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version 1.53, 2002/08/15 00:19:52 version 1.64, 2002/08/19 12:59:28
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 <?xml version="1.0"?> <?xml version="1.0"?>
 <!DOCTYPE archimedes SYSTEM "../dtd/archimedes.dtd" ><archimedes>      <info> <!DOCTYPE archimedes SYSTEM "../dtd/archimedes.dtd" >
  <archimedes xmlns:xlink="http://www.w3.org/1999/xlink">      <info>
         <author>Biancani, Giuseppe</author>         <author>Biancani, Giuseppe</author>
         <title>Aristotelis loca mathematica</title>         <title>Aristotelis loca mathematica</title>
         <date>1615</date>         <date>1615</date>
         <place>Bologna</place>         <place>Bologna</place>
         <translator></translator>         <translator/>
         <lang>la</lang>         <lang>la</lang>
         <cvs_file>bianc_locam_01_la_1615</cvs_file>         <cvs_file>bianc_locam_01_la_1615</cvs_file>
         <cvs_version></cvs_version>         <cvs_version/>
         <locator>0000000009.xml</locator>         <locator>0000000009.xml</locator>
 </info>      <text>          <front>          </front>          <body>            <chap>        <pb/><p type="head"> </info>      <text>          <front>          </front>          <body>            <chap>        <pb/><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>
  
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 <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>Vale.<emph.end type="italics"/></s></p><p type="main"> <s>Vale.<emph.end type="italics"/></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"/></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"/></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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 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.</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>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>
  
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 <s><emph type="italics"/>Qu&aelig;&longs;t. 18. De Trochlea; error Piccolominei.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Qu&aelig;&longs;t. 18. De Trochlea; error Piccolominei.<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. 19. De Securi. </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">
  
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 <s><emph type="italics"/>Qu&aelig;&longs;t. 26. De ligno humeris gestato.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Qu&aelig;&longs;t. 26. De ligno humeris gestato.<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. 27. De ponderibus humero ge&longs;tatis.<emph.end type="italics"/></s></p><p type="main">
  
 <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. 28. De Tollenone.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Qu&aelig;&longs;t. 28. De Tollenone.<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. 29. De onere &agrave; duobus phalanga ge&longs;iato.<emph.end type="italics"/></s></p><p type="main">
  
 <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. 30. De &longs;urgente &agrave; &longs;e&longs;&longs;ione.<emph.end type="italics"/></s></p><p type="head"> <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">
  
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 <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">
  
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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>
  
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 <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>&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>
  
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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 1919 
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 1947 
Line 1932 
  
 <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>&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>Ex cap.
  
 de Priori <emph type="italics"/>(in &longs;cientijs demon&longs;tratiuis e&longs;t prius, &amp; po&longs;terius ordine, <lb/>elementa enim priora &longs;unt ijs, qu&aelig; de&longs;cribuntur, nam principia prior a &longs;unt theore&shy;<lb/>matibus ordine)<emph.end type="italics"/> verba illa, nam principia, &amp;c. </s> 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. 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>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>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>Ex cap.
  
 de motu <emph type="italics"/>(Quadratum augetur Gnomone circumpo&longs;ito)<emph.end type="italics"/> Gnomon vox <lb/>gr&aelig;ca inter alia &longs;ignificat in&longs;trumentum illud, quod Latini tum amu&longs;&longs;im, <lb/><figure id="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.</s></p><p type="main">
  
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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>
  
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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>Ex cap.
  
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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>
  
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 <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>
  
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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>Et cap.
  
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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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 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>Ex cap.
  
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 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"> 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><arrow.to.target n="marg8"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg8"/></s></p><p type="margin">
  
 <s><margin.target id="marg8"></margin.target>8</s></p><p type="main"> <s><margin.target id="marg8"/>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>Ex cap.
  
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 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>Ex cap.
  
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 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>
  
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 <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"/></s></p><p type="margin">
  
 <s><arrow.to.target n="marg11"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg11"/>11</s></p><p type="main">
  
 <s><margin.target id="marg11"></margin.target>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>Ex cap.
  
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 <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>Ex cap.
  
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 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>
  
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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>Ex cap.
  
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 31. de Abductione.</s></p><p type="main"> 31. de Abductione.</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>Notandum hic cum eruditi&longs;&longs;imo Burana, Abductionem hanc, de qua in hoc <lb/>cap.
  
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 <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. </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>
  
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 <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><margin.target id="marg19"/>19</s></p><p type="main">
  
 <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>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>
  
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 <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>alludit ad demon&longs;trationem quandam, quam ip&longs;e infe&shy;<lb/>rius in exemplum adducet, &amp; qu&aelig; e&longs;t in 3. Elem.
  
 Euclidis 31. in qua talis fi&shy;<lb/>gura proponitur qualis e&longs;t pr&aelig;&longs;ens, in qua vides triangulum A B C. in &longs;e&shy;<lb/><figure id="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><margin.target id="marg20"/>20</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>Tex. 5. <emph type="italics"/>(Vera quidem igitur oporter e&longs;&longs;e, quoniam non e&longs;t non ens &longs;cire, vt quod <lb/>diameter &longs;it commen&longs;urabi is)<emph.end type="italics"/> con&longs;ule ea, qu&aelig; &longs;crip&longs;imus ad cap.
  
 23. primi <lb/>Priorum, &longs;ecto 1. &longs;ine quibus locus hic &longs;atis intelligi nequit; ijs autem per&shy;<lb/>ceptis &longs;ic <expan abbr="loc&utilde;">locum</expan> hunc explicare po&longs;&longs;umus, cum diameter quadrati &longs;it incom&shy;<pb 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"> 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><arrow.to.target n="marg21"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg21"/></s></p><p type="margin">
  
 <s><margin.target id="marg21"></margin.target>21</s></p><p type="main"> <s><margin.target id="marg21"/>21</s></p><p type="main">
  
 <s>Hoc eodem cap.  <s>Hoc eodem cap.
  
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 Euclidis percipi pote&longs;t. </s> Euclidis percipi pote&longs;t. </s>
  
 <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> <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>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. 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>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>
  
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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><margin.target id="marg25"/>25</s></p><p type="main">
  
 <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>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>
  
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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><margin.target id="marg26"/>26</s></p><p type="main">
  
 <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.  <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">
  
 <s><arrow.to.target n="marg30"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg30"/></s></p><p type="margin">
  
 <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>
  
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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">
  
 <s><arrow.to.target n="marg31"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg31"/></s></p><p type="margin">
  
 <s><margin.target id="marg31"></margin.target>31</s></p><p type="main"> <s><margin.target id="marg31"/>31</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"> <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><arrow.to.target n="marg32"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg32"/></s></p><p type="margin">
  
 <s><margin.target id="marg32"></margin.target>32</s></p><p type="main"> <s><margin.target id="marg32"/>32</s></p><p type="main">
  
 <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>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>
  
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 <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">
  
 <s><arrow.to.target n="marg33"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg33"/></s></p><p type="margin">
  
 <s><margin.target id="marg33"></margin.target>33</s></p><p type="main"> <s><margin.target id="marg33"/>33</s></p><p type="main">
  
 <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.
  
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 <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">
  
 <s><arrow.to.target n="marg34"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg34"/></s></p><p type="margin">
  
 <s><margin.target id="marg34"></margin.target>34</s></p><p type="main"> <s><margin.target id="marg34"/>34</s></p><p type="main">
  
 <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>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.
  
 &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><margin.target id="marg35"/>35</s></p><p type="main">
  
 <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>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. </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>
  
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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><margin.target id="marg39"/>39</s></p><p type="main">
  
 <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>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><margin.target id="marg43"/>43</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. 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><arrow.to.target n="marg44"/></s></p><p type="margin">
  
 <s><margin.target id="marg44"></margin.target>44</s></p><p type="main"> <s><margin.target id="marg44"/>44</s></p><p type="main">
  
 <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>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><arrow.to.target n="marg45"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg45"/></s></p><p type="margin">
  
 <s><margin.target id="marg45"></margin.target>45</s></p><p type="main"> <s><margin.target id="marg45"/>45</s></p><p type="main">
  
 <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. </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. </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>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>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><margin.target id="marg48"/>48</s></p><p type="main">
  
 <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>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>
  
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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>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><margin.target id="marg52"/>52</s></p><p type="main">
  
 <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>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.
  
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 <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. 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>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>
  
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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><arrow.to.target n="marg54"/></s></p><p type="margin">
  
 <s><margin.target id="marg54"></margin.target>54</s></p><p type="main"> <s><margin.target id="marg54"/>54</s></p><p type="main">
  
 <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>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>
  
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 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>
  
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 1.</s></p><p type="main"> 1.</s></p><p type="main">
  
 <s><arrow.to.target n="marg58"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg58"/></s></p><p type="margin">
  
 <s><margin.target id="marg58"></margin.target>58</s></p><p type="main"> <s><margin.target id="marg58"/>58</s></p><p type="main">
  
 <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>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.
  
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 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. 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>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.
  
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 <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><margin.target id="marg63"/>63</s></p><p type="main">
  
 <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>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>
  
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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><margin.target id="marg65"/>65</s></p><p type="main">
  
 <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>Tex. 2. <emph type="italics"/>(Vt quod omnis triangulus duobus rectis &aelig;quales babet)<emph.end type="italics"/> vide anno&shy;<lb/>tata lib.
  
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 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>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.
  
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 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. 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>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><arrow.to.target n="marg70"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg70"/></s></p><p type="margin">
  
 <s><margin.target id="marg70"></margin.target>70</s></p><p type="main"> <s><margin.target id="marg70"/>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><margin.target id="marg71"/>71</s></p><p type="main">
  
 <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/></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 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. 24. <emph type="italics"/>(Vt propter quid re&longs;onat? </s> <s>Tex. 24. <emph type="italics"/>(Vt 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><margin.target id="marg73"/>73</s></p><p type="main">
  
 <s>Tex. 25. <emph type="italics"/>(Vt propter quid, &amp; permutatim proportionale? </s> <s>Tex. 25. <emph type="italics"/>(Vt propter quid, &amp; permutatim proportionale? </s>
  
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 <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>
  
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 <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"/></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>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.
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 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>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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 <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.</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>
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 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>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.
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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>
  
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 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>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. 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>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>
  
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 <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><margin.target id="marg89"/>89</s></p><p type="main">
  
 <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.  <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.
  
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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><margin.target id="marg90"/>90</s></p><p type="main">
  
 <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>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>
  
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 <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. 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>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>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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 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><margin.target id="marg93"/>93</s></p><p type="main">
  
 <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>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>
  
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 <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><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><margin.target id="marg94"/>94</s></p><p type="main">
  
 <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>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.
  
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 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"> 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><arrow.to.target n="marg95"/></s></p><p type="margin">
  
 <s><margin.target id="marg95"></margin.target>95</s></p><p type="main"> <s><margin.target id="marg95"/>95</s></p><p type="main">
  
 <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>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><arrow.to.target n="marg96"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg96"/></s></p><p type="margin">
  
 <s><margin.target id="marg96"></margin.target>96</s></p><p type="main"> <s><margin.target id="marg96"/>96</s></p><p type="main">
  
 <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>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. 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>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.
  
 23.</s></p><figure></figure><pb pagenum="76"/><p type="head"> 23.</s></p><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><margin.target id="marg98"/>98</s></p><p type="main">
  
 <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>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><margin.target id="marg99"/>99</s></p><p type="main">
  
 <s>Tex. 15. <emph type="italics"/>(Etenim triangulus habet tres angulos &aelig;quales duobus rectis angulis)<emph.end type="italics"/><lb/>lib.  <s>Tex. 15. <emph type="italics"/>(Etenim triangulus habet tres angulos &aelig;quales duobus rectis angulis)<emph.end type="italics"/><lb/>lib.
  
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 <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. 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, <lb/>hic euerteret maxima mathematicorum, ide&longs;t maxime ip&longs;orum demon&longs;tra&shy;<lb/>tiones, atque etiam effata euerterentur: v. </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, <lb/>hic euerteret maxima mathematicorum, ide&longs;t maxime ip&longs;orum demon&longs;tra&shy;<lb/>tiones, atque etiam effata euerterentur: v. </s>
  
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 <s>po&longs;tulatum <expan abbr="quoq;">quoque</expan> illud, qualibet data magnitudine &longs;umi po&longs;&longs;e <lb/>minorem pror&longs;us irritum redderetur, quia data atomo, illa minor accipi <lb/>non po&longs;&longs;et.</s></p><p type="main"> <s>po&longs;tulatum <expan abbr="quoq;">quoque</expan> illud, qualibet data magnitudine &longs;umi po&longs;&longs;e <lb/>minorem pror&longs;us irritum redderetur, quia data atomo, illa minor accipi <lb/>non po&longs;&longs;et.</s></p><p type="main">
  
 <s><arrow.to.target n="marg101"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg101"/></s></p><p type="margin">
  
 <s><margin.target id="marg101"></margin.target>101</s></p><p type="main"> <s><margin.target id="marg101"/>101</s></p><p type="main">
  
 <s>Tex. 36. <emph type="italics"/>(Sit <expan abbr="itaq;">itaque</expan> linea, in qua A G E, infinita ad partes E; &amp; alia vtrinque <lb/>infinita, in qua <foreign lang="greek">b</foreign> B; &longs;i <expan abbr="itaq;">itaque</expan> de&longs;cribat circulum linea A G E, cir ca centrum G, fe-<emph.end type="italics"/><lb/><figure id="fig39"></figure><lb/><emph type="italics"/>retur circulariter linea A G E, &longs;ecans ali&shy;<lb/>quando lineam <foreign lang="greek">b</foreign> B, tempore finito; totum <lb/>enim tempus, in quo circulariter latum <lb/>e&longs;t C&oelig;lum finitum e&longs;t, &amp; ablatum igitur, <lb/>quo &longs;ecans ferebatur; erit igitur aliqued <lb/>prmcipium, quo primum linea A G E, li&shy;<lb/>neam <foreign lang="greek">b</foreign> B, &longs;ecuit. </s> <s>Tex. 36. <emph type="italics"/>(Sit <expan abbr="itaq;">itaque</expan> linea, in qua A G E, infinita ad partes E; &amp; alia vtrinque <lb/>infinita, in qua <foreign lang="greek">b</foreign> B; &longs;i <expan abbr="itaq;">itaque</expan> de&longs;cribat circulum linea A G E, cir ca centrum G, fe-<emph.end type="italics"/><lb/><figure id="fig39"/><lb/><emph type="italics"/>retur circulariter linea A G E, &longs;ecans ali&shy;<lb/>quando lineam <foreign lang="greek">b</foreign> B, tempore finito; totum <lb/>enim tempus, in quo circulariter latum <lb/>e&longs;t C&oelig;lum finitum e&longs;t, &amp; ablatum igitur, <lb/>quo &longs;ecans ferebatur; erit igitur aliqued <lb/>prmcipium, quo primum linea A G E, li&shy;<lb/>neam <foreign lang="greek">b</foreign> B, &longs;ecuit. </s>
  
 <s>&longs;ed impo&longs;&longs;ibile est; non <lb/>est igitur circulariter verti infinit&amp;<gap/>, quare <lb/><expan abbr="neq;">neque</expan> mundum, &longs;i e&longs;&longs;et infinitus)<emph.end type="italics"/> quamuis <lb/>textus hic parum &longs;it mathematicus, <lb/>quia tamen &longs;upponit figuram mathe&shy;<lb/>maticam, qu&aelig; in codicibus pariter, ac <lb/>commentarijs de&longs;ideratur, illam pla&shy;<lb/>cuit apponere. </s> <s>&longs;ed impo&longs;&longs;ibile est; non <lb/>est igitur circulariter verti infinit&amp;<gap/>, quare <lb/><expan abbr="neq;">neque</expan> mundum, &longs;i e&longs;&longs;et infinitus)<emph.end type="italics"/> quamuis <lb/>textus hic parum &longs;it mathematicus, <lb/>quia tamen &longs;upponit figuram mathe&shy;<lb/>maticam, qu&aelig; in codicibus pariter, ac <lb/>commentarijs de&longs;ideratur, illam pla&shy;<lb/>cuit apponere. </s>
  
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 <s>du&aelig; line&aelig; infinit&aelig;, quales &longs;unt pr&aelig;dict&aelig; in ip&longs;o, <expan abbr="atq;">atque</expan> cum ip&longs;o moueri alte&shy;<lb/>ra earum A E, intelligatur, alteram <foreign lang="greek">b</foreign> B, manentem in tempore finito, ide&longs;t, <lb/>in diurna conuer&longs;ione pertran&longs;ibit: fieri autem nequit, vt infinita magni&shy;<lb/>tudo finito tempore percurratur; quare dicendum e&longs;t, mundum e&longs;&longs;e finita <lb/>magnitudine pr&aelig;ditum.</s></p><p type="main"> <s>du&aelig; line&aelig; infinit&aelig;, quales &longs;unt pr&aelig;dict&aelig; in ip&longs;o, <expan abbr="atq;">atque</expan> cum ip&longs;o moueri alte&shy;<lb/>ra earum A E, intelligatur, alteram <foreign lang="greek">b</foreign> B, manentem in tempore finito, ide&longs;t, <lb/>in diurna conuer&longs;ione pertran&longs;ibit: fieri autem nequit, vt infinita magni&shy;<lb/>tudo finito tempore percurratur; quare dicendum e&longs;t, mundum e&longs;&longs;e finita <lb/>magnitudine pr&aelig;ditum.</s></p><p type="main">
  
 <s><arrow.to.target n="marg102"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg102"/></s></p><p type="margin">
  
 <s><margin.target id="marg102"></margin.target>102</s></p><p type="main"> <s><margin.target id="marg102"/>102</s></p><p type="main">
  
 <s>Tex. 48. <emph type="italics"/>(Nihil autem refert grauitates, commen&longs;urabiles &longs;int, an incommen&shy;<lb/>&longs;ur abiles)<emph.end type="italics"/> quidnam &longs;it commen&longs;urabilitas, &amp; incommen&longs;urabilitas, expli&shy;<lb/>catum e&longs;t lib.  <s>Tex. 48. <emph type="italics"/>(Nihil autem refert grauitates, commen&longs;urabiles &longs;int, an incommen&shy;<lb/>&longs;ur abiles)<emph.end type="italics"/> quidnam &longs;it commen&longs;urabilitas, &amp; incommen&longs;urabilitas, expli&shy;<lb/>catum e&longs;t lib.
  
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 23.</s></p><p type="main"> 23.</s></p><p type="main">
  
 <s><arrow.to.target n="marg103"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg103"/></s></p><p type="margin">
  
 <s><margin.target id="marg103"></margin.target>103</s></p><p type="main"> <s><margin.target id="marg103"/>103</s></p><p type="main">
  
 <s>Tex. 119. <emph type="italics"/>(Est autem impo&longs;&longs;ibile, &amp; po&longs;&longs;ibile; fal&longs;um, &amp; verum, ex &longs;uppo&longs;itio&shy;<lb/>ne quidem, dico autem, vt triangulum impo&longs;&longs;ibile e&longs;t duos rectos habere, &longs;i h&aelig;c)<emph.end type="italics"/><lb/>ide&longs;t, &longs;i &longs;upponantur fal&longs;a qu&aelig;dam, qu&aelig; &longs;upponi po&longs;&longs;unt, &longs;equetur impo&longs;&longs;i&shy;<lb/>bile e&longs;&longs;e triangulum habere tres angulos &aelig;quales duobus rectis angulis, vi&shy;<lb/>de, qu&aelig; &longs;crip&longs;i lib.  <s>Tex. 119. <emph type="italics"/>(Est autem impo&longs;&longs;ibile, &amp; po&longs;&longs;ibile; fal&longs;um, &amp; verum, ex &longs;uppo&longs;itio&shy;<lb/>ne quidem, dico autem, vt triangulum impo&longs;&longs;ibile e&longs;t duos rectos habere, &longs;i h&aelig;c)<emph.end type="italics"/><lb/>ide&longs;t, &longs;i &longs;upponantur fal&longs;a qu&aelig;dam, qu&aelig; &longs;upponi po&longs;&longs;unt, &longs;equetur impo&longs;&longs;i&shy;<lb/>bile e&longs;&longs;e triangulum habere tres angulos &aelig;quales duobus rectis angulis, vi&shy;<lb/>de, qu&aelig; &longs;crip&longs;i lib.
  
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 impo&longs;&longs;ibile ex &longs;uppo&longs;itione, quia &longs;cilicet impo&longs;&longs;ibile euadit ex quo&shy;<lb/>dam fal&longs;o &longs;uo &longs;uppo&longs;ito, vt in allato exemplo, triangulum habere tres an&shy;<lb/>gulos &aelig;quales duobus rectis, quamuis nece&longs;&longs;arium &longs;it, tamen ex fal&longs;a &longs;up&shy;<lb/>po&longs;itione, impo&longs;&longs;ibile oua&longs;it.</s></p><p type="main"> impo&longs;&longs;ibile ex &longs;uppo&longs;itione, quia &longs;cilicet impo&longs;&longs;ibile euadit ex quo&shy;<lb/>dam fal&longs;o &longs;uo &longs;uppo&longs;ito, vt in allato exemplo, triangulum habere tres an&shy;<lb/>gulos &aelig;quales duobus rectis, quamuis nece&longs;&longs;arium &longs;it, tamen ex fal&longs;a &longs;up&shy;<lb/>po&longs;itione, impo&longs;&longs;ibile oua&longs;it.</s></p><p type="main">
  
 <s><arrow.to.target n="marg104"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg104"/></s></p><p type="margin">
  
 <s><margin.target id="marg104"></margin.target>104</s></p><p type="main"> <s><margin.target id="marg104"/>104</s></p><p type="main">
  
 <s>Ibidem <emph type="italics"/>(Et diameter commen&longs;urabilis est co&longs;t&aelig;, &longs;i b&aelig;c)<emph.end type="italics"/> vide primo Priorum, <lb/>&longs;ecto 3. cap.  <s>Ibidem <emph type="italics"/>(Et diameter commen&longs;urabilis est co&longs;t&aelig;, &longs;i b&aelig;c)<emph.end type="italics"/> vide primo Priorum, <lb/>&longs;ecto 3. cap.
  
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 <s><emph type="italics"/>Ex Secundo de C&aelig;lo.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Ex Secundo de C&aelig;lo.<emph.end type="italics"/></s></p><p type="main">
  
 <s><arrow.to.target n="marg105"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg105"/></s></p><p type="margin">
  
 <s><margin.target id="marg105"></margin.target>105</s></p><p type="main"> <s><margin.target id="marg105"/>105</s></p><p type="main">
  
 <s>Tex. 24. <emph type="italics"/>(Amplius qui &longs;olida diuidunt in plana, <expan abbr="atq;">atque</expan> ex planis corpora <lb/>generant, his te&longs;tes fui&longs;&longs;e videntur: &longs;olam enim figurarum &longs;olidarum <lb/>&longs;ph&aelig;ram non diuidunt, vt non plures &longs;uperficies. </s> <s>Tex. 24. <emph type="italics"/>(Amplius qui &longs;olida diuidunt in plana, <expan abbr="atq;">atque</expan> ex planis corpora <lb/>generant, his te&longs;tes fui&longs;&longs;e videntur: &longs;olam enim figurarum &longs;olidarum <lb/>&longs;ph&aelig;ram non diuidunt, vt non plures &longs;uperficies. </s>
  
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 <s>quando ver&ograve; ex planis corpo&shy;<lb/>ra generant, vt facit Plato in Tim&aelig;o, accip&iacute;unt prim&ograve; triangulum &aelig;quila&shy;<lb/>terum, &amp; ex quatuor triangulis &aelig;quilateris &longs;imul compactis conficiunt py&shy;<lb/>ramidem; &amp; hoc modo alia &longs;olida &agrave; pluribus &longs;uperficiebus ambita con&longs;ti&shy;<lb/>tuunt: verum hac ratione nullo modo po&longs;&longs;unt &longs;ph&aelig;ram componere, quia <lb/>vnica tantum, <expan abbr="ea&qacute;">eaque</expan>; &longs;ph&aelig;rica &longs;uperficie compr&aelig;henditur: <expan abbr="atq;">atque</expan> hoc pacto i&longs;ti <lb/>diuidentes, &amp; componentes corpora fidem faciunt, &longs;ph&aelig;ram, cum ex nullis <lb/>componatur, &longs;olidorum e&longs;&longs;e primam.</s></p><p type="main"> <s>quando ver&ograve; ex planis corpo&shy;<lb/>ra generant, vt facit Plato in Tim&aelig;o, accip&iacute;unt prim&ograve; triangulum &aelig;quila&shy;<lb/>terum, &amp; ex quatuor triangulis &aelig;quilateris &longs;imul compactis conficiunt py&shy;<lb/>ramidem; &amp; hoc modo alia &longs;olida &agrave; pluribus &longs;uperficiebus ambita con&longs;ti&shy;<lb/>tuunt: verum hac ratione nullo modo po&longs;&longs;unt &longs;ph&aelig;ram componere, quia <lb/>vnica tantum, <expan abbr="ea&qacute;">eaque</expan>; &longs;ph&aelig;rica &longs;uperficie compr&aelig;henditur: <expan abbr="atq;">atque</expan> hoc pacto i&longs;ti <lb/>diuidentes, &amp; componentes corpora fidem faciunt, &longs;ph&aelig;ram, cum ex nullis <lb/>componatur, &longs;olidorum e&longs;&longs;e primam.</s></p><p type="main">
  
 <s><arrow.to.target n="marg106"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg106"/></s></p><p type="margin">
  
 <s><margin.target id="marg106"></margin.target>106</s></p><p type="main"> <s><margin.target id="marg106"/>106</s></p><p type="main">
  
 <s>Tex. 25. <emph type="italics"/>(Est autem, &amp; &longs;ecundum numerorum ordinem a&longs;&longs;ignantibus, &longs;ic po&shy;<lb/>nentibus rationabili&longs;&longs;imam, circulum quidem &longs;ecundum vnum; triangulum autem <lb/>&longs;ecundum dualitatem, quoniam duo recti. </s> <s>Tex. 25. <emph type="italics"/>(Est autem, &amp; &longs;ecundum numerorum ordinem a&longs;&longs;ignantibus, &longs;ic po&shy;<lb/>nentibus rationabili&longs;&longs;imam, circulum quidem &longs;ecundum vnum; triangulum autem <lb/>&longs;ecundum dualitatem, quoniam duo recti. </s>
  
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 1. De&shy;<lb/>mum &longs;i primum locum dederimus triangulo, nullus alius remanet pro cir&shy;<lb/>culo, quod e&longs;t inconueniens, ergo circulus prima figura erit.</s></p><p type="main"> 1. De&shy;<lb/>mum &longs;i primum locum dederimus triangulo, nullus alius remanet pro cir&shy;<lb/>culo, quod e&longs;t inconueniens, ergo circulus prima figura erit.</s></p><p type="main">
  
 <s><arrow.to.target n="marg107"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg107"/></s></p><p type="margin">
  
 <s><margin.target id="marg107"></margin.target>107</s></p><p type="main"> <s><margin.target id="marg107"/>107</s></p><p type="main">
  
 <s>Tex. 31. <emph type="italics"/>(At ver&ograve;, quod aqu&aelig; &longs;uperficies talis &longs;it, manife&longs;tum e&longs;t hac &longs;uppo&longs;i&shy;<lb/>tione &longs;umpta, quod apta natura e&longs;t &longs;emper con<gap/>luere aqua ad magis concauum: ma&shy;<lb/>gis autem concauum e&longs;t, quod centro propinquius est. </s> <s>Tex. 31. <emph type="italics"/>(At ver&ograve;, quod aqu&aelig; &longs;uperficies talis &longs;it, manife&longs;tum e&longs;t hac &longs;uppo&longs;i&shy;<lb/>tione &longs;umpta, quod apta natura e&longs;t &longs;emper con<gap/>luere aqua ad magis concauum: ma&shy;<lb/>gis autem concauum e&longs;t, quod centro propinquius est. </s>
  
 <s>ducantur ergo ex centro A,<emph.end type="italics"/><lb/><figure id="fig40"></figure><lb/><emph type="italics"/>linea A B, &amp; linea A C, &amp; producatur, in qua B C, <lb/>duct<gap/> igitur ad ba&longs;im linea, in qua A D, minor e&longs;t eis, <lb/>qu&aelig; ex centro. </s> <s>ducantur ergo ex centro A,<emph.end type="italics"/><lb/><figure id="fig40"/><lb/><emph type="italics"/>linea A B, &amp; linea A C, &amp; producatur, in qua B C, <lb/>duct<gap/> igitur ad ba&longs;im linea, in qua A D, minor e&longs;t eis, <lb/>qu&aelig; ex centro. </s>
  
 <s>magis igitur concauus locus e&longs;t, quare <lb/>influet aqua, donec <expan abbr="vtiq;">vtique</expan> &aelig;quetur. </s> <s>magis igitur concauus locus e&longs;t, quare <lb/>influet aqua, donec <expan abbr="vtiq;">vtique</expan> &aelig;quetur. </s>
  
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 <s>Huius etiam habes acu&shy;<lb/>ti&longs;&longs;imam Archimedis demon&longs;trationem initio libelli de ijs, qu&aelig; vehuntur <lb/>in aqua, quam in &longs;uam &longs;ph&aelig;ram retulit Clauius.</s></p><p type="main"> <s>Huius etiam habes acu&shy;<lb/>ti&longs;&longs;imam Archimedis demon&longs;trationem initio libelli de ijs, qu&aelig; vehuntur <lb/>in aqua, quam in &longs;uam &longs;ph&aelig;ram retulit Clauius.</s></p><p type="main">
  
