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version 1.14, 2002/08/06 17:19:52 version 1.59, 2002/08/18 16:37:00
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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><emph type="italics"/>Cap.  <s><emph type="italics"/>Cap.
  
 24. &longs;ecti 1. lib. </s> 24. &longs;ecti 1. lib.
  
 <s>1. de De&longs;criptionibus.<emph.end type="italics"/></s></p><p type="main"> 1. de De&longs;criptionibus.<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Cap.  <s><emph type="italics"/>Cap.
  
 2. &longs;ect 2. lib. </s> 2. &longs;ect 2. lib.
  
 <s>1. de De&longs;criptionibus.<emph.end type="italics"/></s></p><p type="main"> 1. de De&longs;criptionibus.<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Cap.  <s><emph type="italics"/>Cap.
  
 3. &longs;ecti 2. lib. </s> 3. &longs;ecti 2. lib.
  
 <s>1. de Incommen&longs;urabili.<emph.end type="italics"/></s></p><p type="main"> 1. de Incommen&longs;urabili.<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Cap.  <s><emph type="italics"/>Cap.
  
 1. &longs;ecti 3. lib. </s> 1. &longs;ecti 3. lib.
  
 <s>1. de eo, quod est, omnis triangulus habet tres angulos &aelig;quales <lb/>&aelig;quales duobus rectis: Aequalitas Geometrica, qu&aelig;.<emph.end type="italics"/></s></p><p type="main"> 1. de eo, quod est, omnis triangulus habet tres angulos &aelig;quales <lb/>&aelig;quales duobus rectis: Aequalitas Geometrica, qu&aelig;.<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Cap.  <s><emph type="italics"/>Cap.
  
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 4. loco 86. Elementa geometrica: Numeri capitales.<emph.end type="italics"/></s></p><p type="head"> 4. loco 86. Elementa geometrica: Numeri capitales.<emph.end type="italics"/></s></p><p type="head">
  
 <s>In Elenchorum lib. </s> <s>In Elenchorum lib.
  
 <s>1.</s></p><p type="main"> 1.</s></p><p type="main">
  
 <s><emph type="italics"/>Cap.  <s><emph type="italics"/>Cap.
  
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 <s>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">
  
 <s><emph type="italics"/>Summa prima cap. </s> <s><emph type="italics"/>Summa prima cap.
  
 <s>3. De magnitudine Terr&aelig; ad a&longs;tra, &amp; &longs;olem collata.<emph.end type="italics"/></s></p><p type="main"> 3. De magnitudine Terr&aelig; ad a&longs;tra, &amp; &longs;olem collata.<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Cap.  <s><emph type="italics"/>Cap.
  
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 4. De ordine Luminarium Solis, &amp; Lun&aelig;.<emph.end type="italics"/></s></p><p type="main"> 4. De ordine Luminarium Solis, &amp; Lun&aelig;.<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Summa 2. cap. </s> <s><emph type="italics"/>Summa 2. cap.
  
 <s>3. de Mercurij stella. </s> 3. de Mercurij stella. </s>
  
 <s>Item de Cometa: e&longs;&longs;e in C&oelig;lo.<emph.end type="italics"/></s></p><p type="main"> <s>Item de Cometa: e&longs;&longs;e in C&oelig;lo.<emph.end type="italics"/></s></p><p type="main">
  
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 <s>Ex 2. Meteororum.</s></p><p type="main"> <s>Ex 2. Meteororum.</s></p><p type="main">
  
 <s><emph type="italics"/>Summa 1. cap. </s> <s><emph type="italics"/>Summa 1. cap.
  
 <s>1. De Marirubro.<emph.end type="italics"/></s></p><p type="main"> 1. De Marirubro.<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Summa 2. cap. </s> <s><emph type="italics"/>Summa 2. cap.
  
 <s>2. De ortu stellarum fixarum: Item de occa&longs;u earumdem.<emph.end type="italics"/></s></p><p type="main"> 2. De ortu stellarum fixarum: Item de occa&longs;u earumdem.<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Cap.  <s><emph type="italics"/>Cap.
  
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 <s>Ex 3. Meteor.</s></p><p type="main"> <s>Ex 3. Meteor.</s></p><p type="main">
  
 <s><emph type="italics"/>Summa 2. cap. </s> <s><emph type="italics"/>Summa 2. cap.
  
 <s>2. De Halone, &longs;eu Area, &longs;eu Corona, Mathematica demon&longs;iratio.<emph.end type="italics"/></s></p><p type="main"> 2. De Halone, &longs;eu Area, &longs;eu Corona, Mathematica demon&longs;iratio.<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Cap.  <s><emph type="italics"/>Cap.
  
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 <s>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>Diameter incommen&longs;.<emph.end type="italics"/></s></p><p type="main"> <s>Diameter incommen&longs;.<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Summa 2. cap. </s> <s><emph type="italics"/>Summa 2. cap.
  
 <s>3. Pythagorei Mathematicas c&aelig;teris pr&aelig;ferebant.<emph.end type="italics"/></s></p><p type="main"> 3. Pythagorei Mathematicas c&aelig;teris pr&aelig;ferebant.<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>T. 47. Geometria habet &longs;uas pr&aelig;cognitiones.<emph.end type="italics"/></s></p><p type="head"> <s><emph type="italics"/>T. 47. Geometria habet &longs;uas pr&aelig;cognitiones.<emph.end type="italics"/></s></p><p type="head">
  
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 <s>Tetragoni&longs;mus est inuentio medi&aelig;.<emph.end type="italics"/></s></p><pb pagenum="16"/><p type="main"> <s>Tetragoni&longs;mus est inuentio medi&aelig;.<emph.end type="italics"/></s></p><pb pagenum="16"/><p type="main">
  
 <s><emph type="italics"/>Tex. </s> <s><emph type="italics"/>Tex. 8. Geod&aelig;&longs;ia quid.<emph.end type="italics"/></s></p><p type="head">
  
 <s>8. Geod&aelig;&longs;ia quid.<emph.end type="italics"/></s></p><p type="head"> 
  
 <s>Ex 4. Methaphy&longs;.</s></p><p type="main"> <s>Ex 4. Methaphy&longs;.</s></p><p type="main">
  
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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"/>16. Idem ex contactu circuli cum linea recta.<emph.end type="italics"/></s></p><p type="head"> <s><emph type="italics"/>16. Idem ex contactu circuli cum linea recta.<emph.end type="italics"/></s></p><p type="head">
  
 <s>Ex lib. </s> <s>Ex lib.
  
 <s>9. Hi&longs;tori&aelig; Animalium.</s></p><p type="main"> 9. Hi&longs;tori&aelig; Animalium.</s></p><p type="main">
  
 <s><emph type="italics"/>Cap.  <s><emph type="italics"/>Cap.
  
 39. error Ari&longs;t. </s> 39. error Ari&longs;t. &amp; noua ob&longs;eruatio de admiranda quadam Aranearum indu&longs;tria.<emph.end type="italics"/></s></p><p type="head">
  
 <s>&amp; noua ob&longs;eruatio de admiranda quadam Aranearum indu&longs;tria.<emph.end type="italics"/></s></p><p type="head"> 
  
 <s>De Ince&longs;&longs;u Animal.</s></p><p type="main"> <s>De Ince&longs;&longs;u Animal.</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. </s> 
  
 <s>1. Automata.<emph.end type="italics"/></s></p><p type="main"> 
  
 <s><emph type="italics"/>Lib. </s> 1. Automata.<emph.end type="italics"/></s></p><p type="main">
  
 <s>2. cap. </s> <s><emph type="italics"/>Lib. 2. cap.
  
 <s>4. Omnis triangulus habet tres, &amp;c. </s> 4. Omnis triangulus habet tres, &amp;c. </s>
  
 <s>Ibidem Diametrum e&longs;&longs;e incommen&shy;<lb/>&longs;urabilem co&longs;t&aelig;, habet cau&longs;am, &amp; demon&longs;trationem.<emph.end type="italics"/></s></p><p type="head"> <s>Ibidem Diametrum e&longs;&longs;e incommen&shy;<lb/>&longs;urabilem co&longs;t&aelig;, habet cau&longs;am, &amp; demon&longs;trationem.<emph.end type="italics"/></s></p><p type="head">
  
 <s>In Ethicis ad Nicom.</s></p><p type="main"> <s>In Ethicis ad Nicom.</s></p><p type="main">
  
 <s><emph type="italics"/>Lib. </s> <s><emph type="italics"/>Lib. 1. cap.
  
 <s>1. cap. </s> 
  
 <s>7. Faber, &amp; Geometra diuers&egrave; con&longs;iderant angulum rectum.<emph.end type="italics"/></s></p><p type="main"> 
  
 <s><emph type="italics"/>Lib. </s> 
  
 <s>2. cap. </s> 7. Faber, &amp; Geometra diuers&egrave; con&longs;iderant angulum rectum.<emph.end type="italics"/></s></p><p type="main">
  
 <s>6. De Arithmetica proportione.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Lib. 2. cap.
  
 <s><emph type="italics"/>cap. </s> 6. De Arithmetica proportione.<emph.end type="italics"/></s></p><p type="main">
  
 <s>9. Centrum circuli reperire.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>cap.
  
 <s><emph type="italics"/>Lib. </s> 9. Centrum circuli reperire.<emph.end type="italics"/></s></p><p type="main">
  
 <s>3. cap. </s> <s><emph type="italics"/>Lib. 3. cap. 3. Diameter, &amp; latus incommen&longs;urabilis: Item quid re&longs;olutio Geome&shy;<lb/>trica: Quid de&longs;ignatio.<emph.end type="italics"/></s></p><p type="main">
  
 <s>3. Diameter, &amp; latus incommen&longs;urabilis: Item quid re&longs;olutio Geome&shy;<lb/>trica: Quid de&longs;ignatio.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Lib. 5. cap.
  
 <s><emph type="italics"/>Lib. </s> 3. Vnitarius numerus. </s>
  
 <s>5. cap. </s> 
  
 <s>3. Vnitarius numerus. </s> 
  
 <s>Quid Proportionalitas. </s> <s>Quid Proportionalitas. </s>
  
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Line 1091 
  
 <s>Propor&shy;<lb/>tio continuata, &amp; di&longs;iuncta quid.<emph.end type="italics"/></s></p><p type="main"> <s>Propor&shy;<lb/>tio continuata, &amp; di&longs;iuncta quid.<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>cap. </s> <s><emph type="italics"/>cap.
  
 <s>6. Proportio Geometrica, &amp; Arithmetica.<emph.end type="italics"/></s></p><p type="main"> 
  
 <s><emph type="italics"/>Lib. </s> 6. Proportio Geometrica, &amp; Arithmetica.<emph.end type="italics"/></s></p><p type="main">
  
 <s>6. cap. </s> <s><emph type="italics"/>Lib. 6. cap.
  
 <s>5. Omnis triangulus, &amp;c.<emph.end type="italics"/></s></p><p type="main"> 5. Omnis triangulus, &amp;c.<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>cap. </s> <s><emph type="italics"/>cap.
  
 <s>8. Principia Mathematica non pendere ab experientia.<emph.end type="italics"/></s></p><p type="main"> 8. Principia Mathematica non pendere ab experientia.<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Lib. </s> <s><emph type="italics"/>Lib. 7. cap. 8. De principijs Mathem.<emph.end type="italics"/></s></p><p type="head">
  
 <s>7. cap. </s> 
  
 <s>8. De principijs Mathem.<emph.end type="italics"/></s></p><p type="head"> 
  
 <s>Ex 1. Magnorum Moralium.</s></p><p type="main"> <s>Ex 1. Magnorum Moralium.</s></p><p type="main">
  
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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>
  
Line 1552 
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 <s>Mecha&shy;<lb/>nic. </s> <s>Mecha&shy;<lb/>nic. </s>
  
 <s>&amp; cap. </s> <s>&amp; cap.
  
 <s>7. lib. </s> 7. lib.
  
 <s>1. Eth.</s></p><p type="main"> 1. Eth.</s></p><p type="main">
  
 <s>Ad axioma 10. quamuis Ari&longs;toteles nihil hac de re dicat; &longs;cias tamen velim <lb/>hoc vno axiomate qu&ecedil;&longs;tionem <expan abbr="qu&atilde;dam">quandam</expan> inter Philo&longs;ophos vald&egrave; difficilem, <lb/>facile di&longs;&longs;olui. </s> <s>Ad axioma 10. quamuis Ari&longs;toteles nihil hac de re dicat; &longs;cias tamen velim <lb/>hoc vno axiomate qu&ecedil;&longs;tionem <expan abbr="qu&atilde;dam">quandam</expan> inter Philo&longs;ophos vald&egrave; difficilem, <lb/>facile di&longs;&longs;olui. </s>
  
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 <s>1. primi Po&longs;ter.</s></p><p type="main"> <s>1. primi Po&longs;ter.</s></p><p type="main">
  
 <s>Ad primam primi, po&longs;t ip&longs;ius explicationem, commod&egrave; declarari pote&longs;t, cur <lb/>Ari&longs;t. </s> <s>Ad primam primi, po&longs;t ip&longs;ius explicationem, commod&egrave; declarari pote&longs;t, cur <lb/>Ari&longs;t. Demon&longs;trationes Geometricas appellet De&longs;criptiones, &amp; De&longs;igna&shy;<lb/>tiones, vide cap.
  
 <s>Demon&longs;trationes Geometricas appellet De&longs;criptiones, &amp; De&longs;igna&shy;<lb/>tiones, vide cap. </s> 
  
 <s>de Priori, &amp; cap. </s> de Priori, &amp; cap.
  
 <s>24. &longs;ecti primi, libri primi Priorum, &amp; <lb/>tex. </s> 24. &longs;ecti primi, libri primi Priorum, &amp; <lb/>tex. </s>
  
 <s>4. quinti Methaph. </s> <s>4. quinti Methaph. </s>
  
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 <s>20. &longs;exti Methaph. </s> <s>20. &longs;exti Methaph. </s>
  
 <s>&amp; cap. </s> <s>&amp; cap.
  
 <s>3. lib. </s> 3. lib.
  
 <s>3. Ethic. <lb/></s> 3. Ethic. <lb/></s>
  
 <s>Item ad primam primi, vide tex. </s> <s>Item ad primam primi, vide tex. </s>
  
 <s>7. &longs;ecundi Po&longs;ter. </s> <s>7. &longs;ecundi Po&longs;ter. loco 2.</s></p><p type="main">
  
 <s>loco 2.</s></p><p type="main"> <s>Ad 5. primi, vide cap.
  
 <s>Ad 5. primi, vide cap. </s> 24. &longs;ecti 1 lib.
  
 <s>24. &longs;ecti 1 lib. </s> 1. Priorum.</s></p><p type="main">
  
 <s>1. Priorum.</s></p><p type="main"> 
  
 <s>Ad 21. primi, vide tex. </s> <s>Ad 21. primi, vide tex. </s>
  
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 <s>Ad 22. primi, vide locum 10. de lineis in&longs;ecabilibus.</s></p><p type="main"> <s>Ad 22. primi, vide locum 10. de lineis in&longs;ecabilibus.</s></p><p type="main">
  
 <s>Ad 28. primi, vide cap. </s> <s>Ad 28. primi, vide cap.
  
 <s>21. &amp; cap. </s> 21. &amp; cap.
  
 <s>22. &longs;ecundi <expan abbr="Prior&utilde;">Priorum</expan>, &amp; tex. </s> 22. &longs;ecundi <expan abbr="Prior&utilde;">Priorum</expan>, &amp; tex. </s>
  
 <s>13. primi Po&longs;ter.</s></p><p type="main"> <s>13. primi Po&longs;ter.</s></p><p type="main">
  
 <s>Ad 32. primi, vide cap. </s> <s>Ad 32. primi, vide cap.
  
 <s>1. &longs;ecti 3. lib. </s> 
  
 <s>1. Prior. </s> 1. &longs;ecti 3. lib.
  
 <s>&amp; cap. </s> 1. Prior. </s>
  
 <s>26. &longs;ecundi <expan abbr="Prior&utilde;">Priorum</expan>, &amp; tex. </s> <s>&amp; cap.
  
 <s>2. <lb/>primi Po&longs;ter. </s> 26. &longs;ecundi <expan abbr="Prior&utilde;">Priorum</expan>, &amp; tex. </s>
  
 <s>loco 4. &amp; tex. </s> <s>2. <lb/>primi Po&longs;ter. loco 4. &amp; tex. </s>
  
 <s>23. primi Po&longs;ter. </s> <s>23. primi Po&longs;ter. </s>
  
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 <s>&amp; tex. </s> <s>&amp; tex. </s>
  
 <s>37. primi Po&longs;ter. </s> <s>37. primi Po&longs;ter. &amp; tex. </s>
  
 <s>&amp; tex. </s> 
  
 <s>39. primi Po&longs;ter. </s> <s>39. primi Po&longs;ter. </s>
  
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 <s>&amp; tex. </s> <s>&amp; tex. </s>
  
 <s>89. &longs;e&shy;<lb/>cundi Phy&longs;. </s> <s>89. &longs;e&shy;<lb/>cundi Phy&longs;. &amp; tex. </s>
  
 <s>&amp; tex. </s> 
  
 <s>15. octaui Phy&longs;. </s> <s>15. octaui Phy&longs;. </s>
  
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 <s>tex 11. primi de Anima. </s> <s>tex 11. primi de Anima. </s>
  
 <s>&amp; cap. </s> <s>&amp; cap.
  
 <s>1. de mem. </s> 1. de mem. </s>
  
 <s>&amp; remini&longs;c. <lb/></s> <s>&amp; remini&longs;c. <lb/></s>
  
 <s>&amp; tex. </s> <s>&amp; tex. </s>
  
 <s>35. quinti Methaphy&longs;. </s> <s>35. quinti Methaphy&longs;. &amp; tex. </s>
  
 <s>&amp; tex. </s> 
  
 <s>20. &longs;exti Methaphy&longs;. </s> <s>20. &longs;exti Methaphy&longs;. </s>
  
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 <s>22. &longs;exti <lb/>Methaphy&longs;. </s> <s>22. &longs;exti <lb/>Methaphy&longs;. </s>
  
 <s>&amp; cap. </s> <s>&amp; cap.
  
 <s>4. lib. </s> 4. lib.
  
 <s>2. de Generat. </s> 2. de Generat. </s>
  
 <s>animal. </s> <s>animal. </s>
  
 <s>&amp; cap. </s> <s>&amp; cap.
  
 <s>5. lib. </s> 
  
 <s>6. Ethic. </s> 
  
 <s>&amp; <lb/>cap. </s> 
  
 <s>2. Magnorum Moral. </s> 5. lib.
  
 <s>&amp; cap. </s> 6. Ethic. </s>
  
 <s>10. Mag. </s> 
  
 <s>Moral. </s> 
  
 <s>&amp; cap. </s> <s>&amp; <lb/>cap.
  
 <s>16. Mag. </s> 2. Magnorum Moral. &amp; cap.
  
 <s>Moral. <lb/></s> 10. Mag. Moral. &amp; cap. 16. Mag. Moral. <lb/></s>
  
 <s>&amp; cap. </s> <s>&amp; cap. </s>
  
 <s>7. &longs;ecundi Eudem. </s> <s>7. &longs;ecundi Eudem. &amp; cap. </s>
  
 <s>&amp; cap. </s> 
  
 <s>12. &longs;ecundi Eudem. </s> <s>12. &longs;ecundi Eudem. </s>
  
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 <s>Ad &longs;cholion pr&aelig;cedentis 32. primi, vide tex. </s> <s>Ad &longs;cholion pr&aelig;cedentis 32. primi, vide tex. </s>
  
 <s>39. primi Po&longs;ter. </s> <s>39. primi Po&longs;ter. loco 3. Item <lb/>tex. </s>
  
 <s>loco 3. Item <lb/>tex. </s> 
  
 <s>25. &longs;ecundi Po&longs;ter. </s> <s>25. &longs;ecundi Po&longs;ter. </s>
  
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 <s><emph type="italics"/>In &longs;ecundo Elem.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>In &longs;ecundo Elem.<emph.end type="italics"/></s></p><p type="main">
  
 <s>Ad 2. definitionem 2. Gnomonis, vide cap. </s> <s>Ad 2. definitionem 2. Gnomonis, vide cap.
  
 <s>de Motu in Po&longs;tpr&aelig;dicam. </s> de Motu in Po&longs;tpr&aelig;dicam. </s>
  
 <s>Qua&shy;<lb/>dratum augetur Gnomone circumpo&longs;ito.</s></p><p type="main"> <s>Qua&shy;<lb/>dratum augetur Gnomone circumpo&longs;ito.</s></p><p type="main">
  
 <s>Ad 14. propo&longs;. </s> <s>Ad 14. propo&longs;. </s>
  
 <s>2. opportunum e&longs;t Auditores de Quadratura circuli erudire, <lb/>vide igitur cap. </s> <s>2. opportunum e&longs;t Auditores de Quadratura circuli erudire, <lb/>vide igitur cap.
  
 <s>de relatione in pr&aelig;dicam. </s> de relatione in pr&aelig;dicam. </s>
  
 <s>&amp; cap. </s> <s>&amp; cap.
  
 <s>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">
  
 <s><emph type="italics"/>In tertio Elem.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>In tertio Elem.<emph.end type="italics"/></s></p><p type="main">
  
 <s>Ad primam 3. vide cap. </s> <s>Ad primam 3. vide cap.
  
 <s>9. lib. </s> 9. lib.
  
 <s>2. Ethycorum.</s></p><p type="main"> 2. Ethycorum.</s></p><p type="main">
  
 <s>Ad 2. tertij, vide tex. </s> <s>Ad 2. tertij, vide tex. </s>
  
 <s>13. lib. </s> <s>13. lib.
  
 <s>1. de Anima. </s> 1. de Anima. </s>
  
 <s>&amp; locum 16. de lineis in&longs;ecab.</s></p><p type="main"> <s>&amp; locum 16. de lineis in&longs;ecab.</s></p><p type="main">
  
 <s>Ad 31. tertij, vide tex. </s> <s>Ad 31. tertij, vide tex. </s>
  
 <s>11. &longs;ecundi Po&longs;ter. </s> <s>11. &longs;ecundi Po&longs;ter. &amp; tex. </s>
  
 <s>&amp; tex. </s> 
  
 <s>20. &longs;exti Methaph. </s> <s>20. &longs;exti Methaph. </s>
  
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 <s>Ad commentarium P. </s> <s>Ad commentarium P. </s>
  
 <s>Clauij extremum lib. </s> <s>Clauij extremum lib.
  
 <s>4. elementorum. </s> 4. elementorum. </s>
  
 <s>lege tex. </s> <s>lege tex. </s>
  
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 <s><emph type="italics"/>In quinto.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>In quinto.<emph.end type="italics"/></s></p><p type="main">
  
 <s>Ad 4. definitionem 5. vide cap. </s> <s>Ad 4. definitionem 5. vide cap.
  
