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version 1.15, 2002/08/07 13:08:03 version 1.65, 2002/08/22 15:44:02
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 <?xml version="1.0"?> <?xml version="1.0"?>
 <!DOCTYPE archimedes SYSTEM "../dtd/archimedes.dtd" ><archimedes>      <info>        <author>Bianchini, Giuseppe</author>        <title>Aristotelis loca mathematica</title>        <date>1615</date>         <!DOCTYPE archimedes SYSTEM "../dtd/archimedes.dtd" >
  <archimedes xmlns:xlink="http://www.w3.org/1999/xlink">      <info>
          <author>Biancani, Giuseppe</author>
 <place>Bologna</place>          <translator></translator>        <lang>la</lang>              <cvs_file>bianc_locam_01_la_1615.xml</cvs_file><cvs_version>1.13</cvs_version><locator>0000000009</locator>      </info>      <text>          <front>          </front>          <body>            <chap>        <pb/><p type="head">         <title>Aristotelis loca mathematica</title>
          <date>1615</date>
          <place>Bologna</place>
          <translator/>
          <lang>la</lang>
          <cvs_file>bianc_locam_01_la_1615</cvs_file>
          <cvs_version/>
          <locator>0000000009.xml</locator>
  </info>      <text>          <front>          </front>          <body>            <chap>        <pb/><p type="head">
  
 <s>ARISTOTELIS</s></p><p type="head"> <s>ARISTOTELIS</s></p><p type="head">
  
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 <s>Maie&longs;tatem <lb/>pro Sereni&longs;s. </s> <s>Maie&longs;tatem <lb/>pro Sereni&longs;s. </s>
  
 <s>Parmen&longs;ium Duce Legatum.</s></p><figure></figure><p type="head"> <s>Parmen&longs;ium Duce Legatum.</s></p><figure/><p type="head">
  
 <s>BONONI&AElig; M. </s> <s>BONONI&AElig; M. </s>
  
 <s>D C. </s> <s>D C. <!-- KEEP S--></s>
  
 <s>X V.</s></p><p type="head"> <s>X V.<!-- KEEP S--></s></p><p type="head">
  
 <s>Apud Bartholom&aelig;um Cochium. </s> <s>Apud Bartholom&aelig;um Cochium. <!-- KEEP S--></s>
  
 <s>Superiorum permi&longs;&longs;u.</s></p><p type="head"> <s>Superiorum permi&longs;&longs;u.</s></p><p type="head">
  
 <s>Sumptibus Hieronymi Tamburini.</s></p><pb pagenum="3"/><figure></figure><p type="head"> <s>Sumptibus Hieronymi Tamburini.</s></p><pb pagenum="3"/><figure/><p type="head">
  
 <s>ILLVSTRISSIMO <lb/>AC NOBILISSIMO</s></p><p type="head"> <s>ILLVSTRISSIMO <lb/>AC NOBILISSIMO</s></p><p type="head">
  
 <s>PETROFRANCISCO <lb/>MALASPINAE</s></p><p type="head"> <s>PETROFRANCISCO <lb/>MALASPINAE</s></p><p type="head">
  
 <s>&AElig;DIFICIORVM MARCHIONI.</s></p><figure></figure><p type="main"> <s>&AElig;DIFICIORVM MARCHIONI.</s></p><figure/><p type="main">
  
 <s><emph type="italics"/>En tandem Illustri&szlig;. </s> <s><emph type="italics"/>En tandem Illustri&szlig;. </s>
  
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 <s>long&aelig;uitatem tueatur. <lb/></s> <s>long&aelig;uitatem tueatur. <lb/></s>
  
 <s>Vale.<emph.end type="italics"/></s></p><p type="main"> <s>Vale.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
  
 <s><emph type="italics"/>Parm&aelig; Idibus Maij M. DC. XIIII.<emph.end type="italics"/><lb/><figure id="fig1"></figure></s></p><pb pagenum="5"/><figure></figure><p type="head"> <s><emph type="italics"/>Parm&aelig; Idibus Maij M. DC. XIIII.<emph.end type="italics"/><lb/><figure id="fig1"/><!-- KEEP S--></s></p><pb pagenum="5"/><figure/><p type="head">
  
 <s>Liber de &longs;e ip&longs;o.</s></p><p type="head"> <s>Liber de &longs;e ip&longs;o.</s></p><p type="head">
  
 <s><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"/></s></p><figure></figure><p type="main"> <s><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><figure/><p type="main">
  
 <s>Ego Iordanus Ca&longs;&longs;ini Pr&aelig;po&longs;itus Prouincialis Prouinci&aelig; Venet&aelig; Societatis <lb/>Ie&longs;u, ex auctoritate Adm. </s> <s>Ego Iordanus Ca&longs;&longs;ini Pr&aelig;po&longs;itus Prouincialis Prouinci&aelig; Venet&aelig; Societatis <lb/>Ie&longs;u, ex auctoritate Adm. </s>
  
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 <s>Claudij <lb/>Aqu&aelig;uiu&aelig;, facultatem concedo, vt hoc opus P. </s> <s>Claudij <lb/>Aqu&aelig;uiu&aelig;, facultatem concedo, vt hoc opus P. </s>
  
 <s>Io&longs;ephi Blancani eiu&longs;dem <lb/>Societatis, quod in&longs;cribitur, Ari&longs;t. </s> <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>
  
 <s>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> 
  
 <s>Parm&aelig; die 15. Ianuarij 1615.</s></p><p type="main"> <s>Parm&aelig; die 15. Ianuarij 1615.</s></p><p type="main">
  
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 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> 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>
  
 <s>Auerroes ip&longs;e tantus vir 5. Phy&longs;. </s> <s>Auerroes ip&longs;e tantus vir 5. Phy&longs;. commen. </s>
  
 <s>commen. </s> 
  
 <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></p><p type="main"> <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></p><p type="main">
  
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 <s>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>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>Vale.</s></p><figure></figure><pb pagenum="11"/><p type="head"> <s>Vale.<!-- KEEP S--></s></p><figure/><pb pagenum="11"/><p type="head">
  
 <s>Pr&ecedil;cipua qu&ecedil;dam, aut noua, autre&longs;taurata, <lb/>qu&aelig; obiter pertractantur.<lb/><arrow.to.target n="table1"></arrow.to.target></s></p><table><table.target id="table1"></table.target><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><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"/>S<gap/>ytala 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></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></cell></row></table><figure></figure><pb pagenum="12"/><p type="head"> <s>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"/>S<gap/>ytala 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><figure/><pb pagenum="12"/><p type="head">
  
 <s><emph type="italics"/>PRIMVS INDEX LOCORVM ARIST.<emph.end type="italics"/></s></p><p type="head"> <s><emph type="italics"/>PRIMVS INDEX LOCORVM ARIST.<emph.end type="italics"/></s></p><p type="head">
  
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 <s><emph type="italics"/>Cap.  <s><emph type="italics"/>Cap.
  
 de Motu, vbi de Gnomone.<emph.end type="italics"/></s></p><p type="head"> de Motu, vbi de Gnomone.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="head">
  
 <s>In Primo Priorum Re&longs;olutoriorum.</s></p><p type="main"> <s>In Primo Priorum Re&longs;olutoriorum.</s></p><p type="main">
  
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 <s><emph type="italics"/>Cap.  <s><emph type="italics"/>Cap.
  
 24. &longs;ecti 1. lib. </s> 24. &longs;ecti 1. lib.
  
 <s>1. de De&longs;criptionibus.<emph.end type="italics"/></s></p><p type="main"> 1. de De&longs;criptionibus.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
  
 <s><emph type="italics"/>Cap.  <s><emph type="italics"/>Cap.
  
 2. &longs;ect 2. lib. </s> 2. &longs;ect 2. lib.
  
 <s>1. de De&longs;criptionibus.<emph.end type="italics"/></s></p><p type="main"> 1. de De&longs;criptionibus.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
  
 <s><emph type="italics"/>Cap.  <s><emph type="italics"/>Cap.
  
 3. &longs;ecti 2. lib. </s> 3. &longs;ecti 2. lib.
  
 <s>1. de Incommen&longs;urabili.<emph.end type="italics"/></s></p><p type="main"> 1. de Incommen&longs;urabili.<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Cap.  <s><emph type="italics"/>Cap.
  
 1. &longs;ecti 3. lib. </s> 1. &longs;ecti 3. lib.
  
 <s>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"> 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><emph type="italics"/>Cap.  <s><emph type="italics"/>Cap.
  
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 <s><emph type="italics"/>Cap.  <s><emph type="italics"/>Cap.
  
 31. de Abductione.<emph.end type="italics"/></s></p><p type="main"> 31. de Abductione.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
  
 <s><emph type="italics"/>Cap.  <s><emph type="italics"/>Cap.
  
 codem, de circuli Quadratura, &longs;ecundum Hippocratem Chium.<emph.end type="italics"/></s></p><p type="head"> codem, de circuli Quadratura, &longs;ecundum Hippocratem Chium.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="head">
  
 <s>In primo Po&longs;teriorum.</s></p><p type="main"> <s>In primo Po&longs;teriorum.</s></p><p type="main">
  
 <s><emph type="italics"/>Textu primo, De Pr&aelig;cognitis Mathematicarum.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Textu primo, De Pr&aelig;cognitis Mathematicarum.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
  
 <s><emph type="italics"/>T. 2. Omnis triangulus habet tres, &amp; c.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>T. 2. Omnis triangulus habet tres, &amp; c.<emph.end type="italics"/></s></p><p type="main">
  
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 <s><emph type="italics"/>T. 11. Line&aelig; punctum inest per &longs;e, &amp; c.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>T. 11. Line&aelig; punctum inest per &longs;e, &amp; c.<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>T. 13. De Parallelis. </s> <s><emph type="italics"/>T. 13. De Parallelis. <!-- KEEP S--></s>
  
 <s>De I&longs;o&longs;cele. </s> <s>De I&longs;o&longs;cele. </s>
  
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 <s>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> <s>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>
  
 <s>Per&longs;pectinam, &amp; Mechanicam &longs;ubalternari Geometri&aelig;, Mu&longs;icam, Arithmetic&aelig;.<emph.end type="italics"/></s></p><p type="main"> <s>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><emph type="italics"/>T. 24. De numero pari, impari, quodrangulo, cubo. </s> <s><emph type="italics"/>T. 24. De numero pari, impari, quodrangulo, cubo. </s>
  
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 <s><emph type="italics"/>T. 25. Geometram non mentiri in &longs;uis exemplis.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>T. 25. Geometram non mentiri in &longs;uis exemplis.<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>T. 28. De Parallelis.<emph.end type="italics"/></s></p><pb pagenum="13"/><p type="main"> <s><emph type="italics"/>T. 28. De Parallelis.<emph.end type="italics"/><!-- KEEP S--></s></p><pb pagenum="13"/><p type="main">
  
 <s><emph type="italics"/>T. 29. Cur in Mathematicis non &longs;it Paralogi&longs;mus. </s> <s><emph type="italics"/>T. 29. Cur in Mathematicis non &longs;it Paralogi&longs;mus. <!-- KEEP S--></s>
  
 <s>Item quid multiplicata propor&shy;<lb/>tio. </s> <s>Item quid multiplicata propor&shy;<lb/>tio. </s>
  
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 <s><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><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><emph type="italics"/>T. 38. Quid Mina, quid Die&longs;is.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>T. 38. Quid Mina, quid Die&longs;is.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
  
 <s><emph type="italics"/>T. 39. Habere tres angulos &aelig;quales, &amp;c. </s> <s><emph type="italics"/>T. 39. Habere tres angulos &aelig;quales, &amp;c. </s>
  
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 <s><emph type="italics"/>T. 2. Omnis triangulus habet tres, &amp;c. </s> <s><emph type="italics"/>T. 2. Omnis triangulus habet tres, &amp;c. </s>
  
 <s>Item de Definitionibus Mathematicarum.<emph.end type="italics"/></s></p><p type="main"> <s>Item de Definitionibus Mathematicarum.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
  
 <s><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><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">
  
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 <s>Zabarella correctus.<emph.end type="italics"/></s></p><p type="main"> <s>Zabarella correctus.<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>T. 24. Echo, Imago &egrave; &longs;peculo, Iris.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>T. 24. Echo, Imago &egrave; &longs;peculo, Iris.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
  
 <s><emph type="italics"/>T. 25. Permutatim proportionale quid; exemplum in triangulis.<emph.end type="italics"/></s></p><p type="head"> <s><emph type="italics"/>T. 25. Permutatim proportionale quid; exemplum in triangulis.<emph.end type="italics"/></s></p><p type="head">
  
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 <s><emph type="italics"/>Cap.  <s><emph type="italics"/>Cap.
  
 2. loco 41. V&longs;us Definitionum in Mathematicis.<emph.end type="italics"/></s></p><p type="main"> 2. loco 41. V&longs;us Definitionum in Mathematicis.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
  
 <s><emph type="italics"/>Cap.  <s><emph type="italics"/>Cap.
  
 4. loco 86. Elementa geometrica: Numeri capitales.<emph.end type="italics"/></s></p><p type="head"> 4. loco 86. Elementa geometrica: Numeri capitales.<emph.end type="italics"/></s></p><p type="head">
  
 <s>In Elenchorum lib. </s> <s>In Elenchorum lib.
  
 <s>1.</s></p><p type="main"> 1.</s></p><p type="main">
  
 <s><emph type="italics"/>Cap.  <s><emph type="italics"/>Cap.
  
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 <s><emph type="italics"/>T. 20. Quatenus Per&longs;pectmus con&longs;ideret lineam.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>T. 20. Quatenus Per&longs;pectmus con&longs;ideret lineam.<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>T. 28. Quid con&longs;onantia Diapa&longs;on.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>T. 28. Quid con&longs;onantia Diapa&longs;on.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
  
 <s><emph type="italics"/>T. 68. Mathematicas Demon&longs;trationes babere cau&longs;am, qu&aelig; reducitur ad defini&shy;<lb/>tionem.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>T. 68. Mathematicas Demon&longs;trationes babere cau&longs;am, qu&aelig; reducitur ad defini&shy;<lb/>tionem.<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>T. 8. Denece&longs;&longs;ari<gap/>, quod e&longs;t in Mathematicis. </s> <s><emph type="italics"/>T. 8. Denece&longs;&longs;ari<gap/>, quod e&longs;t in Mathematicis. <!-- KEEP S--></s>
  
 <s>&amp; omnis triangulus habet tres an&shy;<lb/>gulos, &amp;c.<emph.end type="italics"/></s></p><p type="head"> <s>&amp; omnis triangulus habet tres an&shy;<lb/>gulos, &amp;c.<emph.end type="italics"/></s></p><p type="head">
  
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 <s><emph type="italics"/>T. 76. Quinam numeri dicantur Gnomones.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>T. 76. Quinam numeri dicantur Gnomones.<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>T. 31. Quonam infinito vtantur Mathematici.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>T. 31. Quonam infinito vtantur Mathematici.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
  
 <s><emph type="italics"/>T. 71. De infinito Mathematica.<emph.end type="italics"/></s></p><pb pagenum="14"/><p type="head"> <s><emph type="italics"/>T. 71. De infinito Mathematica.<emph.end type="italics"/><!-- KEEP S--></s></p><pb pagenum="14"/><p type="head">
  
 <s>Ex 4. Phy&longs;ic.</s></p><p type="main"> <s>Ex 4. Phy&longs;ic.</s></p><p type="main">
  
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 <s><emph type="italics"/>T. 15. Omnis triangulus habet tres &aelig;quales, &amp;c.<emph.end type="italics"/></s></p><p type="head"> <s><emph type="italics"/>T. 15. Omnis triangulus habet tres &aelig;quales, &amp;c.<emph.end type="italics"/></s></p><p type="head">
  
 <s>Ex 1. de C&oelig;lo.</s></p><p type="main"> <s>Ex 1. de C&oelig;lo.<!-- KEEP S--></s></p><p type="main">
  
 <s><emph type="italics"/>T. 33. De minimo indiui&longs;ibili.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>T. 33. De minimo indiui&longs;ibili.<emph.end type="italics"/></s></p><p type="main">
  
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 <s>Item de commen&longs;urabili.<emph.end type="italics"/></s></p><p type="head"> <s>Item de commen&longs;urabili.<emph.end type="italics"/></s></p><p type="head">
  
 <s>Ex 2. de C&oelig;lo.</s></p><p type="main"> <s>Ex 2. de C&oelig;lo.<!-- KEEP S--></s></p><p type="main">
  
 <s><emph type="italics"/>T. 24. Plato ex planis &longs;olida componebat, qu&igrave;.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>T. 24. Plato ex planis &longs;olida componebat, qu&igrave;.<emph.end type="italics"/></s></p><p type="main">
  
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 <s><emph type="italics"/>T. 111. Mare occidentale coniungi indico.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>T. 111. Mare occidentale coniungi indico.<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>T. 112. De quantitate Terr&aelig;.<emph.end type="italics"/></s></p><p type="head"> <s><emph type="italics"/>T. 112. De quantitate Terr&aelig;.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="head">
  
 <s>Ex 3. de C&oelig;lo.</s></p><p type="main"> <s>Ex 3. de C&oelig;lo.<!-- KEEP S--></s></p><p type="main">
  
 <s><emph type="italics"/>T. 40. Vt componatur &longs;ph&aelig;ra.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>T. 40. Vt componatur &longs;ph&aelig;ra.<emph.end type="italics"/></s></p><p type="main">
  
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 <s><emph type="italics"/>T. 71. Terram e&longs;&longs;e cubum, cur dictum &longs;it.<emph.end type="italics"/></s></p><p type="head"> <s><emph type="italics"/>T. 71. Terram e&longs;&longs;e cubum, cur dictum &longs;it.<emph.end type="italics"/></s></p><p type="head">
  
 <s>Ex 4. de C&oelig;lo.</s></p><p type="main"> <s>Ex 4. de C&oelig;lo.<!-- KEEP S--></s></p><p type="main">
  
 <s><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"> <s><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">
  
 <s><emph type="italics"/>T. 44. &amp; <expan abbr="&longs;eq.">&longs;eque</expan> Cur qu&aelig;dam grautora qu&agrave;m aqua, &longs;upernatent.<emph.end type="italics"/></s></p><p type="head"> <s><emph type="italics"/>T. 44. &amp; <expan abbr="&longs;eq.">&longs;eque</expan> Cur qu&aelig;dam grautora qu&agrave;m aqua, &longs;upernatent.<emph.end type="italics"/></s></p><p type="head">
  
 <s>Ex 2. de Generatione, &amp; Corruptione.</s></p><p type="main"> <s>Ex 2. de Generatione, &amp; Corruptione.<!-- KEEP S--></s></p><p type="main">
  
 <s><emph type="italics"/>Tex. </s> <s><emph type="italics"/>Tex. 56. Cur Planet&aelig; duobus motibus moueri dicantur.<emph.end type="italics"/></s></p><p type="head">
  
 <s>56. Cur Planet&aelig; duobus motibus moueri dicantur.<emph.end type="italics"/></s></p><p type="head"> 
  
 <s>Ex 1. Meteororum.</s></p><p type="main"> <s>Ex 1. Meteororum.<!-- KEEP S--></s></p><p type="main">
  
 <s><emph type="italics"/>Summa prima cap. </s> <s><emph type="italics"/>Summa prima cap.
  
 <s>3. De magnitudine Terr&aelig; ad a&longs;tra, &amp; &longs;olem collata.<emph.end type="italics"/></s></p><p type="main"> 3. De magnitudine Terr&aelig; ad a&longs;tra, &amp; &longs;olem collata.<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Cap.  <s><emph type="italics"/>Cap.
  
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 <s><emph type="italics"/>Cap.  <s><emph type="italics"/>Cap.
  
 4. De ordine Luminarium Solis, &amp; Lun&aelig;.<emph.end type="italics"/></s></p><p type="main"> 4. De ordine Luminarium Solis, &amp; Lun&aelig;.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
  
 <s><emph type="italics"/>Summa 2. cap. </s> <s><emph type="italics"/>Summa 2. cap.
  
 <s>3. de Mercurij stella. </s> 3. de Mercurij stella. </s>
  
 <s>Item de Cometa: e&longs;&longs;e in C&oelig;lo.<emph.end type="italics"/></s></p><p type="main"> <s>Item de Cometa: e&longs;&longs;e in C&oelig;lo.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
  
 <s><emph type="italics"/>Cap.  <s><emph type="italics"/>Cap.
  
 5. De Magnitudine Solis, &amp; de vmbra Terr&aelig;.<emph.end type="italics"/></s></p><p type="main"> 5. De Magnitudine Solis, &amp; de vmbra Terr&aelig;.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
  
 <s><emph type="italics"/>Cap.  <s><emph type="italics"/>Cap.
  
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 <s>Noua ob&longs;eruatio de rotundi&shy;<lb/>tate Terr&aelig;, <expan abbr="atq;">atque</expan> Mundi duratione.<emph.end type="italics"/></s></p><p type="head"> <s>Noua ob&longs;eruatio de rotundi&shy;<lb/>tate Terr&aelig;, <expan abbr="atq;">atque</expan> Mundi duratione.<emph.end type="italics"/></s></p><p type="head">
  
 <s>Ex 2. Meteororum.</s></p><p type="main"> <s>Ex 2. Meteororum.<!-- KEEP S--></s></p><p type="main">
  
 <s><emph type="italics"/>Summa 1. cap. </s> <s><emph type="italics"/>Summa 1. cap.
  
 <s>1. De Marirubro.<emph.end type="italics"/></s></p><p type="main"> 1. De Marirubro.<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Summa 2. cap. </s> <s><emph type="italics"/>Summa 2. cap.
  
 <s>2. De ortu stellarum fixarum: Item de occa&longs;u earumdem.<emph.end type="italics"/></s></p><p type="main"> 2. De ortu stellarum fixarum: Item de occa&longs;u earumdem.<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Cap.  <s><emph type="italics"/>Cap.
  
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 <s>Ex 3. Meteor.</s></p><p type="main"> <s>Ex 3. Meteor.</s></p><p type="main">
  
 <s><emph type="italics"/>Summa 2. cap. </s> <s><emph type="italics"/>Summa 2. cap.
  
 <s>2. De Halone, &longs;eu Area, &longs;eu Corona, Mathematica demon&longs;iratio.<emph.end type="italics"/></s></p><p type="main"> 2. De Halone, &longs;eu Area, &longs;eu Corona, Mathematica demon&longs;iratio.<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Cap.  <s><emph type="italics"/>Cap.
  
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 <s><emph type="italics"/>Cap.  <s><emph type="italics"/>Cap.
  
 5. De Parelio. </s> 5. De Parelio. <!-- KEEP S--></s>
  
 <s>Rationes Ari&longs;totelis refelluntur.<emph.end type="italics"/></s></p><p type="head"> <s>Rationes Ari&longs;totelis refelluntur.<emph.end type="italics"/></s></p><p type="head">
  
 <s>Ex 1. De Anima.</s></p><p type="main"> <s>Ex 1. De Anima.</s></p><p type="main">
  
 <s><emph type="italics"/>Tex. </s> <s><emph type="italics"/>Tex. 11. Quid rectum, quid obliquum. </s>
  
 <s>11. Quid rectum, quid obliquum. </s> 
  
 <s>&amp; omnis triangulus babet tres, &amp;c.<emph.end type="italics"/></s></p><p type="main"> <s>&amp; omnis triangulus babet tres, &amp;c.<emph.end type="italics"/></s></p><p type="main">
  
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 <s>De Sen&longs;u.</s></p><p type="main"> <s>De Sen&longs;u.</s></p><p type="main">
  
 <s><emph type="italics"/>Capite 6. Die&longs;is.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Capite 6. Die&longs;is.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
  
 <s><emph type="italics"/>Cap.  <s><emph type="italics"/>Cap.
  
 8. Nete. </s> 8. Nete. </s>
  
 <s>Diapa&longs;on. </s> <s>Diapa&longs;on. <!-- KEEP S--></s>
  
 <s>Diapen&longs;e.<emph.end type="italics"/></s></p><p type="head"> <s>Diapen&longs;e.<emph.end type="italics"/></s></p><p type="head">
  
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 <s>Ex lib. </s> <s>Ex lib. </s>
  
 <s>De Somnijs.</s></p><p type="main"> <s>De Somnijs.<!-- KEEP S--></s></p><p type="main">
  
 <s><emph type="italics"/>Cap.  <s><emph type="italics"/>Cap.
  
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 <s>Diameter incommen&longs;.<emph.end type="italics"/></s></p><p type="main"> <s>Diameter incommen&longs;.<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Summa 2. cap. </s> <s><emph type="italics"/>Summa 2. cap.
  
 <s>3. Pythagorei Mathematicas c&aelig;teris pr&aelig;ferebant.<emph.end type="italics"/></s></p><p type="main"> 3. Pythagorei Mathematicas c&aelig;teris pr&aelig;ferebant.<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>T. 47. Geometria habet &longs;uas pr&aelig;cognitiones.<emph.end type="italics"/></s></p><p type="head"> <s><emph type="italics"/>T. 47. Geometria habet &longs;uas pr&aelig;cognitiones.<emph.end type="italics"/></s></p><p type="head">
  
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 <s>Tetragoni&longs;mus est inuentio medi&aelig;.<emph.end type="italics"/></s></p><pb pagenum="16"/><p type="main"> <s>Tetragoni&longs;mus est inuentio medi&aelig;.<emph.end type="italics"/></s></p><pb pagenum="16"/><p type="main">
  
 <s><emph type="italics"/>Tex. </s> <s><emph type="italics"/>Tex. 8. Geod&aelig;&longs;ia quid.<emph.end type="italics"/></s></p><p type="head">
  
 <s>8. Geod&aelig;&longs;ia quid.<emph.end type="italics"/></s></p><p type="head"> 
  
 <s>Ex 4. Methaphy&longs;.</s></p><p type="main"> <s>Ex 4. Methaphy&longs;.</s></p><p type="main">
  
 <s><emph type="italics"/>T. 4. Qu&aelig; &longs;int prim&aelig;, &amp; qu&aelig; &longs;ecund&aelig; inter Mathematicas.<emph.end type="italics"/></s></p><p type="main"> <s><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><emph type="italics"/>T. 28. Diameter, commen&longs;urabilis.<emph.end type="italics"/></s></p><p type="head"> <s><emph type="italics"/>T. 28. Diameter, commen&longs;urabilis.<emph.end type="italics"/></s></p><p type="head">
  
 <s>Ex 5. Methaphy&longs;.</s></p><p type="main"> <s>Ex 5. Methaphy&longs;.</s></p><p type="main">
  
 <s><emph type="italics"/>T. 2. Exemplum cau&longs;&aelig; formalis ex Diapa&longs;on. </s> <s><emph type="italics"/>T. 2. Exemplum cau&longs;&aelig; formalis ex Diapa&longs;on. <!-- KEEP S--></s>
  
 <s>Qu&aelig; &longs;int proportiones Mu&longs;icales.<emph.end type="italics"/></s></p><p type="main"> <s>Qu&aelig; &longs;int proportiones Mu&longs;icales.<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>T. 3. Qu&aelig; &longs;it Materia in Mathematicis.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>T. 3. Qu&aelig; &longs;it Materia in Mathematicis.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
  
 <s><emph type="italics"/>T. 4. Quidnam &longs;int elementa apud Geometras.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>T. 4. Quidnam &longs;int elementa apud Geometras.<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>T. 12. Die&longs;is.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>T. 12. Die&longs;is.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
  
 <s><emph type="italics"/>T. 17. Diameter incommen&longs;urab. </s> <s><emph type="italics"/>T. 17. Diameter incommen&longs;urab. </s>
  
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 <s><emph type="italics"/>T. 4. Motum diurnum men&longs;uram reliquorum. </s> <s><emph type="italics"/>T. 4. Motum diurnum men&longs;uram reliquorum. </s>
  
 <s>Die&longs;is.<emph.end type="italics"/></s></p><p type="main"> <s>Die&longs;is.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
  
 <s><emph type="italics"/>T. 11. Similes figur&aelig; qu&aelig;. </s> <s><emph type="italics"/>T. 11. Similes figur&aelig; qu&aelig;. </s>
  
 <s>Diuer&longs;um in Math. </s> <s>Diuer&longs;um in Math. quid.<emph.end type="italics"/></s></p><p type="head">
  
 <s>quid.<emph.end type="italics"/></s></p><p type="head"> 
  
 <s>Ex 11. Methaphy&longs;.</s></p><p type="main"> <s>Ex 11. Methaphy&longs;.</s></p><p type="main">
  
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 2. De Admirandis circuli.<emph.end type="italics"/></s></p><p type="main"> 2. De Admirandis circuli.<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Qu&aelig;&longs;tio 1. De Libra. </s> <s><emph type="italics"/>Qu&aelig;&longs;tio 1. De Libra. <!-- KEEP S--></s>
  
 <s>cur maior, exactior. </s> <s>cur maior, exactior. </s>
  
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 lap&longs;us.<emph.end type="italics"/></s></p><p type="main"> lap&longs;us.<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Qu&aelig;&longs;t. </s> <s><emph type="italics"/>Qu&aelig;&longs;t. 2. Duplex Libra. <!-- KEEP S--></s>
  
 <s>2. Duplex Libra. </s> 
  
 <s>Piccolomineus reiectus.<emph.end type="italics"/></s></p><p type="main"> <s>Piccolomineus reiectus.<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Qu&aelig;&longs;t. </s> <s><emph type="italics"/>Qu&aelig;&longs;t. 3. De Vecte.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
  
 <s>3. De Vecte.<emph.end type="italics"/></s></p><p type="main"> 
  
 <s><emph type="italics"/>Qu&aelig;&longs;t. </s> 
  
 <s>4. De Remo; Petri Non&yuml; in Arist.  <s><emph type="italics"/>Qu&aelig;&longs;t. 4. De Remo; Petri Non&yuml; in Arist.
  
 correctio.<emph.end type="italics"/></s></p><p type="main"> correctio.<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Qu&aelig;&longs;t. </s> <s><emph type="italics"/>Qu&aelig;&longs;t. 5. De Temone Nauis.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
  
 <s>5. De Temone Nauis.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Qu&aelig;&longs;t. 6. De Antenna.<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Qu&aelig;&longs;t. </s> <s><emph type="italics"/>Qu&aelig;&longs;t. 8 De Rota.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
  
 <s>6. De Antenna.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Qu&aelig;&longs;t. 9. De Trochlea, &amp; Scytali. </s>
  
 <s><emph type="italics"/>Qu&aelig;&longs;t. </s> 
  
 <s>8 De Rota.<emph.end type="italics"/></s></p><p type="main"> 
  
 <s><emph type="italics"/>Qu&aelig;&longs;t. </s> 
  
 <s>9. De Trochlea, &amp; Scytali. </s> 
  
 <s>figura antiqu&aelig; &longs;cytalis.<emph.end type="italics"/></s></p><p type="main"> <s>figura antiqu&aelig; &longs;cytalis.<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Qu&aelig;&longs;t. </s> <s><emph type="italics"/>Qu&aelig;&longs;t. 10. De Libra vacua.<emph.end type="italics"/></s></p><p type="main">
  
 <s>10. De Libra vacua.<emph.end type="italics"/></s></p><p type="main"> 
  
 <s><emph type="italics"/>Q&ugrave;&aelig;&longs;t. </s> <s><emph type="italics"/>Q&ugrave;&aelig;&longs;t. </s>
  
 <s>11. De Curru, &amp; &longs;cytala.<emph.end type="italics"/></s></p><p type="main"> <s>11. De Curru, &amp; &longs;cytala.<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Qu&aelig;&longs;t. </s> <s><emph type="italics"/>Qu&aelig;&longs;t. 13. De lugo. </s>
  
 <s>13. De lugo. </s> 
  
 <s>De Succula.<emph.end type="italics"/></s></p><p type="main"> 
  
 <s><emph type="italics"/>Qu&aelig;&longs;t. </s> <s>De Succula.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
  
 <s>15. De Vmbelicis.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Qu&aelig;&longs;t. 15. De Vmbelicis.<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Qu&aelig;&longs;t. </s> <s><emph type="italics"/>Qu&aelig;&longs;t. 16. De ligni oblongi, ac breuis flexura.<emph.end type="italics"/></s></p><pb pagenum="17"/><p type="main">
  
 <s>16. De ligni oblongi, ac breuis flexura.<emph.end type="italics"/></s></p><pb pagenum="17"/><p type="main"> <s><emph type="italics"/>Qu&aelig;&longs;t. 17. De Cuneo.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
  
 <s><emph type="italics"/>Qu&aelig;&longs;t. </s> <s><emph type="italics"/>Qu&aelig;&longs;t. 18. De Trochlea; error Piccolominei.<emph.end type="italics"/></s></p><p type="main">
  
 <s>17. De Cuneo.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Qu&aelig;&longs;t. 19. De Securi. </s>
  
 <s><emph type="italics"/>Qu&aelig;&longs;t. </s> 
  
 <s>18. De Trochlea; error Piccolominei.<emph.end type="italics"/></s></p><p type="main"> 
  
 <s><emph type="italics"/>Qu&aelig;&longs;t. </s> 
  
 <s>19. De Securi. </s> 
  
 <s>Securis veteris figura, &amp; con&longs;tructio; vn&agrave; cum affectione <lb/>eius mirabili.<emph.end type="italics"/></s></p><p type="main"> <s>Securis veteris figura, &amp; con&longs;tructio; vn&agrave; cum affectione <lb/>eius mirabili.<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Qu&aelig;&longs;t. </s> <s><emph type="italics"/>Qu&aelig;&longs;t. 20. De Statera. <!-- KEEP S--></s>
  
 <s>20. De Statera. </s> 
  
 <s>Veteris stater&aelig; figura restaurata.<emph.end type="italics"/></s></p><p type="main"> <s>Veteris stater&aelig; figura restaurata.<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Qu&aelig;&longs;t. </s> <s><emph type="italics"/>Qu&aelig;&longs;t. 21. De Dentiforcipe.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
  
 <s>21. De Dentiforcipe.<emph.end type="italics"/></s></p><p type="main"> 
  
 <s><emph type="italics"/>Qu&aelig;&longs;t. </s> <s><emph type="italics"/>Qu&aelig;&longs;t. 22. De Nucifrago.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
  
 <s>22. De Nucifrago.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Qu&aelig;&longs;t. 23. De Motibus in Rhombo.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
  
 <s><emph type="italics"/>Qu&aelig;&longs;t. </s> <s><emph type="italics"/>Qu&aelig;&longs;t. 24. De duobus circulis concentricis.<emph.end type="italics"/></s></p><p type="main">
  
 <s>23. De Motibus in Rhombo.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Qu&aelig;&longs;t. 25. De funibus lectulorum.<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Qu&aelig;&longs;t. </s> <s><emph type="italics"/>Qu&aelig;&longs;t. 26. De ligno humeris gestato.<emph.end type="italics"/></s></p><p type="main">
  
 <s>24. De duobus circulis concentricis.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Qu&aelig;&longs;t. 27. De ponderibus humero ge&longs;tatis.<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Qu&aelig;&longs;t. </s> <s><emph type="italics"/>Qu&aelig;&longs;t. 28. De Tollenone.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
  
 <s>25. De funibus lectulorum.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Qu&aelig;&longs;t. 29. De onere &agrave; duobus phalanga ge&longs;iato.<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Qu&aelig;&longs;t. </s> <s><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">
  
 <s>26. De ligno humeris gestato.<emph.end type="italics"/></s></p><p type="main"> 
  
 <s><emph type="italics"/>Qu&aelig;&longs;t. </s> 
  
 <s>27. De ponderibus humero ge&longs;tatis.<emph.end type="italics"/></s></p><p type="main"> 
  
 <s><emph type="italics"/>Qu&aelig;&longs;t. </s> 
  
 <s>28. De Tollenone.<emph.end type="italics"/></s></p><p type="main"> 
  
 <s><emph type="italics"/>Qu&aelig;&longs;t. </s> 
  
 <s>29. De onere &agrave; duobus phalanga ge&longs;iato.<emph.end type="italics"/></s></p><p type="main"> 
  
 <s><emph type="italics"/>Qu&aelig;&longs;t. </s> 
  
 <s>30. De &longs;urgente &agrave; &longs;e&longs;&longs;ione.<emph.end type="italics"/></s></p><p type="head"> 
  
 <s>In libello De Mundo ad Alex.</s></p><p type="main"> <s>In libello De Mundo ad Alex.</s></p><p type="main">
  
 <s><emph type="italics"/>Cap.  <s><emph type="italics"/>Cap.
  
 2. Ordo Planetarum.<emph.end type="italics"/></s></p><p type="main"> 2. Ordo Planetarum.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
  
 <s><emph type="italics"/>Cap.  <s><emph type="italics"/>Cap.
  
 3. De Cometis.<emph.end type="italics"/></s></p><p type="main"> 3. De Cometis.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
  
 <s><emph type="italics"/>Cap.  <s><emph type="italics"/>Cap.
  
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 <s><emph type="italics"/>Nu. </s> <s><emph type="italics"/>Nu. </s>
  
 <s>100. De <gap/>&longs;tro, error Ari&longs;t. </s> <s>100. De <gap/>&longs;tro, error Ari&longs;t. &amp; veterum Geographorum.<emph.end type="italics"/></s></p><p type="head">
  
 <s>&amp; veterum Geographorum.<emph.end type="italics"/></s></p><p type="head"> 
  
 <s>In libello De lineis in&longs;ecabilibus.</s></p><p type="main"> <s>In libello De lineis in&longs;ecabilibus.</s></p><p type="main">
  
Line 1052 
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 <s><emph type="italics"/>7. locus. </s> <s><emph type="italics"/>7. locus. </s>
  
 <s>Multum Mathematicis demon&longs;trationibus tribuitur ab Ari&longs;totele.<emph.end type="italics"/></s></p><p type="main"> <s>Multum Mathematicis demon&longs;trationibus tribuitur ab Ari&longs;totele.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
  
 <s><emph type="italics"/>8. locus. </s> <s><emph type="italics"/>8. locus. </s>
  
Line 1080 
Line 1024 
  
 <s><emph type="italics"/>16. Idem ex contactu circuli cum linea recta.<emph.end type="italics"/></s></p><p type="head"> <s><emph type="italics"/>16. Idem ex contactu circuli cum linea recta.<emph.end type="italics"/></s></p><p type="head">
  
 <s>Ex lib. </s> <s>Ex lib.
  
 <s>9. Hi&longs;tori&aelig; Animalium.</s></p><p type="main"> 9. Hi&longs;tori&aelig; Animalium.</s></p><p type="main">
  
 <s><emph type="italics"/>Cap.  <s><emph type="italics"/>Cap.
  
 39. error Ari&longs;t. </s> 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>&amp; noua ob&longs;eruatio de admiranda quadam Aranearum indu&longs;tria.<emph.end type="italics"/></s></p><p type="head"> 
  
 <s>De Ince&longs;&longs;u Animal.</s></p><p type="main"> <s>De Ince&longs;&longs;u Animal.<!-- KEEP S--></s></p><p type="main">
  
 <s><emph type="italics"/>Cap.  <s><emph type="italics"/>Cap.
  
Line 1098 
Line 1040 
  
 <s>&amp; ea quid &longs;it.<emph.end type="italics"/></s></p><p type="head"> <s>&amp; ea quid &longs;it.<emph.end type="italics"/></s></p><p type="head">
  
 <s>De Motu Animal.</s></p><p type="main"> <s>De Motu Animal.<!-- KEEP S--></s></p><p type="main">
  
 <s><emph type="italics"/>Cap.  <s><emph type="italics"/>Cap.
  
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Line 1048 
  
 <s><emph type="italics"/>Cap.  <s><emph type="italics"/>Cap.
  
 3. Automata.<emph.end type="italics"/></s></p><pb pagenum="18"/><p type="head"> 3. Automata.<emph.end type="italics"/><!-- KEEP S--></s></p><pb pagenum="18"/><p type="head">
  
 <s>De Generatione Animal.</s></p><p type="main"> 
  
 <s><emph type="italics"/>Lib. </s> <s>De Generatione Animal.<!-- KEEP S--></s></p><p type="main">
  
 <s>2. cap. </s> <s><emph type="italics"/>Lib. 2. cap.
  
 <s>1. Automata.<emph.end type="italics"/></s></p><p type="main"> 1. Automata.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
  
 <s><emph type="italics"/>Lib. </s> <s><emph type="italics"/>Lib. 2. cap.
  
 <s>2. cap. </s> 4. Omnis triangulus habet tres, &amp;c. </s>
  
 <s>4. Omnis triangulus habet tres, &amp;c. </s> 
  
 <s>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></p><p type="head"> <s>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></p><p type="head">
  
 <s>In Ethicis ad Nicom.</s></p><p type="main"> <s>In Ethicis ad Nicom.</s></p><p type="main">
  
 <s><emph type="italics"/>Lib. </s> <s><emph type="italics"/>Lib. 1. cap.
  