 <s><arrow.to.target n="marg108"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg108"/></s></p><p type="margin">
  
 <s><margin.target id="marg108"></margin.target>108</s></p><p type="main"> <s><margin.target id="marg108"/>108</s></p><p type="main">
  
 <s>Tex. 46. <emph type="italics"/>(Reliquum e&longs;t orbes quidem moueri, stellas ver&ograve; quie&longs;cere, &amp; infixas <lb/>ip&longs;is orbibus ferri; &longs;olum enim &longs;ic nullum ab&longs;urdum accidit. </s> <s>Tex. 46. <emph type="italics"/>(Reliquum e&longs;t orbes quidem moueri, stellas ver&ograve; quie&longs;cere, &amp; infixas <lb/>ip&longs;is orbibus ferri; &longs;olum enim &longs;ic nullum ab&longs;urdum accidit. </s>
  
 <s>celeriorem enim e&longs;&longs;e <lb/>maioris circuli velocitatem, rationabile e&longs;t circa idem centrum infixis: vt enim in <lb/>alijs maius corpus velocius fertur propria latione, &longs;ic, &amp; in circularibus: maius <lb/>enim e&longs;t eorum, qu&aelig; auferuntur <gap/>b eis, qu&aelig; ex centro, maioris circuli &longs;egmentum)<emph.end type="italics"/><lb/>ex intellectione vltim&aelig; periodi textus totius intelligentia pendet: &longs;it igitur <lb/><figure id="fig41"></figure><lb/>figura pr&aelig;&longs;ens, in qua cum &longs;int duo circuli concen&shy;<lb/>trici, vnus altero maior, <expan abbr="educt&aelig;&qacute;">educt&aelig;que</expan>; &longs;int ex <expan abbr="c&etilde;tro">centro</expan> du&aelig; <lb/>&longs;emidiametri A D, A E, qu&aelig; <expan abbr="vtrunq;">vtrunque</expan> circulum &longs;e&shy;<lb/>cant, apparet maius e&longs;&longs;e <expan abbr="&longs;egment&utilde;">&longs;egmentum</expan> D E, quod &egrave; ma&shy;<lb/>iori circulo &longs;emidiametri ex <expan abbr="c&etilde;tro">centro</expan> educt&aelig; auferunt, <lb/>quam &longs;egmentum B C, minoris circuli, quod ei&longs;dem <lb/>&longs;emidia metris intercipitur. </s> <s>celeriorem enim e&longs;&longs;e <lb/>maioris circuli velocitatem, rationabile e&longs;t circa idem centrum infixis: vt enim in <lb/>alijs maius corpus velocius fertur propria latione, &longs;ic, &amp; in circularibus: maius <lb/>enim e&longs;t eorum, qu&aelig; auferuntur <gap/>b eis, qu&aelig; ex centro, maioris circuli &longs;egmentum)<emph.end type="italics"/><lb/>ex intellectione vltim&aelig; periodi textus totius intelligentia pendet: &longs;it igitur <lb/><figure id="fig41"/><lb/>figura pr&aelig;&longs;ens, in qua cum &longs;int duo circuli concen&shy;<lb/>trici, vnus altero maior, <expan abbr="educt&aelig;&qacute;">educt&aelig;que</expan>; &longs;int ex <expan abbr="c&etilde;tro">centro</expan> du&aelig; <lb/>&longs;emidiametri A D, A E, qu&aelig; <expan abbr="vtrunq;">vtrunque</expan> circulum &longs;e&shy;<lb/>cant, apparet maius e&longs;&longs;e <expan abbr="&longs;egment&utilde;">&longs;egmentum</expan> D E, quod &egrave; ma&shy;<lb/>iori circulo &longs;emidiametri ex <expan abbr="c&etilde;tro">centro</expan> educt&aelig; auferunt, <lb/>quam &longs;egmentum B C, minoris circuli, quod ei&longs;dem <lb/>&longs;emidia metris intercipitur. </s>
  
 <s>Verumtamen &longs;i circuli <lb/>ambo &longs;imul moueantur, maior circulus &aelig;quali tem&shy;<lb/>pore maius illud &longs;patium D E, &amp; minor minus B C, <lb/>pertran&longs;ibit: idem igitur de c&oelig;le&longs;tibus orbibus di&shy;<lb/>cendum, qui quamuis omnes diurnum &longs;imul motum <lb/>ab&longs;oluunt, maiores tamen celerius conuertuntur: quo fit, vt &longs;tell&aelig; maiori&shy;<lb/>bus circulis infix&aelig;, <expan abbr="atq;">atque</expan> delat&aelig;, maiori celeritate &longs;uos cur&longs;us peragant, ne&shy;<lb/>que oportet eas, dum mouentur c&oelig;lum di&longs;&longs;ecare, quod accideret, &longs;i pro&shy;<lb/>prio motu veluti pri&longs;ces per aquam progrederentur.</s></p><p type="main"> <s>Verumtamen &longs;i circuli <lb/>ambo &longs;imul moueantur, maior circulus &aelig;quali tem&shy;<lb/>pore maius illud &longs;patium D E, &amp; minor minus B C, <lb/>pertran&longs;ibit: idem igitur de c&oelig;le&longs;tibus orbibus di&shy;<lb/>cendum, qui quamuis omnes diurnum &longs;imul motum <lb/>ab&longs;oluunt, maiores tamen celerius conuertuntur: quo fit, vt &longs;tell&aelig; maiori&shy;<lb/>bus circulis infix&aelig;, <expan abbr="atq;">atque</expan> delat&aelig;, maiori celeritate &longs;uos cur&longs;us peragant, ne&shy;<lb/>que oportet eas, dum mouentur c&oelig;lum di&longs;&longs;ecare, quod accideret, &longs;i pro&shy;<lb/>prio motu veluti pri&longs;ces per aquam progrederentur.</s></p><p type="main">
  
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 <s>His rationibus conantur ip&longs;i proba&shy;<lb/>re C&oelig;lum e&longs;&longs;e liquidum; <expan abbr="atq;">atque</expan> in eo Planetas, veluti aues in aere, permearc: <lb/>quarum &longs;olutio mihi nulla occurrit, alijs forta&longs;&longs;is occurrct.</s></p><p type="main"> <s>His rationibus conantur ip&longs;i proba&shy;<lb/>re C&oelig;lum e&longs;&longs;e liquidum; <expan abbr="atq;">atque</expan> in eo Planetas, veluti aues in aere, permearc: <lb/>quarum &longs;olutio mihi nulla occurrit, alijs forta&longs;&longs;is occurrct.</s></p><p type="main">
  
 <s><arrow.to.target n="marg109"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg109"/></s></p><p type="margin">
  
 <s><margin.target id="marg109"></margin.target>109</s></p><p type="main"> <s><margin.target id="marg109"/>109</s></p><p type="main">
  
 <s>Tex. 57. <emph type="italics"/>(De ordine autem ip&longs;orum, quo quidem modo &longs;ingula di&longs;penantur<gap/>, vt <lb/>qu&aelig;dam &longs;int priora, qu&aelig;dam posteriora, &amp; quomodo &longs;patijs &longs;e h<gap/>be&abreve;<gap/> ad inuicem,<emph.end type="italics"/><pb pagenum="80"/><emph type="italics"/>ex ijs circa A&longs;trologiam, con&longs;ideretur: dicitur enim &longs;ufficienter)<emph.end type="italics"/> &longs;umit hoc loco <lb/>A&longs;trologiam, pro A&longs;tronomia, &longs;i iuxta recentiores loqui velimus. </s> <s>Tex. 57. <emph type="italics"/>(De ordine autem ip&longs;orum, quo quidem modo &longs;ingula di&longs;penantur<gap/>, vt <lb/>qu&aelig;dam &longs;int priora, qu&aelig;dam posteriora, &amp; quomodo &longs;patijs &longs;e h<gap/>be&abreve;<gap/> ad inuicem,<emph.end type="italics"/><pb pagenum="80"/><emph type="italics"/>ex ijs circa A&longs;trologiam, con&longs;ideretur: dicitur enim &longs;ufficienter)<emph.end type="italics"/> &longs;umit hoc loco <lb/>A&longs;trologiam, pro A&longs;tronomia, &longs;i iuxta recentiores loqui velimus. </s>
  
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 <s>quorum princeps fuit ptol&aelig;meus; no&longs;tra <lb/>tamen &aelig;tate Tycho Brahe, qui certis ob&longs;eruationibus, quas maximo labo&shy;<lb/>re, ac &longs;umptu exantlauit, in nonnullis &agrave; Ptol&aelig;meo, ac reliquis di&longs;&longs;entjt: &longs;tan&shy;<lb/>dum autem e&longs;&longs;e recentioribus ob&longs;eruationibus apud A&longs;tronomi&aelig; peritos in <lb/>confe&longs;&longs;o e&longs;t.</s></p><p type="main"> <s>quorum princeps fuit ptol&aelig;meus; no&longs;tra <lb/>tamen &aelig;tate Tycho Brahe, qui certis ob&longs;eruationibus, quas maximo labo&shy;<lb/>re, ac &longs;umptu exantlauit, in nonnullis &agrave; Ptol&aelig;meo, ac reliquis di&longs;&longs;entjt: &longs;tan&shy;<lb/>dum autem e&longs;&longs;e recentioribus ob&longs;eruationibus apud A&longs;tronomi&aelig; peritos in <lb/>confe&longs;&longs;o e&longs;t.</s></p><p type="main">
  
 <s><arrow.to.target n="marg110"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg110"/></s></p><p type="margin">
  
 <s><margin.target id="marg110"></margin.target>110</s></p><p type="main"> <s><margin.target id="marg110"/>110</s></p><p type="main">
  
 <s>Tex. <emph type="italics"/>(Luna autem o&longs;tenditur per ea, qu&aelig; circa vi&longs;um, quod &longs;ph&aelig;rica &longs;it: non <lb/>enim <expan abbr="vtiq;">vtique</expan> fieret accre&longs;cens, &amp; decre&longs;cens, plurim&ubreve; quidem alter a ex parte curua, <lb/>altera concaua, aut <expan abbr="vtrmq;">vtrmque</expan> curua, &longs;emel autem bipartita)<emph.end type="italics"/> ait per ea, qu&aelig; circa <lb/>vi&longs;um, ide&longs;t per opticem probari Lunam e&longs;&longs;e &longs;ph&aelig;ricam: &longs;ed con&longs;ule, qu&aelig; <lb/>primo Po&longs;ter. tex. </s> <s>Tex. <emph type="italics"/>(Luna autem o&longs;tenditur per ea, qu&aelig; circa vi&longs;um, quod &longs;ph&aelig;rica &longs;it: non <lb/>enim <expan abbr="vtiq;">vtique</expan> fieret accre&longs;cens, &amp; decre&longs;cens, plurim&ubreve; quidem alter a ex parte curua, <lb/>altera concaua, aut <expan abbr="vtrmq;">vtrmque</expan> curua, &longs;emel autem bipartita)<emph.end type="italics"/> ait per ea, qu&aelig; circa <lb/>vi&longs;um, ide&longs;t per opticem probari Lunam e&longs;&longs;e &longs;ph&aelig;ricam: &longs;ed con&longs;ule, qu&aelig; <lb/>primo Po&longs;ter. tex. </s>
  
 <s>3. de hac re &longs;crip&longs;i, &amp; plenam etiam huius loci intelligen&shy;<lb/>tiam a&longs;&longs;equeris, pr&aelig;&longs;ertim &longs;i experimentum ibi traditum inieris.</s></p><p type="main"> <s>3. de hac re &longs;crip&longs;i, &amp; plenam etiam huius loci intelligen&shy;<lb/>tiam a&longs;&longs;equeris, pr&aelig;&longs;ertim &longs;i experimentum ibi traditum inieris.</s></p><p type="main">
  
 <s><arrow.to.target n="marg111"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg111"/></s></p><p type="margin">
  
 <s><margin.target id="marg111"></margin.target>111</s></p><p type="main"> <s><margin.target id="marg111"/>111</s></p><p type="main">
  
 <s>Ibidem <emph type="italics"/>(Et rur&longs;us per Astrologica, quia <expan abbr="vtiq;">vtique</expan> non e&longs;&longs;ent &longs;olis eclyp&longs;es lunul&aelig; <lb/>&longs;peciem pr&aelig;&longs;eferentes. </s> <s>Ibidem <emph type="italics"/>(Et rur&longs;us per Astrologica, quia <expan abbr="vtiq;">vtique</expan> non e&longs;&longs;ent &longs;olis eclyp&longs;es lunul&aelig; <lb/>&longs;peciem pr&aelig;&longs;eferentes. </s>
  
 <s>Quare &longs;i vnum est tale, palam e&longs;t, quod &amp; alia <expan abbr="vtiq;">vtique</expan> erunt <lb/>talia)<emph.end type="italics"/> &longs;icuti <expan abbr="pr&aelig;ced&etilde;s">pr&aelig;cedens</expan> &longs;ph&aelig;ricitatis Lun&aelig; ratio ex Per&longs;pectiua de&longs;umpta e&longs;t, <lb/>ita pr&aelig;&longs;ens ex A&longs;tronomia, ex e&ograve; enim, quod eclyp&longs;is Solis habeat figuram <lb/>lunul&aelig;, ide&longs;t, &longs;i in&longs;tar Lun&aelig; falcat&aelig;, probant A&longs;tronomi Lunam e&longs;&longs;e &longs;ph&aelig;ri&shy;<lb/>cam. </s> <s>Quare &longs;i vnum est tale, palam e&longs;t, quod &amp; alia <expan abbr="vtiq;">vtique</expan> erunt <lb/>talia)<emph.end type="italics"/> &longs;icuti <expan abbr="pr&aelig;ced&etilde;s">pr&aelig;cedens</expan> &longs;ph&aelig;ricitatis Lun&aelig; ratio ex Per&longs;pectiua de&longs;umpta e&longs;t, <lb/>ita pr&aelig;&longs;ens ex A&longs;tronomia, ex e&ograve; enim, quod eclyp&longs;is Solis habeat figuram <lb/>lunul&aelig;, ide&longs;t, &longs;i in&longs;tar Lun&aelig; falcat&aelig;, probant A&longs;tronomi Lunam e&longs;&longs;e &longs;ph&aelig;ri&shy;<lb/>cam. </s>
  
 <s>intellige tamen partem illam Solis, qu&aelig; non eclyp&longs;atur, habere figu&shy;<lb/>ram lunul&aelig;, pars enim &agrave; Luna obumbrata non videtur, et&longs;i videretur oua&shy;<lb/>lem quandam &longs;peciem, pr&aelig;&longs;eferret: pars igitur, illa e&longs;t corniculata, quia <lb/><figure id="fig42"></figure><lb/>cum Solis defectio ex interpo&longs;itione Lun&aelig; inter nos, &amp; <lb/>Solem contingat, &amp; Luna &longs;it &longs;ph&aelig;rica, nece&longs;&longs;ari&ograve; &longs;ph&aelig;&shy;<lb/>ric&egrave;, &amp; circulariter Solem obumbrabit; quare pars illa <lb/>non obumbrata remanet falcata, &amp; corniculata, vt in <lb/>pr&aelig;&longs;enti figura vidcre e&longs;t; vbi cernis, Lunam Solem or&shy;<lb/>biculariter offu&longs;care in linea A D C, partem Solis de&shy;<lb/>tectam <expan abbr="content&atilde;">contentam</expan> lineis curuis A B C D, e&longs;&longs;e lunularem, <lb/>&amp; falcatam; cum ergo in hunc modum fiat Solis deli&shy;<lb/>quium, &longs;ignum certum e&longs;t, Lunam e&longs;&longs;e &longs;ph&aelig;ricam.</s></p><p type="main"> <s>intellige tamen partem illam Solis, qu&aelig; non eclyp&longs;atur, habere figu&shy;<lb/>ram lunul&aelig;, pars enim &agrave; Luna obumbrata non videtur, et&longs;i videretur oua&shy;<lb/>lem quandam &longs;peciem, pr&aelig;&longs;eferret: pars igitur, illa e&longs;t corniculata, quia <lb/><figure id="fig42"/><lb/>cum Solis defectio ex interpo&longs;itione Lun&aelig; inter nos, &amp; <lb/>Solem contingat, &amp; Luna &longs;it &longs;ph&aelig;rica, nece&longs;&longs;ari&ograve; &longs;ph&aelig;&shy;<lb/>ric&egrave;, &amp; circulariter Solem obumbrabit; quare pars illa <lb/>non obumbrata remanet falcata, &amp; corniculata, vt in <lb/>pr&aelig;&longs;enti figura vidcre e&longs;t; vbi cernis, Lunam Solem or&shy;<lb/>biculariter offu&longs;care in linea A D C, partem Solis de&shy;<lb/>tectam <expan abbr="content&atilde;">contentam</expan> lineis curuis A B C D, e&longs;&longs;e lunularem, <lb/>&amp; falcatam; cum ergo in hunc modum fiat Solis deli&shy;<lb/>quium, &longs;ignum certum e&longs;t, Lunam e&longs;&longs;e &longs;ph&aelig;ricam.</s></p><p type="main">
  
 <s><arrow.to.target n="marg112"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg112"/></s></p><p type="margin">
  
 <s><margin.target id="marg112"></margin.target>112</s></p><p type="main"> <s><margin.target id="marg112"/>112</s></p><p type="main">
  
 <s>Tex. 107. <emph type="italics"/>(Quod autem dubitatur, hoc e&longs;t; videre autem non e&longs;t difficile, &longs;i pa&shy;<lb/>rum con&longs;iderauerimus, &amp; di&longs;tinxerimus, quonam modo cen&longs;eamus quantamuis ma&shy;<lb/>gnitudinem grauem ad medium ferri. </s> <s>Tex. 107. <emph type="italics"/>(Quod autem dubitatur, hoc e&longs;t; videre autem non e&longs;t difficile, &longs;i pa&shy;<lb/>rum con&longs;iderauerimus, &amp; di&longs;tinxerimus, quonam modo cen&longs;eamus quantamuis ma&shy;<lb/>gnitudinem grauem ad medium ferri. </s>
  
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 <s>Verum enim ver&ograve; ex an&shy;<lb/>tiquorum monumentis manife&longs;tum e&longs;t, Archimedem, qui mult&ograve; po&longs;t Ari&shy;<lb/>&longs;totelem floruit, primum omnium de centro grauitatis e&longs;&longs;e philo&longs;ophatum, <lb/>qua ratione dicendum e&longs;&longs;et, Ari&longs;totelem de centro, molis loquutum e&longs;&longs;e, <lb/>&amp; perinde non <expan abbr="v&longs;quequaq;">v&longs;quequaque</expan> ver&egrave;.</s></p><p type="main"> <s>Verum enim ver&ograve; ex an&shy;<lb/>tiquorum monumentis manife&longs;tum e&longs;t, Archimedem, qui mult&ograve; po&longs;t Ari&shy;<lb/>&longs;totelem floruit, primum omnium de centro grauitatis e&longs;&longs;e philo&longs;ophatum, <lb/>qua ratione dicendum e&longs;&longs;et, Ari&longs;totelem de centro, molis loquutum e&longs;&longs;e, <lb/>&amp; perinde non <expan abbr="v&longs;quequaq;">v&longs;quequaque</expan> ver&egrave;.</s></p><p type="main">
  
 <s><arrow.to.target n="marg113"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg113"/></s></p><p type="margin">
  
 <s><margin.target id="marg113"></margin.target>113</s></p><p type="main"> <s><margin.target id="marg113"/>113</s></p><p type="main">
  
 <s>Tex. 109. <emph type="italics"/>(Pr&aelig;terea <expan abbr="quoq;">quoque</expan> &amp; per ta, qu&aelig; apparent &longs;ecundum &longs;en&longs;um, neque <lb/>enim Lun&aelig; eclyp&longs;es tales <expan abbr="haber&etilde;t">haberent</expan> deci&longs;iones; nunc enim in ijs, qu&aelig; &longs;ecundum men&shy;<lb/>&longs;em fiunt, figurationibus, omnes accipit diui&longs;iones: etenim recta fit, &amp; vtrinque <lb/>curua, &amp; concaua)<emph.end type="italics"/> probat terram e&longs;&longs;e &longs;ph&aelig;ricam ratione a&longs;tronomica, ex <lb/>Lun&aelig; eclyp&longs;ibus de&longs;umpta: nam ni&longs;i terra e&longs;&longs;et rotunda, nunquam Luna in <lb/>eclyp&longs;i haberet tales deci&longs;iones, ide&longs;t non haberet falcatas, aut lunulatas <lb/>partes illas, qu&aelig; in eclyp&longs;i ob&longs;curantur, &amp; quafi &agrave; Luna re&longs;ecantur. </s> <s>Tex. 109. <emph type="italics"/>(Pr&aelig;terea <expan abbr="quoq;">quoque</expan> &amp; per ta, qu&aelig; apparent &longs;ecundum &longs;en&longs;um, neque <lb/>enim Lun&aelig; eclyp&longs;es tales <expan abbr="haber&etilde;t">haberent</expan> deci&longs;iones; nunc enim in ijs, qu&aelig; &longs;ecundum men&shy;<lb/>&longs;em fiunt, figurationibus, omnes accipit diui&longs;iones: etenim recta fit, &amp; vtrinque <lb/>curua, &amp; concaua)<emph.end type="italics"/> probat terram e&longs;&longs;e &longs;ph&aelig;ricam ratione a&longs;tronomica, ex <lb/>Lun&aelig; eclyp&longs;ibus de&longs;umpta: nam ni&longs;i terra e&longs;&longs;et rotunda, nunquam Luna in <lb/>eclyp&longs;i haberet tales deci&longs;iones, ide&longs;t non haberet falcatas, aut lunulatas <lb/>partes illas, qu&aelig; in eclyp&longs;i ob&longs;curantur, &amp; quafi &agrave; Luna re&longs;ecantur. </s>
  
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 <s>vide etiam, qu&aelig; mox &longs;ubdam circa huius loci reliquum.</s></p><p type="main"> <s>vide etiam, qu&aelig; mox &longs;ubdam circa huius loci reliquum.</s></p><p type="main">
  
 <s><arrow.to.target n="marg114"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg114"/></s></p><p type="margin">
  
 <s><margin.target id="marg114"></margin.target>114</s></p><p type="main"> <s><margin.target id="marg114"/>114</s></p><p type="main">
  
 <s>Ibidem <emph type="italics"/>(Circa autem eclyp&longs;es, &longs;emper curuam habet termin&abreve;tem lmeam: qua&shy;<lb/>re qaon'am eclyp&longs;im palitur propter terr&aelig; obiectionem, terr&aelig; <expan abbr="circumfer&etilde;tia">circumferentia</expan> &longs;ph&aelig;&shy;<lb/>rica exi&longs;tens, figur&aelig; cau&longs;a erit)<emph.end type="italics"/> probat rotunditatem terr&aelig; ab eclyp&longs;i lunari, <lb/>ex eo, quod Luna &longs;ph&aelig;ric&egrave; eclyp&longs;etur, quod innuitur illis verbis, &longs;emper <pb pagenum="82"/>curuam hzbet terminantem lineam, linea &longs;cilicet, qu&aelig; terminat partem <lb/>eclyp&longs;atam &agrave; non eclyp&longs;ata, &longs;emper apparet circularis; cum autem h&aelig;c li&shy;<lb/>nea &longs;it terminus vmbr&aelig; terr&aelig;, qu&aelig; lumen obumbrat, &longs;ignum <expan abbr="manife&longs;t&utilde;">manife&longs;tum</expan> e&longs;t <lb/>vmbram ip&longs;am e&longs;&longs;e rotundam; nam cum Luna deficiat propter terr&aelig; obie&shy;<lb/>ctionem inter ip&longs;am, &amp; Solem, ita, vt vmbra terr&aelig; protendatur <expan abbr="v&longs;q;">v&longs;que</expan> ad Lu&shy;<lb/>nam, <expan abbr="eam&qacute;">eamque</expan>; in omni eclyp&longs;atione, &longs;iue eclyp&longs;is &longs;it &longs;upra terram, &longs;iue infra, <lb/>ad quamlibet <expan abbr="deniq;">denique</expan> partem terr&aelig; fiat, orbiculariter eam contegit, &longs;ignum <lb/>per&longs;picuum e&longs;t terram proijcere quoquouer&longs;us vmbram rotundam, qu&aelig; vt <lb/>in &longs;ph&aelig;ra o&longs;tenditur, e&longs;t rotunda ad modum coni; cum ergo vmbra terr&aelig; <lb/>ex quauis parte proijciatur, &longs;it rotunda, cert&ograve; certius colligitur, <expan abbr="terram&qacute;">terramque</expan>; <lb/><expan abbr="quoq;">quoque</expan> ip&longs;am rotunda &longs;igura pr&aelig;ditam e&longs;&longs;e. </s> <s>Ibidem <emph type="italics"/>(Circa autem eclyp&longs;es, &longs;emper curuam habet termin&abreve;tem lmeam: qua&shy;<lb/>re qaon'am eclyp&longs;im palitur propter terr&aelig; obiectionem, terr&aelig; <expan abbr="circumfer&etilde;tia">circumferentia</expan> &longs;ph&aelig;&shy;<lb/>rica exi&longs;tens, figur&aelig; cau&longs;a erit)<emph.end type="italics"/> probat rotunditatem terr&aelig; ab eclyp&longs;i lunari, <lb/>ex eo, quod Luna &longs;ph&aelig;ric&egrave; eclyp&longs;etur, quod innuitur illis verbis, &longs;emper <pb pagenum="82"/>curuam hzbet terminantem lineam, linea &longs;cilicet, qu&aelig; terminat partem <lb/>eclyp&longs;atam &agrave; non eclyp&longs;ata, &longs;emper apparet circularis; cum autem h&aelig;c li&shy;<lb/>nea &longs;it terminus vmbr&aelig; terr&aelig;, qu&aelig; lumen obumbrat, &longs;ignum <expan abbr="manife&longs;t&utilde;">manife&longs;tum</expan> e&longs;t <lb/>vmbram ip&longs;am e&longs;&longs;e rotundam; nam cum Luna deficiat propter terr&aelig; obie&shy;<lb/>ctionem inter ip&longs;am, &amp; Solem, ita, vt vmbra terr&aelig; protendatur <expan abbr="v&longs;q;">v&longs;que</expan> ad Lu&shy;<lb/>nam, <expan abbr="eam&qacute;">eamque</expan>; in omni eclyp&longs;atione, &longs;iue eclyp&longs;is &longs;it &longs;upra terram, &longs;iue infra, <lb/>ad quamlibet <expan abbr="deniq;">denique</expan> partem terr&aelig; fiat, orbiculariter eam contegit, &longs;ignum <lb/>per&longs;picuum e&longs;t terram proijcere quoquouer&longs;us vmbram rotundam, qu&aelig; vt <lb/>in &longs;ph&aelig;ra o&longs;tenditur, e&longs;t rotunda ad modum coni; cum ergo vmbra terr&aelig; <lb/>ex quauis parte proijciatur, &longs;it rotunda, cert&ograve; certius colligitur, <expan abbr="terram&qacute;">terramque</expan>; <lb/><expan abbr="quoq;">quoque</expan> ip&longs;am rotunda &longs;igura pr&aelig;ditam e&longs;&longs;e. </s>
  
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 <s>Clauium in &longs;ph&aelig;ra.</s></p><p type="main"> <s>Clauium in &longs;ph&aelig;ra.</s></p><p type="main">
  
 <s><arrow.to.target n="marg115"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg115"/></s></p><p type="margin">
  
 <s><margin.target id="marg115"></margin.target>115</s></p><p type="main"> <s><margin.target id="marg115"/>115</s></p><p type="main">
  
 <s>Tex. <emph type="italics"/>(Pr&aelig;terea per astrorum apparentiam, non &longs;olum manife&longs;ium e&longs;t, quod re&shy;<lb/>tunda, &longs;ed &amp; quod magnitudine non magna &longs;it; paruo enim facto ncbis tran&longs;itu ad <lb/>meridiem, &amp; Vr&longs;am, manifa&longs;t&egrave; fit alter horizon circulus, ita vt a&longs;tra, qu&aelig; &longs;uper <lb/>caput, magnam habcant mutationem, &amp; non eadem appareant, &amp; ad Vr&longs;am, &amp; ad <lb/>meridiem tran&longs;euntibus, qu&aelig;dam enim in Acgypto quidem stell&aelig; <expan abbr="vid&etilde;tur">videntur</expan>, &amp; cir&shy;<lb/>ca Cyprum, in ijs autem, qu&aelig; ad Vr&longs;am vergunt regionibus, non <expan abbr="via&etilde;tur">viaentur</expan>. </s> <s>Tex. <emph type="italics"/>(Pr&aelig;terea per astrorum apparentiam, non &longs;olum manife&longs;ium e&longs;t, quod re&shy;<lb/>tunda, &longs;ed &amp; quod magnitudine non magna &longs;it; paruo enim facto ncbis tran&longs;itu ad <lb/>meridiem, &amp; Vr&longs;am, manifa&longs;t&egrave; fit alter horizon circulus, ita vt a&longs;tra, qu&aelig; &longs;uper <lb/>caput, magnam habcant mutationem, &amp; non eadem appareant, &amp; ad Vr&longs;am, &amp; ad <lb/>meridiem tran&longs;euntibus, qu&aelig;dam enim in Acgypto quidem stell&aelig; <expan abbr="vid&etilde;tur">videntur</expan>, &amp; cir&shy;<lb/>ca Cyprum, in ijs autem, qu&aelig; ad Vr&longs;am vergunt regionibus, non <expan abbr="via&etilde;tur">viaentur</expan>. </s>
  
