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| <?xml version="1.0"?> | <?xml version="1.0"?> |
| <!DOCTYPE archimedes SYSTEM "../dtd/archimedes.dtd" > | <!DOCTYPE archimedes SYSTEM "../dtd/archimedes.dtd" > |
| <archimedes xmlns:xlink="http://www.w3.org/1999/xlink"> <info> | <archimedes> <info> |
| <author>Borelli, Giovanni Alfonso</author> | <author>Borelli, Giovanni Alfonso</author> |
| <title>De motionibus naturalibus a gravitate pendentibus</title> | <title>De motionibus naturalibus a gravitate pendentibus</title> |
| <date>1670</date> | <date>1670</date> |
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| <s>De ip&longs;is porrò naturalibus motionibus corporum, <lb/>qu&ecedil; in medio fluido fiunt, &longs;cilicèt qua ratione, & qua-</s></p><pb xlink:href="010/01/010.jpg" pagenum="2"/><p type="main"> | <s>De ip&longs;is porrò naturalibus motionibus corporum, <lb/>qu&ecedil; in medio fluido fiunt, &longs;cilicèt qua ratione, & qua-</s></p><pb xlink:href="010/01/010.jpg" pagenum="2"/><p type="main"> |
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| <s><arrow.to.target n="marg1"/><lb/>re corpora varias magnitud<gap/>nes <gap/> pondera, & di­<lb/>uer&longs;as figuras habentia, moueantur maiori, aut mi­<lb/>nori velocìmte, certa quadam proportione in medio <lb/>fluido, nemo (quodl&longs;ciam) differuit. </s> | <s><arrow.to.target n="marg1"/><lb/>re corpora varias magnitudines, pondera, & di­<lb/>uer&longs;as figuras habentia, moueantur maiori, aut mi­<lb/>nori velocìmte, certa quadam proportione in medio <lb/>fluido, nemo (quodl&longs;ciam) differuit. </s> |
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| <s>Igitur hanc <lb/>phy&longs;ico-mechanices partem hactenùs de&longs;iderata&mtail; <lb/>exponere, ac &longs;upplere animus e&longs;t; &longs;ed ne fa&longs;tidio&longs;&atail; <lb/>repetitione earum rerum, quæ ab alijs tradita &longs;unt, <lb/>lectores de tineam, &longs;upponam ea omnia, quæ in ele­<lb/>mentis mechanicis tradita &longs;unt de natura libræ, vec­<lb/>tis, trochleæ, & de reliquis ab hi&longs;ce in&longs;trumentis pen­<lb/>dentibus, eorum que naturam participantibus. </s> | <s>Igitur hanc <lb/>phy&longs;ico-mechanices partem hactenùs de&longs;iderata&mtail; <lb/>exponere, ac &longs;upplere animus e&longs;t; &longs;ed ne fa&longs;tidio&longs;&atail; <lb/>repetitione earum rerum, quæ ab alijs tradita &longs;unt, <lb/>lectores de tineam, &longs;upponam ea omnia, quæ in ele­<lb/>mentis mechanicis tradita &longs;unt de natura libræ, vec­<lb/>tis, trochleæ, & de reliquis ab hi&longs;ce in&longs;trumentis pen­<lb/>dentibus, eorum que naturam participantibus. </s> |
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| <s><margin.target id="marg1"/>Cap. | <s><margin.target id="marg1"/>Cap. |
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| 1. Cor­<lb/>porum mo­<lb/>tus in medio<gap/><lb/>fluido fieri.</s></p><p type="main"> | 1. Cor­<lb/>porum mo­<lb/>tus in medio <lb/>fluido fieri.</s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>De Momentis Grauium con&longs;istentium & fluidorum <lb/>in ij&longs;dem fluidis innatantium.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>De Momentis Grauium con&longs;istentium & fluidorum <lb/>in ij&longs;dem fluidis innatantium.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main"> |
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| <s>Suppono primò quòd quodlibet corpus, &longs;iuè den­<lb/>&longs;um, &longs;iuè fluidum, ex ijs quæ globum terra-queu&mtail; <lb/>componunt, graue e&longs;t, exercetque vim &longs;eù conatum <lb/>fuæ grauitatis, etiam &longs;i in fluido &longs;ibi aut homogeneo, <lb/>aut non, con&longs;tituatur. </s> | <s>Suppono primò quòd quodlibet corpus, &longs;iuè den­<lb/>&longs;um, &longs;iuè fluidum, ex ijs quæ globum terra-queu&mtail; <lb/>componunt, graue e&longs;t, exercetque vim &longs;eù conatum <lb/>fuæ grauitatis, etiam &longs;i in fluido &longs;ibi aut homogeneo, <lb/>aut non, con&longs;tituatur. </s> |
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| <s>hoc autem &longs;uo loco euidenti&longs;­<lb/>&longs;<gap/>is rationibus, ac experimentis confirmabitur. </s></p><p type="main"> | <s>hoc autem &longs;uo loco euidenti&longs;­<lb/>&longs;imis rationibus, ac experimentis confirmabitur. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>SVPPOSITIO II.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>SVPPOSITIO II.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s>hoc mani­<lb/>fe&longs;tum e&longs;t quia cùm omnes partes terrenæ vt graues <lb/>naturali in&longs;tinctu ad terræ centrum accedere conen-<pb xlink:href="010/01/012.jpg" pagenum="4"/><arrow.to.target n="marg3"/><lb/>tur, hocque earum de&longs;iderium expleri minimè po&longs;&longs;it <lb/>ni&longs;i mediante motu, igitur ce&longs;&longs;ante fine nece&longs;&longs;ariò <lb/>medium quoque ce&longs;&longs;at, &longs;cilicet quando non pote&longs;t <lb/>graue aliquod magis, quàm prius ad terræ centrum <lb/>accedere, tunc nequa quam moue bitur. </s> | <s>hoc mani­<lb/>fe&longs;tum e&longs;t quia cùm omnes partes terrenæ vt graues <lb/>naturali in&longs;tinctu ad terræ centrum accedere conen-<pb xlink:href="010/01/012.jpg" pagenum="4"/><arrow.to.target n="marg3"/><lb/>tur, hocque earum de&longs;iderium expleri minimè po&longs;&longs;it <lb/>ni&longs;i mediante motu, igitur ce&longs;&longs;ante fine nece&longs;&longs;ariò <lb/>medium quoque ce&longs;&longs;at, &longs;cilicet quando non pote&longs;t <lb/>graue aliquod magis, quàm prius ad terræ centrum <lb/>accedere, tunc nequa quam moue bitur. </s> |
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| <s>ex quo &longs;e qui­<lb/>tur vt prædicta corpora quie&longs;cant, quandoquidem &longs;i <lb/>mouerentur, aut deberent à centro telluris recedere <lb/>& remoueri, vel lateraliter circumferri, in primo ea­<lb/>&longs;u &longs;e queretur operatio contraria naturali in&longs;tinctui <lb/>grauium, quod e&longs;t impo&longs;&longs;ibile; in &longs;ecundo verò ca&longs;u <lb/>efficeretur operatio vanæ, & &longs;i ti&longs;tratoria, <gap/>il eni&mtail; <lb/>graue præterea acquireret cùm non amplius ad terræ <lb/>centru accedere po&longs;&longs;et ex hy pothe&longs;i, ab&longs;urdum verò <lb/>e&longs;t atque repugnatnaturam operari ca&longs;n, & ab&longs;qu&etail; <lb/>fine; igitur e&longs;t impo&longs;&longs;ibile vt corpora, quæ ad <expan abbr="centrũ">centrum</expan> <lb/>terræ accedere nequeunt, vllo pacto moueantur; qua <lb/>propter nece&longs;&longs;e e&longs;t vt in eodem &longs;itu fixè quie&longs;cant in <lb/>quo prius degebant. </s></p><p type="margin"> | <s>ex quo &longs;equi­<lb/>tur vt prædicta corpora quie&longs;cant, quandoquidem &longs;i <lb/>mouerentur, aut deberent à centro telluris recedere <lb/>& remoueri, vel lateraliter circumferri, in primo ca­<lb/>&longs;u &longs;equeretur operatio contraria naturali in&longs;tinctui <lb/>grauium, quod e&longs;t impo&longs;&longs;ibile; in &longs;ecundo verò ca&longs;u <lb/>efficeretur operatio vanæ, & &longs;i fru&longs;tratoria, nil enim <lb/>graue præterea acquireret cùm non amplius ad terræ <lb/>centru accedere po&longs;&longs;et ex hypothe&longs;i, ab&longs;urdum verò <lb/>e&longs;t atque repugnat naturam operari ca&longs;n, & ab&longs;que <lb/>fine; igitur e&longs;t impo&longs;&longs;ibile vt corpora, quæ ad <expan abbr="centrũ">centrum</expan> <lb/>terræ accedere nequeunt, vllo pacto moueantur; qua <lb/>propter nece&longs;&longs;e e&longs;t vt in eodem &longs;itu fixè quie&longs;cant in <lb/>quo prius degebant. </s></p><p type="margin"> |
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| <s><margin.target id="marg3"/>Cap. | <s><margin.target id="marg3"/>Cap. |
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| <s><emph type="center"/><emph type="italics"/>SVPPOSITIO IV.<emph.end type="italics"/><emph.end type="center"/><lb/><arrow.to.target n="marg4"/><!-- KEEP S--></s></p><p type="margin"> | <s><emph type="center"/><emph type="italics"/>SVPPOSITIO IV.<emph.end type="italics"/><emph.end type="center"/><lb/><arrow.to.target n="marg4"/><!-- KEEP S--></s></p><p type="margin"> |
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| <s><margin.target id="marg4"/>Archimedis <lb/>&longs;<gap/></s></p><p type="main"> | <s><margin.target id="marg4"/>Archimedis <lb/>&longs;suppositio. </s></p><p type="main"> |
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| <s>Præterea Archimedes &longs;uppo&longs;uit vt primum prin­<lb/>cipium per &longs;e notum, quod eiu&longs;dem fluidi con&longs;i&longs;ten­<lb/>tis, partes quæ &longs;int continuat&ecedil; in eodem plano hori­<lb/>zontaliminus pre&longs;&longs;æ debeant eijci expellique &longs;ur&longs;um <lb/><expan abbr="perp&etilde;diculariter">perpendiculariter</expan> à partibus eiu&longs;dem fluidi magis <expan abbr="cõ-pre&longs;&longs;is">con­<lb/>pre&longs;&longs;is</expan>, hoc verò principium, licèt veri&longs;&longs;imum &longs;it, ha­<lb/>bettamen aliquam ob&longs;curitatem, cùm minimè eui­<lb/>dens &longs;it, quamobrem partes ein&longs;dem fluidi po&longs;&longs;int <lb/>magis, <gap/> minus com<gap/>rimi; nec pariter euidenter </s></p><pb xlink:href="010/01/013.jpg" pagenum="5"/><p type="main"> | <s>Præterea Archimedes &longs;uppo&longs;uit vt primum prin­<lb/>cipium per &longs;e notum, quod eiu&longs;dem fluidi con&longs;i&longs;ten­<lb/>tis, partes quæ &longs;int continuat&ecedil; in eodem plano hori­<lb/>zontaliminus pre&longs;&longs;æ debeant eijci expellique &longs;ur&longs;um <lb/><expan abbr="perp&etilde;diculariter">perpendiculariter</expan> à partibus eiu&longs;dem fluidi magis <expan abbr="cõpre&longs;&longs;is">com­<lb/>pre&longs;&longs;is</expan>, hoc verò principium, licèt veri&longs;&longs;imum &longs;it, ha­<lb/>bet tamen aliquam ob&longs;curitatem, cùm minimè eui­<lb/>dens &longs;it, quamobrem partes eiu&longs;dem fluidi po&longs;&longs;int <lb/>magis, aut minus comprimi; nec pariter euidenter </s></p><pb xlink:href="010/01/013.jpg" pagenum="5"/><p type="main"> |
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| <s><arrow.to.target n="marg5"/><lb/>percipitur quomodo à naturali operatione, de&longs;cen­<lb/>&longs;us nempè deor&longs;um, produci debeat operatio <expan abbr="quædã">quædam</expan> <lb/>contraria, a&longs;cen&longs;us nimirum alterius partis eiu&longs;dem <lb/>fluidi &longs;cilicet recedendo a centro telluris. </s> | <s><arrow.to.target n="marg5"/><lb/>percipitur quomodo à naturali operatione, de&longs;cen­<lb/>&longs;us nempè deor&longs;um, produci debeat operatio <expan abbr="quædã">quædam</expan> <lb/>contraria, a&longs;cen&longs;us nimirum alterius partis eiu&longs;dem <lb/>fluidi &longs;cilicet recedendo a centro telluris. </s> |
