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version 1.25, 2002/08/08 09:04:25 version 1.56, 2002/08/15 00:54:45
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 <?xml version="1.0"?> <?xml version="1.0"?>
 <!DOCTYPE archimedes SYSTEM "../dtd/archimedes.dtd" ><archimedes>      <info>        <author>Bianchini, Giuseppe</author>        <title>Aristotelis loca mathematica</title>        <date>1615</date>         <!DOCTYPE archimedes SYSTEM "../dtd/archimedes.dtd" ><archimedes>      <info>
          <author>Biancani, Giuseppe</author>
          <title>Aristotelis loca mathematica</title>
 <place>Bologna</place>          <translator></translator>        <lang>la</lang>              <cvs_file>bianc_locam_01_la_1615.xml</cvs_file><cvs_version>1.13</cvs_version><locator>0000000009</locator>      </info>      <text>          <front>          </front>          <body>            <chap>        <pb/><p type="head">         <date>1615</date>
          <place>Bologna</place>
          <translator></translator>
          <lang>la</lang>
          <cvs_file>bianc_locam_01_la_1615</cvs_file>
          <cvs_version></cvs_version>
          <locator>0000000009.xml</locator>
  </info>      <text>          <front>          </front>          <body>            <chap>        <pb/><p type="head">
  
 <s>ARISTOTELIS</s></p><p type="head"> <s>ARISTOTELIS</s></p><p type="head">
  
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 <s>Claudij <lb/>Aqu&aelig;uiu&aelig;, facultatem concedo, vt hoc opus P. </s> <s>Claudij <lb/>Aqu&aelig;uiu&aelig;, facultatem concedo, vt hoc opus P. </s>
  
 <s>Io&longs;ephi Blancani eiu&longs;dem <lb/>Societatis, quod in&longs;cribitur, Ari&longs;t. </s> <s>Io&longs;ephi Blancani eiu&longs;dem <lb/>Societatis, quod in&longs;cribitur, Ari&longs;t. Loca Mathematica ex vniuer&longs;is ip&longs;ius <lb/>operibus collecta, &amp; explicata, &agrave; deputatis Patribus recognitum, &amp; ap&shy;<lb/>probatum typis mandari po&longs;&longs;it. </s>
  
 <s>Loca Mathematica ex vniuer&longs;is ip&longs;ius <lb/>operibus collecta, &amp; explicata, &agrave; deputatis Patribus recognitum, &amp; ap&shy;<lb/>probatum typis mandari po&longs;&longs;it. </s> 
  
 <s>Parm&aelig; die 15. Ianuarij 1615.</s></p><p type="main"> <s>Parm&aelig; die 15. Ianuarij 1615.</s></p><p type="main">
  
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 ait duo cubi, cu&shy;<lb/>bus, ip&longs;um loqui putant de duplatione Geometrici cubi, nondum in&shy;<lb/>uenta; non intelligentes, eum ibi de numeris cubis &longs;ermonem habere. <lb/></s> ait duo cubi, cu&shy;<lb/>bus, ip&longs;um loqui putant de duplatione Geometrici cubi, nondum in&shy;<lb/>uenta; non intelligentes, eum ibi de numeris cubis &longs;ermonem habere. <lb/></s>
  
 <s>Auerroes ip&longs;e tantus vir 5. Phy&longs;. </s> <s>Auerroes ip&longs;e tantus vir 5. Phy&longs;. commen. </s>
  
 <s>commen. </s> 
  
 <s>15. qu&agrave;m &longs;e Mathematicis, <lb/>reliqui&longs;que Philo&longs;ophis irridendum pr&aelig;bet dum &agrave; permutata propor&shy;<lb/>tione putat &longs;erect&egrave; in hunc modum pluribus apud ip&longs;um verbis explica&shy;<lb/>tum, argumentari,</s></p><p type="main"> <s>15. qu&agrave;m &longs;e Mathematicis, <lb/>reliqui&longs;que Philo&longs;ophis irridendum pr&aelig;bet dum &agrave; permutata propor&shy;<lb/>tione putat &longs;erect&egrave; in hunc modum pluribus apud ip&longs;um verbis explica&shy;<lb/>tum, argumentari,</s></p><p type="main">
  
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 <s>Ex 2. de Generatione, &amp; Corruptione.</s></p><p type="main"> <s>Ex 2. de Generatione, &amp; Corruptione.</s></p><p type="main">
  
 <s><emph type="italics"/>Tex. </s> <s><emph type="italics"/>Tex. 56. Cur Planet&aelig; duobus motibus moueri dicantur.<emph.end type="italics"/></s></p><p type="head">
  
 <s>56. Cur Planet&aelig; duobus motibus moueri dicantur.<emph.end type="italics"/></s></p><p type="head"> 
  
 <s>Ex 1. Meteororum.</s></p><p type="main"> <s>Ex 1. Meteororum.</s></p><p type="main">
  
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 <s>Ex 1. De Anima.</s></p><p type="main"> <s>Ex 1. De Anima.</s></p><p type="main">
  
 <s><emph type="italics"/>Tex. </s> <s><emph type="italics"/>Tex. 11. Quid rectum, quid obliquum. </s>
  
 <s>11. Quid rectum, quid obliquum. </s> 
  
 <s>&amp; omnis triangulus babet tres, &amp;c.<emph.end type="italics"/></s></p><p type="main"> <s>&amp; omnis triangulus babet tres, &amp;c.<emph.end type="italics"/></s></p><p type="main">
  
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 <s>Tetragoni&longs;mus est inuentio medi&aelig;.<emph.end type="italics"/></s></p><pb pagenum="16"/><p type="main"> <s>Tetragoni&longs;mus est inuentio medi&aelig;.<emph.end type="italics"/></s></p><pb pagenum="16"/><p type="main">
  
 <s><emph type="italics"/>Tex. </s> <s><emph type="italics"/>Tex. 8. Geod&aelig;&longs;ia quid.<emph.end type="italics"/></s></p><p type="head">
  
 <s>8. Geod&aelig;&longs;ia quid.<emph.end type="italics"/></s></p><p type="head"> 
  
 <s>Ex 4. Methaphy&longs;.</s></p><p type="main"> <s>Ex 4. Methaphy&longs;.</s></p><p type="main">
  
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 <s><emph type="italics"/>T. 11. Similes figur&aelig; qu&aelig;. </s> <s><emph type="italics"/>T. 11. Similes figur&aelig; qu&aelig;. </s>
  
 <s>Diuer&longs;um in Math. </s> <s>Diuer&longs;um in Math. quid.<emph.end type="italics"/></s></p><p type="head">
  
 <s>quid.<emph.end type="italics"/></s></p><p type="head"> 
  
 <s>Ex 11. Methaphy&longs;.</s></p><p type="main"> <s>Ex 11. Methaphy&longs;.</s></p><p type="main">
  
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 lap&longs;us.<emph.end type="italics"/></s></p><p type="main"> lap&longs;us.<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Qu&aelig;&longs;t. </s> <s><emph type="italics"/>Qu&aelig;&longs;t. 2. Duplex Libra. </s>
  
 <s>2. Duplex Libra. </s> 
  
 <s>Piccolomineus reiectus.<emph.end type="italics"/></s></p><p type="main"> <s>Piccolomineus reiectus.<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Qu&aelig;&longs;t. </s> <s><emph type="italics"/>Qu&aelig;&longs;t. 3. De Vecte.<emph.end type="italics"/></s></p><p type="main">
  
 <s>3. De Vecte.<emph.end type="italics"/></s></p><p type="main"> 
  
 <s><emph type="italics"/>Qu&aelig;&longs;t. </s> <s><emph type="italics"/>Qu&aelig;&longs;t. 4. De Remo; Petri Non&yuml; in Arist.
  
 <s>4. De Remo; Petri Non&yuml; in Arist.  
  
 correctio.<emph.end type="italics"/></s></p><p type="main"> correctio.<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Qu&aelig;&longs;t. </s> <s><emph type="italics"/>Qu&aelig;&longs;t. 5. De Temone Nauis.<emph.end type="italics"/></s></p><p type="main">
  
 <s>5. De Temone Nauis.<emph.end type="italics"/></s></p><p type="main"> 
  
 <s><emph type="italics"/>Qu&aelig;&longs;t. </s> 
  
 <s>6. De Antenna.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Qu&aelig;&longs;t. 6. De Antenna.<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Qu&aelig;&longs;t. </s> <s><emph type="italics"/>Qu&aelig;&longs;t. 8 De Rota.<emph.end type="italics"/></s></p><p type="main">
  
 <s>8 De Rota.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Qu&aelig;&longs;t. 9. De Trochlea, &amp; Scytali. </s>
  
 <s><emph type="italics"/>Qu&aelig;&longs;t. </s> 
  
 <s>9. De Trochlea, &amp; Scytali. </s> 
  
 <s>figura antiqu&aelig; &longs;cytalis.<emph.end type="italics"/></s></p><p type="main"> <s>figura antiqu&aelig; &longs;cytalis.<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Qu&aelig;&longs;t. </s> <s><emph type="italics"/>Qu&aelig;&longs;t. 10. De Libra vacua.<emph.end type="italics"/></s></p><p type="main">
  
 <s>10. De Libra vacua.<emph.end type="italics"/></s></p><p type="main"> 
  
 <s><emph type="italics"/>Q&ugrave;&aelig;&longs;t. </s> <s><emph type="italics"/>Q&ugrave;&aelig;&longs;t. </s>
  
 <s>11. De Curru, &amp; &longs;cytala.<emph.end type="italics"/></s></p><p type="main"> <s>11. De Curru, &amp; &longs;cytala.<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Qu&aelig;&longs;t. </s> <s><emph type="italics"/>Qu&aelig;&longs;t. 13. De lugo. </s>
  
 <s>13. De lugo. </s> 
  
 <s>De Succula.<emph.end type="italics"/></s></p><p type="main"> <s>De Succula.<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. 15. De Vmbelicis.<emph.end type="italics"/></s></p><p type="main">
  
 <s>15. De Vmbelicis.<emph.end type="italics"/></s></p><p type="main"> 
  
 <s><emph type="italics"/>Qu&aelig;&longs;t. </s> 
  
 <s>16. De ligni oblongi, ac breuis flexura.<emph.end type="italics"/></s></p><pb pagenum="17"/><p type="main"> 
  
 <s><emph type="italics"/>Qu&aelig;&longs;t. </s> 
  
 <s>17. De Cuneo.<emph.end type="italics"/></s></p><p type="main"> 
  
 <s><emph type="italics"/>Qu&aelig;&longs;t. </s> <s><emph type="italics"/>Qu&aelig;&longs;t. 16. De ligni oblongi, ac breuis flexura.<emph.end type="italics"/></s></p><pb pagenum="17"/><p type="main">
  
 <s>18. De Trochlea; error Piccolominei.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Qu&aelig;&longs;t. 17. De Cuneo.<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. 18. De Trochlea; error Piccolominei.<emph.end type="italics"/></s></p><p type="main">
  
 <s>19. De Securi. </s> <s><emph type="italics"/>Qu&aelig;&longs;t. 19. De Securi. </s>
  
 <s>Securis veteris figura, &amp; con&longs;tructio; vn&agrave; cum affectione <lb/>eius mirabili.<emph.end type="italics"/></s></p><p type="main"> <s>Securis veteris figura, &amp; con&longs;tructio; vn&agrave; cum affectione <lb/>eius mirabili.<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Qu&aelig;&longs;t. </s> <s><emph type="italics"/>Qu&aelig;&longs;t. 20. De Statera. </s>
  
 <s>20. De Statera. </s> 
  
 <s>Veteris stater&aelig; figura restaurata.<emph.end type="italics"/></s></p><p type="main"> <s>Veteris stater&aelig; figura restaurata.<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Qu&aelig;&longs;t. </s> <s><emph type="italics"/>Qu&aelig;&longs;t. 21. De Dentiforcipe.<emph.end type="italics"/></s></p><p type="main">
  
 <s>21. De Dentiforcipe.<emph.end type="italics"/></s></p><p type="main"> 
  
 <s><emph type="italics"/>Qu&aelig;&longs;t. </s> 
  
 <s>22. De Nucifrago.<emph.end type="italics"/></s></p><p type="main"> 
  
 <s><emph type="italics"/>Qu&aelig;&longs;t. </s> 
  
 <s>23. De Motibus in Rhombo.<emph.end type="italics"/></s></p><p type="main"> 
  
 <s><emph type="italics"/>Qu&aelig;&longs;t. </s> 
  
 <s>24. De duobus circulis concentricis.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Qu&aelig;&longs;t. 22. De Nucifrago.<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. 23. De Motibus in Rhombo.<emph.end type="italics"/></s></p><p type="main">
  
 <s>25. De funibus lectulorum.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Qu&aelig;&longs;t. 24. De duobus circulis concentricis.<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. 25. De funibus lectulorum.<emph.end type="italics"/></s></p><p type="main">
  
 <s>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. </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>28. De Tollenone.<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. </s> 
  
 <s>29. De onere &agrave; duobus phalanga ge&longs;iato.<emph.end type="italics"/></s></p><p type="main"> 
  
 <s><emph type="italics"/>Qu&aelig;&longs;t. </s> 
  
 <s>30. De &longs;urgente &agrave; &longs;e&longs;&longs;ione.<emph.end type="italics"/></s></p><p type="head"> 
  
 <s>In libello De Mundo ad Alex.</s></p><p type="main"> <s>In libello De Mundo ad Alex.</s></p><p type="main">
  
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 <s><emph type="italics"/>Nu. </s> <s><emph type="italics"/>Nu. </s>
  
 <s>100. De <gap/>&longs;tro, error Ari&longs;t. </s> <s>100. De <gap/>&longs;tro, error Ari&longs;t. &amp; veterum Geographorum.<emph.end type="italics"/></s></p><p type="head">
  
 <s>&amp; veterum Geographorum.<emph.end type="italics"/></s></p><p type="head"> 
  
 <s>In libello De lineis in&longs;ecabilibus.</s></p><p type="main"> <s>In libello De lineis in&longs;ecabilibus.</s></p><p type="main">
  
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 <s><emph type="italics"/>Cap.  <s><emph type="italics"/>Cap.
  
 39. error Ari&longs;t. </s> 39. error Ari&longs;t. &amp; noua ob&longs;eruatio de admiranda quadam Aranearum indu&longs;tria.<emph.end type="italics"/></s></p><p type="head">
  
 <s>&amp; noua ob&longs;eruatio de admiranda quadam Aranearum indu&longs;tria.<emph.end type="italics"/></s></p><p type="head"> 
  
 <s>De Ince&longs;&longs;u Animal.</s></p><p type="main"> <s>De Ince&longs;&longs;u Animal.</s></p><p type="main">
  
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 <s>De Generatione Animal.</s></p><p type="main"> <s>De Generatione Animal.</s></p><p type="main">
  
 <s><emph type="italics"/>Lib. </s> <s><emph type="italics"/>Lib. 2. cap.
  
 <s>2. cap.  
  
 1. Automata.<emph.end type="italics"/></s></p><p type="main"> 1. Automata.<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Lib. </s> <s><emph type="italics"/>Lib. 2. cap.
  
 <s>2. cap.  
  
 4. Omnis triangulus habet tres, &amp;c. </s> 4. Omnis triangulus habet tres, &amp;c. </s>
  
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 <s>In Ethicis ad Nicom.</s></p><p type="main"> <s>In Ethicis ad Nicom.</s></p><p type="main">
  
 <s><emph type="italics"/>Lib. </s> <s><emph type="italics"/>Lib. 1. cap.
  
 <s>1. cap.  
  
 7. Faber, &amp; Geometra diuers&egrave; con&longs;iderant angulum rectum.<emph.end type="italics"/></s></p><p type="main"> 7. Faber, &amp; Geometra diuers&egrave; con&longs;iderant angulum rectum.<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Lib. </s> <s><emph type="italics"/>Lib. 2. cap.
  
 <s>2. cap.  
  
 6. De Arithmetica proportione.<emph.end type="italics"/></s></p><p type="main"> 6. De Arithmetica proportione.<emph.end type="italics"/></s></p><p type="main">
  
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 9. Centrum circuli reperire.<emph.end type="italics"/></s></p><p type="main"> 9. Centrum circuli reperire.<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Lib. </s> <s><emph type="italics"/>Lib. 3. cap. 3. Diameter, &amp; latus incommen&longs;urabilis: Item quid re&longs;olutio Geome&shy;<lb/>trica: Quid de&longs;ignatio.<emph.end type="italics"/></s></p><p type="main">
  
 <s>3. cap. </s> 
  
 <s>3. Diameter, &amp; latus incommen&longs;urabilis: Item quid re&longs;olutio Geome&shy;<lb/>trica: Quid de&longs;ignatio.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Lib. 5. cap.
  
 <s><emph type="italics"/>Lib. </s> 
  
 <s>5. cap.  
  
 3. Vnitarius numerus. </s> 3. Vnitarius numerus. </s>
  
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 6. Proportio Geometrica, &amp; Arithmetica.<emph.end type="italics"/></s></p><p type="main"> 6. Proportio Geometrica, &amp; Arithmetica.<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Lib. </s> <s><emph type="italics"/>Lib. 6. cap.
  
 <s>6. cap.  
  
 5. Omnis triangulus, &amp;c.<emph.end type="italics"/></s></p><p type="main"> 5. Omnis triangulus, &amp;c.<emph.end type="italics"/></s></p><p type="main">
  
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 8. Principia Mathematica non pendere ab experientia.<emph.end type="italics"/></s></p><p type="main"> 8. Principia Mathematica non pendere ab experientia.<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Lib. </s> <s><emph type="italics"/>Lib. 7. cap. 8. De principijs Mathem.<emph.end type="italics"/></s></p><p type="head">
  
 <s>7. cap. </s> 
  
 <s>8. De principijs Mathem.<emph.end type="italics"/></s></p><p type="head"> 
  
 <s>Ex 1. Magnorum Moralium.</s></p><p type="main"> <s>Ex 1. Magnorum Moralium.</s></p><p type="main">
  
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 <s><emph type="italics"/>Primo. </s> <s><emph type="italics"/>Primo. </s>
  
 <s>De &longs;ubiecto Mathem. </s> <s>De &longs;ubiecto Mathem. &longs;eu de materia intelligibili: vbi o&longs;tenduntur definitio&shy;<lb/>nes Mathematic&aelig; e&longs;&longs;e perfecti&longs;&longs;im&aelig;.<emph.end type="italics"/></s></p><p type="main">
  
 <s>&longs;eu de materia intelligibili: vbi o&longs;tenduntur definitio&shy;<lb/>nes Mathematic&aelig; e&longs;&longs;e perfecti&longs;&longs;im&aelig;.<emph.end type="italics"/></s></p><p type="main"> 
  
 <s>2. <emph type="italics"/>Demon&longs;trationes Mathematicas e&longs;&longs;e perfecti&longs;&longs;imas.<emph.end type="italics"/></s></p><p type="main"> <s>2. <emph type="italics"/>Demon&longs;trationes Mathematicas e&longs;&longs;e perfecti&longs;&longs;imas.<emph.end type="italics"/></s></p><p type="main">
  
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 <s><emph type="italics"/>Quo loca Aristotelis Geometrica, in hoc Opere explicata, <lb/>ad Euclidem, &longs;ecundum propo&longs;itionum ordinem refe&shy;<lb/>runtur; vt Mathematicarum Profe&longs;&longs;ores habeant, <lb/>vnde &longs;uas pr&aelig;lectiones aliquando valeant locupletare.<emph.end type="italics"/></s></p><p type="head"> <s><emph type="italics"/>Quo loca Aristotelis Geometrica, in hoc Opere explicata, <lb/>ad Euclidem, &longs;ecundum propo&longs;itionum ordinem refe&shy;<lb/>runtur; vt Mathematicarum Profe&longs;&longs;ores habeant, <lb/>vnde &longs;uas pr&aelig;lectiones aliquando valeant locupletare.<emph.end type="italics"/></s></p><p type="head">
  
 <s><emph type="italics"/>In Primo Elem. </s> <s><emph type="italics"/>In Primo Elem.
  
 <s>Euclidis.<emph.end type="italics"/></s></p><p type="main"> Euclidis.<emph.end type="italics"/></s></p><p type="main">
  
 <s>Ad verbum ip&longs;um <emph type="italics"/>(Elementum Euclidis)<emph.end type="italics"/> vide infra tex. </s> <s>Ad verbum ip&longs;um <emph type="italics"/>(Elementum Euclidis)<emph.end type="italics"/> vide infra tex. </s>
  
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 <s>1. primi Po&longs;ter.</s></p><p type="main"> <s>1. primi Po&longs;ter.</s></p><p type="main">
  
 <s>Ad primam primi, po&longs;t ip&longs;ius explicationem, commod&egrave; declarari pote&longs;t, cur <lb/>Ari&longs;t. </s> <s>Ad primam primi, po&longs;t ip&longs;ius explicationem, commod&egrave; declarari pote&longs;t, cur <lb/>Ari&longs;t. Demon&longs;trationes Geometricas appellet De&longs;criptiones, &amp; De&longs;igna&shy;<lb/>tiones, vide cap.
  
 <s>Demon&longs;trationes Geometricas appellet De&longs;criptiones, &amp; De&longs;igna&shy;<lb/>tiones, vide cap.  
  
 de Priori, &amp; cap.  de Priori, &amp; cap.
  
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 <s>Item ad primam primi, vide tex. </s> <s>Item ad primam primi, vide tex. </s>
  
 <s>7. &longs;ecundi Po&longs;ter. </s> <s>7. &longs;ecundi Po&longs;ter. loco 2.</s></p><p type="main">
  
 <s>loco 2.</s></p><p type="main"> 
  
 <s>Ad 5. primi, vide cap.  <s>Ad 5. primi, vide cap.
  
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 26. &longs;ecundi <expan abbr="Prior&utilde;">Priorum</expan>, &amp; tex. </s> 26. &longs;ecundi <expan abbr="Prior&utilde;">Priorum</expan>, &amp; tex. </s>
  
 <s>2. <lb/>primi Po&longs;ter. </s> <s>2. <lb/>primi Po&longs;ter. loco 4. &amp; tex. </s>
  
 <s>loco 4. &amp; tex. </s> 
  
 <s>23. primi Po&longs;ter. </s> <s>23. primi Po&longs;ter. </s>
  
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 <s>&amp; tex. </s> <s>&amp; tex. </s>
  
 <s>37. primi Po&longs;ter. </s> <s>37. primi Po&longs;ter. &amp; tex. </s>
  
 <s>&amp; tex. </s> 
  
 <s>39. primi Po&longs;ter. </s> <s>39. primi Po&longs;ter. </s>
  
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 <s>&amp; tex. </s> <s>&amp; tex. </s>
  
 <s>89. &longs;e&shy;<lb/>cundi Phy&longs;. </s> <s>89. &longs;e&shy;<lb/>cundi Phy&longs;. &amp; tex. </s>
  
 <s>&amp; tex. </s> 
  
 <s>15. octaui Phy&longs;. </s> <s>15. octaui Phy&longs;. </s>
  
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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; <lb/>cap.  <s>&amp; <lb/>cap.
  
 2. Magnorum Moral. </s> 2. Magnorum Moral. &amp; cap.
  
 <s>&amp; cap.  
  
 10. Mag. </s> 
  
 <s>Moral. </s> 10. Mag. Moral. &amp; cap. 16. Mag. Moral. <lb/></s>
  
 <s>&amp; cap. </s> <s>&amp; cap. </s>
  
 <s>16. Mag. </s> <s>7. &longs;ecundi Eudem. &amp; cap. </s>
  
 <s>Moral. <lb/></s> 
  
 <s>&amp; cap. </s> 
  
 <s>7. &longs;ecundi Eudem. </s> 
  
 <s>&amp; cap. </s> 
  
 <s>12. &longs;ecundi Eudem. </s> <s>12. &longs;ecundi Eudem. </s>
  
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 <s>Ad &longs;cholion pr&aelig;cedentis 32. primi, vide tex. </s> <s>Ad &longs;cholion pr&aelig;cedentis 32. primi, vide tex. </s>
  
 <s>39. primi Po&longs;ter. </s> <s>39. primi Po&longs;ter. loco 3. Item <lb/>tex. </s>
  
 <s>loco 3. Item <lb/>tex. </s> 
  
 <s>25. &longs;ecundi Po&longs;ter. </s> <s>25. &longs;ecundi Po&longs;ter. </s>
  
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 31. &longs;ecundi Priorum, &amp; <lb/>tex. </s> 31. &longs;ecundi Priorum, &amp; <lb/>tex. </s>
  
 <s>23. primi Po&longs;ter. </s> <s>23. primi Po&longs;ter. &amp; finem 1. cap. primi Elenchorum. </s>
  
 <s>&amp; finem 1. cap. </s> 
  
 <s>primi Elenchorum. </s> 
  
 <s>lege primam Ar&shy;<lb/>chimedis de dimen&longs;ione circuli.</s></p><p type="head"> <s>lege primam Ar&shy;<lb/>chimedis de dimen&longs;ione circuli.</s></p><p type="head">
  
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 <s>Ad 31. tertij, vide tex. </s> <s>Ad 31. tertij, vide tex. </s>
  
 <s>11. &longs;ecundi Po&longs;ter. </s> <s>11. &longs;ecundi Po&longs;ter. &amp; tex. </s>
  
 <s>&amp; tex. </s> 
  
 <s>20. &longs;exti Methaph. </s> <s>20. &longs;exti Methaph. </s>
  
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 5. Ethyc. </s> 5. Ethyc. </s>
  
 <s>loco 4. &amp; cap. </s> <s>loco 4. &amp; cap. 31. primi Ma&shy;<lb/>gnorum Moralium.</s></p><p type="main">
  
 <s>31. primi Ma&shy;<lb/>gnorum Moralium.</s></p><p type="main"> 
  
 <s>Ad 10. definitionem 5. vide tex. </s> <s>Ad 10. definitionem 5. vide tex. </s>
  
 <s>29. primi Po&longs;ter. </s> <s>29. primi Po&longs;ter. loco 2.</s></p><p type="main">
  
 <s>loco 2.</s></p><p type="main"> 
  
 <s>Ad 12. definitionem 5. vide tex. </s> <s>Ad 12. definitionem 5. vide tex. </s>
  
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 <s>5. vide tex. </s> <s>5. vide tex. </s>
  
 <s>25. &longs;ecundi Po&longs;ter. </s> <s>25. &longs;ecundi Po&longs;ter. loco 2. ex hac Euclidis demon&shy;<lb/>&longs;tratione patet, vitio&longs;am e&longs;&longs;e illam Auerrois argumentationem, 8. Phy&longs;. <lb/></s>
  
 <s>loco 2. ex hac Euclidis demon&shy;<lb/>&longs;tratione patet, vitio&longs;am e&longs;&longs;e illam Auerrois argumentationem, 8. Phy&longs;. <lb/></s> 
  
 <s>comm. </s> <s>comm. </s>
  
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 <s>9. vide tex. </s> <s>9. vide tex. </s>
  
 <s>20. primi Po&longs;ter. </s> <s>20. primi Po&longs;ter. loco 2.</s></p><p type="main">
  
 <s>loco 2.</s></p><p type="main"> 
  
 <s>Ad 8. propo&longs;. </s> <s>Ad 8. propo&longs;. </s>
  
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 23. li&shy;<lb/>bri 1. Priorum. </s> 23. li&shy;<lb/>bri 1. Priorum. </s>
  
 <s>&amp; cap. </s> <s>&amp; cap. 22. lib.
  
 <s>22. lib.  
  
 2. Priorum. </s> 2. Priorum. </s>
  
 <s>&amp; tex. </s> <s>&amp; tex. </s>
  
 <s>5. primi Po&longs;ter. </s> <s>5. primi Po&longs;ter. &amp; tex. </s>
  
 <s>&amp; tex. </s> 
  
 <s>44. <lb/>primi Po&longs;ter. </s> <s>44. <lb/>primi Po&longs;ter. </s>
  
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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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 3. Ethyc. </s> 3. Ethyc. </s>
  
 <s>&amp; cap. </s> <s>&amp; cap. 10. &longs;ecundi Eu&shy;<lb/>dem. </s>
  
 <s>10. &longs;ecundi Eu&shy;<lb/>dem. </s> 
  
 <s>tot Ari&longs;t.  <s>tot Ari&longs;t.
  
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 <s>Multa hac de re Pap&shy;<lb/>pus Alexandrinus lib.  <s>Multa hac de re Pap&shy;<lb/>pus Alexandrinus lib.
  
 4. Math. </s> 4. Math. coll. </s>
  
 <s>coll. </s> 
  
 <s>&amp; Ioannes Buteo vnico volumine om&shy;<lb/>nes quadraturas tain pri&longs;corum, quam recentiorum <expan abbr="c&otilde;prehen&longs;us">comprehen&longs;us</expan> e&longs;t. </s> <s>&amp; Ioannes Buteo vnico volumine om&shy;<lb/>nes quadraturas tain pri&longs;corum, quam recentiorum <expan abbr="c&otilde;prehen&longs;us">comprehen&longs;us</expan> e&longs;t. </s>
  
 <s>Qua&shy;<lb/>re qui plura cupit, eos adeat; nos tamen infra &longs;uis locis explicabimus tres <lb/>illas celebres antiquorum Antiphontis, Bri&longs;&longs;onis, &amp; Hippocratis quadra&shy;<lb/>turas, quamuis fal&longs;as, <expan abbr="quar&utilde;">quarum</expan> &longs;&aelig;pe meminit Ari&longs;t. </s> <s>Qua&shy;<lb/>re qui plura cupit, eos adeat; nos tamen infra &longs;uis locis explicabimus tres <lb/>illas celebres antiquorum Antiphontis, Bri&longs;&longs;onis, &amp; Hippocratis quadra&shy;<lb/>turas, quamuis fal&longs;as, <expan abbr="quar&utilde;">quarum</expan> &longs;&aelig;pe meminit Ari&longs;t. &amp; alij. </s>
  
 <s>&amp; alij. </s> 
  
 <s>&longs;olet autem &agrave; non&shy;<lb/>nullis di&longs;putari, vtrum quadratura i&longs;ta problematica &longs;it po&longs;&longs;ibilis, nec ne, <lb/>cum videant eam &agrave; nemine, quamuis diu magno labore perqui&longs;itam, hacte&shy;<lb/>nus adinuentam e&longs;&longs;e. </s> <s>&longs;olet autem &agrave; non&shy;<lb/>nullis di&longs;putari, vtrum quadratura i&longs;ta problematica &longs;it po&longs;&longs;ibilis, nec ne, <lb/>cum videant eam &agrave; nemine, quamuis diu magno labore perqui&longs;itam, hacte&shy;<lb/>nus adinuentam e&longs;&longs;e. </s>
  
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 de Priori <emph type="italics"/>(in &longs;cientijs demon&longs;tratiuis e&longs;t prius, &amp; po&longs;terius ordine, <lb/>elementa enim priora &longs;unt ijs, qu&aelig; de&longs;cribuntur, nam principia prior a &longs;unt theore&shy;<lb/>matibus ordine)<emph.end type="italics"/> verba illa, nam principia, &amp;c. </s> de Priori <emph type="italics"/>(in &longs;cientijs demon&longs;tratiuis e&longs;t prius, &amp; po&longs;terius ordine, <lb/>elementa enim priora &longs;unt ijs, qu&aelig; de&longs;cribuntur, nam principia prior a &longs;unt theore&shy;<lb/>matibus ordine)<emph.end type="italics"/> verba illa, nam principia, &amp;c. </s>
  
 <s>qu&aelig; non &longs;unt in antiqua tran&shy;<lb/>&longs;latione de&longs;ump&longs;imus ex ca&longs;tigati&longs;&longs;imo gr&aelig;co codice editionis Francfor&shy;<lb/>dien&longs;is, propterea quod totum hunc locum declarant; &longs;unt autem i&longs;ta, <lb/><foreign lang="greek">ai/gar arxai/ pro/terai tw_n qewrhma/twn th ta/xei.</foreign> per &longs;cientias autem demon&longs;tra&shy;<lb/>tiuas intelligendas e&longs;&longs;e hoc loco ip&longs;as Mathematicas ex eo patet, quod illis <lb/>a&longs;&longs;ignet Ari&longs;t. </s> <s>qu&aelig; non &longs;unt in antiqua tran&shy;<lb/>&longs;latione de&longs;ump&longs;imus ex ca&longs;tigati&longs;&longs;imo gr&aelig;co codice editionis Francfor&shy;<lb/>dien&longs;is, propterea quod totum hunc locum declarant; &longs;unt autem i&longs;ta, <lb/><foreign lang="greek">ai/gar arxai/ pro/terai tw_n qewrhma/twn th ta/xei.</foreign> per &longs;cientias autem demon&longs;tra&shy;<lb/>tiuas intelligendas e&longs;&longs;e hoc loco ip&longs;as Mathematicas ex eo patet, quod illis <lb/>a&longs;&longs;ignet Ari&longs;t. De&longs;criptiones; nam hoc verbo, De&longs;criptiones, &longs;eu figuratio&shy;<lb/>nes, &longs;olet ip&longs;e Mathematicas Demon&longs;trationes innuere, quod in ip&longs;is figu&shy;<lb/>rationes, &amp; De&longs;criptiones adhibeantur, vt alijs locis patebit: idcirco ver&shy;<lb/>ba illa &agrave; nobis addita ex gr&aelig;co, optim &egrave; <expan abbr="pr&aelig;ced&etilde;tia">pr&aelig;cedentia</expan> exponunt, cum per ele&shy;<lb/>menta intelligantur principia, qualia funt initio Euclidis, &amp; per de&longs;criptio&shy;<lb/>nes exponant theoremata. </s>
  
 <s>De&longs;criptiones; nam hoc verbo, De&longs;criptiones, &longs;eu figuratio&shy;<lb/>nes, &longs;olet ip&longs;e Mathematicas Demon&longs;trationes innuere, quod in ip&longs;is figu&shy;<lb/>rationes, &amp; De&longs;criptiones adhibeantur, vt alijs locis patebit: idcirco ver&shy;<lb/>ba illa &agrave; nobis addita ex gr&aelig;co, optim &egrave; <expan abbr="pr&aelig;ced&etilde;tia">pr&aelig;cedentia</expan> exponunt, cum per ele&shy;<lb/>menta intelligantur principia, qualia funt initio Euclidis, &amp; per de&longs;criptio&shy;<lb/>nes exponant theoremata. </s> 
  
 <s>quod autem principia illa ordine priora &longs;int de&shy;<lb/>mon&longs;trationibus, &longs;iue ip&longs;as pr&aelig;cedant, ex ip&longs;a primi Euclidis in&longs;pectione <lb/>patere pote&longs;t.</s></p><p type="main"> <s>quod autem principia illa ordine priora &longs;int de&shy;<lb/>mon&longs;trationibus, &longs;iue ip&longs;as pr&aelig;cedant, ex ip&longs;a primi Euclidis in&longs;pectione <lb/>patere pote&longs;t.</s></p><p type="main">
  
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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">
  
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 <s>per&longs;ua&longs;um tamen mihi e&longs;t, rem <lb/>multo aliter &longs;e habere, veram rationem huius tituli petendam e&longs;&longs;e ex peni&shy;<lb/>tiori Mathematicorum eruditione. </s> <s>per&longs;ua&longs;um tamen mihi e&longs;t, rem <lb/>multo aliter &longs;e habere, veram rationem huius tituli petendam e&longs;&longs;e ex peni&shy;<lb/>tiori Mathematicorum eruditione. </s>
  
 <s>Sciendum <expan abbr="itaq;">itaque</expan> id, quod tradit Pappus <lb/>Alex. </s> <s>Sciendum <expan abbr="itaq;">itaque</expan> id, quod tradit Pappus <lb/>Alex. initio &longs;eptimi Mathem. collect. </s>
  
 <s>initio &longs;eptimi Mathem. </s> 
  
 <s>collect. </s> 
  
 <s>antiqui&longs;&longs;imos videlicet Geometras, <lb/>Euclidem, Apollonium Perg&aelig;um, &amp; Ari&longs;t&ecedil;um &longs;crip&longs;i&longs;&longs;e libros de re&longs;olutio&shy;<lb/>ne, in quibus ars tradebatur, qua propo&longs;ito quouis theoremate, aut proble&shy;<lb/>mate po&longs;&longs;ent facile ex eo, tanquam vero accepto inue&longs;tigare aliquam veri&shy;<lb/>tatem, per quam deinde componerent illius, quod qu&aelig;rebatur, Demon&longs;tra&shy;<lb/>tionem; inue&longs;tigationem illam appellabant re&longs;olutionem: compo&longs;itionem <lb/>ver&ograve; nominabant di&longs;cur&longs;um <expan abbr="ill&utilde;">illum</expan>, quo ex vero illo per re&longs;olutionem inuento, <pb pagenum="36"/>o&longs;tendebant conclu&longs;ionem. </s> <s>antiqui&longs;&longs;imos videlicet Geometras, <lb/>Euclidem, Apollonium Perg&aelig;um, &amp; Ari&longs;t&ecedil;um &longs;crip&longs;i&longs;&longs;e libros de re&longs;olutio&shy;<lb/>ne, in quibus ars tradebatur, qua propo&longs;ito quouis theoremate, aut proble&shy;<lb/>mate po&longs;&longs;ent facile ex eo, tanquam vero accepto inue&longs;tigare aliquam veri&shy;<lb/>tatem, per quam deinde componerent illius, quod qu&aelig;rebatur, Demon&longs;tra&shy;<lb/>tionem; inue&longs;tigationem illam appellabant re&longs;olutionem: compo&longs;itionem <lb/>ver&ograve; nominabant di&longs;cur&longs;um <expan abbr="ill&utilde;">illum</expan>, quo ex vero illo per re&longs;olutionem inuento, <pb pagenum="36"/>o&longs;tendebant conclu&longs;ionem. </s>
  
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 <s>definitio <lb/><expan abbr="vtriu&longs;q;">vtriu&longs;que</expan> e&longs;t a pud Euclidem ad primam propo&longs;. </s> <s>definitio <lb/><expan abbr="vtriu&longs;q;">vtriu&longs;que</expan> e&longs;t a pud Euclidem ad primam propo&longs;. </s>
  
 <s>13. Elem.  <s>13. Elem. iuxta tran&longs;latio&shy;<lb/>nem Zamb<gap/>rti, &amp; Commandini; vbi etiam <expan abbr="quinq;">quinque</expan> priora theoremata, pri&shy;<lb/>m&ograve; per re&longs;olutionem, deinde per compo&longs;itionem demon&longs;trantur, qu&aelig; tan&shy;<lb/>quam per&longs;picua exempla rei propo&longs;it&aelig; in&longs;eruire po&longs;&longs;unt. </s>
  
 iuxta tran&longs;latio&shy;<lb/>nem Zamb<gap/>rti, &amp; Commandini; vbi etiam <expan abbr="quinq;">quinque</expan> priora theoremata, pri&shy;<lb/>m&ograve; per re&longs;olutionem, deinde per compo&longs;itionem demon&longs;trantur, qu&aelig; tan&shy;<lb/>quam per&longs;picua exempla rei propo&longs;it&aelig; in&longs;eruire po&longs;&longs;unt. </s> 
  
 <s>&longs;unt pr&aelig;terea fre&shy;<lb/>quentes huiu&longs;modi re&longs;olutiones in operibus Archimedis, Apollonij, &amp; Pap&shy;<lb/>pi. </s> <s>&longs;unt pr&aelig;terea fre&shy;<lb/>quentes huiu&longs;modi re&longs;olutiones in operibus Archimedis, Apollonij, &amp; Pap&shy;<lb/>pi. </s>
  
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 <s>&longs;i linea <lb/>C, men&longs;uraret A, quater &longs;umpta, ter autem &longs;umpta <lb/>non ad&aelig;quaret omnino <expan abbr="line&atilde;">lineam</expan> B, &longs;ed deficeret, vel ex&shy;<lb/>cederet aliquantulum, <expan abbr="atq;">atque</expan> hoc fieret in quauis alia <lb/>men&longs;ura, loco ip&longs;ius C, a&longs;&longs;umpta, &longs;iue maior, &longs;iue <lb/>minor ip&longs;a C, vt <expan abbr="vtranq;">vtranque</expan> nunquam perfect&egrave; metiretur, e&longs;&longs;ent du&aelig; ill&aelig; line&aelig; <lb/>incommen&longs;. </s> <s>&longs;i linea <lb/>C, men&longs;uraret A, quater &longs;umpta, ter autem &longs;umpta <lb/>non ad&aelig;quaret omnino <expan abbr="line&atilde;">lineam</expan> B, &longs;ed deficeret, vel ex&shy;<lb/>cederet aliquantulum, <expan abbr="atq;">atque</expan> hoc fieret in quauis alia <lb/>men&longs;ura, loco ip&longs;ius C, a&longs;&longs;umpta, &longs;iue maior, &longs;iue <lb/>minor ip&longs;a C, vt <expan abbr="vtranq;">vtranque</expan> nunquam perfect&egrave; metiretur, e&longs;&longs;ent du&aelig; ill&aelig; line&aelig; <lb/>incommen&longs;. </s>
  
 <s>Extare porr&ograve; tales lineas, &amp; &longs;uperficies, &amp; corpora, <expan abbr="ea&qacute;">eaque</expan>; quam&shy;<lb/>plurima, ac pen&egrave; infinita ex 10. Elem.  <s>Extare porr&ograve; tales lineas, &amp; &longs;uperficies, &amp; corpora, <expan abbr="ea&qacute;">eaque</expan>; quam&shy;<lb/>plurima, ac pen&egrave; infinita ex 10. Elem. manife&longs;tum e&longs;t. </s>
  
 manife&longs;tum e&longs;t. </s> 
  
 <s>inuentum autem hu&shy;<lb/>ius a&longs;ymmetri&aelig;, quod Pythagoricis veteres attribuunt, mihi &longs;emper vi&longs;um <lb/>e&longs;t omni maius admiratione, cum nulla experientia, <expan abbr="nullus&qacute;">nullusque</expan>; effectus in ip&shy;<lb/>&longs;ius cognitionem potuerit pri&longs;cos illos Geometras inducere. </s> <s>inuentum autem hu&shy;<lb/>ius a&longs;ymmetri&aelig;, quod Pythagoricis veteres attribuunt, mihi &longs;emper vi&longs;um <lb/>e&longs;t omni maius admiratione, cum nulla experientia, <expan abbr="nullus&qacute;">nullusque</expan>; effectus in ip&shy;<lb/>&longs;ius cognitionem potuerit pri&longs;cos illos Geometras inducere. </s>
  
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 <s>latus B C, pr&aelig;cis&egrave; omnino metiatur. </s> <s>latus B C, pr&aelig;cis&egrave; omnino metiatur. </s>
  
 <s>theorema <lb/>i&longs;tud demon&longs;tratur in vltima 10. Elem.  <s>theorema <lb/>i&longs;tud demon&longs;tratur in vltima 10. Elem. eodem me&shy;<lb/>dio, quod ab Ari&longs;totele hic innuitur; Euclides ex <lb/>&longs;uppo&longs;itione alterius partis contradictionis ip&longs;ius <pb pagenum="38"/>propo&longs;itionis, qu&aelig;fal&longs;a e&longs;t, nimirum &longs;uppo&longs;ito pr&aelig;dictas lineas e&longs;&longs;e comm. <lb/></s>
  
 eodem me&shy;<lb/>dio, quod ab Ari&longs;totele hic innuitur; Euclides ex <lb/>&longs;uppo&longs;itione alterius partis contradictionis ip&longs;ius <pb pagenum="38"/>propo&longs;itionis, qu&aelig;fal&longs;a e&longs;t, nimirum &longs;uppo&longs;ito pr&aelig;dictas lineas e&longs;&longs;e comm. <lb/></s> 
  
 <s>deducit ad impo&longs;&longs;ibile, &longs;iue, vt ait hic Ari&longs;t.  <s>deducit ad impo&longs;&longs;ibile, &longs;iue, vt ait hic Ari&longs;t.
  
 fal&longs;um ratiocinatur, quod &longs;ci&shy;<lb/>licet idem numerus e&longs;&longs;et par, &amp; impar, quod Ari&longs;t. </s> fal&longs;um ratiocinatur, quod &longs;ci&shy;<lb/>licet idem numerus e&longs;&longs;et par, &amp; impar, quod Ari&longs;t. &longs;ignificat, quando ait, <lb/>imparia &aelig;qualia paribus fiunt. </s>
  
 <s>&longs;ignificat, quando ait, <lb/>imparia &aelig;qualia paribus fiunt. </s> 
  
 <s>ex quo ab&longs;urdo deducitur fal&longs;am e&longs;&longs;e pr&aelig;di&shy;<lb/>ctam &longs;uppo&longs;itionem, qu&aelig; a&longs;truebat e&longs;&longs;e comm. </s> <s>ex quo ab&longs;urdo deducitur fal&longs;am e&longs;&longs;e pr&aelig;di&shy;<lb/>ctam &longs;uppo&longs;itionem, qu&aelig; a&longs;truebat e&longs;&longs;e comm. </s>
  
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 2. &longs;ecti 2. lib.  2. &longs;ecti 2. lib.
  
 1. <emph type="italics"/>(Secundum veritatem quidem ex ijs, qu&aelig; &longs;ecundum <lb/>veritatem de&longs;cribuntur ine&longs;&longs;e, ad dialecticos autem &longs;yllogi&longs;mos ex propo&longs;itionibus <lb/>&longs;ecundum opinionem)<emph.end type="italics"/> verba illa; ex ijs, qu&aelig; <expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> veritatem de&longs;cribuntur <pb pagenum="39"/>ine&longs;&longs;e; &longs;ic gr&aelig;c&egrave;, <foreign lang="greek">e/a tw_n xata\ aleiq/ei/an diagegramme/non,</foreign> vbi manife&longs;t&egrave; vtitur <lb/>verbo, De&longs;cribere, per quod &longs;uperius annotauimus apud Ari&longs;t. </s> 1. <emph type="italics"/>(Secundum veritatem quidem ex ijs, qu&aelig; &longs;ecundum <lb/>veritatem de&longs;cribuntur ine&longs;&longs;e, ad dialecticos autem &longs;yllogi&longs;mos ex propo&longs;itionibus <lb/>&longs;ecundum opinionem)<emph.end type="italics"/> verba illa; ex ijs, qu&aelig; <expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> veritatem de&longs;cribuntur <pb pagenum="39"/>ine&longs;&longs;e; &longs;ic gr&aelig;c&egrave;, <foreign lang="greek">e/a tw_n xata\ aleiq/ei/an diagegramme/non,</foreign> vbi manife&longs;t&egrave; vtitur <lb/>verbo, De&longs;cribere, per quod &longs;uperius annotauimus apud Ari&longs;t. &longs;ignificari <lb/>Geometricas demon&longs;trationes, nam eas opponit dialecticis &longs;yllogi&longs;mis, &longs;e&shy;<lb/>quentibus verbis, cum dixit (ad diale cticos autem &longs;yllogi&longs;mos ex propo&longs;i&shy;<lb/>tionibus &longs;ecundum opinionem) hac adhibita con&longs;ideratione, quam inter&shy;<lb/>pres non videtur adhibui&longs;&longs;e, &longs;en&longs;us huius loci non erit ob&longs;curus.</s></p><p type="main">
  
 <s>&longs;ignificari <lb/>Geometricas demon&longs;trationes, nam eas opponit dialecticis &longs;yllogi&longs;mis, &longs;e&shy;<lb/>quentibus verbis, cum dixit (ad diale cticos autem &longs;yllogi&longs;mos ex propo&longs;i&shy;<lb/>tionibus &longs;ecundum opinionem) hac adhibita con&longs;ideratione, quam inter&shy;<lb/>pres non videtur adhibui&longs;&longs;e, &longs;en&longs;us huius loci non erit ob&longs;curus.</s></p><p type="main"> 
  
 <s><arrow.to.target n="marg8"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg8"></arrow.to.target></s></p><p type="margin">
  
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 3. <lb/>in comm. </s> 3. <lb/>in comm. </s>
  
 <s>Elem. </s> <s>Elem.
  
