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version 1.1, 2003/09/26 15:37:54

version 1.2, 2003/11/20 19:14:55

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<cvs_file>gueva_mecha_005_la_1627.xml</cvs_file>

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</info> <text> <front> </front> <body> <chap> <pb id="p.0001"/>

</info> <text> <front> </front> <body> <chap> <pb xlink:href="005/01/001.jpg" id="p.0001"/>

<s>IOANNIS <lb/>DE GVEVARA <lb/>CLER. REG. MIN. <lb/>IN ARISTOTELIS MECHANICAS <lb/>Commentarij.</s>

<s><emph type="italics"/>VNA CVM ADDITIONIBVS QVIBVSDAM <lb/>Ad eandem materiam pertinentibus.<emph.end type="italics"/></s><figure/>

<s><emph type="italics"/>VNA CVM ADDITIONIBVS QVIBVSDAM <lb/>Ad eandem materiam pertinentibus.<emph.end type="italics"/></s><figure id="id.005.01.001.1.jpg" xlink:href="005/01/001/1.jpg"/>

<s>ROMAE, Apud Iacobum Ma&longs;cardum, MDCXXVII. <lb/>SVPERIORVM PERMISSV.</s><pb/>

<s>ROMAE, Apud Iacobum Ma&longs;cardum, MDCXXVII. <lb/>SVPERIORVM PERMISSV.</s><pb xlink:href="005/01/002.jpg"/>

<s>Imprimatur &longs;i videbitur Reuerendi&longs;s. P. Mag. Sac. Pal. Apo&longs;t. <emph type="italics"/>A. Epi&longs;c. Hieracen. Vice&longs;g.<emph.end type="italics"/></s>

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<pb/>

<s>ILLVSTRISS^{MO} PRINCIPI</s>

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<s>Q<emph type="italics"/>vod olimopus in Ari<lb/>&longs;totelis Mechanicas, dum <lb/>Philo&longs;ophiæ, & Mathe<lb/>maticis vacarem inter<lb/>mittere coegit nouæ con<lb/>templationis occa&longs;io, hoc <lb/>ip&longs;um præteritis diebus <lb/>(Illu&longs;tri&longs;sime Princeps) dum publicis nego<lb/>tijs, <expan abbr="grauioribusq.">grauioribusque</expan> &longs;tudijs implicatus, ægrè <lb/>aut vix, vt decet aggredi potui&longs;&longs;em, breuiter vt<lb/>cunque perficere, ac prælis mandare, tua me <lb/>compulit ampli&longs;sima gratia. </s>

<s>Cum enim te pri<lb/>mò Magni Patrui, <expan abbr="Summiq.">Summique</expan> Pontificis Lega<lb/>tum ampli&longs;simum, in Galliam nauigantem, <lb/>ac nuper ex Hi&longs;pania redeuntem ad afferen<pb/>dam pacem animis, proflig andumque maxi<lb/>morum Regum auctoritate exortum in Italia <lb/>bellum, quo poteram ob&longs;equio, atque opera eiu&longs;<lb/>dem Pontificis iu&longs;&longs;u pro&longs;equerer, nobili&longs;simo <lb/>in comitatu innumer æ excitabantur quæ&longs;tio<lb/>nes, tùm circa rem nauticam, tùm circa ma<lb/>chinariam, atque vectoriam in vniuer&longs;um<gap/>; <lb/>quarum &longs;olutiones è mechanicis principij spe<lb/>tere oper æpretium erat. </s>

<s>Cum enim te pri<lb/>mò Magni Patrui, <expan abbr="Summiq.">Summique</expan> Pontificis Lega<lb/>tum ampli&longs;simum, in Galliam nauigantem, <lb/>ac nuper ex Hi&longs;pania redeuntem ad afferen<pb xlink:href="005/01/004.jpg"/>dam pacem animis, proflig andumque maxi<lb/>morum Regum auctoritate exortum in Italia <lb/>bellum, quo poteram ob&longs;equio, atque opera eiu&longs;<lb/>dem Pontificis iu&longs;&longs;u pro&longs;equerer, nobili&longs;simo <lb/>in comitatu innumer æ excitabantur quæ&longs;tio<lb/>nes, tùm circa rem nauticam, tùm circa ma<lb/>chinariam, atque vectoriam in vniuer&longs;um<gap/>; <lb/>quarum &longs;olutiones è mechanicis principij spe<lb/>tere oper æpretium erat. </s>

<s><expan abbr="Cumq.">Cumque</expan> hinc orta fui&longs;<lb/>&longs;et mentio de meis hi&longs;ce lucubrationibus eodem <lb/>in genere partis, gratum fore cognoui, &longs;i vlti<lb/>mam ip&longs;is manum imponens legendas eas ti<lb/>bi litter arum amanti&longs;simo pro animi refectio<lb/>ne obtuli&longs;&longs;em. </s>

<s>Infatig abiles namque animi eo<lb/>rum qui in rebus maximis occupantur, non <lb/>ocio, &longs;ed varietate reficiuntur, & oblectantur: <lb/>præ&longs;ertim cum à grauioribus adleuiora (di<lb/>gna tamen, & aliquo in genere præ&longs;tantia) vel <lb/>ab agilibus ad &longs;peculabilia, & è contra, oppor<lb/>tuna quadam vici&longs;situdine conuertuntur. </s>

<s>Sed <lb/>nec &longs;emper leuiora, aut minoris ex &longs;e conditio<lb/>nis dixerim, quæ in contemplationem mecha<lb/>nicam cadunt, vtpotè quænon modò ad res per <lb/>magni momenti, ac nece&longs;&longs;arium humanæ vi<lb/>tæ v&longs;um, &longs;plendoremque ordinantur: quæque <lb/>proinde apud Reges, ac Principes ex quo ge-<pb/>nus hominum capit, incomparabilem obtinue<lb/>runt extimationem; verùm quæ &longs;peciali qua<lb/>dam ratione, in aliam ampliorem, <expan abbr="diuinioremq.">diuinioremque</expan> <lb/>contemplationem, &longs;ummi videlicet rerum ma<lb/>chinatoris nos conducant. </s>

<s>Sed <lb/>nec &longs;emper leuiora, aut minoris ex &longs;e conditio<lb/>nis dixerim, quæ in contemplationem mecha<lb/>nicam cadunt, vtpotè quænon modò ad res per <lb/>magni momenti, ac nece&longs;&longs;arium humanæ vi<lb/>tæ v&longs;um, &longs;plendoremque ordinantur: quæque <lb/>proinde apud Reges, ac Principes ex quo ge-<pb xlink:href="005/01/005.jpg"/>nus hominum capit, incomparabilem obtinue<lb/>runt extimationem; verùm quæ &longs;peciali qua<lb/>dam ratione, in aliam ampliorem, <expan abbr="diuinioremq.">diuinioremque</expan> <lb/>contemplationem, &longs;ummi videlicet rerum ma<lb/>chinatoris nos conducant. </s>

<s>Quippe qui talia hu<lb/>mano ingenio excogitare dedit molimina, qui<lb/>bus multaq<gap/>&longs;upr a naturam &longs;unt, natur am ip<lb/>&longs;am emulando perficeret, arte &longs;uperando ea à <lb/>quibus natur a vincimur, (vt Antipho &longs;cribit<emph.end type="italics"/><arrow.to.target n="marg1"/><lb/><emph type="italics"/>Poeta) & cæle&longs;tem machinam eiu&longs;que mul<lb/>tiplicem, ac inuariabilem motum, orbi&longs;que to<lb/>tius molem imitaretur: vt Archimedes alij<lb/>que permulti in&longs;ignes Mechanici opere præ<lb/>&longs;titerunt, & Cambray publico in foro li<lb/>cet videre. </s>

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<s>Quæ &longs;olis homini<lb/>bus iccirco data e&longs;t, vt perhibet Philo&longs;ophus,<emph.end type="italics"/><arrow.to.target n="marg2"/><lb/><emph type="italics"/>quia &longs;oli inter omnia animalia &longs;umma pru<lb/>dentia, in qua ars tota fundatur præditi &longs;unt. <lb/></s>

<s>Vnde &longs;icut mens ip&longs;a humana imaginem <lb/>diuinæ &longs;apientiæ, ac prouidentiæ refert dum <lb/>cuncta rectè di&longs;ponit; ita, & manus homi<lb/>nis, omnipotentiam quodammodo exprimit <lb/>Creatoris, dum tam varia, ac mira, Me-<pb/>chanica cognitione duce patratur. </s>

<s>Quæ &longs;i <lb/>cunctis ob &longs;ui generis excellentiam maximo <lb/>cum animarum prouentu, atque decore con<lb/>&longs;ideranda &longs;e offerunt: quàm dignè interdùm <lb/>hac in contemplatione morabitur, quem fru<lb/>ctum non ex ea iucundè decerpet, qui diuina<lb/>rum rerum meditationibus a&longs;&longs;uetus, pium<lb/>que in Deum affectum exercens ip&longs;um &longs;um<lb/>mum moderatorem veneratur, ac iugiter in <lb/>mundi regimine imitatur; dum non modo <lb/>firmum &longs;e Eccle&longs;iæ Cardinem præbet, in <lb/>quo eius circumuertitur, ac fulcitur machi<lb/>na gubernationis. </s>

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<s>Tibi igitur Cardinalis Ampli&longs;si<lb/>me dum talia tuum erga Sancti&longs;simum <lb/>Patruum ter optimum Pontificem agis, mu<lb/>neraque penè diuina per&longs;oluis, non mediocris <lb/>prouentus &longs;imul, ac iucunditatis offertur <lb/>occa&longs;io in his, quos dicaui præ&longs;tanti&longs;simæ <lb/>&longs;cientiæ Commentarijs. </s>

<s>Nam, & motus <lb/>orbis, vel cuiu&longs;que globi circa cardines, ac <pb/>circuli circa centrum, admirabile&longs;que eius <lb/>proprietates in ip&longs;is patebunt; & modus quo <lb/>paruo gubernaculo ingentia circumferuntur <lb/>nauigia: quod etiam Iacobus Apo&longs;tolus mi-<emph.end type="italics"/><arrow.to.target n="marg3"/><lb/><emph type="italics"/>ratus e&longs;t, & ad martalia tran&longs;tulit. </s>

<s>Nam, & motus <lb/>orbis, vel cuiu&longs;que globi circa cardines, ac <pb xlink:href="005/01/007.jpg"/>circuli circa centrum, admirabile&longs;que eius <lb/>proprietates in ip&longs;is patebunt; & modus quo <lb/>paruo gubernaculo ingentia circumferuntur <lb/>nauigia: quod etiam Iacobus Apo&longs;tolus mi-<emph.end type="italics"/><arrow.to.target n="marg3"/><lb/><emph type="italics"/>ratus e&longs;t, & ad martalia tran&longs;tulit. </s>

<s>In&longs;uper <lb/>& quo pacto vela dare liceat, ac remigio vti <lb/>contingat ad nauis progre&longs;&longs;um: Quod Petri <lb/>nauim quam in altum ducere Saluator præ<lb/>cepit ob oculis ponit: Et qua denique ratione<emph.end type="italics"/><arrow.to.target n="marg4"/><lb/><emph type="italics"/>exiguo pondere ingentia leuentur onera, vt <lb/>vniuer&longs;aliter di&longs;camus; cum Paulo, quan-<emph.end type="italics"/><arrow.to.target n="marg5"/><lb/><emph type="italics"/>tumuis magnum, ac diuturnum in &longs;e &longs;it, <lb/>quod pro Chri&longs;ti nomine patimur in hac vi<lb/>ta, momentaneum tamen, ac leue in fide<lb/>lium &longs;tatera inueniri, &longs;olo pondere eius quam <lb/>&longs;peramus futuræ gloriæ, ac retributionis: <lb/>Aliaque permulta id genus licebit &longs;pectare, <lb/>non minus forta&longs;&longs;e ad morealem, ac politi<lb/>cam in&longs;tructionem, quàm ad vtilem in reli<lb/>quis, iucundamque Prinoipis exercitatio<lb/>nem. </s>

<s>Quod &longs;i Amplitudini tuæ inter has tem<lb/>porum angu&longs;tias, non &longs;atis digna obtulerim, <lb/>menti&longs;que propo&longs;itum haud plenè a&longs;&longs;ecutus <lb/>fuerim, ob&longs;equenti&longs;simum, grati&longs;simumque <lb/>&longs;altem in eis a&longs;pice votum, dum vix è Tri<lb/>remibus po&longs;t longam nauigationem tecum <pb/>egre&longs;&longs;us, multis, ac varijs honoribus au<lb/>ctus, vt quo poteram pacto ob&longs;equium erga <lb/>te meum illicò præ&longs;tarem, perpetuoque ani<lb/>mo in&longs;eruirem, ea detuli prout iacent; morem <lb/>putans gerere tuæ voluntati.<emph.end type="italics"/></s>

<s>Quod &longs;i Amplitudini tuæ inter has tem<lb/>porum angu&longs;tias, non &longs;atis digna obtulerim, <lb/>menti&longs;que propo&longs;itum haud plenè a&longs;&longs;ecutus <lb/>fuerim, ob&longs;equenti&longs;simum, grati&longs;simumque <lb/>&longs;altem in eis a&longs;pice votum, dum vix è Tri<lb/>remibus po&longs;t longam nauigationem tecum <pb xlink:href="005/01/008.jpg"/>egre&longs;&longs;us, multis, ac varijs honoribus au<lb/>ctus, vt quo poteram pacto ob&longs;equium erga <lb/>te meum illicò præ&longs;tarem, perpetuoque ani<lb/>mo in&longs;eruirem, ea detuli prout iacent; morem <lb/>putans gerere tuæ voluntati.<emph.end type="italics"/></s>

<s><margin.target id="marg1"/>Apud Ari&longs;<lb/>tot. in <lb/>qu&ecedil;&longs;t. </s>

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<s>IOANNIS <lb/>DE GVEVARA <lb/>CLER. REG. MIN. <lb/>IN ARISTOTELIS MECHANICAS <lb/>Commentarii: <lb/><emph type="italics"/>VNA CVM ADDITIONIBVS QVIBVSDAM <lb/>Ad eandem materiam pertinentibus.<emph.end type="italics"/></s>

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<s>Siquidem in re&longs;o<lb/>lutione, ad ea reducuntur & in ip&longs;is fundantur quæcunque <lb/>de mechanicis in&longs;trumentis, <expan abbr="eorumq.">eorumque</expan> motionibus in progre&longs;<lb/>&longs;u demon&longs;trantur, vel quæcunque ad artificio&longs;am motionem, <lb/>aut detentionem grauium & leuium hìc o&longs;tenduntur. </s>

<s>Proin<pb pagenum="2"/><expan abbr="deq.">deque</expan> ex ip&longs;is totam artem mechanicam tanquam ex proprijs <lb/>principijs intelligemus con&longs;urgere. </s>

<s>Proin<pb xlink:href="005/01/010.jpg" pagenum="2"/><expan abbr="deq.">deque</expan> ex ip&longs;is totam artem mechanicam tanquam ex proprijs <lb/>principijs intelligemus con&longs;urgere. </s>

<s>Quamuis huc etiam &longs;pe<lb/>ctent, & inter eadem principia computari debeant, quæ Ar<lb/>chimedes, Hero, ac Pappus cum alijs tradiderunt de centro <lb/>grauitatis, in quibus pariter variæ, ac perplures demon&longs;tra<lb/>tiones mechanicæ fundantur: quæ que propterea à nobis bre<lb/>ui&longs;&longs;imè colligentur, & ad complementum doctrinæ inferius <lb/>in Additionibus afferentur. </s>

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<s>E&longs;t enim in quibu&longs;dam partibus di<lb/>minutum in alijs verò redundans, ac in multis confu&longs;um. <lb/></s>

<s>Quapropter nonnullæ nobis permittendæ erunt tran&longs;po&longs;itio<lb/>num reductiones, <expan abbr="verborumq.">verborumque</expan> re&longs;ecationes, aut additiones <pb pagenum="3"/>circa litteram ip&longs;ius textus, quam penitus & in rigore &longs;emper <lb/>&longs;ectari nequaquam liceret, ob præfatam corruptionem. <lb/></s>

<s>Quapropter nonnullæ nobis permittendæ erunt tran&longs;po&longs;itio<lb/>num reductiones, <expan abbr="verborumq.">verborumque</expan> re&longs;ecationes, aut additiones <pb xlink:href="005/01/011.jpg" pagenum="3"/>circa litteram ip&longs;ius textus, quam penitus & in rigore &longs;emper <lb/>&longs;ectari nequaquam liceret, ob præfatam corruptionem. <lb/></s>

<s>Pro viribus tamen eam &longs;ectabimur, &longs;en&longs;um enucleando, ac <lb/>exponendo, nunc per modum parafra&longs;is, nunc vero per mo<lb/>dum interpretationis & exten&longs;ionis. </s>

<s>Multa in quibu&longs;dam lo<lb/>cis addendo, prout opus fuerit ad complementum doctrinæ, <lb/><expan abbr="multaq.">multaque</expan> pariter &longs;ub Additionum titulo, &longs;eor&longs;um extra com<lb/>mentarios annectendo, vt &longs;iggillatim quæ &longs;citu digna &longs;unt, & <lb/>ad mechanicam contemplationem pertinent pleniùs eluce<lb/>&longs;cant. </s><figure/><pb pagenum="4"/>

<s>PRIMA PARS <lb/>MECHANICES <lb/>ARISTOTELIS STAGIRITAE <lb/>IN QVA EA CONTINENTVR, <lb/>quæ ad naturam Mechanicæ facultatis, <lb/>& principia operationum ip&longs;ius <lb/>pertinent.</s>

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<s>Huiu&longs;modi autem &longs;unt, in quibus & minora &longs;uperant <lb/>maiora: & quæcunque momentum paruum habentia, magna <lb/>moisent pondera; & omnia ferè illa, quæ mechanica nuncupa<lb/>mus & problemata. </s>

<s>Sunt autem hæc neque naturalibus om<lb/>nino quæ&longs;iionibus eadem, neque &longs;eiugata valde: verum ma<lb/>ibematicarum contemplationum, <expan abbr="naturaliumq.">naturaliumque</expan> communia.<emph.end type="italics"/></s><pb pagenum="5"/>

<s>COMMENTARIVS.</s>

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<s>Quia &longs;cilicet non eo<lb/>dem modo nec eadem ratione procedunt problemata me<lb/>chanica, ac naturalia &longs;eu phy&longs;ica. </s>

<s>Siquidem diuer&longs;is vtun<pb pagenum="6"/>tur principijs, vt fu&longs;iùs infra explicabitur; <expan abbr="diuer&longs;asq.">diuer&longs;asque</expan> omnino <lb/>demon&longs;trationes efficiunt. </s>

<s>Siquidem diuer&longs;is vtun<pb xlink:href="005/01/014.jpg" pagenum="6"/>tur principijs, vt fu&longs;iùs infra explicabitur; <expan abbr="diuer&longs;asq.">diuer&longs;asque</expan> omnino <lb/>demon&longs;trationes efficiunt. </s>

<s>Quoniam verò ea, circa quæ me<lb/>chanica facultas ver&longs;atur nempe pondus & vis, qua illud mo<lb/>uetur, &longs;ub obiecto adæquato phy&longs;ices materialiter contine<lb/>tur, ac non &longs;olùm geometricis, &longs;ed naturalibus quoque ratio<lb/>nibus nonnulla de ip&longs;is demon&longs;trantur; hinc e&longs;t, vt mechani<lb/>ca problemata à phy&longs;icis non dicantur valde &longs;eiuncta, nec <lb/>admodum di&longs;tinguantur. </s>

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<s>Vnde etiam apud latinos machina, tam <lb/>animi quoddam inuentum aut molimen, quàm in&longs;trumentum <lb/>aliquod artificio&longs;um quo moles leuantur, aut quocunque <lb/>modo pelluntur denotare vt plurimum con&longs;ueuit, iuxta illud <lb/><arrow.to.target n="marg6"/> Taciti, Nihil tam ignarum barbaris quàm machinamenta, & <lb/>a&longs;tus oppugnationum. </s>

<s><expan abbr="Illudq.">Illudque</expan> Liuij, Turres contabulatas, <pb pagenum="7"/><expan abbr="machinamentaq.">machinamentaque</expan> alia quatiendis muris portabant. </s>

<s><expan abbr="Illudq.">Illudque</expan> Liuij, Turres contabulatas, <pb xlink:href="005/01/015.jpg" pagenum="7"/><expan abbr="machinamentaq.">machinamentaque</expan> alia quatiendis muris portabant. </s>

<s>Nam &longs;iue <lb/>loquendo de machinis bellicis, &longs;iue de machinis nauticis aut <lb/>architectonicis, &longs;emper machina vtrumque &longs;ignificatum in<lb/>uoluit, aut &longs;altem admittit. </s>

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<s>Iam verò &longs;i originem huius facultatis &longs;ecundum lati&longs;&longs;imam <lb/>eius &longs;ignificationem &longs;pectatæ con&longs;ideremus, eam non ni&longs;i <expan abbr="c&utilde;">cum</expan> <lb/>ip&longs;a natura humana ortum habui&longs;&longs;e comperiemus. </s>

<s>Quando<lb/>quidem nec in ip&longs;is mundi primordijs defuerunt <expan abbr="machinam&etilde;-ta">machinamen<lb/>ta</expan> quibus arte quadam innata, vel infu&longs;a primis parentibus, <lb/>ip&longs;i &longs;e&longs;e, & à contrarijs defenderent, & commoda con&longs;ecta<lb/>rentur ad vitam <expan abbr="incolumitatemq.">incolumitatemque</expan> tuendam; Nam & corpora <pb pagenum="8"/>tegere, & domos con&longs;truere, & agros arare, & commeatus <lb/>vehere, aliaue onera per aquas ac terras longius a&longs;portare; <lb/><expan abbr="aquamq.">aquamque</expan> ip&longs;am ex imis haurire, oleum exprimere, triticum <lb/>terere, ligna cedere, ferrum acuere, <expan abbr="aliaq.">aliaque</expan> huiu&longs;modi perage<lb/>re ad varios v&longs;us ex nece&longs;&longs;itate, vel ab initio c&oelig;perunt; quæ <lb/>cum in&longs;trumenta nonnulla mechanica, tùm artem ip&longs;am ma<lb/>chinandi &longs;upponunt. </s>

<s>Quando<lb/>quidem nec in ip&longs;is mundi primordijs defuerunt <expan abbr="machinam&etilde;-ta">machinamen<lb/>ta</expan> quibus arte quadam innata, vel infu&longs;a primis parentibus, <lb/>ip&longs;i &longs;e&longs;e, & à contrarijs defenderent, & commoda con&longs;ecta<lb/>rentur ad vitam <expan abbr="incolumitatemq.">incolumitatemque</expan> tuendam; Nam & corpora <pb xlink:href="005/01/016.jpg" pagenum="8"/>tegere, & domos con&longs;truere, & agros arare, & commeatus <lb/>vehere, aliaue onera per aquas ac terras longius a&longs;portare; <lb/><expan abbr="aquamq.">aquamque</expan> ip&longs;am ex imis haurire, oleum exprimere, triticum <lb/>terere, ligna cedere, ferrum acuere, <expan abbr="aliaq.">aliaque</expan> huiu&longs;modi perage<lb/>re ad varios v&longs;us ex nece&longs;&longs;itate, vel ab initio c&oelig;perunt; quæ <lb/>cum in&longs;trumenta nonnulla mechanica, tùm artem ip&longs;am ma<lb/>chinandi &longs;upponunt. </s>

<s>Quòd &longs;i &longs;ecundum propriam acceptionem loquamur de <lb/>facultate mechanica, quatenus vt diximus ars quædam e&longs;t, <lb/>vel &longs;cientia, quæ geometricis nixa principijs peculiari <expan abbr="quadã">quadam</expan> <lb/>ratione circa &longs;uum obiectum per demon&longs;trationes ver&longs;atur, <lb/>ac præcepta tradit, quibus homo in v&longs;u ac motione grauium, <lb/>& leuium dirigitur ac iuuatur; &longs;ic nullum extat monimentum <lb/>quo ante tempora Eudoxij Architæ, ac Platonis illam c&ecedil;pi&longs;&longs;e <lb/>a&longs;&longs;ereremus. </s>

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<s>Exinde <lb/>igitur mechanica facultas propagari c&oelig;pit, nam Ari&longs;totelem <lb/>&longs;ecuti, vel imitati &longs;unt multi, præ&longs;ertim, qui &longs;equenti &longs;eculo <lb/>maximè claruerunt, vt Archimedes Siracu&longs;anus, cuius do<lb/>ctrina, ac &longs;ummo ingenio huiu&longs;modi facultas maxima incre<lb/>menta &longs;u&longs;cepit. </s>

<s>Item Cte&longs;ibus machinator præ&longs;tanti&longs;&longs;imus <pb pagenum="9"/>qui &longs;piritalia & hydraulicas machinas primus inuenit. </s>

<s>Item Cte&longs;ibus machinator præ&longs;tanti&longs;&longs;imus <pb xlink:href="005/01/017.jpg" pagenum="9"/>qui &longs;piritalia & hydraulicas machinas primus inuenit. </s>

<s>Dein<lb/>de vero Philo Bizantius, cuius mechanica peritia ab Herone <lb/>commemoratur. </s>

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<s>33. <lb/>præcipuè digno&longs;catur, Ob&longs;eruandum in primis e&longs;t, id quod <lb/>per mechanicam facultatem intendimus, & ad quod tanquam <lb/>ad finem con&longs;e quendum omnis mechanica contemplatio or<lb/>dinatur, aliud non e&longs;&longs;e, quàm grauis aut leuis cuiu&longs;que cor<lb/>poris motionem, vel quietem, quæ parua vt plurimum virtu<lb/>te, arte ip&longs;a mirabiliter comparatur, &longs;iue motio &longs;it &longs;ecundum <lb/>naturam, &longs;iue &longs;it præter aut contra naturam ip&longs;ius corporis <lb/>grauis aut leuis. </s>

<s>Porro inductione con&longs;tat, mechanicum om<lb/>nem conatum, <expan abbr="omnemq.">omnemque</expan> tractatum in admirabilem lationem, <lb/>aut &longs;tatum corporum ordinari ex ip&longs;ius artis proprio in&longs;titu<lb/>to, vt ad leuanda, vel detinenda etiam exigua virtute quæ-<pb pagenum="10"/>cunque pondera, ad aerem vel aquam artificiosè pellendam, <lb/>attrahendam, aut continendam, ad mi&longs;&longs;ilia proijcienda, <expan abbr="aliaq.">aliaque</expan> <lb/>&longs;ecundum varias po&longs;itiones locanda, vel de loco ad locum, <lb/>diuer&longs;imodè transferenda, & &longs;imilia, quæ per &longs;e nota erunt <lb/>mechanicamenta omnia ad id præ&longs;tandum accomodata, ac <lb/>&longs;peculationes mechanicas recen&longs;enti. </s>

<s>Porro inductione con&longs;tat, mechanicum om<lb/>nem conatum, <expan abbr="omnemq.">omnemque</expan> tractatum in admirabilem lationem, <lb/>aut &longs;tatum corporum ordinari ex ip&longs;ius artis proprio in&longs;titu<lb/>to, vt ad leuanda, vel detinenda etiam exigua virtute quæ-<pb xlink:href="005/01/018.jpg" pagenum="10"/>cunque pondera, ad aerem vel aquam artificiosè pellendam, <lb/>attrahendam, aut continendam, ad mi&longs;&longs;ilia proijcienda, <expan abbr="aliaq.">aliaque</expan> <lb/>&longs;ecundum varias po&longs;itiones locanda, vel de loco ad locum, <lb/>diuer&longs;imodè transferenda, & &longs;imilia, quæ per &longs;e nota erunt <lb/>mechanicamenta omnia ad id præ&longs;tandum accomodata, ac <lb/>&longs;peculationes mechanicas recen&longs;enti. </s>

<s>Deinde ob&longs;eruandum e&longs;t, ad prædictam motionem, aut <lb/>quietem arte con&longs;equendam, duo poti&longs;&longs;imum con&longs;iderari à <lb/>Mechanico; nimirum & quantitatem ponderis ex parte cor<lb/>poris mouendi, & quantitatem virtutis ex parte mouentis, &longs;i<lb/>ue immediatè ip&longs;e moueat per virtutem intrin&longs;ecam, fiue per <lb/>impre&longs;&longs;ionem impetus, aut per in&longs;trumenta. </s>

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<s>His ergo præmi&longs;&longs;is facile primo intelligetur, &longs;ubiectum ma-<pb pagenum="11"/>teriale adæquatum facultatis mechanicæ e&longs;&longs;e grauia & leuia, <lb/>&longs;eu quantitatem ponderis ip&longs;orum, ac virtutis qua moueri <lb/>debent aut detineri. </s>

<s>His ergo præmi&longs;&longs;is facile primo intelligetur, &longs;ubiectum ma-<pb xlink:href="005/01/019.jpg" pagenum="11"/>teriale adæquatum facultatis mechanicæ e&longs;&longs;e grauia & leuia, <lb/>&longs;eu quantitatem ponderis ip&longs;orum, ac virtutis qua moueri <lb/>debent aut detineri. </s>

<s>Ratio autem e&longs;t, quia in &longs;cientijs, illud <lb/>dicitur &longs;ubiectum materiale adæquatum, quod complectitur <lb/>omnia de quibus in &longs;cientia tractatur; omne autem de quo in <lb/>hac &longs;cientia tractatur, reducitur ad corpus aliquod graue, aut <lb/>leue mouendum aut detinendum, &longs;iue ad quantitatem virtu<lb/>tis qua moueri debet aut detineri; <expan abbr="Proindeq.">Proindeque</expan> ip&longs;a grauia & <lb/>leuia vt &longs;ic, <expan abbr="&longs;imulq.">&longs;imulque</expan> virtus motiua ac detentiua illorum, me<lb/>ritò huius facultatis mechanicæ materiale &longs;ubiectum adæ<lb/>quatum de&longs;ignatur. </s>

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<s>Quo tandem fit tertio, vt obiectum totale, & adæquatum <lb/>mechanicæ facultatis in vniuer&longs;um, &longs;int ip&longs;a grauia & leuia <lb/>prout artificiosè mobilia, & vt ita dicam quie&longs;cibilia, <expan abbr="&longs;imulq.">&longs;imulque</expan> <lb/>omnia quæ de ip&longs;is demon&longs;trantur in hac eadem &longs;cientia. <lb/></s>

<s>Quod certe non ob&longs;curè &longs;umitur ex Pappo Alexandrino lib. <lb/>8. &longs;uarum Collectionum, vbi mechanicam contemplationem <lb/>docet ver&longs;ari circa &longs;tatum & lationem corporum, <expan abbr="motumq.">motumque</expan> <lb/>&longs;ecundum locum in vniuer&longs;o, vt eorum quæ natura fiunt, cau<lb/>&longs;as reddat; eorum verò quæ à natura &longs;ua di&longs;cedere coguntur <lb/>extra propria loca, in contrarios motus per &longs;ua theoremata <pb pagenum="12"/>transferat. </s>

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<s>Nihilominus 1. Metaphi&longs;ices cap.

1. idem <lb/>Philo&longs;ophus artem videtur confundere cum &longs;cientia &longs;altem <lb/>practica; ait enim, artem e&longs;&longs;e de vniuer&longs;alibus, ac propter <lb/>cau&longs;am ea quæ &longs;iunt cogno&longs;cere, exemplum adhibens tum <pb pagenum="13"/>medicinæ, tum architecturæ; imò ip&longs;as mathematicas di&longs;ci<lb/>plinas indefinitè loquendo, quas con&longs;tat e&longs;&longs;e &longs;cientias, artes <lb/>appellat. </s>

1. idem <lb/>Philo&longs;ophus artem videtur confundere cum &longs;cientia &longs;altem <lb/>practica; ait enim, artem e&longs;&longs;e de vniuer&longs;alibus, ac propter <lb/>cau&longs;am ea quæ &longs;iunt cogno&longs;cere, exemplum adhibens tum <pb xlink:href="005/01/021.jpg" pagenum="13"/>medicinæ, tum architecturæ; imò ip&longs;as mathematicas di&longs;ci<lb/>plinas indefinitè loquendo, quas con&longs;tat e&longs;&longs;e &longs;cientias, artes <lb/>appellat. </s>

<s>Ex quibus primò dicendum erit, mechanicam facultatem <lb/>verè & propriè e&longs;&longs;e artem, prout in hoc libello, & in explica<lb/>to textu a&longs;&longs;umitur ab Ari&longs;totele. </s>

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<s>In primis enim e&longs;t <lb/>intellectualis cognitio eorum quæ circa motionem localem, <lb/>aut quietem grauium ac leuium contingunt, orta ex præexi<lb/>&longs;tenti alia cognitione principiorum, quæ &longs;iue &longs;int per &longs;e nota, <lb/>&longs;iue demon&longs;trentur in alia &longs;uperiori &longs;cientia, vt infra dicetur, <lb/>omnino tamen &longs;unt cau&longs;a eius quod a&longs;&longs;eritur in conclu&longs;ione. <lb/></s>

<s>Ideo <expan abbr="namq.">namque</expan> dicimus in motu circulari, partem diametri, quæ <lb/>magis di&longs;tat à centro circuli, velocius moueri; quia hæe ma-<pb pagenum="14"/>gis participat de motu recto, ac naturali à quo prouenit ip&longs;a <lb/>maior velocitas tanquam à cau&longs;a intrin&longs;eca, & hoc ita &longs;e ha<lb/>bere demon&longs;tratur ex principijs geometricis. </s>

<s>Ideo <expan abbr="namq.">namque</expan> dicimus in motu circulari, partem diametri, quæ <lb/>magis di&longs;tat à centro circuli, velocius moueri; quia hæe ma-<pb xlink:href="005/01/022.jpg" pagenum="14"/>gis participat de motu recto, ac naturali à quo prouenit ip&longs;a <lb/>maior velocitas tanquam à cau&longs;a intrin&longs;eca, & hoc ita &longs;e ha<lb/>bere demon&longs;tratur ex principijs geometricis. </s>

<s>Similiter non <lb/>ex alio dicimus rotunda corpora &longs;uper planum, facilius mo<lb/>ueri, ni&longs;i quia parua vel minima &longs;ui parte planum contingám, <lb/>ac minus offen&longs;ant. </s>

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<s>Neque enim contingenter pon<lb/>dus libræ aut vectis magis grauitat in parte remotiori à fulci<lb/>mento ex eo quòd pars diametri, quæ plus à centro circuli <lb/>di&longs;ce&longs;&longs;erit, magis ab eadem virtute moueri &longs;uapte natura <lb/>præualeat: &longs;ed nece&longs;&longs;ariò ac ineffabiliter, cùm nece&longs;&longs;ariò li<lb/>bra aut vectis in &longs;uo proprio motu con&longs;tituatur veluti diame<lb/>ter circuli; & hoc quod e&longs;t pondus in parte di&longs;tantiori à ful<lb/>cimento quod e&longs;t centrum, magis grauitare &longs;eu efficaciùs de<lb/>or&longs;um impellere e&longs;&longs;entialiter dependeat ab eo, quod e&longs;t par<lb/>tem illam di&longs;tantiorem à centro aptiorem e&longs;&longs;e ad motum, vt <lb/>aperti&longs;&longs;imè ex geometricis principijs demon&longs;trabitur. </s>

<s>Nec <lb/>per accidens e&longs;t, longiùs ferri mi&longs;&longs;ilia funda, quàm manu mi&longs;<lb/>&longs;a, quia in motu circulari qui fit per emi&longs;&longs;ionem, &longs;eu proie<lb/>ctionem, magis illa di&longs;tant à centro per fundæ v&longs;um, quàm &longs;i <lb/>&longs;ola manu proijcerentur, vt per &longs;e con&longs;tat; &longs;ed nece&longs;&longs;ariò ex <lb/>tali cau&longs;a talis procedit effectus, qui proinde aliter non pote&longs;t <lb/>&longs;e habere propter eandem rationem, vt in c&oelig;teris quoque <pb pagenum="15"/>facilè erit inductione probare. </s>

<s>Nec <lb/>per accidens e&longs;t, longiùs ferri mi&longs;&longs;ilia funda, quàm manu mi&longs;<lb/>&longs;a, quia in motu circulari qui fit per emi&longs;&longs;ionem, &longs;eu proie<lb/>ctionem, magis illa di&longs;tant à centro per fundæ v&longs;um, quàm &longs;i <lb/>&longs;ola manu proijcerentur, vt per &longs;e con&longs;tat; &longs;ed nece&longs;&longs;ariò ex <lb/>tali cau&longs;a talis procedit effectus, qui proinde aliter non pote&longs;t <lb/>&longs;e habere propter eandem rationem, vt in c&oelig;teris quoque <pb xlink:href="005/01/023.jpg" pagenum="15"/>facilè erit inductione probare. </s>

<s>Cumque ip&longs;æ cau&longs;æ ex qui<lb/>bus mechanica facultas &longs;uas elicit conclu&longs;iones, vel &longs;int per <lb/>&longs;e notæ, vt citius ferri, quod facilius mouetur; Aequalia ab <lb/>æqualibns non moueri, & &longs;imilia; vel fundentur in principijs <lb/>demon&longs;tratis in alia &longs;uperiori &longs;cientia, de quibus habetur ve<lb/>ra certitudo, & euidentia hinc vlterius fit, vt ip&longs;a pariter co<lb/>gnitio mechanicarum conclu&longs;ionum, eandem participet, ac <lb/>&longs;ortiatur euidentiam, vt commune e&longs;t omnibus &longs;cientijs, quæ <lb/>nimirum euidentiam non ni&longs;i ex principijs obtinent per re&longs;o<lb/>lutionem v&longs;que ad elementa, vt &longs;æpè docet Philo&longs;ophus in <lb/>Analiticis. </s>

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<s>Practi<lb/>ca verò &longs;cientia e&longs;t, cuius finis e&longs;t opus; nempè quæ ex &longs;e or<lb/>dinatur ad opus, vel operationem aliquam exercendam præ<lb/>ter ip&longs;am &longs;cientiam. </s>

<s>Mechanica autem facultas nullo modo <lb/>ab&longs;trahere pote&longs;t ab ordine quem e&longs;&longs;entialiter dicit ad <expan abbr="mot&utilde;">motum</expan> <pb pagenum="16"/>localem, aut quietem mobilibus impertiendam, & ad <expan abbr="mod&utilde;">modum</expan> <lb/>quo moueri debent vel quie&longs;cere. </s>

<s>Mechanica autem facultas nullo modo <lb/>ab&longs;trahere pote&longs;t ab ordine quem e&longs;&longs;entialiter dicit ad <expan abbr="mot&utilde;">motum</expan> <pb xlink:href="005/01/024.jpg" pagenum="16"/>localem, aut quietem mobilibus impertiendam, & ad <expan abbr="mod&utilde;">modum</expan> <lb/>quo moueri debent vel quie&longs;cere. </s>

<s>Nam licet nonnullæ pro<lb/>po&longs;itiones mechanicæ, &longs;i per &longs;e &longs;umantur, &longs;int &longs;peculatiuæ, eo <lb/>quod præci&longs;e &longs;i&longs;tere po&longs;&longs;ent in &longs;ola veritate, nihilominus pro<lb/>pter connexionem quam habent cum alijs practicis, & ordi<lb/>nem quem &longs;imul includunt ad praxim, verè con&longs;tituunt <expan abbr="vnã">vnam</expan> <lb/>&longs;cientiam totalem practicam. </s>

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<s>cap.

