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version 1.1, 2003/09/26 15:28:21

version 1.3, 2006/03/27 14:26:18

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<cvs_file>casat_mecha_017_la_1684.xml</cvs_file>

<cvs_version/>

</info> <text> <front> </front> <body> <chap> <pb/>

</info> <text> <front> </front> <body> <chap> <pb xlink:href="017/01/001.jpg"/>

<s><emph type="center"/>R. P. PAULI <lb/>CASATI <lb/>MECHANICA.<emph.end type="center"/></s><pb/><pb/>

<s><emph type="center"/>R. P. PAULI <lb/>CASATI <lb/>MECHANICA.<emph.end type="center"/></s><pb xlink:href="017/01/002.jpg"/><pb xlink:href="017/01/003.jpg"/>

<s><emph type="center"/>R. P. PAULI <lb/>CASATI <lb/>PLACENTINI <lb/>SOCIET. JESU <lb/>MECHANICORUM <lb/>LIBRI OCTO, <lb/>IN QUIBUS UNO EODEMQUE<emph.end type="center"/></s>

<s><emph type="center"/>principio Vectis vires Phy&longs;icè explicantur & Geometricè <lb/>demon&longs;trantur,<emph.end type="center"/></s>

<s><emph type="center"/><emph type="italics"/>Atque Machinarum omnis generis componendarum methodus <lb/>proponitur.<emph.end type="italics"/><emph.end type="center"/></s><figure/>

<s><emph type="center"/><emph type="italics"/>Atque Machinarum omnis generis componendarum methodus <lb/>proponitur.<emph.end type="italics"/><emph.end type="center"/></s><figure id="id.017.01.003.1.jpg" xlink:href="017/01/003/1.jpg"/>

<s><emph type="center"/>LUGDUNI, <lb/>Apud ANISSONIOS, JOAN, POSUEL <lb/>& CLAUDIUM RIGAUD.<emph.end type="center"/></s>

<s>D C. LXXXIV.<emph.end type="italics"/><lb/>CUM PRIVILEGIO REGIS.<emph.end type="center"/></s><pb/><figure/><pb/>

<s>D C. LXXXIV.<emph.end type="italics"/><lb/>CUM PRIVILEGIO REGIS.<emph.end type="center"/></s><pb xlink:href="017/01/004.jpg"/><figure id="id.017.01.004.1.jpg" xlink:href="017/01/004/1.jpg"/><pb xlink:href="017/01/005.jpg"/>

<s><emph type="center"/>CHRISTIANISSIMO <lb/>GALLIARUM <lb/>ET NAVARRÆ REGI <lb/>LUDOVICO <lb/>MAGNO.<emph.end type="center"/></s>

<s><emph type="italics"/>AD Maje&longs;tatis Tuæ pedes,<emph.end type="italics"/><lb/>REX INVICTISSIME, <lb/><emph type="italics"/>me, meámque hanc de rebus <lb/>Mechanicis lucubrationem, <lb/>ignotus homo, vix forta&longs;&longs;e cre<lb/>dibili confidentiâ, &longs;i&longs;to: Sed <lb/>quâ Regiâ comitate omnium <lb/>animos concilias, eâdem &longs;u&longs;tentor, ne repul&longs;am <lb/>timeam. </s>

<s>In Te Orbis univer&longs;i conjecti &longs;unt oculi, <lb/>quos Tuæ Gloriæ &longs;plendor allicit: à communi feli-<emph.end type="italics"/><pb/><emph type="italics"/>citate quid me paterer excludi? </s>

<s>In Te Orbis univer&longs;i conjecti &longs;unt oculi, <lb/>quos Tuæ Gloriæ &longs;plendor allicit: à communi feli-<emph.end type="italics"/><pb xlink:href="017/01/006.jpg"/><emph type="italics"/>citate quid me paterer excludi? </s>

<s>Amplißima <lb/>Tua in Societatem no&longs;tram merita, quorum nullam <lb/>partem, ne cogitandâ quidem gratiâ, con&longs;equi <lb/>po&longs;&longs;umus, hoc &longs;altem officij ab univer&longs;o Ordine re<lb/>petunt, ut &longs;inguli, quem cordi penitißimè impre&longs;&longs;um <lb/>ge&longs;tamus non ingrati LVDOVICVM, in <lb/>libris palàm in&longs;criptum velimus. </s>

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<s>Neque <lb/>illa quidem aut ex rerum magnitudine ac difficul<lb/>tate, aut ex multiplicato numero, aut ex di&longs;simi<lb/>lium varietate, aut ex &longs;erie non interruptâ, me<lb/>tienda duxi, quamquam & in his admirabilitatis <lb/>plurimum in&longs;it: Verùm longè omnem admirationem <lb/>multúmque &longs;uperare mihi videtur, quòd paucis <lb/>lu&longs;tris vel &longs;æcula complexus, unus pluribus Regibus <lb/>par, tot, tantáque perficere valui&longs;ti. </s>

<s>Ingentis pon<lb/>deris gravitatem vincit adhibita Machina, &longs;ed <lb/>diuturno impul&longs;u agitanda, ut proficiat aliquid: At <lb/>plurima immen&longs;is munita difficultatibus exiguo tem<lb/>poris &longs;patio expugnare, atque ad optatum exitum <lb/>perducere, ita Tuum e&longs;t, REX INVICTISSIME, <lb/>ut quemadmodum rerum ge&longs;tarum gloriâ, ac nomi<lb/>nis celebritate, nemini &longs;uperiorum Regum &longs;ecundus<emph.end type="italics"/><pb/><emph type="italics"/>prædicaris, &longs;ic Tibi &longs;ecundum, qui Tuis planè in<lb/>&longs;i&longs;tat ve&longs;tigiis, ventura &longs;æcula &longs;perare vix audeant. </s>

<s>Ingentis pon<lb/>deris gravitatem vincit adhibita Machina, &longs;ed <lb/>diuturno impul&longs;u agitanda, ut proficiat aliquid: At <lb/>plurima immen&longs;is munita difficultatibus exiguo tem<lb/>poris &longs;patio expugnare, atque ad optatum exitum <lb/>perducere, ita Tuum e&longs;t, REX INVICTISSIME, <lb/>ut quemadmodum rerum ge&longs;tarum gloriâ, ac nomi<lb/>nis celebritate, nemini &longs;uperiorum Regum &longs;ecundus<emph.end type="italics"/><pb xlink:href="017/01/007.jpg"/><emph type="italics"/>prædicaris, &longs;ic Tibi &longs;ecundum, qui Tuis planè in<lb/>&longs;i&longs;tat ve&longs;tigiis, ventura &longs;æcula &longs;perare vix audeant. </s>

<lb/><s>Patere igitur pro &longs;ummâ, quâ præditus es, huma<lb/>nitate, qualemcumque hanc rerum Mechanicarum <lb/>tractationem Regio in&longs;igniri Nomine, ut, quos <lb/>meas ha&longs;ce commentationes legere non piguerit, <lb/>vel hinc di&longs;cant, aliud e&longs;&longs;e non imitabile genus <lb/>Facultatis, quâ ingentia citò perficiantur, &longs;i <lb/>LVDOVICI MAGNI mens acce&longs;&longs;erit. </s>

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<s>Parmæ Kal, Maij 1683. </s>

<s>Humillimus atque Ob&longs;equenti&longs;&longs;imus <lb/>Servus <lb/>PAULUS CASATUS è SOC. JESU. <pb/><gap desc="hr tag"/><emph type="center"/><emph type="italics"/>Facultas R. P. Provincialis Societatis Je&longs;u <lb/>in Provincia Veneta.<emph.end type="italics"/><emph.end type="center"/></s>

<s>Humillimus atque Ob&longs;equenti&longs;&longs;imus <lb/>Servus <lb/>PAULUS CASATUS è SOC. JESU. <pb xlink:href="017/01/008.jpg"/><gap desc="hr tag"/><emph type="center"/><emph type="italics"/>Facultas R. P. Provincialis Societatis Je&longs;u <lb/>in Provincia Veneta.<emph.end type="italics"/><emph.end type="center"/></s>

<s>EGo Octavius Rubeus Societatis Je&longs;u in Provincia Veneta <lb/>Præpo&longs;itus Provincialis, pote&longs;tate ad id mihi factâ ab <lb/>Adm. </s>

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<s>JUNQUIERES. </s>

<s>MECHA </s><pb/><figure/>

<s>MECHA </s><pb xlink:href="017/01/009.jpg"/><figure id="id.017.01.009.1.jpg" xlink:href="017/01/009/1.jpg"/>

<s><emph type="center"/>AD LECTOREM.<emph.end type="center"/></s>

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<s>Amico<lb/>rum tamen officio&longs;is &longs;timulis me urgeri pa&longs;&longs;us &longs;um, ut &longs;ub<lb/>ci&longs;ivis, quæ incurrebant, temporibus tentarem, an de&longs;ti<lb/>natam animo tractationem, cujus brevem Synop&longs;im au<lb/>ditoribus meis in Romano Collegio, anno labentis &longs;æculi <lb/>decimi &longs;eptimi quinquage&longs;imo quarto, tradideram, re<lb/>dordiri, & aliquâ ratione perficere liceret. </s>

<s>Licuit autem, <lb/>præter &longs;pem, toties dimi&longs;&longs;um calamum re&longs;umere, ut tan-<pb/>dem de &longs;ingulis Mechanicis Facultatibus aliquid me &longs;crip<lb/>&longs;i&longs;&longs;e invenerim, quod Mathematicarum di&longs;ciplinarum can<lb/>didatis profuturum amici cen&longs;uerunt, &longs;i publici juris fieret. </s>

<s>Licuit autem, <lb/>præter &longs;pem, toties dimi&longs;&longs;um calamum re&longs;umere, ut tan-<pb xlink:href="017/01/010.jpg"/>dem de &longs;ingulis Mechanicis Facultatibus aliquid me &longs;crip<lb/>&longs;i&longs;&longs;e invenerim, quod Mathematicarum di&longs;ciplinarum can<lb/>didatis profuturum amici cen&longs;uerunt, &longs;i publici juris fieret. </s>

<lb/><s>Quapropter alienæ utilitati &longs;erviendum potiùs fuit, quàm <lb/>meæ voluntati. </s>

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<s>Præterquam quod, &longs;i formâ <lb/>illâ Mathematicis familiari u&longs;us fui&longs;&longs;em, animum forta&longs;&longs;e <lb/>induxi&longs;&longs;es, me mihi ineptè blandiri, & qua&longs;i Geometri<lb/>cas ratiocinationes obtrudere ea, quæ &longs;atis probabili con<lb/>jecturâ &longs;tabilire conatus &longs;um. </s>

<s>Quamvis enim non pauca <lb/>attulerim, quæ Geometricas demon&longs;trationes recipiunt, <lb/>nec mihi videar p&longs;eudographis &longs;yllogi&longs;mis deceptus; quia <lb/>tamen & apud Phy&longs;icos & apud Mathematicos agenda <lb/>erat cau&longs;a, multa fuere ad Philo&longs;ophicas rationes revocan<lb/>da; & quidem, quoad ejus fieri potuit, à receptis in &longs;cho-<pb/>lis opinionibus mihi non erat hìc recedendum, ne quid <lb/>temerè &longs;ine argumentis proferrem, aut ne longiùs ab in<lb/>&longs;tituto recederem, &longs;i quid novi, quæ&longs;itâ veri &longs;imilitudine, <lb/>molirer. </s>

<s>Quamvis enim non pauca <lb/>attulerim, quæ Geometricas demon&longs;trationes recipiunt, <lb/>nec mihi videar p&longs;eudographis &longs;yllogi&longs;mis deceptus; quia <lb/>tamen & apud Phy&longs;icos & apud Mathematicos agenda <lb/>erat cau&longs;a, multa fuere ad Philo&longs;ophicas rationes revocan<lb/>da; & quidem, quoad ejus fieri potuit, à receptis in &longs;cho-<pb xlink:href="017/01/011.jpg"/>lis opinionibus mihi non erat hìc recedendum, ne quid <lb/>temerè &longs;ine argumentis proferrem, aut ne longiùs ab in<lb/>&longs;tituto recederem, &longs;i quid novi, quæ&longs;itâ veri &longs;imilitudine, <lb/>molirer. </s>

<s>Hoc videlicet mihi poti&longs;&longs;imum curæ fuit, ut Phy<lb/>&longs;icam admirandorum per Machinas motuum cau&longs;am in<lb/>ve&longs;tigarem: in Phy&longs;icis autem modum &longs;ciendi Geome<lb/>tricum inquirens, ne ab Ari&longs;totele redarguerer, timerem. </s>

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<s>Mihi autem <lb/>non ea e&longs;t memoriæ firmitas, quæ, quid aliquando lege<lb/>rim, aut ubi legerim, &longs;atis explicatâ recordatione &longs;uggerat. </s>

<lb/><s>Quòd &longs;i placui&longs;&longs;et, corrogatis aliunde libris, magnificam <lb/>hanc eruditionis pompam meæ qualicumque commenta<lb/>tioni adhibere, non &longs;atis otii ad legendum &longs;uppetebat, & <lb/>nimium temporis po&longs;tula&longs;&longs;et &longs;criptio, &longs;i exponendæ pri<lb/>mùm, dein confirmandæ aut refellendæ fui&longs;&longs;ent aliorum <pb/>&longs;ententiæ: propterea &longs;atius duxi, quæ animo occurrebant, <lb/>pro meâ con&longs;uetudine breviter &longs;implicitérque &longs;cribere, <lb/>vix aliquando tactâ alicujus Authoris opinione, quam in <lb/>adver&longs;ariis jampridem notatam inveni. </s>

<lb/><s>Quòd &longs;i placui&longs;&longs;et, corrogatis aliunde libris, magnificam <lb/>hanc eruditionis pompam meæ qualicumque commenta<lb/>tioni adhibere, non &longs;atis otii ad legendum &longs;uppetebat, & <lb/>nimium temporis po&longs;tula&longs;&longs;et &longs;criptio, &longs;i exponendæ pri<lb/>mùm, dein confirmandæ aut refellendæ fui&longs;&longs;ent aliorum <pb xlink:href="017/01/012.jpg"/>&longs;ententiæ: propterea &longs;atius duxi, quæ animo occurrebant, <lb/>pro meâ con&longs;uetudine breviter &longs;implicitérque &longs;cribere, <lb/>vix aliquando tactâ alicujus Authoris opinione, quam in <lb/>adver&longs;ariis jampridem notatam inveni. </s>

<s>Nec te pluribus volo, Amice Lector. </s>

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<s>In iis verò, in quibus à me per impru<lb/>dentiam peccatum fuerit, à tuâ Sapientiâ facilè patiar me <lb/>dedoceri. </s>

<s>ELENCHUS </s><pb/><figure/>

<s>ELENCHUS </s><pb xlink:href="017/01/013.jpg"/><figure id="id.017.01.013.1.jpg" xlink:href="017/01/013/1.jpg"/>

<s><emph type="center"/>ELENCHUS CAPITUM.<emph.end type="center"/></s>

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<row><cell>V.</cell><cell><emph type="italics"/>In quo Machinarum vires &longs;ita &longs;int.<emph.end type="italics"/></cell></row>

<row><cell>VI.</cell><cell><emph type="italics"/>Quid attendendum &longs;it in Machinæ collocatione, at que materiæ.<emph.end type="italics"/></cell></row>

<row><cell>VII.</cell><cell><emph type="italics"/>Præ&longs;tetne Machinam augere? an componere?<emph.end type="italics"/></cell></row>

<pb/>

<row><cell>VIII.</cell><cell><emph type="italics"/>Cur majores rotæ motum juvent præ minoribus.<emph.end type="italics"/></cell></row>

<row><cell>IX.</cell><cell><emph type="italics"/>Quid cylindri & Scytalæ ad faciliorem ponderis motum præ&longs;tent.<emph.end type="italics"/></cell></row>

<row><cell>X.</cell><cell><emph type="italics"/>Circulorum Concentricorum motus explicatur.<emph.end type="italics"/></cell></row></table>

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<row><cell>VII.</cell><cell><emph type="italics"/>Quid conferat Potentiæ moventis applicatio ad Vectens.<emph.end type="italics"/></cell></row>

<row><cell>VIII.</cell><cell><emph type="italics"/>Oneris ex Vecte pendentis momentum inquiritur.<emph.end type="italics"/></cell></row>

<row><cell>IX.</cell><cell><emph type="italics"/>An duo pondus ge&longs;tantes æqualiter premantur.<emph.end type="italics"/></cell></row>

<pb/>

<row><cell>X.</cell><cell><emph type="italics"/>An vis Ela&longs;tica ad aliquod Vectis genus pertineat.<emph.end type="italics"/></cell></row>

<row><cell>XI.</cell><cell><emph type="italics"/>Cur longiora corpora faciliùs flectantur, difficiliùs &longs;u&longs;tincantur.<emph.end type="italics"/></cell></row>

<row><cell>XII.</cell><cell><emph type="italics"/>Vnde oriantur forcipum, & forficum vires.<emph.end type="italics"/></cell></row>

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<row><cell>VI.</cell><cell><emph type="italics"/>Trochlearum ope moveri pote&longs;t pondus velociter.<emph.end type="italics"/></cell></row>

<row><cell>VII.</cell><cell><emph type="italics"/>Quàm validum e&longs;&longs;e oporteat Trochlearum retinaculum.<emph.end type="italics"/></cell></row>

<row><cell>VIII.</cell><cell><emph type="italics"/>Aliqui Trochlearum u&longs;us indicantur.<emph.end type="italics"/></cell></row></table>

<pb/>

<s><emph type="center"/>LIBER SEPTIMUS. De Cuneo, & Percu&longs;&longs;ionibus.<emph.end type="center"/></s>

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<row><cell>III.</cell><cell><emph type="italics"/>Cochlea cum Vecte, atque cum Axe componitur.<emph.end type="italics"/></cell></row>

<row><cell>IV.</cell><cell><emph type="italics"/>Cochleæ Infinitæ vires explicantur.<emph.end type="italics"/></cell></row>

<row><cell>V.</cell><cell><emph type="italics"/>Cochlea u&longs;us aliqui indicantur.<emph.end type="italics"/></cell></row></table>

<s><emph type="center"/>MECHANICORUM<emph.end type="center"/></s>

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<s><emph type="center"/><emph type="italics"/>Quid &longs;it Centrum gravium, & levium.<emph.end type="italics"/><emph.end type="center"/></s>

<s>QUoniam hæc rerum univer&longs;itas corpora diver&longs;æ inter &longs;e <lb/>rationis complectitur, eorum ordo aliquis nece&longs;&longs;ariu, fuit

<pb n="2"/>ut &longs;uo unumquodque loco di&longs;poneretur; atque adeò æquum <lb/>fuit, ut &longs;ingulis à natura ea tribueretur facultas, quâ & &longs;e &longs;uo <lb/>in loco, hoc e&longs;t, juxta in&longs;itam propen&longs;ionem &longs;ibi debito, con<lb/>&longs;ervare po&longs;&longs;int, & ad illum &longs;e ip&longs;a promovere, &longs;i fortè indè <lb/>dimota fuerint. </s><s>Quia verò æqualia non ni&longs;i æqualiter, &longs;imili<lb/>que ratione di&longs;ponenda erant, nullum autem corpus præter <lb/>&longs;phæram habet perfectam in partium di&longs;po&longs;itione æqualitatem, <lb/>debuerunt corpora omnia orbem unum con&longs;tituere. </s><s>At in <lb/>&longs;phæra punctum unum e&longs;t, à quo æqualibus radiis extremæ <lb/>&longs;uperficiei partes removentur: igitur ex ordine ad punctum <lb/>hoc, quod Centrum dicitur, comparanda &longs;unt corpora; qua<lb/>tenus cùm naturâ impellente moventur, ut in loco &longs;ibi debito, <lb/>à quo per vim &longs;ejuncta fuere, demum con&longs;i&longs;tant, vel ad cen<lb/>trum hoc accedunt, vel ab eo recedunt. </s>

<pb xlink:href="017/01/018.jpg" n="2"/>ut &longs;uo unumquodque loco di&longs;poneretur; atque adeò æquum <lb/>fuit, ut &longs;ingulis à natura ea tribueretur facultas, quâ & &longs;e &longs;uo <lb/>in loco, hoc e&longs;t, juxta in&longs;itam propen&longs;ionem &longs;ibi debito, con<lb/>&longs;ervare po&longs;&longs;int, & ad illum &longs;e ip&longs;a promovere, &longs;i fortè indè <lb/>dimota fuerint. </s><s>Quia verò æqualia non ni&longs;i æqualiter, &longs;imili<lb/>que ratione di&longs;ponenda erant, nullum autem corpus præter <lb/>&longs;phæram habet perfectam in partium di&longs;po&longs;itione æqualitatem, <lb/>debuerunt corpora omnia orbem unum con&longs;tituere. </s><s>At in <lb/>&longs;phæra punctum unum e&longs;t, à quo æqualibus radiis extremæ <lb/>&longs;uperficiei partes removentur: igitur ex ordine ad punctum <lb/>hoc, quod Centrum dicitur, comparanda &longs;unt corpora; qua<lb/>tenus cùm naturâ impellente moventur, ut in loco &longs;ibi debito, <lb/>à quo per vim &longs;ejuncta fuere, demum con&longs;i&longs;tant, vel ad cen<lb/>trum hoc accedunt, vel ab eo recedunt. </s>

<s>Et quidem &longs;i ad centrum accedant, gravitare dicuntur, &longs;i <lb/>verò recedant, levitare: & quæ propiora centro con&longs;i&longs;tunt, <lb/>graviora, quæ autem remotiora, leviora quoque cen&longs;entur <lb/>&longs;ecundùm &longs;peciem gravitatis, & levitatis: quicquid &longs;it quod <lb/>æqualia e&longs;&longs;e po&longs;&longs;int &longs;ecundùm gravitatem ab&longs;olutam, aut etiam <lb/>&longs;æpè contingat minus habere gravitatis ab&longs;olutæ id, quod e&longs;t <lb/>gravius &longs;ecundùm &longs;peciem. </s><s>Sic libra plumbi æqualis e&longs;t libræ <lb/>aquæ, immò minor centum libris aquæ; quia tamen plum<lb/>bum infra aquam de&longs;cendens fit centro vicinius, etiam gra<lb/>vius e&longs;t &longs;ecundùm &longs;peciem. </s><s>Quod &longs;i comparare velis duo cor<lb/>pora &longs;olida, quæ &longs;ibi &longs;ua duritie ita ob&longs;i&longs;tunt, ut neutrum intra <lb/>alterum moveri po&longs;&longs;it tanquam in medio; illud e&longs;&longs;e &longs;ecundùm <lb/>&longs;peciem gravius affirmabis, quod datâ paritate molis cum alio <lb/>corpore, cum quo comparatur, &longs;taterâ expen&longs;um in eodem <lb/>medio, in quo utrumque gravitat puta in aëre, plus habere <lb/>ponderis deprehendes. </s><s>Sic aurum e&longs;t ferro gravius in &longs;pecie, <lb/>quia ex æqualibus molibus auri & ferri, aurea e&longs;t pondero&longs;ior. </s>

<s>Generatim autem loquendo ea &longs;unt in &longs;pecie graviora, quæ <lb/>&longs;unt den&longs;iora, ea verò in &longs;pecie leviora, quæ rariora: nam & <lb/>inflata ve&longs;ica ob aërem con&longs;tipatum gravior e&longs;t, quàm flaccida; <lb/>& Æolipilam candentem, aëre intus vi caloris raro, leviorem <lb/>primùm, po&longs;teà, ubi refrixerit, graviorem e&longs;&longs;e experimento <lb/>didicimus, aëre a&longs;&longs;umptam <gap/>aritatem abjiciente. </s><s>Cùm enim <lb/>radij à &longs;phæræ centro ad &longs;uperficiem ducti longiùs à &longs;e invi-

<s>Generatim autem loquendo ea &longs;unt in &longs;pecie graviora, quæ <lb/>&longs;unt den&longs;iora, ea verò in &longs;pecie leviora, quæ rariora: nam & <lb/>inflata ve&longs;ica ob aërem con&longs;tipatum gravior e&longs;t, quàm flaccida; <lb/>& Æolipilam candentem, aëre intus vi caloris raro, leviorem <lb/>primùm, po&longs;teà, ubi refrixerit, graviorem e&longs;&longs;e experimento <lb/>didicimus, aëre a&longs;&longs;umptam raritatem abjiciente. </s><s>Cùm enim <lb/>radij à &longs;phæræ centro ad &longs;uperficiem ducti longiùs à &longs;e invi-

<pb n="3"/>cem recedant, æquum fuit, ut quæ plus habent materiæ atque <lb/>&longs;ub&longs;tantiæ &longs;ub minori mole, in angu&longs;tiore &longs;patio collocarentur; <lb/>ea verò, quæ &longs;ub majoribus dimen&longs;ionibus continentur, am<lb/>pliora &longs;patia occuparent, ubi radij magis di&longs;tant: ut videlicet <lb/>hac ratione æqua &longs;ub&longs;tantiæ di&longs;tributio fieret in totâ &longs;phærâ. </s><lb/><s>Hinc vides, cur idem corpus, eo ip&longs;o quod rarum fit, a&longs;cendat, <lb/>ut aqua in vaporem re&longs;oluta (ni&longs;i aliunde ad de&longs;cendendum <lb/>determinetur, ut aurum fulminans) quia materies eadem &longs;ub <lb/>majoribus dimen&longs;ionibus petit longiùs abe&longs;&longs;e à centro, ibiquè <lb/>tanti&longs;per conquie&longs;cit, dum con&longs;tipata, atque minorem in mo<lb/>lem redacta, iterum de&longs;cendat. </s>

<pb xlink:href="017/01/019.jpg" n="3"/>cem recedant, æquum fuit, ut quæ plus habent materiæ atque <lb/>&longs;ub&longs;tantiæ &longs;ub minori mole, in angu&longs;tiore &longs;patio collocarentur; <lb/>ea verò, quæ &longs;ub majoribus dimen&longs;ionibus continentur, am<lb/>pliora &longs;patia occuparent, ubi radij magis di&longs;tant: ut videlicet <lb/>hac ratione æqua &longs;ub&longs;tantiæ di&longs;tributio fieret in totâ &longs;phærâ. </s><lb/><s>Hinc vides, cur idem corpus, eo ip&longs;o quod rarum fit, a&longs;cendat, <lb/>ut aqua in vaporem re&longs;oluta (ni&longs;i aliunde ad de&longs;cendendum <lb/>determinetur, ut aurum fulminans) quia materies eadem &longs;ub <lb/>majoribus dimen&longs;ionibus petit longiùs abe&longs;&longs;e à centro, ibiquè <lb/>tanti&longs;per conquie&longs;cit, dum con&longs;tipata, atque minorem in mo<lb/>lem redacta, iterum de&longs;cendat. </s>

<s>Quare centrum hoc, quod motus, vel quies corporum re&longs;pi<lb/>cit, dicitur <emph type="italics"/>Centrum gravium, & levium<emph.end type="italics"/>; atque idem creditur <lb/>e&longs;&longs;e cum centro univer&longs;i: vel &longs;altem (ne parùm utili nos di&longs;pu<lb/>tatione torqueamus) centrum eorum, quæ in hac &longs;phærâ ele<lb/>mentari gravia, aut levia dicuntur, idem e&longs;t cum centro ter<lb/>raquei hujus globi, ut quotidiana docet experientia: quicquid <lb/>&longs;it, an pars lunaris globi, &longs;i à lunâ &longs;ejungeretur, reditura e&longs;&longs;er <lb/>ad lunam, ut ad centrum &longs;ui motus. </s><s>Tam itaquè, quæ huju&longs;mo<lb/>di centro proxima &longs;unt, deor&longs;um po&longs;ita dicuntur, &longs;ur&longs;um verò, <lb/>quæ ab eo longiùs collocata &longs;unt. </s><s>Hinc telluris &longs;uperficiei in<lb/>&longs;i&longs;tentes caput &longs;ur&longs;um, pedes deor&longs;um habere dicimur. </s><s>Ille <lb/>verò, quamvis rectus, & pedes, & caput &longs;ur&longs;um haberet, cu<lb/>jus umbilicus huic centro univer&longs;i congrueret. </s><s>Per quod pa<lb/>riter centrum &longs;i &longs;cala ducta intelligatur, duo po&longs;&longs;ent &longs;ibi non <lb/>occurrere invicem, licet alter a&longs;cenderet, alter de&longs;cenderet; <lb/>hic &longs;iquidem accederet ad centrum, ille inde recederet: per <lb/>eam verò po&longs;&longs;et uterque a&longs;cendere, & tamen licet, æquali mo<lb/>tu moverentur, &longs;emper invicem di&longs;tarent magis, quò à centro <lb/>ad oppo&longs;itas partes recederent. <lb/><gap desc="hr tag"/></s>

Line 303

<s><emph type="center"/><emph type="italics"/>An corpora prædita &longs;int gravitate, & levitate.<emph.end type="italics"/><emph.end type="center"/></s>

<s>INter ea, quæ planè homogenea &longs;unt, ordo e&longs;&longs;e non pote&longs;t à <lb/>naturâ in&longs;titutus: hinc &longs;i nulla e&longs;&longs;et corporum di&longs;&longs;imilitudo,

<pb n="4"/>&longs;ed ex omninò &longs;imilibus &longs;ub&longs;tantiæ partibus totus hic orbis <lb/>conflaretur, nulla quoque e&longs;&longs;et aut gravitas, aut levitas. </s><s>Quid <lb/>enim hæc potiùs pars, nulla naturæ conditione à cæteris di&longs;cre<lb/>ta, petat abe&longs;&longs;e à centro, illa verò exigat in co conquie&longs;cere? </s><s><lb/>verùm quia multiplici corporum genere coagmentata rerum <lb/>univer&longs;itas inconcinna e&longs;&longs;e non potuit, &longs;uum cuique locum na<lb/>tura tribuit, in quo &longs;e &longs;i&longs;teret, ut infra hæc quidem de&longs;cende<lb/>ret, &longs;uprà illa verò a&longs;cenderet, &longs;i quando &longs;ibi invicem con<lb/>tigua fierent ordine præpo&longs;tero, nec ullus e&longs;&longs;et motui obex. </s><lb/><s>Cùm itaque corpora &longs;ingula in&longs;itam habeant propen&longs;ionem <lb/>(ab Ari&longs;totele dicitur <foreign lang="greek">o(rmh/</foreign>) qua petunt certum locum in uni<lb/>ver&longs;o; con&longs;tat præter de&longs;cendentium gravitatem dari etiam po<lb/>&longs;itivam levitatem, quâ corpus aliquod &longs;e ip&longs;um promovet ad <lb/>&longs;uperiores partes univer&longs;i à centro magis di&longs;tantes, neque &longs;o<lb/>lùm admittendam levitatem negativam, quâ corpora minùs <lb/>gravia cen&longs;entur levia, &longs;i eorum cum gravioribus fiat compa<lb/>ratio. </s><s>Nam &longs;i ea, quæ levia dicuntur, eatenus dicas a&longs;cendere, <lb/>quatenus à gravioribus in inferiorem locum de&longs;cendentibus <lb/>propelluntur; mihi æquè liberum erit tollere omnem po&longs;iti<lb/>vam gravitatem, &longs;olâ levitate admi&longs;sâ; & omnia pariter &longs;ol<lb/>vam dicendo ea gravia cen&longs;eri, quæ minùs levia &longs;unt, atque <lb/>ideò tantùm de&longs;cendere, quòd extrin&longs;ecùs à levioribus a&longs;cen<lb/>dentibus loco pul&longs;a detrudantur, non quòd ab internâ faculta<lb/>te deor&longs;um impellantur. </s><s>Quod &longs;i vel gravitas de medio tollen<lb/>da &longs;it, vel levitas, &longs;atius e&longs;t levitatem relinquere; naturâ vi<lb/>delicet ad altiora &longs;emper, & perfectiora a&longs;pirante, nec adeò <lb/>contendente de infimo loco. </s><s>Quare cùm per gravitatem &longs;olam <lb/>æquè ac per &longs;olam levitatem motus i&longs;ti explicentur, cæteroqui <lb/>autem ingenita &longs;it unicuique corpori &longs;ui loci exigentia; utram<lb/>que admittere rationi maximè con&longs;entaneum fuerit. </s>

<pb xlink:href="017/01/020.jpg" n="4"/>&longs;ed ex omninò &longs;imilibus &longs;ub&longs;tantiæ partibus totus hic orbis <lb/>conflaretur, nulla quoque e&longs;&longs;et aut gravitas, aut levitas. </s><s>Quid <lb/>enim hæc potiùs pars, nulla naturæ conditione à cæteris di&longs;cre<lb/>ta, petat abe&longs;&longs;e à centro, illa verò exigat in co conquie&longs;cere? </s><s><lb/>verùm quia multiplici corporum genere coagmentata rerum <lb/>univer&longs;itas inconcinna e&longs;&longs;e non potuit, &longs;uum cuique locum na<lb/>tura tribuit, in quo &longs;e &longs;i&longs;teret, ut infra hæc quidem de&longs;cende<lb/>ret, &longs;uprà illa verò a&longs;cenderet, &longs;i quando &longs;ibi invicem con<lb/>tigua fierent ordine præpo&longs;tero, nec ullus e&longs;&longs;et motui obex. </s><lb/><s>Cùm itaque corpora &longs;ingula in&longs;itam habeant propen&longs;ionem <lb/>(ab Ari&longs;totele dicitur <foreign lang="greek">o(rmh/</foreign>) qua petunt certum locum in uni<lb/>ver&longs;o; con&longs;tat præter de&longs;cendentium gravitatem dari etiam po<lb/>&longs;itivam levitatem, quâ corpus aliquod &longs;e ip&longs;um promovet ad <lb/>&longs;uperiores partes univer&longs;i à centro magis di&longs;tantes, neque &longs;o<lb/>lùm admittendam levitatem negativam, quâ corpora minùs <lb/>gravia cen&longs;entur levia, &longs;i eorum cum gravioribus fiat compa<lb/>ratio. </s><s>Nam &longs;i ea, quæ levia dicuntur, eatenus dicas a&longs;cendere, <lb/>quatenus à gravioribus in inferiorem locum de&longs;cendentibus <lb/>propelluntur; mihi æquè liberum erit tollere omnem po&longs;iti<lb/>vam gravitatem, &longs;olâ levitate admi&longs;sâ; & omnia pariter &longs;ol<lb/>vam dicendo ea gravia cen&longs;eri, quæ minùs levia &longs;unt, atque <lb/>ideò tantùm de&longs;cendere, quòd extrin&longs;ecùs à levioribus a&longs;cen<lb/>dentibus loco pul&longs;a detrudantur, non quòd ab internâ faculta<lb/>te deor&longs;um impellantur. </s><s>Quod &longs;i vel gravitas de medio tollen<lb/>da &longs;it, vel levitas, &longs;atius e&longs;t levitatem relinquere; naturâ vi<lb/>delicet ad altiora &longs;emper, & perfectiora a&longs;pirante, nec adeò <lb/>contendente de infimo loco. </s><s>Quare cùm per gravitatem &longs;olam <lb/>æquè ac per &longs;olam levitatem motus i&longs;ti explicentur, cæteroqui <lb/>autem ingenita &longs;it unicuique corpori &longs;ui loci exigentia; utram<lb/>que admittere rationi maximè con&longs;entaneum fuerit. </s>

<s>Vitreum globum vacuum, qui in tubulum recurvum de&longs;i<lb/>nat, quoad fieri pote&longs;t, calefactum, ut inclu&longs;us aör rare&longs;cat, <lb/>Hermeticè claude: tum adjiciatur congruens plumbi gravitas, <lb/>quâ infra aquam deprimatur. </s><s>Sit autem globus, unà cum ad<lb/>jecto plumbo, connexus cum exqui&longs;itæ libræ brachio, aut lan<lb/>ce, ejú&longs;que gravitas intrà aquam exploretur: ubi gravitas in<lb/>notuerit, adhuc &longs;ub aquâ retineatur globus, &longs;ed longiore for<lb/>cipe extremum tubuli caput occlu&longs;um frangatur: & animad-

<pb n="5"/>vertes globi vitrci cum appen&longs;o plumbo gravitatem augeri; cu<lb/>jus incrementum indicabitur ab addito in oppo&longs;itâ lance pon<lb/>dere ad con&longs;tituendum æquilibrium. </s><s>Cùm itaque idem maneat <lb/>vitrum, idémque plumbum, & nulla facta &longs;it alicujus gravita<lb/>tis acce&longs;&longs;io, illud unum &longs;upere&longs;t, quòd aör rarus intrà globum <lb/>conclu&longs;us levior, quàm idem aör, aperto tubulo, &longs;ibi re&longs;titu<lb/>tus, plus elidit gravitatis plumbi & vitri; atque moles compo<lb/>&longs;ita ex plumbo, vitro, & aëre raro, &longs;ecundùm &longs;peciem levior <lb/>e&longs;t, quàm moles ex plumbo, vitro, & aëre non raro. </s><s>Aër igi<lb/>tur intra aquam ita levis e&longs;t, ut aliquid gravitatis imminuat: <lb/>Nam &longs;i globum eundem ex aquâ ext<gap/>actum, omni aöre exclu<lb/>&longs;o, aquâ repleveris, & iterum eodem plumbo adjecto eju&longs;dem <lb/>gravitatem intrà aquam examinaveris, illam adhuc majorem <lb/>deprehendes; quia &longs;cilicet nulla levitas aöris ade&longs;t, quæ ali<lb/>quam deterat gravitatem, &longs;ed illa &longs;olùm perire videtur, quam <lb/>infert di&longs;crimen gravitatum &longs;ecundùm &longs;peciem, ut ex Hy<lb/>dro&longs;taticis con&longs;tat. </s><s>Neque &longs;u&longs;piceris hæc gravitatum incre<lb/>menta oriri ex aquâ &longs;ubeunte per apertum tubulum, cùm aër <lb/>a&longs;&longs;umptam ex calore raritatem abjicit, &longs;e in naturalem &longs;uam <lb/>molem re&longs;tituens, &longs;ivè, aëre pror&longs;us exclu&longs;o, ex aquæ globum <lb/>implentis gravitate. </s><s>Si enim vitrum aliud aut nullius, aut mo<lb/>dici&longs;&longs;imæ aquæ capax, &longs;ed eju&longs;dem in aëre ponderis cum a&longs;<lb/>&longs;umpto globo, &longs;imiliter in aquâ expendas, eandem invenies <lb/>gravitatem, &longs;ive multâ, &longs;ive modicâ aquâ repletum fuerit. </s><lb/><s>Non igitur aqua intrà aquam gravitatem auget. </s>

<pb xlink:href="017/01/021.jpg" n="5"/>vertes globi vitrci cum appen&longs;o plumbo gravitatem augeri; cu<lb/>jus incrementum indicabitur ab addito in oppo&longs;itâ lance pon<lb/>dere ad con&longs;tituendum æquilibrium. </s><s>Cùm itaque idem maneat <lb/>vitrum, idémque plumbum, & nulla facta &longs;it alicujus gravita<lb/>tis acce&longs;&longs;io, illud unum &longs;upere&longs;t, quòd aör rarus intrà globum <lb/>conclu&longs;us levior, quàm idem aör, aperto tubulo, &longs;ibi re&longs;titu<lb/>tus, plus elidit gravitatis plumbi & vitri; atque moles compo<lb/>&longs;ita ex plumbo, vitro, & aëre raro, &longs;ecundùm &longs;peciem levior <lb/>e&longs;t, quàm moles ex plumbo, vitro, & aëre non raro. </s><s>Aër igi<lb/>tur intra aquam ita levis e&longs;t, ut aliquid gravitatis imminuat: <lb/>Nam &longs;i globum eundem ex aquâ extractum, omni aëre exclu<lb/>&longs;o, aquâ repleveris, & iterum eodem plumbo adjecto eju&longs;dem <lb/>gravitatem intrà aquam examinaveris, illam adhuc majorem <lb/>deprehendes; quia &longs;cilicet nulla levitas aöris ade&longs;t, quæ ali<lb/>quam deterat gravitatem, &longs;ed illa &longs;olùm perire videtur, quam <lb/>infert di&longs;crimen gravitatum &longs;ecundùm &longs;peciem, ut ex Hy<lb/>dro&longs;taticis con&longs;tat. </s><s>Neque &longs;u&longs;piceris hæc gravitatum incre<lb/>menta oriri ex aquâ &longs;ubeunte per apertum tubulum, cùm aër <lb/>a&longs;&longs;umptam ex calore raritatem abjicit, &longs;e in naturalem &longs;uam <lb/>molem re&longs;tituens, &longs;ivè, aëre pror&longs;us exclu&longs;o, ex aquæ globum <lb/>implentis gravitate. </s><s>Si enim vitrum aliud aut nullius, aut mo<lb/>dici&longs;&longs;imæ aquæ capax, &longs;ed eju&longs;dem in aëre ponderis cum a&longs;<lb/>&longs;umpto globo, &longs;imiliter in aquâ expendas, eandem invenies <lb/>gravitatem, &longs;ive multâ, &longs;ive modicâ aquâ repletum fuerit. </s><lb/><s>Non igitur aqua intrà aquam gravitatem auget. </s>

<s>Sed illud, ut reliqua &longs;ileam, non leviter &longs;uadere pote&longs;t cor<lb/>pora &longs;uis nutibus non deor&longs;um tantùm, &longs;ed etiam &longs;ur&longs;um co<lb/>nari, quod mihi haud ita pridem aliud inve&longs;tiganti contigit <lb/>ob&longs;ervare. </s><s>Cum enim animadverti&longs;&longs;em aliquando, quàm di&longs;<lb/>par e&longs;&longs;et gravitas aquæ dimidiam &longs;itulam implentis, &longs;i illa in &longs;u<lb/>perficie horizontali libraret &longs;e&longs;e, ac quandò &longs;uppo&longs;ita ligneo <lb/>globo firmiter cum &longs;uperiore tigillo cohærenti altiùs ad latera <lb/>a&longs;&longs;urgebat locum globo concedens, quem tamen non &longs;u&longs;tine<lb/>bat; &longs;ubiit animum cupido tentandi, an bubula ve&longs;ica inflata <lb/>tran&longs;ver&longs;is virgulis infra va&longs;is labra depre&longs;&longs;a ita, ut eam aqua <lb/>circumplecteretur, vim haberet pariter augendi momenta gra<lb/>vitatis; aquam &longs;iquidem cogebat a&longs;&longs;urgere ad altitudinem ma<lb/>jorem perpendicularem, ac quandò, ve&longs;icâ liberè innatante,

<pb n="6"/>&longs;ub&longs;idebat. </s><s>Inveni tamen nullum planè ob&longs;ervari po&longs;&longs;e in <lb/>gravitate di&longs;crimen, quamvis tam ampla e&longs;&longs;et ve&longs;ica, ut facilè <lb/>dimidiam va&longs;is capacitatem impleret: in utroque enim ca&longs;u pon<lb/>dus fuit lib. 44 1/2. </s><s>Id mihi, fateor, accidit præter opinionem: <lb/>

<pb xlink:href="017/01/022.jpg" n="6"/>&longs;ub&longs;idebat. </s><s>Inveni tamen nullum planè ob&longs;ervari po&longs;&longs;e in <lb/>gravitate di&longs;crimen, quamvis tam ampla e&longs;&longs;et ve&longs;ica, ut facilè <lb/>dimidiam va&longs;is capacitatem impleret: in utroque enim ca&longs;u pon<lb/>dus fuit lib. 44 1/2. </s><s>Id mihi, fateor, accidit præter opinionem: <lb/>

<figure/><lb/>Nam &longs;i ex pariete extet tigillus, cui adnectatur <lb/>cylindrus P, aut ve&longs;ica ritè firmata, ferè im<lb/>plens capacitatem va&longs;is AB, va&longs;que illi &longs;up<lb/>ponatur ita, ut aqua deinde infu&longs;a po&longs;&longs;it libe<lb/>rè cylindro circumfundi; percipies onus lon<lb/>gè majus, quàm pro gravitate aquæ infu&longs;æ, <lb/>&longs;i permitteretur &longs;ub&longs;idere: & &longs;i vas ex &longs;taterâ <lb/>pendeat, adducto reductóve &longs;acomate appa<lb/>rebunt momenta gravitatis longè majora, quàm &longs;i tota illa <lb/>aqua fundum peteret, & cylindri pars, quæ priùs immerge<lb/>batur, ab&longs;ci&longs;&longs;a, aut ve&longs;ica innataret. </s><s>Intelligebam id ex majori <lb/>altitudine perpendiculari aquæ &longs;upra eandem ba&longs;im oriri; nam <lb/>depre&longs;&longs;o va&longs;e ita, ut paulatim cylindus emcrgat, & aqua &longs;ub<lb/>&longs;idat, &longs;emper minuitur pondus: idem futurum &longs;perabam, &longs;i <lb/>ve&longs;ica intra aquam non ab extrin&longs;eco obice detineretur, &longs;ed à <lb/>virgulis cum va&longs;e ip&longs;o connexis; quandoquidem aqua ad ean<lb/>dem pariter altitudinem a&longs;&longs;urgebat &longs;uper ba&longs;im eandem: at <lb/>&longs;pem fefellit eventus. </s><s>Nec alia mihi &longs;e obtulit probabilior ra<lb/>tio, quàm ut exi&longs;timarem aquam altiorem vehementius qui<lb/>dem deor&longs;um niti, ve&longs;icam tamen leviorem altiùs depre&longs;&longs;am, <lb/>conantem &longs;ur&longs;um, æqualiter contendere, ut emergeret; cùm <lb/>verò ni&longs;us i&longs;te &longs;ur&longs;um oppo&longs;itas virgulas, atque adeò vas cum <lb/>illis connexum urgeret, elidi adver&longs;um impetum deor&longs;um, <lb/>qui à majore altitudine perpendiculari aquæ oriebatur, & &longs;o<lb/>lum remanere conatum ex ip&longs;orum corporum &longs;ub&longs;tantiâ pro<lb/>manantem, quæ &longs;icut eadem &longs;emper erat, &longs;ivè innataret ve&longs;i<lb/>ca, &longs;ivè per vim immergeretur, ita eadem obtinebat gravita<lb/>tis momenta. </s><s>Quo experimento (quamquam non me lateat, <lb/>quid pro &longs;e afferre hîc po&longs;&longs;ent aliter &longs;entientes) vi&longs;us mihi <lb/>&longs;um deprehendere non ob&longs;curum po&longs;itivæ levitatis ve&longs;ti<lb/>gium. </s>

<figure id="id.017.01.022.1.jpg" xlink:href="017/01/022/1.jpg"/><lb/>Nam &longs;i ex pariete extet tigillus, cui adnectatur <lb/>cylindrus P, aut ve&longs;ica ritè firmata, ferè im<lb/>plens capacitatem va&longs;is AB, va&longs;que illi &longs;up<lb/>ponatur ita, ut aqua deinde infu&longs;a po&longs;&longs;it libe<lb/>rè cylindro circumfundi; percipies onus lon<lb/>gè majus, quàm pro gravitate aquæ infu&longs;æ, <lb/>&longs;i permitteretur &longs;ub&longs;idere: & &longs;i vas ex &longs;taterâ <lb/>pendeat, adducto reductóve &longs;acomate appa<lb/>rebunt momenta gravitatis longè majora, quàm &longs;i tota illa <lb/>aqua fundum peteret, & cylindri pars, quæ priùs immerge<lb/>batur, ab&longs;ci&longs;&longs;a, aut ve&longs;ica innataret. </s><s>Intelligebam id ex majori <lb/>altitudine perpendiculari aquæ &longs;upra eandem ba&longs;im oriri; nam <lb/>depre&longs;&longs;o va&longs;e ita, ut paulatim cylindus emcrgat, & aqua &longs;ub<lb/>&longs;idat, &longs;emper minuitur pondus: idem futurum &longs;perabam, &longs;i <lb/>ve&longs;ica intra aquam non ab extrin&longs;eco obice detineretur, &longs;ed à <lb/>virgulis cum va&longs;e ip&longs;o connexis; quandoquidem aqua ad ean<lb/>dem pariter altitudinem a&longs;&longs;urgebat &longs;uper ba&longs;im eandem: at <lb/>&longs;pem fefellit eventus. </s><s>Nec alia mihi &longs;e obtulit probabilior ra<lb/>tio, quàm ut exi&longs;timarem aquam altiorem vehementius qui<lb/>dem deor&longs;um niti, ve&longs;icam tamen leviorem altiùs depre&longs;&longs;am, <lb/>conantem &longs;ur&longs;um, æqualiter contendere, ut emergeret; cùm <lb/>verò ni&longs;us i&longs;te &longs;ur&longs;um oppo&longs;itas virgulas, atque adeò vas cum <lb/>illis connexum urgeret, elidi adver&longs;um impetum deor&longs;um, <lb/>qui à majore altitudine perpendiculari aquæ oriebatur, & &longs;o<lb/>lum remanere conatum ex ip&longs;orum corporum &longs;ub&longs;tantiâ pro<lb/>manantem, quæ &longs;icut eadem &longs;emper erat, &longs;ivè innataret ve&longs;i<lb/>ca, &longs;ivè per vim immergeretur, ita eadem obtinebat gravita<lb/>tis momenta. </s><s>Quo experimento (quamquam non me lateat, <lb/>quid pro &longs;e afferre hîc po&longs;&longs;ent aliter &longs;entientes) vi&longs;us mihi <lb/>&longs;um deprehendere non ob&longs;curum po&longs;itivæ levitatis ve&longs;ti<lb/>gium. </s>

<s>Ut autem levitatem corporibus adimendam a&longs;&longs;ererent in<lb/>genio&longs;i Academici, hoc poti&longs;&longs;imum ducti &longs;unt experimento. </s><s>

<pb n="7"/>Ligneum <expan abbr="cylindr&utilde;">cylindrum</expan> ABC <lb/>

<pb xlink:href="017/01/023.jpg" n="7"/>Ligneum <expan abbr="cylindr&utilde;">cylindrum</expan> ABC <lb/>

<figure/><lb/>plano horizontali D, E, <lb/>perpendicularem &longs;tatue<lb/>runt; & ut cylindri ba<lb/>&longs;is &longs;ubjecto plano exactè <lb/>congrueret, laminas duas <lb/>accurati&longs;&longs;imè lævigatas, <lb/>tùm cylindri ba&longs;i, tùm <lb/>&longs;ubjecto plano firmiter <lb/>adnexas voluerunt. </s><s>Tùm <lb/>ne aër facilè inter utrum<lb/>que &longs;ubiret, erecto &longs;upra <lb/><expan abbr="plan&utilde;">planum</expan> in orbem ex cretâ, <lb/>aut cerâ aggerulo, <expan abbr="argen-t&utilde;">argen<lb/>tum</expan> vivum infuderunt. </s><s>Cylindrum extremo libræ jugo G, alligâ<lb/>runt, addito in oppo&longs;itâ libræ extremitate H pondere L cylin<lb/>dri pondus adæquante; quod utique cylindrum elevare non po<lb/>te&longs;t. </s><s>Additum igitur e&longs;t & aliud pondus M u&longs;que eò, dum cy<lb/>lindrus à &longs;ubjecto plano avelleretur, & fuit librarum circiter <lb/>trium: quam men&longs;uram arguunt e&longs;&longs;e re&longs;i&longs;tentiæ cylindri con<lb/>tiguo plano adhærentis metu vacui. </s><s>His peractis concavum <lb/>vas cylindricum NOP, æqualis aut majoris altitudinis parâ<lb/>runt, laminâ pariter perpolitâ va&longs;is fundo adnexâ, cui impo<lb/>&longs;itus fuit cylindrus, adeoque adhæ&longs;it, ut, pleno-mercurij <lb/>va&longs;e, omninò non avelleretur, ut innataret; &longs;ed tunc demum <lb/>argento vivo innatavit, cùm per vim à va&longs;is fundo avul&longs;us e&longs;t <lb/>cylindrus: cui, ut iterum fundum peteret, & argento vivo <lb/>immergeretur, imponendum fuit pondus Q librarum circiter <lb/>quinque. </s><s>Vis ergò levitatis ligni in mercurio (&longs;i qua levitas <lb/>e&longs;&longs;et) æ&longs;timanda e&longs;&longs;et ut quinque, cùm vis adhæ&longs;ionis metu <lb/>vacui &longs;olùm inventa &longs;it ut tria: debui&longs;&longs;et igitur levitas ita præ<lb/>valere, ut adhæ&longs;ionem vinceret, & cylindrus &longs;ponte elevaretur. </s><lb/><s>Non e&longs;t itaque levitas, quæ ligneum cylindrum innatare cogit, <lb/>&longs;ed mercurij gravitas major ip&longs;a e&longs;t, quæ lignum elevat, cum <lb/>primùm locus patet, in quem de&longs;cendat. </s>

<figure id="id.017.01.023.1.jpg" xlink:href="017/01/023/1.jpg"/><lb/>plano horizontali D, E, <lb/>perpendicularem &longs;tatue<lb/>runt; & ut cylindri ba<lb/>&longs;is &longs;ubjecto plano exactè <lb/>congrueret, laminas duas <lb/>accurati&longs;&longs;imè lævigatas, <lb/>tùm cylindri ba&longs;i, tùm <lb/>&longs;ubjecto plano firmiter <lb/>adnexas voluerunt. </s><s>Tùm <lb/>ne aër facilè inter utrum<lb/>que &longs;ubiret, erecto &longs;upra <lb/><expan abbr="plan&utilde;">planum</expan> in orbem ex cretâ, <lb/>aut cerâ aggerulo, <expan abbr="argen-t&utilde;">argen<lb/>tum</expan> vivum infuderunt. </s><s>Cylindrum extremo libræ jugo G, alligâ<lb/>runt, addito in oppo&longs;itâ libræ extremitate H pondere L cylin<lb/>dri pondus adæquante; quod utique cylindrum elevare non po<lb/>te&longs;t. </s><s>Additum igitur e&longs;t & aliud pondus M u&longs;que eò, dum cy<lb/>lindrus à &longs;ubjecto plano avelleretur, & fuit librarum circiter <lb/>trium: quam men&longs;uram arguunt e&longs;&longs;e re&longs;i&longs;tentiæ cylindri con<lb/>tiguo plano adhærentis metu vacui. </s><s>His peractis concavum <lb/>vas cylindricum NOP, æqualis aut majoris altitudinis parâ<lb/>runt, laminâ pariter perpolitâ va&longs;is fundo adnexâ, cui impo<lb/>&longs;itus fuit cylindrus, adeoque adhæ&longs;it, ut, pleno-mercurij <lb/>va&longs;e, omninò non avelleretur, ut innataret; &longs;ed tunc demum <lb/>argento vivo innatavit, cùm per vim à va&longs;is fundo avul&longs;us e&longs;t <lb/>cylindrus: cui, ut iterum fundum peteret, & argento vivo <lb/>immergeretur, imponendum fuit pondus Q librarum circiter <lb/>quinque. </s><s>Vis ergò levitatis ligni in mercurio (&longs;i qua levitas <lb/>e&longs;&longs;et) æ&longs;timanda e&longs;&longs;et ut quinque, cùm vis adhæ&longs;ionis metu <lb/>vacui &longs;olùm inventa &longs;it ut tria: debui&longs;&longs;et igitur levitas ita præ<lb/>valere, ut adhæ&longs;ionem vinceret, & cylindrus &longs;ponte elevaretur. </s><lb/><s>Non e&longs;t itaque levitas, quæ ligneum cylindrum innatare cogit, <lb/>&longs;ed mercurij gravitas major ip&longs;a e&longs;t, quæ lignum elevat, cum <lb/>primùm locus patet, in quem de&longs;cendat. </s>

<s>Sed antequam experimentum hoc ad examen revocemus, <lb/>ut innote&longs;cat, quid hinc confici po&longs;&longs;it ad levitatem excluden<lb/>dam, haud ægrè permi&longs;erim, cùm in abeuntis &longs;uâ &longs;ponte cor-

<pb n="8"/>poris locum corpus aliud &longs;uapte vi, & naturâ &longs;uccedit, ab hoc <lb/>illud urgeri po&longs;&longs;e, ut velociùs moveatur: duo &longs;cilicet corpora <lb/>diver&longs;æ &longs;ecundùm &longs;peciem gravitatis &longs;i fuerint perturbatè di&longs;<lb/>po&longs;ita intrà medium, in quo utrumque gravitat, nil mirum, &longs;i <lb/>à graviore majori ni&longs;u conante extrudatur minùs grave: id <lb/>quod etiam de duobus levibus dicendum perturbatè di&longs;po&longs;itis <lb/>in medio, ubi utrumque levitat: duobus enim &longs;imul currenti<lb/>bus, ab eo qui ponè &longs;ub&longs;equitur, &longs;i majoribus viribus polleat, <lb/>priorem urgeri atque impelli palam e&longs;t, quamquam motus uni<lb/>ver&longs;us impul&longs;ioni tribuendus non &longs;it. </s><s>Ita quoque a&longs;cendentem <lb/>in mercurio ligneum cylindrum à de&longs;cendente mercurio &longs;ur<lb/>&longs;um urgeri aliquatenus po&longs;&longs;e non diffitebor, &longs;icut & mercu<lb/>rium ip&longs;um repugnare, ne &longs;ur&longs;um propellatur, atque ab eodem <lb/>lignum innatans prohiberi, ne de&longs;cendat: hinc tamen non <lb/>&longs;equitur ligni a&longs;cendentis motum, aut innatantis quietem, <lb/>prægravis mercurij viribus omnino ad&longs;cribi jure debere, nam, <lb/>& &longs;ua vis a&longs;cendendi, atque con&longs;i&longs;tendi, ligno ip&longs;i tribuen<lb/>da e&longs;t. </s>

<pb xlink:href="017/01/024.jpg" n="8"/>poris locum corpus aliud &longs;uapte vi, & naturâ &longs;uccedit, ab hoc <lb/>illud urgeri po&longs;&longs;e, ut velociùs moveatur: duo &longs;cilicet corpora <lb/>diver&longs;æ &longs;ecundùm &longs;peciem gravitatis &longs;i fuerint perturbatè di&longs;<lb/>po&longs;ita intrà medium, in quo utrumque gravitat, nil mirum, &longs;i <lb/>à graviore majori ni&longs;u conante extrudatur minùs grave: id <lb/>quod etiam de duobus levibus dicendum perturbatè di&longs;po&longs;itis <lb/>in medio, ubi utrumque levitat: duobus enim &longs;imul currenti<lb/>bus, ab eo qui ponè &longs;ub&longs;equitur, &longs;i majoribus viribus polleat, <lb/>priorem urgeri atque impelli palam e&longs;t, quamquam motus uni<lb/>ver&longs;us impul&longs;ioni tribuendus non &longs;it. </s><s>Ita quoque a&longs;cendentem <lb/>in mercurio ligneum cylindrum à de&longs;cendente mercurio &longs;ur<lb/>&longs;um urgeri aliquatenus po&longs;&longs;e non diffitebor, &longs;icut & mercu<lb/>rium ip&longs;um repugnare, ne &longs;ur&longs;um propellatur, atque ab eodem <lb/>lignum innatans prohiberi, ne de&longs;cendat: hinc tamen non <lb/>&longs;equitur ligni a&longs;cendentis motum, aut innatantis quietem, <lb/>prægravis mercurij viribus omnino ad&longs;cribi jure debere, nam, <lb/>& &longs;ua vis a&longs;cendendi, atque con&longs;i&longs;tendi, ligno ip&longs;i tribuen<lb/>da e&longs;t. </s>

<s>Quid quòd ip&longs;æ innatantis cylindri portiones, altera quidem <lb/>mercurio immer&longs;a, altera verò extans, levitatem ip&longs;i ligno in<lb/>&longs;itam declarant? </s><s>Quid enim partis immeriæ ad extantem (&longs;i <lb/>moles &longs;pectetur) ea ratio e&longs;t, quæ &longs;pecificæ gravitatis ligni ad <lb/>differentiam gravitatum ligni, atque mercurij? </s><s>ni&longs;i quia por<lb/>tionis mercurio immer&longs;æ levitas, atque extantis in aëre gravi<lb/>tas, æquilibritatem con&longs;tituent; quemadmodum in <emph type="italics"/>Terra ma<lb/>chinis mota di&longs;&longs;ert.<emph.end type="italics"/> 5. <emph type="italics"/>n.<emph.end type="italics"/> 105. explicatum e&longs;t. </s><s>Hanc porrò æqua<lb/>litatem Algebricè &longs;ic o&longs;tendo. </s><s>Ratio gravitatis ligni ad gravi<lb/>tatem mercurij &longs;it ut S. ad R; differentia e&longs;t R—S. Ponatur <lb/>cylindri pars immer&longs;a. A. </s><s>Quia igitur ut &longs;pecifica gravitas <lb/>corporis innatantis ad differentiam gravitatum, hoc e&longs;t ut <lb/>S ad R — S, ita pars cylindri immer&longs;a A, ad extantem <lb/>(R in A—S in A/S); Si pars extans in aëre in &longs;uam gravitatem S du<lb/>catur, pars verò immer&longs;a A in differentiam gravitatum R—S, <lb/>hoc e&longs;t in — R + S, quia e&longs;t deficiens, efficitur hinc quantitas <lb/>R in A — S in A, hinc verò — R in A + S in A, quæ &longs;e invi<lb/>cem elidunt. </s><s>Æqualia igitur &longs;unt levitatis, & gravitatis mo<lb/>menta. </s><s>Sit enim exempli causâ gravitas ligni ad gravitatem

<pb n="9"/>mercurij, ut S. ad 13. differentia e&longs;t 8. </s><s>E&longs;t igitur cylindri <lb/>pars immer&longs;a eju&longs;dem (5/13), extans verò (8/13): at portio immer&longs;a de<lb/>ficit à grayitate mercurij &longs;ecundùm &longs;peciem ut 8; igitur (5/13) in - 8 <lb/>dant (40/13): item partis extantis gravitas in aëre e&longs;t S; igitur (8/13) <lb/>in 5 dant (40/13): confligunt itaque inter &longs;e pari conatu levitas (-40/13) & <lb/>gravitas (40/13), adeóque fit con&longs;i&longs;tentia & innatat lignum. </s>

<pb xlink:href="017/01/025.jpg" n="9"/>mercurij, ut S. ad 13. differentia e&longs;t 8. </s><s>E&longs;t igitur cylindri <lb/>pars immer&longs;a eju&longs;dem (5/13), extans verò (8/13): at portio immer&longs;a de<lb/>ficit à grayitate mercurij &longs;ecundùm &longs;peciem ut 8; igitur (5/13) in - 8 <lb/>dant (40/13): item partis extantis gravitas in aëre e&longs;t S; igitur (8/13) <lb/>in 5 dant (40/13): confligunt itaque inter &longs;e pari conatu levitas (-40/13) & <lb/>gravitas (40/13), adeóque fit con&longs;i&longs;tentia & innatat lignum. </s>

<s>Sed jam ad propo&longs;iti experimenti examen de&longs;cendamus. </s><s>Aio <lb/>cylindri re&longs;i&longs;tentiam ex adhæ&longs;ione metu vacui non &longs;atis explo<lb/>ratam fui&longs;&longs;e per libram; hæc enim dum ex pondere M deor&longs;um <lb/>inclinatur, extremitas G &longs;ur&longs;um elevata arcum de&longs;cribit, ac <lb/>proinde cylindri a&longs;cendentis motus non e&longs;t per lineam horizon<lb/>tali plano perpendiculariter in&longs;i&longs;tentem, &longs;ed per inclinatam: <lb/>Quare cùm A. versùs I libræ centrum trahatur, cylindri ba&longs;is <lb/>non incipit elevari parallela horizonti, &longs;ed cum inclinatione, ita <lb/>ut C priùs elevetur, quàm B: ea autem, quæ &longs;ibi invicem adhæ<lb/>re&longs;cunt, multò faciliùs divelli manife&longs;tum e&longs;t, &longs;i id cum inclina<lb/>tione fiat, quàm &longs;i &longs;ervandus &longs;it paralleli&longs;mus. </s><s>Adde in hac in<lb/>clinatione faciliùs adhuc divelli cylindrum à &longs;uppo&longs;ito plano, <lb/>quò longior cylindrus fuerit; habet &longs;cilicet rationem vectis, <lb/>cujus potentia e&longs;t in A, hypomochlion in B, re&longs;i&longs;tentia vin<lb/>cenda in C. </s><s>Quare pondus M non aptè metitur re&longs;i&longs;tentiam, <lb/>quæ oritur ex corporum adhære&longs;centiâ, metu vacui, &longs;ed hæc <lb/>multò major e&longs;t, &longs;i ad perpendiculum motus fieri debeat; <lb/>quemadmodum & fieri oporteret, &longs;i in va&longs;e NOP mercurij <lb/>pleno cylindrus fundo adhærens rectâ a&longs;cenderet. </s><s>Quamvis <lb/>igitur pondus Q librarum quinque admitteretur men&longs;ura levi<lb/>tatis, non continuò argui pote&longs;t hujus exce&longs;&longs;us &longs;upra re&longs;i&longs;ten<lb/>tiam adhæ&longs;ionis. </s><s>Quin immo affirmare au&longs;im, &longs;i libræ loco <lb/>adhibita fui&longs;&longs;et amplior trochlea, & ex funiculo ejus orbitam <lb/><expan abbr="cõplectente">complectente</expan> hinc cylindrus A, hinc verò pondus M ad perpen<lb/>diculum pependi&longs;&longs;ent, non &longs;atis futurum fui&longs;&longs;e <expan abbr="põdus">pondus</expan> librarum <lb/>trium, &longs;ed multò majus adhibendum fui&longs;&longs;e, ut cylindri re&longs;i&longs;ten<lb/>tiam &longs;uperaret; fui&longs;&longs;et enim avellenda ba&longs;is &longs;ervato paralleli&longs;mo. </s>

<s>Quantum autem virium, ferè &longs;upra fidem, habeat vacui <lb/>horrorad corpora retinenda, &longs;atis apertè declarant gravia, quæ <lb/>&longs;u&longs;penduntur. </s><s>Ego &longs;anè vidi marmoreum mortarium commu<lb/>nis magnitudinis &longs;atis vulgari artificio &longs;u&longs;pendi vitrco cyatho:

<pb n="10"/>mortarij &longs;cilicet fundo exteriùs aptata fuerat ma&longs;&longs;a ex farinâ <lb/>ad formandos panes recens macerata, & aquâ ita &longs;ubacta, ut <lb/>illi tenaciter cohæreret: tum vitreo calici injecta &longs;tuppa admo<lb/>to igne exar&longs;it, applicitu&longs;que calix ma&longs;&longs;æ eam attraxit, &longs;icut & <lb/>medicorum cucurbitulæ carnem attrahunt: quare accepto ca<lb/>licis vitrei pede facile fuit mortarium elevare, & &longs;u&longs;pendere. </s><lb/><s>Quod &longs;i marmoreum mortarium ex metu vacui in aëre pendu<lb/>lum hæ&longs;it, quid mirum &longs;i & ligneus cylindrus &longs;ubjecto plano <lb/>adhære&longs;cens in mercurio &longs;tetit? </s>

