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version 1.2, 2003/11/20 18:08:02

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

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<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 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>

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<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 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 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 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/>

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<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 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>

Line 509

<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 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>

Line 536

<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 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, & <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 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;end<gap/> 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 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 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>

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>

Line 737

<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 1021

<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 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>

Line 1605

<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 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 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 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; & 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 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 xlink:href="017/01/138.jpg" pagenum="122"/><figure id="id.017.01.138.1.jpg" xlink:href="017/01/138/1.jpg"/>

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 xlink:href="017/01/142.jpg" 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 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 1921

<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="id.017.01.146.1.jpg" xlink:href="017/01/146/1.jpg"/><lb/>tuo fulcri, & axis tritu. </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 xlink:href="017/01/148.jpg" 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 2029

<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 2073

<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 2169

<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 2205

<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 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 glo<gap/>us <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 2253

<lb/><s>Provinciâ Fokion, ubi &longs;ermo e&longs;t de flumine Min, quod vio<lb/>lento cur&longs;u per &longs;axa volvitur, ait naves, quibus ibi navigatur, <lb/>ex diverbio vocari <emph type="italics"/>Papyraceas, eo quòd tenuibus ac minime re<lb/>&longs;i&longs;tentibus con&longs;tent a&longs;&longs;eribus, imò ne clavis quidem compaginatis; <lb/>&longs;ed vimine quodam lenti&longs;&longs;imo; unde tamct&longs;i in &longs;axa impingat na<lb/>vis, &longs;apè tamen minimè rumpitur, quia vix re&longs;i&longs;tit.<emph.end type="italics"/></s><s> Et pag.127. <lb/>de catadupis aquarum in flumine per quod ad Jenping naviga<lb/>tur loquens ait. <emph type="italics"/>Cum naves tran&longs;eunt, ne cum aquâ decidentes <lb/>f actionis incurrant periculum, &longs;citè pramittunt nautæ aliquot &longs;tra<lb/>minis &longs;o&longs;ces, ad quos navis leviùs impingat, ac tran&longs;eat.<emph.end type="italics"/></s>

<s>Jam verò ad impetum extrin&longs;ecùs impre&longs;&longs;um mentem ocu<lb/><gap/>e intendente, non illum &longs;emper momento perire animad<lb/><gap/> aut illicò, ac externus agitator ce&longs;&longs;at. </s>

<s>Jam verò ad impetum extrin&longs;ecùs impre&longs;&longs;um mentem ocu<lb/>lo&longs;que intendente, non illum &longs;emper momento perire animad<lb/>vertimus, aut illicò, ac externus agitator ce&longs;&longs;at. </s>

<s><gap/> nim tit, ut concitato navigio, cùm vela nautæ con<lb/><gap/>ut remiges inhibuerunt, retineat tamen ip&longs;a navis <lb/><gap/>ur&longs;um &longs;uum, intermi&longs;&longs;o ventorum incur&longs;u, pulsúve <pb xlink:href="017/01/169.jpg" pagenum="153"/>remorum? </s>

Line 2535

<s>Satis igitur erit, ubi &longs;ingularum machmarum <lb/>vires expendendæ erunt motuum inire rationes, qui ex machi<lb/>næ agitatione oriuntur: nam &longs;i Potentia præ Onere velociùs <lb/>moveatur, operæ pretium faciet Machinator; modò non adeò <lb/>tenuis &longs;it motuum Ratio, ut quiequid utilitatis ex machinæ fi<lb/>gurà accedit, deferatur ex partium &longs;e terentium conflictu; nam <lb/>perinde e&longs;&longs;et, ac &longs;i oneri gravitas adderetur. </s>

<s>Ex his liquet à non paucis plus operæ labori&longs;que con&longs;ump<lb/>tum, quàm par e&longs;&longs;et, ut Ari&longs;toteli adhærerent in referendis <lb/>machinarum viribus in circuli naturam planè admirandam: <lb/><emph type="italics"/>Quapropter<emph.end type="italics"/> inquit initio <expan abbr="qq.">qque</expan> Mechan. <emph type="italics"/>non e&longs;t inconveniens ip&longs;um <lb/>m<gap/>raculorum omnium e&longs;&longs;e prmcipium. </s>

<s>Ex his liquet à non paucis plus operæ labori&longs;que con&longs;ump<lb/>tum, quàm par e&longs;&longs;et, ut Ari&longs;toteli adhærerent in referendis <lb/>machinarum viribus in circuli naturam planè admirandam: <lb/><emph type="italics"/>Quapropter<emph.end type="italics"/> inquit initio <expan abbr="qq.">qque</expan> Mechan. <emph type="italics"/>non e&longs;t inconveniens ip&longs;um <lb/>miraculorum omnium e&longs;&longs;e principium. </s>

<s>Ea igitur quæ circà libram fiunt, <lb/>ad circulum referuntur, quæ verò circa ve<gap/>em, ad ip&longs;am libram; <lb/>alia autem ferè omnia, quæ circa mechanicas &longs;unt motiones, ad <lb/>vectem.<emph.end type="italics"/></s><s> Ni&longs;i enim fucum veritati faciamus, quæ demum mi<lb/>racula ita circulum à reliquo figurarum vulgo &longs;ecernunt, ut in <lb/>cum admiratio omnis corrivata confluat, nec ni&longs;i hinc in cæte<lb/>ras derivetur? </s>

<s>Ea igitur quæ circà libram fiunt, <lb/>ad circulum referuntur, quæ verò circa vectem, ad ip&longs;am libram; <lb/>alia autem ferè omnia, quæ circa mechanicas &longs;unt motiones, ad <lb/>vectem.<emph.end type="italics"/></s><s> Ni&longs;i enim fucum veritati faciamus, quæ demum mi<lb/>racula ita circulum à reliquo figurarum vulgo &longs;ecernunt, ut in <lb/>cum admiratio omnis corrivata confluat, nec ni&longs;i hinc in cæte<lb/>ras derivetur? </s>

<s>An quòd linea eadem, quâ circuli ambitus de<lb/>finitur, omnis latitudinis expers, cava pariter atque convexa <lb/>amico f&oelig;dere copulat, quæ &longs;ibi invicem repugnant? </s>

Line 2837

<s>Quamvis negandum non &longs;it ad huju&longs;modi facili<lb/>tatem, quam experimur in &longs;u&longs;tinendo potiùs, quàm in re<lb/>tinendo onere, conferre plurimum, quòd tellus, cui ful<lb/>crum infigitur, demùm non &longs;ub&longs;idit; at laqueare &longs;eu for<lb/>nix ex quo &longs;olidum pendet onere prægravatum, tantam <lb/>gravitatem non ita facilè ferre pote&longs;t. </s>

<s>Quare ad tollenda <lb/>in &longs;uperiores ædificiorum partes ingentia &longs;axa multo cau<lb/>tiùs atque tutiùs ij operantur, qui longam trabe<gap/>, aut plu<lb/>ra tigna ritè connexa, qua&longs;i navis malum rudentibus u&longs;<lb/>quequaque firmatum, ne à perpendiculo deflectat, &longs;ta<lb/>tuunt, cui &longs;uperiorem trochleam adnectant; quàm qui tra<lb/>bem Horizonti parallelam parieti infigunt ad idem munus <lb/>præ&longs;tandum; hæc &longs;iquidem horizonti parallela magis fractio<lb/>ni obnoxia e&longs;t, quàm perpendicularis; præterquam quod <lb/>parietem aliquatenus labefactare pote&longs;t, cum habeat ratio-<pb xlink:href="017/01/206.jpg" pagenum="190"/>nem vectis in &longs;uperiora propellentis &longs;axo deor&longs;um urgente; <lb/>ni&longs;i huic periculo ex arte obviam eatur. </s>

<s>Quare ad tollenda <lb/>in &longs;uperiores ædificiorum partes ingentia &longs;axa multo cau<lb/>tiùs atque tutiùs ij operantur, qui longam trabem, aut plu<lb/>ra tigna ritè connexa, qua&longs;i navis malum rudentibus u&longs;<lb/>quequaque firmatum, ne à perpendiculo deflectat, &longs;ta<lb/>tuunt, cui &longs;uperiorem trochleam adnectant; quàm qui tra<lb/>bem Horizonti parallelam parieti infigunt ad idem munus <lb/>præ&longs;tandum; hæc &longs;iquidem horizonti parallela magis fractio<lb/>ni obnoxia e&longs;t, quàm perpendicularis; præterquam quod <lb/>parietem aliquatenus labefactare pote&longs;t, cum habeat ratio-<pb xlink:href="017/01/206.jpg" pagenum="190"/>nem vectis in &longs;uperiora propellentis &longs;axo deor&longs;um urgente; <lb/>ni&longs;i huic periculo ex arte obviam eatur. </s>

<s>Comparatis itaque invicem &longs;olidorum frangendorum lon<lb/>gitudinibus, hoc e&longs;t intervallis inter fractionum puncta & <lb/>locum, ubi potentia vim frangendi habens con&longs;tituta intel<lb/>ligitur, quò major e&longs;t longitudo, eò minor e&longs;t re&longs;i&longs;tentia <lb/>&longs;olidi, ne frangatur. </s>

Line 2845

<s>Hinc e&longs;t <lb/>fieri aliquando po&longs;&longs;e, ut &longs;olidum cra&longs;&longs;ius minùs re&longs;i&longs;tat <lb/>fractioni, quàm &longs;ubtilius, &longs;i hoc breve &longs;it, illud verò valdè <lb/>longum, &longs;i videlicet longitudo cra&longs;&longs;ioris ad longitudinem <lb/>&longs;ubtilioris Rationem habeat majorem, quàm &longs;it ea, quæ ex <lb/>Rationibus Ba&longs;ium, & Cra&longs;&longs;itierum componitur. </s>

<s>Sic &longs;i duo <lb/>fuerint cylindri, & alter triplo cra&longs;&longs;ior fuerit reliquo, &longs;ed <lb/>etiam trigecuplo longior fuerit illo, minùs etiam fractioni <lb/>re&longs;i&longs;tet; quia re&longs;i&longs;tentia ab&longs;oluta majoris cylindri ad mino<lb/>tem e&longs;t ut 27 ad 1, &longs;ed re&longs;i&longs;tentia Re&longs;pectiva eju&longs;dem ma<lb/>joris ad minoris re&longs;i&longs;tentiam pariter re&longs;pectivam e&longs;t ut 1 ad <lb/>30: Ratio ergo ex his Rationibus 27 ad 1, & 1 ad 30 <lb/>Compo&longs;ita, e&longs;t Ratio 27 ad 30, hoc e&longs;t 9 ad 10, ac propterea <lb/>major cylindrus re&longs;i&longs;tit fractioni ut 9, minor verò fractioni <lb/>re&longs;i&longs;tit ut 1<gap/>. </s>

<s>De&longs;ine jam mirari, &longs;i quando paxillum maximis viribus <lb/>re&longs;i&longs;tere videris; quia nimirùm potentia, quæ motum co<lb/>natur, proximè applicata e&longs;t parieti aut plano, cui paxil<lb/>lus infigitur: quòd &longs;i remotior illa fuerit, etiam minùs hic <lb/>re&longs;i&longs;tet. </s>

Line 2969

<s>Hinc manife&longs;tum e&longs;t compo&longs;itis tribus, quatuorve, aut plu<lb/>ribus Facultatibus, Rationem Compo&longs;itam motus potentiæ ad <lb/>motum Ponderis fieri multò majorem; cui &longs;i æqualem Ratio<lb/>nem habere velimus unicâ atque &longs;implici Facultate, hujus <lb/>magnitudinem aliquando enormem fieri nece&longs;&longs;e e&longs;&longs;et; ut &longs;uis <lb/>locis infrà declarabitur. </s>

<s>In co igitur elucebit Machinatoris indu&longs;tria, &longs;i Facultates <lb/>ip&longs;as aptè congruenterque di&longs;ponat, atque permi&longs;ceat, &longs;pecta<lb/>tâ materiæ &longs;oliditate, &longs;patij amplitudine, Ponderis po&longs;itione, <lb/>Potentiæ virtute, temporis ad movendum conce&longs;&longs;i opportuni<lb/>tate: hæc enim omnia attenti&longs;&longs;imè perpendenda &longs;unt; ne, dum <lb/>nimis &longs;ollicitè laborem imminuere &longs;tudet, motum plus æquo <lb/>imminuens, tardioremque efficiens temporis jacturam faciat, <lb/>aut totum &longs;patium machina implens in eas angu&longs;tias Potentiam <lb/>moventem conjiciat, ut motum expeditè perficere nequeat. <lb/><gap desc="hr tag"/></s>

<s>In eo igitur elucebit Machinatoris indu&longs;tria, &longs;i Facultates <lb/>ip&longs;as aptè congruenterque di&longs;ponat, atque permi&longs;ceat, &longs;pecta<lb/>tâ materiæ &longs;oliditate, &longs;patij amplitudine, Ponderis po&longs;itione, <lb/>Potentiæ virtute, temporis ad movendum conce&longs;&longs;i opportuni<lb/>tate: hæc enim omnia attenti&longs;&longs;imè perpendenda &longs;unt; ne, dum <lb/>nimis &longs;ollicitè laborem imminuere &longs;tudet, motum plus æquo <lb/>imminuens, tardioremque efficiens temporis jacturam faciat, <lb/>aut totum &longs;patium machina implens in eas angu&longs;tias Potentiam <lb/>moventem conjiciat, ut motum expeditè perficere nequeat. <lb/><gap desc="hr tag"/></s>

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

Line 3107

7. cap.

37. cum Vi<lb/>truvio lib.10. cap. 6, quem tamen idem Plinius lib.36. cap.14. <pb xlink:href="017/01/225.jpg" pagenum="209"/>cum Strabone vocat Cher&longs;iphronem) celeberrimo Dianæ <lb/>templo con&longs;truendo præfectus, & quidem felici eventu: ca<lb/>pitibus enim &longs;caporum, ubi axis extremitates de&longs;inebant, &longs;ub<lb/>&longs;cudis in modum in&longs;eruit, atque implumbavit ferreos axes: <lb/>tùm de materiâ trientali &longs;capos (hoc e&longs;t ligneos tigillos cra&longs;&longs;i<lb/>tudinis unciarum quatuor pedis, &longs;eu pollicum quatuor) duos <lb/>longiores juxtà columnæ longitudinem, duo&longs;que breviores <lb/>tran&longs;ver&longs;arios ita compegit, ut parallelogrammum con&longs;tituen<lb/>tes columnam po&longs;&longs;ent complecti; medii&longs;que tran&longs;ver&longs;ariis <lb/>ferreas armillas in&longs;eruit, quibus axes ferrei infigebantur, <lb/>a<gap/>ò ut liberè ver&longs;ari po&longs;&longs;ent, cum boves traherent; quem<lb/>admodum & in gyrum volvuntur cylindri marmorei aut la<lb/>pidei, quorum u&longs;us e&longs;t in exæquandis ambulationibus. </s>

37. cum Vi<lb/>truvio lib.10. cap. 6, quem tamen idem Plinius lib.36. cap.14. <pb xlink:href="017/01/225.jpg" pagenum="209"/>cum Strabone vocat Cher&longs;iphronem) celeberrimo Dianæ <lb/>templo con&longs;truendo præfectus, & quidem felici eventu: ca<lb/>pitibus enim &longs;caporum, ubi axis extremitates de&longs;inebant, &longs;ub<lb/>&longs;cudis in modum in&longs;eruit, atque implumbavit ferreos axes: <lb/>tùm de materiâ trientali &longs;capos (hoc e&longs;t ligneos tigillos cra&longs;&longs;i<lb/>tudinis unciarum quatuor pedis, &longs;eu pollicum quatuor) duos <lb/>longiores juxtà columnæ longitudinem, duo&longs;que breviores <lb/>tran&longs;ver&longs;arios ita compegit, ut parallelogrammum con&longs;tituen<lb/>tes columnam po&longs;&longs;ent complecti; medii&longs;que tran&longs;ver&longs;ariis <lb/>ferreas armillas in&longs;eruit, quibus axes ferrei infigebantur, <lb/>adeò ut liberè ver&longs;ari po&longs;&longs;ent, cum boves traherent; quem<lb/>admodum & in gyrum volvuntur cylindri marmorei aut la<lb/>pidei, quorum u&longs;us e&longs;t in exæquandis ambulationibus. </s>

<s>E&longs;t <lb/>autem maximè veri&longs;imile, & probabile, ita firmiter <lb/>ligneum illud parallelogrammum fui&longs;&longs;e compactum, ut non <lb/>&longs;olùm extremis tran&longs;ver&longs;ariorum capitibus anterioribus alli<lb/>gari po&longs;&longs;ent boves; &longs;ed etiam per totam anterioris &longs;capi lon<lb/>gitudinem di&longs;tribui, ut faciliùs columna transferretur. </s>

Line 3129

<s>Tùm circà fu&longs;os fu<lb/>nem involvit, qui bobus trahentibus explicabatur, & con<lb/>vertebantur Rotæ. </s>

<s>Verùm quia funis circumvoluti &longs;piræ ad <lb/>unam, aut ad alteram partem &longs;pectabant, non poterat <gap/><lb/>rectâ ad lineam deduci moles illa; &longs;ed modò in hanc, mo<lb/>dò in illam partem deflectebat, ut opus e&longs;&longs;et retroducere, <lb/>adeò ut ducendo & reducendo pecuniam contriverit, & ope<lb/>ram lu&longs;erit Paconius. </s>

<s>Verùm quia funis circumvoluti &longs;piræ ad <lb/>unam, aut ad alteram partem &longs;pectabant, non poterat viâ <lb/>rectâ ad lineam deduci moles illa; &longs;ed modò in hanc, mo<lb/>dò in illam partem deflectebat, ut opus e&longs;&longs;et retroducere, <lb/>adeò ut ducendo & reducendo pecuniam contriverit, & ope<lb/>ram lu&longs;erit Paconius. </s>

<s>Potui&longs;&longs;et tamen huic malo occurrere, <lb/>nec &longs;ui inventi laude fraudari, &longs;i circà fu&longs;os non unicum, <lb/>&longs;ed duplicem funem ita involvi&longs;&longs;et, ut funium &longs;piris vel ab <lb/>extremitatibus fu&longs;orum, vel à medio, incipientibus, funis <lb/>uterque paribus &longs;emper intervallis à &longs;ibi proximâ Rotâ di&longs;ta<lb/>rent; &longs;ic enim factum fui&longs;&longs;et, ut boves æqualiter utrumque <lb/>funem trahentes, æqualiterque evolventes, molem illam rectâ <lb/>viâ deducerent. </s>

Line 3187

<s>Id quod, <lb/>per &longs;e quidem &longs;atis clarum, dilucidiùs explicabitur, &longs;i ex mi<lb/><figure id="id.017.01.230.1.jpg" xlink:href="017/01/230/1.jpg"/><lb/>nore circulo extet particula, cu<lb/>jus altitudo &longs;it ON, ex majore <lb/>autem circulo æqualis altitudo <lb/>emineat IM. </s>

<s>Ductis Tangen<lb/>tibus & Radiis, certum e&longs;t Se<lb/>cantis exce&longs;&longs;um ON &longs;upra Ra<lb/>dium LO minorem, habere <lb/>majorem Rationem ad &longs;uum <lb/>Radium, quàm habeat æqualis <lb/>exce&longs;&longs;us IM ad &longs;uum Radium <lb/>LI majorem ex 8.lib.5. E&longs;t igl<lb/>tur MLP angulus minor angulo NLS, & Complementum <lb/>LMP majus e&longs;t Complemento LNS quare totus angulus <lb/>VMP major e&longs;t toto angulo TNS, ac proinde magis ad ro<lb/>tunditatem accedit. <lb/><gap desc="hr tag"/></s>

<s>Ductis Tangen<lb/>tibus & Radiis, certum e&longs;t Se<lb/>cantis exce&longs;&longs;um ON &longs;upra Ra<lb/>dium LO minorem, habere <lb/>majorem Rationem ad &longs;uum <lb/>Radium, quàm habeat æqualis <lb/>exce&longs;&longs;us IM ad &longs;uum Radium <lb/>LI majorem ex 8.lib.5.  E&longs;t igi<lb/>tur MLP angulus minor angulo NLS, & Complementum <lb/>LMP majus e&longs;t Complemento LNS quare totus angulus <lb/>VMP major e&longs;t toto angulo TNS, ac proinde magis ad ro<lb/>tunditatem accedit. <lb/><gap desc="hr tag"/></s>

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

Line 3253

<s>Et hæc quidem, quando centri motus legem accipit à pe<lb/>ripheriâ majoris circuli; ad cujus motum minor circulus con<lb/>centricus movetur; eo quod major circulus in&longs;i&longs;tit &longs;ubjecto pla<lb/>no, cui orbita &longs;ubinde coaptatur rectam lineam &longs;ibi æqualem <lb/>de&longs;ignans ex hypothe&longs;i, dumque movetur, &longs;ecum rapit interio<lb/>rem circulum. </s><pb xlink:href="017/01/235.jpg" pagenum="219"/>

<s>Quod &longs;i minor circulus in&longs;i&longs;tat &longs;ubjecto &longs;ibi plano, <gap/>n<lb/>que det motui centri; quia minor peripheria de&longs;ignat <gap/>n <lb/>&longs;ibi æqualem, res contrario modo procedit, quia dum ad mi<lb/>noris circuli motum circulus major movetur, hujus orbita de<lb/>&longs;ignat in plano &longs;ubjecto lineam minori peripheriæ æqualem. </s>

<s>Quod &longs;i minor circulus in&longs;i&longs;tat &longs;ubjecto &longs;ibi plano, legem<lb/>que det motui centri; quia minor peripheria de&longs;ignat rectam <lb/>&longs;ibi æqualem, res contrario modo procedit, quia dum ad mi<lb/>noris circuli motum circulus major movetur, hujus orbita de<lb/>&longs;ignat in plano &longs;ubjecto lineam minori peripheriæ æqualem. </s>

<lb/><s>Hinc &longs;i arcus SI de&longs;ignat rectam SG &longs;ibi æqualem, ubi I ve<lb/>nerit in G, etiam D erit in H, atque totus Quadrans BD de<lb/>&longs;ignabit &longs;olùm rectam BH æqualem rectæ SG. </s>

Line 3263

<s>Ex his apertè liquet eam lineam rectam in &longs;ubjecto plano de<lb/>&longs;ignari à peripheriâ tùm majoris, tùm minoris circuli, quæ <lb/>æqualis &longs;it motui centri, prout ille legem accipit à majore aut <lb/>à minore orbitâ, ad cujus motum altera movetur; ac proinde <lb/>modò longiori, modò breviori lineæ rectæ in motu coaptantur <lb/>ambæ peripheriæ; ut enim rectè loquitur Ari&longs;toteles loc. </s>

<s>cit. <lb/><emph type="italics"/>Quando hic quidem movet, ille verò movetur ab i&longs;<gap/>o, quantum uti<lb/>que moverit alter, tantum alter movebitur.<emph.end type="italics"/></s>

<s>cit. <lb/><emph type="italics"/>Quando hic quidem movet, ille verò movetur ab i&longs;to, quantum uti<lb/>que moverit alter, tantum alter movebitur.<emph.end type="italics"/></s>

<s>Cur igitur parem lineam rectam de&longs;ignat in plano utraque <lb/>orbita major & minor? </s>

Line 3423

<s>Subtilitas hæc relinquatur gemmariis, aurifici<lb/>bus, auríque monetalis cu&longs;oribus, quibus damnum e&longs;&longs;et minu<lb/>tias contemnere. </s>

<s>Quamquam nec i&longs;tis author fuerim, ut &longs;in<lb/><gap/>aribus granis uterentur, &longs;ed potiùs ponderibus, quæ plturi<lb/><gap/>anis æquivalerent; &longs;i enim &longs;ingula grana à legitimo pon<lb/>dere <gap/>iciunt per cente&longs;imam grani partem, quæ facilè &longs;ensûs <pb xlink:href="017/01/247.jpg" pagenum="231"/>aciem fugit, additis centum huju&longs;modi granis error e&longs;t inte<lb/>gri grani deficientis; & in uncia libræ Romanæ ponderalis ad <lb/>monetam pertinentis cum grana 576 contineantur, in uncia <lb/>auri error e&longs;&longs;et granorum ferè &longs;ex deficientium, & in integrâ <lb/>librâ, quæ e&longs;t granorum 6912, e&longs;&longs;et error granorum 69; qui <lb/>tamen error vix contingat, &longs;i a&longs;&longs;umatur integra uncia, aut li<lb/>bra: illud &longs;i quidem, quod &longs;olitarium præ &longs;ua tenuitate in con<lb/>&longs;pectum non cadit, cum pluribus &longs;imilibus conjunctum evadit <lb/>demum notabile atque con&longs;picuum. </s>

<s>Quamquam nec i&longs;tis author fuerim, ut &longs;in<lb/>gularibus granis uterentur, &longs;ed potiùs ponderibus, quæ pluri<lb/>bus granis æquivalerent; &longs;i enim &longs;ingula grana à legitimo pon<lb/>dere dificiunt per cente&longs;imam grani partem, quæ facilè &longs;ensûs <pb xlink:href="017/01/247.jpg" pagenum="231"/>aciem fugit, additis centum huju&longs;modi granis error e&longs;t inte<lb/>gri grani deficientis; & in uncia libræ Romanæ ponderalis ad <lb/>monetam pertinentis cum grana 576 contineantur, in uncia <lb/>auri error e&longs;&longs;et granorum ferè &longs;ex deficientium, & in integrâ <lb/>librâ, quæ e&longs;t granorum 6912, e&longs;&longs;et error granorum 69; qui <lb/>tamen error vix contingat, &longs;i a&longs;&longs;umatur integra uncia, aut li<lb/>bra: illud &longs;i quidem, quod &longs;olitarium præ &longs;ua tenuitate in con<lb/>&longs;pectum non cadit, cum pluribus &longs;imilibus conjunctum evadit <lb/>demum notabile atque con&longs;picuum. </s>

<s>Quare ad paranda pon<lb/>dera huju&longs;modi &longs;ubtiliora, a&longs;&longs;ume laminam metallicam ponde<lb/>re unius libræ, &longs;ed æquabiliter exten&longs;am, eju&longs;que duodecimam <lb/>partem accipe; hæc erit Uncia, quam &longs;epones. </s>

Line 3467

<s>TABELLE WAR HIER</s>

<s>Unum hîc, ubi de Ponderibus &longs;ermo e&longs;t, obiter moneo, libræ <lb/>nomen apud Romanos æquivocum fui&longs;&longs;e, alia enim erat libra <lb/>Ponderalis aridorum, alia Men&longs;uralis liquidorum (& poti&longs;&longs;i<lb/>mum olei, quod cornu librali metiebantur) quam inci&longs;is & in<lb/>&longs;culptis lineis in uncias 12 partiebantur, quemadmodum & li<lb/>bra pondo in uncias pariter 12 di&longs;tinguebatur: &longs;ed inter utram<lb/>que libram, &longs;i materia ip&longs;a ad pondus revocabatur, non exi<lb/>guum erat di&longs;crimen; ut enim ex proprio experimento te&longs;t<gap/><pb xlink:href="017/01/251.jpg" pagenum="235"/>tur Galenus lib.

<s>Unum hîc, ubi de Ponderibus &longs;ermo e&longs;t, obiter moneo, libræ <lb/>nomen apud Romanos æquivocum fui&longs;&longs;e, alia enim erat libra <lb/>Ponderalis aridorum, alia Men&longs;uralis liquidorum (& poti&longs;&longs;i<lb/>mum olei, quod cornu librali metiebantur) quam inci&longs;is & in<lb/>&longs;culptis lineis in uncias 12 partiebantur, quemadmodum & li<lb/>bra pondo in uncias pariter 12 di&longs;tinguebatur: &longs;ed inter utram<lb/>que libram, &longs;i materia ip&longs;a ad pondus revocabatur, non exi<lb/>guum erat di&longs;crimen; ut enim ex proprio experimento te&longs;ta-<pb xlink:href="017/01/251.jpg" pagenum="235"/>tur Galenus lib.

6. cap.

8. <emph type="italics"/>de compo&longs;itione medicam. </s>

<s>per genera.<emph.end type="italics"/><lb/>Libra men&longs;ura &longs;olùm uncias decem continebat, quarum li<lb/>bra pondo erat duodecim: quapropter uncia men&longs;uralis ad un<lb/>ciam ponderalem erat ut 5 ad 6 &longs;pectatâ gravitate & quantita<lb/>te materiæ. <lb/><gap desc="hr tag"/></s>

<s>per genera. <emph.end type="italics"/> <lb/>Libra men&longs;ura &longs;olùm uncias decem continebat, quarum li<lb/>bra pondo erat duodecim: quapropter uncia men&longs;uralis ad un<lb/>ciam ponderalem erat ut 5 ad 6 &longs;pectatâ gravitate & quantita<lb/>te materiæ. <lb/><gap desc="hr tag"/></s>

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

Line 3505

<s>Si <lb/>enim pondera e&longs;&longs;ent æqualia, ponderis A re&longs;i&longs;tentia ratione <pb xlink:href="017/01/253.jpg" pagenum="237"/>motûs e&longs;&longs;et &longs;ubquadrupla, &longs;ed quadruplicatur ratione gravita<lb/>tis, ergo re&longs;i&longs;tentia e&longs;t æqualis: item &longs;i longitudines e&longs;&longs;ent <lb/>æquales, re&longs;i&longs;tentia ponderis B e&longs;&longs;et &longs;ubquadrupla ratione <lb/>gravitatis, &longs;ed quadruplicatur ratione di&longs;tantiæ CB; ergo in B <lb/>e&longs;t æqualis. </s>

<s>Neutrum igitur pondus pote&longs;t oppo&longs;ito ponderi impetum <lb/>imprimere, quo elevetur; quia nimirum unaquæque gravitas <lb/>majorem impetum alteri communicare non pote&longs;t, quàm po&longs;<lb/>&longs;it ip&longs;a concipere, ac propterea impetus gravitatis B, quæ e&longs;t <lb/>ut CA, potens conari deor&longs;um ut GE, &longs;i imprimeretur gravi<lb/>tati A, quæ e&longs;t ut CB, deberet illam elevare ut FD: Atqui <lb/>gravitas ip&longs;ius A, quæ e&longs;t ut CB, conatur deorsùm ut FD, & <lb/>ejus impetus &longs;i gravitati B, quæ e&longs;t ut CA, imprimeretur, il<lb/>lam elevare deberet ut GE: igitur in unaqu<gap/>que gravitate <lb/>æqualis e&longs;&longs;et eju&longs;dem conatus deorsùm & vis illata nitens &longs;ur<lb/>sùm, nec plus præ&longs;tare po&longs;&longs;et impetus impre&longs;&longs;us, quàm innatus. </s>

<s>Neutrum igitur pondus pote&longs;t oppo&longs;ito ponderi impetum <lb/>imprimere, quo elevetur; quia nimirum unaquæque gravitas <lb/>majorem impetum alteri communicare non pote&longs;t, quàm po&longs;<lb/>&longs;it ip&longs;a concipere, ac propterea impetus gravitatis B, quæ e&longs;t <lb/>ut CA, potens conari deor&longs;um ut GE, &longs;i imprimeretur gravi<lb/>tati A, quæ e&longs;t ut CB, deberet illam elevare ut FD: Atqui <lb/>gravitas ip&longs;ius A, quæ e&longs;t ut CB, conatur deorsùm ut FD, & <lb/>ejus impetus &longs;i gravitati B, quæ e&longs;t ut CA, imprimeretur, il<lb/>lam elevare deberet ut GE: igitur in unaquâque gravitate <lb/>æqualis e&longs;&longs;et eju&longs;dem conatus deorsùm & vis illata nitens &longs;ur<lb/>sùm, nec plus præ&longs;tare po&longs;&longs;et impetus impre&longs;&longs;us, quàm innatus. </s>

<lb/><s>Utraque igitur con&longs;i&longs;tere debet, & neutra impetum acquirit, <lb/>aut ab alterâ impetum accipit, quia fru&longs;tra e&longs;&longs;et impetus acqui<lb/>&longs;itus aut impre&longs;&longs;us, quem nullus con&longs;equi pote&longs;t motus. </s>

Line 3651

<s>20.00″ æquatur momento BC hoc e&longs;t 1 &rx;, factâ per <lb/>Antithe&longs;in communi &longs;ubtractione (70756/1121481) &rx;, remanet æquatio <lb/>inter pondus unc. </s>

<s>20.00″ & (10507<gap/>5/1121481) &rx;, & factâ divi&longs;ione emer<lb/>git pretium 1 &rx;, hoc e&longs;t momentum BC pondo unc. </s>

<s>20.00″ & (1050725/1121481) &rx;, & factâ divi&longs;ione emer<lb/>git pretium 1 &rx;, hoc e&longs;t momentum BC pondo unc. </s>

Line 3661

<s>20, totum momentum in A <lb/>e&longs;t unc. </s>

<s>21. 347‴, omnino æquale momento ip&longs;ius B: id quod <lb/>ab initio vix &longs;perare audebam, cum hæc operatio à &longs;uperiore <lb/>differat &longs;olùm per (<gap/>/1000). Hîc pariter brachij AC gravitas ab&longs;o<lb/>luta pondo unc. </s>

<s>21. 347‴, omnino æquale momento ip&longs;ius B: id quod <lb/>ab initio vix &longs;perare audebam, cum hæc operatio à &longs;uperiore <lb/>differat &longs;olùm per (1/1000).  Hîc pariter brachij AC gravitas ab&longs;o<lb/>luta pondo unc. </s>

