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version 1.4, 2006/03/28 17:58:11

version 1.13, 2007/01/23 20:05:31

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

<s>Fortè aliquis poten<lb/>tias machanicas de&longs;ideraret, lineas, motus, & cæle&longs;tes <lb/>&longs;piras; &longs;ed hæ quidquid phy&longs;icum habent, &longs;ingulari tra<lb/>ctatui de corpore cæle&longs;ti, reliqua verò A&longs;tronomiæ con<lb/>cedunt: potentiæ mechanicæ ad Staticam pertinent, qua<lb/>re illarum tantùm phy&longs;icum principium in hoc tractatu <lb/>explicamus, lineæ motus nihil phy&longs;icum habent. </s>

<s>Fortè aliquis poten<lb/>tias mechanicas de&longs;ideraret, lineas, motus, & cæle&longs;tes <lb/>&longs;piras; &longs;ed hæ quidquid phy&longs;icum habent, &longs;ingulari tra<lb/>ctatui de corpore cæle&longs;ti, reliqua verò A&longs;tronomiæ con<lb/>cedunt: potentiæ mechanicæ ad Staticam pertinent, qua<lb/>re illarum tantùm phy&longs;icum principium in hoc tractatu <lb/>explicamus, lineæ motus nihil phy&longs;icum habent. </s>

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

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

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

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

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

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

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

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

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

<s>5. Impetus innatus e&longs;t tantùm determinatus ad lineam perpen<lb/>dicularem deor&longs;um; alioquin &longs;i ad aliam determinari po&longs;&longs;et, primo <lb/>e&longs;&longs;et æqualis motus per inclinatam, & perpendicularem; corpus <lb/>graue mi&longs;&longs;um per lineam inclinatam ab eo non declinaret; imò im<lb/>petus &longs;emel productus (&longs;i liberum e&longs;&longs;et medium) non de&longs;trueretur: <lb/>quæ omnia phy&longs;icis hypothe&longs;ibus repugnant: omnis alius impetus, <lb/>etiam acqui&longs;itus motu naturali deor&longs;um, e&longs;t indifferens ad omnem <lb/>lineam, ad vitanda infinita ferè naturæ incommoda. </s>

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

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

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

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

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

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

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

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

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

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

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

<s>5. Quia tamen in&longs;tantia non &longs;unt &longs;en&longs;ibilia, vt Phy&longs;icæ con&longs;u<lb/>latur, quæ res &longs;en&longs;ibiles con&longs;iderat, a&longs;&longs;umi debent partes tempotis <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>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>quam Galileus excogitauit, vt &longs;ine &longs;crupulo hæc a&longs;<lb/>&longs;umi po&longs;&longs;it: hinc &longs;patia &longs;unt ferè vt temporum quadrata: dixi, ferè: <lb/>nam e&longs;t paulò minor proportio, cùm tantùm finita &longs;int in&longs;tantia <lb/>phy&longs;ica, quæ reuerà &longs;i infinita e&longs;&longs;ent in qualibet temporis &longs;en&longs;ibilis <lb/>parte, haud dubiè &longs;patia e&longs;&longs;ent omninò in ratione duplicata tem<lb/>porum: &longs;ed, quia parum pro nihilo computatur, hanc progre&longs;&longs;io<lb/>nem Galilei deinceps v&longs;urpabimus in Phy&longs;ica. </s>

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

<s>Impetus acqui&longs;itus in de&longs;cen&longs;u <lb/>e&longs;t &longs;emper imperfectior, &longs;i a&longs;&longs;umantur &longs;ingula in&longs;tantia, quæ reuerâ <lb/>&longs;unt &longs;emper minora; quia motus fit &longs;emper velocior: cùm graue <lb/>de&longs;cendit in medio, quod re&longs;i&longs;tit, minùs aecuratè &longs;eruantur prædi<lb/>ctæ proportiones, quæ in vacuo modico accurati&longs;&longs;imè &longs;eruaren<lb/>tur. </s>

<s>Impetus acqui&longs;itus in de&longs;cen&longs;u <lb/>e&longs;t &longs;emper imperfectior, &longs;i a&longs;&longs;umantur &longs;ingula in&longs;tantia, quæ reuerâ <lb/>&longs;unt &longs;emper minora; quia motus fit &longs;emper velocior: cùm graue <lb/>de&longs;cendit in medio, quod re&longs;i&longs;tit, minùs accuratè &longs;eruantur prædi<lb/>ctæ proportiones, quæ in vacuo modico accurati&longs;&longs;imè &longs;eruaren<lb/>tur. </s>

<s>7. Re&longs;i&longs;tentia medij non e&longs;t propter vllam formam improportio<lb/>nat am, qua&longs;i verò impetus &longs;it forma improportionata aëri: &longs;ed in <pb xlink:href="026/01/012.jpg"/>duobus præ&longs;ertim con&longs;i&longs;tit; primò, eò quòd medium detrahat ali<lb/>quid grauitationis corporis grauis; &longs;ecundò, eò quòd partes medij <lb/>aliquam implicationem habeant, quæ &longs;olui non pote&longs;t &longs;ine aliqua <lb/>compre&longs;&longs;ione, vel ten&longs;ione; vtraque autem re&longs;i&longs;tit impetui: quod <lb/>&longs;pectat ad primum, &longs;i medium &longs;it æqualis grauitatis cum ip&longs;o cor<lb/>pore, detrahitur tota grauitatio, &longs;i &longs;ubduplæ &longs;ubduplum, &c. </s>

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<s>Sunt etiam tres aliæ con<lb/>iugationes, &longs;cilicet, eiu&longs;dem mobilis cum diuer&longs;is mediis, duorum <lb/>mobilium cum eodem medio, duorum mobilium cum duobus <lb/>mediis. </s>

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

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

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

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

<s>11. Si tamen &longs;int diuer&longs;æ materiæ, hand 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>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>Corpu&longs;cula etiam ex graui&longs;&longs;ima ma<lb/>teria tardi&longs;&longs;imè de&longs;cendunt: tum, quia à filamentis illis, quibus par<lb/>tes aëris implicantur, facilè detinentur; analogiam habes in lapil<lb/>lo, qui ab araneæ tela intercipitur: tum, quia, cùm lati&longs;&longs;imam ali<lb/>quando habeant &longs;uperficiem pro modica mole, minimam habent <pb xlink:href="026/01/013.jpg"/><expan abbr="proportion&etilde;">proportionem</expan> virium ad <expan abbr="re&longs;i&longs;tentiã">re&longs;i&longs;tentiam</expan>: tùm denique, quia, cùm modico <lb/>impetu agitari po&longs;&longs;int ab aëre mobili, vnus motus alium impedit. </s>

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<s>Triplici modo accidere pote&longs;t: primò, &longs;i reuerà <lb/>imprimatur impetus ab extrin&longs;eco, vt, cùm mitto lapidem &longs;ur&longs;um: <lb/>&longs;ecundò, &longs;i corpus deor&longs;um cadens deinde reflectatur &longs;ur&longs;um; tunc <lb/>autem nihil e&longs;t ab extrin&longs;eco, ni&longs;i determinatio noua, quæ e&longs;t à cor<lb/>pore reflectente: tertiò, &longs;i terra vtrinque e&longs;&longs;et peruia; nam lapis haud <lb/>dubiè non &longs;i&longs;teret in centro, &longs;altem po&longs;t primum de&longs;cen&longs;um; igitur <lb/>a&longs;cenderet per eandem lineam; nullum tamen e&longs;t principium ex<lb/>trin&longs;ecum; igitur motus violentus dicit tantùm motum &longs;ur&longs;um <lb/>corporis grauis. </s>

<s>2. Dari autem motum violentum, dubium e&longs;&longs;e non pote&longs;t, qui <lb/>&longs;upponit impetum, vel impre&longs;&longs;um ab extrin&longs;eco, vel in de&longs;centu <lb/>acqui&longs;itum, qui reuerâ ine&longs;t ip&longs;i mobili, cùm ip&longs;um medium hunc <lb/>motum potiùs impediat, quàm iuuet: hinc, &longs;i nullus e&longs;&longs;et impetus <lb/>extrin&longs;ecus, vel acqui&longs;itus, nullus e&longs;&longs;et motus violentus; quia im<lb/>petus innatus illius cau&longs;a e&longs;&longs;e non pote&longs;t. </s>

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

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

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

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

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

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

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

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

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

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

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

<s>3. Hinc producit impetum imperfectiorem impetus acqui&longs;itus <lb/>in hoc eodem plano, quàm acqui&longs;itus in perpendiculari, æqualibus <lb/>&longs;cilicet temporibus, quia cau&longs;a imperfectior imperfectiorem pro<lb/>ducit effectum: motus in plano inclinato deor&longs;um e&longs;t acceleratus <lb/>iuxta eandem proportionem, iuxta quam acceleratur in perpendi-<pb xlink:href="026/01/016.jpg"/>culo: tempora, quibus pereurruntur perpendiculum, & linea plani <lb/>inclinati, &longs;unt vt lineæ; &longs;patia autem, quæ in prædictis lineis acqui<lb/>runtur æqualibus temporibus, &longs;unt vt motus, id e&longs;t, vt lineæ per<lb/>mutando, vt patet ex dictis. </s>

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

<s>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>

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

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

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

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

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

<s>8. Corpus graue in &longs;uperficie quadrantis caua, deor&longs;um cadit <lb/>motu naturaliter accelerato; quia &longs;ingulis in&longs;tantibus accedit nouus <pb xlink:href="026/01/017.jpg"/>impetus; non tamen æqualibus temperibus, acquiruntur æqualia <lb/>velocitatis momenta; quia in &longs;ingulis punctis quadrantis, e&longs;t diuer<lb/>&longs;a tangens; igitur mutatur progre&longs;&longs;io accelerationis, quæ certè ma<lb/>jor e&longs;t initio, & &longs;ub finem minor; quia initio tangentes acce<lb/>dunt propriùs ad perpendiculum, & &longs;ub finem ad horizonta <lb/>lem. </s>

<s>8. Corpus graue in &longs;uperficie quadrantis caua, deor&longs;um cadit <lb/>motu naturaliter accelerato; quia &longs;ingulis in&longs;tantibus accedit nouus <pb xlink:href="026/01/017.jpg"/>impetus; non tamen æqualibus temporibus, acquiruntur æqualia <lb/>velocitatis momenta; quia in &longs;ingulis punctis quadrantis, e&longs;t diuer<lb/>&longs;a tangens; igitur mutatur progre&longs;&longs;io accelerationis, quæ certè ma<lb/>jor e&longs;t initio, & &longs;ub finem minor; quia initio tangentes acce<lb/>dunt propriùs ad perpendiculum, & &longs;ub finem ad horizonta<lb/>lem. </s>

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

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

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

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

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

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

<s>2. <expan abbr="Qo&utilde;">Qoum</expan> minor e&longs;t, vel acutior prædictus angulus, minùs impetus <lb/>de&longs;truitur; quia diagonalis maior e&longs;t; donec tandem conueniant in <lb/>eandem lineam, tunc enim nihil de&longs;truitur: datur de facto hic mo<lb/>tus in rerum natura; talis e&longs;t motus nauis à duobus ventis im pre&longs;<lb/>&longs;us; vel eiu&longs;dem partis aëris; imò & ip&longs;ius venti: motus mixtus ex <lb/>duobus retardatis iuxta eandem progre&longs;&longs;ionem e&longs;t rectus; quia fit <lb/>per hypothenu&longs;im triangulorum proporionalium: idem dico de <lb/>duobus acceleratis. </s>

<s>2. <expan abbr="Qu&utilde;">Quum</expan> minor e&longs;t, vel acutior prædictus angulus, minùs impetus <lb/>de&longs;truitur; quia diagonalis maior e&longs;t; donec tandem conueniant in <lb/>eandem lineam, tunc enim nihil de&longs;truitur: datur de facto hic mo<lb/>tus in rerum natura; talis e&longs;t motus nauis à duobus ventis impre&longs;<lb/>&longs;us; vel eiu&longs;dem partis aëris; imò & ip&longs;ius venti: motus mixtus ex <lb/>duobus retardatis iuxta eandem progre&longs;&longs;ionem e&longs;t rectus; quia fit <lb/>per hypothenu&longs;im triangulorum proportionalium: idem dico de <lb/>duobus acceleratis. </s>

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

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

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

<s>5. Adde, quòd e&longs;t duplex determinatio: igitur aliquid de&longs;trui de<lb/>bet, non acqui&longs;iti; igitur impre&longs;&longs;i: de&longs;trui autem non dicitur acqui<lb/>fitus, quòd, fcilicet, plùs de nouo accedat, quàm percat; e&longs;t enim ac<lb/>celeratus: adde, quòd non infligitur tantus ictus &longs;ub finem; igitur <lb/>de&longs;truitur aliquid impetus, non acqui&longs;iti, eo modo, quo diximus; <lb/>igitur impre&longs;&longs;i: ita tamen &longs;en&longs;im de&longs;truitur, vt pro æquabili per ali<lb/>quod &longs;patium qua&longs;i haberi po&longs;&longs;it. </s>

<s>5. Adde, quòd e&longs;t duplex determinatio: igitur aliquid de&longs;trui de<lb/>bet, non acqui&longs;iti; igitur impre&longs;&longs;i: de&longs;trui autem non dicitur acqui<lb/>&longs;itus, quòd, &longs;cilicet, plùs de nouo accedat, quàm pereat; e&longs;t enim ac<lb/>celeratus: adde, quòd non infligitur tantus ictus &longs;ub finem; igitur <lb/>de&longs;truitur aliquid impetus, non acqui&longs;iti, eo modo, quo diximus; <lb/>igitur impre&longs;&longs;i: ita tamen &longs;en&longs;im de&longs;truitur, vt pro æquabili per ali<lb/>quod &longs;patium qua&longs;i haberi po&longs;&longs;it. </s>

<s>6. Hinc mobile proiectum per horizontalem, ne primo quidem <lb/>in&longs;tanti per horizontalem mouetur, alioqui non e&longs;&longs;et motus mix<lb/>tus: tardiùs cadit mobile ita proiectum in planùm horizontale &longs;ub<lb/>iectum, quàm cum &longs;ua &longs;ponte, ex eadem altitudine de&longs;cendit: cuius <lb/>rei clari&longs;&longs;ima e&longs;t experientia: ratio e&longs;t; quia impetus acqui&longs;itus in <lb/>hoc iactu non e&longs;t eiu&longs;dem perfectionis, cùm acqui&longs;ito in perpendi<lb/>cnlo: cùm proiicitur mobile per inclinatam &longs;ur&longs;um, mouetur motu <lb/>mixto ex naturali æquabili, & violento retardato: patet prima pars; <lb/>quia acceleratur tantùm naturalis deor&longs;um, &longs;altem in inclinata: &longs;e<lb/>cunda pars etiam patet; quia &longs;ub finem minor e&longs;t ictus. </s>

<s>6. Hinc mobile proiectum per horizontalem, ne primo quidem <lb/>in&longs;tanti per horizontalem mouetur, alioqui non e&longs;&longs;et motus mix<lb/>tus: tardiùs cadit mobile ita proiectum in planùm horizontale &longs;ub<lb/>iectum, quàm cum &longs;ua &longs;ponte, ex eadem altitudine de&longs;cendit: cuius <lb/>rei clari&longs;&longs;ima e&longs;t experientia: ratio e&longs;t; quia impetus acqui&longs;itus in <lb/>hoc iactu non e&longs;t eiu&longs;dem perfectionis, cùm acqui&longs;ito in perpendi<lb/>culo: cùm proiicitur mobile per inclinatam &longs;ur&longs;um, mouetur motu <lb/>mixto ex naturali æquabili, & violento retardato: patet prima pars; <lb/>quia acceleratur tantùm naturalis deor&longs;um, &longs;altem in inclinata: &longs;e<lb/>cunda pars etiam patet; quia &longs;ub finem minor e&longs;t ictus. </s>

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

<s>8. A&longs;cen&longs;us proiecti per inclinatam diutiùs durat, quàm de&longs;<lb/>cen&longs;us, ratione ciu&longs;dem plani horizontalis; quia, &longs;cilicer, a&longs;<lb/>cen&longs;us longior e&longs;t, quàm de&longs;cen&longs;us: e&longs;t autem longior; quia, vt <lb/>e&longs;&longs;et æqualis, nihil impetus impre&longs;&longs;i deberet de&longs;trui in a&longs;cen&longs;u <pb xlink:href="026/01/019.jpg"/>porrò in de&longs;cen&longs;u e&longs;t motus mixtus ex accelerato naturali, <lb/>& retardato violento, vt con&longs;tat ex dictis: iactus per incli<lb/>natam ad angulum 45. e&longs;t omnium maximus, ratione eiu&longs;dem <lb/>plani horizontalis: clara e&longs;t experientia. </s>

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

<s>Ratio e&longs;t: quia per verti<lb/>calem &longs;ur&longs;um, nihil acquiritur in plano horizontali, ex quo fit ia<lb/>ctus; nihil etiam per ip&longs;am horizontalem; igitur plùs acquiritur per <lb/>illam, quæ maximè ab vtraque &longs;imul recedit. </s>

<s>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. </s>

<s>45. <lb/>di&longs;tantes. </s>

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

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

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

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

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

<s>12. Cùm è naui mobili emittitur &longs;agitta per horizontalem, quæ fa<lb/>cit anglum rectum cum linea directionis nauis, fertur qua&longs;i per dia<lb/>gonalem vtriu&longs;que, &longs;altem per aliquod &longs;patium: cùm verò emitti-<pb xlink:href="026/01/020.jpg"/>tur per horizontalem, quæ conueniat cum eadem linea directionis, <lb/>&longs;actus e&longs;t longior toto illo &longs;patio, quod nauis decurrit, dum iactus <lb/>durat; breuior tamen, &longs;i in partem oppo&longs;itam fiat iactus in hoc ca<lb/>&longs;u, &longs;i nauis æqualem impetum imprimeret, deor&longs;um rectà ferretur <lb/>mobile motu naturali; imò &longs;agitta po&longs;&longs;et retorqueri in iaculatorem: <lb/>&longs;i terra e&longs;&longs;et vtrimque peruia, lapis demi&longs;&longs;us per multa annorum <lb/>millia libraretur; non tamen e&longs;&longs;et motuus perpetuus. </s><figure id="id.026.01.020.1.jpg" xlink:href="026/01/020/1.jpg"/>

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

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

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

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

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

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

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

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

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>

in problematis, &longs;ect. </s>

<s>17. problem. </s>

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

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

<s>8. Si globus impactus &longs;it minor corpore reflectente, reflectitur <lb/>eriam 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>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>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>

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

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

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

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

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

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<s>13. Cum duo globi in &longs;e&longs;e inuicem impinguntur æquali motu, <lb/>minor retroagitur velociore motu, quàm ante moueretur, vt clarum <lb/>e&longs;t: maior verò, &longs;i duplus e&longs;t alterius, &longs;i&longs;tit immobilis in puncto <lb/>contactus; &longs;i maior duplo &longs;uum iter pro&longs;equitur, &longs;ed tardiore mo<lb/>tu; &longs;i minor duplo, retroagitur: quæ omnia facilè ex dictis demon<lb/>&longs;trantur. </s>

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

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

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

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

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

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

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

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

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

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

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

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

<s>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, co tempore, quo maior decurret vnicam: li<lb/>cèt enim extremitas minoris, quæ impellitur, habeat tantùm du<lb/>plum impetum extremitatis maioris, &longs;itque impetus inten&longs;io in <lb/>minore, dupla inten&longs;ionis impetus in maiore; e&longs;t tamen quadrupla <lb/>illius, quæ e&longs;t in &longs;egmento maioris versùs centrum æquali minori <lb/>acui: porrò motus circulares æquabiles in vtraque cum eodem <lb/>impetu, &longs;unt vt motus recti. </s>

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

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

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<s>10. Si cylindrus in plano horizontali læuigato in alteaa extremi<lb/>tate per tangentem impellatur, mouebitur motu circulati, &longs;cilicet, <pb xlink:href="026/01/026.jpg"/>faciliori, cirra centrum, quod di&longs;tet ab altera extremitate vna <lb/>quarta totius cylindri: ratio e&longs;t: quia faciliùs mouetur circa illud <lb/>centrum, quàm circa alia puncta, quòd, &longs;cilicet, minùs &longs;patij decur<lb/>ratur, po&longs;ito eodem &longs;emper motu alterius extremitatis, cui appli<lb/>catur immediatè potentia motrix. </s>

<s>10. Si cylindrus in plano horizontali læuigato in altera extremi<lb/>tate per tangentem impellatur, mouebitur motu circulati, &longs;cilicet, <pb xlink:href="026/01/026.jpg"/>faciliori, circa centrum, quod di&longs;tet ab altera extremitate vna <lb/>quarta totius cylindri: ratio e&longs;t: quia faciliùs mouetur circa illud <lb/>centrum, quàm circa alia puncta, quòd, &longs;cilicet, minùs &longs;patij decur<lb/>ratur, po&longs;ito eodem &longs;emper motu alterius extremitatis, cui appli<lb/>catur immediatè potentia motrix. </s>

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

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

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

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

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

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

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

<s>6. Vltimum punctum impetus acqui&longs;itus acqui&longs;itum in de&longs;cen&longs;u, <lb/>nullo modo ad de&longs;cen&longs;um concurrit, &longs;ed ad a&longs;cen&longs;um, vnico tan<lb/>tùm in&longs;tanti; quippe e&longs;t omnium imperfecti&longs;&longs;imum; quod reuerà &longs;i <lb/>e&longs;&longs;et eiu&longs;dem perfectionis cum innato, a&longs;cen&longs;us æqualis e&longs;t de&longs;cen<lb/>&longs;ui: &longs;i &longs;int funependula inæqualia, vibrationes non &longs;unt æquè diu<lb/>turnæ: ratio e&longs;t: quia, &longs;i a&longs;&longs;umamtur, v.g.duo quadrantes inæquales, <lb/>&longs;unt eju&longs;dem inclinationis; igitur minor citiùs percurritur. </s>

<s>6. Vltimum punctum impetus acqui&longs;itus acqui&longs;itum in de&longs;cen&longs;u, <lb/>nullo modo ad de&longs;cen&longs;um concurrit, &longs;ed ad a&longs;cen&longs;um, vnico tan<lb/>tùm in&longs;tanti; quippe e&longs;t omnium imperfecti&longs;&longs;imum; quod reuerà &longs;i <lb/>e&longs;&longs;et eiu&longs;dem perfectionis cum innato, a&longs;cen&longs;us æqualis e&longs;t de&longs;cen<lb/>&longs;ui: &longs;i &longs;int funependula inæqualia, vibrationes non &longs;unt æquè diu<lb/>turnæ: ratio e&longs;t: quia, &longs;i a&longs;&longs;umantur, v.g. duo quadrantes inæquales, <lb/>&longs;unt eju&longs;dem inclinationis; igitur minor citiùs percurritur. </s>

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

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

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

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

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

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

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

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

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

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

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

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

<s>&longs;ed poti&longs;&longs;imùm turbinis, qui <pb xlink:href="026/01/030.jpg"/>vel &longs;eutica, vel funiculo in torto circumagitur, in quo clari&longs;&longs;i<lb/>mè apparet motus centri, & orbis: ratio motus orbis e&longs;t impe<lb/>tus impre&longs;&longs;us vtrique extremitati diametri va&longs;is in partes contra<lb/>rias; ratio verò motus centri e&longs;t, quia adducitur funiculo vel ex<lb/>ploditur, &longs;eu expellitur &longs;cutica: huius motus phænomena &longs;unt ferè <lb/>infinita: &longs;ingula ex no&longs;tris principiis facilè explicantur. </s><figure id="id.026.01.030.1.jpg" xlink:href="026/01/030/1.jpg"/>

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

<s>1. CVm &longs;u&longs;tinetur manus, &longs;eu brachium, in &longs;itu horizontali im<lb/>mobile, producitur nece&longs;&longs;aliò impetus æqualis impetui gra<lb/>uitationis; alioquin, &longs;i maior e&longs;&longs;et, &longs;ur&longs;um ferretur brachium; &longs;i verò <lb/>minor, deor&longs;um: quia præualeret grauitatio, porrò hic impetus pro<lb/>ducitur tantùm à potentia motrice animantis, in &longs;ingulari organo; <lb/>non verò in aliis partibus, etiam animatis, ni&longs;i quando mouentur; <lb/>nec in ip&longs;o pondere, &longs;i aliquod &longs;u&longs;tinetur: &longs;ic men&longs;a in pondere &longs;u<lb/>per po&longs;ito impetum nullum producit. </s>

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

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

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<s>Vt feratur cylindrus humeris <expan abbr="cõmodiùs">commodiùs</expan> <lb/>debet &longs;u&longs;tineri in <expan abbr="c&etilde;tro">centro</expan> grauitatis, ad eleuationem anguli 49. quia <lb/><expan abbr="t&utilde;c">tunc</expan> manui, & humero æqualiter <expan abbr="põdus">pondus</expan> di&longs;tribuitur: ideò in circulo <lb/>voluitur &longs;cyphus aqua plenus &longs;ine effu&longs;ione; quia impetus determi<lb/>natus per tangentem circuli aquam ip&longs;am à centro circuli remouet. </s>

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

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

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

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

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

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

<s>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/>norum ten&longs;ione, &c. </s>

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

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

<s>8. Maiore fu&longs;te maior ictus infligitur; quia potentia toto ni&longs;u <lb/>agens, diutiùs manet applicata maiori, quàm minori; &longs;untque ictus <lb/>in ratione &longs;ubduplicata vtriu&longs;que fu&longs;tis; v. g. fu&longs;tis pendens vnam <lb/>libram per maximum arcum impactus, infligit &longs;ubduplum ictum <lb/>alterius, quem infligit fu&longs;tis quatuor pendens libras per eundem <lb/>arcum impactus: idem dicatur de mi&longs;&longs;o lapide: principium huius <lb/>veritatis pendet ex iis, quæ diximus lib.

2. de motu naturali<lb/>ter accelerate, luxta progre&longs;&longs;ionem numerorum imparium, <lb/>1. 3. 5. &c. </s>

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

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

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

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

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

<s>Dico e&longs;&longs;e qualitatem &longs;iue di&longs;tincta &longs;it, &longs;iue non di&longs;tincta; quod hîc <lb/>certè non di&longs;cutio; nec enim affirmo in hac definitione dari impetum; <lb/>&longs;ed definio tantùm quid &longs;it impetus; qui reuera aliud non e&longs;t, &longs;i e&longs;t: <lb/>quippe id tantùm concipio, cum impetum appello; &longs;iue &longs;it, &longs;iue non &longs;it, <lb/>ne quis fortè initio &longs;tatim mihi litem intendat; quemadmodum definit <lb/>circulum Geometra; licèt non a&longs;&longs;erat dari perfectum circulum; ita Phy<lb/>&longs;icus definit impetum, quamuis non affirmet dari impetum; quod tamen <lb/>in &longs;exto Theoremate demon&longs;trabimus; itaque &longs;i e&longs;t impetus, haud dubiè <lb/>nihil omninò præ&longs;tat in &longs;uo &longs;ubiecto ni&longs;i motum; quod quomodò fiat, <lb/>explicabimus in&longs;rà in Theorematis. </s>

<s>Dico e&longs;&longs;e qualitatem &longs;iue di&longs;tincta &longs;it, &longs;iue non di&longs;tincta; quod hîc <lb/>certè non di&longs;cutio; nec enim affirmo in hac definitione dari impetum; <lb/>&longs;ed definio tantùm quid &longs;it impetus; qui reuera aliud non e&longs;t, &longs;i e&longs;t: <lb/>quippe id tantùm concipio, cum impetum appello; &longs;iue &longs;it, &longs;iue non &longs;it, <lb/>ne quis fortè initio &longs;tatim mihi litem intendat; quemadmodum definit <lb/>circulum Geometra; licèt non a&longs;&longs;erat dari perfectum circulum; ita Phy<lb/>&longs;icus definit impetum, quamuis non affirmet dari impetum; quod tamen <lb/>in &longs;exto Theoremate demon&longs;trabimus; itaque &longs;i e&longs;t impetus, haud dubiè <lb/>nihil omninò præ&longs;tat in &longs;uo &longs;ubiecto ni&longs;i motum; quod quomodò fiat, <lb/>explicabimus intrà in Theorematis. </s>

<s><emph type="center"/><emph type="italics"/>Hypothe&longs;is I.<emph.end type="italics"/><emph.end type="center"/></s>

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

<s>&longs;ed hoc e&longs;t moueri per Def. 1. igitur infinitis fe<lb/>rè experimentis nititur hæc hypothe&longs;is, quam veram e&longs;&longs;e nece&longs;&longs;e e&longs;t, &longs;i <lb/>illa vera &longs;unt; &longs;ed illa certa &longs;unt phy&longs;icè, neque citra miraculum fallere <lb/>po&longs;&longs;unt. </s>

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

<s>cum tamen deinde pernici&longs;&longs;imo cur&longs;u rotari demon&longs;tre<lb/>mus; adde alias oculorum fallacias circa motum; &longs;ic rotata &longs;cintilla, vel <lb/>carbo accen&longs;us immotum orbem de&longs;cribere videtur; &longs;ic nota inu&longs;ta <lb/>trocho, dum celerrimè rotatur, orbem etiam immobilem de&longs;cribere iu<lb/>dicatur; &longs;ic &longs;tella cadens, vel exhalatio continenti &longs;ucce&longs;&longs;ione accen&longs;a <lb/>moueri videtur; licet minimè moucatur; idem dicendum de puluere <lb/>tormentario, vel alia qualibet materia; quæ continuata con&longs;ecutione <lb/>accenditur; immò trochus ip&longs;e in orbem celerrimè agitatus, quie&longs;cere <lb/>videtur; &longs;ic qui vertigine laborant, ea moueri exi&longs;timant, quæ quie&longs;cunt; <lb/>idem exemplum habemus in ebrio&longs;is, iracundis, in iis qui ex graui febris <lb/>ardore delirant, & in pueris qui diu in gyros eunt, vbi verti de&longs;ierint; <lb/>&longs;ic corum quæ motu æquali feruntur, remotiora tardiùs moueri viden<lb/>tur; immò &longs;i per eandem lincam 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 co quòd oculis aliquid moucri videatur. </s>

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

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

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

<s>quidquid &longs;it, fateor vltrò hanc hypothe&longs;im in eo tantùm certitudi<lb/>nis gradu e&longs;&longs;e reponendam, in quo reponitur hæc cognitio, quâ modo <lb/>cogno&longs;co me &longs;cribere, manu&longs;que, & calami motum ob&longs;eruo; &longs;iue id tan<lb/>tùm oculis fiat, &longs;iue intellectu ex oculis; quod aliàs di&longs;cutiemus; &longs;i quis <lb/>fortè in Phy&longs;ica maiorem certitudinem po&longs;tularet, cum eo certè conuc<lb/>nire non po&longs;&longs;um. </s>

<s>quidquid &longs;it, fateor vltrò hanc hypothe&longs;im in eo tantùm certitudi<lb/>nis gradu e&longs;&longs;e reponendam, in quo reponitur hæc cognitio, quâ modo <lb/>cogno&longs;co me &longs;cribere, manu&longs;que, & calami motum ob&longs;eruo; &longs;iue id tan<lb/>tùm oculis fiat, &longs;iue intellectu ex oculis; quod aliàs di&longs;cutiemus; &longs;i quis <lb/>fortè in Phy&longs;ica maiorem certitudinem po&longs;tularet, cum eo certè conue<lb/>nire non po&longs;&longs;um. </s>

<s>Porrò quod &longs;pectat ad fallacias illas quæ &longs;upra adductæ &longs;unt; certum <lb/>e&longs;t vel obiectum e&longs;&longs;e remotius, quam par &longs;it; vel moueri celeriùs, vel <lb/>e&longs;&longs;e aliquod impedimentum interius; præ&longs;ertim in iis, qui &longs;eu vertigine, <lb/>vel alio capitis morbo laborant; &longs;ed ne hîc opticum agere videar, harum <lb/>fallaciarum certi&longs;&longs;imas cau&longs;as in &longs;uum locum remittimus. </s>

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<s><emph type="center"/><emph type="italics"/>Hypothe&longs;is II.<emph.end type="italics"/><emph.end type="center"/></s>

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

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

<s>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>

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<s>Diceret fortè aliquis &longs;ententias prædictas non valere in &longs;ententiâ <lb/>Copernici, quæ terræ motum ad&longs;truit; præterea non modò falli &longs;en&longs;us <lb/>circa motum, verùm etiam circa quietem. </s>

<s>Re&longs;pondeo primò illam Copernici &longs;ententiam e&longs;le fal&longs;i&longs;&longs;imam, vt &longs;uo <lb/>loco o&longs;tendemus: &longs;ecundò, licèt terra moueretur &longs;ecundum Coperni<lb/>cum, Sol, & &longs;tellæ quie&longs;cerent. </s>

<s>Re&longs;pondeo primò illam Copernici &longs;ententiam e&longs;&longs;e fal&longs;i&longs;&longs;imam, vt &longs;uo <lb/>loco o&longs;tendemus: &longs;ecundò, licèt terra moueretur &longs;ecundum Coperni<lb/>cum, Sol, & &longs;tellæ quie&longs;cerent. </s>

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

<s>Re&longs;pondeo primò hypothe&longs;un illam e&longs;&longs;e fal&longs;am, vt &longs;uo <lb/>loco videbimus; &longs;ecundò etiam data illa hypothe&longs;i po&longs;&longs;et dari quies; &longs;i <lb/>enim globus eodem ver&longs;us occa&longs;um impetu proiiceretur, quò ver&longs;us or<lb/>tum à terra ip&longs;a rapitur, haùd dubiè quie&longs;ceret: præterea iuxta hanc hy<lb/>pothe&longs;un, quietem appellarem vnius partis cum alia connexionem in ip<lb/>&longs;o toto &longs;eu globo, & quie&longs;cere dicerem lapidem, qui tantùm totius glo<lb/>bi motu mouetur, ex quo profectò tota &longs;oluitur difficultas. </s>

<s>Re&longs;pondeo primò hypothe&longs;im illam e&longs;&longs;e fal&longs;am, vt &longs;uo <lb/>loco videbimus; &longs;ecundò etiam data illa hypothe&longs;i po&longs;&longs;et dari quies; &longs;i <lb/>enim globus eodem ver&longs;us occa&longs;um impetu proiiceretur, quò ver&longs;us or<lb/>tum à terra ip&longs;a rapitur, haùd dubiè quie&longs;ceret: præterea iuxta hanc hy<lb/>pothe&longs;im, quietem appellarem vnius partis cum alia connexionem in ip<lb/>&longs;o toto &longs;eu globo, & quie&longs;cere dicerem lapidem, qui tantùm totius glo<lb/>bi motu mouetur, ex quo profectò tota &longs;oluitur difficultas. </s>

<s>Quod verò &longs;pectat ad fallacias oculi circa quietem; codem pror&longs;us <lb/>modo &longs;oluendæ &longs;unt, quo iam &longs;upra &longs;olutæ &longs;unt aliæ circa motum: <lb/>vtrùm verò motus, & quies dicant aliquid di&longs;tinctum à mobili, dice<lb/>mus infrà. </s>

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

<s><emph type="italics"/>Contradictoria &longs;imul e&longs;&longs;e non po&longs;&longs;unt, vel non e&longs;&longs;e.<emph.end type="italics"/></s><s> Hoc ip&longs;um iam ptæ<lb/>mi&longs;unus Logicæ no&longs;træ demon&longs;tratiuæ, complectiturque prima illa <lb/>principia Metaphy&longs;icæ. </s>

<s><emph type="italics"/>Contradictoria &longs;imul e&longs;&longs;e non po&longs;&longs;unt, vel non e&longs;&longs;e.<emph.end type="italics"/></s><s> Hoc ip&longs;um iam præ<lb/>mi&longs;imus Logicæ no&longs;træ demon&longs;tratiuæ, complectiturque prima illa <lb/>principia Metaphy&longs;icæ. </s>

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

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<s>vides prædicata contradictoria, quæ cum eidem <lb/>&longs;imul ine&longs;&longs;e non po&longs;&longs;int per Ax. 1. diuer&longs;is, & di&longs;tinctis ine&longs;&longs;e nece&longs;&longs;e <lb/>e&longs;t. </s>

<s>Diceret fortè aliquis hominem reproductum in duobus locis e&longs;&longs;e po&longs;<lb/>&longs;e, & dum Romæ e&longs;t à &longs;e ip&longs;o Lugduni exi&longs;tente &longs;eiunctum e&longs;&longs;e; hoc <lb/>ip&longs;um aliàs examinabimus, dum con&longs;tet modò id totum, &longs;i fiat, mira<lb/>culo tribuendum e&longs;&longs;e, cum tamen res phy&longs;icas citra miraculum con&longs;ide<lb/>temus. </s>

<s><emph type="center"/><emph type="italics"/>Axioma III.<emph.end type="italics"/><emph.end type="center"/></s>

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

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

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

<s>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>

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

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

<s><lb/>Aliquis fortè &longs;tatim opponet mihi partes indeterminatas quantitatis: &longs;ed <lb/>pro&longs;ectò nulla pars actu e&longs;t quæ non &longs;it hæc, & non alia; igitur quæ <lb/>non &longs;it determinata, de quo aliàs; quidquid &longs;it, &longs;altem partes illæ fa<lb/>ciunt aliquod totum quod e&longs;t determinatum, quod mihi &longs;atis e&longs;t modò <lb/>ad veritatem huius Axiomatis. </s>

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<s><emph type="center"/><emph type="italics"/>Axioma V.<emph.end type="italics"/><emph.end type="center"/></s>

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

<s>plures e&longs;&longs;e nece&longs;&longs;e e&longs;t; &longs;i enim <lb/>tantùm vnus e&longs;t, certè indifferens non e&longs;t. </s>

<s><emph type="center"/><emph type="italics"/>Axioma VI.<emph.end type="italics"/><emph.end type="center"/></s>

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

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

<s>Igitur tunc effet fru&longs;trà accidens, cum &longs;uo illo effectu careret; <lb/>hinc rationem contrarietatis aliquando petemus, certi&longs;&longs;imam quidem, <lb/>licet nouam, & inde clari&longs;&longs;imè con&longs;tabit, cur, & quomodo vnum contra<lb/>rium ab alio de&longs;trui dicatur; &longs;ed non e&longs;t huius loci: cùm verò audis fi<lb/>nem: ne quæ&longs;o cogites aliquid morale, nec enim illum finem intelligo, ad <lb/>quem ab agente rationabili de&longs;tinatur: &longs;ed eum dumtaxat, ad quem na<lb/>tura ip&longs;a, vel e&longs;&longs;entia rei &longs;pectat, &longs;ed de his &longs;atis. </s>

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<s><emph type="italics"/>Tunc ponenda e&longs;t forma distincta &longs;ub&longs;t antialis vel accidentalis, dum e&longs;t ali<lb/>qua proprietas &longs;en&longs;ibilis, quæ non pote&longs;t tribui ip&longs;i materiæ,<emph.end type="italics"/> hîc res tantùm <lb/>naturales con&longs;idero, nec &longs;uper naturales attingo, quæ &longs;uas regulas diui<lb/>næ fidei debent, non &longs;en&longs;ibus. </s>

<s>Hoc Axioma omninò certum e&longs;t, & per Ax. 3. confirmatur, vt enim <lb/>dicas aliquid di&longs;tinctum ab omni alio exi&longs;tere, vel debet id &longs;en&longs;u percipi, <lb/>vel aliqua ratione probari quod &longs;it; atqui formam &longs;ub&longs;tantialem &longs;en&longs;u <lb/>non percipis immediatè; igitur aliquem eius effectum &longs;en&longs;ibilem vel me<lb/>diatè, vel immediatè; qui certè &longs;i tribui po&longs;&longs;it materiæ, haud dubiè per il<lb/>lum &longs;ormam non probabis, ni&longs;i formæ ip&longs;ius e&longs;&longs;e antè demon&longs;tres; &longs;i ve<lb/>to e&longs;t forma accidentalis, quam &longs;en&longs;u percipis; certè id tantùm accidit ex <pb xlink:href="026/01/040.jpg" pagenum="8"/>aliqua affectione, quâ&longs;en&longs;um ip&longs;um afficit hæc forma, igitur ex effectu il<lb/>lo illam percipis, quod clarum e&longs;t. </s>

<s>Hoc Axioma omninò certum e&longs;t, & per Ax. 3. confirmatur, vt enim <lb/>dicas aliquid di&longs;tinctum ab omni alio exi&longs;tere, vel debet id &longs;en&longs;u percipi, <lb/>vel aliqua ratione probari quod &longs;it; atqui formam &longs;ub&longs;tantialem &longs;en&longs;u <lb/>non percipis immediatè; igitur aliquem eius effectum &longs;en&longs;ibilem vel me<lb/>diatè, vel immediatè; qui certè &longs;i tribui po&longs;&longs;it materiæ, haud dubiè per il<lb/>lum formam non probabis, ni&longs;i formæ ip&longs;ius e&longs;&longs;e antè demon&longs;tres; &longs;i ve<lb/>to e&longs;t forma accidentalis, quam &longs;en&longs;u percipis; certè id tantùm accidit ex <pb xlink:href="026/01/040.jpg" pagenum="8"/>aliqua affectione, quâ &longs;en&longs;um ip&longs;um afficit hæc forma, igitur ex effectu il<lb/>lo illam percipis, quod clarum e&longs;t. </s>