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| <s>SIt graue AB exten&longs;um, vel compo&longs;itum ex dua­<lb/>bus partibus in extremitatibus eiu&longs;dem libræ <lb/>horizontalis AB di&longs;po&longs;itis, & commune centrum gra­<lb/>uitatis earum &longs;it D. &longs;u&longs;ti­<lb/><figure id="id.010.01.013.1.jpg" xlink:href="010/01/013/1.jpg"/><lb/>neatur po&longs;tea, fulciatur­<lb/>que tota libra ex puncto <lb/>C remoto à centro graui­<lb/>tatis D. dico quòd pars <lb/>eius oppo&longs;ita B &longs;ur&longs;u&mtail; <lb/>a&longs;cendet per arcum BF, <lb/>hac &longs;olummodo de cau&longs;&atail; <lb/>quia integrum graue AB magis, quàm prius ad cen­<lb/>trum terræ accedit. </s> | <s>SIt graue AB exten&longs;um, vel compo&longs;itum ex dua­<lb/>bus partibus in extremitatibus eiu&longs;dem libræ <lb/>horizontalis AB di&longs;po&longs;itis, & commune centrum gra­<lb/>uitatis earum &longs;it D. &longs;u&longs;ti­<lb/><figure id="id.010.01.013.1.jpg" xlink:href="010/01/013/1.jpg"/><lb/>neatur po&longs;tea, fulciatur­<lb/>que tota libra ex puncto <lb/>C remoto à centro graui­<lb/>tatis D. dico quòd pars <lb/>eius oppo&longs;ita B &longs;ur&longs;u&mtail; <lb/>a&longs;cendet per arcum BF, <lb/>hac &longs;olummodo de cau&longs;&atail; <lb/>quia integrum graue AB magis, quàm prius ad cen­<lb/>trum terræ accedit. </s> |
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| <s>quia duæ partes graues A & B <lb/>exercent &longs;uam grauitatem & conatum compre&longs;&longs;iuum <lb/>in centro communi earum grauitatum D; e&longs;t que <lb/>prædictum centrum D re mo<gap/>m a fulcimento &longs;tabili <lb/>C, igitur efformabitur veluti fune-pendulum CD <pb xlink:href="010/01/014.jpg" pagenum="6"/><arrow.to.target n="marg6"/><lb/>horizontaliter con&longs;titutum, &longs;u&longs;pen&longs;um, & alligatum <lb/>in centro C & pondus vniuer&longs;um applicatum eriti&ntail; <lb/>centro D extremo fili, vel lineæ CD: &longs;ed penduli na­<lb/>tura talis e&longs;t vt conetur deor&longs;um ferri per arcum qua­<lb/>drantis DE circa centrum eius &longs;ixum C v&longs;que ad lo­<lb/>cum infimum E, quod magis ad centrum terræ appro­<lb/>ximatur, quàm in &longs;itu horizontali D & patet quòd <lb/>vniuer&longs;a hæcoperatio nece&longs;&longs;aria, & naturalis e&longs;t de­<lb/>pendens à de&longs;cen&longs;u totius grauis. </s> | <s>quia duæ partes graues A & B <lb/>exercent &longs;uam grauitatem & conatum compre&longs;&longs;iuum <lb/>in centro communi earum grauitatum D; e&longs;t que <lb/>prædictum centrum D remotum à fulcimento &longs;tabili <lb/>C, igitur efformabitur veluti fune-pendulum CD <pb xlink:href="010/01/014.jpg" pagenum="6"/><arrow.to.target n="marg6"/><lb/>horizontaliter con&longs;titutum, &longs;u&longs;pen&longs;um, & alligatum <lb/>in centro C & pondus vniuer&longs;um applicatum eriti&ntail; <lb/>centro D extremo fili, vel lineæ CD: &longs;ed penduli na­<lb/>tura talis e&longs;t vt conetur deor&longs;um ferri per arcum qua­<lb/>drantis DE circa centrum eius &longs;ixum C v&longs;que ad lo­<lb/>cum infimum E, quod magis ad centrum terræ appro­<lb/>ximatur, quàm in &longs;itu horizontali D & patet quòd <lb/>vniuer&longs;a hæcoperatio nece&longs;&longs;aria, & naturalis e&longs;t de­<lb/>pendens à de&longs;cen&longs;u totius grauis. </s> |
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| <s>& e&longs;t impo&longs;&longs;ibil&etail; <lb/>vt fune pendulum CD ad in fimum &longs;itum CE perduca­<lb/>tur ab&longs;que eo quòd libra rigida &longs;itum perpendicula­<lb/>rem ad horizontem acquirat, quale e&longs;t GCF, hoc ve­<lb/>ro minimè acquiri pote&longs;t ni&longs;i pars minus grauis libræ <lb/>B &longs;ur&longs;um a&longs;cendat per arcum BF, igitur ca&longs;us, & de­<lb/>&longs;cen&longs;us totius corporis grauis AB à &longs;itu eleuato D ad <lb/>infimum E e&longs;t vera & legitima cau&longs;a a&longs;cen&longs;us corpo­<lb/>ris grauis B per arcum BF, quod fuerat o&longs;tendendum. </s></p><p type="margin"> | <s>& e&longs;t impo&longs;&longs;ibil&etail; <lb/>vt fune pendulum CD ad in fimum &longs;itum CE perduca­<lb/>tur ab&longs;que eo quòd libra rigida &longs;itum perpendicula­<lb/>rem ad horizontem acquirat, quale e&longs;t GCF, hoc ve­<lb/>ro minimè acquiri pote&longs;t ni&longs;i pars minus grauis libræ <lb/>B &longs;ur&longs;um a&longs;cendat per arcum BF, igitur ca&longs;us, & de­<lb/>&longs;cen&longs;us totius corporis grauis AB à &longs;itu eleuato D ad <lb/>infimum E e&longs;t vera & legitima cau&longs;a a&longs;cen&longs;us corpo­<lb/>ris grauis B per arcum BF, quod fuerat o&longs;tendendum. </s></p><p type="margin"> |
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| <s>vt <lb/>in appo&longs;ito &longs;chemat&etail;. <lb/></s> | <s>vt <lb/>in appo&longs;ito &longs;chemat&etail;. <lb/></s> |
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| <s>&longs;it tympanum æreum AF <lb/>BG comprehen&longs;um à &longs;u­<lb/>perficie curua cylindrica ærea & à duabus laminis <lb/>planis circularibus inter &longs;e parallelis optimè læuiga­<lb/>tis & cum illa coaptatis conglutinati&longs;que, verùm in­<lb/>tra tympani cauitatem collocetur lamina plana FCG <lb/>quæ v&longs;um diaphragmatis præ&longs;tet & medietas cylin­<lb/>dri FCGA aqua ver hydrargiro repleatur, reliqu&atail; <lb/>verò medictas BFCG oleo velaere oppleta &longs;it; lami­<lb/>na verò FCG axi HC annexa & ferruminata intr&atail; <lb/>tympanum & circa axim fixum C manubrio aliquo <lb/>H fixè retineri & reuolui po&longs;&longs;it, hac lege vt exactè <pb xlink:href="010/01/018.jpg" pagenum="10"/><arrow.to.target n="marg10"/><lb/>tangat &longs;uperficies internas ambarum ba&longs;ium plana­<lb/>rum & cauam &longs;uperficiem curuam eiu&longs;dem tympani: <lb/>oportet auten<gap/> vt ad in&longs;tar epi&longs;tomij exacti&longs;&longs;inrè dia­<lb/>phragn<gap/>a illud reuolutum ab&longs;que vlla rima occludat <lb/>egre&longs;&longs;umque impediat aquæ vel mercurio in &longs;emicy­<lb/>lindro FAG contento, remanente reliquo &longs;patio G <lb/>BF aere, vel oleo oppleto, &longs;itque præterea moles to­<lb/>tius tympani &longs;u&longs;pen&longs;a in ip&longs;o axi C aflixo duobus ful­<lb/>cris vt liberè circumuolui tympanum po&longs;&longs;it in plano <lb/>perpendiculari ad horizontem; tunc &longs;i vi manus ma­<lb/>nubrium H eique annexum diaphragma FCG perpe­<lb/>tuò in &longs;itu verticali ad horizontem retineretur, pro­<lb/>culdubio (dicèbat amicus) haberemus in tali ca&longs;u li­<lb/>bram radiorum æqualium perpetuam imaginaria&mtail; <lb/>ACB quæ ab inæqualibus ponderibus premeretur, <lb/>fcilicèt à pondere emi&longs;phærij mercurialis vel aquei <lb/>FAG radius CA grauaretur, dum oppo&longs;itus radius C <lb/>B à leuiori pondere olei, vel aeris deprimeretur. </s> | <s>&longs;it tympanum æreum AF <lb/>BG comprehen&longs;um à &longs;u­<lb/>perficie curua cylindrica ærea & à duabus laminis <lb/>planis circularibus inter &longs;e parallelis optimè læuiga­<lb/>tis & cum illa coaptatis conglutinati&longs;que, verùm in­<lb/>tra tympani cauitatem collocetur lamina plana FCG <lb/>quæ v&longs;um diaphragmatis præ&longs;tet & medietas cylin­<lb/>dri FCGA aqua ver hydrargiro repleatur, reliqu&atail; <lb/>verò medictas BFCG oleo velaere oppleta &longs;it; lami­<lb/>na verò FCG axi HC annexa & ferruminata intr&atail; <lb/>tympanum & circa axim fixum C manubrio aliquo <lb/>H fixè retineri & reuolui po&longs;&longs;it, hac lege vt exactè <pb xlink:href="010/01/018.jpg" pagenum="10"/><arrow.to.target n="marg10"/><lb/>tangat &longs;uperficies internas ambarum ba&longs;ium plana­<lb/>rum & cauam &longs;uperficiem curuam eiu&longs;dem tympani: <lb/>oportet autem vt ad in&longs;tar epi&longs;tomij exacti&longs;&longs;imè dia­<lb/>phragma illud reuolutum ab&longs;que vlla rima occludat <lb/>egre&longs;&longs;umque impediat aquæ vel mercurio in &longs;emicy­<lb/>lindro FAG contento, remanente reliquo &longs;patio G <lb/>BF aere, vel oleo oppleto, &longs;itque præterea moles to­<lb/>tius tympani &longs;u&longs;pen&longs;a in ip&longs;o axi C aflixo duobus ful­<lb/>cris vt liberè circumuolui tympanum po&longs;&longs;it in plano <lb/>perpendiculari ad horizontem; tunc &longs;i vi manus ma­<lb/>nubrium H eique annexum diaphragma FCG perpe­<lb/>tuò in &longs;itu verticali ad horizontem retineretur, pro­<lb/>culdubio (dicèbat amicus) haberemus in tali ca&longs;u li­<lb/>bram radiorum æqualium perpetuam imaginariam <lb/>ACB quæ ab inæqualibus ponderibus premeretur, <lb/>&longs;cilicèt à pondere emi&longs;phærij mercurialis vel aquei <lb/>FAG radius CA grauaretur, dum oppo&longs;itus radius C <lb/>B à leuiori pondere olei, vel aeris deprimeretur. </s> |
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| <s>& <lb/>quia horum inæqualium ponderum centrum grauita­<lb/>tis &longs;emper in aliquo puncto D intercepto inter C & <lb/>A caderet, igitur &longs;emper libra AB flecti deberet de­<lb/>or&longs;um ad partes A, vel potius con&longs;titueretur pendu­<lb/>lum horizontale CD &longs;u&longs;pen&longs;um in centro C & ideò <lb/>pendulum de&longs;cendere deberet per arcum DE; qui&atail; <lb/>verò fluidum grauius FAG de primi non po&longs;&longs;et ob im­<lb/>pedimentum diaphragmatis FCG in &longs;itu verticali à <lb/>virtute manus retenti, &longs;equeretur vt vniuer&longs;um &longs;e­<lb/>micylindricum mercurij comprimendo & calcando <lb/>curuam &longs;uper&longs;iciem tympani AG, quæ volubilis e&longs;t <pb xlink:href="010/01/019.jpg" pagenum="11"/><arrow.to.target n="marg11"/><lb/>eam impelleret, proindeque deor&longs;um conuerti debe­<lb/>ret ab A ver&longs;us G cum à nullo retinaculo impediatur, <lb/>igitur &longs;emper reuolui po&longs;&longs;et tympanum ab A ver&longs;us <lb/>G quia &longs;emper per&longs;eueraret eadem cau&longs;a vertiginis <lb/>&longs;cilicet perpetuò con&longs;eruaretur pendulum CD in &longs;itu <lb/>horizontali, & ideò &longs;emper premeret & calcaret tym­<lb/>pani &longs;uperficiem AG; quapropter tali artificio con­<lb/>&longs;equi po&longs;&longs;e videtur motus perpetuus prædicti tym­<lb/>pani. </s></p><p type="margin"> | <s>& <lb/>quia horum inæqualium ponderum centrum grauita­<lb/>tis &longs;emper in aliquo puncto D intercepto inter C & <lb/>A caderet, igitur &longs;emper libra AB flecti deberet de­<lb/>or&longs;um ad partes A, vel potius con&longs;titueretur pendu­<lb/>lum horizontale CD &longs;u&longs;pen&longs;um in centro C & ideò <lb/>pendulum de&longs;cendere deberet per arcum DE; qui&atail; <lb/>verò fluidum grauius FAG de primi non po&longs;&longs;et ob im­<lb/>pedimentum diaphragmatis FCG in &longs;itu verticali à <lb/>virtute manus retenti, &longs;equeretur vt vniuer&longs;um &longs;e­<lb/>micylindricum mercurij comprimendo & calcando <lb/>curuam &longs;uper&longs;iciem tympani AG, quæ volubilis e&longs;t <pb xlink:href="010/01/019.jpg" pagenum="11"/><arrow.to.target n="marg11"/><lb/>eam impelleret, proindeque deor&longs;um conuerti debe­<lb/>ret ab A ver&longs;us G cum à nullo retinaculo impediatur, <lb/>igitur &longs;emper reuolui po&longs;&longs;et tympanum ab A ver&longs;us <lb/>G quia &longs;emper per&longs;eueraret eadem cau&longs;a vertiginis <lb/>&longs;cilicet perpetuò con&longs;eruaretur pendulum CD in &longs;itu <lb/>horizontali, & ideò &longs;emper premeret & calcaret tym­<lb/>pani &longs;uperficiem AG; quapropter tali artificio con­<lb/>&longs;equi po&longs;&longs;e videtur motus perpetuus prædicti tym­<lb/>pani. </s></p><p type="margin"> |
