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version 1.25, 2002/08/18 17:04:49 version 1.55, 2003/08/25 12:49:19
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 <?xml version="1.0"?> <?xml version="1.0"?>
 <!DOCTYPE archimedes SYSTEM "../dtd/archimedes.dtd" ><archimedes>      <info> <!DOCTYPE archimedes SYSTEM "../dtd/archimedes.dtd" >
  <archimedes xmlns:xlink="http://www.w3.org/1999/xlink">      <info>
         <author>Monantheuil, Henri de</author>         <author>Monantheuil, Henri de</author>
         <title>Aristotelis Mechanica</title>         <title>Aristotelis Mechanica</title>
         <date>1599</date>         <date>1599</date>
         <place>Paris</place>         <place>Paris</place>
         <translator></translator>         <translator/>
         <lang>la</lang>         <lang>la</lang>
         <cvs_file>monan_mecha_01_la_1599</cvs_file>         <cvs_file>monan_mecha_01_la_1599</cvs_file>
         <cvs_version></cvs_version>         <cvs_version/>
         <locator>0000000035.xml</locator>         <locator>035.xml</locator>
 </info>      <text>          <front>          </front>          <body>            <chap>        <pb/><p type="head"> </info><text><front><section><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.001.jpg"/><p type="head">
  
 <s>ARISTOTELIS <lb/>MECHANICA <lb/>Gr&aelig;ca, emendata, Latina facta, &amp; <lb/>Commentariis illu&longs;trata. <lb/></s> <s id="id.000001">ARISTOTELIS <lb/>MECHANICA <lb/>Gr&aelig;ca, emendata, Latina facta, &amp; <lb/>Commentariis illu&longs;trata. <lb/></s>
  
 <s>A B <lb/><emph type="italics"/>HENRICO MONANTHOLIO <lb/>Medico, &amp; Mathematicarum artium <lb/>Profe&longs;&longs;ore Regio.<emph.end type="italics"/><lb/>A D <lb/>HENRICVM IIII. GALLI&AElig; &amp; NAVARR&AElig; <lb/>Regem Chri&longs;tiani&longs;simum.</s></p><figure></figure><p type="head"> <s id="id.000002">AB <lb/><emph type="italics"/>HENRICO MONANTHOLIO <lb/>Medico, &amp; Mathematicarum artium <lb/>Profe&longs;&longs;ore Regio. </s>
  
 <s>PARISIIS, <lb/>Apud <gap/>EMIAM PERIER via Iacob&aelig;a, &longs;ub &longs;igno Bellerophontis.</s></p><p type="head"> <s><emph.end type="italics"/><lb/>A D <lb/>HENRICVM IIII. GALLI&AElig; &amp; NAVARR&AElig; <lb/>Regem Chri&longs;tiani&longs;simum. </s></p><figure id="id.035.01.001.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.001.1.jpg"/><p type="head">
  
 <s>M. D. XCIX. <lb/><emph type="italics"/>CUM PRIVILEGIO REGIS.<emph.end type="italics"/></s></p><pb/><figure></figure><p type="head"> <s id="id.000003">PARISIIS, <lb/>Apud IEREMIAM PERIER via Iacob&aelig;a, &longs;ub &longs;igno Bellerophontis. </s></p><p type="head">
  
 <s>HENRICO IIII. <lb/>GALLI&AElig; ET NAVARR&AElig; <lb/>REGI CHRISTIANISSIMO. <lb/>S. P. D.</s></p><p type="main"> <s id="id.000004">M. D. XCIX. <lb/><emph type="italics"/>CUM PRIVILEGIO REGIS. <emph.end type="italics"/></s></p><pb/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.002.jpg"/><figure id="id.035.01.002.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.002.1.jpg"/><p type="head">
  
 <s>Ecce maie&longs;tati tu&aelig;, <lb/>Rex Chri&longs;tiani&longs;&longs;ime, <lb/>nouum <expan abbr="fruct&utilde;">fructum</expan>, &amp; tan&shy;<lb/>quam primitias tu&aelig;&agrave;te <lb/>nuper re&longs;titut&aelig; Acade&shy;<lb/>mi&aelig;, Mechanica Ari&shy;<lb/>&longs;totelis philo&longs;ophorum principis Gr&ecedil;&shy;<lb/>ca, emendata, Latina facta, &amp; commen&shy;<lb/>tariis illu&longs;trata offero, dico, con&longs;ecro. <lb/></s> <s id="id.000005">HENRICO IIII. <lb/>GALLI&AElig; ET NAVARR&AElig; <lb/>REGI CHRISTIANISSIMO. <lb/>S. P. D. </s></p><p type="main">
  
 <s>Noli, ob&longs;ecrote, ad Mechanicorum ti&shy;<lb/>tulum munus hoc, qua&longs;i minus inge&shy;<lb/>nuum, nec&longs;atis liberaliingenio, nedum <lb/>imperatorio &amp; regali dignum, &longs;ubhor&shy;<lb/>re&longs;cere, &amp; ex prima i&longs;ta <expan abbr="fr&otilde;te">fronte</expan> de&longs;picere. <lb/></s> <s id="id.000006">Ecce maie&longs;tati tu&aelig;, <lb/>Rex Chri&longs;tiani&longs;&longs;ime, <lb/>nouum <expan abbr="fruct&utilde;">fructum</expan>, &amp; tan&shy;<lb/>quam primitias tu&aelig; &agrave; te <lb/>nuper re&longs;titut&aelig; Acade&shy;<lb/>mi&aelig;, Mechanica Ari&shy;<lb/>&longs;totelis philo&longs;ophorum principis Gr&ecedil;&shy;<lb/>ca, emendata, Latina facta, &amp; commen&shy;<lb/>tariis illu&longs;trata offero, dico, con&longs;ecro. <lb/></s>
  
 <s><expan abbr="Fer&utilde;t">Ferunt</expan> Platonem, quo philo&longs;ophorum <pb/>nemo de Deo diuinius, <expan abbr="neq;">neque</expan> &longs;anctius <expan abbr="s&etilde;-&longs;it">sen&shy;<lb/>&longs;it</expan>, <expan abbr="c&utilde;interrogaretur">cuninterrogaretur</expan>, quid ageret Deus, <lb/>re&longs;pondi&longs;&longs;e <foreign lang="greek">a)eigewmebei_n.</foreign> Hoc verbum Lati&shy;<lb/>n&egrave; expre&longs;&longs;um &longs;ignificat. </s> <s id="id.000007">Noli, ob&longs;ecro te, ad Mechanicorum ti&shy;<lb/>tulum munus hoc, qua&longs;i minus inge&shy;<lb/>nuum, nec &longs;atis liberali ingenio, nedum <lb/>imperatorio &amp; regali dignum, &longs;ubhor&shy;<lb/>re&longs;cere, &amp; ex prima i&longs;ta <expan abbr="fr&otilde;te">fronte</expan> de&longs;picere. <lb/></s>
  
 <s>A&longs;&longs;idu&egrave; terram <lb/>metiri. </s> <s id="id.000008"><expan abbr="Fer&utilde;t">Ferunt</expan> Platonem, quo philo&longs;ophorum <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.003.jpg"/>nemo de Deo diuinius, <expan abbr="neq;">neque</expan> &longs;anctius <expan abbr="s&etilde;&shy;&longs;it">sen&shy;<lb/>&longs;it</expan>, <expan abbr="c&utilde;interrogaretur">cum interrogaretur</expan>, quid ageret Deus, <lb/>re&longs;pondi&longs;&longs;e <foreign lang="el">a)ei gewmetrei=n. </foreign></s>
  
 <s>Qu&aelig;actio &longs;i&longs;impliciter &longs;pecte&shy;<lb/>tur, &amp;&agrave; Geometri&ecedil; nomine ridiculo, vt <lb/>alibi appellat Plato, <expan abbr="exp&etilde;datur">expendatur</expan>, ridicula, <lb/>&amp; Dei maie&longs;tate indigna iudicabitur. <lb/></s> <s id="id.000009">Hoc verbum Lati&shy;<lb/>n&egrave; expre&longs;&longs;um &longs;ignificat, A&longs;&longs;idu&egrave; terram <lb/>metiri. </s>
  
 <s>Sed &longs;i ex ip&longs;ius artis viribus, &amp; magnifi&shy;<lb/>cis promi&longs;&longs;is illud <foreign lang="greek">a)eigewmebei_n</foreign> &aelig;&longs;timetur, <lb/>quode&longs;t vniuer&longs;i <expan abbr="qu&atilde;tumuis">quantumuis</expan> fus&egrave; <expan abbr="lat&eacute;q;">lat&eacute;que</expan> <lb/>patentis, <expan abbr="corpor&utilde;">corporum</expan> in eo omnium, &longs;uper&shy;<lb/>ficierum, linearum, <expan abbr="omni&uacute;mq;">omni&uacute;mque</expan> men&longs;u&shy;<lb/>rabilium <expan abbr="m&etilde;&longs;uram">men&longs;uram</expan> ratione, proportio&shy;<lb/>ne, &longs;imilitudine con&longs;tituere, de&longs;ignare, <lb/>permetiri: actio cert&egrave; erit tant&ograve; priore <lb/>nobilior: quant&ograve; totum <expan abbr="finit&utilde;">finitum</expan> quidem, <lb/>&longs;ed infinito per&longs;imile exigua, &amp; infima <lb/>&longs;ui parte e&longs;t nobilius, &amp; excellentius: &amp; <lb/>qui <expan abbr="h&atilde;c">hanc</expan> actionem accurate ponderibus <lb/>librarit&longs;uis, <expan abbr="nequaqu&atilde;">nequaquam</expan> indignam, circa <lb/>quam Deus ver&longs;etur, &amp; &longs;e&longs;e occupet, iu&shy;<lb/>dicabit. </s> <s id="id.000010">Qu&aelig; actio &longs;i &longs;impliciter &longs;pecte&shy;<lb/>tur, &amp; &agrave; Geometri&ecedil; nomine ridiculo, vt <lb/>alibi appellat Plato, <expan abbr="exp&etilde;datur">expendatur</expan>, ridicula, <lb/>&amp; Dei maie&longs;tate indigna iudicabitur. <lb/></s>
  
 <s>Verumenimuer&ograve; &longs;iad illud <foreign lang="greek">a)eigew&shy;<lb/>mebei_n</foreign> addi&longs;&longs;et Plato, <foreign lang="greek">kai\ a)eimhxana_<gap/>ai,</foreign> luculen-<pb/>tius mult&ograve; meo iudicio, &amp; diuin&aelig; maie&shy;<lb/>&longs;tati congruentius, <expan abbr="atq;">atque</expan> magnificentius <lb/>re&longs;pondi&longs;&longs;et. </s> <s id="id.000011">Sed &longs;i ex ip&longs;ius artis viribus, &amp; magnifi&shy;<lb/>cis promi&longs;&longs;is illud <foreign lang="el">a)ei gewmetrei=n</foreign> &aelig;&longs;timetur, <lb/>quod e&longs;t vniuer&longs;i <expan abbr="qu&atilde;tumuis">quantumuis</expan> fus&egrave; <expan abbr="lat&eacute;q;">lat&eacute;que</expan> <lb/>patentis, <expan abbr="corpor&utilde;">corporum</expan> in eo omnium, &longs;uper&shy;<lb/>ficierum, linearum, <expan abbr="omni&uacute;mq;">omni&uacute;mque</expan> men&longs;u&shy;<lb/>rabilium <expan abbr="m&etilde;&longs;uram">men&longs;uram</expan> ratione, proportio&shy;<lb/>ne, &longs;imilitudine con&longs;tituere, de&longs;ignare, <lb/>permetiri: actio cert&egrave; erit tant&ograve; priore <lb/>nobilior: quant&ograve; totum <expan abbr="finit&utilde;">finitum</expan> quidem, <lb/>&longs;ed infinito per&longs;imile exigua, &amp; infima <lb/>&longs;ui parte e&longs;t nobilius, &amp; excellentius: &amp; <lb/>qui <expan abbr="h&atilde;c">hanc</expan> actionem accurate ponderibus <lb/>librarit &longs;uis, <expan abbr="nequaqu&atilde;">nequaquam</expan> indignam, circa <lb/>quam Deus ver&longs;etur, &amp; &longs;e&longs;e occupet, iu&shy;<lb/>dicabit. </s>
  
 <s>Quid enim e&longs;t Mundum <lb/>huncex nihilo condidi&longs;&longs;e: &longs;uis omnibus <lb/>numeris ab&longs;olui&longs;&longs;e: ponderibus <expan abbr="vndiq;">vndique</expan> <lb/>&longs;uis &aelig;quilibra&longs;&longs;e: longitudine, latitudi&shy;<lb/>ne, altitudine, in omni habitudine, &amp; <lb/>re&longs;pectu commen&longs;uraui&longs;&longs;e: eund&eacute;m&shy;<lb/>que in eodem &longs;tatu &amp; perfectione a&longs;&longs;i&shy;<lb/>du&ograve; retinere, &longs;tabilire, con&longs;eruare, quam <lb/><foreign lang="greek">a)eigewmetrei_n kai\ a)eimhxana_<gap/>ai?</foreign> Mundus enim <lb/>hic machina e&longs;t, &amp; quidem machina&shy;<lb/>rum maxima, efficaci&longs;&longs;ima, firmi&longs;&longs;ima, <lb/>formo&longs;i&longs;&longs;ima. </s> <s id="id.000012">Verumenimuer&ograve; &longs;i ad illud <foreign lang="el">a)ei gew&shy;<lb/>mtrei=n</foreign> addi&longs;&longs;et Plato, <foreign lang="el">kai\ a)eimhxana=sqai,</foreign> luculen&shy;<pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.004.jpg"/>tius mult&ograve; meo iudicio, &amp; diuin&aelig; maie&shy;<lb/>&longs;tati congruentius, <expan abbr="atq;">atque</expan> magnificentius <lb/>re&longs;pondi&longs;&longs;et. </s>
  
 <s>An non omnia corpora <lb/>complectitur, quod eius <expan abbr="imm&etilde;&longs;itatem">immen&longs;itatem</expan> <lb/>arguit? </s> <s id="id.000013">Quid enim e&longs;t Mundum <lb/>hunc ex nihilo condidi&longs;&longs;e: &longs;uis omnibus <lb/>numeris ab&longs;olui&longs;&longs;e: ponderibus <expan abbr="vndiq;">vndique</expan> <lb/>&longs;uis &aelig;quilibra&longs;&longs;e: longitudine, latitudi&shy;<lb/>ne, altitudine, in omni habitudine, &amp; <lb/>re&longs;pectu commen&longs;uraui&longs;&longs;e: eund&eacute;m&shy;<lb/>que in eodem &longs;tatu &amp; perfectione a&longs;&longs;i&shy;<lb/>du&ograve; retinere, &longs;tabilire, con&longs;eruare, quam <lb/><foreign lang="el">a)ei gewmetrei=n kai\ a)eimhxana=sqai?</foreign> Mundus enim <lb/>hic machina e&longs;t, &amp; quidem machina&shy;<lb/>rum maxima, efficaci&longs;&longs;ima, firmi&longs;&longs;ima, <lb/>formo&longs;i&longs;&longs;ima. </s>
  
 <s>An <expan abbr="n&otilde;">non</expan> ad omnium mutabilium <lb/>lationem, alterationem, generationem, <lb/>auctionem, con&longs;eruationem, &amp; <expan abbr="dura-tion&etilde;">dura&shy;<lb/>tionem</expan>, vt Dei &longs;ui auctoris <expan abbr="in&longs;trum&etilde;tum">in&longs;trumentum</expan> <lb/>concurrit, quod eius vim, &amp; efficaciam <lb/>o&longs;tendit? </s> <s id="id.000014">An non omnia corpora <lb/>complectitur, quod eius <expan abbr="imm&etilde;&longs;itatem">immen&longs;itatem</expan> <lb/>arguit? </s>
  
 <s>An non quinquies mille <expan abbr="quin-g&etilde;tos">quin&shy;<lb/>gentos</expan> &longs;exaginta &amp; <expan abbr="vn&utilde;">vnum</expan> annos, quoad &longs;ui <lb/><expan abbr="quinq;">quinque</expan> partes primas, &amp; &longs;implices, per&shy;<lb/>&longs;euerat omnis mutationis expers: quod <pb/>eius <expan abbr="firmitat&etilde;">firmitatem</expan> plu&longs;quam adamantinam <lb/>te&longs;tatur? </s> <s id="id.000015">An <expan abbr="n&otilde;">non</expan> ad omnium mutabilium <lb/>lationem, alterationem, generationem, <lb/>auctionem, con&longs;eruationem, &amp; <expan abbr="dura&shy;tion&etilde;">dura&shy;<lb/>tionem</expan>, vt Dei &longs;ui auctoris <expan abbr="in&longs;trum&etilde;tum">in&longs;trumentum</expan> <lb/>concurrit, quod eius vim, &amp; efficaciam <lb/>o&longs;tendit? </s>
  
 <s>An non huius totius ad omnes <lb/>&longs;uas partes, &amp; omnium <expan abbr="&longs;uar&utilde;">&longs;uarum</expan> partium, <lb/>particularum que cum inter&longs;e, tum ad <lb/>ip&longs;um &longs;ummus e&longs;t con&longs;en&longs;us, con&longs;pira&shy;<lb/>tio &longs;umma, omnium hominum oculis <lb/>&amp; menti iucun di&longs;sima &longs;ymmetria, pro&shy;<lb/>portio, &aelig;quabilitas, vn&agrave; cum totius fi&shy;<lb/>gura pulcherrima, &amp; conuenienti&longs;&longs;ima, <lb/>qu&aelig; vnica e&longs;t &longs;uperficie terminata pari&shy;<lb/>bus ab vno puncto vndique di&longs;tante <lb/>interuallis, &amp; cum tot <expan abbr="a&longs;tror&utilde;">a&longs;trorum</expan> tan quam <lb/>gemmarum pretio&longs;i&longs;&longs;imarum h&icirc;c ill&icirc;c <lb/>in eminentiori, &amp; apparentiori &longs;ui par&shy;<lb/>te collocatorum perenniluce, qua qua&shy;<lb/>litate nec formo&longs;ior, nec <expan abbr="homin&utilde;">hominum</expan> ocu&shy;<lb/>lis gratior, nec v&longs;ibus humanis vtilior <lb/>apparere pote&longs;t: quod eius pulchritudi&shy;<lb/>nem vbique o&longs;tentat, &amp; mirabiles &longs;ui <lb/>ip&longs;i^{9} amores excitat? </s> <s id="id.000016">An non quinquies mille <expan abbr="quin&shy;g&etilde;tos">quin&shy;<lb/>gentos</expan> &longs;exaginta &amp; <expan abbr="vn&utilde;">vnum</expan> annos, quoad &longs;ui <lb/><expan abbr="quinq;">quinque</expan> partes primas, &amp; &longs;implices, per&shy;<lb/>&longs;euerat omnis mutationis expers: quod <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.005.jpg"/>eius <expan abbr="firmitat&etilde;">firmitatem</expan> plu&longs;quam adamantinam <lb/>te&longs;tatur? </s>
  
 <s>Deus igitur, <expan abbr="pr&ecedil;ter-qu&atilde;">pr&ecedil;ter&shy;<lb/>quam</expan> quod e&longs;t accurati&longs;&longs;imus, <expan abbr="a&longs;&longs;iduu&longs;q;">a&longs;&longs;iduu&longs;que</expan> <lb/>Geometra, diuini Platonis <expan abbr="&longs;ent&etilde;tia">&longs;ententia</expan>, e&longs;t <lb/>etiam no&longs;tra, &amp; operum tot magnifi&shy;<lb/>corum euidentia, &longs;apienti&longs;&longs;imus, opti-<pb/>mus, potenti&longs;&longs;imus <foreign lang="greek">mhxanao\s,</foreign> &amp; <foreign lang="greek">mhxanepoio\s.</foreign><lb/>Ip&longs;eidem, qui <foreign lang="greek">makro/kosmon</foreign> magnum mun&shy;<lb/>dum fecit, fecit &amp; <foreign lang="greek">mikro/kosmon</foreign> <expan abbr="paru&utilde;">paruum</expan> mun&shy;<lb/>dum, hominem &longs;cilicet: &amp; fecit ad ima&shy;<lb/>ginem &longs;uam, atque vt &longs;e imitaretur beni&shy;<lb/>gni&longs;&longs;ima liberalitate impertitus e&longs;t ei <lb/>mentem, qu&aelig; e&longs;&longs;et <foreign lang="greek">te/xnh te/xnwn,</foreign> ars artium, <lb/>&amp; manum, qu&aelig; e&longs;&longs;et <foreign lang="greek">o)/rganono)rga/nwn,</foreign> in&longs;tru&shy;<lb/>mentum in&longs;trumentorum, quibus ho&shy;<lb/>mo, quem volebat e&longs;&longs;e &longs;apienti&longs;&longs;imum <lb/>animalium, machinas &amp; in&longs;trumenta <lb/>alia fabricaretur, &amp; iis adiutus &longs;olus, vel <lb/>cum paucis onera quantumuis ingentia <lb/>dimoueret, deduceret, quo vellet collo&shy;<lb/>caret: vrbes, <expan abbr="t&etilde;pla">templa</expan>, palatia, collegia, por&shy;<lb/>ticus, pontes, domos &aelig;dificaret, perde&shy;<lb/>ret, re&longs;tauraret, con&longs;eruaret: terram ver&shy;<lb/>teret, in terr&aelig; vi&longs;cera de&longs;cenderet, terr&aelig; <lb/>campos, valles, montes bigis, quadrigis <lb/>peragraret: maria omnia, fluuios remis, <lb/>velis tranaret: ventis imperaret: anima&shy;<lb/>lium genus omne &longs;ibi &longs;ubiiceret: tantas <lb/><expan abbr="deniq;">denique</expan>, &amp; tam multas resfaceret, vt eas, <lb/>ni&longs;i quotidie fieri, &amp; factas e&longs;&longs;e &longs;&aelig;pius <pb/>alij homines &longs;pectarent, omnin&ograve; fieri <lb/>non po&longs;&longs;e iurarent. </s> <s id="id.000017">An non huius totius ad omnes <lb/>&longs;uas partes, &amp; omnium <expan abbr="&longs;uar&utilde;">&longs;uarum</expan> partium, <lb/>particularum que cum inter &longs;e, tum ad <lb/>ip&longs;um &longs;ummus e&longs;t con&longs;en&longs;us, con&longs;pira&shy;<lb/>tio &longs;umma, omnium hominum oculis <lb/>&amp; menti iucundi&longs;sima &longs;ymmetria, pro&shy;<lb/>portio, &aelig;quabilitas, vn&agrave; cum totius fi&shy;<lb/>gura pulcherrima, &amp; conuenienti&longs;&longs;ima, <lb/>qu&aelig; vnica e&longs;t &longs;uperficie terminata pari&shy;<lb/>bus ab vno puncto vndique di&longs;tante <lb/>interuallis, &amp; cum tot <expan abbr="a&longs;tror&utilde;">a&longs;trorum</expan> tanquam <lb/>gemmarum pretio&longs;i&longs;&longs;imarum h&icirc;c ill&icirc;c <lb/>in eminentiori, &amp; apparentiori &longs;ui par&shy;<lb/>te collocatorum perenni luce, qua qua&shy;<lb/>litate nec formo&longs;ior, nec <expan abbr="homin&utilde;">hominum</expan> ocu&shy;<lb/>lis gratior, nec v&longs;ibus humanis vtilior <lb/>apparere pote&longs;t: quod eius pulchritudi&shy;<lb/>nem vbique o&longs;tentat, &amp; mirabiles &longs;ui <lb/>ip&longs;ius amores excitat? </s>
  
 <s>Iidem cum facta&shy;<lb/>rum rationes, virium que in in&longs;trumen&shy;<lb/>tis, &amp; machinis adhibitis cau&longs;as non in&shy;<lb/>telligunt, miracula e&longs;&longs;e pleno ore pro&shy;<lb/>clamant. </s> <s id="id.000018">Deus igitur, <expan abbr="pr&ecedil;ter&shy;qu&atilde;">pr&ecedil;ter&shy;<lb/>quam</expan> quod e&longs;t accurati&longs;&longs;imus, <expan abbr="a&longs;&longs;iduu&longs;q;">a&longs;&longs;iduu&longs;que</expan> <lb/>Geometra, diuini Platonis <expan abbr="&longs;ent&etilde;tia">&longs;ententia</expan>, e&longs;t <lb/>etiam no&longs;tra, &amp; operum tot magnifi&shy;<lb/>corum euidentia, &longs;apienti&longs;&longs;imus, opti&shy;<pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.006.jpg"/>mus, potenti&longs;&longs;imus <foreign lang="el">mhxaniko\s,</foreign> &amp; <foreign lang="el">mhxanopoio\s. </foreign><lb/></s>
  <s>Ip&longs;e idem, qui <foreign lang="el">makro/kosmon</foreign> magnum mun&shy;<lb/>dum fecit, fecit &amp; <foreign lang="el">mikro/kosmon</foreign> <expan abbr="paru&utilde;">paruum</expan> mun&shy;<lb/>dum, hominem &longs;cilicet: &amp; fecit ad ima&shy;<lb/>ginem &longs;uam, atque vt &longs;e imitaretur beni&shy;<lb/>gni&longs;&longs;ima liberalitate impertitus e&longs;t ei <lb/>mentem, qu&aelig; e&longs;&longs;et <foreign lang="el">te/xnh te/xnwn,</foreign> ars artium, <lb/>&amp; manum, qu&aelig; e&longs;&longs;et <foreign lang="el">o)/rganon o)rga/nwn,</foreign> in&longs;tru&shy;<lb/>mentum in&longs;trumentorum, quibus ho&shy;<lb/>mo, quem volebat e&longs;&longs;e &longs;apienti&longs;&longs;imum <lb/>animalium, machinas &amp; in&longs;trumenta <lb/>alia fabricaretur, &amp; iis adiutus &longs;olus, vel <lb/>cum paucis onera quantumuis ingentia <lb/>dimoueret, deduceret, quo vellet collo&shy;<lb/>caret: vrbes, <expan abbr="t&etilde;pla">templa</expan>, palatia, collegia, por&shy;<lb/>ticus, pontes, domos &aelig;dificaret, perde&shy;<lb/>ret, re&longs;tauraret, con&longs;eruaret: terram ver&shy;<lb/>teret, in terr&aelig; vi&longs;cera de&longs;cenderet, terr&aelig; <lb/>campos, valles, montes bigis, quadrigis <lb/>peragraret: maria omnia, fluuios remis, <lb/>velis tranaret: ventis imperaret: anima&shy;<lb/>lium genus omne &longs;ibi &longs;ubiiceret: tantas <lb/><expan abbr="deniq;">denique</expan>, &amp; tam multas res faceret, vt eas, <lb/>ni&longs;i quotidie fieri, &amp; factas e&longs;&longs;e &longs;&aelig;pius <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.007.jpg"/>alij homines &longs;pectarent, omnin&ograve; fieri <lb/>non po&longs;&longs;e iurarent. </s>
  
 <s>Vndefort&egrave;illud Martialis.</s></p><p type="main"> <s id="id.000019">Iidem cum facta&shy;<lb/>rum rationes, virium que in in&longs;trumen&shy;<lb/>tis, &amp; machinis adhibitis cau&longs;as non in&shy;<lb/>telligunt, miracula e&longs;&longs;e pleno ore pro&shy;<lb/>clamant. </s>
  
 <s><emph type="italics"/>Barbara Pyramidum &longs;ileat miracula <lb/>Memphis.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000020">Vnde fort&egrave; illud Martialis. </s></p><p type="main">
  
 <s>Tum &longs;eptem illa, qu&aelig; vulg&ograve; iactantur <lb/>orbis miracula. </s> <s id="id.000021"><emph type="italics"/>Barbara Pyramidum &longs;ileat miracula <lb/>Memphis. <emph.end type="italics"/></s></p><p type="main">
  
 <s>Qu&aelig; profect&ograve; &longs;apien&shy;<lb/>ter Deus homini dedit &amp; po&longs;&longs;e, &amp; fa&shy;<lb/>bricari: ne mundum hunc &agrave;&longs;e <expan abbr="c&otilde;ditum">conditum</expan>, <lb/>con&longs;eruatum, con&longs;eruandum, quandiu <lb/>voluerit, hominibus foret incredibile. <lb/></s> <s id="id.000022">Tum &longs;eptem illa, qu&aelig; vulg&ograve; iactantur <lb/>orbis miracula. </s>
  
 <s>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/>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.000023">Qu&aelig; profect&ograve; &longs;apien&shy;<lb/>ter Deus homini dedit &amp; po&longs;&longs;e, &amp; fa&shy;<lb/>bricari: ne mundum hunc &agrave; &longs;e <expan abbr="c&otilde;ditum">conditum</expan>, <lb/>con&longs;eruatum, con&longs;eruandum, quandiu <lb/>voluerit, hominibus foret incredibile. <lb/></s>
  
 <s>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.000024">His enim tantis, &amp; tam multis qu&aelig; ab <lb/>homine <foreign lang="el">mhxanopoihtikw=|</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&shy;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="el">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>In quo enim immen&longs;usille au&shy;<lb/>thor, factorque hominis, in proprij <lb/>operis fabricahomini 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.000025">Hic autem quis pote&longs;t e&longs;&longs;e <lb/>alius, pr&aelig;terquam is, quem Deum om&shy;<lb/>nes appellamus. </s>
  
 <s>quan&shy;<lb/>quam po&longs;t &longs;emel &agrave; &longs;e mundum ex nihilo <lb/>creatum, ille liberrimum &longs;emper, &amp; po&shy;<lb/>tenti&longs;&longs;imum agens, cum his adiunctis, <lb/>&amp; &longs;ine his quando, quotie&longs;que vult, ni&shy;<lb/>hilominus operatur. </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>Qu&aelig; &longs;i rect&egrave; &amp; ve&shy;<lb/>r&egrave; Deo, <expan abbr="quant&utilde;">quantum</expan> fas e&longs;t homini, dicta <lb/>&longs;unt: ecquidiam &longs;upere&longs;t, Rex Chri&longs;tia&shy;<pb/>ni&longs;&longs;ime, quapropter ab hoc munere vt <lb/>vili abhorreas, &amp; ip&longs;e reformidem, licet <lb/>Mechanicorum <expan abbr="titul&utilde;">titulum</expan> in fronti&longs;picio <lb/>gerat, hoc ade&ograve; in&longs;igne opus ab Ari&shy;<lb/>&longs;totele profectum, vtile, <expan abbr="iuc&utilde;dum">iucundum</expan>, &longs;ub&shy;<lb/>tili&longs;&longs;im&egrave; tractatum: &longs;ed temporum iniu&shy;<lb/>ria multis mendis f&oelig;dum, ob&longs;curum, <lb/>captu difficile, nunc opera no&longs;tra niti&shy;<lb/>dum, clarum, &amp; captu facile &longs;anct&aelig; ma&shy;<lb/>ie&longs;tati tu&aelig; dicare, ac <expan abbr="c&otilde;&longs;ecrare">con&longs;ecrare</expan>? </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>Ad quod <lb/>faciendum in&longs;uper me inuitauit cau&longs;a <lb/>alia, ni&longs;i me fallit animus, iu&longs;ti&longs;&longs;ima. <lb/></s> <s id="id.000027">quan&shy;<lb/>quam po&longs;t &longs;emel &agrave; &longs;e mundum ex nihilo <lb/>creatum, ille liberrimum &longs;emper, &amp; po&shy;<lb/>tenti&longs;&longs;imum agens, cum his adiunctis, <lb/>&amp; &longs;ine his quando, quotie&longs;que vult, ni&shy;<lb/>hilominus operatur. </s>
  
 <s>Qui&longs;quis enim duas res omnium, qu&aelig; <lb/>&longs;untin vita <expan abbr="homin&utilde;">hominum</expan>, maximas perfecit, <lb/>quar&uacute;mque temporibus atque fabricis <lb/>&longs;ummus e&longs;t &amp; frequenti&longs;&longs;imus machi&shy;<lb/>narum, &amp; <expan abbr="in&longs;trum&etilde;torum">in&longs;trumentorum</expan> v&longs;us: ille non <lb/>pote&longs;t machinamentorum, &amp; <expan abbr="in&longs;tru-m&etilde;torum">in&longs;tru&shy;<lb/>mentorum</expan> formis, rationibus, adinuen&shy;<lb/>tionibus, &amp; virium <expan abbr="eor&utilde;">eorum</expan> admirabilium, <lb/><expan abbr="incredibiliumq;">incredibiliumque</expan> cau&longs;is, ac principiis per <lb/>ceptis non magno pere delectari, atque <lb/>cos, qui de iis &longs;ubtiliter, &amp; ingeniose tra&shy;<lb/>ctarint, libros oblatos non grati&longs;&longs;im&egrave; <pb/>excipere: tu, Rex potenti&longs;&longs;ime, duas il&shy;<lb/>las res perfeci&longs;ti, bellum &longs;cilicet, &amp; pa&shy;<lb/>cem. </s> <s id="id.000028">Qu&aelig; &longs;i rect&egrave; &amp; ve&shy;<lb/>r&egrave; Deo, <expan abbr="quant&utilde;">quantum</expan> fas e&longs;t homini, dicta <lb/>&longs;unt: ecquid iam &longs;upere&longs;t, Rex Chri&longs;tia&shy;<pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.009.jpg"/>ni&longs;&longs;ime, quapropter ab hoc munere vt <lb/>vili abhorreas, &amp; ip&longs;e reformidem, licet <lb/>Mechanicorum <expan abbr="titul&utilde;">titulum</expan> in fronti&longs;picio <lb/>gerat, hoc ade&ograve; in&longs;igne opus ab Ari&shy;<lb/>&longs;totele profectum, vtile, <expan abbr="iuc&utilde;dum">iucundum</expan>, &longs;ub&shy;<lb/>tili&longs;&longs;im&egrave; tractatum: &longs;ed temporum iniu&shy;<lb/>ria multis mendis f&oelig;dum, ob&longs;curum, <lb/>captu difficile, nunc opera no&longs;tra niti&shy;<lb/>dum, clarum, &amp; captu facile &longs;anct&aelig; ma&shy;<lb/>ie&longs;tati tu&aelig; dicare, ac <expan abbr="c&otilde;&longs;ecrare">con&longs;ecrare</expan>? </s>
  
 <s>In vtriu&longs;que tempore a&longs;&longs;iduus ma&shy;<lb/>chinarum, &amp; in&longs;trumentorum v&longs;us, at&shy;<lb/>que opportunitas. </s> <s id="id.000029">Ad quod <lb/>faciendum in&longs;uper me inuitauit cau&longs;a <lb/>alia, ni&longs;i me fallit animus, iu&longs;ti&longs;&longs;ima. <lb/></s>
  
 <s>Tunam que bellum <lb/>(h&icirc;c me patiare, rex potenti&longs;&longs;ime, in me&shy;<lb/>ritas aliquot tuas laudes paul&ograve; amplius, <lb/>non extra rem tamen excurrere, &amp; ex&shy;<lb/>patiari.) Tu inquam bellum (&ocirc; onus <lb/><foreign lang="greek">kolo<gap/>ikw/ta<gap/>on,</foreign> graui&longs;&longs;imum cert&egrave;, &amp; num&shy;<lb/>quam &longs;i fieri po&longs;&longs;et, commouendum: <lb/>vbi, vbitamen nece&longs;&longs;arium e&longs;t, mouen&shy;<lb/>dum, &longs;u&longs;cipiendum, gerendum) ad&shy;<lb/>uer&longs;us dome&longs;ticos in&longs;anientes, rebel&shy;<lb/>le&longs;que: aduer&longs;us extraneos intraneo&shy;<lb/>rum tumultu &longs;uperbientes, ferocien&shy;<lb/>tes, &amp; occa&longs;ionem regni inuadendi <lb/>opportuni&longs;&longs;imam nacto&scedil; &amp; nihil non <lb/>inde &longs;ibi polliciti&scedil; animo plu&longs;quam <lb/>Herculeo &longs;u&longs;cepi&longs;ti: hoc ip&longs;um, li&shy;<lb/>cet omnium bellorum, quorum hi&shy;<lb/>&longs;torias, &amp; annales no&longs;tros legens me&shy;<lb/>mini&longs;&longs;e mihi videor, acerbi&longs;&longs;imum, <pb/>pernitio&longs;i&longs;&longs;imum, exitio&longs;i&longs;&longs;imumque, <lb/>plurium intus &amp; foris contentione, &amp; <lb/><expan abbr="c&otilde;iuratione">coniuratione</expan> vi&longs;um in&longs;uperabile, moui&shy;<lb/>&longs;ti, ge&longs;&longs;i&longs;ti, &longs;uperaui&longs;ti. </s> <s id="id.000030">Qui&longs;quis enim duas res omnium, qu&aelig; <lb/>&longs;unt in vita <expan abbr="homin&utilde;">hominum</expan>, maximas perfecit, <lb/>quar&uacute;mque temporibus atque fabricis <lb/>&longs;ummus e&longs;t &amp; frequenti&longs;&longs;imus machi&shy;<lb/>narum, &amp; <expan abbr="in&longs;trum&etilde;torum">in&longs;trumentorum</expan> v&longs;us: ille non <lb/>pote&longs;t machinamentorum, &amp; <expan abbr="in&longs;tru&shy;m&etilde;torum">in&longs;tru&shy;<lb/>mentorum</expan> formis, rationibus, adinuen&shy;<lb/>tionibus, &amp; virium <expan abbr="eor&utilde;">eorum</expan> admirabilium, <lb/><expan abbr="incredibiliumq;">incredibiliumque</expan> cau&longs;is, ac principiis per<lb/>ceptis non magnopere delectari, atque <lb/>eos, qui de iis &longs;ubtiliter, &amp; ingeniose tra&shy;<lb/>ctarint, libros oblatos non grati&longs;&longs;im&egrave; <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.010.jpg"/>excipere: tu, Rex potenti&longs;&longs;ime, duas il&shy;<lb/>las res perfeci&longs;ti, bellum &longs;cilicet, &amp; pa&shy;<lb/>cem. </s>
  
 <s>Quomodo <expan abbr="aut&etilde;">autem</expan>? <lb/></s> <s id="id.000031">In vtriu&longs;que tempore a&longs;&longs;iduus ma&shy;<lb/>chinarum, &amp; in&longs;trumentorum v&longs;us, at&shy;<lb/>que opportunitas. </s>
  
 <s>dicam pro meo &longs;en&longs;u: tu melius. </s> <s id="id.000032">Tu namque bellum <lb/>(h&icirc;c me patiare, rex potenti&longs;&longs;ime, in me&shy;<lb/>ritas aliquot tuas laudes paul&ograve; amplius, <lb/>non extra rem tamen excurrere, &amp; ex&shy;<lb/>patiari.) Tu inquam bellum (&ocirc; onus <lb/><foreign lang="el">kolossikw/taton,</foreign> graui&longs;&longs;imum cert&egrave;, &amp; num&shy;<lb/>quam &longs;i fieri po&longs;&longs;et, commouendum: <lb/>vbi, vbi tamen nece&longs;&longs;arium e&longs;t, mouen&shy;<lb/>dum, &longs;u&longs;cipiendum, gerendum) ad&shy;<lb/>uer&longs;us dome&longs;ticos in&longs;anientes, rebel&shy;<lb/>le&longs;que: aduer&longs;us extraneos intraneo&shy;<lb/>rum tumultu &longs;uperbientes, ferocien&shy;<lb/>tes, &amp; occa&longs;ionem regni inuadendi <lb/>opportuni&longs;&longs;imam nacto&scedil; &amp; nihil non <lb/>inde &longs;ibi polliciti&scedil; animo plu&longs;quam <lb/>Herculeo &longs;u&longs;cepi&longs;ti: hoc ip&longs;um, li&shy;<lb/>cet omnium bellorum, quorum hi&shy;<lb/>&longs;torias, &amp; annales no&longs;tros legens me&shy;<lb/>mini&longs;&longs;e mihi videor, acerbi&longs;&longs;imum, <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.011.jpg"/>pernitio&longs;i&longs;&longs;imum, exitio&longs;i&longs;&longs;imumque, <lb/>plurium intus &amp; foris contentione, &amp; <lb/><expan abbr="c&otilde;iuratione">coniuratione</expan> vi&longs;um in&longs;uperabile, moui&shy;<lb/>&longs;ti, ge&longs;&longs;i&longs;ti, &longs;uperaui&longs;ti. </s>
  
 <s>Omnes <lb/>omnium tuarum prouinciarum &longs;ubie&shy;<lb/>ctos rebelles, partim armis, qu&aelig; fuit tua <lb/>in pugnando terribilis &longs;emper inimicis <lb/>&amp; audacia, &amp; fortitudo: partim auro ex <lb/>propriis eorum fodinis effo&longs;&longs;o, recto <lb/>&longs;an&egrave; iudicio, qu&aelig; tua fuit &longs;umma cum <lb/>prudentia iu&longs;ticia, vtin po&longs;terum &longs;ciant <lb/>&longs;uis &agrave; Deo datis obtemperare regibus, <lb/>neque vnquam ab illorum contrariis <lb/>&longs;tare partibus: partim benignitate, &amp; <lb/>man&longs;uetudine, qu&aelig; te &longs;uperis pulcher&shy;<lb/>rima &aelig;quat virtus.</s></p><p type="main"> <s id="id.000033">Quomodo <expan abbr="aut&etilde;">autem</expan>? <lb/></s>
  
 <s><emph type="italics"/>Nam<emph.end type="italics"/> (vt ait grauis vnus &egrave; po&euml;tis) <emph type="italics"/>cum <lb/>vincamur in omni<emph.end type="italics"/></s></p><p type="main"> <s id="id.000034">dicam pro meo &longs;en&longs;u: tu melius. </s>
  
 <s><emph type="italics"/>Munere: &longs;ola Deos &aelig;quat clementia nobis.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000035">Omnes <lb/>omnium tuarum prouinciarum &longs;ubie&shy;<lb/>ctos rebelles, partim armis, qu&aelig; fuit tua <lb/>in pugnando terribilis &longs;emper inimicis <lb/>&amp; audacia, &amp; fortitudo: partim auro ex <lb/>propriis eorum fodinis effo&longs;&longs;o, recto <lb/>&longs;an&egrave; iudicio, qu&aelig; tua fuit &longs;umma cum <lb/>prudentia iu&longs;ticia, vt in po&longs;terum &longs;ciant <lb/>&longs;uis &agrave; Deo datis obtemperare regibus, <lb/>neque vnquam ab illorum contrariis <lb/>&longs;tare partibus: partim benignitate, &amp; <lb/>man&longs;uetudine, qu&aelig; te &longs;uperis pulcher&shy;<lb/>rima &aelig;quat virtus. </s></p><p type="main">
  
 <s>Ad concordiam inter &longs;e, &amp; tecum &longs;er&shy;<lb/>uandam: ad beneuolentiam ergate pr&aelig;&shy;<lb/>&longs;tandam, obedientiam, fidelitatem rede<gap/><lb/>gi&longs;ti. </s> <s id="id.000036"><emph type="italics"/>Nam<emph.end type="italics"/> (vt ait grauis vnus &egrave; po&euml;tis) <emph type="italics"/>cum <lb/>vincamur in omni<emph.end type="italics"/></s></p><p type="main">
  
 <s>Extraneos ver&ograve; longo bello: bre-<pb/>uioritamen, quam &longs;perare, aut promit&shy;<lb/>tere nobis au&longs;i fuerimus, fractos, &longs;&aelig;pe <lb/>Marte aperto, &amp; manibus <expan abbr="vtrinq;">vtrinque</expan> con&shy;<lb/>&longs;ertis victos, fugatos, tandem procul <lb/>ab omnibus Galli&aelig; finibus reieci&longs;ti: &amp; <lb/>quan quam ante&agrave; &longs;emperab omni pacis <lb/>conditione alieni&longs;&longs;imos, vt pacem ip&longs;i <lb/>appeterent, &amp; peterent co&euml;gi&longs;ti. </s> <s id="id.000037"><emph type="italics"/>Munere: &longs;ola Deos &aelig;quat clementia nobis. <emph.end type="italics"/></s></p><p type="main">
  
 <s>Quid <lb/>tuilico? </s> <s id="id.000038">Ad concordiam inter &longs;e, &amp; tecum &longs;er&shy;<lb/>uandam: ad beneuolentiam ergate pr&aelig;&shy;<lb/>&longs;tandam, obedientiam, fidelitatem rede&shy;<lb/>gi&longs;ti. </s>
  
 <s>Quandoquidem pax victo &longs;em&shy;<lb/>per &longs;it nece&longs;&longs;aria, &amp; victoriea, qu&aelig; nihil <lb/>po&longs;t &longs;e ferat in&longs;idiarum, &longs;emper expe&shy;<lb/>diat: &longs;tatim eius ineund&aelig;, &amp; cum <expan abbr="po-t&etilde;ti&longs;&longs;imo">po&shy;<lb/>tenti&longs;&longs;imo</expan> ho&longs;te Philippo Hi&longs;paniarum <lb/>rege conciliand&aelig; <expan abbr="occa&longs;ion&etilde;">occa&longs;ionem</expan> qu&aelig;&longs;itam, <lb/>&amp; oblatam &agrave; Clemente VIII. pontifice <lb/>&longs;ummo, ver&egrave; vtriu&longs;que gentis commu&shy;<lb/>ni <expan abbr="par&etilde;te">parente</expan> clementi&longs;&longs;imo, per &longs;uum lega&shy;<lb/>tum Alexandrum de Medicis Cardina&shy;<lb/>lem, &amp; Archiepi&longs;copum Florentinum, <lb/>qui huic paci tractand&aelig;, conficiend&aelig;, <lb/>&amp; ni&longs;i perfectare <expan abbr="n&otilde;">non</expan> relinquend&aelig; &longs;em&shy;<lb/>per interfuit, &amp; qua&longs;i pr&aelig;fuit, arripui&shy;<lb/>&longs;ti. </s> <s id="id.000039">Extraneos ver&ograve; longo bello: bre&shy;<pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.012.jpg"/>uiori tamen, quam &longs;perare, aut promit&shy;<lb/>tere nobis au&longs;i fuerimus, fractos, &longs;&aelig;pe <lb/>Marte aperto, &amp; manibus <expan abbr="vtrinq;">vtrinque</expan> con&shy;<lb/>&longs;ertis victos, fugatos, tandem procul <lb/>ab omnibus Galli&aelig; finibus reieci&longs;ti: &amp; <lb/>quanquam ante&agrave; &longs;emper ab omni pacis <lb/>conditione alieni&longs;&longs;imos, vt pacem ip&longs;i <lb/>appeterent, &amp; peterent co&euml;gi&longs;ti. </s>
  
