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 1.7

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

version 1.7, 2004/08/20 12:19:57

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>

Legend:

Removed from v.1.6
changed lines
	Added in v.1.7