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version 1.3, 2003/12/05 02:02:22 version 1.11, 2007/05/25 17:52:42
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 <?xml version="1.0"?> <?xml version="1.0" encoding="UTF-8"?>
 <!DOCTYPE archimedes SYSTEM "../dtd/archimedes.dtd" > <!DOCTYPE archimedes SYSTEM "../dtd/archimedes.dtd" >
 <archimedes xmlns:xlink="http://www.w3.org/1999/xlink">      <info> <archimedes xmlns:xlink="http://www.w3.org/1999/xlink">
    <info>
         <author>Biancani, Giuseppe</author>         <author>Biancani, Giuseppe</author>
         <title>Aristotelis loca mathematica</title>         <title>Aristotelis loca mathematica</title>
         <date>1615</date>         <date>1615</date>
         <place>Bologna</place>         <place>Bologna</place>
         <translator/>         <translator/>
         <lang>la</lang>         <lang>la</lang>
         <cvs_file>bianc_locam_009_la_1615.xml</cvs_file>     <cvs_file>bianc_locam_009_la_1615</cvs_file>
         <cvs_version/>         <cvs_version/>
         <locator>009.xml</locator>         <locator>009.xml</locator>
 </info>      <text>          <front>                            <pb xlink:href="009/01/001.jpg" /><section><p type="head">   </info>
    <text>
 <s id="id.000001">ARISTOTELIS<lb/>LOCA MATHEMATICA<lb/>Ex vniuer&longs;is ip&longs;ius Operibus collecta, <lb/>&amp; explicata.</s></p><p type="head">     <front>
        <pb xlink:href="009/01/001.jpg"/>
 <s id="id.000002"><emph type="italics"/>Aristotelic&aelig; videlicet expo&longs;itionis complementum <lb/>hactenus de&longs;ideratum.<emph.end type="italics"/></s></p><p type="head">       <section>
          <p type="head">
 <s id="id.000003">Acce&longs;&longs;ere de Natura Mathematicarum &longs;cientiarum Tractatio; <lb/><expan abbr="atq;">atque</expan> Clarorum Mathematicorum Chronologia.</s></p><p type="head">           <s id="s.000001">ARISTOTELIS <lb/>LOCA MATHEMATICA <lb/>
  Ex vniuer&longs;is ip&longs;ius Operibus collecta, <lb/>
 <s id="id.000004"><emph type="italics"/>Authore IOSEPHO BLANCANO Bononien&longs;i &egrave; Societate Ie&longs;u, <lb/>Mathematicarum in Gymna&longs;io Parmen&longs;i Profe&longs;&longs;ore.<emph.end type="italics"/></s></p><p type="head"> &amp; explicata.</s>
          </p>
 <s id="id.000005">Ad Illu&longs;tri&longs;&longs;imum, ac Nobili&longs;&longs;imum<lb/>PETRVMFRANCISCVM MALASPINAM<lb/>Aedificiorum Marchionem, apud C&aelig;&longs;. <!-- REMOVE S-->Maie&longs;tatem <lb/>pro Sereni&longs;s. <!-- REMOVE S-->Parmen&longs;ium Duce Legatum.</s>         <p type="head">
            <s id="s.000002"><emph type="italics"/>Aristotelic&aelig; videlicet expo&longs;itionis complementum <lb/>
  hactenus de&longs;ideratum.<emph.end type="italics"/></s>
          </p>
 </p><p type="head">         <p type="head">
            <s id="s.000003">Acce&longs;&longs;ere de Natura Mathematicarum &longs;cientiarum Tractatio; <lb/>
 <s id="id.000006">BONONI&AElig; M. <!-- REMOVE S-->D C. <!-- KEEP S--><!-- REMOVE S-->X V.<!-- KEEP S--></s> <expan abbr="atq;">atque</expan> Clarorum Mathematicorum Chronologia.</s>
          </p>
          <p type="head">
            <s id="s.000004"><emph type="italics"/>Authore IOSEPHO BLANCANO Bononien&longs;i &egrave; Societate Ie&longs;u, <lb/>
 </p><p type="head"> Mathematicarum in Gymna&longs;io Parmen&longs;i Profe&longs;&longs;ore.<emph.end type="italics"/></s>
          </p>
 <s id="id.000007">Apud Bartholom&aelig;um Cochium. <!-- KEEP S--></s>         <p type="head">
            <s id="s.000005">Ad Illu&longs;tri&longs;&longs;imum, ac Nobili&longs;&longs;imum <lb/>PETRVM FRANCISCVM MALASPINAM <lb/>
 <s id="id.000008">Superiorum permi&longs;&longs;u.</s></p><p type="head"> Aedificiorum Marchionem, apud C&aelig;&longs;. <!-- REMOVE S-->Maie&longs;tatem <lb/>
  pro Sereni&longs;s. <!-- REMOVE S-->Parmen&longs;ium Duce Legatum.</s>
 <s id="id.000009">Sumptibus Hieronymi Tamburini.</s></p><pb xlink:href="009/01/002.jpg" /><pb xlink:href="009/01/003.jpg" pagenum="3"/>         </p>
          <p type="head">
            <s id="s.000006">BONONI&AElig; M. <!-- REMOVE S-->D C. <!-- KEEP S--><!-- REMOVE S-->X V.<!-- KEEP S--></s>
          </p>
          <p type="head">
            <s id="s.000007">Apud Bartholom&aelig;um Cochium. <!-- KEEP S--></s>
            <s id="s.000008">Superiorum permi&longs;&longs;u.</s>
          </p>
          <p type="head">
            <s id="s.000009">Sumptibus Hieronymi Tamburini.</s>
          </p>
          <pb xlink:href="009/01/002.jpg"/>
          <pb pagenum="3" xlink:href="009/01/003.jpg"/>
 </section> </section>
 <section><p type="head"><s id="id.000010">ILLVSTRISSIMO <lb/>AC NOBILISSIMO<lb/>PETROFRANCISCO <lb/>MALASPINAE<lb/>&AElig;DIFICIORVM MARCHIONI.</s></p><p type="main">       <section>
          <p type="head">
 <s id="id.000011"><emph type="italics"/>En tandem Illustri&szlig;. <!-- REMOVE S-->Marchio opus no&shy;<lb/>strum de Locis Mathematicis apud Ari&shy;<lb/>stotelem, vn&agrave; cum Tractatione de natura <lb/>&longs;cientiarum Mathematicarum, necnon <lb/>Clarorum <expan abbr="Mathematicor&utilde;">Mathematicorum</expan> Chronologia; <lb/>quod tibi Mec&oelig;nati meo munificenti&longs;simo iure merit&ograve; <lb/>dicare, ac &longs;ub clari&szlig;imi tui nominis patrocinio in lucem <lb/>dare con&longs;titui. </s>           <s id="s.000010">ILLVSTRISSIMO <lb/>AC NOBILISSIMO <lb/>PETRO FRANCISCO <lb/>MALASPINAE <lb/>
  &AElig;DIFICIORVM MARCHIONI.</s>
          </p>
          <p type="main">
 <s id="id.000012">prim&ugrave;m quidem, vt mei perpetui erga te <lb/>amoris, &amp; ob&longs;eruanti&aelig; hoc vnum &longs;altem specimen exta&shy;<lb/>ret: t&ugrave;m vt idoneum, &aelig;quumque propo&longs;it&aelig; rei iudicem <lb/>nanci&longs;cerer. </s>           <s id="s.000011"><emph type="italics"/>En tandem Illustri&szlig;. <!-- REMOVE S-->Marchio opus no&shy;<lb/>
  strum de Locis Mathematicis apud Ari&shy;<lb/>
 <s id="id.000013">c&ugrave;m enim adiu&longs;tum <expan abbr="arbitr&utilde;">arbitrum</expan> duo poti&szlig;im&ugrave;m <lb/>requirantur, rerum &longs;cilicet cognitio, atque prudentia, quem <lb/>te rei, de qua agitur peritiorem, quemu&egrave; prudentiorem <lb/>inuenire potuerim? </s> stotelem, vn&agrave; cum Tractatione de natura <lb/>
  &longs;cientiarum Mathematicarum, necnon <lb/>
 <s id="id.000014">tu enim c&ugrave;m Phy&longs;iologi&aelig;, ac Mathe&shy;<lb/>maticarum omnium Encyclop&aelig;diam mirum in modum<emph.end type="italics"/><pb xlink:href="009/01/004.jpg" pagenum="4"/><emph type="italics"/>excolueris, adintima Mathematicarum penetralia ita <lb/>per&longs;ua&longs;i&longs;ti, vt Archimedis, &amp; Apollonij admirandis, ac <lb/>&longs;ubtili&szlig;imis Demon&longs;trationibus detinearis. </s> Clarorum <expan abbr="Mathematicor&utilde;">Mathematicorum</expan> Chronologia; <lb/>
  quod tibi Mec&oelig;nati meo munificenti&longs;simo iure merit&ograve; <lb/>
 <s id="id.000015">Quanta por&shy;<lb/>r&ograve; in rebus agendis prudentia valeas, toti pen&egrave; Europ&aelig; <lb/>innotuit, c&ugrave;m pro no&longs;tris Sereni&szlig;. <!-- REMOVE S-->Ducibus, non &longs;ol&ugrave;m ad <lb/>omnes fer&egrave; Itali&aelig;, atque Germani&aelig; Principes, ver&ugrave;m etiam <lb/>ad C&aelig;&longs;aream Maie&longs;tatem rebus f&oelig;liciter ge&longs;tis Legatus <lb/>decim&ugrave;m extiteris; ac dem&ugrave;m &agrave; Sereni&szlig;. <!-- REMOVE S-->Duce Ranutio <lb/>inter primarios de Rep. <!-- KEEP S--></s> dicare, ac &longs;ub clari&szlig;imi tui nominis patrocinio in lucem <lb/>
  dare con&longs;titui. </s>
            <s id="s.000012">prim&ugrave;m quidem, vt mei perpetui erga te <lb/>
  amoris, &amp; ob&longs;eruanti&aelig; hoc vnum &longs;altem specimen exta&shy;<lb/>
  ret: t&ugrave;m vt idoneum, &aelig;quumque propo&longs;it&aelig; rei iudicem <lb/>
  nanci&longs;cerer. </s>
 <s id="id.000016">Con&longs;iliorum Authores ad&longs;citus <lb/>fueris. </s>           <s id="s.000013">c&ugrave;m enim ad iu&longs;tum <expan abbr="arbitr&utilde;">arbitrum</expan> duo poti&szlig;im&ugrave;m <lb/>
  requirantur, rerum &longs;cilicet cognitio, atque prudentia, quem <lb/>
 <s id="id.000017">C&aelig;ter&ugrave;m in Clarorum Mathematicorum Chro&shy;<lb/>nologia perlegenda, &longs;&aelig;pi&szlig;im&egrave; tibi nobili&szlig;imi &aelig;qu&egrave;, ac do&shy;<lb/>cti&szlig;imi Viri, tui omnino per&longs;imiles occurrent, quod tibi <lb/>nonni&longs;i grati&szlig;imum accidere po&longs;&longs;e arbitror. </s> te rei, de qua agitur peritiorem, quemu&egrave; prudentiorem <lb/>
  inuenire potuerim? </s>
 <s id="id.000018">Complectere <lb/>igitur ea benignitate, atque clementia, qua &longs;oles no&longs;tra stu&shy;<lb/>dia promouere, mea h&aelig;c quantulacumque munu&longs;cula. <lb/></s>           <s id="s.000014">tu enim c&ugrave;m Phy&longs;iologi&aelig;, ac Mathe&shy;<lb/>
  maticarum omnium Encyclop&aelig;diam mirum in modum<emph.end type="italics"/> <pb pagenum="4" xlink:href="009/01/004.jpg"/><emph type="italics"/>excolueris, adintima Mathematicarum penetralia ita <lb/>
 <s id="id.000019">qu&aelig; &longs;i tibi accepta e&longs;&longs;e intellexero, iam tandem ma&shy;<lb/>ximorum munerum loco habenda e&longs;&longs;e cen&longs;e&shy;<lb/>bo. </s> per&longs;ua&longs;i&longs;ti, vt Archimedis, &amp; Apollonij admirandis, ac <lb/>
  &longs;ubtili&szlig;imis Demon&longs;trationibus detinearis. </s>
 <s id="id.000020">incolumem tibi, ac f&oelig;licem D. Opt. <lb/><!-- REMOVE S-->Max. <!-- REMOVE S-->long&aelig;uitatem tueatur. <lb/></s>           <s id="s.000015">Quanta por&shy;<lb/>
  r&ograve; in rebus agendis prudentia valeas, toti pen&egrave; Europ&aelig; <lb/>
  innotuit, c&ugrave;m pro no&longs;tris Sereni&szlig;. <!-- REMOVE S-->Ducibus, non &longs;ol&ugrave;m ad <lb/>
  omnes fer&egrave; Itali&aelig;, atque Germani&aelig; Principes, ver&ugrave;m etiam <lb/>
  ad C&aelig;&longs;aream Maie&longs;tatem rebus f&oelig;liciter ge&longs;tis Legatus <lb/>
  decim&ugrave;m extiteris; ac dem&ugrave;m &agrave; Sereni&szlig;. <!-- REMOVE S-->Duce Ranutio <lb/>
 <s id="id.000021">Vale.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main"> inter primarios de Rep. <!-- KEEP S--></s>
            <s id="s.000016">Con&longs;iliorum Authores ad&longs;citus <lb/>
 <s id="id.000022"><emph type="italics"/>Parm&aelig; Idibus Maij M. DC. XIIII.<emph.end type="italics"/><lb/><!-- KEEP S--></s></p></section><pb xlink:href="009/01/005.jpg" pagenum="5"/><section><p type="head"> fueris. </s>
            <s id="s.000017">C&aelig;ter&ugrave;m in Clarorum Mathematicorum Chro&shy;<lb/>
 <s id="id.000023">Liber de &longs;e ip&longs;o.</s></p><p type="head"> nologia perlegenda, &longs;&aelig;pi&szlig;im&egrave; tibi nobili&szlig;imi &aelig;qu&egrave;, ac do&shy;<lb/>
  cti&szlig;imi Viri, tui omnino per&longs;imiles occurrent, quod tibi <lb/>
 <s id="id.000024"><emph type="italics"/>Nec di&longs;cet Lector me &longs;olo interprete totum, <lb/>Nec &longs;ine me totum di&longs;cet Aristotelem.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main"> nonni&longs;i grati&szlig;imum accidere po&longs;&longs;e arbitror. </s>
            <s id="s.000018">Complectere <lb/>
 <s id="id.000025">Ego Iordanus Ca&longs;&longs;ini Pr&aelig;po&longs;itus Prouincialis Prouinci&aelig; Venet&aelig; Societatis <lb/>Ie&longs;u, ex auctoritate Adm. <!-- REMOVE S-->Reuer. <!-- REMOVE S-->P. nc&longs;tro Pr&aelig;po&longs;iti Generalis P. <!-- REMOVE S-->Claudij <lb/>Aqu&aelig;uiu&aelig;, facultatem concedo, vt hoc opus P. <!-- REMOVE S-->Io&longs;ephi Blancani eiu&longs;dem <lb/>Societatis, quod in&longs;cribitur, Ari&longs;t. Loca Mathematica ex vniuer&longs;is ip&longs;ius <lb/>operibus collecta, &amp; explicata, &agrave; deputatis Patribus recognitum, &amp; ap&shy;<lb/>probatum typis mandari po&longs;&longs;it. </s> igitur ea benignitate, atque clementia, qua &longs;oles no&longs;tra stu&shy;<lb/>
  dia promouere, mea h&aelig;c quantulacumque munu&longs;cula. <lb/>
  </s>
            <s id="s.000019">qu&aelig; &longs;i tibi accepta e&longs;&longs;e intellexero, iam tandem ma&shy;<lb/>
  ximorum munerum loco habenda e&longs;&longs;e cen&longs;e&shy;<lb/>
  bo. </s>
            <s id="s.000020">incolumem tibi, ac f&oelig;licem D. Opt. <lb/>
  <!-- REMOVE S-->Max. <!-- REMOVE S-->long&aelig;uitatem tueatur. <lb/>
  </s>
            <s id="s.000021">Vale.<emph.end type="italics"/><!-- KEEP S--></s>
 <s id="id.000026">Parm&aelig; die 15. Ianuarij 1615.</s></p><p type="main">         </p>
          <p type="main">
 <s id="id.000027"><emph type="italics"/>Iordanus Ca&longs;&longs;ini P.<emph.end type="italics"/><!-- REMOVE S-->Don Marcellus Balda&longs;&longs;inus pro Illu&longs;tri&longs;s. </s></p><p type="main">           <s id="s.000022"><emph type="italics"/>Parm&aelig; Idibus Maij M. DC. XIIII.<emph.end type="italics"/><lb/>
  <!-- KEEP S--></s>
          </p>
        </section>
 <s id="id.000028">&amp; Reuerendi&longs;s. <!-- REMOVE S-->Archiepi&longs;c. <!-- REMOVE S-->Bonon.</s>       <pb pagenum="5" xlink:href="009/01/005.jpg"/>
        <section>
          <p type="head">
            <s id="s.000023">Liber de &longs;e ip&longs;o.</s>
 </p><p type="main">         </p>
          <p type="head">
 <s id="id.000029">Imprimatur</s></p><p type="main">           <s id="s.000024"><emph type="italics"/>Nec di&longs;cet Lector me &longs;olo interprete totum, <lb/>
  Nec &longs;ine me totum di&longs;cet Aristotelem.<emph.end type="italics"/><!-- KEEP S--></s>
 <s id="id.000030">Fr. <!-- REMOVE S-->Hieronymus Onuphrius pro Reuerendi&longs;s. <!-- REMOVE S-->P. <!-- REMOVE S-->Inqui&longs;itore Bonon.</s>         </p>
          <p type="main">
            <s id="s.000025">Ego Iordanus Ca&longs;&longs;ini Pr&aelig;po&longs;itus Prouincialis Prouinci&aelig; Venet&aelig; Societatis <lb/>
  Ie&longs;u, ex auctoritate Adm. <!-- REMOVE S-->Reuer. <!-- REMOVE S-->P. no&longs;tro Pr&aelig;po&longs;iti Generalis P. <!-- REMOVE S-->Claudij <lb/>
  Aqu&aelig;uiu&aelig;, facultatem concedo, vt hoc opus P. <!-- REMOVE S-->Io&longs;ephi Blancani eiu&longs;dem <lb/>
  Societatis, quod in&longs;cribitur, Ari&longs;t. Loca Mathematica ex vniuer&longs;is ip&longs;ius <lb/>
 </p></section><pb xlink:href="009/01/006.jpg" pagenum="6"/><section><p type="head"> operibus collecta, &amp; explicata, &agrave; deputatis Patribus recognitum, &amp; ap&shy;<lb/>
  probatum typis mandari po&longs;&longs;it. </s>
 <s id="id.000031">LECTORI.</s></p><p type="main">           <s id="s.000026">Parm&aelig; die 15. Ianuarij 1615.</s>
          </p>
 <s id="id.000032">Qvod pri&longs;cis olim temporibus (humani&longs;&longs;ime Lector) &longs;um&shy;<lb/>mi duo Philo&longs;ophi, Philippus Mendeus, ac Theon Smyr&shy;<lb/>n&aelig;us in Platonis Dialogis egregi&egrave; perfecerunt, vt videli&shy;<lb/>cet qu&aelig; pa&longs;&longs;im &longs;ummus hic Philo&longs;ophus de Mathemati&shy;<lb/>cis &longs;cripta reliquit, eadem ip&longs;a ab illis &longs;electa, &amp; in vnum <lb/>qua&longs;i corpus redacta lucubrationibus illu&longs;trarent: idem ego quoque in <lb/>Ari&longs;totelis operibus efficere &longs;um conatus, vt qu&aelig; de Mathematicis re&shy;<lb/>bus in vniuer&longs;is eiu&longs;dem monumentis &longs;par&longs;a leguntur, eadem in vnum <lb/>&agrave; me collecta, &amp; explicata ijs Philo&longs;ophi&aelig; &longs;tudio&longs;is maxime &longs;eruirent, <lb/>qui pri&longs;ca illa con&longs;uetudine relicta, Mathematicarum omnium ignari <lb/>non &longs;ine graui &longs;tudiorum &longs;uorum detrimento Philo&longs;ophi&aelig; curriculum <lb/>aggrediuntur. </s>         <p type="main">
            <s id="s.000027"><emph type="italics"/>Iordanus Ca&longs;&longs;ini P.<emph.end type="italics"/><!-- REMOVE S--><lb/>
 <s id="id.000033">Vt autem huius operis nece&longs;&longs;itas, <expan abbr="vari&aelig;&qacute;">vari&aelig;que</expan>; vtilitates pla&shy;<lb/>nius cogno&longs;cantur oper&aelig;pretium erit initio illius cau&longs;as exponere; qu&aelig; <lb/>me poti&longs;&longs;imum ad illud con&longs;cribendum compulerunt, quarum</s></p><p type="main"> Don Marcellus Balda&longs;&longs;inus pro Illu&longs;tri&longs;s. </s>
            <s id="s.000028">&amp; Reuerendi&longs;s. <!-- REMOVE S-->Archiepi&longs;c. <!-- REMOVE S-->Bonon.</s>
 <s id="id.000034">Prima &longs;it, quod h&aelig;c Ari&longs;t.          </p>
          <p type="main">
 loca Mathematica, qu&aelig; quidem fer&egrave; 408. <lb/>numerantur, pe&longs;&longs;im&egrave; latinis literis con&longs;ignata &longs;unt v&longs;que ade&ograve;, vt Ari&shy;<lb/>&longs;totelem ip&longs;um, vel inuitum (quod po&longs;tea multis in locis planum fiet) in <lb/>ab&longs;urdi&longs;&longs;ima errata &longs;&aelig;pi&longs;&longs;im&egrave; compellant.</s></p><p type="main">           <s id="s.000029">Imprimatur</s>
            <s id="s.000030">Fr. <!-- REMOVE S-->Hieronymus Onuphrius pro Reuerendi&longs;s. <!-- REMOVE S-->P. <!-- REMOVE S-->Inqui&longs;itore Bonon.</s>
 <s id="id.000035">Secunda, qu&ograve;d plurima huiu&longs;modi loca &agrave; nemine, quod &longs;ciam, adhuc <lb/>declarata in tenebris magno no&longs;trorum malo delite&longs;cunt: cuiu&longs;modi <lb/>&longs;unt ad &longs;exaginta problemata, libellus de lineis in &longs;ecabilibus, libellus <lb/>de mundo, &longs;i tamen Ari&longs;totelis e&longs;t, &amp; Mechanic&aelig; qu&aelig;&longs;tiones, quamuis <lb/>enim Picolomineus in eas paraphra&longs;im ediderit, loca tamen earum dif&shy;<lb/>ficiliora non &longs;atis illu&longs;trauit. </s>         </p>
        </section>
 <s id="id.000036">Vt autem dixi 408. in vniuer&longs;um loca mi&shy;<lb/>nim&ugrave;m numerantur, quibus illud Platonis in&longs;criptum e&longs;t <foreign lang="greek">agaiome/trhtos <lb/>udei/s eisi/to</foreign>; &amp; in quibus Mathematic&aelig; di&longs;ciplin&aelig; rudes, &amp; imperiti, quem <lb/>&longs;equuntur ducem Ari&longs;t.        <pb pagenum="6" xlink:href="009/01/006.jpg"/>
        <section>
 eum &longs;&aelig;pe de&longs;erere non &longs;ine turpi dedecoris no&shy;<lb/>ta coguntur; quo fit vt exempla illa Mathematica lucem rebus aliquan&shy;<lb/>do allatura, tenebras cimmerijs, vt aiunt vmbris cra&longs;&longs;iores ij&longs;dem <lb/>obducant.</s></p><p type="main">         <p type="head">
            <s id="s.000031">LECTORI.</s>
 <s id="id.000037">Tertia, quia Gr&aelig;cieorumdem locorum commentatores breuiter, &amp; <lb/>ob&longs;cur&egrave; admodum ea, qu&aelig; ad Mathematicum &longs;pectant, attingunt, hoc <lb/>enim ab ip&longs;is <expan abbr="cert&utilde;">certum</expan> ponitur, Lectorem e&longs;&longs;e, vt moris tunc erat, omnium <lb/>Philo &longs;ophorum, Mathematicis imbutum; at ver&ograve; no&longs;tra &aelig;tate magna <lb/>cum Philo&longs;ophi&aelig; iactura, quamplurimi earumdem di&longs;ciplinarum de&longs;ti&shy;<lb/>tuti pr&aelig;&longs;idijs, ne Gr&aelig;corum quidem Interpretum explanationes, ne&shy;<lb/>dum Ari&longs;t.          </p>
          <p type="main">
 ob&longs;cur&egrave; dicta intelligunt.</s></p><pb xlink:href="009/01/007.jpg" pagenum="7"/><p type="main">           <s id="s.000032">Qvod pri&longs;cis olim temporibus &lpar;humani&longs;&longs;ime Lector&rpar; &longs;um&shy;<lb/>
  mi duo Philo&longs;ophi, Philippus Mendeus, ac Theon Smyr&shy;<lb/>
 <s id="id.000038">Quarta. </s> n&aelig;us in Platonis Dialogis egregi&egrave; perfecerunt, vt videli&shy;<lb/>
  cet qu&aelig; pa&longs;&longs;im &longs;ummus hic Philo&longs;ophus de Mathemati&shy;<lb/>
 <s id="id.000039">Adde, quod etiam &longs;i quis leuiter &longs;it erudito illo Mathemati&shy;<lb/>corum puluere con&longs;per&longs;us, ade&ograve; tamen peruer&longs;a e&longs;t eorumdem Gr&aelig;co&shy;<lb/>rum in Latinum tran&longs;latio, <expan abbr="tanta&qacute;">tantaque</expan>; figurarum, qu&aelig; nece&longs;&longs;ari&aelig; erant <lb/>confu&longs;io, &amp; deprauatio, vt nec abeo, qui &longs;it Mathematicarum &longs;cientia <lb/>excultus, &longs;ine magno labore percipi po&longs;&longs;int. </s> cis &longs;cripta reliquit, eadem ip&longs;a ab illis &longs;electa, &amp; in vnum <lb/>
  qua&longs;i corpus redacta lucubrationibus illu&longs;trarent: idem ego quoque in <lb/>
 <s id="id.000040">Quin etiam figur&aelig; ill&aelig;, qu&aelig; <lb/>omnino nece&longs;&longs;ari&aelig; &longs;unt ob Scriptorum, &amp; Typographorum in&longs;citiam, <lb/>aut inertiam pluribus in locis de&longs;iderantur. </s> Ari&longs;totelis operibus efficere &longs;um conatus, vt qu&aelig; de Mathematicis re&shy;<lb/>
  bus in vniuer&longs;is eiu&longs;dem monumentis &longs;par&longs;a leguntur, eadem in vnum <lb/>
 <s id="id.000041">Latini ver&ograve; multo minus, <lb/>qu&agrave;m Gr&aelig;ci Mathematic&aelig; periti, qua ratione eadem loca pertractaue&shy;<lb/>rint, facilius e&longs;t conijcere, qu&agrave;m vt dici oporteat.</s></p><p type="main"> &agrave; me collecta, &amp; explicata ijs Philo&longs;ophi&aelig; &longs;tudio&longs;is maxime &longs;eruirent, <lb/>
  qui pri&longs;ca illa con&longs;uetudine relicta, Mathematicarum omnium ignari <lb/>
 <s id="id.000042">Quinta. </s> non &longs;ine graui &longs;tudiorum &longs;uorum detrimento Philo&longs;ophi&aelig; curriculum <lb/>
  aggrediuntur. </s>
 <s id="id.000043">Ex his omnibus in aliud incommodum, vel maximum Phi&shy;<lb/>lo&longs;ophi quidam incidebant; aut enim horum locorum expo&longs;itionem ta&shy;<lb/>citi declinabant: aut eam minime nece&longs;&longs;ariam ad Ari&longs;t.            <s id="s.000033">Vt autem huius operis nece&longs;&longs;itas, <expan abbr="vari&aelig;&qacute;">vari&aelig;que</expan>; vtilitates pla&shy;<lb/>
  nius cogno&longs;cantur oper&aelig;pretium erit initio illius cau&longs;as exponere; qu&aelig; <lb/>
 percipiendam <lb/>&longs;ententiam a&longs;&longs;erebant; quo quid ab&longs;urdius, quid &longs;tudio&longs;orum progre&longs;&shy;<lb/>&longs;ibus pernicio&longs;ius excogitari pote&longs;t? </s> me poti&longs;&longs;imum ad illud con&longs;cribendum compulerunt, quarum</s>
          </p>
 <s id="id.000044">Eorum ver&ograve; nonnulli eorumdem <lb/>locorum expo&longs;itionem audacter nimis aggrediebantur, <expan abbr="atq;">atque</expan> hinc pueri&shy;<lb/>les ill&aelig;, ac ridicul&aelig; expo&longs;itiones pa&longs;&longs;im audit&aelig;, cuiu&longs;modi e&longs;t illa, quan&shy;<lb/>do Ari&longs;toteles ait, quod illi frequenti&longs;&longs;imum e&longs;t, omnis triangulus ha&shy;<lb/>bet tres; nihil aliud &longs;ignificari volunt, qu&agrave;m omnem triangulum habe&shy;<lb/>re tres angulos. </s>         <p type="main">
            <s id="s.000034">Prima &longs;it, quod h&aelig;c Ari&longs;t. loca Mathematica, qu&aelig; quidem fer&egrave; 408. <lb/>
 <s id="id.000045">quod &longs;i dicat, omnis triangulus habet tres &aelig;quales duo&shy;<lb/>bus rectis: hic h&aelig;rent, hinc anguntur: <expan abbr="cumq;">cumque</expan> ex his angu&longs;tijs, ac tricis <lb/>&longs;e minim&egrave; expedire valeant, aurea verba illa, quibus ingentes &longs;apienti&aelig; <lb/>the&longs;auri continentur, alto &longs;ilentij velo contegere Mathematicarum eos <lb/>cogit in&longs;citia: vnde illud, quod Gr&aelig;c&aelig; lingu&aelig; imperitis mutata oratio&shy;<lb/>ne acclamandum illis foret, Mathematicum e&longs;t, non legitur. </s> numerantur, pe&longs;&longs;im&egrave; latinis literis con&longs;ignata &longs;unt v&longs;que ade&ograve;, vt Ari&shy;<lb/>
  &longs;totelem ip&longs;um, vel inuitum &lpar;quod po&longs;tea multis in locis planum fiet&rpar; in <lb/>
 <s id="id.000046">Nec mi&shy;<lb/>nus elegans illa altera expo&longs;itio; Diametrum e&longs;&longs;e incommen&longs;urabilem <lb/>co&longs;t&aelig;; quod &longs;&aelig;pe apud Ari&longs;t.  ab&longs;urdi&longs;&longs;ima errata &longs;&aelig;pi&longs;&longs;im&egrave; compellant.</s>
          </p>
 legentibus occurrit, nihil aliud &longs;ibi velle, <lb/>quam Diametrum e&longs;&longs;e longiorem co&longs;ta, quam quidem a&longs;ymetri&aelig; huius <lb/>ignorantiam Plato de legibus dial. </s>         <p type="main">
            <s id="s.000035">Secunda, qu&ograve;d plurima huiu&longs;modi loca &agrave; nemine, quod &longs;ciam, adhuc <lb/>
 <s id="id.000047">7. non hominum, &longs;ed &longs;uum, <expan abbr="peco-rumq;">peco&shy;<lb/>rumque</expan> appellare non dubitauit. </s> declarata in tenebris magno no&longs;trorum malo delite&longs;cunt: cuiu&longs;modi <lb/>
  &longs;unt ad &longs;exaginta problemata, libellus de lineis in &longs;ecabilibus, libellus <lb/>
 <s id="id.000048">Quid illa? </s> de mundo, &longs;i tamen Ari&longs;totelis e&longs;t, &amp; Mechanic&aelig; qu&aelig;&longs;tiones, quamuis <lb/>
  enim Picolomineus in eas paraphra&longs;im ediderit, loca tamen earum dif&shy;<lb/>
 <s id="id.000049">cum Ari&longs;t.  ficiliora non &longs;atis illu&longs;trauit. </s>
            <s id="s.000036">Vt autem dixi 408. in vniuer&longs;um loca mi&shy;<lb/>
 ait duo cubi, cu&shy;<lb/>bus, ip&longs;um loqui putant de duplatione Geometrici cubi, nondum in&shy;<lb/>uenta; non intelligentes, eum ibi de numeris cubis &longs;ermonem habere. <lb/></s> nim&ugrave;m numerantur, quibus illud Platonis in&longs;criptum e&longs;t <foreign lang="greek">agaiome/trhtos <lb/>
  udei/s eisi/to</foreign>; &amp; in quibus Mathematic&aelig; di&longs;ciplin&aelig; rudes, &amp; imperiti, quem <lb/>
 <s id="id.000050">Auerroes ip&longs;e tantus vir 5. Phy&longs;. commen. <!-- REMOVE S-->15. qu&agrave;m &longs;e Mathematicis, <lb/>reliqui&longs;que Philo&longs;ophis irridendum pr&aelig;bet dum &agrave; permutata propor&shy;<lb/>tione putat &longs;erect&egrave; in hunc modum pluribus apud ip&longs;um verbis explica&shy;<lb/>tum, argumentari,</s> &longs;equuntur ducem Ari&longs;t. eum &longs;&aelig;pe de&longs;erere non &longs;ine turpi dedecoris no&shy;<lb/>
  ta coguntur; quo fit vt exempla illa Mathematica lucem rebus aliquan&shy;<lb/>
 </p><p type="main"> do allatura, tenebras cimmerijs, vt aiunt vmbris cra&longs;&longs;iores ij&longs;dem <lb/>
  obducant.</s>
 <s id="id.000051"><emph type="italics"/>Vt &longs;e habet voluntas noua ad effectum nouum, <lb/>It a voluntas antiqua ad effectum antiquum. <lb/></s>         </p>
          <p type="main">
 <s id="id.000052">Ergo permutatim, vt &longs;e habebit voluntas noua ad effectum <lb/>antiquum, ita voluntas antiqua ad effectum nouum.<emph.end type="italics"/></s></p><p type="main">           <s id="s.000037">Tertia, quia Gr&aelig;ci eorumdem locorum commentatores breuiter, &amp; <lb/>
  ob&longs;cur&egrave; admodum ea, qu&aelig; ad Mathematicum &longs;pectant, attingunt, hoc <lb/>
 <s id="id.000053"><expan abbr="Spectat&utilde;">Spectatum</expan> admi&longs;&longs;i ri&longs;um teneatis amici? </s> enim ab ip&longs;is <expan abbr="cert&utilde;">certum</expan> ponitur, Lectorem e&longs;&longs;e, vt moris tunc erat, omnium <lb/>
  Philo &longs;ophorum, Mathematicis imbutum; at ver&ograve; no&longs;tra &aelig;tate magna <lb/>
 <s id="id.000054">nego, ait; qui&longs;piam con&longs;equen&shy;<pb xlink:href="009/01/008.jpg" pagenum="8"/>tiam, non enim hoc e&longs;t argumentari &agrave; permutata ratione, deberet enim <lb/>inferre, &longs;ic, ergo ita &longs;e habebit voluntas noua ad antiquam, quemad&shy;<lb/>modum effectus nouus ad antiquum. </s> cum Philo&longs;ophi&aelig; iactura, quamplurimi earumdem di&longs;ciplinarum de&longs;ti&shy;<lb/>
  tuti pr&aelig;&longs;idijs, ne Gr&aelig;corum quidem Interpretum explanationes, ne&shy;<lb/>
 <s id="id.000055">qu&aelig; vitio&longs;a argumentatio quan&shy;<lb/>tumuis l&aelig;uis &longs;it, &amp; manife&longs;ta, quo&longs;dam tamen magni nominis philo&longs;o&shy;<lb/>phantes ade&ograve; tor&longs;it, vt adhuc torqueat.</s></p><p type="main"> dum Ari&longs;t. ob&longs;cur&egrave; dicta intelligunt.</s>
          </p>
 <s id="id.000056">Quanta autem mi&longs;eratione digni, qui public&egrave; aliquando apud &longs;uos <lb/>auditores totam Per&longs;pectiuam, qua nihil iucundius e&longs;t, de medio tolle&shy;<lb/>re conati &longs;unt, propterea quod ill&aelig; vi&longs;uales line&aelig;, illi anguli, ill&aelig; pyra&shy;<lb/>mides, aut coni, quibus vi&longs;io perficitur nullibi extarent, &longs;ed e&longs;&longs;ent vana <lb/>qu&aelig;dam opticorum figmenta. </s>         <pb pagenum="7" xlink:href="009/01/007.jpg"/>
          <p type="main">
 <s id="id.000057">Qu&igrave; ver&ograve; fieri potuit, vt non aduerterint <lb/>i&longs;ti &longs;e Ari&longs;toteli &longs;uo manife&longs;te repugnare, qui &longs;&aelig;pius de lineis vi&longs;ualibus <lb/>per&longs;pectiuum pertractare a&longs;&longs;erit, <expan abbr="di&longs;crimen&qacute;">di&longs;crimenque</expan>; inter lineam phy&longs;icam, &amp; <lb/>opticam a&longs;&longs;ignat, <expan abbr="ip&longs;ius&qacute;">ip&longs;iusque</expan>; optices tanquam ver&aelig; &longs;cienti&aelig; mentionem <lb/>&longs;&aelig;pius facit.</s></p><p type="main">           <s id="s.000038">Quarta. </s>
            <s id="s.000039">Adde, quod etiam &longs;i quis leuiter &longs;it erudito illo Mathemati&shy;<lb/>
 <s id="id.000058">Alij ex altera parte contra A&longs;tronomos in &longs;urgunt, eccentricos, <expan abbr="atq;">atque</expan> <lb/>epiciclos omnes de c&oelig;lo detrahere cupientes. </s> corum puluere con&longs;per&longs;us, ade&ograve; tamen peruer&longs;a e&longs;t eorumdem Gr&aelig;co&shy;<lb/>
  rum in Latinum tran&longs;latio, <expan abbr="tanta&qacute;">tantaque</expan>; figurarum, qu&aelig; nece&longs;&longs;ari&aelig; erant <lb/>
 <s id="id.000059">Verum id i&longs;ti nulla ex&shy;<lb/>pre&longs;&longs;a nedum probabili ratione faciunt, fals&ograve; exi&longs;timantes A&longs;tronomos <lb/>admirandam illam C&oelig;lorum fabricam a&longs;&longs;erere, non autem &longs;upponere: <lb/>&longs;ed a&longs;tronomi illam &longs;upponunt, <expan abbr="eam&qacute;">eamque</expan>; propterea hypothe&longs;im <expan abbr="appell&atilde;t">appellant</expan>, <lb/>non a&longs;&longs;erunt. </s> confu&longs;io, &amp; deprauatio, vt nec abeo, qui &longs;it Mathematicarum &longs;cientia <lb/>
  excultus, &longs;ine magno labore percipi po&longs;&longs;int. </s>
 <s id="id.000060">Quod &longs;i aliqua probabili ratione id facerent, vti nonnulli <lb/>ex recentioribus, quorum Ticho Coripheus e&longs;t, laudandi potius, quam <lb/>vituperandi e&longs;&longs;ent. </s>           <s id="s.000040">Quin etiam figur&aelig; ill&aelig;, qu&aelig; <lb/>
  omnino nece&longs;&longs;ari&aelig; &longs;unt ob Scriptorum, &amp; Typographorum in&longs;citiam, <lb/>
 <s id="id.000061">Impugnant <expan abbr="itaq;">itaque</expan> a&longs;tronomachi i&longs;ti hypothe&longs;im pro <lb/>a&longs;&longs;ertione; <expan abbr="tales&qacute;">talesque</expan>; &longs;&aelig;p&egrave; hi &longs;unt, vt non &longs;atis intelligant, quid &longs;it Aequa&shy;<lb/>tor, aut Zodiacus, ne dum quid Epiciclus, aut Eccentricus. </s> aut inertiam pluribus in locis de&longs;iderantur. </s>
            <s id="s.000041">Latini ver&ograve; multo minus, <lb/>
 <s id="id.000062">Nec defuit <lb/>qui viginti duo argumenta excogitarit, <expan abbr="atq;">atque</expan> in medium protulerit, qui&shy;<lb/>bus contra A&longs;tronomos probare conatus e&longs;t, nullo modo Solem, aut <lb/>Lunam moueri po&longs;&longs;e motibus contrarijs, ide&longs;t, ab oriente in <expan abbr="occid&etilde;tem">occidentem</expan> <lb/>motu diurno, &amp; proprio ab occidente in orientem. </s> qu&agrave;m Gr&aelig;ci Mathematic&aelig; periti, qua ratione eadem loca pertractaue&shy;<lb/>
  rint, facilius e&longs;t conijcere, qu&agrave;m vt dici oporteat.</s>
 <s id="id.000063">Sed exi&longs;timandum <lb/>e&longs;t <expan abbr="i&longs;t&utilde;">i&longs;tum</expan> Lunam nouam &agrave; Sole quotidie magis, ac magis ver&longs;us orientem <lb/>recedere, nunquam animaduerti&longs;&longs;e; ab ea enim hanc motuum concor&shy;<lb/>diam didici&longs;&longs;et.</s></p><p type="main">         </p>
          <p type="main">
 <s id="id.000064">Quid tandem <expan abbr="dic&etilde;dum">dicendum</expan> de quodam magni nominis Philo&longs;opho, om&shy;<lb/>nium tamen <expan abbr="Mathematicar&utilde;">Mathematicarum</expan> experte, qui in publica di&longs;putatione axio&shy;<lb/>ma illud Mathematicum, omne totum e&longs;t maius &longs;ua parte, in &longs;en&longs;u in <lb/>quo &agrave; Mathematicis effertur negare non erubuit, e&ograve;, quod in infinito, <lb/>vt aiebat non concederetur ab omnibus. </s>           <s id="s.000042">Quinta. </s>
            <s id="s.000043">Ex his omnibus in aliud incommodum, vel maximum Phi&shy;<lb/>
 <s id="id.000065">&longs;cilicet non intelligebat ma&shy;<lb/>thematicum tantummodo tractare de Quantitate finita, ac terminata, <lb/>in qua axioma pr&aelig;dictum ab omnibus conceditur. </s> lo&longs;ophi quidam incidebant; aut enim horum locorum expo&longs;itionem ta&shy;<lb/>
  citi declinabant: aut eam minime nece&longs;&longs;ariam ad Ari&longs;t. percipiendam <lb/>
 <s id="id.000066">Neque vero hic <lb/>nonnullorum infen&longs;us in Mathematicas animus quieuit, verum etiam <lb/>c&ograve; progre&longs;&longs;us e&longs;t, vt eas omnes omnino conuellere, atque ex albo &longs;cien&shy;<pb xlink:href="009/01/009.jpg" pagenum="9"/>tiarum, quamuis non Ari&longs;totele tantum, &longs;ed ip&longs;a etiam veritate repu&shy;<lb/>gnante, expungere conati &longs;int; <expan abbr="idq;">idque</expan> ne&longs;cio an vlla alia de cau&longs;a egerint, <lb/>qu&agrave;m quod eas non &longs;atis calerent; non &longs;ecus <expan abbr="atq;">atque</expan> Ae&longs;opica illa Vulpes, <lb/>qu&aelig; cum cauda mutilata e&longs;&longs;et, caudarum mutilationem reliquis vulpi&shy;<lb/>bus vafr&egrave; per&longs;uadere conabatur. </s> &longs;ententiam a&longs;&longs;erebant; quo quid ab&longs;urdius, quid &longs;tudio&longs;orum progre&longs;&shy;<lb/>
  &longs;ibus pernicio&longs;ius excogitari pote&longs;t? </s>
 <s id="id.000067">Verum enim ver&ograve; optim&egrave; &longs;cio, ea, <lb/>qu&ecedil; hactenus dicta &longs;unt non in omnes no&longs;tri temporis Philo&longs;ophos qua&shy;<lb/>drare, cum non pauci hodie quoque &longs;int, qui more antiquorum Mathe&shy;<lb/>maticis &longs;uffulti, optim&egrave; &longs;uis &longs;tudijs con&longs;ulentes, reliquam Philo&longs;ophiam <lb/>non &longs;ine magno compendio aggrediuntur. </s>           <s id="s.000044">Eorum ver&ograve; nonnulli eorumdem <lb/>
  locorum expo&longs;itionem audacter nimis aggrediebantur, <expan abbr="atq;">atque</expan> hinc pueri&shy;<lb/>
 <s id="id.000068">Quo fit, vt c&aelig;teros ageo&shy;<lb/>metretos ita antecellant, vt eorum Magi&longs;tri appellari po&longs;&longs;int, &amp; <expan abbr="debe&atilde;t">debeant</expan>; <lb/>tales fuerunt in primis Vicomercatus, Cardanus, Zabarella, Toletus, <lb/>Bonamicus, &amp; alij, quibus paulo antiquiores fuerunt D. Tho. <!-- REMOVE S-->&amp; Scotus, <lb/>Hiomnes Mathematicarum auxilio, quantum inter reliquos philo&longs;o&shy;<lb/>phantes excelluerint, nemo e&longs;t qui non nouerit. </s> les ill&aelig;, ac ridicul&aelig; expo&longs;itiones pa&longs;&longs;im audit&aelig;, cuiu&longs;modi e&longs;t illa, quan&shy;<lb/>
  do Ari&longs;toteles ait, quod illi frequenti&longs;&longs;imum e&longs;t, omnis triangulus ha&shy;<lb/>
  bet tres; nihil aliud &longs;ignificari volunt, qu&agrave;m omnem triangulum habe&shy;<lb/>
  re tres angulos. </s>
 <s id="id.000069">Illud hoc loco minim&egrave; <lb/>tacendum, Iacobum Zabarellam in &longs;uis logic&aelig; commentarijs te&longs;tari &longs;e <lb/>bis &longs;umma diligentia totum Euclidem perlegi&longs;&longs;e, vt perfect&egrave; Ari&longs;t.            <s id="s.000045">quod &longs;i dicat, omnis triangulus habet tres &aelig;quales duo&shy;<lb/>
  bus rectis: hic h&aelig;rent, hinc anguntur: <expan abbr="cumq;">cumque</expan> ex his angu&longs;tijs, ac tricis <lb/>
 de <lb/>demon&longs;tratione &longs;ententiam a&longs;&longs;equi po&longs;&longs;et.</s></p><p type="main"> &longs;e minim&egrave; expedire valeant, aurea verba illa, quibus ingentes &longs;apienti&aelig; <lb/>
  the&longs;auri continentur, alto &longs;ilentij velo contegere Mathematicarum eos <lb/>
 <s id="id.000070">Hi ridiculas illas, ac pueriles expo&longs;itiones &longs;uperius allatas minim&egrave; <lb/>effutierunt, neque reliquis &longs;upra recen&longs;itis incommodis obnoxij fue&shy;<lb/>runt, quibus magno etiam cum dedecore alij Mathematicarum ope ca&shy;<lb/>rentes afficiuntur.</s></p><p type="main"> cogit in&longs;citia: vnde illud, quod Gr&aelig;c&aelig; lingu&aelig; imperitis mutata oratio&shy;<lb/>
  ne acclamandum illis foret, Mathematicum e&longs;t, non legitur. </s>
 <s id="id.000071">In horum igitur gratiam operam diligenter dedi, vt quantum in me <lb/>e&longs;&longs;et damna &agrave; me &longs;upra enarrata aliqua ex parte re&longs;arcirem. </s>           <s id="s.000046">Nec mi&shy;<lb/>
  nus elegans illa altera expo&longs;itio; Diametrum e&longs;&longs;e incommen&longs;urabilem <lb/>
 <s id="id.000072">Quaprop&shy;<lb/>ter loca h&aelig;c mathematica num rect&egrave; e&longs;&longs;ent &egrave; gr&aelig;co in latinum tran&longs;lata  co&longs;t&aelig;; quod &longs;&aelig;pe apud Ari&longs;t. legentibus occurrit, nihil aliud &longs;ibi velle, <lb/>
 <lb/>diligenter prius expendi. </s> quam Diametrum e&longs;&longs;e longiorem co&longs;ta, quam quidem a&longs;ymetri&aelig; huius <lb/>
  ignorantiam Plato de legibus dial. 7. non hominum, &longs;ed &longs;uum, <expan abbr="peco-rumq;">peco&shy;<lb/>
 <s id="id.000073">Deinde claritate, qu&agrave;m potui maxima eadem  rumque</expan> appellare non dubitauit. </s>
 <lb/>loca interpretatus &longs;um, &amp; in horum, de quibus dixi gratiam, qu&aelig;dam            <s id="s.000047">Quid illa? </s>
 <lb/>fan&egrave; tenuia pro&longs;equutus &longs;um, qu&aelig; alioquin libenter omi&longs;i&longs;&longs;em. </s>           <s id="s.000048">cum Ari&longs;t. ait duo cubi, cu&shy;<lb/>
  bus, ip&longs;um loqui putant de duplatione Geometrici cubi, nondum in&shy;<lb/>
 <s id="id.000074">Tum fi&shy; uenta; non intelligentes, eum ibi de numeris cubis &longs;ermonem habere. <lb/>
 <lb/>guras omnes, aut correxi, aut re&longs;titui, aut nouas appo&longs;ui. </s> </s>
            <s id="s.000049">Auerroes ip&longs;e tantus vir 5. Phy&longs;. commen. <!-- REMOVE S-->15. qu&agrave;m &longs;e Mathematicis, <lb/>
 <s id="id.000075">Hocigitur  reliqui&longs;que Philo&longs;ophis irridendum pr&aelig;bet dum &agrave; permutata propor&shy;<lb/>
 <lb/>no&longs;tro qualicunque labore poterit qui&longs;que omnia illa facile intelligere,  tione putat &longs;erect&egrave; in hunc modum pluribus apud ip&longs;um verbis explica&shy;<lb/>
 <lb/><expan abbr="atq;">atque</expan> enumerata incommoda euitare, vnum tantummodo &agrave; Lectore ma&shy; tum, argumentari,</s>
 <lb/>thematicarum experte requiram, vt principia &longs;altem illa, &longs;cilicet defini&shy;         </p>
 <lb/>tiones, po&longs;tulata, &amp; axiomata, qu&aelig; prim&ograve; Euclideis libro pr&aelig;ponuntur,          <p type="main">
 <lb/>diligenter prius perlegat cum illa &longs;ua per&longs;picuitate omnibus &longs;int obuia;            <s id="s.000050"><emph type="italics"/>Vt &longs;e habet voluntas noua ad effectum nouum, <lb/>
 <lb/>c&aelig;tera ego explicanda recipio. </s> It a voluntas antiqua ad effectum antiquum. <lb/>
  </s>
 <s id="id.000076">Obiter etiam auctaria nonnulla partim            <s id="s.000051">Ergo permutatim, vt &longs;e habebit voluntas noua ad effectum <lb/>
 <lb/>mathematica, partim naturalia in&longs;erui, qu&aelig; ob nouitatem, ac pulchri&shy; antiquum, ita voluntas antiqua ad effectum nouum.<emph.end type="italics"/></s>
 <lb/>tudinem grata Lectori, atque iucunda fore exi&longs;timaui.</s></p><p type="main">         </p>
          <p type="main">
 <s id="id.000077">Sciat pr&aelig;terea Lector no&longs;trum in&longs;titutum e&longs;&longs;e loca h&aelig;c mathemati&shy;           <s id="s.000052"><expan abbr="Spectat&utilde;">Spectatum</expan> admi&longs;&longs;i ri&longs;um teneatis amici? </s>
 <lb/>ca, quatenus mathematica &longs;unt declarare, &longs;iue ea &longs;upplere, qu&aelig; ex ma&shy;           <s id="s.000053">nego, ait; qui&longs;piam con&longs;equen&shy;
 <lb/>thematicis petenda e&longs;&longs;ent: reliqua autem me tantum attingere, quan&shy; 
 <lb/>tum harum rerum cum illis connexio po&longs;tulat.</s></p><pb xlink:href="009/01/010.jpg" pagenum="10"/><p type="main"> 
  
 <s id="id.000078">His omnibus placuit appendices opportune nonnullas addere, qua&shy; 
 <lb/>rum prima de natura mathematicarum &longs;cientiarum: altera, qua omnes  
 <lb/>demon&longs;trationes primi libri Euclidis breuiter ad Logicam normam ex&shy; 
 <lb/>penduntur, vt pateat, quonam demon&longs;trationis genere <expan abbr="c&etilde;&longs;eri">cen&longs;eri</expan> <expan abbr="vnaqu&ecedil;q;">vnaqu&ecedil;que</expan>  
 <lb/>debeat, &amp; ex illis de c&aelig;teris iudicium fiat. </s> 
  
 <s id="id.000079">Tandem in gratiam etiam  
 <lb/>Mathematicorum tertiam appendicem appendi, qua omnia loca Ari&longs;t.  
 <lb/><!-- REMOVE S-->Geometrica ad Euclidis ordinem referuntur; vnde &amp; ip&longs;i ad &longs;uas pr&ecedil;le&shy; 
 <lb/>ctiones exornandas aliquid &longs;ubinde depromere queant.</s> 
  
 </p><p type="main"> 
  
 <s id="id.000080">Fruere igitur amice Lector hoc no&longs;tro qualiquali labore, quo ad ple&shy; 
 <lb/>nam totius Ari&longs;t.  
  
 intelligentiam, cui adhuc mathematicarum ignoratio  
 <lb/>ob&longs;titit peruenire tandem po&longs;&longs;is: <expan abbr="illud&qacute;">illudque</expan>; experiaris, quod optimus qui&shy; 
 <lb/>dam Philo&longs;ophus, cum totum hunc librum perlegi&longs;&longs;et, effatus e&longs;t, vide&shy; 
 <lb/>licet, opus hoc <emph type="italics"/>Aristot elic&aelig; expo&longs;itionis complementum ad hanc v&longs;que  
 <lb/>diem de&longs;ideratum<emph.end type="italics"/> iure ac merit&ograve; nuncupari po&longs;&longs;e.</s></p><p type="main"> 
  
 <s id="id.000081">Illud demum tanquam parergon addam, quod ego his elucubran&shy; 
 <lb/>dis experientia didici, ad veram &longs;cilicet, ac perfectam to&shy; 
 <lb/>tius Ari&longs;totelis intelligentiam lingu&aelig; in primis  
 <lb/>gr&aelig;c&aelig;, necnon mathematicarum om&shy; 
 <lb/>nium di&longs;ciplinarum haud medio&shy; 
 <lb/>crem cognitionem ne&shy; 
 <lb/>ce&longs;&longs;ariam e&longs;&longs;e.  
 <lb/></s> 
  
 <s id="id.000082">Vale.<!-- KEEP S--></s></p></section><pb xlink:href="009/01/011.jpg" pagenum="11"/><section><p type="head"> 
  
 <s id="id.000083">Pr&ecedil;cipua qu&ecedil;dam, aut noua, autre&longs;taurata,  
 <lb/>qu&aelig; obiter pertractantur. 
 <lb/><arrow.to.target n="table1"/></s></p><table><table.target id="table1"/><row><cell><emph type="italics"/>1<emph.end type="italics"/></cell><cell><emph type="italics"/>De re&longs;olutione. numero marginali.<emph.end type="italics"/></cell><cell><emph type="italics"/>4<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>2<emph.end type="italics"/></cell><cell><emph type="italics"/>De figuris vacuum replentibus, vbi Aristotelis, &amp; expo-&longs;itorum erratum aperitur. num.<emph.end type="italics"/></cell><cell><emph type="italics"/>121<emph.end type="italics"/></cell></row><row><cell/><cell><emph type="italics"/>Inibi, Apum mirabilis qu&aelig;dam in cellis &longs;uis hexagonis   constituendis indu&longs;tria detegitur. num.<emph.end type="italics"/></cell><cell><emph type="italics"/>120<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>3<emph.end type="italics"/></cell><cell><emph type="italics"/>De ijs, qu&aelig; aqu&aelig; in&longs;ident, vn&agrave; cum noua demonstratione problema-tis illius Archimedis, quo metallorum mixtionem indi&longs;&longs;oluta Co-rona, explorauit. in additione. ante num.<emph.end type="italics"/></cell><cell><emph type="italics"/>124<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>4<emph.end type="italics"/></cell><cell><emph type="italics"/>De Cometa, recentiorum &longs;ententia. num.<emph.end type="italics"/></cell><cell><emph type="italics"/>136<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>5<emph.end type="italics"/></cell><cell><emph type="italics"/>De altitudine montis Cauca&longs;i.<emph.end type="italics"/></cell><cell><emph type="italics"/>148<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>6<emph.end type="italics"/></cell><cell><emph type="italics"/>De Terr&aelig; rotunditate, ac mundi duratione.<emph.end type="italics"/></cell><cell><emph type="italics"/>151<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>7<emph.end type="italics"/></cell><cell><emph type="italics"/>De Iride. in additione.<emph.end type="italics"/></cell><cell><emph type="italics"/>181<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>8<emph.end type="italics"/></cell><cell><emph type="italics"/>Scytala quid.<emph.end type="italics"/></cell><cell><emph type="italics"/>250<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>9<emph.end type="italics"/></cell><cell><emph type="italics"/>Securis antiqua qu&aelig;, &amp; qua ratione fieret.<emph.end type="italics"/></cell><cell><emph type="italics"/>258<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>10<emph.end type="italics"/></cell><cell><emph type="italics"/>Statera antiqua qu&aelig;,<emph.end type="italics"/></cell><cell><emph type="italics"/>259<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>11<emph.end type="italics"/></cell><cell><emph type="italics"/>De Ae&longs;tu Maris.<emph.end type="italics"/></cell><cell><emph type="italics"/>272<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>12<emph.end type="italics"/></cell><cell><emph type="italics"/>Araneorum indu&longs;tria nuper patefacta: vbi Democritus contra Ari&longs;t.   defenditur.<emph.end type="italics"/></cell><cell><emph type="italics"/>293<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>13<emph.end type="italics"/></cell><cell><emph type="italics"/>De Lucis figuratione, &amp; rerum &longs;imulacris in ob&longs;curo loco.<emph.end type="italics"/></cell><cell><emph type="italics"/>345<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>14<emph.end type="italics"/></cell><cell><emph type="italics"/>De Pupilla oculi.<emph.end type="italics"/></cell><cell><emph type="italics"/>408<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>15<emph.end type="italics"/></cell><cell><emph type="italics"/>De Mathematicarum natura. prop&egrave; finem operis.<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>16<emph.end type="italics"/></cell><cell><emph type="italics"/>Clarorum Mathematicorum Chronologia, in fine operis.<emph.end type="italics"/></cell><cell/></row></table></section><pb xlink:href="009/01/012.jpg" pagenum="12"/><section><p type="head"> 
  
 <s id="id.000084"><emph type="italics"/>PRIMVS INDEX LOCORVM ARIST.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="head"> 
  
 <s id="id.000085"><emph type="italics"/>Qu&aelig; in hoc opere explicantur, iuxta ordine librorum  
 <lb/>ip&longs;ius ex vulgata editione Lugdunen&longs;i.<emph.end type="italics"/></s></p><p type="head"> 
  
 <s id="id.000086">In Pr&aelig;dicamentis.</s></p><p type="main"> 
  
 <s id="id.000087"><emph type="italics"/>Gapite s. </s> 
  
 <s id="id.000088">de Relatione, vbi de Quadratura circuli.<emph.end type="italics"/></s></p><p type="main"> 
  
 <s id="id.000089"><emph type="italics"/>Cap.  
  
 de Priori, vbi de Principijs Mathematicarum,<emph.end type="italics"/></s></p><p type="main"> 
  
 <s id="id.000090"><emph type="italics"/>Cap.  
  
 de Motu, vbi de Gnomone.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="head"> 
  
 <s id="id.000091">In Primo Priorum Re&longs;olutoriorum.</s></p><p type="main"> 
  
 <s id="id.000092"><emph type="italics"/>Ad titulum libri de Re&longs;olutione.<emph.end type="italics"/></s></p><p type="main"> 
  
 <s id="id.000093"><emph type="italics"/>Cap.  
  