 <s>Duobus etuo &longs;anctiore con&longs;ilio de&shy;<lb/>lectis con&longs;iliariis tibi, id e&longs;t patri&aelig; <pb/>&longs;aluti addicti&longs;&longs;imis (permittes bona tua <lb/>venia, Rex clementi&longs;&longs;ime, honoris &amp; <lb/>grat&aelig; erga viros tam bene de te, totaque <lb/>Gallia meritos memori&aelig; no&longs;tr&aelig; gratia, <lb/>h&icirc;c illos nominari) Pomponio Belle&shy;<lb/>ureo &amp; Nicolao Brulartio, toto tant&aelig; <lb/>molis negotio perte commi&longs;&longs;o, pacem <lb/>tibi, tuis, toti Galli&aelig; honorificenti&longs;&longs;i&shy;<lb/>mam conciliaui&longs;ti: pacem inquam ab&shy;<lb/>&longs;entem, &amp; ad multos annos exulem re&shy;<lb/>duxi&longs;ti: iureiurando &longs;olemni&longs;&longs;imo, &longs;i&shy;<lb/>gillis vtriu&longs;que regni confirmatam per <lb/>pr&aelig;cones tuos proclamari iu&longs;&longs;i&longs;ti: arma <lb/>de manibus militum, qu&aelig; erant &longs;umpta <lb/>pro te, &amp; contra te &longs;u&longs;tuli&longs;ti: iam tuo&shy;<lb/>rum in ligones, aratrorum dentes, fal&shy;<lb/>ces, vngues ferreos, vectes, trochleas, <lb/>malleos, aliaque in&longs;trumenta vit&aelig; mi&shy;<lb/>tioris, &amp; pacific&aelig; conuerti&longs;ti: iam arua <lb/>feracis Galli&aelig; recoli c&oelig;pta, vbique re&shy;<lb/>uire&longs;cunt: l&aelig;t&aelig; &longs;egetes, agri vberes cul&shy;<lb/>mis ari&longs;ti&longs;que luxuriant: ex &aelig;dificijs &longs;e&shy;<lb/>miruta re&longs;taurantur, dirutorum loco <lb/>noua &longs;tatuuntur: leges liber&egrave; pronun-<pb/>ciant: iu&longs;ticia libritenens fide zygo&longs;tati&shy;<lb/>ca omnia iudicat: linguarum &amp; bona&shy;<lb/>rum <expan abbr="arti&utilde;">artium</expan>, te earum re&longs;tauratore, &amp; vin&shy;<lb/>dice &amp; cu&longs;tode, eruditio in <expan abbr="Academi&atilde;">Academiam</expan> <lb/>reuer&longs;a frequentatur: ingenia, qu&aelig; in ea <lb/>&longs;unt pr&aelig;clara, in variarum artium iam <lb/>redundant elegantiam, f&oelig;tu&longs;que &longs;uos <lb/>producere ge&longs;tiunt: mercatura denique <lb/>tut&ograve; vagatur, peregrinatur, ru&longs;ticatur. <lb/></s> <s id="id.000040">Quid <lb/>tu ilico? </s>
  
 <s>Harum duarum rerum belli, &amp; pacis <lb/>magnitudinem, <expan abbr="difficultat&etilde;">difficultatem</expan>, <expan abbr="impedim&etilde;-ta">impedimen&shy;<lb/>ta</expan> &longs;oli <expan abbr="c&otilde;plectentur">complectentur</expan>, quitam di&longs;&longs;ociatas <lb/>Gallorum &amp; Hi&longs;panorum <expan abbr="vol&utilde;tates">voluntates</expan>: <expan abbr="t&atilde;">tam</expan> <lb/>multa, &amp; multiplici <expan abbr="&longs;imultat&utilde;">&longs;imultatum</expan> <expan abbr="atq;">atque</expan> odio&shy;<lb/>rum crudelitate &longs;auciatas: tot mordaci&shy;<lb/>bus dictis, &longs;criptis, factis in &longs;e&longs;e mutuis <lb/>exulceratas: tam deiecta, <expan abbr="atq;">atque</expan> perturbata <lb/>omnia ip&longs;i &longs;uis oculis viderunt. </s> <s id="id.000041">Quandoquidem pax victo &longs;em&shy;<lb/>per &longs;it nece&longs;&longs;aria, &amp; victori ea, qu&aelig; nihil <lb/>po&longs;t &longs;e ferat in&longs;idiarum, &longs;emper expe&shy;<lb/>diat: &longs;tatim eius ineund&aelig;, &amp; cum <expan abbr="po&shy;t&etilde;ti&longs;&longs;imo">po&shy;<lb/>tenti&longs;&longs;imo</expan> ho&longs;te Philippo Hi&longs;paniarum <lb/>rege conciliand&aelig; <expan abbr="occa&longs;ion&etilde;">occa&longs;ionem</expan> qu&aelig;&longs;itam, <lb/>&amp; oblatam &agrave; Clemente VIII. pontifice <lb/>&longs;ummo, ver&egrave; vtriu&longs;que gentis commu&shy;<lb/>ni <expan abbr="par&etilde;te">parente</expan> clementi&longs;&longs;imo, per &longs;uum lega&shy;<lb/>tum Alexandrum de Medicis Cardina&shy;<lb/>lem, &amp; Archiepi&longs;copum Florentinum, <lb/>qui huic paci tractand&aelig;, conficiend&aelig;, <lb/>&amp; ni&longs;i perfecta re <expan abbr="n&otilde;">non</expan> relinquend&aelig; &longs;em&shy;<lb/>per interfuit, &amp; qua&longs;i pr&aelig;fuit, arripui&shy;<lb/>&longs;ti. </s>
  
 <s><expan abbr="N&atilde;">Nam</expan> qui <lb/><expan abbr="n&otilde;">non</expan> <expan abbr="vider&utilde;t">viderunt</expan>, licet ab alijs recitata <expan abbr="audi&atilde;t">audiant</expan>, <lb/>aut <expan abbr="monum&etilde;tis">monumentis</expan> <expan abbr="c&otilde;m&etilde;data">commendata</expan> <expan abbr="leg&atilde;t">legant</expan>, non ar&shy;<lb/>bitror <expan abbr="tam&etilde;">tamen</expan> vllius vlla <expan abbr="quant&utilde;uis">quantunuis</expan> elegan&shy;<lb/>ti, &amp; probabili narratione adduci po&longs;&longs;e, <lb/>vt <expan abbr="cred&atilde;t">credant</expan>, quando <expan abbr="quid&etilde;">quidem</expan> nos, qui h&aelig;c vi&shy;<lb/>dimus, &longs;i <expan abbr="qu&atilde;do">quando</expan> in <expan abbr="memori&atilde;reducimus">memoriarreducimus</expan>, <pb/>mera &longs;omnia videre nobis videmur: <lb/>Quid igitur ab&longs;urdum? </s> <s id="id.000042">Duobus e tuo &longs;anctiore con&longs;ilio de&shy;<lb/>lectis con&longs;iliariis tibi, id e&longs;t patri&aelig; <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.013.jpg"/>&longs;aluti addicti&longs;&longs;imis (permittes bona tua <lb/>venia, Rex clementi&longs;&longs;ime, honoris &amp; <lb/>grat&aelig; erga viros tam bene de te, totaque <lb/>Gallia meritos memori&aelig; no&longs;tr&aelig; gratia, <lb/>h&icirc;c illos nominari) Pomponio Belle&shy;<lb/>ureo &amp; Nicolao Brulartio, toto tant&aelig; <lb/>molis negotio per te commi&longs;&longs;o, pacem <lb/>tibi, tuis, toti Galli&aelig; honorificenti&longs;&longs;i&shy;<lb/>mam conciliaui&longs;ti: pacem inquam ab&shy;<lb/>&longs;entem, &amp; ad multos annos exulem re&shy;<lb/>duxi&longs;ti: iureiurando &longs;olemni&longs;&longs;imo, &longs;i&shy;<lb/>gillis vtriu&longs;que regni confirmatam per <lb/>pr&aelig;cones tuos proclamari iu&longs;&longs;i&longs;ti: arma <lb/>de manibus militum, qu&aelig; erant &longs;umpta <lb/>pro te, &amp; contra te &longs;u&longs;tuli&longs;ti: iam tuo&shy;<lb/>rum in ligones, aratrorum dentes, fal&shy;<lb/>ces, vngues ferreos, vectes, trochleas, <lb/>malleos, aliaque in&longs;trumenta vit&aelig; mi&shy;<lb/>tioris, &amp; pacific&aelig; conuerti&longs;ti: iam arua <lb/>feracis Galli&aelig; recoli c&oelig;pta, vbique re&shy;<lb/>uire&longs;cunt: l&aelig;t&aelig; &longs;egetes, agri vberes cul&shy;<lb/>mis ari&longs;ti&longs;que luxuriant: ex &aelig;dificijs &longs;e&shy;<lb/>miruta re&longs;taurantur, dirutorum loco <lb/>noua &longs;tatuuntur: leges liber&egrave; pronun&shy;<pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.014.jpg"/>ciant: iu&longs;ticia libritenens fide zygo&longs;tati&shy;<lb/>ca omnia iudicat: linguarum &amp; bona&shy;<lb/>rum <expan abbr="arti&utilde;">artium</expan>, te earum re&longs;tauratore, &amp; vin&shy;<lb/>dice &amp; cu&longs;tode, eruditio in <expan abbr="Academi&atilde;">Academiam</expan> <lb/>reuer&longs;a frequentatur: ingenia, qu&aelig; in ea <lb/>&longs;unt pr&aelig;clara, in variarum artium iam <lb/>redundant elegantiam, f&oelig;tu&longs;que &longs;uos <lb/>producere ge&longs;tiunt: mercatura denique <lb/>tut&ograve; vagatur, peregrinatur, ru&longs;ticatur. <lb/></s>
  
 <s>quidve inele&shy;<lb/>gans facimus? </s> <s id="id.000043">Harum duarum rerum belli, &amp; pacis <lb/>magnitudinem, <expan abbr="difficultat&etilde;">difficultatem</expan>, <expan abbr="impedim&etilde;&shy;ta">impedimen&shy;<lb/>ta</expan> &longs;oli <expan abbr="c&otilde;plectentur">complectentur</expan>, quitam di&longs;&longs;ociatas <lb/>Gallorum &amp; Hi&longs;panorum <expan abbr="vol&utilde;tates">voluntates</expan>: <expan abbr="t&atilde;">tam</expan> <lb/>multa, &amp; multiplici <expan abbr="&longs;imultat&utilde;">&longs;imultatum</expan> <expan abbr="atq;">atque</expan> odio&shy;<lb/>rum crudelitate &longs;auciatas: tot mordaci&shy;<lb/>bus dictis, &longs;criptis, factis in &longs;e&longs;e mutuis <lb/>exulceratas: tam deiecta, <expan abbr="atq;">atque</expan> perturbata <lb/>omnia ip&longs;i &longs;uis oculis viderunt. </s>
  
 <s>&longs;i tibi qui cum tanta glo&shy;<lb/>ria h&aelig;c duo perfeceris, de pacis &amp; belli <lb/>in&longs;trumentis, vel potius de horum in&shy;<lb/>&longs;trumentorum viribus, &amp; virium cau&shy;<lb/>&longs;is, &amp;, quod admirabilius, vno <expan abbr="ear&utilde;">earum</expan> prin <lb/>cipio, quod e&longs;t circulus, librum offeri&shy;<lb/>mus? </s> <s id="id.000044"><expan abbr="N&atilde;">Nam</expan> qui <lb/><expan abbr="n&otilde;">non</expan> <expan abbr="vider&utilde;t">viderunt</expan>, licet ab alijs recitata <expan abbr="audi&atilde;t">audiant</expan>, <lb/>aut <expan abbr="monum&etilde;tis">monumentis</expan> <expan abbr="c&otilde;m&etilde;data">commendata</expan> <expan abbr="leg&atilde;t">legant</expan>, non ar&shy;<lb/>bitror <expan abbr="tam&etilde;">tamen</expan> vllius vlla <expan abbr="quant&utilde;uis">quantumuis</expan> elegan&shy;<lb/>ti, &amp; probabili narratione adduci po&longs;&longs;e, <lb/>vt <expan abbr="cred&atilde;t">credant</expan>, quando <expan abbr="quid&etilde;">quidem</expan> nos, qui h&aelig;c vi&shy;<lb/>dimus, &longs;i <expan abbr="qu&atilde;do">quando</expan> in <expan abbr="memori&atilde;reducimus">memoriam reducimus</expan>, <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.015.jpg"/>mera &longs;omnia videre nobis videmur: <lb/>Quid igitur ab&longs;urdum? </s>
  
 <s>qui te pr&aelig;terea videamus magni&shy;<lb/>ficis &aelig;dificiorum &longs;ub&longs;tructionibus, ita <lb/>delectari, vt nihil, <expan abbr="n&otilde;">non</expan> dicam nunc, cum <lb/>&longs;int h&aelig;c pacis opera: &longs;ed etiam in ip&longs;o <lb/>belli flagranti&longs;&longs;imiardore, ab ijs auocare <lb/>aut retardare potuerit. </s> <s id="id.000045">quidve inele&shy;<lb/>gans facimus? </s>
  
 <s>Porticus diues, <lb/>&longs;uperba, amu&longs;&longs;itata, qu&aelig; &agrave; tua Lupara <lb/>ad tuas &aelig;des lateritias te, <expan abbr="tuo&longs;q;">tuo&longs;que</expan> delatura <lb/>&amp; illinc ad <expan abbr="vrb&etilde;">vrbem</expan> de&longs;uper ventura, te <expan abbr="in-u&etilde;tore">in&shy;<lb/>uentore</expan>, &amp; excogitatore, tuis &longs;umptibus <lb/>extruitur: &AElig;dium lateritiarum cochlea&shy;<lb/>ri&longs;cal&ecedil;, octauo orbis miraculo <expan abbr="coloph&otilde;">colophom</expan> <lb/>impo&longs;itus: Ca&longs;tella Fontisbellaquei, <lb/>Sanctogermani, Moncelli colophoni <lb/>&longs;uo proxima, nuper Reuerendi&longs;&longs;imo <lb/>Legato hinc in Italiam redeunti, nobi <pb/>li&longs;&longs;imis illis Hi&longs;panis, Flandri&longs;que, qui <lb/>ad pacem iureiurando confirmandam <lb/>aduenerant, cum tua incredibili vo&shy;<lb/>luptate o&longs;tentata, &amp; eorum maiori ad&shy;<lb/>miratione ab illis &longs;pectata luculenter te&shy;<lb/>&longs;tantur, <expan abbr="atq;">atque</expan> <expan abbr="h&atilde;c">hanc</expan> animi tui <expan abbr="delectation&etilde;">delectationem</expan> <lb/>rege magnifico <expan abbr="digni&longs;&longs;im&atilde;">digni&longs;&longs;imam</expan> declararunt, <lb/>&amp; vi&longs;uris, quotquot venient in po&longs;te&shy;<lb/>rum, declarabunt. </s> <s id="id.000046">&longs;i tibi qui cum tanta glo&shy;<lb/>ria h&aelig;c duo perfeceris, de pacis &amp; belli <lb/>in&longs;trumentis, vel potius de horum in&shy;<lb/>&longs;trumentorum viribus, &amp; virium cau&shy;<lb/>&longs;is, &amp;, quod admirabilius, vno <expan abbr="ear&utilde;">earum</expan> prin<lb/>cipio, quod e&longs;t circulus, librum offeri&shy;<lb/>mus? </s>
  
 <s>Spemque adferunt <lb/><expan abbr="n&otilde;mediocrem">nommediocrem</expan>, te, pro tuorum in Aca&shy;<lb/>demia profe&longs;&longs;orum collegio, quale edi&shy;<lb/>ta pro eo oratione &agrave; me de&longs;criptum <lb/>e&longs;t: aut ab alio magnificentius de&longs;cribe&shy;<lb/>tur, &aelig;dificando, aliquandoe&longs;&longs;e cogitatu&shy;<lb/>rum, &amp; perfecturum. </s> <s id="id.000047">qui te pr&aelig;terea videamus magni&shy;<lb/>ficis &aelig;dificiorum &longs;ub&longs;tructionibus, ita <lb/>delectari, vt nihil, <expan abbr="n&otilde;">non</expan> dicam nunc, cum <lb/>&longs;int h&aelig;c pacis opera: &longs;ed etiam in ip&longs;o <lb/>belli flagranti&longs;&longs;imi ardore, ab ijs auocare <lb/>aut retardare potuerit. </s>
  
 <s>H&aelig;c igitur mihi <lb/><expan abbr="per&longs;ua&longs;er&utilde;t">per&longs;ua&longs;erunt</expan>, ne quicquam vererer opus <lb/>hoc, ratione opell&aelig; <expan abbr="quali&longs;cunq;">quali&longs;cunque</expan> no&longs;tr&aelig;, <lb/>exiguum &longs;cio: &longs;ed ratione authoris &longs;ui, <lb/>Ari&longs;totelis, magnum, &longs;anct&aelig; maie&longs;tati <lb/>tu&aelig; co&longs;ecrare. </s> <s id="id.000048">Porticus diues, <lb/>&longs;uperba, amu&longs;&longs;itata, qu&aelig; &agrave; tua Lupara <lb/>ad tuas &aelig;des lateritias te, <expan abbr="tuo&longs;q;">tuo&longs;que</expan> delatura <lb/>&amp; illinc ad <expan abbr="vrb&etilde;">vrbem</expan> de&longs;uper ventura, te <expan abbr="in&shy;u&etilde;tore">in&shy;<lb/>uentore</expan>, &amp; excogitatore, tuis &longs;umptibus <lb/>extruitur: &AElig;dium lateritiarum cochlea&shy;<lb/>ri &longs;cal&ecedil;, octauo orbis miraculo <expan abbr="coloph&otilde;">colophon</expan> <lb/>impo&longs;itus: Ca&longs;tella Fontisbellaquei, <lb/>Sanctogermani, Moncelli colophoni <lb/>&longs;uo proxima, nuper Reuerendi&longs;&longs;imo <lb/>Legato hinc in Italiam redeunti, nobi<pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.016.jpg"/>li&longs;&longs;imis illis Hi&longs;panis, Flandri&longs;que, qui <lb/>ad pacem iureiurando confirmandam <lb/>aduenerant, cum tua incredibili vo&shy;<lb/>luptate o&longs;tentata, &amp; eorum maiori ad&shy;<lb/>miratione ab illis &longs;pectata luculenter te&shy;<lb/>&longs;tantur, <expan abbr="atq;">atque</expan> <expan abbr="h&atilde;c">hanc</expan> animi tui <expan abbr="delectation&etilde;">delectationem</expan> <lb/>rege magnifico <expan abbr="digni&longs;&longs;im&atilde;">digni&longs;&longs;imam</expan> declararunt, <lb/>&amp; vi&longs;uris, quotquot venient in po&longs;te&shy;<lb/>rum, declarabunt. </s>
  
 <s>Quod <expan abbr="n&utilde;c">nunc</expan> igitur tam lu&shy;<lb/>benter facio: quam Deum <expan abbr="optim&utilde;">optimum</expan> ma&shy;<lb/>ximum obnix&egrave; precor, vt vitam tibi <lb/>impertiat, in duas annorum quadrage&shy;<lb/>narias ita partitam vt &longs;ecundam, quam <pb/>belli reliquiis, &amp; pace in ea confectis f&oelig;&shy;<lb/>liciter ingre&longs;&longs;us es, tot rebus pacis tam <lb/>magnificis, &amp; glorio&longs;is adhuc aggre&shy;<lb/>diundis, &amp; perficiundis con&longs;umas: quot <lb/>in rebus belli admirabilibus, atque in&shy;<lb/>credibilibus perfectis primam con&longs;um&shy;<lb/>p&longs;i&longs;ti. </s> <s id="id.000049">Spemque adferunt <lb/><expan abbr="n&otilde;mediocrem">non mediocrem</expan>, te, pro tuorum in Aca&shy;<lb/>demia profe&longs;&longs;orum collegio, quale edi&shy;<lb/>ta pro eo oratione &agrave; me de&longs;criptum <lb/>e&longs;t: aut ab alio magnificentius de&longs;cribe&shy;<lb/>tur, &aelig;dificando, aliquando e&longs;&longs;e cogitatu&shy;<lb/>rum, &amp; perfecturum. </s>
  
 <s>Hoc, &longs;i tibi, Deo ita volente, eue&shy;<lb/>niat, haud profect&ograve; verendum erit di&shy;<lb/>cere, &amp; palam, quod omnium hi&longs;tori&aelig; <lb/>conte&longs;tabuntur, proclamare, te <expan abbr="rer&utilde;">rerum</expan> ad&shy;<lb/>mirabili&longs;&longs;imarum regem, &amp; regum, qui <lb/>hactenus in quacunque orbis regione <lb/>regnauere, fore pr&aelig;&longs;tanti&longs;&longs;imum, &amp; ad&shy;<lb/>mirabili&longs;&longs;imum. </s> <s id="id.000050">H&aelig;c igitur mihi <lb/><expan abbr="per&longs;ua&longs;er&utilde;t">per&longs;ua&longs;erunt</expan>, ne quicquam vererer opus <lb/>hoc, ratione opell&aelig; <expan abbr="quali&longs;cunq;">quali&longs;cunque</expan> no&longs;tr&aelig;, <lb/>exiguum &longs;cio: &longs;ed ratione authoris &longs;ui, <lb/>Ari&longs;totelis, magnum, &longs;anct&aelig; maie&longs;tati <lb/>tu&aelig; co&longs;ecrare. </s>
  
 <s>Vale, &amp; duas illas per&shy;<lb/>optatas annorum quadragenarias tibi, <lb/>&amp; nobis &longs;ic viue. </s> <s id="id.000051">Quod <expan abbr="n&utilde;c">nunc</expan> igitur tam lu&shy;<lb/>benter facio: quam Deum <expan abbr="optim&utilde;">optimum</expan> ma&shy;<lb/>ximum obnix&egrave; precor, vt vitam tibi <lb/>impertiat, in duas annorum quadrage&shy;<lb/>narias ita partitam vt &longs;ecundam, quam <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.017.jpg"/>belli reliquiis, &amp; pace in ea confectis f&oelig;&shy;<lb/>liciter ingre&longs;&longs;us es, tot rebus pacis tam <lb/>magnificis, &amp; glorio&longs;is adhuc aggre&shy;<lb/>diundis, &amp; perficiundis con&longs;umas: quot <lb/>in rebus belli admirabilibus, atque in&shy;<lb/>credibilibus perfectis primam con&longs;um&shy;<lb/>p&longs;i&longs;ti. </s>
  
 <s>Scriptum Luteti&aelig; eo <lb/>die, quo quinquennio ante &agrave; te ciui&shy;<lb/>tas Hi&longs;panis erepta, &amp; &longs;uis ciuibus f&oelig;li&shy;<lb/>citer e&longs;t re&longs;tituta.</s></p><p type="main"> <s id="id.000052">Hoc, &longs;i tibi, Deo ita volente, eue&shy;<lb/>niat, haud profect&ograve; verendum erit di&shy;<lb/>cere, &amp; palam, quod omnium hi&longs;tori&aelig; <lb/>conte&longs;tabuntur, proclamare, te <expan abbr="rer&utilde;">rerum</expan> ad&shy;<lb/>mirabili&longs;&longs;imarum regem, &amp; regum, qui <lb/>hactenus in quacunque orbis regione <lb/>regnauere, fore pr&aelig;&longs;tanti&longs;&longs;imum, &amp; ad&shy;<lb/>mirabili&longs;&longs;imum. </s>
  
 <s>MAIESTATIS</s></p><p type="main"> <s id="id.000053">Vale, &amp; duas illas per&shy;<lb/>optatas annorum quadragenarias tibi, <lb/>&amp; nobis &longs;ic viue. </s>
  
 <s>Humillimus &longs;eruus</s></p><p type="main"> <s id="id.000054">Scriptum Luteti&aelig; eo <lb/>die, quo quinquennio ante &agrave; te ciui&shy;<lb/>tas Hi&longs;panis erepta, &amp; &longs;uis ciuibus f&oelig;li&shy;<lb/>citer e&longs;t re&longs;tituta. </s></p><p type="main">
  
 <s>HENRICVS MONANTHOLIVS.</s></p><pb/><p type="head"> <s id="id.000055">MAIESTATIS</s></p><p type="main">
  
 <s>A D <lb/>HENRICVM IIII. <lb/>GALLI&AElig; ET NAVARR&AElig; <lb/>Regem Chri&longs;tiani&longs;&longs;imum.</s></p><p type="main"> <s id="id.000056">Humillimus &longs;eruus</s></p><p type="main">
  
 <s><emph type="italics"/>Pacatos fecit tua nos victoria ciues. <lb/></s> <s id="id.000057">HENRICVS MONANTHOLIVS. </s></p></section><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.018.jpg"/><section><p type="head">
  
 <s>Inde caput Laurus: digitos ornabit Oliua <lb/>Semper, &amp; ingentem per vtr&acirc;que volabis Olympum.<emph.end type="italics"/></s></p><p type="head"> <s id="id.000058">A D <lb/>HENRICVM IIII. <lb/>GALLI&AElig; ET NAVARR&AElig; <lb/>Regem Chri&longs;tiani&longs;&longs;imum. </s></p><p type="main">
  
 <s>THEODORICVS MONANTHOLII filius.</s></p><p type="head"> <s id="id.000059"><emph type="italics"/>Pacatos fecit tua nos victoria ciues. <lb/></s>
  
 <s>De libro <foreign lang="greek"><gap/> mhxanikw_n,</foreign> Ari&longs;totele, <lb/>&amp; Monantholio.</s></p><p type="main"> <s id="id.000060">Inde caput Laurus: digitos ornabit Oliua <lb/>Semper, &amp; ingentem per vtr&acirc;que volabis Olympum. <emph.end type="italics"/></s></p><p type="head">
  
 <s><emph type="italics"/>Inter Ari&longs;totelis libros &longs;ubtilior i&longs;to<emph.end type="italics"/></s></p><p type="main"> <s id="id.000061">THEODORICVS MONANTHOLII filius. </s></p><p type="head">
  
 <s><emph type="italics"/>Nullus<emph.end type="italics"/> <foreign lang="greek">*mhxanikw_n,</foreign> <emph type="italics"/>vtiliorque fuit.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000062">De libro <foreign lang="el">tw=n mhxanikw=n,</foreign> Ari&longs;totele, <lb/>&amp; Monantholio. </s></p><p type="main">
  
 <s><emph type="italics"/>Sed mendis f&oelig;dus merito &longs;ine honore iacebat,<emph.end type="italics"/></s></p><p type="main"> <s id="id.000063"><emph type="italics"/>Inter Ari&longs;totelis libros &longs;ubtilior i&longs;to<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Non authore &longs;uo dignus Aristotele.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000064"><emph type="italics"/>Nullus<emph.end type="italics"/> <foreign lang="el">*mhxanikw=n,</foreign> <emph type="italics"/>vtiliorque fuit. <emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Lectus erat nulli, nulli intellectus agebat<emph.end type="italics"/></s></p><p type="main"> <s id="id.000065"><emph type="italics"/>Sed mendis f&oelig;dus merito &longs;ine honore iacebat,<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Vitam cum blattis, muribus, &amp; tineis.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000066"><emph type="italics"/>Non authore &longs;uo dignus Aristotele. <emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Liber ab his, captu facilis, bene comptus en exit<emph.end type="italics"/></s></p><p type="main"> <s id="id.000067"><emph type="italics"/>Lectus erat nulli, nulli intellectus agebat<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>In lucem, vigilis luce Monantholij.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000068"><emph type="italics"/>Vitam cum blattis, muribus, &amp; tineis. <emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Sic dat Ari&longs;toteli vitam, clar&eacute;que vici&szlig;ine<emph.end type="italics"/></s></p><p type="main"> <s id="id.000069"><emph type="italics"/>Liber ab his, captu facilis, bene comptus en exit<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Accipit ex ip&longs;o, quam dedit ille, parem.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000070"><emph type="italics"/>In lucem, vigilis luce Monantholij. <emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Vna dies ambos &longs;eruabit, &amp; eximet &aelig;uo,<emph.end type="italics"/></s></p><p type="main"> <s id="id.000071"><emph type="italics"/>Sic dat Ari&longs;toteli vitam, clar&eacute;que vici&szlig;im<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Ambor&uacute;mque &longs;imul fama &longs;uper&longs;tes erit.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000072"><emph type="italics"/>Accipit ex ip&longs;o, quam dedit ille, parem. <emph.end type="italics"/></s></p><p type="main">
  
 <s>RICHARDVS MERCES</s></p><p type="main"> <s id="id.000073"><emph type="italics"/>Vna dies ambos &longs;eruabit, &amp; eximet &aelig;uo,<emph.end type="italics"/></s></p><p type="main">
  
 <s>Doct. </s> <s id="id.000074"><emph type="italics"/>Ambor&uacute;mque &longs;imul fama &longs;uper&longs;tes erit. <emph.end type="italics"/></s></p><p type="main">
  
 <s>Med. </s> <s id="id.000075">RICHARDVS MERCES</s></p><p type="main">
  
 <s>Pari&longs;.</s></p><pb/><figure></figure><p type="head"> <s id="id.000076">Doct. Med. Pari&longs;. </s></p></section><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.019.jpg"/>
  
 <s>PRAEFATIO IN <lb/>MECHANICA ARISTO&shy;<lb/>TELIS, AD LECTOREM.</s></p><p type="main"> <section>
  <figure id="id.035.01.019.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.019.1.jpg"/>
  
 <s>Philosophari in vno rerum quo&shy;<lb/>libet genere, <expan abbr="c&atilde;dide">candide</expan> lector, res e&longs;t per&shy;<lb/>quam dulcis. </s> <p type="head">
  
 <s>Philo&longs;ophari appello re&shy;<lb/>rum e&longs;&longs;entiam, cau&longs;as, proprietates, <lb/>facultates inue&longs;tigare, &amp; inuento rum <lb/>qu&aelig; vtilia &longs;unt in opus ad vit&aelig; homi&shy;<lb/>num f&oelig;licius <expan abbr="deg&etilde;d&aelig;">degend&aelig;</expan> commoda edu&shy;<lb/>cere. </s> <s id="id.000077">PRAEFATIO IN <lb/>MECHANICA ARISTO&shy;<lb/>TELIS, AD LECTOREM. </s></p><p type="main">
  
 <s>Ita enim demum ver&egrave; ille erit, vt ait po&euml;ta,</s></p><p type="main"> <s id="id.000078">Philosophari in vno rerum quo&shy;<lb/>libet genere, <expan abbr="c&atilde;dide">candide</expan> lector, res e&longs;t per&shy;<lb/>quam dulcis. </s>
  
 <s><emph type="italics"/>F&oelig;lix, qui poterit rerum cogno&longs;cere cau&longs;as.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000079">Philo&longs;ophari appello re&shy;<lb/>rum e&longs;&longs;entiam, cau&longs;as, proprietates, <lb/>facultates inue&longs;tigare, &amp; inuento rum <lb/>qu&aelig; vtilia &longs;unt in opus ad vit&aelig; homi&shy;<lb/>num f&oelig;licius <expan abbr="deg&etilde;d&aelig;">degend&aelig;</expan> commoda edu&shy;<lb/>cere. </s>
  
 <s>Alio qui inutilia, vel vtilia: &longs;ed inutiliter id e&longs;t &longs;ine actio&shy;<lb/>ne vel opere, qu&ecedil; fines &longs;unt omnis <expan abbr="c&otilde;templationis">contemplationis</expan> vtilis, <lb/>contemplari, &amp; in his philo&longs;ophando plu&longs;quam paucis <lb/>commorari, parum omnino, aut nihil f&oelig;licitatis in hac <lb/>rerum vniuer&longs;itate habere arbitror. </s> <s id="id.000080">Ita enim demum ver&egrave; ille erit, vt ait po&euml;ta,</s></p><p type="main">
  
 <s>Verumenimuer&ograve; re&shy;<lb/>rum quia propemodum e&longs;t infinita multitudo, licet ani&shy;<lb/>mus hominis (quod e&longs;t ab Ari&longs;totele dictum, &amp; ita e&longs;t, <lb/>pote&longs;tate cogno&longs;cendi, &amp; va&longs;is in&longs;tar &longs;pirituales rerum <lb/>formas recipiendi) &longs;it omnia: vix tamen ita qui&longs;quam <lb/>bene animo con&longs;titutus fuit, vt ip&longs;um ad omnia genera <lb/>appellens in &longs;ingulis excelleret, &amp; magnum quid con&longs;e&shy;<lb/>queretur: vt cuique tamen contigit maior: ita quo que <lb/>maiora con&longs;ecutus e&longs;&longs;e legitur. </s> <s id="id.000081"><emph type="italics"/>F&oelig;lix, qui poterit rerum cogno&longs;cere cau&longs;as. <emph.end type="italics"/></s></p><p type="main">
  
 <s>Pythagoram, Hippocra&shy;<lb/>tem medicum, Platonem, Ari&longs;totelem, Theophra&longs;tum, <lb/>Galenum &longs;i non omnia tenui&longs;&longs;e: quamplurima cert&egrave; &amp; <lb/>aliorum libri, &amp; commentarij ab illis po&longs;teritati relicti <lb/>copios&egrave; loquuntur. </s> <s id="id.000082">Alio qui inutilia, vel vtilia: &longs;ed inutiliter id e&longs;t &longs;ine actio&shy;<lb/>ne vel opere, qu&ecedil; fines &longs;unt omnis <expan abbr="c&otilde;templationis">contemplationis</expan> vtilis, <lb/>contemplari, &amp; in his philo&longs;ophando plu&longs;quam paucis <lb/>commorari, parum omnino, aut nihil f&oelig;licitatis in hac <lb/>rerum vniuer&longs;itate habere arbitror. </s>
  
 <s>Sed quibus non ita magnus vel fuit, <pb/>vel e&longs;t animus, illi vel propen&longs;ione naturali, vel iudicio, <lb/>vel ca&longs;u aliquo de multis nonnulla &longs;eligunt, in quibus <lb/>tempus &amp; operam non &longs;ine v&longs;ura collocent &longs;uam. </s> <s id="id.000083">Verumenimuer&ograve; re&shy;<lb/>rum quia propemodum e&longs;t infinita multitudo, licet ani&shy;<lb/>mus hominis (quod e&longs;t ab Ari&longs;totele dictum, &amp; ita e&longs;t, <lb/>pote&longs;tate cogno&longs;cendi, &amp; va&longs;is in&longs;tar &longs;pirituales rerum <lb/>formas recipiendi) &longs;it omnia: vix tamen ita qui&longs;quam <lb/>bene animo con&longs;titutus fuit, vt ip&longs;um ad omnia genera <lb/>appellens in &longs;ingulis excelleret, &amp; magnum quid con&longs;e&shy;<lb/>queretur: vt cuique tamen contigit maior: ita quo que <lb/>maiora con&longs;ecutus e&longs;&longs;e legitur. </s>
  
 <s>Om&shy;<lb/>nium, qu&aelig; &longs;unt, genera quatuor e&longs;&longs;e reperio, &longs;ingula cer&shy;<lb/>t&egrave; digni&longs;&longs;ima hominis contemplatione. </s> <s id="id.000084">Pythagoram, Hippocra&shy;<lb/>tem medicum, Platonem, Ari&longs;totelem, Theophra&longs;tum, <lb/>Galenum &longs;i non omnia tenui&longs;&longs;e: quamplurima cert&egrave; &amp; <lb/>aliorum libri, &amp; commentarij ab illis po&longs;teritati relicti <lb/>copios&egrave; loquuntur. </s>
  
 <s>Diuina, c&oelig;le&shy;<lb/>&longs;tia, elementaria, artificialia. </s> <s id="id.000085">Sed quibus non ita magnus vel fuit, <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.020.jpg"/>vel e&longs;t animus, illi vel propen&longs;ione naturali, vel iudicio, <lb/>vel ca&longs;u aliquo de multis nonnulla &longs;eligunt, in quibus <lb/>tempus &amp; operam non &longs;ine v&longs;ura collocent &longs;uam. </s>
  
 <s>In quorum &longs;ingulis multos <lb/>excellui&longs;&longs;e clarius e&longs;t: quam vt cuiu&longs;quam nominis com&shy;<lb/>memoratione opus &longs;it. </s> <s id="id.000086">Om&shy;<lb/>nium, qu&aelig; &longs;unt, genera quatuor e&longs;&longs;e reperio, &longs;ingula cer&shy;<lb/>t&egrave; digni&longs;&longs;ima hominis contemplatione. </s>
  
 <s>Et cert&egrave; diuina &longs;unt eiu&longs;modi, vt <lb/>licet ad corum intuitum, &longs;icut ad Solis ve&longs;pertilionis: Ita <lb/>mentis no&longs;tr&aelig; oculi caligent, &longs;i quis tamen diuinitatis <lb/><expan abbr="eti&atilde;">etiam</expan> exiguus repente, &amp; &longs;ubinde radius recipiatur &amp; ocu&shy;<lb/>los &longs;ubintret, plus voluptatis menti adferat: quam alio&shy;<lb/>rum quorumlibet plena cognitio. </s> <s id="id.000087">Diuina, c&oelig;le&shy;<lb/>&longs;tia, elementaria, artificialia. </s>
  
 <s>Qu&aelig; vna res adiuncto <lb/>contemplationis diuinorum fine (quem Dei cognitio&shy;<lb/>nem, amorem, &amp; cultum arbitror) fecit, vt philo&longs;ophi&aelig; <lb/>diuinorum quamplurimi homines totos &longs;e&longs;e dediderint, <lb/>dedantque quotidie. </s> <s id="id.000088">In quorum &longs;ingulis multos <lb/>excellui&longs;&longs;e clarius e&longs;t: quam vt cuiu&longs;quam nominis com&shy;<lb/>memoratione opus &longs;it. </s>
  
 <s>Huic philo&longs;ophi&aelig; proxima e&longs;t c&oelig;&shy;<lb/>le&longs;tium &amp; elementariorum id e&longs;t <foreign lang="greek">tou_ maxroxosmou_</foreign> mundi <lb/>&longs;cilicet huius, cuius &longs;ine machinis fabrica in &longs;ub&longs;tantia, <lb/>magnitudine, figura, numero, &longs;itu, connexione, faculta&shy;<lb/>tibus, &amp; v&longs;u partium <expan abbr="omni&utilde;">omnium</expan> &longs;ui fabricatoris bonitatem, <lb/>&longs;apientiam, <expan abbr="pot&etilde;tiam">potentiam</expan>, &longs;umma i&longs;th&aelig;c omnia arguit, &amp; de&shy;<lb/>mon&longs;trat. </s> <s id="id.000089">Et cert&egrave; diuina &longs;unt eiu&longs;modi, vt <lb/>licet ad eorum intuitum, &longs;icut ad Solis ve&longs;pertilionis: Ita <lb/>mentis no&longs;tr&aelig; oculi caligent, &longs;i quis tamen diuinitatis <lb/><expan abbr="eti&atilde;">etiam</expan> exiguus repente, &amp; &longs;ubinde radius recipiatur &amp; ocu&shy;<lb/>los &longs;ubintret, plus voluptatis menti adferat: quam alio&shy;<lb/>rum quorumlibet plena cognitio. </s>
  
 <s>Luculenti&longs;&longs;im&egrave; in&longs;uper o&longs;tendit Deum, &amp; eius <lb/>admini&longs;tram naturam &longs;ine actione, &longs;ine opere nu&longs;quam <lb/>e&longs;&longs;e. </s> <s id="id.000090">Qu&aelig; vna res adiuncto <lb/>contemplationis diuinorum fine (quem Dei cognitio&shy;<lb/>nem, amorem, &amp; cultum arbitror) fecit, vt philo&longs;ophi&aelig; <lb/>diuinorum quamplurimi homines totos &longs;e&longs;e dediderint, <lb/>dedantque quotidie. </s>
  
 <s>Mult&ograve; de his plura: quam de diuinis philo&longs;ophando <lb/>homines con&longs;ecuti &longs;unt, <expan abbr="neq;">neque</expan> &longs;ine incredibili animorum <lb/>&longs;uorum voluptate, &amp; innumerabili ad v&longs;us humanos vti&shy;<lb/>litate. </s> <s id="id.000091">Huic philo&longs;ophi&aelig; proxima e&longs;t c&oelig;&shy;<lb/>le&longs;tium &amp; elementariorum id e&longs;t <foreign lang="el">tou= makrokosmou=</foreign> mundi <lb/>&longs;cilicet huius, cuius &longs;ine machinis fabrica in &longs;ub&longs;tantia, <lb/>magnitudine, figura, numero, &longs;itu, connexione, faculta&shy;<lb/>tibus, &amp; v&longs;u partium <expan abbr="omni&utilde;">omnium</expan> &longs;ui fabricatoris bonitatem, <lb/>&longs;apientiam, <expan abbr="pot&etilde;tiam">potentiam</expan>, &longs;umma i&longs;th&aelig;c omnia arguit, &amp; de&shy;<lb/>mon&longs;trat. </s>
  
 <s>Nam cum h&aelig;c ita e&longs;&longs;e homines <expan abbr="depreh&etilde;di&longs;&longs;ent">deprehendi&longs;&longs;ent</expan>, vt <lb/>ad mult&ograve; plures v&longs;us, quam ad quos <expan abbr="&longs;p&otilde;t&egrave;">&longs;pont&egrave;</expan> nata e&longs;&longs;e com&shy;<lb/>perirentur, <expan abbr="tr&atilde;sferri">transferri</expan> &amp; aptati po&longs;&longs;ent, <expan abbr="perciperentq;">perciperentque</expan> non <lb/>fru&longs;tr&agrave; &longs;uis animis in&longs;itas non <expan abbr="&longs;ol&utilde;">&longs;olum</expan> facultates i&longs;ta transfe&shy;<lb/>rendi &amp; aptandi: &longs;ed etiam congenita corporibus &longs;uis <expan abbr="in-&longs;trum&etilde;ta">in&shy;<lb/>&longs;trumenta</expan>, quibus vel ex&longs;e, vel &agrave; &longs;e factis <expan abbr="in&longs;trum&etilde;tis">in&longs;trumentis</expan> tran&longs;&shy;<lb/>ferrent &amp; aptarent, non &longs;o la cognitione <expan abbr="c&otilde;tenti">contenti</expan> ad agen&shy;<lb/>dum &longs;e <expan abbr="contuler&utilde;t">contulerunt</expan>. </s> <s id="id.000092">Luculenti&longs;&longs;im&egrave; in&longs;uper o&longs;tendit Deum, &amp; eius <lb/>admini&longs;tram naturam &longs;ine actione, &longs;ine opere nu&longs;quam <lb/>e&longs;&longs;e. </s>
  
 <s>Hinc quartum genus illud <expan abbr="rer&utilde;">rerum</expan>, quas <lb/>diximus, artificialium emanauit, prim&ugrave;m vt credibile e&longs;t <pb/>nece&longs;&longs;ariarum, deinde <expan abbr="delectabili&utilde;">delectabilium</expan>, quod e&ograve;, imitatione <lb/>c&oelig;le&longs;tium &amp; <expan abbr="elem&etilde;tarior&utilde;">elementariorum</expan>, &amp; in <expan abbr="hor&utilde;">horum</expan> nonnullis &longs;upera&shy;<lb/>tione proce&longs;&longs;it, vt homo qui manu mentis con&longs;ilio dire&shy;<lb/>cta tot &amp; <expan abbr="t&atilde;ta">tanta</expan>, quanta <expan abbr="n&utilde;c">nunc</expan> po&longs;&longs;idemus, peregerit, ab Ana&shy;<lb/>xagora quia haberet <expan abbr="man&utilde;">manum</expan>, &longs;apienti&longs;&longs;imus fueritiudica&shy;<lb/>tus. </s> <s id="id.000093">Mult&ograve; de his plura: quam de diuinis philo&longs;ophando <lb/>homines con&longs;ecuti &longs;unt, <expan abbr="neq;">neque</expan> &longs;ine incredibili animorum <lb/>&longs;uorum voluptate, &amp; innumerabili ad v&longs;us humanos vti&shy;<lb/>litate. </s>
  
 <s>Ego <expan abbr="quoq;">quoque</expan> <expan abbr="potenti&longs;&longs;im&utilde;">potenti&longs;&longs;imum</expan> <expan abbr="ead&etilde;">eadem</expan> de cau&longs;a <expan abbr="iudic&etilde;">iudicem</expan>. </s> <s id="id.000094">Nam cum h&aelig;c ita e&longs;&longs;e homines <expan abbr="depreh&etilde;di&longs;&longs;ent">deprehendi&longs;&longs;ent</expan>, vt <lb/>ad mult&ograve; plures v&longs;us, quam ad quos <expan abbr="&longs;p&otilde;t&egrave;">&longs;pont&egrave;</expan> nata e&longs;&longs;e com&shy;<lb/>perirentur, <expan abbr="tr&atilde;sferri">transferri</expan> &amp; aptati po&longs;&longs;ent, <expan abbr="perciperentq;">perciperentque</expan> non <lb/>fru&longs;tr&agrave; &longs;uis animis in&longs;itas non <expan abbr="&longs;ol&utilde;">&longs;olum</expan> facultates i&longs;ta transfe&shy;<lb/>rendi &amp; aptandi: &longs;ed etiam congenita corporibus &longs;uis <expan abbr="in&shy;&longs;trum&etilde;ta">in&shy;<lb/>&longs;trumenta</expan>, quibus vel ex &longs;e, vel &agrave; &longs;e factis <expan abbr="in&longs;trum&etilde;tis">in&longs;trumentis</expan> tran&longs;&shy;<lb/>ferrent &amp; aptarent, non &longs;ola cognitione <expan abbr="c&otilde;tenti">contenti</expan> ad agen&shy;<lb/>dum &longs;e <expan abbr="contuler&utilde;t">contulerunt</expan>. </s>
  
 <s>quid <lb/>enim e&longs;t, quod non &longs;uis v&longs;ibus accommodarit? </s> <s id="id.000095">Hinc quartum genus illud <expan abbr="rer&utilde;">rerum</expan>, quas <lb/>diximus, artificialium emanauit, prim&ugrave;m vt credibile e&longs;t <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.021.jpg"/>nece&longs;&longs;ariarum, deinde <expan abbr="delectabili&utilde;">delectabilium</expan>, quod e&ograve;, imitatione <lb/>c&oelig;le&longs;tium &amp; <expan abbr="elem&etilde;tarior&utilde;">elementariorum</expan>, &amp; in <expan abbr="hor&utilde;">horum</expan> nonnullis &longs;upera&shy;<lb/>tione proce&longs;&longs;it, vt homo qui manu mentis con&longs;ilio dire&shy;<lb/>cta tot &amp; <expan abbr="t&atilde;ta">tanta</expan>, quanta <expan abbr="n&utilde;c">nunc</expan> po&longs;&longs;idemus, peregerit, ab Ana&shy;<lb/>xagora quia haberet <expan abbr="man&utilde;">manum</expan>, &longs;apienti&longs;&longs;imus fuerit iudica&shy;<lb/>tus. </s>
  
 <s>quibus &longs;i <lb/><expan abbr="bonitat&etilde;">bonitatem</expan> exemplo Dei Opt. </s> <s id="id.000096">Ego <expan abbr="quoq;">quoque</expan> <expan abbr="potenti&longs;&longs;im&utilde;">potenti&longs;&longs;imum</expan> <expan abbr="ead&etilde;">eadem</expan> de cau&longs;a <expan abbr="iudic&etilde;">iudicem</expan>. </s>
  
 <s>Max. </s> <s id="id.000097">quid <lb/>enim e&longs;t, quod non &longs;uis v&longs;ibus accommodarit? </s>
  