 <s>Euclidis ad primam propo&longs;itionem primi Elementi, pag. <lb/></s> Euclidis ad primam propo&longs;itionem primi Elementi, pag. <lb/></s>
  
 <s>121. &longs;ic ait, Abductio ver&ograve; e&longs;t tran&longs;itus &agrave; propo&longs;ito problemate, vel theo&shy;<lb/>remate ad aliud, quo cognito, aut comparato Propo&longs;itum quoque per&longs;pi&shy;<lb/>cuum e&longs;t. </s> <s>121. &longs;ic ait, Abductio ver&ograve; e&longs;t tran&longs;itus &agrave; propo&longs;ito problemate, vel theo&shy;<lb/>remate ad aliud, quo cognito, aut comparato Propo&longs;itum quoque per&longs;pi&shy;<lb/>cuum e&longs;t. </s>
  
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 <s>&amp; <expan abbr="quo-ni&atilde;">quo&shy;<lb/>niam</expan> diameter L M, dupla e&longs;t <expan abbr="vniu&longs;-cuiu&longs;q;">vniu&longs;&shy;<lb/>cuiu&longs;que</expan> <expan abbr="diametror&utilde;">diametrorum</expan> B C, L Q, Q S, <lb/>S M, erit &longs;emicirculus L O M, &ecedil;qua&shy;<lb/>lis quatuor &longs;emicirculis pr&aelig;dictis <lb/>per 2. duodecimi, &amp; per 4. &longs;ecundi <lb/>ablatis igitur tribus <expan abbr="&longs;egm&etilde;tis">&longs;egmentis</expan> com&shy;<lb/>munibus L N Q, Q O S, S P M, relinquetur trapezium L Q S M, &aelig;quale &longs;e&shy;<lb/>micirculo B A C, &amp; tribus lunulis L H Q N, Q R S O, S X M P, ab&longs;cindan&shy;<lb/>tur <expan abbr="itaq;">itaque</expan> detrapezio tria triangula &aelig;qualia tribus lunulis, eo modo, quo &longs;u&shy;<lb/>pra in prima figura factum e&longs;t, &amp; quod relinquetur &aelig;quale erit &longs;emicirculo <lb/>B A C. quod deinde quadretur per vlt. </s> <s>&amp; <expan abbr="quo-ni&atilde;">quo&shy;<lb/>niam</expan> diameter L M, dupla e&longs;t <expan abbr="vniu&longs;-cuiu&longs;q;">vniu&longs;&shy;<lb/>cuiu&longs;que</expan> <expan abbr="diametror&utilde;">diametrorum</expan> B C, L Q, Q S, <lb/>S M, erit &longs;emicirculus L O M, &ecedil;qua&shy;<lb/>lis quatuor &longs;emicirculis pr&aelig;dictis <lb/>per 2. duodecimi, &amp; per 4. &longs;ecundi <lb/>ablatis igitur tribus <expan abbr="&longs;egm&etilde;tis">&longs;egmentis</expan> com&shy;<lb/>munibus L N Q, Q O S, S P M, relinquetur trapezium L Q S M, &aelig;quale &longs;e&shy;<lb/>micirculo B A C, &amp; tribus lunulis L H Q N, Q R S O, S X M P, ab&longs;cindan&shy;<lb/>tur <expan abbr="itaq;">itaque</expan> detrapezio tria triangula &aelig;qualia tribus lunulis, eo modo, quo &longs;u&shy;<lb/>pra in prima figura factum e&longs;t, &amp; quod relinquetur &aelig;quale erit &longs;emicirculo <lb/>B A C. quod deinde quadretur per vlt. </s>
  
 <s>&longs;ecundi, &longs;ed aduerte, quod quando <lb/>ait, ab&longs;cindantur de trapezio tria triangula &aelig;qualia lunulis, eo modo, quo <lb/>&longs;upra, committit deceptionem, quia eodem modo, quo &longs;upra minim&egrave; id fa&shy;<lb/>cere po&longs;&longs;umus, quia in &longs;uperiori figura triangula erant con&longs;tituta &longs;uper la&shy;<lb/>tus B C, quadrati B C D F, intra circulum de&longs;cripti, qui circulus facit cum <lb/>B C, maius <expan abbr="&longs;egment&utilde;">&longs;egmentum</expan>, quam faciat &longs;emicirculus L O M, cum lateribus L Q, <lb/>Q S, S M. &amp; propterea &longs;emicirculus i&longs;te non habet eandem proportionem <lb/>ad vnamquamque lunularum &longs;uarum, quam habet &longs;emicirculus &longs;uperior <lb/>B C D, ad lunulam B A C E. <expan abbr="atq;">atque</expan> h&aelig;c e&longs;t fallacia, quam authorem &longs;uum mi&shy;<lb/>nim&egrave; latui&longs;&longs;e putandum, cuius Ari&longs;t. </s> <s>&longs;ecundi, &longs;ed aduerte, quod quando <lb/>ait, ab&longs;cindantur de trapezio tria triangula &aelig;qualia lunulis, eo modo, quo <lb/>&longs;upra, committit deceptionem, quia eodem modo, quo &longs;upra minim&egrave; id fa&shy;<lb/>cere po&longs;&longs;umus, quia in &longs;uperiori figura triangula erant con&longs;tituta &longs;uper la&shy;<lb/>tus B C, quadrati B C D F, intra circulum de&longs;cripti, qui circulus facit cum <lb/>B C, maius <expan abbr="&longs;egment&utilde;">&longs;egmentum</expan>, quam faciat &longs;emicirculus L O M, cum lateribus L Q, <lb/>Q S, S M. &amp; propterea &longs;emicirculus i&longs;te non habet eandem proportionem <lb/>ad vnamquamque lunularum &longs;uarum, quam habet &longs;emicirculus &longs;uperior <lb/>B C D, ad lunulam B A C E. <expan abbr="atq;">atque</expan> h&aelig;c e&longs;t fallacia, quam authorem &longs;uum mi&shy;<lb/>nim&egrave; latui&longs;&longs;e putandum, cuius Ari&longs;t. &longs;&aelig;pius mentionem in &longs;equentibus fa&shy;<lb/>ciet : qu&igrave; enim fieri pote&longs;t, vt tam acutus inuentor, adeo manife&longs;tum erro&shy;<lb/>rem non vidi&longs;&longs;et, verum propter adinuenti excellentiam, authori &longs;uo pla&shy;<lb/>cuit paralogy&longs;mus. </s>
  
 <s>&longs;&aelig;pius mentionem in &longs;equentibus fa&shy;<lb/>ciet : qu&igrave; enim fieri pote&longs;t, vt tam acutus inuentor, adeo manife&longs;tum erro&shy;<lb/>rem non vidi&longs;&longs;et, verum propter adinuenti excellentiam, authori &longs;uo pla&shy;<lb/>cuit paralogy&longs;mus. </s> 
  
 <s>mirabilis tamen &longs;emper habita e&longs;t illa &longs;uperior lunul&aelig; <lb/>quadratio. </s> <s>mirabilis tamen &longs;emper habita e&longs;t illa &longs;uperior lunul&aelig; <lb/>quadratio. </s>
  
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 <s><margin.target id="marg19"></margin.target>19</s></p><p type="main"> <s><margin.target id="marg19"></margin.target>19</s></p><p type="main">
  
 <s>Tex. </s> <s>Tex. 2. <emph type="italics"/>(Quod enim omne triangulum habet duobus rectis &aelig;quales, pr&aelig;&longs;ciuit: <lb/>quod autem hoc, quod e&longs;t in &longs;emicirculo triangulum e&longs;t, &longs;imul inducens cognouit)<emph.end type="italics"/><lb/>vide primo, qu&aelig; &longs;upra libro 1. Prior. </s>
  
 <s>2. <emph type="italics"/>(Quod enim omne triangulum habet duobus rectis &aelig;quales, pr&aelig;&longs;ciuit: <lb/>quod autem hoc, quod e&longs;t in &longs;emicirculo triangulum e&longs;t, &longs;imul inducens cognouit)<emph.end type="italics"/><lb/>vide primo, qu&aelig; &longs;upra libro 1. Prior. </s> 
  
 <s>&longs;ecto 3. cap.  <s>&longs;ecto 3. cap.
  
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 ait, hoc, quod e&longs;t in &longs;emicir cu&shy;<lb/>lo triangulum, &amp;c. </s> ait, hoc, quod e&longs;t in &longs;emicir cu&shy;<lb/>lo triangulum, &amp;c. </s>
  
 <s>alludit ad demon&longs;trationem quandam, quam ip&longs;e infe&shy;<lb/>rius in exemplum adducet, &amp; qu&aelig; e&longs;t in 3. Elem. </s> <s>alludit ad demon&longs;trationem quandam, quam ip&longs;e infe&shy;<lb/>rius in exemplum adducet, &amp; qu&aelig; e&longs;t in 3. Elem.
  
 <s>Euclidis 31. in qua talis fi&shy;<lb/>gura proponitur qualis e&longs;t pr&aelig;&longs;ens, in qua vides triangulum A B C. in &longs;e&shy;<lb/><figure id="fig15"></figure><lb/>micirculo. </s> Euclidis 31. in qua talis fi&shy;<lb/>gura proponitur qualis e&longs;t pr&aelig;&longs;ens, in qua vides triangulum A B C. in &longs;e&shy;<lb/><figure id="fig15"></figure><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">
  
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 <s><margin.target id="marg20"></margin.target>20</s></p><p type="main"> <s><margin.target id="marg20"></margin.target>20</s></p><p type="main">
  
 <s>Tex. </s> <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>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">
  
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 <s>Hoc eodem cap.  <s>Hoc eodem cap.
  
 plura dicuntur de Principijs Demon&longs;trationis, &longs;iue &longs;cien&shy;<lb/>ti&aelig;, vt &longs;unt Dignitates, Po&longs;itiones, Definitiones, &amp; &longs;imilia, qu&aelig; quo modo <lb/>&longs;e habeant, &amp; quo modo illis Demon&longs;trationes innitantur, optim&egrave; ex con&shy;<lb/>templatione primi libri Elem. </s> plura dicuntur de Principijs Demon&longs;trationis, &longs;iue &longs;cien&shy;<lb/>ti&aelig;, vt &longs;unt Dignitates, Po&longs;itiones, Definitiones, &amp; &longs;imilia, qu&aelig; quo modo <lb/>&longs;e habeant, &amp; quo modo illis Demon&longs;trationes innitantur, optim&egrave; ex con&shy;<lb/>templatione primi libri Elem.
  
 <s>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> Euclidis percipi pote&longs;t. </s>
  
 <s>Mathematicas &longs;cientias tamquam typum perfecti&longs;simarum &longs;cientiarum <lb/>&longs;ibi ob oculos propo&longs;ui&longs;&longs;e; ex quo typo ver&aelig; &longs;cienti&aelig; de&longs;criptionem his li&shy;<lb/>bris complectaretur.</s></p><p type="main"> <s>vt propterea ben&egrave; ij <lb/>&longs;entiant, inter quos pr&aelig;cipui &longs;unt Toletus, &amp; Zabarella, qui a&longs;&longs;erunt, Ari&longs;t. <lb/>Mathematicas &longs;cientias tamquam typum perfecti&longs;simarum &longs;cientiarum <lb/>&longs;ibi ob oculos propo&longs;ui&longs;&longs;e; ex quo typo ver&aelig; &longs;cienti&aelig; de&longs;criptionem his li&shy;<lb/>bris complectaretur.</s></p><p type="main">
  
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 <s>Tex. </s> <s>Tex. 9. <emph type="italics"/>(Per &longs;e autem, <expan abbr="qu&aelig;cunq;">qu&aelig;cunque</expan> &amp; in&longs;unt in eo, quod quid e&longs;t, vt triangulo li&shy;<lb/>nea, &amp; line&aelig; punctum; &longs;ub&longs;tantia <expan abbr="namq;">namque</expan> ip&longs;orum ex his e&longs;t, &amp; in oratione dicen&shy;<lb/>te, quid e&longs;t, in&longs;unt)<emph.end type="italics"/> aggreditur explicare qu&aelig;nam &longs;int ea, qu&aelig; per &longs;e dicun&shy;<lb/>tur: <expan abbr="quot&qacute;">quotque</expan>; modis dicatur aliquid per &longs;e. </s>
  
 <s>9. <emph type="italics"/>(Per &longs;e autem, <expan abbr="qu&aelig;cunq;">qu&aelig;cunque</expan> &amp; in&longs;unt in eo, quod quid e&longs;t, vt triangulo li&shy;<lb/>nea, &amp; line&aelig; punctum; &longs;ub&longs;tantia <expan abbr="namq;">namque</expan> ip&longs;orum ex his e&longs;t, &amp; in oratione dicen&shy;<lb/>te, quid e&longs;t, in&longs;unt)<emph.end type="italics"/> aggreditur explicare qu&aelig;nam &longs;int ea, qu&aelig; per &longs;e dicun&shy;<lb/>tur: <expan abbr="quot&qacute;">quotque</expan>; modis dicatur aliquid per &longs;e. </s> 
  
 <s>quorum primus e&longs;t, ea &longs;cilicet, <lb/>per &longs;e de aliquo &longs;ubiecto dici, <expan abbr="qu&aelig;cunq;">qu&aelig;cunque</expan> in definitione illius ponuntur, cu&shy;<lb/>iu&longs;modi &longs;unt linea, &amp; punctum, qu&aelig; per &longs;e pr&aelig;dicantur, illa de triangulo, <lb/>i&longs;tud de linea; in de&longs;initione enim trianguli ponitur linea recta, quia linea <lb/>recta dum terminat illam &longs;uperficiem, qu&aelig; dicitur triangulus illi trianguli <lb/>naturam impertitur, &amp; ideo triangulus definitur &longs;ic, triangulus e&longs;t figura <lb/>tribus lineis rectis terminata. </s> <s>quorum primus e&longs;t, ea &longs;cilicet, <lb/>per &longs;e de aliquo &longs;ubiecto dici, <expan abbr="qu&aelig;cunq;">qu&aelig;cunque</expan> in definitione illius ponuntur, cu&shy;<lb/>iu&longs;modi &longs;unt linea, &amp; punctum, qu&aelig; per &longs;e pr&aelig;dicantur, illa de triangulo, <lb/>i&longs;tud de linea; in de&longs;initione enim trianguli ponitur linea recta, quia linea <lb/>recta dum terminat illam &longs;uperficiem, qu&aelig; dicitur triangulus illi trianguli <lb/>naturam impertitur, &amp; ideo triangulus definitur &longs;ic, triangulus e&longs;t figura <lb/>tribus lineis rectis terminata. </s>
  
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 <s>Tex. </s> <s>Tex. 11. <emph type="italics"/>(Per &longs;e autem, &amp; &longs;ecundum quod ip&longs;um, idem, vt per &longs;e line&aelig; inest<emph.end type="italics"/><pb pagenum="49"/><emph type="italics"/>punctum, &amp; rectum; etenim &longs;ecundum quod linea, &amp; triangulo, &longs;ecundum quod <lb/>triangulum duo recti: etenim per &longs;e triangulum duobus rectis &aelig;quale. </s>
  
 <s>11. <emph type="italics"/>(Per &longs;e autem, &amp; &longs;ecundum quod ip&longs;um, idem, vt per &longs;e line&aelig; inest<emph.end type="italics"/><pb pagenum="49"/><emph type="italics"/>punctum, &amp; rectum; etenim &longs;ecundum quod linea, &amp; triangulo, &longs;ecundum quod <lb/>triangulum duo recti: etenim per &longs;e triangulum duobus rectis &aelig;quale. </s> 
  
 <s>Vniuer&longs;ale <lb/>autem e&longs;t tunc, quando in quolibet, &amp; primo mon&longs;tratur, vt duos rectos habere, <lb/><expan abbr="neq;">neque</expan> figur&aelig; e&longs;t vniuer&longs;ale, quamuis e&longs;t mon&longs;irare de figura, quod duos rectos habet, <lb/>&longs;ed non de qualibet figura, <expan abbr="neq;">neque</expan> vtitur qualibet figura monstrans, quadrangulum <lb/>enim figura a quidem est, non habet autem duobus rectis &aelig;quales. </s> <s>Vniuer&longs;ale <lb/>autem e&longs;t tunc, quando in quolibet, &amp; primo mon&longs;tratur, vt duos rectos habere, <lb/><expan abbr="neq;">neque</expan> figur&aelig; e&longs;t vniuer&longs;ale, quamuis e&longs;t mon&longs;irare de figura, quod duos rectos habet, <lb/>&longs;ed non de qualibet figura, <expan abbr="neq;">neque</expan> vtitur qualibet figura monstrans, quadrangulum <lb/>enim figura a quidem est, non habet autem duobus rectis &aelig;quales. </s>
  
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 <s>Tex. </s> <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>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"></figure><lb/>cen&longs;ui. </s>
  
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 <s>Tex. </s> <s>Tex. 20. <emph type="italics"/>(Ni&longs;i magnitudines numeri &longs;int)<emph.end type="italics"/> hoc e&longs;t, ni&longs;i magnitudines &longs;int di&shy;<lb/>fcret&aelig;, ita vt cadant &longs;ub numernm, vt &longs;i linea qu&aelig;piam diuidatur in partes <lb/>decem, vel duodecim, tunc euadit quantitas di&longs;creta, &longs;iue numerus. </s>
  
 <s>20. <emph type="italics"/>(Ni&longs;i magnitudines numeri &longs;int)<emph.end type="italics"/> hoc e&longs;t, ni&longs;i magnitudines &longs;int di&shy;<lb/>fcret&aelig;, ita vt cadant &longs;ub numernm, vt &longs;i linea qu&aelig;piam diuidatur in partes <lb/>decem, vel duodecim, tunc euadit quantitas di&longs;creta, &longs;iue numerus. </s> 
  
 <s>&amp; tunc <lb/>linca numerus e&longs;t. </s> <s>&amp; tunc <lb/>linca numerus e&longs;t. </s>
  
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 <s>Tex. </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>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>
  
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 <s>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>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">
  
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 <s>Tex. </s> <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>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"></arrow.to.target></s></p><p type="margin">
  
 <s><margin.target id="marg44"></margin.target>44</s></p><p type="main"> <s><margin.target id="marg44"></margin.target>44</s></p><p type="main">
  
 <s>Tex. </s> <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>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"></arrow.to.target></s></p><p type="margin">
  
 <s><margin.target id="marg45"></margin.target>45</s></p><p type="main"> <s><margin.target id="marg45"></margin.target>45</s></p><p type="main">
  
 <s>Tex. </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>
  
 <s>29. <emph type="italics"/>(In Matbematicis ver&ograve; non est &longs;imiliter paralogi&longs;mus, quoniam me&shy;<lb/>di&ubreve; e&longs;t &longs;emper, quod duplex, de hoc enim omni, &amp; hoc rur&longs;us de alio dicitur omni)<emph.end type="italics"/><lb/>aduerte, quod quamuis nonnulli codices habeant pro, in mathematicis, in <pb pagenum="58"/>di&longs;cipli<gap/>is, idem tamen apud gr&aelig;cos <foreign lang="greek">maqhmata</foreign> &longs;unt, ac apud latinos di&longs;ci&shy;<lb/>plm&aelig;; verbum autem <foreign lang="greek">maqhmata</foreign> v&longs;urpat hoc loco Ari&longs;toteles. </s> 
  
 <s>Porr&ograve; non <lb/>e&longs;t in mathematicis, &longs;icut in alijs paralogi&longs;mus, quia in omni demon&longs;tra&shy;<lb/>tione maius extremum dicitur de omni medio, &amp; rur&longs;us medium dicitur de <lb/>omni minori extremo, ac &longs;i diceret mathematic&aelig; demon&longs;trationes &longs;unt in <lb/>primo modo, qui barbar&egrave; &agrave; latinis recentioribus Barbara appellatur. </s> <s>Porr&ograve; non <lb/>e&longs;t in mathematicis, &longs;icut in alijs paralogi&longs;mus, quia in omni demon&longs;tra&shy;<lb/>tione maius extremum dicitur de omni medio, &amp; rur&longs;us medium dicitur de <lb/>omni minori extremo, ac &longs;i diceret mathematic&aelig; demon&longs;trationes &longs;unt in <lb/>primo modo, qui barbar&egrave; &agrave; latinis recentioribus Barbara appellatur. </s>
  
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 <s>A&longs;tronomi <expan abbr="quoq;">quoque</expan> demon&longs;trant eclyp&longs;im de Luna, per in&shy;<lb/>rerpo&longs;itionem terr&aelig; inter Lunam, &amp; Solem, qu&aelig; interpo&longs;itio e&longs;t definitio <lb/>cau&longs;alis ip&longs;ius eclyp&longs;is, &longs;cilicet pa&longs;&longs;ionis. </s> <s>A&longs;tronomi <expan abbr="quoq;">quoque</expan> demon&longs;trant eclyp&longs;im de Luna, per in&shy;<lb/>rerpo&longs;itionem terr&aelig; inter Lunam, &amp; Solem, qu&aelig; interpo&longs;itio e&longs;t definitio <lb/>cau&longs;alis ip&longs;ius eclyp&longs;is, &longs;cilicet pa&longs;&longs;ionis. </s>
  
 <s>huiu&longs;modi <expan abbr="&longs;exc&etilde;tas">&longs;excentas</expan> reperies apud <lb/>Geometras, Arithmeticos, A&longs;tronomos, <expan abbr="c&aelig;teros&qacute;">c&aelig;terosque</expan>; Mathematicas demon&shy;<lb/>&longs;trationes: ita vt merit&ograve; dixerit Ari&longs;t. </s> <s>huiu&longs;modi <expan abbr="&longs;exc&etilde;tas">&longs;excentas</expan> reperies apud <lb/>Geometras, Arithmeticos, A&longs;tronomos, <expan abbr="c&aelig;teros&qacute;">c&aelig;terosque</expan>; Mathematicas demon&shy;<lb/>&longs;trationes: ita vt merit&ograve; dixerit Ari&longs;t. Mathematicas alias omnes natura&shy;<lb/>les &longs;cientias, qu&aelig; di&longs;putabilibus rationibus traduntur ex hac parte antecel&shy;<lb/>lere. </s>
  
 <s>Mathematicas alias omnes natura&shy;<lb/>les &longs;cientias, qu&aelig; di&longs;putabilibus rationibus traduntur ex hac parte antecel&shy;<lb/>lere. </s> 
  
 <s>a&longs;&longs;umunt igitur terminos conuertibiles, quia adhibent &longs;&aelig;p&egrave; definitio&shy;<lb/>nes ad demon&longs;trandum. </s> <s>a&longs;&longs;umunt igitur terminos conuertibiles, quia adhibent &longs;&aelig;p&egrave; definitio&shy;<lb/>nes ad demon&longs;trandum. </s>
  
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 <s><margin.target id="marg48"></margin.target>48</s></p><p type="main"> <s><margin.target id="marg48"></margin.target>48</s></p><p type="main">
  
 <s>Tex. </s> <s>Tex. 30. (<emph type="italics"/>Rur&longs;us quemadmodum mon&longs;trant Lunam, quod &longs;ph&aelig;rica &longs;it per aug&shy;<lb/>menta: &longs;i enim quod ita augetur, e&longs;t &longs;ph&aelig;ricum; augetur autem Luna; plan&ubreve; quod <lb/>&longs;ph&aelig;rica<emph.end type="italics"/>) Illius demon&longs;trationis, qu&aelig; ab effectu procedit, affert exemplum <lb/>ex a&longs;tronomia; A&longs;tronomi enim demon&longs;trant Lunam e&longs;&longs;e &longs;ph&aelig;ricam ab ef&shy;<lb/>fectu ip&longs;ius &longs;ph&aelig;ricitatis, qui e&longs;t illuminatio &longs;ph&aelig;rica: &longs;ic enim ratiocinan&shy;<lb/>tur: ea, qu&aelig; &longs;ph&aelig;ric&egrave; illuminantur &longs;unt &longs;ph&aelig;rica, Luna &longs;ph&aelig;ric&egrave; illumina&shy;<lb/>tur, ergo &longs;ph&aelig;rica e&longs;t: qu&aelig; argumentatio fu&longs;ius explicanda e&longs;t; quod ait, <lb/>quod ita augetur, ide&longs;t, &longs;ph&aelig;ric&egrave;, e&longs;t &longs;ph&aelig;ricum, ide&longs;t, quia lumen nou&aelig; Lu&shy;<lb/>n&aelig; augetur &longs;ph&aelig;ric&egrave;, hoc e&longs;t, ad eum modum, quo qu&aelig;uis &longs;ph&aelig;ra obiecta <lb/>corpori lumino&longs;o &longs;olet illuminari. </s>
  
 <s>30. (<emph type="italics"/>Rur&longs;us quemadmodum mon&longs;trant Lunam, quod &longs;ph&aelig;rica &longs;it per aug&shy;<lb/>menta: &longs;i enim quod ita augetur, e&longs;t &longs;ph&aelig;ricum; augetur autem Luna; plan&ubreve; quod <lb/>&longs;ph&aelig;rica<emph.end type="italics"/>) Illius demon&longs;trationis, qu&aelig; ab effectu procedit, affert exemplum <lb/>ex a&longs;tronomia; A&longs;tronomi enim demon&longs;trant Lunam e&longs;&longs;e &longs;ph&aelig;ricam ab ef&shy;<lb/>fectu ip&longs;ius &longs;ph&aelig;ricitatis, qui e&longs;t illuminatio &longs;ph&aelig;rica: &longs;ic enim ratiocinan&shy;<lb/>tur: ea, qu&aelig; &longs;ph&aelig;ric&egrave; illuminantur &longs;unt &longs;ph&aelig;rica, Luna &longs;ph&aelig;ric&egrave; illumina&shy;<lb/>tur, ergo &longs;ph&aelig;rica e&longs;t: qu&aelig; argumentatio fu&longs;ius explicanda e&longs;t; quod ait, <lb/>quod ita augetur, ide&longs;t, &longs;ph&aelig;ric&egrave;, e&longs;t &longs;ph&aelig;ricum, ide&longs;t, quia lumen nou&aelig; Lu&shy;<lb/>n&aelig; augetur &longs;ph&aelig;ric&egrave;, hoc e&longs;t, ad eum modum, quo qu&aelig;uis &longs;ph&aelig;ra obiecta <lb/>corpori lumino&longs;o &longs;olet illuminari. </s> 
  
 <s>illuminatio porr&ograve; Lun&aelig; in &longs;e &longs;emper e&longs;t <lb/>eadem, quia &longs;emper dimidium Lun&aelig; quod Solem a&longs;picit, illuminatur; dici&shy;<lb/>tur tamen augeri re&longs;pectu oculi no&longs;tri, quia &longs;cilicet initio facto &agrave; nouilunio <lb/>pars illuminata incipit quotidie magis vergere ad oculum no&longs;trum, ita vt <lb/>in dies maiorem, ac maiorem illuminationem videamus, donec opponatur <lb/>Soli, in qua oppo&longs;itione totum fer&egrave; Lun&aelig; <expan abbr="illuminat&utilde;">illuminatum</expan> con&longs;picitur. </s> <s>illuminatio porr&ograve; Lun&aelig; in &longs;e &longs;emper e&longs;t <lb/>eadem, quia &longs;emper dimidium Lun&aelig; quod Solem a&longs;picit, illuminatur; dici&shy;<lb/>tur tamen augeri re&longs;pectu oculi no&longs;tri, quia &longs;cilicet initio facto &agrave; nouilunio <lb/>pars illuminata incipit quotidie magis vergere ad oculum no&longs;trum, ita vt <lb/>in dies maiorem, ac maiorem illuminationem videamus, donec opponatur <lb/>Soli, in qua oppo&longs;itione totum fer&egrave; Lun&aelig; <expan abbr="illuminat&utilde;">illuminatum</expan> con&longs;picitur. </s>
  
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 <s>&amp; &longs;imilibus, dicitur Stereometria &agrave; gr&aelig;co <lb/><foreign lang="greek">steoeov,</foreign> ide&longs;t &longs;olidum. </s> <s>&amp; &longs;imilibus, dicitur Stereometria &agrave; gr&aelig;co <lb/><foreign lang="greek">steoeov,</foreign> ide&longs;t &longs;olidum. </s>
  
 <s>Porr&ograve; cur malit Ari&longs;t. </s> <s>Porr&ograve; cur malit Ari&longs;t. Mechanicam &longs;ubalternari Ste&shy;<lb/>reometri&aelig;, quam toti Geometri&aelig;, qua tamen, vt videre e&longs;t apud Archime&shy;<lb/>dem, innititur, fort&egrave; ea ratio e&longs;t, quia Mechanica pr&aelig;cipu&egrave; con&longs;iderat ma&shy;<lb/>chinas, qu&aelig; corpora &longs;unt, &amp; propterea pr&aelig;cipu&egrave;, &amp; prim&ograve; debet Stereome&shy;<lb/>tri&aelig;, qu&aelig; corpora pariter contemplatur, &longs;ubalternari. </s>
  
 <s>Mechanicam &longs;ubalternari Ste&shy;<lb/>reometri&aelig;, quam toti Geometri&aelig;, qua tamen, vt videre e&longs;t apud Archime&shy;<lb/>dem, innititur, fort&egrave; ea ratio e&longs;t, quia Mechanica pr&aelig;cipu&egrave; con&longs;iderat ma&shy;<lb/>chinas, qu&aelig; corpora &longs;unt, &amp; propterea pr&aelig;cipu&egrave;, &amp; prim&ograve; debet Stereome&shy;<lb/>tri&aelig;, qu&aelig; corpora pariter contemplatur, &longs;ubalternari. </s> 
  
 <s>Quod ait Apparen&shy;<lb/>tia ad A&longs;irol. </s> <s>Quod ait Apparen&shy;<lb/>tia ad A&longs;irol. </s>
  
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 <s><margin.target id="marg52"></margin.target>52</s></p><p type="main"> <s><margin.target id="marg52"></margin.target>52</s></p><p type="main">
  
 <s>Tex. </s> <s>Tex. 37. (<emph type="italics"/>Vt &aelig;quicruri, &amp; Scaleno hoc, quod e&longs;t duobus rectis &aelig;quales habere <lb/>&longs;ecandum commune aliquod ine&longs;t<emph.end type="italics"/>) quid &longs;it habcre tres &aelig;quales duobus rect<gap/><lb/>&longs;atis explicatum e&longs;t lib.
  
 <s>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.  
  
 r. </s> r. </s>
  
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 <s><margin.target id="marg53"></margin.target>53</s></p><p type="main"> <s><margin.target id="marg53"></margin.target>53</s></p><p type="main">
  
 <s>Tex. </s> <s>Tex. 38. (<emph type="italics"/>Et quemadmodum in alijs principium &longs;implex, boc autem non idem <lb/>vbique, &longs;ed in pondere quidem mina, in c&abreve;tu ver&ograve; die&longs;is<emph.end type="italics"/>) Die&longs;is apud Muficos e&longs;t <lb/>pars Toni. </s>
  
 <s>38. (<emph type="italics"/>Et quemadmodum in alijs principium &longs;implex, boc autem non idem <lb/>vbique, &longs;ed in pondere quidem mina, in c&abreve;tu ver&ograve; die&longs;is<emph.end type="italics"/>) Die&longs;is apud Muficos e&longs;t <lb/>pars Toni. </s> 
  
 <s>Tonus autem e&longs;t interuallum duarum vocum, quale e&longs;t inter pri&shy;<lb/>mam vocem, Vt, &amp; &longs;ecundam R&egrave;, vt modo loquuntur. </s> <s>Tonus autem e&longs;t interuallum duarum vocum, quale e&longs;t inter pri&shy;<lb/>mam vocem, Vt, &amp; &longs;ecundam R&egrave;, vt modo loquuntur. </s>
  
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 <s><margin.target id="marg54"></margin.target>54</s></p><p type="main"> <s><margin.target id="marg54"></margin.target>54</s></p><p type="main">
  
 <s>Tex. </s> <s>Tex. 39. <emph type="italics"/>(Si enim quod duobus rectis ine&longs;t, non in <lb/>quantum &aelig;quicrus, &longs;ed in quantum triangulus, no&shy;<lb/>&longs;cens, &amp;c.)<emph.end type="italics"/> ide&longs;t, &longs;i enim qui cogno&longs;cit, quod ha&shy;<lb/>bere tres angulos &aelig;quales duobus rectis conuenit <lb/>&aelig;quicruri, non quatenus &aelig;quicrus e&longs;t, &longs;ed quate&shy;<lb/>nus triangulus e&longs;t, &amp;c. </s>
  
 <s>39. <emph type="italics"/>(Si enim quod duobus rectis ine&longs;t, non in <lb/>quantum &aelig;quicrus, &longs;ed in quantum triangulus, no&shy;<lb/>&longs;cens, &amp;c.)<emph.end type="italics"/> ide&longs;t, &longs;i enim qui cogno&longs;cit, quod ha&shy;<lb/>bere tres angulos &aelig;quales duobus rectis conuenit <lb/>&aelig;quicruri, non quatenus &aelig;quicrus e&longs;t, &longs;ed quate&shy;<lb/>nus triangulus e&longs;t, &amp;c. </s> 
  
 <s>quid &longs;it habere tres &aelig;qua&shy;<lb/>les duobus rectis, &amp;c. </s> <s>quid &longs;it habere tres &aelig;qua&shy;<lb/>les duobus rectis, &amp;c. </s>
  
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 <s><margin.target id="marg58"></margin.target>58</s></p><p type="main"> <s><margin.target id="marg58"></margin.target>58</s></p><p type="main">
  
 <s>Tex. </s> <s>Tex. 43. <emph type="italics"/>(Sed planum, quod et&longs;i e&longs;&longs;et &longs;entire triangulum, quod duobus rectis <lb/>&aelig;quales habet angulos)<emph.end type="italics"/> vide &longs;upra lib.
  
 <s>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.  
  
 1. Priorum &longs;ecto 3. cap.  1. Priorum &longs;ecto 3. cap.
  
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 <s><margin.target id="marg62"></margin.target>62</s></p><p type="main"> <s><margin.target id="marg62"></margin.target>62</s></p><p type="main">
  
 <s>Tex. </s> <s>Tex. 44. <emph type="italics"/>(Commen&longs;urabilem namq e&longs;&longs;e diametrum ver&egrave; opinari, ab&longs;urdum e&longs;t)<emph.end type="italics"/><lb/>vide, qu&aelig; de <expan abbr="comm&etilde;&longs;urabilitate">commen&longs;urabilitate</expan> diametri quadrati cum latere expo&longs;uimus <lb/>lib.
  
 <s>44. <emph type="italics"/>(Commen&longs;urabilem namq e&longs;&longs;e diametrum ver&egrave; opinari, ab&longs;urdum e&longs;t)<emph.end type="italics"/><lb/>vide, qu&aelig; de <expan abbr="comm&etilde;&longs;urabilitate">commen&longs;urabilitate</expan> diametri quadrati cum latere expo&longs;uimus <lb/>lib.  
  
 1. Priorum &longs;ecto 1. cap.  1. Priorum &longs;ecto 1. cap.
  
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 <s><margin.target id="marg63"></margin.target>63</s></p><p type="main"> <s><margin.target id="marg63"></margin.target>63</s></p><p type="main">
  
 <s>Tex. </s> <s>Tex. 1. <emph type="italics"/>(Dico autem &longs;impliciter quidem &longs;ubiectum, vt Lunam, aut ter&shy;<lb/>ram, aut Solem, aut triangulum; aliqu<gap/>d ver&ograve; defectum, &aelig;qualitatem, <lb/>in&aelig;qualitatem. </s>
  
 <s>1. <emph type="italics"/>(Dico autem &longs;impliciter quidem &longs;ubiectum, vt Lunam, aut ter&shy;<lb/>ram, aut Solem, aut triangulum; aliqu<gap/>d ver&ograve; defectum, &aelig;qualitatem, <lb/>in&aelig;qualitatem. </s> 
  
 <s>&longs;i in medio, aut non)<emph.end type="italics"/> Zabarella locum hunc, etiam <lb/>quatenus ad Mathematicum attinet, optim&egrave; declarat. </s> <s>&longs;i in medio, aut non)<emph.end type="italics"/> Zabarella locum hunc, etiam <lb/>quatenus ad Mathematicum attinet, optim&egrave; declarat. </s>
  
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 <s><margin.target id="marg65"></margin.target>65</s></p><p type="main"> <s><margin.target id="marg65"></margin.target>65</s></p><p type="main">
  
 <s>Tex. </s> <s>Tex. 2. <emph type="italics"/>(Vt quod omnis triangulus duobus rectis &aelig;quales babet)<emph.end type="italics"/> vide anno&shy;<lb/>tata lib.
  
 <s>2. <emph type="italics"/>(Vt quod omnis triangulus duobus rectis &aelig;quales babet)<emph.end type="italics"/> vide anno&shy;<lb/>tata lib.  
  
 1. Priorum &longs;ecto 3. cap.  1. Priorum &longs;ecto 3. cap.
  
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 <s><margin.target id="marg69"></margin.target>69</s></p><p type="main"> <s><margin.target id="marg69"></margin.target>69</s></p><p type="main">
  
 <s>Tex. </s> <s>Tex. 7. <emph type="italics"/>(Quid enim &longs;ignificat triangulum, accipit Geometra)<emph.end type="italics"/> vt manife&longs;tum <lb/>e&longs;t in 20. dednitione primi Elem.</s></p><p type="main">
  
 <s>7. <emph type="italics"/>(Quid enim &longs;ignificat triangulum, accipit Geometra)<emph.end type="italics"/> vt manife&longs;tum <lb/>e&longs;t in 20. dednitione primi Elem.</s></p><p type="main"> 
  
 <s><arrow.to.target n="marg70"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg70"></arrow.to.target></s></p><p type="margin">
  
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 <s><margin.target id="marg71"></margin.target>71</s></p><p type="main"> <s><margin.target id="marg71"></margin.target>71</s></p><p type="main">
  
 <s>Tex. </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/></s>
  
 <s>11. <emph type="italics"/>(Manife<gap/>tum autem, &amp; &longs;ic, propter quid e&longs;t rectus in &longs;emicirculo)<emph.end type="italics"/><lb/>affert exemplum demon&longs;trationis per cau&longs;am materialem, <expan abbr="id&qacute;">idque</expan>; vti &longs;olet ex <lb/>Mathematicis petitum, e&longs;t enim apud Euclidem 31. demon&longs;tratio 3. Elem. <lb/></s> 
  
 <s>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>
  
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 <s><margin.target id="marg72"></margin.target>72</s></p><p type="main"> <s><margin.target id="marg72"></margin.target>72</s></p><p type="main">
  
 <s>Tex. </s> <s>Tex. 24. <emph type="italics"/>(Vt propter quid re&longs;onat? </s>
  
 <s>24. <emph type="italics"/>(Vt propter quid re&longs;onat? </s> 
  
 <s>aut propter quid apparet? </s> <s>aut propter quid apparet? </s>
  
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 <s><margin.target id="marg73"></margin.target>73</s></p><p type="main"> <s><margin.target id="marg73"></margin.target>73</s></p><p type="main">
  
 <s>Tex. </s> <s>Tex. 25. <emph type="italics"/>(Vt propter quid, &amp; permutatim proportionale? </s>
  
 <s>25. <emph type="italics"/>(Vt propter quid, &amp; permutatim proportionale? </s> 
  
 <s>&amp; c.<emph.end type="italics"/>) quod quan&shy;<lb/>titates, qu&aelig; &longs;unt proportionales, &longs;int etiam alternatim, &longs;eu permutatim <lb/>proportionales explicatum e&longs;t ad tex. </s> <s>&amp; c.<emph.end type="italics"/>) quod quan&shy;<lb/>titates, qu&aelig; &longs;unt proportionales, &longs;int etiam alternatim, &longs;eu permutatim <lb/>proportionales explicatum e&longs;t ad tex. </s>
  
 <s>13. primi Po&longs;ter. </s> <s>13. primi Po&longs;ter. qu&aelig; etiam nece&longs;&longs;a&shy;<lb/>ria &longs;unt ad hunc locum ben&egrave; intelligendum. </s>
  
 <s>qu&aelig; etiam nece&longs;&longs;a&shy;<lb/>ria &longs;unt ad hunc locum ben&egrave; intelligendum. </s> 
  
 <s>Illud autem commune propter <lb/>quod ea, qu&aelig; &longs;unt proportionalia, &longs;int etiam permutatim proportionalia, <lb/>e&longs;t quoddam innominatum, de quo ibi dictum e&longs;t, quod cum conueniat li&shy;<lb/>neis, &amp; numeris, &amp; tamen &longs;eparatim de vtri&longs;que illa pa&longs;&longs;io demon&longs;tretur, <lb/>qu&aelig;rit cuinam prim&ograve;, &amp; per &longs;e conueniat h&aelig;c pa&longs;&longs;io, e&longs;&longs;e permutatim pro&shy;<lb/>portionale; &longs;cilicet quidnam &longs;it illud innominatum; in quo deinde commu&shy;<lb/>nicent line&aelig;, &amp; numeri, vt inde habeant e&longs;&longs;e etiam permutatim propor&shy;<lb/>tionalia.</s></p><p type="main"> <s>Illud autem commune propter <lb/>quod ea, qu&aelig; &longs;unt proportionalia, &longs;int etiam permutatim proportionalia, <lb/>e&longs;t quoddam innominatum, de quo ibi dictum e&longs;t, quod cum conueniat li&shy;<lb/>neis, &amp; numeris, &amp; tamen &longs;eparatim de vtri&longs;que illa pa&longs;&longs;io demon&longs;tretur, <lb/>qu&aelig;rit cuinam prim&ograve;, &amp; per &longs;e conueniat h&aelig;c pa&longs;&longs;io, e&longs;&longs;e permutatim pro&shy;<lb/>portionale; &longs;cilicet quidnam &longs;it illud innominatum; in quo deinde commu&shy;<lb/>nicent line&aelig;, &amp; numeri, vt inde habeant e&longs;&longs;e etiam permutatim propor&shy;<lb/>tionalia.</s></p><p type="main">
  
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 <s>Ibidem (<emph type="italics"/>Vt extrin&longs;ecos &aelig;quales e&longs;&longs;e<emph.end type="italics"/>) ide&longs;t extrin&longs;ecos angulos cuiu&longs;uis fi&shy;<lb/>gur&aelig; rectiline&aelig; &aelig;quales e&longs;&longs;e quatuor rectis angulis: vide qu&aelig; &longs;crip&longs;imus de <lb/>hac re ad tex. </s> <s>Ibidem (<emph type="italics"/>Vt extrin&longs;ecos &aelig;quales e&longs;&longs;e<emph.end type="italics"/>) ide&longs;t extrin&longs;ecos angulos cuiu&longs;uis fi&shy;<lb/>gur&aelig; rectiline&aelig; &aelig;quales e&longs;&longs;e quatuor rectis angulis: vide qu&aelig; &longs;crip&longs;imus de <lb/>hac re ad tex. </s>
  
 <s>39. &longs;ecundi Po&longs;ter. </s> <s>39. &longs;ecundi Po&longs;ter. qu&aelig; huic pariter loco &longs;atisfaciunt.</s></p><p type="head">
  
 <s>qu&aelig; huic pariter loco &longs;atisfaciunt.</s></p><p type="head"> 
  
 <s><emph type="italics"/>EX TOPICIS.<emph.end type="italics"/></s></p><p type="head"> <s><emph type="italics"/>EX TOPICIS.<emph.end type="italics"/></s></p><p type="head">
  
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 31. <lb/>&amp; quo itidem modo Bry&longs;&longs;o lib.  31. <lb/>&amp; quo itidem modo Bry&longs;&longs;o lib.
  
 1. Po&longs;ter. </s> 1. Po&longs;ter. tex. </s>
  
 <s>tex. </s> 
  
 <s>23. <expan abbr="&longs;ol&utilde;modo">&longs;olummodo</expan> id hoc loco no&shy;<lb/>tandum per p&longs;eudographiam intelligere, vt apert&egrave; etiam inferius explicat, <lb/>Geometricam demon&longs;trationem fallacem, e&ograve; quod demon&longs;trationes geo&shy;<lb/>metric&aelig; fiant adhibitis de&longs;criptionibus, &longs;eu figurationibus: p&longs;endographia <lb/>autem latin&egrave; idem e&longs;t, ac fal&longs;a de&longs;criptio; quemadmodum &egrave; contrari&ograve;, &longs;i&shy;<lb/>cuti &longs;upra in Topicis, &amp; alibi ob&longs;eruaui, per de&longs;cribere intelligit geometri&shy;<lb/>c&egrave; demon&longs;trare, &amp; per de&longs;criptiones intelligit demon&longs;trationes geometri&shy;<lb/>cas. </s> <s>23. <expan abbr="&longs;ol&utilde;modo">&longs;olummodo</expan> id hoc loco no&shy;<lb/>tandum per p&longs;eudographiam intelligere, vt apert&egrave; etiam inferius explicat, <lb/>Geometricam demon&longs;trationem fallacem, e&ograve; quod demon&longs;trationes geo&shy;<lb/>metric&aelig; fiant adhibitis de&longs;criptionibus, &longs;eu figurationibus: p&longs;endographia <lb/>autem latin&egrave; idem e&longs;t, ac fal&longs;a de&longs;criptio; quemadmodum &egrave; contrari&ograve;, &longs;i&shy;<lb/>cuti &longs;upra in Topicis, &amp; alibi ob&longs;eruaui, per de&longs;cribere intelligit geometri&shy;<lb/>c&egrave; demon&longs;trare, &amp; per de&longs;criptiones intelligit demon&longs;trationes geometri&shy;<lb/>cas. </s>
  
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 <s><margin.target id="marg88"></margin.target>88</s></p><p type="main"> <s><margin.target id="marg88"></margin.target>88</s></p><p type="main">
  
 <s>Tex. </s> <s>Tex. 11. <emph type="italics"/>(Simul autem <expan abbr="neq;">neque</expan> conuenit omnia &longs;oluere', &longs;ed <expan abbr="qu&aelig;cunq;">qu&aelig;cunque</expan> ex <lb/>principijs aliquis demon&longs;trans <expan abbr="m&etilde;titur">mentitur</expan>; <expan abbr="qu&aelig;cunq;">qu&aelig;cunque</expan> ver&ograve; non, minim&egrave;: <lb/>vt tetragoni&longs;mum, eum quidem, qui per &longs;ectiones Geometrici est di&longs;&shy;<lb/>&longs;oluere: illum autem, qui Antiphontis non Geometrici e&longs;t<emph.end type="italics"/>) Tetrago&shy;<lb/>ni&longs;mum, &longs;eu circuli quadraturam per &longs;ectiones, e&longs;&longs;e illam Hip&shy;<lb/>pocratis Chij exi&longs;timant gr&aelig;ci expo&longs;itores, qui per lunulas, quas Ari&longs;t. &longs;e&shy;<lb/>ctiones appellat, orbem quadrare tentabat. </s>
  
 <s>11. <emph type="italics"/>(Simul autem <expan abbr="neq;">neque</expan> conuenit omnia &longs;oluere', &longs;ed <expan abbr="qu&aelig;cunq;">qu&aelig;cunque</expan> ex <lb/>principijs aliquis demon&longs;trans <expan abbr="m&etilde;titur">mentitur</expan>; <expan abbr="qu&aelig;cunq;">qu&aelig;cunque</expan> ver&ograve; non, minim&egrave;: <lb/>vt tetragoni&longs;mum, eum quidem, qui per &longs;ectiones Geometrici est di&longs;&shy;<lb/>&longs;oluere: illum autem, qui Antiphontis non Geometrici e&longs;t<emph.end type="italics"/>) Tetrago&shy;<lb/>ni&longs;mum, &longs;eu circuli quadraturam per &longs;ectiones, e&longs;&longs;e illam Hip&shy;<lb/>pocratis Chij exi&longs;timant gr&aelig;ci expo&longs;itores, qui per lunulas, quas Ari&longs;t. </s> 
  
 <s>&longs;e&shy;<lb/>ctiones appellat, orbem quadrare tentabat. </s> 
  
 <s>Eius den on&longs;trationem expli&shy;<lb/>caui ad cap.  <s>Eius den on&longs;trationem expli&shy;<lb/>caui ad cap.
  
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 <s>po&longs;&longs;umus addere tertiam rat<gap/> <gap/>cet <lb/>Hippocrates non procedebat per communia alijs &longs;ci<gap/>ad <lb/>tex. </s> <s>po&longs;&longs;umus addere tertiam rat<gap/> <gap/>cet <lb/>Hippocrates non procedebat per communia alijs &longs;ci<gap/>ad <lb/>tex. </s>
  
 <s>23. primi Po&longs;ter. </s> <s>23. primi Po&longs;ter. cap.
  
 <s>cap.  
  
 8. vbi ip&longs;ius p&longs;endographi<gap/>d&shy;<lb/>modum igitur Geometra di&longs;&longs;oluit fal&longs;as tantum<gap/>r&shy;<lb/>uatis Geometricis principijs procedunt; non au<gap/> <gap/>ri&aelig; <lb/>principia conuellunt: ita Phy&longs;ico non incumbit <expan abbr="c&otilde;tra">contra</expan> P<gap/> Me&shy;<lb/>li&longs;&longs;um natur&aelig; principia de&longs;truentes di&longs;ceptare, aut falla<gap/> rationes <lb/>coarguere. </s> 8. vbi ip&longs;ius p&longs;endographi<gap/>d&shy;<lb/>modum igitur Geometra di&longs;&longs;oluit fal&longs;as tantum<gap/>r&shy;<lb/>uatis Geometricis principijs procedunt; non au<gap/> <gap/>ri&aelig; <lb/>principia conuellunt: ita Phy&longs;ico non incumbit <expan abbr="c&otilde;tra">contra</expan> P<gap/> Me&shy;<lb/>li&longs;&longs;um natur&aelig; principia de&longs;truentes di&longs;ceptare, aut falla<gap/> rationes <lb/>coarguere. </s>
  
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 <s><margin.target id="marg89"></margin.target>89</s></p><p type="main"> <s><margin.target id="marg89"></margin.target>89</s></p><p type="main">
  
 <s>Tex. </s> <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>20. (<emph type="italics"/>Geometria enim de phy&longs;ica linea con&longs;iderat, &longs;ed non quatenus <lb/>e&longs;t phy&longs;ici: Per&longs;pectiua autem ma<gap/> hematicam quidem imcam, &longs;ed non <lb/>quatenus phy&longs;ica e&longs;t<emph.end type="italics"/>) quamuis textus hic non pertineat ad Mathe&shy;<lb/>maticum, libuit tamen illum in ordin<gap/>m no&longs;trum recen&longs;ere, ope&shy;<lb/>r&aelig;pretium etenim e&longs;t ea, qu&aelig; in ip&longs;o continentur &agrave; nonnullis recentioribus <lb/>rect&egrave; intelligi, vt ab his moniti, ab inani quadam optices impugnatione ab&shy;<lb/>&longs;tineant, ac tandem ex Ari&longs;t.  
  
 lineas illas vi&longs;uales quas ip&longs;i de medio tollunt, <lb/>per&longs;picu&egrave; videant. </s> lineas illas vi&longs;uales quas ip&longs;i de medio tollunt, <lb/>per&longs;picu&egrave; videant. </s>
  
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 <s><margin.target id="marg90"></margin.target>90</s></p><p type="main"> <s><margin.target id="marg90"></margin.target>90</s></p><p type="main">
  
 <s>Tex. </s> <s>Tex. 28. (<emph type="italics"/>Alio autem modo, &longs;orma, &amp; exemplum: b&aelig;c autem e&longs;t ratio ip&longs;ius, <lb/>quod quid erat e&longs;&longs;e, &amp; huius genera, vt ip&longs;ius diapa&longs;on duo ad vnum, &amp; omnino <lb/>numerus, &amp; partes, qu&aelig; in ratione &longs;unt<emph.end type="italics"/>) vt ben&egrave; intelligas, quod in pr&aelig;&longs;enti <lb/>textu <expan abbr="mathematic&utilde;">mathematicum</expan> e&longs;t, con&longs;ule prius, qu&aelig; &longs;crip&longs;i ad tex. </s>
  
 <s>28. (<emph type="italics"/>Alio autem modo, &longs;orma, &amp; exemplum: b&aelig;c autem e&longs;t ratio ip&longs;ius, <lb/>quod quid erat e&longs;&longs;e, &amp; huius genera, vt ip&longs;ius diapa&longs;on duo ad vnum, &amp; omnino <lb/>numerus, &amp; partes, qu&aelig; in ratione &longs;unt<emph.end type="italics"/>) vt ben&egrave; intelligas, quod in pr&aelig;&longs;enti <lb/>textu <expan abbr="mathematic&utilde;">mathematicum</expan> e&longs;t, con&longs;ule prius, qu&aelig; &longs;crip&longs;i ad tex. </s> 
  
 <s>1. cap.  <s>1. cap.
  
