texts/archimedes/xml/gueva_mecha_005_la_1627.xml - Colored diff

Main History Search Repository tree

Return to gueva_mecha_005_la_1627.xml CVS log

Up to [CVSROOT] / texts / archimedes / xml

Colored diff for /texts/archimedes/xml/gueva_mecha_005_la_1627.xml between version 1.6 and 1.13

version 1.6, 2004/08/19 16:52:33

version 1.13, 2004/09/13 09:57:12

Line 954

<s id="N11E70">Refertur auté hoc quoque in&longs;tru<lb/>mentum ad vecté, eo quod ex duplici <lb/>vecte videatur con&longs;tare, vt infra qu&etail;&longs;t. <lb/></s>

<s id="N11E78">17. ex Ari&longs;totele magis ex profe&longs;&longs;o <lb/>probabitur. </s>

<s id="N11E7D">Etenim &longs;i con&longs;iderentur <lb/>duo eius latera, quæ ex ba&longs;i in aciem <lb/>terminantur, vt CE, & DE non &longs;e<lb/>cus ac duo vectes &longs;ibi inuicem obuer<lb/>&longs;i, & cóntra conantes reperientur, quo<lb/>rum <expan abbr="vtiq;">vtique</expan> fulc menta &longs;unt partes &longs;cin<lb/>dendi corporis vtrinque con&longs;titutæ vt <lb/>GH, quibus intrando cuneus innititur. </s>

<s id="N11E7D">Etenim &longs;i con&longs;iderentur <lb/>duo eius latera, quæ ex ba&longs;i in aciem <lb/>terminantur, vt CE, & DE non &longs;e<lb/>cus ac duo vectes &longs;ibi inuicem obuer<lb/>&longs;i, & cóntra conantes reperientur, quo<lb/>rum <expan abbr="vtiq;">vtique</expan> fulcimenta &longs;unt partes &longs;cin<lb/>dendi corporis vtrinque con&longs;titutæ vt <lb/>GH, quibus intrando cuneus innititur. </s>

<s id="N11E92">Onera verò &longs;unt re<lb/><figure id="id.005.01.070.2.jpg" xlink:href="005/01/070/2.jpg"/><lb/>reliquæ eiu&longs;dem corporis partes <lb/>&longs;ucce&longs;siuè dimouend&etail;, & adinui<lb/>cem &longs;eparádæ per aciem intran<lb/>tem vbi E, vt in propo&longs;ita figu <lb/>ra e&longs;t l, & K. </s>

<s id="N11E92">Onera verò &longs;unt re<lb/><figure id="id.005.01.070.2.jpg" xlink:href="005/01/070/2.jpg"/><lb/>reliquæ eiu&longs;dem corporis partes <lb/>&longs;ucce&longs;siuè dimouend&etail;, & adinui<lb/>cem &longs;eparándæ per aciem intran<lb/>tem vbi E, vt in propo&longs;ita figu<lb/>ra e&longs;t l, & K. </s>

<s id="N11EA6">Nam pars vbi K <lb/>e&longs;t onus re&longs;pectu vectis CE in<lb/>nixæ in G; & pars vbi I, e&longs;t <lb/>onus re&longs;pectu vectis DE innixæ <lb/>in H. </s>

<s id="N11EB2">Et extrema in quibus ap<lb/>plicatur potentia &longs;unt initia ip&longs;o<lb/>rum laterum ex parte ba&longs;is vbi <lb/>fit tota percu&longs;&longs;io, nempe vbi C <lb/>& D, quæ omnia aperti&longs;&longs;imè <lb/>citata quæ&longs;tione amplius con&longs;ta<lb/>bunt. </s>

Line 969

<s id="N11EEA">Etenim &longs;i in principio helicis <lb/>vbi C, onus congruè applicetur, vt <lb/>pila &longs;uper&longs;ignata H; ita tamen vt ex <lb/>aduer&longs;o non po&longs;&longs;it moueri, ni&longs;i &longs;uper <lb/>rectam IK, qua&longs;i intercepta inter cy<lb/>lindrum & planum quoddam paralle<lb/>lum cylindro; ab&longs;que dubio, ad cir<lb/>cumuolutionem manubrij totiu&longs;que <lb/>cylindri, pondus H paulatim a&longs;cendet <lb/>ex C ad D, deinde ad E & F, & &longs;ic <lb/>deinceps. </s>

<s id="N11F03">Idenique pote&longs;t exemplificari in. <lb/></s>

<s id="N11F03">Idemque pote&longs;t exemplificari in. <lb/></s>

<s id="N11F07">alia ip&longs;ius cochleæ figura æquidi&longs;tantis <lb/>ab horizonte, vt AB, &longs;i apponatur <lb/>illi onus CD, tanquam cylindri con<lb/>caui ac &longs;triati, qui & Tylum à Pappo, & alijs Mechanicis, <lb/><figure id="id.005.01.071.2.jpg" xlink:href="005/01/071/2.jpg"/><pb pagenum="64" xlink:href="005/01/072.jpg"/>& Cochleæ f&oelig;mina vulgò appellatur. </s>

<s id="N11F1B">Nam ad conuer&longs;io<lb/>nem manubrij totiu&longs;que cylindri &longs;uper proprium axem, <lb/>mouebitur etiam ip&longs;um Tylum CD. </s>

<s id="N11F23">Quæ omnia fusè Gui<lb/>dus Vbaldus demon&longs;trat. </s>

Line 1010

<s id="N11FF7">Quapropter &longs;i punctum <lb/>A fuerit centrum grauita<lb/><figure id="id.005.01.073.1.jpg" xlink:href="005/01/073/1.jpg"/><lb/>tis corporis BCD <expan abbr="quo-modocumq;">quo<lb/>modocumque</expan> diui&longs;i per <expan abbr="pla-nã">pla<lb/>nam</expan> EF tran&longs;euntem per ip<lb/>&longs;ummet centrum, atque <lb/>idem corpus ex eodem <lb/>puncto &longs;u&longs;penderetur, cer<lb/>tè quo ad po&longs;itionem ac <lb/>di&longs;po&longs;itionem &longs;uarum par<lb/>tium inuariatum omnino maneret; ita vt nullo pacto ip&longs;um <lb/>B, ac D verterentur circa punctum A tanquam circa cen<lb/>trum, &longs;ed eadem qua prius po&longs;itione manerent, &longs;iue pars <lb/>BEFC æqualis dimentionis inueniretur parti EDF, &longs;iue <lb/>inæqualis: &longs;emper enim &longs;ic coniunctæ æqueponderaret, e&longs;<lb/>&longs;entque æqualium momentorum. </s>

<s id="N12026">Cumque in his, quæ &longs;u<lb/>&longs;penduntur ex aliquo puncto, vel etiam &longs;ic &longs;u&longs;pen&longs;æ ferun<lb/>tur non detur motus circumuolutionis ab&longs;que exuperantia <lb/>alterius partis eorum, nec vna po&longs;&longs;it aliam &longs;uperare ni&longs;i per <lb/>exce&longs;&longs;um ponderis ip&longs;ius; hinc e&longs;t, vt immotæ ambæ ip&longs;æ <lb/>partes per&longs;euerarent tanquam in æquilibrio con&longs;titutæ. <lb/></s>

<s id="N12034">Idemque contingeret quocunque alio modo ip&longs;um corpus <pb pagenum="66" xlink:href="005/01/074.jpg"/>&longs;u&longs;pen&longs;um, aut etiam latum à principio con&longs;tirueretur. </s>

<s id="N1203E">Quod &longs;i contra definitionem, &longs;eu de&longs;criptionem tradi<lb/>tam afferatur, multa dari po&longs;&longs;e corpora talis figuræ, vt cen<lb/>trum grauitatis illorum non &longs;it intra, &longs;ed extra, quemadmo<lb/>dum exempli gratia in rota AB cuius quidem centrum <lb/>e&longs;&longs;et in C. </s>

Line 1034

<s id="N120C2"><expan abbr="Nullumq.">Nullumque</expan> e&longs;t inconueniens, idem corpus e&longs;&longs;e <lb/>po&longs;&longs;e mouens & motum, cum in corpore graui &longs;it potentia <lb/>receptiua motus, & grauitas, quæ e&longs;t <expan abbr="pot&etilde;tia">potentia</expan> effectiua illius. </s>

<s id="N120D2">Diximus verò grauia moueri deor&longs;um per <expan abbr="rectã">rectam</expan> lineam, <lb/>quæ centrum grauitatis ip&longs;orum, <expan abbr="centrumq.">centrumque</expan> mundi conne<lb/>ctit: Nam &longs;en&longs;u pariter con&longs;tat, illa non tendere ad ip&longs;um <lb/>mundi centrum per lineam aliquam obliquam, neque per <lb/>lineam rectam, quæ ab exrremo quoddam, vel quauis alia <lb/>parte ip&longs;ius ad mundi centrum extendatur, &longs;ed per <expan abbr="eã">eam</expan>, quam <lb/>diximus <expan abbr="lineã">lineam</expan>, quæ ab eius centro grauitatis rectà ad mun<lb/>di centrum propendet. </s>

<s id="N120D2">Diximus verò grauia moueri deor&longs;um per <expan abbr="rectã">rectam</expan> lineam, <lb/>quæ centrum grauitatis ip&longs;orum, <expan abbr="centrumq.">centrumque</expan> mundi conne<lb/>ctit: Nam &longs;en&longs;u pariter con&longs;tat, illa non tendere ad ip&longs;um <lb/>mundi centrum per lineam aliquam obliquam, neque per <lb/>lineam rectam, quæ ab extremo quoddam, vel quauis alia <lb/>parte ip&longs;ius ad mundi centrum extendatur, &longs;ed per <expan abbr="eã">eam</expan>, quam <lb/>diximus <expan abbr="lineã">lineam</expan>, quæ ab eius centro grauitatis rectà ad mun<lb/>di centrum propendet. </s>

<s id="N120F3">Omnis enim grauitas cuiu&longs;que <lb/>grauis ita in ip&longs;o grauitatis centro colligitur, & coacerua<lb/>tur, vt extra ip&longs;um nihil grauitare propemodum in corpori<lb/>bus videatur: <expan abbr="proindeq.">proindeque</expan> non ni&longs;i ip&longs;omet centro rectà deor<lb/>&longs;um eadem corpora ferri con&longs;picimus naturali propen&longs;io<lb/>ne. </s>

<s id="N12104">Quo pariter fit, vt &longs;i aliundè quàm ab ip&longs;ius grauitatis <lb/>centro graue aliquod &longs;u&longs;pendatur, &longs;tatim grauitatis centro <lb/>deor&longs;um tendente conuertatur, nec manere vnquam po&longs;&longs;it <lb/>donec ip&longs;um grauitatis centrum &longs;ub puncto &longs;u&longs;pen&longs;ionis per <lb/>lineam horizonti perpendicularem con&longs;tituatur. </s>

<s id="N1210F">Quando<lb/>quidem tunc idem e&longs;t, ac &longs;i corpus per ip&longs;ummet grauita<pb pagenum="68" xlink:href="005/01/076.jpg"/>tis centrum &longs;u&longs;penderetur, cum per eandem lineam ei li<lb/>ceat grauitare, vt latius ac rectè pro&longs;equitur Guidus Vbal<lb/>dus loco citato. </s>

Line 1050

<s id="N12147">Con&longs;tat enim hoc cum aperta deductione ex dictis de <lb/>mobilitate naturali, tùm clara ac patenti experientia; <lb/>ita vt nulla ferè indigeat probatione, aut explicatione, præ<lb/>&longs;ertim in doctrina Ari&longs;totelis, qui quantum attinet ad prin<lb/>cipium extrin&longs;ecum, à quo prouenire diximus præternatu<lb/>ralem motionem, cum 8 Phy&longs;icor. tex. 33. dixi&longs;&longs;et: Omnia, <lb/>quæ mouentur, aut natura moueri, aut præter naturam, ac <lb/>violentia; mox addit: Et quæ vi & præter naturam, omnia <lb/>à quodam, & ab alio. </s>

<s id="N1215E">Iuxta commune illud pronunciatum <lb/>à &longs;e prius traditum, & ab omnibus receptum nimirum, om<lb/>ne quod mouetur, ab alio moueri. </s>

<s id="N1215E">Iuxta commune illud pronuntiatum <lb/>à &longs;e prius traditum, & ab omnibus receptum nimirum, om<lb/>ne quod mouetur, ab alio moueri. </s>

<s id="N12165">Quod quippè loquendo <lb/>&longs;altem de motu præternaturali in rebus inanimatis, e&longs;t ir<lb/>refragabile. </s>

<s id="N1216E">Illud tamen apud nonnullos adhuc non e&longs;t omnino ex<lb/>ploratum, ac non paruam habet difficultatem, quo videli<lb/>cet pacto violentia ip&longs;a corporibus ab extrin&longs;eco inferatur; <lb/>quauè ratione, eadem corpora po&longs;tquam ab impul&longs;ore, vel <lb/>proijciente rece&longs;&longs;erint, ex &longs;e præternaturaliter moueantur. <pb pagenum="69" xlink:href="005/01/077.jpg"/>Quod cum partim ad merè phy&longs;icam &longs;peculationem perti<lb/>neat in 7. & 8. de phy&longs;ico auditu; partim verò in&longs;ra cum <lb/>Ari&longs;totele quæ&longs;t. </s>

<s id="N12182">32. & 33. explicandum &longs;it, hìc non erit <lb/>di&longs;cutiendum, &longs;ed tantum ex dicendis, ac probandis &longs;uppo<lb/>nere oportet, nullam vnquam inferri po&longs;&longs;e violentiam per <lb/>motum localem ab&longs;que productione, ac impre&longs;&longs;ione quali<lb/>tatis cuiu&longs;dam in ip&longs;o mobili, quæ communiter appellari &longs;o<lb/>let impetus &longs;iue impul&longs;us, ac de qua &longs;æpe nobis redibit &longs;er<lb/>mo in ijs quæ&longs;tionibus. </s>

Line 1074

<s id="N12209">Ve<lb/>ctionem verò e&longs;&longs;e motum per accidens; nam id quod vehi<lb/>tur ex co mouetur, quia e&longs;t in eo, quod mouetur. </s>

<s id="N12210">Quoniam <lb/>verò id quod vehit mouetur aut pul&longs;um, aut tractum, aut <lb/>vertigine actum, ex hoc infert, vt & Vectio tripliciter fieri <lb/>po&longs;sit, iuxta triplicem motum prædictum. </s>

<s id="N12219">Denique Verti<lb/>ginem ait e&longs;&longs;e motum compo&longs;itum ex tractione, & pul&longs;io<lb/>ne. </s>

<s id="N12220">Ad quas quippe quatuor &longs;pecies reuocari po&longs;&longs;unt aliæ <lb/>quamplures motiones præternaturales, ac violentæ, quibus <lb/>accommodata &longs;unt in&longs;trumenta, ac machinamenta, de qui<lb/>bus Additione prima egimus, cunctaquè alia, quæ ex illis <lb/>con&longs;lantur, vel ad ea reducuntur. </s>

<s id="N12220">Ad quas quippe quatuor &longs;pecies reuocari po&longs;&longs;unt aliæ <lb/>quam plures motiones præternaturales, ac violentæ, quibus <lb/>accommodata &longs;unt in&longs;trumenta, ac machinamenta, de qui<lb/>bus Additione prima egimus, cunctaquè alia, quæ ex illis <lb/>con&longs;tantur, vel ad ea reducuntur. </s>

<s id="N1222D">Quamobrem præternaturalis mobilitas grauium, ac le<lb/>nium pluries vocatur etiam artificio&longs;a. </s>

<s id="N12232">Nam licet interdum <lb/>à cau&longs;is naturalibus, nulla interueniente hominum indu&longs;tria <lb/>aut violentia, vis aliqua corporibus inferatur, qua præterna<lb/>turaliter ip&longs;a compelluntur moueri, vt cum ignitos lapides <lb/>è montibus quibu&longs;dam videmus erumpere, & in altum &longs;u<lb/>&longs;tolli; vel ferrea corpora à magnete &longs;ur&longs;um attrahi, ac pen<lb/>dentia&longs;u&longs;tineri. </s>

<s id="N12241">Sæpius tamen corpora non ni&longs;i artificio&longs;a <lb/>violentia ex indu&longs;tria ip&longs;is illata præternaturaliter, vt dice<lb/>bamus con&longs;tat moueri. </s>

<s id="N12248">Ita vt ctiam motus eorum præter<lb/>naturales, qui ab aliqua cau&longs;a naturali oriuntur, <expan abbr="aliosq.">aliosque</expan> &longs;imi<lb/>les, ad imitationem naturæ, ars ip&longs;a violentiam applicando, <lb/>augendo, minuendo, ac di&longs;tinguendo producat. </s>

<s id="N12248">Ita vt etiam motus eorum præter<lb/>naturales, qui ab aliqua cau&longs;a naturali oriuntur, <expan abbr="aliosq.">aliosque</expan> &longs;imi<lb/>les, ad imitationem naturæ, ars ip&longs;a violentiam applicando, <lb/>augendo, minuendo, ac di&longs;tinguendo producat. </s>

<s id="N12255">Vt per&longs;pi<lb/>cuè ob&longs;eruare e&longs;t in motibus violentis &longs;ulfurei pulueris <lb/>virtute, ac artis magi&longs;terio productis ad euerrendas moles, <lb/>explodendas ingentes pilas, ac diruendas portas vrbium, <lb/>ac munitionum: nec non in motibus, qui aéris, vel aquæ <lb/>bene&longs;icio multimoda cum arte di&longs;po&longs;ito fiunt, ad nauium <lb/>admirabilem lationem, <expan abbr="earumq.">earumque</expan> cur&longs;us moderationem; & <lb/>ad tam varios machinarum &longs;e mouentium, &longs;eu &longs;piritalium <lb/>v&longs;us, de quibus &longs;crip&longs;it Hero, cum in iis omnibus ars natu-<pb pagenum="71" xlink:href="005/01/079.jpg"/>ram æmulando, vel eam comitando magnopere elucear, <lb/>nec minus ad ip&longs;am vim præternaturaliter inferendam con<lb/>ducat. </s>

<s id="N12255">Vt per&longs;pi<lb/>cuè ob&longs;eruare e&longs;t in motibus violentis &longs;ulfurei pulueris <lb/>virtute, ac artis magi&longs;terio productis ad euerrendas moles, <lb/>explodendas ingentes pilas, ac diruendas portas vrbium, <lb/>ac munitionum: nec non in motibus, qui aéris, vel aquæ <lb/>beneficio multimoda cum arte di&longs;po&longs;ito fiunt, ad nauium <lb/>admirabilem lationem, <expan abbr="earumq.">earumque</expan> cur&longs;us moderationem; & <lb/>ad tam varios machinarum &longs;e mouentium, &longs;eu &longs;piritalium <lb/>v&longs;us, de quibus &longs;crip&longs;it Hero, cum in iis omnibus ars natu-<pb pagenum="71" xlink:href="005/01/079.jpg"/>ram æmulando, vel eam comitando magnopere elucear, <lb/>nec minus ad ip&longs;am vim præternaturaliter inferendam con<lb/>ducat. </s>

<s id="N12277">Ad hanc igitur motionem artificio&longs;am, ac præternatura<lb/>lem vniuer&longs;a facultas Mechaniça ordinatur, vt &longs;upra expli<lb/>cuimus: quatenus mirabili &longs;uo magiftcrio rationabiliter per <lb/>cau&longs;as procedendo, docet quo pacto grauia cuncta, aut le<lb/>uia po&longs;&longs;int &longs;ecundum omnem po&longs;itionem moueri, & cuius <lb/>virtute, quauè proportione illius ad pondus; in qua di&longs;tan<lb/>tia, <expan abbr="quibusq.">quibusque</expan> adminiculis, machinis, & in&longs;trumenris, & id ge<lb/>nus alia; quæ non parua ex parte con&longs;tabunt ex is, quæ <lb/>Ari&longs;toteles vltra &longs;uperius allata, & à nobis expo&longs;ita, in &longs;e<lb/>quentibus quæ&longs;tionibus tradit. </s>

<s id="N12277">Ad hanc igitur motionem artificio&longs;am, ac præternatura<lb/>lem vniuer&longs;a facultas Mechaniça ordinatur, vt &longs;upra expli<lb/>cuimus: quatenus mirabili &longs;uo magisterio rationabiliter per <lb/>cau&longs;as procedendo, docet quo pacto grauia cuncta, aut le<lb/>uia po&longs;&longs;int &longs;ecundum omnem po&longs;itionem moueri, & cuius <lb/>virtute, quauè proportione illius ad pondus; in qua di&longs;tan<lb/>tia, <expan abbr="quibusq.">quibusque</expan> adminiculis, machinis, & in&longs;trumentis, & id ge<lb/>nus alia; quæ non parua ex parte con&longs;tabunt ex is, quæ <lb/>Ari&longs;toteles vltra &longs;uperius allata, & à nobis expo&longs;ita, in &longs;e<lb/>quentibus quæ&longs;tionibus tradit. </s>

<s id="N12290">Cum alias exacta, & pe<lb/>culiaris vniu&longs;cuiu&longs;que grauis, aut leuis prout artificiosè mo<lb/>ueri debeat con&longs;ideratio, ad di&longs;tinctas Mechanicæ facul<lb/>tatis partes iam enumeratas, quas ip&longs;e Philo&longs;ophus non e&longs;t <lb/>aggre&longs;&longs;us; quippe qui vniuer&longs;alia duntaxat principia huius <lb/>admirabilis di&longs;ciplin&etail; in hac prima parte afferre &longs;tatuerit, <lb/>cau&longs;as po&longs;tea in &longs;ecunda parte allaturus eorum, quæ in &longs;e<lb/>quentibus quæ&longs;tionibus proponuntur ad maiorem explica<lb/>tionem, & applicationem eorundem principiorum, ex qui<lb/>bus aliæ infinitæ penè conclu&longs;iones po&longs;&longs;unt deduci. </s>

<s id="N122A7">Sed illud hic &longs;ummopere animaduertendum putauimus <lb/><expan abbr="Archimed&etilde;">Archimedem</expan>, quem iure inter huius di&longs;ciplinæ parentes opti<lb/>mos literæ omnes maxima cum laude commemerant, non <lb/>diuer&longs;a ab ijs, qu&etail; Ari&longs;toteles tradidit principia a&longs;&longs;ump&longs;i&longs;&longs;e, <lb/>ac in &longs;uis de æqueponderantibus libris protuli&longs;&longs;e, vt falsò <lb/>nonnulli commini&longs;cuntur; quinimò tradita ab ip&longs;o Philo&longs;o<lb/>pho &longs;uppo&longs;ui&longs;&longs;e, & amplius, ad particularia de&longs;cendendo, <lb/>extendi&longs;&longs;e, ac planiora reddidi&longs;&longs;e, vt ingenuè fatetur Guidus <lb/>Vbaldus in Præfatione primi de æqueponderantibus libri <lb/><expan abbr="eiu&longs;d&etilde;">eiu&longs;dem</expan> Archimedis. </s>

<s id="N122A7">Sed illud hic &longs;ummopere animaduertendum putauimus <lb/><expan abbr="Archimed&etilde;">Archimedem</expan>, quem iure inter huius di&longs;ciplinæ parentes opti<lb/>mos literæ omnes maxima cum laude commemorant, non <lb/>diuer&longs;a ab ijs, qu&etail; Ari&longs;toteles tradidit principia a&longs;&longs;ump&longs;i&longs;&longs;e, <lb/>ac in &longs;uis de æqueponderantibus libris protuli&longs;&longs;e, vt falsò <lb/>nonnulli commini&longs;cuntur; quin imò tradita ab ip&longs;o Philo&longs;o<lb/>pho &longs;uppo&longs;ui&longs;&longs;e, & amplius, ad particularia de&longs;cendendo, <lb/>extendi&longs;&longs;e, ac planiora reddidi&longs;&longs;e, vt ingenuè fatetur Guidus <lb/>Vbaldus in Præfatione primi de æqueponderantibus libri <lb/><expan abbr="eiu&longs;d&etilde;">eiu&longs;dem</expan> Archimedis. </s>

<s id="N122C3">Ari&longs;toteles enim (vt vel vno vtar exem<lb/>plo) loquendo de motione circulati, ad quam reducuntur <lb/>penè omnes motiones, quæ mechanicis in&longs;trumentis, at que <lb/>artibus fiunt, præ&longs;tanti&longs;simum illud con&longs;tituit principium, <lb/>quæ &longs;unt in maiori à centro di&longs;tantia, maiorem quoque ha<pb pagenum="72" xlink:href="005/01/080.jpg"/>bere virtutem ad motum, <expan abbr="velociusq.">velociusque</expan> moueri, vt &longs;upra vidi<lb/>mus tex. 6. Quod &longs;anè principium non &longs;olum admittit Ar<lb/>chimedes, at que &longs;upponit, &longs;ed con&longs;equenter ad illud vlte<lb/>rius inquirit, <expan abbr="tradiditq.">tradiditque</expan> quanto maior &longs;it virtus, quæ habe<lb/>tur in maiori illa di&longs;tantia, eamq ab ip&longs;ius di&longs;tantiæ pro<lb/>portione indagando, recepti&longs;simum aliud fundamentum <lb/><arrow.to.target n="marg17"/> mechanicum &longs;tatuit, nimirum, it a &longs;e habere pondus ad pon<lb/>dus, vt di&longs;tantia ad di&longs;tantiam à puncto vnde pondera &longs;u<lb/>&longs;penduntur, permutata videlicet ratione, vt infra quæ&longs;t. </s>

<s id="N122C3">Ari&longs;toteles enim (vt vel vno vtar exem<lb/>plo) loquendo de motione circulati, ad quam reducuntur <lb/>penè omnes motiones, quæ mechanicis in&longs;trumentis, atque <lb/>artibus fiunt, præ&longs;tanti&longs;simum illud con&longs;tituit principium, <lb/>quæ &longs;unt in maiori à centro di&longs;tantia, maiorem quoque ha<pb pagenum="72" xlink:href="005/01/080.jpg"/>bere virtutem ad motum, <expan abbr="velociusq.">velociusque</expan> moueri, vt &longs;upra vidi<lb/>mus tex. 6. Quod &longs;anè principium non &longs;olum admittit Ar<lb/>chimedes, at que &longs;upponit, &longs;ed con&longs;equenter ad illud vlte<lb/>rius inquirit, <expan abbr="tradiditq.">tradiditque</expan> quanto maior &longs;it virtus, quæ habe<lb/>tur in maiori illa di&longs;tantia, <expan abbr="eamq">eamque</expan> ab ip&longs;ius di&longs;tantiæ pro<lb/>portione indagando, recepti&longs;simum aliud fundamentum <lb/><arrow.to.target n="marg17"/> mechanicum &longs;tatuit, nimirum, it a &longs;e habere pondus ad pon<lb/>dus, vt di&longs;tantia ad di&longs;tantiam à puncto vnde pondera &longs;u<lb/>&longs;penduntur, permutata videlicet ratione, vt infra quæ&longs;t. </s>

<s id="N122F0">3. <lb/>explicabitur. </s>

<s id="N122F5">Cui fundamento tota Archimedis doctrina, <lb/><expan abbr="veraq.">veraque</expan> mechanica innititur contemplatio. </s>

<s id="N122FD">Illud tamen an<lb/>tea patefecerat Ari&longs;toteles in &longs;uis mechanicis, quæ&longs;t. </s>

Line 1107

<s id="N1233D">SECVND A PARS <lb/>MECHANICES <lb/>ARISTOTELIS STAGIRITAE <lb/>IN QVA PLVRES QV AESTIONES <lb/>continentur, ac &longs;oluuntur iuxta principia in <lb/>priori parte tradita.</s>

<s id="N1234C"><emph type="italics"/>Explicata vniuer&longs;ali doctrina principiorum, <lb/>ex quibus tanquam ex iactis fundamen<lb/>tis inconficiendis demon&longs;trationibus omnis <lb/>mechanica &longs;iructura con&longs;urgit, particulares <lb/>quæ&longs;tiones Philo&longs;ophus proponit, in qua<lb/>rum &longs;olutionibus ip&longs;a vniuer&longs;alis doctrina, <lb/>vt præmonuimus, applicatur.<emph.end type="italics"/></s>

<s id="N1234C"><emph type="italics"/>Explicata vniuer&longs;ali doctrina principiorum, <lb/>ex quibus tanquam ex iactis fundamen<lb/>tis inconficiendis demon&longs;trationibus omnis <lb/>mechanica &longs;tructura con&longs;urgit, particulares <lb/>quæ&longs;tiones Philo&longs;ophus proponit, in qua<lb/>rum &longs;olutionibus ip&longs;a vniuer&longs;alis doctrina, <lb/>vt præmonuimus, applicatur.<emph.end type="italics"/></s>

<s id="N12361">Quæ&longs;tio Prima.</s>

<s id="N12366">C<emph type="italics"/>vr autem maiores libræ exactio<lb/>res &longs;unt minoribus, palam e&longs;t ex ÿs. <lb/></s>

<s id="N12366">C<emph type="italics"/>vr autem maiores libræ exactio<lb/>res &longs;unt minoribus, palam e&longs;t ex ijs. <lb/></s>

<s id="N1236F">Spartum enim fit centrum, id namq<lb/>manet. </s>

<s id="N1236F">Spartum enim fit centrum, id <expan abbr="namq.">namque</expan> <lb/>manet. </s>

<s id="N12374">Quod autem libræ vtrinque <lb/>e&longs;t, exeuntes à centro.<emph.end type="italics"/></s>

<s id="N1237D"><emph type="italics"/>Ab eodem igitur pondere citius mo<lb/>ueri nece<32>e e&longs;t extremum libræ, quo <lb/>plus à &longs;parto di&longs;ce&longs;&longs;erit. </s>

<s id="N12386">Et nonnuila <lb/>quidem in paruis libris impo&longs;ita non mani&longs;e&longs;ta &longs;en&longs;ui &longs;unt <lb/>pondera: in magnis autem mani&longs;e&longs;ta. </s>

<s id="N12386">Et nonnulla <lb/>quidem in paruis libris impo&longs;ita non manife&longs;ta &longs;en&longs;ui &longs;unt <lb/>pondera: in magnis autem manife&longs;ta. </s>

<s id="N1238D">Nibil enim prohibet <lb/>minorem moueri magnitudinem, quàm vt vi&longs;ioni &longs;it mani<lb/>fe&longs;ta. </s>

<s id="N1238D">Nihil enim prohibet <lb/>minorem moueri magnitudinem, quàm vt vi&longs;ioni &longs;it mani<lb/>fe&longs;ta. </s>

<s id="N12394">In magna autem hbra idem pondus vi&longs;ibile effieit ma-<emph.end type="italics"/><pb pagenum="74" xlink:href="005/01/082.jpg"/><emph type="italics"/>gnitudo. </s>

<s id="N12394">In magna autem libra idem pondus vi&longs;ibile efficit ma-<emph.end type="italics"/><pb pagenum="74" xlink:href="005/01/082.jpg"/><emph type="italics"/>gnitudo. </s>

<s id="N123A0">Quædam verò manifesta quidem &longs;unt in vtri&longs;que, <lb/>&longs;ed multò magis in maioribus, quoniam multò maior inclina<lb/>tionis fit magnitudo ab eodem pondere in maioribus. </s>

<s id="N123A7">Quam<lb/>obrem machinantur ÿ, qui purpuram vendunt. </s>

<s id="N123AC">vt pendendo <lb/>defraudent, tum ad medium &longs;partum non ponentes, tum plum<lb/>bum in alterutram libræ partem infundentes, aut ligni, quod <lb/>ad radicem vergebat, in eam, quam deferri volunt partem <lb/>con&longs;tituentes: aut &longs;i nodum babuerit. </s>

<s id="N123B7">Ligni enim grauior il<lb/>la est pars, in qua est radix. </s>

<s id="N123BC">Nodus verò radix quædam e&longs;t.<emph.end type="italics"/></s>

Line 1151

<s id="N1248A">Denique ex ijs animaduertit Ati&longs;toteles modum, quo <lb/>nonnulli vendentes purpuram, vel crocum, aut aliud huiu&longs;<lb/>modi, emptores defraudant. </s>

<s id="N12491">Ita namque (vt ip&longs;e ait) con<lb/>&longs;truunt libram, vt &longs;partum quo illa &longs;u&longs;penditur, &longs;eu axis cir<lb/>ca quem illa conuertitur, non &longs;it pror&longs;us in medio iugi, ac <lb/>proinde vnum brachium illius, &longs;it longius altero, æquè ta<lb/>men grauitet, vt tegatur deceptio. </s>

<s id="N1249C">Infundunt enim plum<lb/>bum in brachium, quod minorem habet longitudinem, vel <lb/>illud ex grauiori ligno conficiunt, vt puta nodo&longs;o, aut ad ra<lb/>dicem vergente: & &longs;ic minorem habens longitudinem <lb/>æqueponderat habenti maiorem, <expan abbr="libraq.">libraque</expan> ip&longs;a hau dquaquam <lb/>apparet vitio&longs;a &longs;iue iniu&longs;ta. </s>

<s id="N124AD">Deinde verò mercem in eam <lb/>lancem imponunt, quæ ex longiori brachio pendet; vbi cer<lb/>tè quodlibet pondus magis gtauitare nece&longs;&longs;e e&longs;t, quàm in <lb/>oppo&longs;ita lance. </s>

<s id="N124AD">Deinde verò mercem in eam <lb/>lancem imponunt, quæ ex longiori brachio pendet; vbi cer<lb/>tè quodlibet pondus magis grauitare nece&longs;&longs;e e&longs;t, quàm in <lb/>oppo&longs;ita lance. </s>

<s id="N124B6">Siquidem brach<gap/>j extremum ex quo pen<lb/>det, magis di&longs;tat a centro; <expan abbr="ideoq.">ideoque</expan> quamuis adulterinæ non <lb/>&longs;int <expan abbr="ponder&utilde;">ponderum</expan> notæ, merces maioris ponderis putatur, quàm <lb/>reuera &longs;it, ac tanti ex fraude venditur. </s>

<s id="N124B6">Siquidem brachij extremum ex quo pen<lb/>det, magis di&longs;tat a centro; <expan abbr="ideoq.">ideoque</expan> quamuis adulterinæ non <lb/>&longs;int <expan abbr="ponder&utilde;">ponderum</expan> notæ, merces maioris ponderis putatur, quàm <lb/>reuera &longs;it, ac tanti ex fraude venditur. </s>

<s id="N124C9">Vnde etiam &longs;i libra <lb/>lancibus vacuis æquilibrium demon&longs;tret, & æqualibus in <lb/>pondere, æqualia addantur, æquè illa ponderare non &longs;equi<lb/>tur, dum æquè à centro libræ non di&longs;tant. </s>

<s id="N124D2">Nàm ratione &longs;i<lb/>tus quælibet additio ponderis po&longs;tea in ip&longs;is lancibus facta, <lb/>&longs;emper eandem &longs;eruare debet proportionem, vt magis gra<lb/>uitet in loco di&longs;tantiori, quàm in propinquiori; vt exactius <lb/>adhuc con&longs;tare pote&longs;t ex Archimede in primo lib. Aeque<lb/>ponderan. po&longs;tulat. </s>

<s id="N124E3">2. & explicatione Guidi Vbaldi è Mar<lb/>chionibus Montis ibidem ac tract. de libra prop.

Line 1169

<s id="N12532">Quæ&longs;tio Secunda.</s>

<s id="N12537">C<emph type="italics"/>vr &longs;iquidem cur&longs;um &longs;uerit &longs;partum, qnan<lb/>do deor&longs;um lato pondere qui&longs;piem id amouet, <lb/>rur&longs;um a&longs;cendit libra: &longs;i autem deor&longs;um con<lb/>&longs;titutum fuerit, non a&longs;oendit, &longs;ed manet? </s>

<s id="N12537">C<emph type="italics"/>vr &longs;iquidem cur&longs;um &longs;uerit &longs;partum, quan<lb/>do deor&longs;um lato pondere qui&longs;piam id amouet, <lb/>rur&longs;um a&longs;cendit libra: &longs;i autem deor&longs;um con<lb/>&longs;titutum fuerit, non a&longs;cendit, &longs;ed manet? </s>

<s id="N12543">An <lb/>quia &longs;ur&longs;um quidem &longs;parto <gap/>xi&longs;&longs;ente plus li<lb/>bræ extra perpendiculum fit: quare nece&longs;&longs;e <lb/>e&longs;t deor&longs;um ferri id quod plus e&longs;t, donec a&longs;cendat, quæ bi&longs;a<lb/>riam libram diuidit, ad ip&longs;um perpendiculum, cùm onus in<lb/>cumbat ad libræ partem &longs;ur&longs;um raptum.<emph.end type="italics"/></s>

<s id="N12543">An <lb/>quia &longs;ur&longs;um quidem &longs;parto existente plus li<lb/>bræ extra perpendiculum fit: quare nece&longs;&longs;e <lb/>e&longs;t deor&longs;um ferri id quod plus e&longs;t, donec a&longs;cendat, quæ bifa<lb/>riam libram diuidit, ad ip&longs;um perpendiculum, cùm onus in<lb/>cumbat ad libræ partem &longs;ur&longs;um raptum.<emph.end type="italics"/></s>

<s id="N12556"><emph type="italics"/>Sit libra recta, vbi BC, &longs;partum autem AD. </s>

<s id="N1255C">Hoc igi<lb/>tur deor&longs;um proiecto perpendiculum erit, vbi ADM. </s>

<s id="N12562">Si igi<lb/>tur in ip&longs;o B ponatur onus, B quidem erit, vbi E, C antem <lb/>vbi H s quamobrem ea, quæ bifariam libram &longs;ecat, primò <lb/>quidem erit DM ip&longs;ius perpendi<gap/>uli: incumbente autem <lb/>onere DG, quare libræ ip&longs;ius vbi EH, quòd extra perpen<lb/>diculum e&longs;t AM, vbi e&longs;t PQ, maius e&longs;i dimidio. </s>

<s id="N12562">Si igi<lb/>tur in ip&longs;o B ponatur onus, B quidem erit, vbi E, C autem <lb/>vbi H s quamobrem ea, quæ bifariam libram &longs;ecat, primò <lb/>quidem erit DM ip&longs;ius perpendiculi: incumbente autem <lb/>onere DG, quare libræ ip&longs;ius vbi EH, quòd extra perpen<lb/>diculum e&longs;t AM, vbi e&longs;t PQ, maius e&longs;i dimidio. </s>

<s id="N12571">Si igitur <lb/>amoueatur onus ab ip&longs;o E, nece&longs;&longs;e e&longs;t deor&longs;um ferri H mi<lb/>vus enim e&longs;t E. </s>

<s id="N12571">Si igitur <lb/>amoueatur onus ab ip&longs;o E, nece&longs;&longs;e e&longs;t deor&longs;um ferri H mi<lb/>nus enim e&longs;t E. </s>

<s id="N12579">Siquidem igitur &longs;ur&longs;um babuerit &longs;partum,<emph.end type="italics"/><pb pagenum="78" xlink:href="005/01/086.jpg"/><emph type="italics"/>rur&longs;um propter boc a&longs;cendit libra. </s>

<s id="N12579">Siquidem igitur &longs;ur&longs;um habuerit &longs;partum,<emph.end type="italics"/><pb pagenum="78" xlink:href="005/01/086.jpg"/><emph type="italics"/>rur&longs;um propter hoc a&longs;cendit libra. </s>

<s id="N12585">Si autem deor&longs;um fuerit <lb/>in quod &longs;ub&longs;tat, contrarium facit. </s>

<s id="N1258A">Plus enim dimidio fit li<lb/>bræ, quæ deor&longs;um e&longs;t pars, quàm quod per pendiculum &longs;ecet: <lb/>quapropter non a&longs;cendit. </s>

<s id="N12591">Eleuata enim pars leuior e&longs;t.<emph.end type="italics"/></s>

<s id="N12598"><emph type="italics"/>Sit libra recta vbi NG: perpondiculum autem KLM. <lb/></s>

<s id="N12598"><emph type="italics"/>Sit libra recta vbi NG: perpendiculum autem KLM. <lb/></s>

<s id="N1259F">Bifariam igitur &longs;ecatur KG. </s>

<s id="N125A2">Impo&longs;ilo autem onere in ip&longs;o <lb/>N, erit quidem N vbi O, ip&longs;um autem G, vbi R, KL <lb/>autem vbi LP. </s>

<s id="N125A2">Impo&longs;ito autem onere in ip&longs;o <lb/>N, erit quidem N vbi O, ip&longs;um autem G, vbi R, KL <lb/>autem vbi LP. </s>

<s id="N125A9">Quare maius e&longs;t KO, quam LR, ip&longs;o <lb/>PKL. </s>

<s id="N125AE">Et ablato igitur onere, nete<32>e e&longs;t manere; incumbit <lb/>enim ceu onus exce&longs;&longs;us medietatis eius vbi e&longs;t F.<emph.end type="italics"/></s>

Line 1196

<s id="N125BE">Cvm axis vel &longs;partum, quod gerit vicem axis, & quo <lb/>&longs;u&longs;penditur libra, locari po&longs;&longs;it tum &longs;upra, tum infra <lb/>iugum ip&longs;ius libræ, quærit modo Ari&longs;toteles quid <lb/>cau&longs;æ &longs;it, vt &longs;i locetur &longs;upra, appo&longs;ito in alteram lancem <lb/>pondere, de&longs;cendat quippe illa, &longs;ed eo amoto ex &longs;e iterum <lb/>in pri&longs;tinum locum a&longs;cendat: &longs;i verò axis locetur infra, lanx <lb/>illa maneat, & non reuertatur. </s>

<s id="N125CF">Porrò prima hius quæ&longs;tionis pars &longs;i phy&longs;icè con&longs;idere<lb/>tur, non paruam videtur inuoluere difficultatem. </s>

<s id="N125CF">Porrò prima huius quæ&longs;tionis pars &longs;i phy&longs;icè con&longs;idere<lb/>tur, non paruam videtur inuoluere difficultatem. </s>

<s id="N125D4">Etenim <lb/>nullum apparet agens, à quo talis a&longs;cen&longs;us depre&longs;&longs;æ lancis <lb/>procedat. </s>

<s id="N125DB">Cum enim quodlibet graue tendat deor&longs;um, cau<lb/>&longs;a huiu&longs;modi eleuationis, & a&longs;cen&longs;ionis non pote&longs;t e&longs;&longs;e for<lb/>ma aliqua intrin&longs;eca; nec pro extrin&longs;eca a&longs;&longs;ignari pote&longs;t <lb/>alia, ni&longs;i grauitas alterius lancis, qua &longs;cilicet illa de&longs;cen<lb/>dendo, hanc faciat a&longs;cendere. </s>

<s id="N125E6">Verum cum vtraque lanx <lb/>æqualis molis, & grauitatis con&longs;tituatur, nequit altera alteri <lb/>præponderare, <expan abbr="de&longs;cen&longs;uq.">de&longs;cen&longs;uque</expan> proprio eam eleuare. </s>

Line 1206

<s id="N1260A">Nihilominus etiam phy&longs;icis principijs inhærendo exijs, <lb/>quæ Ari&longs;toteles in præ&longs;entibus docet, optimè huic difficul<lb/>tati pote&longs;t occurri, <expan abbr="primaq.">primaque</expan> pars quæ&longs;tionis re&longs;olui. </s>

<s id="N12615">Nam <lb/>&longs;uppo&longs;ito, quod pars iugi, qu&etail; eleuatur di&longs;tinguatur à parte, <lb/>quæ deprimitur per lineam perpendicularem cadentem à <lb/>centro circa quod conuertitur libra, &longs;eu ab axe, vel &longs;parto <lb/>ad centrum terræ, vt fen&longs;u con&longs;tabit in &longs;equenti figura: &longs;i<lb/>quidem quidquid libræ e&longs;t ad leuam, v.g. talis lineæ, rapi<lb/>tur deor&longs;um; quidquid verò e&longs;t ad dexteram attollitur &longs;ur<lb/>&longs;um: hoc inquam &longs;uppo&longs;ito, ait Ari&longs;toteles, quod &longs;i libra <lb/>axem, &longs;eu centrum habeat &longs;upra iugum, ac per depre&longs;&longs;io<lb/>nem alterius partis illius, altera eleuetur, plus quippe libræ <lb/>e&longs;&longs;et ex parte eleuata, quàm ex parte depre&longs;&longs;a: proindeq<lb/>pars eleuata nece&longs;&longs;eriò de&longs;cendet, & ad de&longs;cen&longs;um illius, <lb/>&longs;equitur depre&longs;&longs;am a&longs;cendere, quou&longs;que vtraque con&longs;titua<lb/>tur æqualis, ac reuertatur ad æquilibrium. </s>

<s id="N12615">Nam <lb/>&longs;uppo&longs;ito, quod pars iugi, qu&etail; eleuatur di&longs;tinguatur à parte, <lb/>quæ deprimitur per lineam perpendicularem cadentem à <lb/>centro circa quod conuertitur libra, &longs;eu ab axe, vel &longs;parto <lb/>ad centrum terræ, vt sen&longs;u con&longs;tabit in &longs;equenti figura: &longs;i<lb/>quidem quidquid libræ e&longs;t ad leuam, v.g. talis lineæ, rapi<lb/>tur deor&longs;um; quidquid verò e&longs;t ad dexteram attollitur &longs;ur<lb/>&longs;um: hoc inquam &longs;uppo&longs;ito, ait Ari&longs;toteles, quod &longs;i libra <lb/>axem, &longs;eu centrum habeat &longs;upra iugum, ac per depre&longs;&longs;io<lb/>nem alterius partis illius, altera eleuetur, plus quippe libræ <lb/>e&longs;&longs;et ex parte eleuata, quàm ex parte depre&longs;&longs;a: <expan abbr="proindeq.">proindeque</expan> <lb/>pars eleuata nece&longs;&longs;eriò de&longs;cendet, & ad de&longs;cen&longs;um illius, <lb/>&longs;equitur depre&longs;&longs;am a&longs;cendere, quou&longs;que vtraque con&longs;titua<lb/>tur æqualis, ac reuertatur ad æquilibrium. </s>

<s id="N12634">Id quod ita &longs;e <lb/>habere &longs;ic probat. </s>

<s id="N12639">Nam &longs;i iugum libræ &longs;it BC in æquilibrio <lb/><figure id="id.005.01.087.1.jpg" xlink:href="005/01/087/1.jpg"/><lb/>con&longs;titutum: &longs;partum <lb/>autem quo <expan abbr="&longs;u&longs;p&etilde;ditur">&longs;u&longs;penditur</expan>, <lb/>AD, ita videlicet, vt <lb/>axis &longs;it ip&longs;um D, quod <lb/>e&longs;t punctum &longs;upra lati<lb/>tudinem iugi. </s>

<s id="N12652">Dein<lb/>de &longs;partum proijciatur <lb/>deor&longs;um, <expan abbr="efficiatq.">efficiatque</expan> per<lb/>pendicularem ADM. <lb/></s>

Line 1214

<s id="N12667">Quamobrem linea, quæ in <lb/>priori &longs;itu libram diuidebat bifariam, e&longs;t ip&longs;a perpendicu<lb/>laris DM. </s>

<s id="N1266F">Illa verò quæ po&longs;tea eodem pacto diuidit in, <lb/>po&longs;teriori &longs;itu propter onus, quod incumbit in E, erit <lb/>DG. </s>

<s id="N12677">Quare ea pars libræ, &longs;eu iugi. </s>

<s id="N1267A">EH, quæ e&longs;t extra <lb/>perpendiculum AM ver&longs;us H maiorerit dimidio nem<lb/>pe quantum importat triangulus DGM, quod &longs;patium <lb/>Ari&longs;toteles &longs;ignauit <expan abbr="Pq.">Pque</expan> Si igitur amoueaturonus, quod <pb pagenum="80" xlink:href="005/01/088.jpg"/>deprimit in E, nece&longs;&longs;e e&longs;t deor&longs;um ferri partem vbi H. <lb/><figure id="id.005.01.088.1.jpg" xlink:href="005/01/088/1.jpg"/><lb/><expan abbr="Siquid&etilde;">Siquidem</expan> pars illa ma<lb/>ior e&longs;t quàm hæc vbi <lb/>E, quæ per <expan abbr="con&longs;equ&etilde;s">con&longs;equens</expan> <lb/>&longs;ur&longs;um a&longs;cen det, & &longs;ic <lb/>rur&longs;us libra con&longs;titue<lb/>tur in æquilibrio quod <lb/>erat probandum. </s>

<s id="N1267A">EH, quæ e&longs;t extra <lb/>perpendiculum AM ver&longs;us H maior erit dimidio nem<lb/>pe quantum importat triangulus DGM, quod &longs;patium <lb/>Ari&longs;toteles &longs;ignauit <expan abbr="Pq.">PQ</expan> Si igitur amoueatur onus, quod <pb pagenum="80" xlink:href="005/01/088.jpg"/>deprimit in E, nece&longs;&longs;e e&longs;t deor&longs;um ferri partem vbi H. <lb/><figure id="id.005.01.088.1.jpg" xlink:href="005/01/088/1.jpg"/><lb/><expan abbr="Siquid&etilde;">Siquidem</expan> pars illa ma<lb/>ior e&longs;t quàm hæc vbi <lb/>E, quæ per <expan abbr="con&longs;equ&etilde;s">con&longs;equens</expan> <lb/>&longs;ur&longs;um a&longs;cendet, & &longs;ic <lb/>rur&longs;us libra con&longs;titue<lb/>tur in æquilibrio quod <lb/>erat probandum. </s>

<s id="N126A7">Se<lb/>cunda verò pars huius <lb/>quæ&longs;tionis facilius ab <lb/>eodem Ari&longs;totele probatur. </s>

<s id="N126B0">Quoniam &longs;i &longs;partum, &longs;eu axis <lb/>infra iugum locetur, maior pars libr&etail; e&longs;&longs;et illa, qu&etail; deor<lb/>&longs;um ex impo&longs;ito pondere reperiretur depre&longs;&longs;a, quàm qu&etail; <lb/>&longs;ur&longs;um e&longs;&longs;et elata. </s>

<s id="N126B9">Porrò plus dimidio contineret, <expan abbr="proin-deq.">proin<lb/>deque</expan> etiam ablato pondere adhuc magis grauitaret, ac pro<lb/>pterea ad equilibrium redire minimè po&longs;&longs;et. </s>

Line 1226

<s id="N1270B">Quandoquidem exce&longs;&longs;us il<lb/>le &longs;upra medietatem, tanquam onus quoddam ei &longs;emper in<lb/>cumbit. </s>

<s id="N12714">Huic autem Ati&longs;totelis demon&longs;trationi addi etiam po-<pb pagenum="81" xlink:href="005/01/089.jpg"/>te&longs;t alia &longs;umpta ex centro grauitatis, vt proprium e&longs;t me<lb/>chanicarum &longs;peculationum. </s>

<s id="N12714">Huic autem Ari&longs;totelis demon&longs;trationi addi etiam po-<pb pagenum="81" xlink:href="005/01/089.jpg"/>te&longs;t alia &longs;umpta ex centro grauitatis, vt proprium e&longs;t me<lb/>chanicarum &longs;peculationum. </s>

<s id="N1271E">Porrò libræ iam explicatæ cen<lb/>trum grauitatis e&longs;t punctum in medio iugi intrapo&longs;itum, vt <lb/>patet ex definitione. </s>

<s id="N12725">Nam circa illud <expan abbr="vndiq.">vndique</expan> partes æqua<lb/>lium &longs;unt momentorum. </s>

<s id="N1272E">Quando autem libra e&longs;t in Aequi<lb/>librio con&longs;tituta, huiu&longs;modi centrum coincidit in eandem <lb/>lineam perpendiculatem, in qua e&longs;t centrum circumuolu<lb/>tionis, &longs;eu axis ip&longs;ius libræ, ac centrum mundi; &longs;iue axis po<lb/>natur &longs;upra, &longs;iue infra <expan abbr="iug&utilde;">iugum</expan>, vt videre e&longs;t in de&longs;criptis figuris. <lb/></s>

Line 1236

<s id="N12769">Qu&etail; <lb/>omnia ab&longs;que alia figura per&longs;picua e&longs;&longs;e po&longs;&longs;unt ex de&longs;cri<lb/>ptis, ac fu&longs;iùs, & exactiùs traduntur, cum à Guidone Vbaldo <lb/>tractatu de libra, tum à Bernardino Baldo in hac quæ&longs;tione, <lb/>qui tantam in centro grauitatis vim e&longs;&longs;e animaduertit ad <lb/>præponderandum, vt hinc colligat, libras quæ axem habent <lb/>&longs;upra iugum, non à quouis paruo pondere moueri, vel peni<lb/>tus declinare, &longs;ed ab eo <expan abbr="tant&utilde;">tantum</expan>, quod &longs;uperet <expan abbr="re&longs;i&longs;tentiã">re&longs;i&longs;tentiam</expan> cen<lb/>tri grauitatis, qu&etail; re&longs;i&longs;tentia proportionaliter eo maior ex<lb/>peritur, quo minus grauitatis <expan abbr="c&etilde;tr&utilde;">centrum</expan> di&longs;tat ab axe, &longs;eu centro <lb/>circa quod ip&longs;a libra conuertitur, vt <expan abbr="ibid&etilde;">ibidem</expan> ip&longs;e demon&longs;trat. </s>

<s id="N12792">Verum quamuis prædicta omnia vera &longs;int, adhuc tamen <lb/>aliquod de&longs;ideratur ad adæquatam omnino rationem tra<lb/>dendam, cur axe exi&longs;tente &longs;upra iugum, &longs;i eleuetur vna pars <pb pagenum="82" xlink:href="005/01/090.jpg"/>illius ad depre&longs;&longs;ionem alterius, <expan abbr="cau&longs;aq.">cau&longs;aque</expan> depre&longs;&longs;ionis remo<lb/>ucatur, &longs;tatim pars illa eleuata præcipiti cur&longs;u de&longs;cendat, <lb/><expan abbr="redeatq.">redeatque</expan> in pri&longs;tinum locum. </s>

<s id="N12792">Verum quamuis prædicta omnia vera &longs;int, adhuc tamen <lb/>aliquod de&longs;ideratur ad adæquatam omnino rationem tra<lb/>dendam, cur axe exi&longs;tente &longs;upra iugum, &longs;i eleuetur vna pars <pb pagenum="82" xlink:href="005/01/090.jpg"/>illius ad depre&longs;&longs;ionem alterius, <expan abbr="cau&longs;aq.">cau&longs;aque</expan> depre&longs;&longs;ionis remo<lb/>ueatur, &longs;tatim pars illa eleuata præcipiti cur&longs;u de&longs;cendat, <lb/><expan abbr="redeatq.">redeatque</expan> in pri&longs;tinum locum. </s>

<s id="N127A9">Siquidem exce&longs;&longs;us ille partis <lb/>eleuatæ, quem ex Ari&longs;totele explicuimus, <expan abbr="rur&longs;umq.">rur&longs;umque</expan> ratio <lb/>centri grauitatis prædicta non videntur &longs;ufficere, nec tanti <lb/>e&longs;&longs;e momenti, vt <expan abbr="tantã">tantam</expan> motionem <expan abbr="tamquã">tamquam</expan> præcipitem de<lb/>&longs;cen&longs;um cau&longs;are præualeant. </s>

<s id="N127C0">Cum & centrum grauitatis <lb/>parum, aut imperceptibiliter remoueatur à linea illa ca<lb/>dente ab axe ad centrum mundi; & exce&longs;&longs;us partis eleuatæ <lb/>non modo paruus &longs;it, &longs;ed paruum etiam ab eadem linea di<lb/>&longs;tet vbi minus præponderantia experitur. </s>

<s id="N127CB">Etenim &longs;i huiu&longs;<lb/>modi exce&longs;&longs;us appenderetur tanquam onus in libra, quæ in <lb/>æquilibrio &longs;it con&longs;tituta, ac prope axem in &longs;imili &longs;itu, ac e&longs;t <lb/>ille, quem in ca&longs;u no&longs;tro retinet, ab&longs;que dubio parum, aut <lb/>nihil præponderaret brachium in quo appenderetur. </s>

Line 1248

<s id="N127F5">Non <lb/>quia ratione &longs;itus re vera maiorem, aut minorem grauita<lb/>tem acquirat, &longs;ed quia magis, vel minus &longs;u&longs;tinetur ab in<lb/>&longs;trumento in illo &longs;itu iuxta maiorem, aut minorem propin<lb/>quitatem, quam &longs;itus habet cum linea explicata, vt Guido <lb/>Vbaldus animaduertit, tractatu de Libra, prop.