 <s>1. cap. </s> 
  
 <s>7. Faber, &amp; Geometra diuers&egrave; con&longs;iderant angulum rectum.<emph.end type="italics"/></s></p><p type="main"> 
  
 <s><emph type="italics"/>Lib. </s> 
  
 <s>2. cap. </s> 7. Faber, &amp; Geometra diuers&egrave; con&longs;iderant angulum rectum.<emph.end type="italics"/></s></p><p type="main">
  
 <s>6. De Arithmetica proportione.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Lib. 2. cap.
  
 <s><emph type="italics"/>cap. </s> 6. De Arithmetica proportione.<emph.end type="italics"/></s></p><p type="main">
  
 <s>9. Centrum circuli reperire.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>cap.
  
 <s><emph type="italics"/>Lib. </s> 9. Centrum circuli reperire.<emph.end type="italics"/></s></p><p type="main">
  
 <s>3. cap. </s> <s><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>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><emph type="italics"/>Lib. 5. cap.
  
 <s><emph type="italics"/>Lib. </s> 3. Vnitarius numerus. </s>
  
 <s>5. cap. </s> <s>Quid Proportionalitas. <!-- KEEP S--></s>
  
 <s>3. Vnitarius numerus. </s> 
  
 <s>Quid Proportionalitas. </s> 
  
 <s>Eam in 4. terminis con&shy;<lb/>&longs;i&longs;tere. </s> <s>Eam in 4. terminis con&shy;<lb/>&longs;i&longs;tere. </s>
  
Line 1164 
Line 1092 
  
 <s>Propor&shy;<lb/>tio continuata, &amp; di&longs;iuncta quid.<emph.end type="italics"/></s></p><p type="main"> <s>Propor&shy;<lb/>tio continuata, &amp; di&longs;iuncta quid.<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>cap. </s> <s><emph type="italics"/>cap.
  
 <s>6. Proportio Geometrica, &amp; Arithmetica.<emph.end type="italics"/></s></p><p type="main"> 
  
 <s><emph type="italics"/>Lib. </s> 6. Proportio Geometrica, &amp; Arithmetica.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
  
 <s>6. cap. </s> <s><emph type="italics"/>Lib. 6. cap.
  
 <s>5. Omnis triangulus, &amp;c.<emph.end type="italics"/></s></p><p type="main"> 5. Omnis triangulus, &amp;c.<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>cap. </s> <s><emph type="italics"/>cap.
  
 <s>8. Principia Mathematica non pendere ab experientia.<emph.end type="italics"/></s></p><p type="main"> 8. Principia Mathematica non pendere ab experientia.<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Lib. </s> <s><emph type="italics"/>Lib. 7. cap. 8. De principijs Mathem.<emph.end type="italics"/></s></p><p type="head">
  
 <s>7. cap. </s> 
  
 <s>8. De principijs Mathem.<emph.end type="italics"/></s></p><p type="head"> 
  
 <s>Ex 1. Magnorum Moralium.</s></p><p type="main"> <s>Ex 1. Magnorum Moralium.</s></p><p type="main">
  
Line 1328 
Line 1250 
  
 <s><emph type="italics"/>10. Cur in defectu Solis etiam illuminationes ip&longs;ius defectiu&aelig; &longs;unt? </s> <s><emph type="italics"/>10. Cur in defectu Solis etiam illuminationes ip&longs;ius defectiu&aelig; &longs;unt? </s>
  
 <s>modus commod&egrave; <lb/>videndi eclyp&longs;im Solis.<emph.end type="italics"/></s></p><p type="main"> <s>modus commod&egrave; <lb/>videndi eclyp&longs;im Solis.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
  
 <s><emph type="italics"/>Sect. </s> <s><emph type="italics"/>Sect. </s>
  
Line 1350 
Line 1272 
  
 <s>reflexio radior&ubreve; pulchr&egrave; comparatur corpor&ubreve; re&longs;ultationi.<emph.end type="italics"/></s></p><p type="head"> <s>reflexio radior&ubreve; pulchr&egrave; comparatur corpor&ubreve; re&longs;ultationi.<emph.end type="italics"/></s></p><p type="head">
  
 <s>Ex &longs;ectione 19. De Mu&longs;ica.</s></p><p type="main"> <s>Ex &longs;ectione 19. De Mu&longs;ica.<!-- KEEP S--></s></p><p type="main">
  
 <s><emph type="italics"/>num. </s> <s><emph type="italics"/>num. </s>
  
Line 1484 
Line 1406 
  
 <s><emph type="italics"/>21. Cur &longs;olam rectitudinem vnico oculo in&longs;piciamus.<emph.end type="italics"/></s></p><p type="head"> <s><emph type="italics"/>21. Cur &longs;olam rectitudinem vnico oculo in&longs;piciamus.<emph.end type="italics"/></s></p><p type="head">
  
 <s>Auctarium De Oculi Pupilla.</s></p><p type="main"> <s>Auctarium De Oculi Pupilla.<!-- KEEP S--></s></p><p type="main">
  
 <s><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"> <s><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">
  
Line 1510 
Line 1432 
  
 <s><emph type="italics"/>Primo. </s> <s><emph type="italics"/>Primo. </s>
  
 <s>De &longs;ubiecto Mathem. </s> <s>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></p><p type="main">
  
 <s>&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></p><p type="main"> 
  
 <s>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"> <s>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">
  
Line 1526 
Line 1446 
  
 <s>7. <emph type="italics"/>Clarorum Mathematicorum Chronicon.<emph.end type="italics"/></s></p><p type="head"> <s>7. <emph type="italics"/>Clarorum Mathematicorum Chronicon.<emph.end type="italics"/></s></p><p type="head">
  
 <s><emph type="bold"/>Finis Primi Indicis.<emph.end type="bold"/></s></p><figure></figure><pb pagenum="22"/><p type="head"> <s><emph type="bold"/>Finis Primi Indicis.<emph.end type="bold"/></s></p><figure/><pb pagenum="22"/><p type="head">
  
 <s><emph type="italics"/>ALTER INDEX<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>ALTER INDEX<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Quo loca Aristotelis Geometrica, in hoc Opere explicata, <lb/>ad Euclidem, &longs;ecundum propo&longs;itionum ordinem refe&shy;<lb/>runtur; vt Mathematicarum Profe&longs;&longs;ores habeant, <lb/>vnde &longs;uas pr&aelig;lectiones aliquando valeant locupletare.<emph.end type="italics"/></s></p><p type="head"> <s><emph type="italics"/>Quo loca Aristotelis Geometrica, in hoc Opere explicata, <lb/>ad Euclidem, &longs;ecundum propo&longs;itionum ordinem refe&shy;<lb/>runtur; vt Mathematicarum Profe&longs;&longs;ores habeant, <lb/>vnde &longs;uas pr&aelig;lectiones aliquando valeant locupletare.<emph.end type="italics"/></s></p><p type="head">
  
 <s><emph type="italics"/>In Primo Elem. </s> <s><emph type="italics"/>In Primo Elem.
  
 <s>Euclidis.<emph.end type="italics"/></s></p><p type="main"> Euclidis.<emph.end type="italics"/></s></p><p type="main">
  
 <s>Ad verbum ip&longs;um <emph type="italics"/>(Elementum Euclidis)<emph.end type="italics"/> vide infra tex. </s> <s>Ad verbum ip&longs;um <emph type="italics"/>(Elementum Euclidis)<emph.end type="italics"/> vide infra tex. </s>
  
Line 1552 
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 <s>Mecha&shy;<lb/>nic. </s> <s>Mecha&shy;<lb/>nic. </s>
  
 <s>&amp; cap. </s> <s>&amp; cap.
  
 <s>7. lib. </s> 7. lib.
  
 <s>1. Eth.</s></p><p type="main"> 1. Eth.</s></p><p type="main">
  
 <s>Ad axioma 10. quamuis Ari&longs;toteles nihil hac de re dicat; &longs;cias tamen velim <lb/>hoc vno axiomate qu&ecedil;&longs;tionem <expan abbr="qu&atilde;dam">quandam</expan> inter Philo&longs;ophos vald&egrave; difficilem, <lb/>facile di&longs;&longs;olui. </s> <s>Ad axioma 10. quamuis Ari&longs;toteles nihil hac de re dicat; &longs;cias tamen velim <lb/>hoc vno axiomate qu&ecedil;&longs;tionem <expan abbr="qu&atilde;dam">quandam</expan> inter Philo&longs;ophos vald&egrave; difficilem, <lb/>facile di&longs;&longs;olui. </s>
  
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 <s>1. primi Po&longs;ter.</s></p><p type="main"> <s>1. primi Po&longs;ter.</s></p><p type="main">
  
 <s>Ad primam primi, po&longs;t ip&longs;ius explicationem, commod&egrave; declarari pote&longs;t, cur <lb/>Ari&longs;t. </s> <s>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.
  
 <s>Demon&longs;trationes Geometricas appellet De&longs;criptiones, &amp; De&longs;igna&shy;<lb/>tiones, vide cap. </s> 
  
 <s>de Priori, &amp; cap. </s> de Priori, &amp; cap.
  
 <s>24. &longs;ecti primi, libri primi Priorum, &amp; <lb/>tex. </s> 24. &longs;ecti primi, libri primi Priorum, &amp; <lb/>tex. </s>
  
 <s>4. quinti Methaph. </s> <s>4. quinti Methaph. </s>
  
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 <s>20. &longs;exti Methaph. </s> <s>20. &longs;exti Methaph. </s>
  
 <s>&amp; cap. </s> <s>&amp; cap.
  
 <s>3. lib. </s> 3. lib.
  
 <s>3. Ethic. <lb/></s> 3. Ethic. <lb/></s>
  
 <s>Item ad primam primi, vide tex. </s> <s>Item ad primam primi, vide tex. </s>
  
 <s>7. &longs;ecundi Po&longs;ter. </s> <s>7. &longs;ecundi Po&longs;ter. loco 2.</s></p><p type="main">
  
 <s>loco 2.</s></p><p type="main"> <s>Ad 5. primi, vide cap.
  
 <s>Ad 5. primi, vide cap. </s> 
  
 <s>24. &longs;ecti 1 lib. </s> 24. &longs;ecti 1 lib.
  
 <s>1. Priorum.</s></p><p type="main"> 1. Priorum.</s></p><p type="main">
  
 <s>Ad 21. primi, vide tex. </s> <s>Ad 21. primi, vide tex. </s>
  
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 <s>Ad 22. primi, vide locum 10. de lineis in&longs;ecabilibus.</s></p><p type="main"> <s>Ad 22. primi, vide locum 10. de lineis in&longs;ecabilibus.</s></p><p type="main">
  
 <s>Ad 28. primi, vide cap. </s> <s>Ad 28. primi, vide cap.
  
 <s>21. &amp; cap. </s> 21. &amp; cap.
  
 <s>22. &longs;ecundi <expan abbr="Prior&utilde;">Priorum</expan>, &amp; tex. </s> 22. &longs;ecundi <expan abbr="Prior&utilde;">Priorum</expan>, &amp; tex. </s>
  
 <s>13. primi Po&longs;ter.</s></p><p type="main"> <s>13. primi Po&longs;ter.</s></p><p type="main">
  
 <s>Ad 32. primi, vide cap. </s> <s>Ad 32. primi, vide cap.
  
 <s>1. &longs;ecti 3. lib. </s> 1. &longs;ecti 3. lib.
  
 <s>1. Prior. </s> 1. Prior. </s>
  
 <s>&amp; cap. </s> 
  
 <s>26. &longs;ecundi <expan abbr="Prior&utilde;">Priorum</expan>, &amp; tex. </s> <s>&amp; cap.
  
 <s>2. <lb/>primi Po&longs;ter. </s> 26. &longs;ecundi <expan abbr="Prior&utilde;">Priorum</expan>, &amp; tex. </s>
  
 <s>loco 4. &amp; tex. </s> <s>2. <lb/>primi Po&longs;ter. loco 4. &amp; tex. </s>
  
 <s>23. primi Po&longs;ter. </s> <s>23. primi Po&longs;ter. </s>
  
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 <s>&amp; tex. </s> <s>&amp; tex. </s>
  
 <s>37. primi Po&longs;ter. </s> <s>37. primi Po&longs;ter. &amp; tex. </s>
  
 <s>&amp; tex. </s> 
  
 <s>39. primi Po&longs;ter. </s> <s>39. primi Po&longs;ter. </s>
  
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 <s>&amp; tex. </s> <s>&amp; tex. </s>
  
 <s>89. &longs;e&shy;<lb/>cundi Phy&longs;. </s> <s>89. &longs;e&shy;<lb/>cundi Phy&longs;. &amp; tex. </s>
  
 <s>&amp; tex. </s> 
  
 <s>15. octaui Phy&longs;. </s> <s>15. octaui Phy&longs;. </s>
  
 <s>&amp; tex. </s> <s>&amp; tex. </s>
  
 <s>119. primi de C&oelig;lo. </s> <s>119. primi de C&oelig;lo. <!-- KEEP S--></s>
  
 <s>&amp; tex. </s> <s>&amp; tex. </s>
  
 <s>25. <lb/>&longs;ecundi de C&oelig;lo. </s> <s>25. <lb/>&longs;ecundi de C&oelig;lo. <!-- KEEP S--></s>
  
 <s>tex 11. primi de Anima. </s> <s>tex 11. primi de Anima. </s>
  
 <s>&amp; cap. </s> <s>&amp; cap.
  
 <s>1. de mem. </s> 1. de mem. </s>
  
 <s>&amp; remini&longs;c. <lb/></s> <s>&amp; remini&longs;c. <lb/></s>
  
 <s>&amp; tex. </s> <s>&amp; tex. </s>
  
 <s>35. quinti Methaphy&longs;. </s> <s>35. quinti Methaphy&longs;. &amp; tex. </s>
  
 <s>&amp; tex. </s> 
  
 <s>20. &longs;exti Methaphy&longs;. </s> <s>20. &longs;exti Methaphy&longs;. </s>
  
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 <s>22. &longs;exti <lb/>Methaphy&longs;. </s> <s>22. &longs;exti <lb/>Methaphy&longs;. </s>
  
 <s>&amp; cap. </s> <s>&amp; cap.
  
 <s>4. lib. </s> 4. lib.
  
 <s>2. de Generat. </s> 2. de Generat. </s>
  
 <s>animal. </s> <s>animal. </s>
  
 <s>&amp; cap. </s> <s>&amp; cap.
  
 <s>5. lib. </s> 
  
 <s>6. Ethic. </s> 
  
 <s>&amp; <lb/>cap. </s> 5. lib.
  
 <s>2. Magnorum Moral. </s> 6. Ethic. </s>
  
 <s>&amp; cap. </s> 
  
 <s>10. Mag. </s> <s>&amp; <lb/>cap.
  
 <s>Moral. </s> 
  
 <s>&amp; cap. </s> 
  
 <s>16. Mag. </s> 2. Magnorum Moral. &amp; cap.
  
 <s>Moral. <lb/></s> 10. Mag. Moral. &amp; cap. 16. Mag. Moral. <lb/></s>
  
 <s>&amp; cap. </s> <s>&amp; cap. </s>
  
 <s>7. &longs;ecundi Eudem. </s> <s>7. &longs;ecundi Eudem. &amp; cap. </s>
  
 <s>&amp; cap. </s> 
  
 <s>12. &longs;ecundi Eudem. </s> <s>12. &longs;ecundi Eudem. </s>
  
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 <s>Ad &longs;cholion pr&aelig;cedentis 32. primi, vide tex. </s> <s>Ad &longs;cholion pr&aelig;cedentis 32. primi, vide tex. </s>
  
 <s>39. primi Po&longs;ter. </s> <s>39. primi Po&longs;ter. loco 3. Item <lb/>tex. </s>
  
 <s>loco 3. Item <lb/>tex. </s> 
  
 <s>25. &longs;ecundi Po&longs;ter. </s> <s>25. &longs;ecundi Po&longs;ter. </s>
  
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 <s><emph type="italics"/>In &longs;ecundo Elem.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>In &longs;ecundo Elem.<emph.end type="italics"/></s></p><p type="main">
  
 <s>Ad 2. definitionem 2. Gnomonis, vide cap. </s> <s>Ad 2. definitionem 2. Gnomonis, vide cap.
  
 <s>de Motu in Po&longs;tpr&aelig;dicam. </s> de Motu in Po&longs;tpr&aelig;dicam. </s>
  
 <s>Qua&shy;<lb/>dratum augetur Gnomone circumpo&longs;ito.</s></p><p type="main"> <s>Qua&shy;<lb/>dratum augetur Gnomone circumpo&longs;ito.</s></p><p type="main">
  
 <s>Ad 14. propo&longs;. </s> <s>Ad 14. propo&longs;. </s>
  
 <s>2. opportunum e&longs;t Auditores de Quadratura circuli erudire, <lb/>vide igitur cap. </s> <s>2. opportunum e&longs;t Auditores de Quadratura circuli erudire, <lb/>vide igitur cap.
  
 <s>de relatione in pr&aelig;dicam. </s> 
  
 <s>&amp; cap. </s> 
  
 <s>31. &longs;ecundi Priorum, &amp; <lb/>tex. </s> de relatione in pr&aelig;dicam. </s>
  
 <s>23. primi Po&longs;ter. </s> <s>&amp; cap.
  
 <s>&amp; finem 1. cap. </s> 31. &longs;ecundi Priorum, &amp; <lb/>tex. </s>
  
 <s>primi Elenchorum. </s> <s>23. primi Po&longs;ter. &amp; finem 1. cap. primi Elenchorum. </s>
  
 <s>lege primam Ar&shy;<lb/>chimedis de dimen&longs;ione circuli.</s></p><p type="head"> <s>lege primam Ar&shy;<lb/>chimedis de dimen&longs;ione circuli.</s></p><p type="head">
  
 <s><emph type="italics"/>In tertio Elem.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>In tertio Elem.<emph.end type="italics"/></s></p><p type="main">
  
 <s>Ad primam 3. vide cap. </s> <s>Ad primam 3. vide cap.
  
 <s>9. lib. </s> 9. lib.
  
 <s>2. Ethycorum.</s></p><p type="main"> 2. Ethycorum.</s></p><p type="main">
  
 <s>Ad 2. tertij, vide tex. </s> <s>Ad 2. tertij, vide tex. </s>
  
 <s>13. lib. </s> <s>13. lib.
  
 <s>1. de Anima. </s> 1. de Anima. </s>
  
 <s>&amp; locum 16. de lineis in&longs;ecab.</s></p><p type="main"> <s>&amp; locum 16. de lineis in&longs;ecab.</s></p><p type="main">
  
 <s>Ad 31. tertij, vide tex. </s> <s>Ad 31. tertij, vide tex. </s>
  
 <s>11. &longs;ecundi Po&longs;ter. </s> <s>11. &longs;ecundi Po&longs;ter. &amp; tex. </s>
  
 <s>&amp; tex. </s> 
  
 <s>20. &longs;exti Methaph. </s> <s>20. &longs;exti Methaph. </s>
  
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 <s>Ad commentarium P. </s> <s>Ad commentarium P. </s>
  
 <s>Clauij extremum lib. </s> <s>Clauij extremum lib.
  
 <s>4. elementorum. </s> 4. elementorum. </s>
  
 <s>lege tex. </s> <s>lege tex. </s>
  
 <s>66. <lb/>tertij de C&oelig;lo.</s></p><p type="head"> <s>66. <lb/>tertij de C&oelig;lo.<!-- KEEP S--></s></p><p type="head">
  
 <s><emph type="italics"/>In quinto.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>In quinto.<emph.end type="italics"/></s></p><p type="main">
  
 <s>Ad 4. definitionem 5. vide cap. </s> <s>Ad 4. definitionem 5. vide cap.
  
 <s>3. lib. </s> 3. lib.
  
 <s>2. Ethyc.</s></p><p type="main"> 2. Ethyc.</s></p><p type="main">
  
 <s>Ad 9. definitionem 5. vide cap. </s> <s>Ad 9. definitionem 5. vide cap.
  
 <s>3. lib. </s> 3. lib.
  
 <s>5. Ethyc. </s> 5. Ethyc. </s>
  
 <s>loco 4. &amp; cap. </s> <s>loco 4. &amp; cap. 31. primi Ma&shy;<lb/>gnorum Moralium.</s></p><p type="main">
  
 <s>31. primi Ma&shy;<lb/>gnorum Moralium.</s></p><p type="main"> 
  
 <s>Ad 10. definitionem 5. vide tex. </s> <s>Ad 10. definitionem 5. vide tex. </s>
  
 <s>29. primi Po&longs;ter. </s> <s>29. primi Po&longs;ter. loco 2.</s></p><p type="main">
  
 <s>loco 2.</s></p><p type="main"> 
  
 <s>Ad 12. definitionem 5. vide tex. </s> <s>Ad 12. definitionem 5. vide tex. </s>
  
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 <s>32. tertij de Anima. </s> <s>32. tertij de Anima. </s>
  
 <s>&amp; cap. </s> <s>&amp; cap.
  
 <s>3. lib. </s> 3. lib.
  
 <s>5. Ethyc. </s> 5. Ethyc. </s>
  
 <s>loco 4.</s></p><p type="main"> <s>loco 4.</s></p><p type="main">
  
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 <s>5. vide tex. </s> <s>5. vide tex. </s>
  
 <s>25. &longs;ecundi Po&longs;ter. </s> <s>25. &longs;ecundi Po&longs;ter. loco 2. ex hac Euclidis demon&shy;<lb/>&longs;tratione patet, vitio&longs;am e&longs;&longs;e illam Auerrois argumentationem, 8. Phy&longs;. <lb/></s>
  
 <s>loco 2. ex hac Euclidis demon&shy;<lb/>&longs;tratione patet, vitio&longs;am e&longs;&longs;e illam Auerrois argumentationem, 8. Phy&longs;. <lb/></s> 
  
 <s>comm. </s> <s>comm. </s>
  
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 <s>Ad 2. propo&longs;it. </s> <s>Ad 2. propo&longs;it. </s>
  
 <s>6. vide cap. </s> <s>6. vide cap.
  
 <s>2. lib. </s> 2. lib.
  
 <s>8. Topicorum loco 41.</s></p><p type="main"> 8. Topicorum loco 41.</s></p><p type="main">
  
 <s>Ad 13. &longs;exti, vide tex. </s> <s>Ad 13. &longs;exti, vide tex. </s>
  
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 <s>5. primi Po&longs;ter.</s></p><p type="main"> <s>5. primi Po&longs;ter.</s></p><p type="main">
  
 <s>Ad 8. definitionem 7. vide cap. </s> <s>Ad 8. definitionem 7. vide cap.
  
 <s>1. lib. </s> 1. lib.
  
 <s>1. Magnorum Moral.</s></p><p type="head"> 1. Magnorum Moral.</s></p><p type="head">
  
 <s><emph type="italics"/>In octauo.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>In octauo.<emph.end type="italics"/></s></p><p type="main">
  
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 <s>9. vide tex. </s> <s>9. vide tex. </s>
  
 <s>20. primi Po&longs;ter. </s> <s>20. primi Po&longs;ter. loco 2.</s></p><p type="main">
  
 <s>loco 2.</s></p><p type="main"> 
  
 <s>Ad 8. propo&longs;. </s> <s>Ad 8. propo&longs;. </s>
  
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 <s><emph type="italics"/>In decimo.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>In decimo.<emph.end type="italics"/></s></p><p type="main">
  
 <s>Ad primam definitionem 10. vide cap. </s> <s>Ad primam definitionem 10. vide cap.
  
 <s>23. &longs;ecti 1. primi Priorum. </s> 23. &longs;ecti 1. primi Priorum. </s>
  
 <s>&amp; tex. </s> <s>&amp; tex. </s>
  
 <s>48. <lb/>primi de C&oelig;lo.</s></p><p type="main"> <s>48. <lb/>primi de C&oelig;lo.<!-- KEEP S--></s></p><p type="main">
  
 <s>Ad 118. decimi, vide cap. </s> <s>Ad 118. decimi, vide cap.
  
 <s>23. &longs;ecti 1. libri 1. Priorum. </s> 23. &longs;ecti 1. libri 1. Priorum. </s>
  
 <s>&amp; &longs;ecto 2. cap. </s> <s>&amp; &longs;ecto 2. cap.
  
 <s>23. li&shy;<lb/>bri 1. Priorum. </s> 23. li&shy;<lb/>bri 1. Priorum. </s>
  
 <s>&amp; cap. </s> <s>&amp; cap. 22. lib.
  
 <s>22. lib. </s> 
  
 <s>2. Priorum. </s> 2. Priorum. </s>
  
 <s>&amp; tex. </s> <s>&amp; tex. </s>
  
 <s>5. primi Po&longs;ter. </s> <s>5. primi Po&longs;ter. &amp; tex. </s>
  
 <s>&amp; tex. </s> 
  
 <s>44. <lb/>primi Po&longs;ter. </s> <s>44. <lb/>primi Po&longs;ter. </s>
  
 <s>&amp; cap. </s> <s>&amp; cap.
  
 <s>15. primi Po&longs;ter. </s> 15. primi Po&longs;ter. </s>
  
 <s>&amp; tex. </s> <s>&amp; tex. </s>
  
 <s>119. primi de C&oelig;lo. </s> <s>119. primi de C&oelig;lo. <!-- KEEP S--></s>
  
 <s>&amp; tex. <lb/></s> <s>&amp; tex. <lb/></s>
  
 <s>120. quarti Phy&longs;. </s> <s>120. quarti Phy&longs;. &amp; tex. </s>
  
 <s>&amp; tex. </s> 
  
 <s>21. tertij de Anima. </s> <s>21. tertij de Anima. </s>
  
 <s>&amp; cap. </s> <s>&amp; cap.
  
 <s>1. primi Methaphy&longs;. <lb/></s> 1. primi Methaphy&longs;. <lb/></s>
  
 <s>&amp; tex. </s> <s>&amp; tex. </s>
  
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 <s>8. &longs;exti Met. </s> <s>8. &longs;exti Met. </s>
  
 <s>&amp; cap. </s> <s>&amp; cap.
  
 <s>4. <lb/>lib. </s> 4. <lb/>lib.
  
 <s>2. de Generat. </s> 2. de Generat. </s>
  
 <s>animal. </s> <s>animal. </s>
  
 <s>&amp; lib. </s> <s>&amp; lib.
  
 <s>3. cap. </s> 
  
 <s>3. Ethyc. </s> 3. cap.
  
 <s>&amp; cap. </s> 3. Ethyc. </s>
  
 <s>10. &longs;ecundi Eu&shy;<lb/>dem. </s> <s>&amp; cap. 10. &longs;ecundi Eu&shy;<lb/>dem. </s>
  
 <s>tot Ari&longs;t.  <s>tot Ari&longs;t.
  
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 <s><emph type="bold"/>Finis Secundi Indicis.<emph.end type="bold"/></s></p><p type="main"> <s><emph type="bold"/>Finis Secundi Indicis.<emph.end type="bold"/></s></p><p type="main">
  
 <s>Qu&aelig; ver&ograve; ad alias Mathematicas, Mu&longs;icam &longs;cilicet, Per&longs;pe&shy;<lb/>ctiuam, Mechanicam, &amp; A&longs;tronomiam pertinens, facil&egrave; <lb/>poterunt ex primo Indice ad vnamquamque earum &longs;eor&shy;<lb/>&longs;um cum libuerit, &longs;ecerni.</s></p><figure></figure><pb pagenum="25"/><p type="head"> <s>Qu&aelig; ver&ograve; ad alias Mathematicas, Mu&longs;icam &longs;cilicet, Per&longs;pe&shy;<lb/>ctiuam, Mechanicam, &amp; A&longs;tronomiam pertinens, facil&egrave; <lb/>poterunt ex primo Indice ad vnamquamque earum &longs;eor&shy;<lb/>&longs;um cum libuerit, &longs;ecerni.</s></p><figure/><pb pagenum="25"/><p type="head">
  
 <s><emph type="italics"/>TERTIVS INDEX ALPHABETICVS,<emph.end type="italics"/></s></p><p type="head"> <s><emph type="italics"/>TERTIVS INDEX ALPHABETICVS,<emph.end type="italics"/></s></p><p type="head">
  
 <s><emph type="italics"/>cuius numeri re&longs;pondent numeris marginalibus Operis.<emph.end type="italics"/><lb/><arrow.to.target n="table2"></arrow.to.target></s></p><table><table.target id="table2"></table.target><row><cell><emph type="italics"/>A<emph.end type="italics"/></cell><cell></cell></row><row><cell><emph type="italics"/>Abductio quid. eius inuentor. numero 16. marginali.<emph.end type="italics"/></cell><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></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></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></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 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></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></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></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></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"/>Fu<gap/>ium l<gap/>ctorum problema.<emph.end type="italics"/></cell><cell>264</cell></row><row><cell><emph type="italics"/>G<emph.end type="italics"/></cell><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 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, ei&queacute; 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></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></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></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></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></cell></row><row><cell><emph type="italics"/>Li<gap/>ea, 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></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></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"/>Mater<gap/>a intelligibilis. fus&egrave; ver&ograve;. explicatur in tract. de nat. Mathem.<emph.end type="italics"/></cell><cell></cell></row><row><cell><emph type="italics"/>Mathema<gap/>ic&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"/>Mathematic<gap/>s 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></cell></row><pb 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></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"/>Monochordiux<gap/>.<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></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></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></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></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></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></cell></row><row><cell><emph type="italics"/>Parhypate<emph.end type="italics"/></cell><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 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 dignita<gap/>em, 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></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 bominibus. probl.<emph.end type="italics"/> 5.</cell><cell></cell></row><row><cell><emph type="italics"/>Cur in Sole euane&longs;<gap/>at. probl.<emph.end type="italics"/> 6.</cell><cell></cell></row><row><cell><emph type="italics"/>Cur modo maior, modo minor appareat.<emph.end type="italics"/></cell><cell></cell></row><row><cell><emph type="italics"/>Pythagorici primi Mathematicis <expan abbr="oper&atilde;">operam</expan> dedere, eas&queacute; 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></cell></row><row><cell><emph type="italics"/>Qv adra<gap/>ura 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></cell></row><row><cell><emph type="italics"/>R<emph.end type="italics"/></cell><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></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<gap/>antiqu&aelig; &longs;<gap/>uris 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></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></cell></row><pb 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<gap/> oculi. 408. in tractatu de Pupi<gap/>la.<emph.end type="italics"/></cell><cell></cell></row><row><cell><emph type="italics"/>V<emph.end type="italics"/></cell><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></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><emph type="italics"/>cuius numeri re&longs;pondent numeris marginalibus Operis.<emph.end type="italics"/><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 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"/>Fu<gap/>ium l<gap/>ctorum 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 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, ei&queacute; 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"/>Li<gap/>ea, 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"/>Mater<gap/>a intelligibilis. fus&egrave; ver&ograve;. explicatur in tract. de nat. Mathem.<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Mathema<gap/>ic&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"/>Mathematic<gap/>s 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><pb 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"/>Monochordiux<gap/>.<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 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 dignita<gap/>em, 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 bominibus. probl.<emph.end type="italics"/> 5.</cell><cell/></row><row><cell><emph type="italics"/>Cur in Sole euane&longs;<gap/>at. 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, eas&queacute; 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"/>Qv adra<gap/>ura 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<gap/>antiqu&aelig; &longs;<gap/>uris 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 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<gap/> oculi. 408. in tractatu de Pupi<gap/>la.<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>Finis Tertij Indicis.</s></p><figure></figure><pb pagenum="31"/><p type="main"> <s>Finis Tertij Indicis.</s></p><figure/><pb pagenum="31"/><p type="main">
  
 <s>Vi&longs;um e&longs;t etiam opportunum Lectori fore, ea &longs;imul in vnum <lb/>loca colligere, in quibus Ari&longs;toteles mihi vi&longs;us e&longs;t in Ma&shy;<lb/>thematicis &longs;copum non attigi&longs;&longs;e, vt alij pr&ecedil;&longs;ertim Peripa&shy;<lb/>tetici facilius ea inuenire, <expan abbr="atq;">atque</expan> de ij&longs;dem iudicium ferre <lb/>po&longs;&longs;int.<lb/><arrow.to.target n="table3"></arrow.to.target></s></p><pb pagenum="33"/><table><table.target id="table3"></table.target><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><figure></figure><p type="head"> <s>Vi&longs;um e&longs;t etiam opportunum Lectori fore, ea &longs;imul in vnum <lb/>loca colligere, in quibus Ari&longs;toteles mihi vi&longs;us e&longs;t in Ma&shy;<lb/>thematicis &longs;copum non attigi&longs;&longs;e, vt alij pr&ecedil;&longs;ertim Peripa&shy;<lb/>tetici facilius ea inuenire, <expan abbr="atq;">atque</expan> de ij&longs;dem iudicium ferre <lb/>po&longs;&longs;int.<lb/><arrow.to.target n="table3"/></s></p><pb pagenum="33"/><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><figure/><p type="head">
  
 <s>LOCA</s></p><p type="head"> <s>LOCA</s></p><p type="head">
  
Line 2032 
Line 1904 
  
 <s>PR&AElig;DICAMENTORVM</s></p><p type="head"> <s>PR&AElig;DICAMENTORVM</s></p><p type="head">
  
 <s>Per ordinem declarata.</s></p><figure></figure><p type="main"> <s>Per ordinem declarata.</s></p><figure/><p type="main">
  
 <s><arrow.to.target n="marg1"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg1"/></s></p><p type="margin">
  
 <s><margin.target id="marg1"></margin.target>1</s></p><p type="main"> <s><margin.target id="marg1"/>1</s></p><p type="main">
  
 <s>Ex c. </s> <s>Ex c. </s>
  
Line 2060 
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 <s>&amp; alij etiam verum a&longs;&longs;erunt, dum negant hacte&shy;<lb/>nus repertam e&longs;&longs;e, &longs;i nimirum de problemate loquantur, theorema Archi&shy;<pb 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;<lb/>tem huiu&longs;modi. </s> <s>&amp; alij etiam verum a&longs;&longs;erunt, dum negant hacte&shy;<lb/>nus repertam e&longs;&longs;e, &longs;i nimirum de problemate loquantur, theorema Archi&shy;<pb 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;<lb/>tem huiu&longs;modi. </s>
  
 <s>Quilibet circulus &aelig;qualis e&longs;t triangulo rectangulo, cuius <lb/>quidem &longs;emidiameter vni laterum, qu&aelig; circa rectum angulum &longs;unt, ambi&shy;<lb/>tus ver&ograve; ba&longs;i eius e&longs;t &aelig;qualis.</s></p><figure></figure><p type="main"> <s>Quilibet circulus &aelig;qualis e&longs;t triangulo rectangulo, cuius <lb/>quidem &longs;emidiameter vni laterum, qu&aelig; circa rectum angulum &longs;unt, ambi&shy;<lb/>tus ver&ograve; ba&longs;i eius e&longs;t &aelig;qualis.</s></p><figure/><p type="main">
  
 <s>Sit, v.g. </s> <s>Sit, v.g. </s>
  
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 <s>Quod &longs;i in modum Problematis ita <lb/>proponatur: Dato circulo &aelig;quale quadratum con&longs;truere, nondum inuenta <lb/>e&longs;t ratio, qu&aelig; demon&longs;tratione confirmetur, qua id geometric&egrave; penitus, hoc <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;<lb/>ficultas po&longs;ita e&longs;&longs;e videtur in inue&longs;tigando, quonam modo exhibeamus li&shy;<lb/>neam rectam B C, &aelig;qualem peripheri&aelig; circuli dati. </s> <s>Quod &longs;i in modum Problematis ita <lb/>proponatur: Dato circulo &aelig;quale quadratum con&longs;truere, nondum inuenta <lb/>e&longs;t ratio, qu&aelig; demon&longs;tratione confirmetur, qua id geometric&egrave; penitus, hoc <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;<lb/>ficultas po&longs;ita e&longs;&longs;e videtur in inue&longs;tigando, quonam modo exhibeamus li&shy;<lb/>neam rectam B C, &aelig;qualem peripheri&aelig; circuli dati. </s>
  
 <s>quam nullus hactenus <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;<lb/>tione comprobare; Quamuis Archimedes acumine &longs;an&egrave; mirabili in lib. </s> <s>quam nullus hactenus <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;<lb/>tione comprobare; Quamuis Archimedes acumine &longs;an&egrave; mirabili in lib.
  
 <s>de <lb/>lineis &longs;piralibus, eam <expan abbr="quoq;">quoque</expan> theorematic&egrave;, non tamen problematic&egrave; inue&shy;<lb/>&longs;tigauit. </s> de <lb/>lineis &longs;piralibus, eam <expan abbr="quoq;">quoque</expan> theorematic&egrave;, non tamen problematic&egrave; inue&shy;<lb/>&longs;tigauit. </s>
  
 <s>nam propo&longs;itione 18. illius <expan abbr="admir&atilde;di">admirandi</expan> operis inuenit lineam rectam <lb/>&aelig;qualem circumferenti&aelig; primi circuli &longs;piralis line&aelig;; propo&longs; ver&ograve; 19. repe&shy;<lb/>rit aliam rectam &aelig;qualem circumferenti&aelig; &longs;ecundi circuli. </s> <s>nam propo&longs;itione 18. illius <expan abbr="admir&atilde;di">admirandi</expan> operis inuenit lineam rectam <lb/>&aelig;qualem circumferenti&aelig; primi circuli &longs;piralis line&aelig;; propo&longs; ver&ograve; 19. repe&shy;<lb/>rit aliam rectam &aelig;qualem circumferenti&aelig; &longs;ecundi circuli. </s>
  
 <s>tu ip&longs;um con&longs;ule, <lb/>&longs;i admirandarum rerum contemplatione delectaris. </s> <s>tu ip&longs;um con&longs;ule, <lb/>&longs;i admirandarum rerum contemplatione delectaris. </s>
  
 <s>Multa hac de re Pap&shy;<lb/>pus Alexandrinus lib. </s> <s>Multa hac de re Pap&shy;<lb/>pus Alexandrinus lib.
  
 <s>4. Math. </s> 
  
 <s>coll. </s> 4. Math. coll. </s>
  
 <s>&amp; Ioannes Buteo vnico volumine om&shy;<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>&amp; Ioannes Buteo vnico volumine om&shy;<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>Qua&shy;<lb/>re qui plura cupit, eos adeat; nos tamen infra &longs;uis locis explicabimus tres <lb/>illas celebres antiquorum Antiphontis, Bri&longs;&longs;onis, &amp; Hippocratis quadra&shy;<lb/>turas, quamuis fal&longs;as, <expan abbr="quar&utilde;">quarum</expan> &longs;&aelig;pe meminit Ari&longs;t. </s> <s>Qua&shy;<lb/>re qui plura cupit, eos adeat; nos tamen infra &longs;uis locis explicabimus tres <lb/>illas celebres antiquorum Antiphontis, Bri&longs;&longs;onis, &amp; Hippocratis quadra&shy;<lb/>turas, quamuis fal&longs;as, <expan abbr="quar&utilde;">quarum</expan> &longs;&aelig;pe meminit Ari&longs;t. &amp; alij. </s>
  
 <s>&amp; alij. </s> 
  
 <s>&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>&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>
  
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 <s>&amp; pr&aelig;terea con&longs;tet<gap/> Hip&shy;<lb/>pocratem quadra&longs;&longs;e lunulam, vt &longs;uo loco dicemus, &amp; Archimedem in libel&shy;<pb 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>&amp; pr&aelig;terea con&longs;tet<gap/> Hip&shy;<lb/>pocratem quadra&longs;&longs;e lunulam, vt &longs;uo loco dicemus, &amp; Archimedem in libel&shy;<pb 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><arrow.to.target n="marg2"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg2"/></s></p><p type="margin">
  
 <s><margin.target id="marg2"></margin.target>2</s></p><p type="main"> <s><margin.target id="marg2"/>2</s></p><p type="main">
  
 <s>Ex cap. </s> <s>Ex cap.
  
 <s>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> 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>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. </s> <s>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>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 funt initio Euclidis, &amp; per de&longs;criptio&shy;<lb/>nes exponant theoremata. </s> 
  
 <s>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>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><arrow.to.target n="marg3"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg3"/></s></p><p type="margin">
  
 <s><margin.target id="marg3"></margin.target>3</s></p><p type="main"> <s><margin.target id="marg3"/>3</s></p><p type="main">
  
 <s>Ex cap. </s> <s>Ex cap.
  