<s>2. 66″. habet momentum unc. </s>

Line 3735

<s>Quod &longs;i ob inæqualem virgæ cra&longs;&longs;itiem non planè <lb/>ad mediam illius longitudinem facta &longs;it &longs;u&longs;pen&longs;io, &longs;ed æquili<lb/>britas contingat in puncto, quod propius e&longs;t cra&longs;&longs;iori extremi<lb/>tati virgæ, factâ alterutrius brachij inflexione tollitur æquili<lb/>brium, quia non jam ampliùs eadem e&longs;t reciprocè Ratio longi<lb/>tudinum, quæ & gravitatum. </s>

<s>Ex his pariter con&longs;equens e&longs;t aliquando minimam virtutem <lb/>&longs;atis e&longs;&longs;e ad dimovenda ab æquilibrio ingentia corpora, &longs;i <gap/><lb/>&longs;u&longs;tineantur, ut fulcrum vel in puncto, vel in lineâ contingant: <lb/>quoniam &longs;i corpus grave in&longs;i&longs;tat apici coni, aut pyramidis, aut <pb xlink:href="017/01/265.jpg" pagenum="249"/>angulo &longs;olido, aut portioni &longs;phæricæ, quam contingat idem <lb/>corpus &longs;ive planâ, &longs;ive &longs;phæricè cavâ, &longs;ive &longs;phæricam æmulan<lb/>te &longs;uperficie, contactus in puncto efficitur, ac propterea qua<lb/>cunque in extremitate corporis addatur vis movendi, æquili<lb/>brium tollitur, & quidem eò faciliùs, quo magis à puncto con<lb/>tactûs extremitas illa removetur; in illâ quippe di&longs;tantiâ vis mo<lb/>vendi apta velociorem motum efficere, quàm &longs;i propior e&longs;&longs;et, <lb/>plus habet momenti: Id quod adhuc faciliùs accidit, &longs;i ab ex<lb/>tremitate, ubi vis movendi applicatur, ductâ per contingentis <lb/>fulcri punctum rectâ lineâ ad oppo&longs;itam extremitatem, inæqua<lb/>liter divi&longs;a &longs;it in puncto contactûs, & vis ip&longs;a movendi in magis <lb/>di&longs;tante extremitate con&longs;tituta fuerit; tunc enim non &longs;ua tan<lb/>tùm momenta addit, &longs;ed illa multiplicat pro Ratione exce&longs;sûs <lb/>&longs;uæ di&longs;tantiæ; quemadmodum de inæqualibus libræ brachiis <lb/>dictum e&longs;t. </s>

<s>Ex his pariter con&longs;equens e&longs;t aliquando minimam virtutem <lb/>&longs;atis e&longs;&longs;e ad dimovenda ab æquilibrio ingentia corpora, &longs;i ita <lb/>&longs;u&longs;tineantur, ut fulcrum vel in puncto, vel in lineâ contingant: <lb/>quoniam &longs;i corpus grave in&longs;i&longs;tat apici coni, aut pyramidis, aut <pb xlink:href="017/01/265.jpg" pagenum="249"/>angulo &longs;olido, aut portioni &longs;phæricæ, quam contingat idem <lb/>corpus &longs;ive planâ, &longs;ive &longs;phæricè cavâ, &longs;ive &longs;phæricam æmulan<lb/>te &longs;uperficie, contactus in puncto efficitur, ac propterea qua<lb/>cunque in extremitate corporis addatur vis movendi, æquili<lb/>brium tollitur, & quidem eò faciliùs, quo magis à puncto con<lb/>tactûs extremitas illa removetur; in illâ quippe di&longs;tantiâ vis mo<lb/>vendi apta velociorem motum efficere, quàm &longs;i propior e&longs;&longs;et, <lb/>plus habet momenti: Id quod adhuc faciliùs accidit, &longs;i ab ex<lb/>tremitate, ubi vis movendi applicatur, ductâ per contingentis <lb/>fulcri punctum rectâ lineâ ad oppo&longs;itam extremitatem, inæqua<lb/>liter divi&longs;a &longs;it in puncto contactûs, & vis ip&longs;a movendi in magis <lb/>di&longs;tante extremitate con&longs;tituta fuerit; tunc enim non &longs;ua tan<lb/>tùm momenta addit, &longs;ed illa multiplicat pro Ratione exce&longs;sûs <lb/>&longs;uæ di&longs;tantiæ; quemadmodum de inæqualibus libræ brachiis <lb/>dictum e&longs;t. </s>

<s>Sin autem fulcrum &longs;u&longs;tinens, quod horizonti paral<lb/>lelum ponitur, &longs;it acies pri&longs;matis, aut latus pyramidis jacentis, <lb/>aut portio cylindrica &longs;eu conica jacens; tunc in lineâ fit con<lb/>tactus, &longs;i vel plana &longs;it, vel circulariter concava corporis in<lb/>&longs;i&longs;tentis &longs;uperficies: &longs;ed &longs;i vis movendi, quantacumque &longs;it, ad<lb/>datur &longs;ecundùm rectam lineam, quæ efficit Gravitatis diame<lb/>trum, puta in A vel N, non mutat æquilibritatem, &longs;i fulcrum <lb/>congruit toti diametro AN: &longs;i verò fulcrum brevius e&longs;t quàm <lb/>AN, & ex. </s>

Line 3755

<s>Idem Atlas Sinicus, cum &longs;ermo e&longs;t de Pro<lb/>vincia Peking, ubi &longs;olum e&longs;&longs;e areno&longs;um atque plani&longs;&longs;imum <lb/>te&longs;tatur, hæc habet pag.28. <emph type="italics"/>Modus itineris faciendi hi&longs;ce locis <lb/>non infrequens, nec incommodus e&longs;t. </s>

<s>Plau&longs;trum adhibent cum <gap/><lb/>rotâ ita con&longs;titutum, ut uni illius medium oceupandi, & qua&longs;i equo <lb/>in&longs;idendi &longs;it locus, aliis duobus ab utroque latere ad&longs;identibus; auri<lb/>ga plau&longs;trum retro ligneis vectibus urget ac promovet non &longs;ecurè mi<lb/>nùs, quàm velociter.<emph.end type="italics"/></s><s> Si rem conjecturis indagare liceat, ego ro<lb/>tam concipio ita inclu&longs;am ligneo loculamento majoris &longs;egmen<lb/>ti circuli figuram habente, ut huic in&longs;itus &longs;it rotæ axis, ad dex<lb/>tram autem & ad lævam extantia tabulata tantæ latitudinis, <lb/>ut quis modò propè rotam, modò longiùs ad&longs;idere queat ad <lb/>æquilibrium con&longs;tituendum inter duos viatores inæqualiter <lb/>graves: Aurigæ locus e&longs;t in &longs;uprema parte loculamenti, cui <lb/>qua&longs;i equitans in&longs;idet, bino&longs;que contos, &longs;eu vectes concinnè <lb/>locatos, ut manubrium ante &longs;e habeat, extremitas altera (for<lb/>ta&longs;sè in acumen de&longs;inens, ut leviter &longs;olo infigatur) po&longs;t &longs;e ter<lb/>ram re&longs;piciat, utrâque manu apprehendens &longs;olum obliquè pre<lb/>mit, & currum in anteriora velociter promovet. </s>

<s>Plau&longs;trum adhibent cum unâ <lb/>rotâ ita con&longs;titutum, ut uni illius medium occupandi, & qua&longs;i equo <lb/>in&longs;idendi &longs;it locus, aliis duobus ab utroque latere ad&longs;identibus; auri<lb/>ga plau&longs;trum retro ligneis vectibus urget ac promovet non &longs;ecurè mi<lb/>nùs, quàm velociter.<emph.end type="italics"/></s><s> Si rem conjecturis indagare liceat, ego ro<lb/>tam concipio ita inclu&longs;am ligneo loculamento majoris &longs;egmen<lb/>ti circuli figuram habente, ut huic in&longs;itus &longs;it rotæ axis, ad dex<lb/>tram autem & ad lævam extantia tabulata tantæ latitudinis, <lb/>ut quis modò propè rotam, modò longiùs ad&longs;idere queat ad <lb/>æquilibrium con&longs;tituendum inter duos viatores inæqualiter <lb/>graves: Aurigæ locus e&longs;t in &longs;uprema parte loculamenti, cui <lb/>qua&longs;i equitans in&longs;idet, bino&longs;que contos, &longs;eu vectes concinnè <lb/>locatos, ut manubrium ante &longs;e habeat, extremitas altera (for<lb/>ta&longs;sè in acumen de&longs;inens, ut leviter &longs;olo infigatur) po&longs;t &longs;e ter<lb/>ram re&longs;piciat, utrâque manu apprehendens &longs;olum obliquè pre<lb/>mit, & currum in anteriora velociter promovet. </s>

<s>Id quod nemi<lb/>ni difficile videatur, qui &longs;æpiùs ob&longs;ervaverit à puero fabri <lb/>lignarij aut ferrarij rotam curulem identidem impul&longs;am per <lb/>urbis vias velociter deduci; quæ dum impre&longs;&longs;o impetu veloci-<pb xlink:href="017/01/267.jpg" pagenum="251"/>ter conver&longs;a in anteriora promovetur, licet huc atque illuc <lb/>nutabunda inclinetur, ob velocem conver&longs;ionem immunis e&longs;t à <lb/>ca&longs;u: quemadmodum etiam &longs;tanneum aut argenteum orbem <lb/>apici cultri impo&longs;itum, &longs;i in gyrum velociter agatur, à ca&longs;u im<lb/>munem videmus, etiam&longs;i punctum &longs;u&longs;tentationis non exacti&longs;&longs;i<lb/>mè centro re&longs;pondeat. </s>

Line 3801

<s>Nam &longs;i corpus BC, cujus centrum gravitatis &longs;it A, &longs;u&longs;pen<lb/>datur &longs;uper polis in I, quando axi &longs;u&longs;tentanti ad perpendiculum <lb/><figure id="id.017.01.270.1.jpg" xlink:href="017/01/270/1.jpg"/><lb/>re&longs;pondet centrum gravitatis A, ma<lb/>net æquilibrium, &longs;ed factâ corporis <lb/>inclinatione, ut A recedat à perpen<lb/>diculo, jam versùs C plures &longs;unt <lb/>partes gravitatis de&longs;cendentes, quàm <lb/>versùs B &longs;int partes a&longs;cendentes, & <lb/>illæ velociùs moventur deor&longs;um, <lb/>quàm hæ &longs;ur&longs;um; quapropter illæ <pb xlink:href="017/01/271.jpg" pagenum="255"/>majora habent momenta, quibus deorium urgentibus corpus <lb/>revolvitur. </s>

<s>Id quod multò magis contingit in Acrobarycis, quæ <lb/>nimirum gravitatem in &longs;ummitate habent, ut &longs;i corpori BC <gap/><lb/>&longs;uperiori parte adnexa e&longs;&longs;et pyramis D; cum enim totius com<lb/>po&longs;itæ molis ex &longs;olido BC, & pyramide D, centrum commu<lb/>ne gravitatis non e&longs;&longs;et in A, &longs;ed adhuc &longs;uperius procul à polo <lb/>I, qui e&longs;t centrum motûs, factâ levi inclinatione multo plus <lb/>gravitatis e&longs;&longs;et ex parte C, quàm ex oppo&longs;ità B, ut con&longs;tat: <lb/>nam quò altius & remotius e&longs;t centrum gravitatis, eò faciliùs <lb/>linea directionis cadit extra punctum vel lineam &longs;u&longs;tentationis, <lb/>facta pari inclinatione. </s>

<s>Id quod multò magis contingit in Acrobarycis, quæ <lb/>nimirum gravitatem in &longs;ummitate habent, ut &longs;i corpori BC in <lb/>&longs;uperiori parte adnexa e&longs;&longs;et pyramis D; cum enim totius com<lb/>po&longs;itæ molis ex &longs;olido BC, & pyramide D, centrum commu<lb/>ne gravitatis non e&longs;&longs;et in A, &longs;ed adhuc &longs;uperius procul à polo <lb/>I, qui e&longs;t centrum motûs, factâ levi inclinatione multo plus <lb/>gravitatis e&longs;&longs;et ex parte C, quàm ex oppo&longs;ità B, ut con&longs;tat: <lb/>nam quò altius & remotius e&longs;t centrum gravitatis, eò faciliùs <lb/>linea directionis cadit extra punctum vel lineam &longs;u&longs;tentationis, <lb/>facta pari inclinatione. </s>

<s>Liceat autem hîc obiter, qua&longs;i cerollarij loco, attingere <lb/>æquilibria corporum humido in&longs;identium, & Acrobary corum <lb/>fluitantium, in quibus pariter Rationes libræ agno&longs;centur, &longs;i <lb/>rectè perpendatur, ubi fiat &longs;u&longs;tentatio. </s>

Line 3911

<s>Quare ut <expan abbr="põdus">pondus</expan> D ad pondus C, ita GB <lb/>ad GF, hoc e&longs;t ita KC ad KD: ac propterea factâ jugi &longs;u&longs;pen<lb/>&longs;ione in K pondera C & D inæqualia &longs;ecundùm Rationem bra<lb/>chiorum reciprocè po&longs;ita æquiponderabunt & con&longs;i&longs;tent. </s>

<s>Cum <lb/>igitur in hac eâdem Ratione &longs;it de&longs;cen&longs;us BH & BG, ut e&longs;t <lb/>pondus C ad pondus D, fiet con&longs;i&longs;tentia in &longs;itu CAD. <emph type="italics"/>Ergo <lb/>per &longs;ub&longs;umptionem patet,<emph.end type="italics"/> &longs;ubdit Keplerus, cujus &longs;uperiorem <lb/>doctrinam conatus &longs;um paulo clariùs exponere, <emph type="italics"/>cur libræ brachia<emph.end type="italics"/><pb xlink:href="017/01/278.jpg" pagenum="262"/><emph type="italics"/>revolvuntur ad æquilibrium; cum cnim æque ponderent, æquales c<gap/><lb/>in circulo fieri de&longs;cen&longs;us par e&longs;t.<emph.end type="italics"/></s>

<s>Cum <lb/>igitur in hac eâdem Ratione &longs;it de&longs;cen&longs;us BH & BG, ut e&longs;t <lb/>pondus C ad pondus D, fiet con&longs;i&longs;tentia in &longs;itu CAD. <emph type="italics"/>Ergo <lb/>per &longs;ub&longs;umptionem patet,<emph.end type="italics"/> &longs;ubdit Keplerus, cujus &longs;uperiorem <lb/>doctrinam conatus &longs;um paulo clariùs exponere, <emph type="italics"/>cur libræ brachia<emph.end type="italics"/><pb xlink:href="017/01/278.jpg" pagenum="262"/><emph type="italics"/>revolvuntur ad æquilibrium; cum enim æque ponderent, æquales etiam <lb/>in circulo fieri de&longs;cen&longs;us par e&longs;t.<emph.end type="italics"/></s>

<s>Meam hebetudinem di&longs;&longs;imulare non po&longs;&longs;um, qui huju&longs;ce <lb/>Keplerianæ argumentationis vim &longs;atis a&longs;&longs;equi non valeo: quid <lb/>enim, &longs;i fieret æquilibrium horizontale ponderum, facta in K <lb/>&longs;u&longs;pen&longs;ione? </s>

Line 3929

<s>At, inquis, quid cau&longs;æ e&longs;t, <pb xlink:href="017/01/279.jpg" pagenum="263"/>cur &longs;imilem libram in quácumque po&longs;itione quie&longs;centem non <lb/>habemus? </s>

<s>&longs;ed omnis libra ea e&longs;t, ut vel ad æquilibrium redeat, <lb/>vel omninò quantum pote&longs;t de&longs;cendat, qua parte habet bra<lb/>chium inclinatum Re&longs;pon&longs;io in promptu e&longs;t; quia &longs;cilicet dif<lb/>ficillimum e&longs;t duo illa puncta exqui&longs;it<gap/> convenire, hoc e&longs;t cen<lb/>trum motus & centrum gravitatis, nimirùm punctum illud, <lb/>quod brachiorum longitudinem di&longs;eriminat. </s>

<s>&longs;ed omnis libra ea e&longs;t, ut vel ad æquilibrium redeat, <lb/>vel omninò quantum pote&longs;t de&longs;cendat, qua parte habet bra<lb/>chium inclinatum Re&longs;pon&longs;io in promptu e&longs;t; quia &longs;cilicet dif<lb/>ficillimum e&longs;t duo illa puncta exqui&longs;itè convenire, hoc e&longs;t cen<lb/>trum motus & centrum gravitatis, nimirùm punctum illud, <lb/>quod brachiorum longitudinem di&longs;criminat. </s>

<s>Quod &longs;i vel mi<lb/>nimum duo illa centra di&longs;crepent, natura omnes &longs;ui juris api<lb/>ces exacti&longs;&longs;imè per&longs;equitur, & e&longs;t &longs;partum non in medio, &longs;ed <lb/>aut in &longs;uperiore, aut in inferiore parte jugi (&longs;i quidem brachia <lb/>&longs;int æqualia; nam &longs;i ad latus e&longs;&longs;et in eadem recta linea, librac&longs;<lb/>&longs;et inæqualium brachiorum, & tunc non adnexorum ponderum <lb/>æqualitas e&longs;&longs;et con&longs;ideranda, &longs;ed corum Ratio, &longs;umpta recipro<lb/>cè brachiorum Ratione) ex quo &longs;equitur aut reditus ad æquili<lb/>brium, aut ulterior de&longs;cen&longs;us brachij inclinati. </s>

Line 4007

<s><emph type="center"/><emph type="italics"/>An fieri po&longs;sit libra Curva.<emph.end type="italics"/><emph.end type="center"/></s>

<s>QUamvis ad ponderum examen in&longs;tituendum rarò contin<lb/>gere po&longs;&longs;it, ut librâ Curvâ uti cogamur, quia tamen in <lb/>machinamentis aliquibus ita aut loci angu&longs;tiæ, aut opportuna <pb xlink:href="017/01/284.jpg" pagenum="268"/>corporum movendorum di&longs;po&longs;itio, exigunt collocari ponde<lb/>la, ut & libræ Rationes &longs;erventur, & tamen jugi rectitudo nul<lb/>la appareat; non erit hic inutile libram curvam examinare, ut, <lb/>&longs;i quando eâ uti contigerit, innote&longs;cat, quænam &longs;int brachio<lb/><gap/>m, & motuum Rationes. </s>

<s>QUamvis ad ponderum examen in&longs;tituendum rarò contin<lb/>gere po&longs;&longs;it, ut librâ Curvâ uti cogamur, quia tamen in <lb/>machinamentis aliquibus ita aut loci angu&longs;tiæ, aut opportuna <pb xlink:href="017/01/284.jpg" pagenum="268"/>corporum movendorum di&longs;po&longs;itio, exigunt collocari ponde<lb/>ra, ut & libræ Rationes &longs;erventur, & tamen jugi rectitudo nul<lb/>la appareat; non erit hî inutile libram curvam examinare, ut, <lb/>&longs;i quando eâ uti contigerit, innote&longs;cat, quænam &longs;int brachio<lb/>ru>m, & motuum Rationes. </s>

<s>Libram autem curvam voco, quæ <lb/>a commun<gap/> deflectens latera habet non in directum po&longs;i<lb/><gap/>, &longs;ed in angulum concurrentia, aut in arcum &longs;inuata, quo<lb/><gap/>m extremitates &longs;ivè &longs;ur&longs;um, &longs;ivè deor&longs;um re&longs;piciunt: factâ <lb/><gap/> &longs;u&longs;pen&longs;ione &longs;ive ubi angulum latera con&longs;tituunt, &longs;ivè in <lb/>aliquo arcus puncto, ea fieri pote&longs;t hinc & hinc ponderum ad<lb/>ditio, quam horizontale æquilibrium con&longs;equatur. </s>

<s>Libram autem curvam voco, quæ <lb/>a communi formâ deflectens latera habet non in directum po&longs;i<lb/>ta, &longs;ed in angulum concurrentia, aut in arcum &longs;inuata, quo<lb/>rum extremitates &longs;ivè &longs;ur&longs;um, &longs;ivè deor&longs;um re&longs;piciunt: factâ <lb/>enim &longs;u&longs;pen&longs;ione &longs;ive ubi angulum latera con&longs;tituunt, &longs;ivè in <lb/>aliquo arcûs puncto, ea fieri pote&longs;t hinc & hinc ponderum ad<lb/>ditio, quam horizontale æquilibrium con&longs;equatur. </s>

<s>Sed quia <lb/>imperitis fucum facere po&longs;&longs;et apparens hæc laterum longitudo, <lb/>caveant, ne ex illis jugum libræ deductum intelligant: contin<lb/>gere &longs;cilicet pote&longs;t, ut planè varia &longs;it huju&longs;modi libræ forma, <lb/>& magnitudo, idem tamen &longs;it &longs;emper libræ jugum, in quo <lb/>brachia de&longs;umenda &longs;unt. </s>

Line 4021

<s>Hinc &longs;i late<lb/>ra AB & AC jungantur tran&longs;ver&longs;ario HI, in eoque &longs;umatur <lb/>punctum &longs;u&longs;pen&longs;ionis D, nil refert æqualia-ne, an inæqualia <lb/>&longs;int latera AB & AC? </s><s>&longs;ed attendenda e&longs;t æqualitas aut in<lb/>æqualitas linearum ex D ductarum ad extremitates B & C. </s>

<s>Neque me arguas, quòd dixerim jugum e&longs;&longs;e BC, & attenden-<pb xlink:href="017/01/285.jpg" pagenum="269"/>dam æqualitatem aut <expan abbr="inæqualitat&etilde;">inæqualitatem</expan> <expan abbr="linear&utilde;">linearum</expan> ex puncto &longs;u&longs;pen&longs;io<lb/>nis ductarum, puta DB & DC; brachia &longs;iquidem in ip<gap/>o jugo <lb/>con&longs;ideranda &longs;unt; illæ <expan abbr="aut&etilde;">autem</expan> lineæ nihil habent cum jugo com<lb/>mune præter puncta extrema B & C. </s>

<s>Neque me arguas, quòd dixerim jugum e&longs;&longs;e BC, & attenden-<pb xlink:href="017/01/285.jpg" pagenum="269"/>dam æqualitatem aut <expan abbr="inæqualitat&etilde;">inæqualitatem</expan> <expan abbr="linear&utilde;">linearum</expan> ex puncto &longs;u&longs;pen&longs;io<lb/>nis ductarum, puta DB & DC; brachia &longs;iquidem in ip&longs;o jugo <lb/>con&longs;ideranda &longs;unt; illæ <expan abbr="aut&etilde;">autem</expan> lineæ nihil habent cum jugo com<lb/>mune præter puncta extrema B & C. </s>

<s>Quamvis enim lineæ hu<lb/>ju&longs;modi brachia libræ non &longs;int, &longs;i res proprie con&longs;ideretur, in&longs;e<lb/>runt tamen æqualitatem aut inæqualitatem brachiorum, qua<lb/>tenus ex puncto &longs;u&longs;pen&longs;ionis D ducta intelligitur ad BC jugum <lb/>perpendicularis DM, quæ jugum dividit in partes BM & CM <lb/>æquales aut inæquales. </s>

Line 4073

<s>Laterum AB & AC longitudine <lb/>metire, tùm ex B ad C extentum funiculum ad &longs;imilem men<lb/>&longs;uram revoca. </s>

<s>His paratis certum e&longs;t hane jugi longitudinem <lb/>communiter majorem e&longs;&longs;e longitudine &longs;ingulorum laterum, <lb/>&longs;emper tamen &longs;altem alterius, tanto exce&longs;&longs;u, ut po&longs;&longs;it ab ea au<lb/>fe<gap/>i pars, de quâ mox dicetur; debet &longs;cilicet excedere me<lb/>diam proportionalem inter aggregatum laterum, & corum dif<lb/>ferentiam. </s>

<s>His paratis certum e&longs;t hanc jugi longitudinem <lb/>communiter majorem e&longs;&longs;e longitudine &longs;ingulorum laterum, <lb/>&longs;emper tamen &longs;altem alterius, tanto exce&longs;&longs;u, ut po&longs;&longs;it ab ea au<lb/>ferri pars, de quâ mox dicetur; debet &longs;cilicet excedere me<lb/>diam proportionalem inter aggregatum laterum, & corum dif<lb/>ferentiam. </s>

<s>Cum enim linea jugi à perpendiculo cadente ex <lb/>angulo verticali dividenda &longs;it, utrumque latus cum jugo facit <lb/>angulos acutos; alioquin &longs;i alteruter angulorum rectus e&longs;&longs;et, <lb/>aut linea jugi non e&longs;&longs;et parallela horizonti, aut latus e&longs;&longs;et idem <lb/>perpendiculum; & &longs;i obtu&longs;us e&longs;&longs;et, perpendiculum caderet ex<lb/>tra lineam extremitates jungentem. </s>

Line 4091

<s>At &longs;i pro ratione tui in&longs;tituti nimia &longs;it hujus perpendiculi <pb xlink:href="017/01/289.jpg" pagenum="273"/>longitudo, & opportuniùs accidat jugum BC horizontale mi<lb/>nus di&longs;tare à puncto &longs;u&longs;pen&longs;ionis A, jam con&longs;tat latera AB <lb/>& AC explicanda in majorem angulum; quapropter etiam <lb/>major erit jugi longitudo, ex 24.lib.1. Sit ergo definita per<lb/>pendiculi AD altitudo partium 4: hujus quadratum 16 aufer <lb/>ex 81 quadrato lateris AC, & re&longs;iduum 65 e&longs;t quadratum bra<lb/>chij minoris DC, quod idcircò e&longs;t partium (8 1/16) &longs;erè. </s>

<s>Simili<lb/>ter ip&longs;ius AD quadratum 16 aufer ex 400 quadrato lateris AB, <lb/>& re&longs;iduum 384 e&longs;t quadratum brachij majoris BD, quod e&longs;t <lb/>partium (19 23/<gap/>9) proximè; & totum jugum BC e&longs;t partium (27 25/39). <lb/>Quare brachi BD ad brachium DC Ratio e&longs;&longs;et ut 764 ad 314, <lb/>quæ reciprocè e&longs;&longs;et & ponderum. </s>

<s>Simili<lb/>ter ip&longs;ius AD quadratum 16 aufer ex 400 quadrato lateris AB, <lb/>& re&longs;iduum 384 e&longs;t quadratum brachij majoris BD, quod e&longs;t <lb/>partium (19 23/39) proximè; & totum jugum BC e&longs;t partium (27 25/39). <lb/>Quare brachi BD ad brachium DC Ratio e&longs;&longs;et ut 764 ad 314, <lb/>quæ reciprocè e&longs;&longs;et & ponderum. </s>

<s>Ex quibus per&longs;picuum e&longs;t, po&longs;itis ii&longs;dem libræ curvæ late<lb/>ribus, di&longs;parem e&longs;&longs;e ponderum Rationem: in priore enim po&longs;i<lb/>tione Ratio e&longs;t 424 ad 105, hoc e&longs;t proxime ut 4 ad 1. in po&longs;te<lb/>riore po&longs;itione, ubi in majorem angulum latera explicantur, <lb/>Ratio e&longs;t 764 ad 314, hoc e&longs;t ut 2. 43 ad 1; quæ minor e&longs;t <lb/>Ratio, quàm prior ut 4 ad 1. Si autem latera eadem e&longs;&longs;ent in <lb/>directum con&longs;tituta, e&longs;&longs;et ponderum Ratio ut 20 ad 9, hoc e&longs;t <lb/>ut 2. 22′ ad 1; quæ e&longs;t minima Ratio omnium, quæ intercede<lb/>re po&longs;&longs;unt inter pondera æquilibrium horizontale con&longs;tituen<lb/>tia ex illorum laterum extremitatibus: quæ extremitates quo<lb/>minus di&longs;tabunt, inflexis &longs;ubinde latcribus, eo majus pondus <lb/>requiretur in extremitate lateris brevioris, ut æquè ponderet <lb/>cum uno eodemque pondere collocato in extremitate lateris <lb/>longioris. </s>

<s>Porrò ubi de ponderum Ratione &longs;ermo e&longs;t, cave ne ip&longs;orum <lb/>laterum inæqualium libræ curvæ gravitatem contemnas; &longs;i <lb/>enim æqualia illa e&longs;&longs;ent, æqualia quoque e&longs;&longs;ent eorum mo<lb/>menta tùm ratione gravitatis, tum tatione po&longs;itionis, nam per<lb/>pendiculum caderet in medium jugum, & latera e&longs;&longs;ent &longs;imi<lb/>liter inclinata, ac proinde &longs;ola ponderum æqualitas &longs;pectaretur: <lb/>at laterum huju&longs;modi inæqualium momenta &longs;unt ex utroque <lb/>capite inæqualia, videlicet & ratione gravitatis in&longs;itæ, quæ ex <lb/>hypothe&longs;i &longs;ingulis lateribus ine&longs;t pro Ratione molis inæqualis, <lb/>& ratione po&longs;itionis, quæ valde diver&longs;a e&longs;t, cùm non &longs;int late<lb/>ra illa &longs;imili angulo ad perpendiculum inclinata; &longs;ed magis in-<pb xlink:href="017/01/290.jpg" pagenum="274"/>clinatur latus longius faciens cum perpendiculo majorem an<lb/>gulum: pro va<gap/>a autem inclinatione ip&longs;am eju&longs;dem lateris gra<lb/>vitatem varia obtinere momenta manife&longs;tum videtur. </s>

<s>Porrò ubi de ponderum Ratione &longs;ermo e&longs;t, cave ne ip&longs;orum <lb/>laterum inæqualium libræ curvæ gravitatem contemnas; &longs;i <lb/>enim æqualia illa e&longs;&longs;ent, æqualia quoque e&longs;&longs;ent eorum mo<lb/>menta tùm ratione gravitatis, tum tatione po&longs;itionis, nam per<lb/>pendiculum caderet in medium jugum, & latera e&longs;&longs;ent &longs;imi<lb/>liter inclinata, ac proinde &longs;ola ponderum æqualitas &longs;pectaretur: <lb/>at laterum huju&longs;modi inæqualium momenta &longs;unt ex utroque <lb/>capite inæqualia, videlicet & ratione gravitatis in&longs;itæ, quæ ex <lb/>hypothe&longs;i &longs;ingulis lateribus ine&longs;t pro Ratione molis inæqualis, <lb/>& ratione po&longs;itionis, quæ valde diver&longs;a e&longs;t, cùm non &longs;int late<lb/>ra illa &longs;imili angulo ad perpendiculum inclinata; &longs;ed magis in-<pb xlink:href="017/01/290.jpg" pagenum="274"/>clinatur latus longius faciens cum perpendiculo majorem an<lb/>gulum: pro variâ autem inclinatione ip&longs;am eju&longs;dem lateris gra<lb/>vitatem varia obtinere momenta manife&longs;tum videtur. </s>

<s>Pona<lb/><figure id="id.017.01.290.1.jpg" xlink:href="017/01/290/1.jpg"/><lb/>mus laminam metallicam AB clavo <lb/>infixam in A, circa quem qua&longs;i cen<lb/>trum de&longs;cribat &longs;emicirculum BDC. </s>

Line 4227

<s>At in priore illa &longs;pecie libræ <lb/>&longs;partum in &longs;uperiore loco habentis, recedente in alterutram <lb/>partem centro gravitatis, de&longs;cendit illud quidem; &longs;ed non ni&longs;i <lb/>pro ratione exce&longs;sûs ponderis; qui de&longs;cen&longs;us inob&longs;ervabilis erit, <lb/>&longs;i exigua &longs;it ponderum differentia. </s>

<s>Hinc non &longs;emel animadver<lb/>ti accurati&longs;&longs;imas bilances, quibus aurearum monetarum ponde<lb/>ra examinantur, eas e&longs;&longs;e, quæ &longs;partum in inferiore loco habent; <lb/>lanx enim, quæ pondere prægravatur, ad imum, quantùm po<lb/>te&longs;t de&longs;cendit: factâ autem libræ conver&longs;ione ita, ut an<gap/>a infe<lb/>riùs &longs;u&longs;tentata libram &longs;u&longs;tineat, ii&longs;demque ponderibus impo&longs;i<lb/>tis, lanx prægravata non de&longs;cendit ad imum locum; &longs;ed manet <lb/>libra in obliquâ po&longs;itione, quæ ponderum inæqualitati congruè <lb/>re&longs;pondet; &, &longs;i ea &longs;it ponderum inæqualitas, quæ omnem ob<lb/>&longs;ervantis &longs;ubtilitatem effugiat, vidctur libra in æquilibrio hori<lb/>zontali po&longs;ita, cum tamen in priore &longs;itu, antequam libra inver<lb/>teretur, non po&longs;&longs;et in ullo æquilibrio con&longs;i&longs;tere. </s>

<s>Hinc non &longs;emel animadver<lb/>ti accurati&longs;&longs;imas bilances, quibus aurearum monetarum ponde<lb/>ra examinantur, eas e&longs;&longs;e, quæ &longs;partum in inferiore loco habent; <lb/>lanx enim, quæ pondere prægravatur, ad imum, quantùm po<lb/>te&longs;t de&longs;cendit: factâ autem libræ conver&longs;ione ita, ut an&longs;a infe<lb/>riùs &longs;u&longs;tentata libram &longs;u&longs;tineat, ii&longs;demque ponderibus impo&longs;i<lb/>tis, lanx prægravata non de&longs;cendit ad imum locum; &longs;ed manet <lb/>libra in obliquâ po&longs;itione, quæ ponderum inæqualitati congruè <lb/>re&longs;pondet; &, &longs;i ea &longs;it ponderum inæqualitas, quæ omnem ob<lb/>&longs;ervantis &longs;ubtilitatem effugiat, vidctur libra in æquilibrio hori<lb/>zontali po&longs;ita, cum tamen in priore &longs;itu, antequam libra inver<lb/>teretur, non po&longs;&longs;et in ullo æquilibrio con&longs;i&longs;tere. </s>

