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Colored diff for /texts/archimedes/xml/Attic/monan_mecha_01_la_1599.xml between version 1.34 and 1.35

version 1.34, 2002/11/12 20:33:31 version 1.35, 2003/01/14 23:43:22
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 <s id="id.000024">His enim tantis, &amp; tam multis qu&aelig; ab <lb/>homine <foreign lang="greek">mhxanqpomtikw_|</foreign> manife&longs;t&egrave; &amp; in om&shy;<lb/>nium oculis fiunt, &amp; con&longs;eruantur, fa&shy;<lb/>cillimum e&longs;t, qui&longs;quis mentem habet, <lb/>credere, cogno&longs;cere, complecti, etiam &longs;i <lb/>cum fieret, abfuerit, mundum <expan abbr="h&utilde;c">hunc</expan>, <expan abbr="ma-xim&utilde;">ma&shy;<lb/>ximum</expan> cert&egrave; operum opus, factum e&longs;&longs;e, <lb/>&amp; con&longs;eruari: non autem ab vllo homi&shy;<lb/>ne, &longs;ed ab alio <foreign lang="greek">mhxanopoihtikw_|</foreign> tant&ograve; homi&shy;<lb/>nem pr&aelig;&longs;tantia, &longs;apientia, potentia, im&ograve; <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.008.jpg"/>infinit&egrave; &longs;uperante: quant&ograve; h&aelig;c mundi <lb/>machina omnium hominum etiam Ar&shy;<lb/>chimedeorum machinas &longs;uperat, atque <lb/>antecellit. </s> <s id="id.000024">His enim tantis, &amp; tam multis qu&aelig; ab <lb/>homine <foreign lang="greek">mhxanqpomtikw_|</foreign> manife&longs;t&egrave; &amp; in om&shy;<lb/>nium oculis fiunt, &amp; con&longs;eruantur, fa&shy;<lb/>cillimum e&longs;t, qui&longs;quis mentem habet, <lb/>credere, cogno&longs;cere, complecti, etiam &longs;i <lb/>cum fieret, abfuerit, mundum <expan abbr="h&utilde;c">hunc</expan>, <expan abbr="ma-xim&utilde;">ma&shy;<lb/>ximum</expan> cert&egrave; operum opus, factum e&longs;&longs;e, <lb/>&amp; con&longs;eruari: non autem ab vllo homi&shy;<lb/>ne, &longs;ed ab alio <foreign lang="greek">mhxanopoihtikw_|</foreign> tant&ograve; homi&shy;<lb/>nem pr&aelig;&longs;tantia, &longs;apientia, potentia, im&ograve; <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.008.jpg"/>infinit&egrave; &longs;uperante: quant&ograve; h&aelig;c mundi <lb/>machina omnium hominum etiam Ar&shy;<lb/>chimedeorum machinas &longs;uperat, atque <lb/>antecellit. </s>
  
 <s id="id.000025">Hic autem quis pote&longs;t e&longs;&longs;e <lb/>alius, pr&aelig;terquam is, quem Deum om&shy;<lb/>nes appellam^{9}. Sed &amp; ex eo fit perquam <lb/>credibile, ad huius magn&aelig; molis archi&shy;<lb/>tecturam <expan abbr="architect&utilde;">architectum</expan> &longs;uum nihil egu&iuml;&longs;&longs;e <lb/>ferramentis, vecte, cuneis, trochleis, axe <lb/>in peritrochio, molitione, conatu, qu&aelig; <lb/>impius i&longs;te Velleius ex Epicuri &longs;enten&shy;<lb/>tia apud Ciceronem di&longs;putans &longs;tult&egrave; re&shy;<lb/>quirebat. </s> <s id="id.000025">Hic autem quis pote&longs;t e&longs;&longs;e <lb/>alius, pr&aelig;terquam is, quem Deum om&shy;<lb/>nes appellam^{9}. </s>
  
  <s>Sed &amp; ex eo fit perquam <lb/>credibile, ad huius magn&aelig; molis archi&shy;<lb/>tecturam <expan abbr="architect&utilde;">architectum</expan> &longs;uum nihil egu&iuml;&longs;&longs;e <lb/>ferramentis, vecte, cuneis, trochleis, axe <lb/>in peritrochio, molitione, conatu, qu&aelig; <lb/>impius i&longs;te Velleius ex Epicuri &longs;enten&shy;<lb/>tia apud Ciceronem di&longs;putans &longs;tult&egrave; re&shy;<lb/>quirebat. </s>
  
 <s id="id.000026">In quo enim immen&longs;us ille au&shy;<lb/>thor, factorque hominis, in proprij <lb/>operis fabrica homini ip&longs;i pr&aelig;polleret, <lb/>&longs;i machinis, &amp; in&longs;trumentis, materia, &amp; <lb/>molimine, vt homo, indigeret? </s> <s id="id.000026">In quo enim immen&longs;us ille au&shy;<lb/>thor, factorque hominis, in proprij <lb/>operis fabrica homini ip&longs;i pr&aelig;polleret, <lb/>&longs;i machinis, &amp; in&longs;trumentis, materia, &amp; <lb/>molimine, vt homo, indigeret? </s>
  
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 <s id="id.000231"><emph type="italics"/>Extraict du Priuilege du Roy.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main"> <s id="id.000231"><emph type="italics"/>Extraict du Priuilege du Roy.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
  
 <s id="id.000232">Par grace &amp; priuilege du Roy, il e&longs;t permis &agrave; Ie&shy;<lb/>remie Perier marchant Libraire &agrave; Paris, d'impri&shy;<lb/>mer ou faire imprimer vn liure intitul&eacute; <emph type="italics"/>Ari&longs;totelis <lb/>Mechanica, Gr&aelig;ca emendata, Latina facta, &amp; commen&shy;<lb/>tar&yuml;s illu&longs;trata, ab Henrico Monantholio Medico, &amp; Ma&shy;<lb/>thematicarum artium Profe&longs;&longs;ore Regio.<emph.end type="italics"/></s><s id="id.000233"> Et deffen&longs;es &longs;ont <lb/>faictes &agrave; toutes per&longs;onnes de quelque e&longs;tat qualit&eacute; &amp; <lb/>condition qu'ils &longs;oyent, en quelques lieux &amp; villes de <lb/>ce Royaume, de ne le faire imprimer ou faire faire im&shy;<lb/>primer &agrave; peine des articles po&longs;&eacute;s &agrave; l'original du pre&shy;<lb/>&longs;ent priuilege, iu&longs;ques au temps &amp; terme de dix ans, <lb/>finis &amp; accomplis &agrave; conter du iour &amp; datte de la pre&shy;<lb/>&longs;ante impre&longs;&longs;ion, nonob&longs;tant toutes oppo&longs;itions ou <lb/>appellations quelconques, &amp; &longs;ans preiudice d'icelle, <lb/>car tel e&longs;t le plai&longs;ir de &longs;a Mage&longs;t&eacute;. </s> <s id="id.000232"><foreign lang="french">Par grace &amp; priuilege du Roy, il e&longs;t permis &agrave; Ie&shy;<lb/>remie Perier marchant Libraire &agrave; Paris, d'impri&shy;<lb/>mer ou faire imprimer vn liure intitul&eacute;</foreign> <emph type="italics"/>Ari&longs;totelis <lb/>Mechanica, Gr&aelig;ca emendata, Latina facta, &amp; commen&shy;<lb/>tarijs illu&longs;trata, ab Henrico Monantholio Medico, &amp; Ma&shy;<lb/>thematicarum artium Profe&longs;&longs;ore Regio.<emph.end type="italics"/> </s>
  
  <s id="id.000233"><foreign lang="french">Et deffen&longs;es &longs;ont <lb/>faictes &agrave; toutes per&longs;onnes de quelque e&longs;tat qualit&eacute; &amp; <lb/>condition qu'ils &longs;oyent, en quelques lieux &amp; villes de <lb/>ce Royaume, de ne le faire imprimer ou faire faire im&shy;<lb/>primer &agrave; peine des articles po&longs;&eacute;s &agrave; l'original du pre&shy;<lb/>&longs;ent priuilege, iu&longs;ques au temps &amp; terme de dix ans, <lb/>finis &amp; accomplis &agrave; conter du iour &amp; datte de la pre&shy;<lb/>&longs;ante impre&longs;&longs;ion, nonob&longs;tant toutes oppo&longs;itions ou <lb/>appellations quelconques, &amp; &longs;ans preiudice d'icelle, <lb/>car tel e&longs;t le plai&longs;ir de &longs;a Mage&longs;t&eacute;. </foreign></s>
  
 <s id="id.000234">Donn&eacute; &agrave; Paris le <lb/>23. de Decembre 1598.</s></p><p type="main"> <s id="id.000234"><foreign lang="french">Donn&eacute; &agrave; Paris le <lb/>23. de Decembre 1598.</foreign></s></p><p type="main">
  
 <s id="id.000235"><emph type="italics"/>Sign&eacute; par le Con&longs;eil<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main"> <s id="id.000235"><foreign lang="french"><emph type="italics"/>Sign&eacute; par le Con&longs;eil<emph.end type="italics"/></foreign></s></p><p type="main">
  
 <s id="id.000236"><emph type="italics"/>D<emph.end type="italics"/>E LAVETS.<!-- KEEP S--></s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.032.jpg"/><p type="head"> <s id="id.000236"><foreign lang="french"><emph type="italics"/>D<emph.end type="italics"/>E LAVETS.</foreign><!-- KEEP S--></s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.032.jpg"/><p type="head">
  
 <s id="id.000237">INDEX MEMORABILIVM <lb/>IN MECHANICIS ARISTOTELIS <lb/>&amp; eorum Commentarijs.<lb/><arrow.to.target n="table1"/><!-- KEEP S--></s></p><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">*abuasos</foreign> unde. pag.<emph.end type="italics"/></cell><cell>209</cell></row><row><cell><emph type="italics"/>Ab&longs;is pro circunferen&shy;tia rot&aelig;.<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;e&szlig;ione  tant&ugrave;m<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"/>Agricultur&aelig; nece&longs;&longs;aria.<emph.end type="italics"/></cell><cell>14</cell></row><row><cell><emph type="italics"/>&AElig;des rotunda mirifica.<emph.end type="italics"/></cell><cell>10</cell></row><row><cell><emph type="italics"/>&AElig;dificium durabile rect&agrave; in&longs;i&longs;tit.<emph.end type="italics"/></cell><cell>196</cell></row><row><cell><emph type="italics"/>&AElig;olus primus v&longs;us velis.<emph.end type="italics"/></cell><cell>92</cell></row><row><cell><emph type="italics"/>&AElig;quale e&longs;t cau&longs;a quietis.<emph.end type="italics"/></cell><cell>193.196</cell></row><row><cell><emph type="italics"/>&AElig;quilibrium 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 &aelig;qualitatis,   ide&oacute;que 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"/>Antemn&aelig; 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 &amp; arte.<emph.end type="italics"/></cell><cell>8. 12</cell></row><row><cell><emph type="italics"/>Arbores, &amp; plant&aelig; in&longs;i&longs;lunt plane terr&aelig;   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"/>Architectur&aelig; 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 &agrave; Nonio.<emph.end type="italics"/></cell><cell>84</cell></row><row><cell><emph type="italics"/>Ars &longs;lectit naturam, &amp; 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, &amp; natur&aelig; differentia.<emph.end type="italics"/></cell><cell>6</cell></row><row><cell><emph type="italics"/>Artium diui&longs;io in liberales, &amp; &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 magn&aelig;.<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 architectonic&aelig;.<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, &amp; 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">*au<gap/>/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 tut&ograve; a&longs;cendunt, pericu-los&egrave; de&longs;cendunt.<emph.end type="italics"/></cell><cell>199</cell></row><row><cell><emph type="italics"/>B. Feratinus Amerinus <expan abbr="c&atilde;cellari&aelig;">cancellari&aelig;</expan> Apo-&longs;tolic&aelig; regens con&longs;ecrat, &amp; 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 &aelig;qualem peripheri&aelig; 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"/>Bo&uuml;m 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 pedib^{9} 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/<gap/>ar</foreign> <emph type="italics"/>in fund a quid &longs;it.<emph.end type="italics"/></cell><cell>117</cell></row><row><cell><emph type="italics"/>Calli&aelig; 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 &agrave; Scaligero.<emph.end type="italics"/></cell><cell>145</cell></row><row><cell><emph type="italics"/>Cardanus ob&longs;cur&egrave; &amp; imper&longs;ect&egrave;: inge-nios&egrave; 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, &amp; &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)ntixeir,</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 D&aelig;dalus.<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,   qu&aelig;&longs;unt in machinis motricibus.<emph.end type="italics"/></cell><cell>15</cell></row><row><cell><emph type="italics"/>Circulus admirabili&szlig;imus.<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, &amp; 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="c&otilde;tingit">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 &aelig;qualem   orbitam reuoluitur &amp; contra.<emph.end type="italics"/></cell><cell>164</cell></row><row><cell><emph type="italics"/>Circuli <expan abbr="c&otilde;centrici">concentrici</expan> in&aelig;quales iuncti &aelig;qua-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   &amp; <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 Acchit&aelig; <expan abbr="n&otilde;">non</expan> e&longs;t fabula.<emph.end type="italics"/></cell><cell>26</cell></row><row><cell><emph type="italics"/>Contraria qu&aelig; &longs;int ver&egrave;.<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 &amp; 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"/>Cochle&aelig; 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"/>Cochle&aelig; 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 magn&aelig; moles diuiduntur.<emph.end type="italics"/></cell><cell>125</cell></row><row><cell><emph type="italics"/>Croc&aelig; Ari&longs;toteliquid.<emph.end type="italics"/></cell><cell>123</cell></row><row><cell><emph type="italics"/>Croc&aelig; rotund&aelig;.<emph.end type="italics"/></cell><cell>122.123</cell></row><row><cell><emph type="italics"/>Cubus &longs;tabili&szlig;ima 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"/>D&aelig;dali &longs;tatu&aelig;liber&aelig;, &amp; ligat&aelig;.<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;or&yuml; &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 &agrave; 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, &amp; Sph&aelig;r&aelig; 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 qu&aelig;ratio.<emph.end type="italics"/></cell><cell>32</cell></row><row><cell><emph type="italics"/>Dies impo&longs;it&aelig; 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 Fontan&aelig; triumphus.<emph.end type="italics"/></cell><cell>142</cell></row><row><cell><emph type="italics"/>Domus integra &agrave; &longs;undamentis &longs;ublata,   &amp; ali&ograve; 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 qu&aelig;.<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"/>Ergat&aelig;, &amp; &longs;uccul&aelig; 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 qu&aelig;.<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 c&aelig;te-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, &amp; natura-les impetus.<emph.end type="italics"/></cell><cell>164</cell></row><row><cell><emph type="italics"/>Figura decubitus humida, &longs;eu medi&aelig;   qu&aelig;.<emph.end type="italics"/></cell><cell>176</cell></row><row><cell><emph type="italics"/>Forceps, &amp; forfex quid.<emph.end type="italics"/></cell><cell>152</cell></row><row><cell><emph type="italics"/>Fortuna in&longs;i&longs;tit Sphar&aelig;.<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 Ph&aelig;nicuno.<emph.end type="italics"/></cell><cell>116</cell></row><row><cell><emph type="italics"/>Fund&aelig; v&longs;us.<emph.end type="italics"/></cell><cell>116.117</cell></row><row><cell><emph type="italics"/>Fund&aelig; cur Balearis.<emph.end type="italics"/></cell><cell>116</cell></row><row><cell><emph type="italics"/>Funda longius pro&yuml;cit, quam manus.<emph.end type="italics"/></cell><cell>115.117</cell></row><row><cell><emph type="italics"/>Fundaiacit lapidem &amp; plumbum.<emph.end type="italics"/></cell><cell>117</cell></row><row><cell><emph type="italics"/>Fu&longs;tis ad genu fractus non l&aelig;dit.<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 &amp; aqu&aelig; 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 Lhuller&yuml; machina.<emph.end type="italics"/></cell><cell>137.138</cell></row><row><cell><emph type="italics"/>Gubernaculum &amp; eius partes.<emph.end type="italics"/></cell><cell>73</cell></row><row><cell><emph type="italics"/>Gubernaculi &amp; 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;t&aelig; 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   Geometri&aelig;,<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, &amp; progre&longs;sio, vs   fiat.<emph.end type="italics"/></cell><cell>198</cell></row><row><cell><emph type="italics"/>Homo <expan abbr="n&otilde;">non</expan> &longs;tatrectus, vt <expan abbr="c&aelig;l&utilde;">c&aelig;lum</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 &amp; 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   &aelig;qualiter premuntur.<emph.end type="italics"/></cell><cell>190.191</cell></row><row><cell><emph type="italics"/>Horologia nostritemporis veterum cle-p&longs;ydras, &amp; gnemones antecellunt.<emph.end type="italics"/></cell><cell>26</cell></row><row><cell><emph type="italics"/>Plorologium Argentorati <expan abbr="magni&longs;ic&utilde;">magni&longs;icum</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 &amp; 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"/>Libr&aelig; finis.<emph.end type="italics"/></cell><cell>4</cell></row><row><cell><emph type="italics"/>Libr&aelig;partes.<emph.end type="italics"/></cell><cell>45.46</cell></row><row><cell><emph type="italics"/>Libr&aelig;fallaci&aelig;.<emph.end type="italics"/></cell><cell>46.47</cell></row><row><cell><emph type="italics"/>Libr&aelig; 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="p&otilde;dere">pondere</expan> facilius mouetur.<emph.end type="italics"/></cell><cell>112</cell></row><row><cell><emph type="italics"/>Librilis brachia vt <expan abbr="mane&atilde;t">maneant</expan>, aut redeant   ad <expan abbr="&aelig;quilibri&utilde;">&aelig;quilibrium</expan> &longs;ublatis <expan abbr="p&otilde;deril^{9}">ponderil^{9}</expan>.<emph.end type="italics"/></cell><cell>49.50</cell></row><row><cell><emph type="italics"/>Librile <expan abbr="ligne&utilde;">ligneum</expan> facili^{9} 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="fcr&utilde;-tur">fcrun-tur</expan> bumere, quam &agrave; medio.<emph.end type="italics"/></cell><cell>183.184</cell></row><row><cell><emph type="italics"/>Lignum vt &egrave; genu facilius <expan abbr="fr&atilde;gatur">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="qu&atilde;">quam</expan> brcue, vt &longs;it <expan abbr="p&otilde;dere">pondere</expan> &aelig;quale.<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 qu&aelig;dam per &longs;e, qu&aelig;dam-non per&longs;e mouentur.<emph.end type="italics"/></cell><cell>10</cell></row><row><cell><emph type="italics"/>Machin&aelig; valenti&szlig;im&aelig; tres ex &longs;ententia   Hippocratis.<emph.end type="italics"/></cell><cell>119</cell></row><row><cell><emph type="italics"/>Machinarum pluribus, &amp; diuer&longs;arum   compo&longs;itio ad&aelig;quat vnam, qu&aelig; tanta,   quanta opus e&longs;&longs;et fierinon pote&longs;t, pro-pter defectum materi&aelig;.<emph.end type="italics"/></cell><cell>138.139</cell></row><row><cell><emph type="italics"/>Machin&aelig; ad &aelig;dificia, &amp; 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 qu&aelig;.<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="l&otilde;gius">longius</expan> <expan abbr="manubri&utilde;">manubrium</expan> graui^{9} 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 &amp; <expan abbr="Fr&atilde;ci&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 qu&aelig; 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"/>Mechanic&aelig; artes vnde dict&aelig;.<emph.end type="italics"/></cell><cell>2.3</cell></row><row><cell><emph type="italics"/>Mechanice pars e&longs;t philo&longs;ophi&aelig;.<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 aggre&szlig;ionem 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">pa<gap/>adosopcioi\.</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 c&aelig;teras.<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 qu&ograve; 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;&aelig;pe magnam vim obti-net.<emph.end type="italics"/></cell><cell>129</cell></row><row><cell><emph type="italics"/>Motus fit in tempore, &amp; &longs;ucce&szlig;iu&egrave;.<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="rect&atilde;">rectam</expan> <expan abbr="line&atilde;">lineam</expan>.<emph.end type="italics"/></cell><cell>30</cell></row><row><cell><emph type="italics"/>Motum duabus lationibus rationem non   habentibus <expan abbr="n&otilde;">non</expan> fertur <expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> <expan abbr="rect&atilde;">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 &agrave; quibus pen-deat.<emph.end type="italics"/></cell><cell>101</cell></row><row><cell><emph type="italics"/>Mulier parua non e&longs;t pulchr&aelig;.<emph.end type="italics"/></cell><cell>19</cell></row><row><cell><emph type="italics"/>Mundus nutans non vere dici de terra &agrave;   po&euml;ta.<emph.end type="italics"/></cell><cell>104</cell></row><row><cell><emph type="italics"/>Mu&longs;culus vecti comparatus &agrave; 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, &amp; 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, &amp; nauigationis pericula.<emph.end type="italics"/></cell><cell>62</cell></row><row><cell><emph type="italics"/>Nauig&yuml; Hieronis de&longs;criptio incredibi-lis.<emph.end type="italics"/></cell><cell>73</cell></row><row><cell><emph type="italics"/>Nauis quid, &amp; partes.<emph.end type="italics"/></cell><cell>62</cell></row><row><cell><emph type="italics"/>Nauis Ptolemaic&aelig; 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 actuari&aelig; promotio.<emph.end type="italics"/></cell><cell>69</cell></row><row><cell><emph type="italics"/>Nauis velocit as &agrave; 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 &egrave; plumbo tenui &longs;upernatat   aqu&aelig;.<emph.end type="italics"/></cell><cell>164</cell></row><row><cell><emph type="italics"/>Naut&aelig; 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 &agrave; 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="Nucifr&atilde;gibuli">Nucifrangibuli</expan> &amp; 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 peripheri&aelig; 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;c^{9} Xy&longs;tiqualis &amp; <expan abbr="qu&atilde;tus">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, &amp; 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 qu&aelig; ma-chin&aelig;, &amp; quot adhibit&aelig;.<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, &amp; &agrave; quibus perfect&aelig;.<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 Ichnographi&aelig;.<emph.end type="italics"/></cell><cell>143</cell></row><row><cell><emph type="italics"/>de Obeli&longs;co &amp; Xy&longs;to V. Summ. Pont. &amp;   cruce Gulielmi Blanci <expan abbr="epigr&atilde;ma">epigramma</expan>.<emph.end type="italics"/></cell><cell>142</cell></row><row><cell><foreign lang="greek">*odonta/g<gap/>a *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 vol&aelig; manus impo&longs;itum   frangitur manu ill&aelig;&longs;a.<emph.end type="italics"/></cell><cell>122</cell></row><row><cell><foreign lang="greek">*ou<gap/>ano/suopcs</foreign> <emph type="italics"/>pi&longs;cis velit nolio videt   c&aelig;lum.<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"/>Percu&szlig;io 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"/>Percu&szlig;io &agrave; quibus fit maior.<emph.end type="italics"/></cell><cell>128</cell></row><row><cell><emph type="italics"/>Percu&szlig;ionis validiores cau&longs;&aelig;.<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 &agrave; peripher&yuml;s in &longs;emi-diametros circulorum in&aelig;qualium   &aelig;quales auferunt &longs;egmenta &longs;emidia-metrorum in&aelig;qualia, quorum maius   e&longs;t quod &egrave; minori aufertur.<emph.end type="italics"/></cell><cell>40</cell></row><row><cell><emph type="italics"/>Peripheri&aelig; maiores &agrave; punctis &agrave; 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"/>Phalangar&yuml; tetraphori, hexaphori.<emph.end type="italics"/></cell><cell>191</cell></row><row><cell><emph type="italics"/>Phalang&yuml; 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 a&euml;re 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">*go/da e)<gap/>ei_n,</foreign> <emph type="italics"/>&amp; canere quid.<emph.end type="italics"/></cell><cell>95</cell></row><row><cell><foreign lang="greek">*go/des, &amp; p<gap/>o/podes.</foreign></cell><cell>96</cell></row><row><cell><foreign lang="greek">*golio<gap/>uitiu*h\</foreign> <emph type="italics"/>pars Mechanices.<emph.end type="italics"/></cell><cell>11</cell></row><row><cell><foreign lang="greek">*golu/w<gap/>ason.</foreign></cell><cell>111. 134</cell></row><row><cell><emph type="italics"/>Pons Luteti&aelig; ab Henrico 111. inchoatus   ab Henrico 1111. perficietur.<emph.end type="italics"/></cell><cell>120</cell></row><row><cell><emph type="italics"/>Pre&szlig;io 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"/>Progre&szlig;io 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 &agrave; 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 &amp; C. L&aelig;lius colligentes cro-cas qu&aelig; 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"/>Rectiline&aelig; figur&aelig;, &amp; 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 differenti&aelig;.<emph.end type="italics"/></cell><cell>64</cell></row><row><cell><emph type="italics"/>Remiges me&longs;onei maxim&egrave; 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 &aelig;qualem <expan abbr="rect&atilde;">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"/>Rot&aelig; bin&aelig; 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"/>Rot&aelig; curruum maiores commodiores ad   facilitatem &amp; 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, &amp; quotuplex.<emph.end type="italics"/></cell><cell>111.114</cell></row><row><cell><emph type="italics"/>Scytal&aelig; 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,   &amp; nequaquam in vnarecta.<emph.end type="italics"/></cell><cell>193</cell></row><row><cell><emph type="italics"/>Sedentari&aelig; artes vtuntur &longs;e&szlig;ione &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"/>Se&szlig;io propri&egrave; dista &amp; lat&egrave;<emph.end type="italics"/></cell><cell>197</cell></row><row><cell><emph type="italics"/>Se&szlig;io 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">*e*h/mwma</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"/>Sph&aelig;ra quale corpus.<emph.end type="italics"/></cell><cell>16</cell></row><row><cell><emph type="italics"/>Sph&aelig;ra corpus e&longs;t mobili&szlig;imum &amp; mo-uenti&szlig;imum.<emph.end type="italics"/></cell><cell>16</cell></row><row><cell><emph type="italics"/>Sph&aelig;ra contingit planum in puncto.<emph.end type="italics"/></cell><cell>101</cell></row><row><cell><emph type="italics"/>Sph&aelig;ra Archimedis per &longs;e mobilis non   e&longs;t fabula.<emph.end type="italics"/></cell><cell>26</cell></row><row><cell><emph type="italics"/>Sph&aelig;ratop&aelig;ia pars e&longs;t mechanices.<emph.end type="italics"/></cell><cell>11</cell></row><row><cell><emph type="italics"/>Stater&aelig; partes.<emph.end type="italics"/></cell><cell>147</cell></row><row><cell><emph type="italics"/>Stater&aelig; 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 &aelig; &longs;unt libr&aelig;.<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"/>Stater&aelig; paruo &aelig;quipondio magna ponde-ra expendunt.<emph.end type="italics"/></cell><cell>146.147.148</cell></row><row><cell><emph type="italics"/>Stater&aelig; dimidium e&longs;t an&longs;a.<emph.end type="italics"/></cell><cell>148</cell></row><row><cell><emph type="italics"/>Per Stateram ponderationis fact&aelig; 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 terr&aelig;.<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 &amp; &longs;e&szlig;io propria <expan abbr="s&utilde;t">sunt</expan> homini.<emph.end type="italics"/></cell><cell>194</cell></row><row><cell><foreign lang="greek">*etata</foreign> <emph type="italics"/>qu&aelig;.<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 &egrave; 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 thor&aelig;ce   &amp; 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, &amp;   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 &agrave; Pythagoreis, &amp;   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">*qanmatou<gap/>gim*h\</foreign> <emph type="italics"/>pars Mechanices.<emph.end type="italics"/></cell><cell>11</cell></row><row><cell><emph type="italics"/>Theorematis &agrave; 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"/>Trochle&aelig; du&aelig; legitim&egrave; compofit&aelig; 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 machin&aelig;   mult&aelig; &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 aqu&aelig; 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 &agrave; nautis vitentar.<emph.end type="italics"/></cell><cell>210</cell></row><row><cell><emph type="italics"/>Vortices inter Roe&longs;t &amp; Loffoet.<emph.end type="italics"/></cell><cell>210</cell></row><row><cell><emph type="italics"/>in Vorticem vt &longs;entiunt naut&aelig; &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 &agrave; 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> qu&ograve; 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 &amp; *zugo\n.</foreign></cell><cell>45.119</cell></row><row><cell><foreign lang="greek">*zugosa/ths.</foreign></cell><cell>45</cell></row><row><cell><emph type="italics"/>Zygostatica fides.<emph.end type="italics"/></cell><cell>45</cell></row></table><p type="head"> <s id="id.000237">INDEX MEMORABILIVM <lb/>IN MECHANICIS ARISTOTELIS <lb/>&amp; eorum Commentarijs.<lb/><arrow.to.target n="table1"/><!-- KEEP S--></s></p><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">*abuasos</foreign> unde. pag.<emph.end type="italics"/></cell><cell>209</cell></row><row><cell><emph type="italics"/>Ab&longs;is pro circunferen&shy;tia rot&aelig;.<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;e&szlig;ione  tant&ugrave;m<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"/>Agricultur&aelig; nece&longs;&longs;aria.<emph.end type="italics"/></cell><cell>14</cell></row><row><cell><emph type="italics"/>&AElig;des rotunda mirifica.<emph.end type="italics"/></cell><cell>10</cell></row><row><cell><emph type="italics"/>&AElig;dificium durabile rect&agrave; in&longs;i&longs;tit.<emph.end type="italics"/></cell><cell>196</cell></row><row><cell><emph type="italics"/>&AElig;olus primus v&longs;us velis.<emph.end type="italics"/></cell><cell>92</cell></row><row><cell><emph type="italics"/>&AElig;quale e&longs;t cau&longs;a quietis.<emph.end type="italics"/></cell><cell>193.196</cell></row><row><cell><emph type="italics"/>&AElig;quilibrium 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 &aelig;qualitatis,   ide&oacute;que 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"/>Antemn&aelig; 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 &amp; arte.<emph.end type="italics"/></cell><cell>8. 12</cell></row><row><cell><emph type="italics"/>Arbores, &amp; plant&aelig; in&longs;i&longs;lunt plane terr&aelig;   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"/>Architectur&aelig; 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 &agrave; Nonio.<emph.end type="italics"/></cell><cell>84</cell></row><row><cell><emph type="italics"/>Ars &longs;lectit naturam, &amp; 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, &amp; natur&aelig; differentia.<emph.end type="italics"/></cell><cell>6</cell></row><row><cell><emph type="italics"/>Artium diui&longs;io in liberales, &amp; &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 magn&aelig;.<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 architectonic&aelig;.<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, &amp; 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">*au<gap/>/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 tut&ograve; a&longs;cendunt, pericu-los&egrave; de&longs;cendunt.<emph.end type="italics"/></cell><cell>199</cell></row><row><cell><emph type="italics"/>B. Feratinus Amerinus <expan abbr="c&atilde;cellari&aelig;">cancellari&aelig;</expan> Apo-&longs;tolic&aelig; regens con&longs;ecrat, &amp; 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 &aelig;qualem peripheri&aelig; 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"/>Bo&uuml;m 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 pedib^{9} 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/<gap/>ar</foreign> <emph type="italics"/>in fund a quid &longs;it.<emph.end type="italics"/></cell><cell>117</cell></row><row><cell><emph type="italics"/>Calli&aelig; 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 &agrave; Scaligero.<emph.end type="italics"/></cell><cell>145</cell></row><row><cell><emph type="italics"/>Cardanus ob&longs;cur&egrave; &amp; imper&longs;ect&egrave;: inge-nios&egrave; 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, &amp; &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)ntixeir,</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 D&aelig;dalus.<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,   qu&aelig;&longs;unt in machinis motricibus.<emph.end type="italics"/></cell><cell>15</cell></row><row><cell><emph type="italics"/>Circulus admirabili&szlig;imus.<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, &amp; 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="c&otilde;tingit">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 &aelig;qualem   orbitam reuoluitur &amp; contra.<emph.end type="italics"/></cell><cell>164</cell></row><row><cell><emph type="italics"/>Circuli <expan abbr="c&otilde;centrici">concentrici</expan> in&aelig;quales iuncti &aelig;qua-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   &amp; <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 Acchit&aelig; <expan abbr="n&otilde;">non</expan> e&longs;t fabula.<emph.end type="italics"/></cell><cell>26</cell></row><row><cell><emph type="italics"/>Contraria qu&aelig; &longs;int ver&egrave;.<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 &amp; 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"/>Cochle&aelig; 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"/>Cochle&aelig; 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 magn&aelig; moles diuiduntur.<emph.end type="italics"/></cell><cell>125</cell></row><row><cell><emph type="italics"/>Croc&aelig; Ari&longs;toteliquid.<emph.end type="italics"/></cell><cell>123</cell></row><row><cell><emph type="italics"/>Croc&aelig; rotund&aelig;.<emph.end type="italics"/></cell><cell>122.123</cell></row><row><cell><emph type="italics"/>Cubus &longs;tabili&szlig;ima 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"/>D&aelig;dali &longs;tatu&aelig;liber&aelig;, &amp; ligat&aelig;.<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 &agrave; 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, &amp; Sph&aelig;r&aelig; 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 qu&aelig;ratio.<emph.end type="italics"/></cell><cell>32</cell></row><row><cell><emph type="italics"/>Dies impo&longs;it&aelig; 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 Fontan&aelig; triumphus.<emph.end type="italics"/></cell><cell>142</cell></row><row><cell><emph type="italics"/>Domus integra &agrave; &longs;undamentis &longs;ublata,   &amp; ali&ograve; 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 qu&aelig;.<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"/>Ergat&aelig;, &amp; &longs;uccul&aelig; 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 qu&aelig;.<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 c&aelig;te-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, &amp; natura-les impetus.<emph.end type="italics"/></cell><cell>164</cell></row><row><cell><emph type="italics"/>Figura decubitus humida, &longs;eu medi&aelig;   qu&aelig;.<emph.end type="italics"/></cell><cell>176</cell></row><row><cell><emph type="italics"/>Forceps, &amp; forfex quid.<emph.end type="italics"/></cell><cell>152</cell></row><row><cell><emph type="italics"/>Fortuna in&longs;i&longs;tit Sphar&aelig;.<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 Ph&aelig;nicuno.<emph.end type="italics"/></cell><cell>116</cell></row><row><cell><emph type="italics"/>Fund&aelig; v&longs;us.<emph.end type="italics"/></cell><cell>116.117</cell></row><row><cell><emph type="italics"/>Fund&aelig; 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 &amp; plumbum.<emph.end type="italics"/></cell><cell>117</cell></row><row><cell><emph type="italics"/>Fu&longs;tis ad genu fractus non l&aelig;dit.<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 &amp; aqu&aelig; 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 &amp; eius partes.<emph.end type="italics"/></cell><cell>73</cell></row><row><cell><emph type="italics"/>Gubernaculi &amp; 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;t&aelig; 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   Geometri&aelig;,<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, &amp; progre&longs;sio, vs   fiat.<emph.end type="italics"/></cell><cell>198</cell></row><row><cell><emph type="italics"/>Homo <expan abbr="n&otilde;">non</expan> &longs;tatrectus, vt <expan abbr="c&aelig;l&utilde;">c&aelig;lum</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 &amp; 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   &aelig;qualiter premuntur.<emph.end type="italics"/></cell><cell>190.191</cell></row><row><cell><emph type="italics"/>Horologia nostritemporis veterum cle-p&longs;ydras, &amp; gnemones antecellunt.<emph.end type="italics"/></cell><cell>26</cell></row><row><cell><emph type="italics"/>Plorologium Argentorati <expan abbr="magni&longs;ic&utilde;">magni&longs;icum</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 &amp; 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"/>Libr&aelig; finis.<emph.end type="italics"/></cell><cell>4</cell></row><row><cell><emph type="italics"/>Libr&aelig;partes.<emph.end type="italics"/></cell><cell>45.46</cell></row><row><cell><emph type="italics"/>Libr&aelig;fallaci&aelig;.<emph.end type="italics"/></cell><cell>46.47</cell></row><row><cell><emph type="italics"/>Libr&aelig; 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="p&otilde;dere">pondere</expan> facilius mouetur.<emph.end type="italics"/></cell><cell>112</cell></row><row><cell><emph type="italics"/>Librilis brachia vt <expan abbr="mane&atilde;t">maneant</expan>, aut redeant   ad <expan abbr="&aelig;quilibri&utilde;">&aelig;quilibrium</expan> &longs;ublatis <expan abbr="p&otilde;deril^{9}">ponderil^{9}</expan>.<emph.end type="italics"/></cell><cell>49.50</cell></row><row><cell><emph type="italics"/>Librile <expan abbr="ligne&utilde;">ligneum</expan> facili^{9} 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="fcr&utilde;-tur">fcrun-tur</expan> bumere, quam &agrave; medio.<emph.end type="italics"/></cell><cell>183.184</cell></row><row><cell><emph type="italics"/>Lignum vt &egrave; genu facilius <expan abbr="fr&atilde;gatur">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="qu&atilde;">quam</expan> brcue, vt &longs;it <expan abbr="p&otilde;dere">pondere</expan> &aelig;quale.<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 qu&aelig;dam per &longs;e, qu&aelig;dam-non per&longs;e mouentur.<emph.end type="italics"/></cell><cell>10</cell></row><row><cell><emph type="italics"/>Machin&aelig; valenti&szlig;im&aelig; tres ex &longs;ententia   Hippocratis.<emph.end type="italics"/></cell><cell>119</cell></row><row><cell><emph type="italics"/>Machinarum pluribus, &amp; diuer&longs;arum   compo&longs;itio ad&aelig;quat vnam, qu&aelig; tanta,   quanta opus e&longs;&longs;et fierinon pote&longs;t, pro-pter defectum materi&aelig;.<emph.end type="italics"/></cell><cell>138.139</cell></row><row><cell><emph type="italics"/>Machin&aelig; ad &aelig;dificia, &amp; 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 qu&aelig;.<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="l&otilde;gius">longius</expan> <expan abbr="manubri&utilde;">manubrium</expan> graui^{9} 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 &amp; <expan abbr="Fr&atilde;ci&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 qu&aelig; 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"/>Mechanic&aelig; artes vnde dict&aelig;.<emph.end type="italics"/></cell><cell>2.3</cell></row><row><cell><emph type="italics"/>Mechanice pars e&longs;t philo&longs;ophi&aelig;.<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 aggre&szlig;ionem 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">pa<gap/>adosopcioi\.</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 c&aelig;teras.<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 qu&ograve; 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;&aelig;pe magnam vim obti-net.<emph.end type="italics"/></cell><cell>129</cell></row><row><cell><emph type="italics"/>Motus fit in tempore, &amp; &longs;ucce&szlig;iu&egrave;.<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="rect&atilde;">rectam</expan> <expan abbr="line&atilde;">lineam</expan>.<emph.end type="italics"/></cell><cell>30</cell></row><row><cell><emph type="italics"/>Motum duabus lationibus rationem non   habentibus <expan abbr="n&otilde;">non</expan> fertur <expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> <expan abbr="rect&atilde;">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 &agrave; quibus pen-deat.<emph.end type="italics"/></cell><cell>101</cell></row><row><cell><emph type="italics"/>Mulier parua non e&longs;t pulchr&aelig;.<emph.end type="italics"/></cell><cell>19</cell></row><row><cell><emph type="italics"/>Mundus nutans non vere dici de terra &agrave;   po&euml;ta.<emph.end type="italics"/></cell><cell>104</cell></row><row><cell><emph type="italics"/>Mu&longs;culus vecti comparatus &agrave; 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, &amp; 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, &amp; 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, &amp; partes.<emph.end type="italics"/></cell><cell>62</cell></row><row><cell><emph type="italics"/>Nauis Ptolemaic&aelig; 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 actuari&aelig; promotio.<emph.end type="italics"/></cell><cell>69</cell></row><row><cell><emph type="italics"/>Nauis velocit as &agrave; 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 &egrave; plumbo tenui &longs;upernatat   aqu&aelig;.<emph.end type="italics"/></cell><cell>164</cell></row><row><cell><emph type="italics"/>Naut&aelig; 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 &agrave; 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="Nucifr&atilde;gibuli">Nucifrangibuli</expan> &amp; 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 peripheri&aelig; 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;c^{9} Xy&longs;tiqualis &amp; <expan abbr="qu&atilde;tus">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, &amp; 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 qu&aelig; ma-chin&aelig;, &amp; quot adhibit&aelig;.<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, &amp; &agrave; quibus perfect&aelig;.<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 Ichnographi&aelig;.<emph.end type="italics"/></cell><cell>143</cell></row><row><cell><emph type="italics"/>de Obeli&longs;co &amp; Xy&longs;to V. Summ. Pont. &amp;   cruce Gulielmi Blanci <expan abbr="epigr&atilde;ma">epigramma</expan>.<emph.end type="italics"/></cell><cell>142</cell></row><row><cell><foreign lang="greek">*odonta/g<gap/>a *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 vol&aelig; manus impo&longs;itum   frangitur manu ill&aelig;&longs;a.<emph.end type="italics"/></cell><cell>122</cell></row><row><cell><foreign lang="greek">*ou<gap/>ano/suopcs</foreign> <emph type="italics"/>pi&longs;cis velit nolio videt   c&aelig;lum.<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"/>Percu&szlig;io 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"/>Percu&szlig;io &agrave; quibus fit maior.<emph.end type="italics"/></cell><cell>128</cell></row><row><cell><emph type="italics"/>Percu&szlig;ionis validiores cau&longs;&aelig;.<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 &agrave; peripherijs in &longs;emi-diametros circulorum in&aelig;qualium   &aelig;quales auferunt &longs;egmenta &longs;emidia-metrorum in&aelig;qualia, quorum maius   e&longs;t quod &egrave; minori aufertur.<emph.end type="italics"/></cell><cell>40</cell></row><row><cell><emph type="italics"/>Peripheri&aelig; maiores &agrave; punctis &agrave; 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 a&euml;re 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">*go/da e)<gap/>ei_n,</foreign> <emph type="italics"/>&amp; canere quid.<emph.end type="italics"/></cell><cell>95</cell></row><row><cell><foreign lang="greek">*go/des, &amp; p<gap/>o/podes.</foreign></cell><cell>96</cell></row><row><cell><foreign lang="greek">*golio<gap/>uitiu*h\</foreign> <emph type="italics"/>pars Mechanices.<emph.end type="italics"/></cell><cell>11</cell></row><row><cell><foreign lang="greek">*golu/w<gap/>ason.</foreign></cell><cell>111. 134</cell></row><row><cell><emph type="italics"/>Pons Luteti&aelig; ab Henrico 111. inchoatus   ab Henrico 1111. perficietur.<emph.end type="italics"/></cell><cell>120</cell></row><row><cell><emph type="italics"/>Pre&szlig;io 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"/>Progre&szlig;io 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 &agrave; 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 &amp; C. L&aelig;lius colligentes cro-cas qu&aelig; 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"/>Rectiline&aelig; figur&aelig;, &amp; 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 differenti&aelig;.<emph.end type="italics"/></cell><cell>64</cell></row><row><cell><emph type="italics"/>Remiges me&longs;onei maxim&egrave; 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 &aelig;qualem <expan abbr="rect&atilde;">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"/>Rot&aelig; bin&aelig; 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"/>Rot&aelig; curruum maiores commodiores ad   facilitatem &amp; 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, &amp; quotuplex.<emph.end type="italics"/></cell><cell>111.114</cell></row><row><cell><emph type="italics"/>Scytal&aelig; 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,   &amp; nequaquam in vnarecta.<emph.end type="italics"/></cell><cell>193</cell></row><row><cell><emph type="italics"/>Sedentari&aelig; artes vtuntur &longs;e&szlig;ione &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"/>Se&szlig;io propri&egrave; dista &amp; lat&egrave;<emph.end type="italics"/></cell><cell>197</cell></row><row><cell><emph type="italics"/>Se&szlig;io 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">*e*h/mwma</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"/>Sph&aelig;ra quale corpus.<emph.end type="italics"/></cell><cell>16</cell></row><row><cell><emph type="italics"/>Sph&aelig;ra corpus e&longs;t mobili&szlig;imum &amp; mo-uenti&szlig;imum.<emph.end type="italics"/></cell><cell>16</cell></row><row><cell><emph type="italics"/>Sph&aelig;ra contingit planum in puncto.<emph.end type="italics"/></cell><cell>101</cell></row><row><cell><emph type="italics"/>Sph&aelig;ra Archimedis per &longs;e mobilis non   e&longs;t fabula.<emph.end type="italics"/></cell><cell>26</cell></row><row><cell><emph type="italics"/>Sph&aelig;ratop&aelig;ia pars e&longs;t mechanices.<emph.end type="italics"/></cell><cell>11</cell></row><row><cell><emph type="italics"/>Stater&aelig; partes.<emph.end type="italics"/></cell><cell>147</cell></row><row><cell><emph type="italics"/>Stater&aelig; 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 &aelig; &longs;unt libr&aelig;.<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"/>Stater&aelig; paruo &aelig;quipondio magna ponde-ra expendunt.<emph.end type="italics"/></cell><cell>146.147.148</cell></row><row><cell><emph type="italics"/>Stater&aelig; dimidium e&longs;t an&longs;a.<emph.end type="italics"/></cell><cell>148</cell></row><row><cell><emph type="italics"/>Per Stateram ponderationis fact&aelig; 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 terr&aelig;.<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 &amp; &longs;e&szlig;io propria <expan abbr="s&utilde;t">sunt</expan> homini.<emph.end type="italics"/></cell><cell>194</cell></row><row><cell><foreign lang="greek">*etata</foreign> <emph type="italics"/>qu&aelig;.<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 &egrave; 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 thor&aelig;ce   &amp; 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, &amp;   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 &agrave; Pythagoreis, &amp;   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">*qanmatou<gap/>gim*h\</foreign> <emph type="italics"/>pars Mechanices.<emph.end type="italics"/></cell><cell>11</cell></row><row><cell><emph type="italics"/>Theorematis &agrave; 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"/>Trochle&aelig; du&aelig; legitim&egrave; compofit&aelig; 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 machin&aelig;   mult&aelig; &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 aqu&aelig; 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 &agrave; nautis vitentar.<emph.end type="italics"/></cell><cell>210</cell></row><row><cell><emph type="italics"/>Vortices inter Roe&longs;t &amp; Loffoet.<emph.end type="italics"/></cell><cell>210</cell></row><row><cell><emph type="italics"/>in Vorticem vt &longs;entiunt naut&aelig; &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 &agrave; 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> qu&ograve; 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 &amp; *zugo\n.</foreign></cell><cell>45.119</cell></row><row><cell><foreign lang="greek">*zugosa/ths.</foreign></cell><cell>45</cell></row><row><cell><emph type="italics"/>Zygostatica fides.<emph.end type="italics"/></cell><cell>45</cell></row></table><p type="head">
  
 <s id="id.000238">FINIS.<!-- KEEP S--></s></p><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"/><p type="head"> <s id="id.000238">FINIS.<!-- KEEP S--></s></p><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"/><p type="head">
  
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 <s id="id.000243"><emph type="italics"/>Quid e&longs;t Mechanice, &amp; de circulo in quo admirabilium, <lb/>qu&aelig; &longs;unt in Mechanicis, cau&longs;a continetur.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000243"><emph type="italics"/>Quid e&longs;t Mechanice, &amp; de circulo in quo admirabilium, <lb/>qu&aelig; &longs;unt in Mechanicis, cau&longs;a continetur.<emph.end type="italics"/></s></p><p type="main">
  
 <s id="id.000244"><gap/></s></p><p type="main"> <s id="id.000244"><foreign lang="greek">*q*a*u*m*a*z*e*t*a*i<gap/></foreign></s></p><p type="main">
  
 <s id="id.000245">MIRA &longs;unt in his, qu&aelig; <lb/><expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> <expan abbr="natur&atilde;">naturam</expan> <expan abbr="eue-ni&utilde;t">eue&shy;<lb/>niunt</expan>, ea: <expan abbr="quor&utilde;">quorum</expan> cau&longs;a igno&shy;<lb/>ratur, &amp; in his qu&aelig; pr&aelig;ter <lb/>naturam, ea, <expan abbr="qu&ecedil;cunq;">qu&ecedil;cunque</expan> arte <lb/>facta hominibus <expan abbr="c&otilde;ferunt">conferunt</expan>.</s></p><p type="head"> <s id="id.000245">MIRA &longs;unt in his, qu&aelig; <lb/><expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> <expan abbr="natur&atilde;">naturam</expan> <expan abbr="eue-ni&utilde;t">eue&shy;<lb/>niunt</expan>, ea: <expan abbr="quor&utilde;">quorum</expan> cau&longs;a igno&shy;<lb/>ratur, &amp; in his qu&aelig; pr&aelig;ter <lb/>naturam, ea, <expan abbr="qu&ecedil;cunq;">qu&ecedil;cunque</expan> arte <lb/>facta hominibus <expan abbr="c&otilde;ferunt">conferunt</expan>.</s></p><p type="head">
  
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 <s id="id.000264">H&aelig;c autem<emph.end type="italics"/> <foreign lang="greek"><gap/> mhxanikw_n</foreign> <emph type="italics"/>titulo recte exprimuntur. <lb/></s> <s id="id.000264">H&aelig;c autem<emph.end type="italics"/> <foreign lang="greek"><gap/> mhxanikw_n</foreign> <emph type="italics"/>titulo recte exprimuntur. <lb/></s>
  
 <s id="id.000265">quia Mechanica dicta &longs;unt<emph.end type="italics"/> <foreign lang="greek"><gap/>po\ th_s mhxanh_s. </foreign></s> <s id="id.000265">quia Mechanica dicta &longs;unt<emph.end type="italics"/> <foreign lang="greek"><gap/>po\ th_s mhxanh_s. </foreign> &amp; <foreign lang="greek">*mhxanh\ <gap/>po\ tou_ <lb/>mh/kous kai\ a)n/ein,</foreign> <emph type="italics"/>id e&longs;t long&egrave; vel mult&ugrave;m a&longs;cendere, pertingere, pene&shy;<lb/>trare, vt e&longs;t apud Platonem in Cratylo, vnde non qu&aelig;libet artifi&shy;<lb/>cia protrita &amp; vulgaria Mechanica dicenda &longs;unt, &longs;ed ea tantum <lb/>qu&aelig; vtiliter &amp; iucund&egrave; &longs;uccurrunt, &amp; adminiculantur difficul&shy;<lb/>tatibus qu&aelig; in actionibus humanis &longs;e&longs;e <expan abbr="obtrud&utilde;t">obtrudunt</expan>, ip&longs;a&longs;que <expan abbr="impedi&utilde;t">impediunt</expan>.<emph.end type="italics"/><lb/><foreign lang="greek">*mhxanh\</foreign> <emph type="italics"/>autem id e&longs;t machina definitur &agrave; Vitruuio, continens ex <lb/>materia coniunctio, qu&aelig; maximas habet, ad onerum motus virtu&shy;<lb/>tes: &amp; &agrave; Plinio in&longs;trumentum, quo moles aliqua facile, quocumque <lb/>volueris impelli pote&longs;t. </s>
  
 <s id="id.000266"><foreign lang="greek">&amp; *mhxanh\ <gap/>po\ tou_ <lb/>mh/kous kai\ a)n/ein,</foreign> <emph type="italics"/>id e&longs;t long&egrave; vel mult&ugrave;m a&longs;cendere, pertingere, pene&shy;<lb/>trare, vt e&longs;t apud Platonem in Cratylo, vnde non qu&aelig;libet artifi&shy;<lb/>cia protrita &amp; vulgaria Mechanica dicenda &longs;unt, &longs;ed ea tantum <lb/>qu&aelig; vtiliter &amp; iucund&egrave; &longs;uccurrunt, &amp; adminiculantur difficul&shy;<lb/>tatibus qu&aelig; in actionibus humanis &longs;e&longs;e <expan abbr="obtrud&utilde;t">obtrudunt</expan>, ip&longs;a&longs;que <expan abbr="impedi&utilde;t">impediunt</expan>.<emph.end type="italics"/><lb/><foreign lang="greek">*mhxanh\</foreign> <emph type="italics"/>autem id e&longs;t machina definitur &agrave; Vitruuio, continens ex <lb/>materia coniunctio, qu&aelig; maximas habet, ad onerum motus virtu&shy;<lb/>tes: &amp; &agrave; Plinio in&longs;trumentum, quo moles aliqua facile, quocumque <lb/>volueris impelli pote&longs;t. </s> 
  
 <s id="id.000267">Igitur tum h&aelig;c in&longs;trumenta &amp; machin&aelig;: <lb/>tum doctrina, qu&aelig; virium, quibus h&aelig;c pollent, rationem docet, &amp; <lb/>explicat, recl&egrave; Mechanica in&longs;cribuntur. </s> <s id="id.000267">Igitur tum h&aelig;c in&longs;trumenta &amp; machin&aelig;: <lb/>tum doctrina, qu&aelig; virium, quibus h&aelig;c pollent, rationem docet, &amp; <lb/>explicat, rect&egrave; Mechanica in&longs;cribuntur. </s>
  
 <s id="id.000268">Sed vereor, ne h&aelig;c libri <lb/>in&longs;criptio, ex vulgari artium diui&longs;ione in liberales &amp; mechanicas, <lb/>quid &longs;ordidi &longs;ubolens multis, ip&longs;os ab huius libri lectione deterruerit <lb/>&amp; deterreat. </s> <s id="id.000268">Sed vereor, ne h&aelig;c libri <lb/>in&longs;criptio, ex vulgari artium diui&longs;ione in liberales &amp; mechanicas, <lb/>quid &longs;ordidi &longs;ubolens multis, ip&longs;os ab huius libri lectione deterruerit <lb/>&amp; deterreat. </s>
  
 <s id="id.000269">At qu&aelig;cum umque, eluenda e&longs;t macula. </s> <s id="id.000269">At qu&aelig;cumque, eluenda e&longs;t macula. </s>
  
 <s id="id.000270">Manauit enim &agrave;<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.042.jpg" pagenum="3"/><emph type="italics"/>quibu&longs;dam philo&longs;ophis, ii&longs;que otio&longs;is, qui vt maiorem dignitatem <lb/>&longs;ibi fingerent, eas artes nobilitatis titulo ornauere, qu&aelig; in &longs;ola con&shy;<lb/>templatione ver&longs;arentur, &amp; contemplantis duntaxat ingenium <lb/>acuerent, atque perficerent: viles autem eas putauere, qu&aelig; ocium fu&shy;<lb/>gientes, in negotio atque efficientia occuparentur. </s> <s id="id.000270">Manauit enim &agrave;<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.042.jpg" pagenum="3"/><emph type="italics"/>quibu&longs;dam philo&longs;ophis, ii&longs;que otio&longs;is, qui vt maiorem dignitatem <lb/>&longs;ibi fingerent, eas artes nobilitatis titulo ornauere, qu&aelig; in &longs;ola con&shy;<lb/>templatione ver&longs;arentur, &amp; contemplantis duntaxat ingenium <lb/>acuerent, atque perficerent: viles autem eas putauere, qu&aelig; ocium fu&shy;<lb/>gientes, in negotio atque efficientia occuparentur. </s>
  
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 <s id="id.000272">Melius e&longs;t ergo rem i&longs;tam paulo altius re-<emph.end type="italics"/><lb/><arrow.to.target n="marg4"/><lb/><emph type="italics"/>petitam aliquantum vltra per &longs;uas &longs;pecies deducere. </s> <s id="id.000272">Melius e&longs;t ergo rem i&longs;tam paulo altius re-<emph.end type="italics"/><lb/><arrow.to.target n="marg4"/><lb/><emph type="italics"/>petitam aliquantum vltra per &longs;uas &longs;pecies deducere. </s>
  
 <s id="id.000273">Cum omnis ars, <lb/>vt e&longs;t apud Ari&longs;totelem, referatur ad bonum, nulla per &longs;e vilis cen&shy;<lb/>&longs;eri debet, immo omnis po&longs;&longs;e&longs;&longs;orem &longs;uum vel meliorem vel vtilio&shy;<lb/>rem &longs;ibi, vel &longs;u&aelig; ciuitati reddit: at inter &longs;e comparat&aelig; ali&aelig; al<gap/>is pr&aelig;&shy;<lb/>&longs;tantiores existimat&aelig; &longs;unt. </s> <s id="id.000273">Cum omnis ars, <lb/>vt e&longs;t apud Ari&longs;totelem, referatur ad bonum, nulla per &longs;e vilis cen&shy;<lb/>&longs;eri debet, immo omnis po&longs;&longs;e&longs;&longs;orem &longs;uum vel meliorem vel vtilio&shy;<lb/>rem &longs;ibi, vel &longs;u&aelig; ciuitati reddit: at inter &longs;e comparat&aelig; ali&aelig; aliis pr&aelig;&shy;<lb/>&longs;tantiores existimat&aelig; &longs;unt. </s>
  
 <s id="id.000274">vnde nata e&longs;t h&aelig;c vulgaris artium diui&shy;<lb/>&longs;io, vt ali&aelig; liberales e&longs;&longs;ent: ali&aelig; mechanic&aelig;. </s> <s id="id.000274">vnde nata e&longs;t h&aelig;c vulgaris artium diui&shy;<lb/>&longs;io, vt ali&aelig; liberales e&longs;&longs;ent: ali&aelig; mechanic&aelig;. </s>
  
 <s id="id.000275">qu&aelig; his duobus ver&longs;ibus <lb/>exprimuntur.<emph.end type="italics"/></s></p><p type="margin"> <s id="id.000275">qu&aelig; his duobus ver&longs;ibus <lb/>exprimuntur.<emph.end type="italics"/></s></p>
  
 <s id="id.000276"><margin.target id="marg4"/>Lib I.cap i. <lb/>Ethic.</s> <p type="margin"><s id="id.000276"><margin.target id="marg4"/>Lib I.cap i. <lb/>Ethic.</s></p>
  
 <s id="id.000277">Lingua, Tropus, Ratio, Numerus, Tonus, Angulus, A&longs;tra: <lb/>Rus, Nemus, Arma, Faber, Vulnera, Lana, Rates. <emph type="italics"/>horum priore &longs;ignificantur Grammatica, Rhetorica, Dialectica, <lb/>Arithmetica, Mu&longs;ica, Geometria, A&longs;trologia, liberales ob id di&shy;<lb/>ct&aelig;, &longs;iue ingenu&aelig;, quod illis excolatur animus, qui libera &amp; ingenua <lb/>pars e&longs;t hominis: Sed &amp; pueriles, quia his ingenui pueri primis an&shy;<lb/>nis, &longs;tatim imbiberentur tanquam pr&aelig;uiis, &amp; ad cape&longs;&longs;endas &longs;cien&shy;<lb/>tias &amp; magnas artes nece&longs;&longs;ariis. </s></p><p type="main"> <p type="main"><s id="id.000277">Lingua, Tropus, Ratio, Numerus, Tonus, Angulus, A&longs;tra: <lb/>   Rus, Nemus, Arma, Faber, Vulnera, Lana, Rates. </s></p>
  
  <p type="main"><s><emph type="italics"/>horum priore &longs;ignificantur Grammatica, Rhetorica, Dialectica, <lb/>Arithmetica, Mu&longs;ica, Geometria, A&longs;trologia, liberales ob id di&shy;<lb/>ct&aelig;, &longs;iue ingenu&aelig;, quod illis excolatur animus, qui libera &amp; ingenua <lb/>pars e&longs;t hominis: Sed &amp; pueriles, quia his ingenui pueri primis an&shy;<lb/>nis, &longs;tatim imbiberentur tanquam pr&aelig;uiis, &amp; ad cape&longs;&longs;endas &longs;cien&shy;<lb/>tias &amp; magnas artes nece&longs;&longs;ariis. </s></p>
  
  <p type="main"><s id="id.000278">Scienti&aelig; autem erant Philo&longs;ophia <lb/>moralis, Phy&longs;ica, Medicina, Iuri&longs;prudentia, Theologia. </s>
 <s id="id.000278">Scienti&aelig; autem erant Philo&longs;ophia <lb/>moralis, Phy&longs;ica, Medicina, Iuri&longs;prudentia, Theologia. </s> 
  
 <s id="id.000279">Poste&shy;<lb/>riore &longs;ignificatur Agricultura, Venatoria, Militaris, Fabrilis, <lb/>Chirurgia, Lanificium, Nautica. </s> <s id="id.000279">Poste&shy;<lb/>riore &longs;ignificatur Agricultura, Venatoria, Militaris, Fabrilis, <lb/>Chirurgia, Lanificium, Nautica. </s>
  
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 <s id="id.000281">Impe&shy;<lb/>rantes, habere debent pr&aelig;uias illas &longs;eptem liberales ante dictas, vt <lb/>videre e&longs;t apud Vitruuium de &longs;uo architecto, &amp; in no&longs;tro com&shy;<lb/>mentario Iuri&longs;iurandi Hipp. <!-- REMOVE S-->de Hippocrateo medico: apud <expan abbr="Virgili&utilde;">Virgilium</expan> <lb/>de &longs;uo agricola: apud Vegetium de &longs;uo imperatore, &amp; eadem ratione <lb/>in reliquis: ita vt, qui imperantibus i&longs;tis artibus pr&aelig;diti fuerint, in&shy;<lb/>ter homines pr&aelig;&longs;tanti&szlig;imi habiti &longs;emper &longs;int, &amp; &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"/>pr&aelig;&longs;tantiora, aut vtiliora, aut certiora exi&longs;tant. </s> <s id="id.000281">Impe&shy;<lb/>rantes, habere debent pr&aelig;uias illas &longs;eptem liberales ante dictas, vt <lb/>videre e&longs;t apud Vitruuium de &longs;uo architecto, &amp; in no&longs;tro com&shy;<lb/>mentario Iuri&longs;iurandi Hipp. <!-- REMOVE S-->de Hippocrateo medico: apud <expan abbr="Virgili&utilde;">Virgilium</expan> <lb/>de &longs;uo agricola: apud Vegetium de &longs;uo imperatore, &amp; eadem ratione <lb/>in reliquis: ita vt, qui imperantibus i&longs;tis artibus pr&aelig;diti fuerint, in&shy;<lb/>ter homines pr&aelig;&longs;tanti&szlig;imi habiti &longs;emper &longs;int, &amp; &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"/>pr&aelig;&longs;tantiora, aut vtiliora, aut certiora exi&longs;tant. </s>
  
  <s id="id.000282">Agricultur&aelig; enim <lb/>opus, quod alimenta &amp; medicamenta hominibus &longs;uppeditat, nece&szlig;i&shy;<lb/>tate vincit c&aelig;tera: victoria, qu&aelig; rebelles &amp; hostes &longs;ubijcit, proprios <lb/>ciues con&longs;eruat, vtilitate &longs;upereminet: Medicina nobilitate &longs;ubiecti, <lb/>&amp; pr&aelig;stantia boni nempe &longs;anitatis, quam procurat, eximia e&longs;t: Cer&shy;<lb/>titudine operis &amp; operationis Fabrilis anteponenda omnibus: vt <lb/>Lanificium, quod ad opes hone&longs;te parandas: &amp; Nautica propter <lb/>mercaturam faciunt omnium maxim&egrave;. </s>
  
 <s id="id.000282">Agricultur&aelig; enim <lb/>opus, quod alimenta &amp; medicamenta hominibus &longs;uppeditat, nece&szlig;i&shy;<lb/>tate vincit c&aelig;tera: victoria, qu&aelig; rebelles &amp; hostes &longs;ub&yuml;cit, proprios <lb/>ciues con&longs;eruat, vtilitate &longs;upereminet: Medicina nobilitate &longs;ubiecti, <lb/>&amp; pr&aelig;stantia boni nempe &longs;anitatis, quam procurat, eximia e&longs;t: Cer&shy;<lb/>titudine operis &amp; operationis Fabrilis anteponenda omnibus: vt <lb/>Lanificium, quod ad opes hone&longs;te parandas: &amp; Nautica propter <lb/>mercaturam faciunt omnium maxim&egrave;. </s> 
  
 <s id="id.000283">Imperantes etiam hoc ha&shy;<lb/>bent, quod eorum, qu&aelig; efficiunt, rationes teneant: Iuueniles corporis <lb/>vires non requirant: vit&aelig; po&longs;&longs;e&longs;&longs;oris &longs;ui &longs;int &aelig;quales. </s> <s id="id.000283">Imperantes etiam hoc ha&shy;<lb/>bent, quod eorum, qu&aelig; efficiunt, rationes teneant: Iuueniles corporis <lb/>vires non requirant: vit&aelig; po&longs;&longs;e&longs;&longs;oris &longs;ui &longs;int &aelig;quales. </s>
  
 <s id="id.000284">Mini&longs;trantes <lb/>non item: &longs;ed v&longs;u potius &amp; con&longs;uetudine di&longs;cantur &amp; exerceantur: <lb/>Iuueniles vires po&longs;tulent, &amp; po&longs;&longs;e&longs;&longs;orem &longs;uum in &longs;enectute de&longs;e&shy;<lb/>rant. </s> <s id="id.000284">Mini&longs;trantes <lb/>non item: &longs;ed v&longs;u potius &amp; con&longs;uetudine di&longs;cantur &amp; exerceantur: <lb/>Iuueniles vires po&longs;tulent, &amp; po&longs;&longs;e&longs;&longs;orem &longs;uum in &longs;enectute de&longs;e&shy;<lb/>rant. </s>
  
 <s id="id.000285">Ex &yuml;s aliis ali&aelig; materias apparant: ali&aelig; in&longs;trumenta fabrican&shy;<lb/>tur. </s> <s id="id.000285">Ex ijs aliis ali&aelig; materias apparant: ali&aelig; in&longs;trumenta fabrican&shy;<lb/>tur. </s>
  
 <s id="id.000286">In&longs;trumentorum omnium ratio con&longs;i&longs;tit in certa quadam figu&shy;<lb/>ra, qua qu&aelig; eam habent, ad v&longs;um commodiora &longs;unt. </s> <s id="id.000286">In&longs;trumentorum omnium ratio con&longs;i&longs;tit in certa quadam figu&shy;<lb/>ra, qua qu&aelig; eam habent, ad v&longs;um commodiora &longs;unt. </s>
  
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 <s id="id.000298">F&oelig;lix, qui potuit rerum cogno&longs;cere cau&longs;as.</s></p><p type="main"> <s id="id.000298">F&oelig;lix, qui potuit rerum cogno&longs;cere cau&longs;as.</s></p><p type="main">
  
 <s id="id.000299"><emph type="italics"/>Ab hac admirandi facultate Ari&longs;toteles <expan abbr="principi&utilde;">principium</expan> Philo&longs;ophi&aelig; re-<emph.end type="italics"/><lb/><arrow.to.target n="marg5"/><lb/><emph type="italics"/>pet&yuml;t. </s> <s id="id.000299"><emph type="italics"/>Ab hac admirandi facultate Ari&longs;toteles <expan abbr="principi&utilde;">principium</expan> Philo&longs;ophi&aelig; re-<emph.end type="italics"/><lb/><arrow.to.target n="marg5"/><lb/><emph type="italics"/>petijt. </s>
  
 <s id="id.000300">Qui enim, inquit, admiratur, putat &longs;e ignorare, &amp; <expan abbr="dubit&atilde;s">dubitans</expan> co&shy;<lb/>natur dubitationibus &longs;uis &longs;uccurrere. </s> <s id="id.000300">Qui enim, inquit, admiratur, putat &longs;e ignorare, &amp; <expan abbr="dubit&atilde;s">dubitans</expan> co&shy;<lb/>natur dubitationibus &longs;uis &longs;uccurrere. </s>
  
 <s id="id.000301">Homo natura fugiens e&longs;t igno&shy;<lb/>ranti&aelig;. </s> <s id="id.000301">Homo natura fugiens e&longs;t igno&shy;<lb/>ranti&aelig;. </s>
  
 <s id="id.000302"><expan abbr="Itaq;">Itaque</expan> prim&ograve; &egrave; dubitatis faciliora inqui &longs;iuit, deinde paulatim <lb/>vlterius procedens <expan abbr="eti&atilde;">etiam</expan> maiora, vt de affectionibus Lun&aelig;, &amp; &yuml;s qu&aelig; <lb/>circa Solem &amp; &longs;tellas fiunt, ac de generatione vniuer &longs;i: atque &longs;ic <lb/>Philo&longs;ophia orta e&longs;t, &longs;icque Philo&longs;ophus non &longs;olum rara &amp; ingen&shy;<lb/>tia, vt vulgus, &longs;ed etiam frequentia &amp; exigua, &longs;i cau&longs;as latentes ha&shy;<lb/>beant, admiratur, &amp; quidem cum voluptate: in quo etiam di&longs;&longs;entit &agrave; <lb/>vulg&ograve;, qui qu&aelig; admiratur, &longs;&aelig;pe horret, vt Eclip&longs;es Solis &amp; Lun&aelig;,<emph.end type="italics"/><lb/><arrow.to.target n="marg6"/><lb/><emph type="italics"/>quod de Archelao rege Seneca memorat rerum natur&aelig; ade&ograve; ignaro, <lb/>vt quo die Solis defectio fuit, regiam clau&longs;erit, &amp; filium, quod in <lb/>luctu &agrave; rebus aduer&longs;is moris e&longs;t, totunderit. </s> <s id="id.000302"><expan abbr="Itaq;">Itaque</expan> prim&ograve; &egrave; dubitatis faciliora inqui &longs;iuit, deinde paulatim <lb/>vlterius procedens <expan abbr="eti&atilde;">etiam</expan> maiora, vt de affectionibus Lun&aelig;, &amp; ijs qu&aelig; <lb/>circa Solem &amp; &longs;tellas fiunt, ac de generatione vniuer&longs;i: atque &longs;ic <lb/>Philo&longs;ophia orta e&longs;t, &longs;icque Philo&longs;ophus non &longs;olum rara &amp; ingen&shy;<lb/>tia, vt vulgus, &longs;ed etiam frequentia &amp; exigua, &longs;i cau&longs;as latentes ha&shy;<lb/>beant, admiratur, &amp; quidem cum voluptate: in quo etiam di&longs;&longs;entit &agrave; <lb/>vulg&ograve;, qui qu&aelig; admiratur, &longs;&aelig;pe horret, vt Eclip&longs;es Solis &amp; Lun&aelig;,<emph.end type="italics"/><lb/><arrow.to.target n="marg6"/><lb/><emph type="italics"/>quod de Archelao rege Seneca memorat rerum natur&aelig; ade&ograve; ignaro, <lb/>vt quo die Solis defectio fuit, regiam clau&longs;erit, &amp; filium, quod in <lb/>luctu &agrave; rebus aduer&longs;is moris e&longs;t, totunderit. </s>
  
 <s id="id.000303">quam contra Thales <lb/>rerum natur&aelig; gnarus in aperto fixis in peluim oculis magna cum <lb/>animi l&aelig;titia intuitus e&longs;&longs;et.<emph.end type="italics"/></s></p><p type="margin"> <s id="id.000303">quam contra Thales <lb/>rerum natur&aelig; gnarus in aperto fixis in peluim oculis magna cum <lb/>animi l&aelig;titia intuitus e&longs;&longs;et.<emph.end type="italics"/></s></p><p type="margin">
  
  
 <s id="id.000304"><margin.target id="marg5"/>Cap.  <s id="id.000304"><margin.target id="marg5"/>Cap. 2. lib. 2. <lb/>Metaph.<!-- REMOVE S--></s>
  
  
 2. lib.  
  