 23. &longs;ect 1. libri 1. de Incommen &longs;ur abilibus.<emph.end type="italics"/></s></p><p type="main"> 
  
 <s id="id.000094"><emph type="italics"/>Cap.  
  
 24. &longs;ecti 1. lib.  
  
 1. de De&longs;criptionibus.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main"> 
  
 <s id="id.000095"><emph type="italics"/>Cap.  
  
 2. &longs;ect 2. lib.  
  
 1. de De&longs;criptionibus.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main"> 
  
 <s id="id.000096"><emph type="italics"/>Cap.  
  
 3. &longs;ecti 2. lib.  
  
 1. de Incommen&longs;urabili.<emph.end type="italics"/></s></p><p type="main"> 
  
 <s id="id.000097"><emph type="italics"/>Cap.  
  
 1. &longs;ecti 3. lib.  
  
 1. de eo, quod est, omnis triangulus habet tres angulos &aelig;quales  
 <lb/>&aelig;quales duobus rectis: Aequalitas Geometrica, qu&aelig;.<emph.end type="italics"/></s></p><p type="main"> 
  
 <s id="id.000098"><emph type="italics"/>Cap.  
  
 eodem, de exemplis, quibus vtuntar Geometr&aelig;.<emph.end type="italics"/></s></p><p type="head"> 
  
 <s id="id.000099">In &longs;ecundo Priorum Re&longs;ol.<!-- REMOVE S--><emph type="italics"/>Cap.  
  
 21. de lineis Paralellis, &longs;eu Coalternis.<emph.end type="italics"/></s></p><p type="main"> 
  
 <s id="id.000100"><emph type="italics"/>Cap.  
  
 eodem. </s> 
  
 <s id="id.000101">de Paralellis, &amp; de triangulo.<emph.end type="italics"/></s></p><p type="main"> 
  
 <s id="id.000102"><emph type="italics"/>Cap.  
  
 26. Quod omnis triangulus habet tres, &amp; c.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main"> 
  
 <s id="id.000103"><emph type="italics"/>Cap.  
  
 31. de Abductione.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main"> 
  
 <s id="id.000104"><emph type="italics"/>Cap.  
  
 codem, de circuli Quadratura, &longs;ecundum Hippocratem Chium.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="head"> 
  
 <s id="id.000105">In primo Po&longs;teriorum.</s></p><p type="main"> 
  
 <s id="id.000106"><emph type="italics"/>Textu primo, De Pr&aelig;cognitis Mathematicarum.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main"> 
  
 <s id="id.000107"><emph type="italics"/>T. 2. Omnis triangulus habet tres, &amp; c.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main"> 
  
 <s id="id.000108"><emph type="italics"/>T. 5. De Diametro incommen&longs;urabili. </s> 
  
 <s id="id.000109">Item De Mathematicarum Principijs.<emph.end type="italics"/></s></p><p type="main"> 
  
 <s id="id.000110"><emph type="italics"/>T. eodem, De Indiui&longs;ibilitate vnitatis.<emph.end type="italics"/></s></p><p type="main"> 
  
 <s id="id.000111"><emph type="italics"/>T. 9. De Puncto, &amp; linea. </s> 
  
 <s id="id.000112">Item de recto, &amp; circulari. </s> 
  
 <s id="id.000113">Item de numero pari, impari; 
 <lb/>primo, &amp; compo&longs;ito; &aelig;quilatero, &amp; altera parte longiore.<emph.end type="italics"/></s></p><p type="main"> 
  
 <s id="id.000114"><emph type="italics"/>T. 11. Line&aelig; punctum inest per &longs;e, &amp; c.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main"> 
  
 <s id="id.000115"><emph type="italics"/>T. 13. De Parallelis. <!-- KEEP S--></s> 
  
 <s id="id.000116">De I&longs;o&longs;cele. </s> 
  
 <s id="id.000117">De Alterna Proportione,  
 <lb/>Item quod omnis triangulus habet tres, &amp; c.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main"> 
  
 <s id="id.000118"><emph type="italics"/>T. 14. De ij&longs;dem cum pr&aelig;cedentibus.<emph.end type="italics"/></s></p><p type="main"> 
  
 <s id="id.000119"><emph type="italics"/>T. 20. Magnitudines euadunt numeri. </s> 
  
 <s id="id.000120">Item, quod non duo cubi cubus. </s> 
  
 <s id="id.000121">Item de  
 <lb/>Mathematicis &longs;ubalternatis.<emph.end type="italics"/></s></p><p type="main"> 
  
 <s id="id.000122"><emph type="italics"/>T. 23. Quadratura circuli &longs;ecundum Bry&longs;onem. </s> 
  
 <s id="id.000123">Item per&longs;ectam illam e&longs;&longs;e Demon&shy; 
 <lb/>&longs;trationem, qua Geometr&aelig; o&longs;tendunt, quod Omnis triangulus habet tres, &amp; c.  
 <lb/><!-- KEEP S--></s> 
  
 <s id="id.000124">Per&longs;pectinam, &amp; Mechanicam &longs;ubalternari Geometri&aelig;, Mu&longs;icam, Arithmetic&aelig;.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main"> 
  
 <s id="id.000125"><emph type="italics"/>T. 24. De numero pari, impari, quodrangulo, cubo. </s> 
  
 <s id="id.000126">In Geometria quid irrationale,  
 <lb/>refrangi, concurrere. </s> 
  
 <s id="id.000127">Quid Astronomia con&longs;ideret.<emph.end type="italics"/></s></p><p type="main"> 
  
 <s id="id.000128"><emph type="italics"/>T. 25. Geometram non mentiri in &longs;uis exemplis.<emph.end type="italics"/></s></p><p type="main"> 
  
 <s id="id.000129"><emph type="italics"/>T. 28. De Parallelis.<emph.end type="italics"/><!-- KEEP S--></s></p><pb xlink:href="009/01/013.jpg" pagenum="13"/><p type="main"> 
  
 <s id="id.000130"><emph type="italics"/>T. 29. Cur in Mathematicis non &longs;it Paralogi&longs;mus. <!-- KEEP S--></s> 
  
 <s id="id.000131">Item quid multiplicata propor&shy; 
 <lb/>tio. </s> 
  
 <s id="id.000132">Quid C&aelig;neus dixerit. </s> 
  
 <s id="id.000133">Cur Affectiones <expan abbr="Mathematicor&utilde;">Mathematicor&utilde;</expan> maxim&egrave; <expan abbr="conuert&atilde;tur">conuertantur</expan>.<emph.end type="italics"/></s></p><p type="main"> 
  
 <s id="id.000134"><emph type="italics"/>T. 30. De Lun&aelig; &longs;ph&aelig;ricitate. </s> 
  
 <s id="id.000135">Quid &longs;tereometria. </s> 
  
 <s id="id.000136">&amp; De &longs;ubalternatione, &amp;c. </s> 
  
 <s id="id.000137">&amp; Ma&shy; 
 <lb/>thematicorum e&longs;t &longs;cire Propter quid: &longs;en&longs;itiuorum ver&ograve; &longs;cire Quod.<emph.end type="italics"/></s></p><p type="main"> 
  
 <s id="id.000138"><emph type="italics"/>T. 37. I&longs;o&longs;celes, &amp; Scalenum habere tres &aelig;quales, &amp;c.<emph.end type="italics"/></s></p><p type="main"> 
  
 <s id="id.000139"><emph type="italics"/>T. 38. Quid Mina, quid Die&longs;is.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main"> 
  
 <s id="id.000140"><emph type="italics"/>T. 39. Habere tres angulos &aelig;quales, &amp;c. </s> 
  
 <s id="id.000141">Item, quod omnis figura habet &longs;uos angu&shy; 
 <lb/>los externos &aelig;quales quatuor tantum rectis.<emph.end type="italics"/></s></p><p type="main"> 
  
 <s id="id.000142"><emph type="italics"/>T. 43. Triangulum tres &aelig;quales, &amp;c. </s> 
  
 <s id="id.000143">De Eclyp&longs;i.<emph.end type="italics"/></s></p><p type="main"> 
  
 <s id="id.000144"><emph type="italics"/>De combu&longs;tione per refractionem ex &longs;ph&aelig;ra vitrea. </s> 
  
 <s id="id.000145">De principijs &longs;cientiarum.<emph.end type="italics"/></s></p><p type="main"> 
  
 <s id="id.000146"><emph type="italics"/>T. 44. Diameter incommen&longs;urabilis.<emph.end type="italics"/></s></p><p type="head"> 
  
 <s id="id.000147">In 2. Po&longs;teriorum.</s></p><p type="main"> 
  
 <s id="id.000148"><emph type="italics"/>T. 1. Aequalitas, &amp; in&aelig;qualitas. </s> 
  
 <s id="id.000149">Terram e&longs;&longs;e in medio mundi ab A&longs;tronomis per&shy; 
 <lb/>fect&egrave; demon&longs;tratur. </s> 
  
 <s id="id.000150">Item Quid con&longs;onantia.<emph.end type="italics"/></s></p><p type="main"> 
  
 <s id="id.000151"><emph type="italics"/>T. 2. Omnis triangulus habet tres, &amp;c. </s> 
  
 <s id="id.000152">Item de Definitionibus Mathematicarum.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main"> 
  
 <s id="id.000153"><emph type="italics"/>T. 7. Geometra, qu&aelig;dam accipit, qu&aelig;dam demon&longs;trat.<emph.end type="italics"/></s></p><p type="main"> 
  
 <s id="id.000154"><emph type="italics"/>T. 11. Angulum in &longs;emicirculo rectum e&longs;&longs;e probari &agrave; Geometra per cau&longs;am materia&shy; 
 <lb/>lem. </s> 
  
 <s id="id.000155">Zabarella correctus.<emph.end type="italics"/></s></p><p type="main"> 
  
 <s id="id.000156"><emph type="italics"/>T. 24. Echo, Imago &egrave; &longs;peculo, Iris.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main"> 
  
 <s id="id.000157"><emph type="italics"/>T. 25. Permutatim proportionale quid; exemplum in triangulis.<emph.end type="italics"/></s></p><p type="head"> 
  
 <s id="id.000158">In primo lib. <!-- REMOVE S-->Topicorum.</s> 
  
 </p><p type="main"> 
  
 <s id="id.000159"><emph type="italics"/>Cap.  
  
 13. Diameter est incommen&longs;urabilis. </s> 
  
 <s id="id.000160">Vox acuta velox, cur. </s> 
  
 <s id="id.000161">&amp;c. </s> 
  
 <s id="id.000162">Colores in  
 <lb/>Mu&longs;ica, qui. </s> 
  
 <s id="id.000163">tria genera veteris Mu&longs;ic&aelig;.<emph.end type="italics"/></s></p><p type="head"> 
  
 <s id="id.000164">In 4. libro.</s></p><p type="main"> 
  
 <s id="id.000165"><emph type="italics"/>Cap.  
  
 1. loco 1. line&aelig; in&longs;ecabiles.<emph.end type="italics"/></s></p><p type="head"> 
  
 <s id="id.000166">In 6. libro.</s></p><p type="main"> 
  
 <s id="id.000167"><emph type="italics"/>Cap.  
  
 2. loco 32. Definitio line&aelig;.<emph.end type="italics"/></s></p><p type="head"> 
  
 <s id="id.000168">In 8. libro.</s></p><p type="main"> 
  
 <s id="id.000169"><emph type="italics"/>Cap.  
  
 2. loco 41. V&longs;us Definitionum in Mathematicis.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main"> 
  
 <s id="id.000170"><emph type="italics"/>Cap.  
  
 4. loco 86. Elementa geometrica: Numeri capitales.<emph.end type="italics"/></s></p><p type="head"> 
  
 <s id="id.000171">In Elenchorum lib.  
  
 1.<!-- KEEP S--></s></p><p type="main"> 
  
 <s id="id.000172"><emph type="italics"/>Cap.  
  
 10. Quid P&longs;eudographia. </s> 
  
 <s id="id.000173">Quadraturarur&longs;us Hippocratis, &amp; Bry&longs;enis. </s> <pb pagenum="8" xlink:href="009/01/008.jpg"/>tiam, non enim hoc e&longs;t argumentari &agrave; permutata ratione, deberet enim <lb/>
  inferre, &longs;ic, ergo ita &longs;e habebit voluntas noua ad antiquam, quemad&shy;<lb/>
 <s id="id.000174">Mathe&shy; modum effectus nouus ad antiquum. </s>
 <lb/>matic&aelig; non contentio&longs;&aelig;. </s>           <s id="s.000054">qu&aelig; vitio&longs;a argumentatio quan&shy;<lb/>
  tumuis l&aelig;uis &longs;it, &amp; manife&longs;ta, quo&longs;dam tamen magni nominis philo&longs;o&shy;<lb/>
 <s id="id.000175">Quadratio Antiphontis.<emph.end type="italics"/></s></p><p type="head"> phantes ade&ograve; tor&longs;it, vt adhuc torqueat.</s>
          </p>
 <s id="id.000176">Ex 1. Phy&longs;ic.<!-- KEEP S--></s></p><p type="main">         <p type="main">
            <s id="s.000055">Quanta autem mi&longs;eratione digni, qui public&egrave; aliquando apud &longs;uos <lb/>
 <s id="id.000177"><emph type="italics"/>T. 11. De Quadraturis circuli Hippocratis, &amp; Antiphontis.<emph.end type="italics"/></s></p><p type="head"> auditores totam Per&longs;pectiuam, qua nihil iucundius e&longs;t, de medio tolle&shy;<lb/>
  re conati &longs;unt, propterea quod ill&aelig; vi&longs;uales line&aelig;, illi anguli, ill&aelig; pyra&shy;<lb/>
 <s id="id.000178">Ex 2. Phy&longs;ic.<!-- KEEP S--></s></p><p type="main"> mides, aut coni, quibus vi&longs;io perficitur nullibi extarent, &longs;ed e&longs;&longs;ent vana <lb/>
  qu&aelig;dam opticorum figmenta. </s>
 <s id="id.000179"><emph type="italics"/>T. 20. Quatenus Per&longs;pectmus con&longs;ideret lineam.<emph.end type="italics"/></s></p><p type="main">           <s id="s.000056">Qu&igrave; ver&ograve; fieri potuit, vt non aduerterint <lb/>
  i&longs;ti &longs;e Ari&longs;toteli &longs;uo manife&longs;te repugnare, qui &longs;&aelig;pius de lineis vi&longs;ualibus <lb/>
 <s id="id.000180"><emph type="italics"/>T. 28. Quid con&longs;onantia Diapa&longs;on.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main"> per&longs;pectiuum pertractare a&longs;&longs;erit, <expan abbr="di&longs;crimen&qacute;">di&longs;crimenque</expan>; inter lineam phy&longs;icam, &amp; <lb/>
  opticam a&longs;&longs;ignat, <expan abbr="ip&longs;ius&qacute;">ip&longs;iusque</expan>; optices tanquam ver&aelig; &longs;cienti&aelig; mentionem <lb/>
 <s id="id.000181"><emph type="italics"/>T. 68. Mathematicas Demon&longs;trationes babere cau&longs;am, qu&aelig; reducitur ad defini&shy; &longs;&aelig;pius facit.</s>
 <lb/>tionem.<emph.end type="italics"/></s></p><p type="main">         </p>
          <p type="main">
 <s id="id.000182"><emph type="italics"/>T. 8. De nece&longs;&longs;ario, quod e&longs;t in Mathematicis. <!-- KEEP S--></s>           <s id="s.000057">Alij ex altera parte contra A&longs;tronomos in &longs;urgunt, eccentricos, <expan abbr="atq;">atque</expan> <lb/>
  epiciclos omnes de c&oelig;lo detrahere cupientes. </s>
 <s id="id.000183">&amp; omnis triangulus habet tres an&shy;           <s id="s.000058">Verum id i&longs;ti nulla ex&shy;<lb/>
 <lb/>gulos, &amp;c.<emph.end type="italics"/></s></p><p type="head"> pre&longs;&longs;a nedum probabili ratione faciunt, fals&ograve; exi&longs;timantes A&longs;tronomos <lb/>
  admirandam illam C&oelig;lorum fabricam a&longs;&longs;erere, non autem &longs;upponere: <lb/>
 <s id="id.000184">Ex 3. Phy&longs;ic.<!-- KEEP S--></s></p><p type="main"> &longs;ed a&longs;tronomi illam &longs;upponunt, <expan abbr="eam&qacute;">eamque</expan>; propterea hypothe&longs;im <expan abbr="appell&atilde;t">appellant</expan>, <lb/>
  non a&longs;&longs;erunt. </s>
 <s id="id.000185"><emph type="italics"/>T. 76. Quinam numeri dicantur Gnomones.<emph.end type="italics"/></s></p><p type="main">           <s id="s.000059">Quod &longs;i aliqua probabili ratione id facerent, vti nonnulli <lb/>
  ex recentioribus, quorum Ticho Coripheus e&longs;t, laudandi potius, quam <lb/>
 <s id="id.000186"><emph type="italics"/>T. 31. Quonam infinito vtantur Mathematici.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main"> vituperandi e&longs;&longs;ent. </s>
            <s id="s.000060">Impugnant <expan abbr="itaq;">itaque</expan> a&longs;tronomachi i&longs;ti hypothe&longs;im pro <lb/>
 <s id="id.000187"><emph type="italics"/>T. 71. De infinito Mathematica.<emph.end type="italics"/><!-- KEEP S--></s></p><pb xlink:href="009/01/014.jpg" pagenum="14"/><p type="head"> a&longs;&longs;ertione; <expan abbr="tales&qacute;">talesque</expan>; &longs;&aelig;p&egrave; hi &longs;unt, vt non &longs;atis intelligant, quid &longs;it Aequa&shy;<lb/>
  tor, aut Zodiacus, ne dum quid Epiciclus, aut Eccentricus. </s>
 <s id="id.000188">Ex 4. Phy&longs;ic.<!-- KEEP S--></s></p><p type="main">           <s id="s.000061">Nec defuit <lb/>
  qui viginti duo argumenta excogitarit, <expan abbr="atq;">atque</expan> in medium protulerit, qui&shy;<lb/>
 <s id="id.000189"><emph type="italics"/>T. 120. De commen&longs;urab. </s> bus contra A&longs;tronomos probare conatus e&longs;t, nullo modo Solem, aut <lb/>
  Lunam moueri po&longs;&longs;e motibus contrarijs, ide&longs;t, ab oriente in <expan abbr="occid&etilde;tem">occidentem</expan> <lb/>
 <s id="id.000190">&amp; incommen&longs;.<emph.end type="italics"/></s></p><p type="head"> motu diurno, &amp; proprio ab occidente in orientem. </s>
            <s id="s.000062">Sed exi&longs;timandum <lb/>
 <s id="id.000191">Ex 5. Phy&longs;ic.<!-- KEEP S--></s></p><p type="main"> e&longs;t <expan abbr="i&longs;t&utilde;">i&longs;tum</expan> Lunam nouam &agrave; Sole quotidie magis, ac magis ver&longs;us orientem <lb/>
  recedere, nunquam animaduerti&longs;&longs;e; ab ea enim hanc motuum concor&shy;<lb/>
 <s id="id.000192"><emph type="italics"/>T. 6. De chordis, graui, acuta; media, &amp; vltima.<emph.end type="italics"/></s></p><p type="head"> diam didici&longs;&longs;et.</s>
          </p>
 <s id="id.000193">Ex 8. Phy&longs;ic.<!-- KEEP S--></s></p><p type="main">         <p type="main">
            <s id="s.000063">Quid tandem <expan abbr="dic&etilde;dum">dicendum</expan> de quodam magni nominis Philo&longs;opho, om&shy;<lb/>
 <s id="id.000194"><emph type="italics"/>T. 15. Omnis triangulus habet tres &aelig;quales, &amp;c.<emph.end type="italics"/></s></p><p type="head"> nium tamen <expan abbr="Mathematicar&utilde;">Mathematicarum</expan> experte, qui in publica di&longs;putatione axio&shy;<lb/>
  ma illud Mathematicum, omne totum e&longs;t maius &longs;ua parte, in &longs;en&longs;u in <lb/>
 <s id="id.000195">Ex 1. de C&oelig;lo.<!-- KEEP S--></s></p><p type="main"> quo &agrave; Mathematicis effertur negare non erubuit, e&ograve;, quod in infinito, <lb/>
  vt aiebat non concederetur ab omnibus. </s>
 <s id="id.000196"><emph type="italics"/>T. 33. De minimo indiui&longs;ibili.<emph.end type="italics"/></s></p><p type="main">           <s id="s.000064">&longs;cilicet non intelligebat ma&shy;<lb/>
  thematicum tantummodo tractare de Quantitate finita, ac terminata, <lb/>
 <s id="id.000197"><emph type="italics"/>T. 36. Ratione vtitur lineari; vt probet mundum e&longs;&longs;e finitum.<emph.end type="italics"/></s></p><p type="main"> in qua axioma pr&aelig;dictum ab omnibus conceditur. </s>
            <s id="s.000065">Neque vero hic <lb/>
 <s id="id.000198"><emph type="italics"/>T. 48. Commen&longs;urab. <!-- REMOVE S-->&amp; incommen&longs;urab. </s> nonnullorum infen&longs;us in Mathematicas animus quieuit, verum etiam <lb/>
  e&ograve; progre&longs;&longs;us e&longs;t, vt eas omnes omnino conuellere, atque ex albo &longs;cien&shy;
  