<s>Non ita tamen hæc dicta intelligi velim, ut nulla &longs;it habenda <lb/>ratio materiæ, ex qua libra con&longs;tat; hæc &longs;iquidem tantæ gravi<lb/>tatis e&longs;&longs;e pote&longs;t, ut axem vehementiùs premens motum aliqua<lb/>tenus impediat, ac propterea levis illa virtus effectiva motus, <pb xlink:href="017/01/299.jpg" pagenum="283"/>qui ponderum adnexorum inæqualitatem cæteroqui con&longs;eque<lb/>retur, ex hâc pre&longs;&longs;ione, & prominularum particularum &longs;e vi<lb/>ci&longs;&longs;im contingentium conflictu elidatur, atque jugi æquili<lb/>brium horizontale permaneat. </s>

<s>Gravitatem autem motui im<lb/>pedimento e&longs;&longs;e ex eo con&longs;tat, <emph type="italics"/>quòd faciliùs quanào &longs;ine pondere <lb/>e&longs;t, <gap/>r libra, quàm cum pondus habet,<emph.end type="italics"/> ut ob&longs;ervavit <lb/>Ari&longs;toreles 9. 10. Mechan. Cui tamen in a&longs;&longs;ignandâ hujus <lb/>difficultatis causa non aquie&longs;co, licet ultrò concedam <emph type="italics"/>in con<lb/>trarium e<gap/> quod vergit onus, movere difficile e&longs;&longs;e<emph.end type="italics"/>; &longs;i enim libræ <lb/>vacuæ lances minùs graves &longs;unt, impo&longs;ito autem pondere fiunt <lb/>graviores, & proptereà lanx elevanda facta gravior difficiliùs <lb/>movetur contia in&longs;itam gravitati propen&longs;ionem, etiam vici&longs;&longs;im <lb/>lanx deprimenda facta gravior ex adnexo pondere faciliùs ob<lb/>&longs;ecundat naturali gravium propen&longs;ioni, atque adeò augere de<lb/>beret movendi facilitatem, vei &longs;altem hanc imminui non per<lb/>mitteret. </s>

<s>Gravitatem autem motui im<lb/>pedimento e&longs;&longs;e ex eo con&longs;tat, <emph type="italics"/>quòd faciliùs quando &longs;ine pondere <lb/>e&longs;t, movetur libra, quàm cum pondus habet,<emph.end type="italics"/> ut ob&longs;ervavit <lb/>Ari&longs;toteles 9. 10. Mechan. Cui tamen in a&longs;&longs;ignandâ hujus <lb/>difficultatis causa non aquie&longs;co, licet ultrò concedam <emph type="italics"/>in con<lb/>trarium ei, ad quod vergit onus, movere difficile e&longs;&longs;e<emph.end type="italics"/>; &longs;i enim libræ <lb/>vacuæ lances minùs graves &longs;unt, impo&longs;ito autem pondere fiunt <lb/>graviores, & proptereà lanx elevanda facta gravior difficiliùs <lb/>movetur contra in&longs;itam gravitati propen&longs;ionem, etiam vici&longs;&longs;im <lb/>lanx deprimenda facta gravior ex adnexo pondere faciliùs ob<lb/>&longs;ecundat naturali gravium propen&longs;ioni, atque adeò augere de<lb/>beret movendi facilitatem, vel &longs;altem hanc imminui non per<lb/>mitteret. </s>

<s>Non aliunde igitur ortum ducere videtur huju&longs;mo<lb/>di difficultas movendi libram onu&longs;tam, quàm ex majore pre<lb/>mentis gravitatis conatu: pre&longs;&longs;ione autem motum impediri quis <lb/>neget, &longs;i &longs;uper planam &longs;uperficiem continuo lævore lubricam <lb/>ducat regulam metallicam exqui&longs;ite politam, quam nunc te<lb/>nui, nunc validiori conatu premat? </s>

Line 4285

<s>Hinc ulteriùs patet huju&longs;modi <lb/>librâ &longs;atius e&longs;&longs;e multam mercem &longs;imul ponderare, quàm per <lb/>partes: pone enim e&longs;&longs;e uncias 12 legitimi ponderis, cum quo <pb xlink:href="017/01/302.jpg" pagenum="286"/>æquilibrium con&longs;tituitur, merx erit unicarum 14, quia ut 12 <lb/>ad 13, ita unc. </s>

<s>2<gap/> ad 26, & demptis unciis 12 ad brachium & <lb/>lancem &longs;pectantibus, remanent mercis unciæ 14: quare bis <lb/>facta ponderatione erit differentia unc. </s>

<s>24 ad 26, & demptis unciis 12 ad brachium & <lb/>lancem &longs;pectantibus, remanent mercis unciæ 14: quare bis <lb/>facta ponderatione erit differentia unc. </s>

<s>4; unica autem ponde<lb/>ratio dabat tantum uncias 3: quia videlicet &longs;ingulis vicibus ad<lb/>ditui id, qued re&longs;pondet gravitati lancis oppo&longs;itæ; atque adeò <lb/>differentia &longs;æpiùs repetita major e&longs;t, quàm &longs;implex: &longs;ic qua<lb/>tuor libris ponderis legitimi re&longs;ponderent in altera lance mer<lb/>cis lib.4.unc. </s>

Line 5329

<s>ESto anguli BAC Tangens BC, anguli BAK Tangens <lb/>BK; de&longs;cripto arcu COG, differentia &longs;ecantium e&longs;t KO, <pb xlink:href="017/01/357.jpg" pagenum="341"/>& Tangentium differentia e&longs;t CK. </s>

<s>Item anguli BAD Tan<lb/>gens BD, & de&longs;eripto arcu KH, differentia T<gap/><lb/>BK & BD e&longs;t KD, atque &longs;ecantium AK & AD d<gap/><lb/>e&longs;t HD. </s>

<s>Item anguli BAD Tan<lb/>gens BD, & de&longs;eripto arcu KH, differentia Tangentium<lb/>BK & BD e&longs;t KD, atque &longs;ecantium AK & AD differentia <lb/>e&longs;t HD. </s>

<s>Dico majorem Rationem e&longs;&longs;e CK ad KO, <gap/><lb/>KD ad DH. </s>

<s>Dico majorem Rationem e&longs;&longs;e CK ad KO, quàm <lb/>KD ad DH. </s>

<s>Ducantur rectæ CG & KH. </s>

<s>In crianguli<gap/><lb/>&longs;celibus CAG & KAH, anguli ad ba&longs;im CG minores &longs;u<gap/><lb/>angulis ad ba&longs;im KH, quia angulus CAG major e&longs;t ang<gap/><lb/>KAH: quapropter angulo CGA fiat æqualis angulus IH <gap/><lb/>Cum itaque ex 28.lib.1. IH & CG &longs;int parallelæ, per 2.lib.6. <lb/>ut CI ad HG, hoc e&longs;t ad KO, ita ID ad DH: atqui CK ma<lb/>jor e&longs;t quàm CI; ergo major e&longs;t Ratio CK ad KO quàm C<gap/><lb/>ad KO ex 8.lib.5. hoc e&longs;t quàm ID ad DH. </s>

<s>In triangulis i&longs;o<lb/>&longs;celibus CAG & KAH, anguli ad ba&longs;im CG minores &longs;unt <lb/>angulis ad ba&longs;im KH, quia angulus CAG major e&longs;t angulo <lb/>KAH: quapropter angulo CGA fiat æqualis angulus IHA. <lb/>Cum itaque ex 28.lib.I. IH & CG &longs;int parallelæ, per 2.lib.6. <lb/>ut CI ad HG, hoc e&longs;t ad KO, ita ID ad DH: atqui CK ma<lb/>jor e&longs;t quàm CI; ergo major e&longs;t Ratio CK ad KO quàm CI <lb/>ad KO ex 8.lib.5. hoc e&longs;t quàm ID ad DH. </s>

<s>Sed ID e&longs;t ma<lb/>jor quàm KD; ergo per 8.lib.

Line 5631

8. indicata &longs;unt, nam <lb/>eju&longs;dem Tangentis quadrato æqualia &longs;unt, atque adeò & in<lb/>ter &longs;e æqualia, rectangula, quæ fiunt &longs;ub Exce&longs;&longs;u &longs;ecantis & <lb/>aggregato &longs;ecantis & Radij: &longs;unt igitur ex 14. lib.6. Exce&longs;&longs;us <lb/>&longs;ecantium reciprocè in Ratione aggregatorum &longs;ecantis & Ra-<pb xlink:href="017/01/371.jpg" pagenum="355"/>dij: quapropter ubi major e&longs;t Radius & &longs;ecans, ibi minor e&longs;t <lb/>&longs;ecantis Exce&longs;&longs;us, hoc e&longs;t remoti ponderis a&longs;cen&longs;us, & <lb/>contra ubi minor e&longs;t Radius & &longs;ecans, ibi major e&longs;t &longs;ecan<lb/>tis Exce&longs;&longs;us, hoc e&longs;t ponderis proximi a&longs;cen&longs;us. </s>

<s>Cur autem aliquando proximum pondus a&longs;cendat, atque <lb/>remotum de&longs;cendat, quando nimirum valde inæquales &longs;unt <lb/>pond<gap/>is medij à claviculis di&longs;tantiæ, hinc fit, quod idem pon<lb/>dus ex longiore funiculo majorem habet vim de&longs;cendendi, quàm <lb/>ex breviore; cui majori momento cum re&longs;i&longs;tere debeat pondus <lb/>proximum, faciliùs cedit de&longs;cendenti, atque adeò non rectâ de<lb/>or&longs;um tendit pondus medium, &longs;ed obliquè, accedendo ad pon<lb/>dus remotum, quod propterea de&longs;cendit. </s>

<s>Cur autem aliquando proximum pondus a&longs;cendat, atque <lb/>remotum de&longs;cendat, quando nimirum valde inæquales &longs;unt <lb/>ponderis medij à claviculis di&longs;tantiæ, hinc fit, quod idem pon<lb/>dus ex longiore funiculo majorem habet vim de&longs;cendendi, quàm <lb/>ex breviore; cui majori momento cum re&longs;i&longs;tere debeat pondus <lb/>proximum, faciliùs cedit de&longs;cendenti, atque adeò non rectâ de<lb/>or&longs;um tendit pondus medium, &longs;ed obliquè, accedendo ad pon<lb/>dus remotum, quod propterea de&longs;cendit. </s>

<s>Sic po&longs;itum pondus in <lb/>E valde inæqualia habet mo<lb/><figure id="id.017.01.371.1.jpg" xlink:href="017/01/371/1.jpg"/><lb/>menta comparatum cum ex<lb/>tremis ponderibus D & C, <lb/>quæ in punctis B & A exer<lb/>cent &longs;uas vires adversùs pon<lb/>dus medium; quod ubi infrà <lb/>horizontalem AB <expan abbr="de&longs;c&etilde;derit">de&longs;cenderit</expan>, <lb/>illico inæquales angulos cum <lb/>horizontali linea AB con&longs;ti<lb/>tuit inflexus funiculus; ut &longs;i intelligatur pondus ex E veni&longs;&longs;e in <lb/>F, angulus FBA major e&longs;t angulo FAB ex 18. lib.1. quia latus <lb/>AF e&longs;t majus latere FB. </s>

Line 5639

15. pondus in F minora habet <lb/>momenta ad de&longs;cendendum versùs perpendiculum BD, quàm <lb/>ad de&longs;cendendum versùs AC, & quidem duplici titulo, &longs;cilicet <lb/>anguli FBD minoris, & funiculi FB brevioris. </s>

<s>Cum itaque pon<lb/>dus illicò ac ex E de&longs;cendit magis pronum &longs;it ad de&longs;cendendum <lb/>ve<gap/>ù perpendiculum AC, non per rectam EF <expan abbr="perpendicular&etilde;">perpendicularem</expan> <lb/>de&longs;cendit; &longs;ed obliquè per lineam EG, ita ut funiculus GA bre<lb/>vior &longs;it funiculo EA, ac propterca cedit ponderi C deor&longs;um tra<lb/>henti. </s>

<s>Cum itaque pon<lb/>dus illicò ac ex E de&longs;cendit magis pronum &longs;it ad de&longs;cendendum <lb/>versùs perpendiculum AC, non per rectam EF <expan abbr="perpendicular&etilde;">perpendicularem</expan> <lb/>de&longs;cendit; &longs;ed obliquè per lineam EG, ita ut funiculus GA bre<lb/>vior &longs;it funiculo EA, ac propterea cedit ponderi C deor&longs;um tra<lb/>henti. </s>

<s>Et quia funiculus GB longior e&longs;t funiculo FB, & multo <lb/>magis funiculo EB, propterea aliquando contingere pote&longs;t pon<lb/>dus D magis a&longs;cendere, quàm a&longs;cenderet, &longs;i E fui&longs;&longs;et planè in <lb/>mediâ di&longs;tantiâ inter A & B. </s>

Line 5679

<s>Hanc ille ad <lb/>ponderum obliquorum momenta inve&longs;ti<lb/>ganda utilem exi&longs;timavit, camque &longs;æpiùs <lb/>ingerit Static.lib.1.prop.19.& &longs;eqq quam<lb/>vis &longs;emper illam cum elevante directo conjunctam adhibeat. </s>

<lb/><s>Propterea, an aliquid ex illâ emolumenti, &longs;i &longs;olitaria adhibeatur, <lb/>capere po<gap/> mus in ponderum momentis inve&longs;tigandis &longs;ivè &longs;u&longs;<lb/>pen&longs;orum, &longs;ivè in plano inclinato jacentium, hîc examinare ope<lb/>ræ pretium fuerit; nam & à &longs;uperioris capitis argumento non <lb/>ali<gap/>na videtur e&longs;&longs;e præ&longs;ens di&longs;putatio. </s>

<lb/><s>Propterea, an aliquid ex illâ emolumenti, &longs;i &longs;olitaria adhibeatur, <lb/>capere po&longs;&longs;imus in ponderum momentis inve&longs;tigandis &longs;ivè &longs;u&longs;<lb/>pen&longs;orum, &longs;ivè in plano inclinato jacentium, hîc examinare ope<lb/>ræ pretium fuerit; nam & à &longs;uperioris capitis argumento non <lb/>aliena videtur e&longs;&longs;e præ&longs;ens di&longs;putatio. </s>

<s>Antequam verò rem aggrediar, monendum te cen&longs;co, Ami<lb/>ce Lector, opportunius accidere, &longs;i tigilli perforati loco cylin<lb/>drum in cochleam efformatum &longs;tatueris, cui congruat in &longs;imi<lb/>l<gap/>m helicem excavatum foramen S in rotulæ L loculamento: <lb/>&longs;ic enim faciliùs elevabitur aut deprimetur rotula, prout ex<gap/>get <lb/>ip&longs;ius ponderis po&longs;itio. </s>

<s>Antequam verò rem aggrediar, monendum te cen&longs;co, Ami<lb/>ce Lector, opportunius accidere, &longs;i tigilli perforati loco cylin<lb/>drum in cochleam efformatum &longs;tatueris, cui congruat in &longs;imi<lb/>lem helicem excavatum foramen S in rotulæ L loculamento: <lb/>&longs;ic enim faciliùs elevabitur aut deprimetur rotula, prout exiget <lb/>ip&longs;ius ponderis po&longs;itio. </s>

<s>Dupliciter itaque contingere pote&longs;t ponderis obliquitas, &longs;eu <lb/>quia &longs;u&longs;pen&longs;um non in codem perper diculo, in quo e&longs;t punctum <lb/>&longs;u&longs;pen&longs;ioni<gap/>, habet centrum &longs;uæ gravitatis, &longs;eu quia plano incli<lb/>nato incumbit; utroque enim in ca&longs;u momenta habet ad de&longs;cen<lb/>dendum, quæ communi librâ aut &longs;taterâ ve&longs;tigare utique non <lb/>po&longs;&longs;umus: an libræ obliquæ ope id a&longs;&longs;equemur? </s>

<s>Dupliciter itaque contingere pote&longs;t ponderis obliquitas, &longs;eu <lb/>quia &longs;u&longs;pen&longs;um non in codem perpendiculo, in quo e&longs;t punctum <lb/>&longs;u&longs;pen&longs;ionis, habet centrum &longs;uæ gravitatis, &longs;eu quia plano incli<lb/>nato incumbit; utroque enim in ca&longs;u momenta habet ad de&longs;cen<lb/>dendum, quæ communi librâ aut &longs;taterâ ve&longs;tigare utique non <lb/>po&longs;&longs;umus: an libræ obliquæ ope id a&longs;&longs;equemur? </s>

<s>Et primò qui<lb/>dem &longs;i pondus examinandum è funiculo &longs;u&longs;pen&longs;um &longs;ucrit, <gap/>&longs;<lb/>que momenta pro variá declinatione à &longs;uo perpendiculo inqui-<pb xlink:href="017/01/375.jpg" pagenum="359"/>rantur, res manet incerta, &longs;i in praxim deducatur, qum plurimum <lb/>intere&longs;t, quâ obliquitate inclinetur, atque à &longs;uo perpendiculo de<lb/>flectat funiculus libræ obliquæ, &longs;i maxime cum diversa obliqui<lb/>tate jungatur di&longs;par funiculi illius longitudo. </s>

<s>Et primò qui<lb/>dem &longs;i pondus examinandum è funiculo &longs;u&longs;pen&longs;um fuerit, eju&longs;<lb/>que momenta pro variá declinatione à &longs;uo perpendiculo inqui-<pb xlink:href="017/01/375.jpg" pagenum="359"/>rantur, res manet incerta, &longs;i in praxim deducatur, qum plurimum <lb/>intere&longs;t, quâ obliquitate inclinetur, atque à &longs;uo perpendiculo de<lb/>flectat funiculus libræ obliquæ, &longs;i maxime cum diversa obliqui<lb/>tate jungatur di&longs;par funiculi illius longitudo. </s>

<s>Nam ex A &longs;u&longs;<lb/>pendatur pondus B habens BAC <expan abbr="angul&utilde;">angulum</expan> <lb/><figure id="id.017.01.375.1.jpg" xlink:href="017/01/375/1.jpg"/><lb/>declinationis à &longs;uo perpendiculo AC; & <lb/>primùm &longs;it libra obliqua D, itaut <expan abbr="æquip&etilde;-dium">æquipen<lb/>dium</expan> E retineat pondus B in eodem &longs;itu: <lb/>deinde transferatur libra obliqua ex D in <lb/>F, & æquipondium G retineat pariter in <lb/>codem &longs;itu pondus B cum declinationis <lb/>angulo BAC. </s>

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<lb/><s>Quare pondus B, quò acutior e&longs;t angulus, & magis accedit ad <lb/><expan abbr="perpendicul&utilde;">perpendiculum</expan> FG, eò etiam magis conatur contra F, & ad æqui<lb/>librium exigit majorem gravitatem in G, quàm cum angulus e&longs;t <lb/>minù, acutus. </s>

<s>Id quod experimento allato &longs;uperiori capite n<gap/><lb/>ni&longs;e&longs;tum &longs;it; &longs;i enim funiculi extremitates jungant pondera in<gap/><lb/>qualia, pondus intermedium magis accedit ad perpendiculum, in <lb/>quo e&longs;t major gravitas. </s>

<s>Id quod experimento allato &longs;uperiori capite ma<lb/>nife&longs;tum &longs;it; &longs;i enim funiculi extremitates jungant pondera inæ<lb/>qualia, pondus intermedium magis accedit ad perpendiculum, in <lb/>quo e&longs;t major gravitas. </s>

<s>Hinc quia valde incertum e&longs;t in pra<gap/><lb/>utrùm B, D, & F in câdem &longs;int rectá lineâ, propterea <expan abbr="etiã">etiam</expan> <expan abbr="incert&utilde;">incertum</expan> <lb/>erit ex gravitate ponderis G inferre, quanta &longs;int ponderis B <expan abbr="mo-m&etilde;ta">mo<lb/>menta</expan> cum declinatione BAC: Ni&longs;i fortè <expan abbr="duplic&etilde;">duplicem</expan> in&longs;tituas libræ <lb/>obliquæ po&longs;itionem in D, & in F atque <expan abbr="eod&etilde;">eodem</expan> &longs;emper <expan abbr="põdere">pondere</expan> tam <lb/>in E quàm in G retineatur pondus B in po&longs;itione <expan abbr="câd&etilde;">câdem</expan>. </s>

<s>Hinc quia valde incertum e&longs;t in praxi <lb/>utrùm B, D, & F in eâdem &longs;int rectá lineâ, propterea <expan abbr="etiã">etiam</expan> <expan abbr="incert&utilde;">incertum</expan> <lb/>erit ex gravitate ponderis G inferre, quanta &longs;int ponderis B <expan abbr="mo-m&etilde;ta">mo<lb/>menta</expan> cum declinatione BAC: Ni&longs;i fortè <expan abbr="duplic&etilde;">duplicem</expan> in&longs;tituas libræ <lb/>obliquæ po&longs;itionem in D, & in F atque <expan abbr="eod&etilde;">eodem</expan> &longs;emper <expan abbr="põdere">pondere</expan> tam <lb/>in E quàm in G retineatur pondus B in po&longs;itione <expan abbr="câd&etilde;">câdem</expan>. </s>

<s>Ita <expan abbr="tam&etilde;">tamen</expan> <lb/>collocanda e&longs;t libra obliqua, ut angulus ABD &longs;it rectus; ex illo <lb/>quippe æ&longs;timatur <expan abbr="plan&utilde;">planum</expan> <expan abbr="inclinat&utilde;">inclinatum</expan>, in quo pondus B conatur de&longs;<lb/>cendere, ut <expan abbr="dict&utilde;">dictum</expan> e&longs;t lib.1.cap 15.alioquin &longs;i acutus fuerit aut ob<lb/>tu&longs;us ille angulus, quamvis in eâdem declinatione BAC reti<lb/>neatur, valde inæqualia apparebunt momenta. </s>

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<s>Si enim nota &longs;it ponderis dati gravitas ab&longs;oluta, & plani incli<lb/>natio innotuerit, videlicet angulus, quem planum <expan abbr="inclinat&utilde;">inclinatum</expan> cum <lb/>plano horizontali con&longs;tituit, fiat ut Radius ad Sinum noti anguli <lb/>inclinationis, ita gravitas ab&longs;oluta dati ponderis ad <expan abbr="mom&etilde;ta">momenta</expan>, quæ <lb/>habet in plano inclinato: Tum librâ obliquâ exploretur, quanto <lb/>æquipondio opus &longs;it ad <expan abbr="retin&etilde;dum">retinendum</expan> pondus in plano inclinato, ne <lb/>deor&longs;um labatur: nam differentia inter gravitatem æquipondij, & <lb/>momenta inventa pro tali inclinatione indicabit, quantum impe<lb/>dimenti oriatur ex <expan abbr="planor&utilde;">planorum</expan> &longs;e contingentium a&longs;peritate, &longs;i æqui<lb/>pondij gravitas minor &longs;it momentis, quæ ab huju&longs;modi inclina<lb/>tione exiguntur. </s>

<s>Sic ex.gr.&longs;it ponderis dati ab&longs;oluta gravitas un<lb/>ciarum 30, inclinationis angulus dati plani cum plano <expan abbr="horizõtali">horizontali</expan> <lb/>&longs;it gr.60.fiat ut 10000 Radius ad 86603 Sinum gr.60.ita 30 ad <lb/>25.98. Si applicata libra obliqua æquipondium habeat &longs;olùm <lb/>unc.24, manife&longs;tum e&longs;t à planorum a&longs;peritate detrahi momenti <lb/>partem fer<gap/> decimam tertiam, cùm de<gap/>int ju&longs;to æquipondio ferè <lb/>unciæ 2. Verùm & hîc ob&longs;ervandum, opus e&longs;&longs;e funiculi, à quo <lb/>pondus retinetur, paralleli&longs;mum cum plano inclinato, prout ex <lb/>iis, quæ de obliquis tractionibus lib.

<s>Sic ex.gr. &longs;it ponderis dati ab&longs;oluta gravitas un<lb/>ciarum 30, inclinationis angulus dati plani cum plano <expan abbr="horizõtali">horizontali</expan> <lb/>&longs;it gr.60.fiat ut 10000 Radius ad 86603 Sinum gr.60.ita 30 ad <lb/>25.98. Si applicata libra obliqua æquipondium habeat &longs;olùm <lb/>unc. 24, manife&longs;tum e&longs;t à planorum a&longs;peritate detrahi momenti <lb/>partem ferè decimam tertiam, cùm de&longs;int ju&longs;to æquipondio ferè <lb/>unciæ 2. Verùm & hîc ob&longs;ervandum, opus e&longs;&longs;e funiculi, à quo <lb/>pondus retinetur, paralleli&longs;mum cum plano inclinato, prout ex <lb/>iis, quæ de obliquis tractionibus lib. 1. cap.16. dicta &longs;unt, &longs;atis <lb/>con&longs;tat. </s><pb xlink:href="017/01/377.jpg" pagenum="361"/><figure id="id.017.01.377.1.jpg" xlink:href="017/01/377/1.jpg"/>

1. cap.16. dicta &longs;unt, &longs;atis <lb/>con&longs;tat. </s><pb xlink:href="017/01/377.jpg" pagenum="361"/><figure id="id.017.01.377.1.jpg" xlink:href="017/01/377/1.jpg"/>

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

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<s>HACTENUS de in&longs;trumentis ad movenda pondera <lb/>idoncis nihil, ni&longs;i forta&longs;sè obiter, dictum e&longs;t: Jam <lb/>ad illa explicanda accedimus, quibus veteres facul<lb/>tatibus nomen indiderunt. </s>

<s>Quamvis autem in <lb/>quinque facultatibus enumerandis primum locum <lb/>Vecti Pappus lib.

<s>Quamvis autem in <lb/>quinque facultatibus enumerandis primum locum <lb/>Vecti Pappus lib. 8. Collect. Math. non tribuat, placuit tamen <lb/>de Vecte ante cæteras facultates di&longs;&longs;erere, e&longs;t &longs;iquidem paratu <lb/>facillimus, & ad &longs;ubitum u&longs;um prompti&longs;&longs;imus, atque cen&longs;eri <lb/>pote&longs;t, ut idem Pappus loquitur, <emph type="italics"/>forta&longs;&longs;e præmeditatio motús cir<lb/>ca excedentia pondera: &longs;tatuentes enim quidam magna pondera mo<lb/>vere [quoniam primùm à terrâ attollere oportet, an&longs;as autem non <lb/>habebant) quòd omnes partes ba&longs;is ip&longs;ius ponderis &longs;olo incumberent, <lb/>paulum &longs;uffodientes, & ligni longi extremitatem &longs;ubjicientes &longs;ub <lb/>onus, adducebant ex alterâ extremitate, &longs;upponentes ligno propè <lb/>ip&longs;um onus lapidem, qui Hypomochlium appellatur. </s>

8. Collect. Math. non tribuat, placuit tamen <lb/>de Vecte ante cæteras facultates di&longs;&longs;erere, e&longs;t &longs;iquidem paratu <lb/>facillimus, & ad &longs;ubitum u&longs;um prompti&longs;&longs;imus, atque cen&longs;eri <lb/>pote&longs;t, ut idem Pappus loquitur, <emph type="italics"/>forta&longs;&longs;e pram<gap/>ditatlo motús cir<lb/>ca excedentia pondera: &longs;tatuentes enim quidam magna pondera mo<lb/>vere [quoniam primùm à terrâ attollere oportet, an&longs;as autem non <lb/>hahebant) quòd omnes partes ba&longs;is ip&longs;ius ponderis &longs;olo incumberent, <lb/>pau<gap/>um &longs;uffodientes, & ligni longi extremitatem &longs;ubjicientes &longs;ub <lb/>onus, adducebant ex alterâ extremitate, &longs;upponentes ligno propè <lb/>ip&longs;um onus lapiàem, qui Hypomochlium appellatur. </s>

<s>Cúmque illis vi<lb/>&longs;us e&longs;&longs;et hic motus valde facilis, exi&longs;imaverunt fieri pe&longs;&longs;e, ut hoc <lb/>pacio magna pondera moveretur. </s>

<s>Vocatur autem tale lignum Vectis, <lb/>&longs;ive quadratum &longs;it, &longs;ive rotundum, & quanto propinquius oneri poni<lb/>tur hypomochlium, tanto faciliùs pondus movetur.<emph.end type="italics"/> Hæc illc vectis <lb/>ortum & procreationem quodammodo indigitans. </s>

<s>Contingere quidem pote&longs;t, ut Vecte aliquando utamur ad <lb/>&longs;u&longs;tinendum ingens pondus, non autem ad movendum, adeò <lb/>ut potentia exigua &longs;u&longs;tinens, in alterâ vectis extremitate po&longs;ita. <pb xlink:href="017/01/378.jpg" pagenum="362"/>habeat rationem æquipondij retinentis pondus in oppo&longs;itá ex<lb/>tremitate collocatum: & tunc locum habet Ari&longs;totelis &longs;enten<lb/>tia Mechan. quæ &longs;t.3.dicentis, <emph type="italics"/>Ip&longs;e vectis e&longs;t in causá libra ex &longs;iens, <lb/>&longs;partum inferne habens, in inæqualia divi&longs;a; hypomoclion enim e&longs;t <lb/>&longs;p.<gap/>rtum, ambo namque &longs;unt ut centrum.<emph.end type="italics"/></s><s> Verùm cùm propriè, & <lb/>pre&longs;sè tunc facultas e&longs;&longs;e non videatur, neque exerceat munus <lb/>vectis, quia non movet, &longs;ed &longs;it qua&longs;i jugum &longs;tateræ; fru&longs;ira <lb/>Vectis quâ vectis e&longs;t, ad libram revocatur: præ&longs;ertim cùm ali<lb/>quod vectis genus &longs;it, in quo nullum libræ ve&longs;tigium depre<lb/>hendi pote&longs;t, etiam&longs;i pondus cæteroqui <gap/>uiturum &longs;u&longs;tineat; &longs;i <lb/>nimirum pondus ip&longs;um inter vectis extremitates con&longs;titutum <lb/>&longs;u&longs;tineatur, aut potentia ip&longs;a &longs;u&longs;tentans medium locum occu<lb/>pet inter pondus & hypomochlium, ut infra dicetur. </s>

<s>Contingere quidem pote&longs;t, ut Vecte aliquando utamur ad <lb/>&longs;u&longs;tinendum ingens pondus, non autem ad movendum, adeò <lb/>ut potentia exigua &longs;u&longs;tinens, in alterâ vectis extremitate po&longs;ita. <pb xlink:href="017/01/378.jpg" pagenum="362"/>habeat rationem æquipondij retinentis pondus in oppo&longs;itá ex<lb/>tremitate collocatum: & tunc locum habet Ari&longs;totelis &longs;enten<lb/>tia Mechan. quæ &longs;t.3.dicentis, <emph type="italics"/>Ip&longs;e vectis e&longs;t in causá libra ex &longs;iens, <lb/>&longs;partum inferne habens, in inæqualia divi&longs;a; hypomoclion enim e&longs;t <lb/>&longs;partum, ambo namque &longs;unt ut centrum.<emph.end type="italics"/></s><s> Verùm cùm propriè, & <lb/>pre&longs;sè tunc facultas e&longs;&longs;e non videatur, neque exerceat munus <lb/>vectis, quia non movet, &longs;ed &longs;it qua&longs;i jugum &longs;tateræ; fru&longs;tra <lb/>Vectis quâ vectis e&longs;t, ad libram revocatur: præ&longs;ertim cùm ali<lb/>quod vectis genus &longs;it, in quo nullum libræ ve&longs;tigium depre<lb/>hendi pote&longs;t, etiam&longs;i pondus cæteroqui ruiturum &longs;u&longs;tineat; &longs;i <lb/>nimirum pondus ip&longs;um inter vectis extremitates con&longs;titutum <lb/>&longs;u&longs;tineatur, aut potentia ip&longs;a &longs;u&longs;tentans medium locum occu<lb/>pet inter pondus & hypomochlium, ut infra dicetur. </s>

<s>Quid <lb/>enim pariter non revocetur libra aut &longs;tatera ad Vectem, &longs;i ex <lb/>altera jugi extremitate pondus addatur, quod ad oppo&longs;itum <lb/>pondus majorem habeat Rationem, quàm libræ, aut &longs;tateræ <lb/>brachia reciprocè &longs;umpta? </s>

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<s>Quemadmodum igitur libra aut &longs;tatera ad ponderum <lb/>æquilibrium in&longs;titute, non verò ad corum motum, libræ aut <lb/>&longs;tateræ munus non exercent in motu, quâ motus e&longs;t; ita pari<lb/>ter vectis hypomochlium inter extremitates habens non exer<lb/>cet munus vectis in quiete: alioquin & vectis ad libram, & vi<lb/>ci&longs;&longs;im libra ad vectem ab&longs;urdo circulo revocaretur. </s>

