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version 1.42, 2003/07/23 11:04:50

version 1.45, 2003/07/30 14:52:26

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<s id="id.000001">ARISTOTELIS <lb/>MECHANICA <lb/>Græca, emendata, Latina facta, & <lb/>Commentariis illu&longs;trata. <lb/></s>

<s id="id.000002">AB <lb/><emph type="italics"/>HENRICO MONANTHOLIO <lb/>Medico, & Mathematicarum artium <lb/>Profe&longs;&longs;ore Regio.<emph.end type="italics"/><lb/>A D <lb/>HENRICVM IIII. GALLIÆ & NAVARRÆ <lb/>Regem Chri&longs;tiani&longs;simum.</s><figure id="id.035.01.001.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.001.1.jpg"/>

<s id="id.000002">AB <lb/><emph type="italics"/>HENRICO MONANTHOLIO <lb/>Medico, & Mathematicarum artium <lb/>Profe&longs;&longs;ore Regio. </s>

<s><emph.end type="italics"/><lb/>A D <lb/>HENRICVM IIII. GALLIÆ & NAVARRÆ <lb/>Regem Chri&longs;tiani&longs;simum. </s><figure id="id.035.01.001.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.001.1.jpg"/>

<s id="id.000003">PARISIIS, <lb/>Apud IEREMIAM PERIER via Iacobæa, &longs;ub &longs;igno Bellerophontis.</s>

<s id="id.000004">M. D. XCIX. <lb/><emph type="italics"/>CUM PRIVILEGIO REGIS.<emph.end type="italics"/></s><pb/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.002.jpg"/><figure id="id.035.01.002.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.002.1.jpg"/>

<s id="id.000005">HENRICO IIII. <lb/>GALLIÆ ET NAVARRÆ <lb/>REGI CHRISTIANISSIMO. <lb/>S. P. D.</s>

<s id="id.000005">HENRICO IIII. <lb/>GALLIÆ ET NAVARRÆ <lb/>REGI CHRISTIANISSIMO. <lb/>S. P. D. </s>

<s id="id.000006">Ecce maie&longs;tati tuæ, <lb/>Rex Chri&longs;tiani&longs;&longs;ime, <lb/>nouum <expan abbr="fruct&utilde;">fructum</expan>, & tan<lb/>quam primitias tuæ à te <lb/>nuper re&longs;titutæ Acade<lb/>miæ, Mechanica Ari<lb/>&longs;totelis philo&longs;ophorum principis Gr&ecedil;<lb/>ca, emendata, Latina facta, & commen<lb/>tariis illu&longs;trata offero, dico, con&longs;ecro. <lb/></s>

<s id="id.000007">Noli, ob&longs;ecro te, ad Mechanicorum ti<lb/>tulum munus hoc, qua&longs;i minus inge<lb/>nuum, nec &longs;atis liberali ingenio, nedum <lb/>imperatorio & regali dignum, &longs;ubhor<lb/>re&longs;cere, & ex prima i&longs;ta <expan abbr="frõte">fronte</expan> de&longs;picere. <lb/></s>

<s id="id.000008"><expan abbr="Fer&utilde;t">Ferunt</expan> Platonem, quo philo&longs;ophorum <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.003.jpg"/>nemo de Deo diuinius, <expan abbr="neq;">neque</expan> &longs;anctius <expan abbr="s&etilde;-&longs;it">sen<lb/>&longs;it</expan>, <expan abbr="c&utilde;interrogaretur">cum interrogaretur</expan>, quid ageret Deus, <lb/>re&longs;pondi&longs;&longs;e <foreign lang="greek">a)ei gewmetrei=n.</foreign> Hoc verbum Lati<lb/>nè expre&longs;&longs;um &longs;ignificat. </s>

<s id="id.000009">A&longs;&longs;iduè terram <lb/>metiri. </s>

<s id="id.000009">Hoc verbum Lati<lb/>nè expre&longs;&longs;um &longs;ignificat, A&longs;&longs;iduè terram <lb/>metiri. </s>

<s id="id.000010">Quæ actio &longs;i &longs;impliciter &longs;pecte<lb/>tur, & à Geometri&ecedil; nomine ridiculo, vt <lb/>alibi appellat Plato, <expan abbr="exp&etilde;datur">expendatur</expan>, ridicula, <lb/>& Dei maie&longs;tate indigna iudicabitur. <lb/></s>

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<s id="id.000017">An non huius totius ad omnes <lb/>&longs;uas partes, & omnium <expan abbr="&longs;uar&utilde;">&longs;uarum</expan> partium, <lb/>particularum que cum inter &longs;e, tum ad <lb/>ip&longs;um &longs;ummus e&longs;t con&longs;en&longs;us, con&longs;pira<lb/>tio &longs;umma, omnium hominum oculis <lb/>& menti iucundi&longs;sima &longs;ymmetria, pro<lb/>portio, æquabilitas, vnà cum totius fi<lb/>gura pulcherrima, & conuenienti&longs;&longs;ima, <lb/>quæ vnica e&longs;t &longs;uperficie terminata pari<lb/>bus ab vno puncto vndique di&longs;tante <lb/>interuallis, & cum tot <expan abbr="a&longs;tror&utilde;">a&longs;trorum</expan> tanquam <lb/>gemmarum pretio&longs;i&longs;&longs;imarum hîc illîc <lb/>in eminentiori, & apparentiori &longs;ui par<lb/>te collocatorum perenni luce, qua qua<lb/>litate nec formo&longs;ior, nec <expan abbr="homin&utilde;">hominum</expan> ocu<lb/>lis gratior, nec v&longs;ibus humanis vtilior <lb/>apparere pote&longs;t: quod eius pulchritudi<lb/>nem vbique o&longs;tentat, & mirabiles &longs;ui <lb/>ip&longs;ius amores excitat? </s>

<s id="id.000018">Deus igitur, <expan abbr="pr&ecedil;ter-quã">pr&ecedil;ter<lb/>quam</expan> quod e&longs;t accurati&longs;&longs;imus, <expan abbr="a&longs;&longs;iduu&longs;q;">a&longs;&longs;iduu&longs;que</expan> <lb/>Geometra, diuini Platonis <expan abbr="&longs;ent&etilde;tia">&longs;ententia</expan>, e&longs;t <lb/>etiam no&longs;tra, & operum tot magnifi<lb/>corum euidentia, &longs;apienti&longs;&longs;imus, opti<pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.006.jpg"/>mus, potenti&longs;&longs;imus <foreign lang="greek">mhxaniko\s,</foreign> & <foreign lang="greek">mhxanopoio\s.</foreign><lb/>Ip&longs;e idem, qui <foreign lang="greek">makro/kosmon</foreign> magnum mun<lb/>dum fecit, fecit & <foreign lang="greek">mikro/kosmon</foreign> <expan abbr="paru&utilde;">paruum</expan> mun<lb/>dum, hominem &longs;cilicet: & fecit ad ima<lb/>ginem &longs;uam, atque vt &longs;e imitaretur beni<lb/>gni&longs;&longs;ima liberalitate impertitus e&longs;t ei <lb/>mentem, quæ e&longs;&longs;et <foreign lang="greek">te/xnh te/xnwn,</foreign> ars artium, <lb/>& manum, quæ e&longs;&longs;et <foreign lang="greek">o)/rganon o)rga/nwn,</foreign> in&longs;tru<lb/>mentum in&longs;trumentorum, quibus ho<lb/>mo, quem volebat e&longs;&longs;e &longs;apienti&longs;&longs;imum <lb/>animalium, machinas & in&longs;trumenta <lb/>alia fabricaretur, & iis adiutus &longs;olus, vel <lb/>cum paucis onera quantumuis ingentia <lb/>dimoueret, deduceret, quo vellet collo<lb/>caret: vrbes, <expan abbr="t&etilde;pla">templa</expan>, palatia, collegia, por<lb/>ticus, pontes, domos ædificaret, perde<lb/>ret, re&longs;tauraret, con&longs;eruaret: terram ver<lb/>teret, in terræ vi&longs;cera de&longs;cenderet, terræ <lb/>campos, valles, montes bigis, quadrigis <lb/>peragraret: maria omnia, fluuios remis, <lb/>velis tranaret: ventis imperaret: anima<lb/>lium genus omne &longs;ibi &longs;ubiiceret: tantas <lb/><expan abbr="deniq;">denique</expan>, & tam multas res faceret, vt eas, <lb/>ni&longs;i quotidie fieri, & factas e&longs;&longs;e &longs;æpius <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.007.jpg"/>alij homines &longs;pectarent, omninò fieri <lb/>non po&longs;&longs;e iurarent. </s>

<s>Ip&longs;e idem, qui <foreign lang="greek">makro/kosmon</foreign> magnum mun<lb/>dum fecit, fecit & <foreign lang="greek">mikro/kosmon</foreign> <expan abbr="paru&utilde;">paruum</expan> mun<lb/>dum, hominem &longs;cilicet: & fecit ad ima<lb/>ginem &longs;uam, atque vt &longs;e imitaretur beni<lb/>gni&longs;&longs;ima liberalitate impertitus e&longs;t ei <lb/>mentem, quæ e&longs;&longs;et <foreign lang="greek">te/xnh te/xnwn,</foreign> ars artium, <lb/>& manum, quæ e&longs;&longs;et <foreign lang="greek">o)/rganon o)rga/nwn,</foreign> in&longs;tru<lb/>mentum in&longs;trumentorum, quibus ho<lb/>mo, quem volebat e&longs;&longs;e &longs;apienti&longs;&longs;imum <lb/>animalium, machinas & in&longs;trumenta <lb/>alia fabricaretur, & iis adiutus &longs;olus, vel <lb/>cum paucis onera quantumuis ingentia <lb/>dimoueret, deduceret, quo vellet collo<lb/>caret: vrbes, <expan abbr="t&etilde;pla">templa</expan>, palatia, collegia, por<lb/>ticus, pontes, domos ædificaret, perde<lb/>ret, re&longs;tauraret, con&longs;eruaret: terram ver<lb/>teret, in terræ vi&longs;cera de&longs;cenderet, terræ <lb/>campos, valles, montes bigis, quadrigis <lb/>peragraret: maria omnia, fluuios remis, <lb/>velis tranaret: ventis imperaret: anima<lb/>lium genus omne &longs;ibi &longs;ubiiceret: tantas <lb/><expan abbr="deniq;">denique</expan>, & tam multas res faceret, vt eas, <lb/>ni&longs;i quotidie fieri, & factas e&longs;&longs;e &longs;æpius <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.007.jpg"/>alij homines &longs;pectarent, omninò fieri <lb/>non po&longs;&longs;e iurarent. </s>

<s id="id.000019">Iidem cum facta<lb/>rum rationes, virium que in in&longs;trumen<lb/>tis, & machinis adhibitis cau&longs;as non in<lb/>telligunt, miracula e&longs;&longs;e pleno ore pro<lb/>clamant. </s>

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<s id="id.000057">HENRICVS MONANTHOLIVS.</s></section><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.018.jpg"/><section>

<s id="id.000058">A D <lb/>HENRICVM IIII. <lb/>GALLIÆ ET NAVARRÆ <lb/>Regem Chri&longs;tiani&longs;&longs;imum.</s>

<s id="id.000058">A D <lb/>HENRICVM IIII. <lb/>GALLIÆ ET NAVARRÆ <lb/>Regem Chri&longs;tiani&longs;&longs;imum. </s>

<s id="id.000059"><emph type="italics"/>Pacatos fecit tua nos victoria ciues. <lb/></s>

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<s id="id.000065"><emph type="italics"/>Sed mendis f&oelig;dus merito &longs;ine honore iacebat,<emph.end type="italics"/></s>

<s id="id.000066"><emph type="italics"/>Non authore &longs;uo dignus Aristotele.<emph.end type="italics"/></s>

<s id="id.000066"><emph type="italics"/>Non authore &longs;uo dignus Aristotele. <emph.end type="italics"/></s>

<s id="id.000067"><emph type="italics"/>Lectus erat nulli, nulli intellectus agebat<emph.end type="italics"/></s>

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<s id="id.000077">PRAEFATIO IN <lb/>MECHANICA ARISTO<lb/>TELIS, AD LECTOREM.</s>

<s id="id.000077">PRAEFATIO IN <lb/>MECHANICA ARISTO<lb/>TELIS, AD LECTOREM. </s>

<s id="id.000078">Philosophari in vno rerum quo<lb/>libet genere, <expan abbr="cãdide">candide</expan> lector, res e&longs;t per<lb/>quam dulcis. </s>

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<s id="id.000097">quid <lb/>enim e&longs;t, quod non &longs;uis v&longs;ibus accommodarit? </s>

<s id="id.000098">quibus &longs;i <lb/><expan abbr="bonitat&etilde;">bonitatem</expan> exemplo Dei Opt. Max. &longs;emper <expan abbr="adi&utilde;xerit">adiunxerit</expan>, alte<lb/>rùm <expan abbr="quoq;">quoque</expan> <expan abbr="De&utilde;">Deum</expan> inter mortales e&longs;&longs;e dicere non recu&longs;em. <lb/></s>

<s id="id.000098">quibus &longs;i <lb/><expan abbr="bonitat&etilde;">bonitatem</expan> exemplo Dei Opt. Max. &longs;emper <expan abbr="adi&utilde;xerit">adiunxerit</expan>, alte<lb/>rùm <expan abbr="quoq;">quoque</expan> <expan abbr="De&utilde;">Deum</expan> inter mortales e&longs;&longs;e dicere non recu&longs;em. <lb/></s>

<s id="id.000099">E&longs;t certè animus in homine ars <expan abbr="arti&utilde;">artium</expan>. </s>

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<s id="id.000155">Da mihi vbi &longs;i&longs;tam pedem, & hanc ego <expan abbr="terrã">terram</expan> loco &longs;uo dimo<lb/>uebo. </s>

<s id="id.000156">cuius admirabilis dicti <expan abbr="c&utilde;">cum</expan> rogatus e&longs;&longs;et à rege, vt &longs;pe<lb/>cimen aliquod ederet, vna manu læua quinquies millenûm <lb/>modiorum <expan abbr="põdus">pondus</expan> attraxit: nauem in &longs;iccum littus eiectam <lb/>& grauiter <expan abbr="oneratã">oneratam</expan> ad &longs;e perinde pertraxit, ac &longs;i in mari re<lb/>mis, veli&longs;ve impul&longs;a fui&longs;&longs;et: aliam po&longs;tea recens <expan abbr="cõ&longs;tructam">con&longs;tructam</expan> <lb/>ingentis magnitudinis ab Herone regi Ægyptiorum Ptolo<lb/>mæo dono mittendam, quam omnes <expan abbr="Syracu&longs;anor&utilde;">Syracu&longs;anorum</expan> ciuium <lb/>vires <expan abbr="cõiunctæ">coniunctæ</expan> dimouere loco non <expan abbr="potuerãt">potuerant</expan>, vt &longs;olus Hiero <lb/>machinis adiutus in mare educerer, perfecit: & <expan abbr="quid&etilde;">quidem</expan> cum <lb/>tanta ip&longs;ius regis admiratione, vt exclamarit, <foreign lang="greek">a)po\ tau/ths th=s <lb/>h(me/ras peri\ p=anto\s *arxhmh/dei le/gonti pisteute/on.</foreign> Ab hoc die <lb/>quicquid dixerit Archimedes huic <expan abbr="credend&utilde;">credendum</expan>. </s>

<s> Ab hoc die <lb/>quicquid dixerit Archimedes huic <expan abbr="credend&utilde;">credendum</expan>. </s>

<s id="id.000157">At ab eo die <lb/>ab Archimede prodijt illud problema inexpertis in credibi<lb/>le, eruditis tamen demon&longs;tratum. </s>

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<s id="id.000198">Terra, inquit, marique &longs;imul c&oelig;ptæ oppugnari <lb/>Syracu&longs;æ, terra ab Hexapylo: mari ab Acradina. </s>

<s id="id.000199">Et habui&longs;<lb/>&longs;et tantò impetu c&oelig;pta res fortunam, ni&longs;i vnus homo Syra<lb/>cu&longs;is ea <expan abbr="t&etilde;pe&longs;tate">tempe&longs;tate</expan> fui&longs;&longs;et Archimedes. </s>

<s id="id.000200">Is erat vnicus &longs;pecta<lb/>tor c&oelig;li &longs;iderum que: mirabilior tamen inuentor ac machi<lb/>nator bellicorum <expan abbr="torm&etilde;torum">tormentorum</expan>, operumque: quibus ea quæ <lb/>ho&longs;tes ingenti mole agerent ip&longs;e perleui momento ludifi<pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.028.jpg"/>caretur. </s>

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<s id="id.000231"><emph type="italics"/>Extraict du Priuilege du Roy.<emph.end type="italics"/></s>

<s id="id.000231"><emph type="italics"/>Extraict du Priuilege du Roy. <emph.end type="italics"/></s>

<s id="id.000232"><foreign lang="fr">Par grace & priuilege du Roy, il e&longs;t permis à Ie<lb/>remie Perier marchant Libraire à Paris, d'impri<lb/>mer ou faire imprimer vn liure intitulé</foreign> <emph type="italics"/>Ari&longs;totelis <lb/>Mechanica, Græca emendata, Latina facta, & commen<lb/>tarijs illu&longs;trata, ab Henrico Monantholio Medico, & Ma<lb/>thematicarum artium Profe&longs;&longs;ore Regio.<emph.end type="italics"/> </s>

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<s id="id.000236"><foreign lang="fr"><emph type="italics"/>D<emph.end type="italics"/>E LAVETS.</foreign></s></section><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.032.jpg"/><section>