4. ante med. <lb/></s>

<s id="N12803">Cum igitur pondus &longs;uperioris lancis in eo loco magis di&longs;tet <lb/>aliena perpendiculari prædicta, quàm pondus inferioris, &longs;e<lb/>quitur magis grauitare &longs;uperiorem lancem, quàm grauitet <lb/>inferior, atque adeo hæc ab illa tanquam ab inæquali pro<lb/>portione vitutis moueri, & &longs;ur&longs;um ferri v&longs;quequo ad æqua-<pb pagenum="83" xlink:href="005/01/091.jpg"/>lem cum illa à cathectu di&longs;tantiam, ac proinde grauitatem <lb/>perueniat, vt in æquilibrio contingit</s>

<s id="N12803">Cum igitur pondus &longs;uperioris lancis in eo loco magis di&longs;tet <lb/>aliena perpendiculari prædicta, quàm pondus inferioris, &longs;e<lb/>quitur magis grauitare &longs;uperiorem lancem, quàm grauitet <lb/>inferior, atque adeo hæc ab illa tanquam ab inæquali pro<lb/>portione virtutis moueri, & &longs;ur&longs;um ferri v&longs;quequo ad æqua-<pb pagenum="83" xlink:href="005/01/091.jpg"/>lem cum illa à cathectu di&longs;tantiam, ac proinde grauitatem <lb/>perueniat, vt in æquilibrio contingit</s>

<s id="N12817">Superiorem autem lancem modo prædicto à linea ca<lb/>thectus magis remoueri, &longs;ic pote&longs;t <expan abbr="demõ&longs;trari">demon&longs;trari</expan> exemplo hu<lb/>ius figuræ. </s>

Line 1277

<s id="N1291F">Quæ&longs;tio Tertia.</s>

<s id="N12925">C<emph type="italics"/>vr exiguæ vires (quemadmodum à principi<gap/><lb/>dictum e&longs;t) vecte, magna mouent pondera, <lb/>vectis in&longs;uper onus accipientes? </s>

<s id="N12925">C<emph type="italics"/>vr exiguæ vires (quemadmodum à principio<lb/>dictum e&longs;t) vecte, magna mouent pondera, <lb/>vectis in&longs;uper onus accipientes? </s>

<s id="N12930">cum faci<lb/>lius &longs;it minorem mouere grauitatem: minor <lb/>autem e&longs;t &longs;ine vecte. </s>

<s id="N12937">An quoniam ip&longs;e ve<lb/>ctis e&longs;t in cau&longs;a libra exi&longs;tens, &longs;partum infer<lb/>nè habens, in inæqualia diui&longs;a. </s>

<s id="N1293E">Hypomochlion enim est &longs;par<lb/>tum: ambo namque stant vt centrum. </s>

<s id="N12943">Quoniam autem ab <lb/>æquali pondere celeriùs mouetur maior earum, quæ à centro <lb/>&longs;unt: duo verò pondera, quod mouet, & quod mouetur: quod <lb/>igitur motum pondus ad mouens, longitudo patitur ad longi<lb/>tudinem. </s>

<s id="N1294E">Semper autem quanto ab hypomochlio di&longs;tabit ma<lb/>gis, tantò faciliùs mouebit. </s>

<s id="N12953">Cau&longs;a autem e&longs;t, quæ retrò com<lb/>memorata est: quoniam quæ plus à centro distat, maiorem <lb/>de&longs;cribit circulum: quare ab eadem potentia plus &longs;eparabitur <lb/>mouens illud, quod plus ab hypomochlio di&longs;tabit. </s>

<s id="N1295C">Sit vectis <lb/>vbi AB, pondus vbi C, quod mouet autem, vbi D, hypo<lb/>mocblion vbi E, quod autem vbi e&longs;t D, mouens vbi F. mo<lb/>tum autem vbi C. pondus vbi G.<emph.end type="italics"/></s>

<s id="N1295C">Sit vectis <lb/>vbi AB, pondus vbi C, quod mouet autem, vbi D, hypo<lb/>mochlion vbi E, quod autem vbi e&longs;t D, mouens vbi F. mo<lb/>tum autem vbi C. pondus vbi G.<emph.end type="italics"/></s>

<s id="N1296A">COMMENTARIVS.</s>

Line 1305

<s id="N129C2">Tunc &longs;i con&longs;ideretur, eadem erit <lb/><figure id="id.005.01.094.1.jpg" xlink:href="005/01/094/1.jpg"/><pb pagenum="87" xlink:href="005/01/095.jpg"/><figure id="id.005.01.095.1.jpg" xlink:href="005/01/095/1.jpg"/><lb/>ratio ac de libra, cuius iugum &longs;it AB, lances verò C, D, <lb/>& axis, &longs;eu fulcimentum E. </s>

<s id="N129D9">Siquidem ip&longs;um D pendens <lb/>ex longiori brachio libræ, præponderat ip&longs;i C. </s>

<s id="N129DF">Quemad<lb/>modum potentia applicata in vecte vbi D, &longs;uperat graui<lb/>tatem ponderis C. </s>

<s id="N129E7">Axis verò <expan abbr="c&utilde;">cum</expan> ponatur infra iugum, &longs;iue <lb/>ip&longs;um ingum &longs;it &longs;u&longs;pen&longs;um per trutinam, aut &longs;partum, &longs;iue <lb/>innixum &longs;it alteri corpori immobili, idem &longs;emper præ&longs;tat, <lb/>ac fulcimentum vectis vbi E. </s>

<s id="N129E7">Axis verò <expan abbr="c&utilde;">cum</expan> ponatur infra iugum, &longs;iue <lb/>ip&longs;um iugum &longs;it &longs;u&longs;pen&longs;um per trutinam, aut &longs;partum, &longs;iue <lb/>innixum &longs;it alteri corpori immobili, idem &longs;emper præ&longs;tat, <lb/>ac fulcimentum vectis vbi E. </s>

<s id="N129F7">Quoniam autem (pro&longs;equitur Ari&longs;toteles) ab æquali <lb/>pondere celerius, &longs;iue facilius mouetur brachium libræ, <lb/>quod magis à centro di&longs;ce&longs;&longs;erit, vt explicatum e&longs;t de libra, <lb/>quæ alterum brachium longius obtinet, eam ad circulum <lb/>reducendo: hinc fit, vt cum duo &longs;int, quæ in ambis extre<lb/>mitatibus vectis præmunt, vel ponderant, nempe mouens <lb/>in vna, & motum in alia; illud magis præponderet, quod <lb/>longiorem vectis extremitatem præ&longs;&longs;erit; &longs;eu quanto magis <lb/>à fulcimento di&longs;ce&longs;&longs;erit, quamuis aliàs ip&longs;a ponderantia in <lb/>&longs;e &longs;int æqualia, hoc e&longs;t virtus mouentis æqualis &longs;it moto <lb/>ponderi, & longior pars vectis æquè grauitet, ac breuior. <lb/></s>

<s id="N129F7">Quoniam autem (pro&longs;equitur Ari&longs;toteles) ab æquali <lb/>pondere celerius, &longs;iue facilius mouetur brachium libræ, <lb/>quod magis à centro di&longs;ce&longs;&longs;erit, vt explicatum e&longs;t de libra, <lb/>quæ alterum brachium longius obtinet, eam ad circulum <lb/>reducendo: hinc fit, vt cum duo &longs;int, quæ in ambis extre<lb/>mitatibus vectis præsunt, vel ponderant, nempe mouens <lb/>in vna, & motum in alia; illud magis præponderet, quod <lb/>longiorem vectis extremitatem præ&longs;&longs;erit; &longs;eu quanto magis <lb/>à fulcimento di&longs;ce&longs;&longs;erit, quamuis aliàs ip&longs;a ponderantia in <lb/>&longs;e &longs;int æqualia, hoc e&longs;t virtus mouentis æqualis &longs;it moto <lb/>ponderi, & longior pars vectis æquè grauitet, ac breuior. <lb/></s>

<s id="N12A0F">Quod totum, vt ip&longs;emet Ari&longs;toteles inquit, de&longs;umitur ab <pb pagenum="88" xlink:href="005/01/096.jpg"/>explicato illo principio; quoniam &longs;cilicet, quæ plus à cen<lb/>tro di&longs;tat linea, &longs;eu extremitas &longs;emidiametri, maiorem de<lb/>&longs;cribit circumferentiam, quæ &longs;anè cum magis ad rectam li<lb/>neam accedat, facilius, ac velocius per ip&longs;am fertur &longs;emidia<lb/>meter, tanquam per viam magis connaturalem, vt ibidem <lb/>explicuimus. </s>

<s id="N12A23">Illud autem, quod Ari&longs;toteles interpo&longs;uit, nempe: Quod <lb/>igitur motum pondus admouens, longitudo patitur ad lon<lb/>gitudinem: idem e&longs;t, ac dicere, eandem proportionem ha<lb/>bere motricem potentiam ad pondus leuandum, quam ha<lb/>bet eius longitudo, &longs;eu di&longs;tantia à centro vectis ad longitu<lb/>dinem, &longs;eu di&longs;tantiam ponderis ab eodem centro vbi e&longs;t <lb/>fulcimentum. </s>

<s id="N12A32">Quare &longs;ubiungit: Semper autem quanto ab <lb/>hypomochlio, ide&longs;t fulcimento, di&longs;tabit magis, tanto facilius <lb/>mouebit. </s>

<s id="N12A39">Hæc ille, quæ po&longs;tea exactius tradita &longs;unt ab<lb/>Archimede in &longs;uo primo libro æqueponderantium propo<lb/>&longs;itione &longs;exta; & acuti&longs;&longs;imè probantur à Guido Vbaldo è <lb/>Marchionibus Montis in &longs;uis Mechanicis tractatu de libra <lb/>propo&longs;itione &longs;exta; ac de vecte propo&longs;itione quarta. </s>

<s id="N12A39">Hæc ille, quæ po&longs;tea exactius tradita &longs;unt ab <lb/>Archimede in &longs;uo primo libro æqueponderantium propo<lb/>&longs;itione &longs;exta; & acuti&longs;&longs;imè probantur à Guido Vbaldo è <lb/>Marchionibus Montis in &longs;uis Mechanicis tractatu de libra <lb/>propo&longs;itione &longs;exta; ac de vecte propo&longs;itione quarta. </s>

<s id="N12A44">De<lb/>mon&longs;trant enim in æquilibrijs, tàm vectis, quàm libræ, ita &longs;e <lb/>habere pondus ad pondus, vt brachium ad brachium ex <lb/>commutata proportione. </s>

<s id="N12A4D">Sit enim vectis, aut libra AB &longs;uf<lb/>fulta, aut &longs;u&longs;pen&longs;a in C. </s>

<s id="N12A53">Brachium autem CA &longs;it verbi <lb/><figure id="id.005.01.096.1.jpg" xlink:href="005/01/096/1.jpg"/><lb/>gratia vnius <lb/>palmi. </s>

Line 1335

<s id="N12AE3">Stant autem vectis, & libra dum manent in æquili<lb/>brio, & nihilominus parua potentia ingens &longs;u&longs;tinet pondus. </s>

<s id="N12AEA">Veruntamen &longs;i verba Ari&longs;totelis exactius pen&longs;entur non <lb/>id &longs;igni&longs;icant, nec ille talem cau&longs;am formaliter in maiori <lb/>velocitate, &longs;ed in maiori grauitate, aut virtute con&longs;tituit, <lb/>quæ brachij maiorem longitudinem con&longs;equitur. </s>

<s id="N12AEA">Veruntamen &longs;i verba Ari&longs;totelis exactius pen&longs;entur non <lb/>id &longs;ignificant, nec ille talem cau&longs;am formaliter in maiori <lb/>velocitate, &longs;ed in maiori grauitate, aut virtute con&longs;tituit, <lb/>quæ brachij maiorem longitudinem con&longs;equitur. </s>

<s id="N12AF3">Etenim <lb/>cum dixit: <emph type="italics"/>Zuoniam autem ab æquali ponaere celerius mo<lb/>uetur maior earum, quæ à centro &longs;unt.<emph.end type="italics"/></s>

<s id="N12AF3">Etenim <lb/>cum dixit: <emph type="italics"/>Quoniam autem ab æquali pondere celerius mo<lb/>uetur maior earum, quæ à centro &longs;unt.<emph.end type="italics"/></s>

<s id="N12AFF"> Idem per <emph type="italics"/>celerius<emph.end type="italics"/> ac <lb/>per <emph type="italics"/>facilius<emph.end type="italics"/> intellexit. </s>

<s id="N12B10">Quandoquidem paulo po&longs;t id ip&longs;um <lb/>repetens, ait. <emph type="italics"/>Semper autem quanio ab hy<gap/>mochlio di<gap/><lb/>bit magis, tanto facilius mouebit.<emph.end type="italics"/></s>

<s id="N12B10">Quandoquidem paulo po&longs;t id ip&longs;um <lb/>repetens, ait. <emph type="italics"/>Semper autem quanto ab hypomochlio dicta<lb/>bit magis, tanto facilius mouebit.<emph.end type="italics"/></s>

<s id="N12B20"> Et quidem in motu locali <lb/>velocitas &longs;emper facilitatem inuoluit, aut &longs;upponit, <expan abbr="ip&longs;aq.">ip&longs;aque</expan> <pb pagenum="90" xlink:href="005/01/098.jpg"/>maior velocitas, ac facilitas motus, maiorem grauitatem, aut <lb/>maiorem virtutem motiuam nece&longs;&longs;ario indicat, vt palam e&longs;t <lb/>in motibus tàm naturalibus, quàm violentis. </s>

<s id="N12B32">Nam corpus <lb/>quò grauius, eò velocius de&longs;cendit, &longs;i non detineatur; & <lb/>proiecta, eò velocius inter medium percurrunt, quo maio<lb/>rem impul&longs;um à proijciente recipiunt. </s>

<s id="N12B3B"><expan abbr="Ip&longs;aq.">Ip&longs;aque</expan> animalia tan<lb/>to progrediuntur velocius, <expan abbr="citiusq.">citiusque</expan> per incu&longs;&longs;ionem impul<lb/>&longs;us grauia mouent, quanto maiorem virtutem motiuam <lb/>adepta fuerit cum pari di&longs;po&longs;itione in&longs;trumentorum. </s>

Line 1348

<s id="N12B58">Quæ&longs;tio Quarta.</s>

<s id="N12B5D">C<emph type="italics"/>vr ÿ, qui in nauis medio &longs;unt remiges, ma<lb/>ximè nauem mouent? </s>

<s id="N12B5D">C<emph type="italics"/>vr ij, qui in nauis medio &longs;unt remiges, ma<lb/>ximè nauem mouent? </s>

<s id="N12B65">an quia remus vectis <lb/>est, hypomochlion autem fit &longs;calmus? </s>

<s id="N12B6A">&longs;tat <lb/>enim ille: pondus verò mare est, quod propel<lb/>lit remus: vectem autem mouens est ip&longs;e re<lb/>mex. </s>

<s id="N12B73">Semper autem plus mouet ponderis, <lb/>quantò magis ab hypomochlio distabit quicumque id mouet. <lb/></s>

<s id="N12B79">Maior enim ita fit, quæ ex centro. </s>

<s id="N12B7C">Scalmus autem hypomo<lb/>chlion exi&longs;tens, centrum e&longs;t. </s>

<s id="N12B81">In medio autem nauis plurimum <lb/>remi intus e&longs;t: illa enim parte lati&longs;&longs;ima e&longs;i nauis: quare ma<lb/>ior vtrinque remi pars vtrorumque nauis parietum intrin&longs;e<lb/>cus e&longs;i. </s>

<s id="N12B8A">Mouetur autem nauis, quoniam appellente ad ma<lb/>re remo, extremum illius, quod intus e&longs;t, in ante proinouetur: <lb/>nauem verò &longs;calmo alligatam &longs;imul promoueri contingit, <lb/>quo remi extremum. </s>

<s id="N12B8A">Mouetur autem nauis, quoniam appellente ad ma<lb/>re remo, extremum illius, quod intus e&longs;t, in ante promouetur: <lb/>nauem verò &longs;calmo alligatam &longs;imul promoueri contingit, <lb/>quo remi extremum. </s>

<s id="N12B93">V bi enim plurimum maris diuidit re<lb/>mus, eò maximè propelli nece&longs;&longs;e e&longs;i. </s>

<s id="N12B98">Plurimùm autem diuidit, <lb/>vbi pars plurima remi à &longs;calmo e&longs;t. </s>

<s id="N12B9D">Et eam ob cau&longs;am remi<lb/>ges, qui in media &longs;unt naui, mouent illam maximè. </s>

Line 1374

<s id="N12BF1">Ex quo Ari&longs;toteles aliam quoque rationem de&longs;umit, <lb/>quam cum priori (perob&longs;curè tamen) connectit: Quia ni<lb/>mirum adhuc foris pars remi in medio nauis con&longs;tituti, lon<lb/>gior e&longs;t iuxta proportionem prædictam, quæ ad commodi<lb/>tatem remigationis &longs;emper &longs;eruatur in v&longs;u. </s>

<s id="N12BFC">Longior autem <lb/>remi pars externa, &longs;eu palmula, maiorem aquæ portionem <lb/>diuidit, ac propellit, magi&longs;que propterea nauem promouet, <lb/>quàm quæ breuior e&longs;t ratione proportionis, ac &longs;itus. </s>

<s id="N12C05">Quare <lb/>ob&longs;eruandum e&longs;t, eam e&longs;&longs;e debitam remorum proportio<lb/>nem inter &longs;e, quæ e&longs;t inter &longs;itum, & &longs;itum nauis vbi con&longs;ti<lb/>tuuntur, ita vt vbi latior fuerit nauis, ibi productiores remi <lb/>con&longs;tituantur ex vtraque parte ip&longs;orum, quæ e&longs;t vtrinque à <lb/>fcalmo. </s>

<s id="N12C12">Hoc e&longs;t tam intus ex parte manubrij, quàm foris <pb pagenum="92" xlink:href="005/01/100.jpg"/>ex parte palmulæ. </s>

<s id="N12C1A">Et &longs;ic qui in medio &longs;unt remi, eo quod ibi <lb/>lati&longs;sima &longs;it nauis, longi&longs;&longs;imi &longs;unt, <expan abbr="maximèq.">maximèque</expan> proinde nauim <lb/>promouent; qui verò puppim ver&longs;us, aliquantulum breuio<lb/>res; ac breui&longs;&longs;imi, qui con&longs;tituuntur ad proram, propter ean<lb/>dem rationem; <expan abbr="ideoq.">ideoque</expan> minus, ac minus proportionaliter na<lb/>uem ip&longs;am valent mouere, &longs;eu vniformiter difformiter. </s>

<s id="N12C31">Explorati&longs;&longs;imum e&longs;t hoc experimentum, <expan abbr="ratioq.">ratioque</expan> vt vidi<lb/>mus manife&longs;ta. </s>

<s id="N12C3A">Sed contra Ari&longs;totelem obijciunt Blanca<lb/>nus, & <gap/>aldus, quòd mare potius, quàm &longs;calmus rationem <lb/>habere videatur fulcimenti. </s>

<s id="N12C3A">Sed contra Ari&longs;totelem obijciunt Blanca<lb/>nus, & Baldus, quòd mare potius, quàm &longs;calmus rationem <lb/>habere videatur fulcimenti. </s>

<s id="N12C43">Siquidem &longs;calmus eo quod af<lb/>fixus &longs;it naui, non manet, vt <expan abbr="propri&utilde;">proprium</expan> e&longs;t fulcimenti, &longs;ed fer<lb/>tur cum illa. </s>

<s id="N12C4E">Quare in ip&longs;orum &longs;ententia, ita remus con&longs;ti<lb/>tuitur vectis, vt <expan abbr="centr&utilde;">centrum</expan> habeat in extremitate palmulæ, qua <lb/>mari adhæret, atque innititur tanquam fulcimento; pondus <lb/><expan abbr="aut&etilde;">autem</expan> &longs;it nauis, & <expan abbr="pot&etilde;tia">potentia</expan> mouentis applicetur in manubrio. </s>

Line 1398

<s id="N12CD4">Sed forta&longs;<lb/>&longs;e difficile poterit hoc penitus determinari. </s>

<s id="N12CD9">Pendet enim <lb/>non modo à proportione partium remi, nempe quomodo <lb/>&longs;e habeat pars, quæ e&longs;t à &longs;calmo ad extremum manubrij ad <lb/>eam, quæ e&longs;t à &longs;calmo ad extremum palmulæ; verùm etiam <lb/>ab applicatione palmulæ in mare, vt &longs;i plus vel minus intro<lb/>mittatur, <expan abbr="maioremq.">maioremque</expan> portionem aquæ depellat. </s>

<s id="N12CEA">Quando<lb/>quidem &longs;i profundè palmula immergatur, <expan abbr="magnamq.">magnamque</expan> por<lb/>tionem aquæ per illam remiger conetur depellere, tunc pro<lb/>culdubio, minus mouebitur aqua retror&longs;um, quàm nauis an<lb/>tror&longs;um. </s>

<s id="N12CF9">Quod ex eo &longs;it palam, nam &longs;i nauis in mare me<lb/>diet inter duos &longs;copulos, ad quos palmulæ po&longs;&longs;int pertinge<lb/>re, &longs;imili conatu remiges &longs;copulos pul&longs;ando <gap/> aquam pul<lb/>&longs;are con&longs;ueuerunt, magis profecto nau<gap/> ip&longs;am mouebunt. <lb/></s>

<s id="N12CF9">Quod ex eo &longs;it palam, nam &longs;i nauis in mare me<lb/>diet inter duos &longs;copulos, ad quos palmulæ po&longs;&longs;int pertinge<lb/>re, &longs;imili conatu remiges &longs;copulos pul&longs;ando ac aquam pul<lb/>&longs;are con&longs;ueuerunt, magis profecto nauem ip&longs;am mouebunt. <lb/></s>

<s id="N12D07">Quod &longs;i alioquin palmulæ minimè immergantur, &longs;ed veluti <lb/>&longs;olam &longs;uper&longs;iciem aquæ depellant, certum etiam e&longs;t, magis <lb/>aquam illam depul&longs;am <expan abbr="totamq.">totamque</expan> ferè in &longs;pumam redactam <lb/>abire, quam nauem vlterius progredi, aut moueri </s>

<s id="N12D07">Quod &longs;i alioquin palmulæ minimè immergantur, &longs;ed veluti <lb/>&longs;olam &longs;uperficiem aquæ depellant, certum etiam e&longs;t, magis <lb/>aquam illam depul&longs;am <expan abbr="totamq.">totamque</expan> ferè in &longs;pumam redactam <lb/>abire, quam nauem vlterius progredi, aut moueri </s>

<s id="N12D16"><margin.target id="marg18"/>Polyb. lib. <lb/>1.longe an<lb/>te med.</s>

Line 1420

<s id="N12D7B">Ari&longs;toteles autem loquitur de motu recto. </s>

<s id="N12D7E">Deinde non ex <lb/>eo, quod punctum C eodem tempore maius &longs;patium per<lb/>currat, quàm punctum D vtpotè magis di&longs;tans à centro B, <lb/>iccirco &longs;equitur, magis mouere nauim remiges, qui ibi &longs;cal<lb/>mum habent affixum. </s>

<s id="N12D89">Etenim alia, per quam plura &longs;unt pun<lb/>cta in ip&longs;a naui, quæ maius adhuc &longs;patium percurrunt, quam <lb/>C, tanquam à centro remotiora; in quibus tamen &longs;i con&longs;ti<lb/>tueretur &longs;calmus, minus nauem remiges valerent mouere, <lb/>vt in cu&longs;pide puppis, vel proræ. </s>

<s id="N12D94">Quare motus ip&longs;ius C, & <lb/>cuiu&longs;libet alterins puncti remotionis à centro, quamuis ve<lb/>locior &longs;it, quàm m<gap/>us ip&longs;ius D, procedere pote&longs;t magis <lb/>ab impul&longs;uimpre&longs;&longs;o in ip&longs;o D, quàm ab impul&longs;u impre&longs;&longs;o <lb/>in eodem C, & &longs;ic magis mouere nauim eos, qui in nauis <lb/>medio &longs;unt remiges, etiam loquendo de motu circulari. </s>

<s id="N12D94">Quare motus ip&longs;ius C, & <lb/>cuiu&longs;libet alterius puncti remotionis à centro, quamuis ve<lb/>locior &longs;it, quàm m<gap/>us ip&longs;ius D, procedere pote&longs;t magis <lb/>ab impul&longs;u impre&longs;&longs;o in ip&longs;o D, quàm ab impul&longs;u impre&longs;&longs;o <lb/>in eodem C, & &longs;ic magis mouere nauim eos, qui in nauis <lb/>medio &longs;unt remiges, etiam loquendo de motu circulari. </s>

<s id="N12DA5">Rur&longs;us ex ip&longs;<gap/> Baldi probatione, atque conclu&longs;ione &longs;e<lb/>queretur, &longs;calmum vnius remi, magis di&longs;tare à &longs;calmo alte-<pb pagenum="95" xlink:href="005/01/103.jpg"/>rius po&longs;t lationem nauis, quàm antea. </s>

<s id="N12DA5">Rur&longs;us ex ip&longs;a Baldi probatione, atque conclu&longs;ione &longs;e<lb/>queretur, &longs;calmum vnius remi, magis di&longs;tare à &longs;calmo alte-<pb pagenum="95" xlink:href="005/01/103.jpg"/>rius po&longs;t lationem nauis, quàm antea. </s>

<s id="N12DB1">Quod &longs;ic pote&longs;t ex <lb/>proprijs di&longs;tinctius expo&longs;itis o&longs;tendi. </s>

<s id="N12DB6">Sint duo remi ante <lb/>motionem duæ <lb/><figure id="id.005.01.103.1.jpg" xlink:href="005/01/103/1.jpg"/><lb/>æquales para<lb/>lellæ, nempe <lb/>ADB in medio <lb/>nauis; & ACB <lb/>ver&longs;us proram. <lb/></s>

<s id="N12DCC"><expan abbr="Quor&utilde;">Quorum</expan> <expan abbr="manu-bri&utilde;">manu<lb/>brium</expan> &longs;it A, pal<lb/>mula verò B <lb/>Sitque fcalmus <lb/>vnius in D, al<lb/>terius verò in <lb/>C, magis <expan abbr="di-&longs;tãs">di<lb/>&longs;tans</expan> à B. </s>

<s id="N12DCC"><expan abbr="Quor&utilde;">Quorum</expan> <expan abbr="manu-bri&utilde;">manu<lb/>brium</expan> &longs;it A, pal<lb/>mula verò B <lb/>Sitque scalmus <lb/>vnius in D, al<lb/>terius verò in <lb/>C, magis <expan abbr="di-&longs;tãs">di<lb/>&longs;tans</expan> à B. </s>

<s id="N12DE8">Dein<lb/>de po&longs;t latio<lb/>nem <expan abbr="cõ&longs;tituan-tur">con&longs;tituan<lb/>tur</expan> ijdem remi <lb/>ADB in EGB, & ACB in EFB, vtrorumque extremis, <lb/>&longs;iue palmulis manentibus in eodem puncto B, & vtrorum<lb/>que manubrijs æqualiter à priori loco <expan abbr="di&longs;tãtibus">di&longs;tantibus</expan> per æqua<lb/>les arcus AE vtriu&longs;que remi. </s>

<s id="N12E01">Scalmus verò D con&longs;citua<lb/>tur in G, & &longs;calmus C in F; &longs;itque maius &longs;patium CF, <lb/>quam DG, vt rectè Baldus a&longs;&longs;umebat. </s>

<s id="N12E01">Scalmus verò D con&longs;titua<lb/>tur in G, & &longs;calmus C in F; &longs;itque maius &longs;patium CF, <lb/>quam DG, vt rectè Baldus a&longs;&longs;umebat. </s>

<s id="N12E0A">Dico igitur punctum G magis di&longs;tare à puncto F (quæ <lb/>e&longs;t di&longs;tantia vnius fcalmi ab altero po&longs;t lationem) quàm <lb/>punctum D di&longs;tet à puncto C, quæ erat di&longs;tantia eorun<lb/>dem ante motionem. </s>

<s id="N12E0A">Dico igitur punctum G magis di&longs;tare à puncto F (quæ <lb/>e&longs;t di&longs;tantia vnius scalmi ab altero po&longs;t lationem) quàm <lb/>punctum D di&longs;tet à puncto C, quæ erat di&longs;tantia eorun<lb/>dem ante motionem. </s>

<s id="N12E13">Ducantur enim rectæ CD & FG <lb/>&longs;ignantes vtramque di&longs;tantiam. </s>

<s id="N12E18">Et à puncto D, vbi prius <lb/>erat &longs;calmus remi exi&longs;tentis in medio nauis, excitetur alia <lb/>recta linea v&longs;que ad G, vbi idem &longs;calmus con&longs;tituitur po&longs;t<lb/>modum, atque &longs;uper ip&longs;a latera CD, & DG fiat paralel<lb/>logrammum CDGH. </s>

<s id="N12E23">Tunc quippe latus GH erit æquale <lb/>lateri CD & latus GD æquale erit lateri HC, eo quod <lb/>&longs;int oppo&longs;ita, vt patet per 34 primi Euclidis. </s>

<s id="N12E2B">Quoniam <pb pagenum="96" xlink:href="005/01/104.jpg"/>verò &longs;patium DG po&longs;itum e&longs;t minus, quam &longs;patium CF, <lb/>&longs;equitur lineam CH pertingere non po&longs;&longs;e v&longs;que ad pun<lb/>ctum F, cum ip&longs;a &longs;it æqualis ad DG. </s>

<s id="N12E38">Cumque ip<lb/><figure id="id.005.01.104.1.jpg" xlink:href="005/01/104/1.jpg"/><lb/>&longs;ius extremum <lb/>vbi H, &longs;it pari<lb/>ter terminus li<lb/>ne&etail;, &longs;eu lateris <lb/>GH, &longs;equitur <lb/>vlterius, vt ne<lb/>que linea GH <lb/>pertingere po&longs;<lb/>&longs;it <expan abbr="v&longs;q;">v&longs;que</expan> ad pun<lb/>ctum P. </s>

<s id="N12E5A">Erit <lb/>igitur maior li<lb/>nea GF quàm <lb/>&longs;it linea GH, & <lb/>linea CD, quæ <lb/>e&longs;t illi æqualis, <lb/>quod erat pro. <lb/></s>

<s id="N12E5A">Erit <lb/>igitur maior li<lb/>nea GF quàm <lb/>&longs;it linea GH, & <lb/>linea CD, quæ <lb/>e&longs;t illi æqualis, <lb/>quod erat pro<lb/></s>

<s id="N12E6A">bandum. </s>

<s id="N12E6F"><expan abbr="It&etilde;">Item</expan> hinc manife&longs;tè apparet fal&longs;um <expan abbr="quoq;">quoque</expan> e&longs;&longs;e, manubrium <lb/>remiad proram, vel puppim exi&longs;tentis, æquale &longs;patium per<lb/>tran&longs;ire, ac manubrium alterius remi in nauis medio con&longs;ti<lb/>tuti, palmulis vtriu&longs;que remi in eodem &longs;itu, &longs;eu puncto ma<lb/>nentibus, vt à Baldo a&longs;&longs;umebatur ad probandam &longs;uam con<lb/>clu&longs;ionem. </s>

<s id="N12E83">Quod ita facilè o&longs;tenditur ex hucu&longs;que demon<lb/>&longs;tratis. </s>

<s id="N12E83">Quod ita facilè o&longs;tenditur ex huiu&longs;que demon<lb/>&longs;tratis. </s>

<s id="N12E88">Nam &longs;i eo tempore quo &longs;calmus D fertur in G, <lb/>&longs;calmus C fertur in H ad æqualem di&longs;tantiam, vt proba<lb/>tum e&longs;t; vtique manubrium ip&longs;ius remi ad proram con&longs;ti<lb/>tuti, non erit in E, &longs;ed in I, vbi de&longs;init recta ducta à <lb/>centro B, per punctum H ad arcum AE. </s>

<s id="N12E94">Cumque AI <lb/>differat ab AE tanquam pars à toto, & vterque arcus AE <lb/>&longs;it alter alteri æqualis ex con&longs;tructione, palam fit, maius <lb/>&longs;patium percurrere manubrium A remi ADB in medio <lb/>nauis con&longs;tituti, dum fertur v&longs;que ad E, quàm manubrium <lb/>alterius remi, quo d fertur v&longs;que ad I. </s>

Line 1461

<s id="N12EE3">Videmus enim per impul&longs;um remigum incu&longs;&longs;um <lb/>in parte dextera &longs;calmum, ac nauigium moueri ad &longs;ini&longs;tram. <lb/></s>

<s id="N12EE9">Et ratio ip&longs;a &longs;uadet, quia cum nauis ita &longs;upernatet in aqua, <lb/>vt quoquouer&longs;um dimoueri valeat, quando nouam po&longs;itio<lb/>nem acquirit, per impul&longs;um in vno tantum latere acceptum <lb/>nece&longs;&longs;ariò intelligitur conuerti circa centrum &longs;uæ grauita<lb/>tis. </s>

<s id="N12EF4">Illi&longs;a igitur palmula in aquam in parte dextera, ab <expan abbr="eaq.">eaque</expan> <lb/>ob re&longs;i&longs;tentiam repul&longs;a, non &longs;ecus ac &longs;emidiametri extre<lb/>mum, nauim tanquam circulum ad &longs;ini&longs;tram mouebit. <lb/></s>

<s id="N12F00">Idem enim efficit aqua remigationi ob&longs;i&longs;tens, ac &longs;i quis pal<lb/>mulam repelleret in contrariam parcem. </s>

<s id="N12F00">Idem enim efficit aqua remigationi ob&longs;i&longs;tens, ac &longs;i quis pal<lb/>mulam repelleret in contrariam partem. </s>

<s id="N12F05">Cumque talis <lb/>remigatio fiat per modum circuli circa &longs;calmum proceden<lb/>do dextror&longs;um, &longs;equitur repul&longs;um accipi, ac &longs;ieri per op<lb/>po&longs;itum procedendo &longs;ini&longs;tror&longs;um. </s>

<s id="N12F05">Cumque talis <lb/>remigatio fiat per modum circuli circa &longs;calmum proceden<lb/>do dextror&longs;um, &longs;equitur repul&longs;um accipi, ac fieri per op<lb/>po&longs;itum procedendo &longs;ini&longs;tror&longs;um. </s>

<s id="N12F0E">Quamobrem ad hoc, <lb/>vt nauigium rectà antror&longs;um procedat, ex vtraque parte <lb/>&longs;imul remiges conantur impellere, vt ex vtroque motu cir<lb/>culari, & contrario, re&longs;ultet vnus rectus, ac mixtus. </s>

<s id="N12F17">Vt cer<lb/>nere e&longs;t in hac figura, in qua &longs;it remus AB, cuius manu<pb pagenum="98" xlink:href="005/01/106.jpg"/>brium A; palmula B, &longs;calmus verò C; ac &longs;patium, <lb/>quod percurrit pal<lb/><figure id="id.005.01.106.1.jpg" xlink:href="005/01/106/1.jpg"/><lb/>mula per motum <lb/>proprium ip&longs;ius re<lb/>mi circa &longs;calmum <lb/><expan abbr="tanquã">tanquam</expan> circa cen<lb/>trum &longs;it arcus BD. <lb/></s>

<s id="N12F38">Dico igitur per im<lb/>pul&longs;um incu&longs;&longs;um in <lb/>arcu BD palmu<lb/>lam nece&longs;&longs;ariò re<lb/>pelli in oppo&longs;itum per arcum BE, ac per con&longs;equens vir<lb/>tute huiu&longs;modi remigationis, &longs;calmum C, non ferri in <lb/>F, &longs;ed in G; ita vt arcus. </s>

<s id="N12F47">CG re&longs;pondeat ip&longs;i BE: Alio<lb/>quin repul&longs;us non opponeretur impul&longs;ui. </s>

<s id="N12F4C">Iam ergo per im<lb/>pul&longs;um incu&longs;&longs;um ex parte dextera, &longs;calmus C, & vnà cum <lb/>illo nauigium mouebitur ad &longs;ini&longs;tram. </s>

<s id="N12F53">Quod cum &longs;imilitet <lb/>verificetur è contra, vt per impetum incu&longs;&longs;um ex parte &longs;i<lb/>ni&longs;tra, nauigium moueatur ad dexteram: hinc &longs;it, vt ex <lb/>contrarijs motionibus vtrinque procedentibus. </s>

<s id="N12F53">Quod cum &longs;imiliter <lb/>verificetur è contra, vt per impetum incu&longs;&longs;um ex parte &longs;i<lb/>ni&longs;tra, nauigium moueatur ad dexteram: hinc &longs;it, vt ex <lb/>contrarijs motionibus vtrinque procedentibus. </s>

<s id="N12F5C">compona<lb/>tur vnus motus rectus, quo nauigium fertur antror&longs;um, vt <lb/>per lineam mediam, ac rectam CH. </s>

<s id="N12F63">Quod valde diuer<lb/>&longs;um e&longs;t ab eo, quod a&longs;&longs;umebatur à Baldo. </s>

Line 1483

<s id="N12F99">Hypomochlion enim in contra<lb/>rium ver&longs;atur: mare verò anteriùs, & illud exteriùs: illud <lb/>autem &longs;equitur nauis, quoniam illi e&longs;t alligata. </s>

<s id="N12FA0">Et remus <lb/>quidem &longs;ecundum latitudinem onus propellens, & ab eodem <lb/>repul&longs;us, in rectum propellit: gubernaculum autem vt obli<lb/>quum iacet, hinc inde in obliquum motionem facit. </s>

<s id="N12FA9">In ex<lb/>tremo autem, & non in medio iacet, quoniam mouenti facilli<lb/>mum e&longs;t ab extremo motum mouere. </s>

<s id="N12FB0">Prima enim pars celer<lb/>rimè fertur, & quoniam quemadmodum in ÿs, quæ ferun<lb/>tur, in fine deficit latio, &longs;ic ip&longs;ius continui, in fine imbecilli&longs;<lb/>&longs;ima e&longs;t latio. </s>

<s id="N12FB0">Prima enim pars celer<lb/>rimè fertur, & quoniam quemadmodum in ijs, quæ ferun<lb/>tur, in fine deficit latio, &longs;ic ip&longs;ius continui, in fine imbecilli&longs;<lb/>&longs;ima e&longs;t latio. </s>

<s id="N12FB9">Imbecilli&longs;sima autem ad expellendum e&longs;t fa<lb/>cilis. </s>

<s id="N12FBE">Propter hæc igitur in puppi gubernaculum ponitur: <lb/>nec minus, quoniam parua ibi motione facta, multò maius <lb/>interuallum fit in vltimo. </s>

<s id="N12FC5">Quia æqualis angulus &longs;emper <lb/>maiorem &longs;pectat, <expan abbr="tantòq.">tantòque</expan> magis, quantò maiores fuerint il<lb/>læ, quæ continent. </s>

<s id="N12FD0">Ex ÿs etiam manife&longs;ium e&longs;t, quam ob <lb/>cau&longs;am magis in contrarium procedit nauigium, quàm re<lb/>mi ip&longs;ius palmula: eadem magnitudo ÿ&longs;dem mota viribus, <lb/>in aere plus, quàm in aqua progreditur. </s>

<s id="N12FD0">Ex ijs etiam manife&longs;tum e&longs;t, quam ob <lb/>cau&longs;am magis in contrarium procedit nauigium, quàm re<lb/>mi ip&longs;ius palmula: eadem magnitudo ij&longs;dem mota viribus, <lb/>in aere plus, quàm in aqua progreditur. </s>

<s id="N12FD9">Sit enim AB remus, <lb/>C verò &longs;calmus. </s>

<s id="N12FDE">A autem in nauigio &longs;it remi principium, B <lb/>verò in mari palmula. </s>

<s id="N12FE3">Si igitur A vbi D <expan abbr="tran&longs;tat&utilde;">tran&longs;tatum</expan> e&longs;t, <expan abbr="nõ">non</expan> erit <lb/>B vbi E; æqualis enim BE ip&longs;i AD; æquale igitur tran&longs;tatum <lb/>erit, &longs;ed erat minus. </s>

Line 1500

<s id="N13019">V bi igitur <lb/>applicatum e&longs;t gubernaculum, id oportet rei motæ ceu quoddam <lb/>intelligere medium, & quemadmodum &longs;calmus remo. </s>

<s id="N13020">Me<lb/>dium autem procedit &longs;ecundum quod gubernaculum tran&longs;-<emph.end type="italics"/><pb pagenum="100" xlink:href="005/01/108.jpg"/><emph type="italics"/>fertur. </s>

<s id="N1302E">Siquidem intror&longs;us agit, & puppis eò transfertur, <lb/>prora verò ad contrarium vergit. </s>

<s id="N13033">In eodem enim exi&longs;tents <lb/>prora, totum transfertur nauigium.<emph.end type="italics"/></s>

<s id="N13033">In eodem enim exi&longs;tente <lb/>prora, totum transfertur nauigium.<emph.end type="italics"/></s>

<s id="N1303C">COMMENTARIVS.</s>

Line 1508

<s id="N13042">Celebris e&longs;t hæc quæ&longs;tio tum propter communem <lb/>admirationem ortam ex paruitate gubernaculi, ac <lb/>temonis re&longs;pectu magnæ molis nauigij, quæ illius <lb/>beneficio circumfertur: tum propter difficultatem, quæ <lb/>circa &longs;olutionem eiu&longs;dem quæ&longs;tionis, ac doctrinam Philo<lb/>&longs;ophi hic &longs;e&longs;e offert. </s>

<s id="N1304F">Quare vt luculentius in expo&longs;itione <lb/>procedamus, di&longs;tinguendum prius nobis erit inter ip&longs;um <lb/>remonem, &longs;eu clauum, & gubernaculum, quamuis ambo ad <lb/>vnicum pertineant in&longs;trumentum, ac &longs;æpe vnum pro alio <lb/>v&longs;urpetur. </s>

<s id="N1305A">Temonem itaque in præ&longs;enti vocamus cum <lb/>Ari&longs;totele alam illam ligneam, &longs;eu tabulam ad alæ veluti <lb/>fimilitudinem efformatam, quæ duplici cardine liberè in <lb/>dor&longs;o puppis affigitur, <expan abbr="mariq.">marique</expan> ex parte immergitur, & pro <lb/>opportunitate huc atque illuc ad directionem nauis con<lb/>uertitur. </s>

<s id="N1305A">Temonem itaque in præ&longs;enti vocamus cum <lb/>Ari&longs;totele alam illam ligneam, &longs;eu tabulam ad alæ veluti <lb/>similitudinem efformatam, quæ duplici cardine liberè in <lb/>dor&longs;o puppis affigitur, <expan abbr="mariq.">marique</expan> ex parte immergitur, & pro <lb/>opportunitate huc atque illuc ad directionem nauis con<lb/>uertitur. </s>

<s id="N1306B">Gubernaculum verò appellamus an&longs;am, qua te<lb/>mo ip&longs;e manu cietur; cuius videlicet alterum extremum <lb/>lato foramine excipit caput temonis; alterum intra nauim <lb/>&longs;e extendit tanquam mamibrium ad v&longs;um Gubernatoris. </s>

<s id="N13076">Deinde duplex con&longs;ideranda erit motio nauis mediante <lb/>huiu&longs;cemodi in&longs;trumento, quod ex gubernaculo, ac temo<lb/>ne con&longs;truitur. </s>

<s id="N1307D">Vna e&longs;t, quæ à gubernatore procedit per <lb/>motum ip&longs;ius gubernaculi, ac temonis, &longs;iue nauis aliunde <lb/>etiam moueatur &longs;iue quie&longs;cat. </s>

<s id="N13084">Quandoquidem dum temo, <lb/>qui rectà manebat mouetur in tran&longs;uer&longs;um pura ad dexte<lb/>ram, vel &longs;ini&longs;tram, nece&longs;&longs;ariò, maris <expan abbr="portion&etilde;">portionem</expan> propellit ver<lb/>&longs;us eam partem, in quam inclinatur, nece&longs;&longs;arioq: ab ea pro<lb/>pter re&longs;i&longs;tentiam repellitur in contrarium: & &longs;ic temo cum <lb/>puppi, cui e&longs;t affixus, repul&longs;o accepto in dextera, mouebi<lb/>tur ad &longs;ini&longs;tram, vel è conuer&longs;o. </s>

<s id="N13084">Quandoquidem dum temo, <lb/>qui rectà manebat mouetur in tran&longs;uer&longs;um pura ad dexte<lb/>ram, vel &longs;ini&longs;tram, nece&longs;&longs;ariò, maris <expan abbr="portion&etilde;">portionem</expan> propellit ver<lb/>&longs;us eam partem, in quam inclinatur, <expan abbr="nece&longs;&longs;arioq:">nece&longs;&longs;arioque</expan> ab ea pro<lb/>pter re&longs;i&longs;tentiam repellitur in contrarium: & &longs;ic temo cum <lb/>puppi, cui e&longs;t affixus, repul&longs;o accepto in dextera, mouebi<lb/>tur ad &longs;ini&longs;tram, vel è conuer&longs;o. </s>

<s id="N13097">Non enim aliter &longs;e habet <lb/>gubernaculum &longs;imul cum temone in hac motione, quàm <lb/>remus con&longs;titutus in cu&longs;pide puppis per longum iuxtare-<pb pagenum="101" xlink:href="005/01/109.jpg"/>ctitudinem carinæ, ita vt &longs;calmus &longs;it in ip&longs;a cu&longs;pide, manu<lb/>brium intra puppim, & palmula foris mari immer&longs;a. </s>

<s id="N130A5">Quia <lb/>nimirum eodem pacto &longs;i remi palmula mare propellerer ad <lb/>dexteram, ab eo vtique per re&longs;i&longs;tentiam repul&longs;a, &longs;imul cum <lb/>toto remo, &longs;calmo, ac puppi pergeret ad &longs;ini&longs;tram prora <lb/>manente immota, vel qua&longs;i immota. </s>

<s id="N130B0">Et hoc pacto magna <lb/>nauigia ab&longs;que remis &longs;olo temone conuerti &longs;olent in <lb/>portu. </s>

Line 1523

<s id="N130B9">Altera verò motio nauis, quæ &longs;it mediante gubernaculo, <lb/>ac temone, e&longs;t illa, quæ non procedit ab ip&longs;o gubernatore <lb/>tanquam à mouente, &longs;ed tanquam à &longs;u&longs;tinente temonem <lb/>in obliqua po&longs;itione ad excipiendum impetum maris oc<lb/>currentis, quo nauis ip&longs;a aliquantulum inclinatur. </s>

<s id="N130C4">Obliquè <lb/>namque con&longs;tituto temone, <expan abbr="nauigioq.">nauigioque</expan> ad anteriora progre<lb/>diente, nece&longs;&longs;ariò mare obuians temonem in ea parte, qua <lb/>tran&longs;uer&longs;um e&longs;t, offendit, <expan abbr="ip&longs;umq.">ip&longs;umque</expan> repellit. </s>

<s id="N130D5">Per quem repul<lb/>&longs;um temo ip&longs;e cum recta in contrarium ferri non po&longs;&longs;it, vi<lb/>delicet retror&longs;um, eo quod puppi &longs;it affixus procedenti an<lb/>tror&longs;um, obliquè &longs;altem ab itinere dimouetur, & cum eo <lb/>tota nauis à latere aliquantulum circumuertitur, vt mox in<lb/>fra latius explicabitur. </s>

<s id="N130E2">Illod interim adnotando, eandem <lb/>e&longs;&longs;e rationem de aqua in contrarium fluente, temonemque <lb/>cum naui &longs;tantem feriente, ac de aqua &longs;tante, inquam temo <lb/>obliquè con&longs;titutus dum fertur cum naui offendat. </s>

<s id="N130E2">Illud interim adnotando, eandem <lb/>e&longs;&longs;e rationem de aqua in contrarium fluente, temonemque <lb/>cum naui &longs;tantem feriente, ac de aqua &longs;tante, inquam temo <lb/>obliquè con&longs;titutus dum fertur cum naui offendat. </s>

<s id="N130EB">Non <lb/>minus enim vim patitur &longs;olidum manens à fluido currente, <lb/>quod excipit, vt velum à vento, quàm &longs;olidum currens à <lb/>fluido manente; vt verticilla ex papiro, quæ dum ge&longs;tantur <lb/>à pueris currentibus, circumaguntur ab aere quie&longs;cente, vel <lb/>tenuiter obuiante. </s>

<s id="N130FA">His ergo prænotatis facilè vim &longs;olutionis Ari&longs;totelis in <lb/>hac quæ&longs;tione percipiemus. </s>

<s id="N130FF">Ait enim ex eo guberna ulum, <lb/>ac temonem tantas vires habere in motione nauis, quod <lb/>vtrunque &longs;e habeat tanquam vectis, mare autem tanquam <lb/>onus, & gubernator, tanquam potentia. </s>

<s id="N130FF">Ait enim ex eo gubernaculum, <lb/>ac temonem tantas vires habere in motione nauis, quod <lb/>vtrunque &longs;e habeat tanquam vectis, mare autem tanquam <lb/>onus, & gubernator, tanquam potentia. </s>

<s id="N13108">Et enim &longs;i loqua<lb/>mur de prima motione &longs;upra explicata, non minus in illa <lb/>habet rationem vectis gubernaculum cum temone, quàm <pb pagenum="102" xlink:href="005/01/110.jpg"/>remus; Nec minus con&longs;tituitur mouens gubernator, quàm <lb/>remiger, vt per &longs;e patet. </s>

<s id="N13116">Si verò loquamur de &longs;ecunda mo<lb/>tione, adhuc idem in&longs;trumentum in illa con&longs;tituitur vectis <lb/>ad &longs;u&longs;tinendum impetum maris; innixum &longs;cilicet fulcimen<lb/>to, &longs;eu cardini, quo puppi coniungitur: Non &longs;ecus, ac quod<lb/>libet lignum alteri quomodolibet innixum ad &longs;u&longs;tinendum <lb/>onus impo&longs;itum. </s>

<s id="N13123">Gubernator autem con&longs;tituitur potentia, <lb/>nam adhibendo gubernaculum, temonem ip&longs;um &longs;u&longs;tentat <lb/>obliquum contra &longs;luctus maris, veluti qui vecte pondus <lb/>quod cumque &longs;u&longs;tinet, etiam &longs;i non moueatur. </s>

<s id="N13123">Gubernator autem con&longs;tituitur potentia, <lb/>nam adhibendo gubernaculum, temonem ip&longs;um &longs;u&longs;tentat <lb/>obliquum contra fluctus maris, veluti qui vecte pondus <lb/>quod cumque &longs;u&longs;tinet, etiam &longs;i non moueatur. </s>

<s id="N1312C">Mare deni<lb/>que in vtraque motione con&longs;tituitur onus; quoniam vel e&longs;t <lb/>id quod propellitur, vel id quod &longs;u&longs;tinetur per temonem <lb/>tran&longs;uer&longs;um ne directè in oppo&longs;itum fluat. </s>

<s id="N13137">Quamobrem immeritò nonnulli Ari&longs;totelem <expan abbr="redargu&utilde;t">redarguunt</expan>, <lb/>dicentes, mare habere potius rationem potentiæ mouentis <lb/>totam puppim cum temone; Nam &longs;icut &longs;axum, vectem cui <lb/>imponitur &longs;emper premit appetendo de&longs;cen&longs;um ad ima, <lb/>& tamen e&longs;t onus re&longs;pectu potentiæ, quæ vectem &longs;u&longs;tinet in <lb/>illo &longs;itu, ita mare, licet &longs;ucce&longs;&longs;iuè temonem impellat, ratio<lb/>nem habet oneris re&longs;pectu potentiæ manutenentis temo<lb/>nem in illo &longs;itu contra ictus eiu&longs;dem maris. </s>

<s id="N1314C">Quod &longs;i ip&longs;e <lb/>temo cum puppi, cui adhæret verè &longs;imul moueatur à mare, <lb/>per accidens e&longs;t, <expan abbr="proceditq.">proceditque</expan> à fluxibilitate aquæ, in qua diu <lb/>permanere non pote&longs;t puppis omnino immota ad &longs;u&longs;tinen<lb/>dum in &longs;uo cardine ip&longs;um temonem. </s>

<s id="N1315B">Motus enim fulcimen<lb/>ti per accidens &longs;e habet ad motum, vel operationem pro<lb/>priam vectis; vt motus &longs;calmi cum naui, cui e&longs;t affixus ad <lb/>motionem remi, qui tanquam vectis fulcitur in illo; vel mo<lb/>tus cuiuflibet fulcimenti, quod a&longs;portatur cum curru, ad <lb/>motionem vectis eidem innixi. </s>

<s id="N1315B">Motus enim fulcimen<lb/>ti per accidens &longs;e habet ad motum, vel operationem pro<lb/>priam vectis; vt motus &longs;calmi cum naui, cui e&longs;t affixus ad <lb/>motionem remi, qui tanquam vectis fulcitur in illo; vel mo<lb/>tus cuiuslibet fulcimenti, quod a&longs;portatur cum curru, ad <lb/>motionem vectis eidem innixi. </s>

<s id="N13168">Vnde potentia re&longs;pectu ve<lb/>ctis dicitur illa, quæ vectem adhibet, onus mouendo, vel &longs;u<lb/>&longs;tentando, non autem illa, quæ mouet fulcimentum. </s>

<s id="N1316F">Quare <lb/>tunc rectè mare diceretur potentia, cum mediante impetu <lb/>incu&longs;&longs;o in temonem, ip&longs;o tanquam vecte adhibito, moueret <lb/><expan abbr="man&utilde;">manum</expan> gubernatoris. </s>

<s id="N1317B"><expan abbr="C&utilde;">Cum</expan> igitur contra accidat, nempe, vt po<lb/>tius gubernator adhibito temone mare ad latus depellat, <pb pagenum="103" xlink:href="005/01/111.jpg"/>vel <expan abbr="&longs;alt&etilde;">&longs;altem</expan> excipiat re&longs;i&longs;tendo, iure & <expan abbr="quid&etilde;">quidem</expan> optimo guberna<lb/>tor ab Ari&longs;totele con&longs;tituitur potentia, mare autem onus. </s>

<s id="N13194">Sic autem explicato principio, ac in&longs;trum ento vtriu&longs;que <lb/>motionis, explicat Ari&longs;toteles modum, quo procedit &longs;ecun<lb/>da motio à nobis prop&longs;ita, quæ poti&longs;&longs;ima e&longs;t, & maioris <lb/>longè momenti quam prima: <expan abbr="aitq.">aitque</expan> temonem (quem cum <lb/>gubernaculo &longs;æpè confundit) non accipere mare &longs;ecundum <lb/>latitudinem nauis, &longs;eu quod ad latera nauis e&longs;t, eo modo <lb/>quo accipit remus, depellendo illud retror&longs;um, vt per repul<lb/>&longs;um inde acceptum, nauigium feratur antror&longs;um, quia nihil <lb/>temo nauigio confert, quo ad motum antror&longs;um, vt in fine <lb/>etiam quæ&longs;tionis idem Philo&longs;ophus animaduertit: Sed ac<lb/>cipere mare commotum, quod illi obuiat &longs;ecundum longi<lb/>tudinem nauis à prora in puppim. </s>