<s>Adde verò <lb/>genus hoc vectis hypomochlium inter extremitates habentis, &longs;i <lb/>adhibeatur ad onus in plano horizontali movendum, non verò <lb/>ad illud &longs;u&longs;tentandum, nihil habere commercij cum librâ, onus <lb/>&longs;i quidem nullam exercet vim &longs;uæ gravitatis adversùs ip&longs;u<gap/><lb/>vectem, nam ce&longs;&longs;ante potentia onus illicò quie&longs;cit; at in libra <lb/>&longs;ublato æquipondio pondus de&longs;cendit. </s>

<s>Adde verò <lb/>genus hoc vectis hypomochlium inter extremitates habentis, &longs;i <lb/>adhibeatur ad onus in plano horizontali movendum, non verò <lb/>ad illud &longs;u&longs;tentandum, nihil habere commercij cum librâ, onus <lb/>&longs;i quidem nullam exercet vim &longs;uæ gravitatis adversùs ip&longs;um <lb/>vectem, nam ce&longs;&longs;ante potentia onus illicò quie&longs;cit; at in libra <lb/>&longs;ublato æquipondio pondus de&longs;cendit. </s>

<s>Quid &longs;i vecte utamur <lb/>ad corpus leve infra aquam deprimendum? </s>

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<s>Quia verò re&longs;i&longs;tentia com<lb/>ponitur ex innatâ ponderis gravitate, & ex motûs violenti tar<lb/>ditate aut velocitate, hoc e&longs;t ex motûs huju&longs;modi quantitate <lb/>intra datam temporis men&longs;uram; propterea ita duo hæc tempe<lb/>rari oportet, ut quod alteri additur, alteri dematur; ne adeò <lb/>re&longs;i&longs;tentia augeatur, ut jam minor non &longs;it virtute potentiæ. </s>

<lb/><s>Quare in vecte, cujus extremitati A potentia applicatur cer<gap/><lb/>virtutis, ita &longs;tatuendus e&longs;t hypomochlio C locus, ut compara<lb/>to motu potentiæ in A cum motu ponderis in B, ea &longs;it motûs B <pb xlink:href="017/01/381.jpg" pagenum="365"/>tarditas; quæ addita gravitati ponderis B re&longs;i&longs;tentiam compo<lb/>nat minorem virtute movendi potentiæ A. </s>

<lb/><s>Quare in vecte, cujus extremitati A potentia applicatur certæ <lb/>virtutis, ita &longs;tatuendus e&longs;t hypomochlio C locus, ut compara<lb/>to motu potentiæ in A cum motu ponderis in B, ea &longs;it motûs B <pb xlink:href="017/01/381.jpg" pagenum="365"/>tarditas; quæ addita gravitati ponderis B re&longs;i&longs;tentiam compo<lb/>nat minorem virtute movendi potentiæ A. </s>

<s>Quoniam enim, <lb/>manente puncto C tanquam centro motús potentiæ de&longs;cenden<lb/>tis & ponderis a&longs;cendentis, manife&longs;tum e&longs;t eam e&longs;&longs;e motuum <lb/>Rationem, quæ e&longs;t Radiorum CA & CB idcirco quò major <lb/>erit huju&longs;medi Radiorum inæqualitas, eò etiam major erit Ra<lb/>tio motûs potentiæ ad motum ponderis, cujus tarditas gravi<lb/>tatem compen&longs;ans minuet re&longs;i&longs;tentiam, ut virtuti potentiæ, pro<lb/>portione re&longs;pondeat. </s>

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<s>Quare pondus unius libræ in hac &longs;ubdecuplâ di&longs;tantiâ <lb/>cùm &longs;ubdecuplo tardius moveatur (percurrit enim tempore eo<lb/>dem &longs;patium &longs;ubdecuplum) indiget &longs;olùm &longs;ubdecuplo impetu <lb/>ejus, quem prius exigebat, ut æqualiter cum potentiâ move<lb/>retur. </s>

<s>Totus igitur impetus ille, quem potentia ponderi unius <lb/>libræ imprimebat, ut æquali velocitate pariter moverentur, illa <lb/>de&longs;cendendo, hoc a&longs;cendendo, &longs;i decem ponderibus &longs;imilibus <lb/>di&longs;tribuatur, <gap/> e&longs;t, ut omnia illa moveantur &longs;ubdecuplâ ve<lb/>locitate. </s>

<s>Totus igitur impetus ille, quem potentia ponderi unius <lb/>libræ imprimebat, ut æquali velocitate pariter moverentur, illa <lb/>de&longs;cendendo, hoc a&longs;cendendo, &longs;i decem ponderibus &longs;imilibus <lb/>di&longs;tribuatur, &longs;atis e&longs;t, ut omnia illa moveantur &longs;ubdecuplâ ve<lb/>locitate. </s>

<s>Quia autem duorum arteriæ pul&longs;uum &longs;patio &longs;ingula <lb/>a&longs;cend<gap/>nt digitum unum, & &longs;unt decem a&longs;cen&longs;us digitales, <lb/>dum potentia de&longs;cendit digitos decem, & dum potentia primo <pb xlink:href="017/01/382.jpg" pagenum="366"/>arteriæ pul&longs;u decurrit digitos quinque, decem illa pondera <lb/>motum quinque digitorum perficiunt, &longs;ingula videlicet per &longs;e<lb/>midigitum (id quod pariter ob&longs;ervari facilè poterit in &longs;ingulis <lb/>minutioribus temporis particulis) tantumdem motus perficit <lb/>potentia ac pondus, &longs;ive toto impetu uni libræ impre&longs;&longs;o libra <lb/>una habeat motum decem digitorum, &longs;ive decimâ impetûs par<lb/>te &longs;ingulis libris impre&longs;sâ, &longs;ingulæ habeant motum digitalem: <lb/>utrobique &longs;cilicet &longs;unt decem motus digitales, &longs;ive unius pon<lb/>deris, &longs;ive decem ponderum eodem tempore. </s>

<s>Quia autem duorum arteriæ pul&longs;uum &longs;patio &longs;ingula <lb/>a&longs;cendunt digitum unum, & &longs;unt decem a&longs;cen&longs;us digitales, <lb/>dum potentia de&longs;cendit digitos decem, & dum potentia primo <pb xlink:href="017/01/382.jpg" pagenum="366"/>arteriæ pul&longs;u decurrit digitos quinque, decem illa pondera <lb/>motum quinque digitorum perficiunt, &longs;ingula videlicet per &longs;e<lb/>midigitum (id quod pariter ob&longs;ervari facilè poterit in &longs;ingulis <lb/>minutioribus temporis particulis) tantumdem motus perficit <lb/>potentia ac pondus, &longs;ive toto impetu uni libræ impre&longs;&longs;o libra <lb/>una habeat motum decem digitorum, &longs;ive decimâ impetûs par<lb/>te &longs;ingulis libris impre&longs;sâ, &longs;ingulæ habeant motum digitalem: <lb/>utrobique &longs;cilicet &longs;unt decem motus digitales, &longs;ive unius pon<lb/>deris, &longs;ive decem ponderum eodem tempore. </s>

<s>Quis verò mi<lb/>retur, &longs;i ille idem, qui decem aureis nobili ho&longs;piti &longs;plendidio<lb/>res epulas parare po&longs;&longs;et, decem hominibus frugalem men&longs;am <lb/>in&longs;trueret &longs;ingulis aureis in &longs;ingulos homines tributis? </s>

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<s>Cuju&longs;modi &longs;it hy<lb/>pomochlium, &longs;ive &longs;it funis vectem retinens, &longs;ive axis infixus, <lb/>circa quem volvatur vectis, &longs;ive quodcumque aliud corpus, cui <lb/>ille incumbat, aut innitatur, modò ab&longs;it incommodi periculum <lb/>ex ejus fragilitate, parum refert: &longs;atis e&longs;t, &longs;i par fuerit ferendo <lb/>oneri, quod vecte elevatur. </s>

<s>Ex ponderis autem gravitate hy<lb/>pomochlij &longs;oliditas atque materies definienda e&longs;t; ex motùs <pb xlink:href="017/01/388.jpg" pagenum="372"/>qualitate (&longs;p<gap/> quo perficiendus e&longs;t, po&longs;itione) <lb/>forma hypomochlij &longs;tatuatur. </s>

<s>Ex ponderis autem gravitate hy<lb/>pomochlij &longs;oliditas atque materies definienda e&longs;t; ex motùs <pb xlink:href="017/01/388.jpg" pagenum="372"/>qualitate (&longs;pectatâ loci, in quo perficiendus e&longs;t, po&longs;itione) <lb/>forma hypomochlij &longs;tatuatur. </s>

<s>Illud examinandum videtur, quandónam præ&longs;ter uti vecte <lb/>primi generis, quando vecte Secundi generis, hoc e&longs;t an plus <lb/>commodi a&longs;&longs;erat &longs;ulcrum in vectis extremitate collocatum, ut <lb/>in &longs;ecundo genere, an verò inter pondus atque potentiam in<lb/>terjectum, ut in primo genere. </s>

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<s>Datâ igitur ponderis movendi gravitate, & datâ potentiæ <lb/>virtute (quæ videlicet tanto conatu adhibito pote&longs;t certam gra<lb/>vitatem &longs;ola &longs;ine vecte movere in &longs;imili plano &longs;ive horizontali, <lb/>&longs;ive inclinato, &longs;ive verticali) di&longs;tinguatur vectis in duas partes <lb/>ita, ut vel pars ad partem, &longs;i &longs;it primi generis, vel totus ad par-<pb xlink:href="017/01/389.jpg" pagenum="373"/>tem, &longs;i &longs;it &longs;ecundi generis, eandem Rationem habeat, quæ <lb/>e&longs;t dati ponderis ad pondus, quod à potentia olâ &longs;ine vecte po<lb/>te&longs;t moveri. </s>

<s>Sic data Potentia virtutem habeat movendi pon<lb/>dus lib.

<s>Sic data Potentia virtutem habeat movendi pon<lb/>dus lib. 6. certo conatu, oporteat autem hoc codem conatu <lb/>movere lib. 30: quia virtus potentiæ e&longs;t &longs;ubquintupla pon<lb/>deris dati, propo&longs;itus vectis intelligatur primùm di&longs;tinctus <lb/>in partes &longs;ex, quarum una tribuatur di&longs;tantiæ ponderi, ab <lb/>hypomochlio, reliquæ quinque tribuantur di&longs;tantiæ poten<lb/>tiæ, ita ut reciprocè &longs;it di&longs;tantia potentiæ ad di&longs;tanuam <lb/>ponderis, ut pondus datum ad virtutem potentiæ: & hic <lb/>e&longs;t vectis primi generis. </s>

6. certo conatu, oporteat autem hoc codem conatu <lb/>movere lib.

30: quia virtus potentiæ e&longs;t &longs;ubquintupla pon<lb/>deris dati, propo&longs;itus vectis intelligatur primùm <gap/><lb/>in partes &longs;ex, quarum una tribuatur di&longs;tantiæ ponderi, ab <lb/>hypomochlio, reliquæ quinque tribuantur di&longs;tantiæ poten<lb/>tiæ, ita ut reciprocè &longs;it di&longs;tantia potentiæ ad di&longs;tanuam <lb/>ponderis, ut pondus datum ad virtutem potentiæ: & hic <lb/>e&longs;t vectis primi generis. </s>

<s>Deinde ut habeatur vectis &longs;ecun<lb/>di generis, di&longs;tinguatur totus vectis in partes quinque, & <lb/>una ex illis &longs;it di&longs;tantia ponderis ab hypomochlio in vectis <lb/>extremitate con&longs;tituto. </s>

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<s>Ex his, quæ de potentia &longs;u&longs;tentante dicta &longs;unt, &longs;atis apparet <lb/>potentiam paulo validiorem &longs;atis e&longs;&longs;e ad pondus movendum. </s>

<lb/><s>Verùm licèt in vecte primi generis ad pondus &longs;u&longs;tentandum <lb/>opportunè animum adverterimus ad libram curvam, hæc ta<lb/>men in vecte &longs;ecundi generis locum habere non po&longs;&longs;unt; <lb/>propterea ad aliam explicandi rationem confugiendum e&longs;t, <lb/>quæ utrique generi communis &longs;it; nec difficile erit ea, quæ &longs;ta<lb/>tim capite &longs;equen<gap/>ciam pro &longs;ecundo vectis genere ad pri-<pb xlink:href="017/01/401.jpg" pagenum="385"/>mum traducere. </s>

<lb/><s>Verùm licèt in vecte primi generis ad pondus &longs;u&longs;tentandum <lb/>opportunè animum adverterimus ad libram curvam, hæc ta<lb/>men in vecte &longs;ecundi generis locum habere non po&longs;&longs;unt; <lb/>propterea ad aliam explicandi rationem confugiendum e&longs;t, <lb/>quæ utrique generi communis &longs;it; nec difficile erit ea, quæ &longs;ta<lb/>tim capite &longs;equenti &longs;ubjiciam pro &longs;ecundo vectis genere ad pri-<pb xlink:href="017/01/401.jpg" pagenum="385"/>mum traducere. </s>

<s>Con&longs;ideratur nimirum motus ponderis com<lb/>paratus cum eodem motu potentiæ: &longs;i enim potentia &longs;it &longs;uâ <lb/>gravitate de&longs;cendens, ejus de&longs;cen&longs;um metitur ZA: pondus <lb/>vecti impo&longs;itum a&longs;cendit, ut &longs;it &longs;upra horizontalem altitudine <lb/>KD; &longs;ed ex hac demenda e&longs;t centri gravitatis di&longs;tantia DE, <lb/>qua eminebat &longs;upra horizontalem, ut habeatur ejus motus <lb/>DK minùs DE, hoc e&longs;t GK. </s>

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8 ad virtutem potentiæ A moventis &longs;ine vecte li<lb/>bras (2 38/53). Tota igitur virtus potentiæ in hac eorumdem pon<lb/>derum inæqualium collocatione &longs;ufficiet, &longs;i fuerit vis movendi <lb/>lib. (5 23/53), quæ minor e&longs;t eâ, quæ requiritur; quando pondera <lb/>&longs;unt æqualia, & differt à virtute, quæ requiritur, quando F <lb/>gravins e&longs;t quàm E, vi movendi ferè uncias 8 1/3. </s>

<s>Simili argumentatione ratiocinando deprehendes, quo mi<lb/>nus fuerit intervallum inter E & F, <gap/>am faciliùs duo illa pon<lb/>dera eodem vecte moveri. </s>

<s>Simili argumentatione ratiocinando deprehendes, quo mi<lb/>nus fuerit intervallum inter E & F, etiam faciliùs duo illa pon<lb/>dera eodem vecte moveri. </s>

<s>Nam &longs;i idem vectis AE 13 adhi<lb/>beatur, atque pondera E & F æqualia fuerint, intervallum ve<lb/>rò EF &longs;it 4, centrum motuum di&longs;tabit ab A intervallo 11, & <lb/>à &longs;ingulis ponderibus intervallo 2: Quare potentia ut 4 move<lb/>bit pondera &longs;ingula ut 11: vel &longs;i ponantur ut prius &longs;ingula <lb/>lib.

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<s>46, & ba&longs;is AK <lb/>part. (139 <gap/>/100): igitur GK part. (25 6/100), quæ tamen priùs erat <lb/>(12 36/100). Deinde in triangulo AMN latera &longs;int eadem, & an<lb/>gulus MAN gr. 45: invenitur angulus MNA gr. 75. m. </s>

<s>46, & ba&longs;is AK <lb/>part. (139 79/100): igitur GK part. (25 6/100), quæ tamen priùs erat <lb/>(12 36/100). Deinde in triangulo AMN latera &longs;int eadem, & an<lb/>gulus MAN gr. 45: invenitur angulus MNA gr. 75. m. </s>

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<s>43′: quare ba&longs;is RI e&longs;t part. <lb/>(10 4<gap/>/100): & quia RS ex hypothe&longs;i e&longs;t &longs;olum part. </s>

<s>43′: quare ba&longs;is RI e&longs;t part. <lb/>(10 4s/100): & quia RS ex hypothe&longs;i e&longs;t &longs;olum part. </s>

<s>10, motus SI <lb/>e&longs;t (42/100) multo minor quàm cum funis brevior ponitur, ac prop<lb/>terea etiam facilior e&longs;t motus, quippe qui minorem Rationem <lb/>habet ad motum potentiæ. </s>

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<s>Potentia itaque motum &longs;uum dirigens ad acutum angulum <lb/>per lineam BH, vi &longs;ui impetûs de&longs;cribit circa centrum C ar<lb/>cum BR; ad angulum rectum per lineam BI de&longs;cribit arcum <pb xlink:href="017/01/427.jpg" pagenum="411"/>BN; ad anguium demum obtu&longs;um per lineam BG de&longs;cribit <lb/>arcum BL, qui e&longs;t æqualis arcui BR, &longs;iangulu; obtu&longs;us GBA <lb/>&longs;it &longs;upplemencum ad duo, recto, anguli acuti HBA, major <lb/>autem, aut mino, eodem arcub R, li angulus obtu&longs;us &longs;it mi<lb/>nor aut major codem Supplemento ad duos recto. </s>

<s>Hæc tamen <lb/>ita dicta intelliga velim, ut hu&longs;ulmodi arcus toti atque integri <lb/>non motum ip<gap/>n exprimant, qui revera fiat, &longs;ed virium Ra<lb/>tionem pro diversa potentiæ applicatione in minimâ arcû de&longs;<lb/>cripti particula; neque enim &longs;ingulis temporis momentis æqua<lb/>lis pars arcus cidem impetui re&longs;pondet, &longs;ingulis nimirum mo<lb/>mentis mutatur vectis inclinatio, & manet eadem motús di<lb/>rectio, atque varia e&longs;t potentiæ ad vectem applicatio, ni&longs;i il<lb/>la impetum concipiat, quo &longs;ua &longs;ponte in gyrum ageretur, <lb/>etiam&longs;i ad motum circularem non determinaretur à vecte. </s>

<s>Hæc tamen <lb/>ita dicta intelligas velim, ut huju&longs;modi arcus toti atque integri <lb/>non motum ip&longs;um exprimant, qui revera fiat, &longs;ed virium Ra<lb/>tionem pro diversa potentiæ applicatione in minimâ arcû de&longs;<lb/>cripti particula; neque enim &longs;ingulis temporis momentis æqua<lb/>lis pars arcus eidem impetui re&longs;pondet, &longs;ingulis nimirum mo<lb/>mentis mutatur vectis inclinatio, & manet eadem motús di<lb/>rectio, atque varia e&longs;t potentiæ ad vectem applicatio, ni&longs;i il<lb/>la impetum concipiat, quo &longs;ua &longs;ponte in gyrum ageretur, <lb/>etiam&longs;i ad motum circularem non determinaretur à vecte. </s>

<lb/><s>Sed quoniam arcus eodem Radio CB à potentiâ de&longs;criptus <lb/>e&longs;t &longs;imilis arcui eodem Radio CA de&longs;cripto à pondere, <lb/>proinde non mutatur Ratio motuum, &longs;ive potentia de&longs;cri<lb/>bat codem impetu minorem, &longs;ive majorem arcum eju&longs;dem <lb/>circuli: propterea non mutatur quidem momentum poten<lb/>tiæ cum pondere abiolutè comparatæ, mutatur tamen &longs;ubinde <lb/>momentum potentiæ, quatenus &longs;ecum ip&longs;a comparatur, faci<lb/>liú&longs;que movere pondus tunc dicitur, quando eodem conatu <lb/>majorem motum ponderi æquali tempore conciliat; id quod <lb/>fit, cùm ad angulum rectum vecti applicatur. </s>

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<s>Id explicare ex iis, quæ &longs;uperiori capite di&longs;putata &longs;unt, non <lb/>erit difficile, &longs;i animadvertamus in vectibus &longs;ecundi & tertij <lb/>generis utrumque genus conjungi: quemadmodum enim po<lb/>tentia conatur adversùs gravitatem ponderis, ita pondus cona<lb/>tur adversùs vim potentiæ: & in hoc conatu vici&longs;&longs;im exercent <lb/>munus potentiæ & ponderis. </s>

<s>Finge &longs;iquidem duos homines ap<lb/>plicari vecti AB, alterum quidem i<gap/> A, alterum verò in C, &longs;ed <lb/>in adver&longs;a conantes; uterque e&longs;t potentia, uterque e&longs;t pondus, <lb/>dum &longs;ibi reluctantur. </s>

<s>Finge &longs;iquidem duos homines ap<lb/>plicari vecti AB, alterum quidem in A, alterum verò in C, &longs;ed <lb/>in adver&longs;a conantes; uterque e&longs;t potentia, uterque e&longs;t pondus, <lb/>dum &longs;ibi reluctantur. </s>

<s>Anne ita hæc vocabula intra certos fines <lb/>co<gap/>rceri exi&longs;timas, ut potentiæ nomine illum &longs;olum donandum <lb/>putes, qui reliquum vincit? </s>

<s>Anne ita hæc vocabula intra certos fines <lb/>coërceri exi&longs;timas, ut potentiæ nomine illum &longs;olum donandum <lb/>putes, qui reliquum vincit? </s>

<s>&longs;ed quid, &longs;i horum hominum co-<pb xlink:href="017/01/438.jpg" pagenum="422"/>natus &longs;int reciprocè ut eorum di&longs;tantiæ ab hypomochlio B, & <lb/>A quidem conciur ut CB, C autem conetur ut AB; utique <lb/>neuter &longs;uperat; nec tamen negari pote&longs;t ideò contingere mo<lb/>mentorum æqualitatem inter inæquales conatus, quia vecti ap<lb/>plicantur: &longs;unt igitur &longs;ibi vici&longs;&longs;im potentia & pondus. </s>

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<s>At &longs;i vectem tertij generis, quatenus ge&longs;tatorum pre&longs;&longs;io ab <lb/>onere efficitur, con&longs;ideremus; po&longs;ito fulcro in A, potentia in C <lb/>aut in D exi&longs;tens non premit ge&longs;tatorem B perinde, atque &longs;i <lb/>nullo intercedente vecte ge&longs;tator e&longs;&longs;et pariter in C aut in D, &longs;ed <lb/>tanto minus, quanto minor e&longs;t CA aut DA, quam BA: idem<lb/>que de ge&longs;tatore A, po&longs;ito fulcro in B, dicendum e&longs;t. </s>

<s>Quarere<lb/>ciprocæ &longs;unt pre&longs;&longs;iones di&longs;tanti<gap/>s ge&longs;tatorum ab onere, & A <lb/>premitur ut CB aut DB, B autem premitur ut CA aut DA. </s>

<s>Quare re<lb/>ciprocæ &longs;unt pre&longs;&longs;iones di&longs;tantiis ge&longs;tatorum ab onere, & A <lb/>premitur ut CB aut DB, B autem premitur ut CA aut DA. </s>

<lb/><s>Cum enim vis ip&longs;a gravitatis oneris deor&longs;um conantis apta &longs;it <lb/>circa centrum A moveri pro ratione di&longs;tantiæ CA aut DA, uti<lb/>que in B motum efficere debet pro ratione di&longs;tantiæ BA: e&longs;t <lb/>autem CA major quam DA ex hypothe&longs;i, igitur, ex 8.lib.5.ma<lb/>jor e&longs;t Ratio momenti CA quàm momenti DA ad idem mo<lb/>mentum BA, ac proinde major pre&longs;&longs;io ge&longs;tatoris B e&longs;&longs;icitur ab <lb/>onere in C, quam in D, collocato. </s>

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<s>Unum adhuc in palangæ ge&longs;tatoribus attendendum e&longs;t, &longs;i vi<lb/>rium inæqualium fuerint, & onus non ita &longs;it palangæ applica<lb/>tum, ut ejus di&longs;tantiæ à ge&longs;tatoribus &longs;int permutatim ut corum<lb/>dem vires; nimirum contingere po&longs;&longs;e, ut validior ge&longs;tator dum <pb xlink:href="017/01/445.jpg" pagenum="429"/>juxta &longs;uas vires conatur adversùs onus, magis premat infirmio<lb/>rem ge&longs;tatorem, quam premeretur fulcrum infirmius, &longs;i unâ <lb/>cum validiore fulcro eandem gravitatem &longs;u&longs;tineret. </s>

<s>Quia vide<lb/>licet in eadem palanga AB vectem primi generis connderare <lb/>po&longs;&longs;umus, in quo onus C deor&longs;um nitens contra vim ge&longs;tatoris <lb/>habeat rationem hypomochlij, & validior ge&longs;tator A &longs;it poton<lb/>tia repellens ge&longs;tatorem infirmiorem B conantem adver&longs;us <lb/>onus, ac proinde illum premat: quemadmodum &longs;i funi deor&longs;um <lb/>firmiter alligato in&longs;ereretur palanga, cui humeros &longs;<gap/>bjicerent <lb/>duo inæqualibus viribus &longs;urium conantes; con&longs;tat enim infir<lb/>miorem à validiore premi, & e&longs;&longs;e vectem primi generis. </s>

<s>Quia vide<lb/>licet in eâdem palanga AB vectem primi generis con&longs;iderare <lb/>po&longs;&longs;umus, in quo onus C deor&longs;um nitens contra vim ge&longs;tatoris <lb/>habeat rationem hypomochlij, & validior ge&longs;tator A &longs;it poten<lb/>tia repellens ge&longs;tatorem infirmiorem B conantem adver&longs;us <lb/>onus, ac proinde illum premat: quemadmodum &longs;i funi deor&longs;um <lb/>firmiter alligato in&longs;ereretur palanga, cui humeros &longs;ubjicerent <lb/>duo inæqualibus viribus &longs;urium conantes; con&longs;tat enim infir<lb/>miorem à validiore premi, & e&longs;&longs;e vectem primi generis. </s>

<s>Ex quo <lb/>vides, cur bajuli dato invicem &longs;igno curent, ne alter alterum <lb/>præveniat in elevanda palanga; ne &longs;cilicet qui &longs;egnior fuent, <lb/>pre&longs;&longs;ionem, non ab onere adhuc jacente & nondum elevato, &longs;ed <lb/>à &longs;ocio diligentiùs &longs;uam palangæ extremitatem elevante, reci<lb/>piat. </s>

<s>Hæc eadem, quæ de onere &longs;ublevando &longs;unt dicta, de eodem <lb/>trahendo pariter intelligantur, &longs;i vecti illigatum &longs;it onus, & <lb/>vectis extremitatibus jungantur trahentes: horum enim cona<lb/>tus e&longs;&longs;e oportet permutatim in Ratione di&longs;tantiarum ab onere, <lb/>hoc e&longs;t à vectis puncto, cui onus adnectitur. </s>

<s>Id non &longs;ine jucun<lb/>d<gap/>quadam animi titillatione vidi aliquando ob<gap/>ervatum a ru&longs;ti<lb/>co, qui alterius equorum currum trahentium defatigati laborem <lb/>mi&longs;eratus, tran&longs;ver&longs;arium, cui ambo adjungebantur, ita tran&longs;tu<lb/>lit, ut in partes inæquales à temone di&longs;tingueretur, & longior <lb/>tran&longs;ver&longs;arij pars ad debiliorem equum &longs;pectaret. </s>

<s>Id non &longs;ine jucun<lb/>dâ quadam animi titillatione vidi aliquando ob&longs;ervatum à ru&longs;ti<lb/>co, qui alterius equorum currum trahentium defatigati laborem <lb/>mi&longs;eratus, tran&longs;ver&longs;arium, cui ambo adjungebantur, ita tran&longs;tu<lb/>lit, ut in partes inæquales à temone di&longs;tingueretur, & longior <lb/>tran&longs;ver&longs;arij pars ad debiliorem equum &longs;pectaret. </s>

<s>Inerant &longs;iqui<lb/>dem tran&longs;ver&longs;ario tria foramina, per quæ temoni nectebatur fer<lb/>reo clavo; unum quidem plane æqualiter ab extremitatibus abe<lb/>rat, reliqua duo hinc & hinc à medio di&longs;tabant modico quidem <lb/>&longs;ed <gap/>ongruo intervallo, ut &longs;i equus dexter defatigaretur, clavus <lb/>immitteietur &longs;ini&longs;tio foramini, aut contra dextro, &longs;i &longs;ini&longs;ter <lb/>equus languidiùs traheret. </s>

<s>Inerant &longs;iqui<lb/>dem tran&longs;ver&longs;ario tria foramina, per quæ temoni nectebatur fer<lb/>reo clavo; unum quidem plane æqualiter ab extremitatibus abe<lb/>rat, reliqua duo hinc & hinc à medio di&longs;tabant modico quidem <lb/>&longs;ed congruo intervallo, ut &longs;i equus dexter defatigaretur, clavus <lb/>immitteietur &longs;ini&longs;tio foramini, aut contra dextro, &longs;i &longs;ini&longs;ter <lb/>equus languidiùs traheret. </s>

<s>Verùm cautè modica intervalla de<lb/>finierat, ne nimia fieret momentorum inæqualitas; quod enim <lb/>alter<gap/> equorum laboris demebatur, addebatur reliquo. </s>

<s>Verùm cautè modica intervalla de<lb/>finierat, ne nimia fieret momentorum inæqualitas; quod enim <lb/>alteri equorum laboris demebatur, addebatur reliquo. </s>

<s>Quando autem non palanga defertur onus, &longs;ed<gap/>um imme<lb/>diate à d<gap/>obus &longs;u&longs;tinetur, eadem pror&longs;us e&longs;t philolophandi ra<lb/>tio, quandoquidem e&longs;t quodammodo onus vecti conjunctum, <lb/>atque juxta vectis longitudinem di&longs;tributum. </s>

<s>Quando autem non palangâ defertur onus, &longs;ed ip&longs;um imme<lb/>diate à duobus &longs;u&longs;tinetur, eadem pror&longs;us e&longs;t philolophandi ra<lb/>tio, quandoquidem e&longs;t quodammodo onus vecti conjunctum, <lb/>atque juxta vectis longitudinem di&longs;tributum. </s>

<s>Quamvis ver<gap/><pb xlink:href="017/01/446.jpg" pagenum="430"/>&longs;ingulis partibus &longs;ua gravitas in&longs;it, quia tamen in unam coale&longs;<lb/>cunt gravitatem, ideò totius molis gravitas ibi intelligenda e&longs;t, <lb/>ubi e&longs;t centrum gravitatis; vectis autem longitudo æ&longs;timanda <lb/>e&longs;t in lineá jungente puncta, quibus ge&longs;tatores aut &longs;u&longs;tinentes <lb/>applicantur: Ex quibus punctis &longs;i ponamus exire lineas paral<lb/>lelas lineæ directionis exeunti ex centro gravitatis, cadent om<lb/>nesad perpendiculum in lineam horizontalem tran&longs;euntem per <lb/>centrum gravitatis, aut illi parallelam. </s>

<s>Quamvis verò <pb xlink:href="017/01/446.jpg" pagenum="430"/>&longs;ingulis partibus &longs;ua gravitas in&longs;it, quia tamen in unam coale&longs;<lb/>cunt gravitatem, ideò totius molis gravitas ibi intelligenda e&longs;t, <lb/>ubi e&longs;t centrum gravitatis; vectis autem longitudo æ&longs;timanda <lb/>e&longs;t in lineá jungente puncta, quibus ge&longs;tatores aut &longs;u&longs;tinentes <lb/>applicantur: Ex quibus punctis &longs;i ponamus exire lineas paral<lb/>lelas lineæ directionis exeunti ex centro gravitatis, cadent om<lb/>nesad perpendiculum in lineam horizontalem tran&longs;euntem per <lb/>centrum gravitatis, aut illi parallelam. </s>

<s>Harum igitur parallela<lb/>rum, quæ directionem conatûs oppo&longs;iti gravitationi ponderis <lb/>referunt, di&longs;tantia à lineâ directionis centri gravitatis, ip&longs;orum <lb/>deferentium conatum in &longs;u&longs;tinendo, permutatim &longs;umpta de<lb/>finiet; quæcumque demùm &longs;it oneris figura. </s>

<s>Sit onus deferendum, cujus centrum gravitatis E; linca per <lb/><figure id="id.017.01.446.1.jpg" xlink:href="017/01/446/1.jpg"/><lb/>ge&longs;tatores tran&longs;iens, haben&longs;que rationem vectis, &longs;it BC, quæ <lb/>intelligatur horizonti parallela. </s>

<s>In hanc igitur ad angulos <lb/>rectos cadit linea directionis EF; & ge&longs;tatores in quocumqut <lb/>puncto lineæ BC fuerint, permutatim habent momenta &longs;u&longs;ti<lb/>nendi, aut recipiunt momenta pre<gap/>onis pro Ratione di&longs;tan<lb/>tiarum à puncto F, in quod cadit linea directionis: cùm cnim <lb/>linea BC ex hypothe&longs;i &longs;it horizonti parallela, omnium ip&longs;i FE <pb xlink:href="017/01/447.jpg" pagenum="431"/>parallelarum di&longs;tantia ab eádem FE, de&longs;umenda e&longs;t ex inter<lb/>valli, ge&longs;tatorum & puncti F. </s>

<s>In hanc igitur ad angulos <lb/>rectos cadit linea directionis EF; & ge&longs;tatores in quocumque <lb/>puncto lineæ BC fuerint, permutatim habent momenta &longs;u&longs;ti<lb/>nendi, aut recipiunt momenta pre&longs;&longs;onis pro Ratione di&longs;tan<lb/>tiarum à puncto F, in quod cadit linea directionis: cùm enim <lb/>linea BC ex hypothe&longs;i &longs;it horizonti parallela, omnium ip&longs;i FE <pb xlink:href="017/01/447.jpg" pagenum="431"/>parallelarum di&longs;tantia ab eádem FE, de&longs;umenda e&longs;t ex inter<lb/>valli, ge&longs;tatorum & puncti F. </s>