 <s>3. lib. </s> 
  
 <s>2. Ethyc.</s></p><p type="main"> 3. lib.
  
 <s>Ad 9. definitionem 5. vide cap. </s> 2. Ethyc.</s></p><p type="main">
  
 <s>3. lib. </s> <s>Ad 9. definitionem 5. vide cap.
  
 <s>5. Ethyc. </s> 3. lib.
  
 <s>loco 4. &amp; cap. </s> 5. Ethyc. </s>
  
 <s>31. primi Ma&shy;<lb/>gnorum Moralium.</s></p><p type="main"> <s>loco 4. &amp; cap. 31. primi Ma&shy;<lb/>gnorum Moralium.</s></p><p type="main">
  
 <s>Ad 10. definitionem 5. vide tex. </s> <s>Ad 10. definitionem 5. vide tex. </s>
  
 <s>29. primi Po&longs;ter. </s> <s>29. primi Po&longs;ter. loco 2.</s></p><p type="main">
  
 <s>loco 2.</s></p><p type="main"> 
  
 <s>Ad 12. definitionem 5. vide tex. </s> <s>Ad 12. definitionem 5. vide tex. </s>
  
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 <s>32. tertij de Anima. </s> <s>32. tertij de Anima. </s>
  
 <s>&amp; cap. </s> <s>&amp; cap.
  
 <s>3. lib. </s> 3. lib.
  
 <s>5. Ethyc. </s> 5. Ethyc. </s>
  
 <s>loco 4.</s></p><p type="main"> <s>loco 4.</s></p><p type="main">
  
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 <s>5. vide tex. </s> <s>5. vide tex. </s>
  
 <s>25. &longs;ecundi Po&longs;ter. </s> <s>25. &longs;ecundi Po&longs;ter. loco 2. ex hac Euclidis demon&shy;<lb/>&longs;tratione patet, vitio&longs;am e&longs;&longs;e illam Auerrois argumentationem, 8. Phy&longs;. <lb/></s>
  
 <s>loco 2. ex hac Euclidis demon&shy;<lb/>&longs;tratione patet, vitio&longs;am e&longs;&longs;e illam Auerrois argumentationem, 8. Phy&longs;. <lb/></s> 
  
 <s>comm. </s> <s>comm. </s>
  
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 <s>Ad 2. propo&longs;it. </s> <s>Ad 2. propo&longs;it. </s>
  
 <s>6. vide cap. </s> <s>6. vide cap.
  
 <s>2. lib. </s> 2. lib.
  
 <s>8. Topicorum loco 41.</s></p><p type="main"> 8. Topicorum loco 41.</s></p><p type="main">
  
 <s>Ad 13. &longs;exti, vide tex. </s> <s>Ad 13. &longs;exti, vide tex. </s>
  
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 <s>5. primi Po&longs;ter.</s></p><p type="main"> <s>5. primi Po&longs;ter.</s></p><p type="main">
  
 <s>Ad 8. definitionem 7. vide cap. </s> <s>Ad 8. definitionem 7. vide cap.
  
 <s>1. lib. </s> 1. lib.
  
 <s>1. Magnorum Moral.</s></p><p type="head"> 1. Magnorum Moral.</s></p><p type="head">
  
 <s><emph type="italics"/>In octauo.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>In octauo.<emph.end type="italics"/></s></p><p type="main">
  
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 <s>9. vide tex. </s> <s>9. vide tex. </s>
  
 <s>20. primi Po&longs;ter. </s> <s>20. primi Po&longs;ter. loco 2.</s></p><p type="main">
  
 <s>loco 2.</s></p><p type="main"> 
  
 <s>Ad 8. propo&longs;. </s> <s>Ad 8. propo&longs;. </s>
  
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 <s><emph type="italics"/>In decimo.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>In decimo.<emph.end type="italics"/></s></p><p type="main">
  
 <s>Ad primam definitionem 10. vide cap. </s> <s>Ad primam definitionem 10. vide cap.
  
 <s>23. &longs;ecti 1. primi Priorum. </s> 23. &longs;ecti 1. primi Priorum. </s>
  
 <s>&amp; tex. </s> <s>&amp; tex. </s>
  
 <s>48. <lb/>primi de C&oelig;lo.</s></p><p type="main"> <s>48. <lb/>primi de C&oelig;lo.</s></p><p type="main">
  
 <s>Ad 118. decimi, vide cap. </s> <s>Ad 118. decimi, vide cap.
  
 <s>23. &longs;ecti 1. libri 1. Priorum. </s> 
  
 <s>&amp; &longs;ecto 2. cap. </s> 23. &longs;ecti 1. libri 1. Priorum. </s>
  
 <s>23. li&shy;<lb/>bri 1. Priorum. </s> <s>&amp; &longs;ecto 2. cap.
  
 <s>&amp; cap. </s> 23. li&shy;<lb/>bri 1. Priorum. </s>
  
 <s>22. lib. </s> <s>&amp; cap. 22. lib.
  
 <s>2. Priorum. </s> 2. Priorum. </s>
  
 <s>&amp; tex. </s> <s>&amp; tex. </s>
  
 <s>5. primi Po&longs;ter. </s> <s>5. primi Po&longs;ter. &amp; tex. </s>
  
 <s>&amp; tex. </s> 
  
 <s>44. <lb/>primi Po&longs;ter. </s> <s>44. <lb/>primi Po&longs;ter. </s>
  
 <s>&amp; cap. </s> <s>&amp; cap.
  
 <s>15. primi Po&longs;ter. </s> 15. primi Po&longs;ter. </s>
  
 <s>&amp; tex. </s> <s>&amp; tex. </s>
  
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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>
  
 <s>&amp; cap. </s> <s>&amp; cap.
  
 <s>1. primi Methaphy&longs;. <lb/></s> 1. primi Methaphy&longs;. <lb/></s>
  
 <s>&amp; tex. </s> <s>&amp; tex. </s>
  
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 <s>8. &longs;exti Met. </s> <s>8. &longs;exti Met. </s>
  
 <s>&amp; cap. </s> <s>&amp; cap.
  
 <s>4. <lb/>lib. </s> 4. <lb/>lib.
  
 <s>2. de Generat. </s> 2. de Generat. </s>
  
 <s>animal. </s> <s>animal. </s>
  
 <s>&amp; lib. </s> <s>&amp; lib.
  
 <s>3. cap. </s> 
  
 <s>3. Ethyc. </s> 3. cap.
  
 <s>&amp; cap. </s> 3. Ethyc. </s>
  
 <s>10. &longs;ecundi Eu&shy;<lb/>dem. </s> <s>&amp; cap. 10. &longs;ecundi Eu&shy;<lb/>dem. </s>
  
 <s>tot Ari&longs;t.  <s>tot Ari&longs;t.
  
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 <s>Quod &longs;i in modum Problematis ita <lb/>proponatur: Dato circulo &aelig;quale quadratum con&longs;truere, nondum inuenta <lb/>e&longs;t ratio, qu&aelig; demon&longs;tratione confirmetur, qua id geometric&egrave; penitus, hoc <lb/>e&longs;t ad &aelig;qualitatem mathematicam, &longs;eu exacti&longs;&longs;imam effici po&longs;&longs;it, <expan abbr="tota&qacute;">totaque</expan>; dif&shy;<lb/>ficultas po&longs;ita e&longs;&longs;e videtur in inue&longs;tigando, quonam modo exhibeamus li&shy;<lb/>neam rectam B C, &aelig;qualem peripheri&aelig; circuli dati. </s> <s>Quod &longs;i in modum Problematis ita <lb/>proponatur: Dato circulo &aelig;quale quadratum con&longs;truere, nondum inuenta <lb/>e&longs;t ratio, qu&aelig; demon&longs;tratione confirmetur, qua id geometric&egrave; penitus, hoc <lb/>e&longs;t ad &aelig;qualitatem mathematicam, &longs;eu exacti&longs;&longs;imam effici po&longs;&longs;it, <expan abbr="tota&qacute;">totaque</expan>; dif&shy;<lb/>ficultas po&longs;ita e&longs;&longs;e videtur in inue&longs;tigando, quonam modo exhibeamus li&shy;<lb/>neam rectam B C, &aelig;qualem peripheri&aelig; circuli dati. </s>
  
 <s>quam nullus hactenus <lb/>geometric&egrave; illi &aelig;qualem potuit exhibere, <expan abbr="atq;">atque</expan> exhibita <expan abbr="euid&etilde;ti">euidenti</expan> demon&longs;tra&shy;<lb/>tione comprobare; Quamuis Archimedes acumine &longs;an&egrave; mirabili in lib. </s> <s>quam nullus hactenus <lb/>geometric&egrave; illi &aelig;qualem potuit exhibere, <expan abbr="atq;">atque</expan> exhibita <expan abbr="euid&etilde;ti">euidenti</expan> demon&longs;tra&shy;<lb/>tione comprobare; Quamuis Archimedes acumine &longs;an&egrave; mirabili in lib.
  
 <s>de <lb/>lineis &longs;piralibus, eam <expan abbr="quoq;">quoque</expan> theorematic&egrave;, non tamen problematic&egrave; inue&shy;<lb/>&longs;tigauit. </s> de <lb/>lineis &longs;piralibus, eam <expan abbr="quoq;">quoque</expan> theorematic&egrave;, non tamen problematic&egrave; inue&shy;<lb/>&longs;tigauit. </s>
  
 <s>nam propo&longs;itione 18. illius <expan abbr="admir&atilde;di">admirandi</expan> operis inuenit lineam rectam <lb/>&aelig;qualem circumferenti&aelig; primi circuli &longs;piralis line&aelig;; propo&longs; ver&ograve; 19. repe&shy;<lb/>rit aliam rectam &aelig;qualem circumferenti&aelig; &longs;ecundi circuli. </s> <s>nam propo&longs;itione 18. illius <expan abbr="admir&atilde;di">admirandi</expan> operis inuenit lineam rectam <lb/>&aelig;qualem circumferenti&aelig; primi circuli &longs;piralis line&aelig;; propo&longs; ver&ograve; 19. repe&shy;<lb/>rit aliam rectam &aelig;qualem circumferenti&aelig; &longs;ecundi circuli. </s>
  
 <s>tu ip&longs;um con&longs;ule, <lb/>&longs;i admirandarum rerum contemplatione delectaris. </s> <s>tu ip&longs;um con&longs;ule, <lb/>&longs;i admirandarum rerum contemplatione delectaris. </s>
  
 <s>Multa hac de re Pap&shy;<lb/>pus Alexandrinus lib. </s> <s>Multa hac de re Pap&shy;<lb/>pus Alexandrinus lib.
  
 <s>4. Math. </s> 
  
 <s>coll. </s> 4. Math. coll. </s>
  
 <s>&amp; Ioannes Buteo vnico volumine om&shy;<lb/>nes quadraturas tain pri&longs;corum, quam recentiorum <expan abbr="c&otilde;prehen&longs;us">comprehen&longs;us</expan> e&longs;t. </s> <s>&amp; Ioannes Buteo vnico volumine om&shy;<lb/>nes quadraturas tain pri&longs;corum, quam recentiorum <expan abbr="c&otilde;prehen&longs;us">comprehen&longs;us</expan> e&longs;t. </s>
  
 <s>Qua&shy;<lb/>re qui plura cupit, eos adeat; nos tamen infra &longs;uis locis explicabimus tres <lb/>illas celebres antiquorum Antiphontis, Bri&longs;&longs;onis, &amp; Hippocratis quadra&shy;<lb/>turas, quamuis fal&longs;as, <expan abbr="quar&utilde;">quarum</expan> &longs;&aelig;pe meminit Ari&longs;t. </s> <s>Qua&shy;<lb/>re qui plura cupit, eos adeat; nos tamen infra &longs;uis locis explicabimus tres <lb/>illas celebres antiquorum Antiphontis, Bri&longs;&longs;onis, &amp; Hippocratis quadra&shy;<lb/>turas, quamuis fal&longs;as, <expan abbr="quar&utilde;">quarum</expan> &longs;&aelig;pe meminit Ari&longs;t. &amp; alij. </s>
  
 <s>&amp; alij. </s> 
  
 <s>&longs;olet autem &agrave; non&shy;<lb/>nullis di&longs;putari, vtrum quadratura i&longs;ta problematica &longs;it po&longs;&longs;ibilis, nec ne, <lb/>cum videant eam &agrave; nemine, quamuis diu magno labore perqui&longs;itam, hacte&shy;<lb/>nus adinuentam e&longs;&longs;e. </s> <s>&longs;olet autem &agrave; non&shy;<lb/>nullis di&longs;putari, vtrum quadratura i&longs;ta problematica &longs;it po&longs;&longs;ibilis, nec ne, <lb/>cum videant eam &agrave; nemine, quamuis diu magno labore perqui&longs;itam, hacte&shy;<lb/>nus adinuentam e&longs;&longs;e. </s>
  
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 <s><margin.target id="marg2"></margin.target>2</s></p><p type="main"> <s><margin.target id="marg2"></margin.target>2</s></p><p type="main">
  
 <s>Ex cap. </s> <s>Ex cap.
  
 <s>de Priori <emph type="italics"/>(in &longs;cientijs demon&longs;tratiuis e&longs;t prius, &amp; po&longs;terius ordine, <lb/>elementa enim priora &longs;unt ijs, qu&aelig; de&longs;cribuntur, nam principia prior a &longs;unt theore&shy;<lb/>matibus ordine)<emph.end type="italics"/> verba illa, nam principia, &amp;c. </s> 
  
 <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> 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>De&longs;criptiones; nam hoc verbo, De&longs;criptiones, &longs;eu figuratio&shy;<lb/>nes, &longs;olet ip&longs;e Mathematicas Demon&longs;trationes innuere, quod in ip&longs;is figu&shy;<lb/>rationes, &amp; De&longs;criptiones adhibeantur, vt alijs locis patebit: idcirco ver&shy;<lb/>ba illa &agrave; nobis addita ex gr&aelig;co, optim &egrave; <expan abbr="pr&aelig;ced&etilde;tia">pr&aelig;cedentia</expan> exponunt, cum per ele&shy;<lb/>menta intelligantur principia, qualia funt initio Euclidis, &amp; per de&longs;criptio&shy;<lb/>nes exponant theoremata. </s> <s>qu&aelig; non &longs;unt in antiqua tran&shy;<lb/>&longs;latione de&longs;ump&longs;imus ex ca&longs;tigati&longs;&longs;imo gr&aelig;co codice editionis Francfor&shy;<lb/>dien&longs;is, propterea quod totum hunc locum declarant; &longs;unt autem i&longs;ta, <lb/><foreign lang="greek">ai/gar arxai/ pro/terai tw_n qewrhma/twn th ta/xei.</foreign> per &longs;cientias autem demon&longs;tra&shy;<lb/>tiuas intelligendas e&longs;&longs;e hoc loco ip&longs;as Mathematicas ex eo patet, quod illis <lb/>a&longs;&longs;ignet Ari&longs;t. De&longs;criptiones; nam hoc verbo, De&longs;criptiones, &longs;eu figuratio&shy;<lb/>nes, &longs;olet ip&longs;e Mathematicas Demon&longs;trationes innuere, quod in ip&longs;is figu&shy;<lb/>rationes, &amp; De&longs;criptiones adhibeantur, vt alijs locis patebit: idcirco ver&shy;<lb/>ba illa &agrave; nobis addita ex gr&aelig;co, optim &egrave; <expan abbr="pr&aelig;ced&etilde;tia">pr&aelig;cedentia</expan> exponunt, cum per ele&shy;<lb/>menta intelligantur principia, qualia 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><margin.target id="marg3"></margin.target>3</s></p><p type="main"> <s><margin.target id="marg3"></margin.target>3</s></p><p type="main">
  
 <s>Ex cap. </s> <s>Ex cap.
  
 <s>de motu <emph type="italics"/>(Quadratum augetur Gnomone circumpo&longs;ito)<emph.end type="italics"/> Gnomon vox <lb/>gr&aelig;ca inter alia &longs;ignificat in&longs;trumentum illud, quod Latini tum amu&longs;&longs;im, <lb/><figure id="fig2"></figure><lb/>tum normam appellant, Itali ver&ograve;, Squadra, ad <lb/>cuius &longs;imilitudinem Geometr&aelig; denominarunt fi&shy;<lb/>guram quandam, &longs;eu portionem cuiu&longs;uis paralle&shy;<lb/>logrammi, vt videre e&longs;t in definitione &longs;ecunda <lb/>2. elem. </s> de motu <emph type="italics"/>(Quadratum augetur Gnomone circumpo&longs;ito)<emph.end type="italics"/> Gnomon vox <lb/>gr&aelig;ca inter alia &longs;ignificat in&longs;trumentum illud, quod Latini tum amu&longs;&longs;im, <lb/><figure id="fig2"></figure><lb/>tum normam appellant, Itali ver&ograve;, Squadra, ad <lb/>cuius &longs;imilitudinem Geometr&aelig; denominarunt fi&shy;<lb/>guram quandam, &longs;eu portionem cuiu&longs;uis paralle&shy;<lb/>logrammi, vt videre e&longs;t in definitione &longs;ecunda <lb/>2. elem. </s>
  
 <s>&amp; in pr&aelig;&longs;enti figura, in qua quadratum <lb/>A B C D, circumpo&longs;ito gnomone E F G, augetur, <lb/>&amp; fit maius quadratum H B I L.</s></p><p type="main"> <s>&amp; in pr&aelig;&longs;enti figura, in qua quadratum <lb/>A B C D, circumpo&longs;ito gnomone E F G, augetur, <lb/>&amp; fit maius quadratum H B I L.</s></p><p type="main">
  
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 <s>addito numero impari. <lb/></s> <s>addito numero impari. <lb/></s>
  
 <s>quemadmodum infra 3. Phy&longs;. </s> <s>quemadmodum infra 3. Phy&longs;. tex. </s>
  
 <s>tex. </s> 
  
 <s>26. fus&egrave; explicabimus.</s></p><p type="head"> <s>26. fus&egrave; explicabimus.</s></p><p type="head">
  
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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> <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>
  
 <s>iuxta tran&longs;latio&shy;<lb/>nem Zamb<gap/>rti, &amp; Commandini; vbi etiam <expan abbr="quinq;">quinque</expan> priora theoremata, pri&shy;<lb/>m&ograve; per re&longs;olutionem, deinde per compo&longs;itionem demon&longs;trantur, qu&aelig; tan&shy;<lb/>quam per&longs;picua exempla rei propo&longs;it&aelig; in&longs;eruire po&longs;&longs;unt. </s> 
  
 <s>&longs;unt pr&aelig;terea fre&shy;<lb/>quentes huiu&longs;modi re&longs;olutiones in operibus Archimedis, Apollonij, &amp; Pap&shy;<lb/>pi. </s> <s>&longs;unt pr&aelig;terea fre&shy;<lb/>quentes huiu&longs;modi re&longs;olutiones in operibus Archimedis, Apollonij, &amp; Pap&shy;<lb/>pi. </s>
  
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 <s>Quod <lb/>porr&ograve; Ari&longs;t.  <s>Quod <lb/>porr&ograve; Ari&longs;t.
  
 ip&longs;e hanc re&longs;olutionem Mathematicam cognouerit e&longs;&longs;e medij <lb/>inqui&longs;itionem manife&longs;tum e&longs;t ex cap. </s> ip&longs;e hanc re&longs;olutionem Mathematicam cognouerit e&longs;&longs;e medij <lb/>inqui&longs;itionem manife&longs;tum e&longs;t ex cap.
  
 <s>3. lib. </s> 3. lib.
  
 <s>3. Ethyc. </s> 3. Ethyc. </s>
  
 <s>vbi &longs;ic ait <emph type="italics"/>(Qui enim <lb/>con&longs;ultat, qu&aelig;rere videtur, &amp; re&longs;oluere pr&aelig;dicto modo, quemadmodum de&longs;igna&shy;<lb/>tiones)<emph.end type="italics"/> vbi per de&longs;ignationes intelligit Geometricas demon&longs;trationes, vt <lb/>&longs;upra innuimus, &amp; infra probabimus; cum ergo con&longs;ultatio nihil aliud &longs;it, <lb/>quam medij idonei ad finem in rebus agendis inqui&longs;itio, eamque dicat e&longs;&longs;e <lb/>&longs;imilem re&longs;olutioni Geometric&aelig;, manife&longs;tum e&longs;t, ip&longs;am <expan abbr="quoq;">quoque</expan> re&longs;olutionem <lb/>e&longs;&longs;e medij in rebus &longs;peculatiuis idonei perue&longs;tigationem. </s> <s>vbi &longs;ic ait <emph type="italics"/>(Qui enim <lb/>con&longs;ultat, qu&aelig;rere videtur, &amp; re&longs;oluere pr&aelig;dicto modo, quemadmodum de&longs;igna&shy;<lb/>tiones)<emph.end type="italics"/> vbi per de&longs;ignationes intelligit Geometricas demon&longs;trationes, vt <lb/>&longs;upra innuimus, &amp; infra probabimus; cum ergo con&longs;ultatio nihil aliud &longs;it, <lb/>quam medij idonei ad finem in rebus agendis inqui&longs;itio, eamque dicat e&longs;&longs;e <lb/>&longs;imilem re&longs;olutioni Geometric&aelig;, manife&longs;tum e&longs;t, ip&longs;am <expan abbr="quoq;">quoque</expan> re&longs;olutionem <lb/>e&longs;&longs;e medij in rebus &longs;peculatiuis idonei perue&longs;tigationem. </s>
  
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 <s>Et <lb/>ver&ograve; cum reliquas appellationes Problematis, Theorematis, Propo&longs;itionis, <lb/>definitionum, po&longs;tulatorum, axiomatum, &amp; alia huiu&longs;modi ex Geometri&shy;<lb/>cis ad omnes &longs;cientias tran&longs;tulerit, quid ni etiam re&longs;olutionem? </s> <s>Et <lb/>ver&ograve; cum reliquas appellationes Problematis, Theorematis, Propo&longs;itionis, <lb/>definitionum, po&longs;tulatorum, axiomatum, &amp; alia huiu&longs;modi ex Geometri&shy;<lb/>cis ad omnes &longs;cientias tran&longs;tulerit, quid ni etiam re&longs;olutionem? </s>
  
 <s>maxim&egrave; <lb/>ver&ograve;, quia &longs;i horum lib. </s> <s>maxim&egrave; <lb/>ver&ograve;, quia &longs;i horum lib.
  
 <s>intentio e&longs;&longs;et docere iam factum &longs;yllogi&longs;mum in &longs;ua <lb/>principia re&longs;oluere, parum e&longs;&longs;et vtilis; im&ograve; nec vtilis, &longs;ed &longs;uperfluum quid. <lb/></s> intentio e&longs;&longs;et docere iam factum &longs;yllogi&longs;mum in &longs;ua <lb/>principia re&longs;oluere, parum e&longs;&longs;et vtilis; im&ograve; nec vtilis, &longs;ed &longs;uperfluum quid. <lb/></s>
  
 <s>at ver&ograve; vbinam docuit hanc re&longs;olutionem? </s> <s>at ver&ograve; vbinam docuit hanc re&longs;olutionem? </s>
  
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 <s><margin.target id="marg5"></margin.target>5</s></p><p type="main"> <s><margin.target id="marg5"></margin.target>5</s></p><p type="main">
  
 <s>Ex cap. </s> <s>Ex cap.
  
