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Colored diff for /texts/archimedes/xml/fabri_tract_026_la_1646.xml between version 1.23 and 1.29

version 1.23, 2007/02/14 17:57:29

version 1.29, 2008/12/14 16:19:08

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

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

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

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

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

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

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

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

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

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

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<s id="N1161D">Quod verò &longs;pectat ad fallacias oculi circa quietem; </s>

<s id="N11621">codem pror&longs;us <lb/>modo &longs;oluendæ &longs;unt, quo iam &longs;upra &longs;olutæ &longs;unt aliæ circa motum: <lb/>vtrùm verò motus, & quies dicant aliquid di&longs;tinctum à mobili, dice<lb/>mus infrà. </s>

<s id="N11621">eodem pror&longs;us <lb/>modo &longs;oluendæ &longs;unt, quo iam &longs;upra &longs;olutæ &longs;unt aliæ circa motum: <lb/>vtrùm verò motus, & quies dicant aliquid di&longs;tinctum à mobili, dice<lb/>mus infrà. </s>

<s id="N1162D"><emph type="center"/><emph type="italics"/>Hypothe&longs;is III.<emph.end type="italics"/><emph.end type="center"/></s>

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<s id="N11681"><emph type="italics"/>Idem mouetur modò tardiùs, modò velociùs.<emph.end type="italics"/></s>

<s id="N11688"> Video rotatum globum, <lb/>qui &longs;en&longs;im quie&longs;cit: &longs;entio ab codem globo modò maiorem, modò mi<lb/>norem ictum infligi, &c. </s>

<s id="N11688"> Video rotatum globum, <lb/>qui &longs;en&longs;im quie&longs;cit: &longs;entio ab eodem globo modò maiorem, modò mi<lb/>norem ictum infligi, &c. </s>

<s id="N11690">igitur e&longs;t certa hypothe&longs;is. </s>

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<s id="N11B75">Re&longs;pondeo, ignem quidem accendi in data di&longs;tantia; </s>

<s id="N11B79">at non &longs;ine <pb pagenum="10" xlink:href="026/01/042.jpg"/>aliqua applicatione, &longs;altem virtutis, in quo non e&longs;t difficultas; </s>

<s id="N11B82">quomo<lb/>do vero ignis accendatur, & quid &longs;it ignem accendi, explicabimus &longs;uo <lb/>loco; quidquid &longs;it, certum e&longs;t ad productionem impetus requiri ali<lb/>quam applicationem, vt patet etiam in magnte. </s>

<s id="N11B91"><emph type="center"/><emph type="italics"/>Axioma XI.<emph.end type="italics"/><emph.end type="center"/></s>

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<s id="N11C0D">Dices produci po&longs;&longs;e ab aliqua cau&longs;a ignota po&longs;ita dumtaxat tali, vel <lb/>tali conditione. </s>

<s id="N11C12">Re&longs;pondeo, hoc reuera geometricè non probari, &longs;ed <lb/>tantùm phy&longs;icè; </s>

<s id="N11C18">quidquid &longs;it, voco cau&longs;am id, ex cuius applicatione <lb/>&longs;equitur &longs;emper effectus, & nunquam aliàs; </s>

<s id="N11C1E">nam phy&longs;icè loquendo, &longs;iue <lb/>&longs;it alia cau&longs;a, &longs;iue non, codem modo &longs;e habet, ac &longs;i e&longs;&longs;et cau&longs;a; quippe <lb/>certum e&longs;t phy&longs;icè ignem calefacere, Solem illuminare, quod &longs;atis e&longs;t. </s>

<s id="N11C1E">nam phy&longs;icè loquendo, &longs;iue <lb/>&longs;it alia cau&longs;a, &longs;iue non, eodem modo &longs;e habet, ac &longs;i e&longs;&longs;et cau&longs;a; quippe <lb/>certum e&longs;t phy&longs;icè ignem calefacere, Solem illuminare, quod &longs;atis e&longs;t. </s>

<s id="N11C28"><emph type="center"/><emph type="italics"/>Axioma XII.<emph.end type="italics"/><emph.end type="center"/></s>

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<s id="N11C51"><lb/>nam &longs;i vnam partem effectus omittat; cur vnam potiùs quam aliam? </s>

<s id="N11C5A">cur non omnes? </s>

<s id="N11C5D">denique video cau&longs;am eandem eidem <lb/>&longs;ubiecto codem modo applicatam, eundem &longs;emper effectum producere <lb/>per Hyp. 8. </s>

<s id="N11C5D">denique video cau&longs;am eandem eidem <lb/>&longs;ubiecto eodem modo applicatam, eundem &longs;emper effectum producere <lb/>per Hyp. 8. </s>

<s id="N11C68"><emph type="center"/><emph type="italics"/>Axioma XIII<emph.end type="italics"/><emph.end type="center"/></s>

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<s id="N11ED9">&longs;i &longs;ecun<lb/>dum, diceretur aliquo modo productus, vel potiùs acqui&longs;itus; </s>

<s id="N11EDF">at vtrum<lb/>que coniunctim, &longs;imulque e&longs;&longs;entialiter dicit motus; </s>

<s id="N11EE5">nec enim conci<lb/>pio aliud, dum concipio motum: </s>

<s id="N11EEB">porrò vtrumque &longs;imul &longs;umptum indi<lb/>ui&longs;ibiliter non pote&longs;t dici, vel de&longs;tructum propriè, vel productum; Di<gap/><lb/>xi propriè; nam impropriè dici pote&longs;t motus productus. </s>

<s id="N11EEB">porrò vtrumque &longs;imul &longs;umptum indi<lb/>ui&longs;ibiliter non pote&longs;t dici, vel de&longs;tructum propriè, vel productum; Di<lb/>xi propriè; nam impropriè dici pote&longs;t motus productus. </s>

<s id="N11EF6">Dices Motus e&longs;t ens, non à &longs;e; igitur ab alio; igitur motus e&longs;t pro<lb/>ductus. </s>

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<s id="N12234"><emph type="italics"/>Impetus est aliquid distinctum à &longs;ubstantiâ mobilis.<emph.end type="italics"/></s>

<s id="N1223B"> Demon&longs;tratur. </s>

<s id="N1223E"><lb/>Quia &longs;ub&longs;tantia mobilis non e&longs;t cau&longs;a exigens motum per Th. 5. Impe<lb/>tus e&longs;t cau&longs;a exigens per Def. 3. & Th. 6. de codem contradictoria dici <lb/>non po&longs;&longs;unt per Ax. 1. n. </s>

<s id="N1223E"><lb/>Quia &longs;ub&longs;tantia mobilis non e&longs;t cau&longs;a exigens motum per Th. 5. Impe<lb/>tus e&longs;t cau&longs;a exigens per Def. 3. & Th. 6. de eodem contradictoria dici <lb/>non po&longs;&longs;unt per Ax. 1. n. </s>

<s id="N12248">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 id="N12251">4. igitur e&longs;t di&longs;tinctus per Ax. 2. </s>

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<s id="N123D0">Ad id quod obiicitur ex Ari&longs;totele; </s>

<s id="N123D4">aliqui putant inclina&longs;&longs;e in cam &longs;en<lb/>tentiam; </s>

<s id="N123DA">cùm tam en no&longs;tram teneant illu&longs;tres Peripatetici, quorum no<lb/>minibus parco, ne tot citationes paginas impleant; vide apud Conim<lb/>bric. </s>

<s id="N123E2">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: </s>

<s id="N123E2">l. 7. Phy&longs;. cap. 2. Aliqui excu&longs;ant ip&longs;um Ari&longs;totelem, putantque <lb/>non e&longs;&longs;e locutum ex propriâ &longs;ententiâ: </s>

<s id="N123EA">Alij dicunt Ari&longs;totelem quidem <lb/>tribui&longs;&longs;e aliquam vim extrin&longs;ecam aëri; </s>

<s id="N123F0">non tamen nega&longs;&longs;e intrin&longs;ecam <lb/>impetus; </s>

<s id="N123F6">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 id="N12552">igitur non e&longs;&longs;et, vt patet, igitur non e&longs;&longs;et; </s>

<s id="N12556">quia quod <lb/>fru&longs;trà e&longs;t, non e&longs;t per Ax. 6. nec ob&longs;tat quod &longs;uprà indicatum e&longs;t de im <lb/>petu naturali primo vel innato (&longs;ic enim deinceps appellabimus vt recti <lb/>di&longs;tinguamus ab acqui&longs;ito quem vocabimus impetum accelerationis) <lb/>qui &longs;ine motu con&longs;eruatur in corpore grauitante; </s>

<s id="N12562">quia ni&longs;i po&longs;&longs;ibilis e&longs;<lb/>&longs;et motus deor&longs;um nulla e&longs;&longs;et grauitatio; </s>

<s id="N12568">quippe grauitare e&longs;t dcor<lb/>&longs;um inclinari, motumque inclinationis impediri; </s>

<s id="N12568">quippe grauitare e&longs;t deor<lb/>&longs;um inclinari, motumque inclinationis impediri; </s>

<s id="N1256E">hinc dicemus <pb pagenum="20" xlink:href="026/01/052.jpg"/>in &longs;ecundo libro impetum innatum &longs;æpiùs e&longs;&longs;e &longs;ine motu; cum &longs;cilicet <lb/>impeditur à corpore &longs;u&longs;tinente? </s>

<s id="N12579">immò dicemus infrà primo in&longs;tanti, <lb/>quo e&longs;t impetus, nondum e&longs;&longs;e motum. </s>

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<s id="N128D9">Hinc &longs;i res aliqua creata per actionem tantæ perfectionis, quæ mille <lb/>annis e&longs;&longs;entialiter re&longs;ponderet, con&longs;eruaretur; </s>

<s id="N128DF">certè per totum illud <lb/>tempus moueri non po&longs;&longs;et; </s>

<s id="N128E5">e&longs;&longs;et enim vnicum in&longs;tans, hoc e&longs;t duratio <pb pagenum="23" xlink:href="026/01/055.jpg"/>tota &longs;imul; </s>

<s id="N128EE">&longs;ed codem in&longs;tanti in pluribus locis e&longs;&longs;e non pote&longs;t; igitur <lb/>nec moueri; </s>

<s id="N128EE">&longs;ed eodem in&longs;tanti in pluribus locis e&longs;&longs;e non pote&longs;t; igitur <lb/>nec moueri; </s>

<s id="N128F4">adde quod per cam actionem &longs;um in loco, per quam &longs;um <lb/>in tempore; </s>

<s id="N128FA">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>

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<s id="N12B54"><lb/>quia ibi non e&longs;t cau&longs;a formalis, vbi non e&longs;t effectus formalis; alioquin <lb/>e&longs;&longs;et fru&longs;trà, contra Ax. 6.2. </s>

<s id="N12B5B">Tu dicis produci impetum in aliquot parti<lb/>bus; hoc dicis, hoc proba? </s>

<s id="N12B61">an potes digno&longs;cere impetum ni&longs;i ex motu? </s>

<s id="N12B64"><lb/>vel con&longs;eruaretur hîc impetus &longs;equentibus in&longs;tantibus, vel &longs;tatim &longs;ecun<lb/>do in&longs;tanti de&longs;trucretur. </s>

<s id="N12B64"><lb/>vel con&longs;eruaretur hîc impetus &longs;equentibus in&longs;tantibus, vel &longs;tatim &longs;ecun<lb/>do in&longs;tanti de&longs;trueretur. </s>

<s id="N12B6A">Primum dicere ab&longs;urdume&longs;t; </s>

<s id="N12B6D">quia &longs;i hoc e&longs;&longs;et <lb/>multisictibus repetitis tandem moueretur totum mobile; &longs;i verò de<lb/>ftrui dicatur. </s>

<s id="N12B6D">quia &longs;i hoc e&longs;&longs;et <lb/>multisictibus repetitis tandem moueretur totum mobile; &longs;i verò de<lb/>&longs;trui dicatur. </s>

<s id="N12B75">Secundo in&longs;tanti; eadem ratio probat non produci. </s>

<s id="N12B78">Pri<lb/>mo in&longs;tanti, quæ probat de&longs;trui. </s>

<s id="N12B7D">Secundo nam ideo de&longs;truitur. </s>

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<s id="N12BB2">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 id="N12BBC">Obiiciet 2. Ignis applicatus agit in nonnullas partes fubiecti, licèt <lb/>non agat in omnes; igitur & potentia motrix. </s>

<s id="N12BBC">Obiiciet 2. Ignis applicatus agit in nonnullas partes &longs;ubiecti, licèt <lb/>non agat in omnes; igitur & potentia motrix. </s>

<s id="N12BC2">Re&longs;pondeo non e&longs;&longs;e pa<lb/>ritatem; </s>

<s id="N12BC8">quia vna pars pote&longs;t calefieri, & re&longs;olui &longs;ine alia, vt con&longs;tat <lb/>non tamen vna moueri &longs;ine alia, cui coniuncta e&longs;t, ni&longs;i &longs;eparetur; igi<lb/>tur nec recipere impetum &longs;ine alia. </s>

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<s id="N12E15"><emph type="italics"/>Primo in&longs;tanti, quo est impetus, non est ille motus, cuius hic impetus e&longs;t <lb/>cau&longs;a.<emph.end type="italics"/></s>

<s id="N12E1E"> Probatur; </s>

<s id="N12E21">quia non pote&longs;t e&longs;&longs;e motus, ni&longs;i &longs;it locus prior reli<lb/>ctus, & nouus acqui&longs;itus, igitur &longs;i eodem in&longs;tanti, quo e&longs;t impetus, <lb/>haberet motum, codem in&longs;tanti e&longs;&longs;et in duobus locis, quod dici non <lb/>pote&longs;t; & iam diximus in Th. 26. igitur impetus primo in&longs;tanti quo <lb/>e&longs;t non habet &longs;uum motum. </s>

<s id="N12E21">quia non pote&longs;t e&longs;&longs;e motus, ni&longs;i &longs;it locus prior reli<lb/>ctus, & nouus acqui&longs;itus, igitur &longs;i eodem in&longs;tanti, quo e&longs;t impetus, <lb/>haberet motum, eodem in&longs;tanti e&longs;&longs;et in duobus locis, quod dici non <lb/>pote&longs;t; & iam diximus in Th. 26. igitur impetus primo in&longs;tanti quo <lb/>e&longs;t non habet &longs;uum motum. </s>

<s id="N12E2F"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 35.<emph.end type="center"/></s>

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<s id="N12F99">Diceret fortè ali<lb/>quis eundem impetum recipi &longs;imul in &longs;ub&longs;tantia & in ip&longs;is accidenti<lb/>bus; </s>

<s id="N12FA1">&longs;ed contra, nam reuera, &longs;i hoc e&longs;&longs;et, dum proijcitur ferrum cali<lb/>dum, & &longs;tatim frigefit, de&longs;trueretur totus impetus, de&longs;tructo &longs;cilicet <lb/>eius &longs;ubiecto: </s>

<s id="N12FA9">2. qui hoc diceret, deberet probare; </s>

<s id="N12FAD">nam codem modo <lb/>mouetur corpus &longs;iue afficiatur pluribus accidentibus, &longs;iue paucioribus; <lb/>igitur non euincit experientia recipi in illis impetum, nec etiam ratio, <lb/>vt dicam paulò po&longs;t. </s>

<s id="N12FAD">nam eodem modo <lb/>mouetur corpus &longs;iue afficiatur pluribus accidentibus, &longs;iue paucioribus; <lb/>igitur non euincit experientia recipi in illis impetum, nec etiam ratio, <lb/>vt dicam paulò po&longs;t. </s>

<s id="N12FB7">Ratio à priori e&longs;&longs;e pote&longs;t; </s>

<s id="N12FBB">quia accidens cum &longs;uo <lb/>&longs;ubiecto coniunctum exigit &longs;emper e&longs;&longs;e præ&longs;ens &longs;ubiecto, cum natura<lb/>liter extra &longs;ubiectum exi&longs;tere non po&longs;&longs;it; </s>

<s id="N12FC3">igitur cum exigat con&longs;erua<lb/>ri, & exi&longs;tere; </s>

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<s id="N13129">&longs;ed motus præuius de <lb/>nihil pre&longs;enti e&longs;t &longs;ecundo quia non pote&longs;t excogitari aliud munus con<lb/>ditionis; </s>

<s id="N13131">ni&longs;i vel vt tollat impedimentum, vel vt applicet cau&longs;am &longs;ubie<lb/>cto apto; </s>

<s id="N13137">præterea motus præuius non e&longs;t; </s>

<s id="N1313B">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 id="N1313B">igitur eodem modo &longs;e <lb/>habet, ac &longs;i nunquam extiti&longs;&longs;et; & &longs;i eo in&longs;tanti quo corpus impa<lb/>ctum primo tangit, amitteret totum impetum, ita vt expræterito motu <lb/>nihil reliquum e&longs;&longs;et, haud dubiè corpus aliud non pelleret. </s>

<s id="N13147">Diceret alius impetum e&longs;&longs;e tantùm conditionem, quæ &longs;emper e&longs;t <lb/>de præ&longs;enti: </s>

<s id="N1314D">ad hanc in&longs;tantiam non valet &longs;uperior re&longs;pon&longs;io; </s>

<s id="N13151">& certè <lb/>&longs;i eo ip&longs;o in&longs;tanti contactus noua fieret impetus acce&longs;&longs;io; </s>

<s id="N13157">haud dubiè <lb/>maior e&longs;&longs;et ictus; </s>

<s id="N1315D">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; </s>

<s id="N1315D">licèt cum eodem 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; </s>

<s id="N1316D">dum &longs;cili<lb/>cet &longs;ubiectum, cui applicatur &longs;it capax motus; </s>

<s id="N13173">ex applicatione corporis <lb/>&longs;eu &longs;ubiecti ip&longs;ius non &longs;emper &longs;equitur; igitur dicendum e&longs;t impetum <lb/>ip&longs;um e&longs;&longs;e cau&longs;am alterius per Ax. 11. n. </s>

<s id="N1317B">1. voco enim illud cau&longs;am, <lb/>ex cuius applicatione &longs;emper &longs;equitur &longs;imilis effectus; alioquin &longs;i hoc <lb/>neges; </s>

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<s id="N1336C">Ob&longs;eruabis quintò nonnullos e&longs;&longs;e, qui volunt motum vnius corporis <lb/>transferri in aliud corpus; </s>

<s id="N13372">&longs;ed mera e&longs;t metaphora; </s>

<s id="N13376">nihil cnim pror&longs;us <lb/>e&longs;t quod ab vno in aliud tran&longs;eat, &longs;eu transferatur; nec aliud dici po<lb/>te&longs;t, ni&longs;i quod dictum e&longs;t, impetum &longs;cilicet nouum produci. </s>

<s id="N13376">nihil enim pror&longs;us <lb/>e&longs;t quod ab vno in aliud tran&longs;eat, &longs;eu transferatur; nec aliud dici po<lb/>te&longs;t, ni&longs;i quod dictum e&longs;t, impetum &longs;cilicet nouum produci. </s>

<s id="N13380">Hinc etiam reiicies commentum illorum, qui dicunt ideo vnum <lb/>corpus ab alio moueri, quia ab vno in aliud deriuantur corpu&longs;cula illa, <lb/>quæ faciunt lumen, & calorem; </s>

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<s id="N134C5">Hinc etiam aliud paradoxon non minus iucundum; </s>

<s id="N134C9">cau&longs;a nece&longs;&longs;aria <pb pagenum="35" xlink:href="026/01/067.jpg"/>appllcata, & non impedita non agit; </s>

<s id="N134C9">cau&longs;a nece&longs;&longs;aria <pb pagenum="35" xlink:href="026/01/067.jpg"/>applicata, & non impedita non agit; </s>

<s id="N134D2">at verò agit impedita; </s>

<s id="N134D6">&longs;cilicet <lb/>impetus qui tantùm agit, vt tollat impedimentum; igitur, &longs;i non <lb/>impediatur non agit. </s>

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<s id="N1367B"><emph type="italics"/>Si linea directionis ducatur per centrum vtriu&longs;que globi, mobilis &longs;cilicet <lb/>& immobilis, impetus producit totum impetum quem pote&longs;t producere &longs;iue in <lb/>maiori globo, &longs;iue in minori, &longs;iue in æquali<emph.end type="italics"/>; patet experientia; cuius ratio <lb/>e&longs;t; </s>

<s id="N1368A">quia impetus e&longs;t cau&longs;a nece&longs;&longs;aria; </s>

<s id="N1368E">Igitur idem impetus codem mo<lb/>do applicatus æquali tempore, æqualem &longs;emper effectum producit, per <lb/>Ax. 12. igitur cum impetus agat tantùm, vt tollat impedimentum per <lb/>Th. 44. & cum in prædicta linea agat quantum pote&longs;t per Th. 50. cer<lb/>tè æqualem effectum producat nece&longs;&longs;e e&longs;t; &longs;iue in maiori &longs;iue in mino<lb/>ri, &longs;iue in æquali globo immobili. </s>

<s id="N1368E">Igitur idem impetus eodem mo<lb/>do applicatus æquali tempore, æqualem &longs;emper effectum producit, per <lb/>Ax. 12. igitur cum impetus agat tantùm, vt tollat impedimentum per <lb/>Th. 44. & cum in prædicta linea agat quantum pote&longs;t per Th. 50. cer<lb/>tè æqualem effectum producat nece&longs;&longs;e e&longs;t; &longs;iue in maiori &longs;iue in mino<lb/>ri, &longs;iue in æquali globo immobili. </s>

<s id="N1369E"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 58.<emph.end type="center"/></s>

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<s id="N136BF">cum enim omnes <lb/>partes impetus maioris globi agant actione communi per Th. 46. & <lb/>cum agant quantùm maximè po&longs;&longs;unt; </s>

<s id="N136C7">in minore globo, tot partes pro<lb/>ducunt impetus, quot in maiore, vt patet; </s>

<s id="N136CD">igitur in minore globo pau<lb/>cioribus partibus &longs;ubiecti di&longs;tribuuntur plures partes impetus; </s>

<s id="N136D3">crgo in <lb/>qualibet parte &longs;ubiecti &longs;unt plures; </s>

<s id="N136D3">ergo in <lb/>qualibet parte &longs;ubiecti &longs;unt plures; </s>

<s id="N136D9">&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>

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<s id="N138C6">Obijci po&longs;&longs;et tertiò inde &longs;equi progre&longs;&longs;um in infinitum, nam globus <lb/>A impactus in globum B impellet cum æquali motu, & B in C etiam <lb/>æquali, C in D, atque ita deinceps; </s>

<s id="N138CE">modò illi globi ita &longs;tatuantur, vt <lb/>linea directionis per omnium centra rectà ducatur; </s>

<s id="N138D4">Re&longs;pondco, vel il-<pb pagenum="39" xlink:href="026/01/071.jpg"/>los omnes globos ita e&longs;&longs;e contiguos, vt mutuo contactu &longs;e inuicem tan<lb/>gant; </s>

<s id="N138D4">Re&longs;pondeo, vel il-<pb pagenum="39" xlink:href="026/01/071.jpg"/>los omnes globos ita e&longs;&longs;e contiguos, vt mutuo contactu &longs;e inuicem tan<lb/>gant; </s>

<s id="N138DF">vel aliquod &longs;patium inter &longs;ingulos intercipi; </s>

<s id="N138E3">&longs;i primum, produci<lb/>tur impetus à potentia motrice in omnibus, &longs;i &longs;ufficiens e&longs;t; </s>

<s id="N138E9">non verò <lb/>vnus globus in alio, vt con&longs;tat; </s>

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<s id="N13995"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 62.<emph.end type="center"/></s>

<s id="N139A3"><emph type="italics"/>Globus minor imprimit maiori remi&longs;&longs;iorem impetum & tardiorem motum <lb/>& æqualis, aqitali æqualem<emph.end type="italics"/>; hæc omnia probantur per Th. 60. & præ-, <lb/>cedentia. </s>

<s id="N139A3"><emph type="italics"/>Globus minor imprimit maiori remi&longs;&longs;iorem impetum & tardiorem motum <lb/>& æqualis, æquali æqualem<emph.end type="italics"/>; hæc omnia probantur per Th. 60. & præ-, <lb/>cedentia. </s>

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<s id="N13B14"><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 3.<emph.end type="center"/></s>

<s id="N13B23">Hinc reiicies aliquos, quorum &longs;ententiam habes apud Doctum Mer<lb/>&longs;emium, <emph type="italics"/>in prop.<emph.end type="italics"/> 20. <emph type="italics"/>phæn. mech. quorum &longs;unt hæc verba; </s>

<s id="N13B23">Hinc reiicies aliquos, quorum &longs;ententiam habes apud Doctum Mer<lb/>&longs;ennium, <emph type="italics"/>in prop.<emph.end type="italics"/> 20. <emph type="italics"/>phæn. mech. quorum &longs;unt hæc verba; </s>

<s id="N13B32">&longs;i malleus pilam <lb/>currentem eodem, ac anteà modo percutiat, nonam &longs;ui motus partem; &longs;i verò <lb/>currentem tertia vice percutiat, vnam vige&longs;imam &longs;eptimam &longs;ui motus par<lb/>tem ei tribuet, atque ita deinceps.<emph.end type="italics"/></s>

<s id="N13B3E"> Supponit primò hæc &longs;ententia mal<lb/>leum e&longs;&longs;e duplum pilæ percu&longs;&longs;æ. </s>

<s id="N13B43">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>

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<s id="N13CBD">igi<lb/>tur &longs;unt quatuor coniugationes; &longs;eu quatuor cla&longs;&longs;es diuer&longs;arum percu&longs;<lb/>&longs;ionum. </s>

<s id="N13CC7">Hinc compen&longs;ari pote&longs;t ratione vnius quod dee&longs;t ratione alterius, <lb/>v. g. &longs;i fiat percu&longs;&longs;io in puncto E per lineam ME, pote&longs;t &longs;ciri punctum <lb/>inter ED, in quo percu&longs;&longs;io per lineam perpendicularem &longs;it æqualis <lb/>percu&longs;&longs;ioni per lineam ME; &longs;ed de his infrà in lib. 10. cum de percu&longs;<lb/>&longs;ione, determinabimus enim vnde proportiones i&longs;tæ petendæ &longs;<gap/>, & <lb/>demon&longs;trabimus totam i&longs;tam rem, quæ multùm curio&longs;itatis habet, & <lb/>vtilitatis. </s>

<s id="N13CC7">Hinc compen&longs;ari pote&longs;t ratione vnius quod dee&longs;t ratione alterius, <lb/>v. g. &longs;i fiat percu&longs;&longs;io in puncto E per lineam ME, pote&longs;t &longs;ciri punctum <lb/>inter ED, in quo percu&longs;&longs;io per lineam perpendicularem &longs;it æqualis <lb/>percu&longs;&longs;ioni per lineam ME; &longs;ed de his infrà in lib. 10. cum de percu&longs;<lb/>&longs;ione, determinabimus enim vnde proportiones i&longs;tæ petendæ &longs;int, & <lb/>demon&longs;trabimus totam i&longs;tam rem, quæ multùm curio&longs;itatis habet, & <lb/>vtilitatis. </s>

<s id="N13CDF">Determinabimus etiam dato puncto percu&longs;&longs;ionis F v.g. cum &longs;equatur <lb/>motus vectis, quodnam &longs;it centrum vectis &longs;eu huius motus. </s>

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<s id="N13EA8">Colligemus etiam quid dicendum &longs;it de malleorum ictu; </s>

<s id="N13EAC">&longs;it enim <lb/>malleus F æqualis malleo G (in his vna fere manubrij longitudinis ha<lb/>betur ratio) ducatur arcus NM, itemque OG; </s>

<s id="N13EB4">ictus mallei G e&longs;t ferè <lb/>&longs;ubduplus alterius, dum vterque malleus &longs;it æqualis; </s>

<s id="N13EBA">dixi ferè, quia <lb/>motus totius mallei G non e&longs;t omninò &longs;ubduplus motus mallci F, quia <lb/>&longs;cilicet trapezus OD e&longs;t minor &longs;ubduplo alterius NE; </s>

<s id="N13EBA">dixi ferè, quia <lb/>motus totius mallei G non e&longs;t omninò &longs;ubduplus motus mallei F, quia <lb/>&longs;cilicet trapezus OD e&longs;t minor &longs;ubduplo alterius NE; </s>

<s id="N13EC2">quotâ vero parte <lb/>&longs;it minor facilè pote&longs;t &longs;ciri opera Geometriæ: &longs;ed hæc omnia determi<lb/>nabimus. </s>

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<s id="N13FE9">Ob&longs;eruabis qualitatem omnem ita &longs;uo &longs;ubjecto coëxtendi, vt æqua<lb/>lem omnino quodlibet eius punctum, &longs;eu pars extentionem habeat ex<lb/>tentioni puncti, &longs;eu partis &longs;ui &longs;ubjecti; </s>

<s id="N13FF1">nec enim alliud e&longs;t, vnde po&longs;&longs;it <lb/>determinari extentio qualitatum, præter ip&longs;am exten&longs;ionem &longs;ubjecti; </s>

<s id="N13FF1">nec enim aliud e&longs;t, vnde po&longs;&longs;it <lb/>determinari extentio qualitatum, præter ip&longs;am exten&longs;ionem &longs;ubjecti; </s>

<s id="N13FF7"><lb/>quod maximè in impetu videre e&longs;t, cuius partes in mobili den&longs;o minori <lb/>extentioni &longs;ubjacent, quàm in mobili raro; </s>