  
 <s id="id.000199">quid.<emph.end type="italics"/></s></p><p type="main"> <pb pagenum="9" xlink:href="009/01/009.jpg"/>tiarum, quamuis non Ari&longs;totele tantum, &longs;ed ip&longs;a etiam veritate repu&shy;<lb/>
  gnante, expungere conati &longs;int; <expan abbr="idq;">idque</expan> ne&longs;cio an vlla alia de cau&longs;a egerint, <lb/>
 <s id="id.000200"><emph type="italics"/>T. 119. Omnis triangulus habet tres, &amp;c. </s> qu&agrave;m quod eas non &longs;atis calerent; non &longs;ecus <expan abbr="atq;">atque</expan> Ae&longs;opica illa Vulpes, <lb/>
  qu&aelig; cum cauda mutilata e&longs;&longs;et, caudarum mutilationem reliquis vulpi&shy;<lb/>
 <s id="id.000201">Item de commen&longs;urabili.<emph.end type="italics"/></s></p><p type="head"> bus vafr&egrave; per&longs;uadere conabatur. </s>
            <s id="s.000066">Verum enim ver&ograve; optim&egrave; &longs;cio, ea, <lb/>
 <s id="id.000202">Ex 2. de C&oelig;lo.<!-- KEEP S--></s></p><p type="main"> qu&etail; hactenus dicta &longs;unt non in omnes no&longs;tri temporis Philo&longs;ophos qua&shy;<lb/>
  drare, cum non pauci hodie quoque &longs;int, qui more antiquorum Mathe&shy;<lb/>
 <s id="id.000203"><emph type="italics"/>T. 24. Plato ex planis &longs;olida componebat, qu&igrave;.<emph.end type="italics"/></s></p><p type="main"> maticis &longs;uffulti, optim&egrave; &longs;uis &longs;tudijs con&longs;ulentes, reliquam Philo&longs;ophiam <lb/>
  non &longs;ine magno compendio aggrediuntur. </s>
 <s id="id.000204"><emph type="italics"/>T. 25. Ordo figurarum planarum.<emph.end type="italics"/></s></p><p type="main">           <s id="s.000067">Quo fit, vt c&aelig;teros ageo&shy;<lb/>
  metretos ita antecellant, vt eorum Magi&longs;tri appellari po&longs;&longs;int, &amp; <expan abbr="debe&atilde;t">debeant</expan>; <lb/>
 <s id="id.000205"><emph type="italics"/>T. 31. Aqu&aelig; &longs;uperficiem e&longs;&longs;e &longs;ph&aelig;ricam.<emph.end type="italics"/></s></p><p type="main"> tales fuerunt in primis Vicomercatus, Cardanus, Zabarella, Toletus, <lb/>
  Bonamicus, &amp; alij, quibus paulo antiquiores fuerunt D. Tho. <!-- REMOVE S-->&amp; Scotus, <lb/>Hi omnes Mathematicarum auxilio, quantum inter reliquos philo&longs;o&shy;<lb/>
 <s id="id.000206"><emph type="italics"/>T. 46. Maiorem circulum velocius moueri. </s> phantes excelluerint, nemo e&longs;t qui non nouerit. </s>
            <s id="s.000068">Illud hoc loco minim&egrave; <lb/>
 <s id="id.000207">Recentiorum ob&longs;eruationes.<emph.end type="italics"/></s></p><p type="main"> tacendum, Iacobum Zabarellam in &longs;uis logic&aelig; commentarijs te&longs;tari &longs;e <lb/>
  bis &longs;umma diligentia totum Euclidem perlegi&longs;&longs;e, vt perfect&egrave; Ari&longs;t. de <lb/>
 <s id="id.000208"><emph type="italics"/>T. 57. De ordine C&oelig;lorum ex &longs;ententia A&longs;tronomorum.<emph.end type="italics"/></s></p><p type="main"> demon&longs;tratione &longs;ententiam a&longs;&longs;equi po&longs;&longs;et.</s>
          </p>
 <s id="id.000209"><emph type="italics"/>T. 59. De rotunditate Lun&aelig;, bis.<emph.end type="italics"/></s></p><p type="main">         <p type="main">
            <s id="s.000069">Hi ridiculas illas, ac pueriles expo&longs;itiones &longs;uperius allatas minim&egrave; <lb/>
 <s id="id.000210"><emph type="italics"/>T. 107. Centrum duplex grauit: &amp; molis. </s> effutierunt, neque reliquis &longs;upra recen&longs;itis incommodis obnoxij fue&shy;<lb/>
  runt, quibus magno etiam cum dedecore alij Mathematicarum ope ca&shy;<lb/>
 <s id="id.000211">Qua ratione grauia ad mundi centrum  rentes afficiuntur.</s>
 <lb/>aptarentur.<emph.end type="italics"/></s></p><p type="main">         </p>
          <p type="main">
 <s id="id.000212"><emph type="italics"/>T. 109. Terram e&longs;&longs;e rotundam. </s>           <s id="s.000070">In horum igitur gratiam operam diligenter dedi, vt quantum in me <lb/>
  e&longs;&longs;et damna &agrave; me &longs;upra enarrata aliqua ex parte re&longs;arcirem. </s>
 <s id="id.000213">alio item modo.<emph.end type="italics"/></s></p><p type="main">           <s id="s.000071">Quaprop&shy;<lb/>
  ter loca h&aelig;c mathematica num rect&egrave; e&longs;&longs;ent &egrave; gr&aelig;co in latinum tran&longs;lata <lb/>
 <s id="id.000214"><emph type="italics"/>T. 110. Terram e&longs;&longs;e paruam re&longs;pectu C&oelig;li.<emph.end type="italics"/></s></p><p type="main"> diligenter prius expendi. </s>
            <s id="s.000072">Deinde claritate, qu&agrave;m potui maxima eadem <lb/>
 <s id="id.000215"><emph type="italics"/>T. 111. Mare occidentale coniungi indico.<emph.end type="italics"/></s></p><p type="main"> loca interpretatus &longs;um, &amp; in horum, de quibus dixi gratiam, qu&aelig;dam <lb/>
  fan&egrave; tenuia pro&longs;equutus &longs;um, qu&aelig; alioquin libenter omi&longs;i&longs;&longs;em. </s>
 <s id="id.000216"><emph type="italics"/>T. 112. De quantitate Terr&aelig;.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="head">           <s id="s.000073">Tum fi&shy;<lb/>
  guras omnes, aut correxi, aut re&longs;titui, aut nouas appo&longs;ui. </s>
 <s id="id.000217">Ex 3. de C&oelig;lo.<!-- KEEP S--></s></p><p type="main">           <s id="s.000074">Hoc igitur <lb/>
  no&longs;tro qualicunque labore poterit qui&longs;que omnia illa facile intelligere, <lb/>
 <s id="id.000218"><emph type="italics"/>T. 40. Vt componatur &longs;ph&aelig;ra.<emph.end type="italics"/></s></p><p type="main"> <expan abbr="atq;">atque</expan> enumerata incommoda euitare, vnum tantummodo &agrave; Lectore ma&shy;<lb/>
  thematicarum experte requiram, vt principia &longs;altem illa, &longs;cilicet defini&shy;<lb/>
 <s id="id.000219"><emph type="italics"/>T. 66. Omne corpus diui&longs;ibile.<emph.end type="italics"/></s></p><p type="main"> tiones, po&longs;tulata, &amp; axiomata, qu&aelig; prim&ograve; Euclideis libro pr&aelig;ponuntur, <lb/>
  diligenter prius perlegat cum illa &longs;ua per&longs;picuitate omnibus &longs;int obuia; <lb/>
 <s id="id.000220"><emph type="italics"/>T. 66. Qu&aelig;nam planarum figurarum totum &longs;patium repleant. </s> c&aelig;tera ego explicanda recipio. </s>
            <s id="s.000075">Obiter etiam auctaria nonnulla partim <lb/>
 <s id="id.000221">Hinc de admirabili  mathematica, partim naturalia in&longs;erui, qu&aelig; ob nouitatem, ac pulchri&shy;<lb/>
 <lb/>Apum mgenio.<emph.end type="italics"/></s></p><p type="main"> tudinem grata Lectori, atque iucunda fore exi&longs;timaui.</s>
          </p>
 <s id="id.000222"><emph type="italics"/>T. eodem. </s>         <p type="main">
            <s id="s.000076">Sciat pr&aelig;terea Lector no&longs;trum in&longs;titutum e&longs;&longs;e loca h&aelig;c mathemati&shy;<lb/>
 <s id="id.000223">Num plures Pyramides locum replere valeant, vbi Ari&longs;totiles, &amp; omnes  ca, quatenus mathematica &longs;unt declarare, &longs;iue ea &longs;upplere, qu&aelig; ex ma&shy;<lb/>
 <lb/>expo&longs;itores erra&longs;&longs;e o&longs;tenduntur.<emph.end type="italics"/></s></p><p type="main"> thematicis petenda e&longs;&longs;ent: reliqua autem me tantum attingere, quan&shy;<lb/>
  tum harum rerum cum illis connexio po&longs;tulat.</s>
 <s id="id.000224"><emph type="italics"/>T. 71. Terram e&longs;&longs;e cubum, cur dictum &longs;it.<emph.end type="italics"/></s></p><p type="head">         </p>
          <pb pagenum="10" xlink:href="009/01/010.jpg"/>
 <s id="id.000225">Ex 4. de C&oelig;lo.<!-- KEEP S--></s></p><p type="main">         <p type="main">
            <s id="s.000077">His omnibus placuit appendices opportune nonnullas addere, qua&shy;<lb/>
 <s id="id.000226"><emph type="italics"/>T. 33. Extare centrum Mundi, qu&ograve; grauia tendunt, &agrave; quo leuia abeant.<emph.end type="italics"/></s></p><p type="main"> rum prima de natura mathematicarum &longs;cientiarum: altera, qua omnes <lb/>
  demon&longs;trationes primi libri Euclidis breuiter ad Logicam normam ex&shy;<lb/>
 <s id="id.000227"><emph type="italics"/>T. 44. &amp; <expan abbr="&longs;eq.">&longs;eque</expan> Cur qu&aelig;dam grauiora qu&agrave;m aqua, &longs;upernatent.<emph.end type="italics"/></s></p><p type="head"> penduntur, vt pateat, quonam demon&longs;trationis genere <expan abbr="c&etilde;&longs;eri">cen&longs;eri</expan> <expan abbr="vnaqu&etail;q;">vnaqu&etail;que</expan> <lb/>
  debeat, &amp; ex illis de c&aelig;teris iudicium fiat. </s>
 <s id="id.000228">Ex 2. de Generatione, &amp; Corruptione.<!-- KEEP S--></s></p><p type="main">           <s id="s.000078">Tandem in gratiam etiam <lb/>
  Mathematicorum tertiam appendicem appendi, qua omnia loca Ari&longs;t. <lb/>
 <s id="id.000229"><emph type="italics"/>Tex. 56. Cur Planet&aelig; duobus motibus moueri dicantur.<emph.end type="italics"/></s></p><p type="head"> <!-- REMOVE S-->Geometrica ad Euclidis ordinem referuntur; vnde &amp; ip&longs;i ad &longs;uas pr&etail;le&shy;<lb/>
  ctiones exornandas aliquid &longs;ubinde depromere queant.</s>
 <s id="id.000230">Ex 1. Meteororum.<!-- KEEP S--></s></p><p type="main">         </p>
          <p type="main">
 <s id="id.000231"><emph type="italics"/>Summa prima cap.            <s id="s.000079">Fruere igitur amice Lector hoc no&longs;tro qua liquali labore, quo ad ple&shy;<lb/>
  nam totius Ari&longs;t. intelligentiam, cui adhuc mathematicarum ignoratio <lb/>
 3. De magnitudine Terr&aelig; ad a&longs;tra, &amp; &longs;olem collata.<emph.end type="italics"/></s></p><p type="main"> ob&longs;titit peruenire tandem po&longs;&longs;is: <expan abbr="illud&qacute;">illudque</expan>; experiaris, quod optimus qui&shy;<lb/>
  dam Philo&longs;ophus, cum totum hunc librum perlegi&longs;&longs;et, effatus e&longs;t, vide&shy;<lb/>
 <s id="id.000232"><emph type="italics"/>Cap.  licet, opus hoc <emph type="italics"/>Aristotelic&aelig; expo&longs;itionis complementum ad hanc v&longs;que <lb/>
  diem de&longs;ideratum<emph.end type="italics"/> iure ac merit&ograve; nuncupari po&longs;&longs;e.</s>
 eodem. </s>         </p>
          <p type="main">
 <s id="id.000233">De magnitudine A&longs;trorum.<emph.end type="italics"/></s></p><p type="main">           <s id="s.000080">Illud demum tanquam parergon addam, quod ego his elucubran&shy;<lb/>
  dis experientia didici, ad veram &longs;cilicet, ac perfectam to&shy;<lb/>
 <s id="id.000234"><emph type="italics"/>Cap.  tius Ari&longs;totelis intelligentiam lingu&aelig; in primis <lb/>
  gr&aelig;c&aelig;, necnon mathematicarum om&shy;<lb/>
 4. De ordine Luminarium Solis, &amp; Lun&aelig;.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main"> nium di&longs;ciplinarum haud medio&shy;<lb/>
  crem cognitionem ne&shy;<lb/>
 <s id="id.000235"><emph type="italics"/>Summa 2. cap.  ce&longs;&longs;ariam e&longs;&longs;e. <lb/>
  </s>
 3. de Mercurij stella. </s>           <s id="s.000081">Vale.<!-- KEEP S--></s>
          </p>
 <s id="id.000236">Item de Cometa: e&longs;&longs;e in C&oelig;lo.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">       </section>
        <pb pagenum="11" xlink:href="009/01/011.jpg"/>
 <s id="id.000237"><emph type="italics"/>Cap.        <section>
          <p type="head">
 5. De Magnitudine Solis, &amp; de vmbra Terr&aelig;.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">           <s id="s.000082">Pr&etail;cipua qu&etail;dam, aut noua, aut re&longs;taurata, <lb/>
  qu&aelig; obiter pertractantur.<lb/>
 <s id="id.000238"><emph type="italics"/>Cap.  <arrow.to.target n="table1"/></s>
          </p>
 5. De Glaxia.<emph.end type="italics"/></s></p><p type="main">         <table>
            <table.target id="table1"/>
 <s id="id.000239"><emph type="italics"/>Cap.            <row>
              <cell><emph type="italics"/>1<emph.end type="italics"/></cell>
 6. Sententia Ari&longs;totelis de Glaxia, partim defenditur: vera, deinde              <cell><emph type="italics"/>De re&longs;olutione. numero marginali.<emph.end type="italics"/></cell>
 <lb/>aperitur.<emph.end type="italics"/></s></p><pb xlink:href="009/01/015.jpg" pagenum="15"/><p type="main">             <cell><emph type="italics"/>4<emph.end type="italics"/></cell>
            </row>
 <s id="id.000240"><emph type="italics"/>Summa 4. cap 1. De Monte Parna&longs;&longs;o, dubia. </s>           <row>
              <cell><emph type="italics"/>2<emph.end type="italics"/></cell>
 <s id="id.000241">Mare extraneum, quod. </s>             <cell><emph type="italics"/>De figuris vacuum replentibus, vbi Aristotelis, &amp; expo-&longs;itorum erratum aperitur. num.<emph.end type="italics"/></cell>
              <cell><emph type="italics"/>121<emph.end type="italics"/></cell>
 <s id="id.000242">Errata qu&aelig;&shy;           </row>
 <lb/>dam veterum Geographorum, &amp; Ari&longs;t.            <row>
              <cell/>
 corriguntur. </s>             <cell><emph type="italics"/>Inibi, Apum mirabilis qu&aelig;dam in cellis &longs;uis hexagonis   constituendis indu&longs;tria detegitur. num.<emph.end type="italics"/></cell>
              <cell><emph type="italics"/>120<emph.end type="italics"/></cell>
 <s id="id.000243">Altitudo montis Cauca&longs;i.<emph.end type="italics"/></s></p><p type="main">           </row>
            <row>
 <s id="id.000244"><emph type="italics"/>Cap.              <cell><emph type="italics"/>3<emph.end type="italics"/></cell>
              <cell><emph type="italics"/>De ijs, qu&aelig; aqu&aelig; in&longs;ident, vn&agrave; cum noua demonstratione problema-tis illius Archimedis, quo metallorum mixtionem indi&longs;&longs;oluta Co-rona, explorauit. in additione. ante num.<emph.end type="italics"/></cell>
 2. De permutatione Aquarum, &amp; continentis. </s>             <cell><emph type="italics"/>124<emph.end type="italics"/></cell>
            </row>
 <s id="id.000245">Noua ob&longs;eruatio de rotundi&shy;           <row>
 <lb/>tate Terr&aelig;, <expan abbr="atq;">atque</expan> Mundi duratione.<emph.end type="italics"/></s></p><p type="head">             <cell><emph type="italics"/>4<emph.end type="italics"/></cell>
              <cell><emph type="italics"/>De Cometa, recentiorum &longs;ententia. num.<emph.end type="italics"/></cell>
 <s id="id.000246">Ex 2. Meteororum.<!-- KEEP S--></s></p><p type="main">             <cell><emph type="italics"/>136<emph.end type="italics"/></cell>
            </row>
 <s id="id.000247"><emph type="italics"/>Summa 1. cap.            <row>
              <cell><emph type="italics"/>5<emph.end type="italics"/></cell>
 1. De Mari rubro.<emph.end type="italics"/></s></p><p type="main">             <cell><emph type="italics"/>De altitudine montis Cauca&longs;i.<emph.end type="italics"/></cell>
              <cell><emph type="italics"/>148<emph.end type="italics"/></cell>
 <s id="id.000248"><emph type="italics"/>Summa 2. cap.            </row>
            <row>
 2. De ortu stellarum fixarum: Item de occa&longs;u earumdem.<emph.end type="italics"/></s></p><p type="main">             <cell><emph type="italics"/>6<emph.end type="italics"/></cell>
              <cell><emph type="italics"/>De Terr&aelig; rotunditate, ac mundi duratione.<emph.end type="italics"/></cell>
 <s id="id.000249"><emph type="italics"/>Cap.              <cell><emph type="italics"/>151<emph.end type="italics"/></cell>
            </row>
 eodem, De Canicula. </s>           <row>
              <cell><emph type="italics"/>7<emph.end type="italics"/></cell>
 <s id="id.000250">De Zonis temperatis. </s>             <cell><emph type="italics"/>De Iride. in additione.<emph.end type="italics"/></cell>
              <cell><emph type="italics"/>181<emph.end type="italics"/></cell>
 <s id="id.000251">Corona Ariadn&aelig;. </s>           </row>
            <row>
 <s id="id.000252">Zonam torridam              <cell><emph type="italics"/>8<emph.end type="italics"/></cell>
 <lb/>fals&ograve; putabant inho&longs;pitalem. </s>             <cell><emph type="italics"/>Scytala quid.<emph.end type="italics"/></cell>
              <cell><emph type="italics"/>250<emph.end type="italics"/></cell>
 <s id="id.000253">cur habitabilis.<emph.end type="italics"/></s></p><p type="main">           </row>
            <row>
 <s id="id.000254"><emph type="italics"/>Cap.              <cell><emph type="italics"/>9<emph.end type="italics"/></cell>
              <cell><emph type="italics"/>Securis antiqua qu&aelig;, &amp; qua ratione fieret.<emph.end type="italics"/></cell>
 3. De Ventorum &longs;itu.<emph.end type="italics"/></s></p><p type="head">             <cell><emph type="italics"/>258<emph.end type="italics"/></cell>
            </row>
 <s id="id.000255">Ex 3. Meteor.<!-- KEEP S--></s></p><p type="main">           <row>
              <cell><emph type="italics"/>10<emph.end type="italics"/></cell>
 <s id="id.000256"><emph type="italics"/>Summa 2. cap.              <cell><emph type="italics"/>Statera antiqua qu&aelig;,<emph.end type="italics"/></cell>
              <cell><emph type="italics"/>259<emph.end type="italics"/></cell>
 2. De Halone, &longs;eu Area, &longs;eu Corona, Mathematica demon&longs;tratio.<emph.end type="italics"/></s></p><p type="main">           </row>
            <row>
 <s id="id.000257"><emph type="italics"/>Cap.              <cell><emph type="italics"/>11<emph.end type="italics"/></cell>
              <cell><emph type="italics"/>De Ae&longs;tu Maris.<emph.end type="italics"/></cell>
 4. De Iridis figura Mathematica demon&longs;tratio, &longs;ed deficiens. </s>             <cell><emph type="italics"/>272<emph.end type="italics"/></cell>
            </row>
 <s id="id.000258">Noua de eadem            <row>
 <lb/>tractatio.<emph.end type="italics"/></s></p><p type="main">             <cell><emph type="italics"/>12<emph.end type="italics"/></cell>
              <cell><emph type="italics"/>Araneorum indu&longs;tria nuper patefacta: vbi Democritus contra Ari&longs;t.   defenditur.<emph.end type="italics"/></cell>
 <s id="id.000259"><emph type="italics"/>Cap.              <cell><emph type="italics"/>293<emph.end type="italics"/></cell>
            </row>
 5. De Parelio. <!-- KEEP S--></s>           <row>
              <cell><emph type="italics"/>13<emph.end type="italics"/></cell>
 <s id="id.000260">Rationes Ari&longs;totelis refelluntur.<emph.end type="italics"/></s></p><p type="head">             <cell><emph type="italics"/>De Lucis figuratione, &amp; rerum &longs;imulacris in ob&longs;curo loco.<emph.end type="italics"/></cell>
              <cell><emph type="italics"/>345<emph.end type="italics"/></cell>
 <s id="id.000261">Ex 1. De Anima.<!-- KEEP S--></s></p><p type="main">           </row>
            <row>
 <s id="id.000262"><emph type="italics"/>Tex. 11. Quid rectum, quid obliquum. </s>             <cell><emph type="italics"/>14<emph.end type="italics"/></cell>
              <cell><emph type="italics"/>De Pupilla oculi.<emph.end type="italics"/></cell>
 <s id="id.000263">&amp; omnis triangulus babet tres, &amp;c.<emph.end type="italics"/></s></p><p type="main">             <cell><emph type="italics"/>408<emph.end type="italics"/></cell>
            </row>
 <s id="id.000264"><emph type="italics"/>T. 13. Sph&aelig;ra planum tangit in puncto.<emph.end type="italics"/></s></p><p type="head">           <row>
              <cell><emph type="italics"/>15<emph.end type="italics"/></cell>
 <s id="id.000265">Ex 2. De Anima.<!-- KEEP S--></s></p><p type="main">             <cell><emph type="italics"/>De Mathematicarum natura. prop&egrave; finem operis.<emph.end type="italics"/></cell>
              <cell/>
 <s id="id.000266"><emph type="italics"/>T. 12. Definitioncm formalem, &amp; cau&longs;alem explicat exemplo Quadrationis Geo&shy;           </row>
 <lb/>metric&aelig;.<emph.end type="italics"/></s></p><p type="main">           <row>
              <cell><emph type="italics"/>16<emph.end type="italics"/></cell>
 <s id="id.000267"><emph type="italics"/>T. 86. Acutum, &amp; Graue, vt differant.<emph.end type="italics"/></s></p><p type="main">             <cell><emph type="italics"/>Clarorum Mathematicorum Chronologia, in fine operis.<emph.end type="italics"/></cell>
              <cell/>
 <s id="id.000268"><emph type="italics"/>T. 159. De Solis magnitudine ad terram.<emph.end type="italics"/></s></p><p type="head">           </row>
          </table>
 <s id="id.000269">Ex 3. De Anima.<!-- KEEP S--></s></p><p type="main">       </section>
        <pb pagenum="12" xlink:href="009/01/012.jpg"/>
 <s id="id.000270"><emph type="italics"/>T. 21. Incommen&longs;urabile.<emph.end type="italics"/></s></p><p type="main">       <section>
          <p type="head">
 <s id="id.000271"><emph type="italics"/>T. 25. Indiui&longs;ibilia e&longs;&longs;e priuationes.<emph.end type="italics"/></s></p><p type="main">           <s id="s.000083"><emph type="italics"/>PRIMVS INDEX LOCORVM ARIST.<emph.end type="italics"/><!-- KEEP S--></s>
          </p>
 <s id="id.000272"><emph type="italics"/>T. 32. Permutata proportio.<emph.end type="italics"/></s></p><p type="head">         <p type="head">
            <s id="s.000084"><emph type="italics"/>Qu&aelig; in hoc opere explicantur, iuxta ordine librorum <lb/>
 <s id="id.000273">Ex lib. <!-- REMOVE S-->De Sen&longs;u.</s> ip&longs;ius ex vulgata editione Lugdunen&longs;i.<emph.end type="italics"/></s>
          </p>
 </p><p type="main">         <p type="head">
            <s id="s.000085">In Pr&aelig;dicamentis.</s>
 <s id="id.000274"><emph type="italics"/>Capite 6. Die&longs;is.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">         </p>
          <p type="main">
 <s id="id.000275"><emph type="italics"/>Cap.            <s id="s.000086"><emph type="italics"/>Capite s. </s>
            <s id="s.000087">de Relatione, vbi de Quadratura circuli.<emph.end type="italics"/></s>
 8. Nete. </s>         </p>
          <p type="main">
 <s id="id.000276">Diapa&longs;on. <!-- KEEP S--></s>           <s id="s.000088"><emph type="italics"/>Cap. de Priori, vbi de Principijs Mathematicarum,<emph.end type="italics"/></s>
          </p>
 <s id="id.000277">Diapen&longs;e.<emph.end type="italics"/></s></p><p type="head">         <p type="main">
            <s id="s.000089"><emph type="italics"/>Cap. de Motu, vbi de Gnomone.<emph.end type="italics"/><!-- KEEP S--></s>
 <s id="id.000278">Ex lib. <!-- REMOVE S-->De Memoria, &amp; Rem.<!-- KEEP S--></s>         </p>
          <p type="head">
 </p><p type="main">           <s id="s.000090">In Primo Priorum Re&longs;olutoriorum.</s>
          </p>
 <s id="id.000279"><emph type="italics"/>Cap.          <p type="main">
            <s id="s.000091"><emph type="italics"/>Ad titulum libri de Re&longs;olutione.<emph.end type="italics"/></s>
 1. Omnis triangulus habet tres, &amp;c.<emph.end type="italics"/></s></p><p type="main">         </p>
          <p type="main">
 <s id="id.000280"><emph type="italics"/>Cap.            <s id="s.000092"><emph type="italics"/>Cap. 23. &longs;ect 1. libri 1. de Incommen&longs;urabilibus.<emph.end type="italics"/></s>
          </p>
 3. Mathemata facile remini&longs;cibilia.<emph.end type="italics"/></s></p><p type="head">         <p type="main">
            <s id="s.000093"><emph type="italics"/>Cap. 24. &longs;ecti 1. lib. 1. de De&longs;criptionibus.<emph.end type="italics"/><!-- KEEP S--></s>
 <s id="id.000281">Ex lib. <!-- REMOVE S-->De Somnijs.<!-- KEEP S--></s>         </p>
          <p type="main">
 </p><p type="main">           <s id="s.000094"><emph type="italics"/>Cap. 2. &longs;ect 2. lib. 1. de De&longs;criptionibus.<emph.end type="italics"/><!-- KEEP S--></s>
          </p>
 <s id="id.000282"><emph type="italics"/>Cap.          <p type="main">
            <s id="s.000095"><emph type="italics"/>Cap. 3. &longs;ecti 2. lib. 1. de Incommen&longs;urabili.<emph.end type="italics"/></s>
 2. Terra, cur nauigantibus moueri videatur.<emph.end type="italics"/></s></p><p type="main">         </p>
          <p type="main">
 <s id="id.000283"><emph type="italics"/>Cap.            <s id="s.000096"><emph type="italics"/>Cap. 1. &longs;ecti 3. lib. 1. de eo, quod est, omnis triangulus habet tres angulos &aelig;quales <lb/>
  &aelig;quales duobus rectis: Aequalitas Geometrica, qu&aelig;.<emph.end type="italics"/></s>
 3. Cur Oculus digito dimotus res geminatas videat.<emph.end type="italics"/></s></p><p type="head">         </p>
          <p type="main">
 <s id="id.000284">Ex 1. Methaphy&longs;.<!-- KEEP S--></s></p><p type="main">           <s id="s.000097"><emph type="italics"/>Cap. eodem, de exemplis, quibus vtuntur Geometr&aelig;.<emph.end type="italics"/></s>
          </p>
 <s id="id.000285"><emph type="italics"/>Cap.          <p type="head">
            <s id="s.000098">In &longs;ecundo Priorum Re&longs;ol.<!-- REMOVE S--><emph type="italics"/>Cap. 21. de lineis Paralellis, &longs;eu Coalternis.<emph.end type="italics"/></s>
 1. Initium Mathematicarum ab Aegyptiorum Saterdotibus. </s>         </p>
          <p type="main">
 <s id="id.000286">Item, Automata,            <s id="s.000099"><emph type="italics"/>Cap. eodem. </s>
 <lb/>qu&aelig; &longs;olstitia. </s>           <s id="s.000100">de Paralellis, &amp; de triangulo.<emph.end type="italics"/></s>
          </p>
 <s id="id.000287">Diameter incommen&longs;.<emph.end type="italics"/></s></p><p type="main">         <p type="main">
            <s id="s.000101"><emph type="italics"/>Cap. 26. Quod omnis triangulus habet tres, &amp; c.<emph.end type="italics"/><!-- KEEP S--></s>
 <s id="id.000288"><emph type="italics"/>Summa 2. cap.          </p>
          <p type="main">
 3. Pythagorei Mathematicas c&aelig;teris pr&aelig;ferebant.<emph.end type="italics"/></s></p><p type="main">           <s id="s.000102"><emph type="italics"/>Cap. 31. de Abductione.<emph.end type="italics"/><!-- KEEP S--></s>
          </p>
 <s id="id.000289"><emph type="italics"/>T. 47. Geometria habet &longs;uas pr&aelig;cognitiones.<emph.end type="italics"/></s></p><p type="head">         <p type="main">
            <s id="s.000103"><emph type="italics"/>Cap. codem, de circuli Quadratura, &longs;ecundum Hippocratem Chium.<emph.end type="italics"/><!-- KEEP S--></s>
 <s id="id.000290">Ex 2. Methaphy&longs;.<!-- KEEP S--></s></p><p type="main">         </p>
          <p type="head">
 <s id="id.000291"><emph type="italics"/>T. 14. Leges apud Mu&longs;icos quid.<emph.end type="italics"/></s></p><p type="head">           <s id="s.000104">In primo Po&longs;teriorum.</s>
          </p>
 <s id="id.000292">Ex 3. Methaphy&longs;.<!-- KEEP S--></s></p><p type="main">         <p type="main">
            <s id="s.000105"><emph type="italics"/>Textu primo, De Pr&aelig;cognitis Mathematicarum.<emph.end type="italics"/><!-- KEEP S--></s>
 <s id="id.000293"><emph type="italics"/>Tex. <!-- KEEP S--></s>         </p>
          <p type="main">
 <s id="id.000294">Mathematicas puras carere cau&longs;is efficiente, &amp; finali. </s>           <s id="s.000106"><emph type="italics"/>T. 2. Omnis triangulus habet tres, &amp; c.<emph.end type="italics"/><!-- KEEP S--></s>
          </p>
 <s id="id.000295">Ari&longs;tippus, vt Mathe&shy;         <p type="main">
 <lb/>maticas &longs;ugillaret. </s>           <s id="s.000107"><emph type="italics"/>T. 5. De Diametro incommen&longs;urabili. </s>
            <s id="s.000108">Item De Mathematicarum Principijs.<emph.end type="italics"/></s>
 <s id="id.000296">Tetragoni&longs;mus est inuentio medi&aelig;.<emph.end type="italics"/></s></p><pb xlink:href="009/01/016.jpg" pagenum="16"/><p type="main">         </p>
          <p type="main">
 <s id="id.000297"><emph type="italics"/>Tex. 8. Geod&aelig;&longs;ia quid.<emph.end type="italics"/></s></p><p type="head">           <s id="s.000109"><emph type="italics"/>T. eodem, De Indiui&longs;ibilitate vnitatis.<emph.end type="italics"/></s>
          </p>
 <s id="id.000298">Ex 4. Methaphy&longs;.<!-- KEEP S--></s></p><p type="main">         <p type="main">
            <s id="s.000110"><emph type="italics"/>T. 9. De Puncto, &amp; linea. </s>
 <s id="id.000299"><emph type="italics"/>T. 4. Qu&aelig; &longs;int prim&aelig;, &amp; qu&aelig; &longs;ecund&aelig; inter Mathematicas.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">           <s id="s.000111">Item de recto, &amp; circulari. </s>
            <s id="s.000112">Item de numero pari, impari; <lb/>
 <s id="id.000300"><emph type="italics"/>T. 28. Diameter, commen&longs;urabilis.<emph.end type="italics"/></s></p><p type="head"> primo, &amp; compo&longs;ito; &aelig;quilatero, &amp; altera parte longiore.<emph.end type="italics"/></s>
          </p>
 <s id="id.000301">Ex 5. Methaphy&longs;.<!-- KEEP S--></s></p><p type="main">         <p type="main">
            <s id="s.000113"><emph type="italics"/>T. 11. Line&aelig; punctum inest per &longs;e, &amp; c.<emph.end type="italics"/><!-- KEEP S--></s>
 <s id="id.000302"><emph type="italics"/>T. 2. Exemplum cau&longs;&aelig; formalis ex Diapa&longs;on. <!-- KEEP S--></s>         </p>
          <p type="main">
 <s id="id.000303">Qu&aelig; &longs;int proportiones Mu&longs;icales.<emph.end type="italics"/></s></p><p type="main">           <s id="s.000114"><emph type="italics"/>T. 13. De Parallelis. <!-- KEEP S--></s>
            <s id="s.000115">De I&longs;o&longs;cele. </s>
 <s id="id.000304"><emph type="italics"/>T. 3. Qu&aelig; &longs;it Materia in Mathematicis.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">           <s id="s.000116">De Alterna Proportione, <lb/>
  Item quod omnis triangulus habet tres, &amp; c.<emph.end type="italics"/><!-- KEEP S--></s>
 <s id="id.000305"><emph type="italics"/>T. 4. Quidnam &longs;int elementa apud Geometras.<emph.end type="italics"/></s></p><p type="main">         </p>
          <p type="main">
 <s id="id.000306"><emph type="italics"/>T. 12. Die&longs;is.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">           <s id="s.000117"><emph type="italics"/>T. 14. De ij&longs;dem cum pr&aelig;cedentibus.<emph.end type="italics"/></s>
          </p>
 <s id="id.000307"><emph type="italics"/>T. 17. Diameter incommen&longs;urab. </s>         <p type="main">
            <s id="s.000118"><emph type="italics"/>T. 20. Magnitudines euadunt numeri. </s>
 <s id="id.000308">Quid potentia vnius line&aelig;.<emph.end type="italics"/></s></p><p type="main">           <s id="s.000119">Item, quod non duo cubi cubus. </s>
            <s id="s.000120">Item de <lb/>
 <s id="id.000309"><emph type="italics"/>T. 34. Diameter incommen&longs;urabilis.<emph.end type="italics"/></s></p><p type="head"> Mathematicis &longs;ubalternatis.<emph.end type="italics"/></s>
          </p>
 <s id="id.000310">Ex 6. Methaphy&longs;.<!-- KEEP S--></s></p><p type="main">         <p type="main">
            <s id="s.000121"><emph type="italics"/>T. 23. Quadratura circuli &longs;ecundum Bry&longs;onem. </s>
 <s id="id.000311"><emph type="italics"/>T. 1. Principia, elementa, &amp; cau&longs;&aelig; in Mathem.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">           <s id="s.000122">Item per&longs;ectam illam e&longs;&longs;e Demon&shy;<lb/>
  &longs;trationem, qua Geometr&aelig; o&longs;tendunt, quod Omnis triangulus habet tres, &amp; c. <lb/>
 <s id="id.000312"><emph type="italics"/>T. 8. Diameter. </s> <!-- KEEP S--></s>
            <s id="s.000123">Per&longs;pectiuam, &amp; Mechanicam &longs;ubalternari Geometri&aelig;, Mu&longs;icam, Arithmetic&aelig;.<emph.end type="italics"/><!-- KEEP S--></s>
 <s id="id.000313">commen&longs;urab.<emph.end type="italics"/></s></p><p type="main">         </p>
          <p type="main">
 <s id="id.000314"><emph type="italics"/>T. 20. De&longs;criptiones. </s>           <s id="s.000124"><emph type="italics"/>T. 24. De numero pari, impari, quadrangulo, cubo. </s>
            <s id="s.000125">In Geometria quid irrationale, <lb/>
 <s id="id.000315">Omnis triangulus habet tres, &amp;c. </s> refrangi, concurrere. </s>
            <s id="s.000126">Quid Astronomia con&longs;ideret.<emph.end type="italics"/></s>
 <s id="id.000316">Cur Angulus in &longs;emicir&shy;         </p>
 <lb/>culo rectus.<emph.end type="italics"/></s></p><p type="main">         <p type="main">
            <s id="s.000127"><emph type="italics"/>T. 25. Geometram non mentiri in &longs;uis exemplis.<emph.end type="italics"/></s>
 <s id="id.000317"><emph type="italics"/>T. 22. Omnis triangulus habet tres, &amp;c.<emph.end type="italics"/></s></p><p type="head">         </p>
          <p type="main">
 <s id="id.000318">Ex 10. Methaphy&longs;.<!-- KEEP S--></s></p><p type="main">           <s id="s.000128"><emph type="italics"/>T. 28. De Parallelis.<emph.end type="italics"/><!-- KEEP S--></s>
          </p>
 <s id="id.000319"><emph type="italics"/>T. 4. Motum diurnum men&longs;uram reliquorum. </s>         <pb pagenum="13" xlink:href="009/01/013.jpg"/>
          <p type="main">
 <s id="id.000320">Die&longs;is.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">           <s id="s.000129"><emph type="italics"/>T. 29. Cur in Mathematicis non &longs;it Paralogi&longs;mus. <!-- KEEP S--></s>
            <s id="s.000130">Item quid multiplicata propor&shy;<lb/>
 <s id="id.000321"><emph type="italics"/>T. 11. Similes figur&aelig; qu&aelig;. </s> tio. </s>
            <s id="s.000131">Quid C&aelig;neus dixerit. </s>
 <s id="id.000322">Diuer&longs;um in Math. quid.<emph.end type="italics"/></s></p><p type="head">           <s id="s.000132">Cur Affectiones <expan abbr="Mathematicor&utilde;">Mathematicor&utilde;</expan> maxim&egrave; <expan abbr="conuert&atilde;tur">conuertantur</expan>.<emph.end type="italics"/></s>
          </p>
 <s id="id.000323">Ex 11. Methaphy&longs;.<!-- KEEP S--></s></p><p type="main">         <p type="main">
            <s id="s.000133"><emph type="italics"/>T. 30. De Lun&aelig; &longs;ph&aelig;ricitate. </s>
 <s id="id.000324"><emph type="italics"/>Cap.            <s id="s.000134">Quid &longs;tereometria. </s>
            <s id="s.000135">&amp; De &longs;ubalternatione, &amp;c. </s>
 2. Ortus punctorum, linearum, &longs;uperficierum.<emph.end type="italics"/></s></p><p type="head">           <s id="s.000136">&amp; Ma&shy;<lb/>
  thematicorum e&longs;t &longs;cire Propter quid: &longs;en&longs;itiuorum ver&ograve; &longs;cire Quod.<emph.end type="italics"/></s>
 <s id="id.000325">Ex 12. Methaphy&longs;.<!-- KEEP S--></s></p><p type="main">         </p>
          <p type="main">
 <s id="id.000326"><emph type="italics"/>T. 44. Peculiari&longs;&longs;imam Philo&longs;ophiam, Mathematicorum videlicet, A&longs;tronomiam            <s id="s.000137"><emph type="italics"/>T. 37. I&longs;o&longs;celes, &amp; Scalenum habere tres &aelig;quales, &amp;c.<emph.end type="italics"/></s>
 <lb/>pluralitatem C&oelig;lorum docere.<emph.end type="italics"/></s></p><p type="main">         </p>
          <p type="main">
 <s id="id.000327"><emph type="italics"/>T. 45. Numerus orbium c&oelig;le&longs;t ium &longs;ecundum Eudoxum.<emph.end type="italics"/></s></p><p type="main">           <s id="s.000138"><emph type="italics"/>T. 38. Quid Mina, quid Die&longs;is.<emph.end type="italics"/><!-- KEEP S--></s>
          </p>
 <s id="id.000328"><emph type="italics"/>T. 46. Itidem ex Eudoxo.<emph.end type="italics"/></s></p><p type="main">         <p type="main">
            <s id="s.000139"><emph type="italics"/>T. 39. Habere tres angulos &aelig;quales, &amp;c. </s>
 <s id="id.000329"><emph type="italics"/>T. 47. Orbium c&oelig;le&longs;tium numerus, &amp; fabrica ex Calippo.<emph.end type="italics"/></s></p><p type="head">           <s id="s.000140">Item, quod omnis figura habet &longs;uos angu&shy;<lb/>
  los externos &aelig;quales quatuor tantum rectis.<emph.end type="italics"/></s>
 <s id="id.000330">Ex 13. Methaphy&longs;.<!-- KEEP S--></s></p><p type="main">         </p>
          <p type="main">
 <s id="id.000331"><emph type="italics"/>Cap.            <s id="s.000141"><emph type="italics"/>T. 43. Triangulum tres &aelig;quales, &amp;c. </s>
            <s id="s.000142">De Eclyp&longs;i.<emph.end type="italics"/></s>
 3. Qua ratione Mathematici tractant de Bono.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="head">         </p>
          <p type="main">
 <s id="id.000332">In Mechanicas Qu&aelig;&longs;tiones.</s></p><p type="main">           <s id="s.000143"><emph type="italics"/>De combu&longs;tione per refractionem ex &longs;ph&aelig;ra vitrea. </s>
            <s id="s.000144">De principijs &longs;cientiarum.<emph.end type="italics"/></s>
 <s id="id.000333"><emph type="italics"/>Cap.          </p>
          <p type="main">
 1. Qu&aelig; &longs;it Mechanica facultas.<emph.end type="italics"/></s></p><p type="main">           <s id="s.000145"><emph type="italics"/>T. 44. Diameter incommen&longs;urabilis.<emph.end type="italics"/></s>
          </p>
 <s id="id.000334"><emph type="italics"/>Cap.          <p type="head">
            <s id="s.000146">In 2. Po&longs;teriorum.</s>
 2. De Admirandis circuli.<emph.end type="italics"/></s></p><p type="main">         </p>
          <p type="main">
 <s id="id.000335"><emph type="italics"/>Qu&aelig;&longs;tio 1. De Libra. <!-- KEEP S--></s>           <s id="s.000147"><emph type="italics"/>T. 1. Aequalitas, &amp; in&aelig;qualitas. </s>
            <s id="s.000148">Terram e&longs;&longs;e in medio mundi ab A&longs;tronomis per&shy;<lb/>
 <s id="id.000336">cur maior, exactior. </s> fect&egrave; demon&longs;tratur. </s>
            <s id="s.000149">Item Quid con&longs;onantia.<emph.end type="italics"/></s>
 <s id="id.000337">inibi Ari&longs;t.          </p>
          <p type="main">
 lap&longs;us.<emph.end type="italics"/></s></p><p type="main">           <s id="s.000150"><emph type="italics"/>T. 2. Omnis triangulus habet tres, &amp;c. </s>
            <s id="s.000151">Item de Definitionibus Mathematicarum.<emph.end type="italics"/><!-- KEEP S--></s>
 <s id="id.000338"><emph type="italics"/>Qu&aelig;&longs;t. 2. Duplex Libra. <!-- KEEP S--></s>         </p>
          <p type="main">
 <s id="id.000339">Piccolomineus reiectus.<emph.end type="italics"/></s></p><p type="main">           <s id="s.000152"><emph type="italics"/>T. 7. Geometra, qu&aelig;dam accipit, qu&aelig;dam demon&longs;trat.<emph.end type="italics"/></s>
          </p>
 <s id="id.000340"><emph type="italics"/>Qu&aelig;&longs;t. 3. De Vecte.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">         <p type="main">
            <s id="s.000153"><emph type="italics"/>T. 11. Angulum in &longs;emicirculo rectum e&longs;&longs;e probari &agrave; Geometra per cau&longs;am materia&shy;<lb/>
 <s id="id.000341"><emph type="italics"/>Qu&aelig;&longs;t. 4. De Remo; Petri Non&yuml; in Arist.  lem. </s>
            <s id="s.000154">Zabarella correctus.<emph.end type="italics"/></s>
 correctio.<emph.end type="italics"/></s></p><p type="main">         </p>
          <p type="main">
 <s id="id.000342"><emph type="italics"/>Qu&aelig;&longs;t. 5. De Temone Nauis.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">           <s id="s.000155"><emph type="italics"/>T. 24. Echo, Imago &egrave; &longs;peculo, Iris.<emph.end type="italics"/><!-- KEEP S--></s>
          </p>
 <s id="id.000343"><emph type="italics"/>Qu&aelig;&longs;t. 6. De Antenna.<emph.end type="italics"/></s></p><p type="main">         <p type="main">
            <s id="s.000156"><emph type="italics"/>T. 25. Permutatim proportionale quid; exemplum in triangulis.<emph.end type="italics"/></s>
 <s id="id.000344"><emph type="italics"/>Qu&aelig;&longs;t. 8 De Rota.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">         </p>
          <p type="head">
 <s id="id.000345"><emph type="italics"/>Qu&aelig;&longs;t. 9. De Trochlea, &amp; Scytali. </s>           <s id="s.000157">In primo lib. <!-- REMOVE S-->Topicorum.</s>
          </p>
 <s id="id.000346">figura antiqu&aelig; &longs;cytalis.<emph.end type="italics"/></s></p><p type="main">         <p type="main">
            <s id="s.000158"><emph type="italics"/>Cap. 13. Diameter est incommen&longs;urabilis. </s>
 <s id="id.000347"><emph type="italics"/>Qu&aelig;&longs;t. 10. De Libra vacua.<emph.end type="italics"/></s></p><p type="main">           <s id="s.000159">Vox acuta velox, cur. </s>
            <s id="s.000160">&amp;c. </s>
 <s id="id.000348"><emph type="italics"/>Q&ugrave;&aelig;&longs;t. <!-- REMOVE S-->11. De Curru, &amp; &longs;cytala.<emph.end type="italics"/></s>           <s id="s.000161">Colores in <lb/>
  Mu&longs;ica, qui. </s>
 </p><p type="main">           <s id="s.000162">tria genera veteris Mu&longs;ic&aelig;.<emph.end type="italics"/></s>
          </p>
 <s id="id.000349"><emph type="italics"/>Qu&aelig;&longs;t. 13. De lugo. </s>         <p type="head">
            <s id="s.000163">In 4. libro.</s>
 <s id="id.000350">De Succula.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">         </p>
          <p type="main">
 <s id="id.000351"><emph type="italics"/>Qu&aelig;&longs;t. 15. De Vmbelicis.<emph.end type="italics"/></s></p><p type="main">           <s id="s.000164"><emph type="italics"/>Cap. 1. loco 1. line&aelig; in&longs;ecabiles.<emph.end type="italics"/></s>
          </p>
 <s id="id.000352"><emph type="italics"/>Qu&aelig;&longs;t. 16. De ligni oblongi, ac breuis flexura.<emph.end type="italics"/></s></p><pb xlink:href="009/01/017.jpg" pagenum="17"/><p type="main">         <p type="head">
            <s id="s.000165">In 6. libro.</s>
 <s id="id.000353"><emph type="italics"/>Qu&aelig;&longs;t. 17. De Cuneo.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">         </p>
          <p type="main">
 <s id="id.000354"><emph type="italics"/>Qu&aelig;&longs;t. 18. De Trochlea; error Piccolominei.<emph.end type="italics"/></s></p><p type="main">           <s id="s.000166"><emph type="italics"/>Cap. 2. loco 32. Definitio line&aelig;.<emph.end type="italics"/></s>
          </p>
 <s id="id.000355"><emph type="italics"/>Qu&aelig;&longs;t. 19. De Securi. </s>         <p type="head">
            <s id="s.000167">In 8. libro.</s>
 <s id="id.000356">Securis veteris figura, &amp; con&longs;tructio; vn&agrave; cum affectione          </p>
 <lb/>eius mirabili.<emph.end type="italics"/></s></p><p type="main">         <p type="main">
            <s id="s.000168"><emph type="italics"/>Cap. 2. loco 41. V&longs;us Definitionum in Mathematicis.<emph.end type="italics"/><!-- KEEP S--></s>
 <s id="id.000357"><emph type="italics"/>Qu&aelig;&longs;t. 20. De Statera. <!-- KEEP S--></s>         </p>
          <p type="main">
 <s id="id.000358">Veteris stater&aelig; figura restaurata.<emph.end type="italics"/></s></p><p type="main">           <s id="s.000169"><emph type="italics"/>Cap. 4. loco 86. Elementa geometrica: Numeri capitales.<emph.end type="italics"/></s>
          </p>
 <s id="id.000359"><emph type="italics"/>Qu&aelig;&longs;t. 21. De Dentiforcipe.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">         <p type="head">
            <s id="s.000170">In Elenchorum lib. 1.<!-- KEEP S--></s>
 <s id="id.000360"><emph type="italics"/>Qu&aelig;&longs;t. 22. De Nucifrago.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">         </p>
          <p type="main">
 <s id="id.000361"><emph type="italics"/>Qu&aelig;&longs;t. 23. De Motibus in Rhombo.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">           <s id="s.000171"><emph type="italics"/>Cap. 10. Quid P&longs;eudographia. </s>
            <s id="s.000172">Quadratura rur&longs;us Hippocratis, &amp; Bry&longs;onis. </s>
 <s id="id.000362"><emph type="italics"/>Qu&aelig;&longs;t. 24. De duobus circulis concentricis.<emph.end type="italics"/></s></p><p type="main">           <s id="s.000173">Mathe&shy;<lb/>
  matic&aelig; non contentio&longs;&aelig;. </s>
 <s id="id.000363"><emph type="italics"/>Qu&aelig;&longs;t. 25. De funibus lectulorum.<emph.end type="italics"/></s></p><p type="main">           <s id="s.000174">Quadratio Antiphontis.<emph.end type="italics"/></s>
          </p>
 <s id="id.000364"><emph type="italics"/>Qu&aelig;&longs;t. 26. De ligno humeris gestato.<emph.end type="italics"/></s></p><p type="main">         <p type="head">
            <s id="s.000175">Ex 1. Phy&longs;ic.<!-- KEEP S--></s>
 <s id="id.000365"><emph type="italics"/>Qu&aelig;&longs;t. 27. De ponderibus humero ge&longs;tatis.<emph.end type="italics"/></s></p><p type="main">         </p>
          <p type="main">
 <s id="id.000366"><emph type="italics"/>Qu&aelig;&longs;t. 28. De Tollenone.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">           <s id="s.000176"><emph type="italics"/>T. 11. De Quadraturis circuli Hippocratis, &amp; Antiphontis.<emph.end type="italics"/></s>
          </p>
 <s id="id.000367"><emph type="italics"/>Qu&aelig;&longs;t. 29. De onere &agrave; duobus phalanga ge&longs;tato.<emph.end type="italics"/></s></p><p type="main">         <p type="head">
            <s id="s.000177">Ex 2. Phy&longs;ic.<!-- KEEP S--></s>
 <s id="id.000368"><emph type="italics"/>Qu&aelig;&longs;t. 30. De &longs;urgente &agrave; &longs;e&longs;&longs;ione.<emph.end type="italics"/></s></p><p type="head">         </p>
          <p type="main">
 <s id="id.000369">In libello De Mundo ad Alex.<!-- REMOVE S--><emph type="italics"/>Cap.            <s id="s.000178"><emph type="italics"/>T. 20. Quatenus Per&longs;pectiuus con&longs;ideret lineam.<emph.end type="italics"/></s>
          </p>
 2. Ordo Planetarum.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">         <p type="main">
            <s id="s.000179"><emph type="italics"/>T. 28. Quid con&longs;onantia Diapa&longs;on.<emph.end type="italics"/><!-- KEEP S--></s>
 <s id="id.000370"><emph type="italics"/>Cap.          </p>
          <p type="main">
 3. De Cometis.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">           <s id="s.000180"><emph type="italics"/>T. 68. Mathematicas Demon&longs;trationes habere cau&longs;am, qu&aelig; reducitur ad defini&shy;<lb/>
  tionem.<emph.end type="italics"/></s>
 <s id="id.000371"><emph type="italics"/>Cap.          </p>
          <p type="main">
 5. De fluxu maris. </s>           <s id="s.000181"><emph type="italics"/>T. 8. De nece&longs;&longs;ario, quod e&longs;t in Mathematicis. <!-- KEEP S--></s>
            <s id="s.000182">&amp; omnis triangulus habet tres an&shy;<lb/>
 <s id="id.000372">noua de maris &aelig;&longs;tu &longs;ententia.<emph.end type="italics"/></s></p><p type="head"> gulos, &amp;c.<emph.end type="italics"/></s>
          </p>
 <s id="id.000373">In libro De Admirandis audit.</s></p><p type="main">         <p type="head">
            <s id="s.000183">Ex 3. Phy&longs;ic.<!-- KEEP S--></s>
 <s id="id.000374"><emph type="italics"/>Num. <!-- REMOVE S-->8. De nouo orbe.<emph.end type="italics"/></s>         </p>
          <p type="main">
 </p><p type="main">           <s id="s.000184"><emph type="italics"/>T. 76. Quinam numeri dicantur Gnomones.<emph.end type="italics"/></s>
          </p>
 <s id="id.000375"><emph type="italics"/>Nu. </s>         <p type="main">
            <s id="s.000185"><emph type="italics"/>T. 31. Quonam infinito vtantur Mathematici.<emph.end type="italics"/><!-- KEEP S--></s>
 <s id="id.000376">100. De I&longs;tro, error Ari&longs;t. &amp; veterum Geographorum.<emph.end type="italics"/></s></p><p type="head">         </p>
          <p type="main">
 <s id="id.000377">In libello De lineis in&longs;ecabilibus.</s></p><p type="main">           <s id="s.000186"><emph type="italics"/>T. 71. De infinito Mathematica.<emph.end type="italics"/><!-- KEEP S--></s>
          </p>
 <s id="id.000378"><emph type="italics"/>Primus locus. </s>         <pb pagenum="14" xlink:href="009/01/014.jpg"/>
          <p type="head">
 <s id="id.000379">De commen&longs;urabili, &amp; incommen&longs;urabili.<emph.end type="italics"/></s></p><p type="main">           <s id="s.000187">Ex 4. Phy&longs;ic.<!-- KEEP S--></s>
          </p>
 <s id="id.000380"><emph type="italics"/>2. locus. </s>         <p type="main">
            <s id="s.000188"><emph type="italics"/>T. 120. De commen&longs;urab. </s>
 <s id="id.000381">De figuris incommen&longs;.<emph.end type="italics"/></s></p><p type="main">           <s id="s.000189">&amp; incommen&longs;.<emph.end type="italics"/></s>
          </p>
 <s id="id.000382"><emph type="italics"/>3. locus. </s>         <p type="head">
            <s id="s.000190">Ex 5. Phy&longs;ic.<!-- KEEP S--></s>
 <s id="id.000383">Qu&aelig; linea rationalis, qu&aelig; irrationalis. </s>         </p>
          <p type="main">
 <s id="id.000384">Binomio, Apotome.<emph.end type="italics"/></s></p><p type="main">           <s id="s.000191"><emph type="italics"/>T. 6. De chordis, graui, acuta; media, &amp; vltima.<emph.end type="italics"/></s>
          </p>
 <s id="id.000385"><emph type="italics"/>4. locus. </s>         <p type="head">
            <s id="s.000192">Ex 8. Phy&longs;ic.<!-- KEEP S--></s>
 <s id="id.000386">De communi men&longs;ura.<emph.end type="italics"/></s></p><p type="main">         </p>
          <p type="main">
 <s id="id.000387"><emph type="italics"/>5. locus. </s>           <s id="s.000193"><emph type="italics"/>T. 15. Omnis triangulus habet tres &aelig;quales, &amp;c.<emph.end type="italics"/></s>
          </p>
 <s id="id.000388">Line&aelig; rect&aelig; motus in &longs;emicirculum.<emph.end type="italics"/></s></p><p type="main">         <p type="head">
            <s id="s.000194">Ex 1. de C&oelig;lo.<!-- KEEP S--></s>
 <s id="id.000389"><emph type="italics"/>6. locus. </s>         </p>
          <p type="main">
 <s id="id.000390">Circulorum &aelig;qualium ab inuicem motus.<emph.end type="italics"/></s></p><p type="main">           <s id="s.000195"><emph type="italics"/>T. 33. De minimo indiui&longs;ibili.<emph.end type="italics"/></s>
          </p>
 <s id="id.000391"><emph type="italics"/>7. locus. </s>         <p type="main">
            <s id="s.000196"><emph type="italics"/>T. 36. Ratione vtitur lineari; vt probet mundum e&longs;&longs;e finitum.<emph.end type="italics"/></s>
 <s id="id.000392">Multum Mathematicis demon&longs;trationibus tribuitur ab Ari&longs;totele.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">         </p>
          <p type="main">
 <s id="id.000393"><emph type="italics"/>8. locus. </s>           <s id="s.000197"><emph type="italics"/>T. 48. Commen&longs;urab. <!-- REMOVE S-->&amp; incommen&longs;urab. </s>
            <s id="s.000198">quid.<emph.end type="italics"/></s>
 <s id="id.000394">Si extarent indiuidua, omnes line&aelig; e&longs;&longs;ent commen&longs;.<emph.end type="italics"/></s></p><p type="main">         </p>
          <p type="main">
 <s id="id.000395"><emph type="italics"/>9. locus. </s>           <s id="s.000199"><emph type="italics"/>T. 119. Omnis triangulus habet tres, &amp;c. </s>
            <s id="s.000200">Item de commen&longs;urabili.<emph.end type="italics"/></s>
 <s id="id.000396">Idem probat alite&racute;.<emph.end type="italics"/></s></p><p type="main">         </p>
          <p type="head">
 <s id="id.000397"><emph type="italics"/>10. locus. </s>           <s id="s.000201">Ex 2. de C&oelig;lo.<!-- KEEP S--></s>
          </p>
 <s id="id.000398">Idem ex triangulo.<emph.end type="italics"/></s></p><p type="main">         <p type="main">
            <s id="s.000202"><emph type="italics"/>T. 24. Plato ex planis &longs;olida componebat, qu&igrave;.<emph.end type="italics"/></s>
 <s id="id.000399"><emph type="italics"/>11. locus. </s>         </p>
          <p type="main">
 <s id="id.000400">Idem ex quadrato.<emph.end type="italics"/></s></p><p type="main">           <s id="s.000203"><emph type="italics"/>T. 25. Ordo figurarum planarum.<emph.end type="italics"/></s>
          </p>
 <s id="id.000401"><emph type="italics"/>12. Ex diui&longs;ione line&aelig; idem confirmatur.<emph.end type="italics"/></s></p><p type="main">         <p type="main">
            <s id="s.000204"><emph type="italics"/>T. 31. Aqu&aelig; &longs;uperficiem e&longs;&longs;e &longs;ph&aelig;ricam.<emph.end type="italics"/></s>
 <s id="id.000402"><emph type="italics"/>13. Idem eodem fer&egrave; modo cum pr&aelig;cedenti.<emph.end type="italics"/></s></p><p type="main">         </p>
          <p type="main">
 <s id="id.000403"><emph type="italics"/>14. A quadrato cuiu&longs;uis line&aelig;.<emph.end type="italics"/></s></p><p type="main">           <s id="s.000205"><emph type="italics"/>T. 46. Maiorem circulum velocius moueri. </s>
            <s id="s.000206">Recentiorum ob&longs;eruationes.<emph.end type="italics"/></s>
 <s id="id.000404"><emph type="italics"/>15. Idem probat ex &longs;uperficie, &amp; ex corpore.<emph.end type="italics"/></s></p><p type="main">         </p>
          <p type="main">
 <s id="id.000405"><emph type="italics"/>16. Idem ex contactu circuli cum linea recta.<emph.end type="italics"/></s></p><p type="head">           <s id="s.000207"><emph type="italics"/>T. 57. De ordine C&oelig;lorum ex &longs;ententia A&longs;tronomorum.<emph.end type="italics"/></s>
          </p>
 <s id="id.000406">Ex lib.          <p type="main">
            <s id="s.000208"><emph type="italics"/>T. 59. De rotunditate Lun&aelig;, bis.<emph.end type="italics"/></s>
 9. Hi&longs;tori&aelig; Animalium.</s></p><p type="main">         </p>
          <p type="main">
 <s id="id.000407"><emph type="italics"/>Cap.            <s id="s.000209"><emph type="italics"/>T. 107. Centrum duplex grauit: &amp; molis. </s>
            <s id="s.000210">Qua ratione grauia ad mundi centrum <lb/>
 39. error Ari&longs;t. &amp; noua ob&longs;eruatio de admiranda quadam Aranearum indu&longs;tria.<emph.end type="italics"/></s></p><p type="head"> aptarentur.<emph.end type="italics"/></s>
          </p>
 <s id="id.000408">De Ince&longs;&longs;u Animal.<!-- KEEP S--></s></p><p type="main">         <p type="main">
            <s id="s.000211"><emph type="italics"/>T. 109. Terram e&longs;&longs;e rotundam. </s>
 <s id="id.000409"><emph type="italics"/>Cap.            <s id="s.000212">alio item modo.<emph.end type="italics"/></s>
          </p>
 7. qua ratione in gre&longs;&longs;u fiat bypotenu&longs;a. </s>         <p type="main">
            <s id="s.000213"><emph type="italics"/>T. 110. Terram e&longs;&longs;e paruam re&longs;pectu C&oelig;li.<emph.end type="italics"/></s>
 <s id="id.000410">&amp; ea quid &longs;it.<emph.end type="italics"/></s></p><p type="head">         </p>
          <p type="main">
 <s id="id.000411">De Motu Animal.<!-- KEEP S--></s></p><p type="main">           <s id="s.000214"><emph type="italics"/>T. 111. Mare occidentale coniungi indico.<emph.end type="italics"/></s>
          </p>
 <s id="id.000412"><emph type="italics"/>Cap.          <p type="main">
            <s id="s.000215"><emph type="italics"/>T. 112. De quantitate Terr&aelig;.<emph.end type="italics"/><!-- KEEP S--></s>
 1. in flexuris animalium e&longs;&longs;e centrum, &amp; circulum.<emph.end type="italics"/></s></p><p type="main">         </p>
          <p type="head">
 <s id="id.000413"><emph type="italics"/>Cap.            <s id="s.000216">Ex 3. de C&oelig;lo.<!-- KEEP S--></s>
          </p>
 3. Automata.<emph.end type="italics"/><!-- KEEP S--></s></p><pb xlink:href="009/01/018.jpg" pagenum="18"/><p type="head">         <p type="main">
            <s id="s.000217"><emph type="italics"/>T. 40. Vt componatur &longs;ph&aelig;ra.<emph.end type="italics"/></s>
 <s id="id.000414">De Generatione Animal.<!-- KEEP S--></s></p><p type="main">         </p>
          <p type="main">
 <s id="id.000415"><emph type="italics"/>Lib. 2. cap.            <s id="s.000218"><emph type="italics"/>T. 66. Omne corpus diui&longs;ibile.<emph.end type="italics"/></s>
          </p>
 1. Automata.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">         <p type="main">
            <s id="s.000219"><emph type="italics"/>T. 66. Qu&aelig;nam planarum figurarum totum &longs;patium repleant. </s>
 <s id="id.000416"><emph type="italics"/>Lib. 2. cap.            <s id="s.000220">Hinc de admirabili <lb/>Apum ingenio.<emph.end type="italics"/></s>
          </p>
 4. Omnis triangulus habet tres, &amp;c. </s>         <p type="main">
            <s id="s.000221"><emph type="italics"/>T. eodem. </s>
 <s id="id.000417">Ibidem Diametrum e&longs;&longs;e incommen&shy;           <s id="s.000222">Num plures Pyramides locum replere valeant, vbi Ari&longs;toteles, &amp; omnes <lb/>
 <lb/>&longs;urabilem co&longs;t&aelig;, habet cau&longs;am, &amp; demon&longs;trationem.<emph.end type="italics"/></s></p><p type="head"> expo&longs;itores erra&longs;&longs;e o&longs;tenduntur.<emph.end type="italics"/></s>
          </p>
 <s id="id.000418">In Ethicis ad Nicom.</s></p><p type="main">         <p type="main">
            <s id="s.000223"><emph type="italics"/>T. 71. Terram e&longs;&longs;e cubum, cur dictum &longs;it.<emph.end type="italics"/></s>
 <s id="id.000419"><emph type="italics"/>Lib. 1. cap.          </p>
          <p type="head">
 7. Faber, &amp; Geometra diuers&egrave; con&longs;iderant angulum rectum.<emph.end type="italics"/></s></p><p type="main">           <s id="s.000224">Ex 4. de C&oelig;lo.<!-- KEEP S--></s>
          </p>
 <s id="id.000420"><emph type="italics"/>Lib. 2. cap.          <p type="main">
            <s id="s.000225"><emph type="italics"/>T. 33. Extare centrum Mundi, qu&ograve; grauia tendunt, &agrave; quo leuia abeant.<emph.end type="italics"/></s>
 6. De Arithmetica proportione.<emph.end type="italics"/></s></p><p type="main">         </p>
          <p type="main">
 <s id="id.000421"><emph type="italics"/>cap.            <s id="s.000226"><emph type="italics"/>T. 44. &amp; <expan abbr="&longs;eq.">&longs;eque</expan> Cur qu&aelig;dam grauiora qu&agrave;m aqua, &longs;upernatent.<emph.end type="italics"/></s>
          </p>
 9. Centrum circuli reperire.<emph.end type="italics"/></s></p><p type="main">         <p type="head">
            <s id="s.000227">Ex 2. de Generatione, &amp; Corruptione.<!-- KEEP S--></s>
 <s id="id.000422"><emph type="italics"/>Lib. 3. cap. 3. Diameter, &amp; latus incommen&longs;urabilis: Item quid re&longs;olutio Geome&shy;         </p>
 <lb/>trica: Quid de&longs;ignatio.<emph.end type="italics"/></s></p><p type="main">         <p type="main">
            <s id="s.000228"><emph type="italics"/>Tex. 56. Cur Planet&aelig; duobus motibus moueri dicantur.<emph.end type="italics"/></s>
 <s id="id.000423"><emph type="italics"/>Lib. 5. cap.          </p>
          <p type="head">
 3. Vnitarius numerus. </s>           <s id="s.000229">Ex 1. Meteororum.<!-- KEEP S--></s>
          </p>
 <s id="id.000424">Quid Proportionalitas. <!-- KEEP S--></s>         <p type="main">
            <s id="s.000230"><emph type="italics"/>Summa prima cap. 3. De magnitudine Terr&aelig; ad a&longs;tra, &amp; &longs;olem collata.<emph.end type="italics"/></s>
 <s id="id.000425">Eam in 4. terminis con&shy;         </p>
 <lb/>&longs;i&longs;tere. </s>         <p type="main">
            <s id="s.000231"><emph type="italics"/>Cap. eodem. </s>
 <s id="id.000426">Item quid Permutata proportio. </s>           <s id="s.000232">De magnitudine A&longs;trorum.<emph.end type="italics"/></s>
          </p>
 <s id="id.000427">Item quid Geometrica proportio. </s>         <p type="main">
            <s id="s.000233"><emph type="italics"/>Cap. 4. De ordine Luminarium Solis, &amp; Lun&aelig;.<emph.end type="italics"/><!-- KEEP S--></s>
 <s id="id.000428">Propor&shy;         </p>
 <lb/>tio continuata, &amp; di&longs;iuncta quid.<emph.end type="italics"/></s></p><p type="main">         <p type="main">
            <s id="s.000234"><emph type="italics"/>Summa 2. cap. 3. de Mercurij stella. </s>
 <s id="id.000429"><emph type="italics"/>cap.            <s id="s.000235">Item de Cometa: e&longs;&longs;e in C&oelig;lo.<emph.end type="italics"/><!-- KEEP S--></s>
          </p>
 6. Proportio Geometrica, &amp; Arithmetica.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">         <p type="main">
            <s id="s.000236"><emph type="italics"/>Cap. 5. De Magnitudine Solis, &amp; de vmbra Terr&aelig;.<emph.end type="italics"/><!-- KEEP S--></s>
 <s id="id.000430"><emph type="italics"/>Lib. 6. cap.          </p>
          <p type="main">
 5. Omnis triangulus, &amp;c.<emph.end type="italics"/></s></p><p type="main">           <s id="s.000237"><emph type="italics"/>Cap. 5. De Glaxia.<emph.end type="italics"/></s>
          </p>
 <s id="id.000431"><emph type="italics"/>cap.          <p type="main">
            <s id="s.000238"><emph type="italics"/>Cap. 6. Sententia Ari&longs;totelis de Glaxia, partim defenditur: vera, deinde <lb/>
 8. Principia Mathematica non pendere ab experientia.<emph.end type="italics"/></s></p><p type="main"> aperitur.<emph.end type="italics"/></s>
          </p>
 <s id="id.000432"><emph type="italics"/>Lib. 7. cap. 8. De principijs Mathem.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="head">         <pb pagenum="15" xlink:href="009/01/015.jpg"/>
          <p type="main">
 <s id="id.000433">Ex 1. Magnorum Moralium.</s></p><p type="main">           <s id="s.000239"><emph type="italics"/>Summa 4. cap 1. De Monte Parna&longs;&longs;o, dubia. </s>
            <s id="s.000240">Mare extraneum, quod. </s>
 <s id="id.000434"><emph type="italics"/>Cap.            <s id="s.000241">Errata qu&aelig;&shy;<lb/>
  dam veterum Geographorum, &amp; Ari&longs;t. corriguntur. </s>
 1. Numerus pariter par.<emph.end type="italics"/></s></p><p type="main">           <s id="s.000242">Altitudo montis Cauca&longs;i.<emph.end type="italics"/></s>
          </p>
 <s id="id.000435"><emph type="italics"/>Cap.          <p type="main">
            <s id="s.000243"><emph type="italics"/>Cap. 2. De permutatione Aquarum, &amp; continentis. </s>
 2. Omnis triangulus habet, &amp;c.<emph.end type="italics"/></s></p><p type="main">           <s id="s.000244">Noua ob&longs;eruatio de rotundi&shy;<lb/>
  tate Terr&aelig;, <expan abbr="atq;">atque</expan> Mundi duratione.<emph.end type="italics"/></s>
 <s id="id.000436"><emph type="italics"/>Cap.          </p>
          <p type="head">
 10 Omnis triangulus habet, &amp;c.<emph.end type="italics"/></s></p><p type="main">           <s id="s.000245">Ex 2. Meteororum.<!-- KEEP S--></s>
          </p>
 <s id="id.000437"><emph type="italics"/>Cap.          <p type="main">
            <s id="s.000246"><emph type="italics"/>Summa 1. cap. 1. De Mari rubro.<emph.end type="italics"/></s>
 16. Quadratum quatuor rectis &aelig;quales habere.<emph.end type="italics"/></s></p><p type="main">         </p>
          <p type="main">
 <s id="id.000438"><emph type="italics"/>Cap.            <s id="s.000247"><emph type="italics"/>Summa 2. cap. 2. De ortu stellarum fixarum: Item de occa&longs;u earumdem.<emph.end type="italics"/></s>
          </p>
 30. Proportionale in quatuor terminis con&longs;i&longs;tit.<emph.end type="italics"/></s></p><p type="head">         <p type="main">
            <s id="s.000248"><emph type="italics"/>Cap. eodem, De Canicula. </s>
 <s id="id.000439">Ex 1. lib. <!-- REMOVE S-->Moralium Eudemiorum.</s>           <s id="s.000249">De Zonis temperatis. </s>
            <s id="s.000250">Corona Ariadn&aelig;. </s>
 </p><p type="main">           <s id="s.000251">Zonam torridam <lb/>
  fals&ograve; putabant inho&longs;pitalem. </s>
 <s id="id.000440"><emph type="italics"/>Cap.            <s id="s.000252">cur habitabilis.<emph.end type="italics"/></s>
          </p>
 5. Duplum inter multiplices rationes primum tenet locum.<emph.end type="italics"/></s></p><p type="head">         <p type="main">