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| <s><emph type="center"/>PROP. IX.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/>PROP. IX.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Corpus aqua grauius in ea demer&longs;um dum de&longs;cendit consti­<lb/>tuit cu<gap/> æqualimole collateralis fluidi libram <expan abbr="æqualiũ">æqualium</expan> <lb/>radiorum, cuius centrum grauitatis continenter <lb/>de&longs;cendende eleuat leuiorem aquam col­<lb/>lateralem, &longs;emperque renouatur <lb/>horizontalis libra.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Corpus aqua grauius in ea demer&longs;um dum de&longs;cendit consti­<lb/>tuit cum æqualimole collateralis fluidi libram <expan abbr="æqualiũ">æqualium</expan> <lb/>radiorum, cuius centrum grauitatis continenter <lb/>de&longs;cendende eleuat leuiorem aquam col­<lb/>lateralem, &longs;emperque renouatur <lb/>horizontalis libra.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main"> |
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| <s>HOc præmi&longs;&longs;o intelligatur iam vas aquà plenum <lb/>RSTX, & intra eius profunditatem appona­<lb/>tur pri&longs;ma marmoreum ABCD, & producantur eius <lb/>ba&longs;es horizontales AB, & CD <lb/><figure id="id.010.01.033.1.jpg" xlink:href="010/01/033/1.jpg"/><lb/>v&longs;que ad G & H, atque planu&mtail; <lb/>AD producatur &longs;ur&longs;um, & deor­<lb/>&longs;um v&longs;que ad M, & V perpendi­<lb/>culariter ad horizontem. </s> | <s>HOc præmi&longs;&longs;o intelligatur iam vas aquà plenum <lb/>RSTX, & intra eius profunditatem appona­<lb/>tur pri&longs;ma marmoreum ABCD, & producantur eius <lb/>ba&longs;es horizontales AB, & CD <lb/><figure id="id.010.01.033.1.jpg" xlink:href="010/01/033/1.jpg"/><lb/>v&longs;que ad G & H, atque planu&mtail; <lb/>AD producatur &longs;ur&longs;um, & deor­<lb/>&longs;um v&longs;que ad M, & V perpendi­<lb/>culariter ad horizontem. </s> |
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| <s>hic iam <lb/>habemus <expan abbr="&longs;iphon&etilde;">&longs;iphonem</expan> oblongum in &longs;e <lb/>ip&longs;um circumductum, vt in pr&ecedil;­<lb/>cedenti propo&longs;itione expo&longs;itum fuit, quia aqua BM <lb/>GHVC ambit pri&longs;ma &longs;upernè, lateraliter, & infernè, <lb/>nec moueri pote&longs;t <expan abbr="de&longs;c&etilde;dendo">de&longs;cendendo</expan> pri&longs;ma AC quin aqua <pb xlink:href="010/01/034.jpg" pagenum="26"/><arrow.to.target n="marg26"/><lb/>&longs;ubiecta CID è &longs;uo loco expellatur, & lateralitèr fluat <lb/>ver&longs;us P, circumfera turque &longs;ur&longs;um v&longs;que ad locu&mtail; <lb/>relictum à pr&ecedil;dicto pri&longs;mate lapideo in E. &longs;unt igitur <lb/>duæ partes MT, & MS veluti duo canales laterales <lb/>&longs;iphonis, quitamen &longs;e&longs;e contingunt in communi la­<lb/>tere MV; prætereà duæ portiones aquæ &longs;upremæ XA, <lb/>& MG cùm &longs;int homogeneæ, æquè graues &longs;pecie, & <lb/>æque altæ, &longs;e mutuò æquilibrantur, pariterque duæ <lb/>portiones aqueæ &longs;ubiectæ CV, & DS pariter æquili­<lb/>brantur, vnde patet quòd tantummodo comparari <lb/>debent inter &longs;e duo corpora collateralia &longs;axum nimi­<lb/>rum BD, & aqua AH, quæ ab ei&longs;dem planis horizon­<lb/>talibus BG, & HC comprehenduntur, & hæc &longs;imiliter <lb/>fulciuntur &longs;u&longs;tentanturque à plano aquæ &longs;ubiectæ H <lb/>C <expan abbr="nõ">non</expan> firmo, & impermeabili, &longs;ed facilè à &longs;uo loco <lb/>amouibili & cedenti. </s> | <s>hic iam <lb/>habemus <expan abbr="&longs;iphon&etilde;">&longs;iphonem</expan> oblongum in &longs;e <lb/>ip&longs;um circumductum, vt in pr&ecedil;­<lb/>cedenti propo&longs;itione expo&longs;itum fuit, quia aqua BM <lb/>GHVC ambit pri&longs;ma &longs;upernè, lateraliter, & infernè, <lb/>nec moueri pote&longs;t <expan abbr="de&longs;c&etilde;dendo">de&longs;cendendo</expan> pri&longs;ma AC quin aqua <pb xlink:href="010/01/034.jpg" pagenum="26"/><arrow.to.target n="marg26"/><lb/>&longs;ubiecta CID è &longs;uo loco expellatur, & lateralitèr fluat <lb/>ver&longs;us P, circumfera turque &longs;ur&longs;um v&longs;que ad locu&mtail; <lb/>relictum à pr&ecedil;dicto pri&longs;mate lapideo in E. &longs;unt igitur <lb/>duæ partes MT, & MS veluti duo canales laterales <lb/>&longs;iphonis, quitamen &longs;e&longs;e contingunt in communi la­<lb/>tere MV; prætereà duæ portiones aquæ &longs;upremæ XA, <lb/>& MG cùm &longs;int homogeneæ, æquè graues &longs;pecie, & <lb/>æque altæ, &longs;e mutuò æquilibrantur, pariterque duæ <lb/>portiones aqueæ &longs;ubiectæ CV, & DS pariter æquili­<lb/>brantur, vnde patet quòd tantummodo comparari <lb/>debent inter &longs;e duo corpora collateralia &longs;axum nimi­<lb/>rum BD, & aqua AH, quæ ab ei&longs;dem planis horizon­<lb/>talibus BG, & HC comprehenduntur, & hæc &longs;imiliter <lb/>fulciuntur &longs;u&longs;tentanturque à plano aquæ &longs;ubiectæ H <lb/>C <expan abbr="nõ">non</expan> firmo, & impermeabili, &longs;ed facilè à &longs;uo loco <lb/>amouibili & cedenti. </s> |
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| <s>in&longs;i&longs;tunt igitur prædicta duo cor <lb/>pora BD, & AH non &longs;ecùs &longs;u&longs;pen&longs;a ac &longs;i &longs;uper libram <lb/>HC inniterentur; huius verò centrum mobile e&longs;&longs;et <lb/>punctum intermedium D, vbi nimirum libra HC bi­<lb/>fariàm &longs;ecatur, & &longs;i à centro grauitatis O &longs;axi BD ad <lb/>centrum P grauitatis aquæ AH recta linea <expan abbr="coniũga-tur">coniunga­<lb/>tur</expan>, eaque &longs;ecetur in Y reciprocè &longs;ecundùm propor­<lb/>tionem grauitatum eorumdem corporum, patet Y e&longs;­<lb/>&longs;e centrum grauitatis communis &longs;axi BD, & aquæ A <lb/>H, cùmque libra PO &longs;ecetur bifariàm à plano MV in <lb/>Q iam con&longs;u<gap/>get fune-pendulum QY horizontaliter <lb/>excen&longs;um versùs O ob exce&longs;&longs;um grauitatis &longs;axi &longs;upra <lb/>aquæ pondus &longs;pecificum, igitur nece&longs;sè e&longs;t vt tot&atail; <lb/>libra flecta<gap/> <expan abbr="deorsũ">deorsum</expan>, & &longs;ic &longs;axum BD <expan abbr="de&longs;c&etilde;det">de&longs;cendet</expan>. </s> | <s>in&longs;i&longs;tunt igitur prædicta duo cor­<lb/>pora BD, & AH non &longs;ecùs &longs;u&longs;pen&longs;a ac &longs;i &longs;uper libram <lb/>HC inniterentur; huius verò centrum mobile e&longs;&longs;et <lb/>punctum intermedium D, vbi nimirum libra HC bi­<lb/>fariàm &longs;ecatur, & &longs;i à centro grauitatis O &longs;axi BD ad <lb/>centrum P grauitatis aquæ AH recta linea <expan abbr="coniũga-tur">coniunga­<lb/>tur</expan>, eaque &longs;ecetur in Y reciprocè &longs;ecundùm propor­<lb/>tionem grauitatum eorumdem corporum, patet Y e&longs;­<lb/>&longs;e centrum grauitatis communis &longs;axi BD, & aquæ A <lb/>H, cùmque libra PO &longs;ecetur bifariàm à plano MV in <lb/>Q iam con&longs;urget fune-pendulum QY horizontaliter <lb/>excen&longs;um versùs O ob exce&longs;&longs;um grauitatis &longs;axi &longs;upra <lb/>aquæ pondus &longs;pecificum, igitur nece&longs;sè e&longs;t vt tot&atail; <lb/>libra flectatur <expan abbr="deorsũ">deorsum</expan>, & &longs;ic &longs;axum BD <expan abbr="de&longs;c&etilde;det">de&longs;cendet</expan>. </s> |
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| <s>Quia <pb xlink:href="010/01/035.jpg" pagenum="27"/><arrow.to.target n="marg27"/><lb/>verò in de&longs;cen&longs;u aqua &longs;ubiecta expul&longs;a ex I curuo iti­<lb/>nere &longs;ur&longs;um fluit per ZF v&longs;que ad E denuò renouatur <lb/>libra horizontalis, comparanturque inter &longs;e &longs;axum B <lb/>D cum aqua collaterali in nouo &longs;itu horizontali de­<lb/>pre&longs;&longs;iori exi&longs;tente, igitur denuò eadem proportione <lb/>di&longs;&longs;ecta libra imaginaria horizontali, <expan abbr="fune-pendulũ">fune-pendulum</expan> <lb/>æquale priori eadem vi flectetur <expan abbr="deorsũ">deorsum</expan>, <expan abbr="de&longs;cendetq;">de&longs;cendetque</expan> <lb/>centrum grauitatis eius motu perpendiculari ad hori­<lb/>zontem quòu&longs;que ad fundum va&longs;is &longs;axum pertingat. </s></p><p type="margin"> | <s>Quia <pb xlink:href="010/01/035.jpg" pagenum="27"/><arrow.to.target n="marg27"/><lb/>verò in de&longs;cen&longs;u aqua &longs;ubiecta expul&longs;a ex I curuo iti­<lb/>nere &longs;ur&longs;um fluit per ZF v&longs;que ad E denuò renouatur <lb/>libra horizontalis, comparanturque inter &longs;e &longs;axum B <lb/>D cum aqua collaterali in nouo &longs;itu horizontali de­<lb/>pre&longs;&longs;iori exi&longs;tente, igitur denuò eadem proportione <lb/>di&longs;&longs;ecta libra imaginaria horizontali, <expan abbr="fune-pendulũ">fune-pendulum</expan> <lb/>æquale priori eadem vi flectetur <expan abbr="deorsũ">deorsum</expan>, <expan abbr="de&longs;cendetq;">de&longs;cendetque</expan> <lb/>centrum grauitatis eius motu perpendiculari ad hori­<lb/>zontem quòu&longs;que ad fundum va&longs;is &longs;axum pertingat. </s></p><p type="margin"> |
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| <s><emph type="center"/>PROP. X.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/>PROP. X.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Idip&longs;um sentingit, &longs;ed inuer&longs;o ordine cum corpus de­<lb/><gap/>er&longs;um minùs graue aqua collaterali fueris.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Idip&longs;um sentingit, &longs;ed inuer&longs;o ordine cum corpus de­<lb/>mer&longs;um minùs graue aqua collaterali fueris.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main"> |