 <s>&longs;em per <expan abbr="adi&utilde;xerit">adiunxerit</expan>, alte&shy;<lb/>r&ugrave;m <expan abbr="quoq;">quoque</expan> <expan abbr="De&utilde;">Deum</expan> inter mortales e&longs;&longs;e dicere non recu&longs;em. <lb/></s> <s id="id.000098">quibus &longs;i <lb/><expan abbr="bonitat&etilde;">bonitatem</expan> exemplo Dei Opt. Max. &longs;emper <expan abbr="adi&utilde;xerit">adiunxerit</expan>, alte&shy;<lb/>r&ugrave;m <expan abbr="quoq;">quoque</expan> <expan abbr="De&utilde;">Deum</expan> inter mortales e&longs;&longs;e dicere non recu&longs;em. <lb/></s>
  
 <s>E&longs;t cert&egrave; animus in homine ars <expan abbr="arti&utilde;">artium</expan>. </s> <s id="id.000099">E&longs;t cert&egrave; animus in homine ars <expan abbr="arti&utilde;">artium</expan>. </s>
  
 <s>Inuenitenim om&shy;<lb/>nia, &amp; manus <expan abbr="organ&utilde;">organum</expan> organorum. </s> <s id="id.000100">Inuenit enim om&shy;<lb/>nia, &amp; manus <expan abbr="organ&utilde;">organum</expan> organorum. </s>
  
 <s>Facit enim omnia. </s> <s id="id.000101">Facit enim omnia. </s>
  
 <s>Et &longs;i <lb/><foreign lang="greek">mhxana_<gap/></foreign> &longs;it moliri &amp; excogitare quibus in&longs;trumentis <lb/>opus ad agendum <expan abbr="propo&longs;it&utilde;">propo&longs;itum</expan> efficiatur, <foreign lang="greek">mhxa/nhma</foreign> erit mo&shy;<lb/>litio &amp; <expan abbr="inu&etilde;tio">inuentio</expan> <expan abbr="in&longs;trumentor&utilde;">in&longs;trumentorum</expan> ad opus. </s> <s id="id.000102">Et &longs;i <lb/><foreign lang="el">mhxana=sqai</foreign> &longs;it moliri &amp; excogitare quibus in&longs;trumentis <lb/>opus ad agendum <expan abbr="propo&longs;it&utilde;">propo&longs;itum</expan> efficiatur, <foreign lang="el">mhxa/nhma</foreign> erit mo&shy;<lb/>litio &amp; <expan abbr="inu&etilde;tio">inuentio</expan> <expan abbr="in&longs;trumentor&utilde;">in&longs;trumentorum</expan> ad opus. </s>
  
 <s>qu&aelig; cum &longs;ine ra&shy;<lb/>tione non po&longs;&longs;int exi&longs;tere, ratio <expan abbr="aut&etilde;">autem</expan> vnius hominis pro&shy;<lb/>pria &longs;it, <foreign lang="greek">mhxanixo\n</foreign> e&longs;&longs;e &longs;olius erit hominis, <expan abbr="quemadmod&utilde;">quemadmodum</expan> <lb/>loqui, ratiocinari, &amp; omnia qu&aelig; &agrave; Dei &longs;olo nutu, &longs;ine ve&shy;<lb/>cte, &longs;ine ferramentis, &longs;ine machina vlla confecta &amp; creata <lb/><expan abbr="s&utilde;t">sunt</expan>, molitione, machinatione &amp; <expan abbr="in&longs;trum&etilde;tis">in&longs;trumentis</expan> imitari, om&shy;<lb/>nia denique ad v&longs;us &longs;uos transferre. </s> <s id="id.000103">qu&aelig; cum &longs;ine ra&shy;<lb/>tione non po&longs;&longs;int exi&longs;tere, ratio <expan abbr="aut&etilde;">autem</expan> vnius hominis pro&shy;<lb/>pria &longs;it, <foreign lang="el">mhxaniko\n</foreign> e&longs;&longs;e &longs;olius erit hominis, <expan abbr="quemadmod&utilde;">quemadmodum</expan> <lb/>loqui, ratiocinari, &amp; omnia qu&aelig; &agrave; Dei &longs;olo nutu, &longs;ine ve&shy;<lb/>cte, &longs;ine ferramentis, &longs;ine machina vlla confecta &amp; creata <lb/><expan abbr="s&utilde;t">sunt</expan>, molitione, machinatione &amp; <expan abbr="in&longs;trum&etilde;tis">in&longs;trumentis</expan> imitari, om&shy;<lb/>nia denique ad v&longs;us &longs;uos transferre. </s>
  
 <s>Archimedes primus <lb/>c&oelig;lum, alteram mundi partem ampli&longs;&longs;imam &amp; pr&aelig;&longs;tan&shy;<lb/>ti&longs;&longs;imam, tanta arte vnius machin&aelig; vitre&aelig; artificio re&shy;<lb/>pr&aelig;&longs;entauit, vt &longs;i Claudiano credimus, artificij elegantia <lb/>voluptatem &amp; admirationem Ioui pepererit. </s> <s id="id.000104">Archimedes primus <lb/>c&oelig;lum, alteram mundi partem ampli&longs;&longs;imam &amp; pr&aelig;&longs;tan&shy;<lb/>ti&longs;&longs;imam, tanta arte vnius machin&aelig; vitre&aelig; artificio re&shy;<lb/>pr&aelig;&longs;entauit, vt &longs;i Claudiano credimus, artificij elegantia <lb/>voluptatem &amp; admirationem Ioui pepererit. </s>
  
 <s>Sed pr&aelig;&longs;tat <lb/>eleganti&longs;&longs;imos huius po&euml;t&aelig; ver&longs;us recitare.</s></p><p type="main"> <s id="id.000105">Sed pr&aelig;&longs;tat <lb/>eleganti&longs;&longs;imos huius po&euml;t&aelig; ver&longs;us recitare. </s></p><p type="main">
  
 <s><emph type="italics"/>Iuppiter, in paruo cum cerneret &aelig;thera vitro, <lb/>Ri&longs;it, &amp; ad &longs;uperos talia dicta dedit.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000106"><emph type="italics"/>Iuppiter, in paruo cum cerneret &aelig;thera vitro, <lb/>Ri&longs;it, &amp; ad &longs;uperos talia dicta dedit. <emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Hoccine mortalis progre&longs;&longs;a potentia cur&aelig;? <lb/></s> <s id="id.000107"><emph type="italics"/>Hoccine mortalis progre&longs;&longs;a potentia cur&aelig;? <lb/></s>
  
 <s>I am meus in fragili luditur orbe labor.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000108">Iam meus in fragili luditur orbe labor. <emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Iura poli, rerumque fidem, lege&longs;que deorum <lb/>Ecce Syracu&longs;ius tran&longs;tulit arte &longs;enex.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000109"><emph type="italics"/>Iura poli, rerumque fidem, lege&longs;que deorum <lb/>Ecce Syracu&longs;ius tran&longs;tulit arte &longs;enex. <emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Inclu&longs;us varijs famulatur &longs;piritus a&longs;tris, <lb/>Et viuum certis motibus vrget opus.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000110"><emph type="italics"/>Inclu&longs;us varijs famulatur &longs;piritus a&longs;tris, <lb/>Et viuum certis motibus vrget opus. <emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Percurrit proprium mentitus &longs;ignifer annum, <lb/>Et &longs;imulata nouo Cynthia men&longs;e redit.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000111"><emph type="italics"/>Percurrit proprium mentitus &longs;ignifer annum, <lb/>Et &longs;imulata nouo Cynthia men&longs;e redit. <emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Iamque &longs;uum voluens audax indu&longs;tria mundum<emph.end type="italics"/><pb/><emph type="italics"/>Gauder, &amp; humana &longs;idera mente regit.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000112"><emph type="italics"/>Iamque &longs;uum voluens audax indu&longs;tria mundum<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.022.jpg"/><emph type="italics"/>Gaudet, &amp; humana &longs;idera mente regit. <emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Quid &longs;al&longs;o in&longs;ontem tonitru Salmonea miror? <lb/></s> <s id="id.000113"><emph type="italics"/>Quid &longs;al&longs;o in&longs;ontem tonitru Salmonea miror? <lb/></s>
  
 <s>AE mula natur&aelig; parua reperta manus.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000114">AEmula natur&aelig; parua reperta manus. <emph.end type="italics"/></s></p><p type="main">
  
 <s>Sal monci huius fal&longs;um tonitru &longs;tatim in memoriam vo&shy;<lb/>cat, non iam fal&longs;a <expan abbr="homin&utilde;">hominum</expan>, qui nunc viuunt to nitrua, <expan abbr="vi-brataq;">vi&shy;<lb/>brataque</expan> &egrave; &longs;uis &longs;clopetis, <expan abbr="b&otilde;bardi&longs;que">bombardi&longs;que</expan> fulmina, &longs;oni frago&shy;<lb/>re, ictus conqua&longs;&longs;atione, &amp; <expan abbr="pluri&utilde;">plurium</expan> &longs;trage non modo Iouis <lb/>fulmen imitantia: &longs;ed longe &longs;uperantia. </s> <s id="id.000115">Sal monei huius fal&longs;um tonitru &longs;tatim in memoriam vo&shy;<lb/>cat, non iam fal&longs;a <expan abbr="homin&utilde;">hominum</expan>, qui nunc viuunt tonitrua, <expan abbr="vi&shy;brataq;">vi&shy;<lb/>brataque</expan> &egrave; &longs;uis &longs;clopetis, <expan abbr="b&otilde;bardi&longs;que">bombardi&longs;que</expan> fulmina, &longs;oni frago&shy;<lb/>re, ictus conqua&longs;&longs;atione, &amp; <expan abbr="pluri&utilde;">plurium</expan> &longs;trage non modo Iouis <lb/>fulmen imitantia: &longs;ed longe &longs;uperantia. </s>
  
 <s>Quoties fulmen <lb/>&longs;uum mittit Iupiter aut <expan abbr="nemin&etilde;">neminem</expan>, aut <expan abbr="vn&utilde;">vnum</expan> atque alterum <lb/>pr&aelig;cipitat: h&aelig;c ver&ograve; certo ictu &longs;emper de&longs;tinata vrbium <lb/>m&oelig;nia deua&longs;tant: quot homines attingunt, perdunt, &amp; <lb/><expan abbr="quid&etilde;">quidem</expan> tanta celeritate, tant&aacute;que vi, vt qu&ecedil; ab antiquis in&shy;<lb/>genios&egrave;, vel ad oppugnandos ho&longs;tes, vel ab his &longs;e <expan abbr="defen-dend&utilde;">defen&shy;<lb/>dendum</expan> inuenta erant <expan abbr="in&longs;trum&etilde;ta">in&longs;trumenta</expan> bellica, Scorpiones, ca&shy;<lb/>tapult&aelig;, bali&longs;t&aelig;, arietes, turres ambulatori&aelig;, te&longs;tudines, <lb/>helepoles, fund&aelig;, &amp; reliqua eiu&longs;modi poliorcetica, pr&aelig; <lb/>illis qua&longs;i in <expan abbr="de&longs;uetudin&etilde;">de&longs;uetudinem</expan>, &amp; <expan abbr="obliuion&etilde;">obliuionem</expan> abierint. </s> <s id="id.000116">Quoties fulmen <lb/>&longs;uum mittit Iupiter aut <expan abbr="nemin&etilde;">neminem</expan>, aut <expan abbr="vn&utilde;">vnum</expan> atque alterum <lb/>pr&aelig;cipitat: h&aelig;c ver&ograve; certo ictu &longs;emper de&longs;tinata vrbium <lb/>m&oelig;nia deua&longs;tant: quot homines attingunt, perdunt, &amp; <lb/><expan abbr="quid&etilde;">quidem</expan> tanta celeritate, tant&aacute;que vi, vt qu&ecedil; ab antiquis in&shy;<lb/>genios&egrave;, vel ad oppugnandos ho&longs;tes, vel ab his &longs;e <expan abbr="defen&shy;dend&utilde;">defen&shy;<lb/>dendum</expan> inuenta erant <expan abbr="in&longs;trum&etilde;ta">in&longs;trumenta</expan> bellica, Scorpiones, ca&shy;<lb/>tapult&aelig;, bali&longs;t&aelig;, arietes, turres ambulatori&aelig;, te&longs;tudines, <lb/>helepoles, fund&aelig;, &amp; reliqua eiu&longs;modi poliorcetica, pr&aelig; <lb/>illis qua&longs;i in <expan abbr="de&longs;uetudin&etilde;">de&longs;uetudinem</expan>, &amp; <expan abbr="obliuion&etilde;">obliuionem</expan> abierint. </s>
  
 <s>Pr&aelig;clara <lb/>&longs;an&egrave; illa &longs;unt <foreign lang="greek">mhxa<gap/>hma<gap/>,</foreign> &longs;i his homines vterentur <expan abbr="tant&utilde;">tantum</expan>, <lb/>vt patria ab ho&longs;tili &longs;eruitute liberetur, &longs;ubacto ho&longs;te fines <lb/>amplificentur, <expan abbr="adi&utilde;ctis">adiunctis</expan> prouincijs <expan abbr="dilat&etilde;tur">dilatentur</expan>, &amp; &longs;ic long&egrave; <lb/>lat&eacute; que optimi regis dominatio <expan abbr="ext&etilde;datur">extendatur</expan>. </s> <s id="id.000117">Pr&aelig;clara <lb/>&longs;an&egrave; illa &longs;unt <foreign lang="el">mhxanh/mata,</foreign> &longs;i his homines vterentur <expan abbr="tant&utilde;">tantum</expan>, <lb/>vt patria ab ho&longs;tili &longs;eruitute liberetur, &longs;ubacto ho&longs;te fines <lb/>amplificentur, <expan abbr="adi&utilde;ctis">adiunctis</expan> prouincijs <expan abbr="dilat&etilde;tur">dilatentur</expan>, &amp; &longs;ic long&egrave; <lb/>lat&eacute; que optimi regis dominatio <expan abbr="ext&etilde;datur">extendatur</expan>. </s>
  
 <s>Vt veteribus <lb/>illis &longs;olis in&longs;tructus cum Alexan der parua hominum ad <lb/>30000 manu tot prouincias, tot regna, tot vrbes &longs;ubegi&longs;&shy;<lb/>&longs;et, dictum &longs;it abillo vtilius fui&longs;&longs;e &longs;ubigi: quam <expan abbr="reg&utilde;">regum</expan> <expan abbr="pri-&longs;tinor&utilde;">pri&shy;<lb/>&longs;tinorum</expan> in&longs;ul&longs;a pote&longs;tate diutius detineri. </s> <s id="id.000118">Vt veteribus <lb/>illis &longs;olis in&longs;tructus cum Alexander parua hominum ad <lb/>30000 manu tot prouincias, tot regna, tot vrbes &longs;ubegi&longs;&shy;<lb/>&longs;et, dictum &longs;it ab illo vtilius fui&longs;&longs;e &longs;ubigi: quam <expan abbr="reg&utilde;">regum</expan> <expan abbr="pri&shy;&longs;tinor&utilde;">pri&shy;<lb/>&longs;tinorum</expan> in&longs;ul&longs;a pote&longs;tate diutius detineri. </s>
  
 <s><expan abbr="Igni&utilde;">Ignium</expan> vero c&oelig;&shy;<lb/>le&longs;tium, &longs;eu <expan abbr="a&longs;tror&utilde;">a&longs;trorum</expan> lumina faces no&longs;tr&aelig; ardentes <expan abbr="quant&utilde;">quantum</expan> <lb/>v&longs;ibus humanis &longs;atis e&longs;t, imitantur. </s> <s id="id.000119"><expan abbr="Igni&utilde;">Ignium</expan> vero c&oelig;&shy;<lb/>le&longs;tium, &longs;eu <expan abbr="a&longs;tror&utilde;">a&longs;trorum</expan> lumina faces no&longs;tr&aelig; ardentes <expan abbr="quant&utilde;">quantum</expan> <lb/>v&longs;ibus humanis &longs;atis e&longs;t, imitantur. </s>
  
 <s>Fontium <expan abbr="per&etilde;nitates">perennitates</expan> <lb/>Heronis inuenta &longs;uppeditant, vt &amp; Cte&longs;ibij hydraulica <lb/>in&longs;trumenta, &amp; merul&aelig; hominum voces <expan abbr="auiumq;">auiumque</expan> cantus <lb/>imitantes, &amp; <foreign lang="greek">e)g<gap/>ei/<gap/>a<gap/></foreign> funiculis, ponderibus, orbiculis, <lb/>&longs;piritu inclu&longs;o humanos motus &longs;ine voce <expan abbr="ed&etilde;tes">edentes</expan> perbell&egrave; <lb/>expre&longs;&longs;erunt. </s> <s id="id.000120">Fontium <expan abbr="per&etilde;nitates">perennitates</expan> <lb/>Heronis inuenta &longs;uppeditant, vt &amp; Cte&longs;ibij hydraulica <lb/>in&longs;trumenta, &amp; merul&aelig; hominum voces <expan abbr="auiumq;">auiumque</expan> cantus <lb/>imitantes, &amp; <foreign lang="el">e)ggei/bata</foreign> funiculis, ponderibus, orbiculis, <lb/>&longs;piritu inclu&longs;o humanos motus &longs;ine voce <expan abbr="ed&etilde;tes">edentes</expan> perbell&egrave; <lb/>expre&longs;&longs;erunt. </s>
  
 <s><expan abbr="No&longs;troq;">No&longs;troque</expan> <expan abbr="t&etilde;pore">tempore</expan> alij multi in oculis no&longs;tris <lb/>&longs;imilia plurima po&longs;uerunt. </s> <s id="id.000121"><expan abbr="No&longs;troq;">No&longs;troque</expan> <expan abbr="t&etilde;pore">tempore</expan> alij multi in oculis no&longs;tris <lb/>&longs;imilia plurima po&longs;uerunt. </s>
  
 <s>quales fuerunt icuncul&aelig; ill&aelig; <lb/>ad <expan abbr="cant&utilde;">cantum</expan> cythar&aelig; &longs;altitantes, manus manibus iungentes, <lb/>in equos, in currus con&longs;cendentes, mod&ograve; rur&longs;us <expan abbr="curr&etilde;tes">currentes</expan>, <lb/>modo re&longs;titantes. </s> <s id="id.000122">quales fuerunt icuncul&aelig; ill&aelig; <lb/>ad <expan abbr="cant&utilde;">cantum</expan> cythar&aelig; &longs;altitantes, manus manibus iungentes, <lb/>in equos, in currus con&longs;cendentes, mod&ograve; rur&longs;us <expan abbr="curr&etilde;tes">currentes</expan>, <lb/>modo re&longs;titantes. </s>
  
 <s>Tum ca&longs;tellum illud mirabile, in quo <lb/><expan abbr="fabror&utilde;">fabrorum</expan> genus omne &longs;uum munus affabr&egrave;, nec o&longs;citanter <pb/>exercebat, quod h&icirc;c Luteti&aelig; vidimus. </s> <s id="id.000123">Tum ca&longs;tellum illud mirabile, in quo <lb/><expan abbr="fabror&utilde;">fabrorum</expan> genus omne &longs;uum munus affabr&egrave;, nec o&longs;citanter <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.023.jpg"/>exercebat, quod h&icirc;c Luteti&aelig; vidimus. </s>
  
 <s>Vt &amp; Noriberg&aelig; <lb/>mu&longs;ca ferrea <expan abbr="c&otilde;memoratur">commemoratur</expan> &egrave; manu artificis &longs;ui cuola&longs;&longs;e, <lb/>&amp; conuiuas circumuolita&longs;&longs;e, <expan abbr="tandemq;">tandemque</expan> veluti defe&longs;&longs;a in <lb/>&longs;ui domini manum redij&longs;&longs;e: tum aquila illa, qu&aelig; in a&euml;re <lb/>&longs;ublimis Carolo imperatori huius nominis quinto ad vr&shy;<lb/>bem aduentanti obuia facta, <expan abbr="v&longs;q;">v&longs;que</expan> ad vrbis <expan abbr="port&atilde;">portam</expan> cundem <lb/>comitata e&longs;t, ne fabulam exi&longs;timemus quod de columba <lb/>Archit&aelig; <expan abbr="vol&atilde;te">volante</expan> &agrave; veteribus <expan abbr="c&otilde;memoratum">commemoratum</expan> e&longs;t: <expan abbr="neq;">neque</expan> illud <lb/>quod fertur de D&aelig;daleis operibus, &amp; Vulcani tripodi&shy;<lb/>bus, pectinibus, malleis, qui iniu&longs;&longs;i ad opus &longs;ponte &longs;ua ve&shy;<lb/>niebant, &amp; ni&longs;i vinculis coercerentur, aufugiebant. </s> <s id="id.000124">Vt &amp; Noriberg&aelig; <lb/>mu&longs;ca ferrea <expan abbr="c&otilde;memoratur">commemoratur</expan> &egrave; manu artificis &longs;ui euola&longs;&longs;e, <lb/>&amp; conuiuas circumuolita&longs;&longs;e, <expan abbr="tandemq;">tandemque</expan> veluti defe&longs;&longs;a in <lb/>&longs;ui domini manum redij&longs;&longs;e: tum aquila illa, qu&aelig; in a&euml;re <lb/>&longs;ublimis Carolo imperatori huius nominis quinto ad vr&shy;<lb/>bem aduentanti obuia facta, <expan abbr="v&longs;q;">v&longs;que</expan> ad vrbis <expan abbr="port&atilde;">portam</expan> eundem <lb/>comitata e&longs;t, ne fabulam exi&longs;timemus quod de columba <lb/>Archit&aelig; <expan abbr="vol&atilde;te">volante</expan> &agrave; veteribus <expan abbr="c&otilde;memoratum">commemoratum</expan> e&longs;t: <expan abbr="neq;">neque</expan> illud <lb/>quod fertur de D&aelig;daleis operibus, &amp; Vulcani tripodi&shy;<lb/>bus, pectinibus, malleis, qui iniu&longs;&longs;i ad opus &longs;ponte &longs;ua ve&shy;<lb/>niebant, &amp; ni&longs;i vinculis coercerentur, aufugiebant. </s>
  
 <s>Sed <lb/>h&aelig;c ad delectationem tantum &longs;unt comparata, vtilia &amp; <lb/>vit&aelig; human&ecedil; <expan abbr="tr&atilde;&longs;ig&etilde;d&aelig;">tran&longs;igend&aelig;</expan> nece&longs;&longs;aria omnino &longs;unt Agricul&shy;<lb/>tur&aelig;, Militaris, Architectur&aelig;, Medicin&aelig;, Nautic&aelig;, Mer&shy;<lb/>catur&aelig; munera: quibus <expan abbr="alim&etilde;ta">alimenta</expan>, tecta, &longs;anitas, ve&longs;titus, di&shy;<lb/>uiti&aelig;, &amp; ab c&oelig;li, <expan abbr="ho&longs;tiumq;">ho&longs;tiumque</expan> iniurijs defen&longs;io qu&aelig;runtur. <lb/></s> <s id="id.000125">Sed <lb/>h&aelig;c ad delectationem tantum &longs;unt comparata, vtilia &amp; <lb/>vit&aelig; human&ecedil; <expan abbr="tr&atilde;&longs;ig&etilde;d&aelig;">tran&longs;igend&aelig;</expan> nece&longs;&longs;aria omnino &longs;unt Agricul&shy;<lb/>tur&aelig;, Militaris, Architectur&aelig;, Medicin&aelig;, Nautic&aelig;, Mer&shy;<lb/>catur&aelig; munera: quibus <expan abbr="alim&etilde;ta">alimenta</expan>, tecta, &longs;anitas, ve&longs;titus, di&shy;<lb/>uiti&aelig;, &amp; ab c&oelig;li, <expan abbr="ho&longs;tiumq;">ho&longs;tiumque</expan> iniurijs defen&longs;io qu&aelig;runtur. <lb/></s>
  
 <s>At quid artes ill&aelig; e&longs;&longs;e po&longs;&longs;ent, ni&longs;i machin&aelig; <expan abbr="inu&etilde;t&aelig;">inuent&aelig;</expan> fui&longs;&shy;<lb/>&longs;ent, &amp; in&longs;trumenta, quibus vn&acirc; <expan abbr="c&utilde;">cum</expan> <expan abbr="homin&utilde;">hominum</expan> parua vi, mo&shy;<lb/>les <expan abbr="lapid&utilde;">lapidum</expan>, <expan abbr="lignor&utilde;">lignorum</expan>, <expan abbr="frug&utilde;">frugum</expan>, <expan abbr="terrar&utilde;">terrarum</expan>, <expan abbr="mari&utilde;">marium</expan> <expan abbr="ing&etilde;tes">ingentes</expan> loco <expan abbr="di-mou&etilde;tur">di&shy;<lb/>mouentur</expan>, pelluntur, trahuntur, <expan abbr="c&otilde;uehuntur">conuehuntur</expan>, in <expan abbr="gyr&utilde;">gyrum</expan> con&shy;<lb/>torquentur, &amp; <expan abbr="t&atilde;dem">tandem</expan> alti&longs;&longs;imis locis &amp; difficilimis repo&shy;<lb/>nuntur? </s> <s id="id.000126">At quid artes ill&aelig; e&longs;&longs;e po&longs;&longs;ent, ni&longs;i machin&aelig; <expan abbr="inu&etilde;t&aelig;">inuent&aelig;</expan> fui&longs;&shy;<lb/>&longs;ent, &amp; in&longs;trumenta, quibus vn&acirc; <expan abbr="c&utilde;">cum</expan> <expan abbr="homin&utilde;">hominum</expan> parua vi, mo&shy;<lb/>les <expan abbr="lapid&utilde;">lapidum</expan>, <expan abbr="lignor&utilde;">lignorum</expan>, <expan abbr="frug&utilde;">frugum</expan>, <expan abbr="terrar&utilde;">terrarum</expan>, <expan abbr="mari&utilde;">marium</expan> <expan abbr="ing&etilde;tes">ingentes</expan> loco <expan abbr="di&shy;mou&etilde;tur">di&shy;<lb/>mouentur</expan>, pelluntur, trahuntur, <expan abbr="c&otilde;uehuntur">conuehuntur</expan>, in <expan abbr="gyr&utilde;">gyrum</expan> con&shy;<lb/>torquentur, &amp; <expan abbr="t&atilde;dem">tandem</expan> alti&longs;&longs;imis locis &amp; difficilimis repo&shy;<lb/>nuntur? </s>
  
 <s>aut <expan abbr="e&aelig;d&etilde;">e&aelig;dem</expan> iu&longs;ta quantitate appen&longs;&aelig;, aut <expan abbr="m&etilde;&longs;urat&aelig;">men&longs;urat&aelig;</expan> <lb/><expan abbr="cuiq;">cuique</expan> &longs;uum qu&aelig;renti di&longs;tribuuntur? </s> <s id="id.000127">aut <expan abbr="e&aelig;d&etilde;">e&aelig;dem</expan> iu&longs;ta quantitate appen&longs;&aelig;, aut <expan abbr="m&etilde;&longs;urat&aelig;">men&longs;urat&aelig;</expan> <lb/><expan abbr="cuiq;">cuique</expan> &longs;uum qu&aelig;renti di&longs;tribuuntur? </s>
  
 <s>Vnde &longs;ex &longs;unt illa ex <lb/>innumeris &agrave; veteribus <expan abbr="inu&etilde;ta">inuenta</expan>, <expan abbr="quor&utilde;">quorum</expan> &longs;ingula &longs;eor&longs;um ma&shy;<lb/>gna vi: <expan abbr="coni&utilde;cta">coniuncta</expan> ver&ograve;, &amp; multiplicata infinitis propemo&shy;<lb/>dum viribus pollere animaduertuntur, libra, vectis, tro&shy;<lb/>chlea, axis in peritrochio, cuncus, &amp; cochlea. </s> <s id="id.000128">Vnde &longs;ex &longs;unt illa ex <lb/>innumeris &agrave; veteribus <expan abbr="inu&etilde;ta">inuenta</expan>, <expan abbr="quor&utilde;">quorum</expan> &longs;ingula &longs;eor&longs;um ma&shy;<lb/>gna vi: <expan abbr="coni&utilde;cta">coniuncta</expan> ver&ograve;, &amp; multiplicata infinitis propemo&shy;<lb/>dum viribus pollere animaduertuntur, libra, vectis, tro&shy;<lb/>chlea, axis in peritrochio, cuneus, &amp; cochlea. </s>
  
 <s>Sed qu&ecedil; au&shy;<lb/>dio h&icirc;c dicet aliquis? </s> <s id="id.000129">Sed qu&ecedil; au&shy;<lb/>dio h&icirc;c dicet aliquis? </s>
  
 <s>Nunquid <expan abbr="in&longs;trum&etilde;ta">in&longs;trumenta</expan> mercatorum, <lb/><expan abbr="c&oelig;m&etilde;tariorum">c&oelig;mentariorum</expan>, baiulorum, <expan abbr="phalangarior&utilde;">phalangariorum</expan>, lignatorum, <lb/>lapicidarum, <expan abbr="vinitor&utilde;">vinitorum</expan>, &amp; eiu&longs;modi <expan abbr="vili&utilde;">vilium</expan> &longs;or dido rum que <lb/><expan abbr="homin&utilde;">hominum</expan>? </s> <s id="id.000130">Nunquid <expan abbr="in&longs;trum&etilde;ta">in&longs;trumenta</expan> mercatorum, <lb/><expan abbr="c&oelig;m&etilde;tariorum">c&oelig;mentariorum</expan>, baiulorum, <expan abbr="phalangarior&utilde;">phalangariorum</expan>, lignatorum, <lb/>lapicidarum, <expan abbr="vinitor&utilde;">vinitorum</expan>, &amp; eiu&longs;modi <expan abbr="vili&utilde;">vilium</expan> &longs;ordidorumque <lb/><expan abbr="homin&utilde;">hominum</expan>? </s>
  
 <s>Audis &longs;an&egrave;: &longs;ed &amp; A&longs;tre&aelig;, &amp; Neptuni, &amp; Mar&shy;<lb/>tis, &amp; Vulcani, &amp; Cereris, &amp; Palladis, qui tanto pere pro&shy;<lb/>pter h&aelig;c &longs;ua inuenta anti quis <expan abbr="placuer&utilde;t">placuerunt</expan>, vt &longs;int ab illis in <lb/>deorum <expan abbr="numer&utilde;">numerum</expan>, eorumque <expan abbr="maior&utilde;">maiorum</expan> relati. </s> <s id="id.000131">Audis &longs;an&egrave;: &longs;ed &amp; A&longs;tre&aelig;, &amp; Neptuni, &amp; Mar&shy;<lb/>tis, &amp; Vulcani, &amp; Cereris, &amp; Palladis, qui tantopere pro&shy;<lb/>pter h&aelig;c &longs;ua inuenta antiquis <expan abbr="placuer&utilde;t">placuerunt</expan>, vt &longs;int ab illis in <lb/>deorum <expan abbr="numer&utilde;">numerum</expan>, eorumque <expan abbr="maior&utilde;">maiorum</expan> relati. </s>
  
 <s>Trutinarum <lb/>librarumque examinatio reperta, inquit Vitruuius, vin&shy;<lb/>dicat ab iniquitate iu&longs;tis moribus <expan abbr="vit&atilde;">vitam</expan>. </s> <s id="id.000132">Trutinarum <lb/>librarumque examinatio reperta, inquit Vitruuius, vin&shy;<lb/>dicat ab iniquitate iu&longs;tis moribus <expan abbr="vit&atilde;">vitam</expan>. </s>
  
 <s>Vnde &longs;tatera do&shy;<lb/>lo&longs;a abhominatio e&longs;t apud Deum, dixit <expan abbr="&longs;api&etilde;s">&longs;apiens</expan>, &amp; pondus <pb/>&aelig;quum voluntas eius, &amp; alibi abhominatio e&longs;t apud Deum <lb/>pondus &amp; pondus. </s> <s id="id.000133">Vnde &longs;tatera do&shy;<lb/>lo&longs;a abhominatio e&longs;t apud Deum, dixit <expan abbr="&longs;api&etilde;s">&longs;apiens</expan>, &amp; pondus <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.024.jpg"/>&aelig;quum voluntas eius, &amp; alibi abhominatio e&longs;t apud Deum <lb/>pondus &amp; pondus. </s>
  
 <s>Itaque libr&aelig; inucntrix A &longs;tr&aelig;a pro dea <lb/>lu&longs;tici&ecedil; culta e&longs;t. </s> <s id="id.000134">Itaque libr&aelig; inuentrix A&longs;tr&aelig;a pro dea <lb/>lu&longs;tici&ecedil; culta e&longs;t. </s>
  
 <s>Libra ip&longs;a iudicum oculis in fori &longs;ui tabu&shy;<lb/>lis, &amp; &longs;ignis propo&longs;ita, ad quam intuerentur, &amp; denique in <lb/>c&oelig;le&longs;te &longs;ignum conuer&longs;a, qu&aelig; diem naturalem, quem Sol <lb/>&aelig;quatorem peragrans circulum conficit, in tempus lucis &amp; <lb/>tenebrarum &aelig;qualiter vbique diuideret. </s> <s id="id.000135">Libra ip&longs;a iudicum oculis in fori &longs;ui tabu&shy;<lb/>lis, &amp; &longs;ignis propo&longs;ita, ad quam intuerentur, &amp; denique in <lb/>c&oelig;le&longs;te &longs;ignum conuer&longs;a, qu&aelig; diem naturalem, quem Sol <lb/>&aelig;quatorem peragrans circulum conficit, in tempus lucis &amp; <lb/>tenebrarum &aelig;qualiter vbique diuideret. </s>
  
 <s>Vnde po&euml;ta,</s></p><p type="main"> <s id="id.000136">Vnde po&euml;ta,</s></p><p type="main">
  
 <s><emph type="italics"/>Libra die, &longs;omnique pares vbi fecerit horas,<emph.end type="italics"/></s></p><p type="main"> <s id="id.000137"><emph type="italics"/>Libra die, &longs;omnique pares vbi fecerit horas,<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Et medium luci atque vmbris iam diuidet orbem.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000138"><emph type="italics"/>Et medium luci atque vmbris iam diuidet orbem. <emph.end type="italics"/></s></p><p type="main">
  
 <s>Neptuno ver&ograve;, cum tridentem antiquitas attribuit, quid <lb/>aliud, quam vectem? </s> <s id="id.000139">Neptuno ver&ograve;, cum tridentem antiquitas attribuit, quid <lb/>aliud, quam vectem? </s>
  
 <s>Gr&aelig;ci appellant <foreign lang="greek">mo/xlon</foreign> vnde ille <foreign lang="greek">mox&shy;<lb/>leuth\s</foreign> vectiarius &agrave; po&euml;tis dictus e&longs;t, &amp; terr&aelig; mati&longs;que con&shy;<lb/>cu&longs;&longs;or, &amp; hac machina Syrtes &longs;ubleuans, quo plus Troianis <lb/>apparerent &agrave; po&euml;ta inducitur,</s></p><p type="main"> <s id="id.000140">Gr&aelig;ci appellant <foreign lang="el">mo/xlon</foreign> vnde ille <foreign lang="el">mox&shy;<lb/>leuth\s</foreign> vectiarius &agrave; po&euml;tis dictus e&longs;t, &amp; terr&aelig; mati&longs;que con&shy;<lb/>cu&longs;&longs;or, &amp; hac machina Syrtes &longs;ubleuans, quo plus Troianis <lb/>apparerent &agrave; po&euml;ta inducitur,</s></p><p type="main">
  
 <s><emph type="italics"/>Leuat ip&longs;e tridenti,<emph.end type="italics"/></s></p><p type="main"> <s id="id.000141"><emph type="italics"/>Leuat ip&longs;e tridenti,<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Et va&longs;tas aperit Syrtes.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000142"><emph type="italics"/>Et va&longs;tas aperit Syrtes. <emph.end type="italics"/></s></p><p type="main">
  
 <s>Cert&egrave; vectis palus e&longs;t <expan abbr="obl&otilde;gior">oblongior</expan>, materi&aelig; firm&aelig;, cu&longs;pide acu&shy;<lb/>ta, &amp; paulo latiori lingu&aelig; in&longs;tar, quam prop&egrave;, quando e&longs;t <lb/>&longs;ubditum hypomochlium, huic pondus in cumbens, id que <lb/>grauius quam quod &agrave; decem hominum &longs;olis manibus di&shy;<lb/>moueri loco po&longs;&longs;et, vnius <expan abbr="tam&etilde;">tamen</expan> viribus caput huius pali de&shy;<lb/>primentibus, vel &longs;i terra &longs;ubdita pro hypomochlio e&longs;t &longs;uble&shy;<lb/>uantibus, dimouetur. </s> <s id="id.000143">Cert&egrave; vectis palus e&longs;t <expan abbr="obl&otilde;gior">oblongior</expan>, materi&aelig; firm&aelig;, cu&longs;pide acu&shy;<lb/>ta, &amp; paulo latiori lingu&aelig; in&longs;tar, quam prop&egrave;, quando e&longs;t <lb/>&longs;ubditum hypomochlium, huic pondus incumbens, id que <lb/>grauius quam quod &agrave; decem hominum &longs;olis manibus di&shy;<lb/>moueri loco po&longs;&longs;et, vnius <expan abbr="tam&etilde;">tamen</expan> viribus caput huius pali de&shy;<lb/>primentibus, vel &longs;i terra &longs;ubdita pro hypomochlio e&longs;t &longs;uble&shy;<lb/>uantibus, dimouetur. </s>
  
 <s>Vnde in magnis <expan abbr="&aelig;dificior&utilde;">&aelig;dificiorum</expan> &longs;ub&longs;tru&shy;<lb/>ctionibus vnus vectis pro multorum manibus, vnus homo <lb/>bimanus pro Briareo centimano, mod&ograve; pondera lapidum, <lb/>trabi&uacute;m que colo&longs;&longs;icotera fabris &amp; architectis loco dimo&shy;<lb/>uet, &amp; &longs;ubleuat: mod&ograve; <expan abbr="ei&longs;d&etilde;">ei&longs;dem</expan> collopis figura &longs;ucculas ver&longs;at: <lb/>modo tollenonis &longs;pecie aquas &egrave; puteis operis &amp; olitoribus <lb/>exhaurit: modo phalang&aelig; forma baiulis &amp; phalangarijs <lb/>proportionalia tanquam in bilance pondera partitur, mo&shy;<lb/>do iugi nomine in aratro bobus &aelig;quum arationis laborem <lb/>di&longs;pen&longs;at &longs;iue &aelig;quales &longs;iue in&aelig;quales.</s></p><p type="main"> <s id="id.000144">Vnde in magnis <expan abbr="&aelig;dificior&utilde;">&aelig;dificiorum</expan> &longs;ub&longs;tru&shy;<lb/>ctionibus vnus vectis pro multorum manibus, vnus homo <lb/>bimanus pro Briareo centimano, mod&ograve; pondera lapidum, <lb/>trabi&uacute;m que colo&longs;&longs;icotera fabris &amp; architectis loco dimo&shy;<lb/>uet, &amp; &longs;ubleuat: mod&ograve; <expan abbr="ei&longs;d&etilde;">ei&longs;dem</expan> collopis figura &longs;ucculas ver&longs;at: <lb/>modo tollenonis &longs;pecie aquas &egrave; puteis operis &amp; olitoribus <lb/>exhaurit: modo phalang&aelig; forma baiulis &amp; phalangarijs <lb/>proportionalia tanquam in bilance pondera partitur, mo&shy;<lb/>do iugi nomine in aratro bobus &aelig;quum arationis laborem <lb/>di&longs;pen&longs;at &longs;iue &aelig;quales &longs;iue in&aelig;quales. </s></p><p type="main">
  
 <s><emph type="italics"/>Veniant ad aratra iuuenci.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000145"><emph type="italics"/>Veniant ad aratra iuuenci. <emph.end type="italics"/></s></p><p type="main">
  
 <s>Sed cum naui tran&longs;mittitur flumen, aut mare tran&longs;meatur, <lb/>quid e&longs;t in ea remus aliud, quam vectis inuer&longs;us, habens in <lb/>&longs;calmo hypomochlium? </s> <s id="id.000146">Sed cum naui tran&longs;mittitur flumen, aut mare tran&longs;meatur, <lb/>quid e&longs;t in ea remus aliud, quam vectis inuer&longs;us, habens in <lb/>&longs;calmo hypomochlium? </s>
  
 <s><expan abbr="aqu&atilde;">aquam</expan> pro pondere loco dimouens? <lb/></s> <s id="id.000147"><expan abbr="aqu&atilde;">aquam</expan> pro pondere loco dimouens? <lb/></s>
  
 <s>vt in eum cedat nauis, &amp; quidem impul&longs;us ille &agrave; remige pro <pb/>vectiatio tanquam tridens &agrave; Neptuno? </s> <s id="id.000148">vt in eum cedat nauis, &amp; quidem impul&longs;us ille &agrave; remige pro <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.025.jpg"/>vectiatio tanquam tridens &agrave; Neptuno? </s>
  
 <s>Quin &amp; guberna&shy;<lb/>calum, quo gubernator in puppi <expan abbr="&longs;ed&etilde;s">&longs;edens</expan> tam facil&egrave; obliquat <lb/>nauim etiam ingentem, &amp; cum magna in prora loci muta&shy;<lb/>tione, licet in puppi ade&ograve; exigua, vt nihil agere, aut <expan abbr="eti&atilde;">etiam</expan> lu&shy;<lb/>dere videatur: aliud <expan abbr="tam&etilde;">tamen</expan> nihil, quam vectis e&longs;&longs;e <expan abbr="c&otilde;perietur">comperietur</expan>. <lb/></s> <s id="id.000149">Quin &amp; guberna&shy;<lb/>calum, quo gubernator in puppi <expan abbr="&longs;ed&etilde;s">&longs;edens</expan> tam facil&egrave; obliquat <lb/>nauim etiam ingentem, &amp; cum magna in prora loci muta&shy;<lb/>tione, licet in puppi ade&ograve; exigua, vt nihil agere, aut <expan abbr="eti&atilde;">etiam</expan> lu&shy;<lb/>dere videatur: aliud <expan abbr="tam&etilde;">tamen</expan> nihil, quam vectis e&longs;&longs;e <expan abbr="c&otilde;perietur">comperietur</expan>. <lb/></s>
  
 <s>Neque malus erectus in medio nauis e&longs;t aliud. </s> <s id="id.000150">Neque malus erectus in medio nauis e&longs;t aliud. </s>
  
 <s>Calx enim, <lb/>&longs;eu edolium e&longs;t hypomochlium, pars &egrave; qua pendet carche&shy;<lb/>&longs;ium cum pa&longs;&longs;is velis, <expan abbr="tanqu&atilde;">tanquam</expan> alis D&aelig;daleis perflante vento <lb/>propul&longs;a propellit pondus, nauim &longs;cilicet, &amp; quod e&longs;t admi&shy;<lb/>rabilius ibi non aliter venti, quam equi reguntur, <expan abbr="d&utilde;">dum</expan> ex car&shy;<lb/>che&longs;ij vt fr&aelig;ni &longs;itu mod&ograve; altiore: mod&ograve; depre&longs;&longs;iore provt <lb/>&longs;unt admi&longs;&longs;i: ita nauis mod&ograve; vehementius, mod&ograve; remi&longs;&longs;ius <lb/>impellitur.</s></p><p type="main"> <s id="id.000151">Calx enim, <lb/>&longs;eu edolium e&longs;t hypomochlium, pars &egrave; qua pendet carche&shy;<lb/>&longs;ium cum pa&longs;&longs;is velis, <expan abbr="tanqu&atilde;">tanquam</expan> alis D&aelig;daleis perflante vento <lb/>propul&longs;a propellit pondus, nauim &longs;cilicet, &amp; quod e&longs;t admi&shy;<lb/>rabilius ibi non aliter venti, quam equi reguntur, <expan abbr="d&utilde;">dum</expan> ex car&shy;<lb/>che&longs;ij vt fr&aelig;ni &longs;itu mod&ograve; altiore: mod&ograve; depre&longs;&longs;iore provt <lb/>&longs;unt admi&longs;&longs;i: ita nauis mod&ograve; vehementius, mod&ograve; remi&longs;&longs;ius <lb/>impellitur. </s></p><p type="main">
  
 <s>Sed h&aelig;c devecte &longs;atis. </s> <s id="id.000152">Sed h&aelig;c devecte &longs;atis. </s>
  
 <s><expan abbr="Trochle&atilde;">Trochleam</expan> ver&ograve;, qu&aelig; orbiculus e&longs;t <lb/>circa axem immobilem fune conuolutus, quantis viribus <lb/><expan abbr="pr&aelig;dit&atilde;">pr&aelig;ditam</expan> e&longs;&longs;e animaduertimus. </s> <s id="id.000153"><expan abbr="Trochle&atilde;">Trochleam</expan> ver&ograve;, qu&aelig; orbiculus e&longs;t <lb/>circa axem immobilem fune conuolutus, quantis viribus <lb/><expan abbr="pr&aelig;dit&atilde;">pr&aelig;ditam</expan> e&longs;&longs;e animaduertimus. </s>
  
 <s>Ex hac multiplicata, factum <lb/>e&longs;t tri&longs;pa&longs;ton, pentepa&longs;ton, poly&longs;pa&longs;ton, viribus <expan abbr="quor&utilde;">quorum</expan> <expan abbr="c&otilde;fi-&longs;us">confi&shy;<lb/>&longs;us</expan> Archimedes cum audiret <expan abbr="aliqu&etilde;">aliquem</expan> <expan abbr="di&longs;put&atilde;tem">di&longs;putantem</expan> plures e&longs;&longs;e <lb/>mundos coram Heronerege Syracu&longs;arum, au&longs;us e&longs;t dicere. <lb/></s> <s id="id.000154">Ex hac multiplicata, factum <lb/>e&longs;t tri&longs;pa&longs;ton, pentepa&longs;ton, poly&longs;pa&longs;ton, viribus <expan abbr="quor&utilde;">quorum</expan> <expan abbr="c&otilde;fi&shy;&longs;us">confi&shy;<lb/>&longs;us</expan> Archimedes cum audiret <expan abbr="aliqu&etilde;">aliquem</expan> <expan abbr="di&longs;put&atilde;tem">di&longs;putantem</expan> plures e&longs;&longs;e <lb/>mundos coram Herone rege Syracu&longs;arum, au&longs;us e&longs;t dicere. <lb/></s>
  
 <s>Da mihi vbi &longs;i&longs;tam pedem, &amp; hanc ego <expan abbr="terr&atilde;">terram</expan> loco &longs;uo dimo&shy;<lb/>uebo. </s> <s id="id.000155">Da mihi vbi &longs;i&longs;tam pedem, &amp; hanc ego <expan abbr="terr&atilde;">terram</expan> loco &longs;uo dimo&shy;<lb/>uebo. </s>
  