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 <s>Quare non &longs;olum ex his manife&longs;tum e&longs;t rotundam e&longs;&longs;e figuram terr&aelig;, &longs;ed &amp; &longs;ph&aelig;r&aelig; <lb/>non magn&aelig;: non enim tam celeriter in&longs;igne quippiam faceret, tran&longs;latis nobis ade&ograve; <lb/>parum)<emph.end type="italics"/> hic textus ei, qui &longs;ph&aelig;ram mundi audiuerit perfacilis e&longs;t: propte&shy;<lb/>rea eum breuiter &longs;ic paraphra&longs;tic&egrave; exponam. </s> <s>Quare non &longs;olum ex his manife&longs;tum e&longs;t rotundam e&longs;&longs;e figuram terr&aelig;, &longs;ed &amp; &longs;ph&aelig;r&aelig; <lb/>non magn&aelig;: non enim tam celeriter in&longs;igne quippiam faceret, tran&longs;latis nobis ade&ograve; <lb/>parum)<emph.end type="italics"/> hic textus ei, qui &longs;ph&aelig;ram mundi audiuerit perfacilis e&longs;t: propte&shy;<lb/>rea eum breuiter &longs;ic paraphra&longs;tic&egrave; exponam. </s>
  
 <s>Terram e&longs;&longs;e rotundam, <expan abbr="atq;">atque</expan> <lb/>re&longs;pectu c&oelig;le&longs;tium corporum non magnam, &longs;ignum e&longs;t, quod facto &agrave; nobis <lb/>paruo itinere &longs;iue ad meridionalem plagam, &longs;iue ad <expan abbr="&longs;ept&etilde;trionalem">&longs;eptentrionalem</expan> (quam <lb/>Vr&longs;am dicit) magnopere mutatur horizon: quod apparet primo ex varia&shy;<lb/>tionc a&longs;trorum, nam qu&aelig; in primo loco &longs;upra no&longs;trum verticem <expan abbr="tr&atilde;&longs;ibant">tran&longs;ibant</expan>, <lb/>in &longs;ecundo loco non amplius, &longs;ed alia, <expan abbr="atq;">atque</expan> alia valde ab inuicem &longs;eiuncta <lb/><figure id="fig43"></figure><lb/>exfacto quamuis paruo itinere tran&longs;eunt. </s> <s>Terram e&longs;&longs;e rotundam, <expan abbr="atq;">atque</expan> <lb/>re&longs;pectu c&oelig;le&longs;tium corporum non magnam, &longs;ignum e&longs;t, quod facto &agrave; nobis <lb/>paruo itinere &longs;iue ad meridionalem plagam, &longs;iue ad <expan abbr="&longs;ept&etilde;trionalem">&longs;eptentrionalem</expan> (quam <lb/>Vr&longs;am dicit) magnopere mutatur horizon: quod apparet primo ex varia&shy;<lb/>tionc a&longs;trorum, nam qu&aelig; in primo loco &longs;upra no&longs;trum verticem <expan abbr="tr&atilde;&longs;ibant">tran&longs;ibant</expan>, <lb/>in &longs;ecundo loco non amplius, &longs;ed alia, <expan abbr="atq;">atque</expan> alia valde ab inuicem &longs;eiuncta <lb/><figure id="fig43"/><lb/>exfacto quamuis paruo itinere tran&longs;eunt. </s>
  
 <s>&longs;it in <lb/>pr&aelig;&longs;enti figura terra, vbi A, in qua facta parua <lb/>mutatione ex loco F, in locum G, fieret magna <lb/>mutatio <expan abbr="a&longs;tror&utilde;">a&longs;trorum</expan> ver&longs;icalium B, in C, qu&aelig; mul&shy;<lb/>tum ab inuicem di&longs;tant. </s> <s>&longs;it in <lb/>pr&aelig;&longs;enti figura terra, vbi A, in qua facta parua <lb/>mutatione ex loco F, in locum G, fieret magna <lb/>mutatio <expan abbr="a&longs;tror&utilde;">a&longs;trorum</expan> ver&longs;icalium B, in C, qu&aelig; mul&shy;<lb/>tum ab inuicem di&longs;tant. </s>
  
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 <s>Clauium in &longs;ph&aelig;ra.</s></p><p type="main"> <s>Clauium in &longs;ph&aelig;ra.</s></p><p type="main">
  
 <s><arrow.to.target n="marg116"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg116"/></s></p><p type="margin">
  
 <s><margin.target id="marg116"></margin.target>116</s></p><p type="main"> <s><margin.target id="marg116"/>116</s></p><p type="main">
  
 <s>Tex. 111. <emph type="italics"/>(Quapropter existimantes eum, qui circa Herculcas columnas e&longs;t lo&shy;<lb/>cum coniungi ei, qui circa Indiam, &amp; boc modo mare vnum e&longs;&longs;e, nen admcdum <lb/>incredibilia exi&longs;timare videntur &amp;c.)<emph.end type="italics"/> exi&longs;timatores ho&longs;ce non perperam exi&shy;<lb/>&longs;tima&longs;&longs;e apert&egrave; <expan abbr="c&otilde;uincunt">conuincunt</expan> Chri&longs;tophori Columbi, Argonautarum principis <lb/>nauigationes; quibus nouus orbis repertus e&longs;t, qui inter columnas Hercu&shy;<lb/>lis, <expan abbr="atq;">atque</expan> orientalem Indiam totus vna <expan abbr="c&utilde;">cum</expan> mari Oceano Atlantico interiacet.</s></p><p type="main"> <s>Tex. 111. <emph type="italics"/>(Quapropter existimantes eum, qui circa Herculcas columnas e&longs;t lo&shy;<lb/>cum coniungi ei, qui circa Indiam, &amp; boc modo mare vnum e&longs;&longs;e, nen admcdum <lb/>incredibilia exi&longs;timare videntur &amp;c.)<emph.end type="italics"/> exi&longs;timatores ho&longs;ce non perperam exi&shy;<lb/>&longs;tima&longs;&longs;e apert&egrave; <expan abbr="c&otilde;uincunt">conuincunt</expan> Chri&longs;tophori Columbi, Argonautarum principis <lb/>nauigationes; quibus nouus orbis repertus e&longs;t, qui inter columnas Hercu&shy;<lb/>lis, <expan abbr="atq;">atque</expan> orientalem Indiam totus vna <expan abbr="c&utilde;">cum</expan> mari Oceano Atlantico interiacet.</s></p><p type="main">
  
 <s><arrow.to.target n="marg117"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg117"/></s></p><p type="margin">
  
 <s><margin.target id="marg117"></margin.target>117</s></p><p type="main"> <s><margin.target id="marg117"/>117</s></p><p type="main">
  
 <s>Tex. 112. <emph type="italics"/>(Matbematicorum etiam, qui circum ferenti&aelig; magnitudinemratio&shy;<lb/>cinari tentant, ad 400. dicunt ftadiorum millia, &amp;c.)<emph.end type="italics"/> quam &longs;ubtilibus rationi&shy;<lb/>bus inue&longs;tigauerint A&longs;tronomi quantitatem terr&aelig;, optim&egrave;, ac dilucid&egrave; ex&shy;<lb/>ponitur &agrave; P. </s> <s>Tex. 112. <emph type="italics"/>(Matbematicorum etiam, qui circum ferenti&aelig; magnitudinemratio&shy;<lb/>cinari tentant, ad 400. dicunt ftadiorum millia, &amp;c.)<emph.end type="italics"/> quam &longs;ubtilibus rationi&shy;<lb/>bus inue&longs;tigauerint A&longs;tronomi quantitatem terr&aelig;, optim&egrave;, ac dilucid&egrave; ex&shy;<lb/>ponitur &agrave; P. </s>
  
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 <s><emph type="italics"/>Ex Tertio de C&oelig;lo.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Ex Tertio de C&oelig;lo.<emph.end type="italics"/></s></p><p type="main">
  
 <s><arrow.to.target n="marg118"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg118"/></s></p><p type="margin">
  
 <s><margin.target id="marg118"></margin.target>118</s></p><p type="main"> <s><margin.target id="marg118"/>118</s></p><p type="main">
  
 <s>Tex. 40. <emph type="italics"/>(Figur&aelig; autem omnes componuntur ex pyramidibus: rectilinea <lb/>quidem ex rectilmeis: fph&aelig;ra ver&ograve; ex octo partibus componitur)<emph.end type="italics"/> Ale&shy;<lb/>xander exiftimat, Ari&longs;totelem dicere &longs;ph&aelig;ram con&longs;tare ex octo <lb/>partibus illis, qu&aelig; de&longs;ignantur per tres circulos, quorum duo &longs;e&shy;<lb/>cant &longs;e mucu&ograve; ad angulos rectos, vt in &longs;ph&aelig;ra mundi faciunt duo coluri; <lb/>tertius ver&ograve; medios illos diuidit &aelig;quidi&longs;tanter &agrave; &longs;ectionibus <expan abbr="illor&utilde;">illorum</expan> mutuis, <lb/>quemadmodum &aelig;quator in &longs;ph&aelig;ra mundi &longs;ecat duos coluros. </s> <s>Tex. 40. <emph type="italics"/>(Figur&aelig; autem omnes componuntur ex pyramidibus: rectilinea <lb/>quidem ex rectilmeis: fph&aelig;ra ver&ograve; ex octo partibus componitur)<emph.end type="italics"/> Ale&shy;<lb/>xander exiftimat, Ari&longs;totelem dicere &longs;ph&aelig;ram con&longs;tare ex octo <lb/>partibus illis, qu&aelig; de&longs;ignantur per tres circulos, quorum duo &longs;e&shy;<lb/>cant &longs;e mucu&ograve; ad angulos rectos, vt in &longs;ph&aelig;ra mundi faciunt duo coluri; <lb/>tertius ver&ograve; medios illos diuidit &aelig;quidi&longs;tanter &agrave; &longs;ectionibus <expan abbr="illor&utilde;">illorum</expan> mutuis, <lb/>quemadmodum &aelig;quator in &longs;ph&aelig;ra mundi &longs;ecat duos coluros. </s>
  
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 <s>qu&aelig; qua <lb/>ratione re&longs;oluantur in plures pyramides, con&longs;tat ex 10. 11. 12. &amp; 13. Ele&shy;<lb/>mentorum Euclidis, at ver&ograve; in &longs;ph&aelig;ra nullum reale compo&longs;itionis, aut di&shy;<lb/>ui&longs;ionis fundamentum reperitur.</s></p><p type="main"> <s>qu&aelig; qua <lb/>ratione re&longs;oluantur in plures pyramides, con&longs;tat ex 10. 11. 12. &amp; 13. Ele&shy;<lb/>mentorum Euclidis, at ver&ograve; in &longs;ph&aelig;ra nullum reale compo&longs;itionis, aut di&shy;<lb/>ui&longs;ionis fundamentum reperitur.</s></p><p type="main">
  
 <s><arrow.to.target n="marg119"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg119"/></s></p><p type="margin">
  
 <s><margin.target id="marg119"></margin.target>119</s></p><p type="main"> <s><margin.target id="marg119"/>119</s></p><p type="main">
  
 <s>Tex. <emph type="italics"/>(Ad h&aelig;c nece&longs;&longs;e e&longs;t non omne corpus e&longs;&longs;e diui&longs;ibile dicere, &longs;ed repugnare <lb/>certi&longs;&longs;i nis &longs;cientijs; nam Mathematic&aelig; ip&longs;um quide&aelig; intelligibile, accipiunt diui&shy;<lb/>&longs;ibile)<emph.end type="italics"/> ip&longs;um intelligibile, ide&longs;t, quantitatem ab&longs;tractam tam continuam, <lb/>quam di&longs;eretam, quam &longs;tatuunt Philo&longs;ophi e&longs;&longs;e &longs;ubiectam materiam ma&shy;<lb/>thematicarum. </s> <s>Tex. <emph type="italics"/>(Ad h&aelig;c nece&longs;&longs;e e&longs;t non omne corpus e&longs;&longs;e diui&longs;ibile dicere, &longs;ed repugnare <lb/>certi&longs;&longs;i nis &longs;cientijs; nam Mathematic&aelig; ip&longs;um quide&aelig; intelligibile, accipiunt diui&shy;<lb/>&longs;ibile)<emph.end type="italics"/> ip&longs;um intelligibile, ide&longs;t, quantitatem ab&longs;tractam tam continuam, <lb/>quam di&longs;eretam, quam &longs;tatuunt Philo&longs;ophi e&longs;&longs;e &longs;ubiectam materiam ma&shy;<lb/>thematicarum. </s>
  
 <s>quam ideo appellant intelligibilem, quia cum &longs;it ab&longs;tracta <lb/>per intellectum &agrave; &longs;en&longs;ibilibus affectionibus, re&longs;tat vt &longs;it tantummodo intel&shy;<pb pagenum="84"/>lectu perceptibilis. </s> <s>quam ideo appellant intelligibilem, quia cum &longs;it ab&longs;tracta <lb/>per intellectum &agrave; &longs;en&longs;ibilibus affectionibus, re&longs;tat vt &longs;it tantummodo intel&shy;<pb pagenum="84"/>lectu perceptibilis. </s>
  
 <s>Hanc eandem &longs;upponunt e&longs;&longs;e diui&longs;ibilem in infinitum, <lb/>vt &longs;upra 3. Phy&longs;. </s> <s>Hanc eandem &longs;upponunt e&longs;&longs;e diui&longs;ibilem in infinitum, <lb/>vt &longs;upra 3. Phy&longs;. textu 31. dictum e&longs;t.</s></p><p type="main">
  
 <s>textu 31. dictum e&longs;t.</s></p><p type="main"> <s><arrow.to.target n="marg120"/></s></p><p type="margin">
  
 <s><arrow.to.target n="marg120"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg120"/>120</s></p><p type="main">
  
 <s><margin.target id="marg120"></margin.target>120</s></p><p type="main"> 
  
 <s>Tex. 66. <emph type="italics"/>(Ommn&ograve; autem eniti &longs;implicibus corporibus figur as tribuere irratio&shy;<lb/>nabile e&longs;t. </s> <s>Tex. 66. <emph type="italics"/>(Ommn&ograve; autem eniti &longs;implicibus corporibus figur as tribuere irratio&shy;<lb/>nabile e&longs;t. </s>
  
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 <s>tales &longs;unt, <lb/>quibus fieri po&longs;&longs;unt pauimenta, oportet enim, vt &longs;imul vnit&aelig; nihil vacui in <lb/>pauimento relinquant. </s> <s>tales &longs;unt, <lb/>quibus fieri po&longs;&longs;unt pauimenta, oportet enim, vt &longs;imul vnit&aelig; nihil vacui in <lb/>pauimento relinquant. </s>
  
 <s>huiu&longs;modi &longs;unt triangula &aelig;quilatera (de his enim <lb/>intelligendus e&longs;t textus) quadrata, &amp; hexagona, &longs;iue &longs;exilatera regularia; <lb/><figure id="fig44"></figure><lb/>nam &longs;ex triangula &aelig;quilatera &longs;imul iuncta in plano paui&shy;<lb/>re po&longs;&longs;unt, vt patet in figura pr&aelig;&longs;enti; ratio huius e&longs;t, <lb/>quia omnes anguli circa idem punctum (y. </s> <s>huiu&longs;modi &longs;unt triangula &aelig;quilatera (de his enim <lb/>intelligendus e&longs;t textus) quadrata, &amp; hexagona, &longs;iue &longs;exilatera regularia; <lb/><figure id="fig44"/><lb/>nam &longs;ex triangula &aelig;quilatera &longs;imul iuncta in plano paui&shy;<lb/>re po&longs;&longs;unt, vt patet in figura pr&aelig;&longs;enti; ratio huius e&longs;t, <lb/>quia omnes anguli circa idem punctum (y. </s>
  
 <s>g. </s> <s>g. </s>
  
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 <s>&longs;ecundo 15. primi Elemen&shy;<lb/>ti: cum igitur &longs;ex anguli, trianguli &aelig;quilateri <expan abbr="&aelig;quiuale&atilde;t">&aelig;quiualeant</expan> <lb/>quatuor rectis angulis, con&longs;tituti omnes circa punctum <lb/>A, totum locum circa illud implere po&longs;&longs;unt. </s> <s>&longs;ecundo 15. primi Elemen&shy;<lb/>ti: cum igitur &longs;ex anguli, trianguli &aelig;quilateri <expan abbr="&aelig;quiuale&atilde;t">&aelig;quiualeant</expan> <lb/>quatuor rectis angulis, con&longs;tituti omnes circa punctum <lb/>A, totum locum circa illud implere po&longs;&longs;unt. </s>
  
 <s>Quadratum etiam replere lo&shy;<lb/><figure id="fig45"></figure><lb/>cum manife&longs;tum e&longs;t, cum enim ip&longs;ius anguli &longs;intrecti, &longs;i <lb/>quatuor quadrata ad idem punctum A, copulentur, vt in <lb/>figura apparet, replebunt eadem de cau&longs;a vacuum.</s></p><p type="main"> <s>Quadratum etiam replere lo&shy;<lb/><figure id="fig45"/><lb/>cum manife&longs;tum e&longs;t, cum enim ip&longs;ius anguli &longs;intrecti, &longs;i <lb/>quatuor quadrata ad idem punctum A, copulentur, vt in <lb/>figura apparet, replebunt eadem de cau&longs;a vacuum.</s></p><p type="main">
  
 <s>Hexagonum quoque regulare, ide&longs;t &aelig;quilaterum, &amp; <lb/>&aelig;quiangulum idem pr&aelig;&longs;tare pote&longs;t; cum enim tres angu&shy;<lb/>li ip&longs;ius &aelig;quiualeant quatuor rectis, &longs;i tria hexagona ad <lb/>idem punctum A, vt in &longs;igura adaptentur, nece&longs;&longs;ari&ograve; ni&shy;<lb/>hil vacui inter ip&longs;a relinquetur, vt in figura hac o&longs;tenditur. </s> <s>Hexagonum quoque regulare, ide&longs;t &aelig;quilaterum, &amp; <lb/>&aelig;quiangulum idem pr&aelig;&longs;tare pote&longs;t; cum enim tres angu&shy;<lb/>li ip&longs;ius &aelig;quiualeant quatuor rectis, &longs;i tria hexagona ad <lb/>idem punctum A, vt in &longs;igura adaptentur, nece&longs;&longs;ari&ograve; ni&shy;<lb/>hil vacui inter ip&longs;a relinquetur, vt in figura hac o&longs;tenditur. </s>
  
 <s>pr&aelig;ter has tres <lb/><figure id="fig46"></figure><lb/>figuras, nulla alia reperitur, qu&aelig; i&longs;tud efficere pol&shy;<lb/>&longs;it. </s> <s>pr&aelig;ter has tres <lb/><figure id="fig46"/><lb/>figuras, nulla alia reperitur, qu&aelig; i&longs;tud efficere pol&shy;<lb/>&longs;it. </s>
  
 <s>cuius demon&longs;trationem perfectam videre pote&shy;<lb/>ris in fine commentarij P. </s> <s>cuius demon&longs;trationem perfectam videre pote&shy;<lb/>ris in fine commentarij P. </s>
  
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 <s>cum igitur tres tantum ex figuris planis <lb/>totum repleant, h&aelig; &longs;ol&aelig; poterunt elementis attri&shy;<lb/>bui, ac propterea non &longs;ufficient, ni&longs;i pro tribus elementis. </s> <s>cum igitur tres tantum ex figuris planis <lb/>totum repleant, h&aelig; &longs;ol&aelig; poterunt elementis attri&shy;<lb/>bui, ac propterea non &longs;ufficient, ni&longs;i pro tribus elementis. </s>
  
 <s>quare quartum <lb/><expan abbr="ab&longs;q;">ab&longs;que</expan> figura relinquetur; quod e&longs;t ab&longs;urdum.</s></p><figure></figure><pb pagenum="85"/><p type="head"> <s>quare quartum <lb/><expan abbr="ab&longs;q;">ab&longs;que</expan> figura relinquetur; quod e&longs;t ab&longs;urdum.</s></p><figure/><pb pagenum="85"/><p type="head">
  
 <s><emph type="italics"/>Admirabilis qu&aelig;dam A&pgrave;um industria.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Admirabilis qu&aelig;dam A&pgrave;um industria.<emph.end type="italics"/></s></p><p type="main">
  
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 <s>hoc ide&ograve; libentius recen&longs;ui, quia animaduerti naturales hi&longs;toriogra&shy;<lb/>phos omnes latere, vel ip&longs;um Aldobrandum no&longs;trum, qui quamuis indu&shy;<lb/>&longs;trio&longs;&aelig; Apis in&longs;tar omnia delibauerit, i&longs;tud tamen de Apibus artificium tan&shy;<lb/>ta &longs;apientia plenum, ne&longs;cio quo modo pr&aelig;termi&longs;it.</s></p><p type="main"> <s>hoc ide&ograve; libentius recen&longs;ui, quia animaduerti naturales hi&longs;toriogra&shy;<lb/>phos omnes latere, vel ip&longs;um Aldobrandum no&longs;trum, qui quamuis indu&shy;<lb/>&longs;trio&longs;&aelig; Apis in&longs;tar omnia delibauerit, i&longs;tud tamen de Apibus artificium tan&shy;<lb/>ta &longs;apientia plenum, ne&longs;cio quo modo pr&aelig;termi&longs;it.</s></p><p type="main">
  
 <s><arrow.to.target n="marg121"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg121"/></s></p><p type="margin">
  
 <s><margin.target id="marg121"></margin.target>121</s></p><p type="main"> <s><margin.target id="marg121"/>121</s></p><p type="main">
  
 <s>Ibidem <emph type="italics"/>(In folidis ver&ograve; du&aelig; &longs;o<gap/>um pyramis, &amp; cubus)<emph.end type="italics"/> ide&longs;t replent locum <lb/>&longs;olidum. </s> <s>Ibidem <emph type="italics"/>(In folidis ver&ograve; du&aelig; &longs;o<gap/>um pyramis, &amp; cubus)<emph.end type="italics"/> ide&longs;t replent locum <lb/>&longs;olidum. </s>
  
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 <s>cum igitur con&longs;tet vnam tan&shy;<lb/>tum ex figuris &longs;olidis, &longs;iue etiam dicas, vt perperam Ari&longs;t. &amp; alij plures exi&shy;<lb/>&longs;timarunt, replere totum &longs;olidum; nulla ratione poterunt <expan abbr="elem&etilde;ta">elementa</expan> quatuor, <lb/>quatuor diuer&longs;is figuris indui, &longs;ed vnum tantummodo, quare reliqua <expan abbr="ab&longs;q;">ab&longs;que</expan> <lb/>figura remanere nece&longs;&longs;e e&longs;&longs;et: quod e&longs;t omnino inconueniens.</s></p><p type="main"> <s>cum igitur con&longs;tet vnam tan&shy;<lb/>tum ex figuris &longs;olidis, &longs;iue etiam dicas, vt perperam Ari&longs;t. &amp; alij plures exi&shy;<lb/>&longs;timarunt, replere totum &longs;olidum; nulla ratione poterunt <expan abbr="elem&etilde;ta">elementa</expan> quatuor, <lb/>quatuor diuer&longs;is figuris indui, &longs;ed vnum tantummodo, quare reliqua <expan abbr="ab&longs;q;">ab&longs;que</expan> <lb/>figura remanere nece&longs;&longs;e e&longs;&longs;et: quod e&longs;t omnino inconueniens.</s></p><p type="main">
  
 <s><arrow.to.target n="marg122"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg122"/></s></p><p type="margin">
  
 <s><margin.target id="marg122"></margin.target>122</s></p><p type="main"> <s><margin.target id="marg122"/>122</s></p><p type="main">
  
 <s>Tex. 71 <emph type="italics"/>(Deinde &longs;i terra e&longs;t cubus &amp;c.)<emph.end type="italics"/> lege definitiones 11. Elem.  <s>Tex. 71 <emph type="italics"/>(Deinde &longs;i terra e&longs;t cubus &amp;c.)<emph.end type="italics"/> lege definitiones 11. Elem.
  
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 <s><emph type="italics"/>Ex Quarto de C&oelig;lo.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Ex Quarto de C&oelig;lo.<emph.end type="italics"/></s></p><p type="main">
  
 <s><arrow.to.target n="marg123"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg123"/></s></p><p type="margin">
  
 <s><margin.target id="marg123"></margin.target>123</s></p><p type="main"> <s><margin.target id="marg123"/>123</s></p><p type="main">
  
 <s>Tex. 33. <emph type="italics"/>(Deinde ad &longs;imiles videtur angulos ignis quidem &longs;ur&longs;um ferri, <lb/>terra autem deor&longs;um, &amp; omnin&ograve; quod grauitatem babet, quare nece&longs;&longs;e <lb/>est ferri ad medium. </s> <s>Tex. 33. <emph type="italics"/>(Deinde ad &longs;imiles videtur angulos ignis quidem &longs;ur&longs;um ferri, <lb/>terra autem deor&longs;um, &amp; omnin&ograve; quod grauitatem babet, quare nece&longs;&longs;e <lb/>est ferri ad medium. </s>
  
 <s>boc autem vtrum accidit ad ip&longs;um tcrr&aelig; medium, <lb/>an ad vniuer&longs;i, quoniam idem ip&longs;orum &longs;it, alius &longs;ermo e&longs;t)<emph.end type="italics"/> cum vellet <lb/><figure id="fig47"></figure><lb/>probare Ari&longs;toteles dari <expan abbr="p&utilde;ctum">punctum</expan> quoddam in m<gap/>dio <lb/>mundi, ad quod grauia de&longs;cendant, &amp; concurrent: <lb/>&amp; &agrave; quo leuia a&longs;c<gap/>ndat; vtitur, pr&aelig;ter alias, etism <lb/>ratione aliqua ex parte mathematica; qu&aelig; e&longs;t huiu&longs;&shy;<lb/>modi. </s> <s>boc autem vtrum accidit ad ip&longs;um tcrr&aelig; medium, <lb/>an ad vniuer&longs;i, quoniam idem ip&longs;orum &longs;it, alius &longs;ermo e&longs;t)<emph.end type="italics"/> cum vellet <lb/><figure id="fig47"/><lb/>probare Ari&longs;toteles dari <expan abbr="p&utilde;ctum">punctum</expan> quoddam in m<gap/>dio <lb/>mundi, ad quod grauia de&longs;cendant, &amp; concurrent: <lb/>&amp; &agrave; quo leuia a&longs;c<gap/>ndat; vtitur, pr&aelig;ter alias, etism <lb/>ratione aliqua ex parte mathematica; qu&aelig; e&longs;t huiu&longs;&shy;<lb/>modi. </s>
  
 <s>videmus ignem, &amp; c&aelig;tera l&ecedil;uia a&longs;cendere &agrave; <lb/>terra &longs;ur&longs;um ad angulos &aelig;quales; &longs;imiliter videmus <lb/>terram, &amp; c&ecedil;tera grauia de&longs;cendere ad terram dcor&shy;<lb/>&longs;um ad angulos &aelig;quales, quod &longs;ignum e&longs;t omnia i&longs;ta <lb/>idem mundi medium re&longs;picere: v.g. </s> <s>videmus ignem, &amp; c&aelig;tera l&ecedil;uia a&longs;cendere &agrave; <lb/>terra &longs;ur&longs;um ad angulos &aelig;quales; &longs;imiliter videmus <lb/>terram, &amp; c&ecedil;tera grauia de&longs;cendere ad terram dcor&shy;<lb/>&longs;um ad angulos &aelig;quales, quod &longs;ignum e&longs;t omnia i&longs;ta <lb/>idem mundi medium re&longs;picere: v.g. </s>
  
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 <s>vide igitur hac de re <lb/>pulchram de&longs;&longs;ertationem apud Clauium in &longs;ph&aelig;ra: qui probat euidenter <lb/>e&longs;&longs;e vnum, &amp; idem.</s></p><p type="main"> <s>vide igitur hac de re <lb/>pulchram de&longs;&longs;ertationem apud Clauium in &longs;ph&aelig;ra: qui probat euidenter <lb/>e&longs;&longs;e vnum, &amp; idem.</s></p><p type="main">
  
 <s><arrow.to.target n="marg124"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg124"/></s></p><p type="margin">
  
 <s><margin.target id="marg124"></margin.target>124</s></p><p type="main"> <s><margin.target id="marg124"/>124</s></p><p type="main">
  
 <s><emph type="italics"/>Hoc loco de&longs;ideratur commentarius in cap.  <s><emph type="italics"/>Hoc loco de&longs;ideratur commentarius in cap.
  