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 <s><margin.target id="marg91"></margin.target>91</s></p><p type="main"> <s><margin.target id="marg91"></margin.target>91</s></p><p type="main">
  
 <s>Tex. </s> <s>Tex. 68. (<emph type="italics"/>Aut enim ad ip&longs;um quid e&longs;t, reducitur ip&longs;um propter quid in immo&shy;<lb/>bihbus, vt in Mathematicis, ad definitionem enim recti, aut commen&longs;urabilis, aut <lb/>alius cuiu&longs;piam reducitur vltimum<emph.end type="italics"/>) ex his manife&longs;t&egrave; videas Mathematicas <expan abbr="de-m&otilde;&longs;trare">de&shy;<lb/>mon&longs;trare</expan> per cau&longs;am formalem, cum cau&longs;am ip&longs;am ad ip&longs;um quid e&longs;t, ide&longs;t, <lb/>ad definitionem reducant. </s>
  
 <s>68. (<emph type="italics"/>Aut enim ad ip&longs;um quid e&longs;t, reducitur ip&longs;um propter quid in immo&shy;<lb/>bihbus, vt in Mathematicis, ad definitionem enim recti, aut commen&longs;urabilis, aut <lb/>alius cuiu&longs;piam reducitur vltimum<emph.end type="italics"/>) ex his manife&longs;t&egrave; videas Mathematicas <expan abbr="de-m&otilde;&longs;trare">de&shy;<lb/>mon&longs;trare</expan> per cau&longs;am formalem, cum cau&longs;am ip&longs;am ad ip&longs;um quid e&longs;t, ide&longs;t, <lb/>ad definitionem reducant. </s> 
  
 <s>quorum exempla in logicis ex Mathematicis at&shy;<lb/>tuli: &longs;ed etiam &longs;equentis loci exemplum de triangulo idem apert&egrave; manife&shy;<lb/>&longs;tat; in quo probat duos angulos A C B, A C D, e&longs;&longs;e rectos, ex definitione <lb/>ip&longs;orum, &longs;iue ex definitione line&aelig; perpendicularis A C, quod idem e&longs;t.</s></p><p type="main"> <s>quorum exempla in logicis ex Mathematicis at&shy;<lb/>tuli: &longs;ed etiam &longs;equentis loci exemplum de triangulo idem apert&egrave; manife&shy;<lb/>&longs;tat; in quo probat duos angulos A C B, A C D, e&longs;&longs;e rectos, ex definitione <lb/>ip&longs;orum, &longs;iue ex definitione line&aelig; perpendicularis A C, quod idem e&longs;t.</s></p><p type="main">
  
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 <s><margin.target id="marg93"></margin.target>93</s></p><p type="main"> <s><margin.target id="marg93"></margin.target>93</s></p><p type="main">
  
 <s>Tex. </s> <s>Tex. 26. <emph type="italics"/>(Et hi quidem infinitum e&longs;&longs;e par; hoc enim compr&aelig;hen&longs;um, &amp; <lb/>ab impari terminatum tribuit ijs, qu&aelig; &longs;unt, infinitatem. </s>
  
 <s>26. <emph type="italics"/>(Et hi quidem infinitum e&longs;&longs;e par; hoc enim compr&aelig;hen&longs;um, &amp; <lb/>ab impari terminatum tribuit ijs, qu&aelig; &longs;unt, infinitatem. </s> 
  
 <s>&longs;ignum autem <lb/>huius id e&longs;&longs;e, quod contingit in numcris, circumpo&longs;it is enim Gnomoni&shy;<lb/>bus circa vnum, &amp; &longs;eor&longs;um, aliquando quidcm &longs;emper aliam fieri &longs;pe&shy;<lb/>ciem, aliquando autem vnam)<emph.end type="italics"/> vt melius percipiantur ea, qu&aelig; &longs;equuntur, lege <lb/>prius, qu&aelig; in cap.  <s>&longs;ignum autem <lb/>huius id e&longs;&longs;e, quod contingit in numcris, circumpo&longs;it is enim Gnomoni&shy;<lb/>bus circa vnum, &amp; &longs;eor&longs;um, aliquando quidcm &longs;emper aliam fieri &longs;pe&shy;<lb/>ciem, aliquando autem vnam)<emph.end type="italics"/> vt melius percipiantur ea, qu&aelig; &longs;equuntur, lege <lb/>prius, qu&aelig; in cap.
  
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 <s>&amp; &longs;ic &longs;emper in infinitum nou&aelig; ac vari&aelig; numerorum <lb/>form&aelig; ex hac additione parium prouenient, quod argumento e&longs;t numerum <lb/>parem infiniti naturam &longs;apere. </s> <s>&amp; &longs;ic &longs;emper in infinitum nou&aelig; ac vari&aelig; numerorum <lb/>form&aelig; ex hac additione parium prouenient, quod argumento e&longs;t numerum <lb/>parem infiniti naturam &longs;apere. </s>
  
 <s>Porr&ograve; reperiri numeros triangulares, pen&shy;<lb/>tagonos, &amp; &longs;imiles, con&longs;tat ex Arithmetica Nicomachi, Boetij, &amp; Iordani, <lb/>citati in definitionibus 7. &longs;u&aelig; Arithmetic&aelig;, atque ex tractatu Diophantis <lb/>Alex. </s> <s>Porr&ograve; reperiri numeros triangulares, pen&shy;<lb/>tagonos, &amp; &longs;imiles, con&longs;tat ex Arithmetica Nicomachi, Boetij, &amp; Iordani, <lb/>citati in definitionibus 7. &longs;u&aelig; Arithmetic&aelig;, atque ex tractatu Diophantis <lb/>Alex. de numeris rectangulis. </s>
  
 <s>de numeris rectangulis. </s> 
  
 <s><expan abbr="atq;">atque</expan> ex his locus hic &longs;atis clarus redditur.</s></p><p type="main"> <s><expan abbr="atq;">atque</expan> ex his locus hic &longs;atis clarus redditur.</s></p><p type="main">
  
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 <s><margin.target id="marg94"></margin.target>94</s></p><p type="main"> <s><margin.target id="marg94"></margin.target>94</s></p><p type="main">
  
 <s>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>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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 <s><margin.target id="marg95"></margin.target>95</s></p><p type="main"> <s><margin.target id="marg95"></margin.target>95</s></p><p type="main">
  
 <s>Tex. </s> <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>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"></arrow.to.target></s></p><p type="margin">
  
 <s><margin.target id="marg96"></margin.target>96</s></p><p type="main"> <s><margin.target id="marg96"></margin.target>96</s></p><p type="main">
  
 <s>Tex. </s> <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>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">
  
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 <s><margin.target id="marg97"></margin.target>97</s></p><p type="main"> <s><margin.target id="marg97"></margin.target>97</s></p><p type="main">
  
 <s>Tex. </s> <s>Tex. 120. ter in hoc textu meminit commen&longs;urabilitatis, &amp; incommen&shy;<lb/>&longs;urabilitatis, qu&aelig; e&longs;t diametri ad co&longs;tam: cuius explicationem vide <lb/>primo Priorum, &longs;ecto primo, cap.
  
 <s>120. ter in hoc textu meminit commen&longs;urabilitatis, &amp; incommen&shy;<lb/>&longs;urabilitatis, qu&aelig; e&longs;t diametri ad co&longs;tam: cuius explicationem vide <lb/>primo Priorum, &longs;ecto primo, cap.  
  
 23.</s></p><figure></figure><pb pagenum="76"/><p type="head"> 23.</s></p><figure></figure><pb pagenum="76"/><p type="head">
  
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 <s><margin.target id="marg98"></margin.target>98</s></p><p type="main"> <s><margin.target id="marg98"></margin.target>98</s></p><p type="main">
  
 <s>Tex. </s> <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>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">
  
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 <s><margin.target id="marg99"></margin.target>99</s></p><p type="main"> <s><margin.target id="marg99"></margin.target>99</s></p><p type="main">
  
 <s>Tex. </s> <s>Tex. 15. <emph type="italics"/>(Etenim triangulus habet tres angulos &aelig;quales duobus rectis angulis)<emph.end type="italics"/><lb/>lib.
  
 <s>15. <emph type="italics"/>(Etenim triangulus habet tres angulos &aelig;quales duobus rectis angulis)<emph.end type="italics"/><lb/>lib.  
  
 1. Priorum, &longs;ecto 3. cap.  1. Priorum, &longs;ecto 3. cap.
  
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 <s><margin.target id="marg100"></margin.target><gap/>0</s></p><p type="main"> <s><margin.target id="marg100"></margin.target><gap/>0</s></p><p type="main">
  
 <s>Tex. </s> <s>Tex. 33. <emph type="italics"/>(Vt &longs;i quis minimam qu&abreve;dam e&longs;&longs;e dicat magnitudinem, hic enim <lb/>minimum introducens, maxima <expan abbr="vbiq;">vbique</expan> amoueret mathematicor&ubreve;)<emph.end type="italics"/> ide&longs;t, <lb/>&longs;i quis, vt Democritus po&longs;uerit in magnitudinibus e&longs;&longs;e minima, <lb/>&longs;eu indiui&longs;ibilia, ex quibus entia mathematica componerentur, <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>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>g. </s> <s>g. </s>
  
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 <s><margin.target id="marg101"></margin.target>101</s></p><p type="main"> <s><margin.target id="marg101"></margin.target>101</s></p><p type="main">
  
 <s>Tex. </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"></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>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>&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><margin.target id="marg102"></margin.target>102</s></p><p type="main"> <s><margin.target id="marg102"></margin.target>102</s></p><p type="main">
  
 <s>Tex. </s> <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>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.  
  
 1. Priorum, &longs;ecto 1. cap.  1. Priorum, &longs;ecto 1. cap.
  
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 <s><margin.target id="marg103"></margin.target>103</s></p><p type="main"> <s><margin.target id="marg103"></margin.target>103</s></p><p type="main">
  
 <s>Tex. </s> <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>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.  
  
 1. Priorum, &longs;ecto 3. cap.  1. Priorum, &longs;ecto 3. cap.
  
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 <s><margin.target id="marg105"></margin.target>105</s></p><p type="main"> <s><margin.target id="marg105"></margin.target>105</s></p><p type="main">
  
 <s>Tex. </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>
  
 <s>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>quam vnam <expan abbr="hab&etilde;um">habenum</expan>. <lb/></s> <s>quam vnam <expan abbr="hab&etilde;um">habenum</expan>. <lb/></s>
  
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 <s><margin.target id="marg106"></margin.target>106</s></p><p type="main"> <s><margin.target id="marg106"></margin.target>106</s></p><p type="main">
  
 <s>Tex. </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>
  
 <s>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>&longs;i autem &longs;ecundum triangulum, vnum. <lb/></s> <s>&longs;i autem &longs;ecundum triangulum, vnum. <lb/></s>
  
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 <s><margin.target id="marg107"></margin.target>107</s></p><p type="main"> <s><margin.target id="marg107"></margin.target>107</s></p><p type="main">
  
 <s>Tex. </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>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"></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>
  
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 <s><margin.target id="marg108"></margin.target>108</s></p><p type="main"> <s><margin.target id="marg108"></margin.target>108</s></p><p type="main">
  
 <s>Tex. </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>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"></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>
  
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 <s><margin.target id="marg109"></margin.target>109</s></p><p type="main"> <s><margin.target id="marg109"></margin.target>109</s></p><p type="main">
  
 <s>Tex. </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>
  
 <s>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>Dicit igi&shy;<lb/>tur ordinem c&oelig;lorum, ac &longs;yderum, item &longs;itum, &amp; proportiones magnitu&shy;<lb/>dinum corundem, cum per naturalis &longs;cienti&aelig; princip ia &longs;ciri nequeant, ex <lb/>rationibus A&longs;tronomorum petenda e&longs;&longs;e, apud quos i&longs;ta &longs;ufficienter <expan abbr="demon-&longs;tr&etilde;tur">demon&shy;<lb/>&longs;trentur</expan>. </s> <s>Dicit igi&shy;<lb/>tur ordinem c&oelig;lorum, ac &longs;yderum, item &longs;itum, &amp; proportiones magnitu&shy;<lb/>dinum corundem, cum per naturalis &longs;cienti&aelig; princip ia &longs;ciri nequeant, ex <lb/>rationibus A&longs;tronomorum petenda e&longs;&longs;e, apud quos i&longs;ta &longs;ufficienter <expan abbr="demon-&longs;tr&etilde;tur">demon&shy;<lb/>&longs;trentur</expan>. </s>
  
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 <s><margin.target id="marg110"></margin.target>110</s></p><p type="main"> <s><margin.target id="marg110"></margin.target>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. </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>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">
  
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 <s><margin.target id="marg112"></margin.target>112</s></p><p type="main"> <s><margin.target id="marg112"></margin.target>112</s></p><p type="main">
  
 <s>Tex. </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>
  
 <s>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>manife&longs;tum enim e&longs;t, quod non quou&longs;que ex&shy;<lb/>tremum tangat ip&longs;um centrum; &longs;ed maior pars vincat, oportet, <expan abbr="quou&longs;q;">quou&longs;que</expan> &longs;uo medio <lb/>ip&longs;um medium compr&aelig;hendat; <expan abbr="hucn&longs;q;">hucn&longs;que</expan> enim habet propen&longs;ioncm)<emph.end type="italics"/> &longs;en&longs;us Ari&longs;to&shy;<lb/>telis e&longs;t, debere nos exi&longs;timare, quod &longs;i qu&aelig;piam grauis magnitudo de&longs;cen&shy;<lb/>dat ad centrum mundi, eam non perman&longs;uram, &longs;latim ac ip&longs;ius extremum <lb/>centrum mundi attigent; &longs;ed c&ograve; <expan abbr="v&longs;q;">v&longs;que</expan> de&longs;cen&longs;uram, <expan abbr="quou&longs;q;">quou&longs;que</expan> ip&longs;ius medium, <lb/>mundi medium, &longs;iue centrum a&longs;&longs;equutum &longs;it; maior enim ip&longs;ius pars, in qua <lb/>&longs;cilicet medium e&longs;t, minorem partem propellit, donec vtrinque &agrave; centro <lb/>mundi &aelig;qu&egrave; emineat; omne enim graue <expan abbr="hucu&longs;q;">hucu&longs;que</expan> habet propen&longs;ionem, &longs;iue <pb pagenum="81"/><expan abbr="hucu&longs;q;">hucu&longs;que</expan> grauitat, v. </s> <s>manife&longs;tum enim e&longs;t, quod non quou&longs;que ex&shy;<lb/>tremum tangat ip&longs;um centrum; &longs;ed maior pars vincat, oportet, <expan abbr="quou&longs;q;">quou&longs;que</expan> &longs;uo medio <lb/>ip&longs;um medium compr&aelig;hendat; <expan abbr="hucn&longs;q;">hucn&longs;que</expan> enim habet propen&longs;ioncm)<emph.end type="italics"/> &longs;en&longs;us Ari&longs;to&shy;<lb/>telis e&longs;t, debere nos exi&longs;timare, quod &longs;i qu&aelig;piam grauis magnitudo de&longs;cen&shy;<lb/>dat ad centrum mundi, eam non perman&longs;uram, &longs;latim ac ip&longs;ius extremum <lb/>centrum mundi attigent; &longs;ed c&ograve; <expan abbr="v&longs;q;">v&longs;que</expan> de&longs;cen&longs;uram, <expan abbr="quou&longs;q;">quou&longs;que</expan> ip&longs;ius medium, <lb/>mundi medium, &longs;iue centrum a&longs;&longs;equutum &longs;it; maior enim ip&longs;ius pars, in qua <lb/>&longs;cilicet medium e&longs;t, minorem partem propellit, donec vtrinque &agrave; centro <lb/>mundi &aelig;qu&egrave; emineat; omne enim graue <expan abbr="hucu&longs;q;">hucu&longs;que</expan> habet propen&longs;ionem, &longs;iue <pb pagenum="81"/><expan abbr="hucu&longs;q;">hucu&longs;que</expan> grauitat, v. </s>
  
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 <s><margin.target id="marg113"></margin.target>113</s></p><p type="main"> <s><margin.target id="marg113"></margin.target>113</s></p><p type="main">
  
 <s>Tex. </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>
  
 <s>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>quam&shy;<lb/>uis enim &longs;ingulis men&longs;ibus Luna terminetur modo linea concaua, vt quan&shy;<lb/>do noua e&longs;t; modo recta, vt quando diuidua e&longs;t: modo vtrinque curua, vt <lb/>cum &agrave; diuidu&aelig;ad plenilunium tendit. </s> <s>quam&shy;<lb/>uis enim &longs;ingulis men&longs;ibus Luna terminetur modo linea concaua, vt quan&shy;<lb/>do noua e&longs;t; modo recta, vt quando diuidua e&longs;t: modo vtrinque curua, vt <lb/>cum &agrave; diuidu&aelig;ad plenilunium tendit. </s>
  
 <s>quod fu&longs;ius primo Po&longs;ter. </s> <s>quod fu&longs;ius primo Po&longs;ter. tex. </s>
  
 <s>tex. </s> 
  
 <s>30. ex&shy;<lb/>po&longs;ui. </s> <s>30. ex&shy;<lb/>po&longs;ui. </s>
  
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 <s><margin.target id="marg116"></margin.target>116</s></p><p type="main"> <s><margin.target id="marg116"></margin.target>116</s></p><p type="main">
  
 <s>Tex. </s> <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>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"></arrow.to.target></s></p><p type="margin">
  
 <s><margin.target id="marg117"></margin.target>117</s></p><p type="main"> <s><margin.target id="marg117"></margin.target>117</s></p><p type="main">
  
 <s>Tex. </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>
  
 <s>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>Clauio in &longs;ph&aelig;ra: quem &longs;i libet, con&longs;ule, ne inani labore opu&shy;<lb/>&longs;culum i&longs;tud exere&longs;cat.</s></p><p type="head"> <s>Clauio in &longs;ph&aelig;ra: quem &longs;i libet, con&longs;ule, ne inani labore opu&shy;<lb/>&longs;culum i&longs;tud exere&longs;cat.</s></p><p type="head">
  
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 <s><margin.target id="marg118"></margin.target>118</s></p><p type="main"> <s><margin.target id="marg118"></margin.target>118</s></p><p type="main">
  
 <s>Tex. </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>
  
 <s>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>ex quibus &longs;e&shy;<lb/>ctionibus tota &longs;ph&aelig;ra in octo partes diuiditur, quibus &longs;ph&aelig;ram componi <lb/>vult Ari&longs;toteles. </s> <s>ex quibus &longs;e&shy;<lb/>ctionibus tota &longs;ph&aelig;ra in octo partes diuiditur, quibus &longs;ph&aelig;ram componi <lb/>vult Ari&longs;toteles. </s>
  
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 <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"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg120"></arrow.to.target></s></p><p type="margin">
  
 <s><margin.target id="marg120"></margin.target>120</s></p><p type="main"> <s><margin.target id="marg120"></margin.target>120</s></p><p type="main">
  
 <s>Tex. </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>
  
 <s>66. <emph type="italics"/>(Ommn&ograve; autem eniti &longs;implicibus corporibus figur as tribuere irratio&shy;<lb/>nabile e&longs;t. </s> 
  
 <s>prim&ograve; quidem, quia accidit non repleri totum; nam in planis tres figur&aelig; <lb/>videntur implere locum, Triangulus, Quadratum, &amp; Sexangulus)<emph.end type="italics"/> per &longs;implicia <lb/>corpora intelligit quatuor elementa. </s> <s>prim&ograve; quidem, quia accidit non repleri totum; nam in planis tres figur&aelig; <lb/>videntur implere locum, Triangulus, Quadratum, &amp; Sexangulus)<emph.end type="italics"/> per &longs;implicia <lb/>corpora intelligit quatuor elementa. </s>
  
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 <s>Vides igitur tanti viri auctoritate confirmari no&longs;tram &longs;ententiam, py&shy;<lb/>ramides videlicet per &longs;e, non replere vacuum. </s> <s>Vides igitur tanti viri auctoritate confirmari no&longs;tram &longs;ententiam, py&shy;<lb/>ramides videlicet per &longs;e, non replere vacuum. </s>
  
 <s>cum igitur con&longs;tet vnam tan&shy;<lb/>tum ex figuris &longs;olidis, &longs;iue etiam dicas, vt perperam Ari&longs;t. </s> <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>&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"></arrow.to.target></s></p><p type="margin">
  
 <s><margin.target id="marg122"></margin.target>122</s></p><p type="main"> <s><margin.target id="marg122"></margin.target>122</s></p><p type="main">
  
 <s>Tex. </s> <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>71 <emph type="italics"/>(Deinde &longs;i terra e&longs;t cubus &amp;c.)<emph.end type="italics"/> lege definitiones 11. Elem.  
  
 qu&aelig; &longs;unt <lb/>admodum faciles, ibi reperies de&longs;initiones quinque corporum regularium, <lb/>quorum figuras Plato elementis tribuebat: qua ver&ograve; id ratione faceret, ha&shy;<lb/>bes in &longs;ph&aelig;ra Clau. </s> qu&aelig; &longs;unt <lb/>admodum faciles, ibi reperies de&longs;initiones quinque corporum regularium, <lb/>quorum figuras Plato elementis tribuebat: qua ver&ograve; id ratione faceret, ha&shy;<lb/>bes in &longs;ph&aelig;ra Clau. </s>
  
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 <s><margin.target id="marg123"></margin.target>123</s></p><p type="main"> <s><margin.target id="marg123"></margin.target>123</s></p><p type="main">
  
 <s>Tex. </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>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"></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>
  
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 <s><margin.target id="marg129"></margin.target>129</s></p><p type="head"> <s><margin.target id="marg129"></margin.target>129</s></p><p type="head">
  
 <s><emph type="italics"/>Ex Lib. </s> <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>2. de Generatione, &amp; Corruptione.<emph.end type="italics"/><lb/><arrow.to.target n="marg130"></arrow.to.target></s></p><p type="margin"> 
  
 <s><margin.target id="marg130"></margin.target>130</s></p><p type="main"> <s><margin.target id="marg130"></margin.target>130</s></p><p type="main">
  
 <s>Tex. </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>
  
 <s>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>per obliquum ver&ograve; circulum in&shy;<lb/>telligit Zodiacum, qui obliquus e&longs;t, quia poli eius &longs;unt alij &agrave; polis mundi, &amp; <lb/>quia non tendit rect&agrave; ab ortu ad occa&longs;um, &longs;ed in &longs;ph&aelig;ra mundi tran&longs;uer&shy;<lb/>&longs;us e&longs;t, &amp; deflectit &agrave; &longs;eptentrione in meridiem, quamuis non rect&agrave;, vt in <lb/>&longs;ph&aelig;ra explicari &longs;olet. </s> <s>per obliquum ver&ograve; circulum in&shy;<lb/>telligit Zodiacum, qui obliquus e&longs;t, quia poli eius &longs;unt alij &agrave; polis mundi, &amp; <lb/>quia non tendit rect&agrave; ab ortu ad occa&longs;um, &longs;ed in &longs;ph&aelig;ra mundi tran&longs;uer&shy;<lb/>&longs;us e&longs;t, &amp; deflectit &agrave; &longs;eptentrione in meridiem, quamuis non rect&agrave;, vt in <lb/>&longs;ph&aelig;ra explicari &longs;olet. </s>
  
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 <s>In pr&aelig;&longs;enti cap. </s> <s>In pr&aelig;&longs;enti cap. </s>
  
 <s>Ari&longs;t. </s> <s>Ari&longs;t. &longs;uam de Cometis &longs;ententiam exponit: Come&shy;<lb/>tam nimirum infra Lunam in elementari mundo procreari, &amp; ignitum <lb/>quoddam Meteoron, ex lenta, pingui, <expan abbr="&longs;icca&qacute;">&longs;iccaque</expan>; materia &agrave; terra in &longs;u&shy;<lb/>prem<gap/>m aeris regionem attracta, exi&longs;tere; <expan abbr="ibi&qacute;">ibique</expan>; rapti aeris calore, <lb/>vel elementi ignis (quod illic e&longs;&longs;e putat) vicinitate, vel etiam vi a&longs;trorum <lb/>incendi, <expan abbr="atq;">atque</expan> impelli. </s>
  
 <s>&longs;uam de Cometis &longs;ententiam exponit: Come&shy;<lb/>tam nimirum infra Lunam in elementari mundo procreari, &amp; ignitum <lb/>quoddam Meteoron, ex lenta, pingui, <expan abbr="&longs;icca&qacute;">&longs;iccaque</expan>; materia &agrave; terra in &longs;u&shy;<lb/>prem<gap/>m aeris regionem attracta, exi&longs;tere; <expan abbr="ibi&qacute;">ibique</expan>; rapti aeris calore, <lb/>vel elementi ignis (quod illic e&longs;&longs;e putat) vicinitate, vel etiam vi a&longs;trorum <lb/>incendi, <expan abbr="atq;">atque</expan> impelli. </s> 
  
 <s>Han&cacute; porr&ograve; opinionem &amp; &longs;i probabilibus tantum ra&shy;<lb/>tionibus confirmatam vulg&ograve; tamen <expan abbr="v&longs;q;">v&longs;que</expan> ad hanc diem receptam, cum fal&shy;<lb/>&longs;am e&longs;&longs;e a&longs;tronomi exi&longs;timent, non erit abs re rationes eas ex &longs;ecundo pro&shy;<lb/>gymn. </s> <s>Han&cacute; porr&ograve; opinionem &amp; &longs;i probabilibus tantum ra&shy;<lb/>tionibus confirmatam vulg&ograve; tamen <expan abbr="v&longs;q;">v&longs;que</expan> ad hanc diem receptam, cum fal&shy;<lb/>&longs;am e&longs;&longs;e a&longs;tronomi exi&longs;timent, non erit abs re rationes eas ex &longs;ecundo pro&shy;<lb/>gymn. </s>
  
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 exponunt, nul&shy;<lb/>lo modo po&longs;&longs;unt &agrave; Mathematicis redargui per rationem de&longs;umptam &agrave; di&shy;<lb/>uer&longs;itate a&longs;pectus (quam po&longs;tea explicabo) quamuis phy&longs;icis rationibus re&shy;<lb/>fellantur. </s> exponunt, nul&shy;<lb/>lo modo po&longs;&longs;unt &agrave; Mathematicis redargui per rationem de&longs;umptam &agrave; di&shy;<lb/>uer&longs;itate a&longs;pectus (quam po&longs;tea explicabo) quamuis phy&longs;icis rationibus re&shy;<lb/>fellantur. </s>
  
 <s>Alij &longs;unt, quorum &longs;ententia magis videtur <expan abbr="improb&atilde;da">improbanda</expan>, c&ograve; quod <lb/>Ari&longs;t. </s> <s>Alij &longs;unt, quorum &longs;ententia magis videtur <expan abbr="improb&atilde;da">improbanda</expan>, c&ograve; quod <lb/>Ari&longs;t. &longs;ummum Philo&longs;ophum pueriliter in a&longs;tronomia lap&longs;um fateri cogan&shy;<lb/>tur. </s>
  
 <s>&longs;ummum Philo&longs;ophum pueriliter in a&longs;tronomia lap&longs;um fateri cogan&shy;<lb/>tur. </s> 
  
 <s>Exi&longs;timant hi Galaxiam hanc Ari&longs;totelicam nihil aliud e&longs;&longs;e, qu&agrave;m ip&shy;<lb/>&longs;as tenues exhalationes in aere &longs;ubuectas, direct&egrave;que infra &longs;tellas illas la&shy;<lb/>cteum circulum in c&oelig;lo con&longs;tituentes nobis obiectas. </s> <s>Exi&longs;timant hi Galaxiam hanc Ari&longs;totelicam nihil aliud e&longs;&longs;e, qu&agrave;m ip&shy;<lb/>&longs;as tenues exhalationes in aere &longs;ubuectas, direct&egrave;que infra &longs;tellas illas la&shy;<lb/>cteum circulum in c&oelig;lo con&longs;tituentes nobis obiectas. </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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 explicat.</s></p><p type="main"> explicat.</s></p><p type="main">
  
 <s>Inquit igitur Ari&longs;t. </s> <s>Inquit igitur Ari&longs;t. &longs;it enim in oriente, &amp;c. </s>
  
 <s>&longs;it enim in oriente, &amp;c. </s> 
  
 <s>vbi aggreditur probare vnum <lb/>ex tribus illis, qu&aelig; &longs;upra propo&longs;uit, nimirum tunc Iridem e&longs;&longs;e &longs;emicircu&shy;<lb/>lum, quando a&longs;trum fuerit in oriente, &longs;iue in horizonte, vbi G. &longs;i igitur per <lb/>triangulum G M K, intelligamus <expan abbr="plan&utilde;">planum</expan> exten&longs;um, in quo A, in figura, adeo <lb/>magnum, vt totum &longs;ece<gap/> hemi&longs;ph&aelig;rium, faciet in &longs;uperficie hemi&longs;ph&aelig;rij &longs;e&shy;<pb pagenum="118"/>ctionem, qu&aelig; erit portio maximi circuli, per 6. Theodo&longs;ij, cum planum &longs;e&shy;<lb/>cans hemi&longs;ph&aelig;rium, tran&longs;eat per <expan abbr="centr&utilde;">centrum</expan> ip&longs;ius, qu&aelig; &longs;ectio, &longs;iue circuli por&shy;<lb/>tio repr&aelig;&longs;entatur in figura, per &longs;emicirculum in quo A, &longs;iue in quo G A M&shy;<lb/>R O. nihil autem refert quodcunque intelligas planum &longs;uper axem G K O, <lb/>tran&longs;iens &longs;iue per triangulum G K M, &longs;iue per aliud illi &longs;imile. </s> <s>vbi aggreditur probare vnum <lb/>ex tribus illis, qu&aelig; &longs;upra propo&longs;uit, nimirum tunc Iridem e&longs;&longs;e &longs;emicircu&shy;<lb/>lum, quando a&longs;trum fuerit in oriente, &longs;iue in horizonte, vbi G. &longs;i igitur per <lb/>triangulum G M K, intelligamus <expan abbr="plan&utilde;">planum</expan> exten&longs;um, in quo A, in figura, adeo <lb/>magnum, vt totum &longs;ece<gap/> hemi&longs;ph&aelig;rium, faciet in &longs;uperficie hemi&longs;ph&aelig;rij &longs;e&shy;<pb pagenum="118"/>ctionem, qu&aelig; erit portio maximi circuli, per 6. Theodo&longs;ij, cum planum &longs;e&shy;<lb/>cans hemi&longs;ph&aelig;rium, tran&longs;eat per <expan abbr="centr&utilde;">centrum</expan> ip&longs;ius, qu&aelig; &longs;ectio, &longs;iue circuli por&shy;<lb/>tio repr&aelig;&longs;entatur in figura, per &longs;emicirculum in quo A, &longs;iue in quo G A M&shy;<lb/>R O. nihil autem refert quodcunque intelligas planum &longs;uper axem G K O, <lb/>tran&longs;iens &longs;iue per triangulum G K M, &longs;iue per aliud illi &longs;imile. </s>
  
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 <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"></arrow.to.target></s></p><p type="margin">
  
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 <s>in <lb/>hac enim conuer&longs;ione angulus Iridis B, de&longs;cribet circulum, qui erit Iris, &amp; <lb/>pertr an&longs;ibit omnes angulos, qui in tali Solis, oculi, ac nubis &longs;itu, arcum ef&shy;<lb/>ficere &longs;unt idonei.</s></p><p type="main"> <s>in <lb/>hac enim conuer&longs;ione angulus Iridis B, de&longs;cribet circulum, qui erit Iris, &amp; <lb/>pertr an&longs;ibit omnes angulos, qui in tali Solis, oculi, ac nubis &longs;itu, arcum ef&shy;<lb/>ficere &longs;unt idonei.</s></p><p type="main">
  
 <s>Sed contra pr&aelig;dicta de angulo Iridis determinato eadem nobis obijcies, <lb/>qu&aelig; nos &longs;upra ad finem numeri 164. Ari&longs;t. </s> <s>Sed contra pr&aelig;dicta de angulo Iridis determinato eadem nobis obijcies, <lb/>qu&aelig; nos &longs;upra ad finem numeri 164. Ari&longs;t. &amp; alijs obiecimus, plures <expan abbr="nimi-r&utilde;">nimi&shy;<lb/>rum</expan> po&longs;&longs;e con&longs;titui angulos &aelig;quales angulo Iridis B, in plano trianguli A B C, <lb/>qui non &longs;int in eodem orbe con&longs;tituti, in quo &longs;unt omnes anguli B. </s>
  
 <s>&amp; alijs obiecimus, plures <expan abbr="nimi-r&utilde;">nimi&shy;<lb/>rum</expan> po&longs;&longs;e con&longs;titui angulos &aelig;quales angulo Iridis B, in plano trianguli A B C, <lb/>qui non &longs;int in eodem orbe con&longs;tituti, in quo &longs;unt omnes anguli B. </s> 
  
 <s>Iridem <lb/>reflectentes, <expan abbr="quiq;">quique</expan> reflexionem faciant ad eundem oculum C, vnde &longs;equitur <lb/>pr&aelig;dictam Iridis altitudinem non e&longs;&longs;e, vti diximus, determinatam, cum <lb/>po&longs;&longs;it angulus B, alios &longs;ibi &aelig;quales tam &longs;upra, qu&agrave;m infra habere, qua ra&shy;<lb/>tione deberet etiam Iris, &amp; altius, &amp; inferius apparere.</s></p><p type="main"> <s>Iridem <lb/>reflectentes, <expan abbr="quiq;">quique</expan> reflexionem faciant ad eundem oculum C, vnde &longs;equitur <lb/>pr&aelig;dictam Iridis altitudinem non e&longs;&longs;e, vti diximus, determinatam, cum <lb/>po&longs;&longs;it angulus B, alios &longs;ibi &aelig;quales tam &longs;upra, qu&agrave;m infra habere, qua ra&shy;<lb/>tione deberet etiam Iris, &amp; altius, &amp; inferius apparere.</s></p><p type="main">
  
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 <s><margin.target id="marg174"></margin.target>183</s></p><p type="main"> <s><margin.target id="marg174"></margin.target>183</s></p><p type="main">
  
 <s>Tex. </s> <s>Tex. 11. <emph type="italics"/>(Videtur autem non &longs;olum ip&longs;um quid e&longs;t cogno&longs;cere vtile e&longs;&longs;e <lb/>ad cogno&longs;cendas cau&longs;as accidentium &longs;ub&longs;tantijs: &longs;icut in Mathemati&shy;<lb/>cis quid rectum, &amp; quid obliqaum, aut quid linea, &amp; planum, ad co&shy;<lb/>gno&longs; cendum quot rectis, trianguli anguli &longs;unt &aelig;quales)<emph.end type="italics"/> quid &longs;it <expan abbr="vnum-quodq;">vnum&shy;<lb/>quodque</expan> ex pr&aelig;dictis patet tum ex definitionibus primi Elem.
  
 <s>11. <emph type="italics"/>(Videtur autem non &longs;olum ip&longs;um quid e&longs;t cogno&longs;cere vtile e&longs;&longs;e <lb/>ad cogno&longs;cendas cau&longs;as accidentium &longs;ub&longs;tantijs: &longs;icut in Mathemati&shy;<lb/>cis quid rectum, &amp; quid obliqaum, aut quid linea, &amp; planum, ad co&shy;<lb/>gno&longs; cendum quot rectis, trianguli anguli &longs;unt &aelig;quales)<emph.end type="italics"/> quid &longs;it <expan abbr="vnum-quodq;">vnum&shy;<lb/>quodque</expan> ex pr&aelig;dictis patet tum ex definitionibus primi Elem.  
  
 tum ex com&shy;<lb/>mentarijs ip&longs;arum; quamuis autem ibi non definiatur <expan abbr="rect&utilde;">rectum</expan>, nec obliquum <lb/>in genere, definitur tamen linea recta, &amp; obliqua, &amp; plana &longs;uperficies, &longs;iue <lb/>planum, ex quibus facil&egrave; definitio recti, &amp; obliqui colligi pote&longs;t: qu&aelig; defi&shy;<lb/>nitiones nece&longs;&longs;ari&aelig; &longs;unt ad cogno&longs;cendum quot rectis angulis &aelig;quales &longs;int <lb/>tres anguli cuiufuis trianguli. </s> tum ex com&shy;<lb/>mentarijs ip&longs;arum; quamuis autem ibi non definiatur <expan abbr="rect&utilde;">rectum</expan>, nec obliquum <lb/>in genere, definitur tamen linea recta, &amp; obliqua, &amp; plana &longs;uperficies, &longs;iue <lb/>planum, ex quibus facil&egrave; definitio recti, &amp; obliqui colligi pote&longs;t: qu&aelig; defi&shy;<lb/>nitiones nece&longs;&longs;ari&aelig; &longs;unt ad cogno&longs;cendum quot rectis angulis &aelig;quales &longs;int <lb/>tres anguli cuiufuis trianguli. </s>
  
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 <s><margin.target id="marg175"></margin.target>184</s></p><p type="main"> <s><margin.target id="marg175"></margin.target>184</s></p><p type="main">
  
 <s>Tex. </s> <s>Tex. 13. <emph type="italics"/>(Si igitur e&longs;t aliqua anim&aelig; operatio, aut pa&longs;&longs;io propria, continget vti&shy;<lb/>que ip&longs;am &longs;eparari: &longs;i ver&ograve; nulla e&longs;t propria ip&longs;ius non vtique erit &longs;eparabilis. </s>
  
 <s>13. <emph type="italics"/>(Si igitur e&longs;t aliqua anim&aelig; operatio, aut pa&longs;&longs;io propria, continget vti&shy;<lb/>que ip&longs;am &longs;eparari: &longs;i ver&ograve; nulla e&longs;t propria ip&longs;ius non vtique erit &longs;eparabilis. </s> 
  
 <s>&longs;ed <lb/>&longs;icut recto in quantum rectum multa accidunt, vt tangere &aelig;<gap/>eam &longs;ph&aelig;ram &longs;ecun&shy;<lb/>dum punctum, non tamen tanget hoc, rectum ip&longs;um &longs;eparatum: in&longs;eparabile enim, <lb/>&longs;i quidem cum corpore quodam &longs;emper e&longs;t)<emph.end type="italics"/> Propo&longs;itio 2. tertij Elem.  <s>&longs;ed <lb/>&longs;icut recto in quantum rectum multa accidunt, vt tangere &aelig;<gap/>eam &longs;ph&aelig;ram &longs;ecun&shy;<lb/>dum punctum, non tamen tanget hoc, rectum ip&longs;um &longs;eparatum: in&longs;eparabile enim, <lb/>&longs;i quidem cum corpore quodam &longs;emper e&longs;t)<emph.end type="italics"/> Propo&longs;itio 2. tertij Elem.
  
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 <s><margin.target id="marg176"></margin.target>185</s></p><p type="main"> <s><margin.target id="marg176"></margin.target>185</s></p><p type="main">
  
 <s>Tex. </s> <s>Tex. 12. <emph type="italics"/>(Non enim &longs;olum ip&longs;um, quod&longs;it, oportet definitiuam rationem <lb/>oftendere, &longs;icut plures definitionum dicunt, &longs;ed &amp; cau&longs;am ine&longs;&longs;e, &amp; ap&shy;<lb/>parere. </s>
  
 <s>12. <emph type="italics"/>(Non enim &longs;olum ip&longs;um, quod&longs;it, oportet definitiuam rationem <lb/>oftendere, &longs;icut plures definitionum dicunt, &longs;ed &amp; cau&longs;am ine&longs;&longs;e, &amp; ap&shy;<lb/>parere. </s> 
  
 <s>nunc autem, vt conclu&longs;iones rationes definitionum &longs;unt, vt quid <lb/>tetragoni&longs;mus? </s> <s>nunc autem, vt conclu&longs;iones rationes definitionum &longs;unt, vt quid <lb/>tetragoni&longs;mus? </s>
  
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 <s><margin.target id="marg177"></margin.target>186</s></p><p type="main"> <s><margin.target id="marg177"></margin.target>186</s></p><p type="main">
  
 <s>Tex. </s> <s>Tex. 86. <emph type="italics"/>(Acutum mouet &longs;en&longs;um in tempore pauco mult&ugrave;m: graue autem in <lb/>multo par&ugrave;m; non igitur velox e&longs;t acutum, graue autem tardum, fed fit illius qui&shy;<lb/>dem propter velocitatem motus huiu&longs;modi, huius autem propter tarditatem)<emph.end type="italics"/> vide <lb/>qu&aelig; de hac re primo topic. </s>
  
 <s>86. <emph type="italics"/>(Acutum mouet &longs;en&longs;um in tempore pauco mult&ugrave;m: graue autem in <lb/>multo par&ugrave;m; non igitur velox e&longs;t acutum, graue autem tardum, fed fit illius qui&shy;<lb/>dem propter velocitatem motus huiu&longs;modi, huius autem propter tarditatem)<emph.end type="italics"/> vide <lb/>qu&aelig; de hac re primo topic. </s> 
  
 <s>cap.  <s>cap.
  
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 <s><margin.target id="marg178"></margin.target>187</s></p><p type="main"> <s><margin.target id="marg178"></margin.target>187</s></p><p type="main">
  
 <s>Tex. </s> <s>Tex. 159. <emph type="italics"/>(Apparent autem, &amp; fal&longs;a, de quibus &longs;imul exi&longs;timationem veram <lb/>habet, vt apparet &longs;ol vnius pedis, per&longs;ua&longs;um autem e&longs;t, eum maiorem e&longs;&longs;e babitata)<emph.end type="italics"/><lb/>habitata, ide&longs;t terra habitata. </s>
  
 <s>159. <emph type="italics"/>(Apparent autem, &amp; fal&longs;a, de quibus &longs;imul exi&longs;timationem veram <lb/>habet, vt apparet &longs;ol vnius pedis, per&longs;ua&longs;um autem e&longs;t, eum maiorem e&longs;&longs;e babitata)<emph.end type="italics"/><lb/>habitata, ide&longs;t terra habitata. </s> 
  
 <s>Vide, qu&aelig; cap.  <s>Vide, qu&aelig; cap.
  
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 <s><margin.target id="marg179"></margin.target>188</s></p><p type="main"> <s><margin.target id="marg179"></margin.target>188</s></p><p type="main">
  
 <s>Tex. </s> <s>Tex. 21. <emph type="italics"/>(Vt incommen&longs;urabile, &amp; diameter)<emph.end type="italics"/> vide, qu&aelig; de incom&shy;<lb/>men&longs;uratione diametri, &amp; co&longs;t&aelig; &longs;cripta &longs;unt lib.
  
 <s>21. <emph type="italics"/>(Vt incommen&longs;urabile, &amp; diameter)<emph.end type="italics"/> vide, qu&aelig; de incom&shy;<lb/>men&longs;uratione diametri, &amp; co&longs;t&aelig; &longs;cripta &longs;unt lib.  
  
 1. Priorum, cap. <lb/></s> 1. Priorum, cap. <lb/>23. vnde &longs;atis huic loco fieri pote&longs;t.</s></p><p type="main">
  
 <s>23. vnde &longs;atis huic loco fieri pote&longs;t.</s></p><p type="main"> 
  
 <s><arrow.to.target n="marg180"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg180"></arrow.to.target></s></p><p type="margin">
  
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 <s><margin.target id="marg181"></margin.target>190</s></p><p type="main"> <s><margin.target id="marg181"></margin.target>190</s></p><p type="main">
  
 <s>Tex. </s> <s>Tex. 32. <emph type="italics"/>(Sit igitur vt A, quidem album, ad B, quod nigrum; &longs;ic C, ad D; qua&shy;<lb/>re &amp; p<gap/>rmutatim)<emph.end type="italics"/> ide&longs;t, quare &amp; permutando (vt aiunt Geometr&aelig;) erit vt <lb/>A, ad C, ita B, ad D, hunc argumentandi modum &agrave; permutata proportio&shy;<lb/>ne explicaui in primo Po&longs;ter. cap.
  
 <s>32. <emph type="italics"/>(Sit igitur vt A, quidem album, ad B, quod nigrum; &longs;ic C, ad D; qua&shy;<lb/>re &amp; p<gap/>rmutatim)<emph.end type="italics"/> ide&longs;t, quare &amp; permutando (vt aiunt Geometr&aelig;) erit vt <lb/>A, ad C, ita B, ad D, hunc argumentandi modum &agrave; permutata proportio&shy;<lb/>ne explicaui in primo Po&longs;ter. </s> 
  
 <s>cap.  
  
 5. tex. </s> 5. tex. </s>
  
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 <s><margin.target id="marg182"></margin.target>191</s></p><p type="main"> <s><margin.target id="marg182"></margin.target>191</s></p><p type="main">
  
 <s>Cap, 6. <emph type="italics"/>(Et qui in Die&longs;i &longs;onus latet, quamuis contin<gap/>um exi&longs;tentem audit <lb/>omnem cantum, di&longs;t antia enim eius ad extremos &longs;onos latet)<emph.end type="italics"/> quid &longs;it <lb/>Die&longs;is apud Mu&longs;icos explicatum e&longs;t primo Po&longs;ter. </s> <s>Cap, 6. <emph type="italics"/>(Et qui in Die&longs;i &longs;onus latet, quamuis contin<gap/>um exi&longs;tentem audit <lb/>omnem cantum, di&longs;t antia enim eius ad extremos &longs;onos latet)<emph.end type="italics"/> quid &longs;it <lb/>Die&longs;is apud Mu&longs;icos explicatum e&longs;t primo Po&longs;ter. tex. </s>
  
 <s>tex. </s> 
  
 <s>38. cum <lb/>autem Die&longs;is &longs;it minima di&longs;tantia, &longs;eu vt loquuntur Mu&longs;ici, mini&shy;<lb/>mum <expan abbr="interuall&utilde;">interuallum</expan> inter duas voces, hinc fit vt h&aelig;c minima di&longs;tantia inter ex&shy;<lb/>tremos &longs;onos non exaudiatur, quemadmodum nec minima particula alicu&shy;<lb/>ius magni corporis &agrave; long&egrave; vi&longs;i <expan abbr="n&otilde;">non</expan> percipitur, &longs;ed latetinter extrema illius.</s></p><p type="main"> <s>38. cum <lb/>autem Die&longs;is &longs;it minima di&longs;tantia, &longs;eu vt loquuntur Mu&longs;ici, mini&shy;<lb/>mum <expan abbr="interuall&utilde;">interuallum</expan> inter duas voces, hinc fit vt h&aelig;c minima di&longs;tantia inter ex&shy;<lb/>tremos &longs;onos non exaudiatur, quemadmodum nec minima particula alicu&shy;<lb/>ius magni corporis &agrave; long&egrave; vi&longs;i <expan abbr="n&otilde;">non</expan> percipitur, &longs;ed latetinter extrema illius.</s></p><p type="main">
  
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 <s><margin.target id="marg184"></margin.target>193</s></p><p type="main"> <s><margin.target id="marg184"></margin.target>193</s></p><p type="main">
  
 <s>Eodem cap. <emph type="italics"/>(Velut Diapa&longs;on, &amp; Diapente)<emph.end type="italics"/> quid &longs;it con&longs;onantia Diapa&shy;<lb/>&longs;on, explicaui in primo Po&longs;ter. </s> <s>Eodem cap. <emph type="italics"/>(Velut Diapa&longs;on, &amp; Diapente)<emph.end type="italics"/> quid &longs;it con&longs;onantia Diapa&shy;<lb/>&longs;on, explicaui in primo Po&longs;ter. tex. </s>
  
 <s>tex. </s> 
  
 <s>1. Diapente ver&ograve; e&longs;t con&longs;onantia ex duo&shy;<lb/><figure id="fig67"></figure><lb/>bus &longs;onis coale&longs;cens, quorum proportio &longs;it vt <lb/>3. ad 2. qu&aelig; dicitur &longs;e&longs;quialtera. </s> <s>1. Diapente ver&ograve; e&longs;t con&longs;onantia ex duo&shy;<lb/><figure id="fig67"></figure><lb/>bus &longs;onis coale&longs;cens, quorum proportio &longs;it vt <lb/>3. ad 2. qu&aelig; dicitur &longs;e&longs;quialtera. </s>
  
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 <s>Cap. 1. <emph type="italics"/>(Sic meminit eos, qui trianguli, quod duobus rectis &aelig;quales)<emph.end type="italics"/> ide&longs;t <lb/>&longs;ic meminit tres angulos cuiu&longs;uis trianguli &longs;imul &longs;umptos &aelig;qua&shy;<lb/>les e&longs;&longs;e duobus angulis rectis &longs;imul &longs;umptis. </s> <s>Cap. 1. <emph type="italics"/>(Sic meminit eos, qui trianguli, quod duobus rectis &aelig;quales)<emph.end type="italics"/> ide&longs;t <lb/>&longs;ic meminit tres angulos cuiu&longs;uis trianguli &longs;imul &longs;umptos &aelig;qua&shy;<lb/>les e&longs;&longs;e duobus angulis rectis &longs;imul &longs;umptis. </s>
  
  
 <s>lege annotata primo <lb/>Po&longs;ter. </s> <s>lege annotata primo <lb/>Po&longs;ter. &longs;ecto 3. cap.
  