<s id="id.000237">INDEX MEMORABILIVM <lb/>IN MECHANICIS ARISTOTELIS <lb/>& eorum Commentarijs.<lb/><arrow.to.target n="table1"/></s><table><table.target id="table1"/><row><cell><emph type="italics"/>A<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/><foreign lang="greek">*abussos</foreign> unde. pag.<emph.end type="italics"/></cell><cell>209</cell></row><row><cell><emph type="italics"/>Ab&longs;is pro circunferentia rotæ.<emph.end type="italics"/></cell><cell>100</cell></row><row><cell><emph type="italics"/>Acatium ante naues.<emph.end type="italics"/></cell><cell>65</cell></row><row><cell><emph type="italics"/>Actiones manuum in opificijs egent &longs;tatione, vel &longs;eßione tantùm<emph.end type="italics"/></cell><cell>194</cell></row><row><cell><emph type="italics"/>Admiratio quid.<emph.end type="italics"/></cell><cell>4.5</cell></row><row><cell><emph type="italics"/>Agriculturæ nece&longs;&longs;aria.<emph.end type="italics"/></cell><cell>14</cell></row><row><cell><emph type="italics"/>Ædes rotunda mirifica.<emph.end type="italics"/></cell><cell>10</cell></row><row><cell><emph type="italics"/>Ædificium durabile rectà in&longs;i&longs;tit.<emph.end type="italics"/></cell><cell>196</cell></row><row><cell><emph type="italics"/>Æolus primus v&longs;us velis.<emph.end type="italics"/></cell><cell>92</cell></row><row><cell><emph type="italics"/>Æquale e&longs;t cau&longs;a quietis.<emph.end type="italics"/></cell><cell>193.196</cell></row><row><cell><emph type="italics"/>Æquilibrium in ponderatione.<emph.end type="italics"/></cell><cell>149</cell></row><row><cell><foreign lang="greek">*alourgopw/lai</foreign> <emph type="italics"/>qui.<emph.end type="italics"/></cell><cell>47</cell></row><row><cell><emph type="italics"/>Ambulare pronum conuenit brutis.<emph.end type="italics"/></cell><cell>194</cell></row><row><cell><emph type="italics"/>Angulus rectus e&longs;t angulus æqualitatis, ideóque quietis.<emph.end type="italics"/></cell><cell>193.196</cell></row><row><cell><emph type="italics"/>Ad angulos rectos omnia <expan abbr="quie&longs;c&utilde;t">quie&longs;cunt</expan>.<emph.end type="italics"/></cell><cell>196</cell></row><row><cell><emph type="italics"/>Antemna quid.<emph.end type="italics"/></cell><cell>92</cell></row><row><cell><emph type="italics"/>Antemnæ motio.<emph.end type="italics"/></cell><cell>92</cell></row><row><cell><emph type="italics"/>Antiperi&longs;ta&longs;is medij confert ad motum proiecti.<emph.end type="italics"/></cell><cell>203</cell></row><row><cell><emph type="italics"/>Antiphonis dictum, cum iret ad &longs;uppli-cium.<emph.end type="italics"/></cell><cell>12</cell></row><row><cell><emph type="italics"/>Antiphonis ver&longs;us de natura & arte.<emph.end type="italics"/></cell><cell>8. 12</cell></row><row><cell><emph type="italics"/>Arbores, & plantæ in&longs;i&longs;lunt plane terræ ad rectos angulos.<emph.end type="italics"/></cell><cell>196</cell></row><row><cell><emph type="italics"/>Archelai regis factum in eclip&longs;i Solis.<emph.end type="italics"/></cell><cell>5</cell></row><row><cell><emph type="italics"/>Archimedeum problema, datum pondus data potentia mouere.<emph.end type="italics"/></cell><cell>60</cell></row><row><cell><emph type="italics"/>Archimedis factum Mechanicum.<emph.end type="italics"/></cell><cell>12</cell></row><row><cell><emph type="italics"/>Architecturæ tres partes.<emph.end type="italics"/></cell><cell>9</cell></row><row><cell><emph type="italics"/>Argo prima nauis.<emph.end type="italics"/></cell><cell>62</cell></row><row><cell><emph type="italics"/>Ari&longs;toteles reprehen&longs;us à Nonio.<emph.end type="italics"/></cell><cell>84</cell></row><row><cell><emph type="italics"/>Ars &longs;lectit naturam, & ad alium &longs;co-pum vertit.<emph.end type="italics"/></cell><cell>6</cell></row><row><cell><emph type="italics"/>Ars e&longs;t admirationis plena.<emph.end type="italics"/></cell><cell>6</cell></row><row><cell><emph type="italics"/>Artis, & naturæ differentia.<emph.end type="italics"/></cell><cell>6</cell></row><row><cell><emph type="italics"/>Artium diui&longs;io in liberales, & &longs;ordi-das.<emph.end type="italics"/></cell><cell>3</cell></row><row><cell><emph type="italics"/>Artes liberales.<emph.end type="italics"/></cell><cell>3</cell></row><row><cell><emph type="italics"/>Artes pueriles.<emph.end type="italics"/></cell><cell>3</cell></row><row><cell><emph type="italics"/>Artes magnæ.<emph.end type="italics"/></cell><cell>3</cell></row><row><cell><emph type="italics"/>Artes imperantes.<emph.end type="italics"/></cell><cell>3.4</cell></row><row><cell><emph type="italics"/>Artes architectonicæ.<emph.end type="italics"/></cell><cell>3</cell></row><row><cell><emph type="italics"/>Ars Typographica nihil e&longs;&longs;et &longs;ine co-chlea.<emph.end type="italics"/></cell><cell>133</cell></row><row><cell><emph type="italics"/>A&longs;inus, & aues longo collo vident c&oelig;-lum, vt homo.<emph.end type="italics"/></cell><cell>195</cell></row><row><cell><emph type="italics"/>Axis in peritrochio.<emph.end type="italics"/></cell><cell>120</cell></row><row><cell><foreign lang="greek">*auto/mata.</foreign></cell><cell>10</cell></row><row><cell><emph type="italics"/>B<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Baiulus cum &longs;uo onere e&longs;t turbo, vel conus inuer&longs;us.<emph.end type="italics"/></cell><cell>199.200</cell></row><row><cell><emph type="italics"/>Baiuli Pari&longs;ien&longs;es facile ferunt ingentia pondera.<emph.end type="italics"/></cell><cell>198.199</cell></row><row><cell><emph type="italics"/>Baiuli cum onere tutò a&longs;cendunt, pericu-losè de&longs;cendunt.<emph.end type="italics"/></cell><cell>199</cell></row><row><cell><emph type="italics"/>B. Feratinus Amerinus <expan abbr="cãcellariæ">cancellariæ</expan> Apo-&longs;tolicæ regens con&longs;ecrat, & compreca-tur multa &longs;uper crucem apici obeli&longs;ci imponendam.<emph.end type="italics"/></cell><cell>142</cell></row><row><cell><emph type="italics"/>Bombi tormentorum multi editi &longs;tatim atque crux impo&longs;ita fuit apici obe-li&longs;ci.<emph.end type="italics"/></cell><cell>142</cell></row><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.033.jpg"/><row><cell><emph type="italics"/>Bouilli error, qui putabat rectam iuuen-tam æqualem peripheriæ ex circuli &longs;uper planum reuolutione.<emph.end type="italics"/></cell><cell>174</cell></row><row><cell><emph type="italics"/>Boues ad <expan abbr="aratr&utilde;">aratrum</expan> pariter &longs;ubiugandi.<emph.end type="italics"/></cell><cell>192</cell></row><row><cell><emph type="italics"/>Boüm in iugo imbecillior &longs;ubleuari po-te&longs;t.<emph.end type="italics"/></cell><cell>192</cell></row><row><cell><emph type="italics"/>Bruta ventrem ad terram conuer&longs;um habent.<emph.end type="italics"/></cell><cell>195</cell></row><row><cell><emph type="italics"/>Bruti&longs;pina pedibus ad rectos imminet.<emph.end type="italics"/></cell><cell>198</cell></row><row><cell><emph type="italics"/>Brutum nihil admiratur.<emph.end type="italics"/></cell><cell>5</cell></row><row><cell><emph type="italics"/>Bruta nonnulla apta <expan abbr="fer&etilde;dis">ferendis</expan> &longs;arcinis.<emph.end type="italics"/></cell><cell>198</cell></row><row><cell><emph type="italics"/>Brutum nullum pote&longs;t &longs;edere.<emph.end type="italics"/></cell><cell>194</cell></row><row><cell><emph type="italics"/>C<emph.end type="italics"/></cell><cell/></row><row><cell><foreign lang="greek">*ka/iar</foreign> <emph type="italics"/>in fund a quid &longs;it.<emph.end type="italics"/></cell><cell>117</cell></row><row><cell><emph type="italics"/>Calliæ Rhodien&longs;is factum <expan abbr="mechanic&utilde;">mechanicum</expan>.<emph.end type="italics"/></cell><cell>12</cell></row><row><cell><emph type="italics"/>Cardanus reprehen&longs;us à Scaligero.<emph.end type="italics"/></cell><cell>145</cell></row><row><cell><emph type="italics"/>Cardanus ob&longs;curè & imper&longs;ectè: inge-niosè tamen&longs;crip&longs;it.<emph.end type="italics"/></cell><cell>180</cell></row><row><cell><emph type="italics"/>Carche&longs;ium quid.<emph.end type="italics"/></cell><cell>92</cell></row><row><cell><emph type="italics"/>Cathelina mu&longs;ca Rhemen&longs;ibus dicta e&longs;t <expan abbr="ex&etilde;plar">exemplar</expan> puncti duabus lationibus eo-dem tempore moti.<emph.end type="italics"/></cell><cell>32.33</cell></row><row><cell><emph type="italics"/>Cauda e&longs;t omnipi&longs;ci progubernaculo.<emph.end type="italics"/></cell><cell>77</cell></row><row><cell><emph type="italics"/>Celeritas duplex.<emph.end type="italics"/></cell><cell>27</cell></row><row><cell><emph type="italics"/>Centrobarica pars Mechanices.<emph.end type="italics"/></cell><cell>11</cell></row><row><cell><emph type="italics"/>Cercopithecus proxime accedit ad figu-ram hominis.<emph.end type="italics"/></cell><cell>195</cell></row><row><cell><emph type="italics"/>Cercopithecus, & &longs;imia e&longs;t ridicula ho-minis imitatio.<emph.end type="italics"/></cell><cell>195</cell></row><row><cell><emph type="italics"/>Cercopitheci manus differt ab hominis manu.<emph.end type="italics"/></cell><cell>195</cell></row><row><cell><emph type="italics"/>Cercopitheci pollex non e&longs;t <foreign lang="greek">a)nti/xeir,</foreign> vt in manu hominis.<emph.end type="italics"/></cell><cell>195</cell></row><row><cell><emph type="italics"/>Centrum duorum circulorum connexo-rum non e&longs;t idem.<emph.end type="italics"/></cell><cell>173</cell></row><row><cell><emph type="italics"/>Chirurgi togati nolunt dentes cuellere, licet&longs;u operatio chirurgica.<emph.end type="italics"/></cell><cell>153</cell></row><row><cell><emph type="italics"/>Circini author Dædalus.<emph.end type="italics"/></cell><cell>17</cell></row><row><cell><emph type="italics"/>Circulus e&longs;t <expan abbr="principi&utilde;">principium</expan> omnium virium, quæ&longs;unt in machinis motricibus.<emph.end type="italics"/></cell><cell>15</cell></row><row><cell><emph type="italics"/>Circulus admirabilißimus.<emph.end type="italics"/></cell><cell>15</cell></row><row><cell><emph type="italics"/>Circulus habet in &longs;e quinque repugnan-tias.<emph.end type="italics"/></cell><cell>16</cell></row><row><cell><emph type="italics"/>Circulus &longs;ecit miracula in templis paga-norum.<emph.end type="italics"/></cell><cell>25</cell></row><row><cell><emph type="italics"/>Circulus ante, & pone mouetur &longs;imul.<emph.end type="italics"/></cell><cell>20.21</cell></row><row><cell><emph type="italics"/>Circulus maior ad minorem &longs;emper nu-tum habet.<emph.end type="italics"/></cell><cell>106</cell></row><row><cell><emph type="italics"/>Circuli nutus e&longs;t perpetuus.<emph.end type="italics"/></cell><cell>107</cell></row><row><cell><emph type="italics"/>Circuli qua&longs;i motus e&longs;t perpetuus.<emph.end type="italics"/></cell><cell>107</cell></row><row><cell><emph type="italics"/>Circuli minores infiniti &longs;unt in maiore circulo.<emph.end type="italics"/></cell><cell>108</cell></row><row><cell><emph type="italics"/>Circuli maiores &longs;unt mouentiores.<emph.end type="italics"/></cell><cell>109</cell></row><row><cell><emph type="italics"/>Circulus <expan abbr="cõtingit">contingit</expan> <expan abbr="plan&utilde;">planum</expan> in vno <expan abbr="p&utilde;cto">puncto</expan>.<emph.end type="italics"/></cell><cell>101</cell></row><row><cell><emph type="italics"/>Circuli maioris minor e&longs;t angulus conta-ctus quam minoris.<emph.end type="italics"/></cell><cell>115</cell></row><row><cell><emph type="italics"/>Circulus maior cum minore per æqualem orbitam reuoluitur & contra.<emph.end type="italics"/></cell><cell>164</cell></row><row><cell><emph type="italics"/>Circuli <expan abbr="cõcentrici">concentrici</expan> inæquales iuncti æqua-lem orbitam <expan abbr="percurr&utilde;t">percurrunt</expan>.<emph.end type="italics"/></cell><cell>166.167.174</cell></row><row><cell><emph type="italics"/>Circuli maioris motus &longs;ecundum natu-ram maior e&longs;t quam minoris.<emph.end type="italics"/></cell><cell>43</cell></row><row><cell><emph type="italics"/>in Circulo in&longs;criptas &longs;i &longs;ecet recta ad re-ctos ab&longs;ci&longs;&longs;a exdiametro erit maxima & <gap/>pinquior remotiore maior.<emph.end type="italics"/></cell><cell>68.69</cell></row><row><cell><emph type="italics"/>Circulum minorem qui datum maiorem interius tangat de&longs;cribere.<emph.end type="italics"/></cell><cell>41</cell></row><row><cell><emph type="italics"/>C&oelig;li motus unde.<emph.end type="italics"/></cell><cell>104</cell></row><row><cell><emph type="italics"/>C&oelig;lum videre quid apud <expan abbr="Platon&etilde;">Platonem</expan>.<emph.end type="italics"/></cell><cell>195</cell></row><row><cell><emph type="italics"/><expan abbr="Col&utilde;ba">Columba</expan> volans Acchitæ <expan abbr="nõ">non</expan> e&longs;t fabula.<emph.end type="italics"/></cell><cell>26</cell></row><row><cell><emph type="italics"/>Contraria quæ &longs;int verè.<emph.end type="italics"/></cell><cell>18</cell></row><row><cell><emph type="italics"/>Commotum facilius mouetur, quam quie&longs;cens.<emph.end type="italics"/></cell><cell>199</cell></row><row><cell><emph type="italics"/>Connexum & concauum non &longs;unt con-traria.<emph.end type="italics"/></cell><cell>19</cell></row><row><cell><emph type="italics"/>Cochlea quid.<emph.end type="italics"/></cell><cell>131</cell></row><row><cell><emph type="italics"/>Cochleæ effecta.<emph.end type="italics"/></cell><cell>133</cell></row><row><cell><emph type="italics"/>Cochlea magnes vires habet.<emph.end type="italics"/></cell><cell>133</cell></row><row><cell><emph type="italics"/>Cochlea infinita.<emph.end type="italics"/></cell><cell>133</cell></row><row><cell><emph type="italics"/>Cochleæ Ari&longs;toteles non meminit.<emph.end type="italics"/></cell><cell>131</cell></row><row><cell><emph type="italics"/>Cochlea e&longs;t cuneus multiplicatus, vel vnus cuneus continuatus.<emph.end type="italics"/></cell><cell>131</cell></row><row><cell><emph type="italics"/>Cuneus e&longs;t vectu duplicatus.<emph.end type="italics"/></cell><cell>127</cell></row><row><cell><emph type="italics"/>Cuneum vicem gerere duorum vectium demon&longs;tratio linearis.<emph.end type="italics"/></cell><cell>130</cell></row><row><cell><emph type="italics"/>Cuneus quid.<emph.end type="italics"/></cell><cell>126</cell></row><row><cell><emph type="italics"/>Cunci v&longs;us.<emph.end type="italics"/></cell><cell>127</cell></row><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.034.jpg"/><row><cell><emph type="italics"/>Cuneimagna vis.<emph.end type="italics"/></cell><cell>127.127</cell></row><row><cell><emph type="italics"/>Cuneo magnæ moles diuiduntur.<emph.end type="italics"/></cell><cell>125</cell></row><row><cell><emph type="italics"/>Crocæ Ari&longs;toteliquid.<emph.end type="italics"/></cell><cell>123</cell></row><row><cell><emph type="italics"/>Crocæ rotundæ.<emph.end type="italics"/></cell><cell>122.123</cell></row><row><cell><emph type="italics"/>Cubus &longs;tabilißima figurarum.<emph.end type="italics"/></cell><cell>103</cell></row><row><cell><emph type="italics"/>Currus iam commotus facilius moue-tur.<emph.end type="italics"/></cell><cell>200</cell></row><row><cell><emph type="italics"/>D<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Dædali &longs;tatuæliberæ, & ligatæ.<emph.end type="italics"/></cell><cell>25</cell></row><row><cell><emph type="italics"/>Decubitus &longs;anorum in lecto.<emph.end type="italics"/></cell><cell>176</cell></row><row><cell><emph type="italics"/>Dens corro&longs;us eximidebet.<emph.end type="italics"/></cell><cell>153</cell></row><row><cell><emph type="italics"/>Dens non temere eximi debet.<emph.end type="italics"/></cell><cell>153</cell></row><row><cell><emph type="italics"/>Dens forcipe facilius, quam manu euelli-tur.<emph.end type="italics"/></cell><cell>153</cell></row><row><cell><emph type="italics"/>Dentiducus quid.<emph.end type="italics"/></cell><cell>132</cell></row><row><cell><emph type="italics"/><expan abbr="D&etilde;tes">Dentes</expan> <expan abbr="animali&utilde;">animalium</expan> inci&longs;ij &longs;unt cunei.<emph.end type="italics"/></cell><cell>129</cell></row><row><cell><emph type="italics"/>Dens priu&longs;quam eximatur duo fieri po-&longs;tulat.<emph.end type="italics"/></cell><cell>154</cell></row><row><cell><emph type="italics"/>Dentis euellendi differentia à clauo in-fixo.<emph.end type="italics"/></cell><cell>154</cell></row><row><cell><emph type="italics"/>Deusnon admiratur.<emph.end type="italics"/></cell><cell>5</cell></row><row><cell><emph type="italics"/>Diaconus &longs;acris ve&longs;tibus indutus imponit crucem apici obeli&longs;ci.<emph.end type="italics"/></cell><cell>142</cell></row><row><cell><emph type="italics"/>Diameter circuli, & Sphæræ in&longs;i&longs;tit plano ad rectos.<emph.end type="italics"/></cell><cell>105</cell></row><row><cell><emph type="italics"/>Diametri ad peripheriam quæratio.<emph.end type="italics"/></cell><cell>32</cell></row><row><cell><emph type="italics"/>Dies impo&longs;itæ crucis obeli&longs;co.<emph.end type="italics"/></cell><cell>142</cell></row><row><cell><emph type="italics"/>Dolabra e&longs;t cuneus.<emph.end type="italics"/></cell><cell>130</cell></row><row><cell><emph type="italics"/>Dominicus Fontana machinator in&longs;i-gnis.<emph.end type="italics"/></cell><cell>139</cell></row><row><cell><emph type="italics"/>Dominici Fontanæ triumphus.<emph.end type="italics"/></cell><cell>142</cell></row><row><cell><emph type="italics"/>Domus integra à &longs;undamentis &longs;ublata, & aliò tran&longs;lata.<emph.end type="italics"/></cell><cell>133</cell></row><row><cell><emph type="italics"/>E<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Elementa quie&longs;icunt adrectos angu-los &longs;ita.<emph.end type="italics"/></cell><cell>196</cell></row><row><cell><emph type="italics"/>En&longs;is e&longs;t cuneus.<emph.end type="italics"/></cell><cell>130</cell></row><row><cell><foreign lang="greek">*epipo/laia</foreign> <emph type="italics"/>vis quæ.<emph.end type="italics"/></cell><cell>201.202</cell></row><row><cell><emph type="italics"/>Equus Troianus machina er at.<emph.end type="italics"/></cell><cell>12</cell></row><row><cell><emph type="italics"/>Ergat a quid.<emph.end type="italics"/></cell><cell>119</cell></row><row><cell><emph type="italics"/>Ergatæ, & &longs;ucculæ di&longs;tinctio.<emph.end type="italics"/></cell><cell>129</cell></row><row><cell><emph type="italics"/>Ergatam collopes maiores minoribus fa-cilius mouent.<emph.end type="italics"/></cell><cell>118.119</cell></row><row><cell><emph type="italics"/>Exercitium militum in exercitu ferian-tium.<emph.end type="italics"/></cell><cell>125</cell></row><row><cell><emph type="italics"/>Exigua quæ.<emph.end type="italics"/></cell><cell>204</cell></row><row><cell><emph type="italics"/>F<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Fabrilis ars certitudine vincit cæte-ras.<emph.end type="italics"/></cell><cell>4</cell></row><row><cell><emph type="italics"/>Figura hominis <expan abbr="dec&utilde;bentis">decumbentis</expan> exirema.<emph.end type="italics"/></cell><cell>176</cell></row><row><cell><emph type="italics"/>Figura <expan abbr="corpor&utilde;iuuat">corporuniuuat</expan>, velimpedit mul-tum corum inclinationes, & natura-les impetus.<emph.end type="italics"/></cell><cell>164</cell></row><row><cell><emph type="italics"/>Figura decubitus humida, &longs;eu mediæ quæ.<emph.end type="italics"/></cell><cell>176</cell></row><row><cell><emph type="italics"/>Forceps, & forfex quid.<emph.end type="italics"/></cell><cell>152</cell></row><row><cell><emph type="italics"/>Fortuna in&longs;i&longs;tit Spharæ.<emph.end type="italics"/></cell><cell>103</cell></row><row><cell><emph type="italics"/>Funda quid.<emph.end type="italics"/></cell><cell>116</cell></row><row><cell><emph type="italics"/>Funda inuentum Phænicuno.<emph.end type="italics"/></cell><cell>116</cell></row><row><cell><emph type="italics"/>Fundæ v&longs;us.<emph.end type="italics"/></cell><cell>116.117</cell></row><row><cell><emph type="italics"/>Fundæ cur Balearis.<emph.end type="italics"/></cell><cell>116</cell></row><row><cell><emph type="italics"/>Funda longius proijcit, quam manus.<emph.end type="italics"/></cell><cell>115.117</cell></row><row><cell><emph type="italics"/>Fundaiacit lapidem & plumbum.<emph.end type="italics"/></cell><cell>117</cell></row><row><cell><emph type="italics"/>Fu&longs;tis ad genu fractus non lædit.<emph.end type="italics"/></cell><cell>122</cell></row><row><cell><emph type="italics"/>Fu&longs;tis duobus cyphis impo&longs;itus frangitur &longs;ine cyphorum fractione & aquæ effu-&longs;ione.<emph.end type="italics"/></cell><cell>122</cell></row><row><cell><emph type="italics"/>G<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Georgij Lhullerij machina.<emph.end type="italics"/></cell><cell>137.138</cell></row><row><cell><emph type="italics"/>Gubernaculum & eius partes.<emph.end type="italics"/></cell><cell>73</cell></row><row><cell><emph type="italics"/>Gubernaculi & remi differentia.<emph.end type="italics"/></cell><cell>76</cell></row><row><cell><emph type="italics"/>Gubernaculi magna vis in nauis motio-ne.<emph.end type="italics"/></cell><cell>71.72</cell></row><row><cell><emph type="italics"/>Gyraphi &longs;oli crura po&longs;teriora prioribus breuiora habent.<emph.end type="italics"/></cell><cell>112</cell></row><row><cell><emph type="italics"/>H<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Ha&longs;tæ ferrum e&longs;t cuneus.<emph.end type="italics"/></cell><cell>190</cell></row><row><cell><emph type="italics"/>Hominem quie&longs;cere, &longs;edare, &longs;urge-re, &longs;tare, ambulare, currere e&longs;t ex v&longs;u Geometriæ,<emph.end type="italics"/></cell><cell>198</cell></row><row><cell><emph type="italics"/>Hominis quies e&longs;t per rectos angulos.<emph.end type="italics"/></cell><cell>196</cell></row><row><cell><emph type="italics"/>Hominis ambulatio, & progre&longs;sio, vs fiat.<emph.end type="italics"/></cell><cell>198</cell></row><row><cell><emph type="italics"/>Homo <expan abbr="nõ">non</expan> &longs;tatrectus, vt <expan abbr="cæl&utilde;">cælum</expan> videus.<emph.end type="italics"/></cell><cell>194</cell></row><row><cell><emph type="italics"/>Homo vnde factus Mechanicus.<emph.end type="italics"/></cell><cell>7.8</cell></row><row><cell><emph type="italics"/>Homo &longs;olus admiratur.<emph.end type="italics"/></cell><cell>5</cell></row><row><cell><emph type="italics"/>Homo &longs;olus artifex.<emph.end type="italics"/></cell><cell>194</cell></row><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.035.jpg"/><row><cell><emph type="italics"/>Homo &longs;oius &longs;edere pote&longs;t.<emph.end type="italics"/></cell><cell>194</cell></row><row><cell><emph type="italics"/>Homo magnus & paruuus quis.<emph.end type="italics"/></cell><cell>19</cell></row><row><cell><emph type="italics"/>Homines duo ferentes pondus cum perti-ca, &longs;i pondus non e&longs;t in eius medio, non æqualiter premuntur.<emph.end type="italics"/></cell><cell>190.191</cell></row><row><cell><emph type="italics"/>Horologia nostritemporis veterum cle-p&longs;ydras, & gnemones antecellunt.<emph.end type="italics"/></cell><cell>26</cell></row><row><cell><emph type="italics"/>Plorologium Argentorati <expan abbr="magni&longs;ic&utilde;">magnificum</expan>.<emph.end type="italics"/></cell><cell>26</cell></row><row><cell><emph type="italics"/>Humero dextro onera difficilius ferun-tur, quam &longs;ini&longs;tro.<emph.end type="italics"/></cell><cell>187</cell></row><row><cell><emph type="italics"/>Hypomochlium quid.<emph.end type="italics"/></cell><cell>14.55</cell></row><row><cell><emph type="italics"/>I<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Iaccre &longs;upinum quid.<emph.end type="italics"/></cell><cell>194</cell></row><row><cell><emph type="italics"/>lacere pronum.<emph.end type="italics"/></cell><cell>194</cell></row><row><cell><emph type="italics"/>Jacere &longs;upinum & pronum commune e&longs;t multis anim antibus.<emph.end type="italics"/></cell><cell>194</cell></row><row><cell><emph type="italics"/>Joannis iucundi problema.<emph.end type="italics"/></cell><cell>145</cell></row><row><cell><emph type="italics"/>L<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Lancea <expan abbr="perp&etilde;dicularis">perpendicularis</expan> facilius fer-tur, quam obliquata.<emph.end type="italics"/></cell><cell>185</cell></row><row><cell><emph type="italics"/>Lecti lateribus cur fiunt dupli.<emph.end type="italics"/></cell><cell>175</cell></row><row><cell><emph type="italics"/>Libra maior e&longs;t exactior minore.<emph.end type="italics"/></cell><cell>27.44. 45</cell></row><row><cell><emph type="italics"/>Libræ finis.<emph.end type="italics"/></cell><cell>4</cell></row><row><cell><emph type="italics"/>Libræpartes.<emph.end type="italics"/></cell><cell>45.46</cell></row><row><cell><emph type="italics"/>Libræfallaciæ.<emph.end type="italics"/></cell><cell>46.47</cell></row><row><cell><emph type="italics"/>Libræ valde exigua examinantis fabri-ca.<emph.end type="italics"/></cell><cell>47</cell></row><row><cell><emph type="italics"/>Librile <expan abbr="ab&longs;q;">ab&longs;que</expan> <expan abbr="põdere">pondere</expan> facilius mouetur.<emph.end type="italics"/></cell><cell>112</cell></row><row><cell><emph type="italics"/>Librilis brachia vt <expan abbr="maneãt">maneant</expan>, aut redeant ad <expan abbr="æquilibri&utilde;">æquilibrium</expan> &longs;ublatis <expan abbr="põderilus">ponderilus</expan>.<emph.end type="italics"/></cell><cell>49.50</cell></row><row><cell><emph type="italics"/>Librile <expan abbr="ligne&utilde;">ligneum</expan> facilius mouetur ferreo.<emph.end type="italics"/></cell><cell>113</cell></row><row><cell><emph type="italics"/>Lignalongiora &longs;unt imbecilliora.<emph.end type="italics"/></cell><cell>124</cell></row><row><cell><emph type="italics"/>Ligna longa ab extremo difficilius <expan abbr="fer&utilde;-tur">ferun-tur</expan> bumere, quam à medio.<emph.end type="italics"/></cell><cell>183.184</cell></row><row><cell><emph type="italics"/>Lignum vt è genu facilius <expan abbr="frãgatur">frangatur</expan>.<emph.end type="italics"/></cell><cell>121</cell></row><row><cell><emph type="italics"/>Linea de&longs;cribens circulum <expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> duas lationes &longs;ertur.<emph.end type="italics"/></cell><cell>28.34</cell></row><row><cell><emph type="italics"/><expan abbr="Long&utilde;">Longum</expan> pondus difficilius fertur humero, <expan abbr="quã">quam</expan> brcue, vt &longs;it <expan abbr="põdere">pondere</expan> æquale.<emph.end type="italics"/></cell><cell>186.187</cell></row><row><cell><emph type="italics"/>Lorain lectis extenduntur non &longs;ecundum diametrum.<emph.end type="italics"/></cell><cell>175.177</cell></row><row><cell><emph type="italics"/>M<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Machina quid.<emph.end type="italics"/></cell><cell>2</cell></row><row><cell><emph type="italics"/>Machinarum quædam per &longs;e, quædam-non per&longs;e mouentur.<emph.end type="italics"/></cell><cell>10</cell></row><row><cell><emph type="italics"/>Machinæ valentißimæ tres ex &longs;ententia Hippocratis.<emph.end type="italics"/></cell><cell>119</cell></row><row><cell><emph type="italics"/>Machinarum pluribus, & diuer&longs;arum compo&longs;itio adæquat vnam, quæ tanta, quanta opus e&longs;&longs;et fierinon pote&longs;t, pro-pter defectum materiæ.<emph.end type="italics"/></cell><cell>138.139</cell></row><row><cell><emph type="italics"/>Machinæ ad ædificia, & ad bellum.<emph.end type="italics"/></cell><cell>10</cell></row><row><cell><emph type="italics"/>in Machinis faciendis lex ob&longs;eruanda.<emph.end type="italics"/></cell><cell>10</cell></row><row><cell><emph type="italics"/>Magnetis vis.<emph.end type="italics"/></cell><cell>129</cell></row><row><cell><emph type="italics"/>Magna quæ.<emph.end type="italics"/></cell><cell>204</cell></row><row><cell><emph type="italics"/>Malus nauis.<emph.end type="italics"/></cell><cell>92</cell></row><row><cell><emph type="italics"/>Mali pterna.<emph.end type="italics"/></cell><cell>92</cell></row><row><cell><emph type="italics"/>Mallei <expan abbr="lõgius">longius</expan> <expan abbr="manubri&utilde;">manubrium</expan> grauius ferit.<emph.end type="italics"/></cell><cell>128</cell></row><row><cell><emph type="italics"/>Manganaria pars Mechanices.<emph.end type="italics"/></cell><cell>11</cell></row><row><cell><emph type="italics"/>Manus e&longs;t <expan abbr="in&longs;trum&etilde;t&utilde;">in&longs;trumentum</expan> <expan abbr="in&longs;trum&etilde;tor&utilde;">in&longs;trumentorum</expan>.<emph.end type="italics"/></cell><cell>194</cell></row><row><cell><emph type="italics"/>Manus tres partes.<emph.end type="italics"/></cell><cell>118</cell></row><row><cell><emph type="italics"/>Mechanica cur non e&longs;&longs;e Aristotelis vi-&longs;um &longs;it Cardano & <expan abbr="Frãci&longs;co">Franci&longs;co</expan> patricio.<emph.end type="italics"/></cell><cell>1</cell></row><row><cell><emph type="italics"/>Mechanica &longs;unt Aristotelis.<emph.end type="italics"/></cell><cell>2</cell></row><row><cell><emph type="italics"/>Mechanicorum diui&longs;io.<emph.end type="italics"/></cell><cell>2</cell></row><row><cell><emph type="italics"/>Mechanica vnde dicta.<emph.end type="italics"/></cell><cell>2.11</cell></row><row><cell><emph type="italics"/>Mechanica quæ dici debeant.<emph.end type="italics"/></cell><cell>2</cell></row><row><cell><emph type="italics"/>Mechanice quid.<emph.end type="italics"/></cell><cell>8.9</cell></row><row><cell><emph type="italics"/>Mechanice partim e&longs;t phy&longs;ica, partim mathematica.<emph.end type="italics"/></cell><cell>4.12.13</cell></row><row><cell><emph type="italics"/>Mechanicæ artes vnde dictæ.<emph.end type="italics"/></cell><cell>2.3</cell></row><row><cell><emph type="italics"/>Mechanice pars e&longs;t philo&longs;ophiæ.<emph.end type="italics"/></cell><cell>9</cell></row><row><cell><emph type="italics"/>Mechanices finis.<emph.end type="italics"/></cell><cell>9</cell></row><row><cell><emph type="italics"/>Mechanicus ante aggreßionem operis quid con&longs;iderare debeat.<emph.end type="italics"/></cell><cell>13</cell></row><row><cell><emph type="italics"/>Mechanice dicendi<emph.end type="italics"/> <foreign lang="greek">paradocopoioi\.</foreign></cell><cell>12</cell></row><row><cell><emph type="italics"/>laus Mechanicorum.<emph.end type="italics"/></cell><cell>142</cell></row><row><cell><emph type="italics"/>Mens e&longs;t ars artium.<emph.end type="italics"/></cell><cell>194</cell></row><row><cell><emph type="italics"/>Men&longs;ura rei cuiu&longs;que debet e&longs;&longs;e deter-minata.<emph.end type="italics"/></cell><cell>44</cell></row><row><cell><emph type="italics"/>Mercatura opulenta.<emph.end type="italics"/></cell><cell>4</cell></row><row><cell><emph type="italics"/>Mercurius in&longs;istit cubo.<emph.end type="italics"/></cell><cell>103</cell></row><row><cell><emph type="italics"/>Milij grana non &longs;unt &longs;impliciter exigua.<emph.end type="italics"/></cell><cell>204</cell></row><row><cell><emph type="italics"/>Militaris ars vtilitate vincit cæteras.<emph.end type="italics"/></cell><cell>4</cell></row><row><cell><emph type="italics"/>Milo cuneum contemnens peryt.<emph.end type="italics"/></cell><cell>127</cell></row><row><cell><emph type="italics"/>Mobile motum quò vergit facile moue<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.036.jpg"/><emph type="italics"/>tur.<emph.end type="italics"/></cell><cell>103</cell></row><row><cell><emph type="italics"/>Mobilis primi velocitas vt intelligatur.<emph.end type="italics"/></cell><cell>104.</cell></row><row><cell><emph type="italics"/>Mobilis primi motus e&longs;t men&longs;ura alio-rum motuum.<emph.end type="italics"/></cell><cell>104</cell></row><row><cell><emph type="italics"/>Mobile latius mouetur difficilius.<emph.end type="italics"/></cell><cell>104</cell></row><row><cell><emph type="italics"/>Moles exigua &longs;æpe magnam vim obti-net.<emph.end type="italics"/></cell><cell>129</cell></row><row><cell><emph type="italics"/>Motus fit in tempore, & &longs;ucceßiuè.<emph.end type="italics"/></cell><cell>205</cell></row><row><cell><emph type="italics"/>Motus minimus quis.<emph.end type="italics"/></cell><cell>104</cell></row><row><cell><emph type="italics"/>Mota duobus motibus ad eundem <expan abbr="ter-min&utilde;">ter-minum</expan> <expan abbr="tend&etilde;tibus">tendentibus</expan> celerius <expan abbr="mou&etilde;tur">mouentur</expan>.<emph.end type="italics"/></cell><cell>163</cell></row><row><cell><emph type="italics"/>Motum duabus lationibus rationem ha-bentibus fertur <expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> <expan abbr="rectã">rectam</expan> <expan abbr="lineã">lineam</expan>.<emph.end type="italics"/></cell><cell>30</cell></row><row><cell><emph type="italics"/>Motum duabus lationibus rationem non habentibus <expan abbr="nõ">non</expan> fertur <expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> <expan abbr="rectã">rectam</expan>.<emph.end type="italics"/></cell><cell>30</cell></row><row><cell><emph type="italics"/>Motus circularis omnium machinatio-num principia continet.<emph.end type="italics"/></cell><cell>60</cell></row><row><cell><emph type="italics"/>Motus difficultas in mobili à quibus pen-deat.<emph.end type="italics"/></cell><cell>101</cell></row><row><cell><emph type="italics"/>Mulier parua non e&longs;t pulchræ.<emph.end type="italics"/></cell><cell>19</cell></row><row><cell><emph type="italics"/>Mundus nutans non vere dici de terra à poëta.<emph.end type="italics"/></cell><cell>104</cell></row><row><cell><emph type="italics"/>Mu&longs;culus vecti comparatus à Galeno.<emph.end type="italics"/></cell><cell>56</cell></row><row><cell><emph type="italics"/>N<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Natura <expan abbr="eod&etilde;">eodem</expan> modo &longs;emper opera-tur, & eundem &longs;copum habet.<emph.end type="italics"/></cell><cell>6</cell></row><row><cell><emph type="italics"/>Natura re&longs;i&longs;tit arti in multis.<emph.end type="italics"/></cell><cell>8</cell></row><row><cell><emph type="italics"/>Nauigandi ars admirabilis ob &longs;ubtilita-tem, & nauigationis pericula.<emph.end type="italics"/></cell><cell>62</cell></row><row><cell><emph type="italics"/>Nauigij Hieronis de&longs;criptio incredibi-lis.<emph.end type="italics"/></cell><cell>73</cell></row><row><cell><emph type="italics"/>Nauis quid, & partes.<emph.end type="italics"/></cell><cell>62</cell></row><row><cell><emph type="italics"/>Nauis Ptolemaicæ magnitudo.<emph.end type="italics"/></cell><cell>63</cell></row><row><cell><emph type="italics"/>Nauis iam mota &longs;acilius mouetur.<emph.end type="italics"/></cell><cell>201</cell></row><row><cell><emph type="italics"/>Nauis plus vehitur antror&longs;um, quam re-mi palmula retror&longs;um.<emph.end type="italics"/></cell><cell>80</cell></row><row><cell><emph type="italics"/>Nauis actuariæ promotio.<emph.end type="italics"/></cell><cell>69</cell></row><row><cell><emph type="italics"/>Nauis velocit as à quibus.<emph.end type="italics"/></cell><cell>93</cell></row><row><cell><emph type="italics"/>Nauium &longs;pecies.<emph.end type="italics"/></cell><cell>63</cell></row><row><cell><emph type="italics"/>Nauicula è plumbo tenui &longs;upernatat aquæ.<emph.end type="italics"/></cell><cell>164</cell></row><row><cell><emph type="italics"/>Nautæ in procellis &longs;olo vtuntur dolone.<emph.end type="italics"/></cell><cell>94</cell></row><row><cell><emph type="italics"/>Nautica ars opulenta.<emph.end type="italics"/></cell><cell>4</cell></row><row><cell><emph type="italics"/>Nuces à nucifrangibulo &longs;ine ictu facilius franguntur, quam cum ictu.<emph.end type="italics"/></cell><cell>155.156</cell></row><row><cell><emph type="italics"/><expan abbr="Nucifrãgibuli">Nucifrangibuli</expan> & forcipis di&longs;tinctio.<emph.end type="italics"/></cell><cell>156</cell></row><row><cell><emph type="italics"/>Nucifrangibulum ferreum facilius nu-cem frangit, quam ligneum.<emph.end type="italics"/></cell><cell>167</cell></row><row><cell><emph type="italics"/>Nutus quid.<emph.end type="italics"/></cell><cell>104.108</cell></row><row><cell><emph type="italics"/>Nutus quotuplex.<emph.end type="italics"/></cell><cell>108</cell></row><row><cell><emph type="italics"/>Nutus maioris peripheriæ maior e&longs;t, quam minoris.<emph.end type="italics"/></cell><cell>108</cell></row><row><cell><emph type="italics"/>O<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Obeli&longs;cus quid.<emph.end type="italics"/></cell><cell>139</cell></row><row><cell><emph type="italics"/>Obeli&longs;cus Xy&longs;tiqualis & <expan abbr="quãtus">quantus</expan>.<emph.end type="italics"/></cell><cell>139</cell></row><row><cell><emph type="italics"/>Obeli&longs;cus Xy&longs;ti cuiprimo &longs;acer.<emph.end type="italics"/></cell><cell>140</cell></row><row><cell><emph type="italics"/>Obeli&longs;cus vbi&longs;itus erat.<emph.end type="italics"/></cell><cell>140</cell></row><row><cell><emph type="italics"/>quid Obeli&longs;cus tran&longs;latus, & Christo &longs;acer cum cruce &longs;uper apice &longs;uo impo&longs;i-ta Christianis &longs;ignificat.<emph.end type="italics"/></cell><cell>140</cell></row><row><cell><emph type="italics"/>molimina circa Obeli&longs;ci tran&longs;lationem quinque, omnia difficillima.<emph.end type="italics"/></cell><cell>140</cell></row><row><cell><emph type="italics"/>ad Obeli&longs;cum transferendum quæ ma-chinæ, & quot adhibitæ.<emph.end type="italics"/></cell><cell>140</cell></row><row><cell><emph type="italics"/>circa <expan abbr="Obeli&longs;c&utilde;">Obeli&longs;cum</expan> molitiones quiuque, quo-modo, & à quibus perfectæ.<emph.end type="italics"/></cell><cell>141</cell></row><row><cell><emph type="italics"/>Obeli&longs;ci in area V aticani ante portam D. Fetri po&longs;iti Ichnographiæ.<emph.end type="italics"/></cell><cell>143</cell></row><row><cell><emph type="italics"/>de Obeli&longs;co & Xy&longs;to V. Summ. Pont. & cruce Gulielmi Blanci <expan abbr="epigrãma">epigramma</expan>.<emph.end type="italics"/></cell><cell>142</cell></row><row><cell><foreign lang="greek">*odonta/gra *h)/ \o)donta/gw=gos</foreign> <emph type="italics"/>quid.<emph.end type="italics"/></cell><cell>152</cell></row><row><cell><foreign lang="greek">*odonta/gw=gos</foreign> <emph type="italics"/><expan abbr="pl&utilde;beus">plumbeus</expan> in <expan abbr="t&etilde;plo">templo</expan> Apol-linis Delphici quid &longs;ignificabat.<emph.end type="italics"/></cell><cell>153</cell></row><row><cell><emph type="italics"/>Ovos quid.<emph.end type="italics"/></cell><cell>119</cell></row><row><cell><emph type="italics"/>Os arietinum volæ manus impo&longs;itum frangitur manu illæ&longs;a.<emph.end type="italics"/></cell><cell>122</cell></row><row><cell><foreign lang="greek">*ourano/skopos</foreign> <emph type="italics"/>pi&longs;cis velit nolio videt cælum.<emph.end type="italics"/></cell><cell>195</cell></row><row><cell><emph type="italics"/>P<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Palang a quid.<emph.end type="italics"/></cell><cell>191</cell></row><row><cell><emph type="italics"/>Pedem facere.<emph.end type="italics"/></cell><cell>95</cell></row><row><cell><emph type="italics"/>Pente&longs;paston.<emph.end type="italics"/></cell><cell>111.134</cell></row><row><cell><emph type="italics"/>Percußio quid.<emph.end type="italics"/></cell><cell>128</cell></row><row><cell><emph type="italics"/>Percu&longs;sionis duo modi.<emph.end type="italics"/></cell><cell>128</cell></row><row><cell><emph type="italics"/>Percußio à quibus fit maior.<emph.end type="italics"/></cell><cell>128</cell></row><row><cell><emph type="italics"/>Percußionis validiores cau&longs;æ.<emph.end type="italics"/></cell><cell>128.129</cell></row><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.037.jpg"/><row><cell><emph type="italics"/>Percu&longs;sionis magna vis ad mouendum, findendum, frangendum, quatien-dum.<emph.end type="italics"/></cell><cell>129</cell></row><row><cell><emph type="italics"/>Perpendiculares à peripherijs in &longs;emi-diametros circulorum inæqualium æquales auferunt &longs;egmenta &longs;emidia-metrorum inæqualia, quorum maius e&longs;t quod è minori aufertur.<emph.end type="italics"/></cell><cell>40</cell></row><row><cell><emph type="italics"/>Peripheriæ maiores à punctis à centro remotioribus de&longs;cribuntur.<emph.end type="italics"/></cell><cell>23</cell></row><row><cell><emph type="italics"/>Petorita Gallorum petoritis Polonorum difficilius mouentur.<emph.end type="italics"/></cell><cell>113</cell></row><row><cell><emph type="italics"/>Phalanga quid.<emph.end type="italics"/></cell><cell>191</cell></row><row><cell><emph type="italics"/>Phalangary qui.<emph.end type="italics"/></cell><cell>191</cell></row><row><cell><emph type="italics"/>Phalangarij tetraphori, hexaphori.<emph.end type="italics"/></cell><cell>191</cell></row><row><cell><emph type="italics"/>Phalangij ictus.<emph.end type="italics"/></cell><cell>129</cell></row><row><cell><emph type="italics"/>Phalanx.<emph.end type="italics"/></cell><cell>146</cell></row><row><cell><emph type="italics"/>Philo&longs;ophia principium duxit ab admi-ratione.<emph.end type="italics"/></cell><cell>5</cell></row><row><cell><emph type="italics"/>Philo&longs;ophia e&longs;t ars generalis omnibus fa-ciendorum difficultatibus &longs;uccurrens.<emph.end type="italics"/></cell><cell>9</cell></row><row><cell><emph type="italics"/>Philo&longs;ophandi, vt admirandi &longs;emper oc-ca&longs;io erit.<emph.end type="italics"/></cell><cell>5</cell></row><row><cell><emph type="italics"/>Plumbum vtri aëre pleno annexum tar-dius de&longs;cendit in aquim, quam &longs;i non e&longs;&longs;et aunexum.<emph.end type="italics"/></cell><cell>170</cell></row><row><cell><foreign lang="greek">*po/da e)rei=n,</foreign> <emph type="italics"/>& canere quid.<emph.end type="italics"/></cell><cell>95</cell></row><row><cell><foreign lang="greek">*po/des, & pro/podes.</foreign></cell><cell>96</cell></row><row><cell><foreign lang="greek">*poliorkitik*h\</foreign> <emph type="italics"/>pars Mechanices.<emph.end type="italics"/></cell><cell>11</cell></row><row><cell><foreign lang="greek">*polu/spaston.</foreign></cell><cell>111. 134</cell></row><row><cell><emph type="italics"/>Pons Lutetiæ ab Henrico 111. inchoatus ab Henrico 1111. perficietur.<emph.end type="italics"/></cell><cell>120</cell></row><row><cell><emph type="italics"/>Preßio porrecta.<emph.end type="italics"/></cell><cell>14</cell></row><row><cell><emph type="italics"/>Problema difficillimum totius libri.<emph.end type="italics"/></cell><cell>166</cell></row><row><cell><emph type="italics"/>Problematis a theoremate di&longs;tinctio.<emph.end type="italics"/></cell><cell>12</cell></row><row><cell><emph type="italics"/>Progreßio in animali vt fit.<emph.end type="italics"/></cell><cell>187</cell></row><row><cell><emph type="italics"/>Proiecta cur moueri de&longs;inunt.<emph.end type="italics"/></cell><cell>201</cell></row><row><cell><emph type="italics"/>in Proiectis impre&longs;&longs;a vis impellens à mo-tore e&longs;t can&longs;a eorum lationis.<emph.end type="italics"/></cell><cell>201</cell></row><row><cell><emph type="italics"/>Proiecta nec exigua nec magna &longs;eruntur procul.<emph.end type="italics"/></cell><cell>203.205</cell></row><row><cell><emph type="italics"/>Publ. Scipio & C. Lælius colligentes cro-cas quæ dicerent.<emph.end type="italics"/></cell><cell>123</cell></row><row><cell><emph type="italics"/>Purpura quid.<emph.end type="italics"/></cell><cell>47.48</cell></row><row><cell><emph type="italics"/>Q<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Qvie&longs;cens vim motoris diminuit.<emph.end type="italics"/></cell><cell>200</cell></row><row><cell><emph type="italics"/>R<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Radius minor plus retrahitur ad centrum, quam maior.<emph.end type="italics"/></cell><cell>38.39</cell></row><row><cell><emph type="italics"/>Rectilineæ figuræ, & cubus difficulter mouentur &longs;uper planum.<emph.end type="italics"/></cell><cell>102</cell></row><row><cell><emph type="italics"/>Remus quid.<emph.end type="italics"/></cell><cell>63</cell></row><row><cell><emph type="italics"/>Remiges qui.<emph.end type="italics"/></cell><cell>63</cell></row><row><cell><emph type="italics"/>Remigum differentiæ.<emph.end type="italics"/></cell><cell>64</cell></row><row><cell><emph type="italics"/>Remiges me&longs;onei maximè mouent na-uim.<emph.end type="italics"/></cell><cell>61</cell></row><row><cell><emph type="italics"/>Remi digitis manuum comparati.<emph.end type="italics"/></cell><cell>65</cell></row><row><cell><emph type="italics"/>Remus vt plurimum maris diuidit.<emph.end type="italics"/></cell><cell>71</cell></row><row><cell><emph type="italics"/>de Remi motione comparata ad motio-nem nauis.<emph.end type="italics"/></cell><cell>84.85.86.87.88.89</cell></row><row><cell><emph type="italics"/>qui <expan abbr="Remig&utilde;">Remigum</expan> plus nauim promoueant.<emph.end type="italics"/></cell><cell>68</cell></row><row><cell><emph type="italics"/>in Rhombo punctum vnum extremum lateris motum duobus motibus minus &longs;paty conficit, quam latus ip&longs;um.<emph.end type="italics"/></cell><cell>159</cell></row><row><cell><emph type="italics"/>Rhombus con&longs;tituitur cuius angulus acu-tus e&longs;t dimidio obtu&longs;i minor.<emph.end type="italics"/></cell><cell>161</cell></row><row><cell><emph type="italics"/>in Rhombo alterum punctorum extre-morum non æqualem <expan abbr="rectã">rectam</expan> tran&longs;it.<emph.end type="italics"/></cell><cell>157</cell></row><row><cell><emph type="italics"/>Rhombus quid.<emph.end type="italics"/></cell><cell>159</cell></row><row><cell><emph type="italics"/>Rotæ binæ quaternis faciliores.<emph.end type="italics"/></cell><cell>111</cell></row><row><cell><emph type="italics"/>in Rotis quaternis po&longs;teriores prioribus maiorese&longs;&longs;e debent.<emph.end type="italics"/></cell><cell>111</cell></row><row><cell><emph type="italics"/>Rotæ curruum maiores commodiores ad facilitatem & celeritatem.<emph.end type="italics"/></cell><cell>110</cell></row><row><cell><emph type="italics"/>Rotunda figura difficulter patitur.<emph.end type="italics"/></cell><cell>124</cell></row><row><cell><emph type="italics"/>Rotunda maiora facilius mouentur mi-noribus.<emph.end type="italics"/></cell><cell>99.100</cell></row><row><cell><emph type="italics"/><expan abbr="Rot&utilde;dorum">Rotundorum</expan> motus accurata diui&longs;io.<emph.end type="italics"/></cell><cell>100</cell></row><row><cell><emph type="italics"/>S<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Sarcina maior in anteriore plaustri parte poni debet.<emph.end type="italics"/></cell><cell>111</cell></row><row><cell><emph type="italics"/>Saxa tritalantaria &longs;impliciter non &longs;unt magna.<emph.end type="italics"/></cell><cell>204</cell></row><row><cell><emph type="italics"/>Scorpionis ictus.<emph.end type="italics"/></cell><cell>129</cell></row><row><cell><emph type="italics"/>Scytala quid, & quotuplex.<emph.end type="italics"/></cell><cell>111.114</cell></row><row><cell><emph type="italics"/>Scytalæ v&longs;us duplex.<emph.end type="italics"/></cell><cell>111</cell></row><row><cell><emph type="italics"/>Super Scytalis onera facilius ge&longs;tantur,<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.038.jpg"/><emph type="italics"/>quam &longs;uper curribus.<emph.end type="italics"/></cell><cell>113</cell></row><row><cell><emph type="italics"/>Securis magna diuidit.<emph.end type="italics"/></cell><cell>145</cell></row><row><cell><emph type="italics"/>Securis feriens diuidit, premens non item.<emph.end type="italics"/></cell><cell>144</cell></row><row><cell><emph type="italics"/>Securis e&longs;t cuneus annexus malleo.<emph.end type="italics"/></cell><cell>145</cell></row><row><cell><emph type="italics"/>Sedere quid.<emph.end type="italics"/></cell><cell>194</cell></row><row><cell><emph type="italics"/>Sedens caput habet ad pedes parallelum, & nequaquam in vnarecta.<emph.end type="italics"/></cell><cell>193</cell></row><row><cell><emph type="italics"/>Sedentariæ artes vtuntur &longs;eßione &longs;ecu-ra.<emph.end type="italics"/></cell><cell>197</cell></row><row><cell><emph type="italics"/>Sedile idem non congruit omni homini.<emph.end type="italics"/></cell><cell>196</cell></row><row><cell><emph type="italics"/>Seßio propriè dista & latè<emph.end type="italics"/></cell><cell>197</cell></row><row><cell><emph type="italics"/>Seßio cum &longs;ecuritate.<emph.end type="italics"/></cell><cell>197</cell></row><row><cell><emph type="italics"/>Sedens altius &longs;urgit facilius.<emph.end type="italics"/></cell><cell>197.198</cell></row><row><cell><foreign lang="greek">*s*h/kwma</foreign> <emph type="italics"/>quid.<emph.end type="italics"/></cell><cell>151</cell></row><row><cell><emph type="italics"/>Spartion pro an&longs;a.<emph.end type="italics"/></cell><cell>148</cell></row><row><cell><emph type="italics"/>Sphæra quale corpus.<emph.end type="italics"/></cell><cell>16</cell></row><row><cell><emph type="italics"/>Sphæra corpus e&longs;t mobilißimum & mo-uentißimum.<emph.end type="italics"/></cell><cell>16</cell></row><row><cell><emph type="italics"/>Sphæra contingit planum in puncto.<emph.end type="italics"/></cell><cell>101</cell></row><row><cell><emph type="italics"/>Sphæra Archimedis per &longs;e mobilis non e&longs;t fabula.<emph.end type="italics"/></cell><cell>26</cell></row><row><cell><emph type="italics"/>Sphæratopæia pars e&longs;t mechanices.<emph.end type="italics"/></cell><cell>11</cell></row><row><cell><emph type="italics"/>Stateræ partes.<emph.end type="italics"/></cell><cell>147</cell></row><row><cell><emph type="italics"/>Stateræ v&longs;us.<emph.end type="italics"/></cell><cell>148</cell></row><row><cell><emph type="italics"/>Statera in pretio&longs;is expendendis non v&longs;urpatur, &longs;ed libra.<emph.end type="italics"/></cell><cell>147</cell></row><row><cell><emph type="italics"/>Statera commodior libra.<emph.end type="italics"/></cell><cell>147</cell></row><row><cell><emph type="italics"/>Statera vna mult æ &longs;unt libræ.<emph.end type="italics"/></cell><cell>148.149</cell></row><row><cell><emph type="italics"/>Statera e&longs;t vectis inuer&longs;us.<emph.end type="italics"/></cell><cell>150</cell></row><row><cell><emph type="italics"/>Stateræ paruo æquipondio magna ponde-ra expendunt.<emph.end type="italics"/></cell><cell>146.147.148</cell></row><row><cell><emph type="italics"/>Stateræ dimidium e&longs;t an&longs;a.<emph.end type="italics"/></cell><cell>148</cell></row><row><cell><emph type="italics"/>Per Stateram ponderationis factæ de-mon&longs;tratio.<emph.end type="italics"/></cell><cell>152</cell></row><row><cell><emph type="italics"/>Stare quid.<emph.end type="italics"/></cell><cell>194</cell></row><row><cell><emph type="italics"/>Stans e&longs;t perpendicularis terræ.<emph.end type="italics"/></cell><cell>193</cell></row><row><cell><emph type="italics"/>Stantis di&longs;po&longs;itio e&longs;t in recta linea.<emph.end type="italics"/></cell><cell>196</cell></row><row><cell><emph type="italics"/>Statio & &longs;eßio propria <expan abbr="s&utilde;t">sunt</expan> homini.<emph.end type="italics"/></cell><cell>194</cell></row><row><cell><foreign lang="greek">*stata</foreign> <emph type="italics"/>quæ.<emph.end type="italics"/></cell><cell>10</cell></row><row><cell><emph type="italics"/>Succula quid.<emph.end type="italics"/></cell><cell>119</cell></row><row><cell><emph type="italics"/>Surrectio e&longs;t motio.<emph.end type="italics"/></cell><cell>194</cell></row><row><cell><emph type="italics"/>Surrectio è iacente indiget acutis angu-lis.<emph.end type="italics"/></cell><cell>197</cell></row><row><cell><emph type="italics"/>Surgentes con&longs;tituunt angulum acutum ex femore cum tibia, tum ex thoræce & femore.<emph.end type="italics"/></cell><cell>193.195.196</cell></row><row><cell><emph type="italics"/>Surrectionis initium fit per acutos angu-los.<emph.end type="italics"/></cell><cell>198</cell></row><row><cell><emph type="italics"/>Surrectionis medium fit per rectum, & obtu&longs;os angulos.<emph.end type="italics"/></cell><cell>198</cell></row><row><cell><emph type="italics"/>Symmetria quid.<emph.end type="italics"/></cell><cell>19</cell></row><row><cell><emph type="italics"/>Symmetria pro analogia.<emph.end type="italics"/></cell><cell>205</cell></row><row><cell><emph type="italics"/>T<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Telum facilius ten&longs;a penetrat, quam laxa.<emph.end type="italics"/></cell><cell>202</cell></row><row><cell><emph type="italics"/>Terra cur immobilis.<emph.end type="italics"/></cell><cell>103.104</cell></row><row><cell><emph type="italics"/>Terra comparata cubo à Pythagoreis, & Platone.<emph.end type="italics"/></cell><cell>103.196</cell></row><row><cell><emph type="italics"/>Textus Ari&longs;totelis omnium mendo&longs;i&longs;-&longs;imus.<emph.end type="italics"/></cell><cell>178.179</cell></row><row><cell><emph type="italics"/>Thaletis factum in eclip&longs;i Solis.<emph.end type="italics"/></cell><cell>5</cell></row><row><cell><foreign lang="greek">*qaumatourgik*h\</foreign> <emph type="italics"/>pars Mechanices.<emph.end type="italics"/></cell><cell>11</cell></row><row><cell><emph type="italics"/>Theorematis à problemate di&longs;tinctio.<emph.end type="italics"/></cell><cell>12</cell></row><row><cell><emph type="italics"/>Tolleno quid.<emph.end type="italics"/></cell><cell>188.189</cell></row><row><cell><emph type="italics"/>Tollenonis v&longs;us.<emph.end type="italics"/></cell><cell>189</cell></row><row><cell><emph type="italics"/>Tollenonis tran&longs;uer &longs;ario pondus adie-ctum.<emph.end type="italics"/></cell><cell>188.190</cell></row><row><cell><emph type="italics"/>Tormenta bellica deducenda plures equos po&longs;tulant.<emph.end type="italics"/></cell><cell>110.111</cell></row><row><cell><emph type="italics"/>Traba quid.<emph.end type="italics"/></cell><cell>115</cell></row><row><cell><emph type="italics"/>Trispa&longs;ton.<emph.end type="italics"/></cell><cell>111.134</cell></row><row><cell><emph type="italics"/>Trochlea quid.<emph.end type="italics"/></cell><cell>111.134</cell></row><row><cell><emph type="italics"/>Trochlea e&longs;t vectis.<emph.end type="italics"/></cell><cell>136</cell></row><row><cell><emph type="italics"/>in Trochleis plures orbiculi facilius, &longs;ed lentius trahunt.<emph.end type="italics"/></cell><cell>137</cell></row><row><cell><emph type="italics"/>Trochleæ duæ legitimè compofitæ magna pondera adducunt.<emph.end type="italics"/></cell><cell>133.134.136</cell></row><row><cell><emph type="italics"/>V<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Vectis quid.<emph.end type="italics"/></cell><cell>14.55</cell></row><row><cell><emph type="italics"/>Vectis, cuneus.<emph.end type="italics"/></cell><cell>119</cell></row><row><cell><emph type="italics"/>Vectis partes.<emph.end type="italics"/></cell><cell>14.15</cell></row><row><cell><emph type="italics"/>Vectis v&longs;us duplex.<emph.end type="italics"/></cell><cell>55</cell></row><row><cell><emph type="italics"/>Vectis refert libram.<emph.end type="italics"/></cell><cell>57</cell></row><row><cell><emph type="italics"/>pro Vecte vnum &longs;tadium longo machinæ multæ &longs;imul.<emph.end type="italics"/></cell><cell>139</cell></row><row><cell><emph type="italics"/>Velum quid.<emph.end type="italics"/></cell><cell>92</cell></row><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.039.jpg"/><row><cell><emph type="italics"/>Veli&longs;pecies.<emph.end type="italics"/></cell><cell>92</cell></row><row><cell><emph type="italics"/>Ventus &longs;ecundui, aduer&longs;us, iran&longs;uer&longs;us, obliquus.<emph.end type="italics"/></cell><cell>96</cell></row><row><cell><emph type="italics"/>Vento vt codem in contrarias partes na-uigatur demonstratio.<emph.end type="italics"/></cell><cell>98</cell></row><row><cell><emph type="italics"/>in Vortice aquarum lata ad medium de-uoluuntur.<emph.end type="italics"/></cell><cell>206.207.209.210</cell></row><row><cell><emph type="italics"/>Vortex aquarum.<emph.end type="italics"/></cell><cell>206</cell></row><row><cell><emph type="italics"/>in Vortice aquo&longs;i multi circuli concentri-ci.<emph.end type="italics"/></cell><cell>206</cell></row><row><cell><emph type="italics"/>Vortex aquæ e&longs;t linea &longs;piralis vnius, aut plurium reuolutionum.<emph.end type="italics"/></cell><cell>209</cell></row><row><cell><emph type="italics"/>Vortices quomodo à nautis vitentar.<emph.end type="italics"/></cell><cell>210</cell></row><row><cell><emph type="italics"/>Vortices inter Roe&longs;t & Loffoet.<emph.end type="italics"/></cell><cell>210</cell></row><row><cell><emph type="italics"/>in Vorticem vt &longs;entiunt nautæ &longs;e impe<gap/>gi&longs;&longs;e.<emph.end type="italics"/></cell><cell>210</cell></row><row><cell><emph type="italics"/>difficile &longs;e liberare à Vortice.<emph.end type="italics"/></cell><cell>210.211</cell></row><row><cell><emph type="italics"/>aquain Vortice <expan abbr="de&longs;c&etilde;d&etilde;s">de&longs;cendens</expan> quò feratur.<emph.end type="italics"/></cell><cell>211</cell></row><row><cell><emph type="italics"/>Vtilitas hominum postulat in operibus &longs;uis varietatem.<emph.end type="italics"/></cell><cell>6</cell></row><row><cell><emph type="italics"/>X<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Xystus V. Pont. Max. obeli&longs;ci tran&longs;-ferendi author.<emph.end type="italics"/></cell><cell>139</cell></row><row><cell><emph type="italics"/>Xysti V. Pontificis laus.<emph.end type="italics"/></cell><cell>142</cell></row><row><cell><emph type="italics"/>Z<emph.end type="italics"/></cell><cell/></row><row><cell><foreign lang="greek">*zugo\s & *zugo\n.</foreign></cell><cell>45.119</cell></row><row><cell><foreign lang="greek">*zugosta/ths.</foreign></cell><cell>45</cell></row><row><cell><emph type="italics"/>Zygostatica fides.<emph.end type="italics"/></cell><cell>45</cell></row></table>