 2. <lb/>Metaph.<!-- REMOVE S--><margin.target id="marg6"/>Cap.  
  
  <s><margin.target id="marg6"/>Cap. 6. lib. 5. <lb/>De benefic.</s></p><p type="main">
 6. lib.  
  
 5. <lb/>De benefic.</s></p><p type="main"> 
  
 <s id="id.000305">Quorum cau&longs;a ign.] <emph type="italics"/>In rebus naturalibus cau&longs;arum omne <lb/>genus ine&longs;t, materia, efficiens, forma, finis. </s> <s id="id.000305">Quorum cau&longs;a ign.] <emph type="italics"/>In rebus naturalibus cau&longs;arum omne <lb/>genus ine&longs;t, materia, efficiens, forma, finis. </s>
  
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 <s id="id.000309">Fas e&longs;t &longs;cire quidem mortalibus omnia: multa</s></p><p type="main"> <s id="id.000309">Fas e&longs;t &longs;cire quidem mortalibus omnia: multa</s></p><p type="main">
  
 <s id="id.000310">Admirare mod&ograve;, nec non venerarc.</s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.045.jpg" pagenum="6"/><p type="main"> <s id="id.000310">Admirare mod&ograve;, nec non venerare.</s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.045.jpg" pagenum="6"/><p type="main">
  
 <s id="id.000311"><emph type="italics"/>abiecti cert&egrave; ac be&longs;tias imitantis hominis e&longs;t, qu&aelig; ne&longs;ciat, non admi&shy;<lb/>rari, &amp; &longs;i curis, negoti&iacute;&longs;que nece&longs;&longs;ar&yuml;s vacuus e&longs;t, non inquirere, <lb/>&amp; venerari.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000311"><emph type="italics"/>abiecti cert&egrave; ac be&longs;tias imitantis hominis e&longs;t, qu&aelig; ne&longs;ciat, non admi&shy;<lb/>rari, &amp; &longs;i curis, negoti&iacute;&longs;que nece&longs;&longs;arijs vacuus e&longs;t, non inquirere, <lb/>&amp; venerari.<emph.end type="italics"/></s></p><p type="main">
  
 <s id="id.000312"><gap/></s></p><p type="main"> <s id="id.000312"><foreign lang="greek"><gap/></foreign></s></p><p type="main">
  
 <s id="id.000313">In multis enim natura ab <lb/>vtilitate no&longs;tra di&longs;cedit. </s> <s id="id.000313">In multis enim natura ab <lb/>vtilitate no&longs;tra di&longs;cedit. </s>
  
 <s id="id.000314"><expan abbr="Si-quid&etilde;">Si&shy;<lb/>quidem</expan> natura <expan abbr="eod&etilde;">eodem</expan> modo <lb/><expan abbr="s&etilde;per">semper</expan> operatur &amp; &longs;implici&shy;<lb/>ter: <expan abbr="Atali&utilde;">Atalium</expan> <expan abbr="atq;">atque</expan> alium ple&shy;<lb/>rumque po&longs;tulat vtilitas. <lb/></s> <s id="id.000314"><expan abbr="Si-quid&etilde;">Si&shy;<lb/>quidem</expan> natura <expan abbr="eod&etilde;">eodem</expan> modo <lb/><expan abbr="s&etilde;per">semper</expan> operatur &amp; &longs;implici&shy;<lb/>ter: at <expan abbr="ali&utilde;">alium</expan> <expan abbr="atq;">atque</expan> alium ple&shy;<lb/>rumque po&longs;tulat vtilitas. <lb/></s>
  
 <s id="id.000315"><expan abbr="Qu&atilde;do">Quando</expan> igitur conuenit fa&shy;<lb/>cere aliquid pr&ecedil;ter <expan abbr="natur&atilde;">naturam</expan>, <lb/><expan abbr="t&utilde;">tum</expan> difficultas h&aelig;&longs;itationem <lb/>adfert, &amp; arte opus e&longs;t.</s></p><p type="head"> <s id="id.000315"><expan abbr="Qu&atilde;do">Quando</expan> igitur conuenit fa&shy;<lb/>cere aliquid pr&ecedil;ter <expan abbr="natur&atilde;">naturam</expan>, <lb/><expan abbr="t&utilde;">tum</expan> difficultas h&aelig;&longs;itationem <lb/>adfert, &amp; arte opus e&longs;t.</s></p><p type="head">
  
 <s id="id.000316">COMMENTARIVS.<!-- KEEP S--></s></p><p type="main"> <s id="id.000316">COMMENTARIVS.<!-- KEEP S--></s></p><p type="main">
  
 <s id="id.000317">In multis enim.] <emph type="italics"/>Secunda ratio e&longs;t ad probandum in arte fa&shy;<lb/>ctis quibu&longs;dam aliquid mirum e&longs;&longs;e, deprompta e&longs;t ex effectis Na&shy;<lb/>tur&aelig; contrar&yuml;s, &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></p><p type="main"> <s id="id.000317">In multis enim.] <emph type="italics"/>Secunda ratio e&longs;t ad probandum in arte fa&shy;<lb/>ctis quibu&longs;dam aliquid mirum e&longs;&longs;e, deprompta e&longs;t ex effectis Na&shy;<lb/>tur&aelig; 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></p><p type="main">
  
 <s id="id.000318"><emph type="italics"/>Naturam ali&ograve; flectere &amp; adducere, quam vergat, mirum e&longs;t, <lb/>quia difficultas ex renixu natur&aelig; dubitationem parit.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000318"><emph type="italics"/>Naturam ali&ograve; flectere &amp; adducere, quam vergat, mirum e&longs;t, <lb/>quia difficultas ex renixu natur&aelig; dubitationem parit.<emph.end type="italics"/></s></p><p type="main">
  
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 <s id="id.000324">Siquidem Natura.] <emph type="italics"/>Naturalia principium in &longs;e habent &longs;ui <lb/>motus, quo &longs;i &longs;implicia &longs;unt, ad vnum &amp; vno modo &longs;impliciter <lb/>mouentur: &longs;i commixta pr&aelig;dominantis vnius motum &longs;equuntur, <lb/>&longs;icque ad vnum feruntur. </s> <s id="id.000324">Siquidem Natura.] <emph type="italics"/>Naturalia principium in &longs;e habent &longs;ui <lb/>motus, quo &longs;i &longs;implicia &longs;unt, ad vnum &amp; vno modo &longs;impliciter <lb/>mouentur: &longs;i commixta pr&aelig;dominantis vnius motum &longs;equuntur, <lb/>&longs;icque ad vnum feruntur. </s>
  
 <s id="id.000325">H&aelig;c &longs;unt demon&longs;trata ab Aristotele<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.046.jpg" pagenum="7"/><emph type="italics"/>lib.  <s id="id.000325">H&aelig;c &longs;unt demon&longs;trata ab Aristotele<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.046.jpg" pagenum="7"/><emph type="italics"/>lib. de C&oelig;lo &amp; de generat. &amp; corrupt.<emph.end type="italics"/></s></p><p type="main">
  
 de C&oelig;lo &amp; de generat. </s> 
  
 <s id="id.000326">&amp; corrupt.<emph.end type="italics"/></s></p><p type="main"> 
  
 <s id="id.000327">At alium atque alium.] <emph type="italics"/>Hominum vtilitas tum ad e&longs;&longs;e tum <lb/>ad bene e&longs;&longs;e multa vari&aacute;que mult&ograve; aliter quam natura pr&aelig;ferat, pe&shy;<lb/>tit &longs;ibi fieri, vt <expan abbr="alim&etilde;ta">alimenta</expan> &amp; copio&longs;iora, &amp; aliter apparata: <expan abbr="qu&atilde;">quam</expan> terra, <lb/>a&euml;r, &amp; mare &longs;ponte &longs;ua &longs;uppeditent: vt ve&longs;titum, quem connexus <lb/>&longs;taminis cum &longs;ubtegmine faciens corpora tegendo, ip&longs;a probe tuetur <lb/>&amp; ornat: vt &aelig;dificia, qu&aelig; trabium, lapidumque pr&aelig;ter naturam ad <lb/>&longs;uperiorem locum euectio &amp; coagmentatio vtilia facit, ad defen&longs;io&shy;<lb/>nem contra c&oelig;li, a&euml;ris, extern&aacute;&longs;que qua&longs;uis iniurias. </s> <s id="id.000327">At alium atque alium.] <emph type="italics"/>Hominum vtilitas tum ad e&longs;&longs;e tum <lb/>ad bene e&longs;&longs;e multa vari&aacute;que mult&ograve; aliter quam natura pr&aelig;ferat, pe&shy;<lb/>tit &longs;ibi fieri, vt <expan abbr="alim&etilde;ta">alimenta</expan> &amp; copio&longs;iora, &amp; aliter apparata: <expan abbr="qu&atilde;">quam</expan> terra, <lb/>a&euml;r, &amp; mare &longs;ponte &longs;ua &longs;uppeditent: vt ve&longs;titum, quem connexus <lb/>&longs;taminis cum &longs;ubtegmine faciens corpora tegendo, ip&longs;a probe tuetur <lb/>&amp; ornat: vt &aelig;dificia, qu&aelig; trabium, lapidumque pr&aelig;ter naturam ad <lb/>&longs;uperiorem locum euectio &amp; coagmentatio vtilia facit, ad defen&longs;io&shy;<lb/>nem contra c&oelig;li, a&euml;ris, extern&aacute;&longs;que qua&longs;uis iniurias. </s>
  
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 <s id="id.000329">Quando igitur.] <emph type="italics"/>Omnia licet habeat homo &longs;ui gratia nata: non <lb/>ita tamet habet, vt qualia naturaliter prodeunt, talibus <expan abbr="c&utilde;ctis">cunctis</expan> com&shy;<lb/>mode vti po&szlig;it. </s> <s id="id.000329">Quando igitur.] <emph type="italics"/>Omnia licet habeat homo &longs;ui gratia nata: non <lb/>ita tamet habet, vt qualia naturaliter prodeunt, talibus <expan abbr="c&utilde;ctis">cunctis</expan> com&shy;<lb/>mode vti po&szlig;it. </s>
  
 <s id="id.000330">Nece&szlig;itate igitur &amp; commoditate vtendi rebus &agrave; <lb/>natura oblatis pre&longs;&longs;us, conuertit ad &longs;uos v&longs;us &amp; <expan abbr="acc&otilde;modat">accommodat</expan>: &longs;ed con&shy;<lb/>uer&longs;io i&longs;ta, cum &longs;it deductio ad aliud, quam qu&ograve; vergit natura, habet <lb/>in &yuml;s naturale principium renitens: hic renixus parit difficultatem <lb/>conuer&longs;ionis: h&aelig;c difficultas huc illuc animum hominis cogitando, <lb/>qu&aelig;rend&oacute;que, quomodo difficultas i&longs;ta &longs;uperetur, di&longs;trahit, facitque, <lb/>vt mente diu ver&longs;et, quid &amp; quomodo agendum, exempli gratia. </s> <s id="id.000330">Nece&szlig;itate igitur &amp; commoditate vtendi rebus &agrave; <lb/>natura oblatis pre&longs;&longs;us, conuertit ad &longs;uos v&longs;us &amp; <expan abbr="acc&otilde;modat">accommodat</expan>: &longs;ed con&shy;<lb/>uer&longs;io i&longs;ta, cum &longs;it deductio ad aliud, quam qu&ograve; vergit natura, habet <lb/>in ijs naturale principium renitens: hic renixus parit difficultatem <lb/>conuer&longs;ionis: h&aelig;c difficultas huc illuc animum hominis cogitando, <lb/>qu&aelig;rend&oacute;que, quomodo difficultas i&longs;ta &longs;uperetur, di&longs;trahit, facitque, <lb/>vt mente diu ver&longs;et, quid &amp; quomodo agendum, exempli gratia. </s>
  
 <s id="id.000331">vt <lb/>onus &longs;ubleuet, alt&egrave; ip&longs;e con&longs;cendat, vehementer quatiat, long&egrave; iacu&shy;<lb/>letur, &amp; ea demum faciat, velit nolit natura, qu&aelig; vtilitati homi&shy;<lb/>num &longs;eruiant. </s> <s id="id.000331">vt <lb/>onus &longs;ubleuet, alt&egrave; ip&longs;e con&longs;cendat, vehementer quatiat, long&egrave; iacu&shy;<lb/>letur, &amp; ea demum faciat, velit nolit natura, qu&aelig; vtilitati homi&shy;<lb/>num &longs;eruiant. </s>
  
 <s id="id.000332">H&aelig;c cura &longs;olicitud&oacute;que vrget imaginationem, vt lu&shy;<lb/>men &agrave; mente mutuantem &amp; &agrave; rationibus mathematicis, nec quodam <lb/>&longs;ucce&longs;szlig;ionis ordine defatigari <expan abbr="ration&etilde;">rationem</expan> &amp; quie&longs;cere &longs;mit, priu&longs;quam <lb/>quod qu&aelig;ritur, inuentum &longs;it. </s> <s id="id.000332">H&aelig;c cura &longs;olicitud&oacute;que vrget imaginationem, vt lu&shy;<lb/>men &agrave; mente mutuantem &amp; &agrave; rationibus mathematicis, nec quodam <lb/>&longs;ucce&szlig;ionis ordine defatigari <expan abbr="ration&etilde;">rationem</expan> &amp; quie&longs;cere &longs;init, priu&longs;quam <lb/>quod qu&aelig;ritur, inuentum &longs;it. </s>
  
 <s id="id.000333">Illud inuentum, mod&uacute;&longs;ve inuenicndi <lb/>generalis e&longs;t. </s> <s id="id.000333">Illud inuentum, mod&uacute;&longs;ve inueniendi <lb/>generalis e&longs;t. </s>
  
 <s id="id.000334">h&icirc;c particulariter ad <expan abbr="machin&atilde;">machinam</expan> <expan abbr="in&longs;trument&aacute;q;">in&longs;trument&aacute;que</expan> refertur, <lb/>quibus <expan abbr="oner&utilde;">onerum</expan> motiones fiant opportun&aelig;, per motiones intellige, qu&aelig; <lb/>fiunt &agrave; loco ad locum, vt impul&longs;iones, tractiones, volutationes, ve&shy;<lb/>ctiones, &amp; in locis altis, med&yuml;s, imis pro v&longs;u &amp; decoro repo&longs;itiones: <lb/>per onera, quicquid ali&ograve; quam qu&ograve; naturaliter vergit, impellitur, vt <lb/>a&euml;rem, cum deor&longs;um de&longs;cendere cogitur, vt aquam, vt terram cum <lb/>&longs;ur&longs;um a&longs;cendere, &amp; eiu&longs;modi, qu&aelig; vulgus cum admiratione &longs;u&longs;pi&shy;<lb/>cit, &amp; ni&longs;i fierent, nulla res no&longs;tra non e&longs;&longs;et impedita Atque &longs;ic ra&shy;<lb/>tio hominis nece&longs;sitate v&longs;us, &amp; vtilitatis &longs;u&aelig; pre&longs;&longs;a, efficiens cau&longs;a<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.047.jpg" pagenum="8"/><emph type="italics"/>Mechanices hic &longs;tatuitur: vt e&longs;t etiam &longs;tatuta &agrave; Vitruuio &longs;ed &amp; per<emph.end type="italics"/><lb/><arrow.to.target n="marg7"/><lb/><emph type="italics"/>imitationem rerum &agrave; natura procreatarum. </s> <s id="id.000334">h&icirc;c particulariter ad <expan abbr="machin&atilde;">machinam</expan> <expan abbr="in&longs;trument&aacute;q;">in&longs;trument&aacute;que</expan> refertur, <lb/>quibus <expan abbr="oner&utilde;">onerum</expan> motiones fiant opportun&aelig;, per motiones intellige, qu&aelig; <lb/>fiunt &agrave; loco ad locum, vt impul&longs;iones, tractiones, volutationes, ve&shy;<lb/>ctiones, &amp; in locis altis, medijs, imis pro v&longs;u &amp; decoro repo&longs;itiones: <lb/>per onera, quicquid ali&ograve; quam qu&ograve; naturaliter vergit, impellitur, vt <lb/>a&euml;rem, cum deor&longs;um de&longs;cendere cogitur, vt aquam, vt terram cum <lb/>&longs;ur&longs;um a&longs;cendere, &amp; eiu&longs;modi, qu&aelig; vulgus cum admiratione &longs;u&longs;pi&shy;<lb/>cit, &amp; ni&longs;i fierent, nulla res no&longs;tra non e&longs;&longs;et impedita Atque &longs;ic ra&shy;<lb/>tio hominis nece&longs;sitate v&longs;us, &amp; vtilitatis &longs;u&aelig; pre&longs;&longs;a, efficiens cau&longs;a<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.047.jpg" pagenum="8"/><emph type="italics"/>Mechanices hic &longs;tatuitur: vt e&longs;t etiam &longs;tatuta &agrave; Vitruuio &longs;ed &amp; per<emph.end type="italics"/><lb/><arrow.to.target n="marg7"/><lb/><emph type="italics"/>imitationem rerum &agrave; natura procreatarum. </s>
  
 <s id="id.000335">Homo enim inquit, ani&shy;<lb/>maduertens Solis, Lun&aelig;, &amp; reliquorum planetarum continentes <lb/>motus, &amp; machinationes naturales, &longs;ine quibus non habui&longs;&longs;et in <lb/>terra lucem, &amp; fructuum maturit ates hinc exempla &longs;ump &longs;it, &amp; ea <lb/>imitans, inductus rebus diuinis, commodas vit&aelig; perfecit explicatio&shy;<lb/>nes. </s> <s id="id.000335">Homo enim inquit, ani&shy;<lb/>maduertens Solis, Lun&aelig;, &amp; reliquorum planetarum continentes <lb/>motus, &amp; machinationes naturales, &longs;ine quibus non habui&longs;&longs;et in <lb/>terra lucem, &amp; fructuum maturit ates hinc exempla &longs;ump &longs;it, &amp; ea <lb/>imitans, inductus rebus diuinis, commodas vit&aelig; perfecit explicatio&shy;<lb/>nes. </s>
  
 <s id="id.000336">Itaque comparauit, vt e&longs;&longs;ent expeditiora alia machinis, &amp; ea&shy;<lb/>rum ver&longs;ationibus: alia organis, qu&aelig;que ob&longs;eruauit ad v&longs;um vtilia <lb/>e&longs;&longs;e &longs;tud&yuml;s, artibus, in&longs;titutis, doctrinis gradatim augenda curauit: <lb/>hinc tandem extat ars qu&aelig;dam generalis qu&aelig; difficultati faciendo&shy;<lb/>rum pr&aelig;ter naturam ad vtiltiatem hominum &longs;uccurrit.<emph.end type="italics"/></s></p><p type="margin"> <s id="id.000336">Itaque comparauit, vt e&longs;&longs;ent expeditiora alia machinis, &amp; ea&shy;<lb/>rum ver&longs;ationibus: alia organis, qu&aelig;que ob&longs;eruauit ad v&longs;um vtilia <lb/>e&longs;&longs;e &longs;tudijs, artibus, in&longs;titutis, doctrinis gradatim augenda curauit: <lb/>hinc tandem extat ars qu&aelig;dam generalis qu&aelig; difficultati faciendo&shy;<lb/>rum pr&aelig;ter naturam ad vtiltiatem hominum &longs;uccurrit.<emph.end type="italics"/></s></p><p type="margin">
  
 <s id="id.000337"><margin.target id="marg7"/>Lib. 10.</s></p><p type="main"> <s id="id.000337"><margin.target id="marg7"/>Lib. 10.</s></p><p type="main">
  
 <s id="id.000338">Tum difficultas.] <emph type="italics"/>Natur&aelig; renixus difficultatem facit. </s> <s id="id.000338">Tum difficultas.] <emph type="italics"/>Natur&aelig; renixus difficultatem facit. </s>
  
 <s id="id.000339">Re&shy;<lb/>nititur autem Natura &longs;ub&longs;tantia, numero, magnitudine, pondere, <lb/>figura, qu&aelig; omnia ars <expan abbr="immut&atilde;do">immutando</expan>, addendo, detrahendo, <expan abbr="tr&atilde;&longs;ponendo">tran&longs;ponendo</expan>, <lb/>poliendo, figurando corrigit, &amp; ad v&longs;us humanos accommodat.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000339">Re&shy;<lb/>nititur autem Natura &longs;ub&longs;tantia, numero, magnitudine, pondere, <lb/>figura, qu&aelig; omnia ars <expan abbr="immut&atilde;do">immutando</expan>, addendo, detrahendo, <expan abbr="tr&atilde;&longs;ponendo">tran&longs;ponendo</expan>, <lb/>poliendo, figurando corrigit, &amp; ad v&longs;us humanos accommodat.<emph.end type="italics"/></s></p>
  
 <s id="id.000340"><gap/><lb/><arrow.to.target n="marg8"/></s></p><p type="margin"> <p type="main"><s id="id.000340"><foreign lang="greek"><gap/></foreign><lb/><arrow.to.target n="marg8"/></s></p><p type="margin">
  
 <s id="id.000341"><margin.target id="marg8"/><foreign lang="greek"><gap/>xanik<gap/>.</foreign></s></p><p type="main"> <s id="id.000341"><margin.target id="marg8"/><foreign lang="greek"><gap/>xanik<gap/>.</foreign></s></p><p type="main">
  
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 <s id="id.000346">COMMENTARIVS.<!-- KEEP S--></s></p><p type="main"> <s id="id.000346">COMMENTARIVS.<!-- KEEP S--></s></p><p type="main">
  
 <s id="id.000347">Illius artis.] <emph type="italics"/>Ars gencralis, cuius hic mentionem facit Ari&shy;<lb/>&longs;toteles, nu&longs;quam ab eo e&longs;t definita, aut nominata. </s> <s id="id.000347">Illius artis.] <emph type="italics"/>Ars generalis, cuius hic mentionem facit Ari&shy;<lb/>&longs;toteles, nu&longs;quam ab eo e&longs;t definita, aut nominata. </s>
  
 <s id="id.000348">Leonicus, qui <lb/>in hunc librum commentarium edidit putat e&longs;&longs;e Architecturam.<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.048.jpg"/><emph type="italics"/>Quod facit ex &longs;ententia Vitruu&yuml;, qui eius tres partes con&longs;tituit, &aelig;di&shy;<lb/>ficationem in explicatione publicorum &amp; priuatorum operum: <lb/>Gnomonicam in de&longs;criptione Horologiorum: &amp; Machinationent <lb/>in cognitione principiorum &amp; di&longs;po&longs;itione machinarum &amp; orga&shy;<lb/>norum. </s> <s id="id.000348">Leonicus, qui <lb/>in hunc librum commentarium edidit putat e&longs;&longs;e Architecturam.<emph.end type="italics"/></s>
  
 <s id="id.000349">H&aelig;c quidem comprehendi Architectur&aelig; nomine Galenus<emph.end type="italics"/></s></p><p type="main"> <s><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01048.jpg"/><emph type="italics"/>Quod facit ex &longs;ententia Vitruuij, qui eius tres partes con&longs;tituit, &aelig;di&shy;<lb/>ficationem in explicatione publicorum &amp; priuatorum operum: <lb/>Gnomonicam in de&longs;criptione Horologiorum: &amp; Machinationem <lb/>in cognitione principiorum &amp; di&longs;po&longs;itione machinarum &amp; orga&shy;<lb/>norum. </s>
  
 <s id="id.000350"><arrow.to.target n="marg9"/><lb/><emph type="italics"/>etiam te&longs;tatus e&longs;t, nomine inquit, artis Architectorum intelligi volo <lb/>Horologiorum, Clep&longs;ydrarum, Hydrocopiarum, Machinamento&shy;<lb/>rumque omnium de&longs;criptiones, quibus etiam, qu&aelig; &longs;pirabilia vocant, <lb/>continentur. </s> <s id="id.000349">H&aelig;c quidem comprehendi Architectur&aelig; nomine Galenus<lb/><arrow.to.target n="marg9"/> etiam te&longs;tatus e&longs;t, nomine inquit, artis Architectorum intelligi volo <lb/>Horologiorum, Clep&longs;ydrarum, Hydrocopiarum, Machinamento&shy;<lb/>rumque omnium de&longs;criptiones, quibus etiam, qu&aelig; &longs;pirabilia vocant, <lb/>continentur. </s>
  
 <s id="id.000351">Sed cum in his qu&aelig; Architectur&aelig; &longs;ubiecta &longs;unt &longs;olis <lb/>natur&aelig; renixus non vincatur: <expan abbr="ver&utilde;">verum</expan> etiam in quibuslibet aliis cuiu&longs;&shy;<lb/>cunque artis &longs;ubiectis, &longs;i qua &longs;it ars, qu&aelig; in vniuer&longs;um id doceat, <lb/>multo generalior e&longs;t Architectura. </s> <s id="id.000351">Sed cum in his qu&aelig; Architectur&aelig; &longs;ubiecta &longs;unt &longs;olis <lb/>natur&aelig; renixus non vincatur: <expan abbr="ver&utilde;">verum</expan> etiam in quibuslibet aliis cuiu&longs;&shy;<lb/>cunque artis &longs;ubiectis, &longs;i qua &longs;it ars, qu&aelig; in vniuer&longs;um id doceat, <lb/>multo generalior e&longs;t Architectura. </s>
  
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 <s id="id.000356">quorum <lb/>omnium rationes &amp; virium gradus in hac Mechanica tanquam <lb/>generali explicantur, vt po&longs;tea cuique facile apparebit.<emph.end type="italics"/></s></p><p type="margin"> <s id="id.000356">quorum <lb/>omnium rationes &amp; virium gradus in hac Mechanica tanquam <lb/>generali explicantur, vt po&longs;tea cuique facile apparebit.<emph.end type="italics"/></s></p><p type="margin">
  
  
 <s id="id.000357"><margin.target id="marg9"/>Cap.  <s id="id.000357"><margin.target id="marg9"/>Cap. 3. lib. <lb/>de cuiu&longs;que <lb/>animi pecc. <lb/>cogno&longs;c.</s></p><p type="main">
  
  
 3. lib. <lb/> 
  
 de cuiu&longs;que <lb/>animi pecc. <lb/></s> 
  
 <s id="id.000358">cogno&longs;c.</s></p><p type="main"> 
  
 <s id="id.000359">Mechanice.] <emph type="italics"/>In Gr&aelig;co Vecheli legitur h&icirc;c<emph.end type="italics"/> <foreign lang="greek">mhxanh\n</foreign>: <emph type="italics"/>vt etiam <lb/>in titulo huius capitis: &longs;ed vtrobique legendum<emph.end type="italics"/> <foreign lang="greek">mhxanikh\n.</foreign> <emph type="italics"/>quia ha&shy;<lb/>ctenus in hoc pro&euml;mio non machina vna: &longs;ed ars machinarum lau&shy;<lb/>data e&longs;t. </s> <s id="id.000359">Mechanice.] <emph type="italics"/>In Gr&aelig;co Vecheli legitur h&icirc;c<emph.end type="italics"/> <foreign lang="greek">mhxanh\n</foreign>: <emph type="italics"/>vt etiam <lb/>in titulo huius capitis: &longs;ed vtrobique legendum<emph.end type="italics"/> <foreign lang="greek">mhxanikh\n.</foreign> <emph type="italics"/>quia ha&shy;<lb/>ctenus in hoc pro&euml;mio non machina vna: &longs;ed ars machinarum lau&shy;<lb/>data e&longs;t. </s>
  
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 <s id="id.000368">Ill&aelig; intra &longs;e principia &longs;u&aelig; mo&shy;<lb/>tionis habent, &amp;<emph.end type="italics"/> <foreign lang="greek">a)uto/ma<gap/>a</foreign> <emph type="italics"/>vocantur: quorum alia Gr&aelig;cis<emph.end type="italics"/> <foreign lang="greek">sa<gap/>a\,</foreign><lb/><emph type="italics"/>Latinis Stataria, fixa, firma dicuntur: alia<emph.end type="italics"/> <foreign lang="greek">u(pa/<gap/>n<gap/>a</foreign> <emph type="italics"/>ambulantia. <lb/></s> <s id="id.000368">Ill&aelig; intra &longs;e principia &longs;u&aelig; mo&shy;<lb/>tionis habent, &amp;<emph.end type="italics"/> <foreign lang="greek">a)uto/ma<gap/>a</foreign> <emph type="italics"/>vocantur: quorum alia Gr&aelig;cis<emph.end type="italics"/> <foreign lang="greek">sa<gap/>a\,</foreign><lb/><emph type="italics"/>Latinis Stataria, fixa, firma dicuntur: alia<emph.end type="italics"/> <foreign lang="greek">u(pa/<gap/>n<gap/>a</foreign> <emph type="italics"/>ambulantia. <lb/></s>
  
 <s id="id.000369">De vtri&longs;que Hero pertractauit, inter qu&aelig; pulchrum e&longs;t illud, quod <lb/>docuit con&longs;truere, &longs;cilicet &aelig;dem rotundam, in qua Bacchus pateram <lb/>alrera manu tenet, altera thyr&longs;um, prop&egrave; ver&ograve; ade&longs;t panthera, &amp; <lb/>ara: circum autem Bacchides tympana tenentes, &longs;upr&agrave; tholum alata <lb/>&amp; coronata Victoria collocatur, atque vno &amp; <expan abbr="eod&etilde;">eodem</expan> tempore in ara <lb/>ignis &longs;uccenditur, Bacchus lac &egrave; patera, vinum &egrave; thyr&longs;o ver&longs;at in <lb/>pantheram, Bacchides circum&longs;alientes tympana pul&longs;ant, Victoria <lb/>&longs;e circumagens, &amp; alas qaatiens tuba &longs;onat. </s> <s id="id.000369">De vtri&longs;que Hero pertractauit, inter qu&aelig; pulchrum e&longs;t illud, quod <lb/>docuit con&longs;truere, &longs;cilicet &aelig;dem rotundam, in qua Bacchus pateram <lb/>altera manu tenet, altera thyr&longs;um, prop&egrave; ver&ograve; ade&longs;t panthera, &amp; <lb/>ara: circum autem Bacchides tympana tenentes, &longs;upr&agrave; tholum alata <lb/>&amp; coronata Victoria collocatur, atque vno &amp; <expan abbr="eod&etilde;">eodem</expan> tempore in ara <lb/>ignis &longs;uccenditur, Bacchus lac &egrave; patera, vinum &egrave; thyr&longs;o ver&longs;at in <lb/>pantheram, Bacchides circum&longs;alientes tympana pul&longs;ant, Victoria <lb/>&longs;e circumagens, &amp; alas qaatiens tuba &longs;onat. </s>
  
 <s id="id.000370">In alia ver&ograve; di&longs;po&longs;i&shy;<lb/>tione fecit inambulantia, &longs;igilla euntia, &amp; redeuntia, motione&longs;&shy;<lb/>que varias reddentia, vt v&longs;us &amp; voluptas po&longs;tulat pro instituto. <lb/></s> <s id="id.000370">In alia ver&ograve; di&longs;po&longs;i&shy;<lb/>tione fecit inambulantia, &longs;igilla euntia, &amp; redeuntia, motione&longs;&shy;<lb/>que varias reddentia, vt v&longs;us &amp; voluptas po&longs;tulat pro instituto. <lb/></s>
  
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 <s id="id.000374">A qua, <lb/>vnde fiunt rot&aelig; etiam ad <expan abbr="molend&utilde;">molendum</expan>, <expan abbr="t&utilde;">tum</expan> tympana, tum &longs;err&aelig; ad trabes <lb/>&longs;ecandas, folles ad <expan abbr="ferr&utilde;">ferrum</expan> tundendum &amp; alia <expan abbr="plera&qacute;">pleraque</expan>;. </s> <s id="id.000374">A qua, <lb/>vnde fiunt rot&aelig; etiam ad <expan abbr="molend&utilde;">molendum</expan>, <expan abbr="t&utilde;">tum</expan> tympana, tum &longs;err&aelig; ad trabes <lb/>&longs;ecandas, folles ad <expan abbr="ferr&utilde;">ferrum</expan> tundendum &amp; alia <expan abbr="plera&qacute;">pleraque</expan>;. </s>
  
 <s id="id.000375">Ignis &longs;eu fumus <lb/>quo verrucula conuoluuntur: animat&aelig; &longs;unt, bruta qu&aelig; trahunt cur&shy;<lb/>rus, ci&longs;ia, quadrigas: homines qui ver&longs;ant, trahunt, erigunt, impel&shy;<lb/>lunt ad varios belli <expan abbr="paci&longs;q;">paci&longs;que</expan> v&longs;us vtentes vectibus, rad&yuml;s, trochleis, <lb/>cochleis, trutinis, lancibus, ergatis, rotis, tympanis, &amp; ad a&longs;cenden&shy;<lb/>dum in altum multiplicibus &longs;calarum formis, tum munitis, tum &longs;ine <lb/>munitione, &amp; ad di&longs;rumpendum, excutiendum, pro&longs;ternendum, <lb/>quatiendum frangendum, iaculandum, arietibus, te&longs;tudinibus, tur&shy;<lb/>ribus ambulator&yuml;s, catapultis, bali&longs;tis, tormentis reliquis. </s> <s id="id.000375">Ignis &longs;eu fumus <lb/>quo verrucula conuoluuntur: animat&aelig; &longs;unt, bruta qu&aelig; trahunt cur&shy;<lb/>rus, ci&longs;ia, quadrigas: homines qui ver&longs;ant, trahunt, erigunt, impel&shy;<lb/>lunt ad varios belli <expan abbr="paci&longs;q;">paci&longs;que</expan> v&longs;us vtentes vectibus, radijs, trochleis, <lb/>cochleis, trutinis, lancibus, ergatis, rotis, tympanis, &amp; ad a&longs;cenden&shy;<lb/>dum in altum multiplicibus &longs;calarum formis, tum munitis, tum &longs;ine <lb/>munitione, &amp; ad di&longs;rumpendum, excutiendum, pro&longs;ternendum, <lb/>quatiendum frangendum, iaculandum, arietibus, te&longs;tudinibus, tur&shy;<lb/>ribus ambulatorijs, catapultis, bali&longs;tis, tormentis reliquis. </s>
  
 <s id="id.000376">in quibus <lb/>&longs;aciendis h&aelig;c lex po&longs;ita e&longs;t, vt omnia fiant ex paratu facilibus quo <lb/>ad materiam: var&yuml;s quoad figuras: exiguis quoad men&longs;uras: leuibus <lb/>quoad pondera. </s> <s id="id.000376">in quibus <lb/>faciendis h&aelig;c lex po&longs;ita e&longs;t, vt omnia fiant ex paratu facilibus quo <lb/>ad materiam: varijs quoad figuras: exiguis quoad men&longs;uras: leuibus <lb/>quoad pondera. </s>
  
 <s id="id.000377">Quipp&egrave; qu&aelig; &agrave; quibu&longs;cumque artificibus cit&ograve; fieri <lb/>queant, erectu interim, <expan abbr="tr&atilde;slat&uacute;que">translat&uacute;que</expan> facilia: in &longs;idiatu, fractuque dif&shy;<lb/>&longs;icilia: &longs;tabilia, ac tandem eiu&longs;modi &longs;int, vt quatenus nece&szlig;itas<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.050.jpg" pagenum="11"/><emph type="italics"/>po&longs;tulauerit, facile componi, facil&eacute;que di&longs;&longs;olui po&szlig;int. </s> <s id="id.000377">Quipp&egrave; qu&aelig; &agrave; quibu&longs;cumque artificibus cit&ograve; fieri <lb/>queant, erectu interim, <expan abbr="tr&atilde;slat&uacute;que">translat&uacute;que</expan> facilia: in&longs;idiatu, fractuque dif&shy;<lb/>ficilia: &longs;tabilia, ac tandem eiu&longs;modi &longs;int, vt quatenus nece&szlig;itas<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.050.jpg" pagenum="11"/><emph type="italics"/>po&longs;tulauerit, facile componi, facil&eacute;que di&longs;&longs;olui po&szlig;int. </s>
  
 <s id="id.000378">Sed neque hic <lb/>pr&aelig;termittenda diui&longs;io Methanices, qu&aelig; aliter &agrave; Politiano ex He-<emph.end type="italics"/><lb/><arrow.to.target n="marg11"/><lb/><emph type="italics"/>rone inducta e&longs;t. </s> <s id="id.000378">Sed neque hic <lb/>pr&aelig;termittenda diui&longs;io Methanices, qu&aelig; aliter &agrave; Politiano ex He-<emph.end type="italics"/><lb/><arrow.to.target n="marg11"/><lb/><emph type="italics"/>rone inducta e&longs;t. </s>
  
 <s id="id.000379">Mechanices, inquit, altera pars rationalis e&longs;t, qu&aelig; <lb/>numerorum, men&longs;urarum, &longs;yderum, natur&aelig; que rationibus perfici&shy;<lb/>tur: altera<emph.end type="italics"/> <foreign lang="greek">xeipourgikh\,</foreign> <emph type="italics"/>cui vel maxim&egrave; artes ill&aelig;, &aelig;raria, &aelig;difica&shy;<lb/>toria, materiaria, picturaque, adminiculantur. </s> <s id="id.000379">Mechanices, inquit, altera pars rationalis e&longs;t, qu&aelig; <lb/>numerorum, men&longs;urarum, &longs;yderum, natur&aelig; que rationibus perfici&shy;<lb/>tur: altera<emph.end type="italics"/> <foreign lang="greek">xeipourgikh\,</foreign> <emph type="italics"/>cui vel maxim&egrave; artes ill&aelig;, &aelig;raria, &aelig;difica&shy;<lb/>toria, materiaria, picturaque, adminiculantur. </s>
  
 <s id="id.000380">Huius autem partes, <lb/>Manganaria per quam pondera immania minima vi tolluntur in <lb/>altum:<emph.end type="italics"/> <foreign lang="greek">mhxanopoihpkh\,</foreign> <emph type="italics"/>qu&aelig; facile aquas antl&yuml;s extrahit:<emph.end type="italics"/> <foreign lang="greek">*or&shy;<lb/>ganopoihtikh\,</foreign> <emph type="italics"/>qu&aelig; bellis accommoda in&longs;trumenta fabricatur, arie&shy;<lb/>tes, te&longs;tudines, turres ambulatorias, helepoleis, &longs;ambucas, exo&longs;tras, <lb/>tollenones &amp; qu&aelig;cunque Gr&aelig;co vocabulo<emph.end type="italics"/> <foreign lang="greek">w_oliorkh<gap/>ika\</foreign> <emph type="italics"/>vocan&shy;<lb/>tur, tormentorumque varia genera, qu&aelig; libris Athen&aelig;i, Bitonis, <lb/>Heronis, Pappi, Philonis, Apollodorique continentur, vt Latinos <lb/>omi&longs;erim. </s> <s id="id.000380">Huius autem partes, <lb/>Manganaria per quam pondera immania minima vi tolluntur in <lb/>altum:<emph.end type="italics"/> <foreign lang="greek">mhxanopoihpkh\,</foreign> <emph type="italics"/>qu&aelig; facile aquas antlijs extrahit:<emph.end type="italics"/> <foreign lang="greek">*or&shy;<lb/>ganopoihtikh\,</foreign> <emph type="italics"/>qu&aelig; bellis accommoda in&longs;trumenta fabricatur, arie&shy;<lb/>tes, te&longs;tudines, turres ambulatorias, helepoleis, &longs;ambucas, exo&longs;tras, <lb/>tollenones &amp; qu&aelig;cunque Gr&aelig;co vocabulo<emph.end type="italics"/> <foreign lang="greek">w_oliorkh<gap/>ika\</foreign> <emph type="italics"/>vocan&shy;<lb/>tur, tormentorumque varia genera, qu&aelig; libris Athen&aelig;i, Bitonis, <lb/>Heronis, Pappi, Philonis, Apollodorique continentur, vt Latinos <lb/>omi&longs;erim. </s>
  
 <s id="id.000381">Mox &amp; qu&aelig;<emph.end type="italics"/> <foreign lang="greek"><gap/>auma<gap/>ourgikh\</foreign> <emph type="italics"/>cuius exempla &longs;unt<emph.end type="italics"/> <foreign lang="greek">u)drau&shy;<lb/>lika\</foreign> <emph type="italics"/>organa, qu&aelig;que per &longs;e ventorum &longs;latu re&longs;onant. </s> <s id="id.000381">Mox &amp; qu&aelig;<emph.end type="italics"/> <foreign lang="greek"><gap/>auma<gap/>ourgikh\</foreign> <emph type="italics"/>cuius exempla &longs;unt<emph.end type="italics"/> <foreign lang="greek">u)drau&shy;<lb/>lika\</foreign> <emph type="italics"/>organa, qu&aelig;que per &longs;e ventorum flatu re&longs;onant. </s>
  
 <s id="id.000382">Et quod vas <lb/>dic&aelig;ometron vocabant, &amp; quod voces variarum auium exprimit, <lb/>&amp; quod indidem merum, mox dilutum vinum, mox aquam cali&shy;<lb/>dam, mox <expan abbr="frigid&atilde;">frigidam</expan>, copio&longs;am <expan abbr="tenu&eacute;mq;">tenu&eacute;mque</expan> vici&szlig;im funditat. </s> <s id="id.000382">Et quod vas <lb/>dic&aelig;ometron vocabant, &amp; quod voces variarum auium exprimit, <lb/>&amp; quod indidem merum, mox dilutum vinum, mox aquam cali&shy;<lb/>dam, mox <expan abbr="frigid&atilde;">frigidam</expan>, copio&longs;am <expan abbr="tenu&eacute;mq;">tenu&eacute;mque</expan> vici&szlig;im funditat. </s>
  
 <s id="id.000383">Et<emph.end type="italics"/> <foreign lang="greek">si/fwnes</foreign><lb/><emph type="italics"/>extinguendis ineend&yuml;s apti, &amp; medicinabiles cacurbitul&aelig; &longs;ine <lb/>ignis ministerio cutem prehendentes, &amp; pil&aelig; &longs;ponte &longs;altantes, &amp; <lb/>lucerna &longs;uas ip&longs;a producens &longs;tuppas: &amp; animal quod &agrave; &longs;tructore dum <lb/>&longs;ecatur in men&longs;a, bibit interim, crepit&ugrave;que &longs;uo quodam, &amp; voce &longs;i&shy;<lb/>tientis repr&aelig;&longs;entat imaginem: milleque alia id genus, qu&aelig; breuita&shy;<lb/>tis &longs;tudio pr&aelig;terimus. </s> <s id="id.000383">Et<emph.end type="italics"/> <foreign lang="greek">si/fanes</foreign><lb/><emph type="italics"/>extinguendis ineendijs apti, &amp; medicinabiles cacurbitul&aelig; &longs;ine <lb/>ignis ministerio cutem prehendentes, &amp; pil&aelig; &longs;ponte &longs;altantes, &amp; <lb/>lucerna &longs;uas ip&longs;a producens &longs;tuppas: &amp; animal quod &agrave; &longs;tructore dum <lb/>&longs;ecatur in men&longs;a, bibit interim, crepit&ugrave;que &longs;uo quodam, &amp; voce &longs;i&shy;<lb/>tientis repr&aelig;&longs;entat imaginem: milleque alia id genus, qu&aelig; breuita&shy;<lb/>tis &longs;tudio pr&aelig;terimus. </s>
  
 <s id="id.000384">H&aelig;c igitur (vt in capita qu&aelig;dam conferatur) <lb/>aut ponderibus vtitur &amp; &longs;piritu, quorum pr&aelig;ponderatio mouet, <lb/>&aelig;quilibrium &longs;i&longs;tit, (&longs;icuti etiam Tim&aelig;us definit): aut neruis &amp; <lb/>funiculis animatos qua&longs;i tractus, ac motus imitatur, ac circa illa <lb/>qu&aelig; &longs;ubnatant aquis, aut circa aquarum vertitur horologia, quo&shy;<lb/>rum quidem generum primum docet in pneumaticis Heron, alte&shy;<lb/>rum idem in automatis &amp; Zyg&yuml;s, quartum rur&longs;us in Hydr&yuml;s, ter&shy;<lb/>tium ver&ograve; in Ochoumenis Archimedes. <!-- KEEP S--></s> <s id="id.000384">H&aelig;c igitur (vt in capita qu&aelig;dam conferatur) <lb/>aut ponderibus vtitur &amp; &longs;piritu, quorum pr&aelig;ponderatio mouet, <lb/>&aelig;quilibrium &longs;i&longs;tit, (&longs;icuti etiam Tim&aelig;us definit): aut neruis &amp; <lb/>funiculis animatos qua&longs;i tractus, ac motus imitatur, ac circa illa <lb/>qu&aelig; &longs;ubnatant aquis, aut circa aquarum vertitur horologia, quo&shy;<lb/>rum quidem generum primum docet in pneumaticis Heron, alte&shy;<lb/>rum idem in automatis &amp; Zygijs, quartum rur&longs;us in Hydrijs, ter&shy;<lb/>tium ver&ograve; in Ochoumenis Archimedes. <!-- KEEP S--></s>
  
 <s id="id.000385">E&longs;t in eadem Mechanic&aelig; <lb/>&longs;erie qu&aelig; Centrobarica pars dicitur, ex qua reliqu&aelig; pendere dicun&shy;<lb/>tur &amp; Sph&aelig;rotop&oelig;ia, qualis illa Archimedea Claudiani laudata <lb/>ver&longs;ibus. </s> <s id="id.000385">E&longs;t in eadem Mechanic&aelig; <lb/>&longs;erie qu&aelig; Centrobarica pars dicitur, ex qua reliqu&aelig; pendere dicun&shy;<lb/>tur &amp; Sph&aelig;rotop&oelig;ia, qualis illa Archimedea Claudiani laudata <lb/>ver&longs;ibus. </s>
  
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 <s id="id.000390">hos enim videns capite coopertos. </s> <s id="id.000390">hos enim videns capite coopertos. </s>
  
 <s id="id.000391">Quid occultamini, inquit, <lb/>Soc&yuml;, 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.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 &amp; &longs;criptore for&shy;<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&shy;<lb/>terpretem, &amp; po&euml;tam refert Suidas. <!-- KEEP S--></s> <s id="id.000392">E&longs;t alius etiam Antipho <lb/>de quo meminit Cicero, vt &longs;omniorum interprete &amp; &longs;criptore for&shy;<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&shy;<lb/>terpretem, &amp; po&euml;tam refert Suidas. <!-- KEEP S--></s>
  
 <s id="id.000393">A quo etiam forta&longs;&longs;e proma&shy;<lb/>nauit Senariolus, qui hic citatur ab Ari&longs;totele, ad probandum <lb/>homines arte vincere ea, &agrave; quibus natura vincuntur. </s> <s id="id.000393">A quo etiam forta&longs;&longs;e proma&shy;<lb/>nauit Senariolus, qui hic citatur ab Ari&longs;totele, ad probandum <lb/>homines arte vincere ea, &agrave; quibus natura vincuntur. </s>
  
 <s id="id.000394">quod cumfa&shy;<lb/>ciunt in &yuml;s, in quibus iudicio omnium longe &agrave; natura &longs;uperantur<emph.end type="italics"/><lb/><foreign lang="greek">w_<gap/>adozo/poioi,</foreign> <emph type="italics"/>cum Galeno vocari poterunt.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000394">quod cum fa&shy;<lb/>ciunt in ijs, in quibus iudicio omnium longe &agrave; natura &longs;uperantur<emph.end type="italics"/><lb/><foreign lang="greek">w_<gap/>adoxo/poioi,</foreign> <emph type="italics"/>cum Galeno vocari poterunt.<emph.end type="italics"/></s></p><p type="main">
  
 <s id="id.000395">Vt in his, qu&aelig; cum] <emph type="italics"/>Vt cum magnas marmorum moles, tra&shy;<lb/>bes, columnas, colo&longs;&longs;os transferimus, &amp; erigimus, naues &longs;ubduci&shy;<lb/>mus in mare, quod fecit Archimedes conspiciente Hierone rege <lb/>Syracu&longs;arum, Helepoles amplas &longs;upra muros attrahimus, quod <lb/>fecit Callias Rhodien&longs;ibus conspicientibus, Equum Troianum in <lb/>vrbem adducimus (erat enim aliud nihil <expan abbr="qu&atilde;">quam</expan> machina, vt ait po&euml;ta,<emph.end type="italics"/></s></p><p type="main"> <s id="id.000395">Vt in his, qu&aelig; cum] <emph type="italics"/>Vt cum magnas marmorum moles, tra&shy;<lb/>bes, columnas, colo&longs;&longs;os transferimus, &amp; erigimus, naues &longs;ubduci&shy;<lb/>mus in mare, quod fecit Archimedes conspiciente Hierone rege <lb/>Syracu&longs;arum, Helepoles amplas &longs;upra muros attrahimus, quod <lb/>fecit Callias Rhodien&longs;ibus conspicientibus, Equum Troianum in <lb/>vrbem adducimus (erat enim aliud nihil <expan abbr="qu&atilde;">quam</expan> machina, vt ait po&euml;ta,<emph.end type="italics"/></s></p><p type="main">
  
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 <s id="id.000397"><emph type="italics"/>quales mult&aelig; apud Vegetium &amp; Heronem mechanicum.) bom&shy;<lb/>bardas ingentes ad locum destinatum conuertimus.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000397"><emph type="italics"/>quales mult&aelig; apud Vegetium &amp; Heronem mechanicum.) bom&shy;<lb/>bardas ingentes ad locum destinatum conuertimus.<emph.end type="italics"/></s></p><p type="main">
  
 <s id="id.000398"><gap/></s></p><p type="main"> <s id="id.000398"><foreign lang="greek"><gap/></foreign></s></p><p type="main">
  
 <s id="id.000399">Sunt vero h&aelig;c proble&shy;<lb/>matis Phy&longs;icis, nec omni&shy;<lb/>no <expan abbr="ead&etilde;">eadem</expan>, nec vald&egrave; di&longs;&longs;imi&shy;<lb/>lia: &longs;ed con&longs;entanea theo&shy;<lb/>tematis, tum mathemati&shy;<lb/>cis, tum Phy&longs;icis. <!-- KEEP S--></s> <s id="id.000399">Sunt vero h&aelig;c proble&shy;<lb/>matis Phy&longs;icis, nec omni&shy;<lb/>no <expan abbr="ead&etilde;">eadem</expan>, nec vald&egrave; di&longs;&longs;imi&shy;<lb/>lia: &longs;ed con&longs;entanea theo&shy;<lb/>tematis, tum mathemati&shy;<lb/>cis, tum Phy&longs;icis. <!-- KEEP S--></s>
  
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 <s id="id.000401">COMMENTARIVS.<!-- KEEP S--></s></p><p type="main"> <s id="id.000401">COMMENTARIVS.<!-- KEEP S--></s></p><p type="main">
  
 <s id="id.000402"><emph type="italics"/>Apud Euclidem problema &agrave; theoremate di&longs;tinguitur, quod <lb/>hoc iubeat aliquid contemplari: illud fieri: pa&szlig;im 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, &amp; al&yuml;s pro vtroque, vt hic, indifferenter legitur. </s> <s id="id.000402"><emph type="italics"/>Apud Euclidem problema &agrave; theoremate di&longs;tinguitur, quod <lb/>hoc iubeat aliquid contemplari: illud fieri: pa&szlig;im 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, &amp; alijs pro vtroque, vt hic, indifferenter legitur. </s>
  
 <s id="id.000403">Qualia <lb/>autem problemata in Mechanicis habeat tractanda explicat Ari&shy;<lb/>&longs;toteles, dicitque ea e&longs;&longs;e, qu&aelig; &longs;int con&longs;entanea Phy&longs;icis &amp; Mathe&shy;<lb/>maticis, vt qu&aelig; habeant &longs;ubiectum petitum &egrave; Phy&longs;icis. <!-- KEEP S--></s> <s id="id.000403">Qualia <lb/>autem problemata in Mechanicis habeat tractanda explicat Ari&shy;<lb/>&longs;toteles, dicitque ea e&longs;&longs;e, qu&aelig; &longs;int con&longs;entanea Phy&longs;icis &amp; Mathe&shy;<lb/>maticis, vt qu&aelig; habeant &longs;ubiectum petitum &egrave; Phy&longs;icis. <!-- KEEP S--></s>
  
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 <s id="id.000412">H&aelig;c enim &longs;i abunde &longs;uppetant, nec ma&shy;<lb/>teria omnino repugnet, nihil non fieri poterit.<emph.end type="italics"/></s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.053.jpg" pagenum="14"/><p type="main"> <s id="id.000412">H&aelig;c enim &longs;i abunde &longs;uppetant, nec ma&shy;<lb/>teria omnino repugnet, nihil non fieri poterit.<emph.end type="italics"/></s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.053.jpg" pagenum="14"/><p type="main">
  
 <s id="id.000413"><gap/></s></p><p type="main"> <s id="id.000413"><foreign lang="greek"><gap/></foreign></s></p><p type="main">
  