<s>Huc reuoca vulgare illud principium, <emph type="italics"/>Frustrà fit per plura, quod po<lb/>test fieri per pauciora,<emph.end type="italics"/> quod ad Tertium etiam reuocatur; quod ita in<lb/>telligi non debet, vt &longs;ine gutta aquæ Oceanus, &longs;ine &longs;tella c&oelig;lum, &longs;ine gra<lb/>nulo arenæ terra, &longs;ine altero oculorum homo &longs;tare non po&longs;&longs;int; quæ <lb/>omnia fal&longs;i&longs;&longs;una e&longs;&longs;e con&longs;tat; &longs;ed tantùm quod illud dicatur exi&longs;tere &longs;iue <lb/>&longs;it &longs;ub&longs;tantia, &longs;iue accidens, quod vel experientia certa euincit, vel nece&longs;<lb/>&longs;itas, vel ratio, vel diuina fides (immò & humana in rebus humanis, non <lb/>tamen in &longs;cientiis.) </s>

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

<s>Igitur nunquam claudicat hic equus Okami, vt vulgò dicitur, &longs;i hoc <lb/>fræno regatur, & præ&longs;cripto ambulet pa&longs;&longs;u. </s>

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

<s><lb/>Tertium e&longs;t veluti communis po&longs;itio, &longs;eu commune po&longs;tulatum, in quo <lb/>docti omnes conucniunt; quippe nihil &longs;ine ratione dici debet à philo&longs;o<lb/>pho; Sextum & Septimum probari po&longs;&longs;unt per Tertium; &longs;ed iam ad <lb/>alia, quæ propiùs ad phy&longs;icam accedunt, veniamus. </s>

<s><lb/>Tertium e&longs;t veluti communis po&longs;itio, &longs;eu commune po&longs;tulatum, in quo <lb/>docti omnes conunciunt; quippe nihil &longs;ine ratione dici debet à philo&longs;o<lb/>pho; Sextum & Septimum probari po&longs;&longs;unt per Tertium; &longs;ed iam ad <lb/>alia, quæ propiùs ad phy&longs;icam accedunt, veniamus. </s>

<s><emph type="center"/><emph type="italics"/>Axioma VIII.<emph.end type="italics"/><emph.end type="center"/></s>

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<s>Re&longs;pondeo, diffu&longs;ionem vel propagationem actioms in<lb/>choari tantum ab ipsâ &longs;uperficie Solis; quippe omnes partes agunt <lb/>actione communi, de quo infrà; atqui actio communis à communi me<lb/>dio incipit. </s>

<s>Re&longs;pondeo, diffu&longs;ionem vel propagationem actionis in<lb/>choari tantum ab ipsâ &longs;uperficie Solis; quippe omnes partes agunt <lb/>actione communi, de quo infrà; atqui actio communis à communi me<lb/>dio incipit. </s>

<s>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>

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<s><emph type="center"/><emph type="italics"/>Axioma XII.<emph.end type="italics"/><emph.end type="center"/></s>

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

<s>8. & per definitionem cau&longs;æ nece&longs;&longs;ariæ, quæ in hoc differt à libe<lb/>tâ: Secunda pars probatur; quia &longs;i partem effectus omitteret, quam ta<lb/>men ponere po&longs;&longs;et; haud dubiè non e&longs;&longs;et cau&longs;a nece&longs;&longs;aria contra hypoth. </s>

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

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<s>Dixi ad intra; quia ad extra multum iuuat exten&longs;io; &longs;ic maior ignis <lb/>longiùs diffundit &longs;uum calorem; corpus grauiùs cadens majorem ictum <lb/>infligit; Ad hoc Axioma reuocatur i&longs;tud. </s>

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

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

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

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<s><emph type="center"/><emph type="italics"/>Axioma XV.<emph.end type="italics"/><emph.end type="center"/></s>

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

<s><lb/>Ratio e&longs;t, quia plùs vel minùs contrarij de&longs;truere, multam habet ex<lb/>ten&longs;ionem. </s>

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

<s>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;alrem ex parte. </s>

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

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

<s>3. & de&longs;init e&longs;&longs;e in mobili, <lb/>in quo antè erat per hypoth.4. igitur mobile e&longs;t, & non e&longs;t motus; igi<lb/>tur à motu &longs;eparatum; igitur realiter di&longs;tinctum per Ax. 2. præterea <lb/>moueri, & non moueri &longs;unt prædicata contradictoria, vt con&longs;tat; igi<lb/>tur cidem &longs;imul ine&longs;&longs;e non po&longs;&longs;unt per Ax. 1. igitur cum co non &longs;unt <lb/>idem; alioquin &longs;imul e&longs;&longs;ent; igitur alterum illorum e&longs;t di&longs;tinctum à <lb/>mobili; non quies, vt con&longs;tat, quæ e&longs;t tantùm negatio motus, &longs;eu per<lb/>&longs;euerantia in codem loco; igitur nullam dicit mutationem; at verò <lb/>motus mutationem dicit, per Def. 1. hoc Theorema fusè demon&longs;trabo <lb/>in Metaph. </s>

<s>3. & de&longs;init e&longs;&longs;e in mobili, <lb/>in quo antè erat per hypoth.4. igitur mobile e&longs;t, & non e&longs;t motus; igi<lb/>tur à motu &longs;eparatum; igitur realiter di&longs;tinctum per Ax. 2. præterea <lb/>moueri, & non moueri &longs;unt prædicata contradictoria, vt con&longs;tat; igi<lb/>tur eidem &longs;imul ine&longs;&longs;e non po&longs;&longs;unt per Ax. 1. igitur cum eo non &longs;unt <lb/>idem; alioquin &longs;imul e&longs;&longs;ent; igitur alterum illorum e&longs;t di&longs;tinctum à <lb/>mobili; non quies, vt con&longs;tat, quæ e&longs;t tantùm negatio motus, &longs;eu per<lb/>&longs;euerantia in eodem loco; igitur nullam dicit mutationem; at verò <lb/>motus mutationem dicit, per Def. 1. hoc Theorema fusè demon&longs;trabo <lb/>in Metaph. </s>

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 2.<emph.end type="center"/></s>

<s><emph type="italics"/>Motus non pote&longs;t dici propriè preductus immediatè, vel effectus immedia<lb/>tus cau&longs;æ efficientis.<emph.end type="italics"/></s><s> Demon&longs;t. </s>

<s><emph type="italics"/>Motus non pote&longs;t dici propriè productus immediatè, vel effectus immedia<lb/>tus cau&longs;æ efficientis.<emph.end type="italics"/></s><s> Demon&longs;t. </s>

<s>Motus e&longs;t mutatio, &longs;eu tran&longs;itus ex loco <lb/>in locum per Def. 1. &longs;ed mutatio propriè non producitur; quippè pro<lb/>ductio tantùm terminatur ad ens; nihil enim ni&longs;i ens produci pote&longs;t; <pb xlink:href="026/01/045.jpg" pagenum="13"/>atqui nulla mutatio dicit tantùm ens; præ&longs;ertim hæc, quæ tantùm dicit <lb/>terminum à quo, ide&longs;t locum relictum; & terminum ad quem, id e&longs;t lo<lb/>cum immediatum acqui&longs;itum; nam &longs;eparato quocunque alio ab ip&longs;o <lb/>mobili; modo &longs;imul, id e&longs;t eodem in&longs;tanti relinquat primum locum, & <lb/>nouum acquirat, omninò mouetur, &longs;ed concretum illud ex loco relicto, <lb/>& acqui&longs;ito produci non pote&longs;t; illud autem e&longs;t motus, qui certè non <lb/>dicit tantùm locum relictum &longs;ine acqui&longs;ito; alioqui &longs;i mobile de&longs;true<lb/>retur, diceretur moueri; nec etiam locum acqui&longs;itum &longs;ine priori relicto: <lb/>alioqui &longs;i mobile primò produceretur, diceretur moueri localiter; igitur <lb/>motus neutrum dicit &longs;eor&longs;im; &longs;i primum, diceretur de&longs;tructus; &longs;i &longs;ecun<lb/>dum, diceretur aliquo modo productus, vel potiùs acqui&longs;itus; at vtrum<lb/>que coniunctim, &longs;imulque e&longs;&longs;entialiter dicit motus; nec enim conci<lb/>pio aliud, dum concipio motum: porrò vtrumque &longs;imul &longs;umptum indi<lb/>ui&longs;ibiliter non pote&longs;t dici, vel de&longs;tructum propriè, vel productum; Di<gap/><lb/>xi propriè; nam impropriè dici pote&longs;t motus productus. </s>

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<s>Re&longs;p. potentiam motricem e&longs;&longs;e actiuam vt dicemus, <lb/>& ab eâ produci impetum, qui deinde exigit motum, vt dicemus <lb/>infrà. </s>

<s>Nec e&longs;t quod aliqui ita mirentur hæc à me dici; cum certum &longs;it effe<lb/>ctus &longs;ormales &longs;ecundarios principum ferè qualitatum tales e&longs;&longs;e, vt mini<lb/>mè producantur; &longs;ed qua&longs;i re&longs;ultent ab exigentia; v. g. effectus calo<lb/>ris in &longs;uo &longs;ubiecto e&longs;t eiu&longs;dem &longs;ubiecti rarefactio, quæ reuerâ non <lb/>producitur, vt con&longs;tat. </s>

<s>Nec e&longs;t quod aliqui ita mirentur hæc à me dici; cum certum &longs;it effe<lb/>ctus formales &longs;ecundarios principum ferè qualitatum tales e&longs;&longs;e, vt mini<lb/>mè producantur; &longs;ed qua&longs;i re&longs;ultent ab exigentia; v. g. effectus calo<lb/>ris in &longs;uo &longs;ubiecto e&longs;t eiu&longs;dem &longs;ubiecti rarefactio, quæ reuerâ non <lb/>producitur, vt con&longs;tat. </s>

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<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 4.<emph.end type="center"/></s>

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

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

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 5.<emph.end type="center"/></s>

<s><emph type="italics"/>Entitas &longs;eu &longs;ubstantia mobilis non e&longs;t cau&longs;a immediata motus,<emph.end type="italics"/> Sit enim <lb/>lapis proiectus per Po&longs;tul. haud dubiè &longs;ub&longs;tantia lapidis non e&longs;t cau&longs;a <lb/>huius motus; quia lapis tandem &longs;i&longs;tit per hypoth.4. igitur non e&longs;t cau&longs;a <lb/>motus, quia e&longs;&longs;et cau&longs;a nece&longs;&longs;aria; igitur &longs;emper cau&longs;aret per Ax.12. præ<lb/>terea potentia motrix proiicientis verè agit, cum etiam defatigetur; igi<lb/>turaliquid producit, non motum immediatè, qui produci non pote&longs;t pro <lb/>prièper Th. 2. Adde quod motus &longs;ecundi generis habet tantùm caulam <lb/>immediatam exigentem, &longs;ed potentia motrix non exigit; quia primò <lb/>non defatigaretur exigendo; &longs;ecundò quia lapis &longs;eparatus à manu etiam <lb/>mouetur, &longs;ed non ad exigentiam potentiæ motricis, vt patet; quia &longs;tatim <lb/>po&longs;t &longs;eparationem pote&longs;t illa potentia de&longs;trui, licèt lapis longo pò&longs;t <lb/>temporemoueatur; &longs;ed quod non e&longs;t, nihil exigit. </s>

<s><emph type="italics"/>Entitas &longs;eu &longs;ubstantia mobilis non e&longs;t cau&longs;a immediata motus,<emph.end type="italics"/> Sit enim <lb/>lapis proiectus per Po&longs;tul. haud dubiè &longs;ub&longs;tantia lapidis non e&longs;t cau&longs;a <lb/>huius motus; quia lapis tandem &longs;i&longs;tit per hypoth.4. igitur non e&longs;t cau&longs;a <lb/>motus, quia e&longs;&longs;et cau&longs;a nece&longs;&longs;aria; igitur &longs;emper cau&longs;aret per Ax.12. præ<lb/>terea potentia motrix proiicientis verè agit, cum etiam defatigetur; igi<lb/>tur aliquid producit, non motum immediatè, qui produci non pote&longs;t pro<lb/>prièper Th. 2. Adde quod motus &longs;ecundi generis habet tantùm cau&longs;am <lb/>immediatam exigentem, &longs;ed potentia motrix non exigit; quia primò <lb/>non defatigaretur exigendo; &longs;ecundò quia lapis &longs;eparatus à manu etiam <lb/>mouetur, &longs;ed non ad exigentiam potentiæ motricis, vt patet; quia &longs;tatim <lb/>po&longs;t &longs;eparationem pote&longs;t illa potentia de&longs;trui, licèt lapis longo pò&longs;t <lb/>tempore moueatur; &longs;ed quod non e&longs;t, nihil exigit. </s>

<s>Aliquis fortè diceret potentiam motri&oelig;m exigere primam partem <lb/>motus, quæ deinde &longs;ecundam exigit, & &longs;ecunda tertiam, tertia quar<lb/>tam, &c. </s>

<s>Aliquis fortè diceret potentiam motricem exigere primam partem <lb/>motus, quæ deinde &longs;ecundam exigit, & &longs;ecunda tertiam, tertia quar<lb/>tam, &c. </s>

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

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<s>Tertiò probatur; pila di&longs;iuncta à manu proiicientis diu adhuc mo<lb/>uetur per hypoth.6. igitur hic motus habet cau&longs;am per Ax. 8. quælibet <lb/>enim pars motus de nouo e&longs;t, neque duæ illius partes &longs;imul e&longs;&longs;e po&longs;&longs;unt. </s>

<s><lb/>atqui potentia motrix non e&longs;t can&longs;a per Ax.10. immò pote&longs;t e&longs;&longs;e de&longs;tru<lb/>cta; igitur non e&longs;t cau&longs;a per Ax. 9. Non e&longs;t etiam cau&longs;a &longs;ub&longs;tantia pilæ <lb/>mobilis per Th.5.5. nec priores pattes motus per re&longs;p. </s>

<s><lb/>atqui potentia motrix non e&longs;t cau&longs;a per Ax.10. immò pote&longs;t e&longs;&longs;e de&longs;tru<lb/>cta; igitur non e&longs;t cau&longs;a per Ax. 9. Non e&longs;t etiam cau&longs;a &longs;ub&longs;tantia pilæ <lb/>mobilis per Th.5.5. nec priores pattes motus per re&longs;p. </s>

<s>ad primam in<lb/>&longs;tantiam Th 5. igitur aliquid aliud; voco impetum. </s>

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

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

<s>Igitur certum e&longs;t dari impetum; qui certè tribui non <lb/>pote&longs;t, vel vlli connotationi, vel alteri exigentiæ, vt con&longs;tat ex <lb/>dictis. </s>

<s>Diceret fortè alius hæc omnia e&longs;&longs;e dubia; nam fieri pote&longs;t vt Deus <lb/>tantùm moueat; quod &longs;ine impetu fieri po&longs;&longs;e certum e&longs;t; Re&longs;p. equi<lb/>dem per miraculum hoc fieri po&longs;&longs;e; &longs;ed quemadmadum certum e&longs;t phy<lb/>ficè 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>Diceret fortè alius hæc omnia e&longs;&longs;e dubia; nam fieri pote&longs;t vt Deus <lb/>tantùm moueat; quod &longs;ine impetu fieri po&longs;&longs;e certum e&longs;t; Re&longs;p. equi<lb/>dem per miraculum hoc fieri po&longs;&longs;e; &longs;ed quemadmadum certum e&longs;t phy<lb/>&longs;icè ignem applicatum calefacere, niuem frigefacere, & modò calamum <lb/>à me hæc &longs;cribente moueri, ita certum o&longs;t phy&longs;icè &longs;agittam à &longs;agittario <lb/>emitti, & pilam à proiiciente, &c. </s>

<s>adde quod Deus, vt auctor naturæ <lb/>e&longs;t, agit tantùm; vel de&longs;init agere iuxta exigentiam cau&longs;arum &longs;ecunda<lb/>rum; denique cau&longs;am phy&longs;icè appello, ex cuius applicatione nunquam <lb/>non &longs;equitur effectus per Ax.11. num.1. </s>

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

<s>vel enim mutantur, vel non mutantur; &longs;ecundum dici <lb/>non pote&longs;t; quia vt excitentur, ex non excitatis mutari debent; igitur <lb/>per aliquid: deinde quid e&longs;t illa excitatio, ni&longs;i impul&longs;io; igitur &longs;i mouen<lb/>tur illa corpu&longs;cula, & excitantur à potentia motrice, etiam partes prius <lb/>immobiles moucbuntur, & excitabuntur per Ax.12. quia &longs;unt applicatæ <lb/>cau&longs;æ nece&longs;&longs;ariæ. </s>

<s>vel enim mutantur, vel non mutantur; &longs;ecundum dici <lb/>non pote&longs;t; quia vt excitentur, ex non excitatis mutari debent; igitur <lb/>per aliquid: deinde quid e&longs;t illa excitatio, ni&longs;i impul&longs;io; igitur &longs;i mouen<lb/>tur illa corpu&longs;cula, & excitantur à potentia motrice, etiam partes prius <lb/>immobiles mouebuntur, & excitabuntur per Ax.12. quia &longs;unt applicatæ <lb/>cau&longs;æ nece&longs;&longs;ariæ. </s>

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

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

<s>3. Igitur impetus non e&longs;t idem cum &longs;ub&longs;tantià <lb/>mobilis; igitur di&longs;tinctus; deinde &longs;eparari pote&longs;t à &longs;ub&longs;tantia mobilis <lb/>per Hypoth. </s>

<s>3. Igitur impetus non e&longs;t idem cum &longs;ub&longs;tantià <lb/>mobilis; igitur di&longs;tinctus; dcinde &longs;eparari pote&longs;t à &longs;ub&longs;tantia mobilis <lb/>per Hypoth. </s>

<s>4. igitur e&longs;t di&longs;tinctus per Ax. 2. </s>

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

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

<s>& ex Hypoth. </s>

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

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

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

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

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<s>Diceret fortè aliquis lapidem proiectum pelli ab aëre à tergo in&longs;tan<lb/>te, vt voluit Ari&longs;toteles pluribus in locis; &longs;ed præ&longs;ertim 8. Ph.c.vlt.& 7. <lb/>cap.2. 3.de C&oelig;lo, cap.

3. Re&longs;pondeo hoc dici non po&longs;&longs;e; Primò quia non <lb/>modò non iuuat aër; &longs;ed ctiam impedit motum proiecti, quod de omni <lb/>medio nece&longs;&longs;ariò dicendum e&longs;t, vt patet experientiâ; vnde quo cra&longs;&longs;ius, <lb/>&longs;eu den&longs;ius e&longs;t <expan abbr="medi&utilde;">medium</expan>, motum potentiùs ratardat, vt videmus in proiectis <lb/>per aquam; rationem à priori afferemus infrà, cum de re&longs;i&longs;tentia medij: <lb/>Secundò, quis dicat pilam rotatam in &longs;olo moueri aëris appul&longs;u? </s>

3. Re&longs;pondeo hoc dici non po&longs;&longs;e; Primò quia non <lb/>modò non iuuat aër; &longs;ed etiam impedit motum proiecti, quod de omni <lb/>medio nece&longs;&longs;ariò dicendum e&longs;t, vt patet experientiâ; vnde quo cra&longs;&longs;ius, <lb/>&longs;eu den&longs;ius e&longs;t <expan abbr="medi&utilde;">medium</expan>, motum potentiùs retardat, vt videmus in proiectis <lb/>per aquam; rationem à priori afferemus infrà, cum de re&longs;i&longs;tentia medij: </s>

<s><lb/>Secundò, quis dicat pilam rotatam in &longs;olo moueri aëris appul&longs;u? cum <lb/>alia corpora, quæ pila rotata præterlambendo qua&longs;i allambit, nullo mo<lb/>do moueantur; præ&longs;ertim granula pulueris. </s>

<s>cum <lb/>alia corpora, quæ pila rotata præterlambendo qua&longs;i allambit, nullo mo<lb/>do moueantur; præ&longs;ertim granula pulueris. </s>

<s>Tertiò, an fortè aër id præ<lb/>&longs;tare pote&longs;t &longs;ine vi impre&longs;&longs;a; igitur non minus ip&longs;i pilæ proiectæ, quam <lb/>aëri ambienti imprimi poterit: </s>

<s>Tertiò, an fortè aër id præ<lb/>&longs;tare pote&longs;t &longs;ine vi impre&longs;&longs;a; igitur non minus ip&longs;i pilæ proiectæ, quam <lb/>aëri ambienti imprimi poterit: Quartò, nullus aër à tergo pellitur; &longs;ed <lb/>potius ip&longs;a pila aducr&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>Quartò, nullus aër à tergo pellitur; &longs;ed <lb/>potius ip&longs;a pila aduer&longs;us aëra pellit, dum emittitur manu; igitur &longs;i aër <lb/>&longs;uccedit à tergo, id totum accidit, vel metu vacui, vel ne aër compri<lb/>matur, vt videbimus infrà. </s>

<s>Quintò denique, cum diu moueatur eadem <lb/>pars aëris, haud dubiè in ca manet vis impre&longs;&longs;a; igitur impetus erit ad<lb/>huc qualitas permanens. </s>

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

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

<s>l. 7. Phy&longs;. cap.

2. Aliqui excu&longs;ant ip&longs;um Ari&longs;torelem, putantque <lb/>non e&longs;&longs;e locutum ex propriâ &longs;ententiâ: Alij dicunt Ari&longs;totelem quidem <lb/>tribui&longs;&longs;e aliquam vim extrin&longs;ecam aëri; non tamen nega&longs;&longs;e intrin&longs;ecam <lb/>impetus; quidquid &longs;it, ip&longs;a verba Ari&longs;totclis 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>

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

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

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

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

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

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

<s>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 veiut <lb/>appetentiâ concupi&longs;cit, vel exigit. </s>

<s>certè &longs;i fru&longs;trà e&longs;t, non <lb/>e&longs;t, per Ax.6.igitur vt &longs;it, debet habere id, &longs;ine quo e&longs;&longs;e non pote&longs;t; igitur <lb/>maximum eius bonum e&longs;t, igitur finis, quem natiuâ vel innatâ velut <lb/>appetentiâ concupi&longs;cit, vel exigit. </s>

<s>Dixi mediatè, vel immediatè; num <lb/>reuera datur fortè aliquis impetus, vt dicemus infrà; &longs;cilicet primus na<lb/>turalis, qui &longs;cilicet duos fines habet di&longs;iunctiuè; quorum alter e&longs;t gra<lb/>uitatio, alter motus deor&longs;um. </s>

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

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

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

<s>immò dicemus infrà primo in&longs;tanti, <lb/>quo e&longs;t impetus, nondum e&longs;&longs;e motum. </s>

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

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

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

<s>quanquam vt verum fatear non e&longs;&longs;et propriè motus, &longs;ed <lb/>qua&longs;i continuæ reproductionis modus; nam motus dicit aliquam pa&longs;<lb/>&longs;ionem; &longs;cilicet actum entis in potentiâ, vt aiunt. </s>

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

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

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

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

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

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

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

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

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

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

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

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

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

<s>Probatur 2.pars; quia in <lb/>eo impetus non e&longs;&longs;et fru&longs;trà per Ax. 6. igitur haberet &longs;uum effectum; <lb/>igitur motum. </s>

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

<s><emph type="italics"/>Quod dur at tantùmvno in&longs;tanti, e&longs;t incapax motus, & impetus.<emph.end type="italics"/></s><s> Pro<lb/>batur, quia non e&longs;t moueri, ni&longs;i relinquat locum, & acquirat alium; &longs;ed <lb/>1. acquirere locum, e&longs;t 1. e&longs;&longs;e in illo loco; & relinquere locum e&longs;t, <lb/>1. non e&longs;&longs;e in co loco; nec &longs;imul e&longs;t in vtroque, quia in duobus locis <lb/>idem &longs;imul e&longs;&longs;e non pote&longs;t; vt demon&longs;tramus in Metaphy&longs;ica; & phy<lb/>ficè certum e&longs;t ex omni hypothe&longs;i; igitur moueri nunc, id e&longs;t, hoc in<lb/>&longs;tanti, id e&longs;t, 1. acquirere nouum locum, & 1. relinquere priorem, <lb/>&longs;upponit nece&longs;&longs;ariò antè fui&longs;&longs;e in loco nunc relicto; &longs;ed quod durat <lb/>tantùm in in&longs;tanti, non habet antè, neque po&longs;t; igitur quod durat tan<lb/>tùm vno in&longs;tanti, moucri non pote&longs;t; igitur e&longs;t incapax motus; igitur <lb/>& impetus. </s>

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

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

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

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

<s>præterea &longs;i &longs;unt, &longs;unt e&longs;&longs;entia<lb/>liter immobiles; igitur valet &longs;emper ratio allata; igitur Deus e&longs;t inca<lb/>pax motus; igitur & impetus. </s>

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

<s>Præterea quod e&longs;t in loco dicit tan<lb/>rùm ens phy&longs;icum; &longs;ed mutatio dicit etiam non ens; <emph type="italics"/>Hinc egregium pa<lb/>radoxum; illud non mouetur per quod cuncta mouentur, quæ mouentur.<emph.end type="italics"/></s>

<s>Præterea quod e&longs;t in loco dicit tan<lb/>tùm ens phy&longs;icum; &longs;ed mutatio dicit etiam non ens; <emph type="italics"/>Hinc egregium pa<lb/>radoxum; illud non mouetur per quod cuncta mouentur, quæ mouentur.<emph.end type="italics"/></s>

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

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

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

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

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 1.<emph.end type="center"/></s>

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<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 2.<emph.end type="center"/></s>

<s>Hinc &longs;unt tantùm duo adæquatè po&longs;itiua, quæ moucri non po&longs;&longs;uat; <lb/>&longs;cilicet Deus, & actio; Deus, qui &longs;emper e&longs;t; actio, quæ tantùm vno <lb/>in&longs;tanti e&longs;t; Deus vbique e&longs;&longs;entialiter; actio hic tantum e&longs;&longs;entialiter; <lb/>Deus primum ens; actio infinitum ens; e&longs;t enim modus; Deus primum <lb/>mouens; actio ip&longs;e motus; &longs;cilicet primi generis, de quo in &longs;ect. </s>

<s>Hinc &longs;unt tantùm duo adæquatè po&longs;itiua, quæ moueri non po&longs;&longs;unt; <lb/>&longs;cilicet Deus, & actio; Deus, qui &longs;emper e&longs;t; actio, quæ tantùm vno <lb/>in&longs;tanti e&longs;t; Deus vbique e&longs;&longs;entialiter; actio hic tantum e&longs;&longs;entialiter; <lb/>Deus primum ens; actio infinitum ens; e&longs;t enim modus; Deus primum <lb/>mouens; actio ip&longs;e motus; &longs;cilicet primi generis, de quo in &longs;ect. </s>

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 3.<emph.end type="center"/></s>

<s>Hinc &longs;i res aliqua creata per actionem tantæ perfectionis, quæ mille <lb/>annis e&longs;&longs;entialiter re&longs;ponderet, con&longs;eruaretur; certè per totum illud <lb/>tempus moucri non po&longs;&longs;et; e&longs;&longs;et enim vnicum in&longs;tans, hoc e&longs;t duratio <pb xlink:href="026/01/055.jpg" pagenum="23"/>tota &longs;imul; &longs;ed codem in&longs;tanti in pluribus locis e&longs;&longs;e non pote&longs;t; igitur <lb/>nec moueri; adde quod per cam actionem &longs;um in loco, per quam &longs;um <lb/>in tempore; igitur &longs;i hæc e&longs;t &longs;emper eadem, illam eandem e&longs;&longs;e nece&longs;&longs;e <lb/>e&longs;t; &longs;ed hæc &longs;unt metaphy&longs;ica, quæ obiter tantùm attingo, aliàs fusè <lb/>de mon&longs;trabo. </s>

<s>Hinc &longs;i res aliqua creata per actionem tantæ perfectionis, quæ mille <lb/>annis e&longs;&longs;entialiter re&longs;ponderet, con&longs;eruaretur; certè per totum illud <lb/>tempus moueri non po&longs;&longs;et; e&longs;&longs;et enim vnicum in&longs;tans, hoc e&longs;t duratio <pb xlink:href="026/01/055.jpg" pagenum="23"/>tota &longs;imul; &longs;ed codem in&longs;tanti in pluribus locis e&longs;&longs;e non pote&longs;t; igitur <lb/>nec moueri; adde quod per cam actionem &longs;um in loco, per quam &longs;um <lb/>in tempore; igitur &longs;i hæc e&longs;t &longs;emper eadem, illam eandem e&longs;&longs;e nece&longs;&longs;e <lb/>e&longs;t; &longs;ed hæc &longs;unt metaphy&longs;ica, quæ obiter tantùm attingo, aliàs fusè <lb/>de mon&longs;trabo. </s>

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

<s>Ob&longs;eruabis primò ex dictis præclarum naturæ in&longs;titutum; cum enim <lb/>corpus moueri &longs;emper non debeat, (quippe hoc e&longs;&longs;et maximè incom<lb/>modum) certè per &longs;uam entitatem moucri non exigit; alioquin &longs;emper <lb/>moueretur; igitur per aliud ab entitate di&longs;tinctum, id e&longs;t per impetum; <lb/>itaque licet per &longs;uam entitatem exigat fluxum in tempore, id e&longs;t con&longs;er<lb/>nari, & durare; id e&longs;t nouam &longs;emper actionem con&longs;eruatiuam; quia <lb/>maximum eius bonum e&longs;t durare vel exi&longs;tere; Igitur per &longs;e ip&longs;um illud <lb/>exigit; quia &longs;emper exigit, non tamen per &longs;e ip&longs;um exigit fluxum in <lb/>loco, id e&longs;t motum; quia moueri non &longs;emper e&longs;t bonum. </s>

<s>Ob&longs;eruabis primò ex dictis præclarum naturæ in&longs;titutum; cum enim <lb/>corpus moueri &longs;emper non debeat, (quippe hoc e&longs;&longs;et maximè incom<lb/>modum) certè per &longs;uam entitatem moueri non exigit; alioquin &longs;emper <lb/>moueretur; igitur per aliud ab entitate di&longs;tinctum, id e&longs;t per impetum; <lb/>itaque licet per &longs;uam entitatem exigat fluxum in tempore, id e&longs;t con&longs;er<lb/>uari, & durare; id e&longs;t nouam &longs;emper actionem con&longs;eruatiuam; quia <lb/>maximum eius bonum e&longs;t durare vel exi&longs;tere; Igitur per &longs;e ip&longs;um illud <lb/>exigit; quia &longs;emper exigit, non tamen per &longs;e ip&longs;um exigit fluxum in <lb/>loco, id e&longs;t motum; quia moueri non &longs;emper e&longs;t bonum. </s>

<s>Ob&longs;eruabis &longs;ecundò, cum idem corpus aliquando velociùs, tardiùs <lb/>aliquando moueri exigat; &longs;i per &longs;uam entitatem moueri exigeret, eo<lb/>dem &longs;emper ferretur motu; quia eadem &longs;emper e&longs;&longs;et exigentia; igitur <lb/>debet e&longs;&longs;e aliquid aliud; illud autem e&longs;t impetus, qui aliquando maior <lb/>&longs;eu perfectior, aliquando verò minor e&longs;t; igitur maiorem &longs;eu velcio<lb/>rem motum aliquando exigit, aliquando minorem, &longs;eu tardiorem; <lb/>cum enim motus &longs;it eius finis intrin&longs;ecus, vt re&longs;olutio e&longs;t finis caloris <lb/>vel rarefactio; quemadmodum maior calor maiorem exigit, &longs;eu præ<lb/>&longs;tat re&longs;olutionem; ita & maior, &longs;eu perfectior impetus maiorem, &longs;eu <lb/>velociorem motum exigit. </s>

<s>Ob&longs;eruabis &longs;ecundò, cum idem corpus aliquando velociùs, tardiùs <lb/>aliquando moueri exigat; &longs;i per &longs;uam entitatem moueri exigeret, eo<lb/>dem &longs;emper ferretur motu; quia eadem &longs;emper e&longs;&longs;et exigentia; igitur <lb/>debet e&longs;&longs;e aliquid aliud; illud autem e&longs;t impetus, qui aliquando maior <lb/>&longs;eu perfectior, aliquando verò minor e&longs;t; igitur maiorem &longs;eu <expan abbr="velciorem">velocio<lb/>rem</expan> motum aliquando exigit, aliquando minorem, &longs;eu tardiorem; <lb/>cum enim motus &longs;it eius finis intrin&longs;ecus, vt re&longs;olutio e&longs;t finis caloris <lb/>vel rarefactio; quemadmodum maior calor maiorem exigit, &longs;eu præ<lb/>&longs;tat re&longs;olutionem; ita & maior, &longs;eu perfectior impetus maiorem, &longs;eu <lb/>velociorem motum exigit. </s>

<s>Ob&longs;eruabis tertiò aliud naturæ in&longs;titutum, quo &longs;cilicet in eo tan<lb/>tùm &longs;ubiecto recipi pote&longs;t cau&longs;a formalis, in quo recipi pote&longs;t cius effe<lb/>ctus formalis &longs;ecundarius: nec alia regula, præter eam excogitari pote&longs;t; <lb/>cum enim aliqua forma ad talem, vel talem finem à natura in&longs;tituta e&longs;t; <lb/>certè propter illum finem e&longs;t, igitur in co non e&longs;t, in quo &longs;uum finem <lb/>con&longs;equi non pote&longs;t; alioquin fru&longs;trà e&longs;&longs;et; & contra in eo e&longs;&longs;e pote&longs;t, <lb/>in quo fru&longs;trà non e&longs;t; cum &longs;cilicet in eo &longs;uum finem con&longs;equatur; ad<lb/>de quod finis ille intrin&longs;ecus phy&longs;icus &longs;cilicet, non moralis, aliquis no<lb/>uus effectus e&longs;t; atqui nouus effectus &longs;ine &longs;ua cau&longs;a e&longs;&longs;e non pote&longs;t, neque <lb/>cau&longs;a nece&longs;&longs;aria &longs;ine e&longs;&longs;ectu; igitur ibi, &longs;cilicet in hoc &longs;ubiecto, in quo <lb/>e&longs;t, vel e&longs;&longs;e pote&longs;t effectus formalis, cau&longs;a formalis e&longs;t, vel e&longs;&longs;e pote&longs;t, <lb/>e&longs;t inquam citra miraculum. </s>

<s>Ob&longs;eruabis tertiò aliud naturæ in&longs;titutum, quo &longs;cilicet in eo tan<lb/>tùm &longs;ubiecto recipi pote&longs;t cau&longs;a formalis, in quo recipi pote&longs;t eius effe<lb/>ctus formalis &longs;ecundarius: nec alia regula, præter eam excogitari pote&longs;t; <lb/>cum enim aliqua forma ad talem, vel talem finem à natura in&longs;tituta e&longs;t; <lb/>certè propter illum finem e&longs;t, igitur in eo non e&longs;t, in quo &longs;uum finem <lb/>con&longs;equi non pote&longs;t; alioquin fru&longs;trà e&longs;&longs;et; & contra in eo e&longs;&longs;e pote&longs;t, <lb/>in quo fru&longs;trà non e&longs;t; cum &longs;cilicet in eo &longs;uum finem con&longs;equatur; ad<lb/>de quod finis ille intrin&longs;ecus phy&longs;icus &longs;cilicet, non moralis, aliquis no<lb/>uus effectus e&longs;t; atqui nouus effectus &longs;ine &longs;ua cau&longs;a e&longs;&longs;e non pote&longs;t, neque <lb/>cau&longs;a nece&longs;&longs;aria &longs;ine 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>

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

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

<s>deinde multiplex iure po&longs;&longs;et exi&longs;timari; denique <lb/>quod vnum e&longs;t in entitate creata, &longs;eu dependente ab eadem cau&longs;a, vnum <lb/>e&longs;t etiam in dependentia; quæ e&longs;t actio, per quam dependet; &longs;ed de his <lb/>aliàs. </s>

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<s><emph type="italics"/>Impetus non producitur in eo mobili, quod moueri non pote&longs;t à potentia <lb/>motrice applicata, licèt à fortiori moueri po&longs;&longs;it.<emph.end type="italics"/></s><s> Probatur, quia impetus <lb/>e&longs;t tantùm propter motum, qui eius effectus e&longs;t, & finis, per Th. 15. <lb/>& 16. Igitur vbi non e&longs;t motus, fru&longs;trà e&longs;t impetus; &longs;ed quod fru&longs;trà <lb/>e&longs;t, non e&longs;t; id e&longs;t non e&longs;t, quod fru&longs;trà e&longs;&longs;et, &longs;i e&longs;&longs;et per Ax. 6. Exci<lb/>pio tamen impetum naturalem innatum, qui nunquam e&longs;t fru&longs;trà, vt <lb/>dictum e&longs;t &longs;uprà in Theorem. </s>

<s>17. adde quod non pote&longs;t cogno&longs;oi <lb/>impetus, ni&longs;i vel ex motu, vel ex ictu, vel ex contrario ni&longs;u, vel <lb/>impul&longs;u; &longs;ed nihil horum cernitur in rupe quam ferio; Igitur non <lb/>e&longs;t dicendum in ea produci impetum, cuius rationem afferemus infrà; <lb/>nunc&longs;atis e&longs;t Ax. 3. id manife&longs;tè probari; nam qui diceret in rupe im<lb/>mobili impetum imprimi; certè po&longs;itiuo argumento probare tenere<lb/>tur, quod tantùm duci pote&longs;t, vel ab experimento; atqui hîc nullum e&longs;t; <lb/>vel à nece&longs;&longs;itate, quæ nulla e&longs;t; vel ex alio quocumque capite, quod <lb/>nullum excogitari pote&longs;t; &longs;ed maiorem lucem huic Th. 3. ex proximè <lb/>&longs;equentibus accer&longs;emus; nec e&longs;t quòd aliqui dicant produci impetum <lb/>inefficacem; qui cum fru&longs;trà &longs;it, &longs;i e&longs;t, ex nullo capite probari pote&longs;t: ad<lb/>de quòd de&longs;truitur impetus, ne &longs;it fru&longs;trà; Igitur non producitur, ne &longs;it <lb/>fru&longs;trà; nam con&longs;eruatio e&longs;t vera actio, vt dicemus &longs;uo loco; Igitur &longs;i <lb/>hæc non ponitur, ne aliquid &longs;it fru&longs;trà; etiam 1. productio poni non <lb/>debet; vnde commentum illud impetus inefficacis pror&longs;us inefficax e&longs;t. </s>

<s>17. adde quod non pote&longs;t cogno&longs;ci <lb/>impetus, ni&longs;i vel ex motu, vel ex ictu, vel ex contrario ni&longs;u, vel <lb/>impul&longs;u; &longs;ed nihil horum cernitur in rupe quam ferio; Igitur non <lb/>e&longs;t dicendum in ea produci impetum, cuius rationem afferemus infrà; <lb/>nunc &longs;atis e&longs;t Ax. 3. id manife&longs;tè probari; nam qui diceret in rupe im<lb/>mobili impetum imprimi; certè po&longs;itiuo argumento probare tenere<lb/>tur, quod tantùm duci pote&longs;t, vel ab experimento; atqui hîc nullum e&longs;t; <lb/>vel à nece&longs;&longs;itate, quæ nulla e&longs;t; vel ex alio quocumque capite, quod <lb/>nullum excogitari pote&longs;t; &longs;ed maiorem lucem huic Th. 3. ex proximè <lb/>&longs;equentibus accer&longs;emus; nec e&longs;t quòd aliqui dicant produci impetum <lb/>inefficacem; qui cum fru&longs;trà &longs;it, &longs;i e&longs;t, ex nullo capite probari pote&longs;t: ad<lb/>de quòd de&longs;truitur impetus, ne &longs;it fru&longs;trà; Igitur non producitur, ne &longs;it <lb/>fru&longs;trà; nam con&longs;eruatio e&longs;t vera actio, vt dicemus &longs;uo loco; Igitur &longs;i <lb/>hæc non ponitur, ne aliquid &longs;it fru&longs;trà; etiam 1. productio poni non <lb/>debet; vnde commentum illud impetus inefficacis pror&longs;us inefficax e&longs;t. </s>

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

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

<s><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> Probatur, & explicatur; quippe debilior potentia minorem ef<lb/>fectum producit per. </s>

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

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

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

<s>Probatur igitur <lb/>1. quia &longs;i non producatur in omnibus partibus, & nulla &longs;eparetur ab <lb/>alijs; certè nulla mouetur, vt certum e&longs;t; igitur nulla habet impetum; <lb/>quia ibi non e&longs;t cau&longs;a formalis, vbi non e&longs;t effectus formalis; alioquin <lb/>e&longs;&longs;et fru&longs;trà, contra Ax. 6.2. </s>