33. Et huiu&longs;inodi <lb/>dicimus e&longs;&longs;e facultatem mechanicam, cum verè pro fine ha<lb/>b<gap/>at opus externum, vt diximus, nempe motum localem & <lb/>arti&longs;icio&longs;um, vel quietem grauibus & leuibus impertiendam, <lb/>non &longs;ecus ac medicina con&longs;tituitur &longs;cientia practica, <lb/>co quod eius finis, ad quem ordinatur <lb/>tanquam ad proprium opus <lb/>&longs;it &longs;anitas anima<lb/>lis ho<lb/>minibus im<lb/>pertien<lb/>da. </s><pb pagenum="17"/>

<s><emph type="italics"/>Mechanicam facultatem vere ac proprie e&longs;&longs;e <lb/>&longs;cientiam Mathematicam.<emph.end type="italics"/></s>

Line 446

<s>Nihilenim prohibet, <lb/>idem diuer&longs;is principijs plurium &longs;cientiarum o&longs;tendi. </s>

<s>Quarto, nam licet mechanica facultas, vt ab alijs traditur, <pb pagenum="18"/>pa&longs;&longs;im vtatur demon&longs;trationibus mathematicis, id tamen fit, <lb/>vt de&longs;cendat ad particularia, & adaptetur ad praxim, vel vt <lb/>clarius innote&longs;cat veritas ab&longs;tractè con&longs;iderata, cum per figu<lb/>ras obijcitur &longs;en&longs;ibus, ac metiri po&longs;&longs;umus magnitudinem & <lb/>di&longs;tantiam, vt appareat proportio requi&longs;ita ad motum ip&longs;o<lb/>rum grauium. </s>

<s>Quarto, nam licet mechanica facultas, vt ab alijs traditur, <pb xlink:href="005/01/026.jpg" pagenum="18"/>pa&longs;&longs;im vtatur demon&longs;trationibus mathematicis, id tamen fit, <lb/>vt de&longs;cendat ad particularia, & adaptetur ad praxim, vel vt <lb/>clarius innote&longs;cat veritas ab&longs;tractè con&longs;iderata, cum per figu<lb/>ras obijcitur &longs;en&longs;ibus, ac metiri po&longs;&longs;umus magnitudinem & <lb/>di&longs;tantiam, vt appareat proportio requi&longs;ita ad motum ip&longs;o<lb/>rum grauium. </s>

<s>Quinto, nam e&longs;tò Mechanica &longs;cientia pluries indigeat au<lb/>xilio mathematico, nec po&longs;&longs;it multa probare, ni&longs;i mutuetur <lb/>aliqua ex principijs geometricis, imò & arithmeticis; non ta<lb/>men per hoc &longs;equitur, Mathematicis &longs;ubalternari, &longs;icut nec <lb/>Phy&longs;ica, & Theologia &longs;ubalternantur Metaphy&longs;icæ, quamuis <lb/>multa petant ex Metaphy&longs;ica. </s>

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<s>Primum e&longs;t, vt quæ tractantur in &longs;cientia &longs;ubalternata, non <lb/>po&longs;&longs;int <expan abbr="euid&etilde;ter">euidenter</expan> cogno&longs;ci, ni&longs;i ex ijs quæ traduntur ac <expan abbr="demõ-&longs;trantur">demon<lb/>&longs;trantur</expan> in &longs;cientia &longs;ubalternante, à qua propterea ip&longs;a &longs;cien<lb/>tia &longs;ubalternata dicitur intrin&longs;ecè & e&longs;&longs;entialiter dependere. <lb/></s>

<s>Ratio autem e&longs;t, quia &longs;cientia &longs;ubalternata cum non habeat <lb/>principia per &longs;e nota, & immediata, &longs;icut illa quæ immediatè <pb pagenum="19"/>pendet ab habitu principiorum, loco illorum nititur conclu<lb/>&longs;ionibus demon&longs;tratis in &longs;uperiori &longs;cientia. </s>

<s>Ratio autem e&longs;t, quia &longs;cientia &longs;ubalternata cum non habeat <lb/>principia per &longs;e nota, & immediata, &longs;icut illa quæ immediatè <pb xlink:href="005/01/027.jpg" pagenum="19"/>pendet ab habitu principiorum, loco illorum nititur conclu<lb/>&longs;ionibus demon&longs;tratis in &longs;uperiori &longs;cientia. </s>

<s>Et hac ratione <lb/>nihil demon&longs;tratur in Per&longs;pectiua, quod <expan abbr="nõ">non</expan> inferatur ex con<lb/>clu&longs;ionibus Geometriæ cui ip&longs;a &longs;ubordinatur; <expan abbr="nihilq.">nihilque</expan> in Mu<lb/>&longs;ica, quod non nitatur conclu&longs;ionibus ac principijs Arithme<lb/>ticæ cui &longs;imiliter ip&longs;a &longs;ubalternatur. </s>

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<s>Quibus po&longs;itis, dicendum e&longs;t, Mechanicam <expan abbr="facultat&etilde;">facultatem</expan> ab<pb pagenum="20"/>&longs;olutè ac totaliter non &longs;ubalternari Philo&longs;ophiæ naturali, &longs;ed <lb/>Mathematicæ; Ita &longs;en&longs;it expre&longs;sè Ari&longs;toteles in principio iam <lb/>explicato huius opu&longs;culi, cum ait, &longs;ubiectum quidem huius <lb/>facultatis e&longs;&longs;e Phy&longs;icum, con&longs;iderationem verò e&longs;&longs;e mathe<lb/>maticam. </s>

<s>Quibus po&longs;itis, dicendum e&longs;t, Mechanicam <expan abbr="facultat&etilde;">facultatem</expan> ab<pb xlink:href="005/01/028.jpg" pagenum="20"/>&longs;olutè ac totaliter non &longs;ubalternari Philo&longs;ophiæ naturali, &longs;ed <lb/>Mathematicæ; Ita &longs;en&longs;it expre&longs;sè Ari&longs;toteles in principio iam <lb/>explicato huius opu&longs;culi, cum ait, &longs;ubiectum quidem huius <lb/>facultatis e&longs;&longs;e Phy&longs;icum, con&longs;iderationem verò e&longs;&longs;e mathe<lb/>maticam. </s>

<s>Quod po&longs;tea omnes Philo&longs;ophi, ac Mathematici <lb/>vniuer&longs;aliter &longs;upponunt in di&longs;tributione, ac &longs;ubalternatione <lb/>Mathcmaticarum di&longs;ciplinarum, &longs;ubordinando hanc &longs;cien<lb/>tiam Geometricæ. </s>

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<s>Quo <lb/>fit vt proxima ratio &longs;ecundum quam de illo agitur, &longs;it tum <lb/>quantitas ponderis illius, ab&longs;trahendo à materia ponderante, <lb/>tùm quantitas virtutis mouentis aut detinentis, prout &longs;cilicet <lb/>vtraque quantitas coaptari, ac proportionari debet in ordine <lb/>ad motionem aut quietem artificio&longs;am: &longs;eu prout quantitas <lb/>ponderis &longs;ub&longs;tat motioni, aut quieti artificio&longs;æ, quam pro<lb/>pterea diximus, vltimò complere, & <expan abbr="cõ&longs;tituere">con&longs;tituere</expan> obiectum for<lb/>male huius &longs;cientiæ. </s>

<s>At huiu&longs;modi ratio formalis &longs;ic expli<lb/>cata, manife&longs;tè inuoluit quantitatem ab&longs;tractam à materia, <lb/>ac &longs;pecialiter pa&longs;&longs;ionem quandam quantitatis continuæ ac <lb/>permanentis, quæ e&longs;t obiectum Geometriæ; nempe artifi<lb/>cio&longs;am mobilitatem & quietem; imò talis mobilitas attendi<lb/>tur iuxta dimen&longs;ionem quantitatiuam ip&longs;ius mobilis, ac pro-<pb pagenum="21"/>portionem quam habet cum mouente, in tanta propinquita<lb/>te vel di&longs;tantia; ac per&longs;æpe fundatur in ip&longs;a figura quantitatis <lb/>mobilis aut mouendæ. </s>

<s>At huiu&longs;modi ratio formalis &longs;ic expli<lb/>cata, manife&longs;tè inuoluit quantitatem ab&longs;tractam à materia, <lb/>ac &longs;pecialiter pa&longs;&longs;ionem quandam quantitatis continuæ ac <lb/>permanentis, quæ e&longs;t obiectum Geometriæ; nempe artifi<lb/>cio&longs;am mobilitatem & quietem; imò talis mobilitas attendi<lb/>tur iuxta dimen&longs;ionem quantitatiuam ip&longs;ius mobilis, ac pro-<pb xlink:href="005/01/029.jpg" pagenum="21"/>portionem quam habet cum mouente, in tanta propinquita<lb/>te vel di&longs;tantia; ac per&longs;æpe fundatur in ip&longs;a figura quantitatis <lb/>mobilis aut mouendæ. </s>

<s>Ergo ratio formalis &longs;ub qua Mecha<lb/>nica facultas circa proprium &longs;ubiectum ver&longs;atur, eandem e&longs;<lb/>&longs;entialiter rationem &longs;ubiecti Geometriæ participat. </s>

Line 520

<s>Quare licet <expan abbr="&longs;ubiect&utilde;">&longs;ubiectum</expan> <lb/>materiale huius facultatis, quod e&longs;t graue, & leue, &longs;eu quan<lb/>titas ponderis cuiu&longs;que corporis mobilis &longs;ecundum locum, <lb/>connotet pa&longs;&longs;ionem quamdam corporis naturalis, quod con <lb/>&longs;tituitur &longs;ubiectum adæquatum Phy&longs;icæ; cum tamen non <expan abbr="cõ-&longs;ideretur">con<lb/>&longs;ideretur</expan> hic per habitudinemad illud, pertinere non pote&longs;t <lb/>ad &longs;cientiam phy&longs;icam; &longs;icut nec ip&longs;a quantitas, quæ con&longs;ti<lb/>tuitur &longs;ubiectum adæ quatum totius facultatis mathematicæ, <lb/>quamuis in &longs;e &longs;it affectio corporis naturalis, & pa&longs;&longs;io &longs;ub&longs;tar<lb/>tiæ corporeæ, de <expan abbr="illaq.">illaque</expan> abundè etiam tractetur in Phy&longs;ica. <lb/></s>

<s><expan abbr="Idemq.">Idemque</expan> exempli&longs;icari pote&longs;t in Mu&longs;ica & Per&longs;pectiua, quarum <pb pagenum="22"/>&longs;ubiecta materialia non minus &longs;unt phy&longs;ica, con&longs;ideratio ve<lb/>rò mathematica. </s>

<s><expan abbr="Idemq.">Idemque</expan> exempli&longs;icari pote&longs;t in Mu&longs;ica & Per&longs;pectiua, quarum <pb xlink:href="005/01/030.jpg" pagenum="22"/>&longs;ubiecta materialia non minus &longs;unt phy&longs;ica, con&longs;ideratio ve<lb/>rò mathematica. </s>

<s>Ac tandem aperti&longs;&longs;imè con&longs;tare pote&longs;t in<lb/>ductione partium eiu&longs;dem facultatis Mechanicæ. </s>

Line 536

<s>Ad tertium Re&longs;pondetur, nec omnia, nec &longs;ntis demon&longs;tra<lb/>ri po&longs;&longs;e ex principijs phy&longs;icis in hac &longs;cientia. </s>

<s>Porrò licet non<lb/>nulla de graui & leui &longs;npponantur, vel etiam probentur ex <lb/><gap/>is, cæteratamen vt plurimum & exactè non <expan abbr="demon&longs;trãtus">demon&longs;trantus</expan> <pb pagenum="23"/>ni&longs;i ex principijs geométricis, quare &longs;lcat de lride multa <lb/>pertractantur in Phy&longs;ica, quod ramen non tollit omnimod am <lb/>eius cognitionem ad Per&longs;pectiram refe<gap/>ita quamuis mul<lb/>ta de graui & lem &longs;umantur ex phy&longs;ic<gap/>, hoc non ob&longs;tat quo<lb/><gap/>s prout artificiosè mobilia &longs;unt, ex pro&longs;e&longs;&longs;o & omnino <lb/>&longs;olum cogno&longs;cantur in hac &longs;cientia ex principijs mathem ati<lb/>cis. </s>

<s>Porrò licet non<lb/>nulla de graui & leui &longs;npponantur, vel etiam probentur ex <lb/><gap/>is, cæteratamen vt plurimum & exactè non <expan abbr="demon&longs;trãtus">demon&longs;trantus</expan> <pb xlink:href="005/01/031.jpg" pagenum="23"/>ni&longs;i ex principijs geométricis, quare &longs;lcat de lride multa <lb/>pertractantur in Phy&longs;ica, quod ramen non tollit omnimod am <lb/>eius cognitionem ad Per&longs;pectiram refe<gap/>ita quamuis mul<lb/>ta de graui & lem &longs;umantur ex phy&longs;ic<gap/>, hoc non ob&longs;tat quo<lb/><gap/>s prout artificiosè mobilia &longs;unt, ex pro&longs;e&longs;&longs;o & omnino <lb/>&longs;olum cogno&longs;cantur in hac &longs;cientia ex principijs mathem ati<lb/>cis. </s>

<s>Et &longs;ic, grauia æ qudlia ex æqualibus di&longs;tan&longs;&longs;js æ què pon<lb/>derare, <expan abbr="vnumq.">vnumque</expan> in libra non po&longs;&longs;e aliud vincere, non &longs;atis <lb/>probatur ex illo principio phyfico, quod àctio debeat e&longs;&longs;e ab <lb/>inæquali proportione. </s>

Line 548

<s>Ex quibus fæcil<gap/> apparet quid re&longs;pandendum &longs;it ad quar<lb/>tum & quintum argumentum, nem peprincipia mathemati<lb/>ca non modo in mechanica &longs;oientia de&longs;eruire ad maiorem <lb/>claritatem doctrinæ, & vt hæc aptetur ad praxim circa parti<lb/>cularia, &longs;ed ab&longs;olutè ad demon&longs;trandas &longs;uas conclu&longs;iones in <lb/>vniuer&longs;um, quas quippe aliter non po&longs;&longs;et omninò probare. <lb/></s>

<s>Id quod non &longs;olum verificatur in vni vel altera conclu&longs;ione, <lb/>&longs;ed ferè in omnibus, vt in progre&longs;&longs;u con&longs;tabit. </s><pb pagenum="24"/>

<s>Id quod non &longs;olum verificatur in vni vel altera conclu&longs;ione, <lb/>&longs;ed ferè in omnibus, vt in progre&longs;&longs;u con&longs;tabit. </s><pb xlink:href="005/01/032.jpg" pagenum="24"/>

<s>Quod <expan abbr="tand&etilde;">tandem</expan> afferebatur de ortu Mechanices ex Phy&longs;ica, <lb/>& Mathematica ad probandum e&longs;&longs;e &longs;cientiam ex vtraque <lb/>conflatam, &longs;i rectè con&longs;ideretur, nullius e&longs;t momenti; nam <lb/>vere dicitur ex Phy&longs;ica &longs;ump&longs;i&longs;&longs;e &longs;ubiectum, & ex Geome<lb/>tria principia quibus in &longs;uis demon&longs;trationibus procederet; <lb/>ex quo tamen non &longs;equitur, ip&longs;am veluti mixtam quandam <lb/>re&longs;ultare &longs;cientiam, partim &longs;cilicet Phy&longs;icam, partim verò <lb/>Mathematicam; tum quia &longs;peci&longs;icatio &longs;cientiarum vt diximus <lb/>non attenditur ex &longs;ubiecto materiali, &longs;ed ex obiecto formali; <lb/>tum etiam, quia nequit vna eademque &longs;cientia, pluribus &longs;cien<lb/>tijs omnino diuer&longs;is &longs;ubalternari, cum vnitas ip&longs;ius attenda<lb/>tur penes vnitatem eiu&longs;dem obiecti formalis, quod mutuari <lb/>debet vel ex vna, vel ex altera &longs;uperiori &longs;cientia. </s>

Line 558

<s>Vnde potius &longs;en&longs;it Philo&longs;ophus, Me<lb/>chanicam facultatem de his rebus agere, quæ communes &longs;unt <lb/>naturalibus ac Mathematicis quæ&longs;tionibus (quamuis &longs;ub di<lb/>uer&longs;a ratione formali) cui&longs;modi &longs;unt quantitas ponderis, &longs;eu <lb/>ip&longs;a ponderantia, quæ dicuntur grauia & leuia, ac virtus qua <lb/>ip&longs;a mouentur aut detinentur. </s>

<s>Siquidem de his omnibus <lb/>multa quæruntur in phy&longs;icis, prout &longs;unt affectiones corporis <lb/>naturalis, vel corpora quædam naturalia; <expan abbr="multaq.">multaque</expan> pa<lb/>riter in mathematicis, prout dimen&longs;ionem habent <lb/>quantitatiuam, aut virtutis, ab&longs;trahendo <lb/>ab hac vel illa materia, <expan abbr="peculiaresq.">peculiaresque</expan> <lb/>fortiuntur pa&longs;&longs;iones in ordine <lb/>ad motum arti&longs;i<lb/>cio&longs;um. </s><pb pagenum="25"/>

<s><emph type="italics"/>Quæ nam de&longs;criptio quidditatiua huius facul<lb/>tatis colligatur ex dictis, & quo pacto <lb/>ab alijs &longs;cientijs di&longs;tinguatur.<emph.end type="italics"/></s>

Line 574

<s>Denique <lb/>per cæteras particulas explicatur vltima differentia, ex pro<lb/>prio obiecto ac fine de&longs;umpta, qua certè huiu&longs;modi &longs;cientia <lb/>optimè di&longs;tinguitur ab illis quæ non ver&longs;antur circa quantita<lb/>tem aliquam; tum ab illa contemplatione Logica, aut Me<lb/>taphi&longs;ica, quæ tantum ver&longs;atur circa quantitatem prædica<lb/>mentalem; item à Phy&longs;ica quæ circa quantitatem &longs;olum <lb/>ver&longs;atur in quantum e&longs;t affectio corporis naturalis, & in ordi<lb/>ne ad principium motus & quietis naturalis. </s>

<s>Rur&longs;us non <lb/>minus di&longs;tinguitur, eadem differentia, à reliquis di&longs;ciplinis <lb/>Mathematicis, nam licet conueniat cum illis in hoc quod e&longs;t <pb pagenum="26"/>ver&longs;ari circa quantitatem modo quodam ab&longs;tracto à materia, <lb/>illam tamen contrahit ad quantitatem ponderis grauium, & <lb/>leuium, ac virtutis qua debent moueri, &longs;icetnon determi<lb/>net materiam ponderantem, aut virtutis mouentis. </s>

<s>Rur&longs;us non <lb/>minus di&longs;tinguitur, eadem differentia, à reliquis di&longs;ciplinis <lb/>Mathematicis, nam licet conueniat cum illis in hoc quod e&longs;t <pb xlink:href="005/01/034.jpg" pagenum="26"/>ver&longs;ari circa quantitatem modo quodam ab&longs;tracto à materia, <lb/>illam tamen contrahit ad quantitatem ponderis grauium, & <lb/>leuium, ac virtutis qua debent moueri, &longs;icetnon determi<lb/>net materiam ponderantem, aut virtutis mouentis. </s>

<s>Per <lb/>quod &longs;anè primo di&longs;tinguitur ab Arithmetica & Mu&longs;ica, quæ <lb/>ver&longs;atur circa quantitatem di&longs;cretam; non autem continuam <lb/>&longs;icut grauium ac lenium; deinde à Geometria propriè dicta, <lb/>& a Stereometria quæ ver&longs;antur circa quantitatem <expan abbr="cõtinuam">continuam</expan> <lb/>planorum ac &longs;olidorum, ab&longs;trahendo à grauitate aut &longs;euitate, <lb/>& à quocunque motu illorum. </s>

Line 590

<s>Qua in re &longs;upponimus primo, &longs;crmonem e&longs;&longs;e <lb/>de &longs;cientia totali, prout e&longs;t aggregatum quoddam ex omni<lb/>bus &longs;cientijs partialibus, &longs;iue actualibus, &longs;iue habitualibus, <lb/>nempe ex omnibus conclu&longs;ionibus demon&longs;tratis de &longs;ubiecto <lb/>adæquato, circa quod huiu&longs;modi facultas ver&longs;atur. </s>

<s>Deinde <lb/>&longs;upponimus vnitatem &longs;cientiæ totalis de &longs;umi, tùm ex vnitate <lb/>ordinis quo conclu&longs;iones ac partes illius coaptantur inter &longs;e, <pb pagenum="27"/>ad componendam integram &longs;cientiam de eodem &longs;ubiecto <lb/>materiali ac pa&longs;&longs;ionibus illios; tum ex vnitate obiecti form<lb/>lis circa quod omnes &longs;cientiæ partiales conueniunt. </s>

<s>Deinde <lb/>&longs;upponimus vnitatem &longs;cientiæ totalis de &longs;umi, tùm ex vnitate <lb/>ordinis quo conclu&longs;iones ac partes illius coaptantur inter &longs;e, <pb xlink:href="005/01/035.jpg" pagenum="27"/>ad componendam integram &longs;cientiam de eodem &longs;ubiecto <lb/>materiali ac pa&longs;&longs;ionibus illios; tum ex vnitate obiecti form<lb/>lis circa quod omnes &longs;cientiæ partiales conueniunt. </s>

<s>Quibus po&longs;itis dicendum e&longs;t, Mechanicam facultatem e&longs;<lb/>&longs;e vnicam &longs;eientiam totalem vnitate ordinis, ac obiecti for<lb/>malis, &longs;ub quà &longs;cientia totali tanquam &longs;ub &longs;pecie atoma con<lb/>tinentur omnes conclu&longs;iones, vel &longs;cientiæ partiales Mecha<lb/>nicæ. </s>

Line 602

<s>Porrò cum eius &longs;ubiectum <lb/>non &longs;it vna & eadem indiui&longs;ibilis entitas, &longs;ed multiplex &longs;ub <lb/>ratione illa communi iam explicata corporis artificiosè mo<lb/>bilis, tot erunt partes huius &longs;cientiæ, quot &longs;unt partes ip&longs;ius <lb/>adæquati &longs;ubiecti de quo demon&longs;trat qua ratione moueri de<lb/>beat aut quie&longs;cere. </s>

<s>Et licet partes ip&longs;æ adæquati &longs;ubiecti <lb/>comparari po&longs;&longs;ent ad illud tanquam &longs;pecies ad genus, &longs;ub <lb/>quo continentur, vt &longs;ingula elementa, aut mixta re&longs;pectu cor<lb/>poris in vniuer&longs;um quod artificiosè moueri pote&longs;t, aut quie<lb/>&longs;cere; nihilominus cum ratio &longs;pecificans &longs;cientiam, in præ&longs;enti <lb/>non attendatur penes propriam differentiam &longs;ubiecti mate<lb/>rialis, &longs;ed penes rationem formalem &longs;ub qua con&longs;ideratur in <pb pagenum="28"/>ip&longs;a &longs;cientia; hinc e&longs;t, vt commodius ac magis propriè &longs;pe<lb/>cies ip&longs;æ corporum grauium; ac leuium comparentur ad gra<lb/>ue & leue in communi, tanquam partes integrantes ad totum <lb/>quod con&longs;tituunt; præ&longs;ertim cum etiam genus dicat totum <lb/>confusè in compo&longs;itione Metaphy&longs;ica vt e&longs;t communis do<lb/>ctrina &longs;umpta ex Ari&longs;totele lib.

<s>Et licet partes ip&longs;æ adæquati &longs;ubiecti <lb/>comparari po&longs;&longs;ent ad illud tanquam &longs;pecies ad genus, &longs;ub <lb/>quo continentur, vt &longs;ingula elementa, aut mixta re&longs;pectu cor<lb/>poris in vniuer&longs;um quod artificiosè moueri pote&longs;t, aut quie<lb/>&longs;cere; nihilominus cum ratio &longs;pecificans &longs;cientiam, in præ&longs;enti <lb/>non attendatur penes propriam differentiam &longs;ubiecti mate<lb/>rialis, &longs;ed penes rationem formalem &longs;ub qua con&longs;ideratur in <pb xlink:href="005/01/036.jpg" pagenum="28"/>ip&longs;a &longs;cientia; hinc e&longs;t, vt commodius ac magis propriè &longs;pe<lb/>cies ip&longs;æ corporum grauium; ac leuium comparentur ad gra<lb/>ue & leue in communi, tanquam partes integrantes ad totum <lb/>quod con&longs;tituunt; præ&longs;ertim cum etiam genus dicat totum <lb/>confusè in compo&longs;itione Metaphy&longs;ica vt e&longs;t communis do<lb/>ctrina &longs;umpta ex Ari&longs;totele lib.

5 Met. cap.

Line 620

<s>Sub Organopetica verò continetur Po<lb/>liorcetica, quæ ver&longs;atur circa bellicas machinas, vt Arietes ad <lb/>quatiendos muros, vel Catapultas & alias quibus &longs;agittæ, la<lb/>pides, ac tela, in longi&longs;&longs;ima viæ &longs;patia emittuntur, & videre <lb/>e&longs;t apud Athenæum, Heronem mechanicum, & Apolliodo<lb/>rum; & in Thaumaturgicam, de qua Hero Alexandrinus, <lb/>quæque tandem diuiditur in tres partes, quarum prima ver<lb/>&longs;atur circa clep&longs;ydras, fi&longs;tulas, vario&longs;que ductus, quibus ex <lb/>vno va&longs;e in aliud aqua transfunditur, aut foris emittitur ad <lb/>con&longs;tituendas fontes artificiales, alia&longs;que commoditates pr&ecedil;<lb/>&longs;tandas. </s>

<s>Secunda verò docet quo pacto rotis, neruis, tim<lb/>panis, <expan abbr="alijsq.">alijsque</expan> in&longs;trumentis motus veluti animatus præ&longs;tetur <pb pagenum="29"/>in&longs;en&longs;ibilibus, vt fertur de &longs;tatua Dedali ac Vulcani, de Ar<lb/>chitæ columba, ac &longs;imilibus. </s>

<s>Secunda verò docet quo pacto rotis, neruis, tim<lb/>panis, <expan abbr="alijsq.">alijsque</expan> in&longs;trumentis motus veluti animatus præ&longs;tetur <pb xlink:href="005/01/037.jpg" pagenum="29"/>in&longs;en&longs;ibilibus, vt fertur de &longs;tatua Dedali ac Vulcani, de Ar<lb/>chitæ columba, ac &longs;imilibus. </s>

<s>Tertia modum tradit, quo ex <lb/>inclu&longs;o aere varij emittantur &longs;onitus ad morum vel percu&longs;&longs;io<lb/>nem aqu&ecedil;, vt de &longs;erpentum &longs;ibilis, ac volucrum cantibus, <expan abbr="hu-manisq.">hu<lb/>manisque</expan> vocibus imitatis, à pluribus enarratur: de que armo<lb/>nia quam reddebant argentei remi celeberrimi illius nauigij <lb/>Cleopatræ Aegypti Reginæ cum aquam offenderent, ob &longs;pi<lb/>ritum inter thecas eorum re&longs;eratum, qui agitatione remigum, <lb/><expan abbr="aquarumq.">aquarumque</expan> percu&longs;&longs;ione per varia <expan abbr="artificio&longs;aq.">artificio&longs;aque</expan> foramina exire <lb/>cogebatur. </s>

Line 630

<s>Verum cum talis <lb/>differentia valde accidentaria &longs;it & ab extrin&longs;eco fine de&longs;um<lb/>pta, non minus forta&longs;&longs;e inter Mechanicas facultates propriè <lb/>poterit <expan abbr="cõputari">computari</expan>. </s>

<s>Non enim apparet in quo e&longs;&longs;entialiter diffe<lb/>rat artificio&longs;a tran&longs;uectio quæ per nauim fit, ab ea, <lb/>quæ per plau&longs;trum, aut currum; neque <lb/>intere&longs;t &longs;i per aquas, an per aera <lb/>moles aut pondera tran<lb/>sferantur. </s><pb pagenum="30"/>

Line 670

<s>Id quod planum fieri pote&longs;t &longs;igillatim di&longs;currendo per &longs;in<lb/>gulas &longs;cientias enumeratas. </s>

<s>Nam quod attinet ad Mathema<lb/>ticas, Arithmeticam, Geometriam, A&longs;trologiam, Mu&longs;icam, <lb/>ac Per&longs;pectiuam, & &longs;i quæ &longs;unt aliæ huiu&longs;modi; nulli dubium <lb/>e&longs;t, eas omnes præ&longs;tantiores e&longs;&longs;e &longs;cientia Mechanica; tum <lb/>quia &longs;unt gratia &longs;ui, hoc e&longs;t merè &longs;peculatiuæ, ac de nobilio-<pb pagenum="31"/>ribus, &longs;eu amplioribus, ac &longs;implicioribus &longs;ubiectis pertractant, <lb/>vt per &longs;e patet; tum etiam quia vel parem, vel maiorem cer<lb/>titudinem, & euidentiam habent, præ&longs;ertim illæ, quibus ip&longs;a <lb/>Mechanica &longs;ubalternatur, & à quibus accipit &longs;ua principia, <lb/>vt Geometria ac Stereometria. </s>

<s>Nam quod attinet ad Mathema<lb/>ticas, Arithmeticam, Geometriam, A&longs;trologiam, Mu&longs;icam, <lb/>ac Per&longs;pectiuam, & &longs;i quæ &longs;unt aliæ huiu&longs;modi; nulli dubium <lb/>e&longs;t, eas omnes præ&longs;tantiores e&longs;&longs;e &longs;cientia Mechanica; tum <lb/>quia &longs;unt gratia &longs;ui, hoc e&longs;t merè &longs;peculatiuæ, ac de nobilio-<pb xlink:href="005/01/039.jpg" pagenum="31"/>ribus, &longs;eu amplioribus, ac &longs;implicioribus &longs;ubiectis pertractant, <lb/>vt per &longs;e patet; tum etiam quia vel parem, vel maiorem cer<lb/>titudinem, & euidentiam habent, præ&longs;ertim illæ, quibus ip&longs;a <lb/>Mechanica &longs;ubalternatur, & à quibus accipit &longs;ua principia, <lb/>vt Geometria ac Stereometria. </s>

<s>Quandoquidem immedia<lb/>tius attingunt primam rationem a&longs;&longs;entiendi, in qua fundatur <lb/>tota euidentia. </s>

Line 696

<s>Quod &longs;i comparemus Mechanicam facultatem cum parti<lb/>bus quibu&longs;dam, ac &longs;ubalternatis &longs;cientijs Phy&longs;icæ, præ&longs;ertim <lb/>practicis, vt Medicina, & Agricultura, alijsq annexis, mixtis, <lb/>vel &longs;ubalternatis etiam Mathematicis, vt Architectura, & <lb/>Nautica; diuer&longs;a omnino ratio e&longs;t. </s>

<s>Nam vel &longs;ubiectum illa<lb/>rum fecundum &longs;uam rationem &longs;pecificam ignobilius e&longs;t gra<lb/>ui, & leui, virtuteque eorum motrici in vniuer&longs;um, vt multa <lb/>de quibus tanquam de &longs;ubiectis partialibus agitur in Medici<lb/>na, & Agricultura: Vel tanta e&longs;t incertitudo, & imperfectio <lb/>inferendi conclu&longs;iones in talibus &longs;cientijs, vt ex genere &longs;uo <lb/>vix &longs;cientiæ <expan abbr="n&utilde;cupari">nuncupari</expan> po&longs;&longs;int, potiu&longs;que ex probabilibus, <expan abbr="quã">quam</expan> <pb pagenum="32"/>ex <expan abbr="demõ&longs;tratis">demon&longs;tratis</expan> con&longs;tare <expan abbr="videãtur">videantur</expan> magna <expan abbr="&longs;alt&etilde;">&longs;altem</expan> ex parte. </s>

<s>Nam vel &longs;ubiectum illa<lb/>rum fecundum &longs;uam rationem &longs;pecificam ignobilius e&longs;t gra<lb/>ui, & leui, virtuteque eorum motrici in vniuer&longs;um, vt multa <lb/>de quibus tanquam de &longs;ubiectis partialibus agitur in Medici<lb/>na, & Agricultura: Vel tanta e&longs;t incertitudo, & imperfectio <lb/>inferendi conclu&longs;iones in talibus &longs;cientijs, vt ex genere &longs;uo <lb/>vix &longs;cientiæ <expan abbr="n&utilde;cupari">nuncupari</expan> po&longs;&longs;int, potiu&longs;que ex probabilibus, <expan abbr="quã">quam</expan> <pb xlink:href="005/01/040.jpg" pagenum="32"/>ex <expan abbr="demõ&longs;tratis">demon&longs;tratis</expan> con&longs;tare <expan abbr="videãtur">videantur</expan> magna <expan abbr="&longs;alt&etilde;">&longs;altem</expan> ex parte. </s>

<s>Vnde <lb/>licet derebus præ&longs;tantioribus agant <expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> <expan abbr="ration&etilde;">rationem</expan> obiecti <lb/>totalis, vt e&longs;t corpus animale &longs;anabile; aut <expan abbr="vegetatiu&utilde;">vegetatiuum</expan> germina<lb/>bile; nullatenus tamen <expan abbr="Mechanicã">Mechanicam</expan> <expan abbr="facultat&etilde;">facultatem</expan>, quæ de familia<lb/>rioribus omnimoda <expan abbr="c&utilde;">cum</expan> <expan abbr="euid&etilde;tia">euidentia</expan> tractat, antecellere <expan abbr="putab&utilde;tur">putabuntur</expan>. </s>

Line 712

<s>Eademque <lb/>directio operationum intellectus, e&longs;t finis Logicæ &longs;cientiæ, & <lb/>ratio &longs;ub qua de ip&longs;is operationibus agitur in illa. </s>

<s>Cum igi<lb/>tur talis, ac tanta &longs;it vtilitas Mechanicæ &longs;cientiæ ad fines præ<lb/>&longs;tanti&longs;&longs;imos admirabili cum artificio con&longs;equendos, vt ad le<lb/>uanda ingentia pondera, parua, & exigua virtute, ad commo<lb/>ditates tam plurimas, <expan abbr="vrbiumq.">vrbiumque</expan> ornatum tam varium: ad &longs;ub<lb/>mini&longs;trandas tot machinas, & in&longs;trumenta in bello, vt belli<lb/>gerare potius Mechanica, quam armis ip&longs;is, homines videan<lb/>tur: ad aptius mouenda Nauigia; ingentes paruo momento <lb/>excitandas moles, <expan abbr="immaniaq.">immaniaque</expan> euertenda ædificia: ad aquas ar<lb/>tifi cio&longs;i&longs;&longs;i<gap/>nè <expan abbr="&longs;ublimãdas">&longs;ublimandas</expan>, <expan abbr="aeremq.">aeremque</expan> perpetuis follibus emitten<lb/>dum; voces tàm varias effingendas, concentum æquabiliter <lb/>efformandum, motum qua&longs;i animalem in&longs;en&longs;ibilibus imper<lb/>tiendum, & &longs;imilia; ingenue fatendum e&longs;t nec e&longs;&longs;e artem, <lb/>quæ &longs;e Mechanicæ arti in dignitate valeat comparari, nec <lb/>e&longs;&longs;e &longs;cientiam practicam, quam ip&longs;a ex certitudine, & euiden<lb/>tia, qua procedit, & ex dignitate, ac præ&longs;tantia finis, non an<lb/>tecellat; ita vt in quo &longs;uperatur ex parte &longs;ubiecti nobilioris à <lb/>Medicina, vel Logica, comoen&longs;etur, aut vincatur ex parte <lb/>digni&longs;&longs;imi finis, & obiecti formalis, dum admirabili artificio <lb/>intendit ip&longs;os naturæ fines Naturam emulando &longs;uperare. </s><pb pagenum="33"/>

<s><emph type="italics"/>De Dignitatibus, <expan abbr="admirandisq.">admirandisque</expan> circuli <lb/>proprietatibus.<emph.end type="italics"/></s>

Line 740

<s>Verumenim<lb/>uero huius ac &longs;imilium miraculorum omnium cau&longs;as refert <lb/>ad naturam circuli. </s>

<s>Nam vt inferius docet, quæ circa libram <lb/>fiunt, ad circulum rediguntur; quæ vero circa vectem, ad ip<lb/>&longs;am libram; alia autem fere omnia quæ circa Mechanicas <pb pagenum="34"/>&longs;unt motiones, ad vectem. </s>

<s>Interim ex admiralibi (inquiens) <lb/>mirandum accidere quippiam non e&longs;&longs;e ab&longs;urdum. </s>

Line 766

<s>Nec ob&longs;tat quod nonnulli obijciunt, centrum in rigore lo<lb/>quendo non e&longs;&longs;e partem &longs;emidiametri, ac proinde nec circuli, <lb/>nam &longs;ufficit e&longs;&longs;e illius terminum intrin&longs;ecum, &longs;iue extremum, <lb/>quo immoto, &longs;i tota longitudo &longs;emidiametri circumducatur, <lb/>circulus con&longs;tituatur. </s>

<s>Cum igitur admirandum valde &longs;it, &longs;i<lb/>mul contraria fieri, aut aliquid effici ex contrarijs, & hoc con<lb/>tingat in ip&longs;a con&longs;titutione circuli; minus admirandum e&longs;&longs;e <pb pagenum="35"/>relinquitur (concludit Ari&longs;toteles) &longs;i ex ip&longs;o circulo con&longs;ti<lb/>tuto, aliæ po&longs;tea oriantur contrarietates, vel alia contraria in <lb/>ip&longs;o con&longs;iderentur, vt mox ex dicendis patebit. </s>

<s>Cum igitur admirandum valde &longs;it, &longs;i<lb/>mul contraria fieri, aut aliquid effici ex contrarijs, & hoc con<lb/>tingat in ip&longs;a con&longs;titutione circuli; minus admirandum e&longs;&longs;e <pb xlink:href="005/01/043.jpg" pagenum="35"/>relinquitur (concludit Ari&longs;toteles) &longs;i ex ip&longs;o circulo con&longs;ti<lb/>tuto, aliæ po&longs;tea oriantur contrarietates, vel alia contraria in <lb/>ip&longs;o con&longs;iderentur, vt mox ex dicendis patebit. </s>

<s><emph type="italics"/>De &longs;ecunda circuli proprieiate.<emph.end type="italics"/></s>

Line 786

<s>Horum enim medium e&longs;t æquale, illorum verò <lb/>rectum. </s>

<s>Quarè &longs;icut cum magnum, & paruum inuicem, <lb/>commutantur, prius perueniunt ad æquale, quàm ad hoc vt <lb/>magnum con&longs;tituatur paruum, & paruum con&longs;tituatur ma<pb pagenum="36"/>gnum: ita quælibet linea curua, &longs;eu conuexa antequam &longs;iat <lb/>concaua, prius debet fieri recta: ab&longs;urdum igitur apparet, ean<lb/>dem omnino circuli periferiam, &longs;imul con&longs;titui concauam, <lb/>& conuexam. </s>

<s>Quarè &longs;icut cum magnum, & paruum inuicem, <lb/>commutantur, prius perueniunt ad æquale, quàm ad hoc vt <lb/>magnum con&longs;tituatur paruum, & paruum con&longs;tituatur ma<pb xlink:href="005/01/044.jpg" pagenum="36"/>gnum: ita quælibet linea curua, &longs;eu conuexa antequam &longs;iat <lb/>concaua, prius debet fieri recta: ab&longs;urdum igitur apparet, ean<lb/>dem omnino circuli periferiam, &longs;imul con&longs;titui concauam, <lb/>& conuexam. </s>

<s>Nec difficultatem euadunt, qui dicunt, concauum, & con<lb/>uexum realiter non e&longs;&longs;e idem in circulo, &longs;eu curuitatem, & <lb/>concauitatem non reperiri in eadem linea, &longs;ed in diuer&longs;is, ità <lb/>vt in circunferentia &longs;it tantum curuitas, &longs;eù conuexum, con<lb/>cauitas verò &longs;it potius in corpore extrin&longs;eco ambiente per li<lb/>neam illi corre&longs;pondentem. </s>

Line 802

<s>A<emph type="italics"/>ltervm autem, quod &longs;imul contrarÿi <lb/>mouetur motionibus: &longs;imul enim ad anterio<lb/>rem mouetur locum, & ad po&longs;teriorem. </s>

<s>Et <lb/>ea, quæ circulum de&longs;cribit, linea eodem &longs;e <lb/>babet modo: Ex que enim incipit loco, illius <lb/>extremum, ad eundem rur&longs;us redit: Illa <lb/>enim continuò commota, extremum rur&longs;us efficitur primum.<emph.end type="italics"/><pb pagenum="37"/><emph type="italics"/>Quamobrem manife&longs;tum, quod inde muiatum e&longs;t. </s>

<s>Et <lb/>ea, quæ circulum de&longs;cribit, linea eodem &longs;e <lb/>babet modo: Ex que enim incipit loco, illius <lb/>extremum, ad eundem rur&longs;us redit: Illa <lb/>enim continuò commota, extremum rur&longs;us efficitur primum.<emph.end type="italics"/><pb xlink:href="005/01/045.jpg" pagenum="37"/><emph type="italics"/>Quamobrem manife&longs;tum, quod inde muiatum e&longs;t. </s>

<s>Quaprop<lb/>ter (vt dictum e&longs;t prius) non e&longs;t inconueniens, ip&longs;um miracutc<lb/>rum omnium e&longs;&longs;e principium.<emph.end type="italics"/></s>

Line 824

<s>Tertio illud quoque admiratione dignum &longs;e&longs;e o&longs;&longs;ert in <lb/>circulo, quod, inquit Ari&longs;toteles, contrarijs &longs;imul fe<lb/>ratur motionibus, antror&longs;um videlicet, ac retror&longs;um, <lb/>&longs;ur&longs;um, ac deor&longs;um. </s>

<s>Dum enim pars circuli &longs;uperior de&longs;cen<lb/>dit, ac mouetur antror&longs;um, v. g. ad dexteram, altera pars illi <pb pagenum="38"/>oppo&longs;ita, quæ e&longs;t inferior, a&longs;cendit, ac mouetur retror&longs;um ad <lb/>leuam. </s>

<s>Dum enim pars circuli &longs;uperior de&longs;cen<lb/>dit, ac mouetur antror&longs;um, v. g. ad dexteram, altera pars illi <pb xlink:href="005/01/046.jpg" pagenum="38"/>oppo&longs;ita, quæ e&longs;t inferior, a&longs;cendit, ac mouetur retror&longs;um ad <lb/>leuam. </s>

Line 832

<s>Quod &longs;i huiu&longs;modi po&longs;itiones formaliter non con<lb/>&longs;tituantur ni&longs;i in quadam relatione, ac re&longs;pectu vnius partis ad <lb/>alteram, hoc parumrefert, cum fundamentaliter &longs;emper im<lb/>portent realem oppo&longs;itionem, ac diuer&longs;itatem loci, in quo <lb/>ip&longs;e partes relatæ con&longs;tituuntur, vel ad quem tendunt <expan abbr="tanquã">tanquam</expan> <lb/>ad terminum &longs;ui motus. </s>

<s>Quapropter idem Philo&longs;ophus &longs;u<lb/><figure id="fig1"/><lb/>biungit ex hac contra<lb/>rietate fieri, vt vnius <lb/>circuli motione, alij cir<lb/>culi in contrarium mo<lb/>ueantur. </s>

<s>Quapropter idem Philo&longs;ophus &longs;u<lb/><figure id="id.005.01.046.1.jpg" xlink:href="005/01/046/1.jpg"/><lb/>biungit ex hac contra<lb/>rietate fieri, vt vnius <lb/>circuli motione, alij cir<lb/>culi in contrarium mo<lb/>ueantur. </s>

<s>Vt &longs;i con&longs;ti<lb/>tuatur circulus, qui pri<lb/>mò moueri debeat in<lb/>ter alios quaruor, <expan abbr="&longs;intq.">&longs;intque</expan> <lb/>omnes denticulati, <lb/>quem admodum videre <lb/>e&longs;t in horologijs, <expan abbr="alijsq.">alijsque</expan> <lb/>&longs;imilibus machinis, vt <lb/>in hac &longs;igura: Nam pars <lb/>&longs;uperor medij circuli, <lb/>quæ de&longs;cendit, impellit partem inferiorem &longs;uperioris circuli, <lb/>facitque eam a&longs;cendere. </s>