 <s>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="fig2"></figure><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> 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="fig2"/><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>&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.</s></p><p type="main"> <s>&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>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>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>
  
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 <s>addito numero impari. <lb/></s> <s>addito numero impari. <lb/></s>
  
 <s>quemadmodum infra 3. Phy&longs;. </s> <s>quemadmodum infra 3. Phy&longs;. tex. </s>
  
 <s>tex. </s> 
  
 <s>26. fus&egrave; explicabimus.</s></p><p type="head"> <s>26. fus&egrave; explicabimus.</s></p><p type="head">
  
 <s><emph type="italics"/>Ex Primo Priorum re&longs;olutoriorum.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Ex Primo Priorum re&longs;olutoriorum.<emph.end type="italics"/></s></p><p type="main">
  
 <s><arrow.to.target n="marg4"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg4"/></s></p><p type="margin">
  
 <s><margin.target id="marg4"></margin.target>4</s></p><p type="main"> <s><margin.target id="marg4"/>4</s></p><p type="main">
  
 <s>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>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>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>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>Sciendum <expan abbr="itaq;">itaque</expan> id, quod tradit Pappus <lb/>Alex. </s> <s>Sciendum <expan abbr="itaq;">itaque</expan> id, quod tradit Pappus <lb/>Alex. initio &longs;eptimi Mathem. collect. </s>
  
 <s>initio &longs;eptimi Mathem. </s> 
  
 <s>collect. </s> 
  
 <s>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 pagenum="36"/>o&longs;tendebant conclu&longs;ionem. </s> <s>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 pagenum="36"/>o&longs;tendebant conclu&longs;ionem. </s>
  
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 <s>definitio <lb/><expan abbr="vtriu&longs;q;">vtriu&longs;que</expan> e&longs;t a pud Euclidem ad primam propo&longs;. </s> <s>definitio <lb/><expan abbr="vtriu&longs;q;">vtriu&longs;que</expan> e&longs;t a pud Euclidem ad primam propo&longs;. </s>
  
 <s>13. Elem.  <s>13. Elem. iuxta tran&longs;latio&shy;<lb/>nem Zamb<gap/>rti, &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>
  
 iuxta tran&longs;latio&shy;<lb/>nem Zamb<gap/>rti, &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>&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>&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>
  
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 <s>Quod <lb/>porr&ograve; Ari&longs;t.  <s>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. </s> 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.
  
 <s>3. lib. </s> 3. lib.
  
 <s>3. Ethyc. </s> 3. Ethyc. </s>
  
 <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>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>
  
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 <s>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>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>maxim&egrave; <lb/>ver&ograve;, quia &longs;i horum lib. </s> <s>maxim&egrave; <lb/>ver&ograve;, quia &longs;i horum lib.
  
 <s>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> 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>at ver&ograve; vbinam docuit hanc re&longs;olutionem? </s> <s>at ver&ograve; vbinam docuit hanc re&longs;olutionem? </s>
  
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 <s>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>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><arrow.to.target n="marg5"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg5"/></s></p><p type="margin">
  
 <s><margin.target id="marg5"></margin.target>5</s></p><p type="main"> <s><margin.target id="marg5"/>5</s></p><p type="main">
  
 <s>Ex cap. </s> <s>Ex cap.
  
 <s>23. &longs;ecti primi lib. </s> 23. &longs;ecti primi lib.
  
 <s>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> 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>&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>&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>
  
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 <s>&longs;ic; commen&longs;. </s> <s>&longs;ic; commen&longs;. </s>
  
 <s>magnitudines dicuntur, quas <lb/><figure id="fig3"></figure><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. </s> <s>magnitudines dicuntur, quas <lb/><figure id="fig3"/><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. </s>
  
 <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. </s> <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. </s>
  
 <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="fig4"></figure><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. </s> <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="fig4"/><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. </s>
  
 <s>g. </s> <s>g. </s>
  
 <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>&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>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.  <s>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>
  
 manife&longs;tum e&longs;t. </s> 
  
 <s>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>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>Quapropter <lb/>non immerit&ograve; diuinus ille Plato lib. </s> <s>Quapropter <lb/>non immerit&ograve; diuinus ille Plato lib.
  
 <s>7. de legib. </s> 7. de legib. </s>
  
 <s>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>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>inter lineas incommen&longs;. </s> <s>inter lineas incommen&longs;. </s>
  
 <s>&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="fig5"></figure><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. </s> <s>&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="fig5"/><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. </s>
  
 <s>g. <lb/></s> <s>g. <lb/></s>
  
 <s>latus B C, pr&aelig;cis&egrave; omnino metiatur. </s> <s>latus B C, pr&aelig;cis&egrave; omnino metiatur. </s>
  
 <s>theorema <lb/>i&longs;tud demon&longs;tratur in vltima 10. Elem.  <s>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 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/></s>
  
 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 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/></s> 
  
 <s>deducit ad impo&longs;&longs;ibile, &longs;iue, vt ait hic Ari&longs;t.  <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. </s> 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>&longs;ignificat, quando ait, <lb/>imparia &aelig;qualia paribus fiunt. </s> 
  
 <s>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. </s> <s>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. </s>
  
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 <s>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>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><arrow.to.target n="marg6"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg6"/></s></p><p type="margin">
  
 <s><margin.target id="marg6"></margin.target>6</s></p><p type="main"> <s><margin.target id="marg6"/>6</s></p><p type="main">
  
 <s>Et cap. </s> <s>Et cap.
  
 <s>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> 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>&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>&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>
  
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 <s>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>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>&longs;it I&longs;o&longs;ce&shy;<lb/><figure id="fig6"></figure><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>&longs;it I&longs;o&longs;ce&shy;<lb/><figure id="fig6"/><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>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>facto centro <lb/>in A, de&longs;cribatur circulus A B C, tran&longs;iens per puncta <lb/>C B, iam &longs;ic. </s>
  
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 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> 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>Qu&aelig;nam vero &longs;it &aelig;qualitas, quam <lb/>Geometr&aelig; con&longs;iderant, infra cap. </s> <s>Qu&aelig;nam vero &longs;it &aelig;qualitas, quam <lb/>Geometr&aelig; con&longs;iderant, infra cap.
  
 <s>1. &longs;ecti 3. explicabicur.</s></p><p type="main"> 1. &longs;ecti 3. explicabicur.</s></p><p type="main">
  
 <s><arrow.to.target n="marg7"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg7"/></s></p><p type="margin">
  
 <s><margin.target id="marg7"></margin.target>7</s></p><p type="main"> <s><margin.target id="marg7"/>7</s></p><p type="main">
  
 <s>Ex cap. </s> <s>Ex cap.
  
 <s>2. &longs;ecti 2. lib. </s> 2. &longs;ecti 2. lib.
  
 <s>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 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. </s> 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 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>&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><arrow.to.target n="marg8"/></s></p><p type="margin">
  
 <s><arrow.to.target n="marg8"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg8"/>8</s></p><p type="main">
  
 <s><margin.target id="marg8"></margin.target>8</s></p><p type="main"> 
  
 <s>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>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>
  
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 <s>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>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><arrow.to.target n="marg9"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg9"/></s></p><p type="margin">
  
 <s><margin.target id="marg9"></margin.target>9</s></p><p type="main"> <s><margin.target id="marg9"/>9</s></p><p type="main">
  
 <s>Ex cap. </s> <s>Ex cap.
  
 <s>3. &longs;ecti 2. lib. </s> 3. &longs;ecti 2. lib.
  
 <s>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. </s> 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.
  
 <s>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"> 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><arrow.to.target n="marg10"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg10"/></s></p><p type="margin">
  
 <s><margin.target id="marg10"></margin.target>10</s></p><p type="main"> <s><margin.target id="marg10"/>10</s></p><p type="main">
  
 <s>Ex cap. </s> <s>Ex cap.
  
 <s>1. &longs;ecti 3. lib. </s> 1. &longs;ecti 3. lib.
  
 <s>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.  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="fig7"></figure><lb/>inclinatio in puncto A, &longs;iue acumen illud, &longs;iue mucro, <lb/>e&longs;t ratio anguli. </s> 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="fig7"/><lb/>inclinatio in puncto A, &longs;iue acumen illud, &longs;iue mucro, <lb/>e&longs;t ratio anguli. </s>
  
 <s>&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 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. </s> <s>&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 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. </s>
  
 <s>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/></s> <s>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>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. </s> <s>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. </s>
  
 <s>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/></s> <s>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/></s>
  
 <s>angulus B A C, diuidatur in duos angulos &agrave; linea A D. tunc enim duo angu&shy;<lb/><figure id="fig8"></figure><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>angulus B A C, diuidatur in duos angulos &agrave; linea A D. tunc enim duo angu&shy;<lb/><figure id="fig8"/><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>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. </s> <s>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. </s>
  
 <s>&longs;int tres anguli trianguli A B C, <expan abbr="&longs;int&qacute;">&longs;intque</expan>; alij duo anguli recti, <lb/><figure id="fig9"></figure><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="fig10"></figure><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. </s> <s>&longs;int tres anguli trianguli A B C, <expan abbr="&longs;int&qacute;">&longs;intque</expan>; alij duo anguli recti, <lb/><figure id="fig9"/><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="fig10"/><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. </s>
  
 <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>&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>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>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>Quam demon&longs;trationem primi om&shy;<lb/>nium Pythagorici perfecerunt, vt refert Proclus ad 32. primi Elem. </s> <s>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>Eucli&shy;<lb/>des deinde ibidem aliter, quam Pythagorici idem demon&longs;trauit. </s> 
  
 <s>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 pagenum="41"/>&aelig;qualitas nullum di&longs;crimen, quantumuis minimum admittat, quod &longs;en&longs;ui <lb/>vitare ob &longs;ui imperfectione<gap/>on licet: vnde inter e&aelig;, qu&aelig; mathematic&egrave; <lb/>&longs;unt &aelig;qualia, nullus intellectus aliquam valeat reper<gap/>re 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>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 pagenum="41"/>&aelig;qualitas nullum di&longs;crimen, quantumuis minimum admittat, quod &longs;en&longs;ui <lb/>vitare ob &longs;ui imperfectione<gap/>on licet: vnde inter e&aelig;, qu&aelig; mathematic&egrave; <lb/>&longs;unt &aelig;qualia, nullus intellectus aliquam valeat reper<gap/>re 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>
  
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 <s>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>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>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/></s> <s>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>optim&egrave; Aegydius, &amp; Niphus in hunc locum.</s></p><p type="main"> 
  
 <s><arrow.to.target n="marg11"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg11"/></s></p><p type="margin">
  
 <s><margin.target id="marg11"></margin.target>11</s></p><p type="main"> <s><margin.target id="marg11"/>11</s></p><p type="main">
  
 <s>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>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>
  
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 <s><emph type="italics"/>Ex Libro &longs;ecundo Priorum.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Ex Libro &longs;ecundo Priorum.<emph.end type="italics"/></s></p><p type="main">
  
 <s><arrow.to.target n="marg12"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg12"/></s></p><p type="margin">
  
 <s><margin.target id="marg12"></margin.target>12</s></p><p type="main"> <s><margin.target id="marg12"/>12</s></p><p type="main">
  
 <s>Ex cap. </s> <s>Ex cap.
  
 <s>21. <emph type="italics"/>(Quod faciunt, qui coalternas putant &longs;cribere, latent enim ip&longs;<gap/><lb/>&longs;e ip&longs;os talia accip entes, qu&aelig; non est po&longs;&longs;ibile monstrare uon exiftentibus <lb/><gap/>o lternis)<emph.end type="italics"/> Vult Ari&longs;t.  21. <emph type="italics"/>(Quod faciunt, qui coalternas putant &longs;cribere, latent enim ip&longs;<gap/><lb/>&longs;e ip&longs;os talia accip entes, qu&aelig; non est po&longs;&longs;ibile monstrare uon exiftentibus <lb/><gap/>o lternis)<emph.end type="italics"/> Vult Ari&longs;t.
  
 exemplo mathematico explicare, quid &longs;it pe&shy;<lb/>titio principij. </s> exemplo mathematico explicare, quid &longs;it pe&shy;<lb/>titio principij. </s>
  
 <s>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>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>quoad <lb/>exempli explicationem vtor figura textibus apponi &longs;olita, qu&aelig; e&longs;t pr&aelig;&longs;ens. <lb/><figure id="fig11"></figure><lb/>probat Euclides in 28. primi Elem.  <s>quoad <lb/>exempli explicationem vtor figura textibus apponi &longs;olita, qu&aelig; e&longs;t pr&aelig;&longs;ens. <lb/><figure id="fig11"/><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> 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>
  
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 <s>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>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><arrow.to.target n="marg13"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg13"/></s></p><p type="margin">
  
 <s><margin.target id="marg13"></margin.target>13</s></p><p type="main"> <s><margin.target id="marg13"/>13</s></p><p type="main">
  
 <s>Ex cap. </s> <s>Ex cap.
  
 <s>22. lib. </s> 22. lib.
  
 <s>2. Priorum <emph type="italics"/>(Vt &longs;i volens mon&longs;trare, quod diameter e&longs;t incom&shy;<lb/>men&longs;. </s> 2. Priorum <emph type="italics"/>(Vt &longs;i volens mon&longs;trare, quod diameter e&longs;t incom&shy;<lb/>men&longs;. </s>
  
 <s>argueret Zenonis rationem, quod non e&longs;t moueri)<emph.end type="italics"/> &longs;uperius &longs;ecto 3. lib. </s> <s>argueret Zenonis rationem, quod non e&longs;t moueri)<emph.end type="italics"/> &longs;uperius &longs;ecto 3. lib.
  
 <s>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.  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"> non cau&longs;am pro cau&longs;a.</s></p><p type="main">
  
 <s><arrow.to.target n="marg14"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg14"/></s></p><p type="margin">
  
 <s><margin.target id="marg14"></margin.target>14</s></p><p type="main"> <s><margin.target id="marg14"/>14</s></p><p type="main">
  
 <s>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>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>per coalternas intellige lineas &aelig;quidi&longs;tantes, &longs;eu pa&shy;<lb/>rallelas, vt in &longs;uperiori cap. </s> <s>per coalternas intellige lineas &aelig;quidi&longs;tantes, &longs;eu pa&shy;<lb/>rallelas, vt in &longs;uperiori cap.
  
 <s>monuimus. </s> monuimus. </s>
  
 <s>C&aelig;terum Euclides propo&longs;. </s> <s>C&aelig;terum Euclides propo&longs;. </s>
  
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 <s><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><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>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="fig12"></figure><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>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="fig12"/><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>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>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>
  
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 videtur &longs;atis clarus.</s></p><p type="main"> videtur &longs;atis clarus.</s></p><p type="main">
  
 <s><arrow.to.target n="marg15"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg15"/></s></p><p type="margin">
  
 <s><margin.target id="marg15"></margin.target>15</s></p><p type="main"> <s><margin.target id="marg15"/>15</s></p><p type="main">
  
 <s>Ex cap. </s> <s>Ex cap.
  
 <s>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> 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>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>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>&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. </s> <s>&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.
  
 <s>1. &longs;ecto 3. cap. </s> 1. &longs;ecto 3. cap.
  
 <s>1. ex quibus quidquid Ma&shy;<lb/>thematicum e&longs;t hic, clarum redditur. </s> 1. ex quibus quidquid Ma&shy;<lb/>thematicum e&longs;t hic, clarum redditur. </s>
  
 <s>reliqua ver&ograve;, qu&aelig; ad Logicum &longs;pe&shy;<lb/>ctant, huius loci commentatores pro&longs;equuntur.</s></p><p type="main"> <s>reliqua ver&ograve;, qu&aelig; ad Logicum &longs;pe&shy;<lb/>ctant, huius loci commentatores pro&longs;equuntur.</s></p><p type="main">
  
 <s>In cap. </s> <s>In cap.
  
 <s>31. de Abductione.</s></p><p type="main"> 31. de Abductione.<!-- KEEP S--></s></p><p type="main">
  
 <s><arrow.to.target n="marg16"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg16"/></s></p><p type="margin">
  
 <s><margin.target id="marg16"></margin.target>16</s></p><p type="main"> <s><margin.target id="marg16"/>16</s></p><p type="main">
  
 <s>Notandum hic cum eruditi&longs;&longs;imo Burana, Abductionem hanc, de qua in hoc <lb/>cap. </s> <s>Notandum hic cum eruditi&longs;&longs;imo Burana, Abductionem hanc, de qua in hoc <lb/>cap.
  
 <s>agitur e&longs;&longs;e vocem mathematicam, <expan abbr="cam&qacute;">camque</expan>; Ari&longs;t.  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> quemadmodum multa <lb/>alia &agrave; Mathematicis mutuatum ad omnes alias &longs;cientias tran&longs;tuli&longs;&longs;e. </s>
  
 <s>e&longs;&longs;e <pb pagenum="44"/>autem terminum mathematicum colligitur manife&longs;t&egrave; ex Proelo, qui lib. </s> <s>e&longs;&longs;e <pb pagenum="44"/>autem terminum mathematicum colligitur manife&longs;t&egrave; ex Proelo, qui lib.
  
 <s>3. <lb/>in comm. </s> 3. <lb/>in comm. </s>
  
 <s>Elem. </s> <s>Elem.
  
 <s>Euclidis ad primam propo&longs;itionem primi Elementi, pag. <lb/></s> Euclidis ad primam propo&longs;itionem primi Elementi, pag. <lb/></s>
  
 <s>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>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>
  
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 <s>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>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>h&aelig;c Proclus. </s> <s>h&aelig;c Proclus. <!-- KEEP S--></s>
  
 <s>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>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">
  
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 <s>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. </s> <s>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. </s>
  
 <s>Cla&shy;<lb/>uium in fine &longs;exti Elem. </s> <s>Cla&shy;<lb/>uium in fine &longs;exti Elem.
  
 <s>&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;<gap/>mus in cap. </s> &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;<gap/>mus in cap.
  
 <s>3. Pr&aelig;&shy;<lb/>dicam. </s> 3. Pr&aelig;&shy;<lb/>dicam. </s>
  
 <s>de hac re, quia plurimum hunc conferunt. </s> <s>de hac re, quia plurimum hunc conferunt. </s>
  
 <s>&longs;ed iam ad textus expli&shy;<lb/>cationem veniamus.</s></p><p type="main"> <s>&longs;ed iam ad textus expli&shy;<lb/>cationem veniamus.</s></p><p type="main">
  
 <s><arrow.to.target n="marg17"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg17"/></s></p><p type="margin">
  
 <s><margin.target id="marg17"></margin.target>17</s></p><p type="main"> <s><margin.target id="marg17"/>17</s></p><p type="main">
  
 <s>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. </s> <s>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. </s>
  
 <s>11. primi Phy&longs;ic. </s> <s>11. primi Phy&longs;ic. </s>
  
 <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 pagenum="45"/><figure id="fig13"></figure><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>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 pagenum="45"/><figure id="fig13"/><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><expan abbr="hucu&longs;q;">hucu&longs;que</expan> be&shy;<lb/>n&egrave; procedit Hippocrates. </s> <s><expan abbr="hucu&longs;q;">hucu&longs;que</expan> be&shy;<lb/>n&egrave; procedit Hippocrates. <!-- KEEP S--></s>
  
 <s>&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="fig14"></figure><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>&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="fig14"/><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>&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>&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>&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. </s> <s>&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>&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>mirabilis tamen &longs;emper habita e&longs;t illa &longs;uperior lunul&aelig; <lb/>quadratio. </s> <s>mirabilis tamen &longs;emper habita e&longs;t illa &longs;uperior lunul&aelig; <lb/>quadratio. </s>
  
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 <s>Hippocrates i&longs;te Chius e&longs;t alter <pb pagenum="46"/>ab illo Hippocrate Coo medicorum Magi&longs;tro, vt colligitur ex Alexandre <lb/>Aphrod. </s> <s>Hippocrates i&longs;te Chius e&longs;t alter <pb pagenum="46"/>ab illo Hippocrate Coo medicorum Magi&longs;tro, vt colligitur ex Alexandre <lb/>Aphrod. </s>
  
 <s>in Primum Meteororum de Cometis.</s></p><p type="head"> <s>in Primum Meteororum de Cometis.<!-- KEEP S--></s></p><p type="head">
  
 <s><emph type="italics"/>Ex Primo Posteriorum re&longs;olutoriorum.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Ex Primo Posteriorum re&longs;olutoriorum.<emph.end type="italics"/></s></p><p type="main">
  
 <s><arrow.to.target n="marg18"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg18"/></s></p><p type="margin">
  
 <s><margin.target id="marg18"></margin.target>18</s></p><p type="main"> <s><margin.target id="marg18"/>18</s></p><p type="main">
  
 <s>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>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>
  
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 <s>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>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><arrow.to.target n="marg19"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg19"/></s></p><p type="margin">
  
 <s><margin.target id="marg19"></margin.target>19</s></p><p type="main"> 
  
 <s>Tex. </s> <s><margin.target id="marg19"/>19</s></p><p type="main">
  
 <s>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. </s> <s>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. </s>
  
 <s>&longs;ecto 3. cap. </s> <s>&longs;ecto 3. cap.
  
 <s>1. explicaui de angulis <lb/>trianguli. </s> 1. explicaui de angulis <lb/>trianguli. </s>
  
 <s>deinde &longs;cias, quod quando Ari&longs;t.  <s>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> ait, hoc, quod e&longs;t in &longs;emicir cu&shy;<lb/>lo triangulum, &amp;c. </s>
  
 <s>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. </s> <s>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.
  
 <s>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="fig15"></figure><lb/>micirculo. </s> 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="fig15"/><lb/>micirculo. </s>
  
 <s>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>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><arrow.to.target n="marg20"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg20"/></s></p><p type="margin">
  
 <s><margin.target id="marg20"></margin.target>20</s></p><p type="main"> 
  
 <s>Tex. </s> 
  
 <s>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. </s> <s><margin.target id="marg20"/>20</s></p><p type="main">
  
 <s>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 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>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.
  
 <s><arrow.to.target n="marg21"></arrow.to.target></s></p><p type="margin"> 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 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><margin.target id="marg21"></margin.target>21</s></p><p type="main"> <s><arrow.to.target n="marg21"/></s></p><p type="margin">
  
 <s>Hoc eodem cap. </s> <s><margin.target id="marg21"/>21</s></p><p type="main">
  
 <s>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. </s> <s>Hoc eodem cap.
  
 <s>Euclidis percipi pote&longs;t. </s> 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.
  
 <s>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/></s> Euclidis percipi pote&longs;t. </s>
  
 <s>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>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><arrow.to.target n="marg22"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg22"/></s></p><p type="margin">
  
 <s><margin.target id="marg22"></margin.target>22</s></p><p type="main"> <s><margin.target id="marg22"/>22</s></p><p type="main">
  
 <s>Eodem tex. </s> <s>Eodem tex. </s>
  
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 <s>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 <gap/>/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>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 <gap/>/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><arrow.to.target n="marg23"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg23"/></s></p><p type="margin">
  
 <s><margin.target id="marg23"></margin.target>23</s></p><p type="main"> <s><margin.target id="marg23"/>23</s></p><p type="main">
  
 <s>Tex. </s> <s>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>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>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>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>
  
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 <s>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>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><arrow.to.target n="marg24"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg24"/></s></p><p type="margin">
  
 <s><margin.target id="marg24"></margin.target>24</s></p><p type="main"> <s><margin.target id="marg24"/>24</s></p><p type="main">
  
 <s>Eodem tex. </s> <s>Eodem tex. </s>
  
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 <s>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>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>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="fig16"></figure><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>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="fig16"/><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>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>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>
  
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 <s><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><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>Per altera parte longius, intelligit numerum, qui producitur &agrave; duobus <lb/><figure id="fig17"></figure><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>Per altera parte longius, intelligit numerum, qui producitur &agrave; duobus <lb/><figure id="fig17"/><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>atque h&aelig;c <lb/>&longs;unt, qu&aelig; ex Mathematicis petenda erant, ad huius <lb/>loci intelligentiam.</s></p><p type="main"> <s>atque h&aelig;c <lb/>&longs;unt, qu&aelig; ex Mathematicis petenda erant, ad huius <lb/>loci intelligentiam.</s></p><p type="main">
  
 <s><arrow.to.target n="marg25"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg25"/></s></p><p type="margin">
  
 <s><margin.target id="marg25"></margin.target>25</s></p><p type="main"> 
  
 <s>Tex. </s> <s><margin.target id="marg25"/>25</s></p><p type="main">
  
 <s>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 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>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 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>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>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>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>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>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. </s> <s>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.
  
 <s>1. <lb/>&longs;crip&longs;imus. </s> 1. <lb/>&longs;crip&longs;imus. </s>
  
 <s>deinde memineris figuram vniuer&longs;aliorem e&longs;&longs;e triangulo, &amp; tri&shy;<lb/>angulum vniuer&longs;alius &aelig;quicrure. </s> <s>deinde memineris figuram vniuer&longs;aliorem e&longs;&longs;e triangulo, &amp; tri&shy;<lb/>angulum vniuer&longs;alius &aelig;quicrure. </s>
  
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 <s>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>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><arrow.to.target n="marg26"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg26"/></s></p><p type="margin">
  
 <s><margin.target id="marg26"></margin.target>26</s></p><p type="main"> 
  
 <s>Tex. </s> <s><margin.target id="marg26"/>26</s></p><p type="main">
  
 <s>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.  <s>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="fig18"></figure><lb/>cen&longs;ui. </s> de&longs;umitur, quam propterea primo loco exponendam <lb/><figure id="fig18"/><lb/>cen&longs;ui. </s>
  
 <s>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>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>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="fig19"></figure><lb/>cti, probabitur de rectis A B, C D, &aelig;quidi&longs;tan&shy;<lb/>tia. </s> <s>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="fig19"/><lb/>cti, probabitur de rectis A B, C D, &aelig;quidi&longs;tan&shy;<lb/>tia. </s>
  
 <s>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 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>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 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>
  
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 <s>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>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><arrow.to.target n="marg27"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg27"/></s></p><p type="margin">
  
 <s><margin.target id="marg27"></margin.target>27</s></p><p type="main"> <s><margin.target id="marg27"/>27</s></p><p type="main">
  
 <s>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>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>
  
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 <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>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><arrow.to.target n="marg28"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg28"/></s></p><p type="margin">
  
 <s><margin.target id="marg28"></margin.target>28</s></p><p type="main"> <s><margin.target id="marg28"/>28</s></p><p type="main">
  
 <s>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>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>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 pagenum="51"/>dum quid &longs;it alterna proportio. </s> <s>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 pagenum="51"/>dum quid &longs;it alterna proportio. </s>
  
 <s>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="fig20"></figure><lb/>&amp; con&longs;equentis ad con&longs;equentem. </s> <s>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="fig20"/><lb/>&amp; con&longs;equentis ad con&longs;equentem. </s>
  
 <s>Explico, exponantur qua&shy;<lb/>tuor quantitates proportionales, v.g. </s> <s>Explico, exponantur qua&shy;<lb/>tuor quantitates proportionales, v.g. </s>
  
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 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;<lb/>&longs;io debetur; qu&aelig; quidem natura communis nomine caret, &amp; propterea e&longs;t <lb/>cau&longs;a erroris.</s></p><p type="main"> 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;<lb/>&longs;io debetur; qu&aelig; quidem natura communis nomine caret, &amp; propterea e&longs;t <lb/>cau&longs;a erroris.</s></p><p type="main">
  
 <s><arrow.to.target n="marg29"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg29"/></s></p><p type="margin">
  
 <s><margin.target id="marg29"></margin.target>29</s></p><p type="main"> <s><margin.target id="marg29"/>29</s></p><p type="main">
  
 <s><emph type="italics"/>Nunc autem vniuer&longs;aliter demon&longs;tratur)<emph.end type="italics"/> nu&longs;quam apud Mathematicos in&shy;<lb/>uenio hanc demon&longs;trationem vniuer&longs;alem de illo communi omnibus pr&aelig;&shy;<lb/>dictis, quare dicendum cum Zabarella, illud, nunc, e&longs;&longs;e intelligendum &longs;ic, <lb/>nunc autem, ide&longs;t, in pr&aelig;&longs;entia autem deberet vniuer&longs;aliter demon&longs;trari, <lb/>quod tamen cum non &longs;iat, contingit nos decipi putantes vniuer&longs;aliter de&shy;<lb/>mon&longs;tra&longs;&longs;e. </s> <s><emph type="italics"/>Nunc autem vniuer&longs;aliter demon&longs;tratur)<emph.end type="italics"/> nu&longs;quam apud Mathematicos in&shy;<lb/>uenio hanc demon&longs;trationem vniuer&longs;alem de illo communi omnibus pr&aelig;&shy;<lb/>dictis, quare dicendum cum Zabarella, illud, nunc, e&longs;&longs;e intelligendum &longs;ic, <lb/>nunc autem, ide&longs;t, in pr&aelig;&longs;entia autem deberet vniuer&longs;aliter demon&longs;trari, <lb/>quod tamen cum non &longs;iat, contingit nos decipi putantes vniuer&longs;aliter de&shy;<lb/>mon&longs;tra&longs;&longs;e. </s>
  
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 <s><expan abbr="atq;">atque</expan> hoc modo explicatum e&longs;t exem&shy;<lb/>plum &longs;ecundi erroris, qui verbis illis <emph type="italics"/>(Vel &longs;it quidem, &longs;ed innominatum &longs;it in <lb/>rebus &longs;pecie differentibus)<emph.end type="italics"/> continebatur.</s></p><p type="main"> <s><expan abbr="atq;">atque</expan> hoc modo explicatum e&longs;t exem&shy;<lb/>plum &longs;ecundi erroris, qui verbis illis <emph type="italics"/>(Vel &longs;it quidem, &longs;ed innominatum &longs;it in <lb/>rebus &longs;pecie differentibus)<emph.end type="italics"/> continebatur.</s></p><p type="main">
  
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 <s><margin.target id="marg30"></margin.target>30</s></p><p type="main"> <s><margin.target id="marg30"/>30</s></p><p type="main">
  
 <s>Ibidem <emph type="italics"/>(Propter hoc &longs;i quis mon&longs;trauerit &longs;ingulum triangulum. </s> <s>Ibidem <emph type="italics"/>(Propter hoc &longs;i quis mon&longs;trauerit &longs;ingulum triangulum. </s>
  
 <s>demon&longs;tratio&shy;<lb/>ne aut vna, aut altera, quod duos rectos habet vnumquodque, <expan abbr="&aelig;quilatei&utilde;">&aelig;quilateium</expan> &longs;eor&longs;um, <lb/>&amp; &longs;calenum, &amp; &aelig;quicrus: nondum nouit triangulum, quod duobus rectis, <gap/>&longs;i &longs;o&shy;<lb/>phi&longs;tico modo, <expan abbr="neq;">neque</expan> vniuer&longs; aliter triangulum, <expan abbr="neq;">neque</expan> &longs;i vllum e&longs;t pr&aelig;ter pr&aelig;dicta <lb/>triangulum alterum. </s> <s>demon&longs;tratio&shy;<lb/>ne aut vna, aut altera, quod duos rectos habet vnumquodque, <expan abbr="&aelig;quilatei&utilde;">&aelig;quilateium</expan> &longs;eor&longs;um, <lb/>&amp; &longs;calenum, &amp; &aelig;quicrus: nondum nouit triangulum, quod duobus rectis, <gap/>&longs;i &longs;o&shy;<lb/>phi&longs;tico modo, <expan abbr="neq;">neque</expan> vniuer&longs; aliter triangulum, <expan abbr="neq;">neque</expan> &longs;i vllum e&longs;t pr&aelig;ter pr&aelig;dicta <lb/>triangulum alterum. </s>
  
 <s>non enim &longs;ecundum quod triangulum, <expan abbr="neq;">neque</expan> omnetriangulum, <lb/>ni&longs;i &longs;ecundum numerum, &longs;ecundum &longs;peciem autem non omne; &amp; &longs;i nullum e&longs;t, quod <lb/>non nouit)<emph.end type="italics"/> vltimo loco ponit exemplum primi erroris, quem &longs;upra verbis il&shy;<lb/>lis <emph type="italics"/>(Quando vel nibil &longs;it accipere &longs;uperius, pr&aelig;ter &longs;ingulare)<emph.end type="italics"/> expre&longs;&longs;erat, quod, <lb/>vt ben&egrave; intelligamus, opus e&longs;t ea, legere, qu&aelig; libro primo Priorum &longs;ecto 3. <lb/>cap. </s> <s>non enim &longs;ecundum quod triangulum, <expan abbr="neq;">neque</expan> omnetriangulum, <lb/>ni&longs;i &longs;ecundum numerum, &longs;ecundum &longs;peciem autem non omne; &amp; &longs;i nullum e&longs;t, quod <lb/>non nouit)<emph.end type="italics"/> vltimo loco ponit exemplum primi erroris, quem &longs;upra verbis il&shy;<lb/>lis <emph type="italics"/>(Quando vel nibil &longs;it accipere &longs;uperius, pr&aelig;ter &longs;ingulare)<emph.end type="italics"/> expre&longs;&longs;erat, quod, <lb/>vt ben&egrave; intelligamus, opus e&longs;t ea, legere, qu&aelig; libro primo Priorum &longs;ecto 3. <lb/>cap.
  
 <s>1. &longs;crip&longs;imus de propriet<gap/>te illa trianguli, quod &longs;cilicet habet tres an&shy;<lb/>gulos &aelig;quales duobus rectis angulis, quibus pr&aelig;mi&longs;&longs;is, &longs;ic deinde locum <lb/>hunc interpretaberis; Propter hoc, quod pr&aelig;cedenti textu dictum e&longs;t; no&shy;<lb/>tandum in primo errore vniuer&longs;ale, tanquam &longs;i non e&longs;&longs;et vniuer&longs;ale o&longs;ten&shy;<lb/>ditur de &longs;ingulari, &longs;i quis igitur mon&longs;trauerit &longs;ingillatim de <expan abbr="vnoquoq;">vnoquoque</expan> trian&shy;<lb/>gulo in &longs;ingulari, &longs;cilicet de vno &aelig;quilatero, tantum, &amp; de vno Scaleno, &amp; <lb/>de vno I&longs;o&longs;cele, &longs;eparatim, vtens auteadem demon&longs;trationc dum de <expan abbr="vno&qacute;">vnoque</expan>; <pb pagenum="52"/>&longs;epatatim o&longs;tendit, aut vtens diuerfis demon&longs;trationibus, vna pro &aelig;quila&shy;<lb/>tero, altera pro I&longs;o&longs;cele, tertia pro Scaleno, o&longs;tendens, quod <expan abbr="vnumquodq;">vnumquodque</expan> <lb/>illorum habet tres angules &aelig;quales duobus rectis angulis; i&longs;te nondum no&shy;<lb/>uit triangulum omne habere talem affectionem, ni&longs;i modo &longs;ophi&longs;tico, quia <lb/>non cogno&longs;cit hanc affectionem illis <expan abbr="c&otilde;petere">competere</expan> propter naturam illam com&shy;<lb/>munem trianguli, cui primo, &amp; per &longs;e competit; &amp; neque vniuer&longs;aliter co&shy;<lb/>gno&longs;cit triangulum omne e&longs;&longs;e tale, etiam &longs;i nullum aliud reperiatur trian&shy;<lb/>gulum, pr&aelig;ter illud &aelig;quilaterum, vel illud I&longs;o&longs;celes, vel illud Scalenum, de <lb/>quibus &longs;eparatim <expan abbr="dem&otilde;&longs;trauit">demon&longs;trauit</expan>, &amp; &longs;ecundum numernm, ide&longs;t de vnoquoque, <lb/>quatenus e&longs;t vnum numero. </s> 1. &longs;crip&longs;imus de propriet<gap/>te illa trianguli, quod &longs;cilicet habet tres an&shy;<lb/>gulos &aelig;quales duobus rectis angulis, quibus pr&aelig;mi&longs;&longs;is, &longs;ic deinde locum <lb/>hunc interpretaberis; Propter hoc, quod pr&aelig;cedenti textu dictum e&longs;t; no&shy;<lb/>tandum in primo errore vniuer&longs;ale, tanquam &longs;i non e&longs;&longs;et vniuer&longs;ale o&longs;ten&shy;<lb/>ditur de &longs;ingulari, &longs;i quis igitur mon&longs;trauerit &longs;ingillatim de <expan abbr="vnoquoq;">vnoquoque</expan> trian&shy;<lb/>gulo in &longs;ingulari, &longs;cilicet de vno &aelig;quilatero, tantum, &amp; de vno Scaleno, &amp; <lb/>de vno I&longs;o&longs;cele, &longs;eparatim, vtens auteadem demon&longs;trationc dum de <expan abbr="vno&qacute;">vnoque</expan>; <pb pagenum="52"/>&longs;epatatim o&longs;tendit, aut vtens diuerfis demon&longs;trationibus, vna pro &aelig;quila&shy;<lb/>tero, altera pro I&longs;o&longs;cele, tertia pro Scaleno, o&longs;tendens, quod <expan abbr="vnumquodq;">vnumquodque</expan> <lb/>illorum habet tres angules &aelig;quales duobus rectis angulis; i&longs;te nondum no&shy;<lb/>uit triangulum omne habere talem affectionem, ni&longs;i modo &longs;ophi&longs;tico, quia <lb/>non cogno&longs;cit hanc affectionem illis <expan abbr="c&otilde;petere">competere</expan> propter naturam illam com&shy;<lb/>munem trianguli, cui primo, &amp; per &longs;e competit; &amp; neque vniuer&longs;aliter co&shy;<lb/>gno&longs;cit triangulum omne e&longs;&longs;e tale, etiam &longs;i nullum aliud reperiatur trian&shy;<lb/>gulum, pr&aelig;ter illud &aelig;quilaterum, vel illud I&longs;o&longs;celes, vel illud Scalenum, de <lb/>quibus &longs;eparatim <expan abbr="dem&otilde;&longs;trauit">demon&longs;trauit</expan>, &amp; &longs;ecundum numernm, ide&longs;t de vnoquoque, <lb/>quatenus e&longs;t vnum numero. </s>
  
 <s>non nouit autem &longs;ecundum &longs;peciem, ideft fecun&shy;<lb/>dum naturam, &amp; formam communem illis tribus indiuiduis, qu&aelig; e&longs;t natu&shy;<lb/>ra trianguli. </s> <s>non nouit autem &longs;ecundum &longs;peciem, ideft fecun&shy;<lb/>dum naturam, &amp; formam communem illis tribus indiuiduis, qu&aelig; e&longs;t natu&shy;<lb/>ra trianguli. </s>
  
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 confu&longs;ionem nulla ra&shy;<lb/>tione, im&ograve; contra omnem rationem imponimus.</s></p><p type="main"> confu&longs;ionem nulla ra&shy;<lb/>tione, im&ograve; contra omnem rationem imponimus.</s></p><p type="main">
  
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 <s>Textu 14. continet quidem qu&aelig;dam mathematica, &longs;ed fer&egrave; eadem cum <lb/>&longs;uperioribus, qu&aelig; quia tum ex pr&aelig;dictis facile intelligi po&longs;&longs;unt, tum quia <lb/>ben&egrave; ab expo&longs;itoribus explicantur, ne actum agamus, pr&aelig;termittimus.</s></p><p type="main"> <s>Textu 14. continet quidem qu&aelig;dam mathematica, &longs;ed fer&egrave; eadem cum <lb/>&longs;uperioribus, qu&aelig; quia tum ex pr&aelig;dictis facile intelligi po&longs;&longs;unt, tum quia <lb/>ben&egrave; ab expo&longs;itoribus explicantur, ne actum agamus, pr&aelig;termittimus.</s></p><p type="main">
  
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 <s>Tex. </s> <s>Tex. 20. <emph type="italics"/>(Ni&longs;i magnitudines numeri &longs;int)<emph.end type="italics"/> hoc e&longs;t, ni&longs;i magnitudines &longs;int di&shy;<lb/>fcret&aelig;, ita vt cadant &longs;ub numernm, vt &longs;i linea qu&aelig;piam diuidatur in partes <lb/>decem, vel duodecim, tunc euadit quantitas di&longs;creta, &longs;iue numerus. </s>
  
 <s>20. <emph type="italics"/>(Ni&longs;i magnitudines numeri &longs;int)<emph.end type="italics"/> hoc e&longs;t, ni&longs;i magnitudines &longs;int di&shy;<lb/>fcret&aelig;, ita vt cadant &longs;ub numernm, vt &longs;i linea qu&aelig;piam diuidatur in partes <lb/>decem, vel duodecim, tunc euadit quantitas di&longs;creta, &longs;iue numerus. </s> 
  
 <s>&amp; tunc <lb/>linca numerus e&longs;t. </s> <s>&amp; tunc <lb/>linca numerus e&longs;t. </s>
  
 <s>idem de &longs;uperficie, ac &longs;olido intelligendum.</s></p><p type="main"> <s>idem de &longs;uperficie, ac &longs;olido intelligendum.</s></p><p type="main">
  
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 <s>Ibidem <emph type="italics"/>(Propter hoc Geometri&aelig; non licet mon&longs;trare, quod contrariorum vna <lb/>e&longs;e &longs;cientia, &longs;ed neque quod duo cubi cubus)<emph.end type="italics"/> quo ad verba illa, duo cubi cubus<gap/><lb/>qu&aelig; ad nos pertinent, vult Ari&longs;t.  <s>Ibidem <emph type="italics"/>(Propter hoc Geometri&aelig; non licet mon&longs;trare, quod contrariorum vna <lb/>e&longs;e &longs;cientia, &longs;ed neque quod duo cubi cubus)<emph.end type="italics"/> quo ad verba illa, duo cubi cubus<gap/><lb/>qu&aelig; ad nos pertinent, vult Ari&longs;t.
  
 docere<gap/>, quod non debet Geometra o&longs;ten&shy;<lb/>dere numerorum affectiones (per enbos enim intelligit numeros quo&longs;dam <lb/>&longs;ic dictos, vt paulo po&longs;t o&longs;tendam) vt &longs;i quis vellet geometric&egrave; o&longs;tendere id, <lb/>quod o&longs;tenditur in 4. noni Elem. </s> docere<gap/>, quod non debet Geometra o&longs;ten&shy;<lb/>dere numerorum affectiones (per enbos enim intelligit numeros quo&longs;dam <lb/>&longs;ic dictos, vt paulo po&longs;t o&longs;tendam) vt &longs;i quis vellet geometric&egrave; o&longs;tendere id, <lb/>quod o&longs;tenditur in 4. noni Elem.
  