<s>Tu dicis produci impetum in aliquot parti<lb/>bus; hoc dicis, hoc proba? </s>

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

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<s>Igitur certum e&longs;tvel produci in omnibus, vel <lb/>in nulla, ni&longs;i forte aliquæ auolent, &longs;ed tunc &longs;eparantur. </s>

<s>Obiiciet aliquis 1. e&longs;&longs;e cau&longs;am nece&longs;&longs;ariam applicatam &longs;ubiecto ap<lb/>to: igitur agit per Ax. 12. Re&longs;pondeo e&longs;&longs;e impeditam; nam re&longs;i&longs;tentia <lb/>&longs;ubiecti &longs;uperat vires potentiæ vt dictum e&longs;t; immò in ip&longs;o motu re<lb/>torqueo argumentum; licèt enim &longs;it applicata cau&longs;a nec&longs;&longs;aria mouens, <lb/>non tamen mouet. </s>

<s>Obiiciet aliquis 1. e&longs;&longs;e cau&longs;am nece&longs;&longs;ariam applicatam &longs;ubiecto ap<lb/>to: igitur agit per Ax. 12. Re&longs;pondeo e&longs;&longs;e impeditam; nam re&longs;i&longs;tentia <lb/>&longs;ubiecti &longs;uperat vires potentiæ vt dictum e&longs;t; immò in ip&longs;o motu re<lb/>torqueo argumentum; licèt enim &longs;it applicata cau&longs;a nece&longs;&longs;aria mouens, <lb/>non tamen mouet. </s>

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

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<s>Obiiciet. </s>

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

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

<s>Dices &longs;i vterque coniunctim producit effectum: &longs;int v. g. 100. par<lb/>tes impetus; Igitur &longs;inguli producunt tantùm 50. Igitur cur potiùs in <lb/>in his partibus &longs;ubiecti, quàm in alijs, cum vtriu&longs;que potentia eidem <lb/>&longs;ubiecti parti po&longs;&longs;et e&longs;&longs;e applicata? </s>

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<s>Obiicies 4. producitur &longs;onus &longs;i ferias rupem; igitur & impetus; Re&longs;<lb/>pondeo ad &longs;onum &longs;olam aëris colli&longs;ionem &longs;ufficere, quam fieri certum <lb/>e&longs;t à prædicto ictu; deinde mallej motus impacti in rupem facit &longs;onum; <lb/>quidquid tandem &longs;it &longs;onus, de quo hîc non di&longs;puto: adde qnod in ru<lb/>pe &longs;unt &longs;emper aliquæ partes trem ulæ, quæ modico tantùm, coque flexi<lb/>bili nexu cum alijs partibus copu lantur; adde aliquam compre&longs;&longs;ionem, <lb/>ex qua modicæ vibrationes &longs;equuntur. </s>

<s>Obiicies 4. producitur &longs;onus &longs;i ferias rupem; igitur & impetus; Re&longs;<lb/>pondeo ad &longs;onum &longs;olam aëris colli&longs;ionem &longs;ufficere, quam fieri certum <lb/>e&longs;t à prædicto ictu; deinde mallej motus impacti in rupem facit &longs;onum; <lb/>quidquid tandem &longs;it &longs;onus, de quo hîc non di&longs;puto: adde 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>

<s>Obiicies 5. Quando aliquæ partes auolant ab ictu, haud dubiè auo<lb/>lant propter impetum impre&longs;&longs;um: Igitur prius e&longs;t imprimi impetum, <lb/>quàm auolare; igitur productus e&longs;t impetus in nonnullis partibus, & <lb/>non in aliis, cum quibus illæ &longs;unt coniunctæ. </s>

<s>Re&longs;pondeo equidem im<lb/>petum produci in illis partibus antequam auolent; &longs;ed ideo produci vt <lb/>deinde auolent nam tota ratio cur non producatur, e&longs;t ne &longs;it fru&longs;trà; &longs;ed <lb/>&longs;i auolent aliquæ partes: certè in ijs non e&longs;t fru&longs;trà, in quibus habet <lb/>&longs;uum effectum, id e&longs;t, motum. </s>

<s>Dices; igitur primo in&longs;tanti impetus ille e&longs;t fru&longs;trà; in quo non <lb/>habet &longs;uum effectum; Re&longs;pondeo nunquam primo in&longs;tanti e&longs;&longs;e fru&longs;trà, <lb/>modò &longs;it motus &longs;ecundo cum etiam primo in&longs;tanti, quo e&longs;t impetus, <lb/>non po&longs;&longs;it e&longs;&longs;e motus, vt demon&longs;trabo infrà; immò ideo ponitur im<lb/>petus primo vt &longs;it motus &longs;ecundo exigendo pro i n&longs;tant i &longs;equenti, de <lb/>cum impetus ponat tantùm motum quo aliàs. </s>

<s>Dices; igitur primo in&longs;tanti impetus ille e&longs;t fru&longs;trà; in quo non <lb/>habet &longs;uum effectum; Re&longs;pondeo nunquam primo in&longs;tanti e&longs;&longs;e fru&longs;trà, <lb/>modò &longs;it motus &longs;ecundo cum etiam primo in&longs;tanti, quo e&longs;t impetus, <lb/>non po&longs;&longs;it e&longs;&longs;e motus, vt demon&longs;trabo infrà; immò ideo ponitur im<lb/>petus primo vt &longs;it motus &longs;ecundo exigendo pro in&longs;tant &longs;equenti, de <lb/>cum impetus ponat tantùm motum quo aliàs. </s>

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

<s>Re&longs;pondeo non &longs;tare per cau&longs;am nece&longs;&longs;ariam, quin &longs;em<lb/>per agat; &longs;ed per &longs;ubiectum, quod &longs;i aptum e&longs;t, & capax e&longs;&longs;ectus; haud <lb/>dubiè co ip&longs;o cau&longs;a nece&longs;&longs;aria applicata in ip&longs;um aget; &longs;i verò ineptum. </s>

<s>Re&longs;pondeo non &longs;tare per cau&longs;am nece&longs;&longs;ariam, quin &longs;em<lb/>per agat; &longs;ed per &longs;ubiectum, quod &longs;i aptum e&longs;t, & capax effectus; 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><lb/>haud dubiè non aget; nam ad hoc vt producatur effectus in &longs;ubiecto; <lb/>non &longs;atis e&longs;t cau&longs;am po&longs;&longs;e producere, ni&longs;i etiam &longs;ubiectum po&longs;&longs;it recipe<lb/>re; igitur cum &longs;it talis ordo à natura in&longs;titutus, ne aliquid &longs;it fru&longs;trà; <lb/>certè &longs;i impetus producibilis &longs;it futurus fru&longs;trà, hauddubiè non produ<lb/>cetur; &longs;ecus verò &longs;i fru&longs;trà non &longs;it futurus, in quo non e&longs;t difficultas. </s>

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<s>Ob&longs;eruabis 1. vix fieri po&longs;&longs;e quin &longs;emper aliquæ partes &longs;eparentur, <lb/>comprimantur, vel dilatentur, vt patet experientiâ. </s>

<s>Ob&longs;eruabis 2. etiam maximam corporis molem à debili potentia mi-<pb xlink:href="026/01/059.jpg" pagenum="27"/>nimo etiam ictu moucri; quod etiam ob&longs;eruauit Galileus in &longs;uis dialo<lb/>gis de motu; quem certè motum ob&longs;eruabis etiam in&longs;en&longs;ibilem, tùm <lb/>operâ radij luminis repercu&longs;&longs;i, & ad aliquod interuallum proiecti; tùm <lb/>operâ &longs;eu pi&longs;orum in tympani membranâ tremulo qua&longs;i motu &longs;ub&longs;ul<lb/>tantium; quâ etiam arte deprehenditur in arce ob&longs;e&longs;&longs;a, &longs;ub quam muri <lb/>partem cuniculi agantur. </s>

<s>Ob&longs;eruabis 2. etiam maximam corporis molem à debili potentia mi-<pb xlink:href="026/01/059.jpg" pagenum="27"/>nimo etiam ictu moueri; quod etiam ob&longs;eruauit Galileus in &longs;uis dialo<lb/>gis de motu; quem certè motum ob&longs;eruabis etiam in&longs;en&longs;ibilem, tùm <lb/>operâ radij luminis repercu&longs;&longs;i, & ad aliquod interuallum proiecti; tùm <lb/>operâ &longs;eu pi&longs;orum in tympani membranâ tremulo qua&longs;i motu &longs;ub&longs;ul<lb/>tantium; quâ etiam arte deprehenditur in arce ob&longs;e&longs;&longs;a, &longs;ub quam muri <lb/>partem cuniculi agantur. </s>

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 1.<emph.end type="center"/></s>

<s>Hinc egregia ratio erui pote&longs;t, cur ingens corporis moles à debili po<lb/>tenria loco moueri non po&longs;&longs;it; cum enim tot &longs;altem requirantur partes <lb/>impetus, quot &longs;unt partes &longs;ubiecti: quia vel in omnibus, vel in nulla <lb/>producitur; certè cum &longs;int plures partes &longs;ubiecti, quàm vt in &longs;ingulis <lb/>ab ea dumtaxat potentiâ impetus produci po&longs;&longs;it; quid mirum e&longs;t, &longs;i mo<lb/>ueri non po&longs;&longs;it. </s>

<s>Hinc egregia ratio erui pote&longs;t, cur ingens corporis moles à debili po<lb/>tentia loco moueri non po&longs;&longs;it; cum enim tot &longs;altem requirantur partes <lb/>impetus, quot &longs;unt partes &longs;ubiecti: quia vel in omnibus, vel in nulla <lb/>producitur; certè cum &longs;int plures partes &longs;ubiecti, quàm vt in &longs;ingulis <lb/>ab ea dumtaxat potentiâ impetus produci po&longs;&longs;it; quid mirum e&longs;t, &longs;i mo<lb/>ueri non po&longs;&longs;it. </s>

<s><emph type="center"/><emph type="italics"/>Collorarium<emph.end type="italics"/> 2.<emph.end type="center"/></s>

<s>Hinc certa ratio alterius vulgaris effectus potentiæ motricis, quæ lapi<lb/>dem 40. librarum tardo tantùm motu impellit, etiam cum &longs;ummo ni&longs;u, <lb/>cum tamen &longs;axo vnius libræ velocioremmotum imprimat; quia &longs;cilicet <lb/>partes impetus producti di&longs;tribuuntur pluribus partibus &longs;ubiecti in ma<lb/>iori lapide, & paucioribus in minori; igitur &longs;ingulæ partes minoris <lb/>habent plures partes impetus, vt manife&longs;tè coa&longs;tat; ergo ille impetus <lb/>inten&longs;ior e&longs;t; igitur maiorem exigit &longs;eu perfectiorem motum per Ax. <lb/>13. num.2. </s>

<s>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; quia &longs;cilicet <lb/>partes impetus producti di&longs;tribuuntur pluribus partibus &longs;ubiecti in ma<lb/>iori lapide, & paucioribus in minori; igitur &longs;ingulæ partes minoris <lb/>habent plures partes impetus, vt manife&longs;tè con&longs;tat; ergo ille impetus <lb/>inten&longs;ior e&longs;t; igitur maiorem exigit &longs;eu perfectiorem motum per Ax. <lb/>13. num.2. </s>

<s><emph type="center"/><emph type="italics"/>Collorarium<emph.end type="italics"/> 3.<emph.end type="center"/></s>

<s>Hinc &longs;ublata ratione diuer&longs;æ re&longs;i&longs;tentiæ medij, dato pondere <lb/>mobilis vtriu&longs;que, datoque ni&longs;u communi potentiæ, pote&longs;t de<lb/>terminari certus velocitatis gradus vtriu&longs;que; nam ratio velocitatum <lb/>e&longs;t inuer&longs;a ponderum v. g. &longs;it pondùs 4. librarum; fit etiam 2. librarum <lb/>&longs;it impetus impre&longs;&longs;us vtrique &longs;uppo&longs;ito communi, & æquali ni&longs;u <lb/>potentiæ, & æquali tempore; haud dubiè velocitas mobilis 2. libra<lb/>rum erit dupla velocitatis mobilis 4. librarum; quia cum &longs;int duplo <lb/>plures partes &longs;ubiecti in hoc mobili quàm in illo (accipio enim vtrum<lb/>que eiu&longs;dem mareriæ, vt omnes lites fugiam) igitur in minori e&longs;t duplo <lb/>inten&longs;ior impetus: Igitur duplo velocior motus; dixi, &longs;i fiat æquali <lb/>ni&longs;u, & æquali tempore; quia reuerâ non fit in tempore æquali, &longs;ed <lb/>inæquali, &longs;i &longs;upponatur idem arcus brachij v. g. iacientis; nam tempo<lb/>ra &longs;unt in ratione &longs;ubduplicata ponderum; vt demon&longs;trabimus lib.

<s>Hinc &longs;ublata ratione diuer&longs;æ re&longs;i&longs;tentiæ medij, dato pondere <lb/>mobilis vtriu&longs;que, datoque ni&longs;u communi potentiæ, pote&longs;t de<lb/>terminari certus velocitatis gradus vtriu&longs;que; nam ratio velocitatum <lb/>e&longs;t inuer&longs;a ponderum v. g. &longs;it pondùs 4. librarum; fit etiam 2. librarum <lb/>&longs;it impetus impre&longs;&longs;us vtrique &longs;uppo&longs;ito communi, & æquali ni&longs;u <lb/>potentiæ, & æquali tempore; haud dubiè velocitas mobilis 2. libra<lb/>rum erit dupla velocitatis mobilis 4. librarum; quia cum &longs;int duplo <lb/>plures partes &longs;ubiecti in hoc mobili quàm in illo (accipio enim vtrum<lb/>que eiu&longs;dem materiæ, vt omnes lites fugiam) igitur in minori e&longs;t duplo <lb/>inten&longs;ior impetus: Igitur duplo velocior motus; dixi, &longs;i fiat æquali <lb/>ni&longs;u, & æquali tempore; quia reuerâ non fit in tempore æquali, &longs;ed <lb/>inæquali, &longs;i &longs;upponatur idem arcus brachij v. g. iacientis; nam tempo<lb/>ra &longs;unt in ratione &longs;ubduplicata ponderum; vt demon&longs;trabimus lib.

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

<s><emph type="center"/><emph type="italics"/>Collorarium<emph.end type="italics"/> 4.<emph.end type="center"/></s>

<s>Hinc facilè determinari pote&longs;t proportio impetus impre&longs;&longs;i cognitâ <lb/>grauitate mobilium; v. g. &longs;it mobile grauc vt4. & aliud graue vt 2. haud <lb/>dubiè vt moucatur 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;cquitur ex dictis; vt enim tot&longs;int gradus impetus <pb xlink:href="026/01/060.jpg" pagenum="28"/>in qualibet parte minoris, quot &longs;unt in qualibet parte minoris; haud <lb/>dubiè impetus maioris habet eandem rationem ad impetum minoris; <lb/>quam habet maius ad minus. </s>

<s>Hinc facilè determinari pote&longs;t proportio impetus impre&longs;&longs;i cognitâ <lb/>grauitate mobilium; v. g. &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; vt enim tot&longs;int gradus impetus <pb xlink:href="026/01/060.jpg" pagenum="28"/>in qualibet parte minoris, quot &longs;unt in qualibet parte minoris; haud <lb/>dubiè impetus maioris habet eandem rationem ad impetum minoris; <lb/>quam habet maius ad minus. </s>

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

<s><emph type="italics"/>Potest impetus aliquo in&longs;tanti non moueri quo mouetur ip&longs;um mobile, in <lb/>quo est.<emph.end type="italics"/></s><s> Nam moueatur mobile quodlibet; & 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. <lb/>35. quo tamen in&longs;tanti mouetur prædictum mobilc. </s>

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<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 2.<emph.end type="center"/></s>

<s>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; quia &longs;cilicet impetus vnius partis non iuuat mo<lb/>tum alterius: præterca tam facilè 2, partes impetus in 2. partibus &longs;ubie<lb/>cti receptæ ca&longs;dem mouent, quàm 100. alias 100. dixi per &longs;e; 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. <emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 38.<emph.end type="center"/></s>

<s>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; quia &longs;cilicet impetus vnius partis non iuuat mo<lb/>tum alterius: 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; 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. <emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 38.<emph.end type="center"/></s>

<s><emph type="italics"/>Impetus recipitur tantùm in ip&longs;a &longs;ub&longs;tantia &longs;ubiecti naturaliter.<emph.end type="italics"/> v. g. &longs;i <lb/>mobile &longs;it ferrum calidum, recipitur in ip&longs;a &longs;ub&longs;tantia ferri; non verò <lb/>in ip&longs;o calore (ex &longs;uppo&longs;itione quod calor &longs;it accidens, vt aliàs demon<lb/>&longs;trabimus; nec in alijs accidentibus, &longs;i quæ &longs;unt, in eodem &longs;ubiecto; 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; plures quoque partes impetus <lb/>producendæ e&longs;&longs;ent; igitur maiori potentiâ opus e&longs;&longs;et per Ax. 13. n. </s>

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<s>Diceret fortè ali<lb/>quis eundem impetum recipi &longs;imul in &longs;ub&longs;tantia & in ip&longs;is accidenti<lb/>bus; &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: 2. qui hoc diceret, deberet probare; nam codem modo <lb/>mouetur corpus &longs;iue afficiatur pluribus accidentibus, &longs;iue paucioribus; <lb/>igitur non euincit experientia recipiin illis impetum, nec etiam ratio, <lb/>vt dicam paulò po&longs;t. </s>

<s>Ratio à priori e&longs;&longs;e pote&longs;t; 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; igitur cum exigat con&longs;erua<lb/>ri, & exi&longs;tere; co tantùm modo, quo pote&longs;t naturaliter con&longs;eruari & <lb/>exi&longs;tere; certè exigit con&longs;eruari, & ine&longs;&longs;e &longs;ubiecto; igitur exi&longs;tere in <lb/>eo loco, in quo exi&longs;tit &longs;ubiectum, vt patet; igitur, &longs;i &longs;ubiectum mutet <lb/>locum etiam accidens cnm co coniu nctum mutare debet. </s>

<s>Ratio à priori e&longs;&longs;e pote&longs;t; 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; igitur cum exigat con&longs;erua<lb/>ri, & exi&longs;tere; eo tantùm modo, quo pote&longs;t naturaliter con&longs;eruari & <lb/>exi&longs;tere; certè exigit con&longs;eruari, & ine&longs;&longs;e &longs;ubiecto; igitur exi&longs;tere in <lb/>eo loco, in quo exi&longs;tit &longs;ubiectum, vt patet; igitur, &longs;i &longs;ubiectum mutet <lb/>locum etiam accidens cum eo coniunctum mutare debet. </s>

<s>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>cum <lb/>hoc ip&longs;um ad omnem vnionem &longs;pectare videatur; Re&longs;pondeo vnam <pb xlink:href="026/01/062.jpg" pagenum="30"/>partem plumbi ita coniungi cum alia, vt etiam &longs;eparata naturaliter <lb/>exi&longs;tere po&longs;&longs;it; igitur non e&longs;t par ratio; præterea vna pars plumbi non <lb/>e&longs;t in loco alterius; nec enim inuicem penetrantur cum &longs;it compene<lb/>tratio accidentium cum &longs;ubiecto; 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; denique non vide<lb/>rur cur potius produceretur in vna parte, quam in alia; quæ omnia <lb/>iam &longs;uprà Th. 33. demon&longs;trauimus. </s>

<s>cum <lb/>hoc ip&longs;um ad omnem vnionem &longs;pectare videatur; Re&longs;pondeo vnam <pb xlink:href="026/01/062.jpg" pagenum="30"/>partem plumbi ita coniungi cum alia, vt etiam &longs;eparata naturaliter <lb/>exi&longs;tere po&longs;&longs;it; igitur non e&longs;t par ratio; præterea vna pars plumbi non <lb/>e&longs;t in loco alterius; nec enim inuicem penetrantur cum &longs;it compene<lb/>tratio accidentium cum &longs;ubiecto; 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; 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>

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

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<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 1.<emph.end type="center"/></s>

<s>Hinc manife&longs;tè patet, quid dicendum &longs;it de anima bruti, quæ mouc<lb/>tur etiam &longs;ine impetu; 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>

<s>Hinc manife&longs;tè patet, quid dicendum &longs;it de anima bruti, quæ moue<lb/>tur etiam &longs;ine impetu; 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>

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 2.<emph.end type="center"/></s>

<s>Idem quoque de Anima rationali dicendum e&longs;&longs;e videtur; licèt <lb/>enim à corpore &longs;eparata naturaliter exi&longs;tere po&longs;&longs;it; tandiù tamen cum <lb/>corpore manet coniuncta, quandiu agere pote&longs;t in organis corporcis; <lb/>ac proinde exigit con&longs;eruari in corpore ip&longs;o, quandiu &longs;uas operatio<lb/>nes organicas in co exercere pote&longs;t. </s>

<s>Idem quoque de Anima rationali dicendum e&longs;&longs;e videtur; licèt <lb/>enim à corpore &longs;eparata naturaliter exi&longs;tere po&longs;&longs;it; 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>

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 3.<emph.end type="center"/></s>

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

<s><emph type="italics"/>Quando corpus pellitur ab alio corpore per impetum impre&longs;&longs;um; band da<lb/>biè impetus ille impre&longs;&longs;us ab aliqua cau&longs;a efficiente producijur<emph.end type="italics"/>; patet <lb/>per Ax. 8. </s><pb xlink:href="026/01/063.jpg" pagenum="31"/>

<s><emph type="italics"/>Quando corpus pellitur ab alio corpore per impetum impre&longs;&longs;um; 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><pb xlink:href="026/01/063.jpg" pagenum="31"/>

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

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

<s><lb/>Dicunt aliqui requiri <expan abbr="mot&utilde;">motum</expan> præuium, vt agat; &longs;ed contra; nam motus <lb/>præuius non requiritur vt cau&longs;a, vt patet; quia cau&longs;a vt agat debet exi<lb/>&longs;tere per Ax. 9. Igitur requiritur, vt conditio, quod dici non pote&longs;t; <lb/>quia primo etiam conditio debet e&longs;&longs;e præ&longs;ens; &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; ni&longs;i vel vt tollat impedimentum, vel vt applicet cau&longs;am &longs;ubie<lb/>cto apto; præterea motus præuius non e&longs;t; igitur codem modo &longs;e <lb/>habet, ac &longs;i nunquam extiti&longs;&longs;et; & &longs;i co 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>

<s><lb/>Dicunt aliqui requiri <expan abbr="mot&utilde;">motum</expan> præuium, vt agat; &longs;ed contra; nam motus <lb/>præuius non requiritur vt cau&longs;a, vt patet; quia cau&longs;a vt agat debet exi<lb/>&longs;tere per Ax. 9. Igitur requiritur, vt conditio, quod dici non pote&longs;t; <lb/>quia primo etiam conditio debet e&longs;&longs;e præ&longs;ens; &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; ni&longs;i vel vt tollat impedimentum, vel vt applicet cau&longs;am &longs;ubie<lb/>cto apto; præterea motus præuius non e&longs;t; igitur codem 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>

<s>Diceret alius impetum e&longs;&longs;e tantùm conditionem, quæ &longs;emper e&longs;t <lb/>de præ&longs;enti: ad hanc in&longs;tantiam non valet &longs;uperior re&longs;pon&longs;io; & certè <lb/>&longs;i eo ip&longs;o in&longs;tanti contactus noua fieret impetus acce&longs;&longs;io; haud dubiè <lb/>maior e&longs;&longs;et ictus; licèt cum codem motu præuio, & tamen idem e&longs;&longs;et <lb/>corpus <expan abbr="impact&utilde;">impactum</expan>, Igitnr 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; dum &longs;cili<lb/>cet &longs;ubiectum, cui applicatur &longs;it capax motus; ex applicatione corporis <lb/>&longs;eu &longs;ubiecti ip&longs;ius non &longs;emper &longs;equitur; igitur dicendum e&longs;t impetum <lb/>ip&longs;um e&longs;&longs;e cau&longs;am alterius per Ax. 11. n. </s>

<s>Diceret alius impetum e&longs;&longs;e tantùm conditionem, quæ &longs;emper e&longs;t <lb/>de præ&longs;enti: ad hanc in&longs;tantiam non valet &longs;uperior re&longs;pon&longs;io; & certè <lb/>&longs;i eo ip&longs;o in&longs;tanti contactus noua fieret impetus acce&longs;&longs;io; haud dubiè <lb/>maior e&longs;&longs;et ictus; licèt cum codem motu præuio, & tamen idem e&longs;&longs;et <lb/>corpus <expan abbr="impact&utilde;">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; dum &longs;cili<lb/>cet &longs;ubiectum, cui applicatur &longs;it capax motus; ex applicatione corporis <lb/>&longs;eu &longs;ubiecti ip&longs;ius non &longs;emper &longs;equitur; igitur dicendum e&longs;t impetum <lb/>ip&longs;um e&longs;&longs;e cau&longs;am alterius per Ax. 11. n. </s>

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

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<s>igitur illius e&longs;t tollere impedimentnm, cuius e&longs;t exigere motum, <lb/>corpus ip&longs;um graue non exigit motum &longs;ur&longs;um, &longs;ed impetus; igitur im<lb/>petus e&longs;t tollerc impedimentum &longs;ui effectus; igitur producere impetum, <lb/>quo vno tolli tantùm pote&longs;t: 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>igitur illius e&longs;t tollere impedimentum, cuius e&longs;t exigere motum, <lb/>corpus ip&longs;um graue non exigit motum &longs;ur&longs;um, &longs;ed impetus; igitur im<lb/>petus e&longs;t tollere impedimentum &longs;ui effectus; igitur producere impetum, <lb/>quo vno tolli tantùm pote&longs;t: 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>quæ ratio? </s>

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

<s>Ob&longs;eruabis primò, hanc primam e&longs;&longs;e difficultatem; cum in hoc im<lb/>petus maximè differat ab alijs qualitalibus &longs;i quæ &longs;unt, quæ agunt in or<lb/>bem, vt dicemus &longs;uo loco. </s>

<s>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>

<s>Ob&longs;eruabis &longs;ecundò, hanc etiam e&longs;&longs;e communem illorum &longs;ententiam, <lb/>qui dicunt imptum 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>

<s>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>

<s>Ob&longs;eruabis tertiò, impetum in vtroque muncre cau&longs;æ &longs;ube&longs;&longs;e tantùm <lb/>vni lineæ; &longs;cilicet exigit motum per vnam lineam; cum per plures &longs;i<lb/>mul motus e&longs;&longs;e non po&longs;&longs;it; ne idem mobile &longs;imul e&longs;&longs;et in pluribus lo<lb/>cis; & producit impetum per vnam lincam; cum producat tantùm pro<lb/>pter motum. </s>

<s>Ob&longs;eruabis tertiò, impetum in vtroque munere cau&longs;æ &longs;ube&longs;&longs;e tantùm <lb/>vni lineæ; &longs;cilicet exigit motum per vnam lineam; cum per plures &longs;i<lb/>mul motus e&longs;&longs;e non po&longs;&longs;it; ne idem mobile &longs;imul e&longs;&longs;et in pluribus lo<lb/>cis; & producit impetum per vnam lineam; cum producat tantùm pro<lb/>pter motum. </s>

<s>Ob&longs;eruabis quartò, alias qualitates, &longs;i quæ &longs;unt, non agere ad extra, <lb/>vt tollant impedimentum &longs;ui effectus ad intra; qui &longs;cilicet ab impedi<lb/>mento extrin&longs;eco impediri non pote&longs;t; vt accidit in ip&longs;o impetu; etenim <lb/>corpus non pote&longs;t moucri 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 amoucri debet, accepto dumtaxat impetu <lb/>ab alio mobili. </s>

<s>Ob&longs;eruabis quartò, alias qualitates, &longs;i quæ &longs;unt, non agere ad extra, <lb/>vt tollant impedimentum &longs;ui effectus ad intra; qui &longs;cilicet ab impedi<lb/>mento extrin&longs;eco impediri non pote&longs;t; vt accidit in ip&longs;o impetu; etenim <lb/>corpus non pote&longs;t moueri ni&longs;i nouum locum acquirat: neque nouum <lb/>locum acquirere ab alio corpore occupatum, ni&longs;i corpus hoc loco ce<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>

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

<s>Hinc etiam reiicies commentum illorum, qui dicunt ideo vnum <lb/>corpus ab alio moueri, quia ab vno in aliud deriuantur corpu&longs;cula illa, <lb/>quæ faciunt lumen, & calorem; quia lumen, & calor &longs;unt veræ qualita<lb/>tates, non corpu&longs;cula, vt demon&longs;trabimus in 5. tractatu: Adde quod li<lb/>cet ferrum candens aliud frigidum impellat, etiam veloci&longs;&longs;imè; hoc ip<lb/>&longs;um æquè frigidum manet; 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>

<s>Hinc etiam reiicies commentum illorum, qui dicunt ideo vnum <lb/>corpus ab alio moueri, quia ab vno in aliud deriuantur corpu&longs;cula illa, <lb/>quæ faciunt lumen, & calorem; quia lumen, & calor &longs;unt veræ qualita<lb/>tes, non corpu&longs;cula, vt demon&longs;trabimus in 5. tractatu: Adde quod li<lb/>cet ferrum candens aliud frigidum impellat, etiam veloci&longs;&longs;imè; hoc ip<lb/>&longs;um æquè frigidum manet; 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>

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

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

<s>1. ni&longs;i enim agerent actione communi &longs;ed quælibet &longs;uam <lb/>produceret; cur potius in hac parte &longs;ubiecti, quam in alia, demde ap<lb/>pìicatur tantùm vna immediatè; Igitur agunt omnes actione commu<lb/>ni; omnes inquam illæ, quæ impediuntur; 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><pb xlink:href="026/01/066.jpg" pagenum="34"/>

<s>1. ni&longs;i enim agerent actione communi &longs;ed quælibet &longs;uam <lb/>produceret; cur potius in hac parte &longs;ubiecti, quam in alia, deinde ap<lb/>plicatur tantùm vna immediatè; Igitur agunt omnes actione commu<lb/>ni; omnes inquam illæ, quæ impediuntur; 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><pb xlink:href="026/01/066.jpg" pagenum="34"/>

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

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<s>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>

<s>Tertiò, Hinc corpora illa, quorum partes vel nullo vel modico nexu <lb/>copulantur, minimo ferè impul&longs;u commouentur; &longs;ic aër & aqua mini<lb/>mo flante vento agitantur, nubes pelluntur; 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 moucri pote&longs;t, quod in aqua gelu concreta minimè accidit. </s>

<s>Tertiò, Hinc corpora illa, quorum partes vel nullo vel modico nexu <lb/>copulantur, minimo ferè impul&longs;u commouentur; &longs;ic aër & aqua mini<lb/>mo flante vento agitantur, nubes pelluntur; 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>

<s>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>

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

<s><emph type="italics"/>Quo minùs impeditur impetus, minùs agit ad extra, & contrà; quo plùs <lb/>impeditur, plùs agit.<emph.end type="italics"/></s><s> Cum enim ideò agat ad extra, vt tollat impedi<lb/>mentum; certè &longs;i nullum e&longs;t, nihil agit, &longs;i minùs, minùs agit; igitur <lb/>agit pro rata, id e&longs;t, pro diucr&longs;a impedimenti ratione. </s>

<s><emph type="italics"/>Quo minùs impeditur impetus, minùs agit ad extra, & contrà; quo plùs <lb/>impeditur, plùs agit.<emph.end type="italics"/></s><s> Cum enim ideò agat ad extra, vt tollat impedi<lb/>mentum; 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>

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

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

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

<s>&longs;int enim duo globi, <lb/>A mobilis, & B. occurrens ip&longs;i A, &longs;itque linea directionis DE ducta <lb/>per centrum vtriu&longs;que AB, & punctum contactus &longs;it C; certè glo<lb/>bus B maximum ponit impedimentum, quod ab co poni po&longs;&longs;it; Igitur <lb/>impetus globi A agit quantùm pote&longs;t in globum B; vt &longs;cilicet maxi<lb/>mum impedimentum remoucat. </s>

<s>&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; certè glo<lb/>bus B maximum ponit impedimentum, quod ab eo poni po&longs;&longs;it; Igitur <lb/>impetus globi A agit quantùm pote&longs;t in globum B; vt &longs;cilicet maxi<lb/>mum impedimentum remoueat. </s>

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

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

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

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

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

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

<s>Hinc pote&longs;t determinari quota pars impetus producatur, & quantus <lb/>&longs;it ictus; cognito &longs;cilicet & &longs;uppo&longs;ito co impetus gradu, qui producitur, <lb/>cum totus producitur, vt fit in perpendiculari; quippe tota men&longs;ura <lb/>impetus continetur in arcu CB; quam proportionem nos infrà demon<lb/>&longs;trabimus. </s>

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

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

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

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

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

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

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

<s>Ob&longs;eruabis primò, &longs;ingularem impetus proprictatem, quæ alijs qua<lb/>litatibus minimè competit; nam aliæ qualitates v. g. calor; lumen in <lb/>cadem di&longs;tantia effectum &longs;emper æquè inten&longs;um producunt; &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; <lb/>cuius ratio ex eo capite petitur; quòd impetus agat tantùm ad extra <lb/>propter &longs;uum effectum ad intra, vt &longs;cilicet tollat impedimentum; igi<lb/>tur in totum, quod impedit, agit; igitur non habet certam, & deter<lb/>minatam &longs;phæram; cum tantùm agat in obicem, &longs;iue &longs;it maior, &longs;iue <lb/>minor: 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; 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/>maiorc. </s>

<s>Ob&longs;eruabis primò, &longs;ingularem impetus proprietatem, quæ alijs qua<lb/>litatibus minimè competit; nam aliæ qualitates v. g. calor; lumen in <lb/>eadem di&longs;tantia effectum &longs;emper æquè inten&longs;um producunt; &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; <lb/>cuius ratio ex eo capite petitur; quòd impetus agat tantùm ad extra <lb/>propter &longs;uum effectum ad intra, vt &longs;cilicet tollat impedimentum; igi<lb/>tur in totum, quod impedit, agit; igitur non habet certam, & deter<lb/>minatam &longs;phæram; cum tantùm agat in obicem, &longs;iue &longs;it maior, &longs;iue <lb/>minor: 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; 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>

<s>Prætereà, cum dixi omnes partcs mobilis actione communi agere ad <lb/>extra; ita primò intelligi debet, vt omnes illæ partes moueantur: &longs;ecun<lb/>dò, vt linea motus, &longs;eu directionis per centra grauitatis vtriu&longs;que glo<lb/>bi v, g. ducatur; alioquin, vel omnes actione communi non agunt, vel <lb/>minus agunt, de quo infrà; &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>Prætereà, cum dixi omnes partes mobilis actione communi agere ad <lb/>extra; ita primò intelligi debet, vt omnes illæ partes moueantur: &longs;ecun<lb/>dò, vt linea motus, &longs;eu directionis per centra grauitatis vtriu&longs;que glo<lb/>bi v, g. ducatur; alioquin, vel omnes actione communi non agunt, vel <lb/>minus agunt, de quo infrà; &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>

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

<s><emph type="italics"/>Impetus globi impacti in alium globum eo modo, quo diximus, id est, linea<lb/>directionis ducta per centra grauitatis vtriu&longs;que producit in eo æqualem<emph.end type="italics"/>; 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 æqualemi. </s>

<s><emph type="italics"/>Impetus globi impacti in alium globum eo modo, quo diximus, id est, linea <lb/>directionis ducta per centra grauitatis vtriu&longs;que producit in eo æqualem<emph.end type="italics"/>; 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>Probatur primò, <lb/>exemplo aliarum qualitatum; &longs;ecundò, quia ideo agit vt tollat impedi<lb/>mentum, hoc e&longs;t vt corpus illud amoueat loco; igitur æquali motu per <lb/>&longs;e; alioquin ni&longs;i æquali motu amoueret, non tolleret impedimentum, <lb/>vt pater; tertiò &longs;int 30. partes impetus, certèvel producent plures vel <lb/>pauciores, vel totidem, non plures; cur enim potius 31. quam 32. <lb/>nec etiam pauciores; cur enim potius 20. quam 18, &c. </s>

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<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 1.<emph.end type="center"/></s>

<s>Hinc reijcics 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; quia duo globi æquales in&longs;tanti contactus <lb/>perinde &longs;e habent, atque &longs;i conflarent vnum corpus; &longs;ed &longs;i conflarent <lb/>vnum corpus quilibet &longs;ubduplum impetum haberet; &longs;i verò globus cum <lb/>alio &longs;ubduplo faceret vnum mobilc; haud dubiè minor, id e&longs;t, &longs;ubduplus <lb/>haberet tantùm &longs;ubtriplum impetum; atque ita deinceps; hoc totum <lb/>fal&longs;i&longs;&longs;imum e&longs;t; nam primò &longs;i globus æqualis acciperet tantùm &longs;ubdu<lb/>plum impetum ab alio, &longs;ubduplo tantùm motu ferretur; 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; 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; nec enim migrat de <lb/>de &longs;ubiecto in &longs;ubiectum, &longs;ed producit &longs;ibi æqualem: 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; &longs;i e&longs;&longs;ent æquales, qui&longs;que &longs;ubduplum: &longs;i alter &longs;ubduplus &longs;ubtri<lb/>plum, &c. </s>

<s>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; quia duo globi æquales in&longs;tanti contactus <lb/>perinde &longs;e habent, atque &longs;i conflarent vnum corpus; &longs;ed &longs;i conflarent <lb/>vnum corpus quilibet &longs;ubduplum impetum haberet; &longs;i verò globus cum <lb/>alio &longs;ubduplo faceret vnum mobile; haud dubiè minor, id e&longs;t, &longs;ubduplus <lb/>haberet tantùm &longs;ubtriplum impetum; atque ita deinceps; hoc totum <lb/>fal&longs;i&longs;&longs;imum e&longs;t; nam primò &longs;i globus æqualis acciperet tantùm &longs;ubdu<lb/>plum impetum ab alio, &longs;ubduplo tantùm motu ferretur; 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; 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; nec enim migrat de <lb/>de &longs;ubiecto in &longs;ubiectum, &longs;ed producit &longs;ibi æqualem: 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; &longs;i e&longs;&longs;ent æquales, qui&longs;que &longs;ubduplum: &longs;i alter &longs;ubduplus &longs;ubtri<lb/>plum, &c. </s>

<s>&longs;ed hæc &longs;unt &longs;atis facilia. </s>

<s>Obijci fortè po&longs;&longs;et ab aliquo primò experientia; videmus enim &longs;æpè <lb/>globum impul&longs;um in ludo Tudiculario moueri tardiùs globo impellen<lb/>te; re&longs;pondeo id &longs;æpè accidere; tùm quia linea directionis non connec<lb/>tit centra vtriu&longs;que globi; igitur minor e&longs;t ictus per Th 52. tùm quia <lb/>globus impellens, vel impul&longs;us deficiunt à perfecta &longs;phæra; 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>

<s>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; igitur illa pars impetus, quæ de&longs;truitur, non <lb/>producit nouum impetum in globo impul&longs;o; Re&longs;pondco de&longs;truiquidem <lb/>aliquid impetus in globo impacto, vt videbimus infrà; cum tamen de<lb/>&longs;truatur tantùm &longs;equenti po&longs;t ictum in&longs;tanti; 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; adde quod illud ip&longs;um repugnat manife&longs;tæ experientiæ; <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>

<s>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; igitur illa pars impetus, quæ de&longs;truitur, non <lb/>producit nouum impetum in globo impul&longs;o; </s><s>Re&longs;pondeo de&longs;truiquidem <lb/>aliquid impetus in globo impacto, vt videbimus infrà; cum tamen de<lb/>&longs;truatur tantùm &longs;equenti po&longs;t ictum in&longs;tanti; 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; adde quod illud ip&longs;um repugnat manife&longs;tæ experientiæ; <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>

<s>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; modò illi globi ita &longs;tatuantur, vt <lb/>linea directionis per omnium centra rectà ducatur; Re&longs;pondco, vel il-<pb xlink:href="026/01/071.jpg" pagenum="39"/>los omnes globos ita e&longs;&longs;e contiguos, vt mutuo contactu &longs;e inuicem tan<lb/>gant; vel aliquod &longs;patium inter &longs;ingulos intercipi; &longs;i primum, produci<lb/>tur impetus à potentia motrice in omnibus, &longs;i &longs;ufficiens e&longs;t; non verò <lb/>vnus globus in alio, vt con&longs;tat; &longs;icut duo pondera &longs;imul attollo, quorum <lb/>vnum alteri incumbit: &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: idem dico de B, & C, vnde &longs;i nihil impetus in co primo motu <lb/>periret & linea directionis omnium centra perfectè connecteret; ita vt <lb/>omnium ictus illi omnino &longs;ine vlla deflexione re&longs;ponderent; 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; &longs;ed vix illa omnia de quibus &longs;uprà po&longs;&longs;unt ob&longs;eruari; 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>