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 <s>cuius loco &igrave;n-<emph.end type="italics"/></s></p><p type="main"> <s>cuius loco &igrave;n-<emph.end type="italics"/></s></p><p type="main">
  
 <s><arrow.to.target n="marg125"></arrow.to.target><lb/><arrow.to.target n="marg126"></arrow.to.target><lb/><emph type="italics"/>terim Lector adeat Di&longs;cur&longs;um Italicum Galil&aelig;i Galil&aelig;i, de his,<emph.end type="italics"/><lb/><arrow.to.target n="marg127"></arrow.to.target><lb/><emph type="italics"/>qu&aelig; in aqua mouentur, ac natant: ubi prop&egrave; finem, plura in hu-<emph.end type="italics"/><lb/><arrow.to.target n="marg128"></arrow.to.target><lb/><emph type="italics"/>ius capitis explicationem affert.<emph.end type="italics"/><lb/><arrow.to.target n="marg129"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg125"/><lb/><arrow.to.target n="marg126"/><lb/><emph type="italics"/>terim Lector adeat Di&longs;cur&longs;um Italicum Galil&aelig;i Galil&aelig;i, de his,<emph.end type="italics"/><lb/><arrow.to.target n="marg127"/><lb/><emph type="italics"/>qu&aelig; in aqua mouentur, ac natant: ubi prop&egrave; finem, plura in hu-<emph.end type="italics"/><lb/><arrow.to.target n="marg128"/><lb/><emph type="italics"/>ius capitis explicationem affert.<emph.end type="italics"/><lb/><arrow.to.target n="marg129"/></s></p><p type="margin">
  
 <s><margin.target id="marg125"></margin.target>125</s></p><p type="margin"> <s><margin.target id="marg125"/>125</s></p><p type="margin">
  
 <s><margin.target id="marg126"></margin.target>126</s></p><p type="margin"> <s><margin.target id="marg126"/>126</s></p><p type="margin">
  
 <s><margin.target id="marg127"></margin.target>127</s></p><p type="margin"> <s><margin.target id="marg127"/>127</s></p><p type="margin">
  
 <s><margin.target id="marg128"></margin.target>128</s></p><p type="margin"> <s><margin.target id="marg128"/>128</s></p><p type="margin">
  
 <s><margin.target id="marg129"></margin.target>129</s></p><p type="head"> <s><margin.target id="marg129"/>129</s></p><p type="head">
  
 <s><emph type="italics"/>Ex Lib. 2. de Generatione, &amp; Corruptione.<emph.end type="italics"/><lb/><arrow.to.target n="marg130"></arrow.to.target></s></p><p type="margin"> <s><emph type="italics"/>Ex Lib. 2. de Generatione, &amp; Corruptione.<emph.end type="italics"/><lb/><arrow.to.target n="marg130"/></s></p><p type="margin">
  
 <s><margin.target id="marg130"></margin.target>130</s></p><p type="main"> <s><margin.target id="marg130"/>130</s></p><p type="main">
  
 <s>Tex. 56. <emph type="italics"/>(ldeo&queacute; non prima latio cau&longs;a Generationis, &amp; Corruptionis e&longs;t, <lb/>&longs;ed qu&aelig; &longs;ecundum obliquum circulum, in hac enim &amp; continuum vnum <lb/>e&longs;t &amp; moueri duobus motibus)<emph.end type="italics"/> per primam lationem intelligit mo&shy;<lb/>tum primi mobilis, qul &longs;it &longs;uper polis mundi, quo Stell&aelig; omnes <lb/>ab oriente in occidentem rect&agrave; feruntur. </s> <s>Tex. 56. <emph type="italics"/>(ldeo&queacute; non prima latio cau&longs;a Generationis, &amp; Corruptionis e&longs;t, <lb/>&longs;ed qu&aelig; &longs;ecundum obliquum circulum, in hac enim &amp; continuum vnum <lb/>e&longs;t &amp; moueri duobus motibus)<emph.end type="italics"/> per primam lationem intelligit mo&shy;<lb/>tum primi mobilis, qul &longs;it &longs;uper polis mundi, quo Stell&aelig; omnes <lb/>ab oriente in occidentem rect&agrave; feruntur. </s>
  
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 <s><emph type="italics"/>EX PRIMO METEORORVM.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>EX PRIMO METEORORVM.<emph.end type="italics"/></s></p><p type="main">
  
 <s><arrow.to.target n="marg131"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg131"/></s></p><p type="margin">
  
 <s><margin.target id="marg131"></margin.target>131</s></p><p type="main"> <s><margin.target id="marg131"/>131</s></p><p type="main">
  
 <s>Svmma 1. cap.  <s>Svmma 1. cap.
  
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 <s>Porr&ograve; facile e&longs;t demon&longs;trare Solem e&longs;&longs;e terra mult&ograve; maiorem, <lb/>terram ver&ograve; maiorem Luna, <expan abbr="id&qacute;">idque</expan>; ex eclyp&longs;i lunari, cuius imaginem habes <lb/>in figura &longs;equenti; vbi vmbra terr&aelig; e&longs;t D B E, in quam Luna nigricans im&shy;<lb/>mergitur, ac lumine deficit, reliqua cognitu &longs;unt facilia: quia igitur A&longs;tro&shy;<lb/>nomi ob&longs;eruarunt vmbram terr&aelig; paul&ograve; &longs;upra Lunam pertingere, cum &longs;upe&shy;<lb/>riora a&longs;tra non adeat, hinc collegerunt eam nece&longs;&longs;ari&ograve; e&longs;&longs;e acuminatam, &longs;eu <lb/>conicam, vt figura refert. </s> <s>Porr&ograve; facile e&longs;t demon&longs;trare Solem e&longs;&longs;e terra mult&ograve; maiorem, <lb/>terram ver&ograve; maiorem Luna, <expan abbr="id&qacute;">idque</expan>; ex eclyp&longs;i lunari, cuius imaginem habes <lb/>in figura &longs;equenti; vbi vmbra terr&aelig; e&longs;t D B E, in quam Luna nigricans im&shy;<lb/>mergitur, ac lumine deficit, reliqua cognitu &longs;unt facilia: quia igitur A&longs;tro&shy;<lb/>nomi ob&longs;eruarunt vmbram terr&aelig; paul&ograve; &longs;upra Lunam pertingere, cum &longs;upe&shy;<lb/>riora a&longs;tra non adeat, hinc collegerunt eam nece&longs;&longs;ari&ograve; e&longs;&longs;e acuminatam, &longs;eu <lb/>conicam, vt figura refert. </s>
  
 <s>Cum ergo terra vmbram proijciat turbinatam, <lb/>nece&longs;&longs;ari&ograve; corpus Solis, quod ip&longs;am illuminat, eadem maior erit: quoti&shy;<lb/>diana enim experientia docemur, corpore illuminante exi&longs;tente maiore <lb/>qu&agrave; &longs;it illuminatum, vmbram proijci fa&longs;tigiatam: cum deinde Solem val&shy;<lb/>de a terra di&longs;tare certum &longs;it, optim&egrave; infertur, eum re&longs;pectu terr&aelig; e&longs;&longs;e maxi&shy;<lb/>mum: quanto enim du&aelig; line&aelig;, &longs;iue radij B A, B C. &agrave; terra ad partes Solis <lb/><figure id="fig48"></figure><lb/>magis elongantur, tan&shy;<lb/>to maius corpus <expan abbr="illu-min&atilde;s">illu&shy;<lb/>minans</expan> intercipiunt. </s> <s>Cum ergo terra vmbram proijciat turbinatam, <lb/>nece&longs;&longs;ari&ograve; corpus Solis, quod ip&longs;am illuminat, eadem maior erit: quoti&shy;<lb/>diana enim experientia docemur, corpore illuminante exi&longs;tente maiore <lb/>qu&agrave; &longs;it illuminatum, vmbram proijci fa&longs;tigiatam: cum deinde Solem val&shy;<lb/>de a terra di&longs;tare certum &longs;it, optim&egrave; infertur, eum re&longs;pectu terr&aelig; e&longs;&longs;e maxi&shy;<lb/>mum: quanto enim du&aelig; line&aelig;, &longs;iue radij B A, B C. &agrave; terra ad partes Solis <lb/><figure id="fig48"/><lb/>magis elongantur, tan&shy;<lb/>to maius corpus <expan abbr="illu-min&atilde;s">illu&shy;<lb/>minans</expan> intercipiunt. </s>
  
 <s>ha&shy;<lb/>ctenus de magnitudine <lb/>terr&aelig; ad Solem. </s> <s>ha&shy;<lb/>ctenus de magnitudine <lb/>terr&aelig; ad Solem. </s>
  
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 <s>harum rerum demon&longs;trationes exactio<gap/>es pertractare non e&longs;t <lb/>huius loci.</s></p><p type="main"> <s>harum rerum demon&longs;trationes exactio<gap/>es pertractare non e&longs;t <lb/>huius loci.</s></p><p type="main">
  
 <s><arrow.to.target n="marg132"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg132"/></s></p><p type="margin">
  
 <s><margin.target id="marg132"></margin.target>132</s></p><p type="main"> <s><margin.target id="marg132"/>132</s></p><p type="main">
  
 <s>Eodem cap. <emph type="italics"/>(Con&longs;iderautes vtique, qu&aelig; nunc c&longs;tenduntur per Mathematica<emph.end type="italics"/><pb pagenum="90"/><emph type="italics"/>&longs;u<gap/>ficienter, for: &egrave; vtique de&longs;isterent ab hac puerili opinione; valde enim &longs;implex <lb/>e&longs;t pu<gap/>re <expan abbr="vnumquodq;">vnumquodque</expan> eorum qu&aelig; feruntur e&longs;&longs;e paruum magnitudinibus, quia vi&shy;<lb/>detur <gap/>&longs;picientibus, binc nobis &longs;ic)<emph.end type="italics"/> vtinam i&longs;ta, necnon alia his &longs;imilia, qu&aelig; <lb/>pa&longs;&longs;im apud Ari&longs;t.  <s>Eodem cap. <emph type="italics"/>(Con&longs;iderautes vtique, qu&aelig; nunc c&longs;tenduntur per Mathematica<emph.end type="italics"/><pb pagenum="90"/><emph type="italics"/>&longs;u<gap/>ficienter, for: &egrave; vtique de&longs;isterent ab hac puerili opinione; valde enim &longs;implex <lb/>e&longs;t pu<gap/>re <expan abbr="vnumquodq;">vnumquodque</expan> eorum qu&aelig; feruntur e&longs;&longs;e paruum magnitudinibus, quia vi&shy;<lb/>detur <gap/>&longs;picientibus, binc nobis &longs;ic)<emph.end type="italics"/> vtinam i&longs;ta, necnon alia his &longs;imilia, qu&aelig; <lb/>pa&longs;&longs;im apud Ari&longs;t.
  
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 alibi &longs;&aelig;pius, &longs;ed hoc <lb/>pr&aelig;cipu&egrave; loco; quippe qui Mathematicis &longs;ufficienter excultus erat; quibus <lb/>i&longs;ti de&longs;tituti, nullo vnquam modo ve&longs;tigia pr&aelig;ceptoris a&longs;&longs;equi poterunt.</s></p><p type="main"> alibi &longs;&aelig;pius, &longs;ed hoc <lb/>pr&aelig;cipu&egrave; loco; quippe qui Mathematicis &longs;ufficienter excultus erat; quibus <lb/>i&longs;ti de&longs;tituti, nullo vnquam modo ve&longs;tigia pr&aelig;ceptoris a&longs;&longs;equi poterunt.</s></p><p type="main">
  
 <s><arrow.to.target n="marg133"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg133"/></s></p><p type="margin">
  
 <s><margin.target id="marg133"></margin.target>133</s></p><p type="main"> <s><margin.target id="marg133"/>133</s></p><p type="main">
  
 <s>Summa 1. cap.  <s>Summa 1. cap.
  
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 deferebat, vnica, vt pu&shy;<lb/>tant ip&longs;ius auctoritate fulti, Solem &longs;ecundum &agrave; Luna locum occupare om&shy;<lb/>ni ope defendunt.</s></p><p type="main"> deferebat, vnica, vt pu&shy;<lb/>tant ip&longs;ius auctoritate fulti, Solem &longs;ecundum &agrave; Luna locum occupare om&shy;<lb/>ni ope defendunt.</s></p><p type="main">
  
 <s><arrow.to.target n="marg134"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg134"/></s></p><p type="margin">
  
 <s><margin.target id="marg134"></margin.target>134</s></p><p type="main"> <s><margin.target id="marg134"/>134</s></p><p type="main">
  
 <s>Summa 2. cap.  <s>Summa 2. cap.
  
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 <s>non me fugit h&aelig;c omnia ab a&longs;trono&shy;<lb/>mis per epiciclum excu&longs;ari; &longs;ed ego mediocritati eorum, in quorum gra&shy;<lb/>tiam h&aelig;c &longs;cribo, con&longs;ultum volo.</s></p><p type="main"> <s>non me fugit h&aelig;c omnia ab a&longs;trono&shy;<lb/>mis per epiciclum excu&longs;ari; &longs;ed ego mediocritati eorum, in quorum gra&shy;<lb/>tiam h&aelig;c &longs;cribo, con&longs;ultum volo.</s></p><p type="main">
  
 <s><arrow.to.target n="marg135"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg135"/></s></p><p type="margin">
  
 <s><margin.target id="marg135"></margin.target>135</s></p><p type="main"> <s><margin.target id="marg135"/>135</s></p><p type="main">
  
 <s>Eodem cap. <emph type="italics"/>(Ad au&longs;trum autem quando feratur, copiam quidem habere tal&iacute;s <lb/>humiditatis, &longs;ed quia parua e&longs;t &longs;ictio circuli, qu&aelig; &longs;uper terram, qu&aelig; autem deor&shy;<lb/>&longs;um multiplex, non po&longs;&longs;e vi&longs;um hominum fractum ferri ad Solem, <expan abbr="neq;">neque</expan> ip&longs;i tropico <lb/>au&longs;trino appropinquanti; <expan abbr="neq;">neque</expan> in &aelig;&longs;tiuis ver&longs;iombus exi&longs;tente Sole. </s> <s>Eodem cap. <emph type="italics"/>(Ad au&longs;trum autem quando feratur, copiam quidem habere tal&iacute;s <lb/>humiditatis, &longs;ed quia parua e&longs;t &longs;ictio circuli, qu&aelig; &longs;uper terram, qu&aelig; autem deor&shy;<lb/>&longs;um multiplex, non po&longs;&longs;e vi&longs;um hominum fractum ferri ad Solem, <expan abbr="neq;">neque</expan> ip&longs;i tropico <lb/>au&longs;trino appropinquanti; <expan abbr="neq;">neque</expan> in &aelig;&longs;tiuis ver&longs;iombus exi&longs;tente Sole. </s>
  
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 <s>de Cometis.<emph.end type="italics"/></s></p><p type="main"> <s>de Cometis.<emph.end type="italics"/></s></p><p type="main">
  
 <s><arrow.to.target n="marg136"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg136"/></s></p><p type="margin">
  
 <s><margin.target id="marg136"></margin.target>136</s></p><p type="main"> <s><margin.target id="marg136"/>136</s></p><p type="main">
  
 <s>In pr&aelig;&longs;enti cap. </s> <s>In pr&aelig;&longs;enti cap. </s>
  
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 <s>3. Ratio, qua etiam ante nouas ob&longs;eruationes vti &longs;olebant, de&longs;umitur <lb/>ex motu comet&aelig; diurno, quo &longs;cilicet oritur, &amp; occidit, quemadmodum c&aelig;&shy;<lb/>tera &longs;ydera, hoc e&longs;t &longs;patio 24. horarum diurnam conuer&longs;ionem circa totam <lb/>terram ab&longs;oluit. </s> <s>3. Ratio, qua etiam ante nouas ob&longs;eruationes vti &longs;olebant, de&longs;umitur <lb/>ex motu comet&aelig; diurno, quo &longs;cilicet oritur, &amp; occidit, quemadmodum c&aelig;&shy;<lb/>tera &longs;ydera, hoc e&longs;t &longs;patio 24. horarum diurnam conuer&longs;ionem circa totam <lb/>terram ab&longs;oluit. </s>
  
 <s>&longs;i igitur comete e&longs;&longs;et in &longs;ublimiori aeris regione, vbi c&aelig;te&shy;<lb/>ra ignita meteora collocantur, <expan abbr="moueretur&qacute;">mouereturque</expan>; diurno motu circa terram, &longs;e&shy;<lb/>queretur nece&longs;&longs;ari&ograve; eum tanta velocitate videri &agrave; nobis circumferri, vt po&shy;<lb/>tius fulgor quidam, &longs;eu radius pertran&longs;iens ab oriente in occidentem appa&shy;<lb/>reret, quam &longs;tella qu&ecedil;dam: <expan abbr="id&qacute;">idque</expan>; propter propinquitatem; a&longs;tra enim ob ni&shy;<lb/>miam di&longs;tantiam videntur tard&egrave; moueri, quamuis veloci&longs;&longs;im&egrave; moueantur.</s></p><figure></figure><p type="main"> <s>&longs;i igitur comete e&longs;&longs;et in &longs;ublimiori aeris regione, vbi c&aelig;te&shy;<lb/>ra ignita meteora collocantur, <expan abbr="moueretur&qacute;">mouereturque</expan>; diurno motu circa terram, &longs;e&shy;<lb/>queretur nece&longs;&longs;ari&ograve; eum tanta velocitate videri &agrave; nobis circumferri, vt po&shy;<lb/>tius fulgor quidam, &longs;eu radius pertran&longs;iens ab oriente in occidentem appa&shy;<lb/>reret, quam &longs;tella qu&ecedil;dam: <expan abbr="id&qacute;">idque</expan>; propter propinquitatem; a&longs;tra enim ob ni&shy;<lb/>miam di&longs;tantiam videntur tard&egrave; moueri, quamuis veloci&longs;&longs;im&egrave; moueantur.</s></p><figure/><p type="main">
  
 <s>Quod melius ex &longs;equenti figura <lb/><expan abbr="c&otilde;uincitur">conuincitur</expan>, vbi circulus interior e&longs;t <lb/>terra, cuius &longs;emidiameter A B. cir&shy;<lb/>culus ver&ograve; exterior e&longs;t comet&aelig; gy&shy;<lb/>rus, quem ip&longs;e &longs;patio 24. horarum <lb/>percurrit, qui &longs;ecundum veram pro&shy;<lb/>portionem deberet adhuc ip&longs;i terr&aelig; <lb/>propinquior, ac proinde minor e&longs;&longs;e, <lb/>iuxta aeris &longs;upremam partem. </s> <s>Quod melius ex &longs;equenti figura <lb/><expan abbr="c&otilde;uincitur">conuincitur</expan>, vbi circulus interior e&longs;t <lb/>terra, cuius &longs;emidiameter A B. cir&shy;<lb/>culus ver&ograve; exterior e&longs;t comet&aelig; gy&shy;<lb/>rus, quem ip&longs;e &longs;patio 24. horarum <lb/>percurrit, qui &longs;ecundum veram pro&shy;<lb/>portionem deberet adhuc ip&longs;i terr&aelig; <lb/>propinquior, ac proinde minor e&longs;&longs;e, <lb/>iuxta aeris &longs;upremam partem. </s>
  
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 <s>Huic memorati A&longs;tro&shy;<lb/>nomi &longs;ic re&longs;ponderent; id quidem mathematica, &amp; infallibili ratione non <lb/>colligi, im&ograve; aliquot parum infra Lunam extiti&longs;&longs;e, non omnin&ograve; negandum <lb/>videri: at ver&ograve; in &longs;uperiori aeris plaga, in tam fluxa, ac in&longs;tabili mundi par&shy;<lb/>te, cometas vnquam efful&longs;i&longs;&longs;e, nemo &longs;ibi ob allatas rationes merit&ograve; per&longs;ua&shy;<lb/>dere po&longs;&longs;e.</s></p><p type="main"> <s>Huic memorati A&longs;tro&shy;<lb/>nomi &longs;ic re&longs;ponderent; id quidem mathematica, &amp; infallibili ratione non <lb/>colligi, im&ograve; aliquot parum infra Lunam extiti&longs;&longs;e, non omnin&ograve; negandum <lb/>videri: at ver&ograve; in &longs;uperiori aeris plaga, in tam fluxa, ac in&longs;tabili mundi par&shy;<lb/>te, cometas vnquam efful&longs;i&longs;&longs;e, nemo &longs;ibi ob allatas rationes merit&ograve; per&longs;ua&shy;<lb/>dere po&longs;&longs;e.</s></p><p type="main">
  
 <s><arrow.to.target n="marg137"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg137"/></s></p><p type="margin">
  
 <s><margin.target id="marg137"></margin.target>137</s></p><p type="main"> <s><margin.target id="marg137"/>137</s></p><p type="main">
  
 <s>Summ&aelig; 2. cap.  <s>Summ&aelig; 2. cap.
  
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 <s>Exactiores ha&shy;<lb/>rum rerum demon&longs;trationes &longs;unt alterius loci.</s></p><p type="main"> <s>Exactiores ha&shy;<lb/>rum rerum demon&longs;trationes &longs;unt alterius loci.</s></p><p type="main">
  
 <s><arrow.to.target n="marg138"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg138"/></s></p><p type="margin">
  
 <s><margin.target id="marg138"></margin.target>138</s></p><p type="main"> <s><margin.target id="marg138"/>138</s></p><p type="main">
  
 <s>Eodem cap. <emph type="italics"/>(Amplius autem e&longs;t tertia qu&aelig;d<gap/>m opinio de ip&longs;o, dicunt enim<emph.end type="italics"/><pb pagenum="95"/><emph type="italics"/>quidam lac e&longs;&longs;e reflexionem no&longs;tri vi&longs;us ad Solem; &longs;icut &amp; &longs;tellam comatam; im&shy;<lb/>po&longs;&longs;ibile autem e&longs;t &amp; hoc, &longs;i enim videns quieuerit &amp; &longs;peculum, &amp; quod videtur <lb/>omne in eodem puncto &longs;peculi eadem apparebit <expan abbr="vtiq;">vtique</expan> pars imaginis, &longs;i autem mo&shy;<lb/>ueatur &longs;peculum, &amp; quod videtur, in eadem quidem di&longs;tantia ad videns, &amp; quie&shy;<lb/>&longs;cens; ad inuicem autem <expan abbr="neq;">neque</expan> &aelig;qu&egrave; velociter, <expan abbr="neq;">neque</expan> in eadem &longs;emper di&longs;tantia im&shy;<lb/>po&longs;&longs;ibile eandem imaginem in eadem e&longs;&longs;e parte &longs;peculi. </s> <s>Eodem cap. <emph type="italics"/>(Amplius autem e&longs;t tertia qu&aelig;d<gap/>m opinio de ip&longs;o, dicunt enim<emph.end type="italics"/><pb pagenum="95"/><emph type="italics"/>quidam lac e&longs;&longs;e reflexionem no&longs;tri vi&longs;us ad Solem; &longs;icut &amp; &longs;tellam comatam; im&shy;<lb/>po&longs;&longs;ibile autem e&longs;t &amp; hoc, &longs;i enim videns quieuerit &amp; &longs;peculum, &amp; quod videtur <lb/>omne in eodem puncto &longs;peculi eadem apparebit <expan abbr="vtiq;">vtique</expan> pars imaginis, &longs;i autem mo&shy;<lb/>ueatur &longs;peculum, &amp; quod videtur, in eadem quidem di&longs;tantia ad videns, &amp; quie&shy;<lb/>&longs;cens; ad inuicem autem <expan abbr="neq;">neque</expan> &aelig;qu&egrave; velociter, <expan abbr="neq;">neque</expan> in eadem &longs;emper di&longs;tantia im&shy;<lb/>po&longs;&longs;ibile eandem imaginem in eadem e&longs;&longs;e parte &longs;peculi. </s>
  
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 ratio confirmabiaur.</s></p><p type="main"> ratio confirmabiaur.</s></p><p type="main">
  
 <s><arrow.to.target n="marg139"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg139"/></s></p><p type="margin">
  
 <s><margin.target id="marg139"></margin.target>139</s></p><p type="main"> <s><margin.target id="marg139"/>139</s></p><p type="main">
  
 <s>Ibidem <emph type="italics"/>(Qu&aelig; autem in lactis cir culo feruntur astra, &amp; Sol, ad quem fit refle&shy;<lb/>xio, mouentur mancntibus nobis, &amp; &longs;imiliter, &amp; &aelig;qualiter ad nos di&longs;t antia &agrave; &longs;e <lb/>ip&longs;is autem non &aelig;qualiter)<emph.end type="italics"/> qu&aelig; hic ab Ari&longs;totele dicuntur <expan abbr="n&otilde;">non</expan> &longs;unt v&longs;quequae; <lb/>vera propter apog&aelig;um, ac porig&aelig;um Solis, qu&aelig; quidem duo ab omnibus <lb/>a&longs;tronomis a&longs;&longs;eruatur: quando igitur Sol e&longs;t in apog&aelig;o, maiori multo in&shy;<pb pagenum="96"/>teruallo di&longs;tat &agrave; nobis, qu&agrave;m quando e&longs;t in perig&aelig;o, interuallum enim illud <lb/>con&longs;tat diametris terr&aelig; duobus, &amp; quadraginta, hoc e&longs;t milliarijs 208000. <lb/>fer&egrave;, ide&longs;t octonis millibus &longs;upra ducenta millia. </s> <s>Ibidem <emph type="italics"/>(Qu&aelig; autem in lactis cir culo feruntur astra, &amp; Sol, ad quem fit refle&shy;<lb/>xio, mouentur mancntibus nobis, &amp; &longs;imiliter, &amp; &aelig;qualiter ad nos di&longs;t antia &agrave; &longs;e <lb/>ip&longs;is autem non &aelig;qualiter)<emph.end type="italics"/> qu&aelig; hic ab Ari&longs;totele dicuntur <expan abbr="n&otilde;">non</expan> &longs;unt v&longs;quequae; <lb/>vera propter apog&aelig;um, ac porig&aelig;um Solis, qu&aelig; quidem duo ab omnibus <lb/>a&longs;tronomis a&longs;&longs;eruatur: quando igitur Sol e&longs;t in apog&aelig;o, maiori multo in&shy;<pb pagenum="96"/>teruallo di&longs;tat &agrave; nobis, qu&agrave;m quando e&longs;t in perig&aelig;o, interuallum enim illud <lb/>con&longs;tat diametris terr&aelig; duobus, &amp; quadraginta, hoc e&longs;t milliarijs 208000. <lb/>fer&egrave;, ide&longs;t octonis millibus &longs;upra ducenta millia. </s>
  
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 i&longs;ta non occurrerunt, vel tunc temporis nondum <lb/>per&longs;pecta erant.</s></p><p type="main"> i&longs;ta non occurrerunt, vel tunc temporis nondum <lb/>per&longs;pecta erant.</s></p><p type="main">
  
 <s><arrow.to.target n="marg140"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg140"/></s></p><p type="margin">
  
 <s><margin.target id="marg140"></margin.target>140</s></p><p type="main"> <s><margin.target id="marg140"/>140</s></p><p type="main">
  
 <s>Ibidem <emph type="italics"/>(Aliquando enim medijs noctibus Delphin oritur)<emph.end type="italics"/> vt probet, Gala&shy;<lb/>xiam non &longs;emper &longs;eruare &agrave; Sole di&longs;tantiam eandem, accipit tanquam huius <lb/>rei &longs;ignum, manife&longs;tum, quod Delphini con&longs;tellatio aliquando medijs no&shy;<lb/>ctibus oriatur &longs;upra horizontem, aliquando ver&ograve; diluculo; non ide&ograve; tamen <lb/>putes hanc rationem &longs;upponere Delphinum e&longs;&longs;e in ip&longs;o lacteo circulo, quod <lb/>tamen verum non e&longs;t, non enim e&longs;t in Galaxia, &longs;ed tamen illi proximus, vt <lb/>noctu videre e&longs;t in c&oelig;lo, vel etiam &longs;i mauis in globo a&longs;tronomico: non ta&shy;<lb/>men ob id Ari&longs;t.  <s>Ibidem <emph type="italics"/>(Aliquando enim medijs noctibus Delphin oritur)<emph.end type="italics"/> vt probet, Gala&shy;<lb/>xiam non &longs;emper &longs;eruare &agrave; Sole di&longs;tantiam eandem, accipit tanquam huius <lb/>rei &longs;ignum, manife&longs;tum, quod Delphini con&longs;tellatio aliquando medijs no&shy;<lb/>ctibus oriatur &longs;upra horizontem, aliquando ver&ograve; diluculo; non ide&ograve; tamen <lb/>putes hanc rationem &longs;upponere Delphinum e&longs;&longs;e in ip&longs;o lacteo circulo, quod <lb/>tamen verum non e&longs;t, non enim e&longs;t in Galaxia, &longs;ed tamen illi proximus, vt <lb/>noctu videre e&longs;t in c&oelig;lo, vel etiam &longs;i mauis in globo a&longs;tronomico: non ta&shy;<lb/>men ob id Ari&longs;t.
  
 ratio minus valida redditur, cum Delphinus &longs;emper Gala&shy;<lb/>xi&aelig; eodem modo &longs;it proximus, <expan abbr="eo&qacute;">eoque</expan>; moto, ip&longs;a pariter moueatur.</s></p><p type="main"> ratio minus valida redditur, cum Delphinus &longs;emper Gala&shy;<lb/>xi&aelig; eodem modo &longs;it proximus, <expan abbr="eo&qacute;">eoque</expan>; moto, ip&longs;a pariter moueatur.</s></p><p type="main">
  
 <s><arrow.to.target n="marg141"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg141"/></s></p><p type="margin">
  
 <s><margin.target id="marg141"></margin.target>141</s></p><p type="main"> <s><margin.target id="marg141"/>141</s></p><p type="main">
  
 <s>Summ&aelig; 2. cap.  <s>Summ&aelig; 2. cap.
  