 <s>&longs;ecto 3. cap.  
  
 1.</s></p><p type="main"> 1.</s></p><p type="main">
  
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 3. propo&longs;it. </s> 3. propo&longs;it. </s>
  
 <s>11. &amp; 12. &amp; infra <lb/>Problem. </s> <s>11. &amp; 12. &amp; infra <lb/>Problem. 7. &longs;ectionis 31.</s></p><figure></figure><pb pagenum="137"/><p type="head">
  
 <s>7. &longs;ectionis 31.</s></p><figure></figure><pb pagenum="137"/><p type="head"> 
  
 <s>EX PRIMO</s></p><p type="head"> <s>EX PRIMO</s></p><p type="head">
  
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 <s><margin.target id="marg194"></margin.target>203</s></p><p type="main"> <s><margin.target id="marg194"></margin.target>203</s></p><p type="main">
  
 <s>Tex. </s> <s>Tex. 47. (<emph type="italics"/>Qui Geometriam di&longs;cit aliqua pr&aelig;&longs;cire contingit<emph.end type="italics"/>) ide&longs;t definitio&shy;<lb/>nes, po&longs;tulata, axiomata, qu&aelig; &longs;unt tria principiorum genera, ex quibus to&shy;<lb/>ta Geometria deducitur.</s></p><p type="head">
  
 <s>47. (<emph type="italics"/>Qui Geometriam di&longs;cit aliqua pr&aelig;&longs;cire contingit<emph.end type="italics"/>) ide&longs;t definitio&shy;<lb/>nes, po&longs;tulata, axiomata, qu&aelig; &longs;unt tria principiorum genera, ex quibus to&shy;<lb/>ta Geometria deducitur.</s></p><p type="head"> 
  
 <s><emph type="italics"/>Ex Secundo Metaphy&longs;ic&aelig;.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Ex Secundo Metaphy&longs;ic&aelig;.<emph.end type="italics"/></s></p><p type="main">
  
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 <s><margin.target id="marg195"></margin.target>204</s></p><p type="main"> <s><margin.target id="marg195"></margin.target>204</s></p><p type="main">
  
 <s>Tex. </s> <s>Tex. 14. (<emph type="italics"/>Quantam ver&ograve; vim con&longs;uetudo habeat, leges declar ant, in qui&shy;<lb/>bus fabulo&longs;a, ac puerilia plus po&longs;&longs;unt propter con&longs;uetudinem, qu&agrave;m &longs;i <lb/>ea cogno&longs;ceremus<emph.end type="italics"/>) per leges intelligit cantilenas illas, quas vete&shy;<lb/>res Mu&longs;ici leges appellabant, e&ograve; qu&ograve;d eas &longs;olas, c&aelig;teris abroga&shy;<lb/>tis liceret lata lege decantari. </s>
  
 <s>14. (<emph type="italics"/>Quantam ver&ograve; vim con&longs;uetudo habeat, leges declar ant, in qui&shy;<lb/>bus fabulo&longs;a, ac puerilia plus po&longs;&longs;unt propter con&longs;uetudinem, qu&agrave;m &longs;i <lb/>ea cogno&longs;ceremus<emph.end type="italics"/>) per leges intelligit cantilenas illas, quas vete&shy;<lb/>res Mu&longs;ici leges appellabant, e&ograve; qu&ograve;d eas &longs;olas, c&aelig;teris abroga&shy;<lb/>tis liceret lata lege decantari. </s> 
  
 <s>Vide declarationem problematis 15. &amp; 28. <lb/>&longs;ect. </s> <s>Vide declarationem problematis 15. &amp; 28. <lb/>&longs;ect. </s>
  
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 <s><margin.target id="marg196"></margin.target>205</s></p><p type="main"> <s><margin.target id="marg196"></margin.target>205</s></p><p type="main">
  
 <s>Tex. </s> <s>Tex. 3. Verba huius textus, cum &longs;atis per&longs;picua &longs;int, ac parum ma&shy;<lb/>thematicis indigeant, omittenda duxi. </s>
  
 <s>3. Verba huius textus, cum &longs;atis per&longs;picua &longs;int, ac parum ma&shy;<lb/>thematicis indigeant, omittenda duxi. </s> 
  
 <s>Quod ad mathematicas <lb/>attinet, ait, eas non demon&longs;trare, nec per cau&longs;am finalem, nec <lb/>per efficientem (quod intelligendum e&longs;t de Mathematicis puris, <lb/>&amp; &longs;peculatiuis nam mathematic&aelig; practic&aelig; reliquas etiam cau&longs;as, efficien&shy;<lb/>tem, &amp; finalem nece&longs;&longs;ari&ograve; habere debent, quapropter &longs;ophi&longs;ta quidam no&shy;<lb/>mine Ari&longs;tippus, eas irridebat, <expan abbr="atq;">atque</expan> adeo illiberalibus, ac &longs;edentarijs arti&shy;<lb/>bus po&longs;thabebat, qu&aelig; cau&longs;am efficientem, quia &longs;cilicet operantur, &amp; fina&shy;<lb/>lem &longs;cilicet qu&aelig;&longs;tum &longs;ibi proponunt. </s> <s>Quod ad mathematicas <lb/>attinet, ait, eas non demon&longs;trare, nec per cau&longs;am finalem, nec <lb/>per efficientem (quod intelligendum e&longs;t de Mathematicis puris, <lb/>&amp; &longs;peculatiuis nam mathematic&aelig; practic&aelig; reliquas etiam cau&longs;as, efficien&shy;<lb/>tem, &amp; finalem nece&longs;&longs;ari&ograve; habere debent, quapropter &longs;ophi&longs;ta quidam no&shy;<lb/>mine Ari&longs;tippus, eas irridebat, <expan abbr="atq;">atque</expan> adeo illiberalibus, ac &longs;edentarijs arti&shy;<lb/>bus po&longs;thabebat, qu&aelig; cau&longs;am efficientem, quia &longs;cilicet operantur, &amp; fina&shy;<lb/>lem &longs;cilicet qu&aelig;&longs;tum &longs;ibi proponunt. </s>
  
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 <s><margin.target id="marg198"></margin.target>207</s></p><p type="main"> <s><margin.target id="marg198"></margin.target>207</s></p><p type="main">
  
 <s>Tex. </s> <s>Tex. 8. (<emph type="italics"/>Si enim in hoc differret &longs;olum Geometria &agrave; Geod&aelig;&longs;ia, quod h&aelig;c quidem <lb/>eorum e&longs;t, qu&aelig; &longs;entimus, illa ver&ograve; non &longs;en&longs;ibilium e&longs;t<emph.end type="italics"/>) Geod&aelig;&longs;ia e&longs;t pars Geo&shy;<lb/>metri&aelig; practic&aelig;, ea &longs;cilicet, qu&aelig; circa diui&longs;ionem &longs;uperficierum ver&longs;atur. <lb/></s>
  
 <s>8. (<emph type="italics"/>Si enim in hoc differret &longs;olum Geometria &agrave; Geod&aelig;&longs;ia, quod h&aelig;c quidem <lb/>eorum e&longs;t, qu&aelig; &longs;entimus, illa ver&ograve; non &longs;en&longs;ibilium e&longs;t<emph.end type="italics"/>) Geod&aelig;&longs;ia e&longs;t pars Geo&shy;<lb/>metri&aelig; practic&aelig;, ea &longs;cilicet, qu&aelig; circa diui&longs;ionem &longs;uperficierum ver&longs;atur. <lb/></s> 
  
 <s>audi Pedia&longs;mum de men&longs;uratione: Terr&aelig; inquit men&longs;uratio in duas partes <lb/>diuiditur, Geometriam &longs;cilicet, &amp; Geod&aelig;&longs;iam: Are&aelig; <expan abbr="namq;">namque</expan> &longs;ecundum ar&shy;<lb/>tem men&longs;uratio, &amp; terr&aelig; men&longs;uratio e&longs;t, &amp; merit&ograve; Geometria vocatur. <lb/></s> <s>audi Pedia&longs;mum de men&longs;uratione: Terr&aelig; inquit men&longs;uratio in duas partes <lb/>diuiditur, Geometriam &longs;cilicet, &amp; Geod&aelig;&longs;iam: Are&aelig; <expan abbr="namq;">namque</expan> &longs;ecundum ar&shy;<lb/>tem men&longs;uratio, &amp; terr&aelig; men&longs;uratio e&longs;t, &amp; merit&ograve; Geometria vocatur. <lb/></s>
  
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 <s><margin.target id="marg199"></margin.target>208</s></p><p type="main"> <s><margin.target id="marg199"></margin.target>208</s></p><p type="main">
  
 <s>Tex. </s> <s>Tex. 4. <emph type="italics"/>(Philo&longs;ophus <expan abbr="namq;">namque</expan> e&longs;t, vt ille, qui Mathematicus dicitur, &amp; <lb/>b&aelig;c enim habet partes: ac prima qu&aelig;dam, &amp; &longs;ecunda &longs;cientia e&longs;t: c&aelig; <lb/>ter&aelig; <expan abbr="quoq;">quoque</expan> con&longs;equenter in mathematibus<emph.end type="italics"/>) inter mathematicas pri&shy;<lb/>m&aelig; &longs;cienti&aelig; &longs;unt Geometria, &amp; Arithmetica, quia ip&longs;&aelig; &agrave; c&aelig;teris <lb/>nulla ratione dependent; im&ograve; c&aelig;ter&aelig; ip&longs;is innituntur, qu&aelig; &longs;ecund&aelig; hoc lo&shy;<lb/>co appellantur, h&aelig; &longs;unt Per&longs;pectiua, Mu&longs;ica, Mechanica, A&longs;tronomia. </s>
  
 <s>4. <emph type="italics"/>(Philo&longs;ophus <expan abbr="namq;">namque</expan> e&longs;t, vt ille, qui Mathematicus dicitur, &amp; <lb/>b&aelig;c enim habet partes: ac prima qu&aelig;dam, &amp; &longs;ecunda &longs;cientia e&longs;t: c&aelig; <lb/>ter&aelig; <expan abbr="quoq;">quoque</expan> con&longs;equenter in mathematibus<emph.end type="italics"/>) inter mathematicas pri&shy;<lb/>m&aelig; &longs;cienti&aelig; &longs;unt Geometria, &amp; Arithmetica, quia ip&longs;&aelig; &agrave; c&aelig;teris <lb/>nulla ratione dependent; im&ograve; c&aelig;ter&aelig; ip&longs;is innituntur, qu&aelig; &longs;ecund&aelig; hoc lo&shy;<lb/>co appellantur, h&aelig; &longs;unt Per&longs;pectiua, Mu&longs;ica, Mechanica, A&longs;tronomia. </s> 
  
 <s>illas <lb/>duas recentiores &longs;ubalternantes, has ver&ograve; &longs;ecundas &longs;ubalternatas vocant. <lb/></s> <s>illas <lb/>duas recentiores &longs;ubalternantes, has ver&ograve; &longs;ecundas &longs;ubalternatas vocant. <lb/></s>
  
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 <s><margin.target id="marg200"></margin.target>209</s></p><p type="main"> <s><margin.target id="marg200"></margin.target>209</s></p><p type="main">
  
 <s>Tex. </s> <s>Tex. 28. (<emph type="italics"/>Vti diametrum commen&longs;urabilem e&longs;&longs;e<emph.end type="italics"/>) legenda &longs;unt ea, qu&aelig; libro <lb/>primo Priorum, &longs;ecto 1. cap.
  
 <s>28. (<emph type="italics"/>Vti diametrum commen&longs;urabilem e&longs;&longs;e<emph.end type="italics"/>) legenda &longs;unt ea, qu&aelig; libro <lb/>primo Priorum, &longs;ecto 1. cap.  
  
 23. de hac commen&longs;urabilitate, &amp; incommen&shy;<lb/>&longs;urabilitate tractata &longs;unt.</s></p><figure></figure><pb pagenum="140"/><p type="head"> 23. de hac commen&longs;urabilitate, &amp; incommen&shy;<lb/>&longs;urabilitate tractata &longs;unt.</s></p><figure></figure><pb pagenum="140"/><p type="head">
  
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 <s><margin.target id="marg201"></margin.target>210</s></p><p type="main"> <s><margin.target id="marg201"></margin.target>210</s></p><p type="main">
  
 <s>Tex. </s> <s>Tex. 2. (<emph type="italics"/>Alia ver&ograve; cau&longs;a e&longs;t forma, &amp; exemplar: h&aelig;c autem e&longs;t ratio ip&shy;<lb/>&longs;ius quid erat e&longs;&longs;e, &amp; borum genera, vt ip&longs;ius Diapa&longs;on duo ad vnum, <lb/>&amp; &longs;impliciter numerus, &amp; partes, qu&aelig; in ra ione &longs;unt<emph.end type="italics"/>) affert exem&shy;<lb/>plum cau&longs;&aelig; formalis ex Mu&longs;ica petitum; <expan abbr="ait&qacute;">aitque</expan>; cau&longs;am formalem <lb/>illius con&longs;onanti&aelig;, qu&aelig; Diapa&longs;on dicitur, <expan abbr="e&longs;t&qacute;">e&longs;tque</expan>; omnium perfecti&longs;&longs;ima, e&longs;&longs;e <lb/>duplam proportionem, ide&longs;t, qu&aelig; e&longs;t inter duo, &amp; vnum, id, quod omnes <lb/>Mu&longs;ici <expan abbr="fat&etilde;tur">fatentur</expan>. </s>
  
 <s>2. (<emph type="italics"/>Alia ver&ograve; cau&longs;a e&longs;t forma, &amp; exemplar: h&aelig;c autem e&longs;t ratio ip&shy;<lb/>&longs;ius quid erat e&longs;&longs;e, &amp; borum genera, vt ip&longs;ius Diapa&longs;on duo ad vnum, <lb/>&amp; &longs;impliciter numerus, &amp; partes, qu&aelig; in ra ione &longs;unt<emph.end type="italics"/>) affert exem&shy;<lb/>plum cau&longs;&aelig; formalis ex Mu&longs;ica petitum; <expan abbr="ait&qacute;">aitque</expan>; cau&longs;am formalem <lb/>illius con&longs;onanti&aelig;, qu&aelig; Diapa&longs;on dicitur, <expan abbr="e&longs;t&qacute;">e&longs;tque</expan>; omnium perfecti&longs;&longs;ima, e&longs;&longs;e <lb/>duplam proportionem, ide&longs;t, qu&aelig; e&longs;t inter duo, &amp; vnum, id, quod omnes <lb/>Mu&longs;ici <expan abbr="fat&etilde;tur">fatentur</expan>. </s> 
  
 <s>quod vtinelius intelligas, repete, qu&aelig; in 2. Po&longs;ter. </s> <s>quod vtinelius intelligas, repete, qu&aelig; in 2. Po&longs;ter. ad tex. </s>
  
 <s>ad tex. </s> 
  
 <s>1. <lb/>&longs;cripta &longs;unt: necnon qu&aelig; in libro de Sen&longs;u in cap.  <s>1. <lb/>&longs;cripta &longs;unt: necnon qu&aelig; in libro de Sen&longs;u in cap.
  
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 <s><margin.target id="marg202"></margin.target>211</s></p><p type="main"> <s><margin.target id="marg202"></margin.target>211</s></p><p type="main">
  
 <s>Tex. </s> <s>Tex. 3. <emph type="italics"/>(Partes <expan abbr="quoq;">quoque</expan> totius<emph.end type="italics"/>) ide&longs;t &longs;unt inateria; loquitur enim de cau&longs;a <lb/>materiali. </s>
  
 <s>3. <emph type="italics"/>(Partes <expan abbr="quoq;">quoque</expan> totius<emph.end type="italics"/>) ide&longs;t &longs;unt inateria; loquitur enim de cau&longs;a <lb/>materiali. </s> 
  
 <s>libuit locum hunc annotare in gratiam Geometricarum demon&shy;<lb/>&longs;trationum, quorum media &longs;&aelig;p&egrave; &longs;unt ex cau&longs;a materiali &longs;umpta, quod ta&shy;<lb/>men non ita ab omnibus ob&longs;eruatur, <expan abbr="quotie&longs;cunq;">quotie&longs;cunque</expan> enim probant affe ctio&shy;<lb/>nem quampiam de aliquo &longs;ubiecto, ex eo, quod &longs;ubiectum illud &longs;it, vel di&shy;<lb/>midium alicuius, vel duplum, vel reliquum, vel tertia pars, &amp; his &longs;imilia, <lb/>erit talis ratio in genere cau&longs;&aelig; materialis. </s> <s>libuit locum hunc annotare in gratiam Geometricarum demon&shy;<lb/>&longs;trationum, quorum media &longs;&aelig;p&egrave; &longs;unt ex cau&longs;a materiali &longs;umpta, quod ta&shy;<lb/>men non ita ab omnibus ob&longs;eruatur, <expan abbr="quotie&longs;cunq;">quotie&longs;cunque</expan> enim probant affe ctio&shy;<lb/>nem quampiam de aliquo &longs;ubiecto, ex eo, quod &longs;ubiectum illud &longs;it, vel di&shy;<lb/>midium alicuius, vel duplum, vel reliquum, vel tertia pars, &amp; his &longs;imilia, <lb/>erit talis ratio in genere cau&longs;&aelig; materialis. </s>
  
 <s><expan abbr="neq;">neque</expan> e&longs;t cur recentiores quidam, <lb/>naturalibus &longs;cientijs a&longs;&longs;ueti, negent huiu&longs;modi materiam veram e&longs;&longs;emate&shy;<lb/>riam, ac proinde neq, Geometricas demon&longs;trationes veras e&longs;&longs;e demon&longs;tra&shy;<lb/>tiones; dicendum enim talem quidem materiam non e&longs;&longs;e veram materiam <lb/>phy&longs;icam, &amp; proinde illas demon&longs;trationes <expan abbr="n&otilde;">non</expan> e&longs;&longs;e veras naturales demon&shy;<lb/>&longs;irationes, e&longs;&longs;e tamen veram materiam intelligibilem, qu&aelig; Geometri&aelig; &longs;u&shy;<lb/>bijcitur, &amp; proinde demon&longs;trationes illas veras e&longs;&longs;e demon&longs;trationes Geo&shy;<lb/>metricas; id quod Ari&longs;t. </s> <s><expan abbr="neq;">neque</expan> e&longs;t cur recentiores quidam, <lb/>naturalibus &longs;cientijs a&longs;&longs;ueti, negent huiu&longs;modi materiam veram e&longs;&longs;emate&shy;<lb/>riam, ac proinde neq, Geometricas demon&longs;trationes veras e&longs;&longs;e demon&longs;tra&shy;<lb/>tiones; dicendum enim talem quidem materiam non e&longs;&longs;e veram materiam <lb/>phy&longs;icam, &amp; proinde illas demon&longs;trationes <expan abbr="n&otilde;">non</expan> e&longs;&longs;e veras naturales demon&shy;<lb/>&longs;irationes, e&longs;&longs;e tamen veram materiam intelligibilem, qu&aelig; Geometri&aelig; &longs;u&shy;<lb/>bijcitur, &amp; proinde demon&longs;trationes illas veras e&longs;&longs;e demon&longs;trationes Geo&shy;<lb/>metricas; id quod Ari&longs;t. &longs;&aelig;pius in libris Po&longs;ter, apert&egrave; &longs;ignificat, tum a&longs;&longs;er&shy;<lb/>tionibus, tum exemplis quamplurimis. </s>
  
 <s>&longs;&aelig;pius in libris Po&longs;ter, apert&egrave; &longs;ignificat, tum a&longs;&longs;er&shy;<lb/>tionibus, tum exemplis quamplurimis. </s> 
  
 <s>Quapropter cauendum e&longs;t illis, ne <lb/>ingrati animi notam incurrant, dum pulcherrimam artem re&longs;olutoriam, <lb/>quam Ari&longs;t. </s> <s>Quapropter cauendum e&longs;t illis, ne <lb/>ingrati animi notam incurrant, dum pulcherrimam artem re&longs;olutoriam, <lb/>quam Ari&longs;t. &agrave; Mathematicis acceptam omnibus &longs;cientijs accommodauit <lb/>(vt initio Priorum o&longs;ten&longs;um e&longs;t) eam ip&longs;i ita alijs facultatibus adaptent, vt <lb/>Mathematicis ip&longs;is, ex quibus orta, &amp; &longs;ub quibus adoleuit, pulla ratione <lb/>conuenire poi&longs;it. </s>
  
 <s>&agrave; Mathematicis acceptam omnibus &longs;cientijs accommodauit <lb/>(vt initio Priorum o&longs;ten&longs;um e&longs;t) eam ip&longs;i ita alijs facultatibus adaptent, vt <lb/>Mathematicis ip&longs;is, ex quibus orta, &amp; &longs;ub quibus adoleuit, pulla ratione <lb/>conuenire poi&longs;it. </s> 
  
 <s>De hac materia fu&longs;ius infra in additamento de natura Ma&shy;<lb/>thematicarum.</s></p><p type="main"> <s>De hac materia fu&longs;ius infra in additamento de natura Ma&shy;<lb/>thematicarum.</s></p><p type="main">
  
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 <s><margin.target id="marg203"></margin.target>212</s></p><p type="main"> <s><margin.target id="marg203"></margin.target>212</s></p><p type="main">
  
 <s>Tex. </s> <s>Tex. 3. (<emph type="italics"/>Et ip&longs;ius Diapa&longs;on duplum, &amp; numerus<emph.end type="italics"/>) &longs;cilicet cau&longs;&aelig; formales <lb/>&longs;unt, quemadmodum &longs;upra tex. </s>
  
 <s>3. (<emph type="italics"/>Et ip&longs;ius Diapa&longs;on duplum, &amp; numerus<emph.end type="italics"/>) &longs;cilicet cau&longs;&aelig; formales <lb/>&longs;unt, quemadmodum &longs;upra tex. </s> 
  
 <s>2. huius cap.  <s>2. huius cap.
  
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 <s><margin.target id="marg204"></margin.target>213</s></p><p type="main"> <s><margin.target id="marg204"></margin.target>213</s></p><p type="main">
  
 <s>Tex. </s> <s>Tex. 4. (<emph type="italics"/>Similiter autem figurationum <expan abbr="quoq;">quoque</expan> elementa dicuntur, ac &longs;impliciter <lb/>demon&longs;trationum prim&aelig; enim demon&longs;trationes, qu&aelig; in pluribus demonstr ationbus <lb/>in&longs;unt, h&aelig;c elementa demon&longs;trationum dicuntur<emph.end type="italics"/>) verbo (<emph type="italics"/>Figurationum<emph.end type="italics"/>) &longs;iue <expan abbr="de-&longs;cription&utilde;">de&shy;<lb/>&longs;criptionum</expan>, Ari&longs;t, intelligere demon&longs;trationes Geometricas, &longs;&aelig;pius dictum <lb/>e&longs;t, pr&aelig;&longs;ertim in Logicis, &amp; ex hoc loco pariter confirmatur. </s>
  
 <s>4. (<emph type="italics"/>Similiter autem figurationum <expan abbr="quoq;">quoque</expan> elementa dicuntur, ac &longs;impliciter <lb/>demon&longs;trationum prim&aelig; enim demon&longs;trationes, qu&aelig; in pluribus demonstr ationbus <lb/>in&longs;unt, h&aelig;c elementa demon&longs;trationum dicuntur<emph.end type="italics"/>) verbo (<emph type="italics"/>Figurationum<emph.end type="italics"/>) &longs;iue <expan abbr="de-&longs;cription&utilde;">de&shy;<lb/>&longs;criptionum</expan>, Ari&longs;t, intelligere demon&longs;trationes Geometricas, &longs;&aelig;pius dictum <lb/>e&longs;t, pr&aelig;&longs;ertim in Logicis, &amp; ex hoc loco pariter confirmatur. </s> 
  
 <s>Ex hoc por&shy;<lb/>r&ograve; loco illud innote&longs;cit dignum, quod pr&aelig;cipu&egrave; &agrave; Mathematico non igno&shy;<lb/>retur, qu&aelig; nam &longs;int demon&longs;trationes ill&aelig;, qu&aelig; nomine <expan abbr="elementor&utilde;">elementorum</expan> debeant <lb/>appelllari, necnon cau&longs;a cur Euclides &longs;uum opus elementa nuncupauerit, <lb/>&longs;unt enim ill&aelig;, qu&aelig; in pluribus demon&longs;trationibus in&longs;unt, ide&longs;t, qu&aelig; &longs;&aelig;pius <lb/>in alijs demon&longs;trationibus citantur, vti &longs;unt pr&aelig;cipu&egrave; &longs;ex priores libri Eu&shy;<lb/>clidis: <expan abbr="atq;">atque</expan> hac ratione elementa appellantur.</s></p><p type="main"> <s>Ex hoc por&shy;<lb/>r&ograve; loco illud innote&longs;cit dignum, quod pr&aelig;cipu&egrave; &agrave; Mathematico non igno&shy;<lb/>retur, qu&aelig; nam &longs;int demon&longs;trationes ill&aelig;, qu&aelig; nomine <expan abbr="elementor&utilde;">elementorum</expan> debeant <lb/>appelllari, necnon cau&longs;a cur Euclides &longs;uum opus elementa nuncupauerit, <lb/>&longs;unt enim ill&aelig;, qu&aelig; in pluribus demon&longs;trationibus in&longs;unt, ide&longs;t, qu&aelig; &longs;&aelig;pius <lb/>in alijs demon&longs;trationibus citantur, vti &longs;unt pr&aelig;cipu&egrave; &longs;ex priores libri Eu&shy;<lb/>clidis: <expan abbr="atq;">atque</expan> hac ratione elementa appellantur.</s></p><p type="main">
  
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 <s><margin.target id="marg205"></margin.target>214</s></p><p type="main"> <s><margin.target id="marg205"></margin.target>214</s></p><p type="main">
  
 <s>Tex. </s> <s>Tex. 12. <emph type="italics"/>(Principium <expan abbr="itaq;">itaque</expan> &longs;cibilis, circa <expan abbr="vnumquodq;">vnumquodque</expan> ip&longs;um vnum, non e&longs;t au&shy;<lb/>tem idem in cunct is generibus vnum, &longs;ed hic quidem die&longs;is, hic ver&ograve; vocalis, aut <lb/>muta)<emph.end type="italics"/> ide&longs;t, in Mu&longs;ica quidem principium omnium, &amp; elementum e&longs;t die&shy;<lb/>&longs;is, qu&aelig; e&longs;t minima vox, aut &longs;onus, qui &longs;ub Mu&longs;ici con&longs;iderationem cadat. <lb/></s>
  
 <s>12. <emph type="italics"/>(Principium <expan abbr="itaq;">itaque</expan> &longs;cibilis, circa <expan abbr="vnumquodq;">vnumquodque</expan> ip&longs;um vnum, non e&longs;t au&shy;<lb/>tem idem in cunct is generibus vnum, &longs;ed hic quidem die&longs;is, hic ver&ograve; vocalis, aut <lb/>muta)<emph.end type="italics"/> ide&longs;t, in Mu&longs;ica quidem principium omnium, &amp; elementum e&longs;t die&shy;<lb/>&longs;is, qu&aelig; e&longs;t minima vox, aut &longs;onus, qui &longs;ub Mu&longs;ici con&longs;iderationem cadat. <lb/></s> 
  
 <s>Porr&ograve; ad tex. </s> <s>Porr&ograve; ad tex. </s>
  
 <s>38. primi Po&longs;ter. </s> <s>38. primi Po&longs;ter. de die&longs;i plura &longs;unt dicta.</s></p><p type="main">
  
 <s>de die&longs;i plura &longs;unt dicta.</s></p><p type="main"> 
  
 <s><arrow.to.target n="marg206"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg206"></arrow.to.target></s></p><p type="margin">
  
 <s><margin.target id="marg206"></margin.target>215</s></p><p type="main"> <s><margin.target id="marg206"></margin.target>215</s></p><p type="main">
  
 <s>Tex. </s> <s>Tex. 17. <emph type="italics"/>(Veluti diametrum commen&longs;urabilem e&longs;&longs;e impo&longs;&longs;ibile est)<emph.end type="italics"/> huius expo&shy;<lb/>&longs;itionem inuenies 1. Priorum, &longs;ecto 1. cap.
  
 <s>17. <emph type="italics"/>(Veluti diametrum commen&longs;urabilem e&longs;&longs;e impo&longs;&longs;ibile est)<emph.end type="italics"/> huius expo&shy;<lb/>&longs;itionem inuenies 1. Priorum, &longs;ecto 1. cap.  
  
 23.</s></p><figure></figure><p type="main"> 23.</s></p><figure></figure><p type="main">
  
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 <s><margin.target id="marg207"></margin.target>216</s></p><p type="main"> <s><margin.target id="marg207"></margin.target>216</s></p><p type="main">
  
 <s>Tex. </s> <s>Tex. eodem <emph type="italics"/>(Metaphoric&egrave; autem, qu&aelig; in Geometria po&shy;<lb/>tentia dicitur)<emph.end type="italics"/> potentiam vnius line&aelig; appellant Geometr&aelig; <lb/>quadratum illius, ide&longs;t quadratum &longs;uper ip&longs;am con&longs;tru&shy;<lb/>ctum. </s>
  
 <s>eodem <emph type="italics"/>(Metaphoric&egrave; autem, qu&aelig; in Geometria po&shy;<lb/>tentia dicitur)<emph.end type="italics"/> potentiam vnius line&aelig; appellant Geometr&aelig; <lb/>quadratum illius, ide&longs;t quadratum &longs;uper ip&longs;am con&longs;tru&shy;<lb/>ctum. </s> 
  
 <s>v. </s> <s>v. </s>
  
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 <s><margin.target id="marg208"></margin.target>217</s></p><p type="main"> <s><margin.target id="marg208"></margin.target>217</s></p><p type="main">
  
 <s>Tex. </s> <s>Tex. 34. (<emph type="italics"/>Quemadmodum dicitur diametrum e&longs;&longs;e commen&longs;urabilem<emph.end type="italics"/>) vide an&shy;<lb/>notata 1. Priorum, fecto 1. cap.
  
 <s>34. (<emph type="italics"/>Quemadmodum dicitur diametrum e&longs;&longs;e commen&longs;urabilem<emph.end type="italics"/>) vide an&shy;<lb/>notata 1. Priorum, fecto 1. cap.  
  
 23.</s></p><p type="main"> 23.</s></p><p type="main">
  
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 <s><margin.target id="marg209"></margin.target>218</s></p><p type="main"> <s><margin.target id="marg209"></margin.target>218</s></p><p type="main">
  
 <s>Tex. </s> <s>Tex. 35. (<emph type="italics"/>Vt triangulo duos rectos habere<emph.end type="italics"/>) ide&longs;t affectio trianguli e&longs;t habe&shy;<lb/>re tres angulos &aelig;quales duobus rectis angulis. </s>
  
 <s>35. (<emph type="italics"/>Vt triangulo duos rectos habere<emph.end type="italics"/>) ide&longs;t affectio trianguli e&longs;t habe&shy;<lb/>re tres angulos &aelig;quales duobus rectis angulis. </s> 
  
 <s>Vide declarationem huius <lb/>lib.  <s>Vide declarationem huius <lb/>lib.
  
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 <s><margin.target id="marg210"></margin.target>219</s></p><p type="main"> <s><margin.target id="marg210"></margin.target>219</s></p><p type="main">
  
 <s>Tex. </s> <s>Tex. 1. (<emph type="italics"/>Mathematicorum quoque principia, elementa, &amp; cau&longs;&aelig; &longs;unt<emph.end type="italics"/>) <lb/>notanda &longs;unt h&aelig;c aduer&longs;us quo&longs;dam, qui negant in Mathemati&shy;<lb/>cis cau&longs;as reperiri, vt hinc <expan abbr="quoq;">quoque</expan> illis &longs;cientiam auferant. </s>
  
 <s>1. (<emph type="italics"/>Mathematicorum quoque principia, elementa, &amp; cau&longs;&aelig; &longs;unt<emph.end type="italics"/>) <lb/>notanda &longs;unt h&aelig;c aduer&longs;us quo&longs;dam, qui negant in Mathemati&shy;<lb/>cis cau&longs;as reperiri, vt hinc <expan abbr="quoq;">quoque</expan> illis &longs;cientiam auferant. </s> 
  
 <s>enim&shy;<lb/>uer&ograve; apert&egrave; patet eos falli ex toto hoc Ari&longs;t.  <s>enim&shy;<lb/>uer&ograve; apert&egrave; patet eos falli ex toto hoc Ari&longs;t.
  
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 <s><margin.target id="marg212"></margin.target>221</s></p><p type="main"> <s><margin.target id="marg212"></margin.target>221</s></p><p type="main">
  
 <s>Tex. </s> <s>Tex. 20. (<emph type="italics"/>De&longs;eriptiones <expan abbr="quoq;">quoque</expan> actu inueniuntur, diuidentes nanque <lb/>inuenirent, quod &longs;i diui&longs;&aelig; e&longs;&longs;ent, manife&longs;i &egrave; e&longs;&longs;ent, nunc autem in&longs;unt potentia, cur <lb/>triangulus duo recti? </s>
  
 <s>20. (<emph type="italics"/>De&longs;eriptiones <expan abbr="quoq;">quoque</expan> actu inueniuntur, diuidentes nanque <lb/>inuenirent, quod &longs;i diui&longs;&aelig; e&longs;&longs;ent, manife&longs;i &egrave; e&longs;&longs;ent, nunc autem in&longs;unt potentia, cur <lb/>triangulus duo recti? </s> 
  
 <s>quia qui circa vnum punctum anguli duobus rectis &aelig;quales<emph.end type="italics"/><pb pagenum="142"/><emph type="italics"/>&longs;unt, &longs;i igitur qu&aelig; ad latus educeretur, videnti mox e&longs;&longs;et manife&longs;tum<emph.end type="italics"/>) per de&longs;cri&shy;<lb/>ptiones, vel figurationes, vel de&longs;ignationes intelligendas e&longs;&longs;e demon&longs;tra&shy;<lb/>tiones Geometricas &longs;&aelig;pius &longs;upra dictum e&longs;t, &amp; pariter ex hoc loco com&shy;<lb/>probatur. </s> <s>quia qui circa vnum punctum anguli duobus rectis &aelig;quales<emph.end type="italics"/><pb pagenum="142"/><emph type="italics"/>&longs;unt, &longs;i igitur qu&aelig; ad latus educeretur, videnti mox e&longs;&longs;et manife&longs;tum<emph.end type="italics"/>) per de&longs;cri&shy;<lb/>ptiones, vel figurationes, vel de&longs;ignationes intelligendas e&longs;&longs;e demon&longs;tra&shy;<lb/>tiones Geometricas &longs;&aelig;pius &longs;upra dictum e&longs;t, &amp; pariter ex hoc loco com&shy;<lb/>probatur. </s>
  
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 <s>A, &longs;unt con&longs;tituti, &aelig;quales &longs;unt <lb/>non duobus, vt e&longs;t in textu, &longs;ed quatuor rectis, <lb/>vt patet ex corollario 2. 15. primi Elem.  <s>A, &longs;unt con&longs;tituti, &aelig;quales &longs;unt <lb/>non duobus, vt e&longs;t in textu, &longs;ed quatuor rectis, <lb/>vt patet ex corollario 2. 15. primi Elem.
  
 quot&shy;<lb/>quot enim anguli con&longs;tituantur ad punctum A, <lb/>omnes &longs;imul erunt &aelig;quales quatuor rectis, quos <lb/>faciunt pr&aelig;&longs;entes line&aelig; B C, D E. vniuer&longs;i enim <lb/>illi congruent his quatuor rectis: &longs;ed Ari&longs;t. </s> quot&shy;<lb/>quot enim anguli con&longs;tituantur ad punctum A, <lb/>omnes &longs;imul erunt &aelig;quales quatuor rectis, quos <lb/>faciunt pr&aelig;&longs;entes line&aelig; B C, D E. vniuer&longs;i enim <lb/>illi congruent his quatuor rectis: &longs;ed Ari&longs;t. &longs;en&shy;<lb/>&longs;us e&longs;t omnes angulos ad ea&longs;dem partes con&longs;ti&shy;<lb/>tutos, v. </s>
  
 <s>&longs;en&shy;<lb/>&longs;us e&longs;t omnes angulos ad ea&longs;dem partes con&longs;ti&shy;<lb/>tutos, v. </s> 
  
 <s>g. </s> <s>g. </s>
  
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 <s>Ibidem (<emph type="italics"/>Cur in &longs;emicirculo vniuer&longs;aliter rectus? </s> <s>Ibidem (<emph type="italics"/>Cur in &longs;emicirculo vniuer&longs;aliter rectus? </s>
  
 <s>quia &longs;i tres &aelig;quales, &amp; qu&aelig; <lb/>ba&longs;is e&longs;t duo, &amp; qu&aelig; ex medio &longs;upra stat recta, videnti manifestum erit ei, qui illud <lb/>&longs;ciat<emph.end type="italics"/>) In 2. Po&longs;ter. </s> <s>quia &longs;i tres &aelig;quales, &amp; qu&aelig; <lb/>ba&longs;is e&longs;t duo, &amp; qu&aelig; ex medio &longs;upra stat recta, videnti manifestum erit ei, qui illud <lb/>&longs;ciat<emph.end type="italics"/>) In 2. Po&longs;ter. tex. </s>
  
 <s>tex. </s> 
  
 <s>11. inuenies hu ius loci expo&longs;itionem. </s> <s>11. inuenies hu ius loci expo&longs;itionem. </s>
  
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 <s><margin.target id="marg214"></margin.target>223</s></p><p type="main"> <s><margin.target id="marg214"></margin.target>223</s></p><p type="main">
  
 <s>Tex. </s> <s>Tex. 22. (<emph type="italics"/>Vt puta &longs;i triangulum non putet mutari, non opinabitur modo duos <lb/>rectos habere, modo non, mutaretur enim<emph.end type="italics"/>) quia nimirum huius habemus &longs;cien&shy;<lb/>tiam per demon&longs;trationem 32. primi Elementorum. </s>
  
 <s>22. (<emph type="italics"/>Vt puta &longs;i triangulum non putet mutari, non opinabitur modo duos <lb/>rectos habere, modo non, mutaretur enim<emph.end type="italics"/>) quia nimirum huius habemus &longs;cien&shy;<lb/>tiam per demon&longs;trationem 32. primi Elementorum. </s> 
  
 <s>quomodo autem tri&shy;<lb/>angulus habeat duos rectos, ide&longs;t tres angulos &aelig;quales duobus rectis angu&shy;<lb/>lis, explicatum e&longs;t primo Priorum, &longs;ecto 3. cap.  <s>quomodo autem tri&shy;<lb/>angulus habeat duos rectos, ide&longs;t tres angulos &aelig;quales duobus rectis angu&shy;<lb/>lis, explicatum e&longs;t primo Priorum, &longs;ecto 3. cap.
  
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 <s><margin.target id="marg216"></margin.target>225</s></p><p type="main"> <s><margin.target id="marg216"></margin.target>225</s></p><p type="main">
  
 <s>Tex. </s> <s>Tex. 4. (<emph type="italics"/>Ac etiam motum &longs;implici, &amp; veloti&longs;&longs;imo motu men&longs;urant, mi&shy;<lb/>nimum enim tempus hic habet. </s>
  
 <s>4. (<emph type="italics"/>Ac etiam motum &longs;implici, &amp; veloti&longs;&longs;imo motu men&longs;urant, mi&shy;<lb/>nimum enim tempus hic habet. </s> 
  
 <s>quapropter in A&longs;trologia tale vn&ubreve; prin&shy;<lb/>cipium, &amp; men&longs;ura e&longs;t. </s> <s>quapropter in A&longs;trologia tale vn&ubreve; prin&shy;<lb/>cipium, &amp; men&longs;ura e&longs;t. </s>
  
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 <s>ad tex. </s> <s>ad tex. </s>
  
 <s>38. primi Po&longs;ter. </s> <s>38. primi Po&longs;ter. &longs;atis dictum e&longs;t de Die&longs;i, qu&aelig; videas.</s></p><p type="main">
  
 <s>&longs;atis dictum e&longs;t de Die&longs;i, qu&aelig; videas.</s></p><p type="main"> 
  
 <s><arrow.to.target n="marg218"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg218"></arrow.to.target></s></p><p type="margin">
  
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 <s>quid die&longs;is <lb/>dictum &longs;it ad tex. </s> <s>quid die&longs;is <lb/>dictum &longs;it ad tex. </s>
  
 <s>38. primi Po&longs;ter. </s> <s>38. primi Po&longs;ter. quando autem ait <emph type="italics"/>(Vt puta du&aelig; die&longs;es)<emph.end type="italics"/><lb/>ide&longs;t du&aelig; die&longs;es &longs;unt men&longs;ura vnius interualli mu&longs;ici, qui tonus appellatur: <lb/>qu&aelig; quidem du&aelig; die&longs;es non &longs;unt men&longs;ura &longs;en&longs;ibilis, qu&aelig; &longs;cilicet auribus per&shy;<lb/>cipiatur, &longs;ed tantummod&ograve; exi&longs;tunt in numerorum proportionibus, ibi per <lb/>intellectum excogitatis, quando ait <emph type="italics"/>(Et voces plures quibus men&longs;uramus)<emph.end type="italics"/><lb/>quando vtimur eodem interuallo, &longs;iue eadem voce ad cantus men&longs;uram, <lb/>tunc &longs;unt plures men&longs;ur&aelig; numero, quamuis vna tantam &longs;pe<gap/> Ait <emph type="italics"/>(Et dia&shy;<lb/>meter duobus men&longs;uratur)<emph.end type="italics"/> v. </s>
  
 <s>quando autem ait <emph type="italics"/>(Vt puta du&aelig; die&longs;es)<emph.end type="italics"/><lb/>ide&longs;t du&aelig; die&longs;es &longs;unt men&longs;ura vnius interualli mu&longs;ici, qui tonus appellatur: <lb/>qu&aelig; quidem du&aelig; die&longs;es non &longs;unt men&longs;ura &longs;en&longs;ibilis, qu&aelig; &longs;cilicet auribus per&shy;<lb/>cipiatur, &longs;ed tantummod&ograve; exi&longs;tunt in numerorum proportionibus, ibi per <lb/>intellectum excogitatis, quando ait <emph type="italics"/>(Et voces plures quibus men&longs;uramus)<emph.end type="italics"/><lb/>quando vtimur eodem interuallo, &longs;iue eadem voce ad cantus men&longs;uram, <lb/>tunc &longs;unt plures men&longs;ur&aelig; numero, quamuis vna tantam &longs;pe<gap/> Ait <emph type="italics"/>(Et dia&shy;<lb/>meter duobus men&longs;uratur)<emph.end type="italics"/> v. </s> 
  
 <s>g. </s> <s>g. </s>
  
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 <s><margin.target id="marg220"></margin.target>229</s></p><p type="main"> <s><margin.target id="marg220"></margin.target>229</s></p><p type="main">
  
 <s>Tex. </s> <s>Tex. 11. <emph type="italics"/>(Similia ver&ograve; &longs;i cum non &longs;int eadem &longs;impliciter, nec &longs;ecundum &longs;ab&longs;t an&shy;<lb/>tiam &longs;ubiectam in d. </s>
  
 <s>11. <emph type="italics"/>(Similia ver&ograve; &longs;i cum non &longs;int eadem &longs;impliciter, nec &longs;ecundum &longs;ab&longs;t an&shy;<lb/>tiam &longs;ubiectam in d. </s> 
  
 <s>fferentia &longs;ecundum formam eadem &longs;it: quemadmodum quadra&shy;<lb/>tum maius minori &longs;imile e&longs;t, &amp; line&aelig; in&aelig;quales, h&aelig; enim &longs;imiles quidem, ver&ubreve; non <lb/>c&aelig;dem &longs;impliciter &longs;unt)<emph.end type="italics"/> Prima definitio &longs;exti definit &longs;imiles figuras eas e&longs;&longs;e, <lb/>qu&aelig; &longs;unt &aelig;quiangul&aelig; inuicem, &amp; qu&aelig; habent latera proportionalia circa <lb/>&aelig;quales angulos. </s> <s>fferentia &longs;ecundum formam eadem &longs;it: quemadmodum quadra&shy;<lb/>tum maius minori &longs;imile e&longs;t, &amp; line&aelig; in&aelig;quales, h&aelig; enim &longs;imiles quidem, ver&ubreve; non <lb/>c&aelig;dem &longs;impliciter &longs;unt)<emph.end type="italics"/> Prima definitio &longs;exti definit &longs;imiles figuras eas e&longs;&longs;e, <lb/>qu&aelig; &longs;unt &aelig;quiangul&aelig; inuicem, &amp; qu&aelig; habent latera proportionalia circa <lb/>&aelig;quales angulos. </s>
  
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 <s><margin.target id="marg224"></margin.target>233</s></p><p type="main"> <s><margin.target id="marg224"></margin.target>233</s></p><p type="main">
  
 <s>Tex. </s> <s>Tex. 44. <emph type="italics"/>(Pluralitatem ver&ograve; lationum ex peculiari&longs;&longs;ima Philo&longs;ophie <lb/>Mathematicarum &longs;cientiarum, videlicet ex A&longs;tronomia con&longs;iderandum <lb/>est: h&aelig;c enim de &longs;ub&longs;tantia &longs;en&longs;ibili quidem, ac &longs;empiterna &longs;peculatur)<emph.end type="italics"/><lb/>pluralitatem nimirum c&oelig;le&longs;tium motuum petendam e&longs;&longs;e a&longs;&longs;erit <lb/>ex pr&aelig;cipua totius Philo&longs;ophi&aelig; parte, quam ait e&longs;&longs;e A&longs;tronomiam. </s>
  
 <s>44. <emph type="italics"/>(Pluralitatem ver&ograve; lationum ex peculiari&longs;&longs;ima Philo&longs;ophie <lb/>Mathematicarum &longs;cientiarum, videlicet ex A&longs;tronomia con&longs;iderandum <lb/>est: h&aelig;c enim de &longs;ub&longs;tantia &longs;en&longs;ibili quidem, ac &longs;empiterna &longs;peculatur)<emph.end type="italics"/><lb/>pluralitatem nimirum c&oelig;le&longs;tium motuum petendam e&longs;&longs;e a&longs;&longs;erit <lb/>ex pr&aelig;cipua totius Philo&longs;ophi&aelig; parte, quam ait e&longs;&longs;e A&longs;tronomiam. </s> <s>dignum <lb/>porr&ograve; con&longs;ideratione e&longs;t, quanti faciat Ari&longs;t. Mathematicas di&longs;ciplinas, ac <lb/>pr&aelig;cipu&egrave; &longs;yderalem &longs;cientiam.</s></p><p type="main">
  
 <s>dignum <lb/>porr&ograve; con&longs;ideratione e&longs;t, quanti faciat Ari&longs;t. </s> 
  
 <s>Mathematicas di&longs;ciplinas, ac <lb/>pr&aelig;cipu&egrave; &longs;yderalem &longs;cientiam.</s></p><p type="main"> 
  
 <s><arrow.to.target n="marg225"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg225"></arrow.to.target></s></p><p type="margin">
  
 <s><margin.target id="marg225"></margin.target>234</s></p><p type="main"> <s><margin.target id="marg225"></margin.target>234</s></p><p type="main">
  
 <s>Tex. </s> <s>Tex. 45. <emph type="italics"/>(Eudoxus igitur Solis, &amp; Lun&aelig; lationem po&longs;uit fieri &agrave; tribus orbibus, <lb/>quorum primus quidem e&longs;&longs;et, qui inerrantium &longs;iellarum; &longs;ecundus ver&ograve; &longs;ecunduns <lb/>id, quod per medium Zodiacum; tertius tandem, &longs;ecundum quem qui in latitudine <lb/>Zodiaci obliquatur. </s>
  
 <s>45. <emph type="italics"/>(Eudoxus igitur Solis, &amp; Lun&aelig; lationem po&longs;uit fieri &agrave; tribus orbibus, <lb/>quorum primus quidem e&longs;&longs;et, qui inerrantium &longs;iellarum; &longs;ecundus ver&ograve; &longs;ecunduns <lb/>id, quod per medium Zodiacum; tertius tandem, &longs;ecundum quem qui in latitudine <lb/>Zodiaci obliquatur. </s> 
  
 <s>in maiori autem latitudine obliquari eum &longs;ecundum quem Lu&shy;<lb/>na, qu&agrave;m eum &longs;ecundum quem Sol &longs;ertur)<emph.end type="italics"/> Eudoxi tempore nondum &longs;atis ex&shy;<lb/>culta fuerat A&longs;tronomia, vt propterea minim&egrave; mirandum &longs;it, eum hoc lo&shy;<lb/>co imperfecta admodum circa c&ecedil;le&longs;tia tradere. </s> <s>in maiori autem latitudine obliquari eum &longs;ecundum quem Lu&shy;<lb/>na, qu&agrave;m eum &longs;ecundum quem Sol &longs;ertur)<emph.end type="italics"/> Eudoxi tempore nondum &longs;atis ex&shy;<lb/>culta fuerat A&longs;tronomia, vt propterea minim&egrave; mirandum &longs;it, eum hoc lo&shy;<lb/>co imperfecta admodum circa c&ecedil;le&longs;tia tradere. </s>
  