<s id="id.000237">INDEX MEMORABILIVM <lb/>IN MECHANICIS ARISTOTELIS <lb/>& eorum Commentarijs. <lb/><arrow.to.target n="table1"/></s><table><table.target id="table1"/><row><cell><emph type="italics"/>A<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/><foreign lang="greek">*abussos</foreign> unde. pag. <emph.end type="italics"/></cell><cell>209</cell></row><row><cell><emph type="italics"/>Ab&longs;is pro circunferentia rotæ. <emph.end type="italics"/></cell><cell>100</cell></row><row><cell><emph type="italics"/>Acatium ante naues. <emph.end type="italics"/></cell><cell>65</cell></row><row><cell><emph type="italics"/>Actiones manuum in opificijs egent &longs;tatione, vel &longs;eßione tantùm<emph.end type="italics"/></cell><cell>194</cell></row><row><cell><emph type="italics"/>Admiratio quid. <emph.end type="italics"/></cell><cell>4.5</cell></row><row><cell><emph type="italics"/>Agriculturæ nece&longs;&longs;aria. <emph.end type="italics"/></cell><cell>14</cell></row><row><cell><emph type="italics"/>Ædes rotunda mirifica. <emph.end type="italics"/></cell><cell>10</cell></row><row><cell><emph type="italics"/>Ædificium durabile rectà in&longs;i&longs;tit. <emph.end type="italics"/></cell><cell>196</cell></row><row><cell><emph type="italics"/>Æolus primus v&longs;us velis. <emph.end type="italics"/></cell><cell>92</cell></row><row><cell><emph type="italics"/>Æquale e&longs;t cau&longs;a quietis. <emph.end type="italics"/></cell><cell>193.196</cell></row><row><cell><emph type="italics"/>Æquilibrium in ponderatione. <emph.end type="italics"/></cell><cell>149</cell></row><row><cell><foreign lang="greek">*alourgopw/lai</foreign> <emph type="italics"/>qui. <emph.end type="italics"/></cell><cell>47</cell></row><row><cell><emph type="italics"/>Ambulare pronum conuenit brutis. <emph.end type="italics"/></cell><cell>194</cell></row><row><cell><emph type="italics"/>Angulus rectus e&longs;t angulus æqualitatis, ideóque quietis. <emph.end type="italics"/></cell><cell>193.196</cell></row><row><cell><emph type="italics"/>Ad angulos rectos omnia <expan abbr="quie&longs;c&utilde;t">quie&longs;cunt</expan>. <emph.end type="italics"/></cell><cell>196</cell></row><row><cell><emph type="italics"/>Antemna quid. <emph.end type="italics"/></cell><cell>92</cell></row><row><cell><emph type="italics"/>Antemnæ motio. <emph.end type="italics"/></cell><cell>92</cell></row><row><cell><emph type="italics"/>Antiperi&longs;ta&longs;is medij confert ad motum proiecti. <emph.end type="italics"/></cell><cell>203</cell></row><row><cell><emph type="italics"/>Antiphonis dictum, cum iret ad &longs;uppli-cium. <emph.end type="italics"/></cell><cell>12</cell></row><row><cell><emph type="italics"/>Antiphonis ver&longs;us de natura & arte. <emph.end type="italics"/></cell><cell>8. 12</cell></row><row><cell><emph type="italics"/>Arbores, & plantæ in&longs;i&longs;lunt plane terræ ad rectos angulos. <emph.end type="italics"/></cell><cell>196</cell></row><row><cell><emph type="italics"/>Archelai regis factum in eclip&longs;i Solis. <emph.end type="italics"/></cell><cell>5</cell></row><row><cell><emph type="italics"/>Archimedeum problema, datum pondus data potentia mouere. <emph.end type="italics"/></cell><cell>60</cell></row><row><cell><emph type="italics"/>Archimedis factum Mechanicum. <emph.end type="italics"/></cell><cell>12</cell></row><row><cell><emph type="italics"/>Architecturæ tres partes. <emph.end type="italics"/></cell><cell>9</cell></row><row><cell><emph type="italics"/>Argo prima nauis. <emph.end type="italics"/></cell><cell>62</cell></row><row><cell><emph type="italics"/>Ari&longs;toteles reprehen&longs;us à Nonio. <emph.end type="italics"/></cell><cell>84</cell></row><row><cell><emph type="italics"/>Ars &longs;lectit naturam, & ad alium &longs;co-pum vertit. <emph.end type="italics"/></cell><cell>6</cell></row><row><cell><emph type="italics"/>Ars e&longs;t admirationis plena. <emph.end type="italics"/></cell><cell>6</cell></row><row><cell><emph type="italics"/>Artis, & naturæ differentia. <emph.end type="italics"/></cell><cell>6</cell></row><row><cell><emph type="italics"/>Artium diui&longs;io in liberales, & &longs;ordi-das. <emph.end type="italics"/></cell><cell>3</cell></row><row><cell><emph type="italics"/>Artes liberales. <emph.end type="italics"/></cell><cell>3</cell></row><row><cell><emph type="italics"/>Artes pueriles. <emph.end type="italics"/></cell><cell>3</cell></row><row><cell><emph type="italics"/>Artes magnæ. <emph.end type="italics"/></cell><cell>3</cell></row><row><cell><emph type="italics"/>Artes imperantes. <emph.end type="italics"/></cell><cell>3.4</cell></row><row><cell><emph type="italics"/>Artes architectonicæ. <emph.end type="italics"/></cell><cell>3</cell></row><row><cell><emph type="italics"/>Ars Typographica nihil e&longs;&longs;et &longs;ine co-chlea. <emph.end type="italics"/></cell><cell>133</cell></row><row><cell><emph type="italics"/>A&longs;inus, & aues longo collo vident c&oelig;-lum, vt homo. <emph.end type="italics"/></cell><cell>195</cell></row><row><cell><emph type="italics"/>Axis in peritrochio. <emph.end type="italics"/></cell><cell>120</cell></row><row><cell><foreign lang="greek">*auto/mata. </foreign></cell><cell>10</cell></row><row><cell><emph type="italics"/>B<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Baiulus cum &longs;uo onere e&longs;t turbo, vel conus inuer&longs;us. <emph.end type="italics"/></cell><cell>199.200</cell></row><row><cell><emph type="italics"/>Baiuli Pari&longs;ien&longs;es facile ferunt ingentia pondera. <emph.end type="italics"/></cell><cell>198.199</cell></row><row><cell><emph type="italics"/>Baiuli cum onere tutò a&longs;cendunt, pericu-losè de&longs;cendunt. <emph.end type="italics"/></cell><cell>199</cell></row><row><cell><emph type="italics"/>B. Feratinus Amerinus <expan abbr="cãcellariæ">cancellariæ</expan> Apo-&longs;tolicæ regens con&longs;ecrat, & compreca-tur multa &longs;uper crucem apici obeli&longs;ci imponendam. <emph.end type="italics"/></cell><cell>142</cell></row><row><cell><emph type="italics"/>Bombi tormentorum multi editi &longs;tatim atque crux impo&longs;ita fuit apici obe-li&longs;ci. <emph.end type="italics"/></cell><cell>142</cell></row><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.033.jpg"/><row><cell><emph type="italics"/>Bouilli error, qui putabat rectam iuuen-tam æqualem peripheriæ ex circuli &longs;uper planum reuolutione. <emph.end type="italics"/></cell><cell>174</cell></row><row><cell><emph type="italics"/>Boues ad <expan abbr="aratr&utilde;">aratrum</expan> pariter &longs;ubiugandi. <emph.end type="italics"/></cell><cell>192</cell></row><row><cell><emph type="italics"/>Boüm in iugo imbecillior &longs;ubleuari po-te&longs;t. <emph.end type="italics"/></cell><cell>192</cell></row><row><cell><emph type="italics"/>Bruta ventrem ad terram conuer&longs;um habent. <emph.end type="italics"/></cell><cell>195</cell></row><row><cell><emph type="italics"/>Bruti&longs;pina pedibus ad rectos imminet. <emph.end type="italics"/></cell><cell>198</cell></row><row><cell><emph type="italics"/>Brutum nihil admiratur. <emph.end type="italics"/></cell><cell>5</cell></row><row><cell><emph type="italics"/>Bruta nonnulla apta <expan abbr="fer&etilde;dis">ferendis</expan> &longs;arcinis. <emph.end type="italics"/></cell><cell>198</cell></row><row><cell><emph type="italics"/>Brutum nullum pote&longs;t &longs;edere. <emph.end type="italics"/></cell><cell>194</cell></row><row><cell><emph type="italics"/>C<emph.end type="italics"/></cell><cell/></row><row><cell><foreign lang="greek">*ka/iar</foreign> <emph type="italics"/>in fund a quid &longs;it. <emph.end type="italics"/></cell><cell>117</cell></row><row><cell><emph type="italics"/>Calliæ Rhodien&longs;is factum <expan abbr="mechanic&utilde;">mechanicum</expan>. <emph.end type="italics"/></cell><cell>12</cell></row><row><cell><emph type="italics"/>Cardanus reprehen&longs;us à Scaligero. <emph.end type="italics"/></cell><cell>145</cell></row><row><cell><emph type="italics"/>Cardanus ob&longs;curè & imper&longs;ectè: inge-niosè tamen&longs;crip&longs;it. <emph.end type="italics"/></cell><cell>180</cell></row><row><cell><emph type="italics"/>Carche&longs;ium quid. <emph.end type="italics"/></cell><cell>92</cell></row><row><cell><emph type="italics"/>Cathelina mu&longs;ca Rhemen&longs;ibus dicta e&longs;t <expan abbr="ex&etilde;plar">exemplar</expan> puncti duabus lationibus eo-dem tempore moti. <emph.end type="italics"/></cell><cell>32.33</cell></row><row><cell><emph type="italics"/>Cauda e&longs;t omnipi&longs;ci progubernaculo. <emph.end type="italics"/></cell><cell>77</cell></row><row><cell><emph type="italics"/>Celeritas duplex. <emph.end type="italics"/></cell><cell>27</cell></row><row><cell><emph type="italics"/>Centrobarica pars Mechanices. <emph.end type="italics"/></cell><cell>11</cell></row><row><cell><emph type="italics"/>Cercopithecus proxime accedit ad figu-ram hominis. <emph.end type="italics"/></cell><cell>195</cell></row><row><cell><emph type="italics"/>Cercopithecus, & &longs;imia e&longs;t ridicula ho-minis imitatio. <emph.end type="italics"/></cell><cell>195</cell></row><row><cell><emph type="italics"/>Cercopitheci manus differt ab hominis manu. <emph.end type="italics"/></cell><cell>195</cell></row><row><cell><emph type="italics"/>Cercopitheci pollex non e&longs;t <foreign lang="greek">a)nti/xeir,</foreign> vt in manu hominis. <emph.end type="italics"/></cell><cell>195</cell></row><row><cell><emph type="italics"/>Centrum duorum circulorum connexo-rum non e&longs;t idem. <emph.end type="italics"/></cell><cell>173</cell></row><row><cell><emph type="italics"/>Chirurgi togati nolunt dentes cuellere, licet&longs;u operatio chirurgica. <emph.end type="italics"/></cell><cell>153</cell></row><row><cell><emph type="italics"/>Circini author Dædalus. <emph.end type="italics"/></cell><cell>17</cell></row><row><cell><emph type="italics"/>Circulus e&longs;t <expan abbr="principi&utilde;">principium</expan> omnium virium, quæ&longs;unt in machinis motricibus. <emph.end type="italics"/></cell><cell>15</cell></row><row><cell><emph type="italics"/>Circulus admirabilißimus. <emph.end type="italics"/></cell><cell>15</cell></row><row><cell><emph type="italics"/>Circulus habet in &longs;e quinque repugnan-tias. <emph.end type="italics"/></cell><cell>16</cell></row><row><cell><emph type="italics"/>Circulus &longs;ecit miracula in templis paga-norum. <emph.end type="italics"/></cell><cell>25</cell></row><row><cell><emph type="italics"/>Circulus ante, & pone mouetur &longs;imul. <emph.end type="italics"/></cell><cell>20.21</cell></row><row><cell><emph type="italics"/>Circulus maior ad minorem &longs;emper nu-tum habet. <emph.end type="italics"/></cell><cell>106</cell></row><row><cell><emph type="italics"/>Circuli nutus e&longs;t perpetuus. <emph.end type="italics"/></cell><cell>107</cell></row><row><cell><emph type="italics"/>Circuli qua&longs;i motus e&longs;t perpetuus. <emph.end type="italics"/></cell><cell>107</cell></row><row><cell><emph type="italics"/>Circuli minores infiniti &longs;unt in maiore circulo. <emph.end type="italics"/></cell><cell>108</cell></row><row><cell><emph type="italics"/>Circuli maiores &longs;unt mouentiores. <emph.end type="italics"/></cell><cell>109</cell></row><row><cell><emph type="italics"/>Circulus <expan abbr="cõtingit">contingit</expan> <expan abbr="plan&utilde;">planum</expan> in vno <expan abbr="p&utilde;cto">puncto</expan>. <emph.end type="italics"/></cell><cell>101</cell></row><row><cell><emph type="italics"/>Circuli maioris minor e&longs;t angulus conta-ctus quam minoris. <emph.end type="italics"/></cell><cell>115</cell></row><row><cell><emph type="italics"/>Circulus maior cum minore per æqualem orbitam reuoluitur & contra. <emph.end type="italics"/></cell><cell>164</cell></row><row><cell><emph type="italics"/>Circuli <expan abbr="cõcentrici">concentrici</expan> inæquales iuncti æqua-lem orbitam <expan abbr="percurr&utilde;t">percurrunt</expan>. <emph.end type="italics"/></cell><cell>166.167.174</cell></row><row><cell><emph type="italics"/>Circuli maioris motus &longs;ecundum natu-ram maior e&longs;t quam minoris. <emph.end type="italics"/></cell><cell>43</cell></row><row><cell><emph type="italics"/>in Circulo in&longs;criptas &longs;i &longs;ecet recta ad re-ctos ab&longs;ci&longs;&longs;a exdiametro erit maxima & <gap/>pinquior remotiore maior. <emph.end type="italics"/></cell><cell>68.69</cell></row><row><cell><emph type="italics"/>Circulum minorem qui datum maiorem interius tangat de&longs;cribere. <emph.end type="italics"/></cell><cell>41</cell></row><row><cell><emph type="italics"/>C&oelig;li motus unde. <emph.end type="italics"/></cell><cell>104</cell></row><row><cell><emph type="italics"/>C&oelig;lum videre quid apud <expan abbr="Platon&etilde;">Platonem</expan>. <emph.end type="italics"/></cell><cell>195</cell></row><row><cell><emph type="italics"/><expan abbr="Col&utilde;ba">Columba</expan> volans Acchitæ <expan abbr="nõ">non</expan> e&longs;t fabula. <emph.end type="italics"/></cell><cell>26</cell></row><row><cell><emph type="italics"/>Contraria quæ &longs;int verè. <emph.end type="italics"/></cell><cell>18</cell></row><row><cell><emph type="italics"/>Commotum facilius mouetur, quam quie&longs;cens. <emph.end type="italics"/></cell><cell>199</cell></row><row><cell><emph type="italics"/>Connexum & concauum non &longs;unt con-traria. <emph.end type="italics"/></cell><cell>19</cell></row><row><cell><emph type="italics"/>Cochlea quid. <emph.end type="italics"/></cell><cell>131</cell></row><row><cell><emph type="italics"/>Cochleæ effecta. <emph.end type="italics"/></cell><cell>133</cell></row><row><cell><emph type="italics"/>Cochlea magnes vires habet. <emph.end type="italics"/></cell><cell>133</cell></row><row><cell><emph type="italics"/>Cochlea infinita. <emph.end type="italics"/></cell><cell>133</cell></row><row><cell><emph type="italics"/>Cochleæ Ari&longs;toteles non meminit. <emph.end type="italics"/></cell><cell>131</cell></row><row><cell><emph type="italics"/>Cochlea e&longs;t cuneus multiplicatus, vel vnus cuneus continuatus. <emph.end type="italics"/></cell><cell>131</cell></row><row><cell><emph type="italics"/>Cuneus e&longs;t vectu duplicatus. <emph.end type="italics"/></cell><cell>127</cell></row><row><cell><emph type="italics"/>Cuneum vicem gerere duorum vectium demon&longs;tratio linearis. <emph.end type="italics"/></cell><cell>130</cell></row><row><cell><emph type="italics"/>Cuneus quid. <emph.end type="italics"/></cell><cell>126</cell></row><row><cell><emph type="italics"/>Cunci v&longs;us. <emph.end type="italics"/></cell><cell>127</cell></row><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.034.jpg"/><row><cell><emph type="italics"/>Cuneimagna vis. <emph.end type="italics"/></cell><cell>127.127</cell></row><row><cell><emph type="italics"/>Cuneo magnæ moles diuiduntur. <emph.end type="italics"/></cell><cell>125</cell></row><row><cell><emph type="italics"/>Crocæ Ari&longs;toteliquid. <emph.end type="italics"/></cell><cell>123</cell></row><row><cell><emph type="italics"/>Crocæ rotundæ. <emph.end type="italics"/></cell><cell>122.123</cell></row><row><cell><emph type="italics"/>Cubus &longs;tabilißima figurarum. <emph.end type="italics"/></cell><cell>103</cell></row><row><cell><emph type="italics"/>Currus iam commotus facilius moue-tur. <emph.end type="italics"/></cell><cell>200</cell></row><row><cell><emph type="italics"/>D<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Dædali &longs;tatuæliberæ, & ligatæ. <emph.end type="italics"/></cell><cell>25</cell></row><row><cell><emph type="italics"/>Decubitus &longs;anorum in lecto. <emph.end type="italics"/></cell><cell>176</cell></row><row><cell><emph type="italics"/>Dens corro&longs;us eximidebet. <emph.end type="italics"/></cell><cell>153</cell></row><row><cell><emph type="italics"/>Dens non temere eximi debet. <emph.end type="italics"/></cell><cell>153</cell></row><row><cell><emph type="italics"/>Dens forcipe facilius, quam manu euelli-tur. <emph.end type="italics"/></cell><cell>153</cell></row><row><cell><emph type="italics"/>Dentiducus quid. <emph.end type="italics"/></cell><cell>132</cell></row><row><cell><emph type="italics"/><expan abbr="D&etilde;tes">Dentes</expan> <expan abbr="animali&utilde;">animalium</expan> inci&longs;ij &longs;unt cunei. <emph.end type="italics"/></cell><cell>129</cell></row><row><cell><emph type="italics"/>Dens priu&longs;quam eximatur duo fieri po-&longs;tulat. <emph.end type="italics"/></cell><cell>154</cell></row><row><cell><emph type="italics"/>Dentis euellendi differentia à clauo in-fixo. <emph.end type="italics"/></cell><cell>154</cell></row><row><cell><emph type="italics"/>Deusnon admiratur. <emph.end type="italics"/></cell><cell>5</cell></row><row><cell><emph type="italics"/>Diaconus &longs;acris ve&longs;tibus indutus imponit crucem apici obeli&longs;ci. <emph.end type="italics"/></cell><cell>142</cell></row><row><cell><emph type="italics"/>Diameter circuli, & Sphæræ in&longs;i&longs;tit plano ad rectos. <emph.end type="italics"/></cell><cell>105</cell></row><row><cell><emph type="italics"/>Diametri ad peripheriam quæratio. <emph.end type="italics"/></cell><cell>32</cell></row><row><cell><emph type="italics"/>Dies impo&longs;itæ crucis obeli&longs;co. <emph.end type="italics"/></cell><cell>142</cell></row><row><cell><emph type="italics"/>Dolabra e&longs;t cuneus. <emph.end type="italics"/></cell><cell>130</cell></row><row><cell><emph type="italics"/>Dominicus Fontana machinator in&longs;i-gnis. <emph.end type="italics"/></cell><cell>139</cell></row><row><cell><emph type="italics"/>Dominici Fontanæ triumphus. <emph.end type="italics"/></cell><cell>142</cell></row><row><cell><emph type="italics"/>Domus integra à &longs;undamentis &longs;ublata, & aliò tran&longs;lata. <emph.end type="italics"/></cell><cell>133</cell></row><row><cell><emph type="italics"/>E<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Elementa quie&longs;icunt adrectos angu-los &longs;ita. <emph.end type="italics"/></cell><cell>196</cell></row><row><cell><emph type="italics"/>En&longs;is e&longs;t cuneus. <emph.end type="italics"/></cell><cell>130</cell></row><row><cell><foreign lang="greek">*epipo/laia</foreign> <emph type="italics"/>vis quæ. <emph.end type="italics"/></cell><cell>201.202</cell></row><row><cell><emph type="italics"/>Equus Troianus machina er at. <emph.end type="italics"/></cell><cell>12</cell></row><row><cell><emph type="italics"/>Ergat a quid. <emph.end type="italics"/></cell><cell>119</cell></row><row><cell><emph type="italics"/>Ergatæ, & &longs;ucculæ di&longs;tinctio. <emph.end type="italics"/></cell><cell>129</cell></row><row><cell><emph type="italics"/>Ergatam collopes maiores minoribus fa-cilius mouent. <emph.end type="italics"/></cell><cell>118.119</cell></row><row><cell><emph type="italics"/>Exercitium militum in exercitu ferian-tium. <emph.end type="italics"/></cell><cell>125</cell></row><row><cell><emph type="italics"/>Exigua quæ. <emph.end type="italics"/></cell><cell>204</cell></row><row><cell><emph type="italics"/>F<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Fabrilis ars certitudine vincit cæte-ras. <emph.end type="italics"/></cell><cell>4</cell></row><row><cell><emph type="italics"/>Figura hominis <expan abbr="dec&utilde;bentis">decumbentis</expan> exirema. <emph.end type="italics"/></cell><cell>176</cell></row><row><cell><emph type="italics"/>Figura <expan abbr="corpor&utilde;iuuat">corporuniuuat</expan>, velimpedit mul-tum corum inclinationes, & natura-les impetus. <emph.end type="italics"/></cell><cell>164</cell></row><row><cell><emph type="italics"/>Figura decubitus humida, &longs;eu mediæ quæ. <emph.end type="italics"/></cell><cell>176</cell></row><row><cell><emph type="italics"/>Forceps, & forfex quid. <emph.end type="italics"/></cell><cell>152</cell></row><row><cell><emph type="italics"/>Fortuna in&longs;i&longs;tit Spharæ. <emph.end type="italics"/></cell><cell>103</cell></row><row><cell><emph type="italics"/>Funda quid. <emph.end type="italics"/></cell><cell>116</cell></row><row><cell><emph type="italics"/>Funda inuentum Phænicuno. <emph.end type="italics"/></cell><cell>116</cell></row><row><cell><emph type="italics"/>Fundæ v&longs;us. <emph.end type="italics"/></cell><cell>116.117</cell></row><row><cell><emph type="italics"/>Fundæ cur Balearis. <emph.end type="italics"/></cell><cell>116</cell></row><row><cell><emph type="italics"/>Funda longius proijcit, quam manus. <emph.end type="italics"/></cell><cell>115.117</cell></row><row><cell><emph type="italics"/>Fundaiacit lapidem & plumbum. <emph.end type="italics"/></cell><cell>117</cell></row><row><cell><emph type="italics"/>Fu&longs;tis ad genu fractus non lædit. <emph.end type="italics"/></cell><cell>122</cell></row><row><cell><emph type="italics"/>Fu&longs;tis duobus cyphis impo&longs;itus frangitur &longs;ine cyphorum fractione & aquæ effu-&longs;ione. <emph.end type="italics"/></cell><cell>122</cell></row><row><cell><emph type="italics"/>G<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Georgij Lhullerij machina. <emph.end type="italics"/></cell><cell>137.138</cell></row><row><cell><emph type="italics"/>Gubernaculum & eius partes. <emph.end type="italics"/></cell><cell>73</cell></row><row><cell><emph type="italics"/>Gubernaculi & remi differentia. <emph.end type="italics"/></cell><cell>76</cell></row><row><cell><emph type="italics"/>Gubernaculi magna vis in nauis motio-ne. <emph.end type="italics"/></cell><cell>71.72</cell></row><row><cell><emph type="italics"/>Gyraphi &longs;oli crura po&longs;teriora prioribus breuiora habent. <emph.end type="italics"/></cell><cell>112</cell></row><row><cell><emph type="italics"/>H<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Ha&longs;tæ ferrum e&longs;t cuneus. <emph.end type="italics"/></cell><cell>190</cell></row><row><cell><emph type="italics"/>Hominem quie&longs;cere, &longs;edare, &longs;urge-re, &longs;tare, ambulare, currere e&longs;t ex v&longs;u Geometriæ,<emph.end type="italics"/></cell><cell>198</cell></row><row><cell><emph type="italics"/>Hominis quies e&longs;t per rectos angulos. <emph.end type="italics"/></cell><cell>196</cell></row><row><cell><emph type="italics"/>Hominis ambulatio, & progre&longs;sio, vs fiat. <emph.end type="italics"/></cell><cell>198</cell></row><row><cell><emph type="italics"/>Homo <expan abbr="nõ">non</expan> &longs;tatrectus, vt <expan abbr="cæl&utilde;">cælum</expan> videus. <emph.end type="italics"/></cell><cell>194</cell></row><row><cell><emph type="italics"/>Homo vnde factus Mechanicus. <emph.end type="italics"/></cell><cell>7.8</cell></row><row><cell><emph type="italics"/>Homo &longs;olus admiratur. <emph.end type="italics"/></cell><cell>5</cell></row><row><cell><emph type="italics"/>Homo &longs;olus artifex. <emph.end type="italics"/></cell><cell>194</cell></row><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.035.jpg"/><row><cell><emph type="italics"/>Homo &longs;oius &longs;edere pote&longs;t. <emph.end type="italics"/></cell><cell>194</cell></row><row><cell><emph type="italics"/>Homo magnus & paruuus quis. <emph.end type="italics"/></cell><cell>19</cell></row><row><cell><emph type="italics"/>Homines duo ferentes pondus cum perti-ca, &longs;i pondus non e&longs;t in eius medio, non æqualiter premuntur. <emph.end type="italics"/></cell><cell>190.191</cell></row><row><cell><emph type="italics"/>Horologia nostritemporis veterum cle-p&longs;ydras, & gnemones antecellunt. <emph.end type="italics"/></cell><cell>26</cell></row><row><cell><emph type="italics"/>Plorologium Argentorati <expan abbr="magni&longs;ic&utilde;">magnificum</expan>. <emph.end type="italics"/></cell><cell>26</cell></row><row><cell><emph type="italics"/>Humero dextro onera difficilius ferun-tur, quam &longs;ini&longs;tro. <emph.end type="italics"/></cell><cell>187</cell></row><row><cell><emph type="italics"/>Hypomochlium quid. <emph.end type="italics"/></cell><cell>14.55</cell></row><row><cell><emph type="italics"/>I<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Iaccre &longs;upinum quid. <emph.end type="italics"/></cell><cell>194</cell></row><row><cell><emph type="italics"/>lacere pronum. <emph.end type="italics"/></cell><cell>194</cell></row><row><cell><emph type="italics"/>Jacere &longs;upinum & pronum commune e&longs;t multis anim antibus. <emph.end type="italics"/></cell><cell>194</cell></row><row><cell><emph type="italics"/>Joannis iucundi problema. <emph.end type="italics"/></cell><cell>145</cell></row><row><cell><emph type="italics"/>L<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Lancea <expan abbr="perp&etilde;dicularis">perpendicularis</expan> facilius fer-tur, quam obliquata. <emph.end type="italics"/></cell><cell>185</cell></row><row><cell><emph type="italics"/>Lecti lateribus cur fiunt dupli. <emph.end type="italics"/></cell><cell>175</cell></row><row><cell><emph type="italics"/>Libra maior e&longs;t exactior minore. <emph.end type="italics"/></cell><cell>27.44. 45</cell></row><row><cell><emph type="italics"/>Libræ finis. <emph.end type="italics"/></cell><cell>4</cell></row><row><cell><emph type="italics"/>Libræpartes. <emph.end type="italics"/></cell><cell>45.46</cell></row><row><cell><emph type="italics"/>Libræfallaciæ. <emph.end type="italics"/></cell><cell>46.47</cell></row><row><cell><emph type="italics"/>Libræ valde exigua examinantis fabri-ca. <emph.end type="italics"/></cell><cell>47</cell></row><row><cell><emph type="italics"/>Librile <expan abbr="ab&longs;q;">ab&longs;que</expan> <expan abbr="põdere">pondere</expan> facilius mouetur. <emph.end type="italics"/></cell><cell>112</cell></row><row><cell><emph type="italics"/>Librilis brachia vt <expan abbr="maneãt">maneant</expan>, aut redeant ad <expan abbr="æquilibri&utilde;">æquilibrium</expan> &longs;ublatis <expan abbr="põderilus">ponderilus</expan>. <emph.end type="italics"/></cell><cell>49.50</cell></row><row><cell><emph type="italics"/>Librile <expan abbr="ligne&utilde;">ligneum</expan> facilius mouetur ferreo. <emph.end type="italics"/></cell><cell>113</cell></row><row><cell><emph type="italics"/>Lignalongiora &longs;unt imbecilliora. <emph.end type="italics"/></cell><cell>124</cell></row><row><cell><emph type="italics"/>Ligna longa ab extremo difficilius <expan abbr="fer&utilde;-tur">ferun-tur</expan> bumere, quam à medio. <emph.end type="italics"/></cell><cell>183.184</cell></row><row><cell><emph type="italics"/>Lignum vt è genu facilius <expan abbr="frãgatur">frangatur</expan>. <emph.end type="italics"/></cell><cell>121</cell></row><row><cell><emph type="italics"/>Linea de&longs;cribens circulum <expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> duas lationes &longs;ertur. <emph.end type="italics"/></cell><cell>28.34</cell></row><row><cell><emph type="italics"/><expan abbr="Long&utilde;">Longum</expan> pondus difficilius fertur humero, <expan abbr="quã">quam</expan> brcue, vt &longs;it <expan abbr="põdere">pondere</expan> æquale. <emph.end type="italics"/></cell><cell>186.187</cell></row><row><cell><emph type="italics"/>Lorain lectis extenduntur non &longs;ecundum diametrum. <emph.end type="italics"/></cell><cell>175.177</cell></row><row><cell><emph type="italics"/>M<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Machina quid. <emph.end type="italics"/></cell><cell>2</cell></row><row><cell><emph type="italics"/>Machinarum quædam per &longs;e, quædam-non per&longs;e mouentur. <emph.end type="italics"/></cell><cell>10</cell></row><row><cell><emph type="italics"/>Machinæ valentißimæ tres ex &longs;ententia Hippocratis. <emph.end type="italics"/></cell><cell>119</cell></row><row><cell><emph type="italics"/>Machinarum pluribus, & diuer&longs;arum compo&longs;itio adæquat vnam, quæ tanta, quanta opus e&longs;&longs;et fierinon pote&longs;t, pro-pter defectum materiæ. <emph.end type="italics"/></cell><cell>138.139</cell></row><row><cell><emph type="italics"/>Machinæ ad ædificia, & ad bellum. <emph.end type="italics"/></cell><cell>10</cell></row><row><cell><emph type="italics"/>in Machinis faciendis lex ob&longs;eruanda. <emph.end type="italics"/></cell><cell>10</cell></row><row><cell><emph type="italics"/>Magnetis vis. <emph.end type="italics"/></cell><cell>129</cell></row><row><cell><emph type="italics"/>Magna quæ. <emph.end type="italics"/></cell><cell>204</cell></row><row><cell><emph type="italics"/>Malus nauis. <emph.end type="italics"/></cell><cell>92</cell></row><row><cell><emph type="italics"/>Mali pterna. <emph.end type="italics"/></cell><cell>92</cell></row><row><cell><emph type="italics"/>Mallei <expan abbr="lõgius">longius</expan> <expan abbr="manubri&utilde;">manubrium</expan> grauius ferit. <emph.end type="italics"/></cell><cell>128</cell></row><row><cell><emph type="italics"/>Manganaria pars Mechanices. <emph.end type="italics"/></cell><cell>11</cell></row><row><cell><emph type="italics"/>Manus e&longs;t <expan abbr="in&longs;trum&etilde;t&utilde;">in&longs;trumentum</expan> <expan abbr="in&longs;trum&etilde;tor&utilde;">in&longs;trumentorum</expan>. <emph.end type="italics"/></cell><cell>194</cell></row><row><cell><emph type="italics"/>Manus tres partes. <emph.end type="italics"/></cell><cell>118</cell></row><row><cell><emph type="italics"/>Mechanica cur non e&longs;&longs;e Aristotelis vi-&longs;um &longs;it Cardano & <expan abbr="Frãci&longs;co">Franci&longs;co</expan> patricio. <emph.end type="italics"/></cell><cell>1</cell></row><row><cell><emph type="italics"/>Mechanica &longs;unt Aristotelis. <emph.end type="italics"/></cell><cell>2</cell></row><row><cell><emph type="italics"/>Mechanicorum diui&longs;io. <emph.end type="italics"/></cell><cell>2</cell></row><row><cell><emph type="italics"/>Mechanica vnde dicta. <emph.end type="italics"/></cell><cell>2.11</cell></row><row><cell><emph type="italics"/>Mechanica quæ dici debeant. <emph.end type="italics"/></cell><cell>2</cell></row><row><cell><emph type="italics"/>Mechanice quid. <emph.end type="italics"/></cell><cell>8.9</cell></row><row><cell><emph type="italics"/>Mechanice partim e&longs;t phy&longs;ica, partim mathematica. <emph.end type="italics"/></cell><cell>4.12.13</cell></row><row><cell><emph type="italics"/>Mechanicæ artes vnde dictæ. <emph.end type="italics"/></cell><cell>2.3</cell></row><row><cell><emph type="italics"/>Mechanice pars e&longs;t philo&longs;ophiæ. <emph.end type="italics"/></cell><cell>9</cell></row><row><cell><emph type="italics"/>Mechanices finis. <emph.end type="italics"/></cell><cell>9</cell></row><row><cell><emph type="italics"/>Mechanicus ante aggreßionem operis quid con&longs;iderare debeat. <emph.end type="italics"/></cell><cell>13</cell></row><row><cell><emph type="italics"/>Mechanice dicendi<emph.end type="italics"/> <foreign lang="greek">paradocopoioi\. </foreign></cell><cell>12</cell></row><row><cell><emph type="italics"/>laus Mechanicorum. <emph.end type="italics"/></cell><cell>142</cell></row><row><cell><emph type="italics"/>Mens e&longs;t ars artium. <emph.end type="italics"/></cell><cell>194</cell></row><row><cell><emph type="italics"/>Men&longs;ura rei cuiu&longs;que debet e&longs;&longs;e deter-minata. <emph.end type="italics"/></cell><cell>44</cell></row><row><cell><emph type="italics"/>Mercatura opulenta. <emph.end type="italics"/></cell><cell>4</cell></row><row><cell><emph type="italics"/>Mercurius in&longs;istit cubo. <emph.end type="italics"/></cell><cell>103</cell></row><row><cell><emph type="italics"/>Milij grana non &longs;unt &longs;impliciter exigua. <emph.end type="italics"/></cell><cell>204</cell></row><row><cell><emph type="italics"/>Militaris ars vtilitate vincit cæteras. <emph.end type="italics"/></cell><cell>4</cell></row><row><cell><emph type="italics"/>Milo cuneum contemnens peryt. <emph.end type="italics"/></cell><cell>127</cell></row><row><cell><emph type="italics"/>Mobile motum quò vergit facile moue<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.036.jpg"/><emph type="italics"/>tur. <emph.end type="italics"/></cell><cell>103</cell></row><row><cell><emph type="italics"/>Mobilis primi velocitas vt intelligatur. <emph.end type="italics"/></cell><cell>104. </cell></row><row><cell><emph type="italics"/>Mobilis primi motus e&longs;t men&longs;ura alio-rum motuum. <emph.end type="italics"/></cell><cell>104</cell></row><row><cell><emph type="italics"/>Mobile latius mouetur difficilius. <emph.end type="italics"/></cell><cell>104</cell></row><row><cell><emph type="italics"/>Moles exigua &longs;æpe magnam vim obti-net. <emph.end type="italics"/></cell><cell>129</cell></row><row><cell><emph type="italics"/>Motus fit in tempore, & &longs;ucceßiuè. <emph.end type="italics"/></cell><cell>205</cell></row><row><cell><emph type="italics"/>Motus minimus quis. <emph.end type="italics"/></cell><cell>104</cell></row><row><cell><emph type="italics"/>Mota duobus motibus ad eundem <expan abbr="ter-min&utilde;">ter-minum</expan> <expan abbr="tend&etilde;tibus">tendentibus</expan> celerius <expan abbr="mou&etilde;tur">mouentur</expan>. <emph.end type="italics"/></cell><cell>163</cell></row><row><cell><emph type="italics"/>Motum duabus lationibus rationem ha-bentibus fertur <expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> <expan abbr="rectã">rectam</expan> <expan abbr="lineã">lineam</expan>. <emph.end type="italics"/></cell><cell>30</cell></row><row><cell><emph type="italics"/>Motum duabus lationibus rationem non habentibus <expan abbr="nõ">non</expan> fertur <expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> <expan abbr="rectã">rectam</expan>. <emph.end type="italics"/></cell><cell>30</cell></row><row><cell><emph type="italics"/>Motus circularis omnium machinatio-num principia continet. <emph.end type="italics"/></cell><cell>60</cell></row><row><cell><emph type="italics"/>Motus difficultas in mobili à quibus pen-deat. <emph.end type="italics"/></cell><cell>101</cell></row><row><cell><emph type="italics"/>Mulier parua non e&longs;t pulchræ. <emph.end type="italics"/></cell><cell>19</cell></row><row><cell><emph type="italics"/>Mundus nutans non vere dici de terra à poëta. <emph.end type="italics"/></cell><cell>104</cell></row><row><cell><emph type="italics"/>Mu&longs;culus vecti comparatus à Galeno. <emph.end type="italics"/></cell><cell>56</cell></row><row><cell><emph type="italics"/>N<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Natura <expan abbr="eod&etilde;">eodem</expan> modo &longs;emper opera-tur, & eundem &longs;copum habet. <emph.end type="italics"/></cell><cell>6</cell></row><row><cell><emph type="italics"/>Natura re&longs;i&longs;tit arti in multis. <emph.end type="italics"/></cell><cell>8</cell></row><row><cell><emph type="italics"/>Nauigandi ars admirabilis ob &longs;ubtilita-tem, & nauigationis pericula. <emph.end type="italics"/></cell><cell>62</cell></row><row><cell><emph type="italics"/>Nauigij Hieronis de&longs;criptio incredibi-lis. <emph.end type="italics"/></cell><cell>73</cell></row><row><cell><emph type="italics"/>Nauis quid, & partes. <emph.end type="italics"/></cell><cell>62</cell></row><row><cell><emph type="italics"/>Nauis Ptolemaicæ magnitudo. <emph.end type="italics"/></cell><cell>63</cell></row><row><cell><emph type="italics"/>Nauis iam mota &longs;acilius mouetur. <emph.end type="italics"/></cell><cell>201</cell></row><row><cell><emph type="italics"/>Nauis plus vehitur antror&longs;um, quam re-mi palmula retror&longs;um. <emph.end type="italics"/></cell><cell>80</cell></row><row><cell><emph type="italics"/>Nauis actuariæ promotio. <emph.end type="italics"/></cell><cell>69</cell></row><row><cell><emph type="italics"/>Nauis velocit as à quibus. <emph.end type="italics"/></cell><cell>93</cell></row><row><cell><emph type="italics"/>Nauium &longs;pecies. <emph.end type="italics"/></cell><cell>63</cell></row><row><cell><emph type="italics"/>Nauicula è plumbo tenui &longs;upernatat aquæ. <emph.end type="italics"/></cell><cell>164</cell></row><row><cell><emph type="italics"/>Nautæ in procellis &longs;olo vtuntur dolone. <emph.end type="italics"/></cell><cell>94</cell></row><row><cell><emph type="italics"/>Nautica ars opulenta. <emph.end type="italics"/></cell><cell>4</cell></row><row><cell><emph type="italics"/>Nuces à nucifrangibulo &longs;ine ictu facilius franguntur, quam cum ictu. <emph.end type="italics"/></cell><cell>155.156</cell></row><row><cell><emph type="italics"/><expan abbr="Nucifrãgibuli">Nucifrangibuli</expan> & forcipis di&longs;tinctio. <emph.end type="italics"/></cell><cell>156</cell></row><row><cell><emph type="italics"/>Nucifrangibulum ferreum facilius nu-cem frangit, quam ligneum. <emph.end type="italics"/></cell><cell>167</cell></row><row><cell><emph type="italics"/>Nutus quid. <emph.end type="italics"/></cell><cell>104.108</cell></row><row><cell><emph type="italics"/>Nutus quotuplex. <emph.end type="italics"/></cell><cell>108</cell></row><row><cell><emph type="italics"/>Nutus maioris peripheriæ maior e&longs;t, quam minoris. <emph.end type="italics"/></cell><cell>108</cell></row><row><cell><emph type="italics"/>O<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Obeli&longs;cus quid. <emph.end type="italics"/></cell><cell>139</cell></row><row><cell><emph type="italics"/>Obeli&longs;cus Xy&longs;tiqualis & <expan abbr="quãtus">quantus</expan>. <emph.end type="italics"/></cell><cell>139</cell></row><row><cell><emph type="italics"/>Obeli&longs;cus Xy&longs;ti cuiprimo &longs;acer. <emph.end type="italics"/></cell><cell>140</cell></row><row><cell><emph type="italics"/>Obeli&longs;cus vbi&longs;itus erat. <emph.end type="italics"/></cell><cell>140</cell></row><row><cell><emph type="italics"/>quid Obeli&longs;cus tran&longs;latus, & Christo &longs;acer cum cruce &longs;uper apice &longs;uo impo&longs;i-ta Christianis &longs;ignificat. <emph.end type="italics"/></cell><cell>140</cell></row><row><cell><emph type="italics"/>molimina circa Obeli&longs;ci tran&longs;lationem quinque, omnia difficillima. <emph.end type="italics"/></cell><cell>140</cell></row><row><cell><emph type="italics"/>ad Obeli&longs;cum transferendum quæ ma-chinæ, & quot adhibitæ. <emph.end type="italics"/></cell><cell>140</cell></row><row><cell><emph type="italics"/>circa <expan abbr="Obeli&longs;c&utilde;">Obeli&longs;cum</expan> molitiones quiuque, quo-modo, & à quibus perfectæ. <emph.end type="italics"/></cell><cell>141</cell></row><row><cell><emph type="italics"/>Obeli&longs;ci in area V aticani ante portam D. Fetri po&longs;iti Ichnographiæ. <emph.end type="italics"/></cell><cell>143</cell></row><row><cell><emph type="italics"/>de Obeli&longs;co & Xy&longs;to V. Summ. Pont. & cruce Gulielmi Blanci <expan abbr="epigrãma">epigramma</expan>. <emph.end type="italics"/></cell><cell>142</cell></row><row><cell><foreign lang="greek">*odonta/gra *h)/ \o)donta/gw=gos</foreign> <emph type="italics"/>quid. <emph.end type="italics"/></cell><cell>152</cell></row><row><cell><foreign lang="greek">*odonta/gw=gos</foreign> <emph type="italics"/><expan abbr="pl&utilde;beus">plumbeus</expan> in <expan abbr="t&etilde;plo">templo</expan> Apol-linis Delphici quid &longs;ignificabat. <emph.end type="italics"/></cell><cell>153</cell></row><row><cell><emph type="italics"/>Ovos quid. <emph.end type="italics"/></cell><cell>119</cell></row><row><cell><emph type="italics"/>Os arietinum volæ manus impo&longs;itum frangitur manu illæ&longs;a. <emph.end type="italics"/></cell><cell>122</cell></row><row><cell><foreign lang="greek">*ourano/skopos</foreign> <emph type="italics"/>pi&longs;cis velit nolio videt cælum. <emph.end type="italics"/></cell><cell>195</cell></row><row><cell><emph type="italics"/>P<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Palang a quid. <emph.end type="italics"/></cell><cell>191</cell></row><row><cell><emph type="italics"/>Pedem facere. <emph.end type="italics"/></cell><cell>95</cell></row><row><cell><emph type="italics"/>Pente&longs;paston. <emph.end type="italics"/></cell><cell>111.134</cell></row><row><cell><emph type="italics"/>Percußio quid. <emph.end type="italics"/></cell><cell>128</cell></row><row><cell><emph type="italics"/>Percu&longs;sionis duo modi. <emph.end type="italics"/></cell><cell>128</cell></row><row><cell><emph type="italics"/>Percußio à quibus fit maior. <emph.end type="italics"/></cell><cell>128</cell></row><row><cell><emph type="italics"/>Percußionis validiores cau&longs;æ. <emph.end type="italics"/></cell><cell>128.129</cell></row><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.037.jpg"/><row><cell><emph type="italics"/>Percu&longs;sionis magna vis ad mouendum, findendum, frangendum, quatien-dum. <emph.end type="italics"/></cell><cell>129</cell></row><row><cell><emph type="italics"/>Perpendiculares à peripherijs in &longs;emi-diametros circulorum inæqualium æquales auferunt &longs;egmenta &longs;emidia-metrorum inæqualia, quorum maius e&longs;t quod è minori aufertur. <emph.end type="italics"/></cell><cell>40</cell></row><row><cell><emph type="italics"/>Peripheriæ maiores à punctis à centro remotioribus de&longs;cribuntur. <emph.end type="italics"/></cell><cell>23</cell></row><row><cell><emph type="italics"/>Petorita Gallorum petoritis Polonorum difficilius mouentur. <emph.end type="italics"/></cell><cell>113</cell></row><row><cell><emph type="italics"/>Phalanga quid. <emph.end type="italics"/></cell><cell>191</cell></row><row><cell><emph type="italics"/>Phalangary qui. <emph.end type="italics"/></cell><cell>191</cell></row><row><cell><emph type="italics"/>Phalangarij tetraphori, hexaphori. <emph.end type="italics"/></cell><cell>191</cell></row><row><cell><emph type="italics"/>Phalangij ictus. <emph.end type="italics"/></cell><cell>129</cell></row><row><cell><emph type="italics"/>Phalanx. <emph.end type="italics"/></cell><cell>146</cell></row><row><cell><emph type="italics"/>Philo&longs;ophia principium duxit ab admi-ratione. <emph.end type="italics"/></cell><cell>5</cell></row><row><cell><emph type="italics"/>Philo&longs;ophia e&longs;t ars generalis omnibus fa-ciendorum difficultatibus &longs;uccurrens. <emph.end type="italics"/></cell><cell>9</cell></row><row><cell><emph type="italics"/>Philo&longs;ophandi, vt admirandi &longs;emper oc-ca&longs;io erit. <emph.end type="italics"/></cell><cell>5</cell></row><row><cell><emph type="italics"/>Plumbum vtri aëre pleno annexum tar-dius de&longs;cendit in aquim, quam &longs;i non e&longs;&longs;et aunexum. <emph.end type="italics"/></cell><cell>170</cell></row><row><cell><foreign lang="greek">*po/da e)rei=n,</foreign> <emph type="italics"/>& canere quid. <emph.end type="italics"/></cell><cell>95</cell></row><row><cell><foreign lang="greek">*po/des, & pro/podes. </foreign></cell><cell>96</cell></row><row><cell><foreign lang="greek">*poliorkitik*h\</foreign> <emph type="italics"/>pars Mechanices. <emph.end type="italics"/></cell><cell>11</cell></row><row><cell><foreign lang="greek">*polu/spaston. </foreign></cell><cell>111. 134</cell></row><row><cell><emph type="italics"/>Pons Lutetiæ ab Henrico 111. inchoatus ab Henrico 1111. perficietur. <emph.end type="italics"/></cell><cell>120</cell></row><row><cell><emph type="italics"/>Preßio porrecta. <emph.end type="italics"/></cell><cell>14</cell></row><row><cell><emph type="italics"/>Problema difficillimum totius libri. <emph.end type="italics"/></cell><cell>166</cell></row><row><cell><emph type="italics"/>Problematis a theoremate di&longs;tinctio. <emph.end type="italics"/></cell><cell>12</cell></row><row><cell><emph type="italics"/>Progreßio in animali vt fit. <emph.end type="italics"/></cell><cell>187</cell></row><row><cell><emph type="italics"/>Proiecta cur moueri de&longs;inunt. <emph.end type="italics"/></cell><cell>201</cell></row><row><cell><emph type="italics"/>in Proiectis impre&longs;&longs;a vis impellens à mo-tore e&longs;t can&longs;a eorum lationis. <emph.end type="italics"/></cell><cell>201</cell></row><row><cell><emph type="italics"/>Proiecta nec exigua nec magna &longs;eruntur procul. <emph.end type="italics"/></cell><cell>203.205</cell></row><row><cell><emph type="italics"/>Publ. Scipio & C. Lælius colligentes cro-cas quæ dicerent. <emph.end type="italics"/></cell><cell>123</cell></row><row><cell><emph type="italics"/>Purpura quid. <emph.end type="italics"/></cell><cell>47.48</cell></row><row><cell><emph type="italics"/>Q<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Qvie&longs;cens vim motoris diminuit. <emph.end type="italics"/></cell><cell>200</cell></row><row><cell><emph type="italics"/>R<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Radius minor plus retrahitur ad centrum, quam maior. <emph.end type="italics"/></cell><cell>38.39</cell></row><row><cell><emph type="italics"/>Rectilineæ figuræ, & cubus difficulter mouentur &longs;uper planum. <emph.end type="italics"/></cell><cell>102</cell></row><row><cell><emph type="italics"/>Remus quid. <emph.end type="italics"/></cell><cell>63</cell></row><row><cell><emph type="italics"/>Remiges qui. <emph.end type="italics"/></cell><cell>63</cell></row><row><cell><emph type="italics"/>Remigum differentiæ. <emph.end type="italics"/></cell><cell>64</cell></row><row><cell><emph type="italics"/>Remiges me&longs;onei maximè mouent na-uim. <emph.end type="italics"/></cell><cell>61</cell></row><row><cell><emph type="italics"/>Remi digitis manuum comparati. <emph.end type="italics"/></cell><cell>65</cell></row><row><cell><emph type="italics"/>Remus vt plurimum maris diuidit. <emph.end type="italics"/></cell><cell>71</cell></row><row><cell><emph type="italics"/>de Remi motione comparata ad motio-nem nauis. <emph.end type="italics"/></cell><cell>84.85.86.87.88.89</cell></row><row><cell><emph type="italics"/>qui <expan abbr="Remig&utilde;">Remigum</expan> plus nauim promoueant. <emph.end type="italics"/></cell><cell>68</cell></row><row><cell><emph type="italics"/>in Rhombo punctum vnum extremum lateris motum duobus motibus minus &longs;paty conficit, quam latus ip&longs;um. <emph.end type="italics"/></cell><cell>159</cell></row><row><cell><emph type="italics"/>Rhombus con&longs;tituitur cuius angulus acu-tus e&longs;t dimidio obtu&longs;i minor. <emph.end type="italics"/></cell><cell>161</cell></row><row><cell><emph type="italics"/>in Rhombo alterum punctorum extre-morum non æqualem <expan abbr="rectã">rectam</expan> tran&longs;it. <emph.end type="italics"/></cell><cell>157</cell></row><row><cell><emph type="italics"/>Rhombus quid. <emph.end type="italics"/></cell><cell>159</cell></row><row><cell><emph type="italics"/>Rotæ binæ quaternis faciliores. <emph.end type="italics"/></cell><cell>111</cell></row><row><cell><emph type="italics"/>in Rotis quaternis po&longs;teriores prioribus maiorese&longs;&longs;e debent. <emph.end type="italics"/></cell><cell>111</cell></row><row><cell><emph type="italics"/>Rotæ curruum maiores commodiores ad facilitatem & celeritatem. <emph.end type="italics"/></cell><cell>110</cell></row><row><cell><emph type="italics"/>Rotunda figura difficulter patitur. <emph.end type="italics"/></cell><cell>124</cell></row><row><cell><emph type="italics"/>Rotunda maiora facilius mouentur mi-noribus. <emph.end type="italics"/></cell><cell>99.100</cell></row><row><cell><emph type="italics"/><expan abbr="Rot&utilde;dorum">Rotundorum</expan> motus accurata diui&longs;io. <emph.end type="italics"/></cell><cell>100</cell></row><row><cell><emph type="italics"/>S<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Sarcina maior in anteriore plaustri parte poni debet. <emph.end type="italics"/></cell><cell>111</cell></row><row><cell><emph type="italics"/>Saxa tritalantaria &longs;impliciter non &longs;unt magna. <emph.end type="italics"/></cell><cell>204</cell></row><row><cell><emph type="italics"/>Scorpionis ictus. <emph.end type="italics"/></cell><cell>129</cell></row><row><cell><emph type="italics"/>Scytala quid, & quotuplex. <emph.end type="italics"/></cell><cell>111.114</cell></row><row><cell><emph type="italics"/>Scytalæ v&longs;us duplex. <emph.end type="italics"/></cell><cell>111</cell></row><row><cell><emph type="italics"/>Super Scytalis onera facilius ge&longs;tantur,<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.038.jpg"/><emph type="italics"/>quam &longs;uper curribus. <emph.end type="italics"/></cell><cell>113</cell></row><row><cell><emph type="italics"/>Securis magna diuidit. <emph.end type="italics"/></cell><cell>145</cell></row><row><cell><emph type="italics"/>Securis feriens diuidit, premens non item. <emph.end type="italics"/></cell><cell>144</cell></row><row><cell><emph type="italics"/>Securis e&longs;t cuneus annexus malleo. <emph.end type="italics"/></cell><cell>145</cell></row><row><cell><emph type="italics"/>Sedere quid. <emph.end type="italics"/></cell><cell>194</cell></row><row><cell><emph type="italics"/>Sedens caput habet ad pedes parallelum, & nequaquam in vnarecta. <emph.end type="italics"/></cell><cell>193</cell></row><row><cell><emph type="italics"/>Sedentariæ artes vtuntur &longs;eßione &longs;ecu-ra. <emph.end type="italics"/></cell><cell>197</cell></row><row><cell><emph type="italics"/>Sedile idem non congruit omni homini. <emph.end type="italics"/></cell><cell>196</cell></row><row><cell><emph type="italics"/>Seßio propriè dista & latè<emph.end type="italics"/></cell><cell>197</cell></row><row><cell><emph type="italics"/>Seßio cum &longs;ecuritate. <emph.end type="italics"/></cell><cell>197</cell></row><row><cell><emph type="italics"/>Sedens altius &longs;urgit facilius. <emph.end type="italics"/></cell><cell>197.198</cell></row><row><cell><foreign lang="greek">*s*h/kwma</foreign> <emph type="italics"/>quid. <emph.end type="italics"/></cell><cell>151</cell></row><row><cell><emph type="italics"/>Spartion pro an&longs;a. <emph.end type="italics"/></cell><cell>148</cell></row><row><cell><emph type="italics"/>Sphæra quale corpus. <emph.end type="italics"/></cell><cell>16</cell></row><row><cell><emph type="italics"/>Sphæra corpus e&longs;t mobilißimum & mo-uentißimum. <emph.end type="italics"/></cell><cell>16</cell></row><row><cell><emph type="italics"/>Sphæra contingit planum in puncto. <emph.end type="italics"/></cell><cell>101</cell></row><row><cell><emph type="italics"/>Sphæra Archimedis per &longs;e mobilis non e&longs;t fabula. <emph.end type="italics"/></cell><cell>26</cell></row><row><cell><emph type="italics"/>Sphæratopæia pars e&longs;t mechanices. <emph.end type="italics"/></cell><cell>11</cell></row><row><cell><emph type="italics"/>Stateræ partes. <emph.end type="italics"/></cell><cell>147</cell></row><row><cell><emph type="italics"/>Stateræ v&longs;us. <emph.end type="italics"/></cell><cell>148</cell></row><row><cell><emph type="italics"/>Statera in pretio&longs;is expendendis non v&longs;urpatur, &longs;ed libra. <emph.end type="italics"/></cell><cell>147</cell></row><row><cell><emph type="italics"/>Statera commodior libra. <emph.end type="italics"/></cell><cell>147</cell></row><row><cell><emph type="italics"/>Statera vna mult æ &longs;unt libræ. <emph.end type="italics"/></cell><cell>148.149</cell></row><row><cell><emph type="italics"/>Statera e&longs;t vectis inuer&longs;us. <emph.end type="italics"/></cell><cell>150</cell></row><row><cell><emph type="italics"/>Stateræ paruo æquipondio magna ponde-ra expendunt. <emph.end type="italics"/></cell><cell>146.147.148</cell></row><row><cell><emph type="italics"/>Stateræ dimidium e&longs;t an&longs;a. <emph.end type="italics"/></cell><cell>148</cell></row><row><cell><emph type="italics"/>Per Stateram ponderationis factæ de-mon&longs;tratio. <emph.end type="italics"/></cell><cell>152</cell></row><row><cell><emph type="italics"/>Stare quid. <emph.end type="italics"/></cell><cell>194</cell></row><row><cell><emph type="italics"/>Stans e&longs;t perpendicularis terræ. <emph.end type="italics"/></cell><cell>193</cell></row><row><cell><emph type="italics"/>Stantis di&longs;po&longs;itio e&longs;t in recta linea. <emph.end type="italics"/></cell><cell>196</cell></row><row><cell><emph type="italics"/>Statio & &longs;eßio propria <expan abbr="s&utilde;t">sunt</expan> homini. <emph.end type="italics"/></cell><cell>194</cell></row><row><cell><foreign lang="greek">*stata</foreign> <emph type="italics"/>quæ. <emph.end type="italics"/></cell><cell>10</cell></row><row><cell><emph type="italics"/>Succula quid. <emph.end type="italics"/></cell><cell>119</cell></row><row><cell><emph type="italics"/>Surrectio e&longs;t motio. <emph.end type="italics"/></cell><cell>194</cell></row><row><cell><emph type="italics"/>Surrectio è iacente indiget acutis angu-lis. <emph.end type="italics"/></cell><cell>197</cell></row><row><cell><emph type="italics"/>Surgentes con&longs;tituunt angulum acutum ex femore cum tibia, tum ex thoræce & femore. <emph.end type="italics"/></cell><cell>193.195.196</cell></row><row><cell><emph type="italics"/>Surrectionis initium fit per acutos angu-los. <emph.end type="italics"/></cell><cell>198</cell></row><row><cell><emph type="italics"/>Surrectionis medium fit per rectum, & obtu&longs;os angulos. <emph.end type="italics"/></cell><cell>198</cell></row><row><cell><emph type="italics"/>Symmetria quid. <emph.end type="italics"/></cell><cell>19</cell></row><row><cell><emph type="italics"/>Symmetria pro analogia. <emph.end type="italics"/></cell><cell>205</cell></row><row><cell><emph type="italics"/>T<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Telum facilius ten&longs;a penetrat, quam laxa. <emph.end type="italics"/></cell><cell>202</cell></row><row><cell><emph type="italics"/>Terra cur immobilis. <emph.end type="italics"/></cell><cell>103.104</cell></row><row><cell><emph type="italics"/>Terra comparata cubo à Pythagoreis, & Platone. <emph.end type="italics"/></cell><cell>103.196</cell></row><row><cell><emph type="italics"/>Textus Ari&longs;totelis omnium mendo&longs;i&longs;-&longs;imus. <emph.end type="italics"/></cell><cell>178.179</cell></row><row><cell><emph type="italics"/>Thaletis factum in eclip&longs;i Solis. <emph.end type="italics"/></cell><cell>5</cell></row><row><cell><foreign lang="greek">*qaumatourgik*h\</foreign> <emph type="italics"/>pars Mechanices. <emph.end type="italics"/></cell><cell>11</cell></row><row><cell><emph type="italics"/>Theorematis à problemate di&longs;tinctio. <emph.end type="italics"/></cell><cell>12</cell></row><row><cell><emph type="italics"/>Tolleno quid. <emph.end type="italics"/></cell><cell>188.189</cell></row><row><cell><emph type="italics"/>Tollenonis v&longs;us. <emph.end type="italics"/></cell><cell>189</cell></row><row><cell><emph type="italics"/>Tollenonis tran&longs;uer &longs;ario pondus adie-ctum. <emph.end type="italics"/></cell><cell>188.190</cell></row><row><cell><emph type="italics"/>Tormenta bellica deducenda plures equos po&longs;tulant. <emph.end type="italics"/></cell><cell>110.111</cell></row><row><cell><emph type="italics"/>Traba quid. <emph.end type="italics"/></cell><cell>115</cell></row><row><cell><emph type="italics"/>Trispa&longs;ton. <emph.end type="italics"/></cell><cell>111.134</cell></row><row><cell><emph type="italics"/>Trochlea quid. <emph.end type="italics"/></cell><cell>111.134</cell></row><row><cell><emph type="italics"/>Trochlea e&longs;t vectis. <emph.end type="italics"/></cell><cell>136</cell></row><row><cell><emph type="italics"/>in Trochleis plures orbiculi facilius, &longs;ed lentius trahunt. <emph.end type="italics"/></cell><cell>137</cell></row><row><cell><emph type="italics"/>Trochleæ duæ legitimè compofitæ magna pondera adducunt. <emph.end type="italics"/></cell><cell>133.134.136</cell></row><row><cell><emph type="italics"/>V<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Vectis quid. <emph.end type="italics"/></cell><cell>14.55</cell></row><row><cell><emph type="italics"/>Vectis, cuneus. <emph.end type="italics"/></cell><cell>119</cell></row><row><cell><emph type="italics"/>Vectis partes. <emph.end type="italics"/></cell><cell>14.15</cell></row><row><cell><emph type="italics"/>Vectis v&longs;us duplex. <emph.end type="italics"/></cell><cell>55</cell></row><row><cell><emph type="italics"/>Vectis refert libram. <emph.end type="italics"/></cell><cell>57</cell></row><row><cell><emph type="italics"/>pro Vecte vnum &longs;tadium longo machinæ multæ &longs;imul. <emph.end type="italics"/></cell><cell>139</cell></row><row><cell><emph type="italics"/>Velum quid. <emph.end type="italics"/></cell><cell>92</cell></row><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.039.jpg"/><row><cell><emph type="italics"/>Veli&longs;pecies. <emph.end type="italics"/></cell><cell>92</cell></row><row><cell><emph type="italics"/>Ventus &longs;ecundui, aduer&longs;us, iran&longs;uer&longs;us, obliquus. <emph.end type="italics"/></cell><cell>96</cell></row><row><cell><emph type="italics"/>Vento vt codem in contrarias partes na-uigatur demonstratio. <emph.end type="italics"/></cell><cell>98</cell></row><row><cell><emph type="italics"/>in Vortice aquarum lata ad medium de-uoluuntur. <emph.end type="italics"/></cell><cell>206.207.209.210</cell></row><row><cell><emph type="italics"/>Vortex aquarum. <emph.end type="italics"/></cell><cell>206</cell></row><row><cell><emph type="italics"/>in Vortice aquo&longs;i multi circuli concentri-ci. <emph.end type="italics"/></cell><cell>206</cell></row><row><cell><emph type="italics"/>Vortex aquæ e&longs;t linea &longs;piralis vnius, aut plurium reuolutionum. <emph.end type="italics"/></cell><cell>209</cell></row><row><cell><emph type="italics"/>Vortices quomodo à nautis vitentar. <emph.end type="italics"/></cell><cell>210</cell></row><row><cell><emph type="italics"/>Vortices inter Roe&longs;t & Loffoet. <emph.end type="italics"/></cell><cell>210</cell></row><row><cell><emph type="italics"/>in Vorticem vt &longs;entiunt nautæ &longs;e impe<gap/>gi&longs;&longs;e. <emph.end type="italics"/></cell><cell>210</cell></row><row><cell><emph type="italics"/>difficile &longs;e liberare à Vortice. <emph.end type="italics"/></cell><cell>210.211</cell></row><row><cell><emph type="italics"/>aquain Vortice <expan abbr="de&longs;c&etilde;d&etilde;s">de&longs;cendens</expan> quò feratur. <emph.end type="italics"/></cell><cell>211</cell></row><row><cell><emph type="italics"/>Vtilitas hominum postulat in operibus &longs;uis varietatem. <emph.end type="italics"/></cell><cell>6</cell></row><row><cell><emph type="italics"/>X<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Xystus V. Pont. Max. obeli&longs;ci tran&longs;-ferendi author. <emph.end type="italics"/></cell><cell>139</cell></row><row><cell><emph type="italics"/>Xysti V. Pontificis laus. <emph.end type="italics"/></cell><cell>142</cell></row><row><cell><emph type="italics"/>Z<emph.end type="italics"/></cell><cell/></row><row><cell><foreign lang="greek">*zugo\s & *zugo\n. </foreign></cell><cell>45.119</cell></row><row><cell><foreign lang="greek">*zugosta/ths. </foreign></cell><cell>45</cell></row><row><cell><emph type="italics"/>Zygostatica fides. <emph.end type="italics"/></cell><cell>45</cell></row></table>