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 <s>Porr&ograve; h&aelig;c ratio quamuis adeo certa, ac no&longs;tra tempe&longs;tate vul&shy;<lb/>gata, parum tamen &agrave; nonnullis de rebus Meteorologicis commentaria con&shy;<lb/>farcinantibus intellecta, minim&egrave; eos ab&longs;terrere potuit, quin pr&aelig;dictam opi&shy;<lb/>nionem, non &longs;olum Ari&longs;toteli imponerent, verum etiam ip&longs;i <expan abbr="t&atilde;quam">tanquam</expan> veram <pb pagenum="97"/>a&longs;truerent: huiu&longs;modi patiuntur incommoda, qui <expan abbr="ab&longs;q;">ab&longs;que</expan> Mathematicarum <lb/>auxilio Philo&longs;ophiam aggrediuntur.</s></p><p type="main"> <s>Porr&ograve; h&aelig;c ratio quamuis adeo certa, ac no&longs;tra tempe&longs;tate vul&shy;<lb/>gata, parum tamen &agrave; nonnullis de rebus Meteorologicis commentaria con&shy;<lb/>farcinantibus intellecta, minim&egrave; eos ab&longs;terrere potuit, quin pr&aelig;dictam opi&shy;<lb/>nionem, non &longs;olum Ari&longs;toteli imponerent, verum etiam ip&longs;i <expan abbr="t&atilde;quam">tanquam</expan> veram <pb pagenum="97"/>a&longs;truerent: huiu&longs;modi patiuntur incommoda, qui <expan abbr="ab&longs;q;">ab&longs;que</expan> Mathematicarum <lb/>auxilio Philo&longs;ophiam aggrediuntur.</s></p><p type="main">
  
 <s><arrow.to.target n="marg142"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg142"/></s></p><p type="margin">
  
 <s><margin.target id="marg142"></margin.target>142</s></p><p type="main"> <s><margin.target id="marg142"/>142</s></p><p type="main">
  
 <s>Eodem cap. <emph type="italics"/>(Ad h&aelig;c autem locus plenus e&longs;t a&longs;tris maximis, &amp; fulgidi&longs;&longs;imis, <lb/>&amp; adhuc &longs;par&longs;is vocatis)<emph.end type="italics"/> non &longs;olum viam hanc lacteam a&longs;tris plurimis refer&shy;<lb/>ti&longs;&longs;imam e&longs;&longs;e videmus, &longs;ed pr&aelig;terea eandem &longs;tellarum admodum feracem <lb/>appellare licebit, &longs;i quidem &longs;tell&aelig; omnes ill&aelig; nou&aelig;, qu&aelig; no&longs;tra tempe&longs;tate <lb/>apparuerunt, omnes in hac via exort&aelig; &longs;unt. </s> <s>Eodem cap. <emph type="italics"/>(Ad h&aelig;c autem locus plenus e&longs;t a&longs;tris maximis, &amp; fulgidi&longs;&longs;imis, <lb/>&amp; adhuc &longs;par&longs;is vocatis)<emph.end type="italics"/> non &longs;olum viam hanc lacteam a&longs;tris plurimis refer&shy;<lb/>ti&longs;&longs;imam e&longs;&longs;e videmus, &longs;ed pr&aelig;terea eandem &longs;tellarum admodum feracem <lb/>appellare licebit, &longs;i quidem &longs;tell&aelig; omnes ill&aelig; nou&aelig;, qu&aelig; no&longs;tra tempe&longs;tate <lb/>apparuerunt, omnes in hac via exort&aelig; &longs;unt. </s>
  
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 <s>h&aelig;c ille.</s></p><p type="main"> <s>h&aelig;c ille.</s></p><p type="main">
  
 <s><arrow.to.target n="marg143"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg143"/></s></p><p type="margin">
  
 <s><margin.target id="marg143"></margin.target>143</s></p><p type="main"> <s><margin.target id="marg143"/>143</s></p><p type="main">
  
 <s>Eodem cap. <emph type="italics"/>(Con&longs;ideretur autem &amp; circulus, &amp; qu&aelig; &longs;unt in ip&longs;o a&longs;tra ex de&shy;<lb/>&longs;criptione)<emph.end type="italics"/> id e&longs;t, con&longs;ideretur Galaxia, &amp; a&longs;tra ip&longs;ius in&longs;piciantur diligenter <lb/>ex de&longs;criptione alicuius Globi a&longs;tronomici, in quo &longs;olent A&longs;tronomi omnes <lb/>con&longs;tellationes, ac &longs;tellas &longs;uis locis reddere, <expan abbr="atq;">atque</expan> etiam lacteum ip&longs;um cir&shy;<lb/>culum graphic&egrave; effingere. </s> <s>Eodem cap. <emph type="italics"/>(Con&longs;ideretur autem &amp; circulus, &amp; qu&aelig; &longs;unt in ip&longs;o a&longs;tra ex de&shy;<lb/>&longs;criptione)<emph.end type="italics"/> id e&longs;t, con&longs;ideretur Galaxia, &amp; a&longs;tra ip&longs;ius in&longs;piciantur diligenter <lb/>ex de&longs;criptione alicuius Globi a&longs;tronomici, in quo &longs;olent A&longs;tronomi omnes <lb/>con&longs;tellationes, ac &longs;tellas &longs;uis locis reddere, <expan abbr="atq;">atque</expan> etiam lacteum ip&longs;um cir&shy;<lb/>culum graphic&egrave; effingere. </s>
  
 <s>huiu&longs;modi globum veteres &longs;ph&ecedil;ram Arat&aelig;am di&shy;<lb/>cebant ab Arato Poeta gr&aelig;co, qui <expan abbr="c&otilde;&longs;tellationes">con&longs;tellationes</expan> omnes carmine pro&longs;e quu&shy;<lb/>tus e&longs;t, ac proinde globum hunc ordine expo&longs;uit:</s></p><p type="main"> <s>huiu&longs;modi globum veteres &longs;ph&ecedil;ram Arat&aelig;am di&shy;<lb/>cebant ab Arato Poeta gr&aelig;co, qui <expan abbr="c&otilde;&longs;tellationes">con&longs;tellationes</expan> omnes carmine pro&longs;e quu&shy;<lb/>tus e&longs;t, ac proinde globum hunc ordine expo&longs;uit:</s></p><p type="main">
  
 <s><arrow.to.target n="marg144"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg144"/></s></p><p type="margin">
  
 <s><margin.target id="marg144"></margin.target>144</s></p><p type="main"> <s><margin.target id="marg144"/>144</s></p><p type="main">
  
 <s>Eodem cap. <emph type="italics"/>(Spar&longs;a autem vocata)<emph.end type="italics"/> put&ograve; &longs;par&longs;a h&aelig;c &longs;ydera illa e&longs;&longs;e, qu&aelig; <lb/>recentiores informia appellant, e&ograve; quod ad aliorum a&longs;teri&longs;morum formas <lb/>minim&egrave; reuocentur.</s></p><p type="main"> <s>Eodem cap. <emph type="italics"/>(Spar&longs;a autem vocata)<emph.end type="italics"/> put&ograve; &longs;par&longs;a h&aelig;c &longs;ydera illa e&longs;&longs;e, qu&aelig; <lb/>recentiores informia appellant, e&ograve; quod ad aliorum a&longs;teri&longs;morum formas <lb/>minim&egrave; reuocentur.</s></p><p type="main">
  
 <s><arrow.to.target n="marg145"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg145"/></s></p><p type="margin">
  
 <s><margin.target id="marg145"></margin.target>145</s></p><p type="main"> <s><margin.target id="marg145"/>145</s></p><p type="main">
  
 <s>Summa 4. cap.  <s>Summa 4. cap.
  
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 15. <lb/>&longs;ic: Indiam &agrave; &longs;eptentrione Tauri extrema terminant, ab Ariana v&longs;que in <lb/>orientale mare, qu&aelig; extrema indigen&aelig; particulatim nominant Poropami&longs;<gap/><pb pagenum="98"/>&longs;um, Emodum, Imauum, &amp; alijs nominibus: Macedones ver&ograve; Cauca&longs;um <lb/>vocant.</s></p><p type="main"> 15. <lb/>&longs;ic: Indiam &agrave; &longs;eptentrione Tauri extrema terminant, ab Ariana v&longs;que in <lb/>orientale mare, qu&aelig; extrema indigen&aelig; particulatim nominant Poropami&longs;<gap/><pb pagenum="98"/>&longs;um, Emodum, Imauum, &amp; alijs nominibus: Macedones ver&ograve; Cauca&longs;um <lb/>vocant.</s></p><p type="main">
  
 <s><arrow.to.target n="marg146"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg146"/></s></p><p type="margin">
  
 <s><margin.target id="marg146"></margin.target>146</s></p><p type="main"> <s><margin.target id="marg146"/>146</s></p><p type="main">
  
 <s>Ibidem <emph type="italics"/>(Apparet mare, quod e&longs;t extra)<emph.end type="italics"/> intelligit illud mare <expan abbr="Ocean&utilde;">Oceanum</expan>, quod <lb/>Arabiam, ac Per&longs;iam alluit, <expan abbr="Indico&qacute;">Indicoque</expan>; Oceano committitur: <expan abbr="quod&qacute;">quodque</expan>; &agrave; pri&shy;<lb/>&longs;cis Geographis Rubrum mare appellatur, cuius alterum Rubrum mare, <lb/>quod inter Africam, &amp; Arabiam &longs;e in&longs;inuat, e&longs;t quidam &longs;inus, quem nunc <lb/>communiter omnes Rubrum mare appellant. </s> <s>Ibidem <emph type="italics"/>(Apparet mare, quod e&longs;t extra)<emph.end type="italics"/> intelligit illud mare <expan abbr="Ocean&utilde;">Oceanum</expan>, quod <lb/>Arabiam, ac Per&longs;iam alluit, <expan abbr="Indico&qacute;">Indicoque</expan>; Oceano committitur: <expan abbr="quod&qacute;">quodque</expan>; &agrave; pri&shy;<lb/>&longs;cis Geographis Rubrum mare appellatur, cuius alterum Rubrum mare, <lb/>quod inter Africam, &amp; Arabiam &longs;e in&longs;inuat, e&longs;t quidam &longs;inus, quem nunc <lb/>communiter omnes Rubrum mare appellant. </s>
  
Line 4803 
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 <s>Dixit autem mare, quod e&longs;t extra, ide&longs;t extra <lb/>terram habitatam, ad di&longs;tinctionem maris Mediterranei, quod e&longs;t intra <lb/>terram habitatam, ac propterea Mediterraneum dictum e&longs;t.</s></p><p type="main"> <s>Dixit autem mare, quod e&longs;t extra, ide&longs;t extra <lb/>terram habitatam, ad di&longs;tinctionem maris Mediterranei, quod e&longs;t intra <lb/>terram habitatam, ac propterea Mediterraneum dictum e&longs;t.</s></p><p type="main">
  
 <s><arrow.to.target n="marg147"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg147"/></s></p><p type="margin">
  
 <s><margin.target id="marg147"></margin.target>147</s></p><p type="main"> <s><margin.target id="marg147"/>147</s></p><p type="main">
  
 <s>Ibidem <emph type="italics"/>(Ex hoc igitur fluunt &amp; alij fluuij, &amp; Bactrus, &amp; Choa&longs;pes, &amp; Ara&shy;<lb/>xes. </s> <s>Ibidem <emph type="italics"/>(Ex hoc igitur fluunt &amp; alij fluuij, &amp; Bactrus, &amp; Choa&longs;pes, &amp; Ara&shy;<lb/>xes. </s>
  
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 <s><emph type="italics"/>De altitudine montis Cauca&longs;i.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>De altitudine montis Cauca&longs;i.<emph.end type="italics"/></s></p><p type="main">
  
 <s><arrow.to.target n="marg148"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg148"/></s></p><p type="margin">
  
 <s><margin.target id="marg148"></margin.target>148</s></p><p type="main"> <s><margin.target id="marg148"/>148</s></p><p type="main">
  
 <s>Eod. </s> <s>Eod. </s>
  
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 <s>videtur enim his verbis velle dicere, quod quan&shy;<lb/>do habitantibus planitiem, qu&aelig; e&longs;t ad pedem montis Cauca&longs;i, vel horizon&shy;<lb/>tem eiu&longs;dem, incipit Crepu&longs;culum, ij&longs;dem etiam tunc tertia montis pars <lb/>appareat illuminata; in quo &longs;en&longs;u errat po&longs;tea in colligenda montis altitu&shy;<lb/>dine, quamuis enim verum e&longs;&longs;et partem illuminatam eminere totam &longs;upra <lb/>52. milliaria, non tamen &longs;equitur ip&longs;am &longs;olam eminere, &longs;ed alia etiam pars <lb/>eminere pote&longs;t, quod &longs;ic geometric&egrave; demon&longs;trabo. </s> <s>videtur enim his verbis velle dicere, quod quan&shy;<lb/>do habitantibus planitiem, qu&aelig; e&longs;t ad pedem montis Cauca&longs;i, vel horizon&shy;<lb/>tem eiu&longs;dem, incipit Crepu&longs;culum, ij&longs;dem etiam tunc tertia montis pars <lb/>appareat illuminata; in quo &longs;en&longs;u errat po&longs;tea in colligenda montis altitu&shy;<lb/>dine, quamuis enim verum e&longs;&longs;et partem illuminatam eminere totam &longs;upra <lb/>52. milliaria, non tamen &longs;equitur ip&longs;am &longs;olam eminere, &longs;ed alia etiam pars <lb/>eminere pote&longs;t, quod &longs;ic geometric&egrave; demon&longs;trabo. </s>
  
 <s>de&longs;cribatur enim figura <lb/><figure id="fig49"></figure><pb pagenum="101"/>illa, qua ad vaporum altitudines indagandas vtuntur Alhazenus, Vitellio, <lb/>&amp; Clauius, in qua terr&aelig; globus e&longs;t F L G E, regi&ograve; vaporum, &amp; exhalatio&shy;<lb/>num M X N T. horizon a&longs;tronomicus O P. phy&longs;icus Q R, tangens terram <lb/>in puncto F, vbi etiam ponendus e&longs;t huius horizontis habitator, vn&agrave; cum. <lb/></s> <s>de&longs;cribatur enim figura <lb/><figure id="fig49"/><pb pagenum="101"/>illa, qua ad vaporum altitudines indagandas vtuntur Alhazenus, Vitellio, <lb/>&amp; Clauius, in qua terr&aelig; globus e&longs;t F L G E, regi&ograve; vaporum, &amp; exhalatio&shy;<lb/>num M X N T. horizon a&longs;tronomicus O P. phy&longs;icus Q R, tangens terram <lb/>in puncto F, vbi etiam ponendus e&longs;t huius horizontis habitator, vn&agrave; cum. <lb/></s>
  
 <s>Cauca&longs;o F V. </s> <s>Cauca&longs;o F V. </s>
  
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Line 4904 
  
 <s>rectil. </s> <s>rectil. </s>
  
 <s>Clauij;<lb/><arrow.to.target n="table4"></arrow.to.target></s></p><table><table.target id="table4"></table.target><row><cell>vt H F, &longs;inus totus,</cell><cell>ad milliar.</cell><cell>ita tangens F K,</cell><cell>ad milliar.</cell></row><row><cell>100000.</cell><cell>3579.</cell><cell>15659.</cell><cell>560.</cell></row></table><p type="main"> <s>Clauij;<lb/><arrow.to.target n="table4"/></s></p><table><table.target id="table4"/><row><cell>vt H F, &longs;inus totus,</cell><cell>ad milliar.</cell><cell>ita tangens F K,</cell><cell>ad milliar.</cell></row><row><cell>100000.</cell><cell>3579.</cell><cell>15659.</cell><cell>560.</cell></row></table><p type="main">
  
 <s>&amp; inueniemus per auream regulam latus F K, continere milliar. </s> <s>&amp; inueniemus per auream regulam latus F K, continere milliar. </s>
  
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Line 4922 
  
 <s>qui &longs;i detra&shy;<lb/>hatur &agrave; duobus rectis, qui &longs;unt deinceps ad lineam F K, reliquus angulus <lb/>F K V, erit gr. </s> <s>qui &longs;i detra&shy;<lb/>hatur &agrave; duobus rectis, qui &longs;unt deinceps ad lineam F K, reliquus angulus <lb/>F K V, erit gr. </s>
  
 <s>17. 48. &longs;i ergo latus F K, notum ponatur &longs;inus totus 100000. <lb/>latus ver&ograve; F V, tangens anguli noti, erit ip&longs;a 32100. fiat igitur,<lb/><arrow.to.target n="table5"></arrow.to.target></s></p><table><table.target id="table5"></table.target><row><cell>vt F K, &longs;inus totus,</cell><cell>ad milliar.</cell><cell>ita F V, tangens</cell><cell>ad milliar.</cell></row><row><cell>100000.</cell><cell>560.</cell><cell>32100.</cell><cell>180.</cell></row></table><p type="main"> <s>17. 48. &longs;i ergo latus F K, notum ponatur &longs;inus totus 100000. <lb/>latus ver&ograve; F V, tangens anguli noti, erit ip&longs;a 32100. fiat igitur,<lb/><arrow.to.target n="table5"/></s></p><table><table.target id="table5"/><row><cell>vt F K, &longs;inus totus,</cell><cell>ad milliar.</cell><cell>ita F V, tangens</cell><cell>ad milliar.</cell></row><row><cell>100000.</cell><cell>560.</cell><cell>32100.</cell><cell>180.</cell></row></table><p type="main">
  
 <s><expan abbr="inueniemus&qacute;">inueniemusque</expan>; latus F V, continere milliar. </s> <s><expan abbr="inueniemus&qacute;">inueniemusque</expan>; latus F V, continere milliar. </s>
  
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 <s>qu&aelig; tamen adhuc omnem veritatem nimium &longs;uperat. <lb/></s> <s>qu&aelig; tamen adhuc omnem veritatem nimium &longs;uperat. <lb/></s>
  
 <s>Cum ergo hinc inde &longs;equantur ab&longs;urda, putat Mazonium excu&longs;andum e&longs;&longs;e <lb/>Ari&longs;tot. </s> <s>Cum ergo hinc inde &longs;equantur ab&longs;urda, putat Mazonium excu&longs;andum e&longs;&longs;e <lb/>Ari&longs;tot. dicendo eum &longs;equutum e&longs;&longs;e famam, <expan abbr="loquutum&qacute;">loquutumque</expan>; e&longs;&longs;e populariter. <lb/></s>
  
  
 <s>dicendo eum &longs;equutum e&longs;&longs;e famam, <expan abbr="loquutum&qacute;">loquutumque</expan>; e&longs;&longs;e populariter. <lb/></s> 
  
 <s>Verumenimuer&ograve; &longs;apientiores iudicent num rect&egrave; philo&longs;ophus, cuius e&longs;t re&shy;<lb/>condita, <expan abbr="atq;">atque</expan> abdita docere, excu&longs;etur, &longs;i dicatur, eum, popularem famam <lb/>&longs;equutum e&longs;&longs;e.</s></p><p type="main"> <s>Verumenimuer&ograve; &longs;apientiores iudicent num rect&egrave; philo&longs;ophus, cuius e&longs;t re&shy;<lb/>condita, <expan abbr="atq;">atque</expan> abdita docere, excu&longs;etur, &longs;i dicatur, eum, popularem famam <lb/>&longs;equutum e&longs;&longs;e.</s></p><p type="main">
  
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 <s><expan abbr="Atq;">Atque</expan> h&aelig;c de Cauca&longs;o &longs;ufficiant.</s></p><p type="main"> <s><expan abbr="Atq;">Atque</expan> h&aelig;c de Cauca&longs;o &longs;ufficiant.</s></p><p type="main">
  
 <s><arrow.to.target n="marg149"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg149"/></s></p><p type="margin">
  
 <s><margin.target id="marg149"></margin.target>149</s></p><p type="main"> <s><margin.target id="marg149"/>149</s></p><p type="main">
  
 <s>Eodem cap. <emph type="italics"/>(Ex Pyreneo autem, hic autem est mons ad occidentem &aelig;quino&shy;<lb/>ctiaiem in Gallia, flaunt l&longs;ter, &amp; Tarte&longs;&longs;us, iste quidem extra columnas, I&longs;ter au&shy;<lb/>tem per totam Europam in Pontum Euxmum)<emph.end type="italics"/> Ari&longs;t.  <s>Eodem cap. <emph type="italics"/>(Ex Pyreneo autem, hic autem est mons ad occidentem &aelig;quino&shy;<lb/>ctiaiem in Gallia, flaunt l&longs;ter, &amp; Tarte&longs;&longs;us, iste quidem extra columnas, I&longs;ter au&shy;<lb/>tem per totam Europam in Pontum Euxmum)<emph.end type="italics"/> Ari&longs;t.
  
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 tunc enim Geographia <expan abbr="nond&utilde;">nondum</expan> adoleuerat.</s></p><p type="main"> tunc enim Geographia <expan abbr="nond&utilde;">nondum</expan> adoleuerat.</s></p><p type="main">
  
 <s><arrow.to.target n="marg150"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg150"/></s></p><p type="margin">
  
 <s><margin.target id="marg150"></margin.target>150</s></p><p type="main"> <s><margin.target id="marg150"/>150</s></p><p type="main">
  
 <s>Ad fin<gap/>m eiu&longs;dem cap. <emph type="italics"/>(Et circa Ligu&longs;ticam non minor Rhodano ab&longs;orbetur <lb/>qui<gap/>am &longs;l<gap/>us, &amp; iterum egreditur &longs;ecundum alium locum)<emph.end type="italics"/> <expan abbr="incompert&utilde;">incompertum</expan> &amp; hoc <pb pagenum="103"/>Ari&longs;t.  <s>Ad fin<gap/>m eiu&longs;dem cap. <emph type="italics"/>(Et circa Ligu&longs;ticam non minor Rhodano ab&longs;orbetur <lb/>qui<gap/>am &longs;l<gap/>us, &amp; iterum egreditur &longs;ecundum alium locum)<emph.end type="italics"/> <expan abbr="incompert&utilde;">incompertum</expan> &amp; hoc <pb pagenum="103"/>Ari&longs;t.
  
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 <s><emph type="italics"/>De Terr&aelig; rotunditate.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>De Terr&aelig; rotunditate.<emph.end type="italics"/></s></p><p type="main">
  
 <s><arrow.to.target n="marg151"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg151"/></s></p><p type="margin">
  
 <s><margin.target id="marg151"></margin.target>151</s></p><p type="main"> <s><margin.target id="marg151"/>151</s></p><p type="main">
  
 <s>Svmma 4. cap.  <s>Svmma 4. cap.
  
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 <s><emph type="italics"/>Ex Secundo Meteororum.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Ex Secundo Meteororum.<emph.end type="italics"/></s></p><p type="main">
  
 <s><arrow.to.target n="marg152"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg152"/></s></p><p type="margin">
  
 <s><margin.target id="marg152"></margin.target>152</s></p><p type="main"> <s><margin.target id="marg152"/>152</s></p><p type="main">
  
  
 <s>Cap. 1. ait multa e&longs;&longs;e maria, qu&aelig; ad inuicem non communicant. <lb/></s> <s>Cap. 1. ait multa e&longs;&longs;e maria, qu&aelig; ad inuicem non communicant. <lb/></s>
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 pro Rubro mari intelligat Oceanum illum, qui <lb/>Arabiam, ac Per&longs;iam alluit, &longs;iue illius &longs;inum, qui Arabiam, <expan abbr="atq;">atque</expan> Aethiopiam <lb/>interluit, fal&longs;um e&longs;t ip&longs;um parum communicare cum occidentali Oceano, <lb/>vt quotidianis Lu&longs;itanorum nauigationibus ad Indos patet. </s> pro Rubro mari intelligat Oceanum illum, qui <lb/>Arabiam, ac Per&longs;iam alluit, &longs;iue illius &longs;inum, qui Arabiam, <expan abbr="atq;">atque</expan> Aethiopiam <lb/>interluit, fal&longs;um e&longs;t ip&longs;um parum communicare cum occidentali Oceano, <lb/>vt quotidianis Lu&longs;itanorum nauigationibus ad Indos patet. </s>
  
 <s>&longs;ed merit&ograve; hoc <lb/>Ari&longs;tot. </s> <s>&longs;ed merit&ograve; hoc <lb/>Ari&longs;tot. condonandum, cum tunc temporis nondum tota Africa e&longs;&longs;et cert&ograve; <lb/>circumlu&longs;trata, <expan abbr="neq;">neque</expan> iter ab Hi&longs;pania ad Indos maritimum, adeo nunc fre&shy;<lb/>quens, patefactum e&longs;&longs;et.</s>
  
 <s>condonandum, cum tunc temporis nondum tota Africa e&longs;&longs;et cert&ograve; <lb/>circumlu&longs;trata, <expan abbr="neq;">neque</expan> iter ab Hi&longs;pania ad Indos maritimum, adeo nunc fre&shy;<lb/>quens, patefactum e&longs;&longs;et.</s></p><p type="main"> </p><p type="main">
  
 <s><arrow.to.target n="marg153"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg153"/></s></p><p type="margin">
  
 <s><margin.target id="marg153"></margin.target>153</s></p><p type="main"> <s><margin.target id="marg153"/>153</s></p><p type="main">
  
 <s>Summ&aelig; 2. cap.  <s>Summ&aelig; 2. cap.
  
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 <s>A&longs;tra ver&ograve; incrrantia, &amp; <lb/>planet&aelig; Sole tardiores oriuntur <expan abbr="vtroq;">vtroque</expan> modo. </s> <s>A&longs;tra ver&ograve; incrrantia, &amp; <lb/>planet&aelig; Sole tardiores oriuntur <expan abbr="vtroq;">vtroque</expan> modo. </s>
  
 <s>nam c&ugrave;m ip&longs;a Sol, quippe il&shy;<lb/>lis velocior primum a&longs;&longs;equitur, ea &longs;uo lumine obtegit, <expan abbr="e&longs;t&qacute;">e&longs;tque</expan>; hic occa&longs;us eo&shy;<lb/>rum heliacus: cum ver&ograve; cadem pr&aelig;terierit, ac po&longs;t &longs;e reliquerit fit, vt mo&shy;<lb/>tu diurno toto c&oelig;lo conuer&longs;o, mane ante Solem effulgeant, &longs;iue heliac&egrave; <lb/>oriantur: &amp; cum quotidie magis Sol ab illis recedat, ip&longs;aque magis &agrave; Sole <pb pagenum="108"/>elongentur, fit, vt quotidie magis ortum Solis anticipent, &amp; citius mane au&shy;<lb/>te Solem videantur. </s> <s>nam c&ugrave;m ip&longs;a Sol, quippe il&shy;<lb/>lis velocior primum a&longs;&longs;equitur, ea &longs;uo lumine obtegit, <expan abbr="e&longs;t&qacute;">e&longs;tque</expan>; hic occa&longs;us eo&shy;<lb/>rum heliacus: cum ver&ograve; eadem pr&aelig;terierit, ac po&longs;t &longs;e reliquerit fit, vt mo&shy;<lb/>tu diurno toto c&oelig;lo conuer&longs;o, mane ante Solem effulgeant, &longs;iue heliac&egrave; <lb/>oriantur: &amp; cum quotidie magis Sol ab illis recedat, ip&longs;aque magis &agrave; Sole <pb pagenum="108"/>elongentur, fit, vt quotidie magis ortum Solis anticipent, &amp; citius mane au&shy;<lb/>te Solem videantur. </s>
  
 <s><expan abbr="&longs;ic&qacute;">&longs;icque</expan>; tanto in dies citius, vt deinde media etiam nocte <lb/>oriantur; tum ante mediam noctem po&longs;tea paul&ograve; ante occa&longs;um Solis. </s> <s><expan abbr="&longs;ic&qacute;">&longs;icque</expan>; tanto in dies citius, vt deinde media etiam nocte <lb/>oriantur; tum ante mediam noctem po&longs;tea paul&ograve; ante occa&longs;um Solis. </s>
  
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 hoc loco, &amp; alij <lb/>auctores, no&longs;tra hac tempe&longs;tate paul&ograve; ante Solis ingre&longs;&longs;um in Cancrum, &longs;i&shy;<lb/>ue ante &longs;ol&longs;titium &aelig;&longs;tiuum circa 22. Iunij.</s></p><p type="main"> hoc loco, &amp; alij <lb/>auctores, no&longs;tra hac tempe&longs;tate paul&ograve; ante Solis ingre&longs;&longs;um in Cancrum, &longs;i&shy;<lb/>ue ante &longs;ol&longs;titium &aelig;&longs;tiuum circa 22. Iunij.</s></p><p type="main">
  
 <s><arrow.to.target n="marg154"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg154"/></s></p><p type="margin">
  
 <s><margin.target id="marg154"></margin.target>154</s></p><p type="main"> <s><margin.target id="marg154"/>154</s></p><p type="main">
  
 <s>Eodem cap. <emph type="italics"/>(Incertus autem, &amp; mole&longs;tus Orion e&longs;&longs;e videtur &amp; occumbens, &amp; <lb/>oriens, quia in tran&longs;mutatione temporis accidit occa&longs;us, &amp; ortus, a&longs;tate, aut hye&shy;<lb/>me, &amp; propter magnitudinem a&longs;tri dierum &longs;it aliqua pluralitas)<emph.end type="italics"/> hoc loco Vico&shy;<lb/>mercatus ex &longs;ententia a&longs;tronomorum occa&longs;um Orionis fieri autumni tem&shy;<lb/>pore, Sole Scorpionem ob&longs;idente docet, quod &amp; verba Ari&longs;t.  <s>Eodem cap. <emph type="italics"/>(Incertus autem, &amp; mole&longs;tus Orion e&longs;&longs;e videtur &amp; occumbens, &amp; <lb/>oriens, quia in tran&longs;mutatione temporis accidit occa&longs;us, &amp; ortus, a&longs;tate, aut hye&shy;<lb/>me, &amp; propter magnitudinem a&longs;tri dierum &longs;it aliqua pluralitas)<emph.end type="italics"/> hoc loco Vico&shy;<lb/>mercatus ex &longs;ententia a&longs;tronomorum occa&longs;um Orionis fieri autumni tem&shy;<lb/>pore, Sole Scorpionem ob&longs;idente docet, quod &amp; verba Ari&longs;t.
  