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| <s>SI po&longs;tea pri&longs;ma BD fuerit ligneum, & minùs gra­<lb/>ue &longs;pecie quam aqua AH, tunc ij&longs;dem manen­<lb/>tibus &longs;olummodò centrum grauitatis communis Y <lb/>cadet ad partes aquæ inter Q & P, & proindè vniuer­<lb/>&longs;um graue compo&longs;itum ex aqua, & ligno vim faciet <lb/><expan abbr="impell&etilde;do">impellendo</expan> deor&longs;um centrum gra­<lb/><figure id="id.010.01.035.1.jpg" xlink:href="010/01/035/1.jpg"/><lb/>uitatis Y, & ideò vehementiùs <expan abbr="cõ-primetur">con­<lb/>primetur</expan> aqua &longs;ubiecta HDVS, <lb/>hæc verò ob eius continuitatem <lb/>& naturam <expan abbr="con&longs;i&longs;t&etilde;tem">con&longs;i&longs;tentem</expan>, quæ pre&longs;­<lb/>&longs;ioni non cedit, nece&longs;&longs;ariò impel­<lb/>letur versùs I, & &longs;ic vim faciet &longs;ur­<lb/>&longs;um exprimendo ligni &longs;uperficiem DC; at dum <expan abbr="lignũ">lignum</expan> <lb/>a&longs;cendit, oportet vt expellat è &longs;uo loco <expan abbr="incumbent&etilde;">incumbentem</expan> <lb/>aquam E, quæ tran&longs;uer&longs;ali & obliquo motu perduce-<pb xlink:href="010/01/036.jpg" pagenum="28"/><arrow.to.target n="marg28"/><lb/>tur ab E per FZ versù<gap/>, & &longs;ic à prædicto motu circu­<lb/>lari aquæ ambiemis lignum expelletur &longs;ursùm; atta­<lb/>men ratio mechanica <gap/>ius actionis pendet ex eo, <lb/>quòd libra horizontalis imaginaria PO flectitur per­<lb/>petuò deorsùm quidem ad partes centri grauitatis Y <lb/>circa centrum Q, & &longs;ursùm ad partes O. &longs;ed &longs;ummo­<lb/>perè animaduerten dum e&longs;t prædictam libram imagi­<lb/>nariam horizontalem renouari &longs;ucce&longs;&longs;iuè prout <expan abbr="lignũ">lignum</expan> <lb/>a&longs;cendit, <expan abbr="comparaturq;">comparaturque</expan> cum alijs lateralibus pri&longs;ma­<lb/>tibus aqueis, quæ &longs;ucce&longs;&longs;iuè offendit intercepta in­<lb/>ter prædicta plana horizontalia GB, & HC: nece&longs;sè <lb/>ergo e&longs;t vt lignum prædictum numquàm quie&longs;cat in­<lb/>tra aquam demer&longs;um quòu&longs;que ad &longs;upremam <expan abbr="libellã">libellam</expan> <lb/>aquæ RX perducatur; in&longs;uperque aliqua eius por­<lb/>tio emineat. </s></p><p type="margin"> | <s>SI po&longs;tea pri&longs;ma BD fuerit ligneum, & minùs gra­<lb/>ue &longs;pecie quam aqua AH, tunc ij&longs;dem manen­<lb/>tibus &longs;olummodò centrum grauitatis communis Y <lb/>cadet ad partes aquæ inter Q & P, & proindè vniuer­<lb/>&longs;um graue compo&longs;itum ex aqua, & ligno vim faciet <lb/><expan abbr="impell&etilde;do">impellendo</expan> deor&longs;um centrum gra­<lb/><figure id="id.010.01.035.1.jpg" xlink:href="010/01/035/1.jpg"/><lb/>uitatis Y, & ideò vehementiùs <expan abbr="cõ-primetur">con­<lb/>primetur</expan> aqua &longs;ubiecta HDVS, <lb/>hæc verò ob eius continuitatem <lb/>& naturam <expan abbr="con&longs;i&longs;t&etilde;tem">con&longs;i&longs;tentem</expan>, quæ pre&longs;­<lb/>&longs;ioni non cedit, nece&longs;&longs;ariò impel­<lb/>letur versùs I, & &longs;ic vim faciet &longs;ur­<lb/>&longs;um exprimendo ligni &longs;uperficiem DC; at dum <expan abbr="lignũ">lignum</expan> <lb/>a&longs;cendit, oportet vt expellat è &longs;uo loco <expan abbr="incumbent&etilde;">incumbentem</expan> <lb/>aquam E, quæ tran&longs;uer&longs;ali & obliquo motu perduce-<pb xlink:href="010/01/036.jpg" pagenum="28"/><arrow.to.target n="marg28"/><lb/>tur ab E per FZ versùs I, & &longs;ic à prædicto motu circu­<lb/>lari aquæ ambiemis lignum expelletur &longs;ursùm; atta­<lb/>men ratio mechanica huius actionis pendet ex eo, <lb/>quòd libra horizontalis imaginaria PO flectitur per­<lb/>petuò deorsùm quidem ad partes centri grauitatis Y <lb/>circa centrum Q, & &longs;ursùm ad partes O. &longs;ed &longs;ummo­<lb/>perè animaduertendum e&longs;t prædictam libram imagi­<lb/>nariam horizontalem renouari &longs;ucce&longs;&longs;iuè prout <expan abbr="lignũ">lignum</expan> <lb/>a&longs;cendit, <expan abbr="comparaturq;">comparaturque</expan> cum alijs lateralibus pri&longs;ma­<lb/>tibus aqueis, quæ &longs;ucce&longs;&longs;iuè offendit intercepta in­<lb/>ter prædicta plana horizontalia GB, & HC: nece&longs;sè <lb/>ergo e&longs;t vt lignum prædictum numquàm quie&longs;cat in­<lb/>tra aquam demer&longs;um quòu&longs;que ad &longs;upremam <expan abbr="libellã">libellam</expan> <lb/>aquæ RX perducatur; in&longs;uperque aliqua eius por­<lb/>tio emineat. </s></p><p type="margin"> |
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| <s><margin.target id="marg28"/>Cap. | <s><margin.target id="marg28"/>Cap. |
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| <s><emph type="center"/>PROP. XI.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/>PROP. XI.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Si verò corpus &longs;olidum po<gap/>tur &longs;upra aquæ libellam, <lb/>tunc de&longs;cen&longs;us commanis centri grauitatis non <lb/>efficietur per lineam perpendicularem ad <lb/>horizon<gap/>m &longs;ed motu curuoper <lb/>parabolam.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Si verò corpus &longs;olidum ponitur &longs;upra aquæ libellam, <lb/>tunc de&longs;cen&longs;us communis centri grauitatis non <lb/>efficietur per lineam perpendicularem ad <lb/>horizontem &longs;ed motu curuo per <lb/>parabolam.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main"> |
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| <s>IN progre&longs;&longs;u prædictæ operationis notabilis e&longs;t va­<lb/>riatio &longs;itus centri grauitatis eius & mechanicæ eius <lb/>operationis. </s></p><p type="main"> | <s>IN progre&longs;&longs;u prædictæ operationis notabilis e&longs;t va­<lb/>riatio &longs;itus centri grauitatis eius & mechanicæ eius <lb/>operationis. </s></p><p type="main"> |
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| <s><emph type="center"/>PROP. XII.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/>PROP. XII.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>I<gap/> a&longs;cen&longs;u, vel de&longs;cen&longs;u &longs;olidi in fluide neque libra linearis <lb/>e&longs;t, neque habet centrum grauitatis in vno puncto <lb/>&longs;ed libra e&longs;&longs;e &longs;olet &longs;uperficialis, cuius fulci­<lb/>mentum e&longs;t linea circa centrum figuræ, <lb/>& grauitas communis exercetur <lb/>quoque in linea aliqua.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>In a&longs;cen&longs;u, vel de&longs;cen&longs;u &longs;olidi in fluide neque libra linearis <lb/>e&longs;t, neque habet centrum grauitatis in vno puncto <lb/>&longs;ed libra e&longs;&longs;e &longs;olet &longs;uperficialis, cuius fulci­<lb/>mentum e&longs;t linea circa centrum figuræ, <lb/>& grauitas communis exercetur <lb/>quoque in linea aliqua.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main"> |
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| <s>SOllummodò indicabo <expan abbr="nõ">non</expan> &longs;emper v&longs;urpari in præ­<lb/>dicta mechanica operatione punctum, quod <expan abbr="cõ-mune">con­<lb/>mune</expan> centrum grauitatis vocari vulgò &longs;olet; propte­<lb/>rea quòd libra compo&longs;ita ex &longs;olido & fluido ambien­<lb/>te non &longs;emper linearis e&longs;t, &longs;ed &longs;uper ficiem aliquando <lb/>componit, in qua nedum fulcimentum, &longs;ed etiam lo­<lb/>cus vbi exercetur communis grauitas linea e&longs;&longs;e &longs;olet <lb/>aliquando recta, aliquando curua, & multoties com­<lb/>po&longs;ita ex pluribus rectis. </s> | <s>SOllummodò indicabo <expan abbr="nõ">non</expan> &longs;emper v&longs;urpari in præ­<lb/>dicta mechanica operatione punctum, quod <expan abbr="cõ-mune">con­<lb/>mune</expan> centrum grauitatis vocari vulgò &longs;olet; propte­<lb/>rea quòd libra compo&longs;ita ex &longs;olido & fluido ambien­<lb/>te non &longs;emper linearis e&longs;t, &longs;ed &longs;uper ficiem aliquando <lb/>componit, in qua nedum fulcimentum, &longs;ed etiam lo­<lb/>cus vbi exercetur communis grauitas linea e&longs;&longs;e &longs;olet <lb/>aliquando recta, aliquando curua, & multoties com­<lb/>po&longs;ita ex pluribus rectis. </s> |
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| <s>præterea &longs;uppo&longs;uimus <lb/>cum eodem Archimede partes eiu&longs;dem fluidi minùs <lb/>pre&longs;&longs;as expelli ac &longs;ubleuari &longs;ur&longs;um à partibus <expan abbr="eiu&longs;d&etilde;">eiu&longs;dem</expan> <lb/>fluidi magis compre&longs;&longs;is, & grauatis; ex qua hypothe­<lb/>&longs;i deducitur quodliber fluidum, veluti aqua e&longs;t, gra­<lb/>uitatem habere eamque exercere etiam in proprio <lb/>loco, & naturali regione, &longs;cilicèt aquam ip&longs;am dum in <lb/>tota aqua quie&longs;cit tunc quoque grauitatem exercere <lb/>&longs;ubiecta corpora comprimendo. <lb/><arrow.to.target n="marg34"/></s></p><p type="margin"> | <s>præterea &longs;uppo&longs;uimus <lb/>cum eodem Archimede partes eiu&longs;dem fluidi minùs <lb/>pre&longs;&longs;as expelli ac &longs;ubleuari &longs;ur&longs;um à partibus <expan abbr="eiu&longs;d&etilde;">eiu&longs;dem</expan> <lb/>fluidi magis compre&longs;&longs;is, & grauatis; ex qua hypothe­<lb/>&longs;i deducitur quodliber fluidum, veluti aqua e&longs;t, gra­<lb/>uitatem habere eamque exercere etiam in proprio <lb/>loco, & naturali regione, &longs;cilicèt aquam ip&longs;am dum in <lb/>tota aqua quie&longs;cit tunc quoque grauitatem exercere <lb/>&longs;ubiecta corpora comprimendo. <lb/><arrow.to.target n="marg34"/></s></p><p type="margin"> |
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| <s><margin.target id="marg34"/>FxArchi­<lb/>mede dedu­<lb/>cunt aqu<gap/><lb/>in ipsa aqu<gap/><lb/>non grauita­<lb/>re, & id <expan abbr="ipsũ">ipsum</expan> <lb/>Petipatetic<gap/><lb/>affirma<gap/>t.</s></p><p type="main"> | <s><margin.target id="marg34"/>Ex Archi­<lb/>mede dedu­<lb/>cunt aquam <lb/>in ipsa aqua <lb/>non grauita­<lb/>re, & id <expan abbr="ipsũ">ipsum</expan> <lb/>Peripatetici <lb/>affirmaret.</s></p><p type="main"> |
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| <s>Hoc autem à plurimis negatur qui putant Archi­<lb/>medem oppo&longs;itum &longs;en&longs;i&longs;&longs;e. </s> | <s>Hoc autem à plurimis negatur qui putant Archi­<lb/>medem oppo&longs;itum &longs;en&longs;i&longs;&longs;e. </s> |