 <s>23. &longs;ecti primi lib. </s> 23. &longs;ecti primi lib.
  
 <s>1. <emph type="italics"/>(Vt quod diameter incommen&longs;urabilis eo, quod <lb/>imparia &aelig;qualia paribus fiant, &longs;i fuerit po&longs;ita commen&longs;ur abilis. </s> 1. <emph type="italics"/>(Vt quod diameter incommen&longs;urabilis eo, quod <lb/>imparia &aelig;qualia paribus fiant, &longs;i fuerit po&longs;ita commen&longs;ur abilis. </s>
  
 <s>&aelig;qualia igitur fieri <lb/>imparia paribus ratiocinantur, diametrum vtr&ograve; incommen&longs;urabilem e&longs;&longs;e ex &longs;uppo&shy;<lb/>&longs;itione <expan abbr="mon&longs;tr&atilde;t">mon&longs;trant</expan>, quoniam fal&longs;um accidit propter contradictionem)<emph.end type="italics"/> Euclides pri&shy;<lb/>mis duabus definitionibus 10. elem. </s> <s>&aelig;qualia igitur fieri <lb/>imparia paribus ratiocinantur, diametrum vtr&ograve; incommen&longs;urabilem e&longs;&longs;e ex &longs;uppo&shy;<lb/>&longs;itione <expan abbr="mon&longs;tr&atilde;t">mon&longs;trant</expan>, quoniam fal&longs;um accidit propter contradictionem)<emph.end type="italics"/> Euclides pri&shy;<lb/>mis duabus definitionibus 10. elem. </s>
  
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 <s>&longs;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> <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>
  
 <s>manife&longs;tum e&longs;t. </s> 
  
 <s>inuentum autem hu&shy;<lb/>ius a&longs;ymmetri&aelig;, quod Pythagoricis veteres attribuunt, mihi &longs;emper vi&longs;um <lb/>e&longs;t omni maius admiratione, cum nulla experientia, <expan abbr="nullus&qacute;">nullusque</expan>; effectus in ip&shy;<lb/>&longs;ius cognitionem potuerit pri&longs;cos illos Geometras inducere. </s> <s>inuentum autem hu&shy;<lb/>ius a&longs;ymmetri&aelig;, quod Pythagoricis veteres attribuunt, mihi &longs;emper vi&longs;um <lb/>e&longs;t omni maius admiratione, cum nulla experientia, <expan abbr="nullus&qacute;">nullusque</expan>; effectus in ip&shy;<lb/>&longs;ius cognitionem potuerit pri&longs;cos illos Geometras inducere. </s>
  
 <s>Quapropter <lb/>non immerit&ograve; diuinus ille Plato lib. </s> <s>Quapropter <lb/>non immerit&ograve; diuinus ille Plato lib.
  
 <s>7. de legib. </s> 7. de legib. </s>
  
 <s>huius a&longs;ymmetri&aelig; ignora&shy;<lb/>tionem, adeo dete&longs;tatus e&longs;t, vt eam non hominum, &longs;ed &longs;uum, pecorumque <lb/>ignorantiam cen&longs;uerit. </s> <s>huius a&longs;ymmetri&aelig; ignora&shy;<lb/>tionem, adeo dete&longs;tatus e&longs;t, vt eam non hominum, &longs;ed &longs;uum, pecorumque <lb/>ignorantiam cen&longs;uerit. </s>
  
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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> <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>
  
 <s>eodem me&shy;<lb/>dio, quod ab Ari&longs;totele hic innuitur; Euclides ex <lb/>&longs;uppo&longs;itione alterius partis contradictionis ip&longs;ius <pb pagenum="38"/>propo&longs;itionis, qu&aelig;fal&longs;a e&longs;t, nimirum &longs;uppo&longs;ito pr&aelig;dictas lineas e&longs;&longs;e comm. <lb/></s> 
  
 <s>deducit ad impo&longs;&longs;ibile, &longs;iue, vt ait hic Ari&longs;t.  <s>deducit ad impo&longs;&longs;ibile, &longs;iue, vt ait hic Ari&longs;t.
  
 fal&longs;um ratiocinatur, quod &longs;ci&shy;<lb/>licet idem numerus e&longs;&longs;et par, &amp; impar, quod Ari&longs;t. </s> fal&longs;um ratiocinatur, quod &longs;ci&shy;<lb/>licet idem numerus e&longs;&longs;et par, &amp; impar, quod Ari&longs;t. &longs;ignificat, quando ait, <lb/>imparia &aelig;qualia paribus fiunt. </s>
  
 <s>&longs;ignificat, quando ait, <lb/>imparia &aelig;qualia paribus fiunt. </s> 
  
 <s>ex quo ab&longs;urdo deducitur fal&longs;am e&longs;&longs;e pr&aelig;di&shy;<lb/>ctam &longs;uppo&longs;itionem, qu&aelig; a&longs;truebat e&longs;&longs;e comm. </s> <s>ex quo ab&longs;urdo deducitur fal&longs;am e&longs;&longs;e pr&aelig;di&shy;<lb/>ctam &longs;uppo&longs;itionem, qu&aelig; a&longs;truebat e&longs;&longs;e comm. </s>
  
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 <s><margin.target id="marg6"></margin.target>6</s></p><p type="main"> <s><margin.target id="marg6"></margin.target>6</s></p><p type="main">
  
 <s>Et cap. </s> <s>Et cap.
  
 <s>24. &longs;ecti primi libri primi <emph type="italics"/>(Sed magis efficitur manife&longs;tum in de&longs;cri&shy;<lb/>ptionibus, vt quod &aelig;quicruris, qui ad ba&longs;im &aelig;quales &longs;int, ad centrum duct&aelig; A B, <lb/>A C, &longs;i igitur &aelig;qualem accipiat A G, angulum ip&longs;i A B D, non omnino ex. </s> 24. &longs;ecti primi libri primi <emph type="italics"/>(Sed magis efficitur manife&longs;tum in de&longs;cri&shy;<lb/>ptionibus, vt quod &aelig;quicruris, qui ad ba&longs;im &aelig;quales &longs;int, ad centrum duct&aelig; A B, <lb/>A C, &longs;i igitur &aelig;qualem accipiat A G, angulum ip&longs;i A B D, non omnino ex. </s>
  
 <s>&longs;timans <lb/>&aelig;quales, qui &longs;emicirculorum, &amp; rur&longs;us G, ip&longs;i D, non omnem a&longs;&longs;umens eum, qui &longs;e&shy;<lb/>cti. </s> <s>&longs;timans <lb/>&aelig;quales, qui &longs;emicirculorum, &amp; rur&longs;us G, ip&longs;i D, non omnem a&longs;&longs;umens eum, qui &longs;e&shy;<lb/>cti. </s>
  
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 infert manife&longs;tum e&longs;&longs;e oportere in omni &longs;yllo&shy;<lb/>gi&longs;mo, reperiri vniuer&longs;ales, &amp; affirmatiuas propo&longs;itiones, vt Factum e&longs;t in <lb/>pr&aelig;cedenti aliter e&longs;&longs;et petitio principij. </s> infert manife&longs;tum e&longs;&longs;e oportere in omni &longs;yllo&shy;<lb/>gi&longs;mo, reperiri vniuer&longs;ales, &amp; affirmatiuas propo&longs;itiones, vt Factum e&longs;t in <lb/>pr&aelig;cedenti aliter e&longs;&longs;et petitio principij. </s>
  
 <s>Qu&aelig;nam vero &longs;it &aelig;qualitas, quam <lb/>Geometr&aelig; con&longs;iderant, infra cap. </s> <s>Qu&aelig;nam vero &longs;it &aelig;qualitas, quam <lb/>Geometr&aelig; con&longs;iderant, infra cap.
  
 <s>1. &longs;ecti 3. explicabicur.</s></p><p type="main"> 1. &longs;ecti 3. explicabicur.</s></p><p type="main">
  
 <s><arrow.to.target n="marg7"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg7"></arrow.to.target></s></p><p type="margin">
  
 <s><margin.target id="marg7"></margin.target>7</s></p><p type="main"> <s><margin.target id="marg7"></margin.target>7</s></p><p type="main">
  
 <s>Ex cap. </s> <s>Ex cap.
  
 <s>2. &longs;ecti 2. lib. </s> 
  
 <s>1. <emph type="italics"/>(Secundum veritatem quidem ex ijs, qu&aelig; &longs;ecundum <lb/>veritatem de&longs;cribuntur ine&longs;&longs;e, ad dialecticos autem &longs;yllogi&longs;mos ex propo&longs;itionibus <lb/>&longs;ecundum opinionem)<emph.end type="italics"/> verba illa; ex ijs, qu&aelig; <expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> veritatem de&longs;cribuntur <pb pagenum="39"/>ine&longs;&longs;e; &longs;ic gr&aelig;c&egrave;, <foreign lang="greek">e/a tw_n xata\ aleiq/ei/an diagegramme/non,</foreign> vbi manife&longs;t&egrave; vtitur <lb/>verbo, De&longs;cribere, per quod &longs;uperius annotauimus apud Ari&longs;t. </s> 2. &longs;ecti 2. lib.
  
 <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"> 1. <emph type="italics"/>(Secundum veritatem quidem ex ijs, qu&aelig; &longs;ecundum <lb/>veritatem de&longs;cribuntur ine&longs;&longs;e, ad dialecticos autem &longs;yllogi&longs;mos ex propo&longs;itionibus <lb/>&longs;ecundum opinionem)<emph.end type="italics"/> verba illa; ex ijs, qu&aelig; <expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> veritatem de&longs;cribuntur <pb pagenum="39"/>ine&longs;&longs;e; &longs;ic gr&aelig;c&egrave;, <foreign lang="greek">e/a tw_n xata\ aleiq/ei/an diagegramme/non,</foreign> vbi manife&longs;t&egrave; vtitur <lb/>verbo, De&longs;cribere, per quod &longs;uperius annotauimus apud Ari&longs;t. &longs;ignificari <lb/>Geometricas demon&longs;trationes, nam eas opponit dialecticis &longs;yllogi&longs;mis, &longs;e&shy;<lb/>quentibus verbis, cum dixit (ad diale cticos autem &longs;yllogi&longs;mos ex propo&longs;i&shy;<lb/>tionibus &longs;ecundum opinionem) hac adhibita con&longs;ideratione, quam inter&shy;<lb/>pres non videtur adhibui&longs;&longs;e, &longs;en&longs;us huius loci non erit ob&longs;curus.</s></p><p type="main">
  
 <s><arrow.to.target n="marg8"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg8"></arrow.to.target></s></p><p type="margin">
  
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 <s><margin.target id="marg9"></margin.target>9</s></p><p type="main"> <s><margin.target id="marg9"></margin.target>9</s></p><p type="main">
  
 <s>Ex cap. </s> <s>Ex cap.
  
 <s>3. &longs;ecti 2. lib. </s> 3. &longs;ecti 2. lib.
  
 <s>1. <emph type="italics"/>(Vt an ne diameter incomm.)<emph.end type="italics"/> loquitur de a&longs;ymme&shy;<lb/>tria diametri, &amp; co&longs;t&aelig; eiu&longs;dem quadrati, de qua fus&egrave; egimus &longs;uperius in <lb/>cap. </s> 1. <emph type="italics"/>(Vt an ne diameter incomm.)<emph.end type="italics"/> loquitur de a&longs;ymme&shy;<lb/>tria diametri, &amp; co&longs;t&aelig; eiu&longs;dem quadrati, de qua fus&egrave; egimus &longs;uperius in <lb/>cap.
  
 <s>23. &longs;ecti 1. huius libri; qu&aelig; &longs;i repetantur, optim&egrave; hunc <expan abbr="loc&utilde;">locum</expan> declarant.</s></p><p type="main"> 23. &longs;ecti 1. huius libri; qu&aelig; &longs;i repetantur, optim&egrave; hunc <expan abbr="loc&utilde;">locum</expan> declarant.</s></p><p type="main">
  
 <s><arrow.to.target n="marg10"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg10"></arrow.to.target></s></p><p type="margin">
  
 <s><margin.target id="marg10"></margin.target>10</s></p><p type="main"> <s><margin.target id="marg10"></margin.target>10</s></p><p type="main">
  
 <s>Ex cap. </s> <s>Ex cap.
  
 <s>1. &longs;ecti 3. lib. </s> 1. &longs;ecti 3. lib.
  
 <s>1. <emph type="italics"/>(Sit A, duo recti, in quo B, triangulus, in quo C, <lb/>&aelig;quicrus, ip&longs;i <expan abbr="itaq;">itaque</expan> C, ine&longs;t A. per B; ip&longs;i vero B, non amplius per aliud, per &longs;e <lb/>namque triangulus habet duos rectos)<emph.end type="italics"/> nullum aliud exemplum tam frequenter <lb/>v&longs;urpat Philo&longs;ophus, quam i&longs;tud ex Mathematicis de&longs;umptum de triangu&shy;<lb/>lo, &longs;cilicet, omnis triangulus habet tres angulos &aelig;quales duobus rectis an&shy;<lb/>gulis, cuius Demon&longs;tratio e&longs;t in 32. primi Elem. </s> 1. <emph type="italics"/>(Sit A, duo recti, in quo B, triangulus, in quo C, <lb/>&aelig;quicrus, ip&longs;i <expan abbr="itaq;">itaque</expan> C, ine&longs;t A. per B; ip&longs;i vero B, non amplius per aliud, per &longs;e <lb/>namque triangulus habet duos rectos)<emph.end type="italics"/> nullum aliud exemplum tam frequenter <lb/>v&longs;urpat Philo&longs;ophus, quam i&longs;tud ex Mathematicis de&longs;umptum de triangu&shy;<lb/>lo, &longs;cilicet, omnis triangulus habet tres angulos &aelig;quales duobus rectis an&shy;<lb/>gulis, cuius Demon&longs;tratio e&longs;t in 32. primi Elem.
  
 <s>quod, vt prob&egrave; intelliga&shy;<lb/>tur, explicandum e&longs;t penes quid attendenda &longs;it &aelig;qualitas inter angulum, &amp; <lb/>angulum, quod facile a&longs;&longs;equemur, &longs;i meminerimus angulum e&longs;&longs;e in clinatio&shy;<lb/>nem illam, quam du&aelig; line&aelig; non in directum po&longs;it&aelig; faciunt: &longs;iue etiam (vt <lb/>melius percipiamus) angulum e&longs;&longs;e acumen illud, &longs;iue mucronem <expan abbr="ill&utilde;">illum</expan>, quem <lb/>du&aelig; line&aelig; non in directum con&longs;titut&aelig; faciunt, vt duarum linearum A B, A C, <lb/><figure id="fig7"></figure><lb/>inclinatio in puncto A, &longs;iue acumen illud, &longs;iue mucro, <lb/>e&longs;t ratio anguli. </s> quod, vt prob&egrave; intelliga&shy;<lb/>tur, explicandum e&longs;t penes quid attendenda &longs;it &aelig;qualitas inter angulum, &amp; <lb/>angulum, quod facile a&longs;&longs;equemur, &longs;i meminerimus angulum e&longs;&longs;e in clinatio&shy;<lb/>nem illam, quam du&aelig; line&aelig; non in directum po&longs;it&aelig; faciunt: &longs;iue etiam (vt <lb/>melius percipiamus) angulum e&longs;&longs;e acumen illud, &longs;iue mucronem <expan abbr="ill&utilde;">illum</expan>, quem <lb/>du&aelig; line&aelig; non in directum con&longs;titut&aelig; faciunt, vt duarum linearum A B, A C, <lb/><figure id="fig7"></figure><lb/>inclinatio in puncto A, &longs;iue acumen illud, &longs;iue mucro, <lb/>e&longs;t ratio anguli. </s>
  
 <s>&longs;olum igitur duo anguli erunt &aelig;qua&shy;<lb/>les, <expan abbr="qu&atilde;do">quando</expan> vnius acumen &aelig;quale erit acumini alterius; <lb/>etiam &longs;i line&aelig; con&longs;tituentes vnum angulum &longs;int lon&shy;<lb/>giores lineis alterum angulum con&longs;tituentibus, quia <lb/>quantitas anguli non attenditur penes longitudinem <pb pagenum="40"/><expan abbr="linear&utilde;">linearum</expan>, &longs;ed penes inclinationem, &amp; mucronem, quem faciunt: vnde etiam&longs;i <lb/>du&aelig; line&aelig; pr&aelig;dict&aelig; A B, A C, product&aelig;, &longs;iue etiam decurtat&aelig; fuerint, dum&shy;<lb/>modo &longs;itus, &longs;iue po&longs;itio ip&longs;arum, quam ad inuicem habent, non varietur, <lb/>erit &longs;emper eadem quantitas anguli A. </s> <s>&longs;olum igitur duo anguli erunt &aelig;qua&shy;<lb/>les, <expan abbr="qu&atilde;do">quando</expan> vnius acumen &aelig;quale erit acumini alterius; <lb/>etiam &longs;i line&aelig; con&longs;tituentes vnum angulum &longs;int lon&shy;<lb/>giores lineis alterum angulum con&longs;tituentibus, quia <lb/>quantitas anguli non attenditur penes longitudinem <pb pagenum="40"/><expan abbr="linear&utilde;">linearum</expan>, &longs;ed penes inclinationem, &amp; mucronem, quem faciunt: vnde etiam&longs;i <lb/>du&aelig; line&aelig; pr&aelig;dict&aelig; A B, A C, product&aelig;, &longs;iue etiam decurtat&aelig; fuerint, dum&shy;<lb/>modo &longs;itus, &longs;iue po&longs;itio ip&longs;arum, quam ad inuicem habent, non varietur, <lb/>erit &longs;emper eadem quantitas anguli A. </s>
  
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 <s>habet igitur omne triangulum &longs;iue &ecedil;quilaterum, &longs;iue &longs;calenum, <lb/>&longs;iue I&longs;o&longs;celes mirabilem hanc proprietatem, vt tres anguli, cuiu&longs;uis trian&shy;<lb/>guli &longs;int &aelig;quales duobus rectis angulis. </s> <s>habet igitur omne triangulum &longs;iue &ecedil;quilaterum, &longs;iue &longs;calenum, <lb/>&longs;iue I&longs;o&longs;celes mirabilem hanc proprietatem, vt tres anguli, cuiu&longs;uis trian&shy;<lb/>guli &longs;int &aelig;quales duobus rectis angulis. </s>
  
 <s>Quam demon&longs;trationem primi om&shy;<lb/>nium Pythagorici perfecerunt, vt refert Proclus ad 32. primi Elem. </s> <s>Quam demon&longs;trationem primi om&shy;<lb/>nium Pythagorici perfecerunt, vt refert Proclus ad 32. primi Elem. Eucli&shy;<lb/>des deinde ibidem aliter, quam Pythagorici idem demon&longs;trauit. </s>
  
 <s>Eucli&shy;<lb/>des deinde ibidem aliter, quam Pythagorici idem demon&longs;trauit. </s> 
  
 <s>Quod &longs;i <lb/>quis huius rei <expan abbr="experi&etilde;tiam">experientiam</expan> aliquam velit; etiam&longs;i non exactam (cum &aelig;qua&shy;<lb/>litas mathematica non cadat &longs;ub &longs;en&longs;um, &longs;ed &longs;ola intelligentia percipiatur, <lb/>quippe qu&aelig; in materia intelligibili, non autem &longs;en&longs;ibili ver&longs;atur, &amp; cuius <pb pagenum="41"/>&aelig;qualitas nullum di&longs;crimen, quantumuis minimum admittat, quod &longs;en&longs;ui <lb/>vitare ob &longs;ui imperfectione<gap/>on licet: vnde inter e&aelig;, qu&aelig; mathematic&egrave; <lb/>&longs;unt &aelig;qualia, nullus intellectus aliquam valeat reper<gap/>re differentiam) &longs;umat <lb/>inquam triangulum quodpiam materiale, vt ex charta, quantum fieri po&shy;<lb/>ce&longs;t perfectum, deinde ducat lineam vnam perpendicularem &longs;uper aliam, <lb/>qu&aelig; &longs;cilicet faciat, cum illa duos angulos rectos. </s> <s>Quod &longs;i <lb/>quis huius rei <expan abbr="experi&etilde;tiam">experientiam</expan> aliquam velit; etiam&longs;i non exactam (cum &aelig;qua&shy;<lb/>litas mathematica non cadat &longs;ub &longs;en&longs;um, &longs;ed &longs;ola intelligentia percipiatur, <lb/>quippe qu&aelig; in materia intelligibili, non autem &longs;en&longs;ibili ver&longs;atur, &amp; cuius <pb pagenum="41"/>&aelig;qualitas nullum di&longs;crimen, quantumuis minimum admittat, quod &longs;en&longs;ui <lb/>vitare ob &longs;ui imperfectione<gap/>on licet: vnde inter e&aelig;, qu&aelig; mathematic&egrave; <lb/>&longs;unt &aelig;qualia, nullus intellectus aliquam valeat reper<gap/>re differentiam) &longs;umat <lb/>inquam triangulum quodpiam materiale, vt ex charta, quantum fieri po&shy;<lb/>ce&longs;t perfectum, deinde ducat lineam vnam perpendicularem &longs;uper aliam, <lb/>qu&aelig; &longs;cilicet faciat, cum illa duos angulos rectos. </s>
  
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 <s>ip&longs;i <lb/>itaque C, ide&longs;t triangulo &aelig;quicru&longs;i, ine&longs;t A, &longs;cilicet duo recti, hoc e&longs;t, ine&longs;t <lb/>&aelig;quicru&longs;i h&aelig;c, pa&longs;&longs;io habere tres angulos &aelig;quales duobus rectis per B, ide&longs;t <lb/>per <expan abbr="triangul&utilde;">triangulum</expan> vniuer&longs;ale, quia h&aelig;c proprietas e&longs;t trianguli propria, &amp; <expan abbr="c&otilde;pe-tit">compe&shy;<lb/>tit</expan> &aelig;quicru&longs;i, non vt &aelig;quicrus e&longs;t, &longs;ed, vt triangulum e&longs;t; quare B, non crit <lb/>medium ip&longs;ius A, quia pr&aelig;dicta pa&longs;&longs;io. </s> <s>ip&longs;i <lb/>itaque C, ide&longs;t triangulo &aelig;quicru&longs;i, ine&longs;t A, &longs;cilicet duo recti, hoc e&longs;t, ine&longs;t <lb/>&aelig;quicru&longs;i h&aelig;c, pa&longs;&longs;io habere tres angulos &aelig;quales duobus rectis per B, ide&longs;t <lb/>per <expan abbr="triangul&utilde;">triangulum</expan> vniuer&longs;ale, quia h&aelig;c proprietas e&longs;t trianguli propria, &amp; <expan abbr="c&otilde;pe-tit">compe&shy;<lb/>tit</expan> &aelig;quicru&longs;i, non vt &aelig;quicrus e&longs;t, &longs;ed, vt triangulum e&longs;t; quare B, non crit <lb/>medium ip&longs;ius A, quia pr&aelig;dicta pa&longs;&longs;io. </s>
  
 <s>A, non competit triangulo B, per <lb/>aliud, &longs;ed per &longs;e, de eo enim primo, &amp; per &longs;e demon&longs;tratur in 32. primi Elem. <lb/></s> <s>A, non competit triangulo B, per <lb/>aliud, &longs;ed per &longs;e, de eo enim primo, &amp; per &longs;e demon&longs;tratur in 32. primi Elem. <lb/>optim&egrave; Aegydius, &amp; Niphus in hunc locum.</s></p><p type="main">
  
 <s>optim&egrave; Aegydius, &amp; Niphus in hunc locum.</s></p><p type="main"> 
  
 <s><arrow.to.target n="marg11"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg11"></arrow.to.target></s></p><p type="margin">
  
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 <s><margin.target id="marg12"></margin.target>12</s></p><p type="main"> <s><margin.target id="marg12"></margin.target>12</s></p><p type="main">
  
 <s>Ex cap. </s> <s>Ex cap.
  