<pb xlink:href="017/01/026.jpg" n="10"/>mortarij &longs;cilicet fundo exteriùs aptata fuerat ma&longs;&longs;a ex farinâ <lb/>ad formandos panes recens macerata, & aquâ ita &longs;ubacta, ut <lb/>illi tenaciter cohæreret: tum vitreo calici injecta &longs;tuppa admo<lb/>to igne exar&longs;it, applicitu&longs;que calix ma&longs;&longs;æ eam attraxit, &longs;icut & <lb/>medicorum cucurbitulæ carnem attrahunt: quare accepto ca<lb/>licis vitrei pede facile fuit mortarium elevare, & &longs;u&longs;pendere. </s><lb/><s>Quod &longs;i marmoreum mortarium ex metu vacui in aëre pendu<lb/>lum hæ&longs;it, quid mirum &longs;i & ligneus cylindrus &longs;ubjecto plano <lb/>adhære&longs;cens in mercurio &longs;tetit? </s>

<s>Nondum itaque ex hoc experimento, aut ex &longs;imilibus, ubi <lb/>metu vacui &longs;uos motus moliri corpora non po&longs;&longs;unt, &longs;atis habe<lb/>mus argumenti, quo levitatem, &longs;olâ gravitate retentâ, expun<lb/>gamus. </s><s>Huju&longs;modi e&longs;t illud, ubi in lignei va&longs;is fundo exca<lb/>vatur &longs;caphium, cui exqui&longs;itè congruat eburneus globus, qui <lb/>&longs;uperinfu&longs;o hydrargyro non a&longs;cendit. </s><s>Neque enim ideò non <lb/>a&longs;cendit, quia rima nulla patet argento vivo, per quam &longs;ubiens <lb/>extrudat eburneum globum, &longs;ed quia ita &longs;ibi exqui&longs;itè con<lb/>gruunt ebur, & lignum, ut vis ip&longs;a a&longs;cendendi vincere non va<lb/>leat vim adhære&longs;centiæ. </s><s>Nam & eadem vis in aöre &longs;u&longs;pendit <lb/>corpora gravia, ne de&longs;cendant. </s><s>Quamvis autem non totum <lb/>hemi&longs;phærium globi eburnei, &longs;ed &longs;olùm ejus maximus circu<lb/>lus congrueret excavato ligno, & cavitas ip&longs;a aëre repleretur, <lb/>non propterea tollitur vis adhære&longs;centiæ illius annularis; quia <lb/>&longs;cilicet vis a&longs;cendendi in hydrargyro tanta non e&longs;t, ut valeat <lb/>inclu&longs;um ibi aërem di&longs;trahere, &longs;icut opus e&longs;&longs;et ad incipiendum <lb/>motum citra periculum vacui, & præterea &longs;uperanda e&longs;t re<lb/>&longs;i&longs;tentia hydrargyri dividendi; corpora enim in motu divi<lb/>dunt medium, pro cujus cra&longs;&longs;itudine re&longs;i&longs;tentiam experiuntur. </s><lb/><s>Adde hemi&longs;phærium inferius in aëre tanquam in loco po&longs;itum <lb/>gravitare non minùs, quàm hemi&longs;phærium &longs;uperius levitet in <lb/>hydrargyro; proinde nil mirum, &longs;i globus non a&longs;cendat. </s><s>Quod <lb/>&longs;i aëre exclu&longs;o locum illum impleveris hydrargyro, & ebur<lb/>neum globum ita foramini aptaveris, ut illi exqui&longs;itè congruat; <lb/>&longs;i in &longs;uperinfu&longs;o hydrargyro globus non a&longs;cendat, indicio e&longs;t <lb/>ita globum e&longs;&longs;e foramini infixum, ut neque valeat elevari à &longs;ub<lb/>jecto hydrargyro in &longs;caphij formam per vim excavato: neque <lb/>enim facilè mihi per&longs;uadebis &longs;pecificarum gravitatum diffe<lb/>rentiam exigere, ut hemi&longs;phærium integrum præcisè extet:

<pb n="11"/>præter quam quod &longs;i non valebat &longs;ubjectum aërem di&longs;trahere, <lb/>multò minùs id in hydrargyro præ&longs;tare pote&longs;t, ut vacuum <lb/>evitetur. </s>

<pb xlink:href="017/01/027.jpg" n="11"/>præter quam quod &longs;i non valebat &longs;ubjectum aërem di&longs;trahere, <lb/>multò minùs id in hydrargyro præ&longs;tare pote&longs;t, ut vacuum <lb/>evitetur. </s>

<s>At, inquis, fi&longs;tulam quadricubitalem &longs;piritu vini plenam <lb/>cum globulo innatante &longs;i clau&longs;eris, & inverteris deor&longs;um, <lb/>a&longs;cendet globulus &longs;patio 200 vibrationum perpendiculi; in eâ<lb/>dem verò fi&longs;tulâ communis, & &longs;implicis aquæ plenâ a&longs;cendet <lb/>&longs;ubduplo tempore 100 vibrationum. </s><s>Cur hoc? </s><s>ni&longs;i quia aqua <lb/>ut pote gravior validiùs extrudit globulum, quàm &longs;piritus vini. </s><lb/><s>Nihilominus: &longs;i gravia in levibus magis gravitant, & velociùs <lb/>de&longs;cendunt, quò major e&longs;t &longs;pecificarum gravitatum differen<lb/>tia; vici&longs;&longs;im levia in gravibus magis levitant, & velociùs <lb/>a&longs;cendunt, quò major e&longs;t &longs;ecundùm &longs;peciem levitatis differen<lb/>tia: Atqui &longs;piritus vini magis accedit ad &longs;pecificam levitatem <lb/>innatantis globuli, aqua autem magis differt; in aquâ igitur <lb/>globulus magis levitat, & velociùs a&longs;cendit, &longs;icut lapis in aëre <lb/>velociùs de&longs;cendit quàm in aqua, aut in melle. </s>

<s>Addis iterum. </s><s>Vitreo va&longs;culo, cui longior fi&longs;tula adhæreat, <lb/>fomitem cum filo &longs;ulphurato ope fili ferrei ingere, ut vitrum <lb/>tangat: totum imple hydrargyro, & conver&longs;o deor&longs;um o&longs;culo <lb/>de&longs;cendit hydrargyrus; atque &longs;ub&longs;i&longs;tit in altitudine cubiti, & <lb/>quadrantis: admotâ lucernâ vitrarij vitrum calefiat, ut fomes <lb/>cum filo &longs;ulphurato accendatur: fumus de&longs;cendit, nec ni&longs;i <lb/>aperto &longs;uperiore va&longs;is o&longs;culo a&longs;cendit, aëre videlicet &longs;ubeunte, <lb/>à quo extrudatur &longs;ur&longs;um. </s><s>Nego fumum ab aëre &longs;ur&longs;um extru<lb/>di, &longs;ed qui gravior &longs;piritu raro mercurij in illo de&longs;cendebat, <lb/>ubi aërem tangit, ut pote levior in illo a&longs;cendit. </s>

<s>Non au&longs;im tamen in lapide, qui gravitatem in aquâ & aëre, <lb/>levitatem in mercurio, aut plumbo liquente obtinet, duplicem <lb/>&longs;tatuere virtutem, quarum altera &longs;ur&longs;um, altera deor&longs;um con<lb/>nitatur: Cum enim impetus motum efficiens (ut infrà con&longs;ta<lb/>bit) eju&longs;dem naturæ &longs;it, in quamcunque demum orbis plagam <lb/>dirigatur motus; &longs;atis video ab uno eodemque principio, pro <lb/>variâ contigui corporis conditione, a&longs;cen&longs;um, de&longs;censúmve <lb/>prodire po&longs;&longs;e. </s><s>Quandoquidem motus, qui in eadem lineâ per<lb/>ficitur, &longs;imiles planè includit ubicationes &longs;ucce&longs;&longs;ivè acqui&longs;i<lb/>tas, &longs;ivè a&longs;cen&longs;us &longs;it, &longs;ivè de&longs;cen&longs;us, ordine tantùm in earum <lb/>adeptione, commutato. </s><s>Quare cum a&longs;cen&longs;us à de&longs;cen&longs;u hoc

<pb n="12"/>uno differat, quòd quam ubicationem lapis demùm obtineret <lb/>po&longs;t alias propè finem motûs, &longs;i fui&longs;&longs;et centro propior quàm <lb/>mercurius, eam acquirat &longs;ub initium motûs ante alias, &longs;i in <lb/>mercurij locum aër aut aqua &longs;urrogetur centro vicinior quàm <lb/>lapis: ad ordinem hunc permutandum non videtur nece&longs;&longs;aria <lb/>virtutis motricis di&longs;&longs;imilitudo; nihil quippe producitur di&longs;&longs;imi<lb/>le. </s><s>Sed &longs;i quis &longs;ufficere dicat conditionum varietatem, nihil <lb/>ab&longs;onum fortè loquatur: debuit enim una virtus activa in &longs;ui <lb/>effectus productione non uni tantùm conditioni alligari, &longs;ed pro <lb/>earum varietate modum quoque operandi mutare po&longs;&longs;e, modò <lb/>præ&longs;titutos fines, quoad &longs;ub&longs;tantiam, non tran&longs;iliret. </s>

<pb xlink:href="017/01/028.jpg" n="12"/>uno differat, quòd quam ubicationem lapis demùm obtineret <lb/>po&longs;t alias propè finem motûs, &longs;i fui&longs;&longs;et centro propior quàm <lb/>mercurius, eam acquirat &longs;ub initium motûs ante alias, &longs;i in <lb/>mercurij locum aër aut aqua &longs;urrogetur centro vicinior quàm <lb/>lapis: ad ordinem hunc permutandum non videtur nece&longs;&longs;aria <lb/>virtutis motricis di&longs;&longs;imilitudo; nihil quippe producitur di&longs;&longs;imi<lb/>le. </s><s>Sed &longs;i quis &longs;ufficere dicat conditionum varietatem, nihil <lb/>ab&longs;onum fortè loquatur: debuit enim una virtus activa in &longs;ui <lb/>effectus productione non uni tantùm conditioni alligari, &longs;ed pro <lb/>earum varietate modum quoque operandi mutare po&longs;&longs;e, modò <lb/>præ&longs;titutos fines, quoad &longs;ub&longs;tantiam, non tran&longs;iliret. </s>

<s>Neque arbitror hoc tantùm &longs;en&longs;u negatam ab aliquibus levi<lb/>tatem po&longs;itivam; potui&longs;&longs;ent enim æquè negare gravitatem, ad<lb/>mi&longs;&longs;a &longs;olùm potentia motrice. </s><s>Sed &longs;i vis i&longs;ta &longs;e movendi deor<lb/>&longs;um gravitas po&longs;itiva dicenda e&longs;t, cùm eadem &longs;it virtus &longs;e mo<lb/>vendi &longs;ursùm, cur levitas po&longs;itiva non fuerit? </s><s>Qui enim levita<lb/>tem à gravitate &longs;ejunctam negat, non illicò levitatem expun<lb/>git: quemadmodum Angelos intelligentiâ aut voluntate dimi<lb/>nutos non a&longs;&longs;erunt ij, qui vitalium facultatum di&longs;tinctionem <lb/>non agno&longs;cunt. </s><s>Nullum igitur corpus &longs;impliciter, & ab&longs;olutè <lb/>grave dicendum e&longs;t, ni&longs;i quod cæteris omnibus ita petat &longs;ube&longs;&longs;e, <lb/>ut nequeat raritatem a&longs;&longs;umere, vi cujus evadat levius corpore <lb/>&longs;imili quidem &longs;ecundùm naturam, di&longs;&longs;imilis tamen raritatis: <lb/>nullum &longs;impliciter, & ab&longs;olutè leve, ni&longs;i quod ita exigat extre<lb/>mam orbis laciniam occupare, ut nunquam con&longs;tipari po&longs;&longs;it, ac <lb/>fieri gravius proximo corpore rariore. </s><s>Reliqua omnia non ni&longs;i <lb/>comparatè gravia, aut levia dici po&longs;&longs;unt: &longs;ic plumbum grave e&longs;t <lb/>in aëre, grave in aqua, at pariter leve in mercurio, leve &longs;i cum <lb/>auro conferatur. </s>

<s>Hinc corpus in loco &longs;ibi debito con&longs;titutum, sèque ibi con<lb/>&longs;ervans (extra tamen &longs;phæræ centrum, nec in extimâ orbis ele<lb/>mentaris &longs;uperficie) ob idip&longs;um, quia ob&longs;i&longs;tit non tantùm, ne <lb/>infra &longs;ubjectum corpus deprimatur, verùm etiam, ne in locum <lb/>&longs;uperioris attollatur, & levitare &longs;imul dicendum e&longs;t, & gravi<lb/>tare. </s><s>At &longs;i in alienum locum transferatur, quia in medio levio<lb/>re ita repugnat a&longs;cen&longs;ui, ut petat de&longs;cendere, &longs;olùm gravitat; <lb/>quia verò in graviore ita depre&longs;&longs;ioni reluctatur, ut exigat ad <lb/>&longs;uperiora evadere, &longs;olùm levitat. </s><s>Quod &longs;i corpora huju&longs;modi

<pb n="13"/>in actu &longs;ecundo gravitare aut levitare tunc &longs;olùm dixeris, quan<lb/>do illa in locum non &longs;uum tran&longs;lata aut de&longs;cendere expetunt, <lb/>aut a&longs;cendere, vel re etiam ipsâ de&longs;cendunt, aut a&longs;cendunt, <lb/>non admodum repugnabo; modò conatum illum, quo &longs;e &longs;uo <lb/>tutantur in loco, gravitationem, & levitationem &longs;altem in actu <lb/>primo, aut pariter a&longs;&longs;eras, aut pariter neges. </s>

<pb xlink:href="017/01/029.jpg" n="13"/>in actu &longs;ecundo gravitare aut levitare tunc &longs;olùm dixeris, quan<lb/>do illa in locum non &longs;uum tran&longs;lata aut de&longs;cendere expetunt, <lb/>aut a&longs;cendere, vel re etiam ipsâ de&longs;cendunt, aut a&longs;cendunt, <lb/>non admodum repugnabo; modò conatum illum, quo &longs;e &longs;uo <lb/>tutantur in loco, gravitationem, & levitationem &longs;altem in actu <lb/>primo, aut pariter a&longs;&longs;eras, aut pariter neges. </s>

<s>Porrò motus omnis gravium, & levium &longs;icut in vacuo exer<lb/>ceri non pote&longs;t (ut in <emph type="italics"/>Vacuo Pro&longs;cripto cap.<emph.end type="italics"/>2. <emph type="italics"/>num.<emph.end type="italics"/>9. o&longs;tendi) ita <lb/>in medio fit, vel tardiùs, vel citiùs, tùm pro majori vel minori <lb/>ip&longs;ius medij re&longs;i&longs;tentia ad &longs;ci&longs;&longs;ionem partium magis, vel minùs <lb/>connexarum, tùm comparatâ gravitate &longs;eu levitate mobilis <lb/>cum levitate &longs;eu gravitate medij. </s><s>Hinc e&longs;t gravibus minus <lb/>re&longs;i&longs;tere leviora, magis verò, quæ minùs levia, cæteris pari<lb/>bus: &longs;ic aër minùs re&longs;i&longs;tit lapidi cadenti, quàm &longs;i idem lapis in<lb/>ciperet moveri in aquâ, quæ minùs levis e&longs;t, quàm aër. </s><lb/><s>Ex oppo&longs;ito autem levibus graviora minùs re&longs;i&longs;tunt, quæ au<lb/>tem minùs gravia, magis re&longs;i&longs;tunt: &longs;ic exhalatio ex fundo <lb/>aquæ, in vitreâ phialâ ad ignem expo&longs;itâ, per aquam a&longs;cendit <lb/>velociùs, quàm deinde extra aquam po&longs;ita a&longs;cendat in aëre, <lb/>ubi fumeam naturam induerit. </s><s>Unde patet non adeò &longs;olidum <lb/>ab aliquibus ex hoc experimento &longs;umi argumentum negandi <lb/>po&longs;itivam levitatem. </s><s>Quæ enim de gravibus ex comparatione <lb/>cum levibus dicuntur, ea de levibus, proportione &longs;ervatâ, di<lb/>cenda &longs;unt, &longs;i cum gravibus conferantur. </s><s>Cur autem gravibus <lb/>leviora, levibus graviora minùs re&longs;i&longs;tant, ratio e&longs;t, quia mo<lb/>bile movetur in medio propter di&longs;&longs;imilitudinem; nam &longs;i corpus <lb/>contiguum e&longs;&longs;et, &longs;imile non moveretur; quando igitur major <lb/>e&longs;t di&longs;&longs;imilitudo, debet velociùs moveri, &longs;egniùs autem, & len<lb/>tiùs, quò propiùs abe&longs;t à &longs;imilitudine, donec in &longs;imili demum <lb/>quie&longs;cat. </s>

<s>E&longs;t itaque in corporibus gravitas, & levitas, vi cujus motus ali<lb/>quos juxta naturæ propen&longs;ionem perficiunt, ut certo denique in <lb/>loco con&longs;i&longs;tant, eju&longs;demque vi re&longs;i&longs;tunt, ne oppo&longs;itis motibus <lb/>cieantur, & à &longs;uæ quietis loco avellantur. </s><s>Quamvis autem <expan abbr="ead&etilde;">eadem</expan> <lb/>maneat gravitas aut levitas, non <expan abbr="id&etilde;">idem</expan> tamen e&longs;t &longs;emper <expan abbr="moment&utilde;">momentum</expan> <lb/>(Græcis <foreign lang="greek"><gap/>ph</foreign>) hoc e&longs;t actualis ad motum inclinatio, dum in actio<lb/>ne e&longs;t; hæc enim, ut infra patebit, ut plurimum ex po&longs;itione, & <lb/>&longs;itu mutatur, vel comparatè ad <expan abbr="medi&utilde;">medium</expan>, in quo perficitur motus.

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

Line 354

<s>QUamvis non minùs levitate, quàm gravitate prædita &longs;int <lb/>corpora, quia tamen frequentiùs gravitatem vincere co<lb/>namur, quàm levitatem; ideò illa poti&longs;&longs;imùm cadit &longs;ub con<lb/>templationem &longs;cie&ngrave;tiæ Machinalis: vix enim aliquando con<lb/>tingere poterit, ut opus &longs;it infra aquam corpus aliquod leve <lb/>per vim deprimere. </s><s>Hinc factum e&longs;t, ut de &longs;olo gravitatis cen<lb/>tro &longs;ermo communiter &longs;it, levitatis autem centrum &longs;ilentio <lb/>obvolvatur: quia nimirùm quæ de gravitate de&longs;cendente ex<lb/>plicantur, ea de levitate a&longs;cendente, pro rata portione, dicta <lb/>facile intelliguntur. </s>

<s>Ad centrum terræ (quod & centrum gravium ac levium <lb/>dicimus) properant corpora quæcumque gravia in medio le<lb/>viore con&longs;tituta &longs;ibi redduntur, ut motus &longs;uos perficiant. </s><s>Quo<lb/>niam verò natura finem propo&longs;itum per media, quæ pote&longs;t, bre<lb/>vi&longs;&longs;ima pro&longs;equitur, ambages, & diverticula fugiens; mo<lb/>ventur per lineam rectam, ut pote brevi&longs;&longs;imam, ni&longs;i externo <lb/>aliquo impedimento cogantur à rectitudine deflectere: Hæc <lb/>autem recta linea intelligi debet ex terræ centro ducta ad cor<lb/>pus ip&longs;um, quod movetur; ac proinde tùm in &longs;phæricam &longs;u<lb/>

<figure/><lb/>perficiem, tùm in planum Horizon<lb/>tis ad perpendiculum cadit. </s><s>Sed quia <lb/>corpus, quod deor&longs;um contendit, <lb/>plures habet partes, quibus con&longs;tat, <lb/>&longs;ingulas &longs;uâ gravitate præditas, lineæ <lb/>verò à &longs;ingulis hi&longs;ce partibus exeun<lb/>tes in terræ centro concurrunt; fieri <lb/>non pote&longs;t, ut &longs;ervatâ corporis figu<lb/>râ, atque continuo partium nexu non <lb/>di&longs;&longs;oluto, per rectam &longs;uam lineam ad <lb/>centrum ductam unaquæque pars <lb/>de&longs;cendat. </s><s>Si enim parallelepipe<lb/>dum AB in aëre dimittatur, ut &longs;pon-

<figure id="id.017.01.030.1.jpg" xlink:href="017/01/030/1.jpg"/><lb/>perficiem, tùm in planum Horizon<lb/>tis ad perpendiculum cadit. </s><s>Sed quia <lb/>corpus, quod deor&longs;um contendit, <lb/>plures habet partes, quibus con&longs;tat, <lb/>&longs;ingulas &longs;uâ gravitate præditas, lineæ <lb/>verò à &longs;ingulis hi&longs;ce partibus exeun<lb/>tes in terræ centro concurrunt; fieri <lb/>non pote&longs;t, ut &longs;ervatâ corporis figu<lb/>râ, atque continuo partium nexu non <lb/>di&longs;&longs;oluto, per rectam &longs;uam lineam ad <lb/>centrum ductam unaquæque pars <lb/>de&longs;cendat. </s><s>Si enim parallelepipe<lb/>dum AB in aëre dimittatur, ut &longs;pon-

<pb n="15"/>te &longs;ua de&longs;cendat, fieri non pote&longs;t, ut A rectam AC percur<lb/>rat, quin oppo&longs;ituni extremum B à recta BC longi&longs;&longs;ime rece<lb/>dat, & contra: utramque verò extremitatem &longs;imul A & B <lb/>rectâ in centrum C tendere non po&longs;&longs;e e&longs;t manife&longs;tum: Quare <lb/>cum &longs;ibi invicem ob&longs;i&longs;tant æqualiter, ob gravitatis æqualita<lb/>tem, eas ex perpendicularibus AC, BC æqualiter &longs;ecedere <lb/>oportet ad latera, atque parallelas BE, AF de&longs;cendendo de&longs;<lb/>cribere. </s><s>Eadem e&longs;t ratio de cæteris partibus æquali intervallo <lb/>&longs;ejunctis à medio D; omnes enim à &longs;uis perpendiculis rece<lb/>dunt, præter punctum medium D, cujus perpendicularis <lb/>DC parallela e&longs;t lineis à reliquis partibus in motu de&longs;criptis. </s><lb/><s>Ex omnibus itaque particulis datum grave componentibus, eæ <lb/>&longs;olùm, quæ puncto D imminent, per rectam DC in centrum <lb/>moventur; quæ tàm plano horizontis in C, quàm &longs;uperficiei <lb/>&longs;phæricæ in H perpendicularis e&longs;t; cæteræ verò parallelæ BE, <lb/>AF perpendiculares quidem in horizontem cadunt, &longs;ed &longs;phæ<lb/>ricam &longs;uperficiem obliquè &longs;ecant. </s>

<pb xlink:href="017/01/031.jpg" n="15"/>te &longs;ua de&longs;cendat, fieri non pote&longs;t, ut A rectam AC percur<lb/>rat, quin oppo&longs;ituni extremum B à recta BC longi&longs;&longs;ime rece<lb/>dat, & contra: utramque verò extremitatem &longs;imul A & B <lb/>rectâ in centrum C tendere non po&longs;&longs;e e&longs;t manife&longs;tum: Quare <lb/>cum &longs;ibi invicem ob&longs;i&longs;tant æqualiter, ob gravitatis æqualita<lb/>tem, eas ex perpendicularibus AC, BC æqualiter &longs;ecedere <lb/>oportet ad latera, atque parallelas BE, AF de&longs;cendendo de&longs;<lb/>cribere. </s><s>Eadem e&longs;t ratio de cæteris partibus æquali intervallo <lb/>&longs;ejunctis à medio D; omnes enim à &longs;uis perpendiculis rece<lb/>dunt, præter punctum medium D, cujus perpendicularis <lb/>DC parallela e&longs;t lineis à reliquis partibus in motu de&longs;criptis. </s><lb/><s>Ex omnibus itaque particulis datum grave componentibus, eæ <lb/>&longs;olùm, quæ puncto D imminent, per rectam DC in centrum <lb/>moventur; quæ tàm plano horizontis in C, quàm &longs;uperficiei <lb/>&longs;phæricæ in H perpendicularis e&longs;t; cæteræ verò parallelæ BE, <lb/>AF perpendiculares quidem in horizontem cadunt, &longs;ed &longs;phæ<lb/>ricam &longs;uperficiem obliquè &longs;ecant. </s>

<s>Jam verò &longs;i eju&longs;dem parallelepipedi aliud planum AO hori<lb/>zonti parallelum moveri versùs C intelligas, erit in eo &longs;imiliter <lb/>aliud punctum unicum, quod rectam DC percurrat; & intra <lb/>corporis &longs;oliditatem unica linea puncto illi imminens viâ eâdem <lb/>in centrum pergetnon declinans à perpendiculo: cæteræ partes, <lb/>tam quæ ad <expan abbr="dextrã">dextram</expan>, quàm quæ ad <expan abbr="levã">levam</expan>, tam quæ antè, quàm quæ <lb/>ponè, &longs;ibi mutuò adver&longs;antes à recto in <expan abbr="centr&utilde;">centrum</expan> itinere deflectent <lb/>æqualiter. </s><s>Cum itaque, in priori po&longs;itione, linea puncto D <lb/>imminens, e&longs;&longs;et in communi &longs;ectione planorum, quorum alte<lb/>rum partes dextras à &longs;ini&longs;tris, alterum anteriores à po&longs;terioribus <lb/>æqualiter &longs;ecernebat; in &longs;ecundâ autem po&longs;itione linea à per<lb/>pendiculo non recedens &longs;it quoquè in duorum planorum com<lb/>muni &longs;ectione, quibus pariter corporis gravitas in æquas tribui<lb/>tur partes; unum verò ex planis &longs;ecantibus &longs;it utrique po&longs;itioni <lb/>commune; unicum e&longs;t punctum tribus planis commune, in quo <lb/>binorum planorum &longs;ectiones &longs;e invicem &longs;ecant, & &longs;it ex. gr. <lb/>punctum I; quod unicum rectâ pergit in centrum C, quemcum<lb/>que tandem &longs;itum in motu obtineat corpus datum AB, ip&longs;um <lb/>enim e&longs;t duabus illis lineis commune, quæ in &longs;ingulis po&longs;itioni<lb/>bus ad &longs;ui perpendiculi latera non recedunt: cætera illarum li<lb/>nearum puncta, mutatâ po&longs;itione corporis, lineam quoque mo<lb/>tûs mutant. </s>

<s>Illud itaquè punctum in quocumque corpore gravi, quod <lb/>&longs;emper in motu de&longs;cribit lineam rectà in terræ centrum <lb/>ductam, dicitur <emph type="italics"/>Centrum Gravitatis<emph.end type="italics"/>; & linea, quæ centrum <lb/>gravitatis conjungit cum terræ centro, <emph type="italics"/>Linea directionis<emph.end type="italics"/> dicitur; <lb/>&longs;ecundùm quam videlicet dirigitur motus, & dimentienda e&longs;t <lb/>corporis à centro terræ di&longs;tantia, &longs;i quatenus grave con&longs;idere<lb/>tur. </s><s>Porrò punctum I centrum gravitatis dicitur, quia centri <lb/>nomen tribuitur puncto, quod e&longs;t medium: & quemadmodum <lb/>magnitudinis alicujus centrum vocatur punctum illud, quod <lb/>æquales magnitudines circun&longs;tant, &longs;i partes, quæ ex adver&longs;o <lb/>&longs;unt, accipiantur; ita in gravibus centrum gravitatis dicitur, <lb/>quod æquales gravitates, vel æqualia gravitatum momenta cir<lb/>cun&longs;tant. </s><s>Quod &longs;i punctum I non haberet hinc, & hinc æqua<lb/>les gravitatum vires, ab alterutrâ parte præ&longs;tante viribus pro<lb/>pelleretur in latus extra lineam directionis, à quâ nunquam re<lb/>cedit, &longs;i liberè moveatur. </s><s>Cave tamen, ne partium æqualita<lb/>tem dimetiaris linearum longitudine à céntro gravitatis exeun<lb/>tium, ita ut &longs;ingulas lineas æqualiter dividendas putes; &longs;ed to<lb/>tum corpus debet intelligi divi&longs;um bifariam à plano per cen<lb/>trum gravitatis ip&longs;ius corporis, & per centrum gravium ac le<lb/>vium tran&longs;eunte, ita ut &longs;i planum à dextrâ in &longs;ini&longs;tram ductum <lb/>&longs;ecernat partes anteriores à po&longs;terioribus, æqualia &longs;int gravita<lb/>tum momenta antè, & ponè; &longs;i aliud planum per eandem di<lb/>rectionis lineam ductum partes dextras à &longs;ini&longs;tris di&longs;tinguat pa<lb/>ria &longs;imiliter hinc & hinc gravitatum momenta relinquat. </s>

<s>Gravitatum, inquam, momenta, non gravitates; ne locus <lb/>pateat æquivocationi; neque enim quoties æqualia &longs;unt mo<lb/>menta, toties æquales &longs;unt gravitates hinc & hinc centrum gra<lb/>vitatis complectentes, ut patebit ex iis, quæ de æquilibrio dice<lb/>mus. </s><s>Unde fit in iis tantùm corporibus, quæ partibus unius eju&longs;<lb/>demque naturæ, ac ductu perpetuo &longs;imiliter con&longs;titutis, <expan abbr="con&longs;tãt">con&longs;tant</expan>, <lb/>

<figure/><lb/>idem e&longs;&longs;e centrum gravitatis atque magni<lb/>tudinis; reliqua certis regulis non circum<lb/>&longs;cripta, aut ex variis naturis compo&longs;ita, in <lb/>alio puncto, molis centrum habere, in alio, <lb/>gravitatis. </s><s>Si enim duo &longs;olida VT, cujus <lb/>centrum gravitatis, & magnitudinis R, <lb/>& MN, cujus centrum S, æqualia &longs;ecun-

<figure id="id.017.01.032.1.jpg" xlink:href="017/01/032/1.jpg"/><lb/>idem e&longs;&longs;e centrum gravitatis atque magni<lb/>tudinis; reliqua certis regulis non circum<lb/>&longs;cripta, aut ex variis naturis compo&longs;ita, in <lb/>alio puncto, molis centrum habere, in alio, <lb/>gravitatis. </s><s>Si enim duo &longs;olida VT, cujus <lb/>centrum gravitatis, & magnitudinis R, <lb/>& MN, cujus centrum S, æqualia &longs;ecun-

<pb n="17"/>dùm gravitatem coagmententur, non erit centrum gravitatis <lb/>totius molis compo&longs;itæ in I, ubi planum tran&longs;iens per VN &longs;e<lb/>cat lineam RS jungentem centra &longs;ingularum gravitatum æqua<lb/>lium, &longs;ed erit in L, ubi recta RS bifariam dividitur: planum <lb/>autem per centrum terræ, & punctum L ductum non ita &longs;ecat <lb/>hanc molem, ut &longs;int æquales hinc, & hinc gravitates, quamvis <lb/>æqualia &longs;int gravitatum inæqualium momenta, quæ ex figuræ <lb/>po&longs;itione poti&longs;&longs;imùm pendent. </s><s>Quod &longs;i corporis VT gravitas <lb/>ad corporis MN gravitatem, eam haberet rationem, quam SI <lb/>ad IR, e&longs;&longs;et I gravitatis centrum molis compo&longs;itæ, quæ à plano <lb/>per terræ centrum, & punctum I ducto non in gravitates æqua<lb/>les, &longs;ed in momenta æqualia divideretur; ut in loco inferiùs ex<lb/>plicabitur. </s>

<pb xlink:href="017/01/033.jpg" n="17"/>dùm gravitatem coagmententur, non erit centrum gravitatis <lb/>totius molis compo&longs;itæ in I, ubi planum tran&longs;iens per VN &longs;e<lb/>cat lineam RS jungentem centra &longs;ingularum gravitatum æqua<lb/>lium, &longs;ed erit in L, ubi recta RS bifariam dividitur: planum <lb/>autem per centrum terræ, & punctum L ductum non ita &longs;ecat <lb/>hanc molem, ut &longs;int æquales hinc, & hinc gravitates, quamvis <lb/>æqualia &longs;int gravitatum inæqualium momenta, quæ ex figuræ <lb/>po&longs;itione poti&longs;&longs;imùm pendent. </s><s>Quod &longs;i corporis VT gravitas <lb/>ad corporis MN gravitatem, eam haberet rationem, quam SI <lb/>ad IR, e&longs;&longs;et I gravitatis centrum molis compo&longs;itæ, quæ à plano <lb/>per terræ centrum, & punctum I ducto non in gravitates æqua<lb/>les, &longs;ed in momenta æqualia divideretur; ut in loco inferiùs ex<lb/>plicabitur. </s>

<s>Ob&longs;erva autem non &longs;emper centrum gravitatis e&longs;&longs;e in ip&longs;o <lb/>corpore gravi, ut patet in corporibus annularibus, aut angulos <lb/>cavos habentibus, in quibus nullum e&longs;t punctum per quod tran<lb/>&longs;euntia plana quæcunque dividant in æquas pattes momenta <lb/>gravitatum: ita tamen e&longs;t extra corporis cavi &longs;oliditatem, ut &longs;it <lb/>intra ip&longs;am cavitatem punctum, ex quo &longs;i intelligatur annulus, <lb/>vel fru&longs;tum annulare &longs;u&longs;pendi, manet po&longs;itionem habens hori<lb/>zonti parallelam, cum habeat æqualia hinc, & hinc gravita<lb/>tum momenta. </s><s>Quod &longs;i corpus in cavos angulos &longs;inuatum ha<lb/>beat particulam aliquam procurrentem, pote&longs;t contingere, ut <lb/>in illius particulæ extremo &longs;it totius molis centrum gravitatis: <lb/>&longs;ic brevioris alicujus bacilli extremitati alteri &longs;i duos cultros in<lb/>fixeris, ut &longs;inguli cum bacillo hinc, & hinc angulum acutum <lb/>ad ea&longs;dem partes con&longs;tituant, ita inclinari po&longs;&longs;unt, ut extremo <lb/>ungue &longs;uppo&longs;ito reliquæ bacilli extremitati tota illa moles &longs;u&longs;ti<lb/>neatur citrà periculum cadendi, cùm gravitatis centrum in illa <lb/>extremitate, intrà cavitatem, quam inclinati cultri faciunt, <lb/>æqualia habeat ex omni parte gravitatum momenta, &longs;i planum <lb/>&longs;ecans per illud tran&longs;eat.

<s><emph type="center"/>CAPUT IV.<emph.end type="center"/></s>

<s><emph type="center"/><emph type="italics"/>An gravia centro vicina minùs gravitent.<emph.end type="italics"/><emph.end type="center"/></s>

<s>COrpora non intelliguntur gravitare ni&longs;i in alieno loco; <lb/>quando &longs;cilicet corpus contiguum inter illa & centrum <lb/>terræ interjectum, quod medii rationem habere pote&longs;t, levius <lb/>e&longs;t; petit enim infra illud e&longs;&longs;e: ni&longs;um autem hunc deorsùm <lb/><emph type="italics"/>Gravitationem<emph.end type="italics"/> dicimus. </s><s>Sed quoniam ni&longs;us i&longs;te videtur idcircò <lb/>à naturâ in&longs;titutu<gap/>, ut perturbatus corporum ordo re&longs;tituatur; <lb/>&longs;i ex fine ratio petenda &longs;it, &longs;atis apparet corpora gravia &cacute;entro <lb/>terræ vicina minùs gravitare. </s><s>Quemadmodum enim quotie&longs;<lb/>cunque aliquis à propo&longs;ito fine magis di&longs;tat, eò magis anxius <lb/>e&longs;t, atque &longs;olicitus de mediis ad illum a&longs;&longs;equendum nece&longs;&longs;ariis, <lb/>& animo æquiore toleratur modica, quàm multa violentia; ita <lb/>natura minorem ordinis debiti perturbationem &longs;entiens, &longs;i gra<lb/>ve parùm ab&longs;it, quàm &longs;i longè abe&longs;&longs;et, à loco, ubi juxta inge<lb/>nitam propen&longs;ionem exigit con&longs;i&longs;tere, minùs &longs;olicita e&longs;&longs;e debet <lb/>de illo re&longs;tituendo, nec adeò vehementi conatu, hoc e&longs;t gravi<lb/>tatione, illud urgere debet in locum &longs;uum. </s>

<s>COrpora non intelliguntur gravitare ni&longs;i in alieno loco; <lb/>quando &longs;cilicet corpus contiguum inter illa & centrum <lb/>terræ interjectum, quod medii rationem habere pote&longs;t, levius <lb/>e&longs;t; petit enim infra illud e&longs;&longs;e: ni&longs;um autem hunc deorsùm <lb/><emph type="italics"/>Gravitationem<emph.end type="italics"/> dicimus. </s><s>Sed quoniam ni&longs;us i&longs;te videtur idcircò <lb/>à naturâ in&longs;titutus, ut perturbatus corporum ordo re&longs;tituatur; <lb/>&longs;i ex fine ratio petenda &longs;it, &longs;atis apparet corpora gravia &cacute;entro <lb/>terræ vicina minùs gravitare. </s><s>Quemadmodum enim quotie&longs;<lb/>cunque aliquis à propo&longs;ito fine magis di&longs;tat, eò magis anxius <lb/>e&longs;t, atque &longs;olicitus de mediis ad illum a&longs;&longs;equendum nece&longs;&longs;ariis, <lb/>& animo æquiore toleratur modica, quàm multa violentia; ita <lb/>natura minorem ordinis debiti perturbationem &longs;entiens, &longs;i gra<lb/>ve parùm ab&longs;it, quàm &longs;i longè abe&longs;&longs;et, à loco, ubi juxta inge<lb/>nitam propen&longs;ionem exigit con&longs;i&longs;tere, minùs &longs;olicita e&longs;&longs;e debet <lb/>de illo re&longs;tituendo, nec adeò vehementi conatu, hoc e&longs;t gravi<lb/>tatione, illud urgere debet in locum &longs;uum. </s>

<s>Ad hæc omnibus aperti&longs;&longs;imè liquet eò majore naturæ impe<lb/>tu corpora deorsùm niti, quò levius e&longs;t corpus, in quo tan<lb/>quam in medio perficiendus e&longs;t motus, &longs;i dimittantur. </s><s>Sic à <lb/>&longs;axo in aëre pendente manum deorsùm validiùs trahi &longs;enti<lb/>mus, quàm ab eodem aquæ immer&longs;o trahatur, & multò lan<lb/>guidiùs conatur deor&longs;um lapis in melle de&longs;cendens, quàm in <lb/>aqua; quia videlicet aqua levior e&longs;t melle, & aër levior aquâ. </s><lb/><s>Hinc e&longs;t quod, &longs;i medij partes fuerint diversâ gravitate prædi<lb/>tæ, pars centro terræ propior etiam erit gravior; atque ideò <lb/>corpus in parte medij graviore minùs gravitabit propè centrum <lb/>terræ, quàm procul. </s><s>E&longs;&longs;e autem eju&longs;dem medij non commoti <lb/>partes graviores in imo, omnium ferè hominum &longs;en&longs;us e&longs;t: <lb/>quotus enim qui&longs;que e&longs;t, qui ne&longs;ciat mellis optimam partem <lb/>e&longs;&longs;e, quæ in va&longs;is fundo, vini quæ in medio, olei quæ in &longs;um<lb/>mo? </s><s>id autem verum non e&longs;&longs;et, ni&longs;i liquoris eju&longs;dem partes <lb/>e&longs;&longs;ent diversâ gravitate delatæ in loca à terræ centro di&longs;pari-

<pb n="19"/>bus intervallis remota: Quia enim oleum eò perfectius e&longs;t, <lb/>quò propiùs aëris levitatem &longs;pirituum &longs;ubtilitate æmulatur, <lb/>ideò quod in &longs;ummo va&longs;e innatat, optimum e&longs;t: At vini &longs;ua<lb/>vitas in exqui&longs;itâ &longs;ui tartari &longs;ufficienti humore diluti cum &longs;pi<lb/>ritibus permi&longs;tione con&longs;i&longs;tens medium locum in va&longs;e exigit, <lb/>&longs;icut media e&longs;t illius gravitas inter vagantium &longs;pirituum levita<lb/>tem, & fæculenti tartari gravitatem: Mellis demùm dulcedo <lb/>ex &longs;ui &longs;alis, &longs;eu &longs;acchari, copiâ proveniens iis partibus poti&longs;&longs;i<lb/>mum ine&longs;t, quæ multo &longs;ale refertæ graviores quoquè &longs;unt, & <lb/>in fundo &longs;ub&longs;idunt. </s><s>Nec e&longs;t iis abroganda fides, qui in alti&longs;&longs;i<lb/>mo mari adeò gravem aquam à &longs;e deprehen&longs;am alicubi te&longs;tan<lb/>tur, ut &longs;upta reliquum maris fundum ambulantes ad alti&longs;&longs;i<lb/>mam fo&longs;&longs;am venerint, in quam penetrare &longs;æpiùs irrito conatu <lb/>tentârint: his enim non ægrè fidem habeo, qui aërem in imis <lb/>vallibus cra&longs;&longs;iorem atquè graviorem, in &longs;ummis verò montibus <lb/>puriorem atque leviorem ab omnibus admitti video. </s><s>Cum ita<lb/>que (&longs;i ex notis ad minùs nota progredi philo&longs;ophando liceat) <lb/>propè centrum gravium ac levium medij partes graviores &longs;int, <lb/>quam procul ab illo; minor e&longs;t gravitatio corporum, &longs;i centro <lb/>propiora fiant, ac quando longè ab illo remota detinebantur. </s><lb/><s>Hinc autem re&longs;ponderi pote&longs;t quærentibus, cur in fodinis lon<lb/>gè faciliùs crudi metalli ma&longs;&longs;a moveatur, quàm in &longs;uperficie <lb/>terræ: aër &longs;cilicet profundis illis cuniculis inclu&longs;us gravior mul<lb/>tò ac cra&longs;&longs;ior e&longs;t aëre i&longs;to, quem in&longs;piramus, atque adeò ibi <lb/>metallum minùs gravitat. </s>

<pb xlink:href="017/01/035.jpg" n="19"/>bus intervallis remota: Quia enim oleum eò perfectius e&longs;t, <lb/>quò propiùs aëris levitatem &longs;pirituum &longs;ubtilitate æmulatur, <lb/>ideò quod in &longs;ummo va&longs;e innatat, optimum e&longs;t: At vini &longs;ua<lb/>vitas in exqui&longs;itâ &longs;ui tartari &longs;ufficienti humore diluti cum &longs;pi<lb/>ritibus permi&longs;tione con&longs;i&longs;tens medium locum in va&longs;e exigit, <lb/>&longs;icut media e&longs;t illius gravitas inter vagantium &longs;pirituum levita<lb/>tem, & fæculenti tartari gravitatem: Mellis demùm dulcedo <lb/>ex &longs;ui &longs;alis, &longs;eu &longs;acchari, copiâ proveniens iis partibus poti&longs;&longs;i<lb/>mum ine&longs;t, quæ multo &longs;ale refertæ graviores quoquè &longs;unt, & <lb/>in fundo &longs;ub&longs;idunt. </s><s>Nec e&longs;t iis abroganda fides, qui in alti&longs;&longs;i<lb/>mo mari adeò gravem aquam à &longs;e deprehen&longs;am alicubi te&longs;tan<lb/>tur, ut &longs;upta reliquum maris fundum ambulantes ad alti&longs;&longs;i<lb/>mam fo&longs;&longs;am venerint, in quam penetrare &longs;æpiùs irrito conatu <lb/>tentârint: his enim non ægrè fidem habeo, qui aërem in imis <lb/>vallibus cra&longs;&longs;iorem atquè graviorem, in &longs;ummis verò montibus <lb/>puriorem atque leviorem ab omnibus admitti video. </s><s>Cum ita<lb/>que (&longs;i ex notis ad minùs nota progredi philo&longs;ophando liceat) <lb/>propè centrum gravium ac levium medij partes graviores &longs;int, <lb/>quam procul ab illo; minor e&longs;t gravitatio corporum, &longs;i centro <lb/>propiora fiant, ac quando longè ab illo remota detinebantur. </s><lb/><s>Hinc autem re&longs;ponderi pote&longs;t quærentibus, cur in fodinis lon<lb/>gè faciliùs crudi metalli ma&longs;&longs;a moveatur, quàm in &longs;uperficie <lb/>terræ: aër &longs;cilicet profundis illis cuniculis inclu&longs;us gravior mul<lb/>tò ac cra&longs;&longs;ior e&longs;t aëre i&longs;to, quem in&longs;piramus, atque adeò ibi <lb/>metallum minùs gravitat. </s>

<s>Quòd &longs;i libeat minorem hanc gravitationem experimento <lb/>deprehendere, &longs;ume vitream fi&longs;tulam &longs;upernè clau&longs;am longio<lb/>rem pedibus tribus Romanis, eam imple argento vivo, digito<lb/>que o&longs;culum accuratè claudens inverte, ac argento vivo &longs;ub<lb/>jecti va&longs;is immerge; tùm amoto digito de&longs;cendet mercurius in <lb/>fi&longs;tulâ, iterúmque a&longs;cendet, & in certâ demum altitudine per<lb/>pendiculari quie&longs;cet. </s><s>Ob&longs;ervatâ igitur altitudine perpendicu<lb/>lari, quam mercurius obtinet, &longs;i in imâ valle experimentum <lb/>in&longs;tituatur, eâque comparatâ cum altitudine perpendiculari, <lb/>in qua con&longs;i&longs;tit, cùm in &longs;ummo montis alti&longs;&longs;imi vertice expe<lb/>rimentum idem &longs;umitur, animadvertes altitudinem mercurij <lb/>per vim in fi&longs;tulâ &longs;u&longs;pen&longs;i minorem e&longs;&longs;e in &longs;ummo monre, quàm

<pb n="20"/>in valle; Quia nimirum mercurius intra fi&longs;tulam detentus tan<lb/>quàm in va&longs;e, e&longs;t in aëre fi&longs;tulam ambiente tanquam in loco; <lb/>in aëre autem leviori cùm magis gravitet, in minori etiam al<lb/>titudine perpendiculari con&longs;i&longs;tit. </s><s>Experimentum hoc in valle, <lb/>& in monte &longs;umere mihi otium non fuit, quamvis in eo &longs;æ<lb/>piùs me exercuerim: &longs;ed de illius veritate ambigere non &longs;inunt <lb/>te&longs;tes in Galliâ luculenti&longs;&longs;imi, qui di&longs;crimen hoc in mercuri; <lb/>altitudine ob&longs;ervârunt in altioribus montibus. </s>

<pb xlink:href="017/01/036.jpg" n="20"/>in valle; Quia nimirum mercurius intra fi&longs;tulam detentus tan<lb/>quàm in va&longs;e, e&longs;t in aëre fi&longs;tulam ambiente tanquam in loco; <lb/>in aëre autem leviori cùm magis gravitet, in minori etiam al<lb/>titudine perpendiculari con&longs;i&longs;tit. </s><s>Experimentum hoc in valle, <lb/>& in monte &longs;umere mihi otium non fuit, quamvis in eo &longs;æ<lb/>piùs me exercuerim: &longs;ed de illius veritate ambigere non &longs;inunt <lb/>te&longs;tes in Galliâ luculenti&longs;&longs;imi, qui di&longs;crimen hoc in mercuri; <lb/>altitudine ob&longs;ervârunt in altioribus montibus. </s>

<s>Verùm, ex alio præteteà capite imminui debet gravitatio <lb/>corporum in minori à centro remotione, habitâ &longs;olùm ratione <lb/>&longs;itûs. </s><s>Cùm enim totius corporis gravitatio conflata &longs;it ex &longs;in<lb/>gularum partium impetu, quo deor&longs;um nituntur, manife&longs;tum <lb/>e&longs;t &longs;ingulis partibus languidiùs deor&longs;um conantibus, totius cor<lb/>poris gravitationem e&longs;&longs;e pariter languidiorem. </s><s>Quoniam verò <lb/>quicquid in motu cogitur à recto &longs;ecundùm naturam tramite <lb/>deflectere, lentiùs atque remi&longs;&longs;iùs pergit ad præ&longs;titutum mo<lb/>tûs terminum; particulæ autem corporis &longs;olidi gravis, propio<lb/>res centro factæ, magis à &longs;uo perpendiculo, &longs;ibi invicem ad<lb/>ver&longs;antes, declinant; &longs;atis con&longs;tat &longs;ingulas fractis quodammo<lb/>do viribus languentes plurimum de conatu remittere. </s><s>Si enim <lb/>

<figure/><lb/>&longs;olidum AB fiat centro vicinius ita, <lb/>ut A &longs;it in K, & B in L, lineæ di<lb/>rectionis partium extremarum &longs;unt <lb/>KC, LC: at coguntur per lineas <lb/>KF, LE parallelas de&longs;cendere, <lb/>fiuntque anguli CKF, CLE ex<lb/>terni majores internis CAK, CBL <lb/>per 16. l. 1. magis igitur in K & L <lb/>recedunt à perpendiculo, quàm re<lb/>cederent in A & B. </s><s>Quia itaque <lb/>pars in K exi&longs;tens magis impeditur <lb/>ab oppo&longs;itâ extremitate, quæ in L, <lb/>ne per KC de&longs;cendat (ni&longs;i enim <lb/>pars, quæ in L, urgeret oppo&longs;itam <lb/>tentans per LC de&longs;cendere, non cogeretur pars in K exi&longs;tens <lb/>adeò recedere à &longs;uâ directionis lineâ) minori etiam impetu <lb/>deor&longs;um fertur. </s><s>E&longs;t autem eadem de reliquis partibus ratio,

<figure id="id.017.01.036.1.jpg" xlink:href="017/01/036/1.jpg"/><lb/>&longs;olidum AB fiat centro vicinius ita, <lb/>ut A &longs;it in K, & B in L, lineæ di<lb/>rectionis partium extremarum &longs;unt <lb/>KC, LC: at coguntur per lineas <lb/>KF, LE parallelas de&longs;cendere, <lb/>fiuntque anguli CKF, CLE ex<lb/>terni majores internis CAK, CBL <lb/>per 16. l. 1. magis igitur in K & L <lb/>recedunt à perpendiculo, quàm re<lb/>cederent in A & B. </s><s>Quia itaque <lb/>pars in K exi&longs;tens magis impeditur <lb/>ab oppo&longs;itâ extremitate, quæ in L, <lb/>ne per KC de&longs;cendat (ni&longs;i enim <lb/>pars, quæ in L, urgeret oppo&longs;itam <lb/>tentans per LC de&longs;cendere, non cogeretur pars in K exi&longs;tens <lb/>adeò recedere à &longs;uâ directionis lineâ) minori etiam impetu <lb/>deor&longs;um fertur. </s><s>E&longs;t autem eadem de reliquis partibus ratio,

<pb n="21"/>præter eas, quæ in eâdem directionis lineâ &longs;unt cum centro <lb/>gravitatis; &longs;ingulæ enim ad centrum terræ accedentes magis à <lb/>&longs;uo perpendiculo recedunt, minú&longs;que deor&longs;um gravitant. </s><s>Quî <lb/>igitur fieri po&longs;&longs;it, ut debilitato &longs;ingularum particularum cona<lb/>tu, atque impetu deor&longs;um, non minuatur pariter totius cor<lb/>poris gravitatio, &longs;i fiat centro vicinius? </s>

<pb xlink:href="017/01/037.jpg" n="21"/>præter eas, quæ in eâdem directionis lineâ &longs;unt cum centro <lb/>gravitatis; &longs;ingulæ enim ad centrum terræ accedentes magis à <lb/>&longs;uo perpendiculo recedunt, minú&longs;que deor&longs;um gravitant. </s><s>Quî <lb/>igitur fieri po&longs;&longs;it, ut debilitato &longs;ingularum particularum cona<lb/>tu, atque impetu deor&longs;um, non minuatur pariter totius cor<lb/>poris gravitatio, &longs;i fiat centro vicinius? </s>

<s>Illud tamen non diffiteor, quod &longs;i medij levitates, aut angu<lb/>lorum CLE, CBL inclinationes eo tantùm di&longs;crimine &longs;ecer<lb/>nantur, quod omnem &longs;en&longs;um fugiat, vel &longs;altem ex medij gra<lb/>vitate, & anguli magnitudine conjunctim &longs;umptis oriri non <lb/>po&longs;&longs;it varietas, quæ &longs;ub &longs;en&longs;um cadat; neque percipietur gra<lb/>vitationis differentia in majori vicinitate. </s><s>Sed hoc non facit, <lb/>quin inter gravitationes di&longs;crimen intercedat; neque enim <lb/>continuò, &longs;i quid &longs;en&longs;um latet, id omninò non e&longs;&longs;e dicendum <lb/>e&longs;t: contingere &longs;i quidem pote&longs;t motum aliquem ita &longs;en&longs;im, & <lb/>&longs;ine &longs;en&longs;u fieri, ut non ni&longs;i elap&longs;o temporis &longs;patio demùm inno<lb/>te&longs;cat. </s><s>Sic &longs;i vinum, cujus gravitas vix minor &longs;it gravitate aquæ <lb/>arte &longs;atis notâ affuderis aquæ ita, ut innatet, & &longs;upremam va<lb/>&longs;is partem occupet, aliudque vas &longs;imili vino plenum, &longs;ed paulò <lb/>altius, habeas, tum ex libra centrum motûs habente in cen<lb/>tro gravitatis jugi pendeant æqualia pondera intrà vinum <lb/>utriu&longs;que va&longs;is; fiet utique ponderum æquilibrium, & con<lb/>&longs;i&longs;tent eo in &longs;itu, quem illis dederis: at &longs;i alterum libræ extre<lb/>mum ita deprimas, ut pondus, quod ex eo pendet, ex vino ad <lb/>aquam vix graviorem tran&longs;eat, reliquo pondere intra vinum <lb/>manente; initio quidem non apparebit motus libræ &longs;e re&longs;ti<lb/>tuentis, quia pondus in vino non excedit gravitationem pon<lb/>deris æqualis in aquâ ni&longs;i eo exce&longs;&longs;u, quo gravitas aquæ &longs;upe<lb/>rat gravitatem vini; hic autem exce&longs;&longs;us cum minimus &longs;it, mo<lb/>tum quoque efficiet, quem ægrè à quiete di&longs;cernas, ni&longs;i ubi <lb/>po&longs;t aliquod tempus deprehenderis pondus altius de&longs;cendi&longs;&longs;e, <lb/>depre&longs;&longs;ius autem a&longs;cendi&longs;&longs;e. </s><s>Haud &longs;ecus philo&longs;ophandum e&longs;t <lb/>de majore, aut minore corporum gravitatione, &longs;i di&longs;paribus in<lb/>tervallis à terræ centro removeantur, diutiùs enim propè cen<lb/>trum incumbere poterunt &longs;u&longs;tinenti, quàm procul: id quod <lb/>&longs;atis erit ad minorem gravitationem patefaciendam, quæ non <lb/>&longs;tatim innote&longs;cat. </s>

<s>Hæc autem non leviter confirmari videntur ex iis, quæ quo<lb/>tidiè ferè videmus; nam &longs;i circinus, quo circulos de&longs;cribere <lb/>&longs;olemus, cadat, &longs;emper nodus prævertit cu&longs;pides, & prior ter<lb/>ram ferit; ni&longs;i fortè nodus ad perpendiculum immineat cru<lb/>ribus: & omnia ferè corpora, quæ centrum gravitatis ex una <lb/>parte habent, &longs;i ex modicâ altitudine dimittantur, videntur <lb/>quidem cadere parallela; &longs;ed ex majori altitudine &longs;i de&longs;cen<lb/>dant, pars gravior prior terram attingit. </s><s>Sit enim corpus ES, <lb/>

<figure/><lb/>cujus gravitatis centrum H, linea <lb/>directionis HA; &longs;i horizonti paral<lb/>lelum de&longs;cenderet, per rectas EI, <lb/>SR parallelas lineæ directionis mo<lb/>veretur; id quod in modicâ tantùm <lb/>altitudine contingere videtur, quia <lb/>nondum facta e&longs;t ea gravitationis <lb/>imminutio in extremitate S, quæ <lb/>percipi po&longs;&longs;it. </s><s>Si enim E per EI <lb/>de&longs;cenderet, S verò per SR, an<lb/>gulus IEA æqualis alterno EAH <lb/>per 29. lib. 1. minor e&longs;&longs;et angulo <lb/>RSA, qui æqualis e&longs;t alterno <lb/>HAS; nam ex hypothe&longs;i minùs <lb/>di&longs;tat E, quàm S, à centro gravi<lb/>tatis H, & e&longs;t angulus EAH minor angulo HAS; pars igi<lb/>tur S magis deflecteret à &longs;uo perpendiculo SA, quàm E de<lb/>flecteret ab EA; cùm itaque S magis in latus propelleretur, <lb/>plus etiam de conatu deor&longs;um remitteret, quàm E; atque adeò <lb/>non po&longs;&longs;et æqualiter de&longs;cendere ac moveri, contra hypothe&longs;im <lb/>paralleli&longs;mi. </s><s>Dicendum e&longs;t igitur non per parallelas EI, SR <lb/>fieri motum, &longs;ed intra illas paulatim partem E graviorem præ<lb/>currere: quia &longs;cilicet partes omnes extra lineam directionis <lb/>AH con&longs;titutæ dum removentur à &longs;uo perpendiculo, aliquid <lb/>amittunt de impetu, quo deor&longs;um nituntur, propiores quidem <lb/>minus, remotiores autem plus; pars &longs;i quidem G in principio <lb/>motûs de&longs;cendens parallela lineæ directionis per GM facit an<lb/>gulum AGM internum per 16.lib.1. minorem externo GMS, <lb/>qui per 29. 1. e&longs;t æqualis alterno MSR. </s><s>Quia ergo AGM

<figure id="id.017.01.038.1.jpg" xlink:href="017/01/038/1.jpg"/><lb/>cujus gravitatis centrum H, linea <lb/>directionis HA; &longs;i horizonti paral<lb/>lelum de&longs;cenderet, per rectas EI, <lb/>SR parallelas lineæ directionis mo<lb/>veretur; id quod in modicâ tantùm <lb/>altitudine contingere videtur, quia <lb/>nondum facta e&longs;t ea gravitationis <lb/>imminutio in extremitate S, quæ <lb/>percipi po&longs;&longs;it. </s><s>Si enim E per EI <lb/>de&longs;cenderet, S verò per SR, an<lb/>gulus IEA æqualis alterno EAH <lb/>per 29. lib. 1. minor e&longs;&longs;et angulo <lb/>RSA, qui æqualis e&longs;t alterno <lb/>HAS; nam ex hypothe&longs;i minùs <lb/>di&longs;tat E, quàm S, à centro gravi<lb/>tatis H, & e&longs;t angulus EAH minor angulo HAS; pars igi<lb/>tur S magis deflecteret à &longs;uo perpendiculo SA, quàm E de<lb/>flecteret ab EA; cùm itaque S magis in latus propelleretur, <lb/>plus etiam de conatu deor&longs;um remitteret, quàm E; atque adeò <lb/>non po&longs;&longs;et æqualiter de&longs;cendere ac moveri, contra hypothe&longs;im <lb/>paralleli&longs;mi. </s><s>Dicendum e&longs;t igitur non per parallelas EI, SR <lb/>fieri motum, &longs;ed intra illas paulatim partem E graviorem præ<lb/>currere: quia &longs;cilicet partes omnes extra lineam directionis <lb/>AH con&longs;titutæ dum removentur à &longs;uo perpendiculo, aliquid <lb/>amittunt de impetu, quo deor&longs;um nituntur, propiores quidem <lb/>minus, remotiores autem plus; pars &longs;i quidem G in principio <lb/>motûs de&longs;cendens parallela lineæ directionis per GM facit an<lb/>gulum AGM internum per 16.lib.1. minorem externo GMS, <lb/>qui per 29. 1. e&longs;t æqualis alterno MSR. </s><s>Quia ergo AGM

<pb n="23"/>minor e&longs;t angulo ASR, pars G minus de &longs;uo impetu deor&longs;um <lb/>amittit, quàm pars S; & quamvis initio di&longs;crimen hoc non <lb/>percipiatur, demum fit, ut additis pluribus differentiis mani<lb/>fe&longs;tè appareat partem S minùs gravitare, quia tardiùs deor<lb/>&longs;um movetur; & tandem ip&longs;a &longs;equitur partem E præcur<lb/>rentem, po&longs;tquam minori illâ gravitatione permi&longs;it parti E, <lb/>ut propiùs accederet ad lineam directionis, fieretquè quæ<lb/>dam virtualis conver&longs;io circa centrum gravitatis H, in qua <lb/>extremitas E occuparet infimum locum, S autem &longs;upre<lb/>mum. </s><s>Quare cùm nos doceat experientia partem HS <lb/>æquiponderantem parti HE, &longs;i &longs;u&longs;pendantur ex H, in mo<lb/>tu tamen minùs gravitare, quàm oppo&longs;itam, ideóque fieri <lb/>illam conver&longs;ionem, ut pars E fiat inferior; neque aptior <lb/>a&longs;&longs;ignari po&longs;&longs;it ratio, quàm quæ petitur ex rece&longs;&longs;u partium <lb/>majori à &longs;uo perpendiculo: &longs;atis liquet, quantum momenti <lb/>habeat hæc declinatio à perpendiculo ad minuendam gra<lb/>vitationem. </s><s>Ex majori igitur declinatione à lineâ perpen<lb/>diculari, quæ con&longs;equitur corpus con&longs;titutum non adeò <lb/>procul à centro terræ ut priùs, non ineptè arguitur minor <lb/>corporis gravitatio in eo &longs;itu, &longs;i cætera &longs;int paria: neque <lb/>enim comparo corpus, quod per motum de&longs;cendit, per&longs;e<lb/>verans in &longs;uo motu, cum corpore in loco altiori tran&longs;eun<lb/>te à quiete ad motum; nam tunc ex impetu per motum <lb/>concepto major e&longs;t gravitatio in loco inferiore, quàm in &longs;u<lb/>periore: &longs;ed tantùm corpora invicem comparo, vel pariter <lb/>quie&longs;centia, vel æquali tempore mota, illudque, quod ter<lb/>ræ vicinius e&longs;t, a&longs;&longs;ero, vel minori ni&longs;u conari à quiete in <lb/>loco alieno tran&longs;ire ad motum, vel æquali tempore, quo præ<lb/>ce&longs;&longs;it motus, minus impetus acqui&longs;ii&longs;&longs;e ac minoribus viribus <lb/>motum continuare. </s>

<pb xlink:href="017/01/039.jpg" n="23"/>minor e&longs;t angulo ASR, pars G minus de &longs;uo impetu deor&longs;um <lb/>amittit, quàm pars S; & quamvis initio di&longs;crimen hoc non <lb/>percipiatur, demum fit, ut additis pluribus differentiis mani<lb/>fe&longs;tè appareat partem S minùs gravitare, quia tardiùs deor<lb/>&longs;um movetur; & tandem ip&longs;a &longs;equitur partem E præcur<lb/>rentem, po&longs;tquam minori illâ gravitatione permi&longs;it parti E, <lb/>ut propiùs accederet ad lineam directionis, fieretquè quæ<lb/>dam virtualis conver&longs;io circa centrum gravitatis H, in qua <lb/>extremitas E occuparet infimum locum, S autem &longs;upre<lb/>mum. </s><s>Quare cùm nos doceat experientia partem HS <lb/>æquiponderantem parti HE, &longs;i &longs;u&longs;pendantur ex H, in mo<lb/>tu tamen minùs gravitare, quàm oppo&longs;itam, ideóque fieri <lb/>illam conver&longs;ionem, ut pars E fiat inferior; neque aptior <lb/>a&longs;&longs;ignari po&longs;&longs;it ratio, quàm quæ petitur ex rece&longs;&longs;u partium <lb/>majori à &longs;uo perpendiculo: &longs;atis liquet, quantum momenti <lb/>habeat hæc declinatio à perpendiculo ad minuendam gra<lb/>vitationem. </s><s>Ex majori igitur declinatione à lineâ perpen<lb/>diculari, quæ con&longs;equitur corpus con&longs;titutum non adeò <lb/>procul à centro terræ ut priùs, non ineptè arguitur minor <lb/>corporis gravitatio in eo &longs;itu, &longs;i cætera &longs;int paria: neque <lb/>enim comparo corpus, quod per motum de&longs;cendit, per&longs;e<lb/>verans in &longs;uo motu, cum corpore in loco altiori tran&longs;eun<lb/>te à quiete ad motum; nam tunc ex impetu per motum <lb/>concepto major e&longs;t gravitatio in loco inferiore, quàm in &longs;u<lb/>periore: &longs;ed tantùm corpora invicem comparo, vel pariter <lb/>quie&longs;centia, vel æquali tempore mota, illudque, quod ter<lb/>ræ vicinius e&longs;t, a&longs;&longs;ero, vel minori ni&longs;u conari à quiete in <lb/>loco alieno tran&longs;ire ad motum, vel æquali tempore, quo præ<lb/>ce&longs;&longs;it motus, minus impetus acqui&longs;ii&longs;&longs;e ac minoribus viribus <lb/>motum continuare. </s>

<s>Ex his quæ de gravibus hactenus di&longs;putata &longs;unt, aliquis <lb/>forta&longs;sè inferat levia à centro remotiora minùs levitare, &longs;i<lb/>cut gravia centro propiora minùs gravitant. </s><s>Verùm res e&longs;t <lb/>pen&longs;iculatiùs examinanda, nec &longs;impliciter ex oppo&longs;itis gra<lb/>vium, ac levium naturis definienda, qua&longs;i ob id ip&longs;um, <lb/>quia &longs;ibi gravitas atque levitas adver&longs;antur, contraria ha<lb/>berent omnia con&longs;equentia. </s><s>Et quidem quod &longs;pectat ad

<pb n="24"/>&longs;olam corporis levioris po&longs;itionem, non minuitur levitatio, <lb/>&longs;ed potiùs augetur in majoribus à terræ centro intervallis; <lb/>ubi minùs à &longs;uo perpendiculo declinant partes centrum le<lb/>vitatis circun&longs;tantes, & idcirco minùs de conatu remit<lb/>tunt, quò nituntur ad &longs;upe<lb/>

<pb xlink:href="017/01/040.jpg" n="24"/>&longs;olam corporis levioris po&longs;itionem, non minuitur levitatio, <lb/>&longs;ed potiùs augetur in majoribus à terræ centro intervallis; <lb/>ubi minùs à &longs;uo perpendiculo declinant partes centrum le<lb/>vitatis circun&longs;tantes, & idcirco minùs de conatu remit<lb/>tunt, quò nituntur ad &longs;upe<lb/>