Line 848

<s>Et &longs;ic <expan abbr="extrem&utilde;">extremum</expan> rur&longs;us effici<lb/>tur <expan abbr="prim&utilde;">primum</expan>. </s>

<s>Quapropter concludit: Non e&longs;t inconueniens ex <lb/>ip&longs;a &longs;emidiametro <expan abbr="de&longs;cript&utilde;">de&longs;criptum</expan>, <expan abbr="miraculor&utilde;">miraculorum</expan> <expan abbr="pluri&utilde;">plurium</expan> e&longs;&longs;e <expan abbr="principi&utilde;">principium</expan>. </s><pb pagenum="39"/>

<s>Quæ autem de libra ac vatia punctorum &longs;emidiametri ve<lb/>locitate hìc docet Ari&longs;toteles, fru&longs;tra interpo&longs;ita &longs;unt ac præ<lb/>ter Auctoris intentum, cum ad rem de qua agitur non perti<lb/>neant, ac alibi proprijs in locis repetantur. </s>

Line 876

<s>Simile <lb/>igitur est proportione paruum quadrilaterum maiori: quam<lb/>obrem & eadem illorum e&longs;t diameter, & A erit ad F. </s>

<s>Eodem <lb/>etiam o&longs;tendetur modo, vbicunque latio deprabendatur; &longs;em-<emph.end type="italics"/><pb pagenum="40"/><emph type="italics"/>per enim &longs;upra diametrum erit. </s>

<s>Eodem <lb/>etiam o&longs;tendetur modo, vbicunque latio deprabendatur; &longs;em-<emph.end type="italics"/><pb xlink:href="005/01/048.jpg" pagenum="40"/><emph type="italics"/>per enim &longs;upra diametrum erit. </s>

<s>Manife&longs;tum igitur, quod id <lb/>quod &longs;ecundum diametrum duabus fertur lationibus, nece&longs;&longs;a<lb/>riò &longs;ecundum laterum proportionem fertur. </s>

Line 904

<s>Et hoc pacto inquit in de&longs;criptione circuli <lb/>contingere vt puncta quæ magis à centro di&longs;tant, velocius <lb/>moueantur. </s>

<s>Siquidem eodem tempore maiorem de&longs;cribunt <pb pagenum="41"/>ambitum. </s>

<s>Siquidem eodem tempore maiorem de&longs;cribunt <pb xlink:href="005/01/049.jpg" pagenum="41"/>ambitum. </s>

<s>Maior enim e&longs;t circum &longs;erentia cireuli continentis, <lb/>quàm contenti. </s>

Line 922

<s>Et confirmari pote&longs;t argumento quod idem Philo&longs;ophus, <lb/>alijs interpo&longs;itis, &longs;equenti textu adiecit; niminum, quia &longs;i <lb/>duobus (inquit) ab eadem potentia latis, hoc quidem plus <lb/>repellatur vel impediatur ab aliquo, illud verò minus; ratio<lb/>ni con&longs;entancum e&longs;t, tardius moueri id quod plus præpedi<lb/>tur, aut repellit ur: Sed lineæ circumductæ in circulo, vel pun<lb/>cta quæ &longs;unt in eius diametro, quò magis appropinquantur <lb/>centro, eò magis repelluntur in motu circulari ac impediun<lb/>tur ab ip&longs;o centro; ergo tardius mouentur. </s>

<s>Minor propo&longs;itio <lb/>huius argumenti probatur; quia cum centrum &longs;it fixum & <lb/>immotum, <expan abbr="eiq.">eique</expan> colligatæ &longs;int omnes partes diametri per lon<lb/>gitudinem exten&longs;æ, illæ quæ magis ei appropinquantur, ma<lb/>gis vinciuntur ac detinentur nè moueantur: quæ verò magis <pb pagenum="42"/>ab eo di&longs;tant, magis relaxantur, <expan abbr="magisq.">magisque</expan> &longs;oluuntur à princi<lb/>pio detinente, ac propterea minus impediuntur nè ad im<lb/>pul&longs;um vel motum alterius moueantur, & &longs;ic velocius fe<lb/>runtur. </s>

<s>Minor propo&longs;itio <lb/>huius argumenti probatur; quia cum centrum &longs;it fixum & <lb/>immotum, <expan abbr="eiq.">eique</expan> colligatæ &longs;int omnes partes diametri per lon<lb/>gitudinem exten&longs;æ, illæ quæ magis ei appropinquantur, ma<lb/>gis vinciuntur ac detinentur nè moueantur: quæ verò magis <pb xlink:href="005/01/050.jpg" pagenum="42"/>ab eo di&longs;tant, magis relaxantur, <expan abbr="magisq.">magisque</expan> &longs;oluuntur à princi<lb/>pio detinente, ac propterea minus impediuntur nè ad im<lb/>pul&longs;um vel motum alterius moueantur, & &longs;ic velocius fe<lb/>runtur. </s>

<s>Verum enimuero, vt primum ac principale Ari&longs;totelis ar<lb/>gumentum omninò concludat id quod intendit, examinanda <lb/>ac probanda &longs;unt nonnulla quæ in eo a&longs;&longs;umuntur, ac difficul<lb/>tatem non paruam inuoluunt. </s>

Line 942

<s>Sit enim corpus &longs;eu pon<lb/>dus quod moueri debeat con&longs;titutum &longs;uper planum vbi A, <lb/>mouentia verò vbi B, C. </s>

<s>Deinde &longs;upponamus æquali virtu<lb/>te & æquali &longs;imul tempore vtrumque mouens ad &longs;e pondus <pb pagenum="43"/><figure id="fig2"/><lb/>ip&longs;um trahere; quod e&longs;t, eandem &longs;emper proportionem ad <lb/>inuicem &longs;eruare, vt bene&longs;icio trochlearum vel alterius in&longs;tru<lb/>menti. </s>

<s>Deinde &longs;upponamus æquali virtu<lb/>te & æquali &longs;imul tempore vtrumque mouens ad &longs;e pondus <pb xlink:href="005/01/051.jpg" pagenum="43"/><figure id="id.005.01.051.1.jpg" xlink:href="005/01/051/1.jpg"/><lb/>ip&longs;um trahere; quod e&longs;t, eandem &longs;emper proportionem ad <lb/>inuicem &longs;eruare, vt bene&longs;icio trochlearum vel alterius in&longs;tru<lb/>menti. </s>

<s>Tunc enim dicimus primo, corpus ip&longs;um mobile A <lb/>moueri motu quodam mixto ex duabus lationibus, nempe <lb/>qua appropinquatur ad B, & qua appropinquantur ad C. <lb/></s>

Line 952

<s>Ftenim &longs;eruata eadem proportione, pon<lb/>dus ip&longs;um, & quælibet eius pars æqualiter vtrique mouenti in <lb/>æquali tempore deberet appropinquari: quia non e&longs;&longs;et maiot <lb/>ratio cur magis aut citius appropinquaretur ad B, quàm ad C. <lb/></s>

<s>At non po&longs;&longs;et æqualiter vtrique appropinquari, ni&longs;i feratur <pb pagenum="44"/>per diamctrom quadranguli A B C D, quæ e&longs;t recta A D; <lb/>&longs;iquidem in nulla alia parte interiecti &longs;pacij, di&longs;tantia e&longs;&longs;et <lb/>æqualis, vt &longs;en&longs;u con&longs;tat: Ergo &longs;eruata eadem proportione in <lb/>ip&longs;a duplici latione re&longs;pectu mobilis & cuiu&longs;que partis ip&longs;ius, <lb/>motus nece&longs;&longs;ariò erit rectus, &longs;eu <expan abbr="põdus">pondus</expan> & quælibet eius pars, <lb/>nonni&longs;i per rectam lineam poterit moueri. </s>

<s>At non po&longs;&longs;et æqualiter vtrique appropinquari, ni&longs;i feratur <pb xlink:href="005/01/052.jpg" pagenum="44"/>per diamctrom quadranguli A B C D, quæ e&longs;t recta A D; <lb/>&longs;iquidem in nulla alia parte interiecti &longs;pacij, di&longs;tantia e&longs;&longs;et <lb/>æqualis, vt &longs;en&longs;u con&longs;tat: Ergo &longs;eruata eadem proportione in <lb/>ip&longs;a duplici latione re&longs;pectu mobilis & cuiu&longs;que partis ip&longs;ius, <lb/>motus nece&longs;&longs;ariò erit rectus, &longs;eu <expan abbr="põdus">pondus</expan> & quælibet eius pars, <lb/>nonni&longs;i per rectam lineam poterit moueri. </s>

<s>Deinde quod infert Ari&longs;toteles, circulare e&longs;&longs;e id quod &longs;e<lb/>cundum nullam proportionem, nullo in tempore duas pati<lb/>tur lationes, fal&longs;um e&longs;&longs;et etiam iuxta præfatam explicationé <lb/>proportionis; ni&longs;i per circulare intelligeremus lato modo, id <lb/>quod e&longs;t curuum. </s>

Line 962

<s>Iam vero vt Geometricis principijs quæ dicta &longs;unt pateát, <lb/>&longs;ic probat Ari&longs;toteles, quidquid fertur duabus lationibus ad <lb/>inuicem proportionatis, &longs;uper rectam nece&longs;&longs;ariò ferri, ac pro<lb/>inde non circulariter. </s>

<s>Sit inquit proportio ip&longs;arum lationum <lb/><figure id="fig3"/><lb/>quam habent inter <lb/>&longs;e latera A B & AC <lb/>in dato rectangulo <lb/>A B C D. </s>

<s>Sit inquit proportio ip&longs;arum lationum <lb/><figure id="id.005.01.052.1.jpg" xlink:href="005/01/052/1.jpg"/><lb/>quam habent inter <lb/>&longs;e latera A B & AC <lb/>in dato rectangulo <lb/>A B C D. </s>

<s>Et A <lb/><expan abbr="quid&etilde;">quidem</expan> duplici motu <lb/>feratur, vno quo <lb/><expan abbr="t&etilde;dat">tendat</expan> ver&longs;us B, qua<lb/>&longs;i ex &longs;e incedendo <lb/>&longs;uper lineam A B: <lb/>altero verò, quo &longs;imul cum ip&longs;a linea A B &longs;ubterferatur ver<lb/>&longs;us C, &longs;eu ver&longs;us lineam C D cum eadem &longs;emper proportio<lb/>ne. </s>

<s>Tunc dicimus punctum A motu ip&longs;o mixto, nece&longs;&longs;ariò <lb/>ferriper rectam A D, quæ e&longs;t diameter eiu&longs;dem quadrilateri <lb/>A B C D. </s>

<s>Etcnim &longs;i <expan abbr="cõ&longs;tituatur">con&longs;tituatur</expan> rectangulus minor A E F G <pb pagenum="45"/>proportionalis maiori A B C D, ac per motum proprium <lb/>ver&longs;us B, ip&longs;um punctum A peragrauerit quantum e&longs;t v&longs;que <lb/>ad E; & per motum totius lineæ A B, ver&longs;us lineam C D, <lb/>peragrauerit quantum e&longs;t ab A, v&longs;que ad F, &longs;eruata eadem <lb/>proportione ip&longs;orum laterum; certe punctum A reperiri non <lb/>po&longs;&longs;et in E, neque in F; &longs;iquidem non fui&longs;&longs;et latum duabus <lb/>lationibus, nec peragra&longs;&longs;et &longs;pacium &longs;ecundum vtramque po<lb/>&longs;itionem, &longs;imul accedendo quantum &longs;ieri pote&longs;t ad B & ad <lb/>C; &longs;ed vna tantùm latione, alterum &longs;olum &longs;pacium percur<lb/>ri&longs;&longs;et. </s>

<s>Etcnim &longs;i <expan abbr="cõ&longs;tituatur">con&longs;tituatur</expan> rectangulus minor A E F G <pb xlink:href="005/01/053.jpg" pagenum="45"/>proportionalis maiori A B C D, ac per motum proprium <lb/>ver&longs;us B, ip&longs;um punctum A peragrauerit quantum e&longs;t v&longs;que <lb/>ad E; & per motum totius lineæ A B, ver&longs;us lineam C D, <lb/>peragrauerit quantum e&longs;t ab A, v&longs;que ad F, &longs;eruata eadem <lb/>proportione ip&longs;orum laterum; certe punctum A reperiri non <lb/>po&longs;&longs;et in E, neque in F; &longs;iquidem non fui&longs;&longs;et latum duabus <lb/>lationibus, nec peragra&longs;&longs;et &longs;pacium &longs;ecundum vtramque po<lb/>&longs;itionem, &longs;imul accedendo quantum &longs;ieri pote&longs;t ad B & ad <lb/>C; &longs;ed vna tantùm latione, alterum &longs;olum &longs;pacium percur<lb/>ri&longs;&longs;et. </s>

<s>Reperietur ergo ip&longs;um. </s>

Line 980

<s>Quod quidem clarius adhuc probari po&longs;&longs;et exemplo hu<lb/>ius quadrati A B C D, cuius latera diui&longs;a &longs;int in quatuor par<lb/>tes æquales, <expan abbr="efficiantq.">efficiantque</expan> ex illis minora quadrata contenta in <lb/>maiori. </s>

<s>Nam &longs;i &longs;up<lb/><figure id="fig4"/><lb/>ponatur punctum A ex <lb/>&longs;e moueri tanquam na<lb/>turali ac proprio motu <lb/>ver&longs;us B, &longs;uper rectam <lb/>A B, & eodem tempo<lb/>re &longs;imul cum ip&longs;a A B, <lb/>qua&longs;i motu alieno de<lb/>&longs;cendere ver&longs;us C D, <lb/>ac &longs;eruata eadem pro<lb/>portione vtriu&longs;que mo<lb/>tus, quæ &longs;it æqualita<lb/>tis: ab&longs;que dubio, eo-<pb pagenum="46"/>dem tempore quo A, peragrauerit &longs;pacium AE, &longs;imul pera<lb/>grabit &longs;pacium AF, & reperietur in G, quandoquidem &longs;unt <lb/>latera eiu&longs;dem quadrati AG, ac proinde æqualia. </s>

<s>Nam &longs;i &longs;up<lb/><figure id="id.005.01.053.1.jpg" xlink:href="005/01/053/1.jpg"/><lb/>ponatur punctum A ex <lb/>&longs;e moueri tanquam na<lb/>turali ac proprio motu <lb/>ver&longs;us B, &longs;uper rectam <lb/>A B, & eodem tempo<lb/>re &longs;imul cum ip&longs;a A B, <lb/>qua&longs;i motu alieno de<lb/>&longs;cendere ver&longs;us C D, <lb/>ac &longs;eruata eadem pro<lb/>portione vtriu&longs;que mo<lb/>tus, quæ &longs;it æqualita<lb/>tis: ab&longs;que dubio, eo-<pb xlink:href="005/01/054.jpg" pagenum="46"/>dem tempore quo A, peragrauerit &longs;pacium AE, &longs;imul pera<lb/>grabit &longs;pacium AF, & reperietur in G, quandoquidem &longs;unt <lb/>latera eiu&longs;dem quadrati AG, ac proinde æqualia. </s>

<s>Et &longs;icut to<lb/>ta linea AB, coincideret cum linea FH, ita punctum E, coin<lb/>cideret cum puncto G. </s>

Line 1008

<s>Omne quidem igitur circulum de<lb/>&longs;cribenti i&longs;tud accidi<gap/>: <expan abbr="ferturq.">ferturque</expan> eam quæ &longs;ecundum naturam <lb/>e&longs;t lationem, &longs;ecundum circumferentiam: illam vero quæ præ<lb/>ter naturam, in tran&longs;uer&longs;um & &longs;ecundum centrum. </s>

<s>Maio-<emph.end type="italics"/><pb pagenum="47"/><emph type="italics"/>tem autem &longs;emper eam quæ præter naturam e&longs;t ip&longs;a minor <lb/>fertur: quia enim centro e&longs;t vicinior quod trahit, vincitur <lb/>magis.<emph.end type="italics"/></s>

<s>Maio-<emph.end type="italics"/><pb xlink:href="005/01/055.jpg" pagenum="47"/><emph type="italics"/>tem autem &longs;emper eam quæ præter naturam e&longs;t ip&longs;a minor <lb/>fertur: quia enim centro e&longs;t vicinior quod trahit, vincitur <lb/>magis.<emph.end type="italics"/></s>

<s>COMMENTARIVS.</s>

Line 1018

<s>Nam &longs;i <lb/>in de&longs;criptione circuli, &longs;emidiameter vnam tantum lationem <lb/>pateretur, vt verbi gratia naturalem, qua rectà tenderet ver<lb/>&longs;us, vnam aliquam differentiam &longs;itus, nunquam ad ip&longs;ius dia<lb/>metri perpendiculum perueniret. </s>

<s>Implicat enim vnica la<lb/>tione, aliquid &longs;imul rectà tendere, ac in tran&longs;uer&longs;um, quem<lb/>admodum &longs;e habet perpendiculum ad diametrum à qua pro<lb/>pendit: At &longs;emidiameter circulum de&longs;cribendo, aliquando <lb/>peruenit ad &longs;uum perpendiculum, ita vt coincidat cum illo: <lb/>Ergo non vnica, &longs;ed duplici latione conuincitur ferri. </s><figure/>

<s>Sit enim circulus de<lb/>&longs;cribendus ABCD, circa <lb/>centrum E. </s>

Line 1028

<s>Per <expan abbr="mot&utilde;">motum</expan> <lb/>autem naturalem ip&longs;a AE, de&longs;cendi&longs;&longs;et in FD, vel aliò rectè <lb/>tran&longs;lata fui&longs;&longs;et. </s>

<s>Non ergo linea circulum de&longs;cribens fertur, <pb pagenum="48"/>vnico tantummodo motu ver&longs;us vnicam differentiam &longs;itus, <lb/>&longs;ed duplici motu, nempe mixto ex naturali & præternaturali; <lb/>ver&longs;us duplicem differentiam &longs;itus. </s>

<s>Non ergo linea circulum de&longs;cribens fertur, <pb xlink:href="005/01/056.jpg" pagenum="48"/>vnico tantummodo motu ver&longs;us vnicam differentiam &longs;itus, <lb/>&longs;ed duplici motu, nempe mixto ex naturali & præternaturali; <lb/>ver&longs;us duplicem differentiam &longs;itus. </s>

<s>Naturali quippe, quo in <lb/>propo&longs;ita figura fertur ver&longs;us latus F D, præternaturali verò, <lb/>quo retrahitur in tran&longs;uer&longs;um ver&longs;us latus E D, co quòd alte<lb/>rum eius extremum detineatur in centro E, vt clarius infra <lb/>patebit. </s>

Line 1044

<s>Vna quidem naturali, qua prout <lb/>accen&longs;a ac leuia corpora, &longs;ur&longs;um rectà tendere debent: <lb/>altera verò præternaturali, qua prout à con&longs;tipan<lb/>te frigore extruduntur ac propelluntur (in<lb/>&longs;pi&longs;&longs;ata &longs;cilicet ac grauitante magis eo<lb/>rum exhalationis materia) deor<lb/>&longs;um inclinant. </s>

<s>Ex his enim <lb/>duabus lationibus <lb/>medius qui<lb/>dam mo<lb/>tus <lb/>re&longs;ultat, quo vt ip&longs;e inquit, &longs;ydera <lb/>videntur volare, & obliquè <lb/>tanquam proiecta <lb/>per aera <lb/>ferri. </s><pb pagenum="49"/>

<s><emph type="italics"/>Qua ratione partes diametri a oentro remotio<lb/>res magis participent de motu naturali, <lb/>propinquiores verò magis de præ<lb/>ternaturali.<emph.end type="italics"/></s>

Line 1062

<s>Est autem ip&longs;a S T æqualis ip&longs;i L <expan abbr="q.">que</expan> In quan<lb/>to autem tempore ip&longs;a AL ip&longs;am ML lata e&longs;t, in tanto tem<lb/>poris &longs;patio in maiori circulo, maiorem, quam &longs;it B S, latum <lb/>erit extremum ip&longs;is AB. </s>

<s>Latio quidem igit ur &longs;ecundum na<lb/>turam æqualis: Ea autem, quæ præter naturam e&longs;t minor, <lb/>videlicet B T, quam M <expan abbr="q.">que</expan> Oportet autem proportiona-<emph.end type="italics"/><pb pagenum="50"/><emph type="italics"/>biliter e&longs;&longs;e, &longs;icut quod est fecundum naturam, ita quod est <lb/>præter naturam, ad id, quod est præter naturan; maiorem <lb/>igitur circumferentiam pertran&longs;iuit, quam &longs;it ip&longs;a S B. </s>

<s>Latio quidem igit ur &longs;ecundum na<lb/>turam æqualis: Ea autem, quæ præter naturam e&longs;t minor, <lb/>videlicet B T, quam M <expan abbr="q.">que</expan> Oportet autem proportiona-<emph.end type="italics"/><pb xlink:href="005/01/058.jpg" pagenum="50"/><emph type="italics"/>biliter e&longs;&longs;e, &longs;icut quod est fecundum naturam, ita quod est <lb/>præter naturam, ad id, quod est præter naturan; maiorem <lb/>igitur circumferentiam pertran&longs;iuit, quam &longs;it ip&longs;a S B. </s>

<s>Ne<lb/>ce&longs;&longs;e autem e&longs;t ip&longs;am F B. in hoc tempore pertran&longs;i<32>e: bic <lb/>enim erit, quando proportion abiliter vtrinque accidis, quod e&longs;t <lb/>præter naturam, ad id quod e&longs;t &longs;ecundum naturam. </s>

Line 1082

<s>Probat autem hoc modo; &longs;it enim, inquit, <lb/>Circulus B C D E; & alter in hoc minor vbi M N O P <lb/>circà idem centrum A. <expan abbr="Sintq.">Sintque</expan> Diametri maioris quidem C. <lb/>D, & B E; minoris verò M O, & N P. </s>

<s>Deinde complea-<pb pagenum="51"/><figure id="fig5"/><lb/>tur quadrangu'um rectangulum D K R C nempe ducen<lb/>do lineam K R. paralellam, & æqualem ip&longs;i D C. per pun<lb/>ctum B, & claudendo ip&longs;as K R & D C per lineas D K <lb/>& C R. </s>

<s>Deinde complea-<pb xlink:href="005/01/059.jpg" pagenum="51"/><figure id="id.005.01.059.1.jpg" xlink:href="005/01/059/1.jpg"/><lb/>tur quadrangu'um rectangulum D K R C nempe ducen<lb/>do lineam K R. paralellam, & æqualem ip&longs;i D C. per pun<lb/>ctum B, & claudendo ip&longs;as K R & D C per lineas D K <lb/>& C R. </s>

<s>Cum igitur motus naturalis cuiu&longs;libet lineæ dica<lb/>tur ille, quo recta fertur ver&longs;us eam partem in quam tendit, <lb/>&longs;i linea A B &longs;tantis circuli de&longs;cripti deo<gap/>&longs;um tenderet &longs;im<lb/>plici motu naturali, ab&longs;que dubio rectè, ac perpendiculari<lb/>ter tota &longs;imul caderet, & coincid et cum C R. </s>

Line 1090

<s>Itaque progre&longs;&longs;as perpendicu<lb/>laris ver&longs;us C R erit motus naturalis, ver&longs;us autem C D erit <lb/>præternaturalis Quod certè videtur &longs;upponere Ari&longs;toteles. <lb/></s>

<s>Nunc autem &longs;ic procedit ad o&longs;tenden lum propo&longs;itum, <lb/>nempè partem dia necri propinquiorem centro, vt A M <pb pagenum="52"/>magis detrahi à motu naturali, ac tardiùs moueri, quàm <lb/>M B quæ magis di&longs;tat ab illo. </s>

<s>Nunc autem &longs;ic procedit ad o&longs;tenden lum propo&longs;itum, <lb/>nempè partem dia necri propinquiorem centro, vt A M <pb xlink:href="005/01/060.jpg" pagenum="52"/>magis detrahi à motu naturali, ac tardiùs moueri, quàm <lb/>M B quæ magis di&longs;tat ab illo. </s>

<s>Ducatur inquit à centro li<lb/>nea A L F; & à puncto L perpendicularis ip&longs;i A B quæ <lb/>&longs;it L Q, & rur&longs;us ab eodem L ducatur L S paralella ei<lb/>dem A B. </s>

Line 1116

<s>Vlterius verò quod punctum B magis moueatur motu <lb/>&longs;ecundum naturam, quam ip&longs;um punctum M probatur ex <lb/>co; Nam quo tempore punctum M latum fuerit v&longs;que ad <lb/>L; punctum B eodem tempore perueniet v&longs;que ad F. </s>

<s>Ete<lb/>nim cum ita &longs;e habere debeat motus naturalis ip&longs;ius B ad <lb/>motum præter naturam eiu&longs;dem B quemadmodum &longs;e ha<lb/>bet motus naturalis ip&longs;ius M ad motum præter naturam <pb pagenum="53"/>eiu&longs;dem M talis proportio &longs;olum verificari pote&longs;t in F, <lb/>nam proportio, quam habet linea F X referens &longs;pacium <lb/>tran&longs;actum &longs;ecundum naturam ad B X, quod ab eodem <lb/>puncto B tran&longs;actum e&longs;t præter naturam in maiori circulo, <lb/>eadem e&longs;t, ac proportio lineæ QL tran&longs;actæ &longs;ecundum <lb/>naturam ad lineam M Q tran&longs;actam præter naturam in mi<lb/>nori circulo. </s>

<s>Ete<lb/>nim cum ita &longs;e habere debeat motus naturalis ip&longs;ius B ad <lb/>motum præter naturam eiu&longs;dem B quemadmodum &longs;e ha<lb/>bet motus naturalis ip&longs;ius M ad motum præter naturam <pb xlink:href="005/01/061.jpg" pagenum="53"/>eiu&longs;dem M talis proportio &longs;olum verificari pote&longs;t in F, <lb/>nam proportio, quam habet linea F X referens &longs;pacium <lb/>tran&longs;actum &longs;ecundum naturam ad B X, quod ab eodem <lb/>puncto B tran&longs;actum e&longs;t præter naturam in maiori circulo, <lb/>eadem e&longs;t, ac proportio lineæ QL tran&longs;actæ &longs;ecundum <lb/>naturam ad lineam M Q tran&longs;actam præter naturam in mi<lb/>nori circulo. </s>

<s>Quod inde patere pote&longs;t, nam &longs;i ducantur re<lb/>ctæ B F, & M L efficientur duo triangula æquiangula <lb/>B X F, & M Q L quæ per 4. &longs;exti habebunt latera pro<lb/>portionalia circà æquales angulos: Vnde &longs;icut &longs;e habet F X <lb/>ad X B circa angulum. </s>

Line 1130

<s>Attenta natura circuli cum &longs;uis proprietatibus modò <lb/>explicatis ad hoc acumen humani ingenij iam pridem <lb/>peruenit, vt machinas qua&longs;dam excogitaret, quæ naturam <lb/>ip&longs;ius circuli participantes, motricem potentiam in motu <lb/>grauium ac leuium iuuarent. </s>

<s>Huiu&longs;modi autem machinas <lb/>in&longs;trumenta mechanica communiter appellamus, vtpotè <lb/>quæ mechanica &longs;peculatione adinuenta &longs;unt, <expan abbr="eademq.">eademque</expan> arte <pb pagenum="54"/>adhibentur tanquam in&longs;trumenta ad leuanda pondera, vel <lb/>quomodolibet mouenda grauia, quæ re&longs;pectiuè dicuntur <lb/>etiam leuia. </s>

<s>Huiu&longs;modi autem machinas <lb/>in&longs;trumenta mechanica communiter appellamus, vtpotè <lb/>quæ mechanica &longs;peculatione adinuenta &longs;unt, <expan abbr="eademq.">eademque</expan> arte <pb xlink:href="005/01/062.jpg" pagenum="54"/>adhibentur tanquam in&longs;trumenta ad leuanda pondera, vel <lb/>quomodolibet mouenda grauia, quæ re&longs;pectiuè dicuntur <lb/>etiam leuia. </s>

<s>Sunt autem hæc in&longs;trumenta præcipua &longs;ex, ad <lb/>quæ cætera omniareducuntur: nempè Libra. </s>

Line 1142

<s>Ex quibus infertur &longs;iue im<lb/>mediate, &longs;iue mediante, alia quadam ab&longs;tracta ratione quam <lb/>ip&longs;a participent, mechanica penè omnia in&longs;trumenta in &longs;uis <lb/>motionibus ad circuli naturam referri. </s>

<s>Quod vt clarius te<lb/>neatur, pauca &longs;altem de &longs;ingulis ip&longs;is in&longs;trumentis hic adij<lb/>cere operepretium putauimus, ea &longs;cilicet tantummo<lb/>do, quæ ad in&longs;titutam textus dilucidationem no<lb/>uerimus pertinere, Cum exacta huiu&longs;modi <lb/>in&longs;trumentum tractatio habeatur apud <lb/>Heronem, Pappum, & alios ve<lb/>teres, noui&longs;simè verò & <lb/>accurati&longs;simè apud <lb/>Guidum Vbal<lb/>dum <lb/><gap/> Marchionibus Montis, qui &longs;i<lb/>gillatim de illis præcla <lb/>rum librum in<lb/>&longs;tituit. </s><pb pagenum="55"/>

<s>DE LIBRA.</s>

Line 1154

<s>Quo autem pacto libra in &longs;ui motione participet natu<lb/>ram circuli per &longs;e con&longs;tat con&longs;ideranti, iugum, diametri vi<lb/>cem gerere, axem verò &longs;eu trutinam, aut <expan abbr="fulciment&utilde;">fulcimentum</expan> quod<lb/>libet, centri locum tenere, circa quod immotum, ip&longs;a dia<lb/>meter vertitur dum circulum de&longs;cribit; &longs;iquidem immoto <lb/>axe, &longs;eu fulcimento ip&longs;ius libræ, iugum, alterius extremita<lb/>tis depre&longs;sione ob exuperantiam <expan abbr="põderis">ponderis</expan>, alterius verò ele<lb/>uatione, circumagitur, non &longs;ecus ac diameter circulum <lb/>con&longs;iciendo. </s>

<s>Quod &longs;i partes iugi vtrinque à centro produ<lb/>ctæ, non &longs;int inter &longs;e <expan abbr="lõgitudine">longitudine</expan> æquales, quamuis æquipon<lb/>derantes; tunc quidem in ip&longs;is iugi conuer&longs;ione, ac circum<pb pagenum="56"/>latione duo circuli de&longs;cribentur alter altero malor, <expan abbr="tanquã">tanquam</expan> <lb/>à duplici &longs;emidiametro circumlato, vt hic erit in&longs;picere. </s><figure/>

<s>Quod &longs;i partes iugi vtrinque à centro produ<lb/>ctæ, non &longs;int inter &longs;e <expan abbr="lõgitudine">longitudine</expan> æquales, quamuis æquipon<lb/>derantes; tunc quidem in ip&longs;is iugi conuer&longs;ione, ac circum<pb xlink:href="005/01/064.jpg" pagenum="56"/>latione duo circuli de&longs;cribentur alter altero malor, <expan abbr="tanquã">tanquam</expan> <lb/>à duplici &longs;emidiametro circumlato, vt hic erit in&longs;picere. </s><figure id="id.005.01.064.1.jpg" xlink:href="005/01/064/1.jpg"/>

<s>DE VECTE.</s>

<s>Vectis &longs;implex <expan abbr="quoddã">quoddam</expan> <expan abbr="in&longs;trument&utilde;">in&longs;trumentum</expan> e&longs;t ligneum, <lb/>vel <expan abbr="ferre&utilde;">ferreum</expan> &longs;atis oblongum veluti palus, aut fu&longs;ti<gap/><lb/>grandior, ad promouenda pondera; cuius vt <expan abbr="plu-rim&utilde;">plu<lb/>rimum</expan> altera extremitas <expan abbr="põderi">ponderi</expan> eleuando &longs;ubijci<lb/>tur, altera verò manu, &longs;eu <expan abbr="pot&etilde;tia">potentia</expan> præmitur, &longs;ub<lb/>&longs;trato inter <expan abbr="vtramq;">vtramque</expan> aliquo fulcimento, cui inni<lb/>tatur, quòd græcè hypomochilion appellatur, quodq <expan abbr="quãto">quanto</expan> pro<lb/>pinquius ponderi locatur, tanto facilius ip&longs;o vecte leuatur. </s>

<s>Ali<lb/>quando verò altera extremitas <expan abbr="nõ">non</expan> ponderi, &longs;ed fulcimento &longs;ubij<lb/>citur, vel ei quoquomodo innititur <expan abbr="tanquã">tanquam</expan> manenti valido, pon-<pb pagenum="57"/><expan abbr="dusq.">dusque</expan> eleuatur, aut deprimitur per vectis <expan abbr="part&etilde;">partem</expan> mediam, quæ e&longs;t <lb/>inter <expan abbr="vtramq.">vtramque</expan> <expan abbr="extremitat&etilde;">extremitatem</expan> iuxta <expan abbr="eleuation&etilde;">eleuationem</expan>, aut <expan abbr="depre&longs;&longs;ion&etilde;">depre&longs;&longs;ionem</expan> al<lb/>terius extremitatis vbi applicatur <expan abbr="pot&etilde;tia">potentia</expan>: vel certè <expan abbr="põdus">pondus</expan> ele<lb/>uatur per <expan abbr="alterã">alteram</expan> extremitatem, &longs;i in illa locetur, <expan abbr="manusq.">manusque</expan> aut po<lb/>tentia in medio adhibeatur. </s>

<s>Ali<lb/>quando verò altera extremitas <expan abbr="nõ">non</expan> ponderi, &longs;ed fulcimento &longs;ubij<lb/>citur, vel ei quoquomodo innititur <expan abbr="tanquã">tanquam</expan> manenti valido, pon-<pb xlink:href="005/01/065.jpg" pagenum="57"/><expan abbr="dusq.">dusque</expan> eleuatur, aut deprimitur per vectis <expan abbr="part&etilde;">partem</expan> mediam, quæ e&longs;t <lb/>inter <expan abbr="vtramq.">vtramque</expan> <expan abbr="extremitat&etilde;">extremitatem</expan> iuxta <expan abbr="eleuation&etilde;">eleuationem</expan>, aut <expan abbr="depre&longs;&longs;ion&etilde;">depre&longs;&longs;ionem</expan> al<lb/>terius extremitatis vbi applicatur <expan abbr="pot&etilde;tia">potentia</expan>: vel certè <expan abbr="põdus">pondus</expan> ele<lb/>uatur per <expan abbr="alterã">alteram</expan> extremitatem, &longs;i in illa locetur, <expan abbr="manusq.">manusque</expan> aut po<lb/>tentia in medio adhibeatur. </s>

<s>Vnde tres nonnulli &longs;pecies <expan abbr="vecti&utilde;">vectium</expan> di<lb/>&longs;tinguunt, quas iuxta prædicta figuris <expan abbr="etiã">etiam</expan> hic &longs;tuduimus expri<lb/>mere; Illud interim admonendo, eas omnes facilè in &longs;uis motio<lb/>nibus ad <expan abbr="circul&utilde;">circulum</expan> referri, cum ip&longs;æ nonni&longs;i <expan abbr="diametr&utilde;">diametrum</expan>, vel <expan abbr="&longs;emidia-metr&utilde;">&longs;emidia<lb/>metrum</expan> <expan abbr="circul&utilde;">circulum</expan> circa <expan abbr="immot&utilde;">immotum</expan> <expan abbr="fulciment&utilde;">fulcimentum</expan> <expan abbr="de&longs;cribent&etilde;">de&longs;cribentem</expan> referant, vt <lb/>per &longs;e patet, ac prima quæ &longs;anè vtilior & frequentius in v&longs;u e&longs;t, <lb/>ad <expan abbr="librã">libram</expan> à <expan abbr="fulcim&etilde;to">fulcimento</expan> inæquales vtrinque partes <expan abbr="habent&etilde;">habentem</expan> eniden<lb/>ti&longs;simè reducatur, vt amplius deinceps <expan abbr="cõ&longs;tabit">con&longs;tabit</expan>. </s>

<s><expan abbr="Nã">Nam</expan> hoc quod e&longs;t <lb/>fulciri per <expan abbr="&longs;u&longs;pen&longs;ion&etilde;">&longs;u&longs;pen&longs;ionem</expan> beneficio trutinæ, vel per <expan abbr="&longs;ubiection&etilde;">&longs;ubiectionem</expan> al<lb/>terius corporis, quod non minus axis, ac centri <expan abbr="vic&etilde;">vicem</expan> &longs;ubeat, e&longs;t <lb/>differentia valde accidentalis. </s><figure/><pb pagenum="58"/>

<s>DE TROCHLEA.</s>

Line 1172

<s>Con&longs;tare autem <lb/>&longs;olet Trochlea ex vno, vel pluribus orbiculis tanquam inter <lb/>thecas in&longs;ertis, non quidem æqualibus, &longs;ed maioribus &longs;uper <lb/>minores adiectis, ne vnius funis circumductus funem alte<lb/>rius impediat. </s>

<s>In&longs;uper ip&longs;i orbiculo, modò bini &longs;uper binos <lb/>locari con&longs;ueuerunt, ita vt in trochlea quatuor, vel &longs;ex or<lb/>biculi, duplici, vel triplici ordine <expan abbr="reperiãtur">reperiantur</expan> di&longs;po&longs;iti; modo <lb/>verò non ni&longs;i &longs;inguli &longs;uper &longs;ingulos, totidem ordinibus con<lb/>tinentur, vt quo potuimus modò hic figuris expre&longs;simus. </s><figure/>

<s>Reducitur autem Trochlea ad Vectem, & con&longs;equen<lb/>ter ad libram, quia vnu&longs;qui&longs;que orbiculus illius per diame<lb/>trum nititur proprio axiculo tanquam fulcimento, quod in<lb/>ter onus leuandum, aut &longs;u&longs;tinendum, & potentiam eleuan<lb/>tem locatur, ita vt ad depre&longs;sionem vnius extremitatis dia-<pb pagenum="59"/>metri, vbi mouentis potentia applicatur, altera extremitas, <lb/>quæ onus &longs;u&longs;tinet, eleuetur; licet hoc nonimmediatè fiat; <lb/>&longs;ed mediante fune ductario, vt hic ad oculos &longs;pectandum <lb/>proponetur ac infra fu&longs;iùs explicabitur quæ&longs;t. </s>

<s>Reducitur autem Trochlea ad Vectem, & con&longs;equen<lb/>ter ad libram, quia vnu&longs;qui&longs;que orbiculus illius per diame<lb/>trum nititur proprio axiculo tanquam fulcimento, quod in<lb/>ter onus leuandum, aut &longs;u&longs;tinendum, & potentiam eleuan<lb/>tem locatur, ita vt ad depre&longs;sionem vnius extremitatis dia-<pb xlink:href="005/01/067.jpg" pagenum="59"/>metri, vbi mouentis potentia applicatur, altera extremitas, <lb/>quæ onus &longs;u&longs;tinet, eleuetur; licet hoc nonimmediatè fiat; <lb/>&longs;ed mediante fune ductario, vt hic ad oculos &longs;pectandum <lb/>proponetur ac infra fu&longs;iùs explicabitur quæ&longs;t. </s>

<s>18. Sit enim <lb/>trochleç orbiculus ABC, dia<lb/><figure id="fig6"/><lb/>meter verò orbiculi linea ho<lb/>rizonti parallela AB, & axicu<lb/>lus C, tanquam centrum lo<lb/>catum in medio: Deinde per <lb/>funem ductarium ab extremo <lb/>A propendeat onus D, & ab <lb/>extremo B idem funis demit<lb/>tatur, cui applicara &longs;it poten<lb/>tia motiua in E. </s>

<s>18. Sit enim <lb/>trochleç orbiculus ABC, dia<lb/><figure id="id.005.01.067.1.jpg" xlink:href="005/01/067/1.jpg"/><lb/>meter verò orbiculi linea ho<lb/>rizonti parallela AB, & axicu<lb/>lus C, tanquam centrum lo<lb/>catum in medio: Deinde per <lb/>funem ductarium ab extremo <lb/>A propendeat onus D, & ab <lb/>extremo B idem funis demit<lb/>tatur, cui applicara &longs;it poten<lb/>tia motiua in E. </s>

<s>Dicimus er<lb/>go totum orbiculum incum<lb/>bere, ac niti axiculo C tan<lb/>quam fulcimento per diame<lb/>trum eius AB in cuius medio <lb/>axiculus e&longs;t locatus, & in cuius <lb/>extremis AB, vtrinque &longs;it tota <lb/>compre&longs;sio, nempe oneris ac potentiæ; <expan abbr="proindeq.">proindeque</expan> ip&longs;am <lb/>diametrum AB, vectis vicem in motione gerere, qua<lb/>tenus nixa in præfato fulcimento C, ad depre&longs;<lb/>&longs;ionem extremimitatis B per vim trahen<lb/>tem in E, extremitas A nece&longs;&longs;ario <lb/>eleuatur, ac &longs;imul cum illa <lb/>pondus D pendens ex <lb/>ip&longs;a, vt per &longs;e <lb/>patet. </s><pb pagenum="60"/>

<s>DE AXE IN PERITROCHIO.</s>

<s>Axis in Peritrochio e&longs;t oblongus quidam <lb/>cylindrus Peritrochio firmiter in&longs;ixus, ac pa<lb/>rallelus horizontis plano locatus, cuius ex<lb/>trema in rotundis foraminibus immoti peg<lb/>matis expeditè vertuntur. </s>

<s>Peritrochium ve<lb/>rò, e&longs;t machina rotunda, ad rotæ &longs;eu tympani &longs;imilitudi<lb/>nem efformata, in cuius conuexa peripheria &longs;tipites qui & <lb/>Scytalæ vocantur, tanquam radij infinguntur; quibus admo<lb/>ta manu tota machina &longs;imul cum axe ver&longs;atur, ac funibus <lb/>circa axem conuolutis, trahuntur pondera illis alligata; vt <lb/>hic licebit in&longs;picere. </s><figure/>