<s id="id.000238">FINIS.</s><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.040.jpg" pagenum="1"/><figure id="id.035.01.040.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.040.1.jpg"/></section></front><body><chap>

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<s id="id.000245">MIRA &longs;unt in his, quæ <lb/><expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> <expan abbr="naturã">naturam</expan> <expan abbr="eue-ni&utilde;t">eue<lb/>niunt</expan>, ea: <expan abbr="quor&utilde;">quorum</expan> cau&longs;a igno<lb/>ratur, & in his quæ præter <lb/>naturam, ea, <expan abbr="qu&ecedil;cunq;">qu&ecedil;cunque</expan> arte <lb/>facta hominibus <expan abbr="cõferunt">conferunt</expan>.</s>

<s id="id.000246">COMMENTARIVS.</s>

<s id="id.000246">COMMENTARIVS. </s>

<s id="id.000247"><emph type="italics"/>Cardanvs librum hunc Ari&longs;totelis peripate<emph.end type="italics"/><lb/><arrow.to.target n="marg2"/><lb/><emph type="italics"/>ticorum principis e&longs;&longs;e non arbitratur, propter man<lb/>cam, & paulo negligentiorem motuum rotundo<lb/>rum in eo po&longs;itam diui&longs;ionem. </s>

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<s id="id.000280">In quarum &longs;ingulis aliæ &longs;unt im<lb/>perantes, quæ & architectonicæ dicuntur: aliæ mini&longs;trantes. </s>

<s id="id.000281">Impe<lb/>rantes, habere debent præuias illas &longs;eptem liberales ante dictas, vt <lb/>videre e&longs;t apud Vitruuium de &longs;uo architecto, & in no&longs;tro com<lb/>mentario Iuri&longs;iurandi Hipp. de Hippocrateo medico: apud <expan abbr="Virgili&utilde;">Virgilium</expan> <lb/>de &longs;uo agricola: apud Vegetium de &longs;uo imperatore, & eadem ratione <lb/>in reliquis: ita vt, qui imperantibus i&longs;tis artibus præditi fuerint, in<lb/>ter homines præ&longs;tantißimi habiti &longs;emper &longs;int, & &longs;emper haberi <lb/>debeant, quanquam aliarum opera aliis aut nece&longs;&longs;aria magis, aut<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.043.jpg" pagenum="4"/><emph type="italics"/>præ&longs;tantiora, aut vtiliora, aut certiora exi&longs;tant. </s>

<s id="id.000281">Impe<lb/>rantes, habere debent præuias illas &longs;eptem liberales ante dictas, vt <lb/>videre e&longs;t apud Vitruuium de &longs;uo architecto, & in no&longs;tro com<lb/>mentario Iuri&longs;iurandi Hipp. de Hippocrateo medico: apud <expan abbr="Virgili&utilde;">Virgilium</expan> <lb/>de &longs;uo agricola: apud Vegetium de &longs;uo imperatore, & eadem ratione <lb/>in reliquis: ita vt, qui imperantibus i&longs;tis artibus præditi fuerint, in<lb/>ter homines præ&longs;tantißimi habiti &longs;emper &longs;int, & &longs;emper haberi <lb/>debeant, quanquam aliarum opera aliis aut nece&longs;&longs;aria magis, aut<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.043.jpg" pagenum="4"/><emph type="italics"/>præ&longs;tantiora, aut vtiliora, aut certiora exi&longs;tant. </s>

<s id="id.000282">Agriculturæ enim <lb/>opus, quod alimenta & medicamenta hominibus &longs;uppeditat, neceßi<lb/>tate vincit cætera: victoria, quæ rebelles & hostes &longs;ubijcit, proprios <lb/>ciues con&longs;eruat, vtilitate &longs;upereminet: Medicina nobilitate &longs;ubiecti, <lb/>& præstantia boni nempe &longs;anitatis, quam procurat, eximia e&longs;t: Cer<lb/>titudine operis & operationis Fabrilis anteponenda omnibus: vt <lb/>Lanificium, quod ad opes hone&longs;te parandas: & Nautica propter <lb/>mercaturam faciunt omnium maximè. </s>

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<s id="id.000303">quam contra Thales <lb/>rerum naturæ gnarus in aperto fixis in peluim oculis magna cum <lb/>animi lætitia intuitus e&longs;&longs;et.<emph.end type="italics"/></s>

<s id="id.000304"><margin.target id="marg5"/>Cap. 2. lib. 2. <lb/>Metaph.</s>

<s id="id.000304"><margin.target id="marg5"/>Cap. 2. lib. 2. <lb/>Metaph. </s>

<s><margin.target id="marg6"/>Cap. 6. lib. 5. <lb/>De benefic.</s>

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<s id="id.000315"><expan abbr="Quãdo">Quando</expan> igitur conuenit fa<lb/>cere aliquid pr&ecedil;ter <expan abbr="naturã">naturam</expan>, <lb/><expan abbr="t&utilde;">tum</expan> difficultas hæ&longs;itationem <lb/>adfert, & arte opus e&longs;t.</s>

<s id="id.000316">COMMENTARIVS.</s>

<s id="id.000316">COMMENTARIVS. </s>

<s id="id.000317">In multis enim.] <emph type="italics"/>Secunda ratio e&longs;t ad probandum in arte fa<lb/>ctis quibu&longs;dam aliquid mirum e&longs;&longs;e, deprompta e&longs;t ex effectis Na<lb/>turæ contrarijs, &longs;altem repugnantibus, &longs;yllogi&longs;mus &longs;ic in&longs;titutus <lb/>rem ip&longs;am illu&longs;trabit.<emph.end type="italics"/></s>

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<s id="id.000345">vt in his, quæ, cum mino<lb/>ra &longs;int, &longs;uperant maiora: & <lb/>paruum momentum, cum <lb/>habeant, ingentia dimo<lb/>uent pondera, cæteri&longs;<lb/>que fere, quæ problemata <lb/>Mechanica nuncupamus.</s>

<s id="id.000346">COMMENTARIVS.</s>

<s id="id.000346">COMMENTARIVS. </s>

<s id="id.000347">Illius artis.] <emph type="italics"/>Ars generalis, cuius hic mentionem facit Ari<lb/>&longs;toteles, nu&longs;quam ab eo e&longs;t definita, aut nominata. </s>

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<s id="id.000383">Et<emph.end type="italics"/> <foreign lang="greek">si/fwnes</foreign><lb/><emph type="italics"/>extinguendis incendijs apti, & medicinabiles cacurbitulæ &longs;ine <lb/>ignis ministerio cutem prehendentes, & pilæ &longs;ponte &longs;altantes, & <lb/>lucerna &longs;uas ip&longs;a producens &longs;tuppas: & animal quod à &longs;tructore dum <lb/>&longs;ecatur in men&longs;a, bibit interim, crepitùque &longs;uo quodam, & voce &longs;i<lb/>tientis repræ&longs;entat imaginem: milleque alia id genus, quæ breuita<lb/>tis &longs;tudio præterimus. </s>

<s id="id.000384">Hæc igitur (vt in capita quædam conferatur) <lb/>aut ponderibus vtitur & &longs;piritu, quorum præponderatio mouet, <lb/>æquilibrium &longs;i&longs;tit, (&longs;icuti etiam Timæus definit): aut neruis & <lb/>funiculis animatos qua&longs;i tractus, ac motus imitatur, ac circa illa <lb/>quæ &longs;ubnatant aquis, aut circa aquarum vertitur horologia, quo<lb/>rum quidem generum primum docet in pneumaticis Heron, alte<lb/>rum idem in automatis & Zygijs, quartum rur&longs;us in Hydrijs, ter<lb/>tium verò in Ochoumenis Archimedes. </s>

<s id="id.000385">E&longs;t in eadem Mechanicæ <lb/>&longs;erie quæ Centrobarica pars dicitur, ex qua reliquæ pendere dicun<lb/>tur & Sphærotop&oelig;ia, qualis illa Archimedea Claudiani laudata <lb/>ver&longs;ibus. </s>

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<s id="id.000391">Quid occultamini, inquit, <lb/>Socij, cum nullius i&longs;torum qui frequentes ad vrbis portam &longs;pectandi <lb/>gratia confluunt, cras vos &longs;it con&longs;pecturus? </s>

<s id="id.000392">E&longs;t alius etiam Antipho <lb/>de quo meminit Cicero, vt &longs;omniorum interprete & &longs;criptore for<lb/>ta&longs;&longs;e is e&longs;t quem fui&longs;&longs;e Athenien&longs;em mon&longs;tro&longs;orum &longs;omniorum in<lb/>terpretem, & poëtam refert Suidas. </s>

<s id="id.000393">A quo etiam forta&longs;&longs;e proma<lb/>nauit Senariolus, qui hic citatur ab Ari&longs;totele, ad probandum <lb/>homines arte vincere ea, à quibus natura vincuntur. </s>

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<s id="id.000399">Sunt vero hæc proble<lb/>matis Phy&longs;icis, nec omni<lb/>no <expan abbr="ead&etilde;">eadem</expan>, nec valdè di&longs;&longs;imi<lb/>lia: &longs;ed con&longs;entanea theo<lb/>tematis, tum mathemati<lb/>cis, tum Phy&longs;icis. </s>

<s id="id.000400">Etenim <lb/>quod ip&longs;um quomodo ad <lb/>mathematica pertineat: <lb/>ip&longs;um vero circa quod, ad <lb/>Phy&longs;ica, manife&longs;tum e&longs;t.</s>

<s id="id.000401">COMMENTARIVS.</s>

<s id="id.000401">COMMENTARIVS. </s>

<s id="id.000402"><emph type="italics"/>Apud Euclidem problema à theoremate di&longs;tinguitur, quod <lb/>hoc iubeat aliquid contemplari: illud fieri: paßim tamen ab <emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.052.jpg" pagenum="13"/><emph type="italics"/>Ari&longs;totele, & alijs pro vtroque, vt hic, indifferenter legitur. </s>

<s id="id.000403">Qualia <lb/>autem problemata in Mechanicis habeat tractanda explicat Ari<lb/>&longs;toteles, dicitque ea e&longs;&longs;e, quæ &longs;int con&longs;entanea Phy&longs;icis & Mathe<lb/>maticis, vt quæ habeant &longs;ubiectum petitum è Phy&longs;icis. </s>

<s id="id.000404">Machina<lb/>rum enim materia lignum e&longs;t vel ferrum & eiu&longs;modi corpora Phy<lb/>&longs;ica: attributum verò è figuris & terminis Mathematicis cuiu&longs;mo<lb/>di &longs;unt in Geometria lineæ, diametri, centra, circuli, & eiu&longs;modi, <lb/>è quibus machinæ con&longs;tare & figuratæ e&longs;&longs;e, & vires &longs;uas accipere, <lb/>augere, diminuere, metiri o&longs;tenduntur. </s>

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<s id="id.000416">quod enim &longs;ine <lb/>vecte qui&longs;piam non po&longs;&longs;et <lb/>mouere, hoc ip&longs;um pon<lb/>dus, in&longs;uper <expan abbr="adijci&etilde;s">adijciens</expan> vectis <lb/>ip&longs;ius <expan abbr="põdus">pondus</expan>, facile mouet.</s>

<s id="id.000417">COMMENTARIVS.</s>

<s id="id.000417">COMMENTARIVS. </s>

<s id="id.000418">Qvæ de vecte.] <emph type="italics"/>Vectis e&longs;t machina &longs;eu in&longs;trumentum in&longs;tar <lb/>pali aut baculi recti longioris, cuius alterum extremum in cu<lb/>spidem <expan abbr="acutã">acutam</expan> & paulò latiorem de&longs;init, <expan abbr="vocaturq;">vocaturque</expan> lingua: alterum <lb/><expan abbr="extrem&utilde;">extremum</expan> caput e&longs;t, aut manubrium. </s>

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<s id="id.000428">Nec enim ab&longs;urdum e&longs;t, <lb/>ex admirabiliori quid ad<lb/>mirabile contingere.</s>

<s id="id.000429">COMMENTARIVS.</s>

<s id="id.000429">COMMENTARIVS. </s>

<s id="id.000430">Omnium verò talium.] <emph type="italics"/>Cau&longs;a quæ latebat in problemate <lb/>de vecte aßignatur hic e&longs;&longs;e circulus: quæ ad alia multa Me<lb/>chanica po&longs;tea transferetur. </s>

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<s id="id.000439">Illùc <expan abbr="itaq;">itaque</expan> in&longs;pi<lb/>cientibus <expan abbr="cõtraria">contraria</expan> ab ip&longs;o <lb/>prouenire minus erit <expan abbr="mir&utilde;">mirum</expan>.</s>

<s id="id.000440">COMMENTARIVS.</s>

<s id="id.000440">COMMENTARIVS. </s>

<s id="id.000441">Maxime verò.] <emph type="italics"/>Circuli admiranda natura declaratur è <lb/>quintuplici contrariorum, quæ in eo præter contrariorum <emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.055.jpg" pagenum="16"/><emph type="italics"/>legem &longs;imul reperiuntur, repugnantia. </s>

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<s id="id.000456"><emph type="italics"/>Sit igitur recta A B inter extrema duo<lb/>rum brachiorum circini A C B diua<lb/>ricati per interuallum lineæ A B, <lb/>cuius extremum A maneat: alterum B <lb/>lineæ motu feratur per D quou&longs;que redeat <lb/>ad B: &longs;icque circulus B D B erit fa<lb/>ctus. </s>

<s id="id.000457">Idque beneficio puncti B cum tota <lb/>linea A B moti, atque puncti A quieti, vt hic vult Ari&longs;toteles.<emph.end type="italics"/></s></chap><chap>

<s id="id.000457">Idque beneficio puncti B cum tota <lb/>linea A B moti, atque puncti A quieti, vt hic vult Ari&longs;toteles. <emph.end type="italics"/></s></chap><chap>

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<s id="id.000494">Igitur & qu&ecedil; circa <lb/>libram eueniunt ad circu<lb/>lum referuntur, & qu&ecedil; cir<lb/>ca vectem ad libram, & <lb/>forta&longs;&longs;is alia omnia, quæ <lb/>circa motiones mechani<lb/>cas, ad vectem.</s>

<s id="id.000495">COMMENTARIVS.</s>

<s id="id.000495">COMMENTARIVS. </s>

<s id="id.000496">Secundum.] <emph type="italics"/>Pro<emph.end type="italics"/> <foreign lang="greek">deu/teron</foreign> <emph type="italics"/>legamus &longs;i placet<emph.end type="italics"/> <foreign lang="greek">trh/ton.</foreign> <emph type="italics"/>Hic enim <lb/>tertia e&longs;t repugnantia in circulo ex contrarijs motionibus, quas <lb/>&longs;imul habet, antè &longs;cilicet cum pars eius vna mouetur: oppo&longs;ita in <lb/>ip&longs;omet tempore ponè mouetur. </s>

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<s id="id.000505">Quia igitur in his &longs;unt antè & ponè, <lb/>mouebitur antè & ponè: quia in&longs;uper &longs;unt &longs;ur&longs;um & deor&longs;um, <lb/>mouebitur etiam &longs;imul &longs;ur&longs;um & deor&longs;um.<emph.end type="italics"/></s>

<s id="id.000506"><emph type="italics"/>Centrum enim in plano circundatur quatuor loci differentijs, <lb/>propter duas quæ in ip&longs;o ad rectos &longs;e &longs;ecant dimen&longs;iones, vt in circu<lb/>lo B C D E, e&longs;to linea fabricans ip&longs;um A B, ibique e&longs;to ante <lb/>B. igitur cum erit in D, erit ponè: & cum in C, &longs;ur&longs;um: & <lb/>in E, deor&longs;um, & perueniens ad A B, eidem loco re&longs;tituetur, <lb/>à quo c&oelig;perat moueri, quod e&longs;t vltimum <emph.end type="italics"/><lb/><figure id="id.035.01.060.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.060.1.jpg"/><lb/><emph type="italics"/>fieri primum. </s>

<s>igitur cum erit in D, erit ponè: & cum in C, &longs;ur&longs;um: & <lb/>in E, deor&longs;um, & perueniens ad A B, eidem loco re&longs;tituetur, <lb/>à quo c&oelig;perat moueri, quod e&longs;t vltimum <emph.end type="italics"/><lb/><figure id="id.035.01.060.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.060.1.jpg"/><lb/><emph type="italics"/>fieri primum. </s>

<s id="id.000507">Vnde cum circulus moue<lb/>tur, pote&longs;t dici ire, & reuerti &longs;imul: &longs;ic <lb/>cum &longs;phæricum corpus mouetur, in fine <lb/>&longs;emper, & principio motus &longs;ui, etiam tum <lb/>ire, tum reuerti veri&longs;imiliter dicetur.<emph.end type="italics"/></s>

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<s id="id.000514">Præterea etiam, quod, <lb/>cum vna &longs;it ea linea, quæ <lb/>ex centro, nullum eorum, <lb/>quæ in ea &longs;unt, <expan abbr="p&utilde;ctorum">punctorum</expan>, <lb/>æquè celeriter fertur: &longs;ed <lb/>hoc, quod longius e&longs;t ab <lb/>extremo eius immobili, <lb/>&longs;emper celerius: miranda <lb/>multa circa motiones cir<lb/>culi contingunt, vt in <expan abbr="&longs;e-qu&etilde;tibus">&longs;e<lb/>quentibus</expan> problematis fiet <lb/>manife&longs;tum.</s>

<s id="id.000515">COMMENTARIVS.</s>

<s id="id.000515">COMMENTARIVS. </s>

<s id="id.000516">Præterea etiam.] <emph type="italics"/>Quarta repugnantia e&longs;t in circulo ex inæ<lb/>qualitate motuum in eiu&longs;dem lineæ circulum de&longs;cribentis diuer<lb/>&longs;is punctis. </s>

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<s id="id.000522"><emph type="italics"/>E&longs;to A B C, peripheria &longs;emidiametri maioris A E: item <lb/>D F G, peripheria &longs;emidiametri D H minoris. </s>

<s id="id.000523">Dico periphe<lb/>riam A B C maiorem peripheria D F G. </s>

<s id="id.000523">Dico periphe<lb/>riam A B C maiorem peripheria D F G. </s>

<s id="id.000524">Producatur enim A E <lb/>recta vt &longs;it A C <lb/>diameter po&longs;tul.<emph.end type="italics"/><lb/><figure id="id.035.01.062.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.062.1.jpg"/><lb/>2. <emph type="italics"/><expan abbr="it&etilde;">item</expan> D H vt &longs;it <lb/>& D G diame<lb/>ter. </s>

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<s id="id.000536">Hinc <lb/>Architecti Fabri, cum <expan abbr="hãc">hanc</expan> <lb/>in circulo naturam depre<lb/>hendi&longs;&longs;ent, <expan abbr="organ&utilde;">organum</expan> fabri<lb/>cantur principium occu<lb/>lentes, vt &longs;it de machina, <lb/>&longs;olum hoc, quod admira<lb/>bile, apertum: quod autem <lb/>cau&longs;a, occultum.</s>

<s id="id.000537">COMMENTARIVS.</s>

<s id="id.000537">COMMENTARIVS. </s>

<s id="id.000538">Qvod autem circulus.] <emph type="italics"/>Tertia repugnantia in vnius cir<lb/>culi contrarijs motionibus ante po&longs;ita amplius declaratur, ab <lb/>exemplo plurium: &longs;ed contiguorum ab vnica vi primaria &longs;ecundum <lb/>motus contrarios motorum. </s>

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<s id="id.000562">Qui enim extra e&longs;t, maior <lb/>e&longs;t eo, qui intus.</s>

<s id="id.000563">COMMENTARIVS.</s>

<s id="id.000563">COMMENTARIVS. </s>

<s id="id.000564">De libra propter.] <emph type="italics"/>In hoc capite Ari&longs;toteles vult o&longs;tendere <lb/>cur libræ longiorum brachiorum &longs;int exactiores: quam libræ <lb/>breuiorum. </s>

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<s id="id.000592">Manife&longs;tum igitur <lb/>quod latum <expan abbr="&longs;ec&utilde;dum">&longs;ecundum</expan> dia<lb/>metrum duabus lationi<lb/>bus nece&longs;&longs;e habet in ratio<lb/>ne laterum ferri.</s>

<s id="id.000593">COMMENTARIVS.</s>

<s id="id.000593">COMMENTARIVS. </s>

<s id="id.000594">Horum vero cau&longs;a.] <emph type="italics"/>Inæqualium <expan abbr="circulor&utilde;">circulorum</expan> ab inæqualibus <lb/>radiis <expan abbr="de&longs;criptor&utilde;">de&longs;criptorum</expan>, & maioris quidem à maiori multo ab&longs;tru<lb/>&longs;ior aßignatur cau&longs;a ex radij de&longs;cribentis circulum duabus lationi<lb/>bus, quæ inter &longs;e <expan abbr="nullã">nullam</expan> <expan abbr="ration&etilde;">rationem</expan> &longs;eruant. </s>