<s id="N13FFE">cum ex maiore ictu &longs;eu per<lb/>cu&longs;&longs;ione in mobili den&longs;o plures impetus agentis partes e&longs;&longs;e con&longs;tet; quia <lb/>&longs;cilicet &longs;unt plures partes &longs;ubiecti. </s>

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<s id="N1426F"><emph type="italics"/>Perfectio impetus non petitur tantùm à perfectione motus &longs;i con&longs;ideretur <lb/>&longs;eor&longs;im entitas eiu&longs;dem impetus; </s>

<s id="N14277">&longs;ed debet comparari tota collectio omniu&mtail; <lb/>partium impetus, quæ in&longs;unt datæ parti &longs;ubiecti, cum tota collectione partium <lb/>quæ alteri porti mobilis in&longs;unt<emph.end type="italics"/>; </s>

<s id="N14277">&longs;ed debet comparari tota collectio omniu&mtail; <lb/>partium impetus, quæ in&longs;unt datæ parti &longs;ubiecti, cum tota collectione partium <lb/>quæ alteri parti mobilis in&longs;unt<emph.end type="italics"/>; </s>

<s id="N14282">quippe plures partes impetus po&longs;&longs;unt ha<lb/>bere eum motum, vel potius eam motus perfectionem, quam pauciores <lb/>haberent; igitur perfectio illarum e&longs;t ab ip&longs;o motu, quatenus cum ip&longs;o <lb/>partium numero comparatur. </s>

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<s id="N14E3E">Ob&longs;eruabis denique triplicem propagationem impetus e&longs;&longs;e legiti<lb/>mam. </s>

<s id="N14E43">Prima e&longs;t in motu recto, cum propagatur per partes æquales, tùm <lb/>in perfectione, tùm in numero in &longs;ingulis partibus &longs;ubjecti per gradus, <lb/>&longs;cilicet heterogencos. </s>

<s id="N14E4A">Secunda e&longs;t in motu circulari, applicata &longs;cilicet <lb/>potentia centro; cum propagatur per partes æquales in perfectione, & <lb/>inæquales in numero. </s>

<s id="N14E52">Tertia e&longs;t in vecte, cum propagatur per partes <lb/>æquales in numero, & inæquales in perfectione. </s>

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<s id="N15DF4">Primò per qualitatem <lb/>quamdam diffu&longs;am, quod dici non pote&longs;t; </s>

<s id="N15DFA">quia capillus traheretur faci<lb/>liùs, quàm ingens &longs;axum, quàm ma&longs;&longs;a, &longs;eu lamina; </s>

<s id="N15E00">& faciliùs eadem po<lb/>tentia motrix minus pondus moueret quàm maius, cæteris paribus; </s>

<s id="N15E06">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; </s>

<s id="N15E06">præ<lb/>terea manum meam æqualiter traheret, &longs;iue &longs;it cum aliquo pondere con<lb/>iuncta, &longs;iue &longs;it nuda &longs;ine pondere; </s>

<s id="N15E0E">deinde illa virtus tractrix ita diffun<lb/>ditur, vt in maiori di&longs;tantia &longs;it infirmior, fortior in minori; </s>

<s id="N15E14">alioqui <lb/>diffunderetur in infinitum, quod dici non pote&longs;t; </s>

<s id="N15E1A">igitur &longs;i idem lapis <lb/>demittatur ex maiore altitudine, tum ex minore; </s>

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<s id="N162F1"><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 id="N162FA"> Probatur primò, non cre&longs;cit <lb/>corporis grauis &longs;eu grauitas, &longs;eu grauitatio, vt con&longs;tat experientiâ; </s>

<s id="N16300">igitur <lb/>non cre&longs;cit impetus; </s>

<s id="N16306">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; </s>

<s id="N16306">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 euidens; </s>

<s id="N1630C">iam demon&longs;tratur <lb/>propter quid &longs;it; </s>

<s id="N16312">impetus &longs;ecundo in&longs;tanti productus e&longs;&longs;et fru&longs;trà; </s>

<s id="N16316">careret <pb pagenum="83" xlink:href="026/01/115.jpg"/>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>

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<s id="N163B9">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 id="N163C5">Impetus naturalis acqui&longs;itus producitur ab codem principio intrin<lb/>&longs;eco; </s>

<s id="N163C5">Impetus naturalis acqui&longs;itus producitur ab eodem principio intrin<lb/>&longs;eco; </s>

<s id="N163CB">hinc dicitur naturalis: </s>

<s id="N163CF">dicitur verò acqui&longs;itus, quia non e&longs;t inna<lb/>tus; </s>

<s id="N163D5">&longs;ed &longs;eparatur à corpore graui; </s>

<s id="N163D9">quod &longs;emper eo caret, quandiu <lb/>quie&longs;cit: </s>

<s id="N163DF">&longs;ed innato tantùm accedit ad motus accelerationem, & ad alia <lb/>quamplurima, quæ ex ea &longs;equuntur; </s>

<s id="N163E5">putà maiorem percu&longs;&longs;ionem, re&longs;i<lb/>&longs;tentiam, vim, & ad tollendum totius naturæ langudiorem; </s>

<s id="N163E5">putà maiorem percu&longs;&longs;ionem, re&longs;i<lb/>&longs;tentiam, vim, & ad tollendum totius naturæ languidiorem; </s>

<s id="N163EB">quo certè af<lb/>ficeretur, &longs;i corpus graue tardi&longs;&longs;imo motu deor&longs;um ferretur, de quo in<lb/>frà; </s>

<s id="N163F3">Porrò impetus acqui&longs;itus in multis differt ab innato; primò quia <pb pagenum="84" xlink:href="026/01/116.jpg"/>de&longs;truitur à corpore re&longs;i&longs;tente eo modo, quo diximus, & dicemus infrà. </s>

<s id="N163FC"><lb/>Secundò, quia determinari pote&longs;t ad omnem lineam. </s>

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<s id="N16441"><emph type="italics"/>Hinc motus naturalis deor&longs;um acceleratur<emph.end type="italics"/>; </s>

<s id="N1644A">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; </s>

<s id="N16450">&longs;ie enim <lb/>hypothe&longs;is in Theorema conuerti pote&longs;t, vt 6longs;æpè monuimus in metho<lb/>do; </s>

<s id="N16450">&longs;ie enim <lb/>hypothe&longs;is in Theorema conuerti pote&longs;t, vt &longs;æpè monuimus in metho<lb/>do; </s>

<s id="N16458">igitur probatur hoc Theorema facilè; </s>

<s id="N1645C">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; </s>

<s id="N16464">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: </s>

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<s id="N1669A"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 29.<emph.end type="center"/></s>

<s id="N166A8"><emph type="italics"/>Si percurrantnr à mobili æqualia &longs;patia, &longs;ed inæquali velocitate, ip&longs;æ ve<lb/>locitates erunt in ratione permutata temporum, ide&longs;t maior velocitas re&longs;pon<lb/>debit minori tempori, & minor maiori<emph.end type="italics"/>; Probatur per Th.23. </s>

<s id="N166A8"><emph type="italics"/>Si percurrantur à mobili æqualia &longs;patia, &longs;ed inæquali velocitate, ip&longs;æ ve<lb/>locitates erunt in ratione permutata temporum, ide&longs;t maior velocitas re&longs;pon<lb/>debit minori tempori, & minor maiori<emph.end type="italics"/>; Probatur per Th.23. </s>

<s id="N166B7"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 30.<emph.end type="center"/></s>

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<s id="N16B10"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 46.<emph.end type="center"/></s>

<s id="N16B1E"><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"/>; </s>

<s id="N16B2B">&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; </s>

<s id="N16B33">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; </s>

<s id="N16B3F">illudque ducere in nu<lb/>merum terminorum per regulam arithmeticam; </s>

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<s id="N16B73">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; </s>

<s id="N16B79"><lb/>primæ parti tria ex prædictis &longs;patiis re&longs;pondeant; </s>

<s id="N16B7E">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; </s>

<s id="N16B88">primæ parti re&longs;pon-<pb pagenum="92" xlink:href="026/01/124.jpg"/>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: </s>

<s id="N16B88">primæ parti re&longs;pon-<pb pagenum="92" xlink:href="026/01/124.jpg"/>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;iue 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: </s>

<s id="N16BA7">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; </s>

<s id="N16BB3">&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 id="N16C4F"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 49.<emph.end type="center"/></s>

<s id="N16C5D"><emph type="italics"/>In progre&longs;&longs;ione arithmetica &longs;i diuidatur numerus terminorum bifariam æ<lb/>qualiter nunquam &longs;umma po&longs;terioris &longs;egmenti e&longs;t tripla prioris<emph.end type="italics"/>; &longs;ed &longs;i acci<lb/>piantur duo termini e&longs;t tantùm 2/1, &longs;i 4. e&longs;t 7/3 &longs;i 6. e&longs;t (15/6), &longs;i 8. e&longs;t (26/10), &longs;i 10<lb/>(40/25), &longs;i 12. (57/21), &longs;i 14. (77/28), atque ita deinceps. </s>

<s id="N16C5D"><emph type="italics"/>In progre&longs;&longs;ione arithmetica &longs;i diuidatur numerus terminorum bifariam æ<lb/>qualiter nunquam &longs;umma po&longs;terioris &longs;egmenti e&longs;t tripla prioris<emph.end type="italics"/>; &longs;ed &longs;i acci<lb/>piantur duo termini e&longs;t tantùm 2/1, &longs;i 4. e&longs;t 7/3 &longs;i 6. e&longs;t (15/6), &longs;i 8. e&longs;t (26/10), &longs;i 10<lb/>(40/15), &longs;i 12. (57/21), &longs;i 14. (77/28), atque ita deinceps. </s>

<s id="N16C6E">Ex quo ob&longs;erua mirabilem con&longs;equutionem; </s>

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<s id="N16F32"><lb/>&longs;ed minima velocitas primi in&longs;tantis pro nihilo reputatur; </s>

<s id="N16F37">igitur acci<lb/>piatur tantùm &longs;ubduplum maximæ, igitur cum velocitate æquali maxi<lb/>mæ, eodem tempore duplum &longs;patium percurretur; </s>

<s id="N16F3F">igitur in vno minuto <lb/>&longs;ecundo, v.g. 24. pedes; </s>

<s id="N16F47">igitur in vno minuto primo codem motu æqua<lb/>bili 1440. pedes percurrentur; </s>

<s id="N16F47">igitur in vno minuto primo eodem motu æqua<lb/>bili 1440. pedes percurrentur; </s>

<s id="N16F4D">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>

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<s id="N172D1">quin vel aliqua puncta in &longs;patiis, vel in&longs;tantia in <lb/>temporibus de&longs;int, vel &longs;uper&longs;int; </s>

<s id="N172D7">&longs;i enim quis diceret &longs;patium e&longs;&longs;e tri<lb/>plum primi minus 100000. punctis, vel &longs;ecundum tempus e&longs;&longs;e maius <lb/>primo 100000. in&longs;tantibus; quis hanc, vel &longs;patij, vel temporis differen<lb/>tiam &longs;en&longs;u percipiat? </s>

<s id="N172E1">cum tamen experimentum omne phy&longs;icum &longs;en&longs;ui <lb/>&longs;ube&longs;&longs;e po&longs;&longs;it; </s>

<s id="N172E7">nec e&longs;t quod aliquis dicat hoc idem toties ob&longs;eruatum <lb/>e&longs;&longs;e, tam multis locis temporibus, totque ac tantis etiam te&longs;tibus, vt mi<lb/>nimè fraus aliqua, vel error &longs;ubrepere potuerit; nam cum parua &longs;it, & <lb/>in&longs;en&longs;ibilis tùm &longs;patiorum, tùm temporum differentia, maius vel minus <lb/>æquali tempus, pro æquali, maius.vel minus triplò &longs;patium pro triplo <pb pagenum="101" xlink:href="026/01/133.jpg"/>facilè accipi pote&longs;t, cum nullum di&longs;erimen &longs;en&longs;ibile e&longs;t. </s>

<s id="N172FA">Adde quod non de&longs;unt viri graui&longs;&longs;imi qui dicant &longs;e vix ob&longs;eruare po<lb/>tui&longs;&longs;e hanc &longs;patiorum progre&longs;&longs;ionem; </s>

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<s id="N17490">dimittantur enim duo funependula æ<lb/>qualia; </s>

<s id="N17496">alterum quidem ex altitudine 90.graduum, alterum ex altitudine <pb pagenum="103" xlink:href="026/01/135.jpg"/>10. vel 15.graduum; </s>

<s id="N1749F">ita vt &longs;imul vibrationes &longs;uas incipiant; </s>

<s id="N174A3">numerentur <lb/>vibrationes vtriu&longs;que, vbi 100. è minoribus numeratç fuerint, numera<lb/>buntur circiter 97. è maioribus, quod &longs;æpiùs ob&longs;eruaui te&longs;tibus etiam <lb/>adhibitis; </s>

<s id="N174A3">numerentur <lb/>vibrationes vtriu&longs;que, vbi 100. è minoribus numerat&ecedil; fuerint, numera<lb/>buntur circiter 97. è maioribus, quod &longs;æpiùs ob&longs;eruaui te&longs;tibus etiam <lb/>adhibitis; </s>

<s id="N174AD">hoc ip&longs;um etiam ob&longs;eruarunt alij; </s>

<s id="N174B1">atque adeo ip&longs;e P.Mer&longs;en<lb/>nus, qui L. 2. &longs;uæ ver&longs;ionis, Ar.17. Galileum arguit parùm acurati &longs;tu<lb/>dij in his ob&longs;eruationibus adhibiti: </s>

<s id="N174B9">rationem huius effectus in libro de <lb/>funependulis explicabimus; </s>

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<s id="N174DD">Secundum, quod &longs;upponitur, e&longs;t quod longitudines funependulorum <lb/>&longs;int pror&longs;us, vt quadrata temporum, quibus vibrationes &longs;ingulorum <lb/>fiunt, v.g. funependulum longitudinis 4. pedum facere vnam vibratio<lb/>nem eo tempore, quo funependulum longitudinis vnius pedis facit duas; </s>

<s id="N174E9"><lb/>quod primò in multis vibrationibus non tàm accuratè ob&longs;eruatur; </s>

<s id="N174EE"><expan abbr="&longs;ec&umacr;-dò">&longs;ecun<lb/>dò</expan> licèt ob&longs;eruaretur &longs;en&longs;ibiliter, id emre&longs;ponderi debet, quod &longs;uprà in <lb/>&longs;ingulis vibrationibus e&longs;&longs;e tantùm di&longs;crimen; </s>

<s id="N174F9">uod etiam in multis &longs;en&longs;i<lb/>bile non e&longs;t; &longs;i enim di&longs;crimen primarum vibrationem v.g.&longs;it (1/100000000) <lb/>certè vltimarum adhuc in&longs;en&longs;ibile erit. </s>

<s id="N174F9">quod etiam in multis &longs;en&longs;i<lb/>bile non e&longs;t; &longs;i enim di&longs;crimen primarum vibrationem v.g.&longs;it (1/100000000) <lb/>certè vltimarum adhuc in&longs;en&longs;ibile erit. </s>

<s id="N17503">Tertium &longs;uppo&longs;itum fuit, minimum arcum minoris quadrantis a&longs;&longs;um<lb/>ptum, & alium minoris quadrantis e&longs;&longs;e ad in&longs;tar perpendicularium; </s>

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<s id="N17521">hinc illa extremitas ma<lb/>ioris, vnde e&longs;t initium motus, planum decliuius facit; altera verò minùs <lb/>decliue; &longs;ed hæc fusè pro&longs;equar &longs;uo loco. </s>

<s id="N1752B">Quartum, quod &longs;upponitur e&longs;t, accelerationem motus fieri in qua<lb/>drante in ea ratione, in qua fit per plana chordarum inclinata, quod <lb/>etiam fai&longs;um e&longs;t; </s>

<s id="N17533">quia in eodem plano inclinato &longs;upponitur eadem <lb/>inclinatio; </s>

<s id="N17539">&longs;ecus in quadrante, cuius &longs;ingula puncta nouam faciunt in<lb/>clinationem: </s>

<s id="N1753F">adde quod quarta pars quadrantis maioris EK non facit <lb/>eandem inclinationem, quam totus quadrans minor DF ip&longs;i EK æqua<lb/>lis; quamquam hoc ip&longs;i vltrò concedent aduer&longs;arij. </s>

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<s id="N17549">Præterea, &longs;it ita vt &longs;upponitur; </s>

<s id="N1754D">ita vt &longs;en&longs;ibiliter differentia huius <lb/>progre&longs;&longs;ionis percipi non po&longs;&longs;it, &longs;intque numeratæ omnes vibrationes <lb/>&longs;en&longs;ibiles dati funependuli ex altitudine 90, grad. demi&longs;&longs;i; </s>

<s id="N17557">quæ vix e&longs;&longs;e <lb/>po&longs;&longs;unt 1800; </s>

<s id="N1755D">&longs;int autem plures &longs;cilicet 2000. dicis confectas e&longs;&longs;e 2000 <lb/>minoris funependuli eo tempore, quo 1000. tantùm in quadruplo fune<lb/>pendulo nnmerantur; </s>

<s id="N17565">annuo quidem, &longs;i res tantùm &longs;en&longs;ibiliter con&longs;ide<lb/>retur; </s>

<s id="N1756B">&longs;in verò &longs;ecùs, id pernego; &longs;ed dico dee&longs;&longs;e v. g. 1000000. puncta <lb/>&longs;patij, quæ di&longs;cerni non po&longs;&longs;unt, ita vt primæ vibrationi 1000. pun<lb/>cta &longs;ecundæ, 2000. tertiæ 3000. &c. </s>

<s id="N17577">vltimæ verò, &longs;eu mille&longs;imæ <pb pagenum="104" xlink:href="026/01/136.jpg"/>1000000. quæ omnia &longs;unt in&longs;en&longs;ibilia, neque maiorem habent diffi<lb/>cultatem, quàm in motu perpendiculari, de quo &longs;uprà; etiam conce&longs;&longs;is <lb/>vltrò omnibus experimétis propo&longs;itis. </s>

<s id="N17584">Igitur &longs;uppo&longs;itâ progre&longs;&longs;ione &longs;pa<lb/>tiorum arithinetica in in&longs;tantibus, tàm propè accedit ad aliam, quàm <lb/>Galileus ponit, &longs;iue in perpendiculari deor&longs;um, &longs;iue in quadrante fune<lb/>penduli; </s>

<s id="N17584">Igitur &longs;uppo&longs;itâ progre&longs;&longs;ione &longs;pa<lb/>tiorum arithmetica in in&longs;tantibus, tàm propè accedit ad aliam, quàm <lb/>Galileus ponit, &longs;iue in perpendiculari deor&longs;um, &longs;iue in quadrante fune<lb/>penduli; </s>

<s id="N1758E">a&longs;&longs;umptis &longs;cilicet partibus temporis &longs;en&longs;ibilibus, vt differentia <lb/>di&longs;cernit non po&longs;&longs;it; </s>

<s id="N17594">immò nec duplum diffetentiæ, nec centuplum, nec <lb/>millecuplum; </s>

<s id="N17594">immò nec duplum differentiæ, nec centuplum, nec <lb/>millecuplum; </s>

<s id="N1759A">&longs;ed de his &longs;atis quæ ex dictis &longs;uprà facilè intelligi po&longs;&longs;unt: <lb/>quare veniemus iam ad rationes. </s>

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<s id="N17614">ducatur in 6.id e&longs;t in numerum termi<lb/>norum, vel in&longs;tantium; &longs;umma erit 21. igitur quod tribuit Galileus &longs;uæ <lb/>progre&longs;&longs;ioni, etiam no&longs;træ competit. </s>

<s id="N1761E">Tertia ratio petitur ex mathe&longs;i &longs;it enim linea AE diui&longs;a in qautuor <lb/>partes æquales, quæ nobis repre&longs;entent 4. partes temporis æquales; </s>

<s id="N1761E">Tertia ratio petitur ex mathe&longs;i &longs;it enim linea AE diui&longs;a in quatuor <lb/>partes æquales, quæ nobis repre&longs;entent 4. partes temporis æquales; </s>

<s id="N17624"><lb/>haud dubiè, cùm acquirantur temporibus æqualibus æqualia velocitatis <lb/>momenta; </s>

<s id="N1762B">haud dubiè, inquam, his 4. temporibus AB, BC, CD, DE, ac-<pb pagenum="105" xlink:href="026/01/137.jpg"/>quirentur æquales velocitatis gradus; </s>

<s id="N17634">&longs;it autem BI, men&longs;ura velocitatis, <lb/>quam acquirit mobile cadens ex &longs;ua quiete in fine primæ partis tempo<lb/>ris AB; </s>

<s id="N1763C">certè in fine &longs;ecundæ partis temporis BC acquiret velocitatem, <lb/>quæ coniuncta cum priore BI faciet duplam CH, & in fine tertiæ par<lb/>tiæ CD triplam DG; </s>

<s id="N17644">denique in fine quartæ DE quadruplam EF; </s>

<s id="N17648">quip<lb/>pe cum in parte BC remaneat tota velocitas B, & acquiratur æqualis; </s>

<s id="N1764E"><lb/>certè in fine BC e&longs;t velocitas CH dupla illius quæ commen&longs;uratur BI. <lb/>&longs;uniliter in parte CD remanebit vtraque, & accedet altera; </s>

<s id="N1764E"><lb/>certè in fine BC e&longs;t velocitas CH dupla illius quæ commen&longs;uratur BI. <lb/>&longs;imiliter in parte CD remanebit vtraque, & accedet altera; </s>

<s id="N17655">igitur e&longs;t ve<lb/>locitas DG tripla BI, & EF e&longs;t quadrupla: Similiter ita &longs;e ratio habet <lb/>cuiu&longs;libet alterius partis inter AB ad aliam alterius partis inter BC, vt <lb/>lineæ ductæ parallelæ BICH, &c. </s>

<s id="N1765F">igitur cum &longs;patium acqui&longs;itum re&longs;<lb/>pondeat exercitio huius velocitatis; </s>

<s id="N17665">&longs;itque in&longs;tanti B vt BI, & in&longs;tanti <lb/>C vt CH; </s>

<s id="N1766B">certè tempore AB e&longs;t vt triangulum AIB; </s>

<s id="N1766F">nam &longs;patium AIB <lb/>e&longs;t collectio omnium linearum, quæ duci po&longs;&longs;unt parallelæ in tempote <lb/>AB; </s>

<s id="N1766F">nam &longs;patium AIB <lb/>e&longs;t collectio omnium linearum, quæ duci po&longs;&longs;unt parallelæ in tempore <lb/>AB; </s>

<s id="N17677">idem dico de trapezo CBIH, qui e&longs;t triplus trianguli IBA; </s>

<s id="N1767B">& de <lb/>trapezo GDCH, qui e&longs;t quintuplus; </s>

<s id="N17681">igitur triangulum HCA e&longs;t qua<lb/>druplum IBA; </s>

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<s id="N17722"><lb/>quippe hæc progre&longs;&longs;io in puris in&longs;tantibus fieri tantùm pote&longs;t, cum &longs;in<lb/>gulis in&longs;tantibus noua fiat acce&longs;&longs;io velocitatis, in hoc enim e&longs;t error, <lb/>quòd in tota parte temporis AC ponatur æquabilis velocitas, eiu&longs;que <lb/>principium A, &longs;it æquale fini C; </s>

<s id="N1772D">nam AB, & GH &longs;unt æquales; </s>

<s id="N17731">cùm ta<lb/>men &longs;it minor velocitas in A, quàm in C, ni&longs;i AC &longs;it tantùm <expan abbr="in&longs;tãs">in&longs;tans</expan>; </s>

<s id="N1773B">vnde <lb/>tota velocitas in hypothe&longs;i Galilci acqui&longs;ita in 4.partibus temporis a&longs;<lb/>&longs;umptis e&longs;t, vt triangulum AFN; </s>

<s id="N1773B">vnde <lb/>tota velocitas in hypothe&longs;i Galilei acqui&longs;ita in 4.partibus temporis a&longs;<lb/>&longs;umptis e&longs;t, vt triangulum AFN; </s>

<s id="N17743">acqui&longs;ita verò in no&longs;tra hypothe&longs;i e&longs;t vt <lb/>&longs;umma rectangulorum CB, CI, EK, EN, quæ &longs;umma e&longs;t ad triangulum <lb/>AFN, vt 10, ad 8. vel vt 5.ad 4. igitur maior 1/4; nam prima pars tempo<lb/>ris addit triangulum ABG, &longs;ecunda GHI. &c. </s>

<s id="N1774F">Si tamen diuidantur i&longs;tæ partes temporis in minores v. g. in 8. tunc <lb/>&longs;umma rectangulorum erit tantùm maior 1/8; </s>

<s id="N17759">&longs;i in 16. (1/16) &longs;i in 32. (1/32); </s>

<s id="N1775D">&longs;i in <lb/>64.(11/64), cuius &longs;eliema hîc habes; &longs;int enim 3.partes temporis &longs;en&longs;ibiles A <lb/>CDFE, & &longs;patium vt triangulum AFN, &longs;patia verò acqui&longs;ita in &longs;ingulis <lb/>partibus, vt portiones trianguli prædicti, quæ ip&longs;is re&longs;pondent v. g. ac<lb/>qui&longs;itum in prima parte ad acqui&longs;itum in &longs;ecunda tantùm, vt triangu<lb/>lum ACG ad trapezum GCDI &c. </s>

<s id="N1775D">&longs;i in <lb/>64.(11/64), cuius &longs;ehema hîc habes; &longs;int enim 3.partes temporis &longs;en&longs;ibiles A <lb/>CDFE, & &longs;patium vt triangulum AFN, &longs;patia verò acqui&longs;ita in &longs;ingulis <lb/>partibus, vt portiones trianguli prædicti, quæ ip&longs;is re&longs;pondent v. g. ac<lb/>qui&longs;itum in prima parte ad acqui&longs;itum in &longs;ecunda tantùm, vt triangu<lb/>lum ACG ad trapezum GCDI &c. </s>

<s id="N1776F">denique acqui&longs;itum in temporibus <lb/>inæqualibus, vt quadrata temporum v. g. acqui&longs;itum in prima parte ad <lb/>acqui&longs;itum in duabus, vt triangulum ACG ad triangulum ADI; </s>

<s id="N1777B">id e&longs;t <lb/>quadratum CA ad quadratum DA; </s>

<s id="N17781">in no&longs;tra verò hypothe&longs;i, &longs;i velocitas <lb/>in tota prima parte AC ponatur vt CG æquabiliter; </s>

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<s id="N17859">&longs;itque velocitas acqui&longs;ita EF in 4. parti<lb/>bus temporis AE, vt iam &longs;uprà dictum e&longs;t, ne cogar repetere: </s>

<s id="N1785F">certè &longs;i du<lb/>catur velocitas EF in tempus AE, vel EL æquale; </s>

<s id="N17865">habebitur rectan<lb/>gulum EK duplum trianguli AFE: </s>

<s id="N1786B">&longs;ed triangulum AFE e&longs;t &longs;umma <lb/>&longs;patiorum motus accelerati tempore AE, & rectangulum EK e&longs;t &longs;um<lb/>ma &longs;patiorum motus æquabilis cum velocitate EF; igitur duplum e&longs;t <lb/>&longs;patium motus quabilis, quod erat demon&longs;trandum. </s>

<s id="N17875">Præterea &longs;i diai<lb/>datur velocitas EF, & eius &longs;ubdupla ducatur in tempus AE; habebitur <lb/>rectangulum æquale triangulo AFE, vt con&longs;tat. </s>

<s id="N17875">Præterea &longs;i diui<lb/>datur velocitas EF, & eius &longs;ubdupla ducatur in tempus AE; habebitur <lb/>rectangulum æquale triangulo AFE, vt con&longs;tat. </s>

<s id="N1787D">Re&longs;pondeo facilè ex di<lb/>ctis, hoc ip&longs;um etiam ex no&longs;tra hypothe&longs;i proxime &longs;equi; </s>

<s id="N17883">&longs;int enim duo <lb/>in&longs;tantia; </s>

<s id="N17889">haud dubie &longs;i non cre&longs;cit velocitas, &longs;ecundo in&longs;tanti æquale <lb/>&longs;patium percurretur; </s>

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<s id="N17A6D">Secunda objectio; </s>

<s id="N17A70">Sed inquiet aliquis, igitur non e&longs;t continua acce<lb/>leratio motus; nam in&longs;tans quo percurritur &longs;ecundum &longs;patium BD, cùm <lb/>&longs;it æquale in&longs;tanti quo percurritur tertium &longs;patium DC, in vtroque &longs;pa<lb/>tio e&longs;t æquabilis motus. </s>

<s id="N17A7A">Re&longs;pondeo in&longs;tans quo percurritur &longs;ecundum <lb/>&longs;patium BD, e&longs;&longs;e maius in&longs;tanti, quo percurritur tertium &longs;patium DC; </s>

<s id="N17A80"><lb/>tà tamen lege, vt vtrumque &longs;imul &longs;umptum &longs;it onminò equale in&longs;tanti, <pb pagenum="110" xlink:href="026/01/142.jpg"/>quo percurritur primum &longs;patíum AB; </s>

<s id="N17A80"><lb/>tà tamen lege, vt vtrumque &longs;imul &longs;umptum &longs;it omninò equale in&longs;tanti, <pb pagenum="110" xlink:href="026/01/142.jpg"/>quo percurritur primum &longs;patíum AB; </s>