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| <s>igitur huiu&longs;­<lb/>modi facultates ordinatæ &longs;unt ad perducenda <expan abbr="elem&etilde;-taria">elemen­<lb/>taria</expan> corpora ad propria loca vt ibidem quie&longs;cant; <lb/>nec vlteriùs v&longs;um aliquem habere po&longs;&longs;unt, quando­<lb/>quidem &longs;i præterea motum pro&longs;e querentur in &longs;uis lo­<lb/>cis perturbarent & confunderent naturalem fituatio-<pb xlink:href="010/01/043.jpg" pagenum="35"/><arrow.to.target n="marg36"/><lb/>nem eorumdem corporum. </s> | <s>igitur huiu&longs;­<lb/>modi facultates ordinatæ &longs;unt ad perducenda <expan abbr="elem&etilde;-taria">elemen­<lb/>taria</expan> corpora ad propria loca vt ibidem quie&longs;cant; <lb/>nec vlteriùs v&longs;um aliquem habere po&longs;&longs;unt, quando­<lb/>quidem &longs;i præterea motum pro&longs;e querentur in &longs;uis lo­<lb/>cis perturbarent & confunderent naturalem fituatio-<pb xlink:href="010/01/043.jpg" pagenum="35"/><arrow.to.target n="marg36"/><lb/>nem eorumdem corporum. </s> |
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| <s>& profectò e&longs;t con&longs;enta­<lb/>neum vt elementa non nitantur de&longs;erere propria lo­<lb/>ca, & propterea careant illo naturali &longs;t<gap/>ulo &longs;eu prin­<lb/>cipio motus quo impellebantur antequam ad &longs;ua na­<lb/>turalia loca perueni&longs;&longs;ent; hinc deducitur nullum ele­<lb/>mentum in proprio loco grauitatem, aut leuitate&mtail; <lb/>habere, &longs;ed aqua in ip&longs;a aqua po&longs;ita in propria, & na­<lb/>turali regione degit & &longs;ic aer in aere, ergo neutru&mtail; <lb/>horum elementorum grauitatem in &longs;uo loco habet, <lb/>aut exercet. </s> | <s>& profectò e&longs;t con&longs;enta­<lb/>neum vt elementa non nitantur de&longs;erere propria lo­<lb/>ca, & propterea careant illo naturali &longs;timulo &longs;eu prin­<lb/>cipio motus quo impellebantur antequam ad &longs;ua na­<lb/>turalia loca perueni&longs;&longs;ent; hinc deducitur nullum ele­<lb/>mentum in proprio loco grauitatem, aut leuitatem <lb/>habere, &longs;ed aqua in ip&longs;a aqua po&longs;ita in propria, & na­<lb/>turali regione degit & &longs;ic aer in aere, ergo neutrum <lb/>horum elementorum grauitatem in &longs;uo loco habet, <lb/>aut exercet. </s> |
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| <s>& primo quoad Archimedem pertinet <lb/>videntur aduer&longs;arij nequaquam tanti viri mente&mtail; <lb/>a&longs;&longs;equuti &longs;ui&longs;&longs;e vt ex eius verbis &longs;atis <expan abbr="&longs;uperq;">&longs;uperque</expan> patet. <lb/></s> | <s>& primo quoad Archimedem pertinet <lb/>videntur aduer&longs;arij nequaquam tanti viri mente&mtail; <lb/>a&longs;&longs;equuti &longs;ui&longs;&longs;e vt ex eius verbis &longs;atis <expan abbr="&longs;uperq;">&longs;uperque</expan> patet. <lb/></s> |
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| <s><emph type="center"/><emph type="italics"/>Aqua va&longs;is fundum çomprimit &longs;ua grauitate.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Aqua va&longs;is fundum çomprimit &longs;ua grauitate.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main"> |
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| <s>SEd hoc euidentius &longs;ic patebit, &longs;it fi&longs;tula vitrea A <lb/>NO perpendiculariter ad horizontem erect&atail;, <lb/>repleaturquè aqua, &longs;eù quolibet alio fluido cor­<lb/>pore, & ductis innumeris planis horizonti <expan abbr="æquidi&longs;tã-tibus">æquidi&longs;tan­<lb/>tibus</expan> &longs;ubdiuidatur vniuer&longs;um fluidum i&ntail; <lb/><figure id="id.010.01.046.1.jpg" xlink:href="010/01/046/1.jpg"/><lb/>laminas gracillimas &longs;eù membranas æquè <lb/>altas AB, BC, CD, DE, EF, FM, & MN. & <lb/>primò &longs;i verum e&longs;t, vt aduer&longs;arij credunt <lb/>aquam in ip&longs;amet aqua collocatam <expan abbr="nõ">non</expan> gra­<lb/>uitare, igitur &longs;uprema laminula aquea AB <lb/>pror&longs;us <expan abbr="nõ">non</expan> comprimet &longs;ubiectam <expan abbr="membra-nã">membra­<lb/>nam</expan> aqueam BC, &longs;cilicet vim nullam &longs;uper eam exer­<lb/>cebit (hoc enim grauitatis nomen indicat) neque eam <lb/>deor&longs;um impellet perinde ac &longs;i aqua &longs;uprema AB non <lb/>ade&longs;&longs;et, proindeque hæc non augebit grauitatem in­<lb/>ferioris laminæ BC, aliàs &longs;uprema aqua AB pondera-<pb xlink:href="010/01/047.jpg" pagenum="39"/><arrow.to.target n="marg40"/><lb/>ret, comprimeretque &longs;ubiectam aquam BC, quod e&longs;t <lb/>contra aduer&longs;arij hypothe&longs;im; eadem ratione vniuer­<lb/>&longs;a aqua ABC nil ponderabit, ne que comprimet &longs;ub­<lb/>iectam laminam aqueam CD, & tota aqua AD nec <lb/>etiam comprimet aut grauitatem inferet &longs;upra infe­<lb/>riorem <expan abbr="aquã">aquam</expan> DE; idip&longs;um procul dubio aflirmari de­<lb/>bet de reliquis omnibus laminulis fluidis totam alti­<lb/>tudinem aquæ componentibus, & hoc optima ratio­<lb/>ne de duximus, <expan abbr="quãdo">quando</expan> quidem &longs;eriem corporum iner­<lb/>tium & nil pror&longs;us deor&longs;um impellentium nemo &longs;anæ <lb/>mentis affirmabit vim compre&longs;&longs;iuam deorsùm exer­<lb/>cere, imò concedet æquè operari ac &longs;i e&longs;&longs;et vnica &longs;in­<lb/>gularis laminula, vel dicet &longs;ubiectum corpus à nihilo <lb/>comprimi, & è contra &longs;eries corporum vim <expan abbr="impul&longs;iuã">impul&longs;iuam</expan> <lb/><expan abbr="habentiũ">habentium</expan> exercet vim pro men&longs;ura multiplicati cor­<lb/>poris, & hoc &longs;anè lumine naturæ <expan abbr="cõ&longs;tat">con&longs;tat</expan>, hinc deduci­<lb/>tur infimam laminam aqueam MN no&longs;tri va&longs;is nullam <lb/>compre&longs;&longs;ionem pati ab vniuer&longs;a aqua &longs;uperpo&longs;it&atail; <lb/>MA non &longs;ecùs ac &longs;i à nihilo premeretur vnde fit vt in­<lb/>ferior pars aquea MN ablata qua MA tanta vi præ­<lb/>cisè comprimat va&longs;is fundum NO ac &longs;i &longs;uper&longs;taret <lb/>immen&longs;a moles aquea NA, &longs;ed illa ob ponderis exi­<lb/>guitatem haud &longs;en&longs;ibilem vim vitreo fundo infert, <lb/>nec ip&longs;um inflectit, aut di&longs;rumpit, igitur neque <expan abbr="vitrũ">vitrum</expan> <lb/>inflectetur aut <expan abbr="cõ&longs;tringetur">con&longs;tringetur</expan> quando alti&longs;&longs;ima moles a­<lb/>quea NA ei &longs;uperponitur; quia verò hoc e<gap/>identiæ <lb/>&longs;en&longs;us repugnat affirmandum e&longs;t, aquam licèt in ip&longs;a­<lb/>met aqua iners & quie&longs;cens videatur, nece&longs;&longs;ariò gra­<lb/>uitatem exercere. <pb xlink:href="010/01/048.jpg" pagenum="40"/><arrow.to.target n="marg41"/></s></p><p type="margin"> | <s>SEd hoc euidentius &longs;ic patebit, &longs;it fi&longs;tula vitrea A <lb/>NO perpendiculariter ad horizontem erect&atail;, <lb/>repleaturquè aqua, &longs;eù quolibet alio fluido cor­<lb/>pore, & ductis innumeris planis horizonti <expan abbr="æquidi&longs;tã-tibus">æquidi&longs;tan­<lb/>tibus</expan> &longs;ubdiuidatur vniuer&longs;um fluidum i&ntail; <lb/><figure id="id.010.01.046.1.jpg" xlink:href="010/01/046/1.jpg"/><lb/>laminas gracillimas &longs;eù membranas æquè <lb/>altas AB, BC, CD, DE, EF, FM, & MN. & <lb/>primò &longs;i verum e&longs;t, vt aduer&longs;arij credunt <lb/>aquam in ip&longs;amet aqua collocatam <expan abbr="nõ">non</expan> gra­<lb/>uitare, igitur &longs;uprema laminula aquea AB <lb/>pror&longs;us <expan abbr="nõ">non</expan> comprimet &longs;ubiectam <expan abbr="membra-nã">membra­<lb/>nam</expan> aqueam BC, &longs;cilicet vim nullam &longs;uper eam exer­<lb/>cebit (hoc enim grauitatis nomen indicat) neque eam <lb/>deor&longs;um impellet perinde ac &longs;i aqua &longs;uprema AB non <lb/>ade&longs;&longs;et, proindeque hæc non augebit grauitatem in­<lb/>ferioris laminæ BC, aliàs &longs;uprema aqua AB pondera-<pb xlink:href="010/01/047.jpg" pagenum="39"/><arrow.to.target n="marg40"/><lb/>ret, comprimeretque &longs;ubiectam aquam BC, quod e&longs;t <lb/>contra aduer&longs;arij hypothe&longs;im; eadem ratione vniuer­<lb/>&longs;a aqua ABC nil ponderabit, ne que comprimet &longs;ub­<lb/>iectam laminam aqueam CD, & tota aqua AD nec <lb/>etiam comprimet aut grauitatem inferet &longs;upra infe­<lb/>riorem <expan abbr="aquã">aquam</expan> DE; idip&longs;um procul dubio aflirmari de­<lb/>bet de reliquis omnibus laminulis fluidis totam alti­<lb/>tudinem aquæ componentibus, & hoc optima ratio­<lb/>ne de duximus, <expan abbr="quãdo">quando</expan> quidem &longs;eriem corporum iner­<lb/>tium & nil pror&longs;us deor&longs;um impellentium nemo &longs;anæ <lb/>mentis affirmabit vim compre&longs;&longs;iuam deorsùm exer­<lb/>cere, imò concedet æquè operari ac &longs;i e&longs;&longs;et vnica &longs;in­<lb/>gularis laminula, vel dicet &longs;ubiectum corpus à nihilo <lb/>comprimi, & è contra &longs;eries corporum vim <expan abbr="impul&longs;iuã">impul&longs;iuam</expan> <lb/><expan abbr="habentiũ">habentium</expan> exercet vim pro men&longs;ura multiplicati cor­<lb/>poris, & hoc &longs;anè lumine naturæ <expan abbr="cõ&longs;tat">con&longs;tat</expan>, hinc deduci­<lb/>tur infimam laminam aqueam MN no&longs;tri va&longs;is nullam <lb/>compre&longs;&longs;ionem pati ab vniuer&longs;a aqua &longs;uperpo&longs;it&atail; <lb/>MA non &longs;ecùs ac &longs;i à nihilo premeretur vnde fit vt in­<lb/>ferior pars aquea MN ablata qua MA tanta vi præ­<lb/>cisè comprimat va&longs;is fundum NO ac &longs;i &longs;uper&longs;taret <lb/>immen&longs;a moles aquea NA, &longs;ed illa ob ponderis exi­<lb/>guitatem haud &longs;en&longs;ibilem vim vitreo fundo infert, <lb/>nec ip&longs;um inflectit, aut di&longs;rumpit, igitur neque <expan abbr="vitrũ">vitrum</expan> <lb/>inflectetur aut <expan abbr="cõ&longs;tringetur">con&longs;tringetur</expan> quando alti&longs;&longs;ima moles a­<lb/>quea NA ei &longs;uperponitur; quia verò hoc euidentiæ <lb/>&longs;en&longs;us repugnat affirmandum e&longs;t, aquam licèt in ip&longs;a­<lb/>met aqua iners & quie&longs;cens videatur, nece&longs;&longs;ariò gra­<lb/>uitatem exercere. <pb xlink:href="010/01/048.jpg" pagenum="40"/><arrow.to.target n="marg41"/></s></p><p type="margin"> |
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| <s><margin.target id="marg40"/>Cap. | <s><margin.target id="marg40"/>Cap. |
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| <s>Et quia vt mox o&longs;ten&longs;um e&longs;t ex <lb/>aduer&longs;arij hypothe&longs;i tota aqua AM <lb/>vim non infert neque impellit infe­<lb/>riorem aqueam laminam MN, cù&mtail; <lb/>nullam grauitatem &longs;uper eam exer­<lb/>ceat; igitur tota moles aquea AM nil prorsùs impel­<lb/>let terminum aquæ O & proindè ab hoc non impelle­<lb/>tur &longs;ur&longs;um oleo&longs;us cylinder OP, igitur oleum OP <lb/>nulla ratione &longs;ubleuari &longs;ursùm deberet, &longs;ed hoc e&longs;t <lb/>fal&longs;um, igitur fal&longs;a e&longs;t quoque hypothe&longs;is a&longs;&longs;umpta, <lb/>quòd aqua in ip&longs;amet aqua po&longs;ita grauitatem no&ntail; <lb/>exerceat. </s></p><p type="main"> | <s>Et quia vt mox o&longs;ten&longs;um e&longs;t ex <lb/>aduer&longs;arij hypothe&longs;i tota aqua AM <lb/>vim non infert neque impellit infe­<lb/>riorem aqueam laminam MN, cù&mtail; <lb/>nullam grauitatem &longs;uper eam exer­<lb/>ceat; igitur tota moles aquea AM nil prorsùs impel­<lb/>let terminum aquæ O & proindè ab hoc non impelle­<lb/>tur &longs;ur&longs;um oleo&longs;us cylinder OP, igitur oleum OP <lb/>nulla ratione &longs;ubleuari &longs;ursùm deberet, &longs;ed hoc e&longs;t <lb/>fal&longs;um, igitur fal&longs;a e&longs;t quoque hypothe&longs;is a&longs;&longs;umpta, <lb/>quòd aqua in ip&longs;amet aqua po&longs;ita grauitatem no&ntail; <lb/>exerceat. </s></p><p type="main"> |