 <s>&longs;cilicet, &longs;i cubus numerus cubum numerum <lb/>multiplicauerit, productus numerus erit pariter cubus. </s> &longs;cilicet, &longs;i cubus numerus cubum numerum <lb/>multiplicauerit, productus numerus erit pariter cubus. </s>
  
 <s>nonnulli latinorum <lb/>perperam textum hunc expo&longs;uerunt putantes reperiri &longs;olummodo cubos <lb/>geometricos, at Euclides definit. </s> <s>nonnulli latinorum <lb/>perperam textum hunc expo&longs;uerunt putantes reperiri &longs;olummodo cubos <lb/>geometricos, at Euclides definit. </s>
  
 <s>19. &longs;eptimi, &longs;ic arithmeticum cubum de&shy;<lb/>finit, cubus numerus e&longs;t, qui &longs;ub tribus numeris &aelig;qualibus continetur, qua&shy;<lb/>lis e&longs;t. </s> <s>19. &longs;eptimi, &longs;ic arithmeticum cubum de&shy;<lb/>finit, cubus numerus e&longs;t, qui &longs;ub tribus numeris &aelig;qualibus continetur, qua&shy;<lb/>lis e&longs;t. </s>
  
 <s>8. qui e&longs;t ad in&longs;tar cubi geometrici, &amp; continetur&longs;ub tribus binarijs <lb/>multiplicatis inuicem, qu&aelig; multiplicatio &longs;ic in&longs;tituitur, exponuntur tres bi&shy;<lb/><figure id="fig21"></figure><lb/>narij, 2, 2, 2, primus ducitur in &longs;ecundum, &amp; producitur. <lb/></s> <s>8. qui e&longs;t ad in&longs;tar cubi geometrici, &amp; continetur&longs;ub tribus binarijs <lb/>multiplicatis inuicem, qu&aelig; multiplicatio &longs;ic in&longs;tituitur, exponuntur tres bi&shy;<lb/><figure id="fig21"/><lb/>narij, 2, 2, 2, primus ducitur in &longs;ecundum, &amp; producitur. <lb/></s>
  
 <s>4. qui e&longs;t numerus quadratus huius figur&aelig;, <figure id="fig22"></figure>, deinde <lb/>tertius binarius ducitur in pr&aelig;dictum quadratum 4. &amp; pro&shy;<lb/>ducitur 8. qui dicitur cubus, quia &longs;i intelligantur duo qua&shy;<lb/>zerna<gap/>ij, vnus &longs;upra alterum, vt in pr&aelig;&longs;enti figura refe&shy;<lb/>runt cubicam figuram, cuius tam longitudo, quam latitudo, <pb pagenum="53"/>&amp; altitudo, e&longs;t 2. Similiter cubus numerus e&longs;t 27. quia &longs;it ex tribus terna&shy;<lb/>rijs inuicem modo pr&aelig;dicto multiplicatis, 3. 3. 3. nam 3. in 3. ductis &longs;it 9. <lb/><figure id="fig23"></figure><lb/>qui e&longs;t quadratus. </s> <s>4. qui e&longs;t numerus quadratus huius figur&aelig;, <figure id="fig22"/>, deinde <lb/>tertius binarius ducitur in pr&aelig;dictum quadratum 4. &amp; pro&shy;<lb/>ducitur 8. qui dicitur cubus, quia &longs;i intelligantur duo qua&shy;<lb/>zerna<gap/>ij, vnus &longs;upra alterum, vt in pr&aelig;&longs;enti figura refe&shy;<lb/>runt cubicam figuram, cuius tam longitudo, quam latitudo, <pb pagenum="53"/>&amp; altitudo, e&longs;t 2. Similiter cubus numerus e&longs;t 27. quia &longs;it ex tribus terna&shy;<lb/>rijs inuicem modo pr&aelig;dicto multiplicatis, 3. 3. 3. nam 3. in 3. ductis &longs;it 9. <lb/><figure id="fig23"/><lb/>qui e&longs;t quadratus. </s>
  
 <s>quo deinde ducto in tertium ter&shy;<lb/>narium, producitur 27. qui e&longs;t cubus, &amp; refert &longs;igu&shy;<lb/>ram cubicam hanc. </s> <s>quo deinde ducto in tertium ter&shy;<lb/>narium, producitur 27. qui e&longs;t cubus, &amp; refert &longs;igu&shy;<lb/>ram cubicam hanc. </s>
  
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 <s>Quod pr&aelig;terea hoc loco intelligendi &longs;int cubi arith&shy;<lb/>metici cert&ograve; certius con&longs;tat, ex &longs;equenti 24. textu, vbi &longs;ic dicitur <emph type="italics"/>(Veluti <lb/>Arithmetica quidem, quid impar, aut par, aut quadrangulum, aut cubus.)<emph.end type="italics"/></s></p><p type="main"> <s>Quod pr&aelig;terea hoc loco intelligendi &longs;int cubi arith&shy;<lb/>metici cert&ograve; certius con&longs;tat, ex &longs;equenti 24. textu, vbi &longs;ic dicitur <emph type="italics"/>(Veluti <lb/>Arithmetica quidem, quid impar, aut par, aut quadrangulum, aut cubus.)<emph.end type="italics"/></s></p><p type="main">
  
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 <s>Ibidem <emph type="italics"/>(<expan abbr="Neq;">Neque</expan> alij &longs;cienti&aelig; quod alterius, ni&longs;i <expan abbr="qu&aelig;cunq;">qu&aelig;cunque</expan> ita &longs;e habent inter &longs;e, <lb/>vt &longs;it alterum &longs;ub altero, vt per&longs;pectiua ad Geometriam, &amp; harmonica ad Arith&shy;<lb/>meticam)<emph.end type="italics"/> excipit ab illa regula (qua prohibetur, quamuis &longs;cientiam in alie&shy;<lb/>nam falcem immittere) &longs;cientias &longs;ubalternatas, qu&aelig; propri&egrave; in Mathemati&shy;<lb/>cis reperiuntur, Per&longs;pectiua enim propri&egrave; &longs;ubalternatur Geometri&aelig;, quia <lb/>vtitur Demon&longs;trationibus linearibus, quas applicat lineis vi&longs;ualibus, &amp; Mu&shy;<lb/>&longs;ica &longs;ubalternatur Arithmetic&aelig;, quia ab ip&longs;a mutuatur <expan abbr="dem&otilde;&longs;trationes">demon&longs;trationes</expan> nu&shy;<lb/>merorum, quas applicat numeris &longs;onoris. </s> <s>Ibidem <emph type="italics"/>(<expan abbr="Neq;">Neque</expan> alij &longs;cienti&aelig; quod alterius, ni&longs;i <expan abbr="qu&aelig;cunq;">qu&aelig;cunque</expan> ita &longs;e habent inter &longs;e, <lb/>vt &longs;it alterum &longs;ub altero, vt per&longs;pectiua ad Geometriam, &amp; harmonica ad Arith&shy;<lb/>meticam)<emph.end type="italics"/> excipit ab illa regula (qua prohibetur, quamuis &longs;cientiam in alie&shy;<lb/>nam falcem immittere) &longs;cientias &longs;ubalternatas, qu&aelig; propri&egrave; in Mathemati&shy;<lb/>cis reperiuntur, Per&longs;pectiua enim propri&egrave; &longs;ubalternatur Geometri&aelig;, quia <lb/>vtitur Demon&longs;trationibus linearibus, quas applicat lineis vi&longs;ualibus, &amp; Mu&shy;<lb/>&longs;ica &longs;ubalternatur Arithmetic&aelig;, quia ab ip&longs;a mutuatur <expan abbr="dem&otilde;&longs;trationes">demon&longs;trationes</expan> nu&shy;<lb/>merorum, quas applicat numeris &longs;onoris. </s>
  
 <s>v.g. </s> <s>v.g. </s>
  
 <s>Per&longs;pectiua dicit, ea, qu&aelig; vi&shy;<lb/>dentur eminus videri minora, quam qu&aelig; videntur cominus, quia illa viden&shy;<lb/>tur &longs;ub angulo minori, h&aelig;c ver&ograve; &longs;ub angulo maiori, quod ver&ograve; remotiora <lb/>videantur &longs;ub angulo minori, quam propinquiora c&aelig;teris paribus probat <lb/><figure id="fig24"></figure><lb/>per 21. primi Elem. </s> <s>Per&longs;pectiua dicit, ea, qu&aelig; vi&shy;<lb/>dentur eminus videri minora, quam qu&aelig; videntur cominus, quia illa viden&shy;<lb/>tur &longs;ub angulo minori, h&aelig;c ver&ograve; &longs;ub angulo maiori, quod ver&ograve; remotiora <lb/>videantur &longs;ub angulo minori, quam propinquiora c&aelig;teris paribus probat <lb/><figure id="fig24"/><lb/>per 21. primi Elem.
  
 <s>&longs;it enim ma&shy;<lb/>gnitudo vi&longs;a A B, remotior ab o&shy;<lb/>culo in C, po&longs;ito, &amp; vi&longs;a propin&shy;<lb/>quior ab oculo in D. ductis lineis <lb/>vi&longs;ualibus C A, C B: D A, D B; ab <lb/>oculis C, &amp; D, ad extremitates <lb/>&longs;pectat&aelig; magnitudinis, erit remo&shy;<lb/>tioris vi&longs;ionis angulus C, minor <lb/>angulo D, propinquioris, vt ex pr&aelig;allegata Demon&longs;tratione pater. </s> &longs;it enim ma&shy;<lb/>gnitudo vi&longs;a A B, remotior ab o&shy;<lb/>culo in C, po&longs;ito, &amp; vi&longs;a propin&shy;<lb/>quior ab oculo in D. ductis lineis <lb/>vi&longs;ualibus C A, C B: D A, D B; ab <lb/>oculis C, &amp; D, ad extremitates <lb/>&longs;pectat&aelig; magnitudinis, erit remo&shy;<lb/>tioris vi&longs;ionis angulus C, minor <lb/>angulo D, propinquioris, vt ex pr&aelig;allegata Demon&longs;tratione pater. </s>
  
 <s>Hine <lb/>per&longs;picu&egrave; vides, qua ratione Per&longs;pectiua Geometri&aelig; &longs;ubalternetur, &longs;iue <lb/>quid &longs;it ip&longs;a &longs;ubalternatio, vbi medium e&longs;t Geometricum, conclu&longs;io autem <lb/>optica. </s> <s>Hine <lb/>per&longs;picu&egrave; vides, qua ratione Per&longs;pectiua Geometri&aelig; &longs;ubalternetur, &longs;iue <lb/>quid &longs;it ip&longs;a &longs;ubalternatio, vbi medium e&longs;t Geometricum, conclu&longs;io autem <lb/>optica. </s>
  
 <s>Exemplum &longs;ubalternationis Mufic&aelig; &longs;it, <expan abbr="con&longs;on&atilde;tia">con&longs;onantia</expan> Diapa&longs;on, quam <lb/>vulg&ograve; octauam appellant in data chorda collocare, hoc e&longs;t, vocem grauio&shy;<lb/>rem facere duplam vocis acutioris &longs;umatur chorda A B, &amp; diuidatur bifa&shy;<lb/>riam, &longs;ine in &aelig;qualia in C; tota igitur chorda A B, ad dimidium A C, haber <pb pagenum="54"/><figure id="fig25"></figure><lb/>proportionem, quam 2. ad 1. <lb/>&longs;iue duplam, ergo etiam &longs;o&shy;<lb/>nus totius chord&aelig; A B, ad <expan abbr="&longs;o-n&utilde;">&longs;o&shy;<lb/>num</expan> chord&aelig; dimidi&aelig; A C, ha&shy;<lb/>bebit eandem rationem, <expan abbr="nimir&utilde;">nimirum</expan> quam 2. ad 1. &longs;iue duplam. </s> <s>Exemplum &longs;ubalternationis Mufic&aelig; &longs;it, <expan abbr="con&longs;on&atilde;tia">con&longs;onantia</expan> Diapa&longs;on, quam <lb/>vulg&ograve; octauam appellant in data chorda collocare, hoc e&longs;t, vocem grauio&shy;<lb/>rem facere duplam vocis acutioris &longs;umatur chorda A B, &amp; diuidatur bifa&shy;<lb/>riam, &longs;ine in &aelig;qualia in C; tota igitur chorda A B, ad dimidium A C, haber <pb pagenum="54"/><figure id="fig25"/><lb/>proportionem, quam 2. ad 1. <lb/>&longs;iue duplam, ergo etiam &longs;o&shy;<lb/>nus totius chord&aelig; A B, ad <expan abbr="&longs;o-n&utilde;">&longs;o&shy;<lb/>num</expan> chord&aelig; dimidi&aelig; A C, ha&shy;<lb/>bebit eandem rationem, <expan abbr="nimir&utilde;">nimirum</expan> quam 2. ad 1. &longs;iue duplam. </s>
  
 <s>&longs;ed &longs;onus chor&shy;<lb/>d&aelig; A B, ad &longs;onum chord&aelig; A C, con&longs;onat diapa&longs;on, &longs;eu octauam, ergo in <lb/>data chorda collocata e&longs;t con&longs;onantia diapa&longs;on, quod oportebat. </s> <s>&longs;ed &longs;onus chor&shy;<lb/>d&aelig; A B, ad &longs;onum chord&aelig; A C, con&longs;onat diapa&longs;on, &longs;eu octauam, ergo in <lb/>data chorda collocata e&longs;t con&longs;onantia diapa&longs;on, quod oportebat. </s>
  
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 <s>de&longs;umptum e&longs;t ex Boetio.</s></p><p type="main"> <s>de&longs;umptum e&longs;t ex Boetio.</s></p><p type="main">
  
 <s><arrow.to.target n="marg35"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg35"/></s></p><p type="margin">
  
 <s><margin.target id="marg35"></margin.target>35</s></p><p type="main"> 
  
 <s>Tex. </s> <s><margin.target id="marg35"/>35</s></p><p type="main">
  
 <s>23. <emph type="italics"/>(Est autem &longs;ic mon&longs;trare, quemadmodum Bry&longs;o quadraturam, &longs;ecun&shy;<lb/>dum enim commune mon&longs;trant tales rationes)<emph.end type="italics"/> cum velit e&longs;tendere veram de&shy;<lb/>mon&longs;trationem con&longs;tare debere ex proprijs, non autem ex communibus; <lb/>primum affert exemplum demon&longs;trationis cuiu&longs;dam Bry&longs;onis, qu&aelig; ex com&shy;<lb/>munibus procedat, vt autem ben&egrave; intelligamus, quale&longs;nam &longs;int huin&longs;modi <lb/>demon&longs;trationes, qu&aelig; per communia o&longs;tendunt, legenda prius ea &longs;unt, qu&aelig; <lb/>&longs;crip&longs;imus de quadratura circuli in pr&ecedil;dicamento relationis. </s> <s>Tex. 23. <emph type="italics"/>(Est autem &longs;ic mon&longs;trare, quemadmodum Bry&longs;o quadraturam, &longs;ecun&shy;<lb/>dum enim commune mon&longs;trant tales rationes)<emph.end type="italics"/> cum velit e&longs;tendere veram de&shy;<lb/>mon&longs;trationem con&longs;tare debere ex proprijs, non autem ex communibus; <lb/>primum affert exemplum demon&longs;trationis cuiu&longs;dam Bry&longs;onis, qu&aelig; ex com&shy;<lb/>munibus procedat, vt autem ben&egrave; intelligamus, quale&longs;nam &longs;int huin&longs;modi <lb/>demon&longs;trationes, qu&aelig; per communia o&longs;tendunt, legenda prius ea &longs;unt, qu&aelig; <lb/>&longs;crip&longs;imus de quadratura circuli in pr&ecedil;dicamento relationis. </s>
  
 <s>Bry&longs;o itaque, <lb/>vt tradit Alexander, in hunc modum conabatur quadrare <expan abbr="circul&utilde;">circulum</expan>. </s> <s>Bry&longs;o itaque, <lb/>vt tradit Alexander, in hunc modum conabatur quadrare <expan abbr="circul&utilde;">circulum</expan>. </s>
  
 <s>&longs;it qua&shy;<lb/>drandus circulus A B C D, cui circum&longs;eribatur quadratum E F G H. per <lb/>7 quarti, &amp; alterum quadratum I L M N, eidem in&longs;cribatur per 6. quarti, <lb/>quid autem &longs;it circum&longs;cribere, &amp; in&longs;cribere figuram circulo, ex definitione <lb/><figure id="fig26"></figure><lb/>3. &amp; 4. eiu&longs;dem libri petatur, quamuis <lb/>ex in&longs;pectione figur&aelig; <expan abbr="pr&ecedil;s&etilde;tis">pr&ecedil;sentis</expan> &longs;atis per&shy;<lb/>cipi po&longs;&longs;it; deinde aliud <expan abbr="quadrat&utilde;">quadratum</expan> me&shy;<lb/>dium inter pr&aelig;dicta duo con&longs;tituatur, <lb/><expan abbr="&longs;it&qacute;">&longs;itque</expan>; O P Q R. </s> <s>&longs;it qua&shy;<lb/>drandus circulus A B C D, cui circum&longs;eribatur quadratum E F G H. per <lb/>7 quarti, &amp; alterum quadratum I L M N, eidem in&longs;cribatur per 6. quarti, <lb/>quid autem &longs;it circum&longs;cribere, &amp; in&longs;cribere figuram circulo, ex definitione <lb/><figure id="fig26"/><lb/>3. &amp; 4. eiu&longs;dem libri petatur, quamuis <lb/>ex in&longs;pectione figur&aelig; <expan abbr="pr&ecedil;s&etilde;tis">pr&ecedil;sentis</expan> &longs;atis per&shy;<lb/>cipi po&longs;&longs;it; deinde aliud <expan abbr="quadrat&utilde;">quadratum</expan> me&shy;<lb/>dium inter pr&aelig;dicta duo con&longs;tituatur, <lb/><expan abbr="&longs;it&qacute;">&longs;itque</expan>; O P Q R. </s>
  
 <s>Iam &longs;ic o&longs;tendebat i&longs;tud <lb/>medium quadratum e&longs;&longs;e &aelig;quale circu&shy;<lb/>lo propo&longs;ito. </s> <s>Iam &longs;ic o&longs;tendebat i&longs;tud <lb/>medium quadratum e&longs;&longs;e &aelig;quale circu&shy;<lb/>lo propo&longs;ito. </s>
  
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 <s>pr&aelig;terea aduertendum e&longs;t, illud e&longs;&longs;e fal&longs;um, nam &longs;ex, <lb/>&amp; quinque, ambo &longs;unt maiores, quam quatuor, &amp; minores, quam &longs;eptem, <lb/>&amp; tamen non &longs;unt &aelig;quales.</s></p><p type="main"> <s>pr&aelig;terea aduertendum e&longs;t, illud e&longs;&longs;e fal&longs;um, nam &longs;ex, <lb/>&amp; quinque, ambo &longs;unt maiores, quam quatuor, &amp; minores, quam &longs;eptem, <lb/>&amp; tamen non &longs;unt &aelig;quales.</s></p><p type="main">
  
 <s><arrow.to.target n="marg36"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg36"/></s></p><p type="margin">
  
 <s><margin.target id="marg36"></margin.target>36</s></p><p type="main"> <s><margin.target id="marg36"/>36</s></p><p type="main">
  
 <s>In codem textu <emph type="italics"/>(<expan abbr="Vnumquodq;">Vnumquodque</expan> autem &longs;cimus, non &longs;ecundum accidens, quando <lb/>&longs;ecundum illud cogno&longs;camus, &longs;ecundum quod ine&longs;t ex principijs illius, &longs;ecundam <lb/>quod illud; vt duobus rectis &aelig;quales, habere, cui ine&longs;t per &longs;e, quod dictum e&longs;t ex<emph.end type="italics"/><pb pagenum="55"/><emph type="italics"/>principijs huius)<emph.end type="italics"/> affert nunc exemplum alterius demon&longs;trationis, qu&aelig; non <lb/>ex communibus, vt pr&aelig;cedens Bry&longs;onis, &longs;ed ex proprijs principijs o&longs;tendit <lb/>affectionem de &longs;ubiecto proprio. </s> <s>In codem textu <emph type="italics"/>(<expan abbr="Vnumquodq;">Vnumquodque</expan> autem &longs;cimus, non &longs;ecundum accidens, quando <lb/>&longs;ecundum illud cogno&longs;camus, &longs;ecundum quod ine&longs;t ex principijs illius, &longs;ecundam <lb/>quod illud; vt duobus rectis &aelig;quales, habere, cui ine&longs;t per &longs;e, quod dictum e&longs;t ex<emph.end type="italics"/><pb pagenum="55"/><emph type="italics"/>principijs huius)<emph.end type="italics"/> affert nunc exemplum alterius demon&longs;trationis, qu&aelig; non <lb/>ex communibus, vt pr&aelig;cedens Bry&longs;onis, &longs;ed ex proprijs principijs o&longs;tendit <lb/>affectionem de &longs;ubiecto proprio. </s>
  
 <s>E&longs;t autem illud exemplum toties decan&shy;<lb/>tatum de triangulo habente tres angulos &aelig;quales duobus rectis angulis; id&shy;<lb/>circo oper&aelig;pretium e&longs;&longs;e puto explicare demon&longs;trationem, 32. primi Eucli&shy;<lb/>dis, qu&aelig; i&longs;tud ex proprijs principijs demon&longs;trat, &amp; quam hoc loco Ari&longs;to&shy;<lb/>teles innuit, hoc enim modo ip&longs;ius Ari&longs;t.  <s>E&longs;t autem illud exemplum toties decan&shy;<lb/>tatum de triangulo habente tres angulos &aelig;quales duobus rectis angulis; id&shy;<lb/>circo oper&aelig;pretium e&longs;&longs;e puto explicare demon&longs;trationem, 32. primi Eucli&shy;<lb/>dis, qu&aelig; i&longs;tud ex proprijs principijs demon&longs;trat, &amp; quam hoc loco Ari&longs;to&shy;<lb/>teles innuit, hoc enim modo ip&longs;ius Ari&longs;t.
  
 mentem prob&egrave; penetrare poteri&shy;<lb/><figure id="fig27"></figure><lb/>mus. </s> mentem prob&egrave; penetrare poteri&shy;<lb/><figure id="fig27"/><lb/>mus. </s>
  
 <s>&longs;it ergo <expan abbr="tri&atilde;gulum">triangulum</expan> A B C. </s> <s>&longs;it ergo <expan abbr="tri&atilde;gulum">triangulum</expan> A B C. <!-- KEEP S--></s>
  
 <s>Dico ag&shy;<lb/>gregatum <expan abbr="tri&utilde;">trium</expan> ip&longs;ius angulorum A, B, C, <lb/>e&longs;&longs;e &aelig;quale aggregato ex duobus angu&shy;<lb/>lis rectis (vt autem melius intelligas, qu&aelig; <lb/>&longs;equuntur, lege prius ea, qu&aelig; dicta &longs;unt <lb/>in lib. </s> <s>Dico ag&shy;<lb/>gregatum <expan abbr="tri&utilde;">trium</expan> ip&longs;ius angulorum A, B, C, <lb/>e&longs;&longs;e &aelig;quale aggregato ex duobus angu&shy;<lb/>lis rectis (vt autem melius intelligas, qu&aelig; <lb/>&longs;equuntur, lege prius ea, qu&aelig; dicta &longs;unt <lb/>in lib.
  
 <s>1. Priorum &longs;ecto 3. cap. </s> 1. Priorum &longs;ecto 3. cap.
  
 <s>1.) produ&shy;<lb/>catur latus B C, <expan abbr="v&longs;q;">v&longs;que</expan> in D, vt fiat angulus <lb/>externus A C D; Iam &longs;ic, quoniam <expan abbr="pro-bat&utilde;">pro&shy;<lb/>batum</expan> e&longs;t in 13. primi, duos angulos, quos <lb/>facit linea A C, cum linea B D, &longs;cilicet angulos A C B, A C D, e&longs;&longs;e pares <lb/>duobus rectis: &amp; quia pariter in prima parte huins propo&longs;. </s> 1.) produ&shy;<lb/>catur latus B C, <expan abbr="v&longs;q;">v&longs;que</expan> in D, vt fiat angulus <lb/>externus A C D; Iam &longs;ic, quoniam <expan abbr="pro-bat&utilde;">pro&shy;<lb/>batum</expan> e&longs;t in 13. primi, duos angulos, quos <lb/>facit linea A C, cum linea B D, &longs;cilicet angulos A C B, A C D, e&longs;&longs;e pares <lb/>duobus rectis: &amp; quia pariter in prima parte huins propo&longs;. </s>
  
 <s>32. probatum <lb/>e&longs;t ab Euclide duos angulos A B, e&longs;&longs;e &aelig;quales externo angulo A C D: &longs;i ter&shy;<lb/>tius angulus reliquus A C B, &longs;umatur bis, &longs;emel cum duobus angulis A, B, <lb/>&amp; &longs;emel cum externo A C D, <expan abbr="add&etilde;tur">addentur</expan> &aelig;qualia &aelig;qualibus, &amp; propterea tres <lb/>anguli A, B, A C B, &longs;imul &longs;umpti, erunt &aelig;quales duobus A C D, A C B, &longs;imul <lb/>&longs;umptis; &longs;ed his duobus &longs;unt &aelig;quales duo recti, ergo cum qu&aelig; &longs;unt &aelig;qualia <lb/>vni tertio, &longs;int etiam &aelig;qualia inuicem, erit aggregatum trium angulorum <lb/>A, B, A C B, &aelig;quale aggregato duorum rectorum; quod erat demon&longs;tran&shy;<lb/>dum. </s> <s>32. probatum <lb/>e&longs;t ab Euclide duos angulos A B, e&longs;&longs;e &aelig;quales externo angulo A C D: &longs;i ter&shy;<lb/>tius angulus reliquus A C B, &longs;umatur bis, &longs;emel cum duobus angulis A, B, <lb/>&amp; &longs;emel cum externo A C D, <expan abbr="add&etilde;tur">addentur</expan> &aelig;qualia &aelig;qualibus, &amp; propterea tres <lb/>anguli A, B, A C B, &longs;imul &longs;umpti, erunt &aelig;quales duobus A C D, A C B, &longs;imul <lb/>&longs;umptis; &longs;ed his duobus &longs;unt &aelig;quales duo recti, ergo cum qu&aelig; &longs;unt &aelig;qualia <lb/>vni tertio, &longs;int etiam &aelig;qualia inuicem, erit aggregatum trium angulorum <lb/>A, B, A C B, &aelig;quale aggregato duorum rectorum; quod erat demon&longs;tran&shy;<lb/>dum. </s>
  
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 <s>eiu&longs;dem recitat.</s></p><p type="main"> <s>eiu&longs;dem recitat.</s></p><p type="main">
  
 <s><arrow.to.target n="marg37"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg37"/></s></p><p type="margin">
  
 <s><margin.target id="marg37"></margin.target>37</s></p><p type="main"> <s><margin.target id="marg37"/>37</s></p><p type="main">
  
 <s>Ibidem <emph type="italics"/>(Sed quemadmod&ubreve; harmonica per Arithmeticam)<emph.end type="italics"/> vide &longs;upra tex. </s> <s>Ibidem <emph type="italics"/>(Sed quemadmod&ubreve; harmonica per Arithmeticam)<emph.end type="italics"/> vide &longs;upra tex. </s>
  
 <s>20.</s></p><p type="main"> <s>20.</s></p><p type="main">
  
 <s><arrow.to.target n="marg38"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg38"/></s></p><p type="margin">
  
 <s><margin.target id="marg38"></margin.target>38</s></p><p type="main"> <s><margin.target id="marg38"/>38</s></p><p type="main">
  
 <s>Ibidem <emph type="italics"/>(Demon&longs;tratio autem non computatur in aliud genus; m&longs;i, vt dictum <lb/>e&longs;t geometric&aelig; demon&longs;trationes in Per&longs;pectiuas, aut Mcchamcas, &amp; arithmetic&aelig; in <lb/>harmonicas)<emph.end type="italics"/> exempla &longs;ubalternationis Per&longs;pectiu&aelig;, &amp; Mu&longs;ic&aelig; in tex. </s> <s>Ibidem <emph type="italics"/>(Demon&longs;tratio autem non computatur in aliud genus; m&longs;i, vt dictum <lb/>e&longs;t geometric&aelig; demon&longs;trationes in Per&longs;pectiuas, aut Mcchamcas, &amp; arithmetic&aelig; in <lb/>harmonicas)<emph.end type="italics"/> exempla &longs;ubalternationis Per&longs;pectiu&aelig;, &amp; Mu&longs;ic&aelig; in tex. </s>
  
 <s>20. at&shy;<lb/>tulimus; nunc Mechanic&aelig; &longs;ubalternationis, quam hic Ari&longs;t.  <s>20. at&shy;<lb/>tulimus; nunc Mechanic&aelig; &longs;ubalternationis, quam hic Ari&longs;t.
  
 in&longs;inuat, exem&shy;<lb/>plum &longs;it illud, quod Archimedes prop. </s> in&longs;inuat, exem&shy;<lb/>plum &longs;it illud, quod Archimedes prop.
  
 <s>14. primi Aequep. </s> 14. primi Aequep. </s>
  
 <s>demon&longs;trat, ni&shy;<lb/>mirum centrum grauitatis omnis trianguli e&longs;&longs;e punctum illud, in quo rect&aelig; <lb/>line&aelig; ab angulis trianguli ad dimidia latera oppo&longs;ita duct&aelig; concurrunt. </s> <s>demon&longs;trat, ni&shy;<lb/>mirum centrum grauitatis omnis trianguli e&longs;&longs;e punctum illud, in quo rect&aelig; <lb/>line&aelig; ab angulis trianguli ad dimidia latera oppo&longs;ita duct&aelig; concurrunt. </s>
  
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 <s>Quoniam enim in 13. <lb/>Aequep. </s> <s>Quoniam enim in 13. <lb/>Aequep. </s>
  
 <s>probauit centrum grauitatis e&longs;&longs;e in ea linea, qu&aelig; ducta ab angulo <lb/>quouis &longs;ecat oppo&longs;itum latus bifariam, crit in linea A D, <expan abbr="centr&utilde;">centrum</expan> grauitatis. <pb pagenum="57"/><figure id="fig28"></figure><lb/>&longs;ed eadem ratione erit etiam in linea B E, er&shy;<lb/>go non ni&longs;i in puncto F, quod <expan abbr="&longs;ol&utilde;">&longs;olum</expan> e&longs;t in vtra&shy;<lb/>que, quod erat demon&longs;trandum. </s> <s>probauit centrum grauitatis e&longs;&longs;e in ea linea, qu&aelig; ducta ab angulo <lb/>quouis &longs;ecat oppo&longs;itum latus bifariam, crit in linea A D, <expan abbr="centr&utilde;">centrum</expan> grauitatis. <pb pagenum="57"/><figure id="fig28"/><lb/>&longs;ed eadem ratione erit etiam in linea B E, er&shy;<lb/>go non ni&longs;i in puncto F, quod <expan abbr="&longs;ol&utilde;">&longs;olum</expan> e&longs;t in vtra&shy;<lb/>que, quod erat demon&longs;trandum. </s>
  
 <s>ex quibus ap&shy;<lb/>paret, qua ratione mechanica conclu&longs;io Geo&shy;<lb/>metri&aelig; &longs;ubiaceat, dum lineari di&longs;cur&longs;u ip&longs;a <lb/>demon&longs;tratio perficitur. </s> <s>ex quibus ap&shy;<lb/>paret, qua ratione mechanica conclu&longs;io Geo&shy;<lb/>metri&aelig; &longs;ubiaceat, dum lineari di&longs;cur&longs;u ip&longs;a <lb/>demon&longs;tratio perficitur. </s>
  
 <s>Scias pr&aelig;terea cen&shy;<lb/>trum grauitatis e&longs;&longs;e tale punctum, ex quo &longs;i &longs;u&shy;<lb/>&longs;pendatur corpus triangulare vniformis cra&longs;&shy;<lb/>&longs;itici, manet &longs;emper horizonti parallelum, &longs;i <lb/>tamen antequam &longs;u&longs;penderetur, iacebat plano horizontis, &aelig;quidi&longs;tans; <lb/><expan abbr="neq;">neque</expan> &longs;i &longs;u&longs;pen&longs;um feratur huc illud nutat, &longs;ed &longs;emper in <expan abbr="cod&etilde;">codem</expan> &longs;itu per&longs;euerat.</s></p><p type="main"> <s>Scias pr&aelig;terea cen&shy;<lb/>trum grauitatis e&longs;&longs;e tale punctum, ex quo &longs;i &longs;u&shy;<lb/>&longs;pendatur corpus triangulare vniformis cra&longs;&shy;<lb/>&longs;itici, manet &longs;emper horizonti parallelum, &longs;i <lb/>tamen antequam &longs;u&longs;penderetur, iacebat plano horizontis, &aelig;quidi&longs;tans; <lb/><expan abbr="neq;">neque</expan> &longs;i &longs;u&longs;pen&longs;um feratur huc illud nutat, &longs;ed &longs;emper in <expan abbr="cod&etilde;">codem</expan> &longs;itu per&longs;euerat.</s></p><p type="main">
  
 <s><arrow.to.target n="marg39"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg39"/></s></p><p type="margin">
  
 <s><margin.target id="marg39"></margin.target>39</s></p><p type="main"> 
  
 <s>Tex. </s> <s><margin.target id="marg39"/>39</s></p><p type="main">
  
 <s>24. <emph type="italics"/>(Veluti Arithmetica quidem quid impar, aut par; aut quadrangu&shy;<lb/>lum, aut cubus)<emph.end type="italics"/> cogno&longs;cas hinc cert&ograve; certius quadrangulum, &amp; cubum e&longs;&longs;e <lb/>&longs;pecies numerorum, &longs;icuti &longs;upra tex. </s> <s>Tex. 24. <emph type="italics"/>(Veluti Arithmetica quidem quid impar, aut par; aut quadrangu&shy;<lb/>lum, aut cubus)<emph.end type="italics"/> cogno&longs;cas hinc cert&ograve; certius quadrangulum, &amp; cubum e&longs;&longs;e <lb/>&longs;pecies numerorum, &longs;icuti &longs;upra tex. </s>
  
 <s>9. &amp; 20. explicauimus, qu&ograve; nunc te vi&shy;<lb/>ci&longs;&longs;im, vt pr&aelig;&longs;entem locum intelligas, remittimus.</s></p><p type="main"> <s>9. &amp; 20. explicauimus, qu&ograve; nunc te vi&shy;<lb/>ci&longs;&longs;im, vt pr&aelig;&longs;entem locum intelligas, remittimus.</s></p><p type="main">
  
 <s><arrow.to.target n="marg40"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg40"/></s></p><p type="margin">
  
 <s><margin.target id="marg40"></margin.target>40</s></p><p type="main"> <s><margin.target id="marg40"/>40</s></p><p type="main">
  
 <s>Ibidem <emph type="italics"/>(Geometrica ver&ograve; quid irrationale, aut refrangi, aut concurrere)<emph.end type="italics"/> per <lb/>verbum, irrationale, non videtur Ari&longs;t.  <s>Ibidem <emph type="italics"/>(Geometrica ver&ograve; quid irrationale, aut refrangi, aut concurrere)<emph.end type="italics"/> per <lb/>verbum, irrationale, non videtur Ari&longs;t.
  
 intellexi&longs;&longs;e proprietatem illam duo&shy;<lb/>rum linearum incommen&longs;urabilium longitudine, &amp; potentia, quia v&longs;us fui&longs;&shy;<lb/>&longs;et verbo, <foreign lang="greek">a/rrpton.</foreign> quod apud Geometras v&longs;urpari &longs;olet in illa &longs;ignificatio&shy;<lb/>ne, &longs;ed v&longs;us e&longs;t verbo, <foreign lang="greek">a\logon,</foreign> quod latin&egrave; redditur improportionale.</s></p><p type="main"> intellexi&longs;&longs;e proprietatem illam duo&shy;<lb/>rum linearum incommen&longs;urabilium longitudine, &amp; potentia, quia v&longs;us fui&longs;&shy;<lb/>&longs;et verbo, <foreign lang="greek">a/rrpton.</foreign> quod apud Geometras v&longs;urpari &longs;olet in illa &longs;ignificatio&shy;<lb/>ne, &longs;ed v&longs;us e&longs;t verbo, <foreign lang="greek">a\logon,</foreign> quod latin&egrave; redditur improportionale.</s></p><p type="main">
  
 <s><arrow.to.target n="marg41"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg41"/></s></p><p type="margin">
  
 <s><margin.target id="marg41"></margin.target>41</s></p><p type="main"> <s><margin.target id="marg41"/>41</s></p><p type="main">
  
 <s>Per verbum <emph type="italics"/>(Refrangi)<emph.end type="italics"/> &longs;eu frangi, intelligit lineam aliquam rectam, non <lb/>in directum rendere, &longs;ed in aliquo puncto frangi, &longs;eu declinari &agrave; rectitudine, <lb/>ita vt con&longs;tituat angulum.</s></p><p type="main"> <s>Per verbum <emph type="italics"/>(Refrangi)<emph.end type="italics"/> &longs;eu frangi, intelligit lineam aliquam rectam, non <lb/>in directum rendere, &longs;ed in aliquo puncto frangi, &longs;eu declinari &agrave; rectitudine, <lb/>ita vt con&longs;tituat angulum.</s></p><p type="main">
  
 <s>Per verbum <emph type="italics"/>(Concurrere)<emph.end type="italics"/> intelligit, non e&longs;&longs;e parallelas, &longs;ed ad idem ali&shy;<lb/>quod punctum coire, &longs;i protrahantur.</s></p><p type="main"> <s>Per verbum <emph type="italics"/>(Concurrere)<emph.end type="italics"/> intelligit, non e&longs;&longs;e parallelas, &longs;ed ad idem ali&shy;<lb/>quod punctum coire, &longs;i protrahantur.</s></p><p type="main">
  
 <s><arrow.to.target n="marg42"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg42"/></s></p><p type="margin">
  
 <s><margin.target id="marg42"></margin.target>42</s></p><p type="main"> <s><margin.target id="marg42"/>42</s></p><p type="main">
  
 <s>Ibidem <emph type="italics"/>(Et Astrologia &longs;imiliter)<emph.end type="italics"/> per A&longs;trologiam intelligit Ari&longs;t.  <s>Ibidem <emph type="italics"/>(Et Astrologia &longs;imiliter)<emph.end type="italics"/> per A&longs;trologiam intelligit Ari&longs;t.
  
 non iu&shy;<lb/>diciariam, quamuis &agrave; recentioribus hoc nomine vocetur, &longs;ed quam hodie <lb/>dicunt A&longs;tronomiam, <expan abbr="ait&qacute;">aitque</expan>; ip&longs;am con&longs;iderare quantitatem, figuram, mo&shy;<lb/>tum, &amp; locum totius Mundi, ac partium ip&longs;ius integrantium, vt &longs;unt C&oelig;li, <lb/>&amp; Elementa.</s></p><p type="main"> non iu&shy;<lb/>diciariam, quamuis &agrave; recentioribus hoc nomine vocetur, &longs;ed quam hodie <lb/>dicunt A&longs;tronomiam, <expan abbr="ait&qacute;">aitque</expan>; ip&longs;am con&longs;iderare quantitatem, figuram, mo&shy;<lb/>tum, &amp; locum totius Mundi, ac partium ip&longs;ius integrantium, vt &longs;unt C&oelig;li, <lb/>&amp; Elementa.</s></p><p type="main">
  
 <s><arrow.to.target n="marg43"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg43"/></s></p><p type="margin">
  
 <s><margin.target id="marg43"></margin.target>43</s></p><p type="main"> 
  
 <s>Tex. </s> 
  
 <s>25. <emph type="italics"/>(<expan abbr="Neq;">Neque</expan> Geometra fal&longs;a &longs;upponit, quemadmodum quidam a&longs;&longs;eruere di&shy;<lb/>centes, quod non oportet fal&longs;o vti: Geometram ver&ograve; mentiri dicentem pedalem, non <lb/>pedalem, aut rectam de&longs;criptam, non rectam <expan abbr="exist&etilde;tem">existentem</expan>: Geometra ver&ograve; nihil con&shy;<lb/>cludit e&ograve;, quod b&aelig;c e&longs;t linea, &longs;ed qu&aelig; per h&aelig;c e&longs;tenduntur)<emph.end type="italics"/> innuit his verbis eam <lb/>materiam intelligibilem, qu&aelig; e&longs;t &longs;ubiectum Geometri&aelig;: eam &longs;cilicet, qu&aelig; <lb/>&longs;ub figuris Geometricis &longs;en&longs;ibilibus, &amp; <expan abbr="plerunq;">plerunque</expan> fal&longs;is latet; nam &longs;&aelig;p&egrave; Geo&shy;<lb/>metra vtitur linea quadam &longs;en&longs;ibili pro recta, qu&aelig; ver&egrave; nec e&longs;t linea mathe&shy;<lb/>matica, nec recta; &longs;upponit aliquando talem lineam e&longs;&longs;e pedalem, qu&aelig; ve&shy;<lb/>r&egrave; non e&longs;t pedalis: Verumtamen non mentitur, quia re&longs;picit ad veram li&shy;<lb/>neam mathematicam, qu&aelig; &longs;ub illa intelligitur, &amp; qu&aelig; recta concipitur; &amp; <lb/>quidem h&aelig;c omnia ver&egrave; concipiuntur, quoniam ita e&longs;&longs;e re vera po&longs;&longs;unt.</s></p><p type="main"> 
  