<s>At verò &longs;i recta BC non fuerit horizonti parallela, vel quia <lb/>deferentes onus non &longs;unt æquè alti, vel quia in clivo con&longs;i&longs;tunt, <lb/>utique linea directionis centri gravitatis E non cadit amplius in <lb/>rectam BC ad angulos rectos in F, &longs;ed obliquè incidit in H. </s>

<lb/><s>Concipiatur itaque per H tran&longs;iens linea GI horizonti paral<lb/>lela, & ip&longs;i EH &longs;int parallelæ CD & BK: &longs;unt igitur di&longs;tan<lb/>ti<gap/> HD & HK, quæ eandem inter &longs;e habent Rationem, quæ <lb/>reperitur inter HC & HB; &longs;unt enim triangula HDC & <lb/>HKB rectangula ad D & K, æquales angulos ad verticem H <lb/>habentia, ac proinde &longs;imilia, & per 4. lib.6 ut HD ad HK, <lb/>ita HC ad HB. </s>

<lb/><s>Concipiatur itaque per H tran&longs;iens linea GI horizonti paral<lb/>lela, & ip&longs;i EH &longs;int parallelæ CD & BK: &longs;unt igitur di&longs;tan<lb/>tiæ HD & HK, quæ eandem inter &longs;e habent Rationem, quæ <lb/>reperitur inter HC & HB; &longs;unt enim triangula HDC & <lb/>HKB rectangula ad D & K, æquales angulos ad verticem H <lb/>habentia, ac proinde &longs;imilia, & per 4. lib.6 ut HD ad HK, <lb/>ita HC ad HB. </s>

<s>Quo igitur magis ab horizonte removetur <lb/>punctum B præ puncto C, etiam linea directionis ex E propior <lb/>cadit puncto C; atque adeò qui inferior e&longs;t, magis gravatur <lb/>ab onere. </s>

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<s>At verò &longs;i linea MN fuerit ad horizontem incli<lb/>nata, & linea directionis &longs;it EO; utique minor e&longs;t di&longs;tantia à <lb/>&longs;uperiore M, quam ab inferiore N, ideoque plus laborabit &longs;u<lb/>periot retinendo, quam inferior. </s>

<s>Id quod pariter ex dictis <lb/>cap.4. confirmatur; nam pondus e&longs;t vecti &longs;ubjectum, & vectis <lb/>MN habens hypomochlium N e&longs;t &longs;upra horizontalem lineam, <pb xlink:href="017/01/448.jpg" pagenum="432"/>ac propterea potentia plus laborat quam in horizontali: contra <lb/>autem vectis NM habens hypomochlium M e&longs;t in&longs;ta horizon<lb/>talem lineam dep<gap/>e&longs;&longs;us, ideoque minu potentia laborat quam <lb/>in horizontali. </s>

<s>Id quod pariter ex dictis <lb/>cap.4. confirmatur; nam pondus e&longs;t vecti &longs;ubjectum, & vectis <lb/>MN habens hypomochlium N e&longs;t &longs;upra horizontalem lineam, <pb xlink:href="017/01/448.jpg" pagenum="432"/>ac propterea potentia plus laborat quam in horizontali: contra <lb/>autem vectis NM habens hypomochlium M e&longs;t in&longs;ta horizon<lb/>talem lineam depre&longs;&longs;us, ideoque minu potentia laborat quam <lb/>in horizontali. </s>

<s>Quæ omnia tam aperte re&longs;pondent quotidia<lb/>no experimento, ut mirum videatur potui&longs;&longs;e aliquos authores <lb/>idem planè opinari, &longs;ive ge&longs;tatores &longs;u&longs;tineant impo&longs;itum onus, <lb/>&longs;ive illud &longs;u&longs;pen&longs;um retineant in po&longs;itione vectis declivi; Si <lb/>enim ducti per O lineâ horizonti parallelâ, ducantur ex M & <lb/>N rectæ MT, & NV parallelæ lineæ directionis centri gravi<lb/>tatis EO, utique di&longs;tantiæ &longs;unt TO & VO: atqui TO ad <lb/>VO e&longs;t ut MO ad NO propter triangulorum OTM & <lb/>OVN &longs;imilitudinem; & MO ad ON habet minorem Ratio<lb/>nem quàm MS ad SN ex 8.lib.5. igitur etiam TO ad OV <lb/>habet minorem Rationem quàm MS ad SN: igitur in po&longs;ino<lb/>ne vectis declivi, M &longs;uperior laborabit ut ON, atque N infe<lb/>rior laborabit ut OM. </s>

<s>Ex his unu&longs;qui&longs;que intelligit non ad duos tantùm ge&longs;tato<lb/>res, &longs;ed etiam ad plures referenda e&longs;&longs;e, quæ hactenus diximus, <lb/>habitâ &longs;cilicet di&longs;tantiarum ratione, quibus &longs;inguli ab&longs;unt a <lb/>pondere, adeò ut qui æqualibus intervallis à pondere di&longs;tant, <lb/>æqualem conatum impendant in eo &longs;u&longs;tinendo. </s>

<s>Sic &longs;i à pon<lb/><figure id="id.017.01.448.1.jpg" xlink:href="017/01/448/1.jpg"/><lb/>dere P æqualiter di&longs;tent A & B, æqua<lb/>liter premuntur: item C & D æquali<lb/>ter di&longs;tantes ab eodem pondere P æqua<lb/>lem pre&longs;&longs;ionem recipiunt: Et &longs;i compa<lb/>rentur invicem D & B, aut C & A, <lb/>manife&longs;tum e&longs;t propinquiore<gap/> premi præ remotioribus; ac <lb/>propterea, &longs;i &longs;olùm po&longs;itionis ratio haberetur, qui robu&longs;tiores <lb/>&longs;unt, collocandi e&longs;&longs;ent in C & D, infirmiores verò in A & B: <lb/>&longs;ed quoniàm contingit inter plures &longs;odales aliquem aliquando <lb/>connivere, ideò ut plurimum extremi A & B validiores &longs;unt, <lb/>ut &longs;i fortè mediorum aliquis languidiùs conetur &longs;u&longs;tinendo, <lb/>illi faciliùs muneri &longs;uo &longs;atisfaciant. <pb xlink:href="017/01/449.jpg" pagenum="433"/><gap desc="hr tag"/></s>

<s>Sic &longs;i à pon<lb/><figure id="id.017.01.448.1.jpg" xlink:href="017/01/448/1.jpg"/><lb/>dere P æqualiter di&longs;tent A & B, æqua<lb/>liter premuntur: item C & D æquali<lb/>ter di&longs;tantes ab eodem pondere P æqua<lb/>lem pre&longs;&longs;ionem recipiunt: Et &longs;i compa<lb/>rentur invicem D & B, aut C & A, <lb/>manife&longs;tum e&longs;t propinquiores premi præ remotioribus; ac <lb/>propterea, &longs;i &longs;olùm po&longs;itionis ratio haberetur, qui robu&longs;tiores <lb/>&longs;unt, collocandi e&longs;&longs;ent in C & D, infirmiores verò in A & B: <lb/>&longs;ed quoniàm contingit inter plures &longs;odales aliquem aliquando <lb/>connivere, ideò ut plurimum extremi A & B validiores &longs;unt, <lb/>ut &longs;i fortè mediorum aliquis languidiùs conetur &longs;u&longs;tinendo, <lb/>illi faciliùs muneri &longs;uo &longs;atisfaciant. <pb xlink:href="017/01/449.jpg" pagenum="433"/><gap desc="hr tag"/></s>

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

<s><emph type="center"/><emph type="italics"/>An vis Ela&longs;tica ad aliquod Vectis genus <lb/>pertineat.<emph.end type="italics"/><emph.end type="center"/></s>

<s>QUoniam Græeis <foreign lang="greek">elatma\</foreign> tùm laminam, tùm plicam &longs;eu <lb/>flexum &longs;ignificat, atque <foreign lang="greek">e)/las<gap/>n</foreign> e&longs;t id, quod impellit; &longs;æ<lb/>pius autem chalybeas laminas in machinulis ita di&longs;ponimus, ut <lb/>primùm flexæ, deinde &longs;ibi dimi&longs;&longs;æ, dum &longs;e&longs;e re&longs;tituunt, aliud <lb/>corpus impeilant, cui motum concilient; propterea Ela&longs;mata, <lb/>&longs;eu Ela&longs;mos, huju&longs;modi laminas dicimus, quas Itali <emph type="italics"/>Su<gap/>c<emph.end type="italics"/> aut <lb/><emph type="italics"/>molle<emph.end type="italics"/> vocamus; & facultatem illam, qua &longs;ibi congiuentem fi<lb/>guram atque po&longs;itionem hæ laminæ reparant, Vim Ela&longs;ticam <lb/>appellamus. </s>

<s>QUoniam Græcis <foreign lang="greek">elatma\</foreign> tùm laminam, tùm plicam &longs;eu <lb/>flexum &longs;ignificat, atque <foreign lang="greek">e)/las<gap/>n</foreign> e&longs;t id, quod impellit; &longs;æ<lb/>pius autem chalybeas laminas in machinulis ita di&longs;ponimus, ut <lb/>primùm flexæ, deinde &longs;ibi dimi&longs;&longs;æ, dum &longs;e&longs;e re&longs;tituunt, aliud <lb/>corpus impellant, cui motum concilient; propterea Ela&longs;mata, <lb/>&longs;eu Ela&longs;mos, huju&longs;modi laminas dicimus, quas Itali <emph type="italics"/>Su&longs;te emph.end type="italics"/> aut <lb/><emph type="italics"/>molle<emph.end type="italics"/> vocamus; & facultatem illam, qua &longs;ibi congruentem fi<lb/>guram atque po&longs;itionem hæ laminæ reparant, Vim Ela&longs;ticam <lb/>appellamus. </s>

<s>Quamquam non &longs;olis laminis, &longs;ed cæteris quoque <lb/>corporibus per vim inflexis, & ad &longs;ibi debitam rectitudinem <lb/>redeuntibus, facultas hæc Ela&longs;tica tribuenda e&longs;t, quemadmo<lb/>dum flexilibus virgultorum ramis, à quibus &longs;ecundus in &longs;ylvâ <lb/>&longs;ibi cavere debet, & perticæ, quâ toreutæ utuntur in toreu<lb/>mate elaboiando, dum tornum circumagunt circumducto fu<lb/>niculo, qui depre&longs;&longs;o &longs;uppedanco perticam flectit, hæc enim, <lb/>ce&longs;&longs;ante pedis pre&longs;&longs;ione, funicuium retrahens &longs;uam &longs;ibi repa<lb/>rat rectitudinem. </s>

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Line 7133

<s>Si enim alterutra pars arcûs majorem <lb/>violentiam pa&longs;&longs;a velociùs atque validiùs præ reliquâ &longs;e move<lb/>ret, à de&longs;tinato &longs;copo &longs;agitta aberraret in dexteram aut in &longs;i<lb/>ni&longs;tram declinans. </s>

<s>Ut igitur hi<gap/>ce prænotatis ad propo&longs;itam quæ&longs;tionem acce<lb/>damus, non e&longs;t hîc &longs;ermo de laminâ in &longs;piram multiplicem in<lb/>flexâ, atque &longs;pi&longs;sè per vim contorta, quæ amoto repagulo &longs;e&longs;e <lb/>in ampliores gyros explicans &longs;ecum rapit aliud corpus extremi<lb/>tati mobili adnexum; cuju&longs;modi e&longs;t Ela&longs;ma in Automatis ho<lb/>ras indicantibus, cujus extremitati adnectitur tympanum &longs;pi<lb/>ram illam includens; dum enim ex dilatatione Ela&longs;matis in am<lb/>pliorem &longs;piram, circumagitur tympanum, adnexam catenu<lb/>lam conum circumplexam trahit, totique machinulæ motum <lb/>conciliat. </s>

<s>Ut igitur hi&longs;ce prænotatis ad propo&longs;itam quæ&longs;tionem acce<lb/>damus, non e&longs;t hîc &longs;ermo de laminâ in &longs;piram multiplicem in<lb/>flexâ, atque &longs;pi&longs;sè per vim contorta, quæ amoto repagulo &longs;e&longs;e <lb/>in ampliores gyros explicans &longs;ecum rapit aliud corpus extremi<lb/>tati mobili adnexum; cuju&longs;modi e&longs;t Ela&longs;ma in Automatis ho<lb/>ras indicantibus, cujus extremitati adnectitur tympanum &longs;pi<lb/>ram illam includens; dum enim ex dilatatione Ela&longs;matis in am<lb/>pliorem &longs;piram, circumagitur tympanum, adnexam catenu<lb/>lam conum circumplexam trahit, totique machinulæ motum <lb/>conciliat. </s>

<s>Hîc &longs;iquidem, uti nulla longitudo in con&longs;ideratio<lb/>nem cadere pote&longs;t, nullam vectis &longs;peciem habere po&longs;&longs;u<lb/>mus; nam facultas movendi non ratione po&longs;itionis exte<lb/>nuatur, ut in vecte, &longs;ed vires initio validæ &longs;en&longs;im lan<lb/>gue&longs;cunt, quia ela&longs;matis partes compre&longs;&longs;æ atque conten<lb/>tæ, pro ratione violentiæ, quam &longs;ubeunt, excutiendæ, ve<lb/>hementiùs primùm, deinde remi&longs;&longs;iùs conantur. </s>

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Line 7169

<s>Semper autem Potentiam minùs <lb/>moveri, quàm corpus, quod impellitur, con&longs;tat, quemadmo<lb/>dum ratio vectis tertij generis exigit. </s>

<s>Neque his, quæ dicta &longs;unt, adver&longs;antur percu&longs;&longs;iones, quæ <lb/>in extremitate longioris ela&longs;matis per vim inflexi, &longs;tatimque di<lb/>mi&longs;&longs;i, validiores fiunt, quam in partibus mediis; &longs;icut <gap/>p&longs;e te <lb/>docere potes, &longs;i longiu&longs;culi virgulti inflexi atque dimi&longs;&longs;i pri<lb/>mùm parti mediæ deinde extremitati manum in eodem plano <lb/>verticali con&longs;titutam opponas, quam percutiat, magis enim ex <lb/>&longs;ecundâ quàm ex primâ percu&longs;&longs;ione dolebis. </s>

<s>Neque his, quæ dicta &longs;unt, adver&longs;antur percu&longs;&longs;iones, quæ <lb/>in extremitate longioris ela&longs;matis per vim inflexi, &longs;tatimque di<lb/>mi&longs;&longs;i, validiores fiunt, quam in partibus mediis; &longs;icut ip&longs;e te <lb/>docere potes, &longs;i longiu&longs;culi virgulti inflexi atque dimi&longs;&longs;i pri<lb/>mùm parti mediæ deinde extremitati manum in eodem plano <lb/>verticali con&longs;titutam opponas, quam percutiat, magis enim ex <lb/>&longs;ecundâ quàm ex primâ percu&longs;&longs;ione dolebis. </s>

<s>Quia &longs;cilicet non <lb/>impetus &longs;olùm primo productus, &longs;ed & velocitas percutientis <lb/>cum impetu acqui&longs;ito ex motu ante percu&longs;&longs;ionem (ut &longs;uo loco <lb/>dicetur) attenditur, ut validior &longs;it ictus: majorem autem e&longs;&longs;e <lb/>partis extremæ quàm mediarum velocitatem con&longs;tat, quamvis <lb/>initio illæ impetu eodem, aut æquali moveantur. </s>

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Line 7203

<s>Unum hîc con&longs;iderandum e&longs;t, quod ad rationes vectis atti<lb/>net, videlicet, &longs;i &longs;uperiori pri&longs;matis parti, quæ re&longs;pondet ip&longs;i <lb/>AC, incumberet onus, quod faciliùs loco moveri po&longs;&longs;it, quàm <lb/>particularum complexio labefactari, aut omnino di&longs;&longs;olvi, prif<lb/>ma neque frangi, aut forta&longs;&longs;e ne flecti quidem contingeret; <pb xlink:href="017/01/456.jpg" pagenum="440"/>&longs;ed rationem vectis primi generis haberet, cujus fulcrum e&longs;&longs;et <lb/>in C, pondus in A, potentia in D. </s>

<s>At &longs;i onus impo&longs;itum nui<lb/>latenus dimoveri queat, quemadmodum cùm pri&longs;ma parieti in<lb/>fig<gap/>ur, &longs;i CB ejus &longs;it longitudinis, ut vis gravitatis ad de&longs;cen<lb/>dendum tali intervallo CD &longs;ejuncta à fulcro C plus habeat <lb/>momenti, quàm particularum coagmentatio, ne compriman<lb/>tur, aut di&longs;trahantur; tunc vectis e&longs;t &longs;ecundi generis, fulcrum <lb/>quidem habens in C, quatenus totum &longs;egmentum AC retine<lb/>tur pror&longs;us immotum, & potentia in D, pondus verò, cujus <lb/>vires vincuntur, eo loco, ubi maxima fit particularum com<lb/>pre&longs;&longs;io atque di&longs;tractio. </s>

<s>At &longs;i onus impo&longs;itum nul<lb/>latenus dimoveri queat, quemadmodum cùm pri&longs;ma parieti in<lb/>figitur, &longs;i CB ejus &longs;it longitudinis, ut vis gravitatis ad de&longs;cen<lb/>dendum tali intervallo CD &longs;ejuncta à fulcro C plus habeat <lb/>momenti, quàm particularum coagmentatio, ne compriman<lb/>tur, aut di&longs;trahantur; tunc vectis e&longs;t &longs;ecundi generis, fulcrum <lb/>quidem habens in C, quatenus totum &longs;egmentum AC retine<lb/>tur pror&longs;us immotum, & potentia in D, pondus verò, cujus <lb/>vires vincuntur, eo loco, ubi maxima fit particularum com<lb/>pre&longs;&longs;io atque di&longs;tractio. </s>

<s>Hinc factum videtur &longs;atis Ari&longs;toteli quærenti, cur faciliùs <lb/>flectatur lignum cra&longs;&longs;um cubitorum centum, quàm tenue bi<lb/>cubitum; quia nimirum in cra&longs;&longs;o ligno cubitorum centum è <lb/>pariete extantium, &longs;i ponatur &longs;imilem atque æquabilem cra&longs;&longs;i<lb/>tiem juxta totam longitudinem habere, gravitatis centrum <lb/>di&longs;tat à fulcro cubitis quinquaginta, tenue verò atque exile <lb/>lignum &longs;imilis figuræ atque materiæ centrum habet uno tantùm <lb/>cubito di&longs;tans à fulcro, & gravitas illius ad hujus gravitatem in <lb/>eâ e&longs;t Ratione, quam habent inter &longs;e ip&longs;orum lignorum moles, <lb/>quæ &longs;cilicet ex Rationibus ba&longs;ium atque longitudinum compo<lb/>nitur. </s>

Line 7295

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56; <lb/>ideóque forcipes, qua&longs;i forvicapes, dictæ &longs;unt, quòd iis for<lb/>va, ide&longs;t calida, capiantur. </s>

<s>Vis autem forcipum in eo &longs;ita e&longs;t, quòd duo vectes primi <lb/>generis AB, & CD in E connexi <lb/><figure id="id.017.01.461.1.jpg" xlink:href="017/01/461/1.jpg"/><lb/>commune hypomochlium E habent; <lb/>potentia verò in B & D longiorum <lb/>brachiorum extremitates adducens eò <lb/>validius &longs;tringit ferrum brevioribus brachiis EA & EC ap<lb/>prehen&longs;um, quo major fuerit Ratio BE ad EA: támque firma <lb/>retentio e&longs;&longs;e pote&longs;t, ut modico pueri conatu extremitates B & D <pb xlink:href="017/01/462.jpg" pagenum="446"/>vici&longs;&longs;im comprimentis, robu&longs;ti&longs;&longs;imi cuju&longs;que vires elid<gap/>ntur, <lb/>ne arreptum ferrum ex AC po&longs;&longs;it eximere. </s>

<s>Vis autem forcipum in eo &longs;ita e&longs;t, quòd duo vectes primi <lb/>generis AB, & CD in E connexi <lb/><figure id="id.017.01.461.1.jpg" xlink:href="017/01/461/1.jpg"/><lb/>commune hypomochlium E habent; <lb/>potentia verò in B & D longiorum <lb/>brachiorum extremitates adducens eò <lb/>validius &longs;tringit ferrum brevioribus brachiis EA & EC ap<lb/>prehen&longs;um, quo major fuerit Ratio BE ad EA: támque firma <lb/>retentio e&longs;&longs;e pote&longs;t, ut modico pueri conatu extremitates B & D <pb xlink:href="017/01/462.jpg" pagenum="446"/>vici&longs;&longs;im comprimentis, robu&longs;ti&longs;&longs;imi cuju&longs;que vires elidantur, <lb/>ne arreptum ferrum ex AC po&longs;&longs;it eximere. </s>

<s>Quòd &longs;i forcipibus <lb/>BA & DC utatur aliquis veterinarius vice Po&longs;tomidis (&longs;eu, ut <lb/>aliquibus Grammaticis placet Pa&longs;tomidis) equi nares, ad frænan<lb/>dam ejus tenaciam, ut loquitur Fe&longs;tus, inter longiora brachia <lb/>BE & DE contingens; jam BE & DE vectes &longs;unt &longs;ecundi ge<lb/>neris, cum illud, quod ponderis vicem &longs;ubit, inter hypomo<lb/>chlium & potentiam interjiciatur. </s>

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<lb/><s>U&longs;que adeò natura ip&longs;a Mechanicen, u&longs;umque vectis, vel pue<lb/>ros docet. </s>

<s>His adde acutas forcipulas, quibus catenularum fabricato<gap/><lb/>extremitatem fili ferrei inflectunt: ratio enim vectis poti&longs;&longs;i<lb/>mùm con&longs;i&longs;tit in validâ & firmâ ip&longs;ius fili ferrei apprehen&longs;io<lb/>ne; nam quo ad eju&longs;dem inflexionem &longs;pectat, non e&longs;t, cur nos <lb/>torqueamus, ut aliquam demum vectis umbram venemur: &longs;a<lb/>tis e&longs;t, &longs;i manubrij amplitudinem con&longs;iderantes, eámque cum-<pb xlink:href="017/01/463.jpg" pagenum="447"/>tenui apice forcipulæ, circa quem filum ferreum contorquetur, <lb/>comparantes motum potentiæ manubrio applicatæ longè ma<lb/>jorem motu particularum fili ferrei, quod flectitur, deprehen<lb/>damus; hinc quippe aucta potentiæ momenta cogno&longs;cimus. </s>

<s>His adde acutas forcipulas, quibus catenularum fabricatores <lb/>extremitatem fili ferrei inflectunt: ratio enim vectis poti&longs;&longs;i<lb/>mùm con&longs;i&longs;tit in validâ & firmâ ip&longs;ius fili ferrei apprehen&longs;io<lb/>ne; nam quo ad eju&longs;dem inflexionem &longs;pectat, non e&longs;t, cur nos <lb/>torqueamus, ut aliquam demum vectis umbram venemur: &longs;a<lb/>tis e&longs;t, &longs;i manubrij amplitudinem con&longs;iderantes, eámque cum-<pb xlink:href="017/01/463.jpg" pagenum="447"/>tenui apice forcipulæ, circa quem filum ferreum contorquetur, <lb/>comparantes motum potentiæ manubrio applicatæ longè ma<lb/>jorem motu particularum fili ferrei, quod flectitur, deprehen<lb/>damus; hinc quippe aucta potentiæ momenta cogno&longs;cimus. </s>

<s>Aliud forcipum genus frequentiùs u&longs;urpatur, quarum poti&longs;<lb/>&longs;imus u&longs;us e&longs;t in eximendis clavis, <lb/><figure id="id.017.01.463.1.jpg" xlink:href="017/01/463/1.jpg"/><lb/>& minora brachia AE & CE non <lb/>recta &longs;unt, &longs;ed curva; non &longs;olùm ut <lb/>clavus tenaciùs apprehendatur ex<lb/>cepto ejus capite intra forcipum &longs;i<lb/>num, verùm etiam ut forcipes aliam <lb/>exerceant vectis curvi rationem: cùm enim arrepto inter A & <lb/>C clauo inclinantur forcipes, ut punctum H tangat &longs;ubjectum <lb/>planum, &longs;ive paries &longs;it, &longs;ive tabula, jam hypomochlium e&longs;t <lb/>in H, & momenta potentiæ in B ad re&longs;i&longs;tentiam clavi evellen<lb/>di, &longs;unt ut BH ad HA, cùm circa punctum H perficiatur <lb/>motus. </s>

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<s>Nam &longs;i pal<lb/>mula B immota maneret, & &longs;calmus e&longs;&longs;et in C, motus remi<lb/>gis AD ad motum navis CE e&longs;&longs;et ut AB ad CB. </s>

<s>Contra <lb/>verò &longs;i aqua nihil pror&longs;us ob&longs;i&longs;teret remo (&longs;icuti continge-<pb xlink:href="017/01/473.jpg" pagenum="457"/>ret, &longs;i ille admodum lentè moveretur, aut palmula nimis <lb/>obliqua aquam finderet) tantúmque palmula retrogrederetur <lb/>per <gap/>H, quantum remex per AD <lb/><figure id="id.017.01.473.1.jpg" xlink:href="017/01/473/1.jpg"/><lb/>progreditur, immota maneret na<lb/>vis in C: id quod etiam continge<lb/>ret, &longs;i regre&longs;&longs;us BH ad progre&longs;<lb/>&longs;um AD e&longs;&longs;et in Ratione CB ad <lb/>CA. </s>

<s>Contra <lb/>verò &longs;i aqua nihil pror&longs;us ob&longs;i&longs;teret remo (&longs;icuti continge-<pb xlink:href="017/01/473.jpg" pagenum="457"/>ret, &longs;i ille admodum lentè moveretur, aut palmula nimis <lb/>obliqua aquam finderet) tantúmque palmula retrogrederetur <lb/>per BH, quantum remex per AD <lb/><figure id="id.017.01.473.1.jpg" xlink:href="017/01/473/1.jpg"/><lb/>progreditur, immota maneret na<lb/>vis in C: id quod etiam continge<lb/>ret, &longs;i regre&longs;&longs;us BH ad progre&longs;<lb/>&longs;um AD e&longs;&longs;et in Ratione CB ad <lb/>CA. </s>

<s>Quod &longs;i palmula à profluen<lb/>te rapta ex B in L majus &longs;patium <lb/>conficeret, quàm remex ex A in D <lb/>(aut &longs;altem BL ad AD e&longs;&longs;et in <lb/>majore Ratione quàm CB ad CA) <lb/>utique navis ip&longs;a retrocederet, & <lb/>&longs;calmus ex C veniret in F. </s>

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<s>Verùm quæ de cylindro in aquâ quie&longs;cente dicuntur &longs;atis <lb/>probabiliter, non omninò congruere po&longs;&longs;unt motui navis, quæ <lb/>præter motum aquæ percutientis gubernaculum promovetur à <lb/>vento aut à remigibus, & præterea non habet æquabili ductu <lb/>con&longs;titutam figuram, quemadmodum cylindrus: propterea <lb/>huic analogiæ non acquie&longs;cendum duxi. </s>

<s>Sed & illud adden-<pb xlink:href="017/01/486.jpg" pagenum="470"/>dum, quod neque de cylindro &longs;atis certus e&longs;&longs;e po&longs;&longs;um; nam &longs;i <lb/>alia fiat hypothe&longs;is, & ad totius longitudinis be&longs;&longs;em &longs;tatuatur <lb/>punctum conver&longs;ionis ita ut &longs;emi&longs;&longs;is AC &longs;it 3, AE verò &longs;it 4, <lb/>& EB &longs;it 2; Sector ACD ad Sectorem AEF e&longs;t ut 9 ad 16, <lb/>& Sector BCO ad Sectorem BEI e&longs;t ut 9 ad 4; igitur &longs;umma <lb/>priorum ad &longs;ummam po&longs;teriorum e&longs;t ut 18 ad 20. Atqui Sector <lb/>AEG ad Sectorem AEF e&longs;t ut 3 ad 4 (id quod de &longs;imili <lb/>Sectore BEH ad Sectorem BEI intelligendum e&longs;t) igitur, cum <lb/>AEF &longs;it 16, AEG e&longs;t 12, & cum BEI &longs;it 4, BEH e&longs;t 3, ac <lb/>propterea &longs;umma Sectorum AEG & BEH e&longs;t ut 15 ad &longs;um<lb/>mam Sectorum ACD & BCO ut 18. In prima autem hypo<lb/>the&longs;i quando erat AC ut 2 & AE ut 3, erat motuum Ratiout <lb/>8 ad 6 2/3, quæ e&longs;t planè eadem cum Ratione 18 ad 15. Cum <lb/>itaque eadem motuum Ratio &longs;equatur, &longs;ive AE &longs;it bes, &longs;ive <lb/>dodrans totius longitudinis AB, cur dodrantem potiùs quàm <lb/>be&longs;&longs;em pronunciemus, ni&longs;i aliunde doceamur? <lb/><gap desc="hr tag"/></s>

<s>Sed & illud adden-<pb xlink:href="017/01/486.jpg" pagenum="470"/>dum, quod neque de cylindro &longs;atis certus e&longs;&longs;e po&longs;&longs;um; nam &longs;i <lb/>alia fiat hypothe&longs;is, & ad totius longitudinis be&longs;&longs;em &longs;tatuatur <lb/>punctum conver&longs;ionis ita ut &longs;emi&longs;&longs;is AC &longs;it 3, AE verò &longs;it 4, <lb/>& EB &longs;it 2; Sector ACD ad Sectorem AEF e&longs;t ut 9 ad 16, <lb/>& Sector BCO ad Sectorem BEI e&longs;t ut 9 ad 4; igitur &longs;umma <lb/>priorum ad &longs;ummam po&longs;teriorum e&longs;t ut 18 ad 20. Atqui Sector <lb/>AEG ad Sectorem AEF e&longs;t ut 3 ad 4 (id quod de &longs;imili <lb/>Sectore BEH ad Sectorem BEI intelligendum e&longs;t) igitur, cum <lb/>AEF &longs;it 16, AEG e&longs;t 12, & cum BEI &longs;it 4, BEH e&longs;t 3, ac <lb/>propterea &longs;umma Sectorum AEG & BEH e&longs;t ut 15 ad &longs;um<lb/>mam Sectorum ACD & BCO ut 18. In prima autem hypo<lb/>the&longs;i quando erat AC ut 2 & AE ut 3, erat motuum Ratio ut <lb/>8 ad 6 2/3, quæ e&longs;t planè eadem cum Ratione 18 ad 15. Cum <lb/>itaque eadem motuum Ratio &longs;equatur, &longs;ive AE &longs;it bes, &longs;ive <lb/>dodrans totius longitudinis AB, cur dodrantem potiùs quàm <lb/>be&longs;&longs;em pronunciemus, ni&longs;i aliunde doceamur? <lb/><gap desc="hr tag"/></s>

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

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<s>Quam<lb/>quam non omnino &longs;ervetur hæc Ratio ponderis anchoræ in in<lb/>gentibus navigiis, quæ nimirum &longs;uâ gravitate maximè re<lb/>&longs;i&longs;tunt fluctuum impul&longs;ioni, ac proinde minore anchorâ opus <lb/>habent. </s>

<s>Primariæ anchoræ poti&longs;&longs;imus u&longs;us communiter e&longs;t, cùm va<lb/>lidior tempe&longs;tas navim aggreditur; &longs;ecundæ, ut navis in &longs;ta<lb/>tione quie&longs;cat; tertiam adhibent nautæ, ut duabus anchoris ad <lb/>diver&longs;a plagas con&longs;titutis (puta, alterâ ad Sub&longs;olanum, alterâ <lb/>ad Boream aut ad Borrhapeliotem<gap/>) vento & fluctibus navis re<lb/>&longs;i&longs;tat validiùs, nec abrepta à fluctibus anchoram pariter &longs;ecum <lb/>rapiat, &longs;ed tantum alternis motibus qua&longs;i circa centrum agite<lb/>tur: Quartam demum lintre transferunt procul à navi juxta lon<lb/>gitudinem funis adnexi ducentorum circiter cubitorum, quem <lb/>machinâ ad id de&longs;tinatâ colligentes accedunt ad anchoram, & <lb/>&longs;tationem commutant, aut portum intrant, &longs;eu ab illo exeunt, <lb/>ubi ce&longs;&longs;at ventus, aut adver&longs;us &longs;pirat. </s>

<s>Primariæ anchoræ poti&longs;&longs;imus u&longs;us communiter e&longs;t, cùm va<lb/>lidior tempe&longs;tas navim aggreditur; &longs;ecundæ, ut navis in &longs;ta<lb/>tione quie&longs;cat; tertiam adhibent nautæ, ut duabus anchoris ad <lb/>diver&longs;a plagas con&longs;titutis (puta, alterâ ad Sub&longs;olanum, alterâ <lb/>ad Boream aut ad Borrhapeliotem,) vento & fluctibus navis re<lb/>&longs;i&longs;tat validiùs, nec abrepta à fluctibus anchoram pariter &longs;ecum <lb/>rapiat, &longs;ed tantum alternis motibus qua&longs;i circa centrum agite<lb/>tur: Quartam demum lintre transferunt procul à navi juxta lon<lb/>gitudinem funis adnexi ducentorum circiter cubitorum, quem <lb/>machinâ ad id de&longs;tinatâ colligentes accedunt ad anchoram, & <lb/>&longs;tationem commutant, aut portum intrant, &longs;eu ab illo exeunt, <lb/>ubi ce&longs;&longs;at ventus, aut adver&longs;us &longs;pirat. </s>