<s>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; modò illi globi ita &longs;tatuantur, vt <lb/>linea directionis per omnium centra rectà ducatur; Re&longs;pondco, vel il-<pb xlink:href="026/01/071.jpg" pagenum="39"/>los omnes globos ita e&longs;&longs;e contiguos, vt mutuo contactu &longs;e inuicem tan<lb/>gant; vel aliquod &longs;patium inter &longs;ingulos intercipi; &longs;i primum, produci<lb/>tur impetus à potentia motrice in omnibus, &longs;i &longs;ufficiens e&longs;t; non verò <lb/>vnus globus in alio, vt con&longs;tat; &longs;icut duo pondera &longs;imul attollo, quorum <lb/>vnum alteri incumbit: &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: idem dico de B, & C, vnde &longs;i nihil impetus in eo primo motu <lb/>periret & linea directionis omnium centra perfectè connecteret; ita vt <lb/>omnium ictus illi omnino &longs;ine vlla deflexione re&longs;ponderent; 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; &longs;ed vix illa omnia de quibus &longs;uprà po&longs;&longs;unt ob&longs;eruari; 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>

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

<s><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; id e&longs;t, nullum corpus po&longs;le maiorem veloci<lb/>tatis gradum alteri corpori imprimere; co &longs;cilicet gradu, quem ip&longs;um <lb/>habet; nec enim inuenio Principium illud apud eos Mechanicos, qui <lb/>mechanica momenta &longs;uarum demon&longs;trationum momentis confirmant; <lb/>quî porro fieri pote&longs;t, vt principium illud admittatur, quod manife&longs;tæ <lb/>experientiæ repugnat? </s>

<s><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; id e&longs;t, nullum corpus po&longs;&longs;e maiorem veloci<lb/>tatis gradum alteri corpori imprimere; eo &longs;cilicet gradu, quem ip&longs;um <lb/>habet; nec enim inuenio Principium illud apud eos Mechanicos, qui <lb/>mechanica momenta &longs;uarum demon&longs;trationum momentis confirmant; <lb/>quî porro fieri pote&longs;t, vt principium illud admittatur, quod manife&longs;tæ <lb/>experientiæ repugnat? </s>

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

<s><lb/>quis non vidit maiores illas onerarias naues etiam pigro, & tardo motu <lb/>labentes maximum impetum minori occurrenti cymbæ ctiam impri<lb/>mere? </s>

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

<s><lb/>Re&longs;pondeo, plures partes impetus non produci in minore globo, quàm <lb/>&longs;int in maiore; igitur nulla pars e&longs;t impetus minoris globi, quæ &longs;ui <lb/>cau&longs;am &longs;ufficientem non habeat; &longs;ed cum partes impetus maioris globi <lb/>di&longs;tribuantur pluribus partibus &longs;ubiecti, faciunt remi&longs;&longs;um impetum, igi<lb/>tur & tardum; cum &longs;cilicct 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><lb/>Re&longs;pondeo, plures partes impetus non produci in minore globo, quàm <lb/>&longs;int in maiore; igitur nulla pars e&longs;t impetus minoris globi, quæ &longs;ui <lb/>cau&longs;am &longs;ufficientem non habeat; &longs;ed cum partes impetus maioris globi <lb/>di&longs;tribuantur pluribus partibus &longs;ubiecti, faciunt remi&longs;&longs;um impetum, igi<lb/>tur & tardum; 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>1. quid clarius. </s>

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

<s>Ob&longs;eruabis primò, vtrumque globum e&longs;&longs;e eiu&longs;dem materiæ; &longs;i enim <lb/>&longs;int diuer&longs;æ materiæ, &longs;ecùs accidit, quàm diximus; &longs;i v. g. æncus mi<lb/>nor pellatur ab cburneo maiore, maiorem motum hic illi non impri<lb/>met; licèt enim &longs;it maior exten&longs;io eburnci; e&longs;t tamen minus pondus; <lb/>igitur pauciores partes. </s>

<s>Ob&longs;eruabis primò, vtrumque globum e&longs;&longs;e eiu&longs;dem materiæ; &longs;i enim <lb/>&longs;int diuer&longs;æ materiæ, &longs;ecùs accidit, quàm diximus; &longs;i v. g. æneus mi<lb/>nor pellatur ab eburneo maiore, maiorem motum hic illi non impri<lb/>met; licèt enim &longs;it maior exten&longs;io eburnei; e&longs;t tamen minus pondus; <lb/>igitur pauciores partes. </s>

<s>Secundò, cos globos accipiendos e&longs;&longs;e, quorum partes, vel non auo<lb/>lent ab ictu, vel non comprimantur; comprimuntur in plumbeis, <lb/>æncis, & auolant in vitreis; cum enim &longs;it compre&longs;&longs;io, vel partium di<lb/>ui&longs;io, de&longs;truitur multùm impetus. </s>

<s>Secundò, eos globos accipiendos e&longs;&longs;e, quorum partes, vel non auo<lb/>lent ab ictu, vel non comprimantur; 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>

<s>Tcrtiò reiice commentum illorum, qui dicunt corpus illud e&longs;&longs;e ma<lb/>joris vclocitatis capax, quod plures habet partes materiæ &longs;ub eadem <lb/>quantitate; nam &longs;uppo&longs;ita eadem re&longs;i&longs;tentiæ ratione, omne corpus e&longs;t <lb/>capax illius vclocitatis, cuius alind e&longs;t capax; cum nullus &longs;it motus, quo <lb/>non po&longs;&longs;it dari velocior, & tardior, vt dicemus infrà; immò &longs;it glo<lb/>bus plumbeus 12. librarum, &longs;it eburncus eiu&longs;dem diametri 2. librarum, <lb/>v. g. haud dubiè eadem potentia producet inten&longs;iorem impetum in <lb/>cburnco, vt patet experientia, & ratio con&longs;tat ex dictis; qua&longs;i verò &longs;it <lb/>aliqua materiæ inertia, quæ motum re&longs;puat; licèt fortè maior &longs;it pro<lb/>portio re&longs;i&longs;tentiæ medij comparatz cum globo cburneo, quàm compa<lb/>ratæ cum plumbeo; &longs;ed de re&longs;i&longs;tentia de percu&longs;&longs;ionc, & de &longs;patio age<lb/>mus infra. </s>

<s>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; 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; cum nullus &longs;it motus, quo <lb/>non po&longs;&longs;it dari velocior, & tardior, vt dicemus infrà; immò &longs;it glo<lb/>bus plumbeus 12. librarum, &longs;it eburneus eiu&longs;dem diametri 2. librarum, <lb/>v. g. haud dubiè eadem potentia producet inten&longs;iorem impetum in <lb/>eburneo, vt patet experientia, & ratio con&longs;tat ex dictis; qua&longs;i verò &longs;it <lb/>aliqua materiæ inertia, quæ motum re&longs;puat; 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>

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

<s><emph type="italics"/>Omnis globus, qui in alium, qui mouetur impingitur, dum hie mouetur, vt<lb/>lociùs mouetur eo &c. </s>

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

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

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

<s><emph type="italics"/>Hie impetus neuus preductus miner e&longs;t eo qus preduceretur in codem glob<lb/>immobili<emph.end type="italics"/>: ratio c&longs;t; quia &longs;i &longs;i&longs;tcret, maius e&longs;&longs;et impedimentum, quia <lb/>totum motum impediret, cuius tantùm partem impedit, dum mouctur, <lb/>licèt paulò tardius; igitur minus agit ad cxtra per Th. 49. </s>

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

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

<s><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> Probatur, quia mobile quod præit, <lb/>non impedit motum &longs;ub&longs;equentis; igitur nullum impetum ab co acci <lb/>pit per Th. 48. </s><pb xlink:href="026/01/073.jpg" pagenum="41"/>

<s><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> 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><pb xlink:href="026/01/073.jpg" pagenum="41"/>

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

<s><emph type="italics"/>Hinc paradoxon egregium &longs;i quod aliud; globus percu&longs;&longs;us ab alio eadem <lb/>&longs;emper velocitate mouetur, &longs;iue moueretur in&longs;tanti percu&longs;&longs;ionis, &longs;iue &longs;i<lb/>&longs;teret.<emph.end type="italics"/> v. g. &longs;it globus A quie&longs;cens, cui unprimantur ab alio B 40. gra<lb/>dus velocitatis: id e&longs;t æqualis impetus impetui percutientis, iam verò <lb/>moueatur A, cum 20. grad. vclocitatis, & B, qui mouetur cum 40. <lb/>impingatur, certè cum impediatur tantùm &longs;ubduplum motus, produce<lb/>tur tantùm &longs;ubduplum impetus, id c&longs;t 20. qui &longs;i addantur 20. grad. erunt <lb/>40. quæ omnia con&longs;tant per Th.49.48.&c. </s>

<s><emph type="italics"/>Hinc paradoxon egregium &longs;i quod aliud; globus percu&longs;&longs;us ab alio eadem <lb/>&longs;emper velocitate mouetur, &longs;iue moueretur in&longs;tanti percu&longs;&longs;ionis, &longs;iue &longs;i<lb/>&longs;teret.<emph.end type="italics"/> v. g. &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. 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. erunt <lb/>40. quæ omnia con&longs;tant per Th.49.48.&c. </s>

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<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 2.<emph.end type="center"/></s>

<s>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 co, 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>

<s>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>

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 3.<emph.end type="center"/></s>

<s>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. </s>

<s>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; &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> Supponit primò hæc &longs;ententia mal<lb/>leum e&longs;&longs;e duplum pilæ percu&longs;&longs;æ. </s>

<s>quorum &longs;unt hæc verba; &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> Supponit primò hæc &longs;ententia mal<lb/>leum e&longs;&longs;e duplum pilæ percu&longs;&longs;æ. </s>

<s>Secundò, mallcum 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>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>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 quictem propiùs accedit; mi<lb/>norem verò paulò po&longs;t initium motus, vt con&longs;tat ex dictis, & exip&longs;a ex<lb/>perientia; potc&longs;t quidem in aliquo puncto &longs;ui motus &longs;ecunda vice per<lb/>cuti, in quo &longs;ubtriplum tantùm motum imprimet; hoc e&longs;t eo in&longs;tanti<lb/>quo tantùm ami&longs;it tertiam fui impetus partem; tum deindc in tertia <lb/>percu&longs;&longs;ione pote&longs;t tantùm (1/27) motus partem illi tribuere; co &longs;cilicet in<lb/>&longs;tanti, quo tantùm ami&longs;it (1/27) &longs;ui impetus partem; &longs;ed in alijs cemporis <lb/>punctis longè alia crit impetus producti ratio; Igitur tota hæc progre&longs;<lb/>&longs;io gratis omninò fuit excogitata. </s>

<s>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; mi<lb/>norem verò paulò po&longs;t initium motus, vt con&longs;tat ex dictis, & ex ip&longs;a ex<lb/>perientia; pote&longs;t quidem in aliquo puncto &longs;ui motus &longs;ecunda vice per<lb/>cuti, in quo &longs;ubtriplum tantùm motum imprimet; hoc e&longs;t eo in&longs;tanti<lb/>quo tantùm ami&longs;it tertiam fui impetus partem; tum deinde in tertia <lb/>percu&longs;&longs;ione pote&longs;t tantùm (1/27) motus partem illi tribuere; eo &longs;cilicet in<lb/>&longs;tanti, quo tantùm ami&longs;it (1/27) &longs;ui impetus partem; &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>

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 4.<emph.end type="center"/></s>

<s>Hinc ctiam po&longs;t &longs;ecundam percu&longs;&longs;ioncm æquale &longs;patium conficier al<lb/>teri, quod iam confecit po&longs;t primam æqualibus temporibus; igitur æqua<lb/>lis e&longs;t velocitas vtriu&longs;que motus; 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><pb xlink:href="026/01/074.jpg" pagenum="42"/>

<s>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; igitur æqua<lb/>lis e&longs;t velocitas vtriu&longs;que motus; 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><pb xlink:href="026/01/074.jpg" pagenum="42"/>

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 5.<emph.end type="center"/></s>

<s>Ex dictis ctiam 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; 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>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; 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>Igitur velocitates motuum &longs;unt in ratiòne ponderum <lb/>permutando. </s>

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

<s><emph type="italics"/>Si corpus percu&longs;&longs;um &longs;it oblongum, & percu&longs;&longs;io fiat in centro grauitatis eiu&longs;<lb/>dem corpois; producitur impetus in percu&longs;&longs;io æqualis impetui percutientis<emph.end type="italics"/>; &longs;ed <lb/>opus e&longs;t aliqua figura: Sit corpus AD, parallelipedum; diuidatur æqua<lb/>liter in E ita vt E &longs;it centrum grauitatis; &longs;i percu&longs;&longs;io &longs;iat in E per lineam <lb/>perpendicularem HE, producetur impetus in corpore AD æqualis im<lb/>petui corporis percutientis; 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>

<s><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; producitur impetus in percu&longs;&longs;io æqualis impetui percutientis<emph.end type="italics"/>; &longs;ed <lb/>opus e&longs;t aliqua figura: Sit corpus AD, parallelipedum; diuidatur æqua<lb/>liter in E ita vt E &longs;it centrum grauitatis; &longs;i percu&longs;&longs;io fiatin E per lineam <lb/>perpendicularem HE, producetur impetus in corpore AD æqualis im<lb/>petui corporis percutientis; 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>

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

<s><emph type="italics"/>Si percu&longs;&longs;io fiat in<emph.end type="italics"/> F <emph type="italics"/>per lineam perpendicularem<emph.end type="italics"/> IF, <emph type="italics"/>minus erit impedi<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; &longs;ed hic <lb/>motus e&longs;t facilior quam ille; igitur minus e&longs;t impedimentum; (&longs;uppono <lb/>autem cylindrum BC vtroque modo moueri po&longs;&longs;e ab applicata potentia) <lb/>igitur minùs impetus producitur, &longs;i percu&longs;&longs;io fiat per IF, quàm &longs;i fiat <lb/>per LK: 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 ficri <lb/>debeat. </s>

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

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

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

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

<s><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 quæntùm pote&longs;t.<emph.end type="italics"/> v. g. &longs;it parallelipedum EB; quod <lb/>moueatur motu recto parallclo, lineis CD, HG, &c. </s>

<s><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. g. &longs;it parallelipedum EB; quod <lb/>moueatur motu recto parallelo, lineis CD, HG, &c. </s>

<s>&longs;itque globus in <lb/>D; 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; impedit <lb/>inquam ratione oppo&longs;itionis; 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>

<s>&longs;itque globus in <lb/>D; 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 parallcli<lb/>pedi, quàm parallclip edum motum globi impacti per lineam ID; impedit <lb/>inquam ratione oppo&longs;itionis; 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>

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

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

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

<s><emph type="italics"/>Si corpus percutiens non &longs;it par allelipedum, &longs;ed alterius &longs;iguræ v.g.<emph.end type="italics"/> <emph type="italics"/>trigo<lb/>non,<emph.end type="italics"/> ADE, &longs;itque maioris facilitatis gratia Orthonium; eiu&longs;que motus <lb/>&longs;it parallelus lineis ED, BC: &longs;it autem DA dupla DE; &longs;itque diui&longs;a to<lb/>ta DA æqualiter in C, in C non erit maximus ictus; quia in C non <pb xlink:href="026/01/076.jpg" pagenum="44"/>e&longs;t centrum grauitatis, vt patet; vt autem habeatur centrum impre&longs;&longs;io<lb/>nis; a&longs;&longs;umatur AN media proportionalis inter totam AD, & &longs;ubdu<lb/>plum AC; certè cum triangulum ANO &longs;it &longs;ubduplum totius ADE, <lb/>vt con&longs;tat ex Geometria, & æquale trapezo ND EO; erit impetus in <lb/>vtroque æqualis; igitur in N erit centrum impre&longs;&longs;ionis, vel impetus; vt <lb/>autem habeatur centrum percu&longs;&longs;ionis; in quo &longs;cilicet maximus ictus in<lb/>fligitur, inueniatur centrum grauitatis H, ducaturque KHI parallela <lb/>DE, centrum percu&longs;&longs;ionis erit in I; quippe in I totus impeditur impetus <lb/>grauitatis vtrimque, cum &longs;it in æquilibrio; 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. </s>

<s><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; eiu&longs;que motus <lb/>&longs;it parallelus lineis ED, BC: &longs;it autem DA dupla DE; &longs;itque diui&longs;a to<lb/>ta DA æqualiter in C, in C non erit maximus ictus; quia in C non <pb xlink:href="026/01/076.jpg" pagenum="44"/>e&longs;t centrum grauitatis, vt patet; vt autem habeatur centrum impre&longs;&longs;io<lb/>nis; a&longs;&longs;umatur AN media proportionalis inter totam AD, & &longs;ubdu<lb/>plum AC; certè cum triangulum ANO &longs;it &longs;ubduplum totius ADE, <lb/>vt con&longs;tat ex Geometria, & æquale trapezo ND EO; erit impetus in <lb/>vtroque æqualis; igitur in N erit centrum impre&longs;&longs;ionis, vel impetus; vt <lb/>autem habeatur centrum percu&longs;&longs;ionis; in quo &longs;cilicet maximus ictus in<lb/>fligitur, inueniatur centrum grauitatis H, ducaturque KHI parallela <lb/>DE, centrum percu&longs;&longs;ionis erit in I; quippe in I totus impeditur impetus <lb/>grauitatis vtrimque, cum &longs;it in æquilibrio; 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. </s>

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

<s><emph type="italics"/>Si circa centrum immobile rotetur corpus parallelipedum<emph.end type="italics"/> CA, <emph type="italics"/>diuer&longs;a e&longs;t <lb/>ratio percu&longs;&longs;ionum ab ea, quàm &longs;uprà propo&longs;uimus<emph.end type="italics"/>; moucatur 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; igitur punctum A duplò velociùs mouetur quàm B, vt con&longs;tat; igi<lb/>tur habet duplò maiorem impetum; cum effectum habeat duplò maio<lb/>rem per Ax. 13. n. </s>

<s><emph type="italics"/>Si circa centrum immobile rotetur corpus parallelipedum<emph.end type="italics"/> CA, <emph type="italics"/>diuer&longs;a e&longs;t <lb/>ratio percu&longs;&longs;ionum ab ea, quàm &longs;uprà propo&longs;uimus<emph.end type="italics"/>; 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; igitur punctum A duplò velociùs mouetur quàm B, vt con&longs;tat; igi<lb/>tur habet duplò maiorem impetum; cum effectum habeat duplò maio<lb/>rem per Ax. 13. n. </s>

<s>4. igitur cum totus motus &longs;egmenti AB &longs;it ad to<lb/>tum motum &longs;egmenti BC, vt &longs;patia acqui&longs;ita; certè &longs;patia acqui&longs;ita <lb/>&longs;unt vt arcus; igitur & trapezus BAED, continet 3/4 totius CAE, vt <lb/>con&longs;tat; &longs;unt enim &longs;ectores &longs;imilis in ratione duplicata radiorum; igi<lb/>tur totus motus &longs;egmenti BC &longs;ubquadruplus motus totius CA;, gitur <lb/>& impetus; vt autem habeatur centrum impre&longs;&longs;ionis, vel impetus; &longs;it &longs;e<lb/>ctor CHI, &longs;ubduplus totius CAE quod quomodo fiat, patet ex Geo<lb/>metria; 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: vt autem habeatur percu&longs;&longs;ionis, a&longs;<lb/>&longs;umatur CY dupla YA; Dico punctum Y e&longs;&longs;c 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>

<s>4. igitur cum totus motus &longs;egmenti AB &longs;it ad to<lb/>tum motum &longs;egmenti BC, vt &longs;patia acqui&longs;ita; certè &longs;patia acqui&longs;ita <lb/>&longs;unt vt arcus; igitur & trapezus BAED, continet 3/4 totius CAE, vt <lb/>con&longs;tat; &longs;unt enim &longs;ectores &longs;imilis in ratione duplicata radiorum; igi<lb/>tur totus motus &longs;egmenti BC &longs;ubquadruplus motus totius CA; igitur <lb/>& impetus; vt autem habeatur centrum impre&longs;&longs;ionis, vel impetus; &longs;it &longs;e<lb/>ctor CHI, &longs;ubduplus totius CAE quod quomodo fiat, patet ex Geo<lb/>metria; 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: vt autem habeatur percu&longs;&longs;ionis, a&longs;<lb/>&longs;umatur CY dupla YA; </s>

<s>Dico punctum Y e&longs;&longs;e centrum percu&longs;&longs;ionis; <lb/>quia perinde &longs;e habet, atque &longs;i e&longs;&longs;et trianguli cadentis ictus, vt demon<lb/>&longs;trabimus aliàs nunc tantùm indica&longs;&longs;e &longs;ufficiat. </s>

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 1.<emph.end type="center"/></s>

<s>Hinc etiam&longs;oluctur, quod proponunt aliqui; &longs;eu potiùs quærunt; <lb/>in quà &longs;cilicet parte maiorem ictum infligat en&longs;is; &longs;i enim &longs;it ciu&longs;dem <lb/>cra&longs;&longs;itici 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>

<s>Hinc etiam &longs;oluetur, quod proponunt aliqui; &longs;eu potiùs quærunt; <lb/>in quà &longs;cilicet parte maiorem ictum infligat en&longs;is; &longs;i enim &longs;it eiu&longs;dem <lb/>cra&longs;&longs;itiei in omnibus &longs;uis partibus, idem dicendum e&longs;t quod de cylin<lb/>dro CA; &longs;i verò in mucronem de&longs;inat, inueniemus etiam centrum <lb/>percu&longs;&longs;ionis. </s>

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 2.<emph.end type="center"/></s>

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

<s>Hîc ob&longs;erua nouum di&longs;crimen, quod intercedit inter impetum, & <lb/>alias qualitates; 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 cumdem &longs;emper effectum pro<lb/>ducit; 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>

<s>Hîc ob&longs;erua nouum di&longs;crimen, quod intercedit inter impetum, & <lb/>alias qualitates; 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; 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>

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

<s><emph type="italics"/>Impetus &longs;imilis, id e&longs;t, ad eamdem lineam determinatus, & æqualis in in<lb/>ten&longs;ione, non pote&longs;t intendere alium &longs;imilem<emph.end type="italics"/>; Probatur, quia agit tantùm ad <lb/>extra, vt tollat impedimentum per Th. 44. &longs;ed eorum mobilium, quæ <lb/>ver&longs;us eamdem partem pari velocitate mouentur, neutrum impedit al<lb/>terius motum, vt con&longs;tat; igitur impetus &longs;imilis, &c. </s>

<s><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"/>; 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>

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

<s>Ob&longs;erua de impetu &longs;imili id tantùm dici; &longs;imili inquam id e&longs;t non <lb/>modò eiu&longs;dem inten&longs;ionis; &longs;ed etiam eiu&longs;dem lineæ: &longs;i enim alterum <lb/>de&longs;it, haud dubiè &longs;imilis impetus non e&longs;t; &longs;ic impetus quatuor grad. in<lb/>tendere pote&longs;t impetum duorum graduum; licèt vterque ad eamdem li<lb/>neam &longs;it determinatus; &longs;i verò ad diuer&longs;as lineas determinentur; etiam <lb/>impetus vt duo pote&longs;t intendere impetum vt quatuor. </s>

<s>Ob&longs;erua de impetu &longs;imili id tantùm dici; &longs;imili inquam id e&longs;t non <lb/>modò eiu&longs;dem inten&longs;ionis; &longs;ed etiam eiu&longs;dem lineæ: &longs;i enim alterum <lb/>de&longs;it, haud dubiè &longs;imilis impetus non e&longs;t; &longs;ic impetus quatuor grad. in<lb/>tendere pote&longs;t impetum duorum graduum; licèt vterque ad <expan abbr="eãdem">eandem</expan> li<lb/>neam &longs;it determinatus; &longs;i verò ad diuer&longs;as lineas determinentur; etiam <lb/>impetus vt duo pote&longs;t intendere impetum vt quatuor. </s>

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

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

<s><emph type="italics"/>Exten&longs;io impetus respondet extentioni &longs;ui &longs;ubiecti, &longs;cilicet mobilis<emph.end type="italics"/>; cum <lb/>enim extra &longs;ubjectum e&longs;&longs;e non po&longs;&longs;it, cum &longs;it qualitas; 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>

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

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

<s><emph type="italics"/>Datur impetus altero impetu perfectior &longs;ecundum entitatem<emph.end type="italics"/>; dixi &longs;ecun<lb/>dum entitatem; quia iam dictum e&longs;t &longs;uprà dari perfectiorem &longs;ecundum <lb/>inten&longs;ionem; huius Theorematis veritas mihi maximè demon&longs;tranda <lb/>e&longs;t, ex quo tàm multa infrà deducemus; &longs;ic autem probamus; 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; 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 fotmali poti&longs;&longs;imum <lb/>dicidebet; præterea-datur aliquod pondus, quod data potentia &longs;ine me<lb/>chanico organo moucre non pote&longs;t, licèt cum organo facilè moueat; hæc <lb/>hypothe&longs;is certa e&longs;t; 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. <lb/>33. cum verò non mouet, non producit tot partes impetus vt con&longs;tat ex <lb/>dictis; igitur producit plures cnm organo in mobili, quàm &longs;ine organo; <lb/>igitur imperfectiores, quod demon&longs;tro: &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; <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; quia pondus quod non pote&longs;t attolli in B, attollitur in <lb/>E, vel in F, vt patet ex dictis; præterea punctum F mouetur tardius, quàm <lb/>B; quia motus &longs;unt vt arcus, atcus vt &longs;emidiametri, hæ demum vt AF, <lb/>ad AB; igitur motus puncti F, e&longs;t tardior, vel imperfectior; 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 entiratis, <lb/>quæ imperfectior e&longs;t; igitur datur impetus altero impetu imperfectior. </s>

<s><emph type="italics"/>Datur impetus altero impetu perfectior &longs;ecundum entitatem<emph.end type="italics"/>; dixi &longs;ecun<lb/>dum entitatem; quia iam dictum e&longs;t &longs;uprà dari perfectiorem &longs;ecundum <lb/>inten&longs;ionem; huius Theorematis veritas mihi maximè demon&longs;tranda <lb/>e&longs;t, ex quo tàm multa infrà deducemus; &longs;ic autem probamus; 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; 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; præterea datur aliquod pondus, quod data potentia &longs;ine me<lb/>chanico organo mouere non pote&longs;t, licèt cum organo facilè moueat; hæc <lb/>hypothe&longs;is certa e&longs;t; 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. <lb/>33. cum verò non mouet, non producit tot partes impetus vt con&longs;tat ex <lb/>dictis; igitur producit plures cum organo in mobili, quàm &longs;ine organo; <lb/>igitur imperfectiores, quod demon&longs;tro: &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; <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; quia pondus quod non pote&longs;t attolli in B, attollitur in <lb/>E, vel in F, vt patet ex dictis; præterea punctum F mouetur tardius, quàm <lb/>B; quia motus &longs;unt vt arcus, arcus vt &longs;emidiametri, hæ demum vt AF, <lb/>ad AB; igitur motus puncti F, e&longs;t tardior, vel imperfectior; 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>

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<s>Tertiò, &longs;i dato quocunque motu pote&longs;t dari tardior: igitur dato quo<lb/>cunque impetu pote&longs;t dari imperfectior. </s>

<s>Quartò, &longs;i daretur punctum impetus in inten&longs;ione: non po&longs;&longs;et dari <lb/>motus tatdior in infinitum &longs;ine diuer&longs;is gradibus perfectionis. </s>

<s>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>

<s>Quintò, &longs;ine hac diuer&longs;a impetus perfectione nonp o&longs;&longs;et explicari <lb/>productio continua impetus, quæ &longs;it temporibus inæqualibus, neque de<lb/>&longs;tructio ciu&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>

<s>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>

<s>Sextò, Denique ratio propo&longs;ita rem i&longs;tam euincit; cum enim in motu <lb/>vectis plures partes producantur ver&longs;us centrum, &longs;cilicet, in maiori pon<lb/>dere, quod attollitur; & cum hæ habeant motum tardiorem, &longs;equitur ne<lb/>ce&longs;&longs;ariò e&longs;&longs;e imperfectiores. </s>

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<s><emph type="italics"/>Non pote&longs;t explicari tarditas motus &longs;ine diuer&longs;a perfectione impetus, per <lb/>pauciores &longs;cilicet eiu&longs;dem impetus partes.<emph.end type="italics"/></s><s> Primò, quia cum retardari po&longs;&longs;it <lb/>hic motus, & de&longs;trui &longs;ucce&longs;&longs;inè hic impetus; cumque in&longs;tantia motus <lb/>velocioris &longs;int breuiora; certè initio motus, breuiori &longs;cilicet tempore <lb/>imperfectior impetus de&longs;trui tantùm pote&longs;t; cum enim æqualis æquali<lb/>bus temporibus; certè inæqualis inæqualibus. </s>

<s>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 ctiam in commune e&longs;t calori, lumini, &c. </s>

<s>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>

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

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<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 1.<emph.end type="center"/></s>

<s>Hinc difficiliùs attollitur pertica CA ex puncto C motu circulari, <lb/>quàm ex puncto B motu recto; quia &longs;cilicet, cum motu recto ex puncto B <lb/>attollitur, omnes partes mouentur motu æquali; igitur impetus æqualiter <lb/>omnibus di&longs;tribuitur; igitur modò producantur tot partes impetus, quot <lb/>&longs;unt partes in mobili; haud dubiè attolletur: at verò, cum motu circulari <lb/>ex puncto C attollitur, omnes partcs inæquali motu attolluntur; igitur <lb/>plures &longs;unt nece&longs;&longs;ariæ, vt attollatur motu circulari; igitur difficiliùs iuxta <lb/>experimentum; adde quod cum applicatur potentia in C, punctum A, <lb/>maius momentum habet, de quo aùàs. </s>

<s>Hinc difficiliùs attollitur pertica CA ex puncto C motu circulari, <lb/>quàm ex puncto B motu recto; quia &longs;cilicet, cum motu recto ex puncto B <lb/>attollitur, omnes partes mouentur motu æquali; igitur impetus æqualiter <lb/>omnibus di&longs;tribuitur; igitur modò producantur tot partes impetus, quot <lb/>&longs;unt partes in mobili; haud dubiè attolletur: at verò, cum motu circulari <lb/>ex puncto C attollitur, omnes partes inæquali motu attolluntur; igitur <lb/>plures &longs;unt nece&longs;&longs;ariæ, vt attollatur motu circulari; igitur difficiliùs iuxta <lb/>experimentum; adde quod cum applicatur potentia in C, punctum A, <lb/>maius momentum habet, de quo aùàs. </s>

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 2.<emph.end type="center"/></s>

<s>Hinc ratio cuidens illius experimenti, quo manife&longs;tè con&longs;tat perti-<pb xlink:href="026/01/080.jpg" pagenum="48"/>cam CA, ex A, facilius attolli motu recto, quàm circulari; cum &longs;ci<lb/>licct cuiu&longs;dam qua&longs;i reflexionis opera eodem tempore vtraque extremi<lb/>tas æquali motu attollitur. </s>

<s>Hinc ratio euidens illius experimenti, quo manife&longs;tè con&longs;tat perti-<pb xlink:href="026/01/080.jpg" pagenum="48"/>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>

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 81.<emph.end type="center"/></s>

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<s><emph type="italics"/>Si verò applicetur potentia extra centrum vectis v. g. in<emph.end type="italics"/> F, <emph type="italics"/>po&longs;ito centro in<emph.end type="italics"/><lb/>A, <emph type="italics"/>producitur impetus minor ab<emph.end type="italics"/> F, <emph type="italics"/>ver&longs;us<emph.end type="italics"/> A; <emph type="italics"/>ab 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/>turenim ex. </s>

<s>gr. vnus tantùm gradus in F, & in E, productus) at verò <lb/>producuntur alij imperfectiones. </s>

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<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 84.<emph.end type="center"/></s>

<s><emph type="italics"/>Impetus perfectus producere pote&longs;t imperfectum<emph.end type="italics"/>; patet in vecte; 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 ciu&longs;dem perfectionis cum impetu producto in ip&longs;a ve<lb/>ctis extremitate, ex qua pendet; cum &longs;it vrriu&longs;que æqualis motus; &longs;ed <lb/>ver&longs;us centrum ciu&longs;dem vectis producitur impetus imperfectior per <lb/>Th.82. igitur imperfectus à perfecto producitur. </s>

<s><emph type="italics"/>Impetus perfectus producere pote&longs;t imperfectum<emph.end type="italics"/>; patet in vecte; 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; 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>

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 85.<emph.end type="center"/></s>

<s><emph type="italics"/>Impetus perfectus nunquam producitur ab imperfecto, per Ax.<emph.end type="italics"/> 3. <emph type="italics"/>num.<emph.end type="italics"/> 2. <lb/>adde quod nunquam effectus perfectio &longs;uperat perfectionem cau&longs;æ; dixi <lb/>perfectum ab imperfecto; &longs;cilicet &longs;i con&longs;ideretur perfectio ratione en-<pb xlink:href="026/01/081.jpg" pagenum="49"/>titatis; cum reuerâ, vt dictum e&longs;t &longs;uprà, remi&longs;&longs;us producat inten&longs;um, <lb/>quod in vecte clari&longs;&longs;unum e&longs;t; 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: Pro quo, ob&longs;eruabis <lb/>impetum imperfectum cum alio perfecto actione communi agentem <lb/>po&longs;&longs;e concurrere ad producendum perfectum, vt patet; non tamen in <lb/>ratione cau&longs;æ totalis: &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>

<s><emph type="italics"/>Impetus perfectus nunquam producitur ab imperfecto, per Ax.<emph.end type="italics"/> 3. <emph type="italics"/>num.<emph.end type="italics"/> 2. <lb/>adde quod nunquam effectus perfectio &longs;uperat perfectionem cau&longs;æ; dixi <lb/>perfectum ab imperfecto; &longs;cilicet &longs;i con&longs;ideretur perfectio ratione en-<pb xlink:href="026/01/081.jpg" pagenum="49"/>titatis; cum 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; 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: Pro quo, ob&longs;eruabis <lb/>impetum imperfectum cum alio perfecto actione communi agentem <lb/>po&longs;&longs;e concurrere ad producendum perfectum, vt patet; non tamen in <lb/>ratione cau&longs;æ totalis: &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>

<s>Ob&longs;eruabis &longs;ecundò præclarum naturæ in&longs;titutum, quo factum e&longs;t; <lb/>vt cum vires hominum maiora pondera leuare non po&longs;&longs;int, &longs;i &longs;eor&longs;un <lb/>con&longs;iderentur; cum organis tamen mechanicis conjunctæ nullum pon<lb/>dus quantumuis immane leuare non po&longs;&longs;int; 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>

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<s>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>

<s>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; &longs;i primum, erit primus tantùm gradus maximæ perfectio<lb/>nis; ita vt perfectiorem producere non po&longs;&longs;it, ad quem e&longs;t determinata <lb/>potentia; imperfectiorem tamen impetu innato, de quo infrà; &longs;i verò <lb/>&longs;ecundum, producet in &longs;ingulis paitibus eumdem gradum perfecti&longs;&longs;i<lb/>mum cum aliis pluribus, vel paucioribus heterogeneis, & imperfectio<lb/>ribus. </s>

<s>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; &longs;i primum, erit primus tantùm gradus maximæ perfectio<lb/>nis; ita vt perfectiorem producere non po&longs;&longs;it, ad quem e&longs;t determinata <lb/>potentia; imperfectiorem tamen impetu innato, de quo infrà; &longs;i verò <lb/>&longs;ecundum, producet in &longs;ingulis partibus <expan abbr="e&utilde;dem">eundem</expan> gradum perfecti&longs;&longs;i<lb/>mum cum aliis pluribus, vel paucioribus heterogeneis, & imperfectio<lb/>ribus. </s>

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 86.<emph.end type="center"/></s>

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<s><emph type="italics"/>Illa progatio non fit per motum localem, ita vt pars impetus producta in <lb/>prima parte &longs;ubiecti tran&longs;eat ad &longs;ecundam,<emph.end type="italics"/> patet; quia cum impetus &longs;it ac<lb/>cidens per Th. 8. de &longs;ubiecto in &longs;ubiectum tran&longs;ire non pote&longs;t per deff. </s>

<s><lb/>accidentis; de qua in Metaphy&longs;icâ; 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; cum ip&longs;is etiam oculis <lb/>qua&longs;i ocrnatur; cum enim percutis corpus oblongum AE, & cadit ictus <lb/>in extremitatem A, corpus ip&longs;um totum &longs;unul 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>

<s><lb/>accidentis; de qua in Metaphy&longs;icâ; 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; cum ip&longs;is etiam oculis <lb/>qua&longs;i cernatur; 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>

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

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<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 96.<emph.end type="center"/></s>

<s><emph type="italics"/>Cum duo corpora &longs;e&longs;e mutuò tangunt, impetus in vtroque propagatur<emph.end type="italics"/> &longs;int <lb/>v. g. 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: <lb/>probatur primò, quia &longs;e habent per modum vnius, vt patet ex re&longs;i&longs;ten<lb/>&longs;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><emph type="italics"/>Cum duo corpora &longs;e&longs;e mutuò tangunt, impetus in vtroque propagatur<emph.end type="italics"/> &longs;int <lb/>v. g. 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: <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>Tertiò, Ratio à priori e&longs;t; quia idco <lb/>producitur, & propagatur impetus in toto A; quia vna pars non pote&longs;t <lb/>moueri &longs;ine alia per Th. 33. &longs;ed non pote&longs;t A moueri ni&longs;i moucatur B; <lb/>igitur in vtroque &longs;imul, & æqualiter propagatur impetus. </s>

<s>Tertiò, Ratio à priori e&longs;t; quia ideo <lb/>producitur, & propagatur impetus in toto A; quia vna pars non pote&longs;t <lb/>moueri &longs;ine alia per Th. 33. &longs;ed non pote&longs;t A moueri ni&longs;i moueatur B; <lb/>igitur in vtroque &longs;imul, & æqualiter propagatur impetus. </s>

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 1.<emph.end type="center"/></s>

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<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 3.<emph.end type="center"/></s>

<s>Hinc percu&longs;&longs;io vel ictus globi B, cui alter A à tergo immediatè in<lb/>&longs;t&longs;tit maior e&longs;t. </s>

<s>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>

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 4.<emph.end type="center"/></s>

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<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 98.<emph.end type="center"/></s>

<s><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"/>; &longs;int enim punctum B, & pnnctum A: ita &longs;e habet inten&longs;io <lb/>impetus puncti A ad inten&longs;ionem impetus puncti B, vt di&longs;tantia AC <lb/>ad BC. Probatur, quia cum impetus &longs;int vt motus, motus vt &longs;patia, &longs;patia <lb/>verò &longs;int arcus AE. BD; arcus &longs;unt, vt &longs;emidiametri AC, BC; igitur vt <lb/>di&longs;tantiæ quòd erat demon&longs;trandum. </s>

<s><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"/>; &longs;int enim punctum B, & punctum A: ita &longs;e habet inten&longs;io <lb/>impetus puncti A ad inten&longs;ionem impetus puncti B, vt di&longs;tantia AC <lb/>ad BC. Probatur, quia cum impetus &longs;int vt motus, motus vt &longs;patia, &longs;patia <lb/>verò &longs;int arcus AE. BD; arcus &longs;unt, vt &longs;emidiametri AC, BC; igitur vt <lb/>di&longs;tantiæ quòd erat demon&longs;trandum. </s>

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 1.<emph.end type="center"/></s>

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<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 100.<emph.end type="center"/></s>

<s><emph type="italics"/>Impetus, qui producitur ver&longs;us centrum vectis in pondere, licèt cre&longs;cat nu<lb/>mero, decre&longs;cit tamen in perfectione.<emph.end type="italics"/></s><s> Probatur per Th.81. ex motu imper<lb/>ctiore, cui re&longs;pondet impetus imperfectior per Ax. 17.num.4. non ratio<lb/>ne numeri, qui maior e&longs;t per Th.99. igitur ratione entitatis, &longs;eu perfe<lb/>ctionis entitatiuæ. </s>

<s><emph type="italics"/>Impetus, qui producitur ver&longs;us centrum vectis in pondere, licèt cre&longs;cat nu<lb/>mero, decre&longs;cit tamen in perfectione.<emph.end type="italics"/></s><s> Probatur per Th.81. ex motu imper<lb/>fectiore, cui re&longs;pondet impetus imperfectior per Ax. 17.num.4. non ratio<lb/>ne numeri, qui maior e&longs;t per Th.99. igitur ratione entitatis, &longs;eu perfe<lb/>ctionis entitatiuæ. </s>

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 101.<emph.end type="center"/></s>

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<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 106.<emph.end type="center"/></s>

<s><emph type="italics"/>Non producuntur plures partes impetus in vecte ver&longs;us centrum, id est, non <lb/>&longs;unt plures in punclo vectis propiùs ad centrum accedente, quàm in co; quod <lb/>longiùs distat:<emph.end type="italics"/> Probatur primò, quia fru&longs;trà e&longs;&longs;ent plures. </s>