 <s><arrow.to.target n="marg44"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg43"/>43</s></p><p type="main">
  
 <s><margin.target id="marg44"></margin.target>44</s></p><p type="main"> <s>Tex. 25. <emph type="italics"/>(<expan abbr="Neq;">Neque</expan> Geometra fal&longs;a &longs;upponit, quemadmodum quidam a&longs;&longs;eruere di&shy;<lb/>centes, quod non oportet fal&longs;o vti: Geometram ver&ograve; mentiri dicentem pedalem, non <lb/>pedalem, aut rectam de&longs;criptam, non rectam <expan abbr="exist&etilde;tem">existentem</expan>: Geometra ver&ograve; nihil con&shy;<lb/>cludit e&ograve;, quod b&aelig;c e&longs;t linea, &longs;ed qu&aelig; per h&aelig;c e&longs;tenduntur)<emph.end type="italics"/> innuit his verbis eam <lb/>materiam intelligibilem, qu&aelig; e&longs;t &longs;ubiectum Geometri&aelig;: eam &longs;cilicet, qu&aelig; <lb/>&longs;ub figuris Geometricis &longs;en&longs;ibilibus, &amp; <expan abbr="plerunq;">plerunque</expan> fal&longs;is latet; nam &longs;&aelig;p&egrave; Geo&shy;<lb/>metra vtitur linea quadam &longs;en&longs;ibili pro recta, qu&aelig; ver&egrave; nec e&longs;t linea mathe&shy;<lb/>matica, nec recta; &longs;upponit aliquando talem lineam e&longs;&longs;e pedalem, qu&aelig; ve&shy;<lb/>r&egrave; non e&longs;t pedalis: Verumtamen non mentitur, quia re&longs;picit ad veram li&shy;<lb/>neam mathematicam, qu&aelig; &longs;ub illa intelligitur, &amp; qu&aelig; recta concipitur; &amp; <lb/>quidem h&aelig;c omnia ver&egrave; concipiuntur, quoniam ita e&longs;&longs;e re vera po&longs;&longs;unt.</s></p><p type="main">
  
 <s>Tex. </s> <s><arrow.to.target n="marg44"/></s></p><p type="margin">
  
 <s>28. <emph type="italics"/>(Coaltern as ver&ograve; coincidere)<emph.end type="italics"/> per coalternas intelligendas e&longs;&longs;e pa&shy;<lb/>rallelas lineas, alias, &amp; nunc <expan abbr="quoq;">quoque</expan> monemus.</s></p><p type="main"> <s><margin.target id="marg44"/>44</s></p><p type="main">
  
 <s><arrow.to.target n="marg45"></arrow.to.target></s></p><p type="margin"> <s>Tex. 28. <emph type="italics"/>(Coaltern as ver&ograve; coincidere)<emph.end type="italics"/> per coalternas intelligendas e&longs;&longs;e pa&shy;<lb/>rallelas lineas, alias, &amp; nunc <expan abbr="quoq;">quoque</expan> monemus.</s></p><p type="main">
  
 <s><margin.target id="marg45"></margin.target>45</s></p><p type="main"> <s><arrow.to.target n="marg45"/></s></p><p type="margin">
  
 <s>Tex. </s> <s><margin.target id="marg45"/>45</s></p><p type="main">
  
 <s>29. <emph type="italics"/>(In Matbematicis ver&ograve; non est &longs;imiliter paralogi&longs;mus, quoniam me&shy;<lb/>di&ubreve; e&longs;t &longs;emper, quod duplex, de hoc enim omni, &amp; hoc rur&longs;us de alio dicitur omni)<emph.end type="italics"/><lb/>aduerte, quod quamuis nonnulli codices habeant pro, in mathematicis, in <pb pagenum="58"/>di&longs;cipli<gap/>is, idem tamen apud gr&aelig;cos <foreign lang="greek">maqhmata</foreign> &longs;unt, ac apud latinos di&longs;ci&shy;<lb/>plm&aelig;; verbum autem <foreign lang="greek">maqhmata</foreign> v&longs;urpat hoc loco Ari&longs;toteles. </s> <s>Tex. 29. <emph type="italics"/>(In Matbematicis ver&ograve; non est &longs;imiliter paralogi&longs;mus, quoniam me&shy;<lb/>di&ubreve; e&longs;t &longs;emper, quod duplex, de hoc enim omni, &amp; hoc rur&longs;us de alio dicitur omni)<emph.end type="italics"/><lb/>aduerte, quod quamuis nonnulli codices habeant pro, in mathematicis, in <pb pagenum="58"/>di&longs;cipli<gap/>is, idem tamen apud gr&aelig;cos <foreign lang="greek">maqhmata</foreign> &longs;unt, ac apud latinos di&longs;ci&shy;<lb/>plm&aelig;; verbum autem <foreign lang="greek">maqhmata</foreign> v&longs;urpat hoc loco Ari&longs;toteles. <!-- KEEP S--></s>
  
 <s>Porr&ograve; non <lb/>e&longs;t in mathematicis, &longs;icut in alijs paralogi&longs;mus, quia in omni demon&longs;tra&shy;<lb/>tione maius extremum dicitur de omni medio, &amp; rur&longs;us medium dicitur de <lb/>omni minori extremo, ac &longs;i diceret mathematic&aelig; demon&longs;trationes &longs;unt in <lb/>primo modo, qui barbar&egrave; &agrave; latinis recentioribus Barbara appellatur. </s> <s>Porr&ograve; non <lb/>e&longs;t in mathematicis, &longs;icut in alijs paralogi&longs;mus, quia in omni demon&longs;tra&shy;<lb/>tione maius extremum dicitur de omni medio, &amp; rur&longs;us medium dicitur de <lb/>omni minori extremo, ac &longs;i diceret mathematic&aelig; demon&longs;trationes &longs;unt in <lb/>primo modo, qui barbar&egrave; &agrave; latinis recentioribus Barbara appellatur. </s>
  
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 <s>In mathematicis, inquit, non accidit &longs;imiliter para&shy;<lb/>logi&longs;mus, ide&longs;t, tam frequenter, quemadmodum in &longs;yllogi&longs;mis dialecticis, <lb/>quia modus argumentandi mathematicarum e&longs;t perfecti&longs;&longs;imus, quippe in <lb/>primo modo prim&aelig; figur&aelig;.</s></p><p type="main"> <s>In mathematicis, inquit, non accidit &longs;imiliter para&shy;<lb/>logi&longs;mus, ide&longs;t, tam frequenter, quemadmodum in &longs;yllogi&longs;mis dialecticis, <lb/>quia modus argumentandi mathematicarum e&longs;t perfecti&longs;&longs;imus, quippe in <lb/>primo modo prim&aelig; figur&aelig;.</s></p><p type="main">
  
 <s><arrow.to.target n="marg46"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg46"/></s></p><p type="margin">
  
 <s><margin.target id="marg46"></margin.target>46</s></p><p type="main"> <s><margin.target id="marg46"/>46</s></p><p type="main">
  
 <s>Eodem tex. <emph type="italics"/>(Contingit autem quo&longs;dam non &longs;yllogi&longs;tic&egrave; dicere, &amp; quod ex vtri&longs;&shy;<lb/>que con&longs;equentia accipiunt, quemadmodum &amp; C&aelig;neus facit, quod ignis in multi&shy;<lb/>plici proportione: etenim ignis celeriter gignitur, vt ait: &amp; h&aelig;c est proportio. </s> <s>Eodem tex. <emph type="italics"/>(Contingit autem quo&longs;dam non &longs;yllogi&longs;tic&egrave; dicere, &amp; quod ex vtri&longs;&shy;<lb/>que con&longs;equentia accipiunt, quemadmodum &amp; C&aelig;neus facit, quod ignis in multi&shy;<lb/>plici proportione: etenim ignis celeriter gignitur, vt ait: &amp; h&aelig;c est proportio. </s>
  
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 <s>porr&ograve; quid inter multiplicem, &amp; multipli&shy;<lb/>catam rationem inter&longs;it, optim&egrave; declarat no&longs;ter Clauius ad 4. definit. </s> <s>porr&ograve; quid inter multiplicem, &amp; multipli&shy;<lb/>catam rationem inter&longs;it, optim&egrave; declarat no&longs;ter Clauius ad 4. definit. </s>
  
 <s>lib. </s> <s>lib.
  
 <s>5. <lb/>Elem.  5. <lb/>Elem.
  
 ex quo etiam loco pauca decerpam, qu&aelig; huic loco declarando con&shy;<lb/>ducunt. </s> ex quo etiam loco pauca decerpam, qu&aelig; huic loco declarando con&shy;<lb/>ducunt. </s>
  
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 <s>argumentaba&shy;<lb/>tur igitur C&aelig;neus in hunc modum; quod in multiplici ratione augetur, ce&shy;<lb/>lerrim&egrave; augetur: ignis celerrim&egrave; augetur, ergo<gap/>gnis in multiplici ratione <lb/>augetur, qu&aelig; argumentatio vitio&longs;a e&longs;t, ex duabus quippe affirmatiuis in &longs;e&shy;<lb/>cunda figura procedens, vt colligitur ex verbis illis tex. <emph type="italics"/>(Ex viri&longs;que con&longs;e&shy;<lb/>quentia accipiunt<emph.end type="italics"/>) ex his mathematica huius locis patere &longs;atis po&longs;&longs;unt.</s></p><p type="main"> <s>argumentaba&shy;<lb/>tur igitur C&aelig;neus in hunc modum; quod in multiplici ratione augetur, ce&shy;<lb/>lerrim&egrave; augetur: ignis celerrim&egrave; augetur, ergo<gap/>gnis in multiplici ratione <lb/>augetur, qu&aelig; argumentatio vitio&longs;a e&longs;t, ex duabus quippe affirmatiuis in &longs;e&shy;<lb/>cunda figura procedens, vt colligitur ex verbis illis tex. <emph type="italics"/>(Ex viri&longs;que con&longs;e&shy;<lb/>quentia accipiunt<emph.end type="italics"/>) ex his mathematica huius locis patere &longs;atis po&longs;&longs;unt.</s></p><p type="main">
  
 <s><arrow.to.target n="marg47"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg47"/></s></p><p type="margin">
  
 <s><margin.target id="marg47"></margin.target>47</s></p><p type="main"> <s><margin.target id="marg47"/>47</s></p><p type="main">
  
 <s>Ibidem (<emph type="italics"/>Conuertuntur autem magis, qu&aelig;&longs;unt in mathematicis, quoniam nul&shy;<lb/>lum accidens accipiunt (m quo quidem ijs pr&aelig;&longs;t&abreve;t, qu&aelig; di&longs;putationibus traduntur) <lb/>&longs;ed definitiones<emph.end type="italics"/>) H&aelig;c e&longs;t altera mathematicarum laus, vnde earum quoque <lb/>pr&aelig;&longs;tantia elucet, quia &longs;cilicet mathematic&aelig; pro medijs vtuntur definitio&shy;<pb pagenum="59"/>nibus &longs;ubiecti, aut pa&longs;&longs;ionis, qu&aelig; nuilo modo &longs;unt accidentalia conclu&longs;ioni, <lb/>v. </s> <s>Ibidem (<emph type="italics"/>Conuertuntur autem magis, qu&aelig;&longs;unt in mathematicis, quoniam nul&shy;<lb/>lum accidens accipiunt (m quo quidem ijs pr&aelig;&longs;t&abreve;t, qu&aelig; di&longs;putationibus traduntur) <lb/>&longs;ed definitiones<emph.end type="italics"/>) H&aelig;c e&longs;t altera mathematicarum laus, vnde earum quoque <lb/>pr&aelig;&longs;tantia elucet, quia &longs;cilicet mathematic&aelig; pro medijs vtuntur definitio&shy;<pb pagenum="59"/>nibus &longs;ubiecti, aut pa&longs;&longs;ionis, qu&aelig; nuilo modo &longs;unt accidentalia conclu&longs;ioni, <lb/>v. </s>
  
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 <s>A&longs;tronomi <expan abbr="quoq;">quoque</expan> demon&longs;trant eclyp&longs;im de Luna, per in&shy;<lb/>rerpo&longs;itionem terr&aelig; inter Lunam, &amp; Solem, qu&aelig; interpo&longs;itio e&longs;t definitio <lb/>cau&longs;alis ip&longs;ius eclyp&longs;is, &longs;cilicet pa&longs;&longs;ionis. </s> <s>A&longs;tronomi <expan abbr="quoq;">quoque</expan> demon&longs;trant eclyp&longs;im de Luna, per in&shy;<lb/>rerpo&longs;itionem terr&aelig; inter Lunam, &amp; Solem, qu&aelig; interpo&longs;itio e&longs;t definitio <lb/>cau&longs;alis ip&longs;ius eclyp&longs;is, &longs;cilicet pa&longs;&longs;ionis. </s>
  
 <s>huiu&longs;modi <expan abbr="&longs;exc&etilde;tas">&longs;excentas</expan> reperies apud <lb/>Geometras, Arithmeticos, A&longs;tronomos, <expan abbr="c&aelig;teros&qacute;">c&aelig;terosque</expan>; Mathematicas demon&shy;<lb/>&longs;trationes: ita vt merit&ograve; dixerit Ari&longs;t. </s> <s>huiu&longs;modi <expan abbr="&longs;exc&etilde;tas">&longs;excentas</expan> reperies apud <lb/>Geometras, Arithmeticos, A&longs;tronomos, <expan abbr="c&aelig;teros&qacute;">c&aelig;terosque</expan>; Mathematicas demon&shy;<lb/>&longs;trationes: ita vt merit&ograve; dixerit Ari&longs;t. Mathematicas alias omnes natura&shy;<lb/>les &longs;cientias, qu&aelig; di&longs;putabilibus rationibus traduntur ex hac parte antecel&shy;<lb/>lere. </s>
  
 <s>Mathematicas alias omnes natura&shy;<lb/>les &longs;cientias, qu&aelig; di&longs;putabilibus rationibus traduntur ex hac parte antecel&shy;<lb/>lere. </s> 
  
 <s>a&longs;&longs;umunt igitur terminos conuertibiles, quia adhibent &longs;&aelig;p&egrave; definitio&shy;<lb/>nes ad demon&longs;trandum. </s> <s>a&longs;&longs;umunt igitur terminos conuertibiles, quia adhibent &longs;&aelig;p&egrave; definitio&shy;<lb/>nes ad demon&longs;trandum. </s>
  
 <s>Reliqua logici expo&longs;itores declarant.</s></p><p type="main"> <s>Reliqua logici expo&longs;itores declarant.</s></p><p type="main">
  
 <s><arrow.to.target n="marg48"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg48"/></s></p><p type="margin">
  
 <s><margin.target id="marg48"></margin.target>48</s></p><p type="main"> 
  
 <s>Tex. </s> <s><margin.target id="marg48"/>48</s></p><p type="main">
  
 <s>30. (<emph type="italics"/>Rur&longs;us quemadmodum mon&longs;trant Lunam, quod &longs;ph&aelig;rica &longs;it per aug&shy;<lb/>menta: &longs;i enim quod ita augetur, e&longs;t &longs;ph&aelig;ricum; augetur autem Luna; plan&ubreve; quod <lb/>&longs;ph&aelig;rica<emph.end type="italics"/>) Illius demon&longs;trationis, qu&aelig; ab effectu procedit, affert exemplum <lb/>ex a&longs;tronomia; A&longs;tronomi enim demon&longs;trant Lunam e&longs;&longs;e &longs;ph&aelig;ricam ab ef&shy;<lb/>fectu ip&longs;ius &longs;ph&aelig;ricitatis, qui e&longs;t illuminatio &longs;ph&aelig;rica: &longs;ic enim ratiocinan&shy;<lb/>tur: ea, qu&aelig; &longs;ph&aelig;ric&egrave; illuminantur &longs;unt &longs;ph&aelig;rica, Luna &longs;ph&aelig;ric&egrave; illumina&shy;<lb/>tur, ergo &longs;ph&aelig;rica e&longs;t: qu&aelig; argumentatio fu&longs;ius explicanda e&longs;t; quod ait, <lb/>quod ita augetur, ide&longs;t, &longs;ph&aelig;ric&egrave;, e&longs;t &longs;ph&aelig;ricum, ide&longs;t, quia lumen nou&aelig; Lu&shy;<lb/>n&aelig; augetur &longs;ph&aelig;ric&egrave;, hoc e&longs;t, ad eum modum, quo qu&aelig;uis &longs;ph&aelig;ra obiecta <lb/>corpori lumino&longs;o &longs;olet illuminari. </s> <s>Tex. 30. (<emph type="italics"/>Rur&longs;us quemadmodum mon&longs;trant Lunam, quod &longs;ph&aelig;rica &longs;it per aug&shy;<lb/>menta: &longs;i enim quod ita augetur, e&longs;t &longs;ph&aelig;ricum; augetur autem Luna; plan&ubreve; quod <lb/>&longs;ph&aelig;rica<emph.end type="italics"/>) Illius demon&longs;trationis, qu&aelig; ab effectu procedit, affert exemplum <lb/>ex a&longs;tronomia; A&longs;tronomi enim demon&longs;trant Lunam e&longs;&longs;e &longs;ph&aelig;ricam ab ef&shy;<lb/>fectu ip&longs;ius &longs;ph&aelig;ricitatis, qui e&longs;t illuminatio &longs;ph&aelig;rica: &longs;ic enim ratiocinan&shy;<lb/>tur: ea, qu&aelig; &longs;ph&aelig;ric&egrave; illuminantur &longs;unt &longs;ph&aelig;rica, Luna &longs;ph&aelig;ric&egrave; illumina&shy;<lb/>tur, ergo &longs;ph&aelig;rica e&longs;t: qu&aelig; argumentatio fu&longs;ius explicanda e&longs;t; quod ait, <lb/>quod ita augetur, ide&longs;t, &longs;ph&aelig;ric&egrave;, e&longs;t &longs;ph&aelig;ricum, ide&longs;t, quia lumen nou&aelig; Lu&shy;<lb/>n&aelig; augetur &longs;ph&aelig;ric&egrave;, hoc e&longs;t, ad eum modum, quo qu&aelig;uis &longs;ph&aelig;ra obiecta <lb/>corpori lumino&longs;o &longs;olet illuminari. </s>
  
 <s>illuminatio porr&ograve; Lun&aelig; in &longs;e &longs;emper e&longs;t <lb/>eadem, quia &longs;emper dimidium Lun&aelig; quod Solem a&longs;picit, illuminatur; dici&shy;<lb/>tur tamen augeri re&longs;pectu oculi no&longs;tri, quia &longs;cilicet initio facto &agrave; nouilunio <lb/>pars illuminata incipit quotidie magis vergere ad oculum no&longs;trum, ita vt <lb/>in dies maiorem, ac maiorem illuminationem videamus, donec opponatur <lb/>Soli, in qua oppo&longs;itione totum fer&egrave; Lun&aelig; <expan abbr="illuminat&utilde;">illuminatum</expan> con&longs;picitur. </s> <s>illuminatio porr&ograve; Lun&aelig; in &longs;e &longs;emper e&longs;t <lb/>eadem, quia &longs;emper dimidium Lun&aelig; quod Solem a&longs;picit, illuminatur; dici&shy;<lb/>tur tamen augeri re&longs;pectu oculi no&longs;tri, quia &longs;cilicet initio facto &agrave; nouilunio <lb/>pars illuminata incipit quotidie magis vergere ad oculum no&longs;trum, ita vt <lb/>in dies maiorem, ac maiorem illuminationem videamus, donec opponatur <lb/>Soli, in qua oppo&longs;itione totum fer&egrave; Lun&aelig; <expan abbr="illuminat&utilde;">illuminatum</expan> con&longs;picitur. </s>
  
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 <s>cum ergo videamus Lunam eo modo lu&shy;<lb/>mine augeri, quo &longs;ph&aelig;ra, hinc ip&longs;am <expan abbr="quoq;">quoque</expan> &longs;ph&aelig;ricam-e&longs;&longs;e argumentamur.</s></p><p type="main"> <s>cum ergo videamus Lunam eo modo lu&shy;<lb/>mine augeri, quo &longs;ph&aelig;ra, hinc ip&longs;am <expan abbr="quoq;">quoque</expan> &longs;ph&aelig;ricam-e&longs;&longs;e argumentamur.</s></p><p type="main">
  
 <s><arrow.to.target n="marg49"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg49"/></s></p><p type="margin">
  
 <s><margin.target id="marg49"></margin.target>49</s></p><p type="main"> <s><margin.target id="marg49"/>49</s></p><p type="main">
  
 <s>Po&longs;t nonnulla (<emph type="italics"/>Vt Per&longs;pectiua ad Geometriam, &amp; Mechanica ad Stereome&shy;<lb/>tricam, &amp; Harmonica ad Arithmeticam, vt Apparentia ad A&longs;trologicam<emph.end type="italics"/>) &longs;upra <lb/>tex. </s> <s>Po&longs;t nonnulla (<emph type="italics"/>Vt Per&longs;pectiua ad Geometriam, &amp; Mechanica ad Stereome&shy;<lb/>tricam, &amp; Harmonica ad Arithmeticam, vt Apparentia ad A&longs;trologicam<emph.end type="italics"/>) &longs;upra <lb/>tex. </s>
  
 <s>20. exempla &longs;ubalternationum Per&longs;pectiu&aelig;, &amp; Mechanic&aelig; cum Geo&shy;<lb/>metria funt allata. </s> <s>20. exempla &longs;ubalternationum Per&longs;pectiu&aelig;, &amp; Mechanic&aelig; cum Geo&shy;<lb/>metria &longs;unt allata. </s>
  
 <s>hic primo notandum Stereometriam non ef&longs;e &longs;cientiam <lb/>di&longs;tinctam &agrave; Geometria, ni&longs;i &longs;icuti partem &agrave; toto: nam cum Geometria <lb/>con&longs;ideret quantitatem, &longs;ecundum tres dimen&longs;iones, longitudinem, latitu&shy;<lb/>dinem, &amp; profunditatem, oritur triplex illius diui&longs;ro, de lineis, de &longs;uperfi&shy;<lb/>ciebus, de &longs;olidis. </s> <s>hic primo notandum Stereometriam non ef&longs;e &longs;cientiam <lb/>di&longs;tinctam &agrave; Geometria, ni&longs;i &longs;icuti partem &agrave; toto: nam cum Geometria <lb/>con&longs;ideret quantitatem, &longs;ecundum tres dimen&longs;iones, longitudinem, latitu&shy;<lb/>dinem, &amp; profunditatem, oritur triplex illius diui&longs;ro, de lineis, de &longs;uperfi&shy;<lb/>ciebus, de &longs;olidis. </s>
  
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 <s>&amp; &longs;imilibus, dicitur Stereometria &agrave; gr&aelig;co <lb/><foreign lang="greek">steoeov,</foreign> ide&longs;t &longs;olidum. </s> <s>&amp; &longs;imilibus, dicitur Stereometria &agrave; gr&aelig;co <lb/><foreign lang="greek">steoeov,</foreign> ide&longs;t &longs;olidum. </s>
  
 <s>Porr&ograve; cur malit Ari&longs;t. </s> <s>Porr&ograve; cur malit Ari&longs;t. Mechanicam &longs;ubalternari Ste&shy;<lb/>reometri&aelig;, quam toti Geometri&aelig;, qua tamen, vt videre e&longs;t apud Archime&shy;<lb/>dem, innititur, fort&egrave; ea ratio e&longs;t, quia Mechanica pr&aelig;cipu&egrave; con&longs;iderat ma&shy;<lb/>chinas, qu&aelig; corpora &longs;unt, &amp; propterea pr&aelig;cipu&egrave;, &amp; prim&ograve; debet Stereome&shy;<lb/>tri&aelig;, qu&aelig; corpora pariter contemplatur, &longs;ubalternari. </s>
  
 <s>Mechanicam &longs;ubalternari Ste&shy;<lb/>reometri&aelig;, quam toti Geometri&aelig;, qua tamen, vt videre e&longs;t apud Archime&shy;<lb/>dem, innititur, fort&egrave; ea ratio e&longs;t, quia Mechanica pr&aelig;cipu&egrave; con&longs;iderat ma&shy;<lb/>chinas, qu&aelig; corpora &longs;unt, &amp; propterea pr&aelig;cipu&egrave;, &amp; prim&ograve; debet Stereome&shy;<lb/>tri&aelig;, qu&aelig; corpora pariter contemplatur, &longs;ubalternari. </s> 
  
 <s>Quod ait Apparen&shy;<lb/>tia ad A&longs;irol. </s> <s>Quod ait Apparen&shy;<lb/>tia ad A&longs;irol. </s>
  
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 <s>Reliqua <expan abbr="v&longs;q;">v&longs;que</expan> ad &longs;inem ca&shy;<lb/>pitis optim&egrave; &agrave; Zabarella explicantur, <expan abbr="neq;">neque</expan> ad nos pertinet, cum de Mathe&shy;<lb/>maticis agant, quatenus ad Logicum &longs;pectant.</s></p><p type="main"> <s>Reliqua <expan abbr="v&longs;q;">v&longs;que</expan> ad &longs;inem ca&shy;<lb/>pitis optim&egrave; &agrave; Zabarella explicantur, <expan abbr="neq;">neque</expan> ad nos pertinet, cum de Mathe&shy;<lb/>maticis agant, quatenus ad Logicum &longs;pectant.</s></p><p type="main">
  
 <s><arrow.to.target n="marg50"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg50"/></s></p><p type="margin">
  
 <s><margin.target id="marg50"></margin.target>50</s></p><p type="main"> <s><margin.target id="marg50"/>50</s></p><p type="main">
  
 <s>Po&longs;t nonnulla (<emph type="italics"/>Hic enim ip&longs;um quidem quod &longs;en&longs;itiuorum e&longs;t &longs;cire, ip&longs;um ve&shy;<lb/>r&ograve; Propter quid Mathematicorum; hi <expan abbr="namq;">namque</expan> habent cau&longs;arum demon&longs;trationes, <lb/>&amp;c.<emph.end type="italics"/>) &longs;en&longs;us e&longs;t in &longs;ubalternatis, &amp; dependentibus di&longs;ciplinis, quas &longs;en&longs;itiuas <lb/>appellat, quia de rebus &longs;en&longs;ibilibus &longs;unt, vt in Per&longs;pectiua de obiectis vifibi&shy;<lb/>libus, &amp; in Mu&longs;ica de &longs;onis cogno&longs;citur Quod, ide&longs;t effectus: cuius effectus <lb/>cau&longs;a, &longs;eu Propter quid &longs;citur auxilio Mathematicarum, ide&longs;t, traditur &agrave; <lb/>&longs;cientijs &longs;ubalternantibus. </s> <s>Po&longs;t nonnulla (<emph type="italics"/>Hic enim ip&longs;um quidem quod &longs;en&longs;itiuorum e&longs;t &longs;cire, ip&longs;um ve&shy;<lb/>r&ograve; Propter quid Mathematicorum; hi <expan abbr="namq;">namque</expan> habent cau&longs;arum demon&longs;trationes, <lb/>&amp;c.<emph.end type="italics"/>) &longs;en&longs;us e&longs;t in &longs;ubalternatis, &amp; dependentibus di&longs;ciplinis, quas &longs;en&longs;itiuas <lb/>appellat, quia de rebus &longs;en&longs;ibilibus &longs;unt, vt in Per&longs;pectiua de obiectis vifibi&shy;<lb/>libus, &amp; in Mu&longs;ica de &longs;onis cogno&longs;citur Quod, ide&longs;t effectus: cuius effectus <lb/>cau&longs;a, &longs;eu Propter quid &longs;citur auxilio Mathematicarum, ide&longs;t, traditur &agrave; <lb/>&longs;cientijs &longs;ubalternantibus. </s>
  
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 fateri manife&longs;t&egrave; Mathematicas &longs;ubalternatas, &longs;eu medias o&longs;tendere <lb/>per cau&longs;as, quas &longs;ubalternantium ope perue&longs;tigant.</s></p><p type="main"> fateri manife&longs;t&egrave; Mathematicas &longs;ubalternatas, &longs;eu medias o&longs;tendere <lb/>per cau&longs;as, quas &longs;ubalternantium ope perue&longs;tigant.</s></p><p type="main">
  
 <s><arrow.to.target n="marg51"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg51"/></s></p><p type="margin">
  
 <s><margin.target id="marg51"></margin.target>51</s></p><p type="main"> <s><margin.target id="marg51"/>51</s></p><p type="main">
  
 <s>Et po&longs;tea (<emph type="italics"/>Se habet autem &amp; ad Per&longs;pectiuam, vt h&aelig;c ad Geometriam, alia ad <lb/>hanc, vt quo&aelig; e&longs;t de Iride ip&longs;um enim quod Naturalis e&longs;t &longs;cire, ip&longs;um vcr&ograve; Prop&shy;<lb/>ter quid Per&longs;pectiui<emph.end type="italics"/>) &longs;icut &longs;e habet, inquit, <expan abbr="&longs;ci&etilde;ti&agrave;">&longs;cienti&agrave;</expan> Naturalis de Iride ad Per&shy;<lb/>&longs;pectiuam, ita Per&longs;pectiua ad Geomettiam. </s> <s>Et po&longs;tea (<emph type="italics"/>Se habet autem &amp; ad Per&longs;pectiuam, vt h&aelig;c ad Geometriam, alia ad <lb/>hanc, vt quo&aelig; e&longs;t de Iride ip&longs;um enim quod Naturalis e&longs;t &longs;cire, ip&longs;um vcr&ograve; Prop&shy;<lb/>ter quid Per&longs;pectiui<emph.end type="italics"/>) &longs;icut &longs;e habet, inquit, <expan abbr="&longs;ci&etilde;ti&agrave;">&longs;cienti&agrave;</expan> Naturalis de Iride ad Per&shy;<lb/>&longs;pectiuam, ita Per&longs;pectiua ad Geomettiam. </s>
  
 <s>qua ver&ograve; ratione cau&longs;a Iridis <lb/>pertineat ad opticam, <expan abbr="atq;">atque</expan> hine tandem ad Geometriam, optim&egrave; patebit <lb/>in Meteoris, cum ip&longs;ius demon&longs;trationem afferemus.</s></p><p type="main"> <s>qua ver&ograve; ratione cau&longs;a Iridis <lb/>pertineat ad opticam, <expan abbr="atq;">atque</expan> hine tandem ad Geometriam, optim&egrave; patebit <lb/>in Meteoris, cum ip&longs;ius demon&longs;trationem afferemus.</s></p><p type="main">
  
 <s><arrow.to.target n="marg52"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg52"/></s></p><p type="margin">
  
 <s><margin.target id="marg52"></margin.target>52</s></p><p type="main"> 
  
 <s>Tex. </s> <s><margin.target id="marg52"/>52</s></p><p type="main">
  
 <s>37. (<emph type="italics"/>Vt &aelig;quicruri, &amp; Scaleno hoc, quod e&longs;t duobus rectis &aelig;quales habere <lb/>&longs;ecandum commune aliquod ine&longs;t<emph.end type="italics"/>) quid &longs;it habcre tres &aelig;quales duobus rect<gap/><lb/>&longs;atis explicatum e&longs;t lib. </s> <s>Tex. 37. (<emph type="italics"/>Vt &aelig;quicruri, &amp; Scaleno hoc, quod e&longs;t duobus rectis &aelig;quales habere <lb/>&longs;ecandum commune aliquod ine&longs;t<emph.end type="italics"/>) quid &longs;it habcre tres &aelig;quales duobus rect<gap/><lb/>&longs;atis explicatum e&longs;t lib.
  
 <s>r. </s> r. </s>
  
 <s>Priorum &longs;ecto 3. cap. </s> <s>Priorum &longs;ecto 3. cap.
  
 <s>r. </s> r. </s>
  
 <s>nunc igitur paraphra<gap/><lb/>&longs;olum huius loci dabo. </s> <s>nunc igitur paraphra<gap/><lb/>&longs;olum huius loci dabo. </s>
  
 <s>Triangnlo I&longs;o&longs;celi, &amp; Scaleno connenit pa&longs;&longs;io i<gap/><lb/>habere tres angulos &aelig;quales duobus rectis angulis &longs;ecundum aliquod<gap/><pb pagenum="61"/>mune, quia illis competit, quatenus ambo &longs;unt figura qu&aelig;dam, ide&longs;t, qua&shy;<lb/>tenus <expan abbr="vtrumq;">vtrumque</expan> illorum triangulum e&longs;t; triangulo <expan abbr="namq;">namque</expan> omni primo com&shy;<lb/>petit habere tres angulos &aelig;quales duobus rectis.</s></p><p type="main"> <s>Triangnlo I&longs;o&longs;celi, &amp; Scaleno connenit pa&longs;&longs;io i<gap/><lb/>habere tres angulos &aelig;quales duobus rectis angulis &longs;ecundum aliquod<gap/><pb pagenum="61"/>mune, quia illis competit, quatenus ambo &longs;unt figura qu&aelig;dam, ide&longs;t, qua&shy;<lb/>tenus <expan abbr="vtrumq;">vtrumque</expan> illorum triangulum e&longs;t; triangulo <expan abbr="namq;">namque</expan> omni primo com&shy;<lb/>petit habere tres angulos &aelig;quales duobus rectis.</s></p><p type="main">
  
 <s><arrow.to.target n="marg53"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg53"/></s></p><p type="margin">
  
 <s><margin.target id="marg53"></margin.target>53</s></p><p type="main"> <s><margin.target id="marg53"/>53</s></p><p type="main">
  
 <s>Tex. </s> <s>Tex. 38. (<emph type="italics"/>Et quemadmodum in alijs principium &longs;implex, boc autem non idem <lb/>vbique, &longs;ed in pondere quidem mina, in c&abreve;tu ver&ograve; die&longs;is<emph.end type="italics"/>) Die&longs;is apud Muficos e&longs;t <lb/>pars Toni. </s>
  
 <s>38. (<emph type="italics"/>Et quemadmodum in alijs principium &longs;implex, boc autem non idem <lb/>vbique, &longs;ed in pondere quidem mina, in c&abreve;tu ver&ograve; die&longs;is<emph.end type="italics"/>) Die&longs;is apud Muficos e&longs;t <lb/>pars Toni. </s> 
  
 <s>Tonus autem e&longs;t interuallum duarum vocum, quale e&longs;t inter pri&shy;<lb/>mam vocem, Vt, &amp; &longs;ecundam R&egrave;, vt modo loquuntur. </s> <s>Tonus autem e&longs;t interuallum duarum vocum, quale e&longs;t inter pri&shy;<lb/>mam vocem, Vt, &amp; &longs;ecundam R&egrave;, vt modo loquuntur. </s>
  
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 <s>&longs;ed fort&egrave; <expan abbr="dic&etilde;dum">dicendum</expan>, <lb/>Ari&longs;t.  <s>&longs;ed fort&egrave; <expan abbr="dic&etilde;dum">dicendum</expan>, <lb/>Ari&longs;t.
  
 con&longs;idera&longs;&longs;e, Minam re&longs;pectu Talenti, re&longs;pectu enim illius dici pote&longs;t <lb/>principium, cum &longs;ex millia minarum in Attico talento continerentur.</s></p><figure></figure><p type="main"> con&longs;idera&longs;&longs;e, Minam re&longs;pectu Talenti, re&longs;pectu enim illius dici pote&longs;t <lb/>principium, cum &longs;ex millia minarum in Attico talento continerentur.</s></p><figure/><p type="main">
  
 <s><arrow.to.target n="marg54"></arrow.to.target></s></p><p type="margin"> 
  
 <s><margin.target id="marg54"></margin.target>54</s></p><p type="main"> <s><arrow.to.target n="marg54"/></s></p><p type="margin">
  
 <s>Tex. </s> <s><margin.target id="marg54"/>54</s></p><p type="main">
  
 <s>39. <emph type="italics"/>(Si enim quod duobus rectis ine&longs;t, non in <lb/>quantum &aelig;quicrus, &longs;ed in quantum triangulus, no&shy;<lb/>&longs;cens, &amp;c.)<emph.end type="italics"/> ide&longs;t, &longs;i enim qui cogno&longs;cit, quod ha&shy;<lb/>bere tres angulos &aelig;quales duobus rectis conuenit <lb/>&aelig;quicruri, non quatenus &aelig;quicrus e&longs;t, &longs;ed quate&shy;<lb/>nus triangulus e&longs;t, &amp;c. </s> <s>Tex. 39. <emph type="italics"/>(Si enim quod duobus rectis ine&longs;t, non in <lb/>quantum &aelig;quicrus, &longs;ed in quantum triangulus, no&shy;<lb/>&longs;cens, &amp;c.)<emph.end type="italics"/> ide&longs;t, &longs;i enim qui cogno&longs;cit, quod ha&shy;<lb/>bere tres angulos &aelig;quales duobus rectis conuenit <lb/>&aelig;quicruri, non quatenus &aelig;quicrus e&longs;t, &longs;ed quate&shy;<lb/>nus triangulus e&longs;t, &amp;c. </s>
  
 <s>quid &longs;it habere tres &aelig;qua&shy;<lb/>les duobus rectis, &amp;c. </s> <s>quid &longs;it habere tres &aelig;qua&shy;<lb/>les duobus rectis, &amp;c. </s>
  
 <s>fus&egrave; explicatum e&longs;t in lib. </s> <s>fus&egrave; explicatum e&longs;t in lib.
  
 <s>1. <lb/>Priorum &longs;ecto 3. cap. </s> 1. <lb/>Priorum &longs;ecto 3. cap.
  
 <s>1. qu&ograve; te nunc mitto.</s></p><p type="main"> 1. qu&ograve; te nunc mitto.</s></p><p type="main">
  
 <s><arrow.to.target n="marg55"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg55"/></s></p><p type="margin">
  
 <s><margin.target id="marg55"></margin.target>55</s></p><p type="main"> <s><margin.target id="marg55"/>55</s></p><p type="main">
  
 <s>Po&longs;t pauca <emph type="italics"/>(Ine&longs;t omni triangulo hoc quod est <lb/>duos, &amp;c.)<emph.end type="italics"/> ide&longs;t, h&aelig;c proprietas, qu&aelig; e&longs;t habere <lb/>duos angulos rectos non actu, &longs;ed per &aelig;quiualen&shy;<lb/>tiam trium angulorum trianguli. </s> <s>Po&longs;t pauca <emph type="italics"/>(Ine&longs;t omni triangulo hoc quod est <lb/>duos, &amp;c.)<emph.end type="italics"/> ide&longs;t, h&aelig;c proprietas, qu&aelig; e&longs;t habere <lb/>duos angulos rectos non actu, &longs;ed per &aelig;quiualen&shy;<lb/>tiam trium angulorum trianguli. </s>
  
 <s>Vide qu&aelig; im&shy;<lb/>mediat&egrave; &longs;upra de hac re dixi, &amp; qu&ograve; te remi&longs;r.</s></p><p type="main"> <s>Vide qu&aelig; im&shy;<lb/>mediat&egrave; &longs;upra de hac re dixi, &amp; qu&ograve; te remi&longs;r.</s></p><p type="main">
  
 <s><arrow.to.target n="marg56"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg56"/></s></p><p type="margin">
  
 <s><margin.target id="marg56"></margin.target>56</s></p><p type="main"> <s><margin.target id="marg56"/>56</s></p><p type="main">
  
 <s>Eodem tex <emph type="italics"/>(Quando igitur cognofcimes, quod&shy;<lb/>quatuor exteriores &longs;unt &aelig;quales, quoniam I&longs;o&longs;celes, <lb/>adhuc defseit, propier quid I&longs;o&longs;celes? </s> <s>Eodem tex <emph type="italics"/>(Quando igitur cognofcimes, quod&shy;<lb/>quatuor exteriores &longs;unt &aelig;quales, quoniam I&longs;o&longs;celes, <lb/>adhuc defseit, propier quid I&longs;o&longs;celes? </s>
  
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 demon&longs;trare.</s></p><p type="main"> demon&longs;trare.</s></p><p type="main">
  
 <s><arrow.to.target n="marg57"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg57"/></s></p><p type="margin">
  
 <s><margin.target id="marg57"></margin.target>57</s></p><p type="main"> <s><margin.target id="marg57"/>57</s></p><p type="main">
  
 <s>Eodem tex. <emph type="italics"/>(Vt &longs;i quis nouit, quod omnis triangulus habet tres duobus rectis <lb/>&aelig;quales)<emph.end type="italics"/> nihil &longs;requentius. </s> <s>Eodem tex. <emph type="italics"/>(Vt &longs;i quis nouit, quod omnis triangulus habet tres duobus rectis <lb/>&aelig;quales)<emph.end type="italics"/> nihil &longs;requentius. </s>
  
 <s>vide &longs;upra lib. </s> <s>vide &longs;upra lib.
  