<s id="N17A8A">&longs;imiliter totum &longs;patium CG ita <lb/>percurritur tertio tempore, vt &longs;ingula &longs;patia CE. EI. FG. &longs;ingulis in<lb/>&longs;tantibus percurrantur; </s>

<s id="N17A92">&longs;ed hæc tria in&longs;tantia &longs;imul &longs;umpta &longs;unt æqualia <lb/>primo in&longs;tanti, quo percurritur &longs;patium; licèt primum quo percurritur <lb/>CE &longs;it maius &longs;ecundo, quo percurritur EF, & hoc maius tertio, quo per<lb/>curritur FG, atque ita deinceps. </s>

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<s id="N17B1A">Quarta objectio; </s>

<s id="N17B1D">&longs;i impetus &longs;ingulis in&longs;titutibus cre&longs;ceret, vel intende<lb/>retur, augeretur grauitatio: </s>

<s id="N17B1D">&longs;i impetus &longs;ingulis in&longs;tantibus cre&longs;ceret, vel intende<lb/>retur, augeretur grauitatio: </s>

<s id="N17B23">quippe &longs;i grauitas primo in&longs;tanti producat <lb/>vnum gradum impetus; </s>

<s id="N17B29">&longs;ecundo æqualem producet, & tertio, atque ita <lb/>deinceps, quod e&longs;&longs;et ab&longs;urdum; alioqui minima atomus quodlibet cor<lb/>pus graue adæquaret, quod e&longs;t ab&longs;urdum. </s>

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<s id="N17F74">&longs;ed de his fusè in primo libro <lb/>à Th.148. ad finem v&longs;que libri: </s>

<s id="N17F7A">nam reuerâ duæ determinationes op<lb/>po&longs;itæ pugnant pro rata per Ax. 15.l.1. & quotie&longs;cunque idem impetus <lb/>e&longs;t ad lineas oppo&longs;itas determinatus eodem modo &longs;e habet, ac &longs;i duplex <lb/>e&longs;&longs;et, & quilibet &longs;uæ &longs;ube&longs;&longs;et determinationi; </s>

<s id="N17F84">atqui &longs;i duplex e&longs;&longs;et oppo<lb/>&longs;itus, pugnarent pro rata; </s>

<s id="N17F8A">igitur tàm pugnant duæ determinationes op<lb/>po&longs;itæ in codem impetu, quàm duo impetus ad oppo&longs;itas lineas deter<lb/>minati; igitur impetus naturalis aduentitius de&longs;truitur, &c. </s>

<s id="N17F8A">igitur tàm pugnant duæ determinationes op<lb/>po&longs;itæ in eodem impetu, quàm duo impetus ad oppo&longs;itas lineas deter<lb/>minati; igitur impetus naturalis aduentitius de&longs;truitur, &c. </s>

<s id="N17F94"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 73.<emph.end type="center"/></s>

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<s id="N17FBD">Dices lignum vi extrin&longs;eca in aqua immer&longs;um &longs;ua &longs;ponte a&longs;cendit; </s>

<s id="N17FC1"><lb/>igitur ille gradus impetus grauitationis de&longs;truitur, & alius producitur; <lb/>hæc quæ&longs;tio ad præ&longs;ens in&longs;titutum non pertinet, &longs;ed ad librum de gra<lb/>uitate, & leuitate. </s>

<s id="N17FCA">Igitur breuiter re&longs;pondeo illum impetum nunquam <lb/>de&longs;trui, quandiu mobile grauitat, vel grauitatione &longs;ingulari, (&longs;ic corpus <lb/>grauitat in manum &longs;u&longs;tinentis,) vel grauitatione communi, (&longs;ic lignum <lb/>humori innatans grauitat, non quidem in aquam, at &longs;imul cum aqua;) <lb/>&longs;ed de grauitate, & grauitatione in Tomo de &longs;tatibus corporum &longs;en&longs;ibi-<pb pagenum="116" xlink:href="026/01/148.jpg"/>libus, in quo o&longs;tendemus ideo lignum &longs;ur&longs;um emergere, quia ab aqua <lb/>extenditur, & idco corpora &longs;ur&longs;um ire, quia alia deor&longs;um eunt. </s>

<s id="N17FCA">Igitur breuiter re&longs;pondeo illum impetum nunquam <lb/>de&longs;trui, quandiu mobile grauitat, vel grauitatione &longs;ingulari, (&longs;ic corpus <lb/>grauitat in manum &longs;u&longs;tinentis,) vel grauitatione communi, (&longs;ic lignum <lb/>humori innatans grauitat, non quidem in aquam, at &longs;imul cum aqua;) <lb/>&longs;ed de grauitate, & grauitatione in Tomo de &longs;tatibus corporum &longs;en&longs;ibi-<pb pagenum="116" xlink:href="026/01/148.jpg"/>libus, in quo o&longs;tendemus ideo lignum &longs;ur&longs;um emergere, quia ab aqua <lb/>extenditur, & ideo corpora &longs;ur&longs;um ire, quia alia deor&longs;um eunt. </s>

<s id="N17FDE"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 74.<emph.end type="center"/></s>

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<s id="N18423">hinc etiam maioris &longs;unt ponderis in aëre quam in <lb/>aqua; </s>

<s id="N18429">hinc &longs;i grauitas alicuius corporis &longs;it ad grauitatem aëris vt 100. <lb/>ad 1. haud dubiè decre&longs;cet eius pondus in aëre (1/100); </s>

<s id="N1842F">id e&longs;t, &longs;i penderet 100. <lb/>libras in vacuo, in aëre penderet 99. & eo tempore quo in vacuo decur<lb/>reret 100. pa&longs;&longs;us, in aëre decurreret 99. &longs;i nulla &longs;it aliunde re&longs;i&longs;tentia, <lb/>qualis reuerâ e&longs;t, vt dicam infrà; </s>

<s id="N18439">&longs;imiliter &longs;i grauitas alicuius corporis <lb/>&longs;it ad grauitatem aquæ, vt 10. ad 1. decre&longs;cet eius pondus in aqua (1/<gap/>), & <lb/>co tempore quo decurreret in vacuo 10. palmos &longs;patij, in aqua decurre <pb pagenum="120" xlink:href="026/01/152.jpg"/>ret tantùm 9. po&longs;ito quod non &longs;it aliud quod re&longs;i&longs;tat; </s>

<s id="N18439">&longs;imiliter &longs;i grauitas alicuius corporis <lb/>&longs;it ad grauitatem aquæ, vt 10. ad 1. decre&longs;cet eius pondus in aqua (1/10), & <lb/>eo tempore quo decurreret in vacuo 10. palmos &longs;patij, in aqua decurre <pb pagenum="120" xlink:href="026/01/152.jpg"/>ret tantùm 9. po&longs;ito quod non &longs;it aliud quod re&longs;i&longs;tat; </s>

<s id="N18448">quanta verò &longs;it <lb/>grauitas omnium corporum tùm duriorum, qualia &longs;unt metalla, tùm li<lb/>quidorum, tùm &longs;pirabilium, dicemus &longs;uo loco; illorum tabulas habes <lb/>apud Gethaldum, & Mer&longs;ennum. </s>

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<s id="N18499">Ob&longs;eruabis dictum e&longs;&longs;e hactenus; </s>

<s id="N1849D">&longs;i nihil aliud de&longs;cen&longs;um corporis <lb/>grauis impedit; </s>

<s id="N184A3">nam certè aliud e&longs;t, de quo infrà, ex cuius ignoratione <lb/>plures haud dubiè in inue&longs;tigandis grauitatum medij rationibus hallu<lb/>cinarentur; </s>

<s id="N184AB">cum enim ob&longs;eruatum &longs;it globum plumbeum, cuius graui<lb/>tas e&longs;t ferè dodecupla grauitatis aquæ, conficere in libero aëre 48. pedes <lb/>&longs;patij tempore duorum &longs;ecundorum, in aqua verò 12. pedes codem tem<lb/>pore; </s>

<s id="N184B5">certè in vacuo ip&longs;o moueretur tardiùs quàm in aëre; </s>

<s id="N184B9">quia eo tem<lb/>pore, quo conficit in aqua 12.pedes in vacuo conficeret (13 1/21), &longs;i tantùm <lb/>detrahitur (1/12) grauitationis, & de&longs;cen&longs;us; </s>

<s id="N184C1">atqui in aëre codem tempore <lb/>conficit 48. pedes; </s>

<s id="N184C1">atqui in aëre eodem tempore <lb/>conficit 48. pedes; </s>

<s id="N184C7">igitur velociùs moueretur in aëre quàm in vacuo; </s>

<s id="N184CB"><lb/>igitur e&longs;t aliquid aliud quod impedit motum; </s>

<s id="N184D0">vt enim optimè monet <lb/>Mer&longs;ennus, &longs;i grauitas aquæ &longs;it ad grauitatem aëris vt 400 ad 1.& graui<lb/>tas plumbi ad grauitatem aquæ vt 12. ad 1.eadem grauitas plumbi e&longs;t ad <lb/>grauitatem aëris vt 4800. igitur &longs;i &longs;patium, quod decurrit plumbum in <lb/>vacuo diuidatur in 4800. partes, decurret in aëre 4799. partes; </s>

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<s id="N18734">hinc pote&longs;t dici quota parte <lb/>firmior &longs;it nexus vnius corporis quàm alterius; </s>

<s id="N1873A">hinc non tantùm copu<lb/>lantur partes metu vacui; </s>

<s id="N18740">alioquin æquè re&longs;i&longs;terent partes aëris, ac par<lb/>tes aquæ ratione nexus; </s>

<s id="N18746">hinc videntur guttulæ illæ &longs;phericæ inuolui te<lb/>nui qua&longs;i membranula, &longs;eu &longs;uperficie, cuius analogiam videmus in aqua<gap/><pb pagenum="123" xlink:href="026/01/155.jpg"/>feruente; </s>

<s id="N18746">hinc videntur guttulæ illæ &longs;phericæ inuolui te<lb/>nui qua&longs;i membranula, &longs;eu &longs;uperficie, cuius analogiam videmus in aqua <pb pagenum="123" xlink:href="026/01/155.jpg"/>feruente; </s>

<s id="N18752">in bullis, quæ ex guttis pluuiæ re&longs;ilientibus na&longs;ci videntur; </s>

<s id="N18756">in <lb/>bullis etiam illis &longs;aponariis, quas leui calamo pueri inter ludendum in<lb/>flant; </s>

<s id="N1875E">hinc ex minimo ferè contactu guttula &longs;pargitur, ni&longs;i fortè cum <lb/>multo a&longs;per&longs;a puluere cru&longs;tam quamdam induit &longs;olidiorem; </s>

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<s id="N187DD"><emph type="italics"/>Hinc quo &longs;unt plures partes diuidendæ, quæ antè uniebantur, maior e&longs;t re&longs;i<lb/>&longs;tentia<emph.end type="italics"/>; </s>

<s id="N187E8">igitur maiore vi opus e&longs;t, igitur maiore grauitate; </s>

<s id="N187EC">&longs;ed in medio <lb/>den&longs;iore ab codem mobili plures &longs;eparantur quàm in rariore; </s>

<s id="N187EC">&longs;ed in medio <lb/>den&longs;iore ab eodem mobili plures &longs;eparantur quàm in rariore; </s>

<s id="N187F2">quia &longs;ci<lb/>licet corpus den&longs;um plures habet &longs;ub minori exten&longs;ione, & rarum è con<lb/>trario, vt videbimus &longs;uo loco; </s>

<s id="N187FA">igitur in medio den&longs;iore idem mobile ma<lb/>jorem re&longs;i&longs;tentiam inuenit, quàm in rariore; </s>

<s id="N18800">licèt vtriu&longs;que partes <lb/>æquali nexu &longs;eu fibula copulentur; </s>

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<s id="N18A68"><emph type="italics"/>Hinc plùs minuitur grauitas, quàm re&longs;i&longs;tentia minoris cubi<emph.end type="italics"/>; </s>

<s id="N18A71">quia grauitas <lb/>re&longs;pondet &longs;olido, & re&longs;i&longs;tentia prim&etail; faciei; </s>

<s id="N18A77">re&longs;i&longs;tentia <expan abbr="inqu&amacr;">inquam</expan> ratione par<lb/>tium medij; </s>

<s id="N18A81">&longs;ed &longs;olidum plus miuuitur quàm facies, vt dictum e&longs;t; </s>

<s id="N18A81">&longs;ed &longs;olidum plus minuitur quàm facies, vt dictum e&longs;t; </s>

<s id="N18A85">igitur <lb/>plus minuitur grauitas, quæ e&longs;t cau&longs;a virium quàm hæc re&longs;i&longs;tentia; ergo <lb/>decre&longs;cunt vires in maiore proportione quàm hæc re&longs;i&longs;tentia, quod be<lb/>nè ob&longs;eruauit Galileus in dìalogis. </s>

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<s id="N18AA7">Scio non dee&longs;&longs;e multos viros doctos qui acriter in hanc &longs;ententiam <pb pagenum="126" xlink:href="026/01/158.jpg"/>in&longs;urgant: </s>

<s id="N18AB0">Obiicient fortè primò, experientiam e&longs;&longs;e contrariam; </s>

<s id="N18AB4">&longs;i enim <lb/>accipiantur duo cubi maior, & minor eiu&longs;dem materiæ, & dimittantur <lb/>ex eadem altitudine codem pror&longs;us momento terram ferient; </s>

<s id="N18AB4">&longs;i enim <lb/>accipiantur duo cubi maior, & minor eiu&longs;dem materiæ, & dimittantur <lb/>ex eadem altitudine eodem pror&longs;us momento terram ferient; </s>

<s id="N18ABC">Re&longs;ponde<lb/>ri pote&longs;t momentum illud &longs;en&longs;u percipi non po&longs;&longs;e; &longs;i enim dicam ma<lb/>iorem tangere terram 1000. in&longs;tantibus ante minorem, an fortè &longs;en&longs;u <lb/>hoc percipies, vi&longs;u &longs;cilicet vel auditu? </s>

<s id="N18AC6">igitur in maxima altitudine hæc <lb/>&longs;patiorum inæqualitas, & temporum &longs;en&longs;u percipi po&longs;&longs;et, quæ in minori <lb/>&longs;ub &longs;en&longs;um non cadit: præterea accipe pulueris granulum eiu&longs;dem ma<lb/>teriæ, tuncque etiam &longs;en&longs;ibilem motuum differentiam videbîs, atqui <lb/>e&longs;t eadem ratio de omni minore. </s>

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<s id="N18FDF"><emph type="italics"/>Hinc cre&longs;cit re&longs;i&longs;tentia iuxta rationem velocitatum &longs;ingulis instantibus<emph.end type="italics"/>; </s>

<s id="N18FE8"><lb/>quæ ratio &longs;equitur progre&longs;&longs;ionem arithmeticam &longs;implicem numerorum <lb/>1.2.3.4.5.6. ex &longs;uppo&longs;itione quòd tempus con&longs;tet ex partibus finitis actu; </s>

<s id="N18FEF"><lb/>nam codem modo cre&longs;cit velocitas, quo cre&longs;cunt numeri prædicti; </s>

<s id="N18FEF"><lb/>nam eodem modo cre&longs;cit velocitas, quo cre&longs;cunt numeri prædicti; </s>

<s id="N18FF4">&longs;ed <lb/>eodem modo cre&longs;cunt &longs;patia, &longs;i dumtaxat accipiantur in &longs;ingulis in&longs;tan<lb/>tibus; </s>

<s id="N18FFC">re&longs;i&longs;tentia cre&longs;cit iuxta rationem &longs;patiorum; igitur iuxta ratio<lb/>nem velocitatum. </s>

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<s id="N1914F"><emph type="italics"/>MOtus violentus e&longs;t, quo corpus graue mouetur &longs;ursùm per li<lb/>neam verticalem à principio extrin&longs;eco mediatè, vel immediatè vt <lb/>plurimùm.<emph.end type="italics"/></s>

<s id="N1915C">Dixi à principio extrin&longs;eco, &longs;iue cunjuncto, vt cum manu attollo &longs;ur<lb/>&longs;um corpus graue, &longs;iue non conjuncto, vt cum quis proiicit lapidem &longs;ur<lb/>sùm, &longs;iue &longs;it verum principium effectiuum, vt cum impetus, quem poten<lb/>tia motrix producit in manu, producit alium in mobili; </s>

<s id="N1915C">Dixi à principio extrin&longs;eco, &longs;iue conjuncto, vt cum manu attollo &longs;ur<lb/>&longs;um corpus graue, &longs;iue non conjuncto, vt cum quis proiicit lapidem &longs;ur<lb/>sùm, &longs;iue &longs;it verum principium effectiuum, vt cum impetus, quem poten<lb/>tia motrix producit in manu, producit alium in mobili; </s>

<s id="N19166">&longs;iue non &longs;it <lb/>principium effectiuum, &longs;ed tantùm determinans, vt cum mobile quod <lb/>cadit deor&longs;um, &longs;ur&longs;um deinde repercutitur; </s>

<s id="N1916E">nec enim corpus repercu<lb/>tiens producit impetum nouum, vt dicemus cum de motu reflexo; </s>

<s id="N19174">quin <lb/>potiùs producti partem de&longs;truit per accidens, & quidquid illius &longs;upere&longs;t, <lb/>ad nouam lineam determinat; quod quomodo fiat fusè &longs;uo loco expli<lb/>cabimus, igitur licèt corpus reflectens &longs;it tantùm principium nouæ de<lb/>terminationis, non verò alicuius impetus producti, dici pote&longs;t princi<lb/>pium huius motus violenti. </s>

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<s id="N19685"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 21.<emph.end type="center"/></s>

<s id="N19693"><emph type="italics"/>Illa cau&longs;a non e&longs;t entitas corporis mobilis, vel ip&longs;a grauitas, di&longs;tincta &longs;cili<lb/>cet ab impetu muato&longs;i quæ e&longs;t de quæ alias,<emph.end type="italics"/> probatur, quia non e&longs;&longs;et potior <lb/>ratiocur vno in&longs;tanti de&longs;truerentur duo gradus impetus, quàm 3. 4. 5. <lb/>quippe grauitas exigeret de&longs;tructionem omnium: præterea omnis impe<lb/>tus de&longs;truitur ne &longs;it fru&longs;trà per Schol, Th.152. & Th.162.l.1. denique &longs;i <pb pagenum="139" xlink:href="026/01/171.jpg"/>ade&longs;t contrarius impetus de&longs;tructiuus eo modo, quo explicuimus l. 1. non <lb/>e&longs;t ponenda alia cau&longs;a de&longs;tructiua. </s>

<s id="N19693"><emph type="italics"/>Illa cau&longs;a non e&longs;t entitas corporis mobilis, vel ip&longs;a grauitas, di&longs;tincta &longs;cili<lb/>cet ab impetu innato &longs;i quæ e&longs;t de quæ alias,<emph.end type="italics"/> probatur, quia non e&longs;&longs;et potior <lb/>ratio cur vno in&longs;tanti de&longs;truerentur duo gradus impetus, quàm 3. 4. 5. <lb/>quippe grauitas exigeret de&longs;tructionem omnium: præterea omnis impe<lb/>tus de&longs;truitur ne &longs;it fru&longs;trà per Schol, Th.152. & Th.162.l.1. denique &longs;i <pb pagenum="139" xlink:href="026/01/171.jpg"/>ade&longs;t contrarius impetus de&longs;tructiuus eo modo, quo explicuimus l. 1. non <lb/>e&longs;t ponenda alia cau&longs;a de&longs;tructiua. </s>

<s id="N196AF"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 22.<emph.end type="center"/></s>

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<s id="N19760"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 27.<emph.end type="center"/></s>

<s id="N1976E"><emph type="italics"/>In eadem proportione retardatur motus violentus, in qua naturaiis accele<lb/>ratur<emph.end type="italics"/>: </s>

<s id="N1976E"><emph type="italics"/>In eadem proportione retardatur motus violentus, in qua naturalis accele<lb/>ratur<emph.end type="italics"/>: </s>

<s id="N19779">probatur quia &longs;ingulis in&longs;tantibus æqualibus acquiritur æqualis <lb/>gradus impetus, vt &longs;æpè dictum e&longs;t &longs;uprà; </s>

<s id="N1977F">atqui &longs;ingulis in&longs;tantibus de<lb/>&longs;truitur vnus gradus impetus violenti per Th.24. &longs;ed ille gradus re&longs;pon<lb/>det impetui innato per Th. 25. igitur æqualibus temporibus tantùm de<lb/>&longs;truitur violenti, quantùm acquiritur naturalis; cum enim primo in<lb/>&longs;tanti &longs;it impetus naturalis, & &longs;ecundo tempore æquali acquiratur æqua<lb/>lis, item tertio, quarto, &c. </s>

<s id="N1978D">certè cum impetus innatus pugnet cum vio<lb/>lento pro rata; </s>

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<s id="N197EA"><emph type="italics"/>Motus violentus durat tot in&longs;tantibus &longs;cilicet æquiualentibus quot &longs;unt ij <lb/>gradus impetus quibus violentus &longs;uperat innatum,<emph.end type="italics"/> v.g. &longs;it vnus gradus im<lb/>petus innati; </s>

<s id="N197F9">producantur 5. gradus violenti, quorum &longs;inguli &longs;int æqua<lb/>les innato etiam <expan abbr="æquiual&etilde;ter">æquiualenter</expan>, motus durabit 4. in&longs;tantibus etiam æqui<lb/>ualenter id e&longs;t 4. temporibus, quorum &longs;ingula erunr æqualia primo in<lb/>&longs;tanti motus naturalis, probatur, cum &longs;ingulis in&longs;tantibus æqualibus de<lb/>&longs;truatur vnus gradus; certè 4. in&longs;tantibus durat motus. </s>

<s id="N197F9">producantur 5. gradus violenti, quorum &longs;inguli &longs;int æqua<lb/>les innato etiam <expan abbr="æquiual&etilde;ter">æquiualenter</expan>, motus durabit 4. in&longs;tantibus etiam æqui<lb/>ualenter id e&longs;t 4. temporibus, quorum &longs;ingula erunt æqualia primo in<lb/>&longs;tanti motus naturalis, probatur, cum &longs;ingulis in&longs;tantibus æqualibus de<lb/>&longs;truatur vnus gradus; certè 4. in&longs;tantibus durat motus. </s>

<s id="N1980B"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 29.<emph.end type="center"/></s>

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<s id="N19FBF">Vnde cum effectus qui ponitur &longs;ecundo in&longs;tanti non re&longs;pondeat per<lb/>fectioni cau&longs;æ totius propter impedimentum, aliquis gradus cau&longs;æ e&longs;&longs;et <lb/>fru&longs;trà; </s>

<s id="N19FC7">igitur eodem in&longs;tanti &longs;ecundo de&longs;trui debet, alioqui ni&longs;i de&longs;true<lb/>retur &longs;ingulis in&longs;tantibus poneretur effectus non re&longs;pondens perfectioni <lb/>cau&longs;æ; </s>

<s id="N19FCF">immò numquam de&longs;trueretur totus motus violentus, vt con&longs;tat; </s>

<s id="N19FD3"><lb/>itaque primo in&longs;tanti omnes gradus impetus qui &longs;unt exigunt motum <lb/>pro &longs;ecundo ne aliquis eo in&longs;tanti &longs;it fru&longs;trà &longs;i non exigeret, & &longs;ecundo <lb/>in&longs;tanti aliquis gradus impetus de&longs;truitur, ne &longs;it fru&longs;trà codem in&longs;tanti <lb/>&longs;ecundo, cum &longs;cilicet non &longs;int tot gradus motus, quot &longs;unt gradus impe<lb/>tus; atque ita deinceps tertio in&longs;tanti de&longs;truitur vnus gradus, vt iam &longs;u<lb/>prà dictum e&longs;t. </s>

<s id="N19FD3"><lb/>itaque primo in&longs;tanti omnes gradus impetus qui &longs;unt exigunt motum <lb/>pro &longs;ecundo ne aliquis eo in&longs;tanti &longs;it fru&longs;trà &longs;i non exigeret, & &longs;ecundo <lb/>in&longs;tanti aliquis gradus impetus de&longs;truitur, ne &longs;it fru&longs;trà eodem in&longs;tanti <lb/>&longs;ecundo, cum &longs;cilicet non &longs;int tot gradus motus, quot &longs;unt gradus impe<lb/>tus; atque ita deinceps tertio in&longs;tanti de&longs;truitur vnus gradus, vt iam &longs;u<lb/>prà dictum e&longs;t. </s>

<s id="N19FE4"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 68.<emph.end type="center"/></s>

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<s id="N1AB22"><emph type="italics"/>Non est mixtus ex naturali accelerato & violento æquabili<emph.end type="italics"/>; </s>

<s id="N1AB2B">demon&longs;tra<lb/>tur, primò, quia &longs;ub finem motus e&longs;&longs;et maior impetus; </s>

<s id="N1AB31">quippè nihil de<lb/>traheretur violento, &longs;ed multùm accederet naturali; igitur e&longs;&longs;et maior, <lb/>igitur e&longs;&longs;et maior ictus contra hyp. </s>

<s id="N1AB39">3. &longs;ecundò, quotie&longs;cunque &longs;unt duo <lb/>impetus in codem mobili ad diuer&longs;as lineas determinati, aliquid illo<lb/>rum de&longs;truitur per Th.141.l.1.tertiò &longs;i e&longs;&longs;et vterque æquabilis, aliquid <lb/>de&longs;trueretur per Theorema 6. igitur potiori iure, &longs;i impetus naturalis <lb/>cre&longs;cat. </s>

<s id="N1AB39">3. &longs;ecundò, quotie&longs;cunque &longs;unt duo <lb/>impetus in eodem mobili ad diuer&longs;as lineas determinati, aliquid illo<lb/>rum de&longs;truitur per Th.141.l.1.tertiò &longs;i e&longs;&longs;et vterque æquabilis, aliquid <lb/>de&longs;trueretur per Theorema 6. igitur potiori iure, &longs;i impetus naturalis <lb/>cre&longs;cat. </s>

<s id="N1AB46">Diceret fortè aliquis impetum de&longs;trui ab aëre, &longs;ed iam &longs;uprà re&longs;pon<lb/>&longs;um e&longs;t modicum inde imminui; </s>

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<s id="N1B4B1">Sed ne Geometriam omninò de&longs;picere videar, in circulo demon&longs;tro <lb/>proportiones omnes in quibus decre&longs;cit motus violentus per quamlibet <lb/>lineam inclinatam &longs;ur&longs;um, vel deor&longs;um; </s>

<s id="N1B4B9">&longs;it ergo circulus ADGQ cen<lb/>tro B; </s>

<s id="N1B4BF">&longs;it motus violentus &longs;ur&longs;um BD coniunctus cum naturali BR, &longs;int<lb/>que ex gr. BR. RQ æquales; </s>

<s id="N1B4C7">hand dubiè linea motus erit BC, quia na<lb/>turalis BR pugnat pro rata per Th.134.l.1. eritque BC &longs;ubdupla BD; <lb/>igitur centro R. &longs;emidiametro RC de&longs;cribatur circulus CLPS, erit <lb/>æqualis priori, ducanturque ex centro B infinitæ lineæ BE. BF. BK. <lb/>BN, & vt res fit clarior, &longs;int omnes anguli DBE. EBF. FBG, &c. <lb/></s>

<s id="N1B4C7">haud dubiè linea motus erit BC, quia na<lb/>turalis BR pugnat pro rata per Th.134.l.1. eritque BC &longs;ubdupla BD; <lb/>igitur centro R. &longs;emidiametro RC de&longs;cribatur circulus CLPS, erit <lb/>æqualis priori, ducanturque ex centro B infinitæ lineæ BE. BF. BK. <lb/>BN, & vt res fit clarior, &longs;int omnes anguli DBE. EBF. FBG, &c. <lb/></s>

<s id="N1B4D4">æquales &longs;cilicet grad. 30. & ex punctis E.F.G.K.N.q. </s>

<s id="N1B4D9">ducantur lineæ <lb/>ad circunferentiam circuli CLPS. parallelæ DP.Dico omnes e&longs;&longs;e æqua<lb/>les DC; </s>

<s id="N1B4E1">nam primò FH. GL. KM. QP &longs;unt æquales, vt patet: </s>

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<s id="N1B554"><emph type="italics"/>Hinc quò iactus propiùs accedit ad horizontalem &longs;eu verticalem, minùs <lb/>acquirit in eodem plano horizontali, &longs;cilicet in eo à cuius extremitate inci<lb/>pit iactus<emph.end type="italics"/>; </s>

<s id="N1B561">probatur, quia cùm iactus verticalis nihil pror&longs;us acqui<lb/>rat in hotizontali plano per Theorema 60. certè quò propiùs ad illum <lb/>iactus inclinatus accedet, minùs acquiret; idem dico de iactu hori<lb/>zontali. </s>

<s id="N1B561">probatur, quia cùm iactus verticalis nihil pror&longs;us acqui<lb/>rat in horizontali plano per Theorema 60. certè quò propiùs ad illum <lb/>iactus inclinatus accedet, minùs acquiret; idem dico de iactu hori<lb/>zontali. </s>

<s id="N1B56D"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 62.<emph.end type="center"/></s>

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<s id="N1C010"><emph type="italics"/>A&longs;cendit hoc motu ad &longs;ubduplam altitudinem illius, ad quam motu mixto <lb/>tantum ex verticali & horizontali &longs;ine naturali a&longs;cenderet<emph.end type="italics"/>; quippe a&longs;cende<lb/>ret in C fig. </s>

<s id="N1C01D">Th.83. &longs;inc impetu naturali, &longs;ed FC & LA æquales &longs;unt; </s>