<s>Reducitur <expan abbr="aut&etilde;">autem</expan> <lb/>tota huiu&longs;modi ma <lb/>china, &longs;eu in&longs;tru<lb/>mentum ad <expan abbr="vect&etilde;">vectem</expan>; <lb/>Nam &longs;i con&longs;idere<lb/>mus <expan abbr="con&longs;titut&utilde;">con&longs;titutum</expan> ex <lb/>diametro axis, ac <lb/>&longs;emidiametro Pe<lb/>ritrochij <expan abbr="coincid&etilde;-te">coinciden<lb/>te</expan> cum illa non ali<lb/>ter in circumuolu<lb/>tione &longs;e habere <expan abbr="cõ-perimus">con<lb/>perimus</expan>, ac <expan abbr="Vect&etilde;">Vectem</expan>, <lb/>qui circa &longs;uum ful<lb/>cimentum vertitur, <lb/>tanquam circa pro<lb/>prium centrum. <lb/></s>

<s>E&longs;to enim Axis &longs;imul, ac Peritrochij immobile centrum <lb/>A, circa quod vtriu&longs;que circumferentia de&longs;cripta &longs;it, nem<lb/>pe tàm Axis, quàm Tympani ip&longs;ius Peritrochij cum &longs;cyta<lb/>lis; Diameter verò Axis &longs;it linea BC; ac &longs;emidiameter Pe<lb/>titrochij AD, con&longs;tituentes integram lineam BD. </s>

<s>Tum <pb pagenum="61"/>ex Axe per funem BE propendeat onus F; <expan abbr="virtusq.">virtusque</expan> mo<lb/>uentis applicetur in &longs;cytala vbi e&longs;t ip&longs;um D. </s>

<s>Tum <pb xlink:href="005/01/069.jpg" pagenum="61"/>ex Axe per funem BE propendeat onus F; <expan abbr="virtusq.">virtusque</expan> mo<lb/>uentis applicetur in &longs;cytala vbi e&longs;t ip&longs;um D. </s>

<s>Ad motum <lb/>igitur deor&longs;um ip&longs;ius D, linea BD, non aliter &longs;e pote&longs;t <lb/>habere, ac vectis firmiter innixa immobili centro A, tan<lb/>quam fulcimento, ac dum pars AD deprimitur, altera. <lb/></s>

<s>nempe AB, eleuabitur &longs;imulque cum puncto B, pondus <lb/>F, quod ab eodem puncto extremo dependet. </s><figure/>

<s>nempe AB, eleuabitur &longs;imulque cum puncto B, pondus <lb/>F, quod ab eodem puncto extremo dependet. </s><figure id="id.005.01.069.1.jpg" xlink:href="005/01/069/1.jpg"/>

<s>DE CVNEO.</s>

Line 1204

<s>Duabus videlicet &longs;ibi oppo&longs;itis <lb/>quadrangularibus, ac altera parte longioribus; duabus verò <lb/>&longs;imiliter oppo&longs;itis, &longs;ed triangularibus in prædictam acutam, <lb/>& oblongam aciem terminantibus. </s>

<s>Quæ &longs;anè acies cum in <lb/>timulam quamlibet <expan abbr="&longs;cind&etilde;dæ">&longs;cindendæ</expan> molis &longs;e in&longs;inuare præualeat, <pb pagenum="62"/>adueniente valida percu&longs;&longs;ione, vt quæ per malleú &longs;uper ba<lb/>&longs;im adactum fieri con&longs;ueuit, facilè totum cuneum cogit ad<lb/>mittere, <expan abbr="proindeq.">proindeque</expan> partes molis ab inuicem &longs;ecedere, quod <lb/>e&longs;t molem<gap/>p&longs;am &longs;cindi, ac diuidi. </s>

<s>Quæ &longs;anè acies cum in <lb/>timulam quamlibet <expan abbr="&longs;cind&etilde;dæ">&longs;cindendæ</expan> molis &longs;e in&longs;inuare præualeat, <pb xlink:href="005/01/070.jpg" pagenum="62"/>adueniente valida percu&longs;&longs;ione, vt quæ per malleú &longs;uper ba<lb/>&longs;im adactum fieri con&longs;ueuit, facilè totum cuneum cogit ad<lb/>mittere, <expan abbr="proindeq.">proindeque</expan> partes molis ab inuicem &longs;ecedere, quod <lb/>e&longs;t molem<gap/>p&longs;am &longs;cindi, ac diuidi. </s>

<s>Cunei ergo figura &longs;ic de<lb/>lineanda cen&longs;uimus ex quadrata ba&longs;i ABCD, excitando <lb/>&longs;operficiem quadrangularem DBEF, ac aliam triangula<lb/>rem CDE, quæ &longs;imul cum &longs;uis oppo&longs;itis omnes quatuor <lb/>de&longs;inant, ac terminentur in aciem EF. </s><figure/>

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

Line 1214

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

<s>Onera verò &longs;unt re<lb/><figure id="fig7"/><lb/>reliquæ eiu&longs;dem corporis partes <lb/>&longs;ucce&longs;siuè dimouend&ecedil;, & adinui<lb/>cem &longs;eparádæ per aciem intran<lb/>tem vbi E, vt in propo&longs;ita figu <lb/>ra e&longs;t l, & K. </s>

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

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

<s>Et extrema in quibus ap<lb/>plicatur potentia &longs;unt initia ip&longs;o<lb/>rum laterum ex parte ba&longs;is vbi <lb/>fit tota percu&longs;&longs;io, nempe vbi C <lb/>& D, quæ omnia aperti&longs;&longs;imè <lb/>citata quæ&longs;tione amplius con&longs;ta<lb/>bunt. </s><pb pagenum="63"/>

<s>DE COCHLEA.</s>

<s>Cochlea in&longs;trumentum e&longs;t veluti com<lb/>po&longs;itum ex cuneo, & cylindro, &longs;eu e&longs;t &longs;tria<lb/>tus quidam cylindrus &longs;trigas habens admo<lb/>dum helicis &longs;pirulatim circumuolutas, cuius <lb/>vertigine pondera helici <lb/><figure id="fig8"/><lb/>congruè applicata, facillimè mouentur. <lb/></s>

<s>Cochlea in&longs;trumentum e&longs;t veluti com<lb/>po&longs;itum ex cuneo, & cylindro, &longs;eu e&longs;t &longs;tria<lb/>tus quidam cylindrus &longs;trigas habens admo<lb/>dum helicis &longs;pirulatim circumuolutas, cuius <lb/>vertigine pondera helici <lb/><figure id="id.005.01.071.1.jpg" xlink:href="005/01/071/1.jpg"/><lb/>congruè applicata, facillimè mouentur. <lb/></s>

<s>Exemplum &longs;it erectus cylindrus AB, <lb/>cuius helices, vel &longs;trigæ cir cumuolutæ, <lb/>&longs;int CD, EF; manubrium verò cylin<lb/>dri G. </s>

Line 1230

<s>Idenique pote&longs;t exemplificari in. <lb/></s>

<s>alia ip&longs;ius cochleæ figura æquidi&longs;tantis <lb/>ab horizonte, vt AB, &longs;i apponatur <lb/>illi onus CD, tanquam cylindri con<lb/>caui ac &longs;triati, qui & Tylum à Pappo, & alijs Mechanicis, <lb/><figure id="fig9"/><pb pagenum="64"/>& Cochleæ f&oelig;mina vulgò appellatur. </s>

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

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

Line 1252

<s>Quod præclarè explicat Federi<lb/>cus Commandinus. </s>

<s>Si enim, inquit, per tale centrum du-<pb pagenum="65"/>catur planum, figuram ip&longs;ius corporis quomodocun que<arrow.to.target n="marg15"/> &longs;e<lb/>cans, &longs;emper in partes æqueponderantes ip&longs;am diuidet, <lb/>quamuis aliquando &longs;int inæqualis dimentionis. </s>

<s>Si enim, inquit, per tale centrum du-<pb xlink:href="005/01/073.jpg" pagenum="65"/>catur planum, figuram ip&longs;ius corporis quomodocun que<arrow.to.target n="marg15"/> &longs;e<lb/>cans, &longs;emper in partes æqueponderantes ip&longs;am diuidet, <lb/>quamuis aliquando &longs;int inæqualis dimentionis. </s>

<s>Porrò in <lb/>diui&longs;ione corporis per eius centrum grauitatis, partes diui<lb/>&longs;æ non &longs;emper &longs;unt eiu&longs;dem magnitudinis, &longs;eu dimentionis, <lb/>&longs;unt tamen eiu&longs;dem ponderis, & grauitatis, vt Guidus<arrow.to.target n="marg16"/> Vbal<lb/>dus &longs;atis demon&longs;trat. </s>

Line 1276

<s>propo&longs;<gap/>lt.</s>

<s>Quapropter &longs;i punctum <lb/>A fuerit centrum grauita<lb/><figure id="fig10"/><lb/>tis corporis BCD <expan abbr="quo-modocumq;">quo<lb/>modocumque</expan> diui&longs;i per <expan abbr="pla-nã">pla<lb/>nam</expan> EF tran&longs;euntem per ip<lb/>&longs;ummet centrum, atque <lb/>idem corpus ex eodem <lb/>puncto &longs;u&longs;penderetur, cer<lb/>tè quo ad po&longs;itionem ac <lb/>di&longs;po&longs;itionem &longs;uarum par<lb/>tium inuariatum omnino maneret; ita vt nullo pacto ip&longs;um <lb/>B, ac D verterentur circa punctum A tanquam circa cen<lb/>trum, &longs;ed eadem qua prius po&longs;itione manerent, &longs;iue pars <lb/>BEFC æqualis dimentionis inueniretur parti EDF, &longs;iue <lb/>inæqualis: &longs;emper enim &longs;ic coniunctæ æqueponderaret, e&longs;<lb/>&longs;entque æqualium momentorum. </s>

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

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

<s>Idemque contingeret quocunque alio modo ip&longs;um corpus <pb pagenum="66"/>&longs;u&longs;pen&longs;um, aut etiam latum à principio con&longs;tirueretur. </s>

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

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

<s>Sicut etiam in corpore irregulari DE cuius <lb/><figure id="fig11"/><lb/>centrum e&longs;&longs;et in F. </s>

<s>Sicut etiam in corpore irregulari DE cuius <lb/><figure id="id.005.01.074.1.jpg" xlink:href="005/01/074/1.jpg"/><lb/>centrum e&longs;&longs;et in F. </s>

<s>Occurrit Guidus Vbaldus dicens, etiam <lb/>prædicta centra intra figuram e&longs;&longs;e quatenus verè continen<lb/>tur ab ambitu eiu&longs;dem figuræ ip&longs;orum corporum. </s>

Line 1292

<s>Id quod aperti&longs;&longs;imè <lb/>con&longs;tabit con&longs;ideranti graue quodcumque &longs;eclu&longs;o omni <lb/>impedimento, ac detentione, &longs;tatim &longs;uo pondere, & ex &longs;e <lb/>centrum vniuer&longs;i expetere, nec vnquam quie&longs;cere donec <lb/>ad illud &longs;i fieri po&longs;&longs;et, perueniat. </s>

<s>Diximus autem huiu&longs;cemodi aptitudinem e&longs;&longs;e ex prin<lb/>cipio intrin&longs;eco tum actiuo tum pa&longs;&longs;iuo; nam id per quod <lb/>grauia formaliter con&longs;tituuntur apta, & in actu primo ad <lb/>motum localem deor&longs;um, non modò e&longs;t potentia pa&longs;&longs;iua <lb/>ip&longs;is innata, &longs;icut cuilibet corpori ad recipiendum talem <lb/>motum, &longs;iue producatur à &longs;eip&longs;o &longs;iue ab alio: &longs;ed præcipuè <pb pagenum="67"/>e&longs;t intrin&longs;eca ip&longs;a grauitas, quæ tanquam proprium ope<lb/>randi principium e&longs;t illis ratio, vt moueantur deor&longs;um, &longs;eu <lb/>forma qua in &longs;e &longs;eclu&longs;is impedimentis, talem motum pro<lb/>ducunt. </s>

<s>Diximus autem huiu&longs;cemodi aptitudinem e&longs;&longs;e ex prin<lb/>cipio intrin&longs;eco tum actiuo tum pa&longs;&longs;iuo; nam id per quod <lb/>grauia formaliter con&longs;tituuntur apta, & in actu primo ad <lb/>motum localem deor&longs;um, non modò e&longs;t potentia pa&longs;&longs;iua <lb/>ip&longs;is innata, &longs;icut cuilibet corpori ad recipiendum talem <lb/>motum, &longs;iue producatur à &longs;eip&longs;o &longs;iue ab alio: &longs;ed præcipuè <pb xlink:href="005/01/075.jpg" pagenum="67"/>e&longs;t intrin&longs;eca ip&longs;a grauitas, quæ tanquam proprium ope<lb/>randi principium e&longs;t illis ratio, vt moueantur deor&longs;um, &longs;eu <lb/>forma qua in &longs;e &longs;eclu&longs;is impedimentis, talem motum pro<lb/>ducunt. </s>

<s>Quod optimè expre&longs;&longs;it Ari&longs;toteles lib.

Line 1322

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

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

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

<s><emph type="italics"/>De præternaturali, & artificio&longs;a mobilitate <lb/>grauium, & leuium.<emph.end type="italics"/></s>

Line 1340

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

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

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

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

Line 1366

<s>Pul&longs;ionem autem di&longs;tin<lb/>guit in Impul&longs;ionem, & Expul&longs;ionem. </s>

<s>Impul&longs;ionem ait e&longs;&longs;e <lb/>cum pellens ita pellit, vt pul&longs;um non de&longs;erat, &longs;ed comite<pb pagenum="70"/>tur: Expul&longs;ionem verò, tum vbi pepulit, pul&longs;um ip&longs;um re<lb/>linquit, de quo genere e&longs;t proiectio. </s>

<s>Impul&longs;ionem ait e&longs;&longs;e <lb/>cum pellens ita pellit, vt pul&longs;um non de&longs;erat, &longs;ed comite<pb xlink:href="005/01/078.jpg" pagenum="70"/>tur: Expul&longs;ionem verò, tum vbi pepulit, pul&longs;um ip&longs;um re<lb/>linquit, de quo genere e&longs;t proiectio. </s>

<s>Tractionem deinde ait <lb/>e&longs;&longs;e motum trahentis non &longs;eparatum à motu eius, quod <lb/>trahitur: <expan abbr="ideoq.">ideoque</expan> e&longs;&longs;e motum ad &longs;eip&longs;um, & ad alterum. </s>

Line 1386

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

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

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

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

Line 1394

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

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

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

Line 1412

<s><margin.target id="marg17"/>Lib. 1. <lb/>Acqui<gap/> <expan abbr="õd">ond</expan>. <lb/></s>

<s>p<gap/>opo&longs;it.6.</s><figure/><pb pagenum="73"/>

<s>p<gap/>opo&longs;it.6.</s><figure id="id.005.01.080.1.jpg" xlink:href="005/01/080/1.jpg"/><pb xlink:href="005/01/081.jpg" pagenum="73"/>

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

Line 1432

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

<s>In magna autem hbra idem pondus vi&longs;ibile effieit ma-<emph.end type="italics"/><pb pagenum="74"/><emph type="italics"/>gnitudo. </s>

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

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

Line 1456

<s>Ergo idem pondus ab extremo libræ propendens <lb/>eò magis illam conuertere, aut mouere valebit, quò maior <lb/>fuerit ip&longs;a libra, &longs;eu quò longioribus brachijs con&longs;tabit. </s>

<s>Si<lb/>quidem extremum vbi appenditur pondus, magis di&longs;tabit <lb/>à centro, <expan abbr="maioremq.">maioremque</expan> proinde portionem circuli eodem <pb pagenum="75"/>tempore, <expan abbr="eademq.">eademque</expan> vi peraget, vt per&longs;picuum e&longs;t in hac fi<lb/>gura &longs;i brachia libræ AB protrahantur v&longs;que ad CD. </s>

<s>Si<lb/>quidem extremum vbi appenditur pondus, magis di&longs;tabit <lb/>à centro, <expan abbr="maioremq.">maioremque</expan> proinde portionem circuli eodem <pb xlink:href="005/01/083.jpg" pagenum="75"/>tempore, <expan abbr="eademq.">eademque</expan> vi peraget, vt per&longs;picuum e&longs;t in hac fi<lb/>gura &longs;i brachia libræ AB protrahantur v&longs;que ad CD. </s>

<s>Quia <lb/>nimirum, &longs;icut maio<lb/><figure id="fig12"/><lb/>rem efficerent circu<lb/>lum, videlicet conti<lb/>nentem, maioremque <lb/>diametrum; ita maio<lb/>rem arcum eorum ex<lb/>trema percurrerent. <lb/></s>

<s>Quia <lb/>nimirum, &longs;icut maio<lb/><figure id="id.005.01.083.1.jpg" xlink:href="005/01/083/1.jpg"/><lb/>rem efficerent circu<lb/>lum, videlicet conti<lb/>nentem, maioremque <lb/>diametrum; ita maio<lb/>rem arcum eorum ex<lb/>trema percurrerent. <lb/></s>

<s>Nam quo tempore <lb/>ac vi A moueretur v&longs; <lb/>que ad F, ip&longs;um C <lb/>moueretur <expan abbr="v&longs;q;">v&longs;que</expan> ad E <lb/>Maior autem e&longs;t CE <lb/>quàm AF, eo quod <lb/>&longs;icut diameter ad dia<lb/>metrum, ita portio ad <lb/>portionem circuli &longs;e <lb/>habeat. </s>

Line 1470

<s>Vnde quæ mani<lb/>fe&longs;ta &longs;unt in vtriu&longs;que libris, multo magis (vt idem inquit) <lb/>manife&longs;ta &longs;e præbent in meioribus, quoniam in illis multo <lb/>maior inclinatio cau&longs;atur ab eodem pondere. </s>

<s>Id quod in <lb/>omnibus in&longs;trumentis verificatur, quæ ad men&longs;urandum de-<pb pagenum="76"/>&longs;eruiunt: Nam quo ampliora eò minus obtutum fallunt, & <lb/>euidentius men&longs;uratorum differentias manife&longs;tant. </s>

<s>Id quod in <lb/>omnibus in&longs;trumentis verificatur, quæ ad men&longs;urandum de-<pb xlink:href="005/01/084.jpg" pagenum="76"/>&longs;eruiunt: Nam quo ampliora eò minus obtutum fallunt, & <lb/>euidentius men&longs;uratorum differentias manife&longs;tant. </s>

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

Line 1500

<s><expan abbr="Quãdoquidem">Quandoquidem</expan> <lb/>&longs;i ita e&longs;&longs;et, lanx illa maiorem longitudinem brachij non re<lb/>quireret ad magis grauitandum. </s>

<s>Quod &longs;i vtroque ex capi-<pb pagenum="77"/>te magis grauitaret, nempe ex plumbo adiuncto, & ex ma<lb/>iori longitudine brachij, nunquam libra ponderibus, ac mer<lb/>cibus vacua, in æquilibrio po&longs;&longs;et con&longs;titui, fed &longs;atis apertè <lb/>huiu&longs;modi lanx &longs;emper deor&longs;um tenderet, altera verò &longs;ur<lb/>&longs;um; <expan abbr="ideoq.">ideoque</expan> nulla ex hoc oriretur deceptio, <expan abbr="nullaq.">nullaque</expan> fraus, <lb/>quæ ex deceptione con&longs;equitur. </s>

<s>Quod &longs;i vtroque ex capi-<pb xlink:href="005/01/085.jpg" pagenum="77"/>te magis grauitaret, nempe ex plumbo adiuncto, & ex ma<lb/>iori longitudine brachij, nunquam libra ponderibus, ac mer<lb/>cibus vacua, in æquilibrio po&longs;&longs;et con&longs;titui, fed &longs;atis apertè <lb/>huiu&longs;modi lanx &longs;emper deor&longs;um tenderet, altera verò &longs;ur<lb/>&longs;um; <expan abbr="ideoq.">ideoque</expan> nulla ex hoc oriretur deceptio, <expan abbr="nullaq.">nullaque</expan> fraus, <lb/>quæ ex deceptione con&longs;equitur. </s>

<s>Quando igitur Ari&longs;tote<lb/>les ait, purpurarios plumbum, vel quid &longs;imile in eam, quam <lb/>deferri volunt partem con&longs;tituere, intelligendus e&longs;t de par<lb/>te, &longs;eu de brachio libræ minori, quod certè &longs;ur&longs;um a&longs;cende<lb/>ret ad de&longs;cen&longs;um maioris, ac deferri non po&longs;&longs;et ad con&longs;ti<lb/>tuendum Aequilibrium, ni&longs;i &longs;imilibus adiumentis quantum <lb/>opus e&longs;t deprimeretur; vt rectè etiam notat Cardanus lib. <lb/>1. de principijs prope finem. </s>

Line 1520

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

<s>Siquidem igitur &longs;ur&longs;um babuerit &longs;partum,<emph.end type="italics"/><pb pagenum="78"/><emph type="italics"/>rur&longs;um propter boc a&longs;cendit libra. </s>

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

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

Line 1554

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

Line 1564

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

<s>Nam &longs;i iugum libræ &longs;it BC in æquilibrio <lb/><figure id="fig13"/><lb/>con&longs;titutum: &longs;partum <lb/>autem quo <expan abbr="&longs;u&longs;p&etilde;ditur">&longs;u&longs;penditur</expan>, <lb/>AD, ita videlicet, vt <lb/>axis &longs;it ip&longs;um D, quod <lb/>e&longs;t punctum &longs;upra lati<lb/>tudinem iugi. </s>

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

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

Line 1576

<s>Quare ea pars libræ, &longs;eu iugi. </s>

<s>EH, quæ e&longs;t extra <lb/>perpendiculum AM ver&longs;us H maiorerit dimidio nem<lb/>pe quantum importat triangulus DGM, quod &longs;patium <lb/>Ari&longs;toteles &longs;ignauit <expan abbr="Pq.">Pque</expan> Si igitur amoueaturonus, quod <pb pagenum="80"/>deprimit in E, nece&longs;&longs;e e&longs;t deor&longs;um ferri partem vbi H. <lb/><figure id="fig14"/><lb/><expan abbr="Siquid&etilde;">Siquidem</expan> pars illa ma<lb/>ior e&longs;t quàm hæc vbi <lb/>E, quæ per <expan abbr="con&longs;equ&etilde;s">con&longs;equens</expan> <lb/>&longs;ur&longs;um a&longs;cen det, & &longs;ic <lb/>rur&longs;us libra con&longs;titue<lb/>tur in æquilibrio quod <lb/>erat probandum. </s>

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

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

Line 1584

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

<s>Id quod &longs;ic <lb/>o&longs;tendit Ari&longs;toteles &longs;it libra in &ecedil;quilibrio con&longs;tituta NG <lb/><figure id="fig15"/><lb/><expan abbr="perpendicul&utilde;">perpendiculum</expan> verò bi<lb/>fariam libram ip&longs;am <lb/>&longs;ecans, ac tendens ad <lb/>centrum mundi, &longs;it ca<lb/>dens KLM. </s>

<s>Id quod &longs;ic <lb/>o&longs;tendit Ari&longs;toteles &longs;it libra in &ecedil;quilibrio con&longs;tituta NG <lb/><figure id="id.005.01.088.2.jpg" xlink:href="005/01/088/2.jpg"/><lb/><expan abbr="perpendicul&utilde;">perpendiculum</expan> verò bi<lb/>fariam libram ip&longs;am <lb/>&longs;ecans, ac tendens ad <lb/>centrum mundi, &longs;it ca<lb/>dens KLM. </s>

<s>Axis verò <lb/>infra <expan abbr="iug&utilde;">iugum</expan> locatus vbi <lb/>L. </s>

Line 1596

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

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

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

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

Line 1612

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

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

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

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

Line 1630

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

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

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

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

Line 1640

<s>Po&longs;tea excitentur à puncto D, & à puncto E <lb/>duæ paralellæ perpendiculariter tendentes ad lineam AB, <lb/>ita vt efficiantur duo triangula AEG, & DGB. </s>

<s>In his au<lb/><figure id="fig16"/><lb/>tem triangulis, an<lb/>gulus DGB &ecedil;qua<lb/>lis e&longs;t angulo EGA <lb/>cum &longs;int ad verti<lb/>cem per 15. primi <lb/>Eucl. </s>

<s>In his au<lb/><figure id="id.005.01.091.1.jpg" xlink:href="005/01/091/1.jpg"/><lb/>tem triangulis, an<lb/>gulus DGB &ecedil;qua<lb/>lis e&longs;t angulo EGA <lb/>cum &longs;int ad verti<lb/>cem per 15. primi <lb/>Eucl. </s>

<s>Angulus <expan abbr="etiã">etiam</expan> <lb/>D. &ecedil;qualis e&longs;t an<lb/>gulo E cum &longs;int al<lb/>terni intra ea&longs;dem <lb/>paralellas, vt patet <lb/>per 29. primi eiu&longs;<lb/>dem Euclidis. </s>

Line 1652

<s>Vnde fit vt cum <lb/>vnum latus ex duobus, quibus angulus E continetur, vide<lb/>licet GE &longs;it maius <expan abbr="quã">quam</expan> latus GD &ecedil;qualis anguli D. </s>

<s>Siqui<lb/>dem GE e&longs;t plu&longs;quam dimidium line&ecedil; DE continet enim <pb pagenum="84"/>amplius <expan abbr="di&longs;tantiã">di&longs;tantiam</expan> GF, eo quod in F ip&longs;a linea DE bifariam <lb/>diui&longs;a &longs;it, <expan abbr="proindeq.">proindeque</expan> latus GD &longs;it minus dimidio, ad quod <lb/>dee&longs;t &longs;patium GF. Ex. hoc inquam fit, vt alterum latus <lb/>eiu&longs;dem anguli E &longs;it etiam maius altero latere &ecedil;qualis an<lb/>guli D, nempe vt AE, maius &longs;it quàm BD. </s>

<s>Siqui<lb/>dem GE e&longs;t plu&longs;quam dimidium line&ecedil; DE continet enim <pb xlink:href="005/01/092.jpg" pagenum="84"/>amplius <expan abbr="di&longs;tantiã">di&longs;tantiam</expan> GF, eo quod in F ip&longs;a linea DE bifariam <lb/>diui&longs;a &longs;it, <expan abbr="proindeq.">proindeque</expan> latus GD &longs;it minus dimidio, ad quod <lb/>dee&longs;t &longs;patium GF. Ex. hoc inquam fit, vt alterum latus <lb/>eiu&longs;dem anguli E &longs;it etiam maius altero latere &ecedil;qualis an<lb/>guli D, nempe vt AE, maius &longs;it quàm BD. </s>

Line 1660

<s>Vnum tandem hic &longs;upere&longs;t explicandum, de quo non <lb/>meminit Ari&longs;toteles; Cur nimirum &longs;i axis non con&longs;tituatur <lb/>&longs;upra, nec infra, &longs;ed pror&longs;us in puncto medio longitudinis, <lb/>ac magnitudinis iugi, vt in puncto A propo&longs;it&ecedil; libr&ecedil; BC <lb/>in æquilibrio con&longs;titut&ecedil;; & alterum extremum illius manu, <lb/>vel pondere deor&longs;um trahatur, ablato pondere, vel ce&longs;&longs;ante <lb/>detentione, rur&longs;us ad &ecedil;quilibrium ip&longs;a libra non reuertatur, <lb/>&longs;ed maneat quomodocumque relinquatur. </s>

<s>Id quod ex eo prouenire comperiemus, quoniam in hu<lb/>iu&longs;modi con&longs;titutione libr&ecedil;, centrum grauitatis coincidit <lb/>cum centro cir cumuolutionis, &longs;eu axis ip&longs;ius libr&ecedil;, <expan abbr="proin-deq.">proin<lb/>deque</expan> habere non pote&longs;t, quo declinet, aut vergat etiam &longs;i <lb/>libra quomodolibet &longs;ituetur, aut moueatur, &longs;ed manebit <lb/><figure id="fig17"/><lb/>&longs;emper in illo <lb/>tanquam in &longs;uo <lb/>fulcimento, à <lb/>quo &longs;u&longs;tentatur. <lb/></s>

<s>Id quod ex eo prouenire comperiemus, quoniam in hu<lb/>iu&longs;modi con&longs;titutione libr&ecedil;, centrum grauitatis coincidit <lb/>cum centro cir cumuolutionis, &longs;eu axis ip&longs;ius libr&ecedil;, <expan abbr="proin-deq.">proin<lb/>deque</expan> habere non pote&longs;t, quo declinet, aut vergat etiam &longs;i <lb/>libra quomodolibet &longs;ituetur, aut moueatur, &longs;ed manebit <lb/><figure id="id.005.01.092.1.jpg" xlink:href="005/01/092/1.jpg"/><lb/>&longs;emper in illo <lb/>tanquam in &longs;uo <lb/>fulcimento, à <lb/>quo &longs;u&longs;tentatur. <lb/></s>

<s>Idem enim <expan abbr="p&utilde;-ctum">pun<lb/>ctum</expan> A e&longs;t cen<lb/>trum grauitatis <lb/>cum &longs;it in me<lb/>dio iugi BC, & <lb/>e&longs;t <expan abbr="c&etilde;trum">centrum</expan> axis <lb/>ex con&longs;tructio<lb/>nis &longs;uppo&longs;itio<lb/>ne. </s>

<s>Quare &longs;i in <lb/>illo iugum diui<lb/>datur per lineam perpendicularem DE, in quo cumque &longs;i-<pb pagenum="85"/>tu ponatur, &longs;iue in &ecedil;quilibrio, vt vbi BC, &longs;iue alibi vt in F G <lb/>&longs;emper diuidetur bifariam, atque adeo in duas partes &ecedil;qui<lb/>ponderantes, quarum altera, alteram mouere non pote&longs;t, <lb/>cum propter &ecedil;quiponderantiam, tum propter <expan abbr="æquidi&longs;tãtiam">æquidi&longs;tantiam</expan> <lb/>quam &longs;emper <expan abbr="retiner&etilde;t">retinerent</expan> à perpendiculo, &longs;eu linea cathectus. </s>

<s>Quare &longs;i in <lb/>illo iugum diui<lb/>datur per lineam perpendicularem DE, in quo cumque &longs;i-<pb xlink:href="005/01/093.jpg" pagenum="85"/>tu ponatur, &longs;iue in &ecedil;quilibrio, vt vbi BC, &longs;iue alibi vt in F G <lb/>&longs;emper diuidetur bifariam, atque adeo in duas partes &ecedil;qui<lb/>ponderantes, quarum altera, alteram mouere non pote&longs;t, <lb/>cum propter &ecedil;quiponderantiam, tum propter <expan abbr="æquidi&longs;tãtiam">æquidi&longs;tantiam</expan> <lb/>quam &longs;emper <expan abbr="retiner&etilde;t">retinerent</expan> à perpendiculo, &longs;eu linea cathectus. </s>

<s>Quæ&longs;tio Tertia.</s>

Line 1686

<s>COMMENTARIVS.</s>

<s>Qvod Ari&longs;toteles tanquam admirandum, ac vnum <lb/>de numero eorum, qu&ecedil; pr&ecedil;ter naturam accidunt in <lb/>principio huius libri textu 2. propo&longs;uerat, hic mo<lb/>do ad inue&longs;tigandam eius cau&longs;am, iterum proponit, qu&ecedil;rens <pb pagenum="86"/>cur exigu&ecedil; vires adhibito vecte, magna moueant pondera, <lb/>qu&ecedil; ab&longs;que vecte mouere minimè po&longs;&longs;ent, cum tamen ip<lb/>&longs;um quoque onus vectis. </s>

<s>Qvod Ari&longs;toteles tanquam admirandum, ac vnum <lb/>de numero eorum, qu&ecedil; pr&ecedil;ter naturam accidunt in <lb/>principio huius libri textu 2. propo&longs;uerat, hic mo<lb/>do ad inue&longs;tigandam eius cau&longs;am, iterum proponit, qu&ecedil;rens <pb xlink:href="005/01/094.jpg" pagenum="86"/>cur exigu&ecedil; vires adhibito vecte, magna moueant pondera, <lb/>qu&ecedil; ab&longs;que vecte mouere minimè po&longs;&longs;ent, cum tamen ip<lb/>&longs;um quoque onus vectis. </s>

<s>dimouendum &longs;u&longs;cipiant? </s>

Line 1706

<s>AB, pondus <lb/>verò vbi C, & potentia mouens vbi D; inter quæ me<lb/>diet fulcimentum in E. </s>

<s>Tunc &longs;i con&longs;ideretur, eadem erit <lb/><figure id="fig18"/><pb pagenum="87"/><figure id="fig19"/><lb/>ratio ac de libra, cuius iugum &longs;it AB, lances verò C, D, <lb/>& axis, &longs;eu fulcimentum E. </s>

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

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

Line 1716

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

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

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

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

Line 1728

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

<s>Brachium autem CA &longs;it verbi <lb/><figure id="fig20"/><lb/>gratia vnius <lb/>palmi. </s>

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

<s>Bra<lb/>chium verò <lb/>CB &longs;it qua<lb/>tuorpalmo<lb/>rum. </s>

<s>Dein<lb/>de <expan abbr="app&etilde;da-tur">appenda<lb/>tur</expan> in <expan abbr="Apõ-dus">Apon<lb/>dus</expan> D, quod <lb/><expan abbr="põderet">ponderet</expan>, vt <lb/>quatuor; & <lb/>in B appen<lb/>datur pondus E, ponderans vt vnum; ita vt ip&longs;um pondus <pb pagenum="89"/>E &longs;e habeat ad pondus D eadem proportione, qua bra<lb/>chium CA &longs;e habet ad brachium CB. </s>

<s>Dein<lb/>de <expan abbr="app&etilde;da-tur">appenda<lb/>tur</expan> in <expan abbr="Apõ-dus">Apon<lb/>dus</expan> D, quod <lb/><expan abbr="põderet">ponderet</expan>, vt <lb/>quatuor; & <lb/>in B appen<lb/>datur pondus E, ponderans vt vnum; ita vt ip&longs;um pondus <pb xlink:href="005/01/097.jpg" pagenum="89"/>E &longs;e habeat ad pondus D eadem proportione, qua bra<lb/>chium CA &longs;e habet ad brachium CB. </s>

<s>Tunc quippe dici<lb/>mus vectem, aut libram man&longs;uram in æquilibrio propter <lb/><expan abbr="cõmutatam">commutatam</expan> proportionem. </s>

Line 1760

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

<s>Quandoquidem paulo po&longs;t id ip&longs;um <lb/>repetens, ait. <emph type="italics"/>Semper autem quanio ab hy<gap/>mochlio di<gap/><lb/>bit magis, tanto facilius mouebit.<emph.end type="italics"/></s><s> Et quidem in motu locali <lb/>velocitas &longs;emper facilitatem inuoluit, aut &longs;upponit, <expan abbr="ip&longs;aq.">ip&longs;aque</expan> <pb pagenum="90"/>maior velocitas, ac facilitas motus, maiorem grauitatem, aut <lb/>maiorem virtutem motiuam nece&longs;&longs;ario indicat, vt palam e&longs;t <lb/>in motibus tàm naturalibus, quàm violentis. </s>

<s>Quandoquidem paulo po&longs;t id ip&longs;um <lb/>repetens, ait. <emph type="italics"/>Semper autem quanio ab hy<gap/>mochlio di<gap/><lb/>bit magis, tanto facilius mouebit.<emph.end type="italics"/></s><s> Et quidem in motu locali <lb/>velocitas &longs;emper facilitatem inuoluit, aut &longs;upponit, <expan abbr="ip&longs;aq.">ip&longs;aque</expan> <pb xlink:href="005/01/098.jpg" pagenum="90"/>maior velocitas, ac facilitas motus, maiorem grauitatem, aut <lb/>maiorem virtutem motiuam nece&longs;&longs;ario indicat, vt palam e&longs;t <lb/>in motibus tàm naturalibus, quàm violentis. </s>

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

Line 1792

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

<s>Maxima <lb/>enim remi pars à &longs;calmo in nauis medio intus e&longs;t.<emph.end type="italics"/></s><pb pagenum="91"/>

<s>Maxima <lb/>enim remi pars à &longs;calmo in nauis medio intus e&longs;t.<emph.end type="italics"/></s><pb xlink:href="005/01/099.jpg" pagenum="91"/>

<s>COMMENTARIVS.</s>

Line 1810

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

<s>Hoc e&longs;t tam intus ex parte manubrij, quàm foris <pb pagenum="92"/>ex parte palmulæ. </s>

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

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

Line 1824

<s>Veruntamen non video cur mobilitas ac latio nauis cum <lb/>&longs;calmo, ob&longs;tet quominus ip&longs;e &longs;calmus habeat rationem ful<lb/>cimenti, <expan abbr="eaq.">eaque</expan> concedatur mari, quod non minus mouetur <lb/>per impul&longs;um acceptum à palmula. </s>

<s>Quapropter vel neu<lb/>trum horum <expan abbr="dicend&utilde;">dicendum</expan> e&longs;t, habere po&longs;&longs;e rationem fulcimen<lb/>ti, hoc e&longs;t nec mare, nec &longs;calmum; vel dicendum e&longs;t vtrum<lb/>que illorum participare huiu&longs;modi rationem, vt exempli <lb/>gratia, &longs;i ponamus vectem AB interpo&longs;itam e&longs;&longs;e inter <lb/><figure id="fig21"/><lb/>duos lapides CD, quorum C &longs;it ver&longs;us extremitatem B <lb/>retror&longs;um, D verò circa medium ip&longs;ius vectis antror&longs;um; <lb/>& potentia applicetur in extremitate A. </s>

<s>Quapropter vel neu<lb/>trum horum <expan abbr="dicend&utilde;">dicendum</expan> e&longs;t, habere po&longs;&longs;e rationem fulcimen<lb/>ti, hoc e&longs;t nec mare, nec &longs;calmum; vel dicendum e&longs;t vtrum<lb/>que illorum participare huiu&longs;modi rationem, vt exempli <lb/>gratia, &longs;i ponamus vectem AB interpo&longs;itam e&longs;&longs;e inter <lb/><figure id="id.005.01.100.1.jpg" xlink:href="005/01/100/1.jpg"/><lb/>duos lapides CD, quorum C &longs;it ver&longs;us extremitatem B <lb/>retror&longs;um, D verò circa medium ip&longs;ius vectis antror&longs;um; <lb/>& potentia applicetur in extremitate A. </s>

<s>Etenim &longs;i extre<lb/>mum A impellatur antror&longs;um ver&longs;us E, D quidem <lb/>&longs;imul feretur in F & C retrocedet in G, vt cuilibet expe<lb/>riri fas e&longs;t. </s>

<s>Quapropter nulla e&longs;&longs;et maior ratio cur potius <pb pagenum="93"/>lapis C. quàm lapis D con&longs;titueretur fulcimentum in hac <lb/>latione vectis. </s>

<s>Quapropter nulla e&longs;&longs;et maior ratio cur potius <pb xlink:href="005/01/101.jpg" pagenum="93"/>lapis C. quàm lapis D con&longs;titueretur fulcimentum in hac <lb/>latione vectis. </s>

<s>Ideoque vtrumque aliquo modo, illam par<lb/>ticipare dicendum erit. </s>

Line 1854

<s>Tandem addit Baldus, fal&longs;um videri, quod a&longs;&longs;erit Ari&longs;to-<pb pagenum="94"/>teles, eos qui in media naui &longs;unt remiges, maximè nauim <lb/>mouere, &longs;i per maximè denotet maximo &longs;pacio, aut velo. <lb/></s>

<s>Tandem addit Baldus, fal&longs;um videri, quod a&longs;&longs;erit Ari&longs;to-<pb xlink:href="005/01/102.jpg" pagenum="94"/>teles, eos qui in media naui &longs;unt remiges, maximè nauim <lb/>mouere, &longs;i per maximè denotet maximo &longs;pacio, aut velo. <lb/></s>

<s>Etenim (inquit) tardius mouent, & minori &longs;patio, <lb/>quod ita probat. </s>

<s>E&longs;to enim Remus AB, qui mari fulcitur <lb/><figure id="fig22"/><lb/>in B Scalmus remi, <lb/>qui ad proram, pup<lb/>pimve C, qui in <lb/>media naui D. </s>

<s>E&longs;to enim Remus AB, qui mari fulcitur <lb/><figure id="id.005.01.102.1.jpg" xlink:href="005/01/102/1.jpg"/><lb/>in B Scalmus remi, <lb/>qui ad proram, pup<lb/>pimve C, qui in <lb/>media naui D. </s>

<s>Ma<lb/>ior autem remi pars <lb/>e&longs;t à &longs;calmo D ad <lb/>A, quàm ip&longs;ius C <lb/>ad A. </s>

Line 1882

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

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

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

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

<s>Sint duo remi ante <lb/>motionem duæ <lb/><figure id="fig23"/><lb/>æquales para<lb/>lellæ, nempe <lb/>ADB in medio <lb/>nauis; & ACB <lb/>ver&longs;us proram. <lb/></s>

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

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

Line 1902

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

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

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

<s>Cumque ip<lb/><figure id="fig24"/><lb/>&longs;ius extremum <lb/>vbi H, &longs;it pari<lb/>ter terminus li<lb/>ne&ecedil;, &longs;eu lateris <lb/>GH, &longs;equitur <lb/>vlterius, vt ne<lb/>que linea GH <lb/>pertingere po&longs;<lb/>&longs;it <expan abbr="v&longs;q;">v&longs;que</expan> ad pun<lb/>ctum P. </s>

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

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

Line 1916

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

<s>Cumque AI <lb/>differat ab AE tanquam pars à toto, & vterque arcus AE <lb/>&longs;it alter alteri æqualis ex con&longs;tructione, palam fit, maius <lb/>&longs;patium percurrere manubrium A remi ADB in medio <lb/>nauis con&longs;tituti, dum fertur v&longs;que ad E, quàm manubrium <lb/>alterius remi, quo d fertur v&longs;que ad I. </s><pb pagenum="97"/>