            <s id="s.000253"><emph type="italics"/>Cap. 3. De Ventorum &longs;itu.<emph.end type="italics"/></s>
 <s id="id.000441">Ex 1. lib. <!-- REMOVE S-->Mor. <!-- REMOVE S-->Eudemiorum.</s>         </p>
          <p type="head">
            <s id="s.000254">Ex 3. Meteor.<!-- KEEP S--></s>
          </p>
 </p><p type="main">         <p type="main">
            <s id="s.000255"><emph type="italics"/>Summa 2. cap. 2. De Halone, &longs;eu Area, &longs;eu Corona, Mathematica demon&longs;tratio.<emph.end type="italics"/></s>
 <s id="id.000442"><emph type="italics"/>Cap.          </p>
 Omnis triangulus habet tres, &amp;c.<emph.end type="italics"/></s></p><p type="main">         <p type="main">
            <s id="s.000256"><emph type="italics"/>Cap. 4. De Iridis figura Mathematica demon&longs;tratio, &longs;ed deficiens. </s>
 <s id="id.000443"><emph type="italics"/>Cap.            <s id="s.000257">Noua de eadem <lb/>
  tractatio.<emph.end type="italics"/></s>
 10. Diametrum commen&longs;. </s>         </p>
          <p type="main">
 <s id="id.000444">e&longs;&longs;e. </s>           <s id="s.000258"><emph type="italics"/>Cap. 5. De Parelio. <!-- KEEP S--></s>
            <s id="s.000259">Rationes Ari&longs;totelis refelluntur.<emph.end type="italics"/></s>
 <s id="id.000445">Circuli quadratio.<emph.end type="italics"/></s></p><p type="main">         </p>
          <p type="head">
 <s id="id.000446"><emph type="italics"/>Cap.            <s id="s.000260">Ex 1. De Anima.<!-- KEEP S--></s>
          </p>
 12. Triangulus habet tres, &amp;c.<emph.end type="italics"/></s></p><p type="head">         <p type="main">
            <s id="s.000261"><emph type="italics"/>Tex. 11. Quid rectum, quid obliquum. </s>
 <s id="id.000447">Ex 7. lib. <!-- REMOVE S-->Mor. <!-- REMOVE S-->Eudemiorum.</s>           <s id="s.000262">&amp; omnis triangulus habet tres, &amp;c.<emph.end type="italics"/></s>
          </p>
          <p type="main">
            <s id="s.000263"><emph type="italics"/>T. 13. Sph&aelig;ra planum tangit in puncto.<emph.end type="italics"/></s>
 </p><p type="main">         </p>
          <p type="head">
 <s id="id.000448"><emph type="italics"/>Cap.            <s id="s.000264">Ex 2. De Anima.<!-- KEEP S--></s>
          </p>
 12. Diametralis oppo&longs;itio.<emph.end type="italics"/></s></p><p type="head">         <p type="main">
            <s id="s.000265"><emph type="italics"/>T. 12. Definitionem formalem, &amp; cau&longs;alem explicat exemplo Quadrationis Geo&shy;<lb/>
 <s id="id.000449">Ex 3. lib. <!-- REMOVE S-->Politicorum.</s> metric&aelig;.<emph.end type="italics"/></s>
          </p>
 </p><p type="main">         <p type="main">
            <s id="s.000266"><emph type="italics"/>T. 86. Acutum, &amp; Graue, vt differant.<emph.end type="italics"/></s>
 <s id="id.000450"><emph type="italics"/>Cap.          </p>
          <p type="main">
 2. Modi Dorius, &amp; Phrygius apud Mu&longs;icos, qu&igrave;.<emph.end type="italics"/></s></p><p type="head">           <s id="s.000267"><emph type="italics"/>T. 159. De Solis magnitudine ad terram.<emph.end type="italics"/></s>
          </p>
 <s id="id.000451">Ex 4. lib. <!-- REMOVE S-->Polit.<!-- KEEP S--></s>         <p type="head">
            <s id="s.000268">Ex 3. De Anima.<!-- KEEP S--></s>
 </p><p type="main">         </p>
          <p type="main">
 <s id="id.000452"><emph type="italics"/>Cap.            <s id="s.000269"><emph type="italics"/>T. 21. Incommen&longs;urabile.<emph.end type="italics"/></s>
          </p>
 3. Modus Doricus, &amp; Phrygius.<emph.end type="italics"/></s></p><p type="head">         <p type="main">
            <s id="s.000270"><emph type="italics"/>T. 25. Indiui&longs;ibilia e&longs;&longs;e priuationes.<emph.end type="italics"/></s>
 <s id="id.000453">Ex 5. lib. <!-- REMOVE S-->Polit.<!-- KEEP S--></s>         </p>
          <p type="main">
 </p><p type="main">           <s id="s.000271"><emph type="italics"/>T. 32. Permutata proportio.<emph.end type="italics"/></s>
          </p>
 <s id="id.000454"><emph type="italics"/>Cap.          <p type="head">
            <s id="s.000272">Ex lib. <!-- REMOVE S-->De Sen&longs;u.</s>
 1. Aequitas Arithmetica, &amp; qu&aelig; &longs;ecundum dignitatem.<emph.end type="italics"/></s></p><p type="head">         </p>
          <p type="main">
 <s id="id.000455">Ex 8. Polit.<!-- KEEP S--></s></p><p type="main">           <s id="s.000273"><emph type="italics"/>Capite 6. Die&longs;is.<emph.end type="italics"/><!-- KEEP S--></s>
          </p>
 <s id="id.000456"><emph type="italics"/>Cap.          <p type="main">
            <s id="s.000274"><emph type="italics"/>Cap. 8. Nete. </s>
 5. Mu&longs;ica nuda, &amp; cum melodia. </s>           <s id="s.000275">Diapa&longs;on. <!-- KEEP S--></s>
            <s id="s.000276">Diapen&longs;e.<emph.end type="italics"/></s>
 <s id="id.000457">Rithmus quid.<emph.end type="italics"/></s></p><p type="main">         </p>
          <p type="head">
 <s id="id.000458"><emph type="italics"/>Harmonia lydia. </s>           <s id="s.000277">Ex lib. <!-- REMOVE S-->De Memoria, &amp; Rem.<!-- KEEP S--></s>
          </p>
 <s id="id.000459">Rithmus quid &longs;it dicetur in Problematibus.<emph.end type="italics"/></s></p><p type="main">         <p type="main">
            <s id="s.000278"><emph type="italics"/>Cap. 1. Omnis triangulus habet tres, &amp;c.<emph.end type="italics"/></s>
 <s id="id.000460"><emph type="italics"/>Cap.          </p>
          <p type="main">
 7. Harmoni&aelig;, &amp; Rithmi, vt in pr&aelig;cedenti.<emph.end type="italics"/></s></p><p type="head">           <s id="s.000279"><emph type="italics"/>Cap. 3. Mathemata facile remini&longs;cibilia.<emph.end type="italics"/></s>
          </p>
 <s id="id.000461">Ex Problematibus.</s></p><p type="main">         <p type="head">
            <s id="s.000280">Ex lib. <!-- REMOVE S-->De Somnijs.<!-- KEEP S--></s>
 <s id="id.000462"><emph type="italics"/>Sectione 1. num. </s>         </p>
          <p type="main">
 <s id="id.000463">3. De ortu &longs;yderum innerrantium: Succul&aelig;, Hypades, Atlantides,            <s id="s.000281"><emph type="italics"/>Cap. 2. Terra, cur nauigantibus moueri videatur.<emph.end type="italics"/></s>
 <lb/>Virgili&aelig;, Pleiades. </s>         </p>
          <p type="main">
 <s id="id.000464">num. </s>           <s id="s.000282"><emph type="italics"/>Cap. 3. Cur Oculus digito dimotus res geminatas videat.<emph.end type="italics"/></s>
          </p>
 <s id="id.000465">17. De occa&longs;u affixarum &longs;tellarum.<emph.end type="italics"/></s></p><p type="main">         <p type="head">
            <s id="s.000283">Ex 1. Methaphy&longs;.<!-- KEEP S--></s>
 <s id="id.000466"><emph type="italics"/>Sectione 15. num. </s>         </p>
          <p type="main">
 <s id="id.000467">1. Diametri ethymon.<emph.end type="italics"/></s></p><p type="main">           <s id="s.000284"><emph type="italics"/>Cap. 1. Initium Mathematicarum ab Aegyptiorum Sacerdotibus. </s>
            <s id="s.000285">Item, Automata, <lb/>
 <s id="id.000468"><emph type="italics"/>num. </s> qu&aelig; &longs;olstitia. </s>
            <s id="s.000286">Diameter incommen&longs;.<emph.end type="italics"/></s>
 <s id="id.000469">2. Iterum Diametri ethymologia.<emph.end type="italics"/></s></p><pb xlink:href="009/01/019.jpg" pagenum="19"/><p type="main">         </p>
          <p type="main">
 <s id="id.000470"><emph type="italics"/>num. </s>           <s id="s.000287"><emph type="italics"/>Summa 2. cap. 3. Pythagorei Mathematicas c&aelig;teris pr&aelig;ferebant.<emph.end type="italics"/></s>
          </p>
 <s id="id.000471">3. Denarius numerus cur perfectus. </s>         <p type="main">
            <s id="s.000288"><emph type="italics"/>T. 47. Geometria habet &longs;uas pr&aelig;cognitiones.<emph.end type="italics"/></s>
 <s id="id.000472">eius dignitates. </s>         </p>
          <p type="head">
 <s id="id.000473">Petri Apponen&longs;is deceptio.<emph.end type="italics"/></s></p><p type="main">           <s id="s.000289">Ex 2. Methaphy&longs;.<!-- KEEP S--></s>
          </p>
 <s id="id.000474"><emph type="italics"/>4. De in&aelig;quali &longs;olis vmbrarum incremento.<emph.end type="italics"/></s></p><p type="main">         <p type="main">
            <s id="s.000290"><emph type="italics"/>T. 14. Leges apud Mu&longs;icos quid.<emph.end type="italics"/></s>
 <s id="id.000475"><emph type="italics"/>5. Cur Solis illuminationes &longs;emper rotund&aelig;, quamuis per angulo&longs;a foramina ingre&shy;         </p>
 <lb/>diantur.<emph.end type="italics"/></s></p><p type="main">         <p type="head">
            <s id="s.000291">Ex 3. Methaphy&longs;.<!-- KEEP S--></s>
 <s id="id.000476"><emph type="italics"/>6. Cur Luna &longs;emiplena videtur linea recta terminari? </s>         </p>
          <p type="main">
 <s id="id.000477">vbi de illuminatione Lun&aelig;,            <s id="s.000292"><emph type="italics"/>Tex. <!-- KEEP S--></s>
 <lb/>qu&aelig; experientia docetur.<emph.end type="italics"/></s></p><p type="main">           <s id="s.000293">Mathematicas puras carere cau&longs;is efficiente, &amp; finali. </s>
            <s id="s.000294">Ari&longs;tippus, vt Mathe&shy;<lb/>
 <s id="id.000478"><emph type="italics"/>7. Cur Sol, &amp; Luna videantur plana?<emph.end type="italics"/></s></p><p type="main"> maticas &longs;ugillaret. </s>
            <s id="s.000295">Tetragoni&longs;mus est inuentio medi&aelig;.<emph.end type="italics"/></s>
 <s id="id.000479"><emph type="italics"/>8. De vmbris Solis orientis, occidentis, meridiantis.<emph.end type="italics"/></s></p><p type="main">         </p>
          <pb pagenum="16" xlink:href="009/01/016.jpg"/>
 <s id="id.000480"><emph type="italics"/>9. Cur Lun&aelig;, qu&agrave;m Solis minores vmbr&aelig;?<emph.end type="italics"/></s></p><p type="main">         <p type="main">
            <s id="s.000296"><emph type="italics"/>Tex. 8. Geod&aelig;&longs;ia quid.<emph.end type="italics"/></s>
 <s id="id.000481"><emph type="italics"/>10. Cur in defectu Solis etiam illuminationes ip&longs;ius defectiu&aelig; &longs;unt? </s>         </p>
          <p type="head">
 <s id="id.000482">modus commod&egrave;            <s id="s.000297">Ex 4. Methaphy&longs;.<!-- KEEP S--></s>
 <lb/>videndi eclyp&longs;im Solis.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">         </p>
          <p type="main">
 <s id="id.000483"><emph type="italics"/>Sect. <!-- REMOVE S-->16. nu. </s>           <s id="s.000298"><emph type="italics"/>T. 4. Qu&aelig; &longs;int prim&aelig;, &amp; qu&aelig; &longs;ecund&aelig; inter Mathematicas.<emph.end type="italics"/><!-- KEEP S--></s>
          </p>
          <p type="main">
            <s id="s.000299"><emph type="italics"/>T. 28. Diameter, commen&longs;urabilis.<emph.end type="italics"/></s>
 <s id="id.000484">1. Cur ba&longs;es bullarum in aquis &longs;unt alb&aelig;?<emph.end type="italics"/></s></p><p type="main">         </p>
          <p type="head">
 <s id="id.000485"><emph type="italics"/>3. Opplumbati tali.<emph.end type="italics"/></s></p><p type="main">           <s id="s.000300">Ex 5. Methaphy&longs;.<!-- KEEP S--></s>
          </p>
 <s id="id.000486"><emph type="italics"/>4. De re&longs;ultu cadentium in terram.<emph.end type="italics"/></s></p><p type="main">         <p type="main">
            <s id="s.000301"><emph type="italics"/>T. 2. Exemplum cau&longs;&aelig; formalis ex Diapa&longs;on. <!-- KEEP S--></s>
 <s id="id.000487"><emph type="italics"/>5. Cur conus, &amp; cylindrus diuers&egrave; moueantur.<emph.end type="italics"/></s></p><p type="main">           <s id="s.000302">Qu&aelig; &longs;int proportiones Mu&longs;icales.<emph.end type="italics"/></s>
          </p>
 <s id="id.000488"><emph type="italics"/>6. De voluminum &longs;ectione.<emph.end type="italics"/></s></p><p type="main">         <p type="main">
            <s id="s.000303"><emph type="italics"/>T. 3. Qu&aelig; &longs;it Materia in Mathematicis.<emph.end type="italics"/><!-- KEEP S--></s>
 <s id="id.000489"><emph type="italics"/>12. Idem cum pr&aelig;cedenti 3.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">         </p>
          <p type="main">
 <s id="id.000490"><emph type="italics"/>13. Idem cum 4 &longs;uperiori. </s>           <s id="s.000304"><emph type="italics"/>T. 4. Quidnam &longs;int elementa apud Geometras.<emph.end type="italics"/></s>
          </p>
 <s id="id.000491">reflexio radior&ubreve; pulchr&egrave; comparatur corpor&ubreve; re&longs;ultationi.<emph.end type="italics"/></s></p><p type="head">         <p type="main">
            <s id="s.000305"><emph type="italics"/>T. 12. Die&longs;is.<emph.end type="italics"/><!-- KEEP S--></s>
 <s id="id.000492">Ex &longs;ectione 19. De Mu&longs;ica.<!-- KEEP S--></s></p><p type="main">         </p>
          <p type="main">
 <s id="id.000493"><emph type="italics"/>num. </s>           <s id="s.000306"><emph type="italics"/>T. 17. Diameter incommen&longs;urab. </s>
            <s id="s.000307">Quid potentia vnius line&aelig;.<emph.end type="italics"/></s>
 <s id="id.000494">2. Line&aelig; dupl&aelig; quadratum quadruplum. </s>         </p>
          <p type="main">
 <s id="id.000495">Hoc loco &longs;equentium probl. </s>           <s id="s.000308"><emph type="italics"/>T. 34. Diameter incommen&longs;urabilis.<emph.end type="italics"/></s>
          </p>
 <s id="id.000496">cau&longs;a,          <p type="head">
 <lb/>pr&aelig;mittitur totius Mu&longs;ic&aelig; ortus breuis tractatio.<emph.end type="italics"/></s></p><p type="main">           <s id="s.000309">Ex 6. Methaphy&longs;.<!-- KEEP S--></s>
          </p>
 <s id="id.000497"><emph type="italics"/>3. Vox tam in hypate, quam in nete cantando rumpitur.<emph.end type="italics"/></s></p><p type="main">         <p type="main">
            <s id="s.000310"><emph type="italics"/>T. 1. Principia, elementa, &amp; cau&longs;&aelig; in Mathem.<emph.end type="italics"/><!-- KEEP S--></s>
 <s id="id.000498"><emph type="italics"/>4. Cur facilius hypate, quam nete canitur?<emph.end type="italics"/></s></p><p type="main">         </p>
          <p type="main">
 <s id="id.000499"><emph type="italics"/>5. Cur &longs;uauius notam cantilenam audimus?<emph.end type="italics"/></s></p><p type="main">           <s id="s.000311"><emph type="italics"/>T. 8. Diameter. </s>
            <s id="s.000312">commen&longs;urab.<emph.end type="italics"/></s>
 <s id="id.000500"><emph type="italics"/>7. Cur veteres hypatem omittebant.<emph.end type="italics"/></s></p><p type="main">         </p>
          <p type="main">
 <s id="id.000501"><emph type="italics"/>8. Cur grauis &longs;onum potest acut&aelig;?<emph.end type="italics"/></s></p><p type="main">           <s id="s.000313"><emph type="italics"/>T. 20. De&longs;criptiones. </s>
            <s id="s.000314">Omnis triangulus habet tres, &amp;c. </s>
 <s id="id.000502"><emph type="italics"/>9. Cur cantus ad tibiam vnam, aut lyram &longs;uauior?<emph.end type="italics"/></s></p><p type="main">           <s id="s.000315">Cur Angulus in &longs;emicir&shy;<lb/>
  culo rectus.<emph.end type="italics"/></s>
 <s id="id.000503"><emph type="italics"/>10. Teretizare, quid.<emph.end type="italics"/></s></p><p type="main">         </p>
          <p type="main">
 <s id="id.000504"><emph type="italics"/>11. Vox de&longs;inens acutior fit.<emph.end type="italics"/></s></p><p type="main">           <s id="s.000316"><emph type="italics"/>T. 22. Omnis triangulus habet tres, &amp;c.<emph.end type="italics"/></s>
          </p>
 <s id="id.000505"><emph type="italics"/>12. Grauior &egrave; fidibus contilenam &longs;u&longs;cipit.<emph.end type="italics"/></s></p><p type="main">         <p type="head">
            <s id="s.000317">Ex 10. Methaphy&longs;.<!-- KEEP S--></s>
 <s id="id.000506"><emph type="italics"/>13. In Diapa&longs;on graue e&longs;t acuti Antiphonum.<emph.end type="italics"/></s></p><p type="main">         </p>
          <p type="main">
 <s id="id.000507"><emph type="italics"/>14. Cur Diapa&longs;on vnica vox videtur. </s>           <s id="s.000318"><emph type="italics"/>T. 4. Motum diurnum men&longs;uram reliquorum. </s>
            <s id="s.000319">Die&longs;is.<emph.end type="italics"/><!-- KEEP S--></s>
 <s id="id.000508">Punicum quid.<emph.end type="italics"/></s></p><p type="main">         </p>
          <p type="main">
 <s id="id.000509"><emph type="italics"/>15. Leges Mu&longs;ic&aelig;, qu&aelig;. </s>           <s id="s.000320"><emph type="italics"/>T. 11. Similes figur&aelig; qu&aelig;. </s>
            <s id="s.000321">Diuer&longs;um in Math. quid.<emph.end type="italics"/></s>
 <s id="id.000510">Genera, Diatonicum, Chromaticum, Encharmonium.          </p>
 <lb/></s>         <p type="head">
            <s id="s.000322">Ex 11. Methaphy&longs;.<!-- KEEP S--></s>
 <s id="id.000511">Tetrachorda qu&aelig;.<emph.end type="italics"/></s></p><p type="main">         </p>
          <p type="main">
 <s id="id.000512"><emph type="italics"/>16. Antiphonum &longs;uauius est &longs;ymphono, cur.<emph.end type="italics"/></s></p><p type="main">           <s id="s.000323"><emph type="italics"/>Cap. 2. Ortus punctorum, linearum, &longs;uperficierum.<emph.end type="italics"/></s>
          </p>
 <s id="id.000513"><emph type="italics"/>17. Cur &longs;ola Diapa&longs;on canitur. </s>         <p type="head">
            <s id="s.000324">Ex 12. Methaphy&longs;.<!-- KEEP S--></s>
 <s id="id.000514">Magadis quid. </s>         </p>
          <p type="main">
 <s id="id.000515">Magadare.<emph.end type="italics"/></s></p><p type="main">           <s id="s.000325"><emph type="italics"/>T. 44. Peculiari&longs;&longs;imam Philo&longs;ophiam, Mathematicorum videlicet, A&longs;tronomiam <lb/>
  pluralitatem C&oelig;lorum docere.<emph.end type="italics"/></s>
 <s id="id.000516"><emph type="italics"/>18. De Antiphonis.<emph.end type="italics"/></s></p><p type="main">         </p>
          <p type="main">
 <s id="id.000517"><emph type="italics"/>19. Cur Diapente, &amp; Diabe&longs;&longs;acon non canunt in Antiphonis.<emph.end type="italics"/></s></p><p type="main">           <s id="s.000326"><emph type="italics"/>T. 45. Numerus orbium c&oelig;le&longs;tium &longs;ecundum Eudoxum.<emph.end type="italics"/></s>
          </p>
 <s id="id.000518"><emph type="italics"/>20. Me&longs;e &longs;ola di&longs;&longs;onante, totum de&longs;&longs;onat p&longs;alterium.<emph.end type="italics"/></s></p><p type="main">         <p type="main">
            <s id="s.000327"><emph type="italics"/>T. 46. Itidem ex Eudoxo.<emph.end type="italics"/></s>
 <s id="id.000519"><emph type="italics"/>21. Vocum grauium errores manifestiores, cur?<emph.end type="italics"/></s></p><p type="main">         </p>
          <p type="main">
 <s id="id.000520"><emph type="italics"/>23. Cur nete duplo acutior, quam hypate?<emph.end type="italics"/></s></p><p type="main">           <s id="s.000328"><emph type="italics"/>T. 47. Orbium c&oelig;le&longs;tium numerus, &amp; fabrica ex Calippo.<emph.end type="italics"/></s>
          </p>
 <s id="id.000521"><emph type="italics"/>24. Nete interpellata, hypate re&longs;onare videtur.<emph.end type="italics"/></s></p><p type="main">         <p type="head">
            <s id="s.000329">Ex 13. Methaphy&longs;.<!-- KEEP S--></s>
 <s id="id.000522"><emph type="italics"/>25. Cur Me&longs;e &longs;ic appellata e&longs;t.<emph.end type="italics"/></s></p><p type="main">         </p>
          <p type="main">
 <s id="id.000523"><emph type="italics"/>27. Cur &longs;ola audibilia mores obtinent. </s>           <s id="s.000330"><emph type="italics"/>Cap. 3. Qua ratione Mathematici tractant de Bono.<emph.end type="italics"/><!-- KEEP S--></s>
          </p>
 <s id="id.000524">Rithmus quid.<emph.end type="italics"/></s></p><p type="main">         <p type="head">
            <s id="s.000331">In Mechanicas Qu&aelig;&longs;tiones.</s>
 <s id="id.000525"><emph type="italics"/>28. Cur cantilen&aelig; qu&aelig;dam leges de cebantur?<emph.end type="italics"/></s></p><p type="main">         </p>
          <p type="main">
 <s id="id.000526"><emph type="italics"/>30. De Harmonijs, &longs;eu Modis, &longs;eu Tonis pri&longs;corum.<emph.end type="italics"/></s></p><pb xlink:href="009/01/020.jpg" pagenum="20"/><p type="main">           <s id="s.000332"><emph type="italics"/>Cap. 1. Qu&aelig; &longs;it Mechanica facultas.<emph.end type="italics"/></s>
          </p>
 <s id="id.000527"><emph type="italics"/>31. Vetustiores fui&longs;&longs;e magis Melop&aelig;os.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">         <p type="main">
            <s id="s.000333"><emph type="italics"/>Cap. 2. De Admirandis circuli.<emph.end type="italics"/></s>
 <s id="id.000528"><emph type="italics"/>32. De ip&longs;ius Diapa&longs;on ethymo.<emph.end type="italics"/></s></p><p type="main">         </p>
          <p type="main">
 <s id="id.000529"><emph type="italics"/>33. Cur apt&egrave; de acuto in graue, non &egrave; contra canitur?<emph.end type="italics"/></s></p><p type="main">           <s id="s.000334"><emph type="italics"/>Qu&aelig;&longs;tio 1. De Libra. <!-- KEEP S--></s>
            <s id="s.000335">cur maior, exactior. </s>
 <s id="id.000530"><emph type="italics"/>34. Cur bi&longs;diapente, aut bi&longs;diate&longs;&longs;aron con&longs;onantia non e&longs;t.<emph.end type="italics"/></s></p><p type="main">           <s id="s.000336">inibi Ari&longs;t. lap&longs;us.<emph.end type="italics"/></s>
          </p>
 <s id="id.000531"><emph type="italics"/>35. Cur diapa&longs;on omnium pulcherrima e&longs;t con&longs;onantia?<emph.end type="italics"/></s></p><p type="main">         <p type="main">
            <s id="s.000337"><emph type="italics"/>Qu&aelig;&longs;t. 2. Duplex Libra. <!-- KEEP S--></s>
 <s id="id.000532"><emph type="italics"/>36. Me&longs;e &longs;ola di&longs;&longs;onante, tota perit harmonia.<emph.end type="italics"/></s></p><p type="main">           <s id="s.000338">Piccolomineus reiectus.<emph.end type="italics"/></s>
          </p>
 <s id="id.000533"><emph type="italics"/>37. Cur difficilius acutum canere, quam graue?<emph.end type="italics"/></s></p><p type="main">         <p type="main">
            <s id="s.000339"><emph type="italics"/>Qu&aelig;&longs;t. 3. De Vecte.<emph.end type="italics"/><!-- KEEP S--></s>
 <s id="id.000534"><emph type="italics"/>38. Cur Rythmo, &amp; harmonij omnes gaudent?<emph.end type="italics"/></s></p><p type="main">         </p>
          <p type="main">
 <s id="id.000535"><emph type="italics"/>39. Cur &longs;uauius e&longs;t &longs;ymphonum vni&longs;ono?<emph.end type="italics"/></s></p><p type="main">           <s id="s.000340"><emph type="italics"/>Qu&aelig;&longs;t. 4. De Remo; Petri Non&yuml; in Arist. correctio.<emph.end type="italics"/></s>
          </p>
 <s id="id.000536"><emph type="italics"/>40. Cur &longs;olam Diapa&longs;on magadari &longs;olent?<emph.end type="italics"/></s></p><p type="main">         <p type="main">
            <s id="s.000341"><emph type="italics"/>Qu&aelig;&longs;t. 5. De Temone Nauis.<emph.end type="italics"/><!-- KEEP S--></s>
 <s id="id.000537"><emph type="italics"/>41. Idem cum 5.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">         </p>
          <p type="main">
 <s id="id.000538"><emph type="italics"/>42. Idem cum 34.<emph.end type="italics"/></s></p><p type="main">           <s id="s.000342"><emph type="italics"/>Qu&aelig;&longs;t. 6. De Antenna.<emph.end type="italics"/></s>
          </p>
 <s id="id.000539"><emph type="italics"/>43. Idem cum 24. Iugum in lyra veteri quodnam fuerit, vna cum figura vete&shy;         <p type="main">
 <lb/>ris lyr&aelig;.<emph.end type="italics"/></s></p><p type="main">           <s id="s.000343"><emph type="italics"/>Qu&aelig;&longs;t. 8 De Rota.<emph.end type="italics"/><!-- KEEP S--></s>
          </p>
 <s id="id.000540"><emph type="italics"/>44. Cur &longs;uauius ad tibiam, quam ad lyram cantatur?<emph.end type="italics"/></s></p><p type="main">         <p type="main">
            <s id="s.000344"><emph type="italics"/>Qu&aelig;&longs;t. 9. De Trochlea, &amp; Scytali. figura antiqu&aelig; &longs;cytalis.<emph.end type="italics"/></s>
 <s id="id.000541"><emph type="italics"/>45. Idem cum 25. &longs;uperiori.<emph.end type="italics"/></s></p><p type="main">         </p>
          <p type="main">
 <s id="id.000542"><emph type="italics"/>46. Idem cum 22.<emph.end type="italics"/></s></p><p type="main">           <s id="s.000345"><emph type="italics"/>Qu&aelig;&longs;t. 10. De Libra vacua.<emph.end type="italics"/></s>
          </p>
 <s id="id.000543"><emph type="italics"/>47. Idem cum 26.<emph.end type="italics"/></s></p><p type="main">         <p type="main">
            <s id="s.000346"><emph type="italics"/>Q&ugrave;&aelig;&longs;t. <!-- REMOVE S-->11. De Curru, &amp; &longs;cytala.<emph.end type="italics"/></s>
 <s id="id.000544"><emph type="italics"/>48. Idem cum 7. quid Grauiden&longs;um.<emph.end type="italics"/></s></p><p type="main">         </p>
          <p type="main">
 <s id="id.000545"><emph type="italics"/>49. Idem cum 30. In choris trag&oelig;diarum, nec &longs;ubdorius, nec &longs;ubphrygius modus            <s id="s.000347"><emph type="italics"/>Qu&aelig;&longs;t. 13. De lugo. </s>
 <lb/>erat in v&longs;u.<emph.end type="italics"/></s></p><p type="main">           <s id="s.000348">De Succula.<emph.end type="italics"/><!-- KEEP S--></s>
          </p>
 <s id="id.000546"><emph type="italics"/>50. Cur grauior Melodia e&longs;t etiam mollior?<emph.end type="italics"/></s></p><p type="main">         <p type="main">
            <s id="s.000349"><emph type="italics"/>Qu&aelig;&longs;t. 15. De Vmbelicis.<emph.end type="italics"/></s>
 <s id="id.000547"><emph type="italics"/>51. Dolia duo &aelig;qualia, quorum alterum plenum &longs;it, alterum dimidium, Diapa&longs;on          </p>
 <lb/>re&longs;onant.<emph.end type="italics"/></s></p><p type="head">         <p type="main">
            <s id="s.000350"><emph type="italics"/>Qu&aelig;&longs;t. 16. De ligni oblongi, ac breuis flexura.<emph.end type="italics"/></s>
 <s id="id.000548">Ex &longs;ectione 23.</s></p><p type="main">         </p>
          <pb pagenum="17" xlink:href="009/01/017.jpg"/>
 <s id="id.000549"><emph type="italics"/>De immer&longs;ione Nauigij.<emph.end type="italics"/></s></p><p type="head">         <p type="main">
            <s id="s.000351"><emph type="italics"/>Qu&aelig;&longs;t. 17. De Cuneo.<emph.end type="italics"/><!-- KEEP S--></s>
 <s id="id.000550">Ex &longs;ectione 30.</s></p><p type="main">         </p>
          <p type="main">
 <s id="id.000551"><emph type="italics"/>6. Omnis triangulus habet tres &aelig;quales, &amp;c.<emph.end type="italics"/></s></p><p type="head">           <s id="s.000352"><emph type="italics"/>Qu&aelig;&longs;t. 18. De Trochlea; error Piccolominei.<emph.end type="italics"/></s>
          </p>
 <s id="id.000552">Ex &longs;ectione 31.</s></p><p type="main">         <p type="main">
            <s id="s.000353"><emph type="italics"/>Qu&aelig;&longs;t. 19. De Securi. </s>
 <s id="id.000553"><emph type="italics"/>7. Cur o culos, <expan abbr="ab&longs;q;">ab&longs;que</expan> vlla vi, ab inuicem di&longs;&longs;ociari nequimus?<emph.end type="italics"/></s></p><p type="main">           <s id="s.000354">Securis veteris figura, &amp; con&longs;tructio; vn&agrave; cum affectione <lb/>
  eius mirabili.<emph.end type="italics"/></s>
 <s id="id.000554"><emph type="italics"/>Cur duobus oculis res vna tantum videatur. </s>         </p>
          <p type="main">
 <s id="id.000555">Cur aliquando rei vi&longs;&aelig; gemina&shy;           <s id="s.000355"><emph type="italics"/>Qu&aelig;&longs;t. 20. De Statera. <!-- KEEP S--></s>
 <lb/>tio accidat.<emph.end type="italics"/></s></p><p type="main">           <s id="s.000356">Veteris stater&aelig; figura restaurata.<emph.end type="italics"/></s>
          </p>
 <s id="id.000556"><emph type="italics"/>11. Cur di&longs;tractis oculis res vna du&aelig; apparent?<emph.end type="italics"/></s></p><p type="main">         <p type="main">
            <s id="s.000357"><emph type="italics"/>Qu&aelig;&longs;t. 21. De Dentiforcipe.<emph.end type="italics"/><!-- KEEP S--></s>
 <s id="id.000557"><emph type="italics"/>17. Oculo in latera contorto, cur non fit geminatio.<emph.end type="italics"/></s></p><p type="main">         </p>
          <p type="main">
 <s id="id.000558"><emph type="italics"/>21. Cur &longs;olam rectitudinem vnico oculo in&longs;piciamus.<emph.end type="italics"/></s></p><p type="head">           <s id="s.000358"><emph type="italics"/>Qu&aelig;&longs;t. 22. De Nucifrago.<emph.end type="italics"/><!-- KEEP S--></s>
          </p>
 <s id="id.000559">Auctarium De Oculi Pupilla.<!-- KEEP S--></s></p><p type="main">         <p type="main">
            <s id="s.000359"><emph type="italics"/>Qu&aelig;&longs;t. 23. De Motibus in Rhombo.<emph.end type="italics"/><!-- KEEP S--></s>
 <s id="id.000560"><emph type="italics"/>Oculi fabrica pr&aelig;mittitur, colores oculi vbi &longs;int: vnde qui noctu vident.<emph.end type="italics"/></s></p><p type="main">         </p>
          <p type="main">
 <s id="id.000561"><emph type="italics"/>Primo. </s>           <s id="s.000360"><emph type="italics"/>Qu&aelig;&longs;t. 24. De duobus circulis concentricis.<emph.end type="italics"/></s>
          </p>
 <s id="id.000562">De pupill&aelig; voce.<emph.end type="italics"/></s></p><p type="main">         <p type="main">
            <s id="s.000361"><emph type="italics"/>Qu&aelig;&longs;t. 25. De funibus lectulorum.<emph.end type="italics"/></s>
 <s id="id.000563"><emph type="italics"/>2. Cur in oculo appareat.<emph.end type="italics"/></s></p><p type="main">         </p>
          <p type="main">
 <s id="id.000564"><emph type="italics"/>3. Cur non in tota cornea.<emph.end type="italics"/></s></p><p type="main">           <s id="s.000362"><emph type="italics"/>Qu&aelig;&longs;t. 26. De ligno humeris gestato.<emph.end type="italics"/></s>
          </p>
 <s id="id.000565"><emph type="italics"/>4. Pupill&aelig; definitio.<emph.end type="italics"/></s></p><p type="main">         <p type="main">
            <s id="s.000363"><emph type="italics"/>Qu&aelig;&longs;t. 27. De ponderibus humero ge&longs;tatis.<emph.end type="italics"/></s>
 <s id="id.000566"><emph type="italics"/>5. Cur mgra in omnibus hominibus.<emph.end type="italics"/></s></p><p type="main">         </p>
          <p type="main">
 <s id="id.000567"><emph type="italics"/>6. Cur in Sole euane&longs; cat.<emph.end type="italics"/></s></p><p type="main">           <s id="s.000364"><emph type="italics"/>Qu&aelig;&longs;t. 28. De Tollenone.<emph.end type="italics"/><!-- KEEP S--></s>
          </p>
 <s id="id.000568"><emph type="italics"/>7. Quantitas ip&longs;ius num videatur?<emph.end type="italics"/></s></p><p type="main">         <p type="main">
            <s id="s.000365"><emph type="italics"/>Qu&aelig;&longs;t. 29. De onere &agrave; duobus phalanga ge&longs;tato.<emph.end type="italics"/></s>
 <s id="id.000569"><emph type="italics"/>8. Cur modo maior, modo minor videatur, &amp; cui&longs;dam lepida deceptio.<emph.end type="italics"/></s></p><pb xlink:href="009/01/021.jpg" pagenum="21"/><p type="main">         </p>
          <p type="main">
 <s id="id.000570">Additamentum de natura Mathematicarum di&longs;ciplinarum.</s></p><p type="main">           <s id="s.000366"><emph type="italics"/>Qu&aelig;&longs;t. 30. De &longs;urgente &agrave; &longs;e&longs;&longs;ione.<emph.end type="italics"/></s>
          </p>
 <s id="id.000571"><emph type="italics"/>Primo. </s>         <p type="head">
            <s id="s.000367">In libello De Mundo ad Alex.<!-- REMOVE S--><emph type="italics"/>Cap. 2. Ordo Planetarum.<emph.end type="italics"/><!-- KEEP S--></s>
 <s id="id.000572">De &longs;ubiecto Mathem. &longs;eu de materia intelligibili: vbi o&longs;tenduntur definitio&shy;         </p>
 <lb/>nes Mathematic&aelig; e&longs;&longs;e perfecti&longs;&longs;im&aelig;.<emph.end type="italics"/></s></p><p type="main">         <p type="main">
            <s id="s.000368"><emph type="italics"/>Cap. 3. De Cometis.<emph.end type="italics"/><!-- KEEP S--></s>
 <s id="id.000573">2. <emph type="italics"/>Demon&longs;trationes Mathematicas e&longs;&longs;e perfecti&longs;&longs;imas.<emph.end type="italics"/></s></p><p type="main">         </p>
          <p type="main">
 <s id="id.000574">3. <emph type="italics"/>Obiectiones: <expan abbr="atq;">atque</expan> etiam calumni&aelig; diluuntur.<emph.end type="italics"/></s></p><p type="main">           <s id="s.000369"><emph type="italics"/>Cap. 5. De fluxu maris. </s>
            <s id="s.000370">noua de maris &aelig;&longs;tu &longs;ententia.<emph.end type="italics"/></s>
 <s id="id.000575">4. <emph type="italics"/>De pr&aelig;stantia cognitionis, quam Geometria, &amp; Arithmetica gignunt.<emph.end type="italics"/></s></p><p type="main">         </p>
          <p type="head">
 <s id="id.000576">5. <emph type="italics"/>De 4. Mathematicis medijs: A&longs;tronomia, Per&longs;pectiua, Mu&longs;ica, Mechanica.<emph.end type="italics"/></s></p><p type="main">           <s id="s.000371">In libro De Admirandis audit.</s>
          </p>
 <s id="id.000577">6. <emph type="italics"/>Appendix de re&longs;olutione omnium demonstrationum primi Euclidis.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">         <p type="main">
            <s id="s.000372"><emph type="italics"/>Num. <!-- REMOVE S-->8. De nouo orbe.<emph.end type="italics"/></s>
 <s id="id.000578">7. <emph type="italics"/>Clarorum Mathematicorum Chronicon.<emph.end type="italics"/></s></p><p type="head">         </p>
          <p type="main">
 <s id="id.000579"><emph type="bold"/>Finis Primi Indicis.<emph.end type="bold"/></s></p></section><pb xlink:href="009/01/022.jpg" pagenum="22"/><section><p type="head">           <s id="s.000373"><emph type="italics"/>Nu. </s>
            <s id="s.000374">100. De I&longs;tro, error Ari&longs;t. &amp; veterum Geographorum.<emph.end type="italics"/></s>
 <s id="id.000580"><emph type="italics"/>ALTER INDEX<emph.end type="italics"/></s></p><p type="main">         </p>
          <p type="head">
 <s id="id.000581"><emph type="italics"/>Quo loca Aristotelis Geometrica, in hoc Opere explicata,            <s id="s.000375">In libello De lineis in&longs;ecabilibus.</s>
 <lb/>ad Euclidem, &longs;ecundum propo&longs;itionum ordinem refe&shy;         </p>
 <lb/>runtur; vt Mathematicarum Profe&longs;&longs;ores habeant,          <p type="main">
 <lb/>vnde &longs;uas pr&aelig;lectiones aliquando valeant locupletare.<emph.end type="italics"/></s></p><p type="head">           <s id="s.000376"><emph type="italics"/>Primus locus. </s>
            <s id="s.000377">De commen&longs;urabili, &amp; incommen&longs;urabili.<emph.end type="italics"/></s>
 <s id="id.000582"><emph type="italics"/>In Primo Elem.          </p>
          <p type="main">
 Euclidis.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">           <s id="s.000378"><emph type="italics"/>2. locus. </s>
            <s id="s.000379">De figuris incommen&longs;.<emph.end type="italics"/></s>
 <s id="id.000583">Ad verbum ip&longs;um <emph type="italics"/>(Elementum Euclidis)<emph.end type="italics"/> vide infra tex. <!-- REMOVE S-->4. quinti          </p>
 <lb/>Methaph.<!-- KEEP S--></s>         <p type="main">
            <s id="s.000380"><emph type="italics"/>3. locus. </s>
 </p><p type="main">           <s id="s.000381">Qu&aelig; linea rationalis, qu&aelig; irrationalis. </s>
            <s id="s.000382">Binomio, Apotome.<emph.end type="italics"/></s>
 <s id="id.000584">Ad principia primi elementorum, vide infra tex. <!-- REMOVE S-->5. pri. <!-- REMOVE S-->Po&longs;ter.<!-- KEEP S--></s>         </p>
          <p type="main">
            <s id="s.000383"><emph type="italics"/>4. locus. </s>
            <s id="s.000384">De communi men&longs;ura.<emph.end type="italics"/></s>
 </p><p type="main">         </p>
          <p type="main">
 <s id="id.000585">Ad definitionem 10. pri. <!-- REMOVE S-->pro angulo recto, vide 30. qu&aelig;&longs;t. </s>           <s id="s.000385"><emph type="italics"/>5. locus. </s>
            <s id="s.000386">Line&aelig; rect&aelig; motus in &longs;emicirculum.<emph.end type="italics"/></s>
          </p>
          <p type="main">
 <s id="id.000586">Mecha&shy;           <s id="s.000387"><emph type="italics"/>6. locus. </s>
 <lb/>nic. <!-- REMOVE S-->&amp; cap.            <s id="s.000388">Circulorum &aelig;qualium ab inuicem motus.<emph.end type="italics"/></s>
          </p>
 7. lib.          <p type="main">
            <s id="s.000389"><emph type="italics"/>7. locus. </s>
 1. Eth.<!-- KEEP S--></s>           <s id="s.000390">Multum Mathematicis demon&longs;trationibus tribuitur ab Ari&longs;totele.<emph.end type="italics"/><!-- KEEP S--></s>
          </p>
 </p><p type="main">         <p type="main">
            <s id="s.000391"><emph type="italics"/>8. locus. </s>
 <s id="id.000587">Ad axioma 10. quamuis Ari&longs;toteles nihil hac de re dicat; &longs;cias tamen velim            <s id="s.000392">Si extarent indiuidua, omnes line&aelig; e&longs;&longs;ent commen&longs;.<emph.end type="italics"/></s>
 <lb/>hoc vno axiomate qu&ecedil;&longs;tionem <expan abbr="qu&atilde;dam">quandam</expan> inter Philo&longs;ophos vald&egrave; difficilem,          </p>
 <lb/>facile di&longs;&longs;olui. </s>         <p type="main">
            <s id="s.000393"><emph type="italics"/>9. locus. </s>
 <s id="id.000588">ea e&longs;t, vtrum marmor, aut adamas, aliudue quidpiam infle&shy;           <s id="s.000394">Idem probat alite&racute;.<emph.end type="italics"/></s>
 <lb/>xibile &longs;ucce&longs;&longs;iu&egrave; findi, &amp; aperiri po&longs;&longs;it. </s>         </p>
          <p type="main">
 <s id="id.000589">qui enim aiunt, &longs;ic refelluntur, quia            <s id="s.000395"><emph type="italics"/>10. locus. </s>
 <lb/>nimirum &longs;equeretur, duas rectas lineas habere &longs;egmentum commune: in&shy;           <s id="s.000396">Idem ex triangulo.<emph.end type="italics"/></s>
 <lb/>telligantur enim du&aelig; line&aelig;, vna in vna &longs;uperficie, altera vero in altera, qu&aelig;          </p>
 <lb/>antequam incipiat apertio, congruant; Quoniam igitur tota illa apertio          <p type="main">
 <lb/>non fit in in&longs;tanti, &longs;ed &longs;ucce&longs;&longs;iu&egrave;, facta iam aliqua apertionis parte con&longs;i&shy;           <s id="s.000397"><emph type="italics"/>11. locus. </s>
 <lb/>derentur pr&aelig;dict&aelig; line&aelig;, erit igitur earum pars aliqua ab inuicem &longs;epara&shy;           <s id="s.000398">Idem ex quadrato.<emph.end type="italics"/></s>
 <lb/>ta, altera ver&ograve; adhuc alteri congruens, ergo &longs;equetur, duas lineas habere          </p>
 <lb/>&longs;egmentum commune, quod e&longs;t impo&longs;&longs;ibile, quia contra 10. axioma.</s></p><p type="main">         <p type="main">
            <s id="s.000399"><emph type="italics"/>12. Ex diui&longs;ione line&aelig; idem confirmatur.<emph.end type="italics"/></s>
 <s id="id.000590">Ad Calcem axiomatum primi accommodetur tex. <!-- REMOVE S-->1. primi Po&longs;ter.<!-- KEEP S--></s>         </p>
          <p type="main">
 </p><p type="main">           <s id="s.000400"><emph type="italics"/>13. Idem eodem fer&egrave; modo cum pr&aelig;cedenti.<emph.end type="italics"/></s>
          </p>
 <s id="id.000591">Ad primam primi, po&longs;t ip&longs;ius explicationem, commod&egrave; declarari pote&longs;t, cur          <p type="main">
 <lb/>Ari&longs;t. Demon&longs;trationes Geometricas appellet De&longs;criptiones, &amp; De&longs;igna&shy;           <s id="s.000401"><emph type="italics"/>14. A quadrato cuiu&longs;uis line&aelig;.<emph.end type="italics"/></s>
 <lb/>tiones, vide cap.          </p>
          <p type="main">
 de Priori, &amp; cap.            <s id="s.000402"><emph type="italics"/>15. Idem probat ex &longs;uperficie, &amp; ex corpore.<emph.end type="italics"/></s>
          </p>
 24. &longs;ecti primi, libri primi Priorum, &amp;          <p type="main">
 <lb/>tex. <!-- REMOVE S-->4. quinti Methaph. <!-- REMOVE S-->&amp; tex. <!-- REMOVE S-->20. &longs;exti Methaph. <!-- REMOVE S-->&amp; cap.            <s id="s.000403"><emph type="italics"/>16. Idem ex contactu circuli cum linea recta.<emph.end type="italics"/></s>
          </p>
 3. lib.          <p type="head">
            <s id="s.000404">Ex lib. 9. Hi&longs;tori&aelig; Animalium.</s>
 3. Ethic.          </p>
 <lb/><!-- KEEP S--></s>         <p type="main">
            <s id="s.000405"><emph type="italics"/>Cap. 39. error Ari&longs;t. &amp; noua ob&longs;eruatio de admiranda quadam Aranearum indu&longs;tria.<emph.end type="italics"/></s>
          </p>
          <p type="head">
            <s id="s.000406">De Ince&longs;&longs;u Animal.<!-- KEEP S--></s>
          </p>
          <p type="main">
            <s id="s.000407"><emph type="italics"/>Cap. 7. qua ratione in gre&longs;&longs;u fiat hypotenu&longs;a. </s>
            <s id="s.000408">&amp; ea quid &longs;it.<emph.end type="italics"/></s>
          </p>
 <s id="id.000592">Item ad primam primi, vide tex. <!-- REMOVE S-->7. &longs;ecundi Po&longs;ter. loco 2.<!-- KEEP S--></s>         <p type="head">
            <s id="s.000409">De Motu Animal.<!-- KEEP S--></s>
 </p><p type="main">         </p>
          <p type="main">
 <s id="id.000593">Ad 5. primi, vide cap.            <s id="s.000410"><emph type="italics"/>Cap. 1. in flexuris animalium e&longs;&longs;e centrum, &amp; circulum.<emph.end type="italics"/></s>
          </p>
 24. &longs;ecti 1 lib.          <p type="main">
            <s id="s.000411"><emph type="italics"/>Cap. 3. Automata.<emph.end type="italics"/><!-- KEEP S--></s>
 1. Priorum.</s></p><p type="main">         </p>
          <pb pagenum="18" xlink:href="009/01/018.jpg"/>
 <s id="id.000594">Ad 21. primi, vide tex. <!-- REMOVE S-->20. primi Po&longs;ter. <!-- REMOVE S-->loco 2.<!-- KEEP S--></s>         <p type="head">
            <s id="s.000412">De Generatione Animal.<!-- KEEP S--></s>
          </p>
          <p type="main">
 </p><p type="main">           <s id="s.000413"><emph type="italics"/>Lib. 2. cap. 1. Automata.<emph.end type="italics"/><!-- KEEP S--></s>
          </p>
 <s id="id.000595">Ad 22. primi, vide locum 10. de lineis in&longs;ecabilibus.</s></p><p type="main">         <p type="main">
            <s id="s.000414"><emph type="italics"/>Lib. 2. cap. 4. Omnis triangulus habet tres, &amp;c. </s>
 <s id="id.000596">Ad 28. primi, vide cap.            <s id="s.000415">Ibidem Diametrum e&longs;&longs;e incommen&shy;<lb/>
  &longs;urabilem co&longs;t&aelig;, habet cau&longs;am, &amp; demon&longs;trationem.<emph.end type="italics"/></s>
 21. &amp; cap.          </p>
          <p type="head">
 22. &longs;ecundi <expan abbr="Prior&utilde;">Priorum</expan>, &amp; tex. <!-- REMOVE S-->13. primi Po&longs;ter.<!-- KEEP S--></s>           <s id="s.000416">In Ethicis ad Nicom.</s>
          </p>
 </p><p type="main">         <p type="main">
            <s id="s.000417"><emph type="italics"/>Lib. 1. cap. 7. Faber, &amp; Geometra diuers&egrave; con&longs;iderant angulum rectum.<emph.end type="italics"/></s>
 <s id="id.000597">Ad 32. primi, vide cap.          </p>
          <p type="main">
 1. &longs;ecti 3. lib.            <s id="s.000418"><emph type="italics"/>Lib. 2. cap. 6. De Arithmetica proportione.<emph.end type="italics"/></s>
          </p>
 1. Prior. <!-- REMOVE S-->&amp; cap.          <p type="main">
            <s id="s.000419"><emph type="italics"/>cap. 9. Centrum circuli reperire.<emph.end type="italics"/></s>
 26. &longs;ecundi <expan abbr="Prior&utilde;">Priorum</expan>, &amp; tex. <!-- REMOVE S-->2.          </p>
 <lb/>primi Po&longs;ter. loco 4. &amp; tex. <!-- REMOVE S-->23. primi Po&longs;ter. <!-- REMOVE S-->vbi ait hanc e&longs;&longs;e poti&longs;&longs;imam          <p type="main">
 <lb/><expan abbr="dem&otilde;&longs;trationem">demon&longs;trationem</expan>. </s>           <s id="s.000420"><emph type="italics"/>Lib. 3. cap. 3. Diameter, &amp; latus incommen&longs;urabilis: Item quid re&longs;olutio Geome&shy;<lb/>
  trica: Quid de&longs;ignatio.<emph.end type="italics"/></s>
          </p>
          <p type="main">
            <s id="s.000421"><emph type="italics"/>Lib. 5. cap. 3. Vnitarius numerus. </s>
            <s id="s.000422">Quid Proportionalitas. <!-- KEEP S--></s>
            <s id="s.000423">Eam in 4. terminis con&shy;<lb/>
  &longs;i&longs;tere. </s>
            <s id="s.000424">Item quid Permutata proportio. </s>
            <s id="s.000425">Item quid Geometrica proportio. </s>
 <s id="id.000598">&amp; tex. <!-- REMOVE S-->37. primi Po&longs;ter. &amp; tex. <!-- REMOVE S-->39. primi Po&longs;ter. <!-- KEEP S--></s>           <s id="s.000426">Propor&shy;<lb/>
  tio continuata, &amp; di&longs;iuncta quid.<emph.end type="italics"/></s>
          </p>
          <p type="main">
            <s id="s.000427"><emph type="italics"/>cap. 6. Proportio Geometrica, &amp; Arithmetica.<emph.end type="italics"/><!-- KEEP S--></s>
          </p>
 <s id="id.000599">Ibidem          <p type="main">
 <lb/>loco 4. &amp; tex. <!-- REMOVE S-->43. primi Po&longs;ter. <!-- REMOVE S-->&amp; tex. <!-- REMOVE S-->2. &longs;ecundi Po&longs;ter. <!-- REMOVE S-->bis. </s>           <s id="s.000428"><emph type="italics"/>Lib. 6. cap. 5. Omnis triangulus, &amp;c.<emph.end type="italics"/></s>
          </p>
          <p type="main">
            <s id="s.000429"><emph type="italics"/>cap. 8. Principia Mathematica non pendere ab experientia.<emph.end type="italics"/></s>
          </p>
          <p type="main">
            <s id="s.000430"><emph type="italics"/>Lib. 7. cap. 8. De principijs Mathem.<emph.end type="italics"/><!-- KEEP S--></s>
          </p>
          <p type="head">
            <s id="s.000431">Ex 1. Magnorum Moralium.</s>
 <s id="id.000600">&amp; tex. <!-- REMOVE S-->89. &longs;e&shy;         </p>
 <lb/>cundi Phy&longs;. &amp; tex. <!-- REMOVE S-->15. octaui Phy&longs;. <!-- REMOVE S-->&amp; tex. <!-- REMOVE S-->119. primi de C&oelig;lo. <!-- KEEP S--></s>         <p type="main">
            <s id="s.000432"><emph type="italics"/>Cap. 1. Numerus pariter par.<emph.end type="italics"/></s>
          </p>
          <p type="main">
            <s id="s.000433"><emph type="italics"/>Cap. 2. Omnis triangulus habet, &amp;c.<emph.end type="italics"/></s>
          </p>
          <p type="main">
            <s id="s.000434"><emph type="italics"/>Cap. 10 Omnis triangulus habet, &amp;c.<emph.end type="italics"/></s>
          </p>
          <p type="main">
 <s id="id.000601">&amp; tex. <!-- REMOVE S-->25.            <s id="s.000435"><emph type="italics"/>Cap. 16. Quadratum quatuor rectis &aelig;quales habere.<emph.end type="italics"/></s>
 <lb/>&longs;ecundi de C&oelig;lo. <!-- KEEP S--></s>         </p>
          <p type="main">
            <s id="s.000436"><emph type="italics"/>Cap. 30. Proportionale in quatuor terminis con&longs;i&longs;tit.<emph.end type="italics"/></s>
          </p>
 <s id="id.000602">tex 11. primi de Anima. <!-- REMOVE S-->&amp; cap.          <p type="head">
            <s id="s.000437">Ex 1. lib. <!-- REMOVE S-->Moralium Eudemiorum.</s>
 1. de mem. </s>         </p>
          <p type="main">
            <s id="s.000438"><emph type="italics"/>Cap. 5. Duplum inter multiplices rationes primum tenet locum.<emph.end type="italics"/></s>
          </p>
 <s id="id.000603">&amp; remini&longs;c.          <p type="head">
 <lb/></s>           <s id="s.000439">Ex 1. lib. <!-- REMOVE S-->Mor. <!-- REMOVE S-->Eudemiorum.</s>
          </p>
 <s id="id.000604">&amp; tex. <!-- REMOVE S-->35. quinti Methaphy&longs;. &amp; tex. <!-- REMOVE S-->20. &longs;exti Methaphy&longs;. <!-- REMOVE S-->&amp; tex. <!-- REMOVE S-->22. &longs;exti          <p type="main">
 <lb/>Methaphy&longs;. <!-- REMOVE S-->&amp; cap.            <s id="s.000440"><emph type="italics"/>Cap. Omnis triangulus habet tres, &amp;c.<emph.end type="italics"/></s>
          </p>
 4. lib.          <p type="main">
            <s id="s.000441"><emph type="italics"/>Cap. 10. Diametrum commen&longs;. </s>
 2. de Generat. <!-- REMOVE S-->animal. <!-- KEEP S--></s>           <s id="s.000442">e&longs;&longs;e. </s>
            <s id="s.000443">Circuli quadratio.<emph.end type="italics"/></s>
          </p>
          <p type="main">
            <s id="s.000444"><emph type="italics"/>Cap. 12. Triangulus habet tres, &amp;c.<emph.end type="italics"/></s>
          </p>
          <p type="head">
            <s id="s.000445">Ex 7. lib. <!-- REMOVE S-->Mor. <!-- REMOVE S-->Eudemiorum.</s>
          </p>
          <p type="main">
            <s id="s.000446"><emph type="italics"/>Cap. 12. Diametralis oppo&longs;itio.<emph.end type="italics"/></s>
          </p>
          <p type="head">
            <s id="s.000447">Ex 3. lib. <!-- REMOVE S-->Politicorum.</s>
 <s id="id.000605">&amp; cap.          </p>
          <p type="main">
 5. lib.            <s id="s.000448"><emph type="italics"/>Cap. 2. Modi Dorius, &amp; Phrygius apud Mu&longs;icos, qu&igrave;.<emph.end type="italics"/></s>
          </p>
 6. Ethic. <!-- REMOVE S-->&amp;          <p type="head">
 <lb/>cap.            <s id="s.000449">Ex 4. lib. <!-- REMOVE S-->Polit.<!-- KEEP S--></s>
          </p>
 2. Magnorum Moral. &amp; cap.          <p type="main">
            <s id="s.000450"><emph type="italics"/>Cap. 3. Modus Doricus, &amp; Phrygius.<emph.end type="italics"/></s>
 10. Mag. Moral. &amp; cap. 16. Mag. Moral.          </p>
 <lb/><!-- REMOVE S-->&amp; cap. <!-- REMOVE S-->7. &longs;ecundi Eudem. &amp; cap. <!-- REMOVE S-->12. &longs;ecundi Eudem. <!-- REMOVE S-->&amp; problema 6. &longs;ectio&shy;<pb xlink:href="009/01/023.jpg" pagenum="23"/>nis 30. tot Ari&longs;totelis loca illu&longs;trat vnica h&aelig;c Euclidis Demon&longs;tratio.</s>         <p type="head">
            <s id="s.000451">Ex 5. lib. <!-- REMOVE S-->Polit.<!-- KEEP S--></s>
          </p>
          <p type="main">
            <s id="s.000452"><emph type="italics"/>Cap. 1. Aequitas Arithmetica, &amp; qu&aelig; &longs;ecundum dignitatem.<emph.end type="italics"/></s>
          </p>
          <p type="head">
            <s id="s.000453">Ex 8. Polit.<!-- KEEP S--></s>
          </p>
          <p type="main">
 </p><p type="main">           <s id="s.000454"><emph type="italics"/>Cap. 5. Mu&longs;ica nuda, &amp; cum melodia. </s>
            <s id="s.000455">Rithmus quid.<emph.end type="italics"/></s>
 <s id="id.000606">Ad &longs;cholion pr&aelig;cedentis 32. primi, vide tex. <!-- REMOVE S-->39. primi Po&longs;ter. loco 3. Item          </p>
 <lb/>tex. <!-- REMOVE S-->25. &longs;ecundi Po&longs;ter. <!-- REMOVE S-->loco vlt.</s>         <p type="main">
            <s id="s.000456"><emph type="italics"/>Harmonia lydia. </s>
            <s id="s.000457">Rithmus quid &longs;it dicetur in Problematibus.<emph.end type="italics"/></s>
          </p>
          <p type="main">
            <s id="s.000458"><emph type="italics"/>Cap. 7. Harmoni&aelig;, &amp; Rithmi, vt in pr&aelig;cedenti.<emph.end type="italics"/></s>
 </p><p type="main">         </p>
          <p type="head">
 <s id="id.000607">Ad 45. primi, vide locum 9. de lineis in&longs;ecabilibus.</s></p><p type="main">           <s id="s.000459">Ex Problematibus.</s>
          </p>
 <s id="id.000608">Ad 46. primi, vide locum 11. de lineis in&longs;ecabilibus.</s></p><p type="main">         <p type="main">
            <s id="s.000460"><emph type="italics"/>Sectione 1. num. </s>
 <s id="id.000609">Ad 47. primi, vide locum 11. de lineis in&longs;ecab. </s>           <s id="s.000461">3. De ortu &longs;yderum inerrantium: Succul&aelig;, Hypades, Atlantides, <lb/>
  Virgili&aelig;, Pleiades. </s>
 <s id="id.000610">Item locum 14. de ij&longs;dem.</s></p><p type="head">           <s id="s.000462">num. </s>
            <s id="s.000463">17. De occa&longs;u affixarum &longs;tellarum.<emph.end type="italics"/></s>
 <s id="id.000611"><emph type="italics"/>In &longs;ecundo Elem.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">         </p>
          <p type="main">
 <s id="id.000612">Ad 2. definitionem 2. Gnomonis, vide cap.            <s id="s.000464"><emph type="italics"/>Sectione 15. num. </s>
            <s id="s.000465">1. Diametri ethymon.<emph.end type="italics"/></s>
 de Motu in Po&longs;tpr&aelig;dicam. </s>         </p>
          <p type="main">
 <s id="id.000613">Qua&shy;           <s id="s.000466"><emph type="italics"/>num. </s>
 <lb/>dratum augetur Gnomone circumpo&longs;ito.</s></p><p type="main">           <s id="s.000467">2. Iterum Diametri ethymologia.<emph.end type="italics"/></s>
          </p>
 <s id="id.000614">Ad 14. propo&longs;. </s>         <pb pagenum="19" xlink:href="009/01/019.jpg"/>
          <p type="main">
 <s id="id.000615">2. opportunum e&longs;t Auditores de Quadratura circuli erudire,            <s id="s.000468"><emph type="italics"/>num. </s>
 <lb/>vide igitur cap.            <s id="s.000469">3. Denarius numerus cur perfectus. </s>
            <s id="s.000470">eius dignitates. </s>
 de relatione in pr&aelig;dicam. </s>           <s id="s.000471">Petri Apponen&longs;is deceptio.<emph.end type="italics"/></s>
          </p>
 <s id="id.000616">&amp; cap.          <p type="main">
            <s id="s.000472"><emph type="italics"/>4. De in&aelig;quali &longs;olis vmbrarum incremento.<emph.end type="italics"/></s>
 31. &longs;ecundi Priorum, &amp;          </p>
 <lb/>tex. <!-- REMOVE S-->23. primi Po&longs;ter. &amp; finem 1. cap. primi Elenchorum. </s>         <p type="main">
            <s id="s.000473"><emph type="italics"/>5. Cur Solis illuminationes &longs;emper rotund&aelig;, quamuis per angulo&longs;a foramina ingre&shy;<lb/>
  diantur.<emph.end type="italics"/></s>
          </p>
 <s id="id.000617">lege primam Ar&shy;         <p type="main">
 <lb/>chimedis de dimen&longs;ione circuli.</s></p><p type="head">           <s id="s.000474"><emph type="italics"/>6. Cur Luna &longs;emiplena videtur linea recta terminari? </s>
            <s id="s.000475">vbi de illuminatione Lun&aelig;, <lb/>
 <s id="id.000618"><emph type="italics"/>In tertio Elem.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main"> qu&aelig; experientia docetur.<emph.end type="italics"/></s>
          </p>
 <s id="id.000619">Ad primam 3. vide cap.          <p type="main">
            <s id="s.000476"><emph type="italics"/>7. Cur Sol, &amp; Luna videantur plana?<emph.end type="italics"/></s>
 9. lib.          </p>
          <p type="main">
 2. Ethycorum.</s></p><p type="main">           <s id="s.000477"><emph type="italics"/>8. De vmbris Solis orientis, occidentis, meridiantis.<emph.end type="italics"/></s>
          </p>
 <s id="id.000620">Ad 2. tertij, vide tex. <!-- REMOVE S-->13. lib.          <p type="main">
            <s id="s.000478"><emph type="italics"/>9. Cur Lun&aelig;, qu&agrave;m Solis minores vmbr&aelig;?<emph.end type="italics"/></s>
 1. de Anima. <!-- REMOVE S-->&amp; locum 16. de lineis in&longs;ecab.</s>         </p>
          <p type="main">
            <s id="s.000479"><emph type="italics"/>10. Cur in defectu Solis etiam illuminationes ip&longs;ius defectiu&aelig; &longs;unt? </s>
            <s id="s.000480">modus commod&egrave; <lb/>
 </p><p type="main"> videndi eclyp&longs;im Solis.<emph.end type="italics"/><!-- KEEP S--></s>
          </p>
 <s id="id.000621">Ad 31. tertij, vide tex. <!-- REMOVE S-->11. &longs;ecundi Po&longs;ter. &amp; tex. <!-- REMOVE S-->20. &longs;exti Methaph. <!-- REMOVE S-->loco 2.<!-- KEEP S--></s>         <p type="main">
            <s id="s.000481"><emph type="italics"/>Sect. <!-- REMOVE S-->16. nu. </s>
            <s id="s.000482">1. Cur ba&longs;es bullarum in aquis &longs;unt alb&aelig;?<emph.end type="italics"/></s>
          </p>
          <p type="main">
            <s id="s.000483"><emph type="italics"/>3. Opplumbati tali.<emph.end type="italics"/></s>
 </p><p type="head">         </p>
          <p type="main">
 <s id="id.000622"><emph type="italics"/>In quarto.<emph.end type="italics"/></s></p><p type="main">           <s id="s.000484"><emph type="italics"/>4. De re&longs;ultu cadentium in terram.<emph.end type="italics"/></s>
          </p>
 <s id="id.000623">Ad commentarium P. <!-- REMOVE S-->Clauij extremum lib.          <p type="main">
            <s id="s.000485"><emph type="italics"/>5. Cur conus, &amp; cylindrus diuers&egrave; moueantur.<emph.end type="italics"/></s>
 4. elementorum. </s>         </p>
          <p type="main">
            <s id="s.000486"><emph type="italics"/>6. De voluminum &longs;ectione.<emph.end type="italics"/></s>
          </p>
 <s id="id.000624">lege tex. <!-- REMOVE S-->66.          <p type="main">
 <lb/>tertij de C&oelig;lo.<!-- KEEP S--></s>           <s id="s.000487"><emph type="italics"/>12. Idem cum pr&aelig;cedenti 3.<emph.end type="italics"/><!-- KEEP S--></s>
          </p>
 </p><p type="head">         <p type="main">
            <s id="s.000488"><emph type="italics"/>13. Idem cum 4 &longs;uperiori. </s>
 <s id="id.000625"><emph type="italics"/>In quinto.<emph.end type="italics"/></s></p><p type="main">           <s id="s.000489">reflexio radior&ubreve;m pulchr&egrave; comparatur corpor&ubreve;m re&longs;ultationi.<emph.end type="italics"/></s>
          </p>
 <s id="id.000626">Ad 4. definitionem 5. vide cap.          <p type="head">
            <s id="s.000490">Ex &longs;ectione 19. De Mu&longs;ica.<!-- KEEP S--></s>
 3. lib.          </p>
          <p type="main">
 2. Ethyc.<!-- KEEP S--></s></p><p type="main">           <s id="s.000491"><emph type="italics"/>num. </s>
            <s id="s.000492">2. Line&aelig; dupl&aelig; quadratum quadruplum. </s>
 <s id="id.000627">Ad 9. definitionem 5. vide cap.            <s id="s.000493">Hoc loco &longs;equentium probl. </s>
            <s id="s.000494">cau&longs;a, <lb/>
 3. lib.  pr&aelig;mittitur totius Mu&longs;ic&aelig; ortus breuis tractatio.<emph.end type="italics"/></s>
          </p>
 5. Ethyc. <!-- REMOVE S-->loco 4. &amp; cap. 31. primi Ma&shy;         <p type="main">
 <lb/>gnorum Moralium.</s>           <s id="s.000495"><emph type="italics"/>3. Vox tam in hypate, quam in nete cantando rumpitur.<emph.end type="italics"/></s>
          </p>
 </p><p type="main">         <p type="main">
            <s id="s.000496"><emph type="italics"/>4. Cur facilius hypate, quam nete canitur?<emph.end type="italics"/></s>
 <s id="id.000628">Ad 10. definitionem 5. vide tex. <!-- REMOVE S-->29. primi Po&longs;ter. loco 2.<!-- KEEP S--></s>         </p>
          <p type="main">
 </p><p type="main">           <s id="s.000497"><emph type="italics"/>5. Cur &longs;uauius notam cantilenam audimus?<emph.end type="italics"/></s>
          </p>
 <s id="id.000629">Ad 12. definitionem 5. vide tex. <!-- REMOVE S-->13. primi Po&longs;ter. <!-- REMOVE S-->loco 3. &amp; tex. <!-- REMOVE S-->25. &longs;ecundi          <p type="main">
 <lb/>Po&longs;ter. <!-- REMOVE S-->&amp; tex. <!-- REMOVE S-->32. tertij de Anima. <!-- REMOVE S-->&amp; cap.            <s id="s.000498"><emph type="italics"/>7. Cur veteres hypatem omittebant.<emph.end type="italics"/></s>
          </p>
 3. lib.          <p type="main">
            <s id="s.000499"><emph type="italics"/>8. Cur grauis &longs;onum potest acut&aelig;?<emph.end type="italics"/></s>
 5. Ethyc. <!-- REMOVE S-->loco 4.<!-- KEEP S--></s>         </p>
          <p type="main">
            <s id="s.000500"><emph type="italics"/>9. Cur cantus ad tibiam vnam, aut lyram &longs;uauior?<emph.end type="italics"/></s>
          </p>
          <p type="main">
            <s id="s.000501"><emph type="italics"/>10. Teretizare, quid.<emph.end type="italics"/></s>
          </p>
          <p type="main">
            <s id="s.000502"><emph type="italics"/>11. Vox de&longs;inens acutior fit.<emph.end type="italics"/></s>
          </p>
          <p type="main">
            <s id="s.000503"><emph type="italics"/>12. Grauior &egrave; fidibus cantilenam &longs;u&longs;cipit.<emph.end type="italics"/></s>
          </p>
          <p type="main">
 </p><p type="main">           <s id="s.000504"><emph type="italics"/>13. In Diapa&longs;on graue e&longs;t acuti Antiphonum.<emph.end type="italics"/></s>
          </p>
 <s id="id.000630">Ad 16. propo&longs;. </s>         <p type="main">
            <s id="s.000505"><emph type="italics"/>14. Cur Diapa&longs;on vnica vox videtur. </s>
 <s id="id.000631">5. vide tex. <!-- REMOVE S-->25. &longs;ecundi Po&longs;ter. loco 2. ex hac Euclidis demon&shy;           <s id="s.000506">Punicum quid.<emph.end type="italics"/></s>
 <lb/>&longs;tratione patet, vitio&longs;am e&longs;&longs;e illam Auerrois argumentationem, 8. Phy&longs;.          </p>
 <lb/><!-- REMOVE S-->comm. <!-- REMOVE S-->15. &longs;cilicet.</s>         <p type="main">
            <s id="s.000507"><emph type="italics"/>15. Leges Mu&longs;ic&aelig;, qu&aelig;. </s>
            <s id="s.000508">Genera, Diatonicum, Chromaticum, Encharmonium. <lb/>
  </s>
            <s id="s.000509">Tetrachorda qu&aelig;.<emph.end type="italics"/></s>
          </p>
 </p><p type="main">         <p type="main">
            <s id="s.000510"><emph type="italics"/>16. Antiphonum &longs;uauius est &longs;ymphono, cur.<emph.end type="italics"/></s>
 <s id="id.000632">Vt &longs;e habet voluntas antiqua ad antiquum effectum,          </p>
 <lb/>Ita &longs;e habet etiam voluntas noua ad effectum nouum:          <p type="main">
 <lb/>Ergo permutando, ita &longs;e habebit voluntas antiqua ad effectum nouum.            <s id="s.000511"><emph type="italics"/>17. Cur &longs;ola Diapa&longs;on canitur. </s>
 <lb/></s>           <s id="s.000512">Magadis quid. </s>
            <s id="s.000513">Magadare.<emph.end type="italics"/></s>
 <s id="id.000633">Quemadmodum voluntas noua ad effectum antiquum.</s></p><p type="main">         </p>
          <p type="main">
 <s id="id.000634">Non enim in permutando confert antecedentem ad antecedentem, &amp; con&shy;           <s id="s.000514"><emph type="italics"/>18. De Antiphonis.<emph.end type="italics"/></s>
 <lb/>&longs;equentem ad con&longs;equentem, vt par erat, &longs;ed confert antecedentem ad          </p>
 <lb/>con&longs;equentem, quod non licet.</s></p><p type="head">         <p type="main">
            <s id="s.000515"><emph type="italics"/>19. Cur Diapente, &amp; Diabe&longs;&longs;acon non canunt in Antiphonis.<emph.end type="italics"/></s>
 <s id="id.000635"><emph type="italics"/>In &longs;exto.<emph.end type="italics"/></s></p><p type="main">         </p>
          <p type="main">
 <s id="id.000636">Ad 2. propo&longs;it. </s>           <s id="s.000516"><emph type="italics"/>20. Me&longs;e &longs;ola di&longs;&longs;onante, totum de&longs;&longs;onat p&longs;alterium.<emph.end type="italics"/></s>
          </p>
 <s id="id.000637">6. vide cap.          <p type="main">
            <s id="s.000517"><emph type="italics"/>21. Vocum grauium errores manifestiores, cur?<emph.end type="italics"/></s>
 2. lib.          </p>
          <p type="main">
 8. Topicorum loco 41.</s></p><p type="main">           <s id="s.000518"><emph type="italics"/>23. Cur nete duplo acutior, quam hypate?<emph.end type="italics"/></s>
          </p>