<s id="N1C01D">Th.83. &longs;ine impetu naturali, &longs;ed FC & LA æquales &longs;unt; </s>

<s id="N1C021"><lb/>atqui motu violento puro, ni&longs;i naturalis obe&longs;&longs;et, a&longs;cenderet in A; </s>

<s id="N1C026">at ve<lb/>rò &longs;i obe&longs;t naturalis; </s>

<s id="N1C02C">a&longs;cendit tantùm motu violento in K, & mixto in <lb/>in D; </s>

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<s id="N1C095"><emph type="italics"/>Hinc &longs;en&longs;ibiliter ex a&longs;cen&longs;u & de&longs;cen&longs;u fit<emph.end type="italics"/> <emph type="italics"/>integra Parabola<emph.end type="italics"/>; </s>

<s id="N1C0A4">nam pro<lb/>iiciatur ex L in A, eo tempore, quo nauis mouetur ex L in F, certè &longs;i <lb/>tempus illud diuidatur bifariam prima parte mobile percurret LI tri<lb/>plam IK in verticali, & LM &longs;ubduplam LF in horizontali; </s>

<s id="N1C0AE">igitur erit <lb/>in G; </s>

<s id="N1C0B4">&longs;ecunda verò perte temporis in verticali percurrit IK, & MF in <lb/>horizontali; </s>

<s id="N1C0B4">&longs;ecunda verò parte temporis in verticali percurrit IK, & MF in <lb/>horizontali; </s>

<s id="N1C0BA">igitur erit in D; </s>

<s id="N1C0BE">præterea &longs;i accipiantur duæ aliæ partes tem<lb/>poris æquales; </s>

<s id="N1C0C4">prima in perpendiculari deor&longs;um percurret DE æqua<lb/>lem LK, & in horizontali DO; </s>

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<s id="N1C1E6">quippe, &longs;i terra quie&longs;cit, eadem manu cadentem excipio lapi<lb/>dem, quæ &longs;ur&longs;um rectà proiicit; </s>

<s id="N1C1EC">igitur quemadmodum ex hoc non infero <lb/>terræ quietem, &longs;ed aliunde; </s>

<s id="N1C1F2">ita neque ex hoc inferri pote&longs;t terræ motus; </s>

<s id="N1C1F6"><lb/>cum enim duplex hypothe&longs;is codem ph&oelig;nomeno &longs;tare pote&longs;t, neutra ex <lb/>eo euincitur; igitur &longs;icuti fateor ex hoc ph&oelig;nomeno minimè demon<lb/>&longs;trari terræ quietem ita & tu fateri debes ex eo minimè ad&longs;trui po&longs;&longs;e <lb/>terræ motum. </s>

<s id="N1C1F6"><lb/>cum enim duplex hypothe&longs;is eodem ph&oelig;nomeno &longs;tare pote&longs;t, neutra ex <lb/>eo euincitur; igitur &longs;icuti fateor ex hoc ph&oelig;nomeno minimè demon<lb/>&longs;trari terræ quietem ita & tu fateri debes ex eo minimè ad&longs;trui po&longs;&longs;e <lb/>terræ motum. </s>

<s id="N1C203">Adde quod, haud dubiè &longs;i terra quie&longs;cit citiùs proiectus lapis &longs;ur&longs;um <lb/>de&longs;cendit, quàm &longs;i mouetur; </s>

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<s id="N1C3D6"><emph type="italics"/>Hinc vt quis maiore ni&longs;u lapidem v. g. proijciat, tùm longiore tempore <lb/>brachium rotat, tùm præuio cur&longs;u impetum auget,<emph.end type="italics"/> quia non tantùm impe<lb/>tus brachij imprimitur mobili, &longs;ed etiam impetus totius corporis; </s>

<s id="N1C3E7">hinc <lb/>etiam &longs;i præmittatur cur&longs;us longiore &longs;altu <gap/> plano horizontali maius <lb/>&longs;patium traiicitur; quæ omnia ex ii&longs;dem principiis manife&longs;tè &longs;e<lb/>quuntur. </s>

<s id="N1C3E7">hinc <lb/>etiam &longs;i præmittatur cur&longs;us longiore &longs;altu in plano horizontali maius <lb/>&longs;patium traiicitur; quæ omnia ex ii&longs;dem principiis manife&longs;tè &longs;e<lb/>quuntur. </s>

<s id="N1C3F5"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 100.<emph.end type="center"/></s>

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<s id="N1C593">haud dubiè ML e&longs;t æqualis AM, vt <lb/>patet; </s>

<s id="N1C599">& &longs;i motus e&longs;&longs;et tantum mixtus ex AC & AP fieret per diagona<lb/>lem AF, quam mobile eodem tempore percurreret quo vel AC vel AP; </s>

<s id="N1C59F"><lb/>igitur &longs;i dum percurrit AF percurrit AM, motu naturali, certè dum per<lb/>currit AN &longs;ubdupla AF, percurret tantùm &longs;ubquadruplam AM; </s>

<s id="N1C5A6">a&longs;&longs;uma<lb/>tur ergo NO æqualis AS, & FG æqualis AM; <expan abbr="ducaturq;">ducaturque</expan> curua AOG, hæc <lb/>e&longs;t linea quç&longs;ita. </s>

<s id="N1C5A6">a&longs;&longs;uma<lb/>tur ergo NO æqualis AS, & FG æqualis AM; <expan abbr="ducaturq;">ducaturque</expan> curua AOG, hæc <lb/>e&longs;t linea qu&ecedil;&longs;ita. </s>

<s id="N1C5B4">Itaque idem dicendum e&longs;t de his inclinatis, quod de aliis &longs;uprà di<lb/>ctum e&longs;t Th.72. ni&longs;i quod accipitur inclinata mixta ex horizontali & da<lb/>ta inclinata, v.g. ANF ex AC & AP; </s>

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<s id="N1C5F9"><lb/>diuidatur AE bifariam in D; </s>

<s id="N1C5FE">ducatur DG, tùm DC, AC, hæc e&longs;t linea mo<lb/>tus mixti ex inclinata AG, & horizontali AD; </s>

<s id="N1C604">&longs;equitur deinde Parabola; </s>

<s id="N1C608"><lb/>nam &longs;ico tempore quo percurritur AD, percurritur AG, & LM vel FA; </s>

<s id="N1C608"><lb/>nam &longs;i eo tempore quo percurritur AD, percurritur AG, & LM vel FA; </s>

<s id="N1C60D"><pb pagenum="190" xlink:href="026/01/222.jpg"/>certè eodem percurritur AC, igitur &longs;ubduplo tempore <expan abbr="percurr&etilde;tur">percurrentur</expan> AN; </s>

<s id="N1C619"><lb/>igitur FO, quæ e&longs;t &longs;ubquadrupla FA; </s>

<s id="N1C61E">igitur a&longs;&longs;umatur NH æqualis FO, & <lb/>CK æqualis FA, & ducatur curua per puncta AHK; hæc e&longs;t &longs;emiparabo<lb/>la, nam KI e&longs;t ad KE vt quadratum IH ad quadratum EA. </s>

<s id="N1C628">Vnde vides omnes inclinatas &longs;ur&longs;um v&longs;que ab horizontali DB ad <lb/>verticalem DA inclu&longs;iuè e&longs;&longs;e Parabolas; omnes verò inclinatas ab ca<lb/>dem horizontali DB ad perpendicularem DC inclu&longs;iuè non e&longs;&longs;e Para<lb/>bolas, &longs;ed propiùs accedere ad rectam, vnde aliquis &longs;u&longs;picari po&longs;&longs;et e&longs;&longs;e <lb/>Hyperbolas. </s>

<s id="N1C628">Vnde vides omnes inclinatas &longs;ur&longs;um v&longs;que ab horizontali DB ad <lb/>verticalem DA inclu&longs;iuè e&longs;&longs;e Parabolas; omnes verò inclinatas ab ea<lb/>dem horizontali DB ad perpendicularem DC inclu&longs;iuè non e&longs;&longs;e Para<lb/>bolas, &longs;ed propiùs accedere ad rectam, vnde aliquis &longs;u&longs;picari po&longs;&longs;et e&longs;&longs;e <lb/>Hyperbolas. </s>

<s id="N1C636"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 105.<emph.end type="center"/></s>

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<s id="N1C6C5">quamquàm &longs;uppono iam e&longs;&longs;e perpendi<lb/>cularem deor&longs;um AB; </s>

<s id="N1C6CB">denique cum AG &longs;ubquadrupla AF a&longs;&longs;umatur <lb/>ED æqualis AG perpendiculariter ducta in AD, & KL æqualis AF <lb/>parallela ED, & per puncta AEL ducatur curua, hæc e&longs;t linea motus <lb/>quæ&longs;ita; </s>

<s id="N1C6D5">voluatur autem triangulum AKL, donec &longs;it parallelum circulo <lb/>verticali vel alteri, ACO erit in proprio &longs;itu; </s>

<s id="N1C6DB">vnde eo tempore, quo e&longs;<lb/>&longs;et in DE punctum nauis A e&longs;&longs;et in B, & co, quo e&longs;&longs;et in KL, punctum A <lb/>e&longs;&longs;et in C; hoc e&longs;t &longs;ingula puncta AK, è regione AC ductis parallelis <pb pagenum="191" xlink:href="026/01/223.jpg"/>BD, CK, ac proinde nauis & mobile &longs;emper e&longs;&longs;ent è regione in linea <lb/>ver&longs;us ortum. </s>

<s id="N1C6DB">vnde eo tempore, quo e&longs;<lb/>&longs;et in DE punctum nauis A e&longs;&longs;et in B, & eo, quo e&longs;&longs;et in KL, punctum A <lb/>e&longs;&longs;et in C; hoc e&longs;t &longs;ingula puncta AK, è regione AC ductis parallelis <pb pagenum="191" xlink:href="026/01/223.jpg"/>BD, CK, ac proinde nauis & mobile &longs;emper e&longs;&longs;ent è regione in linea <lb/>ver&longs;us ortum. </s>

<s id="N1C6EC">Hinc &longs;i ex A dirigas <expan abbr="&longs;agittã">&longs;agittam</expan> in H feris punctum K, quam artem probè <lb/>no&longs;&longs;e debent rei tormentariæ præfecti; </s>

<s id="N1C6F6">quippe &longs;agitta aberrabit à &longs;copo <lb/>ver&longs;us Boream declinans toto eo &longs;patio, quod conficit nauis codem tem<lb/>pore, quo mouetur &longs;agitta; ita pror&longs;us &longs;i moueatur H ver&longs;us K, vt attin<lb/>gas ex puncto immobili A debes dirigere ictum in K, &longs;i quo tempore <lb/>&longs;agitta conficit AK &longs;copus H percurrit HK.Idem pror&longs;us dicendum e&longs;t <lb/>de iaculatione per lineam oppo&longs;itam ver&longs;us occa&longs;um. </s>

<s id="N1C6F6">quippe &longs;agitta aberrabit à &longs;copo <lb/>ver&longs;us Boream declinans toto eo &longs;patio, quod conficit nauis eodem tem<lb/>pore, quo mouetur &longs;agitta; ita pror&longs;us &longs;i moueatur H ver&longs;us K, vt attin<lb/>gas ex puncto immobili A debes dirigere ictum in K, &longs;i quo tempore <lb/>&longs;agitta conficit AK &longs;copus H percurrit HK.Idem pror&longs;us dicendum e&longs;t <lb/>de iaculatione per lineam oppo&longs;itam ver&longs;us occa&longs;um. </s>

<s id="N1C706">Si verò proiiciatur mobile per lineam inter Boream, & Ortum, linea <lb/>motus erit Parabola cuius Tangens erit mixta ex horizontali ver&longs;us <lb/>Boream, & declinante ver&longs;us Ortum, v. g. &longs;it horizontalis ver&longs;us Boream <lb/>AF, quam hactenus a&longs;&longs;ump&longs;i pro linea directionis; </s>

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<s id="N1CD29">hoc po&longs;ito. </s>

<s id="N1CD2E">Dico pondus affixum P æquale ponderi L facere aquilibrium; cum <lb/>enim linea directionis &longs;it PO, &longs;i de&longs;cenderet liberè per PO. </s>

<s id="N1CD2E">Dico pondus affixum P æquale ponderi L facere æquilibrium; cum <lb/>enim linea directionis &longs;it PO, &longs;i de&longs;cenderet liberè per PO. </s>

<s id="N1CD34">L eodem <lb/>tempore attolleretur per LS, quod certè applicatis planis SL PO facilè <lb/>fieri po&longs;&longs;et; </s>

<s id="N1CD3C">&longs;ed eodem modo P grauitat, quo &longs;i de&longs;cenderet per PO; </s>

<s id="N1CD40">e&longs;t <lb/>enim eius linea directionis; </s>

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<s id="N1CD7A"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 6.<emph.end type="center"/></s>

<s id="N1CD89"><emph type="italics"/>Ex hoc &longs;equitur nece&longs;&longs;ariò motum in plano inclinato e&longs;&longs;e ad motum in per<lb/>pendiculari, vt ip&longs;a perpendicularis ad ip&longs;um planum inclinatum,<emph.end type="italics"/> v.g. velo<lb/>citas motus per AE e&longs;t ad velocitatem motus per AB, vt ip&longs;a AB e&longs;t <lb/>ad ip&longs;am AE, &longs;it enim AE dupla AB, velocitas per AB e&longs;t dupla veloci<lb/>atis per AE. </s>

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<s id="N1D2DA"><lb/>v. g. &longs;it enim cylindrus AE horizontalis, &longs;u&longs;tineaturque in A immo<lb/>biliter, itemque in E; </s>

<s id="N1D2E5">certè qui &longs;u&longs;tinet in E æqualiter &longs;u&longs;tinet; </s>

<s id="N1D2E9">at verò <lb/>&longs;i attollatur in AD; </s>

<s id="N1D2EF">certè potentia quæ in D &longs;u&longs;tinet, e&longs;t ad potentiam <lb/>quæ &longs;u&longs;tinet in E, vt AF ad AE, quia pondus grauitaret in D & in E in <lb/>cadem ratione per Th. 16. &longs;ed potentia &longs;u&longs;tinens adæquat ponderis ra<lb/>tionem, &longs;u&longs;tinens inquam, per DH; </s>

<s id="N1D2EF">certè potentia quæ in D &longs;u&longs;tinet, e&longs;t ad potentiam <lb/>quæ &longs;u&longs;tinet in E, vt AF ad AE, quia pondus grauitaret in D & in E in <lb/>eadem ratione per Th. 16. &longs;ed potentia &longs;u&longs;tinens adæquat ponderis ra<lb/>tionem, &longs;u&longs;tinens inquam, per DH; </s>

<s id="N1D2F9">nam reuerà &longs;u&longs;tinens per DF æqua<lb/>lis e&longs;&longs;e debet potentiæ in E: </s>

<s id="N1D2FF">idem dico &longs;i attollatur in AP, nam potentia <lb/>trahens in P, per CP, e&longs;t ad potentiam in E, vt QA ad AP, vel AE; <lb/>igitur pondus in D e&longs;t ad pondus in P vt FA ad QA. </s>

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<s id="N1D341">Octauò &longs;i attollendum &longs;it rectangulum non quidem circa axem; </s>

<s id="N1D345">&longs;ed <lb/>circa angulum immobilem, etiam decre&longs;cit proportio ponderis, &longs;it enim <lb/>v.g. <expan abbr="quadrat&utilde;">quadratum</expan> ACFD, &longs;itque AD horizontalis, AI perpendicularis, duca<lb/>tur diagonalis AF, attollatur circa punctum A, ita vt trans&longs;eratur in AG, <lb/>ducatur GB perpendicularis: </s>

<s id="N1D345">&longs;ed <lb/>circa angulum immobilem, etiam decre&longs;cit proportio ponderis, &longs;it enim <lb/>v.g. <expan abbr="quadrat&utilde;">quadratum</expan> ACFD, &longs;itque AD horizontalis, AI perpendicularis, duca<lb/>tur diagonalis AF, attollatur circa punctum A, ita vt transferatur in AG, <lb/>ducatur GB perpendicularis: </s>

<s id="N1D355">dico potentiam in G e&longs;&longs;e ad potentiam in <lb/>in A, vt AB ad AD; quippe res eodem modo &longs;e habet, ac &longs;i AF a&longs;cenderet <pb pagenum="207" xlink:href="026/01/239.jpg"/>per arcum FM, donec vbi AF traducta &longs;it in AM, tunc enim nulla erit <lb/>potentia in M propter æquilibrium. </s>

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<s id="N1D4FE">igitur æqua<lb/>lis in D & in B, &longs;ed AB e&longs;t ad BC vt AD ad DE; </s>

<s id="N1D504">igitur &longs;i cre&longs;cit impe<lb/>tus per partes &longs;ubduplas in AC, nece&longs;&longs;ariò cre&longs;cit per partes duplas in <lb/>&longs;patio, atque in tempore; </s>

<s id="N1D50C">cùm enim motus &longs;it &longs;ubduplus, tarditas e&longs;t &longs;ub<lb/>dupla; </s>

<s id="N1D512">igitur acquiritur in AC &longs;patium AB &longs;ubduplum AE eo tempore, <lb/>quo percurtitur AE, &longs;i enim accipiantur æqualia tempora, &longs;patia &longs;unt vt <lb/>motus; </s>

<s id="N1D512">igitur acquiritur in AC &longs;patium AB &longs;ubduplum AE eo tempore, <lb/>quo percurritur AE, &longs;i enim accipiantur æqualia tempora, &longs;patia &longs;unt vt <lb/>motus; </s>

<s id="N1D51A">&longs;ed motus per AC e&longs;t &longs;ubduplus; </s>

<s id="N1D51E">igitur &longs;patium AB e&longs;t &longs;ubdu<lb/>plum AE; </s>

<s id="N1D524">&longs;ed tempore æquali conficit BC triplum AB, igitur tota AC <lb/>e&longs;t dupla AE; </s>

<s id="N1D52A">&longs;ed percurritur tempore duplo; </s>

<s id="N1D52E">igitur tempora &longs;unt vt <lb/><expan abbr="lõgitudines">longitudines</expan> planorum; </s>

<s id="N1D537">&longs;ed clariùs, & brcuiùs illud demon&longs;tro; </s>

<s id="N1D537">&longs;ed clariùs, & breuiùs illud demon&longs;tro; </s>

<s id="N1D53B">In ea pro<lb/>portione erit maius tempus per AC quàm per AE, in qua minor e&longs;t <lb/>motus per AC quàm per AE; </s>

<s id="N1D543">&longs;i enim motus per AF e&longs;&longs;et ad motum per <lb/>AE vt AF ad AE, certè æquali tempore AF & AE percurrerentur; </s>

<s id="N1D549">igitur <lb/>qua proportione motus per AF e&longs;t minor, tempus e&longs;t maius; </s>

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<s id="N1D586">&longs;i 12. 2′. </s>

<s id="N1D589">&longs;i 24. 4″. </s>

<s id="N1D58C">atque ita dein<lb/>ceps; </s>

<s id="N1D591">hinc po&longs;&longs;et dari planum inclinatum quod tantùm 100. annis per<lb/>curretur, &longs;cilicet &longs;i longitudo plani a&longs;&longs;umpti &longs;it æquemultiplex longitu<lb/>dinis 12. pedum atque 100. anni vnius &longs;ecundi; quod facilè e&longs;t, imò da<lb/>to plano cuiu&longs;cunque longitudinis, pote&longs;t dari tempus quodcunque quo <lb/>porcurratur, de quo infrà. </s>

<s id="N1D591">hinc po&longs;&longs;et dari planum inclinatum quod tantùm 100. annis per<lb/>curretur, &longs;cilicet &longs;i longitudo plani a&longs;&longs;umpti &longs;it æque multiplex longitu<lb/>dinis 12. pedum atque 100. anni vnius &longs;ecundi; quod facilè e&longs;t, imò da<lb/>to plano cuiu&longs;cunque longitudinis, pote&longs;t dari tempus quodcunque quo <lb/>percurratur, de quo infrà. </s>

<s id="N1D59F"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 25.<emph.end type="center"/></s>

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<s id="N1D5AD"><emph type="italics"/>Determinari pote&longs;t quantum &longs;patium conficiat mobile in plano inclinato; <lb/>dum conficit perpendicularem<emph.end type="italics"/>; </s>

<s id="N1D5B8">&longs;it enim perpendiculum AE, inclinata AC; </s>

<s id="N1D5BC"><lb/>ducatus, EB perpendicularis in AC; </s>

<s id="N1D5C1">dico quod codem tempore percur<lb/>ret AE & AB, quod demon&longs;tro; </s>

<s id="N1D5C1">dico quod eodem tempore percur<lb/>ret AE & AB, quod demon&longs;tro; </s>

<s id="N1D5C7">quia triangula EAB, EAC &longs;unt pro<lb/>portionalia: </s>

<s id="N1D5CD">igitur AB e&longs;t ad AE vt AE ad AC; </s>

<s id="N1D5D1">igitur motus in AB <lb/>e&longs;t ad motum in DE vt AB ad AE; </s>

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<s id="N1D959">Octauò, &longs;i accipiantur æquales horizontalis, & perpendicularis, v.g. <lb/>BA AC, ducaturque BC: </s>

<s id="N1D960">Dico nullum duci po&longs;&longs;e planum incliuatum à <lb/>puncto B ad perpendiculum AEM, quod breuiori tempore percurratur, <lb/>quàm BC, nec intra angulum vt BR, nec extra vt BM; </s>

<s id="N1D960">Dico nullum duci po&longs;&longs;e planum inclinatum à <lb/>puncto B ad perpendiculum AEM, quod breuiori tempore percurratur, <lb/>quàm BC, nec intra angulum vt BR, nec extra vt BM; </s>

<s id="N1D968">&longs;it enim vt BC ad <lb/>BI ita BI ad BH, e&longs;t autem BI æqualis BA, igitur &longs;i BA, &longs;it 4.BC e&longs;t v.g. <lb/>32. & BH radix q.8.igitur HI e&longs;t ferè I paulò plùs; igitur cum BH percur<lb/>ratur æquali tempore cum AC, e&longs;t tempus, quo percurritur BH ad tem<lb/>pus quo percurritur HC vt BH ad HI. </s>

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<s id="N1DBAA">certè eodem tempore <lb/>de&longs;cendit per AFC, quo de&longs;cenderet per AG duplam AF; </s>

<s id="N1DBB0">&longs;ed eo tem<lb/>pore, quo de&longs;cendit per AF inclinatam, conficit AD per Th.27. quæ e&longs;t <lb/>ad AF vt AF ad BA; </s>

<s id="N1DBB8">&longs;it autem dupla: </s>

<s id="N1DBBC">&longs;imiliter codem tempore conficit <lb/>AFG vel AFG, quo conficit AE duplam AG; denique eo tempore, <lb/>quo conficit AF CHD, vel AGD, conficit duplam AE. </s>

<s id="N1DBBC">&longs;imiliter eodem tempore conficit <lb/>AFG vel AFG, quo conficit AE duplam AG; denique eo tempore, <lb/>quo conficit AF CHD, vel AGD, conficit duplam AE. </s>

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<s id="N1E100"><emph type="italics"/>Globus ab O ver&longs;us E rotatus &longs;emper acceleraret &longs;uum motum.<emph.end type="italics"/></s>

<s id="N1E107"> Demon<lb/>&longs;tro, quia impetus productus in O con&longs;eruaretur etiam in G, & nouns <lb/>produceretur, igitur acceleraret &longs;uum motum; </s>

<s id="N1E107"> Demon<lb/>&longs;tro, quia impetus productus in O con&longs;eruaretur etiam in G, & nouus <lb/>produceretur, igitur acceleraret &longs;uum motum; </s>

<s id="N1E10F">&longs;uppono enim planum E <lb/>N e&longs;&longs;e læuigati&longs;&longs;imum; </s>

<s id="N1E115">igitur nihil e&longs;&longs;et, à quo de&longs;trueretur: </s>

<s id="N1E119">adde quòd <pb pagenum="221" xlink:href="026/01/253.jpg"/>&longs;emper haberet &longs;uum effectum; </s>

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<s id="N1E314"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 66.<emph.end type="center"/></s>

<s id="N1E322"><emph type="italics"/>Determinari pote&longs;t velocitas acqui&longs;ita in de&longs;cen&longs;u OE,<emph.end type="italics"/> e&longs;t enim vt trian<lb/>gulum <expan abbr="mixt&utilde;">mixtum</expan> cuius alterum latus rectum &longs;it ad OE, alterum ad angulos <lb/>rectos PX, tertium curua connectens &longs;inus rectos infra PX ver&longs;us vt E <lb/>vides in figura EO 4. e&longs;t autem hæc velocitas ad velocitatem acqui&longs;i<lb/>&longs;itam in perpendiculari æquali OE vt prædictum triangulum EO 4. ad <lb/>rectangulum &longs;ub OEA. </s>

<s id="N1E322"><emph type="italics"/>Determinari pote&longs;t velocitas acqui&longs;ita in de&longs;cen&longs;u OE,<emph.end type="italics"/> e&longs;t enim vt trian<lb/>gulum <expan abbr="mixt&utilde;">mixtum</expan> cuius alterum latus rectum &longs;it ad OE, alterum ad angulos <lb/>rectos PX, tertium curua connectens &longs;inus rectos infra PX ver&longs;us vt E <lb/>vides in figura EO 4. e&longs;t autem hæc velocitas ad velocitatem acqui&longs;i<lb/>tam in perpendiculari æquali OE vt prædictum triangulum EO 4. ad <lb/>rectangulum &longs;ub OEA. </s>

<s id="N1E33A"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 67.<emph.end type="center"/></s>

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<s id="N1E981">Ratio e&longs;t, quia accederet &longs;emper propiùs ad cen<lb/>trum A; </s>

<s id="N1E987">igitur e&longs;&longs;et planum inclinatum per Th. 2. igitur per illud de<lb/>&longs;cenderet, nec vlla e&longs;&longs;et difficultas; </s>

<s id="N1E98D">quod autem accedat &longs;emper propiùs <lb/>ad A per &longs;emicirculum QLA, certum e&longs;t; </s>

<s id="N1E993">quia PA minor e&longs;t QA; nam <lb/>diamcter e&longs;t maxima &longs;ubten&longs;arum in circulo. </s>

<s id="N1E993">quia PA minor e&longs;t QA; nam <lb/>diameter e&longs;t maxima &longs;ubten&longs;arum in circulo. </s>

<s id="N1E999">Immò per alium &longs;emi<lb/>circulum ASQ a&longs;cenderet denuóque de&longs;cenderet repetitis pluribus vi<lb/>brationibus; nunquam tamen a&longs;cenderet v&longs;que ad punctum Q propter <lb/>tamdem rationem, quam in Theoremate 92. adduximus. </s>

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<s id="N1EF37"><emph type="center"/><emph type="italics"/>Definitio<emph.end type="italics"/> 7.<emph.end type="center"/></s>

<s id="N1EF45"><emph type="italics"/>Angulus reflexionis e&longs;t, quem facit linea reflexionis cum codem plano.<emph.end type="italics"/></s>

<s id="N1EF45"><emph type="italics"/>Angulus reflexionis e&longs;t, quem facit linea reflexionis cum eodem plano.<emph.end type="italics"/></s>

<s id="N1EF4E"><emph type="center"/><emph type="italics"/>Definitio<emph.end type="italics"/> 8.<emph.end type="center"/></s>

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<s id="N1F077"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 1.<emph.end type="center"/></s>

<s id="N1F086"><emph type="italics"/>Datur motus re&longs;lexus<emph.end type="italics"/>; </s>

<s id="N1F086"><emph type="italics"/>Datur motus reflexus<emph.end type="italics"/>; </s>

<s id="N1F08F">nemo dubitat: </s>

<s id="N1F093">quippe aliquod corpus in aliud <lb/>impactum reflectitur per Ax. primum &longs;ed &longs;i corpus reflectitur e&longs;t motus <lb/>reflexus; </s>

<s id="N1F09B">igitur certum e&longs;t de motu reflexo quod &longs;it; infrà verò videbi<lb/>mus propter quid &longs;it. </s>

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<s id="N1F377">In omni reflexione determinatur noua linea motus; </s>

<s id="N1F37B">clarum e&longs;t, quia <lb/>non e&longs;t motus &longs;ine linea determinata, vt patet; </s>

<s id="N1F381">&longs;ed non remanet prior <pb pagenum="240" xlink:href="026/01/272.jpg"/>linea; </s>

<s id="N1F38A">igitur e&longs;t noua, igitur illa determinatur; cur enim potiùs, quàm <lb/>alia, ni&longs;i determinarectur vna. </s>

<s id="N1F38A">igitur e&longs;t noua, igitur illa determinatur; cur enim potiùs, quàm <lb/>alia, ni&longs;i determinaretur vna. </s>

<s id="N1F392"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 16.<emph.end type="center"/></s>

<s id="N1F3A0"><emph type="italics"/>Non determinatur à puncto contactus <expan abbr="tam&utilde;m">tamtum</expan><emph.end type="italics"/>; </s>

<s id="N1F3A0"><emph type="italics"/>Non determinatur à puncto contactus <expan abbr="tam&utilde;m">tantum</expan><emph.end type="italics"/>; </s>

<s id="N1F3AC">quia ab eodem puncto <lb/>plures lineæ reflexionis procedere po&longs;&longs;unt; </s>

<s id="N1F3B2">non à linea incidentiæ tan<lb/>tùm; </s>

<s id="N1F3B8">quia &longs;i tantillùm inclinetur planum eadem linea incidentiæ pote&longs;t <lb/>habere diuer&longs;as lineas reflexionis; </s>