<s>Præterea contra experientiam &longs;upponitur à Baldo, remi <lb/>palmulam ceu centrum manere immotam in ip&longs;a remiga<lb/>tione, qua nauis fertur antror&longs;um. </s>

Line 1946

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

<s>Vt cer<lb/>nere e&longs;t in hac figura, in qua &longs;it remus AB, cuius manu<pb pagenum="98"/>brium A; palmula B, &longs;calmus verò C; ac &longs;patium, <lb/>quod percurrit pal<lb/><figure id="fig25"/><lb/>mula per motum <lb/>proprium ip&longs;ius re<lb/>mi circa &longs;calmum <lb/><expan abbr="tanquã">tanquam</expan> circa cen<lb/>trum &longs;it arcus BD. <lb/></s>

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

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

Line 1966

<s>An quoniam guber<lb/>naculum vectis e&longs;t, onus autem mare, guber<lb/>nator verò mouens e&longs;t? </s>

<s>Non autem &longs;ecundum latitudinem, <lb/>veluti remus, mare accipit gubernaculum: non enim in ante <lb/>nauigium mouet, &longs;ed ip&longs;um commotum mare accipiens incli-<emph.end type="italics"/><pb pagenum="99"/><emph type="italics"/>nat obliquè. </s>

<s>Non autem &longs;ecundum latitudinem, <lb/>veluti remus, mare accipit gubernaculum: non enim in ante <lb/>nauigium mouet, &longs;ed ip&longs;um commotum mare accipiens incli-<emph.end type="italics"/><pb xlink:href="005/01/107.jpg" pagenum="99"/><emph type="italics"/>nat obliquè. </s>

<s>Quoniam enim pondus e&longs;t mare, contrario inni<lb/>xum modo nauem inclinat. </s>

Line 2006

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

<s>Me<lb/>dium autem procedit &longs;ecundum quod gubernaculum tran&longs;-<emph.end type="italics"/><pb pagenum="100"/><emph type="italics"/>fertur. </s>

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

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

Line 2028

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

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

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

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

Line 2048

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

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

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

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

Line 2066

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

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

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

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

Line 2074

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

<s>Cum igitur nec auferri po&longs;&longs;it à puppi, nec retro<lb/>cedere in <expan abbr="direct&utilde;">directum</expan> <expan abbr="cõtra">contra</expan> cur&longs;um nauigij, hinc fit, vt cedendo <lb/><expan abbr="&longs;alt&etilde;">&longs;altem</expan> in parte quoad po&longs;itionem, <expan abbr="quã">quam</expan> prius habebat, nauem <lb/><expan abbr="ipsã">ipsam</expan> inclinet obliquè; &longs;iqui<lb/><figure id="fig26"/><lb/>dem dimoto vno latere an<lb/>guli à &longs;ua po&longs;itione, <expan abbr="alter&utilde;">alterum</expan> <lb/>dimoueri nece&longs;&longs;e e&longs;t, cu&longs;pi<lb/>de manente in eodem &longs;itu. <lb/></s>

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

<s>Quod &longs;ic pote&longs;t amplius <lb/>explicari. </s>

Line 2082

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

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

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

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

Line 2096

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

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

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

<s>Prima enim. <lb/></s>

Line 2124

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

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

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

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

Line 2144

<s>Aliam deinde, ac &longs;olidiorem rationem eiu&longs;dem &longs;ituatio<lb/>nis temonis Ari&longs;toteles &longs;ubnectit. </s>

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

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

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

<s>Quod quippe non contingeret <lb/>&longs;i alibi temo con&longs;titutus <lb/>fui&longs;&longs;et, indeq talismotio <lb/><figure id="fig27"/><lb/>initium &longs;umeret. </s>

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

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

Line 2170

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

<s>Sitremus AB, &longs;cal-<pb pagenum="108"/><figure id="fig28"/><lb/>mus verò C, remi manubrium A, palmula in mari B. <lb/></s>

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

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

Line 2188

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

<s>Hæc paucis mutatis, vel adiunctis Ari&longs;toteles profert, <lb/>quæ &longs;anè licet probent maius e&longs;&longs;e &longs;patium AD, quod ma-<pb pagenum="109"/>nubrium conficit antror&longs;um; quam &longs;patium BF, quod pal<lb/>mula tran&longs;mittit retror&longs;um; non tamen probant prout opus <lb/>erat, &longs;patium quoque CH, quod à &longs;calmo cum naui per<lb/>curritur, maius e&longs;&longs;e, quàm &longs;patium, quod in contrarium pr&ecedil;<lb/>terit palmula, vt BF, vel aliud &longs;imile. </s>

<s>Hæc paucis mutatis, vel adiunctis Ari&longs;toteles profert, <lb/>quæ &longs;anè licet probent maius e&longs;&longs;e &longs;patium AD, quod ma-<pb xlink:href="005/01/117.jpg" pagenum="109"/>nubrium conficit antror&longs;um; quam &longs;patium BF, quod pal<lb/>mula tran&longs;mittit retror&longs;um; non tamen probant prout opus <lb/>erat, &longs;patium quoque CH, quod à &longs;calmo cum naui per<lb/>curritur, maius e&longs;&longs;e, quàm &longs;patium, quod in contrarium pr&ecedil;<lb/>terit palmula, vt BF, vel aliud &longs;imile. </s>

<s>Quare occa&longs;ionem <lb/>nobis tribuunt explicandi, num &longs;emper hoc accidat, vt ma<lb/>gis in anteriora progrediatur nauigium, quàm ip&longs;ius remi <lb/>palmula retrocedat, an verò quandoque tantum, & qua. <lb/></s>

Line 2214

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

<s>Semper enim plus mouetur ma-<pb pagenum="110"/>nubrium, quam &longs;calmus eodem tempore ad impullum il<lb/>lius; nauis autem mouetur ad motum &longs;calmi. </s>

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

<s>Quod clarius <lb/>patebit in &longs;ubiecta figura; in qua &longs;it remus AB, cuius ma<lb/>nubrium A, pal<lb/><figure id="fig29"/><lb/>mula B, &longs;calmus <lb/>verò &longs;it in pun<lb/>cto medio vbi C. <lb/></s>

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

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

Line 2232

<s>Quod &longs;i illucu&longs;que pertingat, id certè contin<lb/>gere debet virtute alterius impul&longs;us aliunde incu&longs;&longs;i in <expan abbr="ips&utilde;">ipsum</expan> <lb/>nauigium. </s>

<s>Qua virtute <expan abbr="eod&etilde;">eodem</expan> tempore &longs;imul ac manubrium <lb/>motu proprio perueni&longs;&longs;et v&longs;que ad D, reperiatur in G; & <lb/>&longs;calmus qui e&longs;&longs;et in F, pertingat v&longs;que ad E; quod e&longs;t <pb pagenum="111"/>vtrumque, duplum &longs;patium percurrere re&longs;pectu illius, quod <lb/>virtute &longs;olius prædictæ remigationis percurri&longs;&longs;et. </s>

<s>Qua virtute <expan abbr="eod&etilde;">eodem</expan> tempore &longs;imul ac manubrium <lb/>motu proprio perueni&longs;&longs;et v&longs;que ad D, reperiatur in G; & <lb/>&longs;calmus qui e&longs;&longs;et in F, pertingat v&longs;que ad E; quod e&longs;t <pb xlink:href="005/01/119.jpg" pagenum="111"/>vtrumque, duplum &longs;patium percurrere re&longs;pectu illius, quod <lb/>virtute &longs;olius prædictæ remigationis percurri&longs;&longs;et. </s>

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

Line 2252

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

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

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

<s>Quæ omnia Geometricè at que exactius con&longs;tare po&longs;&longs;unt <lb/>ex his, quæ Petrus Nonius acuti&longs;&longs;imè demon&longs;trat in &longs;ua <lb/>Annotatione &longs;uper hunc ip&longs;um locum Ari&longs;totelis. </s>

Line 2266

<s>His tandem ita con&longs;titutis de motione remi, applican<lb/>do Ari&longs;toteles eandem ob&longs;eruationem, non ab&longs;imile e&longs;&longs;e <lb/>docet, quod contingit in motione gubernaculi, ac temonis, <lb/>vt &longs;cilicet &longs;icut &longs;calmus, qui con&longs;tituitur medium inter ex<lb/>trema ip&longs;ius remi, quæ mouentur in contrarium, illuc tran&longs;<lb/>fertur vbi remi e&longs;t principium, nempe antror&longs;um, quo remi <lb/>manubrium pergit, ac nauem propellit: ita locus vbi ap<lb/>plicatur gubernaculum, ac primo attingit temonem (qui <lb/>certè locus e&longs;t in linea cadenti, qua temo puppi adhæret in <lb/>cu&longs;pide, & vbi con&longs;tituitur etiam cardo) cum &longs;e habeat <lb/>tanquam medium inter duo extrema, quæ mouentur in <lb/>contrarium, videlicet manubrium gubernaculi, & alam te<lb/>monis, qua mare propellitur, illuc intelligetur transferri, <lb/>quo ip&longs;um gubernaculi manubrium erat. </s>

<s>Quemadmodum <lb/>enim &longs;calmus, temo, ait Ari&longs;toteles, nempe &longs;ecundum præ<lb/>dictam lineam circa quam qua&longs;i immotam, conuertitur la<lb/>titudo ip&longs;ius temonis ex vna parte, & guberna culi manu<lb/>brium ex alia, vt patet in hac prima figura; in qua cadens <pb pagenum="113"/>AB, <expan abbr="lineã">lineam</expan> o&longs;tendit <lb/><figure id="fig30"/><lb/>circa cuius prin<lb/>cipium guberna-<lb/>culum applicatur, <lb/>ac primo attingit <lb/>temonem, quæ li<lb/>nea in motione <lb/>gubernaculi ma-<lb/>net immota, &longs;icut <lb/>&longs;calmus in motio<lb/>ne remi. </s>

<s>Quemadmodum <lb/>enim &longs;calmus, temo, ait Ari&longs;toteles, nempe &longs;ecundum præ<lb/>dictam lineam circa quam qua&longs;i immotam, conuertitur la<lb/>titudo ip&longs;ius temonis ex vna parte, & guberna culi manu<lb/>brium ex alia, vt patet in hac prima figura; in qua cadens <pb xlink:href="005/01/121.jpg" pagenum="113"/>AB, <expan abbr="lineã">lineam</expan> o&longs;tendit <lb/><figure id="id.005.01.121.1.jpg" xlink:href="005/01/121/1.jpg"/><lb/>circa cuius prin<lb/>cipium guberna-<lb/>culum applicatur, <lb/>ac primo attingit <lb/>temonem, quæ li<lb/>nea in motione <lb/>gubernaculi ma-<lb/>net immota, &longs;icut <lb/>&longs;calmus in motio<lb/>ne remi. </s>

<s>Pars ve<lb/>rò AC &longs;ignat fa<lb/>ciem dexteram <lb/>temonis; & AD <lb/>manubrium gu-<lb/>bernaculi. </s>

Line 2276

<s>Cumque &longs;imul naui<lb/>gium, cui temo e&longs;t alligatus, procedat antror&longs;um, ip&longs;um <lb/>A non con&longs;titueretur in G, &longs;ed in E, vbi prius erat ma<lb/>nubrium gubernaculi. </s>

<s>Quare gubernaculum nihil naui<lb/>gio ad id, quod in ante progredi e&longs;t, conferre ait Ari&longs;to<lb/>teles, &longs;ed &longs;olum puppim in obliquum pellere, aliquantu<lb/>lum &longs;cilicet ad latus, qua parua motione puppis, pro<lb/>ra in contrarium vergit, nempe ad latus oppo&longs;itum, vt <lb/>ip&longs;emet Philo&longs;ophus docet, & con&longs;iderare licebit in hac <pb pagenum="114"/><figure id="fig31"/><lb/>figura nauiculæ, cuius <lb/>puppis A, prora D, <lb/><expan abbr="gubernacul&utilde;">gubernaculum</expan> verò EF <lb/>obliquè con&longs;titutum; <lb/>Nam certè ad impul<lb/>&longs;um aquæ in alam ob<lb/>uer&longs;am FA, ip&longs;a pup<lb/>pis A cum retrocede<lb/>re non po&longs;&longs;it ob <expan abbr="pro-gre&longs;s&utilde;">pro<lb/>gre&longs;sum</expan> nauiculæ (dum<lb/>modo aliquantulum cedere debeat impul&longs;ui) declinabit in <lb/>E, vbi erat gubernaculi manubrium, qua parua motione <lb/>puppis, ob rationes in principio po&longs;itas, prora ad contra<lb/>rium verget, inquit Ari&longs;toteles, &longs;cilicet ad latus oppo&longs;itum, <lb/><expan abbr="proindeq.">proindeque</expan> con&longs;tituetur in H, ni&longs;i validum aliquod ventum <lb/>inde &longs;pirans <expan abbr="paruaq.">paruaque</expan> conuer&longs;io temonis non ob&longs;tet. </s>

<s>Quare gubernaculum nihil naui<lb/>gio ad id, quod in ante progredi e&longs;t, conferre ait Ari&longs;to<lb/>teles, &longs;ed &longs;olum puppim in obliquum pellere, aliquantu<lb/>lum &longs;cilicet ad latus, qua parua motione puppis, pro<lb/>ra in contrarium vergit, nempe ad latus oppo&longs;itum, vt <lb/>ip&longs;emet Philo&longs;ophus docet, & con&longs;iderare licebit in hac <pb xlink:href="005/01/122.jpg" pagenum="114"/><figure id="id.005.01.122.1.jpg" xlink:href="005/01/122/1.jpg"/><lb/>figura nauiculæ, cuius <lb/>puppis A, prora D, <lb/><expan abbr="gubernacul&utilde;">gubernaculum</expan> verò EF <lb/>obliquè con&longs;titutum; <lb/>Nam certè ad impul<lb/>&longs;um aquæ in alam ob<lb/>uer&longs;am FA, ip&longs;a pup<lb/>pis A cum retrocede<lb/>re non po&longs;&longs;it ob <expan abbr="pro-gre&longs;s&utilde;">pro<lb/>gre&longs;sum</expan> nauiculæ (dum<lb/>modo aliquantulum cedere debeat impul&longs;ui) declinabit in <lb/>E, vbi erat gubernaculi manubrium, qua parua motione <lb/>puppis, ob rationes in principio po&longs;itas, prora ad contra<lb/>rium verget, inquit Ari&longs;toteles, &longs;cilicet ad latus oppo&longs;itum, <lb/><expan abbr="proindeq.">proindeque</expan> con&longs;tituetur in H, ni&longs;i validum aliquod ventum <lb/>inde &longs;pirans <expan abbr="paruaq.">paruaque</expan> conuer&longs;io temonis non ob&longs;tet. </s>

<s>Quo ex principio intelligi pote&longs;t cur ex tran&longs;uer&longs;o per<lb/>flante admodum vento, ac directè nihilominus nauigia <lb/>procedendo, tandem non pertingant, quo præcisè tende<lb/>bant, &longs;ed inferius multo, &longs;eu ad partem vento magis oppo<lb/>&longs;itam. </s>

<s>Porro cum aliquantulum à latere vento perflante, <lb/>alam temonis illi &longs;atis obuer&longs;am nautæ con&longs;tituere tenean<lb/>tur, validi&longs;simè ip&longs;am &longs;imul cum puppi fluctus repellunt, <lb/>quo &longs;anè repul&longs;o circumagerent totam nauim, ni&longs;i &longs;imul in <lb/>latus ver&longs;us proram inciderent, nam hinc inde coadæquato <lb/>repul&longs;u, ac gubernaculo moderante, dum nauis pergit an<lb/>tror&longs;um &longs;emper eandem, quam prius in &longs;e po&longs;itionem, ac <lb/><expan abbr="direction&etilde;">directionem</expan> &longs;eruat. </s>

<s>Cum <expan abbr="itaq;">itaque</expan> fluctus ip&longs;i nauem circumage<lb/>re nequeant, <expan abbr="nauisq.">nauisque</expan> aliquid pati debeat ex ip&longs;o repul&longs;u, to<lb/>ta &longs;imul cogitur &longs;en&longs;im declinare ad latus <expan abbr="v&etilde;to">vento</expan> oppo&longs;itum; <lb/>Vt exempli gratia data po&longs;itione, quam modo tenet de&longs;cri<lb/>pta nauicula in AD, ac perflante vento ex tran&longs;uer&longs;o, vt <lb/>ex H, certè ad motum ip&longs;ius puppis ex A in E, prora <lb/>non conuerteretur à D in H, (ni&longs;i ob maiorem conuer<lb/>&longs;ionem temonis, &longs;ed potius nonnihil cedendo &longs;icut puppis, <pb pagenum="115"/>declinaret in I; Quare nauis à &longs;itu AD con&longs;tituta in EI, <lb/>eandem quippe &longs;eruaret po&longs;itionem, ac directionem, tran&longs;<lb/>lata tamen e&longs;&longs;et inferius ver&longs;us partem vento oppo&longs;itam, <lb/>&longs;icque vlterius incedendo quamuis ab initio de&longs;tinatum &longs;i<lb/>bi locum per proram in&longs;piceret, illuc tamen peruenire ne<lb/>quiret, ni&longs;i altius, &longs;eu magis ad partem vnde ventus validè <lb/>&longs;pirat, proram direxerit, vt &longs;patium, quod coacta declinatio<lb/>ne deperdit, compen&longs;etur anticipata &longs;itus po&longs;itione, ac di<lb/>rectione. </s>

<s>Cum <expan abbr="itaq;">itaque</expan> fluctus ip&longs;i nauem circumage<lb/>re nequeant, <expan abbr="nauisq.">nauisque</expan> aliquid pati debeat ex ip&longs;o repul&longs;u, to<lb/>ta &longs;imul cogitur &longs;en&longs;im declinare ad latus <expan abbr="v&etilde;to">vento</expan> oppo&longs;itum; <lb/>Vt exempli gratia data po&longs;itione, quam modo tenet de&longs;cri<lb/>pta nauicula in AD, ac perflante vento ex tran&longs;uer&longs;o, vt <lb/>ex H, certè ad motum ip&longs;ius puppis ex A in E, prora <lb/>non conuerteretur à D in H, (ni&longs;i ob maiorem conuer<lb/>&longs;ionem temonis, &longs;ed potius nonnihil cedendo &longs;icut puppis, <pb xlink:href="005/01/123.jpg" pagenum="115"/>declinaret in I; Quare nauis à &longs;itu AD con&longs;tituta in EI, <lb/>eandem quippe &longs;eruaret po&longs;itionem, ac directionem, tran&longs;<lb/>lata tamen e&longs;&longs;et inferius ver&longs;us partem vento oppo&longs;itam, <lb/>&longs;icque vlterius incedendo quamuis ab initio de&longs;tinatum &longs;i<lb/>bi locum per proram in&longs;piceret, illuc tamen peruenire ne<lb/>quiret, ni&longs;i altius, &longs;eu magis ad partem vnde ventus validè <lb/>&longs;pirat, proram direxerit, vt &longs;patium, quod coacta declinatio<lb/>ne deperdit, compen&longs;etur anticipata &longs;itus po&longs;itione, ac di<lb/>rectione. </s>

<s>Demum illud, quod Ari&longs;toteles vltimo loco adiecit. </s>

Line 2292

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

<s>Nam <lb/>dato quod extremum temonis B, mare dextror&longs;um exci<lb/>piens, aut propellens transferatur in D per motum guber<lb/>naculi ab A in E, vtique cu&longs;pis puppis, quæ e&longs;t in C <lb/>transferetur &longs;ini&longs;tror&longs;um vnà cum tota nauicula ver&longs;us F, <lb/>prora ip&longs;a in eodem puncto manente, vel parum inde di<lb/>mota, vt v&longs;que ad punctum H; ita vt nauicula, quæ erat <pb pagenum="116"/><figure id="fig32"/><lb/>in CG, con&longs;tituatur in FG, vel in <lb/>FH. </s>

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

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

Line 2300

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

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

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

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

Line 2316

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

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

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

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

Line 2334

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

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

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

<s>COMMENTARIVS.</s>

Line 2352

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

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

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

<s>Siquidem ibi tota ferè vis incuti<lb/>tur naui ad progrediendum antror&longs;um, vt videre e&longs;t in hac <lb/>figura, in qua extremum mali fundo innixum &longs;it A, cuius <lb/>facies puppim <lb/>re&longs;piciens B; <lb/><figure id="fig33"/><lb/>pars verò ip<lb/>&longs;ius mali, quæ <lb/><expan abbr="flãtibus">flantibus</expan> ventis <lb/>à tergo naui<lb/>gium præmit, <lb/>vel vrget in an<lb/>te, vbi C, è <expan abbr="cõ-&longs;pectu">con<lb/>&longs;pectu</expan> pror&ecedil;; & <lb/>locus antennæ <lb/>in ip&longs;o malo, &longs;it <lb/>D; vbi tota pe<lb/>nè virtus im<lb/>pellentis &longs;piri<lb/>tus refunditur, <lb/>vt diximus ra<lb/>tione veli <expan abbr="ill&utilde;">illum</expan> <lb/>excipientis. </s>

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

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

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

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

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

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

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

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

<s>Et ex vtri&longs;que fit angulus ABC, <lb/>ip&longs;o malleo in extractione clauorum <lb/>cu&longs;pidi innixo vbi B. </s><figure id="id.005.01.129.1.jpg" xlink:href="005/01/129/1.jpg"/>

<s>Similiter ergo malus in naui con&longs;i<lb/>derari pote&longs;t tanquam brachium ve<lb/>ctis, quod alteri coniungatur, nempe <lb/>illi parti carin&ecedil;, qu&ecedil; vergit ad puppim, <lb/>& cum qua con&longs;tituit <expan abbr="angul&utilde;">angulum</expan> in pun<lb/>cto vbi de&longs;init altitudo ip&longs;ius mali. </s>

<s><expan abbr="Nã">Nam</expan> <lb/>impetu in <expan abbr="alter&utilde;">alterum</expan> extremum ip&longs;ius ma<lb/>li incu&longs;&longs;o, nempe circa locum vbi vr<lb/>get antenna velo agitata à ventis, ip&longs;a <lb/>&longs;ummitas mali declinaret &longs;i po&longs;&longs;et ad <lb/>proram, tanquam per conuer&longs;ionem <lb/>circa punctum explicatum, in quo con&longs;tituitur angulus, <expan abbr="&longs;i-mulq.">&longs;i<lb/>mulque</expan> eleuaretur &longs;i po&longs;&longs;et carina ex parte puppis. </s>

<s>Quemad<lb/><figure id="fig34"/><lb/>modum in propo&longs;ito an<lb/>gulo ABC; &longs;i latus AB <lb/>declinaret in BD per <lb/>impul&longs;um acceptum in <lb/>A; latus etiam BC ele<lb/>uaretur in BE. </s>

<s>Quemad<lb/><figure id="id.005.01.129.2.jpg" xlink:href="005/01/129/2.jpg"/><lb/>modum in propo&longs;ito an<lb/>gulo ABC; &longs;i latus AB <lb/>declinaret in BD per <lb/>impul&longs;um acceptum in <lb/>A; latus etiam BC ele<lb/>uaretur in BE. </s>

<s>Quoniam <lb/>verò declinare non po<lb/>te&longs;t malus, nec pars illa <lb/>carinæ per con&longs;equens <lb/>eleuari ab&longs;que immer<lb/>&longs;ione proræ, totus impe<lb/>tus incu&longs;&longs;us refunditur <lb/>in lationem antror&longs;um, eo quod mare cum &longs;it fluidum non <pb pagenum="122"/>re&longs;i&longs;tat lationi, &longs;icut ip&longs;ius proræ immer&longs;ioni, quæ contra <lb/>naturam ligni &longs;equeretur ex declinatione mali. </s>

<s>Quoniam <lb/>verò declinare non po<lb/>te&longs;t malus, nec pars illa <lb/>carinæ per con&longs;equens <lb/>eleuari ab&longs;que immer<lb/>&longs;ione proræ, totus impe<lb/>tus incu&longs;&longs;us refunditur <lb/>in lationem antror&longs;um, eo quod mare cum &longs;it fluidum non <pb xlink:href="005/01/130.jpg" pagenum="122"/>re&longs;i&longs;tat lationi, &longs;icut ip&longs;ius proræ immer&longs;ioni, quæ contra <lb/>naturam ligni &longs;equeretur ex declinatione mali. </s>

<s>Accedit <lb/>quia neque pars carinæ, quæ e&longs;t à malo ad puppim po&longs;&longs;et <lb/>eleuari; tum propter grauitatem puppis, quæ &longs;e habet tan<lb/>quam onus in extremo vectis, <expan abbr="ibiq.">ibique</expan> maximè præponderat <lb/>impul&longs;ui contrario; tum propter naturalem re&longs;i&longs;tentiam ca<lb/>rinæ <expan abbr="totiusq.">totiusque</expan> fundi ne &longs;eparetur ab aqua, cui connaturalius <lb/>ligna præ&longs;ertim plana adhærent; vt patet ex difficultate, <lb/>qua &longs;upernatantes tabulæ extrahuntur ex aqua. </s>

Line 2390

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

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

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

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

Line 2406

<s>Tunc enim &longs;i antenna in <lb/>illo <expan abbr="di&longs;tãtiori">di&longs;tantiori</expan> &longs;itu con&longs;tituatur, ac &longs;emel cum nauigio admo<lb/>dum inclinetur malus, ad totalem potius euer&longs;ionem con<lb/>duceret. </s>

<s>Quandoquidem linea perpendicularis, qua onus <lb/>antennæ mundi centrum petit ob talem inclinationem, non <lb/>caderet intra nauigium, &longs;ed foris à latere, quò propen&longs;ius <pb pagenum="124"/>tendendo antenna ip&longs;a non modo amplius inclinationi ni<lb/>hil ob&longs;taret, &longs;ed vicem &longs;ubiret potentiæ inclinantis eundem <lb/>malum tanquam vectem, & cum illo totum nauigium cui <lb/>malus affigitur, eleuando &longs;cilicet alterum latus tanquam <lb/>onus impo&longs;itum, alterum comprimendo veluti hypomo<lb/>chlion cui innititur, ex quo &longs;equeretur euer&longs;io, atque &longs;um<lb/>mer&longs;io. </s>

<s>Quandoquidem linea perpendicularis, qua onus <lb/>antennæ mundi centrum petit ob talem inclinationem, non <lb/>caderet intra nauigium, &longs;ed foris à latere, quò propen&longs;ius <pb xlink:href="005/01/132.jpg" pagenum="124"/>tendendo antenna ip&longs;a non modo amplius inclinationi ni<lb/>hil ob&longs;taret, &longs;ed vicem &longs;ubiret potentiæ inclinantis eundem <lb/>malum tanquam vectem, & cum illo totum nauigium cui <lb/>malus affigitur, eleuando &longs;cilicet alterum latus tanquam <lb/>onus impo&longs;itum, alterum comprimendo veluti hypomo<lb/>chlion cui innititur, ex quo &longs;equeretur euer&longs;io, atque &longs;um<lb/>mer&longs;io. </s>

<s>Quæ&longs;tio Septima.</s>

Line 2420

<s>Cau&longs;am hic inquirit Ari&longs;toteles cur nautæ ex puppi <lb/>antror&longs;um velo nauigare cupientes non flante ex <lb/>puppi vento, &longs;ed puta ex latere, &longs;eu ex tran&longs;uer&longs;o, <lb/>velo quidem in altero atque oppo&longs;ito nauis latere con&longs;titu<lb/>to, partem eius, quæ ad puppim vergit vbi gubernator ad <lb/>clauum moderandum a&longs;&longs;i&longs;tit, quantum fieri pote&longs;t exten<lb/>dunt, ac fune reducto eius extrema con&longs;tringunt: illam ve<lb/>rò quæ proram ver&longs;us e&longs;t, ac tanquam inferiorem, pedem <lb/>ip&longs;ius veli con&longs;tituunt, altero fune producto relaxant, &longs;eu <lb/>laxiorem e&longs;&longs;e &longs;inunt. </s>

<s><expan abbr="Docetq.">Docetque</expan> ex eo id fieri, nam &longs;uppo&longs;ito <lb/>quod gubernaculum cum temone, multum impellente ven-<pb pagenum="125"/>to inclinare non po&longs;&longs;it nauigium qua&longs;i in contrarium, &longs;icut cum <lb/>parum vel minus impellit; velo &longs;ic con&longs;tituto vt diximus, totus <lb/>penè impetus venti in eius partem, quæ ad puppim extenditur <lb/><expan abbr="tanquã">tanquam</expan> in &longs;inu excipitur atque colligitur, vbi propellit quidem <lb/>ex tran&longs;uer&longs;o, &longs;ed cum magis appropinquetur temoni, quo ob<lb/>uiantibus fluctibus maris, nauis retrahitur in contrarium, minus <lb/>præualet, quàm &longs;i imprimeretur ver&longs;us proram, vel in totum ip<lb/>&longs;um velum vniformiter ten&longs;um. </s>

<s><expan abbr="Docetq.">Docetque</expan> ex eo id fieri, nam &longs;uppo&longs;ito <lb/>quod gubernaculum cum temone, multum impellente ven-<pb xlink:href="005/01/133.jpg" pagenum="125"/>to inclinare non po&longs;&longs;it nauigium qua&longs;i in contrarium, &longs;icut cum <lb/>parum vel minus impellit; velo &longs;ic con&longs;tituto vt diximus, totus <lb/>penè impetus venti in eius partem, quæ ad puppim extenditur <lb/><expan abbr="tanquã">tanquam</expan> in &longs;inu excipitur atque colligitur, vbi propellit quidem <lb/>ex tran&longs;uer&longs;o, &longs;ed cum magis appropinquetur temoni, quo ob<lb/>uiantibus fluctibus maris, nauis retrahitur in contrarium, minus <lb/>præualet, quàm &longs;i imprimeretur ver&longs;us proram, vel in totum ip<lb/>&longs;um velum vniformiter ten&longs;um. </s>

<s><expan abbr="Dumq.">Dumque</expan> nautæ mediante gu<lb/>bernaculo, ac temone, cum vento contendunt, in contrariam <lb/>partem proram reclinando, medium iter tenet nauigium, <expan abbr="per-gitq.">per<lb/>gitque</expan> antror&longs;um, quo ip&longs;emet de&longs;tinauerint nautæ. </s>

<s>Hæc ex Ari&longs;totele, quæ vt clarius dilucidentur, &longs;it nauis AB, <lb/>cuius puppis A, prora verò B, gubernaculum obliquè con&longs;ti<lb/>tutum AC; temo &longs;imili<lb/><figure id="fig35"/><lb/>ter AD, malus E, ac ve<lb/>lum &longs;ecundum <expan abbr="infimã">infimam</expan> &longs;ui <lb/>oram, &longs;it curua linea FG, <lb/>lateraliter ventum exci<lb/>piens ex parte dextera <lb/>vbi H. </s>

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

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

Line 2434

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

<s>Cau&longs;a verò cur neutrum præualeat hæc e&longs;t: Nam ex vno ca<lb/>pite, licet temo, nauis <expan abbr="po&longs;ition&etilde;">po&longs;itionem</expan> immutet, ac inclinare eam va-<pb pagenum="126"/>leat obliquè, promouere tamen eam ip&longs;am nequit, quo proram <lb/>re&longs;picientem con&longs;tituit, <expan abbr="multoq.">multoque</expan> minus dum ventus inde validè <lb/>&longs;pirat. </s>

<s>Cau&longs;a verò cur neutrum præualeat hæc e&longs;t: Nam ex vno ca<lb/>pite, licet temo, nauis <expan abbr="po&longs;ition&etilde;">po&longs;itionem</expan> immutet, ac inclinare eam va-<pb xlink:href="005/01/134.jpg" pagenum="126"/>leat obliquè, promouere tamen eam ip&longs;am nequit, quo proram <lb/>re&longs;picientem con&longs;tituit, <expan abbr="multoq.">multoque</expan> minus dum ventus inde validè <lb/>&longs;pirat. </s>

<s>Quare in ca&longs;u propo&longs;ito, hoc tantum præ&longs;tat ala illa ob<lb/>uer&longs;a temonis, quod e&longs;t, eandem nauis <expan abbr="po&longs;ition&etilde;">po&longs;itionem</expan> obliquam &longs;er<lb/>uare contra impetum &longs;piritus, quo certè prora <expan abbr="nõ">non</expan> minus quàm <lb/>puppis ad latus retrocedere cogeretur, <expan abbr="pariterq.">pariterque</expan> in oppo&longs;itam <lb/><expan abbr="part&etilde;">partem</expan> abire. </s>

<s>Ex alio verò capite licet ventus æquè incidat in to<lb/>tum <expan abbr="vel&utilde;">velum</expan>, ac vehementer pellat ex tran&longs;uer&longs;o: nihilominus pro<lb/>pter explicatam veli po&longs;itionem totum ferè &longs;e confert in par<lb/>tem ad puppim <expan abbr="vergent&etilde;">vergentem</expan>, quæ &longs;ublimior, ac latior e&longs;t, <expan abbr="&longs;inumq.">&longs;inumque</expan> <lb/>maiorem efficit, ex quo impetus qua&longs;i retortus refunditur in <lb/>latus ver&longs;us proram, vt in LB, quo proinde latere nauis fertur <lb/>antror&longs;um &longs;uper lineam E K. </s><figure/>

<s>Retorqueri autem im<lb/>pul&longs;um pr&ecedil;dictum ex eo <lb/>contingit, quia <expan abbr="tã">tam</expan> infima <lb/>veli ora ab E <expan abbr="v&longs;q;">v&longs;que</expan> ad G, <lb/>quàm <expan abbr="ant&etilde;na">antenna</expan> à loco vbi <lb/>malo alligatur v&longs;que ad <lb/><expan abbr="ceruch&utilde;">ceruchum</expan>, &longs;eu cornu eius, <lb/>quod in <expan abbr="alt&utilde;">altum</expan> extollitur, <lb/>&longs;emper patitur magis à <lb/>vento perflante, quàm <lb/>pars tam veli; quàm an<lb/>tennæ, quæ e&longs;t ab E in F <lb/>ver&longs;us <expan abbr="prorã">proram</expan>: nam inde <lb/>potius fugit <expan abbr="atq;">atque</expan> elabitur <lb/>ventus ob maiorem di<lb/>rectionem, quam &longs;eruat <lb/>erga ip&longs;um ventum, quem non ita in faciem excipit, &longs;icut pars <lb/>concaua, quæ ad puppim vergit. </s>

<s>Dum autem patitur, ac percu<lb/>titur magis cum velo, antennæ pars, quæ e&longs;t à malo ad cornu, <lb/>verbi gratia in &longs;ini&longs;tra, tanquam &longs;i moueretur circa ip&longs;um <expan abbr="mal&utilde;">malum</expan> <lb/>veluti &longs;emidiameter circa centrum, vertere nititur nauigium in <lb/><expan abbr="contrari&utilde;">contrarium</expan>, hoc e&longs;t dextror&longs;um, quia vim accipit à &longs;ini&longs;tra. </s>

<s>Vnde <lb/>impul&longs;us qua&longs;i retortus aliquantulum in gyrum, nauem ip&longs;am <pb pagenum="127"/>non quidem &longs;ini&longs;tror&longs;um, &longs;ed antror&longs;um præualet commouere. <lb/></s>

<s>Vnde <lb/>impul&longs;us qua&longs;i retortus aliquantulum in gyrum, nauem ip&longs;am <pb xlink:href="005/01/135.jpg" pagenum="127"/>non quidem &longs;ini&longs;tror&longs;um, &longs;ed antror&longs;um præualet commouere. <lb/></s>

<s>Id quod clariùs hic licebit in&longs;picere in delineata figura ei&longs;dem <lb/>fermè litteris, quibus &longs;uperior con&longs;ignata. </s><figure/>

<s>Id quod clariùs hic licebit in&longs;picere in delineata figura ei&longs;dem <lb/>fermè litteris, quibus &longs;uperior con&longs;ignata. </s><figure id="id.005.01.135.1.jpg" xlink:href="005/01/135/1.jpg"/>

<s>Cæterum ex his <lb/>patet, quàm rectè <lb/>Ari&longs;toteles docuerit <lb/>ex eo nautas veli <lb/>partem ver&longs;us <expan abbr="prorã">proram</expan> <lb/>pedem facere, ac re<lb/>laxare, hoc e&longs;t ex eo <lb/>partem veli inferio<lb/>rem <expan abbr="tanquã">tanquam</expan> pedem <lb/>ver&longs;us <expan abbr="prorã">proram</expan> collo<lb/>care, ac funibus mi<lb/>nus adducere; &longs;upe<lb/>riorem verò quæ <expan abbr="lõ-gè">lon<lb/>gè</expan> maior e&longs;t ver&longs;us <lb/>puppim retrahere, & <lb/>alligare, quia &longs;i vtramque partem veli &ecedil;quatame&longs;&longs;e paterentur, <lb/>malus vtrinque propul&longs;us æquè etiam propelleretur. </s>

Line 2462

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

<s>Tum etiam quia ventus præcipuè non &longs;u&longs;tinetur in prora, &longs;ed <lb/>potius in parte veli, quæ vergit ad puppim, vt dictum e&longs;t. </s><pb pagenum="128"/>

<s>Tum etiam quia ventus præcipuè non &longs;u&longs;tinetur in prora, &longs;ed <lb/>potius in parte veli, quæ vergit ad puppim, vt dictum e&longs;t. </s><pb xlink:href="005/01/136.jpg" pagenum="128"/>

<s>Ex dictis etiam licebit duas alias veluti affines quæ&longs;tiones <lb/>diluere. </s>

Line 2480

<s>Sed facilis e&longs;t re&longs;pon&longs;io; <expan abbr="nã">nam</expan> velo ad pro<lb/>ram laxato, <expan abbr="ventisq.">ventisque</expan> &longs;ecundis <expan abbr="obtume&longs;c&etilde;ti">obtume&longs;centi</expan>, plus <expan abbr="quandoq.">quandoque</expan> <expan abbr="cõ-tingit">con<lb/>tingit</expan> &longs;e ad vnum, quam ad <expan abbr="alter&utilde;">alterum</expan> latus inflectere, eo quod ne<lb/>queat tam antenna, quàm velum exactè in duas partes &ecedil;quales <lb/>vtrinque ad malum di&longs;tribui. </s>

<s>Cumque in hac latione qua nauis <lb/>recta è puppimouetur in proram, temo &longs;cindat quidem mare <lb/>obuium eodem pacto in <expan abbr="direct&utilde;">directum</expan>, &longs;ed illud non excipiat ad dex<lb/>teram, aut &longs;ini&longs;tram, nec ideo vim alienam inferat naui circa <lb/>cur&longs;us <expan abbr="moderation&etilde;">moderationem</expan> per proræ <expan abbr="conuer&longs;ion&etilde;">conuer&longs;ionem</expan>: hinc fit, vt repen<lb/>tino &longs;uperueniente impetu vehementi, atque in vnam magis <lb/>quàm in alteram veli partem incu&longs;&longs;o, ob aptiorem po&longs;itionem <lb/>illius, aut magnitudinem maiorem; facilè totum nauigium à re-<pb pagenum="129"/>ctitudine viæ deuiet, <expan abbr="moxq.">moxque</expan> &longs;e vnà cum malo ad latus, ad <lb/>quod pars illa maior vergerit, omnino declinando demer<lb/>gat; ni&longs;i protinus ob&longs;tauerit gubernator per conuer&longs;ionem <lb/>temonis, compellendo proram, ac reclinando illam ver<lb/>&longs;us eandem partem, in qua &longs;equeretur &longs;ubmer&longs;io, ac vn<lb/>de deflexerat, vt ventus à tergo &longs;pirans, ex æquo velum fe<lb/>riat in prora, <expan abbr="propellatq.">propellatque</expan> recta nauigium &longs;icut prius. </s>

<s>Cumque in hac latione qua nauis <lb/>recta è puppimouetur in proram, temo &longs;cindat quidem mare <lb/>obuium eodem pacto in <expan abbr="direct&utilde;">directum</expan>, &longs;ed illud non excipiat ad dex<lb/>teram, aut &longs;ini&longs;tram, nec ideo vim alienam inferat naui circa <lb/>cur&longs;us <expan abbr="moderation&etilde;">moderationem</expan> per proræ <expan abbr="conuer&longs;ion&etilde;">conuer&longs;ionem</expan>: hinc fit, vt repen<lb/>tino &longs;uperueniente impetu vehementi, atque in vnam magis <lb/>quàm in alteram veli partem incu&longs;&longs;o, ob aptiorem po&longs;itionem <lb/>illius, aut magnitudinem maiorem; facilè totum nauigium à re-<pb xlink:href="005/01/137.jpg" pagenum="129"/>ctitudine viæ deuiet, <expan abbr="moxq.">moxque</expan> &longs;e vnà cum malo ad latus, ad <lb/>quod pars illa maior vergerit, omnino declinando demer<lb/>gat; ni&longs;i protinus ob&longs;tauerit gubernator per conuer&longs;ionem <lb/>temonis, compellendo proram, ac reclinando illam ver<lb/>&longs;us eandem partem, in qua &longs;equeretur &longs;ubmer&longs;io, ac vn<lb/>de deflexerat, vt ventus à tergo &longs;pirans, ex æquo velum fe<lb/>riat in prora, <expan abbr="propellatq.">propellatque</expan> recta nauigium &longs;icut prius. </s>

<s>Quæ&longs;tio Octaua.</s>

Line 2514

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

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

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

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

Line 2534

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

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

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

Line 2548

<s>Hoc e&longs;t, quia motor <lb/>dum huiu&longs;modi corpora rotunda, vel &longs;phærica &longs;ecundum <lb/>ab&longs;idem mouet, eo profectò impellit, quo &longs;tatim ip&longs;orum <lb/>pondus propendit &longs;iue inclinat. </s>

