> 20. <emph type="italics"/>& &longs;i dentur puncta &longs;ubiecti, quod ad præ&longs;ens in&longs;titutum non <lb/>pertinet<emph.end type="italics"/>; </s> <s id="N1438D"><!-- NEW -->Probatur, quia fru&longs;trà e&longs;&longs;ent plura puncta impetus; nec enim <lb/>&longs;unt multiplicandæ formæ &longs;ine nece&longs;&longs;itate, ratione &c. </s> <s id="N14393">per Ax. 7. & 3. <lb/>n. </s> <s id="N14398">1. Præterea non e&longs;t, cur potius produceret 2. quàm 3. 4. &c. </s> <s id="N1439B">atqui <lb/>quod vnum e&longs;t, determinatum e&longs;t per Ax. 5. <!-- KEEP S--></s> </p> <p id="N143A1" type="main"> <s id="N143A3"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 87.<emph.end type="center"/></s> </p> <p id="N143AF" type="main"> <s id="N143B1"><!-- NEW --><emph type="italics"/>Potentia motrix animantium etiam vno in&longs;tanti plura puncta, &longs;en partes <lb/>impetus in eadem parte &longs;ubiecti producere potest<emph.end type="italics"/>; </s> <s id="N143BC"><!-- NEW -->Probatur in proiectis, <lb/>quorum impetus aliquando plùs, aliquando minùs durat licèt &longs;en&longs;im <lb/>&longs;ingulis in&longs;tantibus aliquid illius de&longs;truatur; </s> <s id="N143C4"><!-- NEW -->determinatur autem <pb pagenum="50" xlink:href="026/01/082.jpg"/>numerus punctorum, &longs;eu partium ab ea potentia, cui &longs;ube&longs;t potentia <lb/>motrix; quia modò maior e&longs;t ni&longs;us, modò minor. </s> </p> <p id="N143CF" type="main"> <s id="N143D1"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 88.<emph.end type="center"/></s> </p> <p id="N143DD" type="main"> <s id="N143DF"><!-- NEW --><emph type="italics"/>Eadem potentia inæqualibus temporibus impetum inæqualem in perfectio­<lb/>ne producit<emph.end type="italics"/>; </s> <s id="N143EA"><!-- NEW -->accipiatur enim totum illud tempus, quo vnicum tantùm <lb/>punctum impetus producit (vocetur in&longs;tans) de quo in Th. 86; certè <lb/>&longs;i in minori tempore agat, minùs aget, per Ax. 13. num. </s> <s id="N143F2"><!-- NEW -->4. &longs;ed non <lb/>pote&longs;t minùs agere ratione numeri, vt patet; igitur ratione perfectio­<lb/>nis. </s> </p> <p id="N143FA" type="main"> <s id="N143FC"><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N14408" type="main"> <s id="N1440A">Ob&longs;eruabis &longs;ine hoc Theoremate explicari non po&longs;&longs;e accelerationem <lb/>motus naturalis, vel augmentum impetus, vt videbimus. </s> </p> <p id="N1440F" type="main"> <s id="N14411"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 89.<emph.end type="center"/></s> </p> <p id="N1441D" type="main"> <s id="N1441F"><!-- NEW --><emph type="italics"/>Impetus violenti, qui &longs;en&longs;im de&longs;truitur in proiectis, po&longs;itis ij&longs;dem circum­<lb/>&longs;tantiis medij, & re&longs;i&longs;tentiæ, minori tempore minùs de&longs;truitur; </s> <s id="N14427"><!-- NEW -->plus verò ma­<lb/>jori:<emph.end type="italics"/> Quia hæc de&longs;tructio habet cau&longs;am; nam quidquid de&longs;truitur, ad <lb/>exigentiam alicuius de&longs;truitur, per Ax. 14. num. </s> <s id="N14432">2. igitur minori <lb/>tempore minùs de&longs;truitur per Ax. <!-- REMOVE S-->13. 