 <s id="id.000414">Dubitantur <expan abbr="aut&etilde;">autem</expan> in hoc <lb/>genere ea, qu&aelig; de vecte di&shy;<lb/>cuntur. </s> <s id="id.000414">Dubitantur <expan abbr="aut&etilde;">autem</expan> in hoc <lb/>genere ea, qu&aelig; de vecte di&shy;<lb/>cuntur. </s>
  
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 <s id="id.000422">Fieri tamen ratio repugnat. </s> <s id="id.000422">Fieri tamen ratio repugnat. </s>
  
 <s id="id.000423">Nam in omni motu mouens pr&aelig;ua&shy;<lb/>lere debet mobili: h&icirc;c exigua potentia e&longs;t mouens: magnum pondus <lb/>e&longs;t mobile: illa quatenus exigua e&longs;t, &amp; ante per &longs;e impotens, atque <lb/>infirma, e&longs;t in&aelig;quale minus: hoc quatenus magnum, e&longs;t in&aelig;quale <lb/>maius, &amp; ei addito vectis onere maius adhuc effici videtur: non <lb/>igitur exigua potentia magno oneri &amp; adaucto in motu pr&aelig;ualer&shy;<lb/>debet. </s> <s id="id.000423">Nam in omni motu mouens pr&aelig;ua&shy;<lb/>lere debet mobili: h&icirc;c exigua potentia e&longs;t mouens: magnum pondus <lb/>e&longs;t mobile: illa quatenus exigua e&longs;t, &amp; ante per &longs;e impotens, atque <lb/>infirma, e&longs;t in&aelig;quale minus: hoc quatenus magnum, e&longs;t in&aelig;quale <lb/>maius, &amp; ei addito vectis onere maius adhuc effici videtur: non <lb/>igitur exigua potentia magno oneri &amp; adaucto in motu pr&aelig;ua&shy;<lb/>lere debet. </s>
  
 <s id="id.000424">Si non pr&aelig;ualet, non mouet: mouet tamen: Relinquitur <lb/>ergo vt exi&longs;timemus aliquam cau&longs;am in hoc problemate motus eius <lb/>apparentis latentem &longs;ube&longs;&longs;e, dignam Philo&longs;ophi indagatione.<emph.end type="italics"/></s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.054.jpg" pagenum="15"/><p type="main"> <s id="id.000424">Si non pr&aelig;ualet, non mouet: mouet tamen: Relinquitur <lb/>ergo vt exi&longs;timemus aliquam cau&longs;am in hoc problemate motus eius <lb/>apparentis latentem &longs;ube&longs;&longs;e, dignam Philo&longs;ophi indagatione.<emph.end type="italics"/></s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.054.jpg" pagenum="15"/><p type="main">
  
 <s id="id.000425"><gap/></s></p><p type="main"> <s id="id.000425"><foreign lang="greek"><gap/></foreign></s></p><p type="main">
  
 <s id="id.000426"><expan abbr="Omni&utilde;">Omnium</expan> ver&ograve; talium cir&shy;<lb/>culus continet cau&longs;&aelig; prin&shy;<lb/>cipium. </s> <s id="id.000426"><expan abbr="Omni&utilde;">Omnium</expan> ver&ograve; talium cir&shy;<lb/>culus continet cau&longs;&aelig; prin&shy;<lb/>cipium. </s>
  
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 <s id="id.000435"><emph type="italics"/>Ergo &agrave; circulo prodire id quod e&longs;t admirabile in vecte, mechani&shy;<lb/>ci&longs;que problematis non e&longs;t alienum.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000435"><emph type="italics"/>Ergo &agrave; circulo prodire id quod e&longs;t admirabile in vecte, mechani&shy;<lb/>ci&longs;que problematis non e&longs;t alienum.<emph.end type="italics"/></s></p><p type="main">
  
 <s id="id.000436"><gap/></s></p><p type="main"> <s id="id.000436"><foreign lang="greek"><gap/></foreign></s></p><p type="main">
  
 <s id="id.000437">Maxim&egrave; ver&ograve; mirabile <lb/>e&longs;t contraria fibi inuicem <lb/>&longs;imul fieri: Atqui circulus <lb/>ex iis con&longs;titutus e&longs;t. </s> <s id="id.000437">Maxim&egrave; ver&ograve; mirabile <lb/>e&longs;t contraria sibi inuicem <lb/>&longs;imul fieri: Atqui circulus <lb/>ex iis con&longs;titutus e&longs;t. </s>
  
 <s id="id.000438">Sta&shy;<lb/>tim enim factus e&longs;t ex mo&shy;<lb/>to, &amp; immobili, quorum <lb/>natura &longs;ibi inuicem con&shy;<lb/>traria e&longs;t. </s> <s id="id.000438">Sta&shy;<lb/>tim enim factus e&longs;t ex mo&shy;<lb/>to, &amp; immobili, quorum <lb/>natura &longs;ibi inuicem con&shy;<lb/>traria e&longs;t. </s>
  
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 <s id="id.000442">Ex his triplex deprehenditur <lb/>in circulo dum fit: duplex vero dum factus e&longs;t. </s> <s id="id.000442">Ex his triplex deprehenditur <lb/>in circulo dum fit: duplex vero dum factus e&longs;t. </s>
  
 <s id="id.000443">Primum enim dum fit <lb/>habet hoc admirabile, quod fiat ab vna recta, cuius vnum extremo&shy;<lb/>rum quie&longs;cit &amp; fixum e&longs;t: alterum vn&agrave; cum tota linea mouetur: &longs;e&shy;<lb/>cundum quod in mota linea puncta, cum infinita &longs;int, &amp; omnia &longs;i&shy;<lb/>mul moueantur, in&aelig;qualiter tamen moueantur: Tertium quod extre&shy;<lb/>mum motum eodem tempore duobus motibus contrar&yuml;s, vno natu&shy;<lb/>rali ad peripheriam &longs;cilicet, altero violento ad centrum moueatur. </s> <s id="id.000443">Primum enim dum fit <lb/>habet hoc admirabile, quod fiat ab vna recta, cuius vnum extremo&shy;<lb/>rum quie&longs;cit &amp; fixum e&longs;t: alterum vn&agrave; cum tota linea mouetur: &longs;e&shy;<lb/>cundum quod in mota linea puncta, cum infinita &longs;int, &amp; omnia &longs;i&shy;<lb/>mul moueantur, in&aelig;qualiter tamen moueantur: Tertium quod extre&shy;<lb/>mum motum eodem tempore duobus motibus contrarijs, vno natu&shy;<lb/>rali ad peripheriam &longs;cilicet, altero violento ad centrum moueatur. </s>
  
 <s id="id.000444">In <lb/>facto ver&ograve; hoc admirabile e&longs;t, quod eius terminus vna linea exi&shy;<lb/>&longs;tens, ob&iacute;dque latitudinis expers, concauum tamen &amp; conuexum, <lb/>qu&aelig; quodammodo contraria &longs;unt, admittat: pr&aelig;terea mobilitas, <lb/>qu&aelig; ine&longs;t, admirabilis e&longs;t, quia eodem tempore ad contrarias loci dif&shy;<lb/>ferentias, vt &longs;ur&longs;um deor&longs;um: dextror&longs;um &longs;inistror&longs;um, fiat. </s> <s id="id.000444">In <lb/>facto ver&ograve; hoc admirabile e&longs;t, quod eius terminus vna linea exi&shy;<lb/>&longs;tens, ob&iacute;dque latitudinis expers, concauum tamen &amp; conuexum, <lb/>qu&aelig; quodammodo contraria &longs;unt, admittat: pr&aelig;terea mobilitas, <lb/>qu&aelig; ine&longs;t, admirabilis e&longs;t, quia eodem tempore ad contrarias loci dif&shy;<lb/>ferentias, vt &longs;ur&longs;um deor&longs;um: dextror&longs;um &longs;inistror&longs;um, fiat. </s>
  
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 <s id="id.000446">Sed pr&aelig;ter h&aelig;c, <lb/>qu&aelig; ab Ari&longs;totele de circulo dicuntur, valde notabilia &longs;unt &amp; alia, <lb/>qu&aelig; in Geometria in eo ine&longs;&longs;e, partim ponuntur, partim demon&longs;trata <lb/>&longs;unt. </s> <s id="id.000446">Sed pr&aelig;ter h&aelig;c, <lb/>qu&aelig; ab Ari&longs;totele de circulo dicuntur, valde notabilia &longs;unt &amp; alia, <lb/>qu&aelig; in Geometria in eo ine&longs;&longs;e, partim ponuntur, partim demon&longs;trata <lb/>&longs;unt. </s>
  
 <s id="id.000447">Primum quod vna linea terminetur, e&acirc;que &longs;implici, &longs;imilari <lb/>vniformi, &amp; carente principio, &amp; fine, neque tamen infinita, vt <lb/>cuius, cum partes aliquot &longs;umpt&aelig; &longs;unt, qu&aelig; re&longs;tant, minus &longs;int, quam <lb/>ante quam &longs;umpt&aelig; e&longs;&longs;ent, quod repugnat infinito in magnitudine: &longs;ed <lb/>tota e&longs;t, &amp; perfecta: vnde circulus figura e&longs;t planarum &longs;implici&szlig;i&shy;<lb/>ma, regulari&szlig;ima, perfecti&szlig;ima: Deinde quod ea linea non &longs;it an&shy;<lb/>gulus, ad angulum tamen proxime accedat, vt o&longs;tendimus in no&longs;tro <lb/>libello de angulo contactus, &amp; ob id quod&abreve;modo vndequaque angu&shy;<lb/>lata, cum nu&longs;quam &longs;it, dici po&szlig;it, &amp; figura<emph.end type="italics"/> <foreign lang="greek">w_an/gwnos &amp; o(lo/gwnos,</foreign><lb/><emph type="italics"/>tum prima figurarum &amp; vltima: po&longs;tea, quod ex infinitis punctis <lb/>qu&aelig; in &longs;patio ab ea comprehen&longs;o &longs;unt, vnum e&longs;t tantum, &agrave; quo omnes <lb/>rect&aelig; ad peripheriam duct&aelig;, &longs;unt &aelig;quales: quod Diametro bifariam <lb/>&longs;ecetur: quod hinc &longs;emicirculus circa Diametrum manentem <lb/>voluens, quou&longs;que redierit ad eum locum vnde moueri c&oelig;pit, &longs;ph&aelig;&shy;<lb/>ram constituat, corporum &longs;implici&szlig;imum, capaci&szlig;imum, mobili&szlig;i&shy;<lb/>mum, mouenti&szlig;imum: quod circulus omnium figurarum eiu&longs;dem <lb/>perimetri &longs;it capaci&szlig;ima: quod vno puncto lineam rectam attin&shy;<lb/>gat, &longs;icque o&longs;&longs;en&longs;ationibus &amp; occur&longs;ationibus minimum pateat, <lb/>&longs;icque in&longs;i&longs;tens dimidia &longs;ui totius parte nutet, vnde propen&longs;i&szlig;imus <lb/>e&longs;t ad motum, &amp; dimotus cum moueat annexa, apti&szlig;imus quoque<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.056.jpg" pagenum="17"/><emph type="italics"/>erit ad mouendum: po&longs;trem&ograve; quod inter rectam circulum tangen&shy;<lb/>tem, &amp; circuli peripheriam altera recta &longs;ine &longs;ectione cadere non <lb/>po&szlig;it. </s> <s id="id.000447">Primum quod vna linea terminetur, e&acirc;que &longs;implici, &longs;imilari <lb/>vniformi, &amp; carente principio, &amp; fine, neque tamen infinita, vt <lb/>cuius, cum partes aliquot &longs;umpt&aelig; &longs;unt, qu&aelig; re&longs;tant, minus &longs;int, quam <lb/>ante quam &longs;umpt&aelig; e&longs;&longs;ent, quod repugnat infinito in magnitudine: &longs;ed <lb/>tota e&longs;t, &amp; perfecta: vnde circulus figura e&longs;t planarum &longs;implici&szlig;i&shy;<lb/>ma, regulari&szlig;ima, perfecti&szlig;ima: Deinde quod ea linea non &longs;it an&shy;<lb/>gulus, ad angulum tamen proxime accedat, vt o&longs;tendimus in no&longs;tro <lb/>libello de angulo contactus, &amp; ob id <expan abbr= "quod&atilde;modo">quodammodo</expan> vndequaque angu&shy;<lb/>lata, cum nu&longs;quam &longs;it, dici po&szlig;it, &amp; figura<emph.end type="italics"/> <foreign lang="greek">w_an/gwnos &amp; o(lo/gwnos,</foreign><lb/><emph type="italics"/>tum prima figurarum &amp; vltima: po&longs;tea, quod ex infinitis punctis <lb/>qu&aelig; in &longs;patio ab ea comprehen&longs;o &longs;unt, vnum e&longs;t tantum, &agrave; quo omnes <lb/>rect&aelig; ad peripheriam duct&aelig;, &longs;unt &aelig;quales: quod Diametro bifariam <lb/>&longs;ecetur: quod hinc &longs;emicirculus circa Diametrum manentem <lb/>voluens, quou&longs;que redierit ad eum locum vnde moueri c&oelig;pit, &longs;ph&aelig;&shy;<lb/>ram constituat, corporum &longs;implici&szlig;imum, capaci&szlig;imum, mobili&szlig;i&shy;<lb/>mum, mouenti&szlig;imum: quod circulus omnium figurarum eiu&longs;dem <lb/>perimetri &longs;it capaci&szlig;ima: quod vno puncto lineam rectam attin&shy;<lb/>gat, &longs;icque offen&longs;ationibus &amp; occur&longs;ationibus minimum pateat, <lb/>&longs;icque in&longs;i&longs;tens dimidia &longs;ui totius parte nutet, vnde propen&longs;i&szlig;imus <lb/>e&longs;t ad motum, &amp; dimotus cum moueat annexa, apti&szlig;imus quoque<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.056.jpg" pagenum="17"/><emph type="italics"/>erit ad mouendum: po&longs;trem&ograve; quod inter rectam circulum tangen&shy;<lb/>tem, &amp; circuli peripheriam altera recta &longs;ine &longs;ectione cadere non <lb/>po&szlig;it. </s>
  
 <s id="id.000448">quod 16. prop.  <s id="id.000448">quod 16. prop. lib. 3. elem. e&longs;t demon&longs;tratum.<emph.end type="italics"/></s></p><p type="main">
  
 lib.  
  
 3. elem. </s> 
  
 <s id="id.000449">e&longs;t demon&longs;tratum.<emph.end type="italics"/></s></p><p type="main"> 
  
 <s id="id.000450">Imprimis enim] <emph type="italics"/>Prima repugnantia e&longs;t in circulo, quod fiat <lb/>&egrave; moto &amp; quieto, qu&aelig; &longs;unt oppo&longs;ita ex genere priuantium, vnde rur&shy;<lb/>&longs;us concluditur, minus e&longs;&longs;e mirum, id e&longs;t minus ab&longs;urdum &agrave; circulo <lb/>produci contraria. </s> <s id="id.000450">Imprimis enim] <emph type="italics"/>Prima repugnantia e&longs;t in circulo, quod fiat <lb/>&egrave; moto &amp; quieto, qu&aelig; &longs;unt oppo&longs;ita ex genere priuantium, vnde rur&shy;<lb/>&longs;us concluditur, minus e&longs;&longs;e mirum, id e&longs;t minus ab&longs;urdum &agrave; circulo <lb/>produci contraria. </s>
  
 <s id="id.000451">Circulum autem fieri ex moto &amp; quieto patet his, <lb/>qui eius fabricam repetent &egrave; 3. po&longs;tulato element. </s> <s id="id.000451">Circulum autem fieri ex moto &amp; quieto patet his, <lb/>qui eius fabricam repetent &egrave; 3. po&longs;tulato element.Eucl.</s>
  
 <s id="id.000452">Eucl. <!-- REMOVE S-->Ibi enim po&shy;<lb/>&longs;tulatur, vt &egrave; dato centro &amp; interuallo circulum de&longs;cribere conce&shy;<lb/>datur. </s> <s id="id.000452">Ibi enim po&shy;<lb/>&longs;tulatur, vt &egrave; dato centro &amp; interuallo circulum de&longs;cribere conce&shy;<lb/>datur. </s>
  
  
  
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 <s id="id.000455">Altera pars &longs;taret, pars altera du&shy;<lb/>ceret orbem.</s></p><p type="main"> <s id="id.000455">Altera pars &longs;taret, pars altera du&shy;<lb/>ceret orbem.</s></p><p type="main">
  
 <s id="id.000456"><emph type="italics"/>Sit igitur recta A B inter extrema due&shy;<lb/>rum brachiorum circini A C B diua&shy;<lb/>ricati per interuallum line&aelig; A B, <lb/>cuius extremum A maneat: alterum B <lb/>line&aelig; motu feratur per D quou&longs;que redeat <lb/>ad B: &longs;icque circulus B D B erit fa&shy;<lb/>ctus. </s> <s id="id.000456"><emph type="italics"/>Sit igitur recta A B inter extrema duo&shy;<lb/>rum brachiorum circini A C B diua&shy;<lb/>ricati per interuallum line&aelig; A B, <lb/>cuius extremum A maneat: alterum B <lb/>line&aelig; motu feratur per D quou&longs;que redeat <lb/>ad B: &longs;icque circulus B D B erit fa&shy;<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"/><!-- KEEP S--></s></p><p type="main"> <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"/><!-- KEEP S--></s></p><p type="main">
  
 <s id="id.000458"><gap/></s></p><p type="main"> <s id="id.000458"><foreign lang="greek"><gap/></foreign></s></p><p type="main">
  
  <s id="id.000459">Primum &longs;iquidem line&aelig; <lb/>ip&longs;um circulum <expan abbr="compre-hend&etilde;ti">compre&shy;<lb/>hendenti</expan>, licet latitudinem <lb/>nullam habeat, contraria <lb/>quodammodo, cauum &amp; <lb/>conuexum ine&longs;&longs;e <expan abbr="appar&etilde;t">apparent</expan>. <lb/></s>
  
  <s id="id.000460">H&aelig;c autem ita inter &longs;e di&shy;<lb/>&longs;tant, vt <expan abbr="magn&utilde;">magnum</expan> &amp; paruum. <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.057.jpg" pagenum="18"/></s>
  
 <s id="id.000459">Primum &longs;iquidem line&aelig; <lb/>ip&longs;um circulum <expan abbr="compre-hend&etilde;ti">compre&shy;<lb/>hendenti</expan>, licet latitudinem <lb/>nullam habeat, contraria <lb/>quodammodo, cauum &amp; <lb/>conuexum ine&longs;le <expan abbr="appar&etilde;t">apparent</expan>. <lb/></s> <s><foreign lang="greek"><gap/></foreign></s>
  
 <s id="id.000460">H&aelig;c autem ita inter&longs;e di&shy;<lb/>&longs;tant, vt <expan abbr="magn&utilde;">magnum</expan> &amp; paruum. <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.057.jpg" pagenum="18"/><gap/><lb/>horum enim medium e&longs;t <lb/>&aelig;quale: illorum ver&ograve; re&shy;<lb/>ctum. </s> <s>horum enim medium e&longs;t <lb/>&aelig;quale: illorum ver&ograve; re&shy;<lb/>ctum. </s>
  
 <s id="id.000461">Ide&ograve; inuicem cum <lb/>commutantur, pri&ugrave;s ne&shy;<lb/>ce&longs;&longs;e e&longs;t &aelig;qualia fieri: li&shy;<lb/>neam &longs;an&egrave; rectam, cum ex <lb/>conuexa fit caua: &amp; rur&longs;us <lb/>ex ip&longs;a fit conuexa &amp; ro&shy;<lb/>tunda. </s> <s id="id.000461">Ide&ograve; inuicem cum <lb/>commutantur, pri&ugrave;s ne&shy;<lb/>ce&longs;&longs;e e&longs;t &aelig;qualia fieri: li&shy;<lb/>neam &longs;an&egrave; rectam, cum ex <lb/>conuexa fit caua: &amp; rur&longs;us <lb/>ex ip&longs;a fit conuexa &amp; ro&shy;<lb/>tunda. </s>
  
 <s id="id.000462">Atque vnum hoc <lb/>e&longs;t ex ab&longs;urdis qu&ecedil; in&longs;unt <lb/>circulo.</s></p><p type="head"> <s id="id.000462">Atque vnum hoc <lb/>e&longs;t ex ab&longs;urdis qu&ecedil; in&longs;unt <lb/>circulo.</s></p><p type="head">
  
 <s id="id.000463">COMMENTARIVS.<!-- KEEP S--></s></p><p type="main"> <s id="id.000463">COMMENTARIVS.</s></p><p type="main">
  
 <s id="id.000464">Primum &longs;iquidem.] <emph type="italics"/>Vetu&longs;tatis iniuria multas veterum li&shy;<lb/>bris, &amp; huic &longs;ane irrep&longs;i&longs;&longs;e mendas, non e&longs;t res dubia, vt hoc loco<emph.end type="italics"/><lb/><foreign lang="greek">w_rw/ton</foreign> <emph type="italics"/>pro<emph.end type="italics"/> <foreign lang="greek">deu/teron.</foreign> <emph type="italics"/>Namque h&icirc;cnon prima, vtiam patuit: &longs;ed &longs;e&shy;<lb/>cunda e&longs;t in circulo repugnantia. </s> <s id="id.000464">Primum &longs;iquidem.] <emph type="italics"/>Vetu&longs;tatis iniuria multas veterum li&shy;<lb/>bris, &amp; huic &longs;ane irrep&longs;i&longs;&longs;e mendas, non e&longs;t res dubia, vt hoc loco<emph.end type="italics"/><lb/><foreign lang="greek">w_rw/ton</foreign> <emph type="italics"/>pro<emph.end type="italics"/> <foreign lang="greek">deu/teron.</foreign> <emph type="italics"/>Namque h&icirc;cnon prima, vtiam patuit: &longs;ed &longs;e&shy;<lb/>cunda e&longs;t in circulo repugnantia. </s>
  
 <s id="id.000465">Eaque ex eo quod cum circuli peri&shy;<lb/>pheria &longs;ir vna linea def. </s> <s id="id.000465">Eaque ex eo quod cum circuli peri&shy;<lb/>pheria &longs;it vna linea def. 15. lib. 1. elem. &amp; idcirco latitudinis expers <lb/>def. 2. lib. eiu&longs;dem: habeat tamen in &longs;e contraria conuexum &longs;cilicet, <lb/>&amp; concauum: illud quidem qu&agrave; &longs;pectat foras: hoc vero qu&agrave; intra. <lb/></s>
  
 <s id="id.000466">15. lib.  
  
 1. elem. </s> 
  
 <s id="id.000467">&amp; idcirco latitudinis expers <lb/>def. </s> 
  
 <s id="id.000468">2. lib. <!-- REMOVE S-->eiu&longs;dem: habeat tamen in &longs;econtraria conuexum &longs;cilicet, <lb/>&amp; concauum: illud quidem qu&agrave; &longs;pectat foras: hoc vero qu&agrave; intra. <lb/></s> 
  
  <s id="id.000469">vbi nota Ari&longs;totelem dixi&longs;&longs;e h&aelig;c<emph.end type="italics"/> <foreign lang="greek">en)an<gap/>ia w_<gap/>s</foreign> <emph type="italics"/>contraria quodam&shy;<lb/>modo. </s>
  
  <s id="id.000470">Nec enim vere contraria &longs;unt, quia vere contraria &longs;unt ea, <lb/>qu&aelig; &longs;ecundum &longs;eip&longs;a &longs;umpta, ex &longs;eip&longs;is extreme di&longs;tant, &amp; vnde &longs;e <lb/>expellere nata &longs;int, habent: at h&aelig;c conuexum &amp; concauum non &longs;ic <lb/>extreme di&longs;tant: &longs;ed ratione &longs;itus partium in diuer&longs;is locorum diffe&shy;<lb/>rentijs, quod &longs;cilicet ali&aelig; al&yuml;s &longs;int al-<emph.end type="italics"/><lb/><figure id="id.035.01.057.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.057.1.jpg"/><lb/><emph type="italics"/>tiores, vel depre&szlig;iores. </s>
  
 <s id="id.000469">vbinota Ari&longs;totelem dixi&longs;&longs;e h&aelig;e<emph.end type="italics"/> <foreign lang="greek">en)an<gap/>ia w_<gap/>s</foreign> <emph type="italics"/>contraria quodam&shy;<lb/>modo. </s> <s id="id.000471">Cum enim re&shy;<lb/>ctum &longs;it id in lineis quod ex &aelig;quo iacet <lb/>inter &longs;ua extrema def. 2. lib. 1. &amp; vt <lb/>linea A B, curuum erit quod non ex <lb/>&aelig;quo iacebit, &longs;ed altius aut depre&szlig;ius: <lb/>idque &longs;i inter extrema vbique attollatur: <lb/>conuexum vt C E D: &longs;i vero vbique <lb/>deprimatur concauum, vt C F D qu&aelig; eadem e&longs;t linea ex &longs;e, &longs;ed <lb/>ex locis E E &amp; F F partium mutata. </s>
  
 <s id="id.000470">Nec enim vere contraria &longs;unt, quia vere contraria &longs;untea, <lb/>qu&aelig; &longs;ecundum &longs;eip&longs;a &longs;umpta, ex &longs;eip&longs;is extreme di&longs;tant, &amp; vnde &longs;e <lb/>expellere nata &longs;int, habent: at h&aelig;c conuexum &amp; concauum non &longs;ic <lb/>extreme di&longs;tant: &longs;ed ratione &longs;itus partium in diuer&longs;is locorum diffe&shy;<lb/>rent&yuml;s, quod &longs;cilicet ali&aelig; al&yuml;s &longs;int al-<emph.end type="italics"/><lb/><figure id="id.035.01.057.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.057.1.jpg"/><lb/><emph type="italics"/>tiores, vel depre&szlig;iores. </s> <s>Cum igitur ab eadem C D<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.058.jpg" pagenum="19"/><emph type="italics"/>non &longs;e expellant non erunt ver&egrave; contraria: qualia tamen apparent ex <lb/>di&longs;tantia &amp; differentiis locorum &longs;ur&longs;um deor&longs;um.<emph.end type="italics"/></s></p><p type="main">
  
 <s id="id.000471">Cum enim re&shy;<lb/>ctum &longs;it id in lineis quod ex &aelig;quo iacet <lb/>inter &longs;ua extrema def. </s> 
  
 <s id="id.000472">2. lib.  
  
 1. &amp; vt <lb/>linea A B, curuum erit quod non ex <lb/>&aelig;quo iacebit, &longs;ed altius aut depre&szlig;ius: <lb/>idque &longs;i inter extrema vbique attollatur: <lb/>conuexum vt C E D: &longs;i vero vbique <lb/>deprimatur concauum, vt C F D qu&aelig; eadem e&longs;t linea ex &longs;e, &longs;ed <lb/>ex locis E E &amp; F F partium mutata, Cum igitur ab eadem C D<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.058.jpg" pagenum="19"/><emph type="italics"/>non &longs;e expellant non erunt ver&egrave; contraria: qualia tamen apparent ex <lb/>di&longs;tantia &amp; differentiis locorum &longs;ur&longs;um deor&longs;um.<emph.end type="italics"/></s></p><p type="main"> 
  
 <s id="id.000473">H&aelig;c autem ita.] <emph type="italics"/>Similitudine comprobatur conuexum &amp; <lb/>concauum contraria e&longs;&longs;e. </s> <s id="id.000473">H&aelig;c autem ita.] <emph type="italics"/>Similitudine comprobatur conuexum &amp; <lb/>concauum contraria e&longs;&longs;e. </s>
  
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 <s id="id.000475">&longs;unt igitur conuexum &amp; concauum <lb/>contraria. </s> <s id="id.000475">&longs;unt igitur conuexum &amp; concauum <lb/>contraria. </s>
  
 <s id="id.000476">Sed &amp; hic a&longs;&longs;umemus per eandem definitionem contra&shy;<lb/>riorum ante po&longs;itam, &amp; ex &longs;ententia Ari&longs;totelis in categ. <!-- KEEP S--></s> <s id="id.000476">Sed &amp; hic a&longs;&longs;umemus per eandem definitionem contra&shy;<lb/>riorum ante po&longs;itam, &amp; ex &longs;ententia Ari&longs;totelis in categ. Quanti&shy;<lb/>tatis, magnum &amp; paruum apparenter duntaxat e&longs;&longs;e contraria. </s>
  
 <s id="id.000477">Quanti&shy;<lb/>tatis, magnum &amp; paruum apparenter duntaxat e&longs;&longs;e contraria. </s> 
  
 <s id="id.000478">Ap&shy;<lb/>parenter dico vt illa priora, quia habent aliquid de definitione con&shy;<lb/>trariorum, quod &longs;ibi conueniat, &longs;cilicet di&longs;tare inter&longs;e in eodem ge&shy;<lb/>nere, &amp; habere medium: &longs;ed non vere tamen e&longs;&longs;e. </s> <s id="id.000478">Ap&shy;<lb/>parenter dico vt illa priora, quia habent aliquid de definitione con&shy;<lb/>trariorum, quod &longs;ibi conueniat, &longs;cilicet di&longs;tare inter&longs;e in eodem ge&shy;<lb/>nere, &amp; habere medium: &longs;ed non vere tamen e&longs;&longs;e. </s>
  
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 <s id="id.000487">Atque vnum hoc e&longs;t.] <foreign lang="greek">to\ a)/topcn.</foreign> <emph type="italics"/>Hic vt &amp; alibi &longs;&aelig;pius <lb/>pro<emph.end type="italics"/> <foreign lang="greek"><gap/>auma/ sion</foreign> <emph type="italics"/>&longs;umitur, id e&longs;t igitur e&longs;&longs;e conuexum &amp; concauum <lb/>in linea vnum e&longs;t ex admirabilibus circuli.<emph.end type="italics"/></s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.059.jpg" pagenum="20"/><p type="main"> <s id="id.000487">Atque vnum hoc e&longs;t.] <foreign lang="greek">to\ a)/topcn.</foreign> <emph type="italics"/>Hic vt &amp; alibi &longs;&aelig;pius <lb/>pro<emph.end type="italics"/> <foreign lang="greek"><gap/>auma/ sion</foreign> <emph type="italics"/>&longs;umitur, id e&longs;t igitur e&longs;&longs;e conuexum &amp; concauum <lb/>in linea vnum e&longs;t ex admirabilibus circuli.<emph.end type="italics"/></s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.059.jpg" pagenum="20"/><p type="main">
  
 <s id="id.000488"><gap/></s></p><p type="main"> <s id="id.000488"><foreign lang="greek"><gap/></foreign></s></p><p type="main">
  
 <s id="id.000489">Secundum e&longs;t, quod con&shy;<lb/>trariis motionibus &longs;imul <lb/>moueatur. </s> <s id="id.000489">Secundum e&longs;t, quod con&shy;<lb/>trariis motionibus &longs;imul <lb/>moueatur. </s>
  
 <s id="id.000490">Simul enim an&shy;<lb/>tror&longs;um &amp; retror&longs;um mo&shy;<lb/>uetur: atque linea circu&shy;<lb/>lum <expan abbr="de&longs;crib&etilde;s">de&longs;cribens</expan> &longs;ic &longs;e haber, <lb/>vt ex quo loco extremum <lb/>illius incipiat, rur&longs;us ad <lb/>eundem redeat. </s> <s id="id.000490">Simul enim an&shy;<lb/>tror&longs;um &amp; retror&longs;um mo&shy;<lb/>uetur: atque linea circu&shy;<lb/>lum <expan abbr="de&longs;crib&etilde;s">de&longs;cribens</expan> &longs;ic &longs;e habet, <lb/>vt ex quo loco extremum <lb/>illius incipiat, rur&longs;us ad <lb/>eundem redeat. </s>
  
 <s id="id.000491">Id ip&longs;um <lb/>enim quod in ip&longs;a conti&shy;<lb/>nenter mota e&longs;t vltimum, <lb/>rur&longs;us primum euadit. </s> <s id="id.000491">Id ip&longs;um <lb/>enim quod in ip&longs;a conti&shy;<lb/>nenter mota e&longs;t vltimum, <lb/>rur&longs;us primum euadit. </s>
  
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 <s id="id.000497">Hoc autem e&longs;t contrarias motiones <lb/>&longs;imul habere. </s> <s id="id.000497">Hoc autem e&longs;t contrarias motiones <lb/>&longs;imul habere. </s>
  
 <s id="id.000498">Contrari&aelig; enim &longs;unt motiones apud Ari&longs;totelem in <lb/>categoria vbi &amp; li. </s> <s>Contrari&aelig; enim &longs;unt motiones apud Ari&longs;totelem in <lb/>categoria vbi &amp; li. 5. de Phy&longs;ico auditu ex diametralibus locorum, <lb/>ad qu&aelig; fiunt, di&longs;tantijs dextror&longs;um, &longs;ini&longs;tror&longs;um: &longs;ur&longs;um, deor&longs;um: <lb/>&amp; antror&longs;um, retror&longs;um.<emph.end type="italics"/></s></p><p type="main">
  
 <s id="id.000499">5. de Phy&longs;ico auditu ex diametralibus locorum, <lb/>ad qu&aelig; fiunt, di&longs;tant&yuml;s dextror&longs;um, &longs;ini&longs;tror&longs;um: &longs;ur&longs;um, deor&longs;um: <lb/>&amp; antror&longs;um, retror&longs;um.<emph.end type="italics"/></s></p><p type="main"> 
  
 <s id="id.000500">Atque linea circulum.] <emph type="italics"/>Cur circulus ant&egrave; &amp; pon&egrave; mouea-<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.060.jpg" pagenum="21"/><emph type="italics"/>tur, ratio adducitur &longs;umpta ab efficiente circuli cau&longs;a. </s> <s id="id.000500">Atque linea circulum.] <emph type="italics"/>Cur circulus ant&egrave; &amp; pon&egrave; mouea-<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.060.jpg" pagenum="21"/><emph type="italics"/>tur, ratio adducitur &longs;umpta ab efficiente circuli cau&longs;a. </s>
  
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 <s id="id.000502">Vt fit circulus ita mouetur.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000502">Vt fit circulus ita mouetur.<emph.end type="italics"/></s></p><p type="main">
  
 <s id="id.000503"><emph type="italics"/>Fit circulus &agrave; linea continenter mota circa fixum extremor<gap/>m <lb/>vnum, quou&longs;que redeat ad eum locum vnde moueri c&oelig;pit, quod <lb/>fieri non pote&longs;t ni&longs;i per loca qu&aelig; &longs;unt circa extremum fixum oppo&longs;i&shy;<lb/>ta deducatur, &amp; quod e&longs;t vltimum, rur&longs;us fiat primum.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000503"><emph type="italics"/>Fit circulus &agrave; linea continenter mota circa fixum extremorum <lb/>vnum, quou&longs;que redeat ad eum locum vnde moueri c&oelig;pit, quod <lb/>fieri non pote&longs;t ni&longs;i per loca qu&aelig; &longs;unt circa extremum fixum oppo&longs;i&shy;<lb/>ta deducatur, &amp; quod e&longs;t vltimum, rur&longs;us fiat primum.<emph.end type="italics"/></s></p><p type="main">
  
 <s id="id.000504"><emph type="italics"/>Ergo circulus mouetur per loca &egrave; diametro oppo&longs;ita circa extre&shy;<lb/>mum line&aelig; &agrave; qua fit fixum. </s> <s id="id.000504"><emph type="italics"/>Ergo circulus mouetur per loca &egrave; diametro oppo&longs;ita circa extre&shy;<lb/>mum line&aelig; &agrave; qua fit fixum. </s>
  
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 <s id="id.000506"><emph type="italics"/>Centrum enim in plano circundatur quatuor loci different&yuml;s, <lb/>propter duas qu&aelig; in ip&longs;o ad rectos &longs;e &longs;ecant dimen&longs;iones, vt in circu&shy;<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 pon&egrave;: &amp; cum in C, &longs;ur&longs;um: &amp; <lb/>in E, deor&longs;um, &amp; perueniens ad A B, eidem loco re&longs;tituetur, <lb/>&agrave; 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.000506"><emph type="italics"/>Centrum enim in plano circundatur quatuor loci different&yuml;s, <lb/>propter duas qu&aelig; in ip&longs;o ad rectos &longs;e &longs;ecant dimen&longs;iones, vt in circu&shy;<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 pon&egrave;: &amp; cum in C, &longs;ur&longs;um: &amp; <lb/>in E, deor&longs;um, &amp; perueniens ad A B, eidem loco re&longs;tituetur, <lb/>&agrave; 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 circulu<gap/>oue&shy;<lb/>tur, pote&longs;t dici ire, &amp; reuerti &longs;imul: &longs;ic <lb/>cum &longs;ph&aelig;ricum corpus mouetur, in fine <lb/>&longs;emper, &amp; principio motus &longs;ui, etiam tum <lb/>ire, tum reuerti veri&longs;imiliter dicetur.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000507">Vnde cum circulus moue&shy;<lb/>tur, pote&longs;t dici ire, &amp; reuerti &longs;imul: &longs;ic <lb/>cum &longs;ph&aelig;ricum corpus mouetur, in fine <lb/>&longs;emper, &amp; principio motus &longs;ui, etiam tum <lb/>ire, tum reuerti veri&longs;imiliter dicetur.<emph.end type="italics"/></s></p><p type="main">
  
 <s id="id.000508"><emph type="italics"/>C&aelig;terum notandum quod motiones dict&aelig; <lb/>e&longs;&longs;e in circulo, in&longs;unt quidem: &longs;ed non &longs;i&shy;<lb/>mul &longs;ecundum eandem partem. </s> <s id="id.000508"><emph type="italics"/>C&aelig;terum notandum quod motiones dict&aelig; <lb/>e&longs;&longs;e in circulo, in&longs;unt quidem: &longs;ed non &longs;i&shy;<lb/>mul &longs;ecundum eandem partem. </s>
  
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 <s id="id.000511">ex cuius tamen natura magnorum effe&shy;<lb/>ctuum po&longs;tea cau&longs;&aelig; repetuntur, cum diametri B D, vt inflexilis <lb/>circa A, centrum fixum mot&aelig;, &longs;i B, deprimatur, nece&longs;&longs;e e&longs;t a<gap/>e&shy;<lb/>rum extremum D, attolli: &amp; contra.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000511">ex cuius tamen natura magnorum effe&shy;<lb/>ctuum po&longs;tea cau&longs;&aelig; repetuntur, cum diametri B D, vt inflexilis <lb/>circa A, centrum fixum mot&aelig;, &longs;i B, deprimatur, nece&longs;&longs;e e&longs;t a<gap/>e&shy;<lb/>rum extremum D, attolli: &amp; contra.<emph.end type="italics"/></s></p><p type="main">
  
 <s id="id.000512">Propterea vt e&longs;t prius.] <emph type="italics"/>Conclu&longs;io generalis e&longs;t, huc, vt exi&shy;<lb/>&longs;timo, &egrave; fine primi huius capitis, vbi melius collocaretur, tr&agrave;spo&longs;ita, <lb/>quod amplius declarant ea, qu&aelig; &longs;ub&yuml;ciuntur de vecte &amp; libra, ad <lb/>qu&aelig; cum referat omnia Mechanica, &amp; ip&longs;a vectis &amp; libra referan-<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.061.jpg" pagenum="22"/><emph type="italics"/>tur ad circulum, &longs;equenti etiam capite, quod erat proximum, libr&aelig; <lb/>motiones explicat.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000512">Propterea vt e&longs;t prius.] <emph type="italics"/>Conclu&longs;io generalis e&longs;t, huc, vt exi&shy;<lb/>&longs;timo, &egrave; fine primi huius capitis, vbi melius collocaretur, <expan abbrev="tr&atilde;spo&longs;ita">transpo&longs;ita</expan>, <lb/>quod amplius declarant ea, qu&aelig; &longs;ubijciuntur de vecte &amp; libra, ad <lb/>qu&aelig; cum referat omnia Mechanica, &amp; ip&longs;a vectis &amp; libra referan-<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.061.jpg" pagenum="22"/><emph type="italics"/>tur ad circulum, &longs;equenti etiam capite, quod erat proximum, libr&aelig; <lb/>motiones explicat.<emph.end type="italics"/></s></p><p type="main">
  
 <s id="id.000513"><gap/></s></p><p type="main"> <s id="id.000513"><foreign lang="greek"><gap/></foreign></s></p><p type="main">
  
 <s id="id.000514">Pr&aelig;terea etiam, quod, <lb/>cum vna &longs;it ea linea, qu&aelig; <lb/>ex centro, nullum eorum, <lb/>qu&aelig; in ea &longs;unt, <expan abbr="p&utilde;ctorum">punctorum</expan>, <lb/>&aelig;qu&egrave; celeriter fertur: fed <lb/>hoc, quod longius e&longs;t ab <lb/>extremo eius immobili, <lb/>&longs;emper celerius: miranda <lb/>multa circa motiones cir&shy;<lb/>culi contingunt, vt in <expan abbr="&longs;e-qu&etilde;tibus">&longs;e&shy;<lb/>quentibus</expan> problematis fiet <lb/>manifc&longs;tum.</s></p><p type="head"> <s id="id.000514">Pr&aelig;terea etiam, quod, <lb/>cum vna &longs;it ea linea, qu&aelig; <lb/>ex centro, nullum eorum, <lb/>qu&aelig; in ea &longs;unt, <expan abbr="p&utilde;ctorum">punctorum</expan>, <lb/>&aelig;qu&egrave; 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&shy;<lb/>culi contingunt, vt in <expan abbr="&longs;e-qu&etilde;tibus">&longs;e&shy;<lb/>quentibus</expan> problematis fiet <lb/>manife&longs;tum.</s></p><p type="head">
  
 <s id="id.000515">COMMENTARIVS.<!-- KEEP S--></s></p><p type="main"> <s id="id.000515">COMMENTARIVS.<!-- KEEP S--></s></p><p type="main">
  
 <s id="id.000516">Pr&aelig;terea ctiam.] <emph type="italics"/>Quarta repugnantia e&longs;t in circulo ex in&aelig;&shy;<lb/>qualitate motuum in eiu&longs;dem line&aelig; circulum de&longs;cribentis diuer&shy;<lb/>&longs;is punctis. </s> <s id="id.000516">Pr&aelig;terea etiam.] <emph type="italics"/>Quarta repugnantia e&longs;t in circulo ex in&aelig;&shy;<lb/>qualitate motuum in eiu&longs;dem line&aelig; circulum de&longs;cribentis diuer&shy;<lb/>&longs;is punctis. </s>
  
 <s id="id.000517">In&aelig;qualiter enim moueri dicuntur, &amp; qu&aelig; eodem tem&shy;<lb/>pore diuer&longs;a permeant &longs;patia, &amp; qu&aelig;in &aelig;qualibus temporibus idem: <lb/>atque hoc celerius, quod eodem tempore maius &longs;patium permeat, vel <lb/>breuiori tempore idem: Tardius contra. </s> <s id="id.000517">In&aelig;qualiter enim moueri dicuntur, &amp; qu&aelig; eodem tem&shy;<lb/>pore diuer&longs;a permeant &longs;patia, &amp; qu&aelig;in &aelig;qualibus temporibus idem: <lb/>atque hoc celerius, quod eodem tempore maius &longs;patium permeat, vel <lb/>breuiori tempore idem: Tardius contra. </s>
  
 <s id="id.000518">Punctorum autem, qu&aelig; in&shy;<lb/>&longs;unt in vna eademque linea circulum de&longs;cribente, illud quod remo&shy;<lb/>tius e&longs;t &agrave; centro, maius &longs;patium conficit: quam quod propinquius, li&shy;<lb/>cet vtraque eodem tempore &longs;uum perficiant. </s> <s id="id.000518">Punctorum autem, qu&aelig; in&shy;<lb/>&longs;unt in vna eademque linea circulum de&longs;cribente, illud quod remo&shy;<lb/>tius e&longs;t &agrave; centro, maius &longs;patium conficit: quam quod propinquius, li&shy;<lb/>cet vtraque eodem tempore &longs;uum perficiant. </s>
  
 <s id="id.000519">Linea enim circulum <lb/>de&longs;cribens, quo tempore punctis centro propinquis red&yuml;t ad locum, <lb/>vnde &yuml;&longs;dem moueri c&oelig;perat, eodem remotis redit. </s> <s id="id.000519">Linea enim circulum <lb/>de&longs;cribens, quo tempore punctis centro propinquis red&yuml;t ad locum, <lb/>vnde ij&longs;dem moueri c&oelig;perat, eodem remotis redit. </s>
  
 <s id="id.000520">Spatium autem <lb/>illud e&longs;t peripheria, qu&aelig; ab vnoquoque eorum qu&aelig; &longs;unt in &longs;emidia&shy;<lb/>metro punctorum, de&longs;cribitur, &longs;i quodlibet <expan abbr="p&utilde;ctorum">punctorum</expan> in motu line&aelig; <lb/>intelligatur &longs;ui, vt puncti, ve&longs;tigium relinquere, vt in eo quod circu&shy;<lb/>lum vndiquaque comprehendit. </s> <s id="id.000520">Spatium autem <lb/>illud e&longs;t peripheria, qu&aelig; ab vnoquoque eorum qu&aelig; &longs;unt in &longs;emidia&shy;<lb/>metro punctorum, de&longs;cribitur, &longs;i quodlibet <expan abbr="p&utilde;ctorum">punctorum</expan> in motu line&aelig; <lb/>intelligatur &longs;ui, vt puncti, ve&longs;tigium relinquere, vt in eo quod circu&shy;<lb/>lum vndiquaque comprehendit. </s>
  
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 <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/>&amp; D G diame&shy;<lb/>ter. </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/>&amp; D G diame&shy;<lb/>ter. </s>
  
 <s id="id.000525">Quia igi&shy;<lb/>tur vt diameter <lb/>A C ad <expan abbr="&longs;u&atilde;">&longs;uam</expan> <expan abbr="pe-ripheri&atilde;">pe&shy;<lb/>ripheriam</expan> A B C: <lb/>ita &amp; D G diameter ad &longs;uam peripheriam D F G, per ea qu&aelig; <lb/>demon&longs;trata &longs;unt ab Archimede prop.  <s id="id.000525">Quia igi&shy;<lb/>tur vt diameter <lb/>A C ad <expan abbr="&longs;u&atilde;">&longs;uam</expan> <expan abbr="pe-ripheri&atilde;">pe&shy;<lb/>ripheriam</expan> A B C: <lb/>ita &amp; D G diameter ad &longs;uam peripheriam D F G, per ea qu&aelig; <lb/>demon&longs;trata &longs;unt ab Archimede prop. 3. lib. de dimen&longs;. circuli, &amp; <lb/>vici&szlig;im proportionales erunt A C diameter ad D G diametrum: <lb/>vt peripheria A B C ad peripheriam D F G prop. 16. lib. 5. &amp; <lb/>quia A E &amp; D H partes &longs;unt pariter multiplicium A C, D G <lb/>vtpote &longs;emidiametri &longs;uarum diametrorum, erit A E ad D H vt <lb/>A C ad D G prop. 15. lib. 5. ergo &amp; peripheria A B C ad peri&shy;<lb/>pheriam D F G: vt A E ad D H prop. 11. lib. eiu&longs;dem. </s>
  
 3. lib.  
  
 de dimen&longs;. </s> 
  
 <s id="id.000526">circuli, &amp; <lb/>vici&szlig;im proportionales erunt A C diameter ad D G diametrum: <lb/>vt peripheria A B C ad peripheriam D F G prop. </s> 
  
 <s id="id.000527">16. lib.  
  
 5. &amp; <lb/>quia A E &amp; D H partes &longs;unt pariter multiplicium A C, D G <lb/>vtpote &longs;emidiametri &longs;uarum diametrorum, erit A E ad D H vt <lb/>A C ad D G prop.  
  
 15. lib.  
  
 5. ergo &amp; peripheria A B C ad peri&shy;<lb/>pheriam D F G: vt A E ad D H prop. </s> 
  
 <s id="id.000528">11. lib. <!-- REMOVE S-->eiu&longs;dem. </s> 
  
  
  
 <s id="id.000529">E&longs;t <lb/>autem A E maior: quam D H ex hypothe&longs;i. </s> <s id="id.000529">E&longs;t <lb/>autem A E maior: quam D H ex hypothe&longs;i. </s>
  
 <s id="id.000530">Erit igitur peri&shy;<lb/>pheria A B C maior: quam peripheria D F G. <!-- KEEP S--></s> <s id="id.000530">Erit igitur peri&shy;<lb/>pheria A B C maior: quam peripheria D F G. </s>
  
 <s id="id.000531">Et &longs;ic peripheria <lb/>remotioris puncti &agrave; centro maior e&longs;t peripheria puncti centro pro&shy;<lb/>pinquioris, quod fuit demon&longs;trandum.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000531">Et &longs;ic peripheria <lb/>remotioris puncti &agrave; centro maior e&longs;t peripheria puncti centro pro&shy;<lb/>pinquioris, quod fuit demon&longs;trandum.<emph.end type="italics"/></s></p><p type="main">
  
 <s id="id.000532"><gap/></s></p><p type="main"> <s id="id.000532"><foreign lang="greek"><gap/></foreign></s></p><p type="main">
  
 <s id="id.000533">Quod autem circulus <lb/><expan abbr="c&otilde;trariis">contrariis</expan> cieatur motibus, <lb/>&amp; alterum extremorum <lb/>diametri in quo e&longs;t A, dum <lb/>mouetur antror&longs;um, alte&shy;<lb/>rum in quo e&longs;t B mouea&shy;<lb/>tur retror&longs;um, ideo non&shy;<lb/>nulli <expan abbr="faci&utilde;t">faciunt</expan>, vt ab vna mo&shy;<lb/>tione multi circuli &longs;imul <lb/>in contraria moueantur: <lb/>vt quos in deorum templis <lb/>&longs;tatuunt, efficientes circu-<pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.063.jpg" pagenum="24"/><gap/><lb/>los &aelig;reos &amp; ferreos. </s> <s id="id.000533">Quod autem circulus <lb/><expan abbr="c&otilde;trariis">contrariis</expan> cieatur motibus, <lb/>&amp; alterum extremorum <lb/>diametri in quo e&longs;t A, dum <lb/>mouetur antror&longs;um, alte&shy;<lb/>rum in quo e&longs;t B mouea&shy;<lb/>tur retror&longs;um, ideo non&shy;<lb/>nulli <expan abbr="faci&utilde;t">faciunt</expan>, vt ab vna mo&shy;<lb/>tione multi circuli &longs;imul <lb/>in contraria moueantur: <lb/>vt quos in deorum templis <lb/>&longs;tatuunt, efficientes circu-<pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.063.jpg" pagenum="24"/><foreign lang="greek"><gap/></foreign><lb/>los &aelig;reos &amp; ferreos. </s>
  
 <s id="id.000534">Si <lb/>enim circulum in quo e&longs;t <lb/>A B, alter circulus in quo <lb/>e&longs;t G D attigerit, diamc&shy;<lb/>tro circuli A B antror&shy;<lb/>&longs;um mota, diameter circu&shy;<lb/>li G D retror&longs;um moue&shy;<lb/>bitur, circuli in quo e&longs;t A <lb/>diametro circa idem mo&shy;<lb/>ta. </s> <s id="id.000534">Si <lb/>enim circulum in quo e&longs;t <lb/>A B, alter circulus in quo <lb/>e&longs;t G D attigerit, diame&shy;<lb/>tro circuli A B antror&shy;<lb/>&longs;um mota, diameter circu&shy;<lb/>li G D retror&longs;um moue&shy;<lb/>bitur, circuli in quo e&longs;t A <lb/>diametro circa idem mo&shy;<lb/>ta. </s>
  
 <s id="id.000535">Circulus igitur in quo <lb/>e&longs;t G D, contr&agrave;, quam is, <lb/>in quo e&longs;t A B moucbi&shy;<lb/>tur: idemque &longs;equentem <lb/>in quo e&longs;t E Z propter <lb/>eandem cau&longs;am contra &longs;e <lb/>mouebit, &amp; eodem modo <lb/>&longs;i plures fuerint vno com&shy;<lb/>moto itidem <expan abbr="faci&etilde;t">facient</expan>. </s> <s id="id.000535">Circulus igitur in quo <lb/>e&longs;t G D, contr&agrave;, quam is, <lb/>in quo e&longs;t A B mouebi&shy;<lb/>tur: idemque &longs;equentem <lb/>in quo e&longs;t E Z propter <lb/>eandem cau&longs;am contra &longs;e <lb/>mouebit, &amp; eodem modo <lb/>&longs;i plures fuerint vno com&shy;<lb/>moto itidem <expan abbr="faci&etilde;t">facient</expan>. </s>
  
 <s id="id.000536">Hinc <lb/>Architecti Fabri, cum <expan abbr="h&atilde;c">hanc</expan> <lb/>in circulo naturam depre&shy;<lb/>hendi&longs;&longs;ent, <expan abbr="organ&utilde;">organum</expan> fabri&shy;<lb/>cantur principium occu&shy;<lb/>lentes, vt &longs;it de machina, <lb/>&longs;olum hoc, quod admira&shy;<lb/>bile, apertum: quod autem <lb/>cau&longs;a, occultum.</s></p><p type="head"> <s id="id.000536">Hinc <lb/>Architecti Fabri, cum <expan abbr="h&atilde;c">hanc</expan> <lb/>in circulo naturam depre&shy;<lb/>hendi&longs;&longs;ent, <expan abbr="organ&utilde;">organum</expan> fabri&shy;<lb/>cantur principium occu&shy;<lb/>lentes, vt &longs;it de machina, <lb/>&longs;olum hoc, quod admira&shy;<lb/>bile, apertum: quod autem <lb/>cau&longs;a, occultum.</s></p><p type="head">
  
 <s id="id.000537">COMMENTARIVS.<!-- KEEP S--></s></p><p type="main"> <s id="id.000537">COMMENTARIVS.<!-- KEEP S--></s></p><p type="main">
  
 <s id="id.000538">Qvod autem circulus.] <emph type="italics"/>Tertia repugnantia in vnius cir&shy;<lb/>culi contrar&yuml;s 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> <s id="id.000538">Qvod autem circulus.] <emph type="italics"/>Tertia repugnantia in vnius cir&shy;<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>
  
 <s id="id.000539">Vt &longs;unto tres circuli contingentes quod&shy;<lb/>que fer&egrave; fit denticulis pectinis in&longs;tar &longs;e&longs;e &longs;ubingredientibus in peri&shy;<lb/>phcria pr&aelig;diti, quorum primus A B, moueatur antror&longs;um, &longs;eu&longs;e&shy;<lb/>cundum &longs;uperiorem peripheriam, vt A feratur ver&longs;us C: alter<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.064.jpg" pagenum="25"/><emph type="italics"/>G D ad illius motum nece&longs;&longs;ario mouebitur propter denticulos, &longs;ed <lb/><expan abbr="retrors&utilde;">retrorsum</expan><emph.end type="italics"/><lb/><figure id="id.035.01.064.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.064.1.jpg"/><lb/><emph type="italics"/>&longs;eu <expan abbr="&longs;ec&utilde;-dum">&longs;ecun&shy;<lb/>dum</expan> <expan abbr="in-ferior&etilde;">in&shy;<lb/>feriorem</expan> <lb/><expan abbr="periphe-ri&atilde;">periphe&shy;<lb/>riam</expan>, vt <lb/>G ad B: <lb/>tum ter&shy;<lb/>tius E Z ad &longs;ecundi motum mouebitur etiam, &longs;ed antror&longs;um, vt E <lb/>ad F, &amp; &longs;int deinceps alternatim infiniti denticulis &longs;e&longs;e &longs;ubinui&shy;<lb/>cem ingredientibus, &longs;emper mouebuntur. </s> <s id="id.000539">Vt &longs;unto tres circuli contingentes quod&shy;<lb/>que fer&egrave; fit denticulis pectinis in&longs;tar &longs;e&longs;e &longs;ubingredientibus in peri&shy;<lb/>phcria pr&aelig;diti, quorum primus A B, moueatur antror&longs;um, &longs;eu&longs;e&shy;<lb/>cundum &longs;uperiorem peripheriam, vt A feratur ver&longs;us C: alter<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.064.jpg" pagenum="25"/><emph type="italics"/>G D ad illius motum nece&longs;&longs;ario mouebitur propter denticulos, &longs;ed <lb/><expan abbr="retrors&utilde;">retrorsum</expan><emph.end type="italics"/><lb/><figure id="id.035.01.064.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.064.1.jpg"/><lb/><emph type="italics"/>&longs;eu <expan abbr="&longs;ec&utilde;-dum">&longs;ecun&shy;<lb/>dum</expan> <expan abbr="in-ferior&etilde;">in&shy;<lb/>feriorem</expan> <lb/><expan abbr="periphe-ri&atilde;">periphe&shy;<lb/>riam</expan>, vt <lb/>G ad B: <lb/>tum ter&shy;<lb/>tius E Z ad &longs;ecundi motum mouebitur etiam, &longs;ed antror&longs;um, vt E <lb/>ad F, &amp; &longs;int deinceps alternatim infiniti denticulis &longs;e&longs;e &longs;ubinui&shy;<lb/>cem ingredientibus, &longs;emper mouebuntur. </s>
  
 <s id="id.000540">Vnde tunc &agrave; Fabro dato <lb/>principio motionis, vertebra vertebram continenter mouet, vltim&aacute;&shy;<lb/>que ab illis &longs;imulacrorum excita fit pr&aelig;teruectio, non aliter quans in <lb/>animalium genere &agrave; &longs;en&longs;u, vel intellectione motionum exorto prin&shy;<lb/>cipio intrin&longs;ecis commotis cau&longs;is, &longs;eque inuicem mouentibus, vt alij <lb/>po&longs;tmodum extrin&longs;ecus, cum partium ip&longs;arum, tum etiam vniuer&longs;i <lb/>corporis vi&longs;untur motus.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000540">Vnde tunc &agrave; Fabro dato <lb/>principio motionis, vertebra vertebram continenter mouet, vltim&aacute;&shy;<lb/>que ab illis &longs;imulacrorum excita fit pr&aelig;teruectio, non aliter quam in <lb/>animalium genere &agrave; &longs;en&longs;u, vel intellectione motionum exorto prin&shy;<lb/>cipio intrin&longs;ecis commotis cau&longs;is, &longs;eque inuicem mouentibus, vt alij <lb/>po&longs;tmodum extrin&longs;ecus, cum partium ip&longs;arum, tum etiam vniuer&longs;i <lb/>corporis vi&longs;untur motus.<emph.end type="italics"/></s></p><p type="main">
  
 <s id="id.000541">Hinc architecti.] <emph type="italics"/>Sicuti ante ex vnius circuli contrar&yuml;s mo&shy;<lb/>tibus libram, vectem, mechanic&aacute;que in&longs;trumenta magnam habere <lb/>vim ad onera mouendum &longs;ubindicauit: &longs;ic nunc ex circulorum con&shy;<lb/>tiguorum &amp; vari&egrave; multiplicatorum contrar&yuml;s motionibus machi&shy;<lb/>nas quamplurimas effici <expan abbr="o&longs;t&etilde;dit">o&longs;tendit</expan>, quibus credibile e&longs;t veteres paganos, <lb/>qui veris miraculis <expan abbr="de&longs;titueb&atilde;tur">de&longs;tituebantur</expan>, in templis &longs;uorum <expan abbr="deor&utilde;">deorum</expan> collocatis, <lb/>&amp; etiam per vrbium vicos, &amp; plateas ge&longs;tatis, <expan abbr="authoritat&etilde;">authoritatem</expan> d&yuml;s &longs;uis <lb/><expan abbr="c&otilde;flaui&longs;&longs;e">conflaui&longs;&longs;e</expan>, &amp; ignaro vulgo mirificis modis ita impo&longs;ui&longs;&longs;e. </s> 
  
 <s id="id.000542">Huius rci <lb/>fecit mentionem Galenus, qui miracula inquit moliuntur principio <lb/>motionis exhibito di&longs;cedunt, Machin&aelig; vero ip&longs;&aelig; aliquanti&longs;per, non <lb/>multo tamen tempore per &longs;e ip&longs;&aelig; arti&longs;icios&egrave; impelluntur. </s> 
  
 <s id="id.000543">cap.  <s id="id.000541">Hinc architecti.] <emph type="italics"/>Sicuti ante ex vnius circuli contrarijs mo&shy;<lb/>tibus libram, vectem, mechanic&aacute;que in&longs;trumenta magnam habere <lb/>vim ad onera mouendum &longs;ubindicauit: &longs;ic nunc ex circulorum con&shy;<lb/>tiguorum &amp; vari&egrave; multiplicatorum contrarij;s motionibus machi&shy;<lb/>nas quamplurimas effici <expan abbr="o&longs;t&etilde;dit">o&longs;tendit</expan>, quibus credibile e&longs;t veteres paganos, <lb/>qui veris miraculis <expan abbr="de&longs;titueb&atilde;tur">de&longs;tituebantur</expan>, in templis &longs;uorum <expan abbr="deor&utilde;">deorum</expan> collocatis, <lb/>&amp; etiam per vrbium vicos, &amp; plateas ge&longs;tatis, <expan abbr="authoritat&etilde;">authoritatem</expan> dijs &longs;uis <lb/><expan abbr="c&otilde;flaui&longs;&longs;e">conflaui&longs;&longs;e</expan>, &amp; ignaro vulgo mirificis modis ita impo&longs;ui&longs;&longs;e. </s>
  
 6. lib.  <s id="id.000542">Huius rei <lb/>fecit mentionem Galenus, qui miracula inquit moliuntur principio <lb/>motionis exhibito di&longs;cedunt, Machin&aelig; vero ip&longs;&aelig; aliquanti&longs;per, non <lb/>multo tamen tempore per &longs;e ip&longs;&aelig; arti&longs;icios&egrave; impelluntur. cap. 6. lib. de <lb/>f&oelig;t. format. </s>
  
 de <lb/>f&oelig;t. </s> <s id="id.000545">Herodotus hi&longs;toria &longs;ecunda videtur ex his aliqua<emph.end type="italics"/> <foreign lang="greek">neu&shy;<lb/>ro/sdpaza</foreign> <emph type="italics"/>appella&longs;&longs;e: qua&longs;i diceremus, per funiculos tanquam neruos <lb/>circa rotulas inuolutos, varijs motibus agitata. </s>
  