<s>Etenim &longs;i con&longs;tituatur &longs;u<lb/>per planum AB horizonti <lb/><figure id="fig36"/><lb/>paralellum erecta aliqua <lb/>rota, vt CDEF tanquam <lb/>circulus, eius diameter à <lb/>contactu plani vbi C per<lb/>pendiculariter ad angulos <lb/>rectos per centrum &longs;upra <lb/>tra&longs;cendens ad D, totam <lb/>rotam eiu&longs;que pondus in <lb/>duas partes æquales di&longs;tri<lb/>buet, nempe in DFC, & <lb/>DEC. <expan abbr="Eritq.">Eritque</expan> ip&longs;a rota in <pb pagenum="132"/>æquilibrio, quia non magis vna quam altera pars vtrinque <lb/>à perpendiculo DC grauitare pote&longs;t. </s>

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

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

Line 2574

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

<s>Vt per&longs;picuè apparebit in propo&longs;ita &longs;phæra <pb pagenum="133"/>vel rota ABC, &longs;i decliue <lb/><figure id="fig37"/><lb/>planum DE contingat in <lb/>C ad angulos rectos ip&longs;ius <lb/>diametri BC: linea verò <lb/>cadens per centrum ip&longs;ius <lb/>&longs;phæræ ad centrum mundi, <lb/>&longs;it AF. </s>

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

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

Line 2588

<s>Celerius enim (inquit) ab æqua<lb/>li mouentur potentia, <expan abbr="mouentq.">mouentque</expan> onera. </s>

<s><expan abbr="Cau&longs;amq.">Cau&longs;amque</expan> eam e&longs;&longs;e <pb pagenum="134"/>&longs;ubnectit; quoniam &longs;emper angulus circuli maioris, nutum <lb/>quendam habet ad angulum circuli minoris (in eo &longs;cilicet <lb/>contenti circa idem centrum.) Et &longs;icut diameter ad diame<lb/>trum, ita maior circulus, &longs;eu potius circumferentia ad mino<lb/>rem: In quolibet autem circulo maiori, infiniti circuli mi<lb/>nores continentur. </s>

<s><expan abbr="Cau&longs;amq.">Cau&longs;amque</expan> eam e&longs;&longs;e <pb xlink:href="005/01/142.jpg" pagenum="134"/>&longs;ubnectit; quoniam &longs;emper angulus circuli maioris, nutum <lb/>quendam habet ad angulum circuli minoris (in eo &longs;cilicet <lb/>contenti circa idem centrum.) Et &longs;icut diameter ad diame<lb/>trum, ita maior circulus, &longs;eu potius circumferentia ad mino<lb/>rem: In quolibet autem circulo maiori, infiniti circuli mi<lb/>nores continentur. </s>

<s>Quo igitur maiores fuerint ip&longs;i circuli, <lb/><expan abbr="maioremq.">maioremque</expan> proinde nutum, &longs;eu inclinationem ad minores <lb/>contentos habuerint, eo facilius, ac celerius mouebuntur. </s>

Line 2608

tertij. </s>

<s>Etenim iuxta hanc acceptionem angulus cir<lb/>culi maioris non e&longs;t idem cum angulo circuli minoris, opti<lb/>mèque intelligitur; & explicatur nutus, quem Philo&longs;ophus <pb pagenum="135"/>docet habere i&longs;tum ad illum. </s>

<s>Etenim iuxta hanc acceptionem angulus cir<lb/>culi maioris non e&longs;t idem cum angulo circuli minoris, opti<lb/>mèque intelligitur; & explicatur nutus, quem Philo&longs;ophus <pb xlink:href="005/01/143.jpg" pagenum="135"/>docet habere i&longs;tum ad illum. </s>

<s>Hoc e&longs;t propen&longs;io, quam an<lb/>gulus circuli maioris habet &longs;upra angulum circuli minoris <lb/>circa idem centrum de&longs;cripti, vt celerius, ac facilius cum. <lb/></s>

Line 2618

<s>Diameter au<lb/>tem maioris circuli &longs;it AC, minoris EG. </s>

<s>Angulus item <lb/>maioris ACD; minoris ve<lb/><figure id="fig38"/><lb/>rò EGH. </s>

<s>Angulus item <lb/>maioris ACD; minoris ve<lb/><figure id="id.005.01.143.1.jpg" xlink:href="005/01/143/1.jpg"/><lb/>rò EGH. </s>

<s>Dicimus ergo an<lb/>gulum ACD habere nu<lb/>tum quendam, & inclina<lb/>tionem &longs;upra angulum <lb/>EGH, qua, & &longs;eip&longs;um, & <lb/>illum procliuiorem reddit <lb/>ad motum &longs;ecundum ab&longs;i<lb/>dem &longs;uper planum KL, &longs;i <lb/>circulus ip&longs;e maior per im<lb/>pul&longs;um motoris ver&longs;us L <lb/>moueatur. </s>

Line 2632

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

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

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

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

Line 2652

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

<s>Quod verò adducit ad probandum potius minores circu-<pb pagenum="137"/>los videri ad motum faciliores, eo quod maior e&longs;t angulus <lb/>contingentiæ ad planum, circumferentiæ minotis, quàm <lb/>maioris circuli, vt in &longs;ubiecta figura maior e&longs;t angulus ABC, <lb/>quàm DBC: probat quidem mi<lb/><figure id="fig39"/><lb/>nores circulos minus offen&longs;are <lb/>propter maiorem eleuationem <lb/>ip&longs;ius anguli à terra, vt &longs;upra ex <lb/>plicuimus; &longs;ed non probat per &longs;e <lb/>facilius moueri; imò oppo&longs;itum. <lb/></s>

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

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

Line 2668

<s>Si<lb/>cut verbigratia quodlibet graue ad <expan abbr="mot&utilde;">motum</expan> deor&longs;um. </s>

<s>Quam<lb/>obrem qui mouent ip&longs;um circulum &longs;ecundum cir cumferen-<pb pagenum="138"/>tiam, parum aut nihil conantur re&longs;pectu huius lationis &longs;e<lb/>cundum naturam; &longs;ed mouent ip&longs;um, veluti motum ab in<lb/>trin&longs;eco propter explicatam propen&longs;ionem, quam habet <lb/>ad eandem lationem. </s>

<s>Quam<lb/>obrem qui mouent ip&longs;um circulum &longs;ecundum cir cumferen-<pb xlink:href="005/01/146.jpg" pagenum="138"/>tiam, parum aut nihil conantur re&longs;pectu huius lationis &longs;e<lb/>cundum naturam; &longs;ed mouent ip&longs;um, veluti motum ab in<lb/>trin&longs;eco propter explicatam propen&longs;ionem, quam habet <lb/>ad eandem lationem. </s>

<s>Non &longs;ecus ac &longs;i mouerent onus deor<lb/>&longs;um, quo ex &longs;e illud naturaliter tendit. </s>

Line 2682

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

<s>Sit enim circulus ABCD <lb/><figure id="fig40"/><lb/>circa centrum E, cuius &longs;emi<lb/>diameter EC. </s>

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

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

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

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

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

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

Line 2708

<s>COMMENTARIVS.</s>

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

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

Line 2734

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

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

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

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

Line 2744

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

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

<s>His itaque &longs;ic &longs;e habentibus breuiter ac per&longs;picuè quæ<lb/>&longs;tionem diluit Ari&longs;toteles, inquiens, maiorem hanc facilita<lb/>tem, ac velocitatem motus procedere à maiori di&longs;tantia, <pb pagenum="142"/>quam à centro habet extremum diametri amplioris circu<lb/>li, aut rotæ re&longs;pectu minoris, ob principium illud &longs;æpè re<lb/>petitum, & à nobis pluries explicatum, quod iterum in libra <lb/>hic exemplificat. </s>

<s>His itaque &longs;ic &longs;e habentibus breuiter ac per&longs;picuè quæ<lb/>&longs;tionem diluit Ari&longs;toteles, inquiens, maiorem hanc facilita<lb/>tem, ac velocitatem motus procedere à maiori di&longs;tantia, <pb xlink:href="005/01/150.jpg" pagenum="142"/>quam à centro habet extremum diametri amplioris circu<lb/>li, aut rotæ re&longs;pectu minoris, ob principium illud &longs;æpè re<lb/>petitum, & à nobis pluries explicatum, quod iterum in libra <lb/>hic exemplificat. </s>

<s>Quoniam (inquit) &longs;icut exactiores &longs;unt <lb/>maiores libræ, quam minores, <expan abbr="magisq.">magisque</expan> aut facilius mouen<lb/>tur; ita maiores circuli, vel rotæ, æquali exi&longs;tente onere, <lb/><expan abbr="cæterisq.">cæterisque</expan> paribus, vt dictum e&longs;t: Cum rotæ ex totidem li<lb/>bris, &longs;eu brachijs libræ videantur compactæ, quot &longs;unt dia<lb/>metri ex quibus con&longs;tant. </s>

Line 2764

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

<s>Primò <lb/>nimirum quia per maiores diametros tanquam per longio<lb/>res vectes aptius &longs;uperatur impedimentum, quod experimur <lb/>tam ex parte axis, quàm ex parte foraminis rotæ vbi inditur <lb/>ip&longs;e axis, ad expeditum motum circumuolutionis illius, <lb/>dum propter vtriu&longs;que corporis a&longs;peritatem adinuicem co-<pb pagenum="143"/>guntur fricari, vnde non parum circumuolutio retardatur. <lb/></s>

<s>Primò <lb/>nimirum quia per maiores diametros tanquam per longio<lb/>res vectes aptius &longs;uperatur impedimentum, quod experimur <lb/>tam ex parte axis, quàm ex parte foraminis rotæ vbi inditur <lb/>ip&longs;e axis, ad expeditum motum circumuolutionis illius, <lb/>dum propter vtriu&longs;que corporis a&longs;peritatem adinuicem co-<pb xlink:href="005/01/151.jpg" pagenum="143"/>guntur fricari, vnde non parum circumuolutio retardatur. <lb/></s>

<s>Secundo quia quæ minor e&longs;t rota, &longs;icut pluries, quàm ma<lb/>ior debet conuolui ad eleuandum, vel trahendum aliquod <lb/>pondus, ita pluries e&longs;t illi &longs;uperanda huiu&longs;modi re&longs;i&longs;tentia, <lb/>&longs;eu impedimentum fricationis; <expan abbr="proindeq.">proindeque</expan> difficilius id præ<lb/>&longs;tabit: &longs;icut è contra facilius, quæ maior e&longs;t, <expan abbr="paucioribusq.">paucioribusque</expan> <lb/>circumuolutionibus indiget. </s>

Line 2788

<s>COMMENTARIVS.</s>

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

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

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

Line 2802

<s>Nam licet grauius pondus &longs;i deor&longs;um fe<lb/>ratur, violentius quidem de&longs;cendet, non tamen per hoc fa<lb/>cilius à loco &longs;uo, vel quiete dimouetur. </s>

<s>Deinde quia &longs;icut <lb/>maius pondus auget procliuitatem ad motum perpendicu<lb/>larem ver&longs;us mundi centrum; ita difficultatem auget re-<pb pagenum="145"/>&longs;pectu motus contrarij, vel obliqui, vt e&longs;t motus cir cularis <lb/>libræ, vel rotæ. </s>

<s>Deinde quia &longs;icut <lb/>maius pondus auget procliuitatem ad motum perpendicu<lb/>larem ver&longs;us mundi centrum; ita difficultatem auget re-<pb xlink:href="005/01/153.jpg" pagenum="145"/>&longs;pectu motus contrarij, vel obliqui, vt e&longs;t motus cir cularis <lb/>libræ, vel rotæ. </s>

<s>Rur&longs;umque nec &longs;ub&longs;i&longs;tit contradictio, quam Blancanus <lb/>Philo&longs;opho attribuit, qua&longs;i in præcedenti quæ&longs;tione di<lb/>xerit, maiores trochleas, ac &longs;cytalas, minoribus facilius <lb/>moueri; hic autem a&longs;&longs;erat, maiorem rotam difficilius mo<lb/>ueri, quam minorem. </s>

Line 2820

<s>Sed ad concilianda principia Archimedis cum principijs <lb/>Ari&longs;totelis in propo&longs;ito di&longs;cur&longs;u explicandum &longs;uper e&longs;t, cur <lb/>quando libra, vel rota con&longs;ideratur &longs;u&longs;pen&longs;a per centrum <lb/>&longs;uæ grauitatis indiui&longs;ibiliter, non requiratur eadem propor<lb/>tio inter exce&longs;&longs;um partis præponderantis, & grauitatem ma<lb/>iorem, aut minorem alterius, &longs;ed &longs;ufficiat quilibet exce&longs;&longs;us. <lb/></s>

<s>Siquidem etiam in i&longs;to ca&longs;u ab&longs;tracto maior grauitas partis <pb pagenum="146"/>eleuandæ, maiorem exce&longs;&longs;um ponderis, aut virtutis videre<lb/>tur requirere in parte eleuante. </s>

<s>Siquidem etiam in i&longs;to ca&longs;u ab&longs;tracto maior grauitas partis <pb xlink:href="005/01/154.jpg" pagenum="146"/>eleuandæ, maiorem exce&longs;&longs;um ponderis, aut virtutis videre<lb/>tur requirere in parte eleuante. </s>

<s>Dicimus ergo huiu&longs;modi di&longs;paritatem de&longs;umendam e&longs;&longs;e <lb/>ex propria conditione materiæ. </s>

Line 2834

<s>Imo &longs;emper quie&longs;ceret, nec vlla e&longs;&longs;et re&longs;i<lb/>&longs;tentia partium axis explicata, &longs;iue pondus incumbens e&longs;&longs;et <lb/>grauius, &longs;iue leuius. </s>

<s>Ideoque nullo negotio ad quem<lb/>libet exiguum impul&longs;um, vel modicam additio<lb/>nem ponderis &longs;tatim ab æquilibrio, & à <lb/>quiete dimoueretur omnis quan<lb/>tumuis ingens, & graui&longs;&longs;i<lb/>ma libra, vel <lb/>rota. </s><pb pagenum="147"/>

<s>Quæ&longs;tio Vndecima.</s>

Line 2856

<s>Maximo autem adiumento hu<lb/>iu&longs;modi &longs;cytalæ e&longs;&longs;e &longs;olent cum binæ, vel ternæ æquidi<lb/>&longs;tantes oneribus &longs;upponuntur, vt ea facilius moueantur, <lb/>præ&longs;ertim &longs;uper &longs;olum &longs;atis con&longs;i&longs;tens, & æquatum, à <lb/>quo nulla vnquam &longs;upereminentia, aut cauitate rotarum <lb/>paruitas ab&longs;orbeatur. </s>

<s>Licet non minus imò frequentius <lb/>vtamur &longs;cytalis &longs;implicibus, ac non rotatis, quarum memi<pb pagenum="148"/>nit Pappus lib.

<s>Licet non minus imò frequentius <lb/>vtamur &longs;cytalis &longs;implicibus, ac non rotatis, quarum memi<pb xlink:href="005/01/156.jpg" pagenum="148"/>nit Pappus lib.

8. Vtrarumque autem figuram hic erit in<lb/>&longs;picere delineatam. </s><figure/>

8. Vtrarumque autem figuram hic erit in<lb/>&longs;picere delineatam. </s><figure id="id.005.01.156.1.jpg" xlink:href="005/01/156/1.jpg"/>

<s>Quærit igitur Ari&longs;toteles quid &longs;it in cau&longs;a, vt huiu&longs;modi <lb/>&longs;cytalis, quæ minores valde rotas obtinent, quàm currus, <lb/>facilius quàm ip&longs;is curribus onera a&longs;portentur cum quæ<lb/>&longs;tione nona con&longs;titerit, maiores rotas facilius, ac celerius <lb/>onera mouere. </s>

Line 2866

<s>Axis enim currus duplici ex parte præmitur, <lb/>nempe de&longs;uper ab oneribus incumbentibus, & ex latere <lb/>dum ante, vel retro trahitur à mouentibus. </s>

<s>Quare in dupli<lb/>ci etiam & corre&longs;pondenti parte præmit rotas intra ip&longs;arum <lb/>modiolum, vbi cum rotæ &longs;eiunctæ ab eo &longs;int, ac di&longs;&longs;imili mo<lb/>do moueantur, nece&longs;&longs;ario &longs;e&longs;e ad inuicem &longs;ecundum vtram<lb/>que partem offen&longs;ant atque collidunt, eo quod diuer&longs;o &longs;ibi <pb pagenum="149"/>motu atque impul&longs;u occurrant. </s>

<s>Quare in dupli<lb/>ci etiam & corre&longs;pondenti parte præmit rotas intra ip&longs;arum <lb/>modiolum, vbi cum rotæ &longs;eiunctæ ab eo &longs;int, ac di&longs;&longs;imili mo<lb/>do moueantur, nece&longs;&longs;ario &longs;e&longs;e ad inuicem &longs;ecundum vtram<lb/>que partem offen&longs;ant atque collidunt, eo quod diuer&longs;o &longs;ibi <pb xlink:href="005/01/157.jpg" pagenum="149"/>motu atque impul&longs;u occurrant. </s>

<s>Quod non ita &longs;e habet in <lb/>&longs;cytalis, in quibus cum non &longs;it axis di&longs;tinctus, nec motus di<lb/>uer&longs;us, & ab eodem pondere, quod &longs;u&longs;tinent ip&longs;æ anterius <lb/>&longs;uper planum impellantur, nullus fit in rotatione occur&longs;us <lb/>nullaque offen&longs;atio, &longs;eclu&longs;o omni offendiculo extrin&longs;eco, de <lb/>quo non loquimur. </s>

Line 2888

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

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

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

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

Line 2910

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

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

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

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

Line 2926

<s>Altera verò cau&longs;a propo&longs;iti experimenti, quam Ari&longs;tote<lb/>les a&longs;signat, eaque potior e&longs;t, quia in fundæ v&longs;u manus (&longs;eu <lb/>potius pars vbi brachium humero iungitur, vt optimè Bal<lb/>dus adnotauit) con&longs;tituitur qua&longs;i centrum circuli de&longs;cripti <lb/>per eius motum, funda verò (&longs;cilicet &longs;imul cum brachio) <lb/>&longs;e habet tanquam linea, quæ à centro ad peripheriam ex<lb/>tenditur. </s>

<s>Quanto autem productior, ac longior e&longs;t linea, <pb pagenum="152"/>quæ à centro ad periferiam tendit, vt illa, quæ ex brachio, & <lb/>funda con&longs;tituitur in rotatione; tanto velocius mouetur. <lb/></s>

<s>Quanto autem productior, ac longior e&longs;t linea, <pb xlink:href="005/01/160.jpg" pagenum="152"/>quæ à centro ad periferiam tendit, vt illa, quæ ex brachio, & <lb/>funda con&longs;tituitur in rotatione; tanto velocius mouetur. <lb/></s>

<s>Cumque ex maiori velocitate i&longs;tius motus, maior impetus <lb/>producatur; hinc fit, vt quod funda iacitur, tanquam per <lb/>velociorem iaculationem, maiorem impetum à funditore <lb/>recipiat, quàm &longs;i manu mittatur, longiu&longs;que valde proinde <lb/>feratur. </s>

Line 2942

<s>Quare cum grauitas fundæ, vel nullius momenti in &longs;e &longs;it, <lb/>vel ad &longs;ummum &longs;it grauitas in&longs;trumenti, nullam pariter &longs;u<lb/>pra pondus proiecti augere pote&longs;t difficultatem, ad quam <lb/>&longs;uperandam maior conatus potentiæ requiratur, minu&longs;que <lb/>propterea funda, quàm &longs;ola manu, proiectum mittatur. </s>

<s>Vna tamen adhuc &longs;upere&longs;t difficultas, quæ non mediocris <lb/>e&longs;t momenti; nimirum quo pacto motus circularis, quo <pb pagenum="153"/>funda circumducitur mi&longs;sile, antequam proijciatur, ad mo<lb/>tum rectum proiectionis vim ac robur adijcere po&longs;sit; ita vt <lb/>impetus in circumlatione acqui&longs;itus, in impetum proie<lb/>ctionis refundatur. </s>

<s>Vna tamen adhuc &longs;upere&longs;t difficultas, quæ non mediocris <lb/>e&longs;t momenti; nimirum quo pacto motus circularis, quo <pb xlink:href="005/01/161.jpg" pagenum="153"/>funda circumducitur mi&longs;sile, antequam proijciatur, ad mo<lb/>tum rectum proiectionis vim ac robur adijcere po&longs;sit; ita vt <lb/>impetus in circumlatione acqui&longs;itus, in impetum proie<lb/>ctionis refundatur. </s>

<s>Siquidem quilibet ex ijs duobus im<lb/>pul&longs;ibus, natura &longs;ua ad <expan abbr="mot&utilde;">motum</expan> valde <expan abbr="diuers&utilde;">diuersum</expan> videtur ordinari. </s>

Line 2960

<s>Quod &longs;i ignes mi&longs;siles &longs;ulphureo puluere artificio&longs;i&longs;simè <lb/>compactos videamus huc illuc variis <expan abbr="tortuo&longs;isq.">tortuo&longs;isque</expan> itineribus <lb/>di&longs;currere; id ex eo fit, quia &longs;ulphureus puluis, ita e&longs;t intra <lb/>cartaceos eorum anfractus artificiosè di&longs;po&longs;itus, vt accen<lb/>&longs;us, diuer&longs;is ex lateribus vim inferat, ex quibus illi in oppo<lb/>&longs;ita loca ferantur, ac veluti per obliquos calles &longs;erpendo <lb/>di&longs;currere videantur. </s>

<s>Quod quippe tantum arguit mixtio<lb/>nem ip&longs;ius motus procedentem à varia &longs;ituatione pulueris, <lb/>&longs;eu cau&longs;æ impellentis; cum alias etiam quilibet impetus ab <lb/>accen&longs;o puluere productus directè tendat, ac moueat ver&longs;us <lb/>eam partem in quam &longs;e&longs;e dilatando confert, & qua e&longs;t illi <lb/>additus, vt ex angu&longs;tia elabatur, ac foris erumpat. </s><pb pagenum="154"/>

<s>His ergo &longs;ic &longs;tabilitis, facilè &longs;oluetur difficultas propo&longs;i<lb/>ta, nam impetus mi&longs;&longs;ili incu&longs;&longs;us dum funda circumageretur <lb/>non corrumpitur, nec de&longs;init e&longs;&longs;e per aduentum noui impe<lb/>tus, quo recta illud proijcitur, cum neque natura &longs;ua, neque <lb/>po&longs;itione ei opponatur. </s>

Line 2988

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

<s>Oblongum itaque ac teres quod<lb/>dam lignum e&longs;t &longs;uper tran&longs;uer&longs;a ip&longs;ius textrinæ locatum, <pb pagenum="155"/>bina circa <lb/><figure id="fig41"/><lb/><expan abbr="vtramq.">vtramque</expan> ex<lb/>tremitatem <lb/><expan abbr="hab&etilde;s">habens</expan> fora<lb/>mina, qui<lb/>bus toti<lb/>dem collo<lb/>pes, &longs;eu fu<lb/>&longs;tes infigun<lb/>tur, vt faci<lb/>liùs iugum ip&longs;um eorum beneficio cum opus fuerit conuer<lb/>tatur, vt præ&longs;efert &longs;ub&longs;trata figura. </s>

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

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

<s>Quæritigitur Ari<lb/><figure id="fig42"/><lb/>&longs;toteles cur &longs;i lon<lb/>giores fuerint collo<lb/>pes facilius iugum <lb/>circumagatur, quam <lb/>&longs;i minores, ac bre<lb/>uiores extiterint. <lb/></s>

<s>Quæritigitur Ari<lb/><figure id="id.005.01.163.2.jpg" xlink:href="005/01/163/2.jpg"/><lb/>&longs;toteles cur &longs;i lon<lb/>giores fuerint collo<lb/>pes facilius iugum <lb/>circumagatur, quam <lb/>&longs;i minores, ac bre<lb/>uiores extiterint. <lb/></s>

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

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

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

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

Line 3008

<s>Nam <lb/>eodem pacto præcedenti quæ&longs;tione apud ip&longs;um Philo&longs;o<lb/>phum legimus, manum, non iuncturam brachij habere <lb/>rationem centri in motu circulari, quo circumuertitur fun<lb/>da. </s>

<s>Et tamen ibi vt vidimus &longs;icut hic omnino diuer&longs;us e&longs;t <lb/>&longs;en&longs;us, qui &longs;anè potius ex contextu aliorum omniumque <lb/>verborum, quàm ex vno tantum verbo fortè mendo&longs;o eli-<pb pagenum="157"/>ciendus e&longs;t. </s>

<s>Cum igitur vtrobique iuxta &longs;en&longs;um explica<lb/>tum con&longs;onent reliqua verba, vi&longs;que argumenti non aliter <lb/>appareat, quàm quo expo&longs;uimus modo, &longs;eclu&longs;o omni con<lb/>tentionis pruritu, nullus ambigendi locus relinquitur de <lb/>mente Ari&longs;totelis in his, quæ illum interpretando retuli<lb/>mus. </s>

Line 3028

<s>Qvoniam fracturus qui&longs;piam manibus, ac &longs;imul ge<lb/>nu, aut pede aliquod lignum, dupliciter pote&longs;t ad <lb/>hoc præ&longs;tandum &longs;e gerere; nempe vel æquè dedu<lb/>ctis manibus extrema ligni comprehendens, <expan abbr="genuq.">genuque</expan> aut pe<lb/>de circamedium tanquam fulcimento adhibito, illa ad &longs;e <lb/>retrahendo: vel manibus non ni&longs;i iuxta genu àcprope me<lb/>dium vtrinque admotis, vtrunque ip&longs;ius ligni dimidium in<lb/>clinando: Quærit hic Ari&longs;toteles, cur facilius priori, quàm <lb/>po&longs;teriori modo &longs;equatur præruptio, etiam &longs;i eiu&longs;dem ma<lb/>gnitudinis &longs;it lignum, <expan abbr="eademq.">eademque</expan> virtus in fractione adhibea<lb/>tur. </s>

<s><expan abbr="Idemq.">Idemque</expan> contingat &longs;i humi lignum ip&longs;um &longs;ub&longs;ternatur <lb/><expan abbr="pedeq.">pedeque</expan> circa medium &longs;uperimpo&longs;ito, manus ad tollendum <lb/><expan abbr="&longs;ur&longs;umq.">&longs;ur&longs;umque</expan> curuandum alterum, vel vtrumque eius extremum <lb/>admoueatur, vt &longs;cilicet quò longius à pede lignum com-<pb pagenum="158"/>prehenderit, eo facilius tollat atque confringat. </s>

<s><expan abbr="Idemq.">Idemque</expan> contingat &longs;i humi lignum ip&longs;um &longs;ub&longs;ternatur <lb/><expan abbr="pedeq.">pedeque</expan> circa medium &longs;uperimpo&longs;ito, manus ad tollendum <lb/><expan abbr="&longs;ur&longs;umq.">&longs;ur&longs;umque</expan> curuandum alterum, vel vtrumque eius extremum <lb/>admoueatur, vt &longs;cilicet quò longius à pede lignum com-<pb xlink:href="005/01/166.jpg" pagenum="158"/>prehenderit, eo facilius tollat atque confringat. </s>

<s>Huius igitur cau&longs;am eam e&longs;&longs;e, inquit Ari&longs;toteles. </s>

Line 3050

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

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

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

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

<s>Quod vt planius con&longs;tet, e&longs;to lignum, quod frangitur AB. <lb/></s>

<s>Centrum vbi fulcitur C, <expan abbr="&longs;intq.">&longs;intque</expan> fracta, vel frangenda dimi<lb/>dia AD, & EB &longs;emicirculum de&longs;cribentia AFB circa <lb/><figure id="fig43"/><lb/>ip&longs;um C. </s>

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

Line 3066

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

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

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

<s>Nam ab&longs;tractè loquendo de ip<lb/>&longs;is lineis, quæ ante diui&longs;ionem coincidebant in vnam, non <lb/>po&longs;&longs;et intelligi, prius &longs;eparari vnam partem illarum, quàm <lb/>aliam cum &longs;imul omnes, magis aut minus di&longs;tando di&longs;iungi <lb/>deberent con&longs;tituendo angulum DCE. </s>

Line 3094

<s>COMMENTARIVS.</s>

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

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

Line 3108

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

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

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

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

Line 3128

<s>Sicut nares, ac digiti manu&longs;que <lb/>vel pedes in marmoreis &longs;tatuis, quæ propterea &longs;æpius mu<lb/>tilatæ reperiuntur effo&longs;&longs;æ. </s>

<s>Cum igitur reliquiæ lapidum, <lb/>ac o&longs;trearum a&longs;sidua maris agitatione in littoribus vo<lb/>lutentur, atque inuicem illidantur, extremas <lb/><expan abbr="eminentesq.">eminentesque</expan> earum partes retundi nece&longs;<lb/>&longs;e e&longs;t, ob idque eas in orbicularem <lb/>formam redigi, vel ad ip<lb/>&longs;am quantum fieri <lb/>pote&longs;t acce<lb/>dere. </s><pb pagenum="163"/>

<s>Quæ&longs;tio Decima&longs;exta.</s>

Line 3156

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

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

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

<s>Sit enim <lb/>&longs;ari&longs;&longs;a decem cubitorum longitudinis aliquantulum incli<lb/><figure id="fig44"/><lb/>nata ip&longs;a AB, cuius manubrium A, cu&longs;pis B, &longs;uffulta di<lb/>gitis vbi C, pollice præmente in A tanquam potentia <lb/>eleuante. </s>

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

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

Line 3170

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

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

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

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

Line 3194

<s>Vtrum verò &longs;eruata eadem proportione cra&longs;sitiei ad lon<lb/>gitudinem, æquè facilè inclinetur magnum, ac paruum, &longs;eu <lb/>longum, ac breue, non &longs;atis videtur con&longs;tare. </s>

<s>Probabiliter <lb/>tamen dici pote&longs;t, &longs;pectandum primò e&longs;&longs;e qualitatem, ac di<pb pagenum="166"/>&longs;po&longs;itionem materiæ, vt &longs;i grauior, aut leuior; den&longs;ior, aut <lb/>rarior; fortior, aut imbecillior in &longs;e &longs;it. </s>

<s>Probabiliter <lb/>tamen dici pote&longs;t, &longs;pectandum primò e&longs;&longs;e qualitatem, ac di<pb xlink:href="005/01/174.jpg" pagenum="166"/>&longs;po&longs;itionem materiæ, vt &longs;i grauior, aut leuior; den&longs;ior, aut <lb/>rarior; fortior, aut imbecillior in &longs;e &longs;it. </s>

<s>Nam frequenter ex <lb/>ijs pendet, vt nonnulla corpora plus facilitatis ad &longs;e incli<lb/>nandum acquirant ex maiori longitudine, quàm difficulta<lb/>tis ex maiori cra&longs;&longs;itie: Alia verò contra. </s>

Line 3212

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

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

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

Line 3246

<s>Quærit enim cur paruo exi&longs;tente cuneo, tam valida <lb/>eius adminiculo fiat virtutis impre&longs;sio, vt facilè magna &longs;cin<lb/>dantur corpora, quæ alijs <expan abbr="maioribusq.">maioribusque</expan> adhibitis in&longs;trumen<lb/>tis vix &longs;cindi aliquo modo po&longs;&longs;ent. </s>

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

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

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

Line 3262

<s>Fulcimentum verò I circa in<lb/>gre&longs;&longs;um cunei, &longs;eu principium rimæ. </s>

<s>Huic autem vecti alius <lb/><figure id="fig45"/><lb/>oppo&longs;itus vectis <lb/><expan abbr="cõ&longs;tituatur">con&longs;tituatur</expan> BC, <lb/>cuius <expan abbr="põdus">pondus</expan> &longs;u<lb/>pra verticem B <lb/>ad partes FG <lb/>vbi K, fulcimen<lb/>tum verò in L. <lb/></s>

<s>Huic autem vecti alius <lb/><figure id="id.005.01.176.1.jpg" xlink:href="005/01/176/1.jpg"/><lb/>oppo&longs;itus vectis <lb/><expan abbr="cõ&longs;tituatur">con&longs;tituatur</expan> BC, <lb/>cuius <expan abbr="põdus">pondus</expan> &longs;u<lb/>pra verticem B <lb/>ad partes FG <lb/>vbi K, fulcimen<lb/>tum verò in L. <lb/></s>

<s>Valde igitur per<lb/>cu&longs;&longs;o cuneo in <lb/>AC, vectis AB fulta in I &longs;imul fulcimentum præmens, mo<lb/>uebit ver&longs;us G; onus autem H ver&longs;us M. </s>

Line 3274

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

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

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

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

Line 3288

<s>Quod e&longs;t ip&longs;um ver<lb/>ticem, &longs;eu apicem fungi officio extremorum vtriu&longs;que ve<lb/>ctis ad remouendas vtrinque partes corporis &longs;cindendi tan<lb/>quam ad leuanda pondera virtute impetus in contrarium <lb/>impre&longs;si in alterutro extremo, vt in AC vbi applicatur po<lb/>tentia mouentis, &longs;eu percutientis. </s>

<s>Non igitur res ita e&longs;t con<lb/>cipienda qua&longs;i vertex B tanquam extremum duorum ve<lb/>ctium contra nit entium &longs;imul moueretur ad oppo&longs;ita ad <lb/>partes M, & N: Sed vt dum ip&longs;e vertex B mouetur &longs;u<lb/>per lineam BO, partes cunei vtrinque &longs;equentes, ac paula-<pb pagenum="170"/>tim &longs;e dilatantes, & ab inuicem recedentes, nece&longs;&longs;ariò im<lb/>pingant in partes molis, quas ab eodem loco di&longs;terminant, <lb/>vt ibidem ip&longs;æ &longs;uccedant. </s>

<s>Non igitur res ita e&longs;t con<lb/>cipienda qua&longs;i vertex B tanquam extremum duorum ve<lb/>ctium contra nit entium &longs;imul moueretur ad oppo&longs;ita ad <lb/>partes M, & N: Sed vt dum ip&longs;e vertex B mouetur &longs;u<lb/>per lineam BO, partes cunei vtrinque &longs;equentes, ac paula-<pb xlink:href="005/01/178.jpg" pagenum="170"/>tim &longs;e dilatantes, & ab inuicem recedentes, nece&longs;&longs;ariò im<lb/>pingant in partes molis, quas ab eodem loco di&longs;terminant, <lb/>vt ibidem ip&longs;æ &longs;uccedant. </s>

<s>Non enim ab&longs;que impul&longs;u inde <lb/>po&longs;&longs;ent eas expellere, nec ab&longs;que expul&longs;ione in earum lo<lb/>cum &longs;uccedere. </s>

Line 3302

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

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

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

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

Line 3326

<s>COMMENTARIVS.</s>

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

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

Line 3344

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

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

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

<s>Quare inquit Ari&longs;tote<lb/>les in re ædificatoria, multiplicatis trochleis &longs;uculis, ac ve<lb/><figure id="fig46"/><lb/>ctibus magna <expan abbr="mou&etilde;tur">mouentur</expan> <expan abbr="põde">ponde</expan> <lb/>ra non &longs;ecus ac multiplicatis <lb/>tantummodo trochleis, qu&ecedil; <lb/>vectis <expan abbr="vic&etilde;">vicem</expan> <expan abbr="ger&utilde;t">gerunt</expan> vt diximus. </s>

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

<s>Sed vt prædicta ad oculos <lb/>etiam pateant, &longs;int duæ tro<lb/>chleæ ex oppo&longs;ito <expan abbr="cõ&longs;titutæ">con&longs;titutæ</expan>, <lb/>vna &longs;upernè ac &longs;tabiliter ap<lb/>pen&longs;a vbi A; altera verò in<lb/>fernè locata vbi B, cui pon <lb/>dus C &longs;it <expan abbr="religat&utilde;">religatum</expan>, <expan abbr="habeatq.">habeatque</expan> <lb/><expan abbr="vtraq;">vtraque</expan> trochlea <expan abbr="&longs;u&utilde;">&longs;uum</expan> <expan abbr="orbicul&utilde;">orbiculum</expan> <lb/>inditum, cuifunis ductarius <lb/><expan abbr="circ&utilde;ducatur">circunducatur</expan>; <expan abbr="alligeturq.">alligeturque</expan> al<lb/>terum extremum ip&longs;ius funis <lb/>in parte inferiori &longs;uperioris <lb/>trochleæ vbi D. </s>

Line 3354

<s>Tunc dicimus cum Ari&longs;tote<lb/>le, quòd &longs;i quis manu trahat <lb/>funis caput vbi E, facilè au<lb/>xilio ip&longs;arum trochlearum <lb/>eleuabit pondus C, eo quod <lb/>trochlearum orbiculi, vectis <lb/>vicem, ac virtutem &longs;ubeant. </s>

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

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

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

Line 3382

<s>Re&longs;pondetur, &longs;uperio<lb/>rem trochleam non tam auxilium, quàm commoditatem, <lb/>ac facilitatem ad trahendum illi præbere. </s>

<s>Vt enim patet ex <lb/>Guido Vbaldo de trochlea propo&longs;itione prima, beneficio <lb/>ip&longs;ius trochleæ &longs;uperioris &longs;upernè videlicet appen&longs;æ quan<lb/>do potentia æqualis e&longs;t ponderi inferius alligato, nullatenus <lb/>eleuare illud poterit, cum ita &longs;e habeat, ac &longs;i aliud e&longs;&longs;et ap<lb/>pen&longs;um pondus, æquale ponderi prædicto cum æquali di<lb/>&longs;tantia à centro, &longs;iue axiculo, circa quem diameter orbiculi <lb/>non &longs;ecus ac libra conuertitur, vt clarius videre e&longs;t in hac <lb/>figura, in qua linea AB diametrum referat orbiculi ABC <pb pagenum="175"/>de&longs;cripta circa axiculum C, nam &longs;i funis ex vtroque dia<lb/>metri extremo à centro æquidi&longs;tanti propendeat, & hinc <lb/>pondus D, illinc potentia E æqualiter præmat, idem erit, ac <lb/><figure id="fig47"/><lb/>&longs;i in libra æqualibus prædita <lb/>brachijs æqualia pondera ap<lb/>pendantur, quorum vnum, alte<lb/>rum per proprium de&longs;cen&longs;um <lb/>eleuare non po&longs;&longs;et, cum actio <lb/>debeat e&longs;&longs;e ab inæquali propor<lb/>tione, vt docet idem Ari&longs;t. </s>

<s>Vt enim patet ex <lb/>Guido Vbaldo de trochlea propo&longs;itione prima, beneficio <lb/>ip&longs;ius trochleæ &longs;uperioris &longs;upernè videlicet appen&longs;æ quan<lb/>do potentia æqualis e&longs;t ponderi inferius alligato, nullatenus <lb/>eleuare illud poterit, cum ita &longs;e habeat, ac &longs;i aliud e&longs;&longs;et ap<lb/>pen&longs;um pondus, æquale ponderi prædicto cum æquali di<lb/>&longs;tantia à centro, &longs;iue axiculo, circa quem diameter orbiculi <lb/>non &longs;ecus ac libra conuertitur, vt clarius videre e&longs;t in hac <lb/>figura, in qua linea AB diametrum referat orbiculi ABC <pb xlink:href="005/01/183.jpg" pagenum="175"/>de&longs;cripta circa axiculum C, nam &longs;i funis ex vtroque dia<lb/>metri extremo à centro æquidi&longs;tanti propendeat, & hinc <lb/>pondus D, illinc potentia E æqualiter præmat, idem erit, ac <lb/><figure id="id.005.01.183.1.jpg" xlink:href="005/01/183/1.jpg"/><lb/>&longs;i in libra æqualibus prædita <lb/>brachijs æqualia pondera ap<lb/>pendantur, quorum vnum, alte<lb/>rum per proprium de&longs;cen&longs;um <lb/>eleuare non po&longs;&longs;et, cum actio <lb/>debeat e&longs;&longs;e ab inæquali propor<lb/>tione, vt docet idem Ari&longs;t. </s>

<s>Quare tota vis quæ adiungi<lb/>tur potentiæ, pondus aliquod <lb/>eleuanti prædictarum trochlea<lb/>rum beneficio, petenda e&longs;t ex <lb/>trochlea inferiori. </s>

Line 3392

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

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

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

<s>Quo fit vt cum <lb/>potentia ad pondus attollendum, ip&longs;a inferiori trochlea vti<lb/>tur tanquam vecte non paruam virtutem ab ip&longs;a trochlea <lb/>mutuetur, <expan abbr="nõ">non</expan> &longs;ecus ac à vecte, cuius alterum extremum fir<lb/>miter alicubi &longs;it innixum, ad eleuandum pondus, quod ex <lb/>eius medio pendeat, vt con&longs;tare pote&longs;t in de&longs;cripto vecte <lb/><figure id="fig48"/><lb/>ABC, cuius extre<lb/>mum C fulciatur in <lb/>D, extremum verò <lb/>A &longs;it à <expan abbr="pot&etilde;tia">potentia</expan> ele<lb/>uandum, & ex pun<lb/>cto medio B <expan abbr="prop&etilde;-deat">propen<lb/>deat</expan> onus <expan abbr="alligat&utilde;">alligatum</expan>, <lb/>quod &longs;it ip&longs;um E. <lb/></s>

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

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

Line 3406

<s>Et &longs;i quis multiplicatis trochleis, &longs;u<lb/>culis, ac vectibus, vt hic idem Philo&longs;ophus ait, magna vide<lb/>rit pondera eb exigua virtute moueri, aut eleuari, de&longs;inat <lb/>admirari. </s>

<s>Nam & ore tantum perflando vidi pondus tre-<pb pagenum="177"/>centorum quinquaginta axium, & eius loco hominem &longs;tan<lb/>tem &longs;uper tabulam dimoueri, trochleis, ac &longs;cytalis, axeque <lb/>in paruo peritrochio adhibitis, quod idem vnciali pondere <lb/>præponderante contigerat, vt vtrumque cernere e&longs;t in <lb/>&longs;ub&longs;trata figura. </s><figure/>