<s><emph type="italics"/>Non producuntur plures partes impetus in vecte ver&longs;us centrum, id est, non <lb/>&longs;unt plures in puncto vectis propiùs ad centrum accedente, quàm in co; quod <lb/>longiùs distat:<emph.end type="italics"/> Probatur primò, quia fru&longs;trà e&longs;&longs;ent plures. </s>

<s>Secundò, cur <lb/>potiùs in vna proportione, quàm in alia? </s>

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<s>Primò producentur in co partes 8. <lb/>impetus perfectionis &longs;ubquadruplæ; &longs;i comparentur cum partibus A, <lb/>tum producentur 16. quæ æquiualent 4 A; igitur 24. at verò in A pro<lb/>ducentur primò 4. tum deinde 2. quæ æquiualent 8. productis in B; igitur <lb/>6. igitur pondus, quod leuari pote&longs;t in B, e&longs;t ad pondus, quod leuari pote&longs;t <lb/>in A, vt 24. ad 6.id e&longs;t, in ratione quadrupla quod omninò fal&longs;um e&longs;t. </s>

<s>Primò producentur in eo partes 8. <lb/>impetus perfectionis &longs;ubquadruplæ; &longs;i comparentur cum partibus A, <lb/>tum producentur 16. quæ æquiualent 4 A; igitur 24. at verò in A pro<lb/>ducentur primò 4. tum deinde 2. quæ æquiualent 8. productis in B; igitur <lb/>6. igitur pondus, quod leuari pote&longs;t in B, e&longs;t ad pondus, quod leuari pote&longs;t <lb/>in A, vt 24. ad 6.id e&longs;t, in ratione quadrupla quod omninò fal&longs;um e&longs;t. </s>

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 108.<emph.end type="center"/></s>

<s><emph type="italics"/>Iam facilè explicatur ex dictis, quomodo, & cuius rationis pondera attol<lb/>lantur ex diuer&longs;is punctis vectis<emph.end type="italics"/>; &longs;it enim idem vectis AC, & producan<lb/>tur.v.g. </s>

<s>in &longs;ingulis punctis vectis &longs;ingula puncta impetus, &longs;ed diuer&longs;æ <lb/>perfectionis; haud dubiè plures partes impetus imperfecti po&longs;&longs;unt face<lb/>re impetum æqualem in perfectione alteri, qui con&longs;tat paucioribus, &longs;ed <lb/>perfectioribus; igitur cum impetus B &longs;it imperfectior duplò quàm im<lb/>petus in A, duplò plures partes impetus producentur in B, quàm in A, er<lb/>go duplò maius pondus moucbitur; atque ita deinceps; eum enim ap<lb/>ponitur pondus in B, producuntur in eo partes impetus omnes eiu&longs;dem <lb/>perfectionis; quæ &longs;cilicet re&longs;pondet B, id e&longs;t, quæ e&longs;t &longs;ubdupla perfectio<lb/>nis impetus A; igitur plures partes producuntur, quàm &longs;i e&longs;&longs;ent perfe<lb/>ctionis A; &longs;ed pauciores quàm &longs;i e&longs;&longs;ent perfectionis O, quæ minor e&longs;t; <lb/>quippe eadem potentia, &longs;eu cau&longs;a, quæ agit quantum pote&longs;t (quod &longs;up<lb/>pono modò) producit æqualem effectum in perfectione, per Ax. 13. n. </s>

<s>in &longs;ingulis punctis vectis &longs;ingula puncta impetus, &longs;ed diuer&longs;æ <lb/>perfectionis; haud dubiè plures partes impetus imperfecti po&longs;&longs;unt face<lb/>re impetum æqualem in perfectione alteri, qui con&longs;tat paucioribus, &longs;ed <lb/>perfectioribus; igitur cum impetus B &longs;it imperfectior duplò quàm im<lb/>petus in A, duplò plures partes impetus producentur in B, quàm in A, er<lb/>go duplò maius pondus mouebitur; atque ita deinceps; eum enim ap<lb/>ponitur pondus in B, producuntur in eo partes impetus omnes eiu&longs;dem <lb/>perfectionis; quæ &longs;cilicet re&longs;pondet B, id e&longs;t, quæ e&longs;t &longs;ubdupla perfectio<lb/>nis impetus A; igitur plures partes producuntur, quàm &longs;i e&longs;&longs;ent perfe<lb/>ctionis A; &longs;ed pauciores quàm &longs;i e&longs;&longs;ent perfectionis O, quæ minor e&longs;t; <lb/>quippe eadem potentia, &longs;eu cau&longs;a, quæ agit quantum pote&longs;t (quod &longs;up<lb/>pono modò) producit æqualem effectum in perfectione, per Ax. 13. n. </s>

<s><lb/>4. &longs;ed æqualis perfectio pote&longs;t con&longs;tare pluribus, vel paucioribus parti<lb/>bus perfectionis, nam 4. pattes perfectionis vt 4. faciunt æqualem effe<lb/>ctum alteri qui con&longs;tat 8. partibus perfectionis vt 2. quod certum e&longs;t; &longs;ed <lb/>de his plura aliàs. </s>

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 109.<emph.end type="center"/></s>

<s><emph type="italics"/>Perfectio decre&longs;cit ver&longs;us centrum iuxta diuer&longs;am rationem longitudinum <lb/>vectis, &longs;eu distantiarum.<emph.end type="italics"/> v.g.&longs;it idem vectis AC, ita decre&longs;cit ab A ver&longs;us <lb/>centrum C; vt impetus puncti B &longs;it &longs;ubduplus in perfectione, puncti R <lb/>fubtriplus: iam verò &longs;it vectis &longs;ubduplus prioris BC, &longs;ectus bifariam in <lb/>Z; &longs;i impetus productus in B, qu&ecedil; e&longs;t extremitas minoris vectis B &longs;it æqua<lb/>lis perfectionis cum impetu producto in A (& reuera &longs;unt æquales) &longs;i <lb/>æquali æmpore percurrant arcus æquales, &longs;cilicet AV, & BD) certè im-<pb xlink:href="026/01/091.jpg" pagenum="59"/>pertus productus in Z e&longs;t æqualis producto in B, cum B pertinet ad ma<lb/>iorem vectem; quia vt AC totus maior vectis e&longs;t ad BC ita BC ad <lb/>ZC: igitur decre&longs;cit perfectio versùs centrum iuxta rationem longi<lb/>tudinum. </s>

<s><emph type="italics"/>Perfectio decre&longs;cit ver&longs;us centrum iuxta diuer&longs;am rationem longitudinum <lb/>vectis, &longs;eu distantiarum.<emph.end type="italics"/> v.g.&longs;it idem vectis AC, ita decre&longs;cit ab A ver&longs;us <lb/>centrum C; vt impetus puncti B &longs;it &longs;ubduplus in perfectione, puncti R <lb/>&longs;ubtriplus: iam verò &longs;it vectis &longs;ubduplus prioris BC, &longs;ectus bifariam in <lb/>Z; &longs;i impetus productus in B, qu&ecedil; e&longs;t extremitas minoris vectis B &longs;it æqua<lb/>lis perfectionis cum impetu producto in A (& reuera &longs;unt æquales) &longs;i <lb/>æquali tempore percurrant arcus æquales, &longs;cilicet AV, & BD) certè im-<pb xlink:href="026/01/091.jpg" pagenum="59"/>petus productus in Z e&longs;t æqualis producto in B, cum B pertinet ad ma<lb/>iorem vectem; quia vt AC totus maior vectis e&longs;t ad BC ita BC ad <lb/>ZC: igitur decre&longs;cit perfectio versùs centrum iuxta rationem longi<lb/>tudinum. </s>

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 110.<emph.end type="center"/></s>

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<s>Ob&longs;erua tamen quacumque data potentia po&longs;&longs;e dari minorem; quia <lb/>quocumque dato motu, etiam recto, pote&longs;t dari tardior; igitur quocum<lb/>que impetu imperfectior; igitur quando appellaui potentiam minimam; <lb/>intellige illam quæ comparatur cum vnico puncto impetus talis perfe<lb/>ctionis; hæc enim reuera minima e&longs;t illarum omnium, quæ po&longs;&longs;unt pro<lb/>ducere impetum talis perfectionis, &longs;i verò comparetur cum impetu im<lb/>perfectiore, haud dubiè minima non e&longs;t. </s>

<s>Ob&longs;erua præterea &longs;uppo&longs;itum e&longs;&longs;e hactenus in extremitate vectis &longs;iue <lb/>maioris, &longs;iue minoris, produci impetum ciu&longs;dem perfectionis, ciu&longs;que <lb/>vnicum punctum, &longs;eu partem, vnde potentia quæ applicatur maiori vecti <lb/>conuenit quidem cum ea, quæ applicatur minori in eo, quòd vtraque in <lb/>extremitate &longs;ui vectis producat vnum punctum impetus eiu&longs;dem perfe<lb/>ctionis; differt tamen in eo, quòd illa, quæ applicatur maiori vecti, &longs;it <lb/>maior iuxta rationes prædictas in Theoremate. </s>

<s>Ob&longs;erua præterea &longs;uppo&longs;itum e&longs;&longs;e hactenus in extremitate vectis &longs;iue <lb/>maioris, &longs;iue minoris, produci impetum eiu&longs;dem perfectionis, eiu&longs;que <lb/>vnicum punctum, &longs;eu partem, vnde potentia quæ applicatur maiori vecti <lb/>conuenit quidem cum ea, quæ applicatur minori in eo, quòd vtraque in <lb/>extremitate &longs;ui vectis producat vnum punctum impetus eiu&longs;dem perfe<lb/>ctionis; differt tamen in eo, quòd illa, quæ applicatur maiori vecti, &longs;it <lb/>maior iuxta rationes prædictas in Theoremate. </s>

<s>v. g. illa, quæ applicatur <lb/>vecti. </s>

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<s>2. punctorum e&longs;t ad eam, quæ applicatur vecti trium punctorum, <lb/>&longs;cu partium, vt 1. 1/2 ad 2. & &longs;i vectis &longs;it 4. punctorum ad 2. 1/2; &longs;i 5. ad 3. <lb/>&longs;i 6. ad 3. 1/2; &longs;i 7. ad 4. &longs;i 8. ad 4. 1/2. Vides egregiam progre&longs;&longs;ionem; &longs;it <lb/>enim vectis 2. punctorum AB, in puncto A, quod e&longs;t extremitas, produ<lb/>catur punctum impetus datæ perfectionis, in B producetur aliud, cuius <lb/>perfectio e&longs;t &longs;ubdupla prioris per Th. 109. igitur caracter, &longs;eu momen<lb/>tum totius impetus e&longs;t 1. 1/2. &longs;it porrò vectis 4. punctorum CDEF, in <lb/>C, quod e&longs;t extremitas; producatur vnum punctum impetus ciu&longs;dem <lb/>perfectionis cum eo, quod productum e&longs;t in A; certè in D producetur <lb/>aliud cuius perfectio erit ad priorem vt 3.ad 4. per idem Th. &longs;ic autem <lb/>notetur 1/4, in E 2/4, in F 3/4, in C vero 4/4; perfectiones enim &longs;unt vt lon-<pb xlink:href="026/01/092.jpg" pagenum="60"/>gitudines; quæ &longs;i colligantur, habebis characterem totius impetus, 2 1/2: <lb/>igitur totus impetus productus in minore vecte, qui con&longs;tat 2. punctis, <lb/>e&longs;t ad impetum, qui producitur in maiore con&longs;tante 4.punctis, vt 1. 1/2 ad <lb/>2. 1/2; igitur vectis maior maiorem potentiam ad mouendum ip&longs;um ve<lb/>ctem requirit; non certè in de&longs;cen&longs;u; quippe &longs;uo pondere de&longs;cendit, &longs;ed <lb/>in plano horizontali; ni&longs;i enim potentia po&longs;&longs;it mouere vectem; haud <lb/>dubiè nullum pondus vecte mouebit. </s>

<s>2. punctorum e&longs;t ad eam, quæ applicatur vecti trium punctorum, <lb/>&longs;cu partium, vt 1. 1/2 ad 2. & &longs;i vectis &longs;it 4. punctorum ad 2. 1/2; &longs;i 5. ad 3. <lb/>&longs;i 6. ad 3. 1/2; &longs;i 7. ad 4. &longs;i 8. ad 4. 1/2. Vides egregiam progre&longs;&longs;ionem; &longs;it <lb/>enim vectis 2. punctorum AB, in puncto A, quod e&longs;t extremitas, produ<lb/>catur punctum impetus datæ perfectionis, in B producetur aliud, cuius <lb/>perfectio e&longs;t &longs;ubdupla prioris per Th. 109. igitur caracter, &longs;eu momen<lb/>tum totius impetus e&longs;t 1. 1/2. &longs;it porrò vectis 4. punctorum CDEF, in <lb/>C, quod e&longs;t extremitas; producatur vnum punctum impetus eiu&longs;dem <lb/>perfectionis cum eo, quod productum e&longs;t in A; certè in D producetur <lb/>aliud cuius perfectio erit ad priorem vt 3.ad 4. per idem Th. &longs;ic autem <lb/>notetur 1/4, in E 2/4, in F 3/4, in C vero 4/4; perfectiones enim &longs;unt vt lon-<pb xlink:href="026/01/092.jpg" pagenum="60"/>gitudines; quæ &longs;i colligantur, habebis characterem totius impetus, 2 1/2: <lb/>igitur totus impetus productus in minore vecte, qui con&longs;tat 2. punctis, <lb/>e&longs;t ad impetum, qui producitur in maiore con&longs;tante 4.punctis, vt 1. 1/2 ad <lb/>2. 1/2; igitur vectis maior maiorem potentiam ad mouendum ip&longs;um ve<lb/>ctem requirit; non certè in de&longs;cen&longs;u; quippe &longs;uo pondere de&longs;cendit, &longs;ed <lb/>in plano horizontali; ni&longs;i enim potentia po&longs;&longs;it mouere vectem; haud <lb/>dubiè nullum pondus vecte mouebit. </s>

<s>At verò &longs;i potentia &longs;it tantùm dupla minimæ, quæ datum vectem mo<lb/>uere po&longs;&longs;it; haud dubiè dato illo vecte datum ferè quodcumque pondus <lb/>mouere poterit; cum ip&longs;e vectis con&longs;tet ferè infinitis punctis in longi<lb/>tudine, vt patet ex dictis, & con&longs;ideranti patebit. </s>

<s>Ob&longs;eruabis demum in mechanicis nullam ferè haberi rationem pon<lb/>deris ip&longs;ius vectis; parum enim pro nihilo computatur: Ex his tamen <lb/>erui po&longs;&longs;unt veri&longs;&longs;imæ rationes Phy&longs;icæ proportionum vectis AH; &longs;ia<lb/>que A extremitas, H centrum; &longs;itque BH 1/2. CH 1/4, DH 1/2, EH (1/16), <lb/>FH (1/32), GH (1/64) pondus I applicetur in A, & moueatur; certè in B moue<lb/>bitur pondus K duplum I; quia, cum impetus productus in B, &longs;it &longs;ubdu<lb/>plus in perfectione illius, qui producitur in A; vt æqualis producatur in <lb/>B, & in A, debent produci in B duplò plures partes impetus; igitur du<lb/>plò maius pondus mouebit; at verò in C mouebitur pondus L quadru<lb/>plum I, in D octuplum, atque ita deinceps; donec tandem in G mot ea<lb/>tur pondus, quod &longs;it ad I vt 64. ad 1. & cum adhuc po&longs;&longs;int accipi inter <lb/>GH, partes aliquotæ minores, & minores ferè in infinitum, non mirum <lb/>e&longs;t &longs;i pondus maius po&longs;&longs;it adhuc moueri. </s>

<s>Ob&longs;eruabis demum in mechanicis nullam ferè haberi rationem pon<lb/>deris ip&longs;ius vectis; parum enim pro nihilo computatur: Ex his tamen <lb/>erui po&longs;&longs;unt veri&longs;&longs;imæ rationes Phy&longs;icæ proportionum vectis AH; &longs;ia<lb/>que A extremitas, H centrum; &longs;itque BH 1/2. CH 1/4, DH 1/2, EH (1/16), <lb/>FH (1/32), GH (1/64) pondus I applicetur in A, & moueatur; certè in B moue<lb/>bitur pondus K duplum I; quia, cum impetus productus in B, &longs;it &longs;ubdu<lb/>plus in perfectione illius, qui producitur in A; vt æqualis producatur in <lb/>B, & in A, debent produci in B duplò plures partes impetus; igitur du<lb/>plò maius pondus mouebit; at verò in C mouebitur pondus L quadru<lb/>plum I, in D octuplum, atque ita deinceps; donec tandem in G mouea<lb/>tur pondus, quod &longs;it ad I vt 64. ad 1. & cum adhuc po&longs;&longs;int accipi inter <lb/>GH, partes aliquotæ minores, & minores ferè in infinitum, non mirum <lb/>e&longs;t &longs;i pondus maius po&longs;&longs;it adhuc moueri. </s>

<s>Ob&longs;eruabis etiam in omni vecte ab&longs;trahendo ab eius pondere, & ap<lb/>plicata eadem potentia, hoc e&longs;&longs;e commune; vt po&longs;&longs;it quodcumque pon<lb/>dus attolli, licèt difficiliùs in minore; quia hic non pote&longs;t in tam mul<lb/>tas partes aliquotas &longs;en&longs;ibiliter diuidi, in medio tamen vecte duplum <lb/>femper pondus mouetur; &longs;iue ip&longs;e vectis &longs;it maior, &longs;iue minor. </s>

<s>Ob&longs;eruabis etiam in omni vecte ab&longs;trahendo ab eius pondere, & ap<lb/>plicata eadem potentia, hoc e&longs;&longs;e commune; vt po&longs;&longs;it quodcumque pon<lb/>dus attolli, licèt difficiliùs in minore; quia hic non pote&longs;t in tam mul<lb/>tas partes aliquotas &longs;en&longs;ibiliter diuidi, in medio tamen vecte duplum <lb/>&longs;emper pondus mouetur; &longs;iue ip&longs;e vectis &longs;it maior, &longs;iue minor. </s>

<s>Ob&longs;eruabis deinde, &longs;i centrum vectis non &longs;it in altera extremitate, <lb/>&longs;ed. </s>

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<s><emph type="italics"/>Potentia verò motrix determinatur vel à &longs;uo fine intrin&longs;eco, vel potius ab <lb/>ip&longs;a &longs;ua natura<emph.end type="italics"/>; &longs;ic grauitas &longs;eu potentia motrix grauium determinata <lb/>e&longs;t ad motum deor&longs;um perpendicularem, dum in medio libero corpus <lb/>graue mouetur; vel à plano inclinato; pro cuius diuer&longs;a inclinatione <lb/>diuer&longs;a e&longs;t linea motus deor&longs;um; vel ab ip&longs;a via, &longs;eu exitu patefacto; <lb/>&longs;ic potentia motrix compre&longs;&longs;orum &longs;uas vires exerit, & mobile ip&longs;um <lb/>agit, quâ patet viâ, &longs;ur&longs;um, deor&longs;um &c. </s>

<s>vel ab appetitu &longs;eu libero, &longs;eu <lb/>&longs;en&longs;itiuo; &longs;ic potentia progre&longs;&longs;iua animantium cò corpus agit, quò iu<lb/>bet appetitus, vel ab aliqua affectione intrin&longs;eca intrin&longs;ecùs vel extrin<lb/>&longs;ecùs adueniente; &longs;ic dilatatur pupilla, vel contrahitur pro diuer&longs;a lu<lb/>minis appul&longs;i vi, vel obiecti di&longs;tantia: Huc reuoca motus illos natura<lb/>les, qui animalibus competunt v. g. tu&longs;&longs;is, &longs;ingultus, &longs;ternuationis, &c. </s>

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<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 120.<emph.end type="center"/></s>

<s><emph type="italics"/>Corpus proiectum in aliud ita illud impellit, vt determinet lineam motus <lb/>ratione puncti contactus<emph.end type="italics"/>; Sit enim, ne mnltiplicemus figuras, globus, <lb/>cuius linea directionis &longs;it DC, punctum contactus C, ita globus A im<lb/>pellet globum B, vt linea motus, ad quam determinatur, &longs;it CB, id e&longs;t <lb/>ducta à puncto contactus ad centrum globi impul&longs;i; &longs;it etiam globus <lb/>P impactus in globum A punctum contactus &longs;it D, linea motus, ad <lb/>quam determinatur, e&longs;t DA, quæ &longs;cilicet à puncto contactus ducitur <lb/>per centrum grauitatis corporis impul&longs;i: experientia huius rei certa <lb/>e&longs;t, nec ignorant qui in ludo minoris tudiculæ ver&longs;ati &longs;unt; ratio au<lb/>tem inde tantùm duci pote&longs;t, quod &longs;cilicet ab ip&longs;o puncto contactus ita <lb/>diffunditur impetus, vt hinc inde æqualiter in vtroque hemi&longs;phærio <lb/>diffundatur; coniungitur autem vtrumque hemi&longs;phærium circulo A, <lb/>vel B, in priore figura, e&longs;tque vtriu&longs;que communis &longs;ectio; cum autem <lb/>vtrimque &longs;it æqualis impetus, nulla e&longs;t ratio, cur linea directionis in<lb/>clinet potiùs in vnum hemi&longs;phærium, quàm in aliud: præterea cum <lb/>motus orbis globi determinetur à motu centri; cum &longs;cilicet globus in <lb/>globum impingitur; haud dubiè non pote&longs;t e&longs;&longs;e alius motus centri, ni&longs;i <lb/>qui determinatur à puncto contactus, à quo vnica tantùm linea ad cen<lb/>trum duci pote&longs;t, vt con&longs;tat; & hæc ratio veri&longs;&longs;ima e&longs;t, & totam rem <lb/>ip&longs;am cuincit. </s>

<s><emph type="italics"/>Corpus proiectum in aliud ita illud impellit, vt determinet lineam motus <lb/>ratione puncti contactus<emph.end type="italics"/>; Sit enim, ne multiplicemus figuras, globus, <lb/>cuius linea directionis &longs;it DC, punctum contactus C, ita globus A im<lb/>pellet globum B, vt linea motus, ad quam determinatur, &longs;it CB, id e&longs;t <lb/>ducta à puncto contactus ad centrum globi impul&longs;i; &longs;it etiam globus <lb/>P impactus in globum A punctum contactus &longs;it D, linea motus, ad <lb/>quam determinatur, e&longs;t DA, quæ &longs;cilicet à puncto contactus ducitur <lb/>per centrum grauitatis corporis impul&longs;i: experientia huius rei certa <lb/>e&longs;t, nec ignorant qui in ludo minoris tudiculæ ver&longs;ati &longs;unt; ratio au<lb/>tem inde tantùm duci pote&longs;t, quod &longs;cilicet ab ip&longs;o puncto contactus ita <lb/>diffunditur impetus, vt hinc inde æqualiter in vtroque hemi&longs;phærio <lb/>diffundatur; coniungitur autem vtrumque hemi&longs;phærium circulo A, <lb/>vel B, in priore figura, e&longs;tque vtriu&longs;que communis &longs;ectio; cum autem <lb/>vtrimque &longs;it æqualis impetus, nulla e&longs;t ratio, cur linea directionis in<lb/>clinet potiùs in vnum hemi&longs;phærium, quàm in aliud: præterea cum <lb/>motus orbis globi determinetur à motu centri; cum &longs;cilicet globus in <lb/>globum impingitur; haud dubiè non pote&longs;t e&longs;&longs;e alius motus centri, ni&longs;i <lb/>qui determinatur à puncto contactus, à quo vnica tantùm linea ad cen<lb/>trum duci pote&longs;t, vt con&longs;tat; & hæc ratio veri&longs;&longs;ima e&longs;t, & totam rem <lb/>ip&longs;am euincit. </s>

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 121.<emph.end type="center"/></s>

<s><emph type="italics"/>Hinc licèt diuer&longs;æ &longs;int linea motus globi impellentis, &longs;i tamen &longs;it idem pun<lb/>ctum contactus ad eamdem lineam globus impul&longs;us determinabitur,<emph.end type="italics"/> v. g. li<lb/>cet globus P. ciu&longs;dem figuræ tangat globum A in D per lineam PD &longs;iue <lb/>per lineam HD &longs;iue per quamlibet aliam, globus A mouebitur &longs;emper <lb/>per lineam directionis DA propter rationem propo&longs;itam, quod etiam <lb/>mille experimentis conuincitur. </s>

<s><emph type="italics"/>Hinc licèt diuer&longs;æ &longs;int linea motus globi impellentis, &longs;i tamen &longs;it idem pun<lb/>ctum contactus ad <expan abbr="eãdem">eandem</expan> lineam globus impul&longs;us determinabitur,<emph.end type="italics"/> v. g. li<lb/>cet globus P. eiu&longs;dem figuræ tangat globum A in D per lineam PD &longs;iue <lb/>per lineam HD &longs;iue per quamlibet aliam, globus A mouebitur &longs;emper <lb/>per lineam directionis DA propter rationem propo&longs;itam, quod etiam <lb/>mille experimentis conuincitur. </s>

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<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 132.<emph.end type="center"/></s>

<s><emph type="italics"/>Si globus major in minorem impingatur per lineam directionis, quæ conne<lb/>ctat centra, &longs;eruat eamdem lineam<emph.end type="italics"/>; patet etiam experientiâ, cuius ratio e&longs;t <lb/>minor re&longs;i&longs;tentia minoris globi; &longs;i verò &longs;it alia linea directionis, omni<lb/>nò reflectitur &longs;uo modo; id e&longs;t mutat lineam; &longs;ed de his omnibus fusè <lb/>aliàs; hîc tantùm &longs;ufficiat indica&longs;&longs;e; (&longs;uppo&longs;ita linea directionis cen<lb/>trali &longs;eu connectente centra, &longs;ic enim deinceps eam appellabimus, in <lb/>quo ca&longs;u duplex determinatio tertiam mediam conflare non pote&longs;t) in<lb/>dica&longs;&longs;e inquam &longs;ufficiat nouam determinationem, vel e&longs;&longs;e æqualem prio<lb/>ri, vel maiorem, vel minorem; &longs;i æqualis e&longs;t, globus impactus &longs;i&longs;tit; &longs;i <lb/>maior, reflectitur; &longs;i minor, eamdem lineam, &longs;ed lentiùs pro rata pro<lb/>&longs;equitur. </s>

<s><emph type="italics"/>Si globus major in minorem impingatur per lineam directionis, quæ conne<lb/>ctat centra, &longs;eruat <expan abbr="eãdem">eandem</expan> lineam<emph.end type="italics"/>; patet etiam experientiâ, cuius ratio e&longs;t <lb/>minor re&longs;i&longs;tentia minoris globi; &longs;i verò &longs;it alia linea directionis, omni<lb/>nò reflectitur &longs;uo modo; id e&longs;t mutat lineam; &longs;ed de his omnibus fusè <lb/>aliàs; hîc tantùm &longs;ufficiat indica&longs;&longs;e; (&longs;uppo&longs;ita linea directionis cen<lb/>trali &longs;eu connectente centra, &longs;ic enim deinceps eam appellabimus, in <lb/>quo ca&longs;u duplex determinatio tertiam mediam conflare non pote&longs;t) in<lb/>dica&longs;&longs;e inquam &longs;ufficiat nouam determinationem, vel e&longs;&longs;e æqualem prio<lb/>ri, vel maiorem, vel minorem; &longs;i æqualis e&longs;t, globus impactus &longs;i&longs;tit; &longs;i <lb/>maior, reflectitur; &longs;i minor, <expan abbr="eãdem">eandem</expan> lineam, &longs;ed lentiùs pro rata pro<lb/>&longs;equitur. </s>

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 133.<emph.end type="center"/></s>

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<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 135.<emph.end type="center"/></s>

<s><emph type="italics"/>Siduo globi projecti &longs;ibi inuicem occurrant in lineæ directionis connectente <lb/>centra, reflectitur vterque æquali motu, quo antè.<emph.end type="italics"/></s><s> Probatur; &longs;unt enim globi <pb xlink:href="026/01/098.jpg" pagenum="66"/>A & B, & A feratur per lineam DE, & B per lineam ED, punctum con<lb/>tactus &longs;it C, haud dubiè globus A impactus in B amittit totum &longs;uum im<lb/>petum per Th.127. & 128. B, item impactus in A amittit totum &longs;uum per <lb/>camdem rationem; globus A producit impetum in B æqualem &longs;uo per <lb/>Th.60. item B producit in A æqualem per idem Th. igitur tantùm perit <lb/>impetus quantùm accedit; igitur in vtroque globo remanet æqualis im<lb/>petus priori; igitur æquali motu vterque mouetur, quod erat dem. </s>

<s><emph type="italics"/>Si duo globi projecti &longs;ibi inuicem occurrant in lineæ directionis connectente <lb/>centra, reflectitur vterque æquali motu, quo antè.<emph.end type="italics"/></s><s> Probatur; &longs;unt enim globi <pb xlink:href="026/01/098.jpg" pagenum="66"/>A & B, & A feratur per lineam DE, & B per lineam ED, punctum con<lb/>tactus &longs;it C, haud dubiè globus A impactus in B amittit totum &longs;uum im<lb/>petum per Th.127. & 128. B, item impactus in A amittit totum &longs;uum per <lb/>eandem rationem; globus A producit impetum in B æqualem &longs;uo per <lb/>Th.60. item B producit in A æqualem per idem Th. igitur tantùm perit <lb/>impetus quantùm accedit; igitur in vtroque globo remanet æqualis im<lb/>petus priori; igitur æquali motu vterque mouetur, quod erat dem. </s>

<s>& hæc <lb/>e&longs;t ratio veri&longs;&longs;ima toties probatæ experientiæ. </s>

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<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 138.<emph.end type="center"/></s>

<s><emph type="italics"/>Si &longs;it duplex impetus in eodem mobili ad eamdem lineam determinatus, non <lb/>mutabitur linea; &longs;ed cre&longs;cet motus & &longs;patium<emph.end type="italics"/> Imprimatur impetus in A, <lb/>per AB, quo dato tempore percurratur &longs;patium AB; deinde produca<lb/>tur &longs;imul alius impetus æqualis priori in eodem mobili per lineam AB; <lb/>Dico quod eodem tempore percurretur tota AE, dupla &longs;cilicet AB; <lb/>quia &longs;cilicet dupla cau&longs;a non impedita duplum effectum habet per Ax. <lb/>13. num.1. duplus impetus duplum motum; igitur duplum &longs;patium; &longs;i <lb/>verò &longs;it triplus impetus, triplum erit &longs;patium, &c. </s>

<s><emph type="italics"/>Si &longs;it duplex impetus in eodem mobili ad <expan abbr="eãdem">eandem</expan> lineam determinatus, non <lb/>mutabitur linea; &longs;ed cre&longs;cet motus & &longs;patium<emph.end type="italics"/> Imprimatur impetus in A, <lb/>per AB, quo dato tempore percurratur &longs;patium AB; deinde produca<lb/>tur &longs;imul alius impetus æqualis priori in eodem mobili per lineam AB; <lb/>Dico quod eodem tempore percurretur tota AE, dupla &longs;cilicet AB; <lb/>quia &longs;cilicet dupla cau&longs;a non impedita duplum effectum habet per Ax. <lb/>13. num.1. duplus impetus duplum motum; igitur duplum &longs;patium; &longs;i <lb/>verò &longs;it triplus impetus, triplum erit &longs;patium, &c. </s>

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 139.<emph.end type="center"/></s>

<s><emph type="italics"/>Si lineæ duplicis impetus, faciunt angulum acutiorem, longius erit &longs;patium<emph.end type="italics"/><pb xlink:href="026/01/099.jpg" pagenum="67"/><emph type="italics"/>acqui&longs;itum<emph.end type="italics"/>: &longs;int duæ lineæ IK IL, mobili &longs;eilicet &longs;tatuto in I; <lb/>haud dubiè noua linea erit IM; & quo angulus KIL, erit acutior (&longs;up<lb/>po&longs;itis æqualibus &longs;emper lateribus IK IL) Diagonalis IM, erit ma<lb/>ior; donec tandem IL & IK coeant in eandem lineam; tunc enim li<lb/>nea erit dupla IK per Th. &longs;uperius: quandiu verò e&longs;t aliquis angulus in <lb/>I quantumuis acutus, linea motus erit minor dupla IK, ad quam tamen <lb/>propiùs &longs;emper accedit; quæ omnia con&longs;tant ex elementis. </s>

<s><emph type="italics"/>Si lineæ duplicis impetus, faciunt angulum acutiorem, longius erit &longs;patium<emph.end type="italics"/><pb xlink:href="026/01/099.jpg" pagenum="67"/><emph type="italics"/>acqui&longs;itum<emph.end type="italics"/>: &longs;int duæ lineæ IK IL, mobili &longs;cilicet &longs;tatuto in I; <lb/>haud dubiè noua linea erit IM; & quo angulus KIL, erit acutior (&longs;up<lb/>po&longs;itis æqualibus &longs;emper lateribus IK IL) Diagonalis IM, erit ma<lb/>ior; donec tandem IL & IK coeant in eandem lineam; tunc enim li<lb/>nea erit dupla IK per Th. &longs;uperius: quandiu verò e&longs;t aliquis angulus in <lb/>I quantumuis acutus, linea motus erit minor dupla IK, ad quam tamen <lb/>propiùs &longs;emper accedit; quæ omnia con&longs;tant ex elementis. </s>

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 140.<emph.end type="center"/></s>

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<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 141.<emph.end type="center"/></s>

<s><emph type="italics"/>Ex his nece&longs;&longs;aria ducitur ratio, cur impetus duplus ad diuer&longs;as lineas de<lb/>terminatus non habeat motum duplum, & con&longs;equenter &longs;patium duplum<emph.end type="italics"/>; nec <lb/>enim AE e&longs;t dupla AB, vt con&longs;tat; nam &longs;i lineæ &longs;int oppo&longs;itæ ex <lb/>diametro vt BA BE totus de&longs;truitur impetus, per Th.133. &longs;i verò vna <lb/>in eamdem lineam coëat cum aliâ, nihil impetus de&longs;truitur, nec impedi<lb/>tur per Th.138. igitur quà proportione propiùs accedet ad oppo&longs;itas; <lb/>plùs de&longs;truetur, & minus erit &longs;patium; & quâ proportione accedent <lb/>propiùs ad coëuntes, minùs de&longs;truetur, & maius erit &longs;patium, vt con&longs;tat <lb/>ex dictis. </s>

<s><emph type="italics"/>Ex his nece&longs;&longs;aria ducitur ratio, cur impetus duplus ad diuer&longs;as lineas de<lb/>terminatus non habeat motum duplum, & con&longs;equenter &longs;patium duplum<emph.end type="italics"/>; nec <lb/>enim AE e&longs;t dupla AB, vt con&longs;tat; nam &longs;i lineæ &longs;int oppo&longs;itæ ex <lb/>diametro vt BA BE totus de&longs;truitur impetus, per Th.133. &longs;i verò vna <lb/>in <expan abbr="eãdem">eandem</expan> lineam coëat cum aliâ, nihil impetus de&longs;truitur, nec impedi<lb/>tur per Th.138. igitur quà proportione propiùs accedet ad oppo&longs;itas; <lb/>plùs de&longs;truetur, & minus erit &longs;patium; & quâ proportione accedent <lb/>propiùs ad coëuntes, minùs de&longs;truetur, & maius erit &longs;patium, vt con&longs;tat <lb/>ex dictis. </s>

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 142.<emph.end type="center"/></s>

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<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 149.<emph.end type="center"/></s>

<s><emph type="italics"/>In lineis oppo&longs;itis impetus de&longs;truitur ab impetu &longs;uo modo<emph.end type="italics"/>; &longs;it enim globus <lb/>proiectus ver&longs;us au&longs;trum; cui deinde imprimatur nouus impetus ver<lb/>&longs;us Boream; de&longs;truitur prior vt con&longs;tat, igitur ad exigentiam alicuius, <lb/>&longs;ed nihil e&longs;t quod po&longs;&longs;it exigere, ni&longs;i nouus impetus, &longs;cilicet mediatè; <lb/>nihil enim aliud e&longs;t applicatum, igitar nihil aliud exigit per Ax. 10. <lb/>hæc porrò exigentia non e&longs;t immediata, &longs;ed mediata, vt dixi. </s>

<s><emph type="italics"/>In lineis oppo&longs;itis impetus de&longs;truitur ab impetu &longs;uo modo<emph.end type="italics"/>; &longs;it enim globus <lb/>proiectus ver&longs;us au&longs;trum; cui deinde imprimatur nouus impetus ver<lb/>&longs;us Boream; de&longs;truitur prior vt con&longs;tat, igitur ad exigentiam alicuius, <lb/>&longs;ed nihil e&longs;t quod po&longs;&longs;it exigere, ni&longs;i nouus impetus, &longs;cilicet mediatè; <lb/>nihil enim aliud e&longs;t applicatum, igitur nihil aliud exigit per Ax. 10. <lb/>hæc porrò exigentia non e&longs;t immediata, &longs;ed mediata, vt dixi. </s>

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 150.<emph.end type="center"/></s>

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<s>Sextò, Impetus naturalis innatus nunquam de&longs;truitur; quia nunquam <lb/>e&longs;t fru&longs;trà; quippe &longs;emper habet alterum &longs;uorum effectuum formalium, <lb/>id e&longs;t vel motum deor&longs;um, vel grauitationem, adde quod fru&longs;trà de<lb/>&longs;trueretur, cum &longs;it &longs;emper applicata potentia, id e&longs;t ip&longs;a grauitas, &longs;ed de <lb/>his infrâ fusè. </s><pb xlink:href="026/01/103.jpg" pagenum="71"/>

<s>Septimò, Impetus &longs;ur&longs;um de&longs;truitur etiam, quia e&longs;t fru&longs;trà; quippe <lb/>naturalis detrahit aliquid &longs;patij pro rata; igitur ne aliquid impetus &longs;it <lb/>fru&longs;trà, de&longs;truitur; idem dico de impetu per inclinatam &longs;ur&longs;um, licèt <lb/>minùs de&longs;truatur quàm in perpendiculari &longs;ur&longs;um; idem de impetu per <lb/>inclinatam deor&longs;um, &longs;ed minùs adhuc, &longs;ed hæc acuratiori medita ioni <lb/>&longs;unt relinquenda; quod reuerâ præ&longs;tabimus in lib.4. de motu mixto; <lb/>quidquid &longs;it, con&longs;tat ex dictis per idem Principium probari po&longs;&longs;e de<lb/>&longs;tructionem impetus, &longs;cilicet ne &longs;it fru&longs;trà; &longs;ed de his aliàs fusè. </s>

<s>Septimò, Impetus &longs;ur&longs;um de&longs;truitur etiam, quia e&longs;t fru&longs;trà; quippe <lb/>naturalis detrahit aliquid &longs;patij pro rata; igitur ne aliquid impetus &longs;it <lb/>fru&longs;trà, de&longs;truitur; idem dico de impetu per inclinatam &longs;ur&longs;um, licèt <lb/>minùs de&longs;truatur quàm in perpendiculari &longs;ur&longs;um; idem de impetu per <lb/>inclinatam deor&longs;um, &longs;ed minùs adhuc, &longs;ed hæc acuratiori meditationi <lb/>&longs;unt relinquenda; quod reuerâ præ&longs;tabimus in lib.4. de motu mixto; <lb/>quidquid &longs;it, con&longs;tat ex dictis per idem Principium probari po&longs;&longs;e de<lb/>&longs;tructionem impetus, &longs;cilicet ne &longs;it fru&longs;trà; &longs;ed de his aliàs fusè. </s>

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 153.<emph.end type="center"/></s>

<s><emph type="italics"/>Impetus productus ab extrin&longs;eco e&longs;t tantùm contrarius ratione diuer&longs;æ de<lb/>terminationis, &longs;eu diuer&longs;æ lineæ<emph.end type="italics"/>; Probatur primò, quia vterque ad omnem <lb/>lineam e&longs;t indifferens per Th.113. igitur vnus non c&longs;t alteri contrarius <lb/>ratione entitatis; cùm vterque &longs;imilem motum, immò eumdem habere <lb/>po&longs;&longs;it, vt patet ex dictis: Igitur ratione tanuùn lineæ vnus alteri e&longs;t <lb/>contrarius; hinc minùs e&longs;t contrarietatis, quo minùs e&longs;t oppo&longs;itionis <lb/>inter lineas & contrà. </s>

<s><emph type="italics"/>Impetus productus ab extrin&longs;eco e&longs;t tantùm contrarius ratione diuer&longs;æ de<lb/>terminationis, &longs;eu diuer&longs;æ lineæ<emph.end type="italics"/>; Probatur primò, quia vterque ad omnem <lb/>lineam e&longs;t indifferens per Th.113. igitur vnus non e&longs;t alteri contrarius <lb/>ratione entitatis; cùm vterque &longs;imilem motum, immò <expan abbr="e&utilde;dem">eundem</expan> habere <lb/>po&longs;&longs;it, vt patet ex dictis: </s>