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<s id="id.000612">Nunc igitur ponatur<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>extremum radij duabus lationibus <lb/>de&longs;cribere circulum non digrediens à recta producere rectam, quod <lb/>e&longs;t contra naturam circuli. </s>

<s id="id.000613">Non igitur duæ lationes ip&longs;ius<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>ferun<lb/>tur in ratione<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">a g.</foreign> <emph type="italics"/>Sed hîc obiici pote&longs;t quod Sol motu pri<lb/>mi mobilis mouetur ab Oriente in Occidentem in 24. horis, & motu <lb/>proprio ab Occidente in Orientem in aliquo tempore quantum e&longs;t <lb/>quod re&longs;pondet æquatori coa&longs;cendenti cum 59'. 8". Eclypticæ. </s>

<s id="id.000613">Non igitur duæ lationes ip&longs;ius<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>ferun<lb/>tur in ratione<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">a g. </foreign><emph type="italics"/>Sed hîc obiici pote&longs;t quod Sol motu pri<lb/>mi mobilis mouetur ab Oriente in Occidentem in 24. horis, & motu <lb/>proprio ab Occidente in Orientem in aliquo tempore quantum e&longs;t <lb/>quod re&longs;pondet æquatori coa&longs;cendenti cum 59'. 8". Eclypticæ. </s>

<s id="id.000614">Et &longs;ic <lb/>eius duæ lationes &longs;unt in ratione aliqua, nec tamen Sol fertur &longs;ecun<lb/>dum rectam &longs;ed <expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> arcum Eclypticæ. </s>

<s id="id.000615">Ita e&longs;t, ob id <expan abbr="dicend&utilde;">dicendum</expan> hic <lb/>dictas ab Ari&longs;totele duæ lationes non &longs;impliciter <expan abbr="intellig&etilde;das">intelligendas</expan>: &longs;ed ta<lb/>les, quæ <expan abbr="ferãtur">ferantur</expan> ambæ <expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> rectam. </s>

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<s id="id.000623">Hoc enim prius fuit <lb/>demon&longs;tratum. </s>

<s id="id.000624">Non igi<lb/>tur &longs;ecundum rectam pro<lb/>gredietur, id quod fertur <lb/>in nulla ratione, nulloque <lb/>in tempore. [Si enim <expan abbr="&longs;e-c&utilde;dum">&longs;e<lb/>cundum</expan> rationem aliquam <lb/>latum &longs;it in aliquo tempo<lb/>re, nece&longs;&longs;e e&longs;t illud tempus <lb/>rectam e&longs;&longs;e lationem, pro<lb/>pter ea quæ ante dicta &longs;unt.] Itaque circulare e&longs;t quod <lb/>&longs;ecundum duas lationes latum e&longs;t in nulla ratione nullo <lb/>in tempore.</s>

<s id="id.000624">Non igi<lb/>tur &longs;ecundum rectam pro<lb/>gredietur, id quod fertur <lb/>in nulla ratione, nulloque <lb/>in tempore. </s>

<s>[Si enim <expan abbr="&longs;e-c&utilde;dum">&longs;e<lb/>cundum</expan> rationem aliquam <lb/>latum &longs;it in aliquo tempo<lb/>re, nece&longs;&longs;e e&longs;t illud tempus <lb/>rectam e&longs;&longs;e lationem, pro<lb/>pter ea quæ ante dicta &longs;unt.] </s>

<s>Itaque circulare e&longs;t quod <lb/>&longs;ecundum duas lationes latum e&longs;t in nulla ratione nullo <lb/>in tempore. </s>

<s id="id.000625">COMMENTARIVS.</s>

<s id="id.000625">COMMENTARIVS. </s>

<s id="id.000626">Si enim in alia.] <emph type="italics"/>Locus hic paulo ob&longs;curior, debet &longs;ic intelligi, <lb/>vt &longs;i exempli gratia, a duabus lationibus latum non feratur in <lb/>ratione quidem data<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">a g</foreign>: <emph type="italics"/>&longs;ed<emph.end type="italics"/><lb/><figure id="id.035.01.070.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.070.1.jpg"/><lb/><emph type="italics"/>in alia, non feretur &longs;ecundum diame<lb/>trum<emph.end type="italics"/> <foreign lang="greek">a h,</foreign> <emph type="italics"/>nihilominus tamen feretur <lb/>&longs;ecundum rectam, quæ erit diameter <lb/>figuræ à lateribus alterius rationis <lb/>con&longs;titutæ, vt e&longs;t in præ&longs;enti dia<lb/>grammate<emph.end type="italics"/> <foreign lang="greek">a x</foreign> <emph type="italics"/>diameter quadrilateri <lb/>&longs;ub<emph.end type="italics"/> <foreign lang="greek">a d, a e</foreign> <emph type="italics"/>comprehen&longs;i.<emph.end type="italics"/></s><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.071.jpg" pagenum="32"/>

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<s>[Si igi<lb/>tur ferebatur in ratione <lb/>quam habet <foreign lang="greek">b e</foreign> ad <foreign lang="greek">e g,</foreign> fe<lb/>rebatur &longs;ecundum diame<lb/>trum <foreign lang="greek">b g</foreign>: At nunc cum in <lb/>nulla ratione feratur, &longs;e<lb/>cundum peripheriam <foreign lang="greek">b e g</foreign><lb/>feretur.]</s>

<s id="id.000660">COMMENTARIVS.</s>

<s id="id.000660">COMMENTARIVS. </s>

<s id="id.000661">Qvod vero recta.] <emph type="italics"/>Quia &longs;uperioris &longs;yllogi&longs;mi a&longs;&longs;umptio a&longs;&longs;u<lb/>mebat <expan abbr="Radi&utilde;">Radium</expan> duabus &longs;imul ferri lationibus, id ip&longs;um hîc breui<lb/>ter, ideo valde ob&longs;curè confirmatur. </s>

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<s id="id.000666">Non igitur vna latione tantum fer<lb/>tur: fertur ergo pluribus. </s>

<s id="id.000667">Et quidem vna, vt <lb/>antror&longs;um: qua qua &longs;i diffunditur, & ab&longs;ce<lb/>dit foras, vt<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>ver&longs;us E in hoc diagrammate: altera vt retror<emph.end type="italics"/><lb/><figure id="id.035.01.073.2.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.073.2.jpg"/><lb/><emph type="italics"/>&longs;um ver&longs;us centrum: qua retrahitur, ne euage<lb/>tur longius, quam æqualitas di&longs;tantiæ vndi<lb/>que à centro &longs;eruandæ permittit, vt idem<emph.end type="italics"/> <foreign lang="greek">b</foreign><lb/><emph type="italics"/>ver&longs;us L. </s>

<s id="id.000668">Vtraque autem hæc latio quanta &longs;it <lb/>men&longs;uratur lineis rectis, quarum altera in po&longs;te<lb/>riore diagrammate e&longs;t &longs;inus rectus<emph.end type="italics"/> <foreign lang="greek">g e,</foreign> <emph type="italics"/>altera <lb/>verò e&longs;t &longs;inus ver&longs;us<emph.end type="italics"/> <foreign lang="greek">b g.</foreign></s><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.074.jpg" pagenum="35"/>

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<s id="id.000676">Omni igitur circu<lb/>lum de&longs;cribenti hoc con<lb/>tingit.</s>

<s id="id.000677">COMMENTARIVS.</s>

<s id="id.000677">COMMENTARIVS. </s>

<s id="id.000678">Si vero duorum.] <emph type="italics"/>Vbi confirmauit in omni radio circulum <lb/>de&longs;cribente duas lationes ine&longs;&longs;e, nunc eas comparat in radijs inæ<lb/>qualibus, quod ad celeritatem & tarditatem attinet. </s>

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<s id="id.000692">quia <lb/>enim centro vicinior e&longs;t ad <lb/>&longs;e <expan abbr="reuell&etilde;ti">reuellenti</expan>, vincitur magis.</s>

<s id="id.000693">COMMENTARIVS.</s>

<s id="id.000693">COMMENTARIVS. </s>

<s id="id.000694">Et fertur motu.] <emph type="italics"/>E duobus motibus in extremo radij mobili <lb/>alterum &longs;ecundum naturam e&longs;&longs;e dicit, nempe qui e&longs;t &longs;ecundum <lb/>peripheriam, alterum præter naturam, qui e&longs;t in tran&longs;uer&longs;um, & <lb/>ver&longs;us centrum. </s>

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<s id="id.000707">E&longs;t autem <foreign lang="greek">w n</foreign> æqualis ip&longs;i <lb/><foreign lang="greek">q z.</foreign> In quanto vero tempo<lb/>re <foreign lang="greek">a x</foreign> peragrauit <foreign lang="greek">x q,</foreign> in <lb/><expan abbr="tãto">tanto</expan> in maiore circulo ex<lb/>tremum <foreign lang="greek">a b</foreign> non maiorem <lb/><foreign lang="greek">b w</foreign> peragrauit (etenim <lb/>motus &longs;ecundum naturam <lb/>æqualis e&longs;&longs;et) præter na<lb/>turam vero minor erat, nempe <foreign lang="greek">b n</foreign> quam <foreign lang="greek">x z.</foreign></s>

<s id="id.000708">COMMENTARIVS.</s>

<s id="id.000708">COMMENTARIVS. </s>

<s id="id.000709">Qvod vero minor.] <emph type="italics"/>Altera e&longs;t confirmatio &longs;ed<emph.end type="italics"/> <foreign lang="greek">grammikh\</foreign><lb/><emph type="italics"/>linearis a&longs;&longs;umptionis &longs;yllogi&longs;mi præcedentis. </s>

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<s><emph type="italics"/>Spatia enim cum metiatur perpendicu<lb/>laris, vtpote optima <expan abbr="m&etilde;&longs;ura">men&longs;ura</expan>, quia minima, & &longs;ola regularis & nota. <lb/></s>

<s id="id.000721">Sint autem<emph.end type="italics"/> <foreign lang="greek">w n, q z</foreign> <emph type="italics"/>perpendiculares ex fab. & æquales, quia late<lb/>ra oppo&longs;ita in parallelogrammo<emph.end type="italics"/> <foreign lang="greek">w n z q</foreign> <emph type="italics"/>prop. 34. lib. 1. Erant vtro<lb/>bique &longs;patia<emph.end type="italics"/> <foreign lang="greek">b w & x q</foreign> <emph type="italics"/>æqualia.<emph.end type="italics"/></s>

<s>Erant vtro<lb/>bique &longs;patia<emph.end type="italics"/> <foreign lang="greek">b w & x q</foreign> <emph type="italics"/>æqualia. <emph.end type="italics"/></s>

<s id="id.000723"><foreign lang="greek">b n</foreign> <emph type="italics"/>vero eadem ratione metitur &longs;patium motus præter naturam <lb/>ip&longs;ius<emph.end type="italics"/> <foreign lang="greek">b, & x z</foreign> <emph type="italics"/>ip&longs;ius<emph.end type="italics"/> <foreign lang="greek">x.</foreign> <emph type="italics"/>&longs;i igitur<emph.end type="italics"/> <foreign lang="greek">x z</foreign> (<emph type="italics"/>quod po&longs;tea demon&longs;tra<lb/>bitur) maior &longs;it quam<emph.end type="italics"/> <foreign lang="greek">b n,</foreign> <emph type="italics"/>erit puncti<emph.end type="italics"/> <foreign lang="greek">x</foreign> <emph type="italics"/>motus præter naturam <lb/>maior in eodem &longs;patio motus naturalis: quam puncti<emph.end type="italics"/> <foreign lang="greek">b.</foreign></s><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.079.jpg" pagenum="40"/>

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<s id="id.000731">Sunt vero <foreign lang="greek">w n</foreign> &] <emph type="italics"/>Quia<emph.end type="italics"/> <foreign lang="greek">q w</foreign> <emph type="italics"/>parallela e&longs;t ip&longs;i<emph.end type="italics"/> <foreign lang="greek">z n</foreign> <emph type="italics"/>ex fabrica: <lb/>tùm<emph.end type="italics"/> <foreign lang="greek">w n</foreign> <emph type="italics"/>etiam parallela e&longs;t ip&longs;i<emph.end type="italics"/> <foreign lang="greek">q z,</foreign> <emph type="italics"/>quia in eas incidens<emph.end type="italics"/> <foreign lang="greek">z n</foreign> <emph type="italics"/>facit an<lb/>gulos internos ad <expan abbr="ea&longs;d&etilde;">ea&longs;dem</expan> partes rectos, ex fab. proinde æquales ax. 10. <lb/><expan abbr="itaq;">itaque</expan> parallelæ prop. 28. lib. 1. </s>

<s><expan abbr="parallelogrãm&utilde;">parallelogramum</expan> erit<emph.end type="italics"/> <foreign lang="greek">w n z <expan abbr="q.">que</expan></foreign> <emph type="italics"/>per def. pa<lb/>rall.</s>

<s><expan abbr="parallelogrãm&utilde;">parallelogramum</expan> erit<emph.end type="italics"/> <foreign lang="greek">w n z q. </foreign><emph type="italics"/>per def. pa<lb/>rall. </s>

<s id="id.000735">quare eius latera oppo&longs;ita<emph.end type="italics"/> <foreign lang="greek">w n & q z</foreign> <emph type="italics"/><expan abbr="er&utilde;t">erunt</expan> æqualia prop. 34. lib. 1.<emph.end type="italics"/></s>

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<s id="id.000738">Expo<lb/><figure id="id.035.01.079.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.079.1.jpg"/><lb/>&longs;itio.</s>

<s id="id.000739"><emph type="italics"/>Sunto <lb/>duo cir<lb/>culi in<lb/>æqua<lb/>les A <lb/>B C ma<lb/>ior & <lb/>D E F <lb/>minor, perpendiculares &longs;int B K, E I & ablatæ A K, D I.<emph.end type="italics"/></s><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.080.jpg" pagenum="41"/>

<s id="id.000739"><emph type="italics"/>Sunto <lb/>duo cir<lb/>culi in<lb/>æqua<lb/>les A <lb/>B C ma<lb/>ior & <lb/>D E F <lb/>minor, perpendiculares &longs;int B K, E I & ablatæ A K, D I. <emph.end type="italics"/></s><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.080.jpg" pagenum="41"/>

<s id="id.000740">Deter. <emph type="italics"/>Dico D I e&longs;&longs;e maiorem ip&longs;a A K quæ e&longs;t &longs;egmentum in <lb/>maiori circulo. </s>

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<s id="id.000742"><emph type="italics"/>De&longs;cribere circulum minorem qui alterum datum maiorem <lb/>interius tangat.<emph.end type="italics"/></s>

<s id="id.000743"><emph type="italics"/>Sit datus circulus A B K C maior, ab A per D centrum reper<lb/>tum prop. 1. lib. 3. ducatur A k diameter. </s>

<s id="id.000743"><emph type="italics"/>Sit datus circulus A B K C maior, ab A per D centrum reper<lb/>tum prop. 1. lib. 3. </s>

<s>ducatur A k diameter. </s>

<s id="id.000744">De&longs;cribendus autem &longs;it eo <lb/>minor, cuius accipiatur E <expan abbr="centr&utilde;">centrum</expan> <emph.end type="italics"/><lb/><figure id="id.035.01.080.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.080.1.jpg"/><lb/><emph type="italics"/>inter A & D, & interuallo <lb/>E A de&longs;cribatur A F G. </s>

<s>hic <lb/>tanget interius circulum A B k <lb/>C datum in puncto A. </s>

<s id="id.000745">Nam &longs;i <lb/>& &longs;ecet, vt in puncto H, ducta <lb/>H E. </s>

<s>erit æqualis ip&longs;i E A def. <lb/>15. lib. 1. non erit igitur E A mi<lb/>nima omnium quæ ab E puncto <lb/>extra D centrum circuli A B <lb/>K C cadunt in eius concauam pe<lb/>ripheriam, quod e&longs;t contra prop. <lb/>7. lib. 3. </s>

<s id="id.000745">Nam &longs;i <lb/>& &longs;ecet, vt in puncto H, ducta <lb/>H E. erit æqualis ip&longs;i E A def. <lb/>15. lib. 1. non erit igitur E A mi<lb/>nima omnium quæ ab E puncto <lb/>extra D centrum circuli A B <lb/>K C cadunt in eius concauam pe<lb/>ripheriam, quod e&longs;t contra prop. <lb/>7. lib. 3. non erat igitur H punctum commune vtrique circulo, & <lb/>&longs;ic de alijs. </s>

<s>non erat igitur H punctum commune vtrique circulo, & <lb/>&longs;ic de alijs. </s>

<s id="id.000748">Circulus igitur A F G, tangit circulum A B K C <lb/>in puncto A prop. 11. lib. 3. quod oportuit facere.<emph.end type="italics"/></s>

<s id="id.000748">Circulus igitur A F G, tangit circulum A B K C <lb/>in puncto A prop. 11. lib. 3. </s>

<s>quod oportuit facere. <emph.end type="italics"/></s>

<s id="id.000749"><emph type="italics"/>Iam nunc de A G maiori &longs;emidiametro detrahatur portio A H <lb/>æqualis D H minori prop. 3. lib. 1. centro H interuallo A H de&longs;<lb/>cribatur circulus A M L po&longs;tul. </s>

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<s id="id.000754">E I ax. 1. connectantur M H, <lb/>E H po&longs;t. 1.<emph.end type="italics"/></s>

<s id="id.000757">Demon&longs;t. <emph type="italics"/>Po&longs;tquam ax. 3. A N, D I æquales &longs;unt quia reli<lb/>quæ ex æqualibus A H, D H ex fab. demptis æqualibus N H, <lb/>I H quæ latera &longs;unt &longs;ub æqualibus angulis duorum triangulorum <lb/>M N H & I E H habentium duos angulos duobus angulis <lb/>æquales, & latus lateri æquale vt e&longs;t in 26. prop. lib. 1. nempe angu<lb/>lus qui ad N rectus e&longs;t prop. 29. lib. 1. & qui ad I, rectus ex hypoth. <lb/>ideo æquales ax. 10. tum angulus M H N ad centrum con&longs;titutus <emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.081.jpg" pagenum="42"/><emph type="italics"/>& angulus E H I ad centrum con&longs;titutus in æqualibus circulis ex <lb/>fab. &longs;unt æquales prop. 27. lib. 3. quia æquales &longs;unt peripheriæ A M, <lb/>D E ablatæ &longs;cilicet ab æqualibus &longs;emißibus M N & E I ex <lb/>fab. prop. 3. & 29. lib. 3. & &longs;ic reliquum latus N H æquale e&longs;t re<lb/>liquo I H. </s>

<s id="id.000757">Demon&longs;t. </s>

<s><emph type="italics"/>Po&longs;tquam ax. 3. A N, D I æquales &longs;unt quia reli<lb/>quæ ex æqualibus A H, D H ex fab. demptis æqualibus N H, <lb/>I H quæ latera &longs;unt &longs;ub æqualibus angulis duorum triangulorum <lb/>M N H & I E H habentium duos angulos duobus angulis <lb/>æquales, & latus lateri æquale vt e&longs;t in 26. prop. lib. 1. </s>

<s>nempe angu<lb/>lus qui ad N rectus e&longs;t prop. 29. lib. 1. & qui ad I, rectus ex hypoth. <lb/>ideo æquales ax. 10. </s>

<s>tum angulus M H N ad centrum con&longs;titutus <emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.081.jpg" pagenum="42"/><emph type="italics"/>& angulus E H I ad centrum con&longs;titutus in æqualibus circulis ex <lb/>fab. &longs;unt æquales prop. 27. lib. 3. quia æquales &longs;unt peripheriæ A M, <lb/>D E ablatæ &longs;cilicet ab æqualibus &longs;emißibus M N & E I ex <lb/>fab. prop. 3. & 29. lib. 3. </s>

<s>& &longs;ic reliquum latus N H æquale e&longs;t re<lb/>liquo I H. </s>

<s id="id.000765">Ergo cum tota A N æqualis D I &longs;it maior A K <lb/>parte &longs;ua ax. 9. erit & D I maior ip&longs;a A K.<emph.end type="italics"/></s>

<s id="id.000767">Concl. <emph type="italics"/>Ergo perpendiculares à peripherijs in &longs;emidiametros & <lb/>ct. quod fuit demon&longs;trandum. </s>

<s id="id.000767">Concl. </s>

<s><emph type="italics"/>Ergo perpendiculares à peripherijs in &longs;emidiametros & <lb/>ct. </s>

<s>quod fuit demon&longs;trandum. </s>

<s id="id.000769">Hoc autem theorema videtur <expan abbr="quo-dãmodo">quo<lb/>dammodo</expan><emph.end type="italics"/> <foreign lang="greek">para/docon.</foreign> <emph type="italics"/>Erat enim veri&longs;imilius in maiore circulo <expan abbr="&longs;eg-ment&utilde;">&longs;eg<lb/>mentum</expan> &longs;emidiametri e&longs;&longs;e maius, & in minore minus: at non ita e&longs;t vt <lb/>patuit. </s>

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<s id="id.000783"><margin.target id="marg13"/>Verba &longs;i<lb/>gnis inclu&longs;a <lb/>in <expan abbr="cõtextu">contextu</expan> <lb/>Gr&ecedil;co quia <lb/>redundant <lb/>non verti<lb/>mus.</s>

<s id="id.000784">COMMENTARIVS.</s>

<s id="id.000784">COMMENTARIVS. </s>

<s id="id.000785">At oportet.] <emph type="italics"/>Nunc o&longs;tendit in maiore circulo motum &longs;ecun<lb/>dum naturam maiorem e&longs;&longs;e motu &longs;ecundum naturam in mino<lb/>re circulo eodem tempore factum. </s>

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<s id="id.000802">Nihil enim <lb/>prohibet <expan abbr="minor&etilde;">minorem</expan> permea<lb/>ri magnitudinem: quam vt <lb/>vi&longs;ui &longs;it manife&longs;ta.</s>

<s id="id.000803">COMMENTARIVS.</s>

<s id="id.000803">COMMENTARIVS. </s>

<s id="id.000804">Qvod vero propterea libræ.] <foreign lang="greek">zugo\s</foreign> <emph type="italics"/>vel<emph.end type="italics"/> <foreign lang="greek">zugo\n</foreign> <emph type="italics"/>præter iu<lb/>gum, remigum &longs;edes, & tran&longs;tra curruum & nauium &longs;ignifi<lb/>cat etiam libram & &longs;tateram, hinc illud Pythagoræ<emph.end type="italics"/> <foreign lang="greek">mh\ zugo\n u(per<lb/>bai/nein</foreign> <emph type="italics"/>&longs;tateram ne tran&longs;grediaris & vt annotat Budæus<emph.end type="italics"/> <foreign lang="greek">zugosta/<lb/>tai</foreign> <emph type="italics"/>&longs;unt libripendes per vrbes con&longs;tituti, qui <expan abbr="põderibus">ponderibus</expan> præfecti ap<lb/>pellantur, vnde Zygo&longs;tatica fides pro plena & examinata æquitate <lb/>à Zygo quod e&longs;t libra publice temperata & con&longs;tituta, vt quemad<lb/>modum ait Vitruuius, vindicet ab iniquitate iu&longs;tis moribus vitam.<emph.end type="italics"/><lb/><arrow.to.target n="marg14"/><lb/><emph type="italics"/>Statera enim dolo&longs;a, vt dixit Sapiens, abhominatio e&longs;t apud Deum, <lb/>& pondus æquum voluntas eius.<emph.end type="italics"/></s>

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<s id="id.000818">Ligni <expan abbr="en&itilde;">enim</expan> <lb/>grauior e&longs;t illa pars, vbi ra<lb/>dix, E&longs;t vero nodus quæ<lb/>dam radix.</s><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.086.jpg" pagenum="47"/>

<s id="id.000819">COMMENTARIVS.</s>

<s id="id.000819">COMMENTARIVS. </s>

<s id="id.000820">In magno autem.] <emph type="italics"/>Ex his colligitur fieri po&longs;&longs;e libram, quæ <lb/>examinabit granum vnum, immo grani &longs;ecundam, tertiam, <lb/>quartam partem. </s>

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<s id="id.000840"><margin.target id="marg15"/>Lib. 1. de <lb/>&longs;ubt,</s>

<s id="id.000841"><margin.target id="marg16"/>Prouerb. c. <lb/>10.</s>

<s id="id.000841"><margin.target id="marg16"/>Prouerb. c. <lb/>10. </s>

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<s id="id.000860">E&longs;to librile <foreign lang="greek">n c</foreign> re<lb/>ctum, perpendicularis vero <lb/><foreign lang="greek">k l m,</foreign> quæ bifariam diui<lb/>dat <foreign lang="greek">n c,</foreign> & impo&longs;ito pon<lb/>dere in <foreign lang="greek">n,</foreign> &longs;it <foreign lang="greek">n</foreign> vbi e&longs;t <foreign lang="greek">o, & <lb/>x</foreign> vbi e&longs;t <foreign lang="greek">r, & k l</foreign> vbi <foreign lang="greek">l q</foreign>.<lb/></s>

<s>Itaque maior erit <foreign lang="greek">l o</foreign> quam <lb/><foreign lang="greek">l r</foreign> ip&longs;o <foreign lang="greek">x l <expan abbr="q.">que</expan></foreign> Igitur &longs;u<lb/>blato pondere nece&longs;&longs;e e&longs;t <lb/>manere. </s>

<s>Itaque maior erit <foreign lang="greek">l o</foreign> quam <lb/><foreign lang="greek">l r</foreign> ip&longs;o <foreign lang="greek">x l q. </foreign></s>

<s>Igitur &longs;u<lb/>blato pondere nece&longs;&longs;e e&longs;t <lb/>manere. </s>

<s id="id.000861">Incumbit enim <lb/>ceu pondus exce&longs;&longs;us medietatis, qui e&longs;t in <foreign lang="greek">l o.</foreign></s>

<s id="id.000862">COMMENTARIVS.</s>

<s id="id.000862">COMMENTARIVS. </s>

<s id="id.000863">Propter quid.] <emph type="italics"/>In hoc capite proponitur aliud di&longs;cutiendum <lb/>problema de libra. </s>

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<s id="id.000870">Sine horum enim altero <lb/>modo intelligi <expan abbr="nõ">non</expan> pote&longs;t, <lb/>quomodo librile, quod <lb/>&longs;ecundum longitudinem <lb/>e&longs;t, vt vna recta li<lb/>nea, admittat dif<emph.end type="italics"/><lb/><figure id="id.035.01.089.2.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.089.2.jpg"/><lb/><emph type="italics"/>ferentias illas loci <lb/><expan abbr="&longs;urs&utilde;">&longs;ursum</expan> deor&longs;um. </s>

<s id="id.000871">At <lb/>&longs;iue hoc: &longs;iue illo <lb/>modo librile con<lb/>&longs;tituatur problema <lb/>hîc ab Ari&longs;totele <lb/><expan abbr="po&longs;it&utilde;">po&longs;itum</expan> habebit non <lb/>&longs;olum <expan abbr="experientiã">experientiam</expan>, <lb/>&longs;ed & rationem <lb/>&longs;ibi &longs;uffragantem, <lb/>Exemplum igitur <lb/>librilis primi mo<lb/>di <expan abbr="c&utilde;">cum</expan> latitudine &longs;it <lb/>A B, cuius <expan abbr="centr&utilde;">centrum</expan> <lb/>in &longs;uperiori parte <lb/>latitudinis &longs;it C,<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.090.jpg" pagenum="51"/><emph type="italics"/>cum &longs;uo &longs;u&longs;pen&longs;orio &longs;eu trutina C D: vel &longs;it & in inferiori parte C <lb/>centrum cum &longs;uo fulcro quod pro trutina e&longs;t etiam C D, & <lb/>in vtroque in<emph.end type="italics"/><lb/><figure id="id.035.01.090.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.090.1.jpg"/><lb/><emph type="italics"/>telligatur linea <lb/>recta per cen<lb/>trum tran&longs;ire <lb/>perpendiculari<lb/>ter ad planum <lb/><expan abbr="horizõtis">horizontis</expan> D E.<emph.end type="italics"/></s>

<s id="id.000872"><emph type="italics"/>Exemplum li<lb/>brilis <expan abbr="c&utilde;">cum</expan> truti<lb/>na immobiliter <lb/>connexi &longs;it vbi <emph.end type="italics"/><lb/><figure id="id.035.01.090.2.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.090.2.jpg"/><lb/><emph type="italics"/>e&longs;t librile GH, <lb/>& trutina K <lb/>L, & centrum <lb/>libræ L.<emph.end type="italics"/></s>

<s id="id.000873">An quia &longs;u<lb/>perne.] <emph type="italics"/>In<lb/>tellectis libræ <lb/>generibus ad propo&longs;itum problema accommodatis, nunc eius partis <lb/>prioris adfertur &longs;olutio. </s>

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<s id="id.000887">Centro &longs;iquidem L, <lb/>& interuallo L K circu<lb/>lus de&longs;cribatur, & K <lb/><expan abbr="mot&utilde;">motum</expan> &longs;it in P propter vim <lb/>allatam: tum L K per<lb/>pendicularis intellecta pro<lb/>ducta &longs;ecabit brachium <lb/>P H, id e&longs;t K H, vt in <lb/>M: &longs;icque P M accre&longs;cet pro longitudine ideo & grauitate ad <lb/>P G, redibit igitur G P M.<emph.end type="italics"/></s><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.092.jpg" pagenum="53"/><figure id="id.035.01.092.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.092.1.jpg"/>

<s id="id.000888"><emph type="italics"/>Contra in alte<lb/>ro diagrammate <lb/>eiu&longs;modi &longs;ectio <lb/>fiet, vt in O, & <lb/>&longs;ic pars O P ac<lb/>cre&longs;cet ad P H: <lb/>&longs;icque tota O P <lb/>H vt longior, ita <lb/>grauior O G. <lb/></s>

<s id="id.000889">Manebit igitur <lb/>(præ&longs;uppo&longs;ito hoc <lb/>quod ab H <expan abbr="app&etilde;&longs;a">appen&longs;a</expan> <emph.end type="italics"/><lb/><figure id="id.035.01.092.2.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.092.2.jpg"/><lb/><emph type="italics"/>lanx in&longs;ideat ter<lb/>ræ vel alicui ful<lb/>cro. </s>

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<s>Sunt vero tria circa <expan abbr="vect&etilde;">vectem</expan> <lb/>pre&longs;&longs;io quidem e&longs;t agina & <lb/><expan abbr="centr&utilde;">centrum</expan>, duo etiam pondera <lb/>mouens &longs;cilicet, & mobile.</s>

<s id="id.000909">COMMENTARIVS.</s>

<s id="id.000909">COMMENTARIVS. </s>

<s id="id.000910">Potentiæ vectis cau&longs;a.] <emph type="italics"/>Vectis definitus e&longs;t à Budæo bacu<lb/><arrow.to.target n="marg19"/><lb/>lus validus per mediam machinam traiectus, quo manuducto <lb/>machina, dum ver&longs;atur, funem ductarium aduoluit. </s>

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<s id="id.000916">Primus cum lingula &longs;ubditur oneri commouendo, & vecti ip&longs;i <lb/>quam proxime lingulæ &longs;ubditur corpu&longs;culum firmum, quod Græcis<emph.end type="italics"/><lb/><foreign lang="greek">u(pomo/xlion,</foreign> <emph type="italics"/>Vitruuio preßio dicitur. </s>

<s id="id.000917">Huius figura e&longs;t ferè quæ<lb/>uis obuia: expeditior tamen e&longs;t, &longs;i &longs;it pri&longs;mation, cuius aduer&longs;a duo <lb/>plana æqualia &longs;imilia, parallela, &longs;int trian<emph.end type="italics"/><lb/><figure id="id.035.01.094.2.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.094.2.jpg"/><lb/><emph type="italics"/>gula, vte&longs;t A D B C E F. </s>

<s id="id.000918">Huius enim <lb/>pri&longs;matis lateri vni tanquam centro, &longs;i <lb/>vectis innitentis caput deprimatur, nece&longs;&longs;e <lb/>erit ilico lingulam, & con&longs;equenter lin<lb/>guæ innixum onus attolli, & ideo com<lb/>moueri. </s>

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<s id="id.000924">Item &longs;i &longs;ub onus vectis ferrei lingula &longs;ubiecta fuerit, neque <lb/>caput eius preßione in imum: &longs;ed aduer&longs;us in altitudinem extolletur, <lb/>lingula fulcta in areæ &longs;olo habebit eam pro onere, oneris <expan abbr="aut&etilde;">autem</expan> ip&longs;ius <lb/>angulum pro preßione: ita non tam faciliter quam per preßionem, <lb/>&longs;ed aduer&longs;us nihilominus in pondus oneris erit <expan abbr="excitat&utilde;">excitatum</expan>. </s>

<s id="id.000925">Hæc Vitr. <lb/>à quo parum di&longs;&longs;entimus dum in &longs;ecundo v&longs;u vectis ponit &longs;olum &longs;eu <lb/>aream pro onere, nos pro centro & hypomochlio, quor&longs;um, dicemus<emph.end type="italics"/><lb/><arrow.to.target n="marg20"/><lb/><emph type="italics"/>alibi. </s>

<s id="id.000925">Hæc Vitr. <lb/>à quo parum di&longs;&longs;entimus dum in &longs;ecundo v&longs;u vectis ponit &longs;olum &longs;eu <lb/>aream pro onere, nos pro centro & hypomochlio, quor&longs;um, dicemus<emph.end type="italics"/><lb/><arrow.to.target n="marg20"/><lb/><emph type="italics"/>alibi. </s>

<s id="id.000926">Galenus comparauit mu&longs;culum, qui e&longs;t in&longs;trumentum motus <lb/>voluntarij vecti. </s>

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<s id="id.000954">Sit vectis <foreign lang="greek">a b,</foreign> pondus <lb/>vero <foreign lang="greek">g,</foreign> mouens autem <foreign lang="greek">d,</foreign><lb/>pre&longs;&longs;io <foreign lang="greek">e.</foreign> Ip&longs;um vero quod <lb/>mouerit <foreign lang="greek">d,</foreign> &longs;it vbi <foreign lang="greek">h,</foreign> & pon<lb/>dus <foreign lang="greek">g</foreign> motum vbi <foreign lang="greek">k.</foreign></s>

<s id="id.000955">COMMENTARIVS.</s>

<s id="id.000955">COMMENTARIVS. </s>

<s id="id.000956"><emph type="italics"/>Locus hic breuißimè totam vectis rationem explicat, vt &longs;ciatur <lb/>vectis v&longs;us, & quæ vires, ad quod onus mouendum &longs;ufficiant, <lb/>vel non &longs;ufficiant. </s>

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<s id="id.000959">Sit vectis A B, & huius hypo<lb/>mochlium C:<emph.end type="italics"/><lb/><figure id="id.035.01.097.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.097.1.jpg"/><lb/><emph type="italics"/><expan abbr="&longs;icq;">&longs;icque</expan> vectis duæ <lb/>partes C A ver<lb/>&longs;us linguam, C <lb/>B ver&longs;us caput: <lb/>&longs;it quoque pon<lb/>dus D &longs;u&longs;pen&longs;um ex perpendiculari A D: potentia autem &longs;u&longs;tinens <lb/>&longs;it in B. </s>

<s id="id.000960">Dico potentiam in B e&longs;&longs;e ad pondus D: vt A C ad B <lb/>C (quod hic vocatur reciprocè) fiat ergo vt B C ad A C: ita <lb/>pondus D ad aliud, vt E. hoc igitur pondus E loco potentiæ ap<lb/>pen&longs;um in B, ip&longs;um D pondere æquabit. </s>

<s id="id.000960">Dico potentiam in B e&longs;&longs;e ad pondus D: vt A C ad B <lb/>C (quod hic vocatur reciprocè) fiat ergo vt B C ad A C: ita <lb/>pondus D ad aliud, vt E. </s>

<s>hoc igitur pondus E loco potentiæ ap<lb/>pen&longs;um in B, ip&longs;um D pondere æquabit. </s>

<s id="id.000961">Magnitudines enim in gra<lb/>uitate commen&longs;urabiles æquiponderant, &longs;i permutatim &longs;u&longs;pendantur <lb/>in di&longs;tantijs &longs;ecundum grauitatum rationem <expan abbr="cõ&longs;titutæ">con&longs;titutæ</expan> prop. 6. lib. 1. <lb/>Archim. de æquipond. </s>

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<s id="id.000964">Sed E habet eam ad D, quam A C ad B C, ex <lb/>fab. </s>

<s id="id.000965">ergo potentia in B ad pondus D eam rationem habebit, quam <lb/>A C ad B C. </s>

<s id="id.000965">ergo potentia in B ad pondus D eam rationem habebit, quam <lb/>A C ad B C. </s>

<s id="id.000966">Itaque vt e&longs;t potentia ad pondus &longs;u&longs;tentum: ita e&longs;t <lb/>pars vectis &c. </s>

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<s id="id.000980">Et <lb/>&longs;ic &longs;i minor potentia ad &longs;u&longs;tinendum vel dimouendum &longs;ufficiet, <lb/>etiam alia quæuis paulo maior vis tanto facilius &longs;u&longs;tinebit, aut mo<lb/>uebit pondus: quanto pars ad caput maior erit. </s>

<s id="id.000981">Inæqualium enim <lb/>maior ad eandem maiorem rationem habet prop. 8. lib. 5. Sed & <lb/>huius rei cau&longs;a adfertur ex his quæ ante demon&longs;trata &longs;unt, nempe à <lb/>radio maiore maiorem de&longs;cribi circulum. </s>

<s id="id.000981">Inæqualium enim <lb/>maior ad eandem maiorem rationem habet prop. 8. lib. 5. </s>

<s>Sed & <lb/>huius rei cau&longs;a adfertur ex his quæ ante demon&longs;trata &longs;unt, nempe à <lb/>radio maiore maiorem de&longs;cribi circulum. </s>

<s id="id.000982">Pars enim vectis ab hy<lb/>pomochlio ad caput radij in&longs;tar e&longs;t maioris, qui depre&longs;&longs;us & ideo vo<lb/>lutus circa hypomochlium fixum tanquam <expan abbr="c&etilde;trum">centrum</expan>, de&longs;cribit arcum <lb/>tanto maiorem: quanto ip&longs;e radius maior erat. </s>

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<s id="id.000989">Apertius igitur &longs;ic. </s>

<s id="id.000990">Sit vectis<emph.end type="italics"/> <foreign lang="greek">a b,</foreign> <emph type="italics"/>pondus vero<emph.end type="italics"/> <foreign lang="greek">g,</foreign><lb/><emph type="italics"/>mouens autem<emph.end type="italics"/> <foreign lang="greek">d,</foreign> <emph type="italics"/>preßio<emph.end type="italics"/> <foreign lang="greek">e.</foreign> <emph type="italics"/>Cum ip&longs;um<emph.end type="italics"/> <foreign lang="greek">d,</foreign> <emph type="italics"/>quod moueat, &longs;it vbi<emph.end type="italics"/> <foreign lang="greek">h</foreign><emph type="italics"/>: <lb/>& pondus<emph.end type="italics"/> <foreign lang="greek">g</foreign> <emph type="italics"/>motum erit vbi<emph.end type="italics"/> <foreign lang="greek">k.</foreign> <emph type="italics"/>quod ita &longs;e habere o&longs;tendit tertia <lb/>proprietas circuli, ex qua cap. 1. huius lib. o&longs;ten&longs;um e&longs;t diametri ex<lb/>tremo vno deor&longs;um moto, alterum eodem tempore &longs;ur&longs;um moueri. </s>

<s>Cum ip&longs;um<emph.end type="italics"/> <foreign lang="greek">d,</foreign> <emph type="italics"/>quod moueat, &longs;it vbi<emph.end type="italics"/> <foreign lang="greek">h</foreign><emph type="italics"/>: <lb/>& pondus<emph.end type="italics"/> <foreign lang="greek">g</foreign> <emph type="italics"/>motum erit vbi<emph.end type="italics"/> <foreign lang="greek">k. </foreign></s>

<s><emph type="italics"/>quod ita &longs;e habere o&longs;tendit tertia <lb/>proprietas circuli, ex qua cap. 1. huius lib. o&longs;ten&longs;um e&longs;t diametri ex<lb/>tremo vno deor&longs;um moto, alterum eodem tempore &longs;ur&longs;um moueri. </s>

<s id="id.000991">E&longs;t <lb/>autem hic vectis<emph.end type="italics"/> <foreign lang="greek">b a,</foreign> <emph type="italics"/>vt diameter circuli cuius extremum<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>deor<lb/>&longs;um cum ad<emph.end type="italics"/> <foreign lang="greek">h</foreign> <emph type="italics"/>mouetur, alterum<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>&longs;ur&longs;um &longs;imul moueri vt ad<emph.end type="italics"/> <foreign lang="greek">k,</foreign> <emph type="italics"/>ne<lb/>ce&longs;&longs;um e&longs;t. </s>

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<s id="id.001008">Maxima <lb/>enim remi pars à &longs;calmo intus e&longs;t in medio nauis.</s><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.101.jpg" pagenum="62"/>

<s id="id.001009">COMMENTARIVS.</s>

<s id="id.001009">COMMENTARIVS. </s>

<s id="id.001010">Cvr remiges.] <emph type="italics"/>Specialia deinceps &longs;unt vndecim de vecte pro<lb/>blemata, è quibus priora &longs;ex pertinent ad nauigandi artem, quæ <lb/>mirabilior &longs;it propter audaciam, an propter &longs;ubtilitatem inuentorum <lb/>ad bene <expan abbr="nauigãdum">nauigandum</expan> vtilium, dubium e&longs;t. </s>

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<s id="id.001091">E&longs;to circu<lb/>lus A D B E, in quo rectam A B diametrum &longs;ecet chorda D <lb/>E ad rectos vt & K I, L H: & &longs;int &longs;egmenta C B, è dia<lb/>metro: F I è propinquiore: G H è remotiore. </s>

<s id="id.001092">Dico C B e&longs;&longs;e <lb/>maiorem quam F I: & F I quam G H. </s>

<s id="id.001092">Dico C B e&longs;&longs;e <lb/>maiorem quam F I: & F I quam G H. </s>