<s id="N13194">Sic autem explicato principio, ac in&longs;trumento vtriu&longs;que <lb/>motionis, explicat Ari&longs;toteles modum, quo procedit &longs;ecun<lb/>da motio à nobis propo&longs;ita, quæ poti&longs;&longs;ima e&longs;t, & maioris <lb/>longè momenti quam prima: <expan abbr="aitq.">aitque</expan> temonem (quem cum <lb/>gubernaculo &longs;æpè confundit) non accipere mare &longs;ecundum <lb/>latitudinem nauis, &longs;eu quod ad latera nauis e&longs;t, eo modo <lb/>quo accipit remus, depellendo illud retror&longs;um, vt per repul<lb/>&longs;um inde acceptum, nauigium feratur antror&longs;um, quia nihil <lb/>temo nauigio confert, quo ad motum antror&longs;um, vt in fine <lb/>etiam quæ&longs;tionis idem Philo&longs;ophus animaduertit: Sed ac<lb/>cipere mare commotum, quod illi obuiat &longs;ecundum longi<lb/>tudinem nauis à prora in puppim. </s>

<s id="N131B1">Nam qua parte temo <lb/>vergit foris, <expan abbr="matiq.">matique</expan> eius ala obuertitur ad alterum latus na<lb/>uigij, mare &longs;ecundum longitudinem nauis ei obuians exci<lb/>pit intra <expan abbr="angul&utilde;">angulum</expan>, quem cum naui con&longs;tituit. </s>

<s id="N131C2">Excipiendo au<lb/>tem iliud vim patitur in <expan abbr="contrari&utilde;">contrarium</expan>, tollereturq ni&longs;i fulciretur <lb/>in cardine. </s>

<s id="N131C2">Excipiendo au<lb/>tem illud vim patitur in <expan abbr="contrari&utilde;">contrarium</expan>, <expan abbr="tollereturq">tollereturque</expan> ni&longs;i fulciretur <lb/>in cardine. </s>

<s id="N131CD">Cum igitur nec auferri po&longs;&longs;it à puppi, nec retro<lb/>cedere in <expan abbr="direct&utilde;">directum</expan> <expan abbr="cõtra">contra</expan> cur&longs;um nauigij, hinc fit, vt cedendo <lb/><expan abbr="&longs;alt&etilde;">&longs;altem</expan> in parte quoad po&longs;itionem, <expan abbr="quã">quam</expan> prius habebat, nauem <lb/><expan abbr="ipsã">ipsam</expan> inclinet obliquè; &longs;iqui<lb/><figure id="id.005.01.111.1.jpg" xlink:href="005/01/111/1.jpg"/><lb/>dem dimoto vno latere an<lb/>guli à &longs;ua po&longs;itione, <expan abbr="alter&utilde;">alterum</expan> <lb/>dimoueri nece&longs;&longs;e e&longs;t, cu&longs;pi<lb/>de manente in eodem &longs;itu. <lb/></s>

<s id="N131FB">Quod &longs;ic pote&longs;t amplius <lb/>explicari. </s>

<s id="N13200">E&longs;to nauis AB; <lb/>cuius puppis A, prora B, te<lb/>mo verò AC obliquè con<lb/>&longs;titutus ad &longs;ini&longs;tram, ac &longs;uf<lb/>fultus in A, vbi eius cardo <lb/>ad puppim po&longs;itus e&longs;t, & <lb/>vbi <expan abbr="angul&utilde;">angulum</expan> efficiat <expan abbr="c&utilde;">cum</expan> <expan abbr="lõgi-tudine">longi<lb/>tudine</expan> nauis, qui &longs;it BAC. <lb/></s>

<s id="N1321E">Deinde mare obuians incidat in ip&longs;am AC. </s>

<s id="N13222">Tunc dicimus <pb pagenum="104" xlink:href="005/01/112.jpg"/>punctum C fore, vt transferatur ver&longs;us D; punctum verò <lb/>B, quod proram de&longs;ignat, ver&longs;us E, cardine manente <lb/>immoto vbi A. </s>

<s id="N1322F">Etenim cum mare &longs;olum impellat temo<lb/>nem inquantum obliquè con&longs;tituitur, & à nauis rectitudine <lb/>deuiat, efficacius impellit extremum vbi C, quod magis <lb/>elongatur ab ea, quàm reliquas partes, quæ minus, ac mi<lb/>nus di&longs;tant. </s>

<s id="N1323A">Proindeq remi&longs;&longs;ius, ac remi&longs;&longs;ius agit in illas <lb/>vniformiter difformiter v&longs;que ad punctum A, vbi &longs;icut ter<lb/>minatur di&longs;tantia, ac diuiatio, ita etiam deficit impul&longs;us. </s>

<s id="N1323A"><expan abbr="Proindeq">Proindeque</expan> remi&longs;&longs;ius, ac remi&longs;&longs;ius agit in illas <lb/>vniformiter difformiter v&longs;que ad punctum A, vbi &longs;icut ter<lb/>minatur di&longs;tantia, ac diuitatio, ita etiam deficit impul&longs;us. </s>

<s id="N13241">Ex <lb/>quo &longs;equitur punctum A, per&longs;e non moueri ad talem im<lb/>pul&longs;um, &longs;ed tantum lineam AC circa illud tanquam &longs;emi<lb/>diametrum circa centrum conuerti, ac declinare ver&longs;us D. <lb/></s>

<s id="N1324C">Cumque longitudo nauis angulum cum ip&longs;a latitudine te<lb/>monis efficiat, &longs;equitur vlterius, vt tran&longs;lato ip&longs;o latere <lb/>AC, in AD, &longs;imul transferatur AB in AE, quod e&longs;t na<lb/>uem declinare à &longs;ua rectitudine, ad obliquam po&longs;itionem <lb/>temonis mare intra angulum excipienris. </s>

<s id="N13257">Diximus punctum <lb/>A per &longs;e non moueri ob talem impul&longs;um, nam per acci<lb/>dens, nempe propter maris incon&longs;tantiam, ac fluxibilitatem <lb/>etiam ip&longs;um puppis extremum aliquantulum dimouetur <lb/>cum cardine, quo temo fulcitur, &longs;icut quodlibet fulcimen<lb/>tum ad motum vectis ob incon&longs;tantiam &longs;oli. </s>

<s id="N13266">Contrario autem modo temonem innixum, ait Ari&longs;toce<lb/>les nauem inclinare, quoniam temo rationem habet vectis, <lb/>vt dictum e&longs;t cardini innixi tanquam fulcimento, mare au<lb/>tem &longs;e habet, vt onus: At omnis vectis mediat inter fulci<lb/>mentum, & onus, nec aliter quam fulcimento tanquam cen<lb/>tro inhærendo, onus per modum circuli in contrarium mo<lb/>uet, aut certè &longs;u&longs;tinet in tali po&longs;itione; Ergo dum temo &longs;u<lb/>&longs;tinet mare cardini innixus tamquam fulcimento, & angu<lb/>lum cum naui efficit ad excipiendum mare interius, cardo <lb/>manebit exterius tanquam ex alia parte ip&longs;ius vectis illi <lb/>contraria, ad quam facit nauem inclinarc. </s>

<s id="N13266">Contrario autem modo temonem innixum, ait Ari&longs;tote<lb/>les nauem inclinare, quoniam temo rationem habet vectis, <lb/>vt dictum e&longs;t cardini innixi tanquam fulcimento, mare au<lb/>tem &longs;e habet, vt onus: At omnis vectis mediat inter fulci<lb/>mentum, & onus, nec aliter quam fulcimento tanquam cen<lb/>tro inhærendo, onus per modum circuli in contrarium mo<lb/>uet, aut certè &longs;u&longs;tinet in tali po&longs;itione; Ergo dum temo &longs;u<lb/>&longs;tinet mare cardini innixus tamquam fulcimento, & angu<lb/>lum cum naui efficit ad excipiendum mare interius, cardo <lb/>manebit exterius tanquam ex alia parte ip&longs;ius vectis illi <lb/>contraria, ad quam facit nauem inclinari. </s>

<s id="N1327F">Ad hæc Ari&longs;toteles rationem quandam affert cur in ex<lb/>tremo nauigij, & non in medio temo, &longs;eu clauus locetur, <lb/><expan abbr="aitq.">aitque</expan> eam e&longs;&longs;e, quoniam id quod fertur, facilius ab incepto <pb pagenum="105" xlink:href="005/01/113.jpg"/>itinere, &longs;eu à rectitudine &longs;ui motus declinat, cum in po&longs;tre<lb/>ma eius parte ex latere diuer&longs;um aliquem impul&longs;um acce<lb/>pit, quàm &longs;i accip at in alia parte anteriori. </s>

<s id="N13292">Prima enim. <lb/></s>

<s id="N13296">&longs;eu anterior pars lati <expan abbr="cõtinui">continui</expan>, inten&longs;iori impetu fertur, quàm <lb/>partes &longs;ub&longs;equentes, <expan abbr="validiu&longs;q.">validiu&longs;que</expan> propterea in &longs;uo motu per&longs;i<lb/>&longs;tit, <expan abbr="contrarijsq.">contrarijsque</expan> omnibus ob&longs;i&longs;tit. </s>

<s id="N132A9">E contra verò vltima. <lb/></s>

<s id="N132AD">pars, tanquam remi&longs;&longs;iorem vim con&longs;ecuta, imbecillius mo<lb/>uetur, ac facilius cædit. </s>

<s id="N132B2">Id quod maximè in proiectis ob<lb/>&longs;eruare licebit. </s>

<s id="N132B7">Impetus namque in ea à proijciente im<lb/>pre&longs;&longs;us, &longs;emper maior e&longs;t in eorum parte anteriori, quàm in <lb/>&longs;equentibus: &longs;eu illa pars eorum con&longs;t tuitur anteriot, cæ<lb/>terasq in latione præcedit, in qua maior impetus fuerit <lb/>impre&longs;&longs;us. </s>

<s id="N132B7">Impetus namque in ea à proijciente im<lb/>pre&longs;&longs;us, &longs;emper maior e&longs;t in eorum parte anteriori, quàm in <lb/>&longs;equentibus: &longs;eu illa pars eorum con&longs;tituitur anterior, cæ<lb/><expan abbr="terasq">terasque</expan> in latione præcedit, in qua maior impetus fuerit <lb/>impre&longs;&longs;us. </s>

<s id="N132C2">Vnde cum den&longs;itas materiæ, aut grauitas &longs;ubie<lb/>cti, inten&longs;ioris impetus capax redat ip&longs;um proiectum, hinc <lb/>fit, vt etiam &longs;i in principio motus pars grauior, vel den&longs;ior <lb/>fuerit po&longs;terior in progre&longs;&longs;u euadat anterior. </s>

<s id="N132CB">Quod apertè <lb/>in proiectione baculi experimur quando anteponitur extre<lb/>mum leuius, & po&longs;ponitur grauius; nam ex &longs;e ip&longs;a extrema <lb/>permutantur in aere, <expan abbr="priusq.">priusque</expan> grauius quàm leuius quo ten<lb/>debant pertingit. </s>

<s id="N132DA">Certum ergo relinquitur, vt quo <gap/>nte<lb/>riores fuerint partes ip&longs;is lati continui, eo validius ferantur <lb/>tanquam maiorem adeptæ, aut &longs;ortitæ impetum, quo verò <lb/>po&longs;teriores, eo imbecillius, vnde etiam facilius vincantur. <lb/></s>

<s id="N132DA">Certum ergo relinquitur, vt quo ante<lb/>riores fuerint partes ip&longs;is lati continui, eo validius ferantur <lb/>tanquam maiorem adeptæ, aut &longs;ortitæ impetum, quo verò <lb/>po&longs;teriores, eo imbecillius, vnde etiam facilius vincantur. <lb/></s>

<s id="N132E6">Hoc ip&longs;um itaque applicando in latione nauis, ait Ari&longs;tote<lb/>les, quod cum nauis rectà fertur antror&longs;um, facilius e&longs;t illam <lb/>à cur&longs;u deflectere puppim à latere impellendo, quàm aliam <lb/>eiu&longs;dem nauis partem mediam, aut proram. </s>

<s id="N132EF">Siquidem in <lb/>puppi tanquam in po&longs;trema lati corpotis parte imbecilli&longs;&longs;i<lb/>ma virtus e&longs;t impetus impre&longs;&longs;i, in <expan abbr="eaq.">eaque</expan> terminatur, ac deficit <lb/>latio. </s>

<s id="N132EF">Siquidem in <lb/>puppi tanquam in po&longs;trema lati corporis parte imbecilli&longs;&longs;i<lb/>ma virtus e&longs;t impetus impre&longs;&longs;i, in <expan abbr="eaq.">eaque</expan> terminatur, ac deficit <lb/>latio. </s>

<s id="N132FC">Quare appo&longs;itè clauus in puppilocatur ad excipien<lb/>dos ibi maris impul&longs;us, vt facilius à rectitudine itineris na<lb/>uis ip&longs;a deflectat. </s>

<s id="N13305">Quæ profectò Ari&longs;totelis doctrina, eiusq applicatio, &longs;a<lb/>no modo intelligenda e&longs;t. </s>

<s id="N13305">Quæ profectò Ari&longs;totelis doctrina, <expan abbr="eiusq">eiusque</expan> applicatio, &longs;a<lb/>no modo intelligenda e&longs;t. </s>

<s id="N1330A">Nam licet quando nauigia vni<lb/>co velo in prora locato feruntur, præcipuus impetus per <lb/>malum circa ip&longs;am proram incutiatur; nihilominus quando <pb pagenum="106" xlink:href="005/01/114.jpg"/>remis, vel pluribus velis nauigare contingit, <expan abbr="puppisq.">puppisque</expan> pari<lb/>ter obtinet &longs;uum; res aliter &longs;e habet, cum pari, aut maiori <lb/>impetu, tunc puppis quàm prora feratur, quippe quæ illum <lb/>refundere etiam valeat vlterius in ip&longs;am proram. </s>

<s id="N13320">Id quod <lb/>patet cum ex maiori velocitate, qua mouetur nauigium, ac <lb/>ip&longs;a prora adhibitis etiam velis, aut remis in puppi, &longs;eu pro<lb/>pe illam; tum ex maiori conatu, quem adhibent remiges, <lb/>quò magis prope puppim remigauerint; vt hinc in triremi<lb/>bus ad priores &longs;ingulos remos promouendos con&longs;tituantur <lb/>remiges quini, aut &longs;eni, ad reliquos verò, proram ver&longs;us pro<lb/>cedendo, quaterni, ac tandem terni. </s>

<s id="N13331">Vbi autem maior co<lb/>natus adhibetur, ibi maior imprimitur impetus. </s>

Line 1592

<s id="N1337A">Quia nimirum parua mo<lb/>tione per temonem facta in eo &longs;itu, multo maius interual<lb/>lum prora obliquè declinando percurrit, vt patere pote&longs;t <lb/>ex præcedenti figura <expan abbr="tantoq.">tantoque</expan> magis, quanto longior fuerit <pb pagenum="107" xlink:href="005/01/115.jpg"/>ip&longs;a nauis. </s>

<s id="N1338C">Etenim idem, vel æqualis angulus, quo in<lb/>ter longiores lineas continetur, eo maiorem ba&longs;im &longs;ubten<lb/>dit, &longs;eu &longs;pectat, vt con&longs;tare etiam pote&longs;t per quartam propo<lb/>&longs;itionem &longs;exti Euclidis. </s>

<s id="N13396">Cum igitur longitudo nauis con&longs;i<lb/>derata in priori &longs;itu, deinde in po&longs;teriori po&longs;t <expan abbr="motion&etilde;">motionem</expan> <expan abbr="cir-cular&etilde;">cir<lb/>cularem</expan>, immota ferè manente cu&longs;pide puppis, <expan abbr="angul&utilde;">angulum</expan> quen<lb/>dam efficiat, vt BAE, cuius ba&longs;is EB: tanto maiorem ip&longs;a <lb/>prora veluti ba&longs;im tran&longs;mittet ad motionem temonis quan<lb/>to longior fuerit ip&longs;a nauis. </s>

<s id="N133AF">Quod quippe non contingeret <lb/>&longs;i alibi temo con&longs;titutus <lb/>fui&longs;&longs;et, indeq talismotio <lb/><figure id="id.005.01.115.1.jpg" xlink:href="005/01/115/1.jpg"/><lb/>initium &longs;umeret. </s>

<s id="N133AF">Quod quippe non contingeret <lb/>&longs;i alibi temo con&longs;titutus <lb/>fui&longs;&longs;et, <expan abbr="indeq">indeque</expan> talis motio <lb/><figure id="id.005.01.115.1.jpg" xlink:href="005/01/115/1.jpg"/><lb/>initium &longs;umeret. </s>

<s id="N133BE">Quam<lb/>obrem con&longs;entanea idem <lb/>Ari&longs;toteles protulit lib.

de <lb/>motu animal. </s>

Line 1605

<s id="N133E3">Ari&longs;toteles pertran&longs;it, cuius &longs;olutionem hic in&longs;erit, vt po<lb/>&longs;tea ex ea melius præfata confirmet. </s>

<s id="N133E8">Ait igitur ex ijs etiam <lb/>manife&longs;tum e&longs;&longs;e, quam ob cau&longs;am magis procedat naui<lb/>gium antror&longs;um, quàm ip&longs;ius remi palmula mare reijciens <lb/>cædat retror&longs;um. </s>

<s id="N133F1">Eadem enim (inquit) magnitudo, ij&longs;<lb/>dem mota viribus, plus in aere progreditur, quàm in aqua; <lb/>eo &longs;cilicet, quod minorem in aere inueniat re&longs;i&longs;tentiam. <lb/></s>

<s id="N133F9">Quod ip&longs;e quamuis ob&longs;curè propter defectum quorundam <lb/>verborum, ac fal&longs;itatem characterum, quibus figuram pro<lb/>pont, &longs;ic ferè explicat in propo&longs;ito. </s>

<s id="N133F9">Quod ip&longs;e quamuis ob&longs;curè propter defectum quorundam <lb/>verborum, ac fal&longs;itatem characterum, quibus figuram pro<lb/>ponit, &longs;ic ferè explicat in propo&longs;ito. </s>

<s id="N13400">Sitremus AB, &longs;cal-<pb pagenum="108" xlink:href="005/01/116.jpg"/><figure id="id.005.01.116.1.jpg" xlink:href="005/01/116/1.jpg"/><lb/>mus verò C, remi manubrium A, palmula in mari B. <lb/></s>

<s id="N1340F">Si igitur manubrium A per aerem transferatur in D; vti<lb/>que palmula B transferri non poterit per aquam in E. <lb/></s>

<s id="N13416">Quandoquidem non po&longs;&longs;et cum maiori re&longs;i&longs;tentia æquale <lb/>&longs;patium pertran&longs;ire, quemadmodum e&longs;t &longs;patium BE ip&longs;i <lb/>AD. </s>

Line 1614

<s id="N13436">Addit præterea Ari&longs;toteles, quod inter i&longs;tos duos motus <lb/>contrarios id quod &longs;tabit, &longs;eu manebit, erit medium pun<lb/>ctum vbi C, nempe vbi con&longs;tituitur &longs;calmus circa quem <lb/>remus conuertitur. </s>

<s id="N1343F">Siquidem verè re&longs;pectu manubrij, ac <lb/>palmulæ, tanquam ex<gap/>remorum diametri circulariter du<lb/>ctæ, &longs;calmus ip&longs;e tanquam <expan abbr="c&etilde;trum">centrum</expan> manebit. </s>

<s id="N1343F">Siquidem verè re&longs;pectu manubrij, ac <lb/>palmulæ, tanquam extremorum diametri circulariter du<lb/>ctæ, &longs;calmus ip&longs;e tanquam <expan abbr="c&etilde;trum">centrum</expan> manebit. </s>

<s id="N1344C">Quare &longs;calmus <lb/>C nunquam procederet ad partes D, nempe antror&longs;um, <lb/>ni&longs;i commoueretur nauigium, cui e&longs;t affixus, & eo transfer<lb/>retur, vbi remi e&longs;t principium, cum &longs;emper nauigium per <lb/>impul&longs;um in ip&longs;a remigatione acceptum, &longs;equatur motum. <lb/></s>

<s id="N13458">principij mouentis nempe manubrij à quo fertur antror<lb/>&longs;um, & &longs;ic impo&longs;ito per motum manubrij ab A v&longs;que ad <lb/>D, &longs;calmus, qui erat in C, con&longs;tituetur in H, palmula re<lb/>trocedente à B v&longs;que ad F. </s>

Line 1624

<s id="N13480">ratione fiat. </s>

<s id="N13485">Dicendum ergo e&longs;t, <expan abbr="aliquãdo">aliquando</expan> <expan abbr="nauigi&utilde;">nauigium</expan> in <expan abbr="anter&itilde;ora">anterinora</expan> moue<lb/><gap/>i ab&longs;que eo, quod palmula rettocedat, aliquando verò tan<lb/>tum prouehi nauigium, quantum palmula retroce&longs;&longs;erit; &longs;ed <lb/>vt plurimum, magis procedinauigium, quàm palmula in. <lb/></s>

<s id="N13485">Dicendum ergo e&longs;t, <expan abbr="aliquãdo">aliquando</expan> <expan abbr="nauigi&utilde;">nauigium</expan> in <expan abbr="anter&itilde;ora">anterinora</expan> moue<lb/>ri ab&longs;que eo, quod palmula retrocedat, aliquando verò tan<lb/>tum prouehi nauigium, quantum palmula retroce&longs;&longs;erit; &longs;ed <lb/>vt plurimum, magis procedi nauigium, quàm palmula in. <lb/></s>

<s id="N1349C">contrarium cædat. </s>

<s id="N134A1">Prima pars huius a&longs;&longs;ertionis in duobus ca&longs;ibus verifica<lb/>tur. </s>

<s id="N134A6">Prior e&longs;t, cum æquale &longs;patium pertran&longs;ierit nauigium, <lb/>ac remi manubrium motu proprio, quo &longs;eilicet circa &longs;cal<lb/>mum conuertitur: tunc eorum palmula manet immota. <lb/></s>

<s id="N134A6">Prior e&longs;t, cum æquale &longs;patium pertran&longs;ierit nauigium, <lb/>ac remi manubrium motu proprio, quo &longs;cilicet circa &longs;cal<lb/>mum conuertitur: tunc eorum palmula manet immota. <lb/></s>

<s id="N134AE">Nam &longs;i exempli gratia nauigium pertran&longs;eat palmum &longs;pa<lb/>tij, manubrium verò &longs;imul &longs;uo motu proprio alterum, iam, <lb/>in fine ip&longs;ius remigationis ip&longs;urn manubrium per duos pal<lb/>mos di&longs;tabit à loco priori vnde di&longs;ce&longs;&longs;erat. </s>

<s id="N134AE">Nam &longs;i exempli gratia nauigium pertran&longs;eat palmum &longs;pa<lb/>tij, manubrium verò &longs;imul &longs;uo motu proprio alterum, iam, <lb/>in fine ip&longs;ius remigationis ip&longs;um manubrium per duos pal<lb/>mos di&longs;tabit à loco priori vnde di&longs;ce&longs;&longs;erat. </s>

<s id="N134B7">At palmula cum <lb/>per motum quidem nauigij anterius tran&longs;lata e&longs;&longs;et ad &longs;pa<lb/>tium vnius palmi, per motum verò manubrij &longs;imul retro<lb/>ee&longs;&longs;i&longs;&longs;et ad alium palmum (fiquidem tantum retrocedit pal<lb/>mula quantum antecedit manubrium motu proprio, &longs;uppo<lb/>&longs;&longs;to, quod æquè di&longs;tent à &longs;calmo) &longs;equitur verè ac &longs;implici<lb/>ter ip&longs;am palmulam dimotam non fui&longs;&longs;e. </s>

<s id="N134B7">At palmula cum <lb/>per motum quidem nauigij anterius tran&longs;lata e&longs;&longs;et ad &longs;pa<lb/>tium vnius palmi, per motum verò manubrij &longs;imul retro<lb/>ce&longs;&longs;i&longs;&longs;et ad alium palmum (siquidem tantum retrocedit pal<lb/>mula quantum antecedit manubrium motu proprio, &longs;uppo<lb/>&longs;ito, quod æquè di&longs;tent à &longs;calmo) &longs;equitur verè ac &longs;implici<lb/>ter ip&longs;am palmulam dimotam non fui&longs;&longs;e. </s>

<s id="N134C6">Sicut homo qui <lb/>pari pa&longs;&longs;a graditur contra cur&longs;um nauigij à prora in pup<lb/>pim, &longs;impliciter non mouetur, quia &longs;emper eandem &longs;eruat <lb/>di&longs;tantiam à punctis fixis, vt a terra, vel cælo. </s>

<s id="N134D1">Notand<gap/>m tamen e&longs;t in ca&longs;u de&longs;cripto, nauigium non. <lb/></s>

<s id="N134D1">Notandum tamen e&longs;t in ca&longs;u de&longs;cripto, nauigium non. <lb/></s>

<s id="N134D7">moueri &longs;ola virtute eiu&longs;dem remigationis. </s>

<s id="N134DA">Nam &longs;patium, <lb/>quod percurrit virtute illius, nec computari po&longs;&longs;et vltra il<lb/>&longs;ud, quod &longs;imul percurrit manubrium motu proprio; nec <lb/>vnquam e&longs;&longs;et illi equale. </s>

<s id="N134DA">Nam &longs;patium, <lb/>quod percurrit virtute illius, nec computari po&longs;&longs;et vltra il<lb/>lud, quod &longs;imul percurrit manubrium motu proprio; nec <lb/>vnquam e&longs;&longs;et illi equale. </s>

<s id="N134E3">Semper enim plus mouetur ma-<pb pagenum="110" xlink:href="005/01/118.jpg"/>nubrium, quam &longs;calmus eodem tempore ad impullum il<lb/>lius; nauis autem mouetur ad motum &longs;calmi. </s>

<s id="N134E3">Semper enim plus mouetur ma-<pb pagenum="110" xlink:href="005/01/118.jpg"/>nubrium, quam &longs;calmus eodem tempore ad impulsum il<lb/>lius; nauis autem mouetur ad motum &longs;calmi. </s>

<s id="N134ED">Quod clarius <lb/>patebit in &longs;ubiecta figura; in qua &longs;it remus AB, cuius ma<lb/>nubrium A, pal<lb/><figure id="id.005.01.118.1.jpg" xlink:href="005/01/118/1.jpg"/><lb/>mula B, &longs;calmus <lb/>verò &longs;it in pun<lb/>cto medio vbi C. <lb/></s>

<s id="N13502">Deinde promo-<lb/>ueatur manubrium <lb/>A motu proprio <lb/>v&longs;que ad D, palmnla manente in B. </s>

<s id="N13502">Deinde promo-<lb/>ueatur manubrium <lb/>A motu proprio <lb/>v&longs;que ad D, palmula manente in B. </s>

<s id="N1350B">Scalmus verò C, <lb/>eodem tempore pertran&longs;eat &longs;patium CE, quod &longs;it æquale <lb/>ip&longs;i AD; <expan abbr="&longs;ubtendanturq.">&longs;ubtendanturque</expan> æquales rectæ ip&longs;is arcubus AD, <lb/>& CE, & con&longs;tituatur paralellogrammum DECA, &longs;u<lb/>per ip&longs;um AB. </s>

<s id="N1351B">Tunc dico &longs;calmum C vnà cum nauigio <lb/>tran&longs;latum non fui&longs;&longs;e v&longs;que ad E virtute &longs;ola eiu&longs;dem re<lb/>migationis, &longs;eu proprij motus manubrij ab A v&longs;que ad D, <lb/>palmula manente in B. </s>

<s id="N13524">Siquidem hoc &longs;olo motu remus <lb/>AB con&longs;titueretur in recta DB, cuius punctum medium <lb/>vbi&longs;calmus po&longs;itus e&longs;t e&longs;&longs;et in F, non autem in E, qua <lb/>pertran&longs;ire non pote&longs;t recta DB. </s>

Line 1651

<s id="N1356D">Po&longs;terior verò ca&longs;us, in quo verificatur palmulam ad mo<lb/>tum antror&longs;um nauigij <expan abbr="nõ">non</expan> retrocedere, e&longs;t cum celerius fer<lb/>tur nauigium, quàm remi manubrium. </s>

<s id="N13578"><expan abbr="Siquid&etilde;">Siquidem</expan> cum in tan<lb/>tum palmula po&longs;&longs;it retrocedere, inquantum manubrium <lb/>motu proprio in anteriora amplius progreditur quàm naui<lb/>gium, &longs;i celerius feratur nauigium quàm manubrium, ma<lb/>in&longs;que proinde &longs;patium percurrat, palmula nullo modo po<lb/>terit retrocedere. </s>

<s id="N13578"><expan abbr="Siquid&etilde;">Siquidem</expan> cum in tan<lb/>tum palmula po&longs;&longs;it retrocedere, in quantum manubrium <lb/>motu proprio in anteriora amplius progreditur quàm naui<lb/>gium, &longs;i celerius feratur nauigium quàm manubrium, ma<lb/>iu&longs;que proinde &longs;patium percurrat, palmula nullo modo po<lb/>terit retrocedere. </s>

<s id="N13588">Etenim po&longs;ito, quod manubrium motu <lb/>proprio decurrat &longs;patium bipalmare, per totidem palmos <lb/>palmula retrocederet, &longs;i nauigium maneret immotum: At <lb/>&longs;i &longs;imul nauigium percurrat &longs;patium quadripalmare, nihil <lb/>palmula retrocedet. </s>

<s id="N13593">Nam quo tempore retrocederet <expan abbr="vn&utilde;">vnum</expan>, <lb/>duplum progrederetur in contrarium. </s>

Line 1662

<s id="N135C0">Tertia denique a&longs;&longs;ertionis pars, nempe magis, vt pluri<lb/>mum prògre di nauigium, quàm palmulam incontrarium, <lb/>ex dictis ferè o&longs;tenditur aperti&longs;simè. </s>

<s id="N135C7">Quia licet maius &longs;pa<lb/>tium decurrat remi manubrium, quàm nauigium, quando <lb/>ip&longs;um nauigium mouetur &longs;olùm in virtute eiu&longs;dem remiga<lb/>tionis, vt frequentius accidit: rarò tamen exce&longs;&longs;us ad dimi<lb/>dium videtur pertingere, ita vt manubrium motu proprio <lb/>duplum conficiat &longs;patium, quàm nauigium. </s>

<s id="N135D4">Cum autem <lb/>huiu&longs;modi exce&longs;&longs;us ad dimidium non pertingit, neque pal<lb/>mula per æquale &longs;patium retrocedet, &longs;ed minns. </s>

<s id="N135D4">Cum autem <lb/>huiu&longs;modi exce&longs;&longs;us ad dimidium non pertingit, neque pal<lb/>mula per æquale &longs;patium retrocedet, &longs;ed minus. </s>

<s id="N135DB">Vnde &longs;i <lb/>manubrium progrediatur vt tria; nauigium vero vt duo, pal-<pb pagenum="112" xlink:href="005/01/120.jpg"/>mula retrocedet vt vnum: tantum &longs;cilicet quantum e&longs;t <lb/>&longs;patium, quo excedit illud, quod conficitur per motum <lb/>contrarium. </s>

Line 1692

<s id="N1374C">Etenim &longs;i temo per &longs;ui con<lb/>uer&longs;ionem, vel obliquam po&longs;itionem fluctus maris à dex<lb/>tris excipiat, ab&longs;que dubio puppis ad &longs;ini&longs;tram declinabit, <lb/>prora manente ferè immota, eo quod impetus obliquè &longs;it <lb/>impre&longs;&longs;us, & illuc v&longs;que pertingere nequeat, vel ob &longs;uam <lb/>imbecillitatem ibi tandem langue&longs;cat. </s>

<s id="N13759">Quod facilè con<lb/>templari e&longs;t in &longs;ubiecta, quam delineauimus nauicula, cuius <lb/>linea AB refert gubernaculum cum temone affixo in ip&longs;a <lb/>cu&longs;pide puppis vbi C, ac prora con&longs;tituitur in G. </s>

<s id="N13763">Nam <lb/>dato quod extremum temonis B, mare dextror&longs;um exci<lb/>piens, aut propellens transferatur in D per motum guber<lb/>naculi ab A in E, vtique cu&longs;pis puppis, quæ e&longs;t in C <lb/>transferetur &longs;ini&longs;tror&longs;um vnà cum tota nauicula ver&longs;us F, <lb/>prora ip&longs;a in eodem puncto manente, vel parum inde di<lb/>mota, vt v&longs;que ad punctum H; ita vt nauicula, quæ erat <pb pagenum="116" xlink:href="005/01/124.jpg"/><figure id="id.005.01.124.1.jpg" xlink:href="005/01/124/1.jpg"/><lb/>in CG, con&longs;tituatur in FG, vel in <lb/>FH. </s>

<s id="N1377F">Licet hoc non &longs;emper veri<lb/>ficetur cum &longs;æpius impetus per <lb/>remonem incu&longs;&longs;us à mare in hu<lb/>iu&longs;modi ca&longs;u &longs;uperare, ac tran&longs;<lb/>ferre nequeat centrum grauitatis <lb/>totius nauis, quod e&longs;t circa me<lb/>dium illius, <expan abbr="proindeq.">proindeque</expan> tota longi<lb/>tudo nauis conuerti non po&longs;&longs;it <lb/>tanquam &longs;emidiameter circa ter<lb/>minum prorar, tanquam circa cen<lb/>trum, &longs;ed potius centrum huius <lb/>conuer&longs;ionis con&longs;tituatur in ip&longs;o centro grauitatis totius <lb/>nauis, vel in alio puncto lineæ per ip&longs;um ad centrum mundi <lb/>cadentis. </s>

<s id="N1377F">Licet hoc non &longs;emper veri<lb/>ficetur cum &longs;æpius impetus per <lb/>remonem incu&longs;&longs;us à mare in hu<lb/>iu&longs;modi ca&longs;u &longs;uperare, ac tran&longs;<lb/>ferre nequeat centrum grauitatis <lb/>totius nauis, quod e&longs;t circa me<lb/>dium illius, <expan abbr="proindeq.">proindeque</expan> tota longi<lb/>tudo nauis conuerti non po&longs;&longs;it <lb/>tanquam &longs;emidiameter circa ter<lb/>minum prorae, tanquam circa cen<lb/>trum, &longs;ed potius centrum huius <lb/>conuer&longs;ionis con&longs;tituatur in ip&longs;o centro grauitatis totius <lb/>nauis, vel in alio puncto lineæ per ip&longs;um ad centrum mundi <lb/>cadentis. </s>

<s id="N137A2">In prædictis ergo ca&longs;ibus, & cum explicata limitatione <lb/>loquendo de nauigio, quod nullo pacto fertur antror&longs;um <lb/>intelligitur verificari, quod docuit Ari&longs;toteles. </s>

<s id="N137AA">In eodem <lb/>exi&longs;tente prora, totum transferri nauigium; Alioquin &longs;i &longs;er<lb/>mo fui&longs;&longs;et de nauigio, quod plenis velis, aut remis mare <lb/>tran&longs;mittit, verificari certè non po&longs;&longs;et; cum talis ac tanta <lb/>&longs;it vis eiu&longs;dem cur&longs;us, quo recta in anteriora citi&longs;simè fer<lb/>tur, vt non &longs;inat ip&longs;am puppim per occur&longs;um maris, quod <lb/>incidit in temonem à &longs;uo recto tramite admodum &longs;altem <lb/>diuerti, &longs;icut à puncto &longs;uæ quietis facilè ip&longs;a dimouetur cum <lb/>nauis quie&longs;cit. </s>

<s id="N137BD">Licet enim promoto &longs;ernel antror&longs;um naui<lb/>gio, temo per obliquam &longs;ui con&longs;titutionem, & immediatum <lb/>repul&longs;nm quem patitur, omnino re&longs;i&longs;tere nequeat occur<lb/>rentibus fluctibus, <expan abbr="cogaturq.">cogaturque</expan> moueri, velut in gyrum circa <lb/>ip&longs;ius puppis extremum; vim tamen quam patitur transfun<lb/>dit in longitudinem nauis, tanquam in alterum latus, cum <lb/>quo efficit angulum, vt in principio cum &longs;ua figura expre&longs;si<lb/>mus: Vnde cum non &longs;olum ad motum vnius lateris in an<lb/>gulo, moueatur alterum, &longs;ed facilius &longs;it, vtrumque latus cir<lb/>culariter moueri, cu&longs;pide anguli tanquam centro manente <pb pagenum="117" xlink:href="005/01/125.jpg"/>immota ob aliquo <expan abbr="limpediment&utilde;">limpedimentum</expan>, quàm <expan abbr="tot&utilde;">totum</expan> <expan abbr="angul&utilde;">angulum</expan> &longs;imul <lb/>transferri; hinc e&longs;t, vt re&longs;i&longs;tentia nouis orta ex impetu indi<lb/>rectum tendente, &longs;ufficiat vt cu&longs;pis prædicti anguli, quæ in <lb/>propo&longs;ito e&longs;t vbi puppis extremum; minimè dimoueatur à <lb/>tramite &longs;uper <expan abbr="qu&etilde;">quem</expan> fertur, <expan abbr="nõ">non</expan> <expan abbr="aut&etilde;">autem</expan> &longs;ufficiat quin prora <expan abbr="tanquã">tanquam</expan> <lb/>extremum alterius lateris moueatur ad motum lateris, quod <lb/>con&longs;tituitur à temone, ita vt temone ad leuam repul&longs;o lon<lb/>gitudo nauis cum prora ad dexteram vergat. </s>

<s id="N137BD">Licet enim promoto &longs;emel antror&longs;um naui<lb/>gio, temo per obliquam &longs;ui con&longs;titutionem, & immediatum <lb/>repul&longs;um quem patitur, omnino re&longs;i&longs;tere nequeat occur<lb/>rentibus fluctibus, <expan abbr="cogaturq.">cogaturque</expan> moueri, velut in gyrum circa <lb/>ip&longs;ius puppis extremum; vim tamen quam patitur transfun<lb/>dit in longitudinem nauis, tanquam in alterum latus, cum <lb/>quo efficit angulum, vt in principio cum &longs;ua figura expre&longs;si<lb/>mus: Vnde cum non &longs;olum ad motum vnius lateris in an<lb/>gulo, moueatur alterum, &longs;ed facilius &longs;it, vtrumque latus cir<lb/>culariter moueri, cu&longs;pide anguli tanquam centro manente <pb pagenum="117" xlink:href="005/01/125.jpg"/>immota ob aliquod <expan abbr="limpediment&utilde;">impedimentum</expan>, quàm <expan abbr="tot&utilde;">totum</expan> <expan abbr="angul&utilde;">angulum</expan> &longs;imul <lb/>transferri; hinc e&longs;t, vt re&longs;i&longs;tentia nouis orta ex impetu indi<lb/>rectum tendente, &longs;ufficiat vt cu&longs;pis prædicti anguli, quæ in <lb/>propo&longs;ito e&longs;t vbi puppis extremum; minimè dimoueatur à <lb/>tramite &longs;uper <expan abbr="qu&etilde;">quem</expan> fertur, <expan abbr="nõ">non</expan> <expan abbr="aut&etilde;">autem</expan> &longs;ufficiat quin prora <expan abbr="tanquã">tanquam</expan> <lb/>extremum alterius lateris moueatur ad motum lateris, quod <lb/>con&longs;tituitur à temone, ita vt temone ad leuam repul&longs;o lon<lb/>gitudo nauis cum prora ad dexteram vergat. </s>

<s id="N13805">Prouenit au<lb/>tem maior hæc facilitas motus lateris vtriu&longs;que, circa pro<lb/>priam cu&longs;pidem, tum ex facilitate motus circularis in vni<lb/>uer&longs;um, tum ex ip&longs;a re&longs;i&longs;tentia, qua cu&longs;pis anguli, quem effi<lb/>ciunt detinetur ab impul&longs;o in directum nè moueatur obli<lb/>què in tran&longs;uer&longs;um. </s>

<s id="N13812">Innititur enim ei tanquam fulcimento, <lb/>ip&longs;aque latera induunt rationem vectis cuiu&longs;dam angulo&longs;i <lb/>in medio fulti, qui &longs;anè facilius conuertitur circa fulcimen<lb/>tum ad motum alterius extremi, quàm &longs;imul &longs;ecundum &longs;e <lb/>totum aliò transferatur. </s>

<s id="N1381D">Antror&longs;um ergo naui promota, <lb/>ip&longs;e impetus promotionis, &longs;eu cur&longs;us impedit ne puppis ex<lb/>tremum in tran&longs;uer&longs;um dimoueatur, non autem ob&longs;tat quin <lb/>ad motionem obliquam temonis, conuertatur &longs;ecum & <lb/>prora, cum propter vim illatam, quæ vrgentibus fluctibus, in <lb/>illam transfunditur; tum propter facilitatem conuer&longs;ionis <lb/>explicatam, con&longs;entaneè ad doctrinam &longs;upra traditam, <expan abbr="men-temq.">men<lb/>temque</expan> Ari&longs;totelis aientis. </s>

Line 1709

<s id="N13851">Idem <lb/>enim e&longs;t vtrinque æqualia pondera &longs;u&longs;tinere, ac impetus <lb/>pariter æquales. </s>

<s id="N13858">Cum autem à dextris, vel à &longs;ini&longs;tris ex na<pb pagenum="118" xlink:href="005/01/126.jpg"/>ui lignum aliquod, vt temo, vel aliud non ab&longs;imile promi<lb/>nuerit, cui mare obuians, maiorem impetum incutiat, iam <lb/>non e&longs;t amplius æqualis impetus vtrinque incu&longs;&longs;us. </s>

<s id="N13864">Ac &longs;icut <lb/>libram cum ip&longs;a maius pondus altero brachio &longs;u&longs;tinet incli<lb/>nari nece&longs;&longs;e e&longs;t, ac cedere &longs;ecundum illud brachium ex quo <lb/>maius pondus propendet: ita nauim inclinari oportet &longs;e<lb/>cundum illam partem, in qua maiorem impetum excipit, <lb/>quod &longs;it per circumuer&longs;ionem totius longitudinis nauis ad <lb/>latus ip&longs;um vnde magis percutitur, prout paulò ante de&longs;cri<lb/>p&longs;imus. </s>

<s id="N13875">Licet hic dicendi modus, ip&longs;umq, fundamentum, <lb/>quo nititur verificari po&longs;&longs;it, tum &longs;i centrum motionis circu<lb/>laris, quam experimur in naui con&longs;tituatur in cu&longs;pide pup<lb/>pis, tum &longs;i con&longs;tituatur in prora, vt per &longs;e patet. </s>

<s id="N13875">Licet hic dicendi modus, <expan abbr="ip&longs;umq,">ip&longs;umque</expan> fundamentum, <lb/>quo nititur verificari po&longs;&longs;it, tum &longs;i centrum motionis circu<lb/>laris, quam experimur in naui con&longs;tituatur in cu&longs;pide pup<lb/>pis, tum &longs;i con&longs;tituatur in prora, vt per &longs;e patet. </s>

<s id="N1387E">Sed forta&longs;<lb/>&longs;e multo melius &longs;i con&longs;tituatur in medio, &longs;eu in centro gra<lb/>uitatis totius nauis, circa quod facilius e&longs;t intelligere ip&longs;am <lb/>muis conuer&longs;ionem, &longs;iue inquiete, &longs;iue in motu. </s>

<s id="N1387E">Sed forta&longs;<lb/>&longs;e multo melius &longs;i con&longs;tituatur in medio, &longs;eu in centro gra<lb/>uitatis totius nauis, circa quod facilius e&longs;t intelligere ip&longs;am <lb/>nauis conuer&longs;ionem, &longs;iue inquiete, &longs;iue in motu. </s>

<s id="N13887">Quomo<lb/>docunque enim temo obliquè con&longs;titutus vim patiatur ab <lb/>aqua; Nimirum &longs;iue excipiendo illam fluentem, & obuian<lb/>tem; &longs;iue impingendo in illam quie&longs;centem, &longs;emper dimo<lb/>tio illa circularis intelligetur pertingere v&longs;que ad cen<lb/>trum grauitatis totius nauis, cum quatemo vnum corpus <lb/>efficitur. </s>

<s id="N13896">At in re tam occulta, quæ etiam dum ante ocu<lb/>los ver&longs;atur, adhuc imaginationem comprehen&longs;ionemque <lb/>ob&longs;eruantis fugit, con&longs;ultius erit ab Ari&longs;totelis doctrina non <lb/>di&longs;cedere. </s>

Line 1718

<s id="N138A1">Quæ&longs;tio Sexta.</s>

<s id="N138A6">C<emph type="italics"/>vr quanto antenna &longs;ublimior fuerit, y&longs;dem <lb/>velis, & vento eodem cæle, iùs feruntur na<lb/>uigia? </s>

<s id="N138A6">C<emph type="italics"/>vr quanto antenna &longs;ublimior fuerit, ij&longs;dem <lb/>velis, & vento eodem cæle, iùs feruntur na<lb/>uigia? </s>

<s id="N138B0">An quia malus quidem fit vectis, hy<lb/>pomocblion verò mali &longs;edes, in qua colloca<lb/>tur: pondus autem quod moueri debet, ip&longs;um <lb/>nauigium; mouens verò is, qui vela tendit, <lb/>&longs;piritus? </s>

<s id="N138B0">An quia malus quidem fit vectis, hy<lb/>pomochlion verò mali &longs;edes, in qua colloca<lb/>tur: pondus autem quod moueri debet, ip&longs;um <lb/>nauigium; mouens verò is, qui vela tendit, <lb/>&longs;piritus? </s>

<s id="N138BB">Si igitur quando remotius fuerit hypomocblion,<emph.end type="italics"/><pb pagenum="119" xlink:href="005/01/127.jpg"/><emph type="italics"/>facilius eadem potentia, & citius idem mouet pondus, altius <lb/>sertè &longs;ublata antenna velum à mali &longs;ede, quæ h<gap/>pomochlion <lb/>e&longs;t, remotius faciens, id efficiet.<emph.end type="italics"/></s>

<s id="N138BB">Si igitur quando remotius fuerit hypomochlion,<emph.end type="italics"/><pb pagenum="119" xlink:href="005/01/127.jpg"/><emph type="italics"/>facilius eadem potentia, & citius idem mouet pondus, altius <lb/>sertè &longs;ublata antenna velum à mali &longs;ede, quæ hypomochlion <lb/>e&longs;t, remotius faciens, id efficiet.<emph.end type="italics"/></s>

<s id="N138D1">COMMENTARIVS.</s>

Line 1737

<s id="N13934">Porrò malus ab&longs;olutè con&longs;ideratus in latione nauis, <lb/>virtute ventorum, fulcimentum obtinet circa profundam <lb/>&longs;edem vbi locatur in nauis carina, <expan abbr="eiq.">eique</expan> innititur per &longs;ui ex<lb/>tremum infimum, qua parte, &longs;eu facie vergit ad puppim. <lb/></s>

<s id="N13942">Onus autem &longs;eu nauem promouet per partem ip&longs;ius altio<pb pagenum="120" xlink:href="005/01/128.jpg"/>rem ex ijs, quæ intra foramen continentur, vnde ip&longs;e malus <lb/>foris prodit in altum, tanquam arbor è terra; <expan abbr="vrgetq.">vrgetque</expan> &longs;ecun<lb/>dum eam ip&longs;ius partis faciem, quæ ad proram re&longs;picit vbi <lb/>vltimo foramen de&longs;init. </s>

<s id="N13954">Siquidem ibi tota ferè vis incuti<lb/>tur naui ad progrediendum antror&longs;um, vt videre e&longs;t in hac <lb/>figura, in qua extremum mali fundo innixum &longs;it A, cuius <lb/>facies puppim <lb/>re&longs;piciens B; <lb/><figure id="id.005.01.128.1.jpg" xlink:href="005/01/128/1.jpg"/><lb/>pars verò ip<lb/>&longs;ius mali, quæ <lb/><expan abbr="flãtibus">flantibus</expan> ventis <lb/>à tergo naui<lb/>gium præmit, <lb/>vel vrget in an<lb/>te, vbi C, è <expan abbr="cõ-&longs;pectu">con<lb/>&longs;pectu</expan> pror&etail;; & <lb/>locus antennæ <lb/>in ip&longs;o malo, &longs;it <lb/>D; vbi tota pe<lb/>nè virtus im<lb/>pellentis &longs;piri<lb/>tus refunditur, <lb/>vt diximus ra<lb/>tione veli <expan abbr="ill&utilde;">illum</expan> <lb/>excipientis. </s>

<s id="N13992"><expan abbr="Iã">Iam</expan> <lb/>igitur <expan abbr="cõ&longs;tat">con&longs;tat</expan> ex <lb/>hoc, malum <lb/>per &longs;e &longs;umptum propriè vectem con&longs;titui in ip&longs;a ventorum <lb/>impul&longs;ione, cum fulcimentum habeat in parte di&longs;tincta ab <lb/>ea, qua nauem promouet, & ab ea, qua mouetur à vento, vt <lb/>in &longs;imili commune e&longs;t omnibus vectibus; vndc quo altius <lb/>con&longs;tituetur antenna, vt verbi gratia &longs;i eleuaretur v&longs;que ad <lb/>E, eo celerius moueretur nauigium, quia virtutem impellen<lb/>tem reciperet in parte à centro vectis di&longs;tantiori. </s>

<s id="N13992"><expan abbr="Iã">Iam</expan> <lb/>igitur <expan abbr="cõ&longs;tat">con&longs;tat</expan> ex <lb/>hoc, malum <lb/>per &longs;e &longs;umptum propriè vectem con&longs;titui in ip&longs;a ventorum <lb/>impul&longs;ione, cum fulcimentum habeat in parte di&longs;tincta ab <lb/>ea, qua nauem promouet, & ab ea, qua mouetur à vento, vt <lb/>in &longs;imili commune e&longs;t omnibus vectibus; vnde quo altius <lb/>con&longs;tituetur antenna, vt verbi gratia &longs;i eleuaretur v&longs;que ad <lb/>E, eo celerius moueretur nauigium, quia virtutem impellen<lb/>tem reciperet in parte à centro vectis di&longs;tantiori. </s>

<s id="N139B0">Altera verò vectis ratio, quæ con&longs;ideratur in malo con<lb/>iunctim cum nauis carina, e&longs;t huiu&longs;modi. </s>

<s id="N139B5">Quoniam vt rectè <pb pagenum="121" xlink:href="005/01/129.jpg"/>prænotat Baldus, e&longs;t quædam vectium &longs;pecies, cuius bra<lb/>chia in angulum de&longs;inunt, <expan abbr="ip&longs;iusq.">ip&longs;iusque</expan> anguli cu&longs;pis in operatio<lb/>ne con&longs;tituitur centrum, ac fulcimentum circa quod bra<lb/>chia conuertuntur. </s>

<s id="N139C7">Ad quam &longs;peciem reducitur ferreus <lb/>malleus prout eam partem continet, qua clauos reuellit. <lb/></s>

<s id="N139CD">Etenim vt ob&longs;eruari pote&longs;t in hac &longs;igura, mallei manubrium <lb/>con&longs;tituit vnum brachium AB; alterum verò pars qua cla<lb/>uos reuellit, nempe BC. </s>

<s id="N139CD">Etenim vt ob&longs;eruari pote&longs;t in hac figura, mallei manubrium <lb/>con&longs;tituit vnum brachium AB; alterum verò pars qua cla<lb/>uos reuellit, nempe BC. </s>

<s id="N139D5">Et ex vtri&longs;que fit angulus ABC, <lb/>ip&longs;o malleo in extractione clauorum <lb/>cu&longs;pidi innixo vbi B. </s>

Line 1763

<s id="N13A93">Denique ex his expediri etiam pote&longs;t alia quæ&longs;tio, cur <lb/>nimirum fluctuante aliquantulum mare, ac minimè velis <lb/>munito, aut progrediente nauigio, quo altius &longs;ublimatur an<lb/>tenna, minus ip&longs;um commoueatur; vt in &longs;tatione nauium at<lb/>que triremium extra portum &longs;olet contingere. </s>

<s id="N13A9E">Etenim <lb/>iuxta prædicta facilè re&longs;pondetur, tunc quoque malum, ve<lb/>ctis rationem habere, altero in extremo &longs;uffulti prope na<lb/>uis carinam: antennam verò oneris vicem &longs;ubire, ac mare <lb/>fluctuans, potentiæ mouentis, cuius virtus mediante naui-<pb pagenum="123" xlink:href="005/01/131.jpg"/>gio applicatur vecti inter fulcimentum, & onus; nempe vbi <lb/>malus ip&longs;e vltimo intra corpus nauigij continetur, vt paul<gap/><lb/>ante de&longs;crip&longs;imus. </s>

<s id="N13AB3">Dum enim iactatur &longs;imul cum nauigio <lb/>malus, ac propterea cogitur inclinari, ob&longs;tat quantum po<lb/>te&longs;t antenna in &longs;uperiori eius parte alligata tanquam onus <lb/>incumbens, quod perpendiculariter ad mundi centrum gra<lb/>uitans, re&longs;i&longs;tit inclinationi, ne contra propriam rectitudinem, <lb/>ac naturalem propen&longs;ionem à perpendiculo deuians, obli<lb/>què ad latera vergat. </s>

<s id="N13AC4">Magis autem, aut minus vale<gap/>tre&longs;i&longs;tere, iuxta maiorem, <lb/>aut minorem di&longs;tantiam, quam habet à &longs;ede mali, vbi con<lb/>&longs;tituitur centrum ip&longs;ius motus circularis, quem ad commo<lb/>tionem nauigij per varios arcus conficit malus. </s>

<s id="N13AC4">Magis autem, aut minus valet re&longs;i&longs;tere, iuxta maiorem, <lb/>aut minorem di&longs;tantiam, quam habet à &longs;ede mali, vbi con<lb/>&longs;tituitur centrum ip&longs;ius motus circularis, quem ad commo<lb/>tionem nauigij per varios arcus conficit malus. </s>

<s id="N13ACF">Quo enim <lb/>plus à centro, &longs;eu fulcimento di&longs;ce&longs;&longs;erit onus, eo difficilius <lb/>dimouetur: di&longs;tabit autem tanto magis à &longs;ede mali, ac fun<lb/>do nauis antenna, quantò altius &longs;ublimatur. </s>

<s id="N13AD8">Accedit quia <lb/>&longs;imul magis di&longs;tabit à parte vbi vis incutitur malo in &longs;um<lb/>mo foramine nauis hinc inde illum impellentis: potentia <lb/>verò remotius ab onere applicata, quàm à fulcimento ve<lb/>ctis, minus illud mouere pote&longs;t quando fulcimentum con<lb/>&longs;tituitur in altero vectis extremo: Vt &longs;i qui&longs;piam extremo <lb/>&longs;ari&longs;&longs;æ alicubi obfirmato, ac manu prope ip&longs;um extremum <lb/>illi admota, aliquod pondus altero extremo dimouere co<lb/>netur. </s>

<s id="N13AEB">Antenna ergo remoti&longs;&longs;imè à loco vbi virtus impul<lb/>&longs;iua in malo refunditur collocata, difficillimè commouetur, <lb/>proindeq &longs;imul cum illa totum nauigium cuius commotio<lb/>ni magis valebit ob&longs;tare. </s>

<s id="N13AEB">Antenna ergo remoti&longs;&longs;imè à loco vbi virtus impul<lb/>&longs;iua in malo refunditur collocata, difficillimè commouetur, <lb/><expan abbr="proindeq">proindeque</expan> &longs;imul cum illa totum nauigium cuius commotio<lb/>ni magis valebit ob&longs;tare. </s>