 <s id="id.000638">Ad 13. &longs;exti, vide tex. <!-- REMOVE S-->12. &longs;ecundi de Anima, &amp; tex. <!-- REMOVE S-->3. tertij Methaphy&longs;.<!-- REMOVE S--><emph type="italics"/>In &longs;eptimo.<emph.end type="italics"/></s>         <p type="main">
            <s id="s.000519"><emph type="italics"/>24. Nete interpellata, hypate re&longs;onare videtur.<emph.end type="italics"/></s>
          </p>
          <p type="main">
 </p><p type="main">           <s id="s.000520"><emph type="italics"/>25. Cur Me&longs;e &longs;ic appellata e&longs;t.<emph.end type="italics"/></s>
          </p>
 <s id="id.000639">Ad primam definitionem 7. vide tex. <!-- REMOVE S-->5. primi Po&longs;ter.<!-- KEEP S--></s>         <p type="main">
            <s id="s.000521"><emph type="italics"/>27. Cur &longs;ola audibilia mores obtinent. </s>
 </p><p type="main">           <s id="s.000522">Rithmus quid.<emph.end type="italics"/></s>
          </p>
 <s id="id.000640">Ad 8. definitionem 7. vide cap.          <p type="main">
            <s id="s.000523"><emph type="italics"/>28. Cur cantilen&aelig; qu&aelig;dam leges decebantur?<emph.end type="italics"/></s>
 1. lib.          </p>
          <p type="main">
 1. Magnorum Moral.<!-- KEEP S--></s></p><p type="head">           <s id="s.000524"><emph type="italics"/>30. De Harmonijs, &longs;eu Modis, &longs;eu Tonis pri&longs;corum.<emph.end type="italics"/></s>
          </p>
 <s id="id.000641"><emph type="italics"/>In octauo.<emph.end type="italics"/></s></p><p type="main">         <pb pagenum="20" xlink:href="009/01/020.jpg"/>
          <p type="main">
 <s id="id.000642">Ad 4. propo&longs;. </s>           <s id="s.000525"><emph type="italics"/>31. Vetustiores fui&longs;&longs;e magis Melop&aelig;os.<emph.end type="italics"/><!-- KEEP S--></s>
          </p>
 <s id="id.000643">9. vide tex. <!-- REMOVE S-->20. primi Po&longs;ter. loco 2.<!-- KEEP S--></s>         <p type="main">
            <s id="s.000526"><emph type="italics"/>32. De ip&longs;ius Diapa&longs;on ethymo.<emph.end type="italics"/></s>
 </p><p type="main">         </p>
          <p type="main">
 <s id="id.000644">Ad 8. propo&longs;. </s>           <s id="s.000527"><emph type="italics"/>33. Cur apt&egrave; de acuto in graue, non &egrave; contra canitur?<emph.end type="italics"/></s>
          </p>
 <s id="id.000645">9. vide problem. </s>         <p type="main">
            <s id="s.000528"><emph type="italics"/>34. Cur bi&longs;diapente, aut bi&longs;diate&longs;&longs;aron con&longs;onantia non e&longs;t.<emph.end type="italics"/></s>
 <s id="id.000646">3. &longs;ectionis 15. loco 4.<!-- KEEP S--></s></p><pb xlink:href="009/01/024.jpg" pagenum="24"/><p type="head">         </p>
          <p type="main">
 <s id="id.000647"><emph type="italics"/>In decimo.<emph.end type="italics"/></s></p><p type="main">           <s id="s.000529"><emph type="italics"/>35. Cur diapa&longs;on omnium pulcherrima e&longs;t con&longs;onantia?<emph.end type="italics"/></s>
          </p>
 <s id="id.000648">Ad primam definitionem 10. vide cap.          <p type="main">
            <s id="s.000530"><emph type="italics"/>36. Me&longs;e &longs;ola di&longs;&longs;onante, tota perit harmonia.<emph.end type="italics"/></s>
 23. &longs;ecti 1. primi Priorum. </s>         </p>
          <p type="main">
 <s id="id.000649">&amp; tex. <!-- REMOVE S-->48.            <s id="s.000531"><emph type="italics"/>37. Cur difficilius acutum canere, quam graue?<emph.end type="italics"/></s>
 <lb/>primi de C&oelig;lo.<!-- KEEP S--></s>         </p>
          <p type="main">
 </p><p type="main">           <s id="s.000532"><emph type="italics"/>38. Cur Rythmo, &amp; harmonij omnes gaudent?<emph.end type="italics"/></s>
          </p>
 <s id="id.000650">Ad 118. decimi, vide cap.          <p type="main">
            <s id="s.000533"><emph type="italics"/>39. Cur &longs;uauius e&longs;t &longs;ymphonum vni&longs;ono?<emph.end type="italics"/></s>
 23. &longs;ecti 1. libri 1. Priorum. </s>         </p>
          <p type="main">
 <s id="id.000651">&amp; &longs;ecto 2. cap.            <s id="s.000534"><emph type="italics"/>40. Cur &longs;olam Diapa&longs;on magadari &longs;olent?<emph.end type="italics"/></s>
          </p>
 23. li&shy;         <p type="main">
 <lb/>bri 1. Priorum. </s>           <s id="s.000535"><emph type="italics"/>41. Idem cum 5.<emph.end type="italics"/><!-- KEEP S--></s>
          </p>
 <s id="id.000652">&amp; cap. 22. lib.          <p type="main">
            <s id="s.000536"><emph type="italics"/>42. Idem cum 34.<emph.end type="italics"/></s>
 2. Priorum. </s>         </p>
          <p type="main">
 <s id="id.000653">&amp; tex. <!-- REMOVE S-->5. primi Po&longs;ter. &amp; tex. <!-- REMOVE S-->44.            <s id="s.000537"><emph type="italics"/>43. Idem cum 24. Iugum in lyra veteri quodnam fuerit, vna cum figura vete&shy;<lb/>
 <lb/>primi Po&longs;ter. <!-- REMOVE S-->&amp; cap.  ris lyr&aelig;.<emph.end type="italics"/></s>
          </p>
 15. primi Po&longs;ter. <!-- REMOVE S-->&amp; tex. <!-- REMOVE S-->119. primi de C&oelig;lo. <!-- KEEP S--></s>         <p type="main">
            <s id="s.000538"><emph type="italics"/>44. Cur &longs;uauius ad tibiam, quam ad lyram cantatur?<emph.end type="italics"/></s>
          </p>
          <p type="main">
            <s id="s.000539"><emph type="italics"/>45. Idem cum 25. &longs;uperiori.<emph.end type="italics"/></s>
          </p>
          <p type="main">
            <s id="s.000540"><emph type="italics"/>46. Idem cum 22.<emph.end type="italics"/></s>
          </p>
          <p type="main">
            <s id="s.000541"><emph type="italics"/>47. Idem cum 26.<emph.end type="italics"/></s>
          </p>
 <s id="id.000654">&amp; tex.          <p type="main">
 <lb/><!-- REMOVE S-->120. quarti Phy&longs;. &amp; tex. <!-- REMOVE S-->21. tertij de Anima. <!-- REMOVE S-->&amp; cap.            <s id="s.000542"><emph type="italics"/>48. Idem cum 7. quid Grauiden&longs;um.<emph.end type="italics"/></s>
          </p>
 1. primi Methaphy&longs;.          <p type="main">
 <lb/><!-- REMOVE S-->&amp; tex. <!-- REMOVE S-->28. quarti Met. <!-- REMOVE S-->&amp; tex. <!-- REMOVE S-->34. quinti Met. <!-- REMOVE S-->&amp; tex. <!-- REMOVE S-->8. &longs;exti Met. <!-- REMOVE S-->&amp; cap.            <s id="s.000543"><emph type="italics"/>49. Idem cum 30. In choris trag&oelig;diarum, nec &longs;ubdorius, nec &longs;ubphrygius modus <lb/>
  erat in v&longs;u.<emph.end type="italics"/></s>
 4.          </p>
 <lb/>lib.          <p type="main">
            <s id="s.000544"><emph type="italics"/>50. Cur grauior Melodia e&longs;t etiam mollior?<emph.end type="italics"/></s>
 2. de Generat. <!-- REMOVE S-->animal. <!-- KEEP S--></s>         </p>
          <p type="main">
            <s id="s.000545"><emph type="italics"/>51. Dolia duo &aelig;qualia, quorum alterum plenum &longs;it, alterum dimidium, Diapa&longs;on <lb/>
  re&longs;onant.<emph.end type="italics"/></s>
          </p>
          <p type="head">
            <s id="s.000546">Ex &longs;ectione 23.</s>
          </p>
          <p type="main">
            <s id="s.000547"><emph type="italics"/>De immer&longs;ione Nauigij.<emph.end type="italics"/></s>
          </p>
          <p type="head">
            <s id="s.000548">Ex &longs;ectione 30.</s>
          </p>
          <p type="main">
            <s id="s.000549"><emph type="italics"/>6. Omnis triangulus habet tres &aelig;quales, &amp;c.<emph.end type="italics"/></s>
          </p>
          <p type="head">
            <s id="s.000550">Ex &longs;ectione 31.</s>
          </p>
          <p type="main">
            <s id="s.000551"><emph type="italics"/>7. Cur o culos, <expan abbr="ab&longs;q;">ab&longs;que</expan> vlla vi, ab inuicem di&longs;&longs;ociari nequimus?<emph.end type="italics"/></s>
          </p>
          <p type="main">
 <s id="id.000655">&amp; lib.            <s id="s.000552"><emph type="italics"/>Cur duobus oculis res vna tantum videatur. </s>
            <s id="s.000553">Cur aliquando rei vi&longs;&aelig; gemina&shy;<lb/>
 3. cap.  tio accidat.<emph.end type="italics"/></s>
          </p>
 3. Ethyc. <!-- REMOVE S-->&amp; cap. 10. &longs;ecundi Eu&shy;         <p type="main">
 <lb/>dem. <!-- KEEP S--></s>           <s id="s.000554"><emph type="italics"/>11. Cur di&longs;tractis oculis res vna du&aelig; apparent?<emph.end type="italics"/></s>
          </p>
          <p type="main">
            <s id="s.000555"><emph type="italics"/>17. Oculo in latera contorto, cur non fit geminatio.<emph.end type="italics"/></s>
 <s id="id.000656">tot Ari&longs;t.          </p>
          <p type="main">
 loca ab hac vna Euclidis Demon&longs;tratione illu&longs;trantur.</s></p><p type="head">           <s id="s.000556"><emph type="italics"/>21. Cur &longs;olam rectitudinem vnico oculo in&longs;piciamus.<emph.end type="italics"/></s>
          </p>
 <s id="id.000657"><emph type="italics"/>In decimotertio.<emph.end type="italics"/></s></p><p type="main">         <p type="head">
            <s id="s.000557">Auctarium De Oculi Pupilla.<!-- KEEP S--></s>
 <s id="id.000658">Ad primam propo&longs;. </s>         </p>
          <p type="main">
 <s id="id.000659">13. &longs;ecundum editionem Commandini, aut Zamberti.            <s id="s.000558"><emph type="italics"/>Oculi fabrica pr&aelig;mittitur, colores oculi vbi &longs;int: vnde qui noctu vident.<emph.end type="italics"/></s>
 <lb/><!-- KEEP S--></s>         </p>
          <p type="main">
 <s id="id.000660">vide initio Priorum, in verbum (Re&longs;olutio)</s></p><p type="main">           <s id="s.000559"><emph type="italics"/>Primo. </s>
            <s id="s.000560">De pupill&aelig; voce.<emph.end type="italics"/></s>
 <s id="id.000661">Atqne h&aelig;c &longs;unt, qu&aelig; ex Elementorum opere Ari&longs;toteles pa&longs;&longs;im v&longs;urpauit,          </p>
 <lb/>qu&aelig;que nos infra explicabimus.</s></p><p type="head">         <p type="main">
            <s id="s.000561"><emph type="italics"/>2. Cur in oculo appareat.<emph.end type="italics"/></s>
 <s id="id.000662"><emph type="bold"/>Finis Secundi Indicis.<emph.end type="bold"/></s></p><p type="main">         </p>
          <p type="main">
 <s id="id.000663">Qu&aelig; ver&ograve; ad alias Mathematicas, Mu&longs;icam &longs;cilicet, Per&longs;pe&shy;           <s id="s.000562"><emph type="italics"/>3. Cur non in tota cornea.<emph.end type="italics"/></s>
 <lb/>ctiuam, Mechanicam, &amp; A&longs;tronomiam pertinens, facil&egrave;          </p>
 <lb/>poterunt ex primo Indice ad vnamquamque earum &longs;eor&shy;         <p type="main">
 <lb/>&longs;um cum libuerit, &longs;ecerni.</s></p></section><pb xlink:href="009/01/025.jpg" pagenum="25"/><section><p type="head">           <s id="s.000563"><emph type="italics"/>4. Pupill&aelig; definitio.<emph.end type="italics"/></s>
          </p>
 <s id="id.000664"><emph type="italics"/>TERTIVS INDEX ALPHABETICVS,<emph.end type="italics"/></s></p><p type="head">         <p type="main">
            <s id="s.000564"><emph type="italics"/>5. Cur nigra in omnibus hominibus.<emph.end type="italics"/></s>
 <s id="id.000665"><emph type="italics"/>cuius numeri re&longs;pondent numeris marginalibus Operis.<emph.end type="italics"/>         </p>
 <lb/><arrow.to.target n="table2"/></s></p><table><table.target id="table2"/><row><cell><emph type="italics"/>A<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Abductio quid. eius inuentor. numero 16. marginali.<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Acuti den&longs;um quid.<emph.end type="italics"/></cell><cell>399</cell></row><row><cell><emph type="italics"/>Aequalitas mathematica, qu&aelig;.<emph.end type="italics"/></cell><cell>10</cell></row><row><cell><emph type="italics"/>Ae&longs;tus maris natura.<emph.end type="italics"/></cell><cell>272</cell></row><row><cell><emph type="italics"/>Aequitas arithmetica, &amp; &aelig;quitas &longs;ecundum dignitatem.<emph.end type="italics"/></cell><cell>330</cell></row><row><cell><emph type="italics"/>Agathir&longs;i populi.<emph.end type="italics"/></cell><cell>382</cell></row><row><cell><emph type="italics"/>Angulus quid. vt nominari debeat 10. angulum in &longs;emicirculo e&longs;&longs;e rectum o&longs;tendi   per cau&longs;am materialem.<emph.end type="italics"/></cell><cell>71</cell></row><row><cell><emph type="italics"/>Angulus rectus vari&egrave; con&longs;ideratur &agrave; Geometra, &amp; &agrave; Fabro.<emph.end type="italics"/></cell><cell>301</cell></row><row><cell><emph type="italics"/>Antiphontis quadratura circuli.<emph.end type="italics"/></cell><cell>13</cell></row><row><cell><emph type="italics"/>Antenn&aelig; nauis problema.<emph.end type="italics"/></cell><cell>248</cell></row><row><cell><emph type="italics"/>Antipbon&aelig; voces.<emph.end type="italics"/> 358. 363. 370. 371.</cell><cell>373</cell></row><row><cell><emph type="italics"/>Apum mirabilis indu&longs;tria.<emph.end type="italics"/></cell><cell>120</cell></row><row><cell><emph type="italics"/>Apotome linea, qu&aelig;.<emph.end type="italics"/></cell><cell>279</cell></row><row><cell><emph type="italics"/>Aqu&aelig; &longs;uperficiem e&longs;&longs;e &longs;ph&aelig;ricam ratione mathematica.<emph.end type="italics"/></cell><cell>107</cell></row><row><cell><emph type="italics"/>Arithmetica proportio.<emph.end type="italics"/></cell><cell>302</cell></row><row><cell><emph type="italics"/>Aranei industria patefacta, qua ad res inaca&longs;&longs; as tran&longs;eat.<emph.end type="italics"/></cell><cell>293</cell></row><row><cell><emph type="italics"/>filum emittit ex &longs;ece&longs;&longs;u contra Ari&longs;totelem pro Democrito.<emph.end type="italics"/></cell><cell><emph type="italics"/>ibidem.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>Astronomi&aelig; principia duo, Apparentia, &amp; Ob&longs;eruatio.<emph.end type="italics"/></cell><cell>8</cell></row><row><cell><emph type="italics"/>Automata, qu&aelig;.<emph.end type="italics"/> 199. 298.</cell><cell><emph type="italics"/>a. b.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>B<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Ba&longs;is ballarum in aqua, cur &longs;it alba, &amp; cur non faciat vmbram.<emph.end type="italics"/></cell><cell>351</cell></row><row><cell><emph type="italics"/>Binomium linea, qu&aelig;.<emph.end type="italics"/></cell><cell>279</cell></row><row><cell><emph type="italics"/>Bra&longs;ilien&longs;es, qua ratione numer are &longs;oliti.<emph.end type="italics"/></cell><cell>340</cell></row><row><cell><emph type="italics"/>Bry&longs;onis quadratura circuli.<emph.end type="italics"/></cell><cell>35</cell></row><row><cell><emph type="italics"/>C<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Calippi opinio de numero C&oelig;lorum.<emph.end type="italics"/></cell><cell>236</cell></row><row><cell><emph type="italics"/>Cantilenam notam &longs;uauius, quam ignotam audimus.<emph.end type="italics"/></cell><cell>362</cell></row><row><cell><emph type="italics"/>Centrum circuli reperire. 303. Centrum mundi mathematic&egrave; o&longs;tenditur. 123. Cen-trum grauitatis, &amp; molis.<emph.end type="italics"/> 38.</cell><cell>112</cell></row><row><cell><emph type="italics"/>Chordarum veterum nomina.<emph.end type="italics"/></cell><cell>359</cell></row><row><cell><emph type="italics"/>Circuli quadratura quid. an po&longs;&longs;ibilis. num. 1. Circulorum concentricorum maiores   velocius moueri. 108. Circuli admiranda. 239. De circulorum concentricorum   volutatione.<emph.end type="italics"/></cell><cell>263</cell></row><row><cell><emph type="italics"/>Coaltern&aelig; line&aelig;, qu&aelig;.<emph.end type="italics"/> 12. 14.</cell><cell>44</cell></row><row><cell><emph type="italics"/>C&oelig;lorum ordinem petendum ex A&longs;tronomis 109. item numerum<emph.end type="italics"/></cell><cell>233</cell></row><row><cell><emph type="italics"/>Colores in mu&longs;ica 78. Colores oculorum vnde.<emph.end type="italics"/></cell><cell>408</cell></row><row><cell><emph type="italics"/>Cometarum tractatiuncula ex recentioribus, qui eas in C&oelig;lo collocant. 136. e&longs;&longs;e &longs;u-pra aerem longi&longs;&longs;imo &longs;altem interuallo o&longs;tenditur mathematic&egrave;. 129. in additione.<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Con&longs;onantia, quid. 64. quibus numeris con&longs;onanti&aelig; con&longs;tent.<emph.end type="italics"/></cell><cell>210</cell></row><row><cell><emph type="italics"/>Conus, &amp; cylindrus, cur vari&egrave; mouentur.<emph.end type="italics"/></cell><cell>355</cell></row><pb xlink:href="009/01/026.jpg" pagenum="26"/><row><cell><emph type="italics"/>Cubus numerus. duo cubi cubus, quid &longs;ignificet.<emph.end type="italics"/></cell><cell>33</cell></row><row><cell><emph type="italics"/>Curru problema.<emph.end type="italics"/></cell><cell>252</cell></row><row><cell><emph type="italics"/>Cunei problema.<emph.end type="italics"/></cell><cell>256</cell></row><row><cell><emph type="italics"/>Cylindri, &amp; coni motus comparatio problematica.<emph.end type="italics"/></cell><cell>335</cell></row><row><cell><emph type="italics"/>D<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Definitiones mathematic&aelig; e&longs;&longs;e e&longs;&longs;entiales, &amp; perfe&longs;&longs;imas. cap. 1. de nat. Math.   definitionum v&longs;us in Mathematicis.<emph.end type="italics"/></cell><cell>81</cell></row><row><cell><emph type="italics"/>De&longs;criptio, &amp; de&longs;cribere, quid.<emph.end type="italics"/> 2. 6. 7.</cell><cell>205</cell></row><row><cell><emph type="italics"/>De&longs;ignatio pro demon&longs;tratione mathematica.<emph.end type="italics"/></cell><cell>305</cell></row><row><cell><emph type="italics"/>Demon&longs;trationis perfect&aelig; exemplum. 36. demon&longs;trationum mathematicarum pr&aelig;-&longs;tantia. cap. 4. de nat. Mathem.<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Dentiforcipis problema.<emph.end type="italics"/></cell><cell>260</cell></row><row><cell><emph type="italics"/>Denarij numeri perfectio. 339. cur <expan abbr="v&longs;q;">v&longs;que</expan> ad denari&ubreve; omnes <expan abbr="g&etilde;tes">gentes</expan> <expan abbr="numer&etilde;t">numerent</expan>.<emph.end type="italics"/></cell><cell>339. 8. <emph type="italics"/>&amp;c.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>Diameter incommen&longs;urabilis cost&aelig;. 5. diametri etymon.<emph.end type="italics"/></cell><cell>337</cell></row><row><cell><emph type="italics"/>Diapa&longs;on quid. 90. 350. omnium con&longs;onantiarum pulcberrima.<emph.end type="italics"/></cell><cell>388</cell></row><row><cell><emph type="italics"/>Diapa&longs;on diapente.<emph.end type="italics"/></cell><cell>359</cell></row><row><cell><emph type="italics"/>Diapente con&longs;onantia, qu&aelig;.<emph.end type="italics"/></cell><cell>359</cell></row><row><cell><emph type="italics"/>Diate&longs;&longs;aron con&longs;onantia, qu&aelig;.<emph.end type="italics"/></cell><cell>359</cell></row><row><cell><emph type="italics"/>Di&longs;d apa&longs;on con&longs;onantia, qu&aelig;.<emph.end type="italics"/></cell><cell>359</cell></row><row><cell><emph type="italics"/>Die&longs;is, quid.<emph.end type="italics"/> 53.</cell><cell>226</cell></row><row><cell><emph type="italics"/>Dolia duo, quomodo aliquando Diapa&longs;on re&longs;onent.<emph.end type="italics"/></cell><cell>402</cell></row><row><cell><emph type="italics"/>Duplum inter multiplicia primum e&longs;t.<emph.end type="italics"/></cell><cell>322</cell></row><row><cell><emph type="italics"/>E<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Elementa mundi non componi ex figuris geometricis.<emph.end type="italics"/></cell><cell>120</cell></row><row><cell><emph type="italics"/>Elementa geometrica, qu&aelig;.<emph.end type="italics"/> 82.</cell><cell>213</cell></row><row><cell><emph type="italics"/>Eudoxi opinio de numero C&oelig;lorum.<emph.end type="italics"/></cell><cell>234</cell></row><row><cell><emph type="italics"/>Exempla mathematicorum, qualia. 11. non e&longs;&longs;e fal&longs;a.<emph.end type="italics"/></cell><cell>43</cell></row><row><cell><emph type="italics"/>Exemplorum veritas, &amp; conformitas, quatenus requirantur.<emph.end type="italics"/></cell><cell>36</cell></row><row><cell><emph type="italics"/>F<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Figuram omnem planam habere &longs;uos angulos externos <expan abbr="quotc&ubreve;q;">quotc&ubreve;que</expan> &aelig;quales quatuor   rectis angulis, qu&aelig; e&longs;t mira proprietas.<emph.end type="italics"/></cell><cell>59</cell></row><row><cell><emph type="italics"/>Figur&aelig; &longs;imiles, qu&aelig;.<emph.end type="italics"/></cell><cell>70</cell></row><row><cell><emph type="italics"/>Figurarum planarum ordo 88. qu&aelig; nam totum locum repleant.<emph.end type="italics"/></cell><cell>96</cell></row><row><cell><emph type="italics"/>Figurarum &longs;olidarum, qu&aelig;nam totum locum repleant: vbi Ari&longs;t. &amp; omnium expo&longs;i-torum rratum aperitur.<emph.end type="italics"/></cell><cell>121</cell></row><row><cell><emph type="italics"/>Figuratio lucis.<emph.end type="italics"/></cell><cell>345</cell></row><row><cell><emph type="italics"/>Figurationes pro demonftrationibus Mathem.<emph.end type="italics"/></cell><cell>194</cell></row><row><cell><emph type="italics"/>Filum Araneorum, ex qua parte corporis exeat, &amp; ex qua materia.<emph.end type="italics"/></cell><cell>293</cell></row><row><cell><emph type="italics"/>Fluxus, ac refluxus maris.<emph.end type="italics"/></cell><cell>272</cell></row><row><cell><emph type="italics"/>Funium lectorum problema.<emph.end type="italics"/></cell><cell>264</cell></row><row><cell><emph type="italics"/>G<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Galaxia quid. 131. Ari&longs;toteles defen&longs;us.<emph.end type="italics"/> 132.</cell><cell>140</cell></row><row><cell><emph type="italics"/>Galibei recens ob&longs;eruatio.<emph.end type="italics"/></cell><cell>141</cell></row><row><cell><emph type="italics"/>Generatria Mu&longs;ic&aelig; veteris. 78. Fus&egrave; explicantur.<emph.end type="italics"/></cell><cell>371</cell></row><row><cell><emph type="italics"/>Geod&aelig;&longs;ia.<emph.end type="italics"/></cell><cell>207</cell></row><row><cell><emph type="italics"/>Geographi&aelig; veteris plura errata,<emph.end type="italics"/> 145. 146. 147. 148.</cell><cell>149</cell></row><pb xlink:href="009/01/027.jpg" pagenum="27"/><row><cell><emph type="italics"/>Gnomon, quid. 3. &amp;<emph.end type="italics"/></cell><cell>331</cell></row><row><cell><emph type="italics"/>Gnomones numeri.<emph.end type="italics"/></cell><cell>93</cell></row><row><cell><emph type="italics"/>Graue qua ratione ad centrum mundi de&longs;cenderet, eiqu&eacute; aptaretur.<emph.end type="italics"/></cell><cell>112</cell></row><row><cell><emph type="italics"/>Grauiden&longs;um, quid.<emph.end type="italics"/></cell><cell>399</cell></row><row><cell><emph type="italics"/>H<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Halonis demonfiratio.<emph.end type="italics"/></cell><cell>161</cell></row><row><cell><emph type="italics"/>Hippocratis chij quadratura circuli. 17. <expan abbr="eiu&longs;d&etilde;">eiu&longs;dem</expan> quadratura lunul&aelig; optima.<emph.end type="italics"/></cell><cell>17</cell></row><row><cell><emph type="italics"/>Hyades, Atlantides, &amp; Succul&aelig;.<emph.end type="italics"/></cell><cell>335</cell></row><row><cell><emph type="italics"/>Hypate, quid.<emph.end type="italics"/></cell><cell>360</cell></row><row><cell><emph type="italics"/>Hypotenu&longs;a in ince&longs;&longs;u animalium.<emph.end type="italics"/></cell><cell>294</cell></row><row><cell><emph type="italics"/>I<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Illuminationes Solis deficientis per foramina tran&longs;euntes, eur &longs;int defectiu&aelig;.<emph.end type="italics"/></cell><cell>350</cell></row><row><cell><emph type="italics"/>modus videndi eclyp&longs;im facilis, ac iucundus.<emph.end type="italics"/></cell><cell><emph type="italics"/>ibidem.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>Ince&longs;&longs;us animalium lineis explicatur.<emph.end type="italics"/></cell><cell>294. <emph type="italics"/>&amp; <expan abbr="&longs;eqq.">&longs;eqque</expan><emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>Incommen&longs;urabilia, qu&aelig;, &amp; eorum inuentores.<emph.end type="italics"/></cell><cell>5</cell></row><row><cell><emph type="italics"/>Indiui&longs;ibilia mathematica e&longs;&longs;e priuationes. 189. oriri ex diui&longs;ione. 231. eorum duo   genera.<emph.end type="italics"/></cell><cell>276</cell></row><row><cell><emph type="italics"/>Infinito, qua ratione vtantur Mathematici.<emph.end type="italics"/> 94.</cell><cell>96</cell></row><row><cell><emph type="italics"/>Iridis demon&longs;tratio &longs;ecundum Ari&longs;t. 163. &amp; &longs;equentibus. Item noua de Iride tra-ctatio. ibidem in additione.<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Iugum in lyra quid, &amp; eius figura.<emph.end type="italics"/></cell><cell>396</cell></row><row><cell><emph type="italics"/>L<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Leges mu&longs;icales.<emph.end type="italics"/></cell><cell>204</cell></row><row><cell><emph type="italics"/>Libra maior, cur exactior. initio Mechanicarum qu&aelig;&longs;t.<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Linea, qu&aelig; terminus est illuminationis in Luna, cur modo recta, modo curua vi-deatur.<emph.end type="italics"/></cell><cell>346</cell></row><row><cell><emph type="italics"/>Line&aelig; rationales, &amp; irrationales, &amp;c.<emph.end type="italics"/></cell><cell>279</cell></row><row><cell><emph type="italics"/>Lumen oculorum noctu videntium, in qua oculi parte manet. in addit. de Pupilla.<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Lumen Solis, cur &longs;it circulare, quamuis per foramina angulo&longs;a ingrediatur.<emph.end type="italics"/></cell><cell>345</cell></row><row><cell><emph type="italics"/>Luna plana, cur appareat, cum &longs;it &longs;ph&aelig;rica. 347. cur in eadem altitudine cum Sole   &longs;upra horizontem, maiorem vmbram efficiat.<emph.end type="italics"/></cell><cell>349</cell></row><row><cell><emph type="italics"/>Lunam e&longs;&longs;e &longs;ph&aelig;ricam. 48. illuminari &longs;ph&aelig;ric&egrave; quid: ibidem &amp; de illuminatione Lu-n&aelig;. iterum e&longs;&longs;e &longs;ph&aelig;ricam ab eclyp&longs;ibus.<emph.end type="italics"/></cell><cell>111</cell></row><row><cell><emph type="italics"/>Luminarium Solis, &amp; Lun&aelig; ordo.<emph.end type="italics"/></cell><cell>133</cell></row><row><cell><emph type="italics"/>Lychanos, quid.<emph.end type="italics"/></cell><cell>360</cell></row><row><cell><emph type="italics"/>Lyr&aelig; veteris figura.<emph.end type="italics"/></cell><cell>396</cell></row><row><cell><emph type="italics"/>M<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Magalis, &longs;eu magas, &amp; magadi&longs;&longs;are.<emph.end type="italics"/> 373.</cell><cell>393</cell></row><row><cell><emph type="italics"/>Materia intelligibilis. fus&egrave; ver&ograve;. explicatur in tract. de nat. Mathem.<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Mathematic&aelig; medi&aelig;, &longs;eu &longs;ubalternat&aelig; habent propter quid &longs;uarum demon&longs;iratio-nem.<emph.end type="italics"/></cell><cell>50</cell></row><row><cell><emph type="italics"/>Mathematici negant reperiri quantitatem indiui&longs;ibilem, &longs;eu minimam.<emph.end type="italics"/></cell><cell>100</cell></row><row><cell><emph type="italics"/>Mathematic&aelig; non &longs;unt contentio&longs;&aelig;. 83. ostendunt per cau&longs;am formalcm.<emph.end type="italics"/></cell><cell>91</cell></row><row><cell><emph type="italics"/>Mathematicas inuenerunt Aegyptij Sacerdotes.<emph.end type="italics"/></cell><cell>198</cell></row><row><cell><emph type="italics"/>Mathematic&aelig; o&longs;tendunt per cau&longs;am materialem, &amp; formalem. 205. earum vtilitas.   ibidem. De earum natura. in proprio tractatu.<emph.end type="italics"/></cell><cell/></row>         <p type="main">
 <pb xlink:href="009/01/028.jpg" pagenum="28"/><row><cell><emph type="italics"/>Mathematic&aelig; maxim&egrave; tractant de Bono, &amp; Pulcro, qua ratione.<emph.end type="italics"/></cell><cell>237</cell></row><row><cell><emph type="italics"/>Mechanica facultas, qu&aelig;.<emph.end type="italics"/></cell><cell>238</cell></row><row><cell><emph type="italics"/>Melodia.<emph.end type="italics"/></cell><cell>331</cell></row><row><cell><emph type="italics"/>Melopeia quid.<emph.end type="italics"/></cell><cell>384</cell></row><row><cell><emph type="italics"/>Medium Demonstrationum Mathem. in earum tractatu.<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Me&longs;e quid.<emph.end type="italics"/></cell><cell>360</cell></row><row><cell><emph type="italics"/>Mina in men&longs;uris quid.<emph.end type="italics"/></cell><cell>53</cell></row><row><cell><emph type="italics"/>Monochordium.<emph.end type="italics"/></cell><cell>359</cell></row><row><cell><emph type="italics"/>Motus nauigij, &amp; remi comparatio. 247. Pulchra P. Nonij in id annotatio con-tra Ari&longs;t.<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Modi mu&longs;ici.<emph.end type="italics"/></cell><cell>383</cell></row><row><cell><emph type="italics"/>Modorum antiquorum ordo, numerus, &amp;c.<emph.end type="italics"/></cell><cell>383</cell></row><row><cell><emph type="italics"/>Motus primi mobilis, &longs;eu diurnus e&longs;t men&longs;ura c&oelig;lestium motuum.<emph.end type="italics"/></cell><cell>225</cell></row><row><cell><emph type="italics"/>Mu&longs;ici recentiores reprehen&longs;i. 331. &amp; in fine Chronologi&aelig;.<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Mu&longs;ic&aelig; totius elementa.<emph.end type="italics"/></cell><cell>359</cell></row><row><cell><emph type="italics"/>Mu&longs;ica nuda, &amp; cum melodia.<emph.end type="italics"/></cell><cell>331</cell></row><row><cell><emph type="italics"/>N<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Nete quid.<emph.end type="italics"/></cell><cell>360</cell></row><row><cell><emph type="italics"/>Nucifragi in&longs;trumenti problema.<emph.end type="italics"/></cell><cell>261</cell></row><row><cell><emph type="italics"/>Numerus, par, impar, primus, &amp; compo&longs;itus, quadratus, &longs;eu &aelig;quilaterus, altera   parte longior. 24. Cubus num.<emph.end type="italics"/></cell><cell>33</cell></row><row><cell><emph type="italics"/>Numeri capitales, qui.<emph.end type="italics"/></cell><cell>82</cell></row><row><cell><emph type="italics"/>Numerum parem e&longs;&longs;e cau&longs;am infiniti: imparem ver&ograve; finiti.<emph.end type="italics"/></cell><cell>93</cell></row><row><cell><emph type="italics"/>Numerorum parium alij &longs;unt primi, alij non.<emph.end type="italics"/></cell><cell>224</cell></row><row><cell><emph type="italics"/>Numerus vnitarius.<emph.end type="italics"/></cell><cell>307</cell></row><row><cell><emph type="italics"/>O<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Oculi cur moueantur con&longs;imiliter.<emph.end type="italics"/></cell><cell>405</cell></row><row><cell><emph type="italics"/>Oculi anathome.<emph.end type="italics"/></cell><cell>408. <emph type="italics"/>&amp;c.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>Omophon&aelig; voces.<emph.end type="italics"/> 372.</cell><cell>392</cell></row><row><cell><emph type="italics"/>Oppo&longs;itio diametralis e&longs;t omnium maxima.<emph.end type="italics"/></cell><cell>327</cell></row><row><cell><emph type="italics"/>Ortus, &amp; occa&longs;us &longs;yderum, quid, &amp; quotuplex: vbide Orione, &amp; Canicula.<emph.end type="italics"/></cell><cell>153</cell></row><row><cell><emph type="italics"/>P<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Paranete qu&aelig; voces, aut chord&aelig;.<emph.end type="italics"/></cell><cell>360</cell></row><row><cell><emph type="italics"/>Parame&longs;e<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Parhypate<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Parelia, cur appareant nondum &longs;atis explicari.<emph.end type="italics"/></cell><cell>182</cell></row><row><cell><emph type="italics"/>Parna&longs;&longs;us mons, vbinam &longs;it. Item paropame&longs;&longs;us.<emph.end type="italics"/></cell><cell>145</cell></row><row><cell><emph type="italics"/>Partes quantitatis &longs;unt materia illius.<emph.end type="italics"/></cell><cell>211</cell></row><row><cell><emph type="italics"/>Per&longs;pectiuus, quatenus con&longs;ideret lineam.<emph.end type="italics"/></cell><cell>89</cell></row><row><cell><emph type="italics"/>Pa&longs;&longs;iones Mathematicorum cum &longs;ubiecto conuertuntur.<emph.end type="italics"/></cell><cell>47</cell></row><row><cell><emph type="italics"/>Pila chri&longs;tallina, vel vitrea, qua ratione comburat.<emph.end type="italics"/></cell><cell>60</cell></row><row><cell><emph type="italics"/>Planet&aelig;, qua ratione moueantur duplici motu.<emph.end type="italics"/></cell><cell>130</cell></row><row><cell><emph type="italics"/>Plato &longs;olida ex planis componebat. 105. cur Elementis figuras Geometricas attri-bueret.<emph.end type="italics"/></cell><cell>122</cell></row><row><cell><emph type="italics"/>Planetarum ordo.<emph.end type="italics"/></cell><cell>271</cell></row><row><cell><emph type="italics"/>Principia Mathematicorum.<emph.end type="italics"/> 2.</cell><cell>118</cell></row><pb xlink:href="009/01/029.jpg" pagenum="29"/><row><cell><emph type="italics"/>Principia &longs;cientiarum duplicia. Ex quibus, &amp; circa quod.<emph.end type="italics"/></cell><cell>61</cell></row><row><cell><emph type="italics"/>Principia Mathematica non pendere ab experientia.<emph.end type="italics"/></cell><cell>315</cell></row><row><cell><emph type="italics"/>Proportio alterna. 28. multiplicata, &longs;eu multiplex &longs;ecundum C&aelig;neum.<emph.end type="italics"/></cell><cell>46</cell></row><row><cell><emph type="italics"/>P&longs;eudographia quid.<emph.end type="italics"/></cell><cell>83</cell></row><row><cell><emph type="italics"/>Proportionalitas quid.<emph.end type="italics"/></cell><cell>308</cell></row><row><cell><emph type="italics"/>Proportio continuata, &amp; di&longs;iuncta quid. 310. alterna, &longs;eu permutata quid.<emph.end type="italics"/></cell><cell><emph type="italics"/>inibi.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>Proportio Geometrica. 311. Arithmetica.<emph.end type="italics"/></cell><cell>302</cell></row><row><cell><emph type="italics"/>Proportio &longs;ecundum dignitatem, e&longs;t Geometrica.<emph.end type="italics"/></cell><cell>330</cell></row><row><cell><emph type="italics"/>Problemata mu&longs;icalia varia &agrave; 360. <expan abbr="v&longs;q;">v&longs;que</expan> ad finem &longs;ectionis 19. problematum.<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Punicum, mu&longs;icum in&longs;trumentum.<emph.end type="italics"/></cell><cell>370</cell></row><row><cell><emph type="italics"/>Pupill&aelig; oculi etymon., &amp; natura. 408. cur in oculo no&longs;tro imago pupill&aelig; appareat.   problem.<emph.end type="italics"/> 2.</cell><cell><emph type="italics"/>ibidem.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>Cur nigra in omnibus hominibus. probl.<emph.end type="italics"/> 5.</cell><cell/></row><row><cell><emph type="italics"/>Cur in Sole euane&longs;cat. probl.<emph.end type="italics"/> 6.</cell><cell/></row><row><cell><emph type="italics"/>Cur modo maior, modo minor appareat.<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Pythagorici primi Mathematicis <expan abbr="oper&atilde;">operam</expan> dedere, easqu&eacute; ceteris &longs;cientijs pr&aelig;poneb&abreve;t.<emph.end type="italics"/></cell><cell>202</cell></row><row><cell><emph type="italics"/>Q<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Qvadratura circuli. vide circulus. de quadratura figurarum rectangularum, &amp;   quadratur&aelig; duplex definitio cau&longs;alis, &amp; formalis.<emph.end type="italics"/></cell><cell>185</cell></row><row><cell><emph type="italics"/>Quantitas an conctet ex indiui&longs;ibili. toto libello de lineis in&longs;ecabilibus argumentis   mathematicis.<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>R<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Remi problema.<emph.end type="italics"/></cell><cell>245</cell></row><row><cell><emph type="italics"/>Re&longs;olutio logica, &amp; mathematica, vt conueniant. 4. &amp;<emph.end type="italics"/></cell><cell>305</cell></row><row><cell><emph type="italics"/>Re&longs;ultus cadentium in terram, quibus angulis fiat.<emph.end type="italics"/></cell><cell>354</cell></row><row><cell><emph type="italics"/>Rythmus fus&egrave; explicatur.<emph.end type="italics"/></cell><cell>381</cell></row><row><cell><emph type="italics"/>Rubrum mare duplex.<emph.end type="italics"/></cell><cell>152</cell></row><row><cell><emph type="italics"/>S<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Scythala quid, &amp; eius figura 250. &amp;<emph.end type="italics"/></cell><cell>252</cell></row><row><cell><emph type="italics"/>Securis problema, vbi de antiqu&aelig; &longs;euris figura, &amp; angulo pulchra demon&longs;tran-tur.<emph.end type="italics"/></cell><cell>258</cell></row><row><cell><emph type="italics"/>Semitonium, quid.<emph.end type="italics"/></cell><cell>360</cell></row><row><cell><emph type="italics"/>Solem e&longs;&longs;e terra multo maiorem: probatur.<emph.end type="italics"/></cell><cell>131</cell></row><row><cell><emph type="italics"/>Sph&aelig;ram planum tangit in puncto. demon&longs;tratur.<emph.end type="italics"/></cell><cell>184</cell></row><row><cell><emph type="italics"/>Statera antiqua, qu&aelig;: eius figura, &amp; problema.<emph.end type="italics"/></cell><cell>259</cell></row><row><cell><emph type="italics"/>Stereomatria, vt differat &agrave; Geometria.<emph.end type="italics"/></cell><cell>49</cell></row><row><cell><emph type="italics"/>Succula.<emph.end type="italics"/></cell><cell>253</cell></row><row><cell><emph type="italics"/>Symphon&aelig; voces.<emph.end type="italics"/> 372.</cell><cell>392</cell></row><row><cell><emph type="italics"/>Symphonia.<emph.end type="italics"/></cell><cell>391</cell></row><row><cell><emph type="italics"/>T<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Temonis nauis problema.<emph.end type="italics"/></cell><cell>246</cell></row><row><cell><emph type="italics"/>Terram e&longs;&longs;e rotundam ex eclyp&longs;i. 114. Item aliter. 115. e&longs;&longs;e re&longs;pectu C&oelig;li   paruam valde. 115. e&longs;&longs;e cubum cur Plato voluerit.<emph.end type="italics"/></cell><cell>122</cell></row><row><cell><emph type="italics"/>Terr&aelig; quantitas.<emph.end type="italics"/></cell><cell>115</cell></row><row><cell><emph type="italics"/>Terram paulatim reduci ad peff&eacute;ctam rotunditatem.<emph.end type="italics"/></cell><cell>151</cell></row><row><cell><emph type="italics"/>Tetragoni&longs;mus. vide Quadratura.<emph.end type="italics"/></cell><cell/></row><pb xlink:href="009/01/030.jpg" pagenum="30"/><row><cell><emph type="italics"/>Teretizare, quid.<emph.end type="italics"/></cell><cell>366</cell></row><row><cell><emph type="italics"/>Tetrachordon, quid.<emph.end type="italics"/></cell><cell>386</cell></row><row><cell><emph type="italics"/>Tollenonis problema.<emph.end type="italics"/></cell><cell>267</cell></row><row><cell><emph type="italics"/>Tonus mu&longs;icus, qui; vnde oriatur.<emph.end type="italics"/></cell><cell>360</cell></row><row><cell><emph type="italics"/>Trochle&aelig; problemata.<emph.end type="italics"/> 249. 250.</cell><cell>251</cell></row><row><cell><emph type="italics"/>Tunic&aelig; oculi. 408. in tractatu de Pupilla.<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>V<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Ventorum nomina, &amp; &longs;itus.<emph.end type="italics"/></cell><cell>160. <emph type="italics"/>a.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>Vectis quotuplex, &amp; c.<emph.end type="italics"/></cell><cell>244</cell></row><row><cell><emph type="italics"/>Veteres canere &longs;olitos non &longs;olum in choris, &longs;ed etiam in &longs;cenis.<emph.end type="italics"/> 371. 384.</cell><cell>400</cell></row><row><cell><emph type="italics"/>Virgili&aelig;, Pleiades.<emph.end type="italics"/></cell><cell>335</cell></row><row><cell><emph type="italics"/>Vi&longs;&aelig; res gemmantur di&longs;tractis oculis.<emph.end type="italics"/></cell><cell>406</cell></row><row><cell><emph type="italics"/>Vi&longs;&aelig; rei geminatio non fit altero oculo in latera torto, cur.<emph.end type="italics"/></cell><cell>407</cell></row><row><cell><emph type="italics"/>Vi&longs;us res vi&longs;as, cur non duplicet, etiam &longs;i duos oculos habeamus.<emph.end type="italics"/></cell><cell>405</cell></row><row><cell><emph type="italics"/>Vmbelici litoralis problema.<emph.end type="italics"/></cell><cell>254</cell></row><row><cell><emph type="italics"/>Vmbram terr&aelig; parum &longs;upra Lunam tran&longs;cendere.<emph.end type="italics"/></cell><cell>137</cell></row><row><cell><emph type="italics"/>Vmbrarum incrementa, &amp; decrementa, cur in&aelig;qualia.<emph.end type="italics"/> 344.</cell><cell>348</cell></row><row><cell><emph type="italics"/>Vi&longs;us res geminat, &longs;i alter oculorum digito pellatur, cur.<emph.end type="italics"/></cell><cell>197</cell></row><row><cell><emph type="italics"/>Vocum mu&longs;icalium antiqu&aelig; appellationes.<emph.end type="italics"/></cell><cell>360</cell></row><row><cell><emph type="italics"/>Vox acuta velocior, grauis ver&ograve; tarda, cur.<emph.end type="italics"/></cell><cell>77</cell></row><row><cell><emph type="italics"/>Voluminum &longs;ectio modo rectam lineam, modo curuam refert, cur.<emph.end type="italics"/></cell><cell>356</cell></row><row><cell><emph type="italics"/>Vnitas, cur indiui&longs;ibilis.<emph.end type="italics"/></cell><cell>22</cell></row><row><cell><emph type="italics"/>Z<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Zonas terr&aelig;, vt Arist. de&longs;ignet: &amp; qu&aelig; &longs;ecundum ip&longs;um &longs;int habitabiles.<emph.end type="italics"/></cell><cell>156</cell></row><row><cell><emph type="italics"/>Zonam torridam quatuor reddunt habitabilem.<emph.end type="italics"/></cell><cell>159</cell></row></table><p type="head"><s id="id.000666">Finis Tertij Indicis.</s></p><pb xlink:href="009/01/031.jpg" pagenum="31"/>           <s id="s.000565"><emph type="italics"/>6. Cur in Sole euane&longs;cat.<emph.end type="italics"/></s>
       </section><section><p type="main">         </p>
          <p type="main">
 <s id="id.000667">Vi&longs;um e&longs;t etiam opportunum Lectori fore, ea &longs;imul in vnum            <s id="s.000566"><emph type="italics"/>7. Quantitas ip&longs;ius num videatur?<emph.end type="italics"/></s>
 <lb/>loca colligere, in quibus Ari&longs;toteles mihi vi&longs;us e&longs;t in Ma&shy;         </p>
 <lb/>thematicis &longs;copum non attigi&longs;&longs;e, vt alij pr&ecedil;&longs;ertim Peripa&shy;         <p type="main">
 <lb/>tetici facilius ea inuenire, <expan abbr="atq;">atque</expan> de ij&longs;dem iudicium ferre            <s id="s.000567"><emph type="italics"/>8. Cur modo maior, modo minor videatur, &amp; cui&longs;dam lepida deceptio.<emph.end type="italics"/></s>
 <lb/>po&longs;&longs;int.         </p>
 <lb/><arrow.to.target n="table3"/></s></p><table><table.target id="table3"/><row><cell><emph type="italics"/>121<emph.end type="italics"/></cell><cell><emph type="italics"/>Nvmero marginali: vbi ait plura Octaedra, &longs;eu Pyramides re-plere locum: in quo omnes pariter expo&longs;itores lap&longs;i &longs;unt.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>124<emph.end type="italics"/></cell><cell><emph type="italics"/>Latitudinem figura, ait, cau&longs;am e&longs;&longs;e &longs;upernatationis. &amp; aquam   re&longs;i&longs;tere &longs;impliciter diui&longs;ioni.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>136<emph.end type="italics"/></cell><cell><emph type="italics"/>Cometas in &longs;uprema aeris regione collocat; cuius contrarium ibi   line ari demonctratione ostenditur.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>147<emph.end type="italics"/></cell><cell><emph type="italics"/>Ait Tanaim, &amp; Indum oriri ex monte Paropami&longs;&longs;o. &amp; c.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>148<emph.end type="italics"/></cell><cell><emph type="italics"/>Ait, tertia parte noctis Cauca&longs;i verticem illuminari &agrave; Sole.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>149<emph.end type="italics"/></cell><cell><emph type="italics"/>Ait Danubium ex Pyreneo monte defluere.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>150<emph.end type="italics"/></cell><cell><emph type="italics"/>Ait fluuium quendam non minorem Rhodano in Liguria ab&longs;orberi,   &amp; iterum egredi.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>152<emph.end type="italics"/></cell><cell><emph type="italics"/>Ait Rubrum mare parum Atlantico Oceano commi&longs;ceri.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>159<emph.end type="italics"/></cell><cell><emph type="italics"/>Zonam torridam inhabit abilem exi&longs;timat.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>164<emph.end type="italics"/></cell><cell><emph type="italics"/>Putat Iridis angulos non po&longs;&longs;e vnum &longs;upra alterum collocari, &longs;ed   tantummodo in orbem.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>182<emph.end type="italics"/></cell><cell><emph type="italics"/>Rationes, quas in Parelij dubitationibus affert, videntur inanes.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>236<emph.end type="italics"/></cell><cell><emph type="italics"/>In &longs;ubducendo c&oelig;le&longs;tium orbium numero, memoria labitur.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>243<emph.end type="italics"/></cell><cell><emph type="italics"/>Ait lineam O L, &longs;uperare lineam L R, quantitate P L, vt in figura.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>245<emph.end type="italics"/></cell><cell><emph type="italics"/>Remum ad vectem primi generis reducit.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>246<emph.end type="italics"/></cell><cell><emph type="italics"/>Temonem nauis reducit ad vectem primi generis.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>247<emph.end type="italics"/></cell><cell><emph type="italics"/>In motu Remi collato cum motu Nauigij, &agrave; Nonio erroris manifest&egrave;   arguitur. eodem modo in motu Temonis.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>250<emph.end type="italics"/></cell><cell><emph type="italics"/>Ait maioribus trochleis, aut rotulis facilius onera &longs;ubleuari.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>256<emph.end type="italics"/></cell><cell><emph type="italics"/>Reducit cuneum ad vectem primi generis.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>270<emph.end type="italics"/></cell><cell><emph type="italics"/>Cur res in vorticibus ad medium ferantur, veram cau&longs;am a&longs;signa-re non videtur.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>275<emph.end type="italics"/></cell><cell><emph type="italics"/>Ait Danubium altero ramo in Mediterraneum, altero in Pontum   effluere.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>293<emph.end type="italics"/></cell><cell><emph type="italics"/>Negat Araneum filum ab intrin&longs;eco emittere, Democritum iniuria   refellens. quamuis hoc vltimum ad Phy&longs;icum pertineat.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>403<emph.end type="italics"/></cell><cell><emph type="italics"/>Problem. 2. &longs;ect. 2 3. non ben&egrave; videtur a&longs;signare cau&longs;am vari&aelig; im-mer&longs;ionis nauigij.<emph.end type="italics"/></cell></row></table><pb xlink:href="009/01/032.jpg" /><!--blank page --></section></front><body><chap> <pb xlink:href="009/01/033.jpg" pagenum="33"/>         <pb pagenum="21" xlink:href="009/01/021.jpg"/>
          <p type="main">
 <p type="head"><s id="id.000668">LOCA           <s id="s.000568">Additamentum de natura Mathematicarum di&longs;ciplinarum.</s>
 <lb/>MATHEMATICA         </p>
 <lb/>EX LIBRO         <p type="main">
 <lb/>PR&AElig;DICAMENTORVM           <s id="s.000569"><emph type="italics"/>Primo. </s>
 <lb/>Per ordinem declarata.</s></p><p type="main">           <s id="s.000570">De &longs;ubiecto Mathem. &longs;eu de materia intelligibili: vbi o&longs;tenduntur definitio&shy;<lb/>
  nes Mathematic&aelig; e&longs;&longs;e perfecti&longs;&longs;im&aelig;.<emph.end type="italics"/></s>
 <s id="id.000669"><arrow.to.target n="marg1"/></s></p><p type="margin">         </p>
          <p type="main">
 <s id="id.000670"><margin.target id="marg1"/>1</s></p>           <s id="s.000571">2. <emph type="italics"/>Demon&longs;trationes Mathematicas e&longs;&longs;e perfecti&longs;&longs;imas.<emph.end type="italics"/></s>
 <p type="main">         </p>
 <s id="id.000671">Ex c. <!-- REMOVE S-->3. De his, qu&aelig; ad aliquid. </s>         <p type="main">
            <s id="s.000572">3. <emph type="italics"/>Obiectiones: <expan abbr="atq;">atque</expan> etiam calumni&aelig; diluuntur.<emph.end type="italics"/></s>
          </p>
 <s id="id.000672">Porr&ograve; quemadmodum vnus angulus vni angulo &aelig;qualis e&longs;t, ita          <p type="main">
 <lb/><expan abbr="aliqu&atilde;do">aliquando</expan> duo anguli &longs;unt vni angulo &aelig;quales, vt patet, &longs;i vnus angulus, v.g.            <s id="s.000573">4. <emph type="italics"/>De pr&aelig;stantia cognitionis, quam Geometria, &amp; Arithmetica gignunt.<emph.end type="italics"/></s>
 <lb/><!-- REMOVE S-->angulus B A C, vbi ait <emph type="italics"/>(Scientia ver&ograve; &longs;i non &longs;it,          </p>
 <lb/>nihil probibet e&longs;&longs;e &longs;cibile, vt circuli quadratura, &longs;i e&longs;t &longs;cibilis,          <p type="main">
 <lb/>&longs;cientia quidem eius nondum e&longs;t)<emph.end type="italics"/> Cum velit Ari&longs;t.            <s id="s.000574">5. <emph type="italics"/>De 4. Mathematicis medijs: A&longs;tronomia, Per&longs;pectiua, Mu&longs;ica, Mechanica.<emph.end type="italics"/></s>
          </p>
 o&longs;tendere,          <p type="main">
 <lb/>n&oacute; omnia correlatiua &longs;imul e&longs;&longs;e natura, id de &longs;cibili, &amp; &longs;cien&shy;           <s id="s.000575">6. <emph type="italics"/>Appendix de re&longs;olutione omnium demonstrationum primi Euclidis.<emph.end type="italics"/><!-- KEEP S--></s>
 <lb/>tia vari&egrave; probat, pr&aelig;&longs;ertim ver&ograve;, quia multa &longs;int &longs;cibilia,          </p>
 <lb/>qu&aelig; tamen nondum &longs;ciantur, vt patet, inquit, in Quadratu&shy;         <p type="main">
 <lb/>ra circuli, &amp; &longs;cientia ip&longs;ius, quia quamuis ip&longs;a circuli quadratura &longs;it &longs;cibi&shy;           <s id="s.000576">7. <emph type="italics"/>Clarorum Mathematicorum Chronicon.<emph.end type="italics"/></s>
 <lb/>lis, nondum tamen &longs;imul cum ip&longs;a, &longs;cientia illius extat. </s>         </p>
          <p type="head">
 <s id="id.000673">Qu&aelig; vt perfect&egrave;            <s id="s.000577"><emph type="bold"/>Finis Primi Indicis.<emph.end type="bold"/></s>
 <lb/>intelligantur, &longs;ciendum e&longs;t, quadraturam circuli, qu&aelig; &agrave; Gr&aelig;cis tetrago&shy;         </p>
 <lb/>ni&longs;mus dicitur, nihil aliud e&longs;&longs;e, qu&agrave;m propo&longs;ito cuilibet circulo exhibere        </section>
 <lb/>quadratum &aelig;quale. </s>       <pb pagenum="22" xlink:href="009/01/022.jpg"/>
        <section>
 <s id="id.000674">Qu&aelig; &aelig;qualitas debet intelligi de areis, &longs;eu &longs;patijs, ita          <p type="head">
 <lb/>vt area circuli, &longs;eu &longs;patium illud, &longs;iue &longs;uperficies illa circularis, &longs;it &aelig;qualis            <s id="s.000578"><emph type="italics"/>ALTER INDEX<emph.end type="italics"/></s>
 <lb/>are&aelig;, &longs;eu &longs;uperficiei quadrat&aelig;. </s>         </p>
          <p type="main">
 <s id="id.000675">Qua in re plurimi decipiuntur exi&longs;timantes            <s id="s.000579"><emph type="italics"/>Quo loca Aristotelis Geometrica, in hoc Opere explicata, <lb/>
 <lb/>per quadraturam cir culi inquiri &aelig;qualitatem linearum, ita vt circumferen&shy; ad Euclidem, &longs;ecundum propo&longs;itionum ordinem refe&shy;<lb/>
 <lb/>tia circuli debeat e&longs;&longs;e &aelig;qualis ambitui, &longs;eu quatuor lateribus quadrati:  runtur; vt Mathematicarum Profe&longs;&longs;ores habeant, <lb/>
 <lb/>quod omnino fal&longs;um e&longs;t.</s></p><p type="main"> vnde &longs;uas pr&aelig;lectiones aliquando valeant locupletare.<emph.end type="italics"/></s>
          </p>
 <s id="id.000676">Quadratio porr&ograve; circuli dupliciter proponi pote&longs;t, vel tanquam Theo&shy;         <p type="head">
 <lb/>rema, vel tanquam Problema <emph type="italics"/>(theorema autem e&longs;t propo&longs;itio, in qua nihil fa&shy;           <s id="s.000580"><emph type="italics"/>In Primo Elem. Euclidis.<emph.end type="italics"/><!-- KEEP S--></s>
 <lb/>ciendum proponitur; problema ver&ograve; aliquid fieri expo&longs;cit)<emph.end type="italics"/> neutrum autem tem&shy;         </p>
 <lb/>pore Ari&longs;t.          <p type="main">
            <s id="s.000581">Ad verbum ip&longs;um <emph type="italics"/>&lpar;Elementum Euclidis&rpar;<emph.end type="italics"/> vide infra tex. <!-- REMOVE S-->4. quinti <lb/>
 erat adinuentum nam theorema inuentum e&longs;t po&longs;t ip&longs;um ducen&shy; Methaph.<!-- KEEP S--></s>
 <lb/>tis circiter annis ab Archimede: problema ver&ograve; nondum &agrave; quoquam per&shy;         </p>
 <lb/>fect&egrave; potuit reperiri. </s>         <p type="main">
            <s id="s.000582">Ad principia primi elementorum, vide infra tex. <!-- REMOVE S-->5. pri. <!-- REMOVE S-->Po&longs;ter.<!-- KEEP S--></s>
 <s id="id.000677">qua di&longs;tinctione &longs;aluari po&longs;&longs;unt nonnulli, vt Boetius          </p>
 <lb/>hocloco, qui aiunt, &longs;e vidi&longs;&longs;e Demon&longs;trationem quadratur&aelig; huius, &longs;i nimi&shy;         <p type="main">
 <lb/>rum intelligant theorema. </s>           <s id="s.000583">Ad definitionem 10. pri. <!-- REMOVE S-->pro angulo recto, vide 30. qu&aelig;&longs;t. </s>
            <s id="s.000584">Mecha&shy;<lb/>
 <s id="id.000678">&amp; alij etiam verum a&longs;&longs;erunt, dum negant hacte&shy; nic. <!-- REMOVE S-->&amp; cap. 7. lib. 1. Eth.<!-- KEEP S--></s>
 <lb/>nus repertam e&longs;&longs;e, &longs;i nimirum de problemate loquantur, theorema Archi&shy;<pb xlink:href="009/01/034.jpg" pagenum="34"/>medis e&longs;t propo&longs;itio prima acuti&longs;&longs;imi libelli de Dimen&longs;ione circuli; e&longs;t au&shy;         </p>
 <lb/>tem huiu&longs;modi. </s>         <p type="main">
            <s id="s.000585">Ad axioma 10. quamuis Ari&longs;toteles nihil hac de re dicat; &longs;cias tamen velim <lb/>
 <s id="id.000679">Quilibet circulus &aelig;qualis e&longs;t triangulo rectangulo, cuius  hoc vno axiomate qu&etail;&longs;tionem <expan abbr="qu&atilde;dam">quandam</expan> inter Philo&longs;ophos vald&egrave; difficilem, <lb/>
 <lb/>quidem &longs;emidiameter vni laterum, qu&aelig; circa rectum angulum &longs;unt, ambi&shy; facile di&longs;&longs;olui. </s>
 <lb/>tus ver&ograve; ba&longs;i eius e&longs;t &aelig;qualis.</s></p><figure id="id.009.01.034.1.jpg" xlink:href="009/01/034/1.jpg" place="text"/><p type="main">           <s id="s.000586">ea e&longs;t, vtrum marmor, aut adamas, aliudue quidpiam infle&shy;<lb/>
  xibile &longs;ucce&longs;&longs;iu&egrave; findi, &amp; aperiri po&longs;&longs;it. </s>
 <s id="id.000680">Sit, v.g. <!-- REMOVE S-->datus circulus, cuius &longs;emidiameter A B; &amp; fit trian gulum rectangu&shy;           <s id="s.000587">qui enim aiunt, &longs;ic refelluntur, quia <lb/>
 <lb/>lum A B C, cuius angulus B, &longs;it rectus, &amp; latus B A, <expan abbr="con&longs;titu&etilde;s">con&longs;tituens</expan> angulum re&shy; nimirum &longs;equeretur, duas rectas lineas habere &longs;egmentum commune: in&shy;<lb/>
 <lb/>ctum B, cum ba&longs;i B C, &longs;it &aelig;quale &longs;emidiametro A B; ba&longs;is ver&ograve; B C, &longs;it &aelig;qua&shy; telligantur enim du&aelig; line&aelig;, vna in vna &longs;uperficie, altera vero in altera, qu&aelig; <lb/>
 <lb/>lis peripheri&aelig; eiu&longs;dem circuli dati. </s> antequam incipiat apertio, congruant; Quoniam igitur tota illa apertio <lb/>
  non fit in in&longs;tanti, &longs;ed &longs;ucce&longs;&longs;iu&egrave;, facta iam aliqua apertionis parte con&longs;i&shy;<lb/>
  derentur pr&aelig;dict&aelig; line&aelig;, erit igitur earum pars aliqua ab inuicem &longs;epara&shy;<lb/>
  ta, altera ver&ograve; adhuc alteri congruens, ergo &longs;equetur, duas lineas habere <lb/>
 <s id="id.000681">demon&longs;trat iam ibi Archimedes acuta  &longs;egmentum commune, quod e&longs;t impo&longs;&longs;ibile, quia contra 10. axioma.</s>
 <lb/>&aelig;qu&egrave;, ac euidenti demon&longs;tratione triangulum i&longs;tud &aelig;quale e&longs;&longs;e circulo illi.          </p>
 <lb/></s>         <p type="main">
            <s id="s.000588">Ad Calcem axiomatum primi accommodetur tex. <!-- REMOVE S-->1. primi Po&longs;ter.<!-- KEEP S--></s>
 <s id="id.000682">quod perinde e&longs;t, ac &longs;i o&longs;tendi&longs;&longs;et cuinam quadrato &longs;it &aelig;qualis, cum per vl&shy;         </p>
 <lb/>timam 2. Eucl. <!-- REMOVE S-->po&longs;&longs;imus triangulo huic quadratum &aelig;quale con&longs;truere, quod          <p type="main">
 <lb/>con&longs;equenter dato circulo &aelig;quale erit. </s>           <s id="s.000589">Ad primam primi, po&longs;t ip&longs;ius explicationem, commod&egrave; declarari pote&longs;t, cur <lb/>
  Ari&longs;t. Demon&longs;trationes Geometricas appellet De&longs;criptiones, &amp; De&longs;igna&shy;<lb/>
  tiones, vide cap. de Priori, &amp; cap. 24. &longs;ecti primi, libri primi Priorum, &amp; <lb/>
  tex. <!-- REMOVE S-->4. quinti Methaph. <!-- REMOVE S-->&amp; tex. <!-- REMOVE S-->20. &longs;exti Methaph. <!-- REMOVE S-->&amp; cap. 3. lib. 3. Ethic. <lb/>
 <s id="id.000683">Quod &longs;i in modum Problematis ita  <!-- KEEP S--></s>
 <lb/>proponatur: Dato circulo &aelig;quale quadratum con&longs;truere, nondum inuenta            <s id="s.000590">Item ad primam primi, vide tex. <!-- REMOVE S-->7. &longs;ecundi Po&longs;ter. loco 2.<!-- KEEP S--></s>
 <lb/>e&longs;t ratio, qu&aelig; demon&longs;tratione confirmetur, qua id geometric&egrave; penitus, hoc          </p>
 <lb/>e&longs;t ad &aelig;qualitatem mathematicam, &longs;eu exacti&longs;&longs;imam effici po&longs;&longs;it, <expan abbr="tota&qacute;">totaque</expan>; dif&shy;         <p type="main">
 <lb/>ficultas po&longs;ita e&longs;&longs;e videtur in inue&longs;tigando, quonam modo exhibeamus li&shy;           <s id="s.000591">Ad 5. primi, vide cap. 24. &longs;ecti 1 lib. 1. Priorum.</s>
 <lb/>neam rectam B C, &aelig;qualem peripheri&aelig; circuli dati. </s>         </p>
          <p type="main">
 <s id="id.000684">quam nullus hactenus            <s id="s.000592">Ad 21. primi, vide tex. <!-- REMOVE S-->20. primi Po&longs;ter. <!-- REMOVE S-->loco 2.<!-- KEEP S--></s>
 <lb/>geometric&egrave; illi &aelig;qualem potuit exhibere, <expan abbr="atq;">atque</expan> exhibita <expan abbr="euid&etilde;ti">euidenti</expan> demon&longs;tra&shy;         </p>
 <lb/>tione comprobare; Quamuis Archimedes acumine &longs;an&egrave; mirabili in lib.          <p type="main">
            <s id="s.000593">Ad 22. primi, vide locum 10. de lineis in&longs;ecabilibus.</s>
 de          </p>
 <lb/>lineis &longs;piralibus, eam <expan abbr="quoq;">quoque</expan> theorematic&egrave;, non tamen problematic&egrave; inue&shy;         <p type="main">
 <lb/>&longs;tigauit. </s>           <s id="s.000594">Ad 28. primi, vide cap. 21. &amp; cap. 22. &longs;ecundi <expan abbr="Prior&utilde;">Priorum</expan>, &amp; tex. <!-- REMOVE S-->13. primi Po&longs;ter.<!-- KEEP S--></s>
          </p>
 <s id="id.000685">nam propo&longs;itione 18. illius <expan abbr="admir&atilde;di">admirandi</expan> operis inuenit lineam rectam          <p type="main">
 <lb/>&aelig;qualem circumferenti&aelig; primi circuli &longs;piralis line&aelig;; propo&longs; ver&ograve; 19. repe&shy;           <s id="s.000595">Ad 32. primi, vide cap. 1. &longs;ecti 3. lib. 1. Prior. <!-- REMOVE S-->&amp; cap. 26. &longs;ecundi <expan abbr="Prior&utilde;">Priorum</expan>, &amp; tex. <!-- REMOVE S-->2. <lb/>
 <lb/>rit aliam rectam &aelig;qualem circumferenti&aelig; &longs;ecundi circuli. </s> primi Po&longs;ter. loco 4. &amp; tex. <!-- REMOVE S-->23. primi Po&longs;ter. <!-- REMOVE S-->vbi ait hanc e&longs;&longs;e poti&longs;&longs;imam <lb/>
  <expan abbr="dem&otilde;&longs;trationem">demon&longs;trationem</expan>. </s>
 <s id="id.000686">tu ip&longs;um con&longs;ule,            <s id="s.000596">&amp; tex. <!-- REMOVE S-->37. primi Po&longs;ter. &amp; tex. <!-- REMOVE S-->39. primi Po&longs;ter. <!-- KEEP S--></s>
 <lb/>&longs;i admirandarum rerum contemplatione delectaris. </s>           <s id="s.000597">Ibidem <lb/>
  loco 4. &amp; tex. <!-- REMOVE S-->43. primi Po&longs;ter. <!-- REMOVE S-->&amp; tex. <!-- REMOVE S-->2. &longs;ecundi Po&longs;ter. <!-- REMOVE S-->bis. </s>
 <s id="id.000687">Multa hac de re Pap&shy;           <s id="s.000598">&amp; tex. <!-- REMOVE S-->89. &longs;e&shy;<lb/>
 <lb/>pus Alexandrinus lib.  cundi Phy&longs;. &amp; tex. <!-- REMOVE S-->15. octaui Phy&longs;. <!-- REMOVE S-->&amp; tex. <!-- REMOVE S-->119. primi de C&oelig;lo. <!-- KEEP S--></s>
            <s id="s.000599">&amp; tex. <!-- REMOVE S-->25. <lb/>
 4. Math. coll. </s> &longs;ecundi de C&oelig;lo. <!-- KEEP S--></s>
            <s id="s.000600">tex 11. primi de Anima. <!-- REMOVE S-->&amp; cap. 1. de mem. </s>
 <s id="id.000688">&amp; Ioannes Buteo vnico volumine om&shy;           <s id="s.000601">&amp; remini&longs;c. <lb/>
 <lb/>nes quadraturas tain pri&longs;corum, quam recentiorum <expan abbr="c&otilde;prehen&longs;us">comprehen&longs;us</expan> e&longs;t. </s> </s>
            <s id="s.000602">&amp; tex. <!-- REMOVE S-->35. quinti Methaphy&longs;. &amp; tex. <!-- REMOVE S-->20. &longs;exti Methaphy&longs;. <!-- REMOVE S-->&amp; tex. <!-- REMOVE S-->22. &longs;exti <lb/>
 <s id="id.000689">Qua&shy; Methaphy&longs;. <!-- REMOVE S-->&amp; cap. 4. lib. 2. de Generat. <!-- REMOVE S-->animal. <!-- KEEP S--></s>
 <lb/>re qui plura cupit, eos adeat; nos tamen infra &longs;uis locis explicabimus tres            <s id="s.000603">&amp; cap. 5. lib. 6. Ethic. <!-- REMOVE S-->&amp; <lb/>
 <lb/>illas celebres antiquorum Antiphontis, Bri&longs;&longs;onis, &amp; Hippocratis quadra&shy; cap. 2. Magnorum Moral. &amp; cap. 10. Mag. Moral. &amp; cap. 16. Mag. Moral. <lb/>
 <lb/>turas, quamuis fal&longs;as, <expan abbr="quar&utilde;">quarum</expan> &longs;&aelig;pe meminit Ari&longs;t. &amp; alij. </s> <!-- REMOVE S-->&amp; cap. <!-- REMOVE S-->7. &longs;ecundi Eudem. &amp; cap. <!-- REMOVE S-->12. &longs;ecundi Eudem. <!-- REMOVE S-->&amp; problema 6. &longs;ectio&shy;
  