 <s>cuius admirabilis dicti <expan abbr="c&utilde;">cum</expan> rogatus e&longs;&longs;et &agrave; rege, vt &longs;pe&shy;<lb/>cimen aliquod ederet, vna manu l&aelig;ua quinquies millen&ucirc;m <lb/>modiorum <expan abbr="p&otilde;dus">pondus</expan> attraxit: nauem in &longs;iccum littus eiectam <lb/>&amp; grauiter <expan abbr="onerat&atilde;">oneratam</expan> ad &longs;e perinde pertraxit, ac &longs;i in mari re&shy;<lb/>mis, veli&longs;ve impul&longs;a fui&longs;&longs;et: aliam po&longs;tea recens <expan abbr="c&otilde;&longs;tructam">con&longs;tructam</expan> <lb/>ingentis magnitudinis ab Herone regi &AElig;gyptiorum Ptolo&shy;<lb/>m&aelig;o dono mittendam, quam omnes <expan abbr="Syracu&longs;anor&utilde;">Syracu&longs;anorum</expan> ciuium <lb/>vires <expan abbr="c&otilde;iunct&aelig;">coniunct&aelig;</expan> dimouere loco non <expan abbr="potuer&atilde;t">potuerant</expan>, vt &longs;olus Hiero <lb/>machinis adiutus in mare educerer, perfecit: &amp; <expan abbr="quid&etilde;">quidem</expan> cum <lb/>tanta ip&longs;ius regis admiratione, vt exclamarit, <foreign lang="greek"><gap/>po\ tau/ths <gap/><lb/>k(me/<gap/>as w_<gap/>i\ w_anto\s *arxhmh/<gap/> le/<gap/>n<gap/>i pi<gap/>eute/on.</foreign> Ab hoc die <lb/>quic quid dixerit Archimedes huic <expan abbr="credend&utilde;">credendum</expan>. </s> <s id="id.000156">cuius admirabilis dicti <expan abbr="c&utilde;">cum</expan> rogatus e&longs;&longs;et &agrave; rege, vt &longs;pe&shy;<lb/>cimen aliquod ederet, vna manu l&aelig;ua quinquies millen&ucirc;m <lb/>modiorum <expan abbr="p&otilde;dus">pondus</expan> attraxit: nauem in &longs;iccum littus eiectam <lb/>&amp; grauiter <expan abbr="onerat&atilde;">oneratam</expan> ad &longs;e perinde pertraxit, ac &longs;i in mari re&shy;<lb/>mis, veli&longs;ve impul&longs;a fui&longs;&longs;et: aliam po&longs;tea recens <expan abbr="c&otilde;&longs;tructam">con&longs;tructam</expan> <lb/>ingentis magnitudinis ab Herone regi &AElig;gyptiorum Ptolo&shy;<lb/>m&aelig;o dono mittendam, quam omnes <expan abbr="Syracu&longs;anor&utilde;">Syracu&longs;anorum</expan> ciuium <lb/>vires <expan abbr="c&otilde;iunct&aelig;">coniunct&aelig;</expan> dimouere loco non <expan abbr="potuer&atilde;t">potuerant</expan>, vt &longs;olus Hiero <lb/>machinis adiutus in mare educerer, perfecit: &amp; <expan abbr="quid&etilde;">quidem</expan> cum <lb/>tanta ip&longs;ius regis admiratione, vt exclamarit, <foreign lang="el">a)po\ tau/ths th=s <lb/>h(me/ras peri\ p=anto\s *arxhmh/dei le/gonti pisteute/on. </foreign></s>
  
 <s>At ab eo die <lb/>ab Archimede prodijt illud problema inexpertis in credibi&shy;<lb/>le, cruditis tamen demon&longs;tratum. </s> <s> Ab hoc die <lb/>quicquid dixerit Archimedes huic <expan abbr="credend&utilde;">credendum</expan>. </s>
  
 <s>Datum pondus &agrave; data <lb/>potentia moueri. </s> <s id="id.000157">At ab eo die <lb/>ab Archimede prodijt illud problema inexpertis in credibi&shy;<lb/>le, eruditis tamen demon&longs;tratum. </s>
  
 <s>quod in vectc, trochlea, &amp; axe in peritro&shy;<lb/>chio nuper &agrave; Guidone Vbaldo demon&longs;trationibus geome&shy;<lb/>tricis habemus confirmatum. </s> <s id="id.000158">Datum pondus &agrave; data <lb/>potentia moueri. </s>
  
 <s>Vectis &longs;olus pondera de loco <pb/>propellit &longs;uo, trochlea euellit, &amp; eadem ad alti&longs;&longs;imas &aelig;di&shy;<lb/>ficiorum vbi opus e&longs;t &longs;edes trahit. </s> <s id="id.000159">quod in vecte, trochlea, &amp; axe in peritro&shy;<lb/>chio nuper &agrave; Guidone Vbaldo demon&longs;trationibus geome&shy;<lb/>tricis habemus confirmatum. </s>
  
 <s>Sit in polo horizontis qui <lb/>trochle&aelig; appendiculum firmet, &amp; ad eum homo ip&longs;e &longs;e &longs;u&shy;<lb/>bleuabit. </s> <s id="id.000160">Vectis &longs;olus pondera de loco <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.026.jpg"/>propellit &longs;uo, trochlea euellit, &amp; eadem ad alti&longs;&longs;imas &aelig;di&shy;<lb/>ficiorum vbi opus e&longs;t &longs;edes trahit. </s>
  
 <s>Sed longior &longs;um in troch&longs;ea, in reliquis ero bre&shy;<lb/>uior. </s> <s id="id.000161">Sit in polo horizontis qui <lb/>trochle&aelig; appendiculum firmet, &amp; ad eum homo ip&longs;e &longs;e &longs;u&shy;<lb/>bleuabit. </s>
  
 <s>Axis in peritrochio cylindrus e&longs;t duobus fulcris per <lb/>extrema &longs;u&longs;tentatus, habens prop&egrave; vnum extremorum tym&shy;<lb/>panum &longs;cytalis aliquot in peripheria in fixis perforatum, ita <lb/>quidem, vt <expan abbr="pot&etilde;tia">potentia</expan>, qu&aelig; &longs;emper in &longs;cytalis e&longs;t, dum circum&shy;<lb/>uertit tympanum &amp; axem, &longs;ur&longs;um etiam ex inferis euehat <lb/>pondus quodlibet axi fune circa ip&longs;um axem reuoluto <lb/>appen&longs;um. </s> <s id="id.000162">Sed longior &longs;um in trochlea, in reliquis ero bre&shy;<lb/>uior. </s>
  
 <s>Huius machin&aelig; beneficio de&longs;cenditur in vi&longs;ce&shy;<lb/>ra terr&aelig;, &amp; illinc effo&longs;&longs;&aelig; opes, non vt Ouidius ait, &longs;emper</s></p><p type="main"> <s id="id.000163">Axis in peritrochio cylindrus e&longs;t duobus fulcris per <lb/>extrema &longs;u&longs;tentatus, habens prop&egrave; vnum extremorum tym&shy;<lb/>panum &longs;cytalis aliquot in peripheria in fixis perforatum, ita <lb/>quidem, vt <expan abbr="pot&etilde;tia">potentia</expan>, qu&aelig; &longs;emper in &longs;cytalis e&longs;t, dum circum&shy;<lb/>uertit tympanum &amp; axem, &longs;ur&longs;um etiam ex inferis euehat <lb/>pondus quodlibet axi fune circa ip&longs;um axem reuoluto <lb/>appen&longs;um. </s>
  
 <s><emph type="italics"/>Irritamenta malorum:<emph.end type="italics"/></s></p><p type="main"> <s id="id.000164">Huius machin&aelig; beneficio de&longs;cenditur in vi&longs;ce&shy;<lb/>ra terr&aelig;, &amp; illinc effo&longs;&longs;&aelig; opes, non vt Ouidius ait, &longs;emper</s></p><p type="main">
  
 <s>quin potius occa&longs;iones &amp; adiumenta bonorum multorum, <lb/>&longs;i <expan abbr="bon&utilde;">bonum</expan> <expan abbr="po&longs;&longs;e&longs;&longs;or&etilde;">po&longs;&longs;e&longs;&longs;orem</expan> nact&aelig; &longs;int. </s> <s id="id.000165"><emph type="italics"/>Irritamenta malorum:<emph.end type="italics"/></s></p><p type="main">
  
 <s>Nam vt recte dixit Pindarus,</s></p><p type="main"> <s id="id.000166">quin potius occa&longs;iones &amp; adiumenta bonorum multorum, <lb/>&longs;i <expan abbr="bon&utilde;">bonum</expan> <expan abbr="po&longs;&longs;e&longs;&longs;or&etilde;">po&longs;&longs;e&longs;&longs;orem</expan> nact&aelig; &longs;int. </s>
  
 <s><emph type="italics"/>Qu&aelig; Virtute pecunia<emph.end type="italics"/></s></p><p type="main"> <s id="id.000167">Nam vt recte dixit Pindarus,</s></p><p type="main">
  
 <s><emph type="italics"/>Exornata nitet, &longs;uppeditat Vias<emph.end type="italics"/></s></p><p type="main"> <s id="id.000168"><emph type="italics"/>Qu&aelig; Virtute pecunia<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Non vnas, bene agas, quibus<emph.end type="italics"/></s></p><p type="main"> <s id="id.000169"><emph type="italics"/>Exornata nitet, &longs;uppeditat Vias<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Qu&aelig; &longs;ors cunque ferens obtulerit tibi:<emph.end type="italics"/></s></p><p type="main"> <s id="id.000170"><emph type="italics"/>Non vnas, bene agas, quibus<emph.end type="italics"/></s></p><p type="main">
  
 <s>Et vt Antiphanes,</s></p><p type="main"> <s id="id.000171"><emph type="italics"/>Qu&aelig; &longs;ors cunque ferens obtulerit tibi:<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Per deos cur optet quis dite&longs;cere?<emph.end type="italics"/></s></p><p type="main"> <s id="id.000172">Et vt Antiphanes,</s></p><p type="main">
  
 <s><emph type="italics"/>Pecuni&aelig; cur optet habere plurimum:<emph.end type="italics"/></s></p><p type="main"> <s id="id.000173"><emph type="italics"/>Per deos cur optet quis dite&longs;cere?<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Quam po&longs;sit auxiliari vt amicis? </s> <s id="id.000174"><emph type="italics"/>Pecuni&aelig; cur optet habere plurimum:<emph.end type="italics"/></s></p><p type="main">
  
 <s>Grati&aelig;<emph.end type="italics"/></s></p><p type="main"> <s id="id.000175"><emph type="italics"/>Quam po&longs;sit auxiliari vt amicis? </s>
  
 <s><emph type="italics"/>Fruct&uacute;mque &longs;erere Diuarum &longs;uaui&longs;sim&aelig;?<emph.end type="italics"/></s></p><p type="main"> <s id="id.000176">Grati&aelig;<emph.end type="italics"/></s></p><p type="main">
  
 <s>Illinc in quam effo&longs;&longs;&aelig; opes, &longs;ucci, terr&aelig; medicat&aelig;, metalli <lb/>omne genus, lapides, arena, ad &aelig;dificiorum &longs;ub&longs;tructiones, <lb/>ad medicamenta prauarum &amp; contumacium affectionum, <lb/>ad ornamenta in altum, luc&eacute;m que euehuntur.</s></p><p type="main"> <s id="id.000177"><emph type="italics"/>Fruct&uacute;mque &longs;erere Diuarum &longs;uaui&longs;sim&aelig;?<emph.end type="italics"/></s></p><p type="main">
  
 <s>Cuneus vero e&longs;t <expan abbr="in&longs;trum&etilde;tum">in&longs;trumentum</expan> exiguum in formam pyra&shy;<lb/>midis quadrangul&ecedil;, ad vnam <expan abbr="rect&atilde;">rectam</expan> <expan abbr="line&atilde;">lineam</expan> fa&longs;tigiat&aelig; ad diui&shy;<lb/>dendum ligna factum. </s> <s id="id.000178">Illinc in quam effo&longs;&longs;&aelig; opes, &longs;ucci, terr&aelig; medicat&aelig;, metalli <lb/>omne genus, lapides, arena, ad &aelig;dificiorum &longs;ub&longs;tructiones, <lb/>ad medicamenta prauarum &amp; contumacium affectionum, <lb/>ad ornamenta in altum, luc&eacute;m que euehuntur. </s></p><p type="main">
  
 <s>Hoc <expan abbr="c&utilde;">cum</expan> malleo lignator in&longs;tructus, <lb/>&longs;yluam breuiori tempore integram diui&longs;erit: quam &longs;ine ijs <lb/>arboris vnius vnum truncum. </s> <s id="id.000179">Cuneus vero e&longs;t <expan abbr="in&longs;trum&etilde;tum">in&longs;trumentum</expan> exiguum in formam pyra&shy;<lb/>midis quadrangul&ecedil;, ad vnam <expan abbr="rect&atilde;">rectam</expan> <expan abbr="line&atilde;">lineam</expan> fa&longs;tigiat&aelig; ad diui&shy;<lb/>dendum ligna factum. </s>
  
 <s>Milo Crotoniates Athleta <lb/>ille ro bu&longs;ti&longs;&longs;imus fertur cum arborem bifurcatam proprijs <lb/>viribus diuellere contenderet, &amp; diuelli in c&oelig;ptam retinere <lb/>non po&longs;&longs;et, quin partes diuul&longs;&aelig; &longs;umma celeritate in &longs;e&longs;e re&shy;<lb/>dirent, vn&acirc;que raptas manus interciperent, pr&aelig;da vt im&shy;<pb/>bellis ouis fui&longs;&longs;e lupis. </s> <s id="id.000180">Hoc <expan abbr="c&utilde;">cum</expan> malleo lignator in&longs;tructus, <lb/>&longs;yluam breuiori tempore integram diui&longs;erit: quam &longs;ine ijs <lb/>arboris vnius vnum truncum. </s>
  
 <s>Itaque proprijs,</s></p><p type="main"> <s id="id.000181">Milo Crotoniates Athleta <lb/>ille robu&longs;ti&longs;&longs;imus fertur cum arborem bifurcatam proprijs <lb/>viribus diuellere contenderet, &amp; diuelli in c&oelig;ptam retinere <lb/>non po&longs;&longs;et, quin partes diuul&longs;&aelig; &longs;umma celeritate in &longs;e&longs;e re&shy;<lb/>dirent, vn&acirc;que raptas manus interciperent, pr&aelig;da vt im&shy;<pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.027.jpg"/>bellis ouis fui&longs;&longs;e lupis. </s>
  
 <s><emph type="italics"/>viribus ille<emph.end type="italics"/></s></p><p type="main"> <s id="id.000182">Itaque proprijs,</s></p><p type="main">
  
 <s><emph type="italics"/>Confi&longs;us per&yuml;t,<emph.end type="italics"/></s></p><p type="main"> <s id="id.000183"><emph type="italics"/>viribus ille<emph.end type="italics"/></s></p><p type="main">
  
 <s>qui &longs;i cuneo id ip&longs;um facere volui&longs;&longs;et, in eam calamitatem <lb/>non incidi&longs;&longs;et. </s> <s id="id.000184"><emph type="italics"/>Confi&longs;us perijt,<emph.end type="italics"/></s></p><p type="main">
  
 <s>Quis vero <expan abbr="n&otilde;">non</expan> intelligit Martis, Cereris, Vul&shy;<lb/>canique arma &amp; in&longs;trumenta en&longs;es, gladios, mucrones, &longs;e&shy;<lb/>cures, aratra, ligones, a&longs;cias, falces, vngues ferreos &amp; &longs;imilia, <lb/>qu&aelig; percu&longs;&longs;ione, &longs;iue impul&longs;u incidunt, diuidunt, <expan abbr="perfor&atilde;t">perforant</expan>, <lb/>ad huiu&longs;modi facultatis in&longs;trumentum commode referri <lb/>po&longs;&longs;e? </s> <s id="id.000185">qui &longs;i cuneo id ip&longs;um facere volui&longs;&longs;et, in eam calamitatem <lb/>non incidi&longs;&longs;et. </s>
  
 <s>Ligones agricolarum quid &longs;unt aliud, quam cunei <lb/>mallco connexi? </s> <s id="id.000186">Quis vero <expan abbr="n&otilde;">non</expan> intelligit Martis, Cereris, Vul&shy;<lb/>canique arma &amp; in&longs;trumenta en&longs;es, gladios, mucrones, &longs;e&shy;<lb/>cures, aratra, ligones, a&longs;cias, falces, vngues ferreos &amp; &longs;imilia, <lb/>qu&aelig; percu&longs;&longs;ione, &longs;iue impul&longs;u incidunt, diuidunt, <expan abbr="perfor&atilde;t">perforant</expan>, <lb/>ad huiu&longs;modi facultatis in&longs;trumentum commode referri <lb/>po&longs;&longs;e? </s>
  
 <s>Forfex ver&ograve; ad Palladis &amp; &AElig;&longs;culapij Ma&shy;<lb/>chaoni&longs;que artes <expan abbr="t&atilde;">tam</expan> nece&longs;&longs;arius, quid aliud, <expan abbr="qu&atilde;">quam</expan> duplex cu&shy;<lb/>neus, &amp; totuplex vectis? </s> <s id="id.000187">Ligones agricolarum quid &longs;unt aliud, quam cunei <lb/>malleo connexi? </s>
  
 <s>&longs;icuti forceps tantum vectis e&longs;t du&shy;<lb/>plicatus. </s> <s id="id.000188">Forfex ver&ograve; ad Palladis &amp; &AElig;&longs;culapij Ma&shy;<lb/>chaoni&longs;que artes <expan abbr="t&atilde;">tam</expan> nece&longs;&longs;arius, quid aliud, <expan abbr="qu&atilde;">quam</expan> duplex cu&shy;<lb/>neus, &amp; totuplex vectis? </s>
  
 <s>In&longs;trumentum Vulcani perpetu&ograve; in manibus, qu&ograve; <lb/>pruna, ferrum candens, &aelig;s, <expan abbr="argent&utilde;">argentum</expan>, aurum apprehenditur.</s></p><p type="main"> <s id="id.000189">&longs;icuti forceps tantum vectis e&longs;t du&shy;<lb/>plicatus. </s>
  
 <s><emph type="italics"/>Pren&longs;ant<emph.end type="italics"/> (enim vt po&euml;ta ait,) <emph type="italics"/>ver&longs;antque tenaci<emph.end type="italics"/></s></p><p type="main"> <s id="id.000190">In&longs;trumentum Vulcani perpetu&ograve; in manibus, qu&ograve; <lb/>pruna, ferrum candens, &aelig;s, <expan abbr="argent&utilde;">argentum</expan>, aurum apprehenditur. </s></p><p type="main">
  
 <s><emph type="italics"/>Forcipe ferrum.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000191"><emph type="italics"/>Pren&longs;ant<emph.end type="italics"/> (enim vt po&euml;ta ait,) <emph type="italics"/>ver&longs;antque tenaci<emph.end type="italics"/></s></p><p type="main">
  
 <s>At cuneus &longs;implex percu&longs;&longs;ione mallei adigitur. </s> <s id="id.000192"><emph type="italics"/>Forcipe ferrum. <emph.end type="italics"/></s></p><p type="main">
  
 <s>Idem mul&shy;<lb/>tiplicatus &longs;ine percu&longs;&longs;ione rota cum &longs;cytalis in cochlea ita <lb/>penetrare cogitur, vt vu&aelig;, ole&aelig;, nuces, mala, pyra, c&aelig;tera&shy;<lb/>que humida pr&oelig;lis &longs;ubiecta quicquid &longs;ucci &amp; liquoris ha&shy;<lb/>bent, Domino per&longs;oluere cogantur. </s> <s id="id.000193">At cuneus &longs;implex percu&longs;&longs;ione mallei adigitur. </s>
  
 <s>Hoc beneficium ma&shy;<lb/>gni e&longs;t momenti ad vit&aelig; commoda. </s> <s id="id.000194">Idem mul&shy;<lb/>tiplicatus &longs;ine percu&longs;&longs;ione rota cum &longs;cytalis in cochlea ita <lb/>penetrare cogitur, vt vu&aelig;, ole&aelig;, nuces, mala, pyra, c&aelig;tera&shy;<lb/>que humida pr&oelig;lis &longs;ubiecta quicquid &longs;ucci &amp; liquoris ha&shy;<lb/>bent, Domino per&longs;oluere cogantur. </s>
  
 <s>At vt long&aelig;ua v&longs;que in <lb/>&longs;ecula &longs;int &longs;empiterni doctorum hominum commentarij, <lb/>&amp; con&longs;cript&aelig; cogitationes, quantum confert pr&oelig;lum ty&shy;<lb/>pographicum cochle&aelig; vnius beneficio compre&longs;&longs;um? </s> <s id="id.000195">Hoc beneficium ma&shy;<lb/>gni e&longs;t momenti ad vit&aelig; commoda. </s>
  
 <s>Quid <lb/>dicam ab his fontibus etiam deducta omnia poliorcetica, <lb/>quorum &longs;olorum op&egrave; vnus Archimedes Marcelli Syracu&shy;<lb/>&longs;as terra marique <expan abbr="ob&longs;id&etilde;tis">ob&longs;identis</expan> vires diu, <expan abbr="multumq;">multumque</expan> ludificatus <lb/>e&longs;t, pro qua re h&ucirc;c Titi Liuij lubet conferre admirabile re&shy;<lb/>&longs;timonium. </s> <s id="id.000196">At vt long&aelig;ua v&longs;que in <lb/>&longs;ecula &longs;int &longs;empiterni doctorum hominum commentarij, <lb/>&amp; con&longs;cript&aelig; cogitationes, quantum confert pr&oelig;lum ty&shy;<lb/>pographicum cochle&aelig; vnius beneficio compre&longs;&longs;um? </s>
  
 <s>Terra, inquit, marique &longs;imul c&oelig;pt&aelig; oppugnari <lb/>Syracu&longs;&aelig;, terra ab Hexapylo: mari ab Acradina. </s> <s id="id.000197">Quid <lb/>dicam ab his fontibus etiam deducta omnia poliorcetica, <lb/>quorum &longs;olorum op&egrave; vnus Archimedes Marcelli Syracu&shy;<lb/>&longs;as terra marique <expan abbr="ob&longs;id&etilde;tis">ob&longs;identis</expan> vires diu, <expan abbr="multumq;">multumque</expan> ludificatus <lb/>e&longs;t, pro qua re h&ucirc;c Titi Liuij lubet conferre admirabile te&shy;<lb/>&longs;timonium. </s>
  
 <s>Et habui&longs;&shy;<lb/>&longs;et tant&ograve; impetu c&oelig;pta res fortunam, ni&longs;i vnus homo Syra&shy;<lb/>cu&longs;is ea <expan abbr="t&etilde;pe&longs;tate">tempe&longs;tate</expan> fui&longs;&longs;et Archimedes. </s> <s id="id.000198">Terra, inquit, marique &longs;imul c&oelig;pt&aelig; oppugnari <lb/>Syracu&longs;&aelig;, terra ab Hexapylo: mari ab Acradina. </s>
  
 <s>Is erat vnicus &longs;pecta&shy;<lb/>tor c&oelig;li &longs;iderum que: mirabilior tamen inuentor ac machi&shy;<lb/>nator bellicorum <expan abbr="torm&etilde;torum">tormentorum</expan>, operumque: quibus ea qu&aelig; <lb/>ho&longs;tes ingenti mole agerent ip&longs;e perleui momento ludi&longs;i-<pb/>caretur. </s> <s id="id.000199">Et habui&longs;&shy;<lb/>&longs;et tant&ograve; impetu c&oelig;pta res fortunam, ni&longs;i vnus homo Syra&shy;<lb/>cu&longs;is ea <expan abbr="t&etilde;pe&longs;tate">tempe&longs;tate</expan> fui&longs;&longs;et Archimedes. </s>
  
 <s>Murum per in&ecedil;quales ductum colles, pleraque alta <lb/>&amp; difficilia aditu, &longs;ummi&longs;&longs;a qu&aelig;dam, &amp; qu&aelig; planis vallibus <lb/>adiri po&longs;&longs;ent, vt cuique aptum vi&longs;um e&longs;t loco, ita omni ge&shy;<lb/>nere tormento rum in&longs;truxit. </s> <s id="id.000200">Is erat vnicus &longs;pecta&shy;<lb/>tor c&oelig;li &longs;iderum que: mirabilior tamen inuentor ac machi&shy;<lb/>nator bellicorum <expan abbr="torm&etilde;torum">tormentorum</expan>, operumque: quibus ea qu&aelig; <lb/>ho&longs;tes ingenti mole agerent ip&longs;e perleui momento ludifi&shy;<pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.028.jpg"/>caretur. </s>
  
 <s>A cradin&aelig; murum, qui, vt ante <lb/>dictum e&longs;t, mari alluitur ex quinqueremibus Marcellus <lb/>oppugnabat. </s> <s id="id.000201">Murum per in&ecedil;quales ductum colles, pleraque alta <lb/>&amp; difficilia aditu, &longs;ummi&longs;&longs;a qu&aelig;dam, &amp; qu&aelig; planis vallibus <lb/>adiri po&longs;&longs;ent, vt cuique aptum vi&longs;um e&longs;t loco, ita omni ge&shy;<lb/>nere tormento rum in&longs;truxit. </s>
  
 <s>ex c&aelig;teris nauibus &longs;agittarij, funditore&longs;que, <lb/>&amp; velites etiam quorum telum inhabile ad remittendum <lb/>imperitis e&longs;t: vix quenquam &longs;ine vulnere con&longs;i&longs;tere in muro <lb/>patiebantur. </s> <s id="id.000202">Acradin&aelig; murum, qui, vt ante <lb/>dictum e&longs;t, mari alluitur ex quinqueremibus Marcellus <lb/>oppugnabat. </s>
  
 <s>Hi, quia &longs;patio mi&longs;&longs;ilibus opus e&longs;t: procul mu&shy;<lb/>ro <expan abbr="teneb&atilde;t">tenebant</expan> naues. </s> <s id="id.000203">ex c&aelig;teris nauibus &longs;agittarij, funditore&longs;que, <lb/>&amp; velites etiam quorum telum inhabile ad remittendum <lb/>imperitis e&longs;t: vix quenquam &longs;ine vulnere con&longs;i&longs;tere in muro <lb/>patiebantur. </s>
  
 <s>Iunct&aelig; ali&aelig; bin&aelig; ad quinqueremes dem&shy;<lb/>ptis interioribus remis, vt latus lateri appropinquaretur: <lb/>cum exteriore ordine remorum velut naues agerentur: tur&shy;<lb/>res contabulatas, machinament&aacute; que alia quatiendis muris <lb/>portabant. </s> <s id="id.000204">Hi, quia &longs;patio mi&longs;&longs;ilibus opus e&longs;t: procul mu&shy;<lb/>ro <expan abbr="teneb&atilde;t">tenebant</expan> naues. </s>
  
 <s>A duer&longs;us hunc naualem apparatum Archime&shy;<lb/>des vari&aelig; magnitudinis tormenta in muris di&longs;po&longs;uit. </s> <s id="id.000205">Iunct&aelig; ali&aelig; bin&aelig; ad quinqueremes dem&shy;<lb/>ptis interioribus remis, vt latus lateri appropinquaretur: <lb/>cum exteriore ordine remorum velut naues agerentur: tur&shy;<lb/>res contabulatas, machinament&aacute; que alia quatiendis muris <lb/>portabant. </s>
  
 <s>In eas <lb/>qu&aelig; procul erant, naues &longs;axa ingenti pondere emittebat: <lb/>propiores leuioribus, e&oacute;que magis crebris petebat telis. </s> <s id="id.000206">Aduer&longs;us hunc naualem apparatum Archime&shy;<lb/>des vari&aelig; magnitudinis tormenta in muris di&longs;po&longs;uit. </s>
  
 <s>Po&shy;<lb/>&longs;trem&ograve; vt &longs;ui vulnere intacti tela in ho&longs;tem ingererent: mu&shy;<lb/>rum ab imo &longs;ummum crebris cubitalibus fer&egrave; caueis ape&shy;<lb/>ruit. </s> <s id="id.000207">In eas <lb/>qu&aelig; procul erant, naues &longs;axa ingenti pondere emittebat: <lb/>propiores leuioribus, e&oacute;que magis crebris petebat telis. </s>
  
 <s>per qu&aelig; caua pars &longs;agittis: pars &longs;corpionibus modicis <lb/>ex occulto petebant ho&longs;tem. </s> <s id="id.000208">Po&shy;<lb/>&longs;trem&ograve; vt &longs;ui vulnere intacti tela in ho&longs;tem ingererent: mu&shy;<lb/>rum ab imo &longs;ummum crebris cubitalibus fer&egrave; caueis ape&shy;<lb/>ruit. </s>
  
 <s>Qu&aelig; propius <expan abbr="quid&etilde;">quidem</expan> &longs;ubibant <lb/>naues, quo interiores ictibus <expan abbr="torm&etilde;torum">tormentorum</expan> e&longs;&longs;ent: in eas tol&shy;<lb/>lendas de&longs;uper murum eminentem ferrea manus firm&aelig; ca&shy;<lb/>then&aelig; illigata, cum iniecta pror&aelig; e&longs;&longs;et, grauique libramen&shy;<lb/>to plumbi recelleret ad &longs;olum: <expan abbr="&longs;u&longs;p&etilde;&longs;a">&longs;u&longs;pen&longs;a</expan> prora, nauim in pup&shy;<lb/>pim &longs;tatuebat. </s> <s id="id.000209">per qu&aelig; caua pars &longs;agittis: pars &longs;corpionibus modicis <lb/>ex occulto petebant ho&longs;tem. </s>
  
 <s>Dein remi&longs;&longs;a &longs;ubit&ograve;, velut ex muro caden&shy;<lb/>tem nauim cum ingenti trepidatione nautarum ita vnd&aelig; <lb/>affligebant: vt etiam&longs;i recta recideret aliquantum aqu&aelig; ac&shy;<lb/>ciperet. </s> <s id="id.000210">Qu&aelig; propius <expan abbr="quid&etilde;">quidem</expan> &longs;ubibant <lb/>naues, quo interiores ictibus <expan abbr="torm&etilde;torum">tormentorum</expan> e&longs;&longs;ent: in eas tol&shy;<lb/>lendas de&longs;uper murum eminentem ferrea manus firm&aelig; ca&shy;<lb/>then&aelig; illigata, cum iniecta pror&aelig; e&longs;&longs;et, grauique libramen&shy;<lb/>to plumbi recelleret ad &longs;olum: <expan abbr="&longs;u&longs;p&etilde;&longs;a">&longs;u&longs;pen&longs;a</expan> prora, nauim in pup&shy;<lb/>pim &longs;tatuebat. </s>
  
 <s>Ita maritima oppugnatio e&longs;t elu&longs;a, omni&longs;que vis e&longs;t <lb/>auer&longs;a, vt totis viribus terra aggrederentur. </s> <s id="id.000211">Dein remi&longs;&longs;a &longs;ubit&ograve;, velut ex muro caden&shy;<lb/>tem nauim cum ingenti trepidatione nautarum ita vnd&aelig; <lb/>affligebant: vt etiam&longs;i recta recideret aliquantum aqu&aelig; ac&shy;<lb/>ciperet. </s>
  
 <s>Sed ea quoque <lb/>pars eodem omni apparatu tormentorum in&longs;tructa erat, <lb/>Hieronis impen&longs;is, curaque per multos annos Archimedis <lb/>vnica arte. </s> <s id="id.000212">Ita maritima oppugnatio e&longs;t elu&longs;a, omni&longs;que vis e&longs;t <lb/>auer&longs;a, vt totis viribus terra aggrederentur. </s>
  
 <s>Ita con&longs;ilio habito, cum omnis conatus ludibrio <lb/>e&longs;&longs;et: ab&longs;i&longs;tere oppugnatione atque ob&longs;idendo tantum ar&shy;<lb/>cere terra marique commeatibus ho&longs;tem placuit. </s> <s id="id.000213">Sed ea quoque <lb/>pars eodem omni apparatu tormentorum in&longs;tructa erat, <lb/>Hieronis impen&longs;is, curaque per multos annos Archimedis <lb/>vnica arte. </s>
  
 <s>H&aelig;c Ti&shy;<lb/>tus Liuius lib.  <s id="id.000214">Ita con&longs;ilio habito, cum omnis conatus ludibrio <lb/>e&longs;&longs;et: ab&longs;i&longs;tere oppugnatione atque ob&longs;idendo tantum ar&shy;<lb/>cere terra marique commeatibus ho&longs;tem placuit. </s>
  
 4. decad. </s> <s id="id.000215">H&aelig;c Ti&shy;<lb/>tus Liuius lib.4.decad.3. </s>
  
 <s>3. Vilium igitur, &longs;ordidorum que ho&shy;<lb/>minum ne dixerimus ea e&longs;&longs;e in&longs;trumenta, qu&aelig; vel &agrave; dijs, vel <pb/>&agrave; nobili&longs;&longs;imis hominibus inuenta, &amp; v&longs;urpata &longs;unt, &amp; nunc <lb/>ad v&longs;us humanos perquam nece&longs;&longs;aria hone&longs;ti&longs;&longs;imum qu&aelig;&shy;<lb/>&longs;tum, &amp; qualem agricultura dominis agricolis &longs;uppeditant. <lb/></s> <s id="id.000216">Vilium igitur, &longs;ordidorum que ho&shy;<lb/>minum ne dixerimus ea e&longs;&longs;e in&longs;trumenta, qu&aelig; vel &agrave; dijs, vel <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.029.jpg"/>&agrave; nobili&longs;&longs;imis hominibus inuenta, &amp; v&longs;urpata &longs;unt, &amp; nunc <lb/>ad v&longs;us humanos perquam nece&longs;&longs;aria hone&longs;ti&longs;&longs;imum qu&aelig;&shy;<lb/>&longs;tum, &amp; qualem agricultura dominis agricolis &longs;uppeditant. <lb/></s>
  
 <s>Quanquam non co animo &agrave; nobis h&aelig;c dicuntur, vt ad eas <lb/>artes, quarum &longs;unt in&longs;trumenta, ve&longs;tras animi, corpori&longs;que <lb/>vires &longs;uadeam conferatis: vos dico,</s></p><p type="main"> <s id="id.000217">Quanquam non eo animo &agrave; nobis h&aelig;c dicuntur, vt ad eas <lb/>artes, quarum &longs;unt in&longs;trumenta, ve&longs;tras animi, corpori&longs;que <lb/>vires &longs;uadeam conferatis: vos dico,</s></p><p type="main">
  
 <s><emph type="italics"/>Queis meliore luto finxit pr&aelig;cordia Titan:<emph.end type="italics"/></s></p><p type="main"> <s id="id.000218"><emph type="italics"/>Queis meliore luto finxit pr&aelig;cordia Titan:<emph.end type="italics"/></s></p><p type="main">
  
 <s>atque quos ad his altiora pr&aelig;meditanda iamdudum euexit <lb/>animus, vbi tamen nihil aliud e&longs;&longs;et, quod ageretur, cur non <lb/>aliquod horum relaxamenti gratia etiam qu&aelig;ratis? </s> <s id="id.000219">atque quos ad his altiora pr&aelig;meditanda iamdudum euexit <lb/>animus, vbi tamen nihil aliud e&longs;&longs;et, quod ageretur, cur non <lb/>aliquod horum relaxamenti gratia etiam qu&aelig;ratis? </s>
  
 <s>vel &longs;i rei <lb/>familiaris exiguitas po&longs;tulat, cum ijs agatis, potius, quam <lb/>nihil? </s> <s id="id.000220">vel &longs;i rei <lb/>familiaris exiguitas po&longs;tulat, cum ijs agatis, potius, quam <lb/>nihil? </s>
  
 <s>Neque enim magis horum aliquod nobis indecorum <lb/>putare debemus: quam &longs;ibi A&longs;cr&aelig;us ille po&euml;ta,</s></p><p type="main"> <s id="id.000221">Neque enim magis horum aliquod nobis indecorum <lb/>putare debemus: quam &longs;ibi A&longs;cr&aelig;us ille po&euml;ta,</s></p><p type="main">
  
 <s><emph type="italics"/>Qui alium ditem cernens, cum dee&longs;t quod agatur,<emph.end type="italics"/></s></p><p type="main"> <s id="id.000222"><emph type="italics"/>Qui alium ditem cernens, cum dee&longs;t quod agatur,<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Ip&longs;e &longs;olum vertit tauris, &amp; &longs;emina ponit.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000223"><emph type="italics"/>Ip&longs;e &longs;olum vertit tauris, &amp; &longs;emina ponit. <emph.end type="italics"/></s></p><p type="main">
  
 <s>Sed co animo h&ecedil;c pr&ecedil;&longs;ertim <expan abbr="n&utilde;c">nunc</expan> &agrave; me dicuntur, vt audacter <lb/>&amp; &longs;ine rubore aliquando ingrediamur officinas fabrorum <lb/>generis omnis, vt &amp; in&longs;trumenta, &amp; machinas quibus vtun&shy;<lb/>tur in &longs;uis operibus con&longs;icien dis primum digno&longs;camus, mi&shy;<lb/>rificas ex i&longs;ta dignotione voluptates con&longs;ecuturi, maxim&egrave; <lb/>cum eas, qu&aelig; magna vi pollent, &longs;ummo&longs;que habent v&longs;us <lb/>cognouerimus, ma<gap/>ores adhuc multo po&longs;tea percepturi, &longs;i <lb/>tant&aelig; efficaci&aelig; adiumenti que cau&longs;as inue&longs;tigantes inuene&shy;<lb/><gap/>imus, quod feci&longs;&longs;e Ari&longs;totelem non puduit, qui vno hoc li&shy;<lb/>bello <foreign lang="greek"><gap/>i\ mnxanika_n</foreign> cert&egrave; iucundo &amp; vtili edito tanta inge&shy;<lb/>nij &longs;ubtilitate atque diligentia per&longs;ecutus e&longs;t, vt omnia ad <lb/>vnum princip<gap/>um, quod e&longs;t circulus, reuocari po&longs;&longs;e inue&shy;<lb/>nerit, &amp; reuocanda e&longs;&longs;e non quidem leuibus probabilium <lb/>argumentorum: &longs;ed graui&longs;&longs;imis demon&longs;trationum geome&shy;<lb/>tricarum momentis o&longs;tenderit. </s> <s id="id.000224">Sed eo animo h&ecedil;c pr&ecedil;&longs;ertim <expan abbr="n&utilde;c">nunc</expan> &agrave; me dicuntur, vt audacter <lb/>&amp; &longs;ine rubore aliquando ingrediamur officinas fabrorum <lb/>generis omnis, vt &amp; in&longs;trumenta, &amp; machinas quibus vtun&shy;<lb/>tur in &longs;uis operibus conficiendis primum digno&longs;camus, mi&shy;<lb/>rificas ex i&longs;ta dignotione voluptates con&longs;ecuturi, maxim&egrave; <lb/>cum eas, qu&aelig; magna vi pollent, &longs;ummo&longs;que habent v&longs;us <lb/>cognouerimus, maiores adhuc multo po&longs;tea percepturi, &longs;i <lb/>tant&aelig; efficaci&aelig; adiumenti que cau&longs;as inue&longs;tigantes inuene&shy;<lb/>rimus, quod feci&longs;&longs;e Ari&longs;totelem non puduit, qui vno hoc li&shy;<lb/>bello <foreign lang="el">peri\ mhxanikw=n</foreign> cert&egrave; iucundo &amp; vtili edito tanta inge&shy;<lb/>nij &longs;ubtilitate atque diligentia per&longs;ecutus e&longs;t, vt omnia ad <lb/>vnum principium, quod e&longs;t circulus, reuocari po&longs;&longs;e inue&shy;<lb/>nerit, &amp; reuocanda e&longs;&longs;e non quidem leuibus probabilium <lb/>argumentorum: &longs;ed graui&longs;&longs;imis demon&longs;trationum geome&shy;<lb/>tricarum momentis o&longs;tenderit. </s>
  
 <s>Itaque &longs;i quis audito huius <lb/>libelli titulo, &longs;tatim ab huius lectione volens aufugere, in&longs;u&shy;<lb/>per pue<gap/>iliter irrideat, quod regius mathem aticarum ar&shy;<lb/>tium profe&longs;&longs;or in rebus, vt putabit, vili&longs;&longs;imis philo&longs;ophari, <lb/>&amp; <foreign lang="greek">g<gap/>wmebu_n</foreign> contenderit. </s> <s id="id.000225">Itaque &longs;i quis audito huius <lb/>libelli titulo, &longs;tatim ab huius lectione volens aufugere, in&longs;u&shy;<lb/>per pueriliter irrideat, quod regius mathematicarum ar&shy;<lb/>tium profe&longs;&longs;or in rebus, vt putabit, vili&longs;&longs;imis philo&longs;ophari, <lb/>&amp; <foreign lang="el">gewmetrei=n</foreign> contenderit. </s>
  
 <s>Huic re&longs;pondebimus, quod ali&shy;<lb/>quando Hera clitum dixi&longs;&longs;c ferunt ijs, qui cum alioqui evm <lb/>vellent, quod forte in ca&longs;a furnatia caloris gratia &longs;edentem <lb/>vid<gap/>&longs;&longs;ent, accedere temperarunt, &amp; ingredi fidenter cum <pb/>iu&longs;&longs;i&longs;&longs;et. </s> <s id="id.000226">Huic re&longs;pondebimus, quod ali&shy;<lb/>quando Heraclitum dixi&longs;&longs;e ferunt ijs, qui cum alioqui evm <lb/>vellent, quod forte in ca&longs;a furnaria caloris gratia &longs;edentem <lb/>vidi&longs;&longs;ent, accedere temperarunt, &amp; ingredi fidenter cum <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.030.jpg"/>iu&longs;&longs;i&longs;&longs;et. </s>
  
 <s>Ne quidem, inquit ille, huic loco dij de&longs;unt im&shy;<lb/>mortales: &longs;ic nec i&longs;ti rerum generi dulci&longs;&longs;ima &amp; vtili&longs;&longs;ima, <lb/>&amp; <expan abbr="c&utilde;">cum</expan> &longs;umma ingenij humani voluptate coniuncta &longs;ua dee&longs;t <lb/>philo&longs;ophia, vt in qua explicanda, &amp; <expan abbr="exorn&atilde;da">exornanda</expan> pr&aelig;ter Ari&shy;<lb/>&longs;totelem multi viri pr&aelig;clari &longs;tudium &longs;uum collocauerint, <lb/>Cliades, Architas, Archimedes, Cte&longs;ibius, Nymphodorus, <lb/>Philo byzanteus, Diphilas, Charidas, Polyides, Phyrus, <lb/>Age&longs;i&longs;tratus, ex quorum <expan abbr="c&otilde;mentarijs">commentarijs</expan> qu&aelig; vtilia e&longs;&longs;ent &aelig;di&shy;<lb/>ficationi collecta in vnum Vitruuius corpus co&euml;git: &longs;ed &amp; <lb/>pr&aelig;ter illos quorum fer&egrave; nobis <expan abbr="re&longs;t&atilde;t">re&longs;tant</expan> &longs;ola nomina Pappus, <lb/>Hero vterque, Tzetzes, Iordanus, &amp; &egrave; recentio ribus Leoni&shy;<lb/>cus, Picolominus, Cardanus, Guido Vbaldus, quorum in&shy;<lb/>genia &longs;eruilia nunquam rect&egrave; quis dixerit aut putarit. </s> <s id="id.000227">Ne quidem, inquit ille, huic loco dij de&longs;unt im&shy;<lb/>mortales: &longs;ic nec i&longs;ti rerum generi dulci&longs;&longs;ima &amp; vtili&longs;&longs;ima, <lb/>&amp; <expan abbr="c&utilde;">cum</expan> &longs;umma ingenij humani voluptate coniuncta &longs;ua dee&longs;t <lb/>philo&longs;ophia, vt in qua explicanda, &amp; <expan abbr="exorn&atilde;da">exornanda</expan> pr&aelig;ter Ari&shy;<lb/>&longs;totelem multi viri pr&aelig;clari &longs;tudium &longs;uum collocauerint, <lb/>Cliades, Architas, Archimedes, Cte&longs;ibius, Nymphodorus, <lb/>Philo byzanteus, Diphilas, Charidas, Polyides, Phyrus, <lb/>Age&longs;i&longs;tratus, ex quorum <expan abbr="c&otilde;mentarijs">commentarijs</expan> qu&aelig; vtilia e&longs;&longs;ent &aelig;di&shy;<lb/>ficationi collecta in vnum Vitruuius corpus co&euml;git: &longs;ed &amp; <lb/>pr&aelig;ter illos quorum fer&egrave; nobis <expan abbr="re&longs;t&atilde;t">re&longs;tant</expan> &longs;ola nomina Pappus, <lb/>Hero vterque, Tzetzes, Iordanus, &amp; &egrave; recentioribus Leoni&shy;<lb/>cus, Picolominus, Cardanus, Guido Vbaldus, quorum in&shy;<lb/>genia &longs;eruilia nunquam rect&egrave; quis dixerit aut putarit. </s>
  
 <s>quin <lb/>&amp; Hippocratcs magnus ille medicus &agrave; &longs;e nonnulla luxatio&shy;<lb/>nibus, &amp; fracturis reponendis inuenta commoda gloriatur, <lb/>cuiu&longs;modi &longs;unt <foreign lang="greek">o)/noi, o)/<gap/>iskoi\,</foreign> &amp; &longs;camnum, qu&aelig; vn&agrave; cum alijs <lb/>Galenus quo que paruis eorum exemplaribus vtens &longs;uos &longs;e <lb/>di&longs;cipulos docere te&longs;tatus e&longs;t. </s> <s id="id.000228">quin <lb/>&amp; Hippocratcs magnus ille medicus &agrave; &longs;e nonnulla luxatio&shy;<lb/>nibus, &amp; fracturis reponendis inuenta commoda gloriatur, <lb/>cuiu&longs;modi &longs;unt <foreign lang="el">o)/noi, o)/niskoi\,</foreign> &amp; &longs;camnum, qu&aelig; vn&agrave; cum alijs <lb/>Galenus quo que paruis eorum exemplaribus vtens &longs;uos &longs;e <lb/>di&longs;cipulos docere te&longs;tatus e&longs;t. </s>
  
 <s>In i&longs;tam igitur inqui&longs;itio&shy;<lb/>nem, tractationem, commentationem nobilem, ingenuam <lb/>&amp; philo&longs;ophi non vulgariter vt multi: &longs;ed in Geometria <lb/>magnopere eruditi ingenio digni&longs;&longs;imam, tot magnorum <lb/>virorum exemplo, &longs;i, can dide lector, me hortante atque his <lb/>no&longs;trorum commentariorum vigilijs, vtcunque adiuuante, <lb/>diligenter incubueris, tui te laboris, mihi crede, penitebit <lb/>numquam. </s> <s id="id.000229">In i&longs;tam igitur inqui&longs;itio&shy;<lb/>nem, tractationem, commentationem nobilem, ingenuam <lb/>&amp; philo&longs;ophi non vulgariter vt multi: &longs;ed in Geometria <lb/>magnopere eruditi ingenio digni&longs;&longs;imam, tot magnorum <lb/>virorum exemplo, &longs;i, candide lector, me hortante atque his <lb/>no&longs;trorum commentariorum vigilijs, vtcunque adiuuante, <lb/>diligenter incubueris, tui te laboris, mihi crede, penitebit <lb/>numquam. </s>
  
 <s>Vale.</s></p><pb/><p type="head"> <s id="id.000230">Vale. </s></p></section><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.031.jpg"/><section><p type="head">
  