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 <s>&amp; <expan abbr="quemadmod&utilde;">quemadmodum</expan> temporis illius initium, <lb/>quo primo de nocte apparere incipiunt, dicitur ab&longs;olut&egrave; ortus cuiu&longs;uis &longs;y&shy;<lb/>deris; &longs;ic etiam initium temporis illius, quo primum per noctem ea occide&shy;<lb/>re videmus, &longs;impliciter occa&longs;um appellamus.</s></p><p type="main"> <s>&amp; <expan abbr="quemadmod&utilde;">quemadmodum</expan> temporis illius initium, <lb/>quo primo de nocte apparere incipiunt, dicitur ab&longs;olut&egrave; ortus cuiu&longs;uis &longs;y&shy;<lb/>deris; &longs;ic etiam initium temporis illius, quo primum per noctem ea occide&shy;<lb/>re videmus, &longs;impliciter occa&longs;um appellamus.</s></p><p type="main">
  
 <s><arrow.to.target n="marg155"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg155"/></s></p><p type="margin">
  
 <s><margin.target id="marg155"></margin.target>155</s></p><p type="main"> <s><margin.target id="marg155"/>155</s></p><p type="main">
  
 <s>Eodem cap. <emph type="italics"/>(Ete&longs;i&aelig; autem flant post ver&longs;iones, &amp; Canis ortum)<emph.end type="italics"/> per ver&longs;io&shy;<lb/>nes intelligit tropicos, quod &amp; tropici etymon confirmat, <expan abbr="c&utilde;">cum</expan> tropicus idem <lb/>valeat, ac conuer&longs;iuus. </s> <s>Eodem cap. <emph type="italics"/>(Ete&longs;i&aelig; autem flant post ver&longs;iones, &amp; Canis ortum)<emph.end type="italics"/> per ver&longs;io&shy;<lb/>nes intelligit tropicos, quod &amp; tropici etymon confirmat, <expan abbr="c&utilde;">cum</expan> tropicus idem <lb/>valeat, ac conuer&longs;iuus. </s>
  
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 <s>Ex Magini tabulis ante ephemerides.</s></p><p type="main"> <s>Ex Magini tabulis ante ephemerides.</s></p><p type="main">
  
 <s><arrow.to.target n="marg156"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg156"/></s></p><p type="margin">
  
 <s><margin.target id="marg156"></margin.target>156</s></p><p type="main"> <s><margin.target id="marg156"/>156</s></p><p type="main">
  
 <s>Eodem cap. <emph type="italics"/>(Duobus enim exi&longs;tentibus &longs;egmentis habitabilis regionis: vno <lb/>quidem ad &longs;uperiorem polum, qui no&longs;ter e&longs;t; altero ad alterum, &amp; ad meridiem: <lb/><expan abbr="ea&qacute;">eaque</expan>, tympani &longs;peciem habeant, talem enim figuram terr&aelig; excidunt ex centro ip&longs;ius <lb/>duct&aelig; line&aelig;, &amp; faciunt duos conos, bunc quidem habentem ba&longs;im tropicum, alte&shy;<lb/>rum autem habentem ba&longs;im circulum &longs;emper manifestum, verticem autem in me&shy;<lb/>dio terr&aelig;. </s> <s>Eodem cap. <emph type="italics"/>(Duobus enim exi&longs;tentibus &longs;egmentis habitabilis regionis: vno <lb/>quidem ad &longs;uperiorem polum, qui no&longs;ter e&longs;t; altero ad alterum, &amp; ad meridiem: <lb/><expan abbr="ea&qacute;">eaque</expan>, tympani &longs;peciem habeant, talem enim figuram terr&aelig; excidunt ex centro ip&longs;ius <lb/>duct&aelig; line&aelig;, &amp; faciunt duos conos, bunc quidem habentem ba&longs;im tropicum, alte&shy;<lb/>rum autem habentem ba&longs;im circulum &longs;emper manifestum, verticem autem in me&shy;<lb/>dio terr&aelig;. </s>
  
 <s>eodem autem modo ad inferiorem polum alij duo coni terr&aelig; &longs;egmenta fa&shy;<lb/>ciunt)<emph.end type="italics"/> vt ben&egrave; duas ha&longs;ce terr&aelig; portiones, quas &longs;olas habitabiles putat Ari&shy;<lb/>&longs;tot. </s> <s>eodem autem modo ad inferiorem polum alij duo coni terr&aelig; &longs;egmenta fa&shy;<lb/>ciunt)<emph.end type="italics"/> vt ben&egrave; duas ha&longs;ce terr&aelig; portiones, quas &longs;olas habitabiles putat Ari&shy;<lb/>&longs;tot. concipias, <expan abbr="reliquaq;">reliquaque</expan> huius loci intelligas, in&longs;pice &longs;equentem figuram. <lb/><figure id="fig50"/><lb/>Maior circulus &longs;it c&oelig;lum, in quo polus L, articus; M, antarticus, ille eleua&shy;<lb/>tus &longs;upra no&longs;trum horizontem S N, 45. gradibus, i&longs;te ver&ograve; totidem infra <lb/>depre&longs;&longs;us. </s>
  
  
 <s>concipias, <expan abbr="reliquaq;">reliquaque</expan> huius loci intelligas, in&longs;pice &longs;equentem figuram. <lb/><figure id="fig50"></figure><lb/>Maior circulus &longs;it c&oelig;lum, in quo polus L, articus; M, antarticus, ille eleua&shy;<lb/>tus &longs;upra no&longs;trum horizontem S N, 45. gradibus, i&longs;te ver&ograve; totidem infra <lb/>depre&longs;&longs;us. </s> 
  
 <s><expan abbr="&longs;int&qacute;">&longs;intque</expan>; diametri circuli &longs;emper apparentium maximi S R, necnon <pb pagenum="110"/>diametri &longs;emper occultorum maximi Y N: tropicorum item T Q, Cancri, <lb/>X O, Capricorni, vt vides in figura. </s> <s><expan abbr="&longs;int&qacute;">&longs;intque</expan>; diametri circuli &longs;emper apparentium maximi S R, necnon <pb pagenum="110"/>diametri &longs;emper occultorum maximi Y N: tropicorum item T Q, Cancri, <lb/>X O, Capricorni, vt vides in figura. </s>
  
 <s>Terra &longs;it A B C H G F E D Z K. &agrave; cu&shy;<lb/>ius centro Z, educantur primo du&aelig; line&aelig; rect&aelig; Z R, Z S. ad circulum &longs;em&shy;<lb/>per apparentium maximum, qu&aelig; in terra tran&longs;eant per puncta B, K. &amp; iun&shy;<lb/>gatur linea B K: iam vides conum S R Z, cuius ba&longs;is e&longs;t circulus &longs;emper ap&shy;<lb/>parens S R, vertex autem Z, in centro terr&aelig;, vt ait Ari&longs;tot. </s> <s>Terra &longs;it A B C H G F E D Z K. &agrave; cu&shy;<lb/>ius centro Z, educantur primo du&aelig; line&aelig; rect&aelig; Z R, Z S. ad circulum &longs;em&shy;<lb/>per apparentium maximum, qu&aelig; in terra tran&longs;eant per puncta B, K. &amp; iun&shy;<lb/>gatur linea B K: iam vides conum S R Z, cuius ba&longs;is e&longs;t circulus &longs;emper ap&shy;<lb/>parens S R, vertex autem Z, in centro terr&aelig;, vt ait Ari&longs;tot. <!-- KEEP S--></s>
  
 <s>educantur nunc <lb/>du&aelig; ali&aelig; rect&aelig; ad tropicum Cancri Z T, Z Q, qu&aelig; in terra faciant puncta <lb/>I, C, <expan abbr="iungatur&qacute;">iungaturque</expan>; recta I C; hic pariter vides conum alterum T Q Z, cuius ba&shy;<lb/>&longs;is e&longs;t circulus Cancri, vertex ver&ograve; centrum terr&aelig; Z. con&longs;idera iam figuram <lb/>B K I C, inter duas rectas B K, I C, &amp; duos circuli terr&aelig; arcus contentam; <lb/>hanc Ari&longs;t.  <s>educantur nunc <lb/>du&aelig; ali&aelig; rect&aelig; ad tropicum Cancri Z T, Z Q, qu&aelig; in terra faciant puncta <lb/>I, C, <expan abbr="iungatur&qacute;">iungaturque</expan>; recta I C; hic pariter vides conum alterum T Q Z, cuius ba&shy;<lb/>&longs;is e&longs;t circulus Cancri, vertex ver&ograve; centrum terr&aelig; Z. con&longs;idera iam figuram <lb/>B K I C, inter duas rectas B K, I C, &amp; duos circuli terr&aelig; arcus contentam; <lb/>hanc Ari&longs;t.
  
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 tympano a&longs;&longs;imilatur.</s></p><p type="main"> tympano a&longs;&longs;imilatur.</s></p><p type="main">
  
 <s><arrow.to.target n="marg157"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg157"/></s></p><p type="margin">
  
 <s><margin.target id="marg157"></margin.target>157</s></p><p type="main"> <s><margin.target id="marg157"/>157</s></p><p type="main">
  
 <s>Eodem cap. <emph type="italics"/>(H&aelig; autem habitari &longs;ol&aelig; po&longs;&longs;ibiles: &amp; <expan abbr="neq;">neque</expan> vltra ver&longs;iones; vm&shy;<lb/>bra enim non <expan abbr="vtiq;">vtique</expan> e&longs;&longs;et ad Vr&longs;am: nunc autem inhabitabilia prius fiunt loca, qu&agrave;m <lb/>&longs;ubdeficiat, aut permutetur vmbra ad meridiem. </s> <s>Eodem cap. <emph type="italics"/>(H&aelig; autem habitari &longs;ol&aelig; po&longs;&longs;ibiles: &amp; <expan abbr="neq;">neque</expan> vltra ver&longs;iones; vm&shy;<lb/>bra enim non <expan abbr="vtiq;">vtique</expan> e&longs;&longs;et ad Vr&longs;am: nunc autem inhabitabilia prius fiunt loca, qu&agrave;m <lb/>&longs;ubdeficiat, aut permutetur vmbra ad meridiem. </s>
  
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 <s>Verumtamen, qu&aelig; &longs;ub <expan abbr="vtroq;">vtroque</expan> polo partes &longs;unt adhuc incognit&aelig; manent.</s></p><p type="main"> <s>Verumtamen, qu&aelig; &longs;ub <expan abbr="vtroq;">vtroque</expan> polo partes &longs;unt adhuc incognit&aelig; manent.</s></p><p type="main">
  
 <s><arrow.to.target n="marg158"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg158"/></s></p><p type="margin">
  
 <s><margin.target id="marg158"></margin.target>158</s></p><p type="main"> <s><margin.target id="marg158"/>158</s></p><p type="main">
  
 <s>Eodem cap: <emph type="italics"/>(Fertur autem, &amp; corona &longs;ecundam hunc locum, videtur enim &longs;u&shy;<lb/>per caput e&longs;&longs;e nohis, cum fuerit &longs;ecundum meridianum)<emph.end type="italics"/> con&longs;tellatio videlicet, <lb/>qu&aelig; corona Ariadn&aelig; dicitur, h&aelig;c cum in c&oelig;lo manife&longs;t&egrave; &longs;it Borealis, <expan abbr="no-&longs;tro&qacute;">no&shy;<lb/>&longs;troque</expan>; vertici noctu, quando meridianum pertran&longs;it, incumbat: clar&egrave; indi&shy;<lb/>cat nos <expan abbr="quoq;">quoque</expan> e&longs;&longs;e Boreales.</s></p><p type="main"> <s>Eodem cap: <emph type="italics"/>(Fertur autem, &amp; corona &longs;ecundam hunc locum, videtur enim &longs;u&shy;<lb/>per caput e&longs;&longs;e nohis, cum fuerit &longs;ecundum meridianum)<emph.end type="italics"/> con&longs;tellatio videlicet, <lb/>qu&aelig; corona Ariadn&aelig; dicitur, h&aelig;c cum in c&oelig;lo manife&longs;t&egrave; &longs;it Borealis, <expan abbr="no-&longs;tro&qacute;">no&shy;<lb/>&longs;troque</expan>; vertici noctu, quando meridianum pertran&longs;it, incumbat: clar&egrave; indi&shy;<lb/>cat nos <expan abbr="quoq;">quoque</expan> e&longs;&longs;e Boreales.</s></p><p type="main">
  
 <s><arrow.to.target n="marg159"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg159"/></s></p><p type="margin">
  
 <s><margin.target id="marg159"></margin.target>159</s></p><p type="main"> <s><margin.target id="marg159"/>159</s></p><p type="main">
  
 <s>Eodem cap. <emph type="italics"/>(Et quidem ad latitudinem <expan abbr="v&longs;q;">v&longs;que</expan> ad inhabitabilia &longs;cimus hahita-<emph.end type="italics"/><pb pagenum="111"/><emph type="italics"/>tam, hic enim propter frigus non amplius habitant, illic autem propter &aelig;&longs;tum)<emph.end type="italics"/><lb/>illic autem, ide&longs;t &longs;ub Zona torrida, compertum autem e&longs;t nunc totam fer&egrave; <lb/>torridam Zonam, &amp; quidem alicubi percommod&egrave; habitari, cuius cau&longs;&aelig; &longs;unt <lb/>quatuor, qu&aelig; ip&longs;um latuerunt. </s> <s>Eodem cap. <emph type="italics"/>(Et quidem ad latitudinem <expan abbr="v&longs;q;">v&longs;que</expan> ad inhabitabilia &longs;cimus hahita-<emph.end type="italics"/><pb pagenum="111"/><emph type="italics"/>tam, hic enim propter frigus non amplius habitant, illic autem propter &aelig;&longs;tum)<emph.end type="italics"/><lb/>illic autem, ide&longs;t &longs;ub Zona torrida, compertum autem e&longs;t nunc totam fer&egrave; <lb/>torridam Zonam, &amp; quidem alicubi percommod&egrave; habitari, cuius cau&longs;&aelig; &longs;unt <lb/>quatuor, qu&aelig; ip&longs;um latuerunt. </s>
  
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 <s>qu&aelig; quatuor torridam hanc pa&longs;&longs;im refrigerant, <lb/>atque habitabilem reddunt.</s></p><p type="main"> <s>qu&aelig; quatuor torridam hanc pa&longs;&longs;im refrigerant, <lb/>atque habitabilem reddunt.</s></p><p type="main">
  
 <s><arrow.to.target n="marg160"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg160"/></s></p><p type="margin">
  
 <s><margin.target id="marg160"></margin.target>160.a</s></p><p type="main"> <s><margin.target id="marg160"/>160.a</s></p><p type="main">
  
 <s>Summ&aelig; 2. cap.  <s>Summ&aelig; 2. cap.
  
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 figuras, im&ograve; demon&longs;tratio&shy;<lb/>nes ip&longs;as Mathematicorum, de&longs;criptiones appellare, vt &longs;&aelig;pius in Logicis <lb/>monuimus.</s></p><p type="main"> figuras, im&ograve; demon&longs;tratio&shy;<lb/>nes ip&longs;as Mathematicorum, de&longs;criptiones appellare, vt &longs;&aelig;pius in Logicis <lb/>monuimus.</s></p><p type="main">
  
 <s><emph type="italics"/>De&longs;criptus &longs;it igitur, vt clarior res euadat horizontis circulus quapropter, &amp; <lb/>rotundus)<emph.end type="italics"/> vt in &longs;equenti figura circulus A G B H, de&longs;criptus horizontem <lb/>referret,</s></p><figure></figure><pb pagenum="112"/><p type="main"> <s><emph type="italics"/>De&longs;criptus &longs;it igitur, vt clarior res euadat horizontis circulus quapropter, &amp; <lb/>rotundus)<emph.end type="italics"/> vt in &longs;equenti figura circulus A G B H, de&longs;criptus horizontem <lb/>referret,</s></p><figure/><pb pagenum="112"/><p type="main">
  
 <s><emph type="italics"/>Oportet autem ip&longs;ius alteram portionem intelligere, qu&aelig; nobis habitatur; qu&aelig; <lb/>eodem modo diuidi poterit)<emph.end type="italics"/> ide&longs;t oportet intelligere ip&longs;ius horizontis, vel ter&shy;<lb/>r&aelig; habitat&aelig; partem, qu&aelig; quamuis rotunda non &longs;it, poterit tamen, ac &longs;i ro&shy;<lb/>tunda e&longs;&longs;et in figura circulari repre&longs;entari, <expan abbr="atq;">atque</expan> in plures partes eo modo, <lb/>quo circulus &longs;ecatur, &longs;ecari.</s></p><p type="main"> <s><emph type="italics"/>Oportet autem ip&longs;ius alteram portionem intelligere, qu&aelig; nobis habitatur; qu&aelig; <lb/>eodem modo diuidi poterit)<emph.end type="italics"/> ide&longs;t oportet intelligere ip&longs;ius horizontis, vel ter&shy;<lb/>r&aelig; habitat&aelig; partem, qu&aelig; quamuis rotunda non &longs;it, poterit tamen, ac &longs;i ro&shy;<lb/>tunda e&longs;&longs;et in figura circulari repre&longs;entari, <expan abbr="atq;">atque</expan> in plures partes eo modo, <lb/>quo circulus &longs;ecatur, &longs;ecari.</s></p><p type="main">
  
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 <s><emph type="italics"/>Ex Tertio Meteororum.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Ex Tertio Meteororum.<emph.end type="italics"/></s></p><p type="main">
  
 <s><arrow.to.target n="marg161"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg161"/></s></p><p type="margin">
  
 <s><margin.target id="marg161"></margin.target>160.b</s></p><p type="main"> <s><margin.target id="marg161"/>160.b</s></p><p type="main">
  
 <s>Antequam textuum explicationem aggrediar, illud animaduerten <lb/>dum e&longs;t, <expan abbr="vbicunq;">vbicunque</expan> interpretatio antiqua vtitur verbis, refractio, <lb/>&amp; refrangere; ibi Vicomercatum in &longs;ua interpretatione merit&ograve;, <lb/>&amp; propri&egrave; v&longs;um e&longs;&longs;e verbis; reflexio, &amp; reflecti: differunt enim <lb/>vald&egrave; apud Opticos refractio, &amp; reflexio, vt etiam refrangere, &amp; reflectere. <lb/></s> <s>Antequam textuum explicationem aggrediar, illud animaduerten <lb/>dum e&longs;t, <expan abbr="vbicunq;">vbicunque</expan> interpretatio antiqua vtitur verbis, refractio, <lb/>&amp; refrangere; ibi Vicomercatum in &longs;ua interpretatione merit&ograve;, <lb/>&amp; propri&egrave; v&longs;um e&longs;&longs;e verbis; reflexio, &amp; reflecti: differunt enim <lb/>vald&egrave; apud Opticos refractio, &amp; reflexio, vt etiam refrangere, &amp; reflectere. <lb/></s>
  
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 <s>Vicomerca&shy;<lb/>tus igitur quamuis vtatur voce reflexionis in Halone, non tamen ex pr&aelig;di&shy;<lb/>ctis videtur reprchenden dus.</s></p><p type="main"> <s>Vicomerca&shy;<lb/>tus igitur quamuis vtatur voce reflexionis in Halone, non tamen ex pr&aelig;di&shy;<lb/>ctis videtur reprchenden dus.</s></p><p type="main">
  
 <s><arrow.to.target n="marg162"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg162"/></s></p><p type="margin">
  
 <s><margin.target id="marg162"></margin.target>161</s></p><p type="main"> <s><margin.target id="marg162"/>161</s></p><p type="main">
  
 <s>Summ&aelig; 2. cap.  <s>Summ&aelig; 2. cap.
  
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 <s>ab co&shy;<lb/>dem enim &longs;igno ad idem &longs;ignum &aelig;quales frangentur &longs;uper circuli lineam &longs;emper. </s> <s>ab co&shy;<lb/>dem enim &longs;igno ad idem &longs;ignum &aelig;quales frangentur &longs;uper circuli lineam &longs;emper. </s>
  
 <s>&longs;it<emph.end type="italics"/><lb/><figure id="fig51"></figure><lb/><emph type="italics"/>enim &agrave; puncto, in quo A, ad B, fracta, &amp; ea, qu&aelig; est <lb/>A C B, &amp; qu&aelig; A F B, &amp; qu&aelig; A D B, &aelig;quales autem <lb/>&amp; h&aelig; A C, A F, A D, inuiccm. </s> <s>&longs;it<emph.end type="italics"/><lb/><figure id="fig51"/><lb/><emph type="italics"/>enim &agrave; puncto, in quo A, ad B, fracta, &amp; ea, qu&aelig; est <lb/>A C B, &amp; qu&aelig; A F B, &amp; qu&aelig; A D B, &aelig;quales autem <lb/>&amp; h&aelig; A C, A F, A D, inuiccm. </s>
  
 <s>&amp; qu&aelig; ad B, inui&shy;<lb/>cem &longs;cilicet C B, E B, D B. &amp; protrahatur A E B, <lb/>quare trianguli &aelig;quales, etenim &longs;uper &aelig;qualem, qu&aelig; <lb/>e&longs;t A E B, ducantur autem <expan abbr="perp&etilde;diculares">perpendiculares</expan> ad A E B, <lb/>ex angulis; &agrave; C, quidem, qu&aelig; e&longs;t C E; ab F, autem, <lb/>qu&aelig; e&longs;t F E; &agrave; D, autem, qu&aelig; e&longs;t D E, &aelig;quales itaque <lb/>h&aelig;, in &aelig;qualibus enim tri&abreve;gulis, &amp; in vno plano om&shy;<lb/>nes, ad rectum emm omnes ei, qu&aelig; e&longs;t A E B. &amp; ad <lb/>vnum punctum E, copulantur, circulus igitur erit <lb/>de&longs;cripta, centrum autem E. &longs;it autem B, quidem Sol, <lb/>A, autem vi&longs;us, qu&aelig; autem e&longs;t circa C D F, circun&shy;<lb/>ferentia nubes, &agrave; qua refrangitur vi&longs;us ad Solem)<emph.end type="italics"/><lb/>quia &longs;uppono Aream, &longs;iue Halonem fieri per re&shy;<lb/>fractionem, vt vult etiam Vitellio, propterea <lb/><expan abbr="pr&aelig;mitt&etilde;dum">pr&aelig;mittendum</expan> e&longs;t principium quoddam, quo tra&shy;<lb/>ctatio de refractione innititur; e&longs;t autem huiu&longs;&shy;<lb/>modi; ea, qu&aelig; <expan abbr="vid&etilde;tur">videntur</expan> per refractionem, &longs;iue &longs;ub <lb/>aliquo refractionis angulo, manentibus nobis &amp; <lb/>a&longs;tro, &amp; medio ij&longs;dem in locis, non po&longs;&longs;unt vide&shy;<lb/>ri &longs;ub diuer&longs;o angulo &agrave; priori, ncc per con&longs;<gap/><expan abbr="qu&etilde;s">quens</expan> <lb/>alibi apparere. </s> <s>&amp; qu&aelig; ad B, inui&shy;<lb/>cem &longs;cilicet C B, E B, D B. &amp; protrahatur A E B, <lb/>quare trianguli &aelig;quales, etenim &longs;uper &aelig;qualem, qu&aelig; <lb/>e&longs;t A E B, ducantur autem <expan abbr="perp&etilde;diculares">perpendiculares</expan> ad A E B, <lb/>ex angulis; &agrave; C, quidem, qu&aelig; e&longs;t C E; ab F, autem, <lb/>qu&aelig; e&longs;t F E; &agrave; D, autem, qu&aelig; e&longs;t D E, &aelig;quales itaque <lb/>h&aelig;, in &aelig;qualibus enim tri&abreve;gulis, &amp; in vno plano om&shy;<lb/>nes, ad rectum emm omnes ei, qu&aelig; e&longs;t A E B. &amp; ad <lb/>vnum punctum E, copulantur, circulus igitur erit <lb/>de&longs;cripta, centrum autem E. &longs;it autem B, quidem Sol, <lb/>A, autem vi&longs;us, qu&aelig; autem e&longs;t circa C D F, circun&shy;<lb/>ferentia nubes, &agrave; qua refrangitur vi&longs;us ad Solem)<emph.end type="italics"/><lb/>quia &longs;uppono Aream, &longs;iue Halonem fieri per re&shy;<lb/>fractionem, vt vult etiam Vitellio, propterea <lb/><expan abbr="pr&aelig;mitt&etilde;dum">pr&aelig;mittendum</expan> e&longs;t principium quoddam, quo tra&shy;<lb/>ctatio de refractione innititur; e&longs;t autem huiu&longs;&shy;<lb/>modi; ea, qu&aelig; <expan abbr="vid&etilde;tur">videntur</expan> per refractionem, &longs;iue &longs;ub <lb/>aliquo refractionis angulo, manentibus nobis &amp; <lb/>a&longs;tro, &amp; medio ij&longs;dem in locis, non po&longs;&longs;unt vide&shy;<lb/>ri &longs;ub diuer&longs;o angulo &agrave; priori, ncc per con&longs;<gap/><expan abbr="qu&etilde;s">quens</expan> <lb/>alibi apparere. </s>
  
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 <s>Nunc ad textus declarationem, in <lb/>quo continetur Geometrica demon&longs;tratio rotunditatis Are&aelig;, quam &longs;ic bre&shy;<lb/>uiter prius veteres excogitarunt: Viderunt prim&ograve; Solem in Area apparere <lb/>in orbem, &amp; con&longs;imiliter: hinc intulerunt nece&longs;&longs;e e&longs;&longs;e apparere etiam per <lb/>con&longs;imiles, &longs;iue &aelig;quales refractionis angulos; quia diuer&longs;i anguli, diuer&longs;am <lb/>etiam <expan abbr="appar&etilde;tiam">apparentiam</expan> efficiunt: atqui con&longs;imiles, &longs;iue &aelig;quales refractionis an&shy;<lb/>gulos nece&longs;&longs;e e&longs;t in circulum <expan abbr="c&otilde;&longs;titui">con&longs;titui</expan>, vt mox con&longs;tabit; cau&longs;a igitur rotun&shy;<lb/>ditatis huius, e&longs;t angulorum refractionis &aelig;qualitas. </s> <s>Nunc ad textus declarationem, in <lb/>quo continetur Geometrica demon&longs;tratio rotunditatis Are&aelig;, quam &longs;ic bre&shy;<lb/>uiter prius veteres excogitarunt: Viderunt prim&ograve; Solem in Area apparere <lb/>in orbem, &amp; con&longs;imiliter: hinc intulerunt nece&longs;&longs;e e&longs;&longs;e apparere etiam per <lb/>con&longs;imiles, &longs;iue &aelig;quales refractionis angulos; quia diuer&longs;i anguli, diuer&longs;am <lb/>etiam <expan abbr="appar&etilde;tiam">apparentiam</expan> efficiunt: atqui con&longs;imiles, &longs;iue &aelig;quales refractionis an&shy;<lb/>gulos nece&longs;&longs;e e&longs;t in circulum <expan abbr="c&otilde;&longs;titui">con&longs;titui</expan>, vt mox con&longs;tabit; cau&longs;a igitur rotun&shy;<lb/>ditatis huius, e&longs;t angulorum refractionis &aelig;qualitas. </s>
  
 <s>Sed iam textum Ari&longs;t. <lb/></s> <s>Sed iam textum Ari&longs;t. <lb/>qui geometricam huius rci continet demon&longs;trationem, explicemus. </s>
  
 <s>qui geometricam huius rci continet demon&longs;trationem, explicemus. </s> 
  
 <s>Suppo&shy;<lb/>nit igitur prim&ograve; Ari&longs;t.  <s>Suppo&shy;<lb/>nit igitur prim&ograve; Ari&longs;t.
  