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| <s>Et profectò methodus ac criterium digno&longs;cendi, <lb/>an corpus aliquod grauitet, atque impellat alterum, <lb/>erit huiu&longs;modi; con&longs;iderari nimirum debent effectus <lb/>ab eo producti, & quanta vis contraria requiritur, <lb/>vt vnum à con&longs;ortio, & contactu alterius diuellatur, <lb/>& &longs;eparetur, & quia &longs;i nauis natando lateraliter &longs;co­<lb/>pulum contigeret, po&longs;&longs;et à quacumque exigua vi tra­<lb/>hi, diuelli, & &longs;eparari ab eodem &longs;copulo, hinc i<gap/>r&etail; <lb/>optimo inferemus nauim omninò carere vi motiua, & <pb xlink:href="010/01/049.jpg" pagenum="41"/><arrow.to.target n="marg42"/><lb/>i<gap/>pul&longs;iua tendendi ver&longs;us &longs;copulum, è contra, quia <lb/>videmus, quòd pila ferrea non pote&longs;t à contactu &longs;oli <lb/>&longs;eiungi, ac diuelli ni&longs;i æqualis facultas, & energi&atail; <lb/>contraria adhibeatur, &longs;cilicet ni&longs;i apponatur pondus <lb/>in altera extremitate libræ, quod æquale &longs;it grauita­<lb/>ti prædictæ pilæ ferre&ecedil;, &longs;icuti cùm homo robu&longs;tus co­<lb/>lumnam aliquam impellit, non pote&longs;t ab ea &longs;eiungi, <lb/>ni&longs;i adhibeatur vis motiua prorsùs æqualis ei, quam <lb/>homo exercet; hinc de ducemus pilam vim grauitatis, <lb/>& hominem vim mu&longs;culorum exercere. </s></p><p type="margin"> | <s>Et profectò methodus ac criterium digno&longs;cendi, <lb/>an corpus aliquod grauitet, atque impellat alterum, <lb/>erit huiu&longs;modi; con&longs;iderari nimirum debent effectus <lb/>ab eo producti, & quanta vis contraria requiritur, <lb/>vt vnum à con&longs;ortio, & contactu alterius diuellatur, <lb/>& &longs;eparetur, & quia &longs;i nauis natando lateraliter &longs;co­<lb/>pulum contigeret, po&longs;&longs;et à quacumque exigua vi tra­<lb/>hi, diuelli, & &longs;eparari ab eodem &longs;copulo, hinc in re <lb/>optimo inferemus nauim omninò carere vi motiua, & <pb xlink:href="010/01/049.jpg" pagenum="41"/><arrow.to.target n="marg42"/><lb/>i<gap/>pul&longs;iua tendendi ver&longs;us &longs;copulum, è contra, quia <lb/>videmus, quòd pila ferrea non pote&longs;t à contactu &longs;oli <lb/>&longs;eiungi, ac diuelli ni&longs;i æqualis facultas, & energi&atail; <lb/>contraria adhibeatur, &longs;cilicet ni&longs;i apponatur pondus <lb/>in altera extremitate libræ, quod æquale &longs;it grauita­<lb/>ti prædictæ pilæ ferre&ecedil;, &longs;icuti cùm homo robu&longs;tus co­<lb/>lumnam aliquam impellit, non pote&longs;t ab ea &longs;eiungi, <lb/>ni&longs;i adhibeatur vis motiua prorsùs æqualis ei, quam <lb/>homo exercet; hinc de ducemus pilam vim grauitatis, <lb/>& hominem vim mu&longs;culorum exercere. </s></p><p type="margin"> |
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| <s><margin.target id="marg42"/>Cap. | <s><margin.target id="marg42"/>Cap. |
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| 3. flui­<lb/>dum in &longs;uo <lb/>toto quie­<lb/>&longs;cens pon­<lb/>derat.</s></p><p type="main"> | 3. flui­<lb/>dum in &longs;uo <lb/>toto quie­<lb/>&longs;cens pon­<lb/>derat.</s></p><p type="main"> |
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| <s>Contra hoc euidenti&longs;&longs;imum ratiocinium afferri <lb/>&longs;olet difficultas valdè &longs;pecio&longs;a, quam examinare, ac <lb/>di&longs;&longs;oluere erit operæ pretium, vtque ea<gap/>itè percipi­<lb/>atur, con&longs;ideretur hæc figura. </s> | <s>Contra hoc euidenti&longs;&longs;imum ratiocinium afferri <lb/>&longs;olet difficultas valdè &longs;pecio&longs;a, quam examinare, ac <lb/>di&longs;&longs;oluere erit operæ pretium, vtque ea ritè percipi­<lb/>atur, con&longs;ideretur hæc figura. </s> |
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| <s>Sit vas cylindricu&mtail; <lb/><arrow.to.target n="marg48"/><lb/>ABDC aqua plenum &longs;it que eius altitudo <lb/><figure id="id.010.01.054.1.jpg" xlink:href="010/01/054/1.jpg"/><lb/>di&longs;&longs;ecta in quotcumque partes æquales, <lb/>ductis nempè planis imaginarijs MO, & <lb/>HI, erit igitur moles aquea AI dupl&atail; <lb/>aque &ecedil; molis HD; igitur pondus aquæ AI <lb/>duplum e&longs;t ponderis aquæ HD. quia ve­<lb/>rò corpus grauius minùs graue &longs;uperare <lb/>debet, hocque è &longs;uo loco expellere (cùm in eo con&longs;i­<lb/>&longs;tat vis, & energìa grauitatis, vt tendat deorsùm, <lb/>& &longs;ic è loco infimo corpora minùs grauia expellat) & <lb/>po&longs;tquàm aqua AI translata e&longs;t ad locum HD, atque <lb/>aquam ibidem collocatam expulit denuò in &longs;itu &longs;u­<lb/>periori fi&longs;tulæ AI aqua dupli ponderis, & molis ibi­<lb/>dem re&longs;tituitur quæ pariter &longs;uperat grauitatem &longs;ub­<lb/>duplam aquæ, quæ ad occupandum infimum locum <lb/>HD &longs;ucce&longs;&longs;it, igitur denuò aqua &longs;uprema vt grauior <lb/>in&longs;imam è &longs;uo loco extrudere, atque expellere de-<pb xlink:href="010/01/055.jpg" pagenum="47"/><arrow.to.target n="marg49"/><lb/>bet, & quia hoc &longs;emper repetitur, &longs;cilicèt perpetuò <lb/>re&longs;tituitur in &longs;uperioriloco AI aqua duplò grauior, <lb/>quàm ea, quæ in loco infimo HD reponitur, igitur <lb/>vt contingit in libra efficientur perpetuæ, & conti­<lb/>nuatæ vibrationes, veluti in pendulo, & in aqua fie­<lb/>ri&longs;olent plures vndulationes, &longs;ic in aqua perpetuo <lb/>motu agitarentur eius partes a&longs;cendendo, & de&longs;cen­<lb/>dendo. </s> | <s>Sit vas cylindricu&mtail; <lb/><arrow.to.target n="marg48"/><lb/>ABDC aqua plenum &longs;it que eius altitudo <lb/><figure id="id.010.01.054.1.jpg" xlink:href="010/01/054/1.jpg"/><lb/>di&longs;&longs;ecta in quotcumque partes æquales, <lb/>ductis nempè planis imaginarijs MO, & <lb/>HI, erit igitur moles aquea AI dupl&atail; <lb/>aque &ecedil; molis HD; igitur pondus aquæ AI <lb/>duplum e&longs;t ponderis aquæ HD. quia ve­<lb/>rò corpus grauius minùs graue &longs;uperare <lb/>debet, hocque è &longs;uo loco expellere (cùm in eo con&longs;i­<lb/>&longs;tat vis, & energìa grauitatis, vt tendat deorsùm, <lb/>& &longs;ic è loco infimo corpora minùs grauia expellat) & <lb/>po&longs;tquàm aqua AI translata e&longs;t ad locum HD, atque <lb/>aquam ibidem collocatam expulit denuò in &longs;itu &longs;u­<lb/>periori fi&longs;tulæ AI aqua dupli ponderis, & molis ibi­<lb/>dem re&longs;tituitur quæ pariter &longs;uperat grauitatem &longs;ub­<lb/>duplam aquæ, quæ ad occupandum infimum locum <lb/>HD &longs;ucce&longs;&longs;it, igitur denuò aqua &longs;uprema vt grauior <lb/>in&longs;imam è &longs;uo loco extrudere, atque expellere de-<pb xlink:href="010/01/055.jpg" pagenum="47"/><arrow.to.target n="marg49"/><lb/>bet, & quia hoc &longs;emper repetitur, &longs;cilicèt perpetuò <lb/>re&longs;tituitur in &longs;uperioriloco AI aqua duplò grauior, <lb/>quàm ea, quæ in loco infimo HD reponitur, igitur <lb/>vt contingit in libra efficientur perpetuæ, & conti­<lb/>nuatæ vibrationes, veluti in pendulo, & in aqua fie­<lb/>ri&longs;olent plures vndulationes, &longs;ic in aqua perpetuo <lb/>motu agitarentur eius partes a&longs;cendendo, & de&longs;cen­<lb/>dendo. </s> |
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| <s>hoc verò &longs;en&longs;us euidentia redarguit, igitur <lb/>fatendum e&longs;t &longs;upremam aquam AI &longs;u&longs;tentatam ab <lb/>inferiori aqua &longs;uper eam non exercere vim vlla&mtail;, <lb/>nec pre&longs;&longs;ionem, proinde que non grauitare, hac &longs;cili­<lb/>cet de cau&longs;a, quia nimirùm in eius loco naturali col­<lb/>locatare quie&longs;cit, ac &longs;i&longs;titur. </s></p><p type="margin"> | <s>hoc verò &longs;en&longs;us euidentia redarguit, igitur <lb/>fatendum e&longs;t &longs;upremam aquam AI &longs;u&longs;tentatam ab <lb/>inferiori aqua &longs;uper eam non exercere vim vlla&mtail;, <lb/>nec pre&longs;&longs;ionem, proinde que non grauitare, hac &longs;cili­<lb/>cet de cau&longs;a, quia nimirùm in eius loco naturali col­<lb/>locatare quie&longs;cit, ac &longs;i&longs;titur. </s></p><p type="margin"> |
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| <s><margin.target id="marg48"/>Coatra do­<lb/>ctrinam &longs;u­<lb/>periùs addu­<lb/>ctam ade&longs;t <lb/>noua difficul <lb/>tas, quod ni­<lb/>mirum mo­<lb/>tu perpetuo <lb/>aqua ag<gap/>ari <lb/><gap/>beret.</s></p><p type="margin"> | <s><margin.target id="marg48"/>Contra do­<lb/>ctrinam &longs;u­<lb/>periùs addu­<lb/>ctam ade&longs;t <lb/>noua difficul­<lb/>tas, quod ni­<lb/>mirum mo­<lb/>tu perpetuo <lb/>aqua agitari <lb/>deberet.</s></p><p type="margin"> |
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| <s><margin.target id="marg49"/>Cap. | <s><margin.target id="marg49"/>Cap. |
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| <s>VT verò huiu&longs;modi paralogi&longs;mus detegatur, a­<lb/>nima <expan abbr="duert&etilde;d">duertend</expan> um e&longs;t minimè verum e&longs;&longs;e, quòd <lb/>quælibet aquæ moles maior alterà, <expan abbr="n&etilde;pe">nempe</expan> dupla, exer­<lb/>ceat quoque duplam vim grauitantem quotie&longs;cum­<lb/>que maior &longs;upra minorem in&longs;i&longs;tat, & ab ea fulciatur, <lb/>&longs;ed tunc &longs;olummodò propo&longs;itio verificatur quando <lb/>earum ba&longs;es <expan abbr="cõtiguæ">contiguæ</expan> æquales fuerint, ac in&longs;uper in <lb/>eodem plano horizonti parallelo con&longs;titerint. </s> | <s>VT verò huiu&longs;modi paralogi&longs;mus detegatur, a­<lb/>nima <expan abbr="duert&etilde;d">duertend</expan> um e&longs;t minimè verum e&longs;&longs;e, quòd <lb/>quælibet aquæ moles maior alterà, <expan abbr="n&etilde;pe">nempe</expan> dupla, exer­<lb/>ceat quoque duplam vim grauitantem quotie&longs;cum­<lb/>que maior &longs;upra minorem in&longs;i&longs;tat, & ab ea fulciatur, <lb/>&longs;ed tunc &longs;olummodò propo&longs;itio verificatur quando <lb/>earum ba&longs;es <expan abbr="cõtiguæ">contiguæ</expan> æquales fuerint, ac in&longs;uper in <lb/>eodem plano horizonti parallelo con&longs;titerint. </s> |