 <s id="id.000544">format. </s> <s id="id.000546">Eiu&longs;modi erant ade&ograve; <lb/>celebrat&aelig; D&aelig;dali &longs;tatu&aelig;, qu&aelig; inquit Plato ni&longs;i ligat&aelig; aufugiebant,<emph.end type="italics"/><lb/><arrow.to.target n="marg12"/><lb/><emph type="italics"/>&amp; vago quodam &longs;inuo&longs;oque impetu ferebantur in fugam: ligat&aelig; <lb/>vero permanebant, vnde ill&aelig; non magno pretio emebantur in&longs;tar <lb/>&longs;erui fugitiui: h&aelig; contra magno. </s>
  
 <s id="id.000545">Herodotus hi&longs;toria &longs;ecunda videtur ex his aliqua<emph.end type="italics"/> <foreign lang="greek">neu&shy;<lb/>ro/dpasa</foreign> <emph type="italics"/>appella&longs;&longs;e: qua&longs;i diceremus, per funiculos tanquam neruos <lb/>circa rotulas inuolutos, var&yuml;s motibus agitata. </s> <s id="id.000547">Erant enim pr&aelig;clara opera.<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.065.jpg" pagenum="26"/><emph type="italics"/>Hodie etiam no&longs;tri artifices ex hac plurium rotularum mira in&shy;<lb/>ter &longs;e coniunctione, aliquoque ex &longs;e mobili vt animali, vento, fu&shy;<lb/>mo, aqua, lamina chalybea primum motum &longs;uppeditante commota<emph.end type="italics"/><lb/><foreign lang="greek">au)to/mat>a</foreign> <emph type="italics"/>faciunt non &longs;olum admirabilia: &longs;ed etiam maxim&egrave; vti&shy;<lb/>lia, qualia &longs;unt horologia veterum clep&longs;ydras, &amp; gnomones &longs;ine luce <lb/>&amp; &longs;erenitate inutiles, commoditate &amp; perpetuitate long&egrave; &longs;uperan&shy;<lb/>tia, quibus hodie dies ciuilis in 24. partes, quas horas vocant, di&shy;<lb/>&longs;tribuitur. </s>
  
 <s id="id.000546">Eiu&longs;modij erant ade&ograve; <lb/>celebrat&aelig; D&aelig;dali &longs;tatu&aelig;, qu&aelig; inquit Plato ni&longs;i ligat&aelig; aufugiebant,<emph.end type="italics"/><lb/><arrow.to.target n="marg12"/><lb/><emph type="italics"/>&amp; vago quodam &longs;inuo&longs;oque impetu ferebantur in fugam: ligar&aelig; <lb/>vero permanebant, vnde ill&aelig; non magno pretio emebantur in&longs;tar <lb/>&longs;erui fugitiui: h&aelig; contra magno. </s> 
  
 <s id="id.000547">Erant enim pr&aelig;clara opera.<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.065.jpg" pagenum="26"/><emph type="italics"/>Hodie etiam no&longs;tri artifices ex hac plurium rotularum mira in&shy;<lb/>ter &longs;e coniunctione, aliquoque ex &longs;e mobili vt animali, vento, fu&shy;<lb/>mo, aqua, lamina chalybea primum motum &longs;uppeditante commota<emph.end type="italics"/><lb/><foreign lang="greek">ao)to/ma<gap/>a</foreign> <emph type="italics"/>faciunt non &longs;olum admirabilia: &longs;ed etiam maxim&egrave; vti&shy;<lb/>lia, qualia &longs;unt horologia veterum clep&longs;ydras, &amp; gnomones &longs;ine luce <lb/>&amp; &longs;erenitate inutiles, commoditate &amp; perpetuitate long&egrave; &longs;uperan&shy;<lb/>tia, quibus hodie dies ciuilis in 24. partes, quas horas vocant, di&shy;<lb/>&longs;tribuitur. </s> 
  
 <s id="id.000548">Ex quibus alia &longs;unt &longs;tataria, &amp; in &longs;ummis templorum no&shy;<lb/>&longs;trorum partibus collocata: alia in <expan abbr="homin&utilde;">hominum</expan> collis, Zon&iacute;&longs;ue <expan abbr="app&etilde;&longs;a">appen&longs;a</expan> pr&aelig; <lb/>exiguitate ponderis nullo modo mole&longs;ta, <expan abbr="circunfer&utilde;tur">circunferuntur</expan>. </s> <s id="id.000548">Ex quibus alia &longs;unt &longs;tataria, &amp; in &longs;ummis templorum no&shy;<lb/>&longs;trorum partibus collocata: alia in <expan abbr="homin&utilde;">hominum</expan> collis, Zon&iacute;&longs;ue <expan abbr="app&etilde;&longs;a">appen&longs;a</expan> pr&aelig; <lb/>exiguitate ponderis nullo modo mole&longs;ta, <expan abbr="circunfer&utilde;tur">circunferuntur</expan>. </s>
  
 <s id="id.000549">Sed ne&longs;cio an <lb/>fama, an fide nobilius &longs;it illud, quod A&racute;gentorati in loco ciuitatis <lb/>eminenti&szlig;imo po&longs;itum e&longs;t, in quo vniuer&longs;i mundi c&aelig;le&longs;tis com&shy;<lb/>pago, orbibus &longs;uis in &longs;uas partes di&longs;tincta vi&longs;itur, In hoc enim <lb/>octaui orbis tardi&szlig;imum motum, Zodiaci duodccim &longs;igna, Solis per <lb/>puncta ecliptica tran&longs;itum, Lun&aelig; varias apparitiones, &longs;ingulorum <lb/>planetarum progre&longs;&longs;us, regre&longs;&longs;us, &longs;tationes, latitudines, altitudines, <lb/>innumeraque alia pr&aelig;ter temporum momenta, &amp; horastum &aelig;qua&shy;<lb/>les, tum in&aelig;quales intueri licet. </s> <s id="id.000549">Sed ne&longs;cio an <lb/>fama, an fide nobilius &longs;it illud, quod A&racute;gentorati in loco ciuitatis <lb/>eminenti&szlig;imo po&longs;itum e&longs;t, in quo vniuer&longs;i mundi c&aelig;le&longs;tis com&shy;<lb/>pago, orbibus &longs;uis in &longs;uas partes di&longs;tincta vi&longs;itur, In hoc enim <lb/>octaui orbis tardi&szlig;imum motum, Zodiaci duodecim &longs;igna, Solis per <lb/>puncta ecliptica tran&longs;itum, Lun&aelig; varias apparitiones, &longs;ingulorum <lb/>planetarum progre&longs;&longs;us, regre&longs;&longs;us, &longs;tationes, latitudines, altitudines, <lb/>innumeraque alia pr&aelig;ter temporum momenta, &amp; horas tum &aelig;qua&shy;<lb/>les, tum in&aelig;quales intueri licet. </s>
  
 <s id="id.000550">Ita tamen, vt quod hic dicitur, quic&shy;<lb/>quid e&longs;t rotarum, ponderum, molarum, denticulorum, nolarum, vir&shy;<lb/>garum, <expan abbr="funi&utilde;">funium</expan>, atque aliorum <expan abbr="in&longs;trumentor&utilde;">in&longs;trumentorum</expan> magna ex parte intus <lb/>delite&longs;cat, &amp; occultetur, qu&aelig; ver&ograve; in tanta machina tot admirabilia <lb/>&longs;unt, <expan abbr="appare&atilde;t">appareant</expan>. </s> <s id="id.000550">Ita tamen, vt quod hic dicitur, quic&shy;<lb/>quid e&longs;t rotarum, ponderum, molarum, denticulorum, nolarum, vir&shy;<lb/>garum, <expan abbr="funi&utilde;">funium</expan>, atque aliorum <expan abbr="in&longs;trumentor&utilde;">in&longs;trumentorum</expan> magna ex parte intus <lb/>delite&longs;cat, &amp; occultetur, qu&aelig; ver&ograve; in tanta machina tot admirabilia <lb/>&longs;unt, <expan abbr="appare&atilde;t">appareant</expan>. </s>
  
 <s id="id.000551">H&aelig;c, &amp; qu&aelig; imaguncularum ince&longs;&longs;um, &longs;altum, cho&shy;<lb/>reas repr&aelig;&longs;entant, faciunt, vt qu&aelig; de Archit&aelig; columba volatili, &amp; <lb/>de Archimedis &longs;ph&aelig;ra ver&longs;atili memori&aelig; reliquit antiquitas, pre <lb/>fal&longs;is minime habeamus.<emph.end type="italics"/></s></p><p type="margin"> <s id="id.000551">H&aelig;c, &amp; qu&aelig; imaguncularum ince&longs;&longs;um, &longs;altum, cho&shy;<lb/>reas repr&aelig;&longs;entant, faciunt, vt qu&aelig; de Archit&aelig; columba volatili, &amp; <lb/>de Archimedis &longs;ph&aelig;ra ver&longs;atili memori&aelig; reliquit antiquitas, pro <lb/>fal&longs;is minime habeamus.<emph.end type="italics"/></s></p><p type="margin">
  
 <s id="id.000552"><margin.target id="marg12"/>In Menone</s></p><p type="main"> <s id="id.000552"><margin.target id="marg12"/>In Menone</s></p><p type="main">
  
 <s id="id.000553"><gap/></s></p><p type="main"> <s id="id.000553"><foreign lang="greek"><gap/></foreign></s></p><p type="main">
  
 <s id="id.000554">2. De libra propter quid <lb/>maior linea in circulo <lb/>celerius fertur, minore. <lb/></s> <s id="id.000554">2. De libra propter quid <lb/>maior linea in circulo <lb/>celerius fertur, minore. <lb/></s>
  
 <s id="id.000555">Ex quo fit vt libr&aelig; ma&shy;<lb/>iores minoribus &longs;int <lb/>exactiores.</s></p><p type="main"> <s id="id.000555">Ex quo fit vt libr&aelig; ma&shy;<lb/>iores minoribus &longs;int <lb/>exactiores.</s></p><p type="main">
  
 <s id="id.000556"><gap/></s></p><p type="main"> <s id="id.000556"><foreign lang="greek"><gap/></foreign></s></p><p type="main">
  
 <s id="id.000557"><expan abbr="Prim&utilde;">Primum</expan> igitur qu&ecedil; circa <expan abbr="li-br&atilde;">li&shy;<lb/>bram</expan> <expan abbr="c&otilde;tingunt">contingunt</expan>, <expan abbr="difficultat&etilde;">difficultatem</expan> <lb/><expan abbr="adfer&utilde;t">adferunt</expan>. </s> <s id="id.000557"><expan abbr="Prim&utilde;">Primum</expan> igitur qu&ecedil; circa <expan abbr="li-br&atilde;">li&shy;<lb/>bram</expan> <expan abbr="c&otilde;tingunt">contingunt</expan>, <expan abbr="difficultat&etilde;">difficultatem</expan> <lb/><expan abbr="adfer&utilde;t">adferunt</expan>. </s>
  
 <s id="id.000558">Ob quam cau&longs;am <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.066.jpg" pagenum="27"/><gap/><lb/>libr&aelig; maiores minoribus <lb/>&longs;int exactiores. </s> <s id="id.000558">Ob quam cau&longs;am <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.066.jpg" pagenum="27"/><foreign lang="greek"><gap/></foreign><lb/>libr&aelig; maiores minoribus <lb/>&longs;int exactiores. </s>
  
 <s id="id.000559">Huius vero <lb/><expan abbr="principi&utilde;">principium</expan> e&longs;t quare in cir&shy;<lb/>culo <expan abbr="di&longs;t&atilde;tior">di&longs;tantior</expan> linea &agrave; cen&shy;<lb/>tro, ei propinquiore <expan abbr="ead&etilde;">eadem</expan> <lb/>vi mota celerius fertur. <lb/></s> <s id="id.000559">Huius vero <lb/><expan abbr="principi&utilde;">principium</expan> e&longs;t quare in cir&shy;<lb/>culo <expan abbr="di&longs;t&atilde;tior">di&longs;tantior</expan> linea &agrave; cen&shy;<lb/>tro, ei propinquiore <expan abbr="ead&etilde;">eadem</expan> <lb/>vi mota celerius fertur. <lb/></s>
  
 <s id="id.000560">Celerius autem dicitur bi&shy;<lb/>fariam, &longs;iue enim in mino&shy;<lb/>ri tempore &ecedil;quale &longs;patium <lb/>tran&longs;ierit, celerius e&longs;le di&shy;<lb/>cimus: &longs;iue in <expan abbr="t&etilde;pore">tempore</expan> &ecedil;qua&shy;<lb/>li, maius. </s> <s id="id.000560">Celerius autem dicitur bi&shy;<lb/>fariam, &longs;iue enim in mino&shy;<lb/>ri tempore &ecedil;quale &longs;patium <lb/>tran&longs;ierit, celerius e&longs;&longs;e di&shy;<lb/>cimus: &longs;iue in <expan abbr="t&etilde;pore">tempore</expan> &ecedil;qua&shy;<lb/>li, maius. </s>
  
 <s id="id.000561">Maior autem li&shy;<lb/>nea in &aelig;quali <expan abbr="t&etilde;pore">tempore</expan> ma&shy;<lb/>iorem circulum de&longs;cribit. <lb/></s> <s id="id.000561">Maior autem li&shy;<lb/>nea in &aelig;quali <expan abbr="t&etilde;pore">tempore</expan> ma&shy;<lb/>iorem circulum de&longs;cribit. <lb/></s>
  
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 <s id="id.000564">De libra propter.] <emph type="italics"/>In hoc capite Ari&longs;toteles vult o&longs;tendere <lb/>cur libr&aelig; longiorum brachiorum &longs;int exactiores: quam libr&aelig; <lb/>breuiorum. </s> <s id="id.000564">De libra propter.] <emph type="italics"/>In hoc capite Ari&longs;toteles vult o&longs;tendere <lb/>cur libr&aelig; longiorum brachiorum &longs;int exactiores: quam libr&aelig; <lb/>breuiorum. </s>
  
 <s id="id.000565">Et huius problematis cau&longs;am refert ad circulum, circu&shy;<lb/>lique eam proprietatem, qua rad&yuml; longiores celerius, id e&longs;t eodem <lb/>tempore maius &longs;patium conficiunt, quam breuiores. </s> <s id="id.000565">Et huius problematis cau&longs;am refert ad circulum, circu&shy;<lb/>lique eam proprietatem, qua radij longiores celerius, id e&longs;t eodem <lb/>tempore maius &longs;patium conficiunt, quam breuiores. </s>
  
 <s id="id.000566">Quod quia futu&shy;<lb/>rum e&longs;t fundamentum multorum aliorum problematum po&longs;tea ex&shy;<lb/>plicandorum, diligenter imprimis demon&longs;trat. </s> <s id="id.000566">Quod quia futu&shy;<lb/>rum e&longs;t fundamentum multorum aliorum problematum po&longs;tea ex&shy;<lb/>plicandorum, diligenter imprimis demon&longs;trat. </s>
  
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 <s id="id.000572">Huius vero.] <emph type="italics"/>Cau&longs;a exactiorum librarum refertur ad circuli<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.067.jpg" pagenum="28"/><emph type="italics"/>radios longiores, qui celerius feruntur minoribus, id e&longs;t qui &aelig;quali <lb/>tempore maius &longs;patium, &amp; proinde &longs;en &longs;ibilius tran&longs;eunt.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000572">Huius vero.] <emph type="italics"/>Cau&longs;a exactiorum librarum refertur ad circuli<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.067.jpg" pagenum="28"/><emph type="italics"/>radios longiores, qui celerius feruntur minoribus, id e&longs;t qui &aelig;quali <lb/>tempore maius &longs;patium, &amp; proinde &longs;en &longs;ibilius tran&longs;eunt.<emph.end type="italics"/></s></p><p type="main">
  
 <s id="id.000573">Celerius enim.] <emph type="italics"/>Celeritatis lationum duos modos adfert &longs;i&shy;<lb/>miles &yuml;s quos cap.  <s id="id.000573">Celerius enim.] <emph type="italics"/>Celeritatis lationum duos modos adfert &longs;i&shy;<lb/>miles ijs quos cap. 2. lib. 6. de Phy&longs;. auditu attulit, vt vtro longioris <lb/>radij celeritas accipi debeat, intelligatur.<emph.end type="italics"/></s></p><p type="main">
  
 2. lib.  
  
 6. de Phy&longs;. auditu attulit, vt vtro longioris <lb/>rad&yuml; celeritas accipi debeat, intelligatur.<emph.end type="italics"/></s></p><p type="main"> 
  
 <s id="id.000574">Qui enim extra.] <emph type="italics"/>E duobus circulis concentricis, qui extra e&longs;t, <lb/>e&longs;t quoddam <expan abbr="tot&utilde;">totum</expan>, &amp; internus e&longs;t externi vna pars. </s> <s id="id.000574">Qui enim extra.] <emph type="italics"/>E duobus circulis concentricis, qui extra e&longs;t, <lb/>e&longs;t quoddam <expan abbr="tot&utilde;">totum</expan>, &amp; internus e&longs;t externi vna pars. </s>
  
 <s id="id.000575">Cum <expan abbr="itaq;">itaque</expan> totum <lb/>maius &longs;it &longs;ua parte ex 9. axiom. </s> <s id="id.000575">Cum <expan abbr="itaq;">itaque</expan> totum <lb/>maius &longs;it &longs;ua parte ex 9. axiom. lib. 1. ele. externus circulus interno <lb/>concentrico erit maior. </s>
  
 <s id="id.000576">lib.  
  
 1. ele. </s> 
  
 <s id="id.000577">externus circulus interno <lb/>concentrico erit maior. </s> 
  
 <s id="id.000578">Pr&aelig;terea <expan abbr="c&utilde;">cum</expan> circuli &aelig;quales &longs;int, <expan abbr="quor&utilde;">quorum</expan> &longs;emi&shy;<lb/>diametri &longs;int &aelig;quales def. </s> 
  
 <s id="id.000579">1. lib.  <s id="id.000578">Pr&aelig;terea <expan abbr="c&utilde;">cum</expan> circuli &aelig;quales &longs;int, <expan abbr="quor&utilde;">quorum</expan> &longs;emi&shy;<lb/>diametri &longs;int &aelig;quales def. 1. lib. 3. ele. </s>
  
 3. ele. </s> 
  
 <s id="id.000580">Illi quorum &longs;emidiametri &longs;unt <lb/>in&aelig;quales, erunt &amp; in&aelig;quales, &amp; ille maior, euius &longs;emidiameter <lb/>maior. </s> <s id="id.000580">Illi quorum &longs;emidiametri &longs;unt <lb/>in&aelig;quales, erunt &amp; in&aelig;quales, &amp; ille maior, euius &longs;emidiameter <lb/>maior. </s>
  
 <s id="id.000581">Qu&aelig; licet vera &longs;int non tamen &longs;tatim &longs;equitur figur&aelig; plan&aelig; <lb/>cuius area maior e&longs;t, e&longs;&longs;e &amp; perimetrum maiorem vt ex 36. 37. <lb/>prop.  <s id="id.000581">Qu&aelig; licet vera &longs;int non tamen &longs;tatim &longs;equitur figur&aelig; plan&aelig; <lb/>cuius area maior e&longs;t, e&longs;&longs;e &amp; perimetrum maiorem vt ex 36. 37. <lb/>prop. lib. 1. elem. demon&longs;trari facile pote&longs;t: neque &longs;i rur&longs;us perimeter <lb/>contineat perimetrum, vt continens contento &longs;it maior, vt patere <lb/>pote&longs;t ex eo, quod e&longs;t &agrave; Proclo adductum ad prop. 21. lib. 1. elem. </s>
  
 lib.  
  
 1. elem. </s> 
  
 <s id="id.000582">demon&longs;trari facile pote&longs;t: neque &longs;i rur&longs;us perimeter <lb/>contineat perimetrum, vt continens contento &longs;it maior, vt patere <lb/>pote&longs;t ex eo, quod e&longs;t &agrave; Proclo adductum ad prop.  
  
 21. lib.  <s id="id.000583">De <lb/>duabus rectis intra triangulum, rectangulum vel amblygonium <lb/>comprehen&longs;is, qu&aelig; maiores con&longs;titui po&longs;&longs;unt ijs &agrave; quibus ambiuntur. <lb/></s>
  
 1. elem. </s> 
  
 <s id="id.000583">De <lb/>duabus rectis intra triangulum, rectangulum vel amblygonium <lb/>comprehen&longs;is, qu&aelig; maiores con&longs;titui po&longs;&longs;unt &yuml;s &agrave; quibus ambiuntur. <lb/></s> 
  
 <s id="id.000584">Ob h&aelig;c igitur, cum hic locus non tam debeat intelligi de circulis, <lb/>quam circulorum peripherijs, merit&ograve; ante, cum huius proprietatis <lb/>mentio fieret, capite pr&aelig;cedenti peripheriam maioris circuli periphe&shy;<lb/>ria minoris maiorem e&longs;&longs;e demon&longs;trauimus, &longs;ed etiam huius magni&shy;<lb/>tudinis maioris cau&longs;a, hic ab Ari&longs;totele &longs;ubiungitur.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000584">Ob h&aelig;c igitur, cum hic locus non tam debeat intelligi de circulis, <lb/>quam circulorum peripherijs, merit&ograve; ante, cum huius proprietatis <lb/>mentio fieret, capite pr&aelig;cedenti peripheriam maioris circuli periphe&shy;<lb/>ria minoris maiorem e&longs;&longs;e demon&longs;trauimus, &longs;ed etiam huius magni&shy;<lb/>tudinis maioris cau&longs;a, hic ab Ari&longs;totele &longs;ubiungitur.<emph.end type="italics"/></s></p><p type="main">
  
 <s id="id.000585"><gap/></s></p><p type="main"> <s id="id.000585"><foreign lang="greek"><gap/></foreign></s></p><p type="main">
  
 <s id="id.000586">Horum vero cau&longs;a e&longs;t, <lb/>quod recta de&longs;cribens <expan abbr="cir-cul&utilde;">cir&shy;<lb/>culum</expan> <expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> duas latio&shy;<lb/>nes fertur. </s> <s id="id.000586">Horum vero cau&longs;a e&longs;t, <lb/>quod recta de&longs;cribens <expan abbr="cir-cul&utilde;">cir&shy;<lb/>culum</expan> <expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> duas latio&shy;<lb/>nes fertur. </s>
  
 <s id="id.000587"><expan abbr="C&utilde;">Cum</expan> igitur in ali&shy;<lb/>qua ratione du&ecedil; <expan abbr="s&utilde;t">sunt</expan> ill&aelig; la&shy;<lb/>tiones, nece&longs;&longs;e e&longs;t id, quod <lb/>fertur <expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> <expan abbr="rect&atilde;">rectam</expan> ferri, <lb/>qu&aelig; fit diameter figur&aelig;, <lb/><expan abbr="qu&atilde;">quam</expan> rect&aelig; in ea ratione <expan abbr="c&otilde;-&longs;titut&aelig;">con&shy;<lb/>&longs;titut&aelig;</expan>, <expan abbr="c&otilde;prehendunt">comprehendunt</expan>. </s> <s id="id.000587"><expan abbr="C&utilde;">Cum</expan> igitur in ali&shy;<lb/>qua ratione du&ecedil; <expan abbr="s&utilde;t">sunt</expan> ill&aelig; la&shy;<lb/>tiones, nece&longs;&longs;e e&longs;t id, quod <lb/>fertur <expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> <expan abbr="rect&atilde;">rectam</expan> ferri, <lb/>qu&aelig; fit diameter figur&aelig;, <lb/><expan abbr="qu&atilde;">quam</expan> rect&aelig; in ea ratione <expan abbr="c&otilde;-&longs;titut&aelig;">con&shy;<lb/>&longs;titut&aelig;</expan>, <expan abbr="c&otilde;prehendunt">comprehendunt</expan>. </s>
  
 <s id="id.000588">Sit <lb/>enim ratio <expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> quam <lb/>mobile fertur ea: quam ha-<pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.068.jpg" pagenum="29"/><gap/><lb/>bet <foreign lang="greek">a b</foreign> ad <foreign lang="greek">a g,</foreign> &amp; quidem <lb/><foreign lang="greek">a</foreign> feratur ad <foreign lang="greek">b,</foreign> &amp; <foreign lang="greek">a b_</foreign><lb/>etiam feratur ad <foreign lang="greek">h g</foreign>: la&shy;<lb/>tum vero &longs;it <foreign lang="greek">a</foreign> ad <foreign lang="greek">d,</foreign> &amp; <lb/><foreign lang="greek">a b</foreign> ad <foreign lang="greek">e.</foreign> Igitur cum latio&shy;<lb/>nis ratio erat ea quam ha&shy;<lb/>bet <foreign lang="greek">a b</foreign> ad <foreign lang="greek">a g</foreign>: nece&longs;&longs;e <lb/>e&longs;t &amp; ip&longs;am <foreign lang="greek">a d</foreign> ad <foreign lang="greek">a e</foreign> ean&shy;<lb/>dem habere rationcm. </s> <s id="id.000588">Sit <lb/>enim ratio <expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> quam <lb/>mobile fertur ea: quam ha-<pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.068.jpg" pagenum="29"/><foreign lang="greek"><gap/></foreign><lb/>bet <foreign lang="greek">a b</foreign> ad <foreign lang="greek">a g,</foreign> &amp; quidem <lb/><foreign lang="greek">a</foreign> feratur ad <foreign lang="greek">b,</foreign> &amp; <foreign lang="greek">a b_</foreign><lb/>etiam feratur ad <foreign lang="greek">h g</foreign>: la&shy;<lb/>tum vero &longs;it <foreign lang="greek">a</foreign> ad <foreign lang="greek">d,</foreign> &amp; <lb/><foreign lang="greek">a b</foreign> ad <foreign lang="greek">e.</foreign> Igitur cum latio&shy;<lb/>nis ratio erat ea quam ha&shy;<lb/>bet <foreign lang="greek">a b</foreign> ad <foreign lang="greek">a g</foreign>: nece&longs;&longs;e <lb/>e&longs;t &amp; ip&longs;am <foreign lang="greek">a d</foreign> ad <foreign lang="greek">a e</foreign> ean&shy;<lb/>dem habere rationcm. </s>
  
 <s id="id.000589">Si&shy;<lb/>mile e&longs;t enim ratione par&shy;<lb/>uum quadrilaterum maio&shy;<lb/>ri. </s> <s id="id.000589">Si&shy;<lb/>mile e&longs;t enim ratione par&shy;<lb/>uum quadrilaterum maio&shy;<lb/>ri. </s>
  
 <s id="id.000590">Itaque &amp; eadem diame&shy;<lb/>ter vtriu&longs;que, &amp; ip&longs;um <foreign lang="greek">a</foreign><lb/>erat vbi <foreign lang="greek">z.</foreign> Eodem modo <lb/>demon&longs;trabitur <expan abbr="vbic&utilde;que">vbicunque</expan> <lb/>latio deprehen&longs;a fuerit. </s> <s id="id.000590">Itaque &amp; eadem diame&shy;<lb/>ter vtriu&longs;que, &amp; ip&longs;um <foreign lang="greek">a</foreign><lb/>erat vbi <foreign lang="greek">z.</foreign></s>
  
 <s id="id.000591"><expan abbr="S&etilde;-per">Sen&shy;<lb/>per</expan> enim &longs;upra diametrum <lb/>erit. </s> <s>Eodem modo <lb/>demon&longs;trabitur <expan abbr="vbic&utilde;que">vbicunque</expan> <lb/>latio deprehen&longs;a fuerit. </s>
  
  <s id="id.000591"><expan abbr="S&etilde;-per">Sem&shy;<lb/>per</expan> enim &longs;upra diametrum <lb/>erit. </s>
  
 <s id="id.000592">Manife&longs;tum igitur <lb/>quod latum <expan abbr="&longs;ec&utilde;dum">&longs;ecundum</expan> dia&shy;<lb/>metrum duabus lationi&shy;<lb/>bus nece&longs;&longs;e habet in ratio&shy;<lb/>ne laterum ferri.</s></p><p type="head"> <s id="id.000592">Manife&longs;tum igitur <lb/>quod latum <expan abbr="&longs;ec&utilde;dum">&longs;ecundum</expan> dia&shy;<lb/>metrum duabus lationi&shy;<lb/>bus nece&longs;&longs;e habet in ratio&shy;<lb/>ne laterum ferri.</s></p><p type="head">
  
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 <s id="id.000598">Circuli igitur radius, qui his duabus ita fertur in de&longs;cri&shy;<lb/>ptione circuli, &amp; circulus, qui &agrave; radio tali efficitur, erit admirabilis.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000598">Circuli igitur radius, qui his duabus ita fertur in de&longs;cri&shy;<lb/>ptione circuli, &amp; circulus, qui &agrave; radio tali efficitur, erit admirabilis.<emph.end type="italics"/></s></p><p type="main">
  
 <s id="id.000599">Cum igitur in.] <emph type="italics"/>Aggreditur demon&longs;trare rad&yuml; duas lationes <lb/>nullam habere rationem inter &longs;e. </s> <s id="id.000599">Cum igitur in.] <emph type="italics"/>Aggreditur demon&longs;trare radij duas lationes <lb/>nullam habere rationem inter &longs;e. </s>
  
 <s id="id.000600">Syllog. <!-- REMOVE S-->&longs;ic e&longs;t. </s> 
  
  
  <s id="id.000600">Syllog. &longs;ic e&longs;t. </s>
  
 <s id="id.000601">Omne duabus latio&shy;<lb/>nibus rationem aliquam inter &longs;e &longs;eruantibus latum, fertur &longs;ecundum<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.069.jpg" pagenum="30"/><emph type="italics"/>rectam. </s> <s id="id.000601">Omne duabus latio&shy;<lb/>nibus rationem aliquam inter &longs;e &longs;eruantibus latum, fertur &longs;ecundum<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.069.jpg" pagenum="30"/><emph type="italics"/>rectam. </s>
  
 <s id="id.000602">Radius de&longs;cribens circulum duabus &longs;uis lationibus, non <lb/>Jertur &longs;ecundum rectam. </s> <s id="id.000602">Radius de&longs;cribens circulum duabus &longs;uis lationibus, non <lb/>fertur &longs;ecundum rectam. </s>
  
 <s id="id.000603">Radij igitur iationes in nulla &longs;unt ra&shy;<lb/>tione. </s> <s id="id.000603">Radij igitur lationes in nulla &longs;unt ra&shy;<lb/>tione. </s>
  
 <s id="id.000604">Propo&longs;itio confirmatur cum&verbar; &longs;equenti diagrammate. <lb/></s> <s id="id.000604">Propo&longs;itio confirmatur cum &longs;equenti diagrammate. <lb/></s>
  
 <s id="id.000605">E&longs;to rectangulum<emph.end type="italics"/> <foreign lang="greek">a b h g</foreign> <emph type="italics"/>com-<emph.end type="italics"/><lb/><figure id="id.035.01.069.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.069.1.jpg"/><lb/><emph type="italics"/>prehen&longs;um &longs;ub rectis<emph.end type="italics"/> <foreign lang="greek">a b, a g,</foreign><lb/><emph type="italics"/>qu&aelig; &longs;int inter &longs;e in ratione, quam <lb/>du&aelig; lationes ip&longs;ius<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>habent. <lb/></s> <s id="id.000605">E&longs;to rectangulum<emph.end type="italics"/> <foreign lang="greek">a b h g</foreign> <emph type="italics"/>com-<emph.end type="italics"/><lb/><figure id="id.035.01.069.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.069.1.jpg"/><lb/><emph type="italics"/>prehen&longs;um &longs;ub rectis<emph.end type="italics"/> <foreign lang="greek">a b, a g,</foreign><lb/><emph type="italics"/>qu&aelig; &longs;int inter &longs;e in ratione, quam <lb/>du&aelig; lationes ip&longs;ius<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>habent. <lb/></s>
  
 <s id="id.000606">Et intelligatur a latum ver&longs;us<emph.end type="italics"/><lb/><foreign lang="greek">b</foreign> <emph type="italics"/>perueni&longs;&longs;e ad<emph.end type="italics"/> <foreign lang="greek">d,</foreign> <emph type="italics"/>&amp; ver&longs;us<emph.end type="italics"/><lb/><foreign lang="greek">g</foreign> <emph type="italics"/>perueni&longs;&longs;e ad<emph.end type="italics"/> <foreign lang="greek">e</foreign>: <emph type="italics"/>&longs;icque cum <lb/>lationum ip&longs;ius<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>ratio &longs;it vt<emph.end type="italics"/><lb/><foreign lang="greek">a b</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">a g,</foreign> <emph type="italics"/>ergo erit &amp;<emph.end type="italics"/> <foreign lang="greek">a d</foreign><lb/><emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">a e</foreign>: <emph type="italics"/>vt<emph.end type="italics"/> <foreign lang="greek">a <gap/></foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">a y,</foreign> <emph type="italics"/>&amp; rectrangulum minus<emph.end type="italics"/> <foreign lang="greek">a d z e</foreign> <emph type="italics"/>com&shy;<lb/>munem angulum<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>cum maiori<emph.end type="italics"/> <foreign lang="greek">a b h g</foreign> <emph type="italics"/>habens &amp; &longs;imile erit <lb/>def. </s> <s id="id.000606">Et intelligatur a latum ver&longs;us<emph.end type="italics"/><lb/><foreign lang="greek">b</foreign> <emph type="italics"/>perueni&longs;&longs;e ad<emph.end type="italics"/> <foreign lang="greek">d,</foreign> <emph type="italics"/>&amp; ver&longs;us<emph.end type="italics"/><lb/><foreign lang="greek">g</foreign> <emph type="italics"/>perueni&longs;&longs;e ad<emph.end type="italics"/> <foreign lang="greek">e</foreign>: <emph type="italics"/>&longs;icque cum <lb/>lationum ip&longs;ius<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>ratio &longs;it vt<emph.end type="italics"/><lb/><foreign lang="greek">a b</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">a g,</foreign> <emph type="italics"/>ergo erit &amp;<emph.end type="italics"/> <foreign lang="greek">a d</foreign><lb/><emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">a e</foreign>: <emph type="italics"/>vt<emph.end type="italics"/> <foreign lang="greek">a <gap/></foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">a y,</foreign> <emph type="italics"/>&amp; rectrangulum minus<emph.end type="italics"/> <foreign lang="greek">a d z e</foreign> <emph type="italics"/>com&shy;<lb/>munem angulum<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>cum maiori<emph.end type="italics"/> <foreign lang="greek">a b h g</foreign> <emph type="italics"/>habens &amp; &longs;imile erit <lb/>def. 1. lib. 6. &amp; proinde circa eandem dimentientem conuer&longs;. prop. <lb/>24. lib. 6. </s>
  
 <s id="id.000607">1. lib.  
  
 6. &amp; proinde circa eandem dimentientem conuer&longs;. </s> 
  
 <s id="id.000608">prop.<emph.end type="italics"/><lb/>24. <emph type="italics"/>lib.  
  
 6. Et &longs;ic<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>duabus &longs;uis &longs;ic lationibus latum erit in<emph.end type="italics"/> <foreign lang="greek">z,</foreign> <emph type="italics"/>vt vbi&shy;<lb/>cumque lationes ip&longs;ius<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>&longs;i&longs;tentur, &longs;emper &longs;int &longs;upra diametrum<emph.end type="italics"/><lb/><foreign lang="greek">a h.</foreign> <emph type="italics"/>&longs;iquidem lationes i&longs;t&aelig; &longs;unt 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"/>proinde <lb/>&longs;upra rectam, quia omnis diameter rectanguli recta e&longs;t. </s> <s><emph type="italics"/>Et &longs;ic<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>duabus &longs;uis &longs;ic lationibus latum erit in<emph.end type="italics"/> <foreign lang="greek">z,</foreign> <emph type="italics"/>vt vbi&shy;<lb/>cumque lationes ip&longs;ius<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>&longs;i&longs;tentur, &longs;emper &longs;int &longs;upra diametrum<emph.end type="italics"/><lb/><foreign lang="greek">a h.</foreign> <emph type="italics"/>&longs;iquidem lationes i&longs;t&aelig; &longs;unt 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"/>proinde <lb/>&longs;upra rectam, quia omnis diameter rectanguli recta e&longs;t. </s>
  
 <s id="id.000609">Huic con&shy;<lb/>&longs;entit quod &agrave; Proclo ex Gemino acceptum &longs;ic expo&longs;itum e&longs;t. </s> <s id="id.000609">Huic con&shy;<lb/>&longs;entit quod &agrave; Proclo ex Gemino acceptum &longs;ic expo&longs;itum e&longs;t. </s>
  
 <s id="id.000610">Si qua&shy;<lb/>drangulum duo&longs;que motus qui &aelig;quali celeritate fiant, alterum qui&shy;<lb/>dem per longitudinem: alterum vero per latitudinem intellexeris <lb/>dimetiens producetur recta exi&longs;tens linea, lib.  <s id="id.000610">Si qua&shy;<lb/>drangulum duo&longs;que motus qui &aelig;quali celeritate fiant, alterum qui&shy;<lb/>dem per longitudinem: alterum vero per latitudinem intellexeris <lb/>dimetiens producetur recta exi&longs;tens linea, lib. 2. comm. in def. rect&aelig; <lb/>line&aelig;. </s>
  
 2. comm. <!-- REMOVE S-->in def. </s> 
  
  
  
 <s id="id.000611">rect&aelig; <lb/>line&aelig;. </s> 
  
 <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 &agrave; recta producere rectam, quod <lb/>e&longs;t contra naturam circuli. </s> <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 &agrave; recta producere rectam, quod <lb/>e&longs;t contra naturam circuli. </s>
  
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 <s id="id.000616">Et &longs;it manebit demon&longs;tratio.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000616">Et &longs;it manebit demon&longs;tratio.<emph.end type="italics"/></s></p><p type="main">
  
 <s id="id.000617">Simile e&longs;t enim.] <foreign lang="greek">tw_ lo/gw,</foreign> <emph type="italics"/>id e&longs;t ratione, redundat quia qu&aelig; <lb/>&longs;imilia &longs;unt quadrangula, habent latera, qu&aelig; circum &aelig;quales angu&shy;<lb/>los propertionalia, ex def. </s> <s id="id.000617">Simile e&longs;t enim.] <foreign lang="greek">tw_ lo/gw,</foreign> <emph type="italics"/>id e&longs;t ratione, redundat quia qu&aelig; <lb/>&longs;imilia &longs;unt quadrangula, habent latera, qu&aelig; circum &aelig;quales angu&shy;<lb/>los propertionalia, ex def. 1. lib. 6. elem.<emph.end type="italics"/></s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.070.jpg" pagenum="31"/><p type="main">
  
 <s id="id.000618">1. lib.  <s id="id.000619"><foreign lang="greek"><gap/></foreign></s></p><p type="main">
  
 6. elem.<emph.end type="italics"/></s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.070.jpg" pagenum="31"/><p type="main"> 
  
 <s id="id.000619"><gap/></s></p><p type="main"> 
  
 <s id="id.000620">Si enim in alia aliqua, <lb/>non feretur <expan abbr="&longs;ec&utilde;dum">&longs;ecundum</expan> dia&shy;<lb/>metrum. </s> <s id="id.000620">Si enim in alia aliqua, <lb/>non feretur <expan abbr="&longs;ec&utilde;dum">&longs;ecundum</expan> dia&shy;<lb/>metrum. </s>
  
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 <s id="id.000625">COMMENTARIVS.<!-- KEEP S--></s></p><p type="main"> <s id="id.000625">COMMENTARIVS.<!-- KEEP S--></s></p><p type="main">
  
 <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 excmpli 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&shy;<lb/>trum<emph.end type="italics"/> <foreign lang="greek">a h,</foreign> <emph type="italics"/>nihilominus tamen feretur <lb/>&longs;ecundum rectam, qu&aelig; erit diameter <lb/>figur&aelig; &agrave; lateribus alterius rationis <lb/>con&longs;titut&aelig;, vt e&longs;t in pr&aelig;&longs;enti dia&shy;<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></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.071.jpg" pagenum="32"/><p type="main"> <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&shy;<lb/>trum<emph.end type="italics"/> <foreign lang="greek">a h,</foreign> <emph type="italics"/>nihilominus tamen feretur <lb/>&longs;ecundum rectam, qu&aelig; erit diameter <lb/>figur&aelig; &agrave; lateribus alterius rationis <lb/>con&longs;titut&aelig;, vt e&longs;t in pr&aelig;&longs;enti dia&shy;<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></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.071.jpg" pagenum="32"/><p type="main">
  
 <s id="id.000627">Si vero mobilis.] <emph type="italics"/>Conclu&longs;io e&longs;t confirmata reiterato propo&longs;i&shy;<lb/>tionis pr&aelig;cedentis pro&longs;yllogi&longs;mo, &longs;ic. </s> <s id="id.000627">Si vero mobilis.] <emph type="italics"/>Conclu&longs;io e&longs;t confirmata reiterato propo&longs;i&shy;<lb/>tionis pr&aelig;cedentis pro&longs;yllogi&longs;mo, &longs;ic. </s>
  
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 <s id="id.000638">Demon&longs;trauit enim Ari&longs;toteles in Phy&longs;icis, omnem mo&shy;<lb/>tum e&longs;&longs;e in tempore: alterum, cum amb&aelig; lationes &longs;int in eodem ge&shy;<lb/>nere motus, &longs;cilicet localis, qu&icirc; fiet, vt rationem non habeant. </s> <s id="id.000638">Demon&longs;trauit enim Ari&longs;toteles in Phy&longs;icis, omnem mo&shy;<lb/>tum e&longs;&longs;e in tempore: alterum, cum amb&aelig; lationes &longs;int in eodem ge&shy;<lb/>nere motus, &longs;cilicet localis, qu&icirc; fiet, vt rationem non habeant. </s>
  
 <s id="id.000639">Hoc <lb/>enim repugnat def. </s> <s id="id.000639">Hoc <lb/>enim repugnat def. 3. lib. 5. elem. </s>
  
 <s id="id.000640">3. lib.  
  
 5. elem. </s> 
  
 <s id="id.000641">quantitas enim motus vnius mul&shy;<lb/>tiplicata, alterius vici&szlig;im quantitatem &longs;uperare pote&longs;t. </s> <s id="id.000641">quantitas enim motus vnius mul&shy;<lb/>tiplicata, alterius vici&szlig;im quantitatem &longs;uperare pote&longs;t. </s>
  
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 <s id="id.000643">vt cum duarum rectarum, qu&aelig; parallelogrammum con&longs;tituunt, vna <lb/>e&longs;t latus quadrati alicuius, altera e&longs;t eius diameter. </s> <s id="id.000643">vt cum duarum rectarum, qu&aelig; parallelogrammum con&longs;tituunt, vna <lb/>e&longs;t latus quadrati alicuius, altera e&longs;t eius diameter. </s>
  
 <s id="id.000644">Tunc enim ratio <lb/>e&longs;t rectis illis licet incommen&longs;erabilibus prop.  <s id="id.000644">Tunc enim ratio <lb/>e&longs;t rectis illis licet incommen&longs;erabilibus prop. 116. lib. 10. expre&longs;&longs;a. <lb/></s>
  
 116. lib.  
  
 10. expre&longs;&longs;a. <lb/></s> 
  
 <s id="id.000645">At h&icirc;c vt inter peripheriam &amp; diametrum &longs;it aliqua ratio, veluti <lb/>inter arcum &amp; &longs;ubtendentem: h&aelig;c tamen neque numeris exprimi <lb/>pote&longs;t, nec rectis lineis Geometrice vt videre e&longs;t ex Archimede <lb/>lib.<emph.end type="italics"/> <foreign lang="greek">w_<gap/>i\ uetsh/d. </foreign></s> 
  
 <s id="id.000646"><foreign lang="greek">kuk,</foreign> <emph type="italics"/>&amp; Ptol. <!-- REMOVE S-->lib.  
  
 1.<emph.end type="italics"/> <foreign lang="greek">me/gal. </foreign></s> 
  
  <s id="id.000645">At h&icirc;c vt inter peripheriam &amp; diametrum &longs;it aliqua ratio, veluti <lb/>inter arcum &amp; &longs;ubtendentem: h&aelig;c tamen neque numeris exprimi <lb/>pote&longs;t, nec rectis lineis Geometrice vt videre e&longs;t ex Archimede <lb/>lib.<emph.end type="italics"/> <foreign lang="greek">w_<gap/>i\ uetsh/d. kuk,</foreign><emph type="italics"/>&amp; Ptol. lib. 1.<emph.end type="italics"/> <foreign lang="greek">me/gal. dw<gap/>.</foreign> <emph type="italics"/>quod autem ad <lb/>prius attinet in lationibus illis tempus admittitur, &longs;ed hoc e&longs;t eiu&longs;mo&shy;<lb/>di, vt nullum eius detur in&longs;tans, quo vna latio fiat, quo etiam non <lb/>&amp; altera itidem fiat: quod prioribus licet commune e&longs;&longs;e po&szlig;it: pro&shy;<lb/>pter tamen laterum in&aelig;qualitatem vbi in &aelig;qualia dantur, non ita <lb/>&longs;implex &amp; indiui&longs;ibile e&longs;t. </s>
  
  <s id="id.000648">C&aelig;terum duas has motiones facile ani&shy;<lb/>mo concipiet, qui viderit pueros no&longs;trates &longs;ub medio vere, quo genus <lb/>hoc in&longs;ecti in ro&longs;arijs no&longs;tris abundat, captam vnam grandiorem <lb/>mu&longs;cam viridem Cathelinam ip&longs;i vocant, pede adfuniculum alliga-<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.072.jpg" pagenum="33"/><emph type="italics"/>tam permittere volare: ita tamen vt digitis alterum extremum funi&shy;<lb/>culi retineant. </s>
  
 <s id="id.000647"><foreign lang="greek">dw<gap/>.</foreign> <emph type="italics"/>quod autem ad <lb/>prius attinet in lationibus illis tempus admittitur, &longs;ed hoc e&longs;t eiu&longs;mo&shy;<lb/>di, vt nullum eius detur in&longs;tans, quo vna latio fiat, quo etiam non <lb/>&amp; altera itidem fiat: quod prioribus licet commune e&longs;&longs;e po&szlig;it: pro&shy;<lb/>pter tamen laterum in&aelig;qualitatem vbi in &aelig;qualia dantur, non ita <lb/>&longs;implex &amp; indiui&longs;ibile e&longs;t. </s> <s id="id.000649">H&aelig;c enim in altero extremo mu&longs;ca, tanquam in ex&shy;<lb/>tremo radij circulum de&longs;cribentis volatu &longs;uo de&longs;cribit circulum: hic <lb/>volatus compo&longs;itus e&longs;t &egrave; duobus motibus: vno, quo h&aelig;c mu&longs;ca pro&shy;<lb/>prio fertur, <expan abbr="&longs;ec&utilde;dum">&longs;ecundum</expan> quem &longs;e&longs;e &egrave; vinculo liberare conatur: altero, quo <lb/>per vinculum retinetur, ne euagetur longius, quam longitudo <lb/>funiculi permittit. </s>
  
 <s id="id.000648">C&aelig;terum duas has motiones facile ani&shy;<lb/>mo concipiet, qui viderit pueros no&longs;trates &longs;ub medio vere, quo genus <lb/>hoc in&longs;ecti in ro&longs;ar&yuml;s no&longs;tris abundat, captam vnam grandiorem <lb/>mu&longs;cam viridem Cathelinam ip&longs;i vocant, pede adfuniculum alliga-<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.072.jpg" pagenum="33"/><emph type="italics"/>tam permittere volare: ita tamen vt digitis alterum extremum funi&shy;<lb/>culi retineant. </s> 
  
 <s id="id.000649">H&aelig;c enim in altero extremo mu&longs;ca, tanquam in ex&shy;<lb/>tremo rad&yuml; circulum de&longs;cribentis volatu &longs;uo de&longs;cribit circulum: hic <lb/>volatus compo&longs;itus e&longs;t &egrave; duobus motibus: vno, quo h&aelig;c mu&longs;ca pro&shy;<lb/>prio fertur, <expan abbr="&longs;ec&utilde;dum">&longs;ecundum</expan> quem &longs;e&longs;e &egrave; vinculo liberare conatur: altero, quo <lb/>per vinculum retinetur, ne euagetur longius, quam longitudo <lb/>funiculi permittit. </s> 
  
 <s id="id.000650">Ibi motus mu&longs;c&aelig; violentus e&longs;t, &amp; non naturalis <lb/>vt &agrave; quo etiam cum pes abrumpitur pr&aelig; &longs;uo conatu, aut nodus for&shy;<lb/>tuit&ograve; laxatur, &longs;i liberatur, &longs;tatim rect&agrave; aufugit.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000650">Ibi motus mu&longs;c&aelig; violentus e&longs;t, &amp; non naturalis <lb/>vt &agrave; quo etiam cum pes abrumpitur pr&aelig; &longs;uo conatu, aut nodus for&shy;<lb/>tuit&ograve; laxatur, &longs;i liberatur, &longs;tatim rect&agrave; aufugit.<emph.end type="italics"/></s></p><p type="main">
  
 <s id="id.000651">Si enim &longs;ecundum.] <emph type="italics"/>Hanc particulam parenthe&longs;i &longs;ic [ ] in&shy;<lb/>tercludendam curauimus, quod eam &longs;uperuacuam e&longs;&longs;e cum Leonico <lb/>exi&longs;timemus.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000651">Si enim &longs;ecundum.] <emph type="italics"/>Hanc particulam parenthe&longs;i &longs;ic [ ] in&shy;<lb/>tercludendam curauimus, quod eam &longs;uperuacuam e&longs;&longs;e cum Leonico <lb/>exi&longs;timemus.<emph.end type="italics"/></s></p><p type="main">
  
 <s id="id.000652">Itaque circulare.] <emph type="italics"/>Proinde e&longs;t ac &longs;i diceret, cum via &longs;eu linea <lb/>per quam fertur rad&yuml; extremum mobile &longs;it maxime vniformis, vt <lb/>ex definitione circuli con&longs;tat, nec tamen recta: re&longs;tat, vt &longs;it circula&shy;<lb/>ris &longs;eu rotunda, &agrave; medio &longs;cilicet comprehen&longs;i &longs;pat&yuml; &aelig;qualiter ex omni <lb/>parte di&longs;tans. </s> <s id="id.000652">Itaque circulare.] <emph type="italics"/>Proinde e&longs;t ac &longs;i diceret, cum via &longs;eu linea <lb/>per quam fertur radij extremum mobile &longs;it maxime vniformis, vt <lb/>ex definitione circuli con&longs;tat, nec tamen recta: re&longs;tat, vt &longs;it circula&shy;<lb/>ris &longs;eu rotunda, &agrave; medio &longs;cilicet comprehen&longs;i &longs;patij &aelig;qualiter ex omni <lb/>parte di&longs;tans. </s>
  
 <s id="id.000653">quod nulli alij obliquarum linearum conuenire pore&longs;t: <lb/>non ellip&longs;i quidem, quia licet vna &longs;it linea, &amp; extremum in ea fiat <lb/>primum, vt in peripheria: nullum tamen punctum in eius medio e&longs;t, <lb/>&agrave; quo omnes rect&aelig; ad ellip&longs;is peripheriam &longs;int &aelig;quales: non parabo&shy;<lb/>l&aelig;, non hyperbol&aelig;, non &longs;pirali &longs;eu volut&aelig;. </s> <s id="id.000653">quod nulli alij obliquarum linearum conuenire pore&longs;t: <lb/>non ellip&longs;i quidem, quia licet vna &longs;it linea, &amp; extremum in ea fiat <lb/>primum, vt in peripheria: nullum tamen punctum in eius medio e&longs;t, <lb/>&agrave; quo omnes rect&aelig; ad ellip&longs;is peripheriam &longs;int &aelig;quales: non parabo&shy;<lb/>l&aelig;, non hyperbol&aelig;, non &longs;pirali &longs;eu volut&aelig;. </s>
  
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 <s id="id.000656">Agitur h&icirc;c autem de &longs;implicibus tantum, <lb/>qu&aelig; vno &longs;implici motu, vel &longs;i duobus, ijs &longs;imilibus creantur, &amp; &longs;i&shy;<lb/>milares &longs;unt: quales cum du&aelig; tantum &longs;int recta &longs;cilicet &amp; circula&shy;<lb/>ris, inde bene inferetur &egrave; po&longs;ita &longs;implic&egrave; &longs;i recta non e&longs;t, e&longs;&longs;e cir&shy;<lb/>cularis.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000656">Agitur h&icirc;c autem de &longs;implicibus tantum, <lb/>qu&aelig; vno &longs;implici motu, vel &longs;i duobus, ijs &longs;imilibus creantur, &amp; &longs;i&shy;<lb/>milares &longs;unt: quales cum du&aelig; tantum &longs;int recta &longs;cilicet &amp; circula&shy;<lb/>ris, inde bene inferetur &egrave; po&longs;ita &longs;implic&egrave; &longs;i recta non e&longs;t, e&longs;&longs;e cir&shy;<lb/>cularis.<emph.end type="italics"/></s></p><p type="main">
  
 <s id="id.000657"><gap/></s></p><p type="main"> <s id="id.000657"><foreign lang="greek"><gap/></foreign></s></p><p type="main">
  
 <s id="id.000658">Quod vero recta <expan abbr="de&longs;cri-b&etilde;s">de&longs;cri&shy;<lb/>bens</expan> circulum duabus &longs;imul <lb/>lationib^{9} feratur, <expan abbr="c&utilde;">cum</expan> ex his <lb/>e&longs;t <expan abbr="manife&longs;t&utilde;">manife&longs;tum</expan>, <expan abbr="t&utilde;">tum</expan> quod lata <lb/><expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> <expan abbr="rect&atilde;">rectam</expan> fieret num&shy;<lb/>quam perpendicularis. </s> <s id="id.000658">Quod vero recta <expan abbr="de&longs;cri-b&etilde;s">de&longs;cri&shy;<lb/>bens</expan> circulum duabus &longs;imul <lb/>lationib^{9} feratur, <expan abbr="c&utilde;">cum</expan> ex his <lb/>e&longs;t <expan abbr="manife&longs;t&utilde;">manife&longs;tum</expan>, <expan abbr="t&utilde;">tum</expan> quod lata <lb/><expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> <expan abbr="rect&atilde;">rectam</expan> fieret num&shy;<lb/>quam perpendicularis. </s>
  
 <s id="id.000659">Et <lb/>fieri &agrave; <expan abbr="c&etilde;tro">centro</expan> <expan abbr="perpendicula-r&etilde;">perpendicula&shy;<lb/>rem</expan> [dem&otilde;&longs;trem^{9}]. Sit circu&shy;<pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.073.jpg" pagenum="34"/><gap/><lb/>lus <foreign lang="greek">a b g,</foreign> &amp; extremum <foreign lang="greek">b</foreign><lb/>feratur ad <foreign lang="greek">d,</foreign> perueniet &longs;a&shy;<lb/>ne aliquando ad <foreign lang="greek">g.</foreign> [Si igi&shy;<lb/>tur ferebatur in ratione <lb/>quam habet <foreign lang="greek">b e</foreign> ad <foreign lang="greek">e g,</foreign> fe&shy;<lb/>rebatur &longs;ecundum diame&shy;<lb/>trum <foreign lang="greek"><gap/> g</foreign>: Atnunc cum in <lb/>nulla ratione feratur, &longs;e&shy;<lb/>cundum peripheriam <foreign lang="greek">b e g</foreign><lb/>feretur.]</s></p><p type="head"> <s id="id.000659">Et <lb/>fieri &agrave; <expan abbr="c&etilde;tro">centro</expan> <expan abbr="perpendicula-r&etilde;">perpendicula&shy;<lb/>rem</expan> [<expan abbr="dem&otilde;&longs;trem">demon&longs;trem</expan>^{9}].</s>
  
  <s>Sit circu&shy;<pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.073.jpg" pagenum="34"/><foreign lang="greek"><gap/></foreign><lb/>lus <foreign lang="greek">a b g,</foreign> &amp; extremum <foreign lang="greek">b</foreign><lb/>feratur ad <foreign lang="greek">d,</foreign> perueniet &longs;a&shy;<lb/>ne aliquando ad <foreign lang="greek">g.</foreign></s>
  
  <s>[Si igi&shy;<lb/>tur ferebatur in ratione <lb/>quam habet <foreign lang="greek">b e</foreign> ad <foreign lang="greek">e g,</foreign> fe&shy;<lb/>rebatur &longs;ecundum diame&shy;<lb/>trum <foreign lang="greek"><gap/> g</foreign>: At nunc cum in <lb/>nulla ratione feratur, &longs;e&shy;<lb/>cundum peripheriam <foreign lang="greek">b e g</foreign><lb/>feretur.]</s></p><p type="head">
  
 <s id="id.000660">COMMENTARIVS.<!-- KEEP S--></s></p><p type="main"> <s id="id.000660">COMMENTARIVS.<!-- KEEP S--></s></p><p type="main">
  
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 <s id="id.000662">Confirmatio apertior &longs;ic erit. <lb/></s> <s id="id.000662">Confirmatio apertior &longs;ic erit. <lb/></s>
  
 <s id="id.000663">Radius de&longs;cribens circulum vna tantum latione fertur, aut pluri&shy;<lb/>bus: non vna tantum, quia ad vnam tantum loci differentiam, <lb/>cum &longs;it quid &longs;implici&szlig;imum, ferretur (probat enim hoc Ari&longs;toteles <lb/>cap.  <s id="id.000663">Radius de&longs;cribens circulum vna tantum latione fertur, aut pluri&shy;<lb/>bus: non vna tantum, quia ad vnam tantum loci differentiam, <lb/>cum &longs;it quid &longs;implici&szlig;imum, ferretur (probat enim hoc Ari&longs;toteles <lb/>cap. 2. lib. 1. de C&oelig;lo) Quinetiam &longs;i &longs;ic. </s>
  
 2. lib.  
  