<s id="id.001093">Per punctum M cen<lb/>trum circuli repertum prop. 1. lib. 3. ducatur parallela M N O P <emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.108.jpg" pagenum="69"/><emph type="italics"/>rectæ C D prop. 31. lib. 1. &longs;icque parallelogramma &longs;unt O F & <emph.end type="italics"/><lb/><figure id="id.035.01.108.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.108.1.jpg"/><lb/><emph type="italics"/>N C. </s>

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<s id="id.001124">Quia in tribus prioribus &longs;calmus mani<lb/>fe&longs;tè e&longs;t hypomochlium, pondus mouendum e&longs;t aqua, vel pars extre<lb/>ma remi cum e&longs;t extra aquam. </s>

<s id="id.001125">De his igitur pote&longs;t intelligi Ari&longs;to<lb/>teles tum Vitruuius. </s>

<s id="id.001125">De his igitur pote&longs;t intelligi Ari&longs;to<lb/>teles tum Vitruuius. </s>

<s id="id.001126">At in quarto aqua renitens palmulæ e&longs;t hypo<lb/>mochlium, nauis vero pondus mouendum, vt diximus. </s>

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<s id="id.001146">Igitur remus <lb/>&longs;ecundum latitudinem im<lb/>pellens pondus, & ab illo <lb/>contra repul&longs;us in rectum <lb/>agit: at <expan abbr="gubernacul&utilde;">gubernaculum</expan> qua&longs;i <lb/><expan abbr="trã&longs;uer&longs;um">tran&longs;uer&longs;um</expan> iaceat, in tran&longs;<lb/>uer&longs;um etiam hinc inde motionem facit.</s>

<s id="id.001147">COMMENTARIVS.</s>

<s id="id.001147">COMMENTARIVS. </s>

<s id="id.001148">Potentiæ guber.] <emph type="italics"/>In hoc capite proponuntur tria &longs;pecialia de <lb/>vecte problemata quorum duo &longs;unt de gubernaculo & tertium <lb/>de remo. </s>

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<s id="id.001225">Angulus enim <lb/>æqualis à maiori &longs;ubtendi<lb/>tur, & quanto maiores quæ <lb/>angulum comprehenderunt lineæ.</s>

<s id="id.001226">COMMENTARIVS.</s>

<s id="id.001226">COMMENTARIVS. </s>

<s id="id.001227">In extremo autem.] <emph type="italics"/>Solutio e&longs;t &longs;ecundi problematis duplex, <lb/>&longs;ic.<emph.end type="italics"/></s>

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<s id="id.001245"><emph type="italics"/>Si duo I&longs;o&longs;celia æqualia angulis, inæqualium crurum fuerint: <lb/>erunt & inæqualia <emph.end type="italics"/><lb/><figure id="id.035.01.117.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.117.1.jpg"/><lb/><emph type="italics"/>ba&longs;ibus: & huius ba<lb/>&longs;is maior, cuius crura <lb/>maiora. </s>

<s id="id.001246">Sint A B E <lb/>& A D C duo i&longs;o&longs;<lb/>celia æqualia angulis <lb/>qui ad A, & A D <lb/>crus e&longs;to maius crure <lb/>A B &longs;icut & A C <lb/>ip&longs;o A E. </s>

<s id="id.001246">Sint A B E <lb/>& A D C duo i&longs;o&longs;<lb/>celia æqualia angulis <lb/>qui ad A, & A D <lb/>crus e&longs;to maius crure <lb/>A B &longs;icut & A C <lb/>ip&longs;o A E. </s>

<s id="id.001247">Dico ba&longs;im D C maiorem e&longs;&longs;e ba&longs;i B E. </s>

<s id="id.001247">Dico ba&longs;im D C maiorem e&longs;&longs;e ba&longs;i B E. </s>

<s id="id.001248">Nam quia <emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.118.jpg" pagenum="79"/><emph type="italics"/>tres anguli vnius triangulorum &longs;unt æquales tribus alterius prop. <lb/>32. lib. 1. & anguli qui ad A æquales ex hypothe&longs;i, anguli ad ba<lb/>&longs;im duo duobus &longs;unt æquales ax. 3. & quia A D C & A C D <lb/>&longs;unt ad ba&longs;im I&longs;o&longs;celis, ij inter &longs;e erunt æquales prop. 5. lib. 1. & per <lb/>eandem anguli A B E & A E B. </s>

<s>& anguli qui ad A æquales ex hypothe&longs;i, anguli ad ba<lb/>&longs;im duo duobus &longs;unt æquales ax. 3. </s>

<s>& quia A D C & A C D <lb/>&longs;unt ad ba&longs;im I&longs;o&longs;celis, ij inter &longs;e erunt æquales prop. 5. lib. 1. & per <lb/>eandem anguli A B E & A E B. </s>

<s id="id.001251">Sicque A E B dimidius <lb/>cum &longs;it horum <expan abbr="duor&utilde;">duorum</expan>, angulo A C D etiam dimidio <expan abbr="æquali&utilde;">æqualium</expan> æqua<lb/>lis erit ax. 6. & per idem reliquus reliquo. </s>

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<s>E&longs;t autem maius A D ip&longs;o A B <lb/>ex hypothe&longs;i. </s>

<s id="id.001256">Ergo Ba&longs;is D C maior erit ip&longs;a B E. </s>

<s id="id.001256">Ergo Ba&longs;is D C maior erit ip&longs;a B E. </s>

<s id="id.001257">Igitur &longs;i duo <lb/>I&longs;o&longs;celia æqualia angulis, inæqualia cruribus fuerint &c. </s>

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<s id="id.001259"><emph type="italics"/>Patet igitur ex his quod cum B C &longs;it vt longitudo nauis, &longs;i pup<lb/>pis B peruenerit ad E manente A cardine. </s>

<s id="id.001261">Sicque fiunt duo triangula I&longs;o&longs;celia A B E & A D C æqualia <lb/>angulis ad verticem A oppo&longs;itis prop. 15. lib. 1. </s>

<s>Et inæqualia cruri<lb/>bus. </s>

<s id="id.001262">Nam rectæ ab A puncto Cardini re&longs;pondente in ima parte na<lb/>uis propè puppis extremum ad extremum proræ id e&longs;t A D, A C <lb/>longè maiores &longs;unt breuißimis ijs, quæ &longs;unt ab <expan abbr="eod&etilde;">eodem</expan> puncto A ad ex<lb/>tremum puppis A B, A E. </s>

<s id="id.001263">Peragrabit igitur prora D lineam C B <lb/>longè maiorem, cum B peragrabit B E multo minorem.<emph.end type="italics"/></s></chap><chap>

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<s id="id.001267">Sit enim remus <foreign lang="greek">a b</foreign><lb/>& &longs;calmus <foreign lang="greek">g,</foreign> & intra nauim <lb/>caput remi <foreign lang="greek">a</foreign> palmula intra <lb/>mare <foreign lang="greek">b.</foreign> Si itaque <foreign lang="greek">a</foreign> <expan abbr="tran&longs;la-t&utilde;">tran&longs;la<lb/>tum</expan> &longs;it eò, vbi e&longs;t <foreign lang="greek">d</foreign>: ip&longs;um <foreign lang="greek">b</foreign><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.119.jpg" pagenum="80"/><foreign lang="greek"><gap/></foreign><lb/><arrow.to.target n="marg21"/><lb/>non erit vbi e&longs;t <foreign lang="greek">e.</foreign> E&longs;t enim <lb/><foreign lang="greek">b e</foreign> æqualis ip&longs;i <foreign lang="greek">a d.</foreign> Ex <lb/>æquo igítur tran&longs;latum e&longs;<lb/>&longs;et, &longs;ed minus erat. </s>

<s id="id.001268">E&longs;t igi<lb/>tur vbi <foreign lang="greek">z.</foreign> Minor enim e&longs;t <lb/><foreign lang="greek">b z</foreign>: <expan abbr="quã">quam</expan> <foreign lang="greek">a d.</foreign> Itaque etiam <lb/><foreign lang="greek">q z</foreign> quam <foreign lang="greek">d <expan abbr="q.">que</expan></foreign> Similia enim <lb/>&longs;unt triangula. </s>

<s id="id.001268">E&longs;t igi<lb/>tur vbi <foreign lang="greek">z. </foreign>Minor enim e&longs;t <lb/><foreign lang="greek">b z</foreign>: <expan abbr="quã">quam</expan> <foreign lang="greek">a d. </foreign>Itaque etiam <lb/><foreign lang="greek">q z</foreign> quam <foreign lang="greek">d q. </foreign></s>

<s>Similia enim <lb/>&longs;unt triangula. </s>

<s id="id.001269">Con&longs;i&longs;tens <lb/>vero erit medium vbi e&longs;t <foreign lang="greek">g.</foreign><lb/>In contrarium enim extre<lb/>mo <foreign lang="greek">b,</foreign> quod in mari e&longs;t <lb/>procedit <expan abbr="extrem&utilde;">extremum</expan> <foreign lang="greek">a,</foreign> quod <lb/>in nauigio e&longs;t. </s>

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<s id="id.001271"><margin.target id="marg21"/>Inclu&longs;a his <lb/>notis [] ni<lb/>hil faciunt <lb/>ad rem.</s>

<s id="id.001272">COMMENTARIVS.</s>

<s id="id.001272">COMMENTARIVS. </s>

<s id="id.001273">Ex hoc autem.] <emph type="italics"/>Hic continetur tertium è tribus, quæ hoc <lb/>capite diximus contineri problemata. </s>

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<s id="id.001294"><emph type="italics"/>Ergo nauis plus antror&longs;um mouetur: quam palmula retror&longs;um.<emph.end type="italics"/></s>

<s id="id.001295"><emph type="italics"/>Huius &longs;yllogi&longs;mi propo&longs;itio &longs;ine confirmatione de&longs;erta e&longs;t ab Ari<lb/>&longs;totele. </s>

<s id="id.001295"><emph type="italics"/>Huius &longs;yllogi&longs;mi propo&longs;itio &longs;ine confirmatione de&longs;erta e&longs;t ab Ari<lb/>&longs;totele. </s>

<s id="id.001296">Etiam&longs;i <expan abbr="principi&utilde;">principium</expan> non &longs;it. </s>

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<s><emph type="italics"/>Ex hoc rur&longs;us <expan abbr="cõcludit">concludit</expan> Ari<lb/>&longs;toteles ex figura à Victore Fau&longs;to & ab alijs paßim rectam<emph.end type="italics"/> <foreign lang="greek">d q</foreign><lb/><emph type="italics"/>maiorem e&longs;&longs;e: quam<emph.end type="italics"/> <foreign lang="greek">q z.</foreign> </s>

<s><emph type="italics"/>Et ita e&longs;&longs;e o&longs;tendamus, quia duorum trian<lb/>gulorum<emph.end type="italics"/> <foreign lang="greek">a q d & b q z</foreign> <emph type="italics"/>anguli, qui ad<emph.end type="italics"/> <foreign lang="greek">q</foreign> <emph type="italics"/>ad verticem oppo&longs;iti, <lb/>&longs;unt æquales prop. 15. lib. 1. tum<emph.end type="italics"/> <foreign lang="greek">q a d</foreign> <emph type="italics"/>æqualis e&longs;t<emph.end type="italics"/> <foreign lang="greek">q b z</foreign> <emph type="italics"/>vel quia <lb/>&longs;unt alterni facti à recta<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>incidente in parallelas<emph.end type="italics"/> <foreign lang="greek">a d, b e.</foreign> </s>

<s>tum<emph.end type="italics"/> <foreign lang="greek">q a d</foreign> <emph type="italics"/>æqualis e&longs;t<emph.end type="italics"/> <foreign lang="greek">q b z</foreign> <emph type="italics"/>vel quia <lb/>&longs;unt alterni facti à recta<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>incidente in parallelas<emph.end type="italics"/> <foreign lang="greek">a d, b e.</foreign> </s>

<s><emph type="italics"/>Ex <lb/>præcedenti <expan abbr="demõ&longs;tratione">demon&longs;tratione</expan>. </s>

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<s id="id.001314">qua demon<lb/>&longs;trat cum A caput remi <lb/>remigatione facta e&longs;t in <lb/>D, palmulam B remi A <lb/>B e&longs;&longs;e non in <emph.end type="italics"/><foreign lang="greek"> z</foreign><emph type="italics"/>: &longs;ed in K <lb/>vltra <emph.end type="italics"/><foreign lang="greek"> z</foreign>. </s>

<s id="id.001315"><emph type="italics"/>Nihilominu&longs;que <lb/>B K motum palmulæ B <lb/>retror&longs;um minorem e&longs;&longs;e A <lb/>D motu capitis A an<lb/>tror&longs;um, &longs;ecundum &longs;enten<lb/>tiam Ari&longs;totelis. </s>

<s id="id.001316">Et &longs;ic <lb/>Nonius remigatione facta <lb/>& tran&longs;uecta naui ponit <lb/>&longs;calmum C tran&longs;uectum e&longs;&longs;e in T: vel ex &longs;uperiori Victoris figura <emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.122.jpg" pagenum="83"/><emph type="italics"/>ex<emph.end type="italics"/> <foreign lang="greek">g</foreign> <emph type="italics"/>in<emph.end type="italics"/> <foreign lang="greek">q.</foreign> </s>

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<s id="id.001318">At contrà latum <lb/>pro&longs;perè nauigium &longs;eruat eundem &longs;calmum, &longs;eu &longs;pondam &longs;uam &longs;em<lb/>per æquidi&longs;tantem aquæ, ni&longs;i quod verius e&longs;t, arcum peripheriæ, &longs;ed <lb/>non &longs;implicem, vt po&longs;tea docebimus, de&longs;cribat, cuius extrema &longs;unt in <lb/>&longs;uperficie aquæ. <emph.end type="italics"/><lb/></s><figure id="id.035.01.122.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.122.1.jpg"/>

<s><emph type="italics"/>vt, &longs;it &longs;ponda <lb/>nauis G H, & <lb/>&longs;calmus C, cui <lb/>alligatus remus <lb/>per medium &longs;it <lb/>A B exi&longs;tens in <lb/>principio remi<lb/>gationis, & in <lb/>fine &longs;it vbi D E, <lb/>tran&longs;lato C per <lb/>motum nauigij <lb/>impul&longs;i in T: <lb/>&longs;icque motionis <lb/>intra aquam pal<lb/>mulæ B &longs;patium erit B E: nauigij vero erit C T: tum capitis <lb/>remi A erit A D. </s>

<s id="id.001319">Et quidem cum anguli qui ad E &longs;int &longs;emper <lb/>æquales prop. 15. lib. 1. </s>

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<s id="id.001320">Hæc igi<lb/>tur cum expendo cogor aliud &longs;entire quam Nonius licet timidè (quia <lb/>viro huic propter &longs;cientiam præ&longs;tantem, & quod in loco natus &longs;it, <lb/>vixeritque ad nauigandum opportunißimo, multò plura quam mihi <lb/>tribuere &longs;oleo) dicam tamen quod &longs;entio nempe conclu&longs;ionem i&longs;tam<emph.end type="italics"/><lb/><foreign lang="greek">d q</foreign> <emph type="italics"/>maiorem e&longs;&longs;e<emph.end type="italics"/> <foreign lang="greek">q z,</foreign> <emph type="italics"/>pertinere eò, vt inferatur caput remi A <lb/>tran&longs;uecti non con&longs;i&longs;tere in<emph.end type="italics"/> <foreign lang="greek">d</foreign>: <emph type="italics"/>&longs;ed vltra. </s>

<s id="id.001321">vt in figuræ no&longs;træ pun<lb/>cto F. </s>

<s id="id.001321">vt in figuræ no&longs;træ pun<lb/>cto F. </s>

<s id="id.001322">Sicque caput A multo anterius latum erit, quam B retrò. <lb/></s>

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<s id="id.001338">Nauis vero idem interuallum conficiet quod &longs;calmus B. <lb/></s>

<s id="id.001339">Dico igitur rectam A E maiorem e&longs;&longs;e recta B D. </s>

<s id="id.001339">Dico igitur rectam A E maiorem e&longs;&longs;e recta B D. </s>

<s id="id.001340">Secet enim re<lb/>cta A C rectam E F in G. </s>

<s id="id.001340">Secet enim re<lb/>cta A C rectam E F in G. </s>

<s id="id.001341">Quia igitur A G E, & B G D <lb/>triangula &longs;unt æquiangula, erit &longs;icut A G ad B G: &longs;ic A E <lb/>ad B D prop. 4. lib. 6. </s>

<s>Maior e&longs;t autem A G ip&longs;a B G, ax. 9. <lb/></s>

<s id="id.001342">Erit igitur A E maior quam B D. </s>

<s id="id.001342">Erit igitur A E maior quam B D. </s>

<s id="id.001343">Itaque caput remi A maius <lb/>percurrit &longs;patium: quam nauis. </s>

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<s id="id.001353"><emph type="italics"/>Remus in principio motus habeat <lb/>po&longs;itionem A B C, ducaturque per <lb/>punctum C, in quo remi palmula <lb/>recta C G rectos efficiens angulos <lb/>in puncto G cum recta per quam ad <lb/>motum nauis &longs;calmus B mouetur. </s>

<s id="id.001354">Et <lb/>eadem recta C G producatur v&longs;que <lb/>ad E, ita vt G E &longs;it æqualis rectæ <lb/>B A (quæ e&longs;t dimidium remi) rur<lb/>&longs;us per punctum B ducatur recta Q <lb/>B F ad rectos cum ip&longs;a B G, & in <lb/>Q B F incidant perpendiculares A <lb/>Q C F. </s>

<s id="id.001355">Quoniam igitur triangu<lb/>lorum A B Q & F B C anguli, <lb/>qui ad B ad verticem oppo&longs;iti &longs;unt <lb/>æquales, prop. 15. lib. 1. </s>

<s id="id.001355">Quoniam igitur triangu<lb/>lorum A B Q & F B C anguli, <lb/>qui ad B ad verticem oppo&longs;iti &longs;unt <lb/>æquales, prop. 15. lib. 1. & anguli qui ad Q & F recti &longs;unt, tum <lb/>latus A B lateri B C, &longs;unt enim dimidia remi, æquale e&longs;t, erit & <lb/>latus A Q æquale lateri F C prop. 26. lib. 1. </s>

<s>& anguli qui ad Q & F recti &longs;unt, tum <lb/>latus A B lateri B C, &longs;unt enim dimidia remi, æquale e&longs;t, erit & <lb/>latus A Q æquale lateri F C prop. 26. lib. 1. </s>

<s>Ip&longs;i autem F C recta <lb/>B G, latus parallelogrammi oppo&longs;itum, æqualis e&longs;t prop. 34. lib. 1. <lb/></s>

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<s id="id.001359">Et nauis tantum confecit quan<lb/>tum A caput remi ex hypothe&longs;i. </s>

<s id="id.001360">A autem conficit &longs;patium A <expan abbr="q.">que</expan> <lb/>Igitur B &longs;calmus conficiet &longs;patium B G. </s>

<s id="id.001360">A autem conficit &longs;patium A q. <lb/></s>

<s>Igitur B &longs;calmus conficiet &longs;patium B G. </s>

<s id="id.001361">Et quia anguli ad G <lb/>recti &longs;unt, ideo cum &longs;calmus peruenerit ad G, habebit remus A C <lb/>rectitudinis &longs;itum E C, quo in loco illius remigationis finis erit. </s>

<s id="id.001362">Sic <lb/>igitur palmula C à loco &longs;uo dimota non fuit, quod demon&longs;trandum <lb/>erat. </s>

<s id="id.001363">Cæterum Nonius hîc aduertit rectam G C minorem e&longs;&longs;e B C <lb/>remi dimidio, pro quantitate C T. </s>

<s id="id.001363">Cæterum Nonius hîc aduertit rectam G C minorem e&longs;&longs;e B C <lb/>remi dimidio, pro quantitate C T. </s>

<s id="id.001364">Vnde concludit quo tempore <lb/>&longs;calmus B transfertur in G, palmulam quidem C excurrere in <lb/>ip&longs;am longitudinem C T. </s>

<s id="id.001364">Vnde concludit quo tempore <lb/>&longs;calmus B transfertur in G, palmulam quidem C excurrere in <lb/>ip&longs;am longitudinem C T. </s>

<s id="id.001365">Sed neque antror&longs;um neque retror&longs;um, <lb/>quod Ari&longs;toteles puto vocauit antè, palmulam diuidere mare, quod <lb/>&longs;olum demon&longs;trare intendebat. </s>

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<s id="id.001369"><emph type="italics"/>Manife&longs;ta e&longs;t, quia &longs;i remi palmula dimota non fuerit à loco &longs;uo, <lb/>ibique tandiu per&longs;i&longs;tat, donec remus &longs;itum rectitudinis obtineat, tan<lb/>tum &longs;patium conficiet caput remi motu proprio: quantum nauis. <lb/></s>

<s id="id.001370">Recta enim C F æqualis e&longs;t A Q prop. 26. lib. 1. æqualis etiam <lb/>B G prop. 34. lib. 1. igitur A Q & B G æquales erunt ax. 1.<emph.end type="italics"/></s>

<s id="id.001370">Recta enim C F æqualis e&longs;t A Q prop. 26. lib. 1. </s>

<s>æqualis etiam <lb/>B G prop. 34. lib. 1. </s>

<s>igitur A Q & B G æquales erunt ax. 1. <emph.end type="italics"/></s>

<s id="id.001373">Propo&longs;itio tertia.</s>

<s id="id.001374"><emph type="italics"/>Capite remi proprio motu conficiente &longs;patium duplum &longs;patij nauis: <lb/>tunc nauis tantùm promouebitur, quantùm palmula retrocedet.<emph.end type="italics"/></s><figure id="id.035.01.126.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.126.1.jpg"/>

<s id="id.001375"><emph type="italics"/>Remus incipiente motu &longs;it A C, <lb/>de&longs;inente vero habeat rectitudinis <lb/>&longs;itum F G. </s>

<s id="id.001375"><emph type="italics"/>Remus incipiente motu &longs;it A C, <lb/>de&longs;inente vero habeat rectitudinis <lb/>&longs;itum F G. </s>

<s id="id.001376">Et &longs;ic &longs;calmus B pro<lb/>pter nauis motum conficiet interual<lb/>lum B D. </s>

<s id="id.001376">Et &longs;ic &longs;calmus B pro<lb/>pter nauis motum conficiet interual<lb/>lum B D. </s>

<s id="id.001377">Excitetur igitur à puncto <lb/>B in vtramque partem perpendicu<lb/>laris E E, prop. 11. lib. 1. </s>

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<s id="id.001390"><emph type="italics"/>Si enim C H æqualis ponatur B D, quoniam eidem B D æqua<lb/>lis e&longs;t H E in parallelogrammo, æquales igitur erunt C H & <lb/>H E ax. 1. </s>

<s id="id.001391">Et &longs;ic dupla erit C E ip&longs;ius H E: & eadem C E <lb/>dupla ip&longs;ius B D. æquales porro &longs;unt C E & A E prop 26. lib. 1. <lb/></s>

<s id="id.001391">Et &longs;ic dupla erit C E ip&longs;ius H E: & eadem C E <lb/>dupla ip&longs;ius B D. </s>

<s>æquales porro &longs;unt C E & A E prop 26. lib. 1. <lb/></s>

<s>Dupla ergo erit A E rectæ B D. </s>

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<s id="id.001396"><emph type="italics"/>In po&longs;tremo diagrammate ponatur B D minor, quam A E: <lb/>&longs;ed eius dimidio maior. </s>

<s id="id.001397">Dico quod ip&longs;a B D maior e&longs;t, quam C H. <lb/></s>

<s id="id.001397">Dico quod ip&longs;a B D maior e&longs;t, quam C H. <lb/></s>

<s id="id.001398">Nam B D & H E æquales &longs;unt, ad hæc A E & C E æqua<lb/>les &longs;unt. </s>

<s id="id.001399">maior igitur erit H E dimidio ip&longs;ius A E. </s>

<s>quapropter <lb/>reliqua C H minor dimidio erit eiu&longs;dem A E. </s>

<s>quapropter <lb/>reliqua C H minor dimidio erit eiu&longs;dem A E. </s>

<s id="id.001400">Et minor igitur <lb/>erit C H quam B D. </s>

<s id="id.001400">Et minor igitur <lb/>erit C H quam B D. </s>

<s id="id.001401">Interuallum autem B D, id e&longs;t quod nauis <lb/>confecit, interuallum vero C H remi palmula in contrarium de<lb/>currit. </s>

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<s id="id.001403">Po&longs;terior autem &longs;imiliter <lb/>o&longs;tendetur. </s>

<s id="id.001404">Si enim B D minor e&longs;t dimidio ip&longs;ius A E, minor <lb/>igitur erit & H E dimidio eiu&longs;dem A E. </s>

<s id="id.001404">Si enim B D minor e&longs;t dimidio ip&longs;ius A E, minor <lb/>igitur erit & H E dimidio eiu&longs;dem A E. </s>

<s id="id.001405">Et quoniam A E & <lb/>C E æquales &longs;unt. </s>

<s id="id.001406">Reliqua igitur C H dimidio eiu&longs;dem A E <lb/>maior erit. </s>

<s id="id.001407">Et proinde minor erit B D quam C H. </s>

<s id="id.001407">Et proinde minor erit B D quam C H. </s>

<s id="id.001408">Nauis igitur <lb/>minus interuallum decurret in anteriora: quam remi palmula in <lb/>contrarium. </s>

<s id="id.001409">quod fuit demon&longs;trandum.<emph.end type="italics"/></s>

<s id="id.001410">Corollarium.</s>

<s id="id.001410">Corollarium. </s>

<s id="id.001411"><emph type="italics"/>Hinc & ex præcedenti infertur, quod &longs;i caput remi motu pro<lb/>prio decurrat interuallum maius, quam nauis, &longs;iue duplum, &longs;iue du<lb/>plo minus, &longs;iue maius: &longs;emper interuallum nauis adiuncto ei quod <lb/>palmula retroce&longs;&longs;erit, æquale erit ei, quod à capite remi motu proprio <lb/>conficitur.<emph.end type="italics"/></s><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.128.jpg" pagenum="89"/>

<s id="id.001412"><emph type="italics"/>Semper enim B D æqualis e&longs;t H E: tota vero C E quæ æqua<lb/>lis e&longs;t A E ex&longs;uis con&longs;tabit partibus C H, H E.<emph.end type="italics"/></s>

<s id="id.001413">Propo&longs;itionis conuer&longs;io.</s>

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<s id="id.001417"><emph type="italics"/>Naui celerius mota quam caput remi: palmula antror&longs;um moue<lb/>bitur, nec quicquam retrocedet, idque &longs;patij decurret quo nauis motus <lb/>motum capitis remi &longs;uperat.<emph.end type="italics"/></s><figure id="id.035.01.128.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.128.1.jpg"/>

<s id="id.001418"><emph type="italics"/>Habeat remus inci<lb/>piente motu po&longs;itionem <lb/>A C: de&longs;inente vero <lb/><expan abbr="&longs;it&utilde;">&longs;itum</expan> rectitudinis F G. <lb/></s>

<s id="id.001419">Scalmus igitur B pro<lb/>pter nauis motum tran&longs;<lb/>latus erit in D. </s>

<s id="id.001419">Scalmus igitur B pro<lb/>pter nauis motum tran&longs;<lb/>latus erit in D. </s>

<s id="id.001420">Sit ita<lb/>que interuallum B D <lb/>maius: <expan abbr="quã">quam</expan> A H, quod <lb/>e&longs;t à capite remi motu <lb/>proprio decur&longs;um. </s>

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<s id="id.001422">Dico quod palmu<lb/>la C in vlteriora mouebitur. </s>

<s id="id.001423">Nam cum &longs;calmus B prouectus fue<lb/>rit in D, tran&longs;lata erit ip&longs;a palmula A C, vbi G in rectitudinis <lb/>&longs;itu, interuallumque conficiet C G curuilineum, cui re&longs;pondet C K. <lb/></s>

<s id="id.001424">Mouebitur igitur palmula in anteriora. </s>

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<s>celerius igitur feretur C ad K: quam ad <emph.end type="italics"/><foreign lang="greek">z</foreign><emph type="italics"/>. <lb/></s>

<s>quapropter nihil vnquam retrocedet ip&longs;um C. </s>

<s>quapropter nihil vnquam retrocedet ip&longs;um C. </s>

<s id="id.001429">Imo vero in vlte<lb/>riora progredietur, interuallumque decurret C K, quod quidem re<lb/>linquitur, detracto <emph.end type="italics"/><foreign lang="greek">z</foreign><emph type="italics"/> C ex <emph.end type="italics"/><foreign lang="greek">z</foreign><emph type="italics"/> K. </s>

<s id="id.001430">Si enim remi palmula tota ip&longs;a <emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.129.jpg" pagenum="90"/><emph type="italics"/>nauigij celeritate moueretur, vltra k progrederetur, cum B perue<lb/>niret ad D: &longs;ed retrahitur interim, propter eum motum, qui fit cir<lb/>ca B. </s>

<s id="id.001431">Sic igitur palmulæ celeritate, quæ à motu nauigij prouenit, re<lb/>tardata, decur&longs;um interuallum erit C K. </s>

<s id="id.001431">Sic igitur palmulæ celeritate, quæ à motu nauigij prouenit, re<lb/>tardata, decur&longs;um interuallum erit C K. </s>

<s id="id.001432">Videtur autem &longs;olo remo<lb/>rum impul&longs;u hoc fieri non po&longs;&longs;e: &longs;ed alia in&longs;uper virtute impellente <lb/>opus e&longs;&longs;e: vt vento, vel impetu eò fluentis aquæ.<emph.end type="italics"/></s>

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<s id="id.001443">In eodem <lb/>enim exi&longs;tente prora, nauis <lb/>tota transfertur.</s>

<s id="id.001444">COMMENTARIVS.</s>

<s id="id.001444">COMMENTARIVS. </s>

<s id="id.001445">Id etiam ip&longs;um.] <emph type="italics"/>Ari&longs;toteles a&longs;&longs;erit gubernaculum idem fa<lb/>cere quod remus. </s>

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<s id="id.001460">Igitur &longs;i quan<lb/>to remotior fuerit pre&longs;&longs;io, <lb/>facilius & celerius vis <expan abbr="ead&etilde;">eadem</expan> <lb/>pondus ip&longs;um mouet: an<lb/>temna &longs;ublimius po&longs;ita à <lb/>calce mali, quæ pre&longs;&longs;io e&longs;t, <lb/>magis di&longs;tare velum faciet.</s>

<s id="id.001461">COMMENTARIVS.</s>

<s id="id.001461">COMMENTARIVS. </s>

<s id="id.001462">Antemnæ.] <emph type="italics"/>Antemna lignum e&longs;t per tran&longs;uer&longs;um in malo <lb/>nauis po&longs;itum, à quo velum dependet. </s>

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<s id="id.001481">Ex anteced.<emph.end type="italics"/></s>

<s id="id.001482"><emph type="italics"/>Quò autem antemna, intellige cum velo expan&longs;o, &longs;uperior e&longs;t in <lb/>malo: eò pars ab hypomochlio ad caput vectis e&longs;t longior. </s>

<s id="id.001482"><emph type="italics"/>Quò autem antemna, intellige cum velo expan&longs;o, &longs;uperior e&longs;t in <lb/>malo: eò pars ab hypomochlio ad caput vectis e&longs;t longior. ax. 9. <lb/></s>

<s id="id.001484">E&longs;t enim malus vectis, & mali pterna &longs;eu calx e&longs;t hypo<lb/>mochlium.<emph.end type="italics"/></s>

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<s id="id.001503"><expan abbr="v&etilde;tus">ventus</expan> <lb/>igitur perpellit, quem &longs;e<lb/>cundum facit gubernacu<lb/>lum, auertens & compel<lb/>lens mare, &longs;imul & nautæ <lb/>pugnant cum vento, & in <lb/>contrariam nituntur par<lb/>tem.</s>

<s id="id.001504">COMMENTARIVS.</s>

<s id="id.001504">COMMENTARIVS. </s>

<s id="id.001505">E Cornu volunt nauigare.] <emph type="italics"/>Diximus antemnarum extrema <lb/>appellari cornua. </s>

<s id="id.001506">Hinc è cornu nauigare e&longs;t cum vento cornu <lb/>antemnarum obijcitur. </s>

<s id="id.001507">Quod feci&longs;&longs;e &longs;ignificabat Troianos Virgi<emph.end type="italics"/><arrow.to.target n="marg23"/><lb/><emph type="italics"/>lius hoc ver&longs;u,<emph.end type="italics"/></s>

<s id="id.001507">Quod feci&longs;&longs;e &longs;ignificabat Troianos Virgi<emph.end type="italics"/><arrow.to.target n="marg23"/><lb/><emph type="italics"/>lius hoc ver&longs;u,<emph.end type="italics"/></s>

<s id="id.001508"><margin.target id="marg23"/>Lib. 3. <lb/>Æneid.</s>

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<s>Ii&longs;dem <lb/>autem ventis in contrarium nauigatur prolatis pedibus vt noctu <lb/>plerumque vela concurrant.<emph.end type="italics"/></s>

<s id="id.001528">Cur quando.] <emph type="italics"/>Sextum e&longs;t problema &longs;peciale de vecte in naui<lb/>gatione obliqua, quod &longs;oluitur triplici ope nempe veli obliqui ex par<lb/>te contracti, parteque expan&longs;i gubernaculi tanquam vectis, & re<lb/>migum renixus.<emph.end type="italics"/></s>

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<s id="id.001530">At cum ventus &longs;ecundus non <lb/>e&longs;t, antemnarum ope rectum nihilominus tenere cur&longs;um poßibile e&longs;t, <lb/>Et id vt fiat & quibus de cau&longs;is, explicatur hîc ab Ari&longs;torele.<emph.end type="italics"/></s>

<s id="id.001531">Vento &longs;ecundo.] <emph type="italics"/>Ventus &longs;ecundus e&longs;t cum vt ait Poëta,<emph.end type="italics"/></s>

<s id="id.001531">Vento &longs;ecundo.] <emph type="italics"/>Ventus &longs;ecundus e&longs;t cum vt ait Poëta,<emph.end type="italics"/></s>

<s id="id.001532">A tergo comitatur euntes,</s>

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<s>ventus ex <lb/>C recta feratur ad D, tanquam ad centrum. </s>

<s id="id.001570">Itaque vento pro<lb/>pul&longs;a nauis A, feretur in E, & B in F. </s>

<s id="id.001570">Itaque vento pro<lb/>pul&longs;a nauis A, feretur in E, & B in F. </s>

<s id="id.001571">Fiat igitur in naui per <lb/>temonem mutatum angulus G A K, qui &longs;it æqualis angulo G <lb/>A E: tum H B L æqualis angulo H B F.<emph.end type="italics"/></s>

<s id="id.001571">Fiat igitur in naui per <lb/>temonem mutatum angulus G A K, qui &longs;it æqualis angulo G <lb/>A E: tum H B L æqualis angulo H B F. <emph.end type="italics"/></s>

<s id="id.001572"><emph type="italics"/>Quia igitur nauis A à vento fertur in E, & per temonis muta<lb/>tionem in K, feretur recta in G, & eadem ratione B in H. <lb/></s>

<s id="id.001572"><emph type="italics"/>Quia igitur nauis A à vento fertur in E, & per temonis muta<lb/>tionem in K, feretur recta in G, & eadem ratione B in H. <lb/></s>

<s id="id.001573">Neuter enim cum &longs;uo impul&longs;u præualeat, medium teneat A G ne<lb/>ce&longs;&longs;e e&longs;t, quod &longs;i ventus præualet, adiungitur remigum renixus, qui <lb/>&longs;i non &longs;atis &longs;it, vento cedendum, aut anchora iacienda. </s>

<s id="id.001574">Tum autem <lb/>vix remiges re&longs;i&longs;tunt, <expan abbr="c&utilde;">cum</expan> nauis e&longs;t in centro, vel radio perpendicula<lb/>ri venti, quo in loco propter vim venti maiorem, & anguli per te<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.138.jpg" pagenum="99"/><emph type="italics"/>monem faciendi magnitudinem, vt qui rectum æquare debeat, dif<lb/>ficillimè ad locum de&longs;tinatum dirigitur: at quantò fuerit remotior <lb/>à puncto D, velocius & facilius feretur, quia ventus rectius tan<lb/>get puppim, minor enim erit &longs;emper angulus per temonem facien<lb/>dus, vt intelligitur ex G P Q minore: quam G A E, & G I <lb/>M minore: quam G P <expan abbr="q.">que</expan> Sunt enim duo C A G & G A E, <lb/>quia facti à recta G A in rectam C E duobus rectis æquales <lb/>prop. 13. lib. 1. & per eandem etiam duo C P G & G P Q duobus <lb/>rectis æquales. </s>

<s>Sunt enim duo C A G & G A E, <lb/>quia facti à recta G A in rectam C E duobus rectis æquales <lb/>prop. 13. lib. 1. & per eandem etiam duo C P G & G P Q duobus <lb/>rectis æquales. </s>

<s id="id.001575">Ergo duo C A G & G A E duobus C P G & <lb/>G P Q &longs;unt æquales axiom. 1. </s>

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<s id="id.001587">At &longs;i recti lineum e&longs;<lb/>&longs;et, rectitudine &longs;ua mul<lb/>tum plani attingeret.</s>

<s id="id.001588">COMMENTARIVS.</s>

<s id="id.001588">COMMENTARIVS. </s>

<s id="id.001589">Cvr quæ figurarum.] <emph type="italics"/>In hoc capite redit Ari&longs;toteles ad fi<lb/>guras rotundas, & quærit generaliter cau&longs;as facilitatis motus <lb/>earum, ea&longs;que quinque aßignat <expan abbr="modic&utilde;">modicum</expan> tactum, offen&longs;ationem exi<lb/>guam, nutum dimidiæ partis, motum <expan abbr="perpetu&utilde;">perpetuum</expan>, motum naturalem.<emph.end type="italics"/></s>

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<s id="id.001631">Sit enim <lb/>ABCD <lb/><figure id="id.035.01.141.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.141.1.jpg"/><lb/><expan abbr="rectili-ne&utilde;">rectili<lb/>neum</expan> pla<lb/>no E F <lb/><expan abbr="in&longs;i&longs;t&etilde;s">in&longs;i&longs;tens</expan>, <lb/>& <expan abbr="qui-d&etilde;">qui<lb/>dem</expan> &longs;i na<lb/>turale e&longs;t <lb/>in&longs;ita grauitate verget ver&longs;us G, & ad rectos in&longs;i&longs;tet rectis A C <lb/>& B D & omnibus inter illas interiectis vt H I, K L, M N, <lb/>&longs;icque totidem momentis ver&longs;us G contendit. </s>

<s id="id.001632">Præterea aër vel <lb/>aqua medium occurrens lateri A C, quantum in &longs;e, e&longs;t impedit tot <lb/>punctis, quot &longs;unt in A C.<emph.end type="italics"/></s>

<s id="id.001633"><emph type="italics"/>Sit & cubus A D, planum K L, vna &longs;uperficierum &longs;uarum <lb/>E D attingens, tum habeat rectas A E, C F, B D, H G, ad<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.142.jpg" pagenum="103"/><emph type="italics"/>rectos in&longs;i&longs;ten<emph.end type="italics"/><lb/><figure id="id.035.01.142.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.142.1.jpg"/><lb/><emph type="italics"/>tes, vt totidem <lb/>alias, quot &longs;unt <lb/>puncta in &longs;u<lb/>perficie E D <lb/>nixu naturali <lb/>coniunctæ. </s>

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<s id="id.001644">Sed id nullum locum ha<lb/>bet, quia quæ hactenus dicta &longs;unt im<lb/>pedimenta figurarum, &longs;unt <expan abbr="figurar&utilde;">figurarum</expan> in <lb/>plano <expan abbr="nõ">non</expan> <expan abbr="aut&etilde;">autem</expan> in concauo &longs;imili & <expan abbr="cõ-">con</expan><emph.end type="italics"/><lb/><figure id="id.035.01.142.3.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.142.3.jpg"/><lb/><emph type="italics"/>gruenti <expan abbr="exi&longs;tenti&utilde;">exi&longs;tentium</expan>, cuiu&longs;modi e&longs;t terra, <lb/>cuiu&longs;que omnes partes <expan abbr="rot&utilde;dæ">rotundæ</expan> exi&longs;ten<lb/>tis æquabilius coniuncto nixu ad cen<lb/>trum contendunt: quam &longs;i alterius e&longs;&longs;et <lb/>cuiu&longs;cunque figuræ. </s>

<s id="id.001645">Sit enim cubica <lb/>cuius centrum A & B punctum an<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.143.jpg" pagenum="104"/><emph type="italics"/>gulare, & ita remotius quam C laterale, non tanto nixu contendet: <lb/>quam ip&longs;um C. </s>

<s id="id.001646">Quò enim mobile naturale propius e&longs;t, eò obnixius <lb/>incumbit. </s>

<s id="id.001647">Eadem e&longs;t ratio cuiu&longs;cumque figuræ præterquam &longs;phæri<lb/>cæ, cuius puncta B, C, D, in eadem &longs;uperficie æqualiter à centro <lb/>&longs;emper di&longs;tant. </s>

<s id="id.001648">Itaque terra, vt medium vndiquaque obtineret, & <lb/>vt quæ in ea omnia puncta æquali nixu ad eius centrum niteren<lb/>tur, debuit e&longs;&longs;e &longs;phærica: ob idque immobilißima e&longs;t, nullibique <lb/>nutat, contrà quam dixit Poëta,<emph.end type="italics"/></s>

<s id="id.001649">A&longs;pice nutantem conuexo pondere mundum. <lb/></s>

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<s id="id.001670">Quandoquidem &longs;i in <lb/>contrarium: quam quò <lb/>vergat, moueatur, difficulter mouebitur.</s>

<s id="id.001671">COMMENTARIVS.</s>

<s id="id.001671">COMMENTARIVS. </s>

<s id="id.001672">Præterea quò.] <emph type="italics"/>Tertia cau&longs;a facilitatis e&longs;t motus, quando mo<lb/>bile in omni po&longs;itu &longs;uper plano dimidia &longs;ui parte quoquouer&longs;um <lb/>ad planum ip&longs;um acclinat, vt fit in rotundo, quod ip&longs;um tangit in <lb/>puncto, vt ante docuimus, &longs;icque quoquouer&longs;um vergit. </s>