 <s><emph type="italics"/>Extraict du Priuilege du Roy.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000231"><emph type="italics"/>Extraict du Priuilege du Roy. <emph.end type="italics"/></s></p><p type="main">
  
 <s>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> 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="fr">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>Donn&eacute; &agrave; Paris le <lb/>23. de Decembre 1598.</s></p><p type="main"> <s id="id.000233"><foreign lang="fr">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><emph type="italics"/>Sign&eacute; par le Con&longs;eil<emph.end type="italics"/></s></p><p type="main"> <s id="id.000234"><foreign lang="fr">Donn&eacute; &agrave; Paris le <lb/>23. de Decembre 1598. </foreign></s></p><p type="main">
  
 <s><emph type="italics"/>D<emph.end type="italics"/>E LAVETS.</s></p><pb/><p type="head"> <s id="id.000235"><foreign lang="fr"><emph type="italics"/>Sign&eacute; par le Con&longs;eil<emph.end type="italics"/></foreign></s></p><p type="main">
  
 <s>INDEX MEMOR ABILIVM <lb/>IN MECHANICIS ARISTOTELIS <lb/>&amp; eorum Commentarijs.<lb/><arrow.to.target n="table1"></arrow.to.target></s></p><table><table.target id="table1"></table.target><row><cell><emph type="italics"/>A<emph.end type="italics"/></cell><cell></cell></row><row><cell><emph type="italics"/><foreign lang="greek">*abuasos vnde.</foreign> pag.<emph.end type="italics"/></cell><cell>209</cell></row><row><cell><emph type="italics"/>Ab&longs;is pro circunferen-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   opi&longs;ic&ydot;s egent &longs;tatione, vel &longs;ebione   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 ponder atione.<emph.end type="italics"/></cell><cell>149</cell></row><row><cell><foreign lang="greek">*alou<gap/>gopw/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 angubus &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&aelig; <expan abbr="quit&longs;c&utilde;t">quit&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 med&yuml; 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"/>Archelairegis factum in edip&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"/>Architecture&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 plen&aelig;.<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></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/><row><cell><emph type="italics"/>Bouilli error, qui put abat rectam iuuen-tam equalem 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 admir atur.<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></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/><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></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></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></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></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></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/><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></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></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></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/><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></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></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></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/><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></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></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></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/><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></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></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/><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></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></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.000236"><foreign lang="fr"><emph type="italics"/>D<emph.end type="italics"/>E LAVETS. </foreign></s></p></section><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.032.jpg"/><section><p type="head">
  
 <s>FINIS.</s></p><pb pagenum="1"/><figure></figure><p type="head"> <s id="id.000237">INDEX MEMORABILIVM <lb/>IN MECHANICIS ARISTOTELIS <lb/>&amp; eorum Commentarijs. <lb/><arrow.to.target n="table1"/></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="el">*abussos</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="el">*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&shy;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&shy;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&shy;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&shy;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;&shy;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="el">*auto/mata. </foreign></cell><cell>10</cell></row><row><cell><emph type="italics"/>B<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Baiulus cum &longs;uo onere e&longs;t turbo, vel   conus inuer&longs;us. <emph.end type="italics"/></cell><cell>199.200</cell></row><row><cell><emph type="italics"/>Baiuli Pari&longs;ien&longs;es facile ferunt ingentia   pondera. <emph.end type="italics"/></cell><cell>198.199</cell></row><row><cell><emph type="italics"/>Baiuli cum onere tut&ograve; a&longs;cendunt, pericu&shy;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&shy;&longs;tolic&aelig; regens con&longs;ecrat, &amp; compreca&shy;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&shy;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&shy;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&shy;te&longs;t. <emph.end type="italics"/></cell><cell>192</cell></row><row><cell><emph type="italics"/>Bruta ventrem ad terram conuer&longs;um   habent. <emph.end type="italics"/></cell><cell>195</cell></row><row><cell><emph type="italics"/>Bruti&longs;pina pedibus ad rectos imminet. <emph.end type="italics"/></cell><cell>198</cell></row><row><cell><emph type="italics"/>Brutum nihil admiratur. <emph.end type="italics"/></cell><cell>5</cell></row><row><cell><emph type="italics"/>Bruta nonnulla apta <expan abbr="fer&etilde;dis">ferendis</expan> &longs;arcinis. <emph.end type="italics"/></cell><cell>198</cell></row><row><cell><emph type="italics"/>Brutum nullum pote&longs;t &longs;edere. <emph.end type="italics"/></cell><cell>194</cell></row><row><cell><emph type="italics"/>C<emph.end type="italics"/></cell><cell/></row><row><cell><foreign lang="el">*ka/iar</foreign> <emph type="italics"/>in fund a quid &longs;it. <emph.end type="italics"/></cell><cell>117</cell></row><row><cell><emph type="italics"/>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&shy;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&shy;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="el">a)nti/xeir,</foreign> vt   in manu hominis. <emph.end type="italics"/></cell><cell>195</cell></row><row><cell><emph type="italics"/>Centrum duorum circulorum connexo-rum non e&longs;t idem. <emph.end type="italics"/></cell><cell>173</cell></row><row><cell><emph type="italics"/>Chirurgi togati nolunt dentes cuellere,   licet&longs;u operatio chirurgica. <emph.end type="italics"/></cell><cell>153</cell></row><row><cell><emph type="italics"/>Circini author 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="el">*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;">magnificum</expan>. <emph.end type="italics"/></cell><cell>26</cell></row><row><cell><emph type="italics"/>Humero dextro onera difficilius ferun-tur, quam &longs;ini&longs;tro. <emph.end type="italics"/></cell><cell>187</cell></row><row><cell><emph type="italics"/>Hypomochlium quid. <emph.end type="italics"/></cell><cell>14.55</cell></row><row><cell><emph type="italics"/>I<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Iaccre &longs;upinum quid. <emph.end type="italics"/></cell><cell>194</cell></row><row><cell><emph type="italics"/>lacere pronum. <emph.end type="italics"/></cell><cell>194</cell></row><row><cell><emph type="italics"/>Jacere &longs;upinum &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;derilus">ponderilus</expan>. <emph.end type="italics"/></cell><cell>49.50</cell></row><row><cell><emph type="italics"/>Librile <expan abbr="ligne&utilde;">ligneum</expan> facilius mouetur ferreo. <emph.end type="italics"/></cell><cell>113</cell></row><row><cell><emph type="italics"/>Lignalongiora &longs;unt imbecilliora. <emph.end type="italics"/></cell><cell>124</cell></row><row><cell><emph type="italics"/>Ligna longa ab extremo difficilius <expan abbr="fer&utilde;-tur">ferun-tur</expan> bumere, quam &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> grauius ferit. <emph.end type="italics"/></cell><cell>128</cell></row><row><cell><emph type="italics"/>Manganaria pars Mechanices. <emph.end type="italics"/></cell><cell>11</cell></row><row><cell><emph type="italics"/>Manus e&longs;t <expan abbr="in&longs;trum&etilde;t&utilde;">in&longs;trumentum</expan> <expan abbr="in&longs;trum&etilde;tor&utilde;">in&longs;trumentorum</expan>. <emph.end type="italics"/></cell><cell>194</cell></row><row><cell><emph type="italics"/>Manus tres partes. <emph.end type="italics"/></cell><cell>118</cell></row><row><cell><emph type="italics"/>Mechanica cur non e&longs;&longs;e Aristotelis vi-&longs;um &longs;it Cardano &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="el">paradocopoioi\. </foreign></cell><cell>12</cell></row><row><cell><emph type="italics"/>laus Mechanicorum. <emph.end type="italics"/></cell><cell>142</cell></row><row><cell><emph type="italics"/>Mens e&longs;t ars artium. <emph.end type="italics"/></cell><cell>194</cell></row><row><cell><emph type="italics"/>Men&longs;ura rei cuiu&longs;que debet e&longs;&longs;e deter-minata. <emph.end type="italics"/></cell><cell>44</cell></row><row><cell><emph type="italics"/>Mercatura opulenta. <emph.end type="italics"/></cell><cell>4</cell></row><row><cell><emph type="italics"/>Mercurius in&longs;istit cubo. <emph.end type="italics"/></cell><cell>103</cell></row><row><cell><emph type="italics"/>Milij grana non &longs;unt &longs;impliciter exigua. <emph.end type="italics"/></cell><cell>204</cell></row><row><cell><emph type="italics"/>Militaris ars vtilitate vincit 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&shy;<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;cus 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="el">*odonta/gra *h)/ \o)donta/gw=gos</foreign> <emph type="italics"/>quid. <emph.end type="italics"/></cell><cell>152</cell></row><row><cell><foreign lang="el">*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="el">*ourano/skopos</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="el">*po/da e)rei=n,</foreign> <emph type="italics"/>&amp; canere quid. <emph.end type="italics"/></cell><cell>95</cell></row><row><cell><foreign lang="el">*po/des, &amp; pro/podes. </foreign></cell><cell>96</cell></row><row><cell><foreign lang="el">*poliorkitik*h\</foreign> <emph type="italics"/>pars Mechanices. <emph.end type="italics"/></cell><cell>11</cell></row><row><cell><foreign lang="el">*polu/spaston. </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="el">*s*h/kwma</foreign> <emph type="italics"/>quid. <emph.end type="italics"/></cell><cell>151</cell></row><row><cell><emph type="italics"/>Spartion pro an&longs;a. <emph.end type="italics"/></cell><cell>148</cell></row><row><cell><emph type="italics"/>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="el">*stata</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="el">*qaumatourgik*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&shy;<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="el">*zugo\s &amp; *zugo\n. </foreign></cell><cell>45.119</cell></row><row><cell><foreign lang="el">*zugosta/ths. </foreign></cell><cell>45</cell></row><row><cell><emph type="italics"/>Zygostatica fides. <emph.end type="italics"/></cell><cell>45</cell></row></table><p type="head">
  
 <s><foreign lang="greek">*a*r*i*s*t*o*t*e*l*o*u<gap/></foreign><lb/>MHX ANIKA. <lb/>ARISTOTELIS <lb/>MECHANICA.</s></p><p type="main"> <s id="id.000238">FINIS. </s><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.040.jpg" pagenum="1"/><figure id="id.035.01.040.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.040.1.jpg"/></p></section></front><body><chap><subchap1><p type="head">
  
 <s><arrow.to.target n="marg1"></arrow.to.target></s></p><p type="margin"> <s id="id.000239"><foreign lang="el">*a*r*i*s*t*o*t*e*l*o*u*s <lb/>*m*h*x*a*n*i*k*a</foreign>. <lb/>ARISTOTELIS <lb/>MECHANICA. </s></p><p type="main">
  
 <s><margin.target id="marg1"></margin.target>Pro <foreign lang="greek">mhxanh\,</foreign><lb/>lege <foreign lang="greek">mhxani&shy;<lb/>kh/.</foreign></s></p><p type="head"> <s id="id.000241"><foreign lang="el">Ti/ e)sti mhxanh\, kai=\ peri\ ku/klou, tw=n e)n toi=s mhxanikoi=s <lb/>qaumasi/wn ai)ti/an e)/xontos. <arrow.to.target n="marg1"/></foreign></s></p><p type="head">
  
 <s><foreign lang="greek">Ti<gap/>st mhxanh\, kai_\ w<gap/>i\ ku/klou, <gap/> c)n toi_s mhxanikoi_s <lb/><gap/>ow masi/wn ai)ti/an e)/xontos.</foreign></s></p><p type="head"> <s id="id.000242"><margin.target id="marg1"/>Pro <foreign lang="el">mhxanh\,</foreign><lb/>lege <foreign lang="el">mhxani&shy;<lb/>kh/. </foreign></s></p><p type="head">
  
 <s><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><gap/></s></p><p type="main"> <s id="id.000244"><foreign lang="el">*q*a*u*m*a*z*e*t*a*i tw=n me\n kata\ fu/sin sumbaino/ntwn, o(/swn  <lb/>a)gnoei=tai to\ ai)/tion, tw=n de\ para\ fu/sin, o(/sa gi/netai dia\ <lb/>te/xnhn pro\s to\ sumfe/ron toi=s a)nqrw/pois.</foreign></s></p><p type="main">
  
 <s>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&shy;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>COMMENTARIVS.</s></p><p type="main"> <s id="id.000246">COMMENTARIVS. </s></p><p type="main">
  
 <s><emph type="italics"/>Cardanvs librum hunc Ari&longs;totelis peripate-<emph.end type="italics"/><lb/><arrow.to.target n="marg2"></arrow.to.target><lb/><emph type="italics"/>ticorum principis e&longs;&longs;e non arbitratur, propter man&shy;<lb/>cam, &amp; paulo negligentiorem motuum rotundo&shy;<lb/>rum in eo po&longs;itam diui&longs;ionem. </s> <s id="id.000247"><emph type="italics"/>Cardanvs librum hunc Ari&longs;totelis peripate&shy;<emph.end type="italics"/><lb/><arrow.to.target n="marg2"/><lb/><emph type="italics"/>ticorum principis e&longs;&longs;e non arbitratur, propter man&shy;<lb/>cam, &amp; paulo negligentiorem motuum rotundo&shy;<lb/>rum in eo po&longs;itam diui&longs;ionem. </s>
  
 <s>Franci&longs;cus Patri-<emph.end type="italics"/><lb/><arrow.to.target n="marg3"></arrow.to.target><lb/><emph type="italics"/>cius vbi in omnes Ari&longs;totelis libros diligenter in&shy;<lb/>quirit, ab eorum numero exclu&longs;it, cau&longs;am tamen attulit nullam, ni&longs;i <lb/>quod multi libri magnorum virorum nomine circumferantur, quo&shy;<lb/>rum ip&longs;i authores non &longs;unt. </s> <s id="id.000248">Franci&longs;cus Patri&shy;<emph.end type="italics"/><lb/><arrow.to.target n="marg3"/><lb/><emph type="italics"/>cius vbi in omnes Ari&longs;totelis libros diligenter in&shy;<lb/>quirit, ab eorum numero exclu&longs;it, cau&longs;am tamen attulit nullam, ni&longs;i <lb/>quod multi libri magnorum virorum nomine circumferantur, quo&shy;<lb/>rum ip&longs;i authores non &longs;unt. </s>
  
 <s>quod licet verum e&longs;&longs;e multis rationibus,<emph.end type="italics"/><pb pagenum="2"/><emph type="italics"/>testimoniis, &amp; exemplis coufirmarit: ob id tamen hunc Ari&longs;toteli <lb/>detrahendum e&longs;&longs;e, non e&longs;t nece&longs;&longs;e. </s> <s id="id.000249">quod licet verum e&longs;&longs;e multis rationibus,<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.041.jpg" pagenum="2"/><emph type="italics"/>testimoniis, &amp; exemplis confirmarit: ob id tamen hunc Ari&longs;toteli <lb/>detrahendum e&longs;&longs;e, non e&longs;t nece&longs;&longs;e. </s>
  
 <s>Quid ita? </s> <s id="id.000250">Quid ita? </s>
  
 <s>Ip&longs;emet Patricius fate&shy;<lb/>tur hunc<emph.end type="italics"/> <foreign lang="greek"><gap/> mhxanikw_n</foreign> <emph type="italics"/>librum doctum e&longs;&longs;e, &amp; elegantem: addo <lb/>&amp; &longs;ubtilem, &amp; ab Ari&longs;totelis <expan abbr="ver&utilde;">verum</expan> in vnaquaque re, &longs;implex. </s> <s id="id.000251">Ip&longs;emet Patricius fate&shy;<lb/>tur hunc<emph.end type="italics"/> <foreign lang="el">tw=n mhxanikw=n</foreign> <emph type="italics"/>librum doctum e&longs;&longs;e, &amp; elegantem: addo <lb/>&amp; &longs;ubtilem, &amp; ab Ari&longs;totelis <expan abbr="ver&utilde;">verum</expan> in vnaquaque re, &longs;implex. </s>
  
 <s>&longs;yn&shy;<lb/>cerumque exquirentis ingenio minime abhorrentem, vt ip&longs;um, &amp; <lb/>no&longs;tros in ip&longs;um commentarios cuique legenti manife&longs;tum euadet. <lb/></s> <s id="id.000252">&longs;yn&shy;<lb/>cerumque exquirentis ingenio minime abhorrentem, vt ip&longs;um, &amp; <lb/>no&longs;tros in ip&longs;um commentarios cuique legenti manife&longs;tum euadet. <lb/></s>
  
 <s>Phra&longs;is non repugnat, &longs;i cumea <expan abbr="c&otilde;feratur">conferatur</expan>, qu&aelig; fuit familiaris Ari&shy;<lb/>&longs;toteli in mathematicis, vt cum de Iride, aut de lineis in&longs;ecabilibus <lb/>di&longs;putat. </s> <s id="id.000253">Phra&longs;is non repugnat, &longs;i cum ea <expan abbr="c&otilde;feratur">conferatur</expan>, qu&aelig; fuit familiaris Ari&shy;<lb/>&longs;toteli in mathematicis, vt cum de Iride, aut de lineis in&longs;ecabilibus <lb/>di&longs;putat. </s>
  
 <s>Diogenes La&euml;rtiusinter Ari&longs;totelis monumenta<emph.end type="italics"/> <foreign lang="greek">mhxani&shy;<lb/>kw_n</foreign> <emph type="italics"/>vnum recen&longs;uit. </s> <s id="id.000254">Diogenes La&euml;rtius inter Ari&longs;totelis monumenta<emph.end type="italics"/> <foreign lang="el">mhxani&shy;<lb/>kw=n</foreign> <emph type="italics"/>vnum recen&longs;uit. </s>
  
 <s>Multi clari viri no&longs;tri temporis vt Daniel <lb/>Barbarus &amp; Guidus Vbaldus &longs;&aelig;pe velut ab Ari&longs;totele citant. </s> <s id="id.000255">Multi clari viri no&longs;tri temporis vt Daniel <lb/>Barbarus &amp; Guidus Vbaldus &longs;&aelig;pe velut ab Ari&longs;totele citant. </s>
  
 <s>No&shy;<lb/>nius interpretatus e&longs;t&longs;uis di&longs;cipulis. </s> <s id="id.000256">No&shy;<lb/>nius interpretatus e&longs;t &longs;uis di&longs;cipulis. </s>
  
 <s>Cardaniratio parui e&longs;t <expan abbr="mom&etilde;ti">momenti</expan>. <lb/></s> <s id="id.000257">Cardani ratio parui e&longs;t <expan abbr="mom&etilde;ti">momenti</expan>. <lb/></s>
  
 <s>quia Ari&longs;toteles etiam in his, qui genuini &longs;unt eius libri &longs;ine contro&shy;<lb/>uer&longs;ia, non &longs;emper rerum exqui&longs;itas diui&longs;iones in&longs;tituit. </s> <s id="id.000258">quia Ari&longs;toteles etiam in his, qui genuini &longs;unt eius libri &longs;ine contro&shy;<lb/>uer&longs;ia, non &longs;emper rerum exqui&longs;itas diui&longs;iones in&longs;tituit. </s>
  
 <s>Quare hunc <lb/>librum Ari&longs;totelis e&longs;&longs;e putabimus, quou&longs;que exoriatur aliquis, qui <lb/>vel hunc &longs;ibi vendicare, vel al&yuml; tribuere, potiori iure po&szlig;it.<emph.end type="italics"/></s></p><p type="margin"> <s id="id.000259">Quare hunc <lb/>librum Ari&longs;totelis e&longs;&longs;e putabimus, quou&longs;que exoriatur aliquis, qui <lb/>vel hunc &longs;ibi vendicare, vel alij tribuere, potiori iure po&szlig;it. <emph.end type="italics"/></s></p><p type="margin">
  
 <s><margin.target id="marg2"></margin.target>Lib.  <s id="id.000260"><margin.target id="marg2"/>Lib. de pro&shy;<lb/>port. </s></p><p type="margin">
  
 de pro&shy;<lb/>port.</s></p><p type="margin"> <s id="id.000261"><margin.target id="marg3"/>Tom.I.li.3. <lb/>Di&longs;cu&longs;&longs;io&shy;<lb/>num peri&shy;<lb/>patetic. </s></p><p type="main">
  
 <s><margin.target id="marg3"></margin.target>Tom.I.li.3. <lb/>Di&longs;cu&longs;&longs;io&shy;<lb/>num pori&shy;<lb/>patctic.</s></p><p type="main"> <s id="id.000262">Mechanica] <emph type="italics"/>Huius libri du&aelig; &longs;unt partes. </s>
  
 <s>Mechanica] <emph type="italics"/>Huius libri du&aelig; &longs;unt partes. </s> <s id="id.000263">prior generalis e&longs;t <lb/>in explicatione cau&longs;arum &amp; principiorum, quibus machin&aelig; in mo&shy;<lb/>uendo magnas, &amp; admirabiles vires habent: po&longs;terior &longs;pecialis e&longs;t <lb/>in explicatione 25. qu&aelig;stionum de quarundam machinarum viribus <lb/>&amp; effectis. </s>
  
 <s>prior generalis e&longs;t <lb/>in explicatione cau&longs;arum &amp; principiorum, quibus machin&aelig; in mo&shy;<lb/>uendo magnas, &amp; admirabiles vires habent: po&longs;terior &longs;pecialis e&longs;t <lb/>in explicatione 25. qu&aelig;stionum de quarundam machinarum viribus <lb/>&amp; effectis. </s> <s id="id.000264">H&aelig;c autem <emph.end type="italics"/><foreign lang="el">tw=n mhxanikw=n</foreign> <emph type="italics"/>titulo recte exprimuntur. <lb/></s>
  
 <s>H&aelig;cautem<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="el">a)po\ th=s mhxanh=s. </foreign>&amp; <foreign lang="el">*mhxanh\ a)po\ tou= <lb/>mh/kous kai\ a)/nein,</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/></s>
  
 <s>quia Mechanica dicta&longs;unt<emph.end type="italics"/> <foreign lang="greek"><gap/>po\ th_s mhxanh_s. </foreign></s> <s><foreign lang="el">*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><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; incund&egrave; &longs;uccurrunt, &amp; adminioulantur 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 ide&longs;t machina definitur &agrave; Vitruuio, continens ex <lb/>materia coniunctio, qu&aelig; maximas habet, ad onerum motus virtu&shy;<lb/>tes: &amp; &agrave; P<gap/>nio in&longs;trumentum, quo moles aliquafacile, quocumque <lb/>volueris imp<gap/>lli 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, rect&egrave; Mechanica in&longs;cribuntur. </s>
  
 <s>Igitur tum h&aelig;c in&longs;trumenta &amp; machin&aelig;: <lb/>tum doctrina, qu&aelig; virium, quibus h&aelig;cpollent, rationem docet, &amp; <lb/>explicat, recl&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>Sed vereor, ne h&aelig;clibri <lb/>in&longs;criptio, ex vulgari <gap/>tium diui&longs;ione in liberales &amp; mechanicas, <lb/>quid &longs;or<gap/>di &longs;ubolens multis, ip&longs;os ab huius libri lectione deterruerit <lb/>&amp; deterrea<gap/>. </s> <s id="id.000269">At qu&aelig;cumque, eluenda e&longs;t macula. </s>
  
 <s>At qu&aelig;<gap/> umque, cluenda 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>Manauit enim &agrave;<emph.end type="italics"/><pb 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 ornduere, qu&aelig; in &longs;ola con&shy;<lb/>templatione ver&longs;arentur, &amp; contemplantis duntaxat ingenium <lb/>acuerent, atque perficerent: viles autem eas putduere, qu&aelig; ocium fu&shy;<lb/>gientes, in negotio atque efficientia occuparentur. </s> <s id="id.000271">At ij melius <lb/>meo iudicio feci&longs;&longs;ent, &longs;i eas, qu&aelig; ita corporis adminiculo exercen&shy;<lb/>tur, vt animi &longs;tudium non multum requirant, cum Gr&aelig;cis appel&shy;<lb/>la&longs;&longs;ent, non<emph.end type="italics"/> <foreign lang="el">mhxanika\s,</foreign> <emph type="italics"/>(neque enim h&icirc;c id vocabuli v&longs;urpant) <lb/>&longs;ed<emph.end type="italics"/> <foreign lang="el">fau/las, a)neleuqe/rous banau/sous a)gorai/ous</foreign> <emph type="italics"/>viles, illiberales, <lb/>&longs;ordidas, circunforaneas. </s>
  
 <s>At &yuml; melius <lb/>meo iudicio feci&longs;&longs;ent, &longs;i eas, qu&aelig; ita corporis adminiculo exercen&shy;<lb/>tur, vt animi &longs;tudium non multum requirant, cum Gr&aelig;cis appel&shy;<lb/>la&longs;&longs;ent, non<emph.end type="italics"/> <foreign lang="greek">mhxanika\s,</foreign> <emph type="italics"/>(neque enim h&icirc;c id vocabuli v&longs;urpant) <lb/>&longs;ed<emph.end type="italics"/> <foreign lang="greek">fau/las, a)neleuqirous <gap/>anow/oous a)<gap/>ai/ous</foreign> <emph type="italics"/>viles, illiberales, <lb/>&longs;ordidas, circunforaneas. </s> <s id="id.000272">Melius e&longs;t ergo rem i&longs;tam paulo altius re&shy;<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>Melius e&longs;t ergo rem i&longs;tam paulo altius re-<emph.end type="italics"/><lb/><arrow.to.target n="marg4"></arrow.to.target><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; aliis pr&aelig;&shy;<lb/>&longs;tantiores existimat&aelig; &longs;unt. </s>
  
 <s>Cum omnis ars, <lb/>vt e&longs;t apud Ari&longs;totelem, referatur ad bonum, nulla per &longs;e vilis cen&shy;<lb/>&longs;eridebt, 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.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>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>
  
 <s>qu&aelig; his duobus ver&longs;ibus <lb/>exprimuntur.<emph.end type="italics"/></s></p><p type="margin"> <p type="margin"><s id="id.000276"><margin.target id="marg4"/>Lib I.cap i. <lb/>Ethic. </s></p>
  
 <s><margin.target id="marg4"></margin.target>Lib I.cap i. <lb/></s> <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>
  
 <s>Ethic.</s></p><p type="main"> <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>
  
 <s>Lingua, Tropus, Ratio, Numerus, Tonus, Angulus, A&longs;tra: <lb/>Rus, Nemus, Arma, Faber, Vulnera, Lana, Rates.</s></p><p type="main"> <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><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> <s id="id.000279">Poste&shy;<lb/>riore &longs;ignificatur Agricultura, Venatoria, Militaris, Fabrilis, <lb/>Chirurgia, Lanificium, Nautica. </s>
  
 <s>Scienti&aelig; autem erant Philo&longs;ophia <lb/>moralis, Phy&longs;ica, Medicina, Iuri&longs;prudentia, Theologia. </s> <s id="id.000280">In quarum &longs;ingulis ali&aelig; &longs;unt im&shy;<lb/>perantes, qu&aelig; &amp; architectonic&aelig; dicuntur: ali&aelig; mini&longs;trantes. </s>
  
 <s>Poste&shy;<lb/>riore &longs;ignificatur Agricultura, Venatoria, Militaris, Fabrilis, <lb/>Chirurgia, Lanificium, Nautica. </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. 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>In quarum &longs;ingulis ali&aelig; &longs;unt im&shy;<lb/>perantes, qu&aelig; &amp; architectonic&aelig; dicuntur: ali&aelig; mini&longs;trantes. </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>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. </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>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 pagenum="4"/><emph type="italics"/>pr&aelig;&longs;tantiora, aut vtiliora, aut certiora exi&longs;tant. </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>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.000285">Ex ijs aliis ali&aelig; materias apparant: ali&aelig; in&longs;trumenta fabrican&shy;<lb/>tur. </s>
  
 <s>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.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>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.000287">Cur autem h&aelig; <lb/>figur&aelig; apti&szlig;im&aelig; &longs;int nulla <expan abbr="mini&longs;tr&atilde;tium">mini&longs;trantium</expan> rationem inue&longs;tigat: Satis <lb/>habent, &longs;i modum fabricandi &amp; vtendi tenuerint. </s>
  
 <s>Ex &yuml;s aliis ali&aelig; materias apparant: ali&aelig; in&longs;trumenta fabrican&shy;<lb/>tur. </s> <s id="id.000288">harum tamen <lb/>aliquot, cum cert&aelig; rationes e&longs;&longs;ent &longs;ubtiles, &amp; &agrave; fontibus Geometri&aelig; <lb/>petit&aelig;, ip&longs;as hoc libello ver&egrave; aureo, &amp; intelligentibus periucundo <lb/>Ari&longs;toteles partim generaliter, &amp; ex &longs;uis principiis, partim per ali&shy;<lb/>quot <expan abbr="ex&etilde;pla">exempla</expan>, &agrave; rebus multis vari&iacute;&longs;que petita explicuit. </s>
  
 <s>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.000289">Ob quod liber <lb/>rect&egrave; in&longs;cribitur<emph.end type="italics"/> <foreign lang="el">mhxa/nika,</foreign> <emph type="italics"/>quia hic explicet cau&longs;as virium in&shy;<lb/>&longs;trumentorum ad Mechanicas artes pr&aelig;dictas pertinentium. </s>
  
 <s>Cur autem h&aelig; <lb/>figur&aelig; apti&szlig;im&aelig; &longs;int nulla <expan abbr="mini&longs;tr&atilde;tium">mini&longs;trantium</expan> rationem inue&longs;tigat: Satis <lb/>habent, &longs;i modum fabricandi &amp; vtendi tenuerint. </s> <s id="id.000290">cur <lb/>&longs;cilicet ea, quam habent, pr&aelig;dita figura v&longs;ui, &amp; effectui commodio&shy;<lb/>ra exi&longs;tant. <emph.end type="italics"/></s></p><p type="main">
  
 <s>harum tamen <lb/>aliquot, cum cert&aelig; rationes e&longs;&longs;ent &longs;ubtiles, &amp; &agrave; fontibus Geometri&aelig; <lb/>petit&aelig;, ip&longs;as hoclibello ver&egrave; aureo, &amp; intelligentibus periucundo <lb/>Ari&longs;toteles partim generaliter, &amp; ex &longs;uis principiis, partim per ali&shy;<lb/>quot <expan abbr="ex&etilde;pla">exempla</expan>, &agrave; rebus multis vari&iacute;&longs;que petita explicuit. </s> <s id="id.000291">Quid e&longs;t Mechan.] <emph type="italics"/>Summa e&longs;t eorum, qu&aelig; hoc primo capite <lb/>explicantur, &longs;ed imperfectior: quia non, quid &longs;it mechanice, &longs;ed <lb/>quod &longs;it ars admirabilis, &amp; quod circulus omnium, qu&aelig; fiunt in <lb/>Mechanica, admirabilium e&longs;&longs;e cau&longs;a o&longs;tenditur: pr&aelig;ter qu&aelig; etiam <lb/>docetur problemata mechanica partim e&longs;&longs;e Phy&longs;ica, partim e&longs;&longs;e Ma&shy;<lb/>thematica. <emph.end type="italics"/></s></p><p type="main">
  
 <s>Ob quod liber <lb/>rect&egrave; in&longs;cribitur<emph.end type="italics"/> <foreign lang="greek">mhxa/nika,</foreign> <emph type="italics"/>quia hic explicet cau&longs;as virium in&shy;<lb/>&longs;trumentorum ad Mechanicas artes pr&aelig;dictas pertinentium. </s> <s id="id.000292">Mira &longs;unt in his:] <emph type="italics"/>Similitudo h&icirc;c qu&aelig;dam e&longs;t: &longs;ed &longs;ine notis <lb/>&longs;imilitudinis expre&longs;&longs;a. </s>
  
 <s>cur <lb/>&longs;cilicet ea, quam habent, pr&aelig;dita figura v&longs;ui, &amp; effectui commodio&shy;<lb/>ra exi&longs;tant.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000293">&longs;ic igitur erit clarior. </s>
  
 <s>Quid e&longs;t Mechan.] <emph type="italics"/>Summa e&longs;t eorum, qu&aelig; hoc primo capite <lb/>explicantur, &longs;ed imperfectior: quia non, quid &longs;it mechanice, &longs;ed <lb/>quod &longs;it ars admirabilis, &amp; quod circulus omnium, qu&aelig; fiunt in <lb/>Mechanica, admirabilium e&longs;&longs;e cau&longs;a o&longs;tenditur: pr&aelig;ter qu&aelig; etiam <lb/>docetur problemata mechanica partim e&longs;&longs;e Phy&longs;ica, partim e&longs;&longs;e Ma&shy;<lb/>thematica.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000294">Quemadmodum in re&shy;<lb/>bus naturalibus mir&aelig; &longs;unt ill&aelig;, quarum cau&longs;a ignoratur: ita &amp; in <lb/>his, qu&aelig; pr&aelig;ter naturam arte fact&aelig; hominibus conferunt, &longs;i &amp; ea&shy;<lb/>rum cau&longs;a lateat, vbi notandum admirationem e&longs;&longs;e animi in rem<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.044.jpg" pagenum="5"/><emph type="italics"/>propo&longs;itam intuitionem cum cupiditate cau&longs;am cogno&longs;cendi: ex quo <lb/>intelligitur Deum qui cogno&longs;cit &amp; tenet cau&longs;as <expan abbr="omni&utilde;">omnium</expan>, Bruta quia <lb/><expan abbr="ne&longs;ci&utilde;t">ne&longs;ciunt</expan>, nec &longs;cire cupiunt, nihil admirari: <expan abbr="&longs;ol&utilde;">&longs;olum</expan> hominem inter vtro&longs;&shy;<lb/>que po&longs;itum, qui ne&longs;ciat, &longs;cire autem cupiat, admirationis e&longs;&longs;e capa&shy;<lb/>cem, vnde non &longs;unt &longs;impliciter intelligendi hi ver&longs;us Horatiani,<emph.end type="italics"/></s></p><p type="main">
  
 <s>Mira &longs;unt in his:] <emph type="italics"/>Similitudo h&icirc;c qu&aelig;dam e&longs;t: &longs;ed &longs;ine notis <lb/>&longs;imilitudinis expre&longs;&longs;a. </s> <s id="id.000295">Nil admirari prop&egrave; res e&longs;t vna Numici,</s></p><p type="main">
  
 <s>&longs;ic igitur erit clarior. </s> <s id="id.000296">Sol&aacute;que qu&aelig; po&longs;&longs;it facere &amp; &longs;eruare beatum. </s></p><p type="main">
  
 <s>Quemadmodum in re&shy;<lb/>bus naturalibus mir&aelig; &longs;unt ill&aelig;, quarum cau&longs;a ignoratur: ita &amp; in <lb/>his, qu&aelig; pr&aelig;ter naturam arte fact&aelig; hominibus conferunt, &longs;i &amp; ea&shy;<lb/>rum cau&longs;a lateat, vbi notandum admirationem e&longs;&longs;e animi in rem<emph.end type="italics"/><pb pagenum="5"/><emph type="italics"/>propo&longs;itam intuitionem cum cupiditate cau&longs;am cogno&longs;cendi: ex quo <lb/>intelligitur Deum qui cogno&longs;cit &amp; tenet cau&longs;as <expan abbr="omni&utilde;">omnium</expan>, Bruta quia <lb/><expan abbr="ne&longs;ci&utilde;t">ne&longs;ciunt</expan>, nec &longs;cire cupiunt, nihil admirari: <expan abbr="&longs;ol&utilde;">&longs;olum</expan> hominem inter vtro&longs;&shy;<lb/>que po&longs;itum, qui ne&longs;ciat, &longs;cire autem cupiat, admirationis e&longs;&longs;e capa&shy;<lb/>cem, vnde non &longs;unt &longs;impliciter intelligendi hi ver&longs;us Horatiani,<emph.end type="italics"/></s></p><p type="main"> <s id="id.000297"><emph type="italics"/>Nec enim h&aelig;c res facit Bruta, nec homines, qui ignorant, &longs;ed &longs;cire <lb/>&longs;eputant, aut &longs;cire non cupiunt, f&oelig;lices: &longs;ed eos, qui cogno&longs;cunt, iux&shy;<lb/>ta illud<emph.end type="italics"/></s></p><p type="main">
  
 <s>Nil admirari prop&egrave; res e&longs;t vna Numici,</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>Sol&aacute;que qu&aelig; po&longs;&longs;it facere &amp; &longs;eruare beatum.</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&shy;<emph.end type="italics"/><lb/><arrow.to.target n="marg5"/><lb/><emph type="italics"/>petijt. </s>
  
 <s><emph type="italics"/>Nec enim h&aelig;c res facit Bruta, nec homines, qui ignorant, &longs;ed &longs;cire <lb/>&longs;eputant, aut &longs;cire non cupiunt, f&oelig;lices: &longs;ed eos, qui cogno&longs;cunt, iux&shy;<lb/>ta illud<emph.end type="italics"/></s></p><p type="main"> <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>F&oelig;lix, qui potuit rerum cogno&longs;cere cau&longs;as.</s></p><p type="main"> <s id="id.000301">Homo natura fugiens e&longs;t igno&shy;<lb/>ranti&aelig;. </s>
  
 <s><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"></arrow.to.target><lb/><emph type="italics"/>pet&yuml;t. </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>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.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>Homo natura fugiens e&longs;t igno&shy;<lb/>ranti&aelig;. </s> 
  
 <s><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"></arrow.to.target><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.000304"><margin.target id="marg5"/>Cap. 2. lib. 2. <lb/>Metaph. </s>
  
 <s>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><margin.target id="marg6"/>Cap. 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><margin.target id="marg5"></margin.target>Cap.  <s id="id.000306">Et in &longs;ingularium conti&shy;<lb/>nentium &amp; proximarum inuentione, &amp; earum ad primam redu&shy;<lb/>ctione Philo&longs;ophia con&longs;i&longs;tit. </s>
  
  <s id="id.000307">Sunt autem eiu&longs;modi, vt ex his ali&aelig; <lb/>not&aelig; iam &longs;int, ali&aelig; adhuc ignot&aelig; per&longs;i&longs;tant, vnde numquam &longs;tudio&shy;<lb/>&longs;is deerit admirandi, &amp; propterea philo&longs;ophandi occa&longs;io: difficiles <lb/>tantum, &longs;alebro&longs;o&longs;que aditus habens, &longs;iquidem<emph.end type="italics"/></s></p><p type="main">
  
 2. lib.  <s id="id.000308">Multa tegit &longs;acro inuolucro Natura, neque vllis</s></p><p type="main">
  
 2. <lb/>Metaph.</s></p><p type="margin"> <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 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><margin.target id="marg6"></margin.target>Cap.  <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></subchap1><subchap1><p type="main">
  
  <s id="id.000312"><foreign lang="el">e)n polloi=s ga\r <lb/>h( fu/sis u(penanti/on pro\s to\ xrh/simon h(mi=n poiei=. </foreign></s>
  <s id="g0110103"><foreign lang="el">h( me\n <lb/>ga\r fu/sis a)ei\ to\n au)to\n e)/xei tro/pon kai\ a(plw=s, to\ de\ <lb/>xrh/simon metaba/llei pollaxw=s.</foreign></s>
  <s id="g0110201"><foreign lang="el">o(/tan ou)=n de/h| ti para\ <lb/>fu/sin pra=cai, dia\ to\ xalepo\n a)pori/an pare/xei kai\ dei=tai <lb/>te/xnhs.</foreign></s></p><p type="main">
  
 6. lib.  <s id="id.000313">In multis enim natura ab <lb/>vtilitate no&longs;tra di&longs;cedit. </s>
  
 5. <lb/>De benefic.</s></p><p type="main"> <s id="id.000314"><expan abbr="Si&shy;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>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.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>Et in &longs;ingularium conti&shy;<lb/>nentium &amp; proximarum inuentione, &amp; earum ad primam redu&shy;<lb/>ctione Philo&longs;ophia con&longs;i&longs;tit. </s> <s id="id.000316">COMMENTARIVS. </s></p><p type="main">
  
 <s>Sunt autem eiu&longs;modi, vt ex his ali&aelig; <lb/>not&aelig; iam &longs;int, ali&aelig; adhuc ignot&aelig; per&longs;i&longs;tant, vnde numquam &longs;tudio&shy;<lb/>&longs;is deerit admirandi, &amp; propterea philo&longs;ophandi occa&longs;io: difficiles <lb/>tantum, &longs;alebro&longs;o&longs;que aditus habens, &longs;iquidem<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>Multa tegit &longs;acro inuolucro Natura, neque vllis</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>Fas e&longs;t &longs;cire quidem mortalibus omnia: multa</s></p><p type="main"> <s id="id.000319"><emph type="italics"/>In his qu&aelig; arte fiunt ali&ograve; natura flectitur &amp; adducitur, quam <lb/>vergat. </s>
  
 <s>Admirare mod&ograve;, nec non venerarc.</s></p><pb pagenum="6"/><p type="main"> <s id="id.000320">Natura enim eodem modo &longs;emper agit, v&longs;us autem re&shy;<lb/>rum humanarum varios modos po&longs;tulat. <emph.end type="italics"/></s></p><p type="main">
  
 <s><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.000321"><emph type="italics"/>Igitur in arte factis aliquid mirum e&longs;t. </s>
  
 <s><gap/></s></p><p type="main"> <s id="id.000322">Pro a&longs;&longs;umptione a&longs;&longs;um&shy;<lb/>ptionis confirmatio est ex effectis, &amp; effectorum modo natur&aelig; &amp; <lb/>artis. </s>
  
 <s>In multis enim natura ab <lb/>vtilitate no&longs;tra di&longs;cedit. </s> <s id="id.000323">Natura enim in multis inclinat ali&ograve;, quam vtilitas hominum <lb/>po&longs;tulat: Natura item vno modo &longs;emper operatur: contra Ars vti&shy;<lb/>litatem hominem &longs;emper &longs;pectat, &amp; varios operandi modos pro&shy;<lb/>&longs;equitur. <emph.end type="italics"/></s></p><p type="main">
  
 <s><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.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><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.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">
  
 <s>COMMENTARIVS.</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>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.000328">Quinetiam va&shy;<lb/>rietas <expan abbr="c&otilde;tra">contra</expan> natur&aelig; cur&longs;um expetitur in delectabilibus vt hydrauli&shy;<lb/>cis, engebatis, merulis, &amp; icunculis voces, cantus, ge&longs;tus hominum, <lb/>auium, aliorumque animalium imitantibus. <emph.end type="italics"/></s></p><p type="main">
  
 <s><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.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><emph type="italics"/>In his qu&aelig; arte fiunt ali&ograve; natura flectitur &amp; adducitur, quam <lb/>vergat. </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>Natura enim eodem modo &longs;emper agit, v&longs;us autem re&shy;<lb/>rum humanarum varios modos po&longs;tulat.<emph.end type="italics"/></s></p><p type="main"> <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><emph type="italics"/>Igitur in arte factis aliquid mirum e&longs;t. </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>Pro a&longs;&longs;umptione a&longs;&longs;um&shy;<lb/>ptionis confirmatio est ex effectis, &amp; effectorum modo natur&aelig; &amp; <lb/>artis. </s> <s id="id.000333">Illud inuentum, mod&uacute;&longs;ve inueniendi <lb/>generalis e&longs;t. </s>
  
 <s>Natura enim in multis inclinat ali&ograve;, quam vtilitas hominum <lb/>po&longs;tulat: Natura item vno modo &longs;emper operatur: contra Ars vti&shy;<lb/>litatem hominem &longs;emper &longs;pectat, &amp; varios operandi modos pro&shy;<lb/>&longs;equitur.<emph.end type="italics"/></s></p><p type="main"> <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>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.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 maturitates hinc exempla &longs;ump&longs;it, &amp; ea <lb/>imitans, inductus rebus diuinis, commodas vit&aelig; perfecit explicatio&shy;<lb/>nes. </s>
  
 <s>H&aelig;c &longs;unt demon&longs;trata ab Aristotele<emph.end type="italics"/><pb pagenum="7"/><emph type="italics"/>lib.  <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">
  
 de C&oelig;lo &amp; de generat. </s> <s id="id.000337"><margin.target id="marg7"/>Lib. 10. </s></p><p type="main">
  
 <s>&amp; corrupt.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000338">Tum difficultas.] <emph type="italics"/>Natur&aelig; renixus difficultatem facit. </s>
  
 <s>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.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></subchap1><subchap1>
  
 <s>Quinetiam va&shy;<lb/>rietas <expan abbr="c&otilde;tra">contra</expan> natur&aelig; cur&longs;um expetitur in delectabilibus vt hydrauli&shy;<lb/>cis, engebatis, merulis, &amp; icunculis voces, cantus, ge&longs;tus hominum, <lb/>auium, aliorumque animalium imitantibus.<emph.end type="italics"/></s></p><p type="main"> <p type="main"><s id="id.000340"><foreign lang="el">dio\ kai\ kalou=men th=s te/xnhs, to\ pro\s ta\s toiau/tas <lb/>a)pori/as bohqou=n me/ros, mhxanh/n, <arrow.to.target n="marg8"/>kaqa/per ga\r e)poi/hsen <lb/>*)antifw=n o( poihth/s, ou(/tw kai\ e)/xei: te/xnh| ga\r kratou=men, <lb/>w(=n fu/sei nikw/meqa.</foreign></s>
  <s id="g0110203"><foreign lang="el">toiau=ta de/ e)stin e)n oi(=s ta/ te e)la/ttona <lb/>kratei= tw=n meizo/nwn, kai\ ta\ r(oph\n e)/xonta mikra\n kinei= <lb/>ba/rh mega/la, kai\ pa/nta sxedo\n o(/sa tw=n problhma/twn <lb/>mhxanika\ prosagoreu/omen.</foreign></s><lb/></p><p type="margin">
  
 <s>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.000341"><margin.target id="marg8"/><foreign lang="el">mhxanikh\n. </foreign></s></p><p type="main">
  
 <s>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.000342">Atque propterea partem <lb/>illius artis qu&aelig; h&aelig;&longs;itationi <lb/>i&longs;ti &longs;uccurrit Mechanicem <lb/>vocamus. </s>
  
 <s>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.000343"><expan abbr="Quemadmod&utilde;">Quemadmodum</expan> <lb/>enim Antipho po&euml;ta di&shy;<lb/>xit, ita &longs;e res habet. </s></p><p type="main">
  
 <s>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.000344"><emph type="italics"/>Natura vincit: hanc arte <lb/>vincimus. <emph.end type="italics"/></s></p><p type="main">
  
 <s>Illud inuentum, mod&uacute;&longs;ve inuenicndi <lb/>generalis e&longs;t. </s> <s id="id.000345">vt in his, qu&aelig;, cum mino&shy;<lb/>ra &longs;int, &longs;uperant maiora: &amp; <lb/>paruum momentum, cum <lb/>habeant, ingentia dimo&shy;<lb/>uent pondera, c&aelig;teri&longs;&shy;<lb/>que fere, qu&aelig; problemata <lb/>Mechanica nuncupamus. </s></p><p type="head">
  
 <s>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 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"></arrow.to.target><lb/><emph type="italics"/>imitationem rerum &agrave; natura procreatarum. </s> <s id="id.000346">COMMENTARIVS. </s></p><p type="main">
  
 <s>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.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>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.000348">Leonicus, qui <lb/>in hunc librum commentarium edidit putat e&longs;&longs;e Architecturam. <emph.end type="italics"/></s>
  