 <s id="id.000690">&longs;olet autem &agrave; non&shy; 
 <lb/>nullis di&longs;putari, vtrum quadratura i&longs;ta problematica &longs;it po&longs;&longs;ibilis, nec ne,  
 <lb/>cum videant eam &agrave; nemine, quamuis diu magno labore perqui&longs;itam, hacte&shy; 
 <lb/>nus adinuentam e&longs;&longs;e. </s> 
  
 <s id="id.000691">ego quidem e&longs;&longs;e po&longs;&longs;ibilem exi&longs;timo, quis enim dubi&shy; 
 <lb/>tare pote&longs;t, po&longs;&longs;e exi&longs;tere quadratum &aelig;quale circulo propo&longs;ito? </s> 
  
 <s id="id.000692">Quod &longs;i po&shy; 
 <lb/>te&longs;t fieri, quare non etiam demon&longs;trari? </s> 
  
 <s id="id.000693">pr&ecedil;fertim cum videamus ab Archi&shy; 
 <lb/>mede iam inuentam e&longs;&longs;e, quatenus Theorema e&longs;t. </s> 
  
 <s id="id.000694">&amp; pr&aelig;terea con&longs;tet, Hip&shy; 
 <lb/>pocratem quadra&longs;&longs;e lunulam, vt &longs;uo loco dicemus, &amp; Archimedem in libel&shy;<pb xlink:href="009/01/035.jpg" pagenum="35"/>lo de quadratura Paraboles, quadra&longs;&longs;e ip&longs;am Parabolem, qu&aelig; tamen du&aelig; fi&shy; 
 <lb/>gur&aelig;, lunula &longs;cilicet, &amp; parabola &longs;unt curuiline&aelig;.</s></p><p type="main"> 
  
 <s id="id.000695"><arrow.to.target n="marg2"/></s></p><p type="margin"> 
  
 <s id="id.000696"><margin.target id="marg2"/>2</s></p><p type="main"> 
  
 <s id="id.000697">Ex cap.  
  
 de Priori <emph type="italics"/>(in &longs;cientijs demon&longs;tratiuis e&longs;t prius, &amp; po&longs;terius ordine,  
 <lb/>elementa enim priora &longs;unt ijs, qu&aelig; de&longs;cribuntur, nam principia prior a &longs;unt theore&shy; 
 <lb/>matibus ordine)<emph.end type="italics"/> verba illa, nam principia, &amp;c. </s> 
  
 <s id="id.000698">qu&aelig; non &longs;unt in antiqua tran&shy; 
 <lb/>&longs;latione de&longs;ump&longs;imus ex ca&longs;tigati&longs;&longs;imo gr&aelig;co codice editionis Francfor&shy; 
 <lb/>dien&longs;is, propterea quod totum hunc locum declarant; &longs;unt autem i&longs;ta,  
 <lb/><foreign lang="greek">ai/gar arxai/ pro/terai tw_n qewrhma/twn th ta/xei.</foreign> per &longs;cientias autem demon&longs;tra&shy; 
 <lb/>tiuas intelligendas e&longs;&longs;e hoc loco ip&longs;as Mathematicas ex eo patet, quod illis  
 <lb/>a&longs;&longs;ignet Ari&longs;t. De&longs;criptiones; nam hoc verbo, De&longs;criptiones, &longs;eu figuratio&shy; 
 <lb/>nes, &longs;olet ip&longs;e Mathematicas Demon&longs;trationes innuere, quod in ip&longs;is figu&shy; 
 <lb/>rationes, &amp; De&longs;criptiones adhibeantur, vt alijs locis patebit: idcirco ver&shy; 
 <lb/>ba illa &agrave; nobis addita ex gr&aelig;co, optim &egrave; <expan abbr="pr&aelig;ced&etilde;tia">pr&aelig;cedentia</expan> exponunt, cum per ele&shy; 
 <lb/>menta intelligantur principia, qualia &longs;unt initio Euclidis, &amp; per de&longs;criptio&shy; 
 <lb/>nes exponant theoremata. </s> 
  
 <s id="id.000699">quod autem principia illa ordine priora &longs;int de&shy; 
 <lb/>mon&longs;trationibus, &longs;iue ip&longs;as pr&aelig;cedant, ex ip&longs;a primi Euclidis in&longs;pectione  
 <lb/>patere pote&longs;t.</s></p><p type="main"> 
  
 <s id="id.000700"><arrow.to.target n="marg3"/></s></p><p type="margin"> 
  
 <s id="id.000701"><margin.target id="marg3"/>3</s></p><p type="main"> 
  
 <s id="id.000702">Ex cap.  
  
 de motu <emph type="italics"/>(Quadratum augetur Gnomone circumpo&longs;ito)<emph.end type="italics"/> Gnomon vox  
 <lb/>gr&aelig;ca inter alia &longs;ignificat in&longs;trumentum illud, quod Latini tum amu&longs;&longs;im,  
 <lb/><figure id="id.009.01.035.1.jpg" xlink:href="009/01/035/1.jpg" place="text"/> 
 <lb/>tum normam appellant, Itali ver&ograve;, Squadra, ad  
 <lb/>cuius &longs;imilitudinem Geometr&aelig; denominarunt fi&shy; 
 <lb/>guram quandam, &longs;eu portionem cuiu&longs;uis paralle&shy; 
 <lb/>logrammi, vt videre e&longs;t in definitione &longs;ecunda  
 <lb/>2. elem. </s> 
  
 <s id="id.000703">&amp; in pr&aelig;&longs;enti figura, in qua quadratum  
 <lb/>A B C D, circumpo&longs;ito gnomone E F G, augetur,  
 <lb/>&amp; fit maius quadratum H B I L.<!-- KEEP S--></s></p><p type="main"> 
  
 <s id="id.000704">Idem etiam verum e&longs;t in quadrato arithmeti&shy; 
 <lb/>co, &longs;iue in numero quadrato: is enim pariter ad&shy; 
 <lb/>dito Gnomone augetur. </s> 
  
 <s id="id.000705">i. </s> 
  
 <s id="id.000706">addito numero impari.  
 <lb/></s> 
  
 <s id="id.000707">quemadmodum infra 3. Phy&longs;. tex. <!-- REMOVE S-->26. fus&egrave; explicabimus.</s> 
  
 </p><p type="head"> 
  
 <s id="id.000708"><emph type="italics"/>Ex Primo Priorum re&longs;olutoriorum.<emph.end type="italics"/></s></p> 
 </chap><chap> 
 <p type="main"> 
 <s id="id.000709"><arrow.to.target n="marg4"/></s></p><p type="margin"> 
  
 <s id="id.000710"><margin.target id="marg4"/>4</s></p><p type="main"> 
  
 <s id="id.000711">Aliquorum opinio e&longs;t, Ari&longs;totelem ho&longs;ce libros appella&longs;&longs;e re&longs;olu&shy; 
 <lb/>torios, quod per illos doceat &longs;yllogi&longs;mum, ac demon&longs;trationem  
 <lb/>iam factam in &longs;ua immediata principia re&longs;oluere, quam opinio&shy; 
 <lb/>nem meum non e&longs;t, nunc refellere. </s> 
  
 <s id="id.000712">per&longs;ua&longs;um tamen mihi e&longs;t, rem  
 <lb/>multo aliter &longs;e habere, veram rationem huius tituli petendam e&longs;&longs;e ex peni&shy; 
 <lb/>tiori Mathematicorum eruditione. </s> 
  
 <s id="id.000713">Sciendum <expan abbr="itaq;">itaque</expan> id, quod tradit Pappus  
 <lb/>Alex. initio &longs;eptimi Mathem. collect. </s> 
  
 <s id="id.000714">antiqui&longs;&longs;imos videlicet Geometras,  
 <lb/>Euclidem, Apollonium Perg&aelig;um, &amp; Ari&longs;t&ecedil;um &longs;crip&longs;i&longs;&longs;e libros de re&longs;olutio&shy; 
 <lb/>ne, in quibus ars tradebatur, qua propo&longs;ito quouis theoremate, aut proble&shy; 
 <lb/>mate po&longs;&longs;ent facile ex eo, tanquam vero accepto inue&longs;tigare aliquam veri&shy; 
 <lb/>tatem, per quam deinde componerent illius, quod qu&aelig;rebatur, Demon&longs;tra&shy; 
 <lb/>tionem; inue&longs;tigationem illam appellabant re&longs;olutionem: compo&longs;itionem  
 <lb/>ver&ograve; nominabant di&longs;cur&longs;um <expan abbr="ill&utilde;">illum</expan>, quo ex vero illo per re&longs;olutionem inuento, <pb xlink:href="009/01/036.jpg" pagenum="36"/>o&longs;tendebant conclu&longs;ionem. </s> 
  
 <s id="id.000715">Porr&ograve; Diogenes Laert. <!-- REMOVE S-->huius re&longs;olutionis in&shy; 
 <lb/>uentorem facit Platonem: &agrave; quo eam Leodamas Tha&longs;ius didicit, cuius be&shy; 
 <lb/>neficio, pluries deinde Geometricas demon&longs;trationes adinuenit. </s> 
  
  
  
 <s id="id.000716">definitio  
 <lb/><expan abbr="vtriu&longs;q;">vtriu&longs;que</expan> e&longs;t a pud Euclidem ad primam propo&longs;. </s> 
  
 <s id="id.000717">13. Elem. iuxta tran&longs;latio&shy; 
 <lb/>nem Zamberti, &amp; Commandini; vbi etiam <expan abbr="quinq;">quinque</expan> priora theoremata, pri&shy; 
 <lb/>m&ograve; per re&longs;olutionem, deinde per compo&longs;itionem demon&longs;trantur, qu&aelig; tan&shy; 
 <lb/>quam per&longs;picua exempla rei propo&longs;it&aelig; in&longs;eruire po&longs;&longs;unt. </s> 
  
 <s id="id.000718">&longs;unt pr&aelig;terea fre&shy; 
 <lb/>quentes huiu&longs;modi re&longs;olutiones in operibus Archimedis, Apollonij, &amp; Pap&shy; 
 <lb/>pi. </s> 
  
 <s id="id.000719">extat adhuc liber Datorum Euclidis, qui geometricis re&longs;olutionibus in&shy; 
 <lb/>&longs;eruiebat. </s> 
  
 <s id="id.000720">vtinam extarent etiam alij de re&longs;olutione, quorum auxilio non  
 <lb/>tantopere recentiores Mathematici in inueniendis Demo&longs;trationibus la&shy; 
 <lb/>borarent; hanc re&longs;olutionem, &longs;ic Pappus fu&longs;ius, quam Euclides explicat;  
 <lb/>re&longs;olutio e&longs;t via &agrave; qu&aelig;&longs;ito tanquam conce&longs;&longs;o per ea, qu&aelig; exip&longs;o con&longs;equun&shy; 
 <lb/>tur ad aliquod certum, &amp; conce&longs;&longs;um: in re&longs;olutione enim id, quod qu&aelig;ritur  
 <lb/>tanquam factum, &amp; verum &longs;upponentes, quid ex hoc &longs;equatur, con&longs;idera&shy; 
 <lb/>mus, quou&longs;que incidamus in aliquod iam cognitum, vel quod &longs;it &egrave; numero  
 <lb/>principiorum. </s> 
  
 <s id="id.000721">Quod quidem erat fignum euidens, qu&aelig;&longs;itum quoque verum  
 <lb/>e&longs;&longs;e. </s> 
  
 <s id="id.000722">eadem omnino habet Proclus in comm. <!-- REMOVE S-->ad &longs;extam primi elem. </s> 
  
  
  
 <s id="id.000723">Quod  
 <lb/>porr&ograve; Ari&longs;t. ip&longs;e hanc re&longs;olutionem Mathematicam cognouerit e&longs;&longs;e medij  
 <lb/>inqui&longs;itionem manife&longs;tum e&longs;t ex cap. 3. lib.  3. Ethyc. <!-- REMOVE S-->vbi &longs;ic ait <emph type="italics"/>(Qui enim  
 <lb/>con&longs;ultat, qu&aelig;rere videtur, &amp; re&longs;oluere pr&aelig;dicto modo, quemadmodum de&longs;igna&shy; 
 <lb/>tiones)<emph.end type="italics"/> vbi per de&longs;ignationes intelligit Geometricas demon&longs;trationes, vt  
 <lb/>&longs;upra innuimus, &amp; infra probabimus; cum ergo con&longs;ultatio nihil aliud &longs;it,  
 <lb/>quam medij idonei ad finem in rebus agendis inqui&longs;itio, eamque dicat e&longs;&longs;e  
 <lb/>&longs;imilem re&longs;olutioni Geometric&aelig;, manife&longs;tum e&longs;t, ip&longs;am <expan abbr="quoq;">quoque</expan> re&longs;olutionem  
 <lb/>e&longs;&longs;e medij in rebus &longs;peculatiuis idonei perue&longs;tigationem. </s> 
  
  
  
 <s id="id.000724">Exi&longs;timo igitur  
 <lb/>cum docti&longs;&longs;imis Zabarella, Burana, Toleto, &amp; alijs, Ari&longs;totilem non &longs;olum  
 <lb/>hanc &longs;uam logicam ad mathematicarum &longs;cientiarum typum compegi&longs;&longs;e,  
 <lb/>verum potius imitatum e&longs;&longs;e opus illud Euclidis de re&longs;olutione, atque ex eo  
 <lb/>non &longs;olum plurima exempla Geometrica, verum etiam titulum de&longs;ump&longs;i&longs;&longs;e,  
 <lb/>pr&aelig;&longs;ertim cum argumentum e&longs;&longs;et fer&egrave; idem vtrobique, &longs;ed Ari&longs;t.  
  
 intentio  
 <lb/>fuerit accommodare re&longs;olutionem omnibus <expan abbr="&longs;ci&etilde;tijs">&longs;cientijs</expan>; Euclidis ver&ograve;, &amp; alio&shy; 
 <lb/>rum Geometri&aelig; &longs;oli. </s> 
  
 <s id="id.000725">hinc patere pote&longs;t, cur hi libri re&longs;olutorij in&longs;cribantur,  
 <lb/>quod &longs;cilicet tradunt methodum, qua valeamus qu&aelig;&longs;itum quoduis re&longs;olue&shy; 
 <lb/>re, ide&longs;t, ex qu&aelig;&longs;ito tanquam vero inue&longs;tare aliquam veritatem, per quam  
 <lb/>deinde propo&longs;it&aelig; qu&aelig;&longs;tionis rationem methodo compo&longs;itiua reddamus. </s> 
  
 <s id="id.000726">Et  
 <lb/>ver&ograve; cum reliquas appellationes Problematis, Theorematis, Propo&longs;itionis,  
 <lb/>definitionum, po&longs;tulatorum, axiomatum, &amp; alia huiu&longs;modi ex Geometri&shy; 
 <lb/>cis ad omnes &longs;cientias tran&longs;tulerit, quid ni etiam re&longs;olutionem? </s> 
  
 <s id="id.000727">maxim&egrave;  
 <lb/>ver&ograve;, quia &longs;i horum lib.  
  
 intentio e&longs;&longs;et docere iam factum &longs;yllogi&longs;mum in &longs;ua  
 <lb/>principia re&longs;oluere, parum e&longs;&longs;et vtilis; im&ograve; nec vtilis, &longs;ed &longs;uperfluum quid.  
 <lb/></s> 
  
 <s id="id.000728">at ver&ograve; vbinam docuit hanc re&longs;olutionem? </s> 
  
 <s id="id.000729">profecto nullibi. </s> 
  
 <s id="id.000730">quid opus e&longs;t  
 <lb/>iam factum &longs;yllogi&longs;mum re&longs;oluere? </s> 
  
 <s id="id.000731">at ver&ograve; propo&longs;itam qu&aelig;&longs;tionem re&longs;ol&shy; 
 <lb/>uere veterum mathematicorum more, hoc opus, hic labor e&longs;t.</s></p><p type="main"> 
  
 <s id="id.000732">Hanc porr&ograve; re&longs;olutionem attendendam e&longs;&longs;e prim&ograve; penes formam, quam  
 <lb/>docet primis duobus analyticis; &longs;ecund&ograve; penes materiam, quam tradit duo&shy;<pb xlink:href="009/01/037.jpg" pagenum="37"/>bus vltimis, non pr&aelig;tereundum. </s> 
  
 <s id="id.000733">reliquas duas logic&aelig; partes, Topicam &longs;ci&shy; 
 <lb/>licet, &amp; Elenchos, qu&aelig; &longs;yllogi&longs;mos probabilem, &amp; apparentem docent, no&shy; 
 <lb/>luit appellare re&longs;olutorios, quamuis inuentionem mediorum doceant, quia  
 <lb/>iam mos i&longs;te inoleuerat apud Philo&longs;ophos, &amp; Mathematicos, vt illa &longs;ola  
 <lb/>pars, qu&aelig; ex materia nece&longs;&longs;aria doceret &longs;yllogi&longs;mum demon&longs;tratiuum con&shy; 
 <lb/>&longs;truere, diceretur re&longs;olutio: cum Mathematici, qui primi de re&longs;olutione  
 <lb/>&longs;crip&longs;erunt, talem materiam &longs;olum con&longs;iderent.</s></p><p type="main"> 
  
 <s id="id.000734"><arrow.to.target n="marg5"/></s></p><p type="margin"> 
  
 <s id="id.000735"><margin.target id="marg5"/>5</s></p><p type="main"> 
  
 <s id="id.000736">Ex cap.  
  
 23. &longs;ecti primi lib.  
  