<s>Nam & ore tantum perflando vidi pondus tre-<pb xlink:href="005/01/185.jpg" pagenum="177"/>centorum quinquaginta axium, & eius loco hominem &longs;tan<lb/>tem &longs;uper tabulam dimoueri, trochleis, ac &longs;cytalis, axeque <lb/>in paruo peritrochio adhibitis, quod idem vnciali pondere <lb/>præponderante contigerat, vt vtrumque cernere e&longs;t in <lb/>&longs;ub&longs;trata figura. </s><figure id="id.005.01.185.1.jpg" xlink:href="005/01/185/1.jpg"/>

<s>Quæ&longs;tio Decimanona.</s>

Line 3416

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

<s>Præterea &longs;e-<emph.end type="italics"/><pb pagenum="178"/><emph type="italics"/>curis ip&longs;a efficitur cuneus. </s>

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

<s>Paruus autem exi&longs;tens cuneus <lb/>magna diuidit, cùm ex duobus &longs;it vectibus, contrario ad &longs;e in<lb/>uicem modo constitutis.<emph.end type="italics"/></s>

Line 3432

<s>Præ&longs;&longs;io namque oneris <lb/>ab vna tantum cau&longs;a grauitante &longs;ine locali motu proce<lb/>dit; percu&longs;&longs;io verò &longs;ecuris à duplici, vel triplici cau&longs;a im<lb/>pellente, à qua mixtus quidam, violenti&longs;simus efficitur <lb/>motus. </s>

<s>Quod autem motus penderi addat pondus, &longs;eu grauitas <lb/>augeatur in motu, ac propterea efficacius operetur, explo<lb/>rati&longs;simum e&longs;t, non modo in ijs, quæ cadunt ex alto (nam <lb/>quò magis à principio motus di&longs;ce&longs;&longs;erint, eò velocius ip&longs;a <lb/>deor&longs;um ferri con&longs;picimus, <expan abbr="magisq.">magisque</expan> impellere non &longs;ecus ac <lb/>corpora grauiora;) &longs;ed in reliquis quoque motibus proie<lb/>ctorum, quorum pondus magis operatur in motu, quam in-<pb pagenum="179"/>quiete, <expan abbr="magisq.">magisque</expan> in velociori motu, quàm in tardiori. </s>

<s>Quod autem motus penderi addat pondus, &longs;eu grauitas <lb/>augeatur in motu, ac propterea efficacius operetur, explo<lb/>rati&longs;simum e&longs;t, non modo in ijs, quæ cadunt ex alto (nam <lb/>quò magis à principio motus di&longs;ce&longs;&longs;erint, eò velocius ip&longs;a <lb/>deor&longs;um ferri con&longs;picimus, <expan abbr="magisq.">magisque</expan> impellere non &longs;ecus ac <lb/>corpora grauiora;) &longs;ed in reliquis quoque motibus proie<lb/>ctorum, quorum pondus magis operatur in motu, quam in-<pb xlink:href="005/01/187.jpg" pagenum="179"/>quiete, <expan abbr="magisq.">magisque</expan> in velociori motu, quàm in tardiori. </s>

<s>Quam<lb/>uis in rigore loquendo virtus illa grauium, quæ augetur in <lb/>motu, non &longs;it eadem propriè ip&longs;a grauitas per maiorem in<lb/>tentionem &longs;ui ip&longs;ius, &longs;eu acqui&longs;itionem aliorum graduum <lb/>eiu&longs;dem qualitatis in &longs;pecie, &longs;ed potius &longs;it impetus ip&longs;orum, <lb/>grauium, vel à proijciente impre&longs;&longs;us, vel per ip&longs;am grauita<lb/>tem de&longs;cendentis oneris in eodem onere productus dum <lb/>præceps fertur ad ima, ac &longs;ucce&longs;siuè in &longs;e impetum au<lb/>get. </s>

Line 3446

<s>Tanto enim fortius corpus quodlibet in aliud impin<lb/>git, quantò celerius fertur, ac magis eius moles agitatur. <lb/></s>

<s>Celerius autem fertur &longs;ecuris per motum circularem, ma<lb/>gi&longs;que agitatur, quàm quolibet alio motu; Alioquin &longs;i <lb/>rectà, verbi gratia moueretur &longs;imul cum manu, tantùm <lb/>&longs;pacij percurreret eodem tempore, quantum ip&longs;a manus; <lb/>vt &longs;i &longs;ecuris ex loco A &longs;imul ac manus manubrio appli<lb/>cata ex loco B, rectà de&longs;cenderent ver&longs;us lineam CD <pb pagenum="180"/><figure id="fig49"/><lb/>paralellam ip&longs;i AB <lb/>ad <expan abbr="percuti&etilde;dum">percutiendum</expan> li<lb/>gnum infra ip&longs;am <lb/>lineam collocatum <lb/>in E. </s>

<s>Celerius autem fertur &longs;ecuris per motum circularem, ma<lb/>gi&longs;que agitatur, quàm quolibet alio motu; Alioquin &longs;i <lb/>rectà, verbi gratia moueretur &longs;imul cum manu, tantùm <lb/>&longs;pacij percurreret eodem tempore, quantum ip&longs;a manus; <lb/>vt &longs;i &longs;ecuris ex loco A &longs;imul ac manus manubrio appli<lb/>cata ex loco B, rectà de&longs;cenderent ver&longs;us lineam CD <pb xlink:href="005/01/188.jpg" pagenum="180"/><figure id="id.005.01.188.1.jpg" xlink:href="005/01/188/1.jpg"/><lb/>paralellam ip&longs;i AB <lb/>ad <expan abbr="percuti&etilde;dum">percutiendum</expan> li<lb/>gnum infra ip&longs;am <lb/>lineam collocatum <lb/>in E. </s>

<s>Mouerentur <lb/>enim per latera op<lb/>po&longs;ita <expan abbr="eiu&longs;d&etilde;">eiu&longs;dem</expan> <expan abbr="para-lellogrãmi">para<lb/>lellogrammi</expan> ABCD, <lb/>quæ &longs;unt æqualia. <lb/></s>

Line 3458

<s>Accedit, quia ip&longs;emet impetus aptius imprimitur per <lb/>motum circularem, <expan abbr="magisq.">magisque</expan> con&longs;eruatur in illo, vt ob&longs;erua<lb/>re licet in rotis, quæ facilius mouentur, ac diu circumuol<lb/>uuntur po&longs;t impul&longs;um acceptum; & in pilis, quæ longius <lb/>rotando feruntur, quàm corpora, quæ non mouentur in gy<lb/>rum. </s>

<s>Deinde aptius in particulari imprimitur impetus per <pb pagenum="181"/>circularem motum &longs;ecuris, quia in tali motu eius manu<lb/>brium, vectis vicem &longs;ubit, cuius alterum extremum, quod <lb/>latet in manu, fulcitur vbi complicantur digiti minores in <lb/>ip&longs;i&longs;met digitis minoribus; alterum verò mouet ip&longs;am &longs;e<lb/>curim tanquam pondus ei alligatum, & pars quæ inter pol<lb/>licem, & indicem continetur, &longs;u&longs;cipit impul&longs;um ab eodem <lb/>indice tanquam à potentia monente. </s>

<s>Deinde aptius in particulari imprimitur impetus per <pb xlink:href="005/01/189.jpg" pagenum="181"/>circularem motum &longs;ecuris, quia in tali motu eius manu<lb/>brium, vectis vicem &longs;ubit, cuius alterum extremum, quod <lb/>latet in manu, fulcitur vbi complicantur digiti minores in <lb/>ip&longs;i&longs;met digitis minoribus; alterum verò mouet ip&longs;am &longs;e<lb/>curim tanquam pondus ei alligatum, & pars quæ inter pol<lb/>licem, & indicem continetur, &longs;u&longs;cipit impul&longs;um ab eodem <lb/>indice tanquam à potentia monente. </s>

<s>Vt videre e&longs;t in de<lb/>&longs;cripto manubrio AB, cuius alterum extremum fulcitur <lb/><figure id="fig50"/><lb/>in A qua&longs;i tanquam in centro &longs;ui motus; alterum verò pro<lb/>mouet &longs;ecurim in B: & pars vbi C, impul&longs;um recipit à <lb/>potentia motrice tendentem in D. </s>

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

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

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

<s>Cum <lb/>itaque omnia, quæ vectis vicem obtinent, ac circulariter &longs;uo <lb/>innixa fulcimento cientur, apti&longs;simè virtutem, &longs;eu impul<lb/>&longs;um à mouente recipiant, &longs;equitur vt hac eciam ratione &longs;e<lb/>curis ip&longs;a per motum circularem magnam vim ad &longs;cinden<lb/>dum adipi&longs;catur. </s><pb pagenum="182"/>

<s>Rur&longs;us accedit, quod intra latitudinem &longs;patij, quo ma<lb/>nus mouere pote&longs;t &longs;ecurim, illud maximum erit &longs;patium, <lb/>quod circumeundo ab ip&longs;a vnà cum &longs;ecuri complectitur. <lb/></s>

Line 3490

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

<s>Iuxta <lb/>quamiationem colligitur, quod & experientia comproba<lb/>tur prædicta omnia in&longs;trumenta maximam, acpræcipuam <lb/>virt utem &longs;ortiri in extremo, quod magis di&longs;tat à centro &longs;ui <lb/>motus. </s><pb pagenum="183"/>

<s>Nec ob&longs;tat, quod Baldus adducit ad probandum ictum <lb/>ex en&longs;e, efficaciorem e&longs;&longs;e à parte, quæ e&longs;t circa medium, ex <lb/>eo quod ibi con&longs;tituatur centrum grauitatis, ac propterea <lb/>cu&longs;pis non ni&longs;i dimidium ponderis habeat re&longs;pectu illius. <lb/></s>

Line 3504

<s>Quandoquidem impetus ita e&longs;t determinatus ad vnam <lb/>po&longs;itionem ex vi &longs;uæ impre&longs;sionis, vt non &longs;u&longs;cipiat contra<lb/>rietatem ni&longs;i ab oppo&longs;ita. </s>

<s><expan abbr="Proindeq.">Proindeque</expan> idem ferè e&longs;t, moue<lb/>re dextror&longs;um, vel &longs;ini&longs;tror&longs;um ip&longs;am cu&longs;pidem circumlati <lb/>en&longs;is de&longs;cendentem, & &longs;tantem, vel quie&longs;centem, eo quod <lb/>tali dimotio non apponatur directè ip&longs;i de&longs;cen&longs;ui, ad quem <lb/>impetus natura &longs;ua e&longs;t determinatus. </s><pb pagenum="184"/>

<s>Quæ&longs;tio Vige&longs;ima.</s>

Line 3530

<s>Cau&longs;am hic inquirit Ari&longs;toteles, ob quam in &longs;tatera <lb/>paruo appendiculo magna leuentur, ac trutinentur <lb/>pondera; Cum quippe &longs;tatera nonni&longs;i libra quæ<lb/>dam e&longs;&longs;e videatur, licet qua&longs;i dimidiata, vtpotè quæ ex <lb/>altera tantum parte lancem pendentem habeat, ex altera <lb/>verò di&longs;currens quoddam appendiculum æquipondij. </s>

<s>Vt <pb pagenum="185"/>videre e&longs;t in de&longs;cripta &longs;tatera AB &longs;u&longs;pen&longs;a in C ex cuius <lb/>extremo A pendet lanx D, & ex B appendiculum E. <lb/></s>

<s>Vt <pb xlink:href="005/01/193.jpg" pagenum="185"/>videre e&longs;t in de&longs;cripta &longs;tatera AB &longs;u&longs;pen&longs;a in C ex cuius <lb/>extremo A pendet lanx D, & ex B appendiculum E. <lb/></s>

<s>Etenim &longs;icutlibra æqualia duntaxat ponderibus onera le<lb/><figure id="fig51"/><lb/>uat, ac trutinat; ita &longs;imiliter &longs;tatera, cum libra quædam <lb/>&longs;it, æqualia tantùm appendiculo onera videtur po&longs;&longs;e leua<lb/>re; quod &longs;ecus experimur contingere. </s>

<s>Etenim &longs;icutlibra æqualia duntaxat ponderibus onera le<lb/><figure id="id.005.01.193.1.jpg" xlink:href="005/01/193/1.jpg"/><lb/>uat, ac trutinat; ita &longs;imiliter &longs;tatera, cum libra quædam <lb/>&longs;it, æqualia tantùm appendiculo onera videtur po&longs;&longs;e leua<lb/>re; quod &longs;ecus experimur contingere. </s>

<s>Nam paruæ molis <lb/>appendiculo, magna videmus onera extolli, ac men&longs;u<lb/>rari. </s>

Line 3542

<s>Q<gap/>muis enim &longs;tatera con&longs;titua<lb/>tur ex inæqualibus br<gap/>nijs, & ex altero tantum lanx vna <lb/>propendeat; vel certè loco lancis vnci nonnulli demittan<lb/>tur, qui mercibus, aut rebus ponderandis compacti, eas non <lb/>minus commodè &longs;u&longs;tinent, vt in &longs;ubiecta figura. </s>

<s>Ex altero <pb pagenum="186"/>verònonni&longs;i appendiculum æquipondij &longs;u&longs;pen&longs;um depen<lb/>deat: Semper tamen ip&longs;a &longs;tatera libram refert, cum eius <lb/>axis, ac fulcimentum &longs;it inter onus, & æquipondium, <expan abbr="ip&longs;iusq.">ip&longs;iusque</expan> <lb/><figure id="fig52"/><lb/>æquipondij appendiculum, alterius lancis, vel vnci cum <lb/>pondere vicem &longs;ubeat; &longs;iue ip&longs;um fulcimentum, aut &longs;par<lb/>tum con&longs;tituatur in puncto omnino medio, &longs;iue &longs;ecus, vnde <lb/>prouenit inæqualitas brachiorum, cum hæc libræ naturam <lb/>non auferat, nec immutet, vt diximus &longs;uo loco. </s>

<s>Ex altero <pb xlink:href="005/01/194.jpg" pagenum="186"/>verònonni&longs;i appendiculum æquipondij &longs;u&longs;pen&longs;um depen<lb/>deat: Semper tamen ip&longs;a &longs;tatera libram refert, cum eius <lb/>axis, ac fulcimentum &longs;it inter onus, & æquipondium, <expan abbr="ip&longs;iusq.">ip&longs;iusque</expan> <lb/><figure id="id.005.01.194.1.jpg" xlink:href="005/01/194/1.jpg"/><lb/>æquipondij appendiculum, alterius lancis, vel vnci cum <lb/>pondere vicem &longs;ubeat; &longs;iue ip&longs;um fulcimentum, aut &longs;par<lb/>tum con&longs;tituatur in puncto omnino medio, &longs;iue &longs;ecus, vnde <lb/>prouenit inæqualitas brachiorum, cum hæc libræ naturam <lb/>non auferat, nec immutet, vt diximus &longs;uo loco. </s>

<s><expan abbr="Rur&longs;umq.">Rur&longs;umque</expan> vectis pariter naturam &longs;imul &longs;ortitur &longs;tatera, <lb/>quia fulcimentum habet vbi incumbit in axe, &longs;eu &longs;parto, <lb/>quod idem e&longs;t, ac punctum vnde &longs;u&longs;penditur, & circa quod <lb/>ip&longs;a conuertitur, <expan abbr="pondusq.">pondusque</expan> leuandum con&longs;tituitur merces <lb/>in lancem inuecta, vel vncis infixa; & potentia mouens, ip<lb/>&longs;um appendiculum æquipondij. </s>

<s>Cum igitur ea &longs;it vectis, ac <lb/>libræ natura <expan abbr="propriaq.">propriaque</expan> conditlo,<gap/> cum alterum eius à ful<lb/>cimento brachium longius protenditur, vt in &longs;tatera contin<lb/>git, paruo in ip&longs;ius extremitate adhibito pondere, magnam <lb/>valeat molem ex altero breuiori brachio pendentem attol<lb/>lere, iuxta proportionem vtriu&longs;que di&longs;tantiæ à centro, vt <pb pagenum="187"/>alibi demon&longs;trauimus; planum profecto relinquitur, qua <lb/>ratione, paruo appendiculo in &longs;tatera, magna leuari po&longs;&longs;int <lb/>pondera, vt intendebat Philo&longs;ophus. </s>

<s>Cum igitur ea &longs;it vectis, ac <lb/>libræ natura <expan abbr="propriaq.">propriaque</expan> conditlo,<gap/> cum alterum eius à ful<lb/>cimento brachium longius protenditur, vt in &longs;tatera contin<lb/>git, paruo in ip&longs;ius extremitate adhibito pondere, magnam <lb/>valeat molem ex altero breuiori brachio pendentem attol<lb/>lere, iuxta proportionem vtriu&longs;que di&longs;tantiæ à centro, vt <pb xlink:href="005/01/195.jpg" pagenum="187"/>alibi demon&longs;trauimus; planum profecto relinquitur, qua <lb/>ratione, paruo appendiculo in &longs;tatera, magna leuari po&longs;&longs;int <lb/>pondera, vt intendebat Philo&longs;ophus. </s>

<s>Quoniam verò in præfato di&longs;cur&longs;u &longs;emel atque iterum <lb/>Ari&longs;toteles docuit, &longs;tateram e&longs;&longs;e velutilibram, in qua plures <lb/>&longs;int libræ, ac totidem quot fuerint &longs;parta, hinc Blancanus <lb/>conijcit, apud Pri&longs;cos, &longs;tateram ex multis trutinis, &longs;eu &longs;par<lb/>tis compactam fui&longs;&longs;e, paribus interuallis per totam longi<lb/>tudinem ip&longs;ius &longs;tateræ di&longs;&longs;eminatis; Ex quibus &longs;ingulis <lb/>prout pondus po&longs;tulabat, illa &longs;u&longs;penderetur, appendiculo <lb/>&longs;emper in extremitate &longs;ui brachij immoto manente; Itaut <lb/>tantum mercis lanci imponeretur, quantum appendiculo <lb/>æquiponderaret, iuxta <expan abbr="&longs;ituation&etilde;">&longs;ituationem</expan> cuiu&longs;libet trutinæ. </s>

Line 3562

<s>Quamobrem hac quoque in &longs;tatera con<gap/>i videntur plu<lb/>res libræ, cum &longs;altem duplex in ea trutina reperiatur, quæ <lb/>tanquam duplex libra de&longs;eruit ad maiora, vel minora one<lb/>ra aptius ponderanda, & vt eadem &longs;ecundum maiores, vel <lb/>minores differentias ponderum quando opus fuerit innote<lb/>&longs;cant. </s>

<s>Et quidem cum Ari&longs;toteles ait: ac &longs;i vna libra multæ <pb pagenum="188"/>&longs;int libræ, eo quod in ea in&longs;int &longs;parta multa: forta&longs;&longs;e idem <lb/>intellexit per multa, vel multas, ac plura, vel plures; cum no<lb/>men Græcum <foreign lang="greek">pollo\s</foreign> vtrumque &longs;ignificet, & à Cierone <lb/><foreign lang="greek">w_olla\</foreign> in Timæo Platonis vertatur plures. </s>

<s>Et quidem cum Ari&longs;toteles ait: ac &longs;i vna libra multæ <pb xlink:href="005/01/196.jpg" pagenum="188"/>&longs;int libræ, eo quod in ea in&longs;int &longs;parta multa: forta&longs;&longs;e idem <lb/>intellexit per multa, vel multas, ac plura, vel plures; cum no<lb/>men Græcum <foreign lang="greek">pollo\s</foreign> vtrumque &longs;ignificet, & à Cierone <lb/><foreign lang="greek">w_olla\</foreign> in Timæo Platonis vertatur plures. </s>

<s>Ni&longs;i etiam cum <lb/>Baldo rectè dixerimus, &longs;tateram tot libras con&longs;titui, quot <lb/>&longs;unt tran&longs;lationes appendiculi de loco ad locum; quia toties <lb/>variatur proportio, <expan abbr="proindeq.">proindeque</expan> etiam libra. </s>

Line 3578

<s>Addit autem Ari&longs;toteles quòd quantò propinquius one<lb/>ri in lance, vel vncis appen&longs;o &longs;partum con&longs;tituitur, tanto <lb/>magis onus ip&longs;um, &longs;eu maius onus valet &longs;tatera leuare. </s>

<s>Id <pb pagenum="189"/>quod experientia con&longs;tat, & ea ratione ab eodem Philo&longs;o<lb/>pho probatur, quia cum <expan abbr="&longs;part&utilde;">&longs;partum</expan> con&longs;tituatur hypomochlion, <lb/>&longs;eu fulcimentum talis vectis, nempe &longs;tateræ; <expan abbr="tantoq.">tantoque</expan> faci<lb/>lius vectis beneficio onera leuentur, quantò productior fue<lb/>rit vectis longitudo à fulcimento; hinc fit, vt &longs;parto magis <lb/>ad <expan abbr="loc&utilde;">locum</expan> vnde onus dependet appropinquato, maior vectis <lb/><expan abbr="lõgitudo">longitudo</expan> relinquatur <expan abbr="v&longs;q;">v&longs;que</expan> ad <expan abbr="appendicul&utilde;">appendiculum</expan>, <expan abbr="faciliusq.">faciliusque</expan> propte<lb/>rea ip&longs;um <expan abbr="appendicul&utilde;">appendiculum</expan> valeat in maiori di&longs;tantia <expan abbr="æquipõde-rare">æquiponde<lb/>rare</expan>, <expan abbr="maioraq.">maioraque</expan> onera trutinare: permutata videlicet <expan abbr="ponder&utilde;">ponderum</expan>, <lb/>ac <expan abbr="brachior&utilde;">brachiorum</expan> proportione, vt ex Archimede lib.

<s>Id <pb xlink:href="005/01/197.jpg" pagenum="189"/>quod experientia con&longs;tat, & ea ratione ab eodem Philo&longs;o<lb/>pho probatur, quia cum <expan abbr="&longs;part&utilde;">&longs;partum</expan> con&longs;tituatur hypomochlion, <lb/>&longs;eu fulcimentum talis vectis, nempe &longs;tateræ; <expan abbr="tantoq.">tantoque</expan> faci<lb/>lius vectis beneficio onera leuentur, quantò productior fue<lb/>rit vectis longitudo à fulcimento; hinc fit, vt &longs;parto magis <lb/>ad <expan abbr="loc&utilde;">locum</expan> vnde onus dependet appropinquato, maior vectis <lb/><expan abbr="lõgitudo">longitudo</expan> relinquatur <expan abbr="v&longs;q;">v&longs;que</expan> ad <expan abbr="appendicul&utilde;">appendiculum</expan>, <expan abbr="faciliusq.">faciliusque</expan> propte<lb/>rea ip&longs;um <expan abbr="appendicul&utilde;">appendiculum</expan> valeat in maiori di&longs;tantia <expan abbr="æquipõde-rare">æquiponde<lb/>rare</expan>, <expan abbr="maioraq.">maioraque</expan> onera trutinare: permutata videlicet <expan abbr="ponder&utilde;">ponderum</expan>, <lb/>ac <expan abbr="brachior&utilde;">brachiorum</expan> proportione, vt ex Archimede lib.

1. æquipon<lb/>derantium propo&longs;it.6. & &longs;equenti; necnon ex <expan abbr="eod&etilde;">eodem</expan> Ari&longs;to<lb/>tele &longs;up. </s>

Line 3606

<s>Qværitur in præ&longs;enti ab Ari&longs;totele, ex quo nam pro<lb/>ueniat, vt facilius dentes extrahantur denti&longs;orcipis <lb/>adhibito in&longs;trumento, quàm &longs;ola manu, immediata <lb/>opera digitorum. </s>

<s>Ac primò ex eo, inquit videri po&longs;&longs;e, id or-<pb pagenum="190"/>tum habere, quòd cum dens lubricus in &longs;e &longs;it, magis for<lb/>&longs;an è manu quæ leuis, & mollis e&longs;t, quàm ex rudi, ac tenaci <lb/>forcipe elabatur. </s>

<s>Ac primò ex eo, inquit videri po&longs;&longs;e, id or-<pb xlink:href="005/01/198.jpg" pagenum="190"/>tum habere, quòd cum dens lubricus in &longs;e &longs;it, magis for<lb/>&longs;an è manu quæ leuis, & mollis e&longs;t, quàm ex rudi, ac tenaci <lb/>forcipe elabatur. </s>

<s><expan abbr="Statimq.">Statimque</expan> hanc ip&longs;am rationem impugnat, <lb/>ac penitus euertit, inquiens, potius ferro, quàm digitis con<lb/>tingere, vt dens ab illis apprehen&longs;us, propteri &longs;ui lubricita<lb/>tem aufugiat. </s>

Line 3622

<s>Proindeq, <expan abbr="hor&utilde;">horum</expan> <expan abbr="vecti&utilde;">vectium</expan> virtute arctius, ac validius, <lb/>quàm digitis <expan abbr="dent&etilde;">dentem</expan> per&longs;tringi, <expan abbr="faciliusq.">faciliusque</expan> <expan abbr="cõ&longs;equenter">con&longs;equenter</expan> auelli. </s>

<s>Sit enim dentiforcipis in&longs;trumentum AB, quod dentem <lb/><expan abbr="quid&etilde;">quidem</expan> comprehen<lb/>dat, & con&longs;tringat <lb/><figure id="fig53"/><lb/>per &longs;ui extremum <lb/>B. </s>

<s>Vectis autem <lb/>vnus &longs;it brachium <lb/>BC. </s>

Line 3630

<s>Pon<lb/>du&longs;que &longs;it ip&longs;um <lb/>dens F. </s>

<s>Vtroque <pb pagenum="191"/>igitur vecte &longs;imul admoto per extrema BD ip&longs;um dentem <lb/>tanquam onus in contrarium repellendo, validi&longs;&longs;imè con<lb/>&longs;tringent adhibita, &longs;cilicet manu in AC, qua extremum <lb/>A compellatur ver&longs;us C, & extremum C ver&longs;us A. </s>

<s>Vtroque <pb xlink:href="005/01/199.jpg" pagenum="191"/>igitur vecte &longs;imul admoto per extrema BD ip&longs;um dentem <lb/>tanquam onus in contrarium repellendo, validi&longs;&longs;imè con<lb/>&longs;tringent adhibita, &longs;cilicet manu in AC, qua extremum <lb/>A compellatur ver&longs;us C, & extremum C ver&longs;us A. </s>

<s>Dens <lb/><expan abbr="aut&etilde;">autem</expan> ita con&longs;trictus facilè dimouetur, ar dimotus extrahi<lb/>tur. </s>

Line 3652

<s>Quippe cum digiti nec tam <lb/>tenaciter dentem apprehendere, nec ita vnum veluti corpus <lb/>oblongum, ac ten&longs;um cum eo po&longs;&longs;int componere; quod to<lb/>tum vnius vectis rationem &longs;ubeat. </s>

<s>Quocirca admittenda non erunt, quæ Baldus aliter Phi<lb/>lo&longs;ophus hac in re profert, quamuis acutè fuerint excogita<lb/>ta, cum ait, dentiforcipis partium, quibus dens apprehendi<lb/>tur, eam quæ longior e&longs;t, potentiæ mouentis loco &longs;uccede<lb/>re, breuiorem verò fulcimentum con&longs;titui: Quandoquidem <lb/>in v&longs;u dentiforcipis ad extrahendum dentem etiam prout <pb pagenum="192"/>ab ip&longs;o explicatur, fulcimentum non pote&longs;t con&longs;titui in ip&longs;a <lb/>breuiori dentiforcipis parte, qua apprehenditur dens; tum <lb/>quia hæc &longs;imul cum altera parte mouetur, licet per mino<lb/>rem circulationem, quæ &longs;anè fit circa punctum illud gingi<lb/>uæ, cui in ab&longs;tractione conuertendo &longs;e&longs;e innititur dens, & à <lb/>quo &longs;emper dentiforcipis extremum aliquantulum di&longs;tat, <lb/>eo quod nequeat ad illam v&longs;que partem gingiuæ interio<lb/>rem, ac &longs;olidam vbi huiu&longs;modi fit nixus pertingere: tum, <lb/>etiam quia e&longs;to pars ip&longs;a breuior per &longs;ui extremum non, <lb/>moueretur ad motum alterius, &longs;ed quie&longs;ceret, non propte<lb/>rea &longs;equeretur con&longs;titui fulcimentum huius motionis. </s>

<s>Quocirca admittenda non erunt, quæ Baldus aliter Phi<lb/>lo&longs;ophus hac in re profert, quamuis acutè fuerint excogita<lb/>ta, cum ait, dentiforcipis partium, quibus dens apprehendi<lb/>tur, eam quæ longior e&longs;t, potentiæ mouentis loco &longs;uccede<lb/>re, breuiorem verò fulcimentum con&longs;titui: Quandoquidem <lb/>in v&longs;u dentiforcipis ad extrahendum dentem etiam prout <pb xlink:href="005/01/200.jpg" pagenum="192"/>ab ip&longs;o explicatur, fulcimentum non pote&longs;t con&longs;titui in ip&longs;a <lb/>breuiori dentiforcipis parte, qua apprehenditur dens; tum <lb/>quia hæc &longs;imul cum altera parte mouetur, licet per mino<lb/>rem circulationem, quæ &longs;anè fit circa punctum illud gingi<lb/>uæ, cui in ab&longs;tractione conuertendo &longs;e&longs;e innititur dens, & à <lb/>quo &longs;emper dentiforcipis extremum aliquantulum di&longs;tat, <lb/>eo quod nequeat ad illam v&longs;que partem gingiuæ interio<lb/>rem, ac &longs;olidam vbi huiu&longs;modi fit nixus pertingere: tum, <lb/>etiam quia e&longs;to pars ip&longs;a breuior per &longs;ui extremum non, <lb/>moueretur ad motum alterius, &longs;ed quie&longs;ceret, non propte<lb/>rea &longs;equeretur con&longs;titui fulcimentum huius motionis. </s>

<s>Nam <lb/>punctum cuiu&longs;libet vectis corre&longs;pondens puncto fulcimen<lb/>ti cui innititur, penetratur cum illo, & &longs;imul cum illo quie<lb/>&longs;cit in motione ip&longs;iusmet vectis; & tamen non pote&longs;t con<lb/>&longs;titui fulcimentum &longs;uæ propriæ motionis. </s>

Line 3666

<s>Quod &longs;anè intellexerim habita ratione ad <lb/>dolorem, quem in dentis ab&longs;tractione qui&longs;que vitare, aut <lb/>&longs;altem minuere intendit; ita vt facilitas ad commoditatem <lb/>patientis, non autem ad ab&longs;olutam effectus con&longs;ecutionem <lb/>referatur. </s>

<s>Quo &longs;en&longs;u id ex eo videtur probari, quoniam &longs;i <lb/>&longs;emel dens fuerit commotus, & à po&longs;itione &longs;uæ &longs;edis dimo-<pb pagenum="193"/>tus, non modò &longs;olis digitis poterit &longs;impliciter auelli, non, <lb/>minus ac &longs;imul adhibito in&longs;trumento; &longs;ed etiam commo<lb/>dius, ac facilius, dolorem &longs;cilicet penitus, vel maiori ex par<lb/>te vitando, eo quod digiti &longs;entire &longs;ecus, ac dentiforcipis <lb/>ferrum, & &longs;uperare magis valeant pro opportunitate ali<lb/>qualem dentis re&longs;i&longs;tentiam. </s>

<s>Quo &longs;en&longs;u id ex eo videtur probari, quoniam &longs;i <lb/>&longs;emel dens fuerit commotus, & à po&longs;itione &longs;uæ &longs;edis dimo-<pb xlink:href="005/01/201.jpg" pagenum="193"/>tus, non modò &longs;olis digitis poterit &longs;impliciter auelli, non, <lb/>minus ac &longs;imul adhibito in&longs;trumento; &longs;ed etiam commo<lb/>dius, ac facilius, dolorem &longs;cilicet penitus, vel maiori ex par<lb/>te vitando, eo quod digiti &longs;entire &longs;ecus, ac dentiforcipis <lb/>ferrum, & &longs;uperare magis valeant pro opportunitate ali<lb/>qualem dentis re&longs;i&longs;tentiam. </s>

<s>Alioquin ab&longs;olutè loquendo <lb/>nulla habita ratione ad dolorem, ip&longs;um dentiforcipis in&longs;tru<lb/>mentum, &longs;icut maiorem præualet &longs;uperare dentis re&longs;i&longs;ten<lb/>tiam firmiter inhærentis; ita & multo magis minorem, vt <lb/>cum iam ille à propria &longs;ede dimotus debiliter tantum gin<lb/>giuæ inhæret. </s>

Line 3692

<s>Quantò igitur ip&longs;um K vicinius <lb/>fuerit angulo ip&longs;ius A, tantò vicinius fit connexioni, vbi est <lb/>A, hoc autem e&longs;t bypomochlion, ab eadem igitur potentia appli<lb/>cante FE plus extolli nece&longs;&longs;e e&longs;t. </s>

<s>Quamobrem quoniam ex <lb/>contario e&longs;t eleuatio, nece&longs;&longs;e e&longs;t magis comprimi, quod autem <lb/>comprimitur magis, citius frangitur.<emph.end type="italics"/></s><pb pagenum="194"/>

<s>COMMENTARIVS.</s>

Line 3712

<s>Nux verò <lb/><expan abbr="confring&etilde;da">confringenda</expan> locetur inter A & C vbi F, nempe inter extre<lb/>ma brachiorum ea parte qua minus di&longs;tant à fulcimento. <lb/></s>

<s>Potentia verò confringentis applicetur in extremis ecrun<lb/>dem brachiorum ea parte, qua magis di&longs;tant a fulcimento, <pb pagenum="195"/><figure id="fig54"/><lb/>tanquam in manubrijs, <expan abbr="nimir&utilde;">nimirum</expan> in BD. </s>

<s>Potentia verò confringentis applicetur in extremis ecrun<lb/>dem brachiorum ea parte, qua magis di&longs;tant a fulcimento, <pb xlink:href="005/01/203.jpg" pagenum="195"/><figure id="id.005.01.203.1.jpg" xlink:href="005/01/203/1.jpg"/><lb/>tanquam in manubrijs, <expan abbr="nimir&utilde;">nimirum</expan> in BD. </s>

<s>Con&longs;ideretur dein<lb/>de vtrum que brachium tanquam duplicem vectem moueri <lb/>circa immotum fulcimentum E; ita vt ad motum B ver&longs;us <lb/>D, alterum extremum nempe C appropinquetur ad A; & è <lb/>conuer&longs;o, ad motum D ver&longs;us B, ip&longs;um A appropinquetur <lb/>ad C. </s>

Line 3720

<s>Addit autem primò Ari&longs;toteles, quo <expan abbr="lõgiora">longiora</expan> fuerint bra<lb/>chia huius in&longs;trumenti à connexione ip&longs;orum &longs;eu <expan abbr="fulcim&etilde;to">fulcimento</expan> <lb/>ad extrema, quibus applicatur potentia: & ex alia parte, quo <lb/>breuiora eadem brachia fuerint à conexione &longs;eu <expan abbr="fulcim&etilde;to">fulcimento</expan> <lb/>ad nucem, eo facilius confractionem fieri; ac proinde à mi<lb/>nori potentia, ita vt id ip&longs;um quod cum percu&longs;&longs;ione feci&longs;&longs;et <lb/>pondus, præ&longs;tetur à binis explicatis vectibus in contrarium <lb/>&longs;e&longs;e conantibus, & comprimentibus ip&longs;am nucem; cuius <lb/>re&longs;i&longs;tentia gerit vicem ponderis. </s>

<s>Secundo verò addit Ari&longs;toteles, eò <expan abbr="maior&etilde;">maiorem</expan> fieri vectium <lb/>&longs;eu brachiorum dilatationem, <expan abbr="quõ">quom</expan> propinquius fulcimento, <lb/>&longs;eu angulo connexionis eorum nux confringenda con&longs;titua<lb/>tur, quia nimirum vterque angulus ad verticem ab illis <expan abbr="cõ-&longs;titutus">con<lb/>&longs;titutus</expan>, per talem appropinquationem dilatatur (nempe <lb/>AEC. & BED.) & cum angulo ip&longs;a quoque brachia, quæ <lb/>angulum con&longs;tituunt, ita vt magis tunc di&longs;tare oporteat in<lb/>ter &longs;e extrema AC, &longs;icut & DB, <expan abbr="c&utilde;">cum</expan> maius &longs;it latus, quod &longs;ub <pb pagenum="196"/>maiori angulo &longs;ubtenditur, vt con&longs;tat ex 18. primi ele<lb/>ment. </s>

<s>Secundo verò addit Ari&longs;toteles, eò <expan abbr="maior&etilde;">maiorem</expan> fieri vectium <lb/>&longs;eu brachiorum dilatationem, <expan abbr="quõ">quom</expan> propinquius fulcimento, <lb/>&longs;eu angulo connexionis eorum nux confringenda con&longs;titua<lb/>tur, quia nimirum vterque angulus ad verticem ab illis <expan abbr="cõ-&longs;titutus">con<lb/>&longs;titutus</expan>, per talem appropinquationem dilatatur (nempe <lb/>AEC. & BED.) & cum angulo ip&longs;a quoque brachia, quæ <lb/>angulum con&longs;tituunt, ita vt magis tunc di&longs;tare oporteat in<lb/>ter &longs;e extrema AC, &longs;icut & DB, <expan abbr="c&utilde;">cum</expan> maius &longs;it latus, quod &longs;ub <pb xlink:href="005/01/204.jpg" pagenum="196"/>maiori angulo &longs;ubtenditur, vt con&longs;tat ex 18. primi ele<lb/>ment. </s>

<s>Dilatatur autem magis ip&longs;e angulus AEC, & con<lb/>&longs;equenter alius ad verticem BED; Nam quò propinquius <lb/>ei acce&longs;&longs;erit nucis magnitudo, cum qua con&longs;tituit veluti <lb/><expan abbr="triangul&utilde;">triangulum</expan> AEC, eò minora &longs;eu breuiora <expan abbr="euad&utilde;t">euadunt</expan> duo latera, <lb/>quibus ip&longs;e angulus E continetur, prædictamque magnitu<lb/>dinem tanquam ba&longs;im &longs;ubtendit. </s>

Line 3736

<s>Siquidem maiorem arcum in <lb/>eodem tempore eadem potentia per talem <expan abbr="mot&utilde;">motum</expan> de&longs;cribet. <lb/></s>

<s>Licet enim eadem &longs;it exten&longs;io, quæ deperditur per com<lb/>pre&longs;&longs;ionem ex parte corporis compre&longs;&longs;i, aut confracti vbi<lb/>cunque fiat ip&longs;a compre&longs;&longs;io, &longs;emper tamen quò propriùs <lb/>centro fit, & amplius brachia dilatata &longs;upponit, eo maiorem <lb/>arcum extrema brachiorum, in quibus applicatur potentia <lb/>comprimendo percurrunt. </s><figure/>

<s>Sint <expan abbr="namq;">namque</expan> tanquam <lb/>brachia dilatata duæ <lb/>diametri AD, & CB <lb/>in circulo ABCD &longs;e&longs;e <lb/>inuicem <expan abbr="bifariã">bifariam</expan> inter<lb/>&longs;ecantes, & connecten<lb/>tes in <expan abbr="c&etilde;tro">centro</expan> E. </s>

<s>Exten<lb/>&longs;io verò corporis con<lb/>fring <expan abbr="&etilde;di">endi</expan>, quæ per <expan abbr="com-pre&longs;&longs;ion&etilde;">com<lb/>pre&longs;&longs;ionem</expan> deperditur, <lb/>&longs;it &longs;patium AF, quod <pb pagenum="197"/>primò con&longs;tituatur inter extrema AC eorundem brachio<lb/>rum. </s>

<s>Exten<lb/>&longs;io verò corporis con<lb/>fring <expan abbr="&etilde;di">endi</expan>, quæ per <expan abbr="com-pre&longs;&longs;ion&etilde;">com<lb/>pre&longs;&longs;ionem</expan> deperditur, <lb/>&longs;it &longs;patium AF, quod <pb xlink:href="005/01/205.jpg" pagenum="197"/>primò con&longs;tituatur inter extrema AC eorundem brachio<lb/>rum. </s>

<s>Et à puncto F per centrum E ducatur recta FG, quæ <lb/>locum, vel&longs;itum de&longs;ignat, in quo con&longs;tituendum e&longs;t bra<lb/>chium AD po&longs;t ip&longs;am compre&longs;&longs;ionem, ita vt extremum A <lb/>transferatur in F, & extremum D transferatur in G. <lb/></s>

Line 3760

<s>&longs;exti. </s>

<s>Cumque ba&longs;is AK longioribus lineis <lb/>&longs;ubtendatur ip&longs;i angulo E, maior erit, quàm ba&longs;is HI ei<lb/>dem angulo &longs;ubten&longs;a breuioribus lineis EH, & EI. </s><pb pagenum="198"/>

<s>Quod autem exempli&longs;icauimus in brachio, &longs;eu vecte AD, <lb/>idem etiam procedit de brachio CB. </s>

Line 3784

<s>Il<lb/>lud verò duabus fertur lationibus. </s>

<s>Feratur enim ex ip&longs;a AB, A<emph.end type="italics"/><pb pagenum="199"/><emph type="italics"/>quidem ad <expan abbr="ips&utilde;">ipsum</expan> B, B verò ad <expan abbr="ips&utilde;">ipsum</expan> D eadem celeritate. </s>

<s>Feratur enim ex ip&longs;a AB, A<emph.end type="italics"/><pb xlink:href="005/01/207.jpg" pagenum="199"/><emph type="italics"/>quidem ad <expan abbr="ips&utilde;">ipsum</expan> B, B verò ad <expan abbr="ips&utilde;">ipsum</expan> D eadem celeritate. </s>