 <s>21. <emph type="italics"/>(Quod faciunt, qui coalternas putant &longs;cribere, latent enim ip&longs;<gap/><lb/>&longs;e ip&longs;os talia accip entes, qu&aelig; non est po&longs;&longs;ibile monstrare uon exiftentibus <lb/><gap/>o lternis)<emph.end type="italics"/> Vult Ari&longs;t.  21. <emph type="italics"/>(Quod faciunt, qui coalternas putant &longs;cribere, latent enim ip&longs;<gap/><lb/>&longs;e ip&longs;os talia accip entes, qu&aelig; non est po&longs;&longs;ibile monstrare uon exiftentibus <lb/><gap/>o lternis)<emph.end type="italics"/> Vult Ari&longs;t.
  
 exemplo mathematico explicare, quid &longs;it pe&shy;<lb/>titio principij. </s> exemplo mathematico explicare, quid &longs;it pe&shy;<lb/>titio principij. </s>
  
 <s>vbi per coalternas intelligit parallelas lineas, vox <lb/>enim gr&aelig;ca <foreign lang="greek">parallhlos,</foreign> idem &longs;ignificat, ac mutuus, &amp; coalternus. </s> <s>vbi per coalternas intelligit parallelas lineas, vox <lb/>enim gr&aelig;ca <foreign lang="greek">parallhlos,</foreign> idem &longs;ignificat, ac mutuus, &amp; coalternus. </s>
  
 <s>quoad <lb/>exempli explicationem vtor figura textibus apponi &longs;olita, qu&aelig; e&longs;t pr&aelig;&longs;ens. <lb/><figure id="fig11"></figure><lb/>probat Euclides in 28. primi Elem. </s> <s>quoad <lb/>exempli explicationem vtor figura textibus apponi &longs;olita, qu&aelig; e&longs;t pr&aelig;&longs;ens. <lb/><figure id="fig11"></figure><lb/>probat Euclides in 28. primi Elem.
  
 <s>quod &longs;i <lb/>linea recta qu&aelig;dam, vti E F, cadens &longs;uper <lb/>duas rectas, vti &longs;unt A B, C D, fe cerit angu&shy;<lb/>los alternos &ecedil;quales, angulos <expan abbr="nimir&utilde;">nimirum</expan> A G H, <lb/>G H D, ij enim dicuntur alterni; &longs;iue alios <lb/>dnos, nimirum B G H, G H C, hi enim &longs;unt <lb/><expan abbr="quoq;">quoque</expan> alterni; probat inquam has duas li&shy;<lb/>neas A B, C D, e&longs;&longs;e inuicem parallelas. </s> quod &longs;i <lb/>linea recta qu&aelig;dam, vti E F, cadens &longs;uper <lb/>duas rectas, vti &longs;unt A B, C D, fe cerit angu&shy;<lb/>los alternos &ecedil;quales, angulos <expan abbr="nimir&utilde;">nimirum</expan> A G H, <lb/>G H D, ij enim dicuntur alterni; &longs;iue alios <lb/>dnos, nimirum B G H, G H C, hi enim &longs;unt <lb/><expan abbr="quoq;">quoque</expan> alterni; probat inquam has duas li&shy;<lb/>neas A B, C D, e&longs;&longs;e inuicem parallelas. </s>
  
 <s>Iam &longs;i quis vellet probare, &longs;e duas <lb/>parallelas duxi&longs;&longs;e, hac ratione, quia &longs;cilicet fa ciunt pr&aelig;dictos angulos al&shy;<lb/>ternos &aelig;quales; &amp; probaret facere angulos alternos &aelig;quales, quia &longs;unt pa&shy;<lb/>rallel&aelig;, hic peteret principium, ide&longs;t, illud, quod principio <expan abbr="proband&utilde;">probandum</expan> erat, <lb/>afferret pro ratione, &amp; cau&longs;a, quod dicitur peti principium, quia tunc pe&shy;<lb/>timus, vt concedatur nobis, id, quod principio, &amp; primo omnium demon&shy;<lb/>&longs;trare propo&longs;ueramus. </s> <s>Iam &longs;i quis vellet probare, &longs;e duas <lb/>parallelas duxi&longs;&longs;e, hac ratione, quia &longs;cilicet fa ciunt pr&aelig;dictos angulos al&shy;<lb/>ternos &aelig;quales; &amp; probaret facere angulos alternos &aelig;quales, quia &longs;unt pa&shy;<lb/>rallel&aelig;, hic peteret principium, ide&longs;t, illud, quod principio <expan abbr="proband&utilde;">probandum</expan> erat, <lb/>afferret pro ratione, &amp; cau&longs;a, quod dicitur peti principium, quia tunc pe&shy;<lb/>timus, vt concedatur nobis, id, quod principio, &amp; primo omnium demon&shy;<lb/>&longs;trare propo&longs;ueramus. </s>
  
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 <s><margin.target id="marg13"></margin.target>13</s></p><p type="main"> <s><margin.target id="marg13"></margin.target>13</s></p><p type="main">
  
 <s>Ex cap. </s> <s>Ex cap.
  
 <s>22. lib. </s> 22. lib.
  
 <s>2. Priorum <emph type="italics"/>(Vt &longs;i volens mon&longs;trare, quod diameter e&longs;t incom&shy;<lb/>men&longs;. </s> 2. Priorum <emph type="italics"/>(Vt &longs;i volens mon&longs;trare, quod diameter e&longs;t incom&shy;<lb/>men&longs;. </s>
  
 <s>argueret Zenonis rationem, quod non e&longs;t moueri)<emph.end type="italics"/> &longs;uperius &longs;ecto 3. lib. </s> <s>argueret Zenonis rationem, quod non e&longs;t moueri)<emph.end type="italics"/> &longs;uperius &longs;ecto 3. lib.
  
 <s>1. <lb/>fus&egrave; explicauimus hanc a&longs;ymmetriam, quam &longs;i quis vellet demon&longs;trare ea&shy;<lb/>dem illa ratione, qua Zeno motum impugnabat, quia &longs;cilicet <expan abbr="m&etilde;&longs;ura">men&longs;ura</expan> com&shy;<lb/>munis, qu&aelig; debet vtramq, quantitatem men&longs;urare, debet in men&longs;urando <lb/>infinitas partes pertran&longs;ire, uimirum medietates medietatum in in&longs;initum, <lb/>e&longs;t autem impo&longs;&longs;ibile pertran&longs;ire infinitas huiu&longs;modi partes, &amp; propterea <lb/>non poterit metiri, <expan abbr="neq;">neque</expan> vnam, <expan abbr="neq;">neque</expan> alteram ex <expan abbr="qu&atilde;titatibus">quantitatibus</expan>, qu&aelig; putaban&shy;<lb/>tur commen&longs;urabiles, afferret hic, inquit Ari&longs;t.  1. <lb/>fus&egrave; explicauimus hanc a&longs;ymmetriam, quam &longs;i quis vellet demon&longs;trare ea&shy;<lb/>dem illa ratione, qua Zeno motum impugnabat, quia &longs;cilicet <expan abbr="m&etilde;&longs;ura">men&longs;ura</expan> com&shy;<lb/>munis, qu&aelig; debet vtramq, quantitatem men&longs;urare, debet in men&longs;urando <lb/>infinitas partes pertran&longs;ire, uimirum medietates medietatum in in&longs;initum, <lb/>e&longs;t autem impo&longs;&longs;ibile pertran&longs;ire infinitas huiu&longs;modi partes, &amp; propterea <lb/>non poterit metiri, <expan abbr="neq;">neque</expan> vnam, <expan abbr="neq;">neque</expan> alteram ex <expan abbr="qu&atilde;titatibus">quantitatibus</expan>, qu&aelig; putaban&shy;<lb/>tur commen&longs;urabiles, afferret hic, inquit Ari&longs;t.
  
 non cau&longs;am pro cau&longs;a.</s></p><p type="main"> non cau&longs;am pro cau&longs;a.</s></p><p type="main">
  
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 <s>Ex eodem cap. <emph type="italics"/>(Quoniam idem <expan abbr="vtiq;">vtique</expan> fal&longs;um per plures petitiones accidere <lb/>nihil forta&longs;&longs;e inconueniens, veluti coalternas coincidere; &amp; &longs;i maior e&longs;t extrin&longs;ecus <lb/>angulus intrin&longs;eco; &amp; &longs;i triangulus habet plures rectos duobus)<emph.end type="italics"/> per plures po&longs;i&shy;<lb/>tiones &longs;ubaudi fal&longs;as. </s> <s>Ex eodem cap. <emph type="italics"/>(Quoniam idem <expan abbr="vtiq;">vtique</expan> fal&longs;um per plures petitiones accidere <lb/>nihil forta&longs;&longs;e inconueniens, veluti coalternas coincidere; &amp; &longs;i maior e&longs;t extrin&longs;ecus <lb/>angulus intrin&longs;eco; &amp; &longs;i triangulus habet plures rectos duobus)<emph.end type="italics"/> per plures po&longs;i&shy;<lb/>tiones &longs;ubaudi fal&longs;as. </s>
  
 <s>per coalternas intellige lineas &aelig;quidi&longs;tantes, &longs;eu pa&shy;<lb/>rallelas, vt in &longs;uperiori cap. </s> <s>per coalternas intellige lineas &aelig;quidi&longs;tantes, &longs;eu pa&shy;<lb/>rallelas, vt in &longs;uperiori cap.
  
 <s>monuimus. </s> monuimus. </s>
  
 <s>C&aelig;terum Euclides propo&longs;. </s> <s>C&aelig;terum Euclides propo&longs;. </s>
  
 <s>28. pri&shy;<lb/>mi Elem. </s> <s>28. pri&shy;<lb/>mi Elem.
  
 <s>o&longs;tendit, quod &longs;i fuerint du&aelig; parallel&aelig; veluti in pr&aelig;cedenti figura, <lb/>A B, C D, &longs;uper quas alia recta E F, incidat, nece&longs;&longs;ario faciet angulum ex&shy;<lb/>trin&longs;ecum E G B, v. </s> o&longs;tendit, quod &longs;i fuerint du&aelig; parallel&aelig; veluti in pr&aelig;cedenti figura, <lb/>A B, C D, &longs;uper quas alia recta E F, incidat, nece&longs;&longs;ario faciet angulum ex&shy;<lb/>trin&longs;ecum E G B, v. </s>
  
 <s>g. </s> <s>g. </s>
  
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 <s><margin.target id="marg15"></margin.target>15</s></p><p type="main"> <s><margin.target id="marg15"></margin.target>15</s></p><p type="main">
  
 <s>Ex cap. </s> <s>Ex cap.
  
 <s>26. <emph type="italics"/>(Vt &longs;i A, duo recti, in quo autem P., triangulus, in quo vero C, <lb/>&longs;en&longs;ibuis triangulus, &longs;u&longs;picari <expan abbr="namq;">namque</expan> po&longs;&longs;et aliquis non e&longs;&longs;e C, &longs;ciens, quod omnis <lb/>triangulus habet duos rectos: quare &longs;imul no&longs;cet, &amp; ignorabit idem. </s> 26. <emph type="italics"/>(Vt &longs;i A, duo recti, in quo autem P., triangulus, in quo vero C, <lb/>&longs;en&longs;ibuis triangulus, &longs;u&longs;picari <expan abbr="namq;">namque</expan> po&longs;&longs;et aliquis non e&longs;&longs;e C, &longs;ciens, quod omnis <lb/>triangulus habet duos rectos: quare &longs;imul no&longs;cet, &amp; ignorabit idem. </s>
  
 <s>no&longs;ce enim <lb/>omnem triangulum, quod duobus rectis, non &longs;implex e&longs;t: &longs;ed hoc quidem eo, quod <lb/>vniuer&longs;alem habet &longs;cientiam: illud autem eo, quod &longs;ingularem. </s> <s>no&longs;ce enim <lb/>omnem triangulum, quod duobus rectis, non &longs;implex e&longs;t: &longs;ed hoc quidem eo, quod <lb/>vniuer&longs;alem habet &longs;cientiam: illud autem eo, quod &longs;ingularem. </s>
  
 <s>&longs;ic igitur, vt vni&shy;<lb/>uer&longs;ale nouit C, quod duo recti; vt autem &longs;ingulare non nouit, quare non habebit <lb/>contrarias)<emph.end type="italics"/> vide, qu&aelig; diximus lib. </s> <s>&longs;ic igitur, vt vni&shy;<lb/>uer&longs;ale nouit C, quod duo recti; vt autem &longs;ingulare non nouit, quare non habebit <lb/>contrarias)<emph.end type="italics"/> vide, qu&aelig; diximus lib.
  
 <s>1. &longs;ecto 3. cap. </s> 1. &longs;ecto 3. cap.
  
 <s>1. ex quibus quidquid Ma&shy;<lb/>thematicum e&longs;t hic, clarum redditur. </s> 1. ex quibus quidquid Ma&shy;<lb/>thematicum e&longs;t hic, clarum redditur. </s>
  
 <s>reliqua ver&ograve;, qu&aelig; ad Logicum &longs;pe&shy;<lb/>ctant, huius loci commentatores pro&longs;equuntur.</s></p><p type="main"> <s>reliqua ver&ograve;, qu&aelig; ad Logicum &longs;pe&shy;<lb/>ctant, huius loci commentatores pro&longs;equuntur.</s></p><p type="main">
  
 <s>In cap. </s> <s>In cap.
  
 <s>31. de Abductione.</s></p><p type="main"> 31. de Abductione.</s></p><p type="main">
  
 <s><arrow.to.target n="marg16"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg16"></arrow.to.target></s></p><p type="margin">
  
 <s><margin.target id="marg16"></margin.target>16</s></p><p type="main"> <s><margin.target id="marg16"></margin.target>16</s></p><p type="main">
  
 <s>Notandum hic cum eruditi&longs;&longs;imo Burana, Abductionem hanc, de qua in hoc <lb/>cap. </s> <s>Notandum hic cum eruditi&longs;&longs;imo Burana, Abductionem hanc, de qua in hoc <lb/>cap.
  
 <s>agitur e&longs;&longs;e vocem mathematicam, <expan abbr="cam&qacute;">camque</expan>; Ari&longs;t.  agitur e&longs;&longs;e vocem mathematicam, <expan abbr="cam&qacute;">camque</expan>; Ari&longs;t.
  
 quemadmodum multa <lb/>alia &agrave; Mathematicis mutuatum ad omnes alias &longs;cientias tran&longs;tuli&longs;&longs;e. </s> quemadmodum multa <lb/>alia &agrave; Mathematicis mutuatum ad omnes alias &longs;cientias tran&longs;tuli&longs;&longs;e. </s>
  
 <s>e&longs;&longs;e <pb pagenum="44"/>autem terminum mathematicum colligitur manife&longs;t&egrave; ex Proelo, qui lib. </s> <s>e&longs;&longs;e <pb pagenum="44"/>autem terminum mathematicum colligitur manife&longs;t&egrave; ex Proelo, qui lib.
  
 <s>3. <lb/>in comm. </s> 3. <lb/>in comm. </s>
  
 <s>Elem. </s> <s>Elem.
  
 <s>Euclidis ad primam propo&longs;itionem primi Elementi, pag. <lb/></s> Euclidis ad primam propo&longs;itionem primi Elementi, pag. <lb/></s>
  
 <s>121. &longs;ic ait, Abductio ver&ograve; e&longs;t tran&longs;itus &agrave; propo&longs;ito problemate, vel theo&shy;<lb/>remate ad aliud, quo cognito, aut comparato Propo&longs;itum quoque per&longs;pi&shy;<lb/>cuum e&longs;t. </s> <s>121. &longs;ic ait, Abductio ver&ograve; e&longs;t tran&longs;itus &agrave; propo&longs;ito problemate, vel theo&shy;<lb/>remate ad aliud, quo cognito, aut comparato Propo&longs;itum quoque per&longs;pi&shy;<lb/>cuum e&longs;t. </s>
  
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 <s>in probatione minoris facta e&longs;t Abductio, cum enim ip&longs;e vellet re&shy;<lb/>ctificare circumferentiam circuli per lunulas, nec valeret, alij per lineam, <lb/>quandam quadratricem, vt e&longs;t apud Pappum <expan abbr="Alexandrin&utilde;">Alexandrinum</expan>, &amp; apud P. </s> <s>in probatione minoris facta e&longs;t Abductio, cum enim ip&longs;e vellet re&shy;<lb/>ctificare circumferentiam circuli per lunulas, nec valeret, alij per lineam, <lb/>quandam quadratricem, vt e&longs;t apud Pappum <expan abbr="Alexandrin&utilde;">Alexandrinum</expan>, &amp; apud P. </s>
  
 <s>Cla&shy;<lb/>uium in fine &longs;exti Elem. </s> <s>Cla&shy;<lb/>uium in fine &longs;exti Elem.
  
 <s>&amp; alij aliter fru&longs;tra conarentur, facta e&longs;t Abductio <lb/>circa probationem minoris, in qua adhuc Mathematici verfantur; qu&aelig; pro&shy;<lb/>batio, &longs;i tandem inueniri po&longs;&longs;et, mox &longs;equeretur principale <expan abbr="propo&longs;it&utilde;">propo&longs;itum</expan> pro&shy;<lb/>blema, nimirum circulus quadraretur; vide qu&aelig; &longs;crip&longs;<gap/>mus in cap. </s> &amp; alij aliter fru&longs;tra conarentur, facta e&longs;t Abductio <lb/>circa probationem minoris, in qua adhuc Mathematici verfantur; qu&aelig; pro&shy;<lb/>batio, &longs;i tandem inueniri po&longs;&longs;et, mox &longs;equeretur principale <expan abbr="propo&longs;it&utilde;">propo&longs;itum</expan> pro&shy;<lb/>blema, nimirum circulus quadraretur; vide qu&aelig; &longs;crip&longs;<gap/>mus in cap.
  
 <s>3. Pr&aelig;&shy;<lb/>dicam. </s> 3. Pr&aelig;&shy;<lb/>dicam. </s>
  
 <s>de hac re, quia plurimum hunc conferunt. </s> <s>de hac re, quia plurimum hunc conferunt. </s>
  
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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> <s>&longs;ecto 3. cap.
  
 <s>1. explicaui de angulis <lb/>trianguli. </s> 1. explicaui de angulis <lb/>trianguli. </s>
  
 <s>deinde &longs;cias, quod quando Ari&longs;t.  <s>deinde &longs;cias, quod quando Ari&longs;t.
  
 ait, hoc, quod e&longs;t in &longs;emicir cu&shy;<lb/>lo triangulum, &amp;c. </s> ait, hoc, quod e&longs;t in &longs;emicir cu&shy;<lb/>lo triangulum, &amp;c. </s>
  
 <s>alludit ad demon&longs;trationem quandam, quam ip&longs;e infe&shy;<lb/>rius in exemplum adducet, &amp; qu&aelig; e&longs;t in 3. Elem. </s> <s>alludit ad demon&longs;trationem quandam, quam ip&longs;e infe&shy;<lb/>rius in exemplum adducet, &amp; qu&aelig; e&longs;t in 3. Elem.
  
 <s>Euclidis 31. in qua talis fi&shy;<lb/>gura proponitur qualis e&longs;t pr&aelig;&longs;ens, in qua vides triangulum A B C. in &longs;e&shy;<lb/><figure id="fig15"></figure><lb/>micirculo. </s> Euclidis 31. in qua talis fi&shy;<lb/>gura proponitur qualis e&longs;t pr&aelig;&longs;ens, in qua vides triangulum A B C. in &longs;e&shy;<lb/><figure id="fig15"></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. </s> 23. primi <lb/>Priorum, &longs;ecto 1. &longs;ine quibus locus hic &longs;atis intelligi nequit; ijs autem per&shy;<lb/>ceptis &longs;ic <expan abbr="loc&utilde;">locum</expan> hunc explicare po&longs;&longs;umus, cum diameter quadrati &longs;it incom&shy;<pb pagenum="47"/>men&longs;urabilis lateri &longs;ui quadrati, fal&longs;um erit dicere diametrum e&longs;&longs;e com&shy;<lb/>men&longs;urabilem pr&aelig;dicto lateri, quod autem fal&longs;um e&longs;t, illud non e&longs;t; igitur <lb/>impo&longs;sibile e&longs;t &longs;cire diametrum e&longs;&longs;e commen&longs;urabile.</s></p><p type="main">
  
 <s>23. primi <lb/>Priorum, &longs;ecto 1. &longs;ine quibus locus hic &longs;atis intelligi nequit; ijs autem per&shy;<lb/>ceptis &longs;ic <expan abbr="loc&utilde;">locum</expan> hunc explicare po&longs;&longs;umus, cum diameter quadrati &longs;it incom&shy;<pb pagenum="47"/>men&longs;urabilis lateri &longs;ui quadrati, fal&longs;um erit dicere diametrum e&longs;&longs;e com&shy;<lb/>men&longs;urabilem pr&aelig;dicto lateri, quod autem fal&longs;um e&longs;t, illud non e&longs;t; igitur <lb/>impo&longs;sibile e&longs;t &longs;cire diametrum e&longs;&longs;e commen&longs;urabile.</s></p><p type="main"> 
  
 <s><arrow.to.target n="marg21"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg21"></arrow.to.target></s></p><p type="margin">
  
 <s><margin.target id="marg21"></margin.target>21</s></p><p type="main"> <s><margin.target id="marg21"></margin.target>21</s></p><p type="main">
  
 <s>Hoc eodem cap. </s> <s>Hoc eodem cap.
  