 1. de C&oelig;lo) Quinetiam &longs;i &longs;ic. </s> 
  
 <s id="id.000664">Idem radius &agrave; diametro cir-<emph.end type="italics"/><lb/><figure id="id.035.01.073.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.073.1.jpg"/><lb/><emph type="italics"/>culi digrediens in tran&longs;itu ab vna &longs;emidia&shy;<lb/>metro ad alteram numquam con&longs;equeretur <lb/>cum &longs;itum, per quem ip&longs;i &agrave; centro perpen&shy;<lb/>dicularis e&longs;&longs;et. </s> <s id="id.000664">Idem radius &agrave; diametro cir-<emph.end type="italics"/><lb/><figure id="id.035.01.073.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.073.1.jpg"/><lb/><emph type="italics"/>culi digrediens in tran&longs;itu ab vna &longs;emidia&shy;<lb/>metro ad alteram numquam con&longs;equeretur <lb/>cum &longs;itum, per quem ip&longs;i &agrave; centro perpen&shy;<lb/>dicularis e&longs;&longs;et. </s>
  
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 <s id="id.000667">Et quidem vna, vt <lb/>antror&longs;um: qua qua &longs;i diffunditur, &amp; ab&longs;ce&shy;<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&shy;<lb/>tur longius, quam &aelig;qualitas di&longs;tanti&aelig; vndi&shy;<lb/>que &agrave; centro &longs;eruand&aelig; permittit, vt idem<emph.end type="italics"/> <foreign lang="greek">b</foreign><lb/><emph type="italics"/>ver&longs;us L. <!-- KEEP S--></s> <s id="id.000667">Et quidem vna, vt <lb/>antror&longs;um: qua qua &longs;i diffunditur, &amp; ab&longs;ce&shy;<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&shy;<lb/>tur longius, quam &aelig;qualitas di&longs;tanti&aelig; vndi&shy;<lb/>que &agrave; centro &longs;eruand&aelig; permittit, vt idem<emph.end type="italics"/> <foreign lang="greek">b</foreign><lb/><emph type="italics"/>ver&longs;us L. <!-- KEEP S--></s>
  
 <s id="id.000668">V traque autem h&aelig;c latio quanta &longs;it <lb/>men&longs;uraturlineisrectis, quarum altera in po&longs;te&shy;<lb/>riore diaorammate e&longs;t &longs;inus rectus<emph.end type="italics"/> <foreign lang="greek">g e,</foreign> <emph type="italics"/>altera <lb/>ver&ograve; e&longs;t &longs;inus ver&longs;us<emph.end type="italics"/> <foreign lang="greek">b g.</foreign><!-- KEEP S--></s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.074.jpg" pagenum="35"/><p type="main"> <s id="id.000668">Vtraque autem h&aelig;c latio quanta &longs;it <lb/>men&longs;uraturlineisrectis, quarum altera in po&longs;te&shy;<lb/>riore diagrammate e&longs;t &longs;inus rectus<emph.end type="italics"/> <foreign lang="greek">g e,</foreign> <emph type="italics"/>altera <lb/>ver&ograve; e&longs;t &longs;inus ver&longs;us<emph.end type="italics"/> <foreign lang="greek">b g.</foreign></s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.074.jpg" pagenum="35"/><p type="main">
  
 <s id="id.000669">Demon&longs;tremus.] <emph type="italics"/>Dee&longs;t hoc vocabulum in Gr&aelig;co &longs;ine quo <lb/>&longs;en&longs;us e&longs;t imperfectus.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000669">Demon&longs;tremus.] <emph type="italics"/>Dee&longs;t hoc vocabulum in Gr&aelig;co &longs;ine quo <lb/>&longs;en&longs;us e&longs;t imperfectus.<emph.end type="italics"/></s></p><p type="main">
  
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 <s id="id.000671">hoc enim e&longs;t quod an&shy;<lb/>teae&longs;t demon&longs;tratum.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000671">hoc enim e&longs;t quod an&shy;<lb/>teae&longs;t demon&longs;tratum.<emph.end type="italics"/></s></p><p type="main">
  
 <s id="id.000672"><gap/></s></p><p type="main"> <s id="id.000672"><foreign lang="greek"><gap/></foreign></s></p><p type="main">
  
 <s id="id.000673">Si vero duorum eadem <lb/>vi latorum vnum plus re&shy;<lb/>pellitur, alterum minus: <lb/>&aelig;quum e&longs;t, plus repul&longs;um, <lb/>altero minus repul&longs;o tar&shy;<lb/>dius ferri. </s> <s id="id.000673">Si vero duorum eadem <lb/>vi latorum vnum plus re&shy;<lb/>pellitur, alterum minus: <lb/>&aelig;quum e&longs;t, plus repul&longs;um, <lb/>altero minus repul&longs;o tar&shy;<lb/>dius ferri. </s>
  
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 <s id="id.000677">COMMENTARIVS.<!-- KEEP S--></s></p><p type="main"> <s id="id.000677">COMMENTARIVS.<!-- KEEP S--></s></p><p type="main">
  
 <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 rad&yuml;s in&aelig;&shy;<lb/>qualibus, quod ad celeritatem &amp; tarditatem attinet. </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 in&aelig;&shy;<lb/>qualibus, quod ad celeritatem &amp; tarditatem attinet. </s>
  
 <s id="id.000679">Et quidem <lb/>eam, qu&aelig; &longs;ecundum naturam e&longs;t in radio maiore, maiorem: eam ve&shy;<lb/>ro, qu&aelig; pr&aelig;ter naturam, minorem e&longs;&longs;e in eodem demon&longs;trat, vt ra&shy;<lb/>dium maiorem celerius ferri minore concludat. </s> <s id="id.000679">Et quidem <lb/>eam, qu&aelig; &longs;ecundum naturam e&longs;t in radio maiore, maiorem: eam ve&shy;<lb/>ro, qu&aelig; pr&aelig;ter naturam, minorem e&longs;&longs;e in eodem demon&longs;trat, vt ra&shy;<lb/>dium maiorem celerius ferri minore concludat. </s>
  
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 <s id="id.000688"><emph type="italics"/>Illu&longs;trari h&aelig;c <expan abbr="c&otilde;clu&longs;io">conclu&longs;io</expan> po&longs;&longs;et &longs;imilitudine ampli &amp; lat&egrave; patentis re&shy;<lb/>gni, in cuius medio tanquam centro, cum rex pr&aelig;&longs;ideat, partes me&shy;<lb/>dio vicin&aelig; regis legibus magis coarctantur &amp; continentur: quam <lb/>remot&aelig;.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000688"><emph type="italics"/>Illu&longs;trari h&aelig;c <expan abbr="c&otilde;clu&longs;io">conclu&longs;io</expan> po&longs;&longs;et &longs;imilitudine ampli &amp; lat&egrave; patentis re&shy;<lb/>gni, in cuius medio tanquam centro, cum rex pr&aelig;&longs;ideat, partes me&shy;<lb/>dio vicin&aelig; regis legibus magis coarctantur &amp; continentur: quam <lb/>remot&aelig;.<emph.end type="italics"/></s></p><p type="main">
  
 <s id="id.000689"><gap/></s></p><p type="main"> <s id="id.000689"><foreign lang="greek"><gap/></foreign></s></p><p type="main">
  
 <s id="id.000690">Et fertur motu <expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> <lb/>naturam per peripheriam: <lb/>pr&aelig;ter <expan abbr="natur&atilde;">naturam</expan> vero in <expan abbr="tr&atilde;&longs;-uer&longs;um">tran&longs;&shy;<lb/>uer&longs;um</expan>, &amp; centrum ver&longs;us. <lb/></s> <s id="id.000690">Et fertur motu <expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> <lb/>naturam per peripheriam: <lb/>pr&aelig;ter <expan abbr="natur&atilde;">naturam</expan> vero in <expan abbr="tr&atilde;&longs;-uer&longs;um">tran&longs;&shy;<lb/>uer&longs;um</expan>, &amp; centrum ver&longs;us. <lb/></s>
  
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 <s id="id.000702">Relinquitur ergo vt ea <lb/>&longs;it contra <expan abbr="natur&atilde;">naturam</expan> &amp; per accidens, qua ad ip&longs;um centrum reuellitur.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000702">Relinquitur ergo vt ea <lb/>&longs;it contra <expan abbr="natur&atilde;">naturam</expan> &amp; per accidens, qua ad ip&longs;um centrum reuellitur.<emph.end type="italics"/></s></p><p type="main">
  
 <s id="id.000703"><gap/></s></p><p type="main"> <s id="id.000703"><foreign lang="greek"><gap/></foreign></s></p><p type="main">
  
 <s id="id.000704">Quod vero minor plus <lb/>pr&aelig;ter naturam moueatur: <lb/>quam maior earum, qu&ecedil; ex <lb/>centro <expan abbr="de&longs;crib&utilde;t">de&longs;cribunt</expan> circulos, <lb/>ex his erit manife&longs;tum. </s> <s id="id.000704">Quod vero minor plus <lb/>pr&aelig;ter naturam moueatur: <lb/>quam maior earum, qu&ecedil; ex <lb/>centro <expan abbr="de&longs;crib&utilde;t">de&longs;cribunt</expan> circulos, <lb/>ex his erit manife&longs;tum. </s>
  
 <s id="id.000705">Sit <lb/>circulus <foreign lang="greek">b g d e,</foreign> &amp; alter <lb/>minor <foreign lang="greek">x n m c,</foreign> eiu&longs;dem <expan abbr="c&etilde;-tri">cen&shy;<lb/>tri</expan> <foreign lang="greek">a,</foreign> Et traduct&aelig; &longs;int dia&shy;<lb/>metri in magno quidem <lb/><foreign lang="greek">g d, &amp; b e</foreign>: in minori <foreign lang="greek">m c &amp; <lb/>x n</foreign>: atque alterolongum <lb/>compleatur <foreign lang="greek">d y r g.</foreign> Si igi&shy;<lb/>tur <foreign lang="greek">a b</foreign> de&longs;cribens <expan abbr="circul&utilde;">circulum</expan> <lb/>perueniet ad id vnde mo&shy;<lb/>ueri c&oelig;pit, manife&longs;tum e&longs;t <lb/>quod fertur ad ip&longs;am [<foreign lang="greek">a b</foreign>] <lb/>&longs;imiliter <foreign lang="greek">a x</foreign> perueniet ad <lb/>ip&longs;am <foreign lang="greek">a x.</foreign> Tardius autem <lb/>fertur <foreign lang="greek">a x</foreign>: quam <foreign lang="greek">a b,</foreign> vt <lb/><expan abbr="dict&utilde;">dictum</expan> e&longs;t, propter maiorem <lb/><expan abbr="repul&longs;ion&etilde;">repul&longs;ionem</expan> &amp; reuul&longs;ionem <lb/>ip&longs;ius <foreign lang="greek">a x.</foreign> Ducatur vero <lb/>recta <foreign lang="greek">a q h, &amp; a q</foreign> excitetur <lb/>perpendicularis ad <foreign lang="greek">a b,</foreign> qu&ecedil; <lb/>&longs;it <foreign lang="greek">q z</foreign> in circulo [minori]. <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.077.jpg" pagenum="38"/><gap/><lb/>Et rur&longs;us per <foreign lang="greek">q</foreign> ducatur pa&shy;<lb/>rallela ip&longs;i <foreign lang="greek">a b</foreign> qu&aelig; &longs;it <foreign lang="greek">q w <lb/>&amp; w n</foreign> perpendicularis ip&longs;i <lb/><foreign lang="greek">a b</foreign> tum &amp; <foreign lang="greek">h k.</foreign> Sunt vero <lb/><foreign lang="greek">w n &amp; q z</foreign> &aelig;quales. </s> <s id="id.000705">Sit <lb/>circulus <foreign lang="greek">b g d e,</foreign> &amp; alter <lb/>minor <foreign lang="greek">x n m c,</foreign> eiu&longs;dem <expan abbr="c&etilde;-tri">cen&shy;<lb/>tri</expan> <foreign lang="greek">a,</foreign> Et traduct&aelig; &longs;int dia&shy;<lb/>metri in magno quidem <lb/><foreign lang="greek">g d, &amp; b e</foreign>: in minori <foreign lang="greek">m c &amp; <lb/>x n</foreign>: atque alterolongum <lb/>compleatur <foreign lang="greek">d y r g.</foreign></s>
  
  <s>Si igi&shy;<lb/>tur <foreign lang="greek">a b</foreign> de&longs;cribens <expan abbr="circul&utilde;">circulum</expan> <lb/>perueniet ad id vnde mo&shy;<lb/>ueri c&oelig;pit, manife&longs;tum e&longs;t <lb/>quod fertur ad ip&longs;am [<foreign lang="greek">a b</foreign>] <lb/>&longs;imiliter <foreign lang="greek">a x</foreign> perueniet ad <lb/>ip&longs;am <foreign lang="greek">a x.</foreign></s>
  
  <s>Tardius autem <lb/>fertur <foreign lang="greek">a x</foreign>: quam <foreign lang="greek">a b,</foreign> vt <lb/><expan abbr="dict&utilde;">dictum</expan> e&longs;t, propter maiorem <lb/><expan abbr="repul&longs;ion&etilde;">repul&longs;ionem</expan> &amp; reuul&longs;ionem <lb/>ip&longs;ius <foreign lang="greek">a x.</foreign></s>
  
  <s>Ducatur vero <lb/>recta <foreign lang="greek">a q h, &amp; a q</foreign> excitetur <lb/>perpendicularis ad <foreign lang="greek">a b,</foreign> qu&ecedil; <lb/>&longs;it <foreign lang="greek">q z</foreign> in circulo [minori].</s><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.077.jpg" pagenum="38"/>
  
  <s><foreign lang="greek"><gap/></foreign></s>
  
  <s>Et rur&longs;us per <foreign lang="greek">q</foreign> ducatur pa&shy;<lb/>rallela ip&longs;i <foreign lang="greek">a b</foreign> qu&aelig; &longs;it <foreign lang="greek">q w <lb/>&amp; w n</foreign> perpendicularis ip&longs;i <lb/><foreign lang="greek">a b</foreign> tum &amp; <foreign lang="greek">h k.</foreign></s>
  
  <s>Sunt vero <lb/><foreign lang="greek">w n &amp; q z</foreign> &aelig;quales. </s>
  
 <s id="id.000706">Rur&longs;us <lb/><foreign lang="greek">b n</foreign> e&longs;t minor: quam <foreign lang="greek">x z.</foreign> In <lb/>circulis enim in&aelig;qualibus <lb/>rect&ecedil; &ecedil;quales ad rectos dia&shy;<lb/>metro excitat&aelig;, de diame&shy;<lb/>tro circulorum maiorum <lb/><expan abbr="&longs;egment&utilde;">&longs;egmentum</expan> minus auferunt. <lb/></s> <s id="id.000706">Rur&longs;us <lb/><foreign lang="greek">b n</foreign> e&longs;t minor: quam <foreign lang="greek">x z.</foreign> In <lb/>circulis enim in&aelig;qualibus <lb/>rect&ecedil; &ecedil;quales ad rectos dia&shy;<lb/>metro excitat&aelig;, de diame&shy;<lb/>tro circulorum maiorum <lb/><expan abbr="&longs;egment&utilde;">&longs;egmentum</expan> minus auferunt. <lb/></s>
  
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 <s id="id.000715"><emph type="italics"/>A puncto<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>ad punctum<emph.end type="italics"/> <foreign lang="greek">q</foreign> <emph type="italics"/>ducatur recta<emph.end type="italics"/> <foreign lang="greek">a q,</foreign> <emph type="italics"/>&amp; producatur in<emph.end type="italics"/><lb/><foreign lang="greek">h</foreign> <emph type="italics"/>&longs;itque<emph.end type="italics"/> <foreign lang="greek">a q h.</foreign></s></p><p type="main"> <s id="id.000715"><emph type="italics"/>A puncto<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>ad punctum<emph.end type="italics"/> <foreign lang="greek">q</foreign> <emph type="italics"/>ducatur recta<emph.end type="italics"/> <foreign lang="greek">a q,</foreign> <emph type="italics"/>&amp; producatur in<emph.end type="italics"/><lb/><foreign lang="greek">h</foreign> <emph type="italics"/>&longs;itque<emph.end type="italics"/> <foreign lang="greek">a q h.</foreign></s></p><p type="main">
  
 <s id="id.000716"><emph type="italics"/>Tum &agrave; puncto<emph.end type="italics"/> <foreign lang="greek">q</foreign> <emph type="italics"/>excitetur perpendicularis line&aelig;<emph.end type="italics"/> <foreign lang="greek">a x</foreign> <emph type="italics"/>prop.  <s id="id.000716"><emph type="italics"/>Tum &agrave; puncto<emph.end type="italics"/> <foreign lang="greek">q</foreign> <emph type="italics"/>excitetur perpendicularis line&aelig;<emph.end type="italics"/> <foreign lang="greek">a x</foreign> <emph type="italics"/>prop. 12. <lb/>lib. 1. &longs;itque<emph.end type="italics"/> <foreign lang="greek">q z.</foreign></s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.078.jpg" pagenum="39"/><p type="main">
  
 12. <lb/>lib.  
  
 1. &longs;itque<emph.end type="italics"/> <foreign lang="greek">q z.</foreign></s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.078.jpg" pagenum="39"/><p type="main"> <s id="id.000717"><emph type="italics"/>Et per punctum<emph.end type="italics"/> <foreign lang="greek">q</foreign> <emph type="italics"/>ducatur parallela rect&aelig;<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>prop. 31. lib. 1. <lb/>qu&aelig; &longs;it<emph.end type="italics"/> <foreign lang="greek">q w.</foreign></s></p><figure id="id.035.01.078.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.078.1.jpg"/><p type="main">
  
 <s id="id.000717"><emph type="italics"/>Et per punctum<emph.end type="italics"/> <foreign lang="greek">q</foreign> <emph type="italics"/>ducatur parallela rect&aelig;<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>prop.  
  
 31. lib.  
  
 1. <lb/>qu&aelig; &longs;it<emph.end type="italics"/> <foreign lang="greek">q w.</foreign></s></p><figure id="id.035.01.078.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.078.1.jpg"/><p type="main"> 
  
 <s id="id.000718"><emph type="italics"/>Rur&longs;us &agrave; puncto<emph.end type="italics"/> <foreign lang="greek">w</foreign> <emph type="italics"/>excitetur perpendicularis line&aelig;<emph.end type="italics"/> <foreign lang="greek">a b,</foreign> <emph type="italics"/>&longs;itque<emph.end type="italics"/><lb/><foreign lang="greek">w n</foreign>: <emph type="italics"/>&amp; &longs;ic parallelogrammum erit<emph.end type="italics"/> <foreign lang="greek">w n z q</foreign> <emph type="italics"/>ex def. </s> <s id="id.000718"><emph type="italics"/>Rur&longs;us &agrave; puncto<emph.end type="italics"/> <foreign lang="greek">w</foreign> <emph type="italics"/>excitetur perpendicularis line&aelig;<emph.end type="italics"/> <foreign lang="greek">a b,</foreign> <emph type="italics"/>&longs;itque<emph.end type="italics"/><lb/><foreign lang="greek">w n</foreign>: <emph type="italics"/>&amp; &longs;ic parallelogrammum erit<emph.end type="italics"/> <foreign lang="greek">w n z q</foreign> <emph type="italics"/>ex def. </s>
  
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 <s id="id.000720"><emph type="italics"/>Sicque<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>motum ad<emph.end type="italics"/> <foreign lang="greek">w</foreign> <emph type="italics"/>tantum confecit &longs;pat&yuml; &longs;ecundum natu&shy;<lb/>ram, quam<emph.end type="italics"/> <foreign lang="greek">x</foreign> <emph type="italics"/>motum ad<emph.end type="italics"/> <foreign lang="greek"><expan abbr="q.">que</expan></foreign> <emph type="italics"/>Spatia enim cum metiatur perpendicu&shy;<lb/>laris, vtpote optima <expan abbr="m&etilde;&longs;ura">men&longs;ura</expan>, quia minima, &amp; &longs;ola regularis &amp; nota. <lb/></s> <s id="id.000720"><emph type="italics"/>Sicque<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>motum ad<emph.end type="italics"/> <foreign lang="greek">w</foreign> <emph type="italics"/>tantum confecit &longs;pat&yuml; &longs;ecundum natu&shy;<lb/>ram, quam<emph.end type="italics"/> <foreign lang="greek">x</foreign> <emph type="italics"/>motum ad<emph.end type="italics"/> <foreign lang="greek"><expan abbr="q.">que</expan></foreign> <emph type="italics"/>Spatia enim cum metiatur perpendicu&shy;<lb/>laris, vtpote optima <expan abbr="m&etilde;&longs;ura">men&longs;ura</expan>, quia minima, &amp; &longs;ola regularis &amp; 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. </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. &amp; &aelig;quales, quia late&shy;<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&shy;<lb/>bique &longs;patia<emph.end type="italics"/> <foreign lang="greek">b w &amp; x q</foreign> <emph type="italics"/>&aelig;qualia.<emph.end type="italics"/></s></p><p type="main">
  
 <s id="id.000722">&amp; &aelig;quales, quia late&shy;<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&shy;<lb/>bique &longs;patia<emph.end type="italics"/> <foreign lang="greek">b w &amp; x q</foreign> <emph type="italics"/>&aelig;qualia.<emph.end type="italics"/></s></p><p type="main"> 
  
 <s id="id.000723"><foreign lang="greek">b n</foreign> <emph type="italics"/>vero eadem ratione metitur &longs;patium motus pr&aelig;ter naturam <lb/>ip&longs;ius<emph.end type="italics"/> <foreign lang="greek">b, &amp; 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&shy;<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 pr&aelig;ter naturam <lb/>maior in eodem &longs;patio motus naturalis: quam puncti<emph.end type="italics"/> <foreign lang="greek">b.</foreign></s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.079.jpg" pagenum="40"/><p type="main"> <s id="id.000723"><foreign lang="greek">b n</foreign> <emph type="italics"/>vero eadem ratione metitur &longs;patium motus pr&aelig;ter naturam <lb/>ip&longs;ius<emph.end type="italics"/> <foreign lang="greek">b, &amp; 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&shy;<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 pr&aelig;ter naturam <lb/>maior in eodem &longs;patio motus naturalis: quam puncti<emph.end type="italics"/> <foreign lang="greek">b.</foreign></s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.079.jpg" pagenum="40"/><p type="main">
  
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 <s id="id.000726"><foreign lang="greek">a q h</foreign>] <emph type="italics"/><expan abbr="Punct&utilde;">Punctum</expan><emph.end type="italics"/> <foreign lang="greek">q</foreign> <emph type="italics"/>vbi libet in peripheria accipitur ad de&longs;ignandum <lb/>quoduis <expan abbr="&longs;pati&utilde;">&longs;patium</expan>, quod confecerit<emph.end type="italics"/> <foreign lang="greek">x</foreign> <emph type="italics"/><expan abbr="extrem&utilde;">extremum</expan> mobile minoris rad&yuml;<emph.end type="italics"/> <foreign lang="greek">a x.</foreign></s></p><p type="main"> <s id="id.000726"><foreign lang="greek">a q h</foreign>] <emph type="italics"/><expan abbr="Punct&utilde;">Punctum</expan><emph.end type="italics"/> <foreign lang="greek">q</foreign> <emph type="italics"/>vbi libet in peripheria accipitur ad de&longs;ignandum <lb/>quoduis <expan abbr="&longs;pati&utilde;">&longs;patium</expan>, quod confecerit<emph.end type="italics"/> <foreign lang="greek">x</foreign> <emph type="italics"/><expan abbr="extrem&utilde;">extremum</expan> mobile minoris rad&yuml;<emph.end type="italics"/> <foreign lang="greek">a x.</foreign></s></p><p type="main">
  
 <s id="id.000727">Et <foreign lang="greek">a q</foreign> excitetur.] <emph type="italics"/>A puncto<emph.end type="italics"/> <foreign lang="greek">q</foreign> <emph type="italics"/>extra lineam<emph.end type="italics"/> <foreign lang="greek">a x</foreign> <emph type="italics"/>dato ex&shy;<lb/>citatur in ip&longs;am perpendicularis, qu&aelig; e&longs;t<emph.end type="italics"/> <foreign lang="greek">q z</foreign> <emph type="italics"/>prop.  <s id="id.000727">Et <foreign lang="greek">a q</foreign> excitetur.] <emph type="italics"/>A puncto<emph.end type="italics"/> <foreign lang="greek">q</foreign> <emph type="italics"/>extra lineam<emph.end type="italics"/> <foreign lang="greek">a x</foreign> <emph type="italics"/>dato ex&shy;<lb/>citatur in ip&longs;am perpendicularis, qu&aelig; e&longs;t<emph.end type="italics"/> <foreign lang="greek">q z</foreign> <emph type="italics"/>prop. 12. lib. 1. elem.<emph.end type="italics"/></s></p><p type="main">
  
 12. lib.  
  
 1. elem.<emph.end type="italics"/></s></p><p type="main"> 
  
 <s id="id.000728">Et rur&longs;us per <foreign lang="greek">q</foreign>] <emph type="italics"/>Per punctum<emph.end type="italics"/> <foreign lang="greek">q</foreign> <emph type="italics"/>datum dat&aelig; rect&aelig;<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>duci&shy;<lb/>tur parallela prop.  
  
 31. lib.  
  
 1. elem.<emph.end type="italics"/></s></p><p type="main"> 
  
 <s id="id.000729">Et <foreign lang="greek">w n</foreign> perpend.] <emph type="italics"/>prop. </s> 
  
 <s id="id.000730">12. lib.  <s id="id.000728">Et rur&longs;us per <foreign lang="greek">q</foreign>] <emph type="italics"/>Per punctum<emph.end type="italics"/> <foreign lang="greek">q</foreign> <emph type="italics"/>datum dat&aelig; rect&aelig;<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>duci&shy;<lb/>tur parallela prop. 31. lib. 1. elem.<emph.end type="italics"/></s></p><p type="main">
  
 1. elem.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000729">Et <foreign lang="greek">w n</foreign> perpend.] <emph type="italics"/>prop. 12. lib. 1. elem.<emph.end type="italics"/></s></p><p type="main">
  
 <s id="id.000731">Sunt vero <foreign lang="greek">w n</foreign> &amp;] <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/>t&ugrave;m<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&shy;<lb/>gulos internos ad <expan abbr="ea&longs;d&etilde;">ea&longs;dem</expan> partes rectos, ex fab. </s> <s id="id.000731">Sunt vero <foreign lang="greek">w n</foreign> &amp;] <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/>t&ugrave;m<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&shy;<lb/>gulos internos ad <expan abbr="ea&longs;d&etilde;">ea&longs;dem</expan> partes rectos, ex fab. proinde &aelig;quales ax. 10. <lb/><expan abbr="itaq;">itaque</expan> parallel&aelig; prop. 28. lib. 1. </s>
  
 <s id="id.000732">proinde &aelig;quales ax. </s> <s><expan abbr="parallelogr&atilde;m&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&shy;<lb/>rall.</s>
  
 <s id="id.000733">10. <lb/><expan abbr="itaq;">itaque</expan> parallel&aelig; prop.  <s id="id.000735">quare eius latera oppo&longs;ita<emph.end type="italics"/> <foreign lang="greek">w n &amp; q z</foreign> <emph type="italics"/><expan abbr="er&utilde;t">erunt</expan> &aelig;qualia prop. 34. lib. 1.<emph.end type="italics"/></s></p><p type="main">
  
 28. lib.  
  
 1. <expan abbr="parallelogr&atilde;m&utilde;">parallelogrammum</expan> erit<emph.end type="italics"/> <foreign lang="greek">w n z <expan abbr="q.">que</expan></foreign> <emph type="italics"/>per def. </s> 
  
 <s id="id.000734">pa&shy;<lb/>rall. </s> 
  
 <s id="id.000735">quare eius latera oppo&longs;ita<emph.end type="italics"/> <foreign lang="greek">w n &amp; q z</foreign> <emph type="italics"/><expan abbr="er&utilde;t">erunt</expan> &aelig;qualia prop.  
  
 34. lib.  
  
 1.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main"> 
  
 <s id="id.000736">In circulis.] <emph type="italics"/>Ex hoc loco elicitur hoc theorema. </s> <s id="id.000736">In circulis.] <emph type="italics"/>Ex hoc loco elicitur hoc theorema. </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></p><p type="main"> <s id="id.000742"><emph type="italics"/>De&longs;cribere circulum minorem qui alterum datum maiorem <lb/>interius tangat.<emph.end type="italics"/></s></p><p type="main">
  
 <s id="id.000743"><emph type="italics"/>Sit datus circulus A B K C maior, ab A per D centrum reper&shy;<lb/>tum prop.  <s id="id.000743"><emph type="italics"/>Sit datus circulus A B K C maior, ab A per D centrum reper&shy;<lb/>tum prop. 1. lib. 3. ducatur A k diameter. </s>
  
 1. lib.  
  
 3. 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 &amp; D, &amp; interuallo <lb/>E A de&longs;cribatur A F G. hic <lb/>tanget interius circulum A B k <lb/>C datum in puncto A. <!-- KEEP S--></s> 
  
 <s id="id.000745">Nam &longs;i <lb/>&amp; &longs;ecet, vt in puncto H, ducta <lb/>H E. erit &aelig;qualis ip&longs;i E A def. <lb/></s> 
  
 <s id="id.000746">15. lib.  
  
 1. non erit igitur E A mi&shy;<lb/>nima omnium qu&aelig; ab E puncto <lb/>extra D centrum circuli A B <lb/>K C cadunt in eius concauam pe&shy;<lb/>ripheriam, quod e&longs;t contra prop. <lb/></s> 
  
 <s id="id.000747">7. lib.  
  
 3. non erat igitur H punctum commune vtrique circulo, &amp; <lb/>&longs;ic de al&yuml;s. </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></p><p type="main"> 
  
 <s id="id.000749"><emph type="italics"/>Iam nunc de A G maiori &longs;emidiametro detrahatur portio A H <lb/>&aelig;qualis D H minori prop.  
  
 3. lib.  
  
 1. centro H interuallo A H de&longs;&shy;<lb/>cribatur circulus A M L po&longs;tul. </s> 
  
 <s id="id.000750">3. qui erit &aelig;qualis dato D E F. <lb/>def. </s> 
  
 <s id="id.000751">1. lib.  
  
 3. Et tanget intus circulum A B C in puncto A exprobl. <lb/></s> 
  
 <s id="id.000752">pr&aelig;&longs;umpto. </s> 
  
 <s id="id.000753">per punctum B ducaeur parallela B M prop.  
  
 31. lib.  
  
 1. <lb/>&amp; per eandem parallela M N qu&aelig; per 34. lib. <!-- REMOVE S-->eiu&longs;dem cum &longs;it <lb/>&aelig;qualis ip&longs;i B K erit &amp; &aelig;qualis ip&longs;i. </s> 
  
  
  
 <s id="id.000754">E I ax. </s> 
  
 <s id="id.000755">1. connectantur M H, <lb/>E H po&longs;t. </s> 
  
 <s id="id.000756">1.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main"> 
  
 <s id="id.000757">Demon&longs;t. <emph type="italics"/>Po&longs;tquam ax. </s> 
  
 <s id="id.000758">3. A N, D I &aelig;quales &longs;unt quia reli&shy;<lb/>qu&aelig; ex &aelig;qualibus A H, D H ex fab. </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 &amp; D, &amp; interuallo <lb/>E A de&longs;cribatur A F G. hic <lb/>tanget interius circulum A B k <lb/>C datum in puncto A. </s>
  
 <s id="id.000759">demptis &aelig;qualibus N H, <lb/>I H qu&aelig; latera &longs;unt &longs;ub &aelig;qualibus angulis duorum triangulorum <lb/>M N H &amp; I E H habentium duos angulos duobus angulis <lb/>&aelig;quales, &amp; latus lateri &aelig;quale vt e&longs;t in 26. prop.  <s id="id.000745">Nam &longs;i <lb/>&amp; &longs;ecet, vt in puncto H, ducta <lb/>H E. erit &aelig;qualis ip&longs;i E A def. <lb/>15. lib. 1. non erit igitur E A mi&shy;<lb/>nima omnium qu&aelig; ab E puncto <lb/>extra D centrum circuli A B <lb/>K C cadunt in eius concauam pe&shy;<lb/>ripheriam, quod e&longs;t contra prop. <lb/>7. lib. 3. non erat igitur H punctum commune vtrique circulo, &amp; <lb/>&longs;ic de alijs. </s>
  
 lib.  <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></p><p type="main">
  
 1. nempe angu&shy;<lb/>lus qui ad N rectus e&longs;t prop. </s> <s id="id.000749"><emph type="italics"/>Iam nunc de A G maiori &longs;emidiametro detrahatur portio A H <lb/>&aelig;qualis D H minori prop. 3. lib. 1. centro H interuallo A H de&longs;&shy;<lb/>cribatur circulus A M L po&longs;tul. </s>
  
 <s id="id.000760">29. lib.  <s id="id.000750">3. qui erit &aelig;qualis dato D E F. <lb/>def. 1. lib. 3. </s>
  
 1. &amp; qui ad I, rectus ex hypoth. <lb/></s> <s>Et tanget intus circulum A B C in puncto A exprobl. <lb/>pr&aelig;&longs;umpto. per punctum B ducaeur parallela B M prop. 31. lib. 1. <lb/>&amp; per eandem parallela M N qu&aelig; per 34. lib. eiu&longs;dem cum &longs;it <lb/>&aelig;qualis ip&longs;i B K erit &amp; &aelig;qualis ip&longs;i. </s>
  
 <s id="id.000761">ideo &aelig;quales ax. </s> <s id="id.000754">E I ax. 1. connectantur M H, <lb/>E H po&longs;t. </s>
  
 <s id="id.000762">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"/>&amp; angulus E H I ad centrum con&longs;titutus in &aelig;qualibus circulis ex <lb/>fab. </s> <s id="id.000756">1.<emph.end type="italics"/></s></p><p type="main">
  
 <s id="id.000763">&longs;unt &aelig;quales prop.  <s id="id.000757">Demon&longs;t. <emph type="italics"/>Po&longs;tquam ax. 3. A N, D I &aelig;quales &longs;unt quia reli&shy;<lb/>qu&aelig; ex &aelig;qualibus A H, D H ex fab. demptis &aelig;qualibus N H, <lb/>I H qu&aelig; latera &longs;unt &longs;ub &aelig;qualibus angulis duorum triangulorum <lb/>M N H &amp; I E H habentium duos angulos duobus angulis <lb/>&aelig;quales, &amp; latus lateri &aelig;quale vt e&longs;t in 26. prop. lib. 1. nempe angu&shy;<lb/>lus qui ad N rectus e&longs;t prop. 29. lib. 1. &amp; qui ad I, rectus ex hypoth. <lb/>ideo &aelig;quales 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"/>&amp; angulus E H I ad centrum con&longs;titutus in &aelig;qualibus circulis ex <lb/>fab. &longs;unt &aelig;quales prop. 27. lib. 3. quia &aelig;quales &longs;unt peripheri&aelig; A M, <lb/>D E ablat&aelig; &longs;cilicet ab &aelig;qualibus &longs;emi&szlig;ibus M N &amp; E I ex <lb/>fab. prop. 3. &amp; 29. lib. 3. &amp; &longs;ic reliquum latus N H &aelig;quale e&longs;t re&shy;<lb/>liquo I H. </s>
  
 27. lib.  <s id="id.000765">Ergo cum tota A N &aelig;qualis D I &longs;it maior A K <lb/>parte &longs;ua ax. 9. erit &amp; D I maior ip&longs;a A K.<emph.end type="italics"/></s></p><p type="main">
  
 3. quia &aelig;quales &longs;unt peripheri&aelig; A M, <lb/>D E ablat&aelig; &longs;cilicet ab &aelig;qualibus &longs;emi&szlig;ibus M N &amp; E I ex <lb/>fab. </s> <s id="id.000767">Concl. <emph type="italics"/>Ergo perpendiculares &agrave; peripher&yuml;s in &longs;emidiametros &amp; <lb/>ct. quod fuit demon&longs;trandum. </s>
  
 <s id="id.000764">prop.  
  
 3. &amp; 29. lib.  
  
 3. &amp; &longs;icreliquum latus N H &aelig;quale e&longs;t re&shy;<lb/>liquo I H. <!-- KEEP S--></s> 
  
 <s id="id.000765">Ergo cum tota A N &aelig;qualis D I &longs;it maior A K <lb/>parte &longs;ua ax. </s> 
  
 <s id="id.000766">9. erit &amp; D I maior ip&longs;a A K.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main"> 
  
 <s id="id.000767">Concl. <emph type="italics"/>Ergo perpendiculares &agrave; peripher&yuml;s in &longs;emidiametros &amp; <lb/>ct. </s> 
  
 <s id="id.000768">quod fuit demon&longs;trandum. </s> 
  
 <s id="id.000769">Hoc autem theorema videtur <expan abbr="quo-d&atilde;modo">quo&shy;<lb/>dammodo</expan><emph.end type="italics"/> <foreign lang="greek"><gap/>a/doxon.</foreign> <emph type="italics"/>Erat enim veri&longs;imilius in maiore circulo <expan abbr="&longs;eg-ment&utilde;">&longs;eg&shy;<lb/>mentum</expan> &longs;emidiametri e&longs;&longs;e maius, &amp; in minore minus: at non ita e&longs;t vt <lb/>patuit. </s> <s id="id.000769">Hoc autem theorema videtur <expan abbr="quo-d&atilde;modo">quo&shy;<lb/>dammodo</expan><emph.end type="italics"/> <foreign lang="greek"><gap/>a/doxon.</foreign> <emph type="italics"/>Erat enim veri&longs;imilius in maiore circulo <expan abbr="&longs;eg-ment&utilde;">&longs;eg&shy;<lb/>mentum</expan> &longs;emidiametri e&longs;&longs;e maius, &amp; in minore minus: at non ita e&longs;t vt <lb/>patuit. </s>
  
Line 1727 
Line 1516 
  
 <s id="id.000774">Et &longs;ic in nulla &longs;unt ratione ad vnguem expre&longs;&longs;a: &longs;unt ta&shy;<lb/>men vt hic quodammodo, &amp; vt aiunt fer&egrave;.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000774">Et &longs;ic in nulla &longs;unt ratione ad vnguem expre&longs;&longs;a: &longs;unt ta&shy;<lb/>men vt hic quodammodo, &amp; vt aiunt fer&egrave;.<emph.end type="italics"/></s></p><p type="main">
  
 <s id="id.000775"><gap/></s></p><p type="main"> <s id="id.000775"><foreign lang="greek"><gap/></foreign></s></p><p type="main">
  
 <s id="id.000776">At oportet analoga e&longs;&longs;e, <lb/>vt id quod <expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> <expan abbr="natur&atilde;">naturam</expan>, <lb/>ad id quod <expan abbr="&longs;ec&utilde;dum">&longs;ecundum</expan> natu&shy;<lb/>ram: &longs;ic quod pr&aelig;ter natu&shy;<lb/>ram, ad id quod pr&aelig;ter <expan abbr="na-tur&atilde;">na&shy;<lb/>turam</expan>. </s> <s id="id.000776">At oportet analoga e&longs;&longs;e, <lb/>vt id quod <expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> <expan abbr="natur&atilde;">naturam</expan>, <lb/>ad id quod <expan abbr="&longs;ec&utilde;dum">&longs;ecundum</expan> natu&shy;<lb/>ram: &longs;ic quod pr&aelig;ter natu&shy;<lb/>ram, ad id quod pr&aelig;ter <expan abbr="na-tur&atilde;">na&shy;<lb/>turam</expan>. </s>
  
Line 1735 
Line 1524 
  
 <s id="id.000778">Nece&longs;&longs;e igitur in eo <lb/>tempore <foreign lang="greek">b h</foreign> tran&longs;ij&longs;&longs;e. </s> <s id="id.000778">Nece&longs;&longs;e igitur in eo <lb/>tempore <foreign lang="greek">b h</foreign> tran&longs;ij&longs;&longs;e. </s>
  
 <s id="id.000779">Ibi <lb/>enim erit, vbi proportiona&shy;<lb/>les <expan abbr="c&otilde;ting&etilde;t">contingent</expan> <expan abbr="vtrinq;">vtrinque</expan> motus <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.082.jpg" pagenum="43"/><gap/><lb/>pr&aelig;ter naturam ad motus <lb/>&longs;ecundum naturam. </s> <s id="id.000779">Ibi <lb/>enim erit, vbi proportiona&shy;<lb/>les <expan abbr="c&otilde;ting&etilde;t">contingent</expan> <expan abbr="vtrinq;">vtrinque</expan> motus <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.082.jpg" pagenum="43"/><foreign lang="greek"><gap/></foreign><lb/>pr&aelig;ter naturam ad motus <lb/>&longs;ecundum naturam. </s>
  
  <s id="id.000780">Si igi&shy;<lb/>tur maius e&longs;t id quod <expan abbr="&longs;ec&utilde;-dum">&longs;ecun&shy;<lb/>dum</expan> <expan abbr="natur&atilde;">naturam</expan> in maiore cir&shy;<lb/>culo, &amp; quod e&longs;t pr&ecedil;ter na&shy;<lb/>turam maius, vtique illuc <lb/>concidet vno modo, ita vt <lb/><foreign lang="greek">b</foreign> &longs;it latum per lineam <foreign lang="greek">b h.</foreign><lb/>eo in tempore quo <expan abbr="p&utilde;ctum">punctum</expan> <lb/><foreign lang="greek">x</foreign> [per <foreign lang="greek">x q</foreign>]. </s>
  
  <s>Ibi enim pun&shy;<lb/>cto <foreign lang="greek">b</foreign> &longs;ecundum <expan abbr="quid&etilde;">quidem</expan> na&shy;<lb/>turam e&longs;t recta <foreign lang="greek">k h,</foreign> ab <foreign lang="greek">h</foreign><lb/>enim e&longs;t ip&longs;a perpendicu&shy;<lb/>laris, pr&aelig;ter naturam vero <lb/><foreign lang="greek">b k.</foreign> </s>
  
 <s id="id.000780">Si igi&shy;<lb/>tur maius e&longs;t id quod <expan abbr="&longs;ec&utilde;-dum">&longs;ecun&shy;<lb/>dum</expan> <expan abbr="natur&atilde;">naturam</expan> in maiore cir&shy;<lb/>culo, &amp; quod e&longs;t pr&ecedil;ter na&shy;<lb/>turam maius, vtique illuc <lb/>concidet vno modo, ita vt <lb/><foreign lang="greek">b</foreign> &longs;it latum per lineam <foreign lang="greek">b h.</foreign><lb/>eo in tempore quo <expan abbr="p&utilde;ctum">punctum</expan> <lb/><foreign lang="greek">x</foreign> [per <foreign lang="greek">x q</foreign>]. Ibi enim pun&shy;<lb/>cto <foreign lang="greek">b</foreign> &longs;ecundum <expan abbr="quid&etilde;">quidem</expan> na&shy;<lb/>turam e&longs;t recta <foreign lang="greek">k h,</foreign> ab <foreign lang="greek">h</foreign><lb/>enim e&longs;t ip&longs;a perpendicu&shy;<lb/>laris, pr&aelig;ter naturam vero <lb/><foreign lang="greek">b k.</foreign> E&longs;t &longs;iquidem vt <foreign lang="greek">h k</foreign> ad <lb/><foreign lang="greek"><gap/> k</foreign>: &longs;ic <foreign lang="greek">q z</foreign> ad <foreign lang="greek">x z,</foreign> quod <lb/>erit manife&longs;tum, &longs;i &agrave; pun&shy;<lb/>ctis <foreign lang="greek">b, x</foreign> ad <foreign lang="greek">h, q</foreign> rect&aelig; adiun&shy;<lb/>ct&aelig; &longs;int. </s> <s>E&longs;t &longs;iquidem vt <foreign lang="greek">h k</foreign> ad <lb/><foreign lang="greek"><gap/> k</foreign>: &longs;ic <foreign lang="greek">q z</foreign> ad <foreign lang="greek">x z,</foreign> quod <lb/>erit manife&longs;tum, &longs;i &agrave; pun&shy;<lb/>ctis <foreign lang="greek">b, x</foreign> ad <foreign lang="greek">h, q</foreign> rect&aelig; adiun&shy;<lb/>ct&aelig; &longs;int. </s>
  
 <s id="id.000781">Si vero minor vel <lb/>maior: quam <foreign lang="greek">h b</foreign> fuerit ea, <lb/>perquam <foreign lang="greek">b</foreign> motum e&longs;t, non <lb/>&longs;imiliter neque proportio&shy;<lb/>naliter in <expan abbr="vtri&longs;q;">vtri&longs;que</expan> erit, quod <lb/><arrow.to.target n="marg13"/><lb/>&longs;ecundum naturam ad id <lb/>quod pr&aelig;ter naturam. </s> <s id="id.000781">Si vero minor vel <lb/>maior: quam <foreign lang="greek">h b</foreign> fuerit ea, <lb/>perquam <foreign lang="greek">b</foreign> motum e&longs;t, non <lb/>&longs;imiliter neque proportio&shy;<lb/>naliter in <expan abbr="vtri&longs;q;">vtri&longs;que</expan> erit, quod <lb/><arrow.to.target n="marg13"/><lb/>&longs;ecundum naturam ad id <lb/>quod pr&aelig;ter naturam. </s>
  
 <s id="id.000782">Ob <lb/><expan abbr="h&atilde;c">hanc</expan> igitur cau&longs;am ex dictis <lb/>manife&longs;tum, quod punctum &agrave; centro di&longs;tantius, vt ea&shy;<lb/>dem vi &longs;it motum, celerius fertur.</s></p><p type="margin"> <s id="id.000782">Ob <lb/><expan abbr="h&atilde;c">hanc</expan> igitur cau&longs;am ex dictis <lb/>manife&longs;tum, quod punctum &agrave; centro di&longs;tantius, vt ea&shy;<lb/>dem vi &longs;it motum, celerius fertur.</s></p><p type="margin">
  
 <s id="id.000783"><margin.target id="marg13"/>Vetba &longs;i&shy;<lb/>gnis inclu&longs;a <lb/>in <expan abbr="c&otilde;textu">contextu</expan> <lb/>Gr&ecedil;co quia <lb/>redundant <lb/>non verti&shy;<lb/>mus.</s></p><p type="head"> <s id="id.000783"><margin.target id="marg13"/>Verba &longs;i&shy;<lb/>gnis inclu&longs;a <lb/>in <expan abbr="c&otilde;textu">contextu</expan> <lb/>Gr&ecedil;co quia <lb/>redundant <lb/>non verti&shy;<lb/>mus.</s></p><p type="head">
  
 <s id="id.000784">COMMENTARIVS.<!-- KEEP S--></s></p><p type="main"> <s id="id.000784">COMMENTARIVS.<!-- KEEP S--></s></p><p type="main">
  
 <s id="id.000785">At oportet.] <emph type="italics"/>Nunc o&longs;tendit in maiore circulo motum &longs;ecun&shy;<lb/>dum naturam maiorem e&longs;&longs;e motu &longs;ecundum naturam in mino&shy;<lb/>re circulo eodem tempore factum. </s> <s id="id.000785">At oportet.] <emph type="italics"/>Nunc o&longs;tendit in maiore circulo motum &longs;ecun&shy;<lb/>dum naturam maiorem e&longs;&longs;e motu &longs;ecundum naturam in mino&shy;<lb/>re circulo eodem tempore factum. </s>
  
 <s id="id.000786">Ratio e&longs;t, Circuli in&aelig;quales eadem <lb/>vi moti &longs;eruant analogiam in motibus &longs;cilicet: vt qu&aelig; ratio &longs;it mo&shy;<lb/>tus in maiore circulo &longs;ecundum naturam ad &longs;uum motum pr&aelig;ter na-<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.083.jpg" pagenum="44"/><emph type="italics"/>turam: eadem &longs;it motus in minore circulo &longs;ecundum naturam ad <lb/>&longs;uum motum pr&aelig;ter naturam: at h&aelig;c analogia tantum reperiri po&shy;<lb/>te&longs;t, &longs;i cum<emph.end type="italics"/> <foreign lang="greek">x</foreign> <emph type="italics"/>delatum e&longs;t in<emph.end type="italics"/> <foreign lang="greek">q,</foreign> <emph type="italics"/>intelligatur etiam<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>delatum in<emph.end type="italics"/> <foreign lang="greek">h,</foreign><lb/><emph type="italics"/>&agrave; quo<emph.end type="italics"/> <foreign lang="greek">h</foreign> <emph type="italics"/>e&longs;t perpendicularis<emph.end type="italics"/> <foreign lang="greek">h k</foreign> <emph type="italics"/>in diametrum<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>metiens motum <lb/>ip&longs;ius<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>per peripheriam<emph.end type="italics"/> <foreign lang="greek">b h.</foreign> <emph type="italics"/>Ergo quo tempore<emph.end type="italics"/> <foreign lang="greek">x</foreign> <emph type="italics"/>delatum e&longs;t ad<emph.end type="italics"/><lb/><foreign lang="greek">q,</foreign> <emph type="italics"/>eodem<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>delatum erit ad<emph.end type="italics"/> <foreign lang="greek">h.</foreign> <emph type="italics"/>C&aelig;terum eadem vis in vtri&longs;que cir&shy;<lb/>culis intelligitur ex &aelig;qualitate angulorum ad centrum con&longs;tituto&shy;<lb/>rum. </s> <s id="id.000786">Ratio e&longs;t, Circuli in&aelig;quales eadem <lb/>vi moti &longs;eruant analogiam in motibus &longs;cilicet: vt qu&aelig; ratio &longs;it mo&shy;<lb/>tus in maiore circulo &longs;ecundum naturam ad &longs;uum motum pr&aelig;ter na-<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.083.jpg" pagenum="44"/><emph type="italics"/>turam: eadem &longs;it motus in minore circulo &longs;ecundum naturam ad <lb/>&longs;uum motum pr&aelig;ter naturam: at h&aelig;c analogia tantum reperiri po&shy;<lb/>te&longs;t, &longs;i cum<emph.end type="italics"/> <foreign lang="greek">x</foreign> <emph type="italics"/>delatum e&longs;t in<emph.end type="italics"/> <foreign lang="greek">q,</foreign> <emph type="italics"/>intelligatur etiam<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>delatum in<emph.end type="italics"/> <foreign lang="greek">h,</foreign><lb/><emph type="italics"/>&agrave; quo<emph.end type="italics"/> <foreign lang="greek">h</foreign> <emph type="italics"/>e&longs;t perpendicularis<emph.end type="italics"/> <foreign lang="greek">h k</foreign> <emph type="italics"/>in diametrum<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>metiens motum <lb/>ip&longs;ius<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>per peripheriam<emph.end type="italics"/> <foreign lang="greek">b h.</foreign> <emph type="italics"/></s>
  
 <s id="id.000787">&AElig;qualis enim e&longs;t angulus<emph.end type="italics"/> <foreign lang="greek"><gap/> a h</foreign> <emph type="italics"/>angulo<emph.end type="italics"/> <foreign lang="greek">x a <expan abbr="q.">que</expan></foreign></s></p><p type="main"> <s>Ergo quo tempore<emph.end type="italics"/> <foreign lang="greek">x</foreign> <emph type="italics"/>delatum e&longs;t ad<emph.end type="italics"/><lb/><foreign lang="greek">q,</foreign> <emph type="italics"/>eodem<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>delatum erit ad<emph.end type="italics"/> <foreign lang="greek">h.</foreign> <emph type="italics"/></s>
  
 <s id="id.000788">Ab <foreign lang="greek">h</foreign> enim e&longs;t.] <emph type="italics"/>Curuas lineas perpendicularis &longs;ola vt breui&longs;&shy;<lb/>&longs;ima, quantum fieri pote&longs;t exacte metitur. </s> 
  
 <s id="id.000789">vt &longs;cribit autem Ptolo&shy;<lb/>m&aelig;us in lib.  <s>C&aelig;terum eadem vis in vtri&longs;que cir&shy;<lb/>culis intelligitur ex &aelig;qualitate angulorum ad centrum con&longs;tituto&shy;<lb/>rum. </s>
  
 de Analemmate, &amp; Simplicius in lib. <!-- REMOVE S-->de Dimen&longs;ione, <lb/>men&longs;ura cuiu&longs;cunque rei debet e&longs;&longs;e &longs;tata, determinata, &amp; non indefi&shy;<lb/>nita. </s> <s id="id.000787">&AElig;qualis enim e&longs;t angulus<emph.end type="italics"/> <foreign lang="greek"><gap/> a h</foreign> <emph type="italics"/>angulo<emph.end type="italics"/> <foreign lang="greek">x a <expan abbr="q.">que</expan></foreign></s></p><p type="main">
  
  <s id="id.000788">Ab <foreign lang="greek">h</foreign> enim e&longs;t.] <emph type="italics"/>Curuas lineas perpendicularis &longs;ola vt breui&longs;&shy;<lb/>&longs;ima, quantum fieri pote&longs;t exacte metitur. </s>
  
  <s id="id.000789">vt &longs;cribit autem Ptolo&shy;<lb/>m&aelig;us in lib. de Analemmate, &amp; Simplicius in lib. de Dimen&longs;ione, <lb/>men&longs;ura cuiu&longs;cunque rei debet e&longs;&longs;e &longs;tata, determinata, &amp; non indefi&shy;<lb/>nita. </s>
  
 <s id="id.000790">Talis autem e&longs;t perpendicularis ad linearum reliquarum dimen&shy;<lb/>&longs;ionem.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000790">Talis autem e&longs;t perpendicularis ad linearum reliquarum dimen&shy;<lb/>&longs;ionem.<emph.end type="italics"/></s></p><p type="main">
  
 <s id="id.000791">E&longs;t &longs;iquidem vt <foreign lang="greek">h k.</foreign>] <emph type="italics"/>Triangula enim<emph.end type="italics"/> <foreign lang="greek">x q z &amp; b h k</foreign> <emph type="italics"/>&longs;unt <lb/>&aelig;quiangula. </s> <s id="id.000791">E&longs;t &longs;iquidem vt <foreign lang="greek">h k.</foreign>] <emph type="italics"/>Triangula enim<emph.end type="italics"/> <foreign lang="greek">x q z &amp; b h k</foreign> <emph type="italics"/>&longs;unt <lb/>&aelig;quiangula. </s>
  
 <s id="id.000792">Nam, qui anguli ad<emph.end type="italics"/> <foreign lang="greek"><gap/> &amp; k,</foreign> <emph type="italics"/>&longs;unt recti ex fab. </s> <s id="id.000792">Nam, qui anguli ad<emph.end type="italics"/> <foreign lang="greek"><gap/> &amp; k,</foreign> <emph type="italics"/>&longs;unt recti ex fab. qui vero <lb/>ad<emph.end type="italics"/> <foreign lang="greek">x &amp; b</foreign> <emph type="italics"/>&longs;unt externus &amp; internus ad ea&longs;dem partes facti &agrave; re&shy;<lb/>cta<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>incidente in parallelas<emph.end type="italics"/> <foreign lang="greek">x q, b h</foreign> <emph type="italics"/>prop. 3. lib. 6. </s>
  
 <s id="id.000793">qui vero <lb/>ad<emph.end type="italics"/> <foreign lang="greek">x &amp; b</foreign> <emph type="italics"/>&longs;unt externus &amp; internus ad ea&longs;dem partes facti &agrave; re&shy;<lb/>cta<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>incidente in parallelas<emph.end type="italics"/> <foreign lang="greek">x q, b h</foreign> <emph type="italics"/>prop.  
  
 3. lib.  
  
 6. Nam<emph.end type="italics"/> <foreign lang="greek">x q</foreign><lb/><emph type="italics"/>proportionaliter &longs;ecat<emph.end type="italics"/> <foreign lang="greek">a b &amp; a h</foreign> <emph type="italics"/>latera trianguli<emph.end type="italics"/> <foreign lang="greek">b a h.</foreign> <emph type="italics"/>Sunt enim<emph.end type="italics"/><lb/><foreign lang="greek">a x, a q</foreign> <emph type="italics"/>&aelig;quales radj,<emph.end type="italics"/> &amp; <foreign lang="greek">x b, q h</foreign> <emph type="italics"/>item &aelig;quales line&aelig;, quia re&shy;<lb/>liqu&aelig; ex &aelig;qualibus rad&yuml;s<emph.end type="italics"/> <foreign lang="greek">a b, a h</foreign>: <emph type="italics"/>habent autem &aelig;quales ad <lb/>&aelig;quales eandem rationem E&longs;t igitur<emph.end type="italics"/> <foreign lang="greek">x q</foreign> <emph type="italics"/>parallela ba&longs;i<emph.end type="italics"/> <foreign lang="greek">b h,</foreign> <emph type="italics"/>&amp; &longs;ic <lb/>anguli qui ad<emph.end type="italics"/> <foreign lang="greek">x</foreign> <emph type="italics"/>externus, &amp; qui ad<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>internus erunt &aelig;quales <lb/>prop.  
  
 29. lib.  <s>Nam<emph.end type="italics"/> <foreign lang="greek">x q</foreign><lb/><emph type="italics"/>proportionaliter &longs;ecat<emph.end type="italics"/> <foreign lang="greek">a b &amp; a h</foreign> <emph type="italics"/>latera trianguli<emph.end type="italics"/> <foreign lang="greek">b a h.</foreign> <emph type="italics"/></s>
  
 1. Ergo &amp; reliqui qui ad<emph.end type="italics"/> <foreign lang="greek">q &amp; h</foreign> <emph type="italics"/>prop. </s> <s>Sunt enim<emph.end type="italics"/><lb/><foreign lang="greek">a x, a q</foreign> <emph type="italics"/>&aelig;quales radj,<emph.end type="italics"/> &amp; <foreign lang="greek">x b, q h</foreign> <emph type="italics"/>item &aelig;quales line&aelig;, quia re&shy;<lb/>liqu&aelig; ex &aelig;qualibus rad&yuml;s<emph.end type="italics"/> <foreign lang="greek">a b, a h</foreign>: <emph type="italics"/>habent autem &aelig;quales ad <lb/>&aelig;quales eandem rationem. </s>
  
 <s id="id.000794">32. lib.  <s>E&longs;t igitur<emph.end type="italics"/> <foreign lang="greek">x q</foreign> <emph type="italics"/>parallela ba&longs;i<emph.end type="italics"/> <foreign lang="greek">b h,</foreign> <emph type="italics"/>&amp; &longs;ic <lb/>anguli qui ad<emph.end type="italics"/> <foreign lang="greek">x</foreign> <emph type="italics"/>externus, &amp; qui ad<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>internus erunt &aelig;quales <lb/>prop. 29. lib. 1. </s>
  
 1. H&aelig;c <lb/>igitur duo triangula circa &aelig;quales angulos habebunt latera propor&shy;<lb/>tionalia prop.  <s>Ergo &amp; reliqui qui ad<emph.end type="italics"/> <foreign lang="greek">q &amp; h</foreign> <emph type="italics"/>prop. 32. lib. 1. </s>
  
 4. lib.  <s>H&aelig;c <lb/>igitur duo triangula circa &aelig;quales angulos habebunt latera propor&shy;<lb/>tionalia prop. 4. lib. 6. </s>
  
 6. Sicque erit vt<emph.end type="italics"/> <foreign lang="greek">q z</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">x z</foreign>: <emph type="italics"/>&longs;ic<emph.end type="italics"/> <foreign lang="greek">h k</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">k b,</foreign><lb/><emph type="italics"/>&amp; alternatim vt<emph.end type="italics"/> <foreign lang="greek">q z</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">h k</foreign><emph type="italics"/>: &longs;ic<emph.end type="italics"/> <foreign lang="greek">x z</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">k b</foreign> <emph type="italics"/>prop.  <s>Sicque erit vt<emph.end type="italics"/> <foreign lang="greek">q z</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">x z</foreign>: <emph type="italics"/>&longs;ic<emph.end type="italics"/> <foreign lang="greek">h k</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">k b,</foreign><lb/><emph type="italics"/>&amp; alternatim vt<emph.end type="italics"/> <foreign lang="greek">q z</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">h k</foreign><emph type="italics"/>: &longs;ic<emph.end type="italics"/> <foreign lang="greek">x z</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">k b</foreign> <emph type="italics"/>prop. 16. lib. 5.<emph.end type="italics"/></s></p><p type="main">
  
 16. lib.  
  