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<s id="id.001700">Eam &longs;iquidem, qua <lb/>mouetur in <expan abbr="obliqu&utilde;">obliquum</expan>, mo<lb/>tor impellit: illa verò, quæ &longs;uper diametro efficitur, ip&longs;e<lb/>met &longs;e circulus mouet.</s>

<s id="id.001701">COMMENTARIVS.</s>

<s id="id.001701">COMMENTARIVS. </s>

<s id="id.001702">Præterea nonnulli.] <emph type="italics"/>Quarta cau&longs;a e&longs;t de perpetuo motu con<lb/>firmata nonnullorum, &longs;ed innominatorum authoritate: & &longs;imi<lb/>litudine e contrarijs &longs;ic. </s>

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<s id="id.001723">Nunc igitur hoc cum ve<lb/>rum e&longs;&longs;e experiamur, & ratio conuincat, quantò quodque remotius <lb/>e&longs;t à loco, in quo naturaliter quie&longs;ceret, tantò ad eum magis conari, <lb/>remotioris maior erit nutus. </s>

<s id="id.001724">In peripheria maiori punctum A re<lb/>motius puncto D. </s>

<s id="id.001724">In peripheria maiori punctum A re<lb/>motius puncto D. </s>

<s id="id.001725">Magis igitur nutat. </s>

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<s id="id.001736">quod erat demon&longs;trandum.<emph.end type="italics"/></s>

<s id="id.001737">Etiam&longs;i curuatura.] <emph type="italics"/>Repetit cau&longs;am perpetui motus, aut nu<lb/>tus ad motum, quæ in circulo e&longs;t, cum &longs;ua ab&longs;ide id e&longs;t curuatura at<lb/>tingit planum, ine&longs;&longs;e, etiam&longs;i non attingat, vt fit in rotis figulorum, <lb/>& in trochleis. de quibus po&longs;tea.<emph.end type="italics"/></s>

<s>de quibus po&longs;tea. <emph.end type="italics"/></s>

<s id="id.001739">Sed ob aliam cau&longs;am.] <emph type="italics"/>Quinta cau&longs;a de naturali motu &longs;e<lb/>cundum peripheriam hîc leuiter attingitur, vel potius ex anteceden<lb/>tibus breuiter repetitur. </s>

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<s id="id.001750">Et lineæ <lb/>in librili, quæ &longs;unt ab agina <lb/>vtrimque, &longs;unt radij.</s>

<s id="id.001751">COMMENTARIVS.</s>

<s id="id.001751">COMMENTARIVS. </s>

<s id="id.001752">Cvr per maiores.] <emph type="italics"/>In hoc capite tractatur problema de ma<lb/>ioribus circulis, & &longs;phæricis. </s>

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<s id="id.001764">Geminatur aliquando, tripli<lb/>catur, & amplius multiplicatur. </s>

<s id="id.001765">Vnde &longs;unt illa tractoria infinita<lb/>rum propemodum virium Tri&longs;pa&longs;ton, Pente&longs;pa&longs;ton, Poly&longs;pa&longs;ton, in <lb/>quibus rotulæ &longs;ibi inuicem &longs;ub&longs;eruientes, & tanquam onus attra<lb/>hendum diuidentes &longs;umma facilitate ip&longs;um attrahunt, de quo qui <lb/>multa admirabilia videre volet, videat apud Guidum Vbaldum.<emph.end type="italics"/></s>

<s id="id.001766">Et&longs;cytalæ.] <emph type="italics"/>Scytala lignum e&longs;t cylindricum cuius pro duplici <lb/>v&longs;u duo genera &longs;tatuuntur. </s>

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<s id="id.001797">At quò propendet, fa<lb/>cile: non propendet autèm in obliquum.</s>

<s id="id.001798">COMMENTARIVS.</s>

<s id="id.001798">COMMENTARIVS. </s>

<s id="id.001799">Cvr librile.] <emph type="italics"/>In hoc capite &longs;peciale tractatur problema, quod <lb/>generale e&longs;&longs;e po&longs;&longs;et. </s>

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<s id="id.001818">In <lb/>vtri&longs;que enim his locis re<lb/>uoluitur circulus, & conci<lb/>tatus impellitur.</s>

<s id="id.001819">COMMENTARIVS.</s>

<s id="id.001819">COMMENTARIVS. </s>

<s id="id.001820">Cvr onera.] <emph type="italics"/>Secundum genus &longs;cytalæ e&longs;t lignum ferrumue <lb/>cylindricum oblongum in extremis rotulas habens intra annu<lb/>los currui <emph.end type="italics"/><lb/><figure id="id.035.01.153.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.153.1.jpg"/><lb/><emph type="italics"/>affixos <lb/>ver&longs;atile, <lb/>vt e&longs;t fi<lb/>gura A <lb/>B quæ <lb/>mota iu<lb/>go rotis annexo, contrà, quam in curribus, in quibus non rotis: &longs;ed <lb/>currui annectitur, omnibus &longs;uis partibus mouetur duobus motibus <lb/>&longs;imul, circumcirca, & antror&longs;um. </s>

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<s id="id.001843">At iactus à manu <lb/>re&longs;pectu fundæ breuis e&longs;t.</s>

<s id="id.001844">COMMENTARIVS.</s>

<s id="id.001844">COMMENTARIVS. </s>

<s id="id.001845">A Funda.] <emph type="italics"/>Funda e&longs;t funiculus duobus capitibus manu captus, <lb/>altero cum an&longs;ula digito circumuoluta ne exeat, altero &longs;ine an<lb/>&longs;ula, vt dimitti poßit. </s>

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<s id="id.001849">Erat autem <lb/>fundæ v&longs;us adeò frequens Balearium in&longs;ularum populis, vt matres <lb/>filios non alijs auibus ve&longs;ci paterentur, quam quas funda &longs;ibi com<lb/>para&longs;&longs;ent. </s>

<s id="id.001850">Vnde & funda balearis appellatur à Poëta,<emph.end type="italics"/></s>

<s id="id.001850">Vnde & funda balearis appellatur à Poëta,<emph.end type="italics"/></s>

<s id="id.001851">Stuppea torquentur balearis verbera fundæ. <lb/></s>

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<s id="id.001872">An propter hoc.] <emph type="italics"/>Alter e&longs;t modus &longs;olutionis problematis <lb/>&longs;umptus è funda tanquam radio longiore. </s>

<s id="id.001873">Syllog. &longs;ic e&longs;t. </s>

<s id="id.001873">Syllog. &longs;ic e&longs;t. </s>

<s id="id.001874">Quantò li<lb/>nea à centro e&longs;t maior, tantò celerius mouet.<emph.end type="italics"/></s>

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<s id="id.001890">Et id linea e&longs;t quæ <lb/>ex centro.</s>

<s id="id.001891">COMMENTARIVS.</s>

<s id="id.001891">COMMENTARIVS. </s>

<s id="id.001892">Cvr circa eandem.] <emph type="italics"/>In hoc capite continentur duo proble<lb/>mata vnum de ergatis, alterum de &longs;ucculis. </s>

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<s id="id.001910">Videat apud Guidum Vbaldum in Mechanicis. </s>

<s id="id.001911">Ad <lb/>hoc genus etiam in&longs;trumenti referantur ingentes illæ rotæ in vno <lb/>axe quarum vna labore vnius atque alterius hominis vertitur: alte<lb/>ra &longs;itulis quibus in &longs;ua circumferentia accommodate dispo&longs;itis con<lb/>ferta e&longs;t &longs;ui conuer&longs;ione ex vna parte aquam Sequanæ &longs;eptis contra<lb/>ctam exhau&longs;it, ex altera aliò refudit, vt ex lapide quadrato firma <lb/><expan abbr="iacer&etilde;tur">iacerentur</expan> fundamenta illius eximij pontis, qui magno ornamento & <lb/>commoditate celeberrimæ vrbium Lutetiæ, iu&longs;&longs;u Henrici III. Regis<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.160.jpg" pagenum="121"/><emph type="italics"/>no&longs;tri Chri&longs;tianißimi inchoatus, & maiori iam ex parte con&longs;tru<lb/>ctus perfectionem ab Henrico IIII. </s>

<s id="id.001912">Rege nunc no&longs;tro magnifi<lb/>centißimo de&longs;iderat, ea in parte, qua flumen à &longs;chola S. Germani <lb/>ad plateam Augu&longs;tinorum traducitur. </s>

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<s id="id.001921">Quod frangitur autem moueri nece&longs;&longs;e e&longs;t.</s>

<s id="id.001922">COMMENTARIVS.</s>

<s id="id.001922">COMMENTARIVS. </s>

<s id="id.001923"><emph type="italics"/>Mos e&longs;t ignem excitare in paruo foco volentium, baculos lon<lb/>giores bifariam frangere. </s>

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<s id="id.001952">Crocis autem <lb/>propter maris motum, cum <lb/>quo etiam mouentur, con<lb/>tingit in perpetua motione <lb/>e&longs;&longs;e, & in conuolutione of<lb/>fen&longs;are, & nece&longs;&longs;e e&longs;t præ<lb/>cipuè id contingere earum <lb/>extremitatibus.</s>

<s id="id.001953">COMMENTARIVS.</s>

<s id="id.001953">COMMENTARIVS. </s>

<s id="id.001954">Cvr circa.] <emph type="italics"/>Credibile e&longs;t duo lumina &longs;apientiæ, & virtutis, <lb/>Pub. Scipionem Africanum minorem, & Caium Lælium cum <lb/>propter actuo&longs;am vitam animi remißioni aliquando acquie&longs;centes, <lb/>& ruri feriantes ad Caietam portum Campaniæ, Lucrinumque la<lb/>cum conchas id e&longs;t duriores te&longs;tas <expan abbr="pi&longs;ci&utilde;">pi&longs;cium</expan>, vt purpuræ, muricis, o&longs;treo<lb/>rum, & vmbilicos id e&longs;t rotundos calculos in &longs;peciem no&longs;tri vmbi<emph.end type="italics"/><arrow.to.target n="marg29"/><lb/><emph type="italics"/>lici puerorum more colligerent (vt recen&longs;ent Cicero & Valerius <lb/>maximus) quæ&longs;i&longs;&longs;eidem quod hî Ari&longs;toteles. </s>

<s id="id.001954">Cvr circa.] <emph type="italics"/>Credibile e&longs;t duo lumina &longs;apientiæ, & virtutis, <lb/>Pub. Scipionem Africanum minorem, & Caium Lælium cum <lb/>propter actuo&longs;am vitam animi remißioni aliquando acquie&longs;centes, <lb/>& ruri feriantes ad Caietam portum Campaniæ, Lucrinumque la<lb/>cum conchas id e&longs;t duriores te&longs;tas <expan abbr="pi&longs;ci&utilde;">pi&longs;cium</expan>, vt purpuræ, muricis, o&longs;treo<lb/>rum, & vmbilicos id e&longs;t rotundos calculos in &longs;peciem no&longs;tri vmbi<emph.end type="italics"/><arrow.to.target n="marg29"/><lb/><emph type="italics"/>lici puerorum more colligerent (vt recen&longs;ent Cicero & Valerius <lb/>maximus) quæ&longs;i&longs;&longs;eidem quod hî Ari&longs;toteles. </s>

<s id="id.001956">Cur &longs;cilicet vmbilici <lb/>illi (crocas Ari&longs;toteles appellat) rotundi &longs;int, cum antea e&longs;&longs;ent lapi<lb/>des maiu&longs;culi minime <expan abbr="rot&utilde;di">rotundi</expan>, &longs;ed angulati, vt & partes concharum <lb/>o&longs;treorum inæquales & a&longs;peræ. </s>

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<s id="id.001974">At in <lb/>breuibus <expan abbr="extrem&utilde;">extremum</expan> fit vici<pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.164.jpg" pagenum="125"/><foreign lang="greek"><gap/></foreign><lb/>num hypomochlio quie&longs;<lb/>centi.</s>

<s id="id.001975">COMMENTARIVS.</s>

<s id="id.001975">COMMENTARIVS. </s>

<s id="id.001976">Cvr quantò.] <emph type="italics"/>In exercitu &longs;æpe milites dum feriantur roboris <lb/>experiundi, vel exercendi gratia longas ha&longs;tas humi iacentes <lb/>vna manu, aut vtraque in alterum extremorum iniecta & compre<lb/>hendente nituntur attollere, quou&longs;que perpendiculares fiant plano <lb/>horizontis: qua in &longs;ublatione videre licet ha&longs;tas illas longas vt cra&longs;<lb/>&longs;iores &longs;int, inflecti tamen magis medio &longs;ublationis tempore: quam <lb/>breues, licet tenuiores &longs;int. </s>

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<s id="id.002001">diuellit enim ip&longs;um <foreign lang="greek">b.</foreign></s>

<s id="id.002002">COMMENTARIVS.</s>

<s id="id.002002">COMMENTARIVS. </s>

<s id="id.002003">Cau&longs;a pote&longs;tatis cunei.] <emph type="italics"/>Cuneus e&longs;t in&longs;trumentum ex ma<lb/>teria firma in&longs;tar pyramidis à ba&longs;i lata in angu&longs;tum fa&longs;tigia<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.166.jpg" pagenum="127"/><figure id="id.035.01.166.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.166.1.jpg"/><lb/><emph type="italics"/>tum. </s>

<s id="id.002005">In <lb/>hac forma duo con&longs;ideranda &longs;unt, <lb/>alterum e&longs;t ex amplitudine ba&longs;is, <lb/>qua cuneus ad &longs;u&longs;cipiendam &longs;u&longs;ti<lb/>nendamque percußionem aptißi<lb/>mus e&longs;t: alterum e&longs;t ex vertice acu<lb/>to, qui ob id facile intrà corpora penetrans &longs;ibi viam facit. </s>

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<s id="id.002055">Sed hanc &longs;ic paulò am<lb/>plius & apertius repetemus. </s>

<s id="id.002056">Sit cuneus A B C cuius vertex B: <lb/>& &longs;it A B æqualis B C, <lb/>quod autem diuidendum<emph.end type="italics"/><lb/><figure id="id.035.01.169.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.169.1.jpg"/><lb/><emph type="italics"/>e&longs;t, &longs;it D E F G, &longs;itque <lb/>pars cunei H B K intra <lb/>D E F G, & H B &longs;it <lb/>æqualis ip&longs;i B K. percu<lb/>tiatur vt fieri &longs;olet cuneus <lb/>in A C. </s>

<s>percu<lb/>tiatur vt fieri &longs;olet cuneus <lb/>in A C. </s>

<s id="id.002057">Dum cuneus in <lb/>A C percutitur, A B fit <lb/>vectis, cuius hypomoch<lb/>lium e&longs;t H, & pondus in <lb/>B, eodemque modo C B <lb/>fit vectis, cuius hypomo<lb/>chlium e&longs;t K, & pondus &longs;imiliter in B. </s>

<s id="id.002058">Sed dum percutitur cuneus <lb/>maiori adhuc ip&longs;ius portione, intra ip&longs;um D E F G ingreditur, <lb/>quam prius e&longs;&longs;et: &longs;it autem portio hæc M B L, &longs;itque M B ip&longs;i <lb/>B L æqualis. </s>

<s id="id.002059">Et cum M B, B L &longs;int ip&longs;is H B, B K maiores: <lb/>erit M L maior H K. </s>

<s id="id.002059">Et cum M B, B L &longs;int ip&longs;is H B, B K maiores: <lb/>erit M L maior H K. </s>

<s id="id.002060">Dum igitur M L erit in &longs;itu H K, opor<lb/>tet vt fiat maior diui&longs;io, & D moueatur ver&longs;us O: G autem ver<lb/>&longs;us N, & quò maior pars cunei intra D E F G ingredietur, eò <lb/>maior fiet diui&longs;io: & D, G magis adhuc impellentur ver&longs;us O, <lb/>N. </s>

<s id="id.002061">Pars igitur K G eius quod diuiditur mouebitur à vecte A B, <lb/>cuius hypomochlium e&longs;t H, & pondus in B, ita vt punctum B <lb/>ip&longs;ius vectis A B impellat partem k G: & pars H D mouebi<lb/>tur à vecte C B, cuius hypomochlium e&longs;t k, ita vt B vecte C B <emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.170.jpg" pagenum="131"/><emph type="italics"/>partem H D impellat. </s>

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<s id="id.002065">Ratio e&longs;t, quia in&longs;trumenta mouent per contactum: vectis autem A <lb/>B tangit partem H D motam in H, non &longs;imiliter tangit in B. <lb/></s>

<s id="id.002066">Id ip&longs;um in&longs;uper comprobat ex cuneo inter duas moles &longs;eparatas in<lb/>terpo&longs;ito: &longs;ed quod pace tanti viri dixerim certum e&longs;t, quod ni&longs;i B <lb/>vertex cunei tangeret molem in B, & ip&longs;am impelleret atque diui<lb/>deret, partes H D, K G non vtrinque cederent in O & N. </s>

<s id="id.002067">Quod <lb/>igitur cedant motus is &longs;ecundarius e&longs;t, & priorem qui e&longs;t in B con<lb/>&longs;equens. </s>

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<s id="id.002074">Cochlea cum matrice.<lb/></s>

<s><emph type="italics"/>nexum: pondus <lb/>mouendum &longs;it <lb/>L M N O ex <lb/>parte M N im<lb/>mobile, vt in <lb/>his quæ <expan abbr="&longs;cind&umacr;-tur">&longs;cindun<lb/>tur</expan>, fieri &longs;olet: <lb/>cunei vero vertex A &longs;it intra rimam R S. </s>

<s id="id.002075">Itaque facile e&longs;t videre <lb/>quod dum K F circumuer&longs;us erit vbi K P, vertex A non erit <lb/>amplius intra R S: &longs;ed cunei pars alia vt T V: quæ cum maior <lb/>&longs;it, quam R S. </s>

<s id="id.002076">E&longs;t enim pars quæque cunei remotior à vertice, latior <lb/>propinquiore: ergo vt T V &longs;it intra K S, oportet vt R cedat, mo<lb/>ueaturque ver&longs;us X, & S ver&longs;us E vt faciunt ea quæ &longs;cindun<lb/>tur. </s>

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<s id="id.002087">Alterum <lb/>quia e&longs;t vectis, quo cochlea circumuertitur, qui etiam quò longior, eò <lb/>facilius: &longs;ed etiam tardius mouet.<emph.end type="italics"/></s>

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<s id="id.002092">Quare &longs;i quis in duobus <lb/>tignis inter &longs;e <expan abbr="i&utilde;ctisè">iunctisè</expan> <expan abbr="cõtra-rio">contra<lb/>rio</expan> duas trochleas <expan abbr="cõpon&etilde;s">componens</expan> <lb/>ip&longs;is in circulo circum du<lb/>xerit funiculum, qui lorum <lb/>quòd &longs;u&longs;pendatur ex altero <lb/>tignorum, & alterum inni<lb/>tatur, aut appo&longs;itum &longs;it ad <lb/>trochleas, atque initium <lb/>funiculi traxerit, vt parua <lb/>vi trahat, magna tamen <lb/>pondera adducet.</s><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.173.jpg" pagenum="134"/>

<s id="id.002093">COMMENTARIVS.</s>

<s id="id.002093">COMMENTARIVS. </s>

<s id="id.002094">De trochleis.] <emph type="italics"/>Trochlea e&longs;t in&longs;trumentum vno aut pluribus <lb/>orbiculis circa &longs;uos axiculos mobilibus & fune ductario con<lb/>&longs;tans ad trahendum, & attollendum onera aptum. </s>

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<s id="id.002102">Si igitur quid <lb/>rei natura, & v&longs;us o&longs;ten<lb/>dat, ponamus: illam parti<lb/>culam &longs;ic <expan abbr="cõmutabimus">commutabimus</expan>, <lb/>vt dicamus vnam è dua<lb/>bus trochleis habere <expan abbr="lor&utilde;">lorum</expan>, <lb/>quod dependeat ab altero <lb/>vel vtroque tignorum: al<lb/>teri vero infixum & <expan abbr="ap-po&longs;it&utilde;">ap<lb/>po&longs;itum</expan> e&longs;&longs;e pondus trahen<lb/>dum vel attollendum. </s>

<s id="id.002103">Vt <lb/>&longs;int duo tigna &longs;e&longs;e ex ad<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.174.jpg" pagenum="135"/><emph type="italics"/>uer&longs;o fulcientia C D & E F <emph.end type="italics"/><lb/><figure id="id.035.01.174.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.174.1.jpg"/><lb/><emph type="italics"/>(plura duobus vt tria, & qua<lb/>tuor, vt &longs;e validius fulciant, vt <lb/>plurimum &longs;tatuuntur) &longs;int & <lb/>duæ trochleæ A & B, qua<lb/>rum altera A ad vtrumque ti<lb/>gnum reuinciatur loro H A, <lb/>alteri vero B appo&longs;itum &longs;it pon<lb/>dus G, tracto loro ab ini<lb/>tio vbi I, pondus G cum tro<lb/>chlea B attolletur ver&longs;us A.<emph.end type="italics"/></s>

<s id="id.002104"><emph type="italics"/>Vel etiam &longs;it trochlea in<lb/>ferior in qua orbiculi duo cui <lb/>pondus A per vncum apponi<lb/>tur, &longs;uperior in qua duo item or<lb/>biculi. </s>

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<s id="id.002115">Itaque à <lb/>prima trahente <expan abbr="põdus">pondus</expan> qua<lb/>tuor librarum, ab vltima <lb/>trahi multo minus.</s>

<s id="id.002116">COMMENTARIVS.</s>

<s id="id.002116">COMMENTARIVS. </s>

<s id="id.002117">An quia idem.] <emph type="italics"/>Solutio e&longs;t propo&longs;iti problematis &longs;umpta è <lb/>vecte multiplicato. </s>

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<s id="id.002140">In X autem &longs;it <lb/>harpago ad apprehendendum pondus E attollendum vel deprimen<lb/>dum. </s>

<s id="id.002141">Si enim extremum L ab harpagone V liberetur, & ad A <lb/>traducatur, de&longs;cendet vno qua&longs;i nictu oculi pondus E, tantum <emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.177.jpg" pagenum="138"/><figure id="id.035.01.177.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.177.1.jpg"/><lb/><emph type="italics"/>&longs;patij, quanti &longs;unt funiculi N M, Q P, <lb/>R S, B T. </s>

<s id="id.002142">Tanti erunt autem, <lb/>quantos loci, ad quem de&longs;cendere, vel <lb/>è quo educere volumus, profunditas, <lb/>po&longs;tulat. </s>

<s id="id.002143">Si autem attollere oporteat, <lb/>extremum L cum erit in A, traduce<lb/>tur ad harpagonem V.<emph.end type="italics"/></s>

<s id="id.002143">Si autem attollere oporteat, <lb/>extremum L cum erit in A, traduce<lb/>tur ad harpagonem V. <emph.end type="italics"/></s>

<s id="id.002144"><emph type="italics"/>In hac machina igitur hæc duo in<lb/>&longs;unt, facilitas motionis ob multitudi<lb/>nem trochlearum, & celeritas motio<lb/>nis. </s>

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<s id="id.002158">Diuo Cæ&longs;ari Diui Iulij. </s>

<s id="id.002159">F. Augu&longs;to: Ti.Cæ&longs;ari Diui Augu&longs;ti. </s>

<s id="id.002159">F. Augu&longs;to: Ti.Cæ&longs;ari Diui Augu&longs;ti. </s>

<s id="id.002160">F. Augu&longs;to &longs;acrum.</s>

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<s id="id.002192">Ænea &longs;erpentis Mo&longs;es &longs;imulachra &longs;acerdos <lb/>Extulit, ægrotis vt medicina foret</s>

<s id="id.002193">Nunc alter Mo&longs;es obeli&longs;ci in vertice Sixtus <lb/>Erigit ægrotis ærea &longs;igna Crucis</s>

<s id="id.002193">Nunc alter Mo&longs;es obeli&longs;ci in vertice Sixtus <lb/>Erigit ægrotis ærea &longs;igna Crucis</s>

<s id="id.002194">Vos ô Romani &longs;u&longs;tollite ad æthera vultus, <lb/>A Cruce nam vobis ve&longs;tra petenda &longs;alus.</s>

<s id="id.002195"><emph type="italics"/>Gulielmus Blancus Albien&longs;i. I. C.<emph.end type="italics"/></s><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.182.jpg" pagenum="143"/><figure id="id.035.01.182.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.182.1.jpg"/>

<s id="id.002195"><emph type="italics"/>Gulielmus Blancus Albien&longs;i. I. C. <emph.end type="italics"/></s><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.182.jpg" pagenum="143"/><figure id="id.035.01.182.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.182.1.jpg"/>

<s id="id.002197">Sancti&longs;&longs;imæ Cruci &longs;acra<lb/>uit Sixtus V. Pont. Max. <lb/>è priore &longs;ede auul&longs;um & <lb/>Cæ&longs;aribus Aug. & Tib. <lb/>11.ablatum.</s>

<s id="id.002198"><emph type="italics"/>Faciata à leuante.<emph.end type="italics"/></s>

<s id="id.002199">Ecce Crux Domini <lb/>fugite partes aduer&longs;æ <lb/>vincit leo de Tribu <lb/>Iuda.</s>

<s id="id.002199">Ecce Crux Domini <lb/>fugite partes aduer&longs;æ <lb/>vincit leo de Tribu <lb/>Iuda. </s>

<s id="id.002200"><emph type="italics"/>Faciata à Tramontana.<emph.end type="italics"/></s>

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<s id="id.002219">Impo&longs;itum igitur non <lb/>mouetur, ni&longs;i motione gra<lb/>uitatis [propriæ]: commotum vero & ip&longs;a & motione <lb/>percutientis.</s>

<s id="id.002220">COMMENTARIVS.</s>

<s id="id.002220">COMMENTARIVS. </s>

<s id="id.002221">Cvr&longs;i quis.] <emph type="italics"/>Problema de &longs;ecuri, quæ &longs;ecat dum percutit, non <lb/>autem dum &longs;impliciter incumbit, duobus modis &longs;oluitur. </s>

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<s id="id.002232">quia <lb/>ex duobus vectibus con&longs;ti<lb/>tutus e&longs;t contrario modo <lb/>collocatis.</s>

<s id="id.002233">COMMENTARIVS.</s>

<s id="id.002233">COMMENTARIVS. </s>

<s id="id.002234">Præterea &longs;ecuris.] <emph type="italics"/>Altera e&longs;t problematis propo&longs;iti &longs;olutio <lb/>&longs;umpta è cunei forma, quæ in &longs;ecuri propter aciem acutam, & &longs;u<lb/>perioris partis latitudinem con&longs;picua e&longs;t. </s>

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<s id="id.002250"><margin.target id="marg34"/>Lib. 17. de <lb/>&longs;ubt.</s>

<s id="id.002251"><margin.target id="marg35"/>Exerc. 331.</s></chap><chap>

<s id="id.002251"><margin.target id="marg35"/>Exerc. 331. </s></chap><chap>

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<s id="id.002263">Vt au<lb/>tem vna libra multæ libræ <lb/>&longs;int in tali libra, multæ an&longs;&ecedil; <lb/>adiectæ &longs;unt, è quibus vna<lb/>quæque ad eas partes, vbi <lb/>e&longs;t æquipondium, dimi<lb/>dium e&longs;t &longs;tateræ.</s>

<s id="id.002264">COMMENTARIVS.</s>

<s id="id.002264">COMMENTARIVS. </s>

<s id="id.002265">De &longs;tateris.] <foreign lang="greek">fa/lagc</foreign> <emph type="italics"/>apud Græcos multa &longs;ignificat vt in<lb/>ternodium in digitis, ordinem & agmem militare longius <lb/>quam latius, ligna teretia, quibus naues in mare deuoluuntur: &longs;ed hîc <emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.186.jpg" pagenum="147"/><emph type="italics"/>&longs;ignificat libræ genus, quod trutina, ab alijs &longs;tatera appellatur. </s>

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<s id="id.002306">Et talis exi&longs;tens multæ &longs;unt <lb/>libræ, & quidem tot, quot <lb/>&longs;unt an&longs;æ.</s>

<s id="id.002307">COMMENTARIVS.</s>

<s id="id.002307">COMMENTARIVS. </s>

<s id="id.002308">Et æquipondium.] <emph type="italics"/>Hic textus interiectus quidem e&longs;&longs;e vide<lb/>tur, non ita tamen inutilis, vt totus reijciendus &longs;it, quod aliquis <lb/>interpres fecit. </s>

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<s id="id.002318">Hîc autem <lb/>&longs;acoma facit & ponderat <lb/>ad æquipondium pondus <lb/>&longs;tateræ.</s>

<s id="id.002319">COMMENTARIVS.</s>

<s id="id.002319">COMMENTARIVS. </s>

<s id="id.002320">Omnino quidem.] <emph type="italics"/>Repetitio e&longs;t a&longs;&longs;umptionum præceden<lb/>tium &longs;yllogi&longs;morum &longs;cilicet,<emph.end type="italics"/></s>

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<s id="id.002331">Vide<lb/>tur tamen Ari&longs;toteles & appo&longs;itè volui&longs;&longs;e &longs;ignificare æquipondium <lb/>e&longs;&longs;e in &longs;tatera, vim mouentem, & vnum actu cum &longs;it, quia tamen <lb/>per varias notas di&longs;currere pote&longs;t in &longs;tatera, præ&longs;tare ad diuer&longs;a pon<lb/>dera pendenda, quod in altera libræ lance diuer&longs;a &longs;acomata. </s>

<s id="id.002332">E&longs;t enim<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.190.jpg" pagenum="151"/><foreign lang="greek">sh/kwma,</foreign> <emph type="italics"/>vt annotauit Budæus in Pandect. quod apponitur in libra <lb/>ad æquilibrium faciendum. </s>

<s id="id.002332">E&longs;t enim<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.190.jpg" pagenum="151"/><foreign lang="greek">sh/kwma,</foreign> <emph type="italics"/>vt annotauit Budæus in Pandect. quod apponitur in libra <lb/>ad æquilibrium faciendum. </s>

<s id="id.002333">Vnde & apud Vitruuium legimus re<emph.end type="italics"/><lb/><arrow.to.target n="marg36"/><lb/><emph type="italics"/>demptorem ad tempus opus manufactum &longs;ubtiliter regi approba<lb/>ui&longs;&longs;e, & ad &longs;acoma pondus coronæ vi&longs;um e&longs;&longs;e præ&longs;titi&longs;&longs;e. </s>

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<s id="id.002342"><emph type="italics"/>Dico grauitatem ponderis D ad grauitatem ponderis G ita e&longs;&longs;e <lb/>vt C F ad C B.<emph.end type="italics"/></s><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.191.jpg" pagenum="152"/>

<s id="id.002343">Demon&longs;t.</s>

<s id="id.002343">Demon&longs;t. </s>

<s id="id.002344"><emph type="italics"/>Quia grauitas ponderis D e&longs;t æqualis grauitati ponderis E ex F <lb/>dependentis, & grauitas ponderis G e&longs;t æqualis grauitati ponderis <lb/>E ex B, erit grauitas ponderis D ad grauitatem E ex F: vt gra<lb/>uitas ponderis G ad grauitatem ponderis E ex B, & permutatim <lb/>prop. 16. lib. 5. </s>

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<s id="id.002358">Vtroque igitur extremo <foreign lang="greek">b <lb/>& z</foreign> &longs;imul capiens dimouet: <lb/>quando vero emotus fuerit, manu facilius: quam in&longs;tru<lb/>mento eximetur.</s>

<s id="id.002359">COMMENTARIVS.</s>

<s id="id.002359">COMMENTARIVS. </s>

<s id="id.002360">De dentiduco.] <foreign lang="greek">o)donta/gran h)\ o)donta/gwgon</foreign> <emph type="italics"/>vertit Cælius <lb/>Aurelianus cap. 4. lib. 2.<emph.end type="italics"/> <foreign lang="greek">xroniw=n</foreign> <emph type="italics"/>paßionum dentiducum: Cel<lb/>&longs;us forficem, & generaliter forcipem. </s>

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<s id="id.002390">Præterea duro & graui <expan abbr="cõ-primens">con<lb/>primens</expan> velocius fregerit: <lb/>quam ligneo & leui in&longs;tru<lb/>mento. </s>

<s id="id.002391">An quia &longs;ic vtrin<lb/>que à duobus vectibus nux <lb/><expan abbr="cõprimitur">comprimitur</expan>, vecte vero fa<lb/>cile pondera diuelluntur, <lb/>in&longs;trumentum enim duo<lb/>bus con&longs;tat vectibus, Idem <lb/>hypomochlium <expan abbr="hab&etilde;tibus">habentibus</expan> <lb/>contactum vbi e&longs;t A. </s>

<s id="id.002392">Vt <lb/>igitur &longs;i lineæ E D, F C <lb/>diductæ e&longs;&longs;ent extremis C, <lb/>D motis, facile ab exigua <lb/>vi coadducerentur. </s>

<s id="id.002393">Quod <lb/>igitur ex ictu pondus feci&longs;<lb/>&longs;et, hoc valentius E D & <lb/>F C vectes <expan abbr="c&utilde;">cum</expan> &longs;int, efficiunt. <lb/></s>

<s id="id.002394">Elatione enim in <expan abbr="aduers&utilde;">aduersum</expan> <lb/>tollunt, & comprimentes <lb/>frangunt, quod e&longs;t vbi K. <lb/></s>

<s id="id.002394">Elatione enim in <expan abbr="aduers&utilde;">aduersum</expan> <lb/>tollunt, & comprimentes <lb/>frangunt, quod e&longs;t vbi K. <lb/></s>

<s id="id.002395">Ob id quantò ip&longs;i K fuerit <lb/>propior commi&longs;&longs;ura A tan<lb/>tò citius conterit. </s>

<s id="id.002396">Quantò <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.195.jpg" pagenum="156"/><foreign lang="greek"><gap/></foreign><lb/>enim plus di&longs;titerit vectis <lb/>ab hypomochlio, tantò fa<lb/>cilius ab eadem vi mouet. <lb/></s>

<s id="id.002397">E&longs;t igitur A <expan abbr="hypomochli&utilde;">hypomochlium</expan>, <lb/>& E A D vectis, vt & F A <lb/>C. </s>

<s id="id.002397">E&longs;t igitur A <expan abbr="hypomochli&utilde;">hypomochlium</expan>, <lb/>& E A D vectis, vt & F A <lb/>C. </s>

<s id="id.002398">Quantò igitur ip&longs;um K <lb/>propius fuerit angulo A, <lb/>tantò propius fit commi&longs;&longs;u<lb/>ræ A. </s>

<s id="id.002398">Quantò igitur ip&longs;um K <lb/>propius fuerit angulo A, <lb/>tantò propius fit commi&longs;&longs;u<lb/>ræ A. </s>

<s id="id.002399">Hæc verò e&longs;t hypo<lb/>mochlium. </s>

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<s id="id.002401">Et quia <lb/>eleuatio ex aduer&longs;o e&longs;t, ma<lb/>gis conteri nece&longs;&longs;e e&longs;t, ma<lb/>gis verò contritum celerius <lb/>frangitur.</s>

<s id="id.002402">COMMENTARIVS.</s>

<s id="id.002402">COMMENTARIVS. </s>

<s id="id.002403">De in&longs;trumentis.] <emph type="italics"/>In&longs;trumentum ad frangendum nuces <lb/>pote&longs;t appellari nucifrangibulum, & hoc non differt à forcipe <lb/>ni&longs;i quia leuiter in extremis excauatur ad excipiendum nucem fran<lb/>gendam commodius, Huiu&longs;mo<emph.end type="italics"/><lb/><figure id="id.035.01.195.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.195.1.jpg"/><lb/><emph type="italics"/>di e&longs;t F A C E A B.<emph.end type="italics"/></s>

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<s id="id.002417">Diductis enim B C extremis <lb/>vectium E A B & F A C à viribus in E & F. <lb/>alteris vectium extremis exi&longs;tentibus, &longs;i ip&longs;a compriman<lb/>tur etiam B & C comprimentur. </s>

<s id="id.002418">Quare & nux D in<lb/>terpo&longs;ita, & valide compre&longs;&longs;a frangitur, tantò celerius: <lb/>quantò extrema B & C minus di&longs;tabunt ab hypomoch<lb/>lio A. </s>

<s id="id.002418">Quare & nux D in<lb/>terpo&longs;ita, & valide compre&longs;&longs;a frangitur, tantò celerius: <lb/>quantò extrema B & C minus di&longs;tabunt ab hypomoch<lb/>lio A. </s>

<s id="id.002419">Sic enim aliæ partes vectium ab ip&longs;o di&longs;tantes <lb/>maiorem rationem habebunt. </s>

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<s id="id.002438">Et &longs;imul <lb/>atque latus pertran&longs;it latus <lb/>etiam ip&longs;um <foreign lang="greek">b,</foreign> ip&longs;um <foreign lang="greek">b g</foreign><lb/>diametrum. </s>

<s id="id.002439">Simile igitur <lb/>ip&longs;um <foreign lang="greek">a</foreign> ip&longs;am <foreign lang="greek">a d</foreign> multò <lb/><expan abbr="maior&etilde;">maiorem</expan> ip&longs;a <foreign lang="greek">b g</foreign> pertran&longs;it, <lb/>& latus <expan abbr="mot&utilde;">motum</expan> eadem celeri<lb/>tate <expan abbr="minor&etilde;">minorem</expan> <expan abbr="lineã">lineam</expan> [tran&longs;it.] <lb/>Et latus <foreign lang="greek">b d</foreign> vna latione <lb/>motum pertran&longs;ijt lineam <lb/>maiorem: quam <foreign lang="greek">b g.</foreign> <expan abbr="quãtò">quantò</expan> <lb/>enim acutior e&longs;t Rhombus, <lb/>diameter <expan abbr="quid&etilde;">quidem</expan> <foreign lang="greek">b g</foreign> fit mi<lb/>nor, <foreign lang="greek">a d</foreign> vero maior, <expan abbr="t&utilde;">tum</expan> & la<lb/>tus <foreign lang="greek">a b</foreign> maius quam <foreign lang="greek">b g.</foreign></s>

<s id="id.002439">Simile igitur <lb/>ip&longs;um <foreign lang="greek">a</foreign> ip&longs;am <foreign lang="greek">a d</foreign> multò <lb/><expan abbr="maior&etilde;">maiorem</expan> ip&longs;a <foreign lang="greek">b g</foreign> pertran&longs;it, <lb/>& latus <expan abbr="mot&utilde;">motum</expan> eadem celeri<lb/>tate <expan abbr="minor&etilde;">minorem</expan> <expan abbr="lineã">lineam</expan> [tran&longs;it.] <lb/>Et latus <foreign lang="greek">b d</foreign> vna latione <lb/>motum pertran&longs;ijt lineam <lb/>maiorem: quam <foreign lang="greek">b g. </foreign><expan abbr="quãtò">quantò</expan> <lb/>enim acutior e&longs;t Rhombus, <lb/>diameter <expan abbr="quid&etilde;">quidem</expan> <foreign lang="greek">b g</foreign> fit mi<lb/>nor, <foreign lang="greek">a d</foreign> vero maior, <expan abbr="t&utilde;">tum</expan> & la<lb/>tus <foreign lang="greek">a b</foreign> maius quam <foreign lang="greek">b g. </foreign></s>

<s id="id.002440"><margin.target id="marg38"/>Quidam le<lb/>gunt <foreign lang="greek">lo/gw</foreign><lb/>pro <foreign lang="greek">ta/xei.</foreign></s>

<s id="id.002441">COMMENTARIVS.</s>

<s id="id.002441">COMMENTARIVS. </s>

<s id="id.002442">Cvr amborum.] <emph type="italics"/>In hoc capite duo continentur problemata, <lb/><expan abbr="eor&utilde;que">eorumque</expan> &longs;olutiones. </s>

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<s id="id.002446">Vtrumque problema vt intelligatur &longs;ciendum e&longs;t e def. <lb/>32. lib. 1. Eucl. </s>

<s id="id.002448">Rhombum e&longs;&longs;e quadrilaterum æquilaterum, & mini<lb/>mè rectangulum: Et tamen omnes eius angulos æquales e&longs;&longs;e quatuor <lb/>rectis per coroll. prop. 32. li. 1. Eucl. </s>

<s id="id.002451"><expan abbr="Cumq;">Cumque</expan> oppo&longs;iti in <expan abbr="parallelogrãmo">parallelogrammo</expan> <lb/>&longs;int æquales prop. 34. lib. <expan abbr="eiu&longs;d&etilde;">eiu&longs;dem</expan> duo &longs;unt acuti, reliqui obtu&longs;i, vt &longs;it <lb/><expan abbr="Rhõbus">Rhombus</expan><emph.end type="italics"/> <foreign lang="greek">a b d g,</foreign> <emph type="italics"/>cuius anguli oppo&longs;iti<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>&<emph.end type="italics"/> <foreign lang="greek">d</foreign> <emph type="italics"/>&longs;int acuti:<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>vero<emph.end type="italics"/> <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.199.jpg" pagenum="160"/><emph type="italics"/>&<emph.end type="italics"/> <foreign lang="greek">g</foreign> <emph type="italics"/>obtu&longs;i. </s>

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<s id="id.002454">Ad <lb/>huius autem <expan abbr="mot&utilde;">motum</expan> moueri etiam<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>ver<lb/>&longs;us<emph.end type="italics"/> <foreign lang="greek">g,</foreign> <emph type="italics"/>&<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>ver&longs;us<emph.end type="italics"/> <foreign lang="greek">d.</foreign> <emph type="italics"/>Sicque<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>&<emph.end type="italics"/> <foreign lang="greek">b</foreign><lb/><emph type="italics"/>mouebuntur duobus motibus, vno per &longs;e: <lb/>altero per accidens. </s>

<s id="id.002455">Et po&longs;ito quod mo<lb/>ueantur in Rhombo. </s>

<s id="id.002455">Et po&longs;ito quod mo<lb/>ueantur in Rhombo. </s>

<s id="id.002456">Id e&longs;t quod motus <lb/>illi &longs;int in ratione laterum quibus Rhombus continetur. </s>