4. alioquin totus &longs;imul debe­<lb/>ret de&longs;trui. </s> </p> <p id="N1443B" type="main"> <s id="N1443D"><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N14449" type="main"> <s id="N1444B">Ob&longs;eruabis etiam &longs;ine hoc Theoremate non po&longs;&longs;e explicari de&longs;tru­<lb/>ctionem impetus violenti, vt videbimus infrà. </s> </p> <p id="N14450" type="main"> <s id="N14452"><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 1.<emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N1445F" type="main"> <s id="N14461">Hinc, quò potentia diutiùs manet applicata (putà malleo) percu&longs;&longs;io ma­<lb/>ior e&longs;t. </s> </p> <p id="N14466" type="main"> <s id="N14468"><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 2.<emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N14475" type="main"> <s id="N14477">Hinc, quò impedimentum diutiùs manet applicatum, illa de&longs;tructio <lb/>e&longs;t maior. </s> </p> <p id="N1447C" type="main"> <s id="N1447E"><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 3.<emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N1448B" type="main"> <s id="N1448D"><!-- NEW -->Hinc præclara eruitur ratio, cur maior lapis, quàm minor impactus <lb/>maiorem ictum infligat; </s> <s id="N14493"><!-- NEW -->licèt tot partes impetus eodem in&longs;tanti produ­<lb/>cantur in vno, quot in alio: </s> <s id="N14499"><!-- NEW -->quia &longs;cilicet diutiùs manet applicatus po­<lb/>tentiæ; &longs;ed hanc rationem explicabimus fusè lib. 10. cum de percu&longs;­<lb/>&longs;ione. </s> </p> <p id="N144A1" type="main"> <s id="N144A3"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 90.<emph.end type="center"/></s> </p> <p id="N144AF" type="main"> <s id="N144B1"><emph type="italics"/>Impetus propagatur nece&longs;&longs;ariò per totum corpus impul&longs;um, &longs;eu proiectum.<emph.end type="italics"/></s> </p> <p id="N144B8" type="main"> <s id="N144BA">Probatur; </s> <s id="N144BD"><!-- NEW -->quia cum omnes eius partes moueantur, nec vlla &longs;ine im­<lb/>petu moueri po&longs;&longs;it per Th. 18. & 33. cum etiam potentia motrix non <lb/>&longs;it omnibus immediatè applicata, vt con&longs;tat; certè &longs;ine propagatione, <lb/>vel diffu&longs;ione non pote&longs;t explicari productio huius motus. </s> </p> <pb pagenum="51" xlink:href="026/01/083.jpg"/> <p id="N144CB" type="main"> <s id="N144CD"><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N144D9" type="main"> <s id="N144DB">Ob&longs;eruabis propagationem impetus, vel alterius qualitatis e&longs;&longs;e tan­<lb/>tùm continuatam eiu&longs;dem productionem, quæ incipit ab ea parte, cui <lb/>potentia e&longs;t immediatè applicata, & propagatur, &longs;eu diffunditur per <lb/>omnes alias donec ad vltimam perueniat eo modo, quo iam definio. </s> </p> <p id="N144E4" type="main"> <s id="N144E6"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 92.<emph.end type="center"/></s> </p> <p id="N144F2" type="main"> <s id="N144F4"><!-- NEW --><emph type="italics"/>Illa progatio non fit per motum localem, ita vt pars impetus producta in <lb/>prima parte &longs;ubiecti tran&longs;eat ad &longs;ecundam,<emph.end type="italics"/> patet; quia cum impetus &longs;it ac­<lb/>cidens per Th. 8. de &longs;ubiecto in &longs;ubiectum tran&longs;ire non pote&longs;t per deff. </s> <s id="N14501"><lb/>accidentis; de qua in Metaphy&longs;icâ; </s> <s id="N14505"><!-- NEW -->nec e&longs;t quod aliqui dicant &longs;e <expan abbr="nõ">non</expan> po&longs;&longs;e <lb/>concipere, quomodo id fiat &longs;ine motu locali; </s> <s id="N1450F"><!