 <s>1. Priorum &longs;ecto 3. cap. </s> 
  
 <s>1.</s></p><p type="main"> 1. Priorum &longs;ecto 3. cap.
  
 <s><arrow.to.target n="marg58"></arrow.to.target></s></p><p type="margin"> 1.</s></p><p type="main">
  
 <s><margin.target id="marg58"></margin.target>58</s></p><p type="main"> <s><arrow.to.target n="marg58"/></s></p><p type="margin">
  
 <s>Tex. </s> <s><margin.target id="marg58"/>58</s></p><p type="main">
  
 <s>43. <emph type="italics"/>(Sed planum, quod et&longs;i e&longs;&longs;et &longs;entire triangulum, quod duobus rectis <lb/>&aelig;quales habet angulos)<emph.end type="italics"/> vide &longs;upra lib. </s> <s>Tex. 43. <emph type="italics"/>(Sed planum, quod et&longs;i e&longs;&longs;et &longs;entire triangulum, quod duobus rectis <lb/>&aelig;quales habet angulos)<emph.end type="italics"/> vide &longs;upra lib.
  
 <s>1. Priorum &longs;ecto 3. cap. </s> 1. Priorum &longs;ecto 3. cap.
  
 <s>1.</s></p><p type="main"> 1.</s></p><p type="main">
  
 <s><arrow.to.target n="marg59"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg59"/></s></p><p type="margin">
  
 <s><margin.target id="marg59"></margin.target>59</s></p><p type="main"> <s><margin.target id="marg59"/>59</s></p><p type="main">
  
 <s>Po&longs;t pauca <emph type="italics"/>(Quare &amp; &longs;i &longs;upra Lunam e&longs;&longs;emus, &amp; videremus obiectam terram, <lb/>non <expan abbr="vtiq;">vtique</expan> &longs;ciremus cau&longs;am eclyp&longs;is)<emph.end type="italics"/> loquitur de defectu Lun&aelig;, qui fit, quando <lb/>terra inter Lunam, &amp; Solem po&longs;ita, impedit, ne lumen Solis feratur in Lu&shy;<lb/>nam, &longs;ed efficit, vt vmbra ip&longs;ius terr&aelig; eam contegat.</s></p><p type="main"> <s>Po&longs;t pauca <emph type="italics"/>(Quare &amp; &longs;i &longs;upra Lunam e&longs;&longs;emus, &amp; videremus obiectam terram, <lb/>non <expan abbr="vtiq;">vtique</expan> &longs;ciremus cau&longs;am eclyp&longs;is)<emph.end type="italics"/> loquitur de defectu Lun&aelig;, qui fit, quando <lb/>terra inter Lunam, &amp; Solem po&longs;ita, impedit, ne lumen Solis feratur in Lu&shy;<lb/>nam, &longs;ed efficit, vt vmbra ip&longs;ius terr&aelig; eam contegat.</s></p><p type="main">
  
 <s><arrow.to.target n="marg60"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg60"/></s></p><p type="margin">
  
 <s><margin.target id="marg60"></margin.target>60</s></p><figure></figure><p type="main"> <s><margin.target id="marg60"/>60</s></p><figure/><p type="main">
  
 <s>Et paulo po&longs;t <emph type="italics"/>(Qutmadmod&ubreve; &longs;t vi&shy;<lb/>trum perforatum videremus, &amp; lumen <lb/>permeans, planum vtique e&longs;&longs;et propter <lb/>quid comburit)<emph.end type="italics"/> Ioquitur de ea com&shy;<lb/>bu&longs;tione, cu&aelig; fit per refractionem <lb/>media &longs;ph&aelig;ra vitrea. </s> <s>Et paulo po&longs;t <emph type="italics"/>(Qutmadmod&ubreve; &longs;t vi&shy;<lb/>trum perforatum videremus, &amp; lumen <lb/>permeans, planum vtique e&longs;&longs;et propter <lb/>quid comburit)<emph.end type="italics"/> Ioquitur de ea com&shy;<lb/>bu&longs;tione, cu&aelig; fit per refractionem <lb/>media &longs;ph&aelig;ra vitrea. </s>
  
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 <s>Si igitur, inquit Ari&longs;t.  <s>Si igitur, inquit Ari&longs;t.
  
 vide&shy;<lb/>remus illos radios &longs;ic permeare, &amp; refrangi, planum <expan abbr="vtiq;">vtique</expan> nobis e&longs;&longs;et pro&shy;<lb/>pter quid incendant.<lb/><arrow.to.target n="marg61"></arrow.to.target></s></p><p type="margin"> vide&shy;<lb/>remus illos radios &longs;ic permeare, &amp; refrangi, planum <expan abbr="vtiq;">vtique</expan> nobis e&longs;&longs;et pro&shy;<lb/>pter quid incendant.<lb/><arrow.to.target n="marg61"/></s></p><p type="margin">
  
 <s><margin.target id="marg61"></margin.target>61</s></p><p type="main"> <s><margin.target id="marg61"/>61</s></p><p type="main">
  
 <s>Ad finem tex. </s> <s>Ad finem tex. </s>
  
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 <s>In &longs;eptimo ver&ograve; traduntur definitiones numerorum, quid &longs;it nu&shy;<lb/>merus, quid impar, quid compo&longs;itus, quadratus, cubus, &amp; reliqu&aelig; nume&shy;<lb/>rorum &longs;pecies, qu&aelig; &longs;unt materia &longs;eptimi, octaui, &amp; noni, in quibus de Arith&shy;<lb/>metica tractatur.</s></p><p type="main"> <s>In &longs;eptimo ver&ograve; traduntur definitiones numerorum, quid &longs;it nu&shy;<lb/>merus, quid impar, quid compo&longs;itus, quadratus, cubus, &amp; reliqu&aelig; nume&shy;<lb/>rorum &longs;pecies, qu&aelig; &longs;unt materia &longs;eptimi, octaui, &amp; noni, in quibus de Arith&shy;<lb/>metica tractatur.</s></p><p type="main">
  
 <s><arrow.to.target n="marg62"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg62"/></s></p><p type="margin">
  
 <s><margin.target id="marg62"></margin.target>62</s></p><p type="main"> <s><margin.target id="marg62"/>62</s></p><p type="main">
  
 <s>Tex. </s> <s>Tex. 44. <emph type="italics"/>(Commen&longs;urabilem namq e&longs;&longs;e diametrum ver&egrave; opinari, ab&longs;urdum e&longs;t)<emph.end type="italics"/><lb/>vide, qu&aelig; de <expan abbr="comm&etilde;&longs;urabilitate">commen&longs;urabilitate</expan> diametri quadrati cum latere expo&longs;uimus <lb/>lib.
  
 <s>44. <emph type="italics"/>(Commen&longs;urabilem namq e&longs;&longs;e diametrum ver&egrave; opinari, ab&longs;urdum e&longs;t)<emph.end type="italics"/><lb/>vide, qu&aelig; de <expan abbr="comm&etilde;&longs;urabilitate">commen&longs;urabilitate</expan> diametri quadrati cum latere expo&longs;uimus <lb/>lib. </s> 1. Priorum &longs;ecto 1. cap.
  
 <s>1. Priorum &longs;ecto 1. cap. </s> 23. ait igitur Ari&longs;t.
  
 <s>23. ait igitur Ari&longs;t.  
  
 ab&longs;urdum e&longs;&longs;e opinari dia&shy;<lb/>metrum e&longs;&longs;e commen&longs;urabilem co&longs;t&aelig;, &longs;eu lateri eiu&longs;dem quadrati, reli&shy;<lb/>qua &longs;unt Logica.</s></p><p type="head"> ab&longs;urdum e&longs;&longs;e opinari dia&shy;<lb/>metrum e&longs;&longs;e commen&longs;urabilem co&longs;t&aelig;, &longs;eu lateri eiu&longs;dem quadrati, reli&shy;<lb/>qua &longs;unt Logica.</s></p><p type="head">
  
 <s><emph type="italics"/>Ex Secundo Posteriorum.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Ex Secundo Posteriorum.<emph.end type="italics"/></s></p><p type="main">
  
 <s><arrow.to.target n="marg63"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg63"/></s></p><p type="margin">
  
 <s><margin.target id="marg63"></margin.target>63</s></p><p type="main"> 
  
 <s>Tex. </s> <s><margin.target id="marg63"/>63</s></p><p type="main">
  
 <s>1. <emph type="italics"/>(Dico autem &longs;impliciter quidem &longs;ubiectum, vt Lunam, aut ter&shy;<lb/>ram, aut Solem, aut triangulum; aliqu<gap/>d ver&ograve; defectum, &aelig;qualitatem, <lb/>in&aelig;qualitatem. </s> <s>Tex. 1. <emph type="italics"/>(Dico autem &longs;impliciter quidem &longs;ubiectum, vt Lunam, aut ter&shy;<lb/>ram, aut Solem, aut triangulum; aliqu<gap/>d ver&ograve; defectum, &aelig;qualitatem, <lb/>in&aelig;qualitatem. </s>
  
 <s>&longs;i in medio, aut non)<emph.end type="italics"/> Zabarella locum hunc, etiam <lb/>quatenus ad Mathematicum attinet, optim&egrave; declarat. </s> <s>&longs;i in medio, aut non)<emph.end type="italics"/> Zabarella locum hunc, etiam <lb/>quatenus ad Mathematicum attinet, optim&egrave; declarat. </s>
  
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 demon&longs;trat Euclides, omne triangulum habcre tres angulos <lb/>&aelig;quales duobus rectis.</s></p><p type="main"> demon&longs;trat Euclides, omne triangulum habcre tres angulos <lb/>&aelig;quales duobus rectis.</s></p><p type="main">
  
 <s><arrow.to.target n="marg64"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg64"/></s></p><p type="margin">
  
 <s><margin.target id="marg64"></margin.target>64</s></p><p type="main"> <s><margin.target id="marg64"/>64</s></p><p type="main">
  
 <s>Ibidem <emph type="italics"/>(Quid e&longs;t con&longs;onantia? </s> <s>Ibidem <emph type="italics"/>(Quid e&longs;t con&longs;onantia? </s>
  
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 <s>definiunt igitur Mu&longs;ici con&longs;onantiam hoc modo; Con&longs;onan&shy;<lb/>tia e&longs;t compo&longs;itio &longs;oni grauis, &amp; acuti, qu&aelig; &longs;uauiter auribus accidit; &amp; quo&shy;<lb/>rum &longs;onorum proportio ad inuicem &longs;it &longs;icuti proportio numerorum, qui <lb/>quaternario includuntur: vt e&longs;t proportio 2. ad 1. vel 3. ad 1. vel 4. ad 1. <lb/>vel 3. ad 2. vel 4. ad 3. <expan abbr="Quotie&longs;eunq;">Quotie&longs;eunque</expan> igitur duo &longs;oni habuerin quampiam <pb pagenum="64"/>ex <expan abbr="quinq;">quinque</expan> pr&aelig;dictis proportionibus, &longs;i &longs;imul coaluerint, ita vt ex eis vnue <lb/>tantum &longs;onus efficiatur; &longs;onus ille erit concordans, &amp; auribus gratus. </s> <s>definiunt igitur Mu&longs;ici con&longs;onantiam hoc modo; Con&longs;onan&shy;<lb/>tia e&longs;t compo&longs;itio &longs;oni grauis, &amp; acuti, qu&aelig; &longs;uauiter auribus accidit; &amp; quo&shy;<lb/>rum &longs;onorum proportio ad inuicem &longs;it &longs;icuti proportio numerorum, qui <lb/>quaternario includuntur: vt e&longs;t proportio 2. ad 1. vel 3. ad 1. vel 4. ad 1. <lb/>vel 3. ad 2. vel 4. ad 3. <expan abbr="Quotie&longs;eunq;">Quotie&longs;eunque</expan> igitur duo &longs;oni habuerin quampiam <pb pagenum="64"/>ex <expan abbr="quinq;">quinque</expan> pr&aelig;dictis proportionibus, &longs;i &longs;imul coaluerint, ita vt ex eis vnue <lb/>tantum &longs;onus efficiatur; &longs;onus ille erit concordans, &amp; auribus gratus. </s>
  
 <s><expan abbr="atq;">atque</expan> <lb/>h&aelig;c e&longs;t &longs;ententia pri&longs;corum pr&aelig;&longs;ertim Pythagoreorum, qui propterea di&shy;<lb/>cebantnon licere Mu&longs;ico vltra quaternarium pertran&longs;ire, e&ograve; quod &longs;ol&aelig; pro&shy;<lb/>portiones, vt diximus, numerorum quaternario contentorum, concordem, <lb/>ac con&longs;onantem concentum efficere poterant: quod vt adhuc melius per&shy;<lb/><figure id="fig29"></figure><lb/>cipiamus, accipe exemplum. </s> <s><expan abbr="atq;">atque</expan> <lb/>h&aelig;c e&longs;t &longs;ententia pri&longs;corum pr&aelig;&longs;ertim Pythagoreorum, qui propterea di&shy;<lb/>cebantnon licere Mu&longs;ico vltra quaternarium pertran&longs;ire, e&ograve; quod &longs;ol&aelig; pro&shy;<lb/>portiones, vt diximus, numerorum quaternario contentorum, concordem, <lb/>ac con&longs;onantem concentum efficere poterant: quod vt adhuc melius per&shy;<lb/><figure id="fig29"/><lb/>cipiamus, accipe exemplum. </s>
  
 <s>Sint du&aelig; chord&aelig; <lb/>A, &amp; B, &aelig;qualis cra&longs;&longs;itici, &amp; &aelig;qu&egrave; ten&longs;&aelig;. </s> <s>Sint du&aelig; chord&aelig; <lb/>A, &amp; B, &aelig;qualis cra&longs;&longs;itici, &amp; &aelig;qu&egrave; ten&longs;&aelig;. </s>
  
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 <s><expan abbr="atq;">atque</expan> h&aelig;c in pr&aelig;&longs;entia &longs;ufficiant, cum plura de his ad &longs;ectionem pro&shy;<lb/>blematum 19. qu&aelig; tota e&longs;t de Mu&longs;ica, dicenda &longs;int.</s></p><p type="main"> <s><expan abbr="atq;">atque</expan> h&aelig;c in pr&aelig;&longs;entia &longs;ufficiant, cum plura de his ad &longs;ectionem pro&shy;<lb/>blematum 19. qu&aelig; tota e&longs;t de Mu&longs;ica, dicenda &longs;int.</s></p><p type="main">
  
 <s><arrow.to.target n="marg65"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg65"/></s></p><p type="margin">
  
 <s><margin.target id="marg65"></margin.target>65</s></p><p type="main"> 
  
 <s>Tex. </s> <s><margin.target id="marg65"/>65</s></p><p type="main">
  
 <s>2. <emph type="italics"/>(Vt quod omnis triangulus duobus rectis &aelig;quales babet)<emph.end type="italics"/> vide anno&shy;<lb/>tata lib. </s> <s>Tex. 2. <emph type="italics"/>(Vt quod omnis triangulus duobus rectis &aelig;quales babet)<emph.end type="italics"/> vide anno&shy;<lb/>tata lib.
  
 <s>1. Priorum &longs;ecto 3. cap. </s> 1. Priorum &longs;ecto 3. cap.
  
 <s>1.</s></p><p type="main"> 1.</s></p><p type="main">
  
 <s><arrow.to.target n="marg66"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg66"/></s></p><p type="margin">
  
 <s><margin.target id="marg66"></margin.target>66</s></p><p type="main"> <s><margin.target id="marg66"/>66</s></p><p type="main">
  
 <s>Eodem tex. <emph type="italics"/>(Definitiones ver&ograve; apparent omnes &longs;upponentes, &amp; accipientes <lb/>ip&longs;um quid e&longs;t, vt Mathematic&aelig;, quid vnitas, quid par, &amp; impar)<emph.end type="italics"/> alludit ad de&shy;<lb/>finitiones 7. Elem.  <s>Eodem tex. <emph type="italics"/>(Definitiones ver&ograve; apparent omnes &longs;upponentes, &amp; accipientes <lb/>ip&longs;um quid e&longs;t, vt Mathematic&aelig;, quid vnitas, quid par, &amp; impar)<emph.end type="italics"/> alludit ad de&shy;<lb/>finitiones 7. Elem.
  
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 <s>Qu&aelig; ver&ograve; hoc loco de principijs <lb/>dicuntur, luculenti&longs;&longs;im&egrave; patent con&longs;ideranti definitiones, &amp; axiomata, qu&aelig; <lb/>Mathematicis demon&longs;trationibus in omnibus fer&egrave; libris pr&aelig;mittuntur; ex <lb/>quibus &longs;tatim demon&longs;trationes deriuantur.</s></p><p type="main"> <s>Qu&aelig; ver&ograve; hoc loco de principijs <lb/>dicuntur, luculenti&longs;&longs;im&egrave; patent con&longs;ideranti definitiones, &amp; axiomata, qu&aelig; <lb/>Mathematicis demon&longs;trationibus in omnibus fer&egrave; libris pr&aelig;mittuntur; ex <lb/>quibus &longs;tatim demon&longs;trationes deriuantur.</s></p><p type="main">
  
 <s><arrow.to.target n="marg67"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg67"/></s></p><p type="margin">
  
 <s><margin.target id="marg67"></margin.target>67</s></p><p type="main"> <s><margin.target id="marg67"/>67</s></p><p type="main">
  
 <s>Et paulo po&longs;t <emph type="italics"/>(<expan abbr="Neq;">Neque</expan> <expan abbr="vtiq;">vtique</expan> de plano figura, non enim e&longs;t planum figura, <expan abbr="neq;">neque</expan> fi&shy;<lb/>gura planum)<emph.end type="italics"/> alludit ad definitiones planarum figurarum, qualis e&longs;t circu&shy;<lb/>lus, cuius definitio e&longs;t inter definitiones primi Elem.  <s>Et paulo po&longs;t <emph type="italics"/>(<expan abbr="Neq;">Neque</expan> <expan abbr="vtiq;">vtique</expan> de plano figura, non enim e&longs;t planum figura, <expan abbr="neq;">neque</expan> fi&shy;<lb/>gura planum)<emph.end type="italics"/> alludit ad definitiones planarum figurarum, qualis e&longs;t circu&shy;<lb/>lus, cuius definitio e&longs;t inter definitiones primi Elem.
  
 15. &amp; e&longs;t huiu&longs;modi: <lb/>circulus e&longs;t figura plana, &longs;ub vnica linea comprehen&longs;a, qu&aelig; periph&aelig;ria ap&shy;<lb/>pellatur, ad quam ab vno puncto eorum, qu&aelig; intra figuram &longs;unt po&longs;ita, ca&shy;<lb/>dentes omnes rect&aelig; line&aelig; inter &longs;e &longs;unt &aelig;quales: in qua quidem definitione <lb/>non pr&aelig;dicatur planum de figura, nec figura de plano: <expan abbr="neq;">neque</expan> enim planum, <lb/>&longs;au plana &longs;uperficies e&longs;t figura &longs;ecundum &longs;e, ni&longs;i terminetur; <expan abbr="neq;">neque</expan> figura e&longs;t <lb/>plana &longs;uperficies, cum plurim&aelig; &longs;int figur&aelig; curu&aelig;, &amp; pr&aelig;terea &longs;olid&aelig; quam&shy;<lb/>plurim&aelig;.</s></p><p type="main"> 15. &amp; e&longs;t huiu&longs;modi: <lb/>circulus e&longs;t figura plana, &longs;ub vnica linea comprehen&longs;a, qu&aelig; periph&aelig;ria ap&shy;<lb/>pellatur, ad quam ab vno puncto eorum, qu&aelig; intra figuram &longs;unt po&longs;ita, ca&shy;<lb/>dentes omnes rect&aelig; line&aelig; inter &longs;e &longs;unt &aelig;quales: in qua quidem definitione <lb/>non pr&aelig;dicatur planum de figura, nec figura de plano: <expan abbr="neq;">neque</expan> enim planum, <lb/>&longs;au plana &longs;uperficies e&longs;t figura &longs;ecundum &longs;e, ni&longs;i terminetur; <expan abbr="neq;">neque</expan> figura e&longs;t <lb/>plana &longs;uperficies, cum plurim&aelig; &longs;int figur&aelig; curu&aelig;, &amp; pr&aelig;terea &longs;olid&aelig; quam&shy;<lb/>plurim&aelig;.</s></p><p type="main">
  
 <s><arrow.to.target n="marg68"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg68"/></s></p><p type="margin">
  
 <s><margin.target id="marg68"></margin.target>68</s></p><p type="main"> <s><margin.target id="marg68"/>68</s></p><p type="main">
  
 <s>Ibidem <emph type="italics"/>(Quoniam mon&longs;tratum e&longs;t I&longs;o&longs;celes habere tres angulos &aelig;quales duo&shy;<lb/>bus rectis, &longs;i id de omni triangulo mon&longs;tratum &longs;it)<emph.end type="italics"/> ex dictis lib. </s> <s>Ibidem <emph type="italics"/>(Quoniam mon&longs;tratum e&longs;t I&longs;o&longs;celes habere tres angulos &aelig;quales duo&shy;<lb/>bus rectis, &longs;i id de omni triangulo mon&longs;tratum &longs;it)<emph.end type="italics"/> ex dictis lib.
  
 <s>1. Priorum &longs;ecto <lb/>3. cap. </s> 1. Priorum &longs;ecto <lb/>3. cap.
  
 <s>1. petatur huius loci declaratio.</s></p><p type="main"> 1. petatur huius loci declaratio.</s></p><p type="main">
  
 <s><arrow.to.target n="marg69"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg69"/></s></p><p type="margin">
  
 <s><margin.target id="marg69"></margin.target>69</s></p><p type="main"> <s><margin.target id="marg69"/>69</s></p><p type="main">
  
 <s>Tex. </s> <s>Tex. 7. <emph type="italics"/>(Quid enim &longs;ignificat triangulum, accipit Geometra)<emph.end type="italics"/> vt manife&longs;tum <lb/>e&longs;t in 20. dednitione primi Elem.</s></p><p type="main">
  
 <s>7. <emph type="italics"/>(Quid enim &longs;ignificat triangulum, accipit Geometra)<emph.end type="italics"/> vt manife&longs;tum <lb/>e&longs;t in 20. dednitione primi Elem.</s></p><p type="main"> <s><arrow.to.target n="marg70"/></s></p><p type="margin">
  
 <s><arrow.to.target n="marg70"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg70"/>70</s></p><p type="main">
  
 <s><margin.target id="marg70"></margin.target>70</s></p><p type="main"> 
  
 <s>Ibidem <emph type="italics"/>(Quod autem &longs;it, monstrat)<emph.end type="italics"/> vt per&longs;picuum e&longs;t in prima <expan abbr="dem&otilde;&longs;tra-tione">demon&longs;tra&shy;<lb/>tione</expan> primi Elem.  <s>Ibidem <emph type="italics"/>(Quod autem &longs;it, monstrat)<emph.end type="italics"/> vt per&longs;picuum e&longs;t in prima <expan abbr="dem&otilde;&longs;tra-tione">demon&longs;tra&shy;<lb/>tione</expan> primi Elem.
  
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 <s>Certum tamen e&longs;t, Geometram luppo&shy;<lb/>nere triangulum in communi, cum inter definitiones ip&longs;ius contineatur, <pb pagenum="65"/>quod tamen non ob&longs;tat, quominus probare po&longs;&longs;it, aliquando po&longs;&longs;e <expan abbr="c&otilde;&longs;trni">con&longs;trni</expan>, <lb/>&amp; e&longs;&longs;e aliquod particulare triangulum, vt fit in pr&aelig;dicta demon&longs;tratione, <lb/>Euclidis.</s></p><p type="main"> <s>Certum tamen e&longs;t, Geometram luppo&shy;<lb/>nere triangulum in communi, cum inter definitiones ip&longs;ius contineatur, <pb pagenum="65"/>quod tamen non ob&longs;tat, quominus probare po&longs;&longs;it, aliquando po&longs;&longs;e <expan abbr="c&otilde;&longs;trni">con&longs;trni</expan>, <lb/>&amp; e&longs;&longs;e aliquod particulare triangulum, vt fit in pr&aelig;dicta demon&longs;tratione, <lb/>Euclidis.</s></p><p type="main">
  
 <s><arrow.to.target n="marg71"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg71"/></s></p><p type="margin">
  
 <s><margin.target id="marg71"></margin.target>71</s></p><p type="main"> 
  
 <s>Tex. </s> 
  
 <s>11. <emph type="italics"/>(Manife<gap/>tum autem, &amp; &longs;ic, propter quid e&longs;t rectus in &longs;emicirculo)<emph.end type="italics"/><lb/>affert exemplum demon&longs;trationis per cau&longs;am materialem, <expan abbr="id&qacute;">idque</expan>; vti &longs;olet ex <lb/>Mathematicis petitum, e&longs;t enim apud Euclidem 31. demon&longs;tratio 3. Elem. <lb/></s> <s><margin.target id="marg71"/>71</s></p><p type="main">
  
 <s>vbi ip&longs;e o&longs;tendit angulum in &longs;emicirculo e&longs;&longs;e rectum. </s> <s>Tex. 11. <emph type="italics"/>(Manife<gap/>tum autem, &amp; &longs;ic, propter quid e&longs;t rectus in &longs;emicirculo)<emph.end type="italics"/><lb/>affert exemplum demon&longs;trationis per cau&longs;am materialem, <expan abbr="id&qacute;">idque</expan>; vti &longs;olet ex <lb/>Mathematicis petitum, e&longs;t enim apud Euclidem 31. demon&longs;tratio 3. Elem. <lb/>vbi ip&longs;e o&longs;tendit angulum in &longs;emicirculo e&longs;&longs;e rectum. </s>
  
 <s>Vbi aduertendum e&longs;t <lb/>propo&longs;itionem hanc 31. ab Euclide demon&longs;trari duobus modis; ex quibus <lb/>&longs;ecundum innuit hoc loco Ari&longs;t.  <s>Vbi aduertendum e&longs;t <lb/>propo&longs;itionem hanc 31. ab Euclide demon&longs;trari duobus modis; ex quibus <lb/>&longs;ecundum innuit hoc loco Ari&longs;t.
  
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 <s>quod fort&egrave; non ben&egrave; aduertens Iacobus Zabarella, <lb/>alioquin in his &longs;atis oculatus incidit in errorem, dicens, &longs;e nullo pacto vi&shy;<lb/>dere medium Euclidian&aelig; demon&longs;trationis e&longs;&longs;e cau&longs;am materialem; quod <lb/>tamen nos mox aperiemus. </s> <s>quod fort&egrave; non ben&egrave; aduertens Iacobus Zabarella, <lb/>alioquin in his &longs;atis oculatus incidit in errorem, dicens, &longs;e nullo pacto vi&shy;<lb/>dere medium Euclidian&aelig; demon&longs;trationis e&longs;&longs;e cau&longs;am materialem; quod <lb/>tamen nos mox aperiemus. </s>
  
 <s>per angulum in &longs;emicirculo intelligas eum, qui <lb/>fit &agrave; lineis ductis ab extremitatibus diametri, &amp; &longs;imul in quoduis punctum <lb/><figure id="fig30"></figure><lb/>circumferenti&aelig; coeuntibus, vt in figura <lb/>pr&aelig;&longs;enti vides lineas A C, B C, ad C, pun&shy;<lb/>ctum conuenire, <expan abbr="ibi&qacute;">ibique</expan>; facere angulum, <lb/>A C B, qui dicitur angulus in &longs;emicircu&shy;<lb/>lo, quia de&longs;criptus e&longs;t in &longs;emicirculo A&shy;<lb/>C B. <expan abbr="e&longs;t&qacute;">e&longs;tque</expan>; &longs;an&egrave; mirabilis h&aelig;c &longs;emicirculi <lb/>proprietas, cum <expan abbr="vbicunq;">vbicunque</expan> punctum C, in <lb/>periph&aelig;ria &longs;umptum fuerit, &longs;emper ta&shy;<lb/>men angulus A C B, fiat rectus. </s> <s>per angulum in &longs;emicirculo intelligas eum, qui <lb/>fit &agrave; lineis ductis ab extremitatibus diametri, &amp; &longs;imul in quoduis punctum <lb/><figure id="fig30"/><lb/>circumferenti&aelig; coeuntibus, vt in figura <lb/>pr&aelig;&longs;enti vides lineas A C, B C, ad C, pun&shy;<lb/>ctum conuenire, <expan abbr="ibi&qacute;">ibique</expan>; facere angulum, <lb/>A C B, qui dicitur angulus in &longs;emicircu&shy;<lb/>lo, quia de&longs;criptus e&longs;t in &longs;emicirculo A&shy;<lb/>C B. <expan abbr="e&longs;t&qacute;">e&longs;tque</expan>; &longs;an&egrave; mirabilis h&aelig;c &longs;emicirculi <lb/>proprietas, cum <expan abbr="vbicunq;">vbicunque</expan> punctum C, in <lb/>periph&aelig;ria &longs;umptum fuerit, &longs;emper ta&shy;<lb/>men angulus A C B, fiat rectus. </s>
  
 <s>quod Euclides eodem pror&longs;us medio, quod <lb/>Ari&longs;t.  <s>quod Euclides eodem pror&longs;us medio, quod <lb/>Ari&longs;t.
  
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 <s>Reliqua ad logicum pertinent, etiam&longs;i per cha&shy;<lb/>racteres more mathematicorum exponantur.</s></p><p type="main"> <s>Reliqua ad logicum pertinent, etiam&longs;i per cha&shy;<lb/>racteres more mathematicorum exponantur.</s></p><p type="main">
  
 <s><arrow.to.target n="marg72"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg72"/></s></p><p type="margin">
  
 <s><margin.target id="marg72"></margin.target>72</s></p><p type="main"> <s><margin.target id="marg72"/>72</s></p><p type="main">
  
 <s>Tex. </s> <s>Tex. 24. <emph type="italics"/>(Vt propter quid re&longs;onat? </s>
  
 <s>24. <emph type="italics"/>(Vt propter quid re&longs;onat? </s> 
  
 <s>aut propter quid apparet? </s> <s>aut propter quid apparet? </s>
  
 <s>aut propter quid <lb/>Iris? </s> <s>aut propter quid <lb/>Iris? <!-- KEEP S--></s>
  
 <s>omnia enim h&aelig;r idem problemata &longs;unt genere, omnia enim &longs;unt refractio, &longs;ed <lb/>&longs;pecie altera)<emph.end type="italics"/> propter quid re&longs;onat? </s> <s>omnia enim h&aelig;r idem problemata &longs;unt genere, omnia enim &longs;unt refractio, &longs;ed <lb/>&longs;pecie altera)<emph.end type="italics"/> propter quid re&longs;onat? </s>
  
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 <s>In fine textus <emph type="italics"/>(Quoniam Luna deficit)<emph.end type="italics"/> non intelligit defectum illum, qui <lb/>eclyp&longs;is appellatur, &longs;ed ilium, quo paulatim lumen Lun&aelig; minus oculis no&shy;<lb/>&longs;tris apparet: decre&longs;cente enim Luna &longs;olent humida augeri.</s></p><p type="main"> <s>In fine textus <emph type="italics"/>(Quoniam Luna deficit)<emph.end type="italics"/> non intelligit defectum illum, qui <lb/>eclyp&longs;is appellatur, &longs;ed ilium, quo paulatim lumen Lun&aelig; minus oculis no&shy;<lb/>&longs;tris apparet: decre&longs;cente enim Luna &longs;olent humida augeri.</s></p><p type="main">
  
 <s><arrow.to.target n="marg73"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg73"/></s></p><p type="margin">
  
 <s><margin.target id="marg73"></margin.target>73</s></p><p type="main"> 
  
 <s>Tex. </s> <s><margin.target id="marg73"/>73</s></p><p type="main">
  
 <s>25. <emph type="italics"/>(Vt propter quid, &amp; permutatim proportionale? </s> <s>Tex. 25. <emph type="italics"/>(Vt propter quid, &amp; permutatim proportionale? </s>
  
 <s>&amp; c.<emph.end type="italics"/>) quod quan&shy;<lb/>titates, qu&aelig; &longs;unt proportionales, &longs;int etiam alternatim, &longs;eu permutatim <lb/>proportionales explicatum e&longs;t ad tex. </s> <s>&amp; c.<emph.end type="italics"/>) quod quan&shy;<lb/>titates, qu&aelig; &longs;unt proportionales, &longs;int etiam alternatim, &longs;eu permutatim <lb/>proportionales explicatum e&longs;t ad tex. </s>
  
 <s>13. primi Po&longs;ter. </s> <s>13. primi Po&longs;ter. qu&aelig; etiam nece&longs;&longs;a&shy;<lb/>ria &longs;unt ad hunc locum ben&egrave; intelligendum. </s>
  
 <s>qu&aelig; etiam nece&longs;&longs;a&shy;<lb/>ria &longs;unt ad hunc locum ben&egrave; intelligendum. </s> 
  
 <s>Illud autem commune propter <lb/>quod ea, qu&aelig; &longs;unt proportionalia, &longs;int etiam permutatim proportionalia, <lb/>e&longs;t quoddam innominatum, de quo ibi dictum e&longs;t, quod cum conueniat li&shy;<lb/>neis, &amp; numeris, &amp; tamen &longs;eparatim de vtri&longs;que illa pa&longs;&longs;io demon&longs;tretur, <lb/>qu&aelig;rit cuinam prim&ograve;, &amp; per &longs;e conueniat h&aelig;c pa&longs;&longs;io, e&longs;&longs;e permutatim pro&shy;<lb/>portionale; &longs;cilicet quidnam &longs;it illud innominatum; in quo deinde commu&shy;<lb/>nicent line&aelig;, &amp; numeri, vt inde habeant e&longs;&longs;e etiam permutatim propor&shy;<lb/>tionalia.</s></p><p type="main"> <s>Illud autem commune propter <lb/>quod ea, qu&aelig; &longs;unt proportionalia, &longs;int etiam permutatim proportionalia, <lb/>e&longs;t quoddam innominatum, de quo ibi dictum e&longs;t, quod cum conueniat li&shy;<lb/>neis, &amp; numeris, &amp; tamen &longs;eparatim de vtri&longs;que illa pa&longs;&longs;io demon&longs;tretur, <lb/>qu&aelig;rit cuinam prim&ograve;, &amp; per &longs;e conueniat h&aelig;c pa&longs;&longs;io, e&longs;&longs;e permutatim pro&shy;<lb/>portionale; &longs;cilicet quidnam &longs;it illud innominatum; in quo deinde commu&shy;<lb/>nicent line&aelig;, &amp; numeri, vt inde habeant e&longs;&longs;e etiam permutatim propor&shy;<lb/>tionalia.</s></p><p type="main">
  
 <s><arrow.to.target n="marg74"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg74"/></s></p><p type="margin">
  
 <s><margin.target id="marg74"></margin.target>74</s></p><p type="main"> <s><margin.target id="marg74"/>74</s></p><p type="main">
  
 <s>Ibidem (<emph type="italics"/>Hic quidem forta&longs;&longs;e proportionaliter habere latera, &amp; angulos<emph.end type="italics"/>) vult <lb/>indicare, in quonam con&longs;i&longs;tat &longs;imilitudo inter duas-figuras rectilineas geo&shy;<lb/>metricas, quam &longs;imilitudinem Euclides definit. </s> <s>Ibidem (<emph type="italics"/>Hic quidem forta&longs;&longs;e proportionaliter habere latera, &amp; angulos<emph.end type="italics"/>) vult <lb/>indicare, in quonam con&longs;i&longs;tat &longs;imilitudo inter duas-figuras rectilineas geo&shy;<lb/>metricas, quam &longs;imilitudinem Euclides definit. </s>
  
 <s>1. &longs;exti, &longs;ic explicat: &longs;imi&shy;<lb/>les figur&aelig; rectil&iacute;ne&aelig; &longs;unt; qu&aelig; &amp; angulos &longs;ingulos, &longs;ingulis angulis &aelig;quales <lb/>habent, <expan abbr="atq;">atque</expan> etiam latera, qu&aelig; circa angulos &aelig;quales &longs;unt proportionalia. <lb/></s> <s>1. &longs;exti, &longs;ic explicat: &longs;imi&shy;<lb/>les figur&aelig; rectil&iacute;ne&aelig; &longs;unt; qu&aelig; &amp; angulos &longs;ingulos, &longs;ingulis angulis &aelig;quales <lb/>habent, <expan abbr="atq;">atque</expan> etiam latera, qu&aelig; circa angulos &aelig;quales &longs;unt proportionalia. <lb/></s>
  
 <s>vt &longs;i duo triangula appo&longs;ita habeant angulos &aelig;quales, <expan abbr="angul&utilde;">angulum</expan> A, angulo D: <lb/>angulum B, angulo E. angulum C, angulo F. &amp; pr&aelig;terea latera, qu&aelig; &longs;une <pb pagenum="67"/><figure id="fig31"></figure><lb/>circa angulos &aelig;quales, v. </s> <s>vt &longs;i duo triangula appo&longs;ita habeant angulos &aelig;quales, <expan abbr="angul&utilde;">angulum</expan> A, angulo D: <lb/>angulum B, angulo E. angulum C, angulo F. &amp; pr&aelig;terea latera, qu&aelig; &longs;une <pb pagenum="67"/><figure id="fig31"/><lb/>circa angulos &aelig;quales, v. </s>
  
 <s>g. </s> <s>g. </s>
  
 <s>cirea an&shy;<lb/>gulos A, &amp; D, habeant proportiona&shy;<lb/>lia, hoc e&longs;t, vt latus A B, ad latus A C; <lb/>ita &longs;it latus D E, ad latus D F; &amp; &longs;ic de <lb/>lateribus alijs circa reliquos angulos <lb/>&aelig;quales; erunt tunc pr&aelig;dicta duo tri&shy;<lb/>angula fimilia.</s></p><p type="main"> <s>cirea an&shy;<lb/>gulos A, &amp; D, habeant proportiona&shy;<lb/>lia, hoc e&longs;t, vt latus A B, ad latus A C; <lb/>ita &longs;it latus D E, ad latus D F; &amp; &longs;ic de <lb/>lateribus alijs circa reliquos angulos <lb/>&aelig;quales; erunt tunc pr&aelig;dicta duo tri&shy;<lb/>angula fimilia.</s></p><p type="main">
  
 <s><arrow.to.target n="marg75"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg75"/></s></p><p type="margin">
  
 <s><margin.target id="marg75"></margin.target>75</s></p><p type="main"> <s><margin.target id="marg75"/>75</s></p><p type="main">
  
 <s>Ibidem (<emph type="italics"/>Vt extrin&longs;ecos &aelig;quales e&longs;&longs;e<emph.end type="italics"/>) ide&longs;t extrin&longs;ecos angulos cuiu&longs;uis fi&shy;<lb/>gur&aelig; rectiline&aelig; &aelig;quales e&longs;&longs;e quatuor rectis angulis: vide qu&aelig; &longs;crip&longs;imus de <lb/>hac re ad tex. </s> <s>Ibidem (<emph type="italics"/>Vt extrin&longs;ecos &aelig;quales e&longs;&longs;e<emph.end type="italics"/>) ide&longs;t extrin&longs;ecos angulos cuiu&longs;uis fi&shy;<lb/>gur&aelig; rectiline&aelig; &aelig;quales e&longs;&longs;e quatuor rectis angulis: vide qu&aelig; &longs;crip&longs;imus de <lb/>hac re ad tex. </s>
  
 <s>39. &longs;ecundi Po&longs;ter. </s> <s>39. &longs;ecundi Po&longs;ter. qu&aelig; huic pariter loco &longs;atisfaciunt.</s></p><p type="head">
  
 <s>qu&aelig; huic pariter loco &longs;atisfaciunt.</s></p><p type="head"> 
  
 <s><emph type="italics"/>EX TOPICIS.<emph.end type="italics"/></s></p><p type="head"> <s><emph type="italics"/>EX TOPICIS.<emph.end type="italics"/></s></p><p type="head">
  
 <s><emph type="italics"/>Ex Primo Libro.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Ex Primo Libro.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main">
  
 <s><arrow.to.target n="marg76"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg76"/></s></p><p type="margin">
  
 <s><margin.target id="marg76"></margin.target>76</s></p><p type="main"> <s><margin.target id="marg76"/>76</s></p><p type="main">
  
  
 <s>Cap. 13. (<emph type="italics"/>Con&longs;iderare, quod diameter est co&longs;t&aelig; incommen&longs;urabilis<emph.end type="italics"/>) vide <lb/>qu&aelig; de hac re &longs;crip&longs;i lib. </s> <s>Cap. 13. (<emph type="italics"/>Con&longs;iderare, quod diameter est co&longs;t&aelig; incommen&longs;urabilis<emph.end type="italics"/>) vide <lb/>qu&aelig; de hac re &longs;crip&longs;i lib.
  