<figure/><lb/>riora evadere. </s><s>Sit namque <lb/>Globus HG, cujus centrum <lb/>levitatis M, & linea di&longs;cretio<lb/>nis OMN; cui parallelæ <lb/>&longs;unt HD & GF, quas de&longs;<lb/>cribunt a&longs;cendendo extremi<lb/>tates H & G, & motum eum<lb/>dem continuabunt, &longs;i globus <lb/>in N tran&longs;latus intelligatur. </s><lb/><s>Quando igitur globus e&longs;t in M, <lb/>extremitas H recedit à per<lb/>pendiculo OI, & cum eo <lb/>facit angulum IHT; quan<lb/>do autem e&longs;t in N, extremi<lb/>tas T a&longs;cendens per TD fa<lb/>cit cum perpendiculo OR an<lb/>gulum RTD, qui per 15.lib.1. <lb/>æqualis e&longs;t angulo HTO ad <lb/>verticem, hic autem, inter<lb/>nus cum &longs;it, per 16. 1. minor <lb/>e&longs;t externo IHT. </s><s>E&longs;t ergo <lb/>RTD minor angulo IHT, <lb/>atque ideò plus habet mo<lb/>menti &longs;ur&longs;um, ubi minus à <lb/>recto &longs;ecundum naturam tra<lb/>mite deflectit. </s>

<figure id="id.017.01.040.1.jpg" xlink:href="017/01/040/1.jpg"/><lb/>riora evadere. </s><s>Sit namque <lb/>Globus HG, cujus centrum <lb/>levitatis M, & linea di&longs;cretio<lb/>nis OMN; cui parallelæ <lb/>&longs;unt HD & GF, quas de&longs;<lb/>cribunt a&longs;cendendo extremi<lb/>tates H & G, & motum eum<lb/>dem continuabunt, &longs;i globus <lb/>in N tran&longs;latus intelligatur. </s><lb/><s>Quando igitur globus e&longs;t in M, <lb/>extremitas H recedit à per<lb/>pendiculo OI, & cum eo <lb/>facit angulum IHT; quan<lb/>do autem e&longs;t in N, extremi<lb/>tas T a&longs;cendens per TD fa<lb/>cit cum perpendiculo OR an<lb/>gulum RTD, qui per 15.lib.1. <lb/>æqualis e&longs;t angulo HTO ad <lb/>verticem, hic autem, inter<lb/>nus cum &longs;it, per 16. 1. minor <lb/>e&longs;t externo IHT. </s><s>E&longs;t ergo <lb/>RTD minor angulo IHT, <lb/>atque ideò plus habet mo<lb/>menti &longs;ur&longs;um, ubi minus à <lb/>recto &longs;ecundum naturam tra<lb/>mite deflectit. </s>

<s>Di&longs;crimen hoc momentorum ab angulorum inæqualitate <lb/>proveniens optimè intelligit natura, quæ ita motum perfi<lb/>cit, ut, &longs;i duo inæqualiter levia coagmentata fuerint, le<lb/>vius præcurrat. </s><s>Sic &longs;i A cortex &longs;uberis coagmentetur ligno <lb/>fagino B, & intra aquam mediocriter profundam horizon<lb/>taliter collocetur &longs;olidum DC, ita per lineam directio-

<pb n="25"/>nis TO a&longs;cendit centrum <lb/>

<pb xlink:href="017/01/041.jpg" n="25"/>nis TO a&longs;cendit centrum <lb/>

<figure/><lb/>levitatis, ut demum A in <lb/>loco &longs;uperiore, B autem in <lb/>inferiore con&longs;tituatur, ex<lb/>tremo D per rectam DO <lb/>a&longs;cendente: Quo in motu <lb/>natura magnum invenit <lb/>compendium. </s><s>Quia enim <lb/>partes centro levitatis vi<lb/>ciniores magis levitant, <lb/>quòd linea parallela lineæ <lb/>directionis faciat minorem <lb/>angulum cum earum per<lb/>pendiculo (&longs;ic &longs;i linea di<lb/>rectionis &longs;it FL, eique pa<lb/>rallelæ NG, RX, angu<lb/>lus NGX internus per <lb/>29. 1. e&longs;t æqualis externo <lb/>RXY, at PGX externus per 16. 1. major e&longs;t interno GXF, <lb/>hoc e&longs;t VXY ad verticem, ergo PGX major e&longs;t angulo <lb/>VXY, & &longs;i uterque auferatur ex æqualibus NGX, RXY, <lb/>remanet NGP minor angulo RXV, ideoque G magis levi<lb/>tat, quam X) ex majore impedimento, quod initio motûs ha<lb/>betur ob anguli HDI magnitudinem, dum pars D minùs le<lb/>vitat, centrum levitatis per SO a&longs;cendens inclinat corpus DC, <lb/>& extremitas D in recta DO con&longs;tituitur, in qua longê ci<lb/>tiùs minuuntur impedimenta, quàm &longs;i per parallelam DI <lb/>a&longs;cenderet: vix enim a&longs;cendit in E, cum impedimenta &longs;unt <lb/>æquè diminuta, ac &longs;i a&longs;cendi&longs;&longs;et in I; quandoquidem angu<lb/>lus KEI per 29. 1. e&longs;t æqualis alterno EID, atque adeò <lb/>etiam angulo, quem in I faceret parallela DI cum perpendi<lb/>culo; e&longs;t igitur angulus KEI minor quocunque alio angulo, <lb/>qui fieret in punctis intermediis lineæ DI; &longs;ed quoniam cen<lb/>trum levitatis a&longs;cendendo acqui&longs;ivit majorem impetum, quàm <lb/>extremitas in E exi&longs;tens, per vim illam rapit extra paralle<lb/>lam EK, trahitque per lineam EO, & perpendiculum facit <lb/>angulum &longs;emper minorem cum lineâ directionis; unde fit <lb/>partem inferiorem &longs;emper faciliùs trahi, quo minùs in diver&longs;a

<figure id="id.017.01.041.1.jpg" xlink:href="017/01/041/1.jpg"/><lb/>levitatis, ut demum A in <lb/>loco &longs;uperiore, B autem in <lb/>inferiore con&longs;tituatur, ex<lb/>tremo D per rectam DO <lb/>a&longs;cendente: Quo in motu <lb/>natura magnum invenit <lb/>compendium. </s><s>Quia enim <lb/>partes centro levitatis vi<lb/>ciniores magis levitant, <lb/>quòd linea parallela lineæ <lb/>directionis faciat minorem <lb/>angulum cum earum per<lb/>pendiculo (&longs;ic &longs;i linea di<lb/>rectionis &longs;it FL, eique pa<lb/>rallelæ NG, RX, angu<lb/>lus NGX internus per <lb/>29. 1. e&longs;t æqualis externo <lb/>RXY, at PGX externus per 16. 1. major e&longs;t interno GXF, <lb/>hoc e&longs;t VXY ad verticem, ergo PGX major e&longs;t angulo <lb/>VXY, & &longs;i uterque auferatur ex æqualibus NGX, RXY, <lb/>remanet NGP minor angulo RXV, ideoque G magis levi<lb/>tat, quam X) ex majore impedimento, quod initio motûs ha<lb/>betur ob anguli HDI magnitudinem, dum pars D minùs le<lb/>vitat, centrum levitatis per SO a&longs;cendens inclinat corpus DC, <lb/>& extremitas D in recta DO con&longs;tituitur, in qua longê ci<lb/>tiùs minuuntur impedimenta, quàm &longs;i per parallelam DI <lb/>a&longs;cenderet: vix enim a&longs;cendit in E, cum impedimenta &longs;unt <lb/>æquè diminuta, ac &longs;i a&longs;cendi&longs;&longs;et in I; quandoquidem angu<lb/>lus KEI per 29. 1. e&longs;t æqualis alterno EID, atque adeò <lb/>etiam angulo, quem in I faceret parallela DI cum perpendi<lb/>culo; e&longs;t igitur angulus KEI minor quocunque alio angulo, <lb/>qui fieret in punctis intermediis lineæ DI; &longs;ed quoniam cen<lb/>trum levitatis a&longs;cendendo acqui&longs;ivit majorem impetum, quàm <lb/>extremitas in E exi&longs;tens, per vim illam rapit extra paralle<lb/>lam EK, trahitque per lineam EO, & perpendiculum facit <lb/>angulum &longs;emper minorem cum lineâ directionis; unde fit <lb/>partem inferiorem &longs;emper faciliùs trahi, quo minùs in diver&longs;a

<pb n="26"/>abit ejus perpendiculum, cum quo &longs;emper minorem, & mi<lb/>norem angulum facit linea motûs DO; donec demùm to<lb/>tum &longs;olidum obtineat &longs;itum perpendicularem; quod initio erat <lb/>in æquilibrio. </s>

<pb xlink:href="017/01/042.jpg" n="26"/>abit ejus perpendiculum, cum quo &longs;emper minorem, & mi<lb/>norem angulum facit linea motûs DO; donec demùm to<lb/>tum &longs;olidum obtineat &longs;itum perpendicularem; quod initio erat <lb/>in æquilibrio. </s>

<s>Cæterum, quamvis habitâ ratione &longs;itûs, levia altiora magis <lb/>levitent, &longs;ivè parallela horizonti jaceant extrema, &longs;ivè incli<lb/>nata, ratione tamen medij, quod in &longs;uperioribus e&longs;t levius, <lb/>quàm in inferioribus, minùs levitant: experientia enim o&longs;ten<lb/>dit ea lentiùs a&longs;cendere, quæ propiùs accedunt ad medij na<lb/>turam &longs;ecundùm levitatem: nam ex tribus globulis &longs;phæricis, <lb/>quorum diameter unc. 2 1/5 pedis Romani, cereus erat ponderis <lb/>drachmarum 24, faginus drachm. 22, vitraëreus drachm. 7. <lb/>in aëre expen&longs;i, &longs;ed eorum motus in aquâ ad altitudinem pe<lb/>dum 14, valdè inæqualis fuit, numeratis vibrationibus eju&longs;<lb/>dem perpendiculi; cereus &longs;iquidem a&longs;cendit lenti&longs;&longs;imè vibra<lb/>tionibus 88, faginus vibrationibus 37, vitraëreus vibrationi<lb/>bus 33: unde patet cereum, qui minimùm ab aquâ differt in <lb/>pondere (aquæ etenim molis æqualis e&longs;t drachm. 25 3/5) minùs <lb/>in eâ levitare. </s><s>Sicut igitur diver&longs;a levia in eodem medio inæ<lb/>qualiter levitant, &longs;ic idem leve in medio di&longs;&longs;imili inæqualiter <lb/>levitabit pro majore aut minore levitatum di&longs;&longs;imilitudine. </s><lb/><s>Conveniunt itaque gravia, & levia, quod hæc procul à cen<lb/>tro offendentia medium levius minùs levitant, illa propè cen<lb/>trum habentia medium gravius minùs gravitant. </s><s>Differunt au<lb/>tem ratione po&longs;itionis, quia, in loco remotiore à centro, per<lb/>pendicula omnia concurrunt ad angulos magis acutos, minú&longs;<lb/>que differunt à lineâ rectâ, ideo qua&longs;i collatis viribus magis <lb/>gravitant, & magis levitant; at prope centrum cum perpendi<lb/>cula magis in diver&longs;a abeant, & levia minùs levitant, & gravia <lb/>minùsgravitant. </s><s>Porrò hanc &longs;imilitudinem gravitationis gra<lb/>vium, & levitationis levium in eodem loco, à me vocari di&longs;cri<lb/>men, & differentiam, quia habita ratione oppo&longs;itorum videba<lb/>tur leve remotius debere minùs levitare, &longs;icut grave propius <lb/>minùs gravitat, ne te moveat; litem de verbo non faciam.

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

Line 411

<s>OPus mechanicum plerunque non indiget puncto illo, <lb/>quod intra corporum &longs;oliditatem latet, ac centrum gra<lb/>vitatis definivimus; &longs;ed &longs;atis e&longs;t &longs;i in extimâ corporis &longs;uperfi<lb/>cie innote&longs;cat punctum, aut linea imminens ip&longs;i gravitatis <lb/>centro, pro ratione &longs;itûs, in quo corpus grave con&longs;i&longs;tere cu<lb/>pimus. </s><s>Ideo geometricum laborem inveniendi punctum illud <lb/>intimum Centrobarycæ relinquens, mechanica tantùm inqui<lb/>&longs;itione, & qua&longs;i tentans, perve&longs;tigo punctum illud, aut li<lb/>neam in corporis &longs;uperficie, cui re&longs;pondet planum per lineam <lb/>directionis ductum, & &longs;ecans corpus in certo &longs;itu con&longs;titu<lb/>tum. </s><s>Et quidem &longs;i corpus &longs;phæricum fuerit ex partibus eju&longs;<lb/>dem naturæ conflatum, aut &longs;altem ex partibus heterogeneis <lb/>quidem, &longs;ed circa &longs;phæræ centrum &longs;imiliter di&longs;po&longs;itis ita, ut <lb/>intima &longs;phærula folliculis quibu&longs;dam obvolvatur; quia idem <lb/>e&longs;t molis atque gravitatis centrum, punctum quodcumque in <lb/>&longs;phærica &longs;uperficie a&longs;&longs;umatur, aptum erit; &longs;ingula enim &longs;i<lb/>milem habent po&longs;itionem. </s><s>Sin autem aut &longs;phæræ &longs;egmentum, <lb/>aut &longs;phæra ex partibus heterogeneis inæqualiter di&longs;po&longs;itis fue<lb/>rit; imponatur plano horizontali accuratè levi, & maximè æqua<lb/>bili; & quod punctum tangetur à &longs;uppo&longs;ito plano, ubi motus <lb/>omnis ce&longs;&longs;averit, illud e&longs;t, quod poti&longs;&longs;imùm quæritur, ac <lb/>punctum &longs;uperius, quod huic è regione e&longs;t, erit pariter aptum <lb/>ad propo&longs;itum finem. </s>

<s>Quod &longs;i cylindricum fuerit oblatum corpus, aut pri&longs;ma quod<lb/>cunque continuo, & &longs;imili ductu productum; &longs;ecetur bifariam <lb/>longitudo, & punctum habebitur cylindri centro gravitatis <lb/>re&longs;pondens: pri&longs;matis autem &longs;ingula plana parallelogramma &longs;i <lb/>dividantur in æquas tum longitudinis, tum latitudinis partes, <lb/>planum per inventa puncta ductum tran&longs;ibit per centrum <lb/>gravitatis pri&longs;matis, dividet enim in partes æquales, & &longs;imi<lb/>liter po&longs;itas, unde oritur momentorum gravitatis æqualitas. </s>

<figure/><lb/><s>Ut &longs;i parallelepipedi BC plana ita <lb/>dividantur, ut habeant puncta me<lb/>dia I, & O, & per ea agatur pla<lb/>num, con&longs;tat æqualia e&longs;&longs;e momenta <lb/>gravitatis partium IB, & IC, cùm <lb/>nullo ex capite po&longs;&longs;it oriri momento<lb/>rum inæqualitas. </s><s>At &longs;i non facies parallelogrammæ pri&longs;matis <lb/>dividendæ &longs;int, &longs;ed potius ba&longs;is, quæ &longs;æpè varia e&longs;t, & irre<lb/>gularis, tunc inveniendum e&longs;t in ea punctum, in quo &longs;ibi oc<lb/>currunt &longs;ectiones planorum &longs;ecantium datum corpus in mo<lb/>menta æqualia, illudque re&longs;pondet centro gravitatis intra &longs;o<lb/>liditatem exi&longs;tenti. </s>

<figure id="id.017.01.044.1.jpg" xlink:href="017/01/044/1.jpg"/><lb/><s>Ut &longs;i parallelepipedi BC plana ita <lb/>dividantur, ut habeant puncta me<lb/>dia I, & O, & per ea agatur pla<lb/>num, con&longs;tat æqualia e&longs;&longs;e momenta <lb/>gravitatis partium IB, & IC, cùm <lb/>nullo ex capite po&longs;&longs;it oriri momento<lb/>rum inæqualitas. </s><s>At &longs;i non facies parallelogrammæ pri&longs;matis <lb/>dividendæ &longs;int, &longs;ed potius ba&longs;is, quæ &longs;æpè varia e&longs;t, & irre<lb/>gularis, tunc inveniendum e&longs;t in ea punctum, in quo &longs;ibi oc<lb/>currunt &longs;ectiones planorum &longs;ecantium datum corpus in mo<lb/>menta æqualia, illudque re&longs;pondet centro gravitatis intra &longs;o<lb/>liditatem exi&longs;tenti. </s>

<s>Sit autem primò ba&longs;is pri&longs;matis <lb/>trigona AHI; dividatur unum <lb/>ex lateribus ex. gr. HI bifariam <lb/>in G, planum enim tran&longs;iens per <lb/>A & G, atque bifariam &longs;ecans pa<lb/>rallelogrammum HV tran&longs;ibit per <lb/>centrum gravitatis pri&longs;matis trigo<lb/>ni. </s><s>Nam &longs;i datum pri&longs;ma &longs;ecetur <lb/>pluribus planis parallelis plano <lb/>HV facientibus &longs;ectiones ML, <lb/>BO, NS, CE, & ex harum <lb/>&longs;ectionum extremis exeant alia <lb/>plana &longs;ecantia parallela plano AG; <lb/>ab&longs;cinduntur ex pri&longs;mate dato pa<lb/>rallelepipeda LF, OK &c. quæ à plano AG dividuntur in <lb/>partes GL, GM æquales ac &longs;imiliter po&longs;itas; item DO, DB, &c. </s><lb/><s>Igitur &longs;ingula in eodem plano AG habent gravitatis centrum, <lb/>ac proinde tota moles ex iis parallelepipedis compo&longs;ita in eo<lb/>dem plano habet centrum gravitatis. </s><s>Quoniam verò, &longs;i adhuc <lb/>plana &longs;ecantia frequentiora &longs;int, plura fiunt parallelepipeda, <lb/>quorum omnium moles compo&longs;ita adhuc minus differt à mole <lb/>totius pri&longs;matis dati, ita ut toties multiplicari po&longs;&longs;it bi&longs;ectio, <lb/>ut demum relinquatur differentia minor quacunque minimâ <lb/>mole excogitabili; hinc fit molem compo&longs;itam ex parallelepi<lb/>pedis illis infinitis (&longs;ic loqui liceat, quia non e&longs;t certus eorum <lb/>numerus explicabilis) habere centrum gravitatis in plano AG;

<pb n="29"/>ac proinde etiam pri&longs;ma trigonum ex iis conflatum parallelepi<lb/>pedis habere in eodem plano AG centrum &longs;uæ gravitatis, <lb/>quandoquidem non differt ab illis ni&longs;i differentiâ minore qua<lb/>cumque minimâ excogitabili. </s><s>Sunt igitur partium AGH, <lb/>AGI momenta æqualia; quia &longs;i inæqualia e&longs;&longs;ent haberent <lb/>differentiam, qua po&longs;&longs;et dari minor (neque enim e&longs;&longs;et indivi<lb/>dua) hæc autem differentia &longs;i e&longs;&longs;et, alia non e&longs;&longs;et, quàm quæ <lb/>intercedit inter pri&longs;ma datum, & omnia parallelepipeda, cu<lb/>jus differentiæ inæquales partes e&longs;&longs;ent in AGH, & AGI: <lb/>igitur differentia partium AGH, AGI e&longs;&longs;et minor diffe<lb/>rentiâ pri&longs;matis, & omnium parallelepipedorum; nam e&longs;&longs;e non <lb/>pote&longs;tmajor, vel illi æqualis: &longs;ed jam ex hypothe&longs;i differentia <lb/>inter molem compo&longs;itam ex omnibus parallelepipedis, & pri&longs;<lb/>ma, e&longs;t minor quacumque minimâ datâ, ergo &longs;i e&longs;&longs;ent inæ<lb/>qualia momenta partium AGH, AGI haberent differen<lb/>tiam minorem, & non minorem eâdem differentiâ inter pri&longs;<lb/>ma & omnia parallelepipeda. </s><s>Non &longs;unt igitur inæqualia. </s><s>Res <lb/>autem forta&longs;sè &longs;ic breviùs explicabitur; &longs;i partes AGH, AGI <lb/>non &longs;unt æquales, &longs;it AGH minor quàm AGI, differentiâ Y. </s><lb/><s>Tot autem fiant bi&longs;ectiones, ut parallelepipeda relinquant <lb/>differentiam minorem quàm Y. </s><s>Quia ergo parallelepipeda <lb/>in AGI habent differentiam minorem quàm Y, à parte pri&longs;<lb/>matis AGI, illa &longs;unt majora quàm pars pri&longs;matis AGH, <lb/>quæ deficit à parte AGI differentiâ Y. </s><s>Atqui parallelepepida <lb/>in AGH &longs;unt æqualia parallelepipedis in AGI, ergo etiam <lb/>parallelepipeda in AGH majora &longs;unt, quàm tota pars AGH, <lb/>quod e&longs;t manife&longs;tè fal&longs;um. </s><s>Non e&longs;t igitur altera pars major, <lb/>altera minor. </s><s>Porrò ex continua bi&longs;ectione laterum AC, <lb/>& CN &c. relinqui &longs;emper minorem differentiam, hoc e&longs;t &longs;e<lb/>mi&longs;&longs;em præcedentis differentiæ, con&longs;tat, quia &longs;i AC &longs;ecetur <lb/>in P, & ducantur plana parallela planis AG, & HV, dividi<lb/>tur CT bi&longs;ariam in Q, & e&longs;t TP parallelepipedum ablatum <lb/>duplum pri&longs;matis trigoni CPQ, cui æquale e&longs;t pri&longs;ma APX; <lb/>adeóque duobus hi&longs;ce pri&longs;matis æquale e&longs;t ablatum parallele<lb/>pipedum TP, quod e&longs;t &longs;emi&longs;&longs;is differentiæ ATC, quæ priùs <lb/>relinquebatur: & eadem e&longs;t de cæteris ratio. </s><s>Quare &longs;i ex datâ <lb/>quantitate auferatur &longs;emi&longs;&longs;is, & iterum &longs;emi&longs;&longs;is re&longs;idui, & &longs;ic <lb/>in infinitum, nece&longs;&longs;e e&longs;t aliquando eò devenire, ut re&longs;idua

<pb xlink:href="017/01/045.jpg" n="29"/>ac proinde etiam pri&longs;ma trigonum ex iis conflatum parallelepi<lb/>pedis habere in eodem plano AG centrum &longs;uæ gravitatis, <lb/>quandoquidem non differt ab illis ni&longs;i differentiâ minore qua<lb/>cumque minimâ excogitabili. </s><s>Sunt igitur partium AGH, <lb/>AGI momenta æqualia; quia &longs;i inæqualia e&longs;&longs;ent haberent <lb/>differentiam, qua po&longs;&longs;et dari minor (neque enim e&longs;&longs;et indivi<lb/>dua) hæc autem differentia &longs;i e&longs;&longs;et, alia non e&longs;&longs;et, quàm quæ <lb/>intercedit inter pri&longs;ma datum, & omnia parallelepipeda, cu<lb/>jus differentiæ inæquales partes e&longs;&longs;ent in AGH, & AGI: <lb/>igitur differentia partium AGH, AGI e&longs;&longs;et minor diffe<lb/>rentiâ pri&longs;matis, & omnium parallelepipedorum; nam e&longs;&longs;e non <lb/>pote&longs;tmajor, vel illi æqualis: &longs;ed jam ex hypothe&longs;i differentia <lb/>inter molem compo&longs;itam ex omnibus parallelepipedis, & pri&longs;<lb/>ma, e&longs;t minor quacumque minimâ datâ, ergo &longs;i e&longs;&longs;ent inæ<lb/>qualia momenta partium AGH, AGI haberent differen<lb/>tiam minorem, & non minorem eâdem differentiâ inter pri&longs;<lb/>ma & omnia parallelepipeda. </s><s>Non &longs;unt igitur inæqualia. </s><s>Res <lb/>autem forta&longs;sè &longs;ic breviùs explicabitur; &longs;i partes AGH, AGI <lb/>non &longs;unt æquales, &longs;it AGH minor quàm AGI, differentiâ Y. </s><lb/><s>Tot autem fiant bi&longs;ectiones, ut parallelepipeda relinquant <lb/>differentiam minorem quàm Y. </s><s>Quia ergo parallelepipeda <lb/>in AGI habent differentiam minorem quàm Y, à parte pri&longs;<lb/>matis AGI, illa &longs;unt majora quàm pars pri&longs;matis AGH, <lb/>quæ deficit à parte AGI differentiâ Y. </s><s>Atqui parallelepepida <lb/>in AGH &longs;unt æqualia parallelepipedis in AGI, ergo etiam <lb/>parallelepipeda in AGH majora &longs;unt, quàm tota pars AGH, <lb/>quod e&longs;t manife&longs;tè fal&longs;um. </s><s>Non e&longs;t igitur altera pars major, <lb/>altera minor. </s><s>Porrò ex continua bi&longs;ectione laterum AC, <lb/>& CN &c. relinqui &longs;emper minorem differentiam, hoc e&longs;t &longs;e<lb/>mi&longs;&longs;em præcedentis differentiæ, con&longs;tat, quia &longs;i AC &longs;ecetur <lb/>in P, & ducantur plana parallela planis AG, & HV, dividi<lb/>tur CT bi&longs;ariam in Q, & e&longs;t TP parallelepipedum ablatum <lb/>duplum pri&longs;matis trigoni CPQ, cui æquale e&longs;t pri&longs;ma APX; <lb/>adeóque duobus hi&longs;ce pri&longs;matis æquale e&longs;t ablatum parallele<lb/>pipedum TP, quod e&longs;t &longs;emi&longs;&longs;is differentiæ ATC, quæ priùs <lb/>relinquebatur: & eadem e&longs;t de cæteris ratio. </s><s>Quare &longs;i ex datâ <lb/>quantitate auferatur &longs;emi&longs;&longs;is, & iterum &longs;emi&longs;&longs;is re&longs;idui, & &longs;ic <lb/>in infinitum, nece&longs;&longs;e e&longs;t aliquando eò devenire, ut re&longs;idua

<pb n="30"/>quantitas minor &longs;it quacunque datâ quantitate, ut colligitur <lb/>ex prop. 1. lib. 10. Eucl. </s><s>Ideo fieri non pote&longs;t, ut pri&longs;mate di<lb/>vi&longs;o à plano AG, altera pars excedat momenta alterius quan<lb/>titate Y, quia tot po&longs;&longs;unt ab&longs;cindi purallelepipeda, ut relin<lb/>quatur differentia illorum à pri&longs;mate minor, quàm &longs;it Y: pla<lb/>num autem AG æqualiter dividit momenta parallelepipedo<lb/>rum, igitur cum tota re&longs;idua differentia minor &longs;it quam Y, <lb/>e&longs;&longs;e omnino non pote&longs;t, ut altera pars habeat exce&longs;&longs;um quan<lb/>titati Y re&longs;pondentem &longs;i enim quantitates illæ differrent, po&longs;<lb/>&longs;et dari quantitas minor illarum differentiâ; &longs;ed non pote&longs;t hu<lb/>ju&longs;modi minor quantitas dari, nam quælibet data e&longs;t major, <lb/>igitur non differunt, &longs;ed &longs;unt æquales. </s>

<pb xlink:href="017/01/046.jpg" n="30"/>quantitas minor &longs;it quacunque datâ quantitate, ut colligitur <lb/>ex prop. 1. lib. 10. Eucl. </s><s>Ideo fieri non pote&longs;t, ut pri&longs;mate di<lb/>vi&longs;o à plano AG, altera pars excedat momenta alterius quan<lb/>titate Y, quia tot po&longs;&longs;unt ab&longs;cindi purallelepipeda, ut relin<lb/>quatur differentia illorum à pri&longs;mate minor, quàm &longs;it Y: pla<lb/>num autem AG æqualiter dividit momenta parallelepipedo<lb/>rum, igitur cum tota re&longs;idua differentia minor &longs;it quam Y, <lb/>e&longs;&longs;e omnino non pote&longs;t, ut altera pars habeat exce&longs;&longs;um quan<lb/>titati Y re&longs;pondentem &longs;i enim quantitates illæ differrent, po&longs;<lb/>&longs;et dari quantitas minor illarum differentiâ; &longs;ed non pote&longs;t hu<lb/>ju&longs;modi minor quantitas dari, nam quælibet data e&longs;t major, <lb/>igitur non differunt, &longs;ed &longs;unt æquales. </s>

<s>His ita con&longs;titutis facilè definitur punctum centro gravitatis <lb/>imminens in ba&longs;i pri&longs;matis: quia enim o&longs;ten&longs;um e&longs;t planum <lb/>ab angulo per medium latus oppo&longs;itum ductum tran&longs;ire per <lb/>centrum gravitatis, & dividere in momenta æqualia totum <lb/>pri&longs;ma, centrum gravitatis erit non &longs;olùm in plano AG, &longs;ed <lb/>etiam in plano IN propter eandem rationem. </s><s>Punctum igi<lb/>

<figure/><lb/>tur D, in quo occurrunt &longs;ibi communes <lb/>&longs;ectiones planorum &longs;ecantium, & ba&longs;is, e&longs;t <lb/>punctum, quod quæritur, imminens centro <lb/>gravitatis. </s><s>Punctum D autem &longs;ecare rectam <lb/>NI ita, ut ND ad DI &longs;it ut 1 ad 2, &longs;ic <lb/>o&longs;tenditur. </s><s>Ducatur recta NG, quæ per 2. lib. 6. e&longs;t paral<lb/>lela ip&longs;i AI; ergo ut HG ad HI, ita NG ad AI per 4. lib. 6. <lb/>ergo NG ad AI e&longs;t ut 1 ad 2: ergo triangula NGA, AGI <lb/>&longs;unt ut 1 ad 2, per 1. lib. 6. </s><s>Cum autem ut ND ad DI, <lb/>ita NDA ad DIA, & NDG ad DIG per 1. 6. erit <lb/>etiam, ex 12. lib. 5. ut ND ad DI, ita NGA ad AGI, <lb/>hoc e&longs;t 1 ad 2. </s><s>Eadem ratione o&longs;tenditur GD ad DA e&longs;&longs;e, <lb/>ut 1 ad 2. </s><s>Vel etiam breviùs: Quia enim NG, AI &longs;unt pa<lb/>rallelæ, triangula NDG, ADI &longs;unt &longs;imilia propter angulo<lb/>rum æqualitatem; ergo ut NG ad AI, hoc e&longs;t ut 1 ad 2, <lb/>ita GD ad DA, & ND ad DI. </s><s>Quare &longs;atis erit latus unum <lb/>trianguli bifariam &longs;ecare, & ab oppo&longs;ito angulo rectam duco<lb/>re; cujus tertia pars ver&longs;us ba&longs;im divi&longs;am dabit centrum gravi<lb/>tatis trianguli. </s>

<figure id="id.017.01.046.1.jpg" xlink:href="017/01/046/1.jpg"/><lb/>tur D, in quo occurrunt &longs;ibi communes <lb/>&longs;ectiones planorum &longs;ecantium, & ba&longs;is, e&longs;t <lb/>punctum, quod quæritur, imminens centro <lb/>gravitatis. </s><s>Punctum D autem &longs;ecare rectam <lb/>NI ita, ut ND ad DI &longs;it ut 1 ad 2, &longs;ic <lb/>o&longs;tenditur. </s><s>Ducatur recta NG, quæ per 2. lib. 6. e&longs;t paral<lb/>lela ip&longs;i AI; ergo ut HG ad HI, ita NG ad AI per 4. lib. 6. <lb/>ergo NG ad AI e&longs;t ut 1 ad 2: ergo triangula NGA, AGI <lb/>&longs;unt ut 1 ad 2, per 1. lib. 6. </s><s>Cum autem ut ND ad DI, <lb/>ita NDA ad DIA, & NDG ad DIG per 1. 6. erit <lb/>etiam, ex 12. lib. 5. ut ND ad DI, ita NGA ad AGI, <lb/>hoc e&longs;t 1 ad 2. </s><s>Eadem ratione o&longs;tenditur GD ad DA e&longs;&longs;e, <lb/>ut 1 ad 2. </s><s>Vel etiam breviùs: Quia enim NG, AI &longs;unt pa<lb/>rallelæ, triangula NDG, ADI &longs;unt &longs;imilia propter angulo<lb/>rum æqualitatem; ergo ut NG ad AI, hoc e&longs;t ut 1 ad 2, <lb/>ita GD ad DA, & ND ad DI. </s><s>Quare &longs;atis erit latus unum <lb/>trianguli bifariam &longs;ecare, & ab oppo&longs;ito angulo rectam duco<lb/>re; cujus tertia pars ver&longs;us ba&longs;im divi&longs;am dabit centrum gravi<lb/>tatis trianguli. </s>

<s>Jam verò &longs;i ba&longs;is pri&longs;matis quadrangula fuerit parallelogram-

<pb n="31"/>ma, ductis diametris apparebit quæ&longs;itum punctum, per quod <lb/>tran&longs;eunt omnia plana dividentia æqualiter corporis dati mo<lb/>menta, cum &longs;int partes utrinque æquales, & &longs;imiliter po&longs;itæ. </s><lb/><s>Et ob eandem rationem &longs;i ba&longs;is pri&longs;matis fuerit aliqua ex figu<lb/>ris ordinatis, &longs;eu æquilateris; centrum figuræ e&longs;t punctum im<lb/>minens centro gravitatis; planum &longs;i <expan abbr="quid&etilde;">quidem</expan> per illud tran&longs;iens, & <lb/>per <expan abbr="un&utilde;">unum</expan> angulorum, dividit <expan abbr="tot&utilde;">totum</expan> pri&longs;ma in partes æquales &longs;imi<lb/>literque po&longs;itas; atque adeò momenta hinc, & hinc &longs;unt æqualia. </s>

<pb xlink:href="017/01/047.jpg" n="31"/>ma, ductis diametris apparebit quæ&longs;itum punctum, per quod <lb/>tran&longs;eunt omnia plana dividentia æqualiter corporis dati mo<lb/>menta, cum &longs;int partes utrinque æquales, & &longs;imiliter po&longs;itæ. </s><lb/><s>Et ob eandem rationem &longs;i ba&longs;is pri&longs;matis fuerit aliqua ex figu<lb/>ris ordinatis, &longs;eu æquilateris; centrum figuræ e&longs;t punctum im<lb/>minens centro gravitatis; planum &longs;i <expan abbr="quid&etilde;">quidem</expan> per illud tran&longs;iens, & <lb/>per <expan abbr="un&utilde;">unum</expan> angulorum, dividit <expan abbr="tot&utilde;">totum</expan> pri&longs;ma in partes æquales &longs;imi<lb/>literque po&longs;itas; atque adeò momenta hinc, & hinc &longs;unt æqualia. </s>

<s>At &longs;i ba&longs;is trapezia fuerit, duc utramque <lb/>

<figure/><lb/>diametrum EC, & BD: tum in ba&longs;i trigo<lb/>nâ BCD pri&longs;matis partialis inveniatur <lb/>punctum centro gravitatis re&longs;pondens (pun<lb/>ctum hoc deinceps, brevitatis gratiâ, dice<lb/>tur centrum gravitatis, quamvis per abu&longs;ionem) & &longs;it H; & in <lb/>oppo&longs;ita ba&longs;i trigona reliqui pri&longs;matis BDE pariter invenia<lb/>tur punctum F; & per utrumque punctum tran&longs;eat planum <lb/>FH; nam in hoc eodem plano e&longs;t centrum gravitatis totius <lb/>pri&longs;matis trapezij, quod dividitur in momenta æqualia: hoc &longs;i<lb/>quidem planum tran&longs;iens per H gravitatis momenta æqualia <lb/>habet hinc, & hinc in pri&longs;mate trigono BDC; &longs;imiliter cum <lb/>tran&longs;eat per F, habet hinc, & hinc momenta æqualia gravitatis <lb/>pri&longs;matis trigoni BED: &longs;i igitur æqualia æqualibus jungantur, <lb/>planum idem æqualiter partitur momenta gravitatis pri&longs;matis <lb/>trapezij EDCB, & in eo e&longs;t centrum gravitatis illius. </s><s>Eadem <lb/>ratione in ba&longs;i trigona EBC inveniatur punctum G, & in ba&longs;i <lb/>EDC punctum S, per quæ &longs;i agatur planum GS, in eo pariter <lb/>erit <expan abbr="centr&utilde;">centrum</expan> gravitatis totius pri&longs;matis trapezij. </s>

<figure id="id.017.01.047.1.jpg" xlink:href="017/01/047/1.jpg"/><lb/>diametrum EC, & BD: tum in ba&longs;i trigo<lb/>nâ BCD pri&longs;matis partialis inveniatur <lb/>punctum centro gravitatis re&longs;pondens (pun<lb/>ctum hoc deinceps, brevitatis gratiâ, dice<lb/>tur centrum gravitatis, quamvis per abu&longs;ionem) & &longs;it H; & in <lb/>oppo&longs;ita ba&longs;i trigona reliqui pri&longs;matis BDE pariter invenia<lb/>tur punctum F; & per utrumque punctum tran&longs;eat planum <lb/>FH; nam in hoc eodem plano e&longs;t centrum gravitatis totius <lb/>pri&longs;matis trapezij, quod dividitur in momenta æqualia: hoc &longs;i<lb/>quidem planum tran&longs;iens per H gravitatis momenta æqualia <lb/>habet hinc, & hinc in pri&longs;mate trigono BDC; &longs;imiliter cum <lb/>tran&longs;eat per F, habet hinc, & hinc momenta æqualia gravitatis <lb/>pri&longs;matis trigoni BED: &longs;i igitur æqualia æqualibus jungantur, <lb/>planum idem æqualiter partitur momenta gravitatis pri&longs;matis <lb/>trapezij EDCB, & in eo e&longs;t centrum gravitatis illius. </s><s>Eadem <lb/>ratione in ba&longs;i trigona EBC inveniatur punctum G, & in ba&longs;i <lb/>EDC punctum S, per quæ &longs;i agatur planum GS, in eo pariter <lb/>erit <expan abbr="centr&utilde;">centrum</expan> gravitatis totius pri&longs;matis trapezij. </s>

<s>E&longs;t igitur centrum gravitatis in communi <lb/>

<figure/><lb/>&longs;ectione planorum FH, & GS; ac proinde <lb/>punctum I illud e&longs;t, quod quæritur. </s><s>Aliter <lb/>etiam, & facillimè in ba&longs;i trapezia ABCD <lb/>invenitur centrum gravitatis: ductis enim <lb/>diametris AC, BD, altera diameter ex. gr. <lb/>AC bifariam &longs;ecetur in E, ducanturque rectæ <lb/>DE, BE; trianguli ADC centrum gravi<lb/>tatis e&longs;t in recta DE, & quidem in F, ita ut EF <lb/>&longs;it tertia pars totius ED, ut con&longs;tat ex paulò <lb/>ante demon&longs;tratis. </s><s>Ducatur igitur FG pa-

<figure id="id.017.01.047.2.jpg" xlink:href="017/01/047/2.jpg"/><lb/>&longs;ectione planorum FH, & GS; ac proinde <lb/>punctum I illud e&longs;t, quod quæritur. </s><s>Aliter <lb/>etiam, & facillimè in ba&longs;i trapezia ABCD <lb/>invenitur centrum gravitatis: ductis enim <lb/>diametris AC, BD, altera diameter ex. gr. <lb/>AC bifariam &longs;ecetur in E, ducanturque rectæ <lb/>DE, BE; trianguli ADC centrum gravi<lb/>tatis e&longs;t in recta DE, & quidem in F, ita ut EF <lb/>&longs;it tertia pars totius ED, ut con&longs;tat ex paulò <lb/>ante demon&longs;tratis. </s><s>Ducatur igitur FG pa-

<pb n="32"/>rallela alteri diametro BD, & erit &longs;imiliter G centrum gravita<lb/>tis trianguli ABC, quia per 2. lib. 6. ut EF ad FD, ita EG <lb/>ad GB; Quia ergo diameter AC &longs;ecatur in H, &longs;umatur FO <lb/>æqualis ip&longs;i GH, & e&longs;t O centrum gravitatis trapezij, e&longs;t enim <lb/>triangulum ABC ad triangulum ADC, ut FO ad OG, hoc <lb/>e&longs;t ut HG ad HF. </s><s>E&longs;t autem HG ad HF ut BI ad ID pro<lb/>pter paralleli&longs;mum linearum GF, BD. </s><s>Porrò con&longs;tat triangu<lb/>lum ABC ad triangulum ADC e&longs;&longs;e ut BI ad ID, nam trian<lb/>gula ABI, ADI &longs;unt ut ba&longs;es BI, DI, item BCI, DCI &longs;unt <lb/>ut eædem ba&longs;es BI, DI per 1. lib. 6; igitur, & totum triangu<lb/>lum ABC ad totum ADC e&longs;t ut BI ad DI: igitur, & trian<lb/>gulum ABC ad triangulum ADC e&longs;t ut FO ad OG. </s>

<pb xlink:href="017/01/048.jpg" n="32"/>rallela alteri diametro BD, & erit &longs;imiliter G centrum gravita<lb/>tis trianguli ABC, quia per 2. lib. 6. ut EF ad FD, ita EG <lb/>ad GB; Quia ergo diameter AC &longs;ecatur in H, &longs;umatur FO <lb/>æqualis ip&longs;i GH, & e&longs;t O centrum gravitatis trapezij, e&longs;t enim <lb/>triangulum ABC ad triangulum ADC, ut FO ad OG, hoc <lb/>e&longs;t ut HG ad HF. </s><s>E&longs;t autem HG ad HF ut BI ad ID pro<lb/>pter paralleli&longs;mum linearum GF, BD. </s><s>Porrò con&longs;tat triangu<lb/>lum ABC ad triangulum ADC e&longs;&longs;e ut BI ad ID, nam trian<lb/>gula ABI, ADI &longs;unt ut ba&longs;es BI, DI, item BCI, DCI &longs;unt <lb/>ut eædem ba&longs;es BI, DI per 1. lib. 6; igitur, & totum triangu<lb/>lum ABC ad totum ADC e&longs;t ut BI ad DI: igitur, & trian<lb/>gulum ABC ad triangulum ADC e&longs;t ut FO ad OG. </s>

<s>Hinc facilis patet via ad inve&longs;ti<lb/>gandum idem punctum in ba&longs;i pri&longs;<lb/>matis pentagoni BDEAC. </s><s>Pri<lb/>mùm enim ducto plano per BE, in<lb/>veniatur in ba&longs;i trigonâ BDE <lb/>punctum R, & in ba&longs;i BEAC qua<lb/>drangulâ punctum P; & ducto plano <lb/>per RP, in eo erit centrum gravi<lb/>tatis pri&longs;matis pentagoni, cum in eo<lb/>dem &longs;int centra gravitatis partium. </s><lb/><s>Deinde ducto per D & A plano, inveniatur in ba&longs;i trigona <lb/>DEA punctum L centrum gravitatis, & in ba&longs;i quadrangu<lb/>lâ ACBD punctum M centrum gravitatis: in plano pariter <lb/>ducto per ML e&longs;t centrum gravitatis totius pri&longs;matis pentago<lb/>ni, quod proinde e&longs;t in communi planorum per PR, & LM <lb/>ductorum &longs;ectione; atque adeò punctum, quod quæritur, e&longs;t O. </s><lb/><s>Eadem e&longs;t methodus in pri&longs;mate hexagono; ducto enim plano <lb/>dividente in duo pri&longs;mata, quorum alterum e&longs;t trigonum, al<lb/>terum pentagonum, inveniatur utriu&longs;que centrum gravitatis, <lb/>& per inventa puncta agatur planum. </s><s>Deinde iterum alio pla<lb/>no &longs;ecetur in duo pri&longs;mata, quorum alterum pariter &longs;it trigo<lb/>num, alterum pentagonum, & per inventa &longs;ingularia gravi<lb/>tatum centra agatur planum: duo &longs;iquidem plana ducta per <lb/>centra gravitatis partium, tran&longs;eunt pariter per centrum gra<lb/>vitatis totius, quod e&longs;t in communi eorum &longs;ectione. </s><s>Eademque <lb/>de reliquis pri&longs;matis e&longs;t ratio. </s>

<s>Sed hæc indica&longs;&longs;e &longs;ufficiat, quæ operi Mechanico &longs;atis e&longs;&longs;e <lb/>po&longs;&longs;unt in omnibus ferè pri&longs;matis: Si enim ba&longs;is non fuerit <lb/>planè rectilinea, in&longs;cripto polygono rectilineo, quod mini<lb/>mùm differat à plano ba&longs;is, quæres ejus centrum gravitatis, <lb/>methodo jam tradita; illoque u&longs;urpato tanquam vero dati pri&longs;<lb/>matis centro quæ&longs;ito, minimùm aberrabis; aliquando tamen <lb/>aberrabis, aliquando continget, ut inventum cum quæ&longs;ito <lb/>conveniat. </s><s>Quod &longs;i accuratiori inve&longs;tigatione opus fuerit: <lb/>quemadmodum in cæteris corporibus, quæ continuum ductum <lb/>non habent, &longs;ed inæquali cra&longs;&longs;itudine cre&longs;cunt, aut decre&longs;<lb/>cunt, ut in obeli&longs;cis, aut pyramidibus truncatis, reliqui&longs;què <lb/>planè inordinatis molibus; tunc ad geometricam Centrobary<lb/>ces methodum confugiendum e&longs;t; quam hic ego non per&longs;e<lb/>quor. </s><s>Praxes igitur aliquæ proponendæ &longs;unt, quibus centrum <lb/>gravitatis phy&longs;icè per&longs;pectum habere po&longs;&longs;imus in corporibus, <lb/>quorum frequentior, vulgari&longs;que u&longs;us e&longs;&longs;e pote&longs;t. </s>

<s>Prima praxis &longs;it ad inveniendum gra<lb/>

<figure/><lb/>vitatis centrum in cingulis, quæ laminis <lb/>quoque communis e&longs;&longs;e pote&longs;t. </s><s>Sit datum <lb/>cingulum AH, quod primùm &longs;u&longs;penda<lb/>tur ex H, & inde pendens perpendicu<lb/>lum &longs;ecet oppo&longs;itum latus IA in C; note<lb/>tur igitur punctum C. </s><s>Deinde iterum <lb/>&longs;u&longs;pendatur ex R, & perpendiculum ca<lb/>dat in punctum F, quod notetur. </s><s>His cognitis ducatur filum <lb/>ex R in F, ibique intentum alligetur; aliud filum &longs;imiliter <lb/>ex H in C ducatur, & &longs;ecans in S filum RF, dabit punctum S <lb/>quæ&longs;itum centrum gravitatis: ex quo &longs;i &longs;u&longs;penderetur datum <lb/>cingulum, maneret horizonti parallelum. </s><s>Quod &longs;i e&longs;&longs;et corpus <lb/>talis figuræ, ut &longs;patium non clauderet, &longs;ed haberet angulum <lb/>cavum, aut e&longs;&longs;et fru&longs;tum annulare, eadem e&longs;t methodus factâ <lb/>&longs;u&longs;pen&longs;ione illius ex duobus punctis, ex quibus perpendiculum <lb/>cadere po&longs;&longs;it intrà corporis &longs;uperficiem; in qua &longs;i notentur <lb/>puncta, per quæ tran&longs;it, & ducantur fila, ut priùs, corum com<lb/>munis &longs;ectio dabit quæ&longs;itum centrum gravitatis. </s><s>Hinc &longs;i vel la<lb/>mina e&longs;&longs;et perforanda, ut axi infigeretur, vel cingulum e&longs;&longs;et <lb/>axi imponendum, in utrâque &longs;uperficie oppo&longs;ita quærere opor<lb/>teret punctum S, ut axis per centrum gravitatis tran&longs;iret, eique

<figure id="id.017.01.049.1.jpg" xlink:href="017/01/049/1.jpg"/><lb/>vitatis centrum in cingulis, quæ laminis <lb/>quoque communis e&longs;&longs;e pote&longs;t. </s><s>Sit datum <lb/>cingulum AH, quod primùm &longs;u&longs;penda<lb/>tur ex H, & inde pendens perpendicu<lb/>lum &longs;ecet oppo&longs;itum latus IA in C; note<lb/>tur igitur punctum C. </s><s>Deinde iterum <lb/>&longs;u&longs;pendatur ex R, & perpendiculum ca<lb/>dat in punctum F, quod notetur. </s><s>His cognitis ducatur filum <lb/>ex R in F, ibique intentum alligetur; aliud filum &longs;imiliter <lb/>ex H in C ducatur, & &longs;ecans in S filum RF, dabit punctum S <lb/>quæ&longs;itum centrum gravitatis: ex quo &longs;i &longs;u&longs;penderetur datum <lb/>cingulum, maneret horizonti parallelum. </s><s>Quod &longs;i e&longs;&longs;et corpus <lb/>talis figuræ, ut &longs;patium non clauderet, &longs;ed haberet angulum <lb/>cavum, aut e&longs;&longs;et fru&longs;tum annulare, eadem e&longs;t methodus factâ <lb/>&longs;u&longs;pen&longs;ione illius ex duobus punctis, ex quibus perpendiculum <lb/>cadere po&longs;&longs;it intrà corporis &longs;uperficiem; in qua &longs;i notentur <lb/>puncta, per quæ tran&longs;it, & ducantur fila, ut priùs, corum com<lb/>munis &longs;ectio dabit quæ&longs;itum centrum gravitatis. </s><s>Hinc &longs;i vel la<lb/>mina e&longs;&longs;et perforanda, ut axi infigeretur, vel cingulum e&longs;&longs;et <lb/>axi imponendum, in utrâque &longs;uperficie oppo&longs;ita quærere opor<lb/>teret punctum S, ut axis per centrum gravitatis tran&longs;iret, eique

<pb n="34"/>uterque polus re&longs;ponderet: in cingulis autem præterea haben<lb/>da e&longs;&longs;et ratio tran&longs;ver&longs;ariorum, per quæ axis infigendus e&longs;&longs;et, <lb/>ea enim po&longs;&longs;unt centrum gravitatis compo&longs;itæ in alio puncto <lb/>con&longs;tituere. </s>

<pb xlink:href="017/01/050.jpg" n="34"/>uterque polus re&longs;ponderet: in cingulis autem præterea haben<lb/>da e&longs;&longs;et ratio tran&longs;ver&longs;ariorum, per quæ axis infigendus e&longs;&longs;et, <lb/>ea enim po&longs;&longs;unt centrum gravitatis compo&longs;itæ in alio puncto <lb/>con&longs;tituere. </s>

<s>Secunda praxis laminis poti&longs;&longs;imùm accommodata, in quibus <lb/>punctum medium &longs;atis accuratè inquiritur, ut &longs;i lamina metal<lb/>lica e&longs;&longs;et in calicem excavanda, hæc e&longs;&longs;e pote&longs;t. </s><s>Impone lami<lb/>nam acutæ cu&longs;pidi cultri, aut &longs;tyli, eamque ultrò citróque <lb/>tanti&longs;per move, dum con&longs;i&longs;tat citrà periculum cadendi: <lb/>punctum enim, quod à cultri aut &longs;tyli cu&longs;pide notatur, cen<lb/>trum e&longs;t quæ&longs;itum. </s>

Line 449

<s>Quarta praxis non multùm di&longs;tat à &longs;uperiore: &longs;i nimirum <lb/>oblatum corpus impo&longs;ueris plano alicui horizontali, quod ta<lb/>men à pavimento ab&longs;it mediocri aliquo intervallo, habeat au<lb/>tem extremum marginem exactè rectum: extra &longs;uppo&longs;iti pla<lb/>ni marginem illud paulatim promove, donec eò venerit, ut &longs;i <lb/>vel minimum ulteriùs promoveretur, &longs;ponte caderet; ibíque <lb/>&longs;ecundùm rectitudinem marginis plani duc &longs;tylo lineam in cor<lb/>pore impo&longs;ito. </s><s>Deinde &longs;uperficie eâdem planum tangente, &longs;i <lb/>corpus, præter longitudinem, non modicam præterea habeat <lb/>latitudinem, convertatur aliquantulum, & &longs;imili methodo in<lb/>venietur linea alia &longs;ecans priorem in puncto quæ&longs;ito, quod &longs;ci<lb/>licet re&longs;pondet centro gravitatis intra corporis &longs;oliditatem de<lb/>lite&longs;centi. </s>

<s>Hæc &longs;unt quæ Mechanices in&longs;tituto &longs;ufficere po&longs;&longs;int ad cen<lb/>trum gravitatis inveniendum; in molibus enim majoribus, quæ <lb/>plerumque vix differunt à pri&longs;matis, non indigemus commu-

<pb n="35"/>niter Geometricâ &longs;ubtilitate. </s><s>Illud re&longs;tat, ut earum, quas at<lb/>tuli praxes, ratio, & cau&longs;æ explicentur, ex quibus clarion ha<lb/>beatur notitia eorum, quæ ad centrum gravitatis pertinent. <lb/><gap desc="hr tag"/></s>

<pb xlink:href="017/01/051.jpg" n="35"/>niter Geometricâ &longs;ubtilitate. </s><s>Illud re&longs;tat, ut earum, quas at<lb/>tuli praxes, ratio, & cau&longs;æ explicentur, ex quibus clarion ha<lb/>beatur notitia eorum, quæ ad centrum gravitatis pertinent. <lb/><gap desc="hr tag"/></s>

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

<s><emph type="center"/><emph type="italics"/>Affertur ratio prædictarum praxeon.<emph.end type="italics"/><emph.end type="center"/></s>

<s>UT palam fiat praxibus capite &longs;uperiore allatis inveniri <lb/>punctum re&longs;pondens centro gravitatis, quod inquiritur, <lb/>indicandi &longs;unt fontes, ex quibus illæ deducuntur. </s><s>Earum ita<lb/>que ratio petenda e&longs;t ex gravium naturâ, quæ extra locum &longs;ibi <lb/>debitum con&longs;tituta, in medio videlicet leviore, conantur de<lb/>or&longs;um pro viribus, ni&longs;i impediantur: quod &longs;i interpellentur <lb/>quidem, non tamen pror&longs;us de&longs;cen&longs;u prohibeantur, de&longs;cen<lb/>dunt, prout fert ob&longs;tantium impedimentorum conditio. </s><s>Sic <lb/>lapis &longs;phæricus in montis clivo po&longs;itus cùm non valeat rectâ; <lb/>&longs;icut in aëre libero, deor&longs;um ferri, per planum illud inclina<lb/>tum de&longs;cendit: Sic plumbum, quod filo adnectitur laqueari, à <lb/>perpendiculo remotum de&longs;cendit circulariter. </s><s>Porrò quæ de <lb/>toto ip&longs;o corpore vera e&longs;&longs;e intelligimus, ejus quoque partibus <lb/>&longs;ingulis conveniunt; cùm enim &longs;ingulæ &longs;uam habeant gravita<lb/>tem, ni&longs;i quid ob&longs;tet, de&longs;cendunt. </s><s>Jam verò &longs;i contingat ita <lb/>corpus grave oppo&longs;ito extrin&longs;ecùs obice impediri, ut cunctæ <lb/>&longs;imul partes, qua&longs;i moles unà de&longs;cendere nequeant; &longs;ublato <lb/>partium nexu de&longs;cendunt, quæcunque carent impedimento: <lb/>ut &longs;i ceream candelam, aut glaciem, quam manu &longs;u&longs;tines, igni <lb/>admoveas; haud dubium, quin partes extremæ igni proximæ <lb/>lique&longs;centes, &longs;olutâ unione cum cæteris, &longs;uis nutibus deor&longs;um <lb/>latæ liberè de&longs;cendant. </s><s>At &longs;i partes omnes colligatæ invicem <lb/>permaneant, eandemque figuram &longs;ervent; corpore illo &longs;u&longs;pen<lb/>&longs;o aut &longs;u&longs;tentato, fieri non pote&longs;t, ut partes aliquæ de&longs;cendant, <lb/>quin aliæ, ouæ è regione &longs;unt trans &longs;u&longs;pen&longs;ionis, aut &longs;u&longs;tenta<lb/>tionis punctum, a&longs;cendant; id autem harum gravitati re<lb/>pugnat: non igitur a&longs;cendere po&longs;&longs;unt, ni&longs;i de&longs;cendentes op<lb/>po&longs;itæ viribus ac momentis præ&longs;tent ita, ut harum gravitati

<pb n="36"/>vim inferre valeant. </s><s>Quare &longs;i fiat corporis &longs;u&longs;pen&longs;i, aut &longs;u&longs;ten<lb/>tati con&longs;i&longs;tentia, argumentum e&longs;t æqualitatis momentorum <lb/>punctum &longs;u&longs;pen&longs;ionis, aut &longs;u&longs;tentationis hinc, & hinc u&longs;que<lb/>quaque circun&longs;tantium; &longs;i qua enim e&longs;&longs;et inæqualitas, alterutra <lb/>pars præponderaret, & ad motum incitaretur. </s>

<pb xlink:href="017/01/052.jpg" n="36"/>vim inferre valeant. </s><s>Quare &longs;i fiat corporis &longs;u&longs;pen&longs;i, aut &longs;u&longs;ten<lb/>tati con&longs;i&longs;tentia, argumentum e&longs;t æqualitatis momentorum <lb/>punctum &longs;u&longs;pen&longs;ionis, aut &longs;u&longs;tentationis hinc, & hinc u&longs;que<lb/>quaque circun&longs;tantium; &longs;i qua enim e&longs;&longs;et inæqualitas, alterutra <lb/>pars præponderaret, & ad motum incitaretur. </s>

<s>Sit corpus grave AB, cujus <lb/>centrum gravitatis H, linea di<lb/>rectionis HT in centrum uni<lb/>ver&longs;i producta. </s><s>Si &longs;u&longs;pendatur <lb/>ex puncto C, quod e&longs;t in eadem <lb/>lineâ directionis, nece&longs;&longs;ariò con<lb/>&longs;i&longs;tit corpus horizonti paralle<lb/>lum, quia rectâ de&longs;cendere non <lb/>pote&longs;t per HT, cum in C reti<lb/>neatur; neque alterutra pars pote&longs;t de&longs;cendere, quia momen<lb/>ta partis HB, quibus deor&longs;um nititur, æqualia &longs;unt momen<lb/>tis, quibus pars HA re&longs;i&longs;tit, no elevetur; & vici&longs;&longs;im viribus <lb/>gravitatis- AH cæteroqui de&longs;cen&longs;uræ reluctatur gravitas HB <lb/>pari ni&longs;u repugnans, ne attollatur; totum ergo con&longs;i&longs;tit. </s><s>At &longs;i <lb/>ex M puncto &longs;u&longs;pendatur, non pote&longs;t quidem per MT per<lb/>pendicularem de&longs;cendere versùs terræ centrum, &longs;ed neque <lb/>con&longs;i&longs;tet horizonti parallelum; quia &longs;i planum intelligatur ex <lb/>terræ centro per rectam MT ductum, non dividitur corpus in <lb/>momenta æqualia, cum non tran&longs;eat per H centrum gravita<lb/>tis; igitur cum majora &longs;int momenta partis MB, quàm par<lb/>tis MA, illa præponderabit, atque de&longs;cendens circa <lb/>punctum M permanens convertetur, donec centrum gra<lb/>vitatis H &longs;it in perpendiculari MT, cui congruat recta <lb/>MO: tunc autem demum con&longs;i&longs;tet, quia planum tran&longs;iens <lb/>per MHO æqualiter di&longs;pertit momenta gravitatis; neutrâ <lb/>autem parte præponderante, utraque quie&longs;cit. </s><s>Idem dicen<lb/>dum, &longs;i corpus ex I puncto &longs;u&longs;penderetur; tunc enim &longs;o<lb/>lùm fieret con&longs;i&longs;tentia, ubi in eadem directionis lineâ <lb/>e&longs;&longs;et punctum I atque H centrum gravitatis. </s><s>Quod &longs;i du<lb/>plici funiculo &longs;u&longs;pendatur pondus, & illi paralleli non &longs;int, <lb/>quia neque horizonti perpendiculares, illi &longs;i producantur, <lb/>concurrent in punctum aliquod lineæ directionis, &longs;ivè &longs;upra <lb/>pondus, &longs;ivè infra, pro ratione angulorum, quos con&longs;tituunt.