 <s>plura dicuntur de Principijs Demon&longs;trationis, &longs;iue &longs;cien&shy;<lb/>ti&aelig;, vt &longs;unt Dignitates, Po&longs;itiones, Definitiones, &amp; &longs;imilia, qu&aelig; quo modo <lb/>&longs;e habeant, &amp; quo modo illis Demon&longs;trationes innitantur, optim&egrave; ex con&shy;<lb/>templatione primi libri Elem. </s> 
  
 <s>Euclidis percipi pote&longs;t. </s> plura dicuntur de Principijs Demon&longs;trationis, &longs;iue &longs;cien&shy;<lb/>ti&aelig;, vt &longs;unt Dignitates, Po&longs;itiones, Definitiones, &amp; &longs;imilia, qu&aelig; quo modo <lb/>&longs;e habeant, &amp; quo modo illis Demon&longs;trationes innitantur, optim&egrave; ex con&shy;<lb/>templatione primi libri Elem.
  
 <s>vt propterea ben&egrave; ij <lb/>&longs;entiant, inter quos pr&aelig;cipui &longs;unt Toletus, &amp; Zabarella, qui a&longs;&longs;erunt, Ari&longs;t. <lb/></s> Euclidis percipi pote&longs;t. </s>
  
 <s>Mathematicas &longs;cientias tamquam typum perfecti&longs;simarum &longs;cientiarum <lb/>&longs;ibi ob oculos propo&longs;ui&longs;&longs;e; ex quo typo ver&aelig; &longs;cienti&aelig; de&longs;criptionem his li&shy;<lb/>bris complectaretur.</s></p><p type="main"> <s>vt propterea ben&egrave; ij <lb/>&longs;entiant, inter quos pr&aelig;cipui &longs;unt Toletus, &amp; Zabarella, qui a&longs;&longs;erunt, Ari&longs;t. <lb/>Mathematicas &longs;cientias tamquam typum perfecti&longs;simarum &longs;cientiarum <lb/>&longs;ibi ob oculos propo&longs;ui&longs;&longs;e; ex quo typo ver&aelig; &longs;cienti&aelig; de&longs;criptionem his li&shy;<lb/>bris complectaretur.</s></p><p type="main">
  
 <s><arrow.to.target n="marg22"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg22"></arrow.to.target></s></p><p type="margin">
  
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 <s><margin.target id="marg23"></margin.target>23</s></p><p type="main"> <s><margin.target id="marg23"></margin.target>23</s></p><p type="main">
  
 <s>Tex. </s> <s>Tex. 9. <emph type="italics"/>(Per &longs;e autem, <expan abbr="qu&aelig;cunq;">qu&aelig;cunque</expan> &amp; in&longs;unt in eo, quod quid e&longs;t, vt triangulo li&shy;<lb/>nea, &amp; line&aelig; punctum; &longs;ub&longs;tantia <expan abbr="namq;">namque</expan> ip&longs;orum ex his e&longs;t, &amp; in oratione dicen&shy;<lb/>te, quid e&longs;t, in&longs;unt)<emph.end type="italics"/> aggreditur explicare qu&aelig;nam &longs;int ea, qu&aelig; per &longs;e dicun&shy;<lb/>tur: <expan abbr="quot&qacute;">quotque</expan>; modis dicatur aliquid per &longs;e. </s>
  
 <s>9. <emph type="italics"/>(Per &longs;e autem, <expan abbr="qu&aelig;cunq;">qu&aelig;cunque</expan> &amp; in&longs;unt in eo, quod quid e&longs;t, vt triangulo li&shy;<lb/>nea, &amp; line&aelig; punctum; &longs;ub&longs;tantia <expan abbr="namq;">namque</expan> ip&longs;orum ex his e&longs;t, &amp; in oratione dicen&shy;<lb/>te, quid e&longs;t, in&longs;unt)<emph.end type="italics"/> aggreditur explicare qu&aelig;nam &longs;int ea, qu&aelig; per &longs;e dicun&shy;<lb/>tur: <expan abbr="quot&qacute;">quotque</expan>; modis dicatur aliquid per &longs;e. </s> 
  
 <s>quorum primus e&longs;t, ea &longs;cilicet, <lb/>per &longs;e de aliquo &longs;ubiecto dici, <expan abbr="qu&aelig;cunq;">qu&aelig;cunque</expan> in definitione illius ponuntur, cu&shy;<lb/>iu&longs;modi &longs;unt linea, &amp; punctum, qu&aelig; per &longs;e pr&aelig;dicantur, illa de triangulo, <lb/>i&longs;tud de linea; in de&longs;initione enim trianguli ponitur linea recta, quia linea <lb/>recta dum terminat illam &longs;uperficiem, qu&aelig; dicitur triangulus illi trianguli <lb/>naturam impertitur, &amp; ideo triangulus definitur &longs;ic, triangulus e&longs;t figura <lb/>tribus lineis rectis terminata. </s> <s>quorum primus e&longs;t, ea &longs;cilicet, <lb/>per &longs;e de aliquo &longs;ubiecto dici, <expan abbr="qu&aelig;cunq;">qu&aelig;cunque</expan> in definitione illius ponuntur, cu&shy;<lb/>iu&longs;modi &longs;unt linea, &amp; punctum, qu&aelig; per &longs;e pr&aelig;dicantur, illa de triangulo, <lb/>i&longs;tud de linea; in de&longs;initione enim trianguli ponitur linea recta, quia linea <lb/>recta dum terminat illam &longs;uperficiem, qu&aelig; dicitur triangulus illi trianguli <lb/>naturam impertitur, &amp; ideo triangulus definitur &longs;ic, triangulus e&longs;t figura <lb/>tribus lineis rectis terminata. </s>
  
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 <s>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>
  
 <s>Aequicrus ver&ograve; <lb/>babet quidem <expan abbr="quodcunq;">quodcunque</expan> duobus rectis &aelig;quales, &longs;ed non prim&ograve;, &longs;ed triangulum <lb/>prius. </s> <s>Aequicrus ver&ograve; <lb/>babet quidem <expan abbr="quodcunq;">quodcunque</expan> duobus rectis &aelig;quales, &longs;ed non prim&ograve;, &longs;ed triangulum <lb/>prius. </s>
  
 <s>quod igitur quoduis primum mon&longs;tratur duos rectos habens, aut <expan abbr="quodcunq;">quodcunque</expan> <lb/>aliud, huic primo ine&longs;t vniuer&longs;ale, &amp; demonstratio de hoc vniuer&longs;aliter e&longs;t, de alijs <lb/>ver&ograve; quodammodo, non per &longs;e, <expan abbr="neq;">neque</expan> de &aelig;quicrure e&longs;t vniuer&longs;aliter, &longs;ed in plus)<emph.end type="italics"/> pro <lb/>quorum intelligentia nece&longs;&longs;aria &longs;unt ea, qu&aelig; primo Priorum &longs;ecto 3. cap. </s> <s>quod igitur quoduis primum mon&longs;tratur duos rectos habens, aut <expan abbr="quodcunq;">quodcunque</expan> <lb/>aliud, huic primo ine&longs;t vniuer&longs;ale, &amp; demonstratio de hoc vniuer&longs;aliter e&longs;t, de alijs <lb/>ver&ograve; quodammodo, non per &longs;e, <expan abbr="neq;">neque</expan> de &aelig;quicrure e&longs;t vniuer&longs;aliter, &longs;ed in plus)<emph.end type="italics"/> pro <lb/>quorum intelligentia nece&longs;&longs;aria &longs;unt ea, qu&aelig; primo Priorum &longs;ecto 3. cap.
  
 <s>1. <lb/>&longs;crip&longs;imus. </s> 1. <lb/>&longs;crip&longs;imus. </s>
  
 <s>deinde memineris figuram vniuer&longs;aliorem e&longs;&longs;e triangulo, &amp; tri&shy;<lb/>angulum vniuer&longs;alius &aelig;quicrure. </s> <s>deinde memineris figuram vniuer&longs;aliorem e&longs;&longs;e triangulo, &amp; tri&shy;<lb/>angulum vniuer&longs;alius &aelig;quicrure. </s>
  
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 <s>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. </s> 
  
 <s>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>
  
 <s>Quando igitur du&aelig; rect&aelig; con&longs;titu&shy;<lb/>t&aelig; fuerint, vt A B, C D, in quas alia recta, <lb/>vt G F, incidens, faciat duos angulos in&shy;<lb/>ternos, re&longs;pectu rectarum A B, C D, &amp; ad <lb/>ea&longs;dem partes rect&aelig; E F, vt &longs;unt ex parte <lb/>&longs;ini&longs;tra anguli A G H, C H G; exparte ve&shy;<lb/>r&ograve; dextra B G H, D H G; &longs;i <expan abbr="inqu&atilde;">inquam</expan> linea E F, <lb/>fecerit duos illos angulos ex parte &longs;ini&longs;tra &longs;imul &longs;umptos, &aelig;quales duobus <lb/>rectis angulis, vel duos ex parte dextra pariter &aelig;quales duobus rectis, pro&shy;<lb/>bat Euclides rectas A B, C D, non concurrere, &longs;iue parallelas e&longs;&longs;e. </s> <s>Quando igitur du&aelig; rect&aelig; con&longs;titu&shy;<lb/>t&aelig; fuerint, vt A B, C D, in quas alia recta, <lb/>vt G F, incidens, faciat duos angulos in&shy;<lb/>ternos, re&longs;pectu rectarum A B, C D, &amp; ad <lb/>ea&longs;dem partes rect&aelig; E F, vt &longs;unt ex parte <lb/>&longs;ini&longs;tra anguli A G H, C H G; exparte ve&shy;<lb/>r&ograve; dextra B G H, D H G; &longs;i <expan abbr="inqu&atilde;">inquam</expan> linea E F, <lb/>fecerit duos illos angulos ex parte &longs;ini&longs;tra &longs;imul &longs;umptos, &aelig;quales duobus <lb/>rectis angulis, vel duos ex parte dextra pariter &aelig;quales duobus rectis, pro&shy;<lb/>bat Euclides rectas A B, C D, non concurrere, &longs;iue parallelas e&longs;&longs;e. </s>
  
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 <s>demon&longs;tratio&shy;<lb/>ne aut vna, aut altera, quod duos rectos habet vnumquodque, <expan abbr="&aelig;quilatei&utilde;">&aelig;quilateium</expan> &longs;eor&longs;um, <lb/>&amp; &longs;calenum, &amp; &aelig;quicrus: nondum nouit triangulum, quod duobus rectis, <gap/>&longs;i &longs;o&shy;<lb/>phi&longs;tico modo, <expan abbr="neq;">neque</expan> vniuer&longs; aliter triangulum, <expan abbr="neq;">neque</expan> &longs;i vllum e&longs;t pr&aelig;ter pr&aelig;dicta <lb/>triangulum alterum. </s> <s>demon&longs;tratio&shy;<lb/>ne aut vna, aut altera, quod duos rectos habet vnumquodque, <expan abbr="&aelig;quilatei&utilde;">&aelig;quilateium</expan> &longs;eor&longs;um, <lb/>&amp; &longs;calenum, &amp; &aelig;quicrus: nondum nouit triangulum, quod duobus rectis, <gap/>&longs;i &longs;o&shy;<lb/>phi&longs;tico modo, <expan abbr="neq;">neque</expan> vniuer&longs; aliter triangulum, <expan abbr="neq;">neque</expan> &longs;i vllum e&longs;t pr&aelig;ter pr&aelig;dicta <lb/>triangulum alterum. </s>
  
 <s>non enim &longs;ecundum quod triangulum, <expan abbr="neq;">neque</expan> omnetriangulum, <lb/>ni&longs;i &longs;ecundum numerum, &longs;ecundum &longs;peciem autem non omne; &amp; &longs;i nullum e&longs;t, quod <lb/>non nouit)<emph.end type="italics"/> vltimo loco ponit exemplum primi erroris, quem &longs;upra verbis il&shy;<lb/>lis <emph type="italics"/>(Quando vel nibil &longs;it accipere &longs;uperius, pr&aelig;ter &longs;ingulare)<emph.end type="italics"/> expre&longs;&longs;erat, quod, <lb/>vt ben&egrave; intelligamus, opus e&longs;t ea, legere, qu&aelig; libro primo Priorum &longs;ecto 3. <lb/>cap. </s> <s>non enim &longs;ecundum quod triangulum, <expan abbr="neq;">neque</expan> omnetriangulum, <lb/>ni&longs;i &longs;ecundum numerum, &longs;ecundum &longs;peciem autem non omne; &amp; &longs;i nullum e&longs;t, quod <lb/>non nouit)<emph.end type="italics"/> vltimo loco ponit exemplum primi erroris, quem &longs;upra verbis il&shy;<lb/>lis <emph type="italics"/>(Quando vel nibil &longs;it accipere &longs;uperius, pr&aelig;ter &longs;ingulare)<emph.end type="italics"/> expre&longs;&longs;erat, quod, <lb/>vt ben&egrave; intelligamus, opus e&longs;t ea, legere, qu&aelig; libro primo Priorum &longs;ecto 3. <lb/>cap.
  
 <s>1. &longs;crip&longs;imus de propriet<gap/>te illa trianguli, quod &longs;cilicet habet tres an&shy;<lb/>gulos &aelig;quales duobus rectis angulis, quibus pr&aelig;mi&longs;&longs;is, &longs;ic deinde locum <lb/>hunc interpretaberis; Propter hoc, quod pr&aelig;cedenti textu dictum e&longs;t; no&shy;<lb/>tandum in primo errore vniuer&longs;ale, tanquam &longs;i non e&longs;&longs;et vniuer&longs;ale o&longs;ten&shy;<lb/>ditur de &longs;ingulari, &longs;i quis igitur mon&longs;trauerit &longs;ingillatim de <expan abbr="vnoquoq;">vnoquoque</expan> trian&shy;<lb/>gulo in &longs;ingulari, &longs;cilicet de vno &aelig;quilatero, tantum, &amp; de vno Scaleno, &amp; <lb/>de vno I&longs;o&longs;cele, &longs;eparatim, vtens auteadem demon&longs;trationc dum de <expan abbr="vno&qacute;">vnoque</expan>; <pb pagenum="52"/>&longs;epatatim o&longs;tendit, aut vtens diuerfis demon&longs;trationibus, vna pro &aelig;quila&shy;<lb/>tero, altera pro I&longs;o&longs;cele, tertia pro Scaleno, o&longs;tendens, quod <expan abbr="vnumquodq;">vnumquodque</expan> <lb/>illorum habet tres angules &aelig;quales duobus rectis angulis; i&longs;te nondum no&shy;<lb/>uit triangulum omne habere talem affectionem, ni&longs;i modo &longs;ophi&longs;tico, quia <lb/>non cogno&longs;cit hanc affectionem illis <expan abbr="c&otilde;petere">competere</expan> propter naturam illam com&shy;<lb/>munem trianguli, cui primo, &amp; per &longs;e competit; &amp; neque vniuer&longs;aliter co&shy;<lb/>gno&longs;cit triangulum omne e&longs;&longs;e tale, etiam &longs;i nullum aliud reperiatur trian&shy;<lb/>gulum, pr&aelig;ter illud &aelig;quilaterum, vel illud I&longs;o&longs;celes, vel illud Scalenum, de <lb/>quibus &longs;eparatim <expan abbr="dem&otilde;&longs;trauit">demon&longs;trauit</expan>, &amp; &longs;ecundum numernm, ide&longs;t de vnoquoque, <lb/>quatenus e&longs;t vnum numero. </s> 1. &longs;crip&longs;imus de propriet<gap/>te illa trianguli, quod &longs;cilicet habet tres an&shy;<lb/>gulos &aelig;quales duobus rectis angulis, quibus pr&aelig;mi&longs;&longs;is, &longs;ic deinde locum <lb/>hunc interpretaberis; Propter hoc, quod pr&aelig;cedenti textu dictum e&longs;t; no&shy;<lb/>tandum in primo errore vniuer&longs;ale, tanquam &longs;i non e&longs;&longs;et vniuer&longs;ale o&longs;ten&shy;<lb/>ditur de &longs;ingulari, &longs;i quis igitur mon&longs;trauerit &longs;ingillatim de <expan abbr="vnoquoq;">vnoquoque</expan> trian&shy;<lb/>gulo in &longs;ingulari, &longs;cilicet de vno &aelig;quilatero, tantum, &amp; de vno Scaleno, &amp; <lb/>de vno I&longs;o&longs;cele, &longs;eparatim, vtens auteadem demon&longs;trationc dum de <expan abbr="vno&qacute;">vnoque</expan>; <pb pagenum="52"/>&longs;epatatim o&longs;tendit, aut vtens diuerfis demon&longs;trationibus, vna pro &aelig;quila&shy;<lb/>tero, altera pro I&longs;o&longs;cele, tertia pro Scaleno, o&longs;tendens, quod <expan abbr="vnumquodq;">vnumquodque</expan> <lb/>illorum habet tres angules &aelig;quales duobus rectis angulis; i&longs;te nondum no&shy;<lb/>uit triangulum omne habere talem affectionem, ni&longs;i modo &longs;ophi&longs;tico, quia <lb/>non cogno&longs;cit hanc affectionem illis <expan abbr="c&otilde;petere">competere</expan> propter naturam illam com&shy;<lb/>munem trianguli, cui primo, &amp; per &longs;e competit; &amp; neque vniuer&longs;aliter co&shy;<lb/>gno&longs;cit triangulum omne e&longs;&longs;e tale, etiam &longs;i nullum aliud reperiatur trian&shy;<lb/>gulum, pr&aelig;ter illud &aelig;quilaterum, vel illud I&longs;o&longs;celes, vel illud Scalenum, de <lb/>quibus &longs;eparatim <expan abbr="dem&otilde;&longs;trauit">demon&longs;trauit</expan>, &amp; &longs;ecundum numernm, ide&longs;t de vnoquoque, <lb/>quatenus e&longs;t vnum numero. </s>
  
 <s>non nouit autem &longs;ecundum &longs;peciem, ideft fecun&shy;<lb/>dum naturam, &amp; formam communem illis tribus indiuiduis, qu&aelig; e&longs;t natu&shy;<lb/>ra trianguli. </s> <s>non nouit autem &longs;ecundum &longs;peciem, ideft fecun&shy;<lb/>dum naturam, &amp; formam communem illis tribus indiuiduis, qu&aelig; e&longs;t natu&shy;<lb/>ra trianguli. </s>
  
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 <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>Ibidem <emph type="italics"/>(Propter hoc Geometri&aelig; non licet mon&longs;trare, quod contrariorum vna <lb/>e&longs;e &longs;cientia, &longs;ed neque quod duo cubi cubus)<emph.end type="italics"/> quo ad verba illa, duo cubi cubus<gap/><lb/>qu&aelig; ad nos pertinent, vult Ari&longs;t.  <s>Ibidem <emph type="italics"/>(Propter hoc Geometri&aelig; non licet mon&longs;trare, quod contrariorum vna <lb/>e&longs;e &longs;cientia, &longs;ed neque quod duo cubi cubus)<emph.end type="italics"/> quo ad verba illa, duo cubi cubus<gap/><lb/>qu&aelig; ad nos pertinent, vult Ari&longs;t.
  
 docere<gap/>, quod non debet Geometra o&longs;ten&shy;<lb/>dere numerorum affectiones (per enbos enim intelligit numeros quo&longs;dam <lb/>&longs;ic dictos, vt paulo po&longs;t o&longs;tendam) vt &longs;i quis vellet geometric&egrave; o&longs;tendere id, <lb/>quod o&longs;tenditur in 4. noni Elem. </s> docere<gap/>, quod non debet Geometra o&longs;ten&shy;<lb/>dere numerorum affectiones (per enbos enim intelligit numeros quo&longs;dam <lb/>&longs;ic dictos, vt paulo po&longs;t o&longs;tendam) vt &longs;i quis vellet geometric&egrave; o&longs;tendere id, <lb/>quod o&longs;tenditur in 4. noni Elem.
  
 <s>&longs;cilicet, &longs;i cubus numerus cubum numerum <lb/>multiplicauerit, productus numerus erit pariter cubus. </s> &longs;cilicet, &longs;i cubus numerus cubum numerum <lb/>multiplicauerit, productus numerus erit pariter cubus. </s>
  
 <s>nonnulli latinorum <lb/>perperam textum hunc expo&longs;uerunt putantes reperiri &longs;olummodo cubos <lb/>geometricos, at Euclides definit. </s> <s>nonnulli latinorum <lb/>perperam textum hunc expo&longs;uerunt putantes reperiri &longs;olummodo cubos <lb/>geometricos, at Euclides definit. </s>
  
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 <s>v.g. </s> <s>v.g. </s>
  
 <s>Per&longs;pectiua dicit, ea, qu&aelig; vi&shy;<lb/>dentur eminus videri minora, quam qu&aelig; videntur cominus, quia illa viden&shy;<lb/>tur &longs;ub angulo minori, h&aelig;c ver&ograve; &longs;ub angulo maiori, quod ver&ograve; remotiora <lb/>videantur &longs;ub angulo minori, quam propinquiora c&aelig;teris paribus probat <lb/><figure id="fig24"></figure><lb/>per 21. primi Elem. </s> <s>Per&longs;pectiua dicit, ea, qu&aelig; vi&shy;<lb/>dentur eminus videri minora, quam qu&aelig; videntur cominus, quia illa viden&shy;<lb/>tur &longs;ub angulo minori, h&aelig;c ver&ograve; &longs;ub angulo maiori, quod ver&ograve; remotiora <lb/>videantur &longs;ub angulo minori, quam propinquiora c&aelig;teris paribus probat <lb/><figure id="fig24"></figure><lb/>per 21. primi Elem.
  