-- NEW -->cum ip&longs;is etiam oculis <lb/>qua&longs;i cernatur; </s> <s id="N14515"><!-- NEW -->cum enim percutis corpus oblongum AE, & cadit ictus <lb/>in extremitatem A, corpus ip&longs;um totum &longs;imul moues; igitur pars impe­<lb/>tus, quæ recipitur in A, non migrat in E, &longs;ed hæc producitur in A, & <lb/>alia in B, alia in C, atque ita deinceps. </s> </p> <p id="N1451F" type="main"> <s id="N14521"><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N1452D" type="main"> <s id="N1452F">Ob&longs;eruabis ex hac propagatione impetus per analogiam rectè om­<lb/>ninò explicari propagationem luminis, & aliarum qualitatum, de qui­<lb/>bus &longs;uo loco. </s> </p> <p id="N14536" type="main"> <s id="N14538"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 92.<emph.end type="center"/></s> </p> <p id="N14544" type="main"> <s id="N14546"><!-- NEW --><emph type="italics"/>In propagatione impetus prima pars<emph.end type="italics"/> A v. <!-- REMOVE S-->g. <emph type="italics"/>non producit partem<emph.end type="italics"/> B, <emph type="italics"/>& <lb/>hæc<emph.end type="italics"/> C; </s> <s id="N1455F"><!-- NEW --><emph type="italics"/>hæc verò<emph.end type="italics"/> D, <emph type="italics"/>atque ita deinceps<emph.end type="italics"/>; Probatur. <!-- KEEP S--></s> <s id="N1456F"><!-- NEW -->Primò, quia &longs;i hoc e&longs;&longs;et, <lb/>omne corpus po&longs;&longs;et moueri à qualibet potentia; nam modò po&longs;&longs;et pro­<lb/>duci vnum punctum impetus, hoc etiam aliud produceret, & hoc aliud, <lb/>atque ita deinceps. </s> <s id="N14579">Secundò, Minimum granum &longs;uperpo&longs;itum rupi, to­<lb/>tam ip&longs;am rupem mouere po&longs;&longs;et. </s> <s id="N1457E"><!-- NEW -->Tertio, Quia vel in omnibus, vel in <lb/>nulla parte impetus producitur per Th.33. Quartò, quia impetus mobi­<lb/>lis projecti intenderetur; nam impetus vnius partis impetum alterius <lb/>intenderet. </s> <s id="N14588"><!-- NEW -->Quintò, quia impetus partis B, tàm ageret in A, trahendo, <lb/>quàm in C pellendo; cum impetus vtroque modo propagetur. </s> <s id="N1458E"><!-- NEW -->Sextò, &longs;i <lb/>applicaretur potentia in C, non video, cur impetus partis C, ageret po­<lb/>tius versùs E, quàm versùs A? alioquin eadem pars impetus plures pro­<lb/>ducere po&longs;&longs;et; igitur impetus potentiæ motricis &longs;ufficiens erit cau&longs;a ad <lb/>producendum totum alium. </s> <s id="N1459A"><!-- NEW -->Septimò, tractionis impetus explicari non <lb/>pote&longs;t, &longs;i impetus vnius partis producat in alia impetum; alioquin dare­<lb/>tur mutua actio infinities repetita, vt con&longs;ideranti patebit. </s> <s id="N145A2"><!-- NEW -->Octauò, &longs;i <lb/>impetus vnius partis producit in alia; </s> <s id="N145A8"><!-- NEW -->&longs;int duo globi contigui; igitur il­<lb/>le, qui impellit alium, reflecti po&longs;&longs;et, quod nunquam accidit quando <lb/>&longs;unt contigui. </s> </p> <p id="N145B0" type="main"> <s id="N145B2"><!-- NEW -->Ob&longs;eruabis illud quidem verum e&longs;&longs;e in motu recto, &longs;ecus in circulari; </s> <s id="N145B6"><!-- NEW --><lb/>nam cum cylindrus circa alteram extremitatem vibratus deor&longs;um cadit; <lb/>partes, quæ propiùs ad extremitatem immobilem accedunt iuuant mo­<lb/>tum aliarum, quæ longiùs ab eadem recedunt. </s> </p> <pb pagenum="52" xlink:href="026/01/084.jpg"/> <p id="N145C3" type="main"> <s id="N145C5"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 93.