 <s><margin.target id="marg7"></margin.target>Lib. 10.</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>Tum difficultas.] <emph type="italics"/>Natur&aelig; renixus difficultatem facit. </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>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.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><gap/><lb/><arrow.to.target n="marg8"></arrow.to.target></s></p><p type="margin"> <s id="id.000352">Et quid obe&longs;t dicere hanc e&longs;&longs;e <lb/>Philo&longs;ophiam? </s>
  
 <s><margin.target id="marg8"></margin.target><foreign lang="greek"><gap/>xanik<gap/>.</foreign></s></p><p type="main"> <s id="id.000353">cum Philo&longs;ophia &longs;it cognitio omnium artium &amp; re&shy;<lb/>rum tam diuinarum: quam humanarum cau&longs;as, proprietates, effecta <lb/>con&longs;ideret. </s>
  
 <s>Atque propterea partem <lb/>illius artis qu&aelig; h&aelig;&longs;itationi <lb/>i&longs;ti &longs;uccurrit Mechanicem <lb/>vocamus. </s> <s id="id.000354">Atque hac diui&longs;a in &longs;uas partes, &amp; partium particulas <lb/>vna ex his erit Mechanice. </s>
  
 <s><expan abbr="Quemadmod&utilde;">Quemadmodum</expan> <lb/>enim Antipho po&euml;ta di&shy;<lb/>xit, ita &longs;e res habet.</s></p><p type="main"> <s id="id.000355">Qu&aelig; ad explicationem motuum violen&shy;<lb/>torum, &amp; admirabilium &longs;e habebit, vt Phy&longs;ica ad explicationem <lb/>motuum naturalium: &amp; vt &longs;ub hac Medicina, Agricultura, &amp; <lb/>ali&aelig;: &longs;ic &longs;ub illa ars fabrilis, Architectura, Sutoria, &amp; omnes qu&aelig; <lb/>in&longs;trumentis artificio&longs;is, indu&longs;trii&longs;que opus &longs;uum peragunt. </s>
  
 <s><emph type="italics"/>Natura vincit: hanc arte <lb/>vincimus.<emph.end type="italics"/></s></p><p type="main"> <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>vt in his, qu&aelig;, cum mino&shy;<lb/>ra &longs;int, &longs;uperant maiora: &amp; <lb/>paruum momentum, cum <lb/>habeant, ingentia dimo&shy;<lb/>uent pondera, c&aelig;teri&longs;&shy;<lb/>que fere, qu&aelig; problemata <lb/>Mechanica nuncupamus.</s></p><p type="head"> 
  
 <s>COMMENTARIVS.</s></p><p type="main"> <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">
  
 <s>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.000359">Mechanice.] <emph type="italics"/>In Gr&aelig;co Vecheli legitur h&icirc;c <emph.end type="italics"/><foreign lang="el">mhxanh\n</foreign>: <emph type="italics"/>vt etiam <lb/>in titulo huius capitis: &longs;ed vtrobique legendum <emph.end type="italics"/><foreign lang="el">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>Leonicus, qui <lb/>in hunc librum commentarium edidit putat e&longs;&longs;e Architecturam.<emph.end type="italics"/><pb/><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.000360">Nec tamen definita, vt titulus pollicebatur. </s>
  
 <s>H&aelig;c quidem comprehendi Architectur&aelig; nomine Galenus<emph.end type="italics"/></s></p><p type="main"> <s id="id.000361">Definitur au&shy;<lb/>tem &longs;ic &agrave; Picolomino. </s>
  
 <s><arrow.to.target n="marg9"></arrow.to.target><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.000362">Mechanice e&longs;t &longs;cientia ex qua cau&longs;&aelig; &amp; prin&shy;<emph.end type="italics"/><lb/><arrow.to.target n="marg10"/><lb/><emph type="italics"/>cipia ad quamplurimas artes &longs;ellularias exhauriri po&longs;&longs;unt. </s>
  
 <s>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.000363">Nos peni&shy;<lb/>tius ip&longs;ius rei, qu&aelig; definitur naturam, &amp; ad ea qu&aelig; cum dicta &longs;unt <lb/>ab Aristotele, qu&aelig;que dicentur intuentes perfecti&ugrave;s opinor, &longs;ic de&shy;<lb/>finiemus. </s>
  
 <s>Et quid obe&longs;t dicere hanc e&longs;&longs;e <lb/>Philo&longs;ophiam? </s> <s id="id.000364">Mechanice e&longs;t ars ad ea qu&aelig; vires humanas &longs;uperant, tra&shy;<lb/>hendum, impellendum, ferendum, machinarum fabricatrix. </s>
  
 <s>cum Philo&longs;ophia &longs;it cognitio omnium artium &amp; re&shy;<lb/>rum tam diuinarum: quam humanarum cau&longs;as, proprietates, effecta <lb/>con&longs;ideret. </s> <s id="id.000365">vel &longs;ic <lb/>Mechanice e&longs;t ars cogendi corpora quantum fieri pote&longs;t vt contra <lb/>nutum ferantur. </s>
  
 <s>Atque hac diui&longs;a in &longs;uas partes, &amp; partium particulas <lb/>vna ex his erit Mechanice. </s> <s id="id.000366">H&aelig;c enim tota po&longs;ita e&longs;t, vt ad v&longs;um, delectatio&shy;<lb/>n&eacute;mue hominum grauia &longs;ur&longs;um, leuia deor&longs;um, tum vtraque in la&shy;<lb/>tus, in orbem &longs;eor&longs;im, atque per mixtim &egrave; loco in locum moueantur. <emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.049.jpg" pagenum="10"/><emph type="italics"/>H&aelig;c enim vt fiant, ip&longs;a ars machinas inuenit, &amp; inuentarum, cur <lb/>h&aelig;c pr&aelig;&longs;tent cau&longs;as reddit. </s>
  
 <s>Qu&aelig; ad explicationem motuum violen&shy;<lb/>torum, &amp; admirabilium &longs;e habebit, vt Phy&longs;ica ad explicationem <lb/>motuum naturalium: &amp; vt &longs;ub hac Medicina, Agricultura, &amp; <lb/>ali&aelig;: &longs;ic&longs;ub illa ars fabrilis, Architectura, Sutoria, &amp; omnes qu&aelig; <lb/>in&longs;trumentis artificio&longs;is, indu&longs;trii&longs;que opus &longs;uum peragunt. </s> <s id="id.000367">C&aelig;ter&ugrave;m ex huius machinis, qu&aelig;dam <lb/>mouentur per &longs;e:qu&aelig;dam non &longs;ponte. </s>
  
 <s>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.000368">Ill&aelig; intra &longs;e principia &longs;u&aelig; mo&shy;<lb/>tionis habent, &amp; <emph.end type="italics"/><foreign lang="el">a)uto/mata</foreign> <emph type="italics"/>vocantur: quorum alia Gr&aelig;cis <emph.end type="italics"/><foreign lang="el">stata\, </foreign><lb/><emph type="italics"/>Latinis Stataria, fixa, firma dicuntur: alia <emph.end type="italics"/><foreign lang="el">u(pa/gonta</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/>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><margin.target id="marg9"></margin.target>Cap.  <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.000371">H&aelig; ver&ograve; motionis principium intra &longs;e non habent: Sed ex his <lb/>ali&aelig; mouentur &agrave; rebus inanimis, ali&aelig; ab animatis. </s>
  
 3. lib. <lb/> <s id="id.000372">Res inani&shy;<lb/>m&aelig; principium motionis exhibentes &longs;unt a&euml;r, &longs;piritus, aqua, ignis, <lb/>&longs;umus. </s>
  
 de cuiu&longs;que <lb/>animi pecc. <lb/></s> <s id="id.000373">Aer &amp; &longs;piritus e&longs;t vel inclu&longs;us, ex qu&ograve; pneumatica ratio ab&shy;<lb/>&longs;oluitur, de qua etiam Hero in&longs;trumenta Mu&longs;ica, qu&aelig; per <emph.end type="italics"/><foreign lang="el">a)ntonoma&shy;<lb/>si/an</foreign><emph type="italics"/> organa vocant: vel liber, vnde &aelig;dificia ad molendum. </s>
  
 <s>cogno&longs;c.</s></p><p type="main"> <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>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.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>Nec tamen definita, vt titulus pollicebatur. </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>Definitur au&shy;<lb/>tem &longs;ic &agrave; Picolomino. </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>Mechanice e&longs;t &longs;cientia ex qua cau&longs;&aelig; &amp; prin-<emph.end type="italics"/><lb/><arrow.to.target n="marg10"></arrow.to.target><lb/><emph type="italics"/>cipia ad quamplurimas artes &longs;ellularias exhauriri po&longs;&longs;unt. </s> <s id="id.000378">Sed neque hic <lb/>pr&aelig;termittenda diui&longs;io Methanices, qu&aelig; aliter &agrave; Politiano ex He&shy;<emph.end type="italics"/><lb/><arrow.to.target n="marg11"/><lb/><emph type="italics"/>rone inducta e&longs;t. </s>
  
 <s>Nos peni&shy;<lb/>tius ip&longs;ius rei, qu&aelig; definitur naturam, &amp; ad ea qu&aelig; cum dicta &longs;unt <lb/>ab Aristotele, qu&aelig;que dicentur intuentes perfecti&ugrave;s opinor, &longs;ic de&shy;<lb/>finiemus. </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="el">xeirourgikh\,</foreign> <emph type="italics"/>cui vel maxim&egrave; artes ill&aelig;, &aelig;raria, &aelig;difica&shy;<lb/>toria, materiaria, picturaque, adminiculantur. </s>
  
 <s>Mechanice e&longs;t ars ad ea qu&aelig; vires humanas &longs;uperant, tra&shy;<lb/>hendum, impellendum, ferendum, machinarum fabricatrix. </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="el">mhxanopoihtikh\,</foreign> <emph type="italics"/>qu&aelig; facile aquas antlijs extrahit:<emph.end type="italics"/> <foreign lang="el">*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="el">poliorkhtika\</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>vel &longs;ic <lb/>Mechanice e&longs;t ars cogendi corpora quantum fieri pote&longs;t vt contra <lb/>nutum ferantur. </s> <s id="id.000381">Mox &amp; qu&aelig;<emph.end type="italics"/> <foreign lang="el">qaumatourgikh\</foreign> <emph type="italics"/>cuius exempla &longs;unt<emph.end type="italics"/> <foreign lang="el">u)drau&shy;<lb/>lika\</foreign> <emph type="italics"/>organa, qu&aelig;que per &longs;e ventorum flatu re&longs;onant. </s>
  
 <s>H&aelig;c enim tota po&longs;ita e&longs;t, vt ad v&longs;um, delectatio&shy;<lb/>n&eacute;mue hominum grauia &longs;ur&longs;um, leuia deor&longs;um, tum vtraque in la&shy;<lb/>tus, in orbem &longs;eor &longs;im, atque per mixtim &egrave; loco in locum moueantur.<emph.end type="italics"/><pb pagenum="10"/><emph type="italics"/>H&aelig;c enim vt fiant, ip&longs;a ars machinas inuenit, &amp; inuentarum, cur <lb/>h&aelig;c pr&aelig;&longs;tent cau&longs;as reddit. </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>C&aelig;ter&ugrave;m ex huius machinis, qu&aelig;dam <lb/>mouentur per &longs;e:qu&aelig;dam non &longs;ponte. </s> <s id="id.000383">Et<emph.end type="italics"/> <foreign lang="el">si/fwnes</foreign><lb/><emph type="italics"/>extinguendis incendijs 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>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.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. </s>
  
 <s>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.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>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.000386">Suppeditat eadem Architectur&aelig; quoque &longs;can&longs;orias, tra&shy;<lb/>ctiles, &amp; &longs;pirituales machinas. <emph.end type="italics"/></s></p><p type="margin">
  
 <s>H&aelig; ver&ograve; motionis principium intra &longs;e non habent: Sed ex his <lb/>ali&aelig; mouentur &agrave; rebus inanimis, ali&aelig; ab animatis. </s> <s id="id.000387"><margin.target id="marg10"/>In parapha&shy;<lb/>&longs;i huius li&shy;<lb/>bri. </s></p><p type="margin">
  
 <s>Res inani&shy;<lb/>m&aelig; principium motionis exhibentes &longs;unt a&euml;r, &longs;piritus, aqua, ignis, <lb/>&longs;umus. </s> <s id="id.000388"><margin.target id="marg11"/>In Pancpi&shy;<lb/>&longs;temone. </s></p><p type="main">
  
 <s>Aer &amp; &longs;piritus e&longs;t vel inclu&longs;us, ex qu&ograve; pneumatica ratio ab&shy;<lb/>&longs;oluitur, de qua etiam Hero in&longs;trumenta Mu&longs;ica, qu&aelig; per<emph.end type="italics"/> <foreign lang="greek">an)tono ma&shy;<lb/>si/an</foreign> <emph type="italics"/>organa vocant: vel liber, vnde &aelig;dificia ad molendum. </s> <s id="id.000389">Natura vincit.] <emph type="italics"/>Senariolus e&longs;t cuiu&longs;dam antiqui po&euml;t&aelig; nomine <emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.051.jpg" pagenum="12"/><emph type="italics"/>tenus in hominum memoria &longs;uper&longs;titis: ni&longs;i &longs;it is, de quo Ari&longs;toteles <lb/>in &longs;uis Rhetoricis meminit, lepidumque eius dictum ad &longs;ocios, qui&shy;<lb/>bu&longs;cum vna ducebatur in &longs;upplicium iu&longs;&longs;u Diony&longs;ij tyranni, reci&shy;<lb/>tat. </s>
  
 <s>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.000390">hos enim videns capite coopertos. </s>
  
 <s>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.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>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.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. </s>
  
 <s>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 pagenum="11"/><emph type="italics"/>po&longs;tulauerit, facile componi, facil&eacute;que di&longs;&longs;olui po&szlig;int. </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>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"></arrow.to.target><lb/><emph type="italics"/>rone inducta e&longs;t. </s> <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="el">paradoxo/poioi,</foreign> <emph type="italics"/>cum Galeno vocari poterunt. <emph.end type="italics"/></s></p><p type="main">
  
 <s>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.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>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.000396">In&longs;pectura domos ventur&aacute;que de&longs;uper vrbi. </s></p><p type="main">
  
 <s>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.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></subchap1><subchap1><p type="main">
  
 <s>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.000398"><foreign lang="el">e)/sti de\ tau=ta toi=s fusikoi=s <lb/>problh/masin, ou)/te tau)ta\ pa/mpan, ou)/te kexwrisme/na li/an, <lb/>a)lla\ koina\ tw=n te maqhmatikw=n qewrhma/twn, kai\ tw=n <lb/>fusikw=n: to\ me\n ga\r w(\s dia\ tw=n maqhmatikw=n dh=lon, to\ <lb/>de\ peri\ o(\, dia\ tw=n fusikw=n.</foreign></s></p><p type="main">
  
 <s>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.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. </s>
  
 <s>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. </s> <s id="id.000400">Etenim <lb/>quod ip&longs;um quomodo ad <lb/>mathematica pertineat: <lb/>ip&longs;um vero circa quod, ad <lb/>Phy&longs;ica, manife&longs;tum e&longs;t. </s></p><p type="head">
  
 <s>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.000401">COMMENTARIVS. </s></p><p type="main">
  
 <s>Suppeditat eadem Architectur&aelig; quoque &longs;can&longs;orias, tra&shy;<lb/>ctiles, &amp; &longs;pirituales machinas.<emph.end type="italics"/></s></p><p type="margin"> <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><margin.target id="marg10"></margin.target>In parapha&shy;<lb/>&longs;i huius li&shy;<lb/>bri.</s></p><p type="margin"> <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. </s>
  
 <s><margin.target id="marg11"></margin.target>In Pancpi&shy;<lb/>&longs;temone.</s></p><p type="main"> <s id="id.000404">Machina&shy;<lb/>rum enim materia lignum e&longs;t vel ferrum &amp; eiu&longs;modi corpora Phy&shy;<lb/>&longs;ica: attributum ver&ograve; &egrave; figuris &amp; terminis Mathematicis cuiu&longs;mo&shy;<lb/>di &longs;unt in Geometria line&aelig;, diametri, centra, circuli, &amp; eiu&longs;modi, <lb/>&egrave; quibus machin&aelig; con&longs;tare &amp; figurat&aelig; e&longs;&longs;e, &amp; vires &longs;uas accipere, <lb/>augere, diminuere, metiri o&longs;tenduntur. </s>
  
 <s>Natura vincit.] <emph type="italics"/>Senariolus e&longs;t cuiu&longs;dam antiqui po&euml;t&aelig; nomine<emph.end type="italics"/><pb pagenum="12"/><emph type="italics"/>tenus in hominum memoria &longs;uper&longs;titis: ni&longs;i &longs;it is, de quo Ari&longs;toteles <lb/>in &longs;uis Rhetoricis meminit, lepidumque eius dictum ad &longs;ocios, qui&shy;<lb/>bu&longs;cum vna ducebatur in &longs;upplicium iu&longs;&longs;u Diony &longs;ij tyranni, reci&shy;<lb/>tat. </s> <s id="id.000405">Vnde Mechanice pars e&longs;t <lb/>mathematicarum non aliter: quam Mu&longs;ica, Optica, A&longs;tronomia, <lb/>quas Ari&longs;toteles dixit e&longs;&longs;e<emph.end type="italics"/> <foreign lang="el">fusikote/ras,</foreign> <emph type="italics"/>ob &longs;ubiecti &longs;cilicet, quod <lb/>tractant naturam Phy&longs;icas: &longs;ed ob<emph.end type="italics"/> <foreign lang="el">gra/mmikas</foreign> <emph type="italics"/>id e&longs;t lineares &amp; <lb/>numerales demon&longs;trationes, quibus ip&longs;um explicant, Mathemati&shy;<lb/>cas. </s>
  
 <s>hos enim videns capite coopertos. </s> <s id="id.000406">C&aelig;terum exeo quod dicit Ari&longs;toteles problemata Mechanica <lb/>e&longs;&longs;e Phy&longs;icis &amp; Mathematicis con&longs;entanea, &longs;ub indicare videtur, <lb/>ne Mechanicus ante existimet machinas, quarum habuerit demon&shy;<lb/>&longs;trationem in v&longs;um venire po&longs;&longs;e, &longs;uamque efficaciam &longs;ortiri: ni&longs;i <lb/>materia Phy&longs;ica existat, qu&aelig; rem patiatur fieri. </s>
  
 <s>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.000407">Quamuis enim <lb/>Geometer demon&longs;tratione concludat, datam rectam lineam infinit&egrave; <lb/>diui&longs;ibilem e&longs;&longs;e, nulla materia lineata apud phy&longs;icos e&longs;t, qu&aelig; non <lb/>continuata diui&longs;ione tandem reducatur ad eam, qu&aelig; &longs;i amplius in&shy;<lb/>telligatur diuidi, amittet formam line&aelig; Phy&longs;ic&aelig; &amp; vi&longs;ibilis: &longs;ic <lb/>licet apud Mechanicos multa demon&longs;trentur de motu in infinitum <lb/>augendo, quale e&longs;t illud problema Archimedeum. </s>
  
 <s>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. </s> <s id="id.000408">Datum pondus <lb/>data potentia mouere. </s>
  
 <s>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.000409">Ita tamen intelligenda &longs;unt, ne exi&longs;timemus <lb/>infinita hominis, <expan abbr="quac&utilde;que">quacunque</expan> arte iuuetur, pote&longs;tati &longs;ube&longs;&longs;e. </s>
  
 <s>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.000410">Sunt enim <lb/>certi fines, vltra quos natura rerum ip&longs;um progredi non patitur. <lb/></s>
  
 <s>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.000411">Sunt pr&aelig;terea vitia materi&aelig; qu&aelig; Geometra, aut Mechanicus de&shy;<lb/>mon&longs;trans non con&longs;iderat: nec etiam ob&longs;tant quo minus qu&aelig; propo&shy;<lb/>&longs;ita &longs;unt, vera &longs;int in intellectu: Mechanicus igitur operans, priu&longs;&shy;<lb/>quam operi &longs;e accingat, ne fru&longs;tretur, con&longs;iderare debet, an quod <lb/>proponitur effici po&szlig;it, habita ratione materi&aelig; ex qua, aut per <expan abbr="qu&atilde;">quam</expan>, <lb/>&amp; circun&longs;tantiarum pr&aelig;&longs;ertim temporis quod pr&aelig;&longs;cribitur, &amp; &longs;um&shy;<lb/>ptuum quos facere oporteret. </s>
  
 <s>In&longs;pectura domos ventur&aacute;que de&longs;uper vrbi.</s></p><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></subchap1><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.053.jpg" pagenum="14"/><subchap1><p type="main">
  
 <s><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.000413"><foreign lang="el">perie/xetai de\ tw=n a)poroume/nwn<lb/> e)n tw=| ge/nei tou/tw| ta\ peri\ to\n moxlo/n.</foreign></s>
  <s id="g0120102"><foreign lang="el">a)/topon ga\r <lb/>ei)=nai dokei= to\ kinei=sqai me/ga ba/ros u(po\ mikra=s i)sxu/os, <lb/>kai\ tau=ta meta\ ba/rous plei/onos: o(\ ga\r a)/neu moxlou= kinei=n <lb/>ou) du/natai/ tis, tou=to au)to\ to\ ba/ros proslabw\n e)/ti to\ <lb/>tou= moxlou= ba/ros, kinei= qa=tton.</foreign></s></p><p type="main">
  
 <s><gap/></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>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. </s> <s id="id.000415">Ab&longs;urdum enim <lb/>videtur ab exigua vi ma&shy;<lb/>gnum pondus moueri, &amp; <lb/>quidem ad pondus addito <lb/>pondere. </s>
  
 <s>Etenim <lb/>quod ip&longs;um quomodo ad <lb/>mathematica pertineat: <lb/>ip&longs;um vero circa quod, ad <lb/>Phy&longs;ica, manife&longs;tum e&longs;t.</s></p><p type="head"> <s id="id.000416">quod enim &longs;ine <lb/>vecte qui&longs;piam non po&longs;&longs;et <lb/>mouere, hoc ip&longs;um pon&shy;<lb/>dus, in&longs;uper <expan abbr="adijci&etilde;s">adijciens</expan> vectis <lb/>ip&longs;ius <expan abbr="p&otilde;dus">pondus</expan>, facile mouet. </s></p><p type="head">
  
 <s>COMMENTARIVS.</s></p><p type="main"> <s id="id.000417">COMMENTARIVS. </s></p><p type="main">
  
 <s><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 pagenum="13"/><emph type="italics"/>Ari&longs;totele, &amp; al&yuml;s pro vtroque, vt hic, indifferenter legitur. </s> <s id="id.000418">Qv&aelig; de vecte.] <emph type="italics"/>Vectis e&longs;t machina &longs;eu in&longs;trumentum in&longs;tar <lb/>pali aut baculi recti longioris, cuius alterum extremum in cu&shy;<lb/>spidem <expan abbr="acut&atilde;">acutam</expan> &amp; paul&ograve; latiorem de&longs;init, <expan abbr="vocaturq;">vocaturque</expan> lingua: alterum <lb/><expan abbr="extrem&utilde;">extremum</expan> caput e&longs;t, aut manubrium. </s>
  
 <s>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. </s> <s id="id.000419">vecti in v&longs;u aliquando &longs;upponi&shy;<lb/>tur fulcimentum, quod Gr&aelig;ci<emph.end type="italics"/> <foreign lang="el">u(pomo/xlion,</foreign> <emph type="italics"/>Vitruuius porrectam <lb/>pre&szlig;ionem appellat. <emph.end type="italics"/></s></p><p type="main">
  
 <s>Machina&shy;<lb/>rum enim materia lignum e&longs;t vel ferrum &amp; eiu&longs;modi corpora Phy&shy;<lb/>&longs;ica: attributum ver&ograve; &egrave; figuris &amp; terminis Mathematicis cuiu&longs;mo&shy;<lb/>di &longs;unt in Geometria line&aelig;, diametri, centra, circuli, &amp; eiu&longs;modi, <lb/>&egrave; quibus machin&aelig; con&longs;tare &amp; figurat&aelig; e&longs;&longs;e, &amp; vires &longs;uas accipere, <lb/>augere, diminuere, metiri o&longs;tenduntur. </s> <s id="id.000420">Ab&longs;urdum enim videtur.] <emph type="italics"/>Ostenditur hic cur problema <lb/>de vecte in Mechanicis, dubitabile, &longs;iue dignum qu&aelig;&longs;itu &longs;it. </s>
  
 <s>Vnde Mechanice pars e&longs;t <lb/>mathematicarum non aliter: quam Mu&longs;ica, Optica, A&longs;tronomia, <lb/>quas Ari&longs;toteles dixit e&longs;&longs;e<emph.end type="italics"/> <foreign lang="greek">fusiko<gap/>e/<gap/>s,</foreign> <emph type="italics"/>ob &longs;ubiecti &longs;cilicet, quod <lb/>tractant naturam Phy&longs;icas: &longs;ed ob<emph.end type="italics"/> <foreign lang="greek">gra/mmikas</foreign> <emph type="italics"/>id e&longs;t lineares &amp; <lb/>numerales demon&longs;trationes, quibus ip&longs;um explicant, Mathemati&shy;<lb/>cas. </s> <s id="id.000421">Du&shy;<lb/>bitabilia enim &longs;unt, qu&aelig; reuera fiunt: vt magnum pondus addito <lb/>pondere vectis ab exigua potentia, &amp; vna hominis manu moue&shy;<lb/>ri. </s>
  
 <s>C&aelig;terum exeo quod dicit Ari&longs;toteles problemata Mechanica <lb/>e&longs;&longs;e Phy&longs;icis &amp; Mathematicis con&longs;entanea, &longs;ub indicare videtur, <lb/>ne Mechanicus ante existimet machinas, quarum habuerit demon&shy;<lb/>&longs;trationem in v&longs;um venire po&longs;&longs;e, &longs;uamque efficaciam &longs;ortiri: ni&longs;i <lb/>materia Phy&longs;ica existat, qu&aelig; rem patiatur fieri. </s> <s id="id.000422">Fieri tamen ratio repugnat. </s>
  
 <s>Quamuis enim <lb/>Geometer demon&longs;tratione concludat, datam rectam lineam infinit&egrave; <lb/>diui&longs;ibilem e&longs;&longs;e, nulla materia lineata apud phy&longs;icos e&longs;t, qu&aelig; non <lb/>continuata diui&longs;ione tandem reducatur ad eam, qu&aelig; &longs;i amplius in&shy;<lb/>telligatur diuidi, amittet formam line&aelig; Phy&longs;ic&aelig; &amp; vi&longs;ibilis: &longs;ic <lb/>licet apud Mechanicos multa demon&longs;trentur de motu in infinitum <lb/>augendo, quale e&longs;t illud problema Archimedeum. </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>Datum pondus <lb/>data potentia mouere. </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></subchap1><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.054.jpg" pagenum="15"/><subchap1><p type="main">
  
 <s>Ita tamen intelligenda &longs;unt, ne exi&longs;timemus <lb/>infinita hominis, <expan abbr="quac&utilde;que">quacunque</expan> arte iuuetur, pote&longs;tati &longs;ube&longs;&longs;e. </s> <s id="id.000425"><foreign lang="el">pa/ntwn de\ tw=n toiou/twn <lb/>e)/xei th=s ai)ti/as th\n a)rxh\n o( ku/klos, kai\ tou=to eu)lo/gws <lb/>sumbe/bhken.</foreign></s>
  <s id="g0120104"><foreign lang="el">e)k me\n ga\r qaumasiwte/rou sumbai/nein ti <lb/>qaumasto\n ou)de\n a)/topon. </foreign></s></p><p type="main">
  
 <s>Sunt enim <lb/>certi fines, vltra quos natura rerum ip&longs;um progredi non patitur. <lb/></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>
  
 <s>Sunt pr&aelig;terea vitia materi&aelig; qu&aelig; Geometra, aut Mechanicus de&shy;<lb/>mon&longs;trans non con&longs;iderat: nec etiam ob&longs;tant quo minus qu&aelig; propo&shy;<lb/>&longs;ita &longs;unt, vera &longs;int in intellectu: Mechanicus igitur operans, priu&longs;&shy;<lb/>quam operi &longs;e accingat, nefru&longs;tretur, con&longs;iderare debet, an quod <lb/>proponitur effici po&szlig;it, habitaratione materi&aelig; ex qua, aut per <expan abbr="qu&atilde;">quam</expan>, <lb/>&amp; circun&longs;tantiarum pr&aelig;&longs;ertim temporis quod pr&aelig;&longs;cribitur, &amp; &longs;um&shy;<lb/>ptuum quos facere oporteret. </s> <s id="id.000427">quod etiam ratio&shy;<lb/>ni valde <expan abbr="c&otilde;&longs;entaneum">con&longs;entaneum</expan> e&longs;t. <lb/></s>
  
 <s>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 pagenum="14"/><p type="main"> <s id="id.000428">Nec enim ab&longs;urdum e&longs;t, <lb/>ex admirabiliori quid ad&shy;<lb/>mirabile contingere. </s></p><p type="head">
  
 <s><gap/></s></p><p type="main"> <s id="id.000429">COMMENTARIVS. </s></p><p type="main">
  
 <s>Dubitantur <expan abbr="aut&etilde;">autem</expan> in hoc <lb/>genere ea, qu&aelig; de vecte di&shy;<lb/>cuntur. </s> <s id="id.000430">Omnium ver&ograve; talium.] <emph type="italics"/>Cau&longs;a qu&aelig; latebat in problemate <lb/>de vecte a&szlig;ignatur hic e&longs;&longs;e circulus: qu&aelig; ad alia multa Me&shy;<lb/>chanica po&longs;tea transferetur. </s>
  
 <s>Ab&longs;urdum enim <lb/>videtur ab exigua vi ma&shy;<lb/>gnum pondus moueri, &amp; <lb/>quidem ad pondus addito <lb/>pondere. </s> <s id="id.000431">Probatur autem id ex forma circuli mi&shy;<lb/>rabili&szlig;ima. </s>
  
 <s>quod enim &longs;ine <lb/>vecte qui&longs;piam non po&longs;&longs;et <lb/>mouere, hoc ip&longs;um pon&shy;<lb/>dus, in&longs;uper <expan abbr="adijci&etilde;s">adijciens</expan> vectis <lb/>ip&longs;ius <expan abbr="p&otilde;dus">pondus</expan>, facile mouet.</s></p><p type="head"> <s id="id.000432">&longs;ic. <emph.end type="italics"/></s></p><p type="main">
  
 <s>COMMENTARIVS.</s></p><p type="main"> <s id="id.000433"><emph type="italics"/>Ex admirabiliori admirabile aliquid fieri non e&longs;t alienum, cau&longs;&aelig; <lb/>enim &longs;ibi &longs;imiles effectus edunt. <emph.end type="italics"/></s></p><p type="main">
  
 <s>Qv&aelig; de vecte.] <emph type="italics"/>Vectis e&longs;t machina &longs;eu in&longs;trumentum in&longs;tar <lb/>pali aut baculi recti longioris, cuius alterum extremum in cu&shy;<lb/>spidem <expan abbr="acut&atilde;">acutam</expan> &amp; paul&ograve; latiorem de&longs;init, <expan abbr="vocaturq;">vocaturque</expan> lingua: alterum <lb/><expan abbr="extrem&utilde;">extremum</expan> caput e&longs;t, aut manubrium. </s> <s id="id.000434"><emph type="italics"/>Circulus e&longs;t admirabilis, &amp; admirabilior, quam vectis: quamque <lb/>ea qu&aelig; &agrave; vecte fiunt. <emph.end type="italics"/></s></p><p type="main">
  
 <s>vecti in v&longs;u aliquando &longs;upponi&shy;<lb/>tur fulcimentum, quod Gr&aelig;ci<emph.end type="italics"/> <foreign lang="greek"><gap/>(w_omo/xlion,</foreign> <emph type="italics"/>Vitruuius porrectam <lb/>pre&szlig;ionem appellat.<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></subchap1><subchap1><p type="main">
  
 <s>Ab&longs;urdum enim videtur.] <emph type="italics"/>Ostenditur hic cur problema <lb/>de vecte in Mechanicis, dubitabile, &longs;iue dignum qu&aelig;&longs;itu &longs;it. </s> <s id="id.000436"><foreign lang="el">qaumasiw/taton de\ to\ tou)nanti/a <lb/>gi/nesqai met' a)llh/lwn.</foreign></s>
  <s id="g0120202"><foreign lang="el">o( de\ ku/klos sune/sthken e)k toiou/twn. </foreign></s>
  <s id="g0120203"><foreign lang="el"><lb/>eu)qu\s ga\r e)k kinoume/nou te gege/nhtai kai\ me/nontos, w(=n h( <lb/>fu/sis e)sti\n u(penanti/a a)llh/lois. </foreign></s>
  <s id="g0120203a"><foreign lang="el">w(/st' e)ntau=qa e)/stin e)pible/yasin <lb/>h(=tton qauma/zein ta\s sumbainou/sas u(penantiw/seis <lb/>peri\ au)to/n.</foreign></s></p><p type="main">
  
 <s>Du&shy;<lb/>bitabilia enim &longs;unt, qu&aelig; reuera fiunt: vt magnum pondus addito <lb/>pondere vectis ab exigua potentia, &amp; vna hominis manu moue&shy;<lb/>ri. </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>Fieri tamen ratio repugnat. </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>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.000439">Ill&ugrave;c <expan abbr="itaq;">itaque</expan> in&longs;pi&shy;<lb/>cientibus <expan abbr="c&otilde;traria">contraria</expan> ab ip&longs;o <lb/>prouenire minus erit <expan abbr="mir&utilde;">mirum</expan>. </s></p><p type="head">
  
 <s>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 pagenum="15"/><p type="main"> <s id="id.000440">COMMENTARIVS. </s></p><p type="main">
  
 <s><gap/></s></p><p type="main"> <s id="id.000441">Maxime ver&ograve;.] <emph type="italics"/>Circuli admiranda natura declaratur &egrave; <lb/>quintuplici contrariorum, qu&aelig; in eo pr&aelig;ter contrariorum <emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.055.jpg" pagenum="16"/><emph type="italics"/>legem &longs;imul reperiuntur, repugnantia. </s>
  
 <s><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.000442">Ex his triplex deprehenditur <lb/>in circulo dum fit: duplex vero dum factus e&longs;t. </s>
  
 <s>quod etiam ratio&shy;<lb/>ni valde <expan abbr="c&otilde;&longs;entaneum">con&longs;entaneum</expan> e&longs;t. <lb/></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>Nec enim ab&longs;urdum e&longs;t, <lb/>ex admirabiliori quid ad&shy;<lb/>mirabile contingere.</s></p><p type="head"> <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>COMMENTARIVS.</s></p><p type="main"> <s id="id.000445">H&aelig;c <lb/>&longs;ingula &longs;uis locis delineabuntur &amp; explicabuntur. </s>
  
 <s>Omnium ver&ograve; talium.] <emph type="italics"/>Cau&longs;a qu&aelig; latebat in problemate <lb/>de vecte a&szlig;ignatur hic e&longs;&longs;e circulus: qu&aelig; ad alia multa Me&shy;<lb/>chanica po&longs;tea transferetur. </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>Probatur autem id ex forma circuli mi&shy;<lb/>rabili&szlig;ima. </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="el">pa/ngwnos &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>&longs;ic.<emph.end type="italics"/></s></p><p type="main"> <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">
  
 <s><emph type="italics"/>Ex admirabiliori admirabile aliquid fieri non e&longs;t alienum, cau&longs;&aelig; <lb/>enim &longs;ibi &longs;imiles effectus edunt.<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><emph type="italics"/>Circulus e&longs;t admirabilis, &amp; admirabilior, quam vectis: quamque <lb/>ea qu&aelig; &agrave; vecte fiunt.<emph.end type="italics"/></s></p><p type="main"> <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><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.000452">Ibi enim po&shy;<lb/>&longs;tulatur, vt &egrave; dato centro &amp; interuallo circulum de&longs;cribere conce&shy;<lb/>datur. </s>
  
 <s><gap/></s></p><p type="main"> <s id="id.000453">De&longs;cribitur autem cum data recta finita, manente eius vno <lb/>extremorum, circummoluitur, quou&longs;que redeat ad locum vnde mo&shy;<lb/>ueri c&oelig;pit, id quod, vt &longs;ine errore fiat inuentus e&longs;t circinus &agrave; Talo <lb/>D&aelig;dali ex &longs;orore nepote, cuius forma &amp; officium ab Ouidio accom&shy;<lb/>modate huic loco, &longs;ic e&longs;t expre&longs;&longs;um,<emph.end type="italics"/></s></p><p type="main">
  
 <s>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.000454">Ex vno duo ferrea brachia nodo <lb/>Iunxit, vt &aelig;quali &longs;patio di&longs;tanti&shy;<lb/><figure id="id.035.01.056.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.056.1.jpg"/><lb/>bus ip&longs;is</s></p><p type="main">
  
 <s>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.000455">Altera pars &longs;taret, pars altera du&shy;<lb/>ceret orbem. </s></p><p type="main">
  
 <s>Ill&ugrave;c <expan abbr="itaq;">itaque</expan> in&longs;pi&shy;<lb/>cientibus <expan abbr="c&otilde;traria">contraria</expan> ab ip&longs;o <lb/>prouenire minus erit <expan abbr="mir&utilde;">mirum</expan>.</s></p><p type="head"> <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>COMMENTARIVS.</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"/></s></p></subchap1><subchap1><p type="main">
  
 <s>Maxime ver&ograve;.] <emph type="italics"/>Circuli admiranda natura declaratur &egrave; <lb/>quintuplici contrariorum, qu&aelig; in eo pr&aelig;ter contrariorum<emph.end type="italics"/><pb pagenum="16"/><emph type="italics"/>legem &longs;imul reperiuntur, repugnantia. </s> <s id="id.000458"><foreign lang="el">prw=ton me\n ga\r th=| periexou/sh| grammh=| to\n <lb/>ku/klon pla/tos ou)qe\n e)xou/sh|, ta)nanti/a pws prosemfai/netai, <lb/>to\ koi=lon kai\ to\ kurto/n.</foreign></s>
  
 <s>Ex his triplex deprehenditur <lb/>in circulo dum fit: duplex vero dum factus e&longs;t. </s> <s id="g0120204"><foreign lang="el">tau=ta de\ die/sthken a)llh/lwn, <lb/>o(\n tro/pon to\ me/ga kai\ to\ mikro/n. </foreign></s>
  
 <s>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="g0120205"><foreign lang="el">e)kei/nwn te ga\r <lb/>me/son to\ i)/son kai\ tou/twn to\ eu)qu/. </foreign></s>
  
 <s>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="g0120205a"><foreign lang="el">dio\ metaba/llonta ei)s <lb/>a)/llhla, ta\ me\n a)nagkai=a i)/sa gene/sqai pro/teron h)\ tw=n<lb/> a)/krwn o(poteronou=n, th\n de\ grammh\n eu)qei=an, o(/tan e)k kurth=s <lb/>ei)s koi=lon h)\ pa/lin e)k tau/ths gi/nhtai kurth\ kai\ periferh/s. <lb/></foreign></s>
  
 <s>H&aelig;c <lb/>&longs;ingula &longs;uis locis delineabuntur &amp; explicabuntur. </s> <s id="g0120205b"><foreign lang="el">e(\n kai\ ou)=n tou=to tw=n a)to/pwn u(pa/rxei peri\ to\n ku/klon.</foreign></s></p><p type="main">
  
 <s>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.000459">Primum &longs;iquidem line&aelig; <lb/>ip&longs;um circulum <expan abbr="compre&shy;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>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 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.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>quod 16. prop.  <s>horum enim medium e&longs;t <lb/>&aelig;quale: illorum ver&ograve; re&shy;<lb/>ctum. </s>
  
 lib.  <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>
  
 3. elem. </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>e&longs;t demon&longs;tratum.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000463">COMMENTARIVS. </s></p><p type="main">
  
 <s>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.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="el">prw/ton</foreign> <emph type="italics"/>pro<emph.end type="italics"/> <foreign lang="el">deu/teron. </foreign><emph type="italics"/>Namque h&icirc;c non prima, vt iam patuit: &longs;ed &longs;e&shy;<lb/>cunda e&longs;t in circulo repugnantia. </s>
  
 <s>Circulum autem fieri ex moto &amp; quieto patet his, <lb/>qui eius fabricam repetent &egrave; 3. po&longs;tulato element. </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>Eucl. </s> <s id="id.000469">vbi nota Ari&longs;totelem dixi&longs;&longs;e h&aelig;c<emph.end type="italics"/> <foreign lang="el">e)nanti/a pws</foreign> <emph type="italics"/>contraria quodam&shy;<lb/>modo. </s>
  
 <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.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; alijs &longs;int al&shy;<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>De&longs;cribitur autem cum data recta finita, manente eius vno <lb/>extremorum, circummoluitur, quou&longs;que redeat ad locum vnde mo&shy;<lb/>ueri c&oelig;pit, id quod, vt &longs;ine errore fiat inuentus e&longs;t circinus &agrave; Talo <lb/>D&aelig;dali ex &longs;orore nepote, cuius forma &amp; officium ab Ouidio accom&shy;<lb/>modate huic loco, &longs;ic e&longs;t expre&longs;&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. 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>Ex vno duo ferrea brachia nodo <lb/>Iunxit, vt &aelig;quali &longs;patio di&longs;tanti&shy;<lb/><figure id="fig1"></figure><lb/>busip&longs;is</s></p><p type="main"> <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>Altera pars &longs;taret, pars altera du&shy;<lb/>ceret orbem.</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><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.000474">Quemadmodum magnum &amp; paruum con&shy;<lb/>traria &longs;unt, quia di&longs;tant, inter &longs;e per medium, quod e&longs;t &aelig;quale, &amp; <lb/>cum commutantur in inuicem nece&longs;&longs;e e&longs;t prius &aelig;quale fieri: &longs;ic con&shy;<lb/>uexum &amp; concauum contraria erunt, quia di&longs;tant inter &longs;e per me&shy;<lb/>dium, quod e&longs;t rectum, &amp; cum commutantur in inuicem prius re&shy;<lb/>ctum etiam fieri nece&longs;&longs;um e&longs;t. </s>
  
 <s>Idque beneficio puncti B cum tota <lb/>linea A B moti, atque puncti A quieti, vt hic vult Ari&longs;toteles.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000475">&longs;unt igitur conuexum &amp; concauum <lb/>contraria. </s>
  
 <s><gap/></s></p><p type="main"> <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>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 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>H&aelig;c autem ita inter&longs;e di&shy;<lb/>&longs;tant, vt <expan abbr="magn&utilde;">magnum</expan> &amp; paruum. <pb pagenum="18"/><gap/><lb/>horum enim medium e&longs;t <lb/>&aelig;quale: illorum ver&ograve; re&shy;<lb/>ctum. </s> <s id="id.000479">Quia non habent <lb/>omnes pr&aelig;dict&aelig; definitionis particulas &longs;ibi conuenientes. </s>
  
 <s>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.000480">H&aelig;c <lb/>enim cum &longs;int in Relatis, vnum idemque non ex &longs;e dicitur magnum <lb/>aut paruum: &longs;ed re&longs;pectu alicuius, vt canis re&longs;pectu elephantis paruus <lb/>e&longs;t, at idem re&longs;pectu mu&longs;c&aelig; magnus e&longs;t. </s>
  
 <s>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.000481">C&oelig;terum hic notandum e&longs;t <lb/>re&longs;pectum i&longs;tum licet fieri po&szlig;it ad quodlibet obuium, cum tamen <lb/>h&aelig;c vocabula, magnum, paruum, &longs;impliciter dicuntur, fieri ad &longs;ym&shy;<lb/>metrum &longs;ui cuiu&longs;que generis. </s>
  
 <s>COMMENTARIVS.</s></p><p type="main"> <s id="id.000482">Symmetrum appello, quod iu&longs;tam ma&shy;<lb/>gnitudinem in &longs;uo genere adeptum e&longs;t. </s>
  
 <s>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.000483">Et hoc e&longs;t quod hic dicitur <lb/>&aelig;quale, medium &longs;cilicet inter <expan abbr="magn&utilde;">magnum</expan> tanquam excedens, &amp; paruum <lb/>tanquam deficiens, neutrobique igitur iu&longs;tum. </s>
  
 <s>Eaque ex eo quod cum circuli peri&shy;<lb/>pheria &longs;ir vna linea def. </s> <s id="id.000484">Vt e&longs;to, quod aiunt <lb/>multi, iu&longs;ta hominis magnitudo &longs;ex pedum. </s>
  
 <s>15. lib.  <s id="id.000485">Qui igitur inter homi&shy;<lb/>nes &longs;eptempedalis e&longs;t, magnus: qui quintumpedalis, paruus &longs;implici&shy;<lb/>ter dicetur. </s>
  
 1. elem. </s> <s id="id.000486">Hinc intellige, vt id obiter annotem, quod apud Ari&longs;to&shy;<lb/>telem memini me legi&longs;&longs;e, nullam paruam mulierem pulchram e&longs;&longs;e, <lb/>quia, quod prima pars e&longs;t pulchritudinis non habet, &longs;ymmetrum &longs;ui <lb/>generis. <emph.end type="italics"/></s></p><p type="main">
  
 <s>&amp; idcirco latitudinis expers <lb/>def. </s> <s id="id.000487">Atque vnum hoc e&longs;t.] <foreign lang="el">to\ a)/topon. </foreign><emph type="italics"/>Hic vt &amp; alibi &longs;&aelig;pius <lb/>pro<emph.end type="italics"/> <foreign lang="el">qauma/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></subchap1><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.059.jpg" pagenum="20"/><subchap1><p type="main">
  
 <s>2. lib. </s> <s id="id.000488"><foreign lang="el">deu/teron de\ o(/ti a(/ma kinei=tai ta\s e)nanti/as kinh/seis: <lb/>a(/ma ga\r ei)s to\n e)/mprosqen kinei=tai to/pon kai\ to\n o)/pisqen: <lb/>h(/ te gra/fousa grammh\ to\n ku/klon w(sau/tws e)/xei. </foreign></s>
  <s id="g0120302a"><foreign lang="el">e)c <lb/>ou(= ga\r a)/rxetai to/pou to\ pe/ras au)th=s, ei)s to\n au)to\n tou=ton to/pon <lb/>e)/rxetai pa/lin: sunexw=s ga\r kinoume/nhs au)th=s to\ e)/sxaton <lb/>pa/lin a)ph=lqe prw=ton, w(/ste kai\ fanero\n o(/ti mete/balen <lb/>e)nteu=qen.</foreign></s>
  <s id="g0120303"><foreign lang="el">dio/, kaqa/per ei)/rhtai pro/teron, ou)de\n a)/topon, to\ <lb/>pa/ntwn ei)=nai tw=n qauma/twn au)to\n a)rxh/n.</foreign></s>
  <s id="g0120401"><foreign lang="el">ta\ me\n ou)=n peri\ <lb/>to\n zugo\n gino/mena, ei)s to\n ku/klon a)na/getai, ta\ de\ peri\ <lb/>to\n moxlo\n ei)s to\n zugo/n. </foreign></s>
  <s id="g0120401a"><foreign lang="el">ta\ d' a)/lla pa/nta sxedo\n ta\ <lb/>peri\ ta\s kinh/seis ta\s mhxanika\s, ei)s to\n moxlo/n.</foreign></s></p><p type="main">
  