 <s>&longs;it enim ma&shy;<lb/>gnitudo vi&longs;a A B, remotior ab o&shy;<lb/>culo in C, po&longs;ito, &amp; vi&longs;a propin&shy;<lb/>quior ab oculo in D. ductis lineis <lb/>vi&longs;ualibus C A, C B: D A, D B; ab <lb/>oculis C, &amp; D, ad extremitates <lb/>&longs;pectat&aelig; magnitudinis, erit remo&shy;<lb/>tioris vi&longs;ionis angulus C, minor <lb/>angulo D, propinquioris, vt ex pr&aelig;allegata Demon&longs;tratione pater. </s> &longs;it enim ma&shy;<lb/>gnitudo vi&longs;a A B, remotior ab o&shy;<lb/>culo in C, po&longs;ito, &amp; vi&longs;a propin&shy;<lb/>quior ab oculo in D. ductis lineis <lb/>vi&longs;ualibus C A, C B: D A, D B; ab <lb/>oculis C, &amp; D, ad extremitates <lb/>&longs;pectat&aelig; magnitudinis, erit remo&shy;<lb/>tioris vi&longs;ionis angulus C, minor <lb/>angulo D, propinquioris, vt ex pr&aelig;allegata Demon&longs;tratione pater. </s>
  
 <s>Hine <lb/>per&longs;picu&egrave; vides, qua ratione Per&longs;pectiua Geometri&aelig; &longs;ubalternetur, &longs;iue <lb/>quid &longs;it ip&longs;a &longs;ubalternatio, vbi medium e&longs;t Geometricum, conclu&longs;io autem <lb/>optica. </s> <s>Hine <lb/>per&longs;picu&egrave; vides, qua ratione Per&longs;pectiua Geometri&aelig; &longs;ubalternetur, &longs;iue <lb/>quid &longs;it ip&longs;a &longs;ubalternatio, vbi medium e&longs;t Geometricum, conclu&longs;io autem <lb/>optica. </s>
  
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 <s><margin.target id="marg35"></margin.target>35</s></p><p type="main"> <s><margin.target id="marg35"></margin.target>35</s></p><p type="main">
  
 <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>&longs;it ergo <expan abbr="tri&atilde;gulum">triangulum</expan> A B C. </s> <s>&longs;it ergo <expan abbr="tri&atilde;gulum">triangulum</expan> A B C. </s>
  
 <s>Dico ag&shy;<lb/>gregatum <expan abbr="tri&utilde;">trium</expan> ip&longs;ius angulorum A, B, C, <lb/>e&longs;&longs;e &aelig;quale aggregato ex duobus angu&shy;<lb/>lis rectis (vt autem melius intelligas, qu&aelig; <lb/>&longs;equuntur, lege prius ea, qu&aelig; dicta &longs;unt <lb/>in lib. </s> <s>Dico ag&shy;<lb/>gregatum <expan abbr="tri&utilde;">trium</expan> ip&longs;ius angulorum A, B, C, <lb/>e&longs;&longs;e &aelig;quale aggregato ex duobus angu&shy;<lb/>lis rectis (vt autem melius intelligas, qu&aelig; <lb/>&longs;equuntur, lege prius ea, qu&aelig; dicta &longs;unt <lb/>in lib.
  
 <s>1. Priorum &longs;ecto 3. cap. </s> 1. Priorum &longs;ecto 3. cap.
  
 <s>1.) produ&shy;<lb/>catur latus B C, <expan abbr="v&longs;q;">v&longs;que</expan> in D, vt fiat angulus <lb/>externus A C D; Iam &longs;ic, quoniam <expan abbr="pro-bat&utilde;">pro&shy;<lb/>batum</expan> e&longs;t in 13. primi, duos angulos, quos <lb/>facit linea A C, cum linea B D, &longs;cilicet angulos A C B, A C D, e&longs;&longs;e pares <lb/>duobus rectis: &amp; quia pariter in prima parte huins propo&longs;. </s> 1.) produ&shy;<lb/>catur latus B C, <expan abbr="v&longs;q;">v&longs;que</expan> in D, vt fiat angulus <lb/>externus A C D; Iam &longs;ic, quoniam <expan abbr="pro-bat&utilde;">pro&shy;<lb/>batum</expan> e&longs;t in 13. primi, duos angulos, quos <lb/>facit linea A C, cum linea B D, &longs;cilicet angulos A C B, A C D, e&longs;&longs;e pares <lb/>duobus rectis: &amp; quia pariter in prima parte huins propo&longs;. </s>
  
 <s>32. probatum <lb/>e&longs;t ab Euclide duos angulos A B, e&longs;&longs;e &aelig;quales externo angulo A C D: &longs;i ter&shy;<lb/>tius angulus reliquus A C B, &longs;umatur bis, &longs;emel cum duobus angulis A, B, <lb/>&amp; &longs;emel cum externo A C D, <expan abbr="add&etilde;tur">addentur</expan> &aelig;qualia &aelig;qualibus, &amp; propterea tres <lb/>anguli A, B, A C B, &longs;imul &longs;umpti, erunt &aelig;quales duobus A C D, A C B, &longs;imul <lb/>&longs;umptis; &longs;ed his duobus &longs;unt &aelig;quales duo recti, ergo cum qu&aelig; &longs;unt &aelig;qualia <lb/>vni tertio, &longs;int etiam &aelig;qualia inuicem, erit aggregatum trium angulorum <lb/>A, B, A C B, &aelig;quale aggregato duorum rectorum; quod erat demon&longs;tran&shy;<lb/>dum. </s> <s>32. probatum <lb/>e&longs;t ab Euclide duos angulos A B, e&longs;&longs;e &aelig;quales externo angulo A C D: &longs;i ter&shy;<lb/>tius angulus reliquus A C B, &longs;umatur bis, &longs;emel cum duobus angulis A, B, <lb/>&amp; &longs;emel cum externo A C D, <expan abbr="add&etilde;tur">addentur</expan> &aelig;qualia &aelig;qualibus, &amp; propterea tres <lb/>anguli A, B, A C B, &longs;imul &longs;umpti, erunt &aelig;quales duobus A C D, A C B, &longs;imul <lb/>&longs;umptis; &longs;ed his duobus &longs;unt &aelig;quales duo recti, ergo cum qu&aelig; &longs;unt &aelig;qualia <lb/>vni tertio, &longs;int etiam &aelig;qualia inuicem, erit aggregatum trium angulorum <lb/>A, B, A C B, &aelig;quale aggregato duorum rectorum; quod erat demon&longs;tran&shy;<lb/>dum. </s>
  
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 <s>20. at&shy;<lb/>tulimus; nunc Mechanic&aelig; &longs;ubalternationis, quam hic Ari&longs;t.  <s>20. at&shy;<lb/>tulimus; nunc Mechanic&aelig; &longs;ubalternationis, quam hic Ari&longs;t.
  
 in&longs;inuat, exem&shy;<lb/>plum &longs;it illud, quod Archimedes prop. </s> in&longs;inuat, exem&shy;<lb/>plum &longs;it illud, quod Archimedes prop.
  
 <s>14. primi Aequep. </s> 14. primi Aequep. </s>
  
 <s>demon&longs;trat, ni&shy;<lb/>mirum centrum grauitatis omnis trianguli e&longs;&longs;e punctum illud, in quo rect&aelig; <lb/>line&aelig; ab angulis trianguli ad dimidia latera oppo&longs;ita duct&aelig; concurrunt. </s> <s>demon&longs;trat, ni&shy;<lb/>mirum centrum grauitatis omnis trianguli e&longs;&longs;e punctum illud, in quo rect&aelig; <lb/>line&aelig; ab angulis trianguli ad dimidia latera oppo&longs;ita duct&aelig; concurrunt. </s>
  
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 <s><margin.target id="marg39"></margin.target>39</s></p><p type="main"> <s><margin.target id="marg39"></margin.target>39</s></p><p type="main">
  
 <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><margin.target id="marg43"></margin.target>43</s></p><p type="main"> <s><margin.target id="marg43"></margin.target>43</s></p><p type="main">
  
 <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>porr&ograve; quid inter multiplicem, &amp; multipli&shy;<lb/>catam rationem inter&longs;it, optim&egrave; declarat no&longs;ter Clauius ad 4. definit. </s> <s>porr&ograve; quid inter multiplicem, &amp; multipli&shy;<lb/>catam rationem inter&longs;it, optim&egrave; declarat no&longs;ter Clauius ad 4. definit. </s>
  
 <s>lib. </s> <s>lib.
  
 <s>5. <lb/>Elem. </s> 5. <lb/>Elem.
  
 <s>ex quo etiam loco pauca decerpam, qu&aelig; huic loco declarando con&shy;<lb/>ducunt. </s> ex quo etiam loco pauca decerpam, qu&aelig; huic loco declarando con&shy;<lb/>ducunt. </s>
  
 <s>Proportio igitur multiplex e&longs;t habitudo inter duas quantitates in&shy;<lb/>&aelig;quales, quarum maior continet minorem, bis, vel ter, vel quater, &amp;c. </s> <s>Proportio igitur multiplex e&longs;t habitudo inter duas quantitates in&shy;<lb/>&aelig;quales, quarum maior continet minorem, bis, vel ter, vel quater, &amp;c. </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. </s> 
  
 <s>r. </s> r. </s>
  
 <s>Priorum &longs;ecto 3. cap. </s> <s>Priorum &longs;ecto 3. cap.
  
 <s>r. </s> r. </s>
  
 <s>nunc igitur paraphra<gap/><lb/>&longs;olum huius loci dabo. </s> <s>nunc igitur paraphra<gap/><lb/>&longs;olum huius loci dabo. </s>
  
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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>
  
 <s>fus&egrave; explicatum e&longs;t in lib. </s> <s>fus&egrave; explicatum e&longs;t in lib.
  
 <s>1. <lb/>Priorum &longs;ecto 3. cap. </s> 1. <lb/>Priorum &longs;ecto 3. cap.
  
 <s>1. qu&ograve; te nunc mitto.</s></p><p type="main"> 1. qu&ograve; te nunc mitto.</s></p><p type="main">
  
 <s><arrow.to.target n="marg55"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg55"></arrow.to.target></s></p><p type="margin">
  
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 <s>Eodem tex <emph type="italics"/>(Quando igitur cognofcimes, quod&shy;<lb/>quatuor exteriores &longs;unt &aelig;quales, quoniam I&longs;o&longs;celes, <lb/>adhuc defseit, propier quid I&longs;o&longs;celes? </s> <s>Eodem tex <emph type="italics"/>(Quando igitur cognofcimes, quod&shy;<lb/>quatuor exteriores &longs;unt &aelig;quales, quoniam I&longs;o&longs;celes, <lb/>adhuc defseit, propier quid I&longs;o&longs;celes? </s>
  
 <s>quoniain trian&shy;<lb/>gulus: &amp; hoc quoniam figura rectilinea, &amp;c.)<emph.end type="italics"/> exem&shy;<lb/>plo geometrico vult o&longs;tendere demon&longs;trationem <lb/>vniuer&longs;alem e&longs;&longs;e particulari pr&aelig;&longs;tantiorem: e&longs;t <lb/>autem exemplum de pulcherrima, <expan abbr="atq;">atque</expan> admira&shy;<lb/>bili proprietate, qu&aelig; omnibus figuris rectilineis <lb/>conuenit, e&longs;t <expan abbr="&qacute;">que</expan>; huiu&longs;modi: Omnis figur&aelig; rectili&shy;<lb/>ne&aelig; anguli externi omnes &longs;imul &longs;umpti, &longs;unt &aelig;qua <lb/>les quatuor rectis angulis, qu&aelig; affectio demon&shy;<lb/>&longs;tratur in &longs;cholio 32. primi Elem. </s> <s>quoniain trian&shy;<lb/>gulus: &amp; hoc quoniam figura rectilinea, &amp;c.)<emph.end type="italics"/> exem&shy;<lb/>plo geometrico vult o&longs;tendere demon&longs;trationem <lb/>vniuer&longs;alem e&longs;&longs;e particulari pr&aelig;&longs;tantiorem: e&longs;t <lb/>autem exemplum de pulcherrima, <expan abbr="atq;">atque</expan> admira&shy;<lb/>bili proprietate, qu&aelig; omnibus figuris rectilineis <lb/>conuenit, e&longs;t <expan abbr="&qacute;">que</expan>; huiu&longs;modi: Omnis figur&aelig; rectili&shy;<lb/>ne&aelig; anguli externi omnes &longs;imul &longs;umpti, &longs;unt &aelig;qua <lb/>les quatuor rectis angulis, qu&aelig; affectio demon&shy;<lb/>&longs;tratur in &longs;cholio 32. primi Elem.
  
 <s>dicuntur autern <lb/>anguli externi, qui productis lateribus fiunt, vt in <lb/>triangulo pra&longs;enti anguli externi &longs;unt, B D C, <pb pagenum="62"/>D F E, F B A, ita vt qu&aelig;libet figura tot angulos externos &longs;ortiatur, quot <lb/>habet latera; cum exproductis lateribus oriantur. </s> dicuntur autern <lb/>anguli externi, qui productis lateribus fiunt, vt in <lb/>triangulo pra&longs;enti anguli externi &longs;unt, B D C, <pb pagenum="62"/>D F E, F B A, ita vt qu&aelig;libet figura tot angulos externos &longs;ortiatur, quot <lb/>habet latera; cum exproductis lateribus oriantur. </s>
  
 <s>Vt autem propo&longs;itio ve&shy;<lb/>rificetur, &longs;ingula latera ordinatim &longs;unt producenda, hoc e&longs;t, ver&longs;us eandem <lb/>partem, vt in figuris appo&longs;itis vides. </s> <s>Vt autem propo&longs;itio ve&shy;<lb/>rificetur, &longs;ingula latera ordinatim &longs;unt producenda, hoc e&longs;t, ver&longs;us eandem <lb/>partem, vt in figuris appo&longs;itis vides. </s>
  
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 <s>Eodem tex. <emph type="italics"/>(Vt &longs;i quis nouit, quod omnis triangulus habet tres duobus rectis <lb/>&aelig;quales)<emph.end type="italics"/> nihil &longs;requentius. </s> <s>Eodem tex. <emph type="italics"/>(Vt &longs;i quis nouit, quod omnis triangulus habet tres duobus rectis <lb/>&aelig;quales)<emph.end type="italics"/> nihil &longs;requentius. </s>
  
 <s>vide &longs;upra lib. </s> <s>vide &longs;upra lib.
  
 <s>1. Priorum &longs;ecto 3. cap. </s> 1. Priorum &longs;ecto 3. cap.
  
 <s>1.</s></p><p type="main"> 1.</s></p><p type="main">
  
 <s><arrow.to.target n="marg58"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg58"></arrow.to.target></s></p><p type="margin">
  
 <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. </s> 
  
 <s>1. Priorum &longs;ecto 3. cap. </s> 1. Priorum &longs;ecto 3. cap.
  
 <s>1.</s></p><p type="main"> 1.</s></p><p type="main">
  
 <s><arrow.to.target n="marg59"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg59"></arrow.to.target></s></p><p type="margin">
  
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 <s>C&aelig;terum per prin&shy;<lb/>cipia, ex quibus intelligit Dignitates, quia ex illis di&longs;currimus. </s> <s>C&aelig;terum per prin&shy;<lb/>cipia, ex quibus intelligit Dignitates, quia ex illis di&longs;currimus. </s>
  
 <s>per princi&shy;<lb/>pia ver&ograve; circa quod, intelligit Definitiones, quibus, vt apparet apud Eucli&shy;<lb/>dem, explicatur &longs;ubiectum, circa quod &longs;cientia ver&longs;atur; vt in definitioni&shy;<lb/>bus primi Elem. </s> <s>per princi&shy;<lb/>pia ver&ograve; circa quod, intelligit Definitiones, quibus, vt apparet apud Eucli&shy;<lb/>dem, explicatur &longs;ubiectum, circa quod &longs;cientia ver&longs;atur; vt in definitioni&shy;<lb/>bus primi Elem.
  
 <s>docemur, quid &longs;it linea, quid triangulum, quid circulus, <lb/>quid magnitudines reliqu&aelig;, qu&aelig; &longs;unt materia, circa quam Geometria &longs;pe&shy;<lb/>culatur. </s> docemur, quid &longs;it linea, quid triangulum, quid circulus, <lb/>quid magnitudines reliqu&aelig;, qu&aelig; &longs;unt materia, circa quam Geometria &longs;pe&shy;<lb/>culatur. </s>
  
 <s>In &longs;eptimo ver&ograve; traduntur definitiones numerorum, quid &longs;it nu&shy;<lb/>merus, quid impar, quid compo&longs;itus, quadratus, cubus, &amp; reliqu&aelig; nume&shy;<lb/>rorum &longs;pecies, qu&aelig; &longs;unt materia &longs;eptimi, octaui, &amp; noni, in quibus de Arith&shy;<lb/>metica tractatur.</s></p><p type="main"> <s>In &longs;eptimo ver&ograve; traduntur definitiones numerorum, quid &longs;it nu&shy;<lb/>merus, quid impar, quid compo&longs;itus, quadratus, cubus, &amp; reliqu&aelig; nume&shy;<lb/>rorum &longs;pecies, qu&aelig; &longs;unt materia &longs;eptimi, octaui, &amp; noni, in quibus de Arith&shy;<lb/>metica tractatur.</s></p><p type="main">
  
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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. </s> 
  
 <s>1. Priorum &longs;ecto 1. cap. </s> 1. Priorum &longs;ecto 1. cap.
  
 <s>23. ait igitur Ari&longs;t.  23. ait igitur Ari&longs;t.
  
 ab&longs;urdum e&longs;&longs;e opinari dia&shy;<lb/>metrum e&longs;&longs;e commen&longs;urabilem co&longs;t&aelig;, &longs;eu lateri eiu&longs;dem quadrati, reli&shy;<lb/>qua &longs;unt Logica.</s></p><p type="head"> ab&longs;urdum e&longs;&longs;e opinari dia&shy;<lb/>metrum e&longs;&longs;e commen&longs;urabilem co&longs;t&aelig;, &longs;eu lateri eiu&longs;dem quadrati, reli&shy;<lb/>qua &longs;unt Logica.</s></p><p type="head">
  
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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>in quo Zabarella non probatur, qui &longs;olum <lb/>ait, terram e&longs;&longs;e in medio mundi, &agrave; Phy&longs;icis demon&longs;trari. </s> <s>in quo Zabarella non probatur, qui &longs;olum <lb/>ait, terram e&longs;&longs;e in medio mundi, &agrave; Phy&longs;icis demon&longs;trari. </s>
  
 <s><expan abbr="tri&atilde;gulum">triangulum</expan> autem, <lb/>&longs;eu angulorum ip&longs;ius <expan abbr="pr&aelig;dicat&utilde;">pr&aelig;dicatum</expan> e&longs;t &aelig;qualitas, &amp; in&aelig;qualitas: vt cum in 32. <lb/>primi Elem. </s> <s><expan abbr="tri&atilde;gulum">triangulum</expan> autem, <lb/>&longs;eu angulorum ip&longs;ius <expan abbr="pr&aelig;dicat&utilde;">pr&aelig;dicatum</expan> e&longs;t &aelig;qualitas, &amp; in&aelig;qualitas: vt cum in 32. <lb/>primi Elem.
  
 <s>demon&longs;trat Euclides, omne triangulum habcre tres angulos <lb/>&aelig;quales duobus rectis.</s></p><p type="main"> demon&longs;trat Euclides, omne triangulum habcre tres angulos <lb/>&aelig;quales duobus rectis.</s></p><p type="main">
  
 <s><arrow.to.target n="marg64"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg64"></arrow.to.target></s></p><p type="margin">
  
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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. </s> 
  
 <s>1. Priorum &longs;ecto 3. cap. </s> 1. Priorum &longs;ecto 3. cap.
  
 <s>1.</s></p><p type="main"> 1.</s></p><p type="main">
  
 <s><arrow.to.target n="marg66"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg66"></arrow.to.target></s></p><p type="margin">
  
 <s><margin.target id="marg66"></margin.target>66</s></p><p type="main"> <s><margin.target id="marg66"></margin.target>66</s></p><p type="main">
  
 <s>Eodem tex. <emph type="italics"/>(Definitiones ver&ograve; apparent omnes &longs;upponentes, &amp; accipientes <lb/>ip&longs;um quid e&longs;t, vt Mathematic&aelig;, quid vnitas, quid par, &amp; impar)<emph.end type="italics"/> alludit ad de&shy;<lb/>finitiones 7. Elem. </s> <s>Eodem tex. <emph type="italics"/>(Definitiones ver&ograve; apparent omnes &longs;upponentes, &amp; accipientes <lb/>ip&longs;um quid e&longs;t, vt Mathematic&aelig;, quid vnitas, quid par, &amp; impar)<emph.end type="italics"/> alludit ad de&shy;<lb/>finitiones 7. Elem.
  
 <s>vbi agitur de numeris. </s> vbi agitur de numeris. </s>
  
 <s>Qu&aelig; ver&ograve; hoc loco de principijs <lb/>dicuntur, luculenti&longs;&longs;im&egrave; patent con&longs;ideranti definitiones, &amp; axiomata, qu&aelig; <lb/>Mathematicis demon&longs;trationibus in omnibus fer&egrave; libris pr&aelig;mittuntur; ex <lb/>quibus &longs;tatim demon&longs;trationes deriuantur.</s></p><p type="main"> <s>Qu&aelig; ver&ograve; hoc loco de principijs <lb/>dicuntur, luculenti&longs;&longs;im&egrave; patent con&longs;ideranti definitiones, &amp; axiomata, qu&aelig; <lb/>Mathematicis demon&longs;trationibus in omnibus fer&egrave; libris pr&aelig;mittuntur; ex <lb/>quibus &longs;tatim demon&longs;trationes deriuantur.</s></p><p type="main">
  
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 <s><margin.target id="marg67"></margin.target>67</s></p><p type="main"> <s><margin.target id="marg67"></margin.target>67</s></p><p type="main">
  
 <s>Et paulo po&longs;t <emph type="italics"/>(<expan abbr="Neq;">Neque</expan> <expan abbr="vtiq;">vtique</expan> de plano figura, non enim e&longs;t planum figura, <expan abbr="neq;">neque</expan> fi&shy;<lb/>gura planum)<emph.end type="italics"/> alludit ad definitiones planarum figurarum, qualis e&longs;t circu&shy;<lb/>lus, cuius definitio e&longs;t inter definitiones primi Elem. </s> <s>Et paulo po&longs;t <emph type="italics"/>(<expan abbr="Neq;">Neque</expan> <expan abbr="vtiq;">vtique</expan> de plano figura, non enim e&longs;t planum figura, <expan abbr="neq;">neque</expan> fi&shy;<lb/>gura planum)<emph.end type="italics"/> alludit ad definitiones planarum figurarum, qualis e&longs;t circu&shy;<lb/>lus, cuius definitio e&longs;t inter definitiones primi Elem.
  