<s>Ad firmandam verò navim plurimum habet momenti longi<lb/>tudo ip&longs;a rudentis; &longs;atis enim manife&longs;tum e&longs;t, quantâ vi opus <lb/>&longs;it, ut longior funis intendatur, qui ce&longs;&longs;ante externâ vi illico <lb/>&longs;inuatur; ac propterea vehementi conatu ventorum ac fluctuum <lb/>navis impellenda e&longs;t, ut rudens intentus anchoram trahat. </s>

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<s>Quare potentia E vecte EI &longs;ecundi generis deprimet em<lb/>bolum, & vecte EH primi generis attollet pondus brachij IF. </s>

<lb/><s>Hinc e&longs;t commodius accidere, &longs;i longitudo EK ferrea &longs;it, in K <pb xlink:href="017/01/501.jpg" pagenum="485"/>verò in&longs;eratur, ut firmiter cohæreat, &longs;atis validus baculus <lb/>ligneus KF; poterit enim longior e&longs;&longs;e, & faciliorem efficere <lb/>antliæ agitation<gap/>m, quin gravitas nimia indigeat multo plum<lb/>bo in E, ut præponderetur. </s>

<lb/><s>Hinc e&longs;t commodius accidere, &longs;i longitudo EK ferrea &longs;it, in K <pb xlink:href="017/01/501.jpg" pagenum="485"/>verò in&longs;eratur, ut firmiter cohæreat, &longs;atis validus baculus <lb/>ligneus KF; poterit enim longior e&longs;&longs;e, & faciliorem efficere <lb/>antliæ agitationem, quin gravitas nimia indigeat multo plum<lb/>bo in E, ut præponderetur. </s>

<s>Quòd &longs;i non placeret addere plumbum in E, & &longs;olo vecte <lb/>primi generis FD uti velles, recurrendum e&longs;&longs;et ad vim ela&longs;ti<lb/>cam, qua vel arcûs X in &longs;uperiore loco firmati nervo, vel <lb/>extremæ perticæ AM longiu&longs;culæ (ut Toreuticen exercen<lb/>tibus &longs;olemne e&longs;t) adnecteretur funis pertingens ad F, ut <lb/>ex tractione Potentiæ GF curvatus arcus, vel inflexa per<lb/>tica, ce&longs;&longs;ante potentiâ, iterum &longs;e &longs;uum in &longs;tatum re&longs;titueret, <lb/>&longs;ursúmque traheret extremitatem F, ac proinde embolum <lb/>intra modiolum B deprimeret. </s>

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<s>In Atlante Sinico hæc lego pag. </s>

<s>125. <emph type="italics"/>In ferendis oneri<lb/>bus &longs;citißimi &longs;ant Sinæ, ac rustici illic non parvum &longs;anè &longs;ta<lb/>ticis no<gap/>ris &longs;peculatoribus face&longs;&longs;erent negotium ad cau&longs;as inve<lb/>niendas ac rationes, &longs;i viderent illos tormenta etiam majora, <lb/>ac &longs;imilia pondera, ita vectibus utrinque &longs;u&longs;pendentes, ut per <lb/>arcti&longs;&longs;imas etiam montium fauces facillimè transferant; ac li<lb/>cèt præcedant alij, alij &longs;ub&longs;equantur, multí&longs;que pa&longs;&longs;ibus à pon<lb/>dere &longs;u&longs;pen&longs;o di&longs;tent, ita tamen illud vectibus ac funibus ex æquo <lb/>nôrunt dividere, ut quilibet æquale ferè &longs;entiat onus, &longs;eu paulò re<lb/>motior &longs;it, &longs;ive vicinior. </s>

<s>125. <emph type="italics"/>In ferendis oneri<lb/>bus &longs;citißimi &longs;unt Sinæ, ac rustici illic non parvum &longs;anè &longs;ta<lb/>ticis no&longs;tris &longs;peculatoribus face&longs;&longs;erent negotium ad cau&longs;as inve<lb/>niendas ac rationes, &longs;i viderent illos tormenta etiam majora, <lb/>ac &longs;imilia pondera, ita vectibus utrinque &longs;u&longs;pendentes, ut per <lb/>arcti&longs;&longs;imas etiam montium fauces facillimè transferant; ac li<lb/>cèt præcedant alij, alij &longs;ub&longs;equantur, multí&longs;que pa&longs;&longs;ibus à pon<lb/>dere &longs;u&longs;pen&longs;o di&longs;tent, ita tamen illud vectibus ac funibus ex æquo <lb/>nôrunt dividere, ut quilibet æquale ferè &longs;entiat onus, &longs;eu paulò re<lb/>motior &longs;it, &longs;ive vicinior. </s>

<s>Hoc pacto ingentia marmora, atque inte<lb/>gras etiam arbores facilè videas humeris ge&longs;tare Sinas.<emph.end type="italics"/> Hæc ibi. </s>

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<s>Verùm quia non rarò tam longus vectis, quanto <lb/>opus e&longs;&longs;et, in promptu non e&longs;t, aut ip&longs;a longitudo illum redde<lb/>ret fractioni, aut &longs;altem flexioni, magis obnoxium, aut, &longs;i peri<lb/>culo huic occurratur, tam immanis e&longs;t vectis moles, ut non levi <lb/>incommodo &longs;it eo utentibus: propterea ars aliqua excogitanda <lb/>e&longs;t, qua oblati vectis brevitatem compen&longs;atione aliquâ &longs;up<lb/>pleamus. </s>

<s>Et primò quidem &longs;i oblatus &longs;it vectis AB, habens hypomo<lb/>chlium in C, & pondus in B tam <lb/><figure id="id.017.01.513.1.jpg" xlink:href="017/01/513/1.jpg"/><lb/>grave, ut unica potentia in A non <lb/>&longs;atis &longs;it ad vincendam oneris re&longs;i<lb/>&longs;tentiam, utique &longs;i altero, aut ter<lb/>tio movente opus &longs;it, non omnes in <lb/>extremitate A vectem apprehen<lb/>dere valent, &longs;ed alter in D, tertius <lb/>in E; qui propterea, licèt &longs;inguli <lb/>æquali robore polleant, non tamen <lb/>æqualia habent momenta, &longs;ed pri<lb/>mus<gap/> AC, &longs;ecundus ut DC, ter<lb/>tius ut EC. </s>

<s>Et primò quidem &longs;i oblatus &longs;it vectis AB, habens hypomo<lb/>chlium in C, & pondus in B tam <lb/><figure id="id.017.01.513.1.jpg" xlink:href="017/01/513/1.jpg"/><lb/>grave, ut unica potentia in A non <lb/>&longs;atis &longs;it ad vincendam oneris re&longs;i<lb/>&longs;tentiam, utique &longs;i altero, aut ter<lb/>tio movente opus &longs;it, non omnes in <lb/>extremitate A vectem apprehen<lb/>dere valent, &longs;ed alter in D, tertius <lb/>in E; qui propterea, licèt &longs;inguli <lb/>æquali robore polleant, non tamen <lb/>æqualia habent momenta, &longs;ed pri<lb/>mus ut AC, &longs;ecundus ut DC, ter<lb/>tius ut EC. </s>

<s>Quapropter alter vectis GH adnectatur extremi<lb/>tati A ad angulos rectos, ut huic applicati motores plus ha<lb/>beant momenti. </s>

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<s>Tum in inferiore loco, prout opportunius ac<lb/>ciderit, vectem alium &longs;tatue HI, cui junge &longs;uperioris Vectis ex<lb/>tremitatem G fune GM: nam Ratio compo&longs;ita ex Rationibus <pb xlink:href="017/01/517.jpg" pagenum="501"/>IH ad MH, & GB ad BF dabit momentum potentiæ in I po<lb/>&longs;itæ ad attollendum pondus in D con&longs;titutum per vectem da<lb/>tum CD habentem potentiam in E. </s>

<s>H<gap/> habes tria vectis genera; nam IH e&longs;t &longs;ecundi generis, quia <lb/>pondus intelligitur in M inter potentiam I & hypomochlium H; <lb/>GF e&longs;t primi generis, quia hypomochlium B e&longs;t inter potentiam <lb/>G & pondus in F; CD e&longs;t tertij generis, quemadmodum ab ini<lb/>tio con&longs;titutum e&longs;t. </s>

<s>Hîc habes tria vectis genera; nam IH e&longs;t &longs;ecundi generis, quia <lb/>pondus intelligitur in M inter potentiam I & hypomochlium H; <lb/>GF e&longs;t primi generis, quia hypomochlium B e&longs;t inter potentiam <lb/>G & pondus in F; CD e&longs;t tertij generis, quemadmodum ab ini<lb/>tio con&longs;titutum e&longs;t. </s>

<s>Si itaque in E requireretur vis attollendi <lb/>lib.800, & &longs;it GB dupla ip&longs;ius BF, requiritur in G vis attollendi <lb/>lib.400. Si verò I H ad MH &longs;it quadrupla, requiritur in I vis <lb/>elevandi lib.100. Quare & uteris vecte tertij generis CD, quo <lb/>&longs;atis notabiliter movetur pondus D; & potentiæ momenta <lb/>auxi&longs;ti adeò, ut non &longs;olùm non requiratur potentia major <lb/>pondere attollendo, &longs;ed &longs;ufficiat potentia minor, habet quippe <lb/>motum duplo majorem, quàm &longs;it motus ponderis D; nam mo<lb/>tus extremitatis F & puncti E &longs;unt æquales; motus potentiæ I <lb/>e&longs;t quadruplus motus ip&longs;ius M; hoc e&longs;t extremitatis G; hæc ve<lb/>rò motum habet duplum motus ip&longs;ius F: igitur motus poten<lb/>tiæ I e&longs;t octuplus motûs puncti E, quod movetur motu &longs;ubqua<lb/>druplo extremitatis D: Motus igitur potentiæ I ad motum <lb/>ponderis D e&longs;t ut 8 ad 4, hoc e&longs;t ut 2 ad 1. </s>

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<s>Præterquam quod pro <lb/>variâ ip&longs;ius vectis inclinatione, onerí&longs;que illi impo&longs;iti, aut <lb/>&longs;ubjecti po&longs;itione, varia quoquè &longs;unt momenta potentiæ <lb/>vectem urgentis. </s>

<s>Hinc alia Facultas excogitata e&longs;t, quæ, <lb/>ut pluribus placet, vectis quidam &longs;it perpetuus, citrà in<lb/>commoda, quæ in &longs;implici Vecte, ut innuebam, occur<lb/>runt. <emph type="italics"/>Vectem<emph.end type="italics"/> autem appellant, quia ad vectis Rationes il<lb/>lius vim revocant; <emph type="italics"/>perpetuum<emph.end type="italics"/> verò, quia nullâ opus e&longs;t <lb/>hypomochlij mutatione: proprio tamen, tritóque jam ve<lb/>tu&longs;tate vocabulo, communiter dicitur <emph type="italics"/>Axis in Peritrochio,<emph.end type="italics"/><lb/>qua&longs;i <emph type="italics"/>Axis in Rota,<emph.end type="italics"/> ut quidam interpretantur; &longs;ed forta&longs;sè <lb/>clariùs, pleniú&longs;que vocabuli vim a&longs;&longs;equeremur, &longs;i <emph type="italics"/>Axem <lb/>Convolutum<emph.end type="italics"/> vocaremus; neque enim &longs;emper ade&longs;t Rota, <lb/>cum tamen &longs;emper inter&longs;it Convolutio, &longs;imul quippe vol<lb/>vitur, & Axis ip&longs;e, & id, cum quo Axis conjungitur. <pb xlink:href="017/01/522.jpg" pagenum="506"/>Neque hic &longs;umitur Axis quemadmodum in Cono, Cylin<lb/>dro, atque Sphærâ, pro linea rectâ, circa quam immo<lb/>tam corpora illa in gyrum aguntur; &longs;ed e&longs;t corpus &longs;uâ <lb/>præditum cra&longs;&longs;itie, cui Axis nomen inditum e&longs;t, quia ro<lb/>tarum axem imitatur, non tamen circà illum fit convolu<lb/>tio, &longs;ed ip&longs;e circa idem centrum volvitur minore motu, <lb/>circa quod potentia motu majore rotatur, quatenus illi ap<lb/>plicatur, ut ex his, quæ dicentur, manife&longs;tum fiet. <lb/><gap desc="hr tag"/></s>

<s>Hinc alia Facultas excogitata e&longs;t, quæ, <lb/>ut pluribus placet, vectis quidam &longs;it perpetuus, citrà in<lb/>commoda, quæ in &longs;implici Vecte, ut innuebam, occur<lb/>runt. <emph type="italics"/>Vectem<emph.end type="italics"/> autem appellant, quia ad vectis Rationes il<lb/>lius vim revocant; <emph type="italics"/>perpetuum<emph.end type="italics"/> verò, quia nullâ opus e&longs;t <lb/>hypomochlij mutatione: proprio tamen, tritóque jam ve<lb/>tu&longs;tate vocabulo, communiter dicitur <emph type="italics"/>Axis in Peritrochio,<emph.end type="italics"/><lb/>qua&longs;i <emph type="italics"/>Axis in Rota,<emph.end type="italics"/> ut quidam interpretantur; &longs;ed forta&longs;sè <lb/>clariùs, pleniú&longs;que vocabuli vim a&longs;&longs;equeremur, &longs;i <emph type="italics"/>Axem <lb/>Convolutum<emph.end type="italics"/> vocaremus; neque enim &longs;emper ade&longs;t Rota, <lb/>cum tamen &longs;emper inter&longs;it Convolutio, &longs;imul quippe vol<lb/>vitur, & Axis ip&longs;e, & id, cum quo Axis conjungitur. <pb xlink:href="017/01/522.jpg" pagenum="506"/>Neque hic &longs;umitur Axis quemadmodum in Cono, Cylin<lb/>dro, atque Sphærâ, pro linea rectâ, circa quam immo<lb/>tam corpora illa in gyrum aguntur; &longs;ed e&longs;t corpus &longs;uâ <lb/>præditum cra&longs;&longs;itie, cui Axis nomen inditum e&longs;t, quia ro<lb/>tarum axem imitatur, non tamen circà illum fit convolu<lb/>tio, &longs;ed ip&longs;e circa idem centrum volvitur minore motu, <lb/>circa quod potentia motu majore rotatur, quatenus illi ap<lb/>plicatur, ut ex his, quæ dicentur, manife&longs;tum fiet. <lb/><gap desc="hr tag"/></s>

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

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<s>Nam quod motus ab&longs;olutè &longs;umptus &longs;it aliquantulo <lb/>major, quia centrum ip&longs;um promovetur, nihil refert, quia <lb/>motus hic & cylindro &longs;ubjecto, & oneri, & Potentiæ commu<lb/>nis e&longs;t. </s>

<s>Præter Succulam Radiis infixis in&longs;tructam, cuju&longs;modi <gap/><lb/>e&longs;t, quæ ad hauriendas è puteis aquas vulgò u&longs;urpatur (quam<lb/>quam ob radiorum brevitatem & ip&longs;ius Axis cra&longs;&longs;itudinem non <lb/>admodum potentiæ momenta augeantur) forma alia cæmenta<lb/>riis maximè familiaris e&longs;t ad attollenda &longs;axa, lateres, & calcem, <lb/>duplici manubrio in oppo&longs;itas partes di&longs;po&longs;ito, ut quædam co<lb/>natuum con&longs;tans &longs;imilitudo &longs;ervetur, dum altero &longs;uum manu<lb/>brium deprimente, &longs;uum alter elevat: cùm enim vi brachio-<pb xlink:href="017/01/529.jpg" pagenum="513"/>deor&longs;um connitentium facilior contingat depre&longs;&longs;io, quàm ele<lb/>vatio, &longs;i manubriorum inflexio ad eandem partem collocaretur, <lb/>uterque &longs;imul deprimendo faciliùs axem converteret, at <lb/>uterque &longs;imul elevans aliquid amplius laboris &longs;ubiret; alternis <lb/>autem elevationibus atque depre&longs;&longs;ionibus labor temperatur. </s>

<s>Præter Succulam Radiis infixis in&longs;tructam, cuju&longs;modi ea <lb/>e&longs;t, quæ ad hauriendas è puteis aquas vulgò u&longs;urpatur (quam<lb/>quam ob radiorum brevitatem & ip&longs;ius Axis cra&longs;&longs;itudinem non <lb/>admodum potentiæ momenta augeantur) forma alia cæmenta<lb/>riis maximè familiaris e&longs;t ad attollenda &longs;axa, lateres, & calcem, <lb/>duplici manubrio in oppo&longs;itas partes di&longs;po&longs;ito, ut quædam co<lb/>natuum con&longs;tans &longs;imilitudo &longs;ervetur, dum altero &longs;uum manu<lb/>brium deprimente, &longs;uum alter elevat: cùm enim vi brachio-<pb xlink:href="017/01/529.jpg" pagenum="513"/>deor&longs;um connitentium facilior contingat depre&longs;&longs;io, quàm ele<lb/>vatio, &longs;i manubriorum inflexio ad eandem partem collocaretur, <lb/>uterque &longs;imul deprimendo faciliùs axem converteret, at <lb/>uterque &longs;imul elevans aliquid amplius laboris &longs;ubiret; alternis <lb/>autem elevationibus atque depre&longs;&longs;ionibus labor temperatur. </s>

<lb/><s>Cæterum quod ad potentiæ momenta attinet, parum intere&longs;t, <lb/>quam po&longs;itionem manubria habeant vici&longs;&longs;im comparata; <lb/>&longs;pectatur videlicet &longs;ingulorum longitudo & cuju&longs;modi motum <lb/>potentia manubrio applicata de&longs;cribat: Sic manubrij longitu<lb/>do GH, hoc e&longs;t potentiæ apprehen<lb/>dentis HO di&longs;tantia perpendicula<lb/>ris ab axe cylindri, qui convolvitur, <lb/><figure id="id.017.01.529.1.jpg" xlink:href="017/01/529/1.jpg"/><lb/>attendenda e&longs;t, & cùm ip&longs;ius cylin<lb/>dri, &longs;emidiametro comparanda, ut <lb/>Ratio motûs Potentiæ ad ponderis <lb/>motum innote&longs;cat, ac proinde Po<lb/>tentiæ momentum de&longs;iniatur. </s>

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<s>Si <lb/>verò non planè rectum &longs;it corpus, &longs;ed qua&longs;i procumbens incli<lb/>netur, tunc potentiæ locus definitur à perpendiculo tran&longs;eunte <lb/>per centrum gravitatis ip&longs;ius hominis. </s>

<s>Id quod dicendum pari<lb/>ter, quando tympano includitur canis (nam & à cane ingens <lb/>tympanum ver&longs;ari vid<gap/>, quo in Solarium attollebatur non me<lb/>diocris ci&longs;ta linteis recens ablutis plena) cujus gravitatis cen<lb/>trum &longs;pectandum e&longs;t, ejú&longs;que di&longs;tantia à perpendiculo tran<lb/>&longs;eunte per tympani centrum. </s>

<s>Id quod dicendum pari<lb/>ter, quando tympano includitur canis (nam & à cane ingens <lb/>tympanum ver&longs;ari vidi, quo in Solarium attollebatur non me<lb/>diocris ci&longs;ta linteis recens ablutis plena) cujus gravitatis cen<lb/>trum &longs;pectandum e&longs;t, ejú&longs;que di&longs;tantia à perpendiculo tran<lb/>&longs;eunte per tympani centrum. </s>

<s>Hinc &longs;i ex navi aliæ atque aliæ &longs;arcinæ hac machinâ extrahan<lb/>tur, is qui tympanum ver&longs;at, etiam&longs;i omnino non videat onus ex<lb/>tra machinæ domunculam po&longs;itum, facilè pronuntiabit major<lb/>ne? </s>

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<s>Acceptis itaque tribus partibus decimis <lb/>quintis addantur gradus 18, & habebitur integer peripheriæ <lb/>Quadrans in gradus 90 di&longs;tributus, qui adeò notabiles erunt, <lb/>ut etiam gradûs partes, cuju&longs;modi e&longs;t &longs;emi&longs;&longs;is, triens, & qua<lb/>drans &longs;atis clar<gap/> digno&longs;ci queant. </s>

<s>Tertiò. </s>

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<s>Hinc quoniam <lb/>ferrum cotis tritu extenuatur, eóque faciliùs, quò celeriùs cos <lb/>movetur, qui re&longs;tituunt obtu&longs;as cultorum aut novacularum <lb/>acies, lapidem ex cotariâ eductum in di&longs;cum rotundant, ut cir<lb/>ca axem centro infixum ver&longs;atilis circumagi po&longs;&longs;it. </s>

<s>Quamvis <lb/>autem non rarò eidem axi cohæreat manubrium, quo circum<lb/>ducto rotatur lapis, ut tamen minori labore adhuc etiam velo<lb/>ciùs rotetur, &longs;apienter in&longs;tituerunt amplioris rotæ ab&longs;idi exca<lb/>vatæ funem in&longs;i&longs;tere, qui<gap/>otulam eumdem cum lapide axem <lb/>habentem circumplectatur, ut minor hæc rotula amplioris ro<lb/>tæ ductum &longs;equens &longs;ecum pariter rapiat cotem; cujus periphe<lb/>ria, cùm adnexam rotulam valdè excedat, velociùs quoquè <lb/>movetur. </s>

<s>Quamvis <lb/>autem non rarò eidem axi cohæreat manubrium, quo circum<lb/>ducto rotatur lapis, ut tamen minori labore adhuc etiam velo<lb/>ciùs rotetur, &longs;apienter in&longs;tituerunt amplioris rotæ ab&longs;idi exca<lb/>vatæ funem in&longs;i&longs;tere, qui rotulam eumdem cum lapide axem <lb/>habentem circumplectatur, ut minor hæc rotula amplioris ro<lb/>tæ ductum &longs;equens &longs;ecum pariter rapiat cotem; cujus periphe<lb/>ria, cùm adnexam rotulam valdè excedat, velociùs quoquè <lb/>movetur. </s>

<s>Quantùm verò motus hic, celeritate &longs;uâ, potentiæ <lb/>motum &longs;uperet, facilè con&longs;tabit, &longs;i motuum &longs;ingulis membris <lb/>convenientium ratio ineatur. </s>

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<s>Igitur puncti in cotis peripheriâ <pb xlink:href="017/01/545.jpg" pagenum="529"/>notati motus triplo velocior e&longs;t motu &longs;imilis puncti in ro<gap/><lb/>peripheriâ: rotulæ motum definit funis, qui in convolutione ex<gap/><lb/>plicatur, hic enim pariter majoris rotæ motum metitur: octi<gap/><lb/>ergo rotula, & cum eâ lapis rotatur, dum amplior rota &longs;emel in <lb/>gyrum agitur. </s>

<s>Igitur puncti in cotis peripheriâ <pb xlink:href="017/01/545.jpg" pagenum="529"/>notati motus triplo velocior e&longs;t motu &longs;imilis puncti in rotæ <lb/>peripheriâ: rotulæ motum definit funis, qui in convolutione ex<lb/>plicatur, hic enim pariter majoris rotæ motum metitur: octies <lb/>ergo rotula, & cum eâ lapis rotatur, dum amplior rota &longs;emel in <lb/>gyrum agitur. </s>

<s>Quoniam verò rotæ &longs;emidiameter e&longs;t ad cotis <lb/>&longs;emidiametrum ut 8 ad 3 ex hypothe&longs;i, dum punctum in rotæ, <lb/>peripheriá notatum movetur velocitate ut 8, &longs;imile punctum <lb/>cotis movetur velocitate ut 24. Atqui motus rotæ cum motu <lb/>potentiæ manubrio applicatæ comparatus e&longs;t ut 4 ad 1, ex hy<lb/>pothe&longs;i; igitur &longs;i duæ Rationes 1 ad 4, & 8 ad 24 componan<lb/>tur, erit Ratio motus potentiæ ad motum cotis ut 1 ad 12. Sunt <lb/>hìc itaque duo Axes in Peritrochiis &longs;uis compo&longs;iti, & Potentia <lb/>Axibus applicata intelligitur; cùm enim in Verticali plano lapis <lb/>ip&longs;e ver&longs;etur &longs;uper polos læves atque politos, non admodum re<lb/>pugnat motui; impre&longs;&longs;us autem impetus aliquandiu manens <lb/>potentiam ip&longs;am juvat. </s>

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<s>Sed & alia potentia hìc con&longs;ideranda occurrit: adjunctum <lb/>enim &longs;phæroides H, quod mediocriter grave &longs;tatuitur, non &longs;o<lb/>lùm &longs;uo pondere juvat, ut cu&longs;pis paulò pre&longs;&longs;iùs adhæreat &longs;ub<lb/>jectæ laminæ, verùm etiam concepto in convolutione impetu <lb/>dum explicatur funis, pergit ad ea&longs;dem partes moveri, expli<lb/>catúmque funem iterum circa baculum contorquens cogit <lb/>tran&longs;ver&longs;arium GI a&longs;cendere versùs B, quo vici&longs;&longs;im ab artificis <lb/>manu depre&longs;&longs;o in contrarias partes volvitur. </s>

<s>Impetus igitur <lb/>&longs;phæroidi H impre&longs;&longs;us, dum illud movet, rationem habet po<lb/>tentiæ cu&longs;pidem in gyrum contorquentis, cujus momenta ex <lb/>di&longs;tantiâ ab axe, circa quem efflcitur motus, definienda &longs;unt. <pb xlink:href="017/01/549.jpg" pagenum="533"/><gap desc="hr tag"/></s>

<s>Impetus igitur <lb/>&longs;phæroidi H impre&longs;&longs;us, dum illud movet, rationem habet po<lb/>tentiæ cu&longs;pidem in gyrum contorquentis, cujus momenta ex <lb/>di&longs;tantiâ ab axe, circa quem efficitur motus, definienda &longs;unt. <pb xlink:href="017/01/549.jpg" pagenum="533"/><gap desc="hr tag"/></s>

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

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<s>Placeat jam triplicem hunc Axem cum unico illo comparate, <lb/>qui &longs;olus adhiberetur, &longs;i machina &longs;implex e&longs;&longs;et, & non compo<lb/>&longs;ita: ille &longs;iquidem &longs;i palmaris diametri e&longs;&longs;et, adjunctum tympa<lb/>num haberet altitudinis palmorum centum; in quo con&longs;truen<lb/>do quàm multâ materiâ opus e&longs;&longs;et, quantoque artificio compin<lb/>genda, ne &longs;uâ mole labefactata di&longs;&longs;olveretur? </s>

<s>Triplex autem hic <lb/>Axis cum &longs;uis duobus tympanis, & manubrio (præterquam quod <lb/>multipliciter di&longs;poni pote&longs;t pro loci opportunitate, & potentiæ <lb/>moventis commodo) non &longs;olùm ad altitudinem <expan abbr="palmor&utilde;">palmorum</expan> viginti <lb/><expan abbr="nõ">non</expan> a&longs;&longs;urgeret, &longs;ed longè infra <expan abbr="illã">illam</expan> &longs;ub&longs;i&longs;teret, à <expan abbr="quoc&utilde;que">quocunque</expan> artifice <lb/>nullo negotio con&longs;trueretur, ab alio in <expan abbr="ali&utilde;loc">aliulloc</expan><gap/> facillimè <expan abbr="trãsfer-retur">transfer<lb/>retur</expan>, levíque <expan abbr="di&longs;p&etilde;dio">di&longs;pendio</expan> pararetur, ut cuique <expan abbr="cõ&longs;iderãti">con&longs;ideranti</expan> <expan abbr="obvi&utilde;">obvium</expan> e&longs;t. </s>

<s>Triplex autem hic <lb/>Axis cum &longs;uis duobus tympanis, & manubrio (præterquam quod <lb/>multipliciter di&longs;poni pote&longs;t pro loci opportunitate, & potentiæ <lb/>moventis commodo) non &longs;olùm ad altitudinem <expan abbr="palmor&utilde;">palmorum</expan> viginti <lb/><expan abbr="nõ">non</expan> a&longs;&longs;urgeret, &longs;ed longè infra <expan abbr="illã">illam</expan> &longs;ub&longs;i&longs;teret, à <expan abbr="quoc&utilde;que">quocunque</expan> artifice <lb/>nullo negotio con&longs;trueretur, ab alio in <expan abbr="ali&utilde;">alium</expan> <expan abbr="loc&utilde;">locum</expan> facillimè <expan abbr="trãsfer-retur">transfer<lb/>retur</expan>, levíque <expan abbr="di&longs;p&etilde;dio">di&longs;pendio</expan> pararetur, ut cuique <expan abbr="cõ&longs;iderãti">con&longs;ideranti</expan> <expan abbr="obvi&utilde;">obvium</expan> e&longs;t. </s>

<s>Hocautem, quod in tribus Axibus explicatum e&longs;t, de pluribus <lb/>etiam <expan abbr="dict&utilde;">dictum</expan> intelligatur: nam &longs;i Rationes &longs;ingulæ peritrochij ad <lb/>&longs;uum axem con&longs;iderentur, & &longs;imul componantur multiplicando <lb/>invicem omnes Rationum terminos Antecedentes, item omnes <lb/>Con&longs;equentes, ut habeatur novus Antecedens & novus Con&longs;e<lb/>quens, apparebit Ratio motûs potentiæ ad <expan abbr="mot&utilde;">motum</expan> ponderis, adeó<lb/>que gravitatis ponderis ad virtutem potentiæ. </s>

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<s>Cum igitur rota movens &longs;uam vim exerceat apice den<lb/>tis, integra &longs;emper illius diameter aut &longs;emidiameter con&longs;i<lb/>deranda e&longs;t; at rota, quæ urgetur, cum non in eodem <lb/>puncto recipiat moventis impul&longs;ionem, non e&longs;t ab&longs;olu<lb/>tè attendenda integra illius diameter aut &longs;emidiameter, <lb/>&longs;ed potiùs mediocris quædam inter maximam & mini<lb/>mam à centro di&longs;tantiam eligenda e&longs;t, ut alter Rationis <lb/>terminus habeatur. </s>

<s>Ex quo vides (&longs;i res &longs;ubtiliter elime<lb/>tur) non parum intere&longs;&longs;e, utrùm minor rota majorem ur<lb/>geat, an <gap/>è contrario major minorem propellat. </s>

<s>Ex quo vides (&longs;i res &longs;ubtiliter elime<lb/>tur) non parum intere&longs;&longs;e, utrùm minor rota majorem ur<lb/>geat, an è contrario major minorem propellat. </s>

<s>Concipe <lb/>enim majoris rotæ integram &longs;emidiametrum e&longs;&longs;e particula<lb/>rum 100, & talem e&longs;&longs;e dentium inci&longs;uram, ut angulus, <lb/>in quo ip&longs;i dentes coëunt, di&longs;tet à centro particulis 94: <lb/>rotæ autem minoris, quæ &longs;uos dentes illius dentibus impli<lb/>cat, &longs;emidiameter integra &longs;it &longs;imilium particuiarum 20, & <lb/>angulus concursûs dentium di&longs;tet à centro particulis 14. Uti<lb/>que &longs;i minor majorem urgeat illius Radius e&longs;t ut 20, hu<lb/>jus verò e&longs;t ut 97: contra autem &longs;i major pellat minorem <lb/>illius Radius e&longs;t ut 100, hujus ut 17. Quare &longs;ingulæ com<lb/>paratæ cum iis, quæ &longs;ecum communem habent axem, di<lb/>ver&longs;am con&longs;tituunt Rationem: &longs;i enim major rota urgea<lb/>tur à minore &longs;ibi proximâ, adeò ut &longs;ecunda minor movea<lb/>tur ad motum majoris in eodem axe, & Ratio &longs;it ut 20 ad <lb/>97, &longs;i majore proximâ urgente minorem moveretur major <lb/>ad motum minoris in eodem axe, hujus minoris motus ad <lb/>motum &longs;uæ majoris non e&longs;&longs;et pariter ut 20 ad 97, &longs;ed ut 17 <lb/>ad 100, quæ e&longs;t minor Ratio. <pb xlink:href="017/01/572.jpg" pagenum="556"/><gap desc="hr tag"/></s>

<s>Concipe <lb/>enim majoris rotæ integram &longs;emidiametrum e&longs;&longs;e particula<lb/>rum 100, & talem e&longs;&longs;e dentium inci&longs;uram, ut angulus, <lb/>in quo ip&longs;i dentes coëunt, di&longs;tet à centro particulis 94: <lb/>rotæ autem minoris, quæ &longs;uos dentes illius dentibus impli<lb/>cat, &longs;emidiameter integra &longs;it &longs;imilium particuiarum 20, & <lb/>angulus concursûs dentium di&longs;tet à centro particulis 14. Uti<lb/>que &longs;i minor majorem urgeat illius Radius e&longs;t ut 20, hu<lb/>jus verò e&longs;t ut 97: contra autem &longs;i major pellat minorem <lb/>illius Radius e&longs;t ut 100, hujus ut 17. Quare &longs;ingulæ com<lb/>paratæ cum iis, quæ &longs;ecum communem habent axem, di<lb/>ver&longs;am con&longs;tituunt Rationem: &longs;i enim major rota urgea<lb/>tur à minore &longs;ibi proximâ, adeò ut &longs;ecunda minor movea<lb/>tur ad motum majoris in eodem axe, & Ratio &longs;it ut 20 ad <lb/>97, &longs;i majore proximâ urgente minorem moveretur major <lb/>ad motum minoris in eodem axe, hujus minoris motus ad <lb/>motum &longs;uæ majoris non e&longs;&longs;et pariter ut 20 ad 97, &longs;ed ut 17 <lb/>ad 100, quæ e&longs;t minor Ratio. <pb xlink:href="017/01/572.jpg" pagenum="556"/><gap desc="hr tag"/></s>