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 <s><margin.target id="marg226"></margin.target>235</s></p><p type="main"> <s><margin.target id="marg226"></margin.target>235</s></p><p type="main">
  
 <s>Tex. </s> <s>Tex. 46. <emph type="italics"/>(Errantium ver&ograve; &longs;tellarum <expan abbr="vniu&longs;cuiu&longs;q;">vniu&longs;cuiu&longs;que</expan> in quatuor &longs;ph&aelig;ris, quarura <lb/>primam quidem, &amp; &longs;ecundam eandem illis e&longs;&longs;e: etenim, qu&aelig; fix arum eft eam illam <lb/>e&longs;&longs;e, qu&aelig;omnes fert: at cam, qu&aelig; &longs;ub ip&longs;a ordinata e&longs;t, ac qu&aelig; &longs;ecuxdum Zodiacum <lb/>lationem habet, communem omnibus e&longs;&longs;e. </s>
  
 <s>46. <emph type="italics"/>(Errantium ver&ograve; &longs;tellarum <expan abbr="vniu&longs;cuiu&longs;q;">vniu&longs;cuiu&longs;que</expan> in quatuor &longs;ph&aelig;ris, quarura <lb/>primam quidem, &amp; &longs;ecundam eandem illis e&longs;&longs;e: etenim, qu&aelig; fix arum eft eam illam <lb/>e&longs;&longs;e, qu&aelig;omnes fert: at cam, qu&aelig; &longs;ub ip&longs;a ordinata e&longs;t, ac qu&aelig; &longs;ecuxdum Zodiacum <lb/>lationem habet, communem omnibus e&longs;&longs;e. </s> 
  
 <s>Terti&aelig; ver&ograve; omnium polos in eo, quod <lb/>per medium Zodiacum e&longs;t. </s> <s>Terti&aelig; ver&ograve; omnium polos in eo, quod <lb/>per medium Zodiacum e&longs;t. </s>
  
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 <s><margin.target id="marg227"></margin.target>236</s></p><p type="main"> <s><margin.target id="marg227"></margin.target>236</s></p><p type="main">
  
 <s>Tex. </s> <s>Tex. 47. <emph type="italics"/>(At Calippus &longs;itum quidem &longs;ph&aelig;rarum eundem Eudoxo ponebat, hoe <lb/>e&longs;t di&longs;tantiarum ordinem. </s>
  
 <s>47. <emph type="italics"/>(At Calippus &longs;itum quidem &longs;ph&aelig;rarum eundem Eudoxo ponebat, hoe <lb/>e&longs;t di&longs;tantiarum ordinem. </s> 
  
 <s>pluralitatem autem &longs;tell&aelig; quidem Iouis, ac Saturni ean&shy;<lb/>dem illi attribuebat. </s> <s>pluralitatem autem &longs;tell&aelig; quidem Iouis, ac Saturni ean&shy;<lb/>dem illi attribuebat. </s>
  
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 <s>Qvidquid Mathematicum in his qu&aelig;&longs;tionibus occurret, illud, vt <lb/>plurimum per paraphra&longs;im exponemus, ita tamen, vt tex. </s> <s>Qvidquid Mathematicum in his qu&aelig;&longs;tionibus occurret, illud, vt <lb/>plurimum per paraphra&longs;im exponemus, ita tamen, vt tex. </s>
  
 <s>Ari&longs;t. <lb/></s> <s>Ari&longs;t. <lb/>&amp; figur&aelig; textui re&longs;pondentes per eam, quantum fieri poterit re&shy;<lb/>&longs;tituantur, &amp; &longs;i qu&aelig; &longs;e offerent difficilia, pro viribus &longs;oluantur. <lb/></s>
  
 <s>&amp; figur&aelig; textui re&longs;pondentes per eam, quantum fieri poterit re&shy;<lb/>&longs;tituantur, &amp; &longs;i qu&aelig; &longs;e offerent difficilia, pro viribus &longs;oluantur. <lb/></s> 
  
 <s>E&longs;t autem nonnullis in locis textus tam gr&aelig;cus, qu&agrave;m latinus ade&ograve; corrup&shy;<lb/>tus, ac deprauatus, vt nullo modo emendari queat.</s></p><p type="head"> <s>E&longs;t autem nonnullis in locis textus tam gr&aelig;cus, qu&agrave;m latinus ade&ograve; corrup&shy;<lb/>tus, ac deprauatus, vt nullo modo emendari queat.</s></p><p type="head">
  
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 <s>vltima illa textus verba <emph type="italics"/>(Quod autem vbi D, mo&shy;<lb/>uens, vbi F, motum autem vbi C, pondus in G,)<emph.end type="italics"/> videntur &longs;uperuacanea, atque <lb/>mendos&egrave; addita.</s></p><p type="main"> <s>vltima illa textus verba <emph type="italics"/>(Quod autem vbi D, mo&shy;<lb/>uens, vbi F, motum autem vbi C, pondus in G,)<emph.end type="italics"/> videntur &longs;uperuacanea, atque <lb/>mendos&egrave; addita.</s></p><p type="main">
  
 <s>In hac qu&aelig;&longs;tione re&longs;pexit Ari&longs;t. </s> <s>In hac qu&aelig;&longs;tione re&longs;pexit Ari&longs;t. &longs;ol&ugrave;m ad primam vectis &longs;peciem. </s>
  
 <s>&longs;ol&ugrave;m ad primam vectis &longs;peciem. </s> 
  
 <s>Illud <lb/>demum, quod dixit eandem habere rationem potentiam ad pondus, qu&agrave;m <lb/>partes vectis inuicem demon&longs;tratum e&longs;t po&longs;tea acuti&longs;&longs;im&egrave; ab Archimede <pb pagenum="159"/>propo&longs;itione 6. &amp; 7. de &aelig;queponderantibus: &amp; no&longs;tra <expan abbr="t&etilde;pe&longs;tate">tempe&longs;tate</expan> alio quam&shy;<lb/>uis modo, &amp; vnica demon&longs;tratione &agrave; Guido Vbaldo in &longs;uis Mechanicis pro&shy;<lb/>po&longs;itione 1. de Vecte, qu&aelig; e&longs;t huiu&longs;modi; Potentia &longs;u&longs;tinens pondus vecti <lb/>appen&longs;um, eandem ad ip&longs;um pondus proportionem habet, quam vectis di&shy;<lb/>&longs;tantia inter fulcimentum, ac ponderis &longs;u&longs;pen&longs;ionem, ad di&longs;tantiam, &agrave; fulci&shy;<lb/>mento ad potentiam interiectam. </s> <s>Illud <lb/>demum, quod dixit eandem habere rationem potentiam ad pondus, qu&agrave;m <lb/>partes vectis inuicem demon&longs;tratum e&longs;t po&longs;tea acuti&longs;&longs;im&egrave; ab Archimede <pb pagenum="159"/>propo&longs;itione 6. &amp; 7. de &aelig;queponderantibus: &amp; no&longs;tra <expan abbr="t&etilde;pe&longs;tate">tempe&longs;tate</expan> alio quam&shy;<lb/>uis modo, &amp; vnica demon&longs;tratione &agrave; Guido Vbaldo in &longs;uis Mechanicis pro&shy;<lb/>po&longs;itione 1. de Vecte, qu&aelig; e&longs;t huiu&longs;modi; Potentia &longs;u&longs;tinens pondus vecti <lb/>appen&longs;um, eandem ad ip&longs;um pondus proportionem habet, quam vectis di&shy;<lb/>&longs;tantia inter fulcimentum, ac ponderis &longs;u&longs;pen&longs;ionem, ad di&longs;tantiam, &agrave; fulci&shy;<lb/>mento ad potentiam interiectam. </s>
  
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 <s>Nam nauiginm interdum maius &longs;pa&shy;<lb/>tium percurret, interdum minus, iuxta remigum vires, &amp; prout mari remi <lb/>palmula immer&longs;a fuerit: remi ver&ograve; manubrium tamet&longs;i ab exiguis viribus <lb/>moueatur haud minorem tamen ambitum de&longs;cribet, qu&agrave;m &longs;i &agrave; multo ma&shy;<lb/>iore virtute moueretur. </s> <s>Nam nauiginm interdum maius &longs;pa&shy;<lb/>tium percurret, interdum minus, iuxta remigum vires, &amp; prout mari remi <lb/>palmula immer&longs;a fuerit: remi ver&ograve; manubrium tamet&longs;i ab exiguis viribus <lb/>moueatur haud minorem tamen ambitum de&longs;cribet, qu&agrave;m &longs;i &agrave; multo ma&shy;<lb/>iore virtute moueretur. </s>
  
 <s>Quapropter, vt huiu&longs;modi Ari&longs;t. </s> <s>Quapropter, vt huiu&longs;modi Ari&longs;t. &longs;ententiam exa&shy;<lb/>minaremus, Theoremata, qu&aelig; &longs;equuntur, demonftrauimus.</s></p><p type="head">
  
 <s>&longs;ententiam exa&shy;<lb/>minaremus, Theoremata, qu&aelig; &longs;equuntur, demonftrauimus.</s></p><p type="head"> 
  
 <s><emph type="italics"/>PROPOSITIO PRIMA.<emph.end type="italics"/></s></p><p type="head"> <s><emph type="italics"/>PROPOSITIO PRIMA.<emph.end type="italics"/></s></p><p type="head">
  
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 <s>figuram &longs;implicis trochle&aelig;, con&shy;<lb/>&longs;tantis &longs;cilicet ex duobus tantum orbiculis, facilita&shy;<lb/>tis cau&longs;a exhibebo, in hac enim melius apparebit, <lb/>qua ratione trochlea ad vectem reducatur. </s> <s>figuram &longs;implicis trochle&aelig;, con&shy;<lb/>&longs;tantis &longs;cilicet ex duobus tantum orbiculis, facilita&shy;<lb/>tis cau&longs;a exhibebo, in hac enim melius apparebit, <lb/>qua ratione trochlea ad vectem reducatur. </s>
  
 <s>vnde, &amp; <lb/>Ari&longs;t. </s> <s>vnde, &amp; <lb/>Ari&longs;t. &longs;en&longs;um, quamuis ob&longs;curi&longs;&longs;imum, ac proinde <lb/>problematis &longs;olutionem optim&egrave; percipere licebit. <lb/></s>
  
 <s>&longs;en&longs;um, quamuis ob&longs;curi&longs;&longs;imum, ac proinde <lb/>problematis &longs;olutionem optim&egrave; percipere licebit. <lb/></s> 
  
 <s>Sit igitur orbiculus &longs;uperior A, qui in pegmate I K&shy;<lb/>L D, voluatur circa axem G, <expan abbr="&longs;it&qacute;">&longs;itque</expan>; pegma i&longs;tud &longs;upe&shy;<lb/>rius fixum, &amp; immobile &agrave; clauo H, pendens. </s> <s>Sit igitur orbiculus &longs;uperior A, qui in pegmate I K&shy;<lb/>L D, voluatur circa axem G, <expan abbr="&longs;it&qacute;">&longs;itque</expan>; pegma i&longs;tud &longs;upe&shy;<lb/>rius fixum, &amp; immobile &agrave; clauo H, pendens. </s>
  
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 <s>quia enim in vecte no&longs;tro L M, dupla e&longs;t proportio <lb/>inter L M, &amp; L B, eadem etiam proportio erit inter pondus, &amp; potentiam, <lb/>quare pondus C, duplum erit potenti&aelig; in M, hoc e&longs;t &agrave; minore potentia &longs;ibi <lb/>&longs;ubdupla &longs;u&longs;tinebitur: &amp; &agrave; quauis adhuc <expan abbr="quantumcunq;">quantumcunque</expan> maiore eleuabitur.</s></p><p type="main"> <s>quia enim in vecte no&longs;tro L M, dupla e&longs;t proportio <lb/>inter L M, &amp; L B, eadem etiam proportio erit inter pondus, &amp; potentiam, <lb/>quare pondus C, duplum erit potenti&aelig; in M, hoc e&longs;t &agrave; minore potentia &longs;ibi <lb/>&longs;ubdupla &longs;u&longs;tinebitur: &amp; &agrave; quauis adhuc <expan abbr="quantumcunq;">quantumcunque</expan> maiore eleuabitur.</s></p><p type="main">
  
 <s>Qui plura de trochlea de&longs;iderat, adeat Guidi Vbaldi, Mechanica, cuius <lb/>auxilio fateor me verum &longs;en&longs;um harum Mechanicarum Ari&longs;t. </s> <s>Qui plura de trochlea de&longs;iderat, adeat Guidi Vbaldi, Mechanica, cuius <lb/>auxilio fateor me verum &longs;en&longs;um harum Mechanicarum Ari&longs;t. &amp; pr&aelig;&longs;ertim <lb/>huius loci enuclea&longs;&longs;e. </s>
  
 <s>&amp; pr&aelig;&longs;ertim <lb/>huius loci enuclea&longs;&longs;e. </s> 
  
 <s>qu&aelig; &longs;i cum Piccolominei expo&longs;itione contuleris, vide&shy;<lb/>bis eum nequaquam cognoui&longs;&longs;e, vbi nam vectis in trochlea lateret, eumque <lb/>tam &longs;uperiorem, qu&agrave;m inferiorem <expan abbr="rotul&atilde;">rotulam</expan> &aelig;qu&egrave; vectem facere; in quo etiam <lb/>Io. </s> <s>qu&aelig; &longs;i cum Piccolominei expo&longs;itione contuleris, vide&shy;<lb/>bis eum nequaquam cognoui&longs;&longs;e, vbi nam vectis in trochlea lateret, eumque <lb/>tam &longs;uperiorem, qu&agrave;m inferiorem <expan abbr="rotul&atilde;">rotulam</expan> &aelig;qu&egrave; vectem facere; in quo etiam <lb/>Io. </s>
  
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 <s>&longs;ed cau&longs;a e&longs;t, quia in <lb/>vortice aqua ip &longs;a &longs;piratim circumcurrens tandem in centrum, vbi demer&shy;<lb/>gitur de&longs;cendit; nece&longs;&longs;e igitur e&longs;t, vt etiam ea, qu&aelig; in ip&longs;a &longs;unt, &longs;imul cum <lb/>illa ad centrum per plures conuolutiones deducantur. </s> <s>&longs;ed cau&longs;a e&longs;t, quia in <lb/>vortice aqua ip &longs;a &longs;piratim circumcurrens tandem in centrum, vbi demer&shy;<lb/>gitur de&longs;cendit; nece&longs;&longs;e igitur e&longs;t, vt etiam ea, qu&aelig; in ip&longs;a &longs;unt, &longs;imul cum <lb/>illa ad centrum per plures conuolutiones deducantur. </s>
  
 <s>C&aelig;terum &longs;i quis ve&shy;<lb/>lit Mechanicam facultatem &longs;eri&ograve; aggredi, nequaquam paucis his ab Ari&longs;t. <lb/></s> <s>C&aelig;terum &longs;i quis ve&shy;<lb/>lit Mechanicam facultatem &longs;eri&ograve; aggredi, nequaquam paucis his ab Ari&longs;t. <lb/>traditis, <expan abbr="eis&qacute;">eisque</expan>; leui brachio pertractatis, contentus &longs;it: ver&ugrave;m Archimedem <lb/>de Aqu&aelig;ponderantibus, Commandinum, ac Lucam Valerium de centro <lb/>grauitatis &longs;olidorum, ac tandem Guidi Vbaldi Mechanica adeat, vbi hu&shy;<lb/>ius &longs;cienti&aelig; admiranda plurima, <expan abbr="ea&qacute;">eaque</expan>; firmi&longs;&longs;im&egrave; demon&longs;trata reperiet.</s></p><figure></figure><p type="head">
  
 <s>traditis, <expan abbr="eis&qacute;">eisque</expan>; leui brachio pertractatis, contentus &longs;it: ver&ugrave;m Archimedem <lb/>de Aqu&aelig;ponderantibus, Commandinum, ac Lucam Valerium de centro <lb/>grauitatis &longs;olidorum, ac tandem Guidi Vbaldi Mechanica adeat, vbi hu&shy;<lb/>ius &longs;cienti&aelig; admiranda plurima, <expan abbr="ea&qacute;">eaque</expan>; firmi&longs;&longs;im&egrave; demon&longs;trata reperiet.</s></p><figure></figure><p type="head"> 
  
 <s><emph type="italics"/>IN LIBELLVM DE MVNDO<emph.end type="italics"/></s></p><p type="head"> <s><emph type="italics"/>IN LIBELLVM DE MVNDO<emph.end type="italics"/></s></p><p type="head">
  
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 <s>&amp; in parte huic auer&longs;a <lb/>tumorem B, ex quo alter flu&shy;<lb/>xus deriuatur. </s> <s>&amp; in parte huic auer&longs;a <lb/>tumorem B, ex quo alter flu&shy;<lb/>xus deriuatur. </s>
  
 <s>&amp; quia in alijs <lb/>duobus mundi lateribus non <lb/><expan abbr="fi&utilde;t">fiunt</expan> huin&longs;modi tumores, im&ograve; <lb/>mare ob refrigerationem <lb/>&longs;ub&longs;idet, ibi fiunt duo reflu&shy;<lb/>xus C, &amp; D, ita vt &longs;emper &longs;int <lb/>in mari pr&aelig;&longs;ertim Oceano <lb/>quatuor pr&aelig;dicti effectus, qui <lb/>&longs;imul, vt ait hic Ari&longs;t. </s> <s>&amp; quia in alijs <lb/>duobus mundi lateribus non <lb/><expan abbr="fi&utilde;t">fiunt</expan> huin&longs;modi tumores, im&ograve; <lb/>mare ob refrigerationem <lb/>&longs;ub&longs;idet, ibi fiunt duo reflu&shy;<lb/>xus C, &amp; D, ita vt &longs;emper &longs;int <lb/>in mari pr&aelig;&longs;ertim Oceano <lb/>quatuor pr&aelig;dicti effectus, qui <lb/>&longs;imul, vt ait hic Ari&longs;t. &amp; ex&shy;<pb pagenum="197"/>perientia te&longs;tatur, &longs;imul cum Luna circa mundum circumaguntur. </s>
  
 <s>&amp; ex&shy;<pb pagenum="197"/>perientia te&longs;tatur, &longs;imul cum Luna circa mundum circumaguntur. </s> 
  
 <s>hoe e&longs;t <lb/>&longs;i Luna, qu&aelig; modo e&longs;t in &longs;uperiori parte meridionali, venerit ad locum E, <lb/>occidentalem, eam fluxus A, &longs;uble quitur, <expan abbr="vergit&qacute;">vergitque</expan>; tumorem &longs;uum ad occi&shy;<lb/>dentem E, vnde, &amp; fluxus B, promouebitur ad orientem, ita vt punctum F, <lb/>orientalem a&longs;piciat.</s></p><p type="main"> <s>hoe e&longs;t <lb/>&longs;i Luna, qu&aelig; modo e&longs;t in &longs;uperiori parte meridionali, venerit ad locum E, <lb/>occidentalem, eam fluxus A, &longs;uble quitur, <expan abbr="vergit&qacute;">vergitque</expan>; tumorem &longs;uum ad occi&shy;<lb/>dentem E, vnde, &amp; fluxus B, promouebitur ad orientem, ita vt punctum F, <lb/>orientalem a&longs;piciat.</s></p><p type="main">
  
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 <s>Idem, &longs;ed paul&ograve; mutatis verbis po&longs;tea repetit, qu&aelig; fort&egrave; ab aliquo per <lb/>errorem addita &longs;unt. </s> <s>Idem, &longs;ed paul&ograve; mutatis verbis po&longs;tea repetit, qu&aelig; fort&egrave; ab aliquo per <lb/>errorem addita &longs;unt. </s>
  
 <s>Verumenimuer&ograve; maxim&egrave; con&longs;iderandum e&longs;t, quan&shy;<lb/>tum hoc loco Ari&longs;t. </s> <s>Verumenimuer&ograve; maxim&egrave; con&longs;iderandum e&longs;t, quan&shy;<lb/>tum hoc loco Ari&longs;t. Mathematicis demon&longs;trationibus tribuat: quod dixe&shy;<lb/>rim propter recentiores quo&longs;dam, qui e&ograve; audaci&aelig; deuenerunt, vt Euclidis <lb/>firmi&longs;&longs;imas, <expan abbr="atq;">atque</expan> Ari&longs;tot. </s>
  
 <s>Mathematicis demon&longs;trationibus tribuat: quod dixe&shy;<lb/>rim propter recentiores quo&longs;dam, qui e&ograve; audaci&aelig; deuenerunt, vt Euclidis <lb/>firmi&longs;&longs;imas, <expan abbr="atq;">atque</expan> Ari&longs;tot. </s> 
  
 <s>te&longs;timonio, <expan abbr="veterum&qacute;">veterumque</expan>; Philo&longs;ophorum omnium <lb/>comprobatas, negare non verentur Demon&longs;trationes.</s></p><p type="main"> <s>te&longs;timonio, <expan abbr="veterum&qacute;">veterumque</expan>; Philo&longs;ophorum omnium <lb/>comprobatas, negare non verentur Demon&longs;trationes.</s></p><p type="main">
  
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 <s><margin.target id="marg283"></margin.target>293</s></p><p type="main"> <s><margin.target id="marg283"></margin.target>293</s></p><p type="main">
  
  
 <s>Cap. 39. <emph type="italics"/>(Aranei &longs;tatim cum editi &longs;unt, fila mittunt, non ab intrin&longs;eco <lb/>tanquam excrementum, vt Democritus ait, &longs;ed ab extrin&longs;eco de &longs;uo cor&shy;<lb/>pore, veluti cortice; aut more eorum animalium, qu&aelig; &longs;uos villos iacu&shy;<lb/>lantur, vt hystricis)<emph.end type="italics"/> Cum olim in hunc locum incidi&longs;&longs;em, ince&longs;&longs;ic <lb/>animum meum illa cupido, vt &longs;cilicet cert&ograve; &longs;cirem, numiure, an iniuria <lb/>Ari&longs;t. </s> <s>Cap. 39. <emph type="italics"/>(Aranei &longs;tatim cum editi &longs;unt, fila mittunt, non ab intrin&longs;eco <lb/>tanquam excrementum, vt Democritus ait, &longs;ed ab extrin&longs;eco de &longs;uo cor&shy;<lb/>pore, veluti cortice; aut more eorum animalium, qu&aelig; &longs;uos villos iacu&shy;<lb/>lantur, vt hystricis)<emph.end type="italics"/> Cum olim in hunc locum incidi&longs;&longs;em, ince&longs;&longs;ic <lb/>animum meum illa cupido, vt &longs;cilicet cert&ograve; &longs;cirem, numiure, an iniuria <lb/>Ari&longs;t. Democritum hoc loco reijceret, Araneum fila ab intrin&longs;eco emitte&shy;<lb/>re a&longs;&longs;erentem: quapropter ad magi&longs;tram rerum experientiam confugi, ac&shy;<lb/>cepto manu bacillo Araneum quendam ex ijs, qui circulares telas, quas <lb/><expan abbr="n&otilde;nulli">nonnulli</expan>, &amp; quidem apt&egrave; labyrinthos appellant, ingenio <expan abbr="vtiq;">vtique</expan> mathematico <lb/>contexunt, lic adij, vt Araneus pro arbittio &longs;uper bacillum liber&egrave; inambu&shy;<lb/>laret, dum ip&longs;e interim curio&longs;ius illum ob&longs;eruarem, quanam videlicet ex <lb/>parte filum foras ederet; cum ecce tibi Araneus experienti mihi vltr&ograve; fa&shy;<lb/>uens &longs;e &longs;e ex baculo demi&longs;it, ita tamen, vt ex filo &longs;uo in aere &longs;u&longs;pen&longs;us re&shy;<lb/>maneret. </s>
  
  
 <s>Democritum hoc loco reijceret, Araneum fila ab intrin&longs;eco emitte&shy;<lb/>re a&longs;&longs;erentem: quapropter ad magi&longs;tram rerum experientiam confugi, ac&shy;<lb/>cepto manu bacillo Araneum quendam ex ijs, qui circulares telas, quas <lb/><expan abbr="n&otilde;nulli">nonnulli</expan>, &amp; quidem apt&egrave; labyrinthos appellant, ingenio <expan abbr="vtiq;">vtique</expan> mathematico <lb/>contexunt, lic adij, vt Araneus pro arbittio &longs;uper bacillum liber&egrave; inambu&shy;<lb/>laret, dum ip&longs;e interim curio&longs;ius illum ob&longs;eruarem, quanam videlicet ex <lb/>parte filum foras ederet; cum ecce tibi Araneus experienti mihi vltr&ograve; fa&shy;<lb/>uens &longs;e &longs;e ex baculo demi&longs;it, ita tamen, vt ex filo &longs;uo in aere &longs;u&longs;pen&longs;us re&shy;<lb/>maneret. </s> 
  
 <s>cum primum ob&longs;eruo ip&longs;um inuer&longs;um, hoc e&longs;t capite deor&longs;um, &amp; <lb/>ventre &longs;ur&longs;um pendere. </s> <s>cum primum ob&longs;eruo ip&longs;um inuer&longs;um, hoc e&longs;t capite deor&longs;um, &amp; <lb/>ventre &longs;ur&longs;um pendere. </s>
  
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 <s><margin.target id="marg289"></margin.target>298.b</s></p><p type="main"> <s><margin.target id="marg289"></margin.target>298.b</s></p><p type="main">
  
 <s>Lib. </s> <s>Lib. 2. cap.
  
 <s>2. cap.  
  
 1. <emph type="italics"/>(Sit&queacute; perinde ac admirabilia illa &longs;pontanea)<emph.end type="italics"/> Intelligit ma&shy;<lb/>chinas illas miro artificio confictas, qu&aelig; &agrave; &longs;e ip&longs;is intrin&longs;eco prin&shy;<lb/>cipio mouebantur, quas Gr&aelig;ci veteres Automata, ide&longs;t &longs;pontanea, <lb/>vel &longs;pontina, vt vertit Interpres vocabant, cuiu&longs;modi &longs;unt Auto&shy;<lb/>mata Heronis Alexandrini, qu&aelig; adhuc extant gr&aelig;ca, <expan abbr="qu&aelig;&qacute;">qu&aelig;que</expan>; ab Abbate Gua&shy;<lb/>&longs;tallen&longs;i in Italicum &longs;unt conuer&longs;a. </s> 1. <emph type="italics"/>(Sit&queacute; perinde ac admirabilia illa &longs;pontanea)<emph.end type="italics"/> Intelligit ma&shy;<lb/>chinas illas miro artificio confictas, qu&aelig; &agrave; &longs;e ip&longs;is intrin&longs;eco prin&shy;<lb/>cipio mouebantur, quas Gr&aelig;ci veteres Automata, ide&longs;t &longs;pontanea, <lb/>vel &longs;pontina, vt vertit Interpres vocabant, cuiu&longs;modi &longs;unt Auto&shy;<lb/>mata Heronis Alexandrini, qu&aelig; adhuc extant gr&aelig;ca, <expan abbr="qu&aelig;&qacute;">qu&aelig;que</expan>; ab Abbate Gua&shy;<lb/>&longs;tallen&longs;i in Italicum &longs;unt conuer&longs;a. </s>
  
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 <s><margin.target id="marg290"></margin.target>299</s></p><p type="main"> <s><margin.target id="marg290"></margin.target>299</s></p><p type="main">
  
 <s>Lib. </s> <s>Lib. 2. cap.
  
 <s>2. cap.  
  
 4. <emph type="italics"/>(Nam &amp; triangula figura duobus rectis &aelig;quale &longs;emper habet)<emph.end type="italics"/><lb/>vide qu&aelig; de hac re &longs;crip&longs;i lib.  4. <emph type="italics"/>(Nam &amp; triangula figura duobus rectis &aelig;quale &longs;emper habet)<emph.end type="italics"/><lb/>vide qu&aelig; de hac re &longs;crip&longs;i lib.
  
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 <s><margin.target id="marg292"></margin.target>301</s></p><p type="main"> <s><margin.target id="marg292"></margin.target>301</s></p><p type="main">
  
 <s>Lib. </s> <s>Lib. 1. cap.
  
 <s>1. cap.  
  
 7. <emph type="italics"/>(Faber enim, &amp; Geometra diuer&longs;o modo rectum angulum <lb/><expan abbr="vtriq;">vtrique</expan> con&longs;iderant: ille quatenus <expan abbr="&longs;ol&utilde;">&longs;olum</expan> ad opus vtile e&longs;t, hic ver&ograve; cum ve&shy;<lb/>ritatis &longs;peculator &longs;it, quid, &amp; qualis &longs;it, indagat)<emph.end type="italics"/> Id quod dicit Ari&longs;t. <lb/></s> 7. <emph type="italics"/>(Faber enim, &amp; Geometra diuer&longs;o modo rectum angulum <lb/><expan abbr="vtriq;">vtrique</expan> con&longs;iderant: ille quatenus <expan abbr="&longs;ol&utilde;">&longs;olum</expan> ad opus vtile e&longs;t, hic ver&ograve; cum ve&shy;<lb/>ritatis &longs;peculator &longs;it, quid, &amp; qualis &longs;it, indagat)<emph.end type="italics"/> Id quod dicit Ari&longs;t. <lb/>confirmatur ex eo, quod Fabri omnes vtuntur amu&longs;&longs;i, &longs;eu norma, <lb/><figure id="fig130"></figure><lb/>qu&aelig; nihil aliud e&longs;t qu&agrave;m angulus rectus, qu&aelig; vulg&ograve; <lb/>&longs;quadra dicitur, vt eius auxilio angulum ip&longs;um re&shy;<lb/>ctum in opus conferant, <expan abbr="&longs;ic&qacute;">&longs;icque</expan>; norm&aelig;, aut amu&longs;&longs;is du&shy;<lb/>ctu &longs;ua ip&longs;i opera ad angulos rectos, ide&longs;t quadrata, <lb/>conficiunt. </s>
  
 <s>confirmatur ex eo, quod Fabri omnes vtuntur amu&longs;&longs;i, &longs;eu norma, <lb/><figure id="fig130"></figure><lb/>qu&aelig; nihil aliud e&longs;t qu&agrave;m angulus rectus, qu&aelig; vulg&ograve; <lb/>&longs;quadra dicitur, vt eius auxilio angulum ip&longs;um re&shy;<lb/>ctum in opus conferant, <expan abbr="&longs;ic&qacute;">&longs;icque</expan>; norm&aelig;, aut amu&longs;&longs;is du&shy;<lb/>ctu &longs;ua ip&longs;i opera ad angulos rectos, ide&longs;t quadrata, <lb/>conficiunt. </s> 
  
 <s>Geometra ver&ograve; con&longs;iderat eundem an&shy;<lb/>gulum, quatenus fit &agrave; linea &longs;uper lineam aliam per&shy;<lb/>pendiculariter in&longs;i&longs;tente, vt e&longs;t in definit. </s> <s>Geometra ver&ograve; con&longs;iderat eundem an&shy;<lb/>gulum, quatenus fit &agrave; linea &longs;uper lineam aliam per&shy;<lb/>pendiculariter in&longs;i&longs;tente, vt e&longs;t in definit. </s>
  
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 <s><margin.target id="marg294"></margin.target>303</s></p><p type="main"> <s><margin.target id="marg294"></margin.target>303</s></p><p type="main">
  
 <s>Lib. </s> <s>Lib. 2. cap.
  
 <s>2. cap.  
  
 9. <emph type="italics"/>(Vt circuli medium deprehendere non <lb/>cuiu&longs;libet, &longs;ed <expan abbr="&longs;ci&etilde;tis">&longs;cientis</expan> &longs;olummodo e&longs;t)<emph.end type="italics"/> Reperire medium, <lb/>&longs;iue centrum dati circuli docet Euclides propo&longs;itio&shy;<lb/>ne prima 3. hoc modo. </s> 9. <emph type="italics"/>(Vt circuli medium deprehendere non <lb/>cuiu&longs;libet, &longs;ed <expan abbr="&longs;ci&etilde;tis">&longs;cientis</expan> &longs;olummodo e&longs;t)<emph.end type="italics"/> Reperire medium, <lb/>&longs;iue centrum dati circuli docet Euclides propo&longs;itio&shy;<lb/>ne prima 3. hoc modo. </s>
  
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 <s><margin.target id="marg295"></margin.target>304</s></p><p type="main"> <s><margin.target id="marg295"></margin.target>304</s></p><p type="main">
  
 <s>Lib. </s> <s>Lib. 3. cap.
  
 <s>3. cap.  
  
 3. <emph type="italics"/>(De &aelig;<gap/>ernis autem nemo con&longs;ultat, vt <lb/>de mundo, aut diametro, &amp; latere, quod nulla inter &longs;e <lb/>&aelig;quabilitate conueniant)<emph.end type="italics"/> Qua ratione diameter, &amp; latus eiu&longs;dem quadrati <lb/>nulia &aelig;quabilitate, ide&longs;t nulla communi men&longs;ura inter &longs;e conueniant, fus&egrave; <lb/>explicatum e&longs;t libro Priorum, &longs;ecto 1. cap.  3. <emph type="italics"/>(De &aelig;<gap/>ernis autem nemo con&longs;ultat, vt <lb/>de mundo, aut diametro, &amp; latere, quod nulla inter &longs;e <lb/>&aelig;quabilitate conueniant)<emph.end type="italics"/> Qua ratione diameter, &amp; latus eiu&longs;dem quadrati <lb/>nulia &aelig;quabilitate, ide&longs;t nulla communi men&longs;ura inter &longs;e conueniant, fus&egrave; <lb/>explicatum e&longs;t libro Priorum, &longs;ecto 1. cap.
  
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 <s><margin.target id="marg298"></margin.target>307</s></p><p type="main"> <s><margin.target id="marg298"></margin.target>307</s></p><p type="main">
  
 <s>Lib. </s> <s>Lib. 5. cap.
  
 <s>5. cap.  
  
 3. <emph type="italics"/>(Quod en m proportione con&longs;tat, id non tam vnitario numero, <lb/>qu&agrave;m numero in vniuer&longs;um proprium e&longs;t)<emph.end type="italics"/> Per vnitarium numerum intelligitur <lb/>numerus ex vnitatibus ab&longs;tractis con&longs;litus, ide&longs;t, cuius vnitates non &longs;int res <lb/>phy&longs;ic&aelig;, &longs;ed &agrave; naturalibus ab&longs;tract&aelig;, qualis con&longs;iderat Arithmeticus: omni <lb/>tamen numero &longs;iue ab&longs;tracto, &longs;iue non, connenit proportiones &longs;u&longs;cipere, <lb/>id e&longs;t &amp; numero, &amp; rebus numeratis.</s></p><pb pagenum="218"/><p type="main"> 3. <emph type="italics"/>(Quod en m proportione con&longs;tat, id non tam vnitario numero, <lb/>qu&agrave;m numero in vniuer&longs;um proprium e&longs;t)<emph.end type="italics"/> Per vnitarium numerum intelligitur <lb/>numerus ex vnitatibus ab&longs;tractis con&longs;litus, ide&longs;t, cuius vnitates non &longs;int res <lb/>phy&longs;ic&aelig;, &longs;ed &agrave; naturalibus ab&longs;tract&aelig;, qualis con&longs;iderat Arithmeticus: omni <lb/>tamen numero &longs;iue ab&longs;tracto, &longs;iue non, connenit proportiones &longs;u&longs;cipere, <lb/>id e&longs;t &amp; numero, &amp; rebus numeratis.</s></p><pb pagenum="218"/><p type="main">
  
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 <s><margin.target id="marg304"></margin.target>313</s></p><p type="main"> <s><margin.target id="marg304"></margin.target>313</s></p><p type="main">
  
 <s>Lib. </s> <s>Lib. 5. cap.
  
 <s>5. cap.  
  
 6. <emph type="italics"/>(Atque id vet propo<gap/>tione vel numero)<emph.end type="italics"/> ide&longs;t, vel proportio&shy;<lb/>nalitate Geometrica, vel Arithmetica; qu&aelig; autem &longs;it proportionalitas <lb/>Geometrica, dictum e&longs;t paul&ograve; ante in prioribus locis Mathematicis huius <lb/>quinti libri; qu&aelig; ver&ograve; &longs;it proportionalitas Arithmetica dictum e&longs;t &longs;uperius <lb/>lib.  6. <emph type="italics"/>(Atque id vet propo<gap/>tione vel numero)<emph.end type="italics"/> ide&longs;t, vel proportio&shy;<lb/>nalitate Geometrica, vel Arithmetica; qu&aelig; autem &longs;it proportionalitas <lb/>Geometrica, dictum e&longs;t paul&ograve; ante in prioribus locis Mathematicis huius <lb/>quinti libri; qu&aelig; ver&ograve; &longs;it proportionalitas Arithmetica dictum e&longs;t &longs;uperius <lb/>lib.
  
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 <s><margin.target id="marg305"></margin.target>314</s></p><p type="main"> <s><margin.target id="marg305"></margin.target>314</s></p><p type="main">
  
 <s>Lib. </s> <s>Lib. 6. cap.
  
 <s>6. cap.  
  
 5. <emph type="italics"/>(Verbi cau&longs;a triangulum tres angulos duobus rectis &aelig;quales ha&shy;<lb/>bere, velnon habere)<emph.end type="italics"/> lib.  5. <emph type="italics"/>(Verbi cau&longs;a triangulum tres angulos duobus rectis &aelig;quales ha&shy;<lb/>bere, velnon habere)<emph.end type="italics"/> lib.
  
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 <s><margin.target id="marg306"></margin.target>315</s></p><p type="main"> <s><margin.target id="marg306"></margin.target>315</s></p><p type="main">
  
 <s>Lib. </s> <s>Lib. 6. cap.
  
 <s>6. cap.  
  
 8. <emph type="italics"/>(Nam illud etiam con&longs;ideratione dignum videtur. </s> 8. <emph type="italics"/>(Nam illud etiam con&longs;ideratione dignum videtur. </s>
  
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 <s><margin.target id="marg307"></margin.target>316</s></p><p type="main"> <s><margin.target id="marg307"></margin.target>316</s></p><p type="main">
  
 <s>Lib. </s> <s>Lib. 7. cap.
  
 <s>7. cap.  
  
 8. <emph type="italics"/>(In actionibus autem principium illud e&longs;t, cuius cau&longs;a res fit, <lb/>&longs;icut in Mathematicis &longs;uppo&longs;itiones; nam neque illic ratio e&longs;t, qu&aelig; doctrinam tra&shy;<lb/>dat principiorum, neque hic<emph.end type="italics"/>) Suppo&longs;itionum, &longs;iue principiorum Mathemati&shy;<lb/>corum tria &longs;unt genera, definitiones, po&longs;tulata, axiomata, qu&aelig; in ip&longs;o primi <lb/>Elementorum ve&longs;tibulo proponuntur: &longs;olaque terminorum explicatione <lb/><expan abbr="ab&longs;q;">ab&longs;que</expan> vllo di&longs;cur&longs;u, addi&longs;cuntur.</s></p><p type="head"> 8. <emph type="italics"/>(In actionibus autem principium illud e&longs;t, cuius cau&longs;a res fit, <lb/>&longs;icut in Mathematicis &longs;uppo&longs;itiones; nam neque illic ratio e&longs;t, qu&aelig; doctrinam tra&shy;<lb/>dat principiorum, neque hic<emph.end type="italics"/>) Suppo&longs;itionum, &longs;iue principiorum Mathemati&shy;<lb/>corum tria &longs;unt genera, definitiones, po&longs;tulata, axiomata, qu&aelig; in ip&longs;o primi <lb/>Elementorum ve&longs;tibulo proponuntur: &longs;olaque terminorum explicatione <lb/><expan abbr="ab&longs;q;">ab&longs;que</expan> vllo di&longs;cur&longs;u, addi&longs;cuntur.</s></p><p type="head">
  
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 <s>hoc &longs;olum addendum ad illorum verborum (<emph type="italics"/>Ex de&shy;<lb/>terminato &longs;ibi principio propter quid a&longs;&longs;ump&longs;erunt<emph.end type="italics"/>) intelligentiam, ide&longs;t ex vna <lb/>conclu&longs;ione demon&longs;trata, tanquam principio alia demon&longs;trant; quod rect&egrave; <lb/>fieri Ari&longs;t.  <s>hoc &longs;olum addendum ad illorum verborum (<emph type="italics"/>Ex de&shy;<lb/>terminato &longs;ibi principio propter quid a&longs;&longs;ump&longs;erunt<emph.end type="italics"/>) intelligentiam, ide&longs;t ex vna <lb/>conclu&longs;ione demon&longs;trata, tanquam principio alia demon&longs;trant; quod rect&egrave; <lb/>fieri Ari&longs;t.
  
 in primo Po&longs;ter. </s> in primo Po&longs;ter. docet.</s></p><p type="main">
  
 <s>docet.</s></p><p type="main"> 
  
 <s><arrow.to.target n="marg312"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg312"></arrow.to.target></s></p><p type="margin">
  
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 <s>ini&shy;<lb/>tium, ac &longs;tatum &longs;ignificare voluerunt. </s> <s>ini&shy;<lb/>tium, ac &longs;tatum &longs;ignificare voluerunt. </s>
  
 <s>Vernmenimuer&ograve; cum numerus hu&shy;<lb/>ius diagrammatis, ide&longs;t huiu&longs;cemodi conditionis, qui e&longs;t 12. factus fuerit <lb/>&longs;olidus, hoc e&longs;t, quando Re&longs;p. </s> <s>Vernmenimuer&ograve; cum numerus hu&shy;<lb/>ius diagrammatis, ide&longs;t huiu&longs;cemodi conditionis, qui e&longs;t 12. factus fuerit <lb/>&longs;olidus, hoc e&longs;t, quando Re&longs;p. ben&egrave; con&longs;tituta ad eam annorum, vel &longs;&aelig;culo&shy;<lb/>rum periodum peruenerit, qui &longs;it numerus &longs;olidus numeri 12. tunc fatali <lb/>ordine, mutationem pati incipiet, atque in peius, c&ugrave;m optimi mutatio &longs;it <lb/>pe&longs;sima, prolabi. </s>
  
 <s>ben&egrave; con&longs;tituta ad eam annorum, vel &longs;&aelig;culo&shy;<lb/>rum periodum peruenerit, qui &longs;it numerus &longs;olidus numeri 12. tunc fatali <lb/>ordine, mutationem pati incipiet, atque in peius, c&ugrave;m optimi mutatio &longs;it <lb/>pe&longs;sima, prolabi. </s> 
  
 <s>pori&ograve; numerus &longs;olidus ip&longs;ius 12. e&longs;t 1728. vti mox expli&shy;<lb/>cabo. </s> <s>pori&ograve; numerus &longs;olidus ip&longs;ius 12. e&longs;t 1728. vti mox expli&shy;<lb/>cabo. </s>
  
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 <s>omnem quamuis optimam, in deterius prolpp&longs;u&shy;<pb pagenum="226"/>ram, c&ugrave;m enim ad &longs;ummam perfectionem peruenerit, qu&aelig; in numero &longs;oli&shy;<lb/>do, &amp; cubico &longs;ignificatur, &longs;i vlterius progre&longs;sura &longs;it, nece&longs;&longs;ari&ograve; &longs;ummam <lb/>perfectionem pr&aelig;teribit, ac derelinquet. </s> <s>omnem quamuis optimam, in deterius prolpp&longs;u&shy;<pb pagenum="226"/>ram, c&ugrave;m enim ad &longs;ummam perfectionem peruenerit, qu&aelig; in numero &longs;oli&shy;<lb/>do, &amp; cubico &longs;ignificatur, &longs;i vlterius progre&longs;sura &longs;it, nece&longs;&longs;ari&ograve; &longs;ummam <lb/>perfectionem pr&aelig;teribit, ac derelinquet. </s>
  
 <s>Qu&ograve;d autem numerus 1728. &longs;it <lb/>numerus &longs;olidus, &amp; cubus ip&longs;ius Duodenarij &longs;ic pal<gap/>m fiet, &longs;i tamen prius, <lb/>ea repetiueris, qu&aelig; &longs;upra in primo Po&longs;ter. </s> <s>Qu&ograve;d autem numerus 1728. &longs;it <lb/>numerus &longs;olidus, &amp; cubus ip&longs;ius Duodenarij &longs;ic pal<gap/>m fiet, &longs;i tamen prius, <lb/>ea repetiueris, qu&aelig; &longs;upra in primo Po&longs;ter. num. </s>
  
 <s>num. </s> 
  
 <s>33. marginali, de numero <lb/>Quadrato, &amp; Cubo dicta &longs;unt: e&longs;t autem cubus numerus is, qui ex gemina&shy;<lb/>to ductu alicuius numeri in &longs;e ip&longs;um, producitur. </s> <s>33. marginali, de numero <lb/>Quadrato, &amp; Cubo dicta &longs;unt: e&longs;t autem cubus numerus is, qui ex gemina&shy;<lb/>to ductu alicuius numeri in &longs;e ip&longs;um, producitur. </s>
  
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 <s>in pr&aelig;&longs;enti <lb/>problemate loquitur. </s> <s>in pr&aelig;&longs;enti <lb/>problemate loquitur. </s>
  
 <s>ex his facil&egrave; e&longs;t verborum Ari&longs;t. </s> <s>ex his facil&egrave; e&longs;t verborum Ari&longs;t. &longs;en&longs;um a&longs;&longs;equi. </s>
  
 <s>&longs;en&longs;um a&longs;&longs;equi. </s> 
  
 <s>Qu&aelig;&shy;<lb/>rit igitur, cur tempore &longs;olaris deliquij, &longs;i Solis illuminationes per cribri fo&shy;<lb/>ramina, aut inter alicuius arboris folia, ex ijs, qu&aelig; lata habent folia, aut <lb/>inter manuum decu&longs;&longs;atos digitos, ingredientes, atque in terra apparentes, <pb pagenum="242"/>&longs;pectemus, easfalcatas, ac lunulatas, videamus; non autem, vt &longs;olemus, <lb/>rotundas. </s> <s>Qu&aelig;&shy;<lb/>rit igitur, cur tempore &longs;olaris deliquij, &longs;i Solis illuminationes per cribri fo&shy;<lb/>ramina, aut inter alicuius arboris folia, ex ijs, qu&aelig; lata habent folia, aut <lb/>inter manuum decu&longs;&longs;atos digitos, ingredientes, atque in terra apparentes, <pb pagenum="242"/>&longs;pectemus, easfalcatas, ac lunulatas, videamus; non autem, vt &longs;olemus, <lb/>rotundas. </s>
  
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 <s>re&longs;pondet inde prouenire, quia h&aelig;c vox <lb/>cantandi principium e&longs;t. </s> <s>re&longs;pondet inde prouenire, quia h&aelig;c vox <lb/>cantandi principium e&longs;t. </s>
  
 <s>vbi per cantandi principium puto ip&longs;um intellige&shy;<lb/>re &longs;emitonium, &longs;iue die&longs;im, nam, vtip&longs;e ait primo <lb/><figure id="fig147"></figure><lb/>re &longs;emitonium, &longs;iue die&longs;im, nam, vt ip&longs;e ait primo <lb/>Po&longs;ter. </s> <s>vbi per cantandi principium puto ip&longs;um intellige&shy;<lb/>re &longs;emitonium, &longs;iue die&longs;im, nam, vtip&longs;e ait primo <lb/><figure id="fig147"></figure><lb/>re &longs;emitonium, &longs;iue die&longs;im, nam, vt ip&longs;e ait primo <lb/>Po&longs;ter. cap.
  
 <s>cap.  
  