  
 <s>1. Priorum &longs;ecto 1. cap. </s> 1. Priorum &longs;ecto 1. cap.
  
 <s>23.</s></p><p type="main"> 23.</s></p><p type="main">
  
 <s><arrow.to.target n="marg77"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg77"/></s></p><p type="margin">
  
 <s><margin.target id="marg77"></margin.target>77</s></p><p type="main"> <s><margin.target id="marg77"/>77</s></p><p type="main">
  
 <s>Eodem cap. (<emph type="italics"/>Similiter autem &amp; acutum; non enim idem &longs;impliciter <lb/>in omnibus dicitur: nam vox acuta quidem velox (&longs;icut dicunt, qui &longs;e&shy;<lb/>cundum numeros harmonici &longs;unt) angulus autem acutus, qui minor e&longs;trecto; gla&shy;<lb/>dius ver&ograve;, qui e&longs;t anguli acuti<emph.end type="italics"/>) affert tres &longs;pecies acuti, aliud dicens e&longs;&longs;e acu&shy;<lb/>tum, quod e&longs;t in voce acuta; aliud, quod e&longs;t in angulo acuto: aliud denique, <lb/>quod e&longs;t in gladio acuto horum enim trium acumen diuer&longs;o modo &longs;e habet. <lb/></s> <s>Eodem cap. (<emph type="italics"/>Similiter autem &amp; acutum; non enim idem &longs;impliciter <lb/>in omnibus dicitur: nam vox acuta quidem velox (&longs;icut dicunt, qui &longs;e&shy;<lb/>cundum numeros harmonici &longs;unt) angulus autem acutus, qui minor e&longs;trecto; gla&shy;<lb/>dius ver&ograve;, qui e&longs;t anguli acuti<emph.end type="italics"/>) affert tres &longs;pecies acuti, aliud dicens e&longs;&longs;e acu&shy;<lb/>tum, quod e&longs;t in voce acuta; aliud, quod e&longs;t in angulo acuto: aliud denique, <lb/>quod e&longs;t in gladio acuto horum enim trium acumen diuer&longs;o modo &longs;e habet. <lb/></s>
  
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 <s>mu&longs;ica&shy;<lb/>lium, ait, &longs;i virga celerius feriat aerem, gigni motum celeriorem in aere, <lb/><expan abbr="atq;">atque</expan> hinc &longs;onum acutiorem reddi, experientia con&longs;tat: &longs;i autem eadem vir&shy;<lb/>ga tardius aerem feriat, gigni motum in aere tardiorem, ex quo etiam &longs;o&shy;<lb/>num grauem, vt experientia docet. </s> <s>mu&longs;ica&shy;<lb/>lium, ait, &longs;i virga celerius feriat aerem, gigni motum celeriorem in aere, <lb/><expan abbr="atq;">atque</expan> hinc &longs;onum acutiorem reddi, experientia con&longs;tat: &longs;i autem eadem vir&shy;<lb/>ga tardius aerem feriat, gigni motum in aere tardiorem, ex quo etiam &longs;o&shy;<lb/>num grauem, vt experientia docet. </s>
  
 <s>Ptol&aelig;meus deinde lib. </s> <s>Ptol&aelig;meus deinde lib.
  
 <s>1. cap. </s> 1. cap.
  
 <s>3. Harm. <lb/></s> 3. Harm. <lb/></s>
  
 <s>cum ex alijs, tum ex celeritate oriri &longs;onum acutum, grauem ver&ograve; ex tardi&shy;<lb/>tate a&longs;&longs;erit; vt &longs;i chorda eadem parum inten&longs;a pul&longs;etur, tardius aerem ver&shy;<lb/>berat, &amp; ideo grauiorem &longs;onum efficit: &longs;i autem magis intendatur, validius <lb/>aerem pul&longs;abit, &amp; proinde citiorem motum illi imprimet, &amp; propterea <lb/>acutiorem &longs;onum reddet. </s> <s>cum ex alijs, tum ex celeritate oriri &longs;onum acutum, grauem ver&ograve; ex tardi&shy;<lb/>tate a&longs;&longs;erit; vt &longs;i chorda eadem parum inten&longs;a pul&longs;etur, tardius aerem ver&shy;<lb/>berat, &amp; ideo grauiorem &longs;onum efficit: &longs;i autem magis intendatur, validius <lb/>aerem pul&longs;abit, &amp; proinde citiorem motum illi imprimet, &amp; propterea <lb/>acutiorem &longs;onum reddet. </s>
  
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 <s>Demum explicat, cur nam gladius dicatur acutus, <lb/>quia nimirum habet angulum acutum &longs;uperficialem, ide&longs;t, quem du&aelig; &longs;uper&shy;<lb/>ficies &longs;imul in acie gladij concurrentes efficiunt.</s></p><pb pagenum="68"/><p type="main"> <s>Demum explicat, cur nam gladius dicatur acutus, <lb/>quia nimirum habet angulum acutum &longs;uperficialem, ide&longs;t, quem du&aelig; &longs;uper&shy;<lb/>ficies &longs;imul in acie gladij concurrentes efficiunt.</s></p><pb pagenum="68"/><p type="main">
  
 <s><arrow.to.target n="marg78"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg78"/></s></p><p type="margin">
  
 <s><margin.target id="marg78"></margin.target>78</s></p><p type="main"> <s><margin.target id="marg78"/>78</s></p><p type="main">
  
 <s>Eodem cap. (<emph type="italics"/>Rur&longs;um &longs;i eorundem; qu&aelig; &longs;unt &longs;ub eodem nomine diuer&longs;&aelig; d ffe&shy;<lb/>renti&aelig; &longs;unt; vt coloris, qui e&longs;t in corporibus, &amp; in melodijs<emph.end type="italics"/>) veteres Mu&longs;ici can&shy;<lb/>tilenas omnes ad tria genera reuocarunt, videlicet Enharmonicum, Chro&shy;<lb/>maticum, &amp; Diatonicum; qu&aelig; diftinguebantur inuicem ex varia diui&longs;ione <lb/>interuallorum, ex quibus ip&longs;orum Monochordia conftabant: &longs;iue ex varijs <lb/>vocum interuallis, v. </s> <s>Eodem cap. (<emph type="italics"/>Rur&longs;um &longs;i eorundem; qu&aelig; &longs;unt &longs;ub eodem nomine diuer&longs;&aelig; d ffe&shy;<lb/>renti&aelig; &longs;unt; vt coloris, qui e&longs;t in corporibus, &amp; in melodijs<emph.end type="italics"/>) veteres Mu&longs;ici can&shy;<lb/>tilenas omnes ad tria genera reuocarunt, videlicet Enharmonicum, Chro&shy;<lb/>maticum, &amp; Diatonicum; qu&aelig; diftinguebantur inuicem ex varia diui&longs;ione <lb/>interuallorum, ex quibus ip&longs;orum Monochordia conftabant: &longs;iue ex varijs <lb/>vocum interuallis, v. </s>
  
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 innuit. </s> innuit. </s>
  
 <s>quod genus for&longs;itan &agrave; calore denomina&shy;<lb/>batur, qu&ograve;d ip&longs;ius not&aelig; mu&longs;icales e&longs;&longs;ent colorat&aelig;, vt hoc modo ab alijs ge&shy;<lb/>neribus digno&longs;eeretur<gap/> quam con&longs;uetudinem exi&longs;timat Zarlinus cap. </s> <s>quod genus for&longs;itan &agrave; calore denomina&shy;<lb/>batur, qu&ograve;d ip&longs;ius not&aelig; mu&longs;icales e&longs;&longs;ent colorat&aelig;, vt hoc modo ab alijs ge&shy;<lb/>neribus digno&longs;eeretur<gap/> quam con&longs;uetudinem exi&longs;timat Zarlinus cap.
  
 <s>46. &longs;e&shy;<lb/>cund&aelig; partis, etiam no&longs;tra tempe&longs;tate aliquo modo per&longs;euerare, cum vi&shy;<lb/>deamus in organis, &amp; alijs huiu&longs;modi in&longs;trumentis, qu&aelig; pinnas, vulg&ograve; ta&shy;<lb/>&longs;tos, habent; illas inquam pinnas, qu&aelig; chromaticis interuallis deputat&aelig; <lb/>&longs;unt, colore nigro tinctas e&longs;&longs;e.</s></p><p type="head"> 46. &longs;e&shy;<lb/>cund&aelig; partis, etiam no&longs;tra tempe&longs;tate aliquo modo per&longs;euerare, cum vi&shy;<lb/>deamus in organis, &amp; alijs huiu&longs;modi in&longs;trumentis, qu&aelig; pinnas, vulg&ograve; ta&shy;<lb/>&longs;tos, habent; illas inquam pinnas, qu&aelig; chromaticis interuallis deputat&aelig; <lb/>&longs;unt, colore nigro tinctas e&longs;&longs;e.</s></p><p type="head">
  
 <s><emph type="italics"/>Libro Quarto.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Libro Quarto.<emph.end type="italics"/></s></p><p type="main">
  
 <s><arrow.to.target n="marg79"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg79"/></s></p><p type="margin">
  
 <s><margin.target id="marg79"></margin.target>79</s></p><p type="main"> <s><margin.target id="marg79"/>79</s></p><p type="main">
  
  
 <s>Cap. 1. loco 10. (<emph type="italics"/>Si quis in&longs;ecabiles ponens lineas<emph.end type="italics"/>) nonnulli antiquorum <lb/>Philo&longs;ophorum putarunt omnia ex indiui&longs;ibilibus componi, vt Demo&shy;<lb/>critus, &amp; Leucippus, &amp; propterea dixerunt, etiam lineas con&longs;tare ex lineis <lb/>quibu&longs;dam ade &ograve; paruis, qu&aelig; omnino e&longs;ient in&longs;ecabiles, &longs;eu indiui&longs;ibiles: de <lb/>quibus plura in libello de line is in&longs;ecabilibus.</s> <s>Cap. 1. loco 10. (<emph type="italics"/>Si quis in&longs;ecabiles ponens lineas<emph.end type="italics"/>) nonnulli antiquorum <lb/>Philo&longs;ophorum putarunt omnia ex indiui&longs;ibilibus componi, vt Demo&shy;<lb/>critus, &amp; Leucippus, &amp; propterea dixerunt, etiam lineas con&longs;tare ex lineis <lb/>quibu&longs;dam ade &ograve; paruis, qu&aelig; omnino e&longs;ient in&longs;ecabiles, &longs;eu indiui&longs;ibiles: de <lb/>quibus plura in libello de line is in&longs;ecabilibus.</s>
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 <s><emph type="italics"/>Libro Sexio.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Libro Sexio.<emph.end type="italics"/></s></p><p type="main">
  
 <s><arrow.to.target n="marg80"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg80"/></s></p><p type="margin">
  
 <s><margin.target id="marg80"></margin.target>80</s></p><p type="main"> <s><margin.target id="marg80"/>80</s></p><p type="main">
  
  
 <s>Cap. 2. loco 32. (<emph type="italics"/>Vt qui lineam definiunt longitudmem &longs;ine latitudine e&longs;&longs;e<emph.end type="italics"/>) <lb/>&longs;uppenimus lectorem inteil exi&longs;&longs;e definitiones &longs;altem primi Elem.  <s>Cap. 2. loco 32. (<emph type="italics"/>Vt qui lineam definiunt longitudinem &longs;ine latitudine e&longs;&longs;e<emph.end type="italics"/>) <lb/>&longs;uppenimus lectorem inteil exi&longs;&longs;e definitiones &longs;altem primi Elem.
  
  
 in&shy;<lb/>ter quas d<gap/>f<gap/>nitio line&aelig; e&longs;t &longs;ecunda, <expan abbr="cadem&qacute;">cademque</expan>; cum hac Ari&longs;totelis.</s></p><p type="head"> in&shy;<lb/>ter quas d<gap/>f<gap/>nitio line&aelig; e&longs;t &longs;ecunda, <expan abbr="cadem&qacute;">cademque</expan>; cum hac Ari&longs;totelis.<!-- KEEP S--></s></p><p type="head">
  
 <s><emph type="italics"/>Libro Octauo.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Libro Octauo.<emph.end type="italics"/></s></p><p type="main">
  
 <s><arrow.to.target n="marg81"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg81"/></s></p><p type="margin">
  
 <s><margin.target id="marg81"></margin.target>81</s></p><p type="main"> <s><margin.target id="marg81"/>81</s></p><p type="main">
  
  
 <s>Cap. 2. loco 41. (<emph type="italics"/>Videntur dutem in di&longs;ciplinis, &longs;eu Mathematicis qu&aelig;dam <lb/>ob de&longs;initionis defectum non facile de&longs;cribi; vt &amp; quoniam, qu&aelig; ad latus &longs;e&shy;<lb/>cat planum linea, &longs;imiliter diuidit &amp; lineam, &amp; locum: definitione autem dicta, <lb/>fi <gap/>m man fe&longs;tu<gap/>t&longs;t, quod dicitur, nam eandem ablationem habent lota, &amp; <gap/>inea, <lb/><gap/>se latus plan&aelig; figur&aelig;, est autem definitio eiu&longs;dem proportionis h&aelig;c<emph.end type="italics"/>) mendos&egrave; <lb/>lugitur &agrave; nonnullis (<emph type="italics"/>E&longs;t distem de&longs;initio eiu&longs;dem orationis h&aelig;c<emph.end type="italics"/>) quos puto de&shy;<lb/>ceptos ab &aelig;quiuoco <foreign lang="greek">lsgous</foreign> quod &amp; orationem, &amp; rationem, &longs;iue proportio&shy;<lb/>nem &longs;ignificat: hic autem &longs;ignificare proportionem res &longs;ubrecta &longs;atis mani&shy;<lb/>fe&longs;tat. </s> <s>Cap. 2. loco 41. (<emph type="italics"/>Videntur dutem in di&longs;ciplinis, &longs;eu Mathematicis qu&aelig;dam <lb/>ob de&longs;initionis defectum non facile de&longs;cribi; vt &amp; quoniam, qu&aelig; ad latus &longs;e&shy;<lb/>cat planum linea, &longs;imiliter diuidit &amp; lineam, &amp; locum: definitione autem dicta, <lb/>fi <gap/>m man fe&longs;tu<gap/>t&longs;t, quod dicitur, nam eandem ablationem habent lota, &amp; <gap/>inea, <lb/><gap/>se latus plan&aelig; figur&aelig;, est autem definitio eiu&longs;dem proportionis h&aelig;c<emph.end type="italics"/>) mendos&egrave; <lb/>lugitur &agrave; nonnullis (<emph type="italics"/>E&longs;t distem de&longs;initio eiu&longs;dem orationis h&aelig;c<emph.end type="italics"/>) quos puto de&shy;<lb/>ceptos ab &aelig;quiuoco <foreign lang="greek">lsgous</foreign> quod &amp; orationem, &amp; rationem, &longs;iue proportio&shy;<lb/>nem &longs;ignificat: hic autem &longs;ignificare proportionem res &longs;ubrecta &longs;atis mani&shy;<lb/>fe&longs;tat. </s>
  
  
 <s>Notandum po&longs;tea cum Alexandro (quod &amp; &longs;uperius alias commo&shy;<lb/>nui in cap. </s> <s>Notandum po&longs;tea cum Alexandro (quod &amp; &longs;uperius alias commo&shy;<lb/>nui in cap.
  
 <s>de Priori, &amp; alibi) per verbum (De&longs;cribi) fignificari hoc loco <lb/>geometric&egrave; demon&longs;trare, quoniam Geometr&aelig; <expan abbr="n&otilde;">non</expan> ni&longs;i adhibit is de&longs;criptio&shy;<lb/>nibus, &longs;<gap/>u figutis demon&longs;trant. </s> de Priori, &amp; alibi) per verbum (De&longs;cribi) fignificari hoc loco <lb/>geometric&egrave; demon&longs;trare, quoniam Geometr&aelig; <expan abbr="n&otilde;">non</expan> ni&longs;i adhibit is de&longs;criptio&shy;<lb/>nibus, &longs;<gap/>u figutis demon&longs;trant. </s>
  
 <s>Vult autem Ari&longs;t.  <s>Vult autem Ari&longs;t.
  
 exemplo mathematico <lb/>o&longs;tendere, difficile e&longs;&longs;e di&longs;putare, aut <gap/> <expan abbr="rgum&etilde;tari">rgumentari</expan>, ni&longs;i prius rect&egrave; a&longs;&longs;ignetur <pb pagenum="69"/>definitio illius rei, de qua di&longs;&longs;eritur. </s> exemplo mathematico <lb/>o&longs;tendere, difficile e&longs;&longs;e di&longs;putare, aut <gap/> <expan abbr="rgum&etilde;tari">rgumentari</expan>, ni&longs;i prius rect&egrave; a&longs;&longs;ignetur <pb pagenum="69"/>definitio illius rei, de qua di&longs;&longs;eritur. </s>
  
 <s>Porr&ograve; exemplum mathematicum hic <lb/>allatum &longs;ic videtur explicandum: Conetur aliquis demon&longs;trare hanc pro&shy;<lb/>po&longs;itionem; &longs;i linea ducta fuerit &aelig;quidi&longs;tans lateri vnius plani trianguli, &longs;e&shy;<lb/>cabit &amp; latera, &amp; locum, ideft &longs;uperficiem illam triangularem &longs;imiliter, ide &longs;t <lb/><figure id="fig32"></figure><lb/>in eadem proportione, vt in triangulo A B C, <lb/>linea D E, parallela ba&longs;i B C, &longs;ecat latera A B, <lb/>&amp; A C, in punctis D, &amp; E, in eadem ratione, <lb/>in qua etiam fecat totum triangulum, ita vt <lb/>eadem &longs;it proportio line&aelig; A D, ad D B, &amp; line&aelig; <lb/>A E, ad E C, qu&aelig; e&longs;t partium totalis trianguli <lb/>A B C, &longs;eilicet qu&aelig; e&longs;t partis A D E, ad partem <lb/>E D C, fiue ad partem D E B. quod con&longs;tat ex <lb/>&longs;ecunda 6. Elem. </s> <s>Porr&ograve; exemplum mathematicum hic <lb/>allatum &longs;ic videtur explicandum: Conetur aliquis demon&longs;trare hanc pro&shy;<lb/>po&longs;itionem; &longs;i linea ducta fuerit &aelig;quidi&longs;tans lateri vnius plani trianguli, &longs;e&shy;<lb/>cabit &amp; latera, &amp; locum, ideft &longs;uperficiem illam triangularem &longs;imiliter, ide &longs;t <lb/><figure id="fig32"/><lb/>in eadem proportione, vt in triangulo A B C, <lb/>linea D E, parallela ba&longs;i B C, &longs;ecat latera A B, <lb/>&amp; A C, in punctis D, &amp; E, in eadem ratione, <lb/>in qua etiam fecat totum triangulum, ita vt <lb/>eadem &longs;it proportio line&aelig; A D, ad D B, &amp; line&aelig; <lb/>A E, ad E C, qu&aelig; e&longs;t partium totalis trianguli <lb/>A B C, &longs;eilicet qu&aelig; e&longs;t partis A D E, ad partem <lb/>E D C, fiue ad partem D E B. quod con&longs;tat ex <lb/>&longs;ecunda 6. Elem. </s>
  
 <s>Inquit ergo Ari&longs;t. </s> <s>Inquit ergo Ari&longs;t. </s>
  
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 <s>Porr&ograve; Euclides definit. </s> <s>Porr&ograve; Euclides definit. </s>
  
 <s>&longs;eptima 5. paulo ali&shy;<lb/>ter definit quantitates proportionales e&longs;&longs;e illas, qu&aelig; candem habent ratio&shy;<lb/>nem, v. </s> <s>&longs;eptima 5. paulo ali&shy;<lb/>ter definit quantitates proportionales e&longs;&longs;e illas, qu&aelig; eandem habent ratio&shy;<lb/>nem, v. </s>
  
 <s>g. </s> <s>g. </s>
  
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 <s>ex quibus <lb/>quoad Mathematicas &longs;pectat, huic loco &longs;atisfactum &longs;it.</s></p><p type="main"> <s>ex quibus <lb/>quoad Mathematicas &longs;pectat, huic loco &longs;atisfactum &longs;it.</s></p><p type="main">
  
 <s><arrow.to.target n="marg82"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg82"/></s></p><p type="margin">
  
 <s><margin.target id="marg82"></margin.target>82</s></p><p type="main"> <s><margin.target id="marg82"/>82</s></p><p type="main">
  
  
 <s>Cap. 4. loco 86. <emph type="italics"/>(Tentandum autem, &amp; ea, in qu&aelig; &longs;&aelig;pi&longs;&longs;im&egrave; incidunt di&longs;puta&shy;<lb/>tiones, tenere, nam quemadmodum in Geometria ante opus e&longs;t circa elementa exer&shy;<lb/>citatum e&longs;&longs;e, &amp; in numeris circa capitales prompt&egrave; &longs;e habere, &amp; multum refert ad <lb/>boc, &amp; alium numerum cogno&longs;cere multiplicatum)<emph.end type="italics"/> Elementa vocabant antiqui <lb/>demon&longs;trationes faciliores, &amp; &longs;impliciores, quales propri&egrave; &longs;unt omnes, qu&aelig; <lb/>&longs;ex prioribus libris Euclidianis continentur: ex illis enim tanquam ex ele&shy;<lb/>mentis ab&longs;tru&longs;iores, &amp; difficiliores demon&longs;trationes deducebant. </s> <s>Cap. 4. loco 86. <emph type="italics"/>(Tentandum autem, &amp; ea, in qu&aelig; &longs;&aelig;pi&longs;&longs;im&egrave; incidunt di&longs;puta&shy;<lb/>tiones, tenere, nam quemadmodum in Geometria ante opus e&longs;t circa elementa exer&shy;<lb/>citatum e&longs;&longs;e, &amp; in numeris circa capitales prompt&egrave; &longs;e habere, &amp; multum refert ad <lb/>boc, &amp; alium numerum cogno&longs;cere multiplicatum)<emph.end type="italics"/> Elementa vocabant antiqui <lb/>demon&longs;trationes faciliores, &amp; &longs;impliciores, quales propri&egrave; &longs;unt omnes, qu&aelig; <lb/>&longs;ex prioribus libris Euclidianis continentur: ex illis enim tanquam ex ele&shy;<lb/>mentis ab&longs;tru&longs;iores, &amp; difficiliores demon&longs;trationes deducebant. </s>
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 <s><emph type="italics"/>Ex Primo Elenchorum.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Ex Primo Elenchorum.<emph.end type="italics"/></s></p><p type="main">
  
 <s><arrow.to.target n="marg83"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg83"/></s></p><p type="margin">
  
 <s><margin.target id="marg83"></margin.target>83</s></p><p type="main"> 
  
  <s><margin.target id="marg83"/>83</s></p><p type="main">
  
 <s>Cap. 10. <emph type="italics"/>(Nam p&longs;eudograpbi&aelig; non contentio&longs;&aelig; (&longs;ecundum enim ea, qu&aelig; <lb/>&longs;ub arte &longs;unt, captio&longs;&aelig; &longs;unt ratiocinationes) <expan abbr="neq;">neque</expan> &longs;i aliqua e&longs;t p&longs;eudogra&shy;<lb/>phia circa verum, vt Hippocratis quadratura, qu&aelig; per lunulas, &longs;ed, vt <lb/>Bry&longs;&longs;o quadrauit circulum; &amp; tamet&longs;i quadretur circulus, quia tamen <lb/>non &longs;ecundum rem, ideo &longs;ophi&longs;ticus)<emph.end type="italics"/> qua ratione Hippocrates orbi quadrum <lb/>exhibere &aelig;quale tentauerit, explicatum e&longs;t abund&egrave; in 2. Priorum cap. </s> 
  
  <s>Cap. 10. <emph type="italics"/>(Nam p&longs;eudograpbi&aelig; non contentio&longs;&aelig; (&longs;ecundum enim ea, qu&aelig; <lb/>&longs;ub arte &longs;unt, captio&longs;&aelig; &longs;unt ratiocinationes) <expan abbr="neq;">neque</expan> &longs;i aliqua e&longs;t p&longs;eudogra&shy;<lb/>phia circa verum, vt Hippocratis quadratura, qu&aelig; per lunulas, &longs;ed, vt <lb/>Bry&longs;&longs;o quadrauit circulum; &amp; tamet&longs;i quadretur circulus, quia tamen <lb/>non &longs;ecundum rem, ideo &longs;ophi&longs;ticus)<emph.end type="italics"/> qua ratione Hippocrates orbi quadrum <lb/>exhibere &aelig;quale tentauerit, explicatum e&longs;t abund&egrave; in 2. Priorum cap.
  
 <s>31. <lb/>&amp; quo itidem modo Bry&longs;&longs;o lib. </s> 
  
 <s>1. Po&longs;ter. </s> 31. <lb/>&amp; quo itidem modo Bry&longs;&longs;o lib.
  
 <s>tex. </s> 1. Po&longs;ter. tex. </s>
  
 <s>23. <expan abbr="&longs;ol&utilde;modo">&longs;olummodo</expan> id hoc loco no&shy;<lb/>tandum per p&longs;eudographiam intelligere, vt apert&egrave; etiam inferius explicat, <lb/>Geometricam demon&longs;trationem fallacem, e&ograve; quod demon&longs;trationes geo&shy;<lb/>metric&aelig; fiant adhibitis de&longs;criptionibus, &longs;eu figurationibus: p&longs;endographia <lb/>autem latin&egrave; idem e&longs;t, ac fal&longs;a de&longs;criptio; quemadmodum &egrave; contrari&ograve;, &longs;i&shy;<lb/>cuti &longs;upra in Topicis, &amp; alibi ob&longs;eruaui, per de&longs;cribere intelligit geometri&shy;<lb/>c&egrave; demon&longs;trare, &amp; per de&longs;criptiones intelligit demon&longs;trationes geometri&shy;<lb/>cas. </s> <s>23. <expan abbr="&longs;ol&utilde;modo">&longs;olummodo</expan> id hoc loco no&shy;<lb/>tandum per p&longs;eudographiam intelligere, vt apert&egrave; etiam inferius explicat, <lb/>Geometricam demon&longs;trationem fallacem, e&ograve; quod demon&longs;trationes geo&shy;<lb/>metric&aelig; fiant adhibitis de&longs;criptionibus, &longs;eu figurationibus: p&longs;endographia <lb/>autem latin&egrave; idem e&longs;t, ac fal&longs;a de&longs;criptio; quemadmodum &egrave; contrari&ograve;, &longs;i&shy;<lb/>cuti &longs;upra in Topicis, &amp; alibi ob&longs;eruaui, per de&longs;cribere intelligit geometri&shy;<lb/>c&egrave; demon&longs;trare, &amp; per de&longs;criptiones intelligit demon&longs;trationes geometri&shy;<lb/>cas. </s>
  
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 <s>At ver&ograve; demon&longs;tratio, &longs;eu p&longs;eudographia Bry&longs;&shy;<lb/>&longs;onis erat contentio&longs;a, quia ex communibus, &amp; extra Geometriam petitis <lb/>argumentabatur: quemadmodum ibi explicatum e&longs;t.</s></p><p type="main"> <s>At ver&ograve; demon&longs;tratio, &longs;eu p&longs;eudographia Bry&longs;&shy;<lb/>&longs;onis erat contentio&longs;a, quia ex communibus, &amp; extra Geometriam petitis <lb/>argumentabatur: quemadmodum ibi explicatum e&longs;t.</s></p><p type="main">
  
 <s><arrow.to.target n="marg84"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg84"/></s></p><p type="margin">
  
 <s><margin.target id="marg84"></margin.target>84</s></p><p type="main"> <s><margin.target id="marg84"/>84</s></p><p type="main">
  
 <s>Eodem cap. <emph type="italics"/>(Quadratura per lunulas non contentio&longs;a)<emph.end type="italics"/> inquit Hippocratis <lb/>tetragoni&longs;mum, de quo in 2. Priorum, qu&aelig; non contentio&longs;a dicitur, quia ex <lb/>proprijs Geometri&aelig; deducebatur.</s></p><p type="main"> <s>Eodem cap. <emph type="italics"/>(Quadratura per lunulas non contentio&longs;a)<emph.end type="italics"/> inquit Hippocratis <lb/>tetragoni&longs;mum, de quo in 2. Priorum, qu&aelig; non contentio&longs;a dicitur, quia ex <lb/>proprijs Geometri&aelig; deducebatur.</s></p><p type="main">
  
 <s><arrow.to.target n="marg85"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg85"/></s></p><p type="margin">
  
 <s><margin.target id="marg85"></margin.target>85</s></p><p type="main"> <s><margin.target id="marg85"/>85</s></p><p type="main">
  
 <s>Ibidem <emph type="italics"/>(Bry&longs;&longs;onis autem contentio&longs;a: &amp; illam quidem non e&longs;t transferre, ni&longs;i <lb/>ad Geometriam &longs;olum; eo quod ex proprijs &longs;it principijs)<emph.end type="italics"/> <expan abbr="qu&atilde;do">quando</expan> ait <emph type="italics"/>(&amp; illam qui&shy;<lb/>dem)<emph.end type="italics"/> intelligit quadrationem Hippocratis. </s> <s>Ibidem <emph type="italics"/>(Bry&longs;&longs;onis autem contentio&longs;a: &amp; illam quidem non e&longs;t transferre, ni&longs;i <lb/>ad Geometriam &longs;olum; eo quod ex proprijs &longs;it principijs)<emph.end type="italics"/> <expan abbr="qu&atilde;do">quando</expan> ait <emph type="italics"/>(&amp; illam qui&shy;<lb/>dem)<emph.end type="italics"/> intelligit quadrationem Hippocratis. </s>
  
 <s>vide 2. Prior cap. </s> <s>vide 2. Prior cap.
  
 <s>31. &amp; qu&aelig; pau&shy;<lb/>lo ante in pr&aelig;cedentibus locis diximus.</s></p><p type="main"> 31. &amp; qu&aelig; pau&shy;<lb/>lo ante in pr&aelig;cedentibus locis diximus.</s></p><p type="main">
  
 <s><arrow.to.target n="marg86"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg86"/></s></p><p type="margin">
  
 <s><margin.target id="marg86"></margin.target>86</s></p><p type="main"> <s><margin.target id="marg86"/>86</s></p><p type="main">
  
 <s>Ibidem <emph type="italics"/>(Hanc autem ad plures)<emph.end type="italics"/> intelligit tetragoni&longs;mum Bry&longs;&longs;onis, qui <lb/>per communia deducebatur. </s> <s>Ibidem <emph type="italics"/>(Hanc autem ad plures)<emph.end type="italics"/> intelligit tetragoni&longs;mum Bry&longs;&longs;onis, qui <lb/>per communia deducebatur. </s>
  
 <s>lege &longs;uperius dicta in pr&aelig;cedentibus locis hu&shy;<lb/>ius capituli.</s></p><p type="main"> <s>lege &longs;uperius dicta in pr&aelig;cedentibus locis hu&shy;<lb/>ius capituli.</s></p><p type="main">
  
 <s><arrow.to.target n="marg87"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg87"/></s></p><p type="margin">
  
 <s><margin.target id="marg87"></margin.target>87</s></p><figure></figure><p type="main"> <s><margin.target id="marg87"/>87</s></p><figure/><p type="main">
  
 <s>Ad &longs;inem cap. <emph type="italics"/>(Aut vt Antiphon quadra&shy;<lb/>uit)<emph.end type="italics"/> &longs;imile peccatum pecca&longs;&longs;e Antiphon&shy;<lb/>tem in orbe quadrando, ac Hippocratem, <lb/>Ari&longs;t.  <s>Ad &longs;inem cap. <emph type="italics"/>(Aut vt Antiphon quadra&shy;<lb/>uit)<emph.end type="italics"/> &longs;imile peccatum pecca&longs;&longs;e Antiphon&shy;<lb/>tem in orbe quadrando, ac Hippocratem, <lb/>Ari&longs;t.
  
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 <s>quod fieri po&longs;&longs;e ille <lb/>fals&ograve; contra Geometri&aelig; principia a&longs;&longs;umebat; e&longs;t enim principium Geome&shy;<lb/>tricum continuum e&longs;&longs;e diui&longs;ibile in infinitum, <expan abbr="neq;">neque</expan> per diui&longs;ionem ab&longs;umi <lb/>po&longs;&longs;e; cui principio aduer&longs;atur, dum putat &longs;e con&longs;umpturum rotum circu&shy;<lb/>lum, diuidendo illud in triangula &longs;emper minora; vel quia putat, lineam <lb/>curuam con&longs;tare ex minimis lineis rectis. </s> <s>quod fieri po&longs;&longs;e ille <lb/>fals&ograve; contra Geometri&aelig; principia a&longs;&longs;umebat; e&longs;t enim principium Geome&shy;<lb/>tricum continuum e&longs;&longs;e diui&longs;ibile in infinitum, <expan abbr="neq;">neque</expan> per diui&longs;ionem ab&longs;umi <lb/>po&longs;&longs;e; cui principio aduer&longs;atur, dum putat &longs;e con&longs;umpturum rotum circu&shy;<lb/>lum, diuidendo illud in triangula &longs;emper minora; vel quia putat, lineam <lb/>curuam con&longs;tare ex minimis lineis rectis. </s>
  
 <s>Similiter igitur <expan abbr="atq;">atque</expan> Hippocra&shy;<lb/>res errauit, q&uacute;i pariter in Geometria fallebatur: Antiphon quidem contra <lb/>principia illius: Hippocrates ver&ograve; a&longs;&longs;umens fal&longs;i quidpiam in Geometria. <lb/></s> <s>Similiter igitur <expan abbr="atq;">atque</expan> Hippocra&shy;<lb/>res errauit, q&uacute;i pariter in Geometria fallebatur: Antiphon quidem contra <lb/>principia illius: Hippocrates ver&ograve; a&longs;&longs;umens fal&longs;i quidpiam in Geometria. <lb/><!-- KEEP S--></s>
  
 <s>At Bry&longs;&longs;o, eo quod per communia alijs &longs;cientijs deduceret ratiocinatio&shy;<lb/>nem propterea p&longs;eudographia Antiphontis non litigio&longs;a quidem, &longs;ed <lb/>tamen fallax extitit, non enim per communia alijs &longs;cientijs <lb/>procedat; vnde nec transferri poterat ip&longs;ius fal&longs;a de&shy;<lb/>&longs;criptio, &longs;eu demon&longs;tratio extra Geometri&aelig; li&shy;<lb/>mites, quod cau&longs;a e&longs;t contentionis.</s></p><p type="head"> <s>At Bry&longs;&longs;o, eo quod per communia alijs &longs;cientijs deduceret ratiocinatio&shy;<lb/>nem propterea p&longs;eudographia Antiphontis non litigio&longs;a quidem, &longs;ed <lb/>tamen fallax extitit, non enim per communia alijs &longs;cientijs <lb/>procedat; vnde nec transferri poterat ip&longs;ius fal&longs;a de&shy;<lb/>&longs;criptio, &longs;eu demon&longs;tratio extra Geometri&aelig; li&shy;<lb/>mites, quod cau&longs;a e&longs;t contentionis.</s></p><p type="head">
  
 <s><emph type="italics"/>Log<gap/>corum locorum finis.<emph.end type="italics"/></s></p><figure></figure><pb pagenum="72"/><p type="head"> <s><emph type="italics"/>Log<gap/>corum locorum finis.<emph.end type="italics"/></s></p><figure/><pb pagenum="72"/><p type="head">
  
 <s>EX PRIMO LIBRO</s></p><p type="head"> <s>EX PRIMO LIBRO</s></p><p type="head">
  
 <s>PHYSICORVM.<lb/><arrow.to.target n="marg88"></arrow.to.target></s></p><p type="margin"> <s>PHYSICORVM.<lb/><arrow.to.target n="marg88"/></s></p><p type="margin">
  
 <s><margin.target id="marg88"></margin.target>88</s></p><p type="main"> <s><margin.target id="marg88"/>88</s></p><p type="main">
  
 <s>Tex. </s> <s>Tex. 11. <emph type="italics"/>(Simul autem <expan abbr="neq;">neque</expan> conuenit omnia &longs;oluere', &longs;ed <expan abbr="qu&aelig;cunq;">qu&aelig;cunque</expan> ex <lb/>principijs aliquis demon&longs;trans <expan abbr="m&etilde;titur">mentitur</expan>; <expan abbr="qu&aelig;cunq;">qu&aelig;cunque</expan> ver&ograve; non, minim&egrave;: <lb/>vt tetragoni&longs;mum, eum quidem, qui per &longs;ectiones Geometrici est di&longs;&shy;<lb/>&longs;oluere: illum autem, qui Antiphontis non Geometrici e&longs;t<emph.end type="italics"/>) Tetrago&shy;<lb/>ni&longs;mum, &longs;eu circuli quadraturam per &longs;ectiones, e&longs;&longs;e illam Hip&shy;<lb/>pocratis Chij exi&longs;timant gr&aelig;ci expo&longs;itores, qui per lunulas, quas Ari&longs;t. &longs;e&shy;<lb/>ctiones appellat, orbem quadrare tentabat. </s>
  
 <s>11. <emph type="italics"/>(Simul autem <expan abbr="neq;">neque</expan> conuenit omnia &longs;oluere', &longs;ed <expan abbr="qu&aelig;cunq;">qu&aelig;cunque</expan> ex <lb/>principijs aliquis demon&longs;trans <expan abbr="m&etilde;titur">mentitur</expan>; <expan abbr="qu&aelig;cunq;">qu&aelig;cunque</expan> ver&ograve; non, minim&egrave;: <lb/>vt tetragoni&longs;mum, eum quidem, qui per &longs;ectiones Geometrici est di&longs;&shy;<lb/>&longs;oluere: illum autem, qui Antiphontis non Geometrici e&longs;t<emph.end type="italics"/>) Tetrago&shy;<lb/>ni&longs;mum, &longs;eu circuli quadraturam per &longs;ectiones, e&longs;&longs;e illam Hip&shy;<lb/>pocratis Chij exi&longs;timant gr&aelig;ci expo&longs;itores, qui per lunulas, quas Ari&longs;t. </s> <s>Eius den on&longs;trationem expli&shy;<lb/>caui ad cap.
  
 <s>&longs;e&shy;<lb/>ctiones appellat, orbem quadrare tentabat. </s> 31. de Abductione in 2. Priorum, quam inibi videas. </s>
  
 <s>Eius den on&longs;trationem expli&shy;<lb/>caui ad cap. </s> 
  
 <s>31. de Abductione in 2. Priorum, quam inibi videas. </s> 
  
 <s>hoc &longs;olum <lb/>hic notandum pertinere ad Geometram, ip&longs;am refellere, quia ex fal&longs;a qua&shy;<lb/>dam pr&aelig;mi&longs;&longs;a ex Geometria de&longs;umpta, ratiocinabatur, idcirco debet (in&shy;<lb/>quit Ari&longs;t.) Geometra illius deceptionem inuenire. </s> <s>hoc &longs;olum <lb/>hic notandum pertinere ad Geometram, ip&longs;am refellere, quia ex fal&longs;a qua&shy;<lb/>dam pr&aelig;mi&longs;&longs;a ex Geometria de&longs;umpta, ratiocinabatur, idcirco debet (in&shy;<lb/>quit Ari&longs;t.) Geometra illius deceptionem inuenire. </s>
  
 <s>Tetragoni&longs;mum autem <lb/>Antiphontis non e&longs;t Geometr&aelig; <expan abbr="c&otilde;futare">confutare</expan>, quia aduer&longs;abatur principijs Geo&shy;<lb/>metri&aelig;, &longs;upponebat enim circuli circumferentiam ex indiu<gap/>s, <expan abbr="minimis&qacute;">minimisque</expan>; <lb/>lineis rectis componi: cuius fal&longs;am demon&longs;trationem exp<gap/>ram i<gap/>uenies <lb/>ad cap. </s> <s>Tetragoni&longs;mum autem <lb/>Antiphontis non e&longs;t Geometr&aelig; <expan abbr="c&otilde;futare">confutare</expan>, quia aduer&longs;abatur principijs Geo&shy;<lb/>metri&aelig;, &longs;upponebat enim circuli circumferentiam ex indiu<gap/>s, <expan abbr="minimis&qacute;">minimisque</expan>; <lb/>lineis rectis componi: cuius fal&longs;am demon&longs;trationem exp<gap/>ram i<gap/>uenies <lb/>ad cap.
  
 <s>10. primi Elench. </s> 10. primi Elench. </s>
  
 <s>po&longs;&longs;umus addere tertiam rat<gap/> <gap/>cet <lb/>Hippocrates non procedebat per communia alijs &longs;ci<gap/>ad <lb/>tex. </s> <s>po&longs;&longs;umus addere tertiam rat<gap/> <gap/>cet <lb/>Hippocrates non procedebat per communia alijs &longs;ci<gap/>ad <lb/>tex. </s>
  
 <s>23. primi Po&longs;ter. </s> <s>23. primi Po&longs;ter. cap.
  