<emph.end type="center"/></s> </p> <p id="N145D1" type="main"> <s id="N145D3"><emph type="italics"/>Impetus propagatur eodem in&longs;tanti, id e&longs;t, &longs;ine temporis &longs;ucce&longs;&longs;ione.<emph.end type="italics"/></s> <s id="N145DA"> Proba­<lb/>tur; </s> <s id="N145DF"><!-- NEW -->&longs;it enim applicata potentia in A, dico &longs;imul produci impetum in <lb/>BCDE; </s> <s id="N145E5"><!-- NEW -->quia &longs;i primo in&longs;tanti produceretur in A, & &longs;ecundo in B, vel <lb/>A moueretur ante B, vel impetus in A e&longs;&longs;et fru&longs;trà; </s> <s id="N145EB"><!-- NEW -->vtrumque e&longs;t ab&longs;ur­<lb/>dum; nam totum AE, &longs;imul mouetur. </s> </p> <p id="N145F1" type="main"> <s id="N145F3"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 94.<emph.end type="center"/></s> </p> <p id="N145FF" type="main"> <s id="N14601"><emph type="italics"/>Tribus tantùm modis propagari pote&longs;t impetus ratione inten&longs;ionis.<emph.end type="italics"/></s> <s id="N14608"><!-- NEW --> Primò <lb/>&longs;i æqualiter omnibus partibus &longs;ubjecti di&longs;tribuatur; id e&longs;t vniformiter. </s> <s id="N1460E"><lb/>Secundò, &longs;i plùs partibus propioribus, & minùs remotioribus. </s> <s id="N14612"><!-- NEW -->Tertiò, è <lb/>contra, &longs;i plùs remotioribus, & minùs propioribus; </s> <s id="N14618"><!-- NEW -->tribus etiam ratione <lb/>perfectionis eo modo, quo diximus de inten&longs;ione; </s> <s id="N1461E"><!-- NEW -->at verò nouem mo­<lb/>dis propagari pote&longs;t ratione vtriu&longs;que; patet ex regula combinationum; </s> <s id="N14624"><!-- NEW --><lb/>&longs;i enim 3. ducantur in 3. habebis 9. Iam &longs;upere&longs;t, vt videamus, an reue­<lb/>rà omnibus i&longs;tis modis impetus re ip&longs;a propagetur; </s> <s id="N1462B"><!-- NEW -->quod licèt difficile <lb/>&longs;it, & vix hactenus explicatum: Audeo tamen polliceri meum &longs;uper hac <lb/>re conatum non pror&longs;us inutilem fore. </s> </p> <p id="N14633" type="main"> <s id="N14635"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 95.<emph.end type="center"/></s> </p> <p id="N14641" type="main"> <s id="N14643"><!-- NEW --><emph type="italics"/>Impetus propagatur vniformiter in mobili, cuius omnes partes mouentur <lb/>æquali motu<emph.end type="italics"/>; </s> <s id="N1464E"><!-- NEW -->probatur, quia impetus non cogno&longs;citur ni&longs;i per motum; <lb/>igitur vbi e&longs;t æqualis motus, debet e&longs;&longs;e æqualis impetus in omnibus par­<lb/>tibus, id e&longs;t æqualis graduum heterogeneorum collectio, in quo non <lb/>e&longs;t difficultas. </s> </p> <p id="N14658" type="main"> <s id="N1465A"><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N14666" type="main"> <s id="N14668"><!-- NEW -->Ob&longs;eruabis illud mobile moueri motu æquali &longs;ecundum omnes &longs;ui <lb/>partes, quod mouetur motu recto; quippe fieri non pote&longs;t, quin omnes <lb/>partes, quæ mouentur motu recto &longs;implici, motu etiam æquali mouean­<lb/>tur. </s> </p> <p id="N14672" type="main"> <s id="N14674"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 96.<emph.end type="center"/></s> </p> <p id="N14680" type="main"> <s id="N14682"><!-- NEW --><emph type="italics"/>Cum duo corpora &longs;e&longs;e mutuò tangunt, impetus in vtroque propagatur<emph.end type="italics"/> &longs;int <lb/>v. <!