 38. die&longs;is h&ecedil;c, &longs;iue &longs;emitonium dicitur <lb/>principium cantus, quia minimum e&longs;t omnium in&shy;<lb/>teruallorum, qu&aelig; voce po&longs;&longs;int exprimi: <expan abbr="atq;">atque</expan> ex eo <lb/>alia interualla con&longs;tant, <expan abbr="e&longs;t&qacute;">e&longs;tque</expan>; veluti illorum ele&shy;<lb/>mentum. </s> 38. die&longs;is h&ecedil;c, &longs;iue &longs;emitonium dicitur <lb/>principium cantus, quia minimum e&longs;t omnium in&shy;<lb/>teruallorum, qu&aelig; voce po&longs;&longs;int exprimi: <expan abbr="atq;">atque</expan> ex eo <lb/>alia interualla con&longs;tant, <expan abbr="e&longs;t&qacute;">e&longs;tque</expan>; veluti illorum ele&shy;<lb/>mentum. </s>
  
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 <s><margin.target id="marg353"></margin.target>361</s></p><p type="main"> <s><margin.target id="marg353"></margin.target>361</s></p><p type="main">
  
 <s>Probl. </s> <s>Probl. 4. <emph type="italics"/>(S&eacute;d cur h&aelig;c difficile, hypate facil&egrave; cantatur, cum non ni&longs;i die&longs;i di&shy;<lb/>&longs;crepent? </s>
  
 <s>4. <emph type="italics"/>(S&eacute;d cur h&aelig;c difficile, hypate facil&egrave; cantatur, cum non ni&longs;i die&longs;i di&shy;<lb/>&longs;crepent? </s> 
  
 <s>An quod hypate remi&longs;&longs;ior e&longs;t, <expan abbr="atq;">atque</expan> etiam l&aelig;uius &agrave; con&longs;titutione a&longs;cendi&shy;<lb/>tur? </s> <s>An quod hypate remi&longs;&longs;ior e&longs;t, <expan abbr="atq;">atque</expan> etiam l&aelig;uius &agrave; con&longs;titutione a&longs;cendi&shy;<lb/>tur? </s>
  
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 <s><margin.target id="marg354"></margin.target>362</s></p><p type="main"> <s><margin.target id="marg354"></margin.target>362</s></p><p type="main">
  
 <s>Probl. </s> <s>Probl. 5. <emph type="italics"/>(Cur &longs;uauius cantilenam, quam nouimus, audire &longs;olemus, quam cam, <lb/>quam ignoramus? </s>
  
 <s>5. <emph type="italics"/>(Cur &longs;uauius cantilenam, quam nouimus, audire &longs;olemus, quam cam, <lb/>quam ignoramus? </s> 
  
 <s>Vtrum, quia c&ugrave;m quod cantatur, agno&longs;cimus, tunc magis ma&shy;<lb/>nife&longs;tus e&longs;t, qui veluti &longs;copum a&longs;&longs;equitur. </s> <s>Vtrum, quia c&ugrave;m quod cantatur, agno&longs;cimus, tunc magis ma&shy;<lb/>nife&longs;tus e&longs;t, qui veluti &longs;copum a&longs;&longs;equitur. </s>
  
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 <s>tertia ratio e&longs;t, quia res &longs;olit&aelig; plerumque, quam in&longs;olit&aelig; iucundio&shy;<lb/>res exi&longs;tunt.</s></p><p type="main"> <s>tertia ratio e&longs;t, quia res &longs;olit&aelig; plerumque, quam in&longs;olit&aelig; iucundio&shy;<lb/>res exi&longs;tunt.</s></p><p type="main">
  
 <s>Probl. </s> <s>Probl. 6. &amp; per &longs;e &longs;atis clarum e&longs;t; &amp; ad harmonicam non &longs;pectat.</s></p><p type="main">
  
 <s>6. &amp; per &longs;e &longs;atis clarum e&longs;t; &amp; ad harmonicam non &longs;pectat.</s></p><p type="main"> 
  
 <s><arrow.to.target n="marg355"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg355"></arrow.to.target></s></p><p type="margin">
  
 <s><margin.target id="marg355"></margin.target>363</s></p><p type="main"> <s><margin.target id="marg355"></margin.target>363</s></p><p type="main">
  
 <s>Probl. </s> <s>Probl. 7. <emph type="italics"/>(Cur veteres cum &longs;eptemfidibus concentus di&longs;ponerent, hypaten, non <lb/>neten relinquebant? </s>
  
 <s>7. <emph type="italics"/>(Cur veteres cum &longs;eptemfidibus concentus di&longs;ponerent, hypaten, non <lb/>neten relinquebant? </s> 
  
 <s>An fals&ograve; id dicitur (earum enim <expan abbr="vtramq;">vtramque</expan> &longs;eruarunt; &longs;edtri&shy;<lb/>ten adimere &longs;olebant) An non? </s> <s>An fals&ograve; id dicitur (earum enim <expan abbr="vtramq;">vtramque</expan> &longs;eruarunt; &longs;edtri&shy;<lb/>ten adimere &longs;olebant) An non? </s>
  
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 <s><margin.target id="marg356"></margin.target>364</s></p><p type="main"> <s><margin.target id="marg356"></margin.target>364</s></p><p type="main">
  
 <s>Probl. </s> <s>Probl. 8. <emph type="italics"/>(Cur grauis &longs;onum pote&longs;t acut&aelig;? </s>
  
 <s>8. <emph type="italics"/>(Cur grauis &longs;onum pote&longs;t acut&aelig;? </s> 
  
 <s>An quia maius e&longs;t; etenim quemad&shy;<lb/>modum graue obtu&longs;o, &longs;ic acutum acuto angulo &longs;imile e&longs;t)<emph.end type="italics"/> Ex intelligentia pr&aelig;&shy;<lb/>cedentis problematis, pr&aelig;&longs;ens fatis fer&egrave; clarum e&longs;t: im&ograve; exillo ortum i&longs;tud <lb/>e&longs;&longs;e videtur. </s> <s>An quia maius e&longs;t; etenim quemad&shy;<lb/>modum graue obtu&longs;o, &longs;ic acutum acuto angulo &longs;imile e&longs;t)<emph.end type="italics"/> Ex intelligentia pr&aelig;&shy;<lb/>cedentis problematis, pr&aelig;&longs;ens fatis fer&egrave; clarum e&longs;t: im&ograve; exillo ortum i&longs;tud <lb/>e&longs;&longs;e videtur. </s>
  
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 <s><margin.target id="marg357"></margin.target>365</s></p><p type="main"> <s><margin.target id="marg357"></margin.target>365</s></p><p type="main">
  
 <s>Probl. </s> <s>Probl. 9. <emph type="italics"/>(Gur &longs;olitarias cantilenas &longs;uauius audire &longs;olemus, &longs;i ad tybiam, aut <lb/>ad lyram vnam cantatur, c&ugrave;m tamen ad fides, canticum&queacute; idem, medo <expan abbr="vtroq;">vtroque</expan> per&shy;<lb/>agatur? </s>
  
 <s>9. <emph type="italics"/>(Gur &longs;olitarias cantilenas &longs;uauius audire &longs;olemus, &longs;i ad tybiam, aut <lb/>ad lyram vnam cantatur, c&ugrave;m tamen ad fides, canticum&queacute; idem, medo <expan abbr="vtroq;">vtroque</expan> per&shy;<lb/>agatur? </s> 
  
 <s>narm &longs;i idem ita amplius fit, plus ad plures tibias, <expan abbr="atq;">atque</expan> etiam &longs;uauius e&longs;&longs;e<emph.end type="italics"/><pb pagenum="253"/><emph type="italics"/>oportet? </s> <s>narm &longs;i idem ita amplius fit, plus ad plures tibias, <expan abbr="atq;">atque</expan> etiam &longs;uauius e&longs;&longs;e<emph.end type="italics"/><pb pagenum="253"/><emph type="italics"/>oportet? </s>
  
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 <s><margin.target id="marg358"></margin.target>366</s></p><p type="main"> <s><margin.target id="marg358"></margin.target>366</s></p><p type="main">
  
 <s>Probl. </s> <s>Probl. 10. &longs;atis clarum ex &longs;e. </s>
  
 <s>10. &longs;atis clarum ex &longs;e. </s> 
  
 <s>illud &longs;olum notatione dignum e&longs;t, Teretiza&shy;<lb/>re, quod e&longs;t canere, vt modo aiunt, non verba, &longs;ed notas, fui&longs;&longs;e idem, quod <lb/>nune &longs;olmifationem, aut lalagen decantare.</s></p><p type="main"> <s>illud &longs;olum notatione dignum e&longs;t, Teretiza&shy;<lb/>re, quod e&longs;t canere, vt modo aiunt, non verba, &longs;ed notas, fui&longs;&longs;e idem, quod <lb/>nune &longs;olmifationem, aut lalagen decantare.</s></p><p type="main">
  
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 <s><margin.target id="marg359"></margin.target>367</s></p><p type="main"> <s><margin.target id="marg359"></margin.target>367</s></p><p type="main">
  
 <s>Probl. </s> <s>Probl. 11. <emph type="italics"/>(Cur vox, aut fonus de&longs;inens a<gap/>utoir fit? </s>
  
 <s>11. <emph type="italics"/>(Cur vox, aut fonus de&longs;inens a<gap/>utoir fit? </s> 
  
 <s>An quia minor, vt qu&aelig; fa&shy;<lb/>cta &longs;it imbecillior?)<emph.end type="italics"/> lege qu&aelig; in probl. </s> <s>An quia minor, vt qu&aelig; fa&shy;<lb/>cta &longs;it imbecillior?)<emph.end type="italics"/> lege qu&aelig; in probl. </s>
  
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 <s><margin.target id="marg360"></margin.target>368</s></p><p type="main"> <s><margin.target id="marg360"></margin.target>368</s></p><p type="main">
  
 <s>Probl. </s> <s>Probl. 12. <emph type="italics"/>(Quamobrem qu&aelig; grauior &egrave; fidibus eft &longs;emper modulationem, aut <lb/>cantilenam &longs;u&longs;cipit: nam &longs;i oporteat canere parame&longs;en c&ugrave;m &longs;ola me&longs;e, nihilominus <lb/>medium gignetur: &longs;i ver&ograve; me&longs;en, nece&longs;&longs;arium ambo, &longs;ola non gignitur? </s>
  
 <s>12. <emph type="italics"/>(Quamobrem qu&aelig; grauior &egrave; fidibus eft &longs;emper modulationem, aut <lb/>cantilenam &longs;u&longs;cipit: nam &longs;i oporteat canere parame&longs;en c&ugrave;m &longs;ola me&longs;e, nihilominus <lb/>medium gignetur: &longs;i ver&ograve; me&longs;en, nece&longs;&longs;arium ambo, &longs;ola non gignitur? </s> 
  
 <s>An quia <lb/>graue magnum e&longs;t, itaque validius: &amp; in magno paruum ine&longs;i. </s> <s>An quia <lb/>graue magnum e&longs;t, itaque validius: &amp; in magno paruum ine&longs;i. </s>
  
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 <s>Sed &longs;i minus, cert&egrave; in graui acutum e&longs;t, maius enim <lb/>graue e&longs;t)<emph.end type="italics"/> Cur inquit, ex duobus &longs;onis, qui Diapa&longs;on efficiant, grauis qui&shy;<lb/>dem habet in &longs;e Antiphonum acuti, ide&longs;t, in &longs;e continet etiam acutum: at <lb/>ver&ograve; acutus non habet antiphonum grauis, ide&longs;t non continet in &longs;e grauem. <lb/></s> <s>Sed &longs;i minus, cert&egrave; in graui acutum e&longs;t, maius enim <lb/>graue e&longs;t)<emph.end type="italics"/> Cur inquit, ex duobus &longs;onis, qui Diapa&longs;on efficiant, grauis qui&shy;<lb/>dem habet in &longs;e Antiphonum acuti, ide&longs;t, in &longs;e continet etiam acutum: at <lb/>ver&ograve; acutus non habet antiphonum grauis, ide&longs;t non continet in &longs;e grauem. <lb/></s>
  
 <s>Ratio e&longs;t, inquit, quia in <expan abbr="vtraq;">vtraque</expan> continetur &longs;onus, &longs;eu modus <expan abbr="vtriu&longs;q;">vtriu&longs;que</expan> qua&shy;<lb/>tenus voces huius con&longs;onanti&aelig; &longs;unt eiu&longs;dem natur&aelig;, vt in 7. Probl. </s> <s>Ratio e&longs;t, inquit, quia in <expan abbr="vtraq;">vtraque</expan> continetur &longs;onus, &longs;eu modus <expan abbr="vtriu&longs;q;">vtriu&longs;que</expan> qua&shy;<lb/>tenus voces huius con&longs;onanti&aelig; &longs;unt eiu&longs;dem natur&aelig;, vt in 7. Probl. dictum <lb/>e&longs;t. </s>
  
 <s>dictum <lb/>e&longs;t. </s> 
  
 <s>Sed melius e&longs;t Dicere, quia in graui tanquam in magno acutum veluti <lb/>paruum includitur, vt paul&ograve; ante fu&longs;ius explicatum e&longs;t.</s></p><p type="main"> <s>Sed melius e&longs;t Dicere, quia in graui tanquam in magno acutum veluti <lb/>paruum includitur, vt paul&ograve; ante fu&longs;ius explicatum e&longs;t.</s></p><p type="main">
  
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 <s>in &longs;onis &aelig;qualitas e&longs;t; <lb/>a quale autem omne ad vnitatem <expan abbr="refer&etilde;dum">referendum</expan> e&longs;t. </s> <s>in &longs;onis &aelig;qualitas e&longs;t; <lb/>a quale autem omne ad vnitatem <expan abbr="refer&etilde;dum">referendum</expan> e&longs;t. </s>
  
 <s>hoc idem in fi&longs;tolis etiam euenit, vt <lb/>falli aures po&longs;&longs;int)<emph.end type="italics"/> Qu&aelig;nam &longs;int voces Antiphon&aelig; in 7. Probl. </s> <s>hoc idem in fi&longs;tolis etiam euenit, vt <lb/>falli aures po&longs;&longs;int)<emph.end type="italics"/> Qu&aelig;nam &longs;int voces Antiphon&aelig; in 7. Probl. dictum e&longs;t. </s>
  
 <s>dictum e&longs;t. </s> 
  
 <s>quod <lb/>ad textum attinet pro verbo, atropo, quod in Gaz&aelig; translatione legitur, <lb/>repo&longs;ui, Homine, Gr&aelig;c&egrave; enim e&longs;t, <foreign lang="greek">agqrwxw)<gap/>,</foreign> ex quo fort&egrave; mendos&egrave; factum <lb/>e&longs;t illud, atropo. </s> <s>quod <lb/>ad textum attinet pro verbo, atropo, quod in Gaz&aelig; translatione legitur, <lb/>repo&longs;ui, Homine, Gr&aelig;c&egrave; enim e&longs;t, <foreign lang="greek">agqrwxw)<gap/>,</foreign> ex quo fort&egrave; mendos&egrave; factum <lb/>e&longs;t illud, atropo. </s>
  
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 <s><margin.target id="marg363"></margin.target>372</s></p><p type="main"> <s><margin.target id="marg363"></margin.target>372</s></p><p type="main">
  
 <s>Probl. </s> <s>Probl. 16. <emph type="italics"/>(Qua de cau&longs;a Antiphonum &longs;uauius est &longs;ymphono? </s>
  
 <s>16. <emph type="italics"/>(Qua de cau&longs;a Antiphonum &longs;uauius est &longs;ymphono? </s> 
  
 <s>An quia in an&shy;<lb/>tiphono manife&longs;tior est ip&longs;a con&longs;onantia, qu&agrave;m e&ugrave;m ad &longs;ympboniam cantatur: ne&shy;<lb/>oe&longs;&longs;e exim e&longs;t in &longs;ymphonia alteram vocem alteri vni&longs;onam e&longs;&longs;e; ita vt du&aelig; in ean&shy;<lb/>dem coale&longs;centes altera alteram offu&longs;care po&longs;&longs;it)<emph.end type="italics"/> Per antiphonum intelligit nunc <lb/>Ari&longs;t.  <s>An quia in an&shy;<lb/>tiphono manife&longs;tior est ip&longs;a con&longs;onantia, qu&agrave;m e&ugrave;m ad &longs;ympboniam cantatur: ne&shy;<lb/>oe&longs;&longs;e exim e&longs;t in &longs;ymphonia alteram vocem alteri vni&longs;onam e&longs;&longs;e; ita vt du&aelig; in ean&shy;<lb/>dem coale&longs;centes altera alteram offu&longs;care po&longs;&longs;it)<emph.end type="italics"/> Per antiphonum intelligit nunc <lb/>Ari&longs;t.
  
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 <s><margin.target id="marg364"></margin.target>373</s></p><p type="main"> <s><margin.target id="marg364"></margin.target>373</s></p><p type="main">
  
 <s>Probl. </s> <s>Probl. 17. <emph type="italics"/>(Cur &longs;ola Diapa&longs;on con&longs;onantia cantatur? </s>
  
 <s>17. <emph type="italics"/>(Cur &longs;ola Diapa&longs;on con&longs;onantia cantatur? </s> 
  
 <s>&longs;ecundum hanc cnim, &amp; <lb/>nullam aliam magadare &longs;olent. </s> <s>&longs;ecundum hanc cnim, &amp; <lb/>nullam aliam magadare &longs;olent. </s>
  
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 <s>hoc <lb/>enim pacto ad ip&longs;um canentes, Diapa&longs;on cum ip&longs;o facil&egrave; effeci&longs;&longs;ent. </s> <s>hoc <lb/>enim pacto ad ip&longs;um canentes, Diapa&longs;on cum ip&longs;o facil&egrave; effeci&longs;&longs;ent. </s>
  
 <s>Notan&shy;<lb/>dum pr&aelig;terea Ari&longs;t. </s> <s>Notan&shy;<lb/>dum pr&aelig;terea Ari&longs;t. &longs;umere in textu Antiphonum pro &longs;ola Diapa&longs;on. </s>
  
 <s>&longs;umere in textu Antiphonum pro &longs;ola Diapa&longs;on. </s> 
  
 <s>Qu&aelig;&shy;<lb/>rit igitur, cur canentes &longs;oliti &longs;int per &longs;olam Diapa&longs;on con&longs;onantiam cane&shy;<lb/>re, quod probat ex v&longs;u Magadis, quod vulg&ograve; ad cantum adhibere &longs;olebant, <lb/>c&ugrave;m eo enim omnes in Diapa&longs;on conueniebant. </s> <s>Qu&aelig;&shy;<lb/>rit igitur, cur canentes &longs;oliti &longs;int per &longs;olam Diapa&longs;on con&longs;onantiam cane&shy;<lb/>re, quod probat ex v&longs;u Magadis, quod vulg&ograve; ad cantum adhibere &longs;olebant, <lb/>c&ugrave;m eo enim omnes in Diapa&longs;on conueniebant. </s>
  
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 <s><margin.target id="marg365"></margin.target>374</s></p><p type="main"> <s><margin.target id="marg365"></margin.target>374</s></p><p type="main">
  
 <s>Probl. </s> <s>Probl. 18. <emph type="italics"/>(Sed cur Solis Antiphonis vocibus hoc ine&longs;t? </s>
  
 <s>18. <emph type="italics"/>(Sed cur Solis Antiphonis vocibus hoc ine&longs;t? </s> 
  
 <s>An quod &longs;ol&ccedil; pari in&shy;<lb/>teruallo di&longs;tant &agrave; Me&longs;e. </s> <s>An quod &longs;ol&ccedil; pari in&shy;<lb/>teruallo di&longs;tant &agrave; Me&longs;e. </s>
  
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 <s><margin.target id="marg366"></margin.target>375</s></p><p type="main"> <s><margin.target id="marg366"></margin.target>375</s></p><p type="main">
  
 <s>Probl. </s> <s>Probl. 19. <emph type="italics"/>(Cur non canunt Diapente, &amp; Diate&longs;&longs;aron in Antiphonis? </s>
  
 <s>19. <emph type="italics"/>(Cur non canunt Diapente, &amp; Diate&longs;&longs;aron in Antiphonis? </s> 
  
 <s>An quod <lb/>non eadem con&longs;onandi ratio ijs ine&longs;t, qu&aelig; in Diapa&longs;on: in qua vox grauis eundem <lb/>habet in grauitate modum, quem acuta in acumine: ita vt, &amp; eadem vox quidem, <lb/>&amp; &longs;imul diuer&longs;a oriatur. </s> <s>An quod <lb/>non eadem con&longs;onandi ratio ijs ine&longs;t, qu&aelig; in Diapa&longs;on: in qua vox grauis eundem <lb/>habet in grauitate modum, quem acuta in acumine: ita vt, &amp; eadem vox quidem, <lb/>&amp; &longs;imul diuer&longs;a oriatur. </s>
  
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 <s><margin.target id="marg367"></margin.target>376</s></p><p type="main"> <s><margin.target id="marg367"></margin.target>376</s></p><p type="main">
  
 <s>Probl. </s> <s>Probl. 20. <emph type="italics"/>(Cur &longs;i quis, mota Me&longs;e, alijs quamuis omnibus chordis ben&egrave; con&shy;<lb/>&longs;onantibus, in&longs;trumento vtatur, non &longs;ol&ubreve; cum ad Me&longs;es &longs;on&ubreve; peruenerit, &longs;ed etiam <lb/>in reliqua melodia, aures anget, modumque <expan abbr="inc&otilde;">incom</expan> innum e&longs;&longs;icient: &longs;i ver&ograve; Lycha&shy;<lb/>nos, aut alia qu&aelig;piam mota fuerit, tunc di&longs;crimen, aut in<gap/><expan abbr="&otilde;">om</expan><gap/>nisas &longs;olum appare-<emph.end type="italics"/><pb pagenum="259"/><emph type="italics"/>bit, c&ugrave;m ip&longs;am, quis pul&longs;auerit? </s>
  
 <s>20. <emph type="italics"/>(Cur &longs;i quis, mota Me&longs;e, alijs quamuis omnibus chordis ben&egrave; con&shy;<lb/>&longs;onantibus, in&longs;trumento vtatur, non &longs;ol&ubreve; cum ad Me&longs;es &longs;on&ubreve; peruenerit, &longs;ed etiam <lb/>in reliqua melodia, aures anget, modumque <expan abbr="inc&otilde;">incom</expan> innum e&longs;&longs;icient: &longs;i ver&ograve; Lycha&shy;<lb/>nos, aut alia qu&aelig;piam mota fuerit, tunc di&longs;crimen, aut in<gap/><expan abbr="&otilde;">om</expan><gap/>nisas &longs;olum appare-<emph.end type="italics"/><pb pagenum="259"/><emph type="italics"/>bit, c&ugrave;m ip&longs;am, quis pul&longs;auerit? </s> 
  
 <s>An non ratione id optima accidit? </s> <s>An non ratione id optima accidit? </s>
  
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 <s>&longs;ic <lb/>etiam &longs;onus me&longs;es e&longs;t veluti aliorum &longs;onorum coniunctio, maximeque pulchrior&ubreve;; <lb/>propterea eius &longs;onus &longs;&aelig;pi&longs;&longs;im&egrave; a&longs;&longs;umi &longs;olet)<emph.end type="italics"/> Si quis ea, qu&aelig; initio dicta &longs;unt, pro&shy;<lb/>b&egrave; tenuerit, facil&egrave; ad huius problematis intelligentiam perueniet; per me&shy;<lb/>&longs;en motam intellige de &longs;uo &longs;ibi conuente &longs;tatu <expan abbr="dimot&atilde;">dimotam</expan>, &amp; ide&ograve; ab alijs chor <lb/>dis di&longs;&longs;onantem. </s> <s>&longs;ic <lb/>etiam &longs;onus me&longs;es e&longs;t veluti aliorum &longs;onorum coniunctio, maximeque pulchrior&ubreve;; <lb/>propterea eius &longs;onus &longs;&aelig;pi&longs;&longs;im&egrave; a&longs;&longs;umi &longs;olet)<emph.end type="italics"/> Si quis ea, qu&aelig; initio dicta &longs;unt, pro&shy;<lb/>b&egrave; tenuerit, facil&egrave; ad huius problematis intelligentiam perueniet; per me&shy;<lb/>&longs;en motam intellige de &longs;uo &longs;ibi conuente &longs;tatu <expan abbr="dimot&atilde;">dimotam</expan>, &amp; ide&ograve; ab alijs chor <lb/>dis di&longs;&longs;onantem. </s>
  
 <s>Idem qu&aelig;rit Probl. </s> <s>Idem qu&aelig;rit Probl. 38.</s></p><p type="main">
  
 <s>38.</s></p><p type="main"> 
  
 <s><arrow.to.target n="marg368"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg368"></arrow.to.target></s></p><p type="margin">
  
 <s><margin.target id="marg368"></margin.target>377</s></p><p type="main"> <s><margin.target id="marg368"></margin.target>377</s></p><p type="main">
  
 <s>Probl. </s> <s>Probl. 21. <emph type="italics"/>(Cur qui grauius c&abreve;tant, &longs;i ab&longs;onant deprehendi facilius po&longs;&longs;unt, qu&abreve;, <lb/>qui cantant acutius: nec ver&ograve; &longs;ecus in rithmis accidit. </s>
  
 <s>21. <emph type="italics"/>(Cur qui grauius c&abreve;tant, &longs;i ab&longs;onant deprehendi facilius po&longs;&longs;unt, qu&abreve;, <lb/>qui cantant acutius: nec ver&ograve; &longs;ecus in rithmis accidit. </s> 
  
 <s>euidentiores enim, qui pec&shy;<lb/>cant in grauiori. </s> <s>euidentiores enim, qui pec&shy;<lb/>cant in grauiori. </s>
  
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 13. reliqua &longs;unt &longs;atis clara.</s></p><p type="main"> 13. reliqua &longs;unt &longs;atis clara.</s></p><p type="main">
  
 <s>Probl. </s> <s>Probl. 22. ex &longs;e manife&longs;tum e&longs;t: atque idem cum &longs;equenti num. </s>
  
 <s>22. ex &longs;e manife&longs;tum e&longs;t: atque idem cum &longs;equenti num. </s> 
  
 <s>46.</s></p><p type="main"> <s>46.</s></p><p type="main">
  
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 <s><margin.target id="marg369"></margin.target>378</s></p><p type="main"> <s><margin.target id="marg369"></margin.target>378</s></p><p type="main">
  
 <s>Probl. </s> <s>Probl. 23. <emph type="italics"/>(Cur Nete duplo acutior e&longs;t bypate? </s>
  
 <s>23. <emph type="italics"/>(Cur Nete duplo acutior e&longs;t bypate? </s> 
  
 <s>An primum, quod cum ner&shy;<lb/>u<gap/>s parte &longs;ui dimidia, &amp; totus &longs;imul pul&longs;atur, Diapa&longs;on concinentia exultat: quod <lb/>pariter in fi&longs;tulis apparet, &longs;onus enim, qui per medium foramen emergit Diapa&longs;on <lb/>cum eo re&longs;onat, qui per totam fi&longs;tulam exit. </s> <s>An primum, quod cum ner&shy;<lb/>u<gap/>s parte &longs;ui dimidia, &amp; totus &longs;imul pul&longs;atur, Diapa&longs;on concinentia exultat: quod <lb/>pariter in fi&longs;tulis apparet, &longs;onus enim, qui per medium foramen emergit Diapa&longs;on <lb/>cum eo re&longs;onat, qui per totam fi&longs;tulam exit. </s>
  
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 <s><margin.target id="marg370"></margin.target>379</s></p><p type="main"> <s><margin.target id="marg370"></margin.target>379</s></p><p type="main">
  
 <s>Probl. </s> <s>Probl. 24. <emph type="italics"/>(Cur &longs;i quis p&longs;allens netem pul&longs;atam apprehenderit, &longs;olam Hypa&shy;<lb/>tem re&longs;onare videbitur? </s>
  
 <s>24. <emph type="italics"/>(Cur &longs;i quis p&longs;allens netem pul&longs;atam apprehenderit, &longs;olam Hypa&shy;<lb/>tem re&longs;onare videbitur? </s> 
  
 <s>An quod tinnitus huius maxim&egrave; connaturalis e&longs;t &longs;ono il&shy;<lb/>lius, ill<gap/> que con&longs;onus. </s> <s>An quod tinnitus huius maxim&egrave; connaturalis e&longs;t &longs;ono il&shy;<lb/>lius, ill<gap/> que con&longs;onus. </s>
  
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 <s><margin.target id="marg371"></margin.target>380</s></p><p type="main"> <s><margin.target id="marg371"></margin.target>380</s></p><p type="main">
  
 <s>Probl. </s> <s>Probl. 25. <emph type="italics"/>(Cur in harmonijs chorda illa, qu&aelig; dicitur Me&longs;e, &longs;eu media, &longs;ic ap&shy;<lb/>pellatz e&longs;t? </s>
  
 <s>25. <emph type="italics"/>(Cur in harmonijs chorda illa, qu&aelig; dicitur Me&longs;e, &longs;eu media, &longs;ic ap&shy;<lb/>pellatz e&longs;t? </s> 
  
 <s>cum inter octo nullum medium &longs;it? </s> <s>cum inter octo nullum medium &longs;it? </s>
  
 <s>An quoniam olim har<gap/>oni&aelig; &longs;ep&shy;<lb/>tem fidibus con&longs;tabant, qui numerus medium habet)<emph.end type="italics"/> Ex ordine chordarum Li&shy;<lb/>chaonis, &amp; <expan abbr="Terp&atilde;dri">Terpandri</expan>, quorum alter &longs;eptem, alter ver&ograve; octo chordis mono&shy;<lb/>chordium conflabat, vt &longs;upra recen&longs;ui, huic loco abund&egrave; &longs;atisfieri pote&longs;t.</s></p><p type="main"> <s>An quoniam olim har<gap/>oni&aelig; &longs;ep&shy;<lb/>tem fidibus con&longs;tabant, qui numerus medium habet)<emph.end type="italics"/> Ex ordine chordarum Li&shy;<lb/>chaonis, &amp; <expan abbr="Terp&atilde;dri">Terpandri</expan>, quorum alter &longs;eptem, alter ver&ograve; octo chordis mono&shy;<lb/>chordium conflabat, vt &longs;upra recen&longs;ui, huic loco abund&egrave; &longs;atisfieri pote&longs;t.</s></p><p type="main">
  
 <s>Probl. </s> <s>Probl. 26. &longs;atis ex &longs;e clarum e&longs;t, <expan abbr="atq;">atque</expan> idem cum num. </s>
  
 <s>26. &longs;atis ex &longs;e clarum e&longs;t, <expan abbr="atq;">atque</expan> idem cum num. </s> 
  
 <s>47.</s></p><p type="main"> <s>47.</s></p><p type="main">
  
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 <s><margin.target id="marg372"></margin.target>381</s></p><p type="main"> <s><margin.target id="marg372"></margin.target>381</s></p><p type="main">
  
 <s>Probl. </s> <s>Probl. 27. <emph type="italics"/>(Cur inter omnia, qu&aelig; &longs;ub &longs;en&longs;us cadunt, &longs;ola audibilia mores obti&shy;<lb/>nent? </s>
  
 <s>27. <emph type="italics"/>(Cur inter omnia, qu&aelig; &longs;ub &longs;en&longs;us cadunt, &longs;ola audibilia mores obti&shy;<lb/>nent? </s> 
  
 <s>quamuis &longs;ine &longs;ermone aliquid modulemur, mores tamen pr&aelig; &longs;e ip&longs;a modela&shy;<lb/>tio fert, &longs;ed nec color, nec odor, nec &longs;apor id habet. </s> <s>quamuis &longs;ine &longs;ermone aliquid modulemur, mores tamen pr&aelig; &longs;e ip&longs;a modela&shy;<lb/>tio fert, &longs;ed nec color, nec odor, nec &longs;apor id habet. </s>
  
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 <s>fubdit po&longs;tea alias fui&longs;&longs;e &longs;imiles illis harmonijs, quas <lb/>nunc &longs;onatas dicimus, fui&longs;&longs;e tamen &longs;tatas, ac determinatas numero, quibus <lb/>&longs;olis vti liceret.</s></p><p type="main"> <s>fubdit po&longs;tea alias fui&longs;&longs;e &longs;imiles illis harmonijs, quas <lb/>nunc &longs;onatas dicimus, fui&longs;&longs;e tamen &longs;tatas, ac determinatas numero, quibus <lb/>&longs;olis vti liceret.</s></p><p type="main">
  
 <s>Probl. </s> <s>Probl. 29. Idem e&longs;t cum pr&aelig;cedenti 27. eadem igitur <expan abbr="quoq;">quoque</expan> &longs;it explicatio.</s></p><p type="main">
  
 <s>29. Idem e&longs;t cum pr&aelig;cedenti 27. eadem igitur <expan abbr="quoq;">quoque</expan> &longs;it explicatio.</s></p><p type="main"> 
  
 <s><arrow.to.target n="marg374"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg374"></arrow.to.target></s></p><p type="margin">
  
 <s><margin.target id="marg374"></margin.target>383</s></p><p type="main"> <s><margin.target id="marg374"></margin.target>383</s></p><p type="main">
  
 <s>Probl. </s> <s>Probl. 30. <emph type="italics"/>(Cur <expan abbr="neq;">neque</expan> hypodorium, <expan abbr="neq;">neque</expan> hypop hrygium est in trag&oelig;diarum obo&shy;<lb/>ro? </s>
  
 <s>30. <emph type="italics"/>(Cur <expan abbr="neq;">neque</expan> hypodorium, <expan abbr="neq;">neque</expan> hypop hrygium est in trag&oelig;diarum obo&shy;<lb/>ro? </s> 
  
 <s>An quia non habet anti&longs;trophon, vtpot&egrave; qu&aelig; &longs;cenica &longs;unt, imitationi&queacute;, accom&shy;<lb/>modata)<emph.end type="italics"/> huc pertinent ea, qu&aelig; ad cap.  <s>An quia non habet anti&longs;trophon, vtpot&egrave; qu&aelig; &longs;cenica &longs;unt, imitationi&queacute;, accom&shy;<lb/>modata)<emph.end type="italics"/> huc pertinent ea, qu&aelig; ad cap.
  
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 <s>Quod ad hunc locum &longs;pe&shy;<lb/>ctat, videndum quales e&longs;&longs;ent Hypodorius, &amp; Hypophrygius: quod Ari&longs;t.  <s>Quod ad hunc locum &longs;pe&shy;<lb/>ctat, videndum quales e&longs;&longs;ent Hypodorius, &amp; Hypophrygius: quod Ari&longs;t.
  
 ip&shy;<lb/>&longs;e infra Problem. </s> ip&shy;<lb/>&longs;e infra Problem. 49. docet, ait enim, modum hypophrygium animos Lym&shy;<lb/>phatis, &longs;imiles reddere, <expan abbr="cogere&qacute;">cogereque</expan>; debacchari: Hypodorium ver&ograve; e&longs;&longs;e mo&shy;<lb/>dum magnificum, con&longs;tantem, grauemque. </s>
  
 <s>49. docet, ait enim, modum hypophrygium animos Lym&shy;<lb/>phatis, &longs;imiles reddere, <expan abbr="cogere&qacute;">cogereque</expan>; debacchari: Hypodorium ver&ograve; e&longs;&longs;e mo&shy;<lb/>dum magnificum, con&longs;tantem, grauemque. </s> 
  
 <s><expan abbr="vtrumq;">vtrumque</expan> autem fui&longs;&longs;e vari&aelig; imi&shy;<lb/>tationi aptum, <expan abbr="ideo&qacute;">ideoque</expan>; carui&longs;&longs;e &longs;trophis: qu&aelig; ad eandem &longs;emper imitatio&shy;<lb/>nem, <expan abbr="eundem&qacute;">eundemque</expan>; morem tendunt: vt &longs;upra Probl. </s> 
  
 <s>15. explicaui. </s> <s><expan abbr="vtrumq;">vtrumque</expan> autem fui&longs;&longs;e vari&aelig; imi&shy;<lb/>tationi aptum, <expan abbr="ideo&qacute;">ideoque</expan>; carui&longs;&longs;e &longs;trophis: qu&aelig; ad eandem &longs;emper imitatio&shy;<lb/>nem, <expan abbr="eundem&qacute;">eundemque</expan>; morem tendunt: vt &longs;upra Probl. 15. explicaui. </s>
  
 <s>ex quibus <lb/>intelligere po&longs;&longs;umus Problema pr&aelig;&longs;ens; modus &longs;cilicet Hypodorius, &amp; Hy&shy;<lb/>pophrygius &agrave; choro Trag&oelig;diarum arcebantur, quia carebant anti&longs;trophis, <lb/>quibus chorus gaudebat; chorus enim non imitabatur varios mores, <expan abbr="va-rios&qacute;">va&shy;<lb/>riosque</expan>; hominum affectus, &longs;ed eodem &longs;eruato affectu per ea&longs;dem &longs;trophas ad <lb/>finem <expan abbr="v&longs;q;">v&longs;que</expan> perueniebat. </s> <s>ex quibus <lb/>intelligere po&longs;&longs;umus Problema pr&aelig;&longs;ens; modus &longs;cilicet Hypodorius, &amp; Hy&shy;<lb/>pophrygius &agrave; choro Trag&oelig;diarum arcebantur, quia carebant anti&longs;trophis, <lb/>quibus chorus gaudebat; chorus enim non imitabatur varios mores, <expan abbr="va-rios&qacute;">va&shy;<lb/>riosque</expan>; hominum affectus, &longs;ed eodem &longs;eruato affectu per ea&longs;dem &longs;trophas ad <lb/>finem <expan abbr="v&longs;q;">v&longs;que</expan> perueniebat. </s>
  
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 <s><margin.target id="marg375"></margin.target>384</s></p><p type="main"> <s><margin.target id="marg375"></margin.target>384</s></p><p type="main">
  
 <s>Probl. </s> <s>Probl. 31. <emph type="italics"/>(Cur Phrynicus, c&aelig;teri&queacute;, illius &aelig;tatis Mu&longs;ici magis Meiop&aelig;i er&abreve;t? <lb/></s>
  
 <s>31. <emph type="italics"/>(Cur Phrynicus, c&aelig;teri&queacute;, illius &aelig;tatis Mu&longs;ici magis Meiop&aelig;i er&abreve;t? <lb/></s> 
  
 <s>An quoniam tunc temporis in trag&aelig;dijs carmine contextis maior erat <expan abbr="c&amacr;tilenarum">cantilenarum</expan> <lb/>v&longs;us)<emph.end type="italics"/> Apud Suidam inter plures Phrynicos, vnus recen&longs;etur patria Athe&shy;<lb/>nicn&longs;is, &amp; Poeta Tragicus, qui circa Olympiadem 67. floruit: quem puto <lb/>hunc e&longs;&longs;c, de quo in hoc problemate agitur. </s> <s>An quoniam tunc temporis in trag&aelig;dijs carmine contextis maior erat <expan abbr="c&amacr;tilenarum">cantilenarum</expan> <lb/>v&longs;us)<emph.end type="italics"/> Apud Suidam inter plures Phrynicos, vnus recen&longs;etur patria Athe&shy;<lb/>nicn&longs;is, &amp; Poeta Tragicus, qui circa Olympiadem 67. floruit: quem puto <lb/>hunc e&longs;&longs;c, de quo in hoc problemate agitur. </s>
  
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 <s><margin.target id="marg376"></margin.target>385</s></p><p type="main"> <s><margin.target id="marg376"></margin.target>385</s></p><p type="main">
  
 <s>Probl. </s> <s>Probl. 32. <emph type="italics"/>(Cur Diapa&longs;on con&longs;onantiam dicimus, non ratione numeri Diao&shy;<lb/>tto, vti Diate&longs;&longs;aron, &amp; Diapente? </s>
  
 <s>32. <emph type="italics"/>(Cur Diapa&longs;on con&longs;onantiam dicimus, non ratione numeri Diao&shy;<lb/>tto, vti Diate&longs;&longs;aron, &amp; Diapente? </s> 
  
 <s>An quod antiquitus non pluribus, qu&agrave;m &longs;ep&shy;<lb/>tem vterentur numeris? </s> <s>An quod antiquitus non pluribus, qu&agrave;m &longs;ep&shy;<lb/>tem vterentur numeris? </s>
  
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 <s><margin.target id="marg377"></margin.target>386</s></p><p type="main"> <s><margin.target id="marg377"></margin.target>386</s></p><p type="main">
  
 <s>Probl. </s> <s>Probl. 33. <emph type="italics"/>(Cur aptius de acuto in graue canitur, quam de graue in acutum? <lb/></s>
  
 <s>33. <emph type="italics"/>(Cur aptius de acuto in graue canitur, quam de graue in acutum? <lb/></s> 
  
 <s>Vtrum, quod ita fit, vt &agrave; &longs;uo inchoetur principio? </s> <s>Vtrum, quod ita fit, vt &agrave; &longs;uo inchoetur principio? </s>
  
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 <s>horum primum illud <lb/>erat, quod in parte graui&longs;&longs;ima <expan abbr="collocat&utilde;">collocatum</expan> erat, cuius h&aelig; erant chord&aelig;, Hy&shy;<lb/>pate, Parhypate, Lychanos, Me&longs;e. </s> <s>horum primum illud <lb/>erat, quod in parte graui&longs;&longs;ima <expan abbr="collocat&utilde;">collocatum</expan> erat, cuius h&aelig; erant chord&aelig;, Hy&shy;<lb/>pate, Parhypate, Lychanos, Me&longs;e. </s>
  
 <s>&longs;i igitur in&longs;trumentum habuerit tantum <lb/>duo tetrachorda, neruns medius crit ip&longs;a Me&longs;e, qu&aelig; e&longs;t acuti&longs;&longs;ima primi te&shy;<lb/>trachordi, e&longs;t pr&aelig;terea h&aelig;c Me&longs;e veluti dux reliquarum chordarum, nam, <lb/>vt dictum e&longs;t in Probl. </s> <s>&longs;i igitur in&longs;trumentum habuerit tantum <lb/>duo tetrachorda, neruns medius crit ip&longs;a Me&longs;e, qu&aelig; e&longs;t acuti&longs;&longs;ima primi te&shy;<lb/>trachordi, e&longs;t pr&aelig;terea h&aelig;c Me&longs;e veluti dux reliquarum chordarum, nam, <lb/>vt dictum e&longs;t in Probl. 20. e&longs;t in medio carum vti dux; &longs;&aelig;pi&longs;&longs;im&egrave; omnium <lb/>pui&longs;atur: ca &longs;ola ab alijs di&longs;&longs;onante, reliqu&aelig; omnes videntur di&longs;&longs;onare. </s>
  
 <s>20. e&longs;t in medio carum vti dux; &longs;&aelig;pi&longs;&longs;im&egrave; omnium <lb/>pui&longs;atur: ca &longs;ola ab alijs di&longs;&longs;onante, reliqu&aelig; omnes videntur di&longs;&longs;onare. </s> 
  
 <s>c&ugrave;m <pb pagenum="265"/>igitur alijs pr&aelig;&longs;tet <expan abbr="&longs;it&qacute;">&longs;itque</expan>; &longs;ui tetrachordi acuti&longs;&longs;ima, <expan abbr="c&otilde;uenienter">conuenienter</expan> natura du&shy;<lb/>ce fit, vt ab acuta voce cantum exordiamur. </s> <s>c&ugrave;m <pb pagenum="265"/>igitur alijs pr&aelig;&longs;tet <expan abbr="&longs;it&qacute;">&longs;itque</expan>; &longs;ui tetrachordi acuti&longs;&longs;ima, <expan abbr="c&otilde;uenienter">conuenienter</expan> natura du&shy;<lb/>ce fit, vt ab acuta voce cantum exordiamur. </s>
  
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 <s><margin.target id="marg378"></margin.target>387</s></p><p type="main"> <s><margin.target id="marg378"></margin.target>387</s></p><p type="main">
  
 <s>Probl. </s> <s>Probl. 34. <emph type="italics"/>(Cur bis Diapente, aut bis Diate&longs;&longs;aron <expan abbr="c&otilde;&longs;onantia">con&longs;onantia</expan> <expan abbr="c&otilde;poni">componi</expan> non pote&longs;t, <lb/>bis a&ubreve;<gap/> Diapa&longs;on pote&longs;t? </s>
  
 <s>34. <emph type="italics"/>(Cur bis Diapente, aut bis Diate&longs;&longs;aron <expan abbr="c&otilde;&longs;onantia">con&longs;onantia</expan> <expan abbr="c&otilde;poni">componi</expan> non pote&longs;t, <lb/>bis a&ubreve;<gap/> Diapa&longs;on pote&longs;t? </s> 
  
 <s>An, qu&ograve;d bis Diapente, non bis Diate&longs;&longs;aron e&longs;t: &longs;ed Dia&shy;<lb/>te&longs;&longs;aron, &amp; Diapente in vn&abreve; Diapa&longs;on concurrunt)<emph.end type="italics"/> Quamuis textus <expan abbr="aliquantul&utilde;">aliquantulum</expan> <lb/><expan abbr="&etilde;t">ent</expan> gr&aelig;cus corruptus &longs;it, verumtamen &longs;en&longs;um Ari&longs;t.  <s>An, qu&ograve;d bis Diapente, non bis Diate&longs;&longs;aron e&longs;t: &longs;ed Dia&shy;<lb/>te&longs;&longs;aron, &amp; Diapente in vn&abreve; Diapa&longs;on concurrunt)<emph.end type="italics"/> Quamuis textus <expan abbr="aliquantul&utilde;">aliquantulum</expan> <lb/><expan abbr="&etilde;t">ent</expan> gr&aelig;cus corruptus &longs;it, verumtamen &longs;en&longs;um Ari&longs;t.
  
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 <s>Iam proportio inter primum 6. &amp; vltimum 3. e&longs;t dupla: qu&aelig; e&longs;t ratio ip&longs;ius <lb/>perfecti&longs;&longs;im&aelig; con&longs;onanti&aelig; Diapa&longs;on. </s> <s>Iam proportio inter primum 6. &amp; vltimum 3. e&longs;t dupla: qu&aelig; e&longs;t ratio ip&longs;ius <lb/>perfecti&longs;&longs;im&aelig; con&longs;onanti&aelig; Diapa&longs;on. </s>
  
 <s>Ex quibus Ari&longs;t. </s> <s>Ex quibus Ari&longs;t. &longs;ententia manife&longs;ta <pb pagenum="266"/>e&longs;t. </s>
  
 <s>&longs;ententia manife&longs;ta <pb pagenum="266"/>e&longs;t. </s> 
  
 <s>idem qu&aelig;rit etiam problemate 42. H&aelig;c de ratione multiplici, &amp; &longs;uper&shy;<lb/>particulari dicta &longs;unt ex veterum &longs;ententia: recentiores enim mu&longs;ic&aelig; de&shy;<lb/>prauatores plures alias rationes perperam inter harmonicas intru&longs;erunt.</s></p><p type="main"> <s>idem qu&aelig;rit etiam problemate 42. H&aelig;c de ratione multiplici, &amp; &longs;uper&shy;<lb/>particulari dicta &longs;unt ex veterum &longs;ententia: recentiores enim mu&longs;ic&aelig; de&shy;<lb/>prauatores plures alias rationes perperam inter harmonicas intru&longs;erunt.</s></p><p type="main">
  
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 <s><margin.target id="marg379"></margin.target>388</s></p><p type="main"> <s><margin.target id="marg379"></margin.target>388</s></p><p type="main">
  
 <s>Probl. </s> <s>Probl. 35. <emph type="italics"/>(Cur Diapa&longs;on con&longs;onantia omnium pulcherrima e&longs;t? </s>
  
 <s>35. <emph type="italics"/>(Cur Diapa&longs;on con&longs;onantia omnium pulcherrima e&longs;t? </s> 
  
 <s>An quod <lb/>integris terminis huius proportiones continentur: c&aelig;terarum autem non integris? <lb/></s> <s>An quod <lb/>integris terminis huius proportiones continentur: c&aelig;terarum autem non integris? <lb/></s>
  
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 <s><margin.target id="marg380"></margin.target>389</s></p><p type="main"> <s><margin.target id="marg380"></margin.target>389</s></p><p type="main">
  
 <s>Probl. </s> <s>Probl. 36. <emph type="italics"/>(Cur &longs;i neruus medius ex &longs;uo intentionis modo dimotus fuerit, c&aelig;te&shy;<lb/>ris <expan abbr="quoq;">quoque</expan> omnes nerui, &longs;onos diffonos reddent: &longs;ed <gap/>i, immoto illo manente, ali&shy;<lb/>quis ex c&aelig;teris dimotus fuerit, &longs;olus hic, qui modo &longs;uo caruerit, aberrabit? </s>
  
 <s>36. <emph type="italics"/>(Cur &longs;i neruus medius ex &longs;uo intentionis modo dimotus fuerit, c&aelig;te&shy;<lb/>ris <expan abbr="quoq;">quoque</expan> omnes nerui, &longs;onos diffonos reddent: &longs;ed <gap/>i, immoto illo manente, ali&shy;<lb/>quis ex c&aelig;teris dimotus fuerit, &longs;olus hic, qui modo &longs;uo caruerit, aberrabit? </s> 
  
 <s>An, <lb/>quod ratio concinendi, aptaneruorum omium intentione continetur, qu&aelig; non ni&longs;v<emph.end type="italics"/><pb pagenum="267"/><emph type="italics"/>per habitudinem quandam ad Me&longs;en, &longs;eu ad Medium, <expan abbr="accommod&amacr;da">accommodanda</expan> omnibus e&longs;t, <lb/>ordo&queacute;, ratione illius di&longs;poni &longs;ingulis debet? </s> <s>An, <lb/>quod ratio concinendi, aptaneruorum omium intentione continetur, qu&aelig; non ni&longs;v<emph.end type="italics"/><pb pagenum="267"/><emph type="italics"/>per habitudinem quandam ad Me&longs;en, &longs;eu ad Medium, <expan abbr="accommod&amacr;da">accommodanda</expan> omnibus e&longs;t, <lb/>ordo&queacute;, ratione illius di&longs;poni &longs;ingulis debet? </s>
  
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 <s>Veruntamen Me&longs;e&longs;ibi con&longs;iante, &longs;i quis alius <lb/>di&longs;creparit, merit&ograve; illius &longs;ola pars dee&longs;t: c&aelig;teri <expan abbr="uamq;">uamque</expan> omnes modum &longs;u&aelig; <expan abbr="concin&etilde;-ti&aelig;">concinen&shy;<lb/>ti&aelig;</expan> &longs;eruant integrum) (Neruus medius)<emph.end type="italics"/> ide&longs;t, Me&longs;e, &longs;ic appellata, quod me&shy;<lb/>dia e&longs;&longs;et. <emph type="italics"/>(Qu&aelig; non ni&longs;i per habitudinem quandam ad Me&longs;en)<emph.end type="italics"/> hypate cum Me&shy;<lb/>&longs;e con&longs;onabat Diate&longs;&longs;aron: nete cum eadem Me&longs;e con&longs;onabat Diapente, <lb/>qu&aelig; &longs;unt du&aelig; pr&aelig;cipu&aelig; con&longs;onanti&aelig;, Diapa&longs;on integrantes; ergo &longs;ublata <lb/>Me&longs;e de &longs;uo &longs;tatu, illas pariter tolli nece&longs;&longs;e e&longs;t. </s> <s>Veruntamen Me&longs;e&longs;ibi con&longs;iante, &longs;i quis alius <lb/>di&longs;creparit, merit&ograve; illius &longs;ola pars dee&longs;t: c&aelig;teri <expan abbr="uamq;">uamque</expan> omnes modum &longs;u&aelig; <expan abbr="concin&etilde;-ti&aelig;">concinen&shy;<lb/>ti&aelig;</expan> &longs;eruant integrum) (Neruus medius)<emph.end type="italics"/> ide&longs;t, Me&longs;e, &longs;ic appellata, quod me&shy;<lb/>dia e&longs;&longs;et. <emph type="italics"/>(Qu&aelig; non ni&longs;i per habitudinem quandam ad Me&longs;en)<emph.end type="italics"/> hypate cum Me&shy;<lb/>&longs;e con&longs;onabat Diate&longs;&longs;aron: nete cum eadem Me&longs;e con&longs;onabat Diapente, <lb/>qu&aelig; &longs;unt du&aelig; pr&aelig;cipu&aelig; con&longs;onanti&aelig;, Diapa&longs;on integrantes; ergo &longs;ublata <lb/>Me&longs;e de &longs;uo &longs;tatu, illas pariter tolli nece&longs;&longs;e e&longs;t. </s>
  
 <s>eandem qu&aelig;&longs;tionem &longs;upra <lb/>Probl. </s> <s>eandem qu&aelig;&longs;tionem &longs;upra <lb/>Probl. 20. pertractauit, qu&agrave;m nunc reui&longs;ere con&longs;ultum erit.</s></p><p type="main">
  
 <s>20. pertractauit, qu&agrave;m nunc reui&longs;ere con&longs;ultum erit.</s></p><p type="main"> 
  
 <s><arrow.to.target n="marg381"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg381"></arrow.to.target></s></p><p type="margin">
  
 <s><margin.target id="marg381"></margin.target>390</s></p><p type="main"> <s><margin.target id="marg381"></margin.target>390</s></p><p type="main">
  
 <s>Probl. </s> <s>Probl. 37. <emph type="italics"/>(Cur existente vocum acumine, &longs;ecundum paruum: grauitate au&shy;<lb/>tem &longs;ecundum multum<emph.end type="italics"/> (<emph type="italics"/>quod enim graue e&longs;t, ob va&longs;titatem graue e&longs;t: quod ver&ograve; <lb/>acutum ob paruitatem<emph.end type="italics"/>) <emph type="italics"/>difficilius e&longs;t acutas voces canere, qu&agrave;m graues; &amp; pauci <lb/>&longs;unt, qui &longs;uperna cantare valeant; &amp; leges orthi&aelig;, &amp; acut&aelig; cantu difficiles &longs;unt, <lb/>quod &longs;int vald&egrave; inten&longs;&aelig;. </s>
  
 <s>37. <emph type="italics"/>(Cur existente vocum acumine, &longs;ecundum paruum: grauitate au&shy;<lb/>tem &longs;ecundum multum<emph.end type="italics"/> (<emph type="italics"/>quod enim graue e&longs;t, ob va&longs;titatem graue e&longs;t: quod ver&ograve; <lb/>acutum ob paruitatem<emph.end type="italics"/>) <emph type="italics"/>difficilius e&longs;t acutas voces canere, qu&agrave;m graues; &amp; pauci <lb/>&longs;unt, qui &longs;uperna cantare valeant; &amp; leges orthi&aelig;, &amp; acut&aelig; cantu difficiles &longs;unt, <lb/>quod &longs;int vald&egrave; inten&longs;&aelig;. </s> 
  
 <s>Quamquam facilius &longs;it mouere exiguum, quam <expan abbr="magn&utilde;">magnum</expan>: <lb/>idem <expan abbr="itaq;">itaque</expan> in aere deberet accidere. </s> <s>Quamquam facilius &longs;it mouere exiguum, quam <expan abbr="magn&utilde;">magnum</expan>: <lb/>idem <expan abbr="itaq;">itaque</expan> in aere deberet accidere. </s>
  
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 <s>Obijces, Ari&longs;t.  <s>Obijces, Ari&longs;t.
  
 in Probl. </s> in Probl. 26. &amp; 47. dixi&longs;&longs;e contrarium, fcilicet facilius <lb/>e&longs;&longs;e canere acutum, quam graue, ibi enim re&longs;pondet: vtrum, quod facilius <lb/>acutum, quam graue cantatur? </s>
  
 <s>26. &amp; 47. dixi&longs;&longs;e contrarium, fcilicet facilius <lb/>e&longs;&longs;e canere acutum, quam graue, ibi enim re&longs;pondet: vtrum, quod facilius <lb/>acutum, quam graue cantatur? </s> 
  
 <s>Re&longs;pondeo prim&ugrave;m, Ari&longs;t.  <s>Re&longs;pondeo prim&ugrave;m, Ari&longs;t.
  