<s id="N13AF6">Quod &longs;anè verificatur in mediocri, vel modica fluctuum <lb/>eleuatione, vt con&longs;ultò innuimus; alioquin nimis extuante <lb/>mare, <expan abbr="nimisq.">nimisque</expan> obtume&longs;centibus vndis, dum validè iactatur <lb/>nauigium, oppo&longs;itum experimur. </s>

Line 1783

<s id="N13B2F">C<emph type="italics"/>vr quando ex puppi nauigare volue<lb/>rint, non flante ex puppi vento, veli qui<lb/>dem partem, quæ ad gubernatorem vergit, <lb/>con&longs;tringunt: illam verò quæ proram v<gap/>r&longs;us <lb/>e&longs;t, pedem facientes relaxant? </s>

<s id="N13B3F">An quia re<lb/>trahere quidem multò exi&longs;tente vento guber<lb/>na culum non potest: pauco autem pote&longs;t, quem con&longs;tringunt? <lb/></s>

<s id="N13B47">Propellit quidem igitur ip&longs;e ventus: in puppim verò illum <lb/>constituit gubernaculum retrabens, & mare compellens: &longs;i<lb/>mul & nautæ ip&longs;i cum vento contendunt: in contrarium enim <lb/>&longs;e reclinant partem.<emph.end type="italics"/></s>

<s id="N13B47">Propellit quidem igitur ip&longs;e ventus: in puppim verò illum <lb/>constituit gubernaculum retrahens, & mare compellens: &longs;i<lb/>mul & nautæ ip&longs;i cum vento contendunt: in contrarium enim <lb/>&longs;e reclinant partem.<emph.end type="italics"/></s>

<s id="N13B54">COMMENTARIVS.</s>

Line 1796

<s id="N13B9F">Hæc ex Ari&longs;totele, quæ vt clarius dilucidentur, &longs;it nauis AB, <lb/>cuius puppis A, prora verò B, gubernaculum obliquè con&longs;ti<lb/>tutum AC; temo &longs;imili<lb/><figure id="id.005.01.133.1.jpg" xlink:href="005/01/133/1.jpg"/><lb/>ter AD, malus E, ac ve<lb/>lum &longs;ecundum <expan abbr="infimã">infimam</expan> &longs;ui <lb/>oram, &longs;it curua linea FG, <lb/>lateraliter ventum exci<lb/>piens ex parte dextera <lb/>vbi H. </s>

<s id="N13BBD">Tunc qua&longs;i pugna <lb/><expan abbr="quædã">quædam</expan> <expan abbr="cõ&longs;ideretur">con&longs;ideretur</expan> inter <lb/><expan abbr="vent&utilde;">ventum</expan>, ac temonem. </s>

<s id="N13BCE"><expan abbr="Nã">Nam</expan> <lb/>flante vento ex H, <expan abbr="naui-gi&utilde;">naui<lb/>gium</expan> transferri deberet in <lb/>oppo&longs;itum, hoc e&longs;t &longs;ini<lb/><gap/>tror&longs;um ver&longs;us I per li<lb/>neam HLI. </s>

<s id="N13BCE"><expan abbr="Nã">Nam</expan> <lb/>flante vento ex H, <expan abbr="naui-gi&utilde;">naui<lb/>gium</expan> transferri deberet in <lb/>oppo&longs;itum, hoc e&longs;t &longs;ini<lb/>&longs;tror&longs;um ver&longs;us I per li<lb/>neam HLI. </s>

<s id="N13BE3">Incidentibus <lb/>autem fluctibus maris in <lb/>alam temonis AD, prora <lb/>ex B conuerti deberet in H, circa ip&longs;um <expan abbr="punct&utilde;">punctum</expan> A <expan abbr="tanquã">tanquam</expan> cen<lb/>trum talis motionis obliquæ, vt probatum e&longs;t. </s>

<s id="N13BF6">Quoniam verò <lb/>neutrum præualet, nauis, medium cur&longs;um tenens, transfertur <lb/>antror&longs;um ver&longs;us K quo pergere, ac velificare cupiunt nautæ, <lb/>qui iccirco in tali po&longs;itione nauim cum velo con&longs;tituunt. </s>

Line 1821

<s id="N13D05">Vnde quo magis velum appropinquatur pup<lb/>pi, eo magis temo præualet contra impul&longs;um ventorum ad <lb/>conuertendam nauim obliquè. </s>

<s id="N13D0E">Quod autem ait Piccolomineus, in hac motione nauis cari<lb/>nam vectis vicem obtinere, quæ centro grauitatis ip&longs;ius nauis <lb/>tanquam fulcimento innixa mare mouente, ac impellente te<lb/>monem, ventum in prora &longs;u&longs;tineat tanquam onus, valde ambi<lb/><gap/>uum e&longs;t. </s>

<s id="N13D1A">Tum quia non minus ventus per velum, quàm ma<lb/>re per temonem pote&longs;t habere rationem potentiæ mouentis. <lb/></s>

<s id="N13D20">Tum etiam quia ventus præcipuè non &longs;u&longs;tinetur in prora, &longs;ed <lb/>potius in parte veli, quæ vergit ad puppim, vt dictum e&longs;t. </s>

Line 1845

<s id="N13E05">C<emph type="italics"/>vr ex figurarum genere quæcunque rotun<lb/>dæ &longs;unt, & circinatæ, facilius mouentur? <lb/></s>

<s id="N13E0E">Trifariam autem circulum rotari contingit. <lb/></s>

<s id="N13E12">Aut enim &longs;ecundum ab&longs;idem centro &longs;imul mo<lb/>to, quemadmodum plau&longs;tri vertitur rota: aut <lb/>circa manens centrum, veluti trochleæ &longs;tante <lb/>centro, aut in pauimento manente centro, &longs;icut figuli rota con<lb/>nertitur: an celerrima quidem huiu&longs;modi &longs;unt, quoniam par<lb/>na &longs;ui parte planum contingunt, veluti circulus &longs;ecundum <lb/>punctum, & quoniam non offen&longs;ant. </s>

<s id="N13E12">Aut enim &longs;ecundum ab&longs;idem centro &longs;imul mo<lb/>to, quemadmodum plau&longs;tri vertitur rota: aut <lb/>circa manens centrum, veluti trochleæ &longs;tante <lb/>centro, aut in pauimento manente centro, &longs;icut figuli rota con<lb/>vertitur: an celerrima quidem huiu&longs;modi &longs;unt, quoniam par<lb/>ia &longs;ui parte planum contingunt, veluti circulus &longs;ecundum <lb/>punctum, & quoniam non offen&longs;ant. </s>

<s id="N13E21">A terra enim &longs;emotus e&longs;t <lb/>angulus. </s>

<s id="N13E26">Præterea etiam cui obuiam fiunt corpori, id rur&longs;um <lb/>&longs;ecundum pu&longs;illum tangunt. </s>

<s id="N13E2B">Si autem rectilineum e&longs;&longs;et, re<lb/>ctitudine &longs;ua multum plani contingeret. </s>

Line 1854

<s id="N13E3D">Cùm autem mouetur plus illico, ad quod mouetur, ceri inde nu<lb/>tans, ab impellente facilius in ante mouetur. </s>

<s id="N13E42">Quo enim vnum<lb/>quodque vergit, mouetur ex facili. </s>

<s id="N13E47">Siquidem difficulter ad <lb/>contrarium nutus &longs;ui mouetur motum. </s>

<s id="N13E4C">Praterea nonnulli <lb/>autumant, quod circult linea in perpeti ver&longs;atur motu, quem<lb/>ædmodum manentia propter contrarium nixum manent: &longs;icut <lb/>maioribus contingit circulis ad minores. </s>

<s id="N13E4C">Praeterea nonnulli <lb/>autumant, quod circule linea in perpeti ver&longs;atur motu, quem<lb/>admodum manentia propter contrarium nixum manent: &longs;icut <lb/>maioribus contingit circulis ad minores. </s>

<s id="N13E55">Celeriùs enim ab <lb/>æquali mouentur potentia maiores circuli, <expan abbr="mouentq.">mouentque</expan> onera, <lb/>quoniam circuli maioris angulus ad minoris angulum, circu<lb/>li nutum babet quendam: & &longs;icut diameter ad diametrum, <lb/>ita maior circulus ad minorem. </s>

<s id="N13E55">Celeriùs enim ab <lb/>æquali mouentur potentia maiores circuli, <expan abbr="mouentq.">mouentque</expan> onera, <lb/>quoniam circuli maioris angulus ad minoris angulum, circu<lb/>li nutum habet quendam: & &longs;icut diameter ad diametrum, <lb/>ita maior circulus ad minorem. </s>

<s id="N13E64">Infiniti autem &longs;unt minores. <lb/></s>

<s id="N13E68">Si autem ad alterum nutum babet circulus, &longs;imiliter e&longs;t benè <lb/>mobilis. </s>

<s id="N13E68">Si autem ad alterum nutum habet circulus, &longs;imiliter e&longs;t benè <lb/>mobilis. </s>

<s id="N13E6D">Et aliam &longs;anè babet inclinationem circulus, & <gap/>a<emph.end type="italics"/><pb pagenum="130" xlink:href="005/01/138.jpg"/><emph type="italics"/>quæ à circulo mouentur, licet planitiem ab&longs;ide non contingat, <lb/>&longs;ed aut iuxta planitiem, aut oeluti trochleæ. </s>

<s id="N13E6D">Et aliam &longs;anè habet inclinationem circulus, & <gap/>a<emph.end type="italics"/><pb pagenum="130" xlink:href="005/01/138.jpg"/><emph type="italics"/>quæ à circulo mouentur, licet planitiem ab&longs;ide non contingat, <lb/>&longs;ed aut iuxta planitiem, aut ueluti trochleæ. </s>

<s id="N13E7D">Etenim hoc &longs;e <lb/>habentes modo facillimè mouentur, & onera commouent. </s>

<s id="N13E82">An <lb/>quia parua &longs;ui portione cùm tangit, tum offen&longs;at circulus, &longs;ed <lb/>aliam ob cau&longs;am? </s>

<s id="N13E89">ea autem e&longs;t, quæ dicta est prius, quod circu<lb/>lus &longs;cilicet ex duabus effectus e&longs;t lationibus: quamobrem il<lb/>larum alteram pro nutu &longs;emper habet, & veluti continuò mo<lb/>tum illum moueat quicumque mouent, quando &longs;ecundum cir<lb/>tumferentiam illum mouerint: latam enim ip&longs;am mouent. <lb/></s>

<s id="N13E89">ea autem e&longs;t, quæ dicta est prius, quod circu<lb/>lus &longs;cilicet ex duabus effectus e&longs;t lationibus: quamobrem il<lb/>larum alteram pro nutu &longs;emper habet, & veluti continuò mo<lb/>tum illum moueat quicumque mouent, quando &longs;ecundum cir<lb/>cumferentiam illum mouerint: latam enim ip&longs;am mouent. <lb/></s>

<s id="N13E95">Eam quidem igilur, quæ in obliquum e&longs;t, motionem, ip&longs;um <lb/>impellit mouens: &longs;ecundum verò illam, quæ &longs;uper diametrum <lb/>est, &longs;eip&longs;um mouet circulus.<emph.end type="italics"/></s>

<s id="N13E95">Eam quidem igitur, quæ in obliquum e&longs;t, motionem, ip&longs;um <lb/>impellit mouens: &longs;ecundum verò illam, quæ &longs;uper diametrum <lb/>est, &longs;e ip&longs;um mouet circulus.<emph.end type="italics"/></s>

<s id="N13EA0">COMMENTARIVS.</s>

<s id="N13EA6">Vt quæ&longs;tioni re&longs;pondeat Ari&longs;toteles cur corpora, <lb/>quæ rotundam, aut orbiculatam figuram obtinent, <lb/>&longs;ecundum illam facilius moueantur, triplicem mo<lb/>dum di&longs;tinguit, quo ip&longs;a moueri rotando contingit. </s>

<s id="N13EAF"><expan abbr="Pri-mumq.">Pri<lb/>mumque</expan> e&longs;&longs;e docet, quo &longs;ecundum ab&longs;idem, &longs;eu extimam ip<lb/>forum curuaturam cientur, moto &longs;imul etiam centro, vt <lb/>plau&longs;trorum rotæ, quæ &longs;imul cum axe feruntur. </s>

<s id="N13EAF"><expan abbr="Pri-mumq.">Pri<lb/>mumque</expan> e&longs;&longs;e docet, quo &longs;ecundum ab&longs;idem, &longs;eu extimam ip<lb/>sorum curuaturam cientur, moto &longs;imul etiam centro, vt <lb/>plau&longs;trorum rotæ, quæ &longs;imul cum axe feruntur. </s>

<s id="N13EBB">Secundum <lb/>verò modum, ait e&longs;&longs;e illum, quo circularia ip&longs;a corpora re<lb/>cta quidem &longs;tantia, &longs;eu rectè ad horizontem con&longs;tituta mo<lb/>uentur circa centrum immotum; veluti &longs;tantes trochlea<lb/>rum rotulæ, quæ circa manentem axem, &longs;eu centrum ad di<lb/>uer&longs;os v&longs;us conuertuntur. </s>

<s id="N13EC8">Tertium denique modum e&longs;&longs;e <lb/>inquit, quo circa immotum pariter centrum mouentur, non <lb/>tamen &longs;tando, &longs;ed qua&longs;i pro&longs;trata iuxta planitiem &longs;oli, aut <lb/>pauimenti horizonti paralellam; &longs;icut rota figuli, quæ ad <lb/>impul&longs;um pedis illius conuertitur, ac circumagitur &longs;upra <lb/>axim pauimento perpendiculariter affixum, &longs;eruando &longs;em<lb/>per eandem di&longs;tantiam ab horizonte. </s>

<s id="N13ED9">Loquendo itaque de primo modo, pluribus ex cau&longs;is, ait <lb/>Ari&longs;toteles præfata corpora celerius, ac facilius moueri <lb/>quàm illa, quæ rectilineas adepta &longs;unt figuras, &longs;eu rectilineis <lb/>figuris terminantur, vt triangulari, vel quadrangulari, pirami-<pb pagenum="131" xlink:href="005/01/139.jpg"/>des, & cubi. </s>

<s id="N13EE7">Prima e&longs;t, quia minima &longs;ui parte planum con<lb/>tingunt hoc e&longs;t minori, quam cuiu&longs;libet alterius figuræ cor<lb/>pora, re&longs;pectu, verbi gratia &longs;phæræ, quæ planum tangit in <lb/>puncto. </s>

<s id="N13EF0">Secunda verò e&longs;t, quia hoc pacto non offendunt, aut <lb/>impingunt ni&longs;i &longs;cilicet rarius, ac difficilius; A terra enim &longs;e<lb/>motus e&longs;t angulus, inquit Ari&longs;toteles, nimnum angulum <lb/>contingentiæ, &longs;eu contactus, quia po&longs;t punctum contingen<lb/>tiæ, totum latus curuilineum ip&longs;orum corporum orbicula<lb/>rium, quod cum plano con&longs;tituit huiu&longs;modi angulum, è ter<lb/>ra eleuatur; ac propterea minus impingunt in offendicula, <lb/>quàm alia corpora, quorum latera <expan abbr="nõ">non</expan> &longs;tatim po&longs;t minimum <lb/>contactum eleuantur, &longs;ed ip&longs;i plano, &longs;eu terræ adhærent. <lb/></s>

<s id="N13EF0">Secunda verò e&longs;t, quia hoc pacto non offendunt, aut <lb/>impingunt ni&longs;i &longs;cilicet rarius, ac difficilius; A terra enim &longs;e<lb/>motus e&longs;t angulus, inquit Ari&longs;toteles, nimirum angulum <lb/>contingentiæ, &longs;eu contactus, quia po&longs;t punctum contingen<lb/>tiæ, totum latus curuilineum ip&longs;orum corporum orbicula<lb/>rium, quod cum plano con&longs;tituit huiu&longs;modi angulum, è ter<lb/>ra eleuatur; ac propterea minus impingunt in offendicula, <lb/>quàm alia corpora, quorum latera <expan abbr="nõ">non</expan> &longs;tatim po&longs;t minimum <lb/>contactum eleuantur, &longs;ed ip&longs;i plano, &longs;eu terræ adhærent. <lb/></s>

<s id="N13F08">Tertia cau&longs;a e&longs;t, nam huiu&longs;modi corpora cuicunque ob<lb/>uient offendiculo, illud pariter nonni&longs;i &longs;ecundum pu&longs;illam <lb/>&longs;ui partem attingunt, eadem ratione, qua planum, &longs;eu &longs;olum <lb/>&longs;uper quod ip&longs;a mouentur, &longs;ecus, ac rectilineam figuram ha<lb/>bentia, quæ &longs;emper &longs;ua rectitudine &longs;ecundum magnam, vel <lb/>&longs;altem maiorem partem contingunt. </s>

Line 1886

<s id="N13F29">Etenim &longs;i con&longs;tituatur &longs;u<lb/>per planum AB horizonti <lb/><figure id="id.005.01.139.1.jpg" xlink:href="005/01/139/1.jpg"/><lb/>paralellum erecta aliqua <lb/>rota, vt CDEF tanquam <lb/>circulus, eius diameter à <lb/>contactu plani vbi C per<lb/>pendiculariter ad angulos <lb/>rectos per centrum &longs;upra <lb/>tra&longs;cendens ad D, totam <lb/>rotam eiu&longs;que pondus in <lb/>duas partes æquales di&longs;tri<lb/>buet, nempe in DFC, & <lb/>DEC. <expan abbr="Eritq.">Eritque</expan> ip&longs;a rota in <pb pagenum="132" xlink:href="005/01/140.jpg"/>æquilibrio, quia non magis vna quam altera pars vtrinque <lb/>à perpendiculo DC grauitare pote&longs;t. </s>

<s id="N13F55">Quod &longs;i impul&longs;us <lb/>quamuis perexiguus in ip&longs;am rotam à motore incutiatur, <lb/>vt ex parte E ver&longs;us F, &longs;tatim pars vbi F nutabit ac pro<lb/>pendet ver&longs;us B; <expan abbr="&longs;uoq.">&longs;uoque</expan> nutu, totam rotam &longs;ecum trahet il<lb/>luc. </s>

<s id="N13F64">Nam quælibet vis pote&longs;t æquiponderantia ab æquili<lb/>brio dimouere. </s>

<s id="N13F69">Semel autem mota ip&longs;a rota, ni&longs;i impe<lb/>diatur deinceps nutabit ad partem ver&longs;us quàm primò fuit <lb/>incitata; ideoq facilè vlterius atque vlterius mouebitur. <lb/></s>

<s id="N13F69">Semel autem mota ip&longs;a rota, ni&longs;i impe<lb/>diatur deinceps nutabit ad partem ver&longs;us quàm primò fuit <lb/>incitata; ideoque facilè vlterius atque vlterius mouebitur. <lb/></s>

<s id="N13F71">Quo enim vnumquodque vergit, mouetur ex facili, &longs;ubdit <lb/>ip&longs;e Philo&longs;ophus, &longs;icut vice ver&longs;a difficulter in contrarium; <lb/>vt fu&longs;ius con&longs;tabit quæ&longs;t. </s>

Line 1899

<s id="N13FA6">Circulus enim vel glo<lb/>bus non tangit planum, ni&longs;i in puncto in quod eius diame<lb/>ter incidit ad angulos rectos; quo &longs;anè pacto cadere non <lb/>pote&longs;t perpendicularis tendens ad mundi centrum in pla<lb/>num, quod non e&longs;t horizonti paralellum. </s>

<s id="N13FB1">Cumque præ<lb/>dictum punctum, cui poti&longs;&longs;imum onus incumbit, &longs;u&longs;tineri <lb/>non po&longs;&longs;it ab eo, quod non contingit; hinc fit, vt &longs;emper <lb/>ver&longs;us inferiores partes decliues propendat, ac nutet, de<lb/>feratque propterea ip&longs;a orbiculata corpora quou&longs;que ab <lb/>alio fulciatur. </s>

<s id="N13FBE">Vt per&longs;picuè apparebit in propo&longs;ita &longs;phæra <pb pagenum="133" xlink:href="005/01/141.jpg"/>vel rota ABC, &longs;i decliue <lb/><figure id="id.005.01.141.1.jpg" xlink:href="005/01/141/1.jpg"/><lb/>planum DE contingat in <lb/>C ad angulos rectos ip&longs;ius <lb/>diametri BC: linea verò <lb/>cadens per centrum ip&longs;ius <lb/>&longs;phæræ ad centrum mundi, <lb/>&longs;it AF. </s>

<s id="N13FD9">Nam &longs;ic totum fe<lb/>rè onus incumberet in pun<lb/>cto G, quod cum fulciri <lb/><expan abbr="nõ">non</expan> po&longs;&longs;it in ip&longs;a DE, quam <lb/>nullo modo tangit, nece&longs;&longs;a<lb/>riò <expan abbr="prop&etilde;det">propendet</expan> in F, <expan abbr="rapietq.">rapietque</expan> <lb/>&longs;ecum ad partes E totum <lb/>globum, qui deinceps rur<lb/>&longs;us eadem ratione nutabit per aliud &longs;imile punctum, <expan abbr="infe-tiusq.">infe<lb/>tiusque</expan> citi&longs;&longs;imo cur&longs;u de&longs;cendet &longs;uccedentibus &longs;ibi ad inui<lb/>cem punctis, ac partibus. </s>

<s id="N13FD9">Nam &longs;ic totum fe<lb/>rè onus incumberet in pun<lb/>cto G, quod cum fulciri <lb/><expan abbr="nõ">non</expan> po&longs;&longs;it in ip&longs;a DE, quam <lb/>nullo modo tangit, nece&longs;&longs;a<lb/>riò <expan abbr="prop&etilde;det">propendet</expan> in F, <expan abbr="rapietq.">rapietque</expan> <lb/>&longs;ecum ad partes E totum <lb/>globum, qui deinceps rur<lb/>&longs;us eadem ratione nutabit per aliud &longs;imile punctum, <expan abbr="infe-tiusq.">infe<lb/>riusque</expan> citi&longs;&longs;imo cur&longs;u de&longs;cendet &longs;uccedentibus &longs;ibi ad inui<lb/>cem punctis, ac partibus. </s>

<s id="N14001">Ex hac autem maxima aptitudine, quam rotæ, vel &longs;imili<gap/><lb/>orbiculata corpora habent ad motum, occa&longs;ionem &longs;ump&longs;i&longs;<lb/>&longs;e videntur nonnulli arbitrandi, circuli periferiam nunquam <lb/>quie&longs;cere, &longs;ed perpetuo motu cieri, vt hic &longs;ubiungit Ari&longs;to<lb/>teles. </s>

<s id="N14001">Ex hac autem maxima aptitudine, quam rotæ, vel &longs;imilia <lb/>orbiculata corpora habent ad motum, occa&longs;ionem &longs;ump&longs;i&longs;<lb/>&longs;e videntur nonnulli arbitrandi, circuli periferiam nunquam <lb/>quie&longs;cere, &longs;ed perpetuo motu cieri, vt hic &longs;ubiungit Ari&longs;to<lb/>teles. </s>

<s id="N1400E">Quia &longs;cilicet circulus contrarium nixum non habet, <lb/>quo re&longs;i&longs;tat motui, aut motori &longs;icut corpora manentia, quæ <lb/>ex eo quie&longs;cunt, velmanent, quia habent, in quo contra ni<lb/>tantur, & quo ob&longs;i&longs;tant motui, ac mouenti. </s>

<s id="N14017">Vbiaddendum <lb/>quippe fui&longs;&longs;et ab Ari&longs;totele, falsò eos ita putare; nam licet <lb/>circuli periferia nixum non habeat, quo retardetur, aut im<lb/>pediatur à proprio motu; non tamen &longs;emper habet in &longs;e <lb/>principium proximum, ac formale &longs;ui motus, quod certè <lb/>cum &longs;it qualitas impetus impre&longs;&longs;i, hæc paulatim ex &longs;e re<lb/>mittitur, ac tandem deficit, vt patet in proiectis, quæ iccirco <lb/>de&longs;i&longs;tunt à motu. </s>

Line 1938

<s id="N14111">Ex parte verò portionis circunferentiæ, &longs;eu la<lb/>teris curui; quia CD magis etiam di&longs;tat ab eodem centro, <lb/>ac minus curuatur, quàm GH; <expan abbr="minusq.">minusque</expan> proinde retrahitur <lb/>nè moueatur motu naturali, ad rectum &longs;cilicet magis ap<lb/>propinquanti ideoque velocius ac facilius. </s>

<s id="N14120">Sed angulus C <lb/>inclinari non pote&longs;t ver&longs;us L quin &longs;ecum rapiat angulum <lb/>G, quem intra &longs;e continet. </s>

<s id="N14127">Igitur angulus ip&longs;e C, nutum, <lb/>& propen&longs;ionem habet ad angulum G, vt &longs;imul ac facilius <lb/>moueantur modo quo diximus ad quemlibet impul&longs;um <lb/>motoris. </s>

<s id="N14130">Cumque in&longs;initi &longs;int huiu&longs;modi anguli in explica<lb/>tis circulis, hinc &longs;it, vt rectè ex illis concludat Ari&longs;toteles, <lb/>mobiliores e&longs;&longs;e circulos maiores, ac celerius moueri ab ea<pb pagenum="136" xlink:href="005/01/144.jpg"/>dem, vel æquali potentia; &longs;icut celerius mouentur maiores <lb/>libræ, quàm minores ab eodem, vel æquali pondere. </s>

<s id="N14130">Cumque infiniti &longs;int huiu&longs;modi anguli in explica<lb/>tis circulis, hinc &longs;it, vt rectè ex illis concludat Ari&longs;toteles, <lb/>mobiliores e&longs;&longs;e circulos maiores, ac celerius moueri ab ea<pb pagenum="136" xlink:href="005/01/144.jpg"/>dem, vel æquali potentia; &longs;icut celerius mouentur maiores <lb/>libræ, quàm minores ab eodem, vel æquali pondere. </s>

<s id="N1413E">Non <lb/>enim aliter &longs;e habet circulus &longs;tans &longs;uper planum, quàm libra <lb/>&longs;upra fulcimentum in æquilibrio con&longs;tituta. </s>

<s id="N14147">At Ari&longs;totelem per angulos circuli intelligere angulo<gap/><lb/>à nobis explicatos, illud confirmat, quod cum dixi&longs;&longs;et an<lb/>gulum circuli maioris habere nutum ad angulum circuli <lb/>minoris, qua&longs;i id probans ait: Et &longs;icut diameter ad diame<lb/>trum, ita circumferentia ad circumferentiam. </s>

<s id="N14147">At Ari&longs;totelem per angulos circuli intelligere angulos <lb/>à nobis explicatos, illud confirmat, quod cum dixi&longs;&longs;et an<lb/>gulum circuli maioris habere nutum ad angulum circuli <lb/>minoris, qua&longs;i id probans ait: Et &longs;icut diameter ad diame<lb/>trum, ita circumferentia ad circumferentiam. </s>

<s id="N14153">In quibus <lb/>verbis vtrumque ip&longs;orum angulorum latus comprehendit <lb/>nempe rectum, & <expan abbr="curu&utilde;">curuum</expan>. </s>

<s id="N1415E"><expan abbr="Idemq.">Idemque</expan> e&longs;t, ac dicere, quia <expan abbr="c&utilde;">cum</expan> præ<lb/>dicti anguli con&longs;tent ex huiu&longs;modi lateribus, &longs;icut latera ma<lb/>iora, eo quod magis di&longs;tent à centro, velocius mouentur; ita <lb/>pariter angulus ex illis con&longs;titutus, velocius mouebitur; ma<lb/>gis enim di&longs;tat à centro extremum diametri maioris, quàm <lb/>minoris, &longs;imiliter que portio maioris circumferentiæ ab illo <lb/>de&longs;criptæ, quàm minoris, vt per &longs;e patet. </s>

<s id="N14176">Quod autem Baldus obijcit Ari&longs;toteli, prædictum nu<lb/>tum, quem ip&longs;e gratis explicat per angulos fectores, nul<lb/>lam arguere maiorem mobilitatem circuli maioris, eo quod <lb/>quantum vnus &longs;ector adiuuat de&longs;cen&longs;um ex vna parte, tan<lb/>tum alter oppo&longs;itus retardet a&longs;cen&longs;um ex alia, nihil con<lb/>uincit. </s>

<s id="N14176">Quod autem Baldus obijcit Ari&longs;toteli, prædictum nu<lb/>tum, quem ip&longs;e gratis explicat per angulos sectores, nul<lb/>lam arguere maiorem mobilitatem circuli maioris, eo quod <lb/>quantum vnus &longs;ector adiuuat de&longs;cen&longs;um ex vna parte, tan<lb/>tum alter oppo&longs;itus retardet a&longs;cen&longs;um ex alia, nihil con<lb/>uincit. </s>

<s id="N14183">Nam idem dici po&longs;&longs;et de extremitate diametri lon<lb/>gius à centro di&longs;tante, vt nihil conferat ad maiorem veloci<lb/>tatem, eo quod altera extremitas tantundem debeat retar<lb/>dare; Quod &longs;anè fal&longs;um e&longs;t, quoniam tam in illo, quàm in <lb/>i&longs;to motu &longs;upponitur impetus aliquis impre&longs;&longs;us, virtute cu<lb/>ius motus ip&longs;e exerceatur, ac vna pars circuli, vel diametri <lb/>&longs;uperet aliam æqualem. </s>

<s id="N14192">Alioquin &longs;icut &longs;ola maior di&longs;tan<lb/>tia extremitatis diametri non &longs;ufficit ad motum illius; ita <lb/>nec maior nutus circuli maioris. </s>

<s id="N14199">Vtrumque tamen confert <lb/>ad velocitatem &longs;uppo&longs;ito motu. </s>

<s id="N1419E">Nam virtus illa impre&longs;&longs;a <lb/>nutu proprio ip&longs;ius circuli adiuta, efficacius operatur in e<gap/><lb/>parte vbi imprimitur, vel in quam prius impre&longs;&longs;a fuerir à <lb/>motore. </s>

<s id="N1419E">Nam virtus illa impre&longs;&longs;a <lb/>nutu proprio ip&longs;ius circuli adiuta, efficacius operatur in ea <lb/>parte vbi imprimitur, vel in quam prius impre&longs;&longs;a fuerit à <lb/>motore. </s>

<s id="N141AA">Quod verò adducit ad probandum potius minores circu-<pb pagenum="137" xlink:href="005/01/145.jpg"/>los videri ad motum faciliores, eo quod maior e&longs;t angulus <lb/>contingentiæ ad planum, circumferentiæ minotis, quàm <lb/>maioris circuli, vt in &longs;ubiecta figura maior e&longs;t angulus ABC, <lb/>quàm DBC: probat quidem mi<lb/><figure id="id.005.01.145.1.jpg" xlink:href="005/01/145/1.jpg"/><lb/>nores circulos minus offen&longs;are <lb/>propter maiorem eleuationem <lb/>ip&longs;ius anguli à terra, vt &longs;upra ex <lb/>plicuimus; &longs;ed non probat per &longs;e <lb/>facilius moueri; imò oppo&longs;itum. <lb/></s>

<s id="N141AA">Quod verò adducit ad probandum potius minores circu-<pb pagenum="137" xlink:href="005/01/145.jpg"/>los videri ad motum faciliores, eo quod maior e&longs;t angulus <lb/>contingentiæ ad planum, circumferentiæ minoris, quàm <lb/>maioris circuli, vt in &longs;ubiecta figura maior e&longs;t angulus ABC, <lb/>quàm DBC: probat quidem mi<lb/><figure id="id.005.01.145.1.jpg" xlink:href="005/01/145/1.jpg"/><lb/>nores circulos minus offen&longs;are <lb/>propter maiorem eleuationem <lb/>ip&longs;ius anguli à terra, vt &longs;upra ex<lb/>plicuimus; &longs;ed non probat per &longs;e <lb/>facilius moueri; imò oppo&longs;itum. <lb/></s>

<s id="N141C9">Nam quo curuior e&longs;t linea, eo re<lb/>motior à moturecto, ac naturali, <lb/><expan abbr="ideoq.">ideoque</expan> tardius mouetur, vt cum <lb/>Ari&longs;totele pariter probauimus in <lb/>principio. </s>

<s id="N141D7">Nec recurrere fas e&longs;tad rotam materialem, quæ <lb/>&longs;i maior fit, maiore &longs;ui parte tangit planum, cum idip&longs;um <lb/>de&longs;truat eius a&longs;&longs;umptum, quod fundatur in eleuatione an<lb/>guli contactus &longs;upra punctum B &longs;upponendo contactum <lb/>fieri in puncto ip&longs;o B, & non in parte diui&longs;ibili. </s>

<s id="N141E2">Quod &longs;i di<lb/>catur reuera fieri in parte diui&longs;ibili tanto maiore, quanto <lb/>maior fuerit circumferentia, tunc variatur &longs;uppo&longs;itio ante<lb/>cedentis in con&longs;equenti, <expan abbr="nihilq.">nihilque</expan> propterea verè concluditur. </s>

Line 1972

<s id="N14247">Vtitur autem Ari&longs;toteles illis verbis: &longs;ecundum verò il<lb/>lam (&longs;cilicet motionem) quæ &longs;upra diametrum e&longs;t, &longs;eip&longs;um <lb/>mouet circulus: ad connotandam ip&longs;am motionem mi&longs;tam, <lb/>ac circularem re&longs;ultantem ex duabus lationibus explicatis. <lb/></s>

<s id="N14251">Quam quidem &longs;uper diametrum quadrilateri exempli&longs;ica<lb/>uerat in principio, non &longs;eruata tamen eadem proportione <lb/>Quod non abs re fuerit in hac figura palam exprimere. </s>

<s id="N14251">Quam quidem &longs;uper diametrum quadrilateri exemplifica<lb/>uerat in principio, non &longs;eruata tamen eadem proportione <lb/>Quod non abs re fuerit in hac figura palam exprimere. </s>

<s id="N1425A">Sit enim circulus ABCD <lb/><figure id="id.005.01.146.1.jpg" xlink:href="005/01/146/1.jpg"/><lb/>circa centrum E, cuius &longs;emi<lb/>diameter EC. </s>

<s id="N14267">A qua excite<lb/>tur quadratum ECFD. <expan abbr="Sitq.">Sitque</expan> <lb/>diameter quadrati recta CD. <lb/></s>

<s id="N14274">Dico igitur quod &longs;i punctum <lb/>C, quod e&longs;t extremum &longs;emi<lb/>diametri, moueri debeat <expan abbr="v&longs;q;">v&longs;que</expan> <lb/>ad D, circa immotum <expan abbr="centr&utilde;">centrum</expan> <lb/>E, nullo ferè conatu mouen<lb/>tis mouebitur per arcum, cui <lb/>&longs;ubtenditur recta CD. <expan abbr="Eo-demq.">Eo<lb/>demque</expan> tempore ip&longs;um D transferetur in A; &longs;icut etiam <lb/>A in B, & B vbinunc e&longs;t punctum C: quod e&longs;t, totum <lb/>circulum nullo, aut paruo negotio, à mouente circulariter <lb/>moueri. </s>

<s id="N14297">Cum enim punctum C per lationem &longs;ecundum <lb/>naturam, ad quam ex &longs;e habet nutum, & propen&longs;io<lb/>nem, qualibet exigua vi moueatur yer&longs;us F; per latio-<pb pagenum="139" xlink:href="005/01/147.jpg"/>nem verò præter naturam retrahatur ver&longs;us centrum E; im<lb/>pellente &longs;cilicet ip&longs;o mouente; vtique &longs;i pari proportione <lb/>ip&longs;orum laterum CF, & CE deduceretur, ip&longs;is duabus <lb/>lationibu proculdubio moueretur per diametrum CD, vt <lb/>cum Ari&longs;totele demon&longs;trauimus in principio. </s>

<s id="N14297">Cum enim punctum C per lationem &longs;ecundum <lb/>naturam, ad quam ex &longs;e habet nutum, & propen&longs;io<lb/>nem, qualibet exigua vi moueatur ver&longs;us F; per latio-<pb pagenum="139" xlink:href="005/01/147.jpg"/>nem verò præter naturam retrahatur ver&longs;us centrum E; im<lb/>pellente &longs;cilicet ip&longs;o mouente; vtique &longs;i pari proportione <lb/>ip&longs;orum laterum CF, & CE deduceretur, ip&longs;is duabus <lb/>lationibus proculdubio moueretur per diametrum CD, vt <lb/>cum Ari&longs;totele demon&longs;trauimus in principio. </s>

<s id="N142AB">At cum non <lb/>&longs;eruetur eadem proportio inter lationem &longs;ecundum natu<lb/>ram, ac præter naturam, vt ibi etiam explicuimus; hinc fit, vt <lb/>punctum C moueatur per arcum CD, cui diameter qua<lb/>drati &longs;ubtenditur, & in quo nulla e&longs;t pars, &longs;uper quam di&longs;ce<lb/>dendo à puncto C, non moueatur vtraque latione, nunc <lb/>magis; nune minus &longs;e appropinquando puncto F, ac &longs;etuan<lb/>do &longs;emper eandem di&longs;tantiam à centro E. </s>

<s id="N142AB">At cum non <lb/>&longs;eruetur eadem proportio inter lationem &longs;ecundum natu<lb/>ram, ac præter naturam, vt ibi etiam explicuimus; hinc fit, vt <lb/>punctum C moueatur per arcum CD, cui diameter qua<lb/>drati &longs;ubtenditur, & in quo nulla e&longs;t pars, &longs;uper quam di&longs;ce<lb/>dendo à puncto C, non moueatur vtraque latione, nunc <lb/>magis; nunc minus &longs;e appropinquando puncto F, ac &longs;eruan<lb/>do &longs;emper eandem di&longs;tantiam à centro E. </s>

<s id="N142BD">Mouetur it a que <lb/>punctum C v&longs;que ad D, motione re&longs;ultante ex duabus <lb/>lationibus explicatis: at que adeo nulla alia adhibita vi, aut <lb/>impul&longs;u, qui corre&longs;pondeat ei &longs;icut illis, vt dictum e&longs;t. </s>

<s id="N142C6">Et <lb/>&longs;ic verificatur, quod ait Ari&longs;toteles: &longs;ecundum hanc motio<lb/>nem, quæ fit &longs;uper diametrum; (nempe per arcum, cui illa <lb/>&longs;ubtenditur) &longs;eip&longs;um mouere circulum. </s>

Line 1987

<s id="N142D1">Quæ&longs;tio Nona.</s>

<s id="N142D6">C<emph type="italics"/>vr ea, quæ per maiores circulos tolluntur, & <lb/>trabuntur, facilius & citius moueri contin<lb/>git, veluti maioribus trocbleis, quàm mino<lb/>ribus, & &longs;cytalis &longs;imiliter? </s>

<s id="N142D6">C<emph type="italics"/>vr ea, quæ per maiores circulos tolluntur, & <lb/>trahuntur, facilius & citius moueri contin<lb/>git, veluti maioribus trochleis, quàm mino<lb/>ribus, & &longs;cytalis &longs;imiliter? </s>

<s id="N142E2">An quoniam <lb/>quantò maior fuerit illa, quæ à centro e&longs;t, in <lb/>æquali tempore maius mouetur &longs;patium? <lb/></s>

<s id="N142EA">Quamobrem æquali inexi&longs;tente onere, idem faciet: quemad<lb/>modum diximas, maiores libras minoribus exactiores e&longs;&longs;e. <lb/></s>

<s id="N142EA">Quamobrem æquali inexi&longs;tente onere, idem faciet: quemad<lb/>modum diximus, maiores libras minoribus exactiores e&longs;&longs;e. <lb/></s>

<s id="N142F0">Spartum enim in illis centrum e&longs;t: libræ autem vtrin que par<lb/>tes, quæ ex centro &longs;unt, exi&longs;tunt.<emph.end type="italics"/></s>

<s id="N142F9">COMMENTARIVS.</s>

<s id="N142FF">Maior e&longs;t difficultas, & controuer&longs;ia circa experien<lb/>tiamhic <expan abbr="&longs;uppo&longs;itã">&longs;uppo&longs;itam</expan> ab Ari&longs;totele, dum quæ&longs;tionem <lb/>proponit, quam circa cau&longs;am ip&longs;ius addnctam in <pb pagenum="140" xlink:href="005/01/148.jpg"/>&longs;olutione. </s>

<s id="N142FF">Maior e&longs;t difficultas, & controuer&longs;ia circa experien<lb/>tiam hic <expan abbr="&longs;uppo&longs;itã">&longs;uppo&longs;itam</expan> ab Ari&longs;totele, dum quæ&longs;tionem <lb/>proponit, quam circa cau&longs;am ip&longs;ius adductam in <pb pagenum="140" xlink:href="005/01/148.jpg"/>&longs;olutione. </s>

<s id="N1430F">Scribit enim facilius ac celerius tolli, ac trahi <lb/>pondera per maiores circulos, quàm per minores. </s>

<s id="N14314">Con&longs;ti<lb/>tuitque exemplum de trochleis, ac &longs;cytalis, quæ &longs;i maiores <lb/>&longs;int, aptius onera mouent. </s>

<s id="N1431B">Quod fal&longs;um omnino e&longs;&longs;e cona<lb/>tur o&longs;tendere Blancanus ex Guido Vbaldo. </s>

<s id="N14320">Nam &longs;implex <lb/>trochlea per rotulam cui funis &longs;upernè inditur nullas addit <lb/>vires potentiæ mouenti, eo quod reducatur ad vectem, cu<lb/>ius fultura e&longs;t in medio ip&longs;ius. </s>

<s id="N14329">Vnde &longs;iue rotula illa magna <lb/>fuerit &longs;iue paiua, &longs;emper eadem ratione nullam augere po<lb/>te&longs;t facilitatem, aut velocitatem in hac motione. </s>

<s id="N14329">Vnde &longs;iue rotula illa magna <lb/>fuerit &longs;iue parua, &longs;emper eadem ratione nullam augere po<lb/>te&longs;t facilitatem, aut velocitatem in hac motione. </s>

<s id="N14330">Subdit que <lb/>Blancanus, experientia quoque con&longs;tare eodem labore <lb/>aquam hauriri, &longs;iue rotula illa magna fuerit &longs;iue parua. </s>

<s id="N14339">Verum &longs;i hoc vniuer&longs;aliter demon&longs;traret experientia, &longs;ru<lb/>&longs;tra pa&longs;&longs;im adhiberentur trochleæ ad leuanda, ac trahenda <lb/>pondera; nec e&longs;&longs;et cur iuxta maiorem ponderum grauita<lb/>tem, maioribus rotis, ac trochleis <expan abbr="vter&etilde;tur">vterentur</expan> Architecti quan<lb/>do minoribus vti po&longs;&longs;ent. </s>

<s id="N14339">Verum &longs;i hoc vniuer&longs;aliter demon&longs;traret experientia, fru<lb/>&longs;tra pa&longs;&longs;im adhiberentur trochleæ ad leuanda, ac trahenda <lb/>pondera; nec e&longs;&longs;et cur iuxta maiorem ponderum grauita<lb/>tem, maioribus rotis, ac trochleis <expan abbr="vter&etilde;tur">vterentur</expan> Architecti quan<lb/>do minoribus vti po&longs;&longs;ent. </s>

<s id="N14348">Quamuis igitur &longs;implex trochlea <lb/>&longs;upernè appen&longs;a nullam addat vim potentiæ motrici, &longs;icut <lb/>nec vectis, cuius fulcimentum non &longs;it propinquius oneri; <lb/>multam tamen affert commoditatem. </s>

<s id="N14351">Vnde eadem quip<lb/>pè vi, &longs;ed; non eodem labore eleuatur onus beneficio tro<lb/>chleæ, aut vectis prædicti, quàm &longs;ine illis. </s>

<s id="N14358">Commoditas enim <lb/>minuit laborem, ac &longs;i non auget potentiam, confert tamen <lb/>ad applicationem, & exercitium illius: id quod e&longs;t augere <lb/>facilitatem. </s>

<s id="N14361">Rur&longs;us quæcumque &longs;it facilitas, qua rotis, vel <lb/>trochleis pondera leuantur, certum e&longs;t velocius ea leuari <lb/>maioribus, quàm minoribus rotis; &longs;ed hoc ip&longs;um e&longs;t faci<lb/>lius mouere, quia licet non omnis facilitas includat veloci<lb/>tatem, vt pater in pluribus machinis tractorijs, quæ facilius, <lb/>&longs;ed tardius mouent; nihilominus velocitas &longs;emper inuoluit <lb/>facilitatem; Ergo nihil contra experientiam a&longs;&longs;ump&longs;it Ari<lb/>&longs;toteles, vt Blancanus contendit. </s>

<s id="N14374">Baldus item ait non e&longs;&longs;e &longs;impliciter verum idip&longs;um, quod <lb/>Philo&longs;ophus a&longs;&longs;erit, vt &longs;cilicet quo maiores fuerint trochleæ, <lb/>cò facilius moueant. </s>

<s id="N1437B">Quia tam maior, quàm minor trochlea <lb/>per eius centrum grauitatis diuiditur à perpendiculari ea-<pb pagenum="141" xlink:href="005/01/149.jpg"/>dente ad centrum mundi in duas partes æquales, & æquè <lb/>ponderantes, ac proinde &longs;emper e&longs;t eadem illarum pro<lb/>portio inter &longs;e, & eadem ponderum ratio, ex qua prouenit <lb/>motus. </s>

<s id="N1438B">Fatetur tamen hoc tantum procedere ab&longs;tractè lo<lb/>quendo cum alioquin in trochleis, ac rotis materialibus ne<lb/>gare non po&longs;&longs;it experientiam quam &longs;upponit Ari&longs;toteles. <lb/></s>

<s id="N14394">Quare totam maiorem facilitatem, quam experimur in ip&longs;is <lb/>trochleis, ac rotis maioribus, ip&longs;e ad maiorem proportio<lb/>nem, quam vt plurimum rota maior habet cum proprio axe <lb/>reducit. </s>

<s id="N1439F">Sed quidquid &longs;it de facilitate, aut difficultate &longs;imul <expan abbr="pro-ueni&etilde;te">pro<lb/>ueniente</expan> ex hoc capite, quam certè admittimus, ac infra <expan abbr="etiã">etiam</expan> <lb/>explicabimus: &longs;i&longs;tendo in &longs;ola ratione maioris, aut minoris <lb/>ambitus rotæ prout hic &longs;upponit Ari&longs;toteles, cæteris &longs;cilicet <lb/>paribus; explorati&longs;&longs;imum e&longs;t, ac negari minimè pote&longs;t, quam <lb/>facilius adhuc &longs;eruata eadem proportione axis, &longs;eu cra&longs;&longs;itiei <lb/>illius ad ambitum rotæ, ferantur <expan abbr="põdera">pondera</expan>, &longs;i maioribus a&longs;por<lb/>tentur, eleuentur; aut trahantur rotis; &longs;icut etiam &longs;cytalis, de <lb/>quibus hic eadem e&longs;t ratio. </s>

<s id="N143BE">Loquitur autem Ari&longs;toteles <lb/>de illo genere <expan abbr="&longs;eytalar&utilde;">&longs;eytalarum</expan>, quæ &longs;imiliter circa axim <expan abbr="coniunct&utilde;">coniunctum</expan> <lb/>ad eleuanda pondera conuertuntur, appo&longs;ito in altera ex<lb/>tremitate <expan abbr="illar&utilde;">illarum</expan> ferreo quoddam manubrio, vt in &longs;pecie e&longs;t <lb/>in &longs;ubiecta figura. </s>

<s id="N143BE">Loquitur autem Ari&longs;toteles <lb/>de illo genere <expan abbr="&longs;eytalar&utilde;">&longs;cytalarum</expan>, quæ &longs;imiliter circa axim <expan abbr="coniunct&utilde;">coniunctum</expan> <lb/>ad eleuanda pondera conuertuntur, appo&longs;ito in altera ex<lb/>tremitate <expan abbr="illar&utilde;">illarum</expan> ferreo quoddam manubrio, vt in &longs;pecie e&longs;t <lb/>in &longs;ubiecta figura. </s>

<s id="N143D5">Scytala enim de &longs;e <expan abbr="tant&utilde;">tantum</expan> &longs;ignificat lignum <lb/>quoddam <expan abbr="oblong&utilde;">oblongum</expan>, ac teres <expan abbr="tanquã">tanquam</expan> <expan abbr="cylindr&utilde;">cylindrum</expan>, cui <expan abbr="quandoq.">quandoque</expan> <lb/>alijs adiunctis diuer&longs;æ machinæ, ac in&longs;trumenta vectoria, &longs;i<lb/>ue tractoria efficiuntur, quorum nonnulla adhuc &longs;oytalæ <lb/>vocantur, vt hæc de qua loquimur, & alia de qua infra quæ<lb/>&longs;tione 11. </s>

<s id="N143D5">Scytala enim de &longs;e <expan abbr="tant&utilde;">tantum</expan> &longs;ignificat lignum <lb/>quoddam <expan abbr="oblong&utilde;">oblongum</expan>, ac teres <expan abbr="tanquã">tanquam</expan> <expan abbr="cylindr&utilde;">cylindrum</expan>, cui <expan abbr="quandoq.">quandoque</expan> <lb/>alijs adiunctis diuer&longs;æ machinæ, ac in&longs;trumenta vectoria, &longs;i<lb/>ue tractoria efficiuntur, quorum nonnulla adhuc &longs;cytalæ <lb/>vocantur, vt hæc de qua loquimur, & alia de qua infra quæ<lb/>&longs;tione 11. </s>

Line 2033

<s id="N14433">Magis <lb/>enim retardat, ac impedit axis cra&longs;&longs;ior, quam &longs;ubtilior. </s>

<s id="N14438">Quod <lb/>adhuc (aliter tamen quàm ille) po&longs;&longs;umus probare; Nimirum <lb/>quia ambitus &longs;ubtilioris axis per minorem &longs;ui partem attin<lb/>git rotam, quàm ambitus cra&longs;&longs;ioris: & &longs;ic minus impedit <lb/>circumuolutionem. </s>

<s id="N14443">Itemque po&longs;t punctum, quod e&longs;t in <lb/>&longs;ummitate circumferentiæ, & cui poti&longs;&longs;imum onus rotæ in<lb/>cumbit, partes vtrinque circulariter declinantes, decliuio<lb/>res &longs;unt in axe &longs;ubtiliori; eo quod minor circumferentia <lb/>magis curuetur; &longs;icut è contra quæ amplior e&longs;t, rectius pro<lb/>cedat, &longs;iue magis rectæ appropinquetur. </s>

<s id="N14450">Cumque partes <lb/>decliuiores, minus valeant onus &longs;u&longs;tinere nè dilabatur, <lb/>quàm partes, quæ minus declinant; hinc fit, vt &longs;ubtilior <lb/>axis ex decliuiotibus con&longs;titutus, minus retardet, aut impe<lb/>diat rotæ circumuolutionem. </s>

<s id="N14450">Cumque partes <lb/>decliuiores, minus valeant onus &longs;u&longs;tinere nè dilabatur, <lb/>quàm partes, quæ minus declinant; hinc fit, vt &longs;ubtilior <lb/>axis ex decliuioribus con&longs;titutus, minus retardet, aut impe<lb/>diat rotæ circumuolutionem. </s>

<s id="N1445D">Cæterum data axium paritate, præter cau&longs;am ab Ari&longs;to<lb/>tele a&longs;&longs;ignatam adhuc duplici ex capite reperiemus, maio<lb/>res rotas citiùs, ac faciliùs quàm minores conuolui. </s>

Line 2048

<s id="N144B8">Quæ&longs;tio Decima.</s>

<s id="N144BD">C<emph type="italics"/>vr facilius quando &longs;ine pondere e&longs;t, moue<lb/>tur libra, quàm cùm pondus babet? </s>

<s id="N144BD">C<emph type="italics"/>vr facilius quando &longs;ine pondere e&longs;t, moue<lb/>tur libra, quàm cùm pondus habet? </s>

<s id="N144C5"><expan abbr="&longs;imiliq.">&longs;imilique</expan> <lb/>modo rota, & buiu&longs;modi quippiam, quod gra<lb/>uius quidem e&longs;t, maius autem minore, & le<lb/>uiore? </s>

<s id="N144C5"><expan abbr="&longs;imiliq.">&longs;imilique</expan> <lb/>modo rota, & huiu&longs;modi quippiam, quod gra<lb/>uius quidem e&longs;t, maius autem minore, & le<lb/>uiore? </s>

<s id="N144D1">An quia non &longs;olum in contrarium, <lb/>quod graue e&longs;t, &longs;ed in obliquum etiam diffi<lb/>culter mouetur? </s>

<s id="N144D8">In contrarium enim ei, ad quod vergit onus, <lb/>mouere difficile e&longs;t: quo autem vergit, e&longs;t facilè: in obliquum <lb/>autem baud quaquam vergit.<emph.end type="italics"/></s>

<s id="N144D8">In contrarium enim ei, ad quod vergit onus, <lb/>mouere difficile e&longs;t: quo autem vergit, e&longs;t facilè: in obliquum <lb/>autem haud quaquam vergit.<emph.end type="italics"/></s>

<s id="N144E3">COMMENTARIVS.</s>

<s id="N144E9">Dvo in vnum collecta quærit hic Ari&longs;toteles, nempe <lb/>cur facilius moueatur ràm libra ponderibus vacua <lb/>re&longs;pectu &longs;ui ip&longs;ius cum pondera &longs;u&longs;tinet; quàm ro-<pb pagenum="144" xlink:href="005/01/152.jpg"/>ta leuior re&longs;pectu grauioris, non &longs;olum æqualis magnitudi<lb/>nis, &longs;ed etiam maioris, quam aliàs quæ&longs;tione præcedenti di<lb/>xerat mouerifacilius, ac velocius minore cæteris paribus. <lb/></s>

<s id="N144E9">Dvo in vnum collecta quærit hic Ari&longs;toteles, nempe <lb/>cur facilius moueatur tàm libra ponderibus vacua <lb/>re&longs;pectu &longs;ui ip&longs;ius cum pondera &longs;u&longs;tinet; quàm ro-<pb pagenum="144" xlink:href="005/01/152.jpg"/>ta leuior re&longs;pectu grauioris, non &longs;olum æqualis magnitudi<lb/>nis, &longs;ed etiam maioris, quam aliàs quæ&longs;tione præcedenti di<lb/>xerat moueri facilius, ac velocius minore cæteris paribus. <lb/></s>

<s id="N144FA"><expan abbr="Cau&longs;amq.">Cau&longs;amque</expan> &longs;ci&longs;citandi eam e&longs;&longs;e videtur, quoniam libra in <lb/>æquilibrio con&longs;tituta, &longs;icut etiam rota &longs;tans perpendicula<lb/>riter &longs;uper planum, aut in axe &longs;uffulta, quæ &longs;imilem habet <lb/>rationem, cuiu&longs;cunque grauitatis fuerit, &longs;tatim atque ex ali<lb/>qua parte impingatur, vel onus aliquod alteri eius extremo <lb/>&longs;uperaddatur; amplius manere non pote&longs;t in illo &longs;itu, aut <lb/>po&longs;itione, eo quod nece&longs;&longs;ariò æquilibrium aufe atur per <lb/>additionem ponderis, vel impetum incu&longs;&longs;um in alteram eius <lb/>extremitatem; <expan abbr="proindeq.">proindeque</expan> &longs;iue ip&longs;a libra &longs;itferrea, &longs;iue li<lb/>gnea grauior, aut leuior, æquè facilè deberet moueri: idem<lb/>que verificari de rota. </s>