-- REMOVE S-->g. <!-- REMOVE S-->globi A & B, æquales &longs;ibi inuicem contigui in C, &longs;it applicata po­<lb/>tentia in D, non modò producet impetum in globo A, &longs;ed etiam in B: </s> <s id="N14693"><!-- NEW --><lb/>probatur primò, quia &longs;e habent per modum vnius, vt patet ex re&longs;i&longs;ten­<lb/>tia, nec enim A moueri pote&longs;t &longs;ine B per lineam DE, quod certè cla­<lb/>ri&longs;&longs;imum e&longs;t; probatur &longs;ecundò quia &longs;i A produceret impetum in B, duo <lb/>globi, vel 3. vel 5. vel infiniti tantùm re&longs;i&longs;terent, quantùm vnicus glo­<lb/>bus, quod fal&longs;um & ab&longs;urdum e&longs;t. </s> <s id="N146A0"><!-- NEW -->Tertiò, Ratio à priori e&longs;t; </s> <s id="N146A4"><!-- NEW -->quia ideo <lb/>producitur, & propagatur impetus in toto A; </s> <s id="N146AA"><!-- NEW -->quia vna pars non pote&longs;t <lb/>moueri &longs;ine alia per Th. 33. &longs;ed non pote&longs;t A moueri ni&longs;i moueatur B; <lb/>igitur in vtroque &longs;imul, & æqualiter propagatur impetus. </s> </p> <p id="N146B2" type="main"> <s id="N146B4"><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 1.<emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N146C1" type="main"> <s id="N146C3">Hinc ratio manife&longs;ta cur maior &longs;it re&longs;i&longs;tentia duorum quàm vnius. </s> </p> <pb pagenum="53" xlink:href="026/01/085.jpg"/> <p id="N146CA" type="main"> <s id="N146CC"><emph type="center"/><emph type="italics"/>Corollarium.<emph.end type="italics"/> 2.<emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N146D9" type="main"> <s id="N146DB"><!-- NEW -->Hinc eadem vis requiritur ad &longs;u&longs;tinenda duo pondera; &longs;iue vtrum­<lb/>que &longs;eor&longs;im humeris incubet, &longs;iue alterum alteri &longs;uperponatur. </s> </p> <p id="N146E1" type="main"> <s id="N146E3"><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 3.<emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N146F0" type="main"> <s id="N146F2">Hinc percu&longs;&longs;io vel ictus globi B, cui alter A à tergo immediatè in­<lb/>&longs;i&longs;tit maior e&longs;t. </s> </p> <p id="N146F7" type="main"> <s id="N146F9"><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 4.<emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N14706" type="main"> <s id="N14708">Hinc pondus alteri &longs;uperpo&longs;itum actione communi cum alio graui­<lb/>tat in &longs;uppo&longs;itam manum. </s> <s id="N1470D">v. <!-- REMOVE S-->g. <!-- REMOVE S--><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 5.<emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N1471E" type="main"> <s id="N14720">Hinc potentia applicata in D, minùs impetus &longs;ingulis imprimit. </s> </p> <p id="N14723" type="main"> <s id="N14725"><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 6.<emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N14732" type="main"> <s id="N14734"><!-- NEW -->Hinc demum licèt impetus ratione inten&longs;ionis &longs;it æqualis in vtroque <lb/>globo; </s> <s id="N1473A"><!-- NEW -->attamen, &longs;i accipiatur numerus partium vtriu&longs;que impetus, im­<lb/>petus &longs;unt vt globi v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;i B e&longs;t æqualis A impetus productus in B e&longs;t <lb/>æqualis producto in A, &longs;i B &longs;it &longs;ubduplus, vel &longs;ubtriplus, impetus e&longs;t <lb/>&longs;ubtriplus, vel &longs;ubduplus; quorum omnium rationes patent ex Th.96. </s> </p> <p id="N14748" type="main"> <s id="N1474A"><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 7.