<pb n="37"/>Sit enim corpus AB, cujus cen<lb/>

<pb xlink:href="017/01/053.jpg" n="37"/>Sit enim corpus AB, cujus cen<lb/>

<figure/><lb/>trum gravitatis O, linea directio<lb/>nis IOC, &longs;i ex I &longs;u&longs;pendatur <lb/>per O, in co &longs;itu manebit; ergo <lb/>etiam, &longs;i funiculi &longs;int IH, IL, <lb/>manebit: ergo etiam, &longs;i &longs;int PH, <lb/>SL, funiculorum enim longitudo <lb/>nihil facit; Idem etiam dicendum <lb/>cum funiculi &longs;unt DH, FL; pro<lb/>ducti enim concurrunt cum linea <lb/>directionis in C, &longs;emper &longs;cilicet <lb/>perinde &longs;e habet atque, &longs;i ex I &longs;u&longs;penderetur. </s>

<figure id="id.017.01.053.1.jpg" xlink:href="017/01/053/1.jpg"/><lb/>trum gravitatis O, linea directio<lb/>nis IOC, &longs;i ex I &longs;u&longs;pendatur <lb/>per O, in co &longs;itu manebit; ergo <lb/>etiam, &longs;i funiculi &longs;int IH, IL, <lb/>manebit: ergo etiam, &longs;i &longs;int PH, <lb/>SL, funiculorum enim longitudo <lb/>nihil facit; Idem etiam dicendum <lb/>cum funiculi &longs;unt DH, FL; pro<lb/>ducti enim concurrunt cum linea <lb/>directionis in C, &longs;emper &longs;cilicet <lb/>perinde &longs;e habet atque, &longs;i ex I &longs;u&longs;penderetur. </s>

<s>Quæ verò de &longs;u&longs;pen&longs;ione dicta &longs;unt, ea, analogiâ &longs;ervatâ, de <lb/>&longs;u&longs;tentatione quoque dicta intelligantur; tunc &longs;olùm videlicet <lb/>corpus con&longs;i&longs;tere, cùm ex centro gravitatis ducta directionis <lb/>linea tran&longs;it per punctum &longs;u&longs;tentationis, quia tunc &longs;olùm æqua<lb/>lia hinc, & hinc &longs;unt momenta virtutis ad de&longs;cendendum, at<lb/>que re&longs;i&longs;tentiæ ad a&longs;cendendum: ut quando corpus aliquod <lb/>imponitur cono, vel pri&longs;ma &longs;phæræ, vel &longs;egmentum &longs;phæri<lb/>cum, plano, vel cylindrus aciei pri&longs;matis trigoni in tran&longs;ver<lb/>&longs;um; cadet enim in alterutram partem impo&longs;itum corpus, ni&longs;i <lb/>in eadem linea fuerint centrum terræ, punctum contactus, & <lb/>centrum gravitatis. </s><s>Quod &longs;i corpus &longs;u&longs;tentans, atque &longs;u&longs;tenta<lb/>tum &longs;e tangant in linea, opus e&longs;t lineam illam e&longs;&longs;e in plano per <lb/>lineam directionis ducto, ut fiat æqualium momentorum con<lb/>&longs;i&longs;tentia. </s><s>Quare &longs;i impo&longs;itum corpus con&longs;i&longs;tat, certi&longs;&longs;imo ar<lb/>gumento con&longs;tabit punctum, &longs;eu lineam, contactûs re&longs;pon<lb/>dere centro gravitatis. </s><s>Hinc patet ratio &longs;ecundæ, & tertiæ <lb/>praxis. </s>

<s>In prima praxi quia facies extima, &longs;upra quam perpendicu<lb/>lum liberè movetur, e&longs;t in plano verticali, perpendiculum HC <lb/>e&longs;t parallelum lineæ directionis corporis gravis, quæ tran&longs;it <lb/>etiam per punctum &longs;u&longs;pen&longs;ionis H: planum igitur tran&longs;iens per <lb/>punctum &longs;u&longs;pen&longs;ionis H, & per perpendiculum HC, tran&longs;it <lb/>quoque per centrum gravitatis corporis. </s><s>Cum verò idem pror<lb/>&longs;us dicendum &longs;it de plano tran&longs;eunte per punctum &longs;u&longs;pen&longs;io<lb/>nis R, & perpendiculum RF, illud &longs;cilicet tran&longs;ire per cen<lb/>trum gravitatis corporis; apertum e&longs;t centrum gravitatis e&longs;&longs;e in

<pb n="38"/>communi illorum planorum &longs;ectione, eique re&longs;pondere <lb/>punctum S inventum. </s>

<pb xlink:href="017/01/054.jpg" n="38"/>communi illorum planorum &longs;ectione, eique re&longs;pondere <lb/>punctum S inventum. </s>

<s>Quia demum, &longs;i corpus quod &longs;u&longs;tinet, & id, quod &longs;u&longs;tine<lb/>tur, in &longs;uperficie &longs;e tangant, corpus impo&longs;itum in alterutram <lb/>partem cadere non pote&longs;t (ni&longs;i fortè &longs;uppo&longs;itum planum fuerit <lb/>inclinatum) quin planum per lineam directionis ductum ita &longs;it <lb/>extra &longs;uperficiem, in qua fit contactus, ut neque illam con<lb/>tingat; con&longs;tat ratio quartæ praxis. </s><s>Si namque planum ex ter<lb/>

<figure/><lb/>ræ centro ductum per C cen<lb/>trum gravitatis dati corporis <lb/>OS, &longs;ecet &longs;ubjectum planum, <lb/>pars corporis extra marginem <lb/>FE in aëre extans minora ha<lb/>bet momenta gravitatis, quàm <lb/>reliqua pars; hæc igitur gra<lb/>vior non pote&longs;t ab illa elevari: <lb/>ubi verò promotum corpus eò <lb/>venerit, ut planum per cen<lb/>trum gravitatis C ductum tangat extremum marginem &longs;ub<lb/>jecti plani ita, ut in eodem plano, in quo e&longs;t centrum gravi<lb/>tatis C, &longs;it etiam FE, æqualia &longs;unt gravitatis momenta par<lb/>tis CS in aëre extantis, ac CO partis plano incumbentis; & <lb/>&longs;i vel minimum ulteriùs promoveretur, pars extra planum &longs;ub<lb/>jectum extans gravior e&longs;&longs;et, adeóque de&longs;cenderet. </s><s>Quare &longs;i in <lb/>corporis OS &longs;uperficie infimâ lineam de&longs;crip&longs;eris &longs;ecundùm <lb/>marginem FE, ea erit in plano tran&longs;eunte per centrum gravi<lb/>tatis. </s><s>Quia verò idem contingit, &longs;i ii&longs;dem &longs;uperficiebus &longs;e con<lb/>tingentibus alium &longs;itum corpori dederis, pariterque eò u&longs;que <lb/>promoveris, ut citrà cadendi periculum promoveri ulteriùs <lb/>non po&longs;&longs;it; alia linea &longs;ecundùm marginem FE ducta erit pari<lb/>ter in plano per gravitatis centrum tran&longs;eunte, &longs;ecabitque <lb/>priorem lineam, punctum mutuæ linearum &longs;ectionis illud e&longs;&longs;e, <lb/>quod quæritur, &longs;atis liquet. </s><s>Hæc e&longs;t di&longs;par philo&longs;ophandi ra<lb/>tio, &longs;i pars CO adeò longa e&longs;&longs;et, ut etiam extaret extra an<lb/>gu&longs;tias &longs;ubjecti plani; &longs;emper enim con&longs;i&longs;tit impo&longs;itum corpus, <lb/>quandiù planum per lineam directionis tran&longs;iens, aut tangit, <lb/>aut &longs;ecat &longs;ubjectum planum. </s><s>Quandocunque enim linea di<lb/>rectionis non tran&longs;it per punctum, vel lineam, vel &longs;uperficiem,

<figure id="id.017.01.054.1.jpg" xlink:href="017/01/054/1.jpg"/><lb/>ræ centro ductum per C cen<lb/>trum gravitatis dati corporis <lb/>OS, &longs;ecet &longs;ubjectum planum, <lb/>pars corporis extra marginem <lb/>FE in aëre extans minora ha<lb/>bet momenta gravitatis, quàm <lb/>reliqua pars; hæc igitur gra<lb/>vior non pote&longs;t ab illa elevari: <lb/>ubi verò promotum corpus eò <lb/>venerit, ut planum per cen<lb/>trum gravitatis C ductum tangat extremum marginem &longs;ub<lb/>jecti plani ita, ut in eodem plano, in quo e&longs;t centrum gravi<lb/>tatis C, &longs;it etiam FE, æqualia &longs;unt gravitatis momenta par<lb/>tis CS in aëre extantis, ac CO partis plano incumbentis; & <lb/>&longs;i vel minimum ulteriùs promoveretur, pars extra planum &longs;ub<lb/>jectum extans gravior e&longs;&longs;et, adeóque de&longs;cenderet. </s><s>Quare &longs;i in <lb/>corporis OS &longs;uperficie infimâ lineam de&longs;crip&longs;eris &longs;ecundùm <lb/>marginem FE, ea erit in plano tran&longs;eunte per centrum gravi<lb/>tatis. </s><s>Quia verò idem contingit, &longs;i ii&longs;dem &longs;uperficiebus &longs;e con<lb/>tingentibus alium &longs;itum corpori dederis, pariterque eò u&longs;que <lb/>promoveris, ut citrà cadendi periculum promoveri ulteriùs <lb/>non po&longs;&longs;it; alia linea &longs;ecundùm marginem FE ducta erit pari<lb/>ter in plano per gravitatis centrum tran&longs;eunte, &longs;ecabitque <lb/>priorem lineam, punctum mutuæ linearum &longs;ectionis illud e&longs;&longs;e, <lb/>quod quæritur, &longs;atis liquet. </s><s>Hæc e&longs;t di&longs;par philo&longs;ophandi ra<lb/>tio, &longs;i pars CO adeò longa e&longs;&longs;et, ut etiam extaret extra an<lb/>gu&longs;tias &longs;ubjecti plani; &longs;emper enim con&longs;i&longs;tit impo&longs;itum corpus, <lb/>quandiù planum per lineam directionis tran&longs;iens, aut tangit, <lb/>aut &longs;ecat &longs;ubjectum planum. </s><s>Quandocunque enim linea di<lb/>rectionis non tran&longs;it per punctum, vel lineam, vel &longs;uperficiem,

<pb n="39"/>in quibus corpus grave tangitur à &longs;u&longs;tentante (idem dic de <lb/>&longs;u&longs;pen&longs;ione) &longs;emper in alterutram partem grave inclinatur, in <lb/>eam &longs;cilicet, in qua reperitur centrum gravitatis, cùm plura <lb/>&longs;int ex ea parte momenta gravitatis. <lb/><gap desc="hr tag"/></s>

<pb xlink:href="017/01/055.jpg" n="39"/>in quibus corpus grave tangitur à &longs;u&longs;tentante (idem dic de <lb/>&longs;u&longs;pen&longs;ione) &longs;emper in alterutram partem grave inclinatur, in <lb/>eam &longs;cilicet, in qua reperitur centrum gravitatis, cùm plura <lb/>&longs;int ex ea parte momenta gravitatis. <lb/><gap desc="hr tag"/></s>

<s><emph type="center"/>CAPUT VII.<emph.end type="center"/></s>

<s><emph type="center"/><emph type="italics"/>Quomodo gravia &longs;pontè a&longs;cendentia de&longs;cendant.<emph.end type="italics"/><emph.end type="center"/></s>

<s>EX his, quæ proximè dicta &longs;unt, grave &longs;u&longs;tentatum in eam <lb/>partem inclinari, in qua e&longs;t gravitatis centrum, oritur ali<lb/>quando a&longs;cen&longs;us gravium, qui rerum naturalium ignaros in <lb/>admirationem adducit non mediocrem, &longs;i maximè tunc cor<lb/>pus de&longs;cendere intelligant, quando illud cernunt altiùs ab ho<lb/>rizonte a&longs;cendere. </s><s>Sit <lb/>

<figure/><lb/>enim &longs;uper planum in<lb/>clinatum RN rota tantæ <lb/>latitudinis, ut po&longs;&longs;it in <lb/>plano verticali erecta <lb/>permanere, dum conver<lb/>titur; habeat autem ad <lb/>PO adnexam laminam <lb/>plumbeam cra&longs;&longs;iorem, <lb/>adeò ut totius rotæ cen<lb/>trum gravitatis &longs;it S. </s><s>Jam <lb/>verò ea &longs;it plani &longs;ubjecti <lb/>inclinatio, ut rotâ illud <lb/>tangente puncto H, li<lb/>nea à terræ centro per H punctum contactûs tran&longs;iens non <lb/>tran&longs;eat per S centrum gravitatis (&longs;eu ut veriùs dicam, quia <lb/>extima &longs;uperficies rotæ cylindrica tangit planum in lineâ, pla<lb/>num ex centro terræ per lineam contactûs in H ductum non <lb/>tran&longs;eat per S) &longs;ed illud relinquat versùs &longs;uperiorem plani par<lb/>tem N; planum per rectam HO perpendicularem ductum <lb/>di&longs;tinguit rotam in momenta gravitatis inæqualia: non pote&longs;t <lb/>igitur rota in H con&longs;i&longs;tere, &longs;ed convertitur, ita ut tangat pla<lb/>num in I primùm, deinde in E, demùm in P, ubi con&longs;i&longs;tet,

<figure id="id.017.01.055.1.jpg" xlink:href="017/01/055/1.jpg"/><lb/>enim &longs;uper planum in<lb/>clinatum RN rota tantæ <lb/>latitudinis, ut po&longs;&longs;it in <lb/>plano verticali erecta <lb/>permanere, dum conver<lb/>titur; habeat autem ad <lb/>PO adnexam laminam <lb/>plumbeam cra&longs;&longs;iorem, <lb/>adeò ut totius rotæ cen<lb/>trum gravitatis &longs;it S. </s><s>Jam <lb/>verò ea &longs;it plani &longs;ubjecti <lb/>inclinatio, ut rotâ illud <lb/>tangente puncto H, li<lb/>nea à terræ centro per H punctum contactûs tran&longs;iens non <lb/>tran&longs;eat per S centrum gravitatis (&longs;eu ut veriùs dicam, quia <lb/>extima &longs;uperficies rotæ cylindrica tangit planum in lineâ, pla<lb/>num ex centro terræ per lineam contactûs in H ductum non <lb/>tran&longs;eat per S) &longs;ed illud relinquat versùs &longs;uperiorem plani par<lb/>tem N; planum per rectam HO perpendicularem ductum <lb/>di&longs;tinguit rotam in momenta gravitatis inæqualia: non pote&longs;t <lb/>igitur rota in H con&longs;i&longs;tere, &longs;ed convertitur, ita ut tangat pla<lb/>num in I primùm, deinde in E, demùm in P, ubi con&longs;i&longs;tet,

<pb n="40"/>cùm linea directionis ex gravitatis centro S ducta in terræ cen<lb/>trum tran&longs;ibit per P locum contactús. </s><s>In hac autem conver<lb/>&longs;ione dum rotæ partes inter H & P deinceps aptantur &longs;ubjecto <lb/>plano, centrum quidem molis a&longs;cendit, &longs;ed centrum gravita<lb/>tis S de&longs;cendit. </s><s>Lineam porrò SP minorem e&longs;&longs;e lineá SE, & <lb/>hanc minorem lineâ SI, & hanc lineâ SH, con&longs;tat ex prop.7. <lb/>lib.3. Eucl. &longs;i nimirum per S, & C centrum agatur diameter. </s><lb/><s>Non e&longs;t tamen cen&longs;endum quamlibet ponderis additionem <lb/>in OP &longs;atis e&longs;&longs;e, ut in quoliber plano inclinato rota a&longs;cendat; <lb/>&longs;i enim di&longs;tantia centri gravitatis à centro rotæ minor fuerit, <lb/>quàm Sinus inclinationis plani, &longs;emper de&longs;cendet; &longs;i eidem <lb/>Sinui æqualis, non a&longs;cendet; &longs;i demum eo &longs;inu major, poterit <lb/>a&longs;cendere. </s>

<pb xlink:href="017/01/056.jpg" n="40"/>cùm linea directionis ex gravitatis centro S ducta in terræ cen<lb/>trum tran&longs;ibit per P locum contactús. </s><s>In hac autem conver<lb/>&longs;ione dum rotæ partes inter H & P deinceps aptantur &longs;ubjecto <lb/>plano, centrum quidem molis a&longs;cendit, &longs;ed centrum gravita<lb/>tis S de&longs;cendit. </s><s>Lineam porrò SP minorem e&longs;&longs;e lineá SE, & <lb/>hanc minorem lineâ SI, & hanc lineâ SH, con&longs;tat ex prop.7. <lb/>lib.3. Eucl. &longs;i nimirum per S, & C centrum agatur diameter. </s><lb/><s>Non e&longs;t tamen cen&longs;endum quamlibet ponderis additionem <lb/>in OP &longs;atis e&longs;&longs;e, ut in quoliber plano inclinato rota a&longs;cendat; <lb/>&longs;i enim di&longs;tantia centri gravitatis à centro rotæ minor fuerit, <lb/>quàm Sinus inclinationis plani, &longs;emper de&longs;cendet; &longs;i eidem <lb/>Sinui æqualis, non a&longs;cendet; &longs;i demum eo &longs;inu major, poterit <lb/>a&longs;cendere. </s>

<s>Sit planum inclinatum <lb/>AB, quod in H contingat <lb/>circulum (hunc &longs;umo cir<lb/>culum, qui tran&longs;eat per <lb/>centrum tum molis tum <lb/>gravitatis rotæ) cujus cen<lb/>trum C, & ducatur recta <lb/>CH, quæ cum perpendi<lb/>culari HO faciat angu<lb/>lum CHO. </s><s>Quia enim <lb/>OH producta cadit in ho<lb/>rizontem AD perpendicularis, & angulus OHA per 32.lib.1. <lb/>æqualis e&longs;t duobus internis HFA, FAH, e&longs;t autem AHC ad <lb/>contingentem factus à &longs;emidiametro rectus per 18.lib. 3. &longs;icut <lb/>& HFA e&longs;t rectus; reliquus CHO æqualis e&longs;t angulo HAF <lb/>inclinationis plani. </s><s>Certum e&longs;t igitur, quòd in eam partem ro<lb/>ra convertetur, in qua fuerit centrum gravitatis. </s><s>Quoniam <lb/>verò CI e&longs;t Sinus anguli CHI, po&longs;ito radio CH, e&longs;t au<lb/>tem CI minima omnium, quæ ex C puncto cadant in rectam <lb/>HO, manife&longs;tum e&longs;t, quòd, &longs;i centrum gravitatis fuerit cen<lb/>tro rotæ vicinius, ut in R, rota &longs;emper de&longs;cendet, quia cen<lb/>trum gravitatis re&longs;picit declivitatem plani: at, &longs;i fuerit <lb/>in I, a&longs;cendere non pote&longs;t, quia pars re&longs;piciens acclivita<lb/>tem plani non præponderat: &longs;i demum longiùs à centro <lb/>di&longs;titerit, ut in S, a&longs;cendere poterit, u&longs;que dum punctum S

<pb n="41"/>fuerit in lineâ perpendiculari ad horizontem tran&longs;eunte per <lb/>punctum contactûs. </s>

<pb xlink:href="017/01/057.jpg" n="41"/>fuerit in lineâ perpendiculari ad horizontem tran&longs;eunte per <lb/>punctum contactûs. </s>

<s>Ex his apertè con&longs;tat futurum, ut rota de&longs;cendat, &longs;i angulus, <lb/>quem in puncto contactûs faciunt lineæ ductæ ex centris mo<lb/>lis, & gravitatis (&longs;uppono molis centrum idem e&longs;&longs;e cum centro <lb/>rotæ, quâ rota e&longs;t) minor fuerit angulo inclinationis plani, <lb/>tunc enim centrum gravitatis re&longs;picit declivitatem plani; fu<lb/>turum autem, ut rota a&longs;cendat, &longs;i angulus ille major fuerit co<lb/>dem angulo inclinationis, quia centrum gravitatis re&longs;picit ac<lb/>clivitatem plani; futurum demùm, ut con&longs;i&longs;tat, &longs;i angulus il<lb/>le fuerit æqualis eidem angulo inclinationis plani, quia nimi<lb/>rum planum perpendiculare dividit æqualiter momenta gravi<lb/>tatis, cum tran&longs;eat per centrum gravitatis exi&longs;tens in lineâ <lb/>perpendiculari. </s>

Line 491

<s>At &longs;i centrum gravitatis fuerit S, ductâ ad CS perpendicu<lb/>lari SM, angulus omnium maximus e&longs;t CMS: hic autem e&longs;t <lb/>æqualis externo CKI, cum IK, & SM parallelæ &longs;int con&longs;ti<lb/>tutæ; angulus verò CKI externus major e&longs;t interno CHI, <lb/>igitur angulus CMS major e&longs;t angulo CHI, hoc e&longs;t angulo <lb/>inclinationis. </s><s>A&longs;cendere igitur poterit rota, quando angulus <lb/>ad contractum factus à lineis ex C, & S exeuntibus major e&longs;t <lb/>angulo inclinationis; &longs;in autem contactus fiat in co puncto, ad <lb/>quod fit angulus æqualis, con&longs;i&longs;tet; &longs;i in iis punctis, ad quæ fit <lb/>angulus minor, de&longs;cendet. </s>

<s>Porrò quamvis iis, qui in A&longs;tronomicarum Pro&longs;taphære&longs;eon

<pb n="42"/>doctrinâ ver&longs;ati &longs;unt, &longs;upervacaneum &longs;it o&longs;tendere angulum <lb/>ad peripheriam factum à Radio circuli, & à linea perpendicu<lb/>lari in diametrum, e&longs;&longs;e maximum omnium, qui fieri po&longs;&longs;int à <lb/>Radio, & à lineâ ductâ ex eodem diametri puncto, in quod <lb/>cadebat perpendicularis; ut omnibus tamen fiat &longs;atis, non pi<lb/>

<pb xlink:href="017/01/058.jpg" n="42"/>doctrinâ ver&longs;ati &longs;unt, &longs;upervacaneum &longs;it o&longs;tendere angulum <lb/>ad peripheriam factum à Radio circuli, & à linea perpendicu<lb/>lari in diametrum, e&longs;&longs;e maximum omnium, qui fieri po&longs;&longs;int à <lb/>Radio, & à lineâ ductâ ex eodem diametri puncto, in quod <lb/>cadebat perpendicularis; ut omnibus tamen fiat &longs;atis, non pi<lb/>

<figure/><lb/>gebit hîc demon&longs;trare. </s><s>Sit in diametro <lb/>circuli punctum R extra centrum C, & <lb/>ad CR ducatur perpendicularis HR, <lb/>quæ producta in G, bifariam dividitur <lb/>in R: & ductis ex centro rectis CH, <lb/>CG æqualibus, &longs;unt anguli CHR, <lb/>CGR æquales, per 5. vel 8. lib.1. </s><s>Fiat <lb/>angulus CER, ductis ex C & R rectis <lb/>lineis ad idem punctum E peripheriæ. </s><lb/><s>Dico angulum CER minorem e&longs;&longs;e an<lb/>gulo CHR. </s><s>Ducatur enim recta EG; & erunt in I&longs;o&longs;cele <lb/>CEG æquales anguli CEG, CGE. </s><s>Quia verò, per 7.lib.3. <lb/>RE major e&longs;t quàm RG, angulus RGE major e&longs;t angulo <lb/>REG, per 18.lib. 1. & ablatis æqualibus remanet REC mi<lb/>nor angulo RGC, hoc e&longs;t RHC. </s><s>Similiter o&longs;tendetur angu<lb/>lum RIC minorem e&longs;&longs;e angulo RHC: ductâ enim IG, angu<lb/>li CIG, CGI &longs;unt æquales: & quoniam per 7.lib.3. RG ma<lb/>jor e&longs;t quàm RI, angulus RIG major e&longs;t angulo RGI, per <lb/>18.lib.1. &longs;i igitur ex æqualibus auferantur inæquales anguli, re<lb/>manet RIC minor, quàm RGC, hoc e&longs;t quam RHC. </s><s>Ea<lb/>dem erit methodus demon&longs;trandi angulos ad puncta periphe<lb/>riæ propiora puncto H e&longs;&longs;e majores angulo CER. </s><s>Ductâ enim <lb/>RD æquali ip&longs;i RE, ad punctum &longs;cilicet D æqualiter di&longs;tans à <lb/>diametro, ac di&longs;tet punctum E, & ducto radio CD, e&longs;t angu<lb/>lus CDR æqualis angulo CER. </s><s>Sit autem puncto H vicinior <lb/>angulus COR, quem dico e&longs;&longs;e majorem angulo CER per <lb/>7.lib.3. & 8.lib.1. </s><s>Ducta lineâ OD, anguli COD, CDO <lb/>&longs;unt æquales, quia latera CO, CD æqualia &longs;unt: at per 7.lib.3. <lb/>RO minor e&longs;t, quàm RE, hoc e&longs;t RD, igitur angulus ROD <lb/>per 18.lib.1. major e&longs;t angulo RDO, & ablatis æqualibus re<lb/>manet ROC major quam RDC, hoc e&longs;t quàm REC. </s><s>Angu<lb/>li itáque recedentes à puncto H &longs;emper fiunt minores, acce<lb/>dentes verò fiunt majores. </s>

<figure id="id.017.01.058.1.jpg" xlink:href="017/01/058/1.jpg"/><lb/>gebit hîc demon&longs;trare. </s><s>Sit in diametro <lb/>circuli punctum R extra centrum C, & <lb/>ad CR ducatur perpendicularis HR, <lb/>quæ producta in G, bifariam dividitur <lb/>in R: & ductis ex centro rectis CH, <lb/>CG æqualibus, &longs;unt anguli CHR, <lb/>CGR æquales, per 5. vel 8. lib.1. </s><s>Fiat <lb/>angulus CER, ductis ex C & R rectis <lb/>lineis ad idem punctum E peripheriæ. </s><lb/><s>Dico angulum CER minorem e&longs;&longs;e an<lb/>gulo CHR. </s><s>Ducatur enim recta EG; & erunt in I&longs;o&longs;cele <lb/>CEG æquales anguli CEG, CGE. </s><s>Quia verò, per 7.lib.3. <lb/>RE major e&longs;t quàm RG, angulus RGE major e&longs;t angulo <lb/>REG, per 18.lib. 1. & ablatis æqualibus remanet REC mi<lb/>nor angulo RGC, hoc e&longs;t RHC. </s><s>Similiter o&longs;tendetur angu<lb/>lum RIC minorem e&longs;&longs;e angulo RHC: ductâ enim IG, angu<lb/>li CIG, CGI &longs;unt æquales: & quoniam per 7.lib.3. RG ma<lb/>jor e&longs;t quàm RI, angulus RIG major e&longs;t angulo RGI, per <lb/>18.lib.1. &longs;i igitur ex æqualibus auferantur inæquales anguli, re<lb/>manet RIC minor, quàm RGC, hoc e&longs;t quam RHC. </s><s>Ea<lb/>dem erit methodus demon&longs;trandi angulos ad puncta periphe<lb/>riæ propiora puncto H e&longs;&longs;e majores angulo CER. </s><s>Ductâ enim <lb/>RD æquali ip&longs;i RE, ad punctum &longs;cilicet D æqualiter di&longs;tans à <lb/>diametro, ac di&longs;tet punctum E, & ducto radio CD, e&longs;t angu<lb/>lus CDR æqualis angulo CER. </s><s>Sit autem puncto H vicinior <lb/>angulus COR, quem dico e&longs;&longs;e majorem angulo CER per <lb/>7.lib.3. & 8.lib.1. </s><s>Ducta lineâ OD, anguli COD, CDO <lb/>&longs;unt æquales, quia latera CO, CD æqualia &longs;unt: at per 7.lib.3. <lb/>RO minor e&longs;t, quàm RE, hoc e&longs;t RD, igitur angulus ROD <lb/>per 18.lib.1. major e&longs;t angulo RDO, & ablatis æqualibus re<lb/>manet ROC major quam RDC, hoc e&longs;t quàm REC. </s><s>Angu<lb/>li itáque recedentes à puncto H &longs;emper fiunt minores, acce<lb/>dentes verò fiunt majores. </s>

<s>Hoc probato con&longs;equens e&longs;t illud, quod in rotæ peripheriâ <lb/>duo &longs;unt puncta, inter quæ quodlibet punctum contingat pla<lb/>num <expan abbr="inclinat&utilde;">inclinatum</expan>, rota a&longs;cendit, &longs;i angulus maximus factus à lineis <lb/>ductis ex centro rotæ, & ex centro gravitatis &longs;it major angulo <lb/>inclinationis; quia nimirum anguli à puncto H recedentes ad <lb/>utramque partem &longs;emper fiunt minores; ergo ad utramque e&longs;t <lb/>angulus unus æqualis angulo inclinationis, & &longs;patium inter <lb/>huju&longs;modi angulos e&longs;t quantitas peripheriæ, quæ a&longs;cendens <lb/>pote&longs;t coaptari plano inclinato: ac proinde ex horum puncto<lb/>rum di&longs;tantia definietur &longs;patium, quod pote&longs;t rota a&longs;cendens <lb/>percurrere. </s>

<s>Sit igitur rota, cujus centrum C, & <lb/>

<figure/><lb/>centrum gravitatis S: &longs;it autem CS par<lb/>tium 11, quarum CH Radius e&longs;t 16: <lb/>e&longs;t igitur CS æqualis Sinui gr. 43. 26′. <lb/>qui erit maximus angulus CIS ad peri<lb/>pheriam factus à Radio, & à lineâ IS <lb/>perpendiculari ad SC. </s><s>Quare in quoli<lb/>bet plano habente minorem inclinatio<lb/>nem poterit a&longs;cendere. </s><s>Ponatur plani <lb/>inclinatio gr. 15, cui æqualis &longs;it angulus CHS. </s><s>Fiat igitur <lb/>ut CS 11 ad CH 16, ita Sinus anguli CHS 25882 ad <lb/>37646 Sinum Anguli CSH gr. 22. 7′; eritque angulus <lb/>SCH gr. 142. 53′. </s><s>Cre&longs;cet ergo &longs;upra angulum H angulus <lb/>ad peripheriam, &longs;i ultra punctum H fiat contactus rotæ <lb/>in alio puncto viciniore puncto I, ex quo ad SC perpendi<lb/>cularis cadit; & ex I decre&longs;cit u&longs;que dum in P fiat angu<lb/>lus SPC grad. 15 æqualis angulo inclinationis. </s><s>In triangu<lb/>lo itaque SPC invenitur ex ii&longs;dem datis angulus PSC <lb/>gr. 157. 53′. & angulus SCP gr. 7. 7′. qui ex angulo SCH <lb/>gr. 142. 53′ ablatus relinquit PCH gr. 135. 46′. quæ e&longs;t quan<lb/>titas arcûs HIP, quæ plano coaptatur in a&longs;cen&longs;u. </s><s>Quoniam <lb/>verò quarum partium CG Radius e&longs;t 16, peripheria e&longs;t 100 1/2 <lb/>earum parirer e&longs;t arcus HP ferè 38, &longs;i Radius rotæ fuerit un<lb/>ciarum pedis 16, rota a&longs;cendet in plano percurrens &longs;patium <lb/>pedum 3, & eo ampliùs. </s><s>Hinc poteris aut rotæ diametrum au<lb/>gere, aut plani inclinationem minuere, &longs;i volveris rotam lon<lb/>giore &longs;patio moveri: auctâ enim rotæ diametro augetur peri-

<figure id="id.017.01.059.1.jpg" xlink:href="017/01/059/1.jpg"/><lb/>centrum gravitatis S: &longs;it autem CS par<lb/>tium 11, quarum CH Radius e&longs;t 16: <lb/>e&longs;t igitur CS æqualis Sinui gr. 43. 26′. <lb/>qui erit maximus angulus CIS ad peri<lb/>pheriam factus à Radio, & à lineâ IS <lb/>perpendiculari ad SC. </s><s>Quare in quoli<lb/>bet plano habente minorem inclinatio<lb/>nem poterit a&longs;cendere. </s><s>Ponatur plani <lb/>inclinatio gr. 15, cui æqualis &longs;it angulus CHS. </s><s>Fiat igitur <lb/>ut CS 11 ad CH 16, ita Sinus anguli CHS 25882 ad <lb/>37646 Sinum Anguli CSH gr. 22. 7′; eritque angulus <lb/>SCH gr. 142. 53′. </s><s>Cre&longs;cet ergo &longs;upra angulum H angulus <lb/>ad peripheriam, &longs;i ultra punctum H fiat contactus rotæ <lb/>in alio puncto viciniore puncto I, ex quo ad SC perpendi<lb/>cularis cadit; & ex I decre&longs;cit u&longs;que dum in P fiat angu<lb/>lus SPC grad. 15 æqualis angulo inclinationis. </s><s>In triangu<lb/>lo itaque SPC invenitur ex ii&longs;dem datis angulus PSC <lb/>gr. 157. 53′. & angulus SCP gr. 7. 7′. qui ex angulo SCH <lb/>gr. 142. 53′ ablatus relinquit PCH gr. 135. 46′. quæ e&longs;t quan<lb/>titas arcûs HIP, quæ plano coaptatur in a&longs;cen&longs;u. </s><s>Quoniam <lb/>verò quarum partium CG Radius e&longs;t 16, peripheria e&longs;t 100 1/2 <lb/>earum parirer e&longs;t arcus HP ferè 38, &longs;i Radius rotæ fuerit un<lb/>ciarum pedis 16, rota a&longs;cendet in plano percurrens &longs;patium <lb/>pedum 3, & eo ampliùs. </s><s>Hinc poteris aut rotæ diametrum au<lb/>gere, aut plani inclinationem minuere, &longs;i volveris rotam lon<lb/>giore &longs;patio moveri: auctâ enim rotæ diametro augetur peri-

<pb n="44"/>pheria, &longs;ervatâ ratione eadem di&longs;tantiæ centri gravitatis. </s><s>At &longs;i <lb/>data fuerit rota (oportet non ignorari di&longs;tantiam centri gravi<lb/>tatis à centro rotæ, poterit autem primâ praxi cap.5. inve&longs;tiga<lb/>ri) certum e&longs;t illam non po&longs;&longs;e a&longs;cendere ni&longs;i per &longs;patium mi<lb/>nus longitudine &longs;emiperipheriæ; con&longs;tituto autem &longs;patio inve<lb/>nietur inclinatio plani nece&longs;&longs;aria, hac methodo. </s><s>Data &longs;patij <lb/>longitudo PH reducatur ad denominationem graduum, & erit <lb/>notus angulus PCH: & quoniam anguli ad H & ad P debent <lb/>e&longs;&longs;e æquales, anguli verò in R ad verticem &longs;unt æquales, erunt <lb/>pariter æquales PCH, & PSH, qui proinde notus e&longs;t. </s><s>Hujus <lb/>&longs;emi&longs;&longs;is auferatur ex recto CSI, & innote&longs;cet angulus CSH, <lb/>cum quo & duobus lateribus CS, CH invenietur per Trigo<lb/>nometriam angulus CHS æqualis angulo inclinationis plani <lb/>nece&longs;&longs;ariæ. </s><s>Quod autem angulus HSI &longs;it &longs;emi&longs;&longs;is totius HSP, <lb/>hoc e&longs;t dati PCH, &longs;ic o&longs;tendo. </s><s>Quia in duobus triangulis <lb/>CSP, CHS idem latus CS opponitur angulis æqualibus ad H, <lb/>& ad P, æqualia autem latera CH, & CP opponuntur angulis <lb/>quæ&longs;itis CSH, & CSP, con&longs;tat horum duorum angulorum <lb/>e&longs;&longs;e unum eundemque &longs;inum; ergo &longs;imul &longs;umpti &longs;unt æquales <lb/>duobus rectis; auferatur ex eorum &longs;ummâ unus rectus, rema<lb/>nebunt duo anguli &longs;imul CSH, ISP æquales uni recto, hoc <lb/>e&longs;t angulo ISC: auferatur communis CSH, remanebit HSI <lb/>æqualis angulo ISP: id quod oportuit demon&longs;trare. </s>

<pb xlink:href="017/01/060.jpg" n="44"/>pheria, &longs;ervatâ ratione eadem di&longs;tantiæ centri gravitatis. </s><s>At &longs;i <lb/>data fuerit rota (oportet non ignorari di&longs;tantiam centri gravi<lb/>tatis à centro rotæ, poterit autem primâ praxi cap.5. inve&longs;tiga<lb/>ri) certum e&longs;t illam non po&longs;&longs;e a&longs;cendere ni&longs;i per &longs;patium mi<lb/>nus longitudine &longs;emiperipheriæ; con&longs;tituto autem &longs;patio inve<lb/>nietur inclinatio plani nece&longs;&longs;aria, hac methodo. </s><s>Data &longs;patij <lb/>longitudo PH reducatur ad denominationem graduum, & erit <lb/>notus angulus PCH: & quoniam anguli ad H & ad P debent <lb/>e&longs;&longs;e æquales, anguli verò in R ad verticem &longs;unt æquales, erunt <lb/>pariter æquales PCH, & PSH, qui proinde notus e&longs;t. </s><s>Hujus <lb/>&longs;emi&longs;&longs;is auferatur ex recto CSI, & innote&longs;cet angulus CSH, <lb/>cum quo & duobus lateribus CS, CH invenietur per Trigo<lb/>nometriam angulus CHS æqualis angulo inclinationis plani <lb/>nece&longs;&longs;ariæ. </s><s>Quod autem angulus HSI &longs;it &longs;emi&longs;&longs;is totius HSP, <lb/>hoc e&longs;t dati PCH, &longs;ic o&longs;tendo. </s><s>Quia in duobus triangulis <lb/>CSP, CHS idem latus CS opponitur angulis æqualibus ad H, <lb/>& ad P, æqualia autem latera CH, & CP opponuntur angulis <lb/>quæ&longs;itis CSH, & CSP, con&longs;tat horum duorum angulorum <lb/>e&longs;&longs;e unum eundemque &longs;inum; ergo &longs;imul &longs;umpti &longs;unt æquales <lb/>duobus rectis; auferatur ex eorum &longs;ummâ unus rectus, rema<lb/>nebunt duo anguli &longs;imul CSH, ISP æquales uni recto, hoc <lb/>e&longs;t angulo ISC: auferatur communis CSH, remanebit HSI <lb/>æqualis angulo ISP: id quod oportuit demon&longs;trare. </s>

<s>Colligere po&longs;&longs;umus ex his, quæ hactenus explicata &longs;unt, fie<lb/>ri quidem po&longs;&longs;e, ut, &longs;i rota in plano inclinato primùm con&longs;ti<lb/>tuta exactè tangat in H, pror&longs;us con&longs;i&longs;tat; id tamen vix po&longs;&longs;e <lb/>&longs;perari, quia &longs;i in alio puncto remotiore ab I tangat, cadet, &longs;i <lb/>in puncto viciniore, a&longs;cendet. </s><s>At ubi venerit in P, &longs;i ex con<lb/>cepto impetu pergat adhuc aliquantulum a&longs;cendere; centro <lb/>gravitatis S tran&longs;lato versùs plani declivitatem, & diminuto <lb/>angulo, de&longs;cendet; & ubi tran&longs;ilierit punctum P, iterùm aucto <lb/>angulo a&longs;cendet, donec omninò in P con&longs;i&longs;tat. </s><s>Ubi licet <lb/>animadvertere non idem e&longs;&longs;e punctum contactus, in quo <lb/>quie&longs;ceret in plano horizontali, ac inclinato; in plano enim <lb/>horizontali quie&longs;ceret in O, ubi linea à centro rotæ C perpen<lb/>dicularis horizonti, ac tran&longs;iens per S centrum gravitatis, ter<lb/>minatur: in eo autem puncto O con&longs;i&longs;tere non po&longs;&longs;e &longs;upra pla<lb/>num inclinatum &longs;atis patet ex dictis. </s><s>Porrò hæc, quæ de rotâ

<pb n="45"/>con&longs;i&longs;tente, aut cadente di&longs;putata &longs;unt, dicenda e&longs;&longs;e de &longs;phæ<lb/>râ quie&longs;cente in plano inclinato, clarius e&longs;t, quàm ut oporteat <lb/>pluribus explicare. </s>

<pb xlink:href="017/01/061.jpg" n="45"/>con&longs;i&longs;tente, aut cadente di&longs;putata &longs;unt, dicenda e&longs;&longs;e de &longs;phæ<lb/>râ quie&longs;cente in plano inclinato, clarius e&longs;t, quàm ut oporteat <lb/>pluribus explicare. </s>

<s>Unum &longs;upere&longs;&longs;e videtur o&longs;tendendum, quî verum &longs;it cen<lb/>trum gravitatis de&longs;cendere ita, ut fiat horizonti vicinius, dum <lb/>rota a&longs;cendit, & fit remotior. </s><s>Id ut manife&longs;tum fiat, primò in<lb/>veniatur HS: & &longs;it ut Sinus anguli CHS gr. 15. ad &longs;inum an<lb/>guli SCH gr. 14.2. 53′. hoc e&longs;t ut 25882 ad 60344, ita CS <lb/>partium 11 ad HS 25 2/3: quæ e&longs;t altitudo centri gravitatis ante <lb/>motum. </s><s>Deinde inveniatur SP; & &longs;it ut Sinus SPC gr. 15 ad <lb/>Sinum SCP gr.7. 7′ hoc e&longs;t, ut 25882 ad 12389, ita CS par<lb/>tium 11 ad SP 5 1/4, quæ in fine motus erit altitudo centri gravi<lb/>tatis &longs;upra planum inclinatum; huic autem addenda e&longs;t altitu<lb/>do, quam &longs;upra horizontem habet punctum illud plani inclinati, <lb/>in quo tanget P. </s><s>Quia ergo inclinatio plani e&longs;t gr. 15, & HP <lb/>e&longs;t partium 38, tantum e&longs;t &longs;patium, quod in plano percurritur <lb/>à rota a&longs;cendente, fiat ut Radius 100000 ad 25882 Sinum an<lb/>guli inclinationis, ita 38 ad 9 4/5 altitudinem &longs;upra horizontem, <lb/>cui &longs;i addas SP 5 1/4, erit in fine motûs altitudo centri gravitatis <lb/>&longs;upra horizontem partium 15, cùm initio di&longs;taret partibus 25 2/3. </s><lb/><s>Centrum igitur gravitatis &longs;impliciter, & ab&longs;olutè de&longs;cendit, <lb/>dum rota in plano inclinato a&longs;cendit. </s>

<s>Po&longs;&longs;em hîc afferre aquam vi &longs;uæ gravitatis a&longs;cendentem in <lb/>cochleâ Archimedis, dum cylindrus, quem cochlea ambit, <lb/>convertitur: ab&longs;tineo tamen, quia non vacat hîc examinare, <lb/>an motus ille compo&longs;itus &longs;it ex conver&longs;ione, quâ pul&longs;u externo <lb/>agitata aqua attollatur, & ex naturali de&longs;cen&longs;u, quo per tubum <lb/>in &longs;piras &longs;inuatum de&longs;cendat; an verò quemadmodum &longs;uppo&longs;i<lb/>to cuneo reluctans pondus elevatur, vel etiam cochleâ trahitur <lb/>in plano horizontali, ita dicendum &longs;it aquam vi &longs;uæ gravitatis <lb/>in imo per&longs;i&longs;tentem à cochleâ &longs;en&longs;im &longs;ubeunte elevari &longs;imul, & <lb/>trahi, quin illa &longs;ponte &longs;ua a&longs;cendat: nam aquæ facilè tribuitur <lb/>aliquando motus, qui &longs;ubjecto corpori, cui illa in&longs;idet, conve<lb/>nit; ut liquet &longs;i ampliorem peluim ex fune &longs;u&longs;penderis, vel lu<lb/>brico in plano horizontali collocaveris, in qua &longs;it non multa <lb/>aqua in depre&longs;&longs;iore fundi parte quie&longs;cens; va&longs;e &longs;iquidem ex <lb/>improvi&longs;o vehementiùs impul&longs;o videtur aqua in oppo&longs;itam par-

<pb n="46"/>tem refluere, cum tamen vas ip&longs;um potiùs infra aquam mo<lb/>veatur, quàm aqua in va&longs;e: quanquam ratione adhæ &longs;ionis aquæ <lb/>ad peluim etiam ip&longs;a motum concipiat. </s><s>Quare in cen&longs;u &longs;ponte <lb/>a&longs;cendentium numeranda non videtur aqua tubo &longs;peciali cy<lb/>lindrum circumplexo elevata. </s>

<pb xlink:href="017/01/062.jpg" n="46"/>tem refluere, cum tamen vas ip&longs;um potiùs infra aquam mo<lb/>veatur, quàm aqua in va&longs;e: quanquam ratione adhæ &longs;ionis aquæ <lb/>ad peluim etiam ip&longs;a motum concipiat. </s><s>Quare in cen&longs;u &longs;ponte <lb/>a&longs;cendentium numeranda non videtur aqua tubo &longs;peciali cy<lb/>lindrum circumplexo elevata. </s>

<s>Videatur forta&longs;&longs;e aqua &longs;ponte a&longs;cen&longs;ura in tubo non æquabi<lb/>li &longs;ed conico, in plano verticali rotæ &longs;piraliter circumducto: <lb/>dum enim aqua æquilibrium &longs;uperficiei faciens in parte tubi <lb/>ampliore præponderat, convertitur rota, & illa iterum æqua<lb/>liter &longs;e librans totius molis compo&longs;itæ centrum gravitatis trans<lb/>fert extra lineam perpendicularem: &longs;i tamen ea cautio adhi<lb/>beatur, ut tanta &longs;it aquæ quantitas, quæ non planam obtineat <lb/>&longs;uperficiem &longs;ed tubi inflexione conformetur; neque ita &longs;it <lb/>&longs;piræ a&longs;cendentis ardua altitudo, ut aqua po&longs;t &longs;uperficiei libra<lb/>tionem ex ea parte ob &longs;ui paucitatem non præponderet; & præ<lb/>terea ejus figuræ &longs;it tubus, ut aqua in parte angu&longs;tiore remo<lb/>tior à perpendiculari, non ita ratione &longs;itûs augeat momenta &longs;ui <lb/>conatû<gap/>s deor&longs;um, ut repugnare valeat aquæ ampliorem tubi <lb/>partem occupanti. </s><s>Si hæc, inquam, ob&longs;erventur (an autem <lb/>ita facile &longs;it ea ob&longs;ervare, ut quidam autumant, hic non de<lb/>finio) & centrum gravitatis transferatur extra perpendicula<lb/>rem versùs ampliorem tubi &longs;piralis partem, futurum quidem <lb/>e&longs;t, ut aqua a&longs;cendat; id tamen non e&longs;t opus centri gravitatis, <lb/>&longs;ed potius virtutis illius, qua humor &longs;e æquabiliter librat. <lb/><gap desc="hr tag"/></s>

<s>Videatur forta&longs;&longs;e aqua &longs;ponte a&longs;cen&longs;ura in tubo non æquabi<lb/>li &longs;ed conico, in plano verticali rotæ &longs;piraliter circumducto: <lb/>dum enim aqua æquilibrium &longs;uperficiei faciens in parte tubi <lb/>ampliore præponderat, convertitur rota, & illa iterum æqua<lb/>liter &longs;e librans totius molis compo&longs;itæ centrum gravitatis trans<lb/>fert extra lineam perpendicularem: &longs;i tamen ea cautio adhi<lb/>beatur, ut tanta &longs;it aquæ quantitas, quæ non planam obtineat <lb/>&longs;uperficiem &longs;ed tubi inflexione conformetur; neque ita &longs;it <lb/>&longs;piræ a&longs;cendentis ardua altitudo, ut aqua po&longs;t &longs;uperficiei libra<lb/>tionem ex ea parte ob &longs;ui paucitatem non præponderet; & præ<lb/>terea ejus figuræ &longs;it tubus, ut aqua in parte angu&longs;tiore remo<lb/>tior à perpendiculari, non ita ratione &longs;itûs augeat momenta &longs;ui <lb/>conatus deor&longs;um, ut repugnare valeat aquæ ampliorem tubi <lb/>partem occupanti. </s><s>Si hæc, inquam, ob&longs;erventur (an autem <lb/>ita facile &longs;it ea ob&longs;ervare, ut quidam autumant, hic non de<lb/>finio) & centrum gravitatis transferatur extra perpendicula<lb/>rem versùs ampliorem tubi &longs;piralis partem, futurum quidem <lb/>e&longs;t, ut aqua a&longs;cendat; id tamen non e&longs;t opus centri gravitatis, <lb/>&longs;ed potius virtutis illius, qua humor &longs;e æquabiliter librat. <lb/><gap desc="hr tag"/></s>

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

<s><emph type="center"/><emph type="italics"/>Cur gravium in plano inclinato de&longs;cendentium <lb/>alia repant, alia rotentur.<emph.end type="italics"/><emph.end type="center"/></s>

<s>QUæ capite &longs;uperiori dixi de globi aut rotæ &longs;uper planum <lb/>inclinatum con&longs;i&longs;tentiâ in puncto, in quo linea à centro <lb/>globi, aut rotæ ducta cum eâ, quæ ex centro gravitatis duci<lb/>tur, facit angulum æqualem angulo inclinationis plani, non ita <lb/>intelligi velim, qua&longs;i motus omnis deor&longs;um adimatur rotæ aut <lb/>globo cuju&longs;libet gravitatis, & in quovis plano inclinato: ibi <lb/>enim con&longs;i&longs;tentiæ, aut quietis nomine &longs;olam conver&longs;ionem

<pb n="47"/>excipio, non lap&longs;um nego. </s><s>Fieri &longs;i quidem pote&longs;t, ut adeò con<lb/>tinuo lævore lubricum &longs;it planum, exactéque rotundatus globus, <lb/>ut nullam ex eminulis particulis moram recipiens deor&longs;um la<lb/>batur, volubilitate ipsâ motum nihil juvante, &longs;ed &longs;olo pondere <lb/>urgente, cum in lineâ ad horizontem perpendiculari &longs;emper <lb/>maneat centrum gravitatis, & punctum contactûs. </s>

<pb xlink:href="017/01/063.jpg" n="47"/>excipio, non lap&longs;um nego. </s><s>Fieri &longs;i quidem pote&longs;t, ut adeò con<lb/>tinuo lævore lubricum &longs;it planum, exactéque rotundatus globus, <lb/>ut nullam ex eminulis particulis moram recipiens deor&longs;um la<lb/>batur, volubilitate ipsâ motum nihil juvante, &longs;ed &longs;olo pondere <lb/>urgente, cum in lineâ ad horizontem perpendiculari &longs;emper <lb/>maneat centrum gravitatis, & punctum contactûs. </s>

<s>Neque e&longs;&longs;et diver&longs;a ratio &longs;phæræ centrum gravitatis haben<lb/>tis extra centrum molis, ac cæterorum corporum non &longs;phæri<lb/>corum: Nam gravia quæcunque in plano inclinato con&longs;tituta <lb/>tantum habent ad de&longs;cendendum momenti, ut a&longs;peritatis re<lb/>&longs;i&longs;tentiam vincant, repunt quidem, &longs;i linea directionis ab eo<lb/>rum gravitatis centro in terræ centrum ducta tran&longs;eat per can<lb/>tactum &longs;ubjecti plani, & impo&longs;iti gravis; rotantur verò, &longs;i di<lb/>rectionis linea in plani declivitatem cadat extra contactum: <lb/>&longs;ivè demùm in puncto, &longs;ivè in lineâ, &longs;ivè in &longs;uperficie con<lb/>tactus fiat. </s><s>E&longs;t autem animadvertendum non e&longs;&longs;e opus, ut una <lb/>continua &longs;uperficies &longs;it, aut linea, &longs;ecundùm quam &longs;e tangant; <lb/>&longs;ed pro &longs;uperficie aut linea contactûs accipitur totum illud &longs;pa<lb/>tium, quod inter extrema contingentia rectis lineis conjuncta <lb/>intercipitur. </s>

<s>Sit planum inclinatum AB, <lb/>

<figure/><lb/>cui globus C incumbit con<lb/>tingens in puncto D. </s><s>Ex cen<lb/>tro gravitatis C, quod & cen<lb/>trum molis e&longs;t ex hypothe&longs;i, <lb/>cadat linea directionis CE <lb/>perpendicularis in horizon<lb/>tem FB; quæ nece&longs;&longs;ariò ca<lb/>dit extra punctum contactûs <lb/>D; alioquin eadem linea CE <lb/>caderet ad angulos rectos &longs;u<lb/>pra planum inclinatum, & &longs;upra horizontale, id quod fieri <lb/>non pote&longs;t, cum huju&longs;modi plana non &longs;int invicem parallela. </s><lb/><s>Per D igitur punctum &longs;u&longs;tentationis ductâ GH parallelâ lineæ <lb/>directionis, &longs;i per utramque plana parallela ducantur, planum <lb/>per GH &longs;ecat &longs;phæram in partes inæqualiter graves; & idcir<lb/>co pars præponderans, in qua e&longs;t centrum gravitatis globi, mo<lb/>vetur circa punctum &longs;u&longs;tentationis D, atque adeò in gyrum

<figure id="id.017.01.063.1.jpg" xlink:href="017/01/063/1.jpg"/><lb/>cui globus C incumbit con<lb/>tingens in puncto D. </s><s>Ex cen<lb/>tro gravitatis C, quod & cen<lb/>trum molis e&longs;t ex hypothe&longs;i, <lb/>cadat linea directionis CE <lb/>perpendicularis in horizon<lb/>tem FB; quæ nece&longs;&longs;ariò ca<lb/>dit extra punctum contactûs <lb/>D; alioquin eadem linea CE <lb/>caderet ad angulos rectos &longs;u<lb/>pra planum inclinatum, & &longs;upra horizontale, id quod fieri <lb/>non pote&longs;t, cum huju&longs;modi plana non &longs;int invicem parallela. </s><lb/><s>Per D igitur punctum &longs;u&longs;tentationis ductâ GH parallelâ lineæ <lb/>directionis, &longs;i per utramque plana parallela ducantur, planum <lb/>per GH &longs;ecat &longs;phæram in partes inæqualiter graves; & idcir<lb/>co pars præponderans, in qua e&longs;t centrum gravitatis globi, mo<lb/>vetur circa punctum &longs;u&longs;tentationis D, atque adeò in gyrum

<pb n="48"/>conver&longs;a circa centrum C de&longs;cendit, ac rotatur. </s><s>Quod &longs;i inæ<lb/>qualis fuerit &longs;phæræ &longs;ub&longs;tantia, & centrum gravitatis I in per<lb/>pendiculari GH, non de&longs;cendet &longs;phæra in gyrum acta, &longs;ed <lb/>tantùm repet, cum neutra pars præponderet. </s>

<pb xlink:href="017/01/064.jpg" n="48"/>conver&longs;a circa centrum C de&longs;cendit, ac rotatur. </s><s>Quod &longs;i inæ<lb/>qualis fuerit &longs;phæræ &longs;ub&longs;tantia, & centrum gravitatis I in per<lb/>pendiculari GH, non de&longs;cendet &longs;phæra in gyrum acta, &longs;ed <lb/>tantùm repet, cum neutra pars præponderet. </s>

<s>Simili ratione parallelepipedum KL, cujus centrum gravi<lb/>tatis M, non repit; quia, cùm linea directionis MN cadat ex<lb/>tra ba&longs;im KO, quæ contingit &longs;ubjectum planum, &longs;i per extre<lb/>mam lineam KP tran&longs;eat planum PQ horizonti perpendicu<lb/>lare, dividitur parallelepipedum in duo pri&longs;mata inæqualia, & <lb/>non æquiponderantia: cum verò pri&longs;ma trapezium QLKP <lb/>præponderet pri&longs;mati trigono KOQ, quod &longs;u&longs;tinetur à ba&longs;i, <lb/>illud nece&longs;&longs;ariò de&longs;cendit, & circa lineam KP convertitur. </s><lb/><s>Contrà autem quando intra ba&longs;im contactûs, ut in cubo PR, <lb/>cujus centrum S, cadit linea directionis ST, tunc repit, & non <lb/>rotatur cubus; quia &longs;cilicet ab extrema &longs;u&longs;tentationis lineâ KP <lb/>ductum planum horizonti perpendiculare dividit cubum in <lb/>partes inæquales ita, ut pars illa, in qua e&longs;t centrum gravitatis, <lb/>& quæ à &longs;ubjecto plano tota &longs;u&longs;tinetur, præponderet, nec po&longs;<lb/>&longs;it à reliquâ parte elevari, ut circa KP convertatur. </s>

<s>Hinc apparet ad quantam altitudinem pertinere po&longs;&longs;it paral<lb/>lelepipedum, ut in dato plano inclinato non rotetur, &longs;ed repat: <lb/>nam ab extremâ &longs;u&longs;tentationis lineâ KP excitatum planum <lb/>horizonti perpendiculare PQ, quod bifariam in partes æqui<lb/>ponderantes dividit parallelepipedum KQ, determinat altitu<lb/>dinem maximam <expan abbr="Xq;">Xque</expan> in omni quippe majori altitudine non <lb/>repit, &longs;ed rotatur, quia linea directionis cadit extra ba&longs;im <lb/>&longs;u&longs;tentationis: in omni verò minori altitudine non rotatur, &longs;ed <lb/>repit, quia linea directionis cadit intra ba&longs;im &longs;u&longs;tentationis. </s><lb/><s>Hoc idem in corporibus cæteris, quamvis non parallelepipe<lb/>dis, ob&longs;ervandum e&longs;t, an &longs;cilicet linea directionis cadat extra <lb/>ba&longs;im &longs;u&longs;tentationis, nec ne. </s>

<s>Quæ tamen de cubo repente dicta &longs;unt, intelligi velim &longs;pecta<lb/>tâ per &longs;e gravium figurâ: quia per accidens fieri pote&longs;t, ut cor<lb/>pus non repat, &longs;ed rotetur, quamvis linea directionis cadat in<lb/>tra ba&longs;im, quæ planum inclinatum contingit. </s><s>Nam &longs;i in motu <lb/>occurrat &longs;uper plano inclinato offendiculum aliquod, cui de<lb/>&longs;cendens corpus illidatur, fieri pote&longs;t, ut impetus ex motu con<lb/>ceptus ita promoveat centrum gravitatis in anteriora, ut linea

<pb n="49"/>directionis cadat extra ba&longs;im ultrà punctum illud, quod proxí<lb/>mum e&longs;t offendiculo, ac proinde circa illud convertatur. </s><s>Hæc <lb/>autem poti&longs;&longs;imùm e&longs;t ratio, cur ex clivis de&longs;cendentes lapides, <lb/>quamquam nec orbiculares, nec admodum alti, rotentur ta<lb/>men; quia &longs;cilicet multa offendicula in clivo occurrunt, & ab <lb/>impetu per motum concepto partes &longs;uperiores promoventur <lb/>ulteriùs, inferioribus retardatis. </s><s>Sic &longs;æpè ce&longs;pitantes cadimus, <lb/>quia ab offendiculo retinentur pedes, cum interim corpus re<lb/>liquum ex concepto impetu ulteriùs promoveatur, ita ut linea <lb/>directionis cadat extra ba&longs;im &longs;u&longs;tentationis. <lb/><gap desc="hr tag"/></s>

<pb xlink:href="017/01/065.jpg" n="49"/>directionis cadat extra ba&longs;im ultrà punctum illud, quod proxí<lb/>mum e&longs;t offendiculo, ac proinde circa illud convertatur. </s><s>Hæc <lb/>autem poti&longs;&longs;imùm e&longs;t ratio, cur ex clivis de&longs;cendentes lapides, <lb/>quamquam nec orbiculares, nec admodum alti, rotentur ta<lb/>men; quia &longs;cilicet multa offendicula in clivo occurrunt, & ab <lb/>impetu per motum concepto partes &longs;uperiores promoventur <lb/>ulteriùs, inferioribus retardatis. </s><s>Sic &longs;æpè ce&longs;pitantes cadimus, <lb/>quia ab offendiculo retinentur pedes, cum interim corpus re<lb/>liquum ex concepto impetu ulteriùs promoveatur, ita ut linea <lb/>directionis cadat extra ba&longs;im &longs;u&longs;tentationis. <lb/><gap desc="hr tag"/></s>

<s><emph type="center"/>CAPUT IX.<emph.end type="center"/></s>

<s><emph type="center"/><emph type="italics"/>Cur turres inclinatæ non corruant.<emph.end type="italics"/><emph.end type="center"/></s>

<s>OB&longs;ervandum e&longs;t, ait Vitruvius lib.6. cap. 11, uti omnes <lb/>&longs;tructuræ perpendiculo re&longs;pondeant, neque habeant in <lb/>ulla parte proclinationes. </s><s>Nemo e&longs;t qui non intelligat præ<lb/>ceptum hoc ad ædificiorum con&longs;i&longs;tentiam pertinere; &longs;ed neque <lb/>defuerunt, qui rem &longs;ubtiliùs, quàm par &longs;it, perpendentes ina<lb/>ni timore &longs;e torquebant, ne fortè aliquando domus corrueret, <lb/>cujus parietes inter &longs;e paralleli fuerant con&longs;tituti; cùm enim <lb/>perpendicula &longs;ibi demum in terræ centro occurrant, fieri non <lb/>po&longs;&longs;e putabant, ut &longs;imul paralleli e&longs;&longs;ent parietes. </s><s>Id quod Geo<lb/>metricè quidem verum e&longs;t; Phy&longs;icè tamen paralleli&longs;mus cum <lb/>perpendiculis con&longs;entit: nam &longs;i funiculos duos longitudinis <lb/>ped. 100. clavo affixos ita extendas, ut extrema eorum palmi <lb/>intervallo di&longs;tent, angulum facient acuti&longs;&longs;imum; & &longs;i lineas <lb/>duas bipedales duxeris eorum extremitatibus congruentes, vix <lb/>different à parallelis, cum intervalla jungentia utro&longs;que linea<lb/>rum terminos differant inter &longs;e &longs;olum palmi parte quinquage<lb/>&longs;ima. </s><s>Longè autem majorem rationem terræ &longs;emidiameter ha<lb/>bet ad quamlibet ædificiorum altitudinem; ut proinde à paral<lb/>leli&longs;mo multo minùs recedant parietes, etiam&longs;i fuerint turrium <lb/>in&longs;tar alti&longs;&longs;imi. </s><s>Ponantur enim parietes duo, aut potiùs turres, <lb/>di&longs;tare inter &longs;e pa&longs;&longs;.300; &longs;it autem parietum, vel turrium alti<lb/>tudo pa&longs;&longs;. 60, hoc e&longs;t ped.300. </s><s>Con&longs;tat mihi, ut aliàs o&longs;tendi, <lb/>terrenam &longs;emidiametrum non e&longs;&longs;e minorem pa&longs;&longs;ibus Rom.

<pb n="50"/><expan abbr="antiq.">antique</expan> 4128635: quarè &longs;i fiat ut terræ &longs;emidiameter 4128635 <lb/>ad altitudinem 60, ita di&longs;tantia parietum, aut turrium in imo <lb/>300, ad aliud, proveniet differentia, qua di&longs;tantia turrium in <lb/>&longs;ummo vertice &longs;uperat earum di&longs;tantiam in imo pede, & <gap/>rit <lb/>partium (4359/1000000) unius pa&longs;&longs;us, quæ e&longs;t minor quàm 2/5 digiti: quis <lb/>autem parallelas non dixerit turres, quæ vix uno aut altero <lb/>hordei grano di&longs;tant à paralleli&longs;mo? </s><s>Quod &longs;i in tanta altitudine <lb/>atque di&longs;tantiâ di&longs;crimen hoc adeò exiguum e&longs;t, &longs;atis patet, <lb/>quid de columnarum paralleli&longs;mo dicendum &longs;it. </s><s>Con&longs;tat autem <lb/>ex his ædificia in alti&longs;&longs;imis montibus con&longs;tituta habere parie<lb/>tes minùs à paralleli&longs;mo recedentes, &longs;i fuerint ad perpendicu<lb/>lum ædificati, quàm in locis depre&longs;&longs;ioribus: atque adeò, &longs;i duæ <lb/>columnæ eandem inter &longs;e po&longs;itionem &longs;ervantes de&longs;cenderent <lb/>cum &longs;ubjecto plano, ita ut alterutra columnarum illarum ad <lb/>perpendiculum de&longs;cenderet, reliqua demùm adeò inclinare<lb/>tur, ut caderet. </s>

<pb xlink:href="017/01/066.jpg" n="50"/><expan abbr="antiq.">antique</expan> 4128635: quarè &longs;i fiat ut terræ &longs;emidiameter 4128635 <lb/>ad altitudinem 60, ita di&longs;tantia parietum, aut turrium in imo <lb/>300, ad aliud, proveniet differentia, qua di&longs;tantia turrium in <lb/>&longs;ummo vertice &longs;uperat earum di&longs;tantiam in imo pede, & erit <lb/>partium (4359/1000000) unius pa&longs;&longs;us, quæ e&longs;t minor quàm 2/5 digiti: quis <lb/>autem parallelas non dixerit turres, quæ vix uno aut altero <lb/>hordei grano di&longs;tant à paralleli&longs;mo? </s><s>Quod &longs;i in tanta altitudine <lb/>atque di&longs;tantiâ di&longs;crimen hoc adeò exiguum e&longs;t, &longs;atis patet, <lb/>quid de columnarum paralleli&longs;mo dicendum &longs;it. </s><s>Con&longs;tat autem <lb/>ex his ædificia in alti&longs;&longs;imis montibus con&longs;tituta habere parie<lb/>tes minùs à paralleli&longs;mo recedentes, &longs;i fuerint ad perpendicu<lb/>lum ædificati, quàm in locis depre&longs;&longs;ioribus: atque adeò, &longs;i duæ <lb/>columnæ eandem inter &longs;e po&longs;itionem &longs;ervantes de&longs;cenderent <lb/>cum &longs;ubjecto plano, ita ut alterutra columnarum illarum ad <lb/>perpendiculum de&longs;cenderet, reliqua demùm adeò inclinare<lb/>tur, ut caderet. </s>

<s>Sed quàm inanem &longs;ibi &longs;truant &longs;olicitudinem, qui nimis exi<lb/>guè, & exiliter ad calculos revocant &longs;tructurarum perpendicu<lb/>la, &longs;atis indicant turres inclinatæ, quæ po&longs;t aliquot &longs;ecula con<lb/>&longs;i&longs;tunt citrà ullum ruinæ periculum, quamvis illam timeant <lb/>imperiti. </s><s>Duas habemus in Italiâ turres ob in&longs;ignem inclina<lb/>tionem con&longs;picuas; altera e&longs;t Bononiæ quadrata opere lateri<lb/>tio, altera Pi&longs;is rotunda ex albo marmore affabrè expolito, & <lb/>columnis 284 rite di&longs;po&longs;itis ornata. </s><s>Ædificari c&oelig;pit anno <lb/>1173 Germano quodam architecto, quem ab aliis Guillel<lb/>mum, ab aliis Joannem OE nipontanum dici reperio. </s><s>Rotunda <lb/>e&longs;t forma duplici muro concludente &longs;calas cochleæ in modum <lb/>ab imo ad &longs;ummum ductas: parietis cra&longs;&longs;ities e&longs;t cubitorum <lb/>6 1/3, turris altitudo cubitorum 78, ambitus in imo pede cubi<lb/>torum 80; unde colligitur diameter cubitorum ferè 25 1/2; incli<lb/>natio, &longs;eu intervallum inter ba&longs;im, & perpendiculum e&longs;t cu<lb/>bitorum 7 1/3, ut ex literis ad me inde datis habeo; quamvis <lb/>apud aliquos legerim tantùm cubitos 7, apud alios 6 1/2. </s><s>Factâ <lb/>ne fuerit illa inclinatio de indu&longs;triâ, an verò &longs;ub&longs;identibus fun<lb/>damentis, incertum e&longs;t. </s><s>Ego non facilè eo in illorum &longs;enten<lb/>tiam, qui id &longs;cribunt contigi&longs;&longs;e ex artificis imperitia, cui non <lb/>&longs;atis per&longs;pecta e&longs;&longs;et &longs;oli natura; tum quia fundamenta altitudi-

<pb n="51"/>nem habent, atque amplitudinem ingentem, quibus con<lb/>&longs;truendis annus &longs;olidus &longs;atis non fuit; tum quia nullam unquam <lb/>egit rimam, id quod &longs;ub&longs;idente &longs;olo rari&longs;&longs;imum e&longs;t; tum quia <lb/>potuit architectus excitari ad artis &longs;pecimen exhibendum à tur<lb/>ri Bononien&longs;i Gari&longs;end<gap/> excitatâ anno 1110. </s>

<pb xlink:href="017/01/067.jpg" n="51"/>nem habent, atque amplitudinem ingentem, quibus con<lb/>&longs;truendis annus &longs;olidus &longs;atis non fuit; tum quia nullam unquam <lb/>egit rimam, id quod &longs;ub&longs;idente &longs;olo rari&longs;&longs;imum e&longs;t; tum quia <lb/>potuit architectus excitari ad artis &longs;pecimen exhibendum à tur<lb/>ri Bononien&longs;i Gari&longs;endâ excitatâ anno 1110. </s>

<s>Turris Bononicn&longs;is altitudinem habet pedum Bonon. 130; <lb/>exteriùs inclinatur ped. 9, interiùs verò ped. 1, & paulo am<lb/>plius: muri cra&longs;&longs;ities in parte infimâ e&longs;t pedum 6 1/2, in &longs;upre<lb/>ma ped. 4; cava turris ped. 7. quare lateris longitudo e&longs;t ped. <lb/>20, & ambitus, quoniam quadrata e&longs;t, ped. 80. Ex his men<lb/>&longs;uris, quas in <emph type="italics"/>Bononïá Perlu<gap/>ratâ<emph.end type="italics"/> anno 1650 typis evulgatâ at<lb/>tulit Antonius Pauli Ma&longs;ini, turris &longs;pe<lb/>

<s>Turris Bononien&longs;is altitudinem habet pedum Bonon. 130; <lb/>exteriùs inclinatur ped. 9, interiùs verò ped. 1, & paulo am<lb/>plius: muri cra&longs;&longs;ities in parte infimâ e&longs;t pedum 6 1/2, in &longs;upre<lb/>ma ped. 4; cava turris ped. 7. quare lateris longitudo e&longs;t ped. <lb/>20, & ambitus, quoniam quadrata e&longs;t, ped. 80. Ex his men<lb/>&longs;uris, quas in <emph type="italics"/>Bononïá Perlu&longs;tratâ<emph.end type="italics"/> anno 1650 typis evulgatâ at<lb/>tulit Antonius Pauli Ma&longs;ini, turris &longs;pe<lb/>

<figure/><lb/>ciem exhibeo, & e&longs;t AB latus unum <lb/>ped. 20, BD inclinationis men&longs;ura <lb/>ped. 9. DC altitudo perpendicularis <lb/>ped.130; EB & AF ped. 6 1/2 cra&longs;&longs;ities <lb/>imi parietis, & CH ped. 4. cra&longs;&longs;ities <lb/>eju&longs;dem parietis EC exteriùs inclinati. </s><lb/><s>At quoniam inclinatio interior FI dici<lb/>tur e&longs;&longs;e ped.1, & paulo ampliùs, erit ID <lb/>paulo major ped.21; erecta autem ex I <lb/>perpendicularis dabit punctum G termi<lb/>num cra&longs;&longs;itiei muri AG in parte &longs;upre<lb/>mâ, & erit CG major ped. 21, cum &longs;it <lb/>æqualis ip&longs;i ID. </s><s>Quare fieri non pote&longs;t, <lb/>ut KG &longs;it ped. 4; quemadmodum HC; <lb/>alioquin e&longs;&longs;et CK &longs;altem ped.25, cum <lb/>ba&longs;is AB &longs;it tantum ped.20. </s><s>Hinc &longs;i li<lb/>ceat conjecturas per&longs;equi (quandoqui<lb/>dem veritatem a&longs;&longs;equi non potui, cum <lb/>non careat periculo a&longs;cen&longs;us per &longs;calas <lb/>ligneas à pluviis maximam partem cor<lb/>ruptas) exi&longs;timo AF majorem e&longs;&longs;e quàm <lb/>EB, hoc e&longs;t majorem pedibus 6 1/2, KG <lb/>verò minorem quam HC, ut turri &longs;ua <lb/>con&longs;tet Eurithmia; id quod obtineretur, &longs;i ID uno, aut alte<lb/>ro pede minor e&longs;&longs;et quàm AB, differentia enim inter ID, <lb/>& AB e&longs;&longs;et cra&longs;&longs;ities KG. </s><s>Et &longs;anè memini aliquando me au-

<figure id="id.017.01.067.1.jpg" xlink:href="017/01/067/1.jpg"/><lb/>ciem exhibeo, & e&longs;t AB latus unum <lb/>ped. 20, BD inclinationis men&longs;ura <lb/>ped. 9. DC altitudo perpendicularis <lb/>ped.130; EB & AF ped. 6 1/2 cra&longs;&longs;ities <lb/>imi parietis, & CH ped. 4. cra&longs;&longs;ities <lb/>eju&longs;dem parietis EC exteriùs inclinati. </s><lb/><s>At quoniam inclinatio interior FI dici<lb/>tur e&longs;&longs;e ped.1, & paulo ampliùs, erit ID <lb/>paulo major ped.21; erecta autem ex I <lb/>perpendicularis dabit punctum G termi<lb/>num cra&longs;&longs;itiei muri AG in parte &longs;upre<lb/>mâ, & erit CG major ped. 21, cum &longs;it <lb/>æqualis ip&longs;i ID. </s><s>Quare fieri non pote&longs;t, <lb/>ut KG &longs;it ped. 4; quemadmodum HC; <lb/>alioquin e&longs;&longs;et CK &longs;altem ped.25, cum <lb/>ba&longs;is AB &longs;it tantum ped.20. </s><s>Hinc &longs;i li<lb/>ceat conjecturas per&longs;equi (quandoqui<lb/>dem veritatem a&longs;&longs;equi non potui, cum <lb/>non careat periculo a&longs;cen&longs;us per &longs;calas <lb/>ligneas à pluviis maximam partem cor<lb/>ruptas) exi&longs;timo AF majorem e&longs;&longs;e quàm <lb/>EB, hoc e&longs;t majorem pedibus 6 1/2, KG <lb/>verò minorem quam HC, ut turri &longs;ua <lb/>con&longs;tet Eurithmia; id quod obtineretur, &longs;i ID uno, aut alte<lb/>ro pede minor e&longs;&longs;et quàm AB, differentia enim inter ID, <lb/>& AB e&longs;&longs;et cra&longs;&longs;ities KG. </s><s>Et &longs;anè memini aliquando me au-

<pb n="52"/>divi&longs;&longs;e &longs;upremam cra&longs;&longs;itiem muri oppo&longs;iti parti inclinatæ <lb/>non excedere integrum pedem. </s><s>Id autem valde opportu<lb/>num accidebat, ut longè faciliùs paries AFGK &longs;uâ mole <lb/>&longs;taret: neque enim ca&longs;u inclinatam fui&longs;&longs;e turrim dicere po<lb/>teris, quam con&longs;tat prope A&longs;inellam recti&longs;&longs;imam ideò fui&longs;&longs;e <lb/>conditam, ut multo clariùs appareret inclinatio: præterquam <lb/>quod inclinatio interior minor externâ &longs;atis o&longs;tendit muros <lb/>nunquam fui&longs;&longs;e parallolos. </s>

<pb xlink:href="017/01/068.jpg" n="52"/>divi&longs;&longs;e &longs;upremam cra&longs;&longs;itiem muri oppo&longs;iti parti inclinatæ <lb/>non excedere integrum pedem. </s><s>Id autem valde opportu<lb/>num accidebat, ut longè faciliùs paries AFGK &longs;uâ mole <lb/>&longs;taret: neque enim ca&longs;u inclinatam fui&longs;&longs;e turrim dicere po<lb/>teris, quam con&longs;tat prope A&longs;inellam recti&longs;&longs;imam ideò fui&longs;&longs;e <lb/>conditam, ut multo clariùs appareret inclinatio: præterquam <lb/>quod inclinatio interior minor externâ &longs;atis o&longs;tendit muros <lb/>nunquam fui&longs;&longs;e parallolos. </s>

<s>Porrò ut con&longs;tet ex huju&longs;modi inclinatione non magis <lb/>e&longs;&longs;e de ruinâ timendum, quàm &longs;i exactè perpendicularis e&longs;<lb/>&longs;et, examinemus, &longs;i placet, centrum gravitatis in turri Bo<lb/>nonien&longs;i; hinc enim facilis erit conjectura de cæteris. </s><s>Et <lb/>

<figure/><lb/>primò parietis maximè inclinati &longs;ectio <lb/>verticalis illum bifariam &longs;ecans ac tran<lb/>&longs;iens per centrum gravitatis &longs;it HCBE: <lb/>cujus latera parallela HC, EB bifariam <lb/>&longs;ecta in V & R jungantur rectâ VR, cu<lb/>jus longitudo inve&longs;tiganda e&longs;t, ut in eâ <lb/>definiatur punctum S centrum gravitatis, <lb/>ac innote&longs;cat utrum perpendicularis SX, <lb/>&longs;cilicet linea directionis cadat intra ba<lb/>&longs;im EB &longs;u&longs;tentantem. </s><s>Et ut à fractioni<lb/>bus minus incommodi &longs;ubeamus, liceat <lb/>a&longs;&longs;umere pedem in partes cente&longs;imas di<lb/>vi&longs;um. </s><s>Cum autem EB &longs;it ped. 6 1/2, &longs;emi&longs;<lb/>&longs;is RB e&longs;t ped. 3. 25″; & quia HC e&longs;t <lb/>ped. 4, VC e&longs;t ped. 200″. </s><s>Et ducatur <lb/>recta BV. </s>

<figure id="id.017.01.068.1.jpg" xlink:href="017/01/068/1.jpg"/><lb/>primò parietis maximè inclinati &longs;ectio <lb/>verticalis illum bifariam &longs;ecans ac tran<lb/>&longs;iens per centrum gravitatis &longs;it HCBE: <lb/>cujus latera parallela HC, EB bifariam <lb/>&longs;ecta in V & R jungantur rectâ VR, cu<lb/>jus longitudo inve&longs;tiganda e&longs;t, ut in eâ <lb/>definiatur punctum S centrum gravitatis, <lb/>ac innote&longs;cat utrum perpendicularis SX, <lb/>&longs;cilicet linea directionis cadat intra ba<lb/>&longs;im EB &longs;u&longs;tentantem. </s><s>Et ut à fractioni<lb/>bus minus incommodi &longs;ubeamus, liceat <lb/>a&longs;&longs;umere pedem in partes cente&longs;imas di<lb/>vi&longs;um. </s><s>Cum autem EB &longs;it ped. 6 1/2, &longs;emi&longs;<lb/>&longs;is RB e&longs;t ped. 3. 25″; & quia HC e&longs;t <lb/>ped. 4, VC e&longs;t ped. 200″. </s><s>Et ducatur <lb/>recta BV. </s>

<s>In triangulo BDC rectangulo datis BD, <lb/>inclinatione ped. 90′0′, & altitudine per<lb/>pendiculari CD ped. 130′0′, additis late<lb/>rum quadratis fit quadratum hypothenu<lb/>&longs;æ BC, quæ e&longs;t ped. 13031″. </s><s>Ex datis autem lateribus BD, <lb/>& DC invenitur angulus CBD gr. 88. 33′, cui æqualis e&longs;t <lb/>inter parallelas VC, BD alternus VCB: angulus verò CBR <lb/>gr. 91. 27′. </s>

<s>In triangulo VCB datis lateribus VC ped. 2.0′0′, CB <lb/>ped. 130. 31″, & angulo verticali VCB gr. 88. 33′, reperitur

<pb n="53"/>CVB gr. 90. 34′. 14″, & VBC gr. 0. 52′. 46″.. </s><s>Ex his autem <lb/>inve&longs;tigatur VB ped. 130. 26″. </s>

<pb xlink:href="017/01/069.jpg" n="53"/>CVB gr. 90. 34′. 14″, & VBC gr. 0. 52′. 46″.. </s><s>Ex his autem <lb/>inve&longs;tigatur VB ped. 130. 26″. </s>

<s>Quoniam autem angulus CBR notus erat gr. 91. 27′, &longs;i de<lb/>matur ex illo angulus VBC gr. 0. 52′. 46″. remanet VBR <lb/>gr. 90. 34′, 14″, æqualis angulo CVB alterno inter parallelas; <lb/>& nota &longs;unt latera illum con&longs;tituentia BR ped 3. 25″. & BV <lb/>ped. 130. 26″. </s><s>Ex quibus datis invenitur angulus BRV gr. 88. <lb/>0′. 2″, BVR gr. 1. 25′. 44″ & ba&longs;is VR ped. 130. 326‴. </s>

Line 565

<row><cell>CBD gr.88.33. m</cell><cell>1,15970,08429</cell><cell>Semi&longs;umma ang.</cell><cell>gr.44.42′.53″,-m</cell><cell>9,99567.51920</cell></row>

<row><cell></cell><cell></cell><cell>differentia</cell><cell>gr.43.17, 9

<row><cell/><cell/><cell>differentia</cell><cell>gr.43.17, 9

m</cell><cell>9,97399,93121</cell></row></table>

<s>Quod &longs;i paries exteriùs inclinatus etiam &longs;olitarius con&longs;i&longs;tere <lb/>po&longs;&longs;et, modò ea e&longs;&longs;et partium connexio, ut unum quid &longs;oli<lb/>dum conflarent, quia directionis linea intra ba&longs;im &longs;u&longs;tentan<lb/>tem cadit, & planum per extremam ba&longs;is lineam, & terræ cen<lb/>trum tran&longs;iens relinquit interiorem parietis partem præponde<lb/>rantem exteriori: quis po&longs;&longs;it de turris ruinâ dubitare, &longs;i eâdem <lb/>methodo deprehendat oppo&longs;iti parietis AG centrum gravita<lb/>tis e&longs;&longs;e in O, ac proinde comparatis reliquorum duorum pa<lb/>rietum centris gravitatum, totius turris centrum gravitatis e&longs;&longs;e <lb/>in intimis turris partibus? </s>

Line 577

<s>Id quod pueris ip&longs;is noti&longs;&longs;imum e&longs;t, <lb/>qui turriculas inclinatas architectantur ex buxeis orbiculis, <lb/>quibus in alveolo ludunt. </s>

<s>Et ut res i&longs;ta plani&longs;&longs;imè o&longs;tendatur, <lb/><figure id="fig1"/><lb/>&longs;it &longs;upra planum inclinatum AB, pa<lb/>rallelepipedum ligneum ID ita, ut <lb/>recta CE ad horizontem perpendicu<lb/>laris tran&longs;eat per centrum gravitatis: <lb/>con&longs;tat ex dictis cap.