<s id="N144FA"><expan abbr="Cau&longs;amq.">Cau&longs;amque</expan> &longs;ci&longs;citandi eam e&longs;&longs;e videtur, quoniam libra in <lb/>æquilibrio con&longs;tituta, &longs;icut etiam rota &longs;tans perpendicula<lb/>riter &longs;uper planum, aut in axe &longs;uffulta, quæ &longs;imilem habet <lb/>rationem, cuiu&longs;cunque grauitatis fuerit, &longs;tatim atque ex ali<lb/>qua parte impingatur, vel onus aliquod alteri eius extremo <lb/>&longs;uperaddatur; amplius manere non pote&longs;t in illo &longs;itu, aut <lb/>po&longs;itione, eo quod nece&longs;&longs;ariò æquilibrium auferatur per <lb/>additionem ponderis, vel impetum incu&longs;&longs;um in alteram eius <lb/>extremitatem; <expan abbr="proindeq.">proindeque</expan> &longs;iue ip&longs;a libra &longs;it ferrea, &longs;iue li<lb/>gnea grauior, aut leuior, æquè facilè deberet moueri: idem<lb/>que verificari de rota. </s>

<s id="N1451A">Quæ&longs;tioni tamen re&longs;pondet Ari&longs;toteles, grauiora corpo<lb/>ra difficilius moueri non modo directè contra proprium <lb/>nutum, quo tendunt deor&longs;um, vt cum fur&longs;um eleuantur; &longs;ed <lb/>etiam obliquè cum feruntur ad latera in tran&longs;uer&longs;um, quo <lb/>certè natura &longs;ua pondus non vergit. </s>

<s id="N1451A">Quæ&longs;tioni tamen re&longs;pondet Ari&longs;toteles, grauiora corpo<lb/>ra difficilius moueri non modo directè contra proprium <lb/>nutum, quo tendunt deor&longs;um, vt cum rur&longs;um eleuantur; &longs;ed <lb/>etiam obliquè cum feruntur ad latera in tran&longs;uer&longs;um, quo <lb/>certè natura &longs;ua pondus non vergit. </s>

<s id="N14525">Quamobrem hoc ip<lb/>&longs;o, quod libra, vel rota dimoueri non po&longs;&longs;it ah æqui<lb/>librio, quin obliquè cireumferatur per motum mi&longs;tum, ac <lb/>præter naturalem circa proprium fulcimentum, vel axim; <lb/>quo grauior fuerit, eo difficilius mouebitur, <expan abbr="magisq.">magisque</expan> huic <lb/>motui repugnabit, grauior autem e&longs;t libra ponderibus onu<lb/>&longs;ta, quàm vacua. </s>

<s id="N14525">Quamobrem hoc ip<lb/>&longs;o, quod libra, vel rota dimoueri non po&longs;&longs;it ab æqui<lb/>librio, quin obliquè circumferatur per motum mi&longs;tum, ac <lb/>præter naturalem circa proprium fulcimentum, vel axim; <lb/>quo grauior fuerit, eo difficilius mouebitur, <expan abbr="magisq.">magisque</expan> huic <lb/>motui repugnabit, grauior autem e&longs;t libra ponderibus onu<lb/>&longs;ta, quàm vacua. </s>

<s id="N14538"><expan abbr="Similiterq.">Similiterque</expan> rota ferrea, quàm lignea, vel <lb/>ferrea, aut lignea quadripalmaris diametri, quàm alia eiu&longs;<lb/>dem materiæ, &longs;ed bipalmaris. </s>

Line 2099

<s id="N1463F">C<emph type="italics"/>vr &longs;uper &longs;cytalas facilius portantur one<lb/>ra, quàm &longs;uper currus, cùm tamen ÿ ma<lb/>gnas habeant rotas, illæ verò pu&longs;illas? </s>

<s id="N14649">An <lb/>quoniam in &longs;cytalis nulla e&longs;t offen&longs;atio, in <lb/>curribus autem axis est, ad quem offen&longs;ant. <lb/></s>

<s id="N14651">De&longs;uper enim illum præmunt, & à lateri<lb/>bus. </s>

<s id="N14651">De&longs;uper enim illum premunt, & à lateri<lb/>bus. </s>

<s id="N14656">Quod autem e&longs;t in &longs;cytalis, ad i&longs;thæc duo mouetur, & <lb/>infernè &longs;ub&longs;trato &longs;patio, & onere &longs;uperimpo&longs;ito. </s>

<s id="N1465B">In viri&longs;<lb/>que enim ÿs reuoluitur locis circulus, & motus impellitur.<emph.end type="italics"/></s>

<s id="N1465B">In viri&longs;<lb/>que enim ijs reuoluitur locis circulus, & motus impellitur.<emph.end type="italics"/></s>

<s id="N14664">COMMENTARIVS.</s>

Line 2132

<s id="N14712">C<emph type="italics"/>vr longiùs feruntur mi&longs;&longs;ilia funda, quàm <lb/>manu mi&longs;&longs;a, cùm alioqui proiector manu <lb/>magis pondus comprehendat, quàm cùm il<lb/>lud &longs;u&longs;pendit? </s>

<s id="N1471E">Præterea &longs;ic quidem duo mo<lb/>uet pondera, fundæ videlicet, & mi&longs;silis: illo <lb/>autem modo &longs;olum mi&longs;sile. </s>

<s id="N14725">An quia in funda <lb/>quidem commotum mi&longs;sile funditor proÿcit? </s>

<s id="N14725">An quia in funda <lb/>quidem commotum mi&longs;sile funditor proijcit? </s>

<s id="N1472A">Fundam enim <lb/>circulo, &longs;ubinde rotans, id iaculatur: ex manu autem, à quie<lb/>te e&longs;t initium: omnia autem cùm in motu &longs;unt, quàm cùm <lb/>quie&longs;cunt, faciliùs mouentur. </s>

<s id="N14733">An & eam ob cau&longs;am est, &longs;ed<emph.end type="italics"/><pb pagenum="150" xlink:href="005/01/158.jpg"/><emph type="italics"/>nec minus etiam, quia in fundæ v&longs;u manus quidem fit cen<lb/>trum: &longs;unda verò, quod à centro exit? </s>

<s id="N14733">An & eam ob cau&longs;am est, &longs;ed <emph.end type="italics"/><pb pagenum="150" xlink:href="005/01/158.jpg"/><emph type="italics"/>nec minus etiam, quia in fundæ v&longs;u manus quidem fit cen<lb/>trum: funda verò, quod à centro exit? </s>

<s id="N14741">Quanto autem pro<lb/>ductius fuerit id, quod à centro e&longs;t, tantò citiùs mouetur. <lb/></s>

<s id="N14747">Toctus autem, qui manu fit, fundæ re&longs;pectu breuis e&longs;t.<emph.end type="italics"/></s>

<s id="N14747">Tactus autem, qui manu fit, fundæ re&longs;pectu breuis e&longs;t.<emph.end type="italics"/></s>

<s id="N1474E">COMMENTARIVS.</s>

<s id="N14754">Dvas hic Ariftoreles rationes dubitandi proponit, <lb/>vt explicet cau&longs;am cur longius ferantur mi&longs;silia <lb/>funda, quàm manu mi&longs;&longs;a. </s>

<s id="N14754">Dvas hic Aristoreles rationes dubitandi proponit, <lb/>vt explicet cau&longs;am cur longius ferantur mi&longs;silia <lb/>funda, quàm manu mi&longs;&longs;a. </s>

<s id="N1475B">Prima e&longs;t, quia proie<lb/>ctor melius mi&longs;&longs;ilia ip&longs;a manu comprehendit, quàm cum <lb/>funda &longs;u&longs;pendit: Quod autem melius comprehenditur, va<lb/>lidius iacitur ac propterea longius mittitur: Potius itaque <lb/>manu mi&longs;&longs;a, quàm funda proiecta mi&longs;silia longius ferri de<lb/>berent. </s>

<s id="N14768">Secunda verò ratio e&longs;t, nam <expan abbr="c&utilde;">cum</expan> funda quis proijcit; <lb/>duo &longs;imul mouet <expan abbr="põdera">pondera</expan>; fundá nempe <expan abbr="ipsã">ipsam</expan>, & mi&longs;sile, quod <lb/>proijcit; <expan abbr="ab&longs;q;">ab&longs;que</expan> autem funda <expan abbr="nõ">non</expan> mouet ni&longs;i proiectum: At am<lb/>plius quilibet mouere valet quando <expan abbr="totã">totam</expan> eius vim applicat <lb/>in vnum, quàm cum di&longs;tribuit in plura: Ergo magis ac remo<lb/>tius proiector manu mittet, ac proijciet, quàm funda. </s>

Line 2152

<s id="N147A9">Omnia autem cum in motu &longs;unt, <lb/>facilius vlterius per nouum impul&longs;um feruntur, quàm cum <lb/>quie&longs;cunt, ac tunc primò moueri coguntur. </s>

<s id="N147B2">Quocirca vt hæc doctrina iuxta rei veritatem clarius elu<lb/>ce&longs;cat, ob&longs;eruandum e&longs;t, proiecta in rigore loquendo non <lb/>&longs;tatim po&longs;t quietem è manu iaculantis elabi; &longs;ed aliquan<lb/>tulum &longs;altem prius manu ip&longs;a comitante moueri antequam <lb/>cmittantur. </s>

<s id="N147BD">Motus enim brachij iaculantis arcum quen<lb/>dam &longs;emper de&longs;cribit, in cuius fine, non autem in principio <lb/>mi&longs;silia proijciuntur; & quò longius proijcienda &longs;unt eò <pb pagenum="151" xlink:href="005/01/159.jpg"/>maiorem arcum brachium ip&longs;um efficit; magis nimirum <lb/>prius retrocedendo, magi&longs;que po&longs;tea antror&longs;um &longs;e exten<lb/>dendo, atque in fine exten&longs;ionis è manu mi&longs;silia dimitten<lb/>do. </s>

<s id="N147CF">Alioqui ni&longs;i manus imò etiam brachium &longs;imul cum il<lb/>lis antea moueretur, nec impetum inferre, nec proijcere <lb/>ip&longs;a valeret. </s>

<s id="N147D6">Quare cum ait Ari&longs;toteles, nullam antecede<lb/>re commotionem in proiectione, quæ fit &longs;ola manu, intelli<lb/>gendus non e&longs;t de commotione immediata coniuncta, & <lb/>qua&longs;i e&longs;&longs;entialiter pertinente ad eundem actum proiectio<lb/>nis: &longs;ed de commotione di&longs;po&longs;itiua accidentali, & qua&longs;i re<lb/>mota ad ip&longs;um actum iaculandi, vt e&longs;t præcedens illa irro<lb/>tatio, & agitatio fundæ. </s>

Line 2217

<s id="N14966">Cvm plura iugum de &longs;e po&longs;&longs;it &longs;ignificare, hoc loco &longs;u<lb/>mitur ab Ari&longs;totele pro <expan abbr="in&longs;trum&etilde;to">in&longs;trumento</expan> quodam ligneo, <lb/>quo textores in machina textoria. </s>

<s id="N14971">vtuntur, vt &longs;ta<lb/>men <expan abbr="telasq.">telasque</expan> conuoluant. </s>

<s id="N1497A">Oblongum itaque ac teres quod<lb/>dam lignum e&longs;t &longs;uper tran&longs;uer&longs;a ip&longs;ius textrinæ locatum, <pb pagenum="155" xlink:href="005/01/163.jpg"/>bina circa <lb/><figure id="id.005.01.163.1.jpg" xlink:href="005/01/163/1.jpg"/><lb/><expan abbr="vtramq.">vtramque</expan> ex<lb/>tremitatem <lb/><expan abbr="hab&etilde;s">habens</expan> fora<lb/>mina, qui<lb/>bus toti<lb/>dem collo<lb/>pes, &longs;eu fu<lb/>&longs;tes infigun<lb/>tur, vt faci<lb/>liùs iugum ip&longs;um eorum beneficio cum opus fuerit conuer<lb/>tatur, vt præ&longs;efert &longs;ub&longs;trata figura. </s>

<s id="N149A8">Sucula item quamuis alia po&longs;&longs;it &longs;ignificare, hic tamen <lb/>machinam &longs;ignificat tractorij generis, quæ ex tereti ligno, <lb/>aut lignorum compagine con&longs;tat, adiuncto axe &longs;uffulta <lb/>æquidi&longs;tante à plano horizontis, duobus, vel pluribus col<lb/>lopibus pari longitudine vtrinque immobiliter ad&longs;tantibus <lb/>tanquam rotæ radijs circa modiolum, quibus admota ma<lb/>nu, &longs;ucula ip&longs;a circa proprium axem obuoluitur, <expan abbr="funeq.">funeque</expan> cir<lb/>cumducto, pondera &longs;ubleuat, vt præoculis hic e&longs;t videre <lb/>in eius figura. </s>

Line 2227

<s id="N149D7"><expan abbr="Itemq.">Itemque</expan> cur gracilio<lb/>res &longs;ucculæ facilius <lb/>pariter ab <expan abbr="ead&etilde;">eadem</expan> po<lb/>tentia circumuoluantur, quàm cra&longs;&longs;iores. </s>

<s id="N149E7">Vtriu&longs;que &longs;ubin<lb/>de cau&longs;am e&longs;&longs;e inquit, quod in vtraque machina quilibet <lb/>collops tanquam vectis &longs;e habet, cuius <expan abbr="centr&utilde;">centrum</expan>, ac fulcimen<lb/>tum e&longs;t in medio iugi, vel &longs;uculæ, &longs;iue in intimo axe coniun<lb/>cto, aut &longs;altem in ip&longs;is concepto: potentia verò in extremi-<pb pagenum="156" xlink:href="005/01/164.jpg"/>tate, quæ extra ip&longs;um iugum, vel &longs;uculam prominet, vbi <lb/>manus communiter adhibetur: ac onus con&longs;tituitur in exti<lb/>ma ip&longs;a vtriu&longs;que corporis &longs;uperficie, quam fortiter præ<lb/>mendo vbi è foramine prodit, &longs;ecum conuoluit, ac ver&longs;at. <lb/></s>

<s id="N14A02">Cuius quippe vectis &longs;imilitudinem, & operationem hacte<lb/>nus etiam in malo expre&longs;simus loquendo de motione nauis <lb/>vento agitatæ. </s>

<s id="N14A09">Cum itaque plus atque celerius transfera<lb/>tur ab eadem potentia extremum &longs;emidiametri, quod ma<lb/>gis à centro di&longs;tat in de&longs;criptione circuli, nec non plus, ac <lb/>facilius mouere valeat extremum vectis, quod longius à <lb/>fulcimento re&longs;pectu oneris leuandi protenditur, quò lon<lb/>giores fuerint collopes, &longs;emidiametri, ac vectis rationem <lb/>adepti, <expan abbr="magisq.">magisque</expan> eorum extrema à fulcimento, &longs;eu centro <lb/>in &longs;uperficie conuoluenda di&longs;tauerint, eò faciliùs iugum, aut <lb/>&longs;uculam contorquendo ver&longs;abune. </s>

<s id="N14A20">Quoniam verò in omni <lb/>vecte maior, aut minor di&longs;tantia, quàm à centro, vel fulci<lb/>mento habet extremum, in quo applicatur potentia, atten<lb/>ditur &longs;olummodo re&longs;pectu di&longs;tantiæ, quam &longs;imul habet onus <lb/>ab eodem centro, vel fulcimento; hinc fit, vt in graciliori<lb/>bus &longs;uculis, minore exi&longs;tente di&longs;tantia à centro ad circum<lb/>ferentiam, &longs;eu extimam &longs;uperficiem conuexam vbi con&longs;ti<lb/>tuitur onus, & vbi fit collopis præ&longs;sio, maior di&longs;tantia relin<lb/>quatur v&longs;que ad alterum extremum eiu&longs;dem collopis, quod <lb/>e&longs;t extra; ac iuxtamaiorem hanc proporrionem, magis pa<lb/>riter collops ip&longs;e mouere &longs;uculam valeat. </s>

<s id="N14A20">Quoniam verò in omni <lb/>vecte maior, aut minor di&longs;tantia, quàm à centro, vel fulci<lb/>mento habet extremum, in quo applicatur potentia, atten<lb/>ditur &longs;olummodo re&longs;pectu di&longs;tantiæ, quam &longs;imul habet onus <lb/>ab eodem centro, vel fulcimento; hinc fit, vt in graciliori<lb/>bus &longs;uculis, minore exi&longs;tente di&longs;tantia à centro ad circum<lb/>ferentiam, &longs;eu extimam &longs;uperficiem conuexam vbi con&longs;ti<lb/>tuitur onus, & vbi fit collopis præ&longs;sio, maior di&longs;tantia relin<lb/>quatur v&longs;que ad alterum extremum eiu&longs;dem collopis, quod <lb/>e&longs;t extra; ac iuxta maiorem hanc proportionem, magis pa<lb/>riter collops ip&longs;e mouere &longs;uculam valeat. </s>

<s id="N14A39">Quod &longs;i contra hanc expo&longs;itionem obijciatur, quòd Ari<lb/>&longs;toteles palàm & ab&longs;olutè docuerit, tàm &longs;uculam, quàm iu<lb/>gum <expan abbr="cõ&longs;titui">con&longs;titui</expan> centrum in collopum motione; ex quo a&longs;&longs;um<lb/>pto minus concluderentur, quæ de ip&longs;ius mente relata &longs;unt; <lb/>Occurrendum e&longs;t, id &longs;ano modo e&longs;&longs;e intelligendum. </s>

Line 2241

<s id="N14A73">C<emph type="italics"/>vr eiu&longs;dem magnitudinis lignum faciliùs <lb/>genu. </s>

<s id="N14A7B">frangitur, &longs;i qui&longs;piam æquè deductis <lb/>manibus extrema comprehendens fregerie, <lb/>quàm &longs;i iuxta genu: & &longs;i terræ illud appli<lb/>cans pelle &longs;uperimpo&longs;ito, manu longè didu<lb/>cta confregerit, quàm propè? </s>

<s id="N14A7B">frangitur, &longs;i qui&longs;piam æquè deductis <lb/>manibus extrema comprehendens fregerit, <lb/>quàm &longs;i iuxta genu: & &longs;i terræ illud appli<lb/>cans pelle &longs;uperimpo&longs;ito, manu longè didu<lb/>cta confregerit, quàm propè? </s>

<s id="N14A86">An quia ibi <lb/>quidem genu centr<gap/> e&longs;t, bìs verò ip&longs;e pes. </s>

<s id="N14A8D">Quantò autem <lb/>remotiùs à centro fuerit, faciliùs mouetur quodcunque. </s>

<s id="N14A92">Mo<lb/>ueri autem quod frangitur, nece&longs;&longs;e est.<emph.end type="italics"/></s>

Line 2262

<s id="N14B05"><expan abbr="Cumq.">Cumque</expan> ex hac motione, & <lb/>inclinatione vtriu&longs;que dimidij procedat ip&longs;a fractio ligni, &longs;e<lb/>quitur etiam facilius longè quàm propè diductis manibus <lb/>ip&longs;um lignum confringi. </s>

<s id="N14B13">Cur autem non ob&longs;tante prædicta di&longs;paritate in modo, <lb/>quo frangitur lignum, cæteris paribus<gap/>difficilius <expan abbr="fuãgatur">fuangatur</expan> <lb/>&longs;i cra&longs;sius ip&longs;um &longs;it, quàm &longs;i gracilius, non docet Ari&longs;tote<lb/>les. </s>

<s id="N14B13">Cur autem non ob&longs;tante prædicta di&longs;paritate in modo, <lb/>quo frangitur lignum, cæteris paribus difficilius <expan abbr="fuãgatur">frangatur</expan> <lb/>&longs;i cra&longs;sius ip&longs;um &longs;it, quàm &longs;i gracilius, non docet Ari&longs;tote<lb/>les. </s>

<s id="N14B23">Ex ip&longs;a <expan abbr="tam&etilde;">tamen</expan> rei natura qui&longs;que &longs;tatim intelliget ab&longs;que <lb/>eo, quod recurrat cum Baldo ad rationem illam angulati <lb/>vectis, quam dicit habere <expan abbr="vtrumq.">vtrumque</expan> dimidium ligni prærupti. <lb/></s>

<s id="N14B33">Siquidem cum tota difficultas, quæ reperitur in fractione <lb/>ligni oriatur ex re&longs;i&longs;tentia partium &longs;eparandarum, eo quod <lb/>hæ inter &longs;e naturali nexu coniunctæ, nece&longs;&longs;ariò ob&longs;tent &longs;e<lb/>parationi ab inuicem: quo plures fuerint ip&longs;æ partes, eo ma<lb/>gis ob&longs;tabunt, <expan abbr="difficiliusq.">difficiliusque</expan> proinde per earum diui&longs;ionem <lb/>lignum quodlibet ex ip&longs;is compo&longs;itum confringetur. </s>

<s id="N14B46">Illud etiam hic quæri po&longs;&longs;et, quod Ari&longs;toteles prætermi<lb/>&longs;it, cur prius ex parte &longs;uperiori, ac extra angulum, quem effi<lb/>ciunt dimidia ligni inclinata, quàm ex parte inferiori in cu<lb/>&longs;pide ip&longs;ius anguli vbi <expan abbr="c&etilde;trum">centrum</expan> motionis con&longs;tituitur, fractio <lb/>ip&longs;a ligni &longs;equatur. </s>

<s id="N14B55">Facilisque erit re&longs;pon&longs;io &longs;i dicamus id <lb/>&longs;ieri, quia illæ partes continui in fractione prius ab inuicem <lb/>&longs;eparantur, quæ & citius & longius coguntur di&longs;cedere: In <lb/>fractione autem ligni per inclinationem, & complicationem <lb/>vtriu&longs;que dimidij, ex partibus cra&longs;sitiei, quæ ab inuicem di-<pb pagenum="159" xlink:href="005/01/167.jpg"/>uelluntur, illæ citius ac longius ab inuicem coguntur di&longs;ce<lb/>dere, quæ magis di&longs;tant à puncto, quod con&longs;tituitur cen<lb/>trum in hac motione; quia nimirum illæ di&longs;cedendo, maio<lb/>rem &longs;emper arcum de&longs;cribunt eodem tempore, quam quæ <lb/>propinquiores &longs;unt centro. </s>

<s id="N14B55">Facilisque erit re&longs;pon&longs;io &longs;i dicamus id <lb/>fieri, quia illæ partes continui in fractione prius ab inuicem <lb/>&longs;eparantur, quæ & citius & longius coguntur di&longs;cedere: In <lb/>fractione autem ligni per inclinationem, & complicationem <lb/>vtriu&longs;que dimidij, ex partibus cra&longs;sitiei, quæ ab inuicem di-<pb pagenum="159" xlink:href="005/01/167.jpg"/>uelluntur, illæ citius ac longius ab inuicem coguntur di&longs;ce<lb/>dere, quæ magis di&longs;tant à puncto, quod con&longs;tituitur cen<lb/>trum in hac motione; quia nimirum illæ di&longs;cedendo, maio<lb/>rem &longs;emper arcum de&longs;cribunt eodem tempore, quam quæ <lb/>propinquiores &longs;unt centro. </s>

<s id="N14B6D">Illæ igitur ip&longs;æ partes cra&longs;&longs;itiei <lb/>di&longs;tantiores a centro prius, ac citius ab inuicem &longs;eparantur, <lb/>ac proinde fractio non ab ip&longs;o centro, vel parte inferiori vbi <lb/>fulcitur, &longs;ed à parte &longs;uperiori, ac remotiori ab illo, initium <lb/>&longs;umere debet. </s>

Line 2277

<s id="N14B91">Partes <lb/>verò quæ ab in<lb/>uicem &longs;eparan<lb/>tur &longs;int illæ, quæ <lb/>exi&longs;tunt in lineis <lb/>DC, & EC re<lb/>pr&etail;&longs;entantes la<lb/>titudinem, vel <lb/>cra&longs;sitiem ligni. <lb/></s>

<s id="N14BA5">Dicimus ergo ex <lb/>huiu&longs;modi par<lb/>tibus, quæ &longs;unt in ip&longs;is lineis DC, & EC, illas quæ magis <lb/>di&longs;tant à puncto C citius moueri, ac per maius interuallum <lb/>ab inuicem &longs;eparari: quod e&longs;t prius confringi, quàm quæ <lb/>prop inquiores &longs;unt puncto C. </s>

<s id="N14BB3">Siquidem ip&longs;um C non <lb/>modo con&longs;tituitur centrum in hac motione re&longs;pectu &longs;emi<lb/>circuli AFB; &longs;ed etiam re&longs;pectu &longs;emicirculi GDEH, qui <lb/>efficitur à punctis DE, vt tandem DA po&longs;t ab&longs;olutam <lb/>complicationem ligni reperiatur in GI; & EB in HK. </s>

<s id="N14BBE">Qua<lb/>propter lineæ DC, & EC con&longs;tituuntur tanquam duo &longs;e<lb/>midiametri, cuius partes quo remotiores fuerint à centro <lb/>C, eo velocius ab eadem potentia mouentur, maiusq &longs;pa<lb/>tium in æquali tempore percurrunt, vt &longs;&etail;pius probatum e&longs;t. </s>

<s id="N14BBE">Qua<lb/>propter lineæ DC, & EC con&longs;tituuntur tanquam duo &longs;e<lb/>midiametri, cuius partes quo remotiores fuerint à centro <lb/>C, eo velocius ab eadem potentia mouentur, <expan abbr="maiusq">maiusque</expan> &longs;pa<lb/>tium in æquali tempore percurrunt, vt &longs;&etail;pius probatum e&longs;t. </s>

<s id="N14BCB">Diximus autem prius &longs;eparari partes di&longs;tantiores à pun-<pb pagenum="160" xlink:href="005/01/168.jpg"/>cto C in ip&longs;is lineis DC, & EC, loquendo de illis prout <lb/>repræ&longs;entant materialem cra&longs;sitiem ligni, quæ non &longs;tatim <lb/>ac tota &longs;imul di&longs;rumpitur. </s>

Line 2305

<s id="N14C38">Crocæ apud Græcosidem &longs;ignificant, ac apud Lati<lb/>nos vmbilici, quorum meminit Cicero 2. de Orato<lb/>re; <expan abbr="&longs;untq.">&longs;untque</expan> expoliti illi calculi, qui in littoribus repe<lb/>riuntur continua maris agitatione attriti, ac inorbicularem, <lb/>vel rotundam figuram redacti, vt qui in glarea arenis vi&longs;un-<pb pagenum="161" xlink:href="005/01/169.jpg"/>tur admi&longs;ti. </s>

<s id="N14C4C">De ijs igitur hic loquens Ari&longs;toteles, quærit, <lb/>qua de cau&longs;a rotundam potius quam aliam figuram per at<lb/>tritionem ac perpetuam illam agitationem adipi&longs;cantur, <lb/>cum frequentius ex lapidibus, ac fragmentis alterius figuræ <lb/>efficiantur. </s>

<s id="N14C57">Quod enim &longs;ecundum omnes &longs;ui partes paula<lb/>tim conteritur, ac minuitur, vniformiter difformiter contun<lb/>di debet, ac &longs;en&longs;im attenuari, eadem partium proportione <lb/>&longs;eruata, <expan abbr="eademq.">eademque</expan> proinde figura. </s>

<s id="N14C64">Non igitur &longs;atis apparet <lb/>cur ex tot tanquam ex diuer&longs;is &longs;iguris te&longs;tarum o&longs;treorum <lb/><expan abbr="concarumq.">concarumque</expan> ac lapidum angularium non ni&longs;i rotundam, & <lb/>orbicularem formam eorum reliquiæ videantur &longs;eruare, <lb/><expan abbr="eiu&longs;demq.">eiu&longs;demque</expan> figuræ penè omnes euadant cuius non erant. </s>

<s id="N14C64">Non igitur &longs;atis apparet <lb/>cur ex tot tanquam ex diuer&longs;is figuris te&longs;tarum o&longs;treorum <lb/><expan abbr="concarumq.">concarumque</expan> ac lapidum angularium non ni&longs;i rotundam, & <lb/>orbicularem formam eorum reliquiæ videantur &longs;eruare, <lb/><expan abbr="eiu&longs;demq.">eiu&longs;demque</expan> figuræ penè omnes euadant cuius non erant. </s>

<s id="N14C77">Huic autem quæ&longs;tioni Ari&longs;toteles re&longs;pondet, partes, quæ <lb/>magis à centro, &longs;eu puncto medio circumlati corporis rece<lb/>dunt, cum celerius in eius circumuolutione ferantur (maius <lb/>videlicet in æquali tempore &longs;patium in rotatione conficien<lb/>do) vehementius impetere, <expan abbr="vicinaq.">vicinaque</expan> corpora rotando per<lb/>cutere, quàm partes centro propinquiores; velocitas enim <lb/>auget impul&longs;um: Quæ autem partes <expan abbr="vehem&etilde;tius">vehementius</expan> impetunt, <lb/>atque impingunt, &longs;i fragiles in &longs;e &longs;int, facilius etiam refran<lb/>guntur. </s>

Line 2315

<s id="N14CA5">Quod &longs;i ex hoc Ari&longs;totelis di&longs;cur&longs;u &longs;equatur maiores <lb/>croceas rotundiores fieri, quàm minores propter maiorem <lb/>à centro di&longs;tantiam, qua in rotatione prominentes partes <lb/>facilius contunduntur; id certè ab experientia non e&longs;t om<lb/>nino alienum, vt Baldus arbitratur; &longs;icut nec ip&longs;as croceas <lb/>circa centrum conuerti, quamuis alijs, ac diuer&longs;is etiam mo<lb/>tionibus agitentur. </s>

<s id="N14CB4">Si enim in pluribus littoribus attentius <lb/>ob&longs;erua&longs;&longs;et, vidi&longs;&longs;et vtique fluctuum iactatione fluxu, ac re<lb/>fluxu, non modo glareas, paruo&longs;que lapillos circa centrum <lb/>omnino conuolui, &longs;ed etiam maiores vmbilicos, & non me<pb pagenum="162" xlink:href="005/01/170.jpg"/>diocria &longs;axa &longs;imiliter in orbem ruere, <expan abbr="&longs;e&longs;eq.">&longs;e&longs;eque</expan> collidere, quæ <lb/>ni&longs;i magna valde &longs;int, vt rotari minus commodè po&longs;sint, <lb/>mutua ip&longs;orum colli&longs;ione, orbiculata euadunt, vel ad orbi<lb/>cularem figuram accedunt magis quàm minores lapilli, vel <lb/>te&longs;tæ. </s>

<s id="N14CCE">Vnde lati&longs;simæ plagæ vi&longs;untur his tantum rotundis <lb/>lapidibus &longs;tratæ, nulla ferè admi&longs;ta arena, parua te&longs;ta, vel <lb/>glarea. </s>

<s id="N14CD5">Quod verò non omnes lapides leuigatos, ac rotun<lb/>dos tanquam torno fabrefactos &longs;e videantur o&longs;tendere; id <lb/>potius materiæ varietati eribuendum e&longs;t, qua non omnes <lb/>partes æquè fiagiles con&longs;tituuntur, vt pariter po&longs;sint &longs;ua <lb/>volubilitate contundi. </s>

<s id="N14CD5">Quod verò non omnes lapides leuigatos, ac rotun<lb/>dos tanquam torno fabrefactos &longs;e videantur o&longs;tendere; id <lb/>potius materiæ varietati tribuendum e&longs;t, qua non omnes <lb/>partes æquè fragiles con&longs;tituuntur, vt pariter po&longs;sint &longs;ua <lb/>volubilitate contundi. </s>

<s id="N14CE0">Imò minores vmbilicos, vt plurimùm <lb/>fragiliorem adeptos e&longs;&longs;e materiam argumento e&longs;&longs;e pote&longs;t <lb/>ip&longs;a eorum paruitas. </s>

<s id="N14CE7">Non enim ex magnis parui facti e&longs;&longs;ent, <lb/>ni&longs;i materia, ex qua con&longs;tant facilè cederet, ac cedendo vni<lb/>formiter attenuaretur, ex quo prouenit leuitas. </s>

Line 2352

<s id="N14D9E">Ex ijs autem duobus quæ&longs;itis, &longs;ecundo tantum <expan abbr="re&longs;põdet">re&longs;pondet</expan> <lb/>Ari&longs;toteles, cum ex eius &longs;olutione facilè patere po&longs;sit &longs;olu<lb/>tio primi. </s>

<s id="N14DA9">Ait igitur ex hoc procedere maiorem inflexio<pb pagenum="164" xlink:href="005/01/172.jpg"/>nem ligni procerioris, quod cum lignum ita &longs;u&longs;pen&longs;um, &longs;i<lb/>mul con&longs;tituatur vectis, & onus, fulcimentum habens prope <lb/>alterum extremum in manu à qua eleuatur; quanto exten<lb/>&longs;ius fuerit id quod à fulcimento e&longs;t ver&longs;us alteram extremi<lb/>tatem, quæ con&longs;tituitur pondus; tanto magis ip&longs;um inflecti <lb/>nece&longs;&longs;e e&longs;t, &longs;uppo&longs;ito quod vectis ip&longs;a &longs;eu lignum, ex &longs;e fle<lb/>ctile &longs;it; id quod non contingit in breuibus lignis, aut vecti<lb/>bus etiam &longs;i eadem &longs;eruetur proportio: Porrò extremum, <lb/>quod grauitat parum &longs;emper di&longs;tat à fulcimento. </s>

<s id="N14DC1">Sit enim <lb/>&longs;ari&longs;&longs;a decem cubitorum longitudinis aliquantulum incli<lb/><figure id="id.005.01.172.1.jpg" xlink:href="005/01/172/1.jpg"/><lb/>nata ip&longs;a AB, cuius manubrium A, cu&longs;pis B, &longs;uffulta di<lb/>gitis vbi C, pollice præmente in A tanquam potentia <lb/>eleuante. </s>

<s id="N14DD2">Eodemq pacto con&longs;tituatur gracilior &longs;urculu<gap/><lb/>bicubitus DE fultus in F. </s>

<s id="N14DD2"><expan abbr="Eodemq">Eodemque</expan> pacto con&longs;tituatur gracilior &longs;urculus <lb/>bicubitus DE fultus in F. </s>

<s id="N14DD9">Dico igitur &longs;ari&longs;&longs;am magis in<lb/>clinari quàm &longs;urculum, eo quod licet vtiumque habeat ra<lb/>tionem vectis &longs;imul & oneris; pondus tamen con&longs;titutus in <lb/>B magis di&longs;tat à fulcimento C, quàm quod <expan abbr="cõ&longs;tituitur">con&longs;tituitur</expan> in E <lb/>ab ip&longs;o F; <expan abbr="magisq.">magisque</expan> propterea grauitat, & inclinat deor&longs;um, <lb/>paulatim recedendo à rectitudine, quam &longs;tans, vel in &longs;olo <lb/>iacens habebat. </s>

<s id="N14DD9">Dico igitur &longs;ari&longs;&longs;am magis in<lb/>clinari quàm &longs;urculum, eo quod licet vtrumque habeat ra<lb/>tionem vectis &longs;imul & oneris; pondus tamen con&longs;titutus in <lb/>B magis di&longs;tat à fulcimento C, quàm quod <expan abbr="cõ&longs;tituitur">con&longs;tituitur</expan> in E <lb/>ab ip&longs;o F; <expan abbr="magisq.">magisque</expan> propterea grauitat, & inclinat deor&longs;um, <lb/>paulatim recedendo à rectitudine, quam &longs;tans, vel in &longs;olo <lb/>iacens habebat. </s>

<s id="N14DF2">Quod non abs re fuerit aliundè etiam confirmare, ac vl<lb/>terius declarare, notando prius ad inflexionem <expan abbr="cõtinui">continui</expan> duo <lb/>nece&longs;&longs;ario requiri. </s>

<s id="N14DFD">Vnum e&longs;t determinata, ac proportiona<lb/>ta quædam virtus &longs;iue ponderis, &longs;iue motricis potentiæ, ita <lb/>vt ab alia minori nulla cau&longs;ari po&longs;&longs;it talis inflexio. </s>

<s id="N14E04"><expan abbr="Quõd">Quond</expan> <lb/>certè <expan abbr="cõmune">commune</expan> e&longs;t omnibus cau&longs;is naturalibus re&longs;pectu pro<lb/>priorum effectuum, ad quos ordinantur. </s>

<s id="N14E04"><expan abbr="Quõd">Quod</expan> <lb/>certè <expan abbr="cõmune">commune</expan> e&longs;t omnibus cau&longs;is naturalibus re&longs;pectu pro<lb/>priorum effectuum, ad quos ordinantur. </s>

<s id="N14E12">Alterum verò e&longs;t <pb pagenum="165" xlink:href="005/01/173.jpg"/>con&longs;tipatio quædam aliquarum partium, aliarumque laxa<lb/>tio in corporibus flexibilibus tanquam conden&longs;atio, ac ra<lb/>refactio. </s>

<s id="N14E1E">Non enim po&longs;&longs;et continuum inflecti ni&longs;i partes il<lb/>lius, quæ concauam &longs;uperficiem con&longs;tituunt vici&longs;&longs;im con&longs;ti<lb/>parentur; illæ verò quæ conuexam, laxarentur; &longs;eu quo fie<lb/>ri pote&longs;t extenderentur. </s>

<s id="N14E27">Cumque &longs;en&longs;im natura ab vno ad <lb/>aliud in omnibus gradum faciat; hinc e&longs;t, vt non in qualibet <lb/>longitudine &longs;iue di&longs;tantia æquè fieri po&longs;&longs;it inflexio, &longs;ed lon<lb/>gè facilius in ea, in qua paulatim procedendo, ita partes va<lb/>lent curuari, vt &longs;ingulæ à rectitudine non videantur recede<lb/>re. </s>

Line 2370

<s id="N14E4B">E contra verò quo bre<lb/>uiora extiterint, eo minor e&longs;t virtus huiu&longs;modi; quæ tandem <lb/>&longs;i minor &longs;it minima, quæ &longs;ufficere po&longs;sit ad motionem, nullo <lb/>pacto valet inflectere, vt patet in &longs;urculis calamis ac paleis, <lb/>quæ cum leuitate materiæ, tùm breuitate corporis, graui<lb/>tare non po&longs;&longs;unt quantum &longs;ufficiat ad motum inflexionis. <lb/></s>

<s id="N14E59">Quod &longs;i breuitas ligni compen&longs;etur magna cra&longs;&longs;itiei, ob&longs;ta<lb/>bit ex alio capite ip&longs;amet eadem cra&longs;sities propter maio<lb/>rem multitudinem partium, quarum aliæ con&longs;tipari, aliæ au<lb/>tem laxari debent cum fit ip&longs;a inflexio. </s>

<s id="N14E62">Secundo verò nam <lb/>quanto maior e&longs;t longitudo ip&longs;ius flexilis, tanto minor con<lb/>&longs;tituitur laxatio, & con&longs;tipatio &longs;ingularum partium, quæ ar<lb/>cum inflexionis efficiunt, meliu&longs;que valent &longs;en&longs;im inflecti. <lb/></s>

<s id="N14E6C">Vice autem ver&longs;a, quò breuior e&longs;t longitudo illius, eò magis <lb/>&longs;ingulæ partes curuari debent, vt totius continui &longs;iat infle<lb/>xio. </s>

<s id="N14E6C">Vice autem ver&longs;a, quò breuior e&longs;t longitudo illius, eò magis <lb/>&longs;ingulæ partes curuari debent, vt totius continui fiat infle<lb/>xio. </s>

<s id="N14E73"><expan abbr="Ideoq.">Ideoque</expan> difficilius curuantur, & inflectuntur etiam &longs;i gra<lb/>cile &longs;it ip&longs;um lignum, quod debet inflecti. </s>

Line 2385

<s id="N14ED1">Quare nihil determinari pote&longs;t quo ad hoc ni&longs;i per<lb/>&longs;pecta, vt diximus di&longs;po&longs;itione materiæ, <expan abbr="variaq.">variaque</expan> proportio<lb/>ne, quæ diuer&longs;imodè iuxta maiorem, aut minorem corpo<lb/>rum magnitudinem operatur. </s>

<s id="N14EE0">Denique vt dictum e&longs;t de eleuatione, ac &longs;u&longs;pen&longs;ione li<lb/>gni, vel alterius corporis oblongi &longs;umpti ab altera tantum <lb/>extremitate, vt exemplificauimus in &longs;ari&longs;&longs;a, idem dicendum <lb/>e&longs;t de eleuatione, ac &longs;u&longs;pen&longs;ione, quæ fit, vel ex ambabus <lb/>extremitatibus; vel ex medio inter illas: Nam &longs;i vtrinque ab <lb/>extremitatibus &longs;u&longs;pendatur aliquod lignum ad paralellum <lb/>horizonti, duo quidem in illo vectes fient in ip&longs;is extremita<lb/>tibus fulti, ponderaq in communi puncto intermedio gra<lb/>uitabunt tanquam in remoti&longs;simo &longs;itu ab vtriu&longs;que fultura. <lb/></s>

<s id="N14EE0">Denique vt dictum e&longs;t de eleuatione, ac &longs;u&longs;pen&longs;ione li<lb/>gni, vel alterius corporis oblongi &longs;umpti ab altera tantum <lb/>extremitate, vt exemplificauimus in &longs;ari&longs;&longs;a, idem dicendum <lb/>e&longs;t de eleuatione, ac &longs;u&longs;pen&longs;ione, quæ fit, vel ex ambabus <lb/>extremitatibus; vel ex medio inter illas: Nam &longs;i vtrinque ab <lb/>extremitatibus &longs;u&longs;pendatur aliquod lignum ad paralellum <lb/>horizonti, duo quidem in illo vectes fient in ip&longs;is extremita<lb/>tibus fulti, <expan abbr="ponderaq">ponderaque</expan> in communi puncto intermedio gra<lb/>uitabunt tanquam in remoti&longs;simo &longs;itu ab vtriu&longs;que fultura. <lb/></s>

<s id="N14EF4">Quapropter ibidem fiet vtriu&longs;que vectis, &longs;eu totius ligni in<lb/>flexio, &longs;uppo&longs;ita vt diximus flexibilitate materiæ, <expan abbr="ip&longs;aq.">ip&longs;aque</expan> ce-<pb pagenum="167" xlink:href="005/01/175.jpg"/>dente &longs;uomet ponderi. </s>

<s id="N14F02">Alioquin lignum ip&longs;um, aut non <lb/>recederet à &longs;ua rectitudine, aut frangeretur. </s>

<s id="N14F07">Quod &longs;i &longs;u<lb/>&longs;pendatur ex medio, in ip&longs;o medio fulcietur vtrumque di<lb/>midium, ceu duplex vectis vtrinque applicatus, extremita<lb/>tibus vtrinque pariter grauitantibus, ac propendentibus <lb/>tanquam in remoti&longs;&longs;imo loco à communi centro &longs;iue fùlci<lb/>mento. </s>

Line 2396

<s id="N14F20">C<emph type="italics"/>vr à paruo existente cuneo magna &longs;cindun<lb/>tur pondera, & corporum moles, <expan abbr="validaq.">validaque</expan> fit <lb/>impre&longs;sio? </s>

<s id="N14F2E">An quia cuneus duo &longs;unt vectes, <lb/>&longs;ibi inuicem contrarÿ? </s>

<s id="N14F2E">An quia cuneus duo &longs;unt vectes, <lb/>&longs;ibi inuicem contrarii? </s>

<s id="N14F33">vterque autem & <lb/>pondus habet, & bypomochlion; quod diuellit, <lb/>& comprimit. </s>

<s id="N14F33">vterque autem & <lb/>pondus habet, & hypomochlion; quod diuellit, <lb/>& comprimit. </s>

<s id="N14F3A">Plagæ quin etiam ip&longs;ius latio <lb/>pondus, quod percutit, & mouet, magnum facit, & quoniam <lb/>motum mouet, ip&longs;a celeritate valentius fit. </s>

<s id="N14F41">Paruo autem exi<lb/>stente vectæ, magnæ illum con&longs;equuntur vires: quamobrem <lb/>vltra magnitudinis decentiam latet mouens. </s>

<s id="N14F48">Sit cuneus vbi <lb/>ABC, quod verò cuneo &longs;cinditur DEFG. </s>

Line 2414

<s id="N14F81"><expan abbr="Soluitq.">Soluitque</expan> &longs;tatim, quia in <pb pagenum="168" xlink:href="005/01/176.jpg"/>cuneo, duo &longs;unt vectes &longs;ibi inuicem aduer&longs;i, quorum vter<lb/>que & pondus habet, & fulcimentum, quod comprimens <lb/>diuellit; impul&longs;u &longs;cilicet accepto ab ip&longs;o motore, qui dum <lb/>cuneum malleo, vel alio corpore percutit, &longs;imul vtroque <lb/>vtitur vecte. </s>

<s id="N14F94">Magna autem vis illi incutitur ex mallei per<lb/>cu&longs;&longs;ione, eo quod malleus celerrimè motus moueat &longs;iue <lb/>percutiat. </s>

<s id="N14F9B">Lationis enim celeritate validius ferit. </s>

<s id="N14F9E">Ob vectis <lb/>igitur naturam, quam cuneus participat, & qua vires augen<lb/>tur, validamque mallei percu&longs;&longs;ionem, magnas contingit <lb/>&longs;cindi, aut &longs;aitem findi corporum moles, paruo adhibito <lb/>cuneo in rimula ip&longs;ius molis. </s>

<s id="N14F9E">Ob vectis <lb/>igitur naturam, quam cuneus participat, & qua vires augen<lb/>tur, validamque mallei percu&longs;&longs;ionem, magnas contingit <lb/>&longs;cindi, aut &longs;altem findi corporum moles, paruo adhibito <lb/>cuneo in rimula ip&longs;ius molis. </s>

<s id="N14FA9">Quod adhuc &longs;chemate decla<lb/>rans, hæc ferè &longs;ubnectit idem Ari&longs;toteles. </s>

Line 2428

<s id="N14FFC">Huic autem Ari&longs;totelis doctrinæ, ac &longs;olutioni duo obijcit <lb/>Baldus. </s>

<s id="N15002">Primum e&longs;t, quia &longs;i darentur explicati vectes in cu<lb/>neo, eorum extremitates inuicem contendentes in puncto <lb/>B altera alteri ne quidquam operarentur e&longs;&longs;et impedimen<lb/><gap/>o, vt late probat Guidus Vbaldus tractatu de cuneo. </s>

<s id="N15002">Primum e&longs;t, quia &longs;i darentur explicati vectes in cu<lb/>neo, eorum extremitates inuicem contendentes in puncto <lb/>B altera alteri ne quidquam operarentur e&longs;&longs;et impedimen<lb/>to, vt late probat Guidus Vbaldus tractatu de cuneo. </s>

<s id="N1500C">Se-<pb pagenum="169" xlink:href="005/01/177.jpg"/>cundum verò e&longs;t, quia in ip&longs;o &longs;ci&longs;&longs;ionis actu, facta aliqua di<lb/>&longs;tractione partium molis adhuc non in totum di&longs;ci&longs;&longs;æ, ver<lb/>tex cunei, quo pondera vtrinque diuelli, ac moueri debe<lb/>rent, nihil vt plurimum tangit in rimula dum ip&longs;a vlterius <lb/>dilatatur. </s>

<s id="N1501E">Ad primum tamen re&longs;pondetur, &longs;i concipiamus in cuneo <lb/>vectes explicatos ex parte A vrgere ver&longs;us G, & ex parte <lb/>C vrgere ver&longs;us D; verticem verò non tran&longs;gredi punctum <lb/>B; &longs;ed in eo quie&longs;cere: tunc quidem &longs;equi, extrema ip&longs;orum <lb/>vectium &longs;ibi inuicem ob&longs;tare in puncto B, nè in contratium <lb/>moueantur, moueantque adiacentia pondera modo de&longs;cri<lb/>pto. </s>

<s id="N1501E">Ad primum tamen re&longs;pondetur, &longs;i concipiamus in cuneo <lb/>vectes explicatos ex parte A vrgere ver&longs;us G, & ex parte <lb/>C vrgere ver&longs;us D; verticem verò non tran&longs;gredi punctum <lb/>B; &longs;ed in eo quie&longs;cere: tunc quidem &longs;equi, extrema ip&longs;orum <lb/>vectium &longs;ibi inuicem ob&longs;tare in puncto B, nè in contrarium <lb/>moueantur, moueantque adiacentia pondera modo de&longs;cri<lb/>pto. </s>

<s id="N1502D">At &longs;i concipiamus, vt re vera e&longs;t apicem ip&longs;um &longs;imul <lb/>pergere ad partes EF: tunc in ip&longs;o motu optimè intellige<lb/>mus, concurrentiam extremorum vtriu&longs;que vectis in vni<lb/>cum illud punctum terminatiuum verticis, nihil ob&longs;tare <lb/>quominus pars vectis, quæ &longs;equitur po&longs;t illud vbi K, impel<lb/>lat aliam &longs;ibi corre&longs;pondentem in mole &longs;cindenda ver&longs;us <lb/>N: & pars vbi H, aliam &longs;imilem ver&longs;us M. </s>

<s id="N1503C">Siquidem hoc <lb/>ip&longs;o, quod vertex vlterius pergit, partes illum vtrinque con<lb/>&longs;equentes in proportionatum &longs;ibi locum &longs;uccedere non po&longs;<lb/>&longs;ent, ni&longs;i prius inde <expan abbr="expeller&etilde;tur">expellerentur</expan> per &longs;ci&longs;&longs;ionem partes molis, <lb/>quæ eundem locum occupabant. </s>

<s id="N1504B">Pars autem vbi K in <lb/>mole &longs;cindenda non expellitur inde virtute vectis AB; &longs;icut <lb/>nec H virtute vectis CB; cum nullam vim vtraque pati <lb/>po&longs;&longs;it à vecte ni&longs;i illa nitatur in contrariam partem. </s>

Line 2450

<s id="N150B3">Cæterum &longs;i quis vrgeat ex Guido Vbaldo, potius verti<lb/>cem cunei e&longs;&longs;e commune <expan abbr="fulciment&utilde;">fulcimentum</expan> vtriu&longs;que vectis pon<lb/>dera verò mediare inter fulcimentum, ac potentiam, ita vt <lb/>vectis AB fulta in ip&longs;o B moueat molis partem vbi e&longs;t I, <lb/>tanquam onus ver&longs;us G. <expan abbr="Similiterq.">Similiterque</expan> vectis CB ibidem <lb/>fulta, partem L ver&longs;us D. </s>

<s id="N150C9">Occurrendum e&longs;t, hoc cum alijs, <lb/>quæ Guidus Vbaldus fusè pro&longs;equitur, probare quidem <lb/>talem pariter vectis rationem competere ip&longs;is AB & <lb/>CB; prout con&longs;tituuntur in cuneo: nihil tamen contra <lb/>Ari&longs;totelem concludere; cuius propterea di&longs;cur&longs;um refe<lb/>rens Guidus Vbaldus minimè improbat. </s>

<s id="N150D6">Nihil enim prohi<lb/>bet, quominus idem numero vectis &longs;ecundum diuer&longs;as ra<lb/>tiones ad duas, ac diuer&longs;as vectium &longs;pecies pertineat, vtriu&longs;-<pb pagenum="171" xlink:href="005/01/179.jpg"/>que &longs;cilicet vices gerendo atque exercendo: <expan abbr="idemq.">idemque</expan> cor<lb/>pus &longs;imul po&longs;&longs;it e&longs;&longs;e fulcimentum, & onus quod mouetur <lb/>per vectem re&longs;pectu diuer&longs;orum, vt in &longs;imili &longs;upra explicui<lb/>mus quæ&longs;t. </s>

<s id="N150EC">3. Optime igitur &longs;ecundum vtranque vectis ra<lb/>tioncm dicere po&longs;&longs;umus, cuneum virtutis incrementum &longs;u<lb/>mere à duplici vecte, quam continet, & ab ictu percu&longs;&longs;ionis, <lb/>qua validius omni alio impul&longs;u ip&longs;e adhibetur. </s>

<s id="N150EC">3. Optime igitur &longs;ecundum vtranque vectis ra<lb/>tionem dicere po&longs;&longs;umus, cuneum virtutis incrementum &longs;u<lb/>mere à duplici vecte, quam continet, & ab ictu percu&longs;&longs;ionis, <lb/>qua validius omni alio impul&longs;u ip&longs;e adhibetur. </s>

<s id="N150F7">Quæ&longs;tio Decimaoctaua.</s>

<s id="N150FC">C<emph type="italics"/>vr &longs;i qui&longs;piam trochleas componens duas in <lb/>&longs;ignis duobus æd &longs;e inuicem iunctis contrario <lb/>ad trochleas moto circulo &longs;unem circumdu<lb/>xerit, cuius alterum quidem caput &longs;ignorum <lb/>appendatur alteri, alterum verò trochleis &longs;it <lb/>innixum, & à funis initio trahere c&oelig;perit, <lb/>magna trahit pondera, licet imbecillium fuerit virium? </s>

<s id="N150FC">C<emph type="italics"/>vr &longs;i qui&longs;piam trochleas componens duas in <lb/>&longs;ignis duobus ad &longs;e inuicem iunctis contrario <lb/>ad trochleas moto circulo funem circumdu<lb/>xerit, cuius alterum quidem caput &longs;ignorum <lb/>appendatur alteri, alterum verò trochleis &longs;it <lb/>innixum, & à funis initio trahere c&oelig;perit, <lb/>magna trahit pondera, licet imbecillium fuerit virium? </s>

<s id="N1510E">An <lb/>quia idem pondus à minori potentia &longs;i mouetur, vecte medio <lb/>transfertur magis, quàm à manu? </s>

<s id="N15115">Trochlea autem idem ve<lb/>cti facit. </s>

<s id="N1511A">Quamobrem &longs;i vna facilius trahet, & ab vnic<gap/><lb/>tractu multò grauius trahet, quàm facere po&longs;sit manus, idip<lb/>fum duæ trochleæ plus quàm in dupla velocitate leuabunt. <lb/></s>

<s id="N1511A">Quamobrem &longs;i vna facilius trahet, & ab vnico <lb/>tractu multò grauius trahet, quàm facere po&longs;sit manus, idip<lb/>sum duæ trochleæ plus quàm in dupla velocitate leuabunt. <lb/></s>

<s id="N15123">Minus enim altera trahit, quàm &longs;i ip&longs;a per &longs;eip&longs;am trahe<lb/>ret, quando circa alteram iniectus fuerit funis, illa namque <lb/>minus etiam pondus effecit. </s>

<s id="N1512A"><expan abbr="Pariq.">Parique</expan> modo &longs;i ad plures iniectus <lb/>fuerit funis in paucis trochleis, multa fit differentia, quamob<lb/>rem à prima pondere quatuor minas trahente, ab vltima trahi <lb/>multò minus. </s>

<s id="N15136">Et in re &etail;dificatoria faciliter magna mouent <lb/>pondera, traducunt enim ab una trochlea ad aliam, & rur&longs;us <lb/>ab illa ad &longs;uculas, & vectes. </s>

Line 2469

<s id="N15146">COMMENTARIVS.</s>

<s id="N1514C">Svppo&longs;ita de&longs;criptione trochleæ, <expan abbr="eiusq.">eiusque</expan> multiplici di<lb/>&longs;tinctione quam &longs;upra prima parte tex. 8. Additione <lb/>prima tradidimus, illud in præ&longs;enti primò notandum <pb pagenum="172" xlink:href="005/01/180.jpg"/>occutrit, <expan abbr="Ari&longs;totel&etilde;">Ari&longs;totelem</expan> hic non agere ni&longs;i de trochlea, quæ vni<lb/>cam, ac &longs;implicem rotulam contineat, quam pariter eodem <lb/>nomine trochleam appellat, ac di&longs;tinguit à tigno, &longs;eu ligno, <lb/>quod illam tanquam conceptaculum quoddam, aut cap&longs;u<lb/>la in&longs;ertam continet; cum re vera communi acceptione <lb/>trochlea, vt diximus vtrumque &longs;imul &longs;ignificet, nempe, & <lb/>rotulam inditam &longs;iue orbiculum, & cap&longs;ulam continentem. <lb/></s>