 5.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main"> 
  
 <s id="id.000795">Ob hanc igitur cau&longs;am.] <emph type="italics"/>Conclu&longs;io qua tandem concludi&shy;<lb/>tur punctum &agrave; centro di&longs;tantius, vt eadem vi &longs;it motum, celerius <lb/>ferri, id e&longs;t eodem tempore maius loci &longs;patium conficere.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000795">Ob hanc igitur cau&longs;am.] <emph type="italics"/>Conclu&longs;io qua tandem concludi&shy;<lb/>tur punctum &agrave; centro di&longs;tantius, vt eadem vi &longs;it motum, celerius <lb/>ferri, id e&longs;t eodem tempore maius loci &longs;patium conficere.<emph.end type="italics"/></s></p><p type="main">
  
 <s id="id.000796"><gap/></s></p><p type="main"> <s id="id.000796"><foreign lang="greek"><gap/></foreign></s></p><p type="main">
  
 <s id="id.000797">Quod vero propterea li&shy;<lb/>br&ecedil; maiores minoribus &longs;int <lb/>exactiores, <expan abbr="manife&longs;t&utilde;">manife&longs;tum</expan> ex his <lb/>erit. </s> <s id="id.000797">Quod vero propterea li&shy;<lb/>br&ecedil; maiores minoribus &longs;int <lb/>exactiores, <expan abbr="manife&longs;t&utilde;">manife&longs;tum</expan> ex his <lb/>erit. </s>
  
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 <s id="id.000799">H&aelig;c enim quie&longs;cit. </s> <s id="id.000799">H&aelig;c enim quie&longs;cit. </s>
  
 <s id="id.000800"><expan abbr="vtr&aelig;q;">vtr&aelig;que</expan> <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.084.jpg" pagenum="45"/><gap/><lb/>vero librilis partes line&aelig; <lb/>&longs;unt ex centro. </s> <s id="id.000800"><expan abbr="vtr&aelig;q;">vtr&aelig;que</expan> <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.084.jpg" pagenum="45"/><foreign lang="greek"><gap/></foreign><lb/>vero librilis partes line&aelig; <lb/>&longs;unt ex centro. </s>
  
 <s id="id.000801">Ab eodem <lb/>igitur pondere nece&longs;&longs;e e&longs;t <lb/>e&ograve; celerius extremum li&shy;<lb/>brilis ferri, qu&ograve; plus ab agi&shy;<lb/>na di&longs;titerit, &amp; nonnulla in <lb/>paruis libris pondera im&shy;<lb/>po&longs;ita non manife&longs;ta &longs;en&shy;<lb/>&longs;ui e&longs;&longs;e, qu&aelig; in magnis ma&shy;<lb/>nife&longs;ta erunt. </s> <s id="id.000801">Ab eodem <lb/>igitur pondere nece&longs;&longs;e e&longs;t <lb/>e&ograve; celerius extremum li&shy;<lb/>brilis ferri, qu&ograve; plus ab agi&shy;<lb/>na di&longs;titerit, &amp; nonnulla in <lb/>paruis libris pondera im&shy;<lb/>po&longs;ita non manife&longs;ta &longs;en&shy;<lb/>&longs;ui e&longs;&longs;e, qu&aelig; in magnis ma&shy;<lb/>nife&longs;ta erunt. </s>
  
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 <s id="id.000804">Qvod vero propterea libr&aelig;.] <foreign lang="greek"><gap/>u<gap/>s</foreign> <emph type="italics"/>vel<emph.end type="italics"/> <foreign lang="greek"><gap/>u<gap/>n</foreign> <emph type="italics"/>pr&aelig;ter iu&shy;<lb/>gum, remigum &longs;edes, &amp; tran&longs;tra curruum &amp; nauium &longs;ignifi&shy;<lb/>cat etiam libram &amp; &longs;tateram, hinc illud Pythagor&aelig;<emph.end type="italics"/> <foreign lang="greek">mh\zu<gap/>n u(per&shy;<lb/><gap/>a/inein</foreign> <emph type="italics"/>&longs;tateram ne tran&longs;grediaris &amp; vt annotat Bud&aelig;us<emph.end type="italics"/> <foreign lang="greek">zu<gap/>a/&shy;<lb/>tai</foreign> <emph type="italics"/>&longs;unt libripendes per vrbes con&longs;tituti, qui <expan abbr="p&otilde;deribus">ponderibus</expan> pr&aelig;fecti ap&shy;<lb/>pellantur, vnde Zygo&longs;tatica fides pro plena &amp; examinata &aelig;quitate <lb/>&agrave; Zygo quod e&longs;t libra publice temperata &amp; con&longs;tituta, vt quemad&shy;<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/>&amp; pondus &aelig;quum voluntas eius.<emph.end type="italics"/></s></p><p type="margin"> <s id="id.000804">Qvod vero propterea libr&aelig;.] <foreign lang="greek"><gap/>u<gap/>s</foreign> <emph type="italics"/>vel<emph.end type="italics"/> <foreign lang="greek"><gap/>u<gap/>n</foreign> <emph type="italics"/>pr&aelig;ter iu&shy;<lb/>gum, remigum &longs;edes, &amp; tran&longs;tra curruum &amp; nauium &longs;ignifi&shy;<lb/>cat etiam libram &amp; &longs;tateram, hinc illud Pythagor&aelig;<emph.end type="italics"/> <foreign lang="greek">mh\zu<gap/>n u(per&shy;<lb/><gap/>a/inein</foreign> <emph type="italics"/>&longs;tateram ne tran&longs;grediaris &amp; vt annotat Bud&aelig;us<emph.end type="italics"/> <foreign lang="greek">zu<gap/>a/&shy;<lb/>tai</foreign> <emph type="italics"/>&longs;unt libripendes per vrbes con&longs;tituti, qui <expan abbr="p&otilde;deribus">ponderibus</expan> pr&aelig;fecti ap&shy;<lb/>pellantur, vnde Zygo&longs;tatica fides pro plena &amp; examinata &aelig;quitate <lb/>&agrave; Zygo quod e&longs;t libra publice temperata &amp; con&longs;tituta, vt quemad&shy;<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/>&amp; pondus &aelig;quum voluntas eius.<emph.end type="italics"/></s></p><p type="margin">
  
 <s id="id.000805"><margin.target id="marg14"/>Initio <lb/>cap.  <s id="id.000805"><margin.target id="marg14"/>Initio <lb/>cap. 11. <lb/>Prouerb.</s></p><p type="main">
  
 11. <lb/>Prouerb.<!-- KEEP S--></s></p><p type="main"> 
  
 <s id="id.000806">Agina fit cen&shy;<lb/><figure id="id.035.01.084.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.084.1.jpg"/><lb/><expan abbr="tr&utilde;">trum</expan>.] <emph type="italics"/><expan abbr="Tand&etilde;">Tandem</expan> Ari&shy;<lb/>&longs;toteles <expan abbr="acc&otilde;modat">accommodat</expan> <lb/>problema <expan abbr="propo&longs;it&utilde;">propo&longs;itum</expan> <lb/>de libra ad circuli <lb/><expan abbr="proprietat&etilde;">proprietatem</expan> vltim&ograve; <lb/><expan abbr="demon&longs;trat&atilde;">demon&longs;tratam</expan>. </s> <s id="id.000806">Agina fit cen&shy;<lb/><figure id="id.035.01.084.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.084.1.jpg"/><lb/><expan abbr="tr&utilde;">trum</expan>.] <emph type="italics"/><expan abbr="Tand&etilde;">Tandem</expan> Ari&shy;<lb/>&longs;toteles <expan abbr="acc&otilde;modat">accommodat</expan> <lb/>problema <expan abbr="propo&longs;it&utilde;">propo&longs;itum</expan> <lb/>de libra ad circuli <lb/><expan abbr="proprietat&etilde;">proprietatem</expan> vltim&ograve; <lb/><expan abbr="demon&longs;trat&atilde;">demon&longs;tratam</expan>. </s>
  
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 <s id="id.000812">id e&longs;t minores <lb/>ponderum differentias patefaciet.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000812">id e&longs;t minores <lb/>ponderum differentias patefaciet.<emph.end type="italics"/></s></p><p type="main">
  
 <s id="id.000813"><gap/></s></p><p type="main"> <s id="id.000813"><foreign lang="greek"><gap/></foreign></s></p><p type="main">
  
 <s id="id.000814">In magno <expan abbr="aut&etilde;">autem</expan> librili <expan abbr="id&etilde;">idem</expan> <lb/><expan abbr="p&otilde;dus">pondus</expan> <expan abbr="magnitudin&etilde;">magnitudinem</expan> reddet <lb/><expan abbr="a&longs;pectabil&etilde;">a&longs;pectabilem</expan>. </s> <s id="id.000814">In magno <expan abbr="aut&etilde;">autem</expan> librili <expan abbr="id&etilde;">idem</expan> <lb/><expan abbr="p&otilde;dus">pondus</expan> <expan abbr="magnitudin&etilde;">magnitudinem</expan> reddet <lb/><expan abbr="a&longs;pectabil&etilde;">a&longs;pectabilem</expan>. </s>
  
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 <s id="id.000838">Fraudem autem i&longs;tam deteget, &longs;i pondus &amp; &aelig;qui&shy;<lb/>pondium tran&longs;mutentur de lance in lancem. </s> <s id="id.000838">Fraudem autem i&longs;tam deteget, &longs;i pondus &amp; &aelig;qui&shy;<lb/>pondium tran&longs;mutentur de lance in lancem. </s>
  
 <s id="id.000839">Quod enim ante &aelig;qui&shy;<lb/>ponderabat, tran&longs;latum in alteram lancem no <gap/>amplius &aelig;quiponde&shy;<lb/>rabit duplici de cau&longs;a, &amp; quod &aelig;quipondium grauius &longs;it, &amp; quod <lb/>librilis in parte maiore &longs;it.<emph.end type="italics"/></s></p><p type="margin"> <s id="id.000839">Quod enim ante &aelig;qui&shy;<lb/>ponderabat, tran&longs;latum in alteram lancem non amplius &aelig;quiponde&shy;<lb/>rabit duplici de cau&longs;a, &amp; quod &aelig;quipondium grauius &longs;it, &amp; quod <lb/>librilis in parte maiore &longs;it.<emph.end type="italics"/></s></p><p type="margin">
  
 <s id="id.000840"><margin.target id="marg15"/>Lib. 1. de <lb/>&longs;ubt,</s></p><p type="margin"> <s id="id.000840"><margin.target id="marg15"/>Lib. 1. de <lb/>&longs;ubt,</s></p><p type="margin">
  
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 <s id="id.000846"><margin.target id="marg17"/>Lib. 9. cap. <lb/>36.</s></p><p type="main"> <s id="id.000846"><margin.target id="marg17"/>Lib. 9. cap. <lb/>36.</s></p><p type="main">
  
 <s id="id.000847"><gap/></s></p><p type="main"> <s id="id.000847">3. <foreign lang="greek"><gap/></foreign></s></p><p type="main">
  
 <s id="id.000848">3. Propter quid, &longs;i in &longs;upe&shy;<lb/>riore librilis parte fuerit <lb/>agina, <expan abbr="qu&atilde;do">quando</expan> <expan abbr="p&otilde;dus">pondus</expan>, ali&shy;<lb/>quod depre&longs;&longs;erit, rur&longs;us <lb/>librile referatur: At &longs;i in <lb/>inferiore, non refertur.</s></p><p type="main"> <s id="id.000848">3. Propter quid, &longs;i in &longs;upe&shy;<lb/>riore librilis parte fuerit <lb/>agina, <expan abbr="qu&atilde;do">quando</expan> <expan abbr="p&otilde;dus">pondus</expan>, ali&shy;<lb/>quod depre&longs;&longs;erit, rur&longs;us <lb/>librile referatur: At &longs;i in <lb/>inferiore, non refertur.</s></p><p type="main">
  
 <s id="id.000849"><gap/></s></p><p type="main"> <s id="id.000849"><foreign lang="greek"><gap/></foreign></s></p><p type="main">
  
 <s id="id.000850">Propter quid &longs;i in &longs;upe&shy;<lb/>riore librilis parte fuerit <lb/>agina, cum pr&aelig; <expan abbr="p&otilde;dere">pondere</expan> <expan abbr="de-mi&longs;s&utilde;">de&shy;<lb/>mi&longs;sum</expan> e&longs;t, hoc &longs;ublato rur&shy;<lb/>&longs;us redit: Sed &longs;i in inferiore <lb/>fuorit, <expan abbr="n&otilde;">non</expan> redit, &longs;ed manet? <lb/></s> <s id="id.000850">Propter quid &longs;i in &longs;upe&shy;<lb/>riore librilis parte fuerit <lb/>agina, cum pr&aelig; <expan abbr="p&otilde;dere">pondere</expan> <expan abbr="de-mi&longs;s&utilde;">de&shy;<lb/>mi&longs;sum</expan> e&longs;t, hoc &longs;ublato rur&shy;<lb/>&longs;us redit: Sed &longs;i in inferiore <lb/>fuerit, <expan abbr="n&otilde;">non</expan> redit, &longs;ed manet? <lb/></s>
  
 <s id="id.000851">an quia &longs;uperne exi&longs;tente <lb/>agina, librilis plus erit ex&shy;<lb/>tra perpendicularem. </s> <s id="id.000851">an quia &longs;uperne exi&longs;tente <lb/>agina, librilis plus erit ex&shy;<lb/>tra perpendicularem. </s>
  
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 <s id="id.000853"><expan abbr="Itaq;">Itaque</expan> nece&longs;&longs;e e&longs;t, quod <lb/>plus e&longs;t deor&longs;um vergere, <lb/>incumbente <expan abbr="p&otilde;dere">pondere</expan> in par&shy;<lb/>te librilis &longs;ur&longs;um rapta, do&shy;<lb/>nec venerit e&ograve;, vbi ad per&shy;<lb/>pendicularem ip&longs;am librile <lb/>bifariam diuiditur. </s> <s id="id.000853"><expan abbr="Itaq;">Itaque</expan> nece&longs;&longs;e e&longs;t, quod <lb/>plus e&longs;t deor&longs;um vergere, <lb/>incumbente <expan abbr="p&otilde;dere">pondere</expan> in par&shy;<lb/>te librilis &longs;ur&longs;um rapta, do&shy;<lb/>nec venerit e&ograve;, vbi ad per&shy;<lb/>pendicularem ip&longs;am librile <lb/>bifariam diuiditur. </s>
  
 <s id="id.000854">E&longs;to li&shy;<lb/>brile rectum <foreign lang="greek">b y,</foreign> trutina <foreign lang="greek">a <lb/>d</foreign>: at hoc deor&longs;um demi&longs;&longs;o <lb/>&longs;it perpendicularis <foreign lang="greek">a d m.</foreign><lb/>Si igitur pondus impona&shy;<lb/>tur in lance <foreign lang="greek">b,</foreign> erit <foreign lang="greek">b</foreign> vbi <foreign lang="greek">e, <lb/>&amp; g</foreign> vbi <foreign lang="greek">z.</foreign> Itaque recta bi&shy;<lb/>fariam diuidens librile, pri. <lb/><!-- REMOVE S-->m&ugrave;m quidem erat <foreign lang="greek">a d m,</foreign><lb/>ip&longs;a <expan abbr="perp&etilde;dicularis">perpendicularis</expan> <expan abbr="exi&longs;t&etilde;s">exi&longs;tens</expan>: <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.088.jpg" pagenum="49"/><gap/><lb/>At cum pondus impo&longs;itum <lb/>e&longs;t, e&longs;t <foreign lang="greek">f p.</foreign> Itaque librilis <lb/><foreign lang="greek">e c</foreign> id quod e&longs;t extra per&shy;<lb/>pendicularem <foreign lang="greek">a m</foreign> in ea <lb/>qu&aelig; e&longs;t <foreign lang="greek">f p</foreign> plus e&longs;t: quam <lb/>dimidium. </s> <s id="id.000854">E&longs;to li&shy;<lb/>brile rectum <foreign lang="greek">b y,</foreign> trutina <foreign lang="greek">a <lb/>d</foreign>: at hoc deor&longs;um demi&longs;&longs;o <lb/>&longs;it perpendicularis <foreign lang="greek">a d m.</foreign><lb/></s>
  
  <s>Si igitur pondus impona&shy;<lb/>tur in lance <foreign lang="greek">b,</foreign> erit <foreign lang="greek">b</foreign> vbi <foreign lang="greek">e, <lb/>&amp; g</foreign> vbi <foreign lang="greek">z.</foreign></s>
  
  <s>Itaque recta bi&shy;<lb/>fariam diuidens librile, pri&shy;<lb/>m&ugrave;m quidem erat <foreign lang="greek">a d m,</foreign><lb/>ip&longs;a <expan abbr="perp&etilde;dicularis">perpendicularis</expan> <expan abbr="exi&longs;t&etilde;s">exi&longs;tens</expan>: <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.088.jpg" pagenum="49"/><foreign lang="greek"><gap/></foreign><lb/>At cum pondus impo&longs;itum <lb/>e&longs;t, e&longs;t <foreign lang="greek">f p.</foreign></s>
  
  <s>Itaque librilis <lb/><foreign lang="greek">e c</foreign> id quod e&longs;t extra per&shy;<lb/>pendicularem <foreign lang="greek">a m</foreign> in ea <lb/>qu&aelig; e&longs;t <foreign lang="greek">f p</foreign> plus e&longs;t: quam <lb/>dimidium. </s>
  
 <s id="id.000855">Si igitur pon&shy;<lb/>dus, quod erat in <foreign lang="greek">e</foreign> tolla&shy;<lb/>tur, nece&longs;&longs;e e&longs;t <foreign lang="greek">z</foreign> deor&longs;um <lb/>ferri. </s> <s id="id.000855">Si igitur pon&shy;<lb/>dus, quod erat in <foreign lang="greek">e</foreign> tolla&shy;<lb/>tur, nece&longs;&longs;e e&longs;t <foreign lang="greek">z</foreign> deor&longs;um <lb/>ferri. </s>
  
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 <s id="id.000859">Leuior enim e&longs;t pars &longs;ur&shy;<lb/>&longs;um lata. </s> <s id="id.000859">Leuior enim e&longs;t pars &longs;ur&shy;<lb/>&longs;um lata. </s>
  
 <s id="id.000860">E&longs;to librile <foreign lang="greek">n c</foreign> re&shy;<lb/>ctum, perpendicularis vero <lb/><foreign lang="greek">k l m,</foreign> qu&aelig; bifariam diui&shy;<lb/>dat <foreign lang="greek">n c,</foreign> &amp; impo&longs;ito pon&shy;<lb/>dere in <foreign lang="greek">n,</foreign> &longs;it <foreign lang="greek">n</foreign> vbi e&longs;t <foreign lang="greek">o, &amp; <lb/>x</foreign> vbi e&longs;t <foreign lang="greek">r, &amp; k l</foreign> vbi <foreign lang="greek">l <expan abbr="q.">que</expan></foreign><lb/>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&shy;<lb/>blato pondere nece&longs;&longs;e e&longs;t <lb/>manere. </s> <s id="id.000860">E&longs;to librile <foreign lang="greek">n c</foreign> re&shy;<lb/>ctum, perpendicularis vero <lb/><foreign lang="greek">k l m,</foreign> qu&aelig; bifariam diui&shy;<lb/>dat <foreign lang="greek">n c,</foreign> &amp; impo&longs;ito pon&shy;<lb/>dere in <foreign lang="greek">n,</foreign> &longs;it <foreign lang="greek">n</foreign> vbi e&longs;t <foreign lang="greek">o, &amp; <lb/>x</foreign> vbi e&longs;t <foreign lang="greek">r, &amp; 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&shy;<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></p><p type="head"> <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></p><p type="head">
  
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 <s id="id.000864">De qua qu&aelig;runtur duo. </s> <s id="id.000864">De qua qu&aelig;runtur duo. </s>
  
 <s id="id.000865">Primum cur &longs;i cen&shy;<lb/>trum libr&aelig; &longs;it in &longs;uperiori parte librilis &longs;itum, cum pondere impo&longs;ito <lb/>deor&longs;um venerit librilis vna pars, altera &longs;ur&longs;um, eodem &longs;ublato, &amp; <lb/>librili libero relicto brachia librilis redeant ad pri&longs;tinum locum.<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.089.jpg" pagenum="50"/><emph type="italics"/>Secundum, cur &longs;i centrum eius &longs;it in inferiori parte librilis &longs;itum, <lb/>&amp; pondere impo&longs;ito, parteque librilis vna deor&longs;um demi&longs;&longs;a, eodem <lb/>&longs;ublato librile liberum relictum non redeat: &longs;ed in eo &longs;itu maneat. <lb/></s> <s id="id.000865">Primum cur &longs;i cen&shy;<lb/>trum libr&aelig; &longs;it in &longs;uperiori parte librilis &longs;itum, cum pondere impo&longs;ito <lb/>deor&longs;um venerit librilis vna pars, altera &longs;ur&longs;um, eodem &longs;ublato, &amp; <lb/>librili libero relicto brachia librilis redeant ad pri&longs;tinum locum.<emph.end type="italics"/></s><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.089.jpg" pagenum="50"/><emph type="italics"/>
  
  <s>Secundum, cur &longs;i centrum eius &longs;it in inferiori parte librilis &longs;itum, <lb/>&amp; pondere impo&longs;ito, parteque librilis vna deor&longs;um demi&longs;&longs;a, eodem <lb/>&longs;ublato librile liberum relictum non redeat: &longs;ed in eo &longs;itu maneat. <lb/></s>
  
 <s id="id.000866">Tertium adiungitur &agrave; Guido V baldo (&egrave; quo qu&aelig; h&icirc;c dicemus omnia <lb/>fer&egrave; depromp &longs;imus) non minus qu&aelig;&longs;itu dignum. </s> <s id="id.000866">Tertium adiungitur &agrave; Guido V baldo (&egrave; quo qu&aelig; h&icirc;c dicemus omnia <lb/>fer&egrave; depromp &longs;imus) non minus qu&aelig;&longs;itu dignum. </s>
  
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 <s id="id.000880">pr&aelig;ponderat igitur. </s> <s id="id.000880">pr&aelig;ponderat igitur. </s>
  
 <s id="id.000881">Non itaque per &longs;eredibit: &longs;ed &longs;itum <lb/>detracta decliuem retinebit: alias id graue, quo excedit, &longs;ur&longs;um &longs;ua <lb/>&longs;ponte a&longs;cenderet, contra def. </s> <s id="id.000881">Non itaque per &longs;e redibit: &longs;ed &longs;itum <lb/>detracta decliuem retinebit: alias id graue, quo excedit, &longs;ur&longs;um &longs;ua <lb/>&longs;ponte a&longs;cenderet, contra def. grauis.<emph.end type="italics"/></s></p><p type="main">
  
 <s id="id.000882">grauis.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000883">Itaque librilis <foreign lang="greek">e z.</foreign>] <emph type="italics"/>Quod pars &longs;uperior librilis in vno &longs;itu <lb/>centri &longs;it maior, in altero &longs;it minor, non e&longs;t probatum ab Ari&longs;totele: <lb/>&longs;ed ex fabrica librilis vtriu&longs;que generis res ilico fit euidens, etiam <lb/>pro Ari&longs;totelis characteribus no&longs;tris ad diagrammata adiunctis.<emph.end type="italics"/></s><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.091.jpg" pagenum="52"/>
  
 <s id="id.000883">Itaque librilis <foreign lang="greek">e z.</foreign>] <emph type="italics"/>Quod pars &longs;uperior librilis in vno &longs;itu <lb/>centri &longs;it maior, in altero &longs;it minor, non e&longs;t probatum ab Ari&longs;totele: <lb/>&longs;ed ex fabrica librilis vtriu&longs;que generis res ilico fit euidens, etiam <lb/>pro Ari&longs;totelis characteribus no&longs;tris ad diagrammata adiunctis.<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.091.jpg" pagenum="52"/><emph type="italics"/>Nam in librili primi modi cum obliquatur C F perpendiculum li&shy;<lb/>brilis, quod ip&longs;um perpetu&ograve; bifariam &longs;ecat, digreditur &agrave; perpendicu&shy;<lb/>lari intellecta, quam &longs;ecat<emph.end type="italics"/><lb/><figure id="id.035.01.091.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.091.1.jpg"/><lb/><emph type="italics"/>in centro, &longs;icque triangu&shy;<lb/>lum con&longs;tituit comprehen&shy;<lb/>dens aliquam partem al&shy;<lb/>terutrius brach&yuml; nempe F <lb/>C E, vel R C F, qu&aelig; &longs;ic <lb/>detracta vni, &amp; alteri ad&shy;<lb/>dita, reddit hoc &agrave; quo de&shy;<lb/>trahitur minus, &amp; eius <lb/>detract&aelig; partis duplo alte&shy;<lb/>rum <expan abbr="brachi&utilde;">brachium</expan> maius. </s> <s><emph type="italics"/>Nam in librili primi modi cum obliquatur C F perpendiculum li&shy;<lb/>brilis, quod ip&longs;um perpetu&ograve; bifariam &longs;ecat, digreditur &agrave; perpendicu&shy;<lb/>lari intellecta, quam &longs;ecat<emph.end type="italics"/><lb/><figure id="id.035.01.091.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.091.1.jpg"/><lb/><emph type="italics"/>in centro, &longs;icque triangu&shy;<lb/>lum con&longs;tituit comprehen&shy;<lb/>dens aliquam partem al&shy;<lb/>terutrius brach&yuml; nempe F <lb/>C E, vel R C F, qu&aelig; &longs;ic <lb/>detracta vni, &amp; alteri ad&shy;<lb/>dita, reddit hoc &agrave; quo de&shy;<lb/>trahitur minus, &amp; eius <lb/>detract&aelig; partis duplo alte&shy;<lb/>rum <expan abbr="brachi&utilde;">brachium</expan> maius. </s>
  
 <s id="id.000884">At&shy;<lb/>que hic modus conuenit <lb/>&longs;en&longs;ui Ari&longs;totelis, vt qui <lb/>eo v&longs;urus &longs;it capite &longs;equen&shy;<lb/>ti in problemate de vecte. <lb/></s> <s id="id.000884">At&shy;<lb/>que hic modus conuenit <lb/>&longs;en&longs;ui Ari&longs;totelis, vt qui <lb/>eo v&longs;urus &longs;it capite &longs;equen&shy;<lb/>ti in problemate de vecte. <lb/></s>
  
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 <s id="id.000889">Manebit igitur <lb/>(pr&aelig;&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&shy;<lb/>r&aelig; vel alicui ful&shy;<lb/>cro. </s> <s id="id.000889">Manebit igitur <lb/>(pr&aelig;&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&shy;<lb/>r&aelig; vel alicui ful&shy;<lb/>cro. </s>
  
 <s id="id.000890">Sed &amp; in li&shy;<lb/>brilibus huius ge&shy;<lb/>neris reditus &amp; <lb/>non reditus alia <lb/><expan abbr="eti&atilde;">etiam</expan> cau&longs;a e&longs;t, &longs;ci&shy;<lb/>licet quia <expan abbr="null&utilde;">nullum</expan> <expan abbr="c&etilde;">cem</expan> <lb/><expan abbr="tr&utilde;">trum</expan> grauitatis ma&shy;<lb/>net ni&longs;i &longs;u&longs;tinea&shy;<lb/>tur &agrave; linea <expan abbr="per-p&etilde;diculari">per&shy;<lb/>pendiculari</expan> ad pla&shy;<lb/>num horizontis. </s> <s id="id.000890">Sed &amp; in li&shy;<lb/>brilibus huius ge&shy;<lb/>neris reditus &amp; <lb/>non reditus alia <lb/><expan abbr="eti&atilde;">etiam</expan> cau&longs;a e&longs;t, &longs;ci&shy;<lb/>licet quia <expan abbr="null&utilde;">nullum</expan> <expan abbr="c&etilde;">cen</expan> <lb/><expan abbr="tr&utilde;">trum</expan> grauitatis ma&shy;<lb/>net ni&longs;i &longs;u&longs;tinea&shy;<lb/>tur &agrave; linea <expan abbr="per-p&etilde;diculari">per&shy;<lb/>pendiculari</expan> ad pla&shy;<lb/>num horizontis. </s>
  
 <s id="id.000891">quod e&longs;t demon&longs;tratum ab V baldo prop.  
  
 1. lib.  
  
 de lib. <lb/><!-- KEEP S--></s> 
  
 <s id="id.000892">Atque P e&longs;t centrum grauitatis magnitudinis compo&longs;it&aelig; &egrave; duobus <lb/>brach&yuml;s librilis G H, &amp; lancibus ponderibu&longs;que vtrimque &aelig;qui&shy;<lb/>ponderantibus, &longs;i intelligantur admota, vt patet ex prop.  
  
 4. lib.  
  
 1. <lb/>Archimed. <!-- REMOVE S-->de &aelig;quipond. </s> 
  
  <s id="id.000891">quod e&longs;t demon&longs;tratum ab V baldo prop. 1. lib. de lib. <lb/></s>
  
  <s id="id.000892">Atque P e&longs;t centrum grauitatis magnitudinis compo&longs;it&aelig; &egrave; duobus <lb/>brach&yuml;s librilis G H, &amp; lancibus ponderibu&longs;que vtrimque &aelig;qui&shy;<lb/>ponderantibus, &longs;i intelligantur admota, vt patet ex prop. 4. lib. 1. <lb/>Archimed. de &aelig;quipond. </s>
  
 <s id="id.000893">L K vero linea e&longs;t perpendicularis ad pla&shy;<lb/>num horizontis. </s> <s id="id.000893">L K vero linea e&longs;t perpendicularis ad pla&shy;<lb/>num horizontis. </s>
  
 <s id="id.000894">Non igitur P liberum relictum manebit ita vt e&longs;t <lb/>G P M H: Sed &amp; redibit ex natura grauium quou&longs;que occupe<gap/><lb/>punctum k in perpendiculari horizontis, &agrave; qua quia per extre&shy;<lb/>mum L fixa e&longs;t, &longs;u&longs;tinebitur. </s> <s id="id.000894">Non igitur P liberum relictum manebit ita vt e&longs;t <lb/>G P M H: Sed &amp; redibit ex natura grauium quou&longs;que occupet<lb/>punctum k in perpendiculari horizontis, &agrave; qua quia per extre&shy;<lb/>mum L fixa e&longs;t, &longs;u&longs;tinebitur. </s>
  
 <s id="id.000895">At G O P H manebit &longs;ic, nec <lb/>redibit ad G k H, quia, quod e&longs;&longs;et contra naturam, a&longs;cenderet. <lb/></s> <s id="id.000895">At G O P H manebit &longs;ic, nec <lb/>redibit ad G k H, quia, quod e&longs;&longs;et contra naturam, a&longs;cenderet. <lb/></s>
  
 <s id="id.000896">Vbiautem centrum librilis e&longs;t exqui&longs;it&egrave; medium, vt C ip&longs;ius A B <lb/>cum trutina C D mobili, &longs;eu &longs;upra, &longs;eu infra po&longs;ita &longs;it, quocunqu<gap/><emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.093.jpg" pagenum="54"/><figure id="id.035.01.093.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.093.1.jpg"/><lb/><emph type="italics"/>in &longs;itu fuerit A B vt <lb/>in G H manebit, tum <lb/>quia brachia manent <lb/>&aelig;qualia, tum quia cen&shy;<lb/>trum grauitatis C &longs;em&shy;<lb/>per erit in perpendicu&shy;<lb/>lari horizontis, &longs;ecun&shy;<lb/>dum quam &amp; ad quam <lb/>magnitudo compo&longs;ita <lb/>exbrach&yuml;s C A, C B &amp; lancibus &amp; ponderibus &aelig;quiponderan&shy;<lb/>tibus, &longs;i impo&longs;ita &longs;int, fertur, &longs;ed &longs;u&longs;tinetur linea C D vel C E <lb/>fixa. </s> <s id="id.000896">Vbiautem centrum librilis e&longs;t exqui&longs;it&egrave; medium, vt C ip&longs;ius A B <lb/>cum trutina C D mobili, &longs;eu &longs;upra, &longs;eu infra po&longs;ita &longs;it, quocunque<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.093.jpg" pagenum="54"/><figure id="id.035.01.093.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.093.1.jpg"/><lb/><emph type="italics"/>in &longs;itu fuerit A B vt <lb/>in G H manebit, tum <lb/>quia brachia manent <lb/>&aelig;qualia, tum quia cen&shy;<lb/>trum grauitatis C &longs;em&shy;<lb/>per erit in perpendicu&shy;<lb/>lari horizontis, &longs;ecun&shy;<lb/>dum quam &amp; ad quam <lb/>magnitudo compo&longs;ita <lb/>exbrach&yuml;s C A, C B &amp; lancibus &amp; ponderibus &aelig;quiponderan&shy;<lb/>tibus, &longs;i impo&longs;ita &longs;int, fertur, &longs;ed &longs;u&longs;tinetur linea C D vel C E <lb/>fixa. </s>
  
 <s id="id.000897">Et &longs;ic patet &longs;olutio terti&aelig; partis huius problematis ab Ari&longs;totele <lb/>pr&aelig;termi&longs;&longs;&aelig;. </s> <s id="id.000897">Et &longs;ic patet &longs;olutio terti&aelig; partis huius problematis ab Ari&longs;totele <lb/>pr&aelig;termi&longs;&longs;&aelig;. </s>
  
 <s id="id.000898">Rar&ograve; tamen huic demon&longs;trationi licet ver&aelig;, experien&shy;<lb/>tia re&longs;pondet, propter in&longs;trumentorum materiam Phy&longs;icam, in qua <lb/>exacte medium con&longs;tituere non datur in puncto geometrico, vtcum&shy;<lb/>que tamen alias re&longs;pondet.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000898">Rar&ograve; tamen huic demon&longs;trationi licet ver&aelig;, experien&shy;<lb/>tia re&longs;pondet, propter in&longs;trumentorum materiam Phy&longs;icam, in qua <lb/>exacte medium con&longs;tituere non datur in puncto geometrico, vtcum&shy;<lb/>que tamen alias re&longs;pondet.<emph.end type="italics"/></s></p><p type="main">
  
 <s id="id.000899"><gap/></s></p><p type="main"> <s id="id.000899"><foreign lang="greek"><gap/></foreign></s></p><p type="main">
  
 <s id="id.000900">4. Potenti&aelig; vectis cau&longs;a.</s></p><p type="main"> <s id="id.000900">4. Potenti&aelig; vectis cau&longs;a.</s></p><p type="main">
  
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 <s id="id.000907">amb&aelig; enim &longs;tant vt <lb/>centrum. </s> <s id="id.000907">amb&aelig; enim &longs;tant vt <lb/>centrum. </s>
  
 <s id="id.000908">Quoniam vero <lb/>celerius ab &aelig;quali ponde&shy;<lb/>re mouetur radius maior. <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.094.jpg" pagenum="55"/><gap/><lb/>Sunt vero tria circa|, <expan abbr="vect&etilde;">vectem</expan> <lb/>pre&longs;&longs;io quidem e&longs;t &verbar;agina &amp; <lb/><expan abbr="centr&utilde;">centrum</expan>, duo etiam pondera <lb/>mouens &longs;cilicet, &amp; mobile.</s></p><p type="head"> <s id="id.000908">Quoniam vero <lb/>celerius ab &aelig;quali ponde&shy;<lb/>re mouetur radius maior. </s><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.094.jpg" pagenum="55"/></p>
  
 <s id="id.000909">COMMENTARIVS.<!-- KEEP S--></s></p><p type="main"> <p type="main"><s><foreign lang="greek"><gap/></foreign></s></p>
  
 <s id="id.000910">Potenti&aelig; vectis cau&longs;a.] <emph type="italics"/>Vectis definitus e&longs;t &agrave; Bud&aelig;o bacu&shy;</s></p><p type="main"> <p type="main"><s>Sunt vero tria circa|, <expan abbr="vect&etilde;">vectem</expan> <lb/>pre&longs;&longs;io quidem e&longs;t &verbar;agina &amp; <lb/><expan abbr="centr&utilde;">centrum</expan>, duo etiam pondera <lb/>mouens &longs;cilicet, &amp; mobile.</s></p><p type="head">
  
 <s id="id.000911"><arrow.to.target n="marg19"/><lb/>lus validus per mediam machinam traiectus, quo manuducto <lb/>machina, dum ver&longs;atur, funem ductarium aduoluit. </s> <s id="id.000909">COMMENTARIVS.<!-- KEEP S--></s></p><p type="main">
  
  <s id="id.000910">Potenti&aelig; vectis cau&longs;a.] <emph type="italics"/>Vectis definitus e&longs;t &agrave; Bud&aelig;o bacu&shy; <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>
  
 <s id="id.000912">H&aelig;c definitio <lb/><expan abbr="nimi&utilde;">nimium</expan> angu&longs;ta e&longs;t, neque huic loco <expan abbr="c&otilde;uenit">conuenit</expan>, neque &longs;atis rei ip&longs;i. </s> <s id="id.000912">H&aelig;c definitio <lb/><expan abbr="nimi&utilde;">nimium</expan> angu&longs;ta e&longs;t, neque huic loco <expan abbr="c&otilde;uenit">conuenit</expan>, neque &longs;atis rei ip&longs;i. </s>
  
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 <s id="id.000919">Atque hic e&longs;t primus modus vtendi vecte frequenti&szlig;imus: <lb/>&longs;ed &amp; e&longs;t alter non mult&ograve; infrequentior, cum lingula oneri, vt an&shy;<lb/>t&egrave;, &longs;ubdita nullo &longs;ubdito pr&aelig;ter &longs;olum immobile vecti ip&longs;i hypo&shy;<lb/>mochlio, vectis caput attollitur. </s> <s id="id.000919">Atque hic e&longs;t primus modus vtendi vecte frequenti&szlig;imus: <lb/>&longs;ed &amp; e&longs;t alter non mult&ograve; infrequentior, cum lingula oneri, vt an&shy;<lb/>t&egrave;, &longs;ubdita nullo &longs;ubdito pr&aelig;ter &longs;olum immobile vecti ip&longs;i hypo&shy;<lb/>mochlio, vectis caput attollitur. </s>
  
 <s id="id.000920">Hoc enim &longs;ur&longs;um lato omnes etiam <lb/>vectis partes attolli nece&longs;&longs;e e&longs;t pr&aelig;ter extremum lingul&aelig; fixum, quo<gap/><lb/>centri immobilis rationem &longs;umit, &amp; terr&aelig; vel al&yuml; corpori immobili <lb/>tanquam hypomachlio innititur. </s> <s id="id.000920">Hoc enim &longs;ur&longs;um lato omnes etiam <lb/>vectis partes attolli nece&longs;&longs;e e&longs;t pr&aelig;ter extremum lingul&aelig; fixum, quod <lb/>centri immobilis rationem &longs;umit, &amp; terr&aelig; vel al&yuml; corpori immobili <lb/>tanquam hypomochlio innititur. </s>
  
 <s id="id.000921">Proinde etiam onus ad partis ve&shy;<lb/>ctis cui impo&longs;itum e&longs;t, motionem mouebitur, &amp; tunc non &longs;olum ele&shy;<lb/>uatur: &longs;ed &amp; &longs;i opus e&longs;t, fiatque vectis perpendicularis &longs;olo, &longs;ecundum<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.095.jpg" pagenum="56"/><emph type="italics"/>latus impellitur. </s> <s id="id.000921">Proinde etiam onus ad partis ve&shy;<lb/>ctis cui impo&longs;itum e&longs;t, motionem mouebitur, &amp; tunc non &longs;olum ele&shy;<lb/>uatur: &longs;ed &amp; &longs;i opus e&longs;t, fiatque vectis perpendicularis &longs;olo, &longs;ecundum<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.095.jpg" pagenum="56"/><emph type="italics"/>latus impellitur. </s>
  
 <s id="id.000922">Vtrumque vectis v&longs;um Vitruuius cap.  <s id="id.000922">Vtrumque vectis v&longs;um Vitruuius cap. 8. lib. 10. &longs;ic <lb/>explicuit. </s>
  
 8. lib.  
  
 10. &longs;ic <lb/>explicuit. </s> 
  
 <s id="id.000923">Ferreus vectis cum e&longs;t commotus ad onus, quod manuum <lb/>multitudo non pote&longs;t mouere, &longs;uppo&longs;ita vti centro cito porrecta pre&longs;&shy;<lb/>&longs;ione, qu&ograve;d Gr&aelig;ci<emph.end type="italics"/> <foreign lang="greek">(w_omo/xlion</foreign> <emph type="italics"/>appellant, &amp; vectis lingua &longs;ub <lb/>onus &longs;ubdita, caput eius vnius hominis viribus pre&longs;&longs;um, id onus ex&shy;<lb/>tollet. </s> <s id="id.000923">Ferreus vectis cum e&longs;t commotus ad onus, quod manuum <lb/>multitudo non pote&longs;t mouere, &longs;uppo&longs;ita vti centro cito porrecta pre&longs;&shy;<lb/>&longs;ione, qu&ograve;d Gr&aelig;ci<emph.end type="italics"/> <foreign lang="greek">(w_omo/xlion</foreign> <emph type="italics"/>appellant, &amp; vectis lingua &longs;ub <lb/>onus &longs;ubdita, caput eius vnius hominis viribus pre&longs;&longs;um, id onus ex&shy;<lb/>tollet. </s>
  
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 <s id="id.000925">H&aelig;c Vitr. <lb/><!-- REMOVE S-->&agrave; 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 &amp; 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">H&aelig;c Vitr. <lb/><!-- REMOVE S-->&agrave; 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 &amp; 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/>voluntar&yuml; vecti. </s> <s id="id.000926">Galenus comparauit mu&longs;culum, qui e&longs;t in&longs;trumentum motus <lb/>voluntar&yuml; vecti. </s>
  
 <s id="id.000927">vtque pondera, inquit, qu&aelig; mouere manibus nequi&shy;<lb/>mus, vectibus admotis mouere &longs;olemus. </s> <s id="id.000927">vtque pondera, inquit, qu&aelig; mouere manibus nequi&shy;<lb/>mus, vectibus admotis mouere &longs;olemus. </s>
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 <s id="id.000931">Itaque <lb/>hic &yuml;s qui anatomen corporis humani re&longs;pexerunt <expan abbr="iucund&utilde;">iucundum</expan> e&longs;t ip&longs;ius <lb/>membra, tanquam onera &longs;excentis mu&longs;culis, tanquam vectibus, tam <lb/>varie flecti, intendi &longs;ur&longs;um, ferri deor&longs;um, demitti ad latera, contor&shy;<lb/>queri, circumuolui, &amp; ad omnes motus, quos voluntas humana vti&shy;<lb/>litate incitata pr&aelig;&longs;cribit, educi, immo vero &yuml;&longs;dem agentibus in quie&shy;<lb/>te, &amp; quam medici appellant in media figura, retineri.<emph.end type="italics"/></s></p><p type="margin"> <s id="id.000931">Itaque <lb/>hic &yuml;s qui anatomen corporis humani re&longs;pexerunt <expan abbr="iucund&utilde;">iucundum</expan> e&longs;t ip&longs;ius <lb/>membra, tanquam onera &longs;excentis mu&longs;culis, tanquam vectibus, tam <lb/>varie flecti, intendi &longs;ur&longs;um, ferri deor&longs;um, demitti ad latera, contor&shy;<lb/>queri, circumuolui, &amp; ad omnes motus, quos voluntas humana vti&shy;<lb/>litate incitata pr&aelig;&longs;cribit, educi, immo vero &yuml;&longs;dem agentibus in quie&shy;<lb/>te, &amp; quam medici appellant in media figura, retineri.<emph.end type="italics"/></s></p><p type="margin">
  
 <s id="id.000932"><margin.target id="marg19"/>Annot. <!-- REMOVE S-->in <lb/>Pandectas.</s> <s id="id.000932"><margin.target id="marg19"/>Annot. in <lb/>Pandectas.</s></p>
  
 </p><p type="margin"> 
  
  
 <s id="id.000933"><margin.target id="marg20"/>Cap.  
  
  
 10 lib. <lb/><!-- REMOVE S-->1 de plac. <lb/><!-- REMOVE S-->H<gap/>pp. <!-- REMOVE S-->&amp; <lb/><gap/></s> 
  
  
  <p type="margin"><s id="id.000933"><margin.target id="marg20"/>Cap. 10 lib. <lb/>1 de plac. <lb/>Hipp. &amp; <lb/>Plat.</s></p><p type="main">
  
  
 </p><p type="main"> 
  
 <s id="id.000934">Cur vires exigu&aelig;.] <emph type="italics"/>Machina libr&aelig; duobus problematis expe&shy;<lb/>dita e&longs;t: vectis deinde duodecim di&longs;&longs;eritur, &egrave; quibus primum e&longs;t ge&shy;<lb/>nerale. </s> <s id="id.000934">Cur vires exigu&aelig;.] <emph type="italics"/>Machina libr&aelig; duobus problematis expe&shy;<lb/>dita e&longs;t: vectis deinde duodecim di&longs;&longs;eritur, &egrave; quibus primum e&longs;t ge&shy;<lb/>nerale. </s>
  
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 <s id="id.000949"><emph type="italics"/>Ergo vectis facile deprimetur, depre&longs;&longs;u&longs;que manebit, &amp; ad eius <lb/>motum pondus incumbens mouebitur.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000949"><emph type="italics"/>Ergo vectis facile deprimetur, depre&longs;&longs;u&longs;que manebit, &amp; ad eius <lb/>motum pondus incumbens mouebitur.<emph.end type="italics"/></s></p><p type="main">
  
 <s id="id.000950"><gap/></s></p><p type="main"> <s id="id.000950"><foreign lang="greek"><gap/></foreign></s></p><p type="main">
  
 <s id="id.000951">Quod autem e&longs;t mobile <lb/>ad mouens, id e&longs;t longitu&shy;<lb/>do ad longitudinem reci&shy;<lb/>proc&egrave;. </s> <s id="id.000951">Quod autem e&longs;t mobile <lb/>ad mouens, id e&longs;t longitu&shy;<lb/>do ad longitudinem reci&shy;<lb/>proc&egrave;. </s>
  
 <s id="id.000952">Semper &longs;ane quant&ograve; <lb/>longitudo magis di&longs;tabit &agrave; <lb/>pre&longs;&longs;ione, facilius mouebit <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.097.jpg" pagenum="58"/><gap/><lb/>Cau&longs;a vero ante dicta e&longs;t: <lb/>quoniam radius maior ma&shy;<lb/>iorem de&longs;cribit circulum. <lb/></s> <s id="id.000952">Semper &longs;ane quant&ograve; <lb/>longitudo magis di&longs;tabit &agrave; <lb/>pre&longs;&longs;ione, facilius mouebit. </s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.097.jpg" pagenum="58"/>
  
  <p type="main"><s><foreign lang="greek"><gap/></foreign></s></p>
  
  <p type="main"><s>Cau&longs;a vero ante dicta e&longs;t: <lb/>quoniam radius maior ma&shy;<lb/>iorem de&longs;cribit circulum. <lb/></s>
  
 <s id="id.000953">Itaque ab eadem vi plus <lb/>mutabitur mouens illud, <lb/>quod plus di&longs;tat &agrave; pre&longs;&longs;io&shy;<lb/>ne. </s> <s id="id.000953">Itaque ab eadem vi plus <lb/>mutabitur mouens illud, <lb/>quod plus di&longs;tat &agrave; pre&longs;&longs;io&shy;<lb/>ne. </s>
  
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 <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 reciproc&egrave;) fiat ergo vt B C ad A C: ita <lb/>pondus D ad aliud, vt E. hoc igitur pondus E loco potenti&aelig; ap&shy;<lb/>pen&longs;um in B, ip&longs;um D pondere &aelig;quabit. </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 reciproc&egrave;) fiat ergo vt B C ad A C: ita <lb/>pondus D ad aliud, vt E. hoc igitur pondus E loco potenti&aelig; ap&shy;<lb/>pen&longs;um in B, ip&longs;um D pondere &aelig;quabit. </s>
  
 <s id="id.000961">Magnitudines enim in gra&shy;<lb/>uitate commen&longs;urabiles &aelig;quiponderant, &longs;i permutatim &longs;u&longs;pendantur <lb/>in di&longs;tantijs &longs;ecundum grauitatum rationem <expan abbr="c&otilde;&longs;titut&aelig;">con&longs;titut&aelig;</expan> prop.  <s id="id.000961">Magnitudines enim in gra&shy;<lb/>uitate commen&longs;urabiles &aelig;quiponderant, &longs;i permutatim &longs;u&longs;pendantur <lb/>in di&longs;tantijs &longs;ecundum grauitatum rationem <expan abbr="c&otilde;&longs;titut&aelig;">con&longs;titut&aelig;</expan> prop. 6. lib. 1. <lb/>Archim. de &aelig;quipond. </s>
  
 6. lib.  
  
 1. <lb/>Archim. <!-- REMOVE S-->de &aelig;quipond. </s> 
  
  
  
 <s id="id.000962">Et &longs;ic potentia &aelig;qualis ip&longs;i E ibidem con&longs;ti&shy;<lb/>tuta pondere &aelig;quabit ip&longs;um D, id e&longs;t ne D deor&longs;um vergat, quod fa-<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.098.jpg" pagenum="59"/><emph type="italics"/>eit pondus E, prohibebit. </s> <s id="id.000962">Et &longs;ic potentia &aelig;qualis ip&longs;i E ibidem con&longs;ti&shy;<lb/>tuta pondere &aelig;quabit ip&longs;um D, id e&longs;t ne D deor&longs;um vergat, quod fa-<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.098.jpg" pagenum="59"/><emph type="italics"/>eit pondus E, prohibebit. </s>
  
 <s id="id.000963">Nam &aelig;qualia ad idem eandem rationem <lb/>habent prop.  <s id="id.000963">Nam &aelig;qualia ad idem eandem rationem <lb/>habent prop. 7. lib. 5. el. </s>
  
 7. lib.  
  
 5. el. </s> 
  
 <s id="id.000964">Sed E habet eam ad D, quam A C and B C, ex <lb/>fab. </s> <s id="id.000964">Sed E habet eam ad D, quam A C and B C, ex <lb/>fab. </s>
  
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 <s id="id.000971">Secundum. <emph type="italics"/>Qu&ograve; pars ab hypomochlio ad lingulam minor erit: <lb/>e&ograve; minor potentia ad &longs;u&longs;tinendum &longs;ufficiet.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000971">Secundum. <emph type="italics"/>Qu&ograve; pars ab hypomochlio ad lingulam minor erit: <lb/>e&ograve; minor potentia ad &longs;u&longs;tinendum &longs;ufficiet.<emph.end type="italics"/></s></p><p type="main">
  
 <s id="id.000972">Reciproce.] <foreign lang="greek">*an<gap/>ipepo/n<gap/>hsis.</foreign> <emph type="italics"/>Reciprocatio quid &longs;it de&longs;umen&shy;<lb/>dum e&longs;t ex Eucl. <!-- REMOVE S-->def. </s> <s id="id.000972">Reciproce.] <foreign lang="greek">*an<gap/>ipepo/n<gap/>hsis.</foreign> <emph type="italics"/>Reciprocatio quid &longs;it de&longs;umen&shy;<lb/>dum e&longs;t ex Eucl. def. 2. lib. 6. vbi reciproc&aelig; figur&aelig; definiuntur cum in <lb/>vtraque figura antecedentes &amp; con&longs;equentes rationum termini fue&shy;<lb/>rint, id e&longs;t quando in altera quidem e&longs;t terminus antecedens prim&aelig; <lb/>rationis, &amp; con&longs;equens &longs;ecund&aelig;: in altera vero e&longs;t con&longs;equens pri&shy;<lb/>m&aelig;, &amp; antecedens &longs;ecund&aelig;. </s>
  
  
  
 <s id="id.000973">2. lib.  
  
 6. vbi reciproc&aelig; figur&aelig; definiuntur cum in <lb/>vtraque figura antecedentes &amp; con&longs;equentes rationum termini fue&shy;<lb/>rint, id e&longs;t quando in altera quidem e&longs;t terminus antecedens prim&aelig; <lb/>rationis, &amp; con&longs;equens &longs;ecund&aelig;: in altera vero e&longs;t con&longs;equens pri&shy;<lb/>m&aelig;, &amp; antecedens &longs;ecund&aelig;. </s> 
  
 <s id="id.000974">Qu&aelig; vt conuenire huic loco intelligan&shy;<lb/>tur, &longs;umendum e&longs;t pondus mouendum &longs;imul cum parte vectis ab hy&shy;<lb/>pomochlio ad lingulam cui appenditur pro vna figura: &amp; potentia <lb/>mouens cum reliqua parte vectis pro altera figura. </s> <s id="id.000974">Qu&aelig; vt conuenire huic loco intelligan&shy;<lb/>tur, &longs;umendum e&longs;t pondus mouendum &longs;imul cum parte vectis ab hy&shy;<lb/>pomochlio ad lingulam cui appenditur pro vna figura: &amp; potentia <lb/>mouens cum reliqua parte vectis pro altera figura. </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 qu&aelig;uis paulo maior vis tanto facilius &longs;u&longs;tinebit, aut mo&shy;<lb/>uebit pondus: quanto pars ad caput maior erit. </s> <s id="id.000980">Et <lb/>&longs;ic &longs;i minor potentia ad &longs;u&longs;tinendum vel dimouendum &longs;ufficiet, <lb/>etiam alia qu&aelig;uis paulo maior vis tanto facilius &longs;u&longs;tinebit, aut mo&shy;<lb/>uebit pondus: quanto pars ad caput maior erit. </s>
  
 <s id="id.000981">In&aelig;qualium enim <lb/>maior ad eandem maiorem rationem habet prop.  <s id="id.000981">In&aelig;qualium enim <lb/>maior ad eandem maiorem rationem habet prop. 8. lib. 5. Sed &amp; <lb/>huius rei cau&longs;a adfertur ex his qu&aelig; ante demon&longs;trata &longs;unt, nempe &agrave; <lb/>radio maiore maiorem de&longs;cribi circulum. </s>
  
 8. lib.  
  
 5. Sed &amp; <lb/>huius rei cau&longs;a adfertur ex his qu&aelig; ante demon&longs;trata &longs;unt, nempt &agrave; <lb/>radio maiore maiorem de&longs;cribi circulum. </s> 
  
 <s id="id.000982">Pars enim vectis ab hy&shy;<lb/>pomochlio ad caput rad&yuml; in&longs;tar e&longs;t maioris, qui depre&longs;&longs;us &amp; ideo vo&shy;<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> <s id="id.000982">Pars enim vectis ab hy&shy;<lb/>pomochlio ad caput rad&yuml; in&longs;tar e&longs;t maioris, qui depre&longs;&longs;us &amp; ideo vo&shy;<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.000987">Quod in quouis dato pondere cum r&egrave;rum natura non <lb/>patiatur, problema alioqui geometric&egrave; demon&longs;tratum, in v&longs;u ob ma&shy;<lb/>teri&aelig; &longs;atis long&aelig; &amp; firm&aelig; <expan abbr="defect&utilde;">defectum</expan> &longs;u&aelig; rationi re&longs;pondere <expan abbr="n&otilde;">non</expan> pote&longs;t.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000987">Quod in quouis dato pondere cum r&egrave;rum natura non <lb/>patiatur, problema alioqui geometric&egrave; demon&longs;tratum, in v&longs;u ob ma&shy;<lb/>teri&aelig; &longs;atis long&aelig; &amp; firm&aelig; <expan abbr="defect&utilde;">defectum</expan> &longs;u&aelig; rationi re&longs;pondere <expan abbr="n&otilde;">non</expan> pote&longs;t.<emph.end type="italics"/></s></p><p type="main">
  
 <s id="id.000988">Sit vectis <foreign lang="greek">a b</foreign>] <emph type="italics"/>huius diagrammatis expo&longs;itio &longs;i non imperfe&shy;<lb/>cta e&longs;t, adfertur tantum ad o&longs;tendendum quod pondus<emph.end type="italics"/> <foreign lang="greek">g</foreign> <emph type="italics"/>ab eo cum<emph.end type="italics"/><lb/><figure id="id.035.01.099.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.099.1.jpg"/><lb/><emph type="italics"/>erat in<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>per depre&szlig;ionem<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">h</foreign> <emph type="italics"/>tran&longs;latum e&longs;t ad<emph.end type="italics"/> <foreign lang="greek">k.</foreign> <emph type="italics"/>Sed adhuc <lb/>paulo ob&longs;curius. </s> <s id="id.000988">Sit vectis <foreign lang="greek">a b</foreign>] <emph type="italics"/>huius diagrammatis expo&longs;itio &longs;i non imperfe&shy;<lb/>cta e&longs;t, adfertur tantum ad o&longs;tendendum quod pondus<emph.end type="italics"/> <foreign lang="greek">g</foreign> <emph type="italics"/>ab eo cum<emph.end type="italics"/><lb/><figure id="id.035.01.099.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.099.1.jpg"/><lb/><emph type="italics"/>erat in<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>per depre&szlig;ionem<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">h</foreign> <emph type="italics"/>tran&longs;latum e&longs;t ad<emph.end type="italics"/> <foreign lang="greek">k.</foreign></s>
  
 <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"/>pre&szlig;io<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/>&amp; 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.  <s><emph type="italics"/>Sed adhuc <lb/>paulo ob&longs;curius. </s>
  
 1. huius lib.  <s id="id.000989">Apertius igitur &longs;ic. </s>
  
 o&longs;ten&longs;um e&longs;t diametri ex&shy;<lb/>tremo vno deor&longs;um moto, alterum eodem tempore &longs;ur&longs;um moueri. </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"/>pre&szlig;io<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/>&amp; 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&shy;<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&shy;<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&shy;<lb/>ce&longs;&longs;um e&longs;t. </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&shy;<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&shy;<lb/>ce&longs;&longs;um e&longs;t. </s>
  
 <s id="id.000992">Et ex his denique contendit Ari&longs;toteles o&longs;tendere circula&shy;<lb/>rem motum omnium machinationum principia in &longs;e continere, vt <lb/>multis po&longs;tea &longs;pecialibus exemplis declarabit, in quibus &amp; alijs om&shy;<lb/>nibus, qui &longs;cit&egrave; di&longs;tinguet, quid oneri re&longs;pondeat, pro quo &longs;it vectis, <lb/>quale &longs;it hypomochlium, vnde vis mouens habeatur, hic habebit <lb/>abund&egrave;, quid &longs;entiendum &longs;it.<emph.end type="italics"/></s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.100.jpg" pagenum="61"/><p type="main"> <s id="id.000992">Et ex his denique contendit Ari&longs;toteles o&longs;tendere circula&shy;<lb/>rem motum omnium machinationum principia in &longs;e continere, vt <lb/>multis po&longs;tea &longs;pecialibus exemplis declarabit, in quibus &amp; alijs om&shy;<lb/>nibus, qui &longs;cit&egrave; di&longs;tinguet, quid oneri re&longs;pondeat, pro quo &longs;it vectis, <lb/>quale &longs;it hypomochlium, vnde vis mouens habeatur, hic habebit <lb/>abund&egrave;, quid &longs;entiendum &longs;it.<emph.end type="italics"/></s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.100.jpg" pagenum="61"/><p type="main">
  
 <s id="id.000993"><gap/></s></p><p type="main"> <s id="id.000993">5. <foreign lang="greek"><gap/></foreign></s></p><p type="main">
  
 <s id="id.000994">5. Cur nauim mouent ma&shy;<lb/>xime remiges, qui in <lb/>media naui &longs;edent.</s></p><p type="main"> <s id="id.000994">5. Cur nauim mouent ma&shy;<lb/>xime remiges, qui in <lb/>media naui &longs;edent.</s></p><p type="main">
  
 <s id="id.000995"><gap/></s></p><p type="main"> 
  
 <s id="id.000996">Cur nauim <expan abbr="mou&etilde;t">mouent</expan> maxi&shy;<lb/>me remiges mediani? </s> <s id="id.000996">Cur nauim <expan abbr="mou&etilde;t">mouent</expan> maxi&shy;<lb/>me remiges mediani? </s>
  
 <s id="id.000997">An qa <lb/>remus e&longs;t vectis, pre&longs;&longs;io <expan abbr="&longs;i-quid&etilde;">&longs;i&shy;<lb/>quidem</expan> &longs;calm^{9} efficitur. </s> <s id="id.000997">An qa <lb/>remus e&longs;t vectis, pre&longs;&longs;io <expan abbr="&longs;i-quid&etilde;">&longs;i&shy;<lb/>quidem</expan> &longs;calm^{9} efficitur. </s>
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 <s id="id.001009">COMMENTARIVS.<!-- KEEP S--></s></p><p type="main"> <s id="id.001009">COMMENTARIVS.<!-- KEEP S--></s></p><p type="main">
  
 <s id="id.001010">Cvr remiges.] <emph type="italics"/>Specialia deinceps &longs;unt vndecim de vecte pro&shy;<lb/>blemata, &egrave; quibus priora &longs;ex pertinent ad nauigandi artem, qu&aelig; <lb/>mirabilior &longs;it propter audaciam, an propter &longs;ubtilitatem inuentornm <lb/>ad bene <expan abbr="nauig&atilde;dum">nauigandum</expan> vtilium, dubium e&longs;t. </s> <s id="id.001010">Cvr remiges.] <emph type="italics"/>Specialia deinceps &longs;unt vndecim de vecte pro&shy;<lb/>blemata, &egrave; quibus priora &longs;ex pertinent ad nauigandi artem, qu&aelig; <lb/>mirabilior &longs;it propter audaciam, an propter &longs;ubtilitatem inuentorum <lb/>ad bene <expan abbr="nauig&atilde;dum">nauigandum</expan> vtilium, dubium e&longs;t. </s>
  
  <s id="id.001011">Quid enim audacius quam <lb/>ventorum furorem, &amp; maris rabiem contemnere, &amp; vt in eo tran&shy;<lb/>quilla &longs;int omnia, &longs;e tantum duorum &longs;patio digitorum &agrave; certa, eaque <lb/>a&szlig;idua morte di&longs;tare cernere! </s>
  
  <s>Semper enim<emph.end type="italics"/></s></p><p type="main">
  
 <s id="id.001011">Quid enim audacius quam <lb/>ventorum furorem, &amp; maris rabiem contemnere, &amp; vt in eo tran&shy;<lb/>quilla &longs;int omnia, &longs;e tantum duorum &longs;patio digitorum &agrave; certa, eaque <lb/>a&szlig;idua morte di&longs;tare cernere! Semper enim<emph.end type="italics"/></s></p><p type="main"> <s id="id.001012">E&longs;t tua tam prop&egrave; mors: quam prop&egrave; cernis aquam. <lb/></s>
  
 <s id="id.001012">E&longs;t tua tam prop&egrave; mors: quam prop&egrave; cernis aquam. <lb/><emph type="italics"/>Et quod audacius e&longs;t tam longum iter, tam infidum ob &longs;copulos, vor&shy;<lb/>tices, charybdes, Syllas, breuia, Syrtes &longs;ine vllis certis ho&longs;pic&yuml;s etiam <lb/>per &longs;ummas tenebras, in quibus homines alioqui domibus &longs;uis vrba&shy;<lb/>nis conclu&longs;i, horrent, peragere? </s> <s><emph type="italics"/>Et quod audacius e&longs;t tam longum iter, tam infidum ob &longs;copulos, vor&shy;<lb/>tices, charybdes, Syllas, breuia, Syrtes &longs;ine vllis certis ho&longs;pic&yuml;s etiam <lb/>per &longs;ummas tenebras, in quibus homines alioqui domibus &longs;uis vrba&shy;<lb/>nis conclu&longs;i, horrent, peragere? </s>
  
 <s id="id.001013">Et denique vbie&longs;t aqu&aelig; &longs;emper &longs;um&shy;<lb/>ma copia, nullius rei tamen magis, quam aqu&aelig; penuria laborare? <lb/></s> <s id="id.001013">Et denique vbie&longs;t aqu&aelig; &longs;emper &longs;um&shy;<lb/>ma copia, nullius rei tamen magis, quam aqu&aelig; penuria laborare? <lb/></s>
  
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 <s id="id.001023">An&shy;<lb/>tiqui&szlig;ima nauium Arg&ocirc; &agrave; Fabro nauali, qui eam &aelig;dificauit, &longs;i <lb/>Apollonio creditur, nuncupata e&longs;t. </s> <s id="id.001023">An&shy;<lb/>tiqui&szlig;ima nauium Arg&ocirc; &agrave; Fabro nauali, qui eam &aelig;dificauit, &longs;i <lb/>Apollonio creditur, nuncupata e&longs;t. </s>
  
 <s id="id.001024">Sic enim in<emph.end type="italics"/> <foreign lang="greek">*argonau<gap/>ikw_n.</foreign></s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.102.jpg" pagenum="63"/><p type="main"> <s id="id.001024">Sic enim in<emph.end type="italics"/> <foreign lang="greek">*argonautikw_n.</foreign></s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.102.jpg" pagenum="63"/><p type="main">
  
 <s id="id.001025"><foreign lang="greek">*nh_a d) )<gap/>pikrate/ws ar)gou_ (w_o<gap/>hmosu/nh|si</foreign></s></p><p type="main"> <s id="id.001025"><foreign lang="greek">*nh_a d) )o)pikrate/ws ar)gou_ (w_othmosu/nh|si</foreign></s></p><p type="main">
  
 <s id="id.001026"><foreign lang="greek">*ezwsan, pa/mw_rw<gap/>on e)u:<gap/>refei_ en)do<gap/>en o(/pl<gap/>.</foreign><lb/><emph type="italics"/>qu&aelig; &longs;ic reddidit Lazarus Bayfius.<emph.end type="italics"/></s></p><p type="main"> <s id="id.001026"><foreign lang="greek">*ezwsan, pa/mw_rw<gap/>on e)u:<gap/>refei_ en)do<gap/>en o(/pl<gap/>.</foreign><lb/><emph type="italics"/>qu&aelig; &longs;ic reddidit Lazarus Bayfius.<emph.end type="italics"/></s></p><p type="main">
  
 <s id="id.001027">Imprimis nauem diuinis artibus Argi,<!-- REMOVE S-->Extructam, intus compingunt habili armamento.</s></p><p type="main"> <s id="id.001027">Imprimis nauem diuinis artibus Argi, </s>
  
 <s id="id.001028"><emph type="italics"/>Tullius tamen in 1. Tu&longs;cula. </s> <s>Extructam, intus compingunt habili armamento.</s></p><p type="main">
  
 <s id="id.001029">dicit nominatam Arg&ocirc;, quia Argiui in <lb/>ea delecti viri vecti petebant Arietis pellem inauratam. </s> <s id="id.001028"><emph type="italics"/>Tullius tamen in 1. Tu&longs;cula. dicit nominatam Arg&ocirc;, quia Argiui in <lb/>ea delecti viri vecti petebant Arietis pellem inauratam. </s>
  
 <s id="id.001030">Ante Ar&shy;<lb/>goratibus, &amp; paruis acat&yuml;s homines tantum vehi &longs;olere, te&longs;tis e&longs;t <lb/>Diodorus &longs;iculus. </s> <s id="id.001030">Ante Ar&shy;<lb/>goratibus, &amp; paruis acat&yuml;s homines tantum vehi &longs;olere, te&longs;tis e&longs;t <lb/>Diodorus &longs;iculus. </s>
  
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 <s id="id.001037">Athen&aelig;us recitat inter <lb/>remos quo&longs;dam fui&longs;&longs;e tant&aelig; longitudinis vt duodequadraginta cu&shy;<lb/>bitos explerent, quod non erit incredibile memoria repetenti quarun&shy;<lb/>dam nauium &agrave; veteribus fabricatarum va&longs;titatem, cuiu&longs;modi idem, <lb/>&amp; Plutarchus memorant fui&longs;&longs;e illam dictam fluuialem Thalame&shy;<lb/>gon, quam Ptolom&aelig;us Philopator in delic&yuml;s habuit, non tam ad <lb/>v&longs;um: quam ad o&longs;tentationem, vt qu&aelig; in longitudinem ducentos ac <lb/>octoginta: &amp; ab imo v&longs;que ad tran&longs;tra duodequinquaginta cubitos <lb/>pateret. </s> <s id="id.001037">Athen&aelig;us recitat inter <lb/>remos quo&longs;dam fui&longs;&longs;e tant&aelig; longitudinis vt duodequadraginta cu&shy;<lb/>bitos explerent, quod non erit incredibile memoria repetenti quarun&shy;<lb/>dam nauium &agrave; veteribus fabricatarum va&longs;titatem, cuiu&longs;modi idem, <lb/>&amp; Plutarchus memorant fui&longs;&longs;e illam dictam fluuialem Thalame&shy;<lb/>gon, quam Ptolom&aelig;us Philopator in delic&yuml;s habuit, non tam ad <lb/>v&longs;um: quam ad o&longs;tentationem, vt qu&aelig; in longitudinem ducentos ac <lb/>octoginta: &amp; ab imo v&longs;que ad tran&longs;tra duodequinquaginta cubitos <lb/>pateret. </s>
  
 <s id="id.001038">Qu&aelig; amplitudo remi &amp; nauis (quod alioqui e&longs;t nunc nobis <lb/>incredibile videntibus tantum naues, qu&aelig; &agrave; numero remigum in <lb/>vnoquoque tran&longs;tro &longs;edentium &longs;unt vniremes, triremes, quadrire&shy;<lb/>mes, quinquiremes) probabile facit fui&longs;&longs;e in v&longs;u apud antiquos naues <lb/>multo plurium remigum decem, vndecim, viginti, mult&ograve; plurium, in <lb/>vnoquoque tran&longs;tro &amp; tran&longs;trorum multos, ordines vnde idem<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.103.jpg" pagenum="64"/><emph type="italics"/>Athen&aelig;us recen&longs;et Philadelphum ad v&longs;um habui&longs;&longs;e trieconteres, id <lb/>e&longs;t tricen&ucirc;m ordinum duas: I co&longs;erem vndm, qu&aelig; vicen&ucirc;m erat, qua&shy;<lb/>tuor qu&aelig; tern&ucirc;m den&ucirc;m, duas qu&aelig; duoden&ucirc;m, quatuordecim qu&aelig; <lb/>vnden&ucirc;m, &amp; alias infra multas. </s> <s id="id.001038">Qu&aelig; amplitudo remi &amp; nauis (quod alioqui e&longs;t nunc nobis <lb/>incredibile videntibus tantum naues, qu&aelig; &agrave; numero remigum in <lb/>vnoquoque tran&longs;tro &longs;edentium &longs;unt vniremes, triremes, quadrire&shy;<lb/>mes, quinquiremes) probabile facit fui&longs;&longs;e in v&longs;u apud antiquos naues <lb/>multo plurium remigum decem, vndecim, viginti, mult&ograve; plurium, in <lb/>vnoquoque tran&longs;tro &amp; tran&longs;trorum multos, ordines vnde idem<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.103.jpg" pagenum="64"/><emph type="italics"/>Athen&aelig;us recen&longs;et Philadelphum ad v&longs;um habui&longs;&longs;e trieconteres, id <lb/>e&longs;t tricen&ucirc;m ordinum duas: I co&longs;erem vnam, qu&aelig; vicen&ucirc;m erat, qua&shy;<lb/>tuor qu&aelig; tern&ucirc;m den&ucirc;m, duas qu&aelig; duoden&ucirc;m, quatuordecim qu&aelig; <lb/>vnden&ucirc;m, &amp; alias infra multas. </s>
  
 <s id="id.001039">Illam autem, qu&aelig; Philopatoris fuit, <lb/>fui&longs;&longs;e quinquaginta ordinum, &amp; in &longs;ingulis tran&longs;tris quadraginta <lb/>remis, id e&longs;t, remigibus (nam &amp; horum po&longs;tea numerum a&szlig;ignat to&shy;<lb/>tius fui&longs;&longs;e 4000.) agi. </s> <s id="id.001039">Illam autem, qu&aelig; Philopatoris fuit, <lb/>fui&longs;&longs;e quinquaginta ordinum, &amp; in &longs;ingulis tran&longs;tris quadraginta <lb/>remis, id e&longs;t, remigibus (nam &amp; horum po&longs;tea numerum a&szlig;ignat to&shy;<lb/>tius fui&longs;&longs;e 4000.) agi. </s>
  
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 <s id="id.001042">V nde nonnulli exi&longs;tima&shy;<lb/>runt fui&longs;&longs;e naues, qu&aelig; in parte laterali &longs;upra aquas eminente, tria fo&shy;<lb/>ramina<emph.end type="italics"/> <foreign lang="greek">xa<gap/>) i)/sin</foreign> <emph type="italics"/>eius partis habui&longs;&longs;e, <expan abbr="quor&utilde;">quorum</expan> &longs;ingula &longs;uum remum <lb/>haberet alligatum. </s> <s id="id.001042">V nde nonnulli exi&longs;tima&shy;<lb/>runt fui&longs;&longs;e naues, qu&aelig; in parte laterali &longs;upra aquas eminente, tria fo&shy;<lb/>ramina<emph.end type="italics"/> <foreign lang="greek">xa<gap/>) i)/sin</foreign> <emph type="italics"/>eius partis habui&longs;&longs;e, <expan abbr="quor&utilde;">quorum</expan> &longs;ingula &longs;uum remum <lb/>haberet alligatum. </s>
  
 <s id="id.001043">Vnde cum hiremi &longs;itu pro differentia loci &longs;ur&shy;<lb/>&longs;um &amp; deor&longs;um e&longs;&longs;ent di&longs;tincti: ita quoque &longs;uos remiges haberen<gap/><lb/>di&longs;tinctos: &longs;ed eam mentem non fui&longs;&longs;e &longs;cholia&longs;tis illius indicat, <lb/>quod paul&ograve; p&ograve;&longs;t &longs;ubiunxit.<emph.end type="italics"/> <foreign lang="greek"><gap/>ani/ths )<gap/>,</foreign> <emph type="italics"/>inquit<emph.end type="italics"/> <foreign lang="greek">o( w_ro\s ti/w\ w_ru/mnan, <lb/><gap/>ugi/ths o( meoos, <gap/>alami/ths o( w_ro\s ti/w\ w_rw/<gap/>an.</foreign> <emph type="italics"/>Thranites e&longs;t is, <lb/>qui ad puppim remigat, Zygites qui in media naui, Thalamites qui <lb/>ad proram, vbi manife&longs;t&egrave; &longs;uperiorem nauis partem explicat ad pup&shy;<lb/>pim in qua &longs;edet gubernator, vt qu&aelig; altior e&longs;t: inferiorem ad proram, <lb/>qu&aelig; inferior e&longs;t, ne gubernatoris ob&longs;truat luminibus: ideo inter istos <lb/><gap/>git&aelig; &longs;unt, quos hic Ari&longs;toteles vocabulo compo&longs;ito<emph.end type="italics"/> <foreign lang="greek">e)x meoh_s kai\ <lb/>ne/ws</foreign> <emph type="italics"/>vocat me&longs;oneos. </s> <s id="id.001043">Vnde cum hi remi &longs;itu pro differentia loci &longs;ur&shy;<lb/>&longs;um &amp; deor&longs;um e&longs;&longs;ent di&longs;tincti: ita quoque &longs;uos remiges haberent <lb/>di&longs;tinctos: &longs;ed eam mentem non fui&longs;&longs;e &longs;cholia&longs;tis illius indicat, <lb/>quod paul&ograve; p&ograve;&longs;t &longs;ubiunxit.<emph.end type="italics"/> <foreign lang="greek"><gap/>ani/ths )<gap/>,</foreign> <emph type="italics"/>inquit<emph.end type="italics"/> <foreign lang="greek">o( w_ro\s ti/w\ w_ru/mnan, <lb/><gap/>ugi/ths o( meoos, <gap/>alami/ths o( w_ro\s ti/w\ w_rw/<gap/>an.</foreign></s>
  
 <s id="id.001044">Sed hic non leuis obrepit controuer &longs;ia, &amp; pro&shy;<lb/>pter pr&aelig;&longs;entem Ari&longs;totelis contextumante di&longs;&longs;oluenda, &longs;i pote&longs;t, ex <lb/>duobus locis, altero Thucydidis, altero Galeni. <!-- KEEP S--></s> 
  
 <s id="id.001045">Ille enim li. </s> 
  
 <s id="id.001046">6. h&aelig;c h&aelig;&shy;<lb/>bet.<emph.end type="italics"/> <foreign lang="greek"><gap/>pihra/fxwn )<gap/>pi<gap/>o<gap/>a\s w_ro\s tw_| )ex dimwoi/ou mi<gap/>w_| dido/ntwn <lb/>pi_s <gap/>ari/tais,</foreign> <emph type="italics"/>Thranit&aelig; pr&aelig;ter &longs;tipendium publicum &agrave; trierarchis <lb/>donatiuum con&longs;equebantur, cuius rei cau&longs;a &longs;ubdita e&longs;t &agrave; &longs;choliaste, <lb/><expan abbr="quoni&atilde;remos">quoniarremos</expan> longiores trahebant, grauioreque labore vexabantur, <lb/>&amp; adhuc hodie e&ograve; loci remigant ex omnibus delecti robu&longs;tiores, &agrave; <lb/>largis &longs;patulis Gallis dicti Eppaliers. <!-- KEEP S--></s> 
  
 <s id="id.001047">Hic ver&ograve; cap.  
  