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

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<lb/><s>Pote&longs;t autem po&longs;t aliquantulum motum &longs;ubinde promoveri <pb xlink:href="017/01/584.jpg" pagenum="568"/>extremitas E vectis, ut manife&longs;tum e&longs;t. </s>

<s>Quod &longs;i Ergatâ ip<gap/><lb/>uteremur ad &longs;en&longs;im demittendum in plano inclinato onus <lb/>quoddam ingens, & timeretur, ne vis gravitatis vinceret co<lb/>natum hominum in D reluctantium, ne præceps delabatur <lb/>onus; adhibeatur vectis EF, quo &longs;en&longs;im dimi&longs;&longs;o certiùs reti<lb/>netur onus, & lentiùs de&longs;cendit. <lb/><gap desc="hr tag"/></s>

<s>Quod &longs;i Ergatâ ipsâ <lb/>uteremur ad &longs;en&longs;im demittendum in plano inclinato onus <lb/>quoddam ingens, & timeretur, ne vis gravitatis vinceret co<lb/>natum hominum in D reluctantium, ne præceps delabatur <lb/>onus; adhibeatur vectis EF, quo &longs;en&longs;im dimi&longs;&longs;o certiùs reti<lb/>netur onus, & lentiùs de&longs;cendit. <lb/><gap desc="hr tag"/></s>

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

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<s>Quod &longs;i pondus traha<lb/>tur in plano horizontali, &longs;ola potentia e&longs;t, quæ adversùs cla<lb/>vum &longs;uam vim exercet &longs;uperando re&longs;i&longs;tentiam ponderis, quod <lb/>nihil agit adversùs clavum, &longs;ed &longs;uâ gravitate urget &longs;ubjectum <lb/>planum. </s>

<s>Ut autem manife&longs;tè deprehendas nihil e&longs;&longs;e Trochleis cum <lb/>Vecte commercij, duo ligna accipe, cuju&longs;cumque tandem fi<lb/>guræ: &longs;ingulis tria in&longs;int foramina, quoad ejus fieri poterit, ex<lb/>qui&longs;itè polita, ut minore conflictu funis excurrere po&longs;&longs;it: de<lb/>inde funis alterno ab uno in alterum lignum ductu per forami<lb/>na trajiciatur: Nam &longs;i alterum lignorum huju&longs;modi certo in lo<lb/>co firmetur, alteri adnectatur pondus, tum funis extremitatem <lb/>arripiens trahas, idem planè præ&longs;tabis, qu<gap/>d adhibitis orbicu<lb/>lis in communibus Trochleis: & tamen nullum hîc vectis ve&longs;ti<lb/>gium apparet. </s>

<s>Ut autem manife&longs;tè deprehendas nihil e&longs;&longs;e Trochleis cum <lb/>Vecte commercij, duo ligna accipe, cuju&longs;cumque tandem fi<lb/>guræ: &longs;ingulis tria in&longs;int foramina, quoad ejus fieri poterit, ex<lb/>qui&longs;itè polita, ut minore conflictu funis excurrere po&longs;&longs;it: de<lb/>inde funis alterno ab uno in alterum lignum ductu per forami<lb/>na trajiciatur: Nam &longs;i alterum lignorum huju&longs;modi certo in lo<lb/>co firmetur, alteri adnectatur pondus, tum funis extremitatem <lb/>arripiens trahas, idem planè præ&longs;tabis, quod adhibitis orbicu<lb/>lis in communibus Trochleis: & tamen nullum hîc vectis ve&longs;ti<lb/>gium apparet. </s>

<s>Certè in majoribus navigiis malus hinc & hinc <pb xlink:href="017/01/609.jpg" pagenum="593"/>navis lateribus alligatur, ut rectam po&longs;itionem &longs;ervet: quia au<lb/>tem rudentes aliquando remittuntur, ut in majore æ&longs;tu, illó&longs;<lb/>que intendi oportet, propterea duo huju&longs;modi ligna in Ellip&longs;im <lb/>ferè deformata (vel potiùs in &longs;phæroides Hyperbolium factâ <lb/>conver&longs;ione non circa Axem, &longs;ed circa ordinatim Applicatam) <lb/>alterum navis lateri, alterum rudenti adnectunt nautæ, & fu<lb/>nem non adeò cra&longs;&longs;um per foramina alterno ductu trajiciunt, <lb/>quem etiam axungiâ, aut aliâ pinguedine inficiunt, ut faciliùs <lb/>excurrat. </s>

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<s>Nemo negat in majoribus <lb/>circulis, quorum major e&longs;t Radius, ab extremitate Radij ma<lb/>jorem arcum de&longs;cribi, quàm à Radio minore, &longs;i tempore eodem <lb/>&longs;imilem arcum de&longs;cribant; &longs;unt &longs;cilicet arcus &longs;imiles in Ratione <lb/>Radiorum; &longs;ed quando rotulæ inæquales commune centrum <lb/>non habent, neque Radij omnino &longs;imul moventur, qua&longs;i minor <lb/>&longs;it pars majoris, quid prohibet eodem tempore arcus quídem <lb/>æquales, &longs;ed di&longs;&longs;imiles, de&longs;cribi? </s>

<s>Nam &longs;i potentia trahens de<lb/>&longs;cendat per &longs;patium palmare, &longs;ive rotula major &longs;it, &longs;ive minor, <lb/><gap/> dus a&longs;cendit per palmum, & punctum in orbitâ rotulæ tam <lb/>majoris quàm minoris notatum de&longs;cribit arcum palmarem: hoc <lb/>autem tantummodo differunt, quod in univer&longs;o ponderis ele<lb/>vati motu rotula minor &longs;æpiùs convertitur quàm major, & con<lb/>ver&longs;ionum numeri &longs;unt reciprocè in Ratione Radiorum: &longs;ic &longs;i <lb/>Radius minor ad majorem &longs;it ut 4 ad 9, novem conver&longs;iones <lb/>minoris eodem tempore fiunt, ac quatuor conver&longs;iones majoris <lb/>rotulæ, &longs;i à Potentiâ æqualiter moveantur. </s>

<s>Nam &longs;i potentia trahens de<lb/>&longs;cendat per &longs;patium palmare, &longs;ive rotula major &longs;it, &longs;ive minor, <lb/>pondus a&longs;cendit per palmum, & punctum in orbitâ rotulæ tam <lb/>majoris quàm minoris notatum de&longs;cribit arcum palmarem: hoc <lb/>autem tantummodo differunt, quod in univer&longs;o ponderis ele<lb/>vati motu rotula minor &longs;æpiùs convertitur quàm major, & con<lb/>ver&longs;ionum numeri &longs;unt reciprocè in Ratione Radiorum: &longs;ic &longs;i <lb/>Radius minor ad majorem &longs;it ut 4 ad 9, novem conver&longs;iones <lb/>minoris eodem tempore fiunt, ac quatuor conver&longs;iones majoris <lb/>rotulæ, &longs;i à Potentiâ æqualiter moveantur. </s>

<s>Quare æquali tem<lb/>pore major Radius non movetur per majus &longs;patium; movetur <lb/>&longs;iquidem æqualiter cum potentiâ trahente & pondere a&longs;cen<lb/>dente, quemadmodum & minor Radius. </s>

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<s>Sed &longs;i quem admiratio capiat duodecim orbiculis in &longs;ex tro<lb/>chleas di&longs;tributis tantum pondus moveri, admiretur adhuc am<lb/>pliùs <expan abbr="ii&longs;d&etilde;">ii&longs;dem</expan> duodecim orbiculis in duodecim &longs;implices trochleas <lb/>di&longs;tinctis, quæ binæ & binæ conjungentur, longè majus pondus <lb/>po&longs;&longs;e trahi. </s>

<s>Nam &longs;i trochleæ mobili, cui alligatur pondus, etiam <lb/>funis extremitas adnectatur, jam &longs;ingulæ Trochlearum conjuga<lb/>tiones dant rationem triplam; &longs;unt igitur &longs;ex Rationes triplæ <lb/>compo&longs;itæ; ac propterea prima conjugatio dat Rationem 3 ad 1; <lb/>&longs;ecunda 9 ad 1; tertia 27 ad 1; quarta 81 ad 1; quinta 243 ad 1; <lb/>&longs;exta 7<gap/>9 ad 1: & hæc e&longs;t Ratio motûs po<lb/><figure id="id.017.01.625.1.jpg" xlink:href="017/01/625/1.jpg"/><lb/>tentiæ ad motum ponderis. </s>

<s>Nam &longs;i trochleæ mobili, cui alligatur pondus, etiam <lb/>funis extremitas adnectatur, jam &longs;ingulæ Trochlearum conjuga<lb/>tiones dant rationem triplam; &longs;unt igitur &longs;ex Rationes triplæ <lb/>compo&longs;itæ; ac propterea prima conjugatio dat Rationem 3 ad 1; <lb/>&longs;ecunda 9 ad 1; tertia 27 ad 1; quarta 81 ad 1; quinta 243 ad 1; <lb/>&longs;exta 729 ad 1: & hæc e&longs;t Ratio motûs po<lb/><figure id="id.017.01.625.1.jpg" xlink:href="017/01/625/1.jpg"/><lb/>tentiæ ad motum ponderis. </s>

<s>Quare &longs;i po<lb/>tentia conetur ut 50, ducatur 729 per 50, <lb/>& potentia trahere valebit pondus libra<lb/>rum 36450. At verò &longs;i duodecim illæ &longs;im<lb/>plices trochleæ <expan abbr="nõ">non</expan> fuerint conjugatæ, &longs;ed <lb/>&longs;ingulæ &longs;eor&longs;im &longs;uos habeant funes, ita ut <lb/>primæ adnectatur <expan abbr="põdus">pondus</expan>, & &longs;ecundæ jun<lb/>gatur extremitas funis ductarij primæ, at<lb/>que ita deinceps, jam multo majus erit <lb/>momentum potentiæ; erunt &longs;cilicet duo<lb/>decim Rationes duplæ <expan abbr="cõpo&longs;itæ">compo&longs;itæ</expan>. </s>

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<s>Verùm hoc fieri omnino non po&longs;&longs;e deprehendes, &longs;i ob&longs;erva<lb/>veris, nunquam hoc pacto adduci pondus ni&longs;i per quintam par<lb/>tem reliqui &longs;patij; quare aliquid &longs;emper relinquitur, quin ad <lb/>de&longs;tinatum locum pondus perveniat. </s>

<s>Si placuerit tamen hunc <lb/>laborem a&longs;&longs;umere in disjungendis po&longs;terioribus trochleis, prio<lb/>restrochleas ita invicem disjunctas initio colloca, ut earum in<lb/>tervallum &longs;it &longs;altem &longs;e&longs;quialterum &longs;patij, per quod pondus mo<lb/>veri oportet; &longs;ic enim repetito quinquies trahendi labore obti<lb/>nebis propo&longs;itum motum: primâ videlicet tractione deducitur <lb/>pondus per totius intervalli 1/5; in &longs;ecunda per eju&longs;dem inter<lb/>valli (4/25); in tertiâ per (16/125); in quartâ per (6<gap/>/625); in quintâ per (256/1125); <lb/>quæ partes &longs;i in &longs;ummam redigantur, dant (2101/3125), hoc e&longs;t paulo <lb/>amplius quàm 2/3 propo&longs;iti intervalli, quantum &longs;atis e&longs;t ad perfi<lb/>ciendum de&longs;tinatum &longs;patium. </s>

<s>Si placuerit tamen hunc <lb/>laborem a&longs;&longs;umere in disjungendis po&longs;terioribus trochleis, prio<lb/>restrochleas ita invicem disjunctas initio colloca, ut earum in<lb/>tervallum &longs;it &longs;altem &longs;e&longs;quialterum &longs;patij, per quod pondus mo<lb/>veri oportet; &longs;ic enim repetito quinquies trahendi labore obti<lb/>nebis propo&longs;itum motum: primâ videlicet tractione deducitur <lb/>pondus per totius intervalli 1/5; in &longs;ecunda per eju&longs;dem inter<lb/>valli (4/25); in tertiâ per (16/125); in quartâ per (64/625); in quintâ per (256/1125); <lb/>quæ partes &longs;i in &longs;ummam redigantur, dant (2101/3125), hoc e&longs;t paulo <lb/>amplius quàm 2/3 propo&longs;iti intervalli, quantum &longs;atis e&longs;t ad perfi<lb/>ciendum de&longs;tinatum &longs;patium. </s>

<s>Ubi vides; &longs;i intervallum a&longs;<lb/>&longs;umptum fui&longs;&longs;et paulo majus quàm duplum de&longs;tinati &longs;patij, ter<lb/>tiâ tractione ab&longs;olvi propo&longs;itum motum; nam 1/5, (1/25), (16/125) &longs;i colli<lb/>gantur in &longs;ummam, dant (61/125), hoc e&longs;t ferè 1/2. At &longs;i duobus &longs;im<lb/>plicibus orbiculis utaris, quibus compo&longs;itis potentia habet mo-<pb xlink:href="017/01/628.jpg" pagenum="612"/>mentum quadruplum, etiam&longs;i &longs;ecundi orbiculi funem &longs;tatuas <lb/>æqualem funi prioris orbiculi, cui adnectitur pondus, facilli<lb/>mum e&longs;t orbiculum &longs;ecundum retrahere ad orbiculum primum, <lb/>po&longs;tquam hic primâ tractione ab&longs;olvit &longs;emi&longs;&longs;em &longs;patij inter pon<lb/>dus & paxillum, cui alligatur funis; & &longs;ecundâ tractione ab<lb/>&longs;olvit quadrantem totius intervalli initio con&longs;tituti: Quare &longs;a<lb/>tis fuerit funem prioris orbiculi æquari intervallo &longs;e&longs;quitertio <lb/>longitudinis &longs;patij, per quod deducendum e&longs;t pondus. </s>

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<s>Quod &longs;i magis arrideret non continua convolutione flabel<lb/>la circumagi, &longs;ed alternâ quadam modò in dextram, modò <lb/>in &longs;ini&longs;tram inflexione agitari; Axi, quem funis ductarius <lb/>complectitur, infige rotam dentatam, cujus dentes incurrant <lb/>in pinnulas fu&longs;i perpendicularis flabella &longs;u&longs;tinentes, quemad<lb/>modum in Tempore horologij: &longs;imili enim ratione, ac Tem<lb/>pus, ultrò citróque remeabunt flabella, & aërem in oppo&longs;itas <lb/>partes commovebunt. </s>

<s>Cùm verò ant<gap/> motum appo&longs;ito manu<lb/>brio convolvendus erit Axis, ut funem ductarium recipiat, at<lb/>que trochlea inferior cum pondere attollatur, ita fu&longs;um pau<lb/>li&longs;per elevare oportebit, ut ejus pinnulæ non occurrant denti<lb/>bus rotæ, ni&longs;i cùm iterum fu&longs;us &longs;uum in locum re&longs;tituetur. </s>

<s>Cùm verò antè motum appo&longs;ito manu<lb/>brio convolvendus erit Axis, ut funem ductarium recipiat, at<lb/>que trochlea inferior cum pondere attollatur, ita fu&longs;um pau<lb/>li&longs;per elevare oportebit, ut ejus pinnulæ non occurrant denti<lb/>bus rotæ, ni&longs;i cùm iterum fu&longs;us &longs;uum in locum re&longs;tituetur. </s>

<lb/><s>Hac alternatione diuturnior erit motus. </s>

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<s><emph type="center"/><emph type="italics"/>De Cuneo & Percu&longs;sionibus.<emph.end type="italics"/><emph.end type="center"/></s>

<s>MECHANICARUM Facultatum Quarta &longs;pecies, <lb/>Cuneus, præ&longs;entem di&longs;putationem exigit: neque <lb/>enim &longs;olam corporum gravitatem, ob id ip&longs;um <lb/>quia gravitas e&longs;t, vincere oportet, ac loco dimo<lb/>vere, quemadmodum Vecte, <gap/>xe, & Trochleis, <lb/>&longs;ed etiam &longs;æpè conjunctas corporum partes, aut cohærentia <lb/>proximè corpora &longs;ejungere atque divellere: id quod Cuneo <lb/>poti&longs;&longs;imùm perficimus, & iis, quæ ad Cunei rationem &longs;pecta<lb/>re videntur. </s>

<s>MECHANICARUM Facultatum Quarta &longs;pecies, <lb/>Cuneus, præ&longs;entem di&longs;putationem exigit: neque <lb/>enim &longs;olam corporum gravitatem, ob id ip&longs;um <lb/>quia gravitas e&longs;t, vincere oportet, ac loco dimo<lb/>vere, quemadmodum Vecte, Axe, & Trochleis, <lb/>&longs;ed etiam &longs;æpè conjunctas corporum partes, aut cohærentia <lb/>proximè corpora &longs;ejungere atque divellere: id quod Cuneo <lb/>poti&longs;&longs;imùm perficimus, & iis, quæ ad Cunei rationem &longs;pecta<lb/>re videntur. </s>

<s>Quoniam verò in iis, in quibus præcipuè Cu<lb/>nei vis elucet, percu&longs;&longs;ione utimur, quæ &longs;anè in paulò lon<lb/>giorem &longs;ermonem nos vocat, non erit abs re aliquanto latiùs <lb/>Percu&longs;&longs;ionis naturam explicare, ut potentiæ Cuneo applicatæ <lb/>virtus manife&longs;ta fiat. </s>

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<lb/><s>Sunt autem corpora illa (quantum quidem ad præ&longs;entem <lb/>tractationem &longs;pectat) partium &longs;eparationi difficiliùs obnoxia, <lb/>quorum materia ita probè &longs;ubacta e&longs;t, ut eorum elementa in <lb/>minuti&longs;&longs;imas particulas conci&longs;a, & qua&longs;i individua corpu&longs;cula <lb/>in unam naturam inob&longs;ervabili permi&longs;tione temperata coalue<lb/>rint eâ tantùm humoris copiâ, quæ &longs;atis fuerit ad illa firmiter <lb/>agglutinanda. </s>

<s>Ex quo fit, ut huju&longs;modi corpora &longs;olidiora &longs;int, <lb/>minú&longs;que con&longs;picuas inanitates admittant, atque proinde, &longs;i <lb/>expoliantur, &longs;uperficiem induant lævem & undique æquabi<lb/>lem<gap/>id quod cæteris non accidit, quorum particulæ frequenti<lb/>bus hiatibus interci&longs;æ, cùm aliæ emineant, aliæ &longs;uperentur, <lb/>&longs;emper aliquid habeant a&longs;peritatis; quemadmodum animadver<lb/>tere poterit, qui&longs;quis lapides cum marmoribus comparaverit. </s>

<s>Ex quo fit, ut huju&longs;modi corpora &longs;olidiora &longs;int, <lb/>minú&longs;que con&longs;picuas inanitates admittant, atque proinde, &longs;i <lb/>expoliantur, &longs;uperficiem induant lævem & undique æquabi<lb/>lem: id quod cæteris non accidit, quorum particulæ frequenti<lb/>bus hiatibus interci&longs;æ, cùm aliæ emineant, aliæ &longs;uperentur, <lb/>&longs;emper aliquid habeant a&longs;peritatis; quemadmodum animadver<lb/>tere poterit, qui&longs;quis lapides cum marmoribus comparaverit. </s>

<s>Si igitur ex &longs;olido corpore avellenda e&longs;t particula aliqua, hæc <lb/>i&longs;táque disjungenda e&longs;t à circum&longs;tantibus particulis, quibus <lb/>conjungitur, neque fieri pote&longs;t, ut illa moveatur, quin proxi<lb/>marum particularum aliæ motui oppo&longs;itæ impellantur, aliæ <lb/>di&longs;trahantur; omnes autem ægrè à &longs;tatu &longs;ibi &longs;ecundùm natu<lb/>ram debito recedentes repugnant: quò verò plures particulæ <lb/>vim &longs;ubire coguntur, eò major e&longs;t re&longs;i&longs;tentia plurium qua&longs;i col<lb/>latis viribus &longs;imul repugnantium. </s>

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<s>Et primò <expan abbr="ob&longs;ervand&utilde;">ob&longs;ervandum</expan> e&longs;t cuneum e&longs;&longs;e LBED, cujus vertex <lb/>e&longs;t angulus <expan abbr="cõtingentiæ">contingentiæ</expan> factus à peripheriâ dati circuli, & à pe<lb/>ripheriâ circuli, quem circa centrum C in motu de&longs;cribit extre<lb/>mitas D. </s>

<s>Deinde &longs;emiperipheria BGH à potentiâ de&longs;cripta in <lb/>motu (& e&longs;t ex hypothe&longs;i <expan abbr="parti&utilde;">partium</expan> 355, <expan abbr="quar&utilde;">quarum</expan> Radius CB e&longs;t 113) <lb/>dividatur in partes æquales duodecim, ita <gap/> &longs;ingulæ re&longs;pon<lb/>deant gradibus 15, & &longs;ingulis competant paetes 29 1/2. Similiter <lb/>&longs;emiperipheria DOL in 12 æquales partes ingulas gr.15. divi<lb/>datur: adeò ut cùm linea BD circa punctum C circumacta an<lb/>gulum gr. 15 de&longs;crip&longs;erit, potentia &longs;it progre&longs;&longs;s per partes 29 1/2. <lb/>Examinandum e&longs;t, quanto &longs;patio interim pro<gap/> ellatur pondus, <lb/>quod erat in D, versùs H. </s>

<s>Deinde &longs;emiperipheria BGH à potentiâ de&longs;cripta in <lb/>motu (& e&longs;t ex hypothe&longs;i <expan abbr="parti&utilde;">partium</expan> 355, <expan abbr="quar&utilde;">quarum</expan> Radius CB e&longs;t 113) <lb/>dividatur in partes æquales duodecim, ita ut &longs;ingulæ re&longs;pon<lb/>deant gradibus 15, & &longs;ingulis competant paetes 29 1/2. Similiter <lb/>&longs;emiperipheria DOL in 12 æquales partes ingulas gr.15. divi<lb/>datur: adeò ut cùm linea BD circa punctum C circumacta an<lb/>gulum gr. 15 de&longs;crip&longs;erit, potentia &longs;it progre&longs;&longs;s per partes 29 1/2. <lb/>Examinandum e&longs;t, quanto &longs;patio interim propellatur pondus, <lb/>quod erat in D, versùs H. </s>

<s>Sit angulus DCO, hoc e&longs;t arcus DO, gr. 1<gap/>: ducta intelli<lb/>gatur recta CO u&longs;que in N peripheriam dati ci <gap/>uli; e&longs;t igitur <lb/>ON motus ponderis ex D ver&longs;us H. </s>

<s>Sit angulus DCO, hoc e&longs;t arcus DO, gr. 15: ducta intelli<lb/>gatur recta CO u&longs;que in N peripheriam dati circuli; e&longs;t igitur <lb/>ON motus ponderis ex D ver&longs;us H. </s>

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<s>Ex his manife&longs;tò con&longs;tat initio motûs in primo quadrante à <lb/>circulo majore paulò ampliùs propelli pondus ex D versùs H, <lb/>quàm à circulo minore, datâ angulorum motûs ad centrum C <lb/>paritate. </s>

<s>Verùm in circulo majoris diametri non &longs;olùm pari <lb/>graduum numero re&longs;pondet longior arcus pro Ratione diame<lb/>trorum, &longs;ed etiam, ut ex &longs;uperioribus calculis con&longs;tat, major <lb/>circulus plures gradus ponderi coapta<gap/>, quàm minor. </s>

<s>Sic in <lb/>motu ad centrum C gr. 15, circulo minori, cujus Radius 100, <lb/>competunt gr. 13. 4′. </s>

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<s>Hinc &longs;i ex laqueari pendeat &longs;tatua ventum <lb/>referens, & in &longs;peciem volantis ingentes das expandens junctas <lb/>jugo KL, atque in &longs;uperiore conclavi ad&longs;it qui cylindrum cir<lb/>cumagat, alis reciprocantibus commovebitur aër, & aura exci<lb/>tabitur ad refrigerandum. </s>

<s>Pro variis demum u&longs;ibus &longs;tatuetur cylindrus modò horizon<lb/>ti, tanquam Ergata, perpendicularis, modò velut Sucula, paral<lb/>lelus: Erítque expediti&longs;&longs;ima ejus conver&longs;io, &longs;i centrum Ellip&longs;is <lb/>nulli polo innitatur, &longs;ed cylindrus ip&longs;e congruo loculamento <lb/>ita in&longs;eratur, ut in eo &longs;it ver&longs;atilis, &, quam primò dederis, po-<pb xlink:href="017/01/679.jpg" pagenum="663"/>&longs;itionem deinceps &longs;ervet, ac neutram ïn partem nutet, Id qui<lb/>dem paulò longiorem cylindrum exigit; non tamen e&longs;t nece&longs;<lb/>&longs;e unius perpetuæ cra&longs;&longs;itiei e&longs;&longs;e cylindrum; &longs;æpè enim nimis <lb/>cra&longs;&longs;um atque incommodum e&longs;&longs;e contingeret; &longs;ed fru&longs;to cy<lb/>lindrico cra&longs;&longs;iori obliquè &longs;ecto firmiter inieri poterit gracilior <lb/>cylindrus, ita ut axis axi conveniat, & rectam lineam con&longs;ti<lb/>tuant, atque hic in foramen immi&longs;&longs;us, in quo ver&longs;atilis e&longs;t, dum <lb/>contorquetur, cra&longs;&longs;iorem cylindrum pariter convolvit. <lb/><gap desc="hr tag"/></s>

<s>Pro variis demum u&longs;ibus &longs;tatuetur cylindrus modò horizon<lb/>ti, tanquam Ergata, perpendicularis, modò velut Sucula, paral<lb/>lelus: Erítque expediti&longs;&longs;ima ejus conver&longs;io, &longs;i centrum Ellip&longs;is <lb/>nulli polo innitatur, &longs;ed cylindrus ip&longs;e congruo loculamento <lb/>ita in&longs;eratur, ut in eo &longs;it ver&longs;atilis, &, quam primò dederis, po-<pb xlink:href="017/01/679.jpg" pagenum="663"/>&longs;itionem deinceps &longs;ervet, ac neutram in partem nutet. Id qui<lb/>dem paulò longiorem cylindrum exigit; non tamen e&longs;t nece&longs;<lb/>&longs;e unius perpetuæ cra&longs;&longs;itiei e&longs;&longs;e cylindrum; &longs;æpè enim nimis <lb/>cra&longs;&longs;um atque incommodum e&longs;&longs;e contingeret; &longs;ed fru&longs;to cy<lb/>lindrico cra&longs;&longs;iori obliquè &longs;ecto firmiter inieri poterit gracilior <lb/>cylindrus, ita ut axis axi conveniat, & rectam lineam con&longs;ti<lb/>tuant, atque hic in foramen immi&longs;&longs;us, in quo ver&longs;atilis e&longs;t, dum <lb/>contorquetur, cra&longs;&longs;iorem cylindrum pariter convolvit. <lb/><gap desc="hr tag"/></s>

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

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<s>Arguebant igitur percu&longs;&longs;ionem globi plumbei duarum <lb/>unciarum ex cubitali altitudine cadentis æquiparari pre&longs;&longs;ioni <lb/>decem librarum. </s>

<s>Ulteriùs autem progrediendo, adhibita e&longs;t ba<lb/>li&longs;ta alia validior, cujus arcus ob duriorem ferri temperation<gap/>m <lb/>minùs erat flexibilis: quapropter cum eju&longs;dem potentiæ eadem <lb/>&longs;it vis, eju&longs;dem globuli ex eâdem altitudine &longs;imiliter cadentis <lb/>non ni&longs;i eædem e&longs;&longs;e poterant vires ad vincendam æqualem re<lb/>&longs;i&longs;tentiam: atque adeò durioris arcûs minor flexio æquè re<lb/>&longs;i&longs;tens, ac major flexio arcûs mollioris, breviore termino de<lb/>finivit de&longs;cen&longs;um globuli plumbei, & ad propius punctum ad<lb/>ducta e&longs;t chorda. </s>

<s>Ulteriùs autem progrediendo, adhibita e&longs;t ba<lb/>li&longs;ta alia validior, cujus arcus ob duriorem ferri temperationem <lb/>minùs erat flexibilis: quapropter cum eju&longs;dem potentiæ eadem <lb/>&longs;it vis, eju&longs;dem globuli ex eâdem altitudine &longs;imiliter cadentis <lb/>non ni&longs;i eædem e&longs;&longs;e poterant vires ad vincendam æqualem re<lb/>&longs;i&longs;tentiam: atque adeò durioris arcûs minor flexio æquè re<lb/>&longs;i&longs;tens, ac major flexio arcûs mollioris, breviore termino de<lb/>finivit de&longs;cen&longs;um globuli plumbei, & ad propius punctum ad<lb/>ducta e&longs;t chorda. </s>

<s>Verùm, ut in eodem flexionis &longs;tatu fortior <lb/>hic arcus retineretur, non &longs;atis fuit decem libras appendere, <lb/>&longs;ed viginti librarum pondere opus fuit. </s>

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<s>Si enim ex lento & flexili vir<lb/>gulto ab&longs;tractam virgam per aërem molli brachio huc, illuc, <lb/>&longs;ur&longs;um, deor&longs;um duxeris, hæc, aëre tenui&longs;&longs;imam aut ferè nul<lb/>lam compre&longs;&longs;ionem &longs;ubeunte, vix, aut ne vix quidem, tantu<lb/>lum à d<gap/>ectâ &longs;uarum partium po&longs;itione deflectet: at &longs;i eam ve<lb/>hementius agitaveris, aëre tantam particularum compre&longs;&longs;io<lb/>nem renuente, manife&longs;tè inflexam videbis, & illatam &longs;ibi vim <lb/><gap/>ör acuto &longs;ibilo prodet. </s>

<s>Sic baculo aquam &longs;en&longs;im ac leniter di<lb/>videns non admodum repugnantem experiris; at velociùs con<lb/>citanti illa validè re&longs;i&longs;tit, eóque validiùs, quò cra&longs;&longs;ior fuerit <lb/><gap/>ulus. </s>

<s>Ex his liquidò conficitur de percu&longs;&longs;ione philo&longs;ophan<lb/>tem fru&longs;tra medij re&longs;i&longs;tentiam mente ab&longs;trahere: Nam &longs;i nulla <lb/>e&longs;t &longs;ine motu percu&longs;&longs;io, nullus motus ni&longs;i per medium, neque <lb/>&longs;inè certa velocitatis aut tarditatis men&longs;urâ, cui medium inæ<lb/>qualiter re&longs;i&longs;tit; utique & motum à percu&longs;&longs;ione ita mente pari<lb/>ter &longs;ejungere poteris, ut nihil pror&longs;us de motu cogites, &longs;i nul<lb/>lam cum medio rationem habendam exi&longs;timas: At motum, ejú&longs;<lb/>que velocitatem attendendam e&longs;&longs;e in percu&longs;&longs;ione nemo negat; <lb/>igitur neque medij re&longs;i&longs;tentiam, quæ velocitati modum ali<lb/>quem &longs;tatuit, omnino contemnere oportet. </s>

<s>Hinc duæ ferè ex diametro oppo&longs;itæ &longs;ententiæ cavendæ <lb/>&longs;unt, quarum altera gravium inæqualium motum &longs;tatuit ip&longs;o<lb/>rum gravitatibus analogum, ut decuplò velociùs moveatur il<lb/>lud, quod e&longs;t decuplò gravius: altera æqualem omnibus velo<lb/>citatem tribuit. </s>

<s>Utramque manife&longs;ta experimenta fal&longs;itatis re<lb/>darguunt, &longs;i ex congruâ altitudine in&longs;tituantur: Si enim ex val<lb/>dè editâ turri inæqualia corpora, aut eju&longs;dem, aut diver&longs;æ &longs;e<lb/>cundùm &longs;peciem gravitatis dimittas, illud, quod gravius e&longs;t, <lb/>terram citiùs attingere ob&longs;ervabis, &longs;ed tam brevi momentorum <lb/>di&longs;crimine, ut nulla &longs;ube&longs;&longs;e po&longs;&longs;it &longs;u&longs;picio &longs;ervatæ velocitatum <lb/>cum gravita<gap/>ibus analogiæ, neque tamen de velocitatum inæ<lb/>qualitati dubitari queat. </s>

<s>Utramque manife&longs;ta experimenta fal&longs;itatis re<lb/>darguunt, &longs;i ex congruâ altitudine in&longs;tituantur: Si enim ex val<lb/>dè editâ turri inæqualia corpora, aut eju&longs;dem, aut diver&longs;æ &longs;e<lb/>cundùm &longs;peciem gravitatis dimittas, illud, quod gravius e&longs;t, <lb/>terram citiùs attingere ob&longs;ervabis, &longs;ed tam brevi momentorum <lb/>di&longs;crimine, ut nulla &longs;ube&longs;&longs;e po&longs;&longs;it &longs;u&longs;picio &longs;ervatæ velocitatum <lb/>cum gravitatibus analogiæ, neque tamen de velocitatum inæ<lb/>qualitati dubitari queat. </s>