<emph.end type="center"/></s> </p> <p id="N14756" type="main"> <s id="N14758">Hinc etiam colligi pote&longs;t manife&longs;tum di&longs;crimen, quod intercedit inter <lb/>propagationem impetus, & aliarum qualitatum, quæ (vt vulgò dicitur) <lb/>vniformiter difformiter propagantur, id e&longs;t, æqualiter in æquali <lb/>di&longs;tantia, & inæqualiter inæquali. </s> </p> <p id="N14761" type="main"> <s id="N14763"><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 8.<emph.end type="center"/></s> </p> <p id="N1476F" type="main"> <s id="N14771"><!-- NEW -->Hinc demum colligi pote&longs;t non modò impetum produci in globo B <lb/>v. <!-- REMOVE S-->g. <!-- REMOVE S-->verùm etiam in aëre ambiente, cui &longs;cilicet globus contiguus e&longs;t; </s> <s id="N1477B"><!-- NEW --><lb/>qui reuera aër facilè amouetur; </s> <s id="N14780"><!-- NEW -->tùm quia propter raritatem pauci&longs;&longs;imæ <lb/>partes mouendæ &longs;unt; </s> <s id="N14786"><!-- NEW -->tùm quia facilè diuiduntur, de quibus alias; </s> <s id="N1478A"><!-- NEW -->tùm <lb/>quia, ne detur vaçuum, &longs;patium à tergo relictum occupare debet, quod <lb/>reuerà præ&longs;tat breui peracto circuitu, vt videre e&longs;t in aqua; </s> <s id="N14792"><!-- NEW -->nec enim <lb/>totus aër agitari debet; </s> <s id="N14798"><!-- NEW -->quis enim id con&longs;equi po&longs;&longs;et; tum denique, quia <lb/>aër non grauitat in aëre, igitur cum non re&longs;i&longs;tat vlla grauitatio, facilè <lb/>moueri pote&longs;t. </s> </p> <p id="N147A0" type="main"> <s id="N147A2"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 97.<emph.end type="center"/></s> </p> <p id="N147AE" type="main"> <s id="N147B0"><!-- NEW --><emph type="italics"/>Cum applicatur potentia centro motus circularis, ita propagatur impetus, vt <lb/>plures partes impetus continuò producantur ver&longs;us <expan abbr="circumferentiã">circumferentiam</expan><emph.end type="italics"/>; &longs;it enim <lb/>cylindrus CA, fig. </s> <s id="N147C0"><!-- NEW -->Th. 73. &longs;it centrum motus C; </s> <s id="N147C4"><!-- NEW -->haud dubiè plures <lb/>partes impetus producuntur in B, quàm in C, & plures in A, quam in B; </s> <s id="N147CA"><!-- NEW --><lb/>quia, cum pars B moueatur velociùs, quàm C, & A quàm B; certè, vbi e&longs;t <lb/>maior motus, vel effectus, ibi debet e&longs;&longs;e maior impetus, vel cau&longs;a per <lb/>Ax. 13. n. </s> <s id="N147D3"><!-- NEW -->4. quod autem &longs;it maior motus, con&longs;tat ex maioribus &longs;patiis, <lb/>vel arcubus æquali tempore confectis; quod verò &longs;it impetus inten&longs;ior <pb pagenum="54" xlink:href="026/01/086.jpg"/>versùs circumferentiam, non perfectior, patet per Th. 8. </s> </p> <p id="N147DE" type="main"> <s id="N147E0"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 98.<emph.end type="center"/></s> </p> <p id="N147EC" type="main"> <s id="N147EE"><!-- NEW --><emph type="italics"/>Inten&longs;io impetus propagati iuxta hunc modum &longs;e habet, vt distantia à cen­<lb/>tro motus<emph.end type="italics"/>; </s> <s id="N147F9"><!-- NEW -->&longs;int enim punctum B, & punctum A: </s> <s id="N147FD"><!