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 4. De Iridis figura.<emph.end type="italics"/></s></p><p type="main"> 4. De Iridis figura.<emph.end type="italics"/></s></p><p type="main">
  
 <s><arrow.to.target n="marg163"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg163"/></s></p><p type="margin">
  
 <s><margin.target id="marg163"></margin.target>162</s></p><p type="main"> <s><margin.target id="marg163"/>162</s></p><p type="main">
  
 <s><emph type="italics"/>Qvod autem <expan abbr="neq;">neque</expan> circulum po&longs;&longs;ibile &longs;it fieri Iridis, <expan abbr="neq;">neque</expan> maiorem &longs;emicir&shy;<lb/>culo portionem, &amp; de alijs accidentibus circa ip&longs;am, ex de&longs;criptione <lb/>erit con&longs;iderantibus manife&longs;tum)<emph.end type="italics"/> In Logicis &longs;&aelig;pius monui Ari&longs;t.  <s><emph type="italics"/>Qvod autem <expan abbr="neq;">neque</expan> circulum po&longs;&longs;ibile &longs;it fieri Iridis, <expan abbr="neq;">neque</expan> maiorem &longs;emicir&shy;<lb/>culo portionem, &amp; de alijs accidentibus circa ip&longs;am, ex de&longs;criptione <lb/>erit con&longs;iderantibus manife&longs;tum)<emph.end type="italics"/> In Logicis &longs;&aelig;pius monui Ari&longs;t.
  
 per <lb/>de&longs;criptiones intelligere geometricas demon&longs;trationes, quod <lb/>etiam hoc loco confirmatur, vbi Geometrica demon&longs;tratione quam de&longs;cri&shy;<lb/>ptionem appellat, Iridis figur&aelig; accidentia o&longs;tendit; nimirum cur &longs;it quidem <lb/>circularis, nunquam tamen circulus integer, im&ograve; <expan abbr="neq;">neque</expan> &longs;emicirculo vnquam <lb/>maior, &longs;ed tamen &longs;emicirculo minor.</s></p><p type="main"> per <lb/>de&longs;criptiones intelligere geometricas demon&longs;trationes, quod <lb/>etiam hoc loco confirmatur, vbi Geometrica demon&longs;tratione quam de&longs;cri&shy;<lb/>ptionem appellat, Iridis figur&aelig; accidentia o&longs;tendit; nimirum cur &longs;it quidem <lb/>circularis, nunquam tamen circulus integer, im&ograve; <expan abbr="neq;">neque</expan> &longs;emicirculo vnquam <lb/>maior, &longs;ed tamen &longs;emicirculo minor.</s></p><p type="main">
  
 <s><arrow.to.target n="marg164"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg164"/></s></p><p type="margin">
  
 <s><margin.target id="marg164"></margin.target>163</s></p><p type="main"> <s><margin.target id="marg164"/>163</s></p><p type="main">
  
 <s>Ibidem <emph type="italics"/>(Hemi&longs;pberio enim exi&longs;t exte &longs;uper horizontis circulum in quo A. cen&shy;<lb/>tro autem K, alio autem quodam oriente puncto, in quo G, &longs;i line&aelig;, qu&aelig; &agrave; K, &longs;ecun&shy;<lb/>dum conum excidentes faciant velut axem lineam in qua G K, &amp; &agrave; K. ad M, co&shy;<lb/>pulat&aelig; refrangantur ab hemi&longs;ph&aelig;rio ad G, &longs;uper maiorem angulum, circuli circun&shy;<lb/>ferentiam incident line&aelig;, qu&aelig; &agrave; K, &amp; &longs;i quidem in ortu, aut in occa&longs;u a&longs;tri reflexio <lb/>fiat, &longs;emicirculus ab <expan abbr="horiz&otilde;te">horizonte</expan> a&longs;&longs;umetur &longs;uper terram factus. </s> <s>Ibidem <emph type="italics"/>(Hemi&longs;pberio enim exi&longs;t exte &longs;uper horizontis circulum in quo A. cen&shy;<lb/>tro autem K, alio autem quodam oriente puncto, in quo G, &longs;i line&aelig;, qu&aelig; &agrave; K, &longs;ecun&shy;<lb/>dum conum excidentes faciant velut axem lineam in qua G K, &amp; &agrave; K. ad M, co&shy;<lb/>pulat&aelig; refrangantur ab hemi&longs;ph&aelig;rio ad G, &longs;uper maiorem angulum, circuli circun&shy;<lb/>ferentiam incident line&aelig;, qu&aelig; &agrave; K, &amp; &longs;i quidem in ortu, aut in occa&longs;u a&longs;tri reflexio <lb/>fiat, &longs;emicirculus ab <expan abbr="horiz&otilde;te">horizonte</expan> a&longs;&longs;umetur &longs;uper terram factus. </s>
  
 <s>&longs;i autem &longs;upra, minor<emph.end type="italics"/><pb pagenum="116"/><figure id="fig52"></figure><lb/><emph type="italics"/>&longs;emper &longs;emicirculo, minus autem, <lb/>cum in meridie fuerit a&longs;trum)<emph.end type="italics"/> quod <lb/>&longs;upra monui, iterum moneo, <expan abbr="re-tin&etilde;dam">re&shy;<lb/>tinendam</expan> vocem reflexionis, <expan abbr="qu&atilde;-uis">quan&shy;<lb/>uis</expan> in antiqua tran&longs;latione lega&shy;<lb/>tur refractio, e&longs;t enim apud om&shy;<lb/>nes in confe&longs;&longs;o Iridem fieri per <lb/>reflexionem. </s> <s>&longs;i autem &longs;upra, minor<emph.end type="italics"/><pb pagenum="116"/><figure id="fig52"/><lb/><emph type="italics"/>&longs;emper &longs;emicirculo, minus autem, <lb/>cum in meridie fuerit a&longs;trum)<emph.end type="italics"/> quod <lb/>&longs;upra monui, iterum moneo, <expan abbr="re-tin&etilde;dam">re&shy;<lb/>tinendam</expan> vocem reflexionis, <expan abbr="qu&atilde;-uis">quan&shy;<lb/>uis</expan> in antiqua tran&longs;latione lega&shy;<lb/>tur refractio, e&longs;t enim apud om&shy;<lb/>nes in confe&longs;&longs;o Iridem fieri per <lb/>reflexionem. </s>
  
 <s>E&longs;t igitur in &longs;upe&shy;<lb/>riori figura, quam textui, vt par <lb/>erat re&longs;titui, horizon G K O. cuius centrum K. in quo e&longs;t vi&longs;us no&longs;ter, <expan abbr="&longs;it&qacute;">&longs;itque</expan>; <lb/>hemi&longs;ph&aelig;rium no&longs;trum in arcu G A M O, repr&aelig;&longs;entatum, <expan abbr="&longs;it&qacute;">&longs;itque</expan>; nubes rori&shy;<lb/>da, in qua Iris appareat, vbi M, quod punctum M, nubem referens, in figu&shy;<lb/>ra ponitur in hemi&longs;ph&aelig;rij ambitu, quod c&oelig;lum repr&aelig;&longs;entat, cum tamen <lb/>nubes parum &agrave; terra &longs;ubuchatur; id enim ad demon&longs;trationem fer&egrave; perinde <lb/>e&longs;t. </s> <s>E&longs;t igitur in &longs;upe&shy;<lb/>riori figura, quam textui, vt par <lb/>erat re&longs;titui, horizon G K O. cuius centrum K. in quo e&longs;t vi&longs;us no&longs;ter, <expan abbr="&longs;it&qacute;">&longs;itque</expan>; <lb/>hemi&longs;ph&aelig;rium no&longs;trum in arcu G A M O, repr&aelig;&longs;entatum, <expan abbr="&longs;it&qacute;">&longs;itque</expan>; nubes rori&shy;<lb/>da, in qua Iris appareat, vbi M, quod punctum M, nubem referens, in figu&shy;<lb/>ra ponitur in hemi&longs;ph&aelig;rij ambitu, quod c&oelig;lum repr&aelig;&longs;entat, cum tamen <lb/>nubes parum &agrave; terra &longs;ubuchatur; id enim ad demon&longs;trationem fer&egrave; perinde <lb/>e&longs;t. </s>
  
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 <s>h&ecedil;c tria &longs;unt, qu&aelig; deinceps <expan abbr="prob&atilde;da">probanda</expan> recipit.</s></p><p type="main"> <s>h&ecedil;c tria &longs;unt, qu&aelig; deinceps <expan abbr="prob&atilde;da">probanda</expan> recipit.</s></p><p type="main">
  
 <s><arrow.to.target n="marg165"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg165"/></s></p><p type="margin">
  
 <s><margin.target id="marg165"></margin.target>264</s></p><figure></figure><p type="main"> <s><margin.target id="marg165"/>264</s></p><figure/><p type="main">
  
 <s>Ibidem <emph type="italics"/>(Sit enim in <expan abbr="ori&etilde;te">oriente</expan> pri&shy;<lb/>mum vbi G, &amp; refracta &longs;it K M, <lb/>ad G, &amp; planum erectum &longs;it in quo <lb/>A, &agrave; triangulo in quo G K M, cir&shy;<lb/>culus igitur erit &longs;ectio &longs;ph&aelig;<gap/>&aelig;, qui <lb/>maximus &longs;it in quo A, differet enim <lb/>mbil &longs;i quod<gap/><expan abbr="&ubreve;q;">&ubreve;que</expan> eorum, qu&aelig; &longs;uper <lb/>G K, &longs;ecundum triangul&ubreve; K M G, <lb/>erectum fuerit planum. </s> <s>Ibidem <emph type="italics"/>(Sit enim in <expan abbr="ori&etilde;te">oriente</expan> pri&shy;<lb/>mum vbi G, &amp; refracta &longs;it K M, <lb/>ad G, &amp; planum erectum &longs;it in quo <lb/>A, &agrave; triangulo in quo G K M, cir&shy;<lb/>culus igitur erit &longs;ectio &longs;ph&aelig;<gap/>&aelig;, qui <lb/>maximus &longs;it in quo A, differet enim <lb/>mbil &longs;i quod<gap/><expan abbr="&ubreve;q;">&ubreve;que</expan> eorum, qu&aelig; &longs;uper <lb/>G K, &longs;ecundum triangul&ubreve; K M G, <lb/>erectum fuerit planum. </s>
  
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 <s>in &longs;uperiori figura, quam <lb/>textui re&longs;tituimus exi&longs;tente Sole in G, oculo in K, &amp; nube in M. ex qua ra&shy;<lb/>dius Solis G M, re&longs;lectatur ad vi&longs;um in K, per <expan abbr="line&atilde;">lineam</expan> M K, &longs;ub angulo G M K, <lb/>impo&longs;&longs;ibile e&longs;t manentibus illis, vt dixi, videri Solem in nube M, &longs;ub diuer&shy;<lb/>&longs;o angulo &agrave; priori, nec alibi apparere. </s> <s>in &longs;uperiori figura, quam <lb/>textui re&longs;tituimus exi&longs;tente Sole in G, oculo in K, &amp; nube in M. ex qua ra&shy;<lb/>dius Solis G M, re&longs;lectatur ad vi&longs;um in K, per <expan abbr="line&atilde;">lineam</expan> M K, &longs;ub angulo G M K, <lb/>impo&longs;&longs;ibile e&longs;t manentibus illis, vt dixi, videri Solem in nube M, &longs;ub diuer&shy;<lb/>&longs;o angulo &agrave; priori, nec alibi apparere. </s>
  
 <s>Alterum e&longs;t apud Opticos vulga&shy;<lb/>tum; ea &longs;cilicet, qu&aelig; per reflexionem (de quorum numero e&longs;t Iris) viden&shy;<lb/>tur, videri, tunc &longs;olum, quando angulus incidenti&aelig; fuerit &aelig;qualis angulo <lb/>reflexionis, quia tunc breui&longs;&longs;imis lineis fit vi&longs;io; quibus &longs;oli, natura (&longs;i fieri <lb/><figure id="fig53"></figure><lb/>pote&longs;t) vtitur. </s> <s>Alterum e&longs;t apud Opticos vulga&shy;<lb/>tum; ea &longs;cilicet, qu&aelig; per reflexionem (de quorum numero e&longs;t Iris) viden&shy;<lb/>tur, videri, tunc &longs;olum, quando angulus incidenti&aelig; fuerit &aelig;qualis angulo <lb/>reflexionis, quia tunc breui&longs;&longs;imis lineis fit vi&longs;io; quibus &longs;oli, natura (&longs;i fieri <lb/><figure id="fig53"/><lb/>pote&longs;t) vtitur. </s>
  
 <s>v. </s> <s>v. </s>
  
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 <s>Iam &longs;i <expan abbr="tri&atilde;gulum">triangulum</expan> G M K, prioris figur&aelig; circumuoluatur circa axem G K O, <lb/>punctum ip&longs;ius M, de&longs;cribit pr&aelig;dictum ambitum L M N. hunc ambitum <lb/>inquit Ariltot. </s> <s>Iam &longs;i <expan abbr="tri&atilde;gulum">triangulum</expan> G M K, prioris figur&aelig; circumuoluatur circa axem G K O, <lb/>punctum ip&longs;ius M, de&longs;cribit pr&aelig;dictum ambitum L M N. hunc ambitum <lb/>inquit Ariltot. </s>
  
 <s>linea K M, attinger, <expan abbr="erit&qacute;">eritque</expan>; hic ambitus datus, vt dictum e&longs;t. <lb/><figure id="fig54"></figure><lb/>Erit pr&aelig;terea &longs;ectio circunferentiarum ho&shy;<lb/>rizontis, &amp; huius amb tus data, cuius extre&shy;<lb/>ma puncta e&longs;&longs;ent L, &amp; N. &longs;i enim <expan abbr="c&otilde;cipiamus">concipiamus</expan> <lb/>in figura non &longs;olum horizontis <gap/>iametrum <lb/>G K O, &longs;ed etiam circunferentiam (in qua <lb/>circunferentia e&longs;&longs;ent duo illa puncta L, &amp; N, <lb/>vt in pr&aelig;&longs;enti de&longs;criptione melius intelli ge&shy;<lb/>tur, in qua horizon G N O L, &amp; ambitus <lb/>pr&aelig;dictus e&longs;t L M N, qui debet intelligi ele&shy;<lb/>uatus &longs;upra horizontem perpendiculariter) <lb/>tunc &longs;ectio ip&longs;ius mutua cum horizonte e&longs;&longs;et <pb pagenum="119"/>linea N P L, cuius extrema puncta &longs;unt L, N, qu&aelig; data erunt, cum &longs;int ex&shy;<lb/>trema line&aelig; K M, circumlat&aelig;; &amp; quemadmodum dabatur &longs;uperius punctum <lb/>M. eadem ratione ex Datis, dabitur punctum N, &amp; L. quare etiam &longs;ectio <lb/>N P L, qu&aelig; inter data puncta continetur, data erit ex 26. Datorum.</s></p><p type="main"> <s>linea K M, attinger, <expan abbr="erit&qacute;">eritque</expan>; hic ambitus datus, vt dictum e&longs;t. <lb/><figure id="fig54"/><lb/>Erit pr&aelig;terea &longs;ectio circunferentiarum ho&shy;<lb/>rizontis, &amp; huius amb tus data, cuius extre&shy;<lb/>ma puncta e&longs;&longs;ent L, &amp; N. &longs;i enim <expan abbr="c&otilde;cipiamus">concipiamus</expan> <lb/>in figura non &longs;olum horizontis <gap/>iametrum <lb/>G K O, &longs;ed etiam circunferentiam (in qua <lb/>circunferentia e&longs;&longs;ent duo illa puncta L, &amp; N, <lb/>vt in pr&aelig;&longs;enti de&longs;criptione melius intelli ge&shy;<lb/>tur, in qua horizon G N O L, &amp; ambitus <lb/>pr&aelig;dictus e&longs;t L M N, qui debet intelligi ele&shy;<lb/>uatus &longs;upra horizontem perpendiculariter) <lb/>tunc &longs;ectio ip&longs;ius mutua cum horizonte e&longs;&longs;et <pb pagenum="119"/>linea N P L, cuius extrema puncta &longs;unt L, N, qu&aelig; data erunt, cum &longs;int ex&shy;<lb/>trema line&aelig; K M, circumlat&aelig;; &amp; quemadmodum dabatur &longs;uperius punctum <lb/>M. eadem ratione ex Datis, dabitur punctum N, &amp; L. quare etiam &longs;ectio <lb/>N P L, qu&aelig; inter data puncta continetur, data erit ex 26. Datorum.</s></p><p type="main">
  
 <s>Illud nunc in memoriam <expan abbr="reuoc&atilde;dum">reuocandum</expan>, quod paul&ograve; ante probaui, nimirum <lb/>proportionem linearum G M, K M, non po&longs;&longs;e &longs;eruari in alijs lineis, qu&aelig; &longs;int <lb/>in eodem plano trianguli G M K, &longs;i ducantur ab ij&longs;dem punctis G, K. pote&longs;t <lb/>tamen &longs;eruari in alijs duabus, qu&aelig; cadant in pr&aelig;dictum ambitum, &longs;iue <expan abbr="cir-cunfer&etilde;tiam">cir&shy;<lb/>cunferentiam</expan> L M N, <expan abbr="qu&aelig;&qacute;">qu&aelig;que</expan>; &longs;int in alio plano, <expan abbr="qu&atilde;">quam</expan> in plano trianguli G M K, <lb/>quod tamen tran&longs;eat per axem G K O, <expan abbr="&longs;it&qacute;">&longs;itque</expan>; vnum ex planis illis, de quibus <lb/>&longs;upra dictum e&longs;t. </s> <s>Illud nunc in memoriam <expan abbr="reuoc&atilde;dum">reuocandum</expan>, quod paul&ograve; ante probaui, nimirum <lb/>proportionem linearum G M, K M, non po&longs;&longs;e &longs;eruari in alijs lineis, qu&aelig; &longs;int <lb/>in eodem plano trianguli G M K, &longs;i ducantur ab ij&longs;dem punctis G, K. pote&longs;t <lb/>tamen &longs;eruari in alijs duabus, qu&aelig; cadant in pr&aelig;dictum ambitum, &longs;iue <expan abbr="cir-cunfer&etilde;tiam">cir&shy;<lb/>cunferentiam</expan> L M N, <expan abbr="qu&aelig;&qacute;">qu&aelig;que</expan>; &longs;int in alio plano, <expan abbr="qu&atilde;">quam</expan> in plano trianguli G M K, <lb/>quod tamen tran&longs;eat per axem G K O, <expan abbr="&longs;it&qacute;">&longs;itque</expan>; vnum ex planis illis, de quibus <lb/>&longs;upra dictum e&longs;t. </s>
  
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 <s>Fort&egrave; etiam addi pote&longs;t, quod alibi exi&longs;ten&shy;<lb/>te puncto R, qu&agrave;m in M, non po&longs;&longs;ent anguli incidenti&aelig;, &amp; reflexionis e&longs;&longs;e <lb/>&aelig;quales, qu&aelig; cau&longs;a e&longs;&longs;et cur &longs;ub alio angulo, quam pr&aelig;dicto G M K, Iris <lb/>non appareret.</s></p><p type="main"> <s>Fort&egrave; etiam addi pote&longs;t, quod alibi exi&longs;ten&shy;<lb/>te puncto R, qu&agrave;m in M, non po&longs;&longs;ent anguli incidenti&aelig;, &amp; reflexionis e&longs;&longs;e <lb/>&aelig;quales, qu&aelig; cau&longs;a e&longs;&longs;et cur &longs;ub alio angulo, quam pr&aelig;dicto G M K, Iris <lb/>non appareret.</s></p><p type="main">
  
 <s>Pr&aelig;dicta omnia &longs;unt &longs;ecundum Ari&longs;tot. </s> <s>Pr&aelig;dicta omnia &longs;unt &longs;ecundum Ari&longs;tot. di&longs;cur&longs;um, &amp; figurationem dicta, <lb/>nam &longs;ecundum veritatem po&longs;&longs;<gap/>nt in eadem nube con&longs;titui plures anguli <lb/>&aelig;quales, nec tamen in eodem orbe, &longs;ed vnus &longs;upra <expan abbr="alter&utilde;">alterum</expan>; vt in figura pr&aelig;&shy;<lb/><figure id="fig55"/><lb/>&longs;enti, &longs;i nubes e&longs;&longs;et vbi B D. <lb/>oculus in C, Sol in A. e&longs;&longs;ent <lb/>duo anguli A B C, A D C, &aelig;&shy;<lb/>quales per 33. 3. qui tamen <lb/>non &longs;unt in gyrum con&longs;tituti, <lb/>po&longs;&longs;et igitur, per <expan abbr="illor&utilde;">illorum</expan> vtrun&shy;<lb/>que Sol Iridem efficere. </s>
  
  
 <s>di&longs;cur&longs;um, &amp; figurationem dicta, <lb/>nam &longs;ecundum veritatem po&longs;&longs;<gap/>nt in eadem nube con&longs;titui plures anguli <lb/>&aelig;quales, nec tamen in eodem orbe, &longs;ed vnus &longs;upra <expan abbr="alter&utilde;">alterum</expan>; vt in figura pr&aelig;&shy;<lb/><figure id="fig55"></figure><lb/>&longs;enti, &longs;i nubes e&longs;&longs;et vbi B D. <lb/>oculus in C, Sol in A. e&longs;&longs;ent <lb/>duo anguli A B C, A D C, &aelig;&shy;<lb/>quales per 33. 3. qui tamen <lb/>non &longs;unt in gyrum con&longs;tituti, <lb/>po&longs;&longs;et igitur, per <expan abbr="illor&utilde;">illorum</expan> vtrun&shy;<lb/>que Sol Iridem efficere. </s> 
  
 <s>atque <lb/>animaduer&longs;io h&ecedil;c videtur ma&shy;<lb/>gni <expan abbr="mom&etilde;ti">momenti</expan> e&longs;&longs;e, ad Iridis <expan abbr="de-mon&longs;tration&etilde;">de&shy;<lb/>mon&longs;trationem</expan> con&longs;tituendam: <lb/>cum hinc v&longs;itat&aelig; demon&longs;tra&shy;<lb/>tiones infringatur. </s> <s>atque <lb/>animaduer&longs;io h&ecedil;c videtur ma&shy;<lb/>gni <expan abbr="mom&etilde;ti">momenti</expan> e&longs;&longs;e, ad Iridis <expan abbr="de-mon&longs;tration&etilde;">de&shy;<lb/>mon&longs;trationem</expan> con&longs;tituendam: <lb/>cum hinc v&longs;itat&aelig; demon&longs;tra&shy;<lb/>tiones infringatur. </s>
  
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 <s>Ita vt non &longs;o&shy;<pb pagenum="120"/>lum requiratur idem angulus, &longs;ed etiam tanta Iridis altitudo, <expan abbr="qu&atilde;ta">quanta</expan> requi&shy;<lb/>ritur vt angulus in orbem con&longs;tituatur, ex quo Iris po&longs;&longs;it apparere. </s> <s>Ita vt non &longs;o&shy;<pb pagenum="120"/>lum requiratur idem angulus, &longs;ed etiam tanta Iridis altitudo, <expan abbr="qu&atilde;ta">quanta</expan> requi&shy;<lb/>ritur vt angulus in orbem con&longs;tituatur, ex quo Iris po&longs;&longs;it apparere. </s>
  
 <s>h&aelig;c &agrave; <lb/>nemine hactenus animaduer&longs;a placuit addere, vt ex ijs demon&longs;tratio Iridis <lb/>omnibus numeris aliquando ab&longs;olui po&longs;&longs;it, quod infra (ni fallor, fauente <lb/>Deo) pr&aelig;&longs;tabimus.<lb/><arrow.to.target n="marg166"></arrow.to.target></s></p><p type="margin"> <s>h&aelig;c &agrave; <lb/>nemine hactenus animaduer&longs;a placuit addere, vt ex ijs demon&longs;tratio Iridis <lb/>omnibus numeris aliquando ab&longs;olui po&longs;&longs;it, quod infra (ni fallor, fauente <lb/>Deo) pr&aelig;&longs;tabimus.<lb/><arrow.to.target n="marg166"/></s></p><p type="margin">
  
 <s><margin.target id="marg166"></margin.target>165</s></p><p type="main"> <s><margin.target id="marg166"/>165</s></p><p type="main">
  
 <s>Ibidem <emph type="italics"/>(Extraponatur igitur qu&aelig;dam linea, qu&aelig; D B, &amp; &longs;eindatur vt M G, ad&shy;<lb/>M K, &longs;ic qu&aelig; D, ad B, maior autem qu&aelig; M G, ea qu&agrave;m M K, quoniam &longs;uper ma&shy;<lb/>iorem angulum reflexio coni, maiori enim angulo &longs;ubtenditur trianguli M K G. <lb/></s> <s>Ibidem <emph type="italics"/>(Extraponatur igitur qu&aelig;dam linea, qu&aelig; D B, &amp; &longs;eindatur vt M G, ad&shy;<lb/>M K, &longs;ic qu&aelig; D, ad B, maior autem qu&aelig; M G, ea qu&agrave;m M K, quoniam &longs;uper ma&shy;<lb/>iorem angulum reflexio coni, maiori enim angulo &longs;ubtenditur trianguli M K G. <lb/></s>
  
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 <s>Dicit <expan abbr="itaq;">itaque</expan> Ari&longs;t.  <s>Dicit <expan abbr="itaq;">itaque</expan> Ari&longs;t.
  
 cum data &longs;it proportio linearum K M, &amp; M G, in &longs;upe&shy;<lb/>riori &longs;ecunda figura numeri 164. quam nunc iterum in&longs;picere opertet; ex&shy;<lb/><figure id="fig56"></figure><lb/>ponatur alia linea recta B D. qu&aelig; diui&shy;<lb/>datur in partes B, &amp; D. proportionales <lb/>cum lineis K M, G M, per 10. 6. cum <lb/>ergo K M, &longs;it minor qu&agrave;m G M, per 19. <lb/>primi, quia in triangulo G M K, oppo&shy;<lb/>nitur minori angulo, erit <expan abbr="quoq;">quoque</expan> B, minor qu&agrave;m D, addatur iam ip&longs;i B. linea <lb/>nea F, ita vt &longs;it tota F B, tertia proportionalis ad duas B, &amp; D, per 11. 6. <lb/>hoc ordine, vt F B, ad D. ita D, ad B. </s> cum data &longs;it proportio linearum K M, &amp; M G, in &longs;upe&shy;<lb/>riori &longs;ecunda figura numeri 164. quam nunc iterum in&longs;picere opertet; ex&shy;<lb/><figure id="fig56"/><lb/>ponatur alia linea recta B D. qu&aelig; diui&shy;<lb/>datur in partes B, &amp; D. proportionales <lb/>cum lineis K M, G M, per 10. 6. cum <lb/>ergo K M, &longs;it minor qu&agrave;m G M, per 19. <lb/>primi, quia in triangulo G M K, oppo&shy;<lb/>nitur minori angulo, erit <expan abbr="quoq;">quoque</expan> B, minor qu&agrave;m D, addatur iam ip&longs;i B. linea <lb/>nea F, ita vt &longs;it tota F B, tertia proportionalis ad duas B, &amp; D, per 11. 6. <lb/>hoc ordine, vt F B, ad D. ita D, ad B. </s>
  
 <s>Deinde vt &longs;e habet F, ad K G. ita &longs;it <lb/>B, ad aliam, qu&aelig; &longs;it K P, in eadem figura per 12. 6. &amp; &agrave; puncto P, ad M, iun&shy;<lb/>gatur recta P M. </s> <s>Deinde vt &longs;e habet F, ad K G. ita &longs;it <lb/>B, ad aliam, qu&aelig; &longs;it K P, in eadem figura per 12. 6. &amp; &agrave; puncto P, ad M, iun&shy;<lb/>gatur recta P M. </s>
  
 <s>Dico P, e&longs;&longs;e polum circuli, quem dixi Iridis, &amp; in quem li&shy;<lb/>ne&aelig; &agrave; K, procedentes turbinis formam effingunt, probatur autem ab Ari&longs;t. <lb/></s> <s>Dico P, e&longs;&longs;e polum circuli, quem dixi Iridis, &amp; in quem li&shy;<lb/>ne&aelig; &agrave; K, procedentes turbinis formam effingunt, probatur autem ab Ari&longs;t. <lb/>in &longs;equentibus.</s></p><p type="main">
  
 <s>in &longs;equentibus.</s></p><p type="main"> 
  
 <s><arrow.to.target n="marg167"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg167"/></s></p><p type="margin">
  
 <s><margin.target id="marg167"></margin.target>166</s></p><p type="main"> <s><margin.target id="marg167"/>166</s></p><p type="main">
  
 <s>Ibidem <emph type="italics"/>(Erit etiam, quod qu&aelig; F, ad K G. &amp; qu&aelig; B, ad K P. &amp; qu&aelig; D, ad P M. <lb/>non enim &longs;it, &longs;ed aut ad minorem, aut ad maiorem ea, qu&aelig; P M, nibil emm differet. <lb/></s> <s>Ibidem <emph type="italics"/>(Erit etiam, quod qu&aelig; F, ad K G. &amp; qu&aelig; B, ad K P. &amp; qu&aelig; D, ad P M. <lb/>non enim &longs;it, &longs;ed aut ad minorem, aut ad maiorem ea, qu&aelig; P M, nibil emm differet. <lb/></s>
  
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 <s>e&longs;t etiam vt G P, ad P R, in maiori triangulo, ita P R, ad K P, in <lb/>minori, ex con&longs;tructione, quare per 6. 6. erunt illa duo triangula &aelig;quian&shy;<lb/>gula; erg&ograve; per 4. 6. erunt latera circum &aelig;quales angulos proportionalia; <lb/>quare erit vt G P, ad P R. ita G R, ad R K: erat autem vt K M, ad G M, ita <lb/>B, ad D. &amp; ita etiam G P, ad P R; erg&ograve; per 11. 5. vt K M, ad M G. ita K R, <lb/>ad R G, intra eandem circunferentiam, &amp; in eodem plano: quod e&longs;&longs;e im&shy;<lb/>po&longs;&longs;ibile &longs;upra o&longs;tendimus, hoc autem impo&longs;&longs;ibile, &longs;equitur &longs;i neges e&longs;&longs;e vt <lb/>F, ad G K; &amp; B, ad K P, ita D, ad P M.</s></p><p type="main"> <s>e&longs;t etiam vt G P, ad P R, in maiori triangulo, ita P R, ad K P, in <lb/>minori, ex con&longs;tructione, quare per 6. 6. erunt illa duo triangula &aelig;quian&shy;<lb/>gula; erg&ograve; per 4. 6. erunt latera circum &aelig;quales angulos proportionalia; <lb/>quare erit vt G P, ad P R. ita G R, ad R K: erat autem vt K M, ad G M, ita <lb/>B, ad D. &amp; ita etiam G P, ad P R; erg&ograve; per 11. 5. vt K M, ad M G. ita K R, <lb/>ad R G, intra eandem circunferentiam, &amp; in eodem plano: quod e&longs;&longs;e im&shy;<lb/>po&longs;&longs;ibile &longs;upra o&longs;tendimus, hoc autem impo&longs;&longs;ibile, &longs;equitur &longs;i neges e&longs;&longs;e vt <lb/>F, ad G K; &amp; B, ad K P, ita D, ad P M.</s></p><p type="main">
  