<s>Feratur <lb/><expan abbr="aut&etilde;">autem</expan> & ip&longs;a AB in ip&longs;i AC iuxta CD <expan abbr="ead&etilde;">eadem</expan> celeritate <expan abbr="c&utilde;">cum</expan> illis. <lb/></s>

Line 3822

<s>Si autem omnino recta <lb/>fieret penitus vtique e&longs;sent contrariæ. </s>

<s>Latus verò &longs;ecundum <lb/>vnicam latam lationem à nullo præpeditur, rationabiliter igi<lb/>tur maiorem pertran&longs;it.<emph.end type="italics"/></s><pb pagenum="200"/>

<s>Latus verò &longs;ecundum <lb/>vnicam latam lationem à nullo præpeditur, rationabiliter igi<lb/>tur maiorem pertran&longs;it.<emph.end type="italics"/></s><pb xlink:href="005/01/208.jpg" pagenum="200"/>

<s>COMMENTARIVS.</s>

Line 3834

<s>31. de<lb/>finitione primi Euclidis Rhombum e&longs;&longs;e figuram quadrila<lb/>teram quidem, & æquilateram, &longs;ed non rectangulam; quip<lb/>pe quæ duos angulos habet acutos, duos verò obtu&longs;os. </s>

<s>Si <lb/><figure id="fig55"/><lb/>igitur in Rhombo ABCD, cuius <lb/>acuti anguli &longs;int A & D, obtu&longs;i <lb/>verò B & C, duo extrema pun<lb/>cta lateris AB, nempe ip&longs;um A, & <lb/>ip&longs;um B, æqua velocitate duabus <lb/>ferantur lationibus, vna qua pun<lb/>ctum A &longs;uper idem latus feratur <lb/>ver&longs;us B, & B feratur ver&longs;us A: <lb/>altera verò qua <expan abbr="d&utilde;">dum</expan> ip&longs;a duo pun<lb/>cta &longs;ibi obuiam procedunt, &longs;imul <lb/>cum toto latere AB, moueantur <lb/>ver&longs;us latus CD, ita vt &longs;emper la<lb/>tus, &longs;eu linea AB, ip&longs;i CD &longs;it pa<lb/>ralella, de&longs;cendatque per latera <lb/>AC, & BD quou&longs;que coincidat <lb/>cum eadem CD: Cum ex duabus lationibus, eadem &longs;em<lb/>per laterum proportione &longs;eruata, recta quædam linea pro<lb/>ducatur, vt &longs;upra demon&longs;tratum e&longs;t ex eodem Ari&longs;totele <lb/>1. par. </s>

<s>Si <lb/><figure id="id.005.01.208.1.jpg" xlink:href="005/01/208/1.jpg"/><lb/>igitur in Rhombo ABCD, cuius <lb/>acuti anguli &longs;int A & D, obtu&longs;i <lb/>verò B & C, duo extrema pun<lb/>cta lateris AB, nempe ip&longs;um A, & <lb/>ip&longs;um B, æqua velocitate duabus <lb/>ferantur lationibus, vna qua pun<lb/>ctum A &longs;uper idem latus feratur <lb/>ver&longs;us B, & B feratur ver&longs;us A: <lb/>altera verò qua <expan abbr="d&utilde;">dum</expan> ip&longs;a duo pun<lb/>cta &longs;ibi obuiam procedunt, &longs;imul <lb/>cum toto latere AB, moueantur <lb/>ver&longs;us latus CD, ita vt &longs;emper la<lb/>tus, &longs;eu linea AB, ip&longs;i CD &longs;it pa<lb/>ralella, de&longs;cendatque per latera <lb/>AC, & BD quou&longs;que coincidat <lb/>cum eadem CD: Cum ex duabus lationibus, eadem &longs;em<lb/>per laterum proportione &longs;eruata, recta quædam linea pro<lb/>ducatur, vt &longs;upra demon&longs;tratum e&longs;t ex eodem Ari&longs;totele <lb/>1. par. </s>

<s>tex. 6. vtraque puncta prædicta eandem laterum ip<lb/>&longs;ius rhombi proportionem in &longs;uo motu &longs;eruando, propriam <pb pagenum="201"/>rectam lineam de&longs;cribent: A quidem lineam AD, B verò <lb/>BC: quæ nimirum erunt diametri eiu&longs;dem rhombi. </s>

<s>tex. 6. vtraque puncta prædicta eandem laterum ip<lb/>&longs;ius rhombi proportionem in &longs;uo motu &longs;eruando, propriam <pb xlink:href="005/01/209.jpg" pagenum="201"/>rectam lineam de&longs;cribent: A quidem lineam AD, B verò <lb/>BC: quæ nimirum erunt diametri eiu&longs;dem rhombi. </s>

Line 3850

<s>Eodem pacto, quod dictum e&longs;t de puncto A, applica<lb/>ri pote&longs;t in puncto B. </s>

<s>Nam &longs;i hoc cum eadem velocitate <lb/>moueatur ver&longs;us A, &longs;icut linea AB ver&longs;us CD, quo tem<lb/>pore per proprium motum percurri&longs;&longs;er v&longs;que ad E, alieno <lb/>motu perueni&longs;&longs;et v&longs;que ad G; <expan abbr="æqualesq.">æqualesque</expan> forent lineæ BE, <pb pagenum="202"/>& BG; producti&longs;que lateribus, EH, & GF, rhombus <lb/>EBGK per illa con&longs;titutus, &longs;imilis e&longs;&longs;et rhombo continen<lb/>ti ABCD: Ideoque GK æqualis oppo&longs;itæ BE, & BG <lb/>æqualis EK. </s>

<s>Nam &longs;i hoc cum eadem velocitate <lb/>moueatur ver&longs;us A, &longs;icut linea AB ver&longs;us CD, quo tem<lb/>pore per proprium motum percurri&longs;&longs;er v&longs;que ad E, alieno <lb/>motu perueni&longs;&longs;et v&longs;que ad G; <expan abbr="æqualesq.">æqualesque</expan> forent lineæ BE, <pb xlink:href="005/01/210.jpg" pagenum="202"/>& BG; producti&longs;que lateribus, EH, & GF, rhombus <lb/>EBGK per illa con&longs;titutus, &longs;imilis e&longs;&longs;et rhombo continen<lb/>ti ABCD: Ideoque GK æqualis oppo&longs;itæ BE, & BG <lb/>æqualis EK. </s>

<s>Quare punctum B vtroque motu<gap/> tran&longs;la<lb/>tum cum eadem proportione æqualitatis, mouebitur motu <lb/>mixto &longs;uper diametrum ip&longs;ius rhombi, & quo tempore <lb/>transferri deberet in E & in G, transfertur in K, quod e&longs;t <lb/>punctum medium diametri BC; cuius reliquum dimidium <lb/>conficiet per motum proprium ab E v&longs;que ad A, & alie<lb/>no à G v&longs;que ad D; ita vt tandem reperiatur in C. </s>

Line 3864

<s>Rationi autem con<lb/>&longs;entaneum e&longs;t, vt punctum contrarijs ferè lationibus &longs;e&longs;e <lb/>impedientibus latum, minori interuallo in eodem tempore <lb/>feratur, quàm punctum, quod duabus lationibus &longs;e&longs;e mutuo <lb/>adiuuantibus a&longs;portatur; mitumque propterea non e&longs;&longs;e &longs;i <lb/>hoc maiorem diametrum, illud verò minorem eodem tem<lb/>pore percurrat. </s>

<s>Vnde etia n &longs;equitur, vt quò acutiores <lb/>con&longs;tituantur anguli A, & D, <expan abbr="proindeq.">proindeque</expan> obtu&longs;iores B, <lb/>& C; tardius ac minori interuallo feratur ip&longs;um B; cele-<pb pagenum="203"/>rius verò ac maiori &longs;patio ip&longs;um A. </s>

<s>Vnde etia n &longs;equitur, vt quò acutiores <lb/>con&longs;tituantur anguli A, & D, <expan abbr="proindeq.">proindeque</expan> obtu&longs;iores B, <lb/>& C; tardius ac minori interuallo feratur ip&longs;um B; cele-<pb xlink:href="005/01/211.jpg" pagenum="203"/>rius verò ac maiori &longs;patio ip&longs;um A. </s>

<s>Quandoquidem ex ma<lb/>iori angu&longs;tia angulorum magis. </s>

Line 3882

<s>Porrò <lb/>hæc non fundatur in eo, quod e&longs;t &longs;ur&longs;um, aut deor&longs;um pun<lb/>cta ip&longs;a duabus lationibus ferri, vt ip&longs;e &longs;upponit, quamuis ad <lb/>explicationem præ dicti motus, <expan abbr="doctrinæq.">doctrinæque</expan> Ari&longs;totelis, om<lb/>nes vtamur exemplo diuer&longs;arum po&longs;itionum, vt &longs;ur&longs;um, aut <lb/>deor&longs;um: &longs;ed ab&longs;trahendo à quacumque po&longs;itione, tota <lb/>&longs;olutionis ratio ab Ari&longs;totele con&longs;tituitur in maiori vnione, <lb/>&longs;eu propinquitate laterum acutranguli, & in maiori &longs;epara<lb/>none, &longs;eu di&longs;tantia laterum anguli obtu&longs;i. </s>

<s>Nam per ip&longs;a <lb/>latera anguli obtu&longs;i; punctum in diuer&longs;as longè partesra<lb/>pitur, qua&longs;i omnino contrario motu: per latera verò anguli <lb/>acuti, in vnam ferè partem, qua&longs;i per eundem motum, qui <lb/>propterea velocior con&longs;tituitur, vt dictum e&longs;t. </s><pb pagenum="204"/>

<s>Deinde propria Baldi &longs;olutio, quam ex proprijs cau&longs;is <lb/>ip&longs;e ait e&longs;&longs;e de&longs;umptam, nullam cau&longs;am affert propo&longs;iti effe<lb/>ctus ad diluendam difficultatem, &longs;eu rationem dubitandi, <lb/>&longs;ed rur&longs;us noua cluntaxat via idip&longs;um demon&longs;trat, quod Ari<lb/>&longs;totelis argumento demon&longs;tratum e&longs;t de veritate ip&longs;ius ef<lb/>fectus, nempe punctum A per longiorem diametrum AD, <lb/>illis duabus lationibus ferri eodem tempore, quo punctum <lb/>B fertur &longs;uper minorem diametrum BC; quod e&longs;t citius <lb/>moueri: nihil attingens de cau&longs;a cur id contingat, &longs;eu ob <lb/>quam punctum A, eodem tempore maiorem valeat li<lb/>neam pertran&longs;ire, <expan abbr="proindeq.">proindeque</expan> velocius moueri; id quod opti<lb/>mè fecit Ari&longs;toteles vt vidimus. </s>

Line 3898

<s>Sed vnde hæc dubitandi ratio de&longs;umpta e&longs;t, inde pariter <lb/>ade&longs;t ratio difficultatem &longs;oluendi. </s>

<s>Etenim hoc ip&longs;o, quod <lb/>punctum B feratur duplici latione explicata &longs;uper diame<lb/>trum BC, latus verò BA vnica vel &longs;implici motione <lb/>vehatur ver&longs;us CD, hoc quidem à nullo motu contrario <pb pagenum="205"/>præpeditur, illud verò contrarijs ferè lationibus detinetur <lb/>ne velocius eodem tempore moueatur, maiu&longs;que proin<lb/>de &longs;patium valeat peragrare. </s>

<s>Etenim hoc ip&longs;o, quod <lb/>punctum B feratur duplici latione explicata &longs;uper diame<lb/>trum BC, latus verò BA vnica vel &longs;implici motione <lb/>vehatur ver&longs;us CD, hoc quidem à nullo motu contrario <pb xlink:href="005/01/213.jpg" pagenum="205"/>præpeditur, illud verò contrarijs ferè lationibus detinetur <lb/>ne velocius eodem tempore moueatur, maiu&longs;que proin<lb/>de &longs;patium valeat peragrare. </s>

<s>Quod per&longs;picuè ex dictis <lb/>iam pote&longs;t patere. </s>

Line 3924

<s>Quare quando BG linea ad ip&longs;um peruenerit <lb/>K, & ip&longs;a FC circumferentia erit in ip&longs;a CL & vniuer&longs;us <lb/>erit conuolutus circulus. </s>

<s><expan abbr="Similiq.">Similique</expan> modo &longs;i magnum mouero, <lb/>illi paruum annectens, eodem existente centro, &longs;imul cum AC <lb/>ip&longs;a AB perpendiculum & recta erit: hac quidem ad ip&longs;am<emph.end type="italics"/><pb pagenum="206"/><emph type="italics"/>FI, illæ verò ad GM. </s>

<s><expan abbr="Similiq.">Similique</expan> modo &longs;i magnum mouero, <lb/>illi paruum annectens, eodem existente centro, &longs;imul cum AC <lb/>ip&longs;a AB perpendiculum & recta erit: hac quidem ad ip&longs;am<emph.end type="italics"/><pb xlink:href="005/01/214.jpg" pagenum="206"/><emph type="italics"/>FI, illæ verò ad GM. </s>

<s>Quamobrem quando bæc quidam <lb/>ip&longs;i GM pertran&longs;iuerit, illa verò ip&longs;i FI, & rur&longs;um facta <lb/>fuerit recta ip&longs;a FA ad ip&longs;am FL, & ip&longs;a AG rur&longs;um re<lb/>cta, velut à principio erant in ip&longs;is MI. </s>

Line 3958

<s>Hoc autem e&longs;t, &longs;i alter ab altero mo<lb/>ueatur, non quam natus e&longs;t, neque peculiarem motionem: nibil <lb/>enim refert cireumponere, & annectere, aut <expan abbr="eõiungere">eoniungere</expan> vtrum<lb/>libet alteri. </s>

<s>Similiter enim quando bic quidem mouet, ille ve<lb/>rò mouelur ab isto, quantum vtique mouerit, alt<gap/>r, tantum<emph.end type="italics"/><pb pagenum="207"/><emph type="italics"/>alter mouebitur. </s>

<s>Similiter enim quando bic quidem mouet, ille ve<lb/>rò mouelur ab isto, quantum vtique mouerit, alt<gap/>r, tantum<emph.end type="italics"/><pb xlink:href="005/01/215.jpg" pagenum="207"/><emph type="italics"/>alter mouebitur. </s>

<s>Quandoquidem igitur adiacens mouerit, aut <lb/>propen&longs;us, non &longs;emper conuoluitur, quando verò circa idem <lb/>po&longs;iti fuerint centrum, alterum ab illo &longs;emper conuolui nece&longs;<lb/>&longs;e est. </s>

Line 3982

<s>Quod vt di&longs;tin<lb/>ctius ob&longs;eruetur addit Ari&longs;toteles, cir culos ip&longs;os circa idem <lb/>centrum coniunctos, <expan abbr="quandoq.">quandoque</expan> in circumuolutione tantam <lb/>lineam &longs;patij pertran&longs;ire, quantam &longs;eor&longs;um pertran&longs;iret cir<lb/>culus minor: quandoque verò quantam eodem pacto per<lb/>curreret circulus maior. </s>

<s>Etenim, vt quilque experiri po-<pb pagenum="208"/>te&longs;t, &longs;i ex ip&longs;is duobus circulis &longs;imul circa idem centrum <lb/>coniunctis volutetur minor &longs;ecundum ab&longs;idem &longs;uam &longs;uper <lb/>aliquod planum, ad motum ip&longs;ius conuoluetur &longs;imul & ma<lb/>ior &longs;uper aliud planum; &longs;ed vtraque linea ab ip&longs;is de&longs;cripta, <lb/>æqualis erit ei quam de&longs;criberet ip&longs;emet circulus minor &longs;i <lb/>&longs;olus per &longs;e ac &longs;eor&longs;um volutaretur. </s>

<s>Etenim, vt quilque experiri po-<pb xlink:href="005/01/216.jpg" pagenum="208"/>te&longs;t, &longs;i ex ip&longs;is duobus circulis &longs;imul circa idem centrum <lb/>coniunctis volutetur minor &longs;ecundum ab&longs;idem &longs;uam &longs;uper <lb/>aliquod planum, ad motum ip&longs;ius conuoluetur &longs;imul & ma<lb/>ior &longs;uper aliud planum; &longs;ed vtraque linea ab ip&longs;is de&longs;cripta, <lb/>æqualis erit ei quam de&longs;criberet ip&longs;emet circulus minor &longs;i <lb/>&longs;olus per &longs;e ac &longs;eor&longs;um volutaretur. </s>

<s>E contra verò &longs;i &longs;uper <lb/>planum eodem pacto volutetur &longs;ecundum ab&longs;idem &longs;uam <lb/>circulus maior, & ad motum ip&longs;ius circumuoluatur etiam <lb/>circulus minor, vtraque linea recta ab ip&longs;is de&longs;cripta æqua<lb/>lis erit ei quam per &longs;e volutatus de&longs;criberet idemmet circu<lb/>lus maior. </s>

Line 3994

<s>Veruntamen &longs;i &longs;en&longs;um eiu&longs;dem textus prout &longs;onat ip&longs;a <lb/>vox (angulus) explicare velimus, non incongrue ad hoc to<lb/>tus Ari&longs;totelis di&longs;cur&longs;us pote&longs;t reduci, vt dicat, &longs;en&longs;u con&longs;ta<lb/>re, angulum cuiu&longs;que circuli (con&longs;titutum &longs;cilicet ex cir<lb/>cumferentia propriæ diametri, & ex ip&longs;a diametro) e&longs;&longs;e <lb/>quidem maiorem &longs;i circulus &longs;it maior, minorem verò &longs;i cir<lb/>culus &longs;it minor. </s>

<s>Atque ex hoc fieri, vt ip&longs;a circumferentia, <lb/>&longs;eu ambitus circuli maioris &longs;it pariter maior, minoris verò, <pb pagenum="209"/>&longs;it minor, iuxta maiorem, vel minorem remotionem ip&longs;ius <lb/>ab altero latere nempe diametro, cum qua con&longs;tituit an<lb/>gulum. </s>

<s>Atque ex hoc fieri, vt ip&longs;a circumferentia, <lb/>&longs;eu ambitus circuli maioris &longs;it pariter maior, minoris verò, <pb xlink:href="005/01/217.jpg" pagenum="209"/>&longs;it minor, iuxta maiorem, vel minorem remotionem ip&longs;ius <lb/>ab altero latere nempe diametro, cum qua con&longs;tituit an<lb/>gulum. </s>

<s>Ac propterea in circumuolutione ip&longs;orum circu<lb/>lorum, etiam ad &longs;en&longs;um con&longs;tare, eandem inter &longs;e propor<lb/>tionem habere lineas, quas ip&longs;i circuli &longs;uper planum de&longs;cri<lb/>bunt, vt &longs;cilicet linea de&longs;cripta à maiori iuxta maiorem cir<lb/>cumferentiam &longs;it maior, quæ verò à minori de&longs;cribitur iux<lb/>ta propriam circumferentiam &longs;it minor. </s>

Line 4002

<s>8. nè maxi<lb/>ma ei tribuatur improprietas locutionis explicando angu<lb/>lum pro Sectore, vt Baldus, vel pro arcu qui &longs;ubtenditur <lb/>angulo, vt Blancanus: Cum vnumquodque i&longs;torum, pro<lb/>prium habeat vocabulum, quod Ari&longs;toteles non ignorabat, <lb/><expan abbr="eoq.">eoque</expan> v&longs;us fui&longs;&longs;et, &longs;i idip&longs;um per illud &longs;ignificare volui&longs;&longs;et </s>

<s>Vlterius verò quod prædicti circuli quando &longs;unt &longs;imul <lb/>coniuncti circa idem centrum, æquale ambo pertran&longs;eant <lb/>&longs;patium, &longs;iue maius illud &longs;it, vt rotando &longs;ecundum ab&longs;idem <lb/>circuli maioris, &longs;iue minus &longs;ecundum ab&longs;idem minoris, hoc <lb/>ferè pacto probat Philo&longs;ophus. </s><figure/>

<s>Sint circa <lb/>idem <expan abbr="p&utilde;ctum">punctum</expan> <lb/>A ip&longs;i duo cir<lb/>culi <expan abbr="coni&utilde;cti">coniuncti</expan>, <lb/>maior <expan abbr="quid&etilde;">quidem</expan> <lb/>BCDE, minor <lb/>verò FGHI. <lb/></s>

Line 4010

<s>Ideo<lb/>que quadrans circuli maioris &longs;it CD, minoris verò GH. <lb/></s>

<s>Deinde con&longs;tituamus vtrunque circulum ad dexteram &longs;i<lb/>mul moueri cum &longs;uo communi centro, rotando alterum <pb pagenum="210"/>quidem per &longs;e &longs;uper rectam lineam DK, alterum verò ad <lb/>motum illius, de&longs;cribendo aliam rectam huic parallelam, <lb/>quæ &longs;it HL. </s>

<s>Deinde con&longs;tituamus vtrunque circulum ad dexteram &longs;i<lb/>mul moueri cum &longs;uo communi centro, rotando alterum <pb xlink:href="005/01/218.jpg" pagenum="210"/>quidem per &longs;e &longs;uper rectam lineam DK, alterum verò ad <lb/>motum illius, de&longs;cribendo aliam rectam huic parallelam, <lb/>quæ &longs;it HL. </s>

<s>Rur&longs;us con&longs;tituamus, maiorem circulum per <lb/>&longs;e moueri &longs;ecundum ab&longs;idem quadrantis CD &longs;uper lineam <lb/>DK, ita vt aliquando punctum C perueniat in M, percur<lb/>rendo &longs;patium DM æquale ip&longs;i CD. </s>

Line 4032

<s>Iam igitur po&longs;t huiu&longs;mo<lb/>di rotationem, quo tempore quadrans minoris circuli con<lb/>fecit &longs;patium HP; quadrans maioris circuli conuoluti ad <lb/>motum illius, confecit &longs;patium. </s>

<s>DR, quod æquale e&longs;t ip&longs;i <pb pagenum="211"/>HP. pereandem 34 primi. </s>

<s>DR, quod æquale e&longs;t ip&longs;i <pb xlink:href="005/01/219.jpg" pagenum="211"/>HP. pereandem 34 primi. </s>

<s>Quod & de tota circumferen<lb/>tia vtriu&longs;que circuli demon&longs;trari pote&longs;t, non ab&longs;que magna <lb/>omnium admiratione, quibus forta&longs;&longs;e videretur, maiorem <lb/>circulum, &longs;emper maiorem lineam de&longs;cribere, quàm circu<lb/>lus minor in ip&longs;a rotatione. </s>

Line 4050

<s>Quod &longs;i magni<lb/>tudo, quæ moueri debet ad motum alterius, cui reperi<lb/>tur connexa, mobilis quidem facilè ex &longs;e &longs;it, nihil tamen <lb/>ex &longs;e moueatur, vel ad motum alterius conferat, perin<lb/>de e&longs;t, ac &longs;i minimè apta e&longs;&longs;et ad motum: vnde & altera, <lb/>quæ &longs;imul cum ip&longs;a moueri debet, tardius non minus mo<lb/>uebitur. </s>

<s>Alterum verò fundamentum à Philo&longs;opho &longs;uppo&longs;itum <lb/>illud e&longs;t, quòd impo&longs;&longs;ibile profectò exi&longs;timandum &longs;it aliquid <lb/>plus moueri, quàm mouens à quo mouetur; Siquidem non <lb/>&longs;ua, &longs;ed illius motione cietur, <expan abbr="nullaq.">nullaque</expan> propria vtitur mobili<lb/>tate intrin&longs;eca, & actiua, qua motus po&longs;&longs;it augeri. </s><pb pagenum="212"/>

<s>Quibus po&longs;itis Ari&longs;toteles quæ&longs;tionem &longs;oluendo prædi<lb/>ctum effectum ex eo inquit contingere. </s>

Line 4074

<s>Siquidem moueri non po&longs;&longs;et circa <lb/>proprium centrum, nec proinde peculiarem, ac proportio<lb/>natam &longs;ibi motionem vendicare, &longs;ed tantum circa alienum <lb/>centrum ip&longs;ius circuli deferentis conuerti: Non &longs;ecus ac <lb/>quælibet alia magnitudo adiacens eidem circulo deferenti, <lb/>vel ei extra centrum quoquo modo appen&longs;a; tantum &longs;cili<lb/>cet &longs;patium tran&longs;mittendo, quantum ip&longs;e circulus, ad cuius <lb/>motum defertur, pertran&longs;ierit. </s>

<s>Verùm cum hic &longs;ermo &longs;it <lb/>de duobus circulis concentricis, qui nimirum circa idem <lb/>commune <expan abbr="centr&utilde;">centrum</expan> &longs;imul conuertuntur, non videntur præfa<lb/>ta, & ab ip&longs;o Philo&longs;opho adducta rectè procedere, autcon-<pb pagenum="213"/>cludere. </s>

<s>Quoniam &longs;icut circulus delatus, non minus ac de<lb/>ferens conuoluitur circa proprium centrum, ac &longs;imul cum <lb/>illo progreditur modo &longs;ibi connaturali; ita nec minus pro<lb/>portionatum &longs;ibi interuallum rotando videtur po&longs;&longs;e tran&longs;<lb/>mittere, de&longs;cribendo lineam rectam æqualem &longs;uæ periphe<lb/>riæ &longs;eu ab&longs;idi &longs;ecundum quam conuoluitur. </s>

Line 4088

<s>Quandoquidem deferens ex &longs;e vtitur pro<lb/>prio centro dum circa illud mouetur, <expan abbr="ip&longs;umq.">ip&longs;umque</expan> &longs;ecum rapit <lb/>dum ad vlteriora &longs;uper planum rectà progreditur: delatus <lb/>verò per accidens circa illud conuertitur; &longs;icut per accidens <lb/>etiam progreditur ad motum deferentis. </s>

<s>Quamobrem &longs;o<lb/>phi&longs;ticè ac deceptiua ratiocinatione inquit argumentari <lb/>eos, qui ab&longs;olutè, idem ambobus circulis e&longs;&longs;e centrum do<lb/>cent, eo quod ambo circa idem reuoluantur, ac inde infe<lb/>runt, vtrumlibet proportionato, & connaturali motu cir<lb/>cumferri debere: Quod e&longs;t vnumquemque illorum æqua<lb/>lem rectam &longs;uæ peripheriæ rotando de&longs;cribere; nempe ma<lb/>iorem circulum rectam maiorem, minorem verò minorem, <lb/>&longs;ecus quàm de facto accidit propter cau&longs;as explicatas. </s><pb pagenum="214"/>

<s>Hucu&longs;que ex mente, ac doctrina Ari&longs;totelis, qui tamen <lb/>mul<gap/>orum iudicio non videtur obiectam &longs;ibi difficultatem <lb/>&longs;atis infringere, vt quæ adhuc magna ex parte maneat in &longs;uo <lb/>robore. </s>

Line 4104

<s><expan abbr="Idemq.">Idemque</expan> è conuer&longs;o applicari pote&longs;t in contactu pe<lb/>ripheriæ maioris circuli cum recta breuiori, quam conficit <lb/>ad motum minoris circuli &longs;uper ab&longs;idem per &longs;e lati. </s>

<s>Ad diluendam igitur omnino prædictam difficultatem, <lb/>quæ multorum quippe vexauit ingenia, & pene in&longs;uperabi-<pb pagenum="215"/>lis apud aliquos extimatur, liceat aliunde totum negocium <lb/>au&longs;picari, nouumque aliquid in medium affere in eiu&longs;dem <lb/>Ari&longs;totelis, ac veterum Philo&longs;ophorum princip<gap/>s funda <lb/>tum. </s>

<s>Ad diluendam igitur omnino prædictam difficultatem, <lb/>quæ multorum quippe vexauit ingenia, & pene in&longs;uperabi-<pb xlink:href="005/01/223.jpg" pagenum="215"/>lis apud aliquos extimatur, liceat aliunde totum negocium <lb/>au&longs;picari, nouumque aliquid in medium affere in eiu&longs;dem <lb/>Ari&longs;totelis, ac veterum Philo&longs;ophorum princip<gap/>s funda <lb/>tum. </s>

<s>Ac primò quidem &longs;tabiliatur, motum cuiu&longs;libet circu<lb/>li &longs;ecundum ab&longs;idem, e&longs;&longs;e motum quendam mixtum ex du<lb/>plici latione; vna qua circumuoluitur, &longs;eu circa proprium <lb/>centrum fertur in gyrum; altera verò qua ad motum axis <lb/>rectà fertur &longs;uper planum quo ver&longs;us tendit ip&longs;emet axis. <lb/></s>

Line 4122

<s>Quamuis per accidens con<lb/>tingat, circulum deferentem, vel alium ex &longs;e, ac &longs;eor&longs;um ro<lb/>tando, tantum &longs;patium &longs;imul cum axe recta tran&longs;inittere, <lb/>quantum ip&longs;emet circulariter eodem tempore peragrare <lb/>valuerit. </s>

<s>Quia &longs;cilicet cum tota progre&longs;&longs;io à &longs;ua ip&longs;ius ro<pb pagenum="216"/>tatione dependeat, &longs;icut motus rectus progre&longs;&longs;ionis nece&longs;<lb/>&longs;ariò proportionatur motui circulari à quo pendet, ita <lb/>etiam linea de&longs;cripta per talem motum proportionari, & <lb/>adæquari debet lineæ de&longs;criptæ, &longs;eu peragratæ per circui<lb/>tionem. </s>

<s>Quia &longs;cilicet cum tota progre&longs;&longs;io à &longs;ua ip&longs;ius ro<pb xlink:href="005/01/224.jpg" pagenum="216"/>tatione dependeat, &longs;icut motus rectus progre&longs;&longs;ionis nece&longs;<lb/>&longs;ariò proportionatur motui circulari à quo pendet, ita <lb/>etiam linea de&longs;cripta per talem motum proportionari, & <lb/>adæquari debet lineæ de&longs;criptæ, &longs;eu peragratæ per circui<lb/>tionem. </s>

<s>His itaque &longs;ic &longs;tabilitis, atque &longs;uppo&longs;itis tanquam certis, <lb/>& cuidentibus, ad primam partem quæ&longs;tionis &longs;imul, ac dif<lb/>ficultatis propo&longs;itæ re&longs;pondetur, circulum delatum &longs;emper <lb/>æquale &longs;patium, ac circulum deferentem &longs;uper planum ro<lb/>tando, rectà tran&longs;initrere, &longs;iue maior eo fuerit, &longs;iue minor; <lb/>quia illud non tran&longs;mittit ex vi &longs;uæ rotationis, ac iuxta <lb/>men&longs;uram &longs;uæ circumferentiæ, &longs;ed ex vi &longs;ui raptus, & a&longs;por<lb/>tationis. </s>

Line 4138

<s>Adhuc tamen ex ei&longs;dem principijs <expan abbr="re&longs;põderi">re&longs;ponderi</expan> pote&longs;t, præ<lb/>fata nos experiri, quia minor circulus quando mouetur ad <lb/>motum alterius maioris motu mixto iam explicato, magis <lb/>participat de latione recta, quàm circulari; citius videlicet <lb/>progrediendo quàm rorando. </s>

<s>Cogitur enim rectà progre-<pb pagenum="217"/>di iuxta progre&longs;&longs;um axis, ac circuli maioris, <expan abbr="&longs;imulq.">&longs;imulque</expan> tardius <lb/>rotari quàm ille, minus &longs;patium eodem tempore tran&longs;init<lb/>tendo in &longs;ua minori circumuolutione: <expan abbr="proindeq.">proindeque</expan> per talem <lb/>rotationem, rectam quandam lineam de&longs;cribit maiorem, <lb/>quam &longs;it eius circunferentia propria. </s>

<s>Cogitur enim rectà progre-<pb xlink:href="005/01/225.jpg" pagenum="217"/>di iuxta progre&longs;&longs;um axis, ac circuli maioris, <expan abbr="&longs;imulq.">&longs;imulque</expan> tardius <lb/>rotari quàm ille, minus &longs;patium eodem tempore tran&longs;init<lb/>tendo in &longs;ua minori circumuolutione: <expan abbr="proindeq.">proindeque</expan> per talem <lb/>rotationem, rectam quandam lineam de&longs;cribit maiorem, <lb/>quam &longs;it eius circunferentia propria. </s>

<s>E contra verò, nam <lb/>cum circulus maior mouetur ad motum minoris, magis par<lb/>ticipat de latione circulari, quàm recta. </s>

Line 4154

<s>Etenim cum <lb/>planum à circulo attingatur per puncta, quæ &longs;unt extremita<lb/>tes diametrorum, & vterque circulus ex infinitis diametris <lb/>con&longs;tet; imò diametri cir culi maioris includant diametros <lb/>minoris; tot erunt puncta terminatiua diametrorum in cir<lb/>culo minori, quot &longs;unt in maiori, &longs;iue delato per quæ &longs;imili<lb/>ter omnia puncta &longs;ui plani valebit attingere. </s>

<s>Rur&longs;us dicendum e&longs;t tam circulum deferentem, quàm <lb/>circulum delatum omnes, ac &longs;ingulas partes diui&longs;ibiles, qu&ecedil; <lb/>&longs;unt in eadem linea plani per totidem partes &longs;uas &longs;ucce&longs;&longs;iuè <pb pagenum="218"/>attingere: hoc tamen di&longs;crimine, quod circulus deferens <lb/>illas attingit commen&longs;uratiuè, & adæquatè, circulus verò <lb/>delatus nonni&longs;i inadæquatè. </s>

<s>Rur&longs;us dicendum e&longs;t tam circulum deferentem, quàm <lb/>circulum delatum omnes, ac &longs;ingulas partes diui&longs;ibiles, qu&ecedil; <lb/>&longs;unt in eadem linea plani per totidem partes &longs;uas &longs;ucce&longs;&longs;iuè <pb xlink:href="005/01/226.jpg" pagenum="218"/>attingere: hoc tamen di&longs;crimine, quod circulus deferens <lb/>illas attingit commen&longs;uratiuè, & adæquatè, circulus verò <lb/>delatus nonni&longs;i inadæquatè. </s>

<s>Sicut enim circulus deferens <lb/>&longs;iue maior &longs;it, &longs;iue minor con&longs;tat ex infinitis partibus inde<lb/>terminatis, quæ mediant inter infinita puncta, ita etiam cir<lb/>culus delatus, per ea&longs;que non minus attingere poterit infi<lb/>nitas partes, quæ &longs;unt in plano. </s>

Line 4164

<s>Quapropter cum tota applicatio partium circumferentiæ <lb/>ad attingendas partes plani &longs;uper quod rotatur, fiat tum ex <lb/>vi ip&longs;ius rotationis, qua &longs;ucce&longs;&longs;iuè ip&longs;æ partes inclinantur <lb/>ad illas, tum ex vi motus recti quo &longs;ucce&longs;&longs;iuè etiam progre<lb/>diendo ad ca&longs;dem perueniunt: hinc fit, vt &longs;i lationes ip&longs;æ <lb/>æqualiter procedant, quemadmo dum in motu mixto circuli <lb/>deferentis, aut alterius per &longs;e &longs;eor&longs;um rotantis, æqualiter <lb/>etiam alterius quantitatis partes, ad partes alterius appli<lb/>centur, ac &longs;e tangendo ad inuicem commen&longs;urentur, & <lb/>adæquentur: E contra verò &longs;i non procedant æqualiter ip<lb/>&longs;æ lationes, &longs;ed vna alteram excedat in velocitate, aut tardi<lb/>tate, vt in motu mixto cuiu&longs;libet circuli delati, inæqualiter <lb/>etiam partes ip&longs;ius ad partes plani applicentur, ac inadæ<lb/>quatè adinuicem commen&longs;urentur. </s>

<s>Quod &longs;i non po&longs;&longs;it coexi&longs;tere in &longs;patio, exempli gratia <lb/>bipalmari cum linea recta bipalmari arcus circumferentiæ <lb/>paimaris, vel tripalmaris, quacunque rotatione ad inuicem <lb/>applicentur; hoc profectò intelligitur in quiete, atque in <lb/>termino ip&longs;ius motus: alioquin in tran&longs;itu, ac &longs;ucce&longs;siuè id <lb/>nullo modo repugnat, &longs;icutnec punctum globirectà &longs;uper <lb/>planum delati po&longs;t punctum ip&longs;ius plani, attingere partem <lb/>diui&longs;ibilem eiu&longs;dem plani, eique coexi&longs;tendo inadæquatè <pb pagenum="219"/>& &longs;ucce&longs;siuè commen&longs;urari, vt omnes penè Philo&longs;ophi fa<lb/>tentur. </s>

<s>Quod &longs;i non po&longs;&longs;it coexi&longs;tere in &longs;patio, exempli gratia <lb/>bipalmari cum linea recta bipalmari arcus circumferentiæ <lb/>paimaris, vel tripalmaris, quacunque rotatione ad inuicem <lb/>applicentur; hoc profectò intelligitur in quiete, atque in <lb/>termino ip&longs;ius motus: alioquin in tran&longs;itu, ac &longs;ucce&longs;siuè id <lb/>nullo modo repugnat, &longs;icutnec punctum globirectà &longs;uper <lb/>planum delati po&longs;t punctum ip&longs;ius plani, attingere partem <lb/>diui&longs;ibilem eiu&longs;dem plani, eique coexi&longs;tendo inadæquatè <pb xlink:href="005/01/227.jpg" pagenum="219"/>& &longs;ucce&longs;siuè commen&longs;urari, vt omnes penè Philo&longs;ophi fa<lb/>tentur. </s>

<s>Maior enim vel minor velocitas atque &longs;ucce&longs;sio in <lb/>tran&longs;itu, & in partium applicatione, ex vi alterius lationis <lb/>æquipollet maiori, vel minori exten&longs;ioni ip&longs;ius quantitatis <lb/>ad replendum æquale &longs;patium ei, quod occupatur ab alia <lb/>quantitate in eodem tempore, qua ratione dicuntur coexi<lb/>&longs;tere, ac inter &longs;e coaptari. </s>

Line 4184

<s>Siquidem velocius rotando, quàm progrediendo, nequit at<lb/>tingere tantam dimen&longs;ionem in plano, quantam ip&longs;e exhi<lb/>bet per circumuolutionem. </s>

<s>Vnde quod ei &longs;upere&longs;t exten<lb/>&longs;ionis circularis compen&longs;atur tardiori &longs;ucce&longs;&longs;ione, & appli-<pb pagenum="220"/>cationem &longs;ecundum lationem rectam ad proportionandum <lb/>&longs;e parti minori. </s>

<s>Vnde quod ei &longs;upere&longs;t exten<lb/>&longs;ionis circularis compen&longs;atur tardiori &longs;ucce&longs;&longs;ione, & appli-<pb xlink:href="005/01/228.jpg" pagenum="220"/>cationem &longs;ecundum lationem rectam ad proportionandum <lb/>&longs;e parti minori. </s>

<s>Atque hæc in re tam ambigua &longs;i minus <lb/>demon&longs;tra&longs;&longs;e, &longs;altem indica&longs;&longs;e, vel tenta&longs;&longs;e &longs;ufficiat. </s>

Line 4198

<s>Quod maximè vide<lb/>tur admirandum <expan abbr="c&umacr;">cum</expan> vterque circulus &longs;impliciter, ac &longs;ecun<lb/>dum &longs;e totum ad motum axis progrediendo, æquale &longs;pa<lb/>rium percurrat, vt vidimus, ac probatum e&longs;t in præcedenti<lb/>bus. </s>

<s>Ita tamen rem &longs;e habere &longs;ic o&longs;tenditur. </s><figure/>

<s>Ita tamen rem &longs;e habere &longs;ic o&longs;tenditur. </s><figure id="id.005.01.228.1.jpg" xlink:href="005/01/228/1.jpg"/>

<s>E&longs;to exempli gratia circulus maior ABCD, minor verò <lb/>EFGH circa commune centrum I &longs;uper planum KL. <expan abbr="Sintq.">Sintque</expan> <lb/>duo diametri maioris ad angulos rectos &longs;e&longs;e inter&longs;ecantes <lb/>AC, & BD; minoris verò in ip&longs;is contenti EG, & FH; ita <pb pagenum="221"/>vt BD &longs;it perpendicularis ip&longs;i KL. </s>

<s>E&longs;to exempli gratia circulus maior ABCD, minor verò <lb/>EFGH circa commune centrum I &longs;uper planum KL. <expan abbr="Sintq.">Sintque</expan> <lb/>duo diametri maioris ad angulos rectos &longs;e&longs;e inter&longs;ecantes <lb/>AC, & BD; minoris verò in ip&longs;is contenti EG, & FH; ita <pb xlink:href="005/01/229.jpg" pagenum="221"/>vt BD &longs;it perpendicularis ip&longs;i KL. </s>

<s>Rotetur autem vterque <lb/>circulus &longs;imul &longs;ecundum <expan abbr="ab&longs;id&etilde;">ab&longs;idem</expan> maioris dextror&longs;um quou&longs;<lb/>que punctum C perueniat, verbi gratia in L, ac &longs;emidiame<lb/>ter IC con&longs;tituatur in ML perpendicularis ip&longs;i KL: ac <lb/>per con&longs;equens IG in MN; ita vt punctum G reperia<lb/>tur in N. </s>

Line 4222

<s>dextror&longs;um promoueatur <lb/>quàm punctum H &longs;ibi corre&longs;pondens circuli minoris. </s>

<s>E contra tamen dicimus punctum A circuli maioris am-<pb pagenum="222"/>plius dextror&longs;um progredi, quàm punctum E circuli mino<lb/>ris quo illi corre&longs;pondet. </s>

<s>E contra tamen dicimus punctum A circuli maioris am-<pb xlink:href="005/01/230.jpg" pagenum="222"/>plius dextror&longs;um progredi, quàm punctum E circuli mino<lb/>ris quo illi corre&longs;pondet. </s>

<s>Po&longs;ita namque eadem reuolu<lb/>tione, I exi&longs;tente in M, ac C in L, A erit in V: con<lb/>&longs;titueretur enim tota diameter AIC in VML, in qua etiam <lb/>linea e&longs;&longs;et punctum E, nempe in X. </s>

Line 4248