 1. <emph type="italics"/>(Vt quod diameter incommen&longs;urabilis eo, quod  
 <lb/>imparia &aelig;qualia paribus fiant, &longs;i fuerit po&longs;ita commen&longs;ur abilis. </s> 
  
 <s id="id.000737">&aelig;qualia igitur fieri  
 <lb/>imparia paribus ratiocinantur, diametrum vtr&ograve; incommen&longs;urabilem e&longs;&longs;e ex &longs;uppo&shy; 
 <lb/>&longs;itione <expan abbr="mon&longs;tr&atilde;t">mon&longs;trant</expan>, quoniam fal&longs;um accidit propter contradictionem)<emph.end type="italics"/> Euclides pri&shy; 
 <lb/>mis duabus definitionibus 10. elem. </s> 
  
 <s id="id.000738">definit, qu&aelig; nam &longs;int magnitudines  
 <lb/>commen&longs;. </s> 
  
 <s id="id.000739">&amp; qu&aelig; incommen&longs;. </s> 
  
 <s id="id.000740">&longs;ic; commen&longs;. </s> 
  
 <s id="id.000741">magnitudines dicuntur, quas  
 <lb/><figure id="id.009.01.037.1.jpg" xlink:href="009/01/037/1.jpg" place="text"/> 
 <lb/>eadem men&longs;ura metitur, vt &longs;i fuerint du&aelig; magnitu&shy; 
 <lb/>dines, A, &amp; B, quas eadem men&longs;ura C, ide&longs;t quan&shy; 
 <lb/>titas C, metiatur, ide&longs;t <expan abbr="qu&atilde;titas">quantitas</expan> C, applicata quan&shy; 
 <lb/>titati A, &amp; per ip&longs;am aliquoties replicata ip&longs;am ad&shy; 
 <lb/>&aelig;quat&egrave; ab&longs;umat, vt &longs;i linea C, quinquies &longs;uper li&shy; 
 <lb/>neam A, replicata eam pr&aelig;cis&egrave;, &amp; perfect&egrave; omnin&ograve;  
 <lb/>ad&aelig;quaret: &amp; eadem linea C, applicata line&aelig; B, &amp; &longs;uper illam ter, v.g. <!-- REMOVE S-->re&shy; 
 <lb/>petita ip&longs;am con&longs;umeret, diceretur <expan abbr="vtranq;">vtranque</expan> metiri, &amp; proinde duas lineas  
 <lb/>A, &amp; B, e&longs;&longs;e comm. <!-- REMOVE S-->definit po&longs;tea <expan abbr="incomm&etilde;&longs;">incommen&longs;</expan> hoc modo, incomm, autem, qua&shy; 
 <lb/>rum nullam contingit communem men&longs;uram reperiri; vt &longs;i duarum linea&shy; 
 <lb/><figure id="id.009.01.037.2.jpg" xlink:href="009/01/037/2.jpg" place="text"/> 
 <lb/>rum, A, B, nunquam po&longs;&longs;et reperiri aliqua men&longs;u&shy; 
 <lb/>ra, qu&aelig; <expan abbr="vtranq;">vtranque</expan> ad&aelig;quat&egrave; metiretur, v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;i linea  
 <lb/>C, men&longs;uraret A, quater &longs;umpta, ter autem &longs;umpta  
 <lb/>non ad&aelig;quaret omnino <expan abbr="line&atilde;">lineam</expan> B, &longs;ed deficeret, vel ex&shy; 
 <lb/>cederet aliquantulum, <expan abbr="atq;">atque</expan> hoc fieret in quauis alia  
 <lb/>men&longs;ura, loco ip&longs;ius C, a&longs;&longs;umpta, &longs;iue maior, &longs;iue  
 <lb/>minor ip&longs;a C, vt <expan abbr="vtranq;">vtranque</expan> nunquam perfect&egrave; metiretur, e&longs;&longs;ent du&aelig; ill&aelig; line&aelig;  
 <lb/>incommen&longs;. </s> 
  
  
  
  
  
  
  
  
  
 <s id="id.000742">Extare porr&ograve; tales lineas, &amp; &longs;uperficies, &amp; corpora, <expan abbr="ea&qacute;">eaque</expan>; quam&shy; 
 <lb/>plurima, ac pen&egrave; infinita ex 10. Elem. manife&longs;tum e&longs;t. </s> 
  
 <s id="id.000743">inuentum autem hu&shy; 
 <lb/>ius a&longs;ymmetri&aelig;, quod Pythagoricis veteres attribuunt, mihi &longs;emper vi&longs;um  
 <lb/>e&longs;t omni maius admiratione, cum nulla experientia, <expan abbr="nullus&qacute;">nullusque</expan>; effectus in ip&shy; 
 <lb/>&longs;ius cognitionem potuerit pri&longs;cos illos Geometras inducere. </s> 
  
 <s id="id.000744">Quapropter  
 <lb/>non immerit&ograve; diuinus ille Plato lib.  
  
 7. de legib. </s> 
  
 <s id="id.000745">huius a&longs;ymmetri&aelig; ignora&shy; 
 <lb/>tionem, adeo dete&longs;tatus e&longs;t, vt eam non hominum, &longs;ed &longs;uum, pecorumque  
 <lb/>ignorantiam cen&longs;uerit. </s> 
  
 <s id="id.000746">inter lineas incommen&longs;. </s> 
  
 <s id="id.000747">&longs;unt diameter, &amp; latus eiu&longs;&shy; 
 <lb/>dem quadrati, quia nulla pote&longs;t reperiri men&longs;ura quantumuis exigua, vti  
 <lb/><figure id="id.009.01.037.3.jpg" xlink:href="009/01/037/3.jpg" place="text"/> 
 <lb/>e&longs;t lineola E, in pr&aelig;&longs;enti quadrato, etiam&longs;i illam in  
 <lb/>infinitum &longs;ubdiuidas, qu&aelig; <expan abbr="vtranq;">vtranque</expan> lineam, diame&shy; 
 <lb/>trum &longs;cilicet A C, &amp; latus quoduis ex quatuor, v. <!-- REMOVE S-->g.  
 <lb/><!-- REMOVE S-->latus B C, pr&aelig;cis&egrave; omnino metiatur. </s> 
  
  
  
  
  
 <s id="id.000748">theorema  
 <lb/>i&longs;tud demon&longs;tratur in vltima 10. Elem. eodem me&shy; 
 <lb/>dio, quod ab Ari&longs;totele hic innuitur; Euclides ex  
 <lb/>&longs;uppo&longs;itione alterius partis contradictionis ip&longs;ius <pb xlink:href="009/01/038.jpg" pagenum="38"/>propo&longs;itionis, qu&aelig;fal&longs;a e&longs;t, nimirum &longs;uppo&longs;ito pr&aelig;dictas lineas e&longs;&longs;e comm.  
 <lb/><!-- REMOVE S-->deducit ad impo&longs;&longs;ibile, &longs;iue, vt ait hic Ari&longs;t.  
  
 fal&longs;um ratiocinatur, quod &longs;ci&shy; 
 <lb/>licet idem numerus e&longs;&longs;et par, &amp; impar, quod Ari&longs;t. &longs;ignificat, quando ait,  
 <lb/>imparia &aelig;qualia paribus fiunt. </s> 
  
  
  
 <s id="id.000749">ex quo ab&longs;urdo deducitur fal&longs;am e&longs;&longs;e pr&aelig;di&shy; 
 <lb/>ctam &longs;uppo&longs;itionem, qu&aelig; a&longs;truebat e&longs;&longs;e comm. <!-- REMOVE S-->&amp; proinde altera pars con&shy; 
 <lb/>tradictionis, qu&aelig; e&longs;t, e&longs;&longs;e incomm. <!-- REMOVE S-->vera a&longs;truitur. </s> 
  
  
  
  
  
 <s id="id.000750">ex quibus &longs;atis videtur ex&shy; 
 <lb/>plicari hic locus. </s> 
  
 <s id="id.000751">videas igitur, qu&agrave;m leuiter nonnulli no&longs;tr&aelig; tempe&longs;tatis  
 <lb/>ageometreti i&longs;tud exponant, dicentes diametrum e&longs;&longs;e incomm. <!-- REMOVE S-->co&longs;t&aelig;, nihil  
 <lb/>aliud &longs;igni&longs;icare, quam diametrum e&longs;&longs;e longiorem co&longs;ta, qua expo&longs;itione  
 <lb/>nihil ineptius. </s> 
  
  
  
 <s id="id.000752">Aduerte tandem figuram vulgat&aelig; editionis e&longs;&longs;e ineptam,  
 <lb/>cum habeat duo quadrata alterum &longs;uper diametro alterius, quorum maius  
 <lb/>&longs;uperuacaneum e&longs;t.</s></p><p type="main"> 
  
 <s id="id.000753"><arrow.to.target n="marg6"/></s></p><p type="margin"> 
  
 <s id="id.000754"><margin.target id="marg6"/>6</s></p><p type="main"> 
  
 <s id="id.000755">Et cap.  
  
 24. &longs;ecti primi libri primi <emph type="italics"/>(Sed magis efficitur manife&longs;tum in de&longs;cri&shy; 
 <lb/>ptionibus, vt quod &aelig;quicruris, qui ad ba&longs;im &aelig;quales &longs;int, ad centrum duct&aelig; A B,  
 <lb/>A C, &longs;i igitur &aelig;qualem accipiat A G, angulum ip&longs;i A B D, non omnino ex. </s> 
  
 <s id="id.000756">&longs;timans  
 <lb/>&aelig;quales, qui &longs;emicirculorum, &amp; rur&longs;us G, ip&longs;i D, non omnem a&longs;&longs;umens eum, qui &longs;e&shy; 
 <lb/>cti. </s> 
  
 <s id="id.000757">amplius ab &aelig;qualibus existentibus totis angulis, &amp; ablatorum &aelig;quales e&longs;&longs;e re&shy; 
 <lb/>tiquos E, F, quod ex principio petet, ni&longs;i acceperit ab &aelig;qualibus demptis &aelig;qualia  
 <lb/>derelinqui.)<emph.end type="italics"/> Primum &longs;cias characteres vulgat&aelig; editionis, vna cum figura ip&shy; 
 <lb/>&longs;is re&longs;pondente, e&longs;&longs;e mendo&longs;os; propterea ex textu gr&aelig;co vtrunque corri&shy; 
 <lb/>gendum putaui in hunc, quem vidi&longs;ti modum. </s> 
  
 <s id="id.000758">Secundo, per de&longs;criptiones  
 <lb/>Ari&longs;t.  
  
 intelligere <expan abbr="dem&otilde;&longs;trationes">demon&longs;trationes</expan> Geometricas &longs;upra diximus, quod ex hoc  
 <lb/>loco euidenter confirmatur, vbi manife&longs;t&egrave; loco de&longs;criptionis &longs;upponit li&shy; 
 <lb/>nearem demon&longs;trationem. </s> 
  
 <s id="id.000759">In hoc <expan abbr="itaq;">itaque</expan> exemplo vult Ari&longs;t.  
  
 illud demon&shy; 
 <lb/>&longs;trare, quod Euclides in 5. primi o&longs;tendit, alio tamen modo, &longs;cilicet I&longs;o&longs;ce&shy; 
 <lb/>lium triangulorum, qui ad ba&longs;im &longs;unt anguli, inter &longs;e &longs;unt &aelig;quales. </s> 
  
 <s id="id.000760">e&longs;t au&shy; 
 <lb/>tem figura in omnibus textibus deprauata, quam &longs;ic puto <expan abbr="r&egrave;&longs;t&imacr;tuendam">r&egrave;&longs;tintuendam</expan> e&longs;&longs;e  
 <lb/>ex quodam gr&aelig;co codice, qui characteres hoc modo appo&longs;uerat. </s> 
  
 <s id="id.000761">&longs;it I&longs;o&longs;ce&shy; 
 <lb/><figure id="id.009.01.038.1.jpg" xlink:href="009/01/038/1.jpg" place="text"/> 
 <lb/>les C A B, cuius ba&longs;is C B, Dico angulos &longs;upra ba&longs;im,  
 <lb/>in quibus liter&aelig; E F, e&longs;&longs;e inuicem &aelig;quales. </s> 
  
 <s id="id.000762">facto centro  
 <lb/>in A, de&longs;cribatur circulus A B C, tran&longs;iens per puncta  
 <lb/>C B, iam &longs;ic. </s> 
  
 <s id="id.000763">omnes anguli &longs;emicirculi &longs;unt &aelig;quales in&shy; 
 <lb/>ter &longs;e, ergo anguli A C G, A B D, &longs;unt &aelig;quales. </s> 
  
 <s id="id.000764">Pr&aelig;te&shy; 
 <lb/>rea c&ugrave;m anguli ciu&longs;dem &longs;ectionis &longs;int &aelig;quales ad inui&shy; 
 <lb/>cem, erunt anguli &longs;ectionis C B D G, nimirum anguli,  
 <lb/>in quibus &longs;unt G, &amp; D, inter &longs;e &aelig;quales: <expan abbr="cum&qacute;">cumque</expan>; hi duo  
 <lb/>anguli &longs;ectionis &longs;int partes <expan abbr="angulor&utilde;">angulorum</expan> &longs;emicirculi A C G,  
 <lb/>A B D, &longs;i illi ab his auferantur, auferuntur &aelig;quales anguli ab &aelig;qualibus an&shy; 
 <lb/>gulis, ergo anguli, qui remanent, &longs;cilicet E, &amp; F, erunt &aelig;quales, quod erat  
 <lb/>demon&longs;trandum. </s> 
  
 <s id="id.000765">hinc Ari&longs;t.  
  
 infert manife&longs;tum e&longs;&longs;e oportere in omni &longs;yllo&shy; 
 <lb/>gi&longs;mo, reperiri vniuer&longs;ales, &amp; affirmatiuas propo&longs;itiones, vt Factum e&longs;t in  
 <lb/>pr&aelig;cedenti aliter e&longs;&longs;et petitio principij. </s> 
  
 <s id="id.000766">Qu&aelig;nam vero &longs;it &aelig;qualitas, quam  
 <lb/>Geometr&aelig; con&longs;iderant, infra cap. 1. &longs;ecti 3. explicabicur.</s></p><p type="main"> 
  
 <s id="id.000767"><arrow.to.target n="marg7"/></s></p><p type="margin"> 
  
 <s id="id.000768"><margin.target id="marg7"/>7</s></p><p type="main"> 
  
 <s id="id.000769">Ex cap.  
  
 2. &longs;ecti 2. lib.  
  
 1. <emph type="italics"/>(Secundum veritatem quidem ex ijs, qu&aelig; &longs;ecundum  
 <lb/>veritatem de&longs;cribuntur ine&longs;&longs;e, ad dialecticos autem &longs;yllogi&longs;mos ex propo&longs;itionibus  
 <lb/>&longs;ecundum opinionem)<emph.end type="italics"/> verba illa; ex ijs, qu&aelig; <expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> veritatem de&longs;cribuntur <pb xlink:href="009/01/039.jpg" pagenum="39"/>ine&longs;&longs;e; &longs;ic gr&aelig;c&egrave;, <foreign lang="greek">e/a tw_n xata\ aleiq/ei/an diagegramme/non,</foreign> vbi manife&longs;t&egrave; vtitur  
 <lb/>verbo, De&longs;cribere, per quod &longs;uperius annotauimus apud Ari&longs;t. &longs;ignificari  
 <lb/>Geometricas demon&longs;trationes, nam eas opponit dialecticis &longs;yllogi&longs;mis, &longs;e&shy; 
 <lb/>quentibus verbis, cum dixit (ad diale cticos autem &longs;yllogi&longs;mos ex propo&longs;i&shy; 
 <lb/>tionibus &longs;ecundum opinionem) hac adhibita con&longs;ideratione, quam inter&shy; 
 <lb/>pres non videtur adhibui&longs;&longs;e, &longs;en&longs;us huius loci non erit ob&longs;curus.</s></p><p type="main"> 
  
 <s id="id.000770"><arrow.to.target n="marg8"/></s></p><p type="margin"> 
  
 <s id="id.000771"><margin.target id="marg8"/>8</s></p><p type="main"> 
  
 <s id="id.000772">Ex eodem loco paulo po&longs;t <emph type="italics"/>(Quare principia quidem, qu&aelig; &longs;ecundum <expan abbr="vnum-quodq;">vnum&shy; 
 <lb/>quodque</expan> &longs;unt experimenti est tradere: dico autem, vt a&longs;trologicam experientiam  
 <lb/>a&longs;trologic&aelig; &longs;cienti&aelig;: acceptis enim apparentibus <expan abbr="&longs;uffici&etilde;ter">&longs;ufficienter</expan>, ita inuent&aelig; &longs;unt a&longs;tro&shy; 
 <lb/>logic&aelig; demonstrationes)<emph.end type="italics"/> Cum rationem tradat inueniendorum mediorum ad  
 <lb/>quodlibet problema demon&longs;trandum; nunc docet, non omnia in &longs;eientijs  
 <lb/>po&longs;&longs;e probari, aut demou&longs;trari: principia enim &longs;cientiarum <expan abbr="n&otilde;">non</expan> demon&longs;tran&shy; 
 <lb/>tur, &longs;ed &longs;ola experientia manife&longs;ta &longs;unt; vt patet in A&longs;tronomia, qu&aelig; ab ex&shy; 
 <lb/>perientia &longs;ua &longs;olet &longs;tabilire principia: principijs autem <expan abbr="experim&etilde;to">experimento</expan> con&longs;ti&shy; 
 <lb/>tutis ex ip&longs;is reliqua problemata <expan abbr="demon&longs;tr&atilde;tur">demon&longs;trantur</expan>. </s> 
  
 <s id="id.000773">duo autem &longs;unt apud a&longs;tro&shy; 
 <lb/>nomos genera experimenti, primum dicitur Ph&aelig;nomena, ide&longs;t, <expan abbr="appar&etilde;ti&aelig;">apparenti&aelig;</expan>;  
 <lb/>&amp; &longs;unt ea, qu&aelig; vulgo omnibus patent, vt Solem oriri, &amp; occidere; a&longs;tra fer&shy; 
 <lb/>ri circulariter, diem augeri modo, modo minui: &amp; his &longs;imilia. </s> 
  
 <s id="id.000774">alterum ge&shy; 
 <lb/>nus dicitur ob&longs;eruationes, qu&aelig; tantummodo a&longs;tronomi&aelig; peritis per ob&longs;er&shy; 
 <lb/>uationem innote&longs;cunt, vt Solem in&aelig;qualiter ferri proprio motu per Zodia&shy; 
 <lb/>cum; aliquando maiorem, aliquando minorem videri; plures dies immo&shy; 
 <lb/>rari citra &aelig;quatiorem in parte Zodiaci boreali, quam in altera vltra &aelig;qua&shy; 
 <lb/>torem au&longs;trali. </s> 
  
 <s id="id.000775">dies naturales e&longs;&longs;e inuicem in&aelig;quales, &amp;c. </s> 
  
 <s id="id.000776">ex quibus deinde  
 <lb/>ponunt eccentricos, &amp; augem, ad &longs;aluandas tum apparentias, tum ob&longs;erua&shy; 
 <lb/>tiones; &amp; hac ratione a&longs;trologica &longs;cientia paulatim reperta e&longs;t, ac in dies  
 <lb/>reperitur.</s></p><p type="main"> 
  
 <s id="id.000777"><arrow.to.target n="marg9"/></s></p><p type="margin"> 
  
 <s id="id.000778"><margin.target id="marg9"/>9</s></p><p type="main"> 
  
 <s id="id.000779">Ex cap.  
  
 3. &longs;ecti 2. lib.  
  
 1. <emph type="italics"/>(Vt an ne diameter incomm.)<emph.end type="italics"/> loquitur de a&longs;ymme&shy; 
 <lb/>tria diametri, &amp; co&longs;t&aelig; eiu&longs;dem quadrati, de qua fus&egrave; egimus &longs;uperius in  
 <lb/>cap.  
  
 23. &longs;ecti 1. huius libri; qu&aelig; &longs;i repetantur, optim&egrave; hunc <expan abbr="loc&utilde;">locum</expan> declarant.</s></p><p type="main"> 
  
 <s id="id.000780"><arrow.to.target n="marg10"/></s></p><p type="margin"> 
  
 <s id="id.000781"><margin.target id="marg10"/>10</s></p><p type="main"> 
  
 <s id="id.000782">Ex cap.  
  
 1. &longs;ecti 3. lib.  
  
 1. <emph type="italics"/>(Sit A, duo recti, in quo B, triangulus, in quo C,  
 <lb/>&aelig;quicrus, ip&longs;i <expan abbr="itaq;">itaque</expan> C, ine&longs;t A. per B; ip&longs;i vero B, non amplius per aliud, per &longs;e  
 <lb/>namque triangulus habet duos rectos)<emph.end type="italics"/> nullum aliud exemplum tam frequenter  
 <lb/>v&longs;urpat Philo&longs;ophus, quam i&longs;tud ex Mathematicis de&longs;umptum de triangu&shy; 
 <lb/>lo, &longs;cilicet, omnis triangulus habet tres angulos &aelig;quales duobus rectis an&shy; 
 <lb/>gulis, cuius Demon&longs;tratio e&longs;t in 32. primi Elem.  
  
 quod, vt prob&egrave; intelliga&shy; 
 <lb/>tur, explicandum e&longs;t penes quid attendenda &longs;it &aelig;qualitas inter angulum, &amp;  
 <lb/>angulum, quod facile a&longs;&longs;equemur, &longs;i meminerimus angulum e&longs;&longs;e in clinatio&shy; 
 <lb/>nem illam, quam du&aelig; line&aelig; non in directum po&longs;it&aelig; faciunt: &longs;iue etiam (vt  
 <lb/>melius percipiamus) angulum e&longs;&longs;e acumen illud, &longs;iue mucronem <expan abbr="ill&utilde;">illum</expan>, quem  
 <lb/>du&aelig; line&aelig; non in directum con&longs;titut&aelig; faciunt, vt duarum linearum A B, A C,  
 <lb/><figure id="id.009.01.039.1.jpg" xlink:href="009/01/039/1.jpg" place="text"/> 
 <lb/>inclinatio in puncto A, &longs;iue acumen illud, &longs;iue mucro,  
 <lb/>e&longs;t ratio anguli. </s> 
  
 <s id="id.000783">&longs;olum igitur duo anguli erunt &aelig;qua&shy; 
 <lb/>les, <expan abbr="qu&atilde;do">quando</expan> vnius acumen &aelig;quale erit acumini alterius;  
 <lb/>etiam &longs;i line&aelig; con&longs;tituentes vnum angulum &longs;int lon&shy; 
 <lb/>giores lineis alterum angulum con&longs;tituentibus, quia  
 <lb/>quantitas anguli non attenditur penes longitudinem <pb xlink:href="009/01/040.jpg" pagenum="40"/><expan abbr="linear&utilde;">linearum</expan>, &longs;ed penes inclinationem, &amp; mucronem, quem faciunt: vnde etiam&longs;i  
 <lb/>du&aelig; line&aelig; pr&aelig;dict&aelig; A B, A C, product&aelig;, &longs;iue etiam decurtat&aelig; fuerint, dum&shy; 
 <lb/>modo &longs;itus, &longs;iue po&longs;itio ip&longs;arum, quam ad inuicem habent, non varietur,  
 <lb/>erit &longs;emper eadem quantitas anguli A. <!-- KEEP S--></s> 
  
 <s id="id.000784">Aduertendum pr&aelig;terea rationem  
 <lb/>anguli non po&longs;&longs;e &longs;aluari in &longs;olo puncto A, in quo line&aelig; concurrunt, &longs;ed ne&shy; 
 <lb/>ce&longs;&longs;ariam e&longs;&longs;e aliquam quantitatem, quamuis exiguam, linearum A B, A C.  
 <lb/><!-- KEEP S--></s> 
  
 <s id="id.000785">Notandum etiam, quod in nominatione angulorum, qu&aelig; fit per tres lite&shy; 
 <lb/>ras, &longs;emper literam illam e&longs;&longs;e medio loco proferendam, qu&aelig; ad acumen ip&shy; 
 <lb/>&longs;um po&longs;ita e&longs;t, vt in &longs;uperiori, litera A, debet &longs;emper media proferri, dicen&shy; 
 <lb/>do angulum B A C, &longs;iue C A B, <expan abbr="n&utilde;quam">nunquam</expan> tamen licet dicere angulum A C B,  
 <lb/>vel C B A. <!-- KEEP S--></s> 
  
 <s id="id.000786">Porr&ograve; quemadmodum vnus angulus vni angulo &aelig;qualis e&longs;t, ita  
 <lb/><expan abbr="aliqu&atilde;do">aliquando</expan> duo anguli &longs;unt vni angulo &aelig;quales, vt patet, &longs;i vnus angulus, v.g.  
 <lb/><!-- REMOVE S-->angulus B A C, diuidatur in duos angulos &agrave; linea A D. tunc enim duo angu&shy; 
 <lb/><figure id="id.009.01.040.1.jpg" xlink:href="009/01/040/1.jpg" place="text"/> 
 <lb/>li partiales B A D, D A C, erunt &aelig;quales totali angulo  
 <lb/>B A C, cum partes omnes &longs;imul &longs;umpt&aelig; &longs;int &longs;uo toti &aelig;qua&shy; 
 <lb/>les. </s> 
  
  
  
 <s id="id.000787">pariter tres anguli po&longs;&longs;unt &aelig;quari &amp; vni, &amp; duobus  
 <lb/>alijs angulis, quando nimirum a cumina, &longs;iue mucrones il&shy; 
 <lb/>li &longs;imul ad vnum punctum con&longs;tituti <expan abbr="ad&aelig;quar&etilde;tur">ad&aelig;quarentur</expan> mucro&shy; 
 <lb/>niilli, quem con&longs;tituerent alij duo anguli, quibus illi tres  
 <lb/>&longs;unt pares, v.g. <!-- REMOVE S-->&longs;int tres anguli trianguli A B C, <expan abbr="&longs;int&qacute;">&longs;intque</expan>; alij duo anguli recti,  
 <lb/><figure id="id.009.01.040.2.jpg" xlink:href="009/01/040/2.jpg" place="text"/> 
 <lb/>quos linea perpendicularis D E, facit cum li&shy; 
 <lb/>nea F G; &longs;it <expan abbr="inqu&atilde;">inquam</expan> anguli recti D E F, D E G,  
 <lb/>tunc tres anguli illius <expan abbr="tri&atilde;guli">trianguli</expan> <expan abbr="dic&etilde;tur">dicentur</expan> &aelig;qua&shy; 
 <lb/>les duobus hi&longs;ce rectis, &longs;i tres illi mucrones  
 <lb/>trianguli fimul &longs;umpti, &amp; vniti ad punctum  
 <lb/>E, ad quod duo <expan abbr="quoq;">quoque</expan> mucrones angulorum  
 <lb/><figure id="id.009.01.040.3.jpg" xlink:href="009/01/040/3.jpg" place="text"/> 
 <lb/>rectorum coeunt, congruent omnino duobus  
 <lb/>pr&aelig;dictis angulis rectis, &longs;iue duobus illis mu&shy; 
 <lb/>cronibus angulorum rectorum, &longs;iue con&longs;ti&shy; 
 <lb/>tuent lineam rectam F E G, &longs;icuti faciunt  
 <lb/>etiam duo illi anguli recti; &longs;iue etiam dica&shy; 
 <lb/>mus, occupabunt idem &longs;patium omnin&ograve;, &amp;  
 <lb/>pr&aelig;cis&egrave;, quod occupant duo recti: v.g. <!-- REMOVE S-->&longs;i mucro B, ibi poneretur, faceret  
 <lb/>angulum F E H, &amp; &longs;i ibi iuxta ip&longs;um apponeretur mucro A, faceret angulum  
 <lb/>H E I. quem &longs;i deinceps &longs;ub&longs;equetur reliquus angulus C, con&longs;titueret <expan abbr="reli-qu&utilde;">reli&shy; 
 <lb/>quum</expan> angulum I E G. iam, vt vides, illi tres anguli ad E, tran&longs;lati, &longs;unt &aelig;qua&shy; 
 <lb/>les duobus rectis ad E, pariter con&longs;titutis, cum illi tres fiant partes duorum  
 <lb/>rector&uacute;, vel quia occupant idem &longs;patium, vel eandem lineam rectam F E G,  
 <lb/>con&longs;tituant. </s> 
  
  
  
  
  
 <s id="id.000788">habet igitur omne triangulum &longs;iue &ecedil;quilaterum, &longs;iue &longs;calenum,  
 <lb/>&longs;iue I&longs;o&longs;celes mirabilem hanc proprietatem, vt tres anguli, cuiu&longs;uis trian&shy; 
 <lb/>guli &longs;int &aelig;quales duobus rectis angulis. </s> 
  
 <s id="id.000789">Quam demon&longs;trationem primi om&shy; 
 <lb/>nium Pythagorici perfecerunt, vt refert Proclus ad 32. primi Elem. Eucli&shy; 
 <lb/>des deinde ibidem aliter, quam Pythagorici idem demon&longs;trauit. </s> 
  
 <s id="id.000790">Quod &longs;i  
 <lb/>quis huius rei <expan abbr="experi&etilde;tiam">experientiam</expan> aliquam velit; etiam&longs;i non exactam (cum &aelig;qua&shy; 
 <lb/>litas mathematica non cadat &longs;ub &longs;en&longs;um, &longs;ed &longs;ola intelligentia percipiatur,  
 <lb/>quippe qu&aelig; in materia intelligibili, non autem &longs;en&longs;ibili ver&longs;atur, &amp; cuius <pb xlink:href="009/01/041.jpg" pagenum="41"/>&aelig;qualitas nullum di&longs;crimen, quantumuis minimum admittat, quod &longs;en&longs;ui  
 <lb/>vitare ob &longs;ui imperfectionem non licet: vnde inter e&aelig;, qu&aelig; mathematic&egrave;  
 <lb/>&longs;unt &aelig;qualia, nullus intellectus aliquam valeat reperire differentiam) &longs;umat  
 <lb/>inquam triangulum quodpiam materiale, vt ex charta, quantum fieri po&shy; 
 <lb/>ce&longs;t perfectum, deinde ducat lineam vnam perpendicularem &longs;uper aliam,  
 <lb/>qu&aelig; &longs;cilicet faciat, cum illa duos angulos rectos. </s> 
  
 <s id="id.000791">po&longs;tea ab&longs;cindat tres an&shy; 
 <lb/>gulos trianguli materialis, <expan abbr="eos&qacute;">eosque</expan>; ita &longs;imul componat, vt mucrones illorum  
 <lb/>&longs;int vniti, &amp; contigui ad punctum line&aelig; perpendicularis cum altera, vti e&longs;t  
 <lb/>in &longs;uperiori figura punctnm E; &amp; illic&ograve; apparebit tres illos angulos mate&shy; 
 <lb/>riales obtegere ad&aelig;quat&egrave; totum illud &longs;patium duorum rectorum, quos per&shy; 
 <lb/>pendicularis con&longs;tituit. </s> 
  
 <s id="id.000792">Hoc autem experiri poteris in diuer&longs;is admodum  
 <lb/>triangulis Scalenis, Rectangulis, I&longs;o&longs;celibus, Aequilateris, &amp;c. </s> 
  
 <s id="id.000793">non &longs;ine de&shy; 
 <lb/>lectatione, atque hic e&longs;t &longs;en&longs;us illorum verborum, omnis triangulus habet  
 <lb/>tres &ecedil;quales duobus rectis. </s> 
  
 <s id="id.000794">Ab&longs;tineo &agrave; demon&longs;trationibus geometricis, quo&shy; 
 <lb/>niam ij, qui Mathematicis &longs;unt imbuti, no&longs;tra hac opera parum indigent.  
 <lb/></s> 
  
 <s id="id.000795">&longs;i quis tamen volet, con&longs;ulat 32. primi Elem. <!-- KEEP S--></s> 
  
 <s id="id.000796">Ex hac igitur declaratione  
 <lb/>licet cogno&longs;cere nonnullos ageometretos locum hunc, &amp; &longs;imiles &longs;ub&longs;equen&shy; 
 <lb/>tes non &longs;atis intelligere, dicentes, nihil aliud verba illa Ari&longs;t.  
  
 velle &longs;ignifi&shy; 
 <lb/>care, qu&agrave;m omnem triangulum habere tres angulos, quod inquiunt, noti&longs;&shy; 
 <lb/>&longs;imum e&longs;t. </s> 
  
 <s id="id.000797">Sed &longs;i incidant in &longs;equentia; &aelig;quales duobus rectis, tunc, cum  
 <lb/>h&aelig;c non intelligant, ab&longs;tinent etiam &agrave; priorum declaratione, quibus pr&aelig;&shy; 
 <lb/>mi&longs;&longs;is facile e&longs;t Ari&longs;t.  
  
 textum percipere. </s> 
  
 <s id="id.000798">&longs;it A, duo recti, ide&longs;t, duo anguli  
 <lb/>recti &longs;int pa&longs;&longs;io demon&longs;tranda, in quo B, triangulus, in quo C, &aelig;quicrus. </s> 
  
 <s id="id.000799">ip&longs;i  
 <lb/>itaque C, ide&longs;t triangulo &aelig;quicru&longs;i, ine&longs;t A, &longs;cilicet duo recti, hoc e&longs;t, ine&longs;t  
 <lb/>&aelig;quicru&longs;i h&aelig;c, pa&longs;&longs;io habere tres angulos &aelig;quales duobus rectis per B, ide&longs;t  
 <lb/>per <expan abbr="triangul&utilde;">triangulum</expan> vniuer&longs;ale, quia h&aelig;c proprietas e&longs;t trianguli propria, &amp; <expan abbr="c&otilde;pe-tit">compe&shy; 
 <lb/>tit</expan> &aelig;quicru&longs;i, non vt &aelig;quicrus e&longs;t, &longs;ed, vt triangulum e&longs;t; quare B, non crit  
 <lb/>medium ip&longs;ius A, quia pr&aelig;dicta pa&longs;&longs;io. </s> 
  
 <s id="id.000800">A, non competit triangulo B, per  
 <lb/>aliud, &longs;ed per &longs;e, de eo enim primo, &amp; per &longs;e demon&longs;tratur in 32. primi Elem.  
 <lb/>optim&egrave; Aegydius, &amp; Niphus in hunc locum.</s></p><p type="main"> 
  
 <s id="id.000801"><arrow.to.target n="marg11"/></s></p><p type="margin"> 
  
 <s id="id.000802"><margin.target id="marg11"/>11</s></p><p type="main"> 
  
 <s id="id.000803">Ex eodem cap. <emph type="italics"/>(Non oportet autem exi&longs;timare penes id, quod exponimus, ali&shy; 
 <lb/>quid accidere ab&longs;urdum, nihil enim vtimur eo, quod e&longs;t hoc aliquid e&longs;&longs;e. </s> 
  
 <s id="id.000804">&longs;ed &longs;icut  
 <lb/>Geometra pedalem, &amp; rectam hanc, &amp; &longs;ine latitudine dicit, qu&aelig; non &longs;unt. </s> 
  
 <s id="id.000805">verum  
 <lb/>non &longs;ic vtitur, tanquam ex his ratiocinans)<emph.end type="italics"/> Quoniam Ari&longs;t.  
  
 in exemplis affert  
 <lb/>pro rebus characteres, A, B, C, po&longs;&longs;et qui&longs;piam &longs;u&longs;picari aliquod propterea  
 <lb/>ab&longs;urdum accidere: cui &longs;u&longs;picioni Ari&longs;t.  
  
 re&longs;pondet, dicens, nihil inde ab&longs;ur&shy; 
 <lb/>di accidere po&longs;&longs;e, quoniam ip&longs;e vtitur hi&longs;ce literis, <expan abbr="n&otilde;">non</expan> quatenus liter&aelig; &longs;unt,  
 <lb/>&longs;ed quatenus rerum vicem, pro quibus exponuntur, gerunt: quemadmodum  
 <lb/>etiam Geometr&aelig; faciunt, qui lineam, qu&aelig; pedalis non e&longs;t, pedalem, &amp; qu&aelig;  
 <lb/>non e&longs;t recta, rectam; &amp; qu&aelig; lata e&longs;t, non latam, &longs;upponunt, &amp; tamen nihil  
 <lb/>inde ab&longs;urdi contingit. </s> 
  
 <s id="id.000806">Ex quibus intelligimus per lineas illas &longs;en&longs;ibiles, &amp;  
 <lb/>phy&longs;icas, quas Geometr&aelig; in &longs;uis figuris ducunt, intelligendas e&longs;&longs;e lineas ve&shy; 
 <lb/>r&egrave; Mathematicas omni latitudine carentes; vtitur enim inquit Ari&longs;t. <!-- REMOVE S-->Geo&shy; 
 <lb/>metra lineis phy&longs;icis, non tanquam phy&longs;icis, nec de eis tanquam de phy&longs;icis  
 <lb/>lineis ratiocinatur, &longs;ed ijs vtitur tanquam ver&egrave; mathematicis. </s> 
  
  
  
 <s id="id.000807">idem dicen&shy; 
 <lb/>dum e&longs;t de &longs;uperficiebus, necnon de corporibus, qu&aelig; ijdem Goometr&aelig; de&shy; 
 <lb/>&longs;cribunt, vt per ea, de ver&egrave; mathematicis di&longs;currant.</s></p></chap><pb xlink:href="009/01/042.jpg" pagenum="42"/> 
 <chap><p type="head"> 
 <s id="id.000808"><emph type="italics"/>Ex Libro &longs;ecundo Priorum.<emph.end type="italics"/></s></p><p type="main"> 
  
 <s id="id.000809"><arrow.to.target n="marg12"/></s></p><p type="margin"> 
  
 <s id="id.000810"><margin.target id="marg12"/>12</s></p><p type="main"> 
  
 <s id="id.000811">Ex cap.  
  
 21. <emph type="italics"/>(Quod faciunt, qui coalternas putant &longs;cribere, latent enim ip&longs;i 
 <lb/>&longs;e ip&longs;os talia accip entes, qu&aelig; non est po&longs;&longs;ibile monstrare uon exi&longs;tentibus 
  
 <lb/>coalternis)<emph.end type="italics"/> Vult Ari&longs;t.  
  
 exemplo mathematico explicare, quid &longs;it pe&shy; 
 <lb/>titio principij. </s> 
  
 <s id="id.000812">vbi per coalternas intelligit parallelas lineas, vox  
 <lb/>enim gr&aelig;ca <foreign lang="greek">parallhlos,</foreign> idem &longs;ignificat, ac mutuus, &amp; coalternus. </s> 
  
 <s id="id.000813">quoad  
 <lb/>exempli explicationem vtor figura textibus apponi &longs;olita, qu&aelig; e&longs;t pr&aelig;&longs;ens.  
 <lb/><figure id="id.009.01.042.1.jpg" xlink:href="009/01/042/1.jpg" place="text"/> 
 <lb/>probat Euclides in 28. primi Elem.  
  
 quod &longs;i  
 <lb/>linea recta qu&aelig;dam, vti E F, cadens &longs;uper  
 <lb/>duas rectas, vti &longs;unt A B, C D, fe cerit angu&shy; 
 <lb/>los alternos &ecedil;quales, angulos <expan abbr="nimir&utilde;">nimirum</expan> A G H,  
 <lb/>G H D, ij enim dicuntur alterni; &longs;iue alios  
 <lb/>dnos, nimirum B G H, G H C, hi enim &longs;unt  
 <lb/><expan abbr="quoq;">quoque</expan> alterni; probat inquam has duas li&shy; 
 <lb/>neas A B, C D, e&longs;&longs;e inuicem parallelas. </s> 
  
 <s id="id.000814">Iam &longs;i quis vellet probare, &longs;e duas  
 <lb/>parallelas duxi&longs;&longs;e, hac ratione, quia &longs;cilicet fa ciunt pr&aelig;dictos angulos al&shy; 
 <lb/>ternos &aelig;quales; &amp; probaret facere angulos alternos &aelig;quales, quia &longs;unt pa&shy; 
 <lb/>rallel&aelig;, hic peteret principium, ide&longs;t, illud, quod principio <expan abbr="proband&utilde;">probandum</expan> erat,  
 <lb/>afferret pro ratione, &amp; cau&longs;a, quod dicitur peti principium, quia tunc pe&shy; 
 <lb/>timus, vt concedatur nobis, id, quod principio, &amp; primo omnium demon&shy; 
 <lb/>&longs;trare propo&longs;ueramus. </s> 
  
 <s id="id.000815">aduerte, quod characteres, qui &longs;unt in &longs;equentibus  
 <lb/>verbis huius loci, non appellant characteres figur&aelig; appo&longs;it&aelig;; in quo quidam  
 <lb/>decepti, nullo pacto poterant locum hunc intelligere.</s></p><p type="main"> 
  
 <s id="id.000816"><arrow.to.target n="marg13"/></s></p><p type="margin"> 
  
 <s id="id.000817"><margin.target id="marg13"/>13</s></p><p type="main"> 
  
 <s id="id.000818">Ex cap.  
  
 22. lib.  
  
 2. Priorum <emph type="italics"/>(Vt &longs;i volens mon&longs;trare, quod diameter e&longs;t incom&shy; 
 <lb/>men&longs;. argueret Zenonis rationem, quod non e&longs;t moueri)<emph.end type="italics"/> &longs;uperius &longs;ecto 3. lib.  
  
 1.  
 <lb/>fus&egrave; explicauimus hanc a&longs;ymmetriam, quam &longs;i quis vellet demon&longs;trare ea&shy; 
 <lb/>dem illa ratione, qua Zeno motum impugnabat, quia &longs;cilicet <expan abbr="m&etilde;&longs;ura">men&longs;ura</expan> com&shy; 
 <lb/>munis, qu&aelig; debet vtramq, quantitatem men&longs;urare, debet in men&longs;urando  
 <lb/>infinitas partes pertran&longs;ire, uimirum medietates medietatum in in&longs;initum,  
 <lb/>e&longs;t autem impo&longs;&longs;ibile pertran&longs;ire infinitas huiu&longs;modi partes, &amp; propterea  
 <lb/>non poterit metiri, <expan abbr="neq;">neque</expan> vnam, <expan abbr="neq;">neque</expan> alteram ex <expan abbr="qu&atilde;titatibus">quantitatibus</expan>, qu&aelig; putaban&shy; 
 <lb/>tur commen&longs;urabiles, afferret hic, inquit Ari&longs;t.  
  
 non cau&longs;am pro cau&longs;a.</s></p><p type="main"> 
  
 <s id="id.000819"><arrow.to.target n="marg14"/></s></p><p type="margin"> 
  
 <s id="id.000820"><margin.target id="marg14"/>14</s></p><p type="main"> 
  
 <s id="id.000821">Ex eodem cap. <emph type="italics"/>(Quoniam idem <expan abbr="vtiq;">vtique</expan> fal&longs;um per plures petitiones accidere  
 <lb/>nihil forta&longs;&longs;e inconueniens, veluti coalternas coincidere; &amp; &longs;i maior e&longs;t extrin&longs;ecus  
 <lb/>angulus intrin&longs;eco; &amp; &longs;i triangulus habet plures rectos duobus)<emph.end type="italics"/> per plures po&longs;i&shy; 
 <lb/>tiones &longs;ubaudi fal&longs;as. </s> 
  
 <s id="id.000822">per coalternas intellige lineas &aelig;quidi&longs;tantes, &longs;eu pa&shy; 
 <lb/>rallelas, vt in &longs;uperiori cap.  
  
 monuimus. </s> 
  
 <s id="id.000823">C&aelig;terum Euclides propo&longs;. </s> 
  
 <s id="id.000824">28. pri&shy; 
 <lb/>mi Elem.  
  
 o&longs;tendit, quod &longs;i fuerint du&aelig; parallel&aelig; veluti in pr&aelig;cedenti figura,  
 <lb/>A B, C D, &longs;uper quas alia recta E F, incidat, nece&longs;&longs;ario faciet angulum ex&shy; 
 <lb/>trin&longs;ecum E G B, v. <!-- REMOVE S-->g. <!-- REMOVE S-->&aelig;qualem interno, &amp; oppo&longs;ito, &amp; ad ea&longs;dem partes,  
 <lb/>angulo videlicet G H D. &longs;i ergo inquit Ari&longs;t &longs;upponamus i&longs;tud fal&longs;um, an&shy; 
 <lb/>gulum &longs;cilicet E G B, externum e&longs;&longs;e maiorem angulo interno G H D, &longs;equi&shy; 
 <lb/>tur etiam fal&longs;um, videlicet lineas <expan abbr="&aelig;quidi&longs;t&atilde;tes">&aelig;quidi&longs;tantes</expan> A B, C D, concurrere. </s> 
  
  
  
  
  
 <s id="id.000825">&amp; pro&shy; 
 <lb/>batur con&longs;equentia hoc modo, quia &longs;i angulus E G B, maior e&longs;t angulo <pb xlink:href="009/01/043.jpg" pagenum="43"/>G H D, appo&longs;ito <expan abbr="vtiq;">vtique</expan> communi angulo B G H, erant primum, duo anguli  
 <lb/>E G B, B G H, maiores, quam &longs;int duo B G H, G H D, quia &longs;i in&aelig;qualibus  
 <lb/>&aelig;qualia addantur, tota erunt in&aelig;qualia, vt prius per 4, axioma: hoc loco  
 <lb/>communis angulus additur &longs;emel maiori angulo, &amp; &longs;emel minori; &amp; ideo  
 <lb/>totum illud, in quo e&longs;t maior angulus, adhuc maius e&longs;t altero toto, in quo  
 <lb/>minor angulus continetur. </s> 
  
 <s id="id.000826">at illi duo E G B, B G H, per 13. primi, &longs;unt  
 <lb/>&aelig;quales duobus rectis angulis, ergo duo <expan abbr="quoq;">quoque</expan> recti erunt maiores duobus  
 <lb/>internis B G H, D H G, &longs;iue hi duo interni erunt minores duobus rectis.  
 <lb/></s> 
  
 <s id="id.000827">At quando hi duo interni &longs;unt minores duobus rectis, tunc line&aelig; A B, C D,  
 <lb/>&longs;unt concurrentes, &longs;i protrahantur ad partes pr&aelig;dictorum <expan abbr="angulor&utilde;">angulorum</expan>. </s> 
  
 <s id="id.000828">quod  
 <lb/>P. <!-- REMOVE S-->Clauius luculenti, &amp; hactenus de&longs;iderata demon&longs;tratione ad 28. primi  
 <lb/>demon&longs;trauit. </s> 
  
  
  
 <s id="id.000829"><expan abbr="Atq;">Atque</expan> hoc pacto ex prima fal&longs;a &longs;uppo&longs;itione, nimirum angu&shy; 
 <lb/>lum illum externum e&longs;&longs;e maiorem interno, &amp; oppo&longs;ito; &longs;equitur fal&longs;um, ni&shy; 
 <lb/>mirum lineas parallelas concurrere.</s></p><p type="main"> 
  
 <s id="id.000830">Pr&aelig;terea &longs;i &longs;upponamus aliam fal&longs;itatem, &longs;cilicet triangulum habere tres  
 <lb/>angulos maiores duobus rectis, &longs;equetur eadem iterum fal&longs;itas, &longs;cilicet pa&shy; 
 <lb/><figure id="id.009.01.043.1.jpg" xlink:href="009/01/043/1.jpg" place="text"/> 
 <lb/>rallelas coincidere, &amp; probatur &longs;ic; &longs;int enim  
 <lb/><expan abbr="tri&atilde;guli">trianguli</expan> A B C, tres anguli maiores, quam duo  
 <lb/>recti anguli, &amp; per punctum C, ducta &longs;it recta  
 <lb/>C D, parallela lateri B A. quia ergo angulus  
 <lb/>A, &aelig;qualis e&longs;t angulo &longs;ibi alterno A C D, per  
 <lb/>29. primi, &amp; quia totalis angulus B C D, &aelig;qua&shy; 
 <lb/>lis e&longs;t duobus angulis B C A, A C D, quos tanquam &longs;uas partes ad&aelig;quatas  
 <lb/>continet, quorum alter, &longs;cilicet A C D, e&longs;t &aelig;qualis angulo A. erit idem to&shy; 
 <lb/>talis angulus B C D, &aelig;qualis duobus angulis A, &amp; A C B, trianguli propo&longs;i&shy; 
 <lb/>ti. </s> 
  
 <s id="id.000831">ergo totus i&longs;te angulus B C D, &longs;imul cum reliquo <expan abbr="tri&atilde;guli">trianguli</expan> angulo B. con&shy; 
 <lb/>flabit compo&longs;itionem ex tribus angulis trianguli dati: &amp; con&longs;equenter ta&shy; 
 <lb/>lis compo&longs;itio trium angulorum erit maior, quam &longs;int duo anguli recti. </s> 
  
 <s id="id.000832">ex  
 <lb/>quo &longs;equitur duas rectas B A, C D, &longs;uper quas cadit linea B C, faciens duos  
 <lb/>angulos internos, &amp; ad ea&longs;dem partes, &longs;cilicet A B D, maiores duobus re&shy; 
 <lb/>ctis non e&longs;&longs;e parallelas, &longs;ed concurrentes (vt patet ex nuper citata demon&shy; 
 <lb/>&longs;tratione P. Clauij) quod fal&longs;um e&longs;t. </s> 
  
 <s id="id.000833">&amp; &longs;equitur ex &longs;ecunda fal&longs;a &longs;uppo&longs;itio&shy; 
 <lb/>ne. </s> 
  
 <s id="id.000834">ex quibus textus Ari&longs;t.  
  
 videtur &longs;atis clarus.</s></p><p type="main"> 
  
 <s id="id.000835"><arrow.to.target n="marg15"/></s></p><p type="margin"> 
  
 <s id="id.000836"><margin.target id="marg15"/>15</s></p><p type="main"> 
  
 <s id="id.000837">Ex cap.  
  
 26. <emph type="italics"/>(Vt &longs;i A, duo recti, in quo autem P., triangulus, in quo vero C,  
 <lb/>&longs;en&longs;ibuis triangulus, &longs;u&longs;picari <expan abbr="namq;">namque</expan> po&longs;&longs;et aliquis non e&longs;&longs;e C, &longs;ciens, quod omnis  
 <lb/>triangulus habet duos rectos: quare &longs;imul no&longs;cet, &amp; ignorabit idem. </s> 
  
 <s id="id.000838">no&longs;ce enim  
 <lb/>omnem triangulum, quod duobus rectis, non &longs;implex e&longs;t: &longs;ed hoc quidem eo, quod  
 <lb/>vniuer&longs;alem habet &longs;cientiam: illud autem eo, quod &longs;ingularem. </s> 
  
 <s id="id.000839">&longs;ic igitur, vt vni&shy; 
 <lb/>uer&longs;ale nouit C, quod duo recti; vt autem &longs;ingulare non nouit, quare non habebit  
 <lb/>contrarias)<emph.end type="italics"/> vide, qu&aelig; diximus lib.  
  
 1. &longs;ecto 3. cap.  
  
 1. ex quibus quidquid Ma&shy; 
 <lb/>thematicum e&longs;t hic, clarum redditur. </s> 
  
 <s id="id.000840">reliqua ver&ograve;, qu&aelig; ad Logicum &longs;pe&shy; 
 <lb/>ctant, huius loci commentatores pro&longs;equuntur.</s></p><p type="main"> 
  
 <s id="id.000841">In cap.  
  
 31. de Abductione.<!-- KEEP S--></s></p><p type="main"> 
  
 <s id="id.000842"><arrow.to.target n="marg16"/></s></p><p type="margin"> 
  
 <s id="id.000843"><margin.target id="marg16"/>16</s></p><p type="main"> 
  
 <s id="id.000844">Notandum hic cum eruditi&longs;&longs;imo Burana, Abductionem hanc, de qua in hoc  
 <lb/>cap.  
  
 agitur e&longs;&longs;e vocem mathematicam, <expan abbr="cam&qacute;">camque</expan>; Ari&longs;t.  
  
 quemadmodum multa  
 <lb/>alia &agrave; Mathematicis mutuatum ad omnes alias &longs;cientias tran&longs;tuli&longs;&longs;e. </s> 
  
 <s id="id.000845">e&longs;&longs;e <pb xlink:href="009/01/044.jpg" pagenum="44"/>autem terminum mathematicum colligitur manife&longs;t&egrave; ex Proelo, qui lib.  
  
 3.  
 <lb/>in comm. <!-- REMOVE S-->Elem.  
  