<s id="N1514C">Svppo&longs;ita de&longs;criptione trochleæ, <expan abbr="eiusq.">eiusque</expan> multiplici di<lb/>&longs;tinctione quam &longs;upra prima parte tex. 8. Additione <lb/>prima tradidimus, illud in præ&longs;enti primò notandum <pb pagenum="172" xlink:href="005/01/180.jpg"/>occurrit, <expan abbr="Ari&longs;totel&etilde;">Ari&longs;totelem</expan> hic non agere ni&longs;i de trochlea, quæ vni<lb/>cam, ac &longs;implicem rotulam contineat, quam pariter eodem <lb/>nomine trochleam appellat, ac di&longs;tinguit à tigno, &longs;eu ligno, <lb/>quod illam tanquam conceptaculum quoddam, aut cap&longs;u<lb/>la in&longs;ertam continet; cum re vera communi acceptione <lb/>trochlea, vt diximus vtrumque &longs;imul &longs;ignificet, nempe, & <lb/>rotulam inditam &longs;iue orbiculum, & cap&longs;ulam continentem. <lb/></s>

<s id="N1516F">Nec audiendus e&longs;t Piccolomineus dum ait tigna hic apud <lb/><expan abbr="Ari&longs;totel&etilde;">Ari&longs;totelem</expan>, non &longs;ignificare ligna prædicta, &longs;eu thecas ligneas, <lb/>rotulas continentes, &longs;ed trabes ad &longs;e inuicem iunctas, qui<lb/>bus trochleæ cum pondere &longs;u&longs;tinentur. </s>

<s id="N1517B">Quandoquidem &longs;i <lb/>hoc e&longs;&longs;et, Philo&longs;ophus <expan abbr="nõ">non</expan> dixi&longs;&longs;et, alterum extremum funis <lb/>ductarij, altero <expan abbr="tignor&utilde;">tignorum</expan> appendi. </s>

<s id="N1518A">Cum certum &longs;it, funem du<lb/>ctarium nullo modo ad trabem aliquam appendi, &longs;ed ad ip<lb/>&longs;um extremum trochleæ &longs;uperioris, &longs;eu ligni, quod rotulam <lb/>tegit, ac per axiculum regit, vt &longs;tatim patebit. </s>

Line 2479

<s id="N151A9">His ergo præmi&longs;&longs;is ad <expan abbr="nomin&utilde;">nominum</expan> dilucidationem, quæritur <lb/>hic ab Ari&longs;totele, qua de cau&longs;a <expan abbr="cõtingat">contingat</expan>, vt &longs;i quis duas tro<lb/>chleas ad <expan abbr="inuic&etilde;">inuicem</expan> ex oppo&longs;ito componat, & fune ad <expan abbr="eor&utilde;">eorum</expan> ro<lb/>tulas circumducto, alterum eius caput alteri trochleæ, &longs;eu <lb/>ligno rotulam continenti appendat, alterum verò manu tra<lb/>hat, magna eleuet pondera, quamuis imbecilla &longs;it virtus tra<lb/>hentis. </s>

<s id="N151C8"><expan abbr="Cau&longs;amq.">Cau&longs;amque</expan> mox red dit; quia nimirum facilius vel po<lb/>tius vectis adiumento quàm &longs;ola manu, mouentur pondera <lb/>à minori potentia; rotula verò in trochlea vectis vicem obti<lb/>net, &longs;eu vectis habet virtutem. </s>

<s id="N151D4">Cumque in trochleis prædi<lb/>cto modo applicatis, non tantum vna, &longs;ed duæ &longs;altem rotu<lb/>læ tanquam totidem vectes adhibeantur, mirum non e&longs;t &longs;i <lb/><expan abbr="ear&utilde;">earum</expan> beneficio, celerius, ac facilius, <expan abbr="maioraq.">maioraque</expan> leuentur pon<lb/>dera quàm &longs;it virtus <expan abbr="trah&etilde;tis">trahentis</expan>. </s>

<s id="N151EA">Imò &longs;i vnius rotulæ adiumen-<pb pagenum="173" xlink:href="005/01/181.jpg"/>to plus <expan abbr="faciliusq.">faciliusque</expan> leuatur quàm &longs;ola manu, &longs;i duæ fuerint ro<lb/>tulæ, plus ac celerius leuabitur, quàm in dupla proportione, <lb/>& &longs;ic deinceps tanto magis, &longs;eu maius pondus, quantò plu<lb/>res extiterint rotulæ in ip&longs;is duabus, vel pluribus trochleis <lb/>adhibitæ; ita vt ex multiplicatio<gap/>o <expan abbr="totular&utilde;">totularum</expan>, intelligatur au<lb/>geri virtutem trahentis, ac pondus imminui, cum certè plu<lb/>ribus impertiatur tanquam diui&longs;um. </s>

<s id="N151EA">Imò &longs;i vnius rotulæ adiumen-<pb pagenum="173" xlink:href="005/01/181.jpg"/>to plus <expan abbr="faciliusq.">faciliusque</expan> leuatur quàm &longs;ola manu, &longs;i duæ fuerint ro<lb/>tulæ, plus ac celerius leuabitur, quàm in dupla proportione, <lb/>& &longs;ic deinceps tanto magis, &longs;eu maius pondus, quantò plu<lb/>res extiterint rotulæ in ip&longs;is duabus, vel pluribus trochleis <lb/>adhibitæ; ita vt ex multiplicatione <expan abbr="totular&utilde;">rotularum</expan>, intelligatur au<lb/>geri virtutem trahentis, ac pondus imminui, cum certè plu<lb/>ribus impertiatur tanquam diui&longs;um. </s>

<s id="N15208">Quare inquit Ari&longs;tote<lb/>les in re ædificatoria, multiplicatis trochleis &longs;uculis, ac ve<lb/><figure id="id.005.01.181.1.jpg" xlink:href="005/01/181/1.jpg"/><lb/>ctibus magna <expan abbr="mou&etilde;tur">mouentur</expan> <expan abbr="põde">ponde</expan> <lb/>ra non &longs;ecus ac multiplicatis <lb/>tantummodo trochleis, qu&etail; <lb/>vectis <expan abbr="vic&etilde;">vicem</expan> <expan abbr="ger&utilde;t">gerunt</expan> vt diximus. </s>

Line 2490

<s id="N15283">Quod vt <expan abbr="palã">palam</expan> omnino fiat, <lb/><expan abbr="di&longs;tinguend&utilde;">di&longs;tinguendum</expan> in primis e&longs;t in<lb/>ter orbiculos &longs;uperioris, & <pb pagenum="174" xlink:href="005/01/182.jpg"/>inferioris trochleæ, <expan abbr="quandoquid&etilde;">quandoquidem</expan> <expan abbr="nõ">non</expan> <expan abbr="vterq.">vterque</expan> idem genus ve<lb/>ctis exprimit, aut participat. </s>

<s id="N152A4">Si igitur <expan abbr="orbicul&utilde;">orbiculum</expan> trochleæ &longs;u<lb/>perioris, hoc e&longs;t &longs;upernè appen&longs;æ con&longs;ideremus, eam ratio<lb/>nem vèctis obtinere comperiemus, quam participat etiam <lb/>libra æqualium brachiorum, nempe, cuius fulcimentum in<lb/>ter pondus, & potentiam collocatur. </s>

<s id="N152B3">Potrò diameter or<lb/>biculi orizonti parallela FG longitudinem vectis refert, <lb/>axiculus verò qui in centro e&longs;t vbi H, fulcimentum. </s>

<s id="N152B3">Porrò diameter or<lb/>biculi orizonti parallela FG longitudinem vectis refert, <lb/>axiculus verò qui in centro e&longs;t vbi H, fulcimentum. </s>

<s id="N152BA">Deinde <lb/>diametri extremum F à quo pondus cum inferiori trochlea <lb/>per funem propendet, vectis extremum exprimit, cui onus <lb/>e&longs;t alligatum. </s>

<s id="N152C3">Alterum verò diametri extremum G, vectis <lb/>extremum de&longs;ignat, cui virtus mouentis applicatur. </s>

Line 2514

<s id="N15368"><expan abbr="videreq.">videreque</expan> e&longs;t in &longs;equenti <lb/>figura. </s>

<s id="N15372">Quoniam &longs;i trochlea ABC &longs;u&longs;pen<lb/>datur per funem eius orbiculo cir<lb/>cumductum, cuius vnum <expan abbr="extrem&utilde;">extremum</expan> &longs;it <lb/>in D &longs;tabiliter alligatum, alterum verò <lb/>à potentia in E con&longs;tituta &longs;u&longs;tineatur; <lb/>ac pondus F ab ip&longs;a inferiori parte <lb/>trochleæ vbi B propendeat &longs;ubliga<lb/>tum, pondus ip&longs;um <expan abbr="tot&utilde;">totum</expan>, non quidem <lb/>à &longs;ola potentia E, nec à &longs;olo &longs;u&longs;ten<gap/><pb pagenum="176" xlink:href="005/01/184.jpg"/>taculo D &longs;u&longs;tineri intelligetur, &longs;ed &longs;imul ab vtroque, ita <lb/>vt dimidium, alterutri re&longs;pondeat virtuti. </s>

<s id="N15372">Quoniam &longs;i trochlea ABC &longs;u&longs;pen<lb/>datur per funem eius orbiculo cir<lb/>cumductum, cuius vnum <expan abbr="extrem&utilde;">extremum</expan> &longs;it <lb/>in D &longs;tabiliter alligatum, alterum verò <lb/>à potentia in E con&longs;tituta &longs;u&longs;tineatur; <lb/>ac pondus F ab ip&longs;a inferiori parte <lb/>trochleæ vbi B propendeat &longs;ubliga<lb/>tum, pondus ip&longs;um <expan abbr="tot&utilde;">totum</expan>, non quidem <lb/>à &longs;ola potentia E, nec à &longs;olo &longs;u&longs;ten<pb pagenum="176" xlink:href="005/01/184.jpg"/>taculo D &longs;u&longs;tineri intelligetur, &longs;ed &longs;imul ab vtroque, ita <lb/>vt dimidium, alterutri re&longs;pondeat virtuti. </s>

<s id="N15395">Quo fit vt cum <lb/>potentia ad pondus attollendum, ip&longs;a inferiori trochlea vti<lb/>tur tanquam vecte non paruam virtutem ab ip&longs;a trochlea <lb/>mutuetur, <expan abbr="nõ">non</expan> &longs;ecus ac à vecte, cuius alterum extremum fir<lb/>miter alicubi &longs;it innixum, ad eleuandum pondus, quod ex <lb/>eius medio pendeat, vt con&longs;tare pote&longs;t in de&longs;cripto vecte <lb/><figure id="id.005.01.184.1.jpg" xlink:href="005/01/184/1.jpg"/><lb/>ABC, cuius extre<lb/>mum C fulciatur in <lb/>D, extremum verò <lb/>A &longs;it à <expan abbr="pot&etilde;tia">potentia</expan> ele<lb/>uandum, & ex pun<lb/>cto medio B <expan abbr="prop&etilde;-deat">propen<lb/>deat</expan> onus <expan abbr="alligat&utilde;">alligatum</expan>, <lb/>quod &longs;it ip&longs;um E. <lb/></s>

<s id="N153CA">Nam & &longs;i pondus <lb/>potentiæ vires excederet, <expan abbr="duplamq.">duplamque</expan> ferè proportionem ha<lb/>beret re&longs;pectu earum, omnino tamen beneficio vectis tolle<lb/>retur, cum dimidium tantùm illius ip&longs;i potentiæ re&longs;ponde<lb/>ret. </s>

<s id="N153D9">Quod &longs;i plures orbiculi in ip&longs;a inferiori trochlea con<lb/>tineantur, idem fiet, ac &longs;i totidem vectibus eiu&longs;dem tationis <lb/>idem pondus ab eadem potentia moueatur. </s>

<s id="N153D9">Quod &longs;i plures orbiculi in ip&longs;a inferiori trochlea con<lb/>tineantur, idem fiet, ac &longs;i totidem vectibus eiu&longs;dem rationis <lb/>idem pondus ab eadem potentia moueatur. </s>

<s id="N153E0">Nam cum &longs;in<lb/>gulis pariter onus leuandum impartiri debeat, quò plures <lb/>fuerint rotulæ &longs;icut vectes, eò minus potentiæ ad leuandum <lb/>propria virtute relinquitur, ac propterea minor, ac minor <lb/>virtus in trahente requiritur iuxta numerum rotularum. </s>

Line 2530

<s id="N1541C">Quæ&longs;tio Decimanona.</s>

<s id="N15421">C<emph type="italics"/>vr &longs;i quis &longs;uper lignum magnam imponat <lb/>&longs;ecurim, <expan abbr="de&longs;uperq.">de&longs;uperque</expan> illi magnum adÿciat pon<lb/>dus, ligni quippiam, quod curandum &longs;it, non <lb/>diuidit: &longs;i verò &longs;ecurim extollens percutiat, <lb/>illud &longs;cindit, cùm alioqui multò minus ha<lb/>beat ponderis id, quod percutit, quàm id quod <lb/>&longs;uperiacet, & premit? </s>

<s id="N15421">C<emph type="italics"/>vr &longs;i quis &longs;uper lignum magnam imponat <lb/>&longs;ecurim, <expan abbr="de&longs;uperq.">de&longs;uperque</expan> illi magnum adijciat pon<lb/>dus, ligni quippiam, quod curandum &longs;it, non <lb/>diuidit: &longs;i verò &longs;ecurim extollens percutiat, <lb/>illud &longs;cindit, cùm alioqui multò minus ha<lb/>beat ponderis id, quod percutit, quàm id quod <lb/>&longs;uperiacet, & premit? </s>

<s id="N15437">An quia omnia cum motu fiunt, & <lb/>graue ip&longs;um, grauitatis magis a&longs;&longs;umit motum dum mouetur, <lb/>quàm dum quie&longs;cit. </s>

<s id="N1543E">Incumbens igitur connatam graui mo<lb/>tionem non mouetur, motum verò & &longs;ecundum hanc moue<lb/>tur, & &longs;ecundum eam, quæ est percutientis. </s>

<s id="N15445">Præterea &longs;e-<emph.end type="italics"/><pb pagenum="178" xlink:href="005/01/186.jpg"/><emph type="italics"/>curis ip&longs;a efficitur cuneus. </s>

Line 2540

<s id="N1545C">COMMENTARIVS.</s>

<s id="N15462">Tam quæ&longs;tionis propo&longs;itio quàm dubitandi ratio <lb/>per &longs;e e&longs;t manife&longs;ta, ex quo nimirum contingat, vt <lb/>&longs;i quis &longs;uper lignum magnam imponat &longs;ecurim, <expan abbr="de-&longs;uperq.">de<lb/>&longs;uperque</expan> ingens illi adi; ciat pondus, nihil con&longs;ideratione di<lb/>gnum, aut alicuius momenti diuidat; &longs;i verò &longs;ecurim ip&longs;am <lb/>extollens percutiat, illud &longs;cindat, etiam &longs;i multo minus illa <lb/>habeat ponderis, quam id quod &longs;uperiacet, ac præmit. <lb/></s>

<s id="N15462">Tam quæ&longs;tionis propo&longs;itio quàm dubitandi ratio <lb/>per &longs;e e&longs;t manife&longs;ta, ex quo nimirum contingat, vt <lb/>&longs;i quis &longs;uper lignum magnam imponat &longs;ecurim, <expan abbr="de-&longs;uperq.">de<lb/>&longs;uperque</expan> ingens illi adijciat pondus, nihil con&longs;ideratione di<lb/>gnum, aut alicuius momenti diuidat; &longs;i verò &longs;ecurim ip&longs;am <lb/>extollens percutiat, illud &longs;cindat, etiam &longs;i multo minus illa <lb/>habeat ponderis, quam id quod &longs;uperiacet, ac præmit. <lb/></s>

<s id="N15476">Quod profecto ex eo euenire docet, quia cum omnia motu <lb/>fiant, & graue ip&longs;um maiorem grauitatem acquirat per mo<lb/>tum, magis etiam mouet dum mouetur, quàm dum quie<lb/>&longs;cit. </s>

<s id="N1547F">Quare licet maior &longs;it grauitas innata totius incumben<lb/>tis oneris quod præmit, nempe &longs;ecuris cum &longs;uperadiecto <lb/>pondere, quàm &longs;it &longs;olius motæ &longs;ecuris; nihilominus dum <lb/>prius elata &longs;ecuris deijcitur, non modò operatur per inna<lb/>tam &longs;ibi grauitatem, &longs;ed per eam, quam in ip&longs;o motu acqui<lb/>rit, & per impetum à percutiente impre&longs;&longs;um. </s>

<s id="N1548C">Vnde mirum <lb/>non e&longs;t, &longs;i tune efficacius percutiat, ac ita percutiendo <lb/>&longs;cindat lignum, quod percutit. </s>

Line 2568

<s id="N155BA">Vt videre e&longs;t in de<lb/>&longs;cripto manubrio AB, cuius alterum extremum fulcitur <lb/><figure id="id.005.01.189.1.jpg" xlink:href="005/01/189/1.jpg"/><lb/>in A qua&longs;i tanquam in centro &longs;ui motus; alterum verò pro<lb/>mouet &longs;ecurim in B: & pars vbi C, impul&longs;um recipit à <lb/>potentia motrice tendentem in D. </s>

<s id="N155CC">Quo fit vt ip&longs;um manu<lb/>brium tanquam vectis, ac &longs;emidiameter circulariter mouea<lb/>tur, <expan abbr="efficiatq.">efficiatque</expan> arcum, &longs;eu lineam BE. </s>

<s id="N155D8">Quamuis contingat <lb/>vltimum extremum A aliquantulum retrocedere ver&longs;us <lb/>F, eo quod fulcimentum non &longs;it omnino &longs;tabile, nec po&longs;sit <lb/>ei tam exactè ip&longs;um extremum manubrij applicari. </s>

<s id="N155E1">Cum <lb/>itaque omnia, quæ vectis vicem obtinent, ac circulariter &longs;uo <lb/>innixa fulcimento cientur, apti&longs;simè virtutem, &longs;eu impul<lb/>&longs;um à mouente recipiant, &longs;equitur vt hac eciam ratione &longs;e<lb/>curis ip&longs;a per motum circularem magnam vim ad &longs;cinden<lb/>dum adipi&longs;catur. </s>

<s id="N155E1">Cum <lb/>itaque omnia, quæ vectis vicem obtinent, ac circulariter &longs;uo <lb/>innixa fulcimento cientur, apti&longs;simè virtutem, &longs;eu impul<lb/>&longs;um à mouente recipiant, &longs;equitur vt hac etiam ratione &longs;e<lb/>curis ip&longs;a per motum circularem magnam vim ad &longs;cinden<lb/>dum adipi&longs;catur. </s>

Line 2587

<s id="N1563F">Maximè autem <lb/>omnium ad &longs;tipites loratos, qui communiter ad enuclean<lb/>dum triticum in area ab agriculis adhibentur. </s>

<s id="N15646">Hi enim im<lb/>petu accepto per motum circularem incredibili vehemen<lb/>tia ac virtute percutiunt. </s>

<s id="N1564D">Porrò cum alter ex alterius extre<lb/>mitate cui loris alligatur liberè pendeat, ac per ip&longs;um tan<lb/>quam per manubrium &longs;atis procerum circulariter agitetur, <lb/>longè à centro, quod e&longs;t in iunctura lacerti cum humero <lb/>percutientis, &longs;uum qua&longs;i circulum perficit; <expan abbr="proindeq.">proindeque</expan> citi&longs;<lb/>&longs;imè fertur, vnde & validi&longs;simè ferit, ac percutit. </s>

<s id="N1565E">Iuxta <lb/>quamiationem colligitur, quod & experientia comproba<lb/>tur prædicta omnia in&longs;trumenta maximam, acpræcipuam <lb/>virt utem &longs;ortiri in extremo, quod magis di&longs;tat à centro &longs;ui <lb/>motus. </s>

<s id="N1565E">Iuxta <lb/>quam rationem colligitur, quod & experientia comproba<lb/>tur prædicta omnia in&longs;trumenta maximam, ac præcipuam <lb/>virtutem &longs;ortiri in extremo, quod magis di&longs;tat à centro &longs;ui <lb/>motus. </s>

Line 2606

<s id="N156CE">Quæ&longs;tio Vige&longs;ima.</s>

<s id="N156D3">C<emph type="italics"/>vr &longs;tatera qua carnes ponderantur, paruo ap<lb/>pendiculo magna trutinat onera cù alioqui <lb/>tota dimidiata exi&longs;tat libra<gap/>vbi enim onus im<lb/>ponitur &longs;olùm &longs;u&longs;penditur lanx: in altera <lb/>verò parte &longs;ola est &longs;tatera. </s>

<s id="N156D3">C<emph type="italics"/>vr &longs;tatera qua carnes ponderantur, paruo ap<lb/>pendiculo magna trutinat onera cùm alioqui <lb/>tota dimidiata exi&longs;tat libra<gap/>vbi enim onus im<lb/>ponitur &longs;olùm &longs;u&longs;penditur lanx: in altera <lb/>verò parte &longs;ola est &longs;tatera. </s>

<s id="N156E3">An quia &longs;imul li<lb/>bra & vectem ip&longs;am contingit e&longs;&longs;e &longs;tateram? <lb/></s>

<s id="N156E9">libram quidem, vbi &longs;partorum quodcumque &longs;tatera fit cen<lb/>trum: in altera enim parte lancem, in altera autem pro lance <lb/>æquipondÿ appendiculum habet, quod libræ incumbit, ceu &longs;i <lb/>quis alteram apponeret lancem, & illi pondus imponeret. </s>

<s id="N156E9">libram quidem, vbi &longs;partorum quodcumque &longs;tatera fit cen<lb/>trum: in altera enim parte lancem, in altera autem pro lance <lb/>æquipondij appendiculum habet, quod libræ incumbit, ceu &longs;i <lb/>quis alteram apponeret lancem, & illi pondus imponeret. </s>

<s id="N156F2">Ma<lb/>nife&longs;tum enim quod tantundem trabit ponderis ei, quod in al<lb/>tera iacet lance. </s>

<s id="N156F2">Ma<lb/>nife&longs;tum enim quod tantundem trahit ponderis ei, quod in al<lb/>tera iacet lance. </s>

<s id="N156F9">Quemadmodum autem &longs;i vna libra multæ <lb/>&longs;int libræ, &longs;ic talia in&longs;unt &longs;parta multa in eiu&longs;modi libra, <lb/>quorum vniu&longs;cuiu&longs;cuiu&longs;que quod intrin&longs;ecus e&longs;t ad appendiculum, <lb/>&longs;tateræ e&longs;t dimidium: & omnino i&longs;thuc libra e&longs;t, vnam qui<lb/>dem habens lancem, in qua pondus appenditur: alteram ve<lb/>rò vbi id &longs;tatera æquipondium. </s>

<s id="N156F9">Quemadmodum autem &longs;i vna libra multæ <lb/>&longs;int libræ, &longs;ic talia in&longs;unt &longs;parta multa in eiu&longs;modi libra, <lb/>quorum vniu&longs;cuiusque quod intrin&longs;ecus e&longs;t ad appendiculum, <lb/>&longs;tateræ e&longs;t dimidium: & omnino i&longs;thuc libra e&longs;t, vnam qui<lb/>dem habens lancem, in qua pondus appenditur: alteram ve<lb/>rò vbi id &longs;tatera æquipondium. </s>

<s id="N15706">Quamobrem appendiculum <lb/>ad alteram &longs;ui partem e&longs;t &longs;tatera. </s>

<s id="N1570B">Huiu&longs;modi autem exi<lb/>&longs;tens multæ &longs;unt libræ, totque quot fuerint &longs;parta. </s>

<s id="N15710">Semper <lb/>autem quod lanci propinquius e&longs;t &longs;partum, <expan abbr="appensòq.">appensòque</expan> oneri, <lb/>maius trahit pondus, quoniam fit quidem omnis &longs;tatera in<lb/>uer&longs;us vectis<gap/>, hypornocblion namque vnumquodque &longs;par<lb/>tum &longs;upernè exi&longs;tens, pondus verò id quod lanci ine&longs;t. </s>

<s id="N15710">Semper <lb/>autem quod lanci propinquius e&longs;t &longs;partum, <expan abbr="appensòq.">appensòque</expan> oneri, <lb/>maius trahit pondus, quoniam fit quidem omnis &longs;tatera in<lb/>uer&longs;us vectis<gap/>, hypornochlion namque vnumquodque &longs;par<lb/>tum &longs;upernè exi&longs;tens, pondus verò id quod lanci ine&longs;t. </s>

<s id="N15721">Quan<lb/>tò autem productior vectis fuerit longitudo ab ip&longs;o hypomo<lb/>chlio, tantò ibi quidem facilius mouet, hic autem æquilibrium <lb/>facit, pondu&longs;que &longs;tateræ trutinat, quod ad æquipondÿ vergit ap<lb/>pendiculam.<emph.end type="italics"/></s>

<s id="N15721">Quan<lb/>tò autem productior vectis fuerit longitudo ab ip&longs;o hypomo<lb/>chlio, tantò ibi quidem facilius mouet, hic autem æquilibrium <lb/>facit, pondu&longs;que &longs;tateræ trutinat, quod ad æquipondij vergit ap<lb/>pendiculam.<emph.end type="italics"/></s>

<s id="N15730">COMMENTARIVS.</s>

Line 2627

<s id="N15767">Mox deinde cau&longs;am ip&longs;am in eo docet con&longs;i&longs;tere, quòd <lb/>&longs;tatera, libræ &longs;imul ac vectis rationem induat, ac vtriu&longs;que <lb/>vicem obtineat. </s>

<s id="N1576E">Libræ nimirum, quia reuera e&longs;t veluti iu<lb/>gum tran&longs;uer&longs;um, &longs;eu ha&longs;ta bilancis ex puncto qua&longs;i medio <lb/>&longs;u&longs;pen&longs;a, atque vtrinque ponderibus pendentibus librata <lb/>circa ip&longs;um punctum <expan abbr="intermedi&utilde;">intermedium</expan>. <gap/> &longs;u&longs;penditur tanquam <lb/>circa centrum, vel axem. </s>

<s id="N1576E">Libræ nimirum, quia reuera e&longs;t veluti iu<lb/>gum tran&longs;uer&longs;um, &longs;eu ha&longs;ta bilancis ex puncto qua&longs;i medio <lb/>&longs;u&longs;pen&longs;a, atque vtrinque ponderibus pendentibus librata <lb/>circa ip&longs;um punctum <expan abbr="intermedi&utilde;">intermedium</expan>. Quo &longs;u&longs;penditur tanquam <lb/>circa centrum, vel axem. </s>

<s id="N1577F">Q<gap/>muis enim &longs;tatera con&longs;titua<lb/>tur ex inæqualibus br<gap/>nijs, & ex altero tantum lanx vna <lb/>propendeat; vel certè loco lancis vnci nonnulli demittan<lb/>tur, qui mercibus, aut rebus ponderandis compacti, eas non <lb/>minus commodè &longs;u&longs;tinent, vt in &longs;ubiecta figura. </s>

<s id="N1577F">Qamuis enim &longs;tatera con&longs;titua<lb/>tur ex inæqualibus brachijs, & ex altero tantum lanx vna <lb/>propendeat; vel certè loco lancis vnci nonnulli demittan<lb/>tur, qui mercibus, aut rebus ponderandis compacti, eas non <lb/>minus commodè &longs;u&longs;tinent, vt in &longs;ubiecta figura. </s>

<s id="N1578E">Ex altero <pb pagenum="186" xlink:href="005/01/194.jpg"/>verònonni&longs;i appendiculum æquipondij &longs;u&longs;pen&longs;um depen<lb/>deat: Semper tamen ip&longs;a &longs;tatera libram refert, cum eius <lb/>axis, ac fulcimentum &longs;it inter onus, & æquipondium, <expan abbr="ip&longs;iusq.">ip&longs;iusque</expan> <lb/><figure id="id.005.01.194.1.jpg" xlink:href="005/01/194/1.jpg"/><lb/>æquipondij appendiculum, alterius lancis, vel vnci cum <lb/>pondere vicem &longs;ubeat; &longs;iue ip&longs;um fulcimentum, aut &longs;par<lb/>tum con&longs;tituatur in puncto omnino medio, &longs;iue &longs;ecus, vnde <lb/>prouenit inæqualitas brachiorum, cum hæc libræ naturam <lb/>non auferat, nec immutet, vt diximus &longs;uo loco. </s>

<s id="N157B0"><expan abbr="Rur&longs;umq.">Rur&longs;umque</expan> vectis pariter naturam &longs;imul &longs;ortitur &longs;tatera, <lb/>quia fulcimentum habet vbi incumbit in axe, &longs;eu &longs;parto, <lb/>quod idem e&longs;t, ac punctum vnde &longs;u&longs;penditur, & circa quod <lb/>ip&longs;a conuertitur, <expan abbr="pondusq.">pondusque</expan> leuandum con&longs;tituitur merces <lb/>in lancem inuecta, vel vncis infixa; & potentia mouens, ip<lb/>&longs;um appendiculum æquipondij. </s>

<s id="N157C4">Cum igitur ea &longs;it vectis, ac <lb/>libræ natura <expan abbr="propriaq.">propriaque</expan> conditlo,<gap/> cum alterum eius à ful<lb/>cimento brachium longius protenditur, vt in &longs;tatera contin<lb/>git, paruo in ip&longs;ius extremitate adhibito pondere, magnam <lb/>valeat molem ex altero breuiori brachio pendentem attol<lb/>lere, iuxta proportionem vtriu&longs;que di&longs;tantiæ à centro, vt <pb pagenum="187" xlink:href="005/01/195.jpg"/>alibi demon&longs;trauimus; planum profecto relinquitur, qua <lb/>ratione, paruo appendiculo in &longs;tatera, magna leuari po&longs;&longs;int <lb/>pondera, vt intendebat Philo&longs;ophus. </s>

<s id="N157C4">Cum igitur ea &longs;it vectis, ac <lb/>libræ natura <expan abbr="propriaq.">propriaque</expan> conditio,<gap/> cum alterum eius à ful<lb/>cimento brachium longius protenditur, vt in &longs;tatera contin<lb/>git, paruo in ip&longs;ius extremitate adhibito pondere, magnam <lb/>valeat molem ex altero breuiori brachio pendentem attol<lb/>lere, iuxta proportionem vtriu&longs;que di&longs;tantiæ à centro, vt <pb pagenum="187" xlink:href="005/01/195.jpg"/>alibi demon&longs;trauimus; planum profecto relinquitur, qua <lb/>ratione, paruo appendiculo in &longs;tatera, magna leuari po&longs;&longs;int <lb/>pondera, vt intendebat Philo&longs;ophus. </s>

<s id="N157E3">Quoniam verò in præfato di&longs;cur&longs;u &longs;emel atque iterum <lb/>Ari&longs;toteles docuit, &longs;tateram e&longs;&longs;e velutilibram, in qua plures <lb/>&longs;int libræ, ac totidem quot fuerint &longs;parta, hinc Blancanus <lb/>conijcit, apud Pri&longs;cos, &longs;tateram ex multis trutinis, &longs;eu &longs;par<lb/>tis compactam fui&longs;&longs;e, paribus interuallis per totam longi<lb/>tudinem ip&longs;ius &longs;tateræ di&longs;&longs;eminatis; Ex quibus &longs;ingulis <lb/>prout pondus po&longs;tulabat, illa &longs;u&longs;penderetur, appendiculo <lb/>&longs;emper in extremitate &longs;ui brachij immoto manente; Itaut <lb/>tantum mercis lanci imponeretur, quantum appendiculo <lb/>æquiponderaret, iuxta <expan abbr="&longs;ituation&etilde;">&longs;ituationem</expan> cuiu&longs;libet trutinæ. </s>

Line 2644

<s id="N15818">Verumenimuerò non &longs;atis id colligitur ex Ari&longs;totele, nec <lb/>videtur nece&longs;&longs;arium ad verificandum dictum illud eiu&longs;dem <lb/>Philo&longs;ophi. </s>

<s id="N1581F">Quandoquidem etiam &longs;tatera prout modò apud <lb/>no&longs;trates e&longs;t in v&longs;u, ex duplici &longs;altem trutina &longs;olet con&longs;tare, <lb/>vna quæ loco vnde lanx pendet e&longs;t propior, altera verò <lb/>quæ aliquantulum e&longs;t remotior, & in oppo&longs;ito, &longs;eu inuer&longs;o <lb/>&longs;tateræ latere locatur: Ac per propiorem vtique onera ma<lb/>iora, per remotiorem verò minora con&longs;ueuerunt librari; li<lb/>bero &longs;emper manente appendiculo, vt per reliquum &longs;tateræ <lb/>brachium iuxta exigentiam ponderis di&longs;currere valeat. <lb/></s>

<s id="N15831">Quamobrem hac quoque in &longs;tatera con<gap/>i videntur plu<lb/>res libræ, cum &longs;altem duplex in ea trutina reperiatur, quæ <lb/>tanquam duplex libra de&longs;eruit ad maiora, vel minora one<lb/>ra aptius ponderanda, & vt eadem &longs;ecundum maiores, vel <lb/>minores differentias ponderum quando opus fuerit innote<lb/>&longs;cant. </s>

<s id="N15831">Quamobrem hac quoque in &longs;tatera contineri videntur plu<lb/>res libræ, cum &longs;altem duplex in ea trutina reperiatur, quæ <lb/>tanquam duplex libra de&longs;eruit ad maiora, vel minora one<lb/>ra aptius ponderanda, & vt eadem &longs;ecundum maiores, vel <lb/>minores differentias ponderum quando opus fuerit innote<lb/>&longs;cant. </s>

<s id="N15840">Et quidem cum Ari&longs;toteles ait: ac &longs;i vna libra multæ <pb pagenum="188" xlink:href="005/01/196.jpg"/>&longs;int libræ, eo quod in ea in&longs;int &longs;parta multa: forta&longs;&longs;e idem <lb/>intellexit per multa, vel multas, ac plura, vel plures; cum no<lb/>men Græcum <foreign lang="greek">pollo\s</foreign> vtrumque &longs;ignificet, & à Cierone <lb/><foreign lang="greek">w_olla\</foreign> in Timæo Platonis vertatur plures. </s>

<s id="N15840">Et quidem cum Ari&longs;toteles ait: ac &longs;i vna libra multæ <pb pagenum="188" xlink:href="005/01/196.jpg"/>&longs;int libræ, eo quod in ea in&longs;int &longs;parta multa: forta&longs;&longs;e idem <lb/>intellexit per multa, vel multas, ac plura, vel plures; cum no<lb/>men Græcum <foreign lang="greek">pollo\s</foreign> vtrumque &longs;ignificet, & à Cicerone <lb/><foreign lang="greek">w_olla\</foreign> in Timæo Platonis vertatur plures. </s>

<s id="N15855">Ni&longs;i etiam cum <lb/>Baldo rectè dixerimus, &longs;tateram tot libras con&longs;titui, quot <lb/>&longs;unt tran&longs;lationes appendiculi de loco ad locum; quia toties <lb/>variatur proportio, <expan abbr="proindeq.">proindeque</expan> etiam libra. </s>

<s id="N15862">Quare gratis ad <lb/>exponenda verba Ari&longs;totelis putat Blancanus &longs;tateræ ap<lb/>pendiculum apud veteres fui&longs;&longs;e immobile, <expan abbr="ip&longs;amq.">ip&longs;amque</expan> &longs;tateram <lb/>ex tot &longs;partis, &longs;eu trutinis con&longs;ta&longs;&longs;e, quot erant metienda <lb/>pondera: Quamuis alioquin id non fuerit impo&longs;&longs;ibile, &longs;ed <lb/>laborio&longs;um duntaxat, & inutile. </s>

<s id="N15875">Diximus, non impo&longs;&longs;ibile: Nam quolibet in lance onere <lb/>impo&longs;ito, e&longs;t adinuenire centrum grauitatis totius &longs;tateræ <lb/>&longs;ic con&longs;titutæ, ex quo &longs;i ip&longs;a per trutinam &longs;u&longs;pendatur, <lb/>&longs;tabit <expan abbr="æquiponderabitq.">æquiponderabitque</expan> appendiculum immobile ip&longs;i one<lb/>ri in lance impo&longs;ito. </s>

<s id="N15884">Vnde &longs;ingula puncta longitudinis &longs;ta<lb/>teræ con&longs;titui po&longs;&longs;unt centra grauitatis re&longs;pectu diuer&longs;orum <lb/>onerum imponibilium, ac in quolibet illorum poterit truti<lb/>na locari, quæ ad determinatum &longs;uum onus librandum de<lb/>&longs;eruiat. </s>

<s id="N1588F">Diximus tamen hoc e&longs;&longs;e laborio&longs;um, & inutile, <lb/>tum quia difficilius e&longs;t multiplicare trutinas, <expan abbr="ip&longs;amq.">ip&longs;amque</expan> totam <lb/>&longs;tateram diuer&longs;is ex punctis &longs;u&longs;pendere ad quamlibet oneris <lb/>differentiam digno&longs;cendam, cum &longs;ola appendiculi mobili<lb/>tate, atque di&longs;cur&longs;u id con&longs;equi po&longs;&longs;it: tum etiam quia ad <lb/>panciora onera libranda, <expan abbr="paucioresq.">paucioresque</expan> admodum ponderum <lb/>differentias percipiendas de&longs;eruire po&longs;&longs;et ip&longs;a huiu&longs;modi <lb/>&longs;tatera. </s>

<s id="N1588F">Diximus tamen hoc e&longs;&longs;e laborio&longs;um, & inutile, <lb/>tum quia difficilius e&longs;t multiplicare trutinas, <expan abbr="ip&longs;amq.">ip&longs;amque</expan> totam <lb/>&longs;tateram diuer&longs;is ex punctis &longs;u&longs;pendere ad quamlibet oneris <lb/>differentiam digno&longs;cendam, cum &longs;ola appendiculi mobili<lb/>tate, atque di&longs;cur&longs;u id con&longs;equi po&longs;&longs;it: tum etiam quia ad <lb/>pauciora onera libranda, <expan abbr="paucioresq.">paucioresque</expan> admodum ponderum <lb/>differentias percipiendas de&longs;eruire po&longs;&longs;et ip&longs;a huiu&longs;modi <lb/>&longs;tatera. </s>

<s id="N158A8">Cum certè multiplicari trutinæ non valeant ad nu<lb/>merum linearum, aut denticulorum, in quos modò diuer<lb/>&longs;um e&longs;t brachium &longs;tateræ, & in quos di&longs;currens appendicu<lb/>lum pro opportimitate transfertur, vt &longs;ingulis notis, &longs;eu li<lb/>neis, &longs;ingula onera trutinentur, ac determinatè quodlibet <lb/>corum pondus di&longs;tincti&longs;&longs;imè innote&longs;cat. </s>

<s id="N158A8">Cum certè multiplicari trutinæ non valeant ad nu<lb/>merum linearum, aut denticulorum, in quos modò diuer<lb/>&longs;um e&longs;t brachium &longs;tateræ, & in quos di&longs;currens appendicu<lb/>lum pro opportunitate transfertur, vt &longs;ingulis notis, &longs;eu li<lb/>neis, &longs;ingula onera trutinentur, ac determinatè quodlibet <lb/>eorum pondus di&longs;tincti&longs;&longs;imè innote&longs;cat. </s>

<s id="N158B7">Addit autem Ari&longs;toteles quòd quantò propinquius one<lb/>ri in lance, vel vncis appen&longs;o &longs;partum con&longs;tituitur, tanto <lb/>magis onus ip&longs;um, &longs;eu maius onus valet &longs;tatera leuare. </s>

Line 2669

<s id="N1591C">C<emph type="italics"/>vr medici facilius dentes extrahunt denti<lb/>forcipis onere adiecto, quàm &longs;i &longs;ola vtantur <lb/>manu? </s>

<s id="N15926">An quia ex mana magis, quàm ex den<lb/>tiforcipe lubricus elabitur dens? </s>

<s id="N1592B">An ferro id <lb/>potius accidit, quàm digitis, quoniam vndique <lb/>dentem non comprehendunt, quod mollis di<lb/>gitorum facit caro, adbæret enim & complectitur magis. </s>

<s id="N1592B">An ferro id <lb/>potius accidit, quàm digitis, quoniam vndique <lb/>dentem non comprehendunt, quod mollis di<lb/>gitorum facit caro, adhæret enim & complectitur magis. </s>

<s id="N15934">An <lb/>quia dentiforcipes duo &longs;unt contrarÿ vectes, vnicum habentes <lb/>hypomochlion, eius &longs;cilicet in&longs;trumenti connexionem? </s>

<s id="N15934">An <lb/>quia dentiforcipes duo &longs;unt contrarij vectes, vnicum habentes <lb/>hypomochlion, eius &longs;cilicet in&longs;trumenti connexionem? </s>

<s id="N1593B">Hoc <lb/>igitur ad extractionem vtuntur organo, vt facilius moueant. <lb/></s>

<s id="N15941">Sit dentiforcipis alterum quidem extremum vbi e&longs;t A; alterum <lb/>autem quod extrahit, B, vectis autem vbi A D F, alter verò <lb/>vectis vbi BCE, hypomochlion autem CGD, connexio verò <lb/>vbi G, dens autem pondus. </s>

<s id="N1594A">V troque igitur B & F &longs;imul com<lb/>prehendentes mouent: quomodo autem commotus fuerit, faci<lb/>lius manu trahitur, quàm instrumento.<emph.end type="italics"/></s>

Line 2681

<s id="N1595B">Qværitur in præ&longs;enti ab Ari&longs;totele, ex quo nam pro<lb/>ueniat, vt facilius dentes extrahantur denti&longs;orcipis <lb/>adhibito in&longs;trumento, quàm &longs;ola manu, immediata <lb/>opera digitorum. </s>

<s id="N15964">Ac primò ex eo, inquit videri po&longs;&longs;e, id or-<pb pagenum="190" xlink:href="005/01/198.jpg"/>tum habere, quòd cum dens lubricus in &longs;e &longs;it, magis for<lb/>&longs;an è manu quæ leuis, & mollis e&longs;t, quàm ex rudi, ac tenaci <lb/>forcipe elabatur. </s>

<s id="N15970"><expan abbr="Statimq.">Statimque</expan> hanc ip&longs;am rationem impugnat, <lb/>ac penitus euertit, inquiens, potius ferro, quàm digitis con<lb/>tingere, vt dens ab illis apprehen&longs;us, propteri &longs;ui lubricita<lb/>tem aufugiat. </s>

<s id="N1597C">Quandoquidem ferrum, &longs;eu ferrei denti&longs;orci<lb/>pes, minus quàm digiti <expan abbr="vndiq.">vndique</expan> dentem valent comprehen<lb/>dere. </s>

<s id="N1597C">Quandoquidem ferrum, &longs;eu ferrei dentiforci<lb/>pes, minus quàm digiti <expan abbr="vndiq.">vndique</expan> dentem valent comprehen<lb/>dere. </s>

<s id="N15987">Mollis enim digitorum caro cedendo, ac flectendo <lb/>&longs;e&longs;e, adhæret, & complectitur magis quàm ferrum præ &longs;ua <lb/>duritic, ac in flexibilitate. </s>

<s id="N15987">Mollis enim digitorum caro cedendo, ac flectendo <lb/>&longs;e&longs;e, adhæret, & complectitur magis quàm ferrum præ &longs;ua <lb/>duritie, ac in flexibilitate. </s>

<s id="N1598E">Vnde perperam huiu&longs;modi Ari&longs;to<lb/>telis verba intelligunt cum ij, qui ea tanquam in confirma<lb/>tionem prioris rationis, aut &longs;olutionis dicta exponunt: tum <lb/>etiam qui ex oppo&longs;ito, ea ip&longs;a propo&longs;itam qu&etail;&longs;tionis &longs;uppo<lb/>&longs;itionem arbitrantur de&longs;truere. </s>

<s id="N15999">Etenim non &longs;uppo&longs;itioni, & <lb/>experientiæ a&longs;&longs;umptæ, &longs;ed priori duntaxat opponuntur &longs;olu<lb/>tioni, vt vidimus, <expan abbr="rationemq.">rationemque</expan> dubitandi non mediocliter au<lb/>gent, vt magis ea, <expan abbr="quã">quam</expan> traditurus e&longs;t vera &longs;olutio eluce&longs;cat. </s>

<s id="N15999">Etenim non &longs;uppo&longs;itioni, & <lb/>experientiæ a&longs;&longs;umptæ, &longs;ed priori duntaxat opponuntur &longs;olu<lb/>tioni, vt vidimus, <expan abbr="rationemq.">rationemque</expan> dubitandi non mediocriter au<lb/>gent, vt magis ea, <expan abbr="quã">quam</expan> traditurus e&longs;t vera &longs;olutio eluce&longs;cat. </s>

<s id="N159AC">Soluit igitur Ari&longs;toteles <expan abbr="quæ&longs;tion&etilde;">quæ&longs;tionem</expan> dicens, id ex eo con<lb/>tingere, quòd in dentiforcipe duo continentur vectes &longs;ibi in<lb/>uicem contrarij, videlicet ip&longs;a dentiforcipis brachia, quorum <lb/>vnicum e&longs;t commune hypomochlion, neinpe ip&longs;a vtriu&longs;que <lb/>connexio, parisq alterius ad <expan abbr="alter&utilde;">alterum</expan> in<gap/> exio, qua <expan abbr="inuic&etilde;">inuicem</expan> ob<lb/>uiantur. </s>

<s id="N159AC">Soluit igitur Ari&longs;toteles <expan abbr="quæ&longs;tion&etilde;">quæ&longs;tionem</expan> dicens, id ex eo con<lb/>tingere, quòd in dentiforcipe duo continentur vectes &longs;ibi in<lb/>uicem contrarij, videlicet ip&longs;a dentiforcipis brachia, quorum <lb/>vnicum e&longs;t commune hypomochlion, nempe ip&longs;a vtriu&longs;que <lb/>connexio, parisque alterius ad <expan abbr="alter&utilde;">alterum</expan> inf<gap/>exio, qua <expan abbr="inuic&etilde;">inuicem</expan> ob<lb/>uiantur. </s>

<s id="N159C7">Proindeq, <expan abbr="hor&utilde;">horum</expan> <expan abbr="vecti&utilde;">vectium</expan> virtute arctius, ac validius, <lb/>quàm digitis <expan abbr="dent&etilde;">dentem</expan> per&longs;tringi, <expan abbr="faciliusq.">faciliusque</expan> <expan abbr="cõ&longs;equenter">con&longs;equenter</expan> auelli. </s>

Line 2697

<s id="N159FE">Alter verò <lb/>AD &longs;uffulti in con<lb/>nexione qua&longs;i axe <lb/><expan abbr="vtriu&longs;q;">vtriu&longs;que</expan> vbi E. </s>

<s id="N15A0B">Pon<lb/>du&longs;que &longs;it ip&longs;um <lb/>dens F. </s>

<s id="N15A13">Vtroque <pb pagenum="191" xlink:href="005/01/199.jpg"/>igitur vecte &longs;imul admoto per extrema BD ip&longs;um dentem <lb/>tanquam onus in contrarium repellendo, validi&longs;&longs;imè con<lb/>&longs;tringent adhibita, &longs;cilicet manu in AC, qua extremum <lb/>A compellatur ver&longs;us C, & extremum C ver&longs;us A. </s>

<s id="N15A22">Dens <lb/><expan abbr="aut&etilde;">autem</expan> ita con&longs;trictus facilè dimouetur, ar dimotus extrahi<lb/>tur. </s>

<s id="N15A22">Dens <lb/><expan abbr="aut&etilde;">autem</expan> ita con&longs;trictus facilè dimouetur, ac dimotus extrahi<lb/>tur. </s>

<s id="N15A2E">Hæc ferè Ari&longs;toteles, quæ tamen vt rectè Baldus ob&longs;er<lb/>uat, con&longs;trictionem potius, quam dimotionem, & ab&longs;tractio<lb/>nem dentis demon&longs;trant. </s>

Line 2714

<s id="N15A7A">Quocirca admittenda non erunt, quæ Baldus aliter Phi<lb/>lo&longs;ophus hac in re profert, quamuis acutè fuerint excogita<lb/>ta, cum ait, dentiforcipis partium, quibus dens apprehendi<lb/>tur, eam quæ longior e&longs;t, potentiæ mouentis loco &longs;uccede<lb/>re, breuiorem verò fulcimentum con&longs;titui: Quandoquidem <lb/>in v&longs;u dentiforcipis ad extrahendum dentem etiam prout <pb pagenum="192" xlink:href="005/01/200.jpg"/>ab ip&longs;o explicatur, fulcimentum non pote&longs;t con&longs;titui in ip&longs;a <lb/>breuiori dentiforcipis parte, qua apprehenditur dens; tum <lb/>quia hæc &longs;imul cum altera parte mouetur, licet per mino<lb/>rem circulationem, quæ &longs;anè fit circa punctum illud gingi<lb/>uæ, cui in ab&longs;tractione conuertendo &longs;e&longs;e innititur dens, & à <lb/>quo &longs;emper dentiforcipis extremum aliquantulum di&longs;tat, <lb/>eo quod nequeat ad illam v&longs;que partem gingiuæ interio<lb/>rem, ac &longs;olidam vbi huiu&longs;modi fit nixus pertingere: tum, <lb/>etiam quia e&longs;to pars ip&longs;a breuior per &longs;ui extremum non, <lb/>moueretur ad motum alterius, &longs;ed quie&longs;ceret, non propte<lb/>rea &longs;equeretur con&longs;titui fulcimentum huius motionis. </s>

<s id="N15AA0">Nam <lb/>punctum cuiu&longs;libet vectis corre&longs;pondens puncto fulcimen<lb/>ti cui innititur, penetratur cum illo, & &longs;imul cum illo quie<lb/>&longs;cit in motione ip&longs;iusmet vectis; & tamen non pote&longs;t con<lb/>&longs;titui fulcimentum &longs;uæ propriæ motionis. </s>

<s id="N15AAB">Nimirum quia, <lb/>nihil in &longs;eip&longs;o pote&longs;t fulciri, &longs;ed &longs;emper inter fulcimentum, <lb/>& &longs;uffultum ea debet e&longs;&longs;e di&longs;tinctio, quæ e&longs;t inter mobile, <lb/>& immobile, vel commotum, & immotum. </s>

<s id="N15AB4">Quare cum, <lb/>con&longs;titutum ex dente, ac forcipe &longs;e habeat per <expan abbr="mod&utilde;">modum</expan> vnius <lb/>vectis, non &longs;ecus ac &longs;i e&longs;&longs;et vnicum corpus continuum, <lb/>etiam &longs;i <expan abbr="&longs;ecund&utilde;m">&longs;ecundumm</expan> punctum aliquod &longs;ibi intrin&longs;ecum quie<lb/>&longs;ceret, ac circa illud &longs;ecundum reliquas &longs;ui partes circulari<lb/>ter moueretur; Non propterea po&longs;&longs;et illi tanquam proprio <lb/>fulcimento in &longs;ua ip&longs;ius motione inniti. </s>

<s id="N15AB4">Quare cum, <lb/>con&longs;titutum ex dente, ac forcipe &longs;e habeat per <expan abbr="mod&utilde;">modum</expan> vnius <lb/>vectis, non &longs;ecus ac &longs;i e&longs;&longs;et vnicum corpus continuum, <lb/>etiam &longs;i <expan abbr="&longs;ecund&utilde;m">&longs;ecundum</expan> punctum aliquod &longs;ibi intrin&longs;ecum quie<lb/>&longs;ceret, ac circa illud &longs;ecundum reliquas &longs;ui partes circulari<lb/>ter moueretur; Non propterea po&longs;&longs;et illi tanquam proprio <lb/>fulcimento in &longs;ua ip&longs;ius motione inniti. </s>

<s id="N15ACB">Potius igitur fulci<lb/>mentum con&longs;tituendum e&longs;t extrin&longs;ecum, in ea gingiuæ par<lb/>te, quam de&longs;crip&longs;imus vbi dens ip&longs;e in auul&longs;ione fulcitur, ac <lb/>præmit, <expan abbr="doloremq.">doloremque</expan> infert non minus, quam vbi ex oppo&longs;ito <lb/>dimotæ cius radicire&longs;i&longs;titur. </s>

<s id="N15ADC">In calce tandem huius quæ&longs;tionis Ari&longs;toteles &longs;ubnectit, <lb/>dentem commotum facilius manu &longs;ola quàm in&longs;trumento <lb/>&longs;imul auferri. </s>

Line 2729

<s id="N15B16">C<emph type="italics"/>vr nuces ab&longs;que ictu facilè confringuntur in<lb/>strumentis, qua ad eum fiunt v&longs;um. </s>

<s id="N15B1E">Multum <lb/>enim aufertur virium, motionis &longs;cilicet & vio<lb/>lentia. </s>

<s id="N15B25">Praterea duro & graui comprimens in<lb/>&longs;trumento citiùs confringet, quàm ligneo & <lb/>leui. </s>

<s id="N15B25">Praeterea duro & graui comprimens in<lb/>&longs;trumento citiùs confringet, quàm ligneo & <lb/>leui. </s>

<s id="N15B2C">An quia &longs;ic vtrunque à duobus compri<lb/>mitur vectibus ip&longs;a nux, à vecte autem facilè <lb/>diuelluntur onera? </s>

<s id="N15B33">Id enim instrumentum ex duobus com<lb/>ponitur vectibus, idem habentibus bypomochlion, connexio<lb/>nem videlicet ip&longs;am, vbi est A, quemadmodum igitur fue<lb/>ro diducta &longs;ecundum extrema molis CD, ip&longs;æ FE &longs;ic à par<lb/>ua faciliter potentia conducuntur, quod igitur cum percu&longs;sio<lb/>ne feci&longs;&longs;et pondus id valentiores illæ EC, & FD vectes effi<lb/>eiunt. </s>

<s id="N15B33">Id enim instrumentum ex duobus com<lb/>ponitur vectibus, idem habentibus hypomochlion, connexio<lb/>nem videlicet ip&longs;am, vbi est A, quemadmodum igitur fue<lb/>ro diducta &longs;ecundum extrema molis CD, ip&longs;æ FE &longs;ic à par<lb/>ua faciliter potentia conducuntur, quod igitur cum percu&longs;sio<lb/>ne feci&longs;&longs;et pondus id valentiores illæ EC, & FD vectes effi<lb/>ciunt. </s>

<s id="N15B42">Eleuatione enim in contrarium elati, & comprimentes <lb/>frangunt vbi e&longs;t K. </s>

<s id="N15B48">Hanc etiam ob cau&longs;am quanto vicinius <lb/>fuerit K ip&longs;um A, confringitur celerius. </s>

<s id="N15B4D">Quantò enim ab bipo<lb/>mochlio plus di&longs;tat vectis, facilius & plus mouet ab codem <lb/>potentia. </s>

<s id="N15B4D">Quantò enim ab hipo<lb/>mochlio plus di&longs;tat vectis, facilius & plus mouet ab codem <lb/>potentia. </s>

<s id="N15B54">E&longs;t igitur A quidem bipomochlion: ip&longs;a autem DAF <lb/>vectis, & item ip&longs;a CAE. </s>

<s id="N15B54">E&longs;t igitur A quidem hipomochlion: ip&longs;a autem DAF <lb/>vectis, & item ip&longs;a CAE. </s>

<s id="N15B59">Quantò igitur ip&longs;um K vicinius <lb/>fuerit angulo ip&longs;ius A, tantò vicinius fit connexioni, vbi est <lb/>A, hoc autem e&longs;t bypomochlion, ab eadem igitur potentia appli<lb/>cante FE plus extolli nece&longs;&longs;e e&longs;t. </s>

<s id="N15B59">Quantò igitur ip&longs;um K vicinius <lb/>fuerit angulo ip&longs;ius A, tantò vicinius fit connexioni, vbi est <lb/>A, hoc autem hypomochlion, ab eadem igitur potentia appli<lb/>cante FE plus extolli nece&longs;&longs;e e&longs;t. </s>