<s>Et ut res i&longs;ta plani&longs;&longs;imè o&longs;tendatur, <lb/><figure id="id.017.01.070.1.jpg" xlink:href="017/01/070/1.jpg"/><lb/>&longs;it &longs;upra planum inclinatum AB, pa<lb/>rallelepipedum ligneum ID ita, ut <lb/>recta CE ad horizontem perpendicu<lb/>laris tran&longs;eat per centrum gravitatis: <lb/>con&longs;tat ex dictis cap.

8. futurum e&longs;&longs;e, <lb/>ut grave ID repat, non autem rote<lb/>tur, quia pars CED non præponderat parti CEI, &longs;iqui<lb/>dem po&longs;&longs;it de&longs;cendere per planum inclinatum; quod &longs;i à lap<lb/>&longs;u impediatur, &longs;ub&longs;i&longs;tet. </s>

Line 589

<s>Quare litteris ad P. Franci&longs;cum Mariam Grimaldum da<lb/>tis rogavi, ut pro eâ, quam ad res omnes conferre &longs;olebat, di<lb/>ligentiâ, accuratè men&longs;uras illas inquireret: hæc igitur ex ejus <lb/>re&longs;pon&longs;ione habui, quibus &longs;uperiùs dicta corrigenda &longs;unt; quæ <lb/>tamen expungere nolui, ut &longs;i lubeat, vulgarem opinionem &longs;e<lb/>qui valeas. </s>

<s>Extimus turris ambitus tam in imâ, quam in &longs;upremâ parte <lb/>æqualis e&longs;t, adeò ut oppo&longs;itæ facies parallelæ excurrant: &longs;in<lb/>gulorum autem laterum ad ba&longs;im latitudo e&longs;t ped. Bonon. 17. <lb/>unc. </s>

Line 605

<s>Cum autem pluviæ per hiantem, & patulum turris verticem <lb/>deciduæ &longs;calas corruperint, nec eò veniri po&longs;&longs;it, ut demi&longs;&longs;o <lb/>perpendiculo altitudo turris inve&longs;tigetur, &longs;ub&longs;idium peten<lb/>dum fuit ex Trigonometriâ, & ex proximâ turri A&longs;inellâ, cu<lb/>jus men&longs;uræ multiplici ob&longs;ervatione innotuerant. </s>

<s>Sit itaque <lb/>turris inclinata DC, &longs;uperioris autem podij <lb/><figure id="fig2"/><lb/>A&longs;inellæ altitudo EB ped.234 1/2, unde ob&longs;er<lb/>vatus e&longs;t angulus CEB gr. 18. 40′. </s>

<s>Sit itaque <lb/>turris inclinata DC, &longs;uperioris autem podij <lb/><figure id="id.017.01.071.1.jpg" xlink:href="017/01/071/1.jpg"/><lb/>A&longs;inellæ altitudo EB ped.234 1/2, unde ob&longs;er<lb/>vatus e&longs;t angulus CEB gr. 18. 40′. </s>

Line 617

<s>Ut igitur innote&longs;cat quæ&longs;i<lb/>ta altitudo, inveniatur in triangulo rectangu<lb/>lo CGE, ex datis latere CE ped. (117 7/12) & <lb/>angulo ob&longs;ervato CEG, gr.18.40′, latus EG <lb/>ped. (111 5/12). Jam verò &longs;i EG ped.(111 5/12) dematur <lb/>ex EB ped. 234 1/2, remanet altitudo GB, hoc e&longs;t CH, <lb/>ped. (123 1/12). </s>

<s>Demum ad inve&longs;tigandam turris inclinationem, applicito <lb/>ad punctum I perpendiculo ob&longs;ervatus e&longs;t angulus DIL <lb/>gr. 3. 10′.: cùm autem IL parallela &longs;it perpendiculari CH, erit <lb/>pariter angulus DCH gr.3.10′. </s>

Line 637

<s>BD autem e&longs;t ped. 6. unc.10, hoc e&longs;t ped.(6 10/12). </s>

<s>In Triangulo BDC rectangulo datis BD <lb/>ped. 6. (10/12), & altitudine perpendiculari CD <lb/>ped. (123 1/12), additis laterum quadratis fit qua<lb/>dratum hypothenu&longs;æ BC, quæ e&longs;t ped.123.27″. </s>

Line 705

<s>Tum fiat ut 17 ad 16; hoc e&longs;t duplum majoris EB cum mi<lb/>nore HC, ad duplum minoris HC cum majore EB, ita VS <lb/>ad SR, & erit SR ped.59.72″. </s>

<s>Ductâ igitur ex S centro gra-<pb pagenum="57"/>vitatis perpendiculari lineâ directionis SX, ex datis latere SR <lb/>ped. 59. 72″, & angulo VRX gr. 86, 35′, 43″, innote&longs;cit RX <lb/>ped. 3. 54″. </s>

<s>Ductâ igitur ex S centro gra-<pb xlink:href="017/01/073.jpg" pagenum="57"/>vitatis perpendiculari lineâ directionis SX, ex datis latere SR <lb/>ped. 59. 72″, & angulo VRX gr. 86, 35′, 43″, innote&longs;cit RX <lb/>ped. 3. 54″. </s>

Line 735

<s>Hîc autem qua&longs;i præteriens &longs;atisfaciam quærenti, cur lon<lb/>giores ha&longs;tas faciliùs, quàm breviores virgas digiti extremitate <lb/>&longs;u&longs;tineamus, quin cadant. </s>

<s>Quia nimirum minimus angulus <lb/>declinationis à perpendiculo &longs;tatim &longs;e prodit ha&longs;tæ vertice ad <lb/>partem unam &longs;ecedente, cui &longs;tatim occurrimus ha&longs;tæ calcem <lb/>manu transferentes, ac &longs;ub vertice collocantes: verùm quia fa<lb/>cilior ha&longs;tæ con&longs;i&longs;tentia innote&longs;cit etiam, quando à &longs;uppo&longs;itâ <lb/>manu calx ejus non movetur (nam &longs;i militarem &longs;ari&longs;&longs;am terræ <lb/>perpendiculariter in&longs;i&longs;tentem con&longs;titueris, potes te &longs;emel in gy<lb/>rum contorquere, & illam qua&longs;i perpendicularem recipere, id <lb/>quod in breviore ha&longs;tâ non obtinebis) alia e&longs;t ratio petenda <lb/>primùm ex dictis, quia &longs;cilicet longior ha&longs;ta, cæteris paribus, <lb/>minùs declinat à perpendiculo, ideóque difficiliùs de&longs;cendit; <pb pagenum="58"/>deinde que madmodum longiorem ha&longs;tam &longs;i in aquá agitaveris <lb/>majorem percipies re&longs;i&longs;tentiam, quàm &longs;i breviorem virgam in<lb/>citares; ita aërem variis &longs;emper motibus turbatum plus etiam <lb/>impedire de&longs;cen&longs;um longioris ha&longs;tæ cen&longs;endum e&longs;t, præ&longs;ertim <lb/>&longs;i in &longs;uperiore parte aër versùs unam, in inferiore autem versùs <lb/>aliam partem moveatur: id quod in breviore virgâ non accidit, <lb/>quam modicus aër contingit, nec pote&longs;t aut adeò re&longs;i&longs;tere di<lb/>vi&longs;ioni, aut adeò diver&longs;is motibus cieri. </s>

<s>Quia nimirum minimus angulus <lb/>declinationis à perpendiculo &longs;tatim &longs;e prodit ha&longs;tæ vertice ad <lb/>partem unam &longs;ecedente, cui &longs;tatim occurrimus ha&longs;tæ calcem <lb/>manu transferentes, ac &longs;ub vertice collocantes: verùm quia fa<lb/>cilior ha&longs;tæ con&longs;i&longs;tentia innote&longs;cit etiam, quando à &longs;uppo&longs;itâ <lb/>manu calx ejus non movetur (nam &longs;i militarem &longs;ari&longs;&longs;am terræ <lb/>perpendiculariter in&longs;i&longs;tentem con&longs;titueris, potes te &longs;emel in gy<lb/>rum contorquere, & illam qua&longs;i perpendicularem recipere, id <lb/>quod in breviore ha&longs;tâ non obtinebis) alia e&longs;t ratio petenda <lb/>primùm ex dictis, quia &longs;cilicet longior ha&longs;ta, cæteris paribus, <lb/>minùs declinat à perpendiculo, ideóque difficiliùs de&longs;cendit; <pb xlink:href="017/01/074.jpg" pagenum="58"/>deinde que madmodum longiorem ha&longs;tam &longs;i in aquá agitaveris <lb/>majorem percipies re&longs;i&longs;tentiam, quàm &longs;i breviorem virgam in<lb/>citares; ita aërem variis &longs;emper motibus turbatum plus etiam <lb/>impedire de&longs;cen&longs;um longioris ha&longs;tæ cen&longs;endum e&longs;t, præ&longs;ertim <lb/>&longs;i in &longs;uperiore parte aër versùs unam, in inferiore autem versùs <lb/>aliam partem moveatur: id quod in breviore virgâ non accidit, <lb/>quam modicus aër contingit, nec pote&longs;t aut adeò re&longs;i&longs;tere di<lb/>vi&longs;ioni, aut adeò diver&longs;is motibus cieri. </s>

<s>Hinc a&longs;ta longior <lb/>tardiùs de&longs;cen&longs;um molitur, & faciliùs &longs;u&longs;tinetur, quia major <lb/>aëris dividendi quantitas, ac motus var us, magis re&longs;i&longs;tit, & <lb/>datâ æqualitate motûs minùs declinat à perpendiculo. <lb/><gap desc="hr tag"/></s>

<s>Hinc a&longs;ta longior <lb/>tardiùs de&longs;cen&longs;um molitur, & faciliùs &longs;u&longs;tinetur, quia major <lb/>aëris dividendi quantitas, ac motus varius, magis re&longs;i&longs;tit, & <lb/>datâ æqualitate motûs minùs declinat à perpendiculo. <lb/><gap desc="hr tag"/></s>

<s><emph type="center"/>CAPUT X.<emph.end type="center"/></s>

Line 747

<s>Et &longs;anè &longs;i planities in &longs;ummo montis jugo con<lb/>&longs;ideretur, certum e&longs;t illam e&longs;&longs;e plurium &longs;tructurarum ca<lb/>pacem, quàm &longs;ubjectum planum in &longs;uperficie globi ter<lb/>re&longs;tris: Quemadmodum enim &longs;uperficies &longs;phæræ majoris <lb/>plura capit ædificia, quàm minor, ita etiam &longs;phærarum <lb/>inæqualium partes &longs;imiles inæqualis &longs;unt capacitatis: Con&longs;tat <lb/>autem planitiem in fummo monte pertinere ad &longs;phæram <lb/>majorem, quàm pertineat &longs;imilis planities illi &longs;ubjecta; ac <lb/>proinde & amplior e&longs;t, & magis capax. </s>

<s>Harum verò pla<lb/>nitierum differentia ea erit, quæ e&longs;t quadratorum di&longs;tan<lb/>tiarum à centro terræ: quòd &longs;i quadratorum huju&longs;modi <lb/>differentia exigua &longs;it & contemnenda, eo quod ad illam <lb/>quadratum &longs;emidiametri terræ habeat nimis magnam ratio<lb/>nem; planitierum pariter differentia fugiet omnem &longs;en&longs;um. <pb pagenum="59"/>Sit terræ &longs;emidiameter CS, altitudo au<lb/><figure id="fig3"/><lb/>tem montis SR, in cujus vertice &longs;it pla<lb/>nities RH, cui &longs;imilis e&longs;t in &longs;uperficie <lb/>globi terreni planities SO illi parallela: <lb/>hæ autem planities &longs;imiles habent, per <lb/>20. lib.

<s>Harum verò pla<lb/>nitierum differentia ea erit, quæ e&longs;t quadratorum di&longs;tan<lb/>tiarum à centro terræ: quòd &longs;i quadratorum huju&longs;modi <lb/>differentia exigua &longs;it & contemnenda, eo quod ad illam <lb/>quadratum &longs;emidiametri terræ habeat nimis magnam ratio<lb/>nem; planitierum pariter differentia fugiet omnem &longs;en&longs;um. <pb xlink:href="017/01/075.jpg" pagenum="59"/>Sit terræ &longs;emidiameter CS, altitudo au<lb/><figure id="id.017.01.075.1.jpg" xlink:href="017/01/075/1.jpg"/><lb/>tem montis SR, in cujus vertice &longs;it pla<lb/>nities RH, cui &longs;imilis e&longs;t in &longs;uperficie <lb/>globi terreni planities SO illi parallela: <lb/>hæ autem planities &longs;imiles habent, per <lb/>20. lib.

6. duplicatam Rationem laterum <lb/>RI, SL, hoc e&longs;t, per 4. lib.

Line 761

<s>Non tamen continuò major dicenda <lb/>e&longs;t capacitas, quæ plura aut ampliora recipiat ædificia; ni&longs;i <lb/>mons ad ingentem altitudinem a&longs;cendat; tunc enim perpendi<lb/>cula non &longs;unt inter &longs;e parallela, propter in&longs;ignem eorum <lb/>di&longs;tantiam. </s>

<s>Nam &longs;i &longs;uper clivo AB <lb/>&longs;it &longs;tructura AL, cujus parietes per<lb/><figure id="fig4"/><lb/>pendiculares, &longs;int etiam paralleli <lb/>LB, DA, illi non magis inter &longs;e <lb/>di&longs;tant, quàm &longs;i &longs;uper plano hori<lb/>zontali NB fui&longs;&longs;ent excitati: quic<lb/>quid &longs;it, quod, &longs;icut linea AB ma<lb/>jor e&longs;t quàm NB, ita planum incli<lb/>natum majus &longs;it plano horizontali. </s>

<s>Nam &longs;i &longs;uper clivo AB <lb/>&longs;it &longs;tructura AL, cujus parietes per<lb/><figure id="id.017.01.075.2.jpg" xlink:href="017/01/075/2.jpg"/><lb/>pendiculares, &longs;int etiam paralleli <lb/>LB, DA, illi non magis inter &longs;e <lb/>di&longs;tant, quàm &longs;i &longs;uper plano hori<lb/>zontali NB fui&longs;&longs;ent excitati: quic<lb/>quid &longs;it, quod, &longs;icut linea AB ma<lb/>jor e&longs;t quàm NB, ita planum incli<lb/>natum majus &longs;it plano horizontali. </s>

<lb/><s>Non igitur plures aut ampliores &longs;tructuras recipit clivus collis, <lb/>quàm &longs;ubjectum planum horizontale. </s>

<s>Quod verò de &longs;tructuris <lb/>dicitur, de cæteris quoque intelligendum e&longs;t, quæ perpendi<lb/>cularia in&longs;i&longs;tunt, & &longs;patium implent; at &longs;i ita &longs;e habeant, ut <pb pagenum="60"/>perpendicularia non in&longs;i&longs;tant, certum e&longs;t plures aut longiores <lb/>homines jacere po&longs;&longs;e in clivo AB, quos non capit planum NB: <lb/>vel &longs;i in clivo &longs;e minùs invicem impediant, tunc plura huju&longs;<lb/>modi corpora in colle e&longs;&longs;e po&longs;&longs;unt quàm in planitie: &longs;i enim ra<lb/>mi arboris inferioris re&longs;pondeant trunco &longs;uperioris, certum e&longs;t <lb/>quod multò viciniores e&longs;&longs;e po&longs;&longs;unt arbores, quàm in planitie, <lb/>ubi rami &longs;e vici&longs;&longs;im impedientes majorem po&longs;tulant truncorum <lb/>di&longs;tantiam; ac proinde etiam multo plures arbores intra ea&longs;<lb/>dem parallelas erunt. </s>

<s>Quod verò de &longs;tructuris <lb/>dicitur, de cæteris quoque intelligendum e&longs;t, quæ perpendi<lb/>cularia in&longs;i&longs;tunt, & &longs;patium implent; at &longs;i ita &longs;e habeant, ut <pb xlink:href="017/01/076.jpg" pagenum="60"/>perpendicularia non in&longs;i&longs;tant, certum e&longs;t plures aut longiores <lb/>homines jacere po&longs;&longs;e in clivo AB, quos non capit planum NB: <lb/>vel &longs;i in clivo &longs;e minùs invicem impediant, tunc plura huju&longs;<lb/>modi corpora in colle e&longs;&longs;e po&longs;&longs;unt quàm in planitie: &longs;i enim ra<lb/>mi arboris inferioris re&longs;pondeant trunco &longs;uperioris, certum e&longs;t <lb/>quod multò viciniores e&longs;&longs;e po&longs;&longs;unt arbores, quàm in planitie, <lb/>ubi rami &longs;e vici&longs;&longs;im impedientes majorem po&longs;tulant truncorum <lb/>di&longs;tantiam; ac proinde etiam multo plures arbores intra ea&longs;<lb/>dem parallelas erunt. </s>

<s>Sic plures homines e&longs;&longs;e po&longs;&longs;unt in gradi<lb/>bus amphitheatri, quàm in &longs;ubjecto plano, quia graciliores, <lb/>partes &longs;uperiorum re&longs;pondent cra&longs;&longs;ioribus inferiorum, & &longs;e <lb/>minùs invicem impedientes minus relinquunt &longs;patij vacui: <lb/>quod &longs;i non homines, &longs;ed parallelepipeda, &longs;tatueres in gradi<lb/>bus, non plura &longs;tatui in iis po&longs;&longs;ent, quàm in planâ areâ gradi<lb/>bus &longs;ubjectâ. </s>

Line 773

<s>Ponamus enim per<lb/>pendicula GC, & OC jam non e&longs;&longs;e parallela, eamque e&longs;&longs;e <lb/>altitudinem KG, ut planum per G tran&longs;iens horizonti <lb/>parallelum majus &longs;it plano per O intra eadem perpendicu<lb/>la intercepto, erit quidem capacitas plani inclinati GOLF <lb/>æqualis capacitati &longs;ubjecti plani EKOL: at ulteriùs a&longs;cen<lb/>dendo capacitas FGMR non erit æqualis capacitati plani <lb/>SK continuati cum priore plano EO, &longs;ederit major, quip<lb/>pe quæ æqualis e&longs;t capacitati plani VG; e&longs;t autem pla<lb/>num VG ad planum &longs;imile SK, ut quadratum GC ad <lb/>quadratum KC: major igitur e&longs;t totius clivi ML capacitas, <lb/>quàm planitiei SO. </s>

<s>Et ut res apertius con&longs;tet, quandoquidem clivi alti&longs;<lb/>&longs;imorum montium, &longs;i eandem &longs;ervent inclinationem, non <lb/>&longs;unt ab imo pede ad &longs;ummum jugum æquabili, & conti<lb/>nuo ductu exten&longs;i, Sit terræ centrum H, & &longs;uperficies <pb pagenum="61"/>AD; cujus arcus dividatur in par<lb/><figure id="fig5"/><lb/>tes AB, BC, CD æquales, ita ut <lb/>&longs;inguli arcus pro rectiâ lineâ, & &longs;u<lb/>perficies pro plano horizontali <lb/>Phy&longs;icè u&longs;urpari po&longs;&longs;int; & tunc <lb/>&longs;olùm intelligatur mutari horizon, <lb/>quando ex A jam venerit in B, <lb/>deinde in C &c. </s>

<s>Et ut res apertius con&longs;tet, quandoquidem clivi alti&longs;<lb/>&longs;imorum montium, &longs;i eandem &longs;ervent inclinationem, non <lb/>&longs;unt ab imo pede ad &longs;ummum jugum æquabili, & conti<lb/>nuo ductu exten&longs;i, Sit terræ centrum H, & &longs;uperficies <pb xlink:href="017/01/077.jpg" pagenum="61"/>AD; cujus arcus dividatur in par<lb/><figure id="id.017.01.077.1.jpg" xlink:href="017/01/077/1.jpg"/><lb/>tes AB, BC, CD æquales, ita ut <lb/>&longs;inguli arcus pro rectiâ lineâ, & &longs;u<lb/>perficies pro plano horizontali <lb/>Phy&longs;icè u&longs;urpari po&longs;&longs;int; & tunc <lb/>&longs;olùm intelligatur mutari horizon, <lb/>quando ex A jam venerit in B, <lb/>deinde in C &c. </s>

<s>Si igitur &longs;it pla<lb/>num inclinatum AE, ubi venerit <lb/>in E punctum perpendiculi HB <lb/>producti, non pote&longs;t rectâ progre<lb/>di, quin mutet inclinationem &longs;upra horizontem novum, ad <lb/>quem venit; quare ut &longs;ervetur &longs;imilis inclinatio, deflectit in EF, <lb/>& e&longs;t angulus HEF æqualis angulo HAE cui demum ubi ve<lb/>nerit in F, debet fieri æqualis angulus HEG. </s>

Line 789

<s>Eademque e&longs;to de cæteris <lb/>ratio. </s>

<s>Hinc manife&longs;tum e&longs;t non omninò in univer&longs;um vera e&longs;&longs;e, <lb/>quæ pa&longs;&longs;im dicuntur de æquali capacitate collium, & planitiei <lb/>&longs;ubjectæ, ni&longs;i hæc certis limitibus circum&longs;cribantur; videlicet <lb/>&longs;i &longs;ermo &longs;it de iis quæ tantùm perpendiculariter in&longs;i&longs;tunt, & <pb pagenum="62"/>intrà illud &longs;patium, ac in eá altitudine, ubi perpendiculorum <lb/>convergentia adeò exigua e&longs;t, ut evane&longs;cat. </s>

<s>Hinc manife&longs;tum e&longs;t non omninò in univer&longs;um vera e&longs;&longs;e, <lb/>quæ pa&longs;&longs;im dicuntur de æquali capacitate collium, & planitiei <lb/>&longs;ubjectæ, ni&longs;i hæc certis limitibus circum&longs;cribantur; videlicet <lb/>&longs;i &longs;ermo &longs;it de iis quæ tantùm perpendiculariter in&longs;i&longs;tunt, & <pb xlink:href="017/01/078.jpg" pagenum="62"/>intrà illud &longs;patium, ac in eá altitudine, ubi perpendiculorum <lb/>convergentia adeò exigua e&longs;t, ut evane&longs;cat. </s>

<s>Cæterùm &longs;atis <lb/>mihi videor o&longs;tendi&longs;&longs;e fieri po&longs;&longs;e, ut clivus aliquis plures <lb/>&longs;tructuras recipere po&longs;&longs;it, quàm &longs;uperficies &longs;phærica globi illi <lb/>re&longs;pondens. </s>

Line 807

<s>Quandoquidem &longs;ive con&longs;i&longs;tentium quie<lb/>tem, &longs;ivè gradientium motum, &longs;ivè reclinantium &longs;e &longs;e inflexio<lb/>nem con&longs;ideres, miram naturæ artem intelliges, quâ præcavit, <lb/>ne corpus ingenitâ gravitate delatum præceps caderet. </s>

<s>Id au<lb/>tem a&longs;&longs;ecuta e&longs;t motus ita di&longs;ponendo, ut linea directionis nun-<pb pagenum="63"/>quam caderet extrà ba&longs;im &longs;u&longs;tentationis, ni&longs;i fortè in cur&longs;u, in <lb/>quo tamen &longs;atis con&longs;ultum e&longs;t animalis incolumitati, dum ab <lb/>anteriore pede, ubi terram attigerit, retinetur, ne ulteriùs <lb/>de&longs;cendat. </s>

<s>Id au<lb/>tem a&longs;&longs;ecuta e&longs;t motus ita di&longs;ponendo, ut linea directionis nun-<pb xlink:href="017/01/079.jpg" pagenum="63"/>quam caderet extrà ba&longs;im &longs;u&longs;tentationis, ni&longs;i fortè in cur&longs;u, in <lb/>quo tamen &longs;atis con&longs;ultum e&longs;t animalis incolumitati, dum ab <lb/>anteriore pede, ubi terram attigerit, retinetur, ne ulteriùs <lb/>de&longs;cendat. </s>

<s>Ba&longs;is autem &longs;u&longs;tentationis non &longs;unt &longs;oli pedes, &longs;ed totum <lb/>illud &longs;patium interceptum à lineis pedum extremitates jun<lb/>gentibus; &longs;ic in quadrupedibus linea directionis debet cadere <lb/>intrà &longs;patium comprehen&longs;um lineis, quæ jungunt extrema <lb/>pedum terram contingentium, ut po&longs;&longs;it animal con&longs;i&longs;tere. </s>

Line 819

<lb/><s>Cum autem difficillimum &longs;it diutiùs con&longs;i&longs;tere ita, ut centrum <lb/>gravitatis &longs;emper immineat funi, ideò funambuli, vel ha&longs;tam <lb/>plumbeis laminis gravem in extremitatibus manu tenent, vel <lb/>brachiis expan&longs;is &longs;e librant, ut ha&longs;tam vel brachia extenden<lb/>tes in partem oppo&longs;itam ei, in quam gravitas inclinat, cen<lb/>trum gravitatis con&longs;tituatur in puncto, quod immineat funi <lb/>&longs;uitentanti. </s>

<s>Hinc oritur difficultas con&longs;i&longs;tendi, quam expe<lb/>riuntur grallatores; cum enim grallæ exiguâ &longs;ui parte tangant <lb/>terram, e&longs;t qua&longs;i linea, in qua fit &longs;u&longs;tentatio, extra quam fa<lb/>cilè cadit linea directionis: ideò tertium ge&longs;tant baculum, cui <pb pagenum="64"/>innitantur, quoties quie&longs;cere voluerint, lineâ directionis ca<lb/>dente intrà &longs;patium triangulare comprehen&longs;um à grallis, & <lb/>baculo. </s>

<s>Hinc oritur difficultas con&longs;i&longs;tendi, quam expe<lb/>riuntur grallatores; cum enim grallæ exiguâ &longs;ui parte tangant <lb/>terram, e&longs;t qua&longs;i linea, in qua fit &longs;u&longs;tentatio, extra quam fa<lb/>cilè cadit linea directionis: ideò tertium ge&longs;tant baculum, cui <pb xlink:href="017/01/080.jpg" pagenum="64"/>innitantur, quoties quie&longs;cere voluerint, lineâ directionis ca<lb/>dente intrà &longs;patium triangulare comprehen&longs;um à grallis, & <lb/>baculo. </s>

<s>Hîc autem maximè &longs;e prodit naturæ providentia in tam va<lb/>riâ pedum conformatione, ut ad &longs;u&longs;tentandum idonei e&longs;&longs;ent: <lb/>quadrupedibus &longs;iquidem non adcò amplos pedes tribuit, quia <lb/>ex eorum inter &longs;e di&longs;tantiâ plurimum &longs;patium intercipitur, cui <lb/>immineat centrum gravitatis: bipedibus verò latiores tribuit <lb/>pedes, quâ parte timeri potuit ca&longs;us: &longs;ic quia ex duorum cru<lb/>rum modicâ divaricatione non facilè periculum erat cadendi <lb/>in alterutrum latus, ideò humanis pedibus minorem dedit la<lb/>titudinem, quàm longitudinem; hanc verò non in æquas <lb/>di&longs;tribuit partes, &longs;ed minimam calci (præterquam in Scauris, <lb/>quos pravis fultos male talis appellat Horatius, talis &longs;cilicet <lb/>extantioribus) maximam anteriori parti conce&longs;&longs;it, ne impetu <lb/>per motum concepto tran&longs;latum centrum gravitatis in anterio<lb/>ra tran&longs;iliret ba&longs;im &longs;u&longs;tentationis. </s>

Line 829

<s>Eandem ob cau&longs;am an&longs;eres, & anates, quæ <lb/>multâ carne abundant, & amplo &longs;unt pectore, alternâ qua<lb/>dam in dextrum, & &longs;ini&longs;trum latus inclinatione gradiuntur, <lb/>ideóque ampliores habent palmas, ut citrà cadendi periculum <lb/>centrum gravitatis faciliùs vel immineat pedi &longs;u&longs;tentanti, vel <lb/>minimùm ab eo declinet, ne majore, quàm par &longs;it, impetu <lb/>de&longs;cendens corpus & anteriori pedi incumbens, tibiæ mu&longs;cu<lb/>los, & tendines lædat. </s>

<s>Aves verò, quæ &longs;ubtilioribus ramu&longs;cu<lb/>lis in&longs;ident non palmipedes &longs;unt, &longs;ed digitatæ (palmæ enim <lb/>avibus amphibiis ad natandum poti&longs;&longs;imum datæ videntur) ut <lb/>ramis tenaciùs inhæreant; quæ præterquàm quod exiguæ &longs;unt <lb/>gravitatis, facilè &longs;e &longs;i&longs;tunt in lineâ directionis, quæ cadat in <lb/>ramu&longs;culum, cui in&longs;i&longs;tunt, majore, vel minore angulo, quem <pb pagenum="65"/>faciunt tibiæ cum coxâ; ideò ubi ramum arripuerint, &longs;ub&longs;ul<lb/>tantes &longs;e librant, ramumque arctè apprehentes prohibent, ne <lb/>repentino ca&longs;u circumagantur à centro gravitatis nondum im<lb/>minente ba&longs;i &longs;u&longs;tentationis. </s>

<s>Aves verò, quæ &longs;ubtilioribus ramu&longs;cu<lb/>lis in&longs;ident non palmipedes &longs;unt, &longs;ed digitatæ (palmæ enim <lb/>avibus amphibiis ad natandum poti&longs;&longs;imum datæ videntur) ut <lb/>ramis tenaciùs inhæreant; quæ præterquàm quod exiguæ &longs;unt <lb/>gravitatis, facilè &longs;e &longs;i&longs;tunt in lineâ directionis, quæ cadat in <lb/>ramu&longs;culum, cui in&longs;i&longs;tunt, majore, vel minore angulo, quem <pb xlink:href="017/01/081.jpg" pagenum="65"/>faciunt tibiæ cum coxâ; ideò ubi ramum arripuerint, &longs;ub&longs;ul<lb/>tantes &longs;e librant, ramumque arctè apprehentes prohibent, ne <lb/>repentino ca&longs;u circumagantur à centro gravitatis nondum im<lb/>minente ba&longs;i &longs;u&longs;tentationis. </s>

<s>Verùm quoniam ad aves delap&longs;us &longs;um, prætereundus non <lb/>e&longs;t u&longs;us centri gravitatis involatu; quia enim avis dum alis <lb/>aërem verberans in volatu &longs;e librat atque &longs;u&longs;pendit, ita alas <lb/>debet extendere, ut centrum gravitatis exi&longs;tat intra illud <lb/>alarum &longs;patium, in quo exercetur &longs;u&longs;tentatio; ideò &longs;i vo<lb/>luerit ad &longs;uperiora volatum dirigere, alas in anteriora ver<lb/>&longs;us caput extendit, ut centro gravitatis in po&longs;terioribus re<lb/>licto, ac deor&longs;um præponderante, caput &longs;ur&longs;um dirigatur: <lb/>contra verò, ut motum deor&longs;um dirigat, alas retrahit, ut <lb/>caput præponderet, ac deor&longs;um feratur. </s>

Line 837

<s>Infinitum e&longs;&longs;et &longs;ingulos animalium motus per&longs;equi, in qui<lb/>bus centri gravitatis ratio habetur; &longs;atis fuerit ob&longs;erva&longs;&longs;e nos <lb/>ex declivi loco de&longs;cendentes non in&longs;i&longs;tere plantis pedum ad <lb/>angulos rectos; &longs;ed paululum in po&longs;teriora inclinari; contra <lb/>verò a&longs;cendentes jugum acclive curvari in anteriora; ut nimi<lb/>rum linea directionis cadat intrà &longs;patium, cui pedes in&longs;i&longs;tunt; <lb/>extra quod illa &longs;i caderet, nec alteri fulcro inniteremur, quod <lb/>unà cum pedibus includeret ba&longs;im &longs;u&longs;tentationis, nece&longs;&longs;ariò <lb/>nobis cadendum e&longs;&longs;et. </s>

<s>Quòd &longs;i quis onus habens dor&longs;o impo<lb/>&longs;itum in montosâ regione iter habeat, multò magis curvari de<lb/>bet, cum a&longs;cendit, ut pedibus immineat centrum gravitatis <lb/>compo&longs;itæ ex corpore, & ex onere: quare &longs;apienti&longs;&longs;imè ru&longs;tici <lb/>aliqui in Alpibus, quæ Germaniam ab Italiá di&longs;terminant, ar<lb/>culam ex levibus a&longs;&longs;erculis, & virgulis compactam habent, cui <lb/>onera immittunt, ba&longs;is autem arculæ, quæ ge&longs;tantis corpori <lb/>adhæret, imitatur Re&longs;c Hebraicum, ita ut pars quidem dor<lb/>&longs;o, pars autem capiti incumbat: unde fit, ut centrum gravita-<pb pagenum="66"/>tis compo&longs;itæ minùs recedat à medio humani corporis, adeó<lb/>que faciliùs etiam motus perficiatur, quin opus &longs;it tantâ corpo<lb/>ris inflexione. </s>

<s>Quòd &longs;i quis onus habens dor&longs;o impo<lb/>&longs;itum in montosâ regione iter habeat, multò magis curvari de<lb/>bet, cum a&longs;cendit, ut pedibus immineat centrum gravitatis <lb/>compo&longs;itæ ex corpore, & ex onere: quare &longs;apienti&longs;&longs;imè ru&longs;tici <lb/>aliqui in Alpibus, quæ Germaniam ab Italiá di&longs;terminant, ar<lb/>culam ex levibus a&longs;&longs;erculis, & virgulis compactam habent, cui <lb/>onera immittunt, ba&longs;is autem arculæ, quæ ge&longs;tantis corpori <lb/>adhæret, imitatur Re&longs;c Hebraicum, ita ut pars quidem dor<lb/>&longs;o, pars autem capiti incumbat: unde fit, ut centrum gravita-<pb xlink:href="017/01/082.jpg" pagenum="66"/>tis compo&longs;itæ minùs recedat à medio humani corporis, adeó<lb/>que faciliùs etiam motus perficiatur, quin opus &longs;it tantâ corpo<lb/>ris inflexione. </s>

<s>Simile quid experimur, &longs;i quis à &longs;ede &longs;urgat; <lb/>caput enim cum thorace in anteriora reclinat; pedes verò in <lb/>po&longs;teriora versùs &longs;edem retrahit, ut nimirum pedes &longs;upponan<lb/>tur centro gravitatis, quod primùm imminet parti digitis proxi<lb/>mæ, deinde corpore erecto linea directionis versùs talos rece<lb/>dit. </s>

Line 851

<s>Caput hoc <lb/>claudo explicatione quæ&longs;tionis, qua quæritur, quantò ma<lb/>jus &longs;patium percurrat caput quàm pedes; certum &longs;iquidem <lb/>e&longs;t hominem in lineâ directionis imminere &longs;emper terræ <lb/>centro; ac proinde &longs;i pedes ex B venerunt in C, caput ex <lb/>F in E tran&longs;latum e&longs;t per arcum FE majorem arcu BC. </s>

<lb/><s>Cum enim uterque arcus BC, FE &longs;ubtendatur eidem an<lb/>gulo ad centrum, &longs;unt &longs;imiles, & ut arcus BC ad totam <lb/>&longs;uam peripheriam, ita arcus FE ad &longs;uam peripheriam; &longs;unt <pb pagenum="67"/>autem peripheriæ inter &longs;e ut &longs;emi<lb/><figure id="fig6"/><lb/>diametri, igitur BC ad FE, ut TB, <lb/>ad TF; atqui TF major e&longs;t quàm <lb/>TB, igitur & FE arcus major arcu <lb/>BC: ab&longs;cindatur FI, quæ ex hypo<lb/>the&longs;i intelligatur æqualis ip&longs;i BC; <lb/>e&longs;t igitur ut TB ad TF, ita FI ad <lb/>FE, & dividendo ut TB ad BF <lb/>ita FI, hoc e&longs;t BC, ad IE. </s>

<lb/><s>Cum enim uterque arcus BC, FE &longs;ubtendatur eidem an<lb/>gulo ad centrum, &longs;unt &longs;imiles, & ut arcus BC ad totam <lb/>&longs;uam peripheriam, ita arcus FE ad &longs;uam peripheriam; &longs;unt <pb xlink:href="017/01/083.jpg" pagenum="67"/>autem peripheriæ inter &longs;e ut &longs;emi<lb/><figure id="id.017.01.083.1.jpg" xlink:href="017/01/083/1.jpg"/><lb/>diametri, igitur BC ad FE, ut TB, <lb/>ad TF; atqui TF major e&longs;t quàm <lb/>TB, igitur & FE arcus major arcu <lb/>BC: ab&longs;cindatur FI, quæ ex hypo<lb/>the&longs;i intelligatur æqualis ip&longs;i BC; <lb/>e&longs;t igitur ut TB ad TF, ita FI ad <lb/>FE, & dividendo ut TB ad BF <lb/>ita FI, hoc e&longs;t BC, ad IE. </s>

<s>Fiat ita<lb/>que ut TB &longs;emidiameter terræ mil<lb/>liar. </s>

Line 883

<s>71, ubi mihi tribuit &longs;ententiam maxi<lb/>mè ab&longs;urdam, qua&longs;i in mechanicâ meâ manu&longs;criptâ (quam <lb/>&longs;cilicet anno 1653. Romæ auditoribus meis tradidi) docuerim <lb/>exce&longs;&longs;um motûs capitis &longs;upra motum pedum <emph type="italics"/>e&longs;&longs;e valde modi<lb/>cum, nimirum &longs;olum pedum &longs;ex cum dimidio, adeò ut in milliaribus<emph.end type="italics"/><lb/>500 <emph type="italics"/>tantum reperiatur exce&longs;&longs;us<emph.end type="italics"/> (15/17) <emph type="italics"/>unius pedis, po&longs;itá hominis altitu<lb/>dine pedum &longs;ex, & terræ ambitu milliariorum<emph.end type="italics"/> 21600. Hæ&longs;i pri<lb/>mùm attonitus, meamque o&longs;citantiam admiratus illicò anti<lb/>quàs illas meas &longs;chedulas per&longs;crutari c&oelig;pi; & nihil minus in<lb/>veniens errorem Typographo, qui pro pa&longs;&longs;ibus pedes &longs;uppo-<pb pagenum="68"/>&longs;uerit, tribuendum cen&longs;ui&longs;&longs;em, ni&longs;i Author ip&longs;e modicum il<lb/>lum exce&longs;&longs;um pedum &longs;ex cum dimidio redargueret. </s>

<s>71, ubi mihi tribuit &longs;ententiam maxi<lb/>mè ab&longs;urdam, qua&longs;i in mechanicâ meâ manu&longs;criptâ (quam <lb/>&longs;cilicet anno 1653. Romæ auditoribus meis tradidi) docuerim <lb/>exce&longs;&longs;um motûs capitis &longs;upra motum pedum <emph type="italics"/>e&longs;&longs;e valde modi<lb/>cum, nimirum &longs;olum pedum &longs;ex cum dimidio, adeò ut in milliaribus<emph.end type="italics"/><lb/>500 <emph type="italics"/>tantum reperiatur exce&longs;&longs;us<emph.end type="italics"/> (15/17) <emph type="italics"/>unius pedis, po&longs;itá hominis altitu<lb/>dine pedum &longs;ex, & terræ ambitu milliariorum<emph.end type="italics"/> 21600. Hæ&longs;i pri<lb/>mùm attonitus, meamque o&longs;citantiam admiratus illicò anti<lb/>quàs illas meas &longs;chedulas per&longs;crutari c&oelig;pi; & nihil minus in<lb/>veniens errorem Typographo, qui pro pa&longs;&longs;ibus pedes &longs;uppo-<pb xlink:href="017/01/084.jpg" pagenum="68"/>&longs;uerit, tribuendum cen&longs;ui&longs;&longs;em, ni&longs;i Author ip&longs;e modicum il<lb/>lum exce&longs;&longs;um pedum &longs;ex cum dimidio redargueret. </s>

<s>Quare <lb/>contingere facile potuit, ut ille, qui tunc Romæ degebat, ex <lb/>aliquo manu&longs;cripto codice meam &longs;ententiam re&longs;cribens, ubi <lb/>men&longs;uram hanc pedibus definiebam, brevitatis ergo ad pa&longs;<lb/>&longs;us revocaverit, quam litera P notatam demùm pro pedibus &longs;it <lb/>interpretatus. </s>

Line 899

5. hæc peripheria æqualis e&longs;t illi exce&longs;&longs;ui periphe<lb/>riæ majoris. </s>

<s>Cum itaque Ratio diametri ad peripheriam &longs;it ut <lb/>7 ad 22, &longs;eu ut 113 ad 355, fiat ut Radius 7 ad peripheriam <lb/>44, &longs;eu ut 113 ad 710, ita BF altitudo ped. 6. ad ped. 37. <lb/>unc.8: qui numerus con&longs;entit cùm &longs;uperiore. <pb pagenum="69"/><gap desc="hr tag"/></s>

Line 919

<s>Quoniam verò huc illuc pa&longs;&longs;im tran&longs;latis corpori<lb/>bus, terra nunc in hanc, nunc in illam partem moveretur, ut <lb/>proinde qua&longs;i trepidaret; hinc factus e&longs;t quæ&longs;tioni locus, an <lb/>tellus moveatur motu trepidationis; quicquid &longs;it an motus i&longs;te <lb/>&longs;ub &longs;en&longs;um cadat, nec ne. </s>

<s>Terram univer&longs;am & &longs;ingulas cjus partes &longs;uâ gravitate re<lb/>pugnare, ne &longs;ur&longs;um moveantur, certum e&longs;t; at univer&longs;i cen<lb/>trum occupare, toti quidem elemento gravi&longs;&longs;imo convenit, &longs;ed <lb/>non partibus &longs;ingulis: neque enim gravitas e&longs;t appetitus &longs;ub<lb/>&longs;i&longs;tendi in centro, quem natura non &longs;atis aptè gravibus &longs;ingu<lb/>lis indidi&longs;&longs;et; cui nimirùm fieri &longs;atis non pote&longs;t, ni&longs;i corpora <lb/>&longs;e invicem penetrent; unum autem grave in centro exi&longs;tens <pb pagenum="70"/>cætera omnia inde excludit. </s>

<s>Re&longs;tituunt &longs;e gravia in locum <lb/>&longs;uum versùs centrum pergendo, non ut ad centrum veniant; <lb/>&longs;ed ut nihil levius infra &longs;e habeant; quemadmodum & levia <lb/>versùs cælum a&longs;cendunt, non ut cælum petant, ibíque demum <lb/>quie&longs;cant, &longs;ed ne quid gravius &longs;upra &longs;e patiantur. </s>

Line 933

<s>Hinc e&longs;t quod terræ con&longs;i&longs;tentiam in loco &longs;uo, non propriè <lb/>ex libræ rationibus explicandam cen&longs;eo; quia in librâ utraque <lb/>lanx non repugnat &longs;olùm, ne attollatur, verùm etiam in aöre <lb/>con&longs;tituta deor&longs;um nititur; terræ autem partes &longs;uperiores nil <lb/>infrà &longs;e levius habentes non conantur deor&longs;um. </s>

<s>Et quemad<lb/>modum &longs;i libræ lanx utraque &longs;ubjecto plano incumberet, ea<lb/>rum con&longs;i&longs;tentia non e&longs;&longs;et æquilibrio tribuenda, quamvis <lb/>æquilibres &longs;int, &longs;ed idcircò &longs;olùm con&longs;i&longs;terent, quia infrà &longs;e <lb/>haberent corpus, quod permeare vel non exigit, vel non po<lb/>te&longs;t earum gravitas: ita terræ partes licèt adeò æqualiter &longs;int <lb/>di&longs;po&longs;itæ circa &longs;uum commune gravitatis centrum (in quo vi<lb/>res &longs;uas exererent tellure totâ in aöris locum tran&longs;latâ) ut ex illo <lb/>&longs;u&longs;pensâ tellure in æquilibrio con&longs;i&longs;terent; re tamen ipsâ non <pb pagenum="71"/>con&longs;i&longs;tunt propter æquilibrium; &longs;ed quia nulla pars habet in<lb/>fra &longs;e aliquid, &longs;ub quo petat exi&longs;tere, atque adeò nulla e&longs;t, <lb/>quæ deor&longs;um nitatur. </s>

<s>Et quemad<lb/>modum &longs;i libræ lanx utraque &longs;ubjecto plano incumberet, ea<lb/>rum con&longs;i&longs;tentia non e&longs;&longs;et æquilibrio tribuenda, quamvis <lb/>æquilibres &longs;int, &longs;ed idcircò &longs;olùm con&longs;i&longs;terent, quia infrà &longs;e <lb/>haberent corpus, quod permeare vel non exigit, vel non po<lb/>te&longs;t earum gravitas: ita terræ partes licèt adeò æqualiter &longs;int <lb/>di&longs;po&longs;itæ circa &longs;uum commune gravitatis centrum (in quo vi<lb/>res &longs;uas exererent tellure totâ in aöris locum tran&longs;latâ) ut ex illo <lb/>&longs;u&longs;pensâ tellure in æquilibrio con&longs;i&longs;terent; re tamen ipsâ non <pb xlink:href="017/01/087.jpg" pagenum="71"/>con&longs;i&longs;tunt propter æquilibrium; &longs;ed quia nulla pars habet in<lb/>fra &longs;e aliquid, &longs;ub quo petat exi&longs;tere, atque adeò nulla e&longs;t, <lb/>quæ deor&longs;um nitatur. </s>

<s>Quare Poëticè &longs;olùm, non verò Philo<lb/>&longs;ophicè dictum e&longs;t. <lb/><emph type="italics"/>Terra pilæ &longs;imilis, nullo fulcimine nixa, <lb/>Aëre &longs;ubjecto tam grave pendet onus.<emph.end type="italics"/><lb/>Aör &longs;i quidem non e&longs;t &longs;ubjectus terræ, &longs;ed circumfu&longs;us; ea <lb/>namque &longs;ubjecta &longs;unt, quæ inferiora; inferiora autem, quæ <lb/>centro propiora. </s>

Line 941

<s>Quæ cum ita &longs;int, nulla unquam continget in terrâ mutatio <lb/>atque gravium tran&longs;latio, quæ efficiat motum trepidationis. </s>

<lb/><s>Sit enim terræ globus AB, cujus cen<lb/><figure id="fig7"/><lb/>trum C &longs;it pariter centrum gravitatis: <lb/>ducto per C plano IL, hemi&longs;phærium <lb/>IAL e&longs;t æquale hemi&longs;phærio IBL; <lb/>ex quo ab&longs;ci&longs;&longs;a intelligatur portio <lb/>&longs;phærica DEB, in cujus locum &longs;uc<lb/>cedat aër. </s>

<lb/><s>Sit enim terræ globus AB, cujus cen<lb/><figure id="id.017.01.087.1.jpg" xlink:href="017/01/087/1.jpg"/><lb/>trum C &longs;it pariter centrum gravitatis: <lb/>ducto per C plano IL, hemi&longs;phærium <lb/>IAL e&longs;t æquale hemi&longs;phærio IBL; <lb/>ex quo ab&longs;ci&longs;&longs;a intelligatur portio <lb/>&longs;phærica DEB, in cujus locum &longs;uc<lb/>cedat aër. </s>

<s>Si qua igitur pars deberet <lb/>deor&longs;um versùs C niti, non alia uti<lb/>que e&longs;&longs;et præter D & E, quæ longiùs <lb/>à centro ab&longs;unt, quàm contiguus aër <lb/>DE. </s>

Line 955

<s>Aio ne dum factam <lb/>e&longs;&longs;e mutationem, quæ ad motum telluri conciliandum &longs;ufficiat. </s>

<lb/><s>Quamvis enim mons ille FHG, quippe quem ambit aër le-<pb pagenum="72"/>vior vicinior centro, conetur deor&longs;um; certum e&longs;t illum de<lb/>&longs;cendere non po&longs;&longs;e, quin totam reliquam terram impellat, eju&longs;<lb/>que re&longs;i&longs;tentiam &longs;uperet; re&longs;i&longs;tit autem primò &longs;egmentum <lb/>IDEL, cujus omnes partes magis à centro removerentur; ni<lb/>&longs;i igitur mons FHG major &longs;it &longs;egmento &longs;phærico IDEL <lb/>(vel &longs;altem non multò minor, &longs;i quidem ob majorem à centro <lb/>di&longs;tantiam augerentur momenta gravitatis, ex dictis cap.

<lb/><s>Quamvis enim mons ille FHG, quippe quem ambit aër le-<pb xlink:href="017/01/088.jpg" pagenum="72"/>vior vicinior centro, conetur deor&longs;um; certum e&longs;t illum de<lb/>&longs;cendere non po&longs;&longs;e, quin totam reliquam terram impellat, eju&longs;<lb/>que re&longs;i&longs;tentiam &longs;uperet; re&longs;i&longs;tit autem primò &longs;egmentum <lb/>IDEL, cujus omnes partes magis à centro removerentur; ni<lb/>&longs;i igitur mons FHG major &longs;it &longs;egmento &longs;phærico IDEL <lb/>(vel &longs;altem non multò minor, &longs;i quidem ob majorem à centro <lb/>di&longs;tantiam augerentur momenta gravitatis, ex dictis cap.