 <s>cap. </s> 
  
 <s>8. vbi ip&longs;ius p&longs;endographi<gap/>d&shy;<lb/>modum igitur Geometra di&longs;&longs;oluit fal&longs;as tantum<gap/>r&shy;<lb/>uatis Geometricis principijs procedunt; non au<gap/> <gap/>ri&aelig; <lb/>principia conuellunt: ita Phy&longs;ico non incumbit <expan abbr="c&otilde;tra">contra</expan> P<gap/> Me&shy;<lb/>li&longs;&longs;um natur&aelig; principia de&longs;truentes di&longs;ceptare, aut falla<gap/> rationes <lb/>coarguere. </s> 8. vbi ip&longs;ius p&longs;endographi<gap/>d&shy;<lb/>modum igitur Geometra di&longs;&longs;oluit fal&longs;as tantum<gap/>r&shy;<lb/>uatis Geometricis principijs procedunt; non au<gap/> <gap/>ri&aelig; <lb/>principia conuellunt: ita Phy&longs;ico non incumbit <expan abbr="c&otilde;tra">contra</expan> P<gap/> Me&shy;<lb/>li&longs;&longs;um natur&aelig; principia de&longs;truentes di&longs;ceptare, aut falla<gap/> rationes <lb/>coarguere. </s>
  
 <s>Hoc volebat Ari&longs;toteles inferre.</s></p><p type="head"> <s>Hoc volebat Ari&longs;toteles inferre.</s></p><p type="head">
  
 <s><emph type="italics"/>Ex Secundo Phy&longs;icorum.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Ex Secundo Phy&longs;icorum.<emph.end type="italics"/></s></p><p type="main">
  
 <s><arrow.to.target n="marg89"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg89"/></s></p><p type="margin">
  
 <s><margin.target id="marg89"></margin.target>89</s></p><p type="main"> 
  
 <s>Tex. </s> <s><margin.target id="marg89"/>89</s></p><p type="main">
  
 <s>20. (<emph type="italics"/>Geometria enim de phy&longs;ica linea con&longs;iderat, &longs;ed non quatenus <lb/>e&longs;t phy&longs;ici: Per&longs;pectiua autem ma<gap/> hematicam quidem imcam, &longs;ed non <lb/>quatenus phy&longs;ica e&longs;t<emph.end type="italics"/>) quamuis textus hic non pertineat ad Mathe&shy;<lb/>maticum, libuit tamen illum in ordin<gap/>m no&longs;trum recen&longs;ere, ope&shy;<lb/>r&aelig;pretium etenim e&longs;t ea, qu&aelig; in ip&longs;o continentur &agrave; nonnullis recentioribus <lb/>rect&egrave; intelligi, vt ab his moniti, ab inani quadam optices impugnatione ab&shy;<lb/>&longs;tineant, ac tandem ex Ari&longs;t.  <s>Tex. 20. (<emph type="italics"/>Geometria enim de phy&longs;ica linea con&longs;iderat, &longs;ed non quatenus <lb/>e&longs;t phy&longs;ici: Per&longs;pectiua autem ma<gap/> hematicam quidem imcam, &longs;ed non <lb/>quatenus phy&longs;ica e&longs;t<emph.end type="italics"/>) quamuis textus hic non pertineat ad Mathe&shy;<lb/>maticum, libuit tamen illum in ordin<gap/>m no&longs;trum recen&longs;ere, ope&shy;<lb/>r&aelig;pretium etenim e&longs;t ea, qu&aelig; in ip&longs;o continentur &agrave; nonnullis recentioribus <lb/>rect&egrave; intelligi, vt ab his moniti, ab inani quadam optices impugnatione ab&shy;<lb/>&longs;tineant, ac tandem ex Ari&longs;t.
  
 lineas illas vi&longs;uales quas ip&longs;i de medio tollunt, <lb/>per&longs;picu&egrave; videant. </s> lineas illas vi&longs;uales quas ip&longs;i de medio tollunt, <lb/>per&longs;picu&egrave; videant. </s>
  
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 de Natura Ma&shy;<lb/>thematicarum habet, &longs;unt pr&aelig;ter no&longs;trum in&longs;titutum.</s></p><p type="main"> de Natura Ma&shy;<lb/>thematicarum habet, &longs;unt pr&aelig;ter no&longs;trum in&longs;titutum.</s></p><p type="main">
  
 <s><arrow.to.target n="marg90"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg90"/></s></p><p type="margin">
  
 <s><margin.target id="marg90"></margin.target>90</s></p><p type="main"> 
  
 <s>Tex. </s> <s><margin.target id="marg90"/>90</s></p><p type="main">
  
 <s>28. (<emph type="italics"/>Alio autem modo, &longs;orma, &amp; exemplum: b&aelig;c autem e&longs;t ratio ip&longs;ius, <lb/>quod quid erat e&longs;&longs;e, &amp; huius genera, vt ip&longs;ius diapa&longs;on duo ad vnum, &amp; omnino <lb/>numerus, &amp; partes, qu&aelig; in ratione &longs;unt<emph.end type="italics"/>) vt ben&egrave; intelligas, quod in pr&aelig;&longs;enti <lb/>textu <expan abbr="mathematic&utilde;">mathematicum</expan> e&longs;t, con&longs;ule prius, qu&aelig; &longs;crip&longs;i ad tex. </s> <s>Tex. 28. (<emph type="italics"/>Alio autem modo, &longs;orma, &amp; exemplum: b&aelig;c autem e&longs;t ratio ip&longs;ius, <lb/>quod quid erat e&longs;&longs;e, &amp; huius genera, vt ip&longs;ius diapa&longs;on duo ad vnum, &amp; omnino <lb/>numerus, &amp; partes, qu&aelig; in ratione &longs;unt<emph.end type="italics"/>) vt ben&egrave; intelligas, quod in pr&aelig;&longs;enti <lb/>textu <expan abbr="mathematic&utilde;">mathematicum</expan> e&longs;t, con&longs;ule prius, qu&aelig; &longs;crip&longs;i ad tex. </s>
  
 <s>1. cap. </s> <s>1. cap.
  
 <s>primi 2. Po&shy;<lb/>&longs;ter. </s> primi 2. Po&shy;<lb/>&longs;ter. </s>
  
 <s>&longs;uper verba illa (<emph type="italics"/>Quid e&longs;t con&longs;onan<gap/>ia?<emph.end type="italics"/>) vbi per&longs;picu&egrave; videbis, cur <expan abbr="con-&longs;on&atilde;ti&aelig;">con&shy;<lb/>&longs;onanti&aelig;</expan>, qu&aelig; dicitur Diapa&longs;on, e&longs;&longs;entia, &amp; definitio &longs;it ip&longs;a proportio dupla, <lb/>qu&aelig; &longs;ub his num. </s> <s>&longs;uper verba illa (<emph type="italics"/>Quid e&longs;t con&longs;onan<gap/>ia?<emph.end type="italics"/>) vbi per&longs;picu&egrave; videbis, cur <expan abbr="con-&longs;on&atilde;ti&aelig;">con&shy;<lb/>&longs;onanti&aelig;</expan>, qu&aelig; dicitur Diapa&longs;on, e&longs;&longs;entia, &amp; definitio &longs;it ip&longs;a proportio dupla, <lb/>qu&aelig; &longs;ub his num. </s>
  
 <s>2.1. continetur: quibus per&longs;pectis facilis erit phy&longs;ico totius <lb/>loci intelligentia.</s></p><pb pagenum="73"/><p type="main"> <s>2.1. continetur: quibus per&longs;pectis facilis erit phy&longs;ico totius <lb/>loci intelligentia.</s></p><pb pagenum="73"/><p type="main">
  
 <s><arrow.to.target n="marg91"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg91"/></s></p><p type="margin">
  
 <s><margin.target id="marg91"></margin.target>91</s></p><p type="main"> <s><margin.target id="marg91"/>91</s></p><p type="main">
  
 <s>Tex. </s> <s>Tex. 68. (<emph type="italics"/>Aut enim ad ip&longs;um quid e&longs;t, reducitur ip&longs;um propter quid in immo&shy;<lb/>bihbus, vt in Mathematicis, ad definitionem enim recti, aut commen&longs;urabilis, aut <lb/>alius cuiu&longs;piam reducitur vltimum<emph.end type="italics"/>) ex his manife&longs;t&egrave; videas Mathematicas <expan abbr="de-m&otilde;&longs;trare">de&shy;<lb/>mon&longs;trare</expan> per cau&longs;am formalem, cum cau&longs;am ip&longs;am ad ip&longs;um quid e&longs;t, ide&longs;t, <lb/>ad definitionem reducant. </s>
  
 <s>68. (<emph type="italics"/>Aut enim ad ip&longs;um quid e&longs;t, reducitur ip&longs;um propter quid in immo&shy;<lb/>bihbus, vt in Mathematicis, ad definitionem enim recti, aut commen&longs;urabilis, aut <lb/>alius cuiu&longs;piam reducitur vltimum<emph.end type="italics"/>) ex his manife&longs;t&egrave; videas Mathematicas <expan abbr="de-m&otilde;&longs;trare">de&shy;<lb/>mon&longs;trare</expan> per cau&longs;am formalem, cum cau&longs;am ip&longs;am ad ip&longs;um quid e&longs;t, ide&longs;t, <lb/>ad definitionem reducant. </s> 
  
 <s>quorum exempla in logicis ex Mathematicis at&shy;<lb/>tuli: &longs;ed etiam &longs;equentis loci exemplum de triangulo idem apert&egrave; manife&shy;<lb/>&longs;tat; in quo probat duos angulos A C B, A C D, e&longs;&longs;e rectos, ex definitione <lb/>ip&longs;orum, &longs;iue ex definitione line&aelig; perpendicularis A C, quod idem e&longs;t.</s></p><p type="main"> <s>quorum exempla in logicis ex Mathematicis at&shy;<lb/>tuli: &longs;ed etiam &longs;equentis loci exemplum de triangulo idem apert&egrave; manife&shy;<lb/>&longs;tat; in quo probat duos angulos A C B, A C D, e&longs;&longs;e rectos, ex definitione <lb/>ip&longs;orum, &longs;iue ex definitione line&aelig; perpendicularis A C, quod idem e&longs;t.</s></p><p type="main">
  
 <s><arrow.to.target n="marg92"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg92"/></s></p><p type="margin">
  
 <s><margin.target id="marg92"></margin.target>92</s></p><p type="main"> <s><margin.target id="marg92"/>92</s></p><p type="main">
  
 <s>Tex 89. (<emph type="italics"/>E&longs;t autem nece&longs;&longs;arium in Mathematicis, &amp; in his, qu&aelig; &longs;ecundum <lb/>natur am fiunt qua&longs;i eodem modo; quoniam enim hocrectum e&longs;t, nece&longs;&longs;e e&longs;t, trian&shy;<lb/>gulum trcs angulos habere &aelig;quales duobus rectis; &longs;ed non, &longs;i hoc, illud; &longs;ed &longs;i hoc <lb/>non e&longs;t, <expan abbr="neq;">neque</expan> rectum e&longs;t.<emph.end type="italics"/>) cum animaduerterim non parum e&longs;&longs;e di&longs;&longs;en&longs;ionis, &amp; <lb/>difficultatis in exemplo hoc mathematico explicando, ita vt recentiores <lb/>quidam textum <expan abbr="h&utilde;c">hunc</expan> pro arbitratu &longs;uo perperam latin&egrave; verterint: ide&ograve; pri&shy;<lb/>mum ex gr&aelig;cis codicibus interpretationem hanc veram attuli. </s> <s>Tex 89. (<emph type="italics"/>E&longs;t autem nece&longs;&longs;arium in Mathematicis, &amp; in his, qu&aelig; &longs;ecundum <lb/>natur am fiunt qua&longs;i eodem modo; quoniam enim hocrectum e&longs;t, nece&longs;&longs;e e&longs;t, trian&shy;<lb/>gulum trcs angulos habere &aelig;quales duobus rectis; &longs;ed non, &longs;i hoc, illud; &longs;ed &longs;i hoc <lb/>non e&longs;t, <expan abbr="neq;">neque</expan> rectum e&longs;t.<emph.end type="italics"/>) cum animaduerterim non parum e&longs;&longs;e di&longs;&longs;en&longs;ionis, &amp; <lb/>difficultatis in exemplo hoc mathematico explicando, ita vt recentiores <lb/>quidam textum <expan abbr="h&utilde;c">hunc</expan> pro arbitratu &longs;uo perperam latin&egrave; verterint: ide&ograve; pri&shy;<lb/>mum ex gr&aelig;cis codicibus interpretationem hanc veram attuli. </s>
  
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 <s>cum velit Ari&longs;t.  <s>cum velit Ari&longs;t.
  
 o&longs;tendere nece&longs;&longs;ita&shy;<lb/>tem, qu&aelig; in &longs;cientijs inter pr&aelig;mi&longs;&longs;as, &longs;cu medium, &amp; conclu&longs;ionem reperi&shy;<lb/>tur, affert exemplum illud mathematicum &longs;ibi familiare, demon&longs;trationem <lb/>&longs;cilicet illam, qua o&longs;tenditur, omne triangulum habere tres angulos &aelig;qua&shy;<lb/>les duobus rectis angulis, cuius fu&longs;i&longs;&longs;imam explicationem inuenies &longs;upra in <lb/>primo Priorum, &longs;ecto 3. cap. </s> o&longs;tendere nece&longs;&longs;ita&shy;<lb/>tem, qu&aelig; in &longs;cientijs inter pr&aelig;mi&longs;&longs;as, &longs;cu medium, &amp; conclu&longs;ionem reperi&shy;<lb/>tur, affert exemplum illud mathematicum &longs;ibi familiare, demon&longs;trationem <lb/>&longs;cilicet illam, qua o&longs;tenditur, omne triangulum habere tres angulos &aelig;qua&shy;<lb/>les duobus rectis angulis, cuius fu&longs;i&longs;&longs;imam explicationem inuenies &longs;upra in <lb/>primo Priorum, &longs;ecto 3. cap.
  
 <s>1. quam nece&longs;&longs;e e&longs;t, con&longs;ulas. </s> 1. quam nece&longs;&longs;e e&longs;t, con&longs;ulas. </s>
  
 <s>pro medio autem <lb/>huius pa&longs;&longs;ionis accipit lineam perpendicularem, quam innuit verbis illis <lb/><emph type="italics"/>(quoniam enim hoc rectum e&longs;t<emph.end type="italics"/>) vt in figura &longs;it triangulum A B C, <expan abbr="&longs;it&qacute;">&longs;itque</expan>; vt latus <lb/><figure id="fig33"></figure><lb/>A C, &longs;it perpendiculare <expan abbr="c&utilde;">cum</expan> latere B C, &amp; pro&shy;<lb/>ducatur B C, in D; tunc triangulum A B C, <lb/>habere tres angulos, A, B, &amp; A C B, &aelig;quales <lb/>duobus rectis planum erit: nam <expan abbr="c&utilde;">cum</expan> latus A C, <lb/>&longs;it perpendiculare (quod Ari&longs;t.  <s>pro medio autem <lb/>huius pa&longs;&longs;ionis accipit lineam perpendicularem, quam innuit verbis illis <lb/><emph type="italics"/>(quoniam enim hoc rectum e&longs;t<emph.end type="italics"/>) vt in figura &longs;it triangulum A B C, <expan abbr="&longs;it&qacute;">&longs;itque</expan>; vt latus <lb/><figure id="fig33"/><lb/>A C, &longs;it perpendiculare <expan abbr="c&utilde;">cum</expan> latere B C, &amp; pro&shy;<lb/>ducatur B C, in D; tunc triangulum A B C, <lb/>habere tres angulos, A, B, &amp; A C B, &aelig;quales <lb/>duobus rectis planum erit: nam <expan abbr="c&utilde;">cum</expan> latus A C, <lb/>&longs;it perpendiculare (quod Ari&longs;t.
  
 dicit, cum <expan abbr="re-ct&utilde;">re&shy;<lb/>ctum</expan> hoc &longs;it) erunt duo anguli deinceps A C B, <lb/>A C D, recti, ex definitione line&aelig; perpendicu&shy;<lb/>laris, cum ergo duo anguli A, &amp; B, externo, <expan abbr="recto&qacute;">rectoque</expan>; A C D, &longs;int &aelig;quales per <lb/>32. primi, &amp; reliquus angulus A C B, communis, ide&longs;t, &longs;it angulus triangu&shy;<lb/>li, &amp; angulus vnus line&aelig; perpendicularis, &amp; ide&ograve; rectus; manife&longs;t&egrave; apparet, <lb/>tres angulos A, B, A C B, e&longs;&longs;e &aelig;quales nece&longs;&longs;ari&ograve; duobus rectis, ex po&longs;itio&shy;<lb/>ne illius recti, &longs;iue lateris perpendicularis, quia ex ver&ograve;, verum nece&longs;&longs;ari&ograve; <lb/>&longs;equitur; non tamen po&longs;ita hac pa&longs;&longs;ione, &longs;iue conclu&longs;ione, habere &longs;cilicet <lb/>tres angulos &aelig;quales duobus rectis, nece&longs;&longs;ari&ograve; &longs;equitur illud e&longs;&longs;e rectum, <lb/>idelt latus illud A C, e&longs;&longs;e perpendiculare ad latus B C, quia verum <lb/>&longs;equi pote&longs;t ex ver&ograve;, &amp; fals&ograve;. </s> dicit, cum <expan abbr="re-ct&utilde;">re&shy;<lb/>ctum</expan> hoc &longs;it) erunt duo anguli deinceps A C B, <lb/>A C D, recti, ex definitione line&aelig; perpendicu&shy;<lb/>laris, cum ergo duo anguli A, &amp; B, externo, <expan abbr="recto&qacute;">rectoque</expan>; A C D, &longs;int &aelig;quales per <lb/>32. primi, &amp; reliquus angulus A C B, communis, ide&longs;t, &longs;it angulus triangu&shy;<lb/>li, &amp; angulus vnus line&aelig; perpendicularis, &amp; ide&ograve; rectus; manife&longs;t&egrave; apparet, <lb/>tres angulos A, B, A C B, e&longs;&longs;e &aelig;quales nece&longs;&longs;ari&ograve; duobus rectis, ex po&longs;itio&shy;<lb/>ne illius recti, &longs;iue lateris perpendicularis, quia ex ver&ograve;, verum nece&longs;&longs;ari&ograve; <lb/>&longs;equitur; non tamen po&longs;ita hac pa&longs;&longs;ione, &longs;iue conclu&longs;ione, habere &longs;cilicet <lb/>tres angulos &aelig;quales duobus rectis, nece&longs;&longs;ari&ograve; &longs;equitur illud e&longs;&longs;e rectum, <lb/>idelt latus illud A C, e&longs;&longs;e perpendiculare ad latus B C, quia verum <lb/>&longs;equi pote&longs;t ex ver&ograve;, &amp; fals&ograve;. </s>
  
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 <s><emph type="italics"/>Ex Tertio Phy&longs;icorum.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Ex Tertio Phy&longs;icorum.<emph.end type="italics"/></s></p><p type="main">
  
 <s><arrow.to.target n="marg93"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg93"/></s></p><p type="margin">
  
 <s><margin.target id="marg93"></margin.target>93</s></p><p type="main"> 
  
 <s>Tex. </s> <s><margin.target id="marg93"/>93</s></p><p type="main">
  
 <s>26. <emph type="italics"/>(Et hi quidem infinitum e&longs;&longs;e par; hoc enim compr&aelig;hen&longs;um, &amp; <lb/>ab impari terminatum tribuit ijs, qu&aelig; &longs;unt, infinitatem. </s> <s>Tex. 26. <emph type="italics"/>(Et hi quidem infinitum e&longs;&longs;e par; hoc enim compr&aelig;hen&longs;um, &amp; <lb/>ab impari terminatum tribuit ijs, qu&aelig; &longs;unt, infinitatem. </s>
  
 <s>&longs;ignum autem <lb/>huius id e&longs;&longs;e, quod contingit in numcris, circumpo&longs;it is enim Gnomoni&shy;<lb/>bus circa vnum, &amp; &longs;eor&longs;um, aliquando quidcm &longs;emper aliam fieri &longs;pe&shy;<lb/>ciem, aliquando autem vnam)<emph.end type="italics"/> vt melius percipiantur ea, qu&aelig; &longs;equuntur, lege <lb/>prius, qu&aelig; in cap. </s> <s>&longs;ignum autem <lb/>huius id e&longs;&longs;e, quod contingit in numcris, circumpo&longs;it is enim Gnomoni&shy;<lb/>bus circa vnum, &amp; &longs;eor&longs;um, aliquando quidcm &longs;emper aliam fieri &longs;pe&shy;<lb/>ciem, aliquando autem vnam)<emph.end type="italics"/> vt melius percipiantur ea, qu&aelig; &longs;equuntur, lege <lb/>prius, qu&aelig; in cap.
  
 <s>de Motu in po&longs;t pr&aelig;dicamentis &longs;crip&longs;i de Gnomone, ad <lb/>&longs;imilitudinem enim Gnomonis illius Geometrici, inueniuntur etiam in nu&shy;<lb/>meris Gnomones Arithmetici. </s> de Motu in po&longs;t pr&aelig;dicamentis &longs;crip&longs;i de Gnomone, ad <lb/>&longs;imilitudinem enim Gnomonis illius Geometrici, inueniuntur etiam in nu&shy;<lb/>meris Gnomones Arithmetici. </s>
  
 <s>Pythagorici enim (&agrave; quibus i&longs;ta mutuatus <lb/>e&longs;t Ari&longs;t.  <s>Pythagorici enim (&agrave; quibus i&longs;ta mutuatus <lb/>e&longs;t Ari&longs;t.
  
 numeros impares &longs;olos appellabant Gnomones, e&ograve; quod in for&shy;<lb/>mam norm&aelig; &aelig;quilater&aelig;, &longs;iue Gnomonis con&longs;titui po&longs;&longs;int, vt patet in his <lb/><figure id="fig34"></figure><lb/>nimirum in ternario, quinario, &longs;eptenario, &amp; &longs;ic de <lb/>reliquis imparibus. </s> numeros impares &longs;olos appellabant Gnomones, e&ograve; quod in for&shy;<lb/>mam norm&aelig; &aelig;quilater&aelig;, &longs;iue Gnomonis con&longs;titui po&longs;&longs;int, vt patet in his <lb/><figure id="fig34"/><lb/>nimirum in ternario, quinario, &longs;eptenario, &amp; &longs;ic de <lb/>reliquis imparibus. </s>
  
 <s>pares autem numeri, quia ne&shy;<lb/>queunt in figuram norm&aelig; &aelig;quilater&aelig; di&longs;poni, cum <lb/>non habeant vnitatem pro angulo, &amp; paria po&longs;tea la&shy;<lb/>tera, vt oportet, non merentur appellari Gnomones, vt quaternarius, &longs;i di&shy;<lb/>&longs;ponatur &longs;ic <figure id="fig35"></figure> non refert Gnomonem, quia lateribus in&ecedil;qualibus con&shy;<lb/>&longs;tat; <expan abbr="neq;">neque</expan> &longs;i hoc modo <figure id="fig36"></figure> quia dee&longs;t huic figur&aelig; angularis vnitas, qu&aelig; <lb/>illi nece&longs;iaria e&longs;t. </s> <s>pares autem numeri, quia ne&shy;<lb/>queunt in figuram norm&aelig; &aelig;quilater&aelig; di&longs;poni, cum <lb/>non habeant vnitatem pro angulo, &amp; paria po&longs;tea la&shy;<lb/>tera, vt oportet, non merentur appellari Gnomones, vt quaternarius, &longs;i di&shy;<lb/>&longs;ponatur &longs;ic <figure id="fig35"/> non refert Gnomonem, quia lateribus in&ecedil;qualibus con&shy;<lb/>&longs;tat; <expan abbr="neq;">neque</expan> &longs;i hoc modo <figure id="fig36"/> quia dee&longs;t huic figur&aelig; angularis vnitas, qu&aelig; <lb/>illi nece&longs;iaria e&longs;t. </s>
  
 <s>Pythagorici igitur dicebant, numerum parem ide&ograve; e&longs;&longs;e <lb/>infinitum ip&longs;um, quia videbant ip&longs;um e&longs;&longs;e cau&longs;am perpetu&aelig; diui&longs;ionis, cum <lb/>qu&aelig;libet res quanta &longs;it diui&longs;ibilis bifariam, ide&longs;t in duo &longs;ecundum numerum <lb/>parem, &amp; &longs;ubdiui&longs;ibilis po&longs;tea bifariam, &amp; &longs;ic in infinitum, vt de linea pro&shy;<lb/>blematic&egrave; probatur in 10. primi Elem.  <s>Pythagorici igitur dicebant, numerum parem ide&ograve; e&longs;&longs;e <lb/>infinitum ip&longs;um, quia videbant ip&longs;um e&longs;&longs;e cau&longs;am perpetu&aelig; diui&longs;ionis, cum <lb/>qu&aelig;libet res quanta &longs;it diui&longs;ibilis bifariam, ide&longs;t in duo &longs;ecundum numerum <lb/>parem, &amp; &longs;ubdiui&longs;ibilis po&longs;tea bifariam, &amp; &longs;ic in infinitum, vt de linea pro&shy;<lb/>blematic&egrave; probatur in 10. primi Elem.
  
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 <s>7. Arith&shy;<lb/>metices lordani, vbi i&longs;tud idem demon&longs;trat, qu&aelig; e&longs;t h&aelig;c. </s> <s>7. Arith&shy;<lb/>metices lordani, vbi i&longs;tud idem demon&longs;trat, qu&aelig; e&longs;t h&aelig;c. </s>
  
 <s>&longs;it vnitas, &amp; &longs;uo or&shy;<lb/>dine &longs;equantur impares, vt in &longs;equenti hac &longs;erie apparet 1. 3. 5. 7. 9. &amp; c. <lb/><figure id="fig37"></figure><lb/>&longs;i igitur vnitati addatur ternarius in Gnomo&shy;<lb/>nis modum, vt vides in prima figura, produ&shy;<lb/>cetur quaternarius numerus, qui e&longs;t numerus <lb/>quadratus (quid &longs;it quadratus numerus expli&shy;<lb/>caui in Logicis tex. </s> <s>&longs;it vnitas, &amp; &longs;uo or&shy;<lb/>dine &longs;equantur impares, vt in &longs;equenti hac &longs;erie apparet 1. 3. 5. 7. 9. &amp; c. <lb/><figure id="fig37"/><lb/>&longs;i igitur vnitati addatur ternarius in Gnomo&shy;<lb/>nis modum, vt vides in prima figura, produ&shy;<lb/>cetur quaternarius numerus, qui e&longs;t numerus <lb/>quadratus (quid &longs;it quadratus numerus expli&shy;<lb/>caui in Logicis tex. </s>
  
 <s>9. primi Po&longs;ter.) etfi huic <lb/>quaternario addatur &longs;equens impar, qui e&longs;t <lb/>quinarius in modum Gnomonis, vt in &longs;ecund<gap/><lb/>figura, &longs;it numerus nouenarius, qui pariter e&longs;t quadratus. </s> <s>9. primi Po&longs;ter.) etfi huic <lb/>quaternario addatur &longs;equens impar, qui e&longs;t <lb/>quinarius in modum Gnomonis, vt in &longs;ecund<gap/><lb/>figura, &longs;it numerus nouenarius, qui pariter e&longs;t quadratus. </s>
  
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 <s>qu&aelig; &longs;ic explicantur: &longs;int ab vnitate pares di&longs;po&longs;iti ordinatim <lb/>hoc modo, 1. 2. 4. 6. &amp;c. </s> <s>qu&aelig; &longs;ic explicantur: &longs;int ab vnitate pares di&longs;po&longs;iti ordinatim <lb/>hoc modo, 1. 2. 4. 6. &amp;c. </s>
  
 <s>&longs;i igitur vnitati binarius coaceruetur, fit numerus <lb/><figure id="fig38"></figure><lb/>triangularis, vt in prima figura. </s> <s>&longs;i igitur vnitati binarius coaceruetur, fit numerus <lb/><figure id="fig38"/><lb/>triangularis, vt in prima figura. </s>
  
 <s>&longs;i huic ternario <lb/>coaceruetur &longs;equens par, fiet altera &longs;pecies, ni&shy;<lb/>mirum <gap/>exagonus numerus, vt in &longs;ecunda figu&shy;<lb/>ra. </s> <s>&longs;i huic ternario <lb/>coaceruetur &longs;equens par, fiet altera &longs;pecies, ni&shy;<lb/>mirum <gap/>exagonus numerus, vt in &longs;ecunda figu&shy;<lb/>ra. </s>
  
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 <s>&amp; &longs;ic &longs;emper in infinitum nou&aelig; ac vari&aelig; numerorum <lb/>form&aelig; ex hac additione parium prouenient, quod argumento e&longs;t numerum <lb/>parem infiniti naturam &longs;apere. </s> <s>&amp; &longs;ic &longs;emper in infinitum nou&aelig; ac vari&aelig; numerorum <lb/>form&aelig; ex hac additione parium prouenient, quod argumento e&longs;t numerum <lb/>parem infiniti naturam &longs;apere. </s>
  
 <s>Porr&ograve; reperiri numeros triangulares, pen&shy;<lb/>tagonos, &amp; &longs;imiles, con&longs;tat ex Arithmetica Nicomachi, Boetij, &amp; Iordani, <lb/>citati in definitionibus 7. &longs;u&aelig; Arithmetic&aelig;, atque ex tractatu Diophantis <lb/>Alex. </s> <s>Porr&ograve; reperiri numeros triangulares, pen&shy;<lb/>tagonos, &amp; &longs;imiles, con&longs;tat ex Arithmetica Nicomachi, Boetij, &amp; Iordani, <lb/>citati in definitionibus 7. &longs;u&aelig; Arithmetic&aelig;, atque ex tractatu Diophantis <lb/>Alex. de numeris rectangulis. </s>
  
 <s>de numeris rectangulis. </s> 
  
 <s><expan abbr="atq;">atque</expan> ex his locus hic &longs;atis clarus redditur.</s></p><p type="main"> <s><expan abbr="atq;">atque</expan> ex his locus hic &longs;atis clarus redditur.</s></p><p type="main">
  
 <s><arrow.to.target n="marg94"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg94"/></s></p><p type="margin">
  
 <s><margin.target id="marg94"></margin.target>94</s></p><p type="main"> 
  
 <s>Tex. </s> <s><margin.target id="marg94"/>94</s></p><p type="main">
  
 <s>31. <emph type="italics"/>(Vtuntur etiam Mathematici infinito)<emph.end type="italics"/> <expan abbr="aliqu&atilde;do">aliquando</expan> Mathematici du&shy;<lb/>cunt lineas quantumuis longas, &longs;eu indefinit&aelig; longitudinis, quas etiam in&shy;<lb/>finitas appellant: &amp; hoc modo vtuntur infinito, vt infra tex. </s> <s>Tex. 31. <emph type="italics"/>(Vtuntur etiam Mathematici infinito)<emph.end type="italics"/> <expan abbr="aliqu&atilde;do">aliquando</expan> Mathematici du&shy;<lb/>cunt lineas quantumuis longas, &longs;eu indefinit&aelig; longitudinis, quas etiam in&shy;<lb/>finitas appellant: &amp; hoc modo vtuntur infinito, vt infra tex. </s>
  
 <s>71. ip&longs;e Ari&longs;t. <lb/></s> <s>71. ip&longs;e Ari&longs;t. <lb/>exponit. </s>
  
 <s>exponit. </s> 
  
 <s>alio pr&aelig;terea modo vtuntur infinito, vt quando &longs;upponunt data <lb/>quauis quantitate po&longs;&longs;e &longs;umi maiorem, vel etiam minorem in infinitum, vt <lb/>patet ex 6. po&longs;tulato primi Elem.  <s>alio pr&aelig;terea modo vtuntur infinito, vt quando &longs;upponunt data <lb/>quauis quantitate po&longs;&longs;e &longs;umi maiorem, vel etiam minorem in infinitum, vt <lb/>patet ex 6. po&longs;tulato primi Elem.
  
 editionis Clauian&aelig;. </s> editionis Clauian&aelig;. </s>
  
 <s>numerum <expan abbr="quoq;">quoque</expan> au&shy;<lb/>geri po&longs;&longs;e in infinitum, e&longs;t &longs;ecundum po&longs;tulatum libri 7. Elem. </s> <s>numerum <expan abbr="quoq;">quoque</expan> au&shy;<lb/>geri po&longs;&longs;e in infinitum, e&longs;t &longs;ecundum po&longs;tulatum libri 7. Elem.
  
 <s>vel demum <lb/>quando probant quamlibet lineam po&longs;&longs;e diuidi bifariam, quia hinc &longs;equitur <lb/>po&longs;&longs;e &longs;ub diuidi in <expan abbr="infinit&utilde;">infinitum</expan>; his igitur modis Mathematicis <expan abbr="infinit&utilde;">infinitum</expan> in v&longs;u e&longs;t.</s></p><p type="main"> 
  
 <s><arrow.to.target n="marg95"></arrow.to.target></s></p><p type="margin"> 
  
 <s><margin.target id="marg95"></margin.target>95</s></p><p type="main"> vel demum <lb/>quando probant quamlibet lineam po&longs;&longs;e diuidi bifariam, quia hinc &longs;equitur <lb/>po&longs;&longs;e &longs;ub diuidi in <expan abbr="infinit&utilde;">infinitum</expan>; his igitur modis Mathematicis <expan abbr="infinit&utilde;">infinitum</expan> in v&longs;u e&longs;t.</s></p><p type="main">
  
 <s>Tex. </s> <s><arrow.to.target n="marg95"/></s></p><p type="margin">
  
 <s>68. &amp; 69. plura de magnitudine, &amp; numero continent; &longs;ed qu&aelig; non <lb/>indigeant opera no&longs;tra.</s></p><p type="main"> <s><margin.target id="marg95"/>95</s></p><p type="main">
  
 <s><arrow.to.target n="marg96"></arrow.to.target></s></p><p type="margin"> <s>Tex. 68. &amp; 69. plura de magnitudine, &amp; numero continent; &longs;ed qu&aelig; non <lb/>indigeant opera no&longs;tra.</s></p><p type="main">
  
 <s><margin.target id="marg96"></margin.target>96</s></p><p type="main"> <s><arrow.to.target n="marg96"/></s></p><p type="margin">
  
 <s>Tex. </s> <s><margin.target id="marg96"/>96</s></p><p type="main">
  
 <s>71. <emph type="italics"/>(Non remouet autem ratio Mathematicos &agrave; contemplatione auferens <lb/>&longs;ic e&longs;&longs;e infinitum, vt actu &longs;it ver&longs;us augmentum, vt intran&longs;ibile, <expan abbr="ncq;">ncque</expan> enim nunc in&shy;<lb/>digent infinito, <expan abbr="neq;">neque</expan> vtuntur, &longs;ed &longs;olum e&longs;&longs;e quantum<gap/><expan abbr="unq;">unque</expan> velint fiaitam)<emph.end type="italics"/> ratio <lb/>phy&longs;ica tollens infinitum actu, non e&longs;t Mathematicis impedimento, quia ip&longs;i <lb/>non vtuntur infinito actu; quam enim ip&longs;i ducunt lineam infinitam, non e&longs;t <lb/>ver&egrave; infinita, &longs;ed indefinit<gap/>, eam enim quantumlibet magnam producunt, vt <lb/>po&longs;&longs;it ad demon&longs;trandum &longs;ufficere.</s></p><p type="head"> <s>Tex. 71. <emph type="italics"/>(Non remouet autem ratio Mathematicos &agrave; contemplatione auferens <lb/>&longs;ic e&longs;&longs;e infinitum, vt actu &longs;it ver&longs;us augmentum, vt intran&longs;ibile, <expan abbr="ncq;">ncque</expan> enim nunc in&shy;<lb/>digent infinito, <expan abbr="neq;">neque</expan> vtuntur, &longs;ed &longs;olum e&longs;&longs;e quantum<gap/><expan abbr="unq;">unque</expan> velint fiaitam)<emph.end type="italics"/> ratio <lb/>phy&longs;ica tollens infinitum actu, non e&longs;t Mathematicis impedimento, quia ip&longs;i <lb/>non vtuntur infinito actu; quam enim ip&longs;i ducunt lineam infinitam, non e&longs;t <lb/>ver&egrave; infinita, &longs;ed indefinit<gap/>, eam enim quantumlibet magnam producunt, vt <lb/>po&longs;&longs;it ad demon&longs;trandum &longs;ufficere.</s></p><p type="head">
  
 <s><emph type="italics"/>Ex Quarto Phy&longs;icorum.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Ex Quarto Phy&longs;icorum.<emph.end type="italics"/></s></p><p type="main">
  
 <s><arrow.to.target n="marg97"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg97"/></s></p><p type="margin">
  
 <s><margin.target id="marg97"></margin.target>97</s></p><p type="main"> <s><margin.target id="marg97"/>97</s></p><p type="main">
  
 <s>Tex. </s> <s>Tex. 120. ter in hoc textu meminit commen&longs;urabilitatis, &amp; incommen&shy;<lb/>&longs;urabilitatis, qu&aelig; e&longs;t diametri ad co&longs;tam: cuius explicationem vide <lb/>primo Priorum, &longs;ecto primo, cap.
  
 <s>120. ter in hoc textu meminit commen&longs;urabilitatis, &amp; incommen&shy;<lb/>&longs;urabilitatis, qu&aelig; e&longs;t diametri ad co&longs;tam: cuius explicationem vide <lb/>primo Priorum, &longs;ecto primo, cap. </s> 23.</s></p><figure/><pb pagenum="76"/><p type="head">
  
 <s>23.</s></p><figure></figure><pb pagenum="76"/><p type="head"> 
  
 <s><emph type="italics"/>Ex Quinto Phy&longs;icorum.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Ex Quinto Phy&longs;icorum.<emph.end type="italics"/></s></p><p type="main">
  
 <s><arrow.to.target n="marg98"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg98"/></s></p><p type="margin">
  
 <s><margin.target id="marg98"></margin.target>98</s></p><p type="main"> 
  
 <s>Tex. </s> <s><margin.target id="marg98"/>98</s></p><p type="main">
  
 <s>6. <emph type="italics"/>(Vt media grauis ad vltimam, &amp; acuta ad primam)<emph.end type="italics"/> alludit ad or&shy;<lb/>dinem chordarum in mu&longs;icis in&longs;trumentis, vbi media chorda edit &longs;o&shy;<lb/>num, re&longs;pectu quidem vltim&aelig;, &amp; &longs;uprem&aelig; chord&aelig; grauem: re&longs;pectu ver&ograve; <lb/>prim&aelig;, &amp; infim&aelig; acutum.</s></p><p type="head"> <s>Tex. 6. <emph type="italics"/>(Vt media grauis ad vltimam, &amp; acuta ad primam)<emph.end type="italics"/> alludit ad or&shy;<lb/>dinem chordarum in mu&longs;icis in&longs;trumentis, vbi media chorda edit &longs;o&shy;<lb/>num, re&longs;pectu quidem vltim&aelig;, &amp; &longs;uprem&aelig; chord&aelig; grauem: re&longs;pectu ver&ograve; <lb/>prim&aelig;, &amp; infim&aelig; acutum.</s></p><p type="head">
  
 <s><emph type="italics"/>Ex Octauo Phy&longs;icorum.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Ex Octauo Phy&longs;icorum.<emph.end type="italics"/></s></p><p type="main">
  
 <s><arrow.to.target n="marg99"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg99"/></s></p><p type="margin">
  
 <s><margin.target id="marg99"></margin.target>99</s></p><p type="main"> 
  
 <s>Tex. </s> <s><margin.target id="marg99"/>99</s></p><p type="main">
  
 <s>15. <emph type="italics"/>(Etenim triangulus habet tres angulos &aelig;quales duobus rectis angulis)<emph.end type="italics"/><lb/>lib. </s> <s>Tex. 15. <emph type="italics"/>(Etenim triangulus habet tres angulos &aelig;quales duobus rectis angulis)<emph.end type="italics"/><lb/>lib.
  
 <s>1. Priorum, &longs;ecto 3. cap. </s> 1. Priorum, &longs;ecto 3. cap.
  
 <s>1. huius rei explicationem reperies.</s></p><p type="head"> 1. huius rei explicationem reperies.</s></p><p type="head">
  
 <s><emph type="italics"/>EX PRIMO DE COELO.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>EX PRIMO DE COELO.<emph.end type="italics"/></s></p><p type="main">
  
 <s><arrow.to.target n="marg100"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg100"/></s></p><p type="margin">
  
 <s><margin.target id="marg100"></margin.target><gap/>0</s></p><p type="main"> <s><margin.target id="marg100"/><gap/>0</s></p><p type="main">
  
 <s>Tex. </s> <s>Tex. 33. <emph type="italics"/>(Vt &longs;i quis minimam qu&abreve;dam e&longs;&longs;e dicat magnitudinem, hic enim <lb/>minimum introducens, maxima <expan abbr="vbiq;">vbique</expan> amoueret mathematicor&ubreve;)<emph.end type="italics"/> ide&longs;t, <lb/>&longs;i quis, vt Democritus po&longs;uerit in magnitudinibus e&longs;&longs;e minima, <lb/>&longs;eu indiui&longs;ibilia, ex quibus entia mathematica componerentur, &