<s>Igitur ratione tantùm lineæ vnus alteri e&longs;t <lb/>contrarius; hinc minùs e&longs;t contrarietatis, quo minùs e&longs;t oppo&longs;itionis <lb/>inter lineas & contrà. </s>

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 154.<emph.end type="center"/></s>

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<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 157.<emph.end type="center"/></s>

<s><emph type="italics"/>Impetus ex non contrario eidem fit contrarius<emph.end type="italics"/>; vt patet in eodem ca&longs;u; <lb/>nam impetus naturalis innatus, qui in de&longs;cen&longs;u non erat contrarius <lb/>ac qui&longs;ito, in inotu &longs;ur&longs;um reflexo fit contrarius. </s>

<s><emph type="italics"/>Impetus ex non contrario eidem fit contrarius<emph.end type="italics"/>; vt patet in eodem ca&longs;u; <lb/>nam impetus naturalis innatus, qui in de&longs;cen&longs;u non erat contrarius <lb/>acqui&longs;ito, in motu &longs;ur&longs;um reflexo fit contrarius. </s>

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 158.<emph.end type="center"/></s>

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<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 161.<emph.end type="center"/></s>

<s>Idem impetus pote&longs;t eumdem alium aliquando plùs, aliquando minùs <lb/>intendere. </s>

<s>Idem impetus pote&longs;t <expan abbr="e&utilde;dem">eundem</expan> alium aliquando plùs, aliquando minùs <lb/>intendere. </s>

<s>v. g. 4. gradus impetus additi aliis 4. per eamdem lineam <lb/>iidem ei&longs;dem, minùs intendunt, vt iam &longs;uprà &longs;atis fusè dictum e&longs;t. </s>

<s>v. g. 4. gradus impetus additi aliis 4. per <expan abbr="eãdem">eandem</expan> lineam <lb/>iidem ei&longs;dem, minùs intendunt, vt iam &longs;uprà &longs;atis fusè dictum e&longs;t. </s>

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<s><emph type="center"/><emph type="italics"/>Axioma<emph.end type="italics"/> 1.<emph.end type="center"/></s>

<s><emph type="italics"/>Impetus additus alteri, & determinatus ad eamdem lineam, facit maiorem <lb/>& inten&longs;iorom impetum<emph.end type="italics"/>; patet, & vici&longs;&longs;im, & detractus alteri minorem <lb/>facit, & vici&longs;&longs;im. </s>

<s><emph type="italics"/>Impetus additus alteri, & determinatus ad <expan abbr="eãdem">eandem</expan> lineam, facit maiorem <lb/>& inten&longs;iorem impetum<emph.end type="italics"/>; patet, & vici&longs;&longs;im, & detractus alteri minorem <lb/>facit, & vici&longs;&longs;im. </s>

<s><emph type="center"/><emph type="italics"/>Axioma<emph.end type="italics"/> 2.<emph.end type="center"/></s>

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<s>hic motus e&longs;t ab intrin&longs;eco, <lb/>quod probatur; non e&longs;t ab vllâ causâ extrin&longs;ecâ; igitur e&longs;t ab intrin&longs;eca <lb/>per Ax.4. antecedens probatur inductione factâ omnium extrin&longs;ecorum. </s>

<s><lb/>Primò non e&longs;t à cau&longs;a prima, vt aliquis fortè minùs prudenter, & magis <lb/>piè, quàm par &longs;it, diceret; quia ille effectus tribui tantùm debet cau&longs;æ <lb/>primæ, qui nullam habere pote&longs;t cau&longs;am &longs;ecundam applicatam, vt patet; <lb/>&longs;ed hic effectus pote&longs;t habere cau&longs;am &longs;ecundam applicatam, quam a&longs;&longs;i<lb/>gnabimus infrà; deinde cau&longs;a prima agit tantùm naturaliter iuxta exi<lb/>gentiam cau&longs;arum &longs;ecundarum; igitur ideo moueret corpus graue deor<lb/>&longs;um; quia tunc motum corpus graue exigeret; &longs;ed lioc milri &longs;u&longs;ficit, vt <lb/>dicatur hic motus e&longs;&longs;e ab intrin&longs;eco; præterea, &longs;i dicatur Deus mouere <lb/>corpus graue deor&longs;um iuxta illius exigentiam, dicetur etiam tùm cale<lb/>facere, tùm illuminare, ad exigentiam ignis; quippe tàm mihi &longs;en&longs;ibile <lb/>e&longs;t corpus graue de&longs;cendere &longs;ine vi impre&longs;&longs;a ab extrin&longs;eco, quàm ignem <lb/>calefacere, & &longs;olem lucere &longs;ine vi extrin&longs;eca; adde quod illud &longs;olenne <lb/>e&longs;t naturæ in&longs;titutum, vt id, quod exigit res aliqua ad finem &longs;uum con&longs;e<lb/>quendum, per virtutem intrin&longs;ecam po&longs;&longs;it ponere, &longs;i dumtaxat excipias <lb/>concur&longs;um diuinum, & ip&longs;am con&longs;oruationem; &longs;ic animal exigit vide<lb/>re, audire, &longs;entire, moueri; igitur habet virtutem intrin&longs;ecam, per quam <lb/>videat, audiat, & moueatur; &longs;ic ignis exigit calefacere, lucere; aër, vel aqua <lb/>frigefacere, quidquid tandem &longs;int i&longs;tæ qualitates, de quibus alibi; &longs;ic <lb/>demum corpus graue exigit moueri deor&longs;um; quis enim neget corpori <lb/>graui tàm natiuum e&longs;&longs;e tendere deor&longs;um, cum &longs;cilicer corpus leuius &longs;ub<lb/>e&longs;t, quàm &longs;it animali progredi, vrere igni, lucere, &c. </s>

<s><lb/>Primò non e&longs;t à cau&longs;a prima, vt aliquis fortè minùs prudenter, & magis <lb/>piè, quàm par &longs;it, diceret; quia ille effectus tribui tantùm debet cau&longs;æ <lb/>primæ, qui nullam habere pote&longs;t cau&longs;am &longs;ecundam applicatam, vt patet; <lb/>&longs;ed hic effectus pote&longs;t habere cau&longs;am &longs;ecundam applicatam, quam a&longs;&longs;i<lb/>gnabimus infrà; deinde cau&longs;a prima agit tantùm naturaliter iuxta exi<lb/>gentiam cau&longs;arum &longs;ecundarum; igitur ideo moueret corpus graue deor<lb/>&longs;um; quia tunc motum corpus graue exigeret; &longs;ed hoc mihi &longs;ufficit, vt <lb/>dicatur hic motus e&longs;&longs;e ab intrin&longs;eco; præterea, &longs;i dicatur Deus mouere <lb/>corpus graue deor&longs;um iuxta illius exigentiam, dicetur etiam tùm cale<lb/>facere, tùm illuminare, ad exigentiam ignis; quippe tàm mihi &longs;en&longs;ibile <lb/>e&longs;t corpus graue de&longs;cendere &longs;ine vi impre&longs;&longs;a ab extrin&longs;eco, quàm ignem <lb/>calefacere, & &longs;olem lucere &longs;ine vi extrin&longs;eca; adde quod illud &longs;olenne <lb/>e&longs;t naturæ in&longs;titutum, vt id, quod exigit res aliqua ad finem &longs;uum con&longs;e<lb/>quendum, per virtutem intrin&longs;ecam po&longs;&longs;it ponere, &longs;i dumtaxat excipias <lb/>concur&longs;um diuinum, & ip&longs;am con&longs;eruationem; &longs;ic animal exigit vide<lb/>re, audire, &longs;entire, moueri; igitur habet virtutem intrin&longs;ecam, per quam <lb/>videat, audiat, & moueatur; &longs;ic ignis exigit calefacere, lucere; aër, vel aqua <lb/>frigefacere, quidquid tandem &longs;int i&longs;tæ qualitates, de quibus alibi; &longs;ic <lb/>demum corpus graue exigit moueri deor&longs;um; quis enim neget corpori <lb/>graui tàm natiuum e&longs;&longs;e tendere deor&longs;um, cum &longs;cilicet corpus leuius &longs;ub<lb/>e&longs;t, quàm &longs;it animali progredi, vrere igni, lucere, &c. </s>

<s>Denique &longs;atis e&longs;t mihi, vt dicatur aliquid cau&longs;a, Phy&longs;icè loquendo, &longs;i <lb/>ex illius applicatione &longs;emper &longs;equatur effectus; nam non nego po&longs;&longs;e fie<lb/>ri effectus omnes, qui no&longs;tris &longs;en&longs;ibus &longs;ubiiciuntur, &longs;altem extrin&longs;ecos, <lb/>e&longs;&longs;e à cau&longs;a prima, quippe &longs;i &longs;emper ex ignis applicatione Deus diffun<lb/>deret lucem, & calorem, quem &longs;olus ip&longs;e produceret, igne ip&longs;o inerte re<lb/>licto, nullam pror&longs;us mutationem perciperemus; & nemo e&longs;&longs;et, qui non <lb/>exi&longs;timaret lucom hanc & calorem ltunc e&longs;&longs;e ab igne; igitur Phy&longs;icè lo<lb/>quendo cau&longs;am appellamus id, ex cuius applicatione &longs;emper &longs;equitur <lb/>effectus, vt iam diximus in Ax. 11.l.1. n.1. Igitur cum ex corpore graui <lb/>po&longs;ito in aëre libero &longs;equatur motus deor&longs;um; dicendum e&longs;t, Phy&longs;icè lo<lb/>quendò, e&longs;&longs;e huius motus cau&longs;am, id e&longs;t in ordine ad Phy&longs;icam, perinde <lb/>omninò &longs;e habere, atque &longs;i e&longs;&longs;et cau&longs;a, licèt cau&longs;a non e&longs;&longs;et. </s><pb xlink:href="026/01/109.jpg" pagenum="77"/>

<s>Denique &longs;atis e&longs;t mihi, vt dicatur aliquid cau&longs;a, Phy&longs;icè loquendo, &longs;i <lb/>ex illius applicatione &longs;emper &longs;equatur effectus; nam non nego po&longs;&longs;e fie<lb/>ri effectus omnes, qui no&longs;tris &longs;en&longs;ibus &longs;ubiiciuntur, &longs;altem extrin&longs;ecos, <lb/>e&longs;&longs;e à cau&longs;a prima, quippe &longs;i &longs;emper ex ignis applicatione Deus diffun<lb/>deret lucem, & calorem, quem &longs;olus ip&longs;e produceret, igne ip&longs;o inerte re<lb/>licto, nullam pror&longs;us mutationem perciperemus; & nemo e&longs;&longs;et, qui non <lb/>exi&longs;timaret lucem hanc & calorem hunc e&longs;&longs;e ab igne; igitur Phy&longs;icè lo<lb/>quendo cau&longs;am appellamus id, ex cuius applicatione &longs;emper &longs;equitur <lb/>effectus, vt iam diximus in Ax. 11.l.1. n.1. Igitur cum ex corpore graui <lb/>po&longs;ito in aëre libero &longs;equatur motus deor&longs;um; dicendum e&longs;t, Phy&longs;icè lo<lb/>quendò, e&longs;&longs;e huius motus cau&longs;am, id e&longs;t in ordine ad Phy&longs;icam, perinde <lb/>omninò &longs;e habere, atque &longs;i e&longs;&longs;et cau&longs;a, licèt cau&longs;a non e&longs;&longs;et. </s><pb xlink:href="026/01/109.jpg" pagenum="77"/>

<s>Secundò hic motus non e&longs;t ab aëre ambiente; probatur, ruderet aër <lb/>deor&longs;um corpus graue, quia leuior e&longs;t, id e&longs;t ne &longs;uprà &longs;e corpus grauins <lb/>haberet; &longs;ed eâdem ratione corpus graue debet remouere &longs;ur&longs;um aëra, <lb/>id e&longs;t corpus leue, ne infrà &longs;e habeat corpus leuius; e&longs;t enim par omni<lb/>nò ratio: Præterea &longs;i aër trudit deor&longs;inn corpus graue, quia ip&longs;i loco <lb/>cedit; certè ip&longs;e aër mouetur, igitur ab intrin&longs;eco; &longs;i enim vna pars aë<lb/>ris pellit aliam, & hæc aliam, tandem ad aliquam peruenitur, quæ &longs;e ip<lb/>&longs;am mouet; igitur motus illius e&longs;t ab intrin&longs;eco; igitur motus natura<lb/>lis; deinde non modò lapis de&longs;cendit per aëra, &longs;ed per mediam aquam; <lb/>igitur &longs;i ab aëre truditur deor&longs;um, idem dicendum e&longs;t de aquâ, a qui <lb/>haud dubiè maiore vi truderetur; nam corpus den&longs;um maiore vi pellit, <lb/>quàm rarum, vt con&longs;tat exprientiâ; cum tamen corpus graue per me<lb/>dium den&longs;ius difficiliùs de cendat; igitur medium ip&longs;um re&longs;i&longs;tit motui, <lb/>quis hoc neget? </s>

<s>Secundò hic motus non e&longs;t ab aëre ambiente; probatur, ruderet aër <lb/>deor&longs;um corpus graue, quia leuior e&longs;t, id e&longs;t ne &longs;uprà &longs;e corpus grauius <lb/>haberet; &longs;ed eâdem ratione corpus graue debet remouere &longs;ur&longs;um aëra, <lb/>id e&longs;t corpus leue, ne infrà &longs;e habeat corpus leuius; e&longs;t enim par omni<lb/>nò ratio: Præterea &longs;i aër trudit deor&longs;inn corpus graue, quia ip&longs;i loco <lb/>cedit; certè ip&longs;e aër mouetur, igitur ab intrin&longs;eco; &longs;i enim vna pars aë<lb/>ris pellit aliam, & hæc aliam, tandem ad aliquam peruenitur, quæ &longs;e ip<lb/>&longs;am mouet; igitur motus illius e&longs;t ab intrin&longs;eco; igitur motus natura<lb/>lis; deinde non modò lapis de&longs;cendit per aëra, &longs;ed per mediam aquam; <lb/>igitur &longs;i ab aëre truditur deor&longs;um, idem dicendum e&longs;t de aquâ, a qui <lb/>haud dubiè maiore vi truderetur; nam corpus den&longs;um maiore vi pellit, <lb/>quàm rarum, vt con&longs;tat exprientiâ; cum tamen corpus graue per me<lb/>dium den&longs;ius difficiliùs decendat; igitur medium ip&longs;um re&longs;i&longs;tit motui, <lb/>quis hoc neget? </s>

<s>igitur non e&longs;t cau&longs;a motus, quem impedit. </s>

<s>Denique &longs;i corpus graue non tendit, fertur que deor&longs;um &longs;uá &longs;ponte, <lb/>&longs;ed ab aëre extru&longs;um; igitur dum vix &longs;u&longs;tineo manu; o. </s>

<s>libras ferri, &longs;eu <lb/>plumbi; hæc vis illata manui, quam probè &longs;entio, e&longs;t ab aëre impel<lb/>lente plumbum, quod e&longs;t ridiculum, cnm eadem quantitas aëris incu<lb/>ber, & &longs;ub&longs;it manui, &longs;iue &longs;u&longs;tineat plumbum, &longs;iue &longs;it vacua; ex hoc, ni <lb/>fallor, euincitur pondus ip&longs;um &longs;ui &longs;ponte deor&longs;unr tendere. </s>

<s>libras ferri, &longs;eu <lb/>plumbi; hæc vis illata manui, quam probè &longs;entio, e&longs;t ab aëre impel<lb/>lente plumbum, quod e&longs;t ridiculum, cum eadem quantitas aëris incu<lb/>ber, & &longs;ub&longs;it manui, &longs;iue &longs;u&longs;tineat plumbum, &longs;iue &longs;it vacua; ex hoc, ni <lb/>fallor, euincitur pondus ip&longs;um &longs;ui &longs;ponte deor&longs;um tendere. </s>

<s>Tertiò non de&longs;unt, qui dicant corpus graue trahi ab ip&longs;a vi quadam <lb/>magneticâ, quod triplici modo fieri pote&longs;t; Primò per qualitatem <lb/>quamdam diffu&longs;am, quod dici non pote&longs;t; quia capillus traheretur faci<lb/>liùs, quàm ingens &longs;axum, quàm ma&longs;&longs;a, &longs;eu lamina; & faciliùs eadem po<lb/>tentia motrix minus pondus moueret quàm maius, cæteris paribus; præ<lb/>terea manum meam æqualiter traheret, &longs;iue &longs;it cum aliquo pondere con<lb/>iuncta, &longs;iuc &longs;it nuda &longs;ine pondere; deinde illa virtus tractrix ita diffun<lb/>ditur, vt in maiori di&longs;tantia &longs;it infirmior, fortior in minori; alioqui <lb/>diffunderetur in infinitum, quod dici non pote&longs;t; igitur &longs;i idem lapis <lb/>demittatur ex maiore altitudine, tum ex minore; haud dubiè morus ille <lb/>primus initio e&longs;&longs;et tardior i&longs;to contra experientiam; deinde in &longs;pecu al<lb/>ti&longs;&longs;ima &longs;ubterranea trahi po&longs;&longs;et corpus virdequaque, &longs;icut in magnete; <lb/>quæ omnia intelligi non po&longs;&longs;unt; denique virtutes illas &longs;eu qualitates <lb/>tractrices refellemus &longs;uo loco. </s>

<s>Tertiò non de&longs;unt, qui dicant corpus graue trahi ab ip&longs;a vi quadam <lb/>magneticâ, quod triplici modo fieri pote&longs;t; Primò per qualitatem <lb/>quamdam diffu&longs;am, quod dici non pote&longs;t; quia capillus traheretur faci<lb/>liùs, quàm ingens &longs;axum, quàm ma&longs;&longs;a, &longs;eu lamina; & faciliùs eadem po<lb/>tentia motrix minus pondus moueret quàm maius, cæteris paribus; præ<lb/>terea manum meam æqualiter traheret, &longs;iue &longs;it cum aliquo pondere con<lb/>iuncta, &longs;iuc &longs;it nuda &longs;ine pondere; deinde illa virtus tractrix ita diffun<lb/>ditur, vt in maiori di&longs;tantia &longs;it infirmior, fortior in minori; alioqui <lb/>diffunderetur in infinitum, quod dici non pote&longs;t; igitur &longs;i idem lapis <lb/>demittatur ex maiore altitudine, tum ex minore; haud dubiè morus ille <lb/>primus initio e&longs;&longs;et tardior i&longs;to contra experientiam; deinde in &longs;pecu al<lb/>ti&longs;&longs;ima &longs;ubterranea trahi po&longs;&longs;et corpus vndequaque, &longs;icut in magnete; <lb/>quæ omnia intelligi non po&longs;&longs;unt; denique virtutes illas &longs;eu qualitates <lb/>tractrices refellemus &longs;uo loco. </s>

<s>Secundò, aliqui dicunt hoc totum fieri per vim quamdam &longs;ympathi<lb/>cam, quod etiam fal&longs;i&longs;&longs;imum e&longs;t; tùm quia hæc &longs;ympathia explicari <lb/>non pote&longs;t; tùm quia vel terra ip&longs;a producit aliquid in corpore graui, <lb/>quod in aëre libratur; vel corpus in &longs;e ip&longs;o; &longs;i primum; refellitur ii&longs;<lb/>dem omninò rationibus, quibus ip&longs;am vim terræ tractricem &longs;uprà expu<lb/>gnauimus; &longs;i verò &longs;ecundum, hoc ip&longs;um e&longs;t, quod &longs;uprà diximus. </s>

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<s>Secundò, corpus vicinius etiam faciliùs abriperetur. </s>

<s>Tertiò, numquid flante vento, vel imbre cadente di&longs;&longs;ipantur hæc &longs;i<lb/>lamenta? </s>

<s>Tertiò, numquid flante vento, vel imbre cadente di&longs;&longs;ipantur hæc fi<lb/>lamenta? </s>

<s>quod etiam videmus in electro. </s>

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<s>Sextò, hæc filamenta, quæ deinde reducuntur, debent habere cau<lb/>&longs;am huius reductionis non extrin&longs;ecam; igitur intrin&longs;ecam; igitur datur <lb/>motus naturalis. </s>

<s>Soptimò, hæc filamenta per mediam flammam non traherent, quod <lb/>etiam fieri videmus in electro. </s>

<s>Septimò, hæc filamenta per mediam flammam non traherent, quod <lb/>etiam fieri videmus in electro. </s>

<s>Quartò, motus naturalis non e&longs;t à virtute quadam pellente, quam <lb/>cælo quidam affingunt; nam vel ab omni parte cæli deor&longs;um trudere<lb/>tur, vel ab vnâ; &longs;i ab vna; igitur in omni cæli plaga corpus non fertur <lb/>deor&longs;um; &longs;i ab omni, ergo cum pellatur corpus per plures lineas etiam <lb/>oppo&longs;itas moueri non pote&longs;t: Præterea debilior e&longs;&longs;et hæc vis in maiori <lb/>di&longs;tantiâ; denique vapores, & alia minutiora corpu&longs;cula in aëre fluitan<lb/>tia faciliùs deor&longs;um truderentur, contra experientiam. </s>

<s>Sed non e&longs;t omittendum, quod aliqui putant ex illis filamentis con<lb/>texi po&longs;&longs;e legitimam rationem, cur atomi etiam plumbeæ materiæ non <lb/>ita facilè de&longs;cendant; quòd &longs;cilicet propter &longs;uam tenuitatem ab illis fi<lb/>lamentis non ita intercipi vel implicari po&longs;&longs;int; &longs;ed qua&longs;i pi&longs;ces per fo<lb/>ramina retium euadant; &longs;ed profectò longè alia ratio e&longs;t, qaàm &longs;uo loco <lb/>afferemus, nam etiam plumæ, fe&longs;tucæ, paleæ, & alia corpu&longs;cula longio<lb/>ra, &longs;ed leui&longs;&longs;ima iis filamentis implicarentur, vt videre e&longs;t in electro. </s>

<s>Sed non e&longs;t omittendum, quod aliqui putant ex illis filamentis con<lb/>texi po&longs;&longs;e legitimam rationem, cur atomi etiam plumbeæ materiæ non <lb/>ita facilè de&longs;cendant; quòd &longs;cilicet propter &longs;uam tenuitatem ab illis fi<lb/>lamentis non ita intercipi vel implicari po&longs;&longs;int; &longs;ed qua&longs;i pi&longs;ces per fo<lb/>ramina retium euadant; &longs;ed profectò longè alia ratio e&longs;t, quàm &longs;uo loco <lb/>afferemus, nam etiam plumæ, fe&longs;tucæ, paleæ, & alia corpu&longs;cula longio<lb/>ra, &longs;ed leui&longs;&longs;ima iis filamentis implicarentur, vt videre e&longs;t in electro. </s>

<s>Quintò, aliqui recentiores exi&longs;timant corpora deor&longs;um trudi ab <lb/>ip&longs;a luce, quæ nihil e&longs;t aliud, quam motio æthereæ cuiu&longs;dam &longs;ub&longs;tan<lb/>tiæ per poros aëris traductæ, vt ip&longs;i volunt; &longs;ed neque hoc probari po<lb/>te&longs;t. </s>

<s>Primò quia de nocte corpora æquali motu deor&longs;um feruntur; pe<lb/>rinde atque de die, nec minùs in ob&longs;curi&longs;&longs;imo conclaui, quàm &longs;ub dio, <lb/>vel aperto cælo. </s>

<s>Secundò, in &longs;ubterraneis locis etiam grauia æquè veloci<lb/>ter de&longs;cendunt; licèr eò lumen non penetret; quod &longs;i aliquis ob&longs;tinatè, <lb/>id a&longs;&longs;ereret; haud dubiè per medium aëra maior huius materiæ copia <lb/>diffunditur, quàm per medias rupes, quis hoc neget; igitur pauci&longs;&longs;imi <lb/>radij v&longs;que ad interius & inferius antrum perueniunt. </s>

<s>Secundò, in &longs;ubterraneis locis etiam grauia æquè veloci<lb/>ter de&longs;cendunt; licèt eò lumen non penetret; quod &longs;i aliquis ob&longs;tinatè, <lb/>id a&longs;&longs;ereret; haud dubiè per medium aëra maior huius materiæ copia <lb/>diffunditur, quàm per medias rupes, quis hoc neget; igitur pauci&longs;&longs;imi <lb/>radij v&longs;que ad interius & inferius antrum perueniunt. </s>

<s>Tertiò, manum <lb/>meam &longs;iue ponderi coniunctam &longs;iue ab eo <expan abbr="&longs;eparatã">&longs;eparatam</expan> æqualis portio illius <lb/>materiæ deor&longs;um pelleret, vt patet; igitur æquali motus vi. </s>

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<s>Nec e&longs;t quod prædicti àuthores confugiant ad experientiam, qua <lb/>&longs;cilicet videmus tripudiantes atomos in radio &longs;olari immer&longs;as; igitur <lb/>agitantur ab ip&longs;o radio, quod maximè accidit in linea v&longs;toria, cuius <lb/>effectus veri&longs;&longs;imam rationem &longs;uo loco afferemus, cum de lumine. </s>

<s>Sextò, &longs;unt denique multi, <expan abbr="ii&qacute;ue">iique</expan> ex &longs;euerioribus Peripateticis, qui <lb/>exi&longs;timant grauia moueri deor&longs;um à generante, quod expre&longs;&longs;rs verbis <lb/>traditum e&longs;t ab <emph type="italics"/>Ari&longs;totele l.<emph.end type="italics"/>8. <emph type="italics"/>phy&longs;. cap.<emph.end type="italics"/>4. <emph type="italics"/>iuxta<emph.end type="italics"/> principium illud vniuer<lb/>fali&longs;&longs;imum; <emph type="italics"/>Quidquid mouetur; ab alio mouetur<emph.end type="italics"/>; &longs;ed profectò ij ip&longs;i, qui <lb/>motum grauium generanti tribuunt, tanquam principi cau&longs;æ, non ne<lb/>gant ine&longs;&longs;e grauibus grauitatem, quæ &longs;it principium actiuum minus <lb/>principale motus; ad quem etiam, vt ip&longs;i exi&longs;timant, forma &longs;ub&longs;tantialis <lb/>concurrit; In hoc quippe conueniunt omnes tùm &longs;ectarum Principes, <lb/>tùm recentiores: quidquid &longs;it etiam ex iis ip&longs;is datur motus naturalis, <lb/>qui e&longs;t à virtute proxima intrin&longs;eca; hoc ip&longs;um etiam &longs;en&longs;it Ari&longs;toteles <lb/>lib.4. de cælo cap.

<s>Sextò, &longs;unt denique multi, <expan abbr="ii&qacute;ue">iique</expan> ex &longs;euerioribus Peripateticis, qui <lb/>exi&longs;timant grauia moueri deor&longs;um à generante, quod expre&longs;&longs;is verbis <lb/>traditum e&longs;t ab <emph type="italics"/>Ari&longs;totele l.<emph.end type="italics"/>8. <emph type="italics"/>phy&longs;. cap.<emph.end type="italics"/>4. <emph type="italics"/>iuxta<emph.end type="italics"/> principium illud vniuer<lb/>&longs;ali&longs;&longs;imum; <emph type="italics"/>Quidquid mouetur; ab alio mouetur<emph.end type="italics"/>; &longs;ed profectò ij ip&longs;i, qui <lb/>motum grauium generanti tribuunt, tanquam principi cau&longs;æ, non ne<lb/>gant ine&longs;&longs;e grauibus grauitatem, quæ &longs;it principium actiuum minus <lb/>principale motus; ad quem etiam, vt ip&longs;i exi&longs;timant, forma &longs;ub&longs;tantialis <lb/>concurrit; In hoc quippe conueniunt omnes tùm &longs;ectarum Principes, <lb/>tùm recentiores: quidquid &longs;it etiam ex iis ip&longs;is datur motus naturalis, <lb/>qui e&longs;t à virtute proxima intrin&longs;eca; hoc ip&longs;um etiam &longs;en&longs;it Ari&longs;toteles <lb/>lib.4. de cælo cap.

3. t. </s>

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<s><emph type="italics"/>Motus naturalis non e&longs;t immediatè ab ip&longs;a grauitate.<emph.end type="italics"/></s><s> Probatur, &longs;int <lb/>enim eædem hypoth.1.2.3. igitur maior ictus in fine motus, & velocior <lb/>motus debent habere cau&longs;am; &longs;ed hæc grauitas non e&longs;t, quæ &longs;emper ea<lb/>dem e&longs;t, vt patet, vtrum verò di&longs;tinguatur grauitas ab ip&longs;a corporis <lb/>&longs;ub&longs;tantia di&longs;cutiemus in tractatu &longs;equenti. </s>

<s>Fuit aliquis non infunæ no<lb/>tæ Philo&longs;ophus, qui diceret maiorem illum ictum e&longs;&longs;e ab ipsâ corporis <lb/>&longs;ub&longs;tantiâ; &longs;ed hoc iam refellimus Theoremate 4. lib.1. Adde quod im<lb/>petu, ad extra producitur ab alio impetu per Th.42.lib.1. Dicebat etiam <lb/>velociorem motum e&longs;&longs;e ab ipsâ grauitate connotante præuium motum, <lb/>quod etiam refellemus infrà. </s>

<s>Fuit aliquis non infimæ no<lb/>tæ Philo&longs;ophus, qui diceret maiorem illum ictum e&longs;&longs;e ab ipsâ corporis <lb/>&longs;ub&longs;tantiâ; &longs;ed hoc iam refellimus Theoremate 4. lib.1. Adde quod im<lb/>petu, ad extra producitur ab alio impetu per Th.42.lib.1. Dicebat etiam <lb/>velociorem motum e&longs;&longs;e ab ipsâ grauitate connotante præuium motum, <lb/>quod etiam refellemus infrà. </s>

<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 5.<emph.end type="center"/></s>

<s><emph type="italics"/>Hinc motus naturalis e&longs;t ab impetu.<emph.end type="italics"/></s><s> Probatur; e&longs;t ab aliqua cau&longs;a per <lb/>Ax.8. lib.1. ab aliqua intrin&longs;eca per Th. 1. non à &longs;ub&longs;tantia corporis <lb/>grauis per Th. 3. non à grauitace per Th. 4. igitur ab impetu, quia <lb/>nihil aliud e&longs;&longs;e pote&longs;t intrin&longs;ecum, à quo &longs;it motus pet definitionem <lb/>3. lib.

<s><emph type="italics"/>Hinc motus naturalis e&longs;t ab impetu.<emph.end type="italics"/></s><s> Probatur; e&longs;t ab aliqua cau&longs;a per <lb/>Ax.8. lib.1. ab aliqua intrin&longs;eca per Th. 1. non à &longs;ub&longs;tantia corporis <lb/>grauis per Th. 3. non à grauitate per Th. 4. igitur ab impetu, quia <lb/>nihil aliud e&longs;&longs;e pote&longs;t intrin&longs;ecum, à quo &longs;it motus per definitionem <lb/>3. lib.

1. </s><pb xlink:href="026/01/113.jpg" pagenum="81"/>

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

<s><emph type="italics"/>Hinc produci tantùm pote&longs;t ab ip&longs;a &longs;ubstantia corporis grauis; nam graui<lb/>tas e&longs;t ip&longs;e impetus innatus, de qua infrà:<emph.end type="italics"/> probatur; quia nihil e&longs;t aliud in<lb/>trin&longs;ecum, à quo produci po&longs;&longs;it; quòd autem non produc tur ab alio im<lb/>petu ad intra, patet per Th.41. lib.

<s><emph type="italics"/>Hinc produci tantùm pote&longs;t ab ip&longs;a &longs;ubstantia corporis grauis; nam graui<lb/>tas e&longs;t ip&longs;e impetus innatus, de qua infrà:<emph.end type="italics"/> probatur; quia nihil e&longs;t aliud in<lb/>trin&longs;ecum, à quo produci po&longs;&longs;it; quòd autem non producatur ab alio im<lb/>petu ad intra, patet per Th.41. lib.

1. </s>

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

<s><emph type="italics"/>Impetus ille innatus, qui durat &longs;ecundo instanti, con&longs;eruatur ab aiiqua cau<lb/>&longs;a<emph.end type="italics"/>; e&longs;t certum per Ax. 14.lib.1.num.1. </s>

<s><emph type="italics"/>Impetus ille innatus, qui durat &longs;ecundo instanti, con&longs;eruatur ab aliqua cau<lb/>&longs;a<emph.end type="italics"/>; e&longs;t certum per Ax. 14.lib.1.num.1. </s>

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

<s><emph type="italics"/>Non con&longs;eruatur à cau&longs;a primò productiua.<emph.end type="italics"/></s><s> Probatur per Th.144. lib.1. <lb/>alioquin non po&longs;&longs;et intendi ab eadem cau&longs;a per Th. 146. lib 1. quippè <lb/>con&longs;eruatio nihil e&longs;t aliud, quàm repetita productio, vt con&longs;tat; nam <lb/>cau&longs;a con&longs;eruans verè influit; igitur &longs;i e&longs;t can&longs;a nece&longs;&longs;aria primo, & &longs;e<lb/>cundo in&longs;tanti æquali ni&longs;u influit; influit enim quantum pote&longs;t per Ax. <lb/>12.lib.1.quòd autem impetus intendatur, demon&longs;trabimus infrà; con&longs;ule <lb/>Schol.Th.146.lib.1.in quo habes rationem præclari natura in&longs;tituti; quo <lb/>&longs;cilicet factum e&longs;t, vt qualitates, quæ contrario carent à causâ primò pro<lb/>ductiua; aliæ verò, quæ contrarium habent, ab alia causà con&longs;er<lb/>uentur. </s>

<s><emph type="italics"/>Non con&longs;eruatur à cau&longs;a primò productiua.<emph.end type="italics"/></s><s> Probatur per Th.144. lib.1. <lb/>alioquin non po&longs;&longs;et intendi ab eadem cau&longs;a per Th. 146. lib 1. quippè <lb/>con&longs;eruatio nihil e&longs;t aliud, quàm repetita productio, vt con&longs;tat; nam <lb/>cau&longs;a con&longs;eruans verè influit; igitur &longs;i e&longs;t cau&longs;a nece&longs;&longs;aria primo, & &longs;e<lb/>cundo in&longs;tanti æquali ni&longs;u influit; influit enim quantum pote&longs;t per Ax. <lb/>12.lib.1.quòd autem impetus intendatur, demon&longs;trabimus infrà; con&longs;ule <lb/>Schol.Th.146.lib.1.in quo habes rationem præclari natura in&longs;tituti; quo <lb/>&longs;cilicet factum e&longs;t, vt qualitates, quæ contrario carent à causâ primò pro<lb/>ductiua; aliæ verò, quæ contrarium habent, ab alia causà con&longs;er<lb/>uentur. </s>

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<s>Probatur &longs;ecundò; cre&longs;cit motus grauium in <lb/>libero medio per hypoth. </s>

<s>1.2.3. igitur cre&longs;cit impetus; quia cum motus <lb/>naturalis &longs;it ab impetu per Th.5. quâ proportionc cre&longs;cit effectus, &longs;cilicet <lb/>&longs;ormalis, & exigentiæ; &longs;ic enim motus e&longs;t effectus impetus per Th. 15. <lb/>lib.1.eàdem cre&longs;cit cau&longs;a per Ax.2. Probatur tertiò, quia corpus graue ex <lb/>maiore altitudine cadens maiorem quoque ictum infligit per hypoth.1. <lb/>igitur maior impetus imprimitur in corpore percu&longs;&longs;o; &longs;ed impetus ad ex<lb/>tra producitur ab alio impetu per Th.42.lib.1. igitur &longs;i cre&longs;cit productus <lb/>inpetus, cre&longs;cit impetus producens. </s>

<s>1.2.3. igitur cre&longs;cit impetus; quia cum motus <lb/>naturalis &longs;it ab impetu per Th.5. quâ proportione cre&longs;cit effectus, &longs;cilicet <lb/>formalis, & exigentiæ; &longs;ic enim motus e&longs;t effectus impetus per Th. 15. <lb/>lib.1.eàdem cre&longs;cit cau&longs;a per Ax.2. Probatur tertiò, quia corpus graue ex <lb/>maiore altitudine cadens maiorem quoque ictum infligit per hypoth.1. <lb/>igitur maior impetus imprimitur in corpore percu&longs;&longs;o; &longs;ed impetus ad ex<lb/>tra producitur ab alio impetu per Th.42.lib.1. igitur &longs;i cre&longs;cit productus <lb/>inpetus, cre&longs;cit impetus producens. </s>

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

<s>Hinc reiicies quorumdam placitum, qui volunt cau&longs;am velociotis <lb/>motus e&longs;&longs;e grauitatem ip&longs;am, quatenus connotat motum præuium; quia <lb/>&longs;cilicet grauitas non producit illum maiorem impetum ad extra, vt con<lb/>&longs;tat; nec &longs;ub&longs;tantia ip&longs;ius corporis grauis per Th.40.lib.1.igitur ip&longs;e im<lb/>petus: præterea &longs;i hoc e&longs;&longs;et, fru&longs;trà requireretur impetus contra Th. 5. <lb/>Denique motus præuius nihil e&longs;t amplius, cum alius &longs;uccedit: Vide Th. <lb/>40.lib.1. vbi hæc fusè di&longs;cu&longs;&longs;imus. </s>

<s>Hinc reiicies quorumdam placitum, qui volunt cau&longs;am velocioris <lb/>motus e&longs;&longs;e grauitatem ip&longs;am, quatenus connotat motum præuium; quia <lb/>&longs;cilicet grauitas non producit illum maiorem impetum ad extra, vt con<lb/>&longs;tat; nec &longs;ub&longs;tantia ip&longs;ius corporis grauis per Th.40.lib.1.igitur ip&longs;e im<lb/>petus: præterea &longs;i hoc e&longs;&longs;et, fru&longs;trà requireretur impetus contra Th. 5. <lb/>Denique motus præuius nihil e&longs;t amplius, cum alius &longs;uccedit: Vide Th. <lb/>40.lib.1. vbi hæc fusè di&longs;cu&longs;&longs;imus. </s>

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

<s><emph type="italics"/>Si impetus innatus impeditur, ita vt moueri non po&longs;&longs;it corpus graue, &longs;e<lb/>cundo instanti non producitur nouus impetus.<emph.end type="italics"/></s><s> Probatur primò, non cre&longs;cit <lb/>corporis grauis &longs;eu grauitas, &longs;cu grauitatio, vt con&longs;tat experientiâ; igitur <lb/>non cre&longs;cit impectus; alioquin &longs;i cre&longs;ceret cau&longs;a, cre&longs;ceret effectus per <lb/>Ax.2. igitur de re, quòd &longs;it, certum e&longs;t, atque cuidens; iam demon&longs;tratur <lb/>propter quid &longs;it; impetus &longs;ecundo in&longs;tanti productus e&longs;&longs;et fru&longs;trà; careret <pb xlink:href="026/01/115.jpg" pagenum="83"/>enim &longs;uo fine, vel effectu formali, id e&longs;t motu; igitur e&longs;&longs;et fru&longs;trà, &longs;ed <lb/>quod fru&longs;trà e&longs;t, non e&longs;t per Ax.6.l.1. </s>

<s><emph type="italics"/>Si impetus innatus impeditur, ita vt moueri non po&longs;&longs;it corpus graue, &longs;e<lb/>cundo instanti non producitur nouus impetus.<emph.end type="italics"/></s><s> Probatur primò, non cre&longs;cit <lb/>corporis grauis &longs;eu grauitas, &longs;eu grauitatio, vt con&longs;tat experientiâ; igitur <lb/>non cre&longs;cit impetus; alioquin &longs;i cre&longs;ceret cau&longs;a, cre&longs;ceret effectus per <lb/>Ax.2. igitur de re, quòd &longs;it, certum e&longs;t, atque cuidens; iam demon&longs;tratur <lb/>propter quid &longs;it; impetus &longs;ecundo in&longs;tanti productus e&longs;&longs;et fru&longs;trà; careret <pb xlink:href="026/01/115.jpg" pagenum="83"/>enim &longs;uo fine, vel effectu formali, id e&longs;t motu; igitur e&longs;&longs;et fru&longs;trà, &longs;ed <lb/>quod fru&longs;trà e&longs;t, non e&longs;t per Ax.6.l.1. </s>

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

<s>Ob&longs;erua quæ&longs;o, quod iam &longs;uprà indicattun e&longs;t, e&longs;&longs;e tres veluti &longs;pecies <lb/>impetus. </s>

<s>Ob&longs;erua quæ&longs;o, quod iam &longs;uprà indicatum e&longs;t, e&longs;&longs;e tres veluti &longs;pecies <lb/>impetus. </s>