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| <s>Sup­<lb/>ponatur vas cylindricum plenum aqua ABDC, &longs;it­<lb/>que portio &longs;uprema, & ideò eius altitudo AH dupla <lb/>infimæ altitudinis HB, licèt ergo reuerà &longs;upremæ <pb xlink:href="010/01/056.jpg" pagenum="48"/><arrow.to.target n="marg50"/><lb/>aquæ AI pondus duplum &longs;it ponderis infimæ aquæ <lb/>HD, non hìnc tamen inferri licet &longs;ubiectam aqua&mtail; <lb/>HD in tali &longs;itu vnicam libram tantummodò pendere <lb/>exi&longs;tente &longs;upremo pondere AI duarum librarum, &longs;ed <lb/>nece&longs;sè e&longs;t vt aqua HD comprimat va&longs;is fundum BD <lb/>ni&longs;u, ac vi non vnius libræ, &longs;ed æquali ei, quæ effi­<lb/>citur à pondere trium librarum, & ratio e&longs;t quia ip­<lb/>&longs;a aqua HD nedùm impellitur deor&longs;umà vi propriæ <lb/>grauitatis vnius libræ, &longs;ed in&longs;uper grauatur compri­<lb/>miturque ab incumbente pondere aquæ AI, quæ <expan abbr="cõ-pre&longs;&longs;io">con­<lb/>pre&longs;&longs;io</expan> &longs;uperaddit aqu&ecedil; HD vim æqualem ei, quæ à <lb/>duabus libris effici pote&longs;t; nec profectò nouum e&longs;t &longs;<gap/><lb/>quis centum laminas ferreas, vellapideas, æquè <expan abbr="põ-derantes">pon­<lb/>derantes</expan>, &longs;cilicet &longs;ingulas vnius libræ vnam &longs;uper al­<lb/>teram imponat, quod in&longs;ima lamina non tantummo­<lb/>dò &longs;uo pondere comprimet planum &longs;ubiectum, &longs;cili­<lb/>cèt non efficiet vim æqualem cente&longs;imæ parti totius <lb/>prædicti aggregati, &longs;ed compre&longs;&longs;io infim&ecedil; laminæ ef­<lb/>ficiet vim centuplo maiorem &longs;cilicèt impellet &longs;ubie­<lb/>ctum planum vi æquali centum libris, & tunc <expan abbr="&longs;olũ-modò">&longs;olun­<lb/>modò</expan> in&longs;ima lamina partem cente&longs;imam totius ag­<lb/>gregati ponderabit, quando illa in vna lance, reli­<lb/>quæ verò 100. in oppo&longs;ita lance eiu&longs;dem libræ ra­<lb/>diorum æqualium &longs;u&longs;penderentur; &longs;ic paritèr &longs;i aqua <lb/>HD &longs;upra planum &longs;ubiectum &longs;iuè &longs;olidum, &longs;iuè flui­<lb/>dum collocaretur iuxtà portionem aquæ AI, itaut &longs;e­<lb/>&longs;e contingerent lateraliter, atque <expan abbr="earũ">earum</expan> ba&longs;es æqua­<lb/>les in eodem plano horizontali collocarentur, tunc <lb/>nece&longs;&longs;ariò dupla moles aquæ AI duplam vim com-<pb xlink:href="010/01/057.jpg" pagenum="49"/><arrow.to.target n="marg51"/><lb/>pre&longs;&longs;iuam, pro men&longs;ura duplæ grauitatis haberet. <lb/></s> | <s>Sup­<lb/>ponatur vas cylindricum plenum aqua ABDC, &longs;it­<lb/>que portio &longs;uprema, & ideò eius altitudo AH dupla <lb/>infimæ altitudinis HB, licèt ergo reuerà &longs;upremæ <pb xlink:href="010/01/056.jpg" pagenum="48"/><arrow.to.target n="marg50"/><lb/>aquæ AI pondus duplum &longs;it ponderis infimæ aquæ <lb/>HD, non hìnc tamen inferri licet &longs;ubiectam aquam <lb/>HD in tali &longs;itu vnicam libram tantummodò pendere <lb/>exi&longs;tente &longs;upremo pondere AI duarum librarum, &longs;ed <lb/>nece&longs;sè e&longs;t vt aqua HD comprimat va&longs;is fundum BD <lb/>ni&longs;u, ac vi non vnius libræ, &longs;ed æquali ei, quæ effi­<lb/>citur à pondere trium librarum, & ratio e&longs;t quia ip­<lb/>&longs;a aqua HD nedùm impellitur deor&longs;um à vi propriæ <lb/>grauitatis vnius libræ, &longs;ed in&longs;uper grauatur compri­<lb/>miturque ab incumbente pondere aquæ AI, quæ <expan abbr="cõ-pre&longs;&longs;io">com­<lb/>pre&longs;&longs;io</expan> &longs;uperaddit aqu&ecedil; HD vim æqualem ei, quæ à <lb/>duabus libris effici pote&longs;t; nec profectò nouum e&longs;t &longs;i­<lb/>quis centum laminas ferreas, vellapideas, æquè <expan abbr="põ-derantes">pon­<lb/>derantes</expan>, &longs;cilicet &longs;ingulas vnius libræ vnam &longs;uper al­<lb/>teram imponat, quod in&longs;ima lamina non tantummo­<lb/>dò &longs;uo pondere comprimet planum &longs;ubiectum, &longs;cili­<lb/>cèt non efficiet vim æqualem cente&longs;imæ parti totius <lb/>prædicti aggregati, &longs;ed compre&longs;&longs;io infim&ecedil; laminæ ef­<lb/>ficiet vim centuplo maiorem &longs;cilicèt impellet &longs;ubie­<lb/>ctum planum vi æquali centum libris, & tunc <expan abbr="&longs;olũ-modò">&longs;olum­<lb/>modò</expan> in&longs;ima lamina partem cente&longs;imam totius ag­<lb/>gregati ponderabit, quando illa in vna lance, reli­<lb/>quæ verò 100. in oppo&longs;ita lance eiu&longs;dem libræ ra­<lb/>diorum æqualium &longs;u&longs;penderentur; &longs;ic paritèr &longs;i aqua <lb/>HD &longs;upra planum &longs;ubiectum &longs;iuè &longs;olidum, &longs;iuè flui­<lb/>dum collocaretur iuxtà portionem aquæ AI, itaut &longs;e­<lb/>&longs;e contingerent lateraliter, atque <expan abbr="earũ">earum</expan> ba&longs;es æqua­<lb/>les in eodem plano horizontali collocarentur, tunc <lb/>nece&longs;&longs;ariò dupla moles aquæ AI duplam vim com-<pb xlink:href="010/01/057.jpg" pagenum="49"/><arrow.to.target n="marg51"/><lb/>pre&longs;&longs;iuam, pro men&longs;ura duplæ grauitatis haberet. <lb/></s> |
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| <s>Verum tamen e&longs;t, quòd alia de cau&longs;a non e&longs;t nece&longs;­<lb/>sè, vt &longs;emper ba&longs;es &longs;int æquales, neque grauitates <lb/>&longs;int in eadem proportione dupla, dummodò altitu­<lb/>do AH dupla &longs;it altitudinis ip&longs;ius HB; & ratio huius <lb/>diuer&longs;itatis pendet ex alibi demon&longs;trandis. </s></p><p type="margin"> | <s>Verum tamen e&longs;t, quòd alia de cau&longs;a non e&longs;t nece&longs;­<lb/>sè, vt &longs;emper ba&longs;es &longs;int æquales, neque grauitates <lb/>&longs;int in eadem proportione dupla, dummodò altitu­<lb/>do AH dupla &longs;it altitudinis ip&longs;ius HB; & ratio huius <lb/>diuer&longs;itatis pendet ex alibi demon&longs;trandis. </s></p><p type="margin"> |
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| <s>Ex &longs;uperiori igitur ratiocinio euinci­<lb/><figure id="id.010.01.057.1.jpg" xlink:href="010/01/057/1.jpg"/><lb/>tur, fal&longs;um e&longs;&longs;e, quòd pronunciabatur, <lb/>nimirùm, duplam aquam AI vt grauio­<lb/>rem, expellere de&longs;cendendo debere &longs;ub­<lb/>duplam aquam &longs;ubiectam HD, cùm ècon <lb/>tra hæc vt grauior, grauitate nempe pro­<lb/>pria, & ea, quæ ei &longs;uperadditur ab aqua <lb/>&longs;uperincumbente AI in eodem loco infimo perma­<lb/>nere debeat, nec vnquam à debiliori compre&longs;&longs;ione <lb/>&longs;uper&longs;tantis aquæ expelli po&longs;&longs;it, ac proindè &longs;equitur <lb/>&longs;umma quies, ac tranquillitas, non verò motus per­<lb/>petuus. <lb/><arrow.to.target n="marg52"/></s></p><p type="margin"> | <s>Ex &longs;uperiori igitur ratiocinio euinci­<lb/><figure id="id.010.01.057.1.jpg" xlink:href="010/01/057/1.jpg"/><lb/>tur, fal&longs;um e&longs;&longs;e, quòd pronunciabatur, <lb/>nimirùm, duplam aquam AI vt grauio­<lb/>rem, expellere de&longs;cendendo debere &longs;ub­<lb/>duplam aquam &longs;ubiectam HD, cùm ècon <lb/>tra hæc vt grauior, grauitate nempe pro­<lb/>pria, & ea, quæ ei &longs;uperadditur ab aqua <lb/>&longs;uperincumbente AI in eodem loco infimo perma­<lb/>nere debeat, nec vnquam à debiliori compre&longs;&longs;ione <lb/>&longs;uper&longs;tantis aquæ expelli po&longs;&longs;it, ac proindè &longs;equitur <lb/>&longs;umma quies, ac tranquillitas, non verò motus per­<lb/>petuus. <lb/><arrow.to.target n="marg52"/></s></p><p type="margin"> |
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| <s><margin.target id="marg52"/>Ex doctrina <lb/>&longs;uperiùs tra <lb/>dita videtur <lb/>deduci po&longs;­<lb/>&longs;e lignu&mtail; <lb/>infra aquam <lb/>po&longs;itum &longs;ur­<lb/>&longs;um <expan abbr="a&longs;c&etilde;de-">a&longs;cende­<lb/></expan><gap/> non po&longs;&longs;e<gap/></s></p><p type="main"> | <s><margin.target id="marg52"/>Ex doctrina <lb/>&longs;uperiùs tra­<lb/>dita videtur <lb/>deduci po&longs;­<lb/>&longs;e lignum <lb/>infra aquam <lb/>po&longs;itum &longs;ur­<lb/>&longs;um <expan abbr="a&longs;c&etilde;de-">a&longs;cende­<lb/>re</expan> non po&longs;&longs;e.</s></p><p type="main"> |
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| <s>Sed dices, &longs;i vera e&longs;&longs;et adducta doctrina, lignum <lb/>deberet in fundo aquæ paritèr retineri, proptere&atail; <lb/>quòd nedum à propria grauitate comprimitur, &longs;ed <lb/>etiam à pondere totius aquæ &longs;uper&longs;tantis, & ideò <lb/>magis grauitaret quàm aqua ei&longs;uperpo&longs;ita, & proin­<lb/>de lignum in fundo aquæ permanere deberet: hoc <lb/>autem fal&longs;um e&longs;t, cùm experientia con&longs;tet, lignum <lb/>&longs;ursùm ferri, nec quie&longs;cere, antequàm ad aquæ &longs;u­<lb/>premam libellam perducatur. </s></p><pb xlink:href="010/01/058.jpg" pagenum="50"/><p type="main"> | <s>Sed dices, &longs;i vera e&longs;&longs;et adducta doctrina, lignum <lb/>deberet in fundo aquæ paritèr retineri, proptere&atail; <lb/>quòd nedum à propria grauitate comprimitur, &longs;ed <lb/>etiam à pondere totius aquæ &longs;uper&longs;tantis, & ideò <lb/>magis grauitaret quàm aqua ei&longs;uperpo&longs;ita, & proin­<lb/>de lignum in fundo aquæ permanere deberet: hoc <lb/>autem fal&longs;um e&longs;t, cùm experientia con&longs;tet, lignum <lb/>&longs;ursùm ferri, nec quie&longs;cere, antequàm ad aquæ &longs;u­<lb/>premam libellam perducatur. </s></p><pb xlink:href="010/01/058.jpg" pagenum="50"/><p type="main"> |
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| <s>Hinc colligitur, quòd quotie&longs;cumque &longs;upremum <lb/>lanæ inuolucrum perpendicularitèt incumbens &longs;u­<lb/>peralterum, &longs;i ip&longs;um non flecteret, nec &longs;tringeret, <lb/>tunc planè affirmandum e&longs;&longs;et lanam &longs;uperpo&longs;ita&mtail; <lb/>minimè &longs;uper &longs;ubiectam lanam grauitatem exercere. </s></p><p type="main"> | <s>Hinc colligitur, quòd quotie&longs;cumque &longs;upremum <lb/>lanæ inuolucrum perpendicularitèt incumbens &longs;u­<lb/>peralterum, &longs;i ip&longs;um non flecteret, nec &longs;tringeret, <lb/>tunc planè affirmandum e&longs;&longs;et lanam &longs;uperpo&longs;ita&mtail; <lb/>minimè &longs;uper &longs;ubiectam lanam grauitatem exercere. </s></p><p type="main"> |