 <s><arrow.to.target n="marg168"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg168"/></s></p><p type="margin">
  
 <s><margin.target id="marg168"></margin.target>167</s></p><p type="main"> <s><margin.target id="marg168"/>167</s></p><p type="main">
  
 <s>Ibidem <emph type="italics"/>(Quoni&abreve; igitur qu&aelig; D, <expan abbr="neq;">neque</expan> ad minorem ea, qu&aelig; P M, <expan abbr="neq;">neque</expan> ad maiorem <lb/>(&longs;imiliter enim demon&longs;ir abimus) palam e&longs;t, quod ad ip&longs;am <expan abbr="vtiq;">vtique</expan> erit, in qua P M, <lb/>quare erit, quod qu&aelig; M P, ad P K, qu&aelig; P G, ad M P. </s> <s>Ibidem <emph type="italics"/>(Quoni&abreve; igitur qu&aelig; D, <expan abbr="neq;">neque</expan> ad minorem ea, qu&aelig; P M, <expan abbr="neq;">neque</expan> ad maiorem <lb/>(&longs;imiliter enim demon&longs;ir abimus) palam e&longs;t, quod ad ip&longs;am <expan abbr="vtiq;">vtique</expan> erit, in qua P M, <lb/>quare erit, quod qu&aelig; M P, ad P K, qu&aelig; P G, ad M P. </s>
  
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 <s>Ex quibus pater P, e&longs;&longs;e polum Iridis, ex <lb/>quo per puncta M, vbi &longs;it reflexio, de&longs;cribitur arcus attingens omnes Iridis <lb/>reflexiones.</s></p><pb pagenum="122"/><p type="main"> <s>Ex quibus pater P, e&longs;&longs;e polum Iridis, ex <lb/>quo per puncta M, vbi &longs;it reflexio, de&longs;cribitur arcus attingens omnes Iridis <lb/>reflexiones.</s></p><pb pagenum="122"/><p type="main">
  
 <s><arrow.to.target n="marg169"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg169"/></s></p><p type="margin">
  
 <s><margin.target id="marg169"></margin.target>168</s></p><p type="main"> <s><margin.target id="marg169"/>168</s></p><p type="main">
  
 <s>Ibidem <emph type="italics"/>(Si igitur circumducas &longs;emicircul&ubreve;, in quo A, circa diametrum in qua <lb/>G K P, que &agrave; G, K, reflex&aelig; ad id in quo M; in omnibus planis &longs;imiliter &longs;e habebunt, <lb/>&amp; &aelig;qualem facient angulam, qui K M G, &amp; quem etiam facient angulum, qu&aelig; <lb/>K P, &amp; P M, &longs;uper eam, qu&aelig; G P, &longs;emper &aelig;qualis erit. </s> <s>Ibidem <emph type="italics"/>(Si igitur circumducas &longs;emicircul&ubreve;, in quo A, circa diametrum in qua <lb/>G K P, que &agrave; G, K, reflex&aelig; ad id in quo M; in omnibus planis &longs;imiliter &longs;e habebunt, <lb/>&amp; &aelig;qualem facient angulam, qui K M G, &amp; quem etiam facient angulum, qu&aelig; <lb/>K P, &amp; P M, &longs;uper eam, qu&aelig; G P, &longs;emper &aelig;qualis erit. </s>
  
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 <s>Atque hoc accidit Sole, vel Luna in horizonte exi&longs;tentibus; quod <lb/>erat primo loco demon&longs;trandum.</s></p><p type="main"> <s>Atque hoc accidit Sole, vel Luna in horizonte exi&longs;tentibus; quod <lb/>erat primo loco demon&longs;trandum.</s></p><p type="main">
  
 <s>Porr&ograve; &longs;ciendum po&longs;&longs;e nos breuius polum pr&aelig;dictum inuenire, &longs;i nimirum <lb/><figure id="fig57"></figure><lb/>ad M, ducatur M P, faciens angulum K P M, &aelig;qua&shy;<lb/>lem angulo G M K, per 23. primi, erunt enim duo <lb/>triangula <expan abbr="&aelig;qui&atilde;gula">&aelig;quiangula</expan> G P M, K P M, angulus enim <lb/>P, e&longs;t communis, angulus ver&ograve; M K P, e&longs;t &aelig;qualis <lb/>duobus G, &amp; G M K, per 32. primi, ergo etiam <lb/>duobus ad M, &longs;iue toti G M P, &amp; reliquus K M P, <lb/>reliquo, quare per 4.6. latera circa angulos &aelig;qua&shy;<lb/>les proportionalia erunt, &amp; omologa G M, ad M K, ita G P, ad P M, qu&aelig; <lb/>&aelig;qualibus augulis &longs;ubtenduntur. </s> <s>Porr&ograve; &longs;ciendum po&longs;&longs;e nos breuius polum pr&aelig;dictum inuenire, &longs;i nimirum <lb/><figure id="fig57"/><lb/>ad M, ducatur M P, faciens angulum K P M, &aelig;qua&shy;<lb/>lem angulo G M K, per 23. primi, erunt enim duo <lb/>triangula <expan abbr="&aelig;qui&atilde;gula">&aelig;quiangula</expan> G P M, K P M, angulus enim <lb/>P, e&longs;t communis, angulus ver&ograve; M K P, e&longs;t &aelig;qualis <lb/>duobus G, &amp; G M K, per 32. primi, ergo etiam <lb/>duobus ad M, &longs;iue toti G M P, &amp; reliquus K M P, <lb/>reliquo, quare per 4.6. latera circa angulos &aelig;qua&shy;<lb/>les proportionalia erunt, &amp; omologa G M, ad M K, ita G P, ad P M, qu&aelig; <lb/>&aelig;qualibus augulis &longs;ubtenduntur. </s>
  
 <s><expan abbr="ea&longs;d&etilde;">ea&longs;dem</expan> autem proprietates habcbant etiam <lb/>triangula Ari&longs;t.  <s><expan abbr="ea&longs;d&etilde;">ea&longs;dem</expan> autem proprietates habcbant etiam <lb/>triangula Ari&longs;t.
  
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 <s>Verba illa <emph type="italics"/>(Qu&aelig; ali&shy;<lb/>b quam in &longs;emicirculo constituuntur)<emph.end type="italics"/> &longs;unt perperam in antiqua tran&longs;latione <lb/>tran&longs;lata, nam Gr&aelig;c&egrave; &longs;ic, <foreign lang="greek">ai alloqi tou_ hmixoxlnou/ sunisamenai,</foreign> transferenda <lb/>e&longs;&longs;ent, qu&aelig; in alio circuli loco concurrunt.</s></p><p type="main"> <s>Verba illa <emph type="italics"/>(Qu&aelig; ali&shy;<lb/>b quam in &longs;emicirculo constituuntur)<emph.end type="italics"/> &longs;unt perperam in antiqua tran&longs;latione <lb/>tran&longs;lata, nam Gr&aelig;c&egrave; &longs;ic, <foreign lang="greek">ai alloqi tou_ hmixoxlnou/ sunisamenai,</foreign> transferenda <lb/>e&longs;&longs;ent, qu&aelig; in alio circuli loco concurrunt.</s></p><p type="main">
  
 <s><arrow.to.target n="marg170"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg170"/></s></p><p type="margin">
  
 <s><margin.target id="marg170"></margin.target>169</s></p><p type="main"> <s><margin.target id="marg170"/>169</s></p><p type="main">
  
 <s>Ibidem <emph type="italics"/>(Iterum &longs;it horizon quidem in quo A C. oriatur autem &longs;upra hunc G, <lb/>axis autem &longs;it nunc in quo G P. </s> <s>Ibidem <emph type="italics"/>(Iterum &longs;it horizon quidem in quo A C. oriatur autem &longs;upra hunc G, <lb/>axis autem &longs;it nunc in quo G P. </s>
  
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 <s>Polus autem circuli, in quo P, erit &longs;ub horizonte eo, in quo A C, eleuato puncto, <lb/>in quo G. in eadem autem &amp; polus, &amp; centrum circuli, &amp; terminantis nunc ortum, <lb/>e&longs;t enim i&longs;te, in quo G P. </s> <s>Polus autem circuli, in quo P, erit &longs;ub horizonte eo, in quo A C, eleuato puncto, <lb/>in quo G. in eadem autem &amp; polus, &amp; centrum circuli, &amp; terminantis nunc ortum, <lb/>e&longs;t enim i&longs;te, in quo G P. </s>
  
 <s>Quoniam autem &longs;upra diametrum, qu&aelig; A C, quod K G, <lb/>centrum vtique erit &longs;ub horizonte priori eius, in quo A C, in linea K P, in quo <foreign lang="greek">w,</foreign><emph.end type="italics"/><pb pagenum="123"/><figure id="fig58"></figure><lb/><emph type="italics"/>Quare minor erit &longs;uperior &longs;ectio &longs;emicir&shy;<lb/>culo, in qua S T, (nam Q S T, &longs;emicir&shy;<lb/>culus est, nunc autem inter&longs;ectus e&longs;t ab <lb/>horizonte A C; <expan abbr="itaq;">itaque</expan> Q S, di&longs;parens erit) <lb/>eleuato ip&longs;o Sole)<emph.end type="italics"/> demon&longs;trat propo&longs;i&shy;<lb/>tionem &longs;ecundam nimirum Sole &longs;upra <lb/>horizontem elcuato, ambitum Iridis <lb/>e&longs;&longs;e minorem circuli portionem, &longs;iue <lb/>&longs;emicirculo minorem. </s> <s>Quoniam autem &longs;upra diametrum, qu&aelig; A C, quod K G, <lb/>centrum vtique erit &longs;ub horizonte priori eius, in quo A C, in linea K P, in quo <foreign lang="greek">w,</foreign><emph.end type="italics"/><pb pagenum="123"/><figure id="fig58"/><lb/><emph type="italics"/>Quare minor erit &longs;uperior &longs;ectio &longs;emicir&shy;<lb/>culo, in qua S T, (nam Q S T, &longs;emicir&shy;<lb/>culus est, nunc autem inter&longs;ectus e&longs;t ab <lb/>horizonte A C; <expan abbr="itaq;">itaque</expan> Q S, di&longs;parens erit) <lb/>eleuato ip&longs;o Sole)<emph.end type="italics"/> demon&longs;trat propo&longs;i&shy;<lb/>tionem &longs;ecundam nimirum Sole &longs;upra <lb/>horizontem elcuato, ambitum Iridis <lb/>e&longs;&longs;e minorem circuli portionem, &longs;iue <lb/>&longs;emicirculo minorem. </s>
  
 <s>&longs;it igitur in fi&shy;<lb/>gura &longs;uperiori, quam textui <expan abbr="c&otilde;gruen-tem">congruen&shy;<lb/>tem</expan> re&longs;tituimus, linea A C, horizon&shy;<lb/>talis, &longs;upra quam Sol &longs;it eleuatus in <lb/>circulo altitudinis in loco G, axis au&shy;<lb/>rem coni, quem reflex&egrave; faciunt &longs;it <lb/>G K <foreign lang="greek">w</foreign> P. alia igitur omnia, qu&aelig; &longs;upra exi&longs;tente in ortu a&longs;tro o&longs;ten&longs;a &longs;unt, hic <lb/>pariter o&longs;tendi po&longs;&longs;unt, &longs;cilicet Iridem fieri tantum per lineas proportiona&shy;<lb/>les, &amp; &aelig;quales lineis G M, M K, quia Iris videri nequit, ni&longs;i in tali, ac deter&shy;<lb/>minata reflexione, &amp; angulo, vt initio &longs;uppo&longs;ui; &amp; quia line&aelig; illis propor&shy;<lb/>tionales non po&longs;&longs;unt alibi con&longs;titui, quam in ambitu circulari, &amp; in diuer&longs;is <lb/>planis, &longs;equitur, vt &longs;upra Iridem e&longs;&longs;e circularem M N L; <expan abbr="eius&qacute;">eiusque</expan>; polum P, &amp; <lb/>centrum <foreign lang="greek">w,</foreign> inueniemus &longs;imiliter in axe G K <foreign lang="greek">w</foreign> P, &amp; quia axis hic &longs;ecat hori&shy;<lb/>zontem in K, in hac vltima figura propter eleuationem Solis &longs;upra A C, in <lb/>G, &longs;equitur partem axis, in qua <foreign lang="greek">w,</foreign> &amp; P, exi&longs;tunt, infra horizontem deprimi. <lb/></s> <s>&longs;it igitur in fi&shy;<lb/>gura &longs;uperiori, quam textui <expan abbr="c&otilde;gruen-tem">congruen&shy;<lb/>tem</expan> re&longs;tituimus, linea A C, horizon&shy;<lb/>talis, &longs;upra quam Sol &longs;it eleuatus in <lb/>circulo altitudinis in loco G, axis au&shy;<lb/>rem coni, quem reflex&egrave; faciunt &longs;it <lb/>G K <foreign lang="greek">w</foreign> P. alia igitur omnia, qu&aelig; &longs;upra exi&longs;tente in ortu a&longs;tro o&longs;ten&longs;a &longs;unt, hic <lb/>pariter o&longs;tendi po&longs;&longs;unt, &longs;cilicet Iridem fieri tantum per lineas proportiona&shy;<lb/>les, &amp; &aelig;quales lineis G M, M K, quia Iris videri nequit, ni&longs;i in tali, ac deter&shy;<lb/>minata reflexione, &amp; angulo, vt initio &longs;uppo&longs;ui; &amp; quia line&aelig; illis propor&shy;<lb/>tionales non po&longs;&longs;unt alibi con&longs;titui, quam in ambitu circulari, &amp; in diuer&longs;is <lb/>planis, &longs;equitur, vt &longs;upra Iridem e&longs;&longs;e circularem M N L; <expan abbr="eius&qacute;">eiusque</expan>; polum P, &amp; <lb/>centrum <foreign lang="greek">w,</foreign> inueniemus &longs;imiliter in axe G K <foreign lang="greek">w</foreign> P, &amp; quia axis hic &longs;ecat hori&shy;<lb/>zontem in K, in hac vltima figura propter eleuationem Solis &longs;upra A C, in <lb/>G, &longs;equitur partem axis, in qua <foreign lang="greek">w,</foreign> &amp; P, exi&longs;tunt, infra horizontem deprimi. <lb/></s>
  
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 propo&longs;itio manife&longs;ta e&longs;t.</s></p><p type="main"> propo&longs;itio manife&longs;ta e&longs;t.</s></p><p type="main">
  
 <s><arrow.to.target n="marg171"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg171"/></s></p><p type="margin">
  
 <s><margin.target id="marg171"></margin.target>180</s></p><p type="main"> <s><margin.target id="marg171"/>180</s></p><p type="main">
  
 <s>Ibidem <emph type="italics"/>(Minima autem cum in meridie, quanto enim &longs;uperius G, tanto in&longs;e&shy;<lb/>rius &amp; polus, &amp; centrum circuli erit)<emph.end type="italics"/> probat tertiam propo&longs;itionem, nimi&shy;<lb/>rum Sole exi&longs;tente in meridie minimam <expan abbr="omni&utilde;">omnium</expan> e&longs;&longs;e Iridis arcus portionem: <lb/>ratio autem e&longs;t, quia tunc G, &longs;iue Sol, e&longs;t alti&longs;&longs;imus &longs;upra horizontem, &amp; <lb/>con&longs;equenter <foreign lang="greek">w;</foreign> centrum Iridis e&longs;t depre&longs;si&longs;&longs;imum, quare tunc maxima cir&shy;<lb/>culi Iridis portio ab&longs;condetur, &amp; proinde minima apparebit, quod erat vl&shy;<lb/>timo <expan abbr="dem&otilde;&longs;trandum">demon&longs;trandum</expan>. </s> <s>Ibidem <emph type="italics"/>(Minima autem cum in meridie, quanto enim &longs;uperius G, tanto in&longs;e&shy;<lb/>rius &amp; polus, &amp; centrum circuli erit)<emph.end type="italics"/> probat tertiam propo&longs;itionem, nimi&shy;<lb/>rum Sole exi&longs;tente in meridie minimam <expan abbr="omni&utilde;">omnium</expan> e&longs;&longs;e Iridis arcus portionem: <lb/>ratio autem e&longs;t, quia tunc G, &longs;iue Sol, e&longs;t alti&longs;&longs;imus &longs;upra horizontem, &amp; <lb/>con&longs;equenter <foreign lang="greek">w;</foreign> centrum Iridis e&longs;t depre&longs;si&longs;&longs;imum, quare tunc maxima cir&shy;<lb/>culi Iridis portio ab&longs;condetur, &amp; proinde minima apparebit, quod erat vl&shy;<lb/>timo <expan abbr="dem&otilde;&longs;trandum">demon&longs;trandum</expan>. </s>
  
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 tra&shy;<lb/>ctationem in gratiam textus illius, vt in&longs;tituti mei ratio po&longs;tulabat, per&longs;e&shy;<lb/>quutus &longs;um.</s></p><p type="main"> tra&shy;<lb/>ctationem in gratiam textus illius, vt in&longs;tituti mei ratio po&longs;tulabat, per&longs;e&shy;<lb/>quutus &longs;um.</s></p><p type="main">
  
 <s><arrow.to.target n="marg172"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg172"/></s></p><p type="margin">
  
 <s><margin.target id="marg172"></margin.target>181</s></p><p type="main"> <s><margin.target id="marg172"/>181</s></p><p type="main">
  
 <s>Ibidem <emph type="italics"/>(Quod autem in minoribus quidem diebus ijs, qui po&longs;t &aelig;quinoctium au&shy;<lb/>tumnale <expan abbr="c&otilde;tingit">contingit</expan> &longs;emper fieri Iridem: in longioribus aurem diebus ijs qui ab &aelig;qui&shy;<lb/>noctio altero, ad &aelig;quinoctium alterum circa meridiem non fit Iris, can&longs;a est, quia <lb/>qu&aelig; ad Vr&longs;am &longs;ectiones omnes maiores &longs;unt &longs;emicirculo, &amp; &longs;emper ad matere<gap/> quod <lb/>autem e&longs;t occultum, paruum: qu&aelig; autem ad &aelig;quatoris meridiem &longs;ectiones, qu&aelig; qui&shy;<lb/>dem &longs;upra &longs;ectio, parua; qu&aelig; autem &longs;ub terra magna, &amp; &longs;emper maiores, qu&aelig; lon&shy;<lb/>gius. </s> <s>Ibidem <emph type="italics"/>(Quod autem in minoribus quidem diebus ijs, qui po&longs;t &aelig;quinoctium au&shy;<lb/>tumnale <expan abbr="c&otilde;tingit">contingit</expan> &longs;emper fieri Iridem: in longioribus aurem diebus ijs qui ab &aelig;qui&shy;<lb/>noctio altero, ad &aelig;quinoctium alterum circa meridiem non fit Iris, can&longs;a est, quia <lb/>qu&aelig; ad Vr&longs;am &longs;ectiones omnes maiores &longs;unt &longs;emicirculo, &amp; &longs;emper ad matere<gap/> quod <lb/>autem e&longs;t occultum, paruum: qu&aelig; autem ad &aelig;quatoris meridiem &longs;ectiones, qu&aelig; qui&shy;<lb/>dem &longs;upra &longs;ectio, parua; qu&aelig; autem &longs;ub terra magna, &amp; &longs;emper maiores, qu&aelig; lon&shy;<lb/>gius. </s>
  
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 <s>45. circiter) quare <lb/>quando a&longs;trum G, con&longs;cenderit meridiem, ade&ograve; P, polus Iridis, &amp; etiam <foreign lang="greek">w,</foreign><lb/>centrum eius infra terram deprimitur, vt aut nihil, aut in&longs;en&longs;ibile quid de <lb/>Iridis ambitu &longs;upra terram eleuari po&longs;&longs;it, contrarium accidit in parallelis <lb/>meridionalibus, quia eorum &longs;ectiones &longs;uperiores &longs;unt &longs;emper inferioribus <lb/>minores, quapropter etiam &longs;i a&longs;trum ad meridiem eleuetur, parum tamen <lb/>attollitur, &amp; con&longs;equenter centrum <foreign lang="greek">w,</foreign> Iridis parum infra horizontem <lb/>de&longs;cendit, ac propterea etiam in meridie pars ip&longs;ius &longs;atis ma&shy;<lb/>gna con&longs;picitur. </s> <s>45. circiter) quare <lb/>quando a&longs;trum G, con&longs;cenderit meridiem, ade&ograve; P, polus Iridis, &amp; etiam <foreign lang="greek">w,</foreign><lb/>centrum eius infra terram deprimitur, vt aut nihil, aut in&longs;en&longs;ibile quid de <lb/>Iridis ambitu &longs;upra terram eleuari po&longs;&longs;it, contrarium accidit in parallelis <lb/>meridionalibus, quia eorum &longs;ectiones &longs;uperiores &longs;unt &longs;emper inferioribus <lb/>minores, quapropter etiam &longs;i a&longs;trum ad meridiem eleuetur, parum tamen <lb/>attollitur, &amp; con&longs;equenter centrum <foreign lang="greek">w,</foreign> Iridis parum infra horizontem <lb/>de&longs;cendit, ac propterea etiam in meridie pars ip&longs;ius &longs;atis ma&shy;<lb/>gna con&longs;picitur. </s>
  
 <s>qu&aelig; omnia adhibita &longs;ph&aelig;ra materia&shy;<lb/>li, eaque a&longs;tronomic&egrave; ad &longs;uam eleuationem <lb/>accommodata, nullo negotio li&shy;<lb/>cebit intueri.</s></p><figure></figure><pb pagenum="125"/><p type="head"> <s>qu&aelig; omnia adhibita &longs;ph&aelig;ra materia&shy;<lb/>li, eaque a&longs;tronomic&egrave; ad &longs;uam eleuationem <lb/>accommodata, nullo negotio li&shy;<lb/>cebit intueri.</s></p><figure/><pb pagenum="125"/><p type="head">
  
 <s><emph type="italics"/>Additio de Iride.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Additio de Iride.<emph.end type="italics"/></s></p><p type="main">
  
 <s>Cvm &longs;uperior Ari&longs;tot. </s> <s>Cvm &longs;uperior Ari&longs;tot. de Iride tractatio ob&longs;cura, ac tricis pluribus <lb/>impedita eua&longs;erit, <expan abbr="cum&qacute;">cumque</expan>; aliorum etiam demon&longs;trationes aliqua <lb/>ex parte vacilient, vi&longs;um e&longs;t breuiter expeditam, <expan abbr="atq;">atque</expan> ab&longs;olutam <lb/>ip&longs;ius apponere demon&longs;trationem. </s>
  
  
 <s>de Iride tractatio ob&longs;cura, ac tricis pluribus <lb/>impedita eua&longs;erit, <expan abbr="cum&qacute;">cumque</expan>; aliorum etiam demon&longs;trationes aliqua <lb/>ex parte vacilient, vi&longs;um e&longs;t breuiter expeditam, <expan abbr="atq;">atque</expan> ab&longs;olutam <lb/>ip&longs;ius apponere demon&longs;trationem. </s> 
  
 <s>Cum igitur in c&oelig;le&longs;ti arcu <lb/>duo poti&longs;&longs;imum &longs;int, qu&aelig; &longs;ui admiratione <expan abbr="Philo&longs;ophor&utilde;">Philo&longs;ophorum</expan> animos in &longs;ui con&shy;<lb/>templationem alliciant, colores, &longs;cilicet, &amp; figura: nos mirabilem illam co&shy;<lb/>lorum triadem, tanquam alienam, phy&longs;icis relinquentes, de figura ip&longs;ius iu&shy;<lb/>re mathematico di&longs;&longs;eremus: rotunditatis &longs;cilicet Iridis cau&longs;am opticis ra&shy;<lb/>tionibus venabimur, cur aliquando &longs;emicirculus, aliquando &longs;emicirculo mi&shy;<lb/>nor appareat. </s> <s>Cum igitur in c&oelig;le&longs;ti arcu <lb/>duo poti&longs;&longs;imum &longs;int, qu&aelig; &longs;ui admiratione <expan abbr="Philo&longs;ophor&utilde;">Philo&longs;ophorum</expan> animos in &longs;ui con&shy;<lb/>templationem alliciant, colores, &longs;cilicet, &amp; figura: nos mirabilem illam co&shy;<lb/>lorum triadem, tanquam alienam, phy&longs;icis relinquentes, de figura ip&longs;ius iu&shy;<lb/>re mathematico di&longs;&longs;eremus: rotunditatis &longs;cilicet Iridis cau&longs;am opticis ra&shy;<lb/>tionibus venabimur, cur aliquando &longs;emicirculus, aliquando &longs;emicirculo mi&shy;<lb/>nor appareat. </s>
  
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 <s>i. </s> <s>i. </s>
  
 <s>non in hoc &longs;itu, &amp; ouali figura, &longs;ed <lb/><figure id="fig59"></figure><lb/>e&longs;&longs;e perfect&egrave; &longs;emicircularem, <expan abbr="habere&qacute;">habereque</expan>; talem po&longs;itionem, vt pars ip&longs;ius B F, <lb/>&longs;it citra chartam eleuata, <expan abbr="ip&longs;i&qacute;">ip&longs;ique</expan>; perpendicularis, pars ver&ograve; E B, vltra pagi&shy;<pb pagenum="126"/>nam rect&agrave; recedat, <expan abbr="&longs;ic&qacute;">&longs;icque</expan>; diameter Iridis E F, faciat angulos rectos cum <lb/>linea horizontali A C L, in quo &longs;itu oculo C, totus ex oppo&longs;ito direct&egrave; &longs;pe&shy;<lb/>ctaretur, non aliter ac Iridem ip&longs;am con&longs;picere &longs;olemus. </s> <s>non in hoc &longs;itu, &amp; ouali figura, &longs;ed <lb/><figure id="fig59"/><lb/>e&longs;&longs;e perfect&egrave; &longs;emicircularem, <expan abbr="habere&qacute;">habereque</expan>; talem po&longs;itionem, vt pars ip&longs;ius B F, <lb/>&longs;it citra chartam eleuata, <expan abbr="ip&longs;i&qacute;">ip&longs;ique</expan>; perpendicularis, pars ver&ograve; E B, vltra pagi&shy;<pb pagenum="126"/>nam rect&agrave; recedat, <expan abbr="&longs;ic&qacute;">&longs;icque</expan>; diameter Iridis E F, faciat angulos rectos cum <lb/>linea horizontali A C L, in quo &longs;itu oculo C, totus ex oppo&longs;ito direct&egrave; &longs;pe&shy;<lb/>ctaretur, non aliter ac Iridem ip&longs;am con&longs;picere &longs;olemus. </s>
  
 <s>Quod autem ne&shy;<lb/>ce&longs;&longs;aria &longs;it nubes ro&longs;cida, pulcherrima hac experientia <expan abbr="c&otilde;probatur">comprobatur</expan>: &longs;i enim <lb/>in Sole po&longs;iti ore aquam efflantes leui a&longs;pergine aerem Soli, ac nobis ad&shy;<lb/>uer&longs;um irroremus, actutum Iridis arcum guttulis illis, quamuis volitanti&shy;<lb/>bus inh&aelig;rcntem &longs;umma voluptate &longs;pectabimus. </s> <s>Quod autem ne&shy;<lb/>ce&longs;&longs;aria &longs;it nubes ro&longs;cida, pulcherrima hac experientia <expan abbr="c&otilde;probatur">comprobatur</expan>: &longs;i enim <lb/>in Sole po&longs;iti ore aquam efflantes leui a&longs;pergine aerem Soli, ac nobis ad&shy;<lb/>uer&longs;um irroremus, actutum Iridis arcum guttulis illis, quamuis volitanti&shy;<lb/>bus inh&aelig;rcntem &longs;umma voluptate &longs;pectabimus. </s>
  
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 <s>Ex his etiam Iridis definitio in hunc modum concinnari pote&longs;t, Iris <lb/>e&longs;t arcus multicolor in nube rorida, ex radiorum Solis, aut Lun&aelig; reflexio&shy;<lb/>ne &longs;ab &longs;tatuto angulo effulgens.</s></p><p type="main"> <s>Ex his etiam Iridis definitio in hunc modum concinnari pote&longs;t, Iris <lb/>e&longs;t arcus multicolor in nube rorida, ex radiorum Solis, aut Lun&aelig; reflexio&shy;<lb/>ne &longs;ab &longs;tatuto angulo effulgens.</s></p><p type="main">
  
 <s>Octauo loco Problemata nonnulla re&longs;oluemus.</s></p><figure></figure><pb pagenum="128"/><p type="head"> <s>Octauo loco Problemata nonnulla re&longs;oluemus.</s></p><figure/><pb pagenum="128"/><p type="head">
  
 <s><emph type="italics"/>Problema Primum.<emph.end type="italics"/></s></p><p type="head"> <s><emph type="italics"/>Problema Primum.<emph.end type="italics"/></s></p><p type="head">
  
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 <s><emph type="italics"/>Problema Secundum.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Problema Secundum.<emph.end type="italics"/></s></p><p type="main">
  
 <s>Maior quidem, im&ograve; etiam integer circulus, &longs;ed ab oculo in &longs;ummitate <lb/>montis con&longs;tituto, <expan abbr="Sole&qacute;">Soleque</expan>; iam multum eleuato videri pote&longs;t, vt in <lb/>hac &longs;ecunda figura cernitur, vbi euecto Sole ad locum E, &longs;upra horizontem <lb/><figure id="fig60"></figure><lb/>A B, poterit oculus in vertice montis C, po&longs;itus Iridem F G H I, comple&shy;<lb/>tam videre, quia infra lineam E C D, in qua exi&a