<s>Prima e&longs;t impetus naturalis innati. </s>

<s>Secunda naturalis acqui&longs;iti. </s>

<s><lb/>Tertia violenti; innatus e&longs;t qui vel à generante &longs;imul cum corpore <lb/>graui productus e&longs;t; qui&longs;quis tandem &longs;it generans, de quo aliàs; vel ab <lb/>ip&longs;o graui qua&longs;i profunditur, id e&longs;t, producitur in &longs;e ip&longs;o &longs;tatim initio, <lb/>quo e&longs;t; porrò cum in corpore graui duplex qua&longs;i proprietas &longs;en&longs;ibilis <lb/>e&longs;&longs;e videatur, &longs;cilicet grauitas, &longs;eu pondus & motus deor&longs;um; certè de<lb/>bet e&longs;&longs;e in co aliquid per quod tùm cogno&longs;ci po&longs;&longs;it eins pondus, tùm in<lb/>cipiat moueri deor&longs;um; quippe maximè corpora ex pondere cogno&longs;ci<lb/>mus, vnumque ab alio di&longs;tinguimus; igitur debet e&longs;&longs;e aliquid, quod &longs;en<lb/>&longs;um afficiat, vt cogno&longs;ci po&longs;&longs;it; atqui illud ip&longs;um non e&longs;t &longs;ub&longs;tantia cor<lb/>poris; nam corpus graue meæ manui &longs;u&longs;tinenti impetum imptimit; <lb/>immò vim alterius impetus infringit; igitur operâ alterius per Th. 40. <lb/>& 42.lib.1. Præterea illud ip&longs;um, quod agit, &longs;eu deor&longs;um pellit &longs;u&longs;tinen<lb/>tem manum, e&longs;t illud ip&longs;um quod inclinat corpus graue deor&longs;um imme<lb/>diatè, &longs;eu quod exigit motum naturalem deor&longs;um; illud autem quod <lb/>immediatè præ&longs;tat hunc motum, nec e&longs;t &longs;ub&longs;tantia corporis grauis per <lb/>Th.3. igitur ip&longs;e impetus per Th.5. adde quod primo in&longs;tanti, quo e&longs;t im<lb/>petus, non e&longs;t motus ille, quem exigit per Th.34. lib.1. igitur præexi&longs;tit <lb/>&longs;emper impetus, qui ne &longs;it fru&longs;trà, habet primum effectum &longs;uum forma<lb/>lem, id e&longs;t grauitationem: Ex his dicendum e&longs;t hunc impetum natiuum <lb/>nunquam de&longs;trui, quia nunquam e&longs;t fru&longs;trà, habet enim &longs;emper aliquem <lb/>effectum, primum quidem &longs;i caret &longs;ecundo; &longs;ecundum verò &longs;i caret pri<lb/>mo; quippe vtrumque &longs;imul habere non pote&longs;t; nam corporis pondus <lb/>cogno&longs;ci non pote&longs;t, dum fertur deor&longs;um accelerato motu, quot verò, <lb/>& quanta commoda ex cognitione ponderis cuiu&longs;libet materiæ proce<lb/>dant, vix explicari pote&longs;t. </s>

<s><lb/>Tertia violenti; innatus e&longs;t qui vel à generante &longs;imul cum corpore <lb/>graui productus e&longs;t; qui&longs;quis tandem &longs;it generans, de quo aliàs; vel ab <lb/>ip&longs;o graui qua&longs;i profunditur, id e&longs;t, producitur in &longs;e ip&longs;o &longs;tatim initio, <lb/>quo e&longs;t; porrò cum in corpore graui duplex qua&longs;i proprietas &longs;en&longs;ibilis <lb/>e&longs;&longs;e videatur, &longs;cilicet grauitas, &longs;eu pondus & motus deor&longs;um; certè de<lb/>bet e&longs;&longs;e in eo aliquid per quod tùm cogno&longs;ci po&longs;&longs;it eius pondus, tùm in<lb/>cipiat moueri deor&longs;um; quippe maximè corpora ex pondere cogno&longs;ci<lb/>mus, vnumque ab alio di&longs;tinguimus; igitur debet e&longs;&longs;e aliquid, quod &longs;en<lb/>&longs;um afficiat, vt cogno&longs;ci po&longs;&longs;it; atqui illud ip&longs;um non e&longs;t &longs;ub&longs;tantia cor<lb/>poris; nam corpus graue meæ manui &longs;u&longs;tinenti impetum imprimit; <lb/>immò vim alterius impetus infringit; igitur operâ alterius per Th. 40. <lb/>& 42.lib.1. Præterea illud ip&longs;um, quod agit, &longs;eu deor&longs;um pellit &longs;u&longs;tinen<lb/>tem manum, e&longs;t illud ip&longs;um quod inclinat corpus graue deor&longs;um imme<lb/>diatè, &longs;eu quod exigit motum naturalem deor&longs;um; illud autem quod <lb/>immediatè præ&longs;tat hunc motum, nec e&longs;t &longs;ub&longs;tantia corporis grauis per <lb/>Th.3. igitur ip&longs;e impetus per Th.5. adde quod primo in&longs;tanti, quo e&longs;t im<lb/>petus, non e&longs;t motus ille, quem exigit per Th.34. lib.1. igitur præexi&longs;tit <lb/>&longs;emper impetus, qui ne &longs;it fru&longs;trà, habet primum effectum &longs;uum forma<lb/>lem, id e&longs;t grauitationem: Ex his dicendum e&longs;t hunc impetum natiuum <lb/>nunquam de&longs;trui, quia nunquam e&longs;t fru&longs;trà, habet enim &longs;emper aliquem <lb/>effectum, primum quidem &longs;i caret &longs;ecundo; &longs;ecundum verò &longs;i caret pri<lb/>mo; quippe vtrumque &longs;imul habere non pote&longs;t; nam corporis pondus <lb/>cogno&longs;ci non pote&longs;t, dum fertur deor&longs;um accelerato motu, quot verò, <lb/>& quanta commoda ex cognitione ponderis cuiu&longs;libet materiæ proce<lb/>dant, vix explicari pote&longs;t. </s>

<s>Ex his verò concludendum &longs;upere&longs;t impetum innatum e&longs;&longs;e proprie<lb/>tatem quarto modo, vt vulgò aiunt, corporis grauis; ac proinde ab illo <lb/>in&longs;eparabilem; quid verò fiat de illo, cum corpus graue fit leuc; &longs;i tamen <lb/>hoc aliquando accidit, dicemus cum de grauitate, & grauitatione, iam <lb/>verò &longs;atis e&longs;t ad præ&longs;ens in&longs;titutum impetum innatum ab ip&longs;o corport <lb/>graui nunquam &longs;eparari, quandiu remanet graue. </s>

<s>Ex his verò concludendum &longs;upere&longs;t impetum innatum e&longs;&longs;e proprie<lb/>tatem quarto modo, vt vulgò aiunt, corporis grauis; ac proinde ab illo <lb/>in&longs;eparabilem; quid verò fiat de illo, cum corpus graue fit leue; &longs;i tamen <lb/>hoc aliquando accidit, dicemus cum de grauitate, & grauitatione, iam <lb/>verò &longs;atis e&longs;t ad præ&longs;ens in&longs;titutum impetum innatum ab ip&longs;o corpori <lb/>graui nunquam &longs;eparari, quandiu remanet graue. </s>

<s>Impetus naturalis acqui&longs;itus producitur ab codem principio intrin<lb/>&longs;eco; hinc dicitur naturalis: dicitur verò acqui&longs;itus, quia non e&longs;t inna<lb/>tus; &longs;ed &longs;eparatur à corpore graui; quod &longs;emper co caret, quandiu <lb/>quie&longs;cit: &longs;ed innato tantùm accedit ad motus accelerationem, & ad alia <lb/>quamplurima, quæ ex ea &longs;equuntur; putà maiorem percu&longs;&longs;ionem, re&longs;i<lb/>&longs;tentiam, vim, & ad tollendum totius naturæ languiorem; quo certè af<lb/>ficeretur, &longs;i corpus grauc tardi&longs;&longs;imo motu deor&longs;um ferretur, de quo in<lb/>frà; Porrò impetus acqui&longs;itus in multis differt ab innato; primò quia <pb xlink:href="026/01/116.jpg" pagenum="84"/>de&longs;truitur à corpore re&longs;i&longs;tente co modo, quo diximus, & dicemus infrà. </s>

<s>Impetus naturalis acqui&longs;itus producitur ab codem principio intrin<lb/>&longs;eco; hinc dicitur naturalis: dicitur verò acqui&longs;itus, quia non e&longs;t inna<lb/>tus; &longs;ed &longs;eparatur à corpore graui; quod &longs;emper eo caret, quandiu <lb/>quie&longs;cit: &longs;ed innato tantùm accedit ad motus accelerationem, & ad alia <lb/>quamplurima, quæ ex ea &longs;equuntur; putà maiorem percu&longs;&longs;ionem, re&longs;i<lb/>&longs;tentiam, vim, & ad tollendum totius naturæ langudiorem; quo certè af<lb/>ficeretur, &longs;i corpus graue tardi&longs;&longs;imo motu deor&longs;um ferretur, de quo in<lb/>frà; Porrò impetus acqui&longs;itus in multis differt ab innato; primò quia <pb xlink:href="026/01/116.jpg" pagenum="84"/>de&longs;truitur à corpore re&longs;i&longs;tente eo modo, quo diximus, & dicemus infrà. </s>

<s><lb/>Secundò, quia determinari pote&longs;t ad omnem lincam. </s>

<s><lb/>Secundò, quia determinari pote&longs;t ad omnem lineam. </s>

<s>Impetus violentus e&longs;t, qui e&longs;t ab extrin&longs;eco, de quo agemus infrà, & <lb/>iam &longs;uprà in lib.1. multa &longs;unt de eo demon&longs;trata. </s>

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

<s><emph type="italics"/>Hinc motus naturalis deor&longs;um acceleratur<emph.end type="italics"/>; hoc ip&longs;um &longs;uppo&longs;ui &longs;uprà <lb/>Quod e&longs;&longs;et in hyp.1.2.3. iam verò demon&longs;tro propter quid e&longs;t; &longs;ie cnim <lb/>hypothe&longs;is in Theorema conuerti pote&longs;t, vt fæpè monuimus in metho<lb/>do; igitur probatur hoc Theorema facilè; cre&longs;cit impetus in corpore gra<lb/>ui, quod tendit deor&longs;um in libero medio per T. 15. igitar cre&longs;cit cau&longs;a <lb/>motus; nam impetus e&longs;t can&longs;a immediata motus naturalis per Th. 51. <lb/>&longs;ed quâ proportione cre&longs;cit cau&longs;a, debet cre&longs;cere effectus per Ax.2. igi<lb/>tur motus naturalis deor&longs;um cre&longs;cit, id e&longs;t acceleratur, id e&longs;t fit velo<lb/>cior, quod erat dem: nec e&longs;t quod aliquis exi&longs;timet hic à me committi <lb/>vitio&longs;um argumentationis circulum; quippe probaui &longs;uprà cre&longs;cere im<lb/>petum, quia cre&longs;cit motus; iam verò probo cre&longs;cere motum, quia cre&longs;<lb/>cit impetus; nam primò probaui produci nouum impetum in Th.12. co <lb/>quod &longs;ecundo in&longs;tanti. </s>

<s><emph type="italics"/>Hinc motus naturalis deor&longs;um acceleratur<emph.end type="italics"/>; hoc ip&longs;um &longs;uppo&longs;ui &longs;uprà <lb/>Quod e&longs;&longs;et in hyp.1.2.3. iam verò demon&longs;tro propter quid e&longs;t; &longs;ie enim <lb/>hypothe&longs;is in Theorema conuerti pote&longs;t, vt 6longs;æpè monuimus in metho<lb/>do; igitur probatur hoc Theorema facilè; cre&longs;cit impetus in corpore gra<lb/>ui, quod tendit deor&longs;um in libero medio per T. 15. igitur cre&longs;cit cau&longs;a <lb/>motus; nam impetus e&longs;t cau&longs;a immediata motus naturalis per Th. 51. <lb/>&longs;ed quâ proportione cre&longs;cit cau&longs;a, debet cre&longs;cere effectus per Ax.2. igi<lb/>tur motus naturalis deor&longs;um cre&longs;cit, id e&longs;t acceleratur, id e&longs;t fit velo<lb/>cior, quod erat dem: nec e&longs;t quod aliquis exi&longs;timet hic à me committi <lb/>vitio&longs;um argumentationis circulum; quippe probaui &longs;uprà cre&longs;cere im<lb/>petum, quia cre&longs;cit motus; iam verò probo cre&longs;cere motum, quia cre&longs;<lb/>cit impetus; nam primò probaui produci nouum impetum in Th.12. eo <lb/>quod &longs;ecundo in&longs;tanti. </s>

<s>v.g. &longs;it eadem cau&longs;a nece&longs;&longs;aria applicata non im<lb/>pedita, igitur tàm debet agere &longs;ecundo quàm primo in&longs;tanti, hæc fuit <lb/>mea probatio à priori; &longs;ecundò verò probaui ex hypothe&longs;i certa; quia <lb/>&longs;cilicet cre&longs;cit motus, cuius veritatem cogno&longs;co &longs;en&longs;ibiliter in &longs;e, vnde <lb/>&longs;uppono tantùm de illa quod &longs;it; igitur nullus committitur circulus; nam <lb/>diuer&longs;a e&longs;t omninò cognitio. </s>

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

<s>Ob&longs;eruabis etiam aliud naturæ in&longs;titutum, quo &longs;cilicet factum e&longs;t, vt <pb xlink:href="026/01/117.jpg" pagenum="85"/>corpora grauia motu naturali accelerato deor&longs;um ferantur; &longs;i enim motu <lb/>ferrentur æquabili, vel e&longs;&longs;et æqualis illi quem initio &longs;ui de&longs;cen&longs;us ha<lb/>bent, qui e&longs;t tardi&longs;&longs;imus, vt con&longs;tat ex ip&longs;a ictuum differentia; atque <lb/>ita infinitum ferè tempus ponerent grauia in minimo etiam de&longs;cen&longs;u, <lb/>quod e&longs;&longs;et maximè incommodum; &longs;i verò motus ille e&longs;&longs;et æqualis mo<lb/>tui v.g. quem acqui&longs;iuit in fpatio 3. vel 4. perticarum, pondera corpo<lb/>rum cre&longs;cerent in immen&longs;um, ide&longs;t in ea proportione, qua ictus, qui in<lb/>fligitur à corpore graui confecto 4. perticarum &longs;patio maior e&longs;t ictu, qui <lb/>infligitur po&longs;t decur&longs;um minimum omnium &longs;patiorum, quod valdè in<lb/>commodum e&longs;&longs;et. </s>

<s>Ob&longs;eruabis etiam aliud naturæ in&longs;titutum, quo &longs;cilicet factum e&longs;t, vt <pb xlink:href="026/01/117.jpg" pagenum="85"/>corpora grauia motu naturali accelerato deor&longs;um ferantur; &longs;i enim motu <lb/>ferrentur æquabili, vel e&longs;&longs;et æqualis illi quem initio &longs;ui de&longs;cen&longs;us ha<lb/>bent, qui e&longs;t tardi&longs;&longs;imus, vt con&longs;tat ex ip&longs;a ictuum differentia; atque <lb/>ita infinitum ferè tempus ponerent grauia in minimo etiam de&longs;cen&longs;u, <lb/>quod e&longs;&longs;et maximè incommodum; &longs;i verò motus ille e&longs;&longs;et æqualis mo<lb/>tui v.g. quem acqui&longs;iuit in &longs;patio 3. vel 4. perticarum, pondera corpo<lb/>rum cre&longs;cerent in immen&longs;um, ide&longs;t in ea proportione, qua ictus, qui in<lb/>fligitur à corpore graui confecto 4. perticarum &longs;patio maior e&longs;t ictu, qui <lb/>infligitur po&longs;t decur&longs;um minimum omnium &longs;patiorum, quod valdè in<lb/>commodum e&longs;&longs;et. </s>

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

<s><emph type="italics"/>Qua proportione cre&longs;cit impetus acceleratur motus<emph.end type="italics"/>; quia quæ proportio<lb/>ne cre&longs;cit cau&longs;a, ctiam cre&longs;cit effectus per Ax.2. </s>

<s><emph type="italics"/>Qua proportione cre&longs;cit impetus acceleratur motus<emph.end type="italics"/>; quia quæ proportio<lb/>ne cre&longs;cit cau&longs;a, etiam cre&longs;cit effectus per Ax.2. </s>

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

<s><emph type="italics"/>Hinc æqualibus temporibus in de&longs;cen&longs;u corpus graue acquirit aqualia ve<lb/>locitatis, vel acce&longs;erationis momenta<emph.end type="italics"/>; hoc ip&longs;um e&longs;t quod definitionis lo<lb/>co Galileus in dialogo tertio de motu naturali a&longs;&longs;umit; quod tamen <lb/>meo iudicio fuit antè demon&longs;trandum quàm &longs;upponendum; quare &longs;ic <lb/>demon&longs;tramus, quâ proportione cre&longs;cit impetus, cre&longs;cit motus per Th. <lb/>18. &longs;ed temporibus æqualibus acquiruntur æquales impetus gradus per <lb/>Th.17. igitur æqualia velocitatis momenta, vel incrementa. </s>

<s><emph type="italics"/>Hinc æqualibus temporibus in de&longs;cen&longs;u corpus graue acquirit aqualia ve<lb/>locitatis, vel accelerationis momenta<emph.end type="italics"/>; hoc ip&longs;um e&longs;t quod definitionis lo<lb/>co Galileus in dialogo tertio de motu naturali a&longs;&longs;umit; quod tamen <lb/>meo iudicio fuit antè demon&longs;trandum quàm &longs;upponendum; quare &longs;ic <lb/>demon&longs;tramus, quâ proportione cre&longs;cit impetus, cre&longs;cit motus per Th. <lb/>18. &longs;ed temporibus æqualibus acquiruntur æquales impetus gradus per <lb/>Th.17. igitur æqualia velocitatis momenta, vel incrementa. </s>

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

<s><emph type="italics"/>Spatia que per curruntur motu aquabili æqualibus temporibus &longs;unt æqualia<emph.end type="italics"/>; <lb/>Probatur per Def.2. </s>

<s><emph type="italics"/>Spatia que per curruntur motu æquabili æqualibus temporibus &longs;unt æqualia<emph.end type="italics"/>; <lb/>Probatur per Def.2. </s>

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

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

<s><emph type="italics"/>Duo motus æquabiles, quibus percurruntur &longs;patia æqualia &longs;unt vt tempora <lb/>permutande<emph.end type="italics"/>;, patet, quia velocior e&longs;t, quò percurritur &longs;patium æquale <lb/>minori tempore per Def.2. l. 1. Igitur eò veiocior, quò minori tem<lb/>pore. </s>

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

<s><emph type="italics"/>Si idem mobile temporibus æqualibus pereurrat duo &longs;patia motu æquabili, <lb/>&longs;ed inæquali velocitate; &longs;patia erunt vt velocitates, & hæ vt illa; imò &longs;i <lb/>&longs;patia &longs;unt vt velocitates, tempora erunt æqualia<emph.end type="italics"/>; pater etiam per <lb/>Th.25. </s>

<s><emph type="italics"/>Si idem mobile temporibus æqualibus percurrat duo &longs;patia motu æquabili, <lb/>&longs;ed inæquali velocitate; &longs;patia erunt vt velocitates, & hæ vt illa; imò &longs;i <lb/>&longs;patia &longs;unt vt velocitates, tempora erunt æqualia<emph.end type="italics"/>; pater etiam per <lb/>Th.25. </s>

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

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

<s><emph type="italics"/>Si duo mobilia ferantur motu æquabili per diuer&longs;a &longs;patia, & diuer&longs;a velo<lb/>eitate, tempora erunt in ratione compo&longs;ita ex ratione &longs;paliorum & ratioue <lb/>velocitatum permutata<emph.end type="italics"/>; probatur eodem modo quo &longs;uperius Th. 30. &longs;it <lb/>ratio &longs;patiorum 4/1, velocitatum 4/2; permutetur hæc 1/4; componetur ex <lb/>vtraque 4/1, ide&longs;t 1/2, quæ e&longs;t ratio temporum. </s>

<s><emph type="italics"/>Si duo mobilia ferantur motu æquabili per diuer&longs;a &longs;patia, & diuer&longs;a velo<lb/>citate, tempora erunt in ratione compo&longs;ita ex ratione &longs;patiorum & ratione <lb/>velocitatum permutata<emph.end type="italics"/>; probatur eodem modo quo &longs;uperius Th. 30. &longs;it <lb/>ratio &longs;patiorum 4/1, velocitatum 4/2; permutetur hæc 1/4; componetur ex <lb/>vtraque 4/1, ide&longs;t 1/2, quæ e&longs;t ratio temporum. </s>

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

<s><emph type="italics"/>Si duo mobilia æquabili motu ferantur per diuer&longs;a &longs;patia, & inæqualibus <lb/>temporibus; ratio velocitatum erit compo&longs;ita ex ratione &longs;patiorum, & ex ra<lb/>tione temporum permutata<emph.end type="italics"/>; Probatur eodem modo; &longs;it ratio &longs;patiorum <lb/>4/2 temporum 1/2, permutetur 2/1, compo&longs;ita ex vtraque crit 2/2, ide&longs;t 4. <lb/>quæ e&longs;t ratio velocitatum. </s>

<s><emph type="italics"/>Si duo mobilia æquabili motu ferantur per diuer&longs;a &longs;patia, & inæqualibus <lb/>temporibus; ratio velocitatum erit compo&longs;ita ex ratione &longs;patiorum, & ex ra<lb/>tione temporum permutata<emph.end type="italics"/>; Probatur eodem modo; &longs;it ratio &longs;patiorum <lb/>4/2 temporum 1/2, permutetur 2/1, compo&longs;ita ex vtraque erit 2/2, ide&longs;t 4. <lb/>quæ e&longs;t ratio velocitatum. </s>

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

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

<s><emph type="italics"/>Hinc &longs;ingalis in&longs;tantibus æqualiter cre&longs;cit & intenditur impetus<emph.end type="italics"/> per Th. <lb/>34. igitur æqualiter etiam &longs;ingulis in&longs;tantibus cre&longs;cit velocitas motus <lb/>per Ax.2. </s>

<s><emph type="italics"/>Hinc &longs;ingulis in&longs;tantibus æqualiter cre&longs;cit & intenditur impetus<emph.end type="italics"/> per Th. <lb/>34. igitur æqualiter etiam &longs;ingulis in&longs;tantibus cre&longs;cit velocitas motus <lb/>per Ax.2. </s>

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

<s><emph type="italics"/>Hinc cre&longs;cit impetus iuxta progre&longs;&longs;ionem arithmeticam; cum &longs;ingula in<lb/>&longs;tantia æqualem impetum addant<emph.end type="italics"/>; &longs;i primo in&longs;tanti &longs;it vnus gradus, crunt <lb/>duo; productus &longs;cilicet alteri additus qui con&longs;eruatur, tertio erunt;. </s>

<s><emph type="italics"/>Hinc cre&longs;cit impetus iuxta progre&longs;&longs;ionem arithmeticam; cum &longs;ingula in<lb/>&longs;tantia æqualem impetum addant<emph.end type="italics"/>; &longs;i primo in&longs;tanti &longs;it vnus gradus, erunt <lb/>duo; productus &longs;cilicet alteri additus qui con&longs;eruatur, tertio erunt;. </s>

<s><lb/>quarto 4. quinto 5. &c. </s>

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

<s><emph type="italics"/>Hinc &longs;patium qucd acquiritur &longs;ecundo in&longs;tanti e&longs;t duplum illius, qaod ac<lb/>quiritur primo.<emph.end type="italics"/></s><s> Probatur, quia velocitas e&longs;t dupla per Th 38. igitur &longs;pa<lb/>tium duplum, & triplum tertio, quadruplum quarto, &c. </s>

<s><emph type="italics"/>Hinc &longs;patium qucd acquiritur &longs;ecundo in&longs;tanti e&longs;t duplum illius, quod ac<lb/>quiritur primo.<emph.end type="italics"/></s><s> Probatur, quia velocitas e&longs;t dupla per Th 38. igitur &longs;pa<lb/>tium duplum, & triplum tertio, quadruplum quarto, &c. </s>

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

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

<s><emph type="italics"/>Hinc &longs;patia cre&longs;cunt &longs;ingulis in&longs;tantibus æqualibus &longs;ecundùm pregre&longs;&longs;io<lb/>nem arithmeticam<emph.end type="italics"/>; quia cre&longs;cit vt velocitas per Th.40. hæc vt impetus <lb/>per Th.38. hic demum iuxta progre&longs;&longs;ionem arithmeticam per Th. 37. <lb/>igitur &longs;i &longs;patium acqui&longs;itum primo in&longs;tanti &longs;it 1. acqui&longs;itum &longs;ecundo crit <lb/>2. tertio 3. quarto 4. &c. </s>

<s><emph type="italics"/>Hinc &longs;patia cre&longs;cunt &longs;ingulis in&longs;tantibus æqualibus &longs;ecundùm progre&longs;&longs;io<lb/>nem arithmeticam<emph.end type="italics"/>; quia cre&longs;cit vt velocitas per Th.40. hæc vt impetus <lb/>per Th.38. hic demum iuxta progre&longs;&longs;ionem arithmeticam per Th. 37. <lb/>igitur &longs;i &longs;patium acqui&longs;itum primo in&longs;tanti &longs;it 1. acqui&longs;itum &longs;ecundo erit <lb/>2. tertio 3. quarto 4. &c. </s>

<s>hinc &longs;patia acqui&longs;ita &longs;ingulis in&longs;tantibus &longs;unt <lb/>vt &longs;eries numerorm, qui componunt progre&longs;&longs;ionem &longs;implicem, &longs;cilicet <lb/>1.2.3.4.5.6. &c. </s>

<s>hinc &longs;patia acqui&longs;ita &longs;ingulis in&longs;tantibus &longs;unt <lb/>vt &longs;eries numerorum, qui componunt progre&longs;&longs;ionem &longs;implicem, &longs;cilicet <lb/>1.2.3.4.5.6. &c. </s>

<s>dixi &longs;ingulis in&longs;tantibus æqualibus, quod e&longs;t apprimè <lb/>tenendum; &longs;i enim a&longs;&longs;umantur partes temporis maiores, perturbatur <lb/>hæc progre&longs;&longs;io, de quo infrà. </s><pb xlink:href="026/01/121.jpg" pagenum="89"/>

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

<s>Ob&longs;eruabis primò hanc &longs;patiorum rationem, quæ e&longs;t eadem cum ra<lb/>tione velocitatum a&longs;&longs;umendam tantùm e&longs;&longs;e in iis &longs;patiis, quæ acquirun<lb/>tur &longs;ingulis in&longs;tantibus; &longs;i enim accipiantur partes temporis maiores, quæ <lb/>conflentur ex multis in&longs;tantibus; haud dubiè maior erit ratio &longs;patio<lb/>rum, quàm velocitatum.v.g.&longs;i primo in&longs;tanti acquiratur primo &longs;patium, <lb/>&longs;ecundo, 2.tertio, 3.quarto 4.igitur &longs;i <expan abbr="cõparetur">comparetur</expan> velocitas primi in&longs;tantis <lb/>cum velocitate quarti æqualis erit, vt ratio &longs;patiorum, id e&longs;t, vt 1. ad 4. <lb/>At verò &longs;i accipiatur pars temporis con&longs;tans duobus in&longs;tantibus, hæc 4. <lb/>in&longs;tantia conflabunt tantùm 2. partes temporis æquales; in prima ac<lb/>quirentur 3.&longs;patia, in &longs;ecunda 7.vt patet: &longs;ed quia velocitas primæ par<lb/>tis temporis non e&longs;t æquabilis, nec etiam velocitas &longs;ecundæ; addantur <lb/>velocitates primi & &longs;ecundi in&longs;tantis, itemque &longs;eor&longs;im velocitates tertij, <lb/>& quarti; certè ratio collectorum crit vt ratio &longs;patiorum; &longs;i enim velo<lb/>citas &longs;ecundi in&longs;tantis comparetur cum velocitate quarti e&longs;t tantùm <lb/>1/2 cum tamen primum &longs;patium &longs;it ad &longs;ecundum in ratione 3/7. </s>

<s>Ob&longs;eruabis primò hanc &longs;patiorum rationem, quæ e&longs;t eadem cum ra<lb/>tione velocitatum a&longs;&longs;umendam tantùm e&longs;&longs;e in iis &longs;patiis, quæ acquirun<lb/>tur &longs;ingulis in&longs;tantibus; &longs;i enim accipiantur partes temporis maiores, quæ <lb/>conflentur ex multis in&longs;tantibus; haud dubiè maior erit ratio &longs;patio<lb/>rum, quàm velocitatum.v.g.&longs;i primo in&longs;tanti acquiratur primo &longs;patium, <lb/>&longs;ecundo, 2.tertio, 3.quarto 4.igitur &longs;i <expan abbr="cõparetur">comparetur</expan> velocitas primi in&longs;tantis <lb/>cum velocitate quarti æqualis erit, vt ratio &longs;patiorum, id e&longs;t, vt 1. ad 4. <lb/>At verò &longs;i accipiatur pars temporis con&longs;tans duobus in&longs;tantibus, hæc 4. <lb/>in&longs;tantia conflabunt tantùm 2. partes temporis æquales; in prima ac<lb/>quirentur 3.&longs;patia, in &longs;ecunda 7.vt patet: &longs;ed quia velocitas primæ par<lb/>tis temporis non e&longs;t æquabilis, nec etiam velocitas &longs;ecundæ; addantur <lb/>velocitates primi & &longs;ecundi in&longs;tantis, itemque &longs;eor&longs;im velocitates tertij, <lb/>& quarti; certè ratio collectorum erit vt ratio &longs;patiorum; &longs;i enim velo<lb/>citas &longs;ecundi in&longs;tantis comparetur cum velocitate quarti e&longs;t tantùm <lb/>1/2 cum tamen primum &longs;patium &longs;it ad &longs;ecundum in ratione 3/7. </s>

<s>Secundò, &longs;i comparentur &longs;patia cum temporibus e&longs;t alia ratio v.g.&longs;pa<lb/>tium acqui&longs;itum vno in&longs;tanti &longs;e habet ad &longs;patium acqui&longs;itum in duobus <lb/>in&longs;tantibus, vt 1, ad 3.in tribus vt 1.ad 6.in 4. vt 1. ad 10. </s>

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

<s><emph type="italics"/>Collectio &longs;patiorum e&longs;t &longs;umma terminorum huius progre&longs;&longs;ionis arithmeticæ<emph.end type="italics"/>; <lb/>Gùm enim ratio &longs;patiorum &longs;it vt ratio velocitatum; dum &longs;cilicet hæc <lb/>progre&longs;&longs;io accipitur in in&longs;tantibus, & ratio velocitatum vt ratio incre<lb/>menti impetuum; vt con&longs;tat ex dictis, & hæc &longs;equatur &longs;implicem <lb/>progre&longs;&longs;ionem 1. 2. 3. 4. &c. </s>

<s><emph type="italics"/>Collectio &longs;patiorum e&longs;t &longs;umma terminorum huius progre&longs;&longs;ionis arithmeticæ<emph.end type="italics"/>; <lb/></s>

<s>Cùm enim ratio &longs;patiorum &longs;it vt ratio velocitatum; dum &longs;cilicet hæc <lb/>progre&longs;&longs;io accipitur in in&longs;tantibus, & ratio velocitatum vt ratio incre<lb/>menti impetuum; vt con&longs;tat ex dictis, & hæc &longs;equatur &longs;implicem <lb/>progre&longs;&longs;ionem 1. 2. 3. 4. &c. </s>

<s>certè collectio &longs;patiorum e&longs;t &longs;umma ter<lb/>minorum. </s>

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

<s><emph type="italics"/>Data &longs;umma progre&longs;&longs;ionis huius &longs;implicis, inuenietur numerus terminorum, <lb/>&longs;i inueniatur numerus, per quem diuidatur, qui &longs;uperet tantùm vnitate du<lb/>plum quotientis<emph.end type="italics"/>; quippe habebis in duplo quotientis numerum termino<lb/>rum v.g. &longs;it &longs;umma 10. diui&longs;or &longs;it 5. quotiens 2. duplus 4. hic e&longs;t nume<lb/>rus terminorum datæ &longs;ummæ; &longs;it alia &longs;umma 21. diui&longs;or &longs;it 7.quotiens 3. <lb/>numerus terminorum 6. &longs;it alia &longs;umma 36. dini&longs;or &longs;it 9. quotiens 4. nu<lb/>merus terminorum 8. &longs;it alia &longs;umma 45. partitor &longs;it 10. quotiens 4 1/2, <lb/>numerus terminorum 9. quomodo verò hic partitor inueniri po&longs;&longs;it, vi<lb/>derint Arithinetici; nec enim e&longs;t huius loci, quamquam datâ &longs;ummâ <lb/>huius progre&longs;&longs;ionis &longs;implicis facilè cogno&longs;ci pote&longs;t numerus termino<lb/>rum; duplicetur enim, & radix 9. neglecto re&longs;iduo dabit numerum ter<lb/>minorum v.g. &longs;it &longs;umma 21. duplicetur, erit 42. rad. </s>

<s><emph type="italics"/>Data &longs;umma progre&longs;&longs;ionis huius &longs;implicis, inuenietur numerus terminorum, <lb/>&longs;i inueniatur numerus, per quem diuidatur, qui &longs;uperet tantùm vnitate du<lb/>plum quotientis<emph.end type="italics"/>; quippe habebis in duplo quotientis numerum termino<lb/>rum v.g. &longs;it &longs;umma 10. diui&longs;or &longs;it 5. quotiens 2. duplus 4. hic e&longs;t nume<lb/>rus terminorum datæ &longs;ummæ; &longs;it alia &longs;umma 21. diui&longs;or &longs;it 7.quotiens 3. <lb/>numerus terminorum 6. &longs;it alia &longs;umma 36. dini&longs;or &longs;it 9. quotiens 4. nu<lb/>merus terminorum 8. &longs;it alia &longs;umma 45. partitor &longs;it 10. quotiens 4 1/2, <lb/>numerus terminorum 9. quomodo verò hic partitor inueniri po&longs;&longs;it, vi<lb/>derint Arithmetici; nec enim e&longs;t huius loci, quamquam datâ &longs;ummâ <lb/>huius progre&longs;&longs;ionis &longs;implicis facilè cogno&longs;ci pote&longs;t numerus termino<lb/>rum; duplicetur enim, & radix 9. neglecto re&longs;iduo dabit numerum ter<lb/>minorum v.g. &longs;it &longs;umma 21. duplicetur, erit 42. rad. </s>

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

<s><emph type="italics"/>Semper decre&longs;cit proportio incrementi velocitatis, id est maior est proportio <lb/>velocitatis &longs;ecundi in&longs;tantis ad primum quàm tertij ad &longs;ecundum, & maior<emph.end type="italics"/><pb xlink:href="026/01/123.jpg" pagenum="91"/><emph type="italics"/>tertij ad &longs;ecundum quàm quarti ad tertium, atque ita deinceps<emph.end type="italics"/>; &longs;it enim <lb/>primo in&longs;tanti velocitas vt 1.&longs;ecundo erit, vt 2.tertio, vt 3.quarto, vt 4. <lb/>&longs;ed maior e&longs;t proportio 2.ad 1.quàm 3.ad 2. & hæc maior quàm 4. ad 3. <lb/>atque ita deinceps; &longs;imiliter maior e&longs;t proportio &longs;patij quod percurritur <lb/>&longs;ecundo in&longs;tanti ad &longs;patium, quod percurritur primo, quàm &longs;patij, quod <lb/>percurritur &longs;ecundo in&longs;tanti ad &longs;patium, quod percurtitur primo quàm <lb/>&longs;patij quod percurritur tertio ad &longs;patium, quod percurritur &longs;ecundo, at<lb/>que ita deinceps; e&longs;t enim eadem ratio &longs;patiorum quæ &longs;ingulis in&longs;tanti<lb/>bus re&longs;pondent, quæ velocitatum, vt demon&longs;tratum e&longs;t &longs;uprà. </s>

<s><emph type="italics"/>Semper decre&longs;cit proportio incrementi velocitatis, id est maior est proportio <lb/>velocitatis &longs;ecundi in&longs;tantis ad primum quàm tertij ad &longs;ecundum, & maior<emph.end type="italics"/><pb xlink:href="026/01/123.jpg" pagenum="91"/><emph type="italics"/>tertij ad &longs;ecundum quàm quarti ad tertium, atque ita deinceps<emph.end type="italics"/>; &longs;it enim <lb/>primo in&longs;tanti velocitas vt 1.&longs;ecundo erit, vt 2.tertio, vt 3.quarto, vt 4. <lb/>&longs;ed maior e&longs;t proportio 2.ad 1.quàm 3.ad 2. & hæc maior quàm 4. ad 3. <lb/>atque ita deinceps; &longs;imiliter maior e&longs;t proportio &longs;patij quod percurritur <lb/>&longs;ecundo in&longs;tanti ad &longs;patium, quod percurritur primo, quàm &longs;patij, quod <lb/>percurritur &longs;ecundo in&longs;tanti ad &longs;patium, quod percurritur primo quàm <lb/>&longs;patij quod percurritur tertio ad &longs;patium, quod percurritur &longs;ecundo, at<lb/>que ita deinceps; e&longs;t enim eadem ratio &longs;patiorum quæ &longs;ingulis in&longs;tanti<lb/>bus re&longs;pondent, quæ velocitatum, vt demon&longs;tratum e&longs;t &longs;uprà. </s>

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

<s><emph type="italics"/>Minor e&longs;t proportio totius &longs;patij, quod acquiritur duobus instantibus ad to, <lb/>tum &longs;patium, quod acquiritur vno, quàm &longs;it illius, quod acquiritur quatuor in<lb/>&longs;tantibus ad aliud, quod acquiritur duobus<emph.end type="italics"/>; patet-ex dictis; &longs;i enim primo <lb/>in&longs;tanti acquiritur vnum &longs;patium, &longs;ecundo acquiruntur 2.igitur duobus <lb/>&longs;imul acquirantur 3. igitur proportio e&longs;t vt 3.ad 1.Sed &longs;i duobus acqui<lb/>runtur 3. &longs;patia; certè 4.in&longs;tantibus acquiruntur 10. igitur proportio e&longs;t <lb/>vt 10.ad 3. &longs;ed proportio 10/3 e&longs;t maior 3/1, erit adhuc maior proportio &longs;pa<lb/>tij quod acquiretur 6. in&longs;tantibus ad illud quod acquiritur tribus; e&longs;t <lb/>enim (21/6) vt patet. </s>

<s><emph type="italics"/>Minor e&longs;t proportio totius &longs;patij, quod acquiritur duobus instantibus ad to<lb/>tum &longs;patium, quod acquiritur vno, quàm &longs;it illius, quod acquiritur quatuor in<lb/>&longs;tantibus ad aliud, quod acquiritur duobus<emph.end type="italics"/>; patet ex dictis; &longs;i enim primo <lb/>in&longs;tanti acquiritur vnum &longs;patium, &longs;ecundo acquiruntur 2.igitur duobus <lb/>&longs;imul acquirantur 3. igitur proportio e&longs;t vt 3.ad 1.Sed &longs;i duobus acqui<lb/>runtur 3. &longs;patia; certè 4.in&longs;tantibus acquiruntur 10. igitur proportio e&longs;t <lb/>vt 10.ad 3. &longs;ed proportio 10/3 e&longs;t maior 3/1, erit adhuc maior proportio &longs;pa<lb/>tij quod acquiretur 6. in&longs;tantibus ad illud quod acquiritur tribus; e&longs;t <lb/>enim (21/6) vt patet. </s>

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

<s><emph type="italics"/>Si componatur æquabilis motus ex &longs;ubdupla velocitate maxima, & mini<lb/>ma, æquali tempore, idem &longs;patium percurretur hoc motu naturaliter aceclera<lb/>to<emph.end type="italics"/>; &longs;it enim maxima velocitas vt 6. minima vt 1. motu naturaliter acce<lb/>lerato percurrentur &longs;patia 21. cuius &longs;ummæ termini &longs;unt 6.igitur 6. in<lb/>&longs;tantibus con&longs;tat hic motus; accipiatur &longs;ubduplum maximæ, & minimæ <lb/>velocitatis, &longs;cilicet 3 1/2. sítque velocitas motus æquabilis in&longs;tantium 6. <lb/>haud dubiè &longs;i ducantur 3 1/2 in 6 erunt 21.ratio ex eo petitur quod &longs;cili<lb/>cet, vt habeatur &longs;umma progre&longs;&longs;ionis arithmeticæ, debet addi primus <lb/>terminus maximo, & a&longs;&longs;umi &longs;ubduplum totius; illudque ducere in nu<lb/>merum terminorum per regulam arithmeticam; atqui eadom e&longs;t ratio <lb/>velocitatum, quæ &longs;patiorum; vt dictum e&longs;t &longs;uprà; &longs;cilice, in &longs;ingulis <lb/>in&longs;tantibus. </s>