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| <s>His po&longs;itis, &longs;upremum lanæ inuolucrum applica­<lb/>ri pote&longs;t &longs;uper infimum dum hoc actu per aerem mo­<lb/>uetur de&longs;cendendo deor&longs;um, vel dum quie&longs;cit à pla­<lb/>no &longs;tabili fultum; in primo ca&longs;u manife&longs;tum e&longs;t, <lb/>quòd inuolucra æqualia eiu&longs;dem lanæ æquales gra­<lb/>dus velocitatum <expan abbr="hab&etilde;t">habent</expan>, quibus naturaliter de&longs;cen­<lb/>dunt; igitur &longs;upremum inu olucrum non de&longs;cendet <lb/>tardiori, vel celeriori motu quàm &longs;ibi <expan abbr="&longs;ubiectũ">&longs;ubiectum</expan>, pro­<lb/>indeque æquali velocitare &longs;uprema lana compri­<lb/>mere conatur &longs;ubiectam lanam, ac i&longs;ta nititur effu­<lb/>gere per&longs;equentem; proptere aque &longs;e mutuo plac<gap/>­<lb/>do contactu &longs;olummodò exo&longs;culantur, nec &longs;ubiecta <lb/>inflectetur, aut comprimetur à &longs;uper&longs;tante lana: <lb/>igitur, ex&longs;uperiùs dictis incumbens lana nequè <expan abbr="põ-dus">pon­<lb/>dus</expan>, neque grauitatem exercebit &longs;upra &longs;ugiente&mtail; <lb/>lanam &longs;ubiectam. </s> | <s>His po&longs;itis, &longs;upremum lanæ inuolucrum applica­<lb/>ri pote&longs;t &longs;uper infimum dum hoc actu per aerem mo­<lb/>uetur de&longs;cendendo deor&longs;um, vel dum quie&longs;cit à pla­<lb/>no &longs;tabili fultum; in primo ca&longs;u manife&longs;tum e&longs;t, <lb/>quòd inuolucra æqualia eiu&longs;dem lanæ æquales gra­<lb/>dus velocitatum <expan abbr="hab&etilde;t">habent</expan>, quibus naturaliter de&longs;cen­<lb/>dunt; igitur &longs;upremum inuolucrum non de&longs;cendet <lb/>tardiori, vel celeriori motu quàm &longs;ibi <expan abbr="&longs;ubiectũ">&longs;ubiectum</expan>, pro­<lb/>indeque æquali velocitare &longs;uprema lana compri­<lb/>mere conatur &longs;ubiectam lanam, ac i&longs;ta nititur effu­<lb/>gere per&longs;equentem; proptereaque &longs;e mutuo placi­<lb/>do contactu &longs;olummodò exo&longs;culantur, nec &longs;ubiecta <lb/>inflectetur, aut comprimetur à &longs;uper&longs;tante lana: <lb/>igitur, ex &longs;uperiùs dictis incumbens lana nequè <expan abbr="põ-dus">pon­<lb/>dus</expan>, neque grauitatem exercebit &longs;upra fugientem <lb/>lanam &longs;ubiectam. </s> |
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| <s>In &longs;ecundo verò ca&longs;u &longs;i po&longs;tquàm <lb/>in quiete &longs;ubiecta lana compre&longs;&longs;a e&longs;t à &longs;uperincum­<lb/>bente ambas demittamus, & liberè deor&longs;um <expan abbr="de&longs;c&etilde;-dere">de&longs;cen­<lb/>dere</expan> concedamus, patete as motum inchoare quan­<lb/>do iam re&longs;trictæ, & con&longs;tipatæ &longs;unt, & ideò in pro­<lb/>gre&longs;&longs;u licèt paribus velocitatibus de&longs;cendant, reti­<lb/>ne bunt tamen eandem con&longs;tipationem, quam prius <pb xlink:href="010/01/061.jpg" pagenum="53"/><arrow.to.target n="marg56"/><lb/>habebant; &longs;ed hinc non licet inferre, &longs;upremam la­<lb/>nam dum mouetur grauitatem exercere, quia ill&atail; <lb/>con&longs;tipatio non dependet ab actione grauitatis in­<lb/>cumbentis lanæ quæactio per&longs;eueret exerceaturque <lb/>tempore de&longs;cen&longs;us, &longs;ed illa con&longs;tipatio e&longs;t effectus <lb/>compre&longs;&longs;ionis in præcedenti quiete factæ, in actu e­<lb/>nim de&longs;cen&longs;us nullo pacto impellere pote&longs;t &longs;uprema <lb/>lana &longs;u biectam pani velocitate ictum fugientem, & <lb/>ideo &longs;u per eam minimè pondus exercebit. </s></p><p type="margin"> | <s>In &longs;ecundo verò ca&longs;u &longs;i po&longs;tquàm <lb/>in quiete &longs;ubiecta lana compre&longs;&longs;a e&longs;t à &longs;uperincum­<lb/>bente ambas demittamus, & liberè deor&longs;um <expan abbr="de&longs;c&etilde;-dere">de&longs;cen­<lb/>dere</expan> concedamus, patete as motum inchoare quan­<lb/>do iam re&longs;trictæ, & con&longs;tipatæ &longs;unt, & ideò in pro­<lb/>gre&longs;&longs;u licèt paribus velocitatibus de&longs;cendant, reti­<lb/>ne bunt tamen eandem con&longs;tipationem, quam prius <pb xlink:href="010/01/061.jpg" pagenum="53"/><arrow.to.target n="marg56"/><lb/>habebant; &longs;ed hinc non licet inferre, &longs;upremam la­<lb/>nam dum mouetur grauitatem exercere, quia ill&atail; <lb/>con&longs;tipatio non dependet ab actione grauitatis in­<lb/>cumbentis lanæ quæactio per&longs;eueret exerceaturque <lb/>tempore de&longs;cen&longs;us, &longs;ed illa con&longs;tipatio e&longs;t effectus <lb/>compre&longs;&longs;ionis in præcedenti quiete factæ, in actu e­<lb/>nim de&longs;cen&longs;us nullo pacto impellere pote&longs;t &longs;uprema <lb/>lana &longs;u biectam pani velocitate ictum fugientem, & <lb/>ideo &longs;u per eam minimè pondus exercebit. </s></p><p type="margin"> |
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| <s>Secùs autem contingit in aqua quie&longs;cente, i&ntail; <lb/>puteo aliquo, vellacu, &longs;i enim diuidatur pariter in <lb/>laminas æque altas, patet quòd &longs;upremane dum <expan abbr="tã-git">tan­<lb/>git</expan> &longs;impliciter &longs;ubiectam aquæ laminam, &longs;ed è con­<lb/>tra eam impellit tanta vi <expan abbr="quãta">quanta</expan> e&longs;t energia eius gra­<lb/>uitatis, & patet quòd infima aqua pati cogitur com­<lb/>pre&longs;&longs;ionem, cùm &longs;u&longs;tinere debeat pondus &longs;upremæ <lb/>aquæ incumbentis: & hoc accidit, quia &longs;ua quiete <lb/>impedit progre&longs;&longs;um, & conatum compre&longs;&longs;iuum <expan abbr="de-orsũ">de­<lb/>orsum</expan> &longs;u perpo&longs;itæ aqu&ecedil;; hac de cau&longs;a &longs;i habue it poro­<lb/>&longs;itates hæ nece&longs;&longs;ario con&longs;tringentur à vi ponderis <lb/>incumbentis aquæ. </s> | <s>Secùs autem contingit in aqua quie&longs;cente, i&ntail; <lb/>puteo aliquo, vellacu, &longs;i enim diuidatur pariter in <lb/>laminas æque altas, patet quòd &longs;upremane dum <expan abbr="tã-git">tan­<lb/>git</expan> &longs;impliciter &longs;ubiectam aquæ laminam, &longs;ed è con­<lb/>tra eam impellit tanta vi <expan abbr="quãta">quanta</expan> e&longs;t energia eius gra­<lb/>uitatis, & patet quòd infima aqua pati cogitur com­<lb/>pre&longs;&longs;ionem, cùm &longs;u&longs;tinere debeat pondus &longs;upremæ <lb/>aquæ incumbentis: & hoc accidit, quia &longs;ua quiete <lb/>impedit progre&longs;&longs;um, & conatum compre&longs;&longs;iuum <expan abbr="de-orsũ">de­<lb/>orsum</expan> &longs;u perpo&longs;itæ aqu&ecedil;; hac de cau&longs;a &longs;i habue it poro­<lb/>&longs;itates hæ nece&longs;&longs;ario con&longs;tringentur à vi ponderis <lb/>incumbentis aquæ. </s> |
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| <s>Modò quia impul&longs;us compre&longs;&longs;i­<lb/>uus factus à &longs;uperiore aqua &longs;upra inferiorem nullo <lb/>alio vocabulo de&longs;ignatur, quàm grauitatis, vel <expan abbr="põ-deris">pon­<lb/>deris</expan>, igitur verum e<gap/>t, quòd aqua &longs;uper aqua&mtail; <lb/><arrow.to.target n="marg58"/><lb/>quie&longs;centem grauitatem exercet non quando in mo­<lb/>tu con&longs;tituitur, & extra &longs;uum naturalem locum, &longs;ed, <lb/>tantummodò, quando &longs;i&longs;titur, & quie&longs;cit in loco &longs;uo <lb/>naturali. </s></p><p type="margin"> | <s>Modò quia impul&longs;us compre&longs;&longs;i­<lb/>uus factus à &longs;uperiore aqua &longs;upra inferiorem nullo <lb/>alio vocabulo de&longs;ignatur, quàm grauitatis, vel <expan abbr="põ-deris">pon­<lb/>deris</expan>, igitur verum erit, quòd aqua &longs;uper aquam <lb/><arrow.to.target n="marg58"/><lb/>quie&longs;centem grauitatem exercet non quando in mo­<lb/>tu con&longs;tituitur, & extra &longs;uum naturalem locum, &longs;ed, <lb/>tantummodò, quando &longs;i&longs;titur, & quie&longs;cit in loco &longs;uo <lb/>naturali. </s></p><p type="margin"> |
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| <s><margin.target id="marg58"/>Contra do­<lb/>ctrinam &longs;u­<lb/>p: riùs addu­<lb/>ctam afferri <lb/>&longs;olet difficul <lb/>tas valdè <lb/>plau&longs;ibilis, <lb/>quod nimi­<lb/>rum vrina­<lb/>tores ingens <lb/>pondus aque <lb/>incumbentis <lb/>nec patian­<lb/>tur, nec &longs;en­<lb/>tiant.</s></p><p type="main"> | <s><margin.target id="marg58"/>Contra do­<lb/>ctrinam &longs;u­<lb/>p: riùs addu­<lb/>ctam afferri <lb/>&longs;olet difficul <lb/>tas valdè <lb/>plau&longs;ibilis, <lb/>quod nimi­<lb/>rum vrina­<lb/>tores ingens <lb/>pondus aque <lb/>incumbentis <lb/>nec patian­<lb/>tur, nec &longs;en­<lb/>tiant.</s></p><p type="main"> |
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| <s>His declaratis pro re&longs;olutione principalis proble­<lb/><arrow.to.target n="marg66"/><lb/>matis <expan abbr="inquir&etilde;dũ">inquirendum</expan> e&longs;t, quo modo, & qua ratione à com­<lb/>pre&longs;&longs;ione ponderis incumbentis pa&longs;&longs;io dolorifica in <lb/>animali &longs;ub&longs;equatur. </s></p><p type="margin"> | <s>His declaratis pro re&longs;olutione principalis proble­<lb/><arrow.to.target n="marg66"/><lb/>matis <expan abbr="inquir&etilde;dũ">inquirendum</expan> e&longs;t, quo modo, & qua ratione à com­<lb/>pre&longs;&longs;ione ponderis incumbentis pa&longs;&longs;io dolorifica in <lb/>animali &longs;ub&longs;equatur. </s></p><p type="margin"> |
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| <s><margin.target id="marg66"/>Inquiritu<gap/><lb/>cau&longs;a qua<gap/><lb/>à pondere in­<lb/>cumbent&etail;<gap/><lb/>producitur<gap/><lb/>compre&longs;&longs;io<gap/><lb/>&longs;ci&longs;&longs;io, diui­<lb/>&longs;io continui<gap/><lb/>& proind&etail; <lb/>dolor.</s></p><p type="main"> | <s><margin.target id="marg66"/>Inquiritur <lb/>cau&longs;a quare <lb/>à pondere in­<lb/>cumbente <lb/>producitur <lb/>compre&longs;&longs;io, <lb/>&longs;ci&longs;&longs;io, diui­<lb/>&longs;io continui, <lb/>& proinde <lb/>dolor.</s></p><p type="main"> |
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| <s>Et primò experientia con&longs;tat, à pondere corporis <lb/>manum v. <!-- REMOVE S-->g. <!-- REMOVE S-->prementis aliquando effici &longs;ci&longs;&longs;ionem, <lb/>vt ab acie &longs;ecuris incumbentis, aliquando <expan abbr="fraction&etilde;">fractionem</expan>; <lb/>multotiès luxari, & di&longs;rumpi articulos tractis nem-<pb xlink:href="010/01/070.jpg" pagenum="62"/><arrow.to.target n="marg67"/><lb/>pèviolentèr tendinibus articulos colligantibus, & <lb/>tandem fieri pote&longs;t contu&longs;io, & diffractio partiu&mtail; <lb/>&longs;olidarum. </s> | <s>Et primò experientia con&longs;tat, à pondere corporis <lb/>manum v. <!-- REMOVE S-->g. <!-- REMOVE S-->prementis aliquando effici &longs;ci&longs;&longs;ionem, <lb/>vt ab acie &longs;ecuris incumbentis, aliquando <expan abbr="fraction&etilde;">fractionem</expan>; <lb/>multotiès luxari, & di&longs;rumpi articulos tractis nem-<pb xlink:href="010/01/070.jpg" pagenum="62"/><arrow.to.target n="marg67"/><lb/>pèviolentèr tendinibus articulos colligantibus, & <lb/>tandem fieri pote&longs;t contu&longs;io, & diffractio partiu&mtail; <lb/>&longs;olidarum. </s> |
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