<s id="N15B62">Quamobrem quoniam ex <lb/>contario e&longs;t eleuatio, nece&longs;&longs;e e&longs;t magis comprimi, quod autem <lb/>comprimitur magis, citius frangitur.<emph.end type="italics"/></s>

Line 2754

<s id="N15BAD">Attamen ip&longs;e Philo&longs;ophus huiu&longs;modi difficultatem ac <lb/>dubitationem exeodem principio, quo præcedentem quæ<lb/>&longs;tionem &longs;oluerat, apti&longs;&longs;imè ac breui&longs;&longs;imè diluit, inquiens, <lb/>explicatum in&longs;trumentum duobus brachijs tanquam duo<lb/>bus vectibus contrarijs, ad &longs;e&longs;e inuicem conuer&longs;is con&longs;tare, <lb/>vnico fulcimento innixis, quod e&longs;t vtriu&longs;que connexio ac <lb/>veluti axis: duorum autem vectium compre&longs;&longs;ione, vt potè <lb/>qui magnam vim habeant comprimendi, æquè facile nuces <lb/>amygdalas, vel id genus alia confringi, ac ictu vel percu&longs;&longs;io<lb/>ne cum impetu. </s>

<s id="N15BC2">Quod vt ad oculos etiam pateat, con&longs;ti<lb/>tuatur primo in&longs;trumentum ABCD, cuius brachia &longs;int AD <lb/>& CB &longs;uffulta in connexione vtriu&longs;que vbi E. </s>

<s id="N15BCA">Nux verò <lb/><expan abbr="confring&etilde;da">confringenda</expan> locetur inter A & C vbi F, nempe inter extre<lb/>ma brachiorum ea parte qua minus di&longs;tant à fulcimento. <lb/></s>

<s id="N15BD5">Potentia verò confringentis applicetur in extremis ecrun<lb/>dem brachiorum ea parte, qua magis di&longs;tant a fulcimento, <pb pagenum="195" xlink:href="005/01/203.jpg"/><figure id="id.005.01.203.1.jpg" xlink:href="005/01/203/1.jpg"/><lb/>tanquam in manubrijs, <expan abbr="nimir&utilde;">nimirum</expan> in BD. </s>

<s id="N15BD5">Potentia verò confringentis applicetur in extremis eorun<lb/>dem brachiorum ea parte, qua magis di&longs;tant a fulcimento, <pb pagenum="195" xlink:href="005/01/203.jpg"/><figure id="id.005.01.203.1.jpg" xlink:href="005/01/203/1.jpg"/><lb/>tanquam in manubrijs, <expan abbr="nimir&utilde;">nimirum</expan> in BD. </s>

<s id="N15BEA">Con&longs;ideretur dein<lb/>de vtrum que brachium tanquam duplicem vectem moueri <lb/>circa immotum fulcimentum E; ita vt ad motum B ver&longs;us <lb/>D, alterum extremum nempe C appropinquetur ad A; & è <lb/>conuer&longs;o, ad motum D ver&longs;us B, ip&longs;um A appropinquetur <lb/>ad C. </s>

<s id="N15BF8">Tunc dicimus nucem, qu&etail; quidem tanquam pondus <lb/>ab vtroque extremo duplicis vectis AC pellitur ac repelli<lb/>tur, facilè comprimi, ac tandem nimia compre&longs;&longs;ione con<lb/>fringi, &longs;iquidem dum magis ac magis ip&longs;a extrema AC ad <lb/>inuicem appropinquantur, nece&longs;&longs;ariò quæ inter ip&longs;a interci<lb/>pitur, nucem comprimunt, & comprimendo confringunt. </s>

Line 2784

<s id="N15D20">Quando igitur corpus <expan abbr="confringend&utilde;">confringendum</expan> col<lb/>locatur inter extrema <expan abbr="brachior&utilde;">brachiorum</expan> præfati in&longs;trumenti longi&longs;<lb/>&longs;ime a centro, <expan abbr="tant&utilde;">tantum</expan> &longs;patium in fractione percurrunt ip&longs;a ex<lb/>trema, <expan abbr="quant&utilde;">quantum</expan> alia oppo&longs;ita in quibus applicatur potentia. </s>

<s id="N15D3B">Quod fi corpus confringendum collocetur propinquius <lb/>centro, &longs;eu connexioni brachiorum E, ita vt exten&longs;io eius <lb/>AF, quæ per confractionem deperditur, con&longs;tituatur exem<lb/>pli gratia in HI, A tran&longs;lato in H &longs;uper eandem lineam, <lb/>AD, & F in I ver&longs;us lineam CB; & per ip&longs;um punctum <lb/>I, & centrum E excitetur alia diagonalis KL, quæ pa<lb/>riter de&longs;ignet locum, ac fitum quo transferri debet idem <lb/>brachium AD po&longs;t confractionem: Tunc maiorem ar<lb/>cum inueniemus de&longs;cribitura in ip&longs;a compre&longs;&longs;ione extrema <lb/>DA, quam &longs;it &longs;patium HI, quod deperditur per illam. <lb/></s>

<s id="N15D3B">Quod fi corpus confringendum collocetur propinquius <lb/>centro, &longs;eu connexioni brachiorum E, ita vt exten&longs;io eius <lb/>AF, quæ per confractionem deperditur, con&longs;tituatur exem<lb/>pli gratia in HI, A tran&longs;lato in H &longs;uper eandem lineam, <lb/>AD, & F in I ver&longs;us lineam CB; & per ip&longs;um punctum <lb/>I, & centrum E excitetur alia diagonalis KL, quæ pa<lb/>riter de&longs;ignet locum, ac situm quo transferri debet idem <lb/>brachium AD po&longs;t confractionem: Tunc maiorem ar<lb/>cum inueniemus de&longs;cribitura in ip&longs;a compre&longs;&longs;ione extrema <lb/>DA, quam &longs;it &longs;patium HI, quod deperditur per illam. <lb/></s>

<s id="N15D51">Quandoquidem A transferetur in K, & D in L: Spatium <lb/>autem DL continet &longs;patium DG, &longs;icut &longs;patium AK con<lb/>tinet &longs;patium AF æquale ip&longs;i HI, quo propterea maius e&longs;t <lb/>ip&longs;um AK, & DL, quæ per rationem &longs;uprafactam &longs;unt <lb/>æqualia. </s>

<s id="N15D5C">Rur&longs;us verò &longs;i excitetur linea recta à puncto A <lb/>ad punctum K, & con&longs;iderentur i&longs;ta duo triangula, nempe <lb/>HEI, & AEK, inuenientur habere latera proportionalia <lb/>circa eundem angulum E; ba&longs;esq &longs;imilis rationis per quar<lb/>tam propo&longs;. </s>

<s id="N15D5C">Rur&longs;us verò &longs;i excitetur linea recta à puncto A <lb/>ad punctum K, & con&longs;iderentur i&longs;ta duo triangula, nempe <lb/>HEI, & AEK, inuenientur habere latera proportionalia <lb/>circa eundem angulum E; ba&longs;esque &longs;imilis rationis per quar<lb/>tam propo&longs;. </s>

<s id="N15D67">&longs;exti. </s>

<s id="N15D6A">Cumque ba&longs;is AK longioribus lineis <lb/>&longs;ubtendatur ip&longs;i angulo E, maior erit, quàm ba&longs;is HI ei<lb/>dem angulo &longs;ubten&longs;a breuioribus lineis EH, & EI. </s>

<s id="N15D77">Quod autem exempli&longs;icauimus in brachio, &longs;eu vecte AD, <lb/>idem etiam procedit de brachio CB. </s>

<s id="N15D7D">Et quod de brachijs <lb/>in m dio ad inuicem connexis, ac bifariam &longs;e&longs;e inter&longs;ecan<lb/>tibus dictum e&longs;t, accommodari pote&longs;t in alijs nonita &longs;e ha<lb/>bentibus &longs;eu alibi connexis. </s>

<s id="N15D7D">Et quod de brachijs <lb/>in medio ad inuicem connexis, ac bifariam &longs;e&longs;e inter&longs;ecan<lb/>tibus dictum e&longs;t, accommodari pote&longs;t in alijs non ita &longs;e ha<lb/>bentibus &longs;eu alibi connexis. </s>

<s id="N15D86">Nam &longs;emper verificabitur ad <lb/>maiorem approximationem corporis confringendi ad cen<lb/>trum connexionis eorum, &longs;eu fulcimentum, magis ip&longs;a bra<lb/>chia dilatari, maiu&longs;que deinde &longs;patium eodem tempore, <lb/>comprimendo percurrere, quod e&longs;t velocius agere, vnde & <lb/>validius colligitur fiangere, vt dicebamus ex Ari&longs;totele. </s>

<s id="N15D86">Nam &longs;emper verificabitur ad <lb/>maiorem approximationem corporis confringendi ad cen<lb/>trum connexionis eorum, &longs;eu fulcimentum, magis ip&longs;a bra<lb/>chia dilatari, maiu&longs;que deinde &longs;patium eodem tempore, <lb/>comprimendo percurrere, quod e&longs;t velocius agere, vnde & <lb/>validius colligitur frangere, vt dicebamus ex Ari&longs;totele. </s>

<s id="N15D96">Alio verò ex capite eadem con&longs;equentia probatur, quia <lb/>cum vectis beneficio eandem proportionem habeat po<lb/>tentia ad pondus leuandum, aut deprimendum, quam habet <lb/>eius di&longs;tantia à fulcimento ad di&longs;tantiam ponderis ab eo<lb/>dem fulcimento, vt quæ&longs;t. </s>

Line 2804

<s id="N15DBE">Quæ&longs;tio Vige&longs;imatertia.</s>

<s id="N15DC3">C<emph type="italics"/>vr &longs;i duo extrema in rhombo puncta duabus <lb/>ferantur lat onibus, baudquaquam æquale <lb/>vtrumque eorum pertran&longs;it rectam, &longs;ed multò <lb/>plus alterum? </s>

<s id="N15DC3">C<emph type="italics"/>vr &longs;i duo extrema in rhombo puncta duabus <lb/>ferantur latonibus, haudquaquam æquale <lb/>vtrumque eorum pertran&longs;it rectam, &longs;ed multò <lb/>plus alterum? </s>

<s id="N15DCF">Idem autem e&longs;t &longs;ermo, cur quod <lb/>&longs;uper latus fertur, minus pertran&longs;it quam <lb/>ip&longs;um latus? </s>

<s id="N15DD6">Illud enim diametrum minorem <lb/>boc vero maius latus. </s>

<s id="N15DD6">Illud enim diametrum minorem <lb/>hoc vero maius latus. </s>

<s id="N15DDB">Et hoc quidem vnica. </s>

<s id="N15DDE">Il<lb/>lud verò duabus fertur lationibus. </s>

<s id="N15DE3">Feratur enim ex ip&longs;a AB, A<emph.end type="italics"/><pb pagenum="199" xlink:href="005/01/207.jpg"/><emph type="italics"/>quidem ad <expan abbr="ips&utilde;">ipsum</expan> B, B verò ad <expan abbr="ips&utilde;">ipsum</expan> D eadem celeritate. </s>

Line 2818

<s id="N15E33">Repleto igitur ab ip&longs;o G quod in<lb/>tus e&longs;t, toti e&longs;t &longs;imile, & ip&longs;um B in ip&longs;a diametro erit &longs;ecun<lb/>dum laterum connexionem. </s>

<s id="N15E3A">Et &longs;imul latus pertran&longs;it latus, & <lb/>B ip&longs;um BC diametrum. </s>

<s id="N15E3F">Simul igitur Amultò plus ip&longs;a AB <lb/>pertran&longs;it, & ip&longs;um latus minus latus eadem lata teleritate: <lb/>& ip&longs;um latus maiorem quàm B pertran&longs;iuit vna <expan abbr="lat&utilde;">latum</expan> latio<lb/>ne. </s>

<s id="N15E4C">Quantò enim acutior fuerit rbombus, diameter quidem <lb/>minor fit, AC autem maior; latus verò ip&longs;ius BC minus. </s>

<s id="N15E4C">Quantò enim acutior fuerit rhombus, diameter quidem <lb/>minor fit, AC autem maior; latus verò ip&longs;ius BC minus. </s>

<s id="N15E51">Ab<lb/>&longs;urdum e&longs;t enim (vt dictum e&longs;t) id quod duabus fertur latio<lb/>nibus, aliquando ferri tardius illo, quo fertur vnica, & vtri&longs;<lb/>que po&longs;itis æquali velocitate punctis, alterum pertran&longs;ire ma<lb/>iorem Cau&longs;a autem e&longs;t quoniam ei, quod ab obtu&longs;o fertur an<lb/>gulo, ambæ ferè contrariæ fiunt lationes, & illa &longs;ecundum <lb/>quam ip&longs;um fertur, & illa &longs;ecundum quam ip&longs;um à latere de<lb/>fertur. </s>

<s id="N15E62">Ei autem quod ab acuto fertur, accidit vt ad idem fe<lb/>ratur. </s>

<s id="N15E67">Coadiuuat enim quæ ip&longs;ius e&longs;t lateris,, illam quæ e&longs;t &longs;u<lb/>per diametrum. </s>

<s id="N15E6C">Et quantò bunc quidem acutiorem feceris, <lb/>illum verò obtu&longs;um magis: bæc quidem tardior erit, illa verò <lb/>celerior. </s>

<s id="N15E6C">Et quantò hunc quidem acutiorem feceris, <lb/>illum verò obtu&longs;um magis: hæc quidem tardior erit, illa verò <lb/>celerior. </s>

<s id="N15E73">Hæ quidem igitur magis contrariæ fiunt, quoniam <lb/>obtu&longs;ior fit angulus: illæ verò ad idem magis, quoniam lineæ <lb/>coarctantur. </s>

<s id="N15E7A">Ip&longs;um enim A ferè ad idem fertur &longs;ecundum <lb/>ambas lationes. </s>

<s id="N15E7F">Coadiuuatur igitur altera & quantò &longs;anè <lb/>acutior fuerit angulus, tantò magis ip&longs;um A ad contrarium, <lb/>ip&longs;um enim ad B fertur, latus autem defert ip&longs;um ad D. </s>

<s id="N15E87">Et <lb/>quantò &longs;anè obtu&longs;ior fuerit angulus, magis contrartæ fiunt <lb/>lationes, rectior enim efficitur linea. </s>

<s id="N15E87">Et <lb/>quantò &longs;anè obtu&longs;ior fuerit angulus, magis contrariæ fiunt <lb/>lationes, rectior enim efficitur linea. </s>

<s id="N15E8E">Si autem omnino recta <lb/>fieret penitus vtique e&longs;sent contrariæ. </s>

<s id="N15E93">Latus verò &longs;ecundum <lb/>vnicam latam lationem à nullo præpeditur, rationabiliter igi<lb/>tur maiorem pertran&longs;it.<emph.end type="italics"/></s>

Line 2839

<s id="N15EC3">Prima difficultas e&longs;t, cur &longs;i duo puncta extrema vnius la<lb/>teris in rhombo duabus &longs;imul ferantur lationibus cum ea<lb/>dem velocitate, vnum maius, alterum minus &longs;patium per<lb/>currit. </s>

<s id="N15ECC">Ad cuius rei explieationem &longs;upponimus ex. </s>

<s id="N15ECC">Ad cuius rei explicationem &longs;upponimus ex. </s>

<s id="N15ECF">31. de<lb/>finitione primi Euclidis Rhombum e&longs;&longs;e figuram quadrila<lb/>teram quidem, & æquilateram, &longs;ed non rectangulam; quip<lb/>pe quæ duos angulos habet acutos, duos verò obtu&longs;os. </s>

<s id="N15ED8">Si <lb/><figure id="id.005.01.208.1.jpg" xlink:href="005/01/208/1.jpg"/><lb/>igitur in Rhombo ABCD, cuius <lb/>acuti anguli &longs;int A & D, obtu&longs;i <lb/>verò B & C, duo extrema pun<lb/>cta lateris AB, nempe ip&longs;um A, & <lb/>ip&longs;um B, æqua velocitate duabus <lb/>ferantur lationibus, vna qua pun<lb/>ctum A &longs;uper idem latus feratur <lb/>ver&longs;us B, & B feratur ver&longs;us A: <lb/>altera verò qua <expan abbr="d&utilde;">dum</expan> ip&longs;a duo pun<lb/>cta &longs;ibi obuiam procedunt, &longs;imul <lb/>cum toto latere AB, moueantur <lb/>ver&longs;us latus CD, ita vt &longs;emper la<lb/>tus, &longs;eu linea AB, ip&longs;i CD &longs;it pa<lb/>ralella, de&longs;cendatque per latera <lb/>AC, & BD quou&longs;que coincidat <lb/>cum eadem CD: Cum ex duabus lationibus, eadem &longs;em<lb/>per laterum proportione &longs;eruata, recta quædam linea pro<lb/>ducatur, vt &longs;upra demon&longs;tratum e&longs;t ex eodem Ari&longs;totele <lb/>1. par. </s>

<s id="N15F0B">tex. 6. vtraque puncta prædicta eandem laterum ip<lb/>&longs;ius rhombi proportionem in &longs;uo motu &longs;eruando, propriam <pb pagenum="201" xlink:href="005/01/209.jpg"/>rectam lineam de&longs;cribent: A quidem lineam AD, B verò <lb/>BC: quæ nimirum erunt diametri eiu&longs;dem rhombi. </s>

Line 2847

<s id="N15F33">Quod mirum proculdubio omnibus cau&longs;am igno<lb/>rantibus videri &longs;olet. </s>

<s id="N15F3A">Verùm quod linea recta, quam de&longs;cribere diximus pun<lb/>ctum A, &longs;it ipfa diameter AD; quam verò punctum B, <lb/>&longs;it diameter BC, facilè demon&longs;tratur ex eo. </s>

<s id="N15F3A">Verùm quod linea recta, quam de&longs;cribere diximus pun<lb/>ctum A, &longs;it ipsa diameter AD; quam verò punctum B, <lb/>&longs;it diameter BC, facilè demon&longs;tratur ex eo. </s>

<s id="N15F41">Nam &longs;i pun<lb/>ctum A, proprio motu delatum fuerit exempli gratia v&longs;que <lb/>ad punctum E medium ip&longs;ius lineæ AB, & linea tota <lb/>AB eodem tempore, æquale &longs;patium pertran&longs;ierit ver&longs;us <lb/>CD, ita vt alterum eius extremum peruenerit ad punctum <lb/>F, medium lateris AC; alterum verò ad punctum G, me<lb/>dium lateris BD: quoniam AF æqualis e&longs;t ip&longs;i AE, &longs;i com<lb/>pleatur figura &longs;imilis toti, productis lineis EH, & FG per <lb/>punctum medium K, nempe rhombus AEKF, &longs;imilis <lb/>rhombo maiori ABCD per 24. &longs;exti elementorum; erit <lb/>recta FK æqualis oppo&longs;itæ AE, & AF ip&longs;i EK; proin<lb/>deque punctum A cum duabus tran&longs;latum &longs;it lationibus <lb/>&longs;emper proportionalibus iuxta rationem æqualitatis; quam <lb/>latera rhomborum habent inter &longs;e, vtique tran&longs;latum erit <lb/>&longs;uper rectam AK in ip&longs;um K, quod e&longs;t punctum medium <lb/>diametri AD; Cuius reliquum dimidium conficiet, tum <lb/>ex motu &longs;uo ab E v&longs;que ad B, tum ex alieno ab F v&longs;que <lb/>ad C, ita vt tandem perueniat ad punctum D. </s>

<s id="N15F69">Eodem pacto, quod dictum e&longs;t de puncto A, applica<lb/>ri pote&longs;t in puncto B. </s>

<s id="N15F6E">Nam &longs;i hoc cum eadem velocitate <lb/>moueatur ver&longs;us A, &longs;icut linea AB ver&longs;us CD, quo tem<lb/>pore per proprium motum percurri&longs;&longs;er v&longs;que ad E, alieno <lb/>motu perueni&longs;&longs;et v&longs;que ad G; <expan abbr="æqualesq.">æqualesque</expan> forent lineæ BE, <pb pagenum="202" xlink:href="005/01/210.jpg"/>& BG; producti&longs;que lateribus, EH, & GF, rhombus <lb/>EBGK per illa con&longs;titutus, &longs;imilis e&longs;&longs;et rhombo continen<lb/>ti ABCD: Ideoque GK æqualis oppo&longs;itæ BE, & BG <lb/>æqualis EK. </s>

<s id="N15F6E">Nam &longs;i hoc cum eadem velocitate <lb/>moueatur ver&longs;us A, &longs;icut linea AB ver&longs;us CD, quo tem<lb/>pore per proprium motum percurri&longs;&longs;et v&longs;que ad E, alieno <lb/>motu perueni&longs;&longs;et v&longs;que ad G; <expan abbr="æqualesq.">æqualesque</expan> forent lineæ BE, <pb pagenum="202" xlink:href="005/01/210.jpg"/>& BG; producti&longs;que lateribus, EH, & GF, rhombus <lb/>EBGK per illa con&longs;titutus, &longs;imilis e&longs;&longs;et rhombo continen<lb/>ti ABCD: Ideoque GK æqualis oppo&longs;itæ BE, & BG <lb/>æqualis EK. </s>

<s id="N15F86">Quare punctum B vtroque motu<gap/> tran&longs;la<lb/>tum cum eadem proportione æqualitatis, mouebitur motu <lb/>mixto &longs;uper diametrum ip&longs;ius rhombi, & quo tempore <lb/>transferri deberet in E & in G, transfertur in K, quod e&longs;t <lb/>punctum medium diametri BC; cuius reliquum dimidium <lb/>conficiet per motum proprium ab E v&longs;que ad A, & alie<lb/>no à G v&longs;que ad D; ita vt tandem reperiatur in C. </s>

<s id="N15F86">Quare punctum B vtroque motum tran&longs;la<lb/>tum cum eadem proportione æqualitatis, mouebitur motu <lb/>mixto &longs;uper diametrum ip&longs;ius rhombi, & quo tempore <lb/>transferri deberet in E & in G, transfertur in K, quod e&longs;t <lb/>punctum medium diametri BC; cuius reliquum dimidium <lb/>conficiet per motum proprium ab E v&longs;que ad A, & alie<lb/>no à G v&longs;que ad D; ita vt tandem reperiatur in C. </s>

<s id="N15F98">Cum <lb/>igitur &longs;patium BC, vt dicebamus, minus &longs;it quam &longs;patium <lb/>AD eodem tempore peragratum à puncto A, difficile vi<lb/>detur qua ratione id po&longs;&longs;it contingere, po&longs;tquam ita rem <lb/>&longs;e habere con&longs;titerit. </s>

<s id="N15FA5">Huius tamen euentus cau&longs;am &longs;oluendo primam partem <lb/>quæ&longs;tionis, <expan abbr="primamq.">primamque</expan> difficultatem, eam e&longs;&longs;e inquit Ari&longs;to<lb/>teles, quia cum in rhombo duo &longs;int obtu&longs;i anguli, duo verò <lb/>acuti, lationes illæ, quibus fertur punctum, quod ab obtu&longs;o <lb/>angulo di&longs;cedit, vt in propo&longs;ita figura e&longs;t punctum B, &longs;unt <lb/>inter &longs;e omnino ferè contrariæ, cum vna, verbi gratia &longs;ur<lb/>&longs;um penè tendat ver&longs;us A, altera verò deor&longs;um ver&longs;us D: <lb/>Quo fit vt mutuo præpediantur, ac retardentur. </s>

<s id="N15FBA">Lationes <lb/>verò quibus fertur punctum, quod ab acuto angulo di&longs;cedit <lb/>vt A; quamuis diuer&longs;æ in &longs;e &longs;int, nullo tamen modo con<lb/>&longs;tituuntur contrariæ, cum ad eandem ferè partem pergere <lb/>teneantur, <expan abbr="parumq.">parumque</expan> aut minus &longs;emper di&longs;tent inter &longs;e termi<lb/>ni ad quos tendunt. </s>

<s id="N15FCB">Quare potius ip&longs;æ ad inuicem iuuan<lb/>tur, quàm aliquo modo impediantur. </s>

<s id="N15FD0">Rationi autem con<lb/>&longs;entaneum e&longs;t, vt punctum contrarijs ferè lationibus &longs;e&longs;e <lb/>impedientibus latum, minori interuallo in eodem tempore <lb/>feratur, quàm punctum, quod duabus lationibus &longs;e&longs;e mutuo <lb/>adiuuantibus a&longs;portatur; mitumque propterea non e&longs;&longs;e &longs;i <lb/>hoc maiorem diametrum, illud verò minorem eodem tem<lb/>pore percurrat. </s>

<s id="N15FD0">Rationi autem con<lb/>&longs;entaneum e&longs;t, vt punctum contrarijs ferè lationibus &longs;e&longs;e <lb/>impedientibus latum, minori interuallo in eodem tempore <lb/>feratur, quàm punctum, quod duabus lationibus &longs;e&longs;e mutuo <lb/>adiuuantibus a&longs;portatur; mirumque propterea non e&longs;&longs;e &longs;i <lb/>hoc maiorem diametrum, illud verò minorem eodem tem<lb/>pore percurrat. </s>

<s id="N15FDF">Vnde etia n &longs;equitur, vt quò acutiores <lb/>con&longs;tituantur anguli A, & D, <expan abbr="proindeq.">proindeque</expan> obtu&longs;iores B, <lb/>& C; tardius ac minori interuallo feratur ip&longs;um B; cele-<pb pagenum="203" xlink:href="005/01/211.jpg"/>rius verò ac maiori &longs;patio ip&longs;um A. </s>

<s id="N15FDF">Vnde etiam &longs;equitur, vt quò acutiores <lb/>con&longs;tituantur anguli A, & D, <expan abbr="proindeq.">proindeque</expan> obtu&longs;iores B, <lb/>& C; tardius ac minori interuallo feratur ip&longs;um B; cele-<pb pagenum="203" xlink:href="005/01/211.jpg"/>rius verò ac maiori &longs;patio ip&longs;um A. </s>

<s id="N15FF0">Quandoquidem ex ma<lb/>iori angu&longs;tia angulorum magis. </s>

<s id="N15FF5">vniuntur latera, magis <expan abbr="q.">que</expan> ad <lb/>vnum, & idem terminum appropinquantur. </s>

<s id="N16000">Quam Ari&longs;totelis &longs;olutionem pluribus euerrere conatur <lb/>Baldus, quæ &longs;ummatim in hoc tantum redigi po&longs;&longs;unt, quòd <lb/>ex ea &longs;equeretur, idem &longs;imiliter dicendum e&longs;&longs;e de duo<lb/>bus punctis v<gap/> ius lateris in quadrato, &longs;i duabus &longs;imul latio<lb/>nibus mouerentur eo pacto quo in rhombo Philo&longs;ophus <lb/>de&longs;crip&longs;it; vt &longs;cilicet punctum, quod duabus lationibus fer<lb/>tur, ambabus deor&longs;um tendentibus &longs;uper de&longs;cendentem <lb/>diametrum ip&longs;ius quadrati, velocius feratur, quàm punctum, <lb/>quod duabus lationibus fertur, vna deor&longs;um tendente, alte<lb/>ra verò &longs;ur&longs;um &longs;uper diametrum tran&longs;uer&longs;am. </s>

<s id="N16000">Quam Ari&longs;totelis &longs;olutionem pluribus euerrere conatur <lb/>Baldus, quæ &longs;ummatim in hoc tantum redigi po&longs;&longs;unt, quòd <lb/>ex ea &longs;equeretur, idem &longs;imiliter dicendum e&longs;&longs;e de duo<lb/>bus punctis vnius lateris in quadrato, &longs;i duabus &longs;imul latio<lb/>nibus mouerentur eo pacto quo in rhombo Philo&longs;ophus <lb/>de&longs;crip&longs;it; vt &longs;cilicet punctum, quod duabus lationibus fer<lb/>tur, ambabus deor&longs;um tendentibus &longs;uper de&longs;cendentem <lb/>diametrum ip&longs;ius quadrati, velocius feratur, quàm punctum, <lb/>quod duabus lationibus fertur, vna deor&longs;um tendente, alte<lb/>ra verò &longs;ur&longs;um &longs;uper diametrum tran&longs;uer&longs;am. </s>

<s id="N16017">Id quod per <lb/>&longs;e fal&longs;um e&longs;&longs;e con&longs;tat; cum æquali tempore; æquale &longs;patium <lb/>vtrumque punctum conficeret Siquidem in quadrato vtra<lb/>que diameter alteri ad inuicem &longs;emper e&longs;t æqualis. </s>

<s id="N16020"><expan abbr="Idemq.">Idemque</expan> <lb/>confirmat: in rhombo inuer&longs;o. </s>

<s id="N16028">Nam &longs;equeretur, punctum <lb/>duabus lationibus latum deor&longs;um per minorem diametrum, <lb/>citius ferri, quàm punctum, quod duabus lationibus, vna <lb/>&longs;ur&longs;um: altera deor&longs;um tendente: pertran&longs;iret diametrum <lb/>tran&longs;uer&longs;am, nempe maiorem, Quod quippe ab&longs;urdum e&longs;<lb/>&longs;e liquet. </s>

<s id="N16037">Verumenimuerò Baldus in his propriam potius appre<lb/>hen&longs;ionem, quam Ari&longs;totelis &longs;olutionem euertit. </s>

<s id="N1603C">Porrò <lb/>hæc non fundatur in eo, quod e&longs;t &longs;ur&longs;um, aut deor&longs;um pun<lb/>cta ip&longs;a duabus lationibus ferri, vt ip&longs;e &longs;upponit, quamuis ad <lb/>explicationem præ dicti motus, <expan abbr="doctrinæq.">doctrinæque</expan> Ari&longs;totelis, om<lb/>nes vtamur exemplo diuer&longs;arum po&longs;itionum, vt &longs;ur&longs;um, aut <lb/>deor&longs;um: &longs;ed ab&longs;trahendo à quacumque po&longs;itione, tota <lb/>&longs;olutionis ratio ab Ari&longs;totele con&longs;tituitur in maiori vnione, <lb/>&longs;eu propinquitate laterum acutranguli, & in maiori &longs;epara<lb/>none, &longs;eu di&longs;tantia laterum anguli obtu&longs;i. </s>

<s id="N1603C">Porrò <lb/>hæc non fundatur in eo, quod e&longs;t &longs;ur&longs;um, aut deor&longs;um pun<lb/>cta ip&longs;a duabus lationibus ferri, vt ip&longs;e &longs;upponit, quamuis ad <lb/>explicationem præ dicti motus, <expan abbr="doctrinæq.">doctrinæque</expan> Ari&longs;totelis, om<lb/>nes vtamur exemplo diuer&longs;arum po&longs;itionum, vt &longs;ur&longs;um, aut <lb/>deor&longs;um: &longs;ed ab&longs;trahendo à quacumque po&longs;itione, tota <lb/>&longs;olutionis ratio ab Ari&longs;totele con&longs;tituitur in maiori vnione, <lb/>&longs;eu propinquitate laterum acuti anguli, & in maiori &longs;epara<lb/>tione, &longs;eu di&longs;tantia laterum anguli obtu&longs;i. </s>

<s id="N16053">Nam per ip&longs;a <lb/>latera anguli obtu&longs;i; punctum in diuer&longs;as longè partesra<lb/>pitur, qua&longs;i omnino contrario motu: per latera verò anguli <lb/>acuti, in vnam ferè partem, qua&longs;i per eundem motum, qui <lb/>propterea velocior con&longs;tituitur, vt dictum e&longs;t. </s>

<s id="N16064">Deinde propria Baldi &longs;olutio, quam ex proprijs cau&longs;is <lb/>ip&longs;e ait e&longs;&longs;e de&longs;umptam, nullam cau&longs;am affert propo&longs;iti effe<lb/>ctus ad diluendam difficultatem, &longs;eu rationem dubitandi, <lb/>&longs;ed rur&longs;us noua cluntaxat via idip&longs;um demon&longs;trat, quod Ari<lb/>&longs;totelis argumento demon&longs;tratum e&longs;t de veritate ip&longs;ius ef<lb/>fectus, nempe punctum A per longiorem diametrum AD, <lb/>illis duabus lationibus ferri eodem tempore, quo punctum <lb/>B fertur &longs;uper minorem diametrum BC; quod e&longs;t citius <lb/>moueri: nihil attingens de cau&longs;a cur id contingat, &longs;eu ob <lb/>quam punctum A, eodem tempore maiorem valeat li<lb/>neam pertran&longs;ire, <expan abbr="proindeq.">proindeque</expan> velocius moueri; id quod opti<lb/>mè fecit Ari&longs;toteles vt vidimus. </s>

<s id="N16064">Deinde propria Baldi &longs;olutio, quam ex proprijs cau&longs;is <lb/>ip&longs;e ait e&longs;&longs;e de&longs;umptam, nullam cau&longs;am affert propo&longs;iti effe<lb/>ctus ad diluendam difficultatem, &longs;eu rationem dubitandi, <lb/>&longs;ed rur&longs;us noua duntaxat via idip&longs;um demon&longs;trat, quod Ari<lb/>&longs;totelis argumento demon&longs;tratum e&longs;t de veritate ip&longs;ius ef<lb/>fectus, nempe punctum A per longiorem diametrum AD, <lb/>illis duabus lationibus ferri eodem tempore, quo punctum <lb/>B fertur &longs;uper minorem diametrum BC; quod e&longs;t citius <lb/>moueri: nihil attingens de cau&longs;a cur id contingat, &longs;eu ob <lb/>quam punctum A, eodem tempore maiorem valeat li<lb/>neam pertran&longs;ire, <expan abbr="proindeq.">proindeque</expan> velocius moueri; id quod opti<lb/>mè fecit Ari&longs;toteles vt vidimus. </s>

<s id="N16083">Secunda autem difficultas, quam Philo&longs;ophus hac in <lb/>quæ&longs;tione proponit, e&longs;t, cur in eodem rhombo punctum B, <lb/>quod vt diximus &longs;ua &longs;ponte fertur &longs;uper latus BA, <expan abbr="totamq.">totamque</expan> <lb/>eius longitudinem percurrit; minus quippe pertran&longs;eat &longs;pa<lb/>tium, quàm totum ip&longs;ummet latus BA, in quo fertur ver&longs;us <lb/>CD; imò quàm &longs;it ip&longs;ummet latus BA, quod percurrit. <lb/></s>

<s id="N16095">Quandoquidem punctum B non conficit ni&longs;i&longs;patium BC: <lb/>totum autem latus BA conficit &longs;patium BD, &longs;eu AC, <lb/>quod maius e&longs;t quàm BC. </s>

<s id="N1609D">Sicut ip&longs;um latus BA maius <lb/>con&longs;tituitur, quàm diameter BC in rhombo propo&longs;ito. <lb/></s>

<s id="N160A3"><expan abbr="Totaq.">Totaque</expan> ratio difficultatis in eo &longs;ita e&longs;t, quoniam punctum <lb/>B, duplici fertur latione, latus verò AB, vnica, & <lb/>vtrunque pari velocitate: Quamobrem potius punctum <lb/>B, quàm latus BA, &longs;equeretur maius &longs;patium pertran&longs;i<lb/>re. </s>

<s id="N160B1">Accedit quia punctum B verè totum latus BA, in <lb/>quo fertur percurrit eodem tempore, quo vehitur cum ip<lb/>&longs;omet latere ve<gap/>&longs;us CD; ideoque &longs;atis arduum videtur, <lb/>minus ip&longs;um B &longs;patium pertran&longs;ire quàm &longs;it latus BA, in <lb/>quo fertur. </s>

<s id="N160B1">Accedit quia punctum B verè totum latus BA, in <lb/>quo fertur percurrit eodem tempore, quo vehitur cum ip<lb/>&longs;omet latere ver&longs;us CD; ideoque &longs;atis arduum videtur, <lb/>minus ip&longs;um B &longs;patium pertran&longs;ire quàm &longs;it latus BA, in <lb/>quo fertur. </s>

<s id="N160C0">Sed vnde hæc dubitandi ratio de&longs;umpta e&longs;t, inde pariter <lb/>ade&longs;t ratio difficultatem &longs;oluendi. </s>

Line 2907

<s id="N16138">Si autem quarta pars æqualem conuol<lb/>uitur, manife&longs;tum e&longs;t, quod totus circulus toti circulo æqualem <lb/>conuoluetur. </s>

<s id="N1613F">Quare quando BG linea ad ip&longs;um peruenerit <lb/>K, & ip&longs;a FC circumferentia erit in ip&longs;a CL & vniuer&longs;us <lb/>erit conuolutus circulus. </s>

<s id="N16146"><expan abbr="Similiq.">Similique</expan> modo &longs;i magnum mouero, <lb/>illi paruum annectens, eodem existente centro, &longs;imul cum AC <lb/>ip&longs;a AB perpendiculum & recta erit: hac quidem ad ip&longs;am<emph.end type="italics"/><pb pagenum="206" xlink:href="005/01/214.jpg"/><emph type="italics"/>FI, illæ verò ad GM. </s>

<s id="N16159">Quamobrem quando bæc quidam <lb/>ip&longs;i GM pertran&longs;iuerit, illa verò ip&longs;i FI, & rur&longs;um facta <lb/>fuerit recta ip&longs;a FA ad ip&longs;am FL, & ip&longs;a AG rur&longs;um re<lb/>cta, velut à principio erant in ip&longs;is MI. </s>

<s id="N16159">Quamobrem quando hæc quidam <lb/>ip&longs;i GM pertran&longs;iuerit, illa verò ip&longs;i FI, & rur&longs;um facta <lb/>fuerit recta ip&longs;a FA ad ip&longs;am FL, & ip&longs;a AG rur&longs;um re<lb/>cta, velut à principio erant in ip&longs;is MI. </s>

<s id="N16162">Hoc autem neque <lb/>alia intercedente mora maioris ad minorem, vbi &longs;eilicet per <lb/>aliquod temporis &longs;patium &longs;taret in eodem puncto, neque tran&longs;i<lb/>liente minore aliquod punctum, maiorem quidem æqualem mi<lb/>nori p<gap/>rtran&longs;ire, bunc autem maiori, ab&longs;urdum e&longs;t. </s>

<s id="N16162">Hoc autem neque <lb/>alia intercedente mora maioris ad minorem, vbi &longs;cilicet per <lb/>aliquod temporis &longs;patium &longs;taret in eodem puncto, neque tran&longs;i<lb/>liente minore aliquod punctum, maiorem quidem æqualem mi<lb/>nori pertran&longs;ire, hunc autem maiori, ab&longs;urdum e&longs;t. </s>

<s id="N1616F">Præterea <lb/>vnica etiam &longs;emper existente motione, centrorum motum inter<lb/>dum quidem magnam, nonnunquam verò minorem conuerti, <lb/>admirandum est. </s>

<s id="N16178">I dem enim celeritate eadem latum æqualem <lb/>natum boc e&longs;t pertran&longs;ire: eadem autem celeritate vtroque <lb/>modo æqualem licet mouere. </s>

<s id="N16178">I dem enim celeritate eadem latum æqualem <lb/>natum hoc e&longs;t pertran&longs;ire: eadem autem celeritate vtroque <lb/>modo æqualem licet mouere. </s>

<s id="N1617F">Principium autem &longs;umendum <lb/>est circa i&longs;torum cau&longs;am, quod eadem potentia, & æqualit <lb/>bans quidem tardius mouet magnitudinem, illam verò cel<gap/><lb/>rius. </s>

<s id="N1617F">Principium autem &longs;umendum <lb/>est circa i&longs;torum cau&longs;am, quod eadem potentia, & æqualis <lb/>hanc quidem tardius mouet magnitudinem, illam verò cele<lb/>rius. </s>

<s id="N1618A">Si enim fuerit quippiam, quod à &longs;eip&longs;o moueri, natum <lb/><gap/>n &longs;it, &longs;i &longs;imul & illud mouerit, quod natum e&longs;t mouert, tar<lb/>dius mouebitur, quàm &longs;i ip&longs;um per &longs;e moueretur. </s>

<s id="N1618A">Si enim fuerit quippiam, quod à &longs;eip&longs;o moueri, natum <lb/>non &longs;it, &longs;i &longs;imul & illud mouerit, quod natum e&longs;t moueri, tar<lb/>dius mouebitur, quàm &longs;i ip&longs;um per &longs;e moueretur. </s>

<s id="N16192">Et &longs;iquidem <lb/><gap/>atum fuerit moueri, non &longs;imul autem moueatur, &longs;imiliter <lb/>&longs;e habebit. </s>

<s id="N16192">Et &longs;iquidem <lb/>natum fuerit moueri, non &longs;imul autem moueatur, &longs;imiliter <lb/>&longs;e habebit. </s>

<s id="N1619A">Et impo&longs;&longs;ibile certè e&longs;t, plus moueri quàm mouem, <lb/><gap/>on enim &longs;uam ip&longs;ius mouetur motionem. </s>

<s id="N1619A">Et impo&longs;&longs;ibile certè e&longs;t, plus moueri quàm mouem, <lb/>non enim &longs;uam ip&longs;ius mouetur motionem. </s>

<s id="N161A0">Sit igitur e reu'us <lb/>maior vbi A, minor autem vbi B, &longs;i minor maiorem impel<lb/>let non reuolutum ex &longs;e, manife&longs;tum e&longs;t, quod tantum ip&longs;ius <lb/>rectæ maior pertran&longs;it, quantum e&longs;t impul&longs;us. </s>

<s id="N161A9">T antum autem <lb/>e&longs;t impul&longs;us, quantum paruus est motus æqualem igitur ip&longs;ius <lb/>rectæ pertran&longs;iuerunt. </s>

<s id="N161B0">Nece&longs;ie igitur e&longs;t &longs;i reuolutus minor <lb/>maiorem impellet, reuoluti &longs;imul cum impul&longs;ione; tantum <lb/>autem, quantum minor reuolutus e&longs;t, &longs;i nibil ip&longs;e &longs;ui ip&longs;ius <lb/>motione mouetur. </s>

<s id="N161B0">Nece&longs;&longs;e igitur e&longs;t &longs;i reuolutus minor <lb/>maiorem impellet, reuoluti &longs;imul cum impul&longs;ione; tantum <lb/>autem, quantum minor reuolutus e&longs;t, &longs;i nihil ip&longs;e &longs;ui ip&longs;ius <lb/>motione mouetur. </s>

<s id="N161B9">Quomodo enim & quantum mouit, tantum <lb/>motum e&longs;&longs;e nece&longs;&longs;e e&longs;t, quod mouetur ab illo. </s>

<s id="N161BE">Sed profectò par<lb/>uus circulus tantum jeip&longs;um circulariter mouit, quantum est <lb/>pedalis quantitas (tantum enim &longs;it id, quod motus e&longs;t) & ma<lb/>gnus igitur tantum motus erit. </s>

<s id="N161BE">Sed profectò par<lb/>uus circulus tantum &longs;eip&longs;um circulariter mouit, quantum est <lb/>pedalis quantitas (tantum enim &longs;it id, quod motus e&longs;t) & ma<lb/>gnus igitur tantum motus erit. </s>

<s id="N161C7"><expan abbr="Similiq.">Similique</expan> modo &longs;i magnus par<lb/>uum mouebit, motus erit paruus quemadmodum maior. </s>

<s id="N161CF">Per <lb/>&longs;e autem motus illorum vtrumlibet, &longs;iue celeriter, &longs;eu tardè <lb/>eadem velocitate, statim quando maior natus e&longs;t circumferri <lb/>lineam, quod difficultatem facit, quod non &longs;imiliter faciunt <lb/>quando fuerint connexi. </s>

<s id="N161DA">Hoc autem e&longs;t, &longs;i alter ab altero mo<lb/>ueatur, non quam natus e&longs;t, neque peculiarem motionem: nibil <lb/>enim refert cireumponere, & annectere, aut <expan abbr="eõiungere">eoniungere</expan> vtrum<lb/>libet alteri. </s>

<s id="N161DA">Hoc autem e&longs;t, &longs;i alter ab altero mo<lb/>ueatur, non quam natus e&longs;t, neque peculiarem motionem: nihil <lb/>enim refert circumponere, & annectere, aut <expan abbr="eõiungere">coniungere</expan> vtrum<lb/>libet alteri. </s>

<s id="N161E7">Similiter enim quando bic quidem mouet, ille ve<lb/>rò mouelur ab isto, quantum vtique mouerit, alt<gap/>r, tantum<emph.end type="italics"/><pb pagenum="207" xlink:href="005/01/215.jpg"/><emph type="italics"/>alter mouebitur. </s>

<s id="N161E7">Similiter enim quando hic quidem mouet, ille ve<lb/>rò mouetur ab isto, quantum vtique mouerit, alter, tantum <emph.end type="italics"/><pb pagenum="207" xlink:href="005/01/215.jpg"/><emph type="italics"/>alter mouebitur. </s>

<s id="N161F7">Quandoquidem igitur adiacens mouerit, aut <lb/>propen&longs;us, non &longs;emper conuoluitur, quando verò circa idem <lb/>po&longs;iti fuerint centrum, alterum ab illo &longs;emper conuolui nece&longs;<lb/>&longs;e est. </s>

<s id="N16200">Sed nihileminus non &longs;uam ip&longs;ius motionem mouetur al<lb/>ter, &longs;ed velut nullam baberet motionem: & &longs;i babuerit, illa <lb/>autem non vtatur, tantundem accidit. </s>

<s id="N16200">Sed nihil e minus non &longs;uam ip&longs;ius motionem mouetur al<lb/>ter, &longs;ed velut nullam haberet motionem: & &longs;i habuerit, illa <lb/>autem non vtatur, tantundem accidit. </s>

<s id="N16207">Quandoquidem igitur <lb/>magnus mouerit &longs;ibi <expan abbr="alligat&utilde;">alligatum</expan> paruum, paruus mouetur quan<lb/>tum ille: quando autem paruus, rur&longs;us magnus quantum i&longs;te, <lb/>&longs;eparatus autem vterque &longs;eip&longs;um mouet. </s>

<s id="N16214">Quod autem eodem <lb/>exi&longs;tente centro, & mouente eadem velocitate, accidit inæqua<lb/>lem illos pertran&longs;ire lineam, paralogi&longs;mo &longs;opbi&longs;ticè vtitur is, <lb/>qui dubitat: idem enim ambobus e&longs;t centrum, verùm per acci<lb/>dens, veluti mu&longs;icum, & album. </s>

<s id="N16214">Quod autem eodem <lb/>exi&longs;tente centro, & mouente eadem velocitate, accidit inæqua<lb/>lem illos pertran&longs;ire lineam, paralogi&longs;mo &longs;ophi&longs;ticè vtitur is, <lb/>qui dubitat: idem enim ambobus e&longs;t centrum, verùm per acci<lb/>dens, veluti mu&longs;icum, & album. </s>

<s id="N1621F">E&longs;&longs;e enim vtriu&longs;que circuli <lb/>centro non eodem vtitur. </s>

<s id="N16224">Quandoquidem igitur mouens fue<lb/>rit paruus, vt illius centrum, & principium: quando verò <lb/>magnus, vt illius. </s>

<s id="N1622B">Non igitur idem &longs;impliciter mouet, &longs;ed e&longs;t <lb/>quo modo.<emph.end type="italics"/></s>

Line 2939

<s id="N1623A">Qvæ&longs;tio hæc admirabilem complectitur difficulta<lb/>tem, vtpotè in&longs;tituta circa rem, quæ vix credi po&longs;&longs;et, <lb/>ni&longs;i ante oculos ob&longs;eruaretur: Vnde inter cæteras <lb/>præcipua ac omnium difficillima exi&longs;timatur, <expan abbr="multumq.">multumque</expan> pa<lb/>riter &longs;icut præcedens ad mixti motus naturam exploran<lb/>dam conducit. </s>

<s id="N1624B">Cau&longs;am igitur &longs;ci&longs;citatur Ari&longs;toteles, cur <lb/>duo circuli alter altero maior circa idem centrum &longs;imul an<lb/>nexi, & coaptati, &longs;i &longs;ecundùm ab&longs;idem volutentur (vt plau<lb/>&longs;trorum progredientium rotæ) ambo æquale pertran&longs;eant <lb/>&longs;patium: &longs;eor&longs;um verò &longs;eparati, &longs;i eodem pacto circum<lb/>uoluantur, non ita &longs;ed maior circulus maiorem lineam, mi<lb/>nor verò minorem percurrat iuxta proportionem circumfe<lb/>rentiæ vnius ad circumferentiam alterius? </s>

<s id="N1625C">Quod vt di&longs;tin<lb/>ctius ob&longs;eruetur addit Ari&longs;toteles, cir culos ip&longs;os circa idem <lb/>centrum coniunctos, <expan abbr="quandoq.">quandoque</expan> in circumuolutione tantam <lb/>lineam &longs;patij pertran&longs;ire, quantam &longs;eor&longs;um pertran&longs;iret cir<lb/>culus minor: quandoque verò quantam eodem pacto per<lb/>curreret circulus maior. </s>

<s id="N1626D">Etenim, vt quilque experiri po-<pb pagenum="208" xlink:href="005/01/216.jpg"/>te&longs;t, &longs;i ex ip&longs;is duobus circulis &longs;imul circa idem centrum <lb/>coniunctis volutetur minor &longs;ecundum ab&longs;idem &longs;uam &longs;uper <lb/>aliquod planum, ad motum ip&longs;ius conuoluetur &longs;imul & ma<lb/>ior &longs;uper aliud planum; &longs;ed vtraque linea ab ip&longs;is de&longs;cripta, <lb/>æqualis erit ei quam de&longs;criberet ip&longs;emet circulus minor &longs;i <lb/>&longs;olus per &longs;e ac &longs;eor&longs;um volutaretur. </s>

<s id="N1626D">Etenim, vt qui&longs;que experiri po-<pb pagenum="208" xlink:href="005/01/216.jpg"/>te&longs;t, &longs;i ex ip&longs;is duobus circulis &longs;imul circa idem centrum <lb/>coniunctis volutetur minor &longs;ecundum ab&longs;idem &longs;uam &longs;uper <lb/>aliquod planum, ad motum ip&longs;ius conuoluetur &longs;imul & ma<lb/>ior &longs;uper aliud planum; &longs;ed vtraque linea ab ip&longs;is de&longs;cripta, <lb/>æqualis erit ei quam de&longs;criberet ip&longs;emet circulus minor &longs;i <lb/>&longs;olus per &longs;e ac &longs;eor&longs;um volutaretur. </s>

<s id="N1627F">E contra verò &longs;i &longs;uper <lb/>planum eodem pacto volutetur &longs;ecundum ab&longs;idem &longs;uam <lb/>circulus maior, & ad motum ip&longs;ius circumuoluatur etiam <lb/>circulus minor, vtraque linea recta ab ip&longs;is de&longs;cripta æqua<lb/>lis erit ei quam per &longs;e volutatus de&longs;criberet idemmet circu<lb/>lus maior. </s>

<s id="N1628E">Manife&longs;tum autem e&longs;&longs;e, ait Ari&longs;toteles, circulum maio<lb/>rem &longs;eor&longs;um reuolutum, maius <expan abbr="&longs;paci&utilde;">&longs;pacium</expan>, &longs;eu maiorem lineam <lb/>pertran&longs;ire, quàm pertran&longs;eat circulus minor. </s>

<s id="N16299">Idque ex eo, <lb/>nam &longs;icut &longs;en&longs;u con&longs;tat, ambitum cuiu&longs;que circuli e&longs;&longs;e, at<lb/>que con&longs;titui per ip&longs;am circumferentiam, &longs;eu circumuolu<lb/>tionem propriæ cliametri eiu&longs;dem circuli, maioris quidem <lb/>maiorem, minoris verò minorem: ita &longs;en&longs;u pariter digno&longs;ci<lb/>tur eandem inter &longs;e proportionem habere lineas, quæ per <lb/>circumuolutionem ip&longs;orum circulorum de&longs;cribuntur in <lb/>plano; vt&longs;cilicet linea de&longs;cripta à maiori circumferentia <lb/>&longs;it maior, quæ verò à minori de&longs;cribitur, &longs;it minor. </s>

<s id="N16299">Idque ex eo, <lb/>nam &longs;icut &longs;en&longs;u con&longs;tat, ambitum cuiu&longs;que circuli e&longs;&longs;e, at<lb/>que con&longs;titui per ip&longs;am circumferentiam, &longs;eu circumuolu<lb/>tionem propriæ diametri eiu&longs;dem circuli, maioris quidem <lb/>maiorem, minoris verò minorem: ita &longs;en&longs;u pariter digno&longs;ci<lb/>tur eandem inter &longs;e proportionem habere lineas, quæ per <lb/>circumuolutionem ip&longs;orum circulorum de&longs;cribuntur in <lb/>plano; vt &longs;cilicet linea de&longs;cripta à maiori circumferentia <lb/>&longs;it maior, quæ verò à minori de&longs;cribitur, &longs;it minor. </s>

<s id="N162AC">Vbi <lb/>autem v&longs;i &longs;umus nomine (ambitus) textus habet (angulus) <lb/>cuius propria &longs;ignificatio difficile cohæret cum &longs;en&longs;u ip&longs;ius <lb/>orationis, <expan abbr="proindeq.">proindeque</expan> non paruam &longs;u&longs;picionem præbuit er<lb/>roris librariorum, qui forta&longs;&longs;e angulum pro ambitu &longs;crip&longs;e<lb/>runt: Cum alioquin vox ambitus contextui planè coh&etail;reat, <lb/><expan abbr="explicetq.">explicetque</expan> magis ac breuius quod auctor intendit. </s>

Line 2960

<s id="N1631A">Sint circa <lb/>idem <expan abbr="p&utilde;ctum">punctum</expan> <lb/>A ip&longs;i duo cir<lb/>culi <expan abbr="coni&utilde;cti">coniuncti</expan>, <lb/>maior <expan abbr="quid&etilde;">quidem</expan> <lb/>BCDE, minor <lb/>verò FGHI. <lb/></s>

<s id="N16336">Sintque dia<lb/>metri maioris <lb/>BD, & EC; <lb/>minoris verò <lb/>FH, & IG &longs;e&longs;e <lb/>inuicem inter&longs;ecantes ad angulos rectos in cenrro A. </s>

<s id="N16336">Sintque dia<lb/>metri maioris <lb/>BD, & EC; <lb/>minoris verò <lb/>FH, & IG &longs;e&longs;e <lb/>inuicem inter&longs;ecantes ad angulos rectos in centro A. </s>

<s id="N16344">Ideo<lb/>que quadrans circuli maioris &longs;it CD, minoris verò GH. <lb/></s>

<s id="N1634A">Deinde con&longs;tituamus vtrunque circulum ad dexteram &longs;i<lb/>mul moueri cum &longs;uo communi centro, rotando alterum <pb pagenum="210" xlink:href="005/01/218.jpg"/>quidem per &longs;e &longs;uper rectam lineam DK, alterum verò ad <lb/>motum illius, de&longs;cribendo aliam rectam huic parallelam, <lb/>quæ &longs;it HL. </s>

<s id="N16358">Rur&longs;us con&longs;tituamus, maiorem circulum per <lb/>&longs;e moueri &longs;ecundum ab&longs;idem quadrantis CD &longs;uper lineam <lb/>DK, ita vt aliquando punctum C perueniat in M, percur<lb/>rendo &longs;patium DM æquale ip&longs;i CD. </s>

Line 2984

<s id="N163F1">Præterea quòd vnica exi&longs;tente motione vtriu&longs;que cir<lb/>culi connexi, centrum commune commotum, interdum <lb/>quidem maiorem, interdum verò minorem lineam percur<lb/>rat iuxta ab&longs;idem, &longs;cilicet maioris, aut minoris circuli &longs;e<lb/>cundum quam mouetur: cum tamen idem eadem celerita<lb/>te latum, æqualem lineam regulariter debeat pertran&longs;ire. </s>