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 <s><margin.target id="marg382"></margin.target>391</s></p><p type="main"> <s><margin.target id="marg382"></margin.target>391</s></p><p type="main">
  
 <s>Probl. </s> <s>Probl. 38. <emph type="italics"/>(Cur rithmo, modulo, cantico, &amp; omnin&ograve; &longs;ymphonijs gaudent om&shy;<lb/>nes? </s>
  
 <s>38. <emph type="italics"/>(Cur rithmo, modulo, cantico, &amp; omnin&ograve; &longs;ymphonijs gaudent om&shy;<lb/>nes? </s> 
  
 <s>An quia motibus naturalibus naturaliter gaudemus. </s> <s>An quia motibus naturalibus naturaliter gaudemus. </s>
  
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 <s><margin.target id="marg383"></margin.target>392</s></p><p type="main"> <s><margin.target id="marg383"></margin.target>392</s></p><p type="main">
  
 <s>Probl. </s> <s>Probl. 39. <emph type="italics"/>(Cur &longs;uauius e&longs;t &longs;ymphonum, qu&agrave;m vni&longs;onum? </s>
  
 <s>39. <emph type="italics"/>(Cur &longs;uauius e&longs;t &longs;ymphonum, qu&agrave;m vni&longs;onum? </s> 
  
 <s>An quod antipho&shy;<lb/>num ip&longs;um quoque <expan abbr="con&longs;on&atilde;">con&longs;onam</expan> e&longs;t per Diapa&longs;on, quippe c&ugrave;m ex pueris, viris&queacute; fiat an&shy;<lb/>tiphonum, qui ita inter &longs;e vocibus distant, vt Nete, &amp; Hypate. </s> <s>An quod antipho&shy;<lb/>num ip&longs;um quoque <expan abbr="con&longs;on&atilde;">con&longs;onam</expan> e&longs;t per Diapa&longs;on, quippe c&ugrave;m ex pueris, viris&queacute; fiat an&shy;<lb/>tiphonum, qui ita inter &longs;e vocibus distant, vt Nete, &amp; Hypate. </s>
  
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 <s>&longs;ententi&aelig; <lb/>minim&egrave; quadrant. </s> <s>&longs;ententi&aelig; <lb/>minim&egrave; quadrant. </s>
  
 <s>Probl. </s> <s>Probl. 16. &longs;uperius e&longs;t fer&egrave; idem cum hoc.</s></p><p type="main">
  
 <s>16. &longs;uperius e&longs;t fer&egrave; idem cum hoc.</s></p><p type="main"> 
  
 <s><arrow.to.target n="marg384"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg384"></arrow.to.target></s></p><p type="margin">
  
 <s><margin.target id="marg384"></margin.target>393</s></p><p type="main"> <s><margin.target id="marg384"></margin.target>393</s></p><p type="main">
  
 <s>Probl. </s> <s>Probl. 40. <emph type="italics"/>(Cur in &longs;ola Diapa&longs;on con&longs;onantia magadari &longs;olitum e&longs;t? </s>
  
 <s>40. <emph type="italics"/>(Cur in &longs;ola Diapa&longs;on con&longs;onantia magadari &longs;olitum e&longs;t? </s> 
  
 <s>An quia, <lb/>vt pedes carminum proportionem, aut &aelig;qualis ad &aelig;qualem, aut duo ad vnum, aut <lb/>aliam cliquam obtinent; ita &longs;oni, quibus con&longs;onantia confiat, motus rationem in&shy;<lb/>ter &longs;e aliquam &longs;eruant. </s> <s>An quia, <lb/>vt pedes carminum proportionem, aut &aelig;qualis ad &aelig;qualem, aut duo ad vnum, aut <lb/>aliam cliquam obtinent; ita &longs;oni, quibus con&longs;onantia confiat, motus rationem in&shy;<lb/>ter &longs;e aliquam &longs;eruant. </s>
  
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 <s><margin.target id="marg385"></margin.target>394</s></p><p type="main"> <s><margin.target id="marg385"></margin.target>394</s></p><p type="main">
  
 <s>Probl. </s> <s>Probl. 41. <emph type="italics"/>(Cur &longs;uauius cantum audimus, quem &longs;cimus, quam quem ignora&shy;<lb/>mus? </s>
  
 <s>41. <emph type="italics"/>(Cur &longs;uauius cantum audimus, quem &longs;cimus, quam quem ignora&shy;<lb/>mus? </s> 
  
 <s>Vtrum, quoniam cum <expan abbr="cantilen&atilde;">cantilenam</expan> agno&longs;cimus, manife&longs;tior e&longs;t, qui veiuti &longs;co&shy;<lb/>pum, a&longs;&longs;equatur. </s> <s>Vtrum, quoniam cum <expan abbr="cantilen&atilde;">cantilenam</expan> agno&longs;cimus, manife&longs;tior e&longs;t, qui veiuti &longs;co&shy;<lb/>pum, a&longs;&longs;equatur. </s>
  
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 <s><margin.target id="marg386"></margin.target>395</s></p><p type="main"> <s><margin.target id="marg386"></margin.target>395</s></p><p type="main">
  
 <s>Probl. </s> <s>Probl. 42. <emph type="italics"/>(Cur nec bis Diapente, nec bis Diate&longs;&longs;aron con&longs;onant, &longs;ed bis Dia&shy;<lb/>pa&longs;on. </s>
  
 <s>42. <emph type="italics"/>(Cur nec bis Diapente, nec bis Diate&longs;&longs;aron con&longs;onant, &longs;ed bis Dia&shy;<lb/>pa&longs;on. </s> 
  
 <s>An quod Diapente con&longs;onantia est in proportione &longs;e&longs;quialtera? </s> <s>An quod Diapente con&longs;onantia est in proportione &longs;e&longs;quialtera? </s>
  
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 <s><margin.target id="marg387"></margin.target>396</s></p><p type="main"> <s><margin.target id="marg387"></margin.target>396</s></p><p type="main">
  
 <s>Probl. </s> <s>Probl. 43. <emph type="italics"/>(Cur &longs;i quis <expan abbr="p&longs;all&etilde;s">p&longs;allens</expan> neten appreh&ecaron;dat, &longs;ola bypate &longs;ub&longs;onarc videtur? <lb/></s>
  
 <s>43. <emph type="italics"/>(Cur &longs;i quis <expan abbr="p&longs;all&etilde;s">p&longs;allens</expan> neten appreh&ecaron;dat, &longs;ola bypate &longs;ub&longs;onarc videtur? <lb/></s> 
  
 <s>An <expan abbr="quoni&atilde;">quoniam</expan> nete de&longs;inens &amp; elangue&longs;cens euadit bypate; <expan abbr="indici&utilde;">indicium</expan>, qu&ograve;d po&longs;i bypaten,<emph.end type="italics"/><pb pagenum="270"/><emph type="italics"/>neten canore apt &longs;&longs;im&egrave; licet. </s> <s>An <expan abbr="quoni&atilde;">quoniam</expan> nete de&longs;inens &amp; elangue&longs;cens euadit bypate; <expan abbr="indici&utilde;">indicium</expan>, qu&ograve;d po&longs;i bypaten,<emph.end type="italics"/><pb pagenum="270"/><emph type="italics"/>neten canore apt &longs;&longs;im&egrave; licet. </s>
  
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 <s><margin.target id="marg388"></margin.target>397</s></p><p type="main"> <s><margin.target id="marg388"></margin.target>397</s></p><p type="main">
  
 <s>Probl. </s> <s>Probl. 44. <emph type="italics"/>(Cur &longs;uauius &longs;olitariam cantilenam audimus, c&ugrave;m ad tibiam, quam <lb/>c&ugrave;m ad lyram cantatur? </s>
  
 <s>44. <emph type="italics"/>(Cur &longs;uauius &longs;olitariam cantilenam audimus, c&ugrave;m ad tibiam, quam <lb/>c&ugrave;m ad lyram cantatur? </s> 
  
 <s>An quod omne &longs;uaue, quod <expan abbr="mixi&utilde;">mixium</expan> est cum &longs;uauiori, &longs;ua&shy;<lb/>uius redditur? </s> <s>An quod omne &longs;uaue, quod <expan abbr="mixi&utilde;">mixium</expan> est cum &longs;uauiori, &longs;ua&shy;<lb/>uius redditur? </s>
  
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 <s><margin.target id="marg389"></margin.target>398</s></p><p type="main"> <s><margin.target id="marg389"></margin.target>398</s></p><p type="main">
  
 <s>Probl. </s> <s>Probl. 45. <emph type="italics"/>(Cur neruum illum, quem Me&longs;en, &longs;eu medium dicimus, &longs;ic appella&shy;<lb/>mus; c&ugrave;m inter &longs;eptem, non autem inter octo &longs;it <expan abbr="medi&utilde;">medium</expan>? </s>
  
 <s>45. <emph type="italics"/>(Cur neruum illum, quem Me&longs;en, &longs;eu medium dicimus, &longs;ic appella&shy;<lb/>mus; c&ugrave;m inter &longs;eptem, non autem inter octo &longs;it <expan abbr="medi&utilde;">medium</expan>? </s> 
  
 <s>An quod olim barmoni&aelig; <lb/>&longs;eptem neruis con&longs;tabant, quorum medium e&longs;t. </s> <s>An quod olim barmoni&aelig; <lb/>&longs;eptem neruis con&longs;tabant, quorum medium e&longs;t. </s>
  
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 <s>prim&ograve;, quemadmodum <lb/>etiam in 25. &longs;ecund&ograve;, re&longs;pondet idcirc&ograve; Me&longs;en ita e&longs;&longs;e appellatam, quod in&shy;<lb/>ter eos &longs;onos inter extrema contentos rationem principij haberet, &longs;olent <lb/>enim ea, qu&aelig; inter extrema aliqua &longs;unt <expan abbr="c&aelig;teror&utilde;">c&aelig;terorum</expan> principia, e&longs;&longs;e <expan abbr="eti&atilde;">etiam</expan> media.</s></p><p type="main"> <s>prim&ograve;, quemadmodum <lb/>etiam in 25. &longs;ecund&ograve;, re&longs;pondet idcirc&ograve; Me&longs;en ita e&longs;&longs;e appellatam, quod in&shy;<lb/>ter eos &longs;onos inter extrema contentos rationem principij haberet, &longs;olent <lb/>enim ea, qu&aelig; inter extrema aliqua &longs;unt <expan abbr="c&aelig;teror&utilde;">c&aelig;terorum</expan> principia, e&longs;&longs;e <expan abbr="eti&atilde;">etiam</expan> media.</s></p><p type="main">
  
 <s>Probl. </s> <s>Probl. 46. e&longs;t idem cum &longs;uperiori 22. <expan abbr="vtrumq;">vtrumque</expan> autem ex &longs;e ita manife&longs;tum <lb/>e&longs;t, vt <expan abbr="ab&longs;q;">ab&longs;que</expan> harmonica fa cultate prob&egrave; intelligatur.</s></p><p type="main">
  
 <s>46. e&longs;t idem cum &longs;uperiori 22. <expan abbr="vtrumq;">vtrumque</expan> autem ex &longs;e ita manife&longs;tum <lb/>e&longs;t, vt <expan abbr="ab&longs;q;">ab&longs;que</expan> harmonica fa cultate prob&egrave; intelligatur.</s></p><p type="main"> 
  
 <s>Probl. </s> 
  
 <s>47. idem cum 26. in quibus ait, facilius e&longs;&longs;e canere acutum, qu&agrave;m <lb/>graue: in 37. ver&ograve; contrarium: difficilius e&longs;&longs;e cantare acutum, qu&agrave;m gra&shy;<lb/>ue. </s> <s>Probl. 47. idem cum 26. in quibus ait, facilius e&longs;&longs;e canere acutum, qu&agrave;m <lb/>graue: in 37. ver&ograve; contrarium: difficilius e&longs;&longs;e cantare acutum, qu&agrave;m gra&shy;<lb/>ue. </s>
  
 <s>&longs;ibi conciliabitur, &longs;i dixeris, h&aelig;c dicta e&longs;&longs;e problematic&egrave;.</s></p><p type="main"> <s>&longs;ibi conciliabitur, &longs;i dixeris, h&aelig;c dicta e&longs;&longs;e problematic&egrave;.</s></p><p type="main">
  
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 <s><margin.target id="marg390"></margin.target>399</s></p><p type="main"> <s><margin.target id="marg390"></margin.target>399</s></p><p type="main">
  
 <s>Probl. </s> <s>Probl. 48. <emph type="italics"/>(Cur veteres c&ugrave;m &longs;eptem neruis concentus facerent, hypaten, non <lb/>neten reliquerunt? </s>
  
 <s>48. <emph type="italics"/>(Cur veteres c&ugrave;m &longs;eptem neruis concentus facerent, hypaten, non <lb/>neten reliquerunt? </s> 
  
 <s>An non hypate, &longs;ed nunc <expan abbr="vocat&atilde;">vocatam</expan> paraneten, toni&queacute; interuallum <lb/>ab&longs;tulerunt, vltima ver&ograve; Acutiden&longs;i pro Me&longs;e vtebantur propterea ip&longs;am Me&longs;en <lb/>appellarunt. </s> <s>An non hypate, &longs;ed nunc <expan abbr="vocat&atilde;">vocatam</expan> paraneten, toni&queacute; interuallum <lb/>ab&longs;tulerunt, vltima ver&ograve; Acutiden&longs;i pro Me&longs;e vtebantur propterea ip&longs;am Me&longs;en <lb/>appellarunt. </s>
  
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 <s><margin.target id="marg391"></margin.target>400</s></p><p type="main"> <s><margin.target id="marg391"></margin.target>400</s></p><p type="main">
  
 <s>Probl. </s> <s>Probl. 49. <emph type="italics"/>(Cur Trag&oelig;diarum choris, <expan abbr="neq;">neque</expan> &longs;ubdorio, <expan abbr="neq;">neque</expan> &longs;ubphrygio ca<gap/>tandi <lb/>genere, vti mos e&longs;t? </s>
  
 <s>49. <emph type="italics"/>(Cur Trag&oelig;diarum choris, <expan abbr="neq;">neque</expan> &longs;ubdorio, <expan abbr="neq;">neque</expan> &longs;ubphrygio ca<gap/>tandi <lb/>genere, vti mos e&longs;t? </s> 
  
 <s>An quod modul&ubreve; pr&aelig;&longs;tare b&aelig; harmoni&aelig; nequeunt, quo choris <lb/>vald&egrave; opus e&longs;t; mores habet bypoph<gap/>ygius practicos (<expan abbr="quamobr&etilde;">quamobrem</expan> in Gerione excur&shy;<lb/>&longs;us, &amp; armatio ip&longs;o per&longs;iciunter) Subdorius ver&ograve; magnificus, constans, <expan abbr="gram&longs;q;">gram&longs;que</expan> <lb/>e&longs;t, quosirca omnium harmoniarum maxim&egrave; cythar&aelig; conuemt. </s> <s>An quod modul&ubreve; pr&aelig;&longs;tare b&aelig; harmoni&aelig; nequeunt, quo choris <lb/>vald&egrave; opus e&longs;t; mores habet bypoph<gap/>ygius practicos (<expan abbr="quamobr&etilde;">quamobrem</expan> in Gerione excur&shy;<lb/>&longs;us, &amp; armatio ip&longs;o per&longs;iciunter) Subdorius ver&ograve; magnificus, constans, <expan abbr="gram&longs;q;">gram&longs;que</expan> <lb/>e&longs;t, quosirca omnium harmoniarum maxim&egrave; cythar&aelig; conuemt. </s>
  
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 <s>magis autem debi&shy;<lb/>les afficiuntur, qu&agrave;m fortes, quapropter ille choris conuenit. </s> <s>magis autem debi&shy;<lb/>les afficiuntur, qu&agrave;m fortes, quapropter ille choris conuenit. </s>
  
 <s>Hypodorio ver&ograve;, &amp; <lb/>hypophrygio agimus, qui choro non conueniunt; est enim chorus, veluti curator <lb/>quidam otio&longs;us, ijs &longs;olum beneuolentiam pr&aelig;bens, quibus ade&longs;t)<emph.end type="italics"/> lege Probl. </s> <s>Hypodorio ver&ograve;, &amp; <lb/>hypophrygio agimus, qui choro non conueniunt; est enim chorus, veluti curator <lb/>quidam otio&longs;us, ijs &longs;olum beneuolentiam pr&aelig;bens, quibus ade&longs;t)<emph.end type="italics"/> lege Probl. 30. <lb/>vbi idem qu&aelig;&longs;iuit. </s>
  
 <s>30. <lb/>vbi idem qu&aelig;&longs;iuit. </s> 
  
 <s>lege pr&aelig;terea, qu&aelig; ad num. </s> <s>lege pr&aelig;terea, qu&aelig; ad num. </s>
  
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 <s><margin.target id="marg392"></margin.target>401</s></p><p type="main"> <s><margin.target id="marg392"></margin.target>401</s></p><p type="main">
  
 <s>Probl. </s> <s>Probl. 50. <emph type="italics"/>(Cur in &longs;onis grauioribus &longs;ymphonia mellior euadit? </s>
  
 <s>50. <emph type="italics"/>(Cur in &longs;onis grauioribus &longs;ymphonia mellior euadit? </s> 
  
 <s>An quod mo&shy;<lb/>dulatus cantus &longs;ua quidem natura mollis e&longs;t, &amp; quietus: &longs;ed admixti numeri, &longs;eu <lb/>rithmi ratione a&longs;perior redditur, &amp; mouentior. </s> <s>An quod mo&shy;<lb/>dulatus cantus &longs;ua quidem natura mollis e&longs;t, &amp; quietus: &longs;ed admixti numeri, &longs;eu <lb/>rithmi ratione a&longs;perior redditur, &amp; mouentior. </s>
  
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 <s><margin.target id="marg393"></margin.target>402</s></p><p type="main"> <s><margin.target id="marg393"></margin.target>402</s></p><p type="main">
  
 <s>Probl. </s> <s>Probl. 51. <emph type="italics"/>(Cur &aelig;qualium, &amp; fimiliam doliorum, &longs;i vnum &longs;it inane; alterum <lb/>ver&ograve; dimidiatum tinnitus eorum Diapa&longs;on re&longs;onabunt? </s>
  
 <s>51. <emph type="italics"/>(Cur &aelig;qualium, &amp; fimiliam doliorum, &longs;i vnum &longs;it inane; alterum <lb/>ver&ograve; dimidiatum tinnitus eorum Diapa&longs;on re&longs;onabunt? </s> 
  
 <s>An quoniam &longs;onus dimi&shy;<lb/>diati cum &longs;ono vacui duplam habent inuicem proportionem: quid enim in i&longs;tis po&shy;<lb/>tius, qu&agrave;m in fi&longs;tulis res euariat? </s> <s>An quoniam &longs;onus dimi&shy;<lb/>diati cum &longs;ono vacui duplam habent inuicem proportionem: quid enim in i&longs;tis po&shy;<lb/>tius, qu&agrave;m in fi&longs;tulis res euariat? </s>
  
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 <s>in maioribus ver&ograve; aer tardius occurrit, vt in duplis dupl&ograve;, &amp; c&aelig;teris <lb/>&longs;ecundum proportionem. </s> <s>in maioribus ver&ograve; aer tardius occurrit, vt in duplis dupl&ograve;, &amp; c&aelig;teris <lb/>&longs;ecundum proportionem. </s>
  
 <s>in vtris etiam, duplus c&ugrave;m dimidio Diapa&longs;on con&longs;onat)<emph.end type="italics"/><lb/>qu&aelig; initio dixi in diui&longs;ione monochordij, &amp; alibi, &longs;ed pr&aelig;&longs;ertim in Probl. </s> <s>in vtris etiam, duplus c&ugrave;m dimidio Diapa&longs;on con&longs;onat)<emph.end type="italics"/><lb/>qu&aelig; initio dixi in diui&longs;ione monochordij, &amp; alibi, &longs;ed pr&aelig;&longs;ertim in Probl. 23. <lb/>locum hunc abund&egrave; declarant. </s>
  
 <s>23. <lb/>locum hunc abund&egrave; declarant. </s> 
  
 <s>Vbicunque enim corpus &longs;onans duplum e&longs;t <lb/>alterius corporis &longs;onantis, &longs;iue &longs;int chord&aelig;, &longs;iue fi&longs;tul&aelig;, &longs;iue dolia, &longs;iue vtres, <lb/>re&longs;onant Diapa&longs;on, cuius forma con&longs;i&longs;tit in proportione dupla, qu&aelig; in hu&shy;<lb/>iu&longs;modi corporum &longs;onis reperitur.</s></p><p type="head"> <s>Vbicunque enim corpus &longs;onans duplum e&longs;t <lb/>alterius corporis &longs;onantis, &longs;iue &longs;int chord&aelig;, &longs;iue fi&longs;tul&aelig;, &longs;iue dolia, &longs;iue vtres, <lb/>re&longs;onant Diapa&longs;on, cuius forma con&longs;i&longs;tit in proportione dupla, qu&aelig; in hu&shy;<lb/>iu&longs;modi corporum &longs;onis reperitur.</s></p><p type="head">
  
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 <s>vis enim ea <lb/>e&longs;t aqu&aelig;. </s> <s>vis enim ea <lb/>e&longs;t aqu&aelig;. </s>
  
 <s>vt &longs;ur&longs;um ver&longs;us compellat inferius; erg&ograve;, vt in portu maris par&ugrave;m, &longs;ic <lb/><gap/>&ugrave;m in alco e&longs;t: <expan abbr="itaq;">itaque</expan> plus oneris conuehi in portu videbitur, etiam mouebitur <lb/>&aelig;grtus, quia magis immergitur, &amp; aqua minus reniti pote&longs;t: at ver&ograve; in alto res <lb/>contra v&longs;u vemt)<emph.end type="italics"/> &longs;en&longs;us verborum Ari&longs;t. </s> <s>vt &longs;ur&longs;um ver&longs;us compellat inferius; erg&ograve;, vt in portu maris par&ugrave;m, &longs;ic <lb/><gap/>&ugrave;m in alco e&longs;t: <expan abbr="itaq;">itaque</expan> plus oneris conuehi in portu videbitur, etiam mouebitur <lb/>&aelig;grtus, quia magis immergitur, &amp; aqua minus reniti pote&longs;t: at ver&ograve; in alto res <lb/>contra v&longs;u vemt)<emph.end type="italics"/> &longs;en&longs;us verborum Ari&longs;t. &longs;atis per&longs;picuus e&longs;t, res tamen &longs;unt <lb/>magis expendend&aelig;. </s>
  
 <s>&longs;atis per&longs;picuus e&longs;t, res tamen &longs;unt <lb/>magis expendend&aelig;. </s> 
  
 <s>prim&ograve; <expan abbr="namq;">namque</expan> maxim&egrave; ambigo de experientia ip&longs;a, qu&aelig; <lb/>huic qu&aelig;&longs;tioni &longs;ubijcitur, &longs;i enim vera &longs;unt ea, qu&aelig; ab A&longs;tronomis afferun&shy;<lb/>tur, vt maris &longs;ph&aelig;ricitatem a&longs;&longs;erant, fal&longs;a nece&longs;&longs;ari&ograve; erit experientia h&aelig;c: <lb/>aiunt autem ip&longs;i pari velocitate nauigia &egrave; portu in altum euehi, <expan abbr="atq;">atque</expan> ex al&shy;<lb/>to in portum appellant; quod fignum manife&longs;tum e&longs;t, &longs;uperficiem maris <expan abbr="ex-tim&atilde;">ex&shy;<lb/>timam</expan> &aelig;qu&egrave; <expan abbr="vndiq;">vndique</expan> &agrave; centro mundi di&longs;tare, ac proinde omnin&ograve; <expan abbr="&longs;ph&aelig;ric&atilde;">&longs;ph&aelig;ricam</expan> e&longs;&longs;e.</s></p><p type="main"> <s>prim&ograve; <expan abbr="namq;">namque</expan> maxim&egrave; ambigo de experientia ip&longs;a, qu&aelig; <lb/>huic qu&aelig;&longs;tioni &longs;ubijcitur, &longs;i enim vera &longs;unt ea, qu&aelig; ab A&longs;tronomis afferun&shy;<lb/>tur, vt maris &longs;ph&aelig;ricitatem a&longs;&longs;erant, fal&longs;a nece&longs;&longs;ari&ograve; erit experientia h&aelig;c: <lb/>aiunt autem ip&longs;i pari velocitate nauigia &egrave; portu in altum euehi, <expan abbr="atq;">atque</expan> ex al&shy;<lb/>to in portum appellant; quod fignum manife&longs;tum e&longs;t, &longs;uperficiem maris <expan abbr="ex-tim&atilde;">ex&shy;<lb/>timam</expan> &aelig;qu&egrave; <expan abbr="vndiq;">vndique</expan> &agrave; centro mundi di&longs;tare, ac proinde omnin&ograve; <expan abbr="&longs;ph&aelig;ric&atilde;">&longs;ph&aelig;ricam</expan> e&longs;&longs;e.</s></p><p type="main">
  
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 <s>quare Galil&aelig;us pag. </s> <s>quare Galil&aelig;us pag. </s>
  
 <s>17. &longs;ic orationem claudit: valeant <lb/>inquit, eorum fals&egrave; opiniones, qui exi&longs;timant nauigium facilius &agrave; magna <lb/>aqu&aelig; copia &longs;u&longs;tineri, qu&agrave;m &agrave; parua: quod Ari&longs;t. </s> <s>17. &longs;ic orationem claudit: valeant <lb/>inquit, eorum fals&egrave; opiniones, qui exi&longs;timant nauigium facilius &agrave; magna <lb/>aqu&aelig; copia &longs;u&longs;tineri, qu&agrave;m &agrave; parua: quod Ari&longs;t. &longs;ect. </s>
  
 <s>&longs;ect. </s> 
  
 <s>23. probl. </s> <s>23. probl. </s>
  
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 1. Priorum, &longs;ecto <lb/>3. cap.  1. Priorum, &longs;ecto <lb/>3. cap.
  
 3. de hac trianguli proprietate annotaui, cuius etiam &longs;&aelig;pius Ari&longs;t. <lb/></s> 3. de hac trianguli proprietate annotaui, cuius etiam &longs;&aelig;pius Ari&longs;t. <lb/>meminit, nunquam tamen verbum illud, internos, pr&aelig;terquam hic, addi&shy;<lb/>dit; vt autem ben&egrave; intelligas quinam &longs;int hi anguli interni, &amp; qui externi, <lb/>&amp; quod etiam rectis externi &aelig;quiualeat, lege qu&aelig; ad tex. </s>
  
 <s>meminit, nunquam tamen verbum illud, internos, pr&aelig;terquam hic, addi&shy;<lb/>dit; vt autem ben&egrave; intelligas quinam &longs;int hi anguli interni, &amp; qui externi, <lb/>&amp; quod etiam rectis externi &aelig;quiualeat, lege qu&aelig; ad tex. </s> 
  
 <s>39. primi Po&longs;ter, <lb/>&longs;unt annotata.</s></p><p type="head"> <s>39. primi Po&longs;ter, <lb/>&longs;unt annotata.</s></p><p type="head">
  
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 <s><margin.target id="marg396"></margin.target>405</s></p><p type="main"> <s><margin.target id="marg396"></margin.target>405</s></p><p type="main">
  
 <s>Probl. </s> <s>Probl. 7. <emph type="italics"/>(Quam ob cau&longs;am <expan abbr="vtrunq;">vtrunque</expan> a&longs;pectum &longs;imul diuertere de&longs;tror&longs;um, &amp; <lb/>&longs;ini&longs;tror&longs;um, &amp; ad nares demittere valemus, &amp; alterum ad dextram, &amp; ad <lb/>&longs;ini&longs;tram, &longs;imul ver&ograve; vnum dextror&longs;um, alterum &longs;ini&longs;tror&longs;um nequimus; &longs;imiliter <lb/><expan abbr="neq;">neque</expan> deor&longs;um, <expan abbr="neq;">neque</expan> &longs;ur&longs;um. </s>
  
 <s>7. <emph type="italics"/>(Quam ob cau&longs;am <expan abbr="vtrunq;">vtrunque</expan> a&longs;pectum &longs;imul diuertere de&longs;tror&longs;um, &amp; <lb/>&longs;ini&longs;tror&longs;um, &amp; ad nares demittere valemus, &amp; alterum ad dextram, &amp; ad <lb/>&longs;ini&longs;tram, &longs;imul ver&ograve; vnum dextror&longs;um, alterum &longs;ini&longs;tror&longs;um nequimus; &longs;imiliter <lb/><expan abbr="neq;">neque</expan> deor&longs;um, <expan abbr="neq;">neque</expan> &longs;ur&longs;um. </s> 
  
 <s>&longs;imul ver&ograve; ad idem po&longs;&longs;umus, &longs;eparatim ver&ograve; ncqua-<emph.end type="italics"/><pb pagenum="275"/><emph type="italics"/>quam? </s> <s>&longs;imul ver&ograve; ad idem po&longs;&longs;umus, &longs;eparatim ver&ograve; ncqua-<emph.end type="italics"/><pb pagenum="275"/><emph type="italics"/>quam? </s>
  
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 <s><margin.target id="marg397"></margin.target>406</s></p><p type="main"> <s><margin.target id="marg397"></margin.target>406</s></p><p type="main">
  
 <s>Probl. </s> <s>Probl. 11. <emph type="italics"/>(<gap/>ur di&longs;tractis oculis res vna du&aelig; apparent? </s>
  
 <s>11. <emph type="italics"/>(<gap/>ur di&longs;tractis oculis res vna du&aelig; apparent? </s> 
  
 <s>An quod radij <expan abbr="vtriu&longs;q;">vtriu&longs;que</expan> <lb/>oculi ad idem <expan abbr="p&utilde;ctum">punctum</expan> non concurrunt? </s> <s>An quod radij <expan abbr="vtriu&longs;q;">vtriu&longs;que</expan> <lb/>oculi ad idem <expan abbr="p&utilde;ctum">punctum</expan> non concurrunt? </s>
  
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 <s><margin.target id="marg398"></margin.target>407</s></p><p type="main"> <s><margin.target id="marg398"></margin.target>407</s></p><p type="main">
  
 <s>Probl. </s> <s>Probl. 17. <emph type="italics"/>(Cur res vna non videtur geminari, &longs;i oculum in latera contorquents <lb/>An quia con&longs;piciendi <expan abbr="principi&utilde;">principium</expan> ab eadem linea &longs;umendum e&longs;t. </s>
  
 <s>17. <emph type="italics"/>(Cur res vna non videtur geminari, &longs;i oculum in latera contorquents <lb/>An quia con&longs;piciendi <expan abbr="principi&utilde;">principium</expan> ab eadem linea &longs;umendum e&longs;t. </s> 
  
 <s>duo autem videntur, <lb/>quando i<gap/>d &longs;ur&longs;ure, aut deor&longs;um mutatur; in latus ver&ograve; nihil refert, ni&longs;i &longs;imul <lb/>&longs;ur&longs;um, aut deor&longs;<gap/>)<emph.end type="italics"/> quod pr&aelig;&longs;enti problemate proponitur, non videtur <expan abbr="v&longs;-quequaq;">v&longs;&shy;<lb/>quequaque</expan> verum, expertus enim &longs;um, moto etiam in latus oculo, res vi&longs;as, <lb/>quamuis magna cum difficultate, geminari. </s> <s>duo autem videntur, <lb/>quando i<gap/>d &longs;ur&longs;ure, aut deor&longs;um mutatur; in latus ver&ograve; nihil refert, ni&longs;i &longs;imul <lb/>&longs;ur&longs;um, aut deor&longs;<gap/>)<emph.end type="italics"/> quod pr&aelig;&longs;enti problemate proponitur, non videtur <expan abbr="v&longs;-quequaq;">v&longs;&shy;<lb/>quequaque</expan> verum, expertus enim &longs;um, moto etiam in latus oculo, res vi&longs;as, <lb/>quamuis magna cum difficultate, geminari. </s>
  
 <s>per lineam illam, &agrave; qua princi&shy;<lb/>pium &longs;umitur con&longs;piciendi, intelligit lineam rectam tran&longs;euntem per cen&shy;<lb/>tra <expan abbr="vcriu&longs;q;">vcriu&longs;que</expan> pupill&aelig;. </s> <s>per lineam illam, &agrave; qua princi&shy;<lb/>pium &longs;umitur con&longs;piciendi, intelligit lineam rectam tran&longs;euntem per cen&shy;<lb/>tra <expan abbr="vcriu&longs;q;">vcriu&longs;que</expan> pupill&aelig;. </s>
  
 <s>quod autem ait nihil referri, &longs;i oculus in latus, &longs;iue ad <lb/>pr&aelig;dictam lineam luxetur, f<gap/>&longs;um omnin&ograve; puto ex dictis &longs;upra ad Probl. </s> <s>quod autem ait nihil referri, &longs;i oculus in latus, &longs;iue ad <lb/>pr&aelig;dictam lineam luxetur, f<gap/>&longs;um omnin&ograve; puto ex dictis &longs;upra ad Probl. 7. <lb/>hoc enim modo alter oculus diffimiliter ab altero collocatur, vnde nece&longs;&longs;e <lb/>e&longs;t <expan abbr="c&otilde;&longs;equi">con&longs;equi</expan> geminationem &longs;ecus ac &longs;i &longs;ur&longs;um, aut deor&longs;um <expan abbr="alter&utilde;">alterum</expan> luxaueris.</s></p><p type="main">
  
 <s>7. <lb/>hoc enim modo alter oculus diffimiliter ab altero collocatur, vnde nece&longs;&longs;e <lb/>e&longs;t <expan abbr="c&otilde;&longs;equi">con&longs;equi</expan> geminationem &longs;ecus ac &longs;i &longs;ur&longs;um, aut deor&longs;um <expan abbr="alter&utilde;">alterum</expan> luxaueris.</s></p><p type="main"> 
  
 <s><arrow.to.target n="marg399"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg399"></arrow.to.target></s></p><p type="margin">
  
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 <s>31.2. <lb/>&amp; tex. </s> <s>31.2. <lb/>&amp; tex. </s>
  
 <s>3. 5. Metaph. </s> <s>3. 5. Metaph.
  
 <s>&amp; omnibus Philo&longs;ophis. </s> &amp; omnibus Philo&longs;ophis. </s>
  
 <s>qu&aelig; quidem materi&aelig; accep&shy;<lb/>tio, &longs;imilis e&longs;t acceptioni materi&aelig; phy&longs;ic&aelig;, ex qua tanquam ex parte <expan abbr="c&otilde;po-&longs;itum">compo&shy;<lb/>&longs;itum</expan> con&longs;latur: conflatur enim ex materia, &amp; forma, tanquam partibus. <lb/></s> <s>qu&aelig; quidem materi&aelig; accep&shy;<lb/>tio, &longs;imilis e&longs;t acceptioni materi&aelig; phy&longs;ic&aelig;, ex qua tanquam ex parte <expan abbr="c&otilde;po-&longs;itum">compo&shy;<lb/>&longs;itum</expan> con&longs;latur: conflatur enim ex materia, &amp; forma, tanquam partibus. <lb/></s>
  
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 <s>Po&longs;trem&ograve; aduertendum, qu&ograve;d magni <expan abbr="mom&etilde;ti">momenti</expan> e&longs;t, definitiones tam Geo&shy;<lb/>metric&aelig;, qu&agrave;m Arithmetic&aelig; e&longs;&longs;e omnino e&longs;&longs;entiales, qu&aelig; &longs;cilicet totam rei <lb/>quidditatem explicent; minim&egrave; ver&ograve; e&longs;&longs;e tantummodo nominis explicatio&shy;<lb/>nes, aut definitiones, vt ijdem perperam exi&longs;timarunt, qui eorum tertius <lb/>e&longs;t error. </s> <s>Po&longs;trem&ograve; aduertendum, qu&ograve;d magni <expan abbr="mom&etilde;ti">momenti</expan> e&longs;t, definitiones tam Geo&shy;<lb/>metric&aelig;, qu&agrave;m Arithmetic&aelig; e&longs;&longs;e omnino e&longs;&longs;entiales, qu&aelig; &longs;cilicet totam rei <lb/>quidditatem explicent; minim&egrave; ver&ograve; e&longs;&longs;e tantummodo nominis explicatio&shy;<lb/>nes, aut definitiones, vt ijdem perperam exi&longs;timarunt, qui eorum tertius <lb/>e&longs;t error. </s>
  
 <s>quod quidem Ari&longs;t. </s> <s>quod quidem Ari&longs;t. &longs;en&longs;i&longs;&longs;e manife&longs;tum e&longs;t, <expan abbr="quotie&longs;cunq;">quotie&longs;cunque</expan> enim in <lb/>Analyticis de &longs;cientiarum principijs loquitur, inter ea definitiones Geome <lb/>tri&aelig;, &amp; Arithmetic&aelig; &longs;emper <expan abbr="c&otilde;numerat">connumerat</expan>, quod minim&egrave; feci&longs;&longs;et, &longs;i &longs;ol&ugrave;m no&shy;<lb/>minis e&longs;&longs;ent explicationes. </s>
  
 <s>&longs;en&longs;i&longs;&longs;e manife&longs;tum e&longs;t, <expan abbr="quotie&longs;cunq;">quotie&longs;cunque</expan> enim in <lb/>Analyticis de &longs;cientiarum principijs loquitur, inter ea definitiones Geome <lb/>tri&aelig;, &amp; Arithmetic&aelig; &longs;emper <expan abbr="c&otilde;numerat">connumerat</expan>, quod minim&egrave; feci&longs;&longs;et, &longs;i &longs;ol&ugrave;m no&shy;<lb/>minis e&longs;&longs;ent explicationes. </s> 
  
 <s>Verum quidem e&longs;t eas, vt plurimum e&longs;&longs;e &longs;imul, <pb pagenum="8"/>&amp; rei, &amp; nominis expo&longs;itiones. </s> <s>Verum quidem e&longs;t eas, vt plurimum e&longs;&longs;e &longs;imul, <pb pagenum="8"/>&amp; rei, &amp; nominis expo&longs;itiones. </s>
  
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 <s>vnde etiam &longs;equitur Mathe&shy;<lb/>maticas ha&longs;ce &agrave; notioribus nobis, &amp; natura, vt vult Auerroes, &amp; c&aelig;teri fer&egrave; <lb/>omnes, &amp; ex no&longs;tris maxim&egrave; Toletus qu&ecedil;&longs;t. </s> <s>vnde etiam &longs;equitur Mathe&shy;<lb/>maticas ha&longs;ce &agrave; notioribus nobis, &amp; natura, vt vult Auerroes, &amp; c&aelig;teri fer&egrave; <lb/>omnes, &amp; ex no&longs;tris maxim&egrave; Toletus qu&ecedil;&longs;t. </s>
  
 <s>4. &longs;ecundi Phy&longs;. </s> <s>4. &longs;ecundi Phy&longs;. procedere. </s>
  
 <s>procedere. </s> 
  
 <s>no&shy;<lb/>rioribus nobis, quia primum omnium manife&longs;ta e&longs;t tota figur&aelig; e&longs;&longs;entia ex <lb/>definitione ip&longs;ius allata, ignotis adhuc ip&longs;ius affectionibus, notioribus na&shy;<lb/>tura, quia prius natura e&longs;t &longs;ubiecti e&longs;&longs;entia, qu&agrave;m pa&longs;siones, qu&aelig; ab ea ma&shy;<lb/>nant, <expan abbr="de&qacute;">deque</expan>; ea demon&longs;trantur: <expan abbr="atq;">atque</expan> h&aelig;c cau&longs;&aelig; e&longs;t, cur &longs;emper tanti fact&aelig; &longs;ine <lb/>Geometric&aelig; demon&longs;trationes, <expan abbr="primum&qacute;">primumque</expan>; certitudinis gradum obtineant.</s></p><p type="head"> <s>no&shy;<lb/>rioribus nobis, quia primum omnium manife&longs;ta e&longs;t tota figur&aelig; e&longs;&longs;entia ex <lb/>definitione ip&longs;ius allata, ignotis adhuc ip&longs;ius affectionibus, notioribus na&shy;<lb/>tura, quia prius natura e&longs;t &longs;ubiecti e&longs;&longs;entia, qu&agrave;m pa&longs;siones, qu&aelig; ab ea ma&shy;<lb/>nant, <expan abbr="de&qacute;">deque</expan>; ea demon&longs;trantur: <expan abbr="atq;">atque</expan> h&aelig;c cau&longs;&aelig; e&longs;t, cur &longs;emper tanti fact&aelig; &longs;ine <lb/>Geometric&aelig; demon&longs;trationes, <expan abbr="primum&qacute;">primumque</expan>; certitudinis gradum obtineant.</s></p><p type="head">
  
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 <s>ver&ograve; 31. <emph type="italics"/>(Figurarum autem maxim&egrave; &longs;cientialis <lb/>est prima, mathematic&aelig; <expan abbr="namq;">namque</expan> <expan abbr="&longs;ci&etilde;ti&aelig;">&longs;cienti&aelig;</expan> per hanc demon&longs;trationes ferunt, vt Arith&shy;<lb/>metica, &amp; Geometria, &amp; Per&longs;pectiua, &amp; fer&egrave; dixerim qu&aelig;cunque ip&longs;ius Propter <lb/>quid con&longs;iderationem faciunt)<emph.end type="italics"/> po&longs;tea tex. </s> <s>ver&ograve; 31. <emph type="italics"/>(Figurarum autem maxim&egrave; &longs;cientialis <lb/>est prima, mathematic&aelig; <expan abbr="namq;">namque</expan> <expan abbr="&longs;ci&etilde;ti&aelig;">&longs;cienti&aelig;</expan> per hanc demon&longs;trationes ferunt, vt Arith&shy;<lb/>metica, &amp; Geometria, &amp; Per&longs;pectiua, &amp; fer&egrave; dixerim qu&aelig;cunque ip&longs;ius Propter <lb/>quid con&longs;iderationem faciunt)<emph.end type="italics"/> po&longs;tea tex. </s>
  
 <s>11. 2. Po&longs;ter. </s> <s>11. 2. Po&longs;ter. a&longs;&longs;erit demon&longs;tratio&shy;<lb/>nemillam, qua Geometra probat, angulum in &longs;emicirculo e&longs;&longs;e rectum, e&longs;&longs;e <lb/>&agrave; cau&longs;a materiali, im&ograve; eam tanquam optimum huiu&longs;modi demon&longs;trationis <lb/>exemplum affert. </s>
  
 <s>a&longs;&longs;erit demon&longs;tratio&shy;<lb/>nemillam, qua Geometra probat, angulum in &longs;emicirculo e&longs;&longs;e rectum, e&longs;&longs;e <lb/>&agrave; cau&longs;a materiali, im&ograve; eam tanquam optimum huiu&longs;modi demon&longs;trationis <lb/>exemplum affert. </s> 
  
 <s>&longs;ed de hac eadem demon&longs;tratione infra iterum dicendum <lb/>erit; vide interim pr&aelig;dicti loci explicationem &longs;upra in locis Mathemat. </s> <s>&longs;ed de hac eadem demon&longs;tratione infra iterum dicendum <lb/>erit; vide interim pr&aelig;dicti loci explicationem &longs;upra in locis Mathemat. </s>
  
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 <s>vide huius loci explicationem &longs;upra &agrave; <lb/>nobis allatam. </s> <s>vide huius loci explicationem &longs;upra &agrave; <lb/>nobis allatam. </s>
  
 <s>6. Metaph. </s> <s>6. Metaph.
  
 <s>tex. </s> 
  
 <s>1. <emph type="italics"/>(Mathematicorum <expan abbr="quoq;">quoque</expan> principia, elements, <lb/>&amp; cau&longs;&aelig; &longs;unt)<emph.end type="italics"/> 11. Metaph. </s> tex. </s>
  
 <s>cap.  <s>1. <emph type="italics"/>(Mathematicorum <expan abbr="quoq;">quoque</expan> principia, elements, <lb/>&amp; cau&longs;&aelig; &longs;unt)<emph.end type="italics"/> 11. Metaph.
  
 1. &longs;umm&aelig; 3. <emph type="italics"/>(Patet igitur tria e&longs;&longs;e genera &longs;pe&shy;<lb/>culatiuarum &longs;cientiarum, Naturalem, Mathematicam, Theologiam)<emph.end type="italics"/> ecce tibi, <lb/>quam clara &longs;it Ari&longs;t. </s> cap.
  
 <s>&longs;ententia.</s></p><p type="main"> 1. &longs;umm&aelig; 3. <emph type="italics"/>(Patet igitur tria e&longs;&longs;e genera &longs;pe&shy;<lb/>culatiuarum &longs;cientiarum, Naturalem, Mathematicam, Theologiam)<emph.end type="italics"/> ecce tibi, <lb/>quam clara &longs;it Ari&longs;t. &longs;ententia.</s></p><p type="main">
  
 <s>Quod ad Platonis auctoritatem attinet, certum e&longs;t, eum in Mathematicis <lb/>cau&longs;am materialem, &amp; formalem agnoui&longs;&longs;e, nam te&longs;te Ari&longs;t.  <s>Quod ad Platonis auctoritatem attinet, certum e&longs;t, eum in Mathematicis <lb/>cau&longs;am materialem, &amp; formalem agnoui&longs;&longs;e, nam te&longs;te Ari&longs;t.
  