 <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.000489">Secundum e&longs;t, quod con&shy;<lb/>trariis motionibus &longs;imul <lb/>moueatur. </s>
  
 <s>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.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>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="fig2"></figure><lb/><emph type="italics"/>tiores, vel depre&szlig;iores. </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>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.000492">Ita&shy;<lb/>que manife&longs;tum, quod in&shy;<lb/>de <expan abbr="mutat&utilde;">mutatum</expan> e&longs;t. </s>
  
 <s>2. lib.  <s id="id.000493">Propterea, <lb/>vt e&longs;t prius dictum, non e&longs;t <lb/>ab&longs;urdum ip&longs;um admira&shy;<lb/>bilium omnium e&longs;&longs;e prin&shy;<lb/>cipium. </s>
  
 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 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.000494">Igitur &amp; qu&ecedil; circa <lb/>libram eueniunt ad circu&shy;<lb/>lum referuntur, &amp; qu&ecedil; cir&shy;<lb/>ca vectem ad libram, &amp; <lb/>forta&longs;&longs;is alia omnia, qu&aelig; <lb/>circa motiones mechani&shy;<lb/>cas, ad vectem. </s></p><p type="head">
  
 <s>H&aelig;c autem ita.] <emph type="italics"/>Similitudine comprobatur conuexum &amp; <lb/>concauum contraria e&longs;&longs;e. </s> <s id="id.000495">COMMENTARIVS. </s></p><p type="main">
  
 <s>Quemadmodum magnum &amp; paruum con&shy;<lb/>traria &longs;unt, quia di&longs;tant, inter &longs;e per medium, quod e&longs;t &aelig;quale, &amp; <lb/>cum commutantur in inuicem nece&longs;&longs;e e&longs;t prius &aelig;quale fieri: &longs;ic con&shy;<lb/>uexum &amp; concauum contraria erunt, quia di&longs;tant inter &longs;e per me&shy;<lb/>dium, quod e&longs;t rectum, &amp; cum commutantur in inuicem prius re&shy;<lb/>ctum etiam fierinece&longs;&longs;um e&longs;t. </s> <s id="id.000496">Secundum.] <emph type="italics"/>Pro<emph.end type="italics"/> <foreign lang="el">deu/teron</foreign> <emph type="italics"/>legamus &longs;i placet<emph.end type="italics"/> <foreign lang="el">trh/ton. </foreign><emph type="italics"/>Hic enim <lb/>tertia e&longs;t repugnantia in circulo ex contrarijs motionibus, quas <lb/>&longs;imul habet, ant&egrave; &longs;cilicet cum pars eius vna mouetur: oppo&longs;ita in <lb/>ip&longs;omet tempore pon&egrave; mouetur. </s>
  
 <s>&longs;unt igitur conuexum &amp; concauum <lb/>contraria. </s> <s id="id.000497">Hoc autem e&longs;t contrarias motiones <lb/>&longs;imul habere. </s>
  
 <s>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. </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>Quanti&shy;<lb/>tatis, magnum &amp; paruum apparenter duntaxat e&longs;&longs;e contraria. </s> <s id="id.000500">Atque linea circulum.] <emph type="italics"/>Cur circulus ant&egrave; &amp; pon&egrave; mouea&shy;<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>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.000501">Sic &longs;yllo&shy;<lb/>gi&longs;mus in&longs;titui pote&longs;t. </s>
  
 <s>Quia non habent <lb/>omnes pr&aelig;dict&aelig; definitionis particulas &longs;ibi conuenientes. </s> <s id="id.000502">Vt fit circulus ita mouetur. <emph.end type="italics"/></s></p><p type="main">
  
 <s>H&aelig;c <lb/>enim cum &longs;int in Relatis, vnum idemque non ex&longs;e dicitur magnum <lb/>aut paruum: &longs;ed re&longs;pectu alicuius, vt canis re&longs;pectu elephantis paruus <lb/>e&longs;t, at idem re&longs;pectu mu&longs;c&aelig; magnus e&longs;t. </s> <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>C&oelig;terum hic notandum e&longs;t <lb/>re&longs;pectum i&longs;tum licet fieri po&szlig;it ad quodlibet obuium, cum tamen <lb/>h&aelig;c vocabula, magnum, paruum, &longs;impliciter dicuntur, fieri ad &longs;ym&shy;<lb/>metrum &longs;ui cuiu&longs;que generis. </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>
  
 <s>Symmetrum appello, quod iu&longs;tam ma&shy;<lb/>gnitudinem in &longs;uo genere adeptum e&longs;t. </s> <s id="id.000505">Quia igitur in his &longs;unt ant&egrave; &amp; pon&egrave;, <lb/>mouebitur ant&egrave; &amp; pon&egrave;: quia in&longs;uper &longs;unt &longs;ur&longs;um &amp; deor&longs;um, <lb/>mouebitur etiam &longs;imul &longs;ur&longs;um &amp; deor&longs;um. <emph.end type="italics"/></s></p><p type="main">
  
 <s>Et hoc e&longs;t quod hic dicitur <lb/>&aelig;quale, medium &longs;cilicet inter <expan abbr="magn&utilde;">magnum</expan> tanquam excedens, &amp; paruum <lb/>tanquam deficiens, neutrobique igitur iu&longs;tum. </s> <s id="id.000506"><emph type="italics"/>Centrum enim in plano circundatur quatuor loci differentijs, <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. </s>
  
 <s>Vt e&longs;to, quod aiunt <lb/>multi, iu&longs;ta hominis magnitudo &longs;ex pedum. </s> <s>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>Qui igitur inter homi&shy;<lb/>nes &longs;eptempedalis e&longs;t, magnus: qui quintumpedalis, paruus &longs;implici&shy;<lb/>ter dicetur. </s> <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>Hinc intellige, vt id obiter annotem, quod apud Ari&longs;to&shy;<lb/>telem memini me legi&longs;&longs;e, nullam paruam mulierem pulchram e&longs;&longs;e, <lb/>quia, quod prima pars e&longs;t pulchritudinis non habet, &longs;ymmetrum &longs;ui <lb/>generis.<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>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 pagenum="20"/><p type="main"> <s id="id.000509">Nam cum B, mouetur &longs;ur&longs;um ver&shy;<lb/>&longs;us C, idem B, eodem tempore non fertur deor&longs;um ver&longs;us E, &longs;ed <lb/>tunc quidem D, altera pars in circulo oppo&longs;ita ip&longs;i B, fertur ver&shy;<lb/>&longs;us E: vt autem ver&egrave; e&longs;&longs;ent motiones contrari&aelig; deberent fieri &longs;e&shy;<lb/>cundum ea&longs;dem partes. </s>
  
 <s><gap/></s></p><p type="main"> <s id="id.000510">E&longs;t h&aelig;c igitur vt ali&aelig; in circulo non vera <lb/>&longs;ed apparens repugnantia. </s>
  
 <s>Secundum e&longs;t, quod con&shy;<lb/>trariis motionibus &longs;imul <lb/>moueatur. </s> <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 alte&shy;<lb/>rum extremum D, attolli: &amp; contra. <emph.end type="italics"/></s></p><p type="main">
  
 <s>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.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 abbr="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&shy;<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></subchap1><subchap1><p type="main">
  
 <s>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.000513"><foreign lang="el">e)/ti de\ <lb/>dia\ to\ mia=s ou)/shs th=s e)k tou= ke/ntrou grammh=s mhqe\n e(/teron <lb/>e(te/rw| fe/resqai tw=n shmei/wn tw=n e)n au)th=| i)sotaxw=s, a)ll' a)ei\ <lb/>to\ tou= me/nontos pe/ratos porrw/teron o)\n qa=tton, polla\ tw=n qaumazome/nwn <lb/>sumbai/nei peri\ ta\s kinh/seis tw=n ku/klwn, peri\ <lb/>w(=n e)n toi=s e(pome/nois problh/masin e)/stai dh=lon.</foreign></s></p><p type="main">
  
 <s>Ita&shy;<lb/>que manife&longs;tum, quod in&shy;<lb/>de <expan abbr="mutat&utilde;">mutatum</expan> e&longs;t. </s> <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&shy;qu&etilde;tibus">&longs;e&shy;<lb/>quentibus</expan> problematis fiet <lb/>manife&longs;tum. </s></p><p type="head">
  
 <s>Propterea, <lb/>vt e&longs;t prius dictum, non e&longs;t <lb/>ab&longs;urdum ip&longs;um admira&shy;<lb/>bilium omnium e&longs;&longs;e prin&shy;<lb/>cipium. </s> <s id="id.000515">COMMENTARIVS. </s></p><p type="main">
  
 <s>Igitur &amp; qu&ecedil; circa <lb/>libram eueniunt ad circu&shy;<lb/>lum referuntur, &amp; qu&ecedil; cir&shy;<lb/>ca vectem ad libram, &amp; <lb/>forta&longs;&longs;is alia omnia, qu&aelig; <lb/>circa motiones mechani&shy;<lb/>cas, ad vectem.</s></p><p type="head"> <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>COMMENTARIVS.</s></p><p type="main"> <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>Secundum.] <emph type="italics"/>Pro<emph.end type="italics"/> <foreign lang="greek">d<gap/>/u<gap/>eron</foreign> <emph type="italics"/>legamus &longs;i placet<emph.end type="italics"/> <foreign lang="greek">trh/ton.</foreign> <emph type="italics"/>Hic enim <lb/>tertia e&longs;t repugnantia in circulo ex contrar&yuml;s motionibus, quas <lb/>&longs;imul habet, ant&egrave; &longs;cilicet cum pars eius vna mouetur: oppo&longs;ita in <lb/>ip&longs;omet tempore pon&egrave; mouetur. </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>Hoc autem e&longs;t contrarias motiones <lb/>&longs;imul habere. </s> <s id="id.000519">Linea enim circulum <lb/>de&longs;cribens, quo tempore punctis centro propinquis redijt ad locum, <lb/>vnde ij&longs;dem moueri c&oelig;perat, eodem remotis redit. </s>
  
 <s>Contrari&aelig; enim &longs;unt motiones apud Ari&longs;totelem in <lb/>categoria vbi &amp; li. </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>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.000521">Peripheriam autem remotioris pun&shy;<lb/>cti &agrave; centro, id e&longs;t &longs;emidiametri maioris e&longs;&longs;e maiorem peripheria pun&shy;<lb/>cti centro propinquioris, id e&longs;t &longs;emidiametri minoris, &longs;ic demon&longs;tra&shy;<lb/>bimus. <emph.end type="italics"/></s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.062.jpg" pagenum="23"/><p type="main">
  
 <s>Atque linea circulum.] <emph type="italics"/>Cur circulus ant&egrave; &amp; pon&egrave; mouea-<emph.end type="italics"/><pb pagenum="21"/><emph type="italics"/>tur, ratio adducitur &longs;umpta ab efficiente circuli cau&longs;a. </s> <s id="id.000522"><emph type="italics"/>E&longs;to A B C, peripheria &longs;emidiametri maioris A E: item <lb/>D F G, peripheria &longs;emidiametri D H minoris. </s>
  
 <s>Sic &longs;yllo&shy;<lb/>gi&longs;mus in&longs;titui pote&longs;t. </s> <s id="id.000523">Dico periphe&shy;<lb/>riam A B C maiorem peripheria D F G. </s>
  
 <s>Vt fit circulus ita mouetur.<emph.end type="italics"/></s></p><p type="main"> <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><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.000525">Quia igi&shy;<lb/>tur vt diameter <lb/>A C ad <expan abbr="&longs;u&atilde;">&longs;uam</expan> <expan abbr="pe&shy;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>
  
 <s><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.000529">E&longs;t <lb/>autem A E maior: quam D H ex hypothe&longs;i. </s>
  
 <s>Quia igitur in his &longs;unt ant&egrave; &amp; pon&egrave;, <lb/>mouebitur ant&egrave; &amp; pon&egrave;: quia in&longs;uper &longs;unt &longs;ur&longs;um &amp; deor&longs;um, <lb/>mouebitur etiam &longs;imul &longs;ur&longs;um &amp; deor&longs;um.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000530">Erit igitur peri&shy;<lb/>pheria A B C maior: quam peripheria D F G. </s>
  
 <s><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="fig3"></figure><lb/><emph type="italics"/>fieri primum. </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></subchap1><subchap1><p type="main">
  
 <s>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.000532"><foreign lang="el">dia\ de\ to\ <lb/>ta\s e)nanti/as kinh/seis a(/ma kinei=sqai to\n ku/klon, kai\ to\ <lb/>me\n e(/teron th=s diame/trou tw=n a)/krwn, e)f' ou(= to\ a, ei)s tou)/mprosqen <lb/>kinei=sqai, qa/teron de/, e)f' ou(= to\ *b ei)s tou)/pisqen <lb/>kataskeua/zousi/ tines, w(/st' a)po\ mia=s kinh/sews pollou\s u(penanti/ous <lb/>a(/ma kinei=sqai ku/klous, w(/sper ou(\s a)natiqe/asin e)n <lb/>toi=s i(eroi=s; poih/santes troxi/skous xalkou=s te kai\ sidhrou=s.</foreign></s>
  <s id="g0120502"><foreign lang="el"><lb/>ei) ga\r ei)/h tou= *a*b ku/klou a(pto/menos e(/teros ku/klos e)f' ou(= <lb/>*g*d, tou= ku/klou, e)f' ou(= *a*b, kinoume/nhs th=s diame/trou <lb/>ei)s tou)/mprosqen, kinhqh/setai h( *g*d ei)s tou)/pisqen tou= ku/klou <lb/>tou= e)f' w(=| *a, kinoume/nhs th=s diame/trou peri\ to\ au)to/.</foreign></s>
  <s id="g0120503"><foreign lang="el">ei)s <lb/>tou)nanti/on a)/ra kinhqh/setai o( e)f' ou(= *g*d ku/klos, tw=| e)f' <lb/>ou(= to\ *a*b: kai\ pa/lin au)to\s to\n e)fech=s, e)f' ou(= *e*z, ei)s <lb/>tou)nanti/on au(tw=| kinh/sei dia\ th\n au)th\n tau/thn ai)ti/an.</foreign></s>
  <s id="g0120601"><foreign lang="el">to\n au)to\n de\ <lb/>tro/pon ka)\n plei/ous w)=si, tou=to poih/sousin e(no\s mo/nou kinhqe/ntos.</foreign></s>
  <s id="g0120602"><foreign lang="el"><lb/>tau/thn ou)=n labo/ntes u(pa/rxousan e)n tw=| ku/klw| th\n <lb/>fu/sin oi( dhmiourgoi\ kataskeua/zousin o)/rganon kru/ptontes <lb/>th\n a)rxh/n, o(/pws h)=| tou= mhxanh/matos fanero\n mo/non to\ <lb/>qaumasto/n, to\ d' ai)/tion a)/dhlon. <lb/></foreign></s></p><p type="main">
  
 <s><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.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&shy;<pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.063.jpg" pagenum="24"/>los &aelig;reos &amp; ferreos. </s>
  
 <s>Nam cum B, mouetur &longs;ur&longs;um ver&shy;<lb/>&longs;us C, idem B, eodem tempore non fertur deor&longs;um ver&longs;us E, &longs;ed <lb/>tunc quidem D, altera pars in circulo oppo&longs;ita ip&longs;i B, fertur ver&shy;<lb/>&longs;us E: vt autem ver&egrave; e&longs;&longs;ent motiones contrari&aelig; deberent fieri &longs;e&shy;<lb/>cundum ea&longs;dem partes. </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>E&longs;t h&aelig;c igitur vt ali&aelig; in circulo non vera <lb/>&longs;ed apparens repugnantia. </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>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.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>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 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.000537">COMMENTARIVS. </s></p><p type="main">
  
 <s><gap/></s></p><p type="main"> <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>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.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;&shy;dum">&longs;ecun&shy;<lb/>dum</expan> <expan abbr="in&shy;ferior&etilde;">in&shy;<lb/>feriorem</expan> <lb/><expan abbr="periphe&shy;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>COMMENTARIVS.</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>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.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>
  
 <s>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.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>
  
 <s>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.000545">Herodotus hi&longs;toria &longs;ecunda videtur ex his aliqua<emph.end type="italics"/> <foreign lang="el">neu&shy;<lb/>ro/spasta</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>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.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>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.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="el">au)to/mata</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>Peripheriam autem remotioris pun&shy;<lb/>cti &agrave; centro, id e&longs;t &longs;emidiametri maioris e&longs;&longs;e maiorem peripheria pun&shy;<lb/>cti centro propinquioris, id e&longs;t &longs;emidiametri minoris, &longs;ic demon&longs;tra&shy;<lb/>bimus.<emph.end type="italics"/></s></p><pb pagenum="23"/><p type="main"> <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><emph type="italics"/>E&longs;to A B C, peripheria &longs;emidiametri maioris A E: item <lb/>D F G, peripheria &longs;emidiametri D H minoris. </s> <s id="id.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>Dico periphe&shy;<lb/>riam A B C maiorem peripheria D F G. </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>Producatur enim A E <lb/>recta vt &longs;it A C <lb/>diameter po&longs;tul.<emph.end type="italics"/><lb/><figure id="fig4"></figure><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.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>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.000552"><margin.target id="marg12"/>In Menone</s></p></subchap1></chap><chap><subchap1><p type="main">
  
 3. lib.  <s id="id.000553">2. <foreign lang="el">*amfi\ zugou= dia\ ti/ e)n tw|= <lb/>ku/klw| h( mei/zwn grammh\ <lb/>qa=tton fe/retai th=s e)lattonos, <lb/>kai\ e)nteu=qen dia\ ti/ ta\ mei/&shy;<lb/>zw zuga\ a)kribetera/ e)sti tw=n <lb/>e)latto/nwn. </foreign></s></p><p type="main">
  
 de dimen&longs;. </s> <s id="id.000554">2. De libra propter quid <lb/>maior linea in circulo <lb/>celerius fertur, minore. <lb/></s>
  
 <s>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.000555">Ex quo fit vt libr&aelig; ma&shy;<lb/>iores minoribus &longs;int <lb/>exactiores. </s></p><p type="main">
  
 <s>16. lib.  <s><foreign lang="el">*prw=ton me\n ou)=n ta\ sumbai/nonta peri\ to\n zugo\n a)porei=tai, <lb/>dia\ ti/na ai)ti/an a)kribe/stera/ e)sti ta\ zuga\ ta\ mei/zw <lb/>tw=n e)latto/nwn.</foreign></s>
  <s id="g0120702"><foreign lang="el">tou/tou de\ a)rxh/, dia\ ti/ pote e)n tw=| ku/klw| <lb/>h( plei=on a)festhkui=a grammh\ tou= ke/ntrou th=s e)ggu\s, th=| <lb/>au)th=| i)sxu/i kinoume/nh qa=tton fe/retai th=s e)la/ttonos, to\ <lb/>ga\r qa=tton le/getai dixw=s.</foreign></s>
  <s id="g0120704"><foreign lang="el">a)/n te ga\r e)n e)la/ttoni xro/nw| <lb/>i)/son to/pon diece/lqh|, qa=tton ei)=nai le/gomen, kai\ e)a\n e)n i)/sw|, <lb/>plei/w.</foreign></s>
  <s id="g0120705"><foreign lang="el">h( de\ mei/zwn e)n i)/sw| xro/nw| gra/fei mei/zona ku/klon: <lb/>o( ga\r e)kto\s mei/zwn tou= e)nto/s.</foreign></s></p><p type="main">
  
 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.  <s id="id.000557"><expan abbr="Prim&utilde;">Primum</expan> igitur qu&ecedil; circa <expan abbr="li&shy;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>
  
 15. lib.  <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"/>libr&aelig; maiores minoribus <lb/>&longs;int exactiores. </s>
  
 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.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>11. lib. </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>eiu&longs;dem. </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>E&longs;t <lb/>autem A E maior: quam D H ex hypothe&longs;i. </s> <s id="id.000562">Qui enim extra e&longs;t, maior <lb/>e&longs;t eo, qui intus. </s></p><p type="head">
  
 <s>Erit igitur peri&shy;<lb/>pheria A B C maior: quam peripheria D F G. </s> <s id="id.000563">COMMENTARIVS. </s></p><p type="main">
  
 <s>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.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><gap/></s></p><p type="main"> <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>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 pagenum="24"/><gap/><lb/>los &aelig;reos &amp; ferreos. </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>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.000567">Et primum quod re&shy;<lb/>cta de&longs;cribens circulum (vno nomine relicta periphra&longs;i radium h&icirc;c <lb/>appellabimus) duabus lationibus feratur, ii&longs;que in nulla ratione &amp; <lb/>nullo tempore. </s>
  
 <s>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.000568">Et ex his alteram e&longs;&longs;e &longs;ecundum naturam, alteram <lb/>pr&aelig;ter naturam. </s>
  
 <s>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.000569">Po&longs;trem&ograve; quod latio &longs;ecundum naturam in maiore <lb/>circulo maior &longs;it: quam in minore. </s>
  
 <s>COMMENTARIVS.</s></p><p type="main"> <s id="id.000570">Latio autem pr&aelig;ter naturam in <lb/>minore circulo maior &longs;it: quam in maiore. <emph.end type="italics"/></s></p><p type="main">
  
 <s>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.000571">Primum igitur.] <emph type="italics"/>Proponitur problema de librarum in&aelig;qua&shy;<lb/>lium exactiore iudicio, quod pendet &agrave; minorum ponderum deprehen&shy;<lb/>&longs;ione, vt ea &longs;it exactior per quam minora pondera expendi po&longs;&longs;unt. <emph.end type="italics"/></s></p><p type="main">
  
 <s>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 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="fig5"></figure><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.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>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.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">
  
 <s>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.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>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.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>cap.  <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>
  
 6. lib.  <s id="id.000580">Illi quorum &longs;emidiametri &longs;unt <lb/>in&aelig;quales, erunt &amp; in&aelig;quales, &amp; ille maior, cuius &longs;emidiameter <lb/>maior. </s>
  
 de <lb/>f&oelig;t. </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. 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>
  
 <s>format. </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 ijs &agrave; quibus ambiuntur. <lb/></s>
  
 <s>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.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></subchap1><subchap1><p type="main">
  
 <s>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"></arrow.to.target><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.000585"><foreign lang="el"> ai)/tion de\ tou/twn, o(/ti fe/retai <lb/>du/o fora\s h( gra/fousa to\n ku/klon.</foreign></s>
  <s id="g0120707"><foreign lang="el">o(/tan me\n ou)=n e)n lo/gw| <lb/>tini\ fe/rhtai, e)p' eu)qei/as a)na/gkh fe/resqai to\ fero/menon, <lb/>kai\ gi/netai dia/metros au)th\ tou= sxh/matos o(\ poiou=sin ai( <lb/>e)n tou/tw| tw=| lo/gw| sunteqei=sai grammai/.</foreign></s>
  <s id="g0120708"><foreign lang="el">e)/stw ga\r o( lo/gos <lb/>o(\n fe/retai to\ fero/menon, o(\n e)/xei h( *a*b, pro\s th\n *a*g, <lb/>kai\ to\ me\n *a*g fere/sqw pro\s to\ *b, h( de\ *a*b u(pofere/sqw <lb/>pro\s th\n *h*g: e)nhne/xqw de\ to\ me\n *a pro\s to\ *d, h( de\ e)f' <lb/>h(=| *a*b pro\s to\ *e. </foreign></s>
  
 <s>Erant enim pr&aelig;clara opera.<emph.end type="italics"/><pb 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="g0120708a"><foreign lang="el">ou)kou=n e)pi\ th=s fora=s o( lo/gos h)=n, o(\n h( <lb/>*a*b e)/xei pro\s th\n *a*g, a)na/gkh kai\ th\n *a*d, pro\s th\n <lb/>*a*e, tou=ton e)/xein to\n lo/gon, o(/moion a)/ra e)sti\ tw=| lo/gw| to\ <lb/>mikro\n tetra/pleuron tw=| mei/zoni, w(/ste kai\ h( au)th\ dia/metros <lb/>au)tw=n, kai\ to\ *a e)/stai pro\s to\ *z.</foreign></s>
  <s id="g0120801"><foreign lang="el">to\n au)to\n dh\ tro/pon <lb/>deixqh/setai ka)\n o(pouou=n dialhfqh=| h( fora/: ai)ei\ ga\r <lb/>e)/stai e)pi\ th=s diame/trou.</foreign></s>
  <s id="g0120802"><foreign lang="el">fanero\n ou)=n o(/ti to\ kata\ th\n dia/metron <lb/>fero/menon e)n du/o forai=s, a)na/gkh to\n tw=n pleurw=n <lb/>fe/resqai lo/gon.</foreign></s></p><p type="main">
  
 <s>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.000586">Horum vero cau&longs;a e&longs;t, <lb/>quod recta de&longs;cribens <expan abbr="cir&shy;cul&utilde;">cir&shy;<lb/>culum</expan> <expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> duas latio&shy;<lb/>nes fertur. </s>
  
 <s>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.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;&shy;&longs;titut&aelig;">con&shy;<lb/>&longs;titut&aelig;</expan>, <expan abbr="c&otilde;prehendunt">comprehendunt</expan>. </s>
  
 <s>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.000588">Sit <lb/>enim ratio <expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> quam <lb/>mobile fertur ea: quam ha&shy;<pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.068.jpg" pagenum="29"/>bet <foreign lang="el">a b</foreign> ad <foreign lang="el">a g,</foreign> &amp; quidem <lb/><foreign lang="el">a</foreign> feratur ad <foreign lang="el">b,</foreign> &amp; <foreign lang="el">a b</foreign><lb/>etiam feratur ad <foreign lang="el">h g</foreign>: la&shy;<lb/>tum vero &longs;it <foreign lang="el">a</foreign> ad <foreign lang="el">d,</foreign> &amp; <lb/><foreign lang="el">a b</foreign> ad <foreign lang="el">e. </foreign>Igitur cum latio&shy;<lb/>nis ratio erat ea quam ha&shy;<lb/>bet <foreign lang="el">a b</foreign> ad <foreign lang="el">a g</foreign>: nece&longs;&longs;e <lb/>e&longs;t &amp; ip&longs;am <foreign lang="el">a d</foreign> ad <foreign lang="el">a e</foreign> ean&shy;<lb/>dem habere rationem. </s>
  
 <s>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.000589">Si&shy;<lb/>mile e&longs;t enim ratione par&shy;<lb/>uum quadrilaterum maio&shy;<lb/>ri. </s>
  
 <s><margin.target id="marg12"></margin.target>In Menone</s></p><p type="main"> <s id="id.000590">Itaque &amp; eadem diame&shy;<lb/>ter vtriu&longs;que, &amp; ip&longs;um <foreign lang="el">a</foreign><lb/>erat vbi <foreign lang="el">z. </foreign></s>
  
 <s><gap/></s></p><p type="main"> <s>Eodem modo <lb/>demon&longs;trabitur <expan abbr="vbic&utilde;que">vbicunque</expan> <lb/>latio deprehen&longs;a fuerit. </s>
  
 <s>2. De libra propter quid <lb/>maior linea in circulo <lb/>celerius fertur, minore. <lb/></s> <s id="id.000591"><expan abbr="S&etilde;&shy;per">Sem&shy;<lb/>per</expan> enim &longs;upra diametrum <lb/>erit. </s>
  
 <s>Ex quo fit vt libr&aelig; ma&shy;<lb/>iores minoribus &longs;int <lb/>exactiores.</s></p><p type="main"> <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><gap/></s></p><p type="main"> <s id="id.000593">COMMENTARIVS. </s></p><p type="main">
  
 <s><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.000594">Horum vero cau&longs;a.] <emph type="italics"/>In&aelig;qualium <expan abbr="circulor&utilde;">circulorum</expan> ab in&aelig;qualibus <lb/>radiis <expan abbr="de&longs;criptor&utilde;">de&longs;criptorum</expan>, &amp; maioris quidem &agrave; maiori multo ab&longs;tru&shy;<lb/>&longs;ior a&szlig;ignatur cau&longs;a ex radij de&longs;cribentis circulum duabus lationi&shy;<lb/>bus, qu&aelig; inter &longs;e <expan abbr="null&atilde;">nullam</expan> <expan abbr="ration&etilde;">rationem</expan> &longs;eruant. </s>
  
 <s>Ob quam cau&longs;am <pb pagenum="27"/><gap/><lb/>libr&aelig; maiores minoribus <lb/>&longs;int exactiores. </s> <s id="id.000595">Atque hinc elicitur quinta in <lb/>circulo repugnantia, ex qua admiratio eius maior: quam ante e&longs;&longs;e <lb/>concluditur. </s>
  
 <s>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.000596">E lationibus enim illis vna e&longs;t &longs;ecundum naturam, <lb/>altera pr&aelig;ter naturam. </s>
  
 <s>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.000597">Et vtri&longs;que vnum idemque ferri in nullo <lb/>tempore, id e&longs;t in in&longs;tanti indiui&longs;ibili, quomodo non e&longs;&longs;et valde ad&shy;<lb/>mirabile? </s>
  
 <s>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.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>Qui enim extra e&longs;t, maior <lb/>e&longs;t eo, qui intus.</s></p><p type="head"> <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>COMMENTARIVS.</s></p><p type="main"> <s id="id.000600">Syllog. &longs;ic e&longs;t. </s>
  
 <s>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.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>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.000602">Radius de&longs;cribens circulum duabus &longs;uis lationibus, non <lb/>fertur &longs;ecundum rectam. </s>
  
 <s>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.000603">Radij igitur lationes in nulla &longs;unt ra&shy;<lb/>tione. </s>
  
 <s>Et primum quod re&shy;<lb/>cta de&longs;cribens circulum (vno nomine relicta periphra&longs;i radium h&icirc;c <lb/>appellabimus) duabus lationibus feratur, ii&longs;que in nulla ratione &amp; <lb/>nullo tempore. </s> <s id="id.000604">Propo&longs;itio confirmatur cum &longs;equenti diagrammate. <lb/></s>
  
 <s>Et ex his alteram e&longs;&longs;e &longs;ecundum naturam, alteram <lb/>pr&aelig;ter naturam. </s> <s id="id.000605">E&longs;to rectangulum<emph.end type="italics"/> <foreign lang="el">a b h g</foreign> <emph type="italics"/>com&shy;<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="el">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="el">a</foreign> <emph type="italics"/>habent. <lb/></s>
  
 <s>Po&longs;trem&ograve; quod latio &longs;ecundum naturam in maiore <lb/>circulo maior &longs;it: quam in minore. </s> <s id="id.000606">Et intelligatur a latum ver&longs;us<emph.end type="italics"/><lb/><foreign lang="el">b</foreign> <emph type="italics"/>perueni&longs;&longs;e ad<emph.end type="italics"/> <foreign lang="el">d,</foreign> <emph type="italics"/>&amp; ver&longs;us<emph.end type="italics"/><lb/><foreign lang="el">g</foreign> <emph type="italics"/>perueni&longs;&longs;e ad<emph.end type="italics"/> <foreign lang="el">e</foreign>: <emph type="italics"/>&longs;icque cum <lb/>lationum ip&longs;ius<emph.end type="italics"/> <foreign lang="el">a</foreign> <emph type="italics"/>ratio &longs;it vt<emph.end type="italics"/><lb/><foreign lang="el">a b</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="el">a g,</foreign> <emph type="italics"/>ergo erit &amp;<emph.end type="italics"/> <foreign lang="el">a d</foreign><lb/><emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="el">a e</foreign>: <emph type="italics"/>vt<emph.end type="italics"/> <foreign lang="el">a b</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="el">a y,</foreign> <emph type="italics"/>&amp; rectrangulum minus<emph.end type="italics"/> <foreign lang="el">a d z e</foreign> <emph type="italics"/>com&shy;<lb/>munem angulum<emph.end type="italics"/> <foreign lang="el">a</foreign> <emph type="italics"/>cum maiori<emph.end type="italics"/> <foreign lang="el">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>Latio autem pr&aelig;ter naturam in <lb/>minore circulo maior &longs;it: quam in maiore.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Et &longs;ic<emph.end type="italics"/> <foreign lang="el">a</foreign> <emph type="italics"/>duabus &longs;uis &longs;ic lationibus latum erit in<emph.end type="italics"/> <foreign lang="el">z,</foreign> <emph type="italics"/>vt vbi&shy;<lb/>cumque lationes ip&longs;ius<emph.end type="italics"/> <foreign lang="el">a</foreign> <emph type="italics"/>&longs;i&longs;tentur, &longs;emper &longs;int &longs;upra diametrum<emph.end type="italics"/><lb/><foreign lang="el">a h. </foreign><emph type="italics"/>&longs;iquidem lationes i&longs;t&aelig; &longs;unt in ratione<emph.end type="italics"/> <foreign lang="el">a b</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="el">a g. </foreign><emph type="italics"/>proinde <lb/>&longs;upra rectam, quia omnis diameter rectanguli recta e&longs;t. </s>
  
 <s>Primum igitur.] <emph type="italics"/>Proponitur problema de librarum in&aelig;qua&shy;<lb/>lium exactiore iudicio, quod pendet &agrave; minorum ponderum deprehen&shy;<lb/>&longs;ione, vt ea &longs;it exactior per quam minora pondera expendi po&longs;&longs;unt.<emph.end type="italics"/></s></p><p type="main"> <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>Huius vero.] <emph type="italics"/>Cau&longs;a exactiorum librarum refertur ad circuli<emph.end type="italics"/><pb 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.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>
  
 <s>Celerius enim.] <emph type="italics"/>Celeritatis lationum duos modos adfert &longs;i&shy;<lb/>miles &yuml;s quos cap.  <s id="id.000612">Nunc igitur ponatur<emph.end type="italics"/> <foreign lang="el">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>
  
 2. lib.  <s id="id.000613">Non igitur du&aelig; lationes ip&longs;ius<emph.end type="italics"/> <foreign lang="el">a</foreign> <emph type="italics"/>ferun&shy;<lb/>tur in ratione<emph.end type="italics"/> <foreign lang="el">a b</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="el">a g. </foreign><emph type="italics"/>Sed h&icirc;c obiici pote&longs;t quod Sol motu pri&shy;<lb/>mi mobilis mouetur ab Oriente in Occidentem in 24. horis, &amp; motu <lb/>proprio ab Occidente in Orientem in aliquo tempore quantum e&longs;t <lb/>quod re&longs;pondet &aelig;quatori coa&longs;cendenti cum 59'. 8&quot;. Eclyptic&aelig;. </s>
  
 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.000614">Et &longs;ic <lb/>eius du&aelig; lationes &longs;unt in ratione aliqua, nec tamen Sol fertur &longs;ecun&shy;<lb/>dum rectam &longs;ed <expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> arcum Eclyptic&aelig;. </s>
  
 <s>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.000615">Ita e&longs;t, ob id <expan abbr="dicend&utilde;">dicendum</expan> hic <lb/>dictas ab Ari&longs;totele du&aelig; lationes non &longs;impliciter <expan abbr="intellig&etilde;das">intelligendas</expan>: &longs;ed ta&shy;<lb/>les, qu&aelig; <expan abbr="fer&atilde;tur">ferantur</expan> amb&aelig; <expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> rectam. </s>
  
 <s>Cum <expan abbr="itaq;">itaque</expan> totum <lb/>maius &longs;it &longs;ua parte ex 9. axiom. </s> <s id="id.000616">Et &longs;it manebit demon&longs;tratio. <emph.end type="italics"/></s></p><p type="main">
  
 <s>lib.  <s id="id.000617">Simile e&longs;t enim.] <foreign lang="el">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></subchap1><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.070.jpg" pagenum="31"/><subchap1><p type="main">
  
 1. ele. </s> <s id="id.000619"><foreign lang="el">ei) ga\r a)/llon tina/, ou)k oi)sqh/setai kata\ <lb/>th\n dia/metron.</foreign></s>
  <s id="g0120804"><foreign lang="el">e)a\n de\ e)n mhdeni\ lo/gw| fe/rhtai du/o fora\s <lb/>kata\ mhde/na xro/non, a)du/naton eu)qei=an ei)=nai th\n fora/n.</foreign></s>
  <s id="g0120805"><foreign lang="el"><lb/>e)/stw ga\r eu)qei=a.</foreign></s>
  <s id="g0120806"><foreign lang="el">teqei/shs ou)=n tau/ths diame/trou, kai\ paraplhrwqeisw=n <lb/>tw=n pleurw=n, a)na/gkh to\n tw=n pleurw=n lo/gon <lb/>fe/resqai to\ fero/menon: tou=to ga\r de/deiktai pro/teron.</foreign></s>
  <s id="g0120807"><foreign lang="el">ou)k <lb/>a)/ra poih/sei eu)qei=an to\ e)n mhdeni\ lo/gw| fero/menon mhde/na <lb/>xro/non.</foreign></s>
  <s id="g0120808"><foreign lang="el">e)a\n ga/r tina lo/gon e)nexqh=| e)n xro/nw| tini/, tou=ton <lb/>a)na/gkh to\n xro/non eu)qei=an ei)=nai fora\n dia\ ta\ proeirhme/na.</foreign></s>
  <s id="g0120809"><foreign lang="el"><lb/>w(/ste perifere\s gi/netai, du/o fero/menon fora\s e)n mhqeni\ <lb/>lo/gw| mhqe/na xro/non.</foreign></s></p><p type="main">
  
 <s>externus circulus interno <lb/>concentrico erit maior. </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>
  
 <s>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.000621">Si vero mobilis <lb/>du&aelig; lationes in nulla &longs;int <lb/>ratione, nulloque in tem&shy;<lb/>pore, impo&longs;&longs;ibile e&longs;t latum <lb/>e&longs;&longs;e &longs;ecundum rectam. </s>
  
 <s>1. lib.  <s id="id.000622">Sit <lb/>enim recta, qua po&longs;ita pro <lb/>diametro, &amp; completis la&shy;<lb/>teribus nece&longs;&longs;e e&longs;t mobile <lb/>in ratione laterum latum <lb/>e&longs;&longs;e. </s>
  
 3. ele. </s> <s id="id.000623">Hoc enim prius fuit <lb/>demon&longs;tratum. </s>
  
 <s>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.000624">Non igi&shy;<lb/>tur &longs;ecundum rectam pro&shy;<lb/>gredietur, id quod fertur <lb/>in nulla ratione, nulloque <lb/>in tempore. </s>
  
 <s>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>[Si enim <expan abbr="&longs;e&shy;c&utilde;dum">&longs;e&shy;<lb/>cundum</expan> rationem aliquam <lb/>latum &longs;it in aliquo tempo&shy;<lb/>re, nece&longs;&longs;e e&longs;t illud tempus <lb/>rectam e&longs;&longs;e lationem, pro&shy;<lb/>pter ea qu&aelig; ante dicta &longs;unt.] </s>
  
 lib.  <s>Itaque circulare e&longs;t quod <lb/>&longs;ecundum duas lationes latum e&longs;t in nulla ratione nullo <lb/>in tempore. </s></p><p type="head">
  
 1. elem. </s> <s id="id.000625">COMMENTARIVS. </s></p><p type="main">
  
 <s>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.  <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="el">a b</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="el">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="el">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="el">a x</foreign> <emph type="italics"/>diameter quadrilateri <lb/>&longs;ub<emph.end type="italics"/> <foreign lang="el">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">
  
 21. lib.  <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>
  
 1. elem. </s> <s id="id.000628">Si du&aelig; lationes puncti mobilis <lb/>&longs;unt in nulla ratione, nulloque in tempore, impo&szlig;ibile e&longs;t mobile hoc <lb/>latum e&longs;&longs;e &longs;ecundum rectam: atqui puncti de&longs;cribentis circulum du&aelig; <lb/>lationes &longs;unt in nulla ratione, null&oacute;que in tempore. </s>
  
 <s>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.000629">Ergo impo&szlig;ibile <lb/>e&longs;t punctum, quod de&longs;cribit circulum, ferri &longs;ecundum rectam. </s>
  
 <s>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.000630">Sint <lb/>enim lationes ill&aelig; in aliqua ratione. </s>
  
 <s><gap/></s></p><p type="main"> <s id="id.000631">Ergo punctum feretur &longs;ecun&shy;<lb/>dum rectam: at non fertur &longs;ecundum rectam. </s>
  
 <s>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.000632">Peripheria enim non <lb/>e&longs;t recta: &longs;ed curua. </s>
  
 <s><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.000633">Non igitur in aliqua ratione &longs;unt illius lationes. <lb/></s>
  
 <s>Sit <lb/>enim ratio <expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> quam <lb/>mobile fertur ea: quam ha-<pb 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.000634">Et &longs;i non in vlla ratione. </s>
  
 <s>Si&shy;<lb/>mile e&longs;t enim ratione par&shy;<lb/>uum quadrilaterum maio&shy;<lb/>ri. </s> <s id="id.000635">nec igitur in tempore, quia tempora moti&shy;<lb/>bus analoga &longs;unt. </s>
  
 <s>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.000636">H&icirc;c duo occurrunt valde difficilia. </s>
  
 <s><expan abbr="S&etilde;-per">Sen&shy;<lb/>per</expan> enim &longs;upra diametrum <lb/>erit. </s> <s id="id.000637">Prius de <lb/>tempore. </s>
  
 <s>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.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>COMMENTARIVS.</s></p><p type="main"> <s id="id.000639">Hoc <lb/>enim repugnat def. 3. lib. 5. elem. </s>
  
 <s>Horum vero cau&longs;a.] <emph type="italics"/>In&aelig;qualium <expan abbr="circulor&utilde;">circulorum</expan> ab in&aelig;qualibus <lb/>radiis <expan abbr="de&longs;criptor&utilde;">de&longs;criptorum</expan>, &amp; maioris quidem &agrave; maiori multo ab&longs;tru&shy;<lb/>&longs;ior a&szlig;ignatur cau&longs;a ex radij de&longs;cribentis circulum duabus lationi&shy;<lb/>bus, qu&aelig; inter &longs;e <expan abbr="null&atilde;">nullam</expan> <expan abbr="ration&etilde;">rationem</expan> &longs;eruant. </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>Atque hinc elicitur quinta in <lb/>circulo repugnantia, ex qua admiratio eius maior: quam ante e&longs;&longs;e <lb/>concluditur. </s> <s id="id.000642">Dicimus <lb/>ergo quod ad hoc po&longs;terius attinet, rationem illas habere: &longs;ed<emph.end type="italics"/> <foreign lang="el">a)/r)r(hton,</foreign><lb/><emph type="italics"/>&amp; non &longs;olum indicibilem, quod numeris exprimi nequeat: &longs;ed &amp; <lb/>quod rectis lineis geometric&egrave; id e&longs;t exact&egrave;, exprimi non po&szlig;it, qualis <lb/>non e&longs;t inter duas lationes &egrave; quibus recta creatur, cum h&aelig;c &longs;i nume&shy;<lb/>ris non po&szlig;it exprimi, at rectis lineis &longs;altem geometric&egrave; exprimitur. <lb/></s>
  
 <s>E lationibus enim illis vna e&longs;t &longs;ecundum naturam, <lb/>altera pr&aelig;ter naturam. </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>Et vtri&longs;que vnum idemque ferri in nullo <lb/>tempore, id e&longs;t in in&longs;tanti indiui&longs;ibili, quomodo non e&longs;&longs;et valde ad&shy;<lb/>mirabile? </s> <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>
  
 <s>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.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="el">peri\ metrh/s. kuk,</foreign><emph type="italics"/>&amp; Ptol. lib. 1. <emph.end type="italics"/> <foreign lang="el">me/gal. sunt. </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>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.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&shy;<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>Syllog. </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>&longs;ic e&longs;t. </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>Omne duabus latio&shy;<lb/>nibus rationem aliquam inter &longs;e &longs;eruantibus latum, fertur &longs;ecundum<emph.end type="italics"/><pb pagenum="30"/><emph type="italics"/>rectam. </s> <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>Radius de&longs;cribens circulum duabus &longs;uis lationibus, non <lb/>Jertur &longs;ecundum rectam. </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>Radij igitur iationes in nulla &longs;unt ra&shy;<lb/>tione. </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>Propo&longs;itio confirmatur cum&verbar; &longs;equenti diagrammate. <lb/></s> <s id="id.000654">Quia in nulla harum, quod <lb/>e&longs;t extremum fit primum, quod peripheri&aelig; conuenit. </s>
  
 <s>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="fig6"></figure><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.000655">Pr&aelig;terea nulla <lb/>harum &longs;implex e&longs;t linea. </s>
  
 <s>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.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></subchap1><subchap1><p type="main">
  
 <s>1. lib.  <s id="id.000657"><foreign lang="el">o(/ti me\n toi/nun h( to\n ku/klon gra/fousa <lb/>fe/retai du/o fora\s a(/ma, fanero\n e)/k te tou/twn, <lb/>kai\ o(/ti to\ fero/menon kat' eu)qei=an e)pi\ th\n ka/qeton a)fi&shy;<lb/>knei=tai, w(/ste ei)=nai pa/lin au)th\n a)po\ tou= ke/ntrou ka/qeton.</foreign></s>
  <s id="g0121001"><foreign lang="el"><lb/>e)/stw ku/klos o( *a*b*g, to\ d' a)/kron to\ e)f' ou(= *b, fere/sqw <lb/>e)pi\ to\ *d: a)fiknei=tai de/ pote e)pi\ to\ *g.</foreign></s>
  <s id="g0121002"><foreign lang="el">ei) me\n ou)=n e)n tw=| <lb/>lo/gw| e)fe/reto o(\n e)/xei h( *b*d, pro\s th\n *d*g, e)fe/reto a)\n <lb/>th\n dia/metron th\n e)f' h(=| *b*g.</foreign></s>
  <s id="g0121003"><foreign lang="el">nu=n de/, e)pei/per e)n ou)deni\ <lb/>lo/gw|, e)pi\ th\n perife/reian fe/retai th\n e)f' h(=| *b e *g.</foreign></s></p><p type="main">
  
 6. &amp; proinde circa eandem dimentientem conuer&longs;. </s> <s id="id.000658">Quod vero recta <expan abbr="de&longs;cri&shy;b&etilde;s">de&longs;cri&shy;<lb/>bens</expan> circulum duabus &longs;imul <lb/>lationibus 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>prop.<emph.end type="italics"/><lb/>24. <emph type="italics"/>lib.  <s id="id.000659">Et <lb/>fieri &agrave; <expan abbr="c&etilde;tro">centro</expan> <expan abbr="perpendicula&shy;r&etilde;">perpendicula&shy;<lb/>rem</expan> [<expan abbr="dem&otilde;&longs;trem">demon&longs;trem</expan>us]. </s>
  
 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>Sit circu&shy;<pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.073.jpg" pagenum="34"/><foreign lang="el">b</foreign><lb/>lus <foreign lang="el">a b g,</foreign> &amp; extremum <foreign lang="el">b</foreign><lb/>feratur ad <foreign lang="el">d,</foreign> perueniet &longs;a&shy;<lb/>ne aliquando ad <foreign lang="el">g. </foreign></s>
  