 <s>15. &amp; e&longs;t huiu&longs;modi: <lb/>circulus e&longs;t figura plana, &longs;ub vnica linea comprehen&longs;a, qu&aelig; periph&aelig;ria ap&shy;<lb/>pellatur, ad quam ab vno puncto eorum, qu&aelig; intra figuram &longs;unt po&longs;ita, ca&shy;<lb/>dentes omnes rect&aelig; line&aelig; inter &longs;e &longs;unt &aelig;quales: in qua quidem definitione <lb/>non pr&aelig;dicatur planum de figura, nec figura de plano: <expan abbr="neq;">neque</expan> enim planum, <lb/>&longs;au plana &longs;uperficies e&longs;t figura &longs;ecundum &longs;e, ni&longs;i terminetur; <expan abbr="neq;">neque</expan> figura e&longs;t <lb/>plana &longs;uperficies, cum plurim&aelig; &longs;int figur&aelig; curu&aelig;, &amp; pr&aelig;terea &longs;olid&aelig; quam&shy;<lb/>plurim&aelig;.</s></p><p type="main"> 15. &amp; e&longs;t huiu&longs;modi: <lb/>circulus e&longs;t figura plana, &longs;ub vnica linea comprehen&longs;a, qu&aelig; periph&aelig;ria ap&shy;<lb/>pellatur, ad quam ab vno puncto eorum, qu&aelig; intra figuram &longs;unt po&longs;ita, ca&shy;<lb/>dentes omnes rect&aelig; line&aelig; inter &longs;e &longs;unt &aelig;quales: in qua quidem definitione <lb/>non pr&aelig;dicatur planum de figura, nec figura de plano: <expan abbr="neq;">neque</expan> enim planum, <lb/>&longs;au plana &longs;uperficies e&longs;t figura &longs;ecundum &longs;e, ni&longs;i terminetur; <expan abbr="neq;">neque</expan> figura e&longs;t <lb/>plana &longs;uperficies, cum plurim&aelig; &longs;int figur&aelig; curu&aelig;, &amp; pr&aelig;terea &longs;olid&aelig; quam&shy;<lb/>plurim&aelig;.</s></p><p type="main">
  
 <s><arrow.to.target n="marg68"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg68"></arrow.to.target></s></p><p type="margin">
  
 <s><margin.target id="marg68"></margin.target>68</s></p><p type="main"> <s><margin.target id="marg68"></margin.target>68</s></p><p type="main">
  
 <s>Ibidem <emph type="italics"/>(Quoniam mon&longs;tratum e&longs;t I&longs;o&longs;celes habere tres angulos &aelig;quales duo&shy;<lb/>bus rectis, &longs;i id de omni triangulo mon&longs;tratum &longs;it)<emph.end type="italics"/> ex dictis lib. </s> <s>Ibidem <emph type="italics"/>(Quoniam mon&longs;tratum e&longs;t I&longs;o&longs;celes habere tres angulos &aelig;quales duo&shy;<lb/>bus rectis, &longs;i id de omni triangulo mon&longs;tratum &longs;it)<emph.end type="italics"/> ex dictis lib.
  
 <s>1. Priorum &longs;ecto <lb/>3. cap. </s> 1. Priorum &longs;ecto <lb/>3. cap.
  
 <s>1. petatur huius loci declaratio.</s></p><p type="main"> 1. petatur huius loci declaratio.</s></p><p type="main">
  
 <s><arrow.to.target n="marg69"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg69"></arrow.to.target></s></p><p type="margin">
  
 <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">
  
 <s><margin.target id="marg70"></margin.target>70</s></p><p type="main"> <s><margin.target id="marg70"></margin.target>70</s></p><p type="main">
  
 <s>Ibidem <emph type="italics"/>(Quod autem &longs;it, monstrat)<emph.end type="italics"/> vt per&longs;picuum e&longs;t in prima <expan abbr="dem&otilde;&longs;tra-tione">demon&longs;tra&shy;<lb/>tione</expan> primi Elem. </s> <s>Ibidem <emph type="italics"/>(Quod autem &longs;it, monstrat)<emph.end type="italics"/> vt per&longs;picuum e&longs;t in prima <expan abbr="dem&otilde;&longs;tra-tione">demon&longs;tra&shy;<lb/>tione</expan> primi Elem.
  
 <s>vbi triangulum &aelig;quilaterum con&longs;truit, &amp; po&longs;tea probat <lb/>illud e&longs;&longs;e triangulum &aelig;quilaterum. </s> vbi triangulum &aelig;quilaterum con&longs;truit, &amp; po&longs;tea probat <lb/>illud e&longs;&longs;e triangulum &aelig;quilaterum. </s>
  
 <s>Certum tamen e&longs;t, Geometram luppo&shy;<lb/>nere triangulum in communi, cum inter definitiones ip&longs;ius contineatur, <pb pagenum="65"/>quod tamen non ob&longs;tat, quominus probare po&longs;&longs;it, aliquando po&longs;&longs;e <expan abbr="c&otilde;&longs;trni">con&longs;trni</expan>, <lb/>&amp; e&longs;&longs;e aliquod particulare triangulum, vt fit in pr&aelig;dicta demon&longs;tratione, <lb/>Euclidis.</s></p><p type="main"> <s>Certum tamen e&longs;t, Geometram luppo&shy;<lb/>nere triangulum in communi, cum inter definitiones ip&longs;ius contineatur, <pb pagenum="65"/>quod tamen non ob&longs;tat, quominus probare po&longs;&longs;it, aliquando po&longs;&longs;e <expan abbr="c&otilde;&longs;trni">con&longs;trni</expan>, <lb/>&amp; e&longs;&longs;e aliquod particulare triangulum, vt fit in pr&aelig;dicta demon&longs;tratione, <lb/>Euclidis.</s></p><p type="main">
  
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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/>vbi ip&longs;e o&longs;tendit angulum in &longs;emicirculo e&longs;&longs;e rectum. </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 aduertendum e&longs;t <lb/>propo&longs;itionem hanc 31. ab Euclide demon&longs;trari duobus modis; ex quibus <lb/>&longs;ecundum innuit hoc loco Ari&longs;t.  <s>Vbi aduertendum e&longs;t <lb/>propo&longs;itionem hanc 31. ab Euclide demon&longs;trari duobus modis; ex quibus <lb/>&longs;ecundum innuit hoc loco Ari&longs;t.
  
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 <s><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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 <s><margin.target id="marg76"></margin.target>76</s></p><p type="main"> <s><margin.target id="marg76"></margin.target>76</s></p><p type="main">
  
  
 <s>Cap. 13. (<emph type="italics"/>Con&longs;iderare, quod diameter est co&longs;t&aelig; incommen&longs;urabilis<emph.end type="italics"/>) vide <lb/>qu&aelig; de hac re &longs;crip&longs;i lib. </s> <s>Cap. 13. (<emph type="italics"/>Con&longs;iderare, quod diameter est co&longs;t&aelig; incommen&longs;urabilis<emph.end type="italics"/>) vide <lb/>qu&aelig; de hac re &longs;crip&longs;i lib.
  
  
 <s>1. Priorum &longs;ecto 1. cap. </s> 1. Priorum &longs;ecto 1. cap.
  
 <s>23.</s></p><p type="main"> 23.</s></p><p type="main">
  
 <s><arrow.to.target n="marg77"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg77"></arrow.to.target></s></p><p type="margin">
  
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 <s>mu&longs;ica&shy;<lb/>lium, ait, &longs;i virga celerius feriat aerem, gigni motum celeriorem in aere, <lb/><expan abbr="atq;">atque</expan> hinc &longs;onum acutiorem reddi, experientia con&longs;tat: &longs;i autem eadem vir&shy;<lb/>ga tardius aerem feriat, gigni motum in aere tardiorem, ex quo etiam &longs;o&shy;<lb/>num grauem, vt experientia docet. </s> <s>mu&longs;ica&shy;<lb/>lium, ait, &longs;i virga celerius feriat aerem, gigni motum celeriorem in aere, <lb/><expan abbr="atq;">atque</expan> hinc &longs;onum acutiorem reddi, experientia con&longs;tat: &longs;i autem eadem vir&shy;<lb/>ga tardius aerem feriat, gigni motum in aere tardiorem, ex quo etiam &longs;o&shy;<lb/>num grauem, vt experientia docet. </s>
  
 <s>Ptol&aelig;meus deinde lib. </s> <s>Ptol&aelig;meus deinde lib.
  
 <s>1. cap. </s> 1. cap.
  
 <s>3. Harm. <lb/></s> 3. Harm. <lb/></s>
  
 <s>cum ex alijs, tum ex celeritate oriri &longs;onum acutum, grauem ver&ograve; ex tardi&shy;<lb/>tate a&longs;&longs;erit; vt &longs;i chorda eadem parum inten&longs;a pul&longs;etur, tardius aerem ver&shy;<lb/>berat, &amp; ideo grauiorem &longs;onum efficit: &longs;i autem magis intendatur, validius <lb/>aerem pul&longs;abit, &amp; proinde citiorem motum illi imprimet, &amp; propterea <lb/>acutiorem &longs;onum reddet. </s> <s>cum ex alijs, tum ex celeritate oriri &longs;onum acutum, grauem ver&ograve; ex tardi&shy;<lb/>tate a&longs;&longs;erit; vt &longs;i chorda eadem parum inten&longs;a pul&longs;etur, tardius aerem ver&shy;<lb/>berat, &amp; ideo grauiorem &longs;onum efficit: &longs;i autem magis intendatur, validius <lb/>aerem pul&longs;abit, &amp; proinde citiorem motum illi imprimet, &amp; propterea <lb/>acutiorem &longs;onum reddet. </s>
  
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 <s>ab hac &longs;ententia po&longs;teriores Mu&longs;ici non recel&shy;<lb/>&longs;erunt, vt videre e&longs;t apud Zarlinum.</s></p><p type="main"> <s>ab hac &longs;ententia po&longs;teriores Mu&longs;ici non recel&shy;<lb/>&longs;erunt, vt videre e&longs;t apud Zarlinum.</s></p><p type="main">
  
 <s>In quo po&longs;tea con&longs;i&longs;tat ratio acnti anguli, explicat <expan abbr="induc&etilde;s">inducens</expan> definitionem <lb/>ip&longs;ius, qu&aelig; e&longs;t inter de&longs;initiones primi Elem. </s> <s>In quo po&longs;tea con&longs;i&longs;tat ratio acnti anguli, explicat <expan abbr="induc&etilde;s">inducens</expan> definitionem <lb/>ip&longs;ius, qu&aelig; e&longs;t inter de&longs;initiones primi Elem.
  
 <s>huiu&longs;modi, Angulus acutus <lb/>e&longs;t, qui minor recto e&longs;t. </s> huiu&longs;modi, Angulus acutus <lb/>e&longs;t, qui minor recto e&longs;t. </s>
  
 <s>Demum explicat, cur nam gladius dicatur acutus, <lb/>quia nimirum habet angulum acutum &longs;uperficialem, ide&longs;t, quem du&aelig; &longs;uper&shy;<lb/>ficies &longs;imul in acie gladij concurrentes efficiunt.</s></p><pb pagenum="68"/><p type="main"> <s>Demum explicat, cur nam gladius dicatur acutus, <lb/>quia nimirum habet angulum acutum &longs;uperficialem, ide&longs;t, quem du&aelig; &longs;uper&shy;<lb/>ficies &longs;imul in acie gladij concurrentes efficiunt.</s></p><pb pagenum="68"/><p type="main">
  
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 innuit. </s> innuit. </s>
  
 <s>quod genus for&longs;itan &agrave; calore denomina&shy;<lb/>batur, qu&ograve;d ip&longs;ius not&aelig; mu&longs;icales e&longs;&longs;ent colorat&aelig;, vt hoc modo ab alijs ge&shy;<lb/>neribus digno&longs;eeretur<gap/> quam con&longs;uetudinem exi&longs;timat Zarlinus cap. </s> <s>quod genus for&longs;itan &agrave; calore denomina&shy;<lb/>batur, qu&ograve;d ip&longs;ius not&aelig; mu&longs;icales e&longs;&longs;ent colorat&aelig;, vt hoc modo ab alijs ge&shy;<lb/>neribus digno&longs;eeretur<gap/> quam con&longs;uetudinem exi&longs;timat Zarlinus cap.
  
 <s>46. &longs;e&shy;<lb/>cund&aelig; partis, etiam no&longs;tra tempe&longs;tate aliquo modo per&longs;euerare, cum vi&shy;<lb/>deamus in organis, &amp; alijs huiu&longs;modi in&longs;trumentis, qu&aelig; pinnas, vulg&ograve; ta&shy;<lb/>&longs;tos, habent; illas inquam pinnas, qu&aelig; chromaticis interuallis deputat&aelig; <lb/>&longs;unt, colore nigro tinctas e&longs;&longs;e.</s></p><p type="head"> 46. &longs;e&shy;<lb/>cund&aelig; partis, etiam no&longs;tra tempe&longs;tate aliquo modo per&longs;euerare, cum vi&shy;<lb/>deamus in organis, &amp; alijs huiu&longs;modi in&longs;trumentis, qu&aelig; pinnas, vulg&ograve; ta&shy;<lb/>&longs;tos, habent; illas inquam pinnas, qu&aelig; chromaticis interuallis deputat&aelig; <lb/>&longs;unt, colore nigro tinctas e&longs;&longs;e.</s></p><p type="head">
  
 <s><emph type="italics"/>Libro Quarto.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Libro Quarto.<emph.end type="italics"/></s></p><p type="main">
  
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 <s>Cap. 2. loco 32. (<emph type="italics"/>Vt qui lineam definiunt longitudmem &longs;ine latitudine e&longs;&longs;e<emph.end type="italics"/>) <lb/>&longs;uppenimus lectorem inteil exi&longs;&longs;e definitiones &longs;altem primi Elem. </s> <s>Cap. 2. loco 32. (<emph type="italics"/>Vt qui lineam definiunt longitudmem &longs;ine latitudine e&longs;&longs;e<emph.end type="italics"/>) <lb/>&longs;uppenimus lectorem inteil exi&longs;&longs;e definitiones &longs;altem primi Elem.
  
  
 <s>in&shy;<lb/>ter quas d<gap/>f<gap/>nitio line&aelig; e&longs;t &longs;ecunda, <expan abbr="cadem&qacute;">cademque</expan>; cum hac Ari&longs;totelis.</s></p><p type="head"> in&shy;<lb/>ter quas d<gap/>f<gap/>nitio line&aelig; e&longs;t &longs;ecunda, <expan abbr="cadem&qacute;">cademque</expan>; cum hac Ari&longs;totelis.</s></p><p type="head">
  
 <s><emph type="italics"/>Libro Octauo.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Libro Octauo.<emph.end type="italics"/></s></p><p type="main">
  
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 <s>Cap. 2. loco 41. (<emph type="italics"/>Videntur dutem in di&longs;ciplinis, &longs;eu Mathematicis qu&aelig;dam <lb/>ob de&longs;initionis defectum non facile de&longs;cribi; vt &amp; quoniam, qu&aelig; ad latus &longs;e&shy;<lb/>cat planum linea, &longs;imiliter diuidit &amp; lineam, &amp; locum: definitione autem dicta, <lb/>fi <gap/>m man fe&longs;tu<gap/>t&longs;t, quod dicitur, nam eandem ablationem habent lota, &amp; <gap/>inea, <lb/><gap/>se latus plan&aelig; figur&aelig;, est autem definitio eiu&longs;dem proportionis h&aelig;c<emph.end type="italics"/>) mendos&egrave; <lb/>lugitur &agrave; nonnullis (<emph type="italics"/>E&longs;t distem de&longs;initio eiu&longs;dem orationis h&aelig;c<emph.end type="italics"/>) quos puto de&shy;<lb/>ceptos ab &aelig;quiuoco <foreign lang="greek">lsgous</foreign> quod &amp; orationem, &amp; rationem, &longs;iue proportio&shy;<lb/>nem &longs;ignificat: hic autem &longs;ignificare proportionem res &longs;ubrecta &longs;atis mani&shy;<lb/>fe&longs;tat. </s> <s>Cap. 2. loco 41. (<emph type="italics"/>Videntur dutem in di&longs;ciplinis, &longs;eu Mathematicis qu&aelig;dam <lb/>ob de&longs;initionis defectum non facile de&longs;cribi; vt &amp; quoniam, qu&aelig; ad latus &longs;e&shy;<lb/>cat planum linea, &longs;imiliter diuidit &amp; lineam, &amp; locum: definitione autem dicta, <lb/>fi <gap/>m man fe&longs;tu<gap/>t&longs;t, quod dicitur, nam eandem ablationem habent lota, &amp; <gap/>inea, <lb/><gap/>se latus plan&aelig; figur&aelig;, est autem definitio eiu&longs;dem proportionis h&aelig;c<emph.end type="italics"/>) mendos&egrave; <lb/>lugitur &agrave; nonnullis (<emph type="italics"/>E&longs;t distem de&longs;initio eiu&longs;dem orationis h&aelig;c<emph.end type="italics"/>) quos puto de&shy;<lb/>ceptos ab &aelig;quiuoco <foreign lang="greek">lsgous</foreign> quod &amp; orationem, &amp; rationem, &longs;iue proportio&shy;<lb/>nem &longs;ignificat: hic autem &longs;ignificare proportionem res &longs;ubrecta &longs;atis mani&shy;<lb/>fe&longs;tat. </s>
  
  
 <s>Notandum po&longs;tea cum Alexandro (quod &amp; &longs;uperius alias commo&shy;<lb/>nui in cap. </s> <s>Notandum po&longs;tea cum Alexandro (quod &amp; &longs;uperius alias commo&shy;<lb/>nui in cap.
  
 <s>de Priori, &amp; alibi) per verbum (De&longs;cribi) fignificari hoc loco <lb/>geometric&egrave; demon&longs;trare, quoniam Geometr&aelig; <expan abbr="n&otilde;">non</expan> ni&longs;i adhibit is de&longs;criptio&shy;<lb/>nibus, &longs;<gap/>u figutis demon&longs;trant. </s> de Priori, &amp; alibi) per verbum (De&longs;cribi) fignificari hoc loco <lb/>geometric&egrave; demon&longs;trare, quoniam Geometr&aelig; <expan abbr="n&otilde;">non</expan> ni&longs;i adhibit is de&longs;criptio&shy;<lb/>nibus, &longs;<gap/>u figutis demon&longs;trant. </s>
  
 <s>Vult autem Ari&longs;t.  <s>Vult autem Ari&longs;t.
  
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 <s>Porr&ograve; Euclides definit. </s> <s>Porr&ograve; Euclides definit. </s>
  
 <s>&longs;eptima 5. paulo ali&shy;<lb/>ter definit quantitates proportionales e&longs;&longs;e illas, qu&aelig; candem habent ratio&shy;<lb/>nem, v. </s> <s>&longs;eptima 5. paulo ali&shy;<lb/>ter definit quantitates proportionales e&longs;&longs;e illas, qu&aelig; eandem habent ratio&shy;<lb/>nem, v. </s>
  
 <s>g. </s> <s>g. </s>
  
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 <s>Cap. 10. <emph type="italics"/>(Nam p&longs;eudograpbi&aelig; non contentio&longs;&aelig; (&longs;ecundum enim ea, qu&aelig; <lb/>&longs;ub arte &longs;unt, captio&longs;&aelig; &longs;unt ratiocinationes) <expan abbr="neq;">neque</expan> &longs;i aliqua e&longs;t p&longs;eudogra&shy;<lb/>phia circa verum, vt Hippocratis quadratura, qu&aelig; per lunulas, &longs;ed, vt <lb/>Bry&longs;&longs;o quadrauit circulum; &amp; tamet&longs;i quadretur circulus, quia tamen <lb/>non &longs;ecundum rem, ideo &longs;ophi&longs;ticus)<emph.end type="italics"/> qua ratione Hippocrates orbi quadrum <lb/>exhibere &aelig;quale tentauerit, explicatum e&longs;t abund&egrave; in 2. Priorum cap. </s> <s>Cap. 10. <emph type="italics"/>(Nam p&longs;eudograpbi&aelig; non contentio&longs;&aelig; (&longs;ecundum enim ea, qu&aelig; <lb/>&longs;ub arte &longs;unt, captio&longs;&aelig; &longs;unt ratiocinationes) <expan abbr="neq;">neque</expan> &longs;i aliqua e&longs;t p&longs;eudogra&shy;<lb/>phia circa verum, vt Hippocratis quadratura, qu&aelig; per lunulas, &longs;ed, vt <lb/>Bry&longs;&longs;o quadrauit circulum; &amp; tamet&longs;i quadretur circulus, quia tamen <lb/>non &longs;ecundum rem, ideo &longs;ophi&longs;ticus)<emph.end type="italics"/> qua ratione Hippocrates orbi quadrum <lb/>exhibere &aelig;quale tentauerit, explicatum e&longs;t abund&egrave; in 2. Priorum cap.
  
  
 <s>31. <lb/>&amp; quo itidem modo Bry&longs;&longs;o lib. </s> 
  
 <s>1. Po&longs;ter. </s> 31. <lb/>&amp; quo itidem modo Bry&longs;&longs;o lib.
  
 <s>tex. </s> 1. Po&longs;ter. tex. </s>
  
 <s>23. <expan abbr="&longs;ol&utilde;modo">&longs;olummodo</expan> id hoc loco no&shy;<lb/>tandum per p&longs;eudographiam intelligere, vt apert&egrave; etiam inferius explicat, <lb/>Geometricam demon&longs;trationem fallacem, e&ograve; quod demon&longs;trationes geo&shy;<lb/>metric&aelig; fiant adhibitis de&longs;criptionibus, &longs;eu figurationibus: p&longs;endographia <lb/>autem latin&egrave; idem e&longs;t, ac fal&longs;a de&longs;criptio; quemadmodum &egrave; contrari&ograve;, &longs;i&shy;<lb/>cuti &longs;upra in Topicis, &amp; alibi ob&longs;eruaui, per de&longs;cribere intelligit geometri&shy;<lb/>c&egrave; demon&longs;trare, &amp; per de&longs;criptiones intelligit demon&longs;trationes geometri&shy;<lb/>cas. </s> <s>23. <expan abbr="&longs;ol&utilde;modo">&longs;olummodo</expan> id hoc loco no&shy;<lb/>tandum per p&longs;eudographiam intelligere, vt apert&egrave; etiam inferius explicat, <lb/>Geometricam demon&longs;trationem fallacem, e&ograve; quod demon&longs;trationes geo&shy;<lb/>metric&aelig; fiant adhibitis de&longs;criptionibus, &longs;eu figurationibus: p&longs;endographia <lb/>autem latin&egrave; idem e&longs;t, ac fal&longs;a de&longs;criptio; quemadmodum &egrave; contrari&ograve;, &longs;i&shy;<lb/>cuti &longs;upra in Topicis, &amp; alibi ob&longs;eruaui, per de&longs;cribere intelligit geometri&shy;<lb/>c&egrave; demon&longs;trare, &amp; per de&longs;criptiones intelligit demon&longs;trationes geometri&shy;<lb/>cas. </s>
  
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 <s>Ibidem <emph type="italics"/>(Bry&longs;&longs;onis autem contentio&longs;a: &amp; illam quidem non e&longs;t transferre, ni&longs;i <lb/>ad Geometriam &longs;olum; eo quod ex proprijs &longs;it principijs)<emph.end type="italics"/> <expan abbr="qu&atilde;do">quando</expan> ait <emph type="italics"/>(&amp; illam qui&shy;<lb/>dem)<emph.end type="italics"/> intelligit quadrationem Hippocratis. </s> <s>Ibidem <emph type="italics"/>(Bry&longs;&longs;onis autem contentio&longs;a: &amp; illam quidem non e&longs;t transferre, ni&longs;i <lb/>ad Geometriam &longs;olum; eo quod ex proprijs &longs;it principijs)<emph.end type="italics"/> <expan abbr="qu&atilde;do">quando</expan> ait <emph type="italics"/>(&amp; illam qui&shy;<lb/>dem)<emph.end type="italics"/> intelligit quadrationem Hippocratis. </s>
  
 <s>vide 2. Prior cap. </s> <s>vide 2. Prior cap.
  