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<s id="N1F4E3"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 22.<emph.end type="center"/></s>

<s id="N1F4F1"><emph type="italics"/>Quando linea incidentiæ cadit perpendicnlariter in planum reflectens e&longs;t <lb/>maximum impedimentum<emph.end type="italics"/>; quia &longs;cilicet e&longs;t maximus ictus, vt probauimus <lb/>lib.1. </s>

<s id="N1F4F1"><emph type="italics"/>Quando linea incidentiæ cadit perpendiculariter in planum reflectens e&longs;t <lb/>maximum impedimentum<emph.end type="italics"/>; quia &longs;cilicet e&longs;t maximus ictus, vt probauimus <lb/>lib.1. </s>

<s id="N1F501"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 23.<emph.end type="center"/></s>

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<s id="N1F801"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 36.<emph.end type="center"/></s>

<s id="N1F80F"><emph type="italics"/>Ex hac angulorum æqualitate tùm Captotrica infinita ferè Theoremata de<lb/>monstrat in radiis vi&longs;ilibus, in &longs;peculis v&longs;toriis, tùm Echometria in re&longs;texione <lb/>&longs;onorum.<emph.end type="italics"/></s>

<s id="N1F80F"><emph type="italics"/>Ex hac angulorum æqualitate tùm Captotrica infinita ferè Theoremata de<lb/>monstrat in radiis vi&longs;ilibus, in &longs;peculis v&longs;toriis, tùm Echometria in reflexione <lb/>&longs;onorum.<emph.end type="italics"/></s>

<s id="N1F81A"> Et verò noua Catoptrica pote&longs;t e&longs;&longs;e in motu, quæ eadem pror<lb/>&longs;us demon&longs;trabit, tùm in &longs;peculis parabolicis, à quibus omnia mi&longs;&longs;ilia <lb/>projecta per parallelas axi Parabolæ in idem punctum reflectentur; </s>

<s id="N1F822">vel <lb/>Ellipticis, à quibus omnia mi&longs;&longs;ilia projecta à dato puncto per omnes li<lb/>neas ad idem punctum reflectentur; </s>

<s id="N1F82A">vel Hyperbolicis, à quibus mi&longs;&longs;ilia <lb/>projecta per plures lineas ad idem punctum ad aliud punctum omnes re<lb/>flectuntur; </s>

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<s id="N1FD52"><emph type="italics"/>Ex his demonstratur acurati&longs;&longs;imè æqualitas anguli reflexionis cum &longs;uo an<lb/>gulo incidentiæ<emph.end type="italics"/>; </s>

<s id="N1FD5D">&longs;it enim linea incidentiæ KD v. g. determinatio noua <lb/>per DG e&longs;t ad priorem per DQ, vt K <foreign lang="greek">q</foreign> vel XQ æqualis ad <expan abbr="Dq;">Dque</expan> igi<lb/>tur vt DZ æqualis QX ad DX; </s>

<s id="N1FD71">&longs;ed quotie&longs;cumque &longs;unt duæ determi<lb/>nationes, fit mixta per diagonalem Parallelo grammatis; </s>

<s id="N1FD77">&longs;ed QZ e&longs;t pa<lb/>rallelogramma, & DX diagonalis; </s>

<s id="N1FD7D">igitur determinatio mixta ex vtra<lb/>que e&longs;t per DX; </s>

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<s id="N2001C"><expan abbr="exempl&utilde;">exemplum</expan> &longs;ecundi in cera molli, vel pingui terrâ; </s>

<s id="N20023">tertii <expan abbr="deniq;">denique</expan> in <expan abbr="m&etilde;-brana">men<lb/>brana</expan> ten&longs;a, vel fune ten&longs;o: </s>

<s id="N20031">&longs;imiliter mobile ip&longs;um tribus modis cedere <lb/>pote&longs;t 1&degree; <expan abbr="c&utilde;">cum</expan> diui&longs;ione partium, & fractione, &longs;ic <expan abbr="d&utilde;">dum</expan> <expan abbr="vitr&utilde;">vitrum</expan> à marmore refle<lb/>ctitur in mille partes abit.2&degree; &longs;ine fractione, &longs;ed non &longs;ine depre&longs;sione; &longs;ic <lb/>plumbum deprimitur in corpus durum impactum, aut cera mollis. </s>

<s id="N20047">3&degree; &longs;ine <lb/>diui&longs;ione, &longs;ed <expan abbr="nõ">non</expan> &longs;ine aliqua compre&longs;sione, &longs;ic ve&longs;icca inflata reflectitui. </s>

<s id="N20047">3&degree; &longs;ine <lb/>diui&longs;ione, &longs;ed <expan abbr="nõ">non</expan> &longs;ine aliqua compre&longs;sione, &longs;ic ve&longs;icca inflata reflectitur. </s>

<s id="N20052">Itaque duo &longs;unt planorum genera. </s>

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<s id="N20077">vel enim mobile reflecti<lb/>tur à mobili, &longs;ed non pellitur à plano, & hæc e&longs;t pura reflexio; vel pellitur <lb/>à plano &longs;ine motu præuio, vel &longs;imul reflectitur, & pellitur à plano, quod <lb/>&longs;imul mouetur. </s>

<s id="N20081">Ob&longs;erua 4&degree; <expan abbr="c&utilde;">cum</expan> mouetur corpus reflectens à mobili im<lb/>pacto tres e&longs;&longs;e quoque <expan abbr="cõbinationes">combinationes</expan>, vel enim cum mouetur corpus refle<lb/>ctens, reflectitur, &longs;eu retroagitur mobile impactum, vel <expan abbr="cõ&longs;i&longs;tit">con&longs;i&longs;tit</expan>, &longs;eu quie<lb/>&longs;cit, vel non retroagitur, &longs;ed idem iter pro&longs;equitur. </s>

<s id="N20096">Ob&longs;erua 5&degree; <expan abbr="c&umacr;">cum</expan> &longs;int <lb/>quinque veluti &longs;tatus corporis reflectentis; </s>

<s id="N200A0">nam vel e&longs;t molle, vel pre&longs;si<lb/>bile, vel durum vel fragile, vel friabile, & totidem &longs;tatus mobilis, e&longs;&longs;e 25. <lb/>combinationes, vt patet ex regula combinationum, in quo non e&longs;t diffi<lb/>cultas; igitur deinceps con&longs;iderabo reflexionem ratione potiùs materiæ <lb/>corporis, tùm re&longs;&longs;exi, tùm reflectentis, &longs;it ergo. </s>

<s id="N200AE"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 51.<emph.end type="center"/></s>

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<s id="N20789"><emph type="italics"/>Si globus in æqualem globum impingatur, qui æquali impetu in eum etiam <lb/>impingitur per lineam connectentem centra<emph.end type="italics"/>; </s>

<s id="N20794">vterque retro agitur æquali <lb/>p&oelig;nitus motu, quo &longs;uam lineam vlteriùs propaga&longs;&longs;et, &longs;i in alterum glo<lb/>bum non incidi&longs;&longs;et per Th.137.lib.1.&longs;i autem inæquali impetu mouean<lb/>tur, non e&longs;t determinatum &longs;uprà; pote&longs;t autem &longs;it determinari, fig. </s>

<s id="N2079E">1. <lb/>Tab.1.&longs;it globus A impactus in alium B motu vt 4. codem tempore, quo <lb/>globus B impingitur in A motu vt 2. certè globus B retrò agetur motu vt <lb/>4. quippè &longs;iue moueatur æquali motu, &longs;iue minori, &longs;iue etiam quie&longs;cat, <lb/>&longs;emper æquali motu à globo A impelletur; quod certè mirabile e&longs;t; pri<lb/>mum con&longs;tat per Th. 135.lib. tertium con&longs;tat per Theor.128.lib.1. </s>

<s id="N2079E">1. <lb/>Tab.1.&longs;it globus A impactus in alium B motu vt 4. eodem tempore, quo <lb/>globus B impingitur in A motu vt 2. certè globus B retrò agetur motu vt <lb/>4. quippè &longs;iue moueatur æquali motu, &longs;iue minori, &longs;iue etiam quie&longs;cat, <lb/>&longs;emper æquali motu à globo A impelletur; quod certè mirabile e&longs;t; pri<lb/>mum con&longs;tat per Th. 135.lib. tertium con&longs;tat per Theor.128.lib.1. </s>

<s id="N207AC">Igi<lb/>tur &longs;ecundum con&longs;tat, &longs;i enim impellitur motu vt 4.dum in contrariam <lb/>partem mouetur vt 4. multò magis &longs;i tantùm mouetur vt 2. & &longs;i tantùm <lb/>impellitur motu vt 4. dum quie&longs;cit multò magis motu vt 4. dum in <pb pagenum="259" xlink:href="026/01/293.jpg"/>contrariam partem mouetur motu vt 2. at verò globus A non retro age<lb/>tur: </s>

<s id="N207BD">motu vt 4. &longs;ed tantùm motu vt 2. vt patet; </s>

<s id="N207C1">quippe omninò con&longs;i&longs;teret, <lb/>&longs;i globus B nullum præuium impetum habui&longs;&longs;et; &longs;i verò habui&longs;&longs;et mo<lb/>tum vt 4. tùm etiam A retroageretur motu vt 4. igitur motu vt duo, &longs;i <lb/>B impre&longs;&longs;it impetum vt duo. </s>

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<s id="N20B70"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 82.<emph.end type="center"/></s>

<s id="N20B7E"><emph type="italics"/>Cum planus lapis per lineam incidentiæ valdè obliquæm in &longs;uperficiem <lb/>aquæ proijcitur, qua&longs;i repit lapis in ip&longs;a &longs;uperficie &longs;eu plurimo &longs;altu di&longs;currit<emph.end type="italics"/>; </s>

<s id="N20B7E"><emph type="italics"/>Cum planus lapis per lineam incidentiæ valdè obliquam in &longs;uperficiem <lb/>aquæ proijcitur, qua&longs;i repit lapis in ip&longs;a &longs;uperficie &longs;eu plurimo &longs;altu di&longs;currit<emph.end type="italics"/>; </s>

<s id="N20B89"><lb/>quia &longs;cilicet modica re&longs;i&longs;tentia &longs;ufficit ad reflexionem, cum angulus in<lb/>cidentiæ e&longs;t obliquior, vt con&longs;tat ex dictis; </s>

<s id="N20B90">vt tamen longiorem tractum <lb/>percurrat lapis, ita proiiciendus e&longs;t, vt eius horizonti planior &longs;uperficies <lb/>&longs;it parallela; </s>

<s id="N20B98">immò tantillùm portio anthica attollatur: cur autem, & <lb/>quomodo re&longs;i&longs;tat &longs;uperficies aquæ, dicemus &longs;uo loco. </s>

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<s id="N20DBF">igitur fiet mixta ex AY <lb/>AB, &longs;cilicet A<foreign lang="greek">u</foreign>; </s>

<s id="N20DC9">non tamen eo tempore conficiet A<foreign lang="greek">u</foreign>, quo conficiet <lb/>A<foreign lang="greek">d</foreign>; </s>

<s id="N20DD7">quia &longs;cilicet omnes partes aquæ re&longs;i&longs;tunt, vt con&longs;tat; </s>

<s id="N20DDB">igitur con<lb/>ficietur A <gap/> æqualis A<foreign lang="greek">d</foreign>; quæ porrò &longs;it proportio re&longs;i&longs;tentiæ, quæ mobi<lb/>le retardat in aqua, & re&longs;i&longs;tentiæ, quæ idem retardat in aëre determina<lb/>ri non pote&longs;t, ni&longs;i primò cogno&longs;catur proportio grauitatis vtriu&longs;que. </s>

<s id="N20DDB">igitur con<lb/>ficietur A <foreign lang="greek">q</foreign> æqualis A<foreign lang="greek">d</foreign>; quæ porrò &longs;it proportio re&longs;i&longs;tentiæ, quæ mobi<lb/>le retardat in aqua, & re&longs;i&longs;tentiæ, quæ idem retardat in aëre determina<lb/>ri non pote&longs;t, ni&longs;i primò cogno&longs;catur proportio grauitatis vtriu&longs;que. </s>

<s id="N20DEB"><lb/>Secundò, ni&longs;i &longs;ciatur in quo po&longs;ita &longs;it hæc re&longs;i&longs;tentia: Tertiò, ni&longs;i per<lb/>&longs;pectum &longs;it, an maiore nexu partes aquæ inter &longs;e copulentur, an mino<lb/>re, vel æquali, de quo alias. </s>

<s id="N20DF4">Equidem P. Mer&longs;ennus lib.1.a.15. &longs;uæ ver<lb/>&longs;ionis a&longs;&longs;erit corpus graue per mediam aquam conficere 12. pedes &longs;patij <lb/>eo <expan abbr="t&etilde;pore">tempore</expan>, quo 48. percurrit in aëre, id e&longs;t, tempore duorum &longs;ecundorum. </s>

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<s id="N20FA8">an fortè potentia motrix intendit <lb/>motum per aliam lineam, quàm per lineam incidentiæ? </s>

<s id="N20FAD">cum ip&longs;a linea <lb/>reflexionis &longs;emper accidat præter intentionem potentiæ motricis natu<lb/>ralis; denique licèt hoc totum verum e&longs;&longs;et, vnde probatur po&longs;&longs;e impe<lb/>tum ad angulum reflexionis æqualem &longs;e ip&longs;um determinare? </s>

<s id="N20FB7">Secundò, <lb/>&longs;upponunt impetum e&longs;&longs;e indifferentem ad diuer&longs;as lineas, quod &longs;anè ve<lb/>rum e&longs;t; </s>

<s id="N20FBF">probarc tamen deberent, & di&longs;cernere impetum innatum ab <lb/>omni aliò, at, e&longs;to id verum &longs;it; cur potiùs determinatur ad lineam quæ <lb/>faciat angulum æqualem, quàm inæqualem angulo incidentiæ? </s>

<s id="N20FBF">probare tamen deberent, & di&longs;cernere impetum innatum ab <lb/>omni aliò, at, e&longs;to id verum &longs;it; cur potiùs determinatur ad lineam quæ <lb/>faciat angulum æqualem, quàm inæqualem angulo incidentiæ? </s>

<s id="N20FC7">ex hoc <lb/>enim principio non probatur hæc æqualitas. </s>

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<s id="N21A10">Hic fortè aliquis de&longs;ideraret &longs;olutionem illius argumenti, quod vul<lb/>gò ducitur ex motu circulari contra puncta phy&longs;ica, quod &longs;ic breuiter <lb/>proponi pote&longs;t. </s>

<s id="N21A17">Sit punctum Q, quod acquirat punctum &longs;patij ver&longs;us R <lb/>vno in&longs;tanti; </s>

<s id="N21A1D">certe punctum C, quod mouetur ver&longs;us S, acquiret codem <pb pagenum="279" xlink:href="026/01/313.jpg"/>illo in&longs;tanti plu&longs;quam punctum &longs;patij; </s>

<s id="N21A1D">certe punctum C, quod mouetur ver&longs;us S, acquiret eodem <pb pagenum="279" xlink:href="026/01/313.jpg"/>illo in&longs;tanti plu&longs;quam punctum &longs;patij; </s>

<s id="N21A26">igitur codem in&longs;tanti erit in <lb/>duobus loris, quod e&longs;t ab&longs;urdum; </s>

<s id="N21A26">igitur eodem in&longs;tanti erit in <lb/>duobus loris, quod e&longs;t ab&longs;urdum; </s>

<s id="N21A2C">nec pote&longs;t dici punctum C moueri <lb/>duobus in&longs;tantibus, &longs;ed minoribus, quæ &longs;cilicet re&longs;pondeant in&longs;tanti, quo <lb/>mouetur punctum <expan abbr="q;">que</expan> quia &longs;i po&longs;t primum in&longs;tans C &longs;i&longs;teret, Q mouere<lb/>tur adhuc, quod e&longs;t ab&longs;urdum; nam &longs;imul incipit, & de&longs;init moueri, <lb/>cum puncto C. </s>

<s id="N21A3D">Equidem non pote&longs;t explicari maior velocitas motus C <lb/>per in&longs;tantia minora, vt patet; igitur per &longs;patia maiora. </s>

<s id="N21A43">Itaque re&longs;pon<lb/>deo &longs;i C & Q mouentur in eodem radio conjunctim non po&longs;&longs;e pun<lb/>ctum K acquirere punctum &longs;patij nullo modo participans cum priori, <lb/>&longs;ed participans; </s>

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<s id="N21C0A">Re&longs;pondeo <lb/>negandam e&longs;&longs;e paritatem; </s>

<s id="N21C10">quia naturalis motus grauium non accelera<lb/>tur fru&longs;trà; </s>

<s id="N21C16">Nunquam enim recedit à &longs;uo fine; </s>

<s id="N21C1A">at verò, &longs;i motus circula<lb/>ris &longs;yderum acceleraretur, tandem abiret in infinitum, quod reuerâ e&longs;&longs;et <lb/>contra finem à natura iu&longs;titutum; quippè carerent &longs;uo fine, & v&longs;u corpo<lb/>ra c&oelig;le&longs;tia, &longs;i longè celeriori motu rotarentur. </s>

<s id="N21C1A">at verò, &longs;i motus circula<lb/>ris &longs;yderum acceleraretur, tandem abiret in infinitum, quod reuerâ e&longs;&longs;et <lb/>contra finem à natura in&longs;titutum; quippè carerent &longs;uo fine, & v&longs;u corpo<lb/>ra c&oelig;le&longs;tia, &longs;i longè celeriori motu rotarentur. </s>

<s id="N21C26">Obiiceret alius, motus circularis naturalis non acceleraretur, igitur <lb/>tardi&longs;&longs;imus e&longs;&longs;et, qualis reuerâ motus naturalis grauium deor&longs;um, quod <lb/>e&longs;t contra experientiam. </s>

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<s id="N220A9">quia etiam&longs;i nullus accederet nouus impetus radio AE, &longs;ed tantùm <lb/>minimum pondus; </s>

<s id="N220AF">haud dubiè attolleret radium EC: </s>

<s id="N220B3">Adde quod ra<lb/>dius EC impedit motum radij FE; </s>

<s id="N220B9">igitur ab impetu huius producitur <lb/><gap/> in illo impetus; igitur tùm ab impetu pugni, vel organi, tùm ab <lb/>impetu radij FE producitur impetus in radio EC. </s>

<s id="N220B9">igitur ab impetu huius producitur <lb/>etiam in illo impetus; igitur tùm ab impetu pugni, vel organi, tùm ab <lb/>impetu radij FE producitur impetus in radio EC. </s>

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<s id="N221EC"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 44.<emph.end type="center"/></s>

<s id="N221FA"><emph type="italics"/>Hinc in vtreque &longs;emicirculo plani producitur impetus ab ip&longs;a potentia ap<lb/>plicata, non vero ab impetu producto in altero &longs;emicirculo producitur impetus <lb/>in alio,<emph.end type="italics"/> vt con&longs;tat ex dictis; </s>

<s id="N221FA"><emph type="italics"/>Hinc in vtroque &longs;emicirculo plani producitur impetus ab ip&longs;a potentia ap<lb/>plicata, non vero ab impetu producto in altero &longs;emicirculo producitur impetus <lb/>in alio,<emph.end type="italics"/> vt con&longs;tat ex dictis; </s>

<s id="N22207">&longs;it enim rota horizonti parallela ABCD, & <lb/>applicetur potentia in A per AO, non pote&longs;t produci impetus in radio <lb/>AE, ni&longs;i tollatur impedimentum; </s>

<s id="N2220F">impedit autem radius EC eo primo <lb/>in&longs;tanti; </s>

<s id="N22215">igitur debet &longs;imul tolli impedimentum, & produci impetus in <lb/>AE; </s>

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<s id="N227AC"><emph type="italics"/>Si pellatur nauis, vel cylindrus BH in puncto T, difficiliùs mouebitur, etiam <lb/>ex &longs;uppo&longs;itione, quòd circa centrum M moueatur<emph.end type="italics"/>; </s>

<s id="N227B7">quod codem modo de<lb/>mon&longs;tratur, quo &longs;uprà; </s>

<s id="N227B7">quod eodem modo de<lb/>mon&longs;tratur, quo &longs;uprà; </s>

<s id="N227BD">accipiatur TZ æqualis BC; </s>

<s id="N227C1">&longs;it autem BT æqua<lb/>lis TA; </s>

<s id="N227C7">certè arcus TS erit æqualis arcui BE; </s>

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<s id="N22DF8">fuit meum pendulum 12. pedes longum. </s>

<s id="N22DFD">Quæreret aliquis primò quanta fucrit differentia temporum Secundò, <lb/>quanto tempore globus pendulus ex N in E peruencrit. </s>

<s id="N22DFD">Quæreret aliquis primò quanta fuerit differentia temporum Secundò, <lb/>quanto tempore globus pendulus ex N in E peruenerit. </s>

<s id="N22E02">Re&longs;pondeo inu<lb/>tilem e&longs;&longs;e quæ&longs;tionem; </s>

<s id="N22E08">nec enim minimas illas temporum differentias <lb/>&longs;en&longs;u metiri po&longs;&longs;umus; </s>

<s id="N22E0E">&longs;i enim affirmarem cum nonnullis corpus graue <lb/>per medium liberum 12. &longs;patij pedes conficere vno temporis &longs;ecundo; </s>

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<s id="N22F33"><emph type="center"/><emph type="italics"/>Lemma<emph.end type="italics"/> 3.<emph.end type="center"/></s>

<s id="N22F42">Po&longs;&longs;unt determinari vel &longs;patia inæqualia temporibus æqualibus, vel <lb/>tempora inæqualia &longs;patiis æqualibus in choidis eiu&longs;dem quadrantis, & <lb/>in perpendiculari, &longs;it tempus DI; </s>

<s id="N22F42">Po&longs;&longs;unt determinari vel &longs;patia inæqualia temporibus æqualibus, vel <lb/>tempora inæqualia &longs;patiis æqualibus in chordis eiu&longs;dem quadrantis, & <lb/>in perpendiculari, &longs;it tempus DI; </s>

<s id="N22F4A">&longs;it motus per ip&longs;am perpendicula<lb/>rem AP, vel DI; </s>

<s id="N22F50">&longs;it motus etiam per chordam inclinatam DP; </s>

<s id="N22F54">velo<lb/>citas primi e&longs;t ad velocitatem &longs;ecundi in tempore DI, vt DP ad DI, <lb/>vel vt AK ad &longs;inum VK, vel vt IP ad NP, vel vt quadratum IA ad <lb/>rectangulum NA; </s>

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<s id="N23154"><emph type="italics"/>Tres chordæ faciliùs percurruntur, quàm duæ<emph.end type="italics"/>; </s>

<s id="N2315D">&longs;int enim tres EILB; </s>

<s id="N23161"><lb/>&longs;int duæ ELB. Primò, duæ EIL citiùs percurruntur quàm EL, quia <lb/>IL codem tempore percurritur, &longs;iue initium motus ducatur ab F, &longs;iue ab <lb/>E; </s>

<s id="N23161"><lb/>&longs;int duæ ELB. Primò, duæ EIL citiùs percurruntur quàm EL, quia <lb/>IL eodem tempore percurritur, &longs;iue initium motus ducatur ab F, &longs;iue ab <lb/>E; </s>

<s id="N2316A">& minor e&longs;t ratio EK ad EL, quàm FI ad FL per Lem.5.EI, & EK <lb/>æquè citò percurruntur per Lem. 7. igitur &longs;it vt FI ad mediam propor<lb/>tionalem inter FI & FL; </s>

<s id="N23174">ita tempus Z ad tempus X, & vt EK ad me<lb/>diam proportionalem inter EK EL, ita tempus Z ad tempus Y; </s>

<s id="N2317A">certè <lb/>tempus Y erit maius tempore X per Lem. 8. igitur citiùs percurrentur <lb/>duæ EIL, quàm EL; </s>

<s id="N23184">&longs;ed &longs;i codem tempore percurrerentur duæ EIL <lb/>cum EL; </s>

<s id="N23184">&longs;ed &longs;i eodem tempore percurrerentur duæ EIL <lb/>cum EL; </s>

<s id="N2318A">certè LB æquali tempore percurreretur, quia e&longs;t idem impetus <lb/>in L, &longs;iue ab E per EL, &longs;iue ab F per FL incipiat motus, vt con&longs;tat, & e&longs;t <lb/>idem in I, &longs;iue ab E, &longs;iue ab F incipiat; </s>

<s id="N23192">igitur idem in L &longs;iue ab E per <lb/>EIL, &longs;iue ab F per FL, &longs;iue ab E per EL; </s>

<s id="N23198">igitur LB æquali tempore <lb/>percurretur, &longs;iue motus &longs;it ab E per ELB, &longs;iue ab E per EI, LB, po&longs;ito <lb/>quòd EIL & EL æquali tempore percurrantur; </s>

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<s id="N2326C"><emph type="center"/><emph type="italics"/>Lemma<emph.end type="italics"/> 12.<emph.end type="center"/></s>

<s id="N2327A"><emph type="italics"/>Velocitas acqui&longs;ita in toto arcu quadrantis ELB non debet a&longs;&longs;umi in area <lb/>tota quadrantis AEB, &longs;ed in linea recta æquali toti arcui ELB, ductis &longs;ci<lb/>licet lineis rectis tran&longs;uer&longs;is, qua &longs;int ip&longs;is &longs;inubus rectis æqusles, cuius con&longs;tru<lb/>ctionis<emph.end type="italics"/>; </s>

<s id="N2327A"><emph type="italics"/>Velocitas acqui&longs;ita in toto arcu quadrantis ELB non debet a&longs;&longs;umi in area <lb/>tota quadrantis AEB, &longs;ed in linea recta æquali toti arcui ELB, ductis &longs;ci<lb/>licet lineis rectis tran&longs;uer&longs;is, qua &longs;int ip&longs;is &longs;inubus rectis æquales, cuius con&longs;tru<lb/>ctionis<emph.end type="italics"/>; </s>

<s id="N23289">&longs;it enim linea AN æqualis arcui quadrantis, & NT radio; </s>

<s id="N2328D">igi<lb/>tur totum triangulum mixtum ex rectis AN, NT, & curua TQH, e&longs;t <lb/>velocitas acqui&longs;ita in toto arcu quadrantis; &longs;it autem A <foreign lang="greek">s</foreign> æqualis lateri <lb/>quadrati in&longs;cripti qua e&longs;t ad AN proximè vt 10. ad 11. e&longs;t enim AB ra<lb/>dix quad. </s>

<s id="N2329D">98. &longs;itque AE &longs;inus rectus quad. </s>

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<s id="N234E1">Præterea &longs;int duæ BGF, BG e&longs;t 100000.&longs;it perpendicularis G 4 cùm <lb/>angulus GB 4.&longs;it grad.30. erit vt 5 G ad GB, ita BG ad B 4. igitur B 4. <lb/>erit 115469. &longs;it 4.3.perpendicularis in BF, quadratum B 4. e&longs;t duplum <lb/>quadrati B 3.igitur B 3. erit 81655. iam verò FN e&longs;t &longs;ecans grad.75. &longs;ci<lb/>licet 386370.igitur GN e&longs;t 334606. detracta &longs;cilicet FG æquali BH; </s>

<s id="N234ED">&longs;it <lb/>antem NG ad 359557. vt hæc ad NF; </s>

<s id="N234ED">&longs;it <lb/>autem NG ad 359557. vt hæc ad NF; </s>

<s id="N234F3">certè tempus per BG e&longs;t ad tem-<pb pagenum="308" xlink:href="026/01/342.jpg"/>pus per NG, vt BG ad NG, & ad tempus per GF, vt BG ad 24951. & <lb/>ad tempus per BGF, vt BG id e&longs;t, 100000. ad 124951. porrò tempus <lb/>per B 3. e&longs;t BG; </s>

<s id="N23500">ergo vt quadratum temporis per BG ad quadratum <lb/>temporis per BGF, &longs;cilicet vt 10000000000. ad 1561475241. ita B 3. <lb/>&longs;cilicet 81655. ad aliam, hæc erit 123496. igitur in BF, quæ e&longs;t partium <lb/>141422. percurruntur partes 123496. eo tempore, quo percurruntur <lb/>BGF; </s>

<s id="N2350C">at verò eo tempore, quo percurruntur BHF; </s>

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<s id="N23598">igitur tempus per HG e&longs;t ad tempus <lb/>per HGF, vt 51764. ad 75628. &longs;ed BX e&longs;t æqualis, eiu&longs;demque incli<lb/>nationis cum HG; </s>

<s id="N235A0">igitur tempus, quo percurritur BX e&longs;t BX. vel HG; </s>

<s id="N235A4"><lb/>&longs;it autem vt BX ad 75628. ita hæc ad aliam 111092. igitur eo tempore, <lb/>quo percurruntur HGF, percurruntur in BF 111092. minor BF; igitur <lb/>citiùs percurruntur HGF quàm BHF, vel BZF, &c. </s>

<s id="N235AD">igitur duæ infe<lb/>riores citiùs, quàm duæ fuperiores. </s>

<s id="N235AD">igitur duæ infe<lb/>riores citiùs, quàm duæ &longs;uperiores. </s>

<s id="N235B4">Ex his manife&longs;tum e&longs;t, quænam &longs;int qua&longs;i termini progre&longs;&longs;ionis in a&longs;<lb/>&longs;umptis duabus chordis; &longs;i enim diuidatur arcus BF in 6.arcus æquales, <lb/>BF tardi&longs;&longs;imè, BHF veloci&longs;&longs;imè, &c. </s>