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 <s>Adhuc autem omnis generis &longs;yl&shy;<lb/>logi&longs;morum modus, alios quidem &agrave; cau&longs;is fidem &longs;u&longs;cipientes, alios ver&ograve; &agrave; certis no&shy;<lb/>tis perfectos, omnes autem inuincibiles, &amp; certos, ad &longs;cientiam&queacute;, accommodatos)<emph.end type="italics"/><lb/>notanda &longs;nnt illa; &agrave; caufis fidem &longs;u&longs;cipientes, quibus pr&aelig;cipu&egrave; indicat, &longs;e in <lb/>Demon&longs;trationibus Euclidianis cau&longs;as agno&longs;cere.</s></p><p type="main"> <s>Adhuc autem omnis generis &longs;yl&shy;<lb/>logi&longs;morum modus, alios quidem &agrave; cau&longs;is fidem &longs;u&longs;cipientes, alios ver&ograve; &agrave; certis no&shy;<lb/>tis perfectos, omnes autem inuincibiles, &amp; certos, ad &longs;cientiam&queacute;, accommodatos)<emph.end type="italics"/><lb/>notanda &longs;nnt illa; &agrave; caufis fidem &longs;u&longs;cipientes, quibus pr&aelig;cipu&egrave; indicat, &longs;e in <lb/>Demon&longs;trationibus Euclidianis cau&longs;as agno&longs;cere.</s></p><p type="main">
  
 <s>Lib. </s> <s>Lib.
  
 <s>deinde 3. in comm. </s> deinde 3. in comm. </s>
  
 <s>ad primam Euclidis propo&longs;it. </s> <s>ad primam Euclidis propo&longs;it. </s>
  
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 <s>&longs;imul <lb/>&amp; quod effectus &longs;it, &amp; cur &longs;it liquid&ograve; innote&longs;cit. </s> <s>&longs;imul <lb/>&amp; quod effectus &longs;it, &amp; cur &longs;it liquid&ograve; innote&longs;cit. </s>
  
 <s>Verum ip&longs;e omnium pri&shy;<lb/>mus ab&longs;olut&egrave; dici pote&longs;t, cum nullus ante iplum, cuius opera extent, id di&shy;<lb/>cat; quamuis ip&longs;e fallo Proclum, Ari&longs;t. </s> <s>Verum ip&longs;e omnium pri&shy;<lb/>mus ab&longs;olut&egrave; dici pote&longs;t, cum nullus ante iplum, cuius opera extent, id di&shy;<lb/>cat; quamuis ip&longs;e fallo Proclum, Ari&longs;t. &amp; Platonem &longs;ibi conetur adiungere. <lb/></s>
  
 <s>&amp; Platonem &longs;ibi conetur adiungere. <lb/></s> 
  
 <s>Po&longs;t ip&longs;um ver&ograve; &longs;oli duo fer&egrave; Pererius, &amp; Conimbric. </s> <s>Po&longs;t ip&longs;um ver&ograve; &longs;oli duo fer&egrave; Pererius, &amp; Conimbric. </s>
  
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 <s>videas Lector, qu&agrave;m &longs;yncer&egrave; natu&shy;<lb/>ralis philo&longs;ophi&aelig; profe&longs;&longs;or vera de Mathematicis loquatur, ita vt etiam eas <lb/>illi pr&aelig;ferat. </s> <s>videas Lector, qu&agrave;m &longs;yncer&egrave; natu&shy;<lb/>ralis philo&longs;ophi&aelig; profe&longs;&longs;or vera de Mathematicis loquatur, ita vt etiam eas <lb/>illi pr&aelig;ferat. </s>
  
 <s>Iacobus autem Zabarella in toto &longs;uo opere logico, perpetu&ograve; <lb/>Mathematicas demon&longs;tcationes, vt poti&longs;&longs;imas agno&longs;cit, <expan abbr="exempla&qacute;">exemplaque</expan>; Ari&longs;t. <lb/></s> <s>Iacobus autem Zabarella in toto &longs;uo opere logico, perpetu&ograve; <lb/>Mathematicas demon&longs;tcationes, vt poti&longs;&longs;imas agno&longs;cit, <expan abbr="exempla&qacute;">exemplaque</expan>; Ari&longs;t. <lb/>geometrica exponit tanquam vera, &amp; omnino rebus ip&longs;is accommodata; <lb/>quare non e&longs;t, cur vnum, aut alterum ip&longs;ius locum hic de&longs;cribamus. </s>
  
 <s>geometrica exponit tanquam vera, &amp; omnino rebus ip&longs;is accommodata; <lb/>quare non e&longs;t, cur vnum, aut alterum ip&longs;ius locum hic de&longs;cribamus. </s> 
  
 <s>illud <lb/>non pr&aelig;termittam, ip&longs;um fateri &longs;e bis, teru&egrave; totum Euclidem &longs;edul&ograve; perle&shy;<lb/>gi&longs;&longs;e, vt prob&egrave; po&longs;&longs;et Ari&longs;t.  <s>illud <lb/>non pr&aelig;termittam, ip&longs;um fateri &longs;e bis, teru&egrave; totum Euclidem &longs;edul&ograve; perle&shy;<lb/>gi&longs;&longs;e, vt prob&egrave; po&longs;&longs;et Ari&longs;t.
  
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 <s>2. Ex Themi&longs;tio cap, 2. &longs;u&aelig; paraphr. </s> <s>2. Ex Themi&longs;tio cap, 2. &longs;u&aelig; paraphr. </s>
  
 <s>2. Po&longs;ter. </s> <s>2. Po&longs;ter. Demon&longs;tratio poti&longs;&longs;ima <lb/>debet o&longs;tendere, &amp; quod, &amp; Propter quid. </s>
  
 <s>Demon&longs;tratio poti&longs;&longs;ima <lb/>debet o&longs;tendere, &amp; quod, &amp; Propter quid. </s> 
  
 <s>quod profect&ograve; c&aelig;teris demon&shy;<lb/>&longs;trationibus melius pr&aelig;&longs;tant Geometric&aelig;, &amp; Arithmetic&aelig;. </s> <s>quod profect&ograve; c&aelig;teris demon&shy;<lb/>&longs;trationibus melius pr&aelig;&longs;tant Geometric&aelig;, &amp; Arithmetic&aelig;. </s>
  
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 <s>&amp; quoniam &longs;upra tex. </s> <s>&amp; quoniam &longs;upra tex. </s>
  
 <s>23. 1. Po&longs;ter. </s> <s>23. 1. Po&longs;ter. nos eam per cau&longs;am ma&shy;<lb/>terralem procedere o&longs;tendimus, ide&ograve; ne actum agamus, <expan abbr="explication&etilde;">explicationem</expan> illam <lb/>nunc opus e&longs;t relegere. </s>
  
 <s>nos eam per cau&longs;am ma&shy;<lb/>terralem procedere o&longs;tendimus, ide&ograve; ne actum agamus, <expan abbr="explication&etilde;">explicationem</expan> illam <lb/>nunc opus e&longs;t relegere. </s> 
  
 <s>Hoc tamen loco partem ip&longs;ius primam, angulum, <lb/>videlicet externum cuiu&longs;uis trianguli, &aelig;qualem e&longs;&longs;e duobus internis, &amp; op&shy;<lb/>po&longs;itis, examin<gap/> bo; cuius medium, &longs;i ad rigorem demon&longs;trationis rediga&shy;<lb/>tur, e&longs;t hoc; externus angulus e&longs;t diui&longs;ibilis in duos angulos, quorum &longs;ingu&shy;<lb/>li &longs;ingulis internis &longs;unt &aelig; quales, ergo <expan abbr="eti&atilde;">etiam</expan> totalis anguius erit &aelig;qualis am&shy;<lb/>bobus internis &longs;imul &longs;umptis. </s> <s>Hoc tamen loco partem ip&longs;ius primam, angulum, <lb/>videlicet externum cuiu&longs;uis trianguli, &aelig;qualem e&longs;&longs;e duobus internis, &amp; op&shy;<lb/>po&longs;itis, examin<gap/> bo; cuius medium, &longs;i ad rigorem demon&longs;trationis rediga&shy;<lb/>tur, e&longs;t hoc; externus angulus e&longs;t diui&longs;ibilis in duos angulos, quorum &longs;ingu&shy;<lb/>li &longs;ingulis internis &longs;unt &aelig; quales, ergo <expan abbr="eti&atilde;">etiam</expan> totalis anguius erit &aelig;qualis am&shy;<lb/>bobus internis &longs;imul &longs;umptis. </s>
  
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 <s>ip&longs;e tex. </s> <s>ip&longs;e tex. </s>
  
 <s>3. 5. Metaph. </s> <s>3. 5. Metaph.
  
 <s>id a&longs;&longs;erit. </s> id a&longs;&longs;erit. </s>
  
 <s>&amp; tex. </s> <s>&amp; tex. </s>
  
 <s>11. 2. Po&longs;ter. </s> <s>11. 2. Po&longs;ter. vtitur &longs;imili <expan abbr="ex&etilde;-plo">exen&shy;<lb/>plo</expan> ad <expan abbr="material&etilde;">materialem</expan> cau&longs;am explicandam. </s>
  
 <s>vtitur &longs;imili <expan abbr="ex&etilde;-plo">exen&shy;<lb/>plo</expan> ad <expan abbr="material&etilde;">materialem</expan> cau&longs;am explicandam. </s> 
  
 <s>quamuis autem Geometr&aelig; non di&shy;<lb/>cant talem angulum, vel talem figuram e&longs;&longs;e <expan abbr="diui&longs;ibil&etilde;">diui&longs;ibilem</expan> in partes &aelig;quales alijs <lb/>quibu&longs;dam, &longs;ed &longs;tatim diuidant, id faciunt breuitatis cau&longs;a; vtuntur enim <lb/>actu pro potentia, quia actus potentiam &longs;upponit, qu&ograve;d optim&egrave; Ari&longs;tot. </s> <s>quamuis autem Geometr&aelig; non di&shy;<lb/>cant talem angulum, vel talem figuram e&longs;&longs;e <expan abbr="diui&longs;ibil&etilde;">diui&longs;ibilem</expan> in partes &aelig;quales alijs <lb/>quibu&longs;dam, &longs;ed &longs;tatim diuidant, id faciunt breuitatis cau&longs;a; vtuntur enim <lb/>actu pro potentia, quia actus potentiam &longs;upponit, qu&ograve;d optim&egrave; Ari&longs;tot. </s>
  
 <s>9. <lb/>Metaphy&longs;. </s> <s>9. <lb/>Metaphy&longs;. tex. </s>
  
 <s>tex. </s> 
  
 <s>20. annotauit, &longs;ic; De&longs;criptiones quoque actu inueniuntur, <lb/>diuidentes namque inueniunt, qu&ograve;d &longs;i diui&longs;&aelig; e&longs;&longs;ent, manife &longs;t&aelig; e&longs;&longs;ent, nunc <lb/>autem in&longs;unt potentia, &amp;c. </s> <s>20. annotauit, &longs;ic; De&longs;criptiones quoque actu inueniuntur, <lb/>diuidentes namque inueniunt, qu&ograve;d &longs;i diui&longs;&aelig; e&longs;&longs;ent, manife &longs;t&aelig; e&longs;&longs;ent, nunc <lb/>autem in&longs;unt potentia, &amp;c. </s>
  
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 <s>Vide huius explicationem tex. </s> <s>Vide huius explicationem tex. </s>
  
 <s>23. <lb/>1. Po&longs;ter. </s> <s>23. <lb/>1. Po&longs;ter. vbi etiam videbis eam po&longs;&longs;e demon&longs;trari modo Pythagoreorum, <lb/>ab&longs;que vlla diui&longs;ione, &longs;ed per partes actu exi&longs;tentes. </s>
  
 <s>vbi etiam videbis eam po&longs;&longs;e demon&longs;trari modo Pythagoreorum, <lb/>ab&longs;que vlla diui&longs;ione, &longs;ed per partes actu exi&longs;tentes. </s> 
  
 <s>hoc dico propter eos, <lb/>qui per ha&longs;ce diui&longs;iones timent, ne non inueniatur medium &aacute; priori. </s> <s>hoc dico propter eos, <lb/>qui per ha&longs;ce diui&longs;iones timent, ne non inueniatur medium &aacute; priori. </s>
  
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 <s>Obiectio 3. Demon&longs;trationes Geometric&aelig; non con&longs;tant ex proprijs, &amp; <lb/>per &longs;e, non enim Geometra con&longs;iderat e&longs;&longs;entiam Quantitatis, neque eius <lb/>pa&longs;siones, quatenus ab illius e&longs;&longs;entia manant, quare ex communibus qui&shy;<lb/>bu&longs;dam, &amp; mer&egrave; extrin&longs;ecis nece&longs;&longs;e e&longs;t procedere. </s> <s>Obiectio 3. Demon&longs;trationes Geometric&aelig; non con&longs;tant ex proprijs, &amp; <lb/>per &longs;e, non enim Geometra con&longs;iderat e&longs;&longs;entiam Quantitatis, neque eius <lb/>pa&longs;siones, quatenus ab illius e&longs;&longs;entia manant, quare ex communibus qui&shy;<lb/>bu&longs;dam, &amp; mer&egrave; extrin&longs;ecis nece&longs;&longs;e e&longs;t procedere. </s>
  
 <s>Re&longs;pondeo ex dictis cap. <lb/></s> <s>Re&longs;pondeo ex dictis cap. <lb/>1. de materia intelligibili, &amp; definitionibus Geometricis huic obiectioni <lb/>abund&egrave; fieri &longs;atis. </s>
  
 <s>1. de materia intelligibili, &amp; definitionibus Geometricis huic obiectioni <lb/>abund&egrave; fieri &longs;atis. </s> 
  
 <s>materia enim Geometri&aelig; non e&longs;t quantitas &longs;ecundum &longs;e, <lb/>&longs;ed quatenus terminata, cuius totam e&longs;&longs;entiam ex definitionibus e&longs;&longs;entiali&shy;<lb/>bus Geometra cogno&longs;cit: quorum <expan abbr="vtrumq;">vtrumque</expan> aduer&longs;arios latuit.</s></p><p type="main"> <s>materia enim Geometri&aelig; non e&longs;t quantitas &longs;ecundum &longs;e, <lb/>&longs;ed quatenus terminata, cuius totam e&longs;&longs;entiam ex definitionibus e&longs;&longs;entiali&shy;<lb/>bus Geometra cogno&longs;cit: quorum <expan abbr="vtrumq;">vtrumque</expan> aduer&longs;arios latuit.</s></p><p type="main">
  
 <s>Pr&aelig;terea fal&longs;um e&longs;t, Geometram ex communibus pluribus &longs;cientijs pro&shy;<lb/>cedere, quod vetat Ari&longs;t. </s> <s>Pr&aelig;terea fal&longs;um e&longs;t, Geometram ex communibus pluribus &longs;cientijs pro&shy;<lb/>cedere, quod vetat Ari&longs;t. 1. Po&longs;ter. procedit enim ex principijs communi&shy;<lb/>bus quantitatibus terminatis, ide&longs;t figuris, &amp; numeris; quod non &longs;olum li&shy;<lb/>cet, &longs;ed etiam debet fieri ex 1. Po&longs;ter. tex. </s>
  
 <s>1. Po&longs;ter. </s> 
  
 <s>procedit enim ex principijs communi&shy;<lb/>bus quantitatibus terminatis, ide&longs;t figuris, &amp; numeris; quod non &longs;olum li&shy;<lb/>cet, &longs;ed etiam debet fieri ex 1. Po&longs;ter. </s> 
  
 <s>tex. </s> 
  
 <s>20. &amp; 25. <expan abbr="neq;">neque</expan> vnquam idem prin&shy;<lb/>cipium repetit, ni&longs;i vbi e&longs;t effectus formalis ip&longs;ius, &amp; non ni&longs;i contrahendo <lb/>ad illud particulare.</s></p><p type="head"> <s>20. &amp; 25. <expan abbr="neq;">neque</expan> vnquam idem prin&shy;<lb/>cipium repetit, ni&longs;i vbi e&longs;t effectus formalis ip&longs;ius, &amp; non ni&longs;i contrahendo <lb/>ad illud particulare.</s></p><p type="head">
  
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 <s><expan abbr="neq;">neque</expan> &longs;olum loca ip&longs;ius clari&longs;sima ex analyticis, phyficis, &amp; <lb/>metaphy&longs;icis, qu&aelig; &longs;uperius recitauimus in alienum &longs;en&longs;um detorquent; &longs;ed <lb/>pr&aelig;ter ea vnicum tantum locum, qui expre&longs;s&egrave; Mathematicis refragari vi&shy;<lb/>deatur, afferunt, <expan abbr="cum&qacute;">cumque</expan>; &longs;ibi fals&ograve; fauere <expan abbr="c&otilde;fingunt">confingunt</expan>. </s> <s><expan abbr="neq;">neque</expan> &longs;olum loca ip&longs;ius clari&longs;sima ex analyticis, phyficis, &amp; <lb/>metaphy&longs;icis, qu&aelig; &longs;uperius recitauimus in alienum &longs;en&longs;um detorquent; &longs;ed <lb/>pr&aelig;ter ea vnicum tantum locum, qui expre&longs;s&egrave; Mathematicis refragari vi&shy;<lb/>deatur, afferunt, <expan abbr="cum&qacute;">cumque</expan>; &longs;ibi fals&ograve; fauere <expan abbr="c&otilde;fingunt">confingunt</expan>. </s>
  
 <s>is e&longs;t in angulo quodam <lb/>operum ip&longs;ius, in &longs;ecund&ograve; videlicet Moral. </s> <s>is e&longs;t in angulo quodam <lb/>operum ip&longs;ius, in &longs;ecund&ograve; videlicet Moral. Eudem. cap.
  
 <s>Eudem. </s> 
  
 <s>cap.  
  
 7. &longs;ic, in immobi&shy;<lb/>libus autem, vt in Mathematicis non per &longs;e, &longs;ed &longs;imilitudine quadam prin&shy;<lb/>cipia appellantur. </s> 7. &longs;ic, in immobi&shy;<lb/>libus autem, vt in Mathematicis non per &longs;e, &longs;ed &longs;imilitudine quadam prin&shy;<lb/>cipia appellantur. </s>
  
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 <s>accedit authoritas Ari&longs;t.  <s>accedit authoritas Ari&longs;t.
  
 qui 6. Eth. </s> qui 6. Eth. cap.
  
 <s>cap.  
  
 8, <lb/>ait, quid e&longs;t, qu&ograve;d puer fieri Mathem. </s> 
  
 <s>pote&longs;t, &longs;apiens, aut naturalis non po&shy;<lb/>te&longs;t? </s> 8, <lb/>ait, quid e&longs;t, qu&ograve;d puer fieri Mathem. pote&longs;t, &longs;apiens, aut naturalis non po&shy;<lb/>te&longs;t? </s>
  
 <s>pr&aelig;terea, quia antiquitus pueris ante alias tradebantur. </s> <s>pr&aelig;terea, quia antiquitus pueris ante alias tradebantur. </s>
  
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 <s>Decima, qua dicunt entia Mathematica non extare: &longs;ed ex initio dictis <lb/>de materia intelligibili h&ecedil;c nota &longs;atis detergitur.</s></p><p type="main"> <s>Decima, qua dicunt entia Mathematica non extare: &longs;ed ex initio dictis <lb/>de materia intelligibili h&ecedil;c nota &longs;atis detergitur.</s></p><p type="main">
  
 <s>Vndecima, ab&longs;tractionem &agrave; materia <expan abbr="mult&utilde;">multum</expan> derogare perfectioni Mathe&shy;<lb/>maticarum demon&longs;trationum; cui re&longs;pondeat eruditi&longs;&longs;imus Toletus, qui <lb/>in 2. Phy&longs;. </s> <s>Vndecima, ab&longs;tractionem &agrave; materia <expan abbr="mult&utilde;">multum</expan> derogare perfectioni Mathe&shy;<lb/>maticarum demon&longs;trationum; cui re&longs;pondeat eruditi&longs;&longs;imus Toletus, qui <lb/>in 2. Phy&longs;. qu&aelig;&longs;t. </s>
  
 <s>qu&aelig;&longs;t. </s> 
  
 <s>4. &longs;ic ait: Phy&longs;icus frequentet vtitur demon&longs;tratione effe&shy;<lb/>ctus, &amp; &longs;igni, quia ip&longs;ius cau&longs;&aelig; frequentius &longs;unt occult&aelig; nec per &longs;e &longs;en&longs;ibiles, <lb/>at Mathematicus frequentius &agrave; prioribus procedit, c&ugrave;m eius cau&longs;&aelig; notio&shy;<lb/>res &longs;int effectibus, &agrave; &longs;en&longs;u .n. </s> <s>4. &longs;ic ait: Phy&longs;icus frequentet vtitur demon&longs;tratione effe&shy;<lb/>ctus, &amp; &longs;igni, quia ip&longs;ius cau&longs;&aelig; frequentius &longs;unt occult&aelig; nec per &longs;e &longs;en&longs;ibiles, <lb/>at Mathematicus frequentius &agrave; prioribus procedit, c&ugrave;m eius cau&longs;&aelig; notio&shy;<lb/>res &longs;int effectibus, &agrave; &longs;en&longs;u .n. </s>
  
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 <s>Po&longs;tea in 4. conclu&longs;. </s> <s>Po&longs;tea in 4. conclu&longs;. </s>
  
 <s>&longs;ic ait: omnem phy&longs;ic&aelig; imperfectionem &agrave; materia <lb/>pendere, vnde Ari&longs;t. </s> <s>&longs;ic ait: omnem phy&longs;ic&aelig; imperfectionem &agrave; materia <lb/>pendere, vnde Ari&longs;t. 2. Metaphy. </s>
  
 <s>2. Metaphy. </s> 
  
 <s>tex. </s> <s>tex. </s>
  
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 dum lib.  dum lib.
  
 13. Metaphy&longs;. </s> 13. Metaphy&longs;. ait: qui dicunt Mathematicas &longs;cientias ni&shy;<lb/>hil de bono, vel pulchro dicere, fal&longs;um dicunt: dicunt enim, &amp; maxim&egrave; <expan abbr="o&longs;t&etilde;-dunt">o&longs;ten&shy;<lb/>dunt</expan>, nam etiam&longs;i non nominant, quia tamen opera, &amp; rationes o&longs;tendunt, <lb/>non ne dicunt de eis? </s>
  
 <s>ait: qui dicunt Mathematicas &longs;cientias ni&shy;<lb/>hil de bono, vel pulchro dicere, fal&longs;um dicunt: dicunt enim, &amp; maxim&egrave; <expan abbr="o&longs;t&etilde;-dunt">o&longs;ten&shy;<lb/>dunt</expan>, nam etiam&longs;i non nominant, quia tamen opera, &amp; rationes o&longs;tendunt, <lb/>non ne dicunt de eis? </s> 
  
 <s>pulchri <expan abbr="nam&qacute;">namque</expan>; maxim&egrave; &longs;pecies &longs;unt, ordo, commen&shy;<lb/>&longs;uratio, &amp; definitum, qu&aelig; maxim&egrave; &agrave; Mathematicis &longs;cientijs o&longs;tenduntur.</s></p><p type="main"> <s>pulchri <expan abbr="nam&qacute;">namque</expan>; maxim&egrave; &longs;pecies &longs;unt, ordo, commen&shy;<lb/>&longs;uratio, &amp; definitum, qu&aelig; maxim&egrave; &agrave; Mathematicis &longs;cientijs o&longs;tenduntur.</s></p><p type="main">
  
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 8. 9. &amp; 10. libri primi Procli, vbi fus&egrave; de vtilitate <expan abbr="ear&utilde;">earum</expan> omnium <lb/>di&longs;&longs;erit. </s> 8. 9. &amp; 10. libri primi Procli, vbi fus&egrave; de vtilitate <expan abbr="ear&utilde;">earum</expan> omnium <lb/>di&longs;&longs;erit. </s>
  
 <s>Quod &longs;i Philo&longs;ophus &longs;it, qui h&aelig;c opponat; huic illa &longs;ufficiat vtili&shy;<lb/>tas, qua loca omnia Ari&longs;t. </s> <s>Quod &longs;i Philo&longs;ophus &longs;it, qui h&aelig;c opponat; huic illa &longs;ufficiat vtili&shy;<lb/>tas, qua loca omnia Ari&longs;t. Mathematica, qu&ecedil; fer&egrave; <expan abbr="quadring&etilde;ta">quadringenta</expan> &longs;unt, facil&egrave; <lb/>Mathematicarum auxilio intelliguntur, <expan abbr="&longs;ic&qacute;">&longs;icque</expan>; ad plenam totius Ari&longs;t.
  
 <s>Mathematica, qu&ecedil; fer&egrave; <expan abbr="quadring&etilde;ta">quadringenta</expan> &longs;unt, facil&egrave; <lb/>Mathematicarum auxilio intelliguntur, <expan abbr="&longs;ic&qacute;">&longs;icque</expan>; ad plenam totius Ari&longs;t.  
  
 intel&shy;<lb/>ligentiam, tandem perueniri pote&longs;t.</s></p><p type="main"> intel&shy;<lb/>ligentiam, tandem perueniri pote&longs;t.</s></p><p type="main">
  
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 <s>Quare ni&longs;i lector ad finem <expan abbr="v&longs;q;">v&longs;que</expan> omnia per&shy;<lb/>legerit, quod rar&ograve; accidit, decipitur, putat enim in omnes Mathematicas <lb/>illa quadrare, c&ugrave;m tamen ip&longs;i fateantur, &longs;e nunquam loquutos e&longs;&longs;e de me&shy;<lb/>dijs A&longs;tronomia, Mu&longs;ica, Optica, Mechanica, quibus ine&longs;&longs;e veram &longs;cienti&aelig; <lb/>demon&longs;tratiu&aelig; rationem libenter concedunt.</s></p><p type="main"> <s>Quare ni&longs;i lector ad finem <expan abbr="v&longs;q;">v&longs;que</expan> omnia per&shy;<lb/>legerit, quod rar&ograve; accidit, decipitur, putat enim in omnes Mathematicas <lb/>illa quadrare, c&ugrave;m tamen ip&longs;i fateantur, &longs;e nunquam loquutos e&longs;&longs;e de me&shy;<lb/>dijs A&longs;tronomia, Mu&longs;ica, Optica, Mechanica, quibus ine&longs;&longs;e veram &longs;cienti&aelig; <lb/>demon&longs;tratiu&aelig; rationem libenter concedunt.</s></p><p type="main">
  
 <s>Decima&longs;eptima, e&longs;t cuiu&longs;dam recenti&longs;&longs;imi Philo&longs;ophi, qu&igrave; vbi pluribus <lb/>contra Mathematicas di&longs;&longs;eruit, nihil, vt fieri &longs;olet, &longs;ibi obijcit, <expan abbr="ver&utilde;">verum</expan> com&shy;<pb pagenum="27"/>plura Ari&longs;t. </s> <s>Decima&longs;eptima, e&longs;t cuiu&longs;dam recenti&longs;&longs;imi Philo&longs;ophi, qu&igrave; vbi pluribus <lb/>contra Mathematicas di&longs;&longs;eruit, nihil, vt fieri &longs;olet, &longs;ibi obijcit, <expan abbr="ver&utilde;">verum</expan> com&shy;<pb pagenum="27"/>plura Ari&longs;t. &amp; veterum philo&longs;ophorum loca &longs;ibi aduer&longs;antia di&longs;&longs;imulat: tan&shy;<lb/>dem, quod nullus adhuc au&longs;us e&longs;t, concludit Mathematicam nullam e&longs;&longs;e <lb/>Philo&longs;ophi&aelig; partem, c&ugrave;m tamen apud Ari&longs;t. &amp; omnes peripateticos nihil <lb/>frequentius occurrat, quam tres e&longs;&longs;e philo&longs;ophi&aelig; partes, Phy&longs;icam, Mathe&shy;<lb/>maticam, &amp; Metaphy&longs;icam. </s>
  
 <s>&amp; veterum philo&longs;ophorum loca &longs;ibi aduer&longs;antia di&longs;&longs;imulat: tan&shy;<lb/>dem, quod nullus adhuc au&longs;us e&longs;t, concludit Mathematicam nullam e&longs;&longs;e <lb/>Philo&longs;ophi&aelig; partem, c&ugrave;m tamen apud Ari&longs;t. </s> 
  
 <s>&amp; omnes peripateticos nihil <lb/>frequentius occurrat, quam tres e&longs;&longs;e philo&longs;ophi&aelig; partes, Phy&longs;icam, Mathe&shy;<lb/>maticam, &amp; Metaphy&longs;icam. </s> 
  
 <s>ait pr&aelig;terea &longs;&aelig;pius certitudinem Mathemati&shy;<lb/>cam ex eo prouenire, quod ad &longs;en&longs;um o&longs;tendant, &longs;eu quod &longs;en&longs;u ip&longs;arum ve&shy;<lb/>ritates percipiantur; quod omnin&ograve; fal&longs;um e&longs;&longs;e &longs;&aelig;pius &longs;upra probatum e&longs;t, <lb/>c&ugrave;m eorum materia &longs;it omnin&ograve; intelligibilis, non autem &longs;en&longs;ibilis, &amp; nullus <lb/>e&longs;t, qui eas, vel leuiter attigerit, qu&igrave; i&longs;tud pal&agrave;m non fateatur.</s></p><p type="main"> <s>ait pr&aelig;terea &longs;&aelig;pius certitudinem Mathemati&shy;<lb/>cam ex eo prouenire, quod ad &longs;en&longs;um o&longs;tendant, &longs;eu quod &longs;en&longs;u ip&longs;arum ve&shy;<lb/>ritates percipiantur; quod omnin&ograve; fal&longs;um e&longs;&longs;e &longs;&aelig;pius &longs;upra probatum e&longs;t, <lb/>c&ugrave;m eorum materia &longs;it omnin&ograve; intelligibilis, non autem &longs;en&longs;ibilis, &amp; nullus <lb/>e&longs;t, qui eas, vel leuiter attigerit, qu&igrave; i&longs;tud pal&agrave;m non fateatur.</s></p><p type="main">
  
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 <s>Finis &longs;cienti&aelig; e&longs;t <lb/>veritas. </s> <s>Finis &longs;cienti&aelig; e&longs;t <lb/>veritas. </s>
  
 <s>quod &amp; Plato confirmat, dum in Sympo&longs;io a&longs;&longs;erit, animi cibum e&longs;&shy;<lb/>&longs;e veritatem, atqui Geometria, &amp; Arithmetica, c&ugrave;m &longs;emper euidentiam <lb/>pariant, &longs;emper etiam veritatem con&longs;equentur, vnde Ari&longs;t. </s> <s>quod &amp; Plato confirmat, dum in Sympo&longs;io a&longs;&longs;erit, animi cibum e&longs;&shy;<lb/>&longs;e veritatem, atqui Geometria, &amp; Arithmetica, c&ugrave;m &longs;emper euidentiam <lb/>pariant, &longs;emper etiam veritatem con&longs;equentur, vnde Ari&longs;t. 1. Ethic. </s>
  
 <s>1. Ethic. </s> 
  
 <s>cap.  <s>cap.
  
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 <s>non dee&longs;t tamen Ari&longs;t.  <s>non dee&longs;t tamen Ari&longs;t.
  
 authoritas 1. Po&longs;ter. </s> authoritas 1. Po&longs;ter. tex. </s>
  
 <s>tex. </s> 
  
 <s>30. a&longs;&longs;erentis eas <lb/>habere cau&longs;as demon&longs;trationum, &longs;ic. </s> <s>30. a&longs;&longs;erentis eas <lb/>habere cau&longs;as demon&longs;trationum, &longs;ic. </s>
  
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 <s>Porr&ograve; inter practicas omnium pr&aelig;&longs;tanti&longs;&longs;i&shy;<lb/>ma e&longs;t Geometria practica; quis enim non admiratur, c&ugrave;m audit Geome&shy;<lb/>tram &longs;olo vi&longs;u inacce&longs;&longs;as etiam magnitudines qua&longs;cunque, vt turres, vel <lb/>montes men&longs;urare?</s></p><p type="main"> <s>Porr&ograve; inter practicas omnium pr&aelig;&longs;tanti&longs;&longs;i&shy;<lb/>ma e&longs;t Geometria practica; quis enim non admiratur, c&ugrave;m audit Geome&shy;<lb/>tram &longs;olo vi&longs;u inacce&longs;&longs;as etiam magnitudines qua&longs;cunque, vt turres, vel <lb/>montes men&longs;urare?</s></p><p type="main">
  
 <s>Ex quibus liquid&ograve; con&longs;tant Mathematicas habere perfecti&longs;&longs;imas <expan abbr="dom&otilde;-&longs;trationes">domon&shy;<lb/>&longs;trationes</expan>, quarum cau&longs;&ecedil; ita ab effectu di&longs;tinguntur, vt nullis calumnijs &longs;int <lb/>obnoxi&aelig;: quare etiam &longs;i aduer&longs;arij conuincant, qu&ograve;d neutiquam faciunt, <lb/>Geometriam, &amp; Arithmeticam illis carere; reliquis tamen pr&aelig;dictis con&shy;<lb/>cedere coguntur: <expan abbr="eas&qacute;">easque</expan>; per omne <expan abbr="cau&longs;ar&utilde;">cau&longs;arum</expan> genus excurrere, qu&ograve;d tan&shy;<lb/>ta pr&aelig;terea euidentia pr&aelig;&longs;tant, vt nibl ambiguum, nihil contro&shy;<lb/>uer&longs;um relinquatur: Mathematic&ecedil; <expan abbr="namq;">namque</expan> te&longs;te etiam Ari&longs;t. <lb/></s> <s>Ex quibus liquid&ograve; con&longs;tant Mathematicas habere perfecti&longs;&longs;imas <expan abbr="dom&otilde;-&longs;trationes">domon&shy;<lb/>&longs;trationes</expan>, quarum cau&longs;&ecedil; ita ab effectu di&longs;tinguntur, vt nullis calumnijs &longs;int <lb/>obnoxi&aelig;: quare etiam &longs;i aduer&longs;arij conuincant, qu&ograve;d neutiquam faciunt, <lb/>Geometriam, &amp; Arithmeticam illis carere; reliquis tamen pr&aelig;dictis con&shy;<lb/>cedere coguntur: <expan abbr="eas&qacute;">easque</expan>; per omne <expan abbr="cau&longs;ar&utilde;">cau&longs;arum</expan> genus excurrere, qu&ograve;d tan&shy;<lb/>ta pr&aelig;terea euidentia pr&aelig;&longs;tant, vt nibl ambiguum, nihil contro&shy;<lb/>uer&longs;um relinquatur: Mathematic&ecedil; <expan abbr="namq;">namque</expan> te&longs;te etiam Ari&longs;t. <lb/>1. Elenchorum non &longs;unt contentio&longs;&aelig;. </s>
  
 <s>1. Elenchorum non &longs;unt contentio&longs;&aelig;. </s> 
  
 <s>Vnde &longs;it, vt to&shy;<lb/>ta h&aelig;c ade&ograve; digna, <expan abbr="atq;">atque</expan> admiranda cognitio &longs;it <lb/>mera veritas, qu&aelig; omnium &longs;cientiarum finis <lb/>atque anim&aelig; no&longs;tr&aelig; cibus e&longs;t.</s></p><p type="head"> <s>Vnde &longs;it, vt to&shy;<lb/>ta h&aelig;c ade&ograve; digna, <expan abbr="atq;">atque</expan> admiranda cognitio &longs;it <lb/>mera veritas, qu&aelig; omnium &longs;cientiarum finis <lb/>atque anim&aelig; no&longs;tr&aelig; cibus e&longs;t.</s></p><p type="head">
  
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 <s>3. lib.  <s>3. lib.
  
 5. Metaph. </s> 5. Metaph.
  
 <s>quem &longs;upra <expan abbr="c&utilde;">cum</expan> alijs <expan abbr="ex-plicat&utilde;">ex&shy;<lb/>plicatum</expan> habes. </s> quem &longs;upra <expan abbr="c&utilde;">cum</expan> alijs <expan abbr="ex-plicat&utilde;">ex&shy;<lb/>plicatum</expan> habes. </s>
  
 <s>&longs;ecund&ograve;, demon&longs;trat de eodem I&longs;o&longs;cele, angulos infra ba&longs;im <lb/>e&longs;&longs;e &aelig;quales, ratio, quia opponuntur &ecedil;qualibus lateribus <expan abbr="triangulor&utilde;">triangulorum</expan> quar&shy;<lb/>t&aelig; pr&aelig;cedentis, qu&aelig; ratio videtur &longs;ignum quoddam &aelig;qualitatis eorum e&longs;&longs;e.</s></p><p type="main"> <s>&longs;ecund&ograve;, demon&longs;trat de eodem I&longs;o&longs;cele, angulos infra ba&longs;im <lb/>e&longs;&longs;e &aelig;quales, ratio, quia opponuntur &ecedil;qualibus lateribus <expan abbr="triangulor&utilde;">triangulorum</expan> quar&shy;<lb/>t&aelig; pr&aelig;cedentis, qu&aelig; ratio videtur &longs;ignum quoddam &aelig;qualitatis eorum e&longs;&longs;e.</s></p><p type="main">
  
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 <s>qu&agrave;m fu&longs;i&longs;&longs;im&egrave; explicaui &longs;upra ad tex. </s> <s>qu&agrave;m fu&longs;i&longs;&longs;im&egrave; explicaui &longs;upra ad tex. </s>
  
 <s>23. primi <lb/>Po&longs;ter. </s> <s>23. primi <lb/>Po&longs;ter. vbi Ari&longs;t.
  
 <s>vbi Ari&longs;t.  
  
 eam in exemplum perfecti&longs;&longs;im&aelig; demon&longs;trationis adducit.</s></p><p type="main"> eam in exemplum perfecti&longs;&longs;im&aelig; demon&longs;trationis adducit.</s></p><p type="main">
  
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 <s>cap.  <s>cap.
  
 5. de natura Mathem. </s> 5. de natura Mathem. patuit. </s>
  
 <s>patuit. </s> 
  
 <s>Et quamuis &longs;&ecedil;p&egrave; demon&longs;trent ab effe&shy;<lb/>ctu, perpetu&ograve; tamen cuidentiam efficiunt eam, vt nullam, vt ait Themi&longs;tius, <lb/>patiantur in&longs;tantiam.</s></p><p type="main"> <s>Et quamuis &longs;&ecedil;p&egrave; demon&longs;trent ab effe&shy;<lb/>ctu, perpetu&ograve; tamen cuidentiam efficiunt eam, vt nullam, vt ait Themi&longs;tius, <lb/>patiantur in&longs;tantiam.</s></p><p type="main">
  
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 <s>&longs;ph&aelig;ram con&longs;truxit. </s> <s>&longs;ph&aelig;ram con&longs;truxit. </s>
  
 <s>Plin. </s> <s>Plin. Laert.</s></p><p type="main">
  
 <s>Laert.</s></p><p type="main"> 
  
 <s>CLEOSTRATVS Zodiacum in 12. &longs;igna diui&longs;it. </s> <s>CLEOSTRATVS Zodiacum in 12. &longs;igna diui&longs;it. </s>
  
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 <s>HIPPOCRATES CHIVS, qui dum circulum quadrare conare&shy;<lb/>tur, lunulam quadrauit. </s> <s>HIPPOCRATES CHIVS, qui dum circulum quadrare conare&shy;<lb/>tur, lunulam quadrauit. </s>
  
 <s>eius circuli quadraturam Ari&longs;t. </s> <s>eius circuli quadraturam Ari&longs;t. &longs;&aelig;p&egrave; in paralogi&longs;mi <lb/>exemplum adducit, <expan abbr="eam&qacute;">eamque</expan>; breuiter expo&longs;uit. </s>
  
 <s>&longs;&aelig;p&egrave; in paralogi&longs;mi <lb/>exemplum adducit, <expan abbr="eam&qacute;">eamque</expan>; breuiter expo&longs;uit. </s> 
  
 <s>primus Elementa Geometri&shy;<lb/>ca con&longs;crip&longs;it. </s> <s>primus Elementa Geometri&shy;<lb/>ca con&longs;crip&longs;it. </s>
  
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 <s>PHRINICVS, cuius Ari&longs;t.  <s>PHRINICVS, cuius Ari&longs;t.
  
 in Problem. </s> in Problem. mu&longs;icis cecinit: in&longs;ignis mu&shy;<lb/>&longs;icus, ac tetrametri carminis inuentor.</s></p><p type="main">
  
 <s>mu&longs;icis cecinit: in&longs;ignis mu&shy;<lb/>&longs;icus, ac tetrametri carminis inuentor.</s></p><p type="main"> 
  
 <s>LASVS HERMIN&AElig;VS primus omnium de Mu&longs;ica &longs;crip&longs;it. </s> <s>LASVS HERMIN&AElig;VS primus omnium de Mu&longs;ica &longs;crip&longs;it. </s>
  
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 <s>EPICVRVS ille Epicureorum Sectarius, de Mu&longs;ica &longs;crip&longs;it.</s></p><p type="main"> <s>EPICVRVS ille Epicureorum Sectarius, de Mu&longs;ica &longs;crip&longs;it.</s></p><p type="main">
  
 <s>METON, &amp; EVCTEMON ante Alex. </s> <s>METON, &amp; EVCTEMON ante Alex. Mag. obitum ann. </s>
  
 <s>Mag. </s> 
  
 <s>obitum ann. </s> 
  
 <s>108. Athenis &longs;ol&longs;ti&shy;<lb/>tium ob&longs;eruarunt. </s> <s>108. Athenis &longs;ol&longs;ti&shy;<lb/>tium ob&longs;eruarunt. </s>
  
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 <s><emph type="italics"/>SEXTVM SECVLVM INCIPIENS<emph.end type="italics"/><lb/><arrow.to.target n="table12"></arrow.to.target></s></p><table><table.target id="table12"></table.target><row><cell>Ab Vrbe cond. ann.</cell><cell>401</cell></row><row><cell>Ante Chri&longs;ti Natiuitatem ann.</cell><cell>352</cell></row><row><cell>Tito Manlio Dictatore.</cell><cell></cell></row></table><p type="main"> <s><emph type="italics"/>SEXTVM SECVLVM INCIPIENS<emph.end type="italics"/><lb/><arrow.to.target n="table12"></arrow.to.target></s></p><table><table.target id="table12"></table.target><row><cell>Ab Vrbe cond. ann.</cell><cell>401</cell></row><row><cell>Ante Chri&longs;ti Natiuitatem ann.</cell><cell>352</cell></row><row><cell>Tito Manlio Dictatore.</cell><cell></cell></row></table><p type="main">
  
 <s><emph type="italics"/>In quo Alex. </s> <s><emph type="italics"/>In quo Alex. Mag. imperauit: <expan abbr="obijt&qacute;">obijtque</expan>; ann. </s>
  
 <s>Mag. </s> 
  
 <s>imperauit: <expan abbr="obijt&qacute;">obijtque</expan>; ann. </s> 
  
 <s>ab Orbe cond. </s> <s>ab Orbe cond. </s>
  
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 <s>ARISTOT. </s> <s>ARISTOT. </s>
  
 <s>Platonis auditor, &amp; Alex. </s> <s>Platonis auditor, &amp; Alex. Magn. </s>
  
 <s>Magn. </s> 
  
 <s>pr&aelig;ceptor, &longs;crip&longs;it Me&shy;<lb/>chanicas qu&aelig;&longs;tiones. </s> <s>pr&aelig;ceptor, &longs;crip&longs;it Me&shy;<lb/>chanicas qu&aelig;&longs;tiones. </s>
  
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 <s>de mu&longs;ic.</s></p><p type="main"> <s>de mu&longs;ic.</s></p><p type="main">
  
 <s>ARCHELAVS Chorographus, omnem terram ab Alex. </s> <s>ARCHELAVS Chorographus, omnem terram ab Alex. Mag. pera&shy;<lb/>gratam de&longs;crip&longs;it. </s>
  
 <s>Mag. </s> 
  
 <s>pera&shy;<lb/>gratam de&longs;crip&longs;it. </s> 
  
 <s>Diog Laert.</s></p><p type="main"> <s>Diog Laert.</s></p><p type="main">
  
 <s>XENOPHANTVS Mu&longs;icus, certis modis Alex. </s> <s>XENOPHANTVS Mu&longs;icus, certis modis Alex. Magn. </s>
  
 <s>Magn. </s> 
  
 <s>ad arma pro <lb/>libito concitabat.</s></p><p type="main"> <s>ad arma pro <lb/>libito concitabat.</s></p><p type="main">
  
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 <s>156. ab obitu ver&ograve; Alexan. <lb/></s> <s>156. ab obitu ver&ograve; Alexan. <lb/></s>
  
 <s>Mag. </s> <s>Mag. ann. </s>
  
 <s>ann. </s> 
  
 <s>41. &longs;uas ob&longs;eruationes habuit, quas Ptol&aelig;meus in Almage&longs;to re&shy;<lb/>cen&longs;et. </s> <s>41. &longs;uas ob&longs;eruationes habuit, quas Ptol&aelig;meus in Almage&longs;to re&shy;<lb/>cen&longs;et. </s>
  
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 <s>L. Po&longs;thumio.</s></p><p type="main"> <s>L. Po&longs;thumio.</s></p><p type="main">
  
 <s>ERATOSTHENES Cyreneus &longs;ub Ptolym&aelig;o Euergete primo, &amp; <lb/>duobus &longs;equentibus regibus, ab obitu Alex. </s> <s>ERATOSTHENES Cyreneus &longs;ub Ptolym&aelig;o Euergete primo, &amp; <lb/>duobus &longs;equentibus regibus, ab obitu Alex. ann. </s>
  
 <s>ann. </s> 
  
 <s>90. &amp; totidem an&shy;<lb/>te Hipparchum, a&longs;tronomicis in Aegypto vacabat, <expan abbr="reperit&qacute;">reperitque</expan>; Solis <lb/>declinationem gr. </s> <s>90. &amp; totidem an&shy;<lb/>te Hipparchum, a&longs;tronomicis in Aegypto vacabat, <expan abbr="reperit&qacute;">reperitque</expan>; Solis <lb/>declinationem gr. </s>
  
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 <s>Aemilius Per&longs;en Regem &longs;upe&shy;<lb/>raret, animos militum ob futuram &longs;equenti die eclyp&longs;im trepidaturos, bre&shy;<lb/>ui futuri euentus, admonitione habita, confirmauit. </s> <s>Aemilius Per&longs;en Regem &longs;upe&shy;<lb/>raret, animos militum ob futuram &longs;equenti die eclyp&longs;im trepidaturos, bre&shy;<lb/>ui futuri euentus, admonitione habita, confirmauit. </s>
  
 <s>Plin. </s> <s>Plin. Val. </s>
  
 <s>Val. </s> 
  
 <s>Max.</s></p><p type="head"> <s>Max.</s></p><p type="head">
  
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 <s>primus igitur &longs;tellas numerauit, <expan abbr="&longs;uis&qacute;">&longs;uisque</expan>; locis a&longs;&longs;ignauit, organis <lb/>ad id excogitatis. </s> <s>primus igitur &longs;tellas numerauit, <expan abbr="&longs;uis&qacute;">&longs;uisque</expan>; locis a&longs;&longs;ignauit, organis <lb/>ad id excogitatis. </s>
  
 <s>Plin. </s> <s>Plin. Scrip&longs;it de motu Lun&aelig; in latitudinem, &amp; de Arati <lb/>ph&aelig;nomenis. </s>
  
 <s>Scrip&longs;it de motu Lun&aelig; in latitudinem, &amp; de Arati <lb/>ph&aelig;nomenis. </s> 
  
 <s>ex Suida. </s> <s>ex Suida. </s>
  
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 <s>&longs;pectandum <lb/>propo&longs;uit. </s> <s>&longs;pectandum <lb/>propo&longs;uit. </s>
  
 <s>Plin. </s> <s>Plin. lib.
  
 <s>lib.  
  
 3. cap.  3. cap.
  
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 <s>fuit Pappi &longs;yncronus.</s></p><p type="main"> <s>fuit Pappi &longs;yncronus.</s></p><p type="main">
  
 <s>HYPATIA Theonis Geometr&aelig; filia Alex. </s> <s>HYPATIA Theonis Geometr&aelig; filia Alex. Diophantis Arithmeticam <lb/>comment. </s>
  
 <s>Diophantis Arithmeticam <lb/>comment. </s> 
  
 <s>illu&longs;trauit. </s> <s>illu&longs;trauit. </s>
  
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 <s>A&longs;trolabium, Per&longs;pe&shy;<lb/>ctiuam, omnia probati&longs;&longs;ima, &amp; proprio marte adinuenta. </s> <s>A&longs;trolabium, Per&longs;pe&shy;<lb/>ctiuam, omnia probati&longs;&longs;ima, &amp; proprio marte adinuenta. </s>
  
 <s>Po&longs;thuma &longs;unt <lb/>Problem. </s> <s>Po&longs;thuma &longs;unt <lb/>Problem. a&longs;tron. </s>
  
 <s>a&longs;tron. </s> 
  
 <s>&amp; opus de Cochlea.</s></p><p type="main"> <s>&amp; opus de Cochlea.</s></p><p type="main">
  
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 <s>Zetetica: &amp; alia nonnulla.</s></p><p type="main"> <s>Zetetica: &amp; alia nonnulla.</s></p><p type="main">
  
 <s>SIMON STEVINIVS Brugen&longs;is, edidit Problem. </s> <s>SIMON STEVINIVS Brugen&longs;is, edidit Problem. Geometric. </s>
  
 <s>Geometric. </s> 
  
 <s>lib.  <s>lib.
  

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