 <s>Huic con&shy;<lb/>&longs;entit quod &agrave; Proclo ex Gemino acceptum &longs;ic expo&longs;itum e&longs;t. </s> <s>[Si igi&shy;<lb/>tur ferebatur in ratione <lb/>quam habet <foreign lang="el">b e</foreign> ad <foreign lang="el">e g,</foreign> fe&shy;<lb/>rebatur &longs;ecundum diame&shy;<lb/>trum <foreign lang="el">b g</foreign>: At nunc cum in <lb/>nulla ratione feratur, &longs;e&shy;<lb/>cundum peripheriam <foreign lang="el">b e g</foreign><lb/>feretur.]</s></p><p type="head">
  
 <s>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.000660">COMMENTARIVS. </s></p><p type="main">
  
 2. comm. </s> <s id="id.000661">Qvod vero recta.] <emph type="italics"/>Quia &longs;uperioris &longs;yllogi&longs;mi a&longs;&longs;umptio a&longs;&longs;u&shy;<lb/>mebat <expan abbr="Radi&utilde;">Radium</expan> duabus &longs;imul ferri lationibus, id ip&longs;um h&icirc;c breui&shy;<lb/>ter, ideo valde ob&longs;cur&egrave; confirmatur. </s>
  
 <s>in def. </s> <s id="id.000662">Confirmatio apertior &longs;ic erit. <lb/></s>
  
 <s>rect&aelig; <lb/>line&aelig;. </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. 2. lib. 1. de C&oelig;lo) Quinetiam &longs;i &longs;ic. </s>
  
 <s>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.000664">Idem radius &agrave; diametro cir&shy;<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>Non igitur du&aelig; lationes ip&longs;ius<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>ferun&shy;<lb/>tur in ratione<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">a g.</foreign> <emph type="italics"/>Sed h&icirc;c obiici pote&longs;t quod Sol motu pri&shy;<lb/>mi mobilis mouetur ab Oriente in Occidentem in 24. horis, &amp; motu <lb/>proprio ab Occidente in Orientem in aliquo tempore quantum e&longs;t <lb/>quod re&longs;pondet &aelig;quatori coa&longs;cendenti cum 59'. 8". Eclyptic&aelig;. </s> <s id="id.000665">Con&longs;equitur autem vt cum <lb/>e&longs;t in L<emph.end type="italics"/> <foreign lang="el">g</foreign> <emph type="italics"/>diagrammatis hic de&longs;cri&shy;<lb/>pti. </s>
  
 <s>Et &longs;ic <lb/>eius du&aelig; lationes &longs;unt in ratione aliqua, nec tamen Sol fertur &longs;ecun&shy;<lb/>dum rectam &longs;ed <expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> arcum Eclyptic&aelig;. </s> <s id="id.000666">Non igitur vna latione tantum fer&shy;<lb/>tur: fertur ergo pluribus. </s>
  
 <s>Ita e&longs;t, ob id <expan abbr="dicend&utilde;">dicendum</expan> hic <lb/>dictas ab Ari&longs;totele du&aelig; lationes non &longs;impliciter <expan abbr="intellig&etilde;das">intelligendas</expan>: &longs;ed ta&shy;<lb/>les, qu&aelig; <expan abbr="fer&atilde;tur">ferantur</expan> amb&aelig; <expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> rectam. </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="el">b</foreign> <emph type="italics"/>ver&longs;us E in hoc diagrammate: altera vt retror&shy;<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="el">b</foreign><lb/><emph type="italics"/>ver&longs;us L. </s>
  
 <s>Et &longs;it manebit demon&longs;tratio.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000668">Vtraque autem h&aelig;c latio quanta &longs;it <lb/>men&longs;uratur lineis rectis, quarum altera in po&longs;te&shy;<lb/>riore diagrammate e&longs;t &longs;inus rectus<emph.end type="italics"/> <foreign lang="el">g e,</foreign> <emph type="italics"/>altera <lb/>ver&ograve; e&longs;t &longs;inus ver&longs;us<emph.end type="italics"/> <foreign lang="el">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>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.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>1. lib.  <s id="id.000670">Si igitur ferebatur.] <emph type="italics"/>Rur&longs;us totum hunc textum his notis <lb/>[ ] interclu&longs;um inaniter repeti arbitramur. </s>
  
 6. elem.<emph.end type="italics"/></s></p><pb pagenum="31"/><p type="main"> <s id="id.000671">hoc enim e&longs;t quod an&shy;<lb/>tea e&longs;t demon&longs;tratum. <emph.end type="italics"/></s></p></subchap1><subchap1><p type="main">
  
 <s><gap/></s></p><p type="main"> <s id="id.000672"><foreign lang="el">e)a\n <lb/>de\ duoi=n ferome/noin a)po\ th=s au)th=s i)sxu/os, to\ me\n e)kkrou/oito <lb/>plei=on, to\ de\ e)/latton, eu)/logon bradu/teron kinhqh=nai <lb/>to\ plei=on e)kkrouo/menon tou= e)/latton e)kkrouome/nou, o(\ dokei= <lb/>sumbai/nein e)pi\ th=s mei/zonos kai\ e)la/ttonos, tw=n e)k tou= <lb/>ke/ntrou grafousw=n tou\s ku/klous.</foreign></s>
  <s id="g0121102"><foreign lang="el">dia\ ga\r to\ e)ggu/teron <lb/>ei)=nai tou= me/nontos th=s e)la/ttonos to\ a)/kron, h)\ to\ th=s mei/zonos, <lb/>w(/sper a)ntispw/menon ei)s tou)nanti/on, e)pi\ to\ me/son bradu/teron <lb/>fe/retai to\ th=s e)la/ttonos a)/kron.</foreign></s>
  <s id="g0121201"><foreign lang="el">pa/sh| me\n ou)=n <lb/>ku/klon grafou/sh| tou=to sumbai/nei.</foreign></s></p><p type="main">
  
 <s>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.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>Si vero mobilis <lb/>du&aelig; lationes in nulla &longs;int <lb/>ratione, nulloque in tem&shy;<lb/>pore, impo&longs;&longs;ibile e&longs;t latum <lb/>e&longs;&longs;e &longs;ecundum rectam. </s> <s id="id.000674">Quod videtur <lb/>contingere maiori &amp; mi&shy;<lb/>nori lineis ab eodem cen&shy;<lb/>tro circulos <expan abbr="de&longs;crib&etilde;tibus">de&longs;cribentibus</expan>. <lb/></s>
  
 <s>Sit <lb/>enim recta, qua po&longs;ita pro <lb/>diametro, &amp; completis la&shy;<lb/>teribus nece&longs;&longs;e e&longs;t mobile <lb/>in ratione laterum latum <lb/>e&longs;&longs;e. </s> <s id="id.000675">Quia enim extremum mi&shy;<lb/>noris propius e&longs;t quie&longs;cen&shy;<lb/>ti, quam &longs;it <expan abbr="extrem&utilde;">extremum</expan> maio&shy;<lb/>ris: qua&longs;i in contrarium re&shy;<lb/>uul&longs;um, in medium tardius <lb/>fertur ip&longs;um minoris extre&shy;<lb/>mum. </s>
  
 <s>Hoc enim prius fuit <lb/>demon&longs;tratum. </s> <s id="id.000676">Omni igitur circu&shy;<lb/>lum de&longs;cribenti hoc con&shy;<lb/>tingit. </s></p><p type="head">
  
 <s>Non igi&shy;<lb/>tur &longs;ecundum rectam pro&shy;<lb/>gredietur, id quod fertur <lb/>in nulla ratione, nulloque <lb/>in tempore. [Si enim <expan abbr="&longs;e-c&utilde;dum">&longs;e&shy;<lb/>cundum</expan> rationem aliquam <lb/>latum &longs;it in aliquo tempo&shy;<lb/>re, nece&longs;&longs;e e&longs;t illud tempus <lb/>rectam e&longs;&longs;e lationem, pro&shy;<lb/>pter ea qu&aelig; ante dicta &longs;unt.] Itaque circulare e&longs;t quod <lb/>&longs;ecundum duas lationes latum e&longs;t in nulla ratione nullo <lb/>in tempore.</s></p><p type="head"> <s id="id.000677">COMMENTARIVS. </s></p><p type="main">
  
 <s>COMMENTARIVS.</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 radijs in&aelig;&shy;<lb/>qualibus, quod ad celeritatem &amp; tarditatem attinet. </s>
  
 <s>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="fig7"></figure><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 pagenum="32"/><p type="main"> <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>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.000680">Syllogi&longs;mus e&longs;t <lb/>connexus &longs;ic. <emph.end type="italics"/></s></p><p type="main">
  
 <s>Si du&aelig; lationes puncti mobilis <lb/>&longs;unt in nulla ratione, nulloque in tempore, impo&szlig;ibile e&longs;t mobile hoc <lb/>latum e&longs;&longs;e &longs;ecundum rectam: atqui puncti de&longs;cribentis circulum du&aelig; <lb/>lationes &longs;unt in nulla ratione, null&oacute;que in tempore. </s> <s id="id.000681"><emph type="italics"/>Si duorum eadem vi motorum vnum plus repellitur, alterum <lb/>minus: quod plus repellitur, tardius fertur. <emph.end type="italics"/></s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.075.jpg" pagenum="36"/><p type="main">
  
 <s>Ergo impo&szlig;ibile <lb/>e&longs;t punctum, quod de&longs;cribit circulum, ferri &longs;ecundum rectam. </s> <s id="id.000682"><emph type="italics"/>Radiorem in&aelig;qualium eadem vi motorum minor plus <lb/>repellitur. <emph.end type="italics"/></s></p><p type="main">
  
 <s>Sint <lb/>enim lationes ill&aelig; in aliqua ratione. </s> <s id="id.000683"><emph type="italics"/>Radius igitur minor tardius feretur. <emph.end type="italics"/></s></p><p type="main">
  
 <s>Ergo punctum feretur &longs;ecun&shy;<lb/>dum rectam: at non fertur &longs;ecundum rectam. </s> <s id="id.000684">Quia enim minoris.] <emph type="italics"/>pro&longs;yllogi&longs;mus e&longs;t a&longs;&longs;umptionis &longs;ic. <emph.end type="italics"/></s></p><p type="main">
  
 <s>Peripheria enim non <lb/>e&longs;t recta: &longs;ed curua. </s> <s id="id.000685"><emph type="italics"/>Quod propius e&longs;t quie&longs;centi &amp; immoto plus retrahitur, quod <lb/>idem e&longs;t ac plus repellitur. <emph.end type="italics"/></s></p><p type="main">
  
 <s>Non igitur in aliqua ratione &longs;unt illius lationes. <lb/></s> <s id="id.000686"><emph type="italics"/>Extremum radij minoris mobile propius e&longs;t centro, alteri <lb/>&longs;cilicet extremo quie&longs;centi &amp; immoto: quam extre&shy;<lb/>mum maioris. <emph.end type="italics"/></s></p><p type="main">
  
 <s>Et &longs;i non in vlla ratione. </s> <s id="id.000687"><emph type="italics"/>Ergo extremum radij minoris mobile plus retrahetur retror&shy;<lb/>&longs;um, &amp; ab anteriori repelletur. <emph.end type="italics"/></s></p><p type="main">
  
 <s>nec igitur in tempore, quia tempora moti&shy;<lb/>bus analoga &longs;unt. </s> <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></subchap1><subchap1><p type="main">
  
 <s>H&icirc;c duo occurrunt valde difficilia. </s> <s id="id.000689"><foreign lang="el">kai\ fe/retai th\n me\n <lb/>kata\ fu/sin, th\n de\ para\ fu/sin kata\ th\n perife/reian <lb/>ei)s to\ pla/gion kai\ to\ ke/ntron. mei/zw d' a)ei\ th\n para\ <lb/>fu/sin h( e)la/ttwn fe/retai: dia\ ga\r to\ e)ggu/teron ei)=nai tou= <lb/>ke/ntrou tou= a)ntispw=ntos, kratei=tai ma=llon.</foreign></s></p><p type="main">
  
 <s>Prius de <lb/>tempore. </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;&shy;uer&longs;um">tran&longs;&shy;<lb/>uer&longs;um</expan>, &amp; centrum ver&longs;us. <lb/></s>
  
 <s>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.000691">Minor vero [linea] &longs;emper <lb/><expan abbr="maior&etilde;">maiorem</expan> motum habet eum, <lb/>qui pr&aelig;ter <expan abbr="natur&atilde;">naturam</expan> e&longs;t. </s>
  
 <s>Hoc <lb/>enim repugnat def. </s> <s id="id.000692">quia <lb/>enim centro vicinior e&longs;t ad <lb/>&longs;e <expan abbr="reuell&etilde;ti">reuellenti</expan>, vincitur magis. </s></p><p type="head">
  
 <s>3. lib.  <s id="id.000693">COMMENTARIVS. </s></p><p type="main">
  
 5. elem. </s> <s id="id.000694">Et fertur motu.] <emph type="italics"/>E duobus motibus in extremo radij mobili <lb/>alterum &longs;ecundum naturam e&longs;&longs;e dicit, nempe qui e&longs;t &longs;ecundum <lb/>peripheriam, alterum pr&aelig;ter naturam, qui e&longs;t in tran&longs;uer&longs;um, &amp; <lb/>ver&longs;us centrum. </s>
  
 <s>quantitas enim motus vnius mul&shy;<lb/>tiplicata, alterius vici&szlig;im quantitatem &longs;uperare pote&longs;t. </s> <s id="id.000695">Sed rationem huius hic nullam profert. </s>
  
 <s>Dicimus <lb/>ergo quod ad hoc po&longs;terius attinet, rationem illas habere: &longs;ed<emph.end type="italics"/> <foreign lang="greek">a)/r)r(n<gap/>ov,</foreign><lb/><emph type="italics"/>&amp; non &longs;olum indicibilem, quod numeris exprimi nequeat: &longs;ed &amp; <lb/>quod rectis lineis geometric&egrave; id e&longs;t exact&egrave;, exprimi non po&szlig;it, qualis <lb/>non e&longs;t inter duas lationes &egrave; quibus recta creatur, cum h&aelig;c &longs;i nume&shy;<lb/>ris non po&szlig;it exprimi, at rectis lineis &longs;altem geometric&egrave; exprimitur. <lb/></s> <s id="id.000696">H&aelig;c au&shy;<lb/>tem alibi ab eo dicta adferri pote&longs;t. </s>
  
 <s>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.000697">quia quicquid &longs;implex exi&longs;tens <lb/>duabus lationibus &longs;imul fertur, alteram naturalem, alteram pr&aelig;ter&shy;<lb/>naturam habere &longs;eu vt ita dicam &longs;ecundariam, &amp; ab alio penden&shy;<lb/>tem nece&longs;&longs;e e&longs;t: &longs;icuti videre e&longs;t in motibus inferiorum orbium c&aelig;le&shy;<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.076.jpg" pagenum="37"/><emph type="italics"/>&longs;tium, qui proprio ab occa&longs;u in Orientem vergunt, &amp; motu primi <lb/>mobilis ab Oriente in occa&longs;um mouentur. </s>
  
 <s>Tunc enim ratio <lb/>e&longs;t rectis illis licet incommen&longs;erabilibus prop.  <s id="id.000698">Ergo cum extremum radij <lb/>mobile aut radius ip&longs;e &longs;it quid &longs;implici&szlig;imum, &amp; &longs;imul duabus la&shy;<lb/>tionibus feratur, altera harum erit ei naturalis, altera ad vim alte&shy;<lb/>rius con&longs;equetur. </s>
  
 116. lib.  <s id="id.000699">Et illa quidem potius naturalis erit qu&aelig; &agrave; termino &agrave; <lb/>quo egredi conatur, &amp; quantum in &longs;e e&longs;t, di&longs;cedit. </s>
  
 10. expre&longs;&longs;a. <lb/></s> <s id="id.000700">Talis autem e&longs;t ea <lb/>qua extremum mobile veluti di&longs;cedens &agrave; centro &longs;ecundum periphe&shy;<lb/>riam fertur. </s>
  
 <s>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.000701">Tum qua forma rei acquiritur, qualis latio per circum&shy;<lb/>ferentiam, cum h&aelig;c &longs;it circuli forma &longs;eu finis. </s>
  
 <s><foreign lang="greek">kuk,</foreign> <emph type="italics"/>&amp; Ptol. </s> <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></subchap1><subchap1><p type="main">
  
 <s>lib.  <s id="id.000703"><foreign lang="el">o(/ti de\ mei=zon <lb/>to\ para\ fu/sin kinei=tai h( e)la/ttwn th=s mei/zonos, tw=n e)k tou= <lb/>ke/ntrou grafousw=n tou\s ku/klous, e)k tw=nde dh=lon.</foreign></s>
  <s id="g0121302"><foreign lang="el">e)/stw <lb/>ku/klos e)f' *b*g*d*e, kai\ a)/llos e)n tou/tw| e)la/ttwn, <lb/>e)f' ou(= *x*n*m*c, peri\ to\ au)to\ ke/ntron to\ *a, kai\ e)kbeblh/sqwsan <lb/>ai( dia/metroi, e)n me\n tw=| mega/lw|, e)f' w(=n *g*d <lb/>kai\ *b*e, e)n de\ tw=| e)la/ttoni ai( *m*x *n*c: kai\ to\ e(tero/mhkes <lb/>parapeplhrw/sqw, to\ *d*y*r*g. </foreign></s>
  
 1.<emph.end type="italics"/> <foreign lang="greek">me/gal. </foreign></s> <s id="g0121302a"><foreign lang="el">ei) dh\ h( *a*b gra/fousa <lb/>ku/klon h(/cei e)pi\ to\ au)to\ o(/qen w(rmh/qh e)pi\ th\n *a*e, dh&shy;<lb/>lono/ti fe/retai pro\s au(th/n.</foreign></s>
  <s id="g0121303"><foreign lang="el">o(moi/ws de\ kai\ h( *a*x, pro\s th\n <lb/>*a*x h(/cei.</foreign></s>
  <s id="g0121304"><foreign lang="el">bradu/teron de\ fe/retai h( *a*x th=s *a*b, w(/sper <lb/>ei)/rhtai, dia\ to\ gi/nesqai mei/zona th\n e)/kkrousin, kai\ a)ntispa=sqai <lb/>ma=llon th\n *a*x.</foreign></s>
  <s id="g0121401"><foreign lang="el">h)/xqw de\ h( *a*q*h, kai\ a)po\ <lb/>tou= *q ka/qetos e)pi\ th\n *a*b h( *q*z e)n tw=| ku/klw|, kai\ pa/lin <lb/>a)po\ tou= *q h)/xqw para\ th\n *a*b h( *q*w, kai\ h( *w*u, <lb/>e)pi\ th\n *a*b ka/qeton, kai\ h( *h*k.</foreign></s>
  <s id="g0121402"><foreign lang="el">ai( dh\ e)f' w(=n *w*u kai\ <lb/>*q*z i)/sai. </foreign></s>
  <s id="g0121402a"><foreign lang="el">h( a)/ra *b*u e)la/ttwn th=s *x*z: ai( ga\r i)/sai <lb/>eu)qei=ai e)p' a)ni/sous ku/klous e)mblhqei=sai pro\s o)rqh=| th=| <lb/>diame/trw|, e)/latton tmh=ma a)pote/mnousi th=s diame/trou e)n <lb/>toi=s mei/zosi ku/klois.</foreign></s>
  <s id="g0121402b"><foreign lang="el">e)/sti de\ h( *w*u i)/sh th=| *q*z.</foreign></s>
  <s id="g0121404"><foreign lang="el">e)n o(/sw|<lb/> dh\ xro/nw| h( *a*q th\n *x*q e)nhne/xqh, e)n tosou/tw| xro/nw| e)n <lb/>tw=| ku/klw| tw=| mei/zoni, mh\ mei/zona th=s *b*w e)nh/nektai to\ a)/kron <lb/>th=s *b*a.</foreign></s>
  <s id="g0121501"><foreign lang="el">h( me\n ga\r kata\ fu/sin fora\, i)/sh: h( de\ para\ <lb/>fu/sin e)la/ttwn, h( *b*u, th=s *z*x.</foreign></s></p><p type="main">
  
 <s><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.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>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 pagenum="33"/><emph type="italics"/>tam permittere volare: ita tamen vt digitis alterum extremum funi&shy;<lb/>culi retineant. </s> <s id="id.000705">Sit <lb/>circulus <foreign lang="el">b g d e,</foreign> &amp; alter <lb/>minor <foreign lang="el">x n m c,</foreign> eiu&longs;dem <expan abbr="c&etilde;&shy;tri">cen&shy;<lb/>tri</expan> <foreign lang="el">a,</foreign> Et traduct&aelig; &longs;int dia&shy;<lb/>metri in magno quidem <lb/><foreign lang="el">g d, &amp; b e</foreign>: in minori <foreign lang="el">m c &amp; <lb/>x n</foreign>: atque alterolongum <lb/>compleatur <foreign lang="el">d y r g. </foreign></s>
  
 <s>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>Si igi&shy;<lb/>tur <foreign lang="el">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="el">a b</foreign>] <lb/>&longs;imiliter <foreign lang="el">a x</foreign> perueniet ad <lb/>ip&longs;am <foreign lang="el">a x. </foreign></s>
  
 <s>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>Tardius autem <lb/>fertur <foreign lang="el">a x</foreign>: quam <foreign lang="el">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="el">a x. </foreign></s>
  
 <s>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>Ducatur vero <lb/>recta <foreign lang="el">a q h, &amp; a q</foreign> excitetur <lb/>perpendicularis ad <foreign lang="el">a b,</foreign> qu&ecedil; <lb/>&longs;it <foreign lang="el">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>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>Et rur&longs;us per <foreign lang="el">q</foreign> ducatur pa&shy;<lb/>rallela ip&longs;i <foreign lang="el">a b</foreign> qu&aelig; &longs;it <foreign lang="el">q w <lb/>&amp; w n</foreign> perpendicularis ip&longs;i <lb/><foreign lang="el">a b</foreign> tum &amp; <foreign lang="el">h k. </foreign></s>
  
 <s>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>Sunt vero <lb/><foreign lang="el">w n &amp; q z</foreign> &aelig;quales. </s>
  
 <s>Quia in nulla harum, quod <lb/>e&longs;t extremum fit primum, quod peripheri&aelig; conuenit. </s> <s id="id.000706">Rur&longs;us <lb/><foreign lang="el">b n</foreign> e&longs;t minor: quam <foreign lang="el">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>Pr&aelig;terea nulla <lb/>harum &longs;implex e&longs;t linea. </s> <s id="id.000707">E&longs;t autem <foreign lang="el">w n</foreign> &aelig;qualis ip&longs;i <lb/><foreign lang="el">q z. </foreign>In quanto vero tempo&shy;<lb/>re <foreign lang="el">a x</foreign> peragrauit <foreign lang="el">x q,</foreign> in <lb/><expan abbr="t&atilde;to">tanto</expan> in maiore circulo ex&shy;<lb/>tremum <foreign lang="el">a b</foreign> non maiorem <lb/><foreign lang="el">b w</foreign> peragrauit (etenim <lb/>motus &longs;ecundum naturam <lb/>&aelig;qualis e&longs;&longs;et) pr&aelig;ter na&shy;<lb/>turam vero minor erat, nempe <foreign lang="el">b n</foreign> quam <foreign lang="el">x z. </foreign></s></p><p type="head">
  
 <s>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.000708">COMMENTARIVS. </s></p><p type="main">
  
 <s><gap/></s></p><p type="main"> <s id="id.000709">Qvod vero minor.] <emph type="italics"/>Altera e&longs;t confirmatio &longs;ed<emph.end type="italics"/> <foreign lang="el">grammikh\</foreign><lb/><emph type="italics"/>linearis a&longs;&longs;umptionis &longs;yllogi&longs;mi pr&aelig;cedentis. </s>
  
 <s>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.000710">Scilicet quod mi&shy;<lb/>nor radius plus retrahatur ad centrum, quam maior. </s>
  
 <s>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 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.000711">Vbi ab vtri&longs;que <lb/>&longs;ecundum peripheriam &aelig;quale &longs;patium confectum e&longs;t. </s>
  
 <s>COMMENTARIVS.</s></p><p type="main"> <s id="id.000712">perpendiculis <lb/>enim &aelig;qualibus ip&longs;um men&longs;urantibus partes ab&longs;ci&longs;&longs;&aelig; de diametris, <lb/>qu&aelig; retractionem vtriu&longs;que ad centrum men&longs;urant, in&aelig;quales &longs;unt, <lb/>&amp; in minore circulo, maior: in maiore vero minor. </s>
  
 <s>Qvod vero recta.] <emph type="italics"/>Quia &longs;uperioris &longs;yllogi&longs;mi a&longs;&longs;umptio a&longs;&longs;u&shy;<lb/>mebat <expan abbr="Radi&utilde;">Radium</expan> duabus &longs;imul ferri lationibus, id ip&longs;um h&icirc;c breui&shy;<lb/>ter, ideo valde ob&longs;cur&egrave; confirmatur. </s> <s id="id.000713">vt videre lice&shy;<lb/>bit in diagrammate hic de&longs;cripto &amp; &longs;uis rationibus nece&longs;&longs;arijs con&shy;<lb/>firmato. <emph.end type="italics"/></s></p><p type="main">
  
 <s>Confirmatio apertior &longs;ic erit. <lb/></s> <s id="id.000714"><emph type="italics"/>Sint duo circuli concentrici maior<emph.end type="italics"/> <foreign lang="el">b d e y,</foreign> <emph type="italics"/>minor<emph.end type="italics"/> <foreign lang="el">x m n c</foreign> <emph type="italics"/>&egrave; cen&shy;<lb/>tro a traiecti diametris<emph.end type="italics"/> <foreign lang="el">x n &amp; b e. </foreign></s></p><p type="main">
  
 <s>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.000715"><emph type="italics"/>A puncto<emph.end type="italics"/> <foreign lang="el">a</foreign> <emph type="italics"/>ad punctum<emph.end type="italics"/> <foreign lang="el">q</foreign> <emph type="italics"/>ducatur recta<emph.end type="italics"/> <foreign lang="el">a q,</foreign> <emph type="italics"/>&amp; producatur in<emph.end type="italics"/><lb/><foreign lang="el">h</foreign> <emph type="italics"/>&longs;itque<emph.end type="italics"/> <foreign lang="el">a q h. </foreign></s></p><p type="main">
  
 2. lib.  <s id="id.000716"><emph type="italics"/>Tum &agrave; puncto<emph.end type="italics"/> <foreign lang="el">q</foreign> <emph type="italics"/>excitetur perpendicularis line&aelig;<emph.end type="italics"/> <foreign lang="el">a x</foreign> <emph type="italics"/>prop. 12. <lb/>lib. 1. &longs;itque<emph.end type="italics"/> <foreign lang="el">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">
  
 1. de C&oelig;lo) Quinetiam &longs;i &longs;ic. </s> <s id="id.000717"><emph type="italics"/>Et per punctum<emph.end type="italics"/> <foreign lang="el">q</foreign> <emph type="italics"/>ducatur parallela rect&aelig;<emph.end type="italics"/> <foreign lang="el">a b</foreign> <emph type="italics"/>prop. 31. lib. 1. <lb/>qu&aelig; &longs;it<emph.end type="italics"/> <foreign lang="el">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>Idem radius &agrave; diametro cir-<emph.end type="italics"/><lb/><figure id="fig8"></figure><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.000718"><emph type="italics"/>Rur&longs;us &agrave; puncto<emph.end type="italics"/> <foreign lang="el">w</foreign> <emph type="italics"/>excitetur perpendicularis line&aelig;<emph.end type="italics"/> <foreign lang="el">a b,</foreign> <emph type="italics"/>&longs;itque<emph.end type="italics"/><lb/><foreign lang="el">w n</foreign>: <emph type="italics"/>&amp; &longs;ic parallelogrammum erit<emph.end type="italics"/> <foreign lang="el">w n z q</foreign> <emph type="italics"/>ex def. </s>
  
 <s>Con&longs;equitur autem vt cum <lb/>e&longs;t in L<emph.end type="italics"/> <foreign lang="greek">g</foreign> <emph type="italics"/>diagrammatis hic de&longs;cri&shy;<lb/>pti. </s> <s id="id.000719">parallelog. <emph.end type="italics"/></s></p><p type="main">
  
 <s>Non igitur vna latione tantum fer&shy;<lb/>tur: fertur ergo pluribus. </s> <s id="id.000720"><emph type="italics"/>Sicque<emph.end type="italics"/> <foreign lang="el">b</foreign> <emph type="italics"/>motum ad<emph.end type="italics"/> <foreign lang="el">w</foreign> <emph type="italics"/>tantum confecit &longs;patij &longs;ecundum natu&shy;<lb/>ram, quam<emph.end type="italics"/> <foreign lang="el">x</foreign> <emph type="italics"/>motum ad<emph.end type="italics"/> <foreign lang="el">q</foreign>. </s>
  
 <s>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="fig9"></figure><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. </s> <s><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>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></s></p><pb pagenum="35"/><p type="main"> <s id="id.000721">Sint autem<emph.end type="italics"/> <foreign lang="el">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="el">w n z q</foreign> <emph type="italics"/>prop. 34. lib. 1. </s>
  
 <s>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>Erant vtro&shy;<lb/>bique &longs;patia<emph.end type="italics"/> <foreign lang="el">b w &amp; x q</foreign> <emph type="italics"/>&aelig;qualia. <emph.end type="italics"/></s></p><p type="main">
  
 <s>Si igitur ferebatur.] <emph type="italics"/>Rur&longs;us totum hunc textum his notis <lb/>[ ] interclu&longs;um inaniter repeti arbitramur. </s> <s id="id.000723"><foreign lang="el">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="el">b, &amp; x z</foreign> <emph type="italics"/>ip&longs;ius<emph.end type="italics"/> <foreign lang="el">x. </foreign><emph type="italics"/>&longs;i igitur<emph.end type="italics"/> <foreign lang="el">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="el">b n,</foreign> <emph type="italics"/>erit puncti<emph.end type="italics"/> <foreign lang="el">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="el">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>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.000724"><emph type="italics"/>Sed &amp; &longs;i perficiantur parallelogramma<emph.end type="italics"/> <foreign lang="el">d s t f &amp; d y r g</foreign>: <lb/><emph type="italics"/>illud erit vtile ad o&longs;tendendum<emph.end type="italics"/> <foreign lang="el">d</foreign> <emph type="italics"/>tralatum vno motu v&longs;que ad<emph.end type="italics"/> <foreign lang="el">s,</foreign><lb/><emph type="italics"/>altero motu, quo retrahitur ad centrum, reductum e&longs;&longs;e ad<emph.end type="italics"/> <foreign lang="el">t</foreign>: <emph type="italics"/>&amp; <lb/>huius retractiones <expan abbr="men&longs;ur&atilde;">men&longs;uram</expan> e&longs;&longs;e<emph.end type="italics"/> <foreign lang="el">s t</foreign> <emph type="italics"/>vel<emph.end type="italics"/> <foreign lang="el">d f</foreign>: <emph type="italics"/>hoc vero vtile <expan abbr="eti&atilde;">etiam</expan> erit <lb/>ad terminandos motus illos duos <expan abbr="natural&etilde;">naturalem</expan>, &longs;cilicet &amp; pr&aelig;ter <expan abbr="natur&atilde;">naturam</expan>. <emph.end type="italics"/></s></p><p type="main">
  
 <s><gap/></s></p><p type="main"> <s id="id.000725">Atque alterolongum.] <emph type="italics"/>Hoc <expan abbr="quadrilater&utilde;">quadrilaterum</expan> <expan abbr="oblong&utilde;">oblongum</expan>, &amp; rectan&shy;<lb/>gulum compleri debui&longs;&longs;e dici pote&longs;t, vt rectus in eo motus appareat, <lb/>quem facturus radius fui&longs;&longs;et, ni&longs;i retraheretur in centrum: tum vt <lb/>terminet motus eos, qui &longs;unt &longs;ecundum naturam &amp; pr&aelig;ter naturam. <emph.end type="italics"/></s></p><p type="main">
  
 <s>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.000726"><foreign lang="el">a q h</foreign>] <emph type="italics"/><expan abbr="Punct&utilde;">Punctum</expan><emph.end type="italics"/> <foreign lang="el">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="el">x</foreign> <emph type="italics"/><expan abbr="extrem&utilde;">extremum</expan> mobile minoris radij<emph.end type="italics"/> <foreign lang="el">a x. </foreign></s></p><p type="main">
  
 <s>Quod videtur <lb/>contingere maiori &amp; mi&shy;<lb/>nori lineis ab eodem cen&shy;<lb/>tro circulos <expan abbr="de&longs;crib&etilde;tibus">de&longs;cribentibus</expan>. <lb/></s> <s id="id.000727">Et <foreign lang="el">a q</foreign> excitetur.] <emph type="italics"/>A puncto<emph.end type="italics"/> <foreign lang="el">q</foreign> <emph type="italics"/>extra lineam<emph.end type="italics"/> <foreign lang="el">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="el">q z</foreign> <emph type="italics"/>prop. 12. lib. 1. elem. <emph.end type="italics"/></s></p><p type="main">
  
 <s>Quia enim extremum mi&shy;<lb/>noris propius e&longs;t quie&longs;cen&shy;<lb/>ti, quam &longs;it <expan abbr="extrem&utilde;">extremum</expan> maio&shy;<lb/>ris: qua&longs;i in contrarium re&shy;<lb/>uul&longs;um, in medium tardius <lb/>fertur ip&longs;um minoris extre&shy;<lb/>mum. </s> <s id="id.000728">Et rur&longs;us per <foreign lang="el">q</foreign>] <emph type="italics"/>Per punctum<emph.end type="italics"/> <foreign lang="el">q</foreign> <emph type="italics"/>datum dat&aelig; rect&aelig;<emph.end type="italics"/> <foreign lang="el">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>Omni igitur circu&shy;<lb/>lum de&longs;cribenti hoc con&shy;<lb/>tingit.</s></p><p type="head"> <s id="id.000729">Et <foreign lang="el">w n</foreign> perpend.] <emph type="italics"/>prop. 12. lib. 1. elem. <emph.end type="italics"/></s></p><p type="main">
  
 <s>COMMENTARIVS.</s></p><p type="main"> <s id="id.000731">Sunt vero <foreign lang="el">w n</foreign> &amp;] <emph type="italics"/>Quia<emph.end type="italics"/> <foreign lang="el">q w</foreign> <emph type="italics"/>parallela e&longs;t ip&longs;i<emph.end type="italics"/> <foreign lang="el">z n</foreign> <emph type="italics"/>ex fabrica: <lb/>t&ugrave;m<emph.end type="italics"/> <foreign lang="el">w n</foreign> <emph type="italics"/>etiam parallela e&longs;t ip&longs;i<emph.end type="italics"/> <foreign lang="el">q z,</foreign> <emph type="italics"/>quia in eas incidens<emph.end type="italics"/> <foreign lang="el">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>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><expan abbr="parallelogr&atilde;m&utilde;">parallelogramum</expan> erit<emph.end type="italics"/> <foreign lang="el">w n z q. </foreign><emph type="italics"/>per def. pa&shy;<lb/>rall. </s>
  
 <s>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.000735">quare eius latera oppo&longs;ita<emph.end type="italics"/> <foreign lang="el">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">
  
 <s>Syllogi&longs;mus e&longs;t <lb/>connexus &longs;ic.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000736">In circulis.] <emph type="italics"/>Ex hoc loco elicitur hoc theorema. </s>
  
 <s><emph type="italics"/>Si duorum eadem vi motorum vnum plus repellitur, alterum <lb/>minus: quod plus repellitur, tardius fertur.<emph.end type="italics"/></s></p><pb pagenum="36"/><p type="main"> <s id="id.000737">Perpendicula&shy;<lb/>res &agrave; peripheriis in &longs;emidiametros circulorum in&aelig;qualium &aelig;quales <lb/>&longs;egmenta auferunt de &longs;emidiametris in&aelig;qualia, &amp; quidem maius in <lb/>minori comprehen&longs;um inter peripheriam &amp; perpendicularem. <emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Radiorem in&aelig;qualium eadem vi motorum minor plus <lb/>repellitur.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000738">Expo&shy;<lb/><figure id="id.035.01.079.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.079.1.jpg"/><lb/>&longs;itio. </s></p><p type="main">
  
 <s><emph type="italics"/>Radius igitur minor tardius feretur.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000739"><emph type="italics"/>Sunto <lb/>duo cir<lb/>culi in&shy;<lb/>&aelig;qua&shy;<lb/>les A <lb/>B C ma<lb/>ior &amp; <lb/>D E F <lb/>minor, perpendiculares &longs;int B K, E I &amp; ablat&aelig; A K, D I. <emph.end type="italics"/></s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.080.jpg" pagenum="41"/><p type="main">
  
 <s>Quia enim minoris.] <emph type="italics"/>pro&longs;yllogi&longs;mus e&longs;t a&longs;&longs;umptionis &longs;ic.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000740">Deter. <emph type="italics"/>Dico D I e&longs;&longs;e maiorem ip&longs;a A K qu&aelig; e&longs;t &longs;egmentum in <lb/>maiori circulo. </s>
  
 <s><emph type="italics"/>Quod propius e&longs;t quie&longs;centi &amp; immoto plus retrahitur, quod <lb/>idem e&longs;t ac plus repellitur.<emph.end type="italics"/></s></p><p type="main"> <s id="id.000741">Ante huius fabricam hoc problema e&longs;t <expan abbr="a&longs;&longs;um&etilde;dum">a&longs;&longs;umendum</expan>. <emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Extremum rad&yuml; minoris mobile propius e&longs;t centro, alteri <lb/>&longs;cilicet extremo quie&longs;centi &amp; immoto: quam extre&shy;<lb/>mum maioris.<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><emph type="italics"/>Ergo extremum rad&yuml; minoris mobile plus retrahetur retror&shy;<lb/>&longs;um, &amp; ab anteriori repelletur.<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. 1. lib. 3. </s>
  
 <s><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>ducatur A k diameter. </s>
  
 <s><gap/></s></p><p type="main"> <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. </s>
  
 <s>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>hic <lb/>tanget interius circulum A B k <lb/>C datum in puncto A. </s>
  
 <s>Minor vero [linea] &longs;emper <lb/><expan abbr="maior&etilde;">maiorem</expan> motum habet eum, <lb/>qui pr&aelig;ter <expan abbr="natur&atilde;">naturam</expan> e&longs;t. </s> <s id="id.000745">Nam &longs;i <lb/>&amp; &longs;ecet, vt in puncto H, ducta <lb/>H E. </s>
  
 <s>quia <lb/>enim centro vicinior e&longs;t ad <lb/>&longs;e <expan abbr="reuell&etilde;ti">reuellenti</expan>, vincitur magis.</s></p><p type="head"> <s>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. </s>
  
 <s>COMMENTARIVS.</s></p><p type="main"> <s>non erat igitur H punctum commune vtrique circulo, &amp; <lb/>&longs;ic de alijs. </s>
  
 <s>Et fertur motu.] <emph type="italics"/>E duobus motibus in extremo rad&yuml; mobili <lb/>alterum &longs;ecundum naturam e&longs;&longs;e dicit, nempe qui e&longs;t &longs;ecundum <lb/>peripheriam, alterum pr&aelig;ter naturam, qui e&longs;t in tran&longs;uer&longs;um, &amp; <lb/>ver&longs;us centrum. </s> <s id="id.000748">Circulus igitur A F G, tangit circulum A B K C <lb/>in puncto A prop. 11. lib. 3. </s>
  
 <s>Sed rationem huius hic nullam profert. </s> <s>quod oportuit facere. <emph.end type="italics"/></s></p><p type="main">
  
 <s>H&aelig;c au&shy;<lb/>tem alibi ab eo dicta adferri pote&longs;t. </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. 3. qui erit &aelig;qualis dato D E F. <lb/>def. 1. lib. 3. </s>
  
 <s>quia quicquid &longs;implex exi&longs;tens <lb/>duabus lationibus &longs;imul fertur, alteram naturalem, alteram pr&aelig;ter&shy;<lb/>naturam habere &longs;eu vt ita dicam &longs;ecundariam, &amp; ab alio penden&shy;<lb/>tem nece&longs;&longs;e e&longs;t: &longs;icuti videre e&longs;t in motibus inferiorum orbium c&aelig;le-<emph.end type="italics"/><pb pagenum="37"/><emph type="italics"/>&longs;tium, qui proprio ab occa&longs;u in Orientem vergunt, &amp; motu primi <lb/>mobilis ab Oriente in occa&longs;um mouentur. </s> <s>Et tanget intus circulum A B C in puncto A ex probl. <lb/>pr&aelig;&longs;umpto. </s>
  
 <s>Ergo cum extremum rad&yuml; <lb/>mobile aut radius ip&longs;e &longs;it quid &longs;implici&szlig;imum, &amp; &longs;imul duabus la&shy;<lb/>tionibus feratur, altera harum erit ei naturalis, altera ad vim alte&shy;<lb/>rius con&longs;equetur. </s> <s>per punctum B <expan abbr="ducaeur">ducatur</expan> 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>Et illa quidem potius naturalis erit qu&aelig; &agrave; termino &agrave; <lb/>quo egredi conatur, &amp; quantum in &longs;e e&longs;t, di&longs;cedit. </s> <s id="id.000754">E I ax. 1. connectantur M H, <lb/>E H po&longs;t. 1. <emph.end type="italics"/></s></p><p type="main">
  
 <s>Talis autem e&longs;t ea <lb/>qua extremum mobile veluti di&longs;cedens &agrave; centro &longs;ecundum periphe&shy;<lb/>riam fertur. </s> <s id="id.000757">Demon&longs;t. </s>
  
 <s>Tum qua forma rei acquiritur, qualis latio per circum&shy;<lb/>ferentiam, cum h&aelig;c &longs;it circuli forma &longs;eu finis. </s> <s><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. </s>
  
 <s>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>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. </s>
  
 <s><gap/></s></p><p type="main"> <s>tum angulus M H N ad centrum con&longs;titutus <emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.081.jpg" pagenum="42"/><emph type="italics"/>&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. </s>
  
 <s>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>&amp; &longs;ic reliquum latus N H &aelig;quale e&longs;t re&shy;<lb/>liquo I H. </s>
  
 <s>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 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.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">
  
 <s>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.000767">Concl. </s>
  
 <s>E&longs;t autem <foreign lang="greek">w n</foreign> &aelig;qualis ip&longs;i <lb/><foreign lang="greek">q z.</foreign> In quanto vero tempo&shy;<lb/>re <foreign lang="greek">a x</foreign> peragrauit <foreign lang="greek">x q,</foreign> in <lb/><expan abbr="t&atilde;to">tanto</expan> in maiore circulo ex&shy;<lb/>tremum <foreign lang="greek">a b</foreign> non maiorem <lb/><foreign lang="greek">b w</foreign> peragrauit (etenim <lb/>motus &longs;ecundum naturam <lb/>&aelig;qualis e&longs;&longs;et) pr&aelig;ter na&shy;<lb/>turam vero minor erat, nempe <foreign lang="greek">b n</foreign> quam <foreign lang="greek">x z.</foreign></s></p><p type="head"> <s><emph type="italics"/>Ergo perpendiculares &agrave; peripherijs in &longs;emidiametros &amp; <lb/>ct. </s>
  
 <s>COMMENTARIVS.</s></p><p type="main"> 
  
 <s>Qvod vero minor.] <emph type="italics"/>Altera e&longs;t confirmatio &longs;ed<emph.end type="italics"/> <foreign lang="greek"><gap/>ammikh\</foreign><lb/><emph type="italics"/>linearis a&longs;&longs;umptionis &longs;yllogi&longs;mi pr&aelig;cedentis. </s> 
  
 <s>Scilicet quod mi&shy;<lb/>norradius plus retrahatur ad centrum, quam maior. </s> 
  
 <s>Vbi ab vtri&longs;que <lb/>&longs;ecundum peripheriam &aelig;quale &longs;patium confectum e&longs;t. </s> 
  
 <s>perpendiculis <lb/>enim &aelig;qualibus ip&longs;um men&longs;urantibus partes ab&longs;ci&longs;&longs;&aelig; de diametris, <lb/>qu&aelig; retractionem vtriu&longs;que ad centrum men&longs;urant, in&aelig;quales &longs;unt, <lb/>&amp; in minore circulo, maior: in maiore vero minor. </s> 
  
 <s>vt videre lice&shy;<lb/>bit in diagrammate hic de&longs;cripto &amp; &longs;uis rationibus nece&longs;&longs;ar&yuml;s con&shy;<lb/>firmato.<emph.end type="italics"/></s></p><p type="main"> 
  
 <s><emph type="italics"/>Sint duo circuli concentrici maior<emph.end type="italics"/> <foreign lang="greek">b d e y,</foreign> <emph type="italics"/>minor<emph.end type="italics"/> <foreign lang="greek">x m n c</foreign> <emph type="italics"/>&egrave; cen&shy;<lb/>tro a traiecti diametris<emph.end type="italics"/> <foreign lang="greek">x n &amp; b e.</foreign></s></p><p type="main"> 
  
 <s><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><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 pagenum="39"/><p type="main"> 
  
 <s><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></figure><p type="main"> 
  
 <s><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>parallelog.<emph.end type="italics"/></s></p><p type="main"> 
  
 <s><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>Sint autem<emph.end type="italics"/> <foreign lang="greek">w n, q z</foreign> <emph type="italics"/>perpendiculares ex fab. </s> 
  
 <s>&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><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 pagenum="40"/><p type="main"> 
  
 <s><emph type="italics"/>Sed &amp; &longs;i perficiantur parallelogramma<emph.end type="italics"/> <foreign lang="greek">d s t f &amp; d y r g</foreign>: <lb/><emph type="italics"/>illud erit vtile ad o&longs;tendendum<emph.end type="italics"/> <foreign lang="greek">d</foreign> <emph type="italics"/>tralatum vno motu v&longs;que ad<emph.end type="italics"/> <foreign lang="greek">s,</foreign><lb/><emph type="italics"/>altero motu, quo retrahitur ad centrum, reductum e&longs;&longs;e ad<emph.end type="italics"/> <foreign lang="greek">t</foreign>: <emph type="italics"/>&amp; <lb/>huius retractiones <expan abbr="men&longs;ur&atilde;">men&longs;uram</expan> e&longs;&longs;e<emph.end type="italics"/> <foreign lang="greek">s t</foreign> <emph type="italics"/>vel<emph.end type="italics"/> <foreign lang="greek">d f</foreign>: <emph type="italics"/>hoc vero vtile <expan abbr="eti&atilde;">etiam</expan> erit <lb/>ad terminandos motus illos duos <expan abbr="natural&etilde;">naturalem</expan>, &longs;cilicet &amp; pr&aelig;ter <expan abbr="natur&atilde;">naturam</expan>.<emph.end type="italics"/></s></p><p type="main"> 
  
 <s>Atque alterolongum.] <emph type="italics"/>Hoc <expan abbr="quadrilater&utilde;">quadrilaterum</expan> <expan abbr="oblong&utilde;">oblongum</expan>, &amp; rectan&shy;<lb/>gulum compleri debui&longs;&longs;e dici pote&longs;t, vt rectus in eo motus appareat, <lb/>quem facturus radius fui&longs;&longs;et, ni&longs;i retraheretur in centrum: tum vt <lb/>terminet motus eos, qui &longs;unt &longs;ecundum naturam &amp; pr&aelig;ter naturam.<emph.end type="italics"/></s></p><p type="main"> 
  
 <s><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 minor