4.) <lb/>non poterit &longs;ubjectam terram loco dimovere. </s>

Line 975

<s>Id quod in libræ lance, cui uncia fue<lb/>rit addita, reperire non poteris; totum &longs;iquidem lancis pon<lb/>dus deor&longs;um nititur. </s>

<s>Quod &longs;i ex librâ &longs;imilitudinem ducere placeat, petenda po-<pb pagenum="73"/>tiùs e&longs;t ex librâ, cujus lanx altera &longs;ubjecto plano incumbat, al<lb/>tera in aëre libera pendeat; &longs;i enim utraque lanx plena æquali<lb/>bu; ponderibus con&longs;i&longs;tat in æquilibrio, & incumbenti lanci ad<lb/>datur ponderis pars, quæ à pendulâ lance detrahatur, lances <lb/>non moventur, nec inter &longs;e mutuò confligunt ponderum gra<lb/>vitates, ni&longs;i quatenùs lanx gravior &longs;emper magis re&longs;i&longs;tit leviori, <lb/>ne ab illâ elevetur: cæterùm gravior lanx non movet leviorem, <lb/>ni&longs;i ubi demum tanto pondere prægravata fuerit, ut &longs;ubjecti <lb/>plani re&longs;i&longs;tentiam vincens illud aut frangat, aut &longs;altem depri<lb/>mat. </s>

<s>Quod &longs;i ex librâ &longs;imilitudinem ducere placeat, petenda po-<pb xlink:href="017/01/089.jpg" pagenum="73"/>tiùs e&longs;t ex librâ, cujus lanx altera &longs;ubjecto plano incumbat, al<lb/>tera in aëre libera pendeat; &longs;i enim utraque lanx plena æquali<lb/>bu; ponderibus con&longs;i&longs;tat in æquilibrio, & incumbenti lanci ad<lb/>datur ponderis pars, quæ à pendulâ lance detrahatur, lances <lb/>non moventur, nec inter &longs;e mutuò confligunt ponderum gra<lb/>vitates, ni&longs;i quatenùs lanx gravior &longs;emper magis re&longs;i&longs;tit leviori, <lb/>ne ab illâ elevetur: cæterùm gravior lanx non movet leviorem, <lb/>ni&longs;i ubi demum tanto pondere prægravata fuerit, ut &longs;ubjecti <lb/>plani re&longs;i&longs;tentiam vincens illud aut frangat, aut &longs;altem depri<lb/>mat. </s>

<s>Sic hemi&longs;phærium IAL habet rationem lancis non tan<lb/>tùm &longs;ubjecto plano incumbentis, &longs;ed, quod potius e&longs;t, &longs;uo in <lb/>loco quie&longs;centis; cui quò plus addideris ponderis, auges qui<lb/>dem re&longs;i&longs;tentiam ne &longs;ursùm versùs H propellatur, ip&longs;um verò <lb/>non conatur deor&longs;um versùs C; &longs;ed totus conatus impo&longs;ito & <lb/>adjecto monti tribuendus e&longs;&longs;et, vel (ut &longs;im maximè liberalis) <lb/>etiam exce&longs;&longs;ui illi, quo hemi&longs;phærium IAL &longs;uperat &longs;egmen<lb/>tum &longs;phæricum IDEL, qui exce&longs;&longs;us e&longs;t æqualis ip&longs;i monti, <lb/>hoc e&longs;t &longs;egmento DEB. </s>

Line 985

<s>Sed unum adhuc &longs;upere&longs;t, quod per di&longs;&longs;imulantiam præ<lb/>tereundum non videtur. </s>

<s>E&longs;to inquis, nulla fiat in tellure gra<lb/>vium tran&longs;latio, quæ tanta &longs;it, ut novum gravitatis centrum in <lb/>univer&longs;i centro con&longs;tituere valeat, ac proinde nulla &longs;it centri <lb/>terræ trepidatio: circa centrum &longs;altem nutabit tellus motu <lb/>conver&longs;ionis, validâ ventorum vi &longs;ummos montes impellente, <lb/>orbemque totum, pro variâ ip&longs;orum incur&longs;ione, modò hanc, <lb/>modò illam partem ver&longs;ante: unde forta&longs;&longs;e ortam acû magne<lb/>ticæ eodem in loco po&longs;t aliquot annos variationem &longs;u&longs;picari <pb pagenum="74"/>quis po&longs;&longs;it. </s>

<s>Cum enim tellus æqualibus circà centrum nutibus <lb/>librata permaneat, multo faciliùs omnem in partem converti <lb/>po&longs;&longs;e videtur, quàm rota ingens &longs;uo in axe &longs;u&longs;pen&longs;a: Rota &longs;ci<lb/>licet &longs;uo pondere axem premens illum, dum convertitur, te<lb/>rit; hancque affrictûs difficultatem vincat nece&longs;&longs;e e&longs;t, quod <lb/>una ex parte additur pondus, vel quæ applicatur Potentia, ut <lb/>conver&longs;ionem efficiat: tellus verò in orbem diffu&longs;a nec cen<lb/>trum premit, nec axem, cum quo ullus fiat affrictus; ac <lb/>proptereà faciliorem præbet conver&longs;ionis an&longs;am Potentiæ unam <lb/>aliquam in partem urgenti. </s>

Line 997

<s>an cælum volvatur; &longs;i igitur diurna cæli conver&longs;io magne<lb/>tis declinationem non mutat, neque ad illam mutandam &longs;uffi<lb/>ceret telluris circa &longs;uum axem conver&longs;io, vi cujus alia atque <lb/>alia &longs;ydera re&longs;piceret: Præterquam quod non id temporum lap<lb/>&longs;u accideret; &longs;ed ubi ventorum impetus elangui&longs;&longs;et, illicò va<lb/>riatio illa declinationis magneticæ deprehenderetur: id quod <lb/>ab omni experimento longè abe&longs;t. </s>

<s>Verùm adeò à no&longs;tris &longs;en<lb/>&longs;ibus &longs;ejunctæ &longs;unt magneticorum &longs;ymptomatum cau&longs;æ, ut ad <pb pagenum="75"/>aliarum difficultatum &longs;olutionem non facilè advocandus &longs;it in <lb/>Philo&longs;ophicam &longs;cenam magneti&longs;mus. </s>

<s>Verùm adeò à no&longs;tris &longs;en<lb/>&longs;ibus &longs;ejunctæ &longs;unt magneticorum &longs;ymptomatum cau&longs;æ, ut ad <pb xlink:href="017/01/091.jpg" pagenum="75"/>aliarum difficultatum &longs;olutionem non facilè advocandus &longs;it in <lb/>Philo&longs;ophicam &longs;cenam magneti&longs;mus. </s>

<s>Illud potius hìc attendendum videtur, quod montis altitu<lb/>do, atque magnitudo ad totius telluris molem Rationem habet <lb/>&longs;atis exiguam. </s>

Line 1017

<s>Quare neque montis altitu<lb/>do con&longs;tituta quicquam detrahet orbicularis figuræ, quod &longs;ub <lb/>Phy&longs;icam con&longs;iderationem cadat; ac proptereà nihil virium ad <lb/>tellurem convertendam obtinet ventus in montem incurrens. </s>

<s>Et quidem conver&longs;ionem hanc re ipsâ non fieri manife&longs;tum <lb/>e&longs;t; &longs;i quidem cum nulla vincenda e&longs;&longs;et gravitas, quæ longiùs <lb/>à centro gravium recederet, vel quæ axem tereret, facillima <lb/>videretur e&longs;&longs;e globi totius conver&longs;io circa centrum, non &longs;olùm <pb pagenum="76"/>validioribus atque incitatioribus, &longs;ed temperatis etiam atque <lb/>mediocribus ventis flantibus. </s>

<s>Et quidem conver&longs;ionem hanc re ipsâ non fieri manife&longs;tum <lb/>e&longs;t; &longs;i quidem cum nulla vincenda e&longs;&longs;et gravitas, quæ longiùs <lb/>à centro gravium recederet, vel quæ axem tereret, facillima <lb/>videretur e&longs;&longs;e globi totius conver&longs;io circa centrum, non &longs;olùm <pb xlink:href="017/01/092.jpg" pagenum="76"/>validioribus atque incitatioribus, &longs;ed temperatis etiam atque <lb/>mediocribus ventis flantibus. </s>

<s>Hi autem aliquando diuturni <lb/>&longs;unt; cuju&longs;modi poti&longs;&longs;imum &longs;unt Ete&longs;iæ, quibus maritimi cur<lb/>&longs;us celeres, & certi diriguntur. </s>

<s>Tot igitur dierum &longs;patio, ven<lb/>to oppo&longs;itos montes vehementiùs urgente, non modica fieret <lb/>terreni globi inclinatio; ac propterea non eadem demum per<lb/>maneret eodem in loco Poli &longs;uprà Horizontem altitudo, quo<lb/>ties ab alterutro cardine Au&longs;trali Boreali<gap/>ve, aut à &longs;ol&longs;titiali <lb/>Brumali-ve limite tam ortivo quàm occiduo ventus &longs;piraret, at<lb/>que multarum ædium facies non eandem ampliùs re&longs;picerent <lb/>cæli plagam; quare & &longs;cietherica Horologia quantumvis ac<lb/>curatè &longs;emel de&longs;cripta po&longs;t non adeò multas temporum inclina<lb/>tiones toto ferè cælo di&longs;creparent; aliis enim, atque aliis &longs;ub<lb/>inde flantibus ventis, varia oriretur orbis conver&longs;io, atque alia <lb/>planorum cum circulis horariis &longs;ectio, quæ de&longs;criptis lineis non <lb/>congrueret. </s>

<s>Tot igitur dierum &longs;patio, ven<lb/>to oppo&longs;itos montes vehementiùs urgente, non modica fieret <lb/>terreni globi inclinatio; ac propterea non eadem demum per<lb/>maneret eodem in loco Poli &longs;uprà Horizontem altitudo, quo<lb/>ties ab alterutro cardine Au&longs;trali Boreali ve, aut à &longs;ol&longs;titiali <lb/>Brumali-ve limite tam ortivo quàm occiduo ventus &longs;piraret, at<lb/>que multarum ædium facies non eandem ampliùs re&longs;picerent <lb/>cæli plagam; quare & &longs;cietherica Horologia quantumvis ac<lb/>curatè &longs;emel de&longs;cripta po&longs;t non adeò multas temporum inclina<lb/>tiones toto ferè cælo di&longs;creparent; aliis enim, atque aliis &longs;ub<lb/>inde flantibus ventis, varia oriretur orbis conver&longs;io, atque alia <lb/>planorum cum circulis horariis &longs;ectio, quæ de&longs;criptis lineis non <lb/>congrueret. </s>

<s>Hujus autem mutationis nullum in toto terra<lb/>rum orbe ve&longs;tigium apparet, ni&longs;i fortè fabulas liceat com<lb/>mini&longs;ci. </s>

Line 1031

<lb/><s>Nam &longs;i ab ortu in occa&longs;um ex. </s>

<s>gr. proce&longs;&longs;erit tellus, minus tem<lb/>poris numerabitur quàm pro ratione cæle&longs;tium motuum; ut <lb/>contigi&longs;&longs;e fertur navi cui à Victoriâ nomen inditum e&longs;t, in ex<lb/>peditione Magellanicâ; cum &longs;cilicet po&longs;t totius orbis ambitum <lb/>redux in Hi&longs;palen&longs;em portum, ex quo ante tres annos &longs;olve<lb/>rat, intraret, tunc primùm ob&longs;ervarunt &longs;e à rectâ temporis nu<lb/>meratione defeci&longs;&longs;e die uno; quippe qui cum juxta diurnam <lb/>cæli conver&longs;ionem ab ortu in occa&longs;um iter in&longs;titui&longs;&longs;ent, ju&longs;to <lb/>tardiùs &longs;emper &longs;ol illis occiderat, exiguo quidem &longs;ingulis die-<pb pagenum="77"/>bus, quibus procedebant, di&longs;crimine, &longs;ed quod demùm modi<lb/>cis illis acce&longs;&longs;ionibus in integrum diem excreverat. </s>

<s>gr. proce&longs;&longs;erit tellus, minus tem<lb/>poris numerabitur quàm pro ratione cæle&longs;tium motuum; ut <lb/>contigi&longs;&longs;e fertur navi cui à Victoriâ nomen inditum e&longs;t, in ex<lb/>peditione Magellanicâ; cum &longs;cilicet po&longs;t totius orbis ambitum <lb/>redux in Hi&longs;palen&longs;em portum, ex quo ante tres annos &longs;olve<lb/>rat, intraret, tunc primùm ob&longs;ervarunt &longs;e à rectâ temporis nu<lb/>meratione defeci&longs;&longs;e die uno; quippe qui cum juxta diurnam <lb/>cæli conver&longs;ionem ab ortu in occa&longs;um iter in&longs;titui&longs;&longs;ent, ju&longs;to <lb/>tardiùs &longs;emper &longs;ol illis occiderat, exiguo quidem &longs;ingulis die-<pb xlink:href="017/01/093.jpg" pagenum="77"/>bus, quibus procedebant, di&longs;crimine, &longs;ed quod demùm modi<lb/>cis illis acce&longs;&longs;ionibus in integrum diem excreverat. </s>

Line 1045

<s>Statue in ingenti lacu compo&longs;itam <lb/>ex trabibus aliquot ratem, quam in littore &longs;tans facilè funiculo <lb/>modereris: Tùm ratem aliam paris quidem latitudinis, &longs;ed cen<lb/>tuplò longiorem, compone: Poteris-ne hanc funiculo eodem, <lb/>ac labore non majori, trahere perinde atque priorem? </s>

<s>Negabis <lb/>utique, quamvis enim utraque lacui &longs;tagnanti innate<gap/>, nec <lb/>vincenda &longs;it alterutrius gravitas, ut à centro gravium magis re<lb/>cedat; licet utraque parem in motu ab aquâ dividendâ re&longs;i&longs;ten<lb/>tiam inveniat (eju&longs;dem quippe &longs;unt latitudinis &longs;olâ di&longs;crepan<lb/>tes longitudine, & æqualis e&longs;t utriu&longs;que immer&longs;io propter ean<lb/>dem &longs;ingularum trabium molem, atque &longs;pecificam gravitatem) <lb/>quia tamen di&longs;par e&longs;t ratium magnitudo, & impetu extrin&longs;e<lb/>cùs accepto utraque eget, ut moveatur, palàm e&longs;t majore im<lb/>petu opus e&longs;&longs;e, ut ratis major trahatur, ac propterea po&longs;&longs;e hanc <lb/>adeò augeri, ut impetus ad illam movendam nece&longs;&longs;arius exce<lb/>dat vires Potentiæ ratem minorem funiculo moderantis. </s>

<s>Negabis <lb/>utique, quamvis enim utraque lacui &longs;tagnanti innatet, nec <lb/>vincenda &longs;it alterutrius gravitas, ut à centro gravium magis re<lb/>cedat; licet utraque parem in motu ab aquâ dividendâ re&longs;i&longs;ten<lb/>tiam inveniat (eju&longs;dem quippe &longs;unt latitudinis &longs;olâ di&longs;crepan<lb/>tes longitudine, & æqualis e&longs;t utriu&longs;que immer&longs;io propter ean<lb/>dem &longs;ingularum trabium molem, atque &longs;pecificam gravitatem) <lb/>quia tamen di&longs;par e&longs;t ratium magnitudo, & impetu extrin&longs;e<lb/>cùs accepto utraque eget, ut moveatur, palàm e&longs;t majore im<lb/>petu opus e&longs;&longs;e, ut ratis major trahatur, ac propterea po&longs;&longs;e hanc <lb/>adeò augeri, ut impetus ad illam movendam nece&longs;&longs;arius exce<lb/>dat vires Potentiæ ratem minorem funiculo moderantis. </s>

<s>Ita <lb/>planè e&longs;t. </s>

<s>Sed jam animum transfer ad in&longs;titutam di&longs;putatio<lb/>nem, ut di&longs;picias, undè irrep&longs;erit dubitatio hæc de relluris <pb pagenum="78"/>conver&longs;ione ex ventorum impul&longs;u, & quàm facilè fucum fece<lb/>rit rota &longs;uo in axe &longs;u&longs;pen&longs;a, quæ levi negotio, nec valido im<lb/>pul&longs;u, volvitur. </s>

<s>Sed jam animum transfer ad in&longs;titutam di&longs;putatio<lb/>nem, ut di&longs;picias, undè irrep&longs;erit dubitatio hæc de relluris <pb xlink:href="017/01/094.jpg" pagenum="78"/>conver&longs;ione ex ventorum impul&longs;u, & quàm facilè fucum fece<lb/>rit rota &longs;uo in axe &longs;u&longs;pen&longs;a, quæ levi negotio, nec valido im<lb/>pul&longs;u, volvitur. </s>

<s>Rota &longs;iquidem tota deor&longs;um gravitat, ac <lb/>proptereà axem premit; quia autem in axe &longs;u&longs;penditur, fieri <lb/>non pote&longs;t, ut pars altera de&longs;cendat, quin oppo&longs;ita a&longs;cendat. </s>

Line 1065

<lb/><s>Adde in telluris conver&longs;ione, &longs;i illa fieret, quò vehementior <lb/>e&longs;&longs;et ventus in montem incurrens, validior e&longs;&longs;et re&longs;i&longs;tentia aëris <lb/>à reliquis montibus dividendi; &longs;ed & multorum ingentium <lb/>fluminum contrariam in partem labentium impetus ob&longs;i&longs;teret, <lb/>ne tellus vento flanti ob&longs;ecundaret. </s>

<s>Quod &longs;i hæc levis e&longs;&longs;e mo<lb/>menti dixeris ad ob&longs;i&longs;tendum, levis pariter momenti e&longs;&longs;e ven<lb/>torum impetum, nece&longs;&longs;e e&longs;t, fatearis: neque hic arduum e&longs;&longs;et <lb/>ventorum atque fluminum vires invicem conferre, aquarum-<pb pagenum="79"/>que impetum multò validiorem o&longs;tendere; &longs;ed ad alia prope<lb/>randum e&longs;t: &longs;atisfuerit monui&longs;&longs;e non mediocrem intercedere <lb/>analogiam inter aquarum guttas in rivulos primùm, deinde in <lb/>majores rivos, ac demum in torrentem concurrentes, atque <lb/>terræ expirationes in ventum congregatas, quæ multum vi<lb/>rium obtinent, &longs;i plurimæ in unum coëant, quemadmodum <lb/>& aquis contingit. <lb/><gap desc="hr tag"/></s>

<s>Quod &longs;i hæc levis e&longs;&longs;e mo<lb/>menti dixeris ad ob&longs;i&longs;tendum, levis pariter momenti e&longs;&longs;e ven<lb/>torum impetum, nece&longs;&longs;e e&longs;t, fatearis: neque hic arduum e&longs;&longs;et <lb/>ventorum atque fluminum vires invicem conferre, aquarum-<pb xlink:href="017/01/095.jpg" pagenum="79"/>que impetum multò validiorem o&longs;tendere; &longs;ed ad alia prope<lb/>randum e&longs;t: &longs;atisfuerit monui&longs;&longs;e non mediocrem intercedere <lb/>analogiam inter aquarum guttas in rivulos primùm, deinde in <lb/>majores rivos, ac demum in torrentem concurrentes, atque <lb/>terræ expirationes in ventum congregatas, quæ multum vi<lb/>rium obtinent, &longs;i plurimæ in unum coëant, quemadmodum <lb/>& aquis contingit. <lb/><gap desc="hr tag"/></s>

<s><emph type="center"/>CAPUT XIII.<emph.end type="center"/></s>

Line 1073

<s>PLanum inclinatum dicitur planum quodcumque non tran<lb/>&longs;it per centrum gravium & levium, hoc e&longs;t per centrum <lb/>univer&longs;i; huju&longs;modi &longs;iquidem planum non cadit ad angulos <lb/>æquales in &longs;phæricam terræ &longs;uperficiem. </s>

<s>Hinc etiam planum <lb/>horizonti parallelum reipsâ e&longs;t inclinatum, ni&longs;i adeò exiguum <lb/>&longs;it ac breve, ut puncti vicem obtineat, &longs;i cum terreni globi &longs;u<lb/><figure id="fig8"/><lb/>perficie conferatur. </s>

<s>Sit univer&longs;i <lb/>centrum A, plana BA, & CA &longs;unt <lb/>verticalia & perpendicularia, qui<lb/>bus &longs;i corpus aliquod grave appli<lb/>cueris, illud non impedietur, quin <lb/>per &longs;uam directionis lineam de&longs;cen<lb/>dat. </s>

Line 1083

<s>Quod &longs;i planum parallelum horizonti ita exiguum &longs;it, <lb/>ut à &longs;phæricâ &longs;uperficie, quam tangit, non recedat; tunc in <lb/>quacumque ejus parte con&longs;tituatur corpus grave, perinde e&longs;t, <lb/>atque &longs;i in puncto D collocatum concipiatur. </s>

<s>Sin autem ita à <pb pagenum="80"/>puncto D di&longs;titerit, ut à &longs;phæricâ &longs;uperficie recedat, quemad<lb/>modum &longs;i e&longs;&longs;et planum DF, illud e&longs;t inclinatum, & fit angulus <lb/>DFA inclinationis. </s>

<s>Sin autem ita à <pb xlink:href="017/01/096.jpg" pagenum="80"/>puncto D di&longs;titerit, ut à &longs;phæricâ &longs;uperficie recedat, quemad<lb/>modum &longs;i e&longs;&longs;et planum DF, illud e&longs;t inclinatum, & fit angulus <lb/>DFA inclinationis. </s>

<s>Ubi ob&longs;ervandum e&longs;t non eandem e&longs;&longs;e <lb/>&longs;ingularum plani partium inclinationem; angulus enim in<lb/>clinationis AEC major e&longs;t inclinatione ABC, per 16. <lb/>lib.

Line 1101

<s>Cogno&longs;citur autem gravitatio ex re&longs;i&longs;tentiâ, quâ corpus <lb/>repugnat contra vires illud retinentis, ne deor&longs;um feratur, <lb/>aut &longs;ur&longs;um trahentis; neque enim alio ni&longs;u gravia gravi<lb/>tant, quàm quo re&longs;i&longs;tunt impedienti motum gravitati <lb/>convenientem. </s>

<s>Et quidem experimento aliquo pote&longs;t gra<lb/>vitationis varietas inve&longs;tigari; &longs;i nimirum planum BO ex <lb/>ligno, aut marmore accuratè lævigetur, & extremitati B <lb/>adnectatur orbiculus D facillimè circa axem ver&longs;atilis, pon-<pb pagenum="81"/>deri autem A &longs;ubjiciantur <lb/><figure id="fig9"/><lb/>rotulæ, & adnectatur funi<lb/>culus per D tran&longs;iens, ex <lb/>cujus extremo pendeat lanx <lb/>E, cui pondera immitti po&longs;<lb/>&longs;int: pro variâ enim plani <lb/>BO inclinatione etiam pon<lb/>dera in lance mutare opor<lb/>tebit, ut pondus A &longs;u&longs;ti<lb/>neatur, & plura erunt, quò magis ad perpendiculare accedet <lb/>planum BO. </s>

<s>Et quidem experimento aliquo pote&longs;t gra<lb/>vitationis varietas inve&longs;tigari; &longs;i nimirum planum BO ex <lb/>ligno, aut marmore accuratè lævigetur, & extremitati B <lb/>adnectatur orbiculus D facillimè circa axem ver&longs;atilis, pon-<pb xlink:href="017/01/097.jpg" pagenum="81"/>deri autem A &longs;ubjiciantur <lb/><figure id="id.017.01.097.1.jpg" xlink:href="017/01/097/1.jpg"/><lb/>rotulæ, & adnectatur funi<lb/>culus per D tran&longs;iens, ex <lb/>cujus extremo pendeat lanx <lb/>E, cui pondera immitti po&longs;<lb/>&longs;int: pro variâ enim plani <lb/>BO inclinatione etiam pon<lb/>dera in lance mutare opor<lb/>tebit, ut pondus A &longs;u&longs;ti<lb/>neatur, & plura erunt, quò magis ad perpendiculare accedet <lb/>planum BO. </s>

<s>Verùm quia nunquam carere poteris &longs;u&longs;picione, <lb/>an corporum affrictus aliquid afferat impedimenti; ideò &longs;eclu<lb/>&longs;is omnibus, quæ extrin&longs;ecùs accidere po&longs;&longs;unt, re&longs;i&longs;tentiam ex <lb/>&longs;olâ gravitate ortam opus e&longs;t con&longs;iderare. </s>

<s>Re&longs;i&longs;tentia verò omnis re&longs;pondet violentiæ, quam patitur <lb/>id quod re&longs;i&longs;tit; minori etenim conatu minorem vim illatam <lb/>propul&longs;are &longs;tudet natura, quæ validiùs ob&longs;i&longs;tit majori violen<lb/>tiæ: id quod ita rationi e&longs;t con&longs;onum, & obviis experimentis <lb/>manife&longs;tum, ut in hoc demon&longs;trando &longs;upervacaneum &longs;it im<lb/>morari. </s>

<s>Con&longs;tituantur itaque duo <lb/><figure id="fig10"/><lb/>æqualis ponderis corpora in D & <lb/>in C; &longs;ingulis alligetur funiculus, <lb/>qui per B tran&longs;eat, & &longs;ur&longs;um tra<lb/>hantur &longs;imul ita, ut æqualiter mo<lb/>veantur. </s>

<s>Con&longs;tituantur itaque duo <lb/><figure id="id.017.01.097.2.jpg" xlink:href="017/01/097/2.jpg"/><lb/>æqualis ponderis corpora in D & <lb/>in C; &longs;ingulis alligetur funiculus, <lb/>qui per B tran&longs;eat, & &longs;ur&longs;um tra<lb/>hantur &longs;imul ita, ut æqualiter mo<lb/>veantur. </s>

<s>Ab&longs;olutâ motûs particu<lb/>lâ, corpus alterum ex D a&longs;cendit <lb/>in H in plano perpendiculari; al<lb/>terum in plano inclinato ex C ve<lb/>nit in E, & CE linea æqualis e&longs;t <lb/>lineæ motûs DH. </s>

<s>Non eandem <lb/>tamen utrumque grave &longs;ubiit vio<lb/>lentiam; nam motus DH fuit &longs;impliciter, & ab&longs;olutè violen<lb/>tus; at motus CE eatenus &longs;olùm gravitati adver&longs;atur, quate<lb/>nus a&longs;cendit; a&longs;cen&longs;um autem metitur linea DG, quam ab<lb/>&longs;cindit EG horizonti parallela. </s>

<s>Hîc &longs;cilicet planum DC in<lb/>tellige horizontale nihil à &longs;phæricá &longs;uperficie di&longs;crepans, ut <lb/>communiter contingit: quòd &longs;i non ita &longs;e haberet; &longs;ed e&longs;&longs;et <lb/>ampli&longs;&longs;imum planum, men&longs;ura violentiæ illatæ ponderi in C <pb pagenum="82"/>con&longs;tituto, in E elevato de&longs;umenda e&longs;&longs;et ex differentiâ inter <lb/>KC & OE. </s>

<s>Hîc &longs;cilicet planum DC in<lb/>tellige horizontale nihil à &longs;phæricá &longs;uperficie di&longs;crepans, ut <lb/>communiter contingit: quòd &longs;i non ita &longs;e haberet; &longs;ed e&longs;&longs;et <lb/>ampli&longs;&longs;imum planum, men&longs;ura violentiæ illatæ ponderi in C <pb xlink:href="017/01/098.jpg" pagenum="82"/>con&longs;tituto, in E elevato de&longs;umenda e&longs;&longs;et ex differentiâ inter <lb/>KC & OE. </s>

<s>E&longs;t itaque gravitatio in plano perpendiculari ad <lb/>gravitationem in plano inclinato, ut re&longs;i&longs;tentia ad a&longs;cenden<lb/>dum in uno ad re&longs;i&longs;tentiam ad a&longs;cendendum in alio; re&longs;i&longs;tentiæ <lb/>autem &longs;unt, ut violentia, quam corpora &longs;ubeunt in motu; vio<lb/>lentia demum e&longs;t ut HD ad GD, hoc e&longs;t per 7. lib.

Line 1133

<s>Sed quia de&longs;cen&longs;us naturæ pro<lb/>pen&longs;ioni congruit, fieri non pote&longs;t, ut in alio atque alio plano <lb/>æquales &longs;int motus i&longs;ochroni; tardior enim e&longs;t, qui in plano in<lb/>clinato perficitur, neque, &longs;i æqualis ponderis corpora de&longs;cen<lb/>dant ex H & E, quando illud ad D pervenit, hoc pote&longs;t attin<lb/>gere punctum C: ideò non ex de&longs;cen&longs;u gravitationem metiri <lb/>oportet, cum motus æquales non habeantur: ni&longs;i fortè ea&longs;dem <lb/>movendi vires tribuas gravitati non impeditæ in perpendicula<lb/>ri, ac impeditæ in plano inclinato. </s>

<s>Qua propter gravitationis <lb/>momenta ad de&longs;cendendum non aliunde meliùs æ&longs;timantur, <lb/>quàm ex repugnantiâ ad a&longs;cendendum: &longs;ic enim vulgari argu-<pb pagenum="83"/>mento &longs;ingulorum corporum gravitates librâ expendimus, tan<lb/>tumque iis ad de&longs;cendendum virium tribuimus, quantum re<lb/>&longs;i&longs;tunt, ne ab oppo&longs;itâ libræ lance deor&longs;um conante eleventur. </s>

<s>Qua propter gravitationis <lb/>momenta ad de&longs;cendendum non aliunde meliùs æ&longs;timantur, <lb/>quàm ex repugnantiâ ad a&longs;cendendum: &longs;ic enim vulgari argu-<pb xlink:href="017/01/099.jpg" pagenum="83"/>mento &longs;ingulorum corporum gravitates librâ expendimus, tan<lb/>tumque iis ad de&longs;cendendum virium tribuimus, quantum re<lb/>&longs;i&longs;tunt, ne ab oppo&longs;itâ libræ lance deor&longs;um conante eleventur. </s>

<lb/><s>Eadem igitur e&longs;t gravitationis Ratio, &longs;eu propen&longs;ionis ad de<lb/>&longs;cendendum, quæ e&longs;t re&longs;i&longs;tentiæ ad a&longs;cendendum: Cum verò <lb/>re&longs;i&longs;tentiam in plano inclinato ad re&longs;i&longs;tentiam in perpendicu<lb/>lari o&longs;ten&longs;um &longs;it e&longs;&longs;e, ut Radius ad Secantem anguli inclinatio<lb/>nis, hoc e&longs;t ut BD ad BC, erit pariter vis de&longs;cendendi in <lb/>plano BC ad vim de&longs;cendendi in plano BD, reciprocè ut BD <lb/>ad BC. </s>

Line 1151

<s>Et hæc e&longs;t ratio, cur violentiam determinans, quam grave <lb/>a&longs;cendens patitur, a&longs;&longs;ump&longs;erim in perpendiculari BA par<lb/>tem GD, quam ab&longs;cindit parallela horizonti; hæc enim <lb/>men&longs;ura phy&longs;icè non di&longs;crepat à verâ men&longs;urâ, quæ a&longs;&longs;umen<lb/>da e&longs;&longs;et, &longs;i mente concipias rectam lineam DC tangere circu<lb/>lum, cujus &longs;emidiameter &longs;it millecuplo major. </s>

<s>Men&longs;ura &longs;i qui<lb/>dem a&longs;censûs petenda e&longs;t ex exce&longs;&longs;u, quo perpendicularis EA <lb/>&longs;uperat perpendicularem AC; illo enim intervallo, quo magis <lb/>rece&longs;&longs;it à centro, a&longs;cendit. </s><pb pagenum="84"/>

<s>Ex quo fit quod, &longs;i planum inclinatum BC cum perpendi<lb/>culari CA faceret angulum acutum ACB, corpus ex C u&longs;que <lb/>in L (in quod punctum cadit perpendicularis AL) de&longs;cende<lb/>ret, quia &longs;emper magis ad centrum accederet: ex L autem in E <lb/>a&longs;cenderet, & a&longs;cen&longs;um metiretur exce&longs;&longs;us perpendiculi EA <lb/>&longs;uprà perpendiculum LA. </s>

Line 1183

<s>26′; <lb/>eju&longs;que Secans AC e&longs;t partium (100000 5017/100000), quarum AD <lb/>po&longs;ita e&longs;t 100000; di&longs;crimen inter AC, & AE &longs;uperiùs in<lb/>ventam, e&longs;t partium (43 46227/100000), quæ e&longs;t proximè eadem men&longs;u<lb/>ra, ac DG po&longs;ita partium 43 1/2. Quod &longs;i in plani inclinati lon<lb/>gitudine <expan abbr="tantã">tantam</expan> Rationem habente ad terræ <expan abbr="&longs;emidiametr&utilde;">&longs;emidiametrum</expan>, quan<lb/>ta con&longs;tit ita e&longs;t, pote&longs;t citrà errorem a&longs;&longs;umi tanquam men&longs;ura <lb/>a&longs;censûs pars perpendiculi BA inte c pta ab horizontali DC, <lb/>& parallelâ EG, &longs;atis patet id multò magis licere in planorum <lb/>longitudinibus minorem Rationem habentibus ad eandem ter<lb/>ræ &longs;emidiametrum. </s>

<s>Manet itaque con&longs;tituta regula gravitatio<lb/>nis, videlicet gravitationem in plano inclinato ad gravitationem <lb/>in perpendiculari e&longs;&longs;e, ut e&longs;t Radius ad &longs;ecantem anguli incli<lb/>nationis. </s><pb pagenum="85"/>

<s>Quamvis verò in partibus inferioribus plani inclinati &longs;it &longs;em<lb/>per major angulus inclinationis, quàm in &longs;uperioribus, & pro<lb/>inde minor &longs;it Ratio, quam habet Radius ad &longs;ecantem anguli <lb/>majoris, ac ea, quam idem Radius habet ad &longs;ecantem anguli <lb/>minoris: non tamen ea e&longs;t gravitationis differentia, cujus ratio <lb/>habenda &longs;it; cum enim adeò exiguus &longs;it angulus BAC, ejus <lb/>quantitas di&longs;tribuitur per omnes inclinationis angulos, qui <lb/>fiunt in punctis intermediis inter B & C; atque adeò contem<lb/>nendum e&longs;t in praxi di&longs;crimen illud, quod oritur ex alio atque <lb/>alio inclinationis angulo in codem plano. </s>

Line 1197

<s>Hinc prætereà fit, ut, &longs;i gravia in planis con&longs;tituta habeant <lb/>Rationem eandem, quam &longs;ecantes angulorum inclinationis ha<lb/>bent inter &longs;e vel ad Radium, eorum gravitatione, &longs;int æquales. </s>

<lb/><s>Sit ad horizontalem, SC per<lb/><figure id="fig11"/><lb/>pendicularis BD, & inclina<lb/>tæ BS, BC, per quas lineas <lb/>ducta intelligantur plana, & <lb/>in planis gravia diver&longs;a, & ut <lb/>BD ad BC ita pondus O ad <lb/>pondus M, & ut BD ad BS <lb/>ita pondus O ad pondus N. </s>

<lb/><s>Sit ad horizontalem, SC per<lb/><figure id="id.017.01.101.1.jpg" xlink:href="017/01/101/1.jpg"/><lb/>pendicularis BD, & inclina<lb/>tæ BS, BC, per quas lineas <lb/>ducta intelligantur plana, & <lb/>in planis gravia diver&longs;a, & ut <lb/>BD ad BC ita pondus O ad <lb/>pondus M, & ut BD ad BS <lb/>ita pondus O ad pondus N. </s>

<lb/><s>Dico ponderum M, O, N, gravitationes in &longs;uis planis e&longs;&longs;e <lb/>æquales. </s>

<s><expan abbr="Quoniã">Quoniam</expan> enim duorum gravium gravitationes in eadem <lb/>perpendiculari BD &longs;unt ut <expan abbr="ip&longs;or&utilde;">ip&longs;orum</expan> pondera, gravitatio M in per<lb/>pendiculari BD, ad gravitationem O in eadem perpendiculari, <lb/>e&longs;t ut M ad O, hoc e&longs;t ut BC ad BD; &longs;ed gravitatio M in per-<pb pagenum="86"/>pendiculari BD, ad gravitationcm eju&longs;dem M in inclinatâ <lb/>BC, e&longs;t pariter ut BC ad BD; igitur per 11. lib.

<s><expan abbr="Quoniã">Quoniam</expan> enim duorum gravium gravitationes in eadem <lb/>perpendiculari BD &longs;unt ut <expan abbr="ip&longs;or&utilde;">ip&longs;orum</expan> pondera, gravitatio M in per<lb/>pendiculari BD, ad gravitationem O in eadem perpendiculari, <lb/>e&longs;t ut M ad O, hoc e&longs;t ut BC ad BD; &longs;ed gravitatio M in per-<pb xlink:href="017/01/102.jpg" pagenum="86"/>pendiculari BD, ad gravitationcm eju&longs;dem M in inclinatâ <lb/>BC, e&longs;t pariter ut BC ad BD; igitur per 11. lib.

5. gravita<lb/>tio M in perpendiculari ad gravitationem O in perpendiculari <lb/>e&longs;t, ut gravitatio M in perpendiculari BD ad gravitationem <lb/>M in inclinatâ BC; igitur per 14. lib.

Line 1247

<s>Quare potentia &longs;u&longs;tinens <lb/>pondus in plano inclinato e&longs;t ad pondus, ut Radius ad Secan<lb/>tem anguli inclinationis; & potentia potens movere cum &longs;it ma<lb/>jor potentiâ &longs;u&longs;tinente, etiam majorem habet Rationem quàm <lb/>habeat Radius ad Secantem. </s>

<s>Id quod intelligitur ex vi præcisè <lb/>gravitationis; quicquid inferat di&longs;criminis partium conflictus. <pb pagenum="87"/><gap desc="hr tag"/></s>

<s>Id quod intelligitur ex vi præcisè <lb/>gravitationis; quicquid inferat di&longs;criminis partium conflictus. <pb xlink:href="017/01/103.jpg" pagenum="87"/><gap desc="hr tag"/></s>

<s><emph type="center"/>CAPUT XIV.<emph.end type="center"/></s>

Line 1267

<s>Eædem <lb/>igitur vires, quæ ad de&longs;cendendum in plano verticali impen<lb/>derentur, in urgendo plano horizontali in&longs;umuntur. </s>

<s>Quæ cum ita &longs;int, &longs;atis con&longs;tat corpora gravia ita in pla<lb/>no inclinato gravitare, & obtinere momenta ad de&longs;cenden-<pb pagenum="88"/>dum, ut etiam in illud, à quo impediuntur, gravitent, il<lb/>ludque urgeant. </s>

<s>Quæ cum ita &longs;int, &longs;atis con&longs;tat corpora gravia ita in pla<lb/>no inclinato gravitare, & obtinere momenta ad de&longs;cenden-<pb xlink:href="017/01/104.jpg" pagenum="88"/>dum, ut etiam in illud, à quo impediuntur, gravitent, il<lb/>ludque urgeant. </s>

<s>Id verò fieri non pote&longs;t ni&longs;i pro ratione impedimenti & mo<lb/>ræ, quam &longs;ubjectum planum motui infert &longs;u&longs;tinendo corpora <lb/>gravia; quæ proinde &longs;ibi relicta à directionis lineâ declinant, <lb/>motúmque deflectunt. </s>

<s>Porrò in plano inclinato quantum &longs;ub<lb/>&longs;it impedimenti, &longs;tatim apparet, ac innote&longs;cit, quantum reli<lb/>quum &longs;it virium ad de&longs;cendendum; vires enim, quæ reliquæ <lb/>&longs;unt, &longs;i adjiciantur viribus impeditis, totam virium omnium <lb/>&longs;ummam conflare debent. </s>

<s>Atqui ex &longs;uperiori capite notæ &longs;unt <lb/>vires, quibus corpus gravitat in plano inclinato; igitur quæ e&longs;t <lb/>differentia gravitationis in plano inclinato, à gravitatione in <lb/>plano verticlai, quod & perpendiculare, ea e&longs;t men&longs;ura im<lb/>pedimenti, quod à &longs;ubjecto plano infertur motui; atque <lb/><figure id="fig12"/><lb/>adeò gravitationis corporis in planum. </s>

<s>Atqui ex &longs;uperiori capite notæ &longs;unt <lb/>vires, quibus corpus gravitat in plano inclinato; igitur quæ e&longs;t <lb/>differentia gravitationis in plano inclinato, à gravitatione in <lb/>plano verticlai, quod & perpendiculare, ea e&longs;t men&longs;ura im<lb/>pedimenti, quod à &longs;ubjecto plano infertur motui; atque <lb/><figure id="id.017.01.104.1.jpg" xlink:href="017/01/104/1.jpg"/><lb/>adeò gravitationis corporis in planum. </s>

<s>Cum itaque o&longs;ten&longs;um fuerit <expan abbr="gravitation&etilde;">gravitationem</expan> <lb/>in plano BS ad gravitationem in plano BD <lb/>e&longs;&longs;e reciprocè ut BD ad BS, hoc e&longs;t, ut Ra<lb/>dius ad &longs;ecantem anguli inclinationis cum <lb/>verticali, hoc e&longs;t ut BV ad BS, patet vires <lb/>non impeditas ad vires impeditas e&longs;&longs;e ut <lb/>BV ad VS, quandoquidem totas gravita<lb/>tis vires refert BS. </s>

Line 1283

<s>Id <lb/>autem, quod de plano BS dictum e&longs;t, de plano quoque BC, & <lb/>cæteris quibu&longs;cunque dictum intelligatur; cum enim gravita<lb/>tio in plano inclinato BC ad gravitationem in perpendiculari <lb/>&longs;it ut BD, hoc e&longs;t BX, ad BC, erit gravitatio in planum ho<lb/>rizontale ad gravitationem in inclinatum ut BC ad XC, hoc <lb/>e&longs;t ut BT ad DT. </s>

<s>Quare gravitatio in planum BS ad gravi<lb/>tationem in planum BC, e&longs;t ut DR Sinus ver&longs;us inclinationis <lb/>DBS, ad DT Sinum ver&longs;um inclinationis DBC; a&longs;&longs;umptis <pb pagenum="89"/>&longs;cilicet numeris tabulatis ad eundem Radium relatis; nam &longs;i li<lb/>neæ &longs;pectentur, non e&longs;t Ratio ut DR ad DT, &longs;ed ut OT <lb/>ad DT; neque enim idem e&longs;t Radius BS & BC; ac proinde <lb/>OT major e&longs;t, quàm DR, &longs;icuti Radius BI major e&longs;t Radio <lb/>BS; vel a&longs;&longs;umpto eodem Radio BD, Ratio e&longs;t ut VS ad XC, <lb/>exce&longs;&longs;us &longs;ecantium &longs;upra Radium. </s>

<s>Quare gravitatio in planum BS ad gravi<lb/>tationem in planum BC, e&longs;t ut DR Sinus ver&longs;us inclinationis <lb/>DBS, ad DT Sinum ver&longs;um inclinationis DBC; a&longs;&longs;umptis <pb xlink:href="017/01/105.jpg" pagenum="89"/>&longs;cilicet numeris tabulatis ad eundem Radium relatis; nam &longs;i li<lb/>neæ &longs;pectentur, non e&longs;t Ratio ut DR ad DT, &longs;ed ut OT <lb/>ad DT; neque enim idem e&longs;t Radius BS & BC; ac proinde <lb/>OT major e&longs;t, quàm DR, &longs;icuti Radius BI major e&longs;t Radio <lb/>BS; vel a&longs;&longs;umpto eodem Radio BD, Ratio e&longs;t ut VS ad XC, <lb/>exce&longs;&longs;us &longs;ecantium &longs;upra Radium. </s>

<s>Id verò ex dictis &longs;ub finem capitis &longs;uperioris videtur mani<lb/>fe&longs;tum: nam &longs;i in plano BC retinetur pondus lib.

Line 1291

40 1/2, pa<lb/>tet à plano &longs;u&longs;tineri lib.9 1/2; ac proinde grave, quod habet gra<lb/>vitatem totam ut 100, in plano BC gravitabit ut 81, & urge<lb/>bit ut 19 &longs;ubjectum planum. </s>

<s>Ex his fieri pote&longs;t &longs;atis quæ<lb/><figure id="fig13"/><lb/>renti, cur &longs;u&longs;tinens columnam <lb/>OR plus gravitatis percipiat, <lb/>quàm qui &longs;u&longs;tinet columnam <lb/>SR: quia nimirum, qui &longs;u&longs;tinet, <lb/>e&longs;t pars plani inclinati, in quo ja<lb/>cens concipitur columna: quan<lb/>do igitur e&longs;t pars plani habentis <lb/>inclinationem LOR, gravitas, <lb/>quæ &longs;u&longs;tinetur à &longs;ubjecto plano, &longs;e habet ad totam gravitatem <lb/>ut Sinus Ver&longs;us anguli LOR ad Radium; Quando autem e&longs;t <lb/>pars plani habentis inclinationem VSR, gravitatio in &longs;ub<lb/>jectum planum &longs;u&longs;tinens e&longs;t ad totam gravitationem ut Sinus <lb/>Ver&longs;us anguli VSR ad eumdem Radium. </s>

<s>Ex his fieri pote&longs;t &longs;atis quæ<lb/><figure id="id.017.01.105.1.jpg" xlink:href="017/01/105/1.jpg"/><lb/>renti, cur &longs;u&longs;tinens columnam <lb/>OR plus gravitatis percipiat, <lb/>quàm qui &longs;u&longs;tinet columnam <lb/>SR: quia nimirum, qui &longs;u&longs;tinet, <lb/>e&longs;t pars plani inclinati, in quo ja<lb/>cens concipitur columna: quan<lb/>do igitur e&longs;t pars plani habentis <lb/>inclinationem LOR, gravitas, <lb/>quæ &longs;u&longs;tinetur à &longs;ubjecto plano, &longs;e habet ad totam gravitatem <lb/>ut Sinus Ver&longs;us anguli LOR ad Radium; Quando autem e&longs;t <lb/>pars plani habentis inclinationem VSR, gravitatio in &longs;ub<lb/>jectum planum &longs;u&longs;tinens e&longs;t ad totam gravitationem ut Sinus <lb/>Ver&longs;us anguli VSR ad eumdem Radium. </s>

<s>Atqui Sinus Ver&longs;us <lb/>anguli VSR minoris minor e&longs;t Sinu Ver&longs;o anguli LOR ma<lb/>joris; igitur minor e&longs;t gravitatio SR, quam OR. </s>

<s>Verum qui<lb/>dem e&longs;t illud, quod &longs;i in R aliquo obice prohibeatur, ne de<lb/>&longs;cendat; variatâ inclinatione, quo fit minor &longs;u&longs;tinentis labor, <lb/>cò augetur magis conatus potentiæ in R detinentis columnam, <lb/>ne juxta plani inclinationem de&longs;cendat. </s>

<s>Hinc &longs;i duo &longs;int co<lb/>lumnam inclinatam deferentes, qui illam in R &longs;u&longs;tinet, plus <lb/>&longs;ubit laboris, quàm qui in O, aut S: quia præter gravitatio<lb/>nem, quam percipit tanquam pars plani inclinati SR aut OR, <lb/>debet præterea retinere columnam proclivem ad de&longs;cen&longs;um <lb/>propter plani inclinationem; ideò cùm &longs;calas, aut montis cli<lb/>vum con&longs;cendunt, qui in &longs;uperiore loco e&longs;t, minimum &longs;ubit <pb pagenum="90"/>laboris. </s>

<s>Huc etiam revocari po&longs;&longs;e videtur ratio, ob quam in <lb/>elevando pontes illos ver&longs;atiles, qui arcium portis opponuntur, <lb/>initio major percipiatur difficultas, &longs;ed demùm facillimè ele<lb/>ventur. </s>

Line 1307

<s>E&longs;t &longs;iquidem certum apud <lb/>omnes mechanicos, tam ubi de libra, quàm ubi de vecte &longs;ermo <lb/>e&longs;t, aliam &longs;ervari Rationem quàm Sinuum Ver&longs;orum in mo<lb/>mento potentiæ, aut ponderis determinando. </s>

<s>Sit vectis, aut <lb/><figure id="fig14"/><lb/>libræ brachium EC, hypomochlion <lb/>&longs;eu centrum C; attollatur in H, aut <lb/>in D; omnes con&longs;entiunt momentum <lb/>potentiæ aut ponderis in E ad mo<lb/>mentum in H, e&longs;&longs;e ut HC ad IC, <lb/>ad momentum verò in D e&longs;&longs;e ut DC <lb/>ad FC. </s>

<s>Sit vectis, aut <lb/><figure id="id.017.01.106.1.jpg" xlink:href="017/01/106/1.jpg"/><lb/>libræ brachium EC, hypomochlion <lb/>&longs;eu centrum C; attollatur in H, aut <lb/>in D; omnes con&longs;entiunt momentum <lb/>potentiæ aut ponderis in E ad mo<lb/>mentum in H, e&longs;&longs;e ut HC ad IC, <lb/>ad momentum verò in D e&longs;&longs;e ut DC <lb/>ad FC. </s>

<s>E&longs;t igitur, inquis, gravitatio <lb/>in planum DC ad gravitationem in <lb/>planum horizontale EC, ut FC ad DC; in planum verò HC, <lb/>ut IC ad HC, hoc e&longs;t ut Sinus Rectus anguli inclinationis ad <lb/>Radium. </s>

Line 1317

<lb/><s>Neque hic liceat ad æqualitatem potentiarum confugere, ut <lb/>&longs;icut per 47. lib.

1. Eucl. linea DC pote&longs;t quadrata linearum <lb/>DF, FC, ita vis totius gravitatis æqualis gravitationibus in <lb/>plano inclinato & in planum inclinatum eandem &longs;ervet pro<lb/>portionem laterum trianguli DFC, adeò ut totam gravitatem <pb pagenum="91"/>Secans anguli inclinationis exprimat, gravitationem in plano <lb/>inclinato Radius, Tangens verò gravitationem in planum in<lb/>clinatum. </s>

1. Eucl. linea DC pote&longs;t quadrata linearum <lb/>DF, FC, ita vis totius gravitatis æqualis gravitationibus in <lb/>plano inclinato & in planum inclinatum eandem &longs;ervet pro<lb/>portionem laterum trianguli DFC, adeò ut totam gravitatem <pb xlink:href="017/01/107.jpg" pagenum="91"/>Secans anguli inclinationis exprimat, gravitationem in plano <lb/>inclinato Radius, Tangens verò gravitationem in planum in<lb/>clinatum. </s>

Line 1337

<s>Nam &longs;i DC &longs;it columna, <lb/>aut pons ver&longs;atilis, retineaturque in C, jam punctum C vicem <lb/>obtinens &longs;ubjecti plani, illiu&longs;que munere fungens, &longs;u&longs;tinet <lb/>ponderis partem EF, reliqua FC, quæ e&longs;t men&longs;ura momenti <lb/>ad de&longs;cendendum, debet &longs;u&longs;tineri à potentia motum impe<lb/>diente per DG. </s>

<s>Sin autem per DC planum columna moveri <lb/>po&longs;&longs;it rectâ & de&longs;cendere, vis de&longs;cendendi ad totam gravitatio<lb/>nem e&longs;t ut DF ad DC, gravitatio autem contra &longs;u&longs;tinentem <lb/>e&longs;t ad totam gravitationem ut Sinus Ver&longs;us anguli inclinationis <pb pagenum="92"/>FDC ad Radium; qui enim &longs;u&longs;tinet grave, dum de&longs;cendit in<lb/>clinatum, habet rationem plani inclinati. </s>

<s>Sin autem per DC planum columna moveri <lb/>po&longs;&longs;it rectâ & de&longs;cendere, vis de&longs;cendendi ad totam gravitatio<lb/>nem e&longs;t ut DF ad DC, gravitatio autem contra &longs;u&longs;tinentem <lb/>e&longs;t ad totam gravitationem ut Sinus Ver&longs;us anguli inclinationis <pb xlink:href="017/01/108.jpg" pagenum="92"/>FDC ad Radium; qui enim &longs;u&longs;tinet grave, dum de&longs;cendit in<lb/>clinatum, habet rationem plani inclinati. </s>

<s>Neque id mirum vi<lb/>deri debet, quandoquidem plurimum refert, an per planum <lb/>DG an verò per DC &longs;it determinatio ad motum, & quâ ra<lb/>tione &longs;u&longs;tinens opponatur virtuti motivæ: quare cùm diversâ <lb/>ratione opponatur motui circa centrum C, ac motui per pla<lb/>num DC, etiam di&longs;par erit in &longs;u&longs;tinendo difficultas. </s>

<s>Ex his, quæ tùm hoc, tùm &longs;uperiori capite di&longs;putata &longs;unt, <lb/>habes quid funambulis re&longs;pondeas volatum mentiri meditanti<lb/>bus, cum pectore in&longs;i&longs;tentes intento funi, diductis cruribus & <lb/>exten&longs;is brachiis, corpus æqualibus momentis librant, séque <lb/>ex editâ turri in depre&longs;&longs;iorem locum præcipites dant; &longs;i fortè, <lb/>ut noverint, quàm &longs;olidus e&longs;&longs;e debeat ac validus funis, quo iis <lb/>utendum e&longs;t, quærant, quantis momentis corpus urgeat &longs;ub<lb/><figure id="fig15"/><lb/>jectum funem. </s>

<s>Datâ enim turris altitudi<lb/>ne BD, & depre&longs;&longs;ioris loci, in quem de<lb/>&longs;cendendum e&longs;t, di&longs;tantiâ DC, collectí&longs;<lb/>que in &longs;ummam harum quadratis, Radix <lb/>&longs;ummæ dabit BC funis longitudinem; ex <lb/>quâ &longs;i auferatur BX turris altitudini BD <lb/>æqualis, erit BC divi&longs;a in X juxtà Ratio<lb/>nem momentorum, quæ corporis gravitas <lb/>exercet in plano inclinato, & in planum <lb/>inclinatum. </s>

<s>Sic po&longs;itâ BD ped. 150, & DC ped. 200, BC e&longs;t <lb/>ped. 250: ex quâ &longs;i auferatur BD, erit BX 150, & XC 100. <lb/>Statue autem totius gravitatis corporis funambuli momenta <lb/>220; hæc dividantur in duas partes, quarum major &longs;it &longs;e&longs;qui<lb/>altera minoris, &longs;icut BX inventa e&longs;t ip&longs;ius XC &longs;e&longs;quialtera, & <lb/>erunt momenta quidem ad de&longs;cendendum in plano inclinato <lb/>132, momenta verò gravitationis in planum inclinatum, hoc <lb/>e&longs;t in &longs;ubjectum funem, 88. Hæc tamen intelligenda &longs;unt eâ <lb/>factâ hypothe&longs;i, quòd funis rectâ intentus permaneret: cæte<lb/>rùm cum & &longs;uopte pondere, & &longs;ub impo&longs;iti corporis mole &longs;ub<lb/>&longs;idat, atque inflectatur, præ&longs;ertim circà medium, &longs;atis apparet <lb/>adhuc majorem &longs;ubjecti plani inclinationem æ&longs;timandam e&longs;&longs;e, <lb/>quàm quæ ex altitudine DB & di&longs;tantiâ DC inferatur, quin <lb/>& illam pro diversâ ab extremitatibus di&longs;tantiâ &longs;ubinde muta<lb/>ri, ac proinde validiori fune opus e&longs;&longs;e. <pb pagenum="93"/><gap desc="hr tag"/></s>

Line 1361

<s>Ex his &longs;i quidem, quæ hactenus di&longs;puta<lb/>ta &longs;unt, lux, opinor, non modica ad hanc, quam examinan<lb/>dam &longs;u&longs;cipimus quæ&longs;tionem, derivabitur. </s>

<s>Pendeat ex clavo C ad perpen<lb/><figure id="fig16"/><lb/>diculum globus ferreus A, quem <lb/>&longs;uppo&longs;itum planum horizontale <lb/>BD ita exactè contingat, ut nihil <lb/>de funiculi CA intentione remit<lb/>tatur. </s>

<s>Pendeat ex clavo C ad perpen<lb/><figure id="id.017.01.109.1.jpg" xlink:href="017/01/109/1.jpg"/><lb/>diculum globus ferreus A, quem <lb/>&longs;uppo&longs;itum planum horizontale <lb/>BD ita exactè contingat, ut nihil <lb/>de funiculi CA intentione remit<lb/>tatur. </s>

<s>Satis apparet &longs;ubjecto pla<lb/>no BD non incumbere globum A, <lb/>&longs;ed omnia &longs;uæ gravitationis, qua <lb/>deor&longs;um nititur, momenta exer<lb/>cere contrà clavum C, ex quo &longs;u&longs;pen&longs;us ad perpendiculum <lb/>pendet. </s>

<s>Quod &longs;i aut clavus C, nemine funem retinente, revel<lb/>leretur, aut funis CA præcideretur, jam tota vis de&longs;cendendi, <lb/>quæ corpori A ine&longs;t, urgeret &longs;ubjectum planum BD; nec ta<lb/>men in motum erumperet globus, quia planum BD; pari u&longs;que<lb/>quaque ad perpendiculum inclinatione libratur, atque adeò <lb/>motui pror&longs;us ob&longs;i&longs;tit. </s>

<s>Jam verò &longs;i globum A pariter ex perpendiculo CA penden<lb/>tem contingat planum aliud non quidem horizontale, &longs;ed in<lb/>clinatum EF, manife&longs;tum e&longs;t totam pariter gravitationem <lb/>exerceri contra clavum C retinentem, planumque contingens <pb pagenum="94"/>omninò non urgeri, ni&longs;i præci&longs;o funiculo &longs;ibi relinquatur glo<lb/>bus, ut in inclinato plano EF ad de&longs;cen&longs;um pronus contra &longs;ub<lb/>jectum planum nitatur, à quo cogitur, ut in motu à recto, quod <lb/>ad univer&longs;i centrum e&longs;t, itinere deflectat. </s>

<s>Jam verò &longs;i globum A pariter ex perpendiculo CA penden<lb/>tem contingat planum aliud non quidem horizontale, &longs;ed in<lb/>clinatum EF, manife&longs;tum e&longs;t totam pariter gravitationem <lb/>exerceri contra clavum C retinentem, planumque contingens <pb xlink:href="017/01/110.jpg" pagenum="94"/>omninò non urgeri, ni&longs;i præci&longs;o funiculo &longs;ibi relinquatur glo<lb/>bus, ut in inclinato plano EF ad de&longs;cen&longs;um pronus contra &longs;ub<lb/>jectum planum nitatur, à quo cogitur, ut in motu à recto, quod <lb/>ad univer&longs;i centrum e&longs;t, itinere deflectat. </s>

<s>Quod &longs;i planum inclinatum EF ita &longs;u&longs;pen&longs;o globo A &longs;ubji<lb/>ciatur, ut recta linea centrum gravitatis A, & punctum &longs;u&longs;<lb/>pen&longs;ionis H conjungens parallela &longs;it lineæ EF, quam in plano <lb/>inclinato de&longs;cendens globus percurreret; momenta quidem <lb/>gravitationis, quæ in eo plano obtineret globus ad de&longs;cenden<lb/>dum, exercebit adversùs clavum retinentem in H, &longs;ubjectum <lb/>verò planum EF perinde urgebitur, atque &longs;i nullo retinente li<lb/>bera e&longs;&longs;et globo de&longs;cendendi facultas: vis enim, quâ prohibe<lb/>tur globus, ne moveatur &longs;ecundùm rectam lineam, ut con&longs;tat, <lb/>opponitur de&longs;cen&longs;ui in plano inclinato; ejus autem directio <lb/>AH non opponitur nitenti in planum, cui parallela e&longs;t. </s>

Line 1379

<s>Quæ verò fuerit inter <lb/>CA & HA, tollet quidem de&longs;cen&longs;um in plano EF inclinato; <lb/>&longs;ed non omninò prohibebit, quin &longs;ubjectum planum, cui aliqua<lb/>tenus nititur, urgeat. </s>

<s>Id quod facilè intelligas, &longs;i plana &longs;ubjecta <lb/>BD horizontale, & EF inclinatum ex maximè flexili mate<lb/>ria, puta, papyro, concipias; in quâlibet enim &longs;u&longs;pen&longs;ione <lb/>inter C, & L, planum BD horizontale flectetur ex pondere, <lb/>non autem inclinatum EF: contrà verò in omni &longs;u&longs;pen&longs;ione <pb pagenum="95"/>inter C & H, planum inclinatum EF flectetur; at non item ho<lb/>rizontale BD, quia nimirum inclinatum EF prohibet, ne recta <lb/>HA ad perpendiculum accedens verticalis fiat. </s>

<s>Id quod facilè intelligas, &longs;i plana &longs;ubjecta <lb/>BD horizontale, & EF inclinatum ex maximè flexili mate<lb/>ria, puta, papyro, concipias; in quâlibet enim &longs;u&longs;pen&longs;ione <lb/>inter C, & L, planum BD horizontale flectetur ex pondere, <lb/>non autem inclinatum EF: contrà verò in omni &longs;u&longs;pen&longs;ione <pb xlink:href="017/01/111.jpg" pagenum="95"/>inter C & H, planum inclinatum EF flectetur; at non item ho<lb/>rizontale BD, quia nimirum inclinatum EF prohibet, ne recta <lb/>HA ad perpendiculum accedens verticalis fiat. </s>

<s>Unum hic præterea con&longs;iderandum venit, quod &longs;uperiori <lb/>capite &longs;ubindicatum fuit; &longs;i videlicet non ex flexili fune deor<lb/>&longs;um pendeat globus, &longs;ed rigido bacillo circà axem inferiùs po<lb/>&longs;itum ver&longs;atili adnectatur &longs;upe<lb/><figure id="fig17"/><lb/>riùs. </s>

<s>Sic rectus bacillus AB, cujus <lb/>extremitas altera adnexum ha<lb/>beat globum B, altera &longs;it circà <lb/>axem A ver&longs;atilis. </s>

Line 1397

<s>Quia tamen in motu globus ex bacilli conver&longs;ione circà <lb/>axem A non pote&longs;t percurrere rectam BC, &longs;ed ita retinetur à <lb/>bacillo, cui adnectitur, ut de&longs;cendat in F, jam in alio plano <lb/>minorem inclinationem habente con&longs;titutus intelligitur, nimi<lb/>rùm in plano FG, quod cum perpendiculo FL efficit angulum <lb/>inclinationis GFL æqualem angulo LAF elevationis: id quod <lb/>eâdem planè methodo, ac &longs;uperiùs factum e&longs;t, demon&longs;tratur. <pb pagenum="96"/>Ex quo fit, quemadmodum in huju&longs;modi conver&longs;ione globus <lb/>in alio atque alio plano inclinato con&longs;tituitur, ita alia atque alia <lb/>obtinere gravitatis momenta: in B &longs;iquidem gravitat ut BD ad <lb/>BE, in F verò ut HF ad FI. </s>

<s>Quia tamen in motu globus ex bacilli conver&longs;ione circà <lb/>axem A non pote&longs;t percurrere rectam BC, &longs;ed ita retinetur à <lb/>bacillo, cui adnectitur, ut de&longs;cendat in F, jam in alio plano <lb/>minorem inclinationem habente con&longs;titutus intelligitur, nimi<lb/>rùm in plano FG, quod cum perpendiculo FL efficit angulum <lb/>inclinationis GFL æqualem angulo LAF elevationis: id quod <lb/>eâdem planè methodo, ac &longs;uperiùs factum e&longs;t, demon&longs;tratur. <pb xlink:href="017/01/112.jpg" pagenum="96"/>Ex quo fit, quemadmodum in huju&longs;modi conver&longs;ione globus <lb/>in alio atque alio plano inclinato con&longs;tituitur, ita alia atque alia <lb/>obtinere gravitatis momenta: in B &longs;iquidem gravitat ut BD ad <lb/>BE, in F verò ut HF ad FI. </s>

<s>Cum igitur Radius utrobique ex <lb/>hypothe&longs;i æqualis &longs;it, videlicet DB, & HF, major autem &longs;it <lb/>BE Secans majoris anguli DBE, quàm FI Secans minoris an<lb/>guli HFI, con&longs;tat ex 8. lib.

Line 1405

<s>Ex his attentè perpen&longs;is facilis e&longs;t tran&longs;itus ad &longs;u&longs;pen&longs;orum <lb/>corporum gravitationem inve&longs;tigandam. </s>

<s>Sit enim jam non in<lb/><figure id="fig18"/><lb/>feriùs, &longs;ed &longs;uperiùs po&longs;itus <lb/>Axis A, circa quem ver&longs;a<lb/>tilis e&longs;t funiculus AB, cui <lb/>globus B adnectitur. </s>

<s>Sit enim jam non in<lb/><figure id="id.017.01.112.1.jpg" xlink:href="017/01/112/1.jpg"/><lb/>feriùs, &longs;ed &longs;uperiùs po&longs;itus <lb/>Axis A, circa quem ver&longs;a<lb/>tilis e&longs;t funiculus AB, cui <lb/>globus B adnectitur. </s>

<s>Con<lb/>&longs;tat &longs;anè non ad perpendi<lb/>culum BD cadere po&longs;&longs;e <lb/>globum B; &longs;ed à recto deor<lb/>&longs;um tramite deflectere, fu<lb/>niculo &longs;cilicet AB eum re<lb/>tinente, quemadmodum ri<lb/>gidus bacillus OB eum ali<lb/>quatenùs &longs;u&longs;tineret. </s>

Line 1413

<s>Momenta igitur gra<lb/>vitatis in eo plano inclinato, ad gravitatis momenta &longs;i corpus <lb/>liberè de&longs;cenderet, in eâ &longs;unt Ratione, quæ e&longs;t DB ad BE; <lb/>hoc e&longs;t DO ad OB per 8. lib.6. hoc e&longs;t KB ad BA per 4.lib.6. <lb/>Haud di&longs;pari methodo ratiocinantes o&longs;tendemus globi in F <lb/>con&longs;tituti momenta ad gravitandum e&longs;&longs;e perinde, atque &longs;i e&longs;<lb/>&longs;et in plano inclinato FI, in quod ad rectos angulos cadit fu<lb/>niculus AF; ac proinde gravitatio in F, &longs;i de&longs;cendendi vis <lb/>præcisè &longs;pectetur, ad gravitationem globi liberi, e&longs;t ut HF <lb/>ad FI, hoc e&longs;t, ut GF ad FA. </s>

<s>Ex quo apertiùs liquet, quàm ut in eo explicando diutiùs <pb pagenum="97"/>immorari oporteat, alia &longs;ubinde atque alia e&longs;&longs;e momenta gra<lb/>vitatis corporis &longs;u&longs;pen&longs;i, pro ut major aut minor e&longs;t angulus <lb/>declinationis à perpendiculo AG, haud aliter quàm &longs;i in aliis <lb/>atque aliis planis inclinatis con&longs;titueretur; quo enim minor e&longs;t <lb/>declinationis angulus GAF, eò major e&longs;t angulus inclinatio<lb/>nis plani, quippe qui e&longs;t illius complementum. </s>

<s>Ex quo apertiùs liquet, quàm ut in eo explicando diutiùs <pb xlink:href="017/01/113.jpg" pagenum="97"/>immorari oporteat, alia &longs;ubinde atque alia e&longs;&longs;e momenta gra<lb/>vitatis corporis &longs;u&longs;pen&longs;i, pro ut major aut minor e&longs;t angulus <lb/>declinationis à perpendiculo AG, haud aliter quàm &longs;i in aliis <lb/>atque aliis planis inclinatis con&longs;titueretur; quo enim minor e&longs;t <lb/>declinationis angulus GAF, eò major e&longs;t angulus inclinatio<lb/>nis plani, quippe qui e&longs;t illius complementum. </s>

<s>Con&longs;tat &longs;i qui<lb/>dem angulos GAF, GFA &longs;imul, e&longs;&longs;e æquales tùm Recto <lb/>AFI, tùm Recto GFH; ac proinde dempto communi GFI, <lb/>remanet HFI angulus inclinationis plani æqualis angulo <lb/>GFA, qui e&longs;t complementum anguli declinationis GAF. </s>

Line 1433

1. ac propterea minor e&longs;t incli<lb/>natio plani FN facientis cum rectâ MF angulum Rectum, <lb/>quàm &longs;it inclinatio plani FI, cui perpendicularis e&longs;t recta <lb/>AF. </s>

<s>Plus igitur momenti ad gravitandum habet glo-<pb pagenum="98"/>bus F, &longs;i ex breviore funiculo MF pendeat, quàm &longs;i ex <lb/>longiore AF. </s>

<s>Plus igitur momenti ad gravitandum habet glo-<pb xlink:href="017/01/114.jpg" pagenum="98"/>bus F, &longs;i ex breviore funiculo MF pendeat, quàm &longs;i ex <lb/>longiore AF. </s>

<s>Quæ cum ita &longs;int, haud &longs;anè incongrua &longs;e nobis offert me<lb/>thodus pondus ex depre&longs;&longs;iore in altiorem locum transferendi; <lb/>&longs;i videlicet id curemus, ut ex &longs;atis valido & longiore fune &longs;u&longs;<lb/>pendatur; &longs;ublato etenim partium attritu, qui fieret, &longs;i per pla<lb/>num raptaretur pondus, minore virium jacturâ trahi pote&longs;t. </s>

<s>Sit corpus grave ubi A, quod at<lb/><figure id="fig19"/><lb/>tollere oporteat, & in &longs;uperiorem <lb/>locum RS transferre. </s>

<s>Sit corpus grave ubi A, quod at<lb/><figure id="id.017.01.114.1.jpg" xlink:href="017/01/114/1.jpg"/><lb/>tollere oporteat, & in &longs;uperiorem <lb/>locum RS transferre. </s>

<s>Si ex C brevio<lb/>ri fune &longs;u&longs;pendatur, trahere illud po<lb/>terit u&longs;que in R, quicumque facto de<lb/>clinationis angulo ACR pote&longs;t illud <lb/>cum aliquo virium exce&longs;&longs;u retinere, <lb/>& ob&longs;i&longs;tere gravitatis momentis, quæ <lb/>obtinet in R. </s>

Line 1453

1. &longs;i ex &longs;ummâ duorum Rectorum au<lb/>ferantur duo majores anguli DAS, DSA, relinquitur ADS <lb/>minor, quàm &longs;i ex eâdem duorum Rectorum &longs;ummâ auferan<lb/>tur duo minores CAR, CRA, hoc e&longs;t minor quàm ACR. </s>

<lb/><s>Ut autem clariùs innote&longs;cat, quænam &longs;it gravitationum Ratio <lb/>pro funiculi longitudine, &longs;it corpus grave in R: & primùm <lb/>quidem ex C pendeat funiculo breviore CR, deinde ex D lon<lb/>giore funiculo DR: qui&longs;quis retineat corpus in R con&longs;titu<lb/>tum, atque de&longs;cen&longs;u prohibeat, faciliùs retinebit, cum ex D, <pb pagenum="99"/>quàm cùm ex C, pendebit; quia declinationis angulus XCR <lb/>major e&longs;t angulo XDR per 16. lib.

<lb/><s>Ut autem clariùs innote&longs;cat, quænam &longs;it gravitationum Ratio <lb/>pro funiculi longitudine, &longs;it corpus grave in R: & primùm <lb/>quidem ex C pendeat funiculo breviore CR, deinde ex D lon<lb/>giore funiculo DR: qui&longs;quis retineat corpus in R con&longs;titu<lb/>tum, atque de&longs;cen&longs;u prohibeat, faciliùs retinebit, cum ex D, <pb xlink:href="017/01/115.jpg" pagenum="99"/>quàm cùm ex C, pendebit; quia declinationis angulus XCR <lb/>major e&longs;t angulo XDR per 16. lib.

1. Verùm qua Ratione, in<lb/>quis, vires, quas in utroque ca&longs;u retinens exerit, di&longs;criminan<lb/>tur? </s>

Line 1467

<lb/><s>Quemcumque enim interrogaveris, quæ &longs;it Ratio 2/7 ad 6/7 illicò <lb/>re&longs;pondebit e&longs;&longs;e &longs;ubtriplam, &longs;ecunda &longs;cilicet ter continet pri<lb/>mam, ut con&longs;tat &longs;i ter po&longs;itam Rationem 2/7 in &longs;ummam colligas; <lb/>neque enim <expan abbr="id&etilde;">idem</expan> e&longs;t Rationem Rationis e&longs;&longs;e &longs;ubtriplam, ac &longs;ub<lb/>triplicatam; Ratio &longs;iquidem 2/7 e&longs;t &longs;ubtriplicata Rationis (8/343). Si <lb/>igitur pariter quæras, quænam &longs;it Ratio 7/2 ad 7/6 rectè re&longs;ponde<lb/>bit eam e&longs;&longs;e triplam, hoc e&longs;t reciprocè ut 6 ad 2: id quod ma<lb/>nife&longs;tè apparebit, &longs;i illas ad denominationem eandem, hoc e&longs;t <lb/>ad eumdem Con&longs;equentem terminum reduxeris, &longs;unt nimirum <lb/>ut (42/12) ad (14/12), hoc e&longs;t ut 6 ad 2. </s>

<s>Ex quibus obiter patet methodus exponendi per lineas pro<lb/>portionem duarum Rationum etiam numeris non explicabi<lb/>lium; &longs;i videlicet fiat ut Antecedens &longs;ecundæ Rationis ad &longs;uum <lb/>Con&longs;equentem, ita Antecedens datus primæ Rationis ad alium <lb/>novum Con&longs;equentem; erit enim prima Ratio data ad &longs;ecun-<pb pagenum="100"/>dam rationem daram reciprocè ut novus Con&longs;equens terminus <lb/>ad datum Con&longs;equentem primæ Rationis: aut etiam &longs;i fiat ut <lb/>Con&longs;equens &longs;ecundæ Rationis ad &longs;uum Antecedentem, ita con<lb/>&longs;equens primæ Rationis ad alium novum Antecedentem; erit <lb/>enim prima ratio data ad &longs;ecundam Rationem datam, directè <lb/>ut datus Antecedens primæ Rationis ad novum Antecedentem. </s>

<s>Ex quibus obiter patet methodus exponendi per lineas pro<lb/>portionem duarum Rationum etiam numeris non explicabi<lb/>lium; &longs;i videlicet fiat ut Antecedens &longs;ecundæ Rationis ad &longs;uum <lb/>Con&longs;equentem, ita Antecedens datus primæ Rationis ad alium <lb/>novum Con&longs;equentem; erit enim prima Ratio data ad &longs;ecun-<pb xlink:href="017/01/116.jpg" pagenum="100"/>dam rationem daram reciprocè ut novus Con&longs;equens terminus <lb/>ad datum Con&longs;equentem primæ Rationis: aut etiam &longs;i fiat ut <lb/>Con&longs;equens &longs;ecundæ Rationis ad &longs;uum Antecedentem, ita con<lb/>&longs;equens primæ Rationis ad alium novum Antecedentem; erit <lb/>enim prima ratio data ad &longs;ecundam Rationem datam, directè <lb/>ut datus Antecedens primæ Rationis ad novum Antecedentem. </s>

<s>Con&longs;ideratâ hactenus unicâ & &longs;implici corporis gravis &longs;u&longs;<lb/>pen&longs;ione, gradum facere oportet ad gravitationis rationes in<lb/>ve&longs;tigandas, &longs;i duplex fuerit &longs;u&longs;pen&longs;io. </s>

<s>Sit enim globus A tùm <lb/><figure id="fig20"/><lb/>ex B, tùm ex C &longs;u&longs;pen&longs;us fu<lb/>niculis BA & CA. </s>

<s>Sit enim globus A tùm <lb/><figure id="id.017.01.116.1.jpg" xlink:href="017/01/116/1.jpg"/><lb/>ex B, tùm ex C &longs;u&longs;pen&longs;us fu<lb/>niculis BA & CA. </s>

<s>Haud du<lb/>bium quin tota corporis gravi<lb/>tas ex B & C pendeat; &longs;ed quâ <lb/>Ratione &longs;ingulæ vires eidem <lb/>gravitati ob&longs;i&longs;tant, de hoc po<lb/>te&longs;t ambigi. </s>

Line 1487

<s>Quare fiat angulus DAF æqualis angulo EAC, & e&longs;t trian<lb/>gulum DAF ob angulorum æqualitatem &longs;imile triangulo <lb/>EAC; ac propterea per 4. lib.