<s id="N16400">Pro &longs;olultione igitur quæ&longs;tionis ad explicandam cau&longs;am <lb/>tam mirifici effectus, duo &longs;upponit Ari&longs;toteles fundamenta. <lb/></s>

<s id="N16400">Pro &longs;olutione igitur quæ&longs;tionis ad explicandam cau&longs;am <lb/>tam mirifici effectus, duo &longs;upponit Ari&longs;toteles fundamenta. <lb/></s>

<s id="N16406">Vnum e&longs;t eandem, vel æqualem potentiam, tardius quidem <lb/>mouere vnam magnitudinem, quàm aliam. </s>

<s id="N1640B">Licet enim illæ <lb/>æquè ex &longs;e mobiles &longs;int, &longs;i tamen vna &longs;imul cum alia ad <lb/>motum inepta vel difficili reperiatur coniuncta, tardius mo<lb/>uebitur, quàm illa, quæ reperitur &longs;oluta, vel quam ip&longs;amet <lb/>&longs;eor&longs;um moueretur ab eadem potentia. </s>

<s id="N16416">Quod &longs;i magni<lb/>tudo, quæ moueri debet ad motum alterius, cui reperi<lb/>tur connexa, mobilis quidem facilè ex &longs;e &longs;it, nihil tamen <lb/>ex &longs;e moueatur, vel ad motum alterius conferat, perin<lb/>de e&longs;t, ac &longs;i minimè apta e&longs;&longs;et ad motum: vnde & altera, <lb/>quæ &longs;imul cum ip&longs;a moueri debet, tardius non minus mo<lb/>uebitur. </s>

Line 2995

<s id="N1643C">Quibus po&longs;itis Ari&longs;toteles quæ&longs;tionem &longs;oluendo prædi<lb/>ctum effectum ex eo inquit contingere. </s>

<s id="N16441">Nam &longs;i circulus ma<lb/>ior non moueatur ni&longs;i ad motum minoris cui e&longs;t annexus, <lb/>tantum &longs;patium poterit pertran&longs;ire, quantum delatus fuerit <lb/>ex impullu illius: tantum autem deferri poterit quantum <lb/>minor ip&longs;e circulus ex &longs;e motus impulerit, & non amplius. <lb/></s>

<s id="N16441">Nam &longs;i circulus ma<lb/>ior non moueatur ni&longs;i ad motum minoris cui e&longs;t annexus, <lb/>tantum &longs;patium poterit pertran&longs;ire, quantum delatus fuerit <lb/>ex impul&longs;u illius: tantum autem deferri poterit quantum <lb/>minor ip&longs;e circulus ex &longs;e motus impulerit, & non amplius. <lb/></s>

<s id="N1644D">Quomodo enim & quantum ex &longs;e motus fuerit mouens, <lb/>tantundem nece&longs;&longs;e e&longs;t moueri, qui mouetur ab illo. </s>

<s id="N16452">Aequa<lb/>lem igitur viam vterque circulus rotando conficiet dum <lb/>maior mouetur ad motum minoris. </s>

<s id="N16459"><expan abbr="Idemq.">Idemque</expan> infert contin<lb/>gere &longs;i minor circulus moueatur ad motum maioris &longs;ibi an<lb/>nexi, & eodem pacto &longs;ecundum ab&longs;idem lati. </s>

<s id="N16463">Nam tantum <lb/>ip&longs;e minor circulus, & non minus moueri poterit, quantum <lb/>à maiori deportabitur. </s>

<s id="N1646A">Rapitur enim iugiter ab illo in &longs;ua <lb/>rotatione v&longs;que ad vltimum terminum, <expan abbr="æqualemq.">æqualemque</expan> propte<lb/>rea lineam rectam <expan abbr="c&utilde;">cum</expan> illo de&longs;cribet, quamuis minorem pe<lb/>ripheriam obtineat. </s>

<s id="N1647B">Quod &longs;i vtrumlibet ip&longs;orum circulo<lb/>rum &longs;eor&longs;um ex &longs;e &longs;ecundum propriam ab&longs;idem eadem ve<lb/>locitate moueatur, tunc maior circulus maiorem rectam, <lb/>minor verò minorem &longs;ua volutatione conficiet iuxta men<lb/>&longs;utam &longs;ecundum quam natus e&longs;t circumferri. </s>

<s id="N1647B">Quod &longs;i vtrumlibet ip&longs;orum circulo<lb/>rum &longs;eor&longs;um ex &longs;e &longs;ecundum propriam ab&longs;idem eadem ve<lb/>locitate moueatur, tunc maior circulus maiorem rectam, <lb/>minor verò minorem &longs;ua volutatione conficiet iuxta men<lb/>&longs;uram &longs;ecundum quam natus e&longs;t circumferri. </s>

<s id="N16488">Cæterum eam, ac profectò <expan abbr="arduã">arduam</expan> difficultatem &longs;ibi obij<lb/>cit Philo&longs;ophus. </s>

Line 3022

<s id="N1652A">Hucu&longs;que ex mente, ac doctrina Ari&longs;totelis, qui tamen <lb/>mul<gap/>orum iudicio non videtur obiectam &longs;ibi difficultatem <lb/>&longs;atis infringere, vt quæ adhuc magna ex parte maneat in &longs;uo <lb/>robore. </s>

<s id="N1652A">Huiu&longs;que ex mente, ac doctrina Ari&longs;totelis, qui tamen <lb/>multorum iudicio non videtur obiectam &longs;ibi difficultatem <lb/>&longs;atis infringere, vt quæ adhuc magna ex parte maneat in &longs;uo <lb/>robore. </s>

<s id="N16535">Nam hoc quod e&longs;t proprio, vel alieno motu cieri, <lb/><expan abbr="centrumq.">centrumque</expan> circuli deferentis per accidens e&longs;&longs;e etiam cen<lb/>trum circuli delati, non tollit, vtrunque circulum &longs;ecun<lb/>dum ab&longs;idem codem pacto rotari, ac propriam lineam <lb/>rectam in &longs;uo plano de&longs;cribere: vnde videtur inferri eodem <lb/>etiam pacto vtramque lineam de&longs;criptam propriæ periphe<lb/>riæ à qua de&longs;cribitur debere commen&longs;urari. </s>

<s id="N16547">Parum enim <lb/>refert, circulum per &longs;e rotari circa proprium centrum ad <lb/>impul&longs;um axis immediatè, vel per accidens mediante alio <lb/>circulo, dummodo eodem pacto per circumuolutionem &longs;u&etail; <lb/>ab&longs;idis circa idem centrum lineam de&longs;cribat, cui illa debeat <lb/>commen&longs;urari. </s>

<s id="N16554">Sphæra namque &longs;uper planum rotando &longs;i<lb/>ue proprio nutu, &longs;iue alieno impul&longs;u, tardius, aut velocius, <lb/>&longs;icut omnes plani partes, per quas tran&longs;it debet attingere; <lb/>ita per totidem partes &longs;uas illis debet corre&longs;pondere, & ad <lb/>æqualitatem in tran&longs;itu adaptari. </s>

Line 3031

<s id="N1657F"><expan abbr="Idemq.">Idemque</expan> è conuer&longs;o applicari pote&longs;t in contactu pe<lb/>ripheriæ maioris circuli cum recta breuiori, quam conficit <lb/>ad motum minoris circuli &longs;uper ab&longs;idem per &longs;e lati. </s>

<s id="N1658B">Ad diluendam igitur omnino prædictam difficultatem, <lb/>quæ multorum quippe vexauit ingenia, & pene in&longs;uperabi-<pb pagenum="215" xlink:href="005/01/223.jpg"/>lis apud aliquos extimatur, liceat aliunde totum negocium <lb/>au&longs;picari, nouumque aliquid in medium affere in eiu&longs;dem <lb/>Ari&longs;totelis, ac veterum Philo&longs;ophorum princip<gap/>s funda <lb/>tum. </s>

<s id="N1659D">Ac primò quidem &longs;tabiliatur, motum cuiu&longs;libet circu<lb/>li &longs;ecundum ab&longs;idem, e&longs;&longs;e motum quendam mixtum ex du<lb/>plici latione; vna qua circumuoluitur, &longs;eu circa proprium <lb/>centrum fertur in gyrum; altera verò qua ad motum axis <lb/>rectà fertur &longs;uper planum quo ver&longs;us tendit ip&longs;emet axis. <lb/></s>

<s id="N165A9">Etenim &longs;i circulus &longs;tans ab&longs;que &longs;ui rotatione raperetur &longs;u<lb/>per <expan abbr="plan&utilde;">planum</expan>, verè moueretur motu recto, ac per vnicum pun<lb/>ctum totam plani longitudinem &longs;uper quam fertur attinge<lb/>ret. </s>

<s id="N165B6">Si verò circumuolueretur ab&longs;que progre&longs;&longs;u, aut latio<lb/>ne axis, verè moueretur circulariter ac per omnes partes, <lb/><expan abbr="punctaq.">punctaque</expan> &longs;uæ peripheriæ, eandem plani partem, vel punctum <lb/>in quo &longs;i&longs;tebat attingeret. </s>

<s id="N165C2">Cum itaque ad motum axis re<lb/>ctà &longs;uper planum trahitur, ac &longs;imul rotatur, ex vtraque la<lb/>tione mixtus quidam motus producitur, per quem tota <lb/>circumferentia toti longitudini &longs;uper quam fertur ada<lb/>ptatur. </s>

<s id="N165CF">Deinde verò &longs;tabiliatur lineam, quæ à circulo, prædicto <lb/>modo de&longs;cribitur &longs;uper planum, ab&longs;trahendo à rotatione <lb/>&longs;pontanea, vel coacta ad motum alterius, ex natura &longs;ua non <lb/>de&longs;cribinisi luxta men&longs;uram lationis, &longs;eu motus recti, qui &longs;imui <lb/>cum axe conficitur in anteriora, & cuius virtute de&longs;cribitur. <lb/></s>

<s id="N165CF">Deinde verò &longs;tabiliatur lineam, quæ à circulo, prædicto <lb/>modo de&longs;cribitur &longs;uper planum, ab&longs;trahendo à rotatione <lb/>&longs;pontanea, vel coacta ad motum alterius, ex natura &longs;ua non <lb/>de&longs;cribi nisi iuxta men&longs;uram lationis, &longs;eu motus recti, qui &longs;imul <lb/>cum axe conficitur in anteriora, & cuius virtute de&longs;cribitur. <lb/></s>

<s id="N165DB">Etenim ip&longs;a de&longs;cribi po&longs;&longs;et ab eodem circulo etiam &longs;ine ro<lb/>tatione, per vnicum punctum vt diximus, non autem &longs;ine re<lb/>cta aliqua latione. </s>

<s id="N165E2">Quamobrem in de&longs;criptione ip&longs;ius lineæ <lb/>rectæ &longs;uper planum, per &longs;e, & ab&longs;olutè loquendo, non habe<lb/>tur ratio de motu circulari, nec de &longs;patio circulariter pera<lb/>grato ab ip&longs;o circulo, &longs;ed de motu recto, ac &longs;patio, quod ip<lb/>&longs;e circulus &longs;imul <expan abbr="c&utilde;">cum</expan> axe percurrit, & ad cuius &longs;emper men<lb/>&longs;uram ip&longs;a recta linea excitatur. </s>

<s id="N165F3">Quamuis per accidens con<lb/>tingat, circulum deferentem, vel alium ex &longs;e, ac &longs;eor&longs;um ro<lb/>tando, tantum &longs;patium &longs;imul cum axe recta tran&longs;inittere, <lb/>quantum ip&longs;emet circulariter eodem tempore peragrare <lb/>valuerit. </s>

<s id="N165F3">Quamuis per accidens con<lb/>tingat, circulum deferentem, vel alium ex &longs;e, ac &longs;eor&longs;um ro<lb/>tando, tantum &longs;patium &longs;imul cum axe recta tran&longs;mittere, <lb/>quantum ip&longs;emet circulariter eodem tempore peragrare <lb/>valuerit. </s>

<s id="N165FE">Quia &longs;cilicet cum tota progre&longs;&longs;io à &longs;ua ip&longs;ius ro<pb pagenum="216" xlink:href="005/01/224.jpg"/>tatione dependeat, &longs;icut motus rectus progre&longs;&longs;ionis nece&longs;<lb/>&longs;ariò proportionatur motui circulari à quo pendet, ita <lb/>etiam linea de&longs;cripta per talem motum proportionari, & <lb/>adæquari debet lineæ de&longs;criptæ, &longs;eu peragratæ per circui<lb/>tionem. </s>

<s id="N16610">His itaque &longs;ic &longs;tabilitis, atque &longs;uppo&longs;itis tanquam certis, <lb/>& cuidentibus, ad primam partem quæ&longs;tionis &longs;imul, ac dif<lb/>ficultatis propo&longs;itæ re&longs;pondetur, circulum delatum &longs;emper <lb/>æquale &longs;patium, ac circulum deferentem &longs;uper planum ro<lb/>tando, rectà tran&longs;initrere, &longs;iue maior eo fuerit, &longs;iue minor; <lb/>quia illud non tran&longs;mittit ex vi &longs;uæ rotationis, ac iuxta <lb/>men&longs;uram &longs;uæ circumferentiæ, &longs;ed ex vi &longs;ui raptus, & a&longs;por<lb/>tationis. </s>

<s id="N16610">His itaque &longs;ic &longs;tabilitis, atque &longs;uppo&longs;itis tanquam certis, <lb/>& cui dentibus, ad primam partem quæ&longs;tionis &longs;imul, ac dif<lb/>ficultatis propo&longs;itæ re&longs;pondetur, circulum delatum &longs;emper <lb/>æquale &longs;patium, ac circulum deferentem &longs;uper planum ro<lb/>tando, rectà tran&longs;mittere, &longs;iue maior eo fuerit, &longs;iue minor; <lb/>quia illud non tran&longs;mittit ex vi &longs;uæ rotationis, ac iuxta <lb/>men&longs;uram &longs;uæ circumferentiæ, &longs;ed ex vi &longs;ui raptus, & a&longs;por<lb/>tationis. </s>

<s id="N16621">Siquidem tantum rectà progreditur, quantum à <lb/>deferente rapitur, & a&longs;portatur, licet aliàs eodem tempore <lb/>maiorem, aut minorem &longs;imul peragrat circuitum, de quo <lb/>nulla per &longs;e haberi debet ratio, vt præmonuimus. </s>

<s id="N1662A">Vnde nec <lb/>requiritur, vt cius motus circumuolutionis &longs;it æqualis mo<lb/>tui recto, nec vt linea recta, quam percurrit &longs;it æqualis cir<lb/>cunferentiæ &longs;ecundum quam rotando conuoluitur. </s>

<s id="N1662A">Vnde nec <lb/>requiritur, vt eius motus circumuolutionis &longs;it æqualis mo<lb/>tui recto, nec vt linea recta, quam percurrit &longs;it æqualis cir<lb/>cunferentiæ &longs;ecundum quam rotando conuoluitur. </s>

<s id="N16635">Ad &longs;ecundam verò partem quæ&longs;tionis re&longs;pondetur, cir<lb/>culum deferentem, vel alium, qui &longs;eor&longs;um per &longs;e &longs;uper pla<lb/>num circumuoluatur, quò maior ip&longs;e fuerit, maius &longs;patium <lb/>rectà in &longs;ua reuolutione percurrere, quò verò minor, minus. <lb/></s>

Line 3056

<s id="N16655">Adhuc tamen ex ei&longs;dem principijs <expan abbr="re&longs;põderi">re&longs;ponderi</expan> pote&longs;t, præ<lb/>fata nos experiri, quia minor circulus quando mouetur ad <lb/>motum alterius maioris motu mixto iam explicato, magis <lb/>participat de latione recta, quàm circulari; citius videlicet <lb/>progrediendo quàm rorando. </s>

<s id="N16664">Cogitur enim rectà progre-<pb pagenum="217" xlink:href="005/01/225.jpg"/>di iuxta progre&longs;&longs;um axis, ac circuli maioris, <expan abbr="&longs;imulq.">&longs;imulque</expan> tardius <lb/>rotari quàm ille, minus &longs;patium eodem tempore tran&longs;init<lb/>tendo in &longs;ua minori circumuolutione: <expan abbr="proindeq.">proindeque</expan> per talem <lb/>rotationem, rectam quandam lineam de&longs;cribit maiorem, <lb/>quam &longs;it eius circunferentia propria. </s>

<s id="N16664">Cogitur enim rectà progre-<pb pagenum="217" xlink:href="005/01/225.jpg"/>di iuxta progre&longs;&longs;um axis, ac circuli maioris, <expan abbr="&longs;imulq.">&longs;imulque</expan> tardius <lb/>rotari quàm ille, minus &longs;patium eodem tempore tran&longs;mit<lb/>tendo in &longs;ua minori circumuolutione: <expan abbr="proindeq.">proindeque</expan> per talem <lb/>rotationem, rectam quandam lineam de&longs;cribit maiorem, <lb/>quam &longs;it eius circunferentia propria. </s>

<s id="N1667C">E contra verò, nam <lb/>cum circulus maior mouetur ad motum minoris, magis par<lb/>ticipat de latione circulari, quàm recta. </s>

<s id="N16683">Siquidem, cogitur <lb/>citius moueri circulariter quàm rectà, cum eodem tempo<lb/>re maiorem ambitum, quàm circulus minor, æqualemque <lb/>rectam debeat percurrere: <expan abbr="ideoq.">ideoque</expan> minorem rectam in &longs;ua <lb/>circumuolutione de&longs;cribit, quàm &longs;it eiu&longs;inet circum&longs;erentia<lb/>qua illam attingit. </s>

<s id="N16683">Siquidem, cogitur <lb/>citius moueri circulariter quàm rectà, cum eodem tempo<lb/>re maiorem ambitum, quàm circulus minor, æqualemque <lb/>rectam debeat percurrere: <expan abbr="ideoq.">ideoque</expan> minorem rectam in &longs;ua <lb/>circumuolutione de&longs;cribit, quàm &longs;it eiu&longs;met circum&longs;erentia<lb/> qua illam attingit. </s>

<s id="N16694">Demum quia &longs;i circulus ex &longs;e, & inde<lb/>pendenter ab alio duplici hac latione feratur, &longs;iue maior &longs;it, <lb/>&longs;iue minor, &longs;emper æquè de vtraque participat. </s>

<s id="N1669B">Etenim tan<lb/>tum rectà progreditur quantum rotatur, nec aliunde rapi<lb/>tur, aut detinetur, vt magis vna quàm altera latione dimo<lb/>ueatur. </s>

<s id="N166A4">Quo fit vt linea quam &longs;uper planum de&longs;cribit, æqua<lb/>lis &longs;it propriæ circumferentiæ eique &longs;ecundum omnes par<lb/>tes commen&longs;urata. </s>

<s id="N166AD">Verum vt non &longs;olum cau&longs;a tam admirabilis effectus, &longs;ed <lb/>etiam modus quo ip&longs;e ab illa procedit expre&longs;&longs;ius innote<lb/>&longs;cat, ac difficultas vltimò propo&longs;ita ex directo penitus eua<lb/>datur, vlterius dicendum e&longs;t, circulum delatum non minus <lb/>ac deferentem, omnia ac &longs;ingula puncta, quæ &longs;unt in linea re<lb/>cta &longs;uper quam fertur per totidem puncta propria &longs;ucce&longs;&longs;i<lb/>uè attingere; ita vt in quolibet in&longs;tanti per nouum punctum <lb/>&longs;<gap/>æ peripheriæ attingat nouum punctum plani. </s>

<s id="N166C0">Etenim cum <lb/>planum à circulo attingatur per puncta, quæ &longs;unt extremita<lb/>tes diametrorum, & vterque circulus ex infinitis diametris <lb/>con&longs;tet; imò diametri cir culi maioris includant diametros <lb/>minoris; tot erunt puncta terminatiua diametrorum in cir<lb/>culo minori, quot &longs;unt in maiori, &longs;iue delato per quæ &longs;imili<lb/>ter omnia puncta &longs;ui plani valebit attingere. </s>

<s id="N166D1">Rur&longs;us dicendum e&longs;t tam circulum deferentem, quàm <lb/>circulum delatum omnes, ac &longs;ingulas partes diui&longs;ibiles, qu&etail; <lb/>&longs;unt in eadem linea plani per totidem partes &longs;uas &longs;ucce&longs;&longs;iuè <pb pagenum="218" xlink:href="005/01/226.jpg"/>attingere: hoc tamen di&longs;crimine, quod circulus deferens <lb/>illas attingit commen&longs;uratiuè, & adæquatè, circulus verò <lb/>delatus nonni&longs;i inadæquatè. </s>

<s id="N166E1">Sicut enim circulus deferens <lb/>&longs;iue maior &longs;it, &longs;iue minor con&longs;tat ex infinitis partibus inde<lb/>terminatis, quæ mediant inter infinita puncta, ita etiam cir<lb/>culus delatus, per ea&longs;que non minus attingere poterit infi<lb/>nitas partes, quæ &longs;unt in plano. </s>

<s id="N166EC">Diximus tamen attingere <lb/>inadæquatè. </s>

<s id="N166F1">Nam contactus adæquatus, & commen&longs;ura<lb/>tus duarum quantitatum, fit per æqualem applicationem <lb/>partium æqualium vtriu&longs;que quantitatis ad coexi&longs;tendum <lb/>&longs;imul in eodem &longs;patio loci: partes autem æqualiter appli<lb/>carinon po&longs;&longs;ant per lationes inæquales, nam ea e&longs;t inæqua<lb/>litas in applicatione, quæ e&longs;t in ip&longs;is lationibus, &longs;iue lationes <lb/>cadant in vtramque quantitatem, &longs;iue in alteram tantùm. <lb/></s>

<s id="N166F1">Nam contactus adæquatus, & commen&longs;ura<lb/>tus duarum quantitatum, fit per æqualem applicationem <lb/>partium æqualium vtriu&longs;que quantitatis ad coexi&longs;tendum <lb/>&longs;imul in eodem &longs;patio loci: partes autem æqualiter appli<lb/>cari non po&longs;&longs;unt per lationes inæquales, nam ea e&longs;t inæqua<lb/>litas in applicatione, quæ e&longs;t in ip&longs;is lationibus, &longs;iue lationes <lb/>cadant in vtramque quantitatem, &longs;iue in alteram tantùm. <lb/></s>

<s id="N16701">Quapropter cum tota applicatio partium circumferentiæ <lb/>ad attingendas partes plani &longs;uper quod rotatur, fiat tum ex <lb/>vi ip&longs;ius rotationis, qua &longs;ucce&longs;&longs;iuè ip&longs;æ partes inclinantur <lb/>ad illas, tum ex vi motus recti quo &longs;ucce&longs;&longs;iuè etiam progre<lb/>diendo ad ca&longs;dem perueniunt: hinc fit, vt &longs;i lationes ip&longs;æ <lb/>æqualiter procedant, quemadmo dum in motu mixto circuli <lb/>deferentis, aut alterius per &longs;e &longs;eor&longs;um rotantis, æqualiter <lb/>etiam alterius quantitatis partes, ad partes alterius appli<lb/>centur, ac &longs;e tangendo ad inuicem commen&longs;urentur, & <lb/>adæquentur: E contra verò &longs;i non procedant æqualiter ip<lb/>&longs;æ lationes, &longs;ed vna alteram excedat in velocitate, aut tardi<lb/>tate, vt in motu mixto cuiu&longs;libet circuli delati, inæqualiter <lb/>etiam partes ip&longs;ius ad partes plani applicentur, ac inadæ<lb/>quatè adinuicem commen&longs;urentur. </s>

<s id="N16701">Quapropter cum tota applicatio partium circumferentiæ <lb/>ad attingendas partes plani &longs;uper quod rotatur, fiat tum ex <lb/>vi ip&longs;ius rotationis, qua &longs;ucce&longs;&longs;iuè ip&longs;æ partes inclinantur <lb/>ad illas, tum ex vi motus recti quo &longs;ucce&longs;&longs;iuè etiam progre<lb/>diendo ad ea&longs;dem perueniunt: hinc fit, vt &longs;i lationes ip&longs;æ <lb/>æqualiter procedant, quemadmodum in motu mixto circuli <lb/>deferentis, aut alterius per &longs;e &longs;eor&longs;um rotantis, æqualiter <lb/>etiam alterius quantitatis partes, ad partes alterius appli<lb/>centur, ac &longs;e tangendo ad inuicem commen&longs;urentur, & <lb/>adæquentur: E contra verò &longs;i non procedant æqualiter ip<lb/>&longs;æ lationes, &longs;ed vna alteram excedat in velocitate, aut tardi<lb/>tate, vt in motu mixto cuiu&longs;libet circuli delati, inæqualiter <lb/>etiam partes ip&longs;ius ad partes plani applicentur, ac inadæ<lb/>quatè adinuicem commen&longs;urentur. </s>

<s id="N16720">Quod &longs;i non po&longs;&longs;it coexi&longs;tere in &longs;patio, exempli gratia <lb/>bipalmari cum linea recta bipalmari arcus circumferentiæ <lb/>paimaris, vel tripalmaris, quacunque rotatione ad inuicem <lb/>applicentur; hoc profectò intelligitur in quiete, atque in <lb/>termino ip&longs;ius motus: alioquin in tran&longs;itu, ac &longs;ucce&longs;siuè id <lb/>nullo modo repugnat, &longs;icutnec punctum globirectà &longs;uper <lb/>planum delati po&longs;t punctum ip&longs;ius plani, attingere partem <lb/>diui&longs;ibilem eiu&longs;dem plani, eique coexi&longs;tendo inadæquatè <pb pagenum="219" xlink:href="005/01/227.jpg"/>& &longs;ucce&longs;siuè commen&longs;urari, vt omnes penè Philo&longs;ophi fa<lb/>tentur. </s>

<s id="N16720">Quod &longs;i non po&longs;&longs;it coexi&longs;tere in &longs;patio, exempli gratia <lb/>bipalmari cum linea recta bipalmari arcus circumferentiæ <lb/>palmaris, vel tripalmaris, quacunque rotatione ad inuicem <lb/>applicentur; hoc profectò intelligitur in quiete, atque in <lb/>termino ip&longs;ius motus: alioquin in tran&longs;itu, ac &longs;ucce&longs;siuè id <lb/>nullo modo repugnat, &longs;icutnec punctum globi rectà &longs;uper <lb/>planum delati po&longs;t punctum ip&longs;ius plani, attingere partem <lb/>diui&longs;ibilem eiu&longs;dem plani, eique coexi&longs;tendo inadæquatè <pb pagenum="219" xlink:href="005/01/227.jpg"/>& &longs;ucce&longs;siuè commen&longs;urari, vt omnes penè Philo&longs;ophi fa<lb/>tentur. </s>

<s id="N16738">Maior enim vel minor velocitas atque &longs;ucce&longs;sio in <lb/>tran&longs;itu, & in partium applicatione, ex vi alterius lationis <lb/>æquipollet maiori, vel minori exten&longs;ioni ip&longs;ius quantitatis <lb/>ad replendum æquale &longs;patium ei, quod occupatur ab alia <lb/>quantitate in eodem tempore, qua ratione dicuntur coexi<lb/>&longs;tere, ac inter &longs;e coaptari. </s>

<s id="N16747">Res itaque &longs;ic e&longs;t concipienda, vt in reuolutione circuli <lb/>minoris ad motum maioris &longs;emper pars minor ip&longs;ius attin, <lb/>gat partem plani maiorem, quia velocius tran&longs;it per illam <lb/>motu recto, quàm rotando æqualem <expan abbr="dimen&longs;ion&etilde;">dimen&longs;ionem</expan> proptiam <lb/>po&longs;sit exponere, atque &longs;ecundum ip&longs;am &longs;e applicare. </s>

<s id="N16747">Res itaque &longs;ic e&longs;t concipienda, vt in reuolutione circuli <lb/>minoris ad motum maioris &longs;emper pars minor ip&longs;ius attin<lb/>gat partem plani maiorem, quia velocius tran&longs;it per illam <lb/>motu recto, quàm rotando æqualem <expan abbr="dimen&longs;ion&etilde;">dimen&longs;ionem</expan> proptiam <lb/>po&longs;sit exponere, atque &longs;ecundum ip&longs;am &longs;e applicare. </s>

<s id="N16756">Vnde <lb/>quod illi dee&longs;t exten&longs;ionis compen&longs;atur velociori &longs;ucce&longs;sio<lb/>ne, & applicatione &longs;ecundum lationem rectam ad coaptan<lb/>dum &longs;e parti majori. </s>

<s id="N1675F">Quod certè non e&longs;t intelligendum <lb/>fieri per raptationem, qua&longs;i per vnicum delati circuli pun<lb/>ctum plura plani puncta, vel per <expan abbr="eand&etilde;">eandem</expan>. </s>

<s id="N1676A">omnino circuli par<lb/>tem, plures plani partes attingerentur; &longs;ed per propriam, <lb/>rotationem. </s>

<s id="N16771">Quia ita rapitur, ac fertur &longs;uper illud motu re<lb/>cto, vt &longs;imul quamuis tardius feratur latione circulari per <lb/>quam partes, ac puncta ip&longs;ius peripheriæ iugiter mutantur. <lb/></s>

<s id="N16779">Cumque numerus in&longs;inities in&longs;initus punctorum, ac indeter<lb/>minatarum partium vtriu&longs;que circuli &longs;ufficiat ad mutatio<lb/>nem ip&longs;am continuam, & corre&longs;pondentiam, quam præ&longs;ta<lb/>re debet infinitis punctis, ac partibus plani, nullum relinqui<lb/>tur inconueniens, minorem circumferentiam maiori &longs;pario, <lb/>plani ob di&longs;parem lationem, & applicationem inadæquatè <lb/>in tran&longs;itu coaptari. </s>

<s id="N16779">Cumque numerus infinities infinitus punctorum, ac indeter<lb/>minatarum partium vtriu&longs;que circuli &longs;ufficiat ad mutatio<lb/>nem ip&longs;am continuam, & corre&longs;pondentiam, quam præ&longs;ta<lb/>re debet infinitis punctis, ac partibus plani, nullum relinqui<lb/>tur inconueniens, minorem circumferentiam maiori &longs;patio, <lb/>plani ob di&longs;parem lationem, & applicationem inadæquatè <lb/>in tran&longs;itu coaptari. </s>

<s id="N16788">Idemque è conuer&longs;o dici pote&longs;t in re<lb/>uolutione circuli maioris ad <expan abbr="mot&utilde;">motum</expan> minoris, vt &longs;cilicet &longs;em<lb/>per pars maior ip&longs;ius co re&longs;pondeat parti minori in plano <lb/>&longs;uper quod fertur, quia tardius tran&longs;it per illam motu recto, <lb/>quàm rotando æ qualem &longs;ibi dimen&longs;ionem po&longs;&longs;it attingere. <lb/></s>

<s id="N16788">Idemque è conuer&longs;o dici pote&longs;t in re<lb/>uolutione circuli maioris ad <expan abbr="mot&utilde;">motum</expan> minoris, vt &longs;cilicet &longs;em<lb/>per pars maior ip&longs;ius eo re&longs;pondeat parti minori in plano <lb/>&longs;uper quod fertur, quia tardius tran&longs;it per illam motu recto, <lb/>quàm rotando æqualem &longs;ibi dimen&longs;ionem po&longs;&longs;it attingere. <lb/></s>

<s id="N16798">Siquidem velocius rotando, quàm progrediendo, nequit at<lb/>tingere tantam dimen&longs;ionem in plano, quantam ip&longs;e exhi<lb/>bet per circumuolutionem. </s>

<s id="N1679F">Vnde quod ei &longs;upere&longs;t exten<lb/>&longs;ionis circularis compen&longs;atur tardiori &longs;ucce&longs;&longs;ione, & appli-<pb pagenum="220" xlink:href="005/01/228.jpg"/>cationem &longs;ecundum lationem rectam ad proportionandum <lb/>&longs;e parti minori. </s>

<s id="N167AB">Atque hæc in re tam ambigua &longs;i minus <lb/>demon&longs;tra&longs;&longs;e, &longs;altem indica&longs;&longs;e, vel tenta&longs;&longs;e &longs;ufficiat. </s>

Line 3095

<s id="N167BB">Nimirum cur in prædicta latione <lb/>duorum circulorum circa idem centrum &longs;ecundùm ab&longs;idem <lb/>circuli maioris, aliqua puncta circumferentiæ maioris, mi<lb/>nus progrediantur, quàm corre&longs;pondentia &longs;ibi puncta cir<lb/>cumferentiæ minoris; aliqua verò magis. </s>

<s id="N167C6">In maiori enim <lb/>circulo puncta vnius &longs;emicirculi minus progrediuntur, quam <lb/>puncta &longs;emicirculi corre&longs;pondentis in circulo minori. </s>

<s id="N167CD">Con<lb/>tra verò, puncta alterius &longs;emicirculi magis progrediuntur in <lb/>circulo maiori, quàm in minori, vt de motu particulari Epi<lb/>cyclorum docere &longs;olent A&longs;tronomi. </s>

<s id="N167D7">Quod maximè vide<lb/>tur admirandum <expan abbr="c&umacr;">cum</expan> vterque circulus &longs;impliciter, ac &longs;ecun<lb/>dum &longs;e totum ad motum axis progrediendo, æquale &longs;pa<lb/>rium percurrat, vt vidimus, ac probatum e&longs;t in præcedenti<lb/>bus. </s>

<s id="N167D7">Quod maximè vide<lb/>tur admirandum <expan abbr="c&umacr;">cum</expan> vterque circulus &longs;impliciter, ac &longs;ecun<lb/>dum &longs;e totum ad motum axis progrediendo, æquale &longs;pa<lb/>tium percurrat, vt vidimus, ac probatum e&longs;t in præcedenti<lb/>bus. </s>

<s id="N167E6">Ita tamen rem &longs;e habere &longs;ic o&longs;tenditur. </s>

Line 3105

<s id="N16815">Dicimus ergo punctum C in hac reuolutione <lb/>minus dextror&longs;um promoueri, quàm punctum G. </s>

<s id="N1681B">Demit<lb/>tatur enim à puncto C linea CO perpendicularis pariter <lb/>ip&longs;i KL, & à puncto G alia perpendicularis GP: & tunc <lb/>apparebit punctum C dextror&longs;um peragra&longs;&longs;e &longs;patium CM, <lb/>vel OL, quæ &longs;unt latera oppo&longs;ita, ac proinde æqualia re<lb/>ctanguli CMLO, vt pater per 34. propo&longs;it. </s>

<s id="N16828">primi. </s>

<s id="N1682B">Pun<lb/>ctum verò G con&longs;tabit peragraffe &longs;patium GM, &longs;eu PL <lb/>æquale huic. </s>

<s id="N1682B">Pun<lb/>ctum verò G con&longs;tabit peragra&longs;&longs;e &longs;patium GM, &longs;eu PL <lb/>æquale huic. </s>

<s id="N16832">At GM maior e&longs;t, quàm CM, eo quod <lb/>illam contineat, &longs;icut PL maior e&longs;t ip&longs;a OL propter ean<lb/>dem rationem. </s>

<s id="N16839">Ergo per talem circumuolutionem minus <lb/>dextror&longs;um progreditur punctum C, quod e&longs;t extremum <lb/>diainetri circuli maioris, quàm punctum G extremum <lb/>diametri contenti cit culi minoris. </s>

<s id="N16839">Ergo per talem circumuolutionem minus <lb/>dextror&longs;um progreditur punctum C, quod e&longs;t extremum <lb/>diametri circuli maioris, quàm punctum G extremum <lb/>diametri contenti sit culi minoris. </s>

<s id="N16844">Rur&longs;us verò dicimus punctum D eiu&longs;dem circuli maio<lb/>ris, minus pariter dextror&longs;um progredi, quam punctum H, <lb/>quod illi corre&longs;pondet in circulo minori. </s>

<s id="N1684B">Etenim po&longs;t præ<lb/>dictam reuolutionem centro I tran&longs;lato in M, ac C in <lb/>L, punctum D erit in linea AM vbi Q, (nempe in loco, <lb/>qui tantum &longs;anè di&longs;ter à puncto M, quantum di&longs;tat extre<lb/>mum D ip&longs;ius &longs;emidiametri DI ab ip&longs;o centro I,) pun<lb/>ctum verò H &longs;imiliter erit in R; ita vt &longs;emidiameter IHD <lb/>reperiatur in <expan abbr="MRq.">MRque</expan> Quapropter &longs;i ex duobus punctis QR <lb/>demittantur duæ perpendiculares in planum DL, quæ &longs;int <lb/>QS, & RT, &longs;patium progre&longs;&longs;ionis ip&longs;ius puncti D, erit <lb/>linea IQ, æqualis ip&longs;i DS: Spatium verò progre&longs;&longs;ionis <lb/>puncti H, erit linea IR, &longs;iue DT. C<gap/> lgitur minor &longs;it linea <lb/>DS ip&longs;a DT, &longs;iquidem continetur in illa, remanet vt pun<lb/>ctum D circuli maioris, minus. </s>

<s id="N1684B">Etenim po&longs;t præ<lb/>dictam reuolutionem centro I tran&longs;lato in M, ac C in <lb/>L, punctum D erit in linea AM vbi Q, (nempe in loco, <lb/>qui tantum &longs;anè di&longs;ter à puncto M, quantum di&longs;tat extre<lb/>mum D ip&longs;ius &longs;emidiametri DI ab ip&longs;o centro I,) pun<lb/>ctum verò H &longs;imiliter erit in R; ita vt &longs;emidiameter IHD <lb/>reperiatur in <expan abbr="MRq.">MRque</expan> Quapropter &longs;i ex duobus punctis QR <lb/>demittantur duæ perpendiculares in planum DL, quæ &longs;int <lb/>QS, & RT, &longs;patium progre&longs;&longs;ionis ip&longs;ius puncti D, erit <lb/>linea IQ, æqualis ip&longs;i DS: Spatium verò progre&longs;&longs;ionis <lb/>puncti H, erit linea IR, &longs;iue DT. Cum igitur minor &longs;it linea <lb/>DS ip&longs;a DT, &longs;iquidem continetur in illa, remanet vt pun<lb/>ctum D circuli maioris, minus. </s>

<s id="N1686C">dextror&longs;um promoueatur <lb/>quàm punctum H &longs;ibi corre&longs;pondens circuli minoris. </s>

Line 3123

<s id="N1689D">Id ip&longs;um tandem demon&longs;tratur de puncto B, quod cer<lb/>tè magis progreditur quàm F. </s>

<s id="N168A3">Quandoquidem in de&longs;cri<lb/>pta reuolutione &longs;emidiarneter IB con&longs;titueretur in MY in <lb/>qua cum contineatur &longs;emidiameter IF, ip&longs;um F con&longs;titue<lb/>retur in Z: completi&longs;que rectangulis BY, & BZ, erit &longs;pa<lb/>tium dextror&longs;um peragratum à B quantum IY; peragra<lb/>tum verò ab F; quantum IZ contentum in ip&longs;o IY, quod <lb/>propterea maius e&longs;t. </s>

<s id="N168A3">Quandoquidem in de&longs;cri<lb/>pta reuolutione &longs;emidiameter IB con&longs;titueretur in MY in <lb/>qua cum contineatur &longs;emidiameter IF, ip&longs;um F con&longs;titue<lb/>retur in Z: completi&longs;que rectangulis BY, & BZ, erit &longs;pa<lb/>tium dextror&longs;um peragratum à B quantum IY; peragra<lb/>tum verò ab F; quantum IZ contentum in ip&longs;o IY, quod <lb/>propterea maius e&longs;t. </s>

<s id="N168B2">Erunt igitur duo puncta circuli maio<lb/>ris, quæ minus dextror&longs;um progrediuntur, quàm puncta &longs;ibi <lb/>corre&longs;pondentia circuli minoris: alia verò duo quæ magis. <lb/></s>

<s id="N168BA">Quod etiam demon&longs;trari poterit de reliquis punctis eiu&longs;<lb/>dem &longs;emicirculi cum &longs;uo corre&longs;pondenti in vtroque circulo <lb/>&longs;i vterque bifariam &longs;ecetur per diametrum 3, 4, cuius extre<lb/>mitates nempe 3, & 4, in circulo maiori medient inter A, <lb/>& D, ac inter B & C. </s>

<s id="N168C6">Sicut in circulo minori extremita<lb/>tes 5, 6. medient inter E, & H, ac inter F, & G. </s>

Line 3143

<s id="N16945">Quod &longs;i puncta, quæ &longs;unt in arcubus 4 C, & 6 G dex<lb/>tror&longs;um vtraque pariter latione ferantur, &longs;icut reliqua pun<lb/>cta, quæ &longs;unt in &longs;emicirculis ABC, & EFG; & tamen pun<lb/>cta inter 4 C circuli maioris minus progrediantur, quàm <lb/>&longs;ibi corre&longs;pondentia in 6 G circuli minoris; hoc quidem <lb/>fit; nam cum ip&longs;i arcus maximè declinent deor&longs;um, parum <lb/>ambo progrediuntur ad dexteram virtute &longs;uæ circumuolu<lb/>tionis; <expan abbr="multumq.">multumque</expan> virtute motus recti, & a&longs;portantis ad mo<lb/>tum axis. </s>

<s id="N1695C">Cumque ratione &longs;itus, terminus à quo incipit mo<lb/>ueri prædictus arcus circuli minoris, magis di&longs;tet à termino, <pb pagenum="224" xlink:href="005/01/232.jpg"/>à quo incipit moueri arcus maioris, quàm &longs;it exce&longs;&longs;us pto<lb/>gre&longs;&longs;ionis ip&longs;ius arcus maioris ratione termini, ad quem <lb/>po&longs;tea pertingit, &longs;equitur ab&longs;olutè loquendo, magis progre<lb/>di dextror&longs;um prædictum arcum circuli minoris, quàm ar<lb/>cum circuli maioris. </s>

<s id="N1695C">Cumque ratione &longs;itus, terminus à quo incipit mo<lb/>ueri prædictus arcus circuli minoris, magis di&longs;tet à termino, <pb pagenum="224" xlink:href="005/01/232.jpg"/>à quo incipit moueri arcus maioris, quàm &longs;it exce&longs;&longs;us pro<lb/>gre&longs;&longs;ionis ip&longs;ius arcus maioris ratione termini, ad quem <lb/>po&longs;tea pertingit, &longs;equitur ab&longs;olutè loquendo, magis progre<lb/>di dextror&longs;um prædictum arcum circuli minoris, quàm ar<lb/>cum circuli maioris. </s>

<s id="N1696E"><expan abbr="Idemq.">Idemque</expan> è conuer&longs;o applicari pote&longs;t in <lb/>arcubus 3 A, 5 E ad o&longs;tendendum, cur puncta arcus <lb/>3 A circuli maioris, magis progrediantur quàm puncta ar<lb/>cus 5 E circuli minoris. </s>

<s id="N1697A">Nam licet vterque arcus per mo<lb/>tum circularem retrocedat, ac retrocedendo velocius mo<lb/>ueatur arcus maioris, quàm minoris; nihilominus ratione <lb/>&longs;itus, ac termini à quo, <expan abbr="c&utilde;">cum</expan> minor &longs;it exce&longs;&longs;us retroce&longs;&longs;ionis, <lb/>quàm antece&longs;&longs;ionis virtute motus rect, eo quod à remotio<lb/>ri termino arcus maioris promoueatur; hinc pariter fit, vt <lb/>maior &longs;it progre&longs;&longs;us dextror&longs;um maioris, quàm minoris ar<lb/>cus prædicti, &longs;icut & totius &longs;emicirculi 3 AB 4, quàm 5 <lb/>EF 6, vt dicebamus. </s>

<s id="N1697A">Nam licet vterque arcus per mo<lb/>tum circularem retrocedat, ac retrocedendo velocius mo<lb/>ueatur arcus maioris, quàm minoris; nihilominus ratione <lb/>&longs;itus, ac termini à quo, <expan abbr="c&utilde;">cum</expan> minor &longs;it exce&longs;&longs;us retroce&longs;&longs;ionis, <lb/>quàm antece&longs;&longs;ionis virtute motus recti, eo quod à remotio<lb/>ri termino arcus maioris promoueatur; hinc pariter fit, vt <lb/>maior &longs;it progre&longs;&longs;us dextror&longs;um maioris, quàm minoris ar<lb/>cus prædicti, &longs;icut & totius &longs;emicirculi 3 AB 4, quàm 5 <lb/>EF 6, vt dicebamus. </s>

<s id="N16993">Quæ&longs;tio Vige&longs;imaquinta.</s>

<s id="N16998">C<emph type="italics"/>vr lectulorum &longs;pondas &longs;ecundum duplam fa<lb/>ciunt proportionem, hanc quidem &longs;ex pedum, <lb/>vel paulò ampliorem, illam verò trium? </s>

<s id="N169A2">Curvè <lb/>non &longs;ecundum diametcum illos restibus exten<lb/>dunt? </s>

<s id="N169A2">Curvè <lb/>non &longs;ecundum diametrum illos restibus exten<lb/>dunt? </s>

<s id="N169A9">An tantos quidem magnitudine faciunt, <lb/>vt corporibus &longs;int proportionem babentes? <lb/></s>

<s id="N169A9">An tantos quidem magnitudine faciunt, <lb/>vt corporibus &longs;int proportionem habentes? <lb/></s>

<s id="N169AF">fiunt enim &longs;ic &longs;ecundum &longs;pondas dupli, longitudine quidem <lb/>cubitorum, latitudine verò duorum. </s>

<s id="N169B4">Extendunt autem illos <lb/>non &longs;ecundum diametrum, &longs;ed ex oppo&longs;ito, vt & ligna <lb/>minus di&longs;trabantur. </s>

<s id="N169B4">Extendunt autem illos <lb/>non &longs;ecundum diametrum, &longs;ed ex oppo&longs;ito, vt & ligna <lb/>minus di&longs;trahantur. </s>

<s id="N169BB">Celerrimè enim &longs;cinduntur &longs;ecundum na<lb/>turam diui&longs;a, & eodem modo distenta laborant maximè. </s>

<s id="N169C0">Am<lb/>plius quonia n opus e&longs;t, vt re&longs;tes pondus ferre po&longs;sint, &longs;i certè <lb/>pondere impo&longs;ito minus <expan abbr="laborab&utilde;t">laborabunt</expan>, &longs;i tran&longs;uer&longs;im, quàm &longs;i obli<lb/>què extendantur. </s>

<s id="N169C0">Am<lb/>plius quoniam opus e&longs;t, vt re&longs;tes pondus ferre po&longs;sint, &longs;i certè <lb/>pondere impo&longs;ito minus <expan abbr="laborab&utilde;t">laborabunt</expan>, &longs;i tran&longs;uer&longs;im, quàm &longs;i obli<lb/>què extendantur. </s>

<s id="N169CD">Præterea hoc etiam modo minus ab&longs;umitur <lb/>restium. </s>

<s id="N169D2">Sit enim lectulus AFGK, & bifariam diuidatur ip<lb/>&longs;a FG &longs;ecundum B: æqualia certè foramina &longs;unt in ip&longs;a <lb/>FA: latera enim &longs;unt æqualia, nam totum FG duplum est. <lb/></s>

<s id="N169DA">Extendunt autem, vt de&longs;criptum e&longs;t, ab ip&longs;o A ad ip&longs;um B: ita <lb/>vbi e&longs;t C ita e&longs;t D, ita vbi H, po&longs;tea vbi E, & <expan abbr="eod&etilde;">eodem</expan> &longs;emper mo-<emph.end type="italics"/><pb pagenum="225" xlink:href="005/01/233.jpg"/><emph type="italics"/>do, donee ad angulum peruenerint <expan abbr="ali&utilde;">alium</expan>. </s>

<s id="N169DA">Extendunt autem, vt de&longs;criptum e&longs;t, ab ip&longs;o A ad ip&longs;um B: ita <lb/>vbi e&longs;t C ita e&longs;t D, ita vbi H, po&longs;tea vbi E, & <expan abbr="eod&etilde;">eodem</expan> &longs;emper mo-<emph.end type="italics"/><pb pagenum="225" xlink:href="005/01/233.jpg"/><emph type="italics"/>do, donec ad angulum peruenerint <expan abbr="ali&utilde;">alium</expan>. </s>

<s id="N169F0">Duo enim anguli restis <lb/>babent capita: æquales autem &longs;unt re&longs;tes &longs;ecundum curuatu<lb/>ras, videlicet AB, & BC, ip&longs;is CD, & DH: & aliæ &longs;imi<lb/>li &longs;e babent modo, quoniam eadem demon&longs;tratio: ip&longs;a enim <lb/>AB æqualis est ip&longs;i HE, æqualia enim &longs;unt latera &longs;patÿ BG, <lb/>MA, & foramina æquè distant. </s>

<s id="N169F0">Duo enim anguli restis <lb/>habent capita: æquales autem &longs;unt re&longs;tes &longs;ecundum curuatu<lb/>ras, videlicet AB, & BC, ip&longs;is CD, & DH: & aliæ &longs;imi<lb/>li &longs;e habent modo, quoniam eadem demon&longs;tratio: ip&longs;a enim <lb/>AB æqualis est ip&longs;i HE, æqualia enim &longs;unt latera &longs;patij BG, <lb/>MA, & foramina æquè distant. </s>

<s id="N169FD">Ip&longs;a autem BG æqualis e&longs;t <lb/>ip&longs;i MA. </s>

<s id="N16A02">Angulus enim B æqualis e&longs;t angulo G. </s>

<s id="N16A06">In æquali<lb/>bus enim hic quidem intus, ille verò extra, & B quidem est <lb/>&longs;emirectus. </s>

<s id="N16A0D">Est enim FB æqualis ip&longs;i FA. </s>

<s id="N16A10">Et angulus vbi <lb/>F, rectus e&longs;t, B autem angulus æqualis ei, vbi e&longs;t G quo<lb/>niam quadratum altera parte longius, duplum e&longs;t: & ad me<lb/>dium e&longs;t curuatura, quamobrem AD ip&longs;i EG e&longs;t æqualis, bui<gap/><lb/>verò ip&longs;a HM. <expan abbr="Similiq.">Similique</expan> modo demon&longs;trantur aliæ, quoniam <lb/>æquales &longs;unt duæ, quæ &longs;ecundum euruaturas &longs;unt, duabus. <lb/></s>

<s id="N16A10">Et angulus vbi <lb/>F, rectus e&longs;t, B autem angulus æqualis ei, vbi e&longs;t G quo<lb/>niam quadratum altera parte longius, duplum e&longs;t: & ad me<lb/>dium e&longs;t curuatura, quamobrem AD ip&longs;i EG e&longs;t æqualis, huic <lb/>verò ip&longs;a HM. <expan abbr="Similiq.">Similique</expan> modo demon&longs;trantur aliæ, quoniam <lb/>æquales &longs;unt duæ, quæ &longs;ecundum curuaturas &longs;unt, duabus. <lb/></s>

<s id="N16A23">Quare manifestum e&longs;t, quod tot &longs;unt re&longs;tes in lectulo, quot <lb/>&longs;unt quatuor, &longs;icut AB. </s>

<s id="N16A29">Quanta autem foraminum e&longs;t mul<lb/>titudo in ip&longs;o FG laters, & in eius dimidio FB e&longs;t medietas. <lb/></s>

<s id="N16A29">Quanta autem foraminum e&longs;t mul<lb/>titudo in ip&longs;o FG latere, & in eius dimidio FB e&longs;t medietas. <lb/></s>

<s id="N16A2F">Quamobrem in dimidiato lectulo tantæ re&longs;tium magnitudines <lb/>erunt, quantum e&longs;t AB, multitudine verò tot, quot in BG &longs;unt <lb/>foramina. </s>

<s id="N16A36">Hoc autem nihil refert dicere, quàm quot &longs;unt in <lb/>ip&longs;is AF, & BF &longs;imul &longs;umptis. </s>

<s id="N16A3B">Si autem &longs;ecundum diame<lb/>trum extendantur re&longs;tes, quemadmodum &longs;e babet in lectulo <lb/>ABCD: dimidia non tot &longs;unt, quot amborum latera FAFG, <lb/>æqualia autem quot in ip&longs;is FB, FA, &longs;unt foramina. </s>

<s id="N16A3B">Si autem &longs;ecundum diame<lb/>trum extendantur re&longs;tes, quemadmodum &longs;e habet in lectulo <lb/>ABCD: dimidia non tot &longs;unt, quot amborum latera FAFG, <lb/>æqualia autem quot in ip&longs;is FB, FA, &longs;unt foramina. </s>

<s id="N16A44">Maio<lb/>res autem &longs;unt ip&longs;æ AF, BF, duæ exi&longs;tentes, quam AB. </s>

<s id="N16A4A">Qua<lb/>re re&longs;tis in tantùm maior, quantùm ambo latera diametro &longs;unt <lb/>maiora.<emph.end type="italics"/></s>

Line 3185

<s id="N16A7F">Philo&longs;ophus de lectulis minoribus cum qui ad vnum dum<lb/>taxat capiendum hominem cubantem efficiuntur, tum qui <lb/>re&longs;tibus, &longs;eu funibus quibu&longs;dam ad &longs;u&longs;tinendam culcitram <lb/>&longs;uper quam ille iaceat &longs;unt intexti, quemadmodum adhuc <lb/>in Italia licet rarò, frequentius tamen in Gallia, atque Hi&longs;pa<lb/>nia con&longs;piciuntur in v&longs;um traducti. </s>

<s id="N16A8E">Hinc itaque rur&longs;us qu<gap/>rit cur in huiu&longs;modi lectulis mu<lb/>niendis, re&longs;tes per tran&longs;uer&longs;um, & ex oppo&longs;ito, non autem <lb/>per diametrum extendantur. </s>

<s id="N16A8E">Hinc itaque rur&longs;us quaerit cur in huiu&longs;modi lectulis mu<lb/>niendis, re&longs;tes per tran&longs;uer&longs;um, & ex oppo&longs;ito, non autem <lb/>per diametrum extendantur. </s>

<s id="N16A97"><expan abbr="Aitq.">Aitque</expan> triplici ex cau&longs;a id fieri; <lb/>vel pariter in con&longs;uetudinem abij&longs;&longs;e. </s>

<s id="N16A9F">Primò nimirum, vt <lb/>&longs;pondarum ligna ab ip&longs;is re&longs;tibus minus di&longs;trahantur atque <lb/>&longs;cindantur; quandoquidem &longs;ci&longs;&longs;ioni magis obnoxia &longs;unt cum <lb/>per diametrum in eis funes inditi fuerint, ac di&longs;tenti. </s>

<s id="N16AA8">Nam <lb/>tunc qua&longs;i per longum iuxta naturales venulas, ac rimulas, <lb/>quibus ob&longs;equendo facilè &longs;equitur &longs;ci&longs;sio, ligna ip&longs;a vim pa<lb/>terentur, ac veluti &longs;ecarentur; &longs;ecus ac &longs;i per tran&longs;uer&longs;um, <lb/>ac &longs;ecundum latitudinem terebrata &longs;int, funesq per ip&longs;a <lb/>foramina <expan abbr="traducãtur">traducantur</expan>. </s>

<s id="N16AA8">Nam <lb/>tunc qua&longs;i per longum iuxta naturales venulas, ac rimulas, <lb/>quibus ob&longs;equendo facilè &longs;equitur &longs;ci&longs;sio, ligna ip&longs;a vim pa<lb/>terentur, ac veluti &longs;ecarentur; &longs;ecus ac &longs;i per tran&longs;uer&longs;um, <lb/>ac &longs;ecundum latitudinem terebrata &longs;int, <expan abbr="funesq">funesque</expan> per ip&longs;a <lb/>foramina <expan abbr="traducãtur">traducantur</expan>. </s>

<s id="N16AB9">Quia &longs;emper lignorum tramites tran&longs;<lb/>uer&longs;i funium pre<gap/>&longs;&longs;ioni magis re&longs;i&longs;tunt. </s>