-- NEW -->ita &longs;e habet inten&longs;io <lb/>impetus puncti A ad inten&longs;ionem impetus puncti B, vt di&longs;tantia AC <lb/>ad BC. Probatur, quia cum impetus &longs;int vt motus, motus vt &longs;patia, &longs;patia <lb/>verò &longs;int arcus AE. BD; </s> <s id="N14807"><!-- NEW -->arcus &longs;unt, vt &longs;emidiametri AC, BC; igitur vt <lb/>di&longs;tantiæ quòd erat demon&longs;trandum. </s> </p> <p id="N1480D" type="main"> <s id="N1480F"><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 1.<emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N1481C" type="main"> <s id="N1481E"><!-- NEW -->Hinc &longs;i di&longs;tantia CA e&longs;t dupla di&longs;tantiæ CB, impetus in A e&longs;t du­<lb/>plus impetus in B: at verò impetus &longs;egmenti e&longs;t ad impetum alterius, <lb/>vt diximus in Th. 73. </s> </p> <p id="N14826" type="main"> <s id="N14828"><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 2.<emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N14835" type="main"> <s id="N14837"><!-- NEW -->Hinc hæc propagatio fit iuxta progre&longs;&longs;ionem arithmeticam id e&longs;t, &longs;i <lb/>in primâ parte ver&longs;us centrum producitur impetus vt 1. in &longs;ecunda pro­<lb/>ducitur vt duo, in tertiâ vt tria, atque ita deinceps; quia proportio <lb/>arithmetica e&longs;t laterum, &longs;eu linearum. </s> </p> <p id="N14841" type="main"> <s id="N14843"><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 3.<emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N14850" type="main"> <s id="N14852">Hinc hæc propagatio e&longs;t omninò inuer&longs;a illius, quæ aliis qualitatibus <lb/>competit, vt patet. </s> </p> <p id="N14857" type="main"> <s id="N14859"><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 4.<emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N14866" type="main"> <s id="N14868">Hinc etiam manife&longs;ta ratio &longs;equitur illius experimenti, quod propo­<lb/>&longs;uimus corol. </s> <s id="N1486D">2. Th. 80. </s> </p> <p id="N14870" type="main"> <s id="N14872"><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 5.<emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N1487F" type="main"> <s id="N14881"><!-- NEW -->Hinc &longs;i tantùm habeatur ratio impetus, facilè pote&longs;t determinari in <lb/>qua proportione cylindrus faciliùs moueatur motu recto, quàm motu <lb/>circulari; </s> <s id="N14889"><!-- NEW -->po&longs;ito &longs;cilicet centro motus in altera extremitate, cui applica­<lb/>tur potentia; </s> <s id="N1488F"><!-- NEW -->quippe impetus propagatus in motu circulari e&longs;t &longs;umma <lb/>terminorum; </s> <s id="N14895"><!-- NEW -->propagatus verò in motu recto e&longs;t vltimus terminorum, <lb/>v.g. <!-- REMOVE S-->&longs;int &longs;ex puncta &longs;ubiecti; </s> <s id="N1489D"><!-- NEW -->in quolibet producatur impetus vt vnum; </s> <s id="N148A1"><!-- NEW --><lb/>haud dubiè erit motus rectus; </s> <s id="N148A6"><!-- NEW -->vt verò &longs;it motus circularis in primo <lb/>puncto; </s> <s id="N148AC"><!-- NEW -->producatur vt 1. in &longs;ecundo vt 2. in tertio, vt 3. atque ita dein­<lb/>ceps; &longs;umma erit 21. cum tamen in motu recto e&longs;&longs;ent tantùm 6. igitur <lb/>vt &longs;e habent 21. ad 6. ita &longs;e habet facilitas motus recti ad facilitatem <lb/>motus circularis. </s> </p> <p id="N148B6" type="main"> <s id="N148B8"><!-- NEW -->Dixi, &longs;i tantùm habeatur ratio impetus; </s> <s id="N148BC"><!