<s><emph type="italics"/>Si componatur æquabilis motus ex &longs;ubdupla velocitate maxima, & mini<lb/>ma, æquali tempore, idem &longs;patium percurretur hoc motu naturaliter aceclera<lb/>to<emph.end type="italics"/>; &longs;it enim maxima velocitas vt 6. minima vt 1. motu naturaliter acce<lb/>lerato percurrentur &longs;patia 21. cuius &longs;ummæ termini &longs;unt 6.igitur 6. in<lb/>&longs;tantibus con&longs;tat hic motus; accipiatur &longs;ubduplum maximæ, & minimæ <lb/>velocitatis, &longs;cilicet 3 1/2. sítque velocitas motus æquabilis in&longs;tantium 6. <lb/>haud dubiè &longs;i ducantur 3 1/2 in 6 erunt 21.ratio ex eo petitur quod &longs;cili<lb/>cet, vt habeatur &longs;umma progre&longs;&longs;ionis arithmeticæ, debet addi primus <lb/>terminus maximo, & a&longs;&longs;umi &longs;ubduplum totius; illudque ducere in nu<lb/>merum terminorum per regulam arithmeticam; atqui eadem e&longs;t ratio <lb/>velocitatum, quæ &longs;patiorum; vt dictum e&longs;t &longs;uprà; &longs;cilice, in &longs;ingulis <lb/>in&longs;tantibus. </s>

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

<s><emph type="italics"/>Si a&longs;&longs;umantur partes temporis majores; quæ &longs;cilicet pluribus in&longs;tantibus <lb/>constent, &longs;erueturque eadem accelerationis progre&longs;&longs;io arithinetica, &longs;patium <lb/>quod ex &longs;umma huius progre&longs;&longs;ionis re&longs;ultabit, erit minus vero,<emph.end type="italics"/> &longs;int enim 6.in<lb/>&longs;tantia, & cuilibet iuxta progre&longs;&longs;ionem prædictam &longs;uum &longs;patium re&longs;pon<lb/>deat, haud dubiè &longs;patium &longs;ecundi erit duplum &longs;patij primi, & tertium <lb/>triplum, &c. </s>

<s><emph type="italics"/>Si a&longs;&longs;umantur partes temporis majores; quæ &longs;cilicet pluribus in&longs;tantibus <lb/>constent, &longs;erueturque eadem accelerationis progre&longs;&longs;io arithmetica, &longs;patium <lb/>quod ex &longs;umma huius progre&longs;&longs;ionis re&longs;ultabit, erit minus vero,<emph.end type="italics"/> &longs;int enim 6.in<lb/>&longs;tantia, & cuilibet iuxta progre&longs;&longs;ionem prædictam &longs;uum &longs;patium re&longs;pon<lb/>deat, haud dubiè &longs;patium &longs;ecundi erit duplum &longs;patij primi, & tertium <lb/>triplum, &c. </s>

<s>vt con&longs;tat ex dictis; igitur erunt &longs;patia 21. iam verò a&longs;&longs;u<lb/>mantur 3. partes temporis, quarum quælibet ex 2. con&longs;tet in&longs;tantibus; <lb/>primæ parti tria ex prædictis &longs;patiis re&longs;pondeant; certè &longs;i &longs;eruetur pro<lb/>gre&longs;&longs;io arithmetica, &longs;ecundæ re&longs;pondebunt 6. & tertiæ 9. igitur totum <lb/>&longs;patium erit 18. minus vero quod erat 21. &longs;i verò a&longs;&longs;umantur tantùm 2. <lb/>partes, quarum quælibet tribus in&longs;tantibus con&longs;tet; primæ parti re&longs;pon-<pb xlink:href="026/01/124.jpg" pagenum="92"/>debunt 6. &longs;ecundæ 12. igitur &longs;umma erit 18. minor vero &longs;patio &longs;cilicet <lb/>21.hinc vides &longs;uppo&longs;ito eodem in&longs;tantium numero &longs;patium e&longs;&longs;e &longs;empet <lb/>æquale, &longs;iue a&longs;&longs;umantur partes maiores temporis, &longs;iuc minores, v. g. &longs;up<lb/>po&longs;itis 6.in&longs;tantibus, ex quibus totum &longs;patium 21.con&longs;equitur, &longs;iue a&longs;&longs;u<lb/>mantur tres partes, quarum quælibet con&longs;tet 2. in&longs;tantibus, &longs;iue duæ, <lb/>quarum quælibet con&longs;tet tribus, &longs;patium quod ex illis re&longs;ultat, e&longs;t &longs;em<lb/>per idem &longs;cilicet 18. a&longs;&longs;umptis verò 8. in&longs;tantibus, & totali &longs;patio, quod <lb/>illis re&longs;pondet 36. &longs;patium quod ex partibus re&longs;ultabit erit 30. &longs;iue &longs;int <lb/>duæ partes, quarum quælibet con&longs;tet 4. in&longs;tantibus, &longs;iue &longs;int 4. quarum <lb/>quælibet con&longs;tet duobus: hinc rur&longs;us vides a&longs;&longs;umpto maiori in&longs;tantium <lb/>numero &longs;patium verum habere maiorem rationem ad non verum, quàm <lb/>a&longs;&longs;umpto minori in&longs;tantium numero, v.g.a&longs;&longs;umantur 4.in&longs;tantia, &longs;umma <lb/>&longs;patiorum erit 10. &longs;i verò a&longs;&longs;umantur 2.partes temporis, quarum quæli<lb/>bet duobus in&longs;tantibus re&longs;pondeat; &longs;umma &longs;patij erit 9.igitur ratio ve<lb/>ri &longs;patij ad non verum e&longs;t (10/9). a&longs;&longs;umantur 6. in&longs;tantia &longs;patij veri, &longs;umma <lb/>erit 21.non veri 18. igitur ratio (21/18) &longs;eu 7/6 quæ maior e&longs;t priori: denique <lb/>a&longs;&longs;umantur 8. in&longs;tantia &longs;patij veri, &longs;umma erit 36. non veri 30 igitur ra<lb/>tio (36/30) &longs;eu 6/3 quæ maior e&longs;t prioribus, atque ita deinceps. </s>

<s>vt con&longs;tat ex dictis; igitur erunt &longs;patia 21. iam verò a&longs;&longs;u<lb/>mantur 3. partes temporis, quarum quælibet ex 2. con&longs;tet in&longs;tantibus; <lb/>primæ parti tria ex prædictis &longs;patiis re&longs;pondeant; certè &longs;i &longs;eruetur pro<lb/>gre&longs;&longs;io arithmetica, &longs;ecundæ re&longs;pondebunt 6. & tertiæ 9. igitur totum <lb/>&longs;patium erit 18. minus vero quod erat 21. &longs;i verò a&longs;&longs;umantur tantùm 2. <lb/>partes, quarum quælibet tribus in&longs;tantibus con&longs;tet; primæ parti re&longs;pon-<pb xlink:href="026/01/124.jpg" pagenum="92"/>debunt 6. &longs;ecundæ 12. igitur &longs;umma erit 18. minor vero &longs;patio &longs;cilicet <lb/>21.hinc vides &longs;uppo&longs;ito eodem in&longs;tantium numero &longs;patium e&longs;&longs;e &longs;emper <lb/>æquale, &longs;iue a&longs;&longs;umantur partes maiores temporis, &longs;iuc minores, v. g. &longs;up<lb/>po&longs;itis 6.in&longs;tantibus, ex quibus totum &longs;patium 21.con&longs;equitur, &longs;iue a&longs;&longs;u<lb/>mantur tres partes, quarum quælibet con&longs;tet 2. in&longs;tantibus, &longs;iue duæ, <lb/>quarum quælibet con&longs;tet tribus, &longs;patium quod ex illis re&longs;ultat, e&longs;t &longs;em<lb/>per idem &longs;cilicet 18. a&longs;&longs;umptis verò 8. in&longs;tantibus, & totali &longs;patio, quod <lb/>illis re&longs;pondet 36. &longs;patium quod ex partibus re&longs;ultabit erit 30. &longs;iue &longs;int <lb/>duæ partes, quarum quælibet con&longs;tet 4. in&longs;tantibus, &longs;iue &longs;int 4. quarum <lb/>quælibet con&longs;tet duobus: hinc rur&longs;us vides a&longs;&longs;umpto maiori in&longs;tantium <lb/>numero &longs;patium verum habere maiorem rationem ad non verum, quàm <lb/>a&longs;&longs;umpto minori in&longs;tantium numero, v.g.a&longs;&longs;umantur 4.in&longs;tantia, &longs;umma <lb/>&longs;patiorum erit 10. &longs;i verò a&longs;&longs;umantur 2.partes temporis, quarum quæli<lb/>bet duobus in&longs;tantibus re&longs;pondeat; &longs;umma &longs;patij erit 9.igitur ratio ve<lb/>ri &longs;patij ad non verum e&longs;t (10/9). a&longs;&longs;umantur 6. in&longs;tantia &longs;patij veri, &longs;umma <lb/>erit 21.non veri 18. igitur ratio (21/18) &longs;eu 7/6 quæ maior e&longs;t priori: denique <lb/>a&longs;&longs;umantur 8. in&longs;tantia &longs;patij veri, &longs;umma erit 36. non veri 30 igitur ra<lb/>tio (36/30) &longs;eu 6/3 quæ maior e&longs;t prioribus, atque ita deinceps. </s>

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

<s><emph type="italics"/>Datis duabus partibus temporis, & cognito &longs;patio quod percurritur in prima, <lb/>matius &longs;patium re&longs;pondebit &longs;ecundæ quo vtraque in plures partes minores diui<lb/>detur, &longs;uppofita &longs;emper eadem proare&longs;&longs;ione arithmetica in ip&longs;o incremento<emph.end type="italics"/>; <lb/>&longs;int enim duæ partes temporis &longs;en&longs;ibiles æquales AG. GH. & &longs;pa<lb/>tium quod percurritur prima parte temporis AG &longs;it HI; in &longs;ecunda <lb/>percurretur IO, id e&longs;t, duplum HI; at verò diuidatur pars temporis <lb/>AG in duas æquales AF, FG, & con&longs;equenter totum tempus AH in 4. <lb/>æquales; haud dubiè in prima AF percurretur NP &longs;ubtripla HI, & in <lb/>&longs;ecunda FG percurretur PK dupla NP; igitur in 4. partibus temporis <lb/>AH percurretur &longs;patium decuplum PN, &longs;ed HO e&longs;t tantùm nouecupla <lb/>NP; igitur re&longs;ultabit maius &longs;patium in 4.partibus temporis, quam in dua<lb/>bus; licèt duæ æquiualeant 4. iuxta progre&longs;&longs;ionem arithmeticam. </s>

<s><emph type="italics"/>Datis duabus partibus temporis, & cognito &longs;patio quod percurritur in prima, <lb/>matius &longs;patium re&longs;pondebit &longs;ecundæ quo vtraque in plures partes minores diui<lb/>detur, &longs;uppo&longs;ita &longs;emper eadem progre&longs;&longs;ione arithmetica in ip&longs;o incremento<emph.end type="italics"/>; <lb/>&longs;int enim duæ partes temporis &longs;en&longs;ibiles æquales AG. GH. & &longs;pa<lb/>tium quod percurritur prima parte temporis AG &longs;it HI; in &longs;ecunda <lb/>percurretur IO, id e&longs;t, duplum HI; at verò diuidatur pars temporis <lb/>AG in duas æquales AF, FG, & con&longs;equenter totum tempus AH in 4. <lb/>æquales; haud dubiè in prima AF percurretur NP &longs;ubtripla HI, & in <lb/>&longs;ecunda FG percurretur PK dupla NP; igitur in 4. partibus temporis <lb/>AH percurretur &longs;patium decuplum PN, &longs;ed HO e&longs;t tantùm nonecupla <lb/>NP; igitur re&longs;ultabit maius &longs;patium in 4.partibus temporis, quam in dua<lb/>bus; licèt duæ æquiualeant 4. iuxta progre&longs;&longs;ionem arithmeticam. </s>

<s>Similiter AF diuidatur bifariam in E. & tota AH in 8. æquales AE; <lb/>certè primis 4.percurretur idem &longs;patium ML æquale NK & HI; igitur <lb/>in prima AE percurretur MR. cuius ML &longs;it decupla; nam 4. terminis <lb/>re&longs;pondet &longs;umma 10. &longs;ed 8. terminis id e&longs;t 8.partibus temporis re&longs;pon<lb/>det &longs;umma; 6. æqualium RM; &longs;ed HO tripla ML e&longs;t tantum 30. <lb/>æqualium MR; igitur in 8.partibus re&longs;ultabit maius &longs;patium, quàm in <lb/>4.quæ æquiualent 8. </s>

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

<s><emph type="italics"/>Hinc quoque ratio maximæ percu&longs;&longs;ionis ex &longs;olo pondere cadentis illius arie<lb/>tis inflictæ<emph.end type="italics"/>; quâ &longs;cilicet altè infiguntur lignei pali, quibus in mediis <lb/>aquis tanquam iacto &longs;undamini &longs;uperædificatur ingens &longs;æpè ædificij <lb/>moles. </s>

<s><emph type="italics"/>Hinc quoque ratio maximæ percu&longs;&longs;ionis ex &longs;olo pondere cadentis illius arie<lb/>tis inflictæ<emph.end type="italics"/>; quâ &longs;cilicet altè infiguntur lignei pali, quibus in mediis <lb/>aquis tanquam iacto fundamini &longs;uperædificatur ingens &longs;æpè ædificij <lb/>moles. </s>

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

<s><emph type="italics"/>Hinc ex minima altitudine cadens corpus graue minimum ferè ictum in<lb/>fligit<emph.end type="italics"/>; quia primus impetus valdè debilis e&longs;t, qui tamen deinde &longs;acta <lb/>acce&longs;&longs;ione maximus ferè euadit. </s>

<s><emph type="italics"/>Hinc ex minima altitudine cadens corpus graue minimum ferè ictum in<lb/>fligit<emph.end type="italics"/>; quia primus impetus valdè debilis e&longs;t, qui tamen deinde facta <lb/>acce&longs;&longs;ione maximus ferè euadit. </s>

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

<s><emph type="italics"/>Hinc ratio, cur tanta &longs;it differentia impetus grauit ationis, & percu&longs;&longs;ionis <lb/>ab eodem mobili<emph.end type="italics"/>; quia &longs;cilicet quantumuis tempore breui&longs;&longs;imo mouea<lb/>tur, plurimis tamen cius motus durat in&longs;tantibus; atqui quolibet in&longs;tan<lb/>ti motus acquiritur impetus æqualis primo impetui grauitationis, vt <lb/>con&longs;tat ex dictis. </s>

<s><emph type="italics"/>Hinc ratio, cur tanta &longs;it differentia impetus grauitationis, & percu&longs;&longs;ionis <lb/>ab eodem mobili<emph.end type="italics"/>; quia &longs;cilicet quantumuis tempore breui&longs;&longs;imo mouea<lb/>tur, plurimis tamen eius motus durat in&longs;tantibus; atqui quolibet in&longs;tan<lb/>ti motus acquiritur impetus æqualis primo impetui grauitationis, vt <lb/>con&longs;tat ex dictis. </s>

<s>v. g. &longs;it mobile quod moueatur per mille in&longs;tantia <lb/>(modicum certè tempus & minimè &longs;en&longs;ibile) po&longs;t hunc motum impetus <lb/>erit millecuplus; igitur effectus etiam millecuplus; quæ omnia con&longs;tant <lb/>ex dictis. </s>

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<s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 38.<emph.end type="center"/></s>

<s><emph type="italics"/>Hinc primo in&longs;tanti grauit ationis nullum ferè &longs;entitur pondus,<emph.end type="italics"/> quia mini<lb/>ma vis e&longs;t, quæ con&longs;equentibus in&longs;tantibus augetur, hinc licèt corpus <lb/>breui tempore quis &longs;u&longs;tineat, paulò po&longs;t tamen ponderi cedit, ratio e&longs;t <lb/>elara ex dictis. </s><pb xlink:href="026/01/127.jpg" pagenum="95"/>

<s><emph type="italics"/>Hinc primo in&longs;tanti grauitationis nullum ferè &longs;entitur pondus,<emph.end type="italics"/> quia mini<lb/>ma vis e&longs;t, quæ con&longs;equentibus in&longs;tantibus augetur, hinc licèt corpus <lb/>breui tempore quis &longs;u&longs;tineat, paulò po&longs;t tamen ponderi cedit, ratio e&longs;t <lb/>clara ex dictis. </s><pb xlink:href="026/01/127.jpg" pagenum="95"/>

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

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<s>Secundò non pote&longs;t ad amu&longs;&longs;im tempus cum tempore componi ad <lb/>æqualitatem, vel aliam datam rationem; licèt enim vnum tempus &longs;en&longs;i<lb/>bile haberet mille in&longs;tantia &longs;upra aliud; illa tamen inæqualitas &longs;en&longs;u <lb/>minimè perciperetur; idem dico de aliis rationibus, in quo, ni fallor, <lb/>maximè peccant, qui temporum æqualitatem perfectam ob&longs;eruari po&longs;&longs;e <lb/>contendunt. </s>

<s>Tertiò, idem dico de percu&longs;&longs;ionum ratione; quippe non pote&longs;t &longs;en&longs;u <lb/>percipi inæqualitas duarum percu&longs;&longs;ionum, licèt vires vnius præualeant <lb/>mille punctis &longs;eu gradibus in&longs;en&longs;ibilibus; quippe non pote&longs;t di&longs;tingui <lb/>ab alia ni&longs;i vel ex &longs;patio; atqui di&longs;cerni non pote&longs;t, an vnum &longs;patium <lb/>&longs;uperet aliud mille punctis; vel ex &longs;ono; atqui &longs;onus pote&longs;t diuidi in in<lb/>finitos ferè gradus &longs;en&longs;u minimè perceptibiles; igitur nulla hypothe&longs;is <lb/>in his experimentis &longs;tatui pote&longs;t, quibus æqualitas vel temporum, vel <lb/>&longs;patiorum cogno&longs;ci dicatur; nec dicas aliquot in&longs;tantia parùm di&longs;cti<lb/>minis importare, nam cùm &longs;ingulis in&longs;tantibus fiat æqualis impetus ac<lb/>ce&longs;&longs;io, mille in&longs;tantia reddunt percu&longs;&longs;ionem millecuplam grauitationis; <lb/>hinc certum e&longs;t ex numero in&longs;tantium cognito cogno&longs;ci tantùm po&longs;&longs;e <lb/>numerum punctorum, & vici&longs;&longs;im; at certè neuter &longs;en&longs;u percipi pote&longs;t; ne<lb/>que tanti e&longs;t hoc &longs;cire. </s>

<s>Tertiò, idem dico de percu&longs;&longs;ionum ratione; quippe non pote&longs;t &longs;en&longs;u <lb/>percipi inæqualitas duarum percu&longs;&longs;ionum, licèt vires vnius præualeant <lb/>mille punctis &longs;eu gradibus in&longs;en&longs;ibilibus; quippe non pote&longs;t di&longs;tingui <lb/>ab alia ni&longs;i vel ex &longs;patio; atqui di&longs;cerni non pote&longs;t, an vnum &longs;patium <lb/>&longs;uperet aliud mille punctis; vel ex &longs;ono; atqui &longs;onus pote&longs;t diuidi in in<lb/>finitos ferè gradus &longs;en&longs;u minimè perceptibiles; igitur nulla hypothe&longs;is <lb/>in his experimentis &longs;tatui pote&longs;t, quibus æqualitas vel temporum, vel <lb/>&longs;patiorum cogno&longs;ci dicatur; nec dicas aliquot in&longs;tantia parùm di&longs;eri<lb/>minis importare, nam cùm &longs;ingulis in&longs;tantibus fiat æqualis impetus ac<lb/>ce&longs;&longs;io, mille in&longs;tantia reddunt percu&longs;&longs;ionem millecuplam grauitationis; <lb/>hinc certum e&longs;t ex numero in&longs;tantium cognito cogno&longs;ci tantùm po&longs;&longs;e <lb/>numerum punctorum, & vici&longs;&longs;im; at certè neuter &longs;en&longs;u percipi pote&longs;t; ne<lb/>que tanti e&longs;t hoc &longs;cire. </s>

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

<s><emph type="italics"/>Hinc &longs;i corpus graue de&longs;cenderet motu æquabili eoque æquali motui primi <lb/>m&longs;tantis; certè vix modicum &longs;patium post multos annos decurreret<emph.end type="italics"/>; &longs;uppo<lb/>namus enim quod plures habent, licèt accuratè experimento &longs;ubii<lb/>ci non po&longs;&longs;it, &longs;cilicet vno &longs;ecundo minuto temporis decurri à corpore <lb/>graui deor&longs;um 12. pedes &longs;patij; in &longs;ecundo minuto &longs;upponamus e&longs;&longs;e <lb/>mille in&longs;tantia, quamuis infinita penè contineat; &longs;itque in primo in<lb/>&longs;tanti motus vnus gradus impetus; &longs;ic enim vocetur illa pars impetus, que <lb/>producitur primo in&longs;tanti; certè po&longs;t mille in&longs;tantia motus, erunt mille <lb/>gradus impetus; iam vcrò &longs;i accipiatur &longs;ubduplum maximæ & minimæ <lb/>velocitatis; id e&longs;t vnius gradus, & mille graduum, &longs;cilicet 500. 1/2 tri<lb/>buaturque motui æquabili; haud dubiè vno fecundo minuto percur<lb/>rentur 12. pedes &longs;patij per Th. 46. Igitur &longs;i cum velocitate vt 500, 1/2 <lb/>percurrentur 12. pedes 1.minuto, cum velocitate vt 1. percurrentur <lb/>12. pedes 500.&longs;ecundis minutis, &; 30. tertiis; &longs;i verò accipiantur plura <lb/>in&longs;tantia, v.g. 1000000.in&longs;tantia, percurrentur 12. pedes 500000. &longs;e<lb/>cundis minutis; &longs;i verò 1000000000000. percurremur 500000000000. <lb/>&longs;ecundis, id e&longs;t 8333333333. minutis, id e&longs;t 138888888. horis <pb xlink:href="026/01/128.jpg" pagenum="96"/>id e&longs;t 5787037. diebus id e&longs;t 89031. annis, omitto minutias; atqui lon<lb/>gè adhuc plura in vno minuto continentur in&longs;tantia. </s>

<s><emph type="italics"/>Hinc &longs;i corpus graue de&longs;cenderet motu æquabili eoque æquali motui primi <lb/>in&longs;tantis; certè vix modicum &longs;patium post multos annos decurreret<emph.end type="italics"/>; &longs;uppo<lb/>namus enim quod plures habent, licèt accuratè experimento &longs;ubii<lb/>ci non po&longs;&longs;it, &longs;cilicet vno &longs;ecundo minuto temporis decurri à corpore <lb/>graui deor&longs;um 12. pedes &longs;patij; in &longs;ecundo minuto &longs;upponamus e&longs;&longs;e <lb/>mille in&longs;tantia, quamuis infinita penè contineat; &longs;itque in primo in<lb/>&longs;tanti motus vnus gradus impetus; &longs;ic enim vocetur illa pars impetus, que <lb/>producitur primo in&longs;tanti; certè po&longs;t mille in&longs;tantia motus, erunt mille <lb/>gradus impetus; iam vcrò &longs;i accipiatur &longs;ubduplum maximæ & minimæ <lb/>velocitatis; id e&longs;t vnius gradus, & mille graduum, &longs;cilicet 500. 1/2 tri<lb/>buaturque motui æquabili; haud dubiè vno fecundo minuto percur<lb/>rentur 12. pedes &longs;patij per Th. 46. Igitur &longs;i cum velocitate vt 500, 1/2 <lb/>percurrentur 12. pedes 1.minuto, cum velocitate vt 1. percurrentur <lb/>12. pedes 500.&longs;ecundis minutis, &; 30. tertiis; &longs;i verò accipiantur plura <lb/>in&longs;tantia, v.g. 1000000.in&longs;tantia, percurrentur 12. pedes 500000. &longs;e<lb/>cundis minutis; &longs;i verò 1000000000000. percurremur 500000000000. <lb/>&longs;ecundis, id e&longs;t 8333333333. minutis, id e&longs;t 138888888. horis <pb xlink:href="026/01/128.jpg" pagenum="96"/>id e&longs;t 5787037. diebus id e&longs;t 89031. annis, omitto minutias; atqui lon<lb/>gè adhuc plura in vno minuto continentur in&longs;tantia. </s>

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

<s><emph type="italics"/>Si corpus graue de&longs;cenderet motu æquabili, eoque æquali motui vltimi in<lb/>stantis, duplum ferè &longs;patium æquali tempore conficeret illius quod conficit <lb/>motu accelerato, duplum inquam ferè &longs;cilicet panlò minùs<emph.end type="italics"/>; quia conficit <lb/>idem motu æquabili; cuius velocitas e&longs;t &longs;ubdupla maximæ & minimæ; <lb/>&longs;ed minima velocitas primi in&longs;tantis pro nihilo reputatur; igitur acci<lb/>piatur tantùm &longs;ubduplum maximæ, igitur cum velocitate æquali maxi<lb/>mæ, eodem tempore duplum &longs;patium percurretur; igitur in vno minuto <lb/>&longs;ecundo, v.g. 24. pedes; igitur in vno minuto primo codem motu æqua<lb/>bili 1440. pedes percurrentur; igitur in vna hora 86400. pedes; hinc <lb/>non e&longs;t quod aliqui adeo mirentur, &longs;eu potiùs reiiciant hanc motus <lb/>accelerationem quod ex ea tùm tardi&longs;&longs;imus motus, tùm veloci&longs;&longs;imus <lb/>con&longs;equatur. </s>

<s><emph type="italics"/>Si corpus graue de&longs;cenderet motu æquabili, eoque æquali motui vltimi in<lb/>stantis, duplum ferè &longs;patium æquali tempore conficeret illius quod conficit <lb/>motu accelerato, duplum inquam ferè &longs;cilicet paulò minùs<emph.end type="italics"/>; quia conficit <lb/>idem motu æquabili; cuius velocitas e&longs;t &longs;ubdupla maximæ & minimæ; <lb/>&longs;ed minima velocitas primi in&longs;tantis pro nihilo reputatur; igitur acci<lb/>piatur tantùm &longs;ubduplum maximæ, igitur cum velocitate æquali maxi<lb/>mæ, eodem tempore duplum &longs;patium percurretur; igitur in vno minuto <lb/>&longs;ecundo, v.g. 24. pedes; igitur in vno minuto primo codem motu æqua<lb/>bili 1440. pedes percurrentur; igitur in vna hora 86400. pedes; hinc <lb/>non e&longs;t quod aliqui adeo mirentur, &longs;eu potiùs reiiciant hanc motus <lb/>accelerationem quod ex ea tùm tardi&longs;&longs;imus motus, tùm veloci&longs;&longs;imus <lb/>con&longs;equatur. </s>

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

<s><emph type="italics"/>Motus naturaliter acceleratus non propagatur per omnes tarditatis gra<lb/>dus<emph.end type="italics"/>; quia tot &longs;unt huius propagationis gradus, quot &longs;unt in&longs;tantia, <lb/>quibus durat hic motus, cum &longs;ingulis in&longs;tantibus noua fiat impetus ac<lb/>ce&longs;&longs;io, &longs;ed non &longs;unt infinita in&longs;tantia, vt demon&longs;trabimus in Metaphy<lb/>&longs;ica; prætereà licèt e&longs;&longs;ent infinita in&longs;tantia, non fieret adhuc per omnes <lb/>tarditatis gradus hæc propagatio; quia daretur aliquis gradus tarditatis, <lb/>quem non comprehenderet hæc graduum &longs;eries; nam incipit moucri <lb/>tardiùs in plano inclinato quàm in libero medio rectà deor&longs;um, vt con<lb/>&longs;tat, & in medio den&longs;o quàm in raro v.g. in aqua quàm in aëre; igitur <lb/>hic tarditatis gradus, quo incipit moueri in plano tantillùm inclinato, <lb/>non continetur inter illos, quibus mouetur rectà deor&longs;um. </s>

<s><emph type="italics"/>Motus naturaliter acceleratus non propagatur per omnes tarditatis gra<lb/>dus<emph.end type="italics"/>; quia tot &longs;unt huius propagationis gradus, quot &longs;unt in&longs;tantia, <lb/>quibus durat hic motus, cum &longs;ingulis in&longs;tantibus noua fiat impetus ac<lb/>ce&longs;&longs;io, &longs;ed non &longs;unt infinita in&longs;tantia, vt demon&longs;trabimus in Metaphy<lb/>&longs;ica; prætereà licèt e&longs;&longs;ent infinita in&longs;tantia, non fieret adhuc per omnes <lb/>tarditatis gradus hæc propagatio; quia daretur aliquis gradus tarditatis, <lb/>quem non comprehenderet hæc graduum &longs;eries; nam incipit moueri <lb/>tardiùs in plano inclinato quàm in libero medio rectà deor&longs;um, vt con<lb/>&longs;tat, & in medio den&longs;o quàm in raro v.g. in aqua quàm in aëre; igitur <lb/>hic tarditatis gradus, quo incipit moueri in plano tantillùm inclinato, <lb/>non continetur inter illos, quibus mouetur rectà deor&longs;um. </s>

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<s><emph type="center"/><emph type="italics"/>Corollarium.<emph.end type="italics"/> 2.<emph.end type="center"/></s>

<s>Secundò reiicies illos, qui volunt accelerationem motus e&longs;&longs;e, vel à vi <lb/>magnetica, quâ terra trahit ad &longs;e omnia grauia; vel ab alia vi occulta, <lb/>quâ c&oelig;lum pellit deor&longs;um; vel à c&oelig;le&longs;ti illa, imò potiùs fabulosâ mate<lb/>riâ; vel demum ab ip&longs;a vi fympathicâ, quâ corpus &longs;uo centro propiùs <lb/>factum totas &longs;uas vires exerit, vt ei &longs;e conjungat; quæ omnia gratis di<lb/>cuntur, & ex dictis plu&longs;quam efficaciter refelli po&longs;&longs;unt, nefru&longs;trà tempus <lb/>in iis iterum refellendis teramus. </s>

<s>Secundò reiicies illos, qui volunt accelerationem motus e&longs;&longs;e, vel à vi <lb/>magnetica, quâ terra trahit ad &longs;e omnia grauia; vel ab alia vi occulta, <lb/>quâ c&oelig;lum pellit deor&longs;um; vel à c&oelig;le&longs;ti illa, imò potiùs fabulosâ mate<lb/>riâ; vel demum ab ip&longs;a vi &longs;ympathicâ, quâ corpus &longs;uo centro propiùs <lb/>factum totas &longs;uas vires exerit, vt ei &longs;e conjungat; quæ omnia gratis di<lb/>cuntur, & ex dictis plu&longs;quam efficaciter refelli po&longs;&longs;unt, ne fru&longs;trà tempus <lb/>in iis iterum refellendis teramus. </s>

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 3.<emph.end type="center"/></s>

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<s><emph type="center"/><emph type="italics"/>Corollarium.<emph.end type="italics"/> 4.<emph.end type="center"/></s>

<s>Quartò ex his &longs;ententia Ari&longs;totelica de motu accelerato optunè vin<lb/>dicatur; quòd &longs;cilicet grauia &longs;ub finem &longs;ui motus velociùs &longs;erantur ver<lb/>sùs centrum; quod ex dictis, & &longs;implici&longs;&longs;imis, certi&longs;&longs;imi&longs;que principiis <lb/>demon&longs;tratum fuit. </s>

<s>Quartò ex his &longs;ententia Ari&longs;totelica de motu accelerato optimè vin<lb/>dicatur; quòd &longs;cilicet grauia &longs;ub finem &longs;ui motus velociùs &longs;erantur ver<lb/>sùs centrum; quod ex dictis, & &longs;implici&longs;&longs;imis, certi&longs;&longs;imi&longs;que principiis <lb/>demon&longs;tratum fuit. </s>

<s><emph type="center"/><emph type="italics"/>Corollarium.<emph.end type="italics"/> 5.<emph.end type="center"/></s>

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<s>fique vno in&longs;tanti acquiritur 1. <lb/>&longs;patium, duobus acquiruntur 4. tribus 9. quatuor 16. atque ita deinceps <lb/>per quadrata, quæ omnia ex dictis falfa e&longs;&longs;e con&longs;tat; quippe &longs;i æqualibus <lb/>temporibus acquiruntur æqualia velocitatis momenta; igitur &longs;i primo <lb/>in&longs;tanti e&longs;t 1.gradus, &longs;ecundo erunt 2. igitur &longs;ecundo tempore cum duo<lb/>bus gradibus velocitatis vel impetus percurrentur duo tantùm &longs;patia, &longs;i <lb/>primò in&longs;tanti æquali cum vno gradu percurritur vnus, &longs;ed de his fusè <lb/>infrà. </s><pb xlink:href="026/01/130.jpg" pagenum="98"/>

<s>fique vno in&longs;tanti acquiritur 1. <lb/>&longs;patium, duobus acquiruntur 4. tribus 9. quatuor 16. atque ita deinceps <lb/>per quadrata, quæ omnia ex dictis fal&longs;a e&longs;&longs;e con&longs;tat; quippe &longs;i æqualibus <lb/>temporibus acquiruntur æqualia velocitatis momenta; igitur &longs;i primo <lb/>in&longs;tanti e&longs;t 1.gradus, &longs;ecundo erunt 2. igitur &longs;ecundo tempore cum duo<lb/>bus gradibus velocitatis vel impetus percurrentur duo tantùm &longs;patia, &longs;i <lb/>primò in&longs;tanti æquali cum vno gradu percurritur vnus, &longs;ed de his fusè <lb/>infrà. </s><pb xlink:href="026/01/130.jpg" pagenum="98"/>

<s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 7.<emph.end type="center"/></s>

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<s>prop.18.&longs;uæ Bali&longs;ticæ &longs;ub finem; illa <lb/>e&longs;t inquam &longs;ententia, quam hactenus meo iudicio &longs;atis luculenter de<lb/>mon&longs;trauimus. </s>

<s>Sunt tres aliæ &longs;ententiæ, quæ ab eodem Mer&longs;enno referuntur; prima <lb/>e&longs;t quæ progre&longs;&longs;ionem &longs;patiorum eamdem e&longs;&longs;e vult cum eâ, quæ e&longs;t &longs;i<lb/>nuum ver&longs;orum, centro quadrantis po&longs;ito in centro terræ, & altero ex<lb/>tremo &longs;inus totius in co punctò, in quo incipit motus. </s>

<s>Sunt tres aliæ &longs;ententiæ, quæ ab eodem Mer&longs;enno referuntur; prima <lb/>e&longs;t quæ progre&longs;&longs;ionem &longs;patiorum <expan abbr="eãdem">eandem</expan> e&longs;&longs;e vult cum eâ, quæ e&longs;t &longs;i<lb/>nuum ver&longs;orum, centro quadrantis po&longs;ito in centro terræ, & altero ex<lb/>tremo &longs;inus totius in eo punctò, in quo incipit motus. </s>

<s>Secunda e&longs;t quo<lb/>rumdam, qui volunt progre&longs;&longs;ionem &longs;patiorum, quæ &longs;ingulis temporibus <lb/>re&longs;pondent, e&longs;&longs;e in progre&longs;&longs;ione geometrica dupla iuxta hos numeros, <lb/>1.2.4.8.32. Tertia e&longs;t alicuius, qui voluit e&longs;&longs;e iuxta proportionem lineæ <lb/>&longs;ectæ in mediam, & extremam rationem. </s>

<s>Tres vltimæ &longs;ententiæ nullo pror&longs;us nituntur fundamento; igitur vel <lb/>inde maximè confutantur, quòd gratis &longs;ine vllo pror&longs;us vel rationis vel <lb/>experimenti momento excogitatæ &longs;int. </s>

<s>Igitur in hac di&longs;&longs;ertatione duæ <lb/>tantùm primæ di&longs;cutiendæ &longs;unt Sententiæ Galilei &longs;chema hic habes <lb/>in linea AF, in qua a&longs;&longs;umitur AB, &longs;patium &longs;cilicet, quod dato tempore <pb xlink:href="026/01/131.jpg" pagenum="99"/>corpus graue &longs;uo motu percurrit; & &longs;ecundo tempore æquali BC, quæ <lb/>tripla e&longs;t AB, tertio CD quintupla quarto DE &longs;eptupla, quinto EF <lb/>nouecupla; vides primò &longs;eriem numerorum imparium 1. 3. 5. 7. 9.atque <lb/>ita deinceps. </s>

<s>Igitur in hac di&longs;&longs;ertatione duæ <lb/>tantùm primæ di&longs;cutiendæ &longs;unt Sententiæ Galilei &longs;chema hic habes <lb/>in linea AF, in qua a&longs;&longs;umitur AB, &longs;patium &longs;cilicet, quod dato tempore <pb xlink:href="026/01/131.jpg" pagenum="99"/>corpus graue &longs;uo motu percurrit; & &longs;ecundo tempore æquali BC, quæ <lb/>tripla e&longs;t AB, tertio CD quintupla quarto DE &longs;eptupla, quinto EF <lb/>nonecupla; vides primò &longs;eriem numerorum imparium 1. 3. 5. 7. 9.atque <lb/>ita deinceps. </s>

<s>Secundò vides &longs;patia e&longs;&longs;e in ratione duplicata temporum, <lb/>hoc e&longs;t vt temporum quadrata. </s>

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<s>Adde quod, vt &longs;e habet tempus, quo de&longs;cendit per totum quadrantem <lb/>DF, ad tempus, quo de&longs;cendit per totum quadrantem EG. &longs;ic &longs;e habet <lb/>tempus, quo de&longs;cendit per arcum DL &longs;ubduplum DF ad tempus, quo <lb/>de&longs;cendit per arcum EI &longs;ubduplum EG; item tempus, quo de&longs;cendit <pb xlink:href="026/01/132.jpg" pagenum="100"/>per arcum DM &longs;ubquadruplum DF.ad tempus, quo de&longs;cendit per arcum <lb/>EK &longs;ubquadruplum EG; denique vt tempus, quo per minimum ar<lb/>cum quadrantis DF, ad tempus, quo de&longs;cendit per alium proportiona<lb/>lem, &longs;cilicet quadruplum in quadrante EG; atqui tam parui arcus po&longs;<lb/>&longs;unt a&longs;&longs;umi, vt &longs;int ad in&longs;tar lineæ rectæ deor&longs;um tangentis &longs;cilicet in D <lb/>& in E; igitur in his rectis de&longs;cendunt grauia iuxta progre&longs;&longs;ionem præ<lb/>dictam; id e&longs;t, cum arcus minimus a&longs;&longs;umptus ab E, qui æquiualet rectæ, <lb/>&longs;it quadruplus arcus minimi a&longs;&longs;umpti à puncto D, tempus, quo percurri<lb/>tur ille primus, e&longs;t ad tempus, quo percurritur hic &longs;ubquadruplus, vt tem<lb/>pus, quo percurritur EG ad tempus, quo percurritur DF vt dictum e&longs;t; <lb/>&longs;ed tempus, quo percurritur EG e&longs;t duplum illius, quo percurritur DF; <lb/>igitur tempus, quo percurritur minimus arcus a&longs;&longs;umptus ab E, & qui e&longs;t <lb/>ad in&longs;tar rectæ, e&longs;t duplum temporis quo percurritur minimus arcus a&longs;<lb/>&longs;umptus à puncto D &longs;ubquadruplus prioris, & qui e&longs;t etiam ad in&longs;tar re<lb/>ctæ; igitur &longs;patia &longs;unt vt temporum quadrata. </s>

<s>Quod autem tempus, quo percurritur EG &longs;it duplum illius, quo per<lb/>curritur DF, patet experientiâ; nam &longs;i numerentur ducentæ vibrationes <lb/>funependuli CD; eodem tempore numerabuntur centum vibrationes <lb/>maioris CE; igitur vibrationum minoris numerus e&longs;t duplus numeri vi<lb/>brationum maioris, dum &longs;imul vibrantur; igitur eo tempore, quo fiunt <lb/>100.maioris, fient 200. minoris; nam ommes vibrationes eiu&longs;dem fune<lb/>penduli &longs;unt æquò diuturnæ, licèt fiant per arcus inæquales ciu&longs;dem. </s>

<s>Quod autem tempus, quo percurritur EG &longs;it duplum illius, quo per<lb/>curritur DF, patet experientiâ; nam &longs;i numerentur ducentæ vibrationes <lb/>funependuli CD; eodem tempore numerabuntur centum vibrationes <lb/>maioris CE; igitur vibrationum minoris numerus e&longs;t duplus numeri vi<lb/>brationum maioris, dum &longs;imul vibrantur; igitur eo tempore, quo fiunt <lb/>100.maioris, fient 200. minoris; nam omnes vibrationes eiu&longs;dem fune<lb/>penduli &longs;unt æquò diuturnæ, licèt fiant per arcus inæquales eiu&longs;dem. </s>

<s><lb/>quadrantis, vt &longs;æpè ob&longs;eruatum e&longs;t. </s>

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<s>iudicio, nec <lb/>&longs;inceriùs exponi po&longs;&longs;unt. </s>

<s>Antequam ratione