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<s id="N23DF0">Denique ob&longs;eruabis, ex hoc etiam po&longs;&longs;e concludi omnes vibrationes <lb/>eiu&longs;dem funependuli non e&longs;&longs;e æquè diuturnas; </s>

<s id="N23DF6">nam reuerà &longs;i æquè diu<lb/>turnæ e&longs;&longs;ent, & nongentæ numeratæ e&longs;&longs;ent &longs;patio 15. minutorum; </s>

<s id="N23DFC">haud <lb/>dubiè &longs;ingulæ &longs;ingulis &longs;ecundis minutis re&longs;ponderent; igitur eo tempore, <lb/>quo tres &longs;patij pedes decurrerentur in perpendiculo, in quadrantis arcu <lb/>4. 3/7 con&longs;icerentur, quod fieri non pote&longs;t. </s>

<s id="N23E08"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 14.<emph.end type="center"/></s>

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<s id="N2423A">Tertiò, &longs;unt tres determinationes in a&longs;cen&longs;u; </s>

<s id="N2423E">prima e&longs;t impetus pro<lb/>ducti in de&longs;cen&longs;u determinati ad Tangentem; &longs;ecunda funis per &longs;uam li<lb/>neam qua&longs;i retrahentis pendulum. </s>

<s id="N24246">tertia ip&longs;ius impetus innati qua&longs;i tra<lb/>hentis deor&longs;um idem pondus; atqui ex pugna trium determinationum in <lb/>codem mobili de&longs;truitur multùm impetus, vt patet ex dictis alibi. </s>

<s id="N24246">tertia ip&longs;ius impetus innati qua&longs;i tra<lb/>hentis deor&longs;um idem pondus; atqui ex pugna trium determinationum in <lb/>eodem mobili de&longs;truitur multùm impetus, vt patet ex dictis alibi. </s>

<s id="N24250">Quartò, cum eo impetu, cuius ope non po&longs;&longs;et corpus a&longs;cendere per <lb/>ip&longs;um perpendiculum EA, a&longs;cendit adhuc per arcum EI; </s>

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<s id="N24C0A"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 43.<emph.end type="center"/></s>

<s id="N24C18"><emph type="italics"/>Hinc &longs;unt paceses vibrationes corporis oblongi, quàm funependuli,<emph.end type="italics"/> cum <lb/>&longs;inguli a&longs;cen&longs;us plùs impetus de&longs;truant in vibrationibus corporis ob<lb/>longi, quàm funependuli: </s>

<s id="N24C18"><emph type="italics"/>Hinc &longs;unt pauciores vibrationes corporis oblongi, quàm funependuli,<emph.end type="italics"/> cum <lb/>&longs;inguli a&longs;cen&longs;us plùs impetus de&longs;truant in vibrationibus corporis ob<lb/>longi, quàm funependuli: </s>

<s id="N24C2B">Hinc citiùs quie&longs;cit corpus oblongum vibra<lb/>tum, quàm funependulum; </s>

<s id="N24C31">licèt vtrumque ex eadem altitudine demitta<lb/>tur; quod etiam multis experimentis comprobatur, & ratio patet ex <lb/>dictis. </s>

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<s id="N25031"><emph type="italics"/>Omnia puncta rotæ AQLZ, quæ rotatur in plano, mouentur inæquali mo<lb/>tu<emph.end type="italics"/>; </s>

<s id="N2503C">de duobus oppo&longs;itis LA con&longs;tat manife&longs;tè, quia æquali tempore <lb/>L acquirit maius &longs;patium, quàm A, v. g. &longs;patium LI eo tempo<lb/>re quo A acquirit &longs;patium AS: </s>

<s id="N25048">de duobus QZ etiam con&longs;tat; </s>

<s id="N2504C">nam <lb/>Z ita mouetur ver&longs;us L, vt inotus orbis addat &longs;inum ver&longs;um motui centri <lb/>Q verò ita mouetur, vt detrahat <expan abbr="e&utilde;dem">eundem</expan> &longs;inum; </s>

<s id="N2504C">nam <lb/>Z ita mouetur ver&longs;us L, vt motus orbis addat &longs;inum ver&longs;um motui centri <lb/>Q verò ita mouetur, vt detrahat <expan abbr="e&utilde;dem">eundem</expan> &longs;inum; </s>

<s id="N25058">igitur Z mouetur velo<lb/>ciùs, quàm <expan abbr="q;">que</expan> de duobus K & 10. certum e&longs;t, nam 10. plùs addit a&longs;cen<lb/>dendo quàm K de&longs;cendendo æquali tempore; </s>

<s id="N25064">nam 10. in arcu 10. L ad<lb/>dit motui centri 10. M, & K in de&longs;cen&longs;u KH addit addit tantùm 14. H; </s>

<s id="N2506A"><lb/>&longs;ed hæc e&longs;t minor.10. M, vt con&longs;tat toto &longs;inu ver&longs;o arcus <expan abbr="Hq;">Hque</expan> & licèt <lb/>punctum 10. in a&longs;cen&longs;u eodem tempore addat 10. M quo punctum L <lb/>in de&longs;cen&longs;u addit MK æqualem; </s>

<s id="N2506A"><lb/>&longs;ed hæc e&longs;t minor.10. M, vt con&longs;tat toto &longs;inu ver&longs;o arcus HQ; & licèt <lb/>punctum 10. in a&longs;cen&longs;u eodem tempore addat 10. M quo punctum L <lb/>in de&longs;cen&longs;u addit MK æqualem; </s>

<s id="N25077">non tamen propterea mouentur æquè <lb/>velociter; </s>

<s id="N2507D">quia punctum L initio mouetur velociùs, & &longs;ub finem tardiùs; </s>

<s id="N25081"><lb/>at verò punctum 10. initio mouetur tardiùs; vnde quocunque arcu a&longs;<lb/>&longs;umpto inter 10. L, & alio æquali inter LK, punctum L mouebitur <lb/>velociùs initio. </s>

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<s id="N2554B">&longs;i primum, &longs;unt nece&longs;&longs;ariò æquales; </s>

<s id="N2554F">&longs;i inæquales illæ &longs;unt <lb/>vel alogæ eædem quæ &longs;uprà, &longs;ic diagonalis <expan abbr="cõparata">comparata</expan> cum latere quadrati <pb pagenum="343" xlink:href="026/01/377.jpg"/>e&longs;t aloga, hoc e&longs;t ita inæqualis, vt nulla &longs;it vtrique pars aliquota commu<lb/>munis; </s>

<s id="N25560">alogæ quidem in ordine ad commen&longs;urationem, non tamen in <lb/>ordines ad partes aliquotas; </s>

<s id="N25566">&longs;ic maior arcus comparatus cum linea recta <lb/>&longs;ubdupla non e&longs;t alogus primo modo &longs;ed <expan abbr="&longs;ec&utilde;do">&longs;ecundo</expan>, id e&longs;t illa linea, quæ e&longs;t <lb/>&longs;ubdupla arcus, non pote&longs;t conuenire cum areu toto, nec cum aliqua <lb/>eius parte; </s>

<s id="N25574">&longs;i verò &longs;int æquales, po&longs;&longs;unt etiam dici alogæ in ordine ad <lb/>commen&longs;urationem, &longs;i nullo modo conuenire po&longs;&longs;unt quamtumuis diui<lb/>dantur; </s>

<s id="N2557C">&longs;ic angulus, quem faciunt duæ circumferentiæ, pote&longs;t quidem e&longs;&longs;e <lb/>&etail;qualis angulo dato rectilineo; </s>

<s id="N25582">nunquam tamen cum eo conuenire po<lb/>te&longs;t; </s>

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<s id="N25937"><lb/>quia non de&longs;truitur ab impetu innato, vt iam dictum e&longs;t; </s>

<s id="N2593C">nec enim &longs;ic <lb/>motus circularis e&longs;t contrarius motui recto; </s>

<s id="N25942">quippe modò centrum <lb/>grauitatis globi feratur motu recto, hoc &longs;atis e&longs;&longs;e videtur, &longs;iue partes mo<lb/>tu circulari ferantur: circa idem centrum, &longs;iue omnes motu recto per <lb/>lineas parallelas ferantur:</s>

<s id="N25943">ratio à priori e&longs;t, quia in tantum vnus impe<lb/>tus de&longs;truit alium in eadem parte mobilis, in quantum impeditur ab eo <lb/>eius motus deor&longs;um totius globi nullo modo impeditur ab illo motu <lb/>circulari, quia glebus æquè citò de&longs;cendit vno, atque alio motu, vt con<lb/>&longs;tat mille experientiæ. </s>

<s id="N25943">ratio à priori e&longs;t, quia in tantum vnus impe<lb/>tus de&longs;truit alium in eadem parte mobilis, in quantum impeditur ab eo <lb/>eius motus deor&longs;um totius globi nullo modo impeditur ab illo motu <lb/>circulari, quia globus æquè citò de&longs;cendit vno, atque alio motu, vt con<lb/>&longs;tat mille experientiæ. </s>

<s id="N25959"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 11.<emph.end type="center"/></s>

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<s id="N25E1B">Tertiò, motus huius rotæ accedit propiùs ad motum rotæ in plano <lb/>rectilineo, quàm motus rotæ &longs;uperioris; quia BF, quæ e&longs;t &longs;uperficies ma<lb/>ioris circuli, accedit propiùs ad lineam rectam. </s>

<s id="N25E25">Quartò, &longs;i &longs;it minor rota radio NR cuius motus dirigatur à motu <lb/>maioris radio NB, de&longs;cribit lineam, quæ accedit propiùs ad lineam <lb/>rectam RSTVX, &longs;eu potiùs ad motum centti, quod mouetur motu <lb/>circulari per arcum NG, à quo non recedit, vt patet: </s>

<s id="N25E25">Quartò, &longs;i &longs;it minor rota radio NR cuius motus dirigatur à motu <lb/>maioris radio NB, de&longs;cribit lineam, quæ accedit propiùs ad lineam <lb/>rectam RSTVX, &longs;eu potiùs ad motum centri, quod mouetur motu <lb/>circulari per arcum NG, à quo non recedit, vt patet: </s>

<s id="N25E2F">porrò minor <lb/>rota percurrit maiorem &longs;uperficiem &longs;ua peripheria, quod etiam expli-<pb pagenum="353" xlink:href="026/01/387.jpg"/>candum e&longs;t per contactus inadæquatos; tunc enim motus centri longè <lb/>&longs;uperat motum orbis. </s>

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<s id="N25E44">vnde omnia puncta <lb/>eiu&longs;dem circuli paralleli mouerentur inæquali motui tardi&longs;&longs;imo qui<lb/>dem punctum contactus hoc e&longs;t meridiano re&longs;pondens, veloci&longs;&longs;imo ve<lb/>rò ip&longs;i oppo&longs;itum, &longs;cilicet de media nocte: porrò in hoc motu motus <lb/>centri e&longs;&longs;et ferè maior motu orbis iuxta communem de diametro ma<lb/>gni orbis &longs;ententiam. </s>

<s id="N25E54">Sextò, &longs;i motus maioris rotæ diragatur à minore res eodem modo <lb/>explicanda e&longs;t, quo explicuimus illam per <expan abbr="cõtactus">contactus</expan> diuer&longs;os inadæquatos <lb/>tùm Th. 15. num. </s>

<s id="N25E54">Sextò, &longs;i motus maioris rotæ dirigatur à minore res eodem modo <lb/>explicanda e&longs;t, quo explicuimus illam per <expan abbr="cõtactus">contactus</expan> diuer&longs;os inadæquatos <lb/>tùm Th. 15. num. </s>

<s id="N25E5F">11. tùm in digre&longs;&longs;ione multis locis: </s>

<s id="N25E63">porrò po&longs;&longs;unt e&longs;&longs;e <lb/>diuer&longs;æ proportiones circuli mobilis, & immobilis; qui &longs;i maximus e&longs;t, <lb/>minimus illius arcus accipi pote&longs;t pro linea recta. </s>

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<s id="N266C2"><emph type="italics"/>Quando voluitur funis circa cylindrum, vel axem, mouetur motu <lb/>&longs;pirali, &longs;ed diuer&longs;o à prioribus<emph.end type="italics"/>; </s>

<s id="N266CF">&longs;unt enim veræ &longs;piræ ad in&longs;tar &longs;apien<lb/>tia in diuer&longs;a volumina contorti; </s>

<s id="N266D5">&longs;ic funis circa digitum fæpè <lb/>rotatur.; </s>

<s id="N266D5">&longs;ic funis circa digitum &longs;æpè <lb/>rotatur.; </s>

<s id="N266DB">e&longs;t enim motus mixtus ex diuer&longs;is circularibus: </s>

<s id="N266E1">quippè <pb pagenum="363" xlink:href="026/01/397.jpg"/>in &longs;ingulis punctis e&longs;t diuer&longs;a determinatio ad nouum circulum, quia <lb/>e&longs;t nouus radius, quia continuò radius huius vertiginis imminuitur; <lb/>porrò duobus modis pote&longs;t funis circa axem vel cylindrum conuolui. </s>

<s id="N266EE"><lb/>Primò, &longs;i &longs;emper circa <expan abbr="e&utilde;dem">eundem</expan> cylindri circulum voluatur; </s>

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<s id="N2679B"><emph type="italics"/>Cum taleola &longs;upra planum rectilineum ita repit, vt etiam circa propriu&mtail; <lb/>centrum voluatur, est motus mixtus ex recto & circulari<emph.end type="italics"/>; </s>

<s id="N267A6">neque hic motus <lb/>diuer&longs;us e&longs;t à motu rotæ in plano, &longs;it enim taleola centro A, circa quod <lb/>vertitur dum centrum A repit motu recto per rectam AD, perinde &longs;e <lb/>habet, atque &longs;i rota in plano BE vel CF rotaretur; </s>

<s id="N267B0">immò pote&longs;t tabella <lb/>GK ita moueri, vt eius centrum A moueatur per AD, dum reliquæ par<lb/>tes circa centrum A voluuntur; </s>

<s id="N267B8">tunc enim punctum H codem motu <lb/>moueretur, quo alia puncta peripheriæ huius rotæ; </s>

<s id="N267B8">tunc enim punctum H eodem motu <lb/>moueretur, quo alia puncta peripheriæ huius rotæ; </s>

<s id="N267BE">punctum verò I eo <lb/>modo quo I in radio BA, dum rota mouetur, quod &longs;uprà fusè explicui-<pb pagenum="364" xlink:href="026/01/398.jpg"/>mus; denique ita moueri pote&longs;t taleola, vt primò B moueatur motu or<lb/>bis ver&longs;us. </s>

<s id="N267CB">Secundò, ver&longs;us K; Tertiò, vt motus centri &longs;it maior vel minor <lb/>motu orbis. </s>

<s id="N267D0">Quartò, vt &longs;it æqualis. </s>

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<s id="N26B63">Quintò, E per arcum EG non mouetur; </s>

<s id="N26B67">alioquin A <lb/>e&longs;&longs;et immobilis: </s>

<s id="N26B6D">præterea F. non mouetur motu circulari, ni&longs;i retineatur <lb/>in A; </s>

<s id="N26B73">&longs;ed non retinetur; igitur non mouetur per EG. Sextò, non mouc<lb/>tur quoque per rectam EF, quia retinetur E ab A, & reliquis partibus, <lb/>quæ minùs habent impetus. </s>

<s id="N26B73">&longs;ed non retinetur; igitur non mouetur per EG. Sextò, non moue<lb/>tur quoque per rectam EF, quia retinetur E ab A, & reliquis partibus, <lb/>quæ minùs habent impetus. </s>

<s id="N26B7B">Septimò, mouetur E per lineam curuam, quæ <lb/>accedit ad ellip&longs;im, &longs;cilicet per EHA; </s>

<s id="N26B81">A verò a&longs;&longs;urgit &longs;upra AE; </s>

<s id="N26B85">ratio <lb/>huius motus petitur ex eo quod, neque per EF, neque per arcum EG <lb/>mouetur extremitas E; igitur per curuam de vtraque participan<lb/>tem. </s>

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<s id="N26D68">Sextò, diu durat i&longs;te motus circularis turbinis, quia non de&longs;truitur <lb/>ab impetu contrario grauitationis, vt iam diximus alibi, &longs;ed tantùm ab <lb/>affrictu ad planum illud, in quo vertitur, & à noua determinatione, quæ <lb/>&longs;ingulis in&longs;tantibus ponitur, quæ pro nihilo ferè haberi debet; hinc quò <lb/>vertex turbinis, politior e&longs;t, & planum in quo &longs;uos gyros agit, læuiga<lb/>tius, diutiùs durat eius motus. </s>

<s id="N26D78">Septimò, aliquando dormire dicitur turbo cum celerrimè mouetur, <lb/>defixo &longs;cilicet axe in codem loco, & &longs;itu, ratio petitur ex eo quòd ver<lb/>tex certè componitur cum ip&longs;o plano factâ &longs;ibi veluti in&longs;en&longs;ibili apo<lb/>theca &longs;eu fo&longs;&longs;ula, cuius tenuis margo impedit motum centri; igitur mo<lb/>tus orbis vnicus e&longs;t, igitur maior. </s>

<s id="N26D78">Septimò, aliquando dormire dicitur turbo cum celerrimè mouetur, <lb/>defixo &longs;cilicet axe in eodem loco, & &longs;itu, ratio petitur ex eo quòd ver<lb/>tex certè componitur cum ip&longs;o plano factâ &longs;ibi veluti in&longs;en&longs;ibili apo<lb/>theca &longs;eu fo&longs;&longs;ula, cuius tenuis margo impedit motum centri; igitur mo<lb/>tus orbis vnicus e&longs;t, igitur maior. </s>

<s id="N26D86">Octauò, verbere adigitur trochus, <expan abbr="ip&longs;i&qacute;ue">ip&longs;ique</expan> imprimitur primò motus <lb/>orbis, quia lora illa &longs;cuticæ trocho aduoluta, vbi deinde explicantur, tro<lb/>chum ip&longs;um circumagunt: </s>

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<s id="N272B2">Decimò, cum manus &longs;u&longs;tinet aliquod pondus immobiliter, non <lb/>producit in eo impetum; </s>

<s id="N272B8">Primò, quia, &longs;i non producitur impe<lb/>tus in alijs partibus vnitis, licèt animatis, multò minùs in alijs; </s>

<s id="N272BE"><lb/>Secundò, quia codem modo &longs;u&longs;tinetur pondus à manu, quo ab alio <lb/>corpore inanimo, v. g. à men&longs;a; </s>

<s id="N272BE"><lb/>Secundò, quia eodem modo &longs;u&longs;tinetur pondus à manu, quo ab alio <lb/>corpore inanimo, v. g. à men&longs;a; </s>

<s id="N272C9">&longs;ed hæc non producit impetum in <lb/>pondere, quod &longs;u&longs;tinet, vt dicam paulò pò&longs;t; </s>

<s id="N272CF">Tertiò, quia fru&longs;trà pro<lb/>duceretur; </s>

<s id="N272D5">quia modò manus &longs;u&longs;tinens &longs;tet immobilis; haud dubiè etiam <lb/>&longs;ublato omni extrin&longs;eco impetu à pondere adhuc &longs;u&longs;tinebitur. </s>

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<s id="N276FA">adde quod mollities manus ad extinguendum ictum poti&longs;&longs;imum <lb/>confert; analogiam habes in lana, quæ tormentorum vim penitus <lb/>eneruat. </s>

<s id="N27704">Quartò, vt longiùs repellatur pila, &longs;ecundus modus adhiberi debet <lb/>critque motus mixtus ex directo & reflexo. </s>

<s id="N27704">Quartò, vt longiùs repellatur pila, &longs;ecundus modus adhiberi debet <lb/>eritque motus mixtus ex directo & reflexo. </s>

<s id="N2770B"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 6.<emph.end type="center"/></s>

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<s id="N2778B">ita <lb/>etiam non producitur quando fru&longs;trà e&longs;&longs;et, &longs;i produceretur; e&longs;t enim <lb/>par vtrimque ratio. </s>

<s id="N27795">Quartò, hinc licèt trahatur ingens rupes, non propterea mouetur, <lb/>quia non pote&longs;t impetus produci in omnibus illius partibus ab applica<lb/>ta potentia; igitut in nulla per Th.33.l.1. </s>

<s id="N2779F">Dices, e&longs;t cau&longs;a nece&longs;&longs;aria applicata. </s>

Line 17604

Line 17603

<s id="N27BAC">impellens producit impetum in &longs;e ip&longs;e; 2&degree;. </s>

<s id="N27BB0">impetus impellentis pro<lb/>ducit impetum in corpore. </s>

<s id="N27BB5">3&degree;. </s>

<s id="N27BB8">&longs;ingulis in&longs;tantibus de&longs;truitur aliquid <lb/>impetus impellentis, & impulfi. </s>

<s id="N27BB8">&longs;ingulis in&longs;tantibus de&longs;truitur aliquid <lb/>impetus impellentis, & impul&longs;i. </s>

<s id="N27BBD">4&degree;. </s>

<s id="N27BC0">initio difficiliùs mobile mouetur <lb/>impul&longs;u. </s>

<s id="N27BC5">5&degree;. </s>

Line 17877

Line 17876

<s id="N280F9">dico H eodem tempore L con<lb/>ficere tantùm &longs;patium prioris &longs;ubquadruplum; </s>

<s id="N280FF">igitur duplo tem<lb/>pore conficit &longs;patium K: </s>

<s id="N28105">&longs;ed æqualibus temporibus acquiruntur <lb/>æqualia velocitatis momenta motu accelerato; </s>

<s id="N2810B">igitur vbi H confi<lb/>cit &longs;patium K, habet &longs;ubduplam velocitatem illius, quam habet I <lb/>confecto codem &longs;patio K; </s>

<s id="N2810B">igitur vbi H confi<lb/>cit &longs;patium K, habet &longs;ubduplam velocitatem illius, quam habet I <lb/>confecto eodem &longs;patio K; </s>

<s id="N28113">&longs;ed moles H e&longs;t quadrupla molis I; </s>

<s id="N28117">igi<lb/>tur impetus H e&longs;t duplus impetu I; </s>

<s id="N2811D">igitur duplò maior ictus: </s>

Line 17991

Line 17990

<s id="N28374">haud dubiè A tanget &longs;olum AB ex G, antequam B de&longs;cendat in B <lb/>ex H; </s>

<s id="N2837A">igitur attemperandus e&longs;t motus fu&longs;tis DA; </s>

<s id="N2837E">præterea pondus in <lb/>de&longs;cen&longs;u auget ictum, deinde B de&longs;cendit deor&longs;um motu orbis & motu <lb/>centri: </s>

<s id="N28386">præterea B pote&longs;t in a&longs;cen&longs;u maiorem arcum &longs;ui orbis decurre<lb/>re, quàm in de&longs;cen&longs;u, vel æqualem: denique maior e&longs;t ictus quando po<lb/>tentia toto ni&longs;u euitente fu&longs;tis AB plùs temporis ante ictum in &longs;uo mo<lb/>tu in&longs;umit. </s>

<s id="N28386">præterea B pote&longs;t in a&longs;cen&longs;u maiorem arcum &longs;ui orbis decurre<lb/>re, quàm in de&longs;cen&longs;u, vel æqualem: denique maior e&longs;t ictus quando po<lb/>tentia toto ni&longs;u euidente fu&longs;tis AB plùs temporis ante ictum in &longs;uo mo<lb/>tu in&longs;umit. </s>

<s id="N28392">Decimotertiò, e&longs;t etiam aliud flagelli genus pluribus catenulis ferreis <lb/>in&longs;tructi, ex quibus &longs;ingulis &longs;inguli ferrei globi aliquando &longs;piculis, & <lb/>clauis armati pendent, quorum graui&longs;&longs;imus e&longs;t ictus propter rationes <lb/>prædictas; </s>

Line 18015

Line 18014

<s id="N2840B">igitur potentia <lb/>manet diutiùs applicata; </s>

<s id="N28411">igitur maiorem effectum producit, vnde re<lb/>uocare pote&longs;t: hunc effectum ad illud phænomenum baculi flexibilis, <lb/>de quo &longs;uprà. </s>

<s id="N28419">Octauò, hinc pueri &longs;trophiolis prædicto modo inflexis <lb/>inter &longs;e contendunt, pro quo e&longs;t eadem ratio. </s>

<s id="N2841E">Nonò, hinc vt excutiatur <lb/>puluis ex pannis, codem modo &longs;uccutiuntur; </s>

<s id="N2841E">Nonò, hinc vt excutiatur <lb/>puluis ex pannis, eodem modo &longs;uccutiuntur; </s>

<s id="N28424">tùm propter ten&longs;ionem <lb/>filorum, quæ pulueri liberiores meatus aperit; </s>

<s id="N2842A">tùm propter vibrationes <lb/>quæ puluerem abigunt: </s>

<s id="N28430">immò flexibus aduer&longs;is tapetes ita &longs;uccutiun<lb/>tur, vt flexus hinc inde currentes qua&longs;i tumentes fluctus, &longs;ibi inuicem <lb/>occurrant in medio tapete, & allidantur; </s>

Line 18049

Line 18048

<s id="N284AF">Quintò, velocitates extremitatum, po&longs;ita diuer&longs;a longitudine manu<lb/>brij, &longs;unt vt ip&longs;æ longitudines permutando: </s>

<s id="N284B5">probatur, quia cùm &longs;it mo<lb/>tus acceleratus, &longs;patia &longs;unt vt quadrata temporum; &longs;ed velocitates <lb/>&longs;unt vt tempora, & tempora &longs;unt in ratione &longs;ubduplicata &longs;patiorum. </s>

<s id="N284BD"><lb/>id e&longs;t, vt diametri quadratorum, id e&longs;t, vt longitudines, &longs;it enim lon<lb/>gitudo AB, quæ dato tempore H decurrat &longs;patium ABF, potentia <pb pagenum="399" xlink:href="026/01/433.jpg"/>&longs;cilicet toto ni&longs;u applicata, &longs;it etiam longitudo AC dupla AB: </s>

<s id="N284C9">dico <lb/>quod eodum tempore H acquiret æquale &longs;patium &longs;cilicet CAD; </s>

<s id="N284C9">dico <lb/>quod eodem tempore H acquiret æquale &longs;patium &longs;cilicet CAD; </s>

<s id="N284CF">igitur <lb/>CAD e&longs;t 1/4 CAG, quia e&longs;t æquale BAF; </s>

<s id="N284D5">igitur CD e&longs;t 1/4 CG, &longs;ed <lb/>CG e&longs;t duplus BF; </s>

<s id="N284DB">igitur CD e&longs;t &longs;ubduplus BF; </s>

Line 18057

Line 18056

<s id="N284E5">adde quod AC cùm <lb/>numerus partium AC &longs;it duplus numeri partium AB, & cùm in eadem <lb/>proportione di&longs;tribuatur impetus AC, & AB; certè partes maioris &longs;i <lb/>comparentur cum partibus proportionalibus minoris, &longs;ubduplam tan<lb/>tùm habebunt portionem. </s>

<s id="N284F3">Sextò, ictus inflicti à malleis, quorum manubria diuer&longs;am longitu<lb/>dinem habent, &longs;uppo&longs;ito codem angulo, &longs;unt vt longitudines; </s>

<s id="N284F3">Sextò, ictus inflicti à malleis, quorum manubria diuer&longs;am longitu<lb/>dinem habent, &longs;uppo&longs;ito eodem angulo, &longs;unt vt longitudines; </s>

<s id="N284F9">&longs;i enim <lb/>eo tempore, quo AB facit &longs;patium BAF, AC facit CAD; </s>

<s id="N284FF">certè æquali <lb/>tempore AC faciet DAG, vt con&longs;tat ex natura motus accelerati; </s>

<s id="N28505"><lb/>igitur acquirit <expan abbr="tant&utilde;dem">tantundem</expan> impetus; </s>

Line 18067

Line 18066

<s id="N28520">igitur ictus &longs;unt in ratione &longs;ubdupli<lb/>cata CAG, BAF; igitur vt ACAB. </s>

<s id="N28528">Septimò, diceret aliquis velocitatem C decur&longs;o CD, e&longs;&longs;e &longs;ubduplam <lb/>vclocitatis B decur&longs;o BF; </s>

<s id="N28528">Septimò, diceret aliquis velocitatem C decur&longs;o CD, e&longs;&longs;e &longs;ubduplam <lb/>velocitatis B decur&longs;o BF; </s>

<s id="N2852E">&longs;ed velocitas C, decur&longs;o CG, e&longs;t dupla velo<lb/>citatis eiu&longs;dem C decur&longs;o CD; </s>

<s id="N28534">igitur velocitas C, decur&longs;o CG, e&longs;t <lb/>æqualis velocitati B, decur&longs;o BF; igitur æqualis ictus. </s>

<s id="N2853A">Re&longs;p. conce&longs;&longs;a <lb/>primâ con&longs;equentiâ, vltimâ verò negatâ; </s>

<s id="N28540">quia non tantùm impetus <lb/>puncti C incutit ictum &longs;ed totius CA, qui cen&longs;etur e&longs;&longs;e collectus in <lb/>malleo in quo e&longs;t qua&longs;i centrum huius impetus, vt iam explicuimus <lb/>aliàs; &longs;ed velocitas totius CA confecto CAD e&longs;t æqualis velocitati <lb/>totius BA confecto BAF, cuius velocitas CA confecto CAG e&longs;t dupla, <lb/>vt iam probatum e&longs;t. </s>