-- NEW -->quia &longs;i addatur ratio graui­<lb/>tationis, &longs;eu momenti; haud dubiè maior erit adhuc difficultas, de <lb/>quo infrà in Schol. <!-- REMOVE S--><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 6.<emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N148D0" type="main"> <s id="N148D2"><!-- NEW -->Hinc quò longior e&longs;t cylindrus, v. <!-- REMOVE S-->g. <!-- REMOVE S-->cre&longs;cit proportio maioris illius <lb/>facilitatis, vt patet inductione; </s> <s id="N148DC"><!-- NEW -->nam &longs;i &longs;int tantùm 2. puncta, proportio <lb/>erit 3. ad 2.; </s> <s id="N148E2"><!-- NEW -->&longs;it tria 6. ad 3.; </s> <s id="N148E6"><!-- NEW -->&longs;i 4. 10. ad 4. &longs;i 5. 15. ad 5.; </s> <s id="N148EA"><!-- NEW -->&longs;i 6. 21. ad 6. <pb pagenum="55" xlink:href="026/01/087.jpg"/>&longs;i 7. 28. ad 7; </s> <s id="N148F3"><!-- NEW -->&longs;i 8. 36. ad 8; </s> <s id="N148F7"><!-- NEW -->&longs;i 9. 45. ad 9; atque ita deinceps; ex quibus primò <lb/>vides cre&longs;cere &longs;emper proportionem. </s> <s id="N148FD"><!-- NEW -->Secundò inter duplam, & triplam <lb/>rationem, &longs;cilicet 6. ad 3. & 15. ad 5. intercedere 2 1/2; </s> <s id="N14903"><!-- NEW -->inter triplam & <lb/>quadruplam intercedere 3. 1/2; </s> <s id="N14909"><!-- NEW -->inter quadruplam & quintuplam inter­<lb/>cedere 4 1/2; atque ita deinceps. </s> </p> <p id="N1490F" type="main"> <s id="N14911"><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 7.<emph.end type="center"/></s> </p> <p id="N1491D" type="main"> <s id="N1491F"><!-- NEW -->Colligo denique po&longs;&longs;e in motu recto cum maiore ni&longs;u produci inten­<lb/>&longs;iorem impetum in data ratione; </s> <s id="N14925"><!-- NEW -->&longs;it enim cylindrus AB, qui moueatur <lb/>circa centrum A, percurrátque B, arcum BD; </s> <s id="N1492B"><!-- NEW -->qui accipiatur vt recta, <lb/>quæ à minimis arcubus &longs;en&longs;u di&longs;tingui non pote&longs;t; </s> <s id="N14931"><!-- NEW -->haud dubiè &longs;i eo <lb/>tempore, vel æquali, quo AB tran&longs;it in AD; </s> <s id="N14937"><!-- NEW -->eadem AB, vel æqualis <lb/>motu recto tran&longs;eat in FD, Dico impetum huius motus e&longs;&longs;e duplò in­<lb/>ten&longs;iorem impetu illius; </s> <s id="N1493F"><!-- NEW -->quia impetus &longs;unt vt motus; </s> <s id="N14943"><!-- NEW -->motus verò vt <lb/>&longs;patia, quæ percurruntur æqualibus temporibus; </s> <s id="N14949"><!-- NEW -->&longs;ed &longs;patium rectanguli <lb/>AD, e&longs;t duplum trianguli ADB; </s> <s id="N1494F"><!-- NEW -->igitur & motus; </s> <s id="N14953"><!-- NEW -->igitur & impetus; </s> <s id="N14957"><!-- NEW -->&longs;i <lb/>verò AB tran&longs;eat in EL, ita vt AF, &longs;it dupla AE; </s> <s id="N1495D"><!-- NEW -->impetus erunt <lb/>æquales; quia rectangulum AC, e&longs;t æquale triangulo ABD. </s> </p> <p id="N14963" type="main"> <s id="N14965"><!-- NEW -->Dixi arcum BD, accipi vt lineam rectam; </s> <s id="N14969"><!-- NEW -->Si enim accipiatur vt ar­<lb/>cus; haud dubiè motus cylindri AB, dum transfertur in FD, e&longs;t ad mo­<lb/>tum eiu&longs;dem AB, dum transfertur in AD, vt rectangulum AD, ad &longs;e­<lb/>ctorem, cuius arcus &longs;it æqualis rectæ BD, & radius ip&longs;i AB. <!-- KEEP S--></s> </p> <p id="N14974" type="main"> <s id="N14976"><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s> </p> <p id="N14982" type="main"> <s id="N14984">Ob&longs;eruabis primò, id quod