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<s>Hoc erit &longs;imile toti<emph.end type="italics"/> <foreign lang="greek">a b d g.</foreign><lb/><emph type="italics"/>prop. 24. lib. 6. </s>

<s>Ergo per conu <expan abbr="eiu&longs;d&etilde;">eiu&longs;dem</expan> prop. &longs;unt circa <expan abbr="eand&etilde;">eandem</expan> <expan abbr="diametr&utilde;">diametrum</expan><emph.end type="italics"/><lb/><foreign lang="greek">a q d,</foreign> <emph type="italics"/>& &longs;ic<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>duobus motibus motum prædictis delineauit<emph.end type="italics"/> <foreign lang="greek">a q</foreign><lb/><emph type="italics"/>cum<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>peruenit ad<emph.end type="italics"/> <foreign lang="greek">z h.</foreign> <emph type="italics"/>proinde &<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>etiam delineauerit<emph.end type="italics"/> <foreign lang="greek">a d</foreign><lb/><emph type="italics"/>cum peruenerit<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">g d.</foreign> <emph type="italics"/></s>

<s><emph type="italics"/>proinde &<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>etiam delineauerit<emph.end type="italics"/> <foreign lang="greek">a d</foreign><lb/><emph type="italics"/>cum peruenerit<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">g d. </foreign><emph type="italics"/></s>

<s>Simili ratiocinatione conficitur<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>eo<lb/>dem tempore peragra&longs;&longs;e diametrum<emph.end type="italics"/> <foreign lang="greek">b g.</foreign> <emph type="italics"/></s>

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<s id="id.002467">Nece&longs;&longs;e igitur.] <emph type="italics"/>Nam parallelogramma quæ toti & inter &longs;e<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.200.jpg" pagenum="161"/><emph type="italics"/>&longs;unt &longs;imilia, &longs;unt circa eandem diametrum. </s>

<s id="id.002469">Æqualis enim e&longs;t.] <emph type="italics"/>Quia in ratione æqualitatis motum e&longs;t<emph.end type="italics"/> <foreign lang="greek">b</foreign><lb/><emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">e</foreign> <emph type="italics"/>&<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">h.</foreign></s>

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<s id="id.002472">In Rhombo enim cuius, qui acutus e&longs;t angulus, maior <lb/>e&longs;t dimidio obtu&longs;i, vt in E<emph.end type="italics"/><lb/><figure id="id.035.01.200.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.200.1.jpg"/><lb/><emph type="italics"/>F G H: quia F H an<lb/>gulum E maiorem &longs;ubten<lb/>dit: quam E H, erit F H <lb/>maior E H prop. 18. lib. 1. <lb/></s>

<s>Sed verum e&longs;t in certo ca<lb/>&longs;u, eo nimirum (licet hîc <lb/>non &longs;it expre&longs;&longs;us) in quo <lb/>Rhombi acutus e&longs;&longs;et mi<lb/>nor: quam dimidius obtu<lb/>&longs;i, vt angulus A Rhombi <lb/>A B C D &longs;it minor: quam dimidius obtu&longs;i B, id e&longs;t quam A B C. <lb/></s>

<s id="id.002473">Dico latus A C maius e&longs;&longs;e diametro B C per eandem prop. 18. <lb/>&longs;ubtendit enim trianguli A B C maiorem angulum. </s>

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<s id="id.002492">Æquum e&longs;t igitur, vt lineam maiorem tran<lb/>&longs;eat.</s><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.202.jpg" pagenum="163"/>

<s id="id.002493">COMMENTARIVS.</s>

<s id="id.002493">COMMENTARIVS. </s>

<s id="id.002494">Ab&longs;urdum enim.] <emph type="italics"/>Repetitio e&longs;t eius, quod problematis &longs;ecun<lb/>di antea iam auxit difficultatem.<emph.end type="italics"/></s>

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<s>Magnus au<lb/>tem connexus e&longs;to. </s>

<s id="id.002522">Quum <lb/>igitur <foreign lang="greek">a b</foreign> ad rectos fiet li<lb/>neæ <foreign lang="greek">h k,</foreign> &longs;imul etiam <foreign lang="greek">a g</foreign><lb/>ad rectos fiet lineæ <foreign lang="greek">z l.</foreign></s>

<s id="id.002523">Quare per æqualem erit <lb/>tran&longs;latio, nempè <foreign lang="greek">h k</foreign> in <lb/>qua e&longs;t <foreign lang="greek">z g.</foreign> Quod &longs;i quarta <lb/>pars per &ecedil;qualem voluitur, <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.205.jpg" pagenum="166"/><gap/><lb/>quod totus circulus æqua<lb/>lem toti circulo reuolua<lb/>tur, manife&longs;tum e&longs;t. </s>

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<s id="id.002525">Si<lb/>militer &longs;i maiorem moue<lb/>ro, cui &longs;it annexus minor <lb/><expan abbr="eod&etilde;">eodem</expan> centro exi&longs;tente, vna <lb/>cum <foreign lang="greek">a g</foreign> etiam <foreign lang="greek">a b</foreign> perpen<lb/>dicularis erit. </s>

<s id="id.002526">Illa quidem <lb/>ad <foreign lang="greek">z i</foreign> hæc verò ad <foreign lang="greek">h <expan abbr="q.">que</expan></foreign> Ita<lb/>que quando per æqualem <lb/>ip&longs;i <foreign lang="greek">h q</foreign> vel <foreign lang="greek">z i</foreign> rur&longs;um erit <lb/>tran&longs;latio etiam <foreign lang="greek">a g</foreign> per<lb/>pendicularis erit ad <foreign lang="greek">z i,</foreign> & <lb/><foreign lang="greek">a b</foreign> ad <foreign lang="greek">h q,</foreign> vt ab initio <lb/>erunt in <foreign lang="greek">q, i</foreign>: atque id nul<lb/>la intercedente mora ma<lb/>ioris ad minorem, qua&longs;i ad <lb/>aliquod tempus in eodem <lb/>ip&longs;o puncto moueret. </s>

<s id="id.002526">Illa quidem <lb/>ad <foreign lang="greek">z i</foreign> hæc verò ad <foreign lang="greek">h q</foreign>. </s>

<s>Ita<lb/>que quando per æqualem <lb/>ip&longs;i <foreign lang="greek">h q</foreign> vel <foreign lang="greek">z i</foreign> rur&longs;um erit <lb/>tran&longs;latio etiam <foreign lang="greek">a g</foreign> per<lb/>pendicularis erit ad <foreign lang="greek">z i,</foreign> & <lb/><foreign lang="greek">a b</foreign> ad <foreign lang="greek">h q,</foreign> vt ab initio <lb/>erunt in <foreign lang="greek">q, i</foreign>: atque id nul<lb/>la intercedente mora ma<lb/>ioris ad minorem, qua&longs;i ad <lb/>aliquod tempus in eodem <lb/>ip&longs;o puncto moueret. </s>

<s id="id.002527">vter<lb/>que enim vtroque modo <lb/>continuè mouetur. </s>

<s id="id.002528">Neque <lb/>minore vllum punctum <lb/>tran&longs;iliente, & maiorem <lb/>minori æqualem tran&longs;ire, & minorem maiori ab&longs;urdum.</s>

<s id="id.002529">COMMENTARIVS.</s>

<s id="id.002529">COMMENTARIVS. </s>

<s id="id.002530">Dvbium e&longs;t.] <emph type="italics"/>Problema quod hoc capite proponitur, omnium <lb/>quæ ante propo&longs;ita &longs;unt, & po&longs;tea proponentur fortaßè e&longs;t &longs;ub<lb/>tilißimum. </s>

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<s id="id.002553">Cæterum princi<lb/>pium &longs;umatur ex vtriu&longs;que <lb/>cau&longs;a, quod eadem vis, & <lb/>æqualis vnam quidem <expan abbr="ma-gnitudin&utilde;">ma<lb/>gnitudinum</expan> tardius: alteram <lb/>celerius moueat. </s>

<s id="id.002554">Si quid <lb/>enim fuerit non à &longs;eip&longs;o <lb/>moueri <expan abbr="nat&utilde;">natum</expan>, & <expan abbr="ips&utilde;">ipsum</expan> aliud <lb/>quod moueri <expan abbr="nat&utilde;">natum</expan> &longs;it mo<lb/>uerit, tardius mouebitur: <lb/><expan abbr="quã">quam</expan> &longs;i <expan abbr="ips&utilde;">ipsum</expan> <expan abbr="p &longs;e">ip&longs;e</expan> moueretur. </s><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.208.jpg" pagenum="169"/>

<s id="id.002554">Si quid <lb/>enim fuerit non à &longs;eip&longs;o <lb/>moueri <expan abbr="nat&utilde;">natum</expan>, & <expan abbr="ips&utilde;">ipsum</expan> aliud <lb/>quod moueri <expan abbr="nat&utilde;">natum</expan> &longs;it mo<lb/>uerit, tardius mouebitur: <lb/><expan abbr="quã">quam</expan> &longs;i <expan abbr="ips&utilde;">ipsum</expan> per &longs;e moueretur. </s><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.208.jpg" pagenum="169"/>

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<s id="id.002555">Et vt plus moueatur: quam <lb/>quod mouet, fieri non po<lb/>te&longs;t. </s>

<s id="id.002556">Non enim &longs;uo ip&longs;ius <lb/>mouetur motu: &longs;ed <expan abbr="mou&etilde;-">mouen<lb/></expan><arrow.to.target n="marg39"/><lb/>tis. [Sit igitur circulus maior <lb/><expan abbr="quid&etilde;">quidem</expan> vbi <foreign lang="greek">g,</foreign> at minor vbi <lb/>b.] </s>

<s id="id.002556">Non enim &longs;uo ip&longs;ius <lb/>mouetur motu: &longs;ed <expan abbr="mou&etilde;-">mouen<lb/></expan><arrow.to.target n="marg39"/><lb/>tis. </s>

<s>[Sit igitur circulus maior <lb/><expan abbr="quid&etilde;">quidem</expan> vbi <foreign lang="greek">g,</foreign> at minor vbi <lb/>b.] </s>

<s>Si impellat minor <expan abbr="maio-r&etilde;">maio<lb/>rem</expan> ip&longs;o &longs;e minime <expan abbr="volu&etilde;te">voluente</expan>, <lb/>manife&longs;tum quod tantam <lb/><expan abbr="rectã">rectam</expan> maior tran&longs;it, ad <expan abbr="quã-tam">quan<lb/>tam</expan> à minore impul&longs;us e&longs;t: <lb/>ad tantam verò impul&longs;us <lb/>e&longs;t, ad quantam minor &longs;e <lb/>mouit. </s>

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<s id="id.002566"><margin.target id="marg39"/>Hæc inter<lb/>po&longs;ita <expan abbr="vid&etilde;-tur">viden<lb/>tur</expan>.</s>

<s id="id.002567">COMMENTARIVS.</s>

<s id="id.002567">COMMENTARIVS. </s>

<s id="id.002568">Præterea vnica.] <emph type="italics"/>Cum &longs;it o&longs;ten&longs;a problematis veritas rur&longs;us <lb/>o&longs;tendit aliquid admirabile contineri. </s>

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<s id="id.002603">Non igitur idem mouet &longs;impliciter: &longs;ed quodammodo.</s>

<s id="id.002604">COMMENTARIVS.</s>

<s id="id.002604">COMMENTARIVS. </s>

<s id="id.002605">Qvod etiam dubit.] <emph type="italics"/>Antea de circulis ad vnum centrum <lb/>connexis <expan abbr="demõ&longs;tratum">demon&longs;tratum</expan> e&longs;t: perinde etiam in inæqualibus ad di<lb/>uer&longs;a puncta connexis &longs;e habere o&longs;tenditur, ni&longs;i <expan abbr="mend&utilde;">mendum</expan> &longs;ub&longs;it aliquod <lb/>in contextu è quo particulam<emph.end type="italics"/> <foreign lang="greek">ou)k</foreign> <emph type="italics"/>expunximus. </s>

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<s id="id.002619">Quæritur ergo quod e&longs;t &longs;uperiori problemate diffici<lb/>lius, vt fieri poßit rectarum æqualium peragratio à circulis inæqua<lb/>libus. </s>

<s id="id.002620">Sit igitur. vt rotæ axis<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>tran&longs;eat in F. </s>

<s id="id.002620">Sit igitur vt rotæ axis<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>tran&longs;eat in F. </s>

<s id="id.002622">Et quia<emph.end type="italics"/> <foreign lang="greek">a h</foreign> <emph type="italics"/>& F G<emph.end type="italics"/><lb/><figure id="id.035.01.213.2.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.213.2.jpg"/><lb/><emph type="italics"/>æquales &longs;unt. </s>

<s id="id.002623">Radij enim &longs;unt eiu&longs;dem circuli minoris &<emph.end type="italics"/> <foreign lang="greek">h</foreign> <emph type="italics"/>G e&longs;t <lb/>æquidi&longs;tans<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>F. </s>

<s id="id.002624">Erit per demon&longs;trata punctum G in linea F H. <lb/></s>

<s id="id.002624">Erit per demon&longs;trata punctum G in linea F H. <lb/></s>

<s id="id.002625">Et ponatur quod punctum fuerit M in maiori circulo, quod tran&longs;la<lb/>tum & retrò reuolutum peruenerit ad H, atque<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>M &longs;ecet circulum <lb/>minorem<emph.end type="italics"/> <foreign lang="greek">h</foreign> <emph type="italics"/>F<emph.end type="italics"/> <foreign lang="greek">e,</foreign> <emph type="italics"/>vt in puncto I. </s>

<s id="id.002626">Dico quod I e&longs;t punctum G. </s>

<s id="id.002626">Dico quod I e&longs;t punctum G. </s>

<s id="id.002627">Nam <lb/>quia M e&longs;t H, & in linea F H: præterea I e&longs;t in linea<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>M, <lb/>erit etiam in linea F H. </s>

<s id="id.002628">E&longs;t etiam in circulo<emph.end type="italics"/> <foreign lang="greek">h</foreign> <emph type="italics"/>F<emph.end type="italics"/> <foreign lang="greek">e.</foreign> <emph type="italics"/>Ergo in puncto <lb/>communi vtrique. </s>

<s id="id.002629">Nullum autem e&longs;t præter G. </s>

<s id="id.002629">Nullum autem e&longs;t præter G. </s>

<s id="id.002630">Igitur I peruenit<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.214.jpg" pagenum="175"/><emph type="italics"/>in G. </s>

<s id="id.002630">Igitur I peruenit<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.214.jpg" pagenum="175"/><emph type="italics"/>in G. </s>

<s id="id.002631">Sicque M retroceßit per angulum M G H. </s>

<s id="id.002631">Sicque M retroceßit per angulum M G H. </s>

<s id="id.002632">Contrà I an<lb/>teceßit per angulum I G F, qui &longs;unt anguli æquales prop. 15. lib. 1. <lb/></s>

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<s id="id.002641">Sic enim lateribus dupli <lb/>efficiuntur, vt longitudine <lb/>quatuor cubitorum, latitu<lb/>dine verò duorum &longs;int.</s>

<s id="id.002642">COMMENTARIVS.</s>

<s id="id.002642">COMMENTARIVS. </s>

<s id="id.002643">Cvr lectos.] <emph type="italics"/>In hoc capite quæruntur duo, quibus apertè &longs;atis<lb/>facit philo&longs;ophus, quod ad primas quæ&longs;tionum rationes attinet. <lb/></s>

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<s id="id.002666">Præterea <expan abbr="etiã">etiam</expan> funium <expan abbr="quã-titas">quan<lb/>titas</expan>: &longs;ic minor erit.</s>

<s id="id.002667">COMMENTARIVS.</s>

<s id="id.002667">COMMENTARIVS. </s>

<s id="id.002668">Non extendunt.] <emph type="italics"/>Po&longs;terior quæ&longs;tio e&longs;t, cur lectus cuius late<lb/>ra &longs;unt in ratione dupla pertendatur loris non &longs;ecundum dia<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.216.jpg" pagenum="177"/><emph type="italics"/>metrum: &longs;ed in obliquum proten&longs;is, ad quam tripliciter re&longs;pondet. <lb/></s>

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<s id="id.002689">Duo <lb/>etenim anguli habent fu<lb/>nis principia. </s>

<s id="id.002690">Sunt verò fu<lb/>nes iuxta curuaturas æqua<lb/>les, nempe <foreign lang="greek">a b</foreign> & <foreign lang="greek">b g</foreign> ip&longs;i <lb/><foreign lang="greek">g d</foreign> & <foreign lang="greek">d <expan abbr="q.">que</expan></foreign> Et alij &longs;unt eiu&longs;<lb/>modi, quod eadem &longs;it de<lb/>mon&longs;tratio. </s>

<s>Et alij &longs;unt eiu&longs;<lb/>modi, quod eadem &longs;it de<lb/>mon&longs;tratio. </s>

<s id="id.002691">Etenim <foreign lang="greek">a b</foreign> æ<lb/>qualis e&longs;t ip&longs;i <foreign lang="greek">e q.</foreign> </s>

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<s>Itaque funis <lb/>tanto maior: quanto ambo <lb/>latera maiora &longs;unt diame<lb/>tro.</s>

<s id="id.002701">COMMENTARIVS.</s>

<s id="id.002701">COMMENTARIVS. </s>

<s id="id.002702">Sit lectus <foreign lang="greek">a z h i.</foreign>] <emph type="italics"/>In tertia ratione &longs;ecundæ quæ&longs;tionis expli<lb/>canda reliquus Ari&longs;totelis contextus totus e&longs;t: &longs;ed adeo mendo&longs;us <lb/>& in verbis, & in diagrammatis, & in diagrammatum characte<lb/>ribus, vt &longs;i Iuppiter cum Æ&longs;culapio mederi, & mendas eluere ve<lb/>lit, non poßit tamen: ideò &longs;atius e&longs;t cum &longs;it nota philo&longs;ophi &longs;enten<lb/>tia, totum adimere, & alium &longs;upplere. </s>

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<s id="id.002710">Sit igitur prima A B C D, cuius la<emph.end type="italics"/><lb/><figure id="id.035.01.219.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.219.1.jpg"/><lb/><emph type="italics"/>tus A B duplum &longs;it lateris A C, & quidem illud 4. pe<lb/>dum, hoc duorum. </s>

<s id="id.002711">In hac lora &longs;ecundum diametrum &longs;int quidem <lb/>&longs;ecundum longitudinem tria K N. </s>

<s id="id.002711">In hac lora &longs;ecundum diametrum &longs;int quidem <lb/>&longs;ecundum longitudinem tria K N. </s>

<s id="id.002712">L O, M P, & &longs;ic inter &longs;e <emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.220.jpg" pagenum="181"/><emph type="italics"/>& lateri A B æqualia prop. 34. lib. 1. </s>

<s>Sint & totidem G Q, <lb/>E F, H R &longs;ecundum latitudinem exten&longs;a, inter&longs;e quoque, & la<lb/>teri A C æqualia per eandem.<emph.end type="italics"/></s>

<s id="id.002713"><emph type="italics"/>Sit &longs;ecunda forma<emph.end type="italics"/> <foreign lang="greek">a b g d</foreign> <emph type="italics"/>in eadem ratione laterum, & ea<lb/>dem magnitudine &longs;eruata, & linearum &longs;ed obliquarum æquali nu<lb/>mero, quæ &longs;int<emph.end type="italics"/> <foreign lang="greek">a c, h k, e d</foreign> <emph type="italics"/>tum.<emph.end type="italics"/> <foreign lang="greek">b c, q i, e g,</foreign> <emph type="italics"/>quæ quia pa<emph.end type="italics"/><lb/><figure id="id.035.01.220.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.220.1.jpg"/><lb/><emph type="italics"/>rallelæ &longs;unt, & aduer&longs;æ in &longs;uis parallelogrammis, omnes inter &longs;e <lb/>æquales &longs;unt prop. 34. lib. 1. </s>

<s id="id.002713"><emph type="italics"/>Sit &longs;ecunda forma<emph.end type="italics"/> <foreign lang="greek">a b g d</foreign> <emph type="italics"/>in eadem ratione laterum, & ea<lb/>dem magnitudine &longs;eruata, & linearum &longs;ed obliquarum æquali nu<lb/>mero, quæ &longs;int<emph.end type="italics"/> <foreign lang="greek">a c, h k, e d</foreign> <emph type="italics"/>tum <emph.end type="italics"/> <foreign lang="greek">b c, q i, e g,</foreign> <emph type="italics"/>quæ quia pa<emph.end type="italics"/><lb/><figure id="id.035.01.220.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.220.1.jpg"/><lb/><emph type="italics"/>rallelæ &longs;unt, & aduer&longs;æ in &longs;uis parallelogrammis, omnes inter &longs;e <lb/>æquales &longs;unt prop. 34. lib. 1. </s>

<s>Nam po&longs;ito quod<emph.end type="italics"/> <foreign lang="greek">a c</foreign> <emph type="italics"/>&longs;it ab angulo<emph.end type="italics"/> <foreign lang="greek">a</foreign><lb/><emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">c</foreign> <emph type="italics"/>medium lateris<emph.end type="italics"/> <foreign lang="greek">g d</foreign><emph type="italics"/>: erit hæc æqualis ip&longs;i<emph.end type="italics"/> <foreign lang="greek">b c,</foreign> <emph type="italics"/>quia latera <lb/>æqualium quadratorum. </s>

<s id="id.002714">Vtrumque enim æquale e&longs;t duobus ex<emph.end type="italics"/> <foreign lang="greek">a g, <lb/>g c,</foreign> <emph type="italics"/>vel quod idem e&longs;t ex<emph.end type="italics"/> <foreign lang="greek">c d, d b</foreign> <emph type="italics"/>prop. 47. lib. 1.<emph.end type="italics"/></s>

<s id="id.002715"><emph type="italics"/>Dico ergo quod lorum K N cum G Q, id e&longs;t A C, A B ma<lb/>ius e&longs;t<emph.end type="italics"/> <foreign lang="greek">a c, c b,</foreign> <emph type="italics"/>& duo pariter accepta duobus pariter acceptis e&longs;&longs;e <lb/>maiora: &longs;icque totum lorum in lecto A B C D maius e&longs;&longs;e toto, <lb/>quod e&longs;t in lecto<emph.end type="italics"/> <foreign lang="greek">a b g d.</foreign></s>

<s id="id.002716"><emph type="italics"/>Demon&longs;tratio. </s>

<s id="id.002717">Quia rectangulum &longs;ub A C, A B comprehen<lb/>&longs;um duplum e&longs;t quadrati ex A C prop. 1. lib. 6. & rectangulum &longs;ub<emph.end type="italics"/><lb/><foreign lang="greek">a c, c b</foreign> <emph type="italics"/>duplum <expan abbr="it&etilde;">item</expan> e&longs;t quadrati ex A C. </s>

<s id="id.002718">Ip&longs;um enim <expan abbr="c&utilde;">cum</expan> quadratum <lb/>&longs;it. </s>

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<s id="id.002748">Ob id ip&longs;um etiam facilius fertur.</s><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.223.jpg" pagenum="184"/>

<s id="id.002749">COMMENTARIVS.</s>

<s id="id.002749">COMMENTARIVS. </s>

<s id="id.002750">Cvr difficilius.] <emph type="italics"/>Huius capitis problema e&longs;t cur lignum lon<lb/>gum difficilius ex humero fertur per extremum: quam per me<lb/>dium. </s>

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<s>Si<lb/>mul autem eleuata idem præ&longs;tant.</s>

<s id="id.002766">COMMENTARIVS.</s>

<s id="id.002766">COMMENTARIVS. </s>

<s id="id.002767">Cau&longs;a vero.] <emph type="italics"/>Confirmatio e&longs;t a&longs;&longs;umptionis ex æquis extremo<lb/>rum ponderibus vicißim ob id &longs;e &longs;ubleuantibus: &longs;i enim vnius <lb/>propen&longs;io vergit deor&longs;um: alterius re&longs;i&longs;tentia ad motum &longs;ur&longs;um im<lb/>pediet. </s>

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<s id="id.002788"><expan abbr="Quãtò">Quantò</expan> igitur fuerit maius <lb/>id, quod ex <expan abbr="c&etilde;tro">centro</expan>, vel ip&longs;um <lb/><foreign lang="greek">a g,</foreign> tantò plus magnitudo <lb/>illa transfertur, quod e&longs;t <lb/>prius demon&longs;tratum.</s>

<s id="id.002789">COMMENTARIVS.</s>

<s id="id.002789">COMMENTARIVS. </s>

<s id="id.002790">Cvr &longs;i fuerint.] <emph type="italics"/>Huius capitis problema e&longs;t. </s>

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<s id="id.002795"><emph type="italics"/>Sit & breuius <emph.end type="italics"/><lb/><figure id="id.035.01.226.2.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.226.2.jpg"/><lb/><emph type="italics"/>D E eiu&longs;dem pon<lb/>deris puta decem librarum è medio F ge&longs;tatum etiam. </s>

<s id="id.002796">Quia partes <lb/>cum pariter multiplicibus &longs;unt in eadem ratione prop. 15. lib. 5. & <lb/>e&longs;t A B maior ip&longs;o D E, erit dimidium A C maius dimidio D F. <lb/></s>

<s id="id.002796">Quia partes <lb/>cum pariter multiplicibus &longs;unt in eadem ratione prop. 15. lib. 5. & <lb/>e&longs;t A B maior ip&longs;o D E, erit dimidium A C maius dimidio D F. <lb/></s>

<s id="id.002797">Et &longs;ic extremum A magis di&longs;tans à centro C immoto plus mouet, <lb/>vel mouetur pro natura &longs;ua deor&longs;um. </s>

<s id="id.002799">Ergo tum A tum B <lb/>plus impediunt ferentem ex C: quam D & E ex F. </s>

<s id="id.002799">Ergo tum A tum B <lb/>plus impediunt ferentem ex C: quam D & E ex F. </s>

<s id="id.002800">Quæri hic <lb/>po&longs;&longs;et cur pondera &longs;ini&longs;tro humero facilius ferantur, quam dextro. <lb/></s>

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<s id="id.002816"><expan abbr="Itaq;">Itaque</expan> hoc modo vtrumque <lb/>factu facilius e&longs;t: quam alterum.</s>

<s id="id.002817">COMMENTARIVS.</s>

<s id="id.002817">COMMENTARIVS. </s>

<s id="id.002818">Cvr in puteis tollenonem.] <foreign lang="greek">Khlo/neion</foreign> <emph type="italics"/>quid &longs;it etiam&longs;i hîc <lb/>Ari&longs;toteles non explicet, non e&longs;t tamen difficile coniectura a&longs;<lb/>&longs;equi, e&longs;&longs;e eam machinam ligneam, qua & antiqui v&longs;i &longs;unt, & qui <lb/>adhuc viuunt vtuntur in hauriendis aquis è puteo ad irrigandos <emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.228.jpg" pagenum="189"/><emph type="italics"/>hortos, vel ad aliud quod volunt. </s>

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<s id="id.002832">Vnde autem tum hæc, tum illud pendeat non dicit Ari&longs;tote<lb/>les, quia ex antecedentibus facile intellectum. </s>

<s id="id.002833">Tignus enim tran&longs;<lb/>uer&longs;us e&longs;t vectis, cuius <expan abbr="fulciment&utilde;">fulcimentum</expan> e&longs;t in axiculo trabis, <expan abbr="atq;">atque</expan> in motu <lb/>immer&longs;ionis pondus <expan abbr="mouend&utilde;">mouendum</expan> e&longs;t in A: mouens vero e&longs;t in B, vel in <lb/>&longs;itula E. </s>

<s id="id.002834">Quò igitur pondus in A erit grauius, eò difficilius attol<lb/>letur, &longs;ic natura grauitatis ferente: & &longs;ic maiore vi opus erit: contrà <lb/>in motu eleuationis, pondus mouendum e&longs;t &longs;itula, mouens e&longs;t in A, <lb/>hic adiutus pondere adiecto natura &longs;ua deor&longs;um vergente, facilius <lb/>tantò deprimet ip&longs;um A: quantò grauius erit G. </s>

<s id="id.002835">Et &longs;ic facilius B <lb/>attolletur cum annexa &longs;itula. </s>

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<s id="id.002842">At po&longs;ito ponde<lb/>re in medio, non alter alteri <lb/>maiori e&longs;t ponderi, nec ma<lb/>gis mouet: &longs;ed <expan abbr="vterq;">vterque</expan> vtri<lb/>que &longs;imile pondus adfert.</s>

<s id="id.002843">COMMENTARIVS.</s>

<s id="id.002843">COMMENTARIVS. </s>

<s id="id.002844">Cvr cum duo.] <emph type="italics"/>Fu&longs;tes teretes nodis carentes ad onera go&longs;tan<lb/>da apti palangæ à Nonio & Varrone dicuntur, vel phalangæ <lb/>à Plinio vnde phalangarij Baiuli ijs <expan abbr="vt&etilde;tes">vtentes</expan>, qui ex numero tetrapho<lb/>ri, & hexaphori dicti &longs;unt. </s>

<s id="id.002845">Quærit igitur hîc Ari&longs;toteles. </s>

<s id="id.002845">Quærit igitur hîc Ari&longs;toteles. </s>

<s id="id.002846">cur è duo<lb/>bus pondus aliquod phalanga ferentibus, quò ponderi propinquior e&longs;t <lb/>alter, eò magis remotiori prematur. </s>

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<s id="id.002857">Erit vna ad alteram vt interualla inter po<lb/>tentias, & pondus reciprocè. </s>

<s id="id.002858">Vt &longs;i &longs;it vectis A B, poten<lb/>tiæ A & B, pondus &longs;u&longs;tentum C E, erit A ad B. vt B C <lb/>ad A C. </s>

<s id="id.002858">Vt &longs;i &longs;it vectis A B, poten<lb/>tiæ A & B, pondus &longs;u&longs;tentum C E, erit A ad B. vt B C <lb/>ad A C. </s>

<s id="id.002859">Sit igitur vt B C &longs;it minor: quam A C. </s>

<s id="id.002859">Sit igitur vt B C &longs;it minor: quam A C. </s>

<s id="id.002860">Ergo A <emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.231.jpg" pagenum="192"/><emph type="italics"/>potentia <emph.end type="italics"/><lb/><figure id="id.035.01.231.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.231.1.jpg"/><lb/><emph type="italics"/>erit mi<lb/>nor: <expan abbr="quã">quam</expan> <lb/>B, id e&longs;t <lb/>potentia <lb/>minor in <lb/>A &longs;ic di <lb/>&longs;tante à <lb/>C &longs;ufficiet &longs;u&longs;tinendo ponderi. </s>

<s id="id.002861">Po&longs;itis igitur A & B potentijs <lb/>æqualibus, A facilius &longs;u&longs;tinebit, & quidem tantò: quantò A di<lb/>&longs;tabit magis ab C. </s>

<s id="id.002861">Po&longs;itis igitur A & B potentijs <lb/>æqualibus, A facilius &longs;u&longs;tinebit, & quidem tantò: quantò A di<lb/>&longs;tabit magis ab C. </s>

<s id="id.002862">Sit præterea vt C &longs;it in medio vectis A B. <lb/>quia B C erit æqualis ip&longs;i A C potentiæ æquales A & B e&longs;&longs;e <lb/>debent, vt æquè pondus idem &longs;u&longs;tineant. </s>

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<s>E&longs;t enim A di&longs;tans <lb/>magis ab C quam B ex hypo<lb/>the&longs;i: erit angulus B maior: quam A prop. 18. lib. 1. </s>

<s id="id.002869">Et &longs;ic E plus <lb/>de&longs;cendit re&longs;pectu B: quam re&longs;pectu A. </s>

<s id="id.002869">Et &longs;ic E plus <lb/>de&longs;cendit re&longs;pectu B: quam re&longs;pectu A. </s>

<s id="id.002870">Igitur E plus grauat B: <lb/>quam A &longs;eu ex cau&longs;a, quod magis premat: &longs;eu ex effectu, quod ma<lb/>gis de&longs;cenderit.<emph.end type="italics"/></s></chap><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.232.jpg" pagenum="193"/><chap>

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<s id="id.002887">Atque habere tum <lb/>caput, tum pedes in eadem <lb/>recta: <foreign lang="greek">g z</foreign> vero cum <foreign lang="greek">b g</foreign><lb/>angulum <expan abbr="acut&utilde;">acutum</expan> con&longs;tituet</s>

<s id="id.002888">COMMENTARIVS.</s>

<s id="id.002888">COMMENTARIVS. </s>

<s id="id.002889">Cvr qui &longs;urgunt.] <emph type="italics"/>Surrectio e&longs;t motio, quia homo è iacente <lb/>vel &longs;edente fit &longs;tans. </s>

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<s id="id.002919">Cur omnes qui &longs;urgunt.] <emph type="italics"/>Quærit hîc Ari&longs;toteles, cur &longs;ur<lb/>gens de &longs;eßione nece&longs;&longs;ario con&longs;tituat angu<lb/>lum acutum ex tibia cum femore, vel ex <lb/>thorace, &longs;eu &longs;pina cum femore, vt in &longs;e&longs;<emph.end type="italics"/><lb/><figure id="id.035.01.234.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.234.1.jpg"/><lb/><emph type="italics"/>&longs;ione &longs;it thorax A B, femur B C, tibia C <lb/>D, anguli A B C & B C D recti. </s>

<s id="id.002920">Ex hoc <lb/>&longs;itu ad &longs;urgendum innitens nece&longs;&longs;e habet addu<lb/>cere C D ad C E, vel A B ad B F, vt è <lb/>rectis A B C, B C D angulis, fiant acuti <lb/>F B C, B C E.<emph.end type="italics"/></s>

<s id="id.002921">An quia quod æquale.] <emph type="italics"/>Quæ&longs;tionem propo&longs;itam &longs;oluit du<lb/>pliciter. </s>

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<s id="id.002958">Is enim qui iacet, vt &longs;urgat, & &longs;tet, quatuor <lb/>acutos efficit, utroque brachio & latere: thorace & cruribus: fe<lb/>moribus & tibiis, vt ia<lb/>ceat A B G D. </s>

<s>vt &longs;ur<emph.end type="italics"/><lb/><figure id="id.035.01.236.2.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.236.2.jpg"/><lb/><emph type="italics"/>gat A B thorax bra<lb/>chiorum in acutos con<lb/>formatorum adminiculo <lb/>adducetur ad E B: &longs;ic<lb/>que E B G erit acutus <lb/>ex thorace & femoribus, <lb/>& G D tibia adducetur in G F: &longs;icque erit acutus B G F.<emph.end type="italics"/></s>

<s id="id.002959"><emph type="italics"/>Cæterum &longs;eßio, de qua hîc Aristoteles, e&longs;t propriè dicta, & hanc <lb/>Galenus cum &longs;ecuritate e&longs;&longs;e dixit. </s>

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<s id="id.002963"><emph type="italics"/>Dico quod ex <emph.end type="italics"/><lb/><figure id="id.035.01.237.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.237.1.jpg"/><lb/><emph type="italics"/>K facilius &longs;ur<lb/>get: quam ex L: <lb/>quamque ex M. <lb/></s>

<s id="id.002964">Ratio e&longs;t, quia <lb/>A B &longs;uper K <lb/>magis e&longs;t parti<lb/>ceps &longs;tationis: <lb/>quam &longs;uper L. <lb/></s>

<s id="id.002964">Ratio e&longs;t, quia <lb/>A B &longs;uper K <lb/>magis e&longs;t parti<lb/>ceps &longs;tationis: <lb/>quam &longs;uper L. <lb/></s>

<s id="id.002965">Et &longs;uper L quam <lb/>quam &longs;uper M. <lb/></s>

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<s id="id.002987">hoc ip&longs;um <lb/>facit id, quod in via commotum e&longs;t.</s><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.239.jpg" pagenum="200"/>

<s id="id.002988">COMMENTARIVS.</s>

<s id="id.002988">COMMENTARIVS. </s>

<s id="id.002989">Cvr commotum.] <emph type="italics"/>Commotum hîc ita capi debet, vt eò, quò <lb/>moueatur, impellatur: non contra, quod ex re&longs;pon&longs;ione colligere <lb/>facilè erit. </s>

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<s id="id.003023">An ab&longs;urdum <lb/>de eo dubitare e&longs;t eum, qui <lb/>principium relinquit.</s>

<s id="id.003024">COMMENTARIVS.</s>

<s id="id.003024">COMMENTARIVS. </s>

<s id="id.003025">Cvr proiecta.] <emph type="italics"/>Proiecta dicuntur, quæ manu, funda, arcu, vel <lb/>aliò in&longs;trumento &longs;ur&longs;um, vel ad latus, vel etiam deor&longs;um vio<lb/>lenter feruntur. </s>

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<s id="id.003052">Et quando <lb/>grauitas eius quod fertur <lb/>deor&longs;um ruit magis: quam <lb/>antror&longs;um impul&longs;oris vis <lb/>po&longs;&longs;it impellere.</s>

<s id="id.003053">COMMENTARIVS.</s>

<s id="id.003053">COMMENTARIVS. </s>

<s id="id.003054">Qvare quidpiam.] <emph type="italics"/>Cum omne proiectum graue quid &longs;it, ideó<lb/>que natura tendens rectà deor&longs;um. </s>

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<s id="id.003070">Alte<lb/>rum enim nihil mouet: alterum nequaquam mouetur.</s>

<s id="id.003071">COMMENTARIVS.</s>

<s id="id.003071">COMMENTARIVS. </s>

<s id="id.003072">Cvr neque exigua.] <emph type="italics"/>Exigua & magna vocabula &longs;unt in re<lb/>latis, & quæ intelligi, vt ante dictum e&longs;t, non po&longs;&longs;unt ni&longs;i rela<lb/>tione facta ad aliud, ad quod referuntur. </s>

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<s id="id.003104">Etenim <lb/>ip&longs;um in vnoquoque circulorum æqualiter di&longs;tat.</s>

<s id="id.003105">COMMENTARIVS.</s>

<s id="id.003105">COMMENTARIVS. </s>

<s id="id.003106">Cvr lata in vortice.] <foreign lang="greek">*dino/menon u(/dwr</foreign> <emph type="italics"/>&longs;eu<emph.end type="italics"/> <foreign lang="greek">di/nh</foreign> <emph type="italics"/>Latinis vor<lb/>tex aquæ, & gurges. </s>

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<s id="id.003111">Quærit igi<emph.end type="italics"/><lb/><figure id="id.035.01.246.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.246.1.jpg"/><lb/><emph type="italics"/>tur Aristoteles cur quæ fe<lb/>runtur in vortico&longs;a aqua, om<lb/>nia tandem ad medium deuol<lb/>uantur. </s>

<s id="id.003112">Sit igitur A medium <lb/>aquæ per circulos B C D, <lb/>E F G, H I K, L M N, <lb/>O P Q volutæ: &longs;it & vt <lb/>nauis R feratur per vorticem <lb/>B C D.<emph.end type="italics"/></s>

<s id="id.003113"><emph type="italics"/>Dico quod ad A medium <lb/>deuoluetur.<emph.end type="italics"/></s>

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<s id="id.003138">Quie&longs;cit enim &longs;olum <lb/>centrum, ad quod omnia nece&longs;&longs;e e&longs;t congregari.</s><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.248.jpg" pagenum="209"/>

<s id="id.003139">COMMENTARIVS.</s>

<s id="id.003139">COMMENTARIVS. </s>

<s id="id.003140">An quia quæ quidem.] <emph type="italics"/>Altera e&longs;t eiu&longs;dem<emph.end type="italics"/> <foreign lang="greek">diorismou=</foreign> <emph type="italics"/>pro<lb/>blematis demon&longs;tratio. </s>

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<s id="id.003158">His <lb/>ita po&longs;itis demon&longs;tratio problematis Aristotelici e&longs;t facilis & <lb/>breuis.<emph.end type="italics"/></s><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.249.jpg" pagenum="210"/>

<s id="id.003159"><emph type="italics"/>Sit A inte<lb/>rius extremum, <lb/><figure id="id.035.01.249.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.249.1.jpg"/><lb/>& B exterius <lb/>lineæ &longs;piralis A <lb/>B plurium reuo<lb/>lutionum, in ex<lb/>tremo B &longs;it na<lb/>uis C. </s>

<s id="id.003160">Dico quod <lb/>C feretur ad A, <lb/>& in&longs;uper quod <lb/>cum erit in A <lb/>&longs;ummergetur in<lb/>tra aby&longs;&longs;um A <lb/>E.<emph.end type="italics"/></s>

<s id="id.003161">Demon&longs;t. <lb/></s>

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<s id="id.003178">quinetiam in &longs;cholis <expan abbr="vulgari&utilde;">vulgarium</expan> illorum philo&longs;ophorum, qui pa<lb/>rum ab&longs;unt, vt omninò<emph.end type="italics"/> <foreign lang="greek">a)gewme/trhtoi</foreign> <emph type="italics"/>non &longs;int, locum eum obtine<lb/>re po&longs;sit, quem cæteri qui ab hoc naturæ & artis etiam omnis atque <lb/>indu&longs;triæ genio libri prodierunt, quémque ij, qui ab illis publicè le<lb/>guntur & explicantur. </s>

<s id="id.003179">Quod in numinis diuini bonorum omnium <lb/>largitoris gloriam: Henrici IIII. </s>

<s id="id.003179">Quod in numinis diuini bonorum omnium <lb/>largitoris gloriam: Henrici IIII. </s>

<s id="id.003180">Regis nostri augu&longs;ti&longs;simi perpe<lb/>tuum decus: Ari&longs;totelis libri huius authoris famam atque authori<lb/>tatem maiorem: Reipub. denique no&longs;træ literariæ vtilitatem cedat, <lb/>de&longs;idero.<emph.end type="italics"/></s>

<s id="id.003180">Regis nostri augu&longs;ti&longs;simi perpe<lb/>tuum decus: Ari&longs;totelis libri huius authoris famam atque authori<lb/>tatem maiorem: Reipub. denique no&longs;træ literariæ vtilitatem cedat, <lb/>de&longs;idero. <emph.end type="italics"/></s>

<s id="id.003181">FINIS.</s>

<s id="id.003181">FINIS. </s>

<s id="id.003182">C&oelig;lo re&longs;tat iter: C&oelig;lo tentabimus ire.</s></chap></body><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.251.jpg"/><back><section>

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