<s id="N28550">Octanò, hinc ictus CA confecto CAD e&longs;t æqualis ictui AB con<lb/>fecto BAF, & ictus CA confecto CI duplo CD e&longs;t ad ictum CA con<lb/>fecto CD, vt radix CA ad radicem CI: </s>

<s id="N28550">Octauò, hinc ictus CA confecto CAD e&longs;t æqualis ictui AB con<lb/>fecto BAF, & ictus CA confecto CI duplo CD e&longs;t ad ictum CA con<lb/>fecto CD, vt radix CA ad radicem CI: </s>

<s id="N28558">hinc vides hunc motum con<lb/>uenire in eo cum recto, quòd &longs;cilicet ictus inflictus motu recto à mi<lb/>nori mole, &longs;it ad ictum maioris, &longs;uppo&longs;ita linea motus æquali in ratio<lb/>ne &longs;ubduplicata ponderum; quòd dicitur etiam de motu circulari duo<lb/>rum fu&longs;tium inæqualium, quorum ictus &longs;unt in ratione &longs;ubduplicata <lb/>longitudinum, a&longs;&longs;umptis duntaxat arcubus æqualibus ab extremitate <lb/>vtriu&longs;que decur&longs;is. </s>

<s id="N2856A">Nonò, cum mallei &longs;unt diucr&longs;i ponderis, & longitudinis, facilè co<lb/>gno&longs;ci poterit proportio ictuum; </s>

<s id="N2856A">Nonò, cum mallei &longs;unt diuer&longs;i ponderis, & longitudinis, facilè co<lb/>gno&longs;ci poterit proportio ictuum; </s>

<s id="N28570">e&longs;t enim compo&longs;ita ex ratione lon<lb/>gitudinum & &longs;ubduplicata ponderum v.g. &longs;it malleus A, cuius longitu<lb/>do &longs;it 2. pondus 4. &longs;it malleus B cuius longitudo &longs;it pondus; </s>

<s id="N2857A">rectè ra<lb/>tio longitudinum e&longs;t 2/3, & &longs;ubduplicata ponderum e&longs;t 2/3; </s>

<s id="N28580">ducatur vna <lb/>in aliam, vt cuadat compo&longs;ita &longs;cilicet 4/1 vel longitudo A &longs;it I, & B 2; </s>

<s id="N28580">ducatur vna <lb/>in aliam, vt euadat compo&longs;ita &longs;cilicet 4/1 vel longitudo A &longs;it I, & B 2; </s>

<s id="N28586"><lb/>habebitur ratio &longs;ubduplicata ponderum 2/<gap/>, & ratio longitudinum 2/1; </s>

<s id="N28586"><lb/>habebitur ratio &longs;ubduplicata ponderum 2/1, & ratio longitudinum 3/2; </s>

<s id="N2858D"><lb/>ducatur v<gap/>a in aliam, habebitur ratio compo&longs;ita 2/2; </s>

<s id="N2858D"><lb/>ducatur vna in aliam, habebitur ratio compo&longs;ita 2/2; </s>

<s id="N28594">igitur &longs;unt æqua-<pb pagenum="400" xlink:href="026/01/434.jpg"/>les, quæ omnia facilè intelliguntur ex dictis; </s>

<s id="N2859D">itaque habes 4. combina<lb/>tiones duorum malleorum; </s>

<s id="N285A3">vel enim e&longs;t idem pondus vtrique, & ea<lb/>dem longitudo, vel idem pondus, &longs;ed diuer&longs;a longitudo, vel eadem lon<lb/>gitudo & diuer&longs;um pondus, vel diuer&longs;um pondus & diuer&longs;a longitudo; <lb/>&longs;i verò e&longs;t diuer&longs;a longitudo &longs;imal, & diuer&longs;um pondus, vel eidem ine&longs;t <lb/>maius pondus, & maior longitudo, vel maior longitudo, & minus pou<lb/>dus, & contrà alteri minor lougitudo, & minus pondus, vel maius pon<lb/>dus, & minor longitudo, quorum omnium proportiones &longs;unt determi<lb/>natæ. </s>

<s id="N285A3">vel enim e&longs;t idem pondus vtrique, & ea<lb/>dem longitudo, vel idem pondus, &longs;ed diuer&longs;a longitudo, vel eadem lon<lb/>gitudo & diuer&longs;um pondus, vel diuer&longs;um pondus & diuer&longs;a longitudo; <lb/>&longs;i verò e&longs;t diuer&longs;a longitudo &longs;imul, & diuer&longs;um pondus, vel eidem ine&longs;t <lb/>maius pondus, & maior longitudo, vel maior longitudo, & minus pon<lb/>dus, & contrà alteri minor longitudo, & minus pondus, vel maius pon<lb/>dus, & minor longitudo, quorum omnium proportiones &longs;unt determi<lb/>natæ. </s>

<s id="N285B7">Decimò, quod &longs;pectat ad cra&longs;&longs;itudinem manubrij, illa haud dubiè <lb/>auget aliquando vim ictus, aliquando imminuit; </s>

Line 18104

Line 18103

<s id="N28605">&longs;i verò &longs;unt eiu&longs;dem ponderis, & cadunt <lb/>ex diuer&longs;a altitudine impetus acqui&longs;iti motu naturali, &longs;unt in ratione <lb/>&longs;ubduplicata altitudinum; </s>

<s id="N2860D">&longs;i verò &longs;unt diuer&longs;i ponderis, & cadunt ex <lb/>diuer&longs;a altitudine, &longs;unt in ratione compo&longs;ita aliquomodo ex vtraque; </s>

<s id="N28613"><lb/>dico aliquo modo, quia non e&longs;t omninò propria compo&longs;itio rationum; </s>

<s id="N28618"><lb/>pote&longs;t tamen facilè proportio ictuum inueniri, v. g. &longs;it malleus A, & <lb/>malleus B, ictns A ratione impetus impre&longs;&longs;i extrin&longs;ecxs &longs;it vt 8, ratione <lb/>ca&longs;us &longs;it vt 2; </s>

<s id="N28618"><lb/>pote&longs;t tamen facilè proportio ictuum inueniri, v. g. &longs;it malleus A, & <lb/>malleus B, ictus A ratione impetus impre&longs;&longs;i extrin&longs;ecus &longs;it vt 8, ratione <lb/>ca&longs;us &longs;it vt 2; </s>

<s id="N28625">at verò ictus B ratione impetus impre&longs;&longs;i &longs;it vt 6, ratione <lb/>ca&longs;us vt 3: </s>

<s id="N2862B">addantur 8, & 2 erunt 10; </s>

<s id="N2862F">adduntur 6, & 3 erunt 9; </s>

<s id="N28633">igitur <lb/>ictus &longs;unt in ratione (10/9), vt con&longs;tat: </s>

<s id="N28639">porrò quemadmodum nouus im<lb/>petus accedit ratione motus naturalis, cum malleus impingitur dcos<lb/>&longs;um, ita aliquid impetus de&longs;truitur cum malleus impingitur &longs;ur&longs;um, vt <lb/>patet; </s>

<s id="N28639">porrò quemadmodum nouus im<lb/>petus accedit ratione motus naturalis, cum malleus impingitur deor<lb/>&longs;um, ita aliquid impetus de&longs;truitur cum malleus impingitur &longs;ur&longs;um, vt <lb/>patet; </s>

<s id="N28643">denique, quia &longs;unt 5 termini, quos re&longs;picit ictus, &longs;cilicet pondus <lb/>mallei, longitudo manubrij, cra&longs;&longs;itudo arcus extremitatis, & linea &longs;ur<lb/>fum vel deor&longs;um, ita &longs;unt 25. combinationes ictuam; &longs;ed hoc fa<lb/>cile e&longs;t. </s>

<s id="N28643">denique, quia &longs;unt 5 termini, quos re&longs;picit ictus, &longs;cilicet pondus <lb/>mallei, longitudo manubrij, cra&longs;&longs;itudo arcus extremitatis, & linea &longs;ur<lb/>&longs;um vel deor&longs;um, ita &longs;unt 25. combinationes ictuum; &longs;ed hoc fa<lb/>cile e&longs;t. </s>

Line 18125

Line 18124

<s id="N28681">&longs;it enim centrum grauitatis clauæ I, in quo &longs;i <lb/>&longs;u&longs;tineatur, &longs;tabit in æquilibrio; </s>

<s id="N28687">ducatur FIE, maiorem ictum <lb/>infliget ex puncto E, quia <expan abbr="tant&utilde;dem">tantundem</expan> e&longs;t impetus in &longs;egmento <lb/>FEK quantum in &longs;egmento FEA; </s>

<s id="N28693">igitur totus impeditur impe<lb/>tus; igitur maximus erit ictus &longs;i infligat ictum motu circulari circa <lb/>aliud e&longs;t centrum percu&longs;&longs;ionis, de quo infrà. </s>

<s id="N2869B">Tertiò, hoe percu&longs;&longs;io<lb/>nis organum validum ictum infligit propter illam extremam cra&longs;<lb/>&longs;itudinem, e&longs;t enim quoddam mallei genus, & valdè periculo&longs;um; </s>

<s id="N2869B">Tertiò, hoc percu&longs;&longs;io<lb/>nis organum validum ictum infligit propter illam extremam cra&longs;<lb/>&longs;itudinem, e&longs;t enim quoddam mallei genus, & valdè periculo&longs;um; </s>

<s id="N286A3"><lb/>præ&longs;ertim &longs;i ferreis clauis armetur; </s>

<s id="N286A8">hinc vulgò tribuitur Herculi tan<lb/>quam in&longs;igne fortitudinis &longs;ymbolum; porrò tàm altè clauum infigit <lb/>&longs;ibi coniunctum, quam infigeret, &longs;i claua ip&longs;a erectum, & qua&longs;i expe<lb/>ctantem ictum feriret. </s>

<s id="N286B4">Decimoquartò, Tudicula maior reuocatur ad malleum. </s>

<s id="N286B7">Primò <lb/>faciunt ad ictum longitudo manubrij, flexibilitas, inæqualitas, mal<lb/>lei pondus, durities materiæ, arcus motus, vegetæ potentiæ vires; </s>

<s id="N286BF"><lb/>omitto ea, quæ cum malleo habet communia, quorum ratio ex <lb/>dictis conftare pote&longs;t; igitur non videntur e&longs;&longs;e repetenda. </s>

<s id="N286BF"><lb/>omitto ea, quæ cum malleo habet communia, quorum ratio ex <lb/>dictis con&longs;tare pote&longs;t; igitur non videntur e&longs;&longs;e repetenda. </s>

<s id="N286C6">Secundò, <lb/>flexibilitas manubrij auget vim ictus, tùm quia potentia diutiùs <lb/>manet applicata, cùm aliquo tempore in ip&longs;a vibratione malleus à <lb/>tergo relinquatur, tùm quia potentia illa media, de qua &longs;upra, &longs;uum <lb/>impetum, impetui alterius adiungit. </s>

<s id="N286D1">Tertiò, ita manubrium fa<lb/>bricatur, vt continua imminutione ver&longs;us malleum decre&longs;cat, quod <lb/>multum facit ad ictum, quia hæc inæqualitas inflexioni re&longs;i&longs;tit ver<lb/>&longs;us caput manubrij; </s>

<s id="N286DB">igitur initio inflectitur manubrium, non pro<lb/>cul à mallco, tùm deinde aucto impetu in partibus remotioribus, <lb/>quæ difficiliùs inflectuntur; </s>

<s id="N286DB">igitur initio inflectitur manubrium, non pro<lb/>cul à malleo, tùm deinde aucto impetu in partibus remotioribus, <lb/>quæ difficiliùs inflectuntur; </s>

<s id="N286E3">igitur inæqualiter partes illæ redeunt, <lb/>atque &longs;e&longs;e pri&longs;tino &longs;tatui re&longs;tituunt; </s>

<s id="N286E9">atqui ex illa inæqualitate diu<lb/>tiùs durat motus; </s>

<s id="N286EF">igitur inde maior cuadit: </s>

<s id="N286EF">igitur inde maior euadit: </s>

<s id="N286F3">&longs;imile quid videmus in <lb/>arcu, cuius medium cra&longs;&longs;ius e&longs;t: adde quod &longs;i æqualis &longs;it cra&longs;&longs;itudo, <lb/>incipit inflexio ver&longs;us illam extremitatem, quæ propiùs accedit ad <lb/>manum, longiùs recedit à malleo, vt patet experientiâ, in fune, <lb/>virgâ &c. </s>

<s id="N286FF">&longs;ed de arcu, ten&longs;ione, compre&longs;&longs;ione fusè agemus <lb/>tractatu &longs;ingulari: </s>

<s id="N28705">hæc tantum obiter indica&longs;&longs;e &longs;ufficiat. <pb pagenum="402" xlink:href="026/01/436.jpg"/>Quartò, maximus e&longs;t ictus, cum malleus eo in&longs;tanti attingic pilam, quo <lb/>manubrium e&longs;t rectum; </s>

<s id="N28710">tunc enim e&longs;t modum vibrationis &longs;eu reditus; <lb/>igitur maximus impetus. </s>

<s id="N28716">Quintò, &longs;i altera extremitas mallei, quæ glo<lb/>bum attingit, &longs;it obliqua, globum ip&longs;um attollit propter punctum con<lb/>tactus; quod certè clarum e&longs;t. </s>

<s id="N2871E">Sextò, durities mallei multùm facit ad <lb/>ictum; </s>

<s id="N28724">&longs;i enim cedat lignum, imminuitur impetus, vt patet; hinc ar<lb/>millâ, vel annulo ferreo armatur vtraque ba&longs;is mallei, vt finnior eua<lb/>dat. </s>

<s id="N28724">&longs;i enim cedat lignum, imminuitur impetus, vt patet; hinc ar<lb/>millâ, vel annulo ferreo armatur vtraque ba&longs;is mallei, vt firmior eua<lb/>dat. </s>

<s id="N2872C">Septimò, globi ratio multa habenda e&longs;t, cui infligitur ictus; </s>

<s id="N28730">quippe <lb/>&longs;i leuior e&longs;t ab aëre ambiente impeditur, & retinetur; </s>

<s id="N28736">&longs;i verò mollior <lb/>minor ictus infligitur, quia cedit materies; </s>

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<s id="N28778"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 14.<emph.end type="center"/></s>

<s id="N28786"><emph type="italics"/>Ex dictis explicaris po&longs;&longs;um omnia ph&oelig;nomena, quæ ob&longs;erumtur in lu<gap/><lb/>rudis gladiatoriæ<emph.end type="italics"/>; </s>

<s id="N28786"><emph type="italics"/>Ex dictis explicaris po&longs;&longs;um omnia ph&oelig;nomena, quæ ob&longs;eruantur in ludo <lb/>rudis gladiatoriæ<emph.end type="italics"/>; </s>

<s id="N28792">Primo, tria &longs;unt in hac arte, ad quæ reliqua facilè re<lb/>ducuntur; </s>

<s id="N28798">primum e&longs;t declinatio; &longs;ecundum petitio; tertium confla<lb/>tum ex vtroque. </s>

<s id="N2879E">Secundò, pote&longs;t declinati, vel auerti ictus, &longs;eu petitio <lb/>duobus modis. </s>

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<s id="N287A5">Primò, &longs;i declinatio cum aliqua impactione coniungatur. </s>

<s id="N287AA">Secundò, &longs;i tantùm cum inera re&longs;i&longs;tentia, vel &longs;implici impul<lb/>&longs;ione. <lb/><arrow.to.target n="note4"/></s>

<s id="N287AA">Secundò, &longs;i tantùm cum mera re&longs;i&longs;tentia, vel &longs;implici impul<lb/>&longs;ione. <lb/><arrow.to.target n="note4"/></s>

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<s id="N287CE">&longs;iue enim duo gladij <lb/>AC, DF, capulares pilæ AD; </s>

<s id="N287D4">&longs;it autem gladius AC declinans petitio<lb/>nem alterius DF; id certè quatuor modis præ&longs;tare pote&longs;t. </s>

<s id="N287DA">Primò, &longs;i <lb/>punctum contactus ad mucronem vtriu&longs;que propiùs accedat. </s>

<s id="N287DF">v.g. &longs;i <lb/>vterque &longs;it in &longs;itu ACDF. Secundò, &longs;i propiùs accedat ad capulum <lb/>vtriu&longs;que, talis e&longs;t &longs;itus DFCH. Tertiò, &longs;i accedat propiùs ad mu<lb/>cronem gladij petentis DF, & propiùs ad capulum declinanti<gap/>. <pb pagenum="403" xlink:href="026/01/437.jpg"/>Quartò, è contrario &longs;i accedat propiùs ad capulum petentis DF, & pro<lb/>piùs ad mucronem declinantis; addi pote&longs;t quinta combinatio, cum <lb/>&longs;cilicet contactus e&longs;t in medio vtriu&longs;que. </s>

<s id="N287DF">v.g. &longs;i <lb/>vterque &longs;it in &longs;itu ACDF. Secundò, &longs;i propiùs accedat ad capulum <lb/>vtriu&longs;que, talis e&longs;t &longs;itus DFCH. Tertiò, &longs;i accedat propiùs ad mu<lb/>cronem gladij petentis DF, & propiùs ad capulum declinantis. <pb pagenum="403" xlink:href="026/01/437.jpg"/>Quartò, è contrario &longs;i accedat propiùs ad capulum petentis DF, & pro<lb/>piùs ad mucronem declinantis; addi pote&longs;t quinta combinatio, cum <lb/>&longs;cilicet contactus e&longs;t in medio vtriu&longs;que. </s>

<s id="N287F8">Quartò, &longs;i &longs;it mera impul&longs;io &longs;ine percu&longs;&longs;ione, vel impactione, maxi<lb/>ma vis e&longs;t declinationis, cum punctum contactus accedit propiùs ad ca<lb/>pulum declinantis, & ad mucronem petentis iuxta tertiam combinatio<lb/>nem, & &longs;itum DFPE, & punctum contactus in B; </s>

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<s id="N28888">Nonò, &longs;i primo modo declinatur ictus repul&longs;o petentis gladio maxi<lb/>ma vis erit; &longs;i punctum contactus fiat circa 2/3 de quo infrà, quod verò <lb/>&longs;pectat ad gladium, qui repellitur, eò faciliùs repellitur, quò punctum <lb/>contactus propiùs ad eius mucronem accedet. </s>

<s id="N28892">Si tertio modo, & gla<lb/>dius &longs;olus ita libraretur maxima vis e&longs;&longs;et circa centrum eius grauitatis; </s>

<s id="N28898"><lb/>in hoc enim puncto maximum ictum infligunt, quæ motu recto mo<lb/>uentur; quia verò totum &longs;egmentum brachij, qnod inter manum, & <pb pagenum="404" xlink:href="026/01/438.jpg"/>caput cubiti intercipitur, mouetur &longs;imul cum gladio motu recto, circa <lb/>capulum erit maxima vis, cùm propiùs accedat ad centrum grauitatis <lb/>totius conflati ex illo &longs;egmento brachij, & gladio. </s>

<s id="N28898"><lb/>in hoc enim puncto maximum ictum infligunt, quæ motu recto mo<lb/>uentur; quia verò totum &longs;egmentum brachij, quod inter manum, & <pb pagenum="404" xlink:href="026/01/438.jpg"/>caput cubiti intercipitur, mouetur &longs;imul cum gladio motu recto, circa <lb/>capulum erit maxima vis, cùm propiùs accedat ad centrum grauitatis <lb/>totius conflati ex illo &longs;egmento brachij, & gladio. </s>

<s id="N288AA">Decimò, denique &longs;i &longs;ecundo modo declinetur ictus, idem dicendum <lb/>e&longs;t quod de motu circulari dictum, mutato dumtaxat centro, v.g. &longs;it gla<lb/>dius declinantis RG, &longs;itque IG 1/4 totius RG circa I &longs;it motus circula<lb/>tis, centrum percu&longs;&longs;ionis erit circa 2/3 IG, vel IR. </s>

<s id="N288B7">Vndecimò, vix tamen ita acuratè hoc &longs;ecundo modo declinatur ictus, <lb/>quin tertius etiam cum &longs;ecundo coniunctus &longs;it, vt patet experientiâ; </s>

<s id="N288BD"><lb/>rotatur autem manus delcinantis vt illo qua&longs;i gyro maiorem impetum <lb/>acquirat, de quo iam &longs;uprà: immò ni&longs;i tertius modus cum &longs;ecundo e&longs;&longs;et <lb/>coniunctus, non po&longs;&longs;et delinari ictus, &longs;i contactus gladiorum fieret in <lb/>centro illius motus, vt patet. </s>

<s id="N288BD"><lb/>rotatur autem manus declinantis vt illo qua&longs;i gyro maiorem impetum <lb/>acquirat, de quo iam &longs;uprà: immò ni&longs;i tertius modus cum &longs;ecundo e&longs;&longs;et <lb/>coniunctus, non po&longs;&longs;et delinari ictus, &longs;i contactus gladiorum fieret in <lb/>centro illius motus, vt patet. </s>

<s id="N288CA">Duodecimò, quò longior e&longs;t gladius declinantis, cum iuxta mucro<lb/>nem fit contactus &longs;ine impactione e&longs;t vis debilior, quàm e&longs;&longs;et in breuio<lb/>re, patet ex vecte; &longs;i verò &longs;it impactio iuxta &longs;ecundum. </s>

<s id="N288D2">n.10. vis maior <lb/>e&longs;t cum gladius longior e&longs;t; </s>

<s id="N288D8">e&longs;t enim maior motus; </s>

<s id="N288DC">igitur maior ictus li<lb/>cèt tardior; </s>

<s id="N288E2">hinc longiore gladiore equidem fortiùs auertitur ictus quàm <lb/>breuiore, &longs;ed tardiùs; breuiore verò citiùs quàm longiore, &longs;ed debiliùs, <lb/>vt patet ex dictis. </s>

<s id="N288E2">hinc longiore gladio equidem fortiùs auertitur ictus quàm <lb/>breuiore, &longs;ed tardiùs; breuiore verò citiùs quàm longiore, &longs;ed debiliùs, <lb/>vt patet ex dictis. </s>

<s id="N288EC">Decimotertiò, longior gladius &longs;u&longs;tinetur facilè opera capularis pilæ, <lb/>quæ momentum longitudinis gladij &longs;upplet, vt con&longs;tat ex &longs;tatera, cuius <lb/>proportiones videbimus lib.&longs;eq. </s>

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<s id="N28924">verùm etiam corpus detegitur: <lb/>adde quod ictus validior e&longs;t per lineam perpendicularem. </s>

<s id="N2892C">Decimo&longs;extò, hinc ita debet extremitas manus per hor&longs;zontalem <lb/>porrigi & brachium contractum explicari, vt maiorem lineam rectam <lb/>de&longs;cribat; </s>

<s id="N2892C">Decimo&longs;extò, hinc ita debet extremitas manus per horizontalem <lb/>porrigi & brachium contractum explicari, vt maiorem lineam rectam <lb/>de&longs;cribat; </s>

<s id="N28934">acquiritur enim maior impetus in maiori &longs;patio, quod per<lb/>curritur motu accelerato, vt con&longs;tat ex dictis, &longs;ed quò brachium con<lb/>tractius e&longs;t, cò maiorem lineam eius extremitas motu recto decurrit: <lb/>adde quod impre&longs;&longs;io totius corporis, quod in <expan abbr="eãdem">eandem</expan> partem agitur, <lb/>multùm auget vim brachij mucronem in aduer&longs;um pectus inten<lb/>tantis. </s>

<s id="N28948">Decimo&longs;eptimò, &longs;i longior e&longs;t gladius impetus, hæc videntur e&longs;&longs;e <lb/>commoda. </s>

<s id="N2894D">Primò, eius mucro longiùs producitur, & procul attingit. <pb pagenum="405" xlink:href="026/01/439.jpg"/>Secundò maiorem ictum infligit, vt iam &longs;upra dictum e&longs;t de &longs;ari&longs;&longs;a, mo<lb/>dò in eadem ratione aucta &longs;it cra&longs;&longs;itudo; non de&longs;unt tamen incommo<lb/>moda. </s>

<s id="N2895A">Primò ratione vectis maius e&longs;t illius pondus. </s>

<s id="N2895D">Secundò faciliùs de<lb/>clinatur ictus propter <expan abbr="eãdem">eandem</expan> ratiodem. </s>

<s id="N2895D">Secundò faciliùs de<lb/>clinatur ictus propter <expan abbr="eãdem">eandem</expan> rationem. </s>

<s id="N28966">Tertiò, &longs;i tantillùm deflecte<lb/>tur, corpus omninò detegit propter maiorem cum, &longs;unt enim arcus <lb/>vt radij, vel longitudines. </s>

<s id="N2896D">Quartò, hinc pugiles faciliùs decu&longs;&longs;atis gla<lb/>dijs &longs;e&longs;e mutuò præhendunt, & luctâ decernunt. </s>

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<s id="N289D0"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 23.<emph.end type="center"/></s>

<s id="N289DE"><emph type="italics"/>Explieari po&longs;&longs;unt omnia ph&oelig;nomena percu&longs;&longs;ionis, quæ infligitur à <lb/>serpore graui deor&longs;um &longs;ua &longs;ponte cadente motu naturaliter accele<lb/>rato.<emph.end type="italics"/></s>

<s id="N289DE"><emph type="italics"/>Explicari po&longs;&longs;unt omnia ph&oelig;nomena percu&longs;&longs;ionis, quæ infligitur à <lb/>corpore graui deor&longs;um &longs;ua &longs;ponte cadente motu naturaliter accele<lb/>rato.<emph.end type="italics"/></s>

<s id="N289EB">Primò, corpus graue cadens ex maiore altitudine fortiùs ferit: ratio <lb/>e&longs;t; </s>

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<s id="N28A03">Secundò, &longs;unt 4. combinationes grauium; </s>

<s id="N28A07">vel enim e&longs;t idem pondus <lb/>e&longs;t altitudo; </s>

<s id="N28A0D">vel idem pondus, diuer&longs;a altitudo; </s>

<s id="N28A11">vel eadem altitudo di<lb/>uer&longs;um poudus; </s>

<s id="N28A11">vel eadem altitudo di<lb/>uer&longs;um pondus; </s>

<s id="N28A17">vel diuer&longs;um pondus & diuer&longs;a altitudo; addi pote&longs;t <lb/>diuer&longs;us incidentiæ angulus, immò diuer&longs;a figura corporis cadentis, quæ <lb/>omnia infrà demon&longs;trabimus. </s>

<s id="N28A21">Tertiò, &longs;i &longs;it æquale pondus, & æqualis altitudo &longs;uppo&longs;ito ca&longs;u <pb pagenum="406" xlink:href="026/01/440.jpg"/>perpendiculari æquales &longs;unt ictus, patet; quia eadem cau&longs;a <expan abbr="e&utilde;dem">eundem</expan> h<gap/><lb/>bet eflectum. </s>

<s id="N28A33">Quartò, &longs;i &longs;it æquale pondus, & inæqualis altitudo, ictus &longs;unt in ra<lb/>tione &longs;ubduplicata altitudinum v.g. &longs;it altitudo 4. cubitorum, & altera <lb/>tautum cubitalis; </s>

<s id="N28A3D">certè cùm acquirantur æqualibus temporibus æqua<lb/>lia velocitatis momenta, velocitates acqui&longs;itæ &longs;unt vt tempora, impetus <lb/>vt velocitates, ictus vt impetus; </s>

<s id="N28A45">&longs;ed tempora &longs;unt in ratione &longs;ubdupli<lb/>cata &longs;patiorum vel altitudinem; </s>

<s id="N28A4B">igitur & ictus; igitur ictus inflictus à <lb/>corpore cadente ex altitudine 4. cubitorum e&longs;t duplus ictus eiu&longs;dem <lb/>corporis cadentis ex altitudine cubitali. </s>

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<s id="N28A67">Sextò, &longs;i &longs;int infinita in&longs;tantia, e&longs;t infinita proportio inter actum in<lb/>flictum à corpore cadente, & vim grauitationis eiu&longs;dem; </s>

<s id="N28A6D">quia dato quo<lb/>cunque tempore po&longs;&longs;et dari minnus, & minus; igitur dato puocunque <lb/>ictu po&longs;&longs;et dari minor, & minor in infinitum, quod ex illa hypothe&longs;i <lb/>nece&longs;&longs;ariò con&longs;equitur. </s>

<s id="N28A6D">quia dato quo<lb/>cunque tempore po&longs;&longs;et dari minus, & minus; igitur dato quocunque <lb/>ictu po&longs;&longs;et dari minor, & minor in infinitum, quod ex illa hypothe&longs;i <lb/>nece&longs;&longs;ariò con&longs;equitur. </s>

<s id="N28A79">Septimò, immò &longs;i &longs;int infinita in&longs;tantia, &longs;ique infinita proportio in<lb/>ter ictum inflictum à corpore cadente, & vim grauitationis eiu&longs;dem, e&longs;t <lb/>etiam infinita proportio inter <expan abbr="eumd&etilde;ictum">eumdenictum</expan>, & vim grauitationis cuiu&longs;<lb/>libet alterius corporis quantumuis immen&longs;i, inter duas grauitationes <lb/>duorum corporum datur proportio, vt con&longs;tat; </s>

<s id="N28A79">Septimò, immò &longs;i &longs;int infinita in&longs;tantia, &longs;ique infinita proportio in<lb/>ter ictum inflictum à corpore cadente, & vim grauitationis eiu&longs;dem, e&longs;t <lb/>etiam infinita proportio inter <expan abbr="eumd&etilde;">eumdem</expan> ictum, & vim grauitationis cuiu&longs;<lb/>libet alterius corporis quantumuis immen&longs;i, inter duas grauitationes <lb/>duorum corporum datur proportio, vt con&longs;tat; </s>