 Euclidis ad primam propo&longs;itionem primi Elementi, pag.  
 <lb/></s> 
  
  
  
 <s id="id.000846">121. &longs;ic ait, Abductio ver&ograve; e&longs;t tran&longs;itus &agrave; propo&longs;ito problemate, vel theo&shy; 
 <lb/>remate ad aliud, quo cognito, aut comparato Propo&longs;itum quoque per&longs;pi&shy; 
 <lb/>cuum e&longs;t. </s> 
  
 <s id="id.000847">Exempli cau&longs;a, cum cubi duplicatio propo&longs;ita e&longs;&longs;et ad inue&longs;ti&shy; 
 <lb/>gandam qu&aelig;&longs;tionem in aliud tran&longs;tulere, quod illud propo&longs;itum con&longs;equi&shy; 
 <lb/>tur, ad duarum nempe mediarum linearum inuentionem tran&longs;lata e&longs;t qu&aelig;&shy; 
 <lb/>&longs;tio, &amp; &longs;ic qu&aelig;rebant deinceps, quonam modo datis duabus rectis lineis,  
 <lb/>du&aelig; medi&aelig; proportionales reperirentur. </s> 
  
 <s id="id.000848">Primum autem dicunt Hippocra&shy; 
 <lb/>tem Chium pr&ecedil;dictorum titulorum, Abductionem feci&longs;&longs;e, qui &amp; lunul&aelig; qua&shy; 
 <lb/>dratum fecit &aelig;quale, &amp; alia multa in Geometria inuenit. </s> 
  
 <s id="id.000849">h&aelig;c Proclus. <!-- KEEP S--></s> 
  
 <s id="id.000850">vbi  
 <lb/>non di&longs;&longs;imulandum nos re&longs;titui&longs;&longs;e verbum, Abductionem, cuius loco inter&shy; 
 <lb/>pres Procli vtitur inductionis voce, &longs;equuti &amp; rationem, &amp; gr&aelig;cum textum,  
 <lb/>qui no&longs;tram hanc expo&longs;itionem euidenter po&longs;tulat, <foreign lang="greek">apagwgh\</foreign> enim valet &amp;  
 <lb/>inductionem, &amp; abductionem, &longs;ed abductio omnino rei propo&longs;it&aelig; quadrat.</s></p><p type="main"> 
  
 <s id="id.000851">Notandum pr&aelig;terea Hippoetatem Chium fui&longs;&longs;e auctorem huius Abdu&shy; 
 <lb/>ctionis, <expan abbr="eum&qacute;">eumque</expan>; feci&longs;&longs;e Abductionem &agrave; propo&longs;ito Problemate quadrandi cir&shy; 
 <lb/>culi, vnde manife&longs;t&egrave; apparet, Ari&longs;totelem ex Mathematicis hunc terminum  
 <lb/>mutu&ograve; accepi&longs;&longs;e, quandoquidem ex ij&longs;dem accepit etiam exemplum Abdu&shy; 
 <lb/>ctionis Mathematic&aelig;, im&ograve; etiam exemplum ip&longs;ius authoris Abductionis 
 <lb/>Mathematic&aelig;. </s> 
  
 <s id="id.000852">&longs;yllogi&longs;mus autem Hippocratis, quo o&longs;tendebat circuli qua&shy; 
 <lb/>draturam reducebatur ad has propo&longs;itiones, omnis rectilinea figura qua&shy; 
 <lb/>dratur, &longs;ed circulus reducitur ad figuram rectilineam, ergo circulus qua&shy; 
 <lb/>dratur. </s> 
  
 <s id="id.000853">in probatione minoris facta e&longs;t Abductio, cum enim ip&longs;e vellet re&shy; 
 <lb/>ctificare circumferentiam circuli per lunulas, nec valeret, alij per lineam,  
 <lb/>quandam quadratricem, vt e&longs;t apud Pappum <expan abbr="Alexandrin&utilde;">Alexandrinum</expan>, &amp; apud P. <!-- REMOVE S-->Cla&shy; 
 <lb/>uium in fine &longs;exti Elem.  
  
 &amp; alij aliter fru&longs;tra conarentur, facta e&longs;t Abductio  
 <lb/>circa probationem minoris, in qua adhuc Mathematici verfantur; qu&aelig; pro&shy; 
 <lb/>batio, &longs;i tandem inueniri po&longs;&longs;et, mox &longs;equeretur principale <expan abbr="propo&longs;it&utilde;">propo&longs;itum</expan> pro&shy; 
 <lb/>blema, nimirum circulus quadraretur; vide qu&aelig; &longs;crip&longs;imus in cap.  
  
 3. Pr&aelig;&shy; 
 <lb/>dicam. <!-- REMOVE S-->de hac re, quia plurimum hunc conferunt. </s> 
  
  
  
  
  
 <s id="id.000854">&longs;ed iam ad textus expli&shy; 
 <lb/>cationem veniamus.</s></p><p type="main"> 
  
 <s id="id.000855"><arrow.to.target n="marg17"/></s></p><p type="margin"> 
  
 <s id="id.000856"><margin.target id="marg17"/>17</s></p><p type="main"> 
  
 <s id="id.000857">Ex eodem cap. <emph type="italics"/>(Veluti &longs;i K, e&longs;&longs;et quadrari, in quo autem E, rectilineum, in  
 <lb/>quo ver&ograve; F, circulus, &longs;i ip&longs;ius E F, vnum &longs;olum e&longs;&longs;et medium, hoc, quod e&longs;t, cum  
 <lb/>lunulis &aelig;qualem fieri circulum rectilineo, e&longs;&longs;e po&longs;&longs;et prop&egrave; ip&longs;um cogno&longs;cere, cum  
 <lb/>vero B C, neque credibilius &longs;it, quam A C, <expan abbr="neq;">neque</expan> pauca media, non dico Abductio&shy; 
 <lb/>nem: <expan abbr="neq;">neque</expan> quando B C, &longs;it immediatum, tale enim &longs;cientia est)<emph.end type="italics"/> Aduerte figuram  
 <lb/>vulgat&aelig; editionis e&longs;&longs;e mendo&longs;am, &amp; propterea re&longs;tituendam e&longs;&longs;e, qualis pri&shy; 
 <lb/>ma &longs;equens ex Simplicio ad tex. <!-- REMOVE S-->11. primi Phy&longs;ic. <!-- REMOVE S-->hoc modo Hippocrates  
 <lb/>Chius conabatur circulum ad quadrum redigere; fit circulus A B G C, qua&shy; 
 <lb/>drandus; con&longs;tituatur <expan abbr="itaq;">itaque</expan> &longs;uper diametro cius B C, quadratum B C D F,  
 <lb/>cuius diameter B D, &longs;ecatur bifariam in G, &agrave; circumferentia circuli dati,  
 <lb/>quod patet ducta &longs;emidiametro H G, perpendiculari ex B C, qu&aelig; &longs;uo extre&shy; 
 <lb/>mo puncto G, &longs;ecat bifariam, &amp; <expan abbr="diametr&utilde;">diametrum</expan> B D, &amp; circumferentiam B G C.  
 <lb/>facto ergo centro G, de&longs;cribatur alter circulus per puncta B C D F, <expan abbr="conne-ctatur&qacute;">conne&shy; 
 <lb/>ctaturque</expan>; recta G C. in triangulo orthogonio B C D, latus B D, &longs;ubtenditur <pb xlink:href="009/01/045.jpg" pagenum="45"/><figure id="id.009.01.045.1.jpg" xlink:href="009/01/045/1.jpg" place="text"/> 
 <lb/>angulo recto C, ergo quadratum eius ex eorol&shy; 
 <lb/>lario 47. primi, duplum erit quadrati B C, quare  
 <lb/>etiam circulus B C D F, duplus erit circuli A B&shy; 
 <lb/>G C, per 2. duodecimi, &amp; &longs;emicirculus B C D,  
 <lb/>duplus erit &longs;emicirculi B A C: &amp; quadrans B E&shy; 
 <lb/>C G, &aelig;qualis erit &longs;emicirculo B A C: ablato igi&shy; 
 <lb/>tur communi &longs;egmento B E C H, remanet lunu&shy; 
 <lb/>la B A C E, &aelig;qualis triangulo B C G, quod trian&shy; 
 <lb/>gulum &longs;i per vltimam &longs;ecundi quadretur, erit lu&shy; 
 <lb/>nula B A C, con&longs;equenter quadrata. </s> 
  
  
  
  
  
 <s id="id.000858"><expan abbr="hucu&longs;q;">hucu&longs;que</expan> be&shy; 
 <lb/>n&egrave; procedit Hippocrates. <!-- KEEP S--></s> 
  
 <s id="id.000859">&longs;ed vt reliquum circu&shy; 
 <lb/>li quadret, &longs;ic pergit, ponatur recta L M, dupla  
 <lb/>ip&longs;ius B C, &longs;upra quam &longs;emicirculus de&longs;cribatur  
 <lb/><figure id="id.009.01.045.2.jpg" xlink:href="009/01/045/2.jpg" place="text"/> 
 <lb/>L O M, cui in&longs;cribatur hexagoni  
 <lb/>&aelig;quilateri dimidium L Q S M, &amp; &longs;u&shy; 
 <lb/>per tribus hexagoni lateribus, &longs;int  
 <lb/>tres &longs;emicirculi, vt in figura. </s> 
  
 <s id="id.000860">&amp; <expan abbr="quo-ni&atilde;">quo&shy; 
 <lb/>niam</expan> diameter L M, dupla e&longs;t <expan abbr="vniu&longs;-cuiu&longs;q;">vniu&longs;&shy; 
 <lb/>cuiu&longs;que</expan> <expan abbr="diametror&utilde;">diametrorum</expan> B C, L Q, Q S,  
 <lb/>S M, erit &longs;emicirculus L O M, &ecedil;qua&shy; 
 <lb/>lis quatuor &longs;emicirculis pr&aelig;dictis  
 <lb/>per 2. duodecimi, &amp; per 4. &longs;ecundi  
 <lb/>ablatis igitur tribus <expan abbr="&longs;egm&etilde;tis">&longs;egmentis</expan> com&shy; 
 <lb/>munibus L N Q, Q O S, S P M, relinquetur trapezium L Q S M, &aelig;quale &longs;e&shy; 
 <lb/>micirculo B A C, &amp; tribus lunulis L H Q N, Q R S O, S X M P, ab&longs;cindan&shy; 
 <lb/>tur <expan abbr="itaq;">itaque</expan> detrapezio tria triangula &aelig;qualia tribus lunulis, eo modo, quo &longs;u&shy; 
 <lb/>pra in prima figura factum e&longs;t, &amp; quod relinquetur &aelig;quale erit &longs;emicirculo  
 <lb/>B A C. quod deinde quadretur per vlt. </s> 
  
 <s id="id.000861">&longs;ecundi, &longs;ed aduerte, quod quando  
 <lb/>ait, ab&longs;cindantur de trapezio tria triangula &aelig;qualia lunulis, eo modo, quo  
 <lb/>&longs;upra, committit deceptionem, quia eodem modo, quo &longs;upra minim&egrave; id fa&shy; 
 <lb/>cere po&longs;&longs;umus, quia in &longs;uperiori figura triangula erant con&longs;tituta &longs;uper la&shy; 
 <lb/>tus B C, quadrati B C D F, intra circulum de&longs;cripti, qui circulus facit cum  
 <lb/>B C, maius <expan abbr="&longs;egment&utilde;">&longs;egmentum</expan>, quam faciat &longs;emicirculus L O M, cum lateribus L Q,  
 <lb/>Q S, S M. &amp; propterea &longs;emicirculus i&longs;te non habet eandem proportionem  
 <lb/>ad vnamquamque lunularum &longs;uarum, quam habet &longs;emicirculus &longs;uperior  
 <lb/>B C D, ad lunulam B A C E. <expan abbr="atq;">atque</expan> h&aelig;c e&longs;t fallacia, quam authorem &longs;uum mi&shy; 
 <lb/>nim&egrave; latui&longs;&longs;e putandum, cuius Ari&longs;t. &longs;&aelig;pius mentionem in &longs;equentibus fa&shy; 
 <lb/>ciet : qu&igrave; enim fieri pote&longs;t, vt tam acutus inuentor, adeo manife&longs;tum erro&shy; 
 <lb/>rem non vidi&longs;&longs;et, verum propter adinuenti excellentiam, authori &longs;uo pla&shy; 
 <lb/>cuit paralogy&longs;mus. </s> 
  
 <s id="id.000862">mirabilis tamen &longs;emper habita e&longs;t illa &longs;uperior lunul&aelig;  
 <lb/>quadratio. </s> 
  
 <s id="id.000863">Ex quibus &longs;atis clara e&longs;&longs;e po&longs;&longs;unt ea, qu&aelig; ad <expan abbr="Mathematic&utilde;">Mathematicum</expan> per&shy; 
 <lb/>tinent, ad locum hunc de Abductione declarandum. </s> 
  
 <s id="id.000864">facta e&longs;t igitur abdu&shy; 
 <lb/>ctio ab Hippocrate in quadratione trium po&longs;teriorum lunularum, in qua&shy; 
 <lb/>rum quadratione diu immoratus, nunquam ni&longs;i cum paralogy&longs;mo quadra&shy; 
 <lb/>re valuit. </s> 
  
 <s id="id.000865">H&aelig;c pluribus, vt &longs;equentibus etiam textibus, in quibus huius te&shy; 
 <lb/>tragoni&longs;mi fit mentio &longs;atisfacere po&longs;&longs;imus. </s> 
  
 <s id="id.000866">Hippocrates i&longs;te Chius e&longs;t alter <pb xlink:href="009/01/046.jpg" pagenum="46"/>ab illo Hippocrate Coo medicorum Magi&longs;tro, vt colligitur ex Alexandre  
 <lb/>Aphrod. <!-- REMOVE S-->in Primum Meteororum de Cometis.<!-- KEEP S--></s> 
  
 </p></chap><chap><p type="head"> 
  
 <s id="id.000867"><emph type="italics"/>Ex Primo Posteriorum re&longs;olutoriorum.<emph.end type="italics"/></s></p><p type="main"> 
  
 <s id="id.000868"><arrow.to.target n="marg18"/></s></p><p type="margin"> 
  
 <s id="id.000869"><margin.target id="marg18"/>18</s></p><p type="main"> 
  
 <s id="id.000870">Textu primo <emph type="italics"/>(Omnis doctrina, &amp; omnis di&longs;ciplina di&longs;cur&longs;iua ex pr&aelig;exi&shy; 
 <lb/>&longs;tenti fit cognitione. </s> 
  
 <s id="id.000871">manife&longs;tum autem hoc &longs;peculantibus in omnibus,  
 <lb/>Mathematic&aelig; <expan abbr="namq;">namque</expan> &longs;cientiarum per hunc modum accedunt)<emph.end type="italics"/> quo mo&shy; 
 <lb/>do Mathematic&aelig; fiant ex pr&aelig;cedenti cognitione, &longs;cilicet Princi&shy; 
 <lb/>piorum per&longs;picu&egrave; quilibet videbit, qui &longs;altem primum <expan abbr="Elem&etilde;torum">Elementorum</expan> Eucli&shy; 
 <lb/>dis, vel &egrave; ianuis in&longs;pexerit; pr&ecedil;cedunt enim primo principiorum tria gene&shy; 
 <lb/>ra, quorum primum continet definitiones &longs;ubiecti Geometri&aelig;, vt definitio&shy; 
 <lb/>nes line&aelig;, &longs;uperficiei, trianguli, &amp;c: Secundum continet Po&longs;tulata. </s> 
  
 <s id="id.000872">Tertium  
 <lb/>Axiomata, &longs;eu communes omnium conceptiones, &amp; &longs;ententias, ex quibus  
 <lb/>tanquam ex vberrimis, &amp; chri&longs;taltinis fontibus Demon&longs;trationes Geome&shy; 
 <lb/>tric&aelig; deriuantur. </s> 
  
 <s id="id.000873">Idem v&igrave;dere licet in operibus aliorum Geometrarum,  
 <lb/>Archimedis, Apollonij, Pappi, &amp; c&aelig;terorum. </s> 
  
 <s id="id.000874">Ali&aelig; &longs;iniliter mathematic&aelig;,  
 <lb/>vt Arithmetica, Per&longs;pectiua, Mu&longs;ica, Mechanica, A&longs;tronomia, non ni&longs;t ex  
 <lb/>pr&aelig;mi&longs;&longs;is, ac manife&longs;ti&longs;simis principijs &longs;uas demon&longs;trationes deducunt.  
 <lb/></s> 
  
 <s id="id.000875">Nulla porr&ograve; alia &longs;cientia tam di&longs;tinct&egrave; &longs;ua pr&aelig;mittit principia, <expan abbr="tam&qacute;">tamque</expan>; per&shy; 
 <lb/>&longs;picua, &longs;icuti Mathematic&aelig;, vt non immerit&ograve; Philo&longs;ophus eas, tamquam  
 <lb/>ver&aelig; &longs;cienti&aelig; <expan abbr="typ&utilde;">typum</expan>, <expan abbr="eum&qacute;">eumque</expan>; omnibus numeris ab&longs;olutum &longs;ibi ob oculos pro&shy; 
 <lb/>po&longs;uerit, ex quo ver&aelig; &longs;cienti&aelig; de&longs;criptionem hi&longs;ce libris complecteretur.</s></p><p type="main"> 
  
 <s id="id.000876"><arrow.to.target n="marg19"/></s></p><p type="margin"> 
  
 <s id="id.000877"><margin.target id="marg19"/>19</s></p><p type="main"> 
  
 <s id="id.000878">Tex. 2. <emph type="italics"/>(Quod enim omne triangulum habet duobus rectis &aelig;quales, pr&aelig;&longs;ciuit:  
 <lb/>quod autem hoc, quod e&longs;t in &longs;emicirculo triangulum e&longs;t, &longs;imul inducens cognouit)<emph.end type="italics"/> 
 <lb/>vide primo, qu&aelig; &longs;upra libro 1. Prior. <!-- REMOVE S-->&longs;ecto 3. cap.  
  
 1. explicaui de angulis  
 <lb/>trianguli. </s> 
  
  
  
 <s id="id.000879">deinde &longs;cias, quod quando Ari&longs;t.  
  
 ait, hoc, quod e&longs;t in &longs;emicir cu&shy; 
 <lb/>lo triangulum, &amp;c. </s> 
  
 <s id="id.000880">alludit ad demon&longs;trationem quandam, quam ip&longs;e infe&shy; 
 <lb/>rius in exemplum adducet, &amp; qu&aelig; e&longs;t in 3. Elem.  
  
 Euclidis 31. in qua talis fi&shy; 
 <lb/>gura proponitur qualis e&longs;t pr&aelig;&longs;ens, in qua vides triangulum A B C. in &longs;e&shy; 
 <lb/><figure id="id.009.01.046.1.jpg" xlink:href="009/01/046/1.jpg" place="text"/> 
 <lb/>micirculo. </s> 
  
 <s id="id.000881">tunc autem dicitur triangulum in  
 <lb/>&longs;emicirculo, quando ba&longs;is ip&longs;ius e&longs;t diameter  
 <lb/>&longs;emicirculi, &amp; reliqua duo latera ita concur&shy; 
 <lb/>runt &longs;imul in angulum B, vt ip&longs;um paricer in  
 <lb/>circumferentia con&longs;tituant, quibus pr&ecedil;mi&longs;sis  
 <lb/>&longs;ic textum explicaueris: quod enim omne  
 <lb/>triangulum habet tres angulos &aelig;quales duo&shy; 
 <lb/>bus rectis angulis pr&aelig;&longs;ciuit vniuer&longs;aliter per  
 <lb/>32. primi; quod autem hoc particulare triangulum A B C, quod e&longs;t in &longs;e&shy; 
 <lb/>micirculo habeat eandem proprietatem, &longs;imul, ac qui&longs;piam animaduertit  
 <lb/>illud e&longs;&longs;e triangulum cogno&longs;cit, <expan abbr="ab&longs;q;">ab&longs;que</expan> vlla demon&longs;tratione, &longs;ed &longs;olum virtu&shy; 
 <lb/>te illius maioris propo&longs;itionis; omne triangulum habet tres, &amp;c.</s></p><p type="main"> 
  
 <s id="id.000882"><arrow.to.target n="marg20"/></s></p><p type="margin"> 
  
 <s id="id.000883"><margin.target id="marg20"/>20</s></p><p type="main"> 
  
 <s id="id.000884">Tex. 5. <emph type="italics"/>(Vera quidem igitur oporter e&longs;&longs;e, quoniam non e&longs;t non ens &longs;cire, vt quod  
 <lb/>diameter &longs;it commen&longs;urabi is)<emph.end type="italics"/> con&longs;ule ea, qu&aelig; &longs;crip&longs;imus ad cap.  
  
 23. primi  
 <lb/>Priorum, &longs;ecto 1. &longs;ine quibus locus hic &longs;atis intelligi nequit; ijs autem per&shy; 
 <lb/>ceptis &longs;ic <expan abbr="loc&utilde;">locum</expan> hunc explicare po&longs;&longs;umus, cum diameter quadrati &longs;it incom&shy;<pb xlink:href="009/01/047.jpg" pagenum="47"/>men&longs;urabilis lateri &longs;ui quadrati, fal&longs;um erit dicere diametrum e&longs;&longs;e com&shy; 
 <lb/>men&longs;urabilem pr&aelig;dicto lateri, quod autem fal&longs;um e&longs;t, illud non e&longs;t; igitur  
 <lb/>impo&longs;sibile e&longs;t &longs;cire diametrum e&longs;&longs;e commen&longs;urabile.</s></p><p type="main"> 
  
 <s id="id.000885"><arrow.to.target n="marg21"/></s></p><p type="margin"> 
  
 <s id="id.000886"><margin.target id="marg21"/>21</s></p><p type="main"> 
  
 <s id="id.000887">Hoc eodem cap.  
  
 plura dicuntur de Principijs Demon&longs;trationis, &longs;iue &longs;cien&shy; 
 <lb/>ti&aelig;, vt &longs;unt Dignitates, Po&longs;itiones, Definitiones, &amp; &longs;imilia, qu&aelig; quo modo  
 <lb/>&longs;e habeant, &amp; quo modo illis Demon&longs;trationes innitantur, optim&egrave; ex con&shy; 
 <lb/>templatione primi libri Elem.  
  
 Euclidis percipi pote&longs;t. </s> 
  
 <s id="id.000888">vt propterea ben&egrave; ij  
 <lb/>&longs;entiant, inter quos pr&aelig;cipui &longs;unt Toletus, &amp; Zabarella, qui a&longs;&longs;erunt, Ari&longs;t.  
 <lb/>Mathematicas &longs;cientias tamquam typum perfecti&longs;simarum &longs;cientiarum  
 <lb/>&longs;ibi ob oculos propo&longs;ui&longs;&longs;e; ex quo typo ver&aelig; &longs;cienti&aelig; de&longs;criptionem his li&shy; 
 <lb/>bris complectaretur.</s></p><p type="main"> 
  
 <s id="id.000889"><arrow.to.target n="marg22"/></s></p><p type="margin"> 
  
 <s id="id.000890"><margin.target id="marg22"/>22</s></p><p type="main"> 
  
 <s id="id.000891">Eodem tex. <!-- REMOVE S-->5. <emph type="italics"/>(Ponit enim Arithmeticus vnitatem indiui&longs;ibilem e&longs;&longs;e &longs;ecun&shy; 
 <lb/>dum quantum)<emph.end type="italics"/> hoc quamquam non ponatur ab Arithmeticis expre&longs;s&egrave;, pr&aelig;&shy; 
 <lb/>&longs;upponitur tamen ab eis: nu&longs;quam enim Euclides in totis tribus Arithme&shy; 
 <lb/>ticis libris, infra vnitatem de&longs;cendit, vt propterea appareat, ip&longs;am in quan&shy; 
 <lb/>titate di&longs;creta e&longs;&longs;e minimum, &amp; indiui&longs;ibile. </s> 
  
  
  
 <s id="id.000892">Verum dubitabit forr&egrave; qui&longs;&shy; 
 <lb/>piam hoc modo, &longs;i vnitas minimum, <expan abbr="atq;">atque</expan> indiui&longs;ibile e&longs;t in quanto di&longs;creto,  
 <lb/>qua igitur ratione Arithmetici practici eam diuidunt in dimidium, in trien&shy; 
 <lb/>tem, in quadrantem, &amp; alijs &longs;imiliter modis, vnde numeri illi, qui fractio&shy; 
 <lb/>nes appellantur, exurgunt? </s> 
  
 <s id="id.000893">Re&longs;pondemus, <expan abbr="quotie&longs;eunq;">quotie&longs;eunque</expan> vnitas diuiditur ab  
 <lb/>Arithmeticis, tunc ip&longs;i eam accipiunt tanquam totum quoddam <expan abbr="c&otilde;tinuum">continuum</expan>  
 <lb/>in plures partes diui&longs;ibile: &longs;iue tanquam aggregatum quoddam vnitatum,  
 <lb/>qu&aelig; vnitates &longs;unt partes illius, vt quando dicunt, vnum hor&aelig; quadrantem,  
 <lb/>vel duos hor&aelig; quadrantes, vel tres hor&aelig; quadrantes, accipiunt horam tan&shy; 
 <lb/>quam aggregatum quatuor quadrantum, &amp; propterea numeri illi 1/4. 2/4. 3/4.  
 <lb/>&amp; &longs;imiles fractiones, nihil aliud &longs;unt, quam numeri partium vnius hor&aelig;: ex  
 <lb/>quo patet huiu&longs;modi fractiones omnes reduci ad numeros integros, qui  
 <lb/>enim dicit tres quadrantes 3/4. dicit tres partes alicuius totius, quod intel&shy; 
 <lb/>ligitur diui&longs;um e&longs;&longs;e in 4. &aelig;quales partes, ex quibus ill&aelig; tres tantummodo  
 <lb/>numerat.</s></p><p type="main"> 
  
 <s id="id.000894"><arrow.to.target n="marg23"/></s></p><p type="margin"> 
  
 <s id="id.000895"><margin.target id="marg23"/>23</s></p><p type="main"> 
  
 <s id="id.000896">Tex. 9. <emph type="italics"/>(Per &longs;e autem, <expan abbr="qu&aelig;cunq;">qu&aelig;cunque</expan> &amp; in&longs;unt in eo, quod quid e&longs;t, vt triangulo li&shy; 
 <lb/>nea, &amp; line&aelig; punctum; &longs;ub&longs;tantia <expan abbr="namq;">namque</expan> ip&longs;orum ex his e&longs;t, &amp; in oratione dicen&shy; 
 <lb/>te, quid e&longs;t, in&longs;unt)<emph.end type="italics"/> aggreditur explicare qu&aelig;nam &longs;int ea, qu&aelig; per &longs;e dicun&shy; 
 <lb/>tur: <expan abbr="quot&qacute;">quotque</expan>; modis dicatur aliquid per &longs;e. </s> 
  
 <s id="id.000897">quorum primus e&longs;t, ea &longs;cilicet,  
 <lb/>per &longs;e de aliquo &longs;ubiecto dici, <expan abbr="qu&aelig;cunq;">qu&aelig;cunque</expan> in definitione illius ponuntur, cu&shy; 
 <lb/>iu&longs;modi &longs;unt linea, &amp; punctum, qu&aelig; per &longs;e pr&aelig;dicantur, illa de triangulo,  
 <lb/>i&longs;tud de linea; in de&longs;initione enim trianguli ponitur linea recta, quia linea  
 <lb/>recta dum terminat illam &longs;uperficiem, qu&aelig; dicitur triangulus illi trianguli  
 <lb/>naturam impertitur, &amp; ideo triangulus definitur &longs;ic, triangulus e&longs;t figura  
 <lb/>tribus lineis rectis terminata. </s> 
  
 <s id="id.000898">&longs;imiliter in definitione line&aelig;, non in&longs;init&aelig;,  
 <lb/>&longs;ed finit&aelig;, &amp; terminat&aelig; ponitur punctum, quia duo puncta, qu&aelig; &longs;unt extre&shy; 
 <lb/>ma illius, faciunt, vt ea &longs;it line a finita, &amp; definitur &longs;ic, linea finita e&longs;t lon&shy; 
 <lb/>gitudo, caius extrema &longs;unt puncta. </s> 
  
 <s id="id.000899">quamuis autem h&aelig;c definitio apud Eu&shy; 
 <lb/>clidem expre&longs;&longs;a non habeatur, tamen ex definitionibus ip&longs;ius pr&aelig;&longs;ertim &longs;e&shy; 
 <lb/>cunda, tertia, &amp; quarta elici pote&longs;t.</s></p><p type="main"> 
  
 <s id="id.000900"><arrow.to.target n="marg24"/></s></p><p type="margin"> 
  
 <s id="id.000901"><margin.target id="marg24"/>24</s></p><p type="main"> 
  
 <s id="id.000902">Eodem tex. <!-- REMOVE S-->9. <emph type="italics"/>(Et <expan abbr="quibu&longs;cunq;">quibu&longs;cunque</expan> iuexi&longs;tentium ip&longs;is, ip&longs;&aelig; &longs;unt in oratione, quid<emph.end type="italics"/><pb xlink:href="009/01/048.jpg" pagenum="48"/><emph type="italics"/>est declarante, quemadmodum rectum ine&longs;t line&aelig;, &amp; circulare: &amp; impar, &amp; par 
 <lb/>numero, &amp; primum, &amp; compo&longs;itum, &amp; &aelig;quilaterum, &amp; altera parte longius. </s> 
  
  
  
 <s id="id.000903">&amp;  
 <lb/><expan abbr="o&itilde;bus">oimbus</expan> bis in&longs;unt in oratione, quid e&longs;t <expan abbr="declar&atilde;te">declarante</expan>, ibi quidem linea, hic vero numerus)<emph.end type="italics"/> 
 <lb/>quia locus hic ben&egrave; exponitur &agrave; Toleto, &amp; melius etiam &agrave; Conymbr. </s> 
  
 <s id="id.000904">addam  
 <lb/>tantummodo qu&aelig;dam, qu&aelig; ad perfectam eius intelligentiam de&longs;iderantur.  
 <lb/></s> 
  
 <s id="id.000905">Sciendum igitur prim&ograve;, nu&longs;quam ab Euclide definiri rectum, circulare,  
 <lb/>impar, par, primum, compo&longs;itum, &aelig;quilaterum, nec altera parte longius:  
 <lb/><expan abbr="ver&utilde;">verum</expan> ab ip&longs;o in definitionibus primi definiri lineam rectam, non tamen cir&shy; 
 <lb/>cularem expre&longs;s&egrave;. </s> 
  
 <s id="id.000906">in definitionibus deinde &longs;eptimi definiri <expan abbr="numer&utilde;">numerum</expan> parem,  
 <lb/>&amp; imparem, item numerum primum, &amp; compofitum, &amp; &aelig;quilaterum, &amp; al&shy; 
 <lb/>tera parte longiorem. </s> 
  
 <s id="id.000907">ex quibus definitionibus po&longs;&longs;unt erui definitiones re&shy; 
 <lb/>cti, circularis, imparis, &amp; c&aelig;terorum, quorum hic Ari&longs;toteles meminit.  
 <lb/></s> 
  
 <s id="id.000908">C&aelig;terum Euclides definitione 11. &longs;eptimi, &longs;ic definit numerum primum:  
 <lb/>primus numerus e&longs;t, quem vnitas &longs;ola metitur. </s> 
  
 <s id="id.000909">numerus autem, vel vnitas  
 <lb/>metiri dicitur alium numerum, quando &longs;&aelig;pius repetita ip&longs;um omnino ad&shy; 
 <lb/>&aelig;quat, vt ternarius metitur nouenarium, quia ter repetitus ip&longs;um ad vn&shy; 
 <lb/>guem explet. </s> 
  
 <s id="id.000910">illi igitur numeri dicuntur ab Arithmeticis primi, qui &agrave; nullo  
 <lb/>alio, pr&aelig;terquam ab vnitate men&longs;urantur, quales &longs;unt, 2. 3. 5. 7. &amp;c. </s> 
  
 <s id="id.000911">Defi&shy; 
 <lb/>nitione ver&ograve; 13. definit numerum compo&longs;itum &longs;ic; compo&longs;itus numerus e&longs;t,  
 <lb/>quem numerus qui&longs;piam metitur, vt &longs;enarius erit compo&longs;itus, quia ip&longs;um  
 <lb/>binarius metitur, nam ter repetitus, ip&longs;i perfect&egrave; ad&aelig;quatur.</s></p><p type="main"> 
  
 <s id="id.000912">Per &aelig;quilaterum, intelligit quadratum, quadratus autem numerus defi&shy; 
 <lb/>nitione 18. &longs;eptimi &longs;ic explicatur: Quadratus numerus e&longs;t, qui &longs;ub duobus  
 <lb/>&aelig;qualibus numeris continetur, ide&longs;t, qui fit ex ductu vnius numeri in &longs;e ip&shy; 
 <lb/><figure id="id.009.01.048.1.jpg" xlink:href="009/01/048/1.jpg" place="text"/> 
 <lb/>&longs;um, vt &longs;i ducantur 3. in 3. fient 9. qui continetur &longs;ub duobus  
 <lb/>ternarijs; omnes autem ternarij &longs;unt &aelig;quales. </s> 
  
 <s id="id.000913">is autem nu&shy; 
 <lb/>merus dicetur quadratus, quia, vt apparet in figura, nouem  
 <lb/>ip&longs;ius vnitates po&longs;&longs;unt in plano ita ad inuicem collocari, vt  
 <lb/>referant quadratum; &amp; &longs;icuti quadratum geometricum ha&shy; 
 <lb/>bet latera &aelig;qualia, ita etiam quadratum arithmeticum: &longs;i&shy; 
 <lb/>ue numerus quadratus, habet &longs;ua latera &aelig;qualia, quot enim vnitates &longs;unt  
 <lb/>in vno, tot etiam &longs;unt in reliquis, vt in pr&aelig;&longs;enti &longs;unt tres vnitates in &longs;ingulis  
 <lb/>lateribus. </s> 
  
 <s id="id.000914">pr&ecedil;terea quemadmodum quadratum geometricum re&longs;olni pote&longs;t  
 <lb/>in plura quadrata, ita etiam arithmeticum, vt pr&aelig;&longs;ens, qui re&longs;oluitur in  
 <lb/>quatuor quadrata arithmetica. </s> 
  
 <s id="id.000915"><expan abbr="Neq;">Neque</expan> enim pote&longs;t quilibet numerus, vt opi&shy; 
 <lb/>nantur ageometreti, in hunc modum di&longs;poni, &longs;ed &longs;olum ij, qui producuntur  
 <lb/>ex multiplicatione numeri alicuius in &longs;e ip&longs;um.</s></p><p type="main"> 
  
 <s id="id.000916">Per altera parte longius, intelligit numerum, qui producitur &agrave; duobus  
 <lb/><figure id="id.009.01.048.2.jpg" xlink:href="009/01/048/2.jpg" place="text"/> 
 <lb/>numeris in&aelig;qualibus inuicem multiplicatis, qualis e&longs;t  
 <lb/>duodenarius, qui ex ductu trium in quatuor produci&shy; 
 <lb/>tur, &amp; refert figuram altera parte longiorem, &longs;iue, vt  
 <lb/>ait Boetius longilateram, cuius vnum latus e&longs;t maius  
 <lb/>altero, vt in appo&longs;ita figura videre licet. </s> 
  
 <s id="id.000917">atque h&aelig;c  
 <lb/>&longs;unt, qu&aelig; ex Mathematicis petenda erant, ad huius  
 <lb/>loci intelligentiam.</s></p><p type="main"> 
  
 <s id="id.000918"><arrow.to.target n="marg25"/></s></p><p type="margin"> 
  
 <s id="id.000919"><margin.target id="marg25"/>25</s></p><p type="main"> 
  
 <s id="id.000920">Tex. 11. <emph type="italics"/>(Per &longs;e autem, &amp; &longs;ecundum quod ip&longs;um, idem, vt per &longs;e line&aelig; inest<emph.end type="italics"/><pb xlink:href="009/01/049.jpg" pagenum="49"/><emph type="italics"/>punctum, &amp; rectum; etenim &longs;ecundum quod linea, &amp; triangulo, &longs;ecundum quod  
 <lb/>triangulum duo recti: etenim per &longs;e triangulum duobus rectis &aelig;quale. </s> 
  
 <s id="id.000921">Vniuer&longs;ale  
 <lb/>autem e&longs;t tunc, quando in quolibet, &amp; primo mon&longs;tratur, vt duos rectos habere,  
 <lb/><expan abbr="neq;">neque</expan> figur&aelig; e&longs;t vniuer&longs;ale, quamuis e&longs;t mon&longs;irare de figura, quod duos rectos habet,  
 <lb/>&longs;ed non de qualibet figura, <expan abbr="neq;">neque</expan> vtitur qualibet figura monstrans, quadrangulum  
 <lb/>enim figura a quidem est, non habet autem duobus rectis &aelig;quales. </s> 
  
 <s id="id.000922">Aequicrus ver&ograve;  
 <lb/>babet quidem <expan abbr="quodcunq;">quodcunque</expan> duobus rectis &aelig;quales, &longs;ed non prim&ograve;, &longs;ed triangulum  
 <lb/>prius. </s> 
  
 <s id="id.000923">quod igitur quoduis primum mon&longs;tratur duos rectos habens, aut <expan abbr="quodcunq;">quodcunque</expan>  
 <lb/>aliud, huic primo ine&longs;t vniuer&longs;ale, &amp; demonstratio de hoc vniuer&longs;aliter e&longs;t, de alijs  
 <lb/>ver&ograve; quodammodo, non per &longs;e, <expan abbr="neq;">neque</expan> de &aelig;quicrure e&longs;t vniuer&longs;aliter, &longs;ed in plus)<emph.end type="italics"/> pro  
 <lb/>quorum intelligentia nece&longs;&longs;aria &longs;unt ea, qu&aelig; primo Priorum &longs;ecto 3. cap.  
  
 1.  
 <lb/>&longs;crip&longs;imus. </s> 
  
 <s id="id.000924">deinde memineris figuram vniuer&longs;aliorem e&longs;&longs;e triangulo, &amp; tri&shy; 
 <lb/>angulum vniuer&longs;alius &aelig;quicrure. </s> 
  
 <s id="id.000925">quando ait (vt duos rectos habere) vult  
 <lb/>dicere, habere duos angulos rectos non actu, &longs;ed potentia; qu&aelig; affectio e&longs;t  
 <lb/>trianguli, quia, vt &longs;uperius diximus, habet tres angulos &aelig;quales duobus  
 <lb/>rectis angulis: qu&aelig; proprietas vniuer&longs;aliter, &amp; prim&ograve; competit triangulo.  
 <lb/></s> 
  
 <s id="id.000926">non autem figur&aelig;, quia figura e&longs;t vniuer&longs;alior. </s> 
  
 <s id="id.000927"><expan abbr="neq;">neque</expan> i&longs;o&longs;celi, quia i&longs;o&longs;celes e&longs;t  
 <lb/>re&longs;trictius triangulo. </s> 
  
 <s id="id.000928">omittimus reliqua &longs;ingillatim exponere, tum quia &longs;a&shy; 
 <lb/>tis clara &longs;unt, tum quia ab interpretibus ben&egrave; explicantur.</s></p><p type="main"> 
  
 <s id="id.000929"><arrow.to.target n="marg26"/></s></p><p type="margin"> 
  
 <s id="id.000930"><margin.target id="marg26"/>26</s></p><p type="main"> 
  
 <s id="id.000931">Tex. 13. <emph type="italics"/>(Si quis igitur mon&longs;trauerit, quod rect&aelig; <expan abbr="n&otilde;">non</expan> coincidunt, videbitur <expan abbr="vtiq;">vtique</expan>  
 <lb/>buius e&longs;&longs;e demonstratio, eo quod in omnibus e&longs;t rectis; non e&longs;t autem: &longs;i quidem  
 <lb/>non quoniam &longs;ic &aelig;quales, fit hoc, &longs;ed &longs;ecundum quod <expan abbr="quomodocunq;">quomodocunque</expan> &aelig;quales)<emph.end type="italics"/> pro&shy; 
 <lb/>ponit tres errores, qui circa demon&longs;trationem de vniuer&longs;ali contingunt,  
 <lb/>quos omnes Geometricis exemplis illu&longs;trat; affert autem primo pro tertio  
 <lb/>errore duo exempla, quorum primum in pr&aelig;mi&longs;&longs;is verbis continetur, <expan abbr="atq;">atque</expan>  
 <lb/>ex 28. primi Elem.  
  
 de&longs;umitur, quam propterea primo loco exponendam  
 <lb/><figure id="id.009.01.049.1.jpg" xlink:href="009/01/049/1.jpg" place="text"/> 
 <lb/>cen&longs;ui. </s> 
  
 <s id="id.000932">Quando igitur du&aelig; rect&aelig; con&longs;titu&shy; 
 <lb/>t&aelig; fuerint, vt A B, C D, in quas alia recta,  
 <lb/>vt G F, incidens, faciat duos angulos in&shy; 
 <lb/>ternos, re&longs;pectu rectarum A B, C D, &amp; ad  
 <lb/>ea&longs;dem partes rect&aelig; E F, vt &longs;unt ex parte  
 <lb/>&longs;ini&longs;tra anguli A G H, C H G; exparte ve&shy; 
 <lb/>r&ograve; dextra B G H, D H G; &longs;i <expan abbr="inqu&atilde;">inquam</expan> linea E F,  
 <lb/>fecerit duos illos angulos ex parte &longs;ini&longs;tra &longs;imul &longs;umptos, &aelig;quales duobus  
 <lb/>rectis angulis, vel duos ex parte dextra pariter &aelig;quales duobus rectis, pro&shy; 
 <lb/>bat Euclides rectas A B, C D, non concurrere, &longs;iue parallelas e&longs;&longs;e. </s> 
  
 <s id="id.000933">Verum,  
 <lb/>quia linea E F, pote&longs;t facere aliquando pr&aelig;dictos angulos non <expan abbr="tant&utilde;">tantum</expan> &aelig;qua&shy; 
 <lb/>les duobus rectis, verum etiam rectos, quo etiam modo <expan abbr="probar&etilde;tur">probarentur</expan> c&aelig;dem  
 <lb/>line&aelig; e&longs;&longs;e parallel&aelig;, vt in &longs;equenti figura, cum &longs;int anguli A G I, C I G, re&shy; 
 <lb/><figure id="id.009.01.049.2.jpg" xlink:href="009/01/049/2.jpg" place="text"/> 
 <lb/>cti, probabitur de rectis A B, C D, &aelig;quidi&longs;tan&shy; 
 <lb/>tia. </s> 
  
 <s id="id.000934">Ex his facile textum in hunc modum expo&shy; 
 <lb/>nemus; &longs;i quis igitur mon&longs;trauerit, quod rect&aelig;  
 <lb/>A B, C D, nunquam coincidunt, etiam&longs;i in in&longs;i&shy; 
 <lb/>nitum producantur, &longs;eu quod &longs;unt &aelig;quidi&longs;tantes,  
 <lb/>quando anguli pr&aelig;dicti interni &longs;unt duo recti,  
 <lb/>videbitur <expan abbr="vtiq;">vtique</expan> huius e&longs;&longs;e demon&longs;tratio de vniuer&longs;ali per &longs;e, &amp; de primo &longs;u&shy;<pb xlink:href="009/01/050.jpg" pagenum="50"/>biecto, vel &longs;ecundum quod ip&longs;um, e&ograve; quod probatur vniuer&longs;aliter de lineis  
 <lb/>omnibus habentibus pr&aelig;dictos angulos rectos. </s> 
  
 <s id="id.000935">non autem de omni, &longs;ecun&shy; 
 <lb/>dum quod ip&longs;um, &longs;i quidem non competit affectio h&aelig;c, e&longs;&longs;e parallelas, li&shy; 
 <lb/>neis habentibus illos angulos rectos actu; &longs;ed prim&ograve;, &amp; vniuer&longs;aliter, &amp; &longs;e&shy; 
 <lb/>cundum quod ip&longs;um competit lineis habentibus illos angulos &aelig;quales duo&shy; 
 <lb/>bus rectis, <expan abbr="quomodocunq;">quomodocunque</expan> &aelig;quales &longs;int duobus rectis, &longs;iue ambo &longs;int recti,  
 <lb/>&longs;iue vnus acutus, alter obtu&longs;us, &longs;ed tamen ambo &longs;imul &aelig;quentur duobus re&shy; 
 <lb/>ctis, quales &longs;unt line&aelig; prim&aelig; figur&aelig;. </s> 
  
 <s id="id.000936">In tertio igitur errore, vniuer&longs;ale exi&shy; 
 <lb/>&longs;tit quidem, &amp; habet nomen, &longs;ed tamen pr&aelig;termittetur, &longs;eu &longs;trictius &longs;ume&shy; 
 <lb/>tur, quam oportet. </s> 
  
 <s id="id.000937">alij latini, quos quidem viderim, pr&aelig;ter Zabarellana  
 <lb/>perperam omnino ob mathematicarum ignorantiam, exemplum i&longs;tud in&shy; 
 <lb/>terpretantur.</s></p><p type="main"> 
  
 <s id="id.000938"><arrow.to.target n="marg27"/></s></p><p type="margin"> 
  
 <s id="id.000939"><margin.target id="marg27"/>27</s></p><p type="main"> 
  
 <s id="id.000940">Ibidem <emph type="italics"/>(Et &longs;i triangulum non e&longs;&longs;et aliud, quam I&longs;o&longs;celes, &longs;ecundum quod I&longs;o&shy; 
 <lb/>&longs;celes videretur <expan abbr="vtiq;">vtique</expan> ine&longs;&longs;e)<emph.end type="italics"/> i&longs;tud e&longs;t &longs;ecundum exemplum tertij erroris. </s> 
  
 <s id="id.000941">Por&shy; 
 <lb/>r&ograve; cum tres &longs;int &longs;pecies triangulorum, &aelig;quilaterum, I&longs;o&longs;celes, Scalenum, &longs;i  
 <lb/>accideret, vt ex illis tribus vna tantum &longs;pecies, v. <!-- REMOVE S-->g. <!-- REMOVE S-->I&longs;o&longs;celes in mundo re&shy; 
 <lb/>periretur; <expan abbr="tunc&qacute;">tuncque</expan>; qui&longs;piam de I&longs;o&longs;cele o&longs;tenderet affectionem quampiam,  
 <lb/>putans &longs;e <expan abbr="o&longs;t&etilde;di&longs;&longs;e">o&longs;tendi&longs;&longs;e</expan> pa&longs;&longs;ionem de proprio &longs;ubiecto, &amp; primo, falleretur, quia  
 <lb/>aifectio illa competeret I&longs;o&longs;celi, non vt huic &longs;peciei I&longs;o&longs;celis, &longs;ed quatenus  
 <lb/>e&longs;t triangulum, cui primo, &amp; per &longs;e, &amp; &longs;ecundum quod ip&longs;um conuenit. </s> 
  
  
  
  
  
 <s id="id.000942">hoc  
 <lb/>loco di&longs;ce&longs;&longs;imus &agrave; Zabarella, qui putat i&longs;tud e&longs;&longs;e exemplum primi erroris,  
 <lb/>cum verba textus adeo clara &longs;int, vt expo&longs;itionem illius nullo modo admit&shy; 
 <lb/>tant. </s> 
  
 <s id="id.000943">&longs;unt autem h&aelig;c textus verba <emph type="italics"/>(Et &longs;i triangulum non e&longs;&longs;et aliud, quam I&longs;o&shy; 
 <lb/>&longs;celes, &longs;ecundum quod I&longs;o&longs;celes videretur <expan abbr="vtiq;">vtique</expan> ine&longs;&longs;e)<emph.end type="italics"/> quibus verbis manife&longs;t&egrave;  
 <lb/>apparet Ari&longs;t.  
  
 accipere pro &longs;ubiecto vniuer&longs;ali non indiuiduum vnum, vt in  
 <lb/>primo errore contingit, &longs;ed &longs;peciem loco generis, &longs;cilicet I&longs;o&longs;celes, quod  
 <lb/>e&longs;t &longs;pecies trianguli pro genere ip&longs;o, nimirum pro Triangulo. </s> 
  
 <s id="id.000944">ait enim, &longs;i  
 <lb/>non e&longs;&longs;et aliud, quam I&longs;o&longs;celes, <expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> quod I&longs;o&longs;celes: quibus verbis cla&shy; 
 <lb/>r&egrave; &longs;peciem, non indiuiduum, &longs;igni&longs;icat, ex his duobus exemplis manife&longs;tus  
 <lb/>e&longs;t tertius error, qui erat, quando erat <emph type="italics"/>(vt in parte totum)<emph.end type="italics"/> <expan abbr="quod&qacute;">quodque</expan>; illis verbis  
 <lb/>expo&longs;uerat <emph type="italics"/>(vei contingit etiam, vt in parte totum, in quo mon&longs;tratur: ijs emm,  
 <lb/>qu&aelig; &longs;unt in parte inerit quidem demon&longs;tratio, &amp; erit de omni, &longs;ed tamen non erit  
 <lb/>buius primi vniuer&longs;aliter demon&longs;tratio. </s> 
  
 <s id="id.000945">dico auttm huius primi, &longs;ecundum quod  
 <lb/>buius demonstrationem, quando &longs;it primi vniuer&longs;aliter)<emph.end type="italics"/> ide&longs;t, quando vniuer&longs;ale  
 <lb/>&longs;ubiectum exi&longs;tit quidem, &longs;ed tamen non de ip&longs;o &longs;it demon&longs;tratio, &longs;ed de ali&shy; 
 <lb/>qua parte ip&longs;ius, v. <!-- REMOVE S-->g. <!-- REMOVE S-->de &longs;pecie aliqua demon&longs;tratur aliquid, quod deberet  
 <lb/>o&longs;tendi prim&ograve; de ip&longs;o vniuer&longs;ali, cum illi prim&ograve; competat.</s> 
  
  
  
 </p><p type="main"> 
  
 <s id="id.000946"><arrow.to.target n="marg28"/></s></p><p type="margin"> 
  
 <s id="id.000947"><margin.target id="marg28"/>28</s></p><p type="main"> 
  
 <s id="id.000948">Ibidem <emph type="italics"/>(Et proportionale, quod alternatim, &longs;ecundum quod numeri, &amp; &longs;ecun&shy; 
 <lb/>dum quod line&aelig;, &amp; &longs;ecundum quod &longs;olida, &amp; &longs;ecundum quod tempora: quemad&shy; 
 <lb/>modum &amp; mon&longs;trabatur aliquando &longs;eor&longs;um, contingens <expan abbr="vtiq;">vtique</expan> de omnibus vnica  
 <lb/>demon&longs;tratione mon&longs;irari; &longs;ed quia non &longs;unt nominatum quidam omnia h&aelig;c vnum,  
 <lb/>numeri, longitudines, tempora &longs;olida, &amp; &longs;pecie differunt &agrave; &longs;einuicem &longs;cor&longs;um <expan abbr="ac-cipieb&atilde;tur">ac&shy; 
 <lb/>cipiebantur</expan>. </s> 
  
 <s id="id.000949">nunc autem vniuer &longs;aliter mon&longs;tratur, <expan abbr="neq;">neque</expan> enim &longs;ecundum quod line&aelig;,  
 <lb/>aut &longs;ecundum quod numeri, inerat; &longs;ed &longs;ecundum quod boc, quod vniuer &longs;ale &longs;up&shy; 
 <lb/>ponunt e&longs;&longs;e)<emph.end type="italics"/> affert exemplum &longs;ecundi erroris, quiaccidit, quando vniuer&longs;a&shy; 
 <lb/>le exi&longs;tit quidem, &longs;ed tamen e&longs;t innominatum, pro cuius explicatione &longs;cien&shy;<pb xlink:href="009/01/051.jpg" pagenum="51"/>dum quid &longs;it alterna proportio. </s> 
  
 <s id="id.000950">Alternam igitur proportionem definit Eu&shy; 
 <lb/>clides definitione 12. quinti, &longs;ic, e&longs;t &longs;umptio antecedentis ad <expan abbr="anteced&etilde;tem">antecedentem</expan>,  
 <lb/><figure id="id.009.01.051.1.jpg" xlink:href="009/01/051/1.jpg" place="text"/> 
 <lb/>&amp; con&longs;equentis ad con&longs;equentem. </s> 
  
 <s id="id.000951">Explico, exponantur qua&shy; 
 <lb/>tuor quantitates proportionales, v.g. <!-- REMOVE S-->vt 6. ad 3. ita &longs;int 4. ad  
 <lb/>2. &longs;i igitur argumentemur &longs;ic, vt 6. ad 3. ita 4. ad 2. ergo al&shy; 
 <lb/>ternatim erit, vt 6. ad 4. ita 3. ad 2. &longs;iue dixerimus, vt pri&shy; 
 <lb/>mum ad &longs;ecundum, ita tertium ad quartum, igitur alterna&shy; 
 <lb/>tim erit, vt primum ad tertium, ita &longs;ecundum ad quartum: valebit con&longs;e&shy; 
 <lb/>quentia; qu&aelig; quidem probatur deinde propo&longs;itione 16. quinti de magnitu&shy; 
 <lb/>dinibus, hoc e&longs;t in vniuer&longs;um de lineis, &longs;uperficiebus, &amp; &longs;olidis. </s> 
  
  
  
 <s id="id.000952">quando igi&shy; 
 <lb/>tur Ari&longs;t.  
  
 ait, mon&longs;tramus proportionale, ide&longs;t, qua&longs;uis quatuor quantita&shy; 
 <lb/>tes proportionales, habere hanc proprietatem, vt &longs;int etiam alternatim  
 <lb/>proportionales, &amp; non mon&longs;tramus vnica demon&longs;tratione de omni quouis  
 <lb/>proportionali, &longs;ed &longs;eparatim de magnitudinibus in 16. quinti, de numeris  
 <lb/>in 13. &longs;eptimi, &amp; &longs;eor&longs;um de temporibus in a&longs;tronomia, vel phy&longs;ica; hoc  
 <lb/>modo non o&longs;tendimus vniuer&longs;aliter de primo &longs;ubiecto, quia talis affectio  
 <lb/>conuenit &longs;ingulis, non vt numeri, aut ma gnitudines, aut tempora &longs;unt, &longs;ed  
 <lb/>&longs;ecundum quandam naturam illis omnibus communem, cui prim&ograve; illa pa&longs;&shy;