6. ut EA ad AC, ita DA ad <pb pagenum="101"/>AF. </s>

6. ut EA ad AC, ita DA ad <pb xlink:href="017/01/117.jpg" pagenum="101"/>AF. </s>

<s>Ergo vis de&longs;cendendi ex CA e&longs;t ut DA ad AF, & vis <lb/>de&longs;cendendi ex BA e&longs;t ut DA ad AB: igitur duæ hæ Ratio<lb/>nes &longs;unt reciprocè ut BA ad AF; atque adeò B quidem reti<lb/>nens, ne de&longs;cendat ex CA, exerit vires ut BA; C verò reti<lb/>nens, ne de&longs;cendat ex BA, adhibet conatum ut FA; & quæ <lb/>componitur ex BA, AF, totum gravitatis momentum, quod <lb/>corpori &longs;u&longs;pen&longs;o ine&longs;t, repræ&longs;entat. </s>

Line 1499

<s>Hic autem hæ&longs;itantem videre mihi videor non neminem ex <lb/>iis, quæ dicebantur, colligentem corpus A primùm ex decli<lb/>nante BA æquè ac ex perpendiculari BD gravitare; deinde <lb/>plus ad de&longs;cendendum momenti obtinere, &longs;i ex duobus funi<lb/>culis, quàm &longs;i ex unico pendeat. </s>

<s>Si enim angulus declinatio<lb/>nis DBA &longs;it gr. 22. 12′; e&longs;t DA &longs;inus dati anguli ad radium <lb/>BA ut 37784 ad 100000: & &longs;i angulus declinationis ECA <lb/>&longs;it gr. 54. 35, e&longs;t EA &longs;inus dati anguli ad Radium CA ut <lb/>81496 ad 100000. At ex con&longs;tructione triangulum DAF &longs;i<lb/>mile e&longs;t triangulo EAC; igitur DA ad AF e&longs;t ut 81496 ad <lb/>100000. E&longs;t autem DA in particulis Radij BA partium 37784; <lb/>igitur &longs;i fiat ut 81496 ad 100000, ita 37784, ad aliud, erit AF <lb/>earumdem particularum 46363, quarum BA e&longs;t 100000. Qua<lb/>re compo&longs;ita BA, AF momenta &longs;unt 146363, cum tamen <lb/>momentum in perpendiculari AD &longs;it tantum 100000. Cum <lb/>verò dictum &longs;it B clavum re&longs;i&longs;tere ponderi A ut BA, C autem <pb pagenum="102"/>ut FA, manife&longs;tum e&longs;t B clavum retinere ut 100000 quando <lb/>declinat BA à perpendiculo: Atqui etiam in perpendiculo BD <lb/>retinet ut 100000, igitur idem e&longs;t ponderis tùm ex BD, tùm <lb/>ex BA momentum; id quod e&longs;t ab&longs;urdum. </s>

<s>Si enim angulus declinatio<lb/>nis DBA &longs;it gr. 22. 12′; e&longs;t DA &longs;inus dati anguli ad radium <lb/>BA ut 37784 ad 100000: & &longs;i angulus declinationis ECA <lb/>&longs;it gr. 54. 35, e&longs;t EA &longs;inus dati anguli ad Radium CA ut <lb/>81496 ad 100000. At ex con&longs;tructione triangulum DAF &longs;i<lb/>mile e&longs;t triangulo EAC; igitur DA ad AF e&longs;t ut 81496 ad <lb/>100000. E&longs;t autem DA in particulis Radij BA partium 37784; <lb/>igitur &longs;i fiat ut 81496 ad 100000, ita 37784, ad aliud, erit AF <lb/>earumdem particularum 46363, quarum BA e&longs;t 100000. Qua<lb/>re compo&longs;ita BA, AF momenta &longs;unt 146363, cum tamen <lb/>momentum in perpendiculari AD &longs;it tantum 100000. Cum <lb/>verò dictum &longs;it B clavum re&longs;i&longs;tere ponderi A ut BA, C autem <pb xlink:href="017/01/118.jpg" pagenum="102"/>ut FA, manife&longs;tum e&longs;t B clavum retinere ut 100000 quando <lb/>declinat BA à perpendiculo: Atqui etiam in perpendiculo BD <lb/>retinet ut 100000, igitur idem e&longs;t ponderis tùm ex BD, tùm <lb/>ex BA momentum; id quod e&longs;t ab&longs;urdum. </s>

Line 1515

<s>At &longs;i globus ex alio <lb/>prætereà funiculo CA pendeat, idem funiculus BA re&longs;i&longs;tit <lb/>etiam momentis illis, quibus globus A de&longs;cenderet in plano in<lb/>clinato, cui CA ad rectos angulos in&longs;i&longs;teret, quæ momenta (ut <lb/>&longs;ummum) &longs;unt ad BA radium ut 81496. Momenta verò qui<lb/>bus urgeret planum inclinatum perpendiculare ad BA, &longs;unt, ex <lb/>dictis &longs;uperiori capite, ut Sinus Ver&longs;us anguli inclinationis pla<lb/>ni; inclinatio autem plani, ut paulò &longs;uperiùs hoc eodem capite <lb/>demon&longs;travimus, e&longs;t complementum anguli declinationis <lb/>DBA. </s>

<s>Quare differentia inter DA 37784 &longs;inum rectum an<lb/>guli declinationis, & radium BA 100000, cum &longs;it Sinus Ver<lb/>&longs;us anguli inclinationis plani, &longs;unt momenta 62216 addenda <pb pagenum="103"/>prioribus 81496; adeò ut &longs;umma &longs;it 143712 momentorum, qui<lb/>bus funiculus BA repugnat, &longs;i pondus pendeat etiam ex CA; <lb/>cum tamen &longs;i ex ip&longs;o tantùm funiculo BA penderet, & aliquis <lb/>e&longs;&longs;et præcisè obluctans viribus ad de&longs;cendendum, idem funicu<lb/>lus BA re&longs;i&longs;teret &longs;olùm momentis 62216. </s>

<s>Quare differentia inter DA 37784 &longs;inum rectum an<lb/>guli declinationis, & radium BA 100000, cum &longs;it Sinus Ver<lb/>&longs;us anguli inclinationis plani, &longs;unt momenta 62216 addenda <pb xlink:href="017/01/119.jpg" pagenum="103"/>prioribus 81496; adeò ut &longs;umma &longs;it 143712 momentorum, qui<lb/>bus funiculus BA repugnat, &longs;i pondus pendeat etiam ex CA; <lb/>cum tamen &longs;i ex ip&longs;o tantùm funiculo BA penderet, & aliquis <lb/>e&longs;&longs;et præcisè obluctans viribus ad de&longs;cendendum, idem funicu<lb/>lus BA re&longs;i&longs;teret &longs;olùm momentis 62216. </s>

<s>Eâdem methodo deprehendes funiculum CA, &longs;i ex eo &longs;olo <lb/>globus pendeat, retinere momenta 18504: at &longs;i etiam ex BA <lb/>globus pendeat, additis momentis 37784, tota momentorum <lb/>&longs;umma e&longs;t 56288. Jam &longs;ummam hanc priori 143712 adde, & <lb/>erit tota momentorum &longs;umma 200000: perinde atque &longs;i corpo<lb/>ris gravitas fui&longs;&longs;et duplicata. </s>

Line 1523

<s>Hæc tamen ut veritati congruant, ita &longs;olùm accipienda &longs;unt, <lb/>ut momenta &longs;ingula ex utrâque funiculorum declinatione orta <lb/>particulatim &longs;umantur: pondus &longs;cilicet ex utroque &longs;u&longs;pen&longs;um <lb/>perinde hactenus con&longs;ideratum e&longs;t, ac &longs;i momenta ip&longs;a de&longs;cen<lb/>dendi in diver&longs;as partes abeuntia momentum quoddam ex <lb/>utri&longs;que temperatum non con&longs;tituerent; re autem ipsa quod ex <lb/>iis componitur momentum, non ex ip&longs;orum momentorum ad<lb/>ditione conflatur, &longs;ed ex ip&longs;is temperatur. </s>

<s>Si enim mobile &longs;it <lb/>ubi A, impetum verò cum tali <lb/><figure id="fig21"/><lb/>directione habeat, quâ deferri <lb/>po&longs;&longs;it æquabiliter per rectam <lb/>AB, alio autem impetu feratur <lb/>æquabiliter directum in C, no<lb/>tum omnibus e&longs;t motum, qui ex <lb/>AB & AC componitur, non fieri ex earum additione, &longs;ed tem<lb/>perari in lineam AD, quæ dimetiens e&longs;t parallelogrammi, quod <lb/>ex earumdem linearum AB, AC longitudine, ac mutuâ incli<lb/>natione formam de&longs;umit. </s>

<s>Si enim mobile &longs;it <lb/>ubi A, impetum verò cum tali <lb/><figure id="id.017.01.119.1.jpg" xlink:href="017/01/119/1.jpg"/><lb/>directione habeat, quâ deferri <lb/>po&longs;&longs;it æquabiliter per rectam <lb/>AB, alio autem impetu feratur <lb/>æquabiliter directum in C, no<lb/>tum omnibus e&longs;t motum, qui ex <lb/>AB & AC componitur, non fieri ex earum additione, &longs;ed tem<lb/>perari in lineam AD, quæ dimetiens e&longs;t parallelogrammi, quod <lb/>ex earumdem linearum AB, AC longitudine, ac mutuâ incli<lb/>natione formam de&longs;umit. </s>

<s>Quâ in re plurimum intere&longs;t, quam <lb/>invicem habeant inclinationem directiones motuum in diver&longs;a <lb/>abeuntium; quò enim acutiorem angulum con&longs;tituunt, eò lon<lb/>giùs provehitur mobile, ut AB, AC in acutum angulum <pb pagenum="104"/>coëuntibus mobile ex A in D venit: quò verò obtu&longs;ior fuerit <lb/>angulus, eò etiam brevius e&longs;t iter ip&longs;ius mobilis, ut contingit, <lb/>&longs;i ex B directum per rectas BA, BD ad obtu&longs;um angulum <lb/>con&longs;titutas moveatur, &longs;i&longs;titur enim in C, & brevior e&longs;t diame<lb/>ter BC quàm AD, ut ex 24. lib.

<s>Quâ in re plurimum intere&longs;t, quam <lb/>invicem habeant inclinationem directiones motuum in diver&longs;a <lb/>abeuntium; quò enim acutiorem angulum con&longs;tituunt, eò lon<lb/>giùs provehitur mobile, ut AB, AC in acutum angulum <pb xlink:href="017/01/120.jpg" pagenum="104"/>coëuntibus mobile ex A in D venit: quò verò obtu&longs;ior fuerit <lb/>angulus, eò etiam brevius e&longs;t iter ip&longs;ius mobilis, ut contingit, <lb/>&longs;i ex B directum per rectas BA, BD ad obtu&longs;um angulum <lb/>con&longs;titutas moveatur, &longs;i&longs;titur enim in C, & brevior e&longs;t diame<lb/>ter BC quàm AD, ut ex 24. lib.

1. &longs;atis manife&longs;tum e&longs;t geo<lb/>metris, & ip&longs;a motuum natura po&longs;tulat; qui nimirum &longs;ibi in<lb/>vicem magis adver&longs;antur, magi&longs;que in diver&longs;a abeunt, &longs;e ma<lb/>gis elidunt, id quod fit ex angulo obtu&longs;o DBA; qui verò mi<lb/>nùs in diver&longs;a abeunt, id quod fit ex angulo acuto CAB, &longs;e pa<lb/>riter minùs elidunt. </s>

Line 1553

<s>Sunt igitur in triangulo AGN nota latera AG, <lb/>GN (e&longs;t enim ex 34. lib.

1. GN oppo&longs;ito lateri AR æquale) <pb pagenum="105"/>unâ cum angulo G comprehen&longs;o, & ex Trigonometriâ inno<lb/>te&longs;cit tertium latus AN. </s>

1. GN oppo&longs;ito lateri AR æquale) <pb xlink:href="017/01/121.jpg" pagenum="105"/>unâ cum angulo G comprehen&longs;o, & ex Trigonometriâ inno<lb/>te&longs;cit tertium latus AN. </s>

<s>Quare cum latus AG &longs;it ex &longs;upe<lb/>riùs con&longs;titutis 81496, & GN, hoc e&longs;t AR, 37784, fiat ut <lb/>laterum AG, GN &longs;umma 119280 ad eorumdem differen<lb/>tiam 43712, ita &longs;emi&longs;ummæ angulorum ad ba&longs;im, hoc e&longs;t <lb/>gr. 51. 36 1/2 Tangens 126205 ad 46249 Tangentem gr. 24. 49′ 2/5 <lb/>differentiæ infra, vel &longs;upra eandem &longs;emi&longs;ummam. </s>

Line 1579

<s>Quemadmodum verò de momentis de&longs;cendendi in planis <lb/>inclinatis ratiocinati &longs;umus, ita pariter in unum coale&longs;cere di<lb/>cenda &longs;unt momenta, quibus funiculi pondus retinentes ip&longs;um <lb/>quodammodo avellere conantur à plano inclinato, ne illud ur<lb/>geat; hæc enim pariter momenta in diver&longs;a abeunt &longs;ecun<lb/>dùm ip&longs;am funiculorum directionem. </s>

<s>Sunt autem momenta <lb/>illa Sinus Ver&longs;i angulorum inclinationis planorum; qui haben<lb/>tur, &longs;i Sinus Recti complementorum, hoc e&longs;t angulorum de-<pb pagenum="106"/><figure id="fig22"/><lb/>clinationis funiculorum, de<lb/>mantur ex Radio. </s>

<s>Sunt autem momenta <lb/>illa Sinus Ver&longs;i angulorum inclinationis planorum; qui haben<lb/>tur, &longs;i Sinus Recti complementorum, hoc e&longs;t angulorum de-<pb xlink:href="017/01/122.jpg" pagenum="106"/><figure id="id.017.01.122.1.jpg" xlink:href="017/01/122/1.jpg"/><lb/>clinationis funiculorum, de<lb/>mantur ex Radio. </s>

<s>Itaque ex <lb/>BA auferatur BF ip&longs;i DA <lb/>æqualis, & e&longs;t FA Sinus Ver<lb/>&longs;us anguli inclinationis: po&longs;ita <lb/>e&longs;t autem declinatio DBA <lb/>gr.22. 12′, igitur FA e&longs;t parti<lb/>cularum 62216; & declinatio <lb/>ECA gr. 54. 35′; igitur factâ <lb/>CG æquali ip&longs;i AE, remanet <lb/>GA particularum 18504, quarum CA e&longs;t 100000. Quare ut <lb/>habeantur particulæ eju&longs;dem rationis cum particulis AF, fiat <lb/>ut CA ad AG, ita BA ad AH, & e&longs;t AH particularum 18504 <lb/>homologarum particulis AF. </s>

Line 1605

<s>Inventa itaque momenta compo&longs;ita tùm in planis inclinatis, <lb/>tùm in plana inclinata, dividantur juxta Rationem momento-<pb pagenum="107"/>rum &longs;implicium, ut innote&longs;cat, quid demum cuique fi<gap/><lb/>tribuendum &longs;it in pondere retinendo. </s>

<s>Inventa itaque momenta compo&longs;ita tùm in planis inclinatis, <lb/>tùm in plana inclinata, dividantur juxta Rationem momento-<pb xlink:href="017/01/123.jpg" pagenum="107"/>rum &longs;implicium, ut innote&longs;cat, quid demum cuique funicolo <lb/>tribuendum &longs;it in pondere retinendo. </s>

<s>Momentum de&longs;cenden<lb/>di compo&longs;itum inventum e&longs;t &longs;u&longs;periùs 81613, &longs;implicia &longs;unt <lb/>81496, & 37784. Fiat ut igitur ut &longs;implicium momentorum <lb/>&longs;umma 119280 ad corum alterutrum, puta ad 37784, ita mo<lb/>mentum compo&longs;itum 81613 ad aliud, & provenit 25852 pars <lb/>illius momenti pertinens ad funiculum CA, qui retinet pon<lb/>dus; cujus vis de&longs;cendendi e&longs;t DA 37784. Reliqua autem mo<lb/>menti 81613 pars 55761 pertinet ad funiculum BA retinentem <lb/>pondus, cujus vis de&longs;cendendi e&longs;t EA 81496. Pari ratione fiat <lb/>ut Sinuum Ver&longs;orum angulorum inclinationis &longs;implicium <lb/>62216, atque 18504 &longs;umma 80720 ad corum alterutrum, pu<lb/>ta ad 18504, ita momentum compo&longs;itum inventum 68852 ad <lb/>aliud, & provenit pro minori 15783, pro majori verò 53069. <lb/>Quare funiculus BA minorem habens declinationem, & plus <lb/>&longs;u&longs;tinet in &longs;uo plano magis inclinato, cui perpendicularis e&longs;t, <lb/>nimirum ut 53069, & plus retinet in plano reliquo minùs in<lb/>clinato, nimirum ut 55761: contra verò funiculus CA, & mi<lb/>nus &longs;u&longs;tinet, &longs;cilicet ut 15783, & minus retinet &longs;cilicet ut <lb/>25852. Funiculus itaque BA exercet vires ut 108830, & fu<lb/>niculus CA ut 41635, & totum corporis &longs;u&longs;pen&longs;i momentum <lb/>e&longs;t 150465. </s>

Line 1613

<s>Illud po&longs;tremò hîc o&longs;tendendum &longs;upere&longs;t, plus &longs;cilicet in<lb/>e&longs;&longs;e po&longs;&longs;e momenti ad de&longs;cendendum corpori ex duobus funi<lb/>culis invicem inclinatis &longs;u&longs;pen&longs;o, quàm &longs;i ex unico ad per<lb/>pendiculum pendeat. </s>

<s>Orbiculo circà &longs;uum axem C ver&longs;atili, <pb pagenum="108"/><figure id="fig23"/><lb/>ac &longs;ecundùm extremam <lb/>oram excavato, in&longs;eratur <lb/>funiculus AFB, ex quo <lb/>æqualia hinc, & hinc <lb/>pondera A, & B pen<lb/>deant: nullus planè &longs;e<lb/>quitur motus, quia utrum<lb/>que ex perpendiculo pen<lb/>det, & quantâ vi alterum conatur deor&longs;um, pari nu&longs;u alterum <lb/>repugnat, ne elevetur. </s>

<s>Orbiculo circà &longs;uum axem C ver&longs;atili, <pb xlink:href="017/01/124.jpg" pagenum="108"/><figure id="id.017.01.124.1.jpg" xlink:href="017/01/124/1.jpg"/><lb/>ac &longs;ecundùm extremam <lb/>oram excavato, in&longs;eratur <lb/>funiculus AFB, ex quo <lb/>æqualia hinc, & hinc <lb/>pondera A, & B pen<lb/>deant: nullus planè &longs;e<lb/>quitur motus, quia utrum<lb/>que ex perpendiculo pen<lb/>det, & quantâ vi alterum conatur deor&longs;um, pari nu&longs;u alterum <lb/>repugnat, ne elevetur. </s>

<s>Quærenti igitur, quantum momenti <lb/>pondus B habeat ad de&longs;cendendum, utique re&longs;pondebis omni<lb/>nò par e&longs;&longs;e momento ponderis A. </s>

Line 1625

<s>Non igitur hoc ab&longs;urdum e&longs;t, <lb/>quod con&longs;titutam à nobis momentorum hypothe&longs;im con&longs;equa<lb/>tur, &longs;ed potiùs ip&longs;i naturæ no&longs;tra con&longs;entit hypothe&longs;is, cui ro<lb/>bur adjicit experientia; nec ex eo capite perperam philo&longs;opha<lb/>ti videmur, quòd in perpendiculo minus momenti, quàm ex <lb/>duplici funiculo &longs;u&longs;pen&longs;um pondus habere dicendum &longs;it. </s>

<s>Ex his, quæ de corpore ex binis funiculis &longs;u&longs;pen&longs;o hactenus <lb/>di&longs;putata &longs;unt, non difficilis erit conjectura eorum, quæ dicen<lb/>da &longs;int, &longs;i ex tribus aut quatuor &longs;u&longs;pendatur, &longs;ivè illi immedia<lb/>tè adnectantur ip&longs;i ponderi, &longs;ivè funiculus unus demum in plu<lb/>ra capita dividatur, ex quibus fiat &longs;u&longs;pen&longs;io: neque enim his <lb/>diutiùs ad nau&longs;eam immorandum cen&longs;eo. <pb pagenum="109"/><gap desc="hr tag"/></s>

<s>Ex his, quæ de corpore ex binis funiculis &longs;u&longs;pen&longs;o hactenus <lb/>di&longs;putata &longs;unt, non difficilis erit conjectura eorum, quæ dicen<lb/>da &longs;int, &longs;i ex tribus aut quatuor &longs;u&longs;pendatur, &longs;ivè illi immedia<lb/>tè adnectantur ip&longs;i ponderi, &longs;ivè funiculus unus demum in plu<lb/>ra capita dividatur, ex quibus fiat &longs;u&longs;pen&longs;io: neque enim his <lb/>diutiùs ad nau&longs;eam immorandum cen&longs;eo. <pb xlink:href="017/01/125.jpg" pagenum="109"/><gap desc="hr tag"/></s>

<s><emph type="center"/>CAPUT XVI.<emph.end type="center"/></s>

Line 1633

<s>PRoxima e&longs;t iis, quæ hactenus di&longs;putata &longs;unt, præ&longs;ens in<lb/>ve&longs;tigatio gravitationis corporum, &longs;ive nisûs, quo motui <lb/>re&longs;i&longs;tunt, cùm obliquè in plano aliquo trahuntur, aut elevan<lb/>tur: &longs;icut enim toto conatu repugnant elevanti ad perpendicu<lb/>lum, & ab&longs;trahenti à plano, cui in&longs;ident, ita pro majori, aut <lb/>minori obliquitate tractionis aut elevationis magis etiam, aut <lb/>minùs, ob&longs;i&longs;tere experimur. </s>

<s>Et primùm quidem &longs;uper plano <lb/><figure id="fig24"/><lb/>inclinato AB duo pondera <lb/>pror&longs;us æqualia, & &longs;imilia <lb/>intelligantur po&longs;ita in B <lb/>& C, atque linea CE &longs;it <lb/>horizonti BE perpendicu<lb/>laris, ac pondus C filo DC <lb/>ad perpendiculum &longs;u&longs;pen<lb/>datur, ita tamen, ut con<lb/>tingat planum in C, & &longs;it <lb/>recta DE. </s>

<s>Et primùm quidem &longs;uper plano <lb/><figure id="id.017.01.125.1.jpg" xlink:href="017/01/125/1.jpg"/><lb/>inclinato AB duo pondera <lb/>pror&longs;us æqualia, & &longs;imilia <lb/>intelligantur po&longs;ita in B <lb/>& C, atque linea CE &longs;it <lb/>horizonti BE perpendicu<lb/>laris, ac pondus C filo DC <lb/>ad perpendiculum &longs;u&longs;pen<lb/>datur, ita tamen, ut con<lb/>tingat planum in C, & &longs;it <lb/>recta DE. </s>

<s>Item ex D <lb/>puncto ducatur filum DB, <lb/>ut &longs;ur&longs;um trahatur B pon<lb/>dus incumbens plano in<lb/>clinato, dum pariter pon<lb/>dus C &longs;ur&longs;um rectâ trahi<lb/>tur, & à plano avellitur: horum autem funiculorum trahatur <lb/>ex D pars æqualis. </s>

Line 1641

<s>Ductâ itaque lineâ ON horizonti pa<lb/>rallelâ, erit EN altitudo perpendicularis, ad quam a&longs;cendit <lb/>pondus B in plano inclinato interea, dum pondus C venit in V, <lb/>aut E venit in M, e&longs;t enim EM a&longs;&longs;umpta ip&longs;i CV æqualis. </s>

<lb/><s>Quare cum pondus B obliquè trahitur &longs;uper planum inclina-<pb pagenum="110"/>tum, minorem &longs;ubit violentiam, quàm cum ab illo perpendi<lb/>culari elevatione avellitur. </s>

<lb/><s>Quare cum pondus B obliquè trahitur &longs;uper planum inclina-<pb xlink:href="017/01/126.jpg" pagenum="110"/>tum, minorem &longs;ubit violentiam, quàm cum ab illo perpendi<lb/>culari elevatione avellitur. </s>

<s>Hoc tamen ita intelligendum e&longs;t, ut ob&longs;ervetur alia e&longs;&longs;e <lb/>momenta, cùm tractionis linea parallela e&longs;t ip&longs;i plano inclina<lb/>to, ac cùm in planum inclinatum cadit obliqua, ut hîc li<lb/>nea DB. </s>

Line 1653

<s>Similiter intelligatur pondus C elevatum fui&longs;&longs;e ex D <lb/>(quod punctum D concipiatur multò altius, quàm in præ<lb/>&longs;enti &longs;chemate) ad perpendiculum altitudine æquali ip&longs;i ET, <lb/>pondus verò B æquali tractione funiculi veni&longs;&longs;e ex B in G, <lb/>demptâ &longs;cilicet longitudine BF ip&longs;i ET æquali, atque <lb/>adeò DF, DG æquales &longs;unt: ip&longs;i autem ET æqualis &longs;u<lb/>matur BI; quæ &longs;imili ratione demon&longs;tratur brevior, quàm <lb/>BG: ex quo pariter &longs;it hîc etiam ad majorem altitudi<lb/>nem perpendicularem EH elevari, quàm &longs;i tractio pa<lb/>rallela fui&longs;&longs;et plano inclinato, & elevatio ad altitudi<lb/>nem EL. </s>

<s>Ex his manife&longs;tum e&longs;t plus virium requiri ad trahendum <pb pagenum="111"/>pondus idem per lineam DB, aut DO, aut DG obli<lb/>quas, quàm per lineam plani inclinati BC, aut illi paral<lb/>lelam: dum enim per obliquas illas lineas fit tractio, pon<lb/>dus quidem non omninò ab&longs;trahitur à plano, &longs;icut in tractio<lb/>ne perpendiculari, &longs;ed nec omninò incumbit plano, &longs;i<lb/>cut in tractione parallelâ ip&longs;i plano; ac propterea, quò ma<lb/>gis tractio ad perpendicularem accedit, eò majorem inve<lb/>nit in pondere re&longs;i&longs;tentiam. </s>

<s>Ex his manife&longs;tum e&longs;t plus virium requiri ad trahendum <pb xlink:href="017/01/127.jpg" pagenum="111"/>pondus idem per lineam DB, aut DO, aut DG obli<lb/>quas, quàm per lineam plani inclinati BC, aut illi paral<lb/>lelam: dum enim per obliquas illas lineas fit tractio, pon<lb/>dus quidem non omninò ab&longs;trahitur à plano, &longs;icut in tractio<lb/>ne perpendiculari, &longs;ed nec omninò incumbit plano, &longs;i<lb/>cut in tractione parallelâ ip&longs;i plano; ac propterea, quò ma<lb/>gis tractio ad perpendicularem accedit, eò majorem inve<lb/>nit in pondere re&longs;i&longs;tentiam. </s>

<s>Patet autem altitudinum per<lb/>pendicularium EH, EL differentiam HL majorem e&longs;&longs;e, <lb/>quàm &longs;it altitudinum perpendicularium EN, ES differen<lb/>tia NS. </s>

Line 1669

<s>Momentum igitur <lb/>perpendicularis tractionis ad momentum obliquæ tractionis <lb/>minorem Rationem habet, quàm ad momentum tractionis pa<lb/>rallelæ plano inclinato. </s>

<s>Ex his ob&longs;ervare e&longs;t aliquod paradoxum, pondus &longs;cilicet obli<lb/>quâ hâc elevatione tractum plus moveri, quàm potentiam tra<lb/>hentem; hæc enim movetur &longs;ecundùm men&longs;uram funiculi <lb/>tracti, hoc e&longs;t BP &longs;eu BR illi æqualis, o&longs;ten&longs;um e&longs;t autem <pb pagenum="112"/>BR minorem e&longs;&longs;e quàm BO. </s>

<s>Ex his ob&longs;ervare e&longs;t aliquod paradoxum, pondus &longs;cilicet obli<lb/>quâ hâc elevatione tractum plus moveri, quàm potentiam tra<lb/>hentem; hæc enim movetur &longs;ecundùm men&longs;uram funiculi <lb/>tracti, hoc e&longs;t BP &longs;eu BR illi æqualis, o&longs;ten&longs;um e&longs;t autem <pb xlink:href="017/01/128.jpg" pagenum="112"/>BR minorem e&longs;&longs;e quàm BO. </s>

<s>Id quod etiam manife&longs;tum e&longs;t, <lb/>&longs;i tractio obliqua non ab&longs;trahat pondus à plano, &longs;ed qua&longs;i il<lb/><figure id="fig25"/><lb/>lud adversùs planum trahat. </s>

<s>Id quod etiam manife&longs;tum e&longs;t, <lb/>&longs;i tractio obliqua non ab&longs;trahat pondus à plano, &longs;ed qua&longs;i il<lb/><figure id="id.017.01.128.1.jpg" xlink:href="017/01/128/1.jpg"/><lb/>lud adversùs planum trahat. </s>

<lb/><s>Sit enim planum AB, &longs;uper <lb/>quo globus C, & funiculus <lb/>obliquus DC; ex D autem <lb/>pendeat ad perpendiculum <lb/>æquale pondus E. </s>

Line 1687

<s>Sed jam trahatur iterum funiculus ita, ut ip&longs;i CG primæ <lb/>tractioni æqualis &longs;it &longs;ecunda tractio HL; & crit centrum globi <lb/>in M, & æquales DM, DL. </s>

<s>Anguli MDH, HDC &longs;i di<lb/>cantur æquales, etiam per 3.lib.6. ut MD ad DC ita MH <lb/>ad HC: e&longs;t igitur MH minor quàm HC, major tamen quàm <lb/>HL, quia &longs;ubten&longs;a e&longs;t angulo MLH obtu&longs;o, ut pote infra ba-<pb pagenum="113"/>&longs;im I&longs;o&longs;celis MDL. </s>

<s>Anguli MDH, HDC &longs;i di<lb/>cantur æquales, etiam per 3.lib.6. ut MD ad DC ita MH <lb/>ad HC: e&longs;t igitur MH minor quàm HC, major tamen quàm <lb/>HL, quia &longs;ubten&longs;a e&longs;t angulo MLH obtu&longs;o, ut pote infra ba-<pb xlink:href="017/01/129.jpg" pagenum="113"/>&longs;im I&longs;o&longs;celis MDL. </s>

<s>Atqui ex hypothe&longs;i anguli MDL, HDG <lb/>&longs;unt æquales; ergo I&longs;o&longs;celium anguli infra ba&longs;es, hoc e&longs;t MLH, <lb/>HGC &longs;unt æquales: angulus autem extermus MHL major e&longs;t <lb/>interno HCD, hoc e&longs;t HCG, per 16.lib.1. igitur reliquus <lb/>HML minor e&longs;t reliquo CHG. </s>

Line 1701

<s>Quandoquidem igitur LMH, GHC non &longs;unt æquales, dica<lb/>tur angulus LMH minor quàm GHC, & quia æqualibus li<lb/>neis HL, CG &longs;ubtenduntur, triangulum HLM e&longs;t in circulo <lb/>majore, triangulum verò CHG in minore. </s>

<s>Cum autem angu-<pb pagenum="114"/>lus MHL, ex &longs;æpiùs dictis, &longs;it major quàm HCG, etiam &longs;ub<lb/>ten&longs;a illius, ut potè in circulo majori, &longs;cilicet ML major e&longs;t <lb/>quàm HG &longs;ubten&longs;a anguli minoris in circulo minori: atque <lb/>hinc idem quod priùs, &longs;equitur ab&longs;urdum angulum verticalem <lb/>MDL, ex hypothe&longs;i minorem, & brevioribus lateribus com<lb/>prehen&longs;um ba&longs;im habere majorem, quàm &longs;it ba&longs;is anguli verti<lb/>calis HDG majoris &longs;ub lateribus longioribus. </s>

<s>Cum autem angu-<pb xlink:href="017/01/130.jpg" pagenum="114"/>lus MHL, ex &longs;æpiùs dictis, &longs;it major quàm HCG, etiam &longs;ub<lb/>ten&longs;a illius, ut potè in circulo majori, &longs;cilicet ML major e&longs;t <lb/>quàm HG &longs;ubten&longs;a anguli minoris in circulo minori: atque <lb/>hinc idem quod priùs, &longs;equitur ab&longs;urdum angulum verticalem <lb/>MDL, ex hypothe&longs;i minorem, & brevioribus lateribus com<lb/>prehen&longs;um ba&longs;im habere majorem, quàm &longs;it ba&longs;is anguli verti<lb/>calis HDG majoris &longs;ub lateribus longioribus. </s>

<s>Sed neque dici pote&longs;t angulus HML major quàm CHG; <lb/>quia, &longs;i MDL minor e&longs;t quàm HDG, angulus DML ad ba<lb/>&longs;im I&longs;o&longs;celis major e&longs;t quàm DHG pariter ad ba&longs;im; ergo &longs;i <lb/>DML majori addatur major HML, & DHG minori adda<lb/>tur minor CHG, erit totus DMH major toto angulo DHC, <lb/>internus &longs;cilicet major externo, contra 16.lib.1. Si igitur an<lb/>gulus HML comparatus cum angulo CHG non pote&longs;t e&longs;&longs;e <lb/>æqualis, neque minor, neque major, factâ hypothe&longs;i anguli <lb/>MDL minoris quàm HDC, nece&longs;&longs;ariâ con&longs;ecutione confici<lb/>tur angulum MDL non e&longs;&longs;e minorem angulo HDG. </s>

Line 1711

<s>Facilè ex dictis colliges, quanto laboris compendio Romæ <lb/>altioribus rotis in&longs;truantur birota (antiquis Ci&longs;ia dicebantur) <lb/>adeò ut unicus equus temoni applicitus, illumque &longs;ubjecto pla<lb/>no proximè parallelum &longs;ervans, dum clivum a&longs;cendit, ingentia <lb/>pondera trahat, quibus &longs;anè par non e&longs;&longs;et, &longs;i rotarum axis mi<lb/>nùs à &longs;ubjecto plano di&longs;taret, & equitractio e&longs;&longs;et obliqua &longs;ur<lb/>&longs;um: quamvis, ut aliàs &longs;uo loco explicabitur, ip&longs;a rotarum am<lb/>plitudo plurimum conferat. </s>

<s>Similiter in navium tractione, quæ <pb pagenum="115"/>adver&longs;o flumine deducuntur fune ab&longs;idi mali conjuncto, ali<lb/>quid juvare funis longitudinem, ut &longs;cilicet minùs obliqua &longs;it <lb/>tractio, ex dictis confirmatur: quamvis enim tractiones in plano <lb/>inclinato confideraverimus, ut gravium elevationem expende<lb/>remus, aliquid etiam facit obliquitas tractionis in plano horizon<lb/>tali, cuju&longs;modi e&longs;t aqua, cui navis innatat; pars &longs;iquidem de<lb/>mer&longs;a ob&longs;tantem undam repellere debet; nec planè inutile e&longs;t, <lb/>&longs;ecundùm quam lineam dirigatur motus potentiæ trahentis, vi <lb/>cujus impedimentum &longs;uperandum e&longs;t. </s>

<s>Similiter in navium tractione, quæ <pb xlink:href="017/01/131.jpg" pagenum="115"/>adver&longs;o flumine deducuntur fune ab&longs;idi mali conjuncto, ali<lb/>quid juvare funis longitudinem, ut &longs;cilicet minùs obliqua &longs;it <lb/>tractio, ex dictis confirmatur: quamvis enim tractiones in plano <lb/>inclinato confideraverimus, ut gravium elevationem expende<lb/>remus, aliquid etiam facit obliquitas tractionis in plano horizon<lb/>tali, cuju&longs;modi e&longs;t aqua, cui navis innatat; pars &longs;iquidem de<lb/>mer&longs;a ob&longs;tantem undam repellere debet; nec planè inutile e&longs;t, <lb/>&longs;ecundùm quam lineam dirigatur motus potentiæ trahentis, vi <lb/>cujus impedimentum &longs;uperandum e&longs;t. </s>

<s>Hactenus nobis de tractione &longs;ermo fuit, quæ motum inferens <lb/>non ni&longs;i &longs;patiis, per quæ motus e&longs;t, determinari potuit. </s>

Line 1719

<s>Quamquam autem <lb/>pondera qua&longs;i molis expertia unico puncto expre&longs;&longs;imus in plano <lb/>ip&longs;o inclinato, ut in 1.fig.hujus cap.

re tamen verâ centrum gra<lb/>vitatis attendendum e&longs;t, ut in 2. &longs;chemate, quod utique di&longs;tat à <lb/>plano, cui corpus grave incumbit: hujus verò di&longs;tantiam nulla <lb/>certior men&longs;ura definit, quàm linea ex eo cadens in &longs;ubjectum <lb/>planum ad angulos rectos, hæc quippe omnium brevi&longs;&longs;ima e&longs;t. <lb/><figure id="fig26"/><lb/>Sit igitur planum inclinatum AB, <lb/>cui impo&longs;itus globus centrum ha<lb/>bet gravitatis C, & contingit pla<lb/>num in D; ac propterea etiam, quæ <lb/>à centro ad contactum ducitur <lb/>recta CD, di&longs;tantiam determinat, <lb/>cum &longs;it plano perpendicularis ex <lb/>18.lib.3. Jam recta CE parallela <lb/>plano ducatur, & &longs;it linea &longs;u&longs;pen<lb/>&longs;ionis, quam claritatis gratiâ paral<lb/>lelam vocemus: & per D punctum, <lb/>in quod cadit linea di&longs;tantiæ cen<lb/>tri gravitatis tran&longs;eat perpendicu<lb/>laris horizonti linea FD quæ in G <lb/>&longs;ecat lineam CE. </s>

re tamen verâ centrum gra<lb/>vitatis attendendum e&longs;t, ut in 2. &longs;chemate, quod utique di&longs;tat à <lb/>plano, cui corpus grave incumbit: hujus verò di&longs;tantiam nulla <lb/>certior men&longs;ura definit, quàm linea ex eo cadens in &longs;ubjectum <lb/>planum ad angulos rectos, hæc quippe omnium brevi&longs;&longs;ima e&longs;t. <lb/><figure id="id.017.01.131.1.jpg" xlink:href="017/01/131/1.jpg"/><lb/>Sit igitur planum inclinatum AB, <lb/>cui impo&longs;itus globus centrum ha<lb/>bet gravitatis C, & contingit pla<lb/>num in D; ac propterea etiam, quæ <lb/>à centro ad contactum ducitur <lb/>recta CD, di&longs;tantiam determinat, <lb/>cum &longs;it plano perpendicularis ex <lb/>18.lib.3. Jam recta CE parallela <lb/>plano ducatur, & &longs;it linea &longs;u&longs;pen<lb/>&longs;ionis, quam claritatis gratiâ paral<lb/>lelam vocemus: & per D punctum, <lb/>in quod cadit linea di&longs;tantiæ cen<lb/>tri gravitatis tran&longs;eat perpendicu<lb/>laris horizonti linea FD quæ in G <lb/>&longs;ecat lineam CE. </s>

<s>Con&longs;tat trian-<pb pagenum="116"/>gulum DGC fimile e&longs;&longs;e triangulo BAS: quia enim GD pa<lb/>rallela e&longs;t lineæ AS pariter perpendiculari ad horizontem, an<lb/>guli SAB, ADG alterni æquales &longs;unt per 27.lib.1. Et quo<lb/>niam angulus CDA ex con&longs;tractione e&longs;t rectus, complemen<lb/>tum CDG æquale e&longs;t angulo complementi ABS; anguli verò <lb/>DCG, BSA &longs;unt recti, hic quidem ex hypothe&longs;i, ille autem <lb/>propter linearum CE, DA paralleli&longs;mum: igitur reliquus <lb/>CGD reliquo BAS æqualis e&longs;t; ac proptereà per 4. lib.

<s>Con&longs;tat trian-<pb xlink:href="017/01/132.jpg" pagenum="116"/>gulum DGC fimile e&longs;&longs;e triangulo BAS: quia enim GD pa<lb/>rallela e&longs;t lineæ AS pariter perpendiculari ad horizontem, an<lb/>guli SAB, ADG alterni æquales &longs;unt per 27.lib.1. Et quo<lb/>niam angulus CDA ex con&longs;tractione e&longs;t rectus, complemen<lb/>tum CDG æquale e&longs;t angulo complementi ABS; anguli verò <lb/>DCG, BSA &longs;unt recti, hic quidem ex hypothe&longs;i, ille autem <lb/>propter linearum CE, DA paralleli&longs;mum: igitur reliquus <lb/>CGD reliquo BAS æqualis e&longs;t; ac proptereà per 4. lib.

6. ut <lb/>BA ad AS, ita DG ad GC. </s>

Line 1741

<s>Sunt itaque æquiangula & &longs;imi<lb/>lia duo triangula BAP & DIC, atque per 4.lib.6. ut BA ad <lb/>AP, ita DI ad IC. </s>

<s>Atqui pondera &longs;uper BA & AP, quæ &longs;int <pb pagenum="117"/>ut BA ad AP, æquiponderant ex dictis cap.

<s>Atqui pondera &longs;uper BA & AP, quæ &longs;int <pb xlink:href="017/01/133.jpg" pagenum="117"/>ut BA ad AP, æquiponderant ex dictis cap.

13. ergo etiam <lb/>æqualium momentorum e&longs;t globus, & potentia retinens per <lb/>HC, &longs;i globus ad potentiam &longs;it ut DI ad IC, hoc e&longs;t ut CN <lb/>ad ND, &longs;i ex D intelligatur exire DN parallela ip&longs;i HC. </s>

Line 1759

<s>Ex his & illud colligitur, quod &longs;i linea, &longs;ecundùm quam <lb/>pondus retinetur in plano inclinato, &longs;it parallela horizonti, <lb/>eadem e&longs;t philo&longs;ophandi methodus. </s>

<s>Si enim &longs;uper plano in<lb/>clinato AB &longs;it pondus tangens in C, cujus gravitatis centrum <lb/>&longs;it D, & linea retentionis DE horizonti parallela, ducatur <pb pagenum="118"/><figure id="fig27"/><lb/>CF perpendicularis horizonti; & Rati<gap/><lb/>ponderis ad vires retinentes erunt ut CF <lb/>ad FD. </s>

<s>Si enim &longs;uper plano in<lb/>clinato AB &longs;it pondus tangens in C, cujus gravitatis centrum <lb/>&longs;it D, & linea retentionis DE horizonti parallela, ducatur <pb xlink:href="017/01/134.jpg" pagenum="118"/><figure id="id.017.01.134.1.jpg" xlink:href="017/01/134/1.jpg"/><lb/>CF perpendicularis horizonti; & Ratio<lb/>ponderis ad vires retinentes erunt ut CF <lb/>ad FD. </s>

<s>Fiat enim angulus BAH æqua<lb/>lis angulo CFD, qui utique e&longs;t rectus, <lb/>cum DE ex hypothe&longs;i &longs;it horizonti pa<lb/>rallela, FC verò perpendicularis: ergo <lb/>&longs;uper AB, AH æquiponderant pondera, <lb/>quæ &longs;int ut AB ad AH; paria igitur &longs;unt <lb/>momenta, &longs;i pondus ad vires potentiæ re<lb/>tinentis in eâdem Ratione &longs;it ut AB ad AH, hoc e&longs;t ut CF ad <lb/>FD. </s>

Line 1769

<s>Concipe autem &longs;ublatum triangulum totum BAH, & DC <lb/>e&longs;&longs;e columnam, quæ in eodem &longs;itu inclinata retineri debeat: <lb/>jam &longs;atis con&longs;tat ex dictis, quâ ratione di&longs;poni oporteat funes, <lb/>ut qui funium extremitates tenent, minus laboris impendant. </s>

<lb/><s>Non e&longs;t tamen eadem funis retinentis, & fulcri &longs;u&longs;tentantis <lb/>ratio: in &longs;upponendis enim fulcris illud poti&longs;&longs;imùm attenditur, <lb/>quòd fulcrum ip&longs;um integrum permaneat, citrà &longs;ci&longs;&longs;ionis aut <lb/>fractionis periculum; id quod habetur, quò magis perpendicu<lb/>lari ad horizontem &longs;itui proximum collocatur; parùm &longs;cilicet <pb pagenum="119"/>intere&longs;t, quanto conatu &longs;ubjectam tellurem urgeat modò certi <lb/>&longs;imus de fulcri ip&longs;ius firmitate. </s>

<lb/><s>Non e&longs;t tamen eadem funis retinentis, & fulcri &longs;u&longs;tentantis <lb/>ratio: in &longs;upponendis enim fulcris illud poti&longs;&longs;imùm attenditur, <lb/>quòd fulcrum ip&longs;um integrum permaneat, citrà &longs;ci&longs;&longs;ionis aut <lb/>fractionis periculum; id quod habetur, quò magis perpendicu<lb/>lari ad horizontem &longs;itui proximum collocatur; parùm &longs;cilicet <pb xlink:href="017/01/135.jpg" pagenum="119"/>intere&longs;t, quanto conatu &longs;ubjectam tellurem urgeat modò certi <lb/>&longs;imus de fulcri ip&longs;ius firmitate. </s>

<s>Cæterùm &longs;i tu ip&longs;e fu&longs;tem <lb/>manu tenens cogaris inclinatam columnam &longs;u&longs;tinere, punctum <lb/>autem &longs;u&longs;tentationis, cui fulcrum applicatur, magis à &longs;ub<lb/>jecto plano di&longs;tet, vel &longs;altem non minùs, quàm centrum gra<lb/>vitatis columnæ, experieris minori conatu opus e&longs;&longs;e, &longs;i ful<lb/>crum axi columnæ perpendiculare &longs;it, qui &longs;itus re&longs;pondet re<lb/>tentioni parallelæ plano inclinato, majorem verò adhiben<lb/>dum e&longs;&longs;e conatum, &longs;i fulcrum cum eodem axe acutum aut ob<lb/>tu&longs;um angulum con&longs;tituat; id quod obliquis elevationibus <lb/>re&longs;pondet. </s>

Line 1779

<s>Cavendum <lb/>autem plurimum e&longs;t ab æquivocationibus, quæ obrepere <lb/>po&longs;&longs;unt, ni&longs;i animum advertas ad gravitatem, &longs;ivè per totam <lb/>longitudinem, quæ movetur, aut ad motum incitari pote&longs;t, <lb/>diffu&longs;am, &longs;ivè qua&longs;i in unum punctum ibi collectam, ubi ele<lb/>vans applicatur, ut in vecte, aut librâ; hinc enim non mo<lb/>dica momentorum inæqualitas oritur. </s>

<s>Nam &longs;i puncto appli<lb/>cationis re&longs;pondeat centrum gravitatis, multò majores ad <lb/>elevandum, aut &longs;u&longs;pendendum corpus requiruntur vires, <lb/>quàm &longs;i centrum gravitatis à puncto applicationis aliquo in<lb/>tervallo &longs;ejungatur. </s><pb pagenum="120"/><figure/>

<s>Hinc &longs;i &longs;it pri&longs;ma AB ho<lb/>rizontaliter collocatum, eju&longs;<lb/>que extremitas A innitatur <lb/>apici pyramidis, altera verò <lb/>extremitas B &longs;u&longs;pendatur per<lb/>pendiculari funiculo CB, vel <lb/>&longs;u&longs;tentetur &longs;uppo&longs;ito ad <expan abbr="per-pendicul&utilde;">per<lb/>pendiculum</expan> fulcro DB, æqua<lb/>liter res &longs;e habet, & pares requiruntur vires tam in &longs;u&longs;penden<lb/>te CB, quàm in &longs;u&longs;tentante DB: hæ tamen vires non pares <lb/>e&longs;&longs;e debent toti ponderi pri&longs;matis; &longs;ed quia centrum gravita<lb/>tis E ab utroque extremo æqualiter di&longs;tare &longs;upponitur, &longs;e<lb/>mi&longs;&longs;is tantùm gravitatis percipitur in B. </s>

Line 1789

<s>Ut autem non hîc perperam nos philo&longs;ophari innote&longs;cat, <lb/>finge &longs;ublatam ex A pyramidem, & con&longs;titutam in G ita, <lb/>ut ex B ad perpendiculum dependeat pondus aliquod æqui<lb/>librium efficiens cum pri&longs;mate: quo perpendiculari pondere <lb/>&longs;ublato, ut pri&longs;ma horizontale permaneat, certum e&longs;t &longs;uper <lb/>plano inclinato BO requiri pondus, quod ad pondus per<lb/>pendiculare ex BD &longs;it ut BO ad BD: igitur &longs;i loco pon<lb/>deris applicentur &longs;ecundùm eandem rectam lineam BO vires <lb/>alicujus viventis, à quo retineatur pri&longs;ma in eodem &longs;itu ho<lb/>rizontali, &longs;atis apparet conatum debere e&longs;&longs;e ut BO ad cona<lb/>tum, qui &longs;ecundùm perpendicularem requireretur ut BD. </s>

<lb/><s>Sicut itaque conatus deor&longs;um trahens, cum fulcrum e&longs;t in <lb/>G citrà centrum gravitatis E, ex inclinatione lineæ, &longs;ecun<lb/>dùm quam fit, de&longs;umitur, ita etiam conatus &longs;u&longs;pendens IB, <pb pagenum="121"/>aut &longs;ur&longs;um urgens OB, cum fulcrum e&longs;t in A ultrà centrum <lb/>gravitatis E, de&longs;umendus e&longs;t pariter ex inclinatione lineæ, &longs;e<lb/>cundùm quam applicatur pri&longs;mati, comparatè ad conatum per<lb/>pendicularem CB, vel DB, habita &longs;emper ratione di&longs;tantiæ <lb/>fulcri à centro gravitatis. </s>

<lb/><s>Sicut itaque conatus deor&longs;um trahens, cum fulcrum e&longs;t in <lb/>G citrà centrum gravitatis E, ex inclinatione lineæ, &longs;ecun<lb/>dùm quam fit, de&longs;umitur, ita etiam conatus &longs;u&longs;pendens IB, <pb xlink:href="017/01/137.jpg" pagenum="121"/>aut &longs;ur&longs;um urgens OB, cum fulcrum e&longs;t in A ultrà centrum <lb/>gravitatis E, de&longs;umendus e&longs;t pariter ex inclinatione lineæ, &longs;e<lb/>cundùm quam applicatur pri&longs;mati, comparatè ad conatum per<lb/>pendicularem CB, vel DB, habita &longs;emper ratione di&longs;tantiæ <lb/>fulcri à centro gravitatis. </s>

<s>Ne quid verò dubitationis <lb/><figure id="fig28"/><lb/>&longs;uper&longs;it, utrum OB deor&longs;um, <lb/>& IB &longs;ur&longs;um trahentium pa<lb/>res &longs;int vires &longs;ecundùm can<lb/>dem rectam lineam OI, &longs;int <lb/>rotulæ duæ H & F circa &longs;uum <lb/>axem ver&longs;atiles infixæ extre<lb/>mitatibus regulæ, aut tigilli, <lb/>& ex funiculo rotularum ca<lb/>vitatibus in&longs;erto dependeant <lb/>æqualia pondera L & G. </s>

<s>Ne quid verò dubitationis <lb/><figure id="id.017.01.137.1.jpg" xlink:href="017/01/137/1.jpg"/><lb/>&longs;uper&longs;it, utrum OB deor&longs;um, <lb/>& IB &longs;ur&longs;um trahentium pa<lb/>res &longs;int vires &longs;ecundùm can<lb/>dem rectam lineam OI, &longs;int <lb/>rotulæ duæ H & F circa &longs;uum <lb/>axem ver&longs;atiles infixæ extre<lb/>mitatibus regulæ, aut tigilli, <lb/>& ex funiculo rotularum ca<lb/>vitatibus in&longs;erto dependeant <lb/>æqualia pondera L & G. </s>

<s>Hæc <lb/>pondera &longs;ibi vici&longs;&longs;im æquipon<lb/>derare manife&longs;tum e&longs;t, quem<lb/>cumque tandem &longs;itum &longs;ivè <lb/>perpendicularem, &longs;ivè incli<lb/>natum, habeat regula, aut ti<lb/>gillus, cui rotulæ infixæ &longs;unt. </s>

Line 1799

<s>Submove pondus L, remanent G <lb/>& D, quorum neutrum prævalere pote&longs;t; &longs;unt enim æqualia <lb/>inter &longs;e, & per lineas &longs;imiliter inclinatas AF, BO agunt. </s>

<s>Re<lb/>pone pondus L, & amove pondus G, item removeatur pon<lb/>dus D, & &longs;ur&longs;um ponatur æquale C; aio libræ jugum AB <lb/>adhuc retinere eumdem &longs;itum; quia &longs;cilicet pondera C & D <lb/><gap/>i&longs;&longs;im æquiponderabant, &longs;icut etiam G & L: igitur quantum <lb/>virium habebat pondus D ad æquiponderandum ip&longs;i G, tan<lb/>tumdem virium habet pondus C ad æquiponderandum ponde<lb/>ri L, hoc e&longs;t cidem ponderi G. </s>

<s>Re<lb/>pone pondus L, & amove pondus G, item removeatur pon<lb/>dus D, & &longs;ur&longs;um ponatur æquale C; aio libræ jugum AB <lb/>adhuc retinere eumdem &longs;itum; quia &longs;cilicet pondera C & D <lb/>vici&longs;&longs;im æquiponderabant, &longs;icut etiam G & L: igitur quantum <lb/>virium habebat pondus D ad æquiponderandum ip&longs;i G, tan<lb/>tumdem virium habet pondus C ad æquiponderandum ponde<lb/>ri L, hoc e&longs;t eidem ponderi G. </s>

<s>Sivè igitur in &longs;uperiori &longs;che<lb/>mate con&longs;iderentur vires deor&longs;um trahentes aut &longs;u&longs;tentantes <lb/>OB, &longs;ive retinentes IB, perinde e&longs;t, & æqualium momento<lb/>rum cen&longs;endæ &longs;unt. </s><pb pagenum="122"/><figure/>

<s>Non jam horizontale &longs;it <lb/>pri&longs;ma AB, &longs;ed inclinatum, <lb/>& puncto A &longs;tabili innixum: <lb/>momenta ad de&longs;cendendum, <lb/>ac proinde repugnantia ad <lb/>a&longs;cendendum, ut &longs;uperiùs in<lb/>nuimus cap.14; æ&longs;timanda <lb/>&longs;unt in plano DC inclinato, <lb/>quod cum AB angulos facit <lb/>rectos, & cum horizonte AE <lb/>concurrit in puncto E. </s>

Line 1817

<s>Ad retinendum igitur pri&longs;ma in eodem &longs;itu in<lb/>clinationis BAE per obliquam GB, vires æquipollentes viri<lb/>bus retinentibus in perpendiculari FB e&longs;&longs;e oportet ut BL ad <lb/>BI, quemadmodum retinentes per rectam DB &longs;unt ut BC. </s>

<s>Quare datâ corporis inclinatione, cujus gravitas retinenda e&longs;t <lb/>in eodem &longs;itu, &longs;umatur eju&longs;dem axis tran&longs;iens per gravitatis <lb/>centrum, & ad axis extremitatem mobilem ducatur ip&longs;i axi per<lb/>pendicularis DB, in quâ a&longs;&longs;umpto quolibet puncto D, ducatur <lb/>prædicto axi parallela DG, quæ &longs;ecans lineas qua&longs;libet obli<lb/>quas, & perpendicularem ad Horizontem, dabit omnium obli<lb/>quarum &longs;u&longs;pen&longs;ionum Rationem: Sic recta DG &longs;ecans perpen<lb/>d cularem FB & obliquam GB determinat Rationem virium in <lb/>utrâque &longs;u&longs;pen&longs;ione, ut &longs;cilicet &longs;int in Ratione BF ad BG, & <lb/>&longs;ic de reliquis. </s><pb pagenum="123"/>

<s>Quòd &longs;i in gradibus data &longs;it inclinatio pri&longs;matis, & funiculi <lb/>oblique &longs;u&longs;pendenti declinatio a perpendiculo, &longs;tatim ex tabu<lb/>lis Sinuum, aut etiam Secantium, apparebit Ratio quæ&longs;ita li<lb/>nearum: angulus enim, quem perpendicularis ad axem facit <lb/>cum perpendiculari ad Horizontem, æqualis e&longs;t angulo incli<lb/>nationis pri&longs;inatis; angulo &longs;iquidem BAE inclinationis pri&longs;ma<lb/>tis, æqualis e&longs;t angulus EBH per 8.lib.6. ac proptereà etiam <lb/>ex 15.lib.1. qui illi e&longs;t ad verticem DBF. </s>

Line 1831

<s>Secundò fieri pote&longs;t, ut pare: vires requirantur, &longs;i linea re<lb/>tentionis faciat cùm axe corporis elevati angulum acutum, ac <lb/>&longs;i faciat cùm eodem angulum obtu&longs;um, ut &longs;i fuerit recta MB; <lb/>ip&longs;a enim pariter opponitur angulo recto BDM, ac proinde <pb pagenum="124"/>eò major e&longs;t quàm recta BD, quò fuerit major angulus MBD, <lb/>qui pote&longs;t e&longs;&longs;e æqualis angulo DBF, vel DBG; quo ca&longs;u <lb/>etiam ip&longs;a BM æqualis erit ip&longs;i BF aut BG. </s>

<s>Secundò fieri pote&longs;t, ut pare: vires requirantur, &longs;i linea re<lb/>tentionis faciat cùm axe corporis elevati angulum acutum, ac <lb/>&longs;i faciat cùm eodem angulum obtu&longs;um, ut &longs;i fuerit recta MB; <lb/>ip&longs;a enim pariter opponitur angulo recto BDM, ac proinde <pb xlink:href="017/01/140.jpg" pagenum="124"/>eò major e&longs;t quàm recta BD, quò fuerit major angulus MBD, <lb/>qui pote&longs;t e&longs;&longs;e æqualis angulo DBF, vel DBG; quo ca&longs;u <lb/>etiam ip&longs;a BM æqualis erit ip&longs;i BF aut BG. </s>

<s>Ex quo <gap/>riàs <lb/>&longs;equitur, &longs;i à retinente obliquè fiat tractio elevando magis ac <lb/>magis pri&longs;ma &longs;ic inclinatum, mutari &longs;ubinde momenta: hoc ta<lb/>men intercedit di&longs;erimen, quod trahentis linea initio applicata, <lb/>ut angulum faciat acutum cum axe pri&longs;matis, in ipsâ t<gap/>ione <lb/>&longs;emper majorem facit cum ip&longs;o axe angulum, donee venrat ad <lb/>angulum rectum con&longs;tituendum, ut &longs;i MB traheretur, donec <lb/>coincidat cùm DB, quæ pariter moveri intelligatur: contrà <lb/>verò trahentis linea applicata, ut cum axe faciat angulum ob<lb/>tu&longs;um, in ipsâ tractione magis adhuc obtu&longs;um angulum con&longs;ti<lb/>tuit, donec tractionis linea (&longs;i tamen fieri id po&longs;&longs;it) in unam <lb/>rectam lineam cum axe pri&longs;matis conveniat. </s>

<s>Quare in primâ <lb/>illâ tractione minuitur conatus, in hac &longs;ecunda augetur. <lb/><figure id="fig29"/></s><pb pagenum="125"/><figure/>

<s>Quare in primâ <lb/>illâ tractione minuitur conatus, in hac &longs;ecunda augetur. <lb/><figure id="id.017.01.140.1.jpg" xlink:href="017/01/140/1.jpg"/></s><pb xlink:href="017/01/141.jpg" pagenum="125"/><figure id="id.017.01.141.1.jpg" xlink:href="017/01/141/1.jpg"/>

<s><emph type="center"/>MECHANICORUM<emph.end type="center"/><emph type="center"/>LIBER SECUNDUS.<emph.end type="center"/></s>

Line 1849

<s>Quapropter ut certâ methodo ma<lb/>chinas oneribus movendis pares con&longs;truere valeamus, motus <lb/>machinalis cau&longs;as antè cognitas habere nece&longs;&longs;e e&longs;t, quàm ma<lb/>chinas ip&longs;as aggrediamur. </s>

<s>His porrò jactis fundamentis ope<lb/>ro&longs;um non erit inædificare, & machinarum &longs;ingularum vires, <lb/>&longs;ivè &longs;implices illæ &longs;int, &longs;ivè compo&longs;itæ, exponere: adeò ut iis <lb/>ritè intellectis, quæ hoc &longs;ecundo libro di&longs;putabuntur, vix qui<gap/><lb/>quam in reliquo opere &longs;uper&longs;it difficultatis. <pb pagenum="126"/><gap desc="hr tag"/></s>

<s>His porrò jactis fundamentis ope<lb/>ro&longs;um non erit inædificare, & machinarum &longs;ingularum vires, <lb/>&longs;ivè &longs;implices illæ &longs;int, &longs;ivè compo&longs;itæ, exponere: adeò ut iis <lb/>ritè intellectis, quæ hoc &longs;ecundo libro di&longs;putabuntur, vix quie<lb/>quam in reliquo opere &longs;uper&longs;it difficultatis. <pb xlink:href="017/01/142.jpg" pagenum="126"/><gap desc="hr tag"/></s>

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

Line 1871

<s>Et quidem &longs;i &longs;olidum in corpus non incumbat <lb/>onus, &longs;ed in aëre &longs;u&longs;pen&longs;um pendeat, ac &longs;ur&longs;um trahere opor<lb/>teat, certos ad calculos revocari gravitatis momenta poterunt, <lb/>quibus machina proportione re&longs;pondeat: nam quamvis aër aëri <lb/>præ&longs;tet tenuitate, non ea tamen e&longs;t in levitatibus differentia, ut <lb/>hinc in gravium corporum momentis di&longs;&longs;imilitudo notabilis <lb/>oriatur. </s>

<s>Quare &longs;icut laberetur turpiter, qui machinam &longs;axo ab <lb/>imo mariad &longs;ummam &longs;uperficiem elevando parem in&longs;trueret, &longs;i <lb/>nullâ factâ virium acce&longs;&longs;ione illud in aërem extrahi po&longs;&longs;e &longs;ibi <pb pagenum="127"/>per&longs;uaderet; ita nimis exiguè & exiliter ad calculos revocaret <lb/>aërem, qui pro di&longs;pari ejus levitate modum machinæ &longs;tatueret; <lb/>in materiâ etenim, ex quâ machina componitur, nullus e&longs;t <lb/>huic minutæ &longs;ubtilitati locus, quæ aciem omnem fugit, ni&longs;i <lb/>cum veritas in di&longs;putatione limatur. </s>

<s>Quare &longs;icut laberetur turpiter, qui machinam &longs;axo ab <lb/>imo mariad &longs;ummam &longs;uperficiem elevando parem in&longs;trueret, &longs;i <lb/>nullâ factâ virium acce&longs;&longs;ione illud in aërem extrahi po&longs;&longs;e &longs;ibi <pb xlink:href="017/01/143.jpg" pagenum="127"/>per&longs;uaderet; ita nimis exiguè & exiliter ad calculos revocaret <lb/>aërem, qui pro di&longs;pari ejus levitate modum machinæ &longs;tatueret; <lb/>in materiâ etenim, ex quâ machina componitur, nullus e&longs;t <lb/>huic minutæ &longs;ubtilitati locus, quæ aciem omnem fugit, ni&longs;i <lb/>cum veritas in di&longs;putatione limatur. </s>

<s>Id quod de eâ pariter <lb/>gravitationis inæqualitate dictum velim, quæ ex inæquali à cen<lb/>tro gravium di&longs;tantiâ ortum habet, ut lib.1. cap.