<s id="N28A89">&longs;unt enim vt pondera; <lb/>igitur &longs;i nullam habet proportionem cum ictu corporis grauis cadentis, <lb/>nullam etiam habebit altera, vt patet ex elementis. </s>

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<s id="N28AA9">Nonò, &longs;i altitudo &longs;it diuer&longs;a, & pondus diuer&longs;um, ictus &longs;unt in ratione <lb/>compo&longs;ita ex ratione ponderum, & &longs;ubduplicata altitudinum, patet ex <lb/>dictis. </s>

<s id="N28AB2">Decimò, &longs;i &longs;int infinita in&longs;tantia dato ictu cuiu&longs;libet corporis caden<lb/>tis ex quacunque altitudine, non pote&longs;t dari vlla corporis mo<gap/>s, qua <lb/>&longs;uo pondere id præ&longs;tat, quod illud præ&longs;titit &longs;uo ca&longs;u. </s>

<s id="N28AB2">Decimò, &longs;i &longs;int infinita in&longs;tantia dato ictu cuiu&longs;libet corporis caden<lb/>tis ex quacunque altitudine, non pote&longs;t dari vlla corporis moles, qua <lb/>&longs;uo pondere id præ&longs;tat, quod illud præ&longs;titit &longs;uo ca&longs;u. </s>

<s id="N28ABB">Probatur ex n. </s>

<s id="N28ABE">7. <lb/>hinc fru&longs;trà proponitur hæc quæ&longs;tio ab ijs, qui agno&longs;cunt infinitos tar<lb/>ditatis gradus, per quos propagatur motus; nam reuerâ ex hac hypothe&longs;i <lb/>e&longs;t infinita proportio inter ictum, & vim grauitationis. </s>

<s id="N28ACA">Vndecimò, &longs;i tamen ponantur finita in&longs;tantia; </s>

<s id="N28ACE">haud dubiè hæcpro<lb/>po&longs;itio non e&longs;t infinita; </s>

<s id="N28AD4">&longs;it enim quodlibet corpus cadens ex quacun<lb/>que data altitudine per 100. in&longs;tantia, &longs;cu partes temporis æquales pri<lb/>mo in&longs;tanti quo mouetur; </s>

<s id="N28AD4">&longs;it enim quodlibet corpus cadens ex quacun<lb/>que data altitudine per 100. in&longs;tantia, &longs;eu partes temporis æquales pri<lb/>mo in&longs;tanti quo mouetur; </s>

<s id="N28ADC">haud dubiè ictus ab eo inflictus cadendo e&longs;t <pb pagenum="407" xlink:href="026/01/441.jpg"/>ad vim grauitationis eiu&longs;dem vt 1001. ad 1. cùm enim &longs;ingulis in&longs;tan<lb/>tibus æqualibus acquirantur æqualia velocitatis momenta, &longs;eu æqualis <lb/>impetus; </s>

<s id="N28AE9">certè 1000. in&longs;tantibus, quibus mouetur acqui&longs;iuit 1000. gra<lb/>uus impetus æquales primo, quem habebat in ptima grauitatione; </s>

<s id="N28AE9">certè 1000. in&longs;tantibus, quibus mouetur acqui&longs;iuit 1000. gra<lb/>dus impetus æquales primo, quem habebat in prima grauitatione; </s>

<s id="N28AEF">& <lb/>qui fuit cau&longs;a motus primi in&longs;tantis; </s>

<s id="N28AF5">igitur &longs;i hic addatur 1000. erunt <lb/>1001. hinc &longs;i corpus moueatur tantùm vno in&longs;tanti, ictus erit duplus <lb/>tantùm grauitationis: &longs;uppono autem nullam e&longs;&longs;e medij re&longs;i&longs;tentiam, <lb/>ictumque infligi per lineam directam. </s>

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<s id="N28B21">Decimotertiò, hinc non pote&longs;t determinari proportio corporis ca<lb/>dentis, & grauitantis, ni&longs;i ex hypothe&longs;i; </s>

<s id="N28B27">quia nemo &longs;cit quot fluxerint <lb/>iu&longs;tantia in dato motu; </s>

<s id="N28B27">quia nemo &longs;cit quot fluxerint <lb/>in&longs;tantia in dato motu; </s>

<s id="N28B2D">qaod reuerâ &longs;ciri po&longs;&longs;et &longs;i po&longs;&longs;et aliqua arte in<lb/>ueniri corpus, cuius grauitatio haberet <expan abbr="effect&utilde;">effectum</expan>, quem habet alteriusictus, <lb/>qnod nec &longs;ciri pote&longs;t per depre&longs;&longs;um cylindrum cereum vel <expan abbr="plumbe&utilde;">plumbeum</expan>, vel <lb/>alterius mollioris materiæ, quia æqualis depre&longs;&longs;io accuratè cogno&longs;ci non <lb/>pote&longs;t; &longs;i quis enim diceret dee&longs;&longs;e, vel &longs;upere&longs;&longs;e 1000. &longs;uperficies, quà <lb/>ratione conuinci po&longs;&longs;et? </s>

<s id="N28B2D">quoad reuerâ &longs;ciri po&longs;&longs;et &longs;i po&longs;&longs;et aliqua arte in<lb/>ueniri corpus, cuius grauitatio haberet <expan abbr="effect&utilde;">effectum</expan>, quem habet alterius ictus, <lb/>quod nec &longs;ciri pote&longs;t per depre&longs;&longs;um cylindrum cereum vel <expan abbr="plumbe&utilde;">plumbeum</expan>, vel <lb/>alterius mollioris materiæ, quia æqualis depre&longs;&longs;io accuratè cogno&longs;ci non <lb/>pote&longs;t; &longs;i quis enim diceret dee&longs;&longs;e, vel &longs;upere&longs;&longs;e 1000. &longs;uperficies, quà <lb/>ratione conuinci po&longs;&longs;et? </s>

<s id="N28B43">non pote&longs;t etiam &longs;ciri operâ libræ, in cuius al<lb/>terum brachium cadat mobile, quia &longs;unt ferè infiniti motus in&longs;en&longs;ibiles, <lb/>vt con&longs;ideranti patebit; igitur proportio hæc tantùm, determinari pote&longs;t <lb/>ex hypothe&longs;i data, vt clari&longs;&longs;imè con&longs;tat ex dictis. </s>

<s id="N28B4F">Decimoquartò, hinc maxima e&longs;t proportio inter ictum, & grauita<lb/>tionem; </s>

<s id="N28B55">cùm modicus malleoli ca&longs;us eum effectum præ&longs;tet, quem in<lb/>gens corporis moles &longs;ua grauitatione præ&longs;tare non po&longs;&longs;et; </s>

<s id="N28B5B">non e&longs;t tamen <lb/>infinita proportio, quia pote&longs;t tanta e&longs;&longs;e moles grauitatis, & tam par<lb/>uum corporis cadentis pondus, vt illa præualeat, vt con&longs;tat experientiâ, <lb/>quæ nobis cuidenti&longs;&longs;imam &longs;uggerit rationem; </s>

<s id="N28B5B">non e&longs;t tamen <lb/>infinita proportio, quia pote&longs;t tanta e&longs;&longs;e moles grauitatis, & tam par<lb/>uum corporis cadentis pondus, vt illa præualeat, vt con&longs;tat experientiâ, <lb/>quæ nobis euidenti&longs;&longs;imam &longs;uggerit rationem; </s>

<s id="N28B65">quia reiicimus infinitos <lb/>illos tarditatis gradus, quos a&longs;&longs;ump&longs;it Galilæus ad probandam &longs;uam <lb/>hypothe&longs;im de motu accelerato, & infinita &longs;iu&longs;dem & aliorum multo<lb/>rum in&longs;tantia, de quibus alibi in Metaphy&longs;icâ; </s>

<s id="N28B65">quia reiicimus infinitos <lb/>illos tarditatis gradus, quos a&longs;&longs;ump&longs;it Galilæus ad probandam &longs;uam <lb/>hypothe&longs;im de motu accelerato, & infinita eiu&longs;dem & aliorum multo<lb/>rum in&longs;tantia, de quibus alibi in Metaphy&longs;icâ; </s>

<s id="N28B6F">e&longs;t tamen maxima illa <lb/>proportio, vt dixi; </s>

<s id="N28B75">quia perexigua temporis pars infinitis ferè in&longs;tanti<lb/>tibus con&longs;tat; </s>

<s id="N28B75">quia perexigua temporis pars infinitis ferè in&longs;tanti<lb/>bus con&longs;tat; </s>

<s id="N28B7B">quorum certè numerum recen&longs;ere po&longs;&longs;emus, &longs;i quis mo<lb/>dum inueniat, quo po&longs;&longs;it ab&longs;olutè adæquare grauitationis dati corporis <lb/>effectum cum effectu ictus alterius cadentis: quod meo iudicio non <lb/>modo geometricè, vetùm etiam mechanicè, &longs;altem accuratè fieri non <lb/>pote&longs;t. </s>

<s id="N28B7B">quorum certè numerum recen&longs;ere po&longs;&longs;emus, &longs;i quis mo<lb/>dum inueniat, quo po&longs;&longs;it ab&longs;olutè adæquare grauitationis dati corporis <lb/>effectum cum effectu ictus alterius cadentis: quod meo iudicio non <lb/>modo geometricè, verùm etiam mechanicè, &longs;altem accuratè fieri non <lb/>pote&longs;t. </s>

<s id="N28B89">Decimoquintò, nec illud, quod habet Dominus Hobs apud Mer&longs;en<lb/>num, in ph&oelig;nom. </s>

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<s id="N28B9D">Secundò, quia dicit cona-<pb pagenum="408" xlink:href="026/01/442.jpg"/>tum primum puncti AC, & totius axis AB, quamdiu de&longs;cendit vterque, <lb/>e&longs;&longs;e æqualem; </s>

<s id="N28BA8">quod tamen dici non pote&longs;t, quia conatus &longs;ingulorum <lb/>punctorum &longs;eor&longs;im &longs;unt æquales; </s>

<s id="N28BAE">&longs;ed conatus omnium coniunctim e&longs;t <lb/>maior conatu &longs;ingulorum; </s>

<s id="N28BB4">nam &longs;ingula habent &longs;uum impetum; verum <lb/>e&longs;t quidem moueri motu æquali, quia &longs;ingula æquali impetu moueutur. </s>

<s id="N28BB4">nam &longs;ingula habent &longs;uum impetum; verum <lb/>e&longs;t quidem moueri motu æquali, quia &longs;ingula æquali impetu mouentur. </s>

<s id="N28BBA"><lb/>Tertiò, quia vult po&longs;ito cylindro &longs;upra ba&longs;im 4. illam immediatè premi <lb/>à puncto EB, hoc verò punctum à puncto DE, & hoc ab CD, & hoc ab <lb/>AC; </s>

<s id="N28BC3">quod tamen dici non pote&longs;t; quis enim dicat granulum &longs;uperpo&longs;i<lb/>tum rupi in illam grauitare? </s>

<s id="N28BC9">Equidem cum illa grauitat grauitatione <lb/>communi, vt dictum e&longs;t &longs;uprà, non tamen in illam. </s>

<s id="N28BCE">Quartò, quia dicit <lb/>pumum B cum conatu totius cylinèri incubantis eo tempore, quo pun<lb/>ctum AC conficeret AC, conficere AB, quod repugnat progre&longs;&longs;ioni <lb/>Galilei, quam &longs;equitur ip&longs;e; </s>

<s id="N28BD8">puia conatus &longs;unt, vt velocitates; </s>

<s id="N28BD8">quia conatus &longs;unt, vt velocitates; </s>

<s id="N28BDC">hæ verò <lb/>vt tempora; &longs;ed &longs;patia in ratione duplicata temporum. </s>

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<s id="N28C61">Decimononò, &longs;i æqualis &longs;it &longs;ecundus ictus. </s>

<s id="N28C64">Primò, pote&longs;t determina<lb/>ri proportio iuxta quam defigitur palus, quod vt melius explicetur, &longs;it<lb/>cuneus BE, cuius &longs;olidum facilè demon&longs;tratur; </s>

<s id="N28C6C">e&longs;t enim &longs;ubduplum pa<lb/>rallelipedi, cuius ba&longs;is &longs;it quadratum AC, & altitudo RE; </s>

<s id="N28C72">&longs;i enim trian<lb/>gulum ADE ducatur in latus AB vel EF habebitur &longs;olidum cunci, vt <lb/>con&longs;tat, vnde cunei eiu&longs;dem latitudinis &longs;unt, vt triangula, v.g. cuneus A <lb/>F ad cumdem YF; </s>

<s id="N28C7E">vt triangulum ADE ad triangulum YHE: </s>

<s id="N28C82">hoc po<lb/>&longs;ito &longs;it triangulum MKN æqualis ADF, & primo ictu tota EI vel N <lb/>Z &longs;ecundo ictu defigitur, non quidem æquali altitudinc, &longs;ed æquali &longs;oli<lb/>do; </s>

<s id="N28C8C">cùm autem triangulum XZN &longs;it &longs;ubquadruplum trianguli QON <lb/>&longs;it media proportionalis Ninter NZNO, triangulum N<foreign lang="greek">b</foreign> Y e&longs;t du<lb/>plum NZX; </s>

<s id="N28C98">igitur &longs;ecundo ictu defigetur N<foreign lang="greek">b</foreign>: </s>

<s id="N28CA0">&longs;imiliter &longs;i vt NZ ad N <lb/><foreign lang="greek">b</foreign>, ita N<foreign lang="greek">b</foreign> ad N. Tertio, ita defigetur NT, & quarto NO dupla NI: ra<lb/>tio e&longs;t, quia æquales ictus æquales habent effectus. </s>

<s id="N28CB1">Vige&longs;imò, &longs;i æquales accipiantur altitudines &longs;ingulis ictibus, ictus <lb/>&longs;unt in ratione duplicata altitudinum, &longs;uppo&longs;itâ prædicta hypothe&longs;i cunei <lb/>v.g.&longs;i dato ictu defigatur NZ, & altero NO, &longs;ecundus e&longs;t ictus quadruplus <lb/>primi; </s>

<s id="N28CBB">&longs;i verò tertio ictu defigatur N<foreign lang="greek">q</foreign> tripla NZ, ictus e&longs;t ad primum <lb/>in ratione 9/1. &longs;i denique dato ictu defigatur NM, ictus e&longs;t ad primum <lb/>in ratione (26/<gap/>), vt patet ex dictis; &longs;i verò primo ictu defigatur NZ, &longs;ecundo <lb/>ZO, tertio O<foreign lang="greek">q</foreign>, quarto <foreign lang="greek">q</foreign>M, ictus &longs;unt, vt numeri impares 1. <lb/>3. 7. 9. </s>

<s id="N28CBB">&longs;i verò tertio ictu defigatur N<foreign lang="greek">q</foreign> tripla NZ, ictus e&longs;t ad primum <lb/>in ratione 9/1. &longs;i denique dato ictu defigatur NM, ictus e&longs;t ad primum <lb/>in ratione 36/3, vt patet ex dictis; &longs;i verò primo ictu defigatur NZ, &longs;ecundo <lb/>ZO, tertio O <foreign lang="greek">q</foreign>, quarto <foreign lang="greek">q</foreign> M, ictus &longs;unt, vt numeri impares 1. <lb/>3. 7. 9. </s>

<s id="N28CD7">Vige&longs;imoprimò, hinc &longs;i dentur duo ictus, & eorum proportio deter<lb/>minari, vt pote&longs;t proportio altitudinum, quæ defiguntur, quæ &longs;unt in <lb/>ratione &longs;ubduplicata ictuum, &longs;uppo&longs;ito cuneo: </s>

<s id="N28CDF">&longs;imiliter, &longs;i dentur alti<lb/>tudines, carumque proportio, determinari pote&longs;t proportio ictum; </s>

<s id="N28CE5">&longs;unt <lb/>enim in ratione duplicata, vt patet ex dictis; porrò vtrumque pote&longs;t <lb/>con&longs;iderari duobus modis. </s>

<s id="N28CED">Primò, coniunctim, &longs;i &longs;ecundus ictus &longs;ucce<lb/>d<gap/> primo, & eius altitudinem augeat. </s>

<s id="N28CED">Primò, coniunctim, &longs;i &longs;ecundus ictus &longs;ucce<lb/>dat primo, & eius altitudinem augeat. </s>

<s id="N28CF4">Secundò, &longs;i &longs;eor&longs;im vterque <lb/>con&longs;ideretur, &c. </s>

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<s id="N28D26">Vige&longs;imotertiò, pote&longs;t explicari quomodo deprimatur cylindrus con<lb/>&longs;tans ex molliori materia; </s>

<s id="N28D2C">nam primò deptimitur prima &longs;uperficies <lb/>cylindri, & extenditur; quia cùm materia. </s>

<s id="N28D2C">nam primò deprimitur prima &longs;uperficies <lb/>cylindri, & extenditur; quia cùm materia. </s>

<s id="N28D32">&longs;it mollior, prematurque a <lb/>duobus corporibus duris vtrinque, &longs;cilicet ab vtraque ba&longs;i, cedit & di<lb/>latatur propter humorem in cauitatibus contentum. </s>

<s id="N28D39">Secundò, aliquan<lb/>do totus cylindrus deprimitur &longs;eruatà &longs;emper cylindri licet cra&longs;&longs;io<lb/>ris figurâ, quod vt fiat, molli&longs;&longs;imam materiam e&longs;&longs;e nece&longs;&longs;e e&longs;t. </s>

<s id="N28D40">Ter-<pb pagenum="410" xlink:href="026/01/444.jpg"/>tiò, aliquando primæ tantùm &longs;uperficies extenduntur, vt videmus in <lb/>capite, &longs;eu ba&longs;i cuncorum; quia materies durior multùm re&longs;i&longs;tit. </s>

<s id="N28D40">Ter-<pb pagenum="410" xlink:href="026/01/444.jpg"/>tiò, aliquando primæ tantùm &longs;uperficies extenduntur, vt videmus in <lb/>capite, &longs;eu ba&longs;i cuneorum; quia materies durior multùm re&longs;i&longs;tit. </s>

<s id="N28D4B">Quartò, <lb/>limbus ba&longs;is dilatatæ contrahitur deinde, &longs;eu retorquetur deor&longs;um; </s>

<s id="N28D51">quia <lb/>cùm interiores circuli dilatentur, deberet facere limbus ille maiorem <lb/>circulum; quod cùm fieri non po&longs;&longs;it, contrahitur &longs;eu incuruatur deor<lb/>&longs;um, quod facilè &longs;ine figura intelligi pote&longs;t. </s>

<s id="N28D5B">Quintò, pote&longs;t deter<lb/>minari proportio ictuum, quibus deprimuntur cyiindri; </s>

<s id="N28D5B">Quintò, pote&longs;t deter<lb/>minari proportio ictuum, quibus deprimuntur cylindri; </s>

<s id="N28D61">&longs;i enim &longs;up<lb/>ponatur eadem altitudo, &longs;eu linea depre&longs;&longs;ionis, & diuer&longs;a cra&longs;&longs;i<lb/>tudo cylindrorum ictus, erunt vt ba&longs;es; </s>

<s id="N28D69">nam quò plures partes de<lb/>primendæ &longs;unt, maiore ictu opus e&longs;t, &longs;i opponatur eadem cra&longs;&longs;itudo <lb/>vtriu&longs;que cylindri &longs;ed diuer&longs;a depre&longs;&longs;ionis linea vel altitudo, ictus <lb/>erunt vt altitudines; </s>

<s id="N28D73">&longs;i vtraque &longs;upponitur diuer&longs;a, ictus erunt in ra<lb/>rione compo&longs;ita ex ratione ba&longs;ium, & altitudinum; quæ omnia con&longs;tant <lb/>ex dictis. </s>

<s id="N28D73">&longs;i vtraque &longs;upponitur diuer&longs;a, ictus erunt in ra<lb/>tione compo&longs;ita ex ratione ba&longs;ium, & altitudinum; quæ omnia con&longs;tant <lb/>ex dictis. </s>

<s id="N28D7D">Ob&longs;eruabis tamen cre&longs;cere re&longs;i&longs;tentiam ex duplici capite. </s>

<s id="N28D80">Primò, <lb/>ex eo quod aliquæ vacuitates occupentur à partibus depre&longs;&longs;is, ac proin<lb/>de cylindrus induretur; &longs;ic incus durior cuadit &longs;ub mallco, & & pila <lb/>lignea &longs;ub ictibus. </s>

<s id="N28D80">Primò, <lb/>ex eo quod aliquæ vacuitates occupentur à partibus depre&longs;&longs;is, ac proin<lb/>de cylindrus induretur; &longs;ic intus durior euadit &longs;ub malleo, & & pila <lb/>lignea &longs;ub ictibus. </s>

<s id="N28D8A">Secundò, latiorem illam &longs;uperficiem impedire di<lb/>latationem aliarum partium: </s>

<s id="N28D90">hinc variè di&longs;cerpitur eius limbus, vt <lb/>videre e&longs;t in cuneo ferreo: </s>

<s id="N28D96">atqui in explicandis &longs;uprà ictuum propor<lb/>tionibus, hoc geminum re&longs;i&longs;tentiæ caput nullo modo con&longs;iderauimus: </s>

<s id="N28D9C"><lb/>&longs;extò, quærunt aliqui dato ictu, quo deprimitur cylindrus data alti<lb/>tudine, quantum pondus e&longs;&longs;e debeat, quod &longs;ua grauitatione cum<lb/>dem præ&longs;tet effectum; &longs;ed profectò id nemo vnquam determinauit, <lb/>ni&longs;i primò inueniat pondus, cuius ca&longs;u prædictus cylindrus codem <lb/>modo deprimatur. </s>

<s id="N28D9C"><lb/>&longs;extò, quærunt aliqui dato ictu, quo deprimitur cylindrus data alti<lb/>tudine, quantum pondus e&longs;&longs;e debeat, quod &longs;ua grauitatione eum<lb/>dem præ&longs;tet effectum; &longs;ed profectò id nemo vnquam determinauit, <lb/>ni&longs;i primò inueniat pondus, cuius ca&longs;u prædictus cylindrus eodem <lb/>modo deprimatur. </s>

<s id="N28DA9">Secundò, ni&longs;i &longs;ciat quot in&longs;tantibus de&longs;cendat, vt <lb/>patet ex his quæ diximus &longs;uprà; vt autem comparetur ictus inflictus <lb/>à brachio cum ictu inflicto à pondere cadente, debet con&longs;uli diuer&longs;a <lb/>depre&longs;&longs;io, vel defixio. </s>

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<s id="N28EC1">ratio e&longs;t, quia maior impetus imprimitur Tudiculæ à potentia <lb/>diutiùs applicata; diutiùs autem applicatur maiori, quia tardiùs moue<lb/>tur, vt &longs;uprà diximus. </s>

<s id="N28ECB">Sextò, pila emi&longs;&longs;a veloci&longs;&longs;imè mouetur eo in&longs;tanti, quo vltimo tan<lb/>gitur à Tudicula; quia deinceps nihil pror&longs;us impetus accedit, ac proin<lb/>de continuò &longs;en&longs;im de&longs;truitur ab eo inftanti. </s>

<s id="N28ED5">Septimò, nunquam mouetur pila emi&longs;&longs;a velociùs ip&longs;a Tudiculâ, cum <lb/>&longs;cilicet emi&longs;&longs;io fit per meram impul&longs;ionem; </s>

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<s id="N28F40"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 17.<emph.end type="center"/></s>

<s id="N28F4E"><emph type="italics"/>Explicari poffunt omnia ph&oelig;nomena emi&longs;&longs;ionum, quæ fiunt cum perco&longs;&longs;ione.<emph.end type="italics"/></s>

<s id="N28F4E"><emph type="italics"/>Explicari po&longs;&longs;unt omnia ph&oelig;nomena emi&longs;&longs;ionum, quæ fiunt cum percu&longs;&longs;ione.<emph.end type="italics"/></s>

<s id="N28F57">Primò, &longs;it percu&longs;&longs;io minoris Tudiculæ v.g. eo maior e&longs;t, quò Tudi<lb/>cula maior e&longs;t; rationem iam attulimus &longs;uprà num.5.Th.16. </s>

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<s id="N28F73">Quartò, quod &longs;pectat ad Tudiculam maiorem, iam &longs;uprà explicuimus <lb/>cuncta illius ph&oelig;nomena, cum de malleo: certum e&longs;t enim primò ma<lb/>iorem à maiore ictum infligi, cæteris partibus, quàm à minore propter <lb/>prædictum rationem. </s>

<s id="N28F7D">Secundò, certum e&longs;t longitudinem manubrij fle<lb/>xibilitatem, inæqnalitatem, materiem, duritiem mallei, æqualitatem ba&longs;is <lb/>&c. </s>

<s id="N28F7D">Secundò, certum e&longs;t longitudinem manubrij fle<lb/>xibilitatem, inæqualitatem, materiem, duritiem mallei, æqualitatem ba&longs;is <lb/>&c. </s>

<s id="N28F84">multùm conferre ad maiorem cùm ictus. </s>

<s id="N28F87">Tertiò certum e&longs;t mino<lb/>rem globum, in quem impingitur Tudicula, citiùs moueri, inaiorem tar<lb/>diùs, cæteris paribus. </s>

<s id="N28F8E">Quartò, globus maior in alium impactus Tudiculâ <lb/>maiorem ictum infligit, vt con&longs;tat experientiâ; ratî; </s>

<s id="N28F94">e&longs;t, quia tardiùs <lb/>mouetur; </s>

<s id="N28F9A">igitur diutiùs applicatur: Equidem globus proiectus in alium <lb/>fortiorem ictum infligit ex duplici capite, vt dicam infrà. </s>

<s id="N28FA0">1&degree;. </s>

<s id="N28FA3">Quia ma<lb/>iorem impetum à potentia diutiùs applicata.2&degree;.Quia diutiùs applicatur <lb/>globo in quem impingitur; at verò quando impigitur Tudiculâ maiore, <lb/>ex duplici quoque capite cre&longs;cit ictus.1&degree;.quia globus globo diutiùs ma<lb/>net applicatus, cùm tardior motus dicat plùs temporis. </s>

<s id="N28FA3">Quia ma<lb/>iorem impetum à potentia diutiùs applicata.2&degree;.Quia diutiùs applicatur <lb/>globo in quem impingitur; at verò quando impingitur Tudiculâ maiore, <lb/>ex duplici quoque capite cre&longs;cit ictus.1&degree;.quia globus globo diutiùs ma<lb/>net applicatus, cùm tardior motus dicat plùs temporis. </s>

<s id="N28FAF">2&degree;. </s>

<s id="N28FB2">quia malleus <lb/>tardiorem motum imprimis globo; </s>

<s id="N28FB8">igitur diutiùs manet applicatus: e&longs;t <lb/>en<gap/>m hæc abta lex agentium, vt longiore tempore maior effectus produ<lb/>catur, minor verò minore, reliqua ex dictis facilè intelligentur. </s>

<s id="N28FB8">igitur diutiùs manet applicatus: e&longs;t <lb/>enim hæc abta lex agentium, vt longiore tempore maior effectus produ<lb/>catur, minor verò minore, reliqua ex dictis facilè intelligentur. </s>

<s id="N28FC4"><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 18.<emph.end type="center"/></s>

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<s id="N2903B">Quartò, leui&longs;&longs;imi lapides vix iaciuntur ad modicam di&longs;tantiam v. g. <lb/>granula &longs;abuli; ratio e&longs;t, 1&degree;. </s>

<s id="N29044">quia accipiunt minùs impetus, quia citiùs <lb/>&longs;eparantur à iaciente manu, vt patet. </s>

<s id="N29049">2&degree;. </s>

<s id="N2904C">quia mouetur initio velociùs i<gap/><lb/>aëre; </s>

<s id="N2904C">quia mouetur initio velociùs in <lb/>aëre; </s>

<s id="N29053">igitur &longs;ingulis in&longs;tantibus plùs impetus de&longs;truitur, vt con&longs;tat; nam <lb/>in maiori &longs;patio aëris e&longs;t maior re&longs;i&longs;tentia. </s>

<s id="N29059">3&degree;.quia cùm aër perpetuo <lb/>motu agitetur, vt certum e&longs;t, in leuiori corpore impetum imprimit; igi<lb/>tur aliam &longs;i&longs;tit vel deflectit. </s>

<s id="N29061">4&degree;.quia manu non pote&longs;t rectè prehendi ia<lb/>ciendus lapillus &c. </s>

<s id="N29068">Quintò, grauior lapis ad modicam tantùm diftantiam iacitur; ratio <lb/>e&longs;t 1&degree;.quia producitur remi&longs;&longs;ior impetus, cùm &longs;cilicet pluribus partibus <lb/>&longs;ubiecti di&longs;tribuatur. </s>

<s id="N29068">Quintò, grauior lapis ad modicam tantùm di&longs;tantiam iacitur; ratio <lb/>e&longs;t 1&degree;.quia producitur remi&longs;&longs;ior impetus, cùm &longs;cilicet pluribus partibus <lb/>&longs;ubiecti di&longs;tribuatur. </s>

<s id="N29070">2&degree;.quia impetus grauitationis citiùs de&longs;truit impe<lb/>tum extrin&longs;ecus aduenientem. </s>

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<s id="N2909D"><lb/>&longs