 24. lib. <!-- REMOVE S-->I, de v&longs;u<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.104.jpg" pagenum="65"/><emph type="italics"/>partium &longs;ic ait, In triremibus <expan abbr="remor&utilde;">remorum</expan> extremitates ad vnam &aelig;qua&shy;<lb/>litatem perueniunt, cum tamen ip&longs;i omnes non &longs;int &aelig;quales, etenim <lb/>etiam ibi medios eandem ob cau&longs;am maximos efficiunt, id e&longs;t, vt vi&shy;<lb/>dere licet ex i&longs;to cap. <!-- REMOVE S-->Galen. <!-- REMOVE S-->citato, vt manus digiti in&aelig; quales &longs;unt, <lb/>&amp; medius longi&szlig;imus ad firmam rerum apprehen &longs;ionem, &amp; ap&shy;<lb/>prehen&longs;arum retentionem, quod illius munus e&longs;t, quod non aliter fit <lb/>quam quum digitorum extremitates ad &aelig;qualitatem perueniunt: &longs;ic <lb/>ob nauigationis perfectionem in valido &amp; faciliori nauis, qu&acirc; prora <lb/>&longs;pectat impul&longs;u po&longs;itam, remi facti &longs;unt in&aelig;quales, &amp; corum me&shy;<lb/>dius maximus: &amp; horum quidem i&longs;ta in&aelig;qualitas ob eandem cau&shy;<lb/>&longs;am, vt &longs;cilicet remorum extremitates &longs;imul omnes in remigatione <lb/>ad &aelig;qualitatem peruenirent. </s> 
  
  
  <s><emph type="italics"/>Thranites e&longs;t is, <lb/>qui ad puppim remigat, Zygites qui in media naui, Thalamites qui <lb/>ad proram, vbi manife&longs;t&egrave; &longs;uperiorem nauis partem explicat ad pup&shy;<lb/>pim in qua &longs;edet gubernator, vt qu&aelig; altior e&longs;t: inferiorem ad proram, <lb/>qu&aelig; inferior e&longs;t, ne gubernatoris ob&longs;truat luminibus: ideo inter istos <lb/>zygit&aelig; &longs;unt, quos hic Ari&longs;toteles vocabulo compo&longs;ito<emph.end type="italics"/> <foreign lang="greek">e)x meoh_s kai\ <lb/>ne/ws</foreign> <emph type="italics"/>vocat me&longs;oneos. </s>
  
  <s id="id.001044">Sed hic non leuis obrepit controuer&longs;ia, &amp; pro&shy;<lb/>pter pr&aelig;&longs;entem Ari&longs;totelis contextum ante di&longs;&longs;oluenda, &longs;i pote&longs;t, ex <lb/>duobus locis, altero Thucydidis, altero Galeni. </s>
  
  <s id="id.001045">Ille enim li. 6. h&aelig;c ha&shy;<lb/>bet.<emph.end type="italics"/></s>
  
  <s><foreign lang="greek"><gap/>pihra/fxwn )<gap/>pi<gap/>o<gap/>a\s w_ro\s tw_| )ex dimwoi/ou mi<gap/>w_| dido/ntwn <lb/>pi_s <gap/>ari/tais,</foreign> <emph type="italics"/>Thranit&aelig; pr&aelig;ter &longs;tipendium publicum &agrave; trierarchis <lb/>donatiuum con&longs;equebantur, cuius rei cau&longs;a &longs;ubdita e&longs;t &agrave; &longs;choliaste, <lb/><expan abbr="quoni&atilde;">quoniam</expan> remos longiores trahebant, grauioreque labore vexabantur, <lb/>&amp; adhuc hodie e&ograve; loci remigant ex omnibus delecti robu&longs;tiores, &agrave; <lb/>largis &longs;patulis Gallis dicti Eppaliers. </s>
  
  <s id="id.001047">Hic ver&ograve; cap. 24. lib. I, de v&longs;u<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.104.jpg" pagenum="65"/><emph type="italics"/>partium &longs;ic ait, In triremibus <expan abbr="remor&utilde;">remorum</expan> extremitates ad vnam &aelig;qua&shy;<lb/>litatem perueniunt, cum tamen ip&longs;i omnes non &longs;int &aelig;quales, etenim <lb/>etiam ibi medios eandem ob cau&longs;am maximos efficiunt, id e&longs;t, vt vi&shy;<lb/>dere licet ex i&longs;to cap. Galen. citato, vt manus digiti in&aelig; quales &longs;unt, <lb/>&amp; medius longi&szlig;imus ad firmam rerum apprehen&longs;ionem, &amp; ap&shy;<lb/>prehen&longs;arum retentionem, quod illius munus e&longs;t, quod non aliter fit <lb/>quam quum digitorum extremitates ad &aelig;qualitatem perueniunt: &longs;ic <lb/>ob nauigationis perfectionem in valido &amp; faciliori nauis, qu&acirc; prora <lb/>&longs;pectat impul&longs;u po&longs;itam, remi facti &longs;unt in&aelig;quales, &amp; eorum me&shy;<lb/>dius maximus: &amp; horum quidem i&longs;ta in&aelig;qualitas ob eandem cau&shy;<lb/>&longs;am, vt &longs;cilicet remorum extremitates &longs;imul omnes in remigatione <lb/>ad &aelig;qualitatem peruenirent. </s>
  
 <s id="id.001048">Ex his locis <expan abbr="vtriq;">vtrique</expan> conueniunt eiu&longs;dem <lb/>lateris remos e&longs;&longs;e in&aelig;quales: &longs;ed in hoc in &longs;igniter di&longs;crepant, quod <lb/>Galenus a&longs;&longs;erat medios, id e&longs;t remos Zygitarum, &longs;eu<emph.end type="italics"/> <foreign lang="greek">meoune/wn</foreign> <emph type="italics"/>e&longs;&longs;e <lb/>maximos: Ari&longs;toteles non hos, &longs;ed <expan abbr="Thranitar&utilde;">Thranitarum</expan>. </s> <s id="id.001048">Ex his locis <expan abbr="vtriq;">vtrique</expan> conueniunt eiu&longs;dem <lb/>lateris remos e&longs;&longs;e in&aelig;quales: &longs;ed in hoc in &longs;igniter di&longs;crepant, quod <lb/>Galenus a&longs;&longs;erat medios, id e&longs;t remos Zygitarum, &longs;eu<emph.end type="italics"/> <foreign lang="greek">meoune/wn</foreign> <emph type="italics"/>e&longs;&longs;e <lb/>maximos: Ari&longs;toteles non hos, &longs;ed <expan abbr="Thranitar&utilde;">Thranitarum</expan>. </s>
  
 <s id="id.001049">Et <expan abbr="ver&utilde;">verum</expan> dicere Gale&shy;<lb/>num cogno&longs;cemus &longs;i prius intellexerimus quomodo remorum extre&shy;<lb/>mitates in remigationis ictu ad &aelig;qualitatem perueniant. </s> <s id="id.001049">Et <expan abbr="ver&utilde;">verum</expan> dicere Gale&shy;<lb/>num cogno&longs;cemus &longs;i prius intellexerimus quomodo remorum extre&shy;<lb/>mitates in remigationis ictu ad &aelig;qualitatem perueniant. </s>
  
 <s id="id.001050">Ad hane <lb/>enim peruenire po&longs;&longs;unt duobus tantum modis, priore &longs;i intelligamus <lb/>tran&longs;trorum ordines<emph.end type="italics"/><lb/><figure id="id.035.01.104.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.104.1.jpg"/><lb/><emph type="italics"/>po&longs;itos e&longs;&longs;e ita, vt de&shy;<lb/>&longs;inant &longs;ecundum re&shy;<lb/>ctam A B parallelam <lb/>rect&aelig;, qu&aelig; in naui ex&shy;<lb/>tenderetur &agrave; prora ad <lb/>puppim cuiu&longs;modi e&longs;to <lb/>C D, cui etiam altera <lb/>E F in mari parallela <lb/>ad quam extremitates <lb/>peruenirent, ita vt <lb/>&longs;ponda nauis ad cuius <lb/>G H T &longs;calmos e&longs;&longs;ent <lb/>alligati remi K G P, <lb/>M H N, O T P. <lb/><!-- KEEP S--></s> <s id="id.001050">Ad hanc <lb/>enim peruenire po&longs;&longs;unt duobus tantum modis, priore &longs;i intelligamus <lb/>tran&longs;trorum ordines<emph.end type="italics"/><lb/><figure id="id.035.01.104.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.104.1.jpg"/><lb/><emph type="italics"/>po&longs;itos e&longs;&longs;e ita, vt de&shy;<lb/>&longs;inant &longs;ecundum re&shy;<lb/>ctam A B parallelam <lb/>rect&aelig;, qu&aelig; in naui ex&shy;<lb/>tenderetur &agrave; prora ad <lb/>puppim cuiu&longs;modi e&longs;to <lb/>C D, cui etiam altera <lb/>E F in mari parallela <lb/>ad quam extremitates <lb/>peruenirent, ita vt <lb/>&longs;ponda nauis ad cuius <lb/>G H T &longs;calmos e&longs;&longs;ent <lb/>alligati remi K G P, <lb/>M H N, O T P. <lb/></s>
  
 <s id="id.001051">Sed &longs;i &longs;ic pr&aelig;terquam <lb/>quod Thalamitarum <lb/>Zygitarum &amp; Thra-<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.105.jpg" pagenum="66"/><emph type="italics"/>nitarum Remi e&longs;&longs;ent &aelig;quales prop.  
  
 33. &amp; 34. lib. <!-- REMOVE S-->I. elem. </s> 
  
  
  
 <s id="id.001052">Eucl. <!-- REMOVE S-->quod <lb/>e&longs;t contra omnium &longs;ententiam, nauigatio e&longs;&longs;et valde impedita, eo <lb/>quod cum aqua ante nauim immota, ideoque difficilius cedens: tum <lb/>po&longs;t nauim etiam immota, minimeque eo rediens non compelleret. <lb/></s> 
  
  
  <s id="id.001051">Sed &longs;i &longs;ic pr&aelig;terquam <lb/>quod Thalamitarum <lb/>Zygitarum &amp; Thra-<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.105.jpg" pagenum="66"/><emph type="italics"/>nitarum Remi e&longs;&longs;ent &aelig;quales prop. 33. &amp; 34. lib. I. elem. Eucl. quod <lb/>e&longs;t contra omnium &longs;ententiam, nauigatio e&longs;&longs;et valde impedita, eo <lb/>quod cum aqua ante nauim immota, ideoque difficilius cedens: tum <lb/>po&longs;t nauim etiam immota, minimeque eo rediens non compelleret. <lb/></s>
  
 <s id="id.001053">Moueretur enim aqua &longs;ecundum rectam E F remorum extremita&shy;<lb/>tes excipientem. </s> <s id="id.001053">Moueretur enim aqua &longs;ecundum rectam E F remorum extremita&shy;<lb/>tes excipientem. </s>
  
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 <s id="id.001055">Quomodo &longs;i pro E F recta <lb/>con&longs;tituamus pe-<emph.end type="italics"/><lb/><figure id="id.035.01.105.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.105.1.jpg"/><lb/><emph type="italics"/><expan abbr="ripheric&atilde;">riphericam</expan> Q L N <lb/>P R ad quam <expan abbr="de-&longs;in&atilde;t">de&shy;<lb/>&longs;inant</expan> pr&aelig;dicti re&shy;<lb/>mi, non &longs;olum re&shy;<lb/>morum erit in&aelig;&shy;<lb/>qualitas, &amp; me&shy;<lb/>dius erit maxi&shy;<lb/>mus, vt in manu <lb/>digitus medius: <lb/>&longs;ed &amp; nauigatio <lb/>facilius procedet <lb/>propter <expan abbr="c&otilde;trarias">contrarias</expan> <lb/>cau&longs;as, quipp&egrave; ve&shy;<lb/>luti circulationes <lb/><expan abbr="vndar&utilde;">vndarum</expan> circa na&shy;<lb/>uim fient, vnde <lb/>qu&aelig; ante e&longs;t pro&shy;<lb/>pul&longs;a aqua viam <lb/>aperiet nauigio, <lb/>&amp; retro compre&longs;&longs;a, comprimen&longs; que nauigium propellet. </s> <s id="id.001055">Quomodo &longs;i pro E F recta <lb/>con&longs;tituamus pe-<emph.end type="italics"/><lb/><figure id="id.035.01.105.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.105.1.jpg"/><lb/><emph type="italics"/><expan abbr="ripheric&atilde;">riphericam</expan> Q L N <lb/>P R ad quam <expan abbr="de-&longs;in&atilde;t">de&shy;<lb/>&longs;inant</expan> pr&aelig;dicti re&shy;<lb/>mi, non &longs;olum re&shy;<lb/>morum erit in&aelig;&shy;<lb/>qualitas, &amp; me&shy;<lb/>dius erit maxi&shy;<lb/>mus, vt in manu <lb/>digitus medius: <lb/>&longs;ed &amp; nauigatio <lb/>facilius procedet <lb/>propter <expan abbr="c&otilde;trarias">contrarias</expan> <lb/>cau&longs;as, quipp&egrave; ve&shy;<lb/>luti circulationes <lb/><expan abbr="vndar&utilde;">vndarum</expan> circa na&shy;<lb/>uim fient, vnde <lb/>qu&aelig; ante e&longs;t pro&shy;<lb/>pul&longs;a aqua viam <lb/>aperiet nauigio, <lb/>&amp; retro compre&longs;&longs;a, comprimen&longs; que nauigium propellet. </s>
  
 <s id="id.001056">Quod autem <lb/>M H N medius remus &longs;it longior remis O I P &amp; K G L fa&shy;<lb/>cile demon&longs;tratur ducta recta G I parallela ip&longs;i K. O. <!-- KEEP S--></s> <s id="id.001056">Quod autem <lb/>M H N medius remus &longs;it longior remis O I P &amp; K G L fa&shy;<lb/>cile demon&longs;tratur ducta recta G I parallela ip&longs;i K. O. </s>
  
 <s id="id.001057">Sic enim <lb/>&aelig;quales &longs;unt G K, S M, I O prop.  
  
 33. &amp; 34. lib.  <s id="id.001057">Sic enim <lb/>&aelig;quales &longs;unt G K, S M, I O prop. 33. &amp; 34. lib. 1. &aelig;quales item <lb/>propter paralleli&longs;mum G L, H N, &amp; I P. </s>
  
 1. &aelig;quales item <lb/>propter paralleli&longs;mum G L, H N, &amp; I P. tot&aelig; igitur ex his <lb/>&aelig;quales axiom. </s> <s>tot&aelig; igitur ex his <lb/>&aelig;quales axiom. 2. lib. 1. &amp; ad earum vnam nempe ex S M, H N<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.106.jpg" pagenum="67"/><emph type="italics"/>cum addatur in&longs;uper S H erit ip&longs;a M S H N remus medius <lb/>in&aelig;qualis, &amp; vtrolibet aliorum maior ax. 4.</s>
  
 <s id="id.001058">2. lib.  <s id="id.001059"> Ergo maximus, quod <lb/>fuit probandum. </s>
  
 1. &amp; ad earum vnam nempe ex S M, H N<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.106.jpg" pagenum="67"/><emph type="italics"/>cum addatur in&longs;uper S H erit ip&longs;a M S H N remus medius <lb/>in&aelig;qualis, &amp; vtrolibet aliorum maior ax. </s> 
  
 <s id="id.001059">4. Ergo maximus, quod <lb/>fuit probandum. </s> 
  
 <s id="id.001060">Dicemus igitur &longs;cholia&longs;tis &amp; Thucydidis locos <lb/>debere intelligi, non de totis remis: &longs;ed remorum partibus, qu&aelig; &longs;unt &agrave; <lb/>&longs;calmo ad mare proportione habita ad eas partes, qu&aelig; &longs;unt &agrave; &longs;calmo <lb/>ad manubrium. </s> <s id="id.001060">Dicemus igitur &longs;cholia&longs;tis &amp; Thucydidis locos <lb/>debere intelligi, non de totis remis: &longs;ed remorum partibus, qu&aelig; &longs;unt &agrave; <lb/>&longs;calmo ad mare proportione habita ad eas partes, qu&aelig; &longs;unt &agrave; &longs;calmo <lb/>ad manubrium. </s>
  
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 <s id="id.001063">Atque &longs;ic &longs;int hi duo loci meo iudicio ex&shy;<lb/>plicati. </s> <s id="id.001063">Atque &longs;ic &longs;int hi duo loci meo iudicio ex&shy;<lb/>plicati. </s>
  
 <s id="id.001064">C&aelig;terum Remiges, vt &amp; hoc notatu pulchrum ad&yuml;ciamus, <lb/>Remigando artificios&egrave; &longs;imul omnes, quamuis quater mille, inter &longs;e <lb/>con&longs;entientes, alioqui illis corium fiagris tam fit maculo&longs;um quam <lb/>nutricis pallium, vel cur&longs;um nauis accelerant, vel inhibent, vel &longs;u&longs;ti&shy;<lb/>nent, &amp; vt ait Poeta,<emph.end type="italics"/></s></p><p type="main"> <s id="id.001064">C&aelig;terum Remiges, vt &amp; hoc notatu pulchrum ad&yuml;ciamus, <lb/>Remigando artificios&egrave; &longs;imul omnes, quamuis quater mille, inter &longs;e <lb/>con&longs;entientes, alioqui illis corium flagris tam fit maculo&longs;um quam <lb/>nutricis pallium, vel cur&longs;um nauis accelerant, vel inhibent, vel &longs;u&longs;ti&shy;<lb/>nent, &amp; vt ait Poeta,<emph.end type="italics"/></s></p><p type="main">
  
 <s id="id.001065">Intentaque brachia rem&iacute;s</s></p><p type="main"> <s id="id.001065">Intentaque brachia rem&iacute;s</s></p><p type="main">
  
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 <s id="id.001073"><emph type="italics"/>Ille remiges inter plus nauim promouet, cuius remi pars &agrave; &longs;cal&shy;<lb/>mo ad manubrium maior e&longs;t: &amp; cuius etiam pars &agrave; &longs;calmo <lb/>ad palmulam plurimum maris diuidit.<emph.end type="italics"/></s></p><p type="main"> <s id="id.001073"><emph type="italics"/>Ille remiges inter plus nauim promouet, cuius remi pars &agrave; &longs;cal&shy;<lb/>mo ad manubrium maior e&longs;t: &amp; cuius etiam pars &agrave; &longs;calmo <lb/>ad palmulam plurimum maris diuidit.<emph.end type="italics"/></s></p><p type="main">
  
 <s id="id.001074"><emph type="italics"/>Sed remi pars &agrave; &longs;calmo ad manubrium cius qui in medio e&longs;t <lb/>maior: &amp; ad palmulam eiu&longs;dem plus maris diuidit, <lb/>quam aliorum.<emph.end type="italics"/></s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.107.jpg" pagenum="68"/><p type="main"> <s id="id.001074"><emph type="italics"/>Sed remi pars &agrave; &longs;calmo ad manubrium eius qui in medio e&longs;t <lb/>maior: &amp; ad palmulam eiu&longs;dem plus maris diuidit, <lb/>quam aliorum.<emph.end type="italics"/></s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.107.jpg" pagenum="68"/><p type="main">
  
 <s id="id.001075"><emph type="italics"/>Ergo qui in medio e&longs;t inter remiges plus promouet nauim.<emph.end type="italics"/></s></p><p type="main"> <s id="id.001075"><emph type="italics"/>Ergo qui in medio e&longs;t inter remiges plus promouet nauim.<emph.end type="italics"/></s></p><p type="main">
  
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 <s id="id.001077"><emph type="italics"/>Quant&ograve; maior e&longs;t vectis pars ab hypomochlio ad caput, tant&ograve; <lb/>vis mouens facilius &amp; plus mouet, quia ibi maior e&longs;t radius. <lb/></s> <s id="id.001077"><emph type="italics"/>Quant&ograve; maior e&longs;t vectis pars ab hypomochlio ad caput, tant&ograve; <lb/>vis mouens facilius &amp; plus mouet, quia ibi maior e&longs;t radius. <lb/></s>
  
 <s id="id.001078">Hoc ita e&longs;&longs;e patuit ex cap.  <s id="id.001078">Hoc ita e&longs;&longs;e patuit ex cap. pr&aelig;ced. libri huius.<emph.end type="italics"/></s></p><p type="main">
  
 pr&aelig;ced.  
  
 libri huius.<emph.end type="italics"/></s></p><p type="main"> 
  
 <s id="id.001079"><emph type="italics"/>Sed pars remi &agrave; Scalmo ad manubrium e&longs;t pars vectis ab <lb/>hypomochlio ad caput. </s> <s id="id.001079"><emph type="italics"/>Sed pars remi &agrave; Scalmo ad manubrium e&longs;t pars vectis ab <lb/>hypomochlio ad caput. </s>
  
 <s id="id.001080">Nam remus e&longs;t vectis. </s> <s id="id.001080">Nam remus e&longs;t vectis. per def. &amp; <lb/>&longs;calmus e&longs;t hypomochlium. </s>
  
 <s id="id.001081">per def. </s> <s id="id.001083">hic enim mouet, pondus vero <lb/>mobile mare, &amp; vectem mouens, Remex.<emph.end type="italics"/></s></p><p type="main">
  
 <s id="id.001082">&amp; <lb/>&longs;calmus e&longs;t hypomochlium. </s> 
  
 <s id="id.001083">hic enim mouet, pondus vero <lb/>mobile mare, &amp; vectem mouens, Remex.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main"> 
  
 <s id="id.001084"><emph type="italics"/>Ergo is plus &amp; facilius nauim promouebit, cuius remi pars &agrave; <lb/>&longs;calmo ad manubrium maior erit.<emph.end type="italics"/></s></p><p type="main"> <s id="id.001084"><emph type="italics"/>Ergo is plus &amp; facilius nauim promouebit, cuius remi pars &agrave; <lb/>&longs;calmo ad manubrium maior erit.<emph.end type="italics"/></s></p><p type="main">
  
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 <s id="id.001087">vt ex penultimo <lb/>diagrammate qualicunque intelligi pote&longs;t. </s> <s id="id.001087">vt ex penultimo <lb/>diagrammate qualicunque intelligi pote&longs;t. </s>
  
 <s id="id.001088">In quo C e&longs;to prora, D <lb/>puppis, G &longs;calmus ad proram, T &longs;calmus ad puppim, H &longs;calmus <lb/>ad medium: vbi nauis latior &amp; depre&szlig;ior e&longs;t, ob id magis di&longs;tans &agrave; <lb/>recta A B, vtpote chorda arcus A G H T B, qu&aelig; de&longs;ignes <lb/>loca tran&longs;trorum &amp; qu&aelig; &agrave; remis partes auferat &aelig;quales &amp; partes <lb/>in&aelig;quales relinquat K G, M H, O T &amp; quidem M H ma&shy;<lb/>iorem. (quod nos &longs;equenti theoremate demon&longs;trabimus) igiur erit <lb/>totum ex M H, &amp; adempto maius quam quod ex K G &amp; <lb/>adempto, velex O T &amp; adempto per ax. </s> <s id="id.001088">In quo C e&longs;to prora, D <lb/>puppis, G &longs;calmus ad proram, T &longs;calmus ad puppim, H &longs;calmus <lb/>ad medium: vbi nauis latior &amp; depre&szlig;ior e&longs;t, ob id magis di&longs;tans &agrave; <lb/>recta A B, vtpote chorda arcus A G H T B, qu&aelig; de&longs;ignes <lb/>loca tran&longs;trorum &amp; qu&aelig; &agrave; remis partes auferat &aelig;quales &amp; partes <lb/>in&aelig;quales relinquat K G, M H, O T &amp; quidem M H ma&shy;<lb/>iorem. </s>
  
 <s id="id.001089">5.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main"> <s>(quod nos &longs;equenti theoremate demon&longs;trabimus) igiur erit <lb/>totum ex M H, &amp; adempto maius quam quod ex K G &amp; <lb/>adempto, velex O T &amp; adempto per ax. 5.<emph.end type="italics"/></s></p><p type="main">
  
 <s id="id.001090">Theorema. <emph type="italics"/>Si chorda rectas in circulo in&longs;criptas ad rectos &longs;e&shy;<lb/>cet: &longs;ectarum pars, qu&aelig; de diametro ab&longs;cinditur, e&longs;t maxima, reli&shy;<lb/>quarum qu&aelig; diametro propinquior remotiore maior e&longs;t. </s> <s id="id.001090">Theorema. <emph type="italics"/>Si chorda rectas in circulo in&longs;criptas ad rectos &longs;e&shy;<lb/>cet: &longs;ectarum pars, qu&aelig; de diametro ab&longs;cinditur, e&longs;t maxima, reli&shy;<lb/>quarum qu&aelig; diametro propinquior remotiore maior e&longs;t. </s>
  
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 <s id="id.001092">Dico C B e&longs;&longs;e <lb/>maiorem quam F I: &amp; F I quam G H. <!-- KEEP S--></s> <s id="id.001092">Dico C B e&longs;&longs;e <lb/>maiorem quam F I: &amp; F I quam G H. <!-- KEEP S--></s>
  
 <s id="id.001093">Per punctum M cen&shy;<lb/>trum circuli repertum prop.  <s id="id.001093">Per punctum M cen&shy;<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"/>rect&aelig; C D prop. 31. lib. 1. &longs;icque parallelogramma &longs;unt O F &amp;<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>
  
 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"/>rect&aelig; C D prop. </s> 
  
 <s id="id.001094">31. lib.  
  
 1. &longs;icque parallelogramma &longs;unt O F &amp;<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. <!-- KEEP S--></s> 
  
 <s id="id.001095">Quoniam igitur diame&shy;<lb/>ter A B maxima e&longs;t in&longs;cripta&shy;<lb/>rum in circulo, &amp; K I propin&shy;<lb/>quior centro ip&longs;i L H remotiore <lb/>maior e&longs;t prop.  
  
 15. lib.  
  
 3. harum <lb/>quoque dimidi&aelig; M B, N I, O <lb/>H prop. </s> <s id="id.001095">Quoniam igitur diame&shy;<lb/>ter A B maxima e&longs;t in&longs;cripta&shy;<lb/>rum in circulo, &amp; K I propin&shy;<lb/>quior centro ip&longs;i L H remotiore <lb/>maior e&longs;t prop. 15. lib. 3. harum <lb/>quoque dimidi&aelig; M B, N I, O <lb/>H prop. 3. lib. eiu&longs;dem erunt in&shy;<lb/>&aelig;quales &amp; M B maior quam <lb/>N I, &amp; N I quam O H. </s>
  
 <s id="id.001096">3. lib. <!-- REMOVE S-->eiu&longs;dem erunt in&shy;<lb/>&aelig;quales &amp; M B maior quam <lb/>N I, &amp; N I quam O H. <!-- KEEP S--></s> 
  
  
  <s id="id.001097">Ab <lb/>his igitur &longs;ublatis &aelig;qualibus M <lb/>C, N F, O G parallelogram&shy;<lb/>morum O F, N C lateribus oppo&longs;itis prop. 34. lib. 1. reliqu&aelig; C&verbar; B, <lb/>F I, G H erunt iu&aelig;quales ax. 5. </s>
  
 <s id="id.001097">Ab <lb/>his igitur &longs;ublatis &aelig;qualibus M <lb/>C, N F, O G parallelogram&shy;<lb/>morum O F, N C lateribus oppo&longs;itis prop.  <s>Et quidem reliqua C B &agrave; maiore M <lb/>B maior: quam F I: &amp; F I eadem ratione maior quam G H, &amp; <lb/>&longs;ic de c&aelig;teris. </s>
  
 34. lib.  
  
 1. reliqu&aelig; C&verbar; B, <lb/>F I, G H erunt iu&aelig;quales ax. </s> 
  
 <s id="id.001098">5. Et quidem reliqua C B &agrave; maiore M <lb/>B maior: quam F I: &amp; F I eadem ratione maior quam G H, &amp; <lb/>&longs;ic de c&aelig;teris. </s> 
  
 <s id="id.001099">Igitur &longs;i chorda rectas, &amp;c. </s> <s id="id.001099">Igitur &longs;i chorda rectas, &amp;c. </s>
  
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 <s id="id.001113">H&aelig;c Cicero. </s> <s id="id.001113">H&aelig;c Cicero. </s>
  
 <s id="id.001114">qu&aelig; non <lb/>abs re vt arbitror h&icirc;c &longs;unt in&longs;erta, vt qu&aelig; plurimum faciant <lb/>ad intelligendum <gap/>e motibus nauis duos rectos concitationem &longs;ci&shy;<lb/>licet, &amp; inhibitionem, &amp; vtramque fieri &agrave; remo tanquam &agrave; <lb/>vecte. </s> <s id="id.001114">qu&aelig; non <lb/>abs re vt arbitror h&icirc;c &longs;unt in&longs;erta, vt qu&aelig; plurimum faciant <lb/>ad intelligendum e motibus nauis duos rectos concitationem &longs;ci&shy;<lb/>licet, &amp; inhibitionem, &amp; vtramque fieri &agrave; remo tanquam &agrave; <lb/>vecte. </s>
  
 <s id="id.001115">non tamen vt antea vecte, in quo eius altero extre&shy;<lb/>mo per vim mouentem depre&longs;&longs;o, eleuetur alterum: &longs;ed in quo cum <lb/>eius alterum extremum &longs;ur&longs;um tollatur, alteri &longs;ubiecta aqua renita&shy;<lb/>tur, &amp; hypomochl&yuml; vicem pr&aelig;&longs;tet: non &longs;calmus. </s> <s id="id.001115">non tamen vt antea vecte, in quo eius altero extre&shy;<lb/>mo per vim mouentem depre&longs;&longs;o, eleuetur alterum: &longs;ed in quo cum <lb/>eius alterum extremum &longs;ur&longs;um tollatur, alteri &longs;ubiecta aqua renita&shy;<lb/>tur, &amp; hypomochl&yuml; vicem pr&aelig;&longs;tet: non &longs;calmus. </s>
  
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 <s id="id.001117">Et aqu&aelig; pars exci&shy;<lb/>piens palmulam, qua patet in latum, vt reuera moueatur: motus ta&shy;<lb/>men hic vel e&longs;t exiguus, &amp; pro nullo ideo cen&longs;endus: vel retrocedit, <lb/>&longs;ed minus quam &longs;calmus procedat, vt po&longs;tea demon&longs;trabitur. </s> <s id="id.001117">Et aqu&aelig; pars exci&shy;<lb/>piens palmulam, qua patet in latum, vt reuera moueatur: motus ta&shy;<lb/>men hic vel e&longs;t exiguus, &amp; pro nullo ideo cen&longs;endus: vel retrocedit, <lb/>&longs;ed minus quam &longs;calmus procedat, vt po&longs;tea demon&longs;trabitur. </s>
  
 <s id="id.001118">Erit <lb/>iginur pro centro, neque etiam nautis animus e&longs;t mare: &longs;ed nauem <lb/>tanquam pondus propellere. </s> <s id="id.001118">Erit <lb/>igitur pro centro, neque etiam nautis animus e&longs;t mare: &longs;ed nauem <lb/>tanquam pondus propellere. </s>
  
 <s id="id.001119">Neque minus interea verum erit, quod <lb/>qui in medio mari remigant, ip&longs;am plus propellant. </s> <s id="id.001119">Neque minus interea verum erit, quod <lb/>qui in medio mari remigant, ip&longs;am plus propellant. </s>
  
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 <s id="id.001125">De his igitur pote&longs;t intelligi Ari&longs;to&shy;<lb/>teles tum Vitruuius. <!-- KEEP S--></s> <s id="id.001125">De his igitur pote&longs;t intelligi Ari&longs;to&shy;<lb/>teles tum Vitruuius. <!-- KEEP S--></s>
  
 <s id="id.001126">At in quarto agua renitens palmul&aelig; e&longs;t hypo&shy;<lb/>mochlium, nauis vero pondus mouendum, vt diximus. </s> <s id="id.001126">At in quarto aqua renitens palmul&aelig; e&longs;t hypo&shy;<lb/>mochlium, nauis vero pondus mouendum, vt diximus. </s>
  
 <s id="id.001127">Si quis tamen <lb/>etiam de hoc po&longs;trem&ograve; remi motu velit &longs;en&longs;i&longs;&longs;e Ari&longs;totelem non re&shy;<lb/>luctabor, dummodo concipiat mare pondus quidem mouendum: &longs;ed <lb/>quod ob renixum qua&longs;i immobile faciat, vt &longs;calmus circa quem tan&shy;<lb/>quam centrum remus voluitur, cedat loco &amp; promoueatur. </s> <s id="id.001127">Si quis tamen <lb/>etiam de hoc po&longs;trem&ograve; remi motu velit &longs;en&longs;i&longs;&longs;e Ari&longs;totelem non re&shy;<lb/>luctabor, dummodo concipiat mare pondus quidem mouendum: &longs;ed <lb/>quod ob renixum qua&longs;i immobile faciat, vt &longs;calmus circa quem tan&shy;<lb/>quam centrum remus voluitur, cedat loco &amp; promoueatur. </s>
  
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 <s id="id.001135">E&longs;t autem palmula eorum <lb/>qui &longs;unt in medio nauis, qu&aelig; intra aquam, radius maior: quam pal&shy;<lb/>mula aliorum, &amp; &longs;ic maius &longs;patium peragrat.<emph.end type="italics"/></s></p><p type="main"> <s id="id.001135">E&longs;t autem palmula eorum <lb/>qui &longs;unt in medio nauis, qu&aelig; intra aquam, radius maior: quam pal&shy;<lb/>mula aliorum, &amp; &longs;ic maius &longs;patium peragrat.<emph.end type="italics"/></s></p><p type="main">
  
 <s id="id.001136">Propter id remiges.] <emph type="italics"/>Conclu&longs;io e&longs;t primar&yuml; &longs;yllogi&longs;mi cuns <lb/>repetione cau&longs;&aelig; eiu&longs;dem.<emph.end type="italics"/></s></p><p type="main"> <s id="id.001136">Propter id remiges.] <emph type="italics"/>Conclu&longs;io e&longs;t primar&yuml; &longs;yllogi&longs;mi cum <lb/>repetione cau&longs;&aelig; eiu&longs;dem.<emph.end type="italics"/></s></p><p type="main">
  
 <s id="id.001137"><gap/></s></p><p type="main"> <s id="id.001137"><foreign lang="greek"><gap/></foreign></s></p><p type="main">
  
 <s id="id.001138">6. Potenti&aelig; gubernaculi <lb/>cau&longs;a, &amp; quod <expan abbr="nauigi&utilde;">nauigium</expan> <lb/>magis in <expan abbr="contrari&utilde;">contrarium</expan> pro&shy;<lb/>cedat: quam remi pal&shy;<lb/>mula.</s></p><p type="main"> <s id="id.001138">6. Potenti&aelig; gubernaculi <lb/>cau&longs;a, &amp; quod <expan abbr="nauigi&utilde;">nauigium</expan> <lb/>magis in <expan abbr="contrari&utilde;">contrarium</expan> pro&shy;<lb/>cedat: quam remi pal&shy;<lb/>mula.</s></p><p type="main">
  
 <s id="id.001139"><gap/></s></p><p type="main"> <s id="id.001139"><foreign lang="greek"><gap/></foreign></s></p><p type="main">
  
 <s id="id.001140">Cur gubernaculum par&shy;<lb/>uum quid exi&longs;tens, &amp; in <lb/>extrema parte nauigij tan&shy;<lb/>tam vim habet, vt ab exi&shy;<lb/>guo temone, &amp; vnius ho&shy;<lb/>minis ctiam propemodum <lb/>quie&longs;centis viribus, magn&aelig; <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.111.jpg" pagenum="72"/><gap/><lb/><expan abbr="nauigior&utilde;">nauigiorum</expan> moles mouean&shy;<lb/>tur? </s> <s id="id.001140">Cur gubernaculum par&shy;<lb/>uum quid exi&longs;tens, &amp; in <lb/>extrema parte nauigij tan&shy;<lb/>tam vim habet, vt ab exi&shy;<lb/>guo temone, &amp; vnius ho&shy;<lb/>minis etiam propemodum <lb/>quie&longs;centis viribus, magn&aelig; <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.111.jpg" pagenum="72"/><foreign lang="greek"><gap/></foreign><lb/><expan abbr="nauigior&utilde;">nauigiorum</expan> moles mouean&shy;<lb/>tur? </s>
  
 <s id="id.001141">An quia <expan abbr="gubernacul&utilde;">gubernaculum</expan> <lb/>e&longs;t vect is: pondus mare, gu&shy;<lb/>bernator mouens. </s> <s id="id.001141">An quia <expan abbr="gubernacul&utilde;">gubernaculum</expan> <lb/>e&longs;t vect is: pondus mare, gu&shy;<lb/>bernator mouens. </s>
  
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 <s id="id.001163">quo dicto nauig&yuml; magnitudinem con&yuml;ciendam nobis reliquit. <lb/></s> <s id="id.001163">quo dicto nauig&yuml; magnitudinem con&yuml;ciendam nobis reliquit. <lb/></s>
  
 <s id="id.001164">Ad nauticum autem in&longs;trumentum cum &aelig;s, ferrum, cannabim, reli&shy;<lb/>quaque, quibus opus erat, partim ex Italia, partim ex Iberia, partim <lb/>Rhodano flumine compara&longs;&longs;et, trecentos operi f<gap/> do fabros, arti&shy;<lb/>fice&longs;que adhibui&longs;&longs;e: ac materi&aelig; dedoland&aelig; pr&aelig;ter admini&longs;tros fabri&shy;<lb/>c&aelig; &longs;ub&longs;eruientes opific&yuml;s, pr&aelig;fecto &longs;umm&aelig; operis architecto Archia <lb/>Corinthio. </s> <s id="id.001164">Ad nauticum autem in&longs;trumentum cum &aelig;s, ferrum, cannabim, reli&shy;<lb/>quaque, quibus opus erat, partim ex Italia, partim ex Iberia, partim <lb/>Rhodano flumine compara&longs;&longs;et, trecentos operi faciendo fabros, arti&shy;<lb/>fice&longs;que adhibui&longs;&longs;e: ac materi&aelig; dedoland&aelig; pr&aelig;ter admini&longs;tros fabri&shy;<lb/>c&aelig; &longs;ub&longs;eruientes opific&yuml;s, pr&aelig;fecto &longs;umm&aelig; operis architecto Archia <lb/>Corinthio. </s>
  
 <s id="id.001165">Quos ip&longs;e cum magnopere hortatus e&longs;&longs;et ad opus aggre&shy;<lb/>diendum, in&longs;uper etiam dies totos operis &longs;e curatorem, exactoremque <lb/>pr&aelig;bui&longs;&longs;e: hac diligentia, his artificibus, hoc architecto, Regem ta&shy;<lb/>men illum dimidium tantum nauis intra &longs;ex men&longs;es perfeci&longs;&longs;e. </s> <s id="id.001165">Quos ip&longs;e cum magnopere hortatus e&longs;&longs;et ad opus aggre&shy;<lb/>diendum, in&longs;uper etiam dies totos operis &longs;e curatorem, exactoremque <lb/>pr&aelig;bui&longs;&longs;e: hac diligentia, his artificibus, hoc architecto, Regem ta&shy;<lb/>men illum dimidium tantum nauis intra &longs;ex men&longs;es perfeci&longs;&longs;e. </s>
  
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 <s id="id.001177">Summa pars nauigij gymna&longs;ium habebat ambulatione&longs;que laxas, <lb/>proportione magnitudinis &longs;u&aelig;, quas etiam ip&longs;as &longs;imul ambientes hor&shy;<lb/>ti omni genere <expan abbr="&longs;tirpi&utilde;">&longs;tirpium</expan> complectebantur, fictilibus in va&longs;is &amp; plum&shy;<lb/>beis con&longs;itorum, &longs;imul heder&aelig; vite&longs;que opacabant pampinis, ac co&shy;<lb/>rymbis inumbrantes, quarum radices <expan abbr="aleb&atilde;t">alebant</expan> dolia terr&aelig; plena: pari&shy;<lb/>ter quidem ill&aelig; cum hortis machinamento irrigu&aelig;. </s> <s id="id.001177">Summa pars nauigij gymna&longs;ium habebat ambulatione&longs;que laxas, <lb/>proportione magnitudinis &longs;u&aelig;, quas etiam ip&longs;as &longs;imul ambientes hor&shy;<lb/>ti omni genere <expan abbr="&longs;tirpi&utilde;">&longs;tirpium</expan> complectebantur, fictilibus in va&longs;is &amp; plum&shy;<lb/>beis con&longs;itorum, &longs;imul heder&aelig; vite&longs;que opacabant pampinis, ac co&shy;<lb/>rymbis inumbrantes, quarum radices <expan abbr="aleb&atilde;t">alebant</expan> dolia terr&aelig; plena: pari&shy;<lb/>ter quidem ill&aelig; cum hortis machinamento irrigu&aelig;. </s>
  
 <s id="id.001178">Ab his erat <lb/>Aphrodi&longs;ium id e&longs;t conclaue Veneri de&aelig; dicatum: in&longs;trumentum <lb/>etiam ip&longs;um tricl&iacute;<gap/>ari lecti&longs;ternio, pauimentoque &longs;tratum achate la&shy;<lb/>pide aly&longs;que var&yuml;s &amp; nitentibus di&longs;tincto. </s> <s id="id.001178">Ab his erat <lb/>Aphrodi&longs;ium id e&longs;t conclaue Veneri de&aelig; dicatum: in&longs;trumentum <lb/>etiam ip&longs;um tricl&iacute;nari lecti&longs;ternio, pauimentoque &longs;tratum achate la&shy;<lb/>pide alij&longs;que var&yuml;s &amp; nitentibus di&longs;tincto. </s>
  
 <s id="id.001179">Cuiu&longs;modi lapidum co&shy;<lb/>pia in Sicilia reperitur. </s> <s id="id.001179">Cuiu&longs;modi lapidum co&shy;<lb/>pia in Sicilia reperitur. </s>
  
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 <s id="id.001193">Sed <lb/>vt &amp; huius nauigij magnitudo va&longs;titas ac onus animo amplius con&shy;<lb/>cipi po&szlig;it, in&longs;uper adijciam tam multis nonnulla, qu&aelig; Athen&aelig;us <lb/>&longs;crip&longs;it ad hoc maxime pertinentia. </s> <s id="id.001193">Sed <lb/>vt &amp; huius nauigij magnitudo va&longs;titas ac onus animo amplius con&shy;<lb/>cipi po&szlig;it, in&longs;uper adijciam tam multis nonnulla, qu&aelig; Athen&aelig;us <lb/>&longs;crip&longs;it ad hoc maxime pertinentia. </s>
  
 <s id="id.001194">Erat, inquit, in eodem nauigio <lb/>&longs;ecundum proram aqu&aelig; conceptaculum conclu&longs;um capax duorum <lb/>milium metretarum a&longs;&longs;amentis &amp; pice &amp; linteorum farctura com&shy;<lb/>pictile, iuxta quod rur&longs;us pi&longs;cina coaxatione &amp; implumbatura <lb/>con&longs;tans plena aqu&aelig; marin&aelig;. </s> <s id="id.001194">Erat, inquit, in eodem nauigio <lb/>&longs;ecundum proram aqu&aelig; conceptaculum conclu&longs;um capax duorum <lb/>milium metretarum a&longs;&longs;amentis &amp; pice &amp; linteorum farctura com&shy;<lb/>pactile, iuxta quod rur&longs;us pi&longs;cina coaxatione &amp; implumbatura <lb/>con&longs;tans plena aqu&aelig; marin&aelig;. </s>
  
 <s id="id.001195">Ita vt in ea commode magna copia <lb/>pi&longs;cium facile aleretur. </s> <s id="id.001195">Ita vt in ea commode magna copia <lb/>pi&longs;cium facile aleretur. </s>
  
 <s id="id.001196">Idem alibi. </s> <s id="id.001196">Idem alibi frumentum negociatorium in <lb/>ea naui exportabant ad millia &longs;exaginta: &longs;al&longs;amenta Sicula ad ca&shy;<lb/>dum decem millia: lanarum talenta viginti millia, &amp; alterius mer&shy;<lb/>cis altera viginti millia, pr&aelig;tere&aacute;que commeatus vectorum nauta&shy;<lb/>rumque &longs;exaginta millia. </s>
  
 <s id="id.001197">frumentum negociatorium in <lb/>ea naui exportabant ad millia &longs;exaginta: &longs;al&longs;amenta Sicula ad ca&shy;<lb/>dum decem millia: lanarum talenta viginti millia, &amp; alterius mer&shy;<lb/>cis altera viginti millia, pr&aelig;tere&aacute;que commeatus vectorum nauta&shy;<lb/>rumque &longs;exaginta millia. </s> 
  
 <s id="id.001198">Horum omnium onus, cum Bud&aelig;us exqui&shy;<lb/>&longs;it&egrave; per&longs;equitur, comperit &longs;ummam librarum ad quinque &amp; &longs;eptua&shy;<lb/>ginta millia excre&longs;cere pr&aelig;ter aquam dulcem, pr&aelig;ter pi&longs;cinam, pr&aelig;&shy;<lb/>ter tot dietarum inte&longs;tinum in&longs;trumentum, pr&aelig;ter annonam vecto-<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.115.jpg" pagenum="76"/><emph type="italics"/>rum, &amp; pabulum equorum, pr&aelig;ter denique onus tanti nauigij. </s> <s id="id.001198">Horum omnium onus, cum Bud&aelig;us exqui&shy;<lb/>&longs;it&egrave; per&longs;equitur, comperit &longs;ummam librarum ad quinque &amp; &longs;eptua&shy;<lb/>ginta millia excre&longs;cere pr&aelig;ter aquam dulcem, pr&aelig;ter pi&longs;cinam, pr&aelig;&shy;<lb/>ter tot dietarum inte&longs;tinum in&longs;trumentum, pr&aelig;ter annonam vecto-<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.115.jpg" pagenum="76"/><emph type="italics"/>rum, &amp; pabulum equorum, pr&aelig;ter denique onus tanti nauigij. </s>
  
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 <s id="id.001217">Mouet igitur obliqu&egrave; nauim (quod e&longs;t intelligendum de <lb/>puppi non de prora qu&aelig; in partem ad quam mare mouetur) &longs;ini&shy;<lb/>&longs;tror&longs;um, &longs;i illud dextror&longs;um: vel dextror&longs;um, &longs;i illud &longs;ini&longs;tror&longs;um <lb/>depul&longs;um e&longs;t.<emph.end type="italics"/></s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.116.jpg" pagenum="77"/><p type="main"> <s id="id.001217">Mouet igitur obliqu&egrave; nauim (quod e&longs;t intelligendum de <lb/>puppi non de prora qu&aelig; in partem ad quam mare mouetur) &longs;ini&shy;<lb/>&longs;tror&longs;um, &longs;i illud dextror&longs;um: vel dextror&longs;um, &longs;i illud &longs;ini&longs;tror&longs;um <lb/>depul&longs;um e&longs;t.<emph.end type="italics"/></s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.116.jpg" pagenum="77"/><p type="main">
  
 <s id="id.001218"><gap/></s></p><p type="main"> <s id="id.001218"><foreign lang="greek"><gap/></foreign></s></p><p type="main">
  
 <s id="id.001219">In extremo autem, non <lb/>in medio po&longs;itum e&longs;t. </s> <s id="id.001219">In extremo autem, non <lb/>in medio po&longs;itum e&longs;t. </s>
  
 <s id="id.001220">quia <lb/>motor, id quodiam moue&shy;<lb/>tur, facillime ab extremo <lb/><expan abbr="c&otilde;mouet">commouet</expan>. </s> <s id="id.001220">quia <lb/>motor, id quodiam moue&shy;<lb/>tur, facillime ab extremo <lb/><expan abbr="c&otilde;mouet">commouet</expan>. </s>
  
 <s id="id.001221">Celetrime enim <lb/>fertur nauis prior pars, <lb/>Quoniam vt in ijs qu&aelig; mo&shy;<lb/>uentur, ad finem latio defi&shy;<lb/>cit: &longs;ic ip&longs;ius continui in ex&shy;<lb/>tremo latio imbecillima <lb/>e&longs;t. </s> <s id="id.001221">Celerrime enim <lb/>fertur nauis prior pars, <lb/>Quoniam vt in ijs qu&aelig; mo&shy;<lb/>uentur, ad finem latio defi&shy;<lb/>cit: &longs;ic ip&longs;ius continui in ex&shy;<lb/>tremo latio imbecillima <lb/>e&longs;t. </s>
  
 <s id="id.001222">E&longs;t autem imbecillima <lb/>facilis repul&longs;u. </s> <s id="id.001222">E&longs;t autem imbecillima <lb/>facilis repul&longs;u. </s>
  
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 <s id="id.001230"><emph type="italics"/>Ergo in puppi non in medio gubernaculum collocandum e&longs;t. <lb/></s> <s id="id.001230"><emph type="italics"/>Ergo in puppi non in medio gubernaculum collocandum e&longs;t. <lb/></s>
  
 <s id="id.001231">Obid etiam&longs;i e pi&longs;cibus quidam parte anteriori homini &amp; quadra&shy;<lb/>pedibus &longs;imiles &longs;unt, vt <expan abbr="Trit&otilde;">Tritom</expan>, Nereis, elephas, &amp; vitulus: po&longs;teriore <lb/>tamen omnes in caudam bifidam de&longs;inunt, paucis admodum exce&shy;<lb/>ptis, atque id non ob aliam cau&longs;am quam quod, velut in nauis puppi <lb/>temo nauim dirigit: Ita pi&longs;cis iter cauda.<emph.end type="italics"/></s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.117.jpg" pagenum="78"/><p type="main"> <s id="id.001231">Ob id etiam&longs;i e pi&longs;cibus quidam parte anteriori homini &amp; quadra&shy;<lb/>pedibus &longs;imiles &longs;unt, vt <expan abbr="Trit&otilde;">Triton</expan>, Nereis, elephas, &amp; vitulus: po&longs;teriore <lb/>tamen omnes in caudam bifidam de&longs;inunt, paucis admodum exce&shy;<lb/>ptis, atque id non ob aliam cau&longs;am quam quod, velut in nauis puppi <lb/>temo nauim dirigit: Ita pi&longs;cis iter cauda.<emph.end type="italics"/></s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.117.jpg" pagenum="78"/><p type="main">
  
 <s id="id.001232">Quia motor.] <emph type="italics"/>Syllogi&longs;mi pr&aelig;cedentis propo&longs;itio nec po&longs;ita, <lb/>nec illu&longs;trata e&longs;t. </s> <s id="id.001232">Quia motor.] <emph type="italics"/>Syllogi&longs;mi pr&aelig;cedentis propo&longs;itio nec po&longs;ita, <lb/>nec illu&longs;trata e&longs;t. </s>
  
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 <s id="id.001240">Quemadmodum eorum qu&aelig; vi <lb/>feruntur latio ad finem deficit, &amp; imbecillior e&longs;t: &longs;ic continui lati <lb/>extremum imbecillius mouetur.<emph.end type="italics"/></s></p><p type="main"> <s id="id.001240">Quemadmodum eorum qu&aelig; vi <lb/>feruntur latio ad finem deficit, &amp; imbecillior e&longs;t: &longs;ic continui lati <lb/>extremum imbecillius mouetur.<emph.end type="italics"/></s></p><p type="main">
  
 <s id="id.001241">Et quoniam exigua.] <emph type="italics"/>Similis &longs;ententia e&longs;t apud Ari&longs;totelem <lb/>lib.  <s id="id.001241">Et quoniam exigua.] <emph type="italics"/>Similis &longs;ententia e&longs;t apud Ari&longs;totelem <lb/>lib. de animalium motu. </s>
  
 de animalium motu. </s> 
  
 <s id="id.001242">Nec vero dubium e&longs;t, inquit, quin parua ad&shy;<lb/>modum initio facta mutatione in corpore multiplices &egrave; longinquo <lb/>varietates &longs;uboriantur, vt cum per temonem paululum tralatum <lb/>long&egrave; diuer&longs;a pror&aelig; po&longs;itio vi&longs;itur. </s> <s id="id.001242">Nec vero dubium e&longs;t, inquit, quin parua ad&shy;<lb/>modum initio facta mutatione in corpore multiplices &egrave; longinquo <lb/>varietates &longs;uboriantur, vt cum per temonem paululum tralatum <lb/>long&egrave; diuer&longs;a pror&aelig; po&longs;itio vi&longs;itur. </s>
  
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 <s id="id.001247">Dico ba&longs;im D C maiorem e&longs;&longs;e ba&longs;i B E. <!-- KEEP S--></s> <s id="id.001247">Dico ba&longs;im D C maiorem e&longs;&longs;e ba&longs;i B E. <!-- KEEP S--></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 &aelig;quales tribus alterius prop. <lb/></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 &aelig;quales tribus alterius prop. <lb/>32. lib. 1. &amp; anguli qui ad A &aelig;quales ex hypothe&longs;i, anguli ad ba&shy;<lb/>&longs;im duo duobus &longs;unt &aelig;quales ax. 3. &amp; quia A D C &amp; A C D <lb/>&longs;unt ad ba&longs;im I&longs;o&longs;celis, &yuml; inter &longs;e erunt &aelig;quales prop. 5. lib. 1. &amp; per <lb/>eandem anguli A B E &amp; A E B. </s>
  
 <s id="id.001249">32. lib.  
  