<s>Meis &longs;cilicet auribus & oculis fidem <lb/>abrogare nequeo, quicquid obtrudant aliqui in contrarium &longs;ua <lb/>aut aliorum experimenta afferentes ex nimis brevi altitudine. <pb xlink:href="017/01/699.jpg" pagenum="683"/>Nam & &longs;æpiùs in profundi&longs;&longs;imum puteum inæquales lapides <lb/>dimi&longs;i &longs;imul, & ictuum &longs;onitum alium alio priorem &longs;emper au<lb/>divi; id quod &longs;atis e&longs;t ad illam velocitatum omnimodam æqua<lb/>litatem rejiciendam, quamvis uter prior aquam attigerit, certò <lb/>digno&longs;cere non valeret auris; quòd &longs;i alter in &longs;ubjectam peluim <lb/>æneam, alter in vas ligneum decidi&longs;&longs;et, potui&longs;&longs;et auris dijudi<lb/>care ex &longs;onitu: Et ex alti&longs;&longs;imâ turri Bononien&longs;i dimi&longs;&longs;a pondera <lb/>inæqualia ob&longs;ervavi initio qua&longs;i æqualiter de&longs;cendere ita, ut <lb/>oculus nullam velocitatum di&longs;&longs;imilitudinem adhuc digno&longs;ce<lb/>ret; deinde procedente de&longs;cen&longs;u paulatim gravitas major præ<lb/>currere notabiliter incipiebat, &longs;empérque magis augebatur ve<lb/>locitas, adeò ut aliquando gravitas major terram attigerit, <lb/>quando minor adhuc aberat intervallo pedum quadraginta, <lb/>quemadmodum ex notâ in turris latere dimetiri licuit. </s>

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<s>Sed quis certum habeat, utrùm quie&longs;cat aër, neque <lb/>corporis impetum frangat, aut reprimat aliena impre&longs;&longs;ione ad<lb/>ver&longs;us, an verò ad ea&longs;dem partes delatus motui ob&longs;ecundet, & <lb/>velocitati faveat? </s>

<s>Quare laudandi quidem quicumque percu&longs;<lb/>&longs;ionum naturam ve&longs;tigantes, & ea, quibus in e<gap/>us notitiam <lb/>deduci po&longs;&longs;ent, conjecturá pro&longs;picientes, in in&longs;tituendi expe<lb/>rimentis &longs;edulò &longs;e exercuerunt; parùm tamen mihi de veritate <lb/>blandiri me po&longs;&longs;e arbitrarer, &longs;i hæc qua&longs;i Apodixes temerè reci<lb/>perem; &longs;ed neque ore tam duro fuerim, ut ea prorsùs rejiciam. </s>

<s>Quare laudandi quidem quicumque percu&longs;<lb/>&longs;ionum naturam ve&longs;tigantes, & ea, quibus in ejus notitiam <lb/>deduci po&longs;&longs;ent, conjecturá pro&longs;picientes, in in&longs;tituendi expe<lb/>rimentis &longs;edulò &longs;e exercuerunt; parùm tamen mihi de veritate <lb/>blandiri me po&longs;&longs;e arbitrarer, &longs;i hæc qua&longs;i Apodixes temerè reci<lb/>perem; &longs;ed neque ore tam duro fuerim, ut ea prorsùs rejiciam. </s>

<lb/><s>Confirmatis igitur experimentis me duci &longs;inam, quatenus ad <lb/>veritatis &longs;imilitudinem me proximè acce&longs;&longs;urum &longs;pero. </s>

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<lb/><s>Quoniam verò gravitas inter eas cau&longs;as enumeratur, in quibus <lb/>ine&longs;t efficiendi nece&longs;&longs;itas, & quandiu opus e&longs;t juxta naturæ pro<lb/>po&longs;itum, quantum po&longs;&longs;unt, efficiunt; &longs;ingulis momentis, qui<lb/>bus pote&longs;t de&longs;cendere, &longs;ingulos impetûs gradus æquales priori<lb/>bus adjicit, adeò ut, quot momenta motum metiuntur, tot gra<lb/>dus impetûs po&longs;tremo momento inten&longs;ionem con&longs;tituant, cui <lb/>motûs velocitas re&longs;pondeat. </s>

<s>Velocitatum igitur incrementa <lb/>fiu<gap/> juxta naturalem numerorum progre&longs;&longs;ionem 1.2.3.4.5, &c. <pb xlink:href="017/01/706.jpg" pagenum="690"/>nam juxta hanc eandem &longs;eriem impetûs, velocitatis cau&longs;a, au<lb/>getur, &longs;ingulis gradibus in &longs;ingula momenta additis. </s>

<s>Velocitatum igitur incrementa <lb/>fiunt juxta naturalem numerorum progre&longs;&longs;ionem 1.2.3.4.5, &c. <pb xlink:href="017/01/706.jpg" pagenum="690"/>nam juxta hanc eandem &longs;eriem impetûs, velocitatis cau&longs;a, au<lb/>getur, &longs;ingulis gradibus in &longs;ingula momenta additis. </s>

<s>Ab omni tamen infinitatis &longs;u&longs;picione recedendum e&longs;t hìc, <lb/>ubi momentorum vocabulum u&longs;urpo, qua&longs;i infinita puncta <lb/>temporis agno&longs;cerem, & ad vim percu&longs;&longs;ionis infinitam ad&longs;truen<lb/>dam, infinitis momentis &longs;ingulis impetûs gradum tribuerem. </s>

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<s>Sit corporis percutientis longitudo AB. </s>

<s>Si motu naturali <lb/><figure id="id.017.01.730.1.jpg" xlink:href="017/01/730/1.jpg"/><lb/>&longs;ponte &longs;uâ d<gap/>&longs;cenderet, & <lb/>in motu po&longs;itionem hori<lb/>zonti parallelam &longs;ervaret, <lb/>utique validi&longs;&longs;imus e&longs;&longs;et <lb/>ictus in D puncto, quod <lb/>re&longs;pondet centro gravita<lb/>tis C; e&longs;&longs;ent enim hinc atque hinc æquales gravitates, & æqua<lb/>lia impetûs momenta, ut &longs;uperiùs dictum e&longs;t. </s>

<s>Si motu naturali <lb/><figure id="id.017.01.730.1.jpg" xlink:href="017/01/730/1.jpg"/><lb/>&longs;ponte &longs;uâ de&longs;cenderet, & <lb/>in motu po&longs;itionem hori<lb/>zonti parallelam &longs;ervaret, <lb/>utique validi&longs;&longs;imus e&longs;&longs;et <lb/>ictus in D puncto, quod <lb/>re&longs;pondet centro gravita<lb/>tis C; e&longs;&longs;ent enim hinc atque hinc æquales gravitates, & æqua<lb/>lia impetûs momenta, ut &longs;uperiùs dictum e&longs;t. </s>

<s>At manente ex<lb/>tremitate A, tanquam centro motûs, & corpore ip&longs;o vi &longs;uæ gra<lb/>vitatis de&longs;cendente, licèt &longs;ingulæ particulæ, utpote naturæ <lb/>eju&longs;dem, paribus viribus &longs;int præditæ, non tamen æquali mo<lb/>mento feruntur; &longs;ed cum in A retineantur, quæ puncto A pro<lb/>piores &longs;unt, magis detorquentur à directione naturalis gravita<lb/>tis, adeóque plus momenti habent partes inter DB, quàm in<lb/>ter AD con&longs;titutæ. </s>

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<s>127. <emph type="italics"/>In flumine, per quod ad Ienping navi<lb/>gatur, Catadupæ aquarum multæ &longs;unt, & periculo&longs;i&longs;&longs;ima Syrtibus <lb/>loca, duo præ&longs;ertim propè Cinglieu, unus Kieulung, alter Changcung <lb/>dictus. </s>

<s>Cum naves tran&longs;eunt, ne cum aquâ decidentes fractionis in<lb/>currant periculum, &longs;citè præmittunt aliquot &longs;traminis fa&longs;ces, ad quos <lb/>navis leviùs impingat, ac tran&longs;eat.<emph.end type="italics"/></s><s> Sic ferreis tormentorum glo<lb/>bis objecti &longs;acci lanâ aut terrâ repleti illorum vim elidunt, ne <lb/>diruant muros huju&longs;modi &longs;accis protectos <gap/> &longs;ic farti go&longs;&longs;ypio <lb/>thoraces non levi munimento &longs;unt digladiantibus. </s>

<s>Cum naves tran&longs;eunt, ne cum aquâ decidentes fractionis in<lb/>currant periculum, &longs;citè præmittunt aliquot &longs;traminis fa&longs;ces, ad quos <lb/>navis leviùs impingat, ac tran&longs;eat.<emph.end type="italics"/></s><s> Sic ferreis tormentorum glo<lb/>bis objecti &longs;acci lanâ aut terrâ repleti illorum vim elidunt, ne <lb/>diruant muros huju&longs;modi &longs;accis protecto: &longs;ic farti go&longs;&longs;ypio <lb/>thoraces non levi munimento &longs;unt digladiantibus. </s>

<s>Quò autem <lb/>mollius fuerit corpus percu&longs;&longs;um, quia magis cedit, minùs læ-<pb xlink:href="017/01/737.jpg" pagenum="721"/>ditur à percutiente; & vici&longs;&longs;im quò durius illud fuerit, magis <lb/>ab eodem percutiente læditur, cujus impul&longs;um excipit. </s>

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<s>Notabili, inquam, ne <lb/>in quæ&longs;tionem vocemus, utrùm flecti dicenda &longs;int illa corpora, <lb/>quæ ex ictu tremorem concipiunt, ut æri campano, cum pul&longs;a<lb/>tur, accidit: nam vix excogitari pote&longs;t corpus aliquod, cui ex <lb/>vi percu&longs;&longs;ionis accidere nequeat tremor; cum & terram ip&longs;am <lb/>licèt altiùs defo&longs;&longs;am in cuniculis concuti & contremi&longs;cere <lb/>o&longs;tendant lapilli, & fabæ in tympani militaris planâ facie &longs;ub&longs;i<lb/>lientes ex profundo illo ligonis ictu. </s>

<s>Certè, &longs;i Atlanti Sinico <lb/>pag.57. credimus, ubi in IV Provinciâ Xantung mentionem <lb/>facit de monte, cui nomen Mingxe, hoc e&longs;t Sonorum lapis; <lb/><emph type="italics"/>in hujus montis vertice cippus erectus &longs;tat centum altus perticas<emph.end type="italics"/><lb/>(Pertica apud Sinas e&longs;t decem cubitorum) <emph type="italics"/>qui vel l<gap/>viter digito <lb/>percu&longs;&longs;us ad tympani modum &longs;onum edere dicitur, à quo monti nomen<emph.end type="italics"/>; <lb/>nullus autem &longs;onus ab&longs;que corporis &longs;onori tremore efficitur. </s>

<s>Certè, &longs;i Atlanti Sinico <lb/>pag.57. credimus, ubi in IV Provinciâ Xantung mentionem <lb/>facit de monte, cui nomen Mingxe, hoc e&longs;t Sonorum lapis; <lb/><emph type="italics"/>in hujus montis vertice cippus erectus &longs;tat centum altus perticas<emph.end type="italics"/><lb/>(Pertica apud Sinas e&longs;t decem cubitorum) <emph type="italics"/>qui vel leviter digito <lb/>percu&longs;&longs;us ad tympani modum &longs;onum edere dicitur, à quo monti nomen<emph.end type="italics"/>; <lb/>nullus autem &longs;onus ab&longs;que corporis &longs;onori tremore efficitur. </s>

<lb/><s>Quod &longs;i non ni&longs;i levi&longs;&longs;imè flecti queat corpus percu&longs;&longs;um, &longs;ed ci-<pb xlink:href="017/01/738.jpg" pagenum="722"/>tra tremorem frangatur, aut frietur, indicium e&longs;t majoris re<lb/>&longs;i&longs;tentiæ, ac proinde, cæteris paribus, vehementiorem futu<lb/>ram percu&longs;&longs;ionem, quàm &longs;i con&longs;picuam flexionem admitteret. </s>

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<s>Sic decidentis ex <lb/>altitudine non modicâ lapidis ictum manu citrà læ&longs;ionem exci<lb/>pimus, &longs;i illius motui, ubi manum attigerit, exiguo minoris <lb/>velocitatis di&longs;crimine ob&longs;ecundemus: hæc &longs;iquidem exigua re<lb/>&longs;i&longs;tentia modicum quid impetûs deterit, & quia aliquot mo<lb/>menta durat, ita &longs;en&longs;im extenuatur impetus, ut demum qui re<lb/>liquus e&longs;t nocere non valeat. </s>

<s>Hoc artificio procul dubio utebatur quidam, qui ante ali<lb/>quot annos, ut ex viro fide digno tanquam rem noti&longs;&longs;imam ac<lb/>cepi, Mutinæ en&longs;em eâ dexteritate in altum proji<gap/>iebat, ut per<lb/>pendicularis recideret mucrone deor&longs;um conver&longs;o, quem ca<lb/>dentem nuda manûs vola innoxiè excipiebat; &longs;ed cum aliquan<lb/>do invitus cogeretur, ut id noctu experiretur in conclavi mul<lb/>tis facibus illu&longs;trato, cùm (deficiente con&longs;tanti & clari&longs;&longs;imâ <lb/>diurnâ luce, quam æmulari non pote&longs;t tremula & incon&longs;tans <lb/>facium, quamvis multarum, flamma) non ita exactè a&longs;&longs;eque<lb/>retur de&longs;cendentis gladij motum & velocitatem, finem fecit lu<lb/>do manum trajectam referens. </s>

<s>Hoc artificio procul dubio utebatur quidam, qui ante ali<lb/>quot annos, ut ex viro fide digno tanquam rem noti&longs;&longs;imam ac<lb/>cepi, Mutinæ en&longs;em eâ dexteritate in altum projiciebat, ut per<lb/>pendicularis recideret mucrone deor&longs;um conver&longs;o, quem ca<lb/>dentem nuda manûs vola innoxiè excipiebat; &longs;ed cum aliquan<lb/>do invitus cogeretur, ut id noctu experiretur in conclavi mul<lb/>tis facibus illu&longs;trato, cùm (deficiente con&longs;tanti & clari&longs;&longs;imâ <lb/>diurnâ luce, quam æmulari non pote&longs;t tremula & incon&longs;tans <lb/>facium, quamvis multarum, flamma) non ita exactè a&longs;&longs;eque<lb/>retur de&longs;cendentis gladij motum & velocitatem, finem fecit lu<lb/>do manum trajectam referens. </s>

<s>Po&longs;tremum caput, ex quo re&longs;i&longs;tentiæ modus de&longs;umitur in <lb/>percu&longs;&longs;ionibus, e&longs;t ip&longs;a po&longs;itio corporis percu&longs;&longs;i, prout directè, <lb/>aut obliquè, ictum excipit, hoc e&longs;t quatenus linea directionis <lb/>motûs, quo fertur corpus percutiens, incurrit in corporis per-<pb xlink:href="017/01/740.jpg" pagenum="724"/>cu&longs;&longs;i &longs;uperficiem ad angulos æquales, aut inæquales. </s>

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<lb/><s>Sic ha&longs;tam &longs;i obliquè contorqueas in rupem, non modò inæ<lb/>qualitatem angulorum deprehendes, &longs;ed vix reflexionem fieri <lb/>admittes; quia videlicet extremo ha&longs;tæ calce rupem tangente, <lb/>reliquæ partes habentes circa centrum gravitatis inæqualia mo<lb/>menta, valdè turbant motum: &longs;olùm autem quando ha&longs;ta in <lb/>planum impingitur, aut cadit, ad perpendiculum, &longs;ervata re<lb/>flexionis regulâ ad angulos rectos re&longs;ilit; quia tunc partes om<lb/>nes circa centrum gravitatis paria habent momenta. </s>

<s>Hæc au<lb/>tem momentorum diver&longs;itas in globo non reperitur, ni&longs;i fortè <lb/>aut deficiat à perfect<gap/> rotunditate, aut centrum magnitudinis <lb/>non &longs;it idem cum centro gravitatis, adeò ut linea punctum <lb/>contactûs cum centro gravitatis, jungens non &longs;it plano re<lb/>flectenti perpendicularis; tunc enim perturbaretur globi <lb/>reflexio. </s>

<s>Hæc au<lb/>tem momentorum diver&longs;itas in globo non reperitur, ni&longs;i fortè <lb/>aut deficiat à perfectâ rotunditate, aut centrum magnitudinis <lb/>non &longs;it idem cum centro gravitatis, adeò ut linea punctum <lb/>contactûs cum centro gravitatis, jungens non &longs;it plano re<lb/>flectenti perpendicularis; tunc enim perturbaretur globi <lb/>reflexio. </s>

<s>Ex dictis &longs;atis apertè con&longs;tat reflexionem non ex impetu de<lb/>&longs;umendam e&longs;&longs;e, &longs;ed ex directione motus, cui opponitur corpus <lb/>reflectens, juxta hu us po&longs;itionem perpendicularem aut obli<lb/>quam: multus enim impetus aliquando officere pote&longs;t æquali<lb/>tati angulorum, &longs;i ex colli&longs;ione corporis impacti cum corpore <lb/>reflectente, aut alterutrum, aut utrumque notabiliter cedat, <lb/>adeò ut non contingat &longs;incera reflexio. </s>

Line 11625

Line 11617

<s>Quare occurrant &longs;ibi <lb/>globi in puncto A; & illo<lb/>rum directiones primò eæ <lb/>&longs;int, quæ &longs;ibi maximè ad<lb/>ver&longs;antes in rectam lineam <lb/>BC coëant: haud dubium <lb/>quin globus V per rectam <lb/>AB, & globus R per rectam <lb/>AC re&longs;iliat, uterque per li<lb/>neam, quâ venit, jungentem <lb/>cum puncto contactûs Centrum impetûs: &longs;implici enim di<lb/>rectione alter adversùs alterum fertur, & &longs;ibi toto conatu re<lb/>pugnant. </s>

<s>Deinde obliquus &longs;it morus, & globi R directio &longs;it DE: <lb/>quapropter RE directio quædam e&longs;t mixta ex lineâ maximæ re<lb/>&longs;i&longs;tentiæ RA, & ex lineâ nullius re&longs;i&longs;tentiæ R<gap/>, ita ut partim <lb/>versùs A, partim versùs I tendat: priorem directionem versùs A <lb/>metitur linea RF, po&longs;teriorem versùs I metitur linea FE. </s>

<s>Deinde obliquus &longs;it morus, & globi R directio &longs;it DE: <lb/>quapropter RE directio quædam e&longs;t mixta ex lineâ maximæ re<lb/>&longs;i&longs;tentiæ RA, & ex lineâ nullius re&longs;i&longs;tentiæ RI, ita ut partim <lb/>versùs A, partim versùs I tendat: priorem directionem versùs A <lb/>metitur linea RF, po&longs;teriorem versùs I metitur linea FE. </s>

<s>Cum <pb xlink:href="017/01/753.jpg" pagenum="737"/>igitur globus V &longs;olùm priori directioni RF opponatur, hæc <lb/>mutatur in oppo&longs;itam RG, manet autem directio versùs I æqua<lb/>lis ip&longs;i FE, & e&longs;t GH: propterea motus centri R e&longs;t RH <lb/>parallelus motui puncti A, quod per lineam KA incidens in <lb/>Tangentem MN, reflecteretur ad angulos æquales KAN & <lb/>LAM percurrendo lineam AL. </s>

Line 12443

Line 12435

<s>Hinc &longs;i plura fuerint Compo&longs;ita Tympana, eorum Ratio, <lb/>quæ ex Rationibus diametrorum tympanorum ad &longs;uorum <lb/>Axium diametros componitur, a&longs;&longs;umenda e&longs;t, atque attenden<lb/>dum quoties volvatur cochlea, ut primum tympanum cochleæ <lb/>proximum circumagatur: deinde per numerum dentium primi <lb/>tympani ducendus e&longs;t motus potentiæ manubrio cochleæ appli<lb/>catæ; & ex Ratione tympanorum, atque ex Ratione Cochleæ, <lb/>componenda e&longs;t Ratio. </s>

<s>Sit cochlea eadem, quæ priùs, eodém<lb/>que manubrio in&longs;tructa, adeò ut potentia &longs;emel cochleam ver<lb/>&longs;ans de&longs;cribat circuli peripheriam digitorum ferè 44; & pri<lb/>mum tympanum habens peripheriam dig.25 in dentes 24 di&longs;tri<lb/>butam, dum &longs;emel volvitur, potentia vicies & quater periphe<lb/>riam dig.44 de&longs;cribens percurrit digitos 10<gap/>6. Sit idem pri<lb/>mum tympanum ad &longs;uum Axem &longs;triatum ut 4 ad 1, &longs;ecundum <lb/>tympanum ad &longs;uum Axem fune ductario involutum &longs;it ut 3 ad 2: <lb/>Ratio compo&longs;ita horum duorum tympanorum e&longs;t ut 6 ad 1. <lb/>Cum verò motus potentiæ manubrio applicatæ ad integrum <lb/>motum peripheriæ tympani primi &longs;it ut 1056 ad 25 (nam &longs;ingu<lb/>læ conver&longs;iones manubrij cochleæ ad motum unius dentis &longs;unt <lb/>ut 44 ad (25/24)) componatur hæc Ratio cum Ratione 6 ad 1, & erit <lb/>motus potentiæ ad motum ponderis axi &longs;ecundi tympani per fu<lb/>nem ductarium applicati, ut 6336 ad 25, hoc e&longs;t ferè ut 253 1/2 <lb/>ad 1: atque adeò quo conatu potentia moveret libras decem; <lb/>hac machinâ movebit libras 2535. </s>

<s>Sit cochlea eadem, quæ priùs, eodém<lb/>que manubrio in&longs;tructa, adeò ut potentia &longs;emel cochleam ver<lb/>&longs;ans de&longs;cribat circuli peripheriam digitorum ferè 44; & pri<lb/>mum tympanum habens peripheriam dig.25 in dentes 24 di&longs;tri<lb/>butam, dum &longs;emel volvitur, potentia vicies & quater periphe<lb/>riam dig.44 de&longs;cribens percurrit digitos 1056. Sit idem pri<lb/>mum tympanum ad &longs;uum Axem &longs;triatum ut 4 ad 1, &longs;ecundum <lb/>tympanum ad &longs;uum Axem fune ductario involutum &longs;it ut 3 ad 2: <lb/>Ratio compo&longs;ita horum duorum tympanorum e&longs;t ut 6 ad 1. <lb/>Cum verò motus potentiæ manubrio applicatæ ad integrum <lb/>motum peripheriæ tympani primi &longs;it ut 1056 ad 25 (nam &longs;ingu<lb/>læ conver&longs;iones manubrij cochleæ ad motum unius dentis &longs;unt <lb/>ut 44 ad 25/24) componatur hæc Ratio cum Ratione 6 ad 1, & erit <lb/>motus potentiæ ad motum ponderis axi &longs;ecundi tympani per fu<lb/>nem ductarium applicati, ut 6336 ad 25, hoc e&longs;t ferè ut 253 1/2 <lb/>ad 1: atque adeò quo conatu potentia moveret libras decem; <lb/>hac machinâ movebit libras 2535. </s>

<s>Verùm adhuc augeri po&longs;&longs;unt vires Cochleæ Infinitæ non <lb/>multiplicatis tympanis dentatis, &longs;ed cum illo unico, quod à <lb/>Cochleâ movetur, componendo Trochleas: &longs;i videlicet alteri <lb/>Trochleæ adnectatur pondus, altera Trochlea alicubi firmetur: <lb/>tum funis ductarius, qui à Potentiâ arripiendus e&longs;&longs;et atque <lb/>trahendus, axi tympani alligetur. </s>

<s>Nam &longs;i Ratio, quam Tro<lb/>chleæ inferunt, componatur cum Ratione Axis in Peritrochio, <lb/>atque Ratione Cochleæ, fit Ratio ex tribus Rationibus trium <pb xlink:href="017/01/803.jpg" pagenum="787"/>Facultatum compo&longs;ita. </s>

<s>Sic Ratio Cochleæ &longs;it, ut priùs, 44 ad (25/24<gap/>) <lb/>Ratio Tympani ad Axem &longs;it 4 ad 1, Ratio Trochlearum, capite <lb/>funis ad trochleam ponderis alligato (&longs;int autem Trochleæ bi<lb/>norum orbiculorum) &longs;it 5 ad 1: tres hæ Rationes Compo&longs;itæ <lb/>con&longs;tituunt Rationem 845 ad 1. Quare quo conatu moveres <lb/>libras decem, movebis libras 8450 tam facili & parabili ma<lb/>chinâ. </s>

<s>Sic Ratio Cochleæ &longs;it, ut priùs, 44 ad 25/24, <lb/>Ratio Tympani ad Axem &longs;it 4 ad 1, Ratio Trochlearum, capite <lb/>funis ad trochleam ponderis alligato (&longs;int autem Trochleæ bi<lb/>norum orbiculorum) &longs;it 5 ad 1: tres hæ Rationes Compo&longs;itæ <lb/>con&longs;tituunt Rationem 845 ad 1. Quare quo conatu moveres <lb/>libras decem, movebis libras 8450 tam facili & parabili ma<lb/>chinâ. </s>

<s>Ob&longs;ervanda &longs;unt autem tam commoda, quàm incommoda, <lb/>quæ hujus machinæ, &longs;cilicet Cochleæ Infinitæ u&longs;um comitan<lb/>tur. </s>

<s>Neque in po&longs;tremis illud numerandum e&longs;t, quod tantul<gap/><lb/>machinula facillimè transferri pote&longs;t, ad pondera &longs;atis magn<gap/><lb/>dimovenda; maximè &longs;i in plano raptanda &longs;int &longs;uppo&longs;itis &longs;cytalis <lb/>& trochleæ adhibeantur, quas non adeò cra&longs;&longs;o fune connect <lb/>oportet, quemadmodum &longs;i in &longs;ublime attollendum e&longs;&longs;et pon<lb/>dus, & fune ip&longs;o retinendum, ne relabatur. </s>

<s>Neque in po&longs;tremis illud numerandum e&longs;t, quod tantula <lb/>machinula facillimè transferri pote&longs;t, ad pondera &longs;atis magna <lb/>dimovenda; maximè &longs;i in plano raptanda &longs;int &longs;uppo&longs;itis &longs;cytalis <lb/>& trochleæ adhibeantur, quas non adeò cra&longs;&longs;o fune connecti <lb/>oportet, quemadmodum &longs;i in &longs;ublime attollendum e&longs;&longs;et pon<lb/>dus, & fune ip&longs;o retinendum, ne relabatur. </s>

<s>Adde non requiri ampliora &longs;patia, ut cochlea huju&longs;modi infi <lb/>nita circumagatur, & vel &longs;edentem hominem &longs;olâ, neque mul<lb/>tâ, lacertorum manubrium ver&longs;antium contentione po&longs;&longs;e mo<lb/>tum quæ&longs;itum perficere: atque &longs;i pondus attollatur, licet poten <lb/>tiæ, quandocumque libitum fuerit, ce&longs;&longs;are à motu, quin pon <lb/>dus &longs;u&longs;pen&longs;um recidat, etiam&longs;i neque illi fulcrum &longs;ubjiciatui <lb/>neque cochleæ manubrium retinaculo aliquo firmetur. </s>

<s>Verùr <lb/>in attollendis ingentibus oneribus non expedit hac machin <lb/>uti, ni&longs;i tympanum dentatum &longs;atis magnum fuerit, ut Axer <lb/>cra&longs;&longs;iorem atque validiorem admittat, cui ductarius funis cir <lb/>cumduci queat; hic autem funis cum <expan abbr="teñuis">tennuis</expan> e&longs;&longs;e non po&longs;&longs;it, n<gap/><lb/>que exilem Axem exigit. </s>

<s>Verùr <lb/>in attollendis ingentibus oneribus non expedit hac machinâ <lb/>uti, ni&longs;i tympanum dentatum &longs;atis magnum fuerit, ut Axem <lb/>cra&longs;&longs;iorem atque validiorem admittat, cui ductarius funis cir <lb/>cumduci queat; hic autem funis cum <expan abbr="teñuis">tennuis</expan> e&longs;&longs;e non po&longs;&longs;it, ne<lb/>que exilem Axem exigit. </s>

<s>Præterea di&longs;&longs;imulandum non e&longs;t per <lb/>culum, ne cochlea inutilis fiat; &longs;i videlicet vel unicus tympan <lb/>dens excutiatur: ubi enim in conver&longs;ione ad cam lacunai <lb/>ventum fuerit, illico ce&longs;&longs;at tympani conver&longs;io, cum nullus ej<gap/><lb/>dens occurrat cochleæ. </s>

<s>Præterea di&longs;&longs;imulandum non e&longs;t per <lb/>culum, ne cochlea inutilis fiat; &longs;i videlicet vel unicus tympano <lb/>dens excutiatur: ubi enim in conver&longs;ione ad cam lacunam <lb/>ventum fuerit, illico ce&longs;&longs;at tympani conver&longs;io, cum nullus ejus <lb/>dens occurrat cochleæ. </s>

<s>Propterea rem prudenter admini&longs;tra<gap/><lb/>oportet, ut congrua machina eligatur. </s>

<s>Propterea rem prudenter admini&longs;trare <lb/>oportet, ut congrua machina eligatur. </s>

<s>Porrò non contemnenda utilitas ex Cochleâ hac infinitâ pe <lb/>cipi pote&longs;t ad augendas communis Cochleæ vires &longs;ivè preme <lb/>tis, &longs;ivè etiam attrahentis. </s>

<s>Eo videlicet loco, ubi aptandus e <lb/>fet Radius ad Cochleæ conver&longs;ionem, tympanum dentatum a<gap/><lb/>jiciatur, ex cujus centro exeat cylindrus in cochleam deform<gap/><lb/>tus, & Matrici in&longs;ertus: tympani verò dentes congruâ cochle<gap/><pb xlink:href="017/01/804.jpg" pagenum="788"/>infinitæ &longs;pirâ excipiantur: Manubrio enim ver&longs;ato cochlea in<lb/>finita convertitur, & &longs;ingulis conver&longs;ionibus &longs;ingulos tympani <lb/>dentes, alios &longs;ubinde atque alios promovens, tympani covolu<lb/>tionem efficit, atque cum eo pariter infixa cochlea ver&longs;atur. </s>

<s>Eo videlicet loco, ubi aptandus e&longs;<lb/>&longs;et Radius ad Cochleæ conver&longs;ionem, tympanum dentatum ad<lb/>jiciatur, ex cujus centro exeat cylindrus in cochleam deforma<lb/>tus, & Matrici in&longs;ertus: tympani verò dentes congruâ cochleæ <pb xlink:href="017/01/804.jpg" pagenum="788"/>infinitæ &longs;pirâ excipiantur: Manubrio enim ver&longs;ato cochlea in<lb/>finita convertitur, & &longs;ingulis conver&longs;ionibus &longs;ingulos tympani <lb/>dentes, alios &longs;ubinde atque alios promovens, tympani covolu<lb/>tionem efficit, atque cum eo pariter infixa cochlea ver&longs;atur. </s>

<lb/><s>Prudenti autem Machinatori non deerit methodus, qua huju&longs;<lb/>modi Cochlea infinita applicetur, & &longs;imul cum tympano den<lb/>tato deprimatur aut attollatur, &longs;i opus fuerit. </s>

Line 12473

Line 12465

<s>gr. <lb/>&longs;pirarum cochleæ prementis intervallum &longs;ubtriplum &longs;emidia<lb/>metri tympani, cui illa infixa e&longs;t: igitur Ratio perimetri tym<lb/>pani ad intervallum &longs;pirarum e&longs;t ut (18 84/100) ad 1. At Cochleæ in<lb/>finitæ manubrium ad eju&longs;dem &longs;pirarum di&longs;tantiam &longs;it ut 10 ad <gap/><lb/>Motus igitur potentiæ manubrium ver&longs;antis e&longs;t ut peripheria <lb/>de&longs;cripta (62 83/100) ad motum unius dentis tympani ut 1. Ratio <lb/>itaque ex his duabus Rationibus Compo&longs;ita e&longs;t (1183 7/10) ad 1. <lb/>Ex quo &longs;atis innote&longs;cit, quanto virium incremento addatur co<lb/>chleæ vulgari cochlea hæc infinita tam brevi manubrio in<lb/>&longs;tructa, loco vectis admodum longi, quem &longs;patij angu&longs;tiæ non <lb/>caperent. </s>

<s>gr. <lb/>&longs;pirarum cochleæ prementis intervallum &longs;ubtriplum &longs;emidia<lb/>metri tympani, cui illa infixa e&longs;t: igitur Ratio perimetri tym<lb/>pani ad intervallum &longs;pirarum e&longs;t ut 18 84/100 ad 1. At Cochleæ in<lb/>finitæ manubrium ad eju&longs;dem &longs;pirarum di&longs;tantiam &longs;it ut 10 ad 1: <lb/>Motus igitur potentiæ manubrium ver&longs;antis e&longs;t ut peripheria <lb/>de&longs;cripta 62 83/100 ad motum unius dentis tympani ut 1. Ratio <lb/>itaque ex his duabus Rationibus Compo&longs;ita e&longs;t 1183 7/10 ad 1. <lb/>Ex quo &longs;atis innote&longs;cit, quanto virium incremento addatur co<lb/>chleæ vulgari cochlea hæc infinita tam brevi manubrio in<lb/>&longs;tructa, loco vectis admodum longi, quem &longs;patij angu&longs;tiæ non <lb/>caperent. </s>

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