Line 1883

<lb/><s>E&longs;t autem tùm &longs;ubjecti corporis con&longs;i&longs;tentis, tùm impo&longs;iti one<lb/>ris movendi &longs;uperficies &longs;pectanda, quatenus &longs;e contingunt: <lb/>Nam &longs;i lapideum globum pondo 100 in planitie con&longs;titutum <lb/>non rotare modo, &longs;ed & rectâ urgere po&longs;&longs;is, non itidem cubum <lb/>pondere parem & materiâ &longs;imilem æquali facilitate urgebis; <lb/>quia &longs;cilicet globus tenui&longs;&longs;imâ &longs;ui parte &longs;uppo&longs;itam planitiem <lb/>contingens minus invenit impedimenti ex proximè &longs;ubjecti <lb/>corporis a&longs;peritate, quæ prominulas impo&longs;iti globi particulas re<lb/>moretur; at cubus longè pluribus &longs;ui partibus plano adhæret, at<lb/>que adeò multiplicatá partium hujus in illius partes incurren<lb/>tium re&longs;i&longs;tentiâ, augeri quoque movendi <expan abbr="difficultat&etilde;">difficultatem</expan> nece&longs;&longs;e e&longs;t. </s>

<s>Quoniam verò obtineri nequit, ut corporum &longs;e contingen<lb/>tium &longs;uperficies &longs;int continuo lævore lubricæ, earum autem <pb pagenum="128"/>a&longs;peritates anomalæ &longs;unt ac multiformes, re&longs;i&longs;tentia indè pro<lb/>veniens &longs;ub certam legem non cadit; &longs;ed quantum conjectura <lb/>a&longs;&longs;equi valemus, illa potius ex antiquis experimentis æ&longs;timanda <lb/>videtur, quàm mathematicis ratiocinationibus indaganda. </s>

<s>Quoniam verò obtineri nequit, ut corporum &longs;e contingen<lb/>tium &longs;uperficies &longs;int continuo lævore lubricæ, earum autem <pb xlink:href="017/01/144.jpg" pagenum="128"/>a&longs;peritates anomalæ &longs;unt ac multiformes, re&longs;i&longs;tentia indè pro<lb/>veniens &longs;ub certam legem non cadit; &longs;ed quantum conjectura <lb/>a&longs;&longs;equi valemus, illa potius ex antiquis experimentis æ&longs;timanda <lb/>videtur, quàm mathematicis ratiocinationibus indaganda. </s>

<s>In <lb/>hoc uno nimirùm facem præferre pote&longs;t Geometria, ut &longs;i reli<lb/>qua pror&longs;us paria &longs;int, nec alia &longs;it quàm molis aut figuræ di&longs;&longs;i<lb/>militudo, quantum ex hoc capite movendi difficultas augea<lb/>tur, minuaturve, innnote&longs;cat: cæterùm plenè atque perfectè <lb/>explicare, quantum re&longs;i&longs;tentiæ ex a&longs;perarum &longs;uperficierum <lb/>conflictione oriatur, quis ni&longs;i temerè conetur? </s>

Line 1897

<s>Verùm nec frequens e&longs;&longs;e pote&longs;t, nec commodum, remedium <lb/>hoc ex pingui liquore petitum; illud certius erit ad imminuen<lb/>dam moram ex tritu corporum ortam, quod ea &longs;e invicem <lb/>quàm minimùm contingant. </s>

<s>Quoniam verò deducendi one<lb/>ris &longs;uperficiem amplam mutare &longs;æpè nequimus, aut illud rap<lb/>tandum trahæ imponimus, quæ non ni&longs;i tigillis duobus læviga-<pb pagenum="129"/>tis &longs;ubjectam planitiem tangit; aut in plau&longs;trum injicimus, cu<lb/>jus rotæ &longs;olum calcantes dum convertuntur, axem tantum<lb/>modo terunt, compendio &longs;anè mirabili; nam dum rotæ modio<lb/>lusaxem &longs;emel terit, pedes circiter viginti provehitur onus, aut <lb/>demum &longs;ublato corporum mutuo tritu cylindros, vel &longs;cytalas <lb/>illi &longs;ubjicimus, ut nihil noceat &longs;oli a&longs;peritas, ni&longs;i quatenus hæc <lb/>cylindrorum vel &longs;cytalarum conver&longs;ionem remoratur. </s>

<s>Quoniam verò deducendi one<lb/>ris &longs;uperficiem amplam mutare &longs;æpè nequimus, aut illud rap<lb/>tandum trahæ imponimus, quæ non ni&longs;i tigillis duobus læviga-<pb xlink:href="017/01/145.jpg" pagenum="129"/>tis &longs;ubjectam planitiem tangit; aut in plau&longs;trum injicimus, cu<lb/>jus rotæ &longs;olum calcantes dum convertuntur, axem tantum<lb/>modo terunt, compendio &longs;anè mirabili; nam dum rotæ modio<lb/>lusaxem &longs;emel terit, pedes circiter viginti provehitur onus, aut <lb/>demum &longs;ublato corporum mutuo tritu cylindros, vel &longs;cytalas <lb/>illi &longs;ubjicimus, ut nihil noceat &longs;oli a&longs;peritas, ni&longs;i quatenus hæc <lb/>cylindrorum vel &longs;cytalarum conver&longs;ionem remoratur. </s>

<s>Huc &longs;pectat id, quod non &longs;ine voluptate ob&longs;ervare aliouan<lb/>do contigit Bononiæ. </s>

Line 1905

<s>Erecto &longs;acco machinulam ap<lb/>plicabant, tùm &longs;accum pariter cum temone reclinabant, & ne <lb/>temoni incumbens juxtà longitudinem &longs;accus in alterutram <lb/>partem inclinaretur, duo hinc & hinc retinebant pariter, ac <lb/>propellebant, ut tertium arrepto temone trahentem labore le<lb/>varent: Hâc ratione alium atque alium &longs;accum tenui&longs;&longs;imo la<lb/>bore in domum importarunt; erectoque iterum temone delap<lb/>&longs;us e&longs;t ex machinulâ &longs;accus, &longs;tetitque erectus. </s>

<s>Ex his itaque con&longs;tat in machinâ in&longs;truendâ non &longs;olùm in<lb/>genitæ corpori movendo gravitatis rationem habendam e&longs;&longs;e; <lb/>&longs;ed & plani, &longs;uper quo illud deducendum e&longs;t, jacens-n<gap/> &longs;it? </s>

<lb/><s>an erectum? </s>

Line 1919

<s>Quamquam & ip&longs;a a&longs;peritas facit aliquod laboris compen<lb/>dium: nam licèt continens ac perpetuus non &longs;it motus, &longs;ed al<lb/>ternâ quiete interruptus &longs;uper arduo clivo, modico tamen co<lb/>natu prohibetur moles, ne prolap&longs;a &longs;i&longs;ipheum crect laborem; <lb/>quia a&longs;pera &longs;uper&longs;icies motui ob&longs;i&longs;tens efficit ne corporis gravi<lb/>tas deor&longs;um conetur pro plani inclinatione. </s>

<s>Satis igitur fuerit <pb pagenum="130"/>ab&longs;olutæ oneris gravitati machinam ita re&longs;pondere, ut illi ad <lb/>perpendiculum &longs;u&longs;tollendo cæteroqui impares vires &longs;ufficiant: <lb/>qui enim valuerit, adhibitâ machinâ, molem attollere, poterit <lb/>illam pariter, eju&longs;dem machinæ ope, in plano quocunque tra<lb/>here aut propellere; &longs;i maximè cylindri aut rotæ ei &longs;ubji<lb/>ciantur. </s>

<s>Satis igitur fuerit <pb xlink:href="017/01/146.jpg" pagenum="130"/>ab&longs;olutæ oneris gravitati machinam ita re&longs;pondere, ut illi ad <lb/>perpendiculum &longs;u&longs;tollendo cæteroqui impares vires &longs;ufficiant: <lb/>qui enim valuerit, adhibitâ machinâ, molem attollere, poterit <lb/>illam pariter, eju&longs;dem machinæ ope, in plano quocunque tra<lb/>here aut propellere; &longs;i maximè cylindri aut rotæ ei &longs;ubji<lb/>ciantur. </s>

<s>Hîc autem fortè nec à præ&longs;enti in&longs;tituto alienum, nec lect<gap/><lb/>ri injucundum accidat, &longs;i quæ, aliquando commini&longs;ci placuit, <lb/>&longs;ubjiciam, cum narrantem quendam audirem de campaná in<lb/>gentis ponderis facillimè agitatâ &longs;ubjectis æneis rotulis, quæ <lb/>demum longo ævo confectæ di&longs;&longs;ipatæ fuere; &longs;ed quonam artifi<lb/>cio, quóve ordine di&longs;po&longs;itæ fui&longs;&longs;ent, ennarrare omninò non <lb/>poterat. </s>

<s>Hîc autem fortè nec à præ&longs;enti in&longs;tituto alienum, nec lecto<lb/>ri injucundum accidat, &longs;i quæ, aliquando commini&longs;ci placuit, <lb/>&longs;ubjiciam, cum narrantem quendam audirem de campaná in<lb/>gentis ponderis facillimè agitatâ &longs;ubjectis æneis rotulis, quæ <lb/>demum longo ævo confectæ di&longs;&longs;ipatæ fuere; &longs;ed quonam artifi<lb/>cio, quóve ordine di&longs;po&longs;itæ fui&longs;&longs;ent, ennarrare omninò non <lb/>poterat. </s>

<s>Quare mecum ip&longs;e reputans, quî fieri id potui&longs;&longs;et, in <lb/>eam incidi &longs;ententiam, ut exi&longs;timarem gravi&longs;&longs;imam campanam <lb/>potui&longs;&longs;e facilè pul&longs;ari, imminutâ re&longs;i&longs;tentiâ, quæ oritur ex mu<lb/><figure id="fig30"/><lb/>tuo fulcri, & axis tritu. </s>

<s>Sint <lb/>enim binæ rotulæ B & C ex <lb/>ære &longs;olido, quarum diameter <lb/>&longs;it in aliquâ Ratione multiplici <lb/>ad diametrum axis, cui cam<lb/>pana innititur. </s>

<s>Axis autem &longs;e<lb/>midiameter &longs;it AE, rotulæ ve<lb/>rò BE in ratione duplâ; ergo <lb/>& periphæriæ &longs;unt in eâdem Ratione: dum igitur punctum I <lb/>in H perficit quadrantem, convertit pariter rotulam; cujus pe<lb/>ripheriæ &longs;emiquadranti coæquatur. </s>

<s>Quare &longs;i rotula infixa e&longs;&longs;et <lb/>axi, cujus &longs;emidiameter BG e&longs;&longs;et æqualis &longs;emidiametro AE, <lb/>fieret affrictus cum octante peripheriæ axis rotulæ B; &longs;ed quia <lb/>etiam in rotulâ C fieret æqualis affrictus cum eju&longs;dem axe, jam <lb/>nihil ferè emolumenti haberetur, quia totus affrictus æquè e&longs;<lb/>&longs;et, ac &longs;i quadrans EO in fulcro &longs;tabili & cavo converteretur: <lb/>& potiùs laboris in agitandâ campanâ compendium e&longs;&longs;et, &longs;i ro<lb/>tulæ fixæ hærerent, axis &longs;i quidem cylindricus cum &longs;it, &longs;ubjectas <lb/>rotulas in lineâ tangeret modico &longs;cilicet tritu; rotularum autem <lb/>axes concavis earum partibus congruunt in &longs;uperficie, quæ te<lb/>ritur, dum rotulæ convertuntur: ni&longs;i fortè cylindrica axis <lb/>BG &longs;uperficies convexa paulò minor e&longs;&longs;et concavâ rotulæ <lb/>&longs;uperficie, eæque propterea &longs;ecundùm lineam &longs;e continge-<pb pagenum="131"/>rent, ut ex 13. lib.3. facilè e&longs;t demon&longs;trare; id quod nec rarò <lb/>contingit. </s>

<s>Quare &longs;i rotula infixa e&longs;&longs;et <lb/>axi, cujus &longs;emidiameter BG e&longs;&longs;et æqualis &longs;emidiametro AE, <lb/>fieret affrictus cum octante peripheriæ axis rotulæ B; &longs;ed quia <lb/>etiam in rotulâ C fieret æqualis affrictus cum eju&longs;dem axe, jam <lb/>nihil ferè emolumenti haberetur, quia totus affrictus æquè e&longs;<lb/>&longs;et, ac &longs;i quadrans EO in fulcro &longs;tabili & cavo converteretur: <lb/>& potiùs laboris in agitandâ campanâ compendium e&longs;&longs;et, &longs;i ro<lb/>tulæ fixæ hærerent, axis &longs;i quidem cylindricus cum &longs;it, &longs;ubjectas <lb/>rotulas in lineâ tangeret modico &longs;cilicet tritu; rotularum autem <lb/>axes concavis earum partibus congruunt in &longs;uperficie, quæ te<lb/>ritur, dum rotulæ convertuntur: ni&longs;i fortè cylindrica axis <lb/>BG &longs;uperficies convexa paulò minor e&longs;&longs;et concavâ rotulæ <lb/>&longs;uperficie, eæque propterea &longs;ecundùm lineam &longs;e continge-<pb xlink:href="017/01/147.jpg" pagenum="131"/>rent, ut ex 13. lib.3. facilè e&longs;t demon&longs;trare; id quod nec rarò <lb/>contingit. </s>

<s>Verum non e&longs;t nece&longs;&longs;e rotulis B & C tàm &longs;olidos axes dare; <lb/>nam &longs;iaxis AE toti campanæ oneri ferendo par e&longs;t, bini æqua<lb/>les axes duplici ponderi re&longs;i&longs;tunt: &longs;atis igitur e&longs;&longs;et, &longs;i axes &longs;in<lb/>guli B & C, oneris &longs;emi&longs;&longs;em &longs;u&longs;tinerent. </s>

Line 1955

<s>Primi igitur 600 quadratum <lb/>360000 duc in 223, & producti 80280000, Radix cubica e&longs;t <lb/>431 1/3 proximè: alterius verò extremi 223 quadratum 49729 <lb/>ductum in 600 dat 29837400, cujus Radix cubica 310 proxi<lb/>mè e&longs;t alter medius. </s>

<s>Sunt igitur quatuor numeri 600. 431 1/<gap/>. <pb pagenum="132"/>31<gap/>. </s>

<s>Sunt igitur quatuor numeri 600. 431 1/3. <pb xlink:href="017/01/148.jpg" pagenum="132"/>31<gap/>. </s>

<s>223 continuè proportionales proximè, &longs;pretis fractiuncu<lb/>lis. </s>

<s>Quare &longs;i &longs;iat ut 60<gap/>′ ad 431″, ita &longs;emidiameter AE ad BN, <lb/>erit hæc &longs;emidiameter quæ&longs;ita &longs;ufficienter re&longs;i&longs;tens. </s>

<s>Quare &longs;i &longs;iat ut 600′ ad 431′, ita &longs;emidiameter AE ad BN, <lb/>erit hæc &longs;emidiameter quæ&longs;ita &longs;ufficienter re&longs;i&longs;tens. </s>

<s>Quoniam itaque BE dupla e&longs;t ip&longs;ius AE, & AE ad BN <lb/>facta e&longs;t ut 600 ad 431, erit BE ad BN ut 1200 ad 431; & &longs;e<lb/>cundùm hane eandem Rationem &longs;e habebunt &longs;emiquadrantes <lb/>ab illis de&longs;eripti. </s>

Line 1977

<lb/><s>Cum ergò onus hærere in &longs;alebrâ, non ex in&longs;itâ vi, &longs;ed ex proxi<lb/>mi etiam atque continentis corporis a&longs;peritate proveniat, & <lb/>in&longs;trumenta, quibus hoc tantummodo impedimentum tollitur, <lb/>idem planè efficiant, quod pinguis humor lubricum parans iter; <lb/>neque hæc machinæ magis dici po&longs;&longs;unt, quàm centones ungui<lb/>ne delibuti, &longs;i ritè &longs;ub&longs;ternantur, neque motus propterea inter <lb/>machinales numerandus videtur, quorum hîc cau&longs;as ye&longs;tigare <lb/>nobis propo&longs;itum e&longs;t. </s>

<s>Quamquam negandum non &longs;it hæc pari-<pb pagenum="133"/>ter ad mechanicam contemplationem pertmere; quippe quæ <lb/>machinis, præcipuo nimirum mechanices &longs;copo. </s>

<s>Quamquam negandum non &longs;it hæc pari-<pb xlink:href="017/01/149.jpg" pagenum="133"/>ter ad mechanicam contemplationem pertmere; quippe quæ <lb/>machinis, præcipuo nimirum mechanices &longs;copo. </s>

<s>affinia &longs;unt; <lb/>etiam&longs;i ad illas non velut &longs;ubjectæ partes ad genus revocentur: <lb/>& in&longs;trumentis huju&longs;modi &longs;i machinæ appellationem tribuere <lb/>placuerit, non admodum de nomine di&longs;putabo; res enim hîc <lb/>&longs;pectatur, non verba penduntur. </s>

<s>Sed neque hîc di&longs;putare velim, utrùm in motuum machina<lb/>lium cen&longs;um irrepant, an verò iis ritè annumerandi &longs;int motus <lb/>illi, quos &longs;ur&longs;um deor&longs;um, ultrò citróque perficiendos eatenus <lb/>expeditè, nec exiguo laboris compendio, molimur, quatenus <lb/>cos intervallis ita di&longs;tinguimus, ut nos quidem corpus deprima<lb/>mus, ut adducamus, ab alio verò extollatur, aut reducatur: in <lb/>his &longs;iquidem &longs;æpè nihil e&longs;t, quod no&longs;tram imminuat operam, <lb/>&longs;i motiones &longs;ingulæ attendantur; quamquam motui univer&longs;o <lb/>adjumentum importat continens illa conatûs no&longs;tri, alienique <lb/>&longs;ub&longs;idij, vici&longs;&longs;itudo. </s>

<s>Hinc &longs;i quis <lb/><figure id="fig31"/><lb/>ad contundendam in æneo morta<lb/>rio A contumacem aliquam mate<lb/>riam graviore pi&longs;tillo ferreo opus <lb/>habeat, haud dubium quin ei mul<lb/>tâ lacertorum vi contendendum <lb/>&longs;it, ut illum extollat; cumque ope<lb/>ro&longs;ius multo &longs;it inflexum corpus <lb/>erigere, quàm erectum inclinare, <lb/>multóque mole&longs;tius brachia tanto <lb/>pondere pregravata attollere, quàm <lb/>eorum gravitati ob&longs;ecundando de<lb/>primere, &longs;atis con&longs;tat, quantum &longs;i<lb/>bi laboris detractum eat, &longs;i &longs;uperio<lb/>re in loco tran&longs;ver&longs;um tigillum <lb/>CD circa axem E ver&longs;atilem &longs;tatuat, paribú&longs;que intervallis <lb/>hinc ex C pendeat fune &longs;u&longs;pen&longs;us pi&longs;tillus B, hinc verò in D <lb/>plumbea ma&longs;&longs;a adnectatur, quâ ita pi&longs;tillus præponderetur, ut, <lb/>nemine hunc retinente aut deprimente, illa aliquanto gravior <lb/>in &longs;ubjectum prodeuntis è pariete tigni caput G recidens &longs;pon<lb/>te &longs;ub&longs;idat. </s>

<s>Hinc &longs;i quis <lb/><figure id="id.017.01.149.1.jpg" xlink:href="017/01/149/1.jpg"/><lb/>ad contundendam in æneo morta<lb/>rio A contumacem aliquam mate<lb/>riam graviore pi&longs;tillo ferreo opus <lb/>habeat, haud dubium quin ei mul<lb/>tâ lacertorum vi contendendum <lb/>&longs;it, ut illum extollat; cumque ope<lb/>ro&longs;ius multo &longs;it inflexum corpus <lb/>erigere, quàm erectum inclinare, <lb/>multóque mole&longs;tius brachia tanto <lb/>pondere pregravata attollere, quàm <lb/>eorum gravitati ob&longs;ecundando de<lb/>primere, &longs;atis con&longs;tat, quantum &longs;i<lb/>bi laboris detractum eat, &longs;i &longs;uperio<lb/>re in loco tran&longs;ver&longs;um tigillum <lb/>CD circa axem E ver&longs;atilem &longs;tatuat, paribú&longs;que intervallis <lb/>hinc ex C pendeat fune &longs;u&longs;pen&longs;us pi&longs;tillus B, hinc verò in D <lb/>plumbea ma&longs;&longs;a adnectatur, quâ ita pi&longs;tillus præponderetur, ut, <lb/>nemine hunc retinente aut deprimente, illa aliquanto gravior <lb/>in &longs;ubjectum prodeuntis è pariete tigni caput G recidens &longs;pon<lb/>te &longs;ub&longs;idat. </s>

<s>Omnis &longs;cilicet extollendi pi&longs;tilli labore &longs;ublato, <lb/>vel &longs;olum brachiorum pondus pi&longs;tillo additum &longs;atis e&longs;&longs;e ali<lb/>quando poterit ad leviu&longs;culè tundendam materiam, licebitque <pb pagenum="134"/>modò contento, modò remi&longs;&longs;o conatu opus urgere. </s>

<s>Omnis &longs;cilicet extollendi pi&longs;tilli labore &longs;ublato, <lb/>vel &longs;olum brachiorum pondus pi&longs;tillo additum &longs;atis e&longs;&longs;e ali<lb/>quando poterit ad leviu&longs;culè tundendam materiam, licebitque <pb xlink:href="017/01/150.jpg" pagenum="134"/>modò contento, modò remi&longs;&longs;o conatu opus urgere. </s>

<s>Id quod <lb/>pariter continget, &longs;i operâ unâ opus duplex efficere placuerit; <lb/>nam &longs;i ex D plumbeæ ma&longs;&longs;æ loco alius pendeat æque, ac plum<lb/>bum, gravis pi&longs;tillus, pondere præpollens elevabit pi&longs;tillum B, <lb/>aliámque vici&longs;&longs;im in altero &longs;ubjecto mortario conteret mate<lb/>riam &longs;ponte &longs;uâ cadens: cumque pi&longs;tillorum gravitates non ad<lb/>modum inter &longs;e di&longs;pares &longs;int, neque multum laboris eum &longs;ubi<lb/>re nece&longs;&longs;e erit, cui pi&longs;tillum B deprimendi munus incumbit. </s>

Line 1997

<s>Nec di&longs;&longs;imilis ineunda videtur dicendi ratio, &longs;i quid alternis <lb/>ciendum motibus &longs;ic di&longs;ponitur, ut, cum primùm quidem mo<lb/>vetur, corpus aliud vi flectatur, quod po&longs;tmodum facultate <lb/>ela&longs;ticâ, &longs;e re&longs;tituens illud vici&longs;&longs;im moveat; quemadmodum <lb/>pa&longs;&longs;im in eorum officinis videre e&longs;t, qui rudes arborum, aut <lb/>elephantini dentis particulas in toreumata elaborant: primùm <lb/>enim artifex pede &longs;ubjectum vectem premens, toreuma in gy<lb/>rum ducit, ha&longs;tulámque &longs;uperiore in loco po&longs;itam pariter in<lb/>flectit; quæ &longs;ibi mox &longs;uam reparans rectitudinem, funiculum<lb/>que cylindrulo ver&longs;atili circumplicatum retrahens, illud iterum <lb/>&longs;ua per ve&longs;tigia ver&longs;at, ut accuratè exqui&longs;itéque tornetur. </s>

<s>Sic <lb/>aliquid &longs;ubtiliter ac delicatè &longs;ecturus, ut &longs;errulam rectâ addu<lb/>cas, reducá&longs;que, operæ tantùm &longs;emi&longs;&longs;em tibi re&longs;ervans, arcum <lb/>intentum ex adver&longs;o &longs;tatuito, ac medio nervo &longs;errulam alliga<lb/>to; hac enim adductâ magis flectetur arcus, qui &longs;e &longs;e mox re&longs;ti<lb/>tuens illam vici&longs;&longs;im reducet. </s><pb pagenum="135"/>

<s>Hæc &longs;anè laboris in movendo compendia ex ela&longs;mate, vel ex <lb/>anti&longs;acomate petita, quemadmodum & ea, quæ mutuum cor<lb/>porum tritum atque conflictum minuunt, ut pote Mechanico <lb/>artificio con&longs;tituta, eumdemque in finem ac machinæ, quibus <lb/>hoc nomen præcipuè tribuitur, videlicet in infirmæ potentiæ <lb/>&longs;ub&longs;idium excogitata, e&longs;to illis primas deferant, non tamen <lb/>omninò rejicerem, &longs;i in machinarum cen&longs;u prodirent, ii&longs;que <lb/>&longs;e peterent ad&longs;cribi. </s>

Line 2009

<s>Alternam autem operam appel<lb/>lo, cum in motu ex duplici motione compo&longs;ito alterutram effi<lb/>cit potentia, &longs;ivè illæ &longs;ibi invicem adver&longs;antes &longs;uccedant, ut <lb/>Ar&longs;is ac The&longs;is, Adductio atque Reductio, &longs;ivè in unam tem<lb/>perentur, ut cum premere &longs;imul oportet ac agitare: &longs;ic plana <lb/>vitra expolientes in &longs;pecula, inter ip&longs;a, & lacunar bacillum in<lb/>flectunt, qui &longs;e re&longs;tituere tentans vi ela&longs;ticâ, &longs;peculum validè, <lb/>quantum opus e&longs;t, admovet atque applicat ad &longs;ubjectum pla<lb/>num, adeò ut ad artificem à pre&longs;&longs;u immunem nil aliud &longs;pectet, <lb/>quàm &longs;peculum urgere, retrahere, contorquere. </s>

<s>Verùm ta<lb/>met&longs;i de his omnibus in hac tractione pa&longs;&longs;im &longs;e offeret dicendi <lb/>locus, primus tamen di&longs;putationis no&longs;træ &longs;copus erit prima illa <lb/>&longs;pecies, ip&longs;æ nimirum facultates, quarum poti&longs;&longs;imum momen<lb/>ta expendimus, cum motûs machinalis cau&longs;as inquirimus. <pb pagenum="136"/><gap desc="hr tag"/></s>

<s>Verùm ta<lb/>met&longs;i de his omnibus in hac tractione pa&longs;&longs;im &longs;e offeret dicendi <lb/>locus, primus tamen di&longs;putationis no&longs;træ &longs;copus erit prima illa <lb/>&longs;pecies, ip&longs;æ nimirum facultates, quarum poti&longs;&longs;imum momen<lb/>ta expendimus, cum motûs machinalis cau&longs;as inquirimus. <pb xlink:href="017/01/152.jpg" pagenum="136"/><gap desc="hr tag"/></s>

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

Line 2025

<s>Cum enim eadem de&longs;cendentis lapidis na<lb/>tura per&longs;everet, nec illa in &longs;uâ pote&longs;tate &longs;it, aut optione delatâ, <lb/>ut eligat utrum velit, motum arbitrio &longs;uo incitare, aut remit<lb/>tere valeat; qui fieri po&longs;&longs;it, ut de&longs;cendens velocitatem augeat, <lb/>ni&longs;i ei, quem primùm produxit, alium atque alium momentis <lb/>&longs;ingulis impetum adjiciat? </s>

<s>Illud certè extrà omnem controver<lb/>&longs;iam po&longs;itum videtur, naturam gravem &longs;ponte &longs;uâ non a&longs;cen-<pb pagenum="137"/>dere: quid ergo illud e&longs;t, quod eburneum globulum in &longs;ub<lb/>jectam rupem delap&longs;um re&longs;ilire cogit, aut &longs;ibi relictum plum<lb/>bum ex fune &longs;u&longs;pen&longs;um ultrà perpendiculum, naturá repugnan<lb/>te, &longs;ur&longs;um provehit, & eò quidem altiùs, quò ex altiore loco <lb/>globulus aut plumbum deciderunt? </s>

<s>Illud certè extrà omnem controver<lb/>&longs;iam po&longs;itum videtur, naturam gravem &longs;ponte &longs;uâ non a&longs;cen-<pb xlink:href="017/01/153.jpg" pagenum="137"/>dere: quid ergo illud e&longs;t, quod eburneum globulum in &longs;ub<lb/>jectam rupem delap&longs;um re&longs;ilire cogit, aut &longs;ibi relictum plum<lb/>bum ex fune &longs;u&longs;pen&longs;um ultrà perpendiculum, naturá repugnan<lb/>te, &longs;ur&longs;um provehit, & eò quidem altiùs, quò ex altiore loco <lb/>globulus aut plumbum deciderunt? </s>

<s>ni&longs;i quia conceptus naturâ <lb/>procurante impetus pergit motum efficere, ipsâ etiam naturâ <lb/>quantum pote&longs;t, ob&longs;i&longs;tente. </s>

<s>Quòd &longs;i corpus alienâ vi longiùs <lb/>emi&longs;&longs;um moveatur, extrin&longs;ecùs impetum imprimi nece&longs;&longs;e e&longs;t: <lb/>quem &longs;anè non concipit, ubi primùm à projiciente &longs;ejunctum <lb/>fuerit; nihil enim prode&longs;&longs;<gap/>t ad longiorem lapidis jactum fun<lb/>dam iterum ac tertiò circumducere, ni&longs;i alium atque alium im<lb/>petum lapis conciperet, quandiù funditori adhærens unâ cum <lb/>ip&longs;o movetur. </s>

<s>Quòd &longs;i corpus alienâ vi longiùs <lb/>emi&longs;&longs;um moveatur, extrin&longs;ecùs impetum imprimi nece&longs;&longs;e e&longs;t: <lb/>quem &longs;anè non concipit, ubi primùm à projiciente &longs;ejunctum <lb/>fuerit; nihil enim prode&longs;&longs;et ad longiorem lapidis jactum fun<lb/>dam iterum ac tertiò circumducere, ni&longs;i alium atque alium im<lb/>petum lapis conciperet, quandiù funditori adhærens unâ cum <lb/>ip&longs;o movetur. </s>

<s>Quæcumque igitur moventur, impetum habent, quo ferun<lb/>tur; cui &longs;atis probabili conjectura, proxima vis motum efficien<lb/>di tribuenda videtur. </s>

Line 2041

<s>Atqui impetum ex eorum &longs;altem genere e&longs;&longs;e, quæ mo<lb/>tum efficiant, con&longs;tat ex velociore motu po&longs;terioribus momen<lb/>tis, naturâ pror&longs;us immutatâ, factoque impetûs incremento: <lb/>contrà verò motu, quâ motus e&longs;t, impetum non augeri &longs;atis <lb/>indicant mi&longs;&longs;ilia, quorum velocitas, dum moventur, &longs;en&longs;im <lb/>elangue&longs;cit. </s>

<s>Igitur & priore illo temporis momento non mo<lb/>tus impetum; &longs;ed impetus motum proximè effecit; impetum <lb/>autem procreavit innata movendi vis; cui id circo motio tri-<pb pagenum="138"/>buitur, quia id illa gignit, quod proximè motus con&longs;equitur, <lb/>& ad motum efficiendum natura de&longs;tinavit. </s>

<s>Igitur & priore illo temporis momento non mo<lb/>tus impetum; &longs;ed impetus motum proximè effecit; impetum <lb/>autem procreavit innata movendi vis; cui id circo motio tri-<pb xlink:href="017/01/154.jpg" pagenum="138"/>buitur, quia id illa gignit, quod proximè motus con&longs;equitur, <lb/>& ad motum efficiendum natura de&longs;tinavit. </s>

Line 2061

<s>Sed quoniam non pauca &longs;unt, quæ motui &longs;æpè adver&longs;antur, <lb/>hinc e&longs;t non &longs;emper eandem e&longs;&longs;e corporis &longs;e moventis velocita<lb/>tem, quamvis pari impetu producto connitatur: deteritur nimi<lb/>rum tantum impetus, quantum &longs;atis e&longs;t ad impedimentum &longs;ub<lb/>movendum. </s>

<s>Sivè enim objectum corpus propellendum &longs;it, &longs;ivè <lb/>medij particulæ locum ægrè dantes divellendæ aut compri<lb/>mendæ &longs;int, &longs;ivè connexam molem pariter rapi oporteat, &longs;ivè <pb pagenum="139"/>quid aliud huju&longs;modi ad&longs;it, cui ni&longs;i vis inferatur, ut ex alio <lb/>in alium locum migret præter naturam, irritus reddatur corpo<lb/>ris in motum propen&longs;i conatus; &longs;atis con&longs;tat illud motu agitan<lb/>dum e&longs;&longs;e exteriùs: atque adeò quantum impetus illi imprimi<lb/>tur oppo&longs;itæ propen&longs;ioni æquale, motui tantumdem &longs;ub<lb/>trahitur. </s>

<s>Sivè enim objectum corpus propellendum &longs;it, &longs;ivè <lb/>medij particulæ locum ægrè dantes divellendæ aut compri<lb/>mendæ &longs;int, &longs;ivè connexam molem pariter rapi oporteat, &longs;ivè <pb xlink:href="017/01/155.jpg" pagenum="139"/>quid aliud huju&longs;modi ad&longs;it, cui ni&longs;i vis inferatur, ut ex alio <lb/>in alium locum migret præter naturam, irritus reddatur corpo<lb/>ris in motum propen&longs;i conatus; &longs;atis con&longs;tat illud motu agitan<lb/>dum e&longs;&longs;e exteriùs: atque adeò quantum impetus illi imprimi<lb/>tur oppo&longs;itæ propen&longs;ioni æquale, motui tantumdem &longs;ub<lb/>trahitur. </s>

<s>In iis &longs;anè, quæ alienâ vi extrin&longs;ecùs moventur, quia infi<lb/>nitè progredi non licet, aliqua demum origo deprehenditur, <lb/>cui naturalis &longs;it motus: natura &longs;iquidem vis e&longs;t ciens motus in <lb/>corporibus nece&longs;&longs;arios; ita tamen certis tenetur legibus uni<lb/>ver&longs;itatis rerum concinnitatem &longs;pectantibus, ut ne ab iis di&longs;ce<lb/>dat, &longs;ingularibus corporibus vim aliquam inferri permittat, ubi <lb/>adver&longs;is propen&longs;ionibus inter &longs;e confligentibus validior præ&longs;tat <lb/>imbecilliori. </s>

Line 2069

<s>Verùm il<lb/>lud firmum ac perpetuum e&longs;t, quòd ubi plus violentiæ opus e&longs;t, <lb/>parem conatum languidior motus con&longs;equitur. </s>

<s>Id quod in <lb/><figure id="fig32"/><lb/>&longs;iphone ABC ob&longs;ervare in promptu e&longs;t, ex <lb/>cujus o&longs;culo C inæqualis aquæ copia de<lb/>fluit paribus temporis intervallis: quò enim <lb/>magis aquæ &longs;uperficies in va&longs;e deprimitur, <lb/>eò lentiùs aqua ex &longs;iphone dilabitur: <lb/>quamvis &longs;cilicet aquæ crus BC implentis <lb/>pares &longs;int &longs;emper ad de&longs;cendendum vires, &longs;i <lb/>nihil, aut &longs;altem non inæqualiter, repugnet, <lb/>aquæ tamen crus BD brevius, & BI longius, & BA adhuc <lb/>longius implentis di&longs;par e&longs;t in afcen&longs;u repugnantia; ac pro<lb/>pterea cum earumdem virium BC minor &longs;it Ratio ad majorem <lb/>re&longs;i&longs;tentiam BI, quàm ad minorem BD, languidior quoque <lb/>motus e&longs;t de&longs;cendentis aquæ ex BC, cùm graviorem aquam <lb/>BI, quàm cùm minùs gravem BD &longs;ursùm trahere oporter. </s>

<s>Id quod in <lb/><figure id="id.017.01.155.1.jpg" xlink:href="017/01/155/1.jpg"/><lb/>&longs;iphone ABC ob&longs;ervare in promptu e&longs;t, ex <lb/>cujus o&longs;culo C inæqualis aquæ copia de<lb/>fluit paribus temporis intervallis: quò enim <lb/>magis aquæ &longs;uperficies in va&longs;e deprimitur, <lb/>eò lentiùs aqua ex &longs;iphone dilabitur: <lb/>quamvis &longs;cilicet aquæ crus BC implentis <lb/>pares &longs;int &longs;emper ad de&longs;cendendum vires, &longs;i <lb/>nihil, aut &longs;altem non inæqualiter, repugnet, <lb/>aquæ tamen crus BD brevius, & BI longius, & BA adhuc <lb/>longius implentis di&longs;par e&longs;t in afcen&longs;u repugnantia; ac pro<lb/>pterea cum earumdem virium BC minor &longs;it Ratio ad majorem <lb/>re&longs;i&longs;tentiam BI, quàm ad minorem BD, languidior quoque <lb/>motus e&longs;t de&longs;cendentis aquæ ex BC, cùm graviorem aquam <lb/>BI, quàm cùm minùs gravem BD &longs;ursùm trahere oporter. </s>

<s>At <pb pagenum="140"/>&longs;i externum &longs;iphonis crus ità decurtatum &longs;it in E, ut o&longs;culum E <lb/>& aquæ in va&longs;e &longs;uperficies I paribus ab&longs;int ab Horizonte inter<lb/>vallis, aquam ideò hærere, nec amplius ex E fluere con&longs;tat, <lb/>quia aquæ BE ad de&longs;cendendum propen&longs;ionem, par aquæ BI <lb/>repugnantia, ne a&longs;cendat, elidit. </s>

<s>At <pb xlink:href="017/01/156.jpg" pagenum="140"/>&longs;i externum &longs;iphonis crus ità decurtatum &longs;it in E, ut o&longs;culum E <lb/>& aquæ in va&longs;e &longs;uperficies I paribus ab&longs;int ab Horizonte inter<lb/>vallis, aquam ideò hærere, nec amplius ex E fluere con&longs;tat, <lb/>quia aquæ BE ad de&longs;cendendum propen&longs;ionem, par aquæ BI <lb/>repugnantia, ne a&longs;cendat, elidit. </s>

<s>Quòd &longs;i demum aquam in <lb/>va&longs;e imminuas, ut ejus &longs;uperficies paulò infra I, atque adeò <lb/>infra E o&longs;culum deprimatur, non jam aqua hæret in E, &longs;ed &longs;ua <lb/>per ve&longs;tigia in EB remeare cogitur, præponderatâ nimirum <lb/>majore gravitate aquæ implentis crus paulo longiùs quàm BI, <lb/>atque adeò quàm BE, quod illi ex hypothe&longs;i con&longs;tituimus <lb/>æquale; tantóque velociùs ab aqu<gap/> interioris cruris raperetur <lb/>exterior, quantò depre&longs;&longs;ior facta fui&longs;&longs;et in va&longs;e aquæ &longs;uper<lb/>ficies. </s>

<s>Quòd &longs;i demum aquam in <lb/>va&longs;e imminuas, ut ejus &longs;uperficies paulò infra I, atque adeò <lb/>infra E o&longs;culum deprimatur, non jam aqua hæret in E, &longs;ed &longs;ua <lb/>per ve&longs;tigia in EB remeare cogitur, præponderatâ nimirum <lb/>majore gravitate aquæ implentis crus paulo longiùs quàm BI, <lb/>atque adeò quàm BE, quod illi ex hypothe&longs;i con&longs;tituimus <lb/>æquale; tantóque velociùs ab aquâ interioris cruris raperetur <lb/>exterior, quantò depre&longs;&longs;ior facta fui&longs;&longs;et in va&longs;e aquæ &longs;uper<lb/>ficies. </s>

<s>Hinc itaque fit, ut pro variâ corporis motui ob&longs;i&longs;tentis re<lb/>pugnantiâ modò plus, modò minus impetûs reliquum &longs;it, quo <lb/>motû, celeritas aut tarditas perficiatur. </s>

Line 2083

<s>Quemadmodum enim &longs;i corporis alicujus <lb/>&longs;pecificam gravitatem in aquâ mutari non po&longs;&longs;e con&longs;tet, infer<lb/>re continuò licet, corpus idem neque raritatem neque den&longs;ita<lb/>tem in aquâ a&longs;&longs;ùmere po&longs;&longs;e; ex his &longs;iquidem &longs;pecificæ gravita<lb/>tis mutatio oriretur: ita pariter ubi nihil haberi pote&longs;t eorum, <lb/>quæ impetum extrin&longs;ecùs impre&longs;&longs;um nece&longs;&longs;ariò con&longs;equuntur, <lb/>impetum quoque abe&longs;&longs;e non immeritò conjectamus. </s>

<s>Si quis tamen animum diligentiùs adverrat, manife&longs;tò de-<pb pagenum="141"/>prehendet corpus idem magis repugnare motui, &longs;i celeriùs mo<lb/>vendum &longs;it, minùs verò, &longs;i tardiùs: &longs;ic ferreæ an&longs;æ cubiculi <lb/>o&longs;tio infixæ magnetem armatum applicui, & &longs;iquidem paulò <lb/>velociùs magnetem traherem, disjungebatur ab ansâ; at len<lb/>tiùs trahentem &longs;ub&longs;equebatur o&longs;tium, magnetis &longs;cilicet vim <lb/>non &longs;uperans, ubi lentè res peragebatur. </s>

<s>Si quis tamen animum diligentiùs adverrat, manife&longs;tò de-<pb xlink:href="017/01/157.jpg" pagenum="141"/>prehendet corpus idem magis repugnare motui, &longs;i celeriùs mo<lb/>vendum &longs;it, minùs verò, &longs;i tardiùs: &longs;ic ferreæ an&longs;æ cubiculi <lb/>o&longs;tio infixæ magnetem armatum applicui, & &longs;iquidem paulò <lb/>velociùs magnetem traherem, disjungebatur ab ansâ; at len<lb/>tiùs trahentem &longs;ub&longs;equebatur o&longs;tium, magnetis &longs;cilicet vim <lb/>non &longs;uperans, ubi lentè res peragebatur. </s>

<s>An non oneri, quod potentia præ &longs;ui tenuitate propellere <lb/>non po&longs;&longs;e videtur, motus, qui momentis &longs;ingulis &longs;en&longs;um om<lb/>nem fugiat, conciliari pote&longs;t, adeò ut, &longs;i illa quidem con&longs;tan<lb/>ter urgeat, elap&longs;o demùm longo temporis intervallo appareat? </s>

Line 2099

<s>Nonnè & agricolæ terram <lb/>&longs;ubigentes fo&longs;&longs;ione glebarum, tam multiplices adhibent operas, <lb/>quàm breviori tempore opus ab&longs;olvere meditantur? </s>

<s>Eò igitur <lb/>magis re&longs;i&longs;tit corpus motui, quò celeriùs agitandum e&longs;t; con<lb/>trà verò minùs repugnat, quò tardiùs. </s><pb pagenum="142"/>

<s>Eò igitur <lb/>magis re&longs;i&longs;tit corpus motui, quò celeriùs agitandum e&longs;t; con<lb/>trà verò minùs repugnat, quò tardiùs. </s><pb xlink:href="017/01/158.jpg" pagenum="142"/>

<s>Quare &longs;i duo &longs;int corpora, quorum alterum alteri præ&longs;tet <lb/>triplo majori gravitate, atque hæc pari celeritate attollenda &longs;int, <lb/>di&longs;parem exigunt conatum pro gravitatis Ratione: &longs;i par &longs;it eo<lb/>rum gravitas, motus autem alterius reliquo triplo velocior e&longs;&longs;e <lb/>debeat, inæqualem pariter exigunt conatum, &longs;ed pro ratione <lb/>velocitatis: &longs;i demùm & di&longs;par &longs;it gravitas, & inæqualis velo<lb/>citas, eam e&longs;&longs;e con&longs;tat repugnantiam, quæ tùm ex gravitate, <lb/>tùm ex velocitate componitur; atque adeò &longs;i corpus alterum <lb/>triplo gravius triplo etiam velociùs movendum e&longs;&longs;et, noncuplex <lb/>e&longs;&longs;et ejus repugnantia; &longs;in autem triplo levius triplo majori <lb/>velocitate quàm corpus triplo gravius, moveretur, par e&longs;&longs;et eo<lb/>rum ob&longs;i&longs;tentia, paremque conatum exigerent. </s>

Line 2113

<s>Quare <lb/>ad movendas libras 5 1/4 velocitate ut 8, requiritur conatus &longs;e&longs;<lb/>quialter conatûs nece&longs;&longs;arij ad movendas libras 4 velocitate <lb/>ut 7. Eadem e&longs;to de reliquis ac &longs;imilibus conjectura. </s>

<s>Ex his præterea manife&longs;tum e&longs;t corporis per vim dimovendi <lb/>re&longs;i&longs;tentiam ex &longs;olâ naturâ, & principio in&longs;ito, quod motui re<lb/>pugnat, ab&longs;olutè definiri non po&longs;&longs;e; motum &longs;i quidem ab omni <lb/>prorsùs celeritatis aut tarditatis men&longs;urâ &longs;ejungere non po&longs;&longs;u<lb/>mus; idcircò non ni&longs;i habitâ ratione celeritatis, aut tarditatis, <pb pagenum="143"/>ex quibus re&longs;i&longs;tentia componitur, re&longs;i&longs;tentia ip&longs;a innote&longs;cere <lb/>poterit. </s>

<s>Ex his præterea manife&longs;tum e&longs;t corporis per vim dimovendi <lb/>re&longs;i&longs;tentiam ex &longs;olâ naturâ, & principio in&longs;ito, quod motui re<lb/>pugnat, ab&longs;olutè definiri non po&longs;&longs;e; motum &longs;i quidem ab omni <lb/>prorsùs celeritatis aut tarditatis men&longs;urâ &longs;ejungere non po&longs;&longs;u<lb/>mus; idcircò non ni&longs;i habitâ ratione celeritatis, aut tarditatis, <pb xlink:href="017/01/159.jpg" pagenum="143"/>ex quibus re&longs;i&longs;tentia componitur, re&longs;i&longs;tentia ip&longs;a innote&longs;cere <lb/>poterit. </s>

<s>Quare & impetus à facultate movendi principium ha<lb/>bente productus major &longs;it nece&longs;&longs;e e&longs;t, quàm dimoti corperis <lb/>repugnantia; quæ varia prorsùs cùm &longs;it, nunc quidem majo<lb/>rem, nunc verò minorem impetum exigit, ut ab eo vincatur; <lb/>nam &longs;i pares confiigerent vires, à neutrâ parte &longs;taret victoria. </s>

Line 2125

<s>Quæcunque igitur ob id ip&longs;um in motum prona &longs;unt, quia <lb/>vim patiuntur, impetum illicò concipiunt, ac vis iis illata e&longs;t, <lb/>quo naturalem locum, &longs;eu &longs;tatum, recipere valeant, licèt &longs;æpè <lb/>irrito conatu, ni&longs;i quatenùs adver&longs;o hoc impetu illatam ab ob<lb/>&longs;i&longs;tente violentiam retundunt, vim aliquam illi vici&longs;&longs;im infe<lb/>rentes. </s>

<s>Sic onera bajulorum humeros, quibus &longs;u&longs;tinentur, <lb/>premunt, aut penduli brachij; ex quo &longs;u&longs;penduntur, mu&longs;cu<lb/>los ac ligamenta fatigant: id quod pariter in corpore inanimo <lb/>cernere licet; quemadmodum enim ex diuturnâ prementis <lb/>deor&longs;um ponderis, ac mu&longs;culorum &longs;ursùm urgentium luctâ, <lb/>di&longs;&longs;ipatis &longs;piritibus, la&longs;&longs;itudo in animali oritur, ita pariter &longs;ub<lb/>jectum a&longs;&longs;erem longâ temporis morâ pondus curvat, aut etiam <lb/>demùm frangit, & funem, ex quo pendet, non intendit &longs;olùm, &longs;ed <lb/>ctiam tandem aliquando corrupto particularum nexu disjicit. </s><pb pagenum="144"/>

<s>Quo id autem pacto contingat, explicare opero&longs;um non fue<lb/>rit funiculi texturam con&longs;ideranti; ex tenui&longs;&longs;imis &longs;cilicet linei <lb/>aut cannabini corticis longâ maceratione, & plurimâ tun&longs;ione <lb/>extenuati particulis in &longs;piram contortis filum cohæret; ex filis <lb/>autem plu&longs;culis in &longs;piram pariter contortis funiculus, & pluri<lb/>bus funiculis cra&longs;&longs;iores rudentes conflantur: quod &longs;i di&longs;&longs;olvatur <lb/>omnis &longs;pira, non cohærent funiculi aut fili partes. </s>

Line 2141

<s>Sic ha&longs;tam <lb/>per vim inflexam &longs;i continuò dimittas, illa &longs;e&longs;e re&longs;tituit, facul<lb/>tate ela&longs;ticâ; at &longs;i dies aliquot, aut etiam diutiù per vim &longs;i<lb/>nuata perman&longs;erit, &longs;ibi dimi&longs;&longs;a antiquam rectitudinem non re<lb/>parat; elanguit nimirùm facultas ela&longs;tica, quæ ex violentâ par<lb/>ticularum compre&longs;&longs;ione aut di&longs;tractione oriebatur. </s>

<s>Cùm enim <lb/>primùm ha&longs;ta flectitur, particulæ concavam curvaturæ partem <lb/>re&longs;picientes comprimuntur, contra verò, quæ convexam re&longs;pi-<pb pagenum="145"/>ciunt, di&longs;trahuntur; quare tùm quæ, raræ, tùm quæ den&longs;æ factæ <lb/>&longs;unt, dum vim illicò prorsùs excutere conantur, con&longs;pirant, ut <lb/>pri&longs;tinam ha&longs;tæ rectitudinem moliantur: Quod &longs;i id non li<lb/>cuerit, hæ quidem aliam ex angu&longs;tiis evadendi, quâ facilior <lb/>patet via, rationem tentant, ita ut demùm &longs;ubtili&longs;&longs;imas in ru<lb/>gas cri&longs;pentur, illæ verò &longs;e&longs;e ad angu&longs;tiora &longs;patia &longs;en&longs;im reci<lb/>pientes mutuum nexum &longs;olvunt, tenui&longs;&longs;imo&longs;que poros relin<lb/>quunt, aut &longs;i qui priùs interjecti fuerint, ampliùs hiare per<lb/>mittunt. </s>

<s>Cùm enim <lb/>primùm ha&longs;ta flectitur, particulæ concavam curvaturæ partem <lb/>re&longs;picientes comprimuntur, contra verò, quæ convexam re&longs;pi-<pb xlink:href="017/01/161.jpg" pagenum="145"/>ciunt, di&longs;trahuntur; quare tùm quæ, raræ, tùm quæ den&longs;æ factæ <lb/>&longs;unt, dum vim illicò prorsùs excutere conantur, con&longs;pirant, ut <lb/>pri&longs;tinam ha&longs;tæ rectitudinem moliantur: Quod &longs;i id non li<lb/>cuerit, hæ quidem aliam ex angu&longs;tiis evadendi, quâ facilior <lb/>patet via, rationem tentant, ita ut demùm &longs;ubtili&longs;&longs;imas in ru<lb/>gas cri&longs;pentur, illæ verò &longs;e&longs;e ad angu&longs;tiora &longs;patia &longs;en&longs;im reci<lb/>pientes mutuum nexum &longs;olvunt, tenui&longs;&longs;imo&longs;que poros relin<lb/>quunt, aut &longs;i qui priùs interjecti fuerint, ampliùs hiare per<lb/>mittunt. </s>

<s>Id quod ubi jam contigerit, fru&longs;trà &longs;ubmoves, quæ <lb/>admoveras impedimenta; & &longs;pontè curvaturam ha&longs;ta &longs;ervat, <lb/>ni&longs;i fortè particulis omnibus adhuc per tempus non licuerit <lb/>vim totam excutere; tunc enim &longs;e &longs;e languidiùs re&longs;tituunt, pro <lb/>ratione reliquæ violentiæ. </s>

Line 2155

<s><emph type="center"/><emph type="italics"/>Quâ ratione &longs;emel conceptus impetus pereat.<emph.end type="italics"/><emph.end type="center"/></s>

<s>UT impetûs natura, quam inquirimus, explicatiùs atque <lb/>di&longs;tinctiùs innote&longs;cat, ex quo pariter, quæ corpora, quâ<lb/>ve ratione, impetum re&longs;puant, intelligamus, hîc nobis e&longs;t <lb/>ve&longs;tigandum, quâ ratione conceptum &longs;emel impetum abji<lb/>ciant: hinc nimirum in uberiorem ip&longs;ius re&longs;i&longs;tentiæ notitiam <lb/>venientes ad explicandam motûs machinalis cau&longs;am propiùs <lb/>accedemus. </s><pb pagenum="146"/>

<s>Et &longs;anè conceptum impetum, naturâ &longs;uâ, nec flabilem &longs;em<lb/>per permanere, nec ad unicum temporis punctum durare, &longs;a<lb/>tis con&longs;tat: &longs;ivè enim &longs;pontè profluat ex naturâ debitum &longs;ibi <lb/>locum quærente, &longs;ivè alienâ vi impre&longs;&longs;us &longs;uo loco corpus ex<lb/>trudat, perpetuus e&longs;&longs;e nequit; omnis &longs;cilicet motus terminum <lb/>habeat nece&longs;&longs;e e&longs;t; nam &longs;i violentus quidem e&longs;t, perennis uti<lb/>que non e&longs;t; &longs;in autem naturalis, quem violentus præce&longs;&longs;erit, <lb/>certis definitur terminis; à loco enim, in quo quietem natura <lb/>indixit, corpus infinito intervallo non abe&longs;t, ac proinde ubi <lb/>eum attigerit, demùm conquie&longs;cet, nec impetu perpetuo opus <lb/>erit, cùm motum ce&longs;&longs;are oporteat. </s>

Line 2167

<s>Impetum hunc, qui <lb/>naturali &longs;e movendi facultati re&longs;pondet, & e&longs;t ip&longs;a gravitatio, <lb/>&longs;eu naturalis ad de&longs;cen&longs;um propen&longs;io, Innatum voco, & is e&longs;t, <lb/>cui extrin&longs;eca cau&longs;a repugnat motum impediens. </s>

<s>Quòd &longs;i &longs;u&longs;<lb/>pen&longs;um corpus &longs;ibi relinquatur, ita &longs;uum in locum contendit, <lb/>ut vis naturalis æquè &longs;emper ad agendum applicata, nec impe<lb/>dita, momentis &longs;ingulis novum impetum acquirat, qui propterea <pb pagenum="147"/>Acqui&longs;itus dicitur, & po&longs;terior priori additus inten&longs;ionem ef<lb/>ficit: &longs;apienti &longs;anè naturæ in&longs;tituto; nam &longs;i corpora per &longs;e ip&longs;a <lb/>ac &longs;uâ &longs;ponte mota non accelerarent; &longs;ed naturalis motus pla<lb/>ne æquabilis e&longs;&longs;et, tardè nimis locum &longs;uum con&longs;equerentur; <lb/>atque adeò augendus continuò fuit impetus, ut & motus in<lb/>crementum acciperet: at &longs;i innatus impetus valdè <expan abbr="int&etilde;&longs;us">inten&longs;us</expan> e&longs;&longs;et, <lb/>corpora nonni&longs;i ægerrimè aliò transferri, aut alieno in loco re<lb/>tineri pro animalium, & hominis utilitate po&longs;&longs;ent; finge &longs;cili<lb/>cet animo tibiam tanto impetu innato repugnare, ne attollatur, <lb/>quanto impetu in aëre ex 200 pa&longs;&longs;uum altitudine de&longs;cenderet; <lb/>quanto id tibi e&longs;&longs;et incommodo? </s>

<s>Quòd &longs;i &longs;u&longs;<lb/>pen&longs;um corpus &longs;ibi relinquatur, ita &longs;uum in locum contendit, <lb/>ut vis naturalis æquè &longs;emper ad agendum applicata, nec impe<lb/>dita, momentis &longs;ingulis novum impetum acquirat, qui propterea <pb xlink:href="017/01/163.jpg" pagenum="147"/>Acqui&longs;itus dicitur, & po&longs;terior priori additus inten&longs;ionem ef<lb/>ficit: &longs;apienti &longs;anè naturæ in&longs;tituto; nam &longs;i corpora per &longs;e ip&longs;a <lb/>ac &longs;uâ &longs;ponte mota non accelerarent; &longs;ed naturalis motus pla<lb/>ne æquabilis e&longs;&longs;et, tardè nimis locum &longs;uum con&longs;equerentur; <lb/>atque adeò augendus continuò fuit impetus, ut & motus in<lb/>crementum acciperet: at &longs;i innatus impetus valdè <expan abbr="int&etilde;&longs;us">inten&longs;us</expan> e&longs;&longs;et, <lb/>corpora nonni&longs;i ægerrimè aliò transferri, aut alieno in loco re<lb/>tineri pro animalium, & hominis utilitate po&longs;&longs;ent; finge &longs;cili<lb/>cet animo tibiam tanto impetu innato repugnare, ne attollatur, <lb/>quanto impetu in aëre ex 200 pa&longs;&longs;uum altitudine de&longs;cenderet; <lb/>quanto id tibi e&longs;&longs;et incommodo? </s>

<s>Quare peropportunum acci<lb/>dit, ut vehemens non e&longs;&longs;et &longs;ingularum particularum impetus <lb/>innatus, qui tamen ubi motum efficeret, novâ acce<gap/>one po&longs;<lb/>&longs;et augeri. </s>

<s>Quare peropportunum acci<lb/>dit, ut vehemens non e&longs;&longs;et &longs;ingularum particularum impetus <lb/>innatus, qui tamen ubi motum efficeret, novâ acce&longs;&longs;ione po&longs;<lb/>&longs;et augeri. </s>

<s>Quod ad impetum Innatum &longs;pectat, quem à gravitatione <lb/>ipsá & proxima motus exigentia non &longs;ejungo, utique fru&longs;trà <lb/>e&longs;&longs;et, &longs;i omni pror&longs;us effectu careret; impetus autem motum <lb/>aut efficit, aut &longs;altem exigit: propterea illum &longs;tatim perire au<lb/>tumo, ac fuerit corpus in loco &longs;uo: Id quod hoc deprehendes <lb/>experimento. </s>

Line 2181

<s>Quæ <lb/>&longs;anè immer&longs;io, ni&longs;i Acqui&longs;itus impetus adhuc duraret, omninò <lb/>non contingeret. </s>

<s>Verùm nihil rem per &longs;e &longs;atis ab&longs;tru&longs;am æquè <lb/>in lucem evocat, ac funependulorum motus; plumbum enim <lb/>ex filo &longs;u&longs;pen&longs;um, & à perpendiculo dimotum, ita de&longs;cendens <pb pagenum="148"/>arcum de&longs;cribit, ut ferè parem arcum, & vix (aut fortè ne vix <lb/>quidem) minori tempore a&longs;cendens de&longs;cribat. </s>

<s>Verùm nihil rem per &longs;e &longs;atis ab&longs;tru&longs;am æquè <lb/>in lucem evocat, ac funependulorum motus; plumbum enim <lb/>ex filo &longs;u&longs;pen&longs;um, & à perpendiculo dimotum, ita de&longs;cendens <pb xlink:href="017/01/164.jpg" pagenum="148"/>arcum de&longs;cribit, ut ferè parem arcum, & vix (aut fortè ne vix <lb/>quidem) minori tempore a&longs;cendens de&longs;cribat. </s>

<s>Cui autem, re<lb/>pugnante plumbi gravitate à naturá in&longs;itâ, tribuatur a&longs;cen&longs;us, <lb/>ni&longs;i impetui acqui&longs;ito dum de&longs;cenderet, adhuc po&longs;t de&longs;cen&longs;um <lb/>duranti? </s>

Line 2191

<s>Cum enim impetus contra<lb/>rium impetum non habeat, &longs;i præci&longs;a quidem impetûs natura <lb/>&longs;pectetur (quippe qui unus & idem contrariorum motuum ori<lb/>go e&longs;t, ut ex funependulis ultrò citróque &longs;ponte vibratis & ex <lb/>pilâ lu&longs;oriâ deor&longs;um cadente, ac vi concepti impetûs &longs;ur&longs;um <lb/>re&longs;iliente, con&longs;tat) reliquum e&longs;t, ut pereat pro ratione eorum, <lb/>quæ aut motui corporis ob&longs;i&longs;tunt, aut illud aliò quoquomodo <lb/>dirigunt. </s>

<s>Præ&longs;tat autem hîc funependuli <lb/><figure id="fig33"/><lb/>motum paulò attentiùs con&longs;iderare. </s>

<s>Præ&longs;tat autem hîc funependuli <lb/><figure id="id.017.01.164.1.jpg" xlink:href="017/01/164/1.jpg"/><lb/>motum paulò attentiùs con&longs;iderare. </s>

<lb/><s>Sit plumbeus globulus B filo AB <lb/>connexus clavo in A. </s>

Line 2201

15 explicatum e&longs;t; hæc autem <lb/>&longs;unt pro Ratione Sinuum angulorum declinationis à perpendi<lb/>culo AK. </s>

<s>Quare totum momentum, quod in B e&longs;&longs;et ut AB, <lb/>fingulis momentis in de&longs;cen&longs;u libero per rectam BC paribus <lb/>&longs;altem incrementis augeretur (Quicquid &longs;it an etiam pro Ra<lb/>tione duplicatâ temporum, de quo alias di&longs;putabimus) &longs;ed <lb/>cum à rectitudine deflectat, cum venerit in D, non additur <lb/>momentum ut EF, &longs;ed ut ED; &longs;imiliter in G momentum non <pb pagenum="149"/>e&longs;t ut HI, &longs;ed ut HG. </s>

<s>Quare totum momentum, quod in B e&longs;&longs;et ut AB, <lb/>fingulis momentis in de&longs;cen&longs;u libero per rectam BC paribus <lb/>&longs;altem incrementis augeretur (Quicquid &longs;it an etiam pro Ra<lb/>tione duplicatâ temporum, de quo alias di&longs;putabimus) &longs;ed <lb/>cum à rectitudine deflectat, cum venerit in D, non additur <lb/>momentum ut EF, &longs;ed ut ED; &longs;imiliter in G momentum non <pb xlink:href="017/01/165.jpg" pagenum="149"/>e&longs;t ut HI, &longs;ed ut HG. </s>

<s>Augetur igitur impetus in de&longs;cen&longs;u <lb/>BK non omninò pro Ratione <expan abbr="momentor&utilde;">momentorum</expan> temporis, quo motus <lb/>durat, &longs;ed pro Ratione momentorum gravitatis, quæ &longs;ubinde <lb/>obtinet minora & minora; pars <expan abbr="&longs;iquid&etilde;">&longs;iquidem</expan> impetûs ab in&longs;itâ globuli <lb/>gravitate producti deteritur in intendendo filo, quo retinetur. </s>

<lb/><s>Q<gap/>ropter ubi in K venerit per arcum BK, non tantum ha<lb/>bet impetûs, quantum &longs;i per lineam perpendicularem arcui <lb/>BK æqualem de&longs;cendi&longs;&longs;et; in motu enim ad perpendiculum <lb/>cum nihil retineat aut impediat, totus impetus ad de&longs;cen&longs;um <lb/>urget velociùs, quàm ubi repugnat aliquid. </s>

<lb/><s>Quapropter ubi in K venerit per arcum BK, non tantum ha<lb/>bet impetûs, quantum &longs;i per lineam perpendicularem arcui <lb/>BK æqualem de&longs;cendi&longs;&longs;et; in motu enim ad perpendiculum <lb/>cum nihil retineat aut impediat, totus impetus ad de&longs;cen&longs;um <lb/>urget velociùs, quàm ubi repugnat aliquid. </s>

<s>Ex quo fit quod, <lb/>cùm arcus BK ad Radium AB, hoc e&longs;t ad BC æqualc<gap/><lb/>proximè ut 11 ad 7, ex Cyclometricis, multò plus t<gap/><lb/>percurrendo arcu BK, quàm in rectâ BC, in&longs;umit<gap/><lb/>&longs;cilicet movetur quàm in perpendiculari, quæ ad BC<gap/> ut <lb/>11 ad 7. manente itaque, quamdiu corpus naturá urg<gap/><lb/>vetur, impetu acqui&longs;ito, qui re&longs;i&longs;tentiam exced<gap/><lb/>de&longs;censûs in K totus impetus e&longs;t ut aggregatum om<gap/><lb/>nuum Quadrantis: at in perpendiculari BC in fin<gap/><lb/>in C e&longs;&longs;et ut aggregatum omnium parallelarum ip&longs;i AB<gap/><lb/>Quadrato AC; ac propterea (in re Phy&longs;icâ &longs;i liceat <gap/><lb/>metrizantibus per Indivi&longs;ibilia ratiocinari) erit impetus pe<gap/><lb/>cum BK acqui&longs;itus ad impetum per rectam BC acqui&longs;i<gap/><lb/>Quadrans ABK ad Quadratum AC, hoc e&longs;t ut 11 ad <gap/><lb/>iis quæ in Cyclometriâ demon&longs;trantur. </s>

Line 2215

<s>Quare tantum abe&longs;t, <lb/>ut novus &longs;ingulis temporis punctis impetus &longs;ur&longs;um directus pro<lb/>ducatur, ut potius ex eo tantumdem dematur, quanta e&longs;t <lb/>a&longs;cendentis plumbi repugnantia. </s>

<s>Hinc e&longs;t a&longs;cen&longs;um initio ve<lb/>lociorem e&longs;&longs;e, quia adhuc multus e&longs;t impetus acqui&longs;itus, & pro <pb pagenum="150"/>Sinuum declinationis brevitate, exigua illius pars deteritur, <lb/>atque adeò motus efficitur celerior: quia verò diminuto &longs;en&longs;im <lb/>impetu, & auctis <expan abbr="cõtrariæ">contrariæ</expan> gravitatis <expan abbr="mom&etilde;tis">momentis</expan> pro Sinuum decli<lb/>nationis <expan abbr="increm&etilde;to">incremento</expan>, minor fit ip&longs;ius impetûs ad <expan abbr="contrari&utilde;">contrarium</expan> ni&longs;um <lb/>Ratio, tardior &longs;equitur motus, & plus acqui&longs;iti impetûs perit, do<lb/>nec demùm pror&longs;us evanuerit, & &longs;uperante gravitate glo<gap/>us <lb/>iterum de&longs;cendat. </s>

<s>Hinc e&longs;t a&longs;cen&longs;um initio ve<lb/>lociorem e&longs;&longs;e, quia adhuc multus e&longs;t impetus acqui&longs;itus, & pro <pb xlink:href="017/01/166.jpg" pagenum="150"/>Sinuum declinationis brevitate, exigua illius pars deteritur, <lb/>atque adeò motus efficitur celerior: quia verò diminuto &longs;en&longs;im <lb/>impetu, & auctis <expan abbr="cõtrariæ">contrariæ</expan> gravitatis <expan abbr="mom&etilde;tis">momentis</expan> pro Sinuum decli<lb/>nationis <expan abbr="increm&etilde;to">incremento</expan>, minor fit ip&longs;ius impetûs ad <expan abbr="contrari&utilde;">contrarium</expan> ni&longs;um <lb/>Ratio, tardior &longs;equitur motus, & plus acqui&longs;iti impetûs perit, do<lb/>nec demùm pror&longs;us evanuerit, & &longs;uperante gravitate globulus <lb/>iterum de&longs;cendat. </s>

<s>Quamvis autem &longs;i po&longs;itio &longs;ola &longs;pectetur, ii&longs;<lb/>dem Reciproce gradibus minui videatur impetus, quibus fuit <lb/>auctus, totidemque momentis temporis, ita ut quantum po&longs;tre<lb/>mo temporis puncto acce&longs;&longs;it, tantumdem primo decedat, adhuc <lb/>tamen aliqua e&longs;t ob&longs;i&longs;tentiæ appendicula ex aëre dividendo, ac <lb/>propterea paulo ampliùs extenuatur impetus acqui&longs;itus, quàm <lb/>pro Ratione incrementi Sinuum declinationis: quò autem ve<lb/>locior e&longs;t motus, magis etiam aër dividendus comprimitur, <lb/>den&longs;atú&longs;que plus ob&longs;i&longs;tit quàm rarus; quòd &longs;i medium non fue<lb/>rit compre&longs;&longs;ionis capax, &longs;altem æquali tempore plures medij <lb/>partes &longs;cinduntur, quàm in motu tardiori, ac propterea etiam <lb/>multiplex e&longs;t medij re&longs;i&longs;tentia: Ex quo fit arcum a&longs;censûs pau<lb/>lò minorem &longs;emper e&longs;&longs;e arcu de&longs;censûs, &, cum vici&longs;&longs;im glo<lb/>bus remaneat ex humiliore loco ac priùs de&longs;cendens, brevio<lb/>rem pariter &longs;ecundi a&longs;censûs arcum perfici, atque ita deinceps, <lb/>ut &longs;ervatâ eâ in motu &longs;emper minori reciprocando con&longs;tantiâ <lb/>demum quie&longs;cat in perpendiculo. </s>

Line 2223

<s>Fateor eburneum globum &longs;egniùs re&longs;ilire delap&longs;um in gle<lb/>bam humore perfu&longs;am, quàm in marmor; non tamen his con<lb/>&longs;equens e&longs;t, ut impetûs acqui&longs;iti diminutioni alius &longs;tatuendus <lb/>&longs;it modus, quàm ex impedimento: ubi enim globus cadens ex<lb/>timam &longs;ubjecti corporis &longs;uperficiem attigerit, non quie&longs;eit, &longs;ed <lb/>pergit moveri, aut deor&longs;um comprimendo corpus molle, aut <lb/>illicò &longs;ursùm reflexum à duro. </s>

<s>Fateor eburneum globum &longs;egniùs re&longs;ilire delap&longs;um in gle<lb/>bam humore perfu&longs;am, quàm in marmor; non tamen his con<lb/>&longs;e