 1. &amp; anguli qui ad A &aelig;quales ex hypothe&longs;i, anguli ad ba&shy;<lb/>&longs;im duo duobus &longs;unt &aelig;quales ax. </s> 
  
 <s id="id.001250">3. &amp; quia A D C &amp; A C D <lb/>&longs;unt ad ba&longs;im I&longs;o&longs;celis, &yuml; inter &longs;e erunt &aelig;quales prop.  
  
 5. lib.  <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="&aelig;quali&utilde;">&aelig;qualium</expan> &aelig; qua&shy;<lb/>lis erit ax. 6. &amp; per idem reliquus reliquo. </s>
  
 1. &amp; per <lb/>eandem anguli A B E &amp; 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="&aelig;quali&utilde;">&aelig;qualium</expan> &aelig; qua&shy;<lb/>lis erit ax. </s> 
  
 <s id="id.001252">6. &amp; per idem reliquus reliquo. </s> 
  
 <s id="id.001253">Sunt igitur A B E &amp; <lb/>A D C triangula &aelig;quiangula, proinde circum &aelig;quales angulos la&shy;<lb/>tera habebunt proportionalia. </s> <s id="id.001253">Sunt igitur A B E &amp; <lb/>A D C triangula &aelig;quiangula, proinde circum &aelig;quales angulos la&shy;<lb/>tera habebunt proportionalia. </s>
  
 <s id="id.001254">prop.  <s id="id.001254">prop. 4. lib. 6. ideo vt A D ad D C: <lb/>&longs;ic A B ad B E: &amp; vici&szlig;im vt A D ad A B: &longs;ic D C ba&shy;<lb/>&longs;is ad ba&longs;im B E prop. 16. lib. 5. </s>
  
 4. lib.  
  
 6. ideo vt A D ad D C: <lb/>&longs;ic A B ad B E: &amp; vici&szlig;im vt A D ad A B: &longs;ic D C ba&shy;<lb/>&longs;is ad ba&longs;im B E prop. </s> 
  
 <s id="id.001255">16. lib.  <s>E&longs;t autem maius A D ip&longs;o A B <lb/>ex hypothe&longs;i. </s>
  
 5. 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. <!-- KEEP S--></s> <s id="id.001256">Ergo Ba&longs;is D C maior erit ip&longs;a B E. <!-- KEEP S--></s>
  
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 <s id="id.001260">Tunc C erit in D. <lb/><!-- KEEP S--></s> <s id="id.001260">Tunc C erit in D. <lb/><!-- KEEP S--></s>
  
 <s id="id.001261">Sicque fiunt duo triangula I&longs;o&longs;celia A B E &amp; A D C &aelig;qualia <lb/>angulis ad verticem A oppo&longs;itis prop.  <s id="id.001261">Sicque fiunt duo triangula I&longs;o&longs;celia A B E &amp; A D C &aelig;qualia <lb/>angulis ad verticem A oppo&longs;itis prop. 15. lib. 1. </s>
  
 15. lib.  
  
 1. Et in&aelig;qualia cruri&shy;<lb/>bus. </s> <s>Et in&aelig;qualia cruri&shy;<lb/>bus. </s>
  
 <s id="id.001262">Namrect&aelig; ab A puncto Cardini re&longs;pondente in ima parte na&shy;<lb/>uis prop&egrave; puppis extremum ad extremum pror&aelig; id e&longs;t A D, A C <lb/>long&egrave; maiores &longs;unt breui&szlig;imis &yuml;s, qu&aelig; &longs;unt ab <expan abbr="eod&etilde;">eodem</expan> puncto A ad ex&shy;<lb/>tremum puppis A B, A E. <!-- KEEP S--></s> <s id="id.001262">Namrect&aelig; ab A puncto Cardini re&longs;pondente in ima parte na&shy;<lb/>uis prop&egrave; puppis extremum ad extremum pror&aelig; id e&longs;t A D, A C <lb/>long&egrave; maiores &longs;unt breui&szlig;imis &yuml;s, qu&aelig; &longs;unt ab <expan abbr="eod&etilde;">eodem</expan> puncto A ad ex&shy;<lb/>tremum puppis A B, A E. <!-- KEEP S--></s>
  
 <s id="id.001263">Peragrabit igitur prora D lineam C B <lb/>long&egrave; maiorem, cum B peragrabit B E multo minorem.<emph.end type="italics"/></s></p><p type="main"> <s id="id.001263">Peragrabit igitur prora D lineam C B <lb/>long&egrave; maiorem, cum B peragrabit B E multo minorem.<emph.end type="italics"/></s></p><p type="main">
  
 <s id="id.001264"><gap/></s></p><p type="main"> <s id="id.001264"><foreign lang="greek"><gap/></foreign></s></p><p type="main">
  
 <s id="id.001265">Ex hoc autem <expan abbr="manife&longs;t&utilde;">manife&longs;tum</expan> <lb/>e&longs;t, ob quam cau&longs;am nauis <lb/>in contrarium magis pro&shy;<lb/>cedat: quam remi palmula. <lb/></s> <s id="id.001265">Ex hoc autem <expan abbr="manife&longs;t&utilde;">manife&longs;tum</expan> <lb/>e&longs;t, ob quam cau&longs;am nauis <lb/>in contrarium magis pro&shy;<lb/>cedat: quam remi palmula. <lb/></s>
  
 <s id="id.001266">Eadem enim moles eadem <lb/>vi mota per aerem plus, <lb/>quam per aquam progre&shy;<lb/>ditur. </s> <s id="id.001266">Eadem enim moles eadem <lb/>vi mota per aerem plus, <lb/>quam per aquam progre&shy;<lb/>ditur. </s>
  
 <s id="id.001267">Sit enim remus <foreign lang="greek">a b</foreign><lb/>&amp; &longs;calm^{9} <foreign lang="greek">g,</foreign> &amp; 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&shy;<lb/>tum</expan> &longs;it e&ograve;, 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"/><gap/><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> &aelig;qualis ip&longs;i <foreign lang="greek">a d.</foreign> Ex <lb/>&aelig;quo ig&iacute;tur tran&longs;latum e&longs;&shy;<lb/>&longs;et, &longs;ed minus erat. </s> <s id="id.001267">Sit enim remus <foreign lang="greek">a b</foreign><lb/>&amp; &longs;calm^{9} <foreign lang="greek">g,</foreign> &amp; 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&shy;<lb/>tum</expan> &longs;it e&ograve;, 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> &aelig;qualis ip&longs;i <foreign lang="greek">a d.</foreign> Ex <lb/>&aelig;quo ig&iacute;tur tran&longs;latum e&longs;&shy;<lb/>&longs;et, &longs;ed minus erat. </s>
  
 <s id="id.001268">E&longs;t igi&shy;<lb/>tur vbi <foreign lang="greek">z.</foreign> Minor enim e&longs;t <lb/><foreign lang="greek">b z</foreign>: <expan abbr="qu&atilde;">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&shy;<lb/>tur vbi <foreign lang="greek">z.</foreign> Minor enim e&longs;t <lb/><foreign lang="greek">b z</foreign>: <expan abbr="qu&atilde;">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>
  
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 <s id="id.001270">Non autem <lb/>ad <foreign lang="greek">d</foreign> procederet, ni&longs;i mo&shy;<lb/>ueretur nauis, &amp; eo vbi e&longs;t <lb/>caput remi, transferretur.</s></p><p type="margin"> <s id="id.001270">Non autem <lb/>ad <foreign lang="greek">d</foreign> procederet, ni&longs;i mo&shy;<lb/>ueretur nauis, &amp; eo vbi e&longs;t <lb/>caput remi, transferretur.</s></p><p type="margin">
  
 <s id="id.001271"><margin.target id="marg21"/>Inclu&longs;a his <lb/>notis [] ni <lb/>hil faciunt <lb/>ad rem.</s></p><p type="head"> <s id="id.001271"><margin.target id="marg21"/>Inclu&longs;a his <lb/>notis [] ni&shy;<lb/>hil faciunt <lb/>ad rem.</s></p><p type="head">
  
 <s id="id.001272">COMMENTARIVS.<!-- KEEP S--></s></p><p type="main"> <s id="id.001272">COMMENTARIVS.<!-- KEEP S--></s></p><p type="main">
  
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 <s id="id.001293">Sed caputremi plus antror&longs;um mouetur: quam palmulare&shy;<lb/>tror&longs;um.<emph.end type="italics"/></s></p><p type="main"> <s id="id.001293">Sed caputremi plus antror&longs;um mouetur: quam palmulare&shy;<lb/>tror&longs;um.<emph.end type="italics"/></s></p><p type="main">
  
 <s id="id.001294"><emph type="italics"/>Ergo nauis plus antror&longs;um mouetur: quam palmula retror&longs;um.<emph.end type="italics"/></s></p><p type="main"> <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&shy;<lb/>&longs;totele. <!-- KEEP S--></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&shy;<lb/>&longs;totele. <!-- KEEP S--></s>
  
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 <s id="id.001303">vnde infert caput remi ab eo loco, in quo erat ante remi&shy;<lb/>gationem, ad alium transferri. </s> <s id="id.001303">vnde infert caput remi ab eo loco, in quo erat ante remi&shy;<lb/>gationem, ad alium transferri. </s>
  
 <s id="id.001304">Ergo<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>caput remi tran&longs;latum &longs;it ad<emph.end type="italics"/><lb/><foreign lang="greek">d.</foreign> <emph type="italics"/>Quo autem tempore<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>tran&longs;latum e&longs;t ad<emph.end type="italics"/> <foreign lang="greek">d,</foreign> <emph type="italics"/>palmula<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>non <lb/>transfertur ad<emph.end type="italics"/> <foreign lang="greek">e</foreign><emph type="italics"/>: alioqui &aelig;qualiter moueretur palmula atque caput, <lb/>contra ea qu&aelig; ante po&longs;ita &longs;unt. </s> <s id="id.001304">Ergo<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>caput remi tran&longs;latum &longs;it ad<emph.end type="italics"/><lb/><foreign lang="greek">d.</foreign> </s>
  
 <s id="id.001305">Intelligatur enim remus<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>vbi e&longs;t<emph.end type="italics"/><lb/><foreign lang="greek">d e,</foreign> <emph type="italics"/>&longs;calmo<emph.end type="italics"/> <foreign lang="greek">g</foreign> <emph type="italics"/>manente. </s> 
  
 <s id="id.001306">fiunt duo triangula<emph.end type="italics"/> <foreign lang="greek">a g d &amp; b g e,</foreign><lb/><emph type="italics"/>quorum anguli quiad<emph.end type="italics"/> <foreign lang="greek">g,</foreign> <emph type="italics"/>quia ad <expan abbr="vertic&etilde;">verticem</expan> oppo&longs;iti, &longs;unt &aelig;quales prop. <lb/></s> <s><emph type="italics"/>Quo autem tempore<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>tran&longs;latum e&longs;t ad<emph.end type="italics"/> <foreign lang="greek">d,</foreign> <emph type="italics"/>palmula<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>non <lb/>transfertur ad<emph.end type="italics"/> <foreign lang="greek">e</foreign><emph type="italics"/>: alioqui &aelig;qualiter moueretur palmula atque caput, <lb/>contra ea qu&aelig; ante po&longs;ita &longs;unt. </s>
  
 <s id="id.001307">15. lib.  <s id="id.001305">Intelligatur enim remus<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>vbi e&longs;t<emph.end type="italics"/><lb/><foreign lang="greek">d e,</foreign> <emph type="italics"/>&longs;calmo<emph.end type="italics"/> <foreign lang="greek">g</foreign> <emph type="italics"/>manente. </s>
  
 1. Tum latera, qu&aelig; ip&longs;os continent<emph.end type="italics"/> <foreign lang="greek">a g, d g,</foreign> <emph type="italics"/>duobus<emph.end type="italics"/> <foreign lang="greek"><gap/> g, <lb/><gap/> g</foreign> <emph type="italics"/>&longs;unt &aelig;qualia, quia partes &longs;unt dimidi&aelig; eiu&longs;dem remi<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>ax. </s> 
  
 <s id="id.001308">6. <lb/>eruntigitur ba&longs;es<emph.end type="italics"/> <foreign lang="greek">a d, b e</foreign> <emph type="italics"/>&aelig;quales, vt reliqui anguli prop.  <s id="id.001306">fiunt duo triangula<emph.end type="italics"/> <foreign lang="greek">a g d &amp; b g e,</foreign><lb/><emph type="italics"/>quorum anguli qui ad<emph.end type="italics"/> <foreign lang="greek">g,</foreign> <emph type="italics"/>quia ad <expan abbr="vertic&etilde;">verticem</expan> oppo&longs;iti, &longs;unt &aelig;quales prop. <lb/>15. lib. 1. </s>
  
 4. lib.  <s>Tum latera, qu&aelig; ip&longs;os continent<emph.end type="italics"/> <foreign lang="greek">a g, d g,</foreign> <emph type="italics"/>duobus<emph.end type="italics"/> <foreign lang="greek"><gap/> g, <lb/>e g</foreign> <emph type="italics"/>&longs;unt &aelig;qualia, quia partes &longs;unt dimidi&aelig; eiu&longs;dem remi<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>ax. 6. <lb/></s>
  
 1.<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.121.jpg" pagenum="82"/><emph type="italics"/>Et &longs;ic palmula perducta ad<emph.end type="italics"/> <foreign lang="greek">e</foreign> <emph type="italics"/>cum<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>caput prouectum e&longs;&longs;et ad<emph.end type="italics"/> <foreign lang="greek">d</foreign><lb/><emph type="italics"/>&aelig;qualiter moueretur, &longs;ed in i&longs;to ca&longs;u<emph.end type="italics"/> <foreign lang="greek">g</foreign> <emph type="italics"/>&longs;calmo manente nauis immo&shy;<lb/>ta e&longs;&longs;et, <expan abbr="c&utilde;">cum</expan> tamen prouecta e&longs;&longs;e &longs;upponatur. </s> <s id="id.001308">erunt igitur ba&longs;es<emph.end type="italics"/> <foreign lang="greek">a d, b e</foreign> <emph type="italics"/>&aelig;quales, vt reliqui anguli prop. 4. lib. 1. <emph.end type="italics"/></s><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.121.jpg" pagenum="82"/>
  
 <s id="id.001309">Intelligatur igitur mini&shy;<lb/>m&ugrave;m, vt ad<emph.end type="italics"/> <foreign lang="greek">z</foreign> <emph type="italics"/>e&longs;&longs;e perducta palmula<emph.end type="italics"/> <foreign lang="greek">b.</foreign> <emph type="italics"/>Ex hoc rur&longs;us <expan abbr="c&otilde;cludit">concludit</expan> Ari&shy;<lb/>&longs;toteles ex figura &agrave; Victore Fau&longs;to &amp; ab al&yuml;s pa&szlig;im 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> <emph type="italics"/>Et ita e&longs;&longs;e o&longs;tendamus, quia duorum trian&shy;<lb/>gulorum<emph.end type="italics"/> <foreign lang="greek">a q d &amp; 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 &aelig;quales prop.  <s><emph type="italics"/>Et &longs;ic palmula perducta ad<emph.end type="italics"/> <foreign lang="greek">e</foreign> <emph type="italics"/>cum<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>caput prouectum e&longs;&longs;et ad<emph.end type="italics"/> <foreign lang="greek">d</foreign><lb/><emph type="italics"/>&aelig;qualiter moueretur, &longs;ed in i&longs;to ca&longs;u<emph.end type="italics"/> <foreign lang="greek">g</foreign> <emph type="italics"/>&longs;calmo manente nauis immo&shy;<lb/>ta e&longs;&longs;et, <expan abbr="c&utilde;">cum</expan> tamen prouecta e&longs;&longs;e &longs;upponatur. </s>
  
 15. lib.  <s id="id.001309">Intelligatur igitur mini&shy;<lb/>m&ugrave;m, vt ad<emph.end type="italics"/> <foreign lang="greek">z</foreign> <emph type="italics"/>e&longs;&longs;e perducta palmula<emph.end type="italics"/> <foreign lang="greek">b.</foreign> </s>
  
 1. tum<emph.end type="italics"/> <foreign lang="greek">q a d</foreign> <emph type="italics"/>&aelig;qualis e&longs;t<emph.end type="italics"/> <foreign lang="greek">q b z</foreign> <emph type="italics"/>vel quia <lb/>&longs;unt alterni facti &agrave; 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, <gap/> e.</foreign> <emph type="italics"/>Ex <lb/>pr&aelig;cedenti <expan abbr="dem&otilde;&longs;tratione">demon&longs;tratione</expan>. </s> <s><emph type="italics"/>Ex hoc rur&longs;us <expan abbr="c&otilde;cludit">concludit</expan> Ari&shy;<lb/>&longs;toteles ex figura &agrave; Victore Fau&longs;to &amp; ab al&yuml;s pa&szlig;im 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 id="id.001310">Ergo reliquus<emph.end type="italics"/> <foreign lang="greek">q d a</foreign> <emph type="italics"/>reliquo<emph.end type="italics"/> <foreign lang="greek">b z q</foreign> <emph type="italics"/>&aelig;qua&shy;<lb/>lis erit prop.  <s><emph type="italics"/>Et ita e&longs;&longs;e o&longs;tendamus, quia duorum trian&shy;<lb/>gulorum<emph.end type="italics"/> <foreign lang="greek">a q d &amp; 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 &aelig;quales prop. 15. lib. 1. tum<emph.end type="italics"/> <foreign lang="greek">q a d</foreign> <emph type="italics"/>&aelig;qualis e&longs;t<emph.end type="italics"/> <foreign lang="greek">q b z</foreign> <emph type="italics"/>vel quia <lb/>&longs;unt alterni facti &agrave; 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, <gap/> e.</foreign> </s>
  
 32. lib.  <s><emph type="italics"/>Ex <lb/>pr&aelig;cedenti <expan abbr="dem&otilde;&longs;tratione">demon&longs;tratione</expan>. </s>
  
 1. Et &longs;ic triangula<emph.end type="italics"/> <foreign lang="greek">a q d &amp; b q z</foreign> <emph type="italics"/>&longs;unt &aelig;quian&shy;<lb/>gula, proinde &amp; circum &aelig;quales angulos latera proportionalia prop. <lb/></s> <s id="id.001310">Ergo reliquus<emph.end type="italics"/> <foreign lang="greek">q d a</foreign> <emph type="italics"/>reliquo<emph.end type="italics"/> <foreign lang="greek">b z q</foreign> <emph type="italics"/>&aelig;qua&shy;<lb/>lis erit prop. 32. lib. 1. </s>
  
 <s id="id.001311">4. lib.  <s>Et &longs;ic triangula<emph.end type="italics"/> <foreign lang="greek">a q d &amp; b q z</foreign> <emph type="italics"/>&longs;unt &aelig;quian&shy;<lb/>gula, proinde &amp; circum &aelig;quales angulos latera proportionalia prop. 4. lib. 6. <lb/></s>
  
 6. E&longs;t igitur vt<emph.end type="italics"/> <foreign lang="greek">a q</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">q d</foreign>: <emph type="italics"/>&longs;ic<emph.end type="italics"/> <foreign lang="greek">b q</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">q z,</foreign> <emph type="italics"/>&amp; vici&szlig;im <lb/>prop.  <s id="id.001311">E&longs;t igitur vt<emph.end type="italics"/> <foreign lang="greek">a q</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">q d</foreign>: <emph type="italics"/>&longs;ic<emph.end type="italics"/> <foreign lang="greek">b q</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">q z,</foreign> <emph type="italics"/>&amp; vici&szlig;im <lb/>prop. 16. lib. 5. vt<emph.end type="italics"/> <foreign lang="greek">a q</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">q b</foreign>: <emph type="italics"/>&longs;ic<emph.end type="italics"/> <foreign lang="greek">d q</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">q z.</foreign> </s>
  
 16. lib.  <s><emph type="italics"/>E&longs;t <expan abbr="aut&etilde;">autem</expan><emph.end type="italics"/> <foreign lang="greek">a q</foreign> <emph type="italics"/>maior: <lb/>quam<emph.end type="italics"/> <foreign lang="greek">q b,</foreign> <emph type="italics"/>quia<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>erat bi&longs;&longs;ecta in<emph.end type="italics"/> <foreign lang="greek">g,</foreign> <emph type="italics"/>&amp; detracta e&longs;t de dimi&shy;<lb/>dia<emph.end type="italics"/> <foreign lang="greek">g b</foreign> <emph type="italics"/>portio<emph.end type="italics"/> <foreign lang="greek">q g,</foreign> <emph type="italics"/>qu&aelig; additur ip&longs;i dimidi&aelig;<emph.end type="italics"/> <foreign lang="greek">a g.</foreign> </s>
  
 5. vt<emph.end type="italics"/> <foreign lang="greek">a q</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">q b</foreign>: <emph type="italics"/>&longs;ic<emph.end type="italics"/> <foreign lang="greek">d q</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">q z.</foreign> <emph type="italics"/>E&longs;t <expan abbr="aut&etilde;">autem</expan><emph.end type="italics"/> <foreign lang="greek">a q</foreign> <emph type="italics"/>maior: <lb/>quam<emph.end type="italics"/> <foreign lang="greek">q b,</foreign> <emph type="italics"/>quia<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>erat bi&longs;&longs;ecta in<emph.end type="italics"/> <foreign lang="greek">g,</foreign> <emph type="italics"/>&amp; detracta e&longs;t de dimi&shy;<lb/>dia<emph.end type="italics"/> <foreign lang="greek">g b</foreign> <emph type="italics"/>portio<emph.end type="italics"/> <foreign lang="greek">q g,</foreign> <emph type="italics"/>qu&aelig; additur ip&longs;i dimidi&aelig;<emph.end type="italics"/> <foreign lang="greek">a g.</foreign> <emph type="italics"/>E&longs;t igitur<emph.end type="italics"/><lb/><foreign lang="greek">d q</foreign> <emph type="italics"/>maior quam<emph.end type="italics"/> <foreign lang="greek">q z.</foreign></s></p><p type="main"> <s><emph type="italics"/>E&longs;t igitur<emph.end type="italics"/><lb/><foreign lang="greek">d q</foreign> <emph type="italics"/>maior quam<emph.end type="italics"/> <foreign lang="greek">q z.</foreign></s></p><p type="main">
  
 <s id="id.001312"><emph type="italics"/>Hoc autem quanquam verum &longs;it, quor&longs;um tamen, dubium e&longs;t. <lb/></s> <s id="id.001312"><emph type="italics"/>Hoc autem quanquam verum &longs;it, quor&longs;um tamen, dubium e&longs;t. <lb/></s>
  
 <s id="id.001313">Exi&longs;timauit Nonius ide&ograve; h&icirc;c po&longs;itum e&longs;&longs;e, vt o&longs;tendatur B per remi-<emph.end type="italics"/><lb/><figure id="id.035.01.121.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.121.1.jpg"/><lb/><emph type="italics"/>gationem factam, non e&longs;&longs;e <lb/>in E: &longs;ed vltra vt in K, <lb/>vnde nouam hane de&longs;cri&shy;<lb/>bit figuram. </s> <s id="id.001313">Exi&longs;timauit Nonius ide&ograve; h&icirc;c po&longs;itum e&longs;&longs;e, vt o&longs;tendatur B per remi-<emph.end type="italics"/><lb/><figure id="id.035.01.121.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.121.1.jpg"/><lb/><emph type="italics"/>gationem factam, non e&longs;&longs;e <lb/>in E: &longs;ed vltra vt in K, <lb/>vnde nouam hanc de&longs;cri&shy;<lb/>bit figuram. </s>
  
 <s id="id.001314">qua demon&shy;<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 E: &longs;ed in K <lb/>vltra E. <!-- KEEP S--></s> <s id="id.001314">qua demon&shy;<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">Nihilominu&longs;que <lb/>B K motum palmul&aelig; B <lb/>retror&longs;um minorem e&longs;&longs;e A <lb/>D motu capitis A an&shy;<lb/>tror&longs;um, &longs;ecundum &longs;enten&shy;<lb/>tiam Ari&longs;totelis. <!-- KEEP S--></s> <s id="id.001315"><emph type="italics"/>Nihilominu&longs;que <lb/>B K motum palmul&aelig; B <lb/>retror&longs;um minorem e&longs;&longs;e A <lb/>D motu capitis A an&shy;<lb/>tror&longs;um, &longs;ecundum &longs;enten&shy;<lb/>tiam Ari&longs;totelis. <!-- KEEP S--></s>
  
 <s id="id.001316">Et &longs;ic <lb/>Nonius remigatione facta <lb/>&amp; 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"><expan abbr="q.">que</expan></foreign> <emph type="italics"/>Sed &longs;i &longs;ice&longs;&longs;et, T idem &longs;calmus qui C, propior cum &longs;it <lb/>aqu&aelig;: quam ip&longs;e C, &longs;equeretur vt in vnius remigationis principio, <lb/>medio, fine nauis plus &amp; minus mergeretur. </s> <s id="id.001316">Et &longs;ic <lb/>Nonius remigatione facta <lb/>&amp; 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>
  
  <s><emph type="italics"/>Sed &longs;i &longs;ic e&longs;&longs;et, T idem &longs;calmus qui C, propior cum &longs;it <lb/>aqu&aelig;: quam ip&longs;e C, &longs;equeretur vt in vnius remigationis principio, <lb/>medio, fine nauis plus &amp; minus mergeretur. </s>
  
 <s id="id.001317">quod &longs;i quando fiat, fit <lb/>exaccidenti, nec citra naufrag&yuml; periculum: imo vero &longs;ic non tam <lb/>nauis ferretur antror&longs;um: quam in profundum. </s> <s id="id.001317">quod &longs;i quando fiat, fit <lb/>exaccidenti, nec citra naufrag&yuml; periculum: imo vero &longs;ic non tam <lb/>nauis ferretur antror&longs;um: quam in profundum. </s>
  
 <s id="id.001318">At contr&agrave; latum <lb/>pro&longs;per&egrave; nauigium &longs;eruat eundem &longs;calmum, &longs;eu &longs;pondam &longs;uam &longs;em&shy;<lb/>per &aelig;quidi&longs;tantem aqu&aelig;, ni&longs;i quod verius e&longs;t, arcum peripheri&aelig;, &longs;ed <lb/>non &longs;implicem, vt po&longs;tea docebimus, de&longs;cribat, cuius extrema &longs;unt in <lb/>&longs;uperficie aqu&aelig;.<emph.end type="italics"/><lb/><figure id="id.035.01.122.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.122.1.jpg"/><lb/><emph type="italics"/>vt, &longs;it &longs;ponda <lb/>nauis G H, &amp; <lb/>&longs;calmus C, cui <lb/>alligatus remus <lb/>per medium &longs;it <lb/>A B exi&longs;tens in <lb/>principio remi&shy;<lb/>gationis, &amp; 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&shy;<lb/>mul&aelig; B &longs;patium erit B E: nauigij vero erit C T: tum capitis <lb/>remi A erit A D. <!-- KEEP S--></s> <s id="id.001318">At contr&agrave; latum <lb/>pro&longs;per&egrave; nauigium &longs;eruat eundem &longs;calmum, &longs;eu &longs;pondam &longs;uam &longs;em&shy;<lb/>per &aelig;quidi&longs;tantem aqu&aelig;, ni&longs;i quod verius e&longs;t, arcum peripheri&aelig;, &longs;ed <lb/>non &longs;implicem, vt po&longs;tea docebimus, de&longs;cribat, cuius extrema &longs;unt in <lb/>&longs;uperficie aqu&aelig;. <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 id="id.001319">Et quidem cum anguli qui ad E &longs;int &longs;emper <lb/>&aelig;quales prop.  <s><emph type="italics"/>vt, &longs;it &longs;ponda <lb/>nauis G H, &amp; <lb/>&longs;calmus C, cui <lb/>alligatus remus <lb/>per medium &longs;it <lb/>A B exi&longs;tens in <lb/>principio remi&shy;<lb/>gationis, &amp; 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&shy;<lb/>mul&aelig; B &longs;patium erit B E: nauigij vero erit C T: tum capitis <lb/>remi A erit A D. <!-- KEEP S--></s>
  
 15. lib.  <s id="id.001319">Et quidem cum anguli qui ad E &longs;int &longs;emper <lb/>&aelig;quales prop. 15. lib. 1. </s>
  
 1. Ba&longs;es erunt &aelig;quales, &longs;i triangula fiant &aelig;qui <lb/>crura, &longs;i iniquicrura, illius trianguli ba&longs;is erit maior, cuius latera <lb/>angulum continentia &longs;unt maiora, vt antea ostendimus. </s> <s>Ba&longs;es erunt &aelig;quales, &longs;i triangula fiant &aelig;qui <lb/>crura, &longs;i iniquicrura, illius trianguli ba&longs;is erit maior, cuius latera <lb/>angulum continentia &longs;unt maiora, vt antea ostendimus. </s>
  
 <s id="id.001320">H&aelig;cigi&shy;<lb/>tur cum expendo cogor aliud &longs;entire quam Nonius licet timid&egrave; (quia <lb/>viro huic propter &longs;cientiam pr&aelig;&longs;tantem, &amp; quod in loco natus &longs;it, <lb/>vixeritque ad nauigandum opportuni&szlig;imo, mult&ograve; 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 e&ograve;, 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.001320">H&aelig;cigi&shy;<lb/>tur cum expendo cogor aliud &longs;entire quam Nonius licet timid&egrave; (quia <lb/>viro huic propter &longs;cientiam pr&aelig;&longs;tantem, &amp; quod in loco natus &longs;it, <lb/>vixeritque ad nauigandum opportuni&szlig;imo, mult&ograve; 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 e&ograve;, 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>
  
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 <s id="id.001322">Sicque caput A multo anterius latum erit, quam B retr&ograve;. <lb/></s> <s id="id.001322">Sicque caput A multo anterius latum erit, quam B retr&ograve;. <lb/></s>
  
 <s id="id.001323">E&longs;t enim A F maior quam A D axiom. </s> <s id="id.001323">E&longs;t enim A F maior quam A D axiom. 9. qu&aelig; demon&longs;trata e&longs;t<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.123.jpg" pagenum="84"/><figure id="id.035.01.123.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.123.1.jpg"/><lb/><emph type="italics"/>e&longs;&longs;e maior ip&longs;a B E: &longs;ic <lb/>etiam C &longs;calmus erit in O, <lb/>&aelig;quedi&longs;tanter cum C ab <lb/>aqua. </s>
  
 <s id="id.001324">9. qu&aelig; demon&longs;trata e&longs;t<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.123.jpg" pagenum="84"/><figure id="id.035.01.123.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.123.1.jpg"/><lb/><emph type="italics"/>e&longs;&longs;e maior ip&longs;a B E: &longs;ic <lb/>etiam C &longs;calmus erit in O, <lb/>&aelig;quedi&longs;tanter cum C ab <lb/>aqua. </s> 
  
 <s id="id.001325">quod fieri oportet in <lb/>artificio&longs;a &amp; pro&longs;pera na&shy;<lb/>uigatione. </s> <s id="id.001325">quod fieri oportet in <lb/>artificio&longs;a &amp; pro&longs;pera na&shy;<lb/>uigatione. </s>
  
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 <s id="id.001340">Secet enim re&shy;<lb/>cta A C rectam E F in G. <!-- KEEP S--></s> <s id="id.001340">Secet enim re&shy;<lb/>cta A C rectam E F in G. <!-- KEEP S--></s>
  
 <s id="id.001341">Quia igitur A G E, &amp; B G D <lb/>triangula &longs;unt &aelig;quiangula, erit &longs;icut A G ad B G: &longs;ic A E <lb/>ad B D prop.  <s id="id.001341">Quia igitur A G E, &amp; B G D <lb/>triangula &longs;unt &aelig;quiangula, erit &longs;icut A G ad B G: &longs;ic A E <lb/>ad B D prop. 4. lib. 6. </s>
  
 4. lib.  <s>Maior e&longs;t autem A G ip&longs;a B G, ax. 9. <lb/></s>
  
 6. Maior e&longs;t autem A G ip&longs;a B G, ax. </s> <s id="id.001342">Erit igitur A E maior quam B D. <!-- KEEP S--></s>
  
 <s id="id.001342">9. <lb/>Erit igitur A E maior quam B D. <!-- KEEP S--></s> 
  
 <s id="id.001343">Itaque caput remi A maius <lb/>percurrit &longs;patium: quam nauis. </s> <s id="id.001343">Itaque caput remi A maius <lb/>percurrit &longs;patium: quam nauis. </s>
  
 <s id="id.001344">quod erat demon&longs;trandum.<emph.end type="italics"/></s></p><figure id="id.035.01.124.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.124.1.jpg"/><p type="main"> <s id="id.001344">quod erat demon&longs;trandum.<emph.end type="italics"/></s></p><figure id="id.035.01.124.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.124.1.jpg"/><p type="main">
  
 <s id="id.001345"><emph type="italics"/>Quod &longs;i per punctum B rectam duca&shy;<lb/>mus H K &aelig;qualem remo, &amp; ad rectos <lb/>cum recta B D, &amp; in&longs;uper &longs;ecantem A<emph.end type="italics"/><lb/>3 <emph type="italics"/>in puncto I, manife&longs;t&egrave; intelligemus <lb/>ip&longs;am rectam A E (qu&aelig; e&longs;t totus motus <lb/>capitis remi in vna remigatione) con&longs;tare <lb/>ex A I, &amp; I E, quarum prior re&longs;pon&shy;<lb/>det curu&aelig; A H de&longs;cript&aelig; per capitis remi <lb/>motum proprium: po&longs;terior vero &aelig;qualis <lb/>e&longs;trect&aelig; B D (&longs;unt enim latera parallelo&shy;<lb/>grammi oppo&longs;ita prop.  <s id="id.001345"><emph type="italics"/>Quod &longs;i per punctum B rectam duca&shy;<lb/>mus H K &aelig;qualem remo, &amp; ad rectos <lb/>cum recta B D, &amp; in&longs;uper &longs;ecantem A<emph.end type="italics"/><lb/>3 <emph type="italics"/>in puncto I, manife&longs;t&egrave; intelligemus <lb/>ip&longs;am rectam A E (qu&aelig; e&longs;t totus motus <lb/>capitis remi in vna remigatione) con&longs;tare <lb/>ex A I, &amp; I E, quarum prior re&longs;pon&shy;<lb/>det curu&aelig; A H de&longs;cript&aelig; per capitis remi <lb/>motum proprium: po&longs;terior vero &aelig;qualis <lb/>e&longs;trect&aelig; B D (&longs;unt enim latera parallelo&shy;<lb/>grammi oppo&longs;ita prop. 34. lib. 1.) qu&aelig; motu <lb/>nauis decur&longs;a e&longs;t.<emph.end type="italics"/></s></p><p type="main">
  
 34. lib.  
  
 1.) qu&aelig; motu <lb/>nauis decur&longs;a e&longs;t.<emph.end type="italics"/></s></p><p type="main"> 
  
 <s id="id.001346"><emph type="italics"/>Et quia Nonius &longs;ine demon&longs;tratione a&longs;&shy;<lb/>&longs;umit nauim tant&ugrave;m decurrere, quant&ugrave;m <lb/>&longs;calmus, id quoque demonstremus. </s> <s id="id.001346"><emph type="italics"/>Et quia Nonius &longs;ine demon&longs;tratione a&longs;&shy;<lb/>&longs;umit nauim tant&ugrave;m decurrere, quant&ugrave;m <lb/>&longs;calmus, id quoque demonstremus. </s>
  
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 <s id="id.001348"><emph type="italics"/>Ante remigationem remi existentis in &longs;calmo B &longs;it nauis prora C <lb/>po&longs;t remigationem &longs;it B<emph.end type="italics"/><lb/><figure id="id.035.01.124.2.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.124.2.jpg"/><lb/><emph type="italics"/>in E &amp; prora in D &longs;ic&shy;<lb/>que C D erit nauis pro&shy;<lb/>motio, &amp; B E &longs;calmi. <lb/></s> <s id="id.001348"><emph type="italics"/>Ante remigationem remi existentis in &longs;calmo B &longs;it nauis prora C <lb/>po&longs;t remigationem &longs;it B<emph.end type="italics"/><lb/><figure id="id.035.01.124.2.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.124.2.jpg"/><lb/><emph type="italics"/>in E &amp; prora in D &longs;ic&shy;<lb/>que C D erit nauis pro&shy;<lb/>motio, &amp; B E &longs;calmi. <lb/></s>
  
 <s id="id.001349">Dico igitur C D &amp; B E &aelig;quales, quia reliqu&aelig; &longs;unt ex &aelig;qualibus <lb/>B C, E D dempto communi E C axio. </s> <s id="id.001349">Dico igitur C D &amp; B E &aelig;quales, quia reliqu&aelig; &longs;unt ex &aelig;qualibus <lb/>B C, E D dempto communi E C axio. 3. </s>
  
 <s id="id.001350">3. Ergo nauis tant&ugrave;m de&shy;<lb/>currit quant&ugrave;m &longs;calmus.<emph.end type="italics"/></s></p><p type="head"> <s id="id.001350">Ergo nauis tant&ugrave;m de&shy;<lb/>currit quant&ugrave;m &longs;calmus.<emph.end type="italics"/></s></p><p type="head">
  
 <s id="id.001351">Propo&longs;itio &longs;ecunda.</s></p><p type="main"> <s id="id.001351">Propo&longs;itio &longs;ecunda.</s></p><p type="main">
  
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 <s id="id.001354">Et <lb/>eadem recta C G producatur v&longs;que <lb/>ad E, ita vt G E &longs;it &aelig;qualis rect&aelig; <lb/>B A (qu&aelig; e&longs;t dimidium remi) rur&shy;<lb/>&longs;us per punctum B ducatur recta Q <lb/>B F ad rectos cum ip&longs;a B G, &amp; in <lb/>Q B F incidant perpendiculares A <lb/>Q C F. <!-- KEEP S--></s> <s id="id.001354">Et <lb/>eadem recta C G producatur v&longs;que <lb/>ad E, ita vt G E &longs;it &aelig;qualis rect&aelig; <lb/>B A (qu&aelig; e&longs;t dimidium remi) rur&shy;<lb/>&longs;us per punctum B ducatur recta Q <lb/>B F ad rectos cum ip&longs;a B G, &amp; in <lb/>Q B F incidant perpendiculares A <lb/>Q C F. <!-- KEEP S--></s>
  
 <s id="id.001355">Quoniam igitur triangu&shy;<lb/>lorum A B Q &amp; F B C anguli, <lb/>qui ad B ad verticem oppo&longs;iti &longs;unt <lb/>&aelig;quales, prop.  <s id="id.001355">Quoniam igitur triangu&shy;<lb/>lorum A B Q &amp; F B C anguli, <lb/>qui ad B ad verticem oppo&longs;iti &longs;unt <lb/>&aelig;quales, prop. 15. lib. 1. &amp; anguli qui ad Q &amp; F recti &longs;unt, tum <lb/>latus A B lateri B C, &longs;unt enim dimidia remi, &aelig;quale e&longs;t, erit &amp; <lb/>latus A Q &aelig;quale lateri F C prop. 26. lib. 1. </s>
  
 15. lib.  
  
 1. &amp; anguli qui ad Q &amp; F recti &longs;unt, tum <lb/>latus A B lateri B C, &longs;unt enim dimidia remi, &aelig;quale e&longs;t, erit &amp; <lb/>latus A Q &aelig;quale lateri F C prop.  <s>Ip&longs;i autem F C recta <lb/>B G, latus parallelogrammi oppo&longs;itum, &aelig;qualis e&longs;t prop. 34. lib. 1. <lb/></s>
  
 26. lib.  <s id="id.001356">A Q igitur erit &aelig;qualis ip&longs;i B G ax. 1. </s>
  
 1. Ip&longs;i autem F C recta <lb/>B G, latus parallelogrammi oppo&longs;itum, &aelig;qualis e&longs;t prop. </s> <s id="id.001357">Atque tantum &longs;patium B <lb/>&longs;calmus: quantum nauis. </s>
  
 <s id="id.001356">34. lib.  <s>ex antec. </s>
  
 1. <lb/>A Qigitur erit &aelig;qualis ip&longs;i B G ax. </s> 
  
 <s id="id.001357">1. Atque tantum &longs;patium B <lb/>&longs;calmus: quantum nauis. </s> 
  
 <s id="id.001358">ex antec. </s> 
  
 <s id="id.001359">Et nauis tantum confecit quan&shy;<lb/>tum A caput remi ex hypothe&longs;i. </s> <s id="id.001359">Et nauis tantum confecit quan&shy;<lb/>tum A caput remi ex hypothe&longs;i. </s>
  
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 <s id="id.001366">vbi etiam aduertes lector ex hoc dia&shy;<lb/>grammate Non&yuml; &amp; c&aelig;teris lineam A L E &agrave; capite remi in hac <lb/>remigatione de&longs;criptam, non e&longs;&longs;e &longs;implicem arcum: &longs;ed duos, vnum <lb/>A L ex motu proprio remi circa B centrum: alterum L E ex motu <lb/>con&longs;equente &longs;calmi B motum. </s> <s id="id.001366">vbi etiam aduertes lector ex hoc dia&shy;<lb/>grammate Non&yuml; &amp; c&aelig;teris lineam A L E &agrave; capite remi in hac <lb/>remigatione de&longs;criptam, non e&longs;&longs;e &longs;implicem arcum: &longs;ed duos, vnum <lb/>A L ex motu proprio remi circa B centrum: alterum L E ex motu <lb/>con&longs;equente &longs;calmi B motum. </s>
  
 <s id="id.001367">quod pulchr&egrave; con&longs;entit cum his qu&aelig;<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.126.jpg" pagenum="87"/><emph type="italics"/>unt&egrave; diximus de remi in vna remigatione varijs motibus.<emph.end type="italics"/></s></p><p type="head"> <s id="id.001367">quod pulchr&egrave; con&longs;entit cum his qu&aelig;<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.126.jpg" pagenum="87"/><emph type="italics"/>ant&egrave; diximus de remi in vna remigatione varijs motibus.<emph.end type="italics"/></s></p><p type="head">
  
 <s id="id.001368">Propo&longs;itionis conuer&longs;io</s></p><p type="main"> <s id="id.001368">Propo&longs;itionis conuer&longs;io</s></p><p type="main">
  
 <s id="id.001369"><emph type="italics"/>Manife&longs;ta e&longs;t, quia &longs;i remi palmula dimota non fuerit &agrave; loco &longs;uo, <lb/>ibique tandiu per&longs;i&longs;tat, donec remus &longs;itum rectitudinis obtineat, tan&shy;<lb/>tum &longs;patium conficiet caput remi motu proprio: quantum nauis. <lb/></s> <s id="id.001369"><emph type="italics"/>Manife&longs;ta e&longs;t, quia &longs;i remi palmula dimota non fuerit &agrave; loco &longs;uo, <lb/>ibique tandiu per&longs;i&longs;tat, donec remus &longs;itum rectitudinis obtineat, tan&shy;<lb/>tum &longs;patium conficiet caput remi motu proprio: quantum nauis. <lb/></s>
  
 <s id="id.001370">Recta enim C F &aelig;qualis e&longs;t A Q prop.  <s id="id.001370">Recta enim C F &aelig;qualis e&longs;t A Q prop. 26. lib. 1. &aelig;qualis etiam <lb/>B G prop. 34. lib. 1. igitur A Q &amp; B G &aelig;quales erunt ax. 1.<emph.end type="italics"/></s></p><p type="head">
  
 26. lib.  
  
 1. &aelig;qualis etiam <lb/>B G prop. </s> 
  
 <s id="id.001371">34. lib.  
  
 1. igitur A Q &amp; B G &aelig;quales erunt ax. </s> 
  
 <s id="id.001372">1.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="head"> 
  
 <s id="id.001373">Propo&longs;itio tertia.</s></p><p type="main"> <s id="id.001373">Propo&longs;itio tertia.</s></p><p type="main">
  
 <s id="id.001374"><emph type="italics"/>Capite remi proprio motu conficiente &longs;patium duplum &longs;pat&yuml; nauis: <lb/>tunc nauis tant&ugrave;m promouebitur, quant&ugrave;m palmula retrocedet.<emph.end type="italics"/></s></p><figure id="id.035.01.126.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.126.1.jpg"/><p type="main"> <s id="id.001374"><emph type="italics"/>Capite remi proprio motu conficiente &longs;patium duplum &longs;pat&yuml; nauis: <lb/>tunc nauis tant&ugrave;m promouebitur, quant&ugrave;m palmula retrocedet.<emph.end type="italics"/></s></p><figure id="id.035.01.126.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.126.1.jpg"/><p type="main">
  
 <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. <!-- KEEP S--></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. <!-- KEEP S--></s>
  
 <s id="id.001376">Et &longs;ic &longs;calmus B pro&shy;<lb/>pter nauis motum conficiet interual&shy;<lb/>lum B D. <!-- KEEP S--></s> 
  
 <s id="id.001377">Excitetur igitur &agrave; puncto <lb/>B in vtramque partem perpendicu&shy;<lb/>laris E E, prop.  
  
 11. lib.  
  
 1. In quam <lb/>perpendiculares incidant &agrave; punctis <lb/>A &amp; C, qu&aelig; &longs;int A E, C E prop. <lb/></s> 
  
 <s id="id.001378">12. lib.  
  
 1. Et &longs;it interuallum A E <lb/>quod e&longs;t decur&longs;um &agrave; capite remi A <lb/>proprio motu, duplum interualli B <lb/>D, &amp; recta linea C H re&longs;pondeat <lb/>curu&aelig; C G &agrave; remi palmula de&longs;cri&shy;<lb/>pt&aelig;. </s> 
  
 <s id="id.001379">Dico rectas lineas B D, C H <lb/>&aelig;quales e&longs;&longs;e. </s> <s id="id.001376">Et &longs;ic &longs;calmus B pro&shy;<lb/>pter nauis motum conficiet interual&shy;<lb/>lum B D. <!-- KEEP S--></s>
  
 <s id="id.001380">Nam triangulorum B <lb/>A E &amp; C B E rect&aelig; A E, C E prop.  <s id="id.001377">Excitetur igitur &agrave; puncto <lb/>B in vtramque partem perpendicu&shy;<lb/>laris E E, prop. 11. lib. 1. </s>
  
 26. lib.  <s>In quam <lb/>perpendiculares incidant &agrave; punctis <lb/>A &amp; C, qu&aelig; &longs;int A E, C E prop. 12. lib. 1. <lb/></s>
  
 1. &amp; in parallelo&shy;<lb/>grammo B H rect&aelig; oppo&longs;it&aelig; B D, E H etiam &aelig;quales prop. </s> <s id="id.001378">Et &longs;it interuallum A E <lb/>quod e&longs;t decur&longs;um &agrave; capite remi A <lb/>proprio motu, duplum interualli B <lb/>D, &amp; recta linea C H re&longs;pondeat <lb/>curu&aelig; C G &agrave; remi palmula de&longs;cri&shy;<lb/>pt&aelig;. </s>
  
 <s id="id.001381">34. <lb/>lib.  <s id="id.001379">Dico rectas lineas B D, C H <lb/>&aelig;quales e&longs;&longs;e. </s>
  
 1. Atqui recta A E dupla e&longs;t rect&aelig; B D ex hypothe&longs;i. </s> <s id="id.001380">Nam triangulorum B <lb/>A E &amp; C B E rect&aelig; A E, C E prop. 26. lib. 1. &amp; in parallelo&shy;<lb/>grammo B H rect&aelig; oppo&longs;it&aelig; B D, E H etiam &aelig;quales prop. 34. <lb/>lib. 1. </s>
  
 <s id="id.001382">Dupla <lb/>igitur &amp; C E rect&aelig; H E, quapropter C H &amp; E H &aelig;qual<gap/>s <lb/>erunt ax. </s> <s id="id.001381">Atqui recta A E dupla e&longs;t rect&aelig; B D ex hypothe&longs;i. </s>
  
 <s id="id.001383">7. Et &longs;ic C H &amp; B D &aelig;quales &longs;unt ax. </s> <s id="id.001382">Dupla <lb/>igitur &amp; C E rect&aelig; H E, quapropter C H &amp; E H &aelig;quales <lb/>erunt ax. 7. </s>
  
 <s id="id.001384">1. Et quia nauis <lb/>tantum interualli decurrit &longs;emper: quantum &longs;calmus. </s> <s id="id.001383">Et &longs;ic C H &amp; B D &aelig;quales &longs;unt ax. 1. </s>
  
 <s id="id.001385">Ex antec. </s> <s id="id.001384">Et quia nauis <lb/>tantum interualli decurrit &longs;emper: quantum &longs;calmus. </s>
  
 <s id="id.001386">igi&shy;<lb/>tur &longs;i caput remi motu proprio duplum confecerit ip&longs;ius nauis inter&shy;<lb/>ualli, tant&ugrave;m prouehetur nauis: quant&ugrave;m palmula retrocedet. </s> <s id="id.001385">Ex antec. igi&shy;<lb/>tur &longs;i caput remi motu proprio duplum confecerit ip&longs;ius nauis inter&shy;<lb/>ualli, tant&ugrave;m prouehetur nauis: quant&ugrave;m palmula retrocedet. </s>
  
 <s id="id.001387">quod <lb/>demon&longs;trandum erat.<emph.end type="italics"/></s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.127.jpg" pagenum="88"/><p type="head"> <s id="id.001387">quod <lb/>demon&longs;trandum erat.<emph.end type="italics"/></s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.127.jpg" pagenum="88"/><p type="head">
  
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 <s id="id.001389"><emph type="italics"/>Naui &aelig;qualiter prouecta, atque palmula retroce&szlig;it: motus capitis <lb/>remi proprius duplus e&longs;t motus nauis.<emph.end type="italics"/></s></p><p type="main"> <s id="id.001389"><emph type="italics"/>Naui &aelig;qualiter prouecta, atque palmula retroce&szlig;it: motus capitis <lb/>remi proprius duplus e&longs;t motus nauis.<emph.end type="italics"/></s></p><p type="main">
  
 <s id="id.001390"><emph type="italics"/>Si enim C H &aelig;qualis ponatur B D, quoniam eidem B D &aelig;qua&shy;<lb/>lis e&longs;t H E in parallelogrammo, &aelig;quales igitur erunt C H &amp; <lb/>H E ax. </s> <s id="id.001390"><emph type="italics"/>Si enim C H &aelig;qualis ponatur B D, quoniam eidem B D &aelig;qua&shy;<lb/>lis e&longs;t H E in parallelogrammo, &aelig;quales igitur erunt C H &amp; <lb/>H E ax. 1. </s>
  
 <s id="id.001391">1. Et &longs;ic dupla erit C E ip&longs;ius H E: &amp; eadem C E <lb/>dupla ip&longs;ius B D. &aelig;quales porro &longs;unt C E &amp; A E prop 26. lib.  <s id="id.001391">Et &longs;ic dupla erit C E ip&longs;ius H E: &amp; eadem C E <lb/>dupla ip&longs;ius B D. &aelig;quales porro &longs;unt C E &amp; A E prop 26. lib. 1. <lb/></s>
  
 1. <lb/>Dupla ergo erit A E rect&aelig; B D. &longs;ed recta A E decur&longs;a e&longs;t &agrave; ca&shy;<lb/>pite remi, &amp; B D &agrave; &longs;calmo, quant&ugrave;m autem prouehitur &longs;calmus, <lb/>tant&ugrave;m &amp; nauis. </s> <s>Dupla ergo erit A E rect&aelig; B D. </s>
  
  <s>&longs;ed recta A E decur&longs;a e&longs;t &agrave; ca&shy;<lb/>pite remi, &amp; B D &agrave; &longs;calmo, quant&ugrave;m autem prouehitur &longs;calmus, <lb/>tant&ugrave;m &amp; nauis. </s>
  
 <s id="id.001392">Igitur &longs;i nauis tant&ugrave;m fuerit prouecta, quant&ugrave;m <lb/>remi palmula retroce&szlig;it, duplum conficit caput remi motu proprio <lb/>eius interualli, quod nauis conficit. </s> <s id="id.001392">Igitur &longs;i nauis tant&ugrave;m fuerit prouecta, quant&ugrave;m <lb/>remi palmula retroce&szlig;it, duplum conficit caput remi motu proprio <lb/>eius interualli, quod nauis conficit. </s>
  
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 <s id="id.001398">Nam B D &amp; H E &aelig;quales &longs;unt, adh&aelig;c A E &amp; C E &aelig;qua&shy;<lb/>les &longs;unt. </s> <s id="id.001398">Nam B D &amp; H E &aelig;quales &longs;unt, adh&aelig;c A E &amp; C E &aelig;qua&shy;<lb/>les &longs;unt. </s>
  
 <s id="id.001399">maior igitur erit H E dimidio ip&longs;ius A E. quapropter <lb/>reliqua C H minor dimidio erit eiu&longs;dem A E. <!-- KEEP S--></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. <!-- KEEP S--></s>
  
 <s id="id.001400">Et minor igitur <lb/>erit C H quam B D. <!-- KEEP S--></s> <s id="id.001400">Et minor igitur <lb/>erit C H quam B D. <!-- KEEP S--></s>
  
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 <s id="id.001425">Nihil autem vnquam re&shy;<lb/>trocedere o&longs;tendetur in hunc modum. </s> <s id="id.001425">Nihil autem vnquam re&shy;<lb/>trocedere o&longs;tendetur in hunc modum. </s>
  
 <s id="id.001426">Eadem celeritate mouentur A <lb/>in H, &amp; C ver&longs;us E circa &longs;calmum. </s> <s id="id.001426">Eadem celeritate mouentur A <lb/>in H, &amp; C ver&longs;us <emph.end type="italics"/><foreign lang="greek">z</foreign><emph type="italics"/> circa &longs;calmum. </s>
  
  <s id="id.001427">Atqui per hypothe&longs;im cele&shy;<lb/>rius fertur nauis: quam C ver&longs;us <emph.end type="italics"/><foreign lang="greek">z</foreign><emph type="italics"/>. </s>
  
  <s id="id.001428">Et mouetur idem C ip&longs;a nauis <lb/>celeritate ver&longs;us K. </s>
  
 <s id="id.001427">Atqui per hypothe&longs;im cele&shy;<lb/>rius fertur nauis: quam C ver&longs;us E. <!-- KEEP S--></s> <s>celerius igitur feretur C ad K: quam ad <emph.end type="italics"/><foreign lang="greek">z</foreign><emph type="italics"/>. <lb/></s>
  
 <s id="id.001428">Et mouetur idem C ip&longs;a nauis <lb/>celeritate ver&longs;us K. celerius igitur feretur C ad K: quam ad E. <lb/>quapropter nihil vnquam retrocedet ip&longs;um C. <!-- KEEP S--></s> <s>quapropter nihil vnquam retrocedet ip&longs;um C. <!-- KEEP S--></s>
  
 <s id="id.001429">Imo vero in vlte&shy;<lb/>riora progredietur, interuallumque decurret C K, quod quidem re&shy;<lb/>linquitur, detracto E C ex E K. <!-- KEEP S--></s> <s id="id.001429">Imo vero in vlte&shy;<lb/>riora progredietur, interuallumque decurret C K, quod quidem re&shy;<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. <!-- KEEP S--></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"/>nauig&yuml; celeritate moueretur, vltra k progrederetur, cum B perue&shy;<lb/>niret ad D: &longs;ed retrahitur interim, propter eum motum, qui fit cir&shy;<lb/>ca B. </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"/>nauig&yuml; celeritate moueretur, vltra k progrederetur, cum B perue&shy;<lb/>niret ad D: &longs;ed retrahitur interim, propter eum motum, qui fit cir&shy;<lb/>ca B. </s>
  
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 <s id="id.001434">Concludit <lb/>etiam hac di&longs;tinctione po&longs;ita Ari&longs;totelem in&longs;cit&egrave;, &amp; fals&ograve; proble&shy;<lb/>mati &longs;atisfeci&longs;&longs;e. </s> <s id="id.001434">Concludit <lb/>etiam hac di&longs;tinctione po&longs;ita Ari&longs;totelem in&longs;cit&egrave;, &amp; fals&ograve; proble&shy;<lb/>mati &longs;atisfeci&longs;&longs;e. </s>
  
 <s id="id.001435">Quandoquidem non continu&ograve; &longs;i nauis in anteriora <lb/>moueatur, remi palmula retrocedet: neque &longs;i retrocedat, minus inter&shy;<lb/>uallum in contrarium tran&longs;naittet: quam nauis progrediatur, vt ex <lb/>&longs;ecunda &amp; tertia propo&longs;itionibus liquet: pr&aelig;tered cum caput remi <lb/>motu proprio, qui circa &longs;calmum fit, vn&acirc; cum nauis motu, maius in&shy;<lb/>teruallum conficiat: quam nauis, &longs;olo autem proprio motu, &longs;i contin&shy;<lb/>gat tantum interuallum conficere: quantum nauis, fieri non po&szlig;it, vt <lb/>palmula moueatur: fru&longs;tr&agrave; Ari&longs;toteles conatus e&longs;t in vniuer&longs;um <lb/>o&longs;tendere remi caput maius &longs;patium decurrere: quam palmulam in <lb/>contrarium. </s> <s id="id.001435">Quandoquidem non continu&ograve; &longs;i nauis in anteriora <lb/>moueatur, remi palmula retrocedet: neque &longs;i retrocedat, minus inter&shy;<lb/>uallum in contrarium tran&longs;mittet: quam nauis progrediatur, vt ex <lb/>&longs;ecunda &amp; tertia propo&longs;itionibus liquet: pr&aelig;terea cum caput remi <lb/>motu proprio, qui circa &longs;calmum fit, vn&acirc; cum nauis motu, maius in&shy;<lb/>teruallum conficiat: quam nauis, &longs;olo autem proprio motu, &longs;i contin&shy;<lb/>gat tantum interuallum conficere: quantum nauis, fieri non po&szlig;it, vt <lb/>palmula moueatur: fru&longs;tr&agrave; Ari&longs;toteles conatus e&longs;t in vniuer&longs;um <lb/>o&longs;tendere remi caput maius &longs;patium decurrere: quam palmulam in <lb/>contrarium. </s>
  
 <s id="id.001436">Po&longs;tremo cum nauis longius progreditur: quam palmula <lb/>regreditur: minus quo que interuallum decurrit: quam caputremi, &amp; <lb/>&longs;ic non &aelig;quale. </s> <s id="id.001436">Po&longs;tremo cum nauis longius progreditur: quam palmula <lb/>regreditur: minus quo que interuallum decurrit: quam caputremi, &amp; <lb/>&longs;ic non &aelig;quale. </s>
  
 <s id="id.001437">Atque h&aelig;c cum &longs;int &longs;uis veris demon&longs;trationibus <lb/>&longs;tabilita Ari&longs;totelem in hoc problemate dormita&longs;&longs;e, quod aliquando <lb/>bono Homero contingit, conuincunt.<emph.end type="italics"/></s></p><p type="main"> <s id="id.001437">Atque h&aelig;c cum &longs;int &longs;uis veris demon&longs;trationibus <lb/>&longs;tabilita Ari&longs;totelem in hoc problemate dormita&longs;&longs;e, quod aliquando <lb/>bono Homero contingit, conuincunt.<emph.end type="italics"/></s></p><p type="main">
  
 <s id="id.001438"><gap/></s></p><p type="main"> <s id="id.001438"><foreign lang="greek"><gap/></foreign></s></p><p type="main">
  
 <s id="id.001439">Id etiam ip&longs;um facit gu&shy;<lb/>bernaculum, ni&longs;i quod an&shy;<lb/>terius non mouet nauim: <lb/>vt antea dictum e&longs;t: &longs;ed <lb/>hinc vel hinc puppim &longs;o&shy;<lb/>lum in tran&longs;uer&longs;um pellit. <lb/></s> <s id="id.001439">Id etiam ip&longs;um facit gu&shy;<lb/>bernaculum, ni&longs;i quod an&shy;<lb/>terius non mouet nauim: <lb/>vt antea dictum e&longs;t: &longs;ed <lb/>hinc vel hinc puppim &longs;o&shy;<lb/>lum in tran&longs;uer&longs;um pellit. <lb/></s>
  
 <s id="id.001440">Sic enim in <expan abbr="c&otilde;trari&utilde;">contrarium</expan> prora <lb/>vergit. </s> <s id="id.001440">Sic enim in <expan abbr="c&otilde;trari&utilde;">contrarium</expan> prora <lb/>vergit. </s>
  
 <s id="id.001441">Vbi igitur <expan abbr="guberna-cul&utilde;">guberna&shy;<lb/>culum</expan> <expan abbr="adi&utilde;ct&utilde;">adiunctum</expan> e&longs;t, ibi opor&shy;<lb/>tet aliquod eius, quod mo&shy;<lb/>uetur <expan abbr="medi&utilde;">medium</expan> intelligere, &amp; <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.130.jpg" pagenum="91"/><gap/><lb/>qualis e&longs;t &longs;calmus remo: <lb/>Illud vero medium proce&shy;<lb/>dit, quo temo transfertur. <lb/></s> <s id="id.001441">Vbi igitur <expan abbr="guberna-cul&utilde;">guberna&shy;<lb/>culum</expan> <expan abbr="adi&utilde;ct&utilde;">adiunctum</expan> e&longs;t, ibi opor&shy;<lb/>tet aliquod eius, quod mo&shy;<lb/>uetur <expan abbr="medi&utilde;">medium</expan> intelligere, &amp; <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.130.jpg" pagenum="91"/><foreign lang="greek"><gap/></foreign><lb/>qualis e&longs;t &longs;calmus remo: <lb/>Illud vero medium proce&shy;<lb/>dit, quo temo transfertur. <lb/></s>
  
 <s id="id.001442">Si quidem intror&longs;us agat, <lb/>etiam puppis e&ograve; transfer&shy;<lb/>tur, prora ver&ograve; in con&shy;<lb/>trarium nutat. </s> <s id="id.001442">Si quidem intror&longs;us agat, <lb/>etiam puppis e&ograve; transfer&shy;<lb/>tur, prora ver&ograve; in con&shy;<lb/>trarium nutat. </s>
  
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 <s id="id.001444">COMME