 <s>31. &amp; qu&aelig; pau&shy;<lb/>lo ante in pr&aelig;cedentibus locis diximus.</s></p><p type="main"> 31. &amp; qu&aelig; pau&shy;<lb/>lo ante in pr&aelig;cedentibus locis diximus.</s></p><p type="main">
  
 <s><arrow.to.target n="marg86"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg86"></arrow.to.target></s></p><p type="margin">
  
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 <s>Tex. </s> <s>Tex. 11. <emph type="italics"/>(Simul autem <expan abbr="neq;">neque</expan> conuenit omnia &longs;oluere', &longs;ed <expan abbr="qu&aelig;cunq;">qu&aelig;cunque</expan> ex <lb/>principijs aliquis demon&longs;trans <expan abbr="m&etilde;titur">mentitur</expan>; <expan abbr="qu&aelig;cunq;">qu&aelig;cunque</expan> ver&ograve; non, minim&egrave;: <lb/>vt tetragoni&longs;mum, eum quidem, qui per &longs;ectiones Geometrici est di&longs;&shy;<lb/>&longs;oluere: illum autem, qui Antiphontis non Geometrici e&longs;t<emph.end type="italics"/>) Tetrago&shy;<lb/>ni&longs;mum, &longs;eu circuli quadraturam per &longs;ectiones, e&longs;&longs;e illam Hip&shy;<lb/>pocratis Chij exi&longs;timant gr&aelig;ci expo&longs;itores, qui per lunulas, quas Ari&longs;t. &longs;e&shy;<lb/>ctiones appellat, orbem quadrare tentabat. </s>
  
 <s>11. <emph type="italics"/>(Simul autem <expan abbr="neq;">neque</expan> conuenit omnia &longs;oluere', &longs;ed <expan abbr="qu&aelig;cunq;">qu&aelig;cunque</expan> ex <lb/>principijs aliquis demon&longs;trans <expan abbr="m&etilde;titur">mentitur</expan>; <expan abbr="qu&aelig;cunq;">qu&aelig;cunque</expan> ver&ograve; non, minim&egrave;: <lb/>vt tetragoni&longs;mum, eum quidem, qui per &longs;ectiones Geometrici est di&longs;&shy;<lb/>&longs;oluere: illum autem, qui Antiphontis non Geometrici e&longs;t<emph.end type="italics"/>) Tetrago&shy;<lb/>ni&longs;mum, &longs;eu circuli quadraturam per &longs;ectiones, e&longs;&longs;e illam Hip&shy;<lb/>pocratis Chij exi&longs;timant gr&aelig;ci expo&longs;itores, qui per lunulas, quas Ari&longs;t. </s> <s>Eius den on&longs;trationem expli&shy;<lb/>caui ad cap.
  
 <s>&longs;e&shy;<lb/>ctiones appellat, orbem quadrare tentabat. </s> 31. de Abductione in 2. Priorum, quam inibi videas. </s>
  
 <s>Eius den on&longs;trationem expli&shy;<lb/>caui ad cap. </s> 
  
 <s>31. de Abductione in 2. Priorum, quam inibi videas. </s> 
  
 <s>hoc &longs;olum <lb/>hic notandum pertinere ad Geometram, ip&longs;am refellere, quia ex fal&longs;a qua&shy;<lb/>dam pr&aelig;mi&longs;&longs;a ex Geometria de&longs;umpta, ratiocinabatur, idcirco debet (in&shy;<lb/>quit Ari&longs;t.) Geometra illius deceptionem inuenire. </s> <s>hoc &longs;olum <lb/>hic notandum pertinere ad Geometram, ip&longs;am refellere, quia ex fal&longs;a qua&shy;<lb/>dam pr&aelig;mi&longs;&longs;a ex Geometria de&longs;umpta, ratiocinabatur, idcirco debet (in&shy;<lb/>quit Ari&longs;t.) Geometra illius deceptionem inuenire. </s>
  
 <s>Tetragoni&longs;mum autem <lb/>Antiphontis non e&longs;t Geometr&aelig; <expan abbr="c&otilde;futare">confutare</expan>, quia aduer&longs;abatur principijs Geo&shy;<lb/>metri&aelig;, &longs;upponebat enim circuli circumferentiam ex indiu<gap/>s, <expan abbr="minimis&qacute;">minimisque</expan>; <lb/>lineis rectis componi: cuius fal&longs;am demon&longs;trationem exp<gap/>ram i<gap/>uenies <lb/>ad cap. </s> <s>Tetragoni&longs;mum autem <lb/>Antiphontis non e&longs;t Geometr&aelig; <expan abbr="c&otilde;futare">confutare</expan>, quia aduer&longs;abatur principijs Geo&shy;<lb/>metri&aelig;, &longs;upponebat enim circuli circumferentiam ex indiu<gap/>s, <expan abbr="minimis&qacute;">minimisque</expan>; <lb/>lineis rectis componi: cuius fal&longs;am demon&longs;trationem exp<gap/>ram i<gap/>uenies <lb/>ad cap.
  
 <s>10. primi Elench. </s> 10. primi Elench. </s>
  
 <s>po&longs;&longs;umus addere tertiam rat<gap/> <gap/>cet <lb/>Hippocrates non procedebat per communia alijs &longs;ci<gap/>ad <lb/>tex. </s> <s>po&longs;&longs;umus addere tertiam rat<gap/> <gap/>cet <lb/>Hippocrates non procedebat per communia alijs &longs;ci<gap/>ad <lb/>tex. </s>
  
 <s>23. primi Po&longs;ter. </s> <s>23. primi Po&longs;ter. cap.
  
 <s>cap. </s> 
  
 <s>8. vbi ip&longs;ius p&longs;endographi<gap/>d&shy;<lb/>modum igitur Geometra di&longs;&longs;oluit fal&longs;as tantum<gap/>r&shy;<lb/>uatis Geometricis principijs procedunt; non au<gap/> <gap/>ri&aelig; <lb/>principia conuellunt: ita Phy&longs;ico non incumbit <expan abbr="c&otilde;tra">contra</expan> P<gap/> Me&shy;<lb/>li&longs;&longs;um natur&aelig; principia de&longs;truentes di&longs;ceptare, aut falla<gap/> rationes <lb/>coarguere. </s> 8. vbi ip&longs;ius p&longs;endographi<gap/>d&shy;<lb/>modum igitur Geometra di&longs;&longs;oluit fal&longs;as tantum<gap/>r&shy;<lb/>uatis Geometricis principijs procedunt; non au<gap/> <gap/>ri&aelig; <lb/>principia conuellunt: ita Phy&longs;ico non incumbit <expan abbr="c&otilde;tra">contra</expan> P<gap/> Me&shy;<lb/>li&longs;&longs;um natur&aelig; principia de&longs;truentes di&longs;ceptare, aut falla<gap/> rationes <lb/>coarguere. </s>
  
 <s>Hoc volebat Ari&longs;toteles inferre.</s></p><p type="head"> <s>Hoc volebat Ari&longs;toteles inferre.</s></p><p type="head">
  
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 <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> <s>1. cap.
  
 <s>primi 2. Po&shy;<lb/>&longs;ter. </s> primi 2. Po&shy;<lb/>&longs;ter. </s>
  
 <s>&longs;uper verba illa (<emph type="italics"/>Quid e&longs;t con&longs;onan<gap/>ia?<emph.end type="italics"/>) vbi per&longs;picu&egrave; videbis, cur <expan abbr="con-&longs;on&atilde;ti&aelig;">con&shy;<lb/>&longs;onanti&aelig;</expan>, qu&aelig; dicitur Diapa&longs;on, e&longs;&longs;entia, &amp; definitio &longs;it ip&longs;a proportio dupla, <lb/>qu&aelig; &longs;ub his num. </s> <s>&longs;uper verba illa (<emph type="italics"/>Quid e&longs;t con&longs;onan<gap/>ia?<emph.end type="italics"/>) vbi per&longs;picu&egrave; videbis, cur <expan abbr="con-&longs;on&atilde;ti&aelig;">con&shy;<lb/>&longs;onanti&aelig;</expan>, qu&aelig; dicitur Diapa&longs;on, e&longs;&longs;entia, &amp; definitio &longs;it ip&longs;a proportio dupla, <lb/>qu&aelig; &longs;ub his num. </s>
  
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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>cum velit Ari&longs;t.  <s>cum velit Ari&longs;t.
  
 o&longs;tendere nece&longs;&longs;ita&shy;<lb/>tem, qu&aelig; in &longs;cientijs inter pr&aelig;mi&longs;&longs;as, &longs;cu medium, &amp; conclu&longs;ionem reperi&shy;<lb/>tur, affert exemplum illud mathematicum &longs;ibi familiare, demon&longs;trationem <lb/>&longs;cilicet illam, qua o&longs;tenditur, omne triangulum habere tres angulos &aelig;qua&shy;<lb/>les duobus rectis angulis, cuius fu&longs;i&longs;&longs;imam explicationem inuenies &longs;upra in <lb/>primo Priorum, &longs;ecto 3. cap. </s> o&longs;tendere nece&longs;&longs;ita&shy;<lb/>tem, qu&aelig; in &longs;cientijs inter pr&aelig;mi&longs;&longs;as, &longs;cu medium, &amp; conclu&longs;ionem reperi&shy;<lb/>tur, affert exemplum illud mathematicum &longs;ibi familiare, demon&longs;trationem <lb/>&longs;cilicet illam, qua o&longs;tenditur, omne triangulum habere tres angulos &aelig;qua&shy;<lb/>les duobus rectis angulis, cuius fu&longs;i&longs;&longs;imam explicationem inuenies &longs;upra in <lb/>primo Priorum, &longs;ecto 3. cap.
  
 <s>1. quam nece&longs;&longs;e e&longs;t, con&longs;ulas. </s> 1. quam nece&longs;&longs;e e&longs;t, con&longs;ulas. </s>
  
 <s>pro medio autem <lb/>huius pa&longs;&longs;ionis accipit lineam perpendicularem, quam innuit verbis illis <lb/><emph type="italics"/>(quoniam enim hoc rectum e&longs;t<emph.end type="italics"/>) vt in figura &longs;it triangulum A B C, <expan abbr="&longs;it&qacute;">&longs;itque</expan>; vt latus <lb/><figure id="fig33"></figure><lb/>A C, &longs;it perpendiculare <expan abbr="c&utilde;">cum</expan> latere B C, &amp; pro&shy;<lb/>ducatur B C, in D; tunc triangulum A B C, <lb/>habere tres angulos, A, B, &amp; A C B, &aelig;quales <lb/>duobus rectis planum erit: nam <expan abbr="c&utilde;">cum</expan> latus A C, <lb/>&longs;it perpendiculare (quod Ari&longs;t.  <s>pro medio autem <lb/>huius pa&longs;&longs;ionis accipit lineam perpendicularem, quam innuit verbis illis <lb/><emph type="italics"/>(quoniam enim hoc rectum e&longs;t<emph.end type="italics"/>) vt in figura &longs;it triangulum A B C, <expan abbr="&longs;it&qacute;">&longs;itque</expan>; vt latus <lb/><figure id="fig33"></figure><lb/>A C, &longs;it perpendiculare <expan abbr="c&utilde;">cum</expan> latere B C, &amp; pro&shy;<lb/>ducatur B C, in D; tunc triangulum A B C, <lb/>habere tres angulos, A, B, &amp; A C B, &aelig;quales <lb/>duobus rectis planum erit: nam <expan abbr="c&utilde;">cum</expan> latus A C, <lb/>&longs;it perpendiculare (quod Ari&longs;t.
  
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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. </s> de Motu in po&longs;t pr&aelig;dicamentis &longs;crip&longs;i de Gnomone, ad <lb/>&longs;imilitudinem enim Gnomonis illius Geometrici, inueniuntur etiam in nu&shy;<lb/>meris Gnomones Arithmetici. </s>
  
 <s>de Motu in po&longs;t pr&aelig;dicamentis &longs;crip&longs;i de Gnomone, ad <lb/>&longs;imilitudinem enim Gnomonis illius Geometrici, inueniuntur etiam in nu&shy;<lb/>meris Gnomones Arithmetici. </s> 
  
 <s>Pythagorici enim (&agrave; quibus i&longs;ta mutuatus <lb/>e&longs;t Ari&longs;t.  <s>Pythagorici enim (&agrave; quibus i&longs;ta mutuatus <lb/>e&longs;t Ari&longs;t.
  
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 <s>pares autem numeri, quia ne&shy;<lb/>queunt in figuram norm&aelig; &aelig;quilater&aelig; di&longs;poni, cum <lb/>non habeant vnitatem pro angulo, &amp; paria po&longs;tea la&shy;<lb/>tera, vt oportet, non merentur appellari Gnomones, vt quaternarius, &longs;i di&shy;<lb/>&longs;ponatur &longs;ic <figure id="fig35"></figure> non refert Gnomonem, quia lateribus in&ecedil;qualibus con&shy;<lb/>&longs;tat; <expan abbr="neq;">neque</expan> &longs;i hoc modo <figure id="fig36"></figure> quia dee&longs;t huic figur&aelig; angularis vnitas, qu&aelig; <lb/>illi nece&longs;iaria e&longs;t. </s> <s>pares autem numeri, quia ne&shy;<lb/>queunt in figuram norm&aelig; &aelig;quilater&aelig; di&longs;poni, cum <lb/>non habeant vnitatem pro angulo, &amp; paria po&longs;tea la&shy;<lb/>tera, vt oportet, non merentur appellari Gnomones, vt quaternarius, &longs;i di&shy;<lb/>&longs;ponatur &longs;ic <figure id="fig35"></figure> non refert Gnomonem, quia lateribus in&ecedil;qualibus con&shy;<lb/>&longs;tat; <expan abbr="neq;">neque</expan> &longs;i hoc modo <figure id="fig36"></figure> quia dee&longs;t huic figur&aelig; angularis vnitas, qu&aelig; <lb/>illi nece&longs;iaria e&longs;t. </s>
  
 <s>Pythagorici igitur dicebant, numerum parem ide&ograve; e&longs;&longs;e <lb/>infinitum ip&longs;um, quia videbant ip&longs;um e&longs;&longs;e cau&longs;am perpetu&aelig; diui&longs;ionis, cum <lb/>qu&aelig;libet res quanta &longs;it diui&longs;ibilis bifariam, ide&longs;t in duo &longs;ecundum numerum <lb/>parem, &amp; &longs;ubdiui&longs;ibilis po&longs;tea bifariam, &amp; &longs;ic in infinitum, vt de linea pro&shy;<lb/>blematic&egrave; probatur in 10. primi Elem. </s> <s>Pythagorici igitur dicebant, numerum parem ide&ograve; e&longs;&longs;e <lb/>infinitum ip&longs;um, quia videbant ip&longs;um e&longs;&longs;e cau&longs;am perpetu&aelig; diui&longs;ionis, cum <lb/>qu&aelig;libet res quanta &longs;it diui&longs;ibilis bifariam, ide&longs;t in duo &longs;ecundum numerum <lb/>parem, &amp; &longs;ubdiui&longs;ibilis po&longs;tea bifariam, &amp; &longs;ic in infinitum, vt de linea pro&shy;<lb/>blematic&egrave; probatur in 10. primi Elem.
  
 <s>quamuis theorematic&egrave; &longs;it axioma. <lb/></s> quamuis theorematic&egrave; &longs;it axioma. <lb/></s>
  
 <s>hunc porr&ograve; numerum parem dicebant terminatum e&longs;&longs;e ab impari, quia ori&shy;<lb/>tur ex diui&longs;ione cuiu&longs;uis rei, qu&aelig; vna &longs;it, &longs;umentes vnitatem pro impari. <lb/></s> <s>hunc porr&ograve; numerum parem dicebant terminatum e&longs;&longs;e ab impari, quia ori&shy;<lb/>tur ex diui&longs;ione cuiu&longs;uis rei, qu&aelig; vna &longs;it, &longs;umentes vnitatem pro impari. <lb/></s>
  
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 <s>&amp; &longs;ic &longs;emper in infinitum nou&aelig; ac vari&aelig; numerorum <lb/>form&aelig; ex hac additione parium prouenient, quod argumento e&longs;t numerum <lb/>parem infiniti naturam &longs;apere. </s> <s>&amp; &longs;ic &longs;emper in infinitum nou&aelig; ac vari&aelig; numerorum <lb/>form&aelig; ex hac additione parium prouenient, quod argumento e&longs;t numerum <lb/>parem infiniti naturam &longs;apere. </s>
  
 <s>Porr&ograve; reperiri numeros triangulares, pen&shy;<lb/>tagonos, &amp; &longs;imiles, con&longs;tat ex Arithmetica Nicomachi, Boetij, &amp; Iordani, <lb/>citati in definitionibus 7. &longs;u&aelig; Arithmetic&aelig;, atque ex tractatu Diophantis <lb/>Alex. </s> <s>Porr&ograve; reperiri numeros triangulares, pen&shy;<lb/>tagonos, &amp; &longs;imiles, con&longs;tat ex Arithmetica Nicomachi, Boetij, &amp; Iordani, <lb/>citati in definitionibus 7. &longs;u&aelig; Arithmetic&aelig;, atque ex tractatu Diophantis <lb/>Alex. de numeris rectangulis. </s>
  
 <s>de numeris rectangulis. </s> 
  
 <s><expan abbr="atq;">atque</expan> ex his locus hic &longs;atis clarus redditur.</s></p><p type="main"> <s><expan abbr="atq;">atque</expan> ex his locus hic &longs;atis clarus redditur.</s></p><p type="main">
  
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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. </s> editionis Clauian&aelig;. </s>
  
 <s>editionis Clauian&aelig;. </s> <s>numerum <expan abbr="quoq;">quoque</expan> au&shy;<lb/>geri po&longs;&longs;e in infinitum, e&longs;t &longs;ecundum po&longs;tulatum libri 7. Elem.
  
 <s>numerum <expan abbr="quoq;">quoque</expan> au&shy;<lb/>geri po&longs;&longs;e in infinitum, e&longs;t &longs;ecundum po&longs;tulatum libri 7. Elem. </s> vel demum <lb/>quando probant quamlibet lineam po&longs;&longs;e diuidi bifariam, quia hinc &longs;equitur <lb/>po&longs;&longs;e &longs;ub diuidi in <expan abbr="infinit&utilde;">infinitum</expan>; his igitur modis Mathematicis <expan abbr="infinit&utilde;">infinitum</expan> in v&longs;u e&longs;t.</s></p><p type="main">
  
 <s>vel demum <lb/>quando probant quamlibet lineam po&longs;&longs;e diuidi bifariam, quia hinc &longs;equitur <lb/>po&longs;&longs;e &longs;ub diuidi in <expan abbr="infinit&utilde;">infinitum</expan>; his igitur modis Mathematicis <expan abbr="infinit&utilde;">infinitum</expan> in v&longs;u e&longs;t.</s></p><p type="main"> 
  
 <s><arrow.to.target n="marg95"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg95"></arrow.to.target></s></p><p type="margin">
  
 <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. </s> 23.</s></p><figure></figure><pb pagenum="76"/><p type="head">
  
 <s>23.</s></p><figure></figure><pb pagenum="76"/><p type="head"> 
  
 <s><emph type="italics"/>Ex Quinto Phy&longs;icorum.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Ex Quinto Phy&longs;icorum.<emph.end type="italics"/></s></p><p type="main">
  
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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. </s> 
  
 <s>1. Priorum, &longs;ecto 3. cap. </s> 1. Priorum, &longs;ecto 3. cap.
  
 <s>1. huius rei explicationem reperies.</s></p><p type="head"> 1. huius rei explicationem reperies.</s></p><p type="head">
  
 <s><emph type="italics"/>EX PRIMO DE COELO.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>EX PRIMO DE COELO.<emph.end type="italics"/></s></p><p type="main">
  
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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>
  
 <s>10. primi Elem. </s> <s>10. primi Elem.
  
 <s>qu&aelig; docet <lb/>quamlibet lineam po&longs;&longs;e diuidi bifariam nulla e&longs;&longs;et, quia linea illa, qu&aelig; con&shy;<lb/>&longs;taret ex tribus Democriti atomis, nulla ratione bifariam &longs;ecari po&longs;&longs;et. </s> qu&aelig; docet <lb/>quamlibet lineam po&longs;&longs;e diuidi bifariam nulla e&longs;&longs;et, quia linea illa, qu&aelig; con&shy;<lb/>&longs;taret ex tribus Democriti atomis, nulla ratione bifariam &longs;ecari po&longs;&longs;et. </s>
  
 <s>pa&shy;<lb/>riter totus fer&egrave; decimus liber Elem. </s> <s>pa&shy;<lb/>riter totus fer&egrave; decimus liber Elem.
  
 <s>deceptiuus, &amp; nullus e&longs;&longs;et, &longs;i enim da&shy;<lb/>rentur ill&aelig; atomi, ex quibus <expan abbr="qu&atilde;titas">quantitas</expan> conflaretur, null&aelig; e&longs;&longs;ent line&aelig; incom&shy;<lb/>men&longs;urabiles, quandoquidem omnes communi illa, ac indiuidua, commen&shy;<lb/>&longs;urarentur. </s> deceptiuus, &amp; nullus e&longs;&longs;et, &longs;i enim da&shy;<lb/>rentur ill&aelig; atomi, ex quibus <expan abbr="qu&atilde;titas">quantitas</expan> conflaretur, null&aelig; e&longs;&longs;ent line&aelig; incom&shy;<lb/>men&longs;urabiles, quandoquidem omnes communi illa, ac indiuidua, commen&shy;<lb/>&longs;urarentur. </s>
  
 <s>po&longs;tulatum <expan abbr="quoq;">quoque</expan> illud, qualibet data magnitudine &longs;umi po&longs;&longs;e <lb/>minorem pror&longs;us irritum redderetur, quia data atomo, illa minor accipi <lb/>non po&longs;&longs;et.</s></p><p type="main"> <s>po&longs;tulatum <expan abbr="quoq;">quoque</expan> illud, qualibet data magnitudine &longs;umi po&longs;&longs;e <lb/>minorem pror&longs;us irritum redderetur, quia data atomo, illa minor accipi <lb/>non po&longs;&longs;et.</s></p><p type="main">
  
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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. </s> 
  
 <s>1. Priorum, &longs;ecto 1. cap. </s> 1. Priorum, &longs;ecto 1. cap.
  
 <s>23.</s></p><p type="main"> 23.</s></p><p type="main">
  
 <s><arrow.to.target n="marg103"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg103"></arrow.to.target></s></p><p type="margin">
  
 <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. </s> 1. Priorum, &longs;ecto 3. cap.
  
 <s>1. Priorum, &longs;ecto 3. cap. </s> 1. de hoc, quod e&longs;t, habere tres <lb/>angulos &aelig;quales duobus rectis. </s>
  
 <s>1. de hoc, quod e&longs;t, habere tres <lb/>angulos &aelig;quales duobus rectis. </s> 
  
 <s>v. </s> <s>v. </s>
  
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 <s><margin.target id="marg104"></margin.target>104</s></p><p type="main"> <s><margin.target id="marg104"></margin.target>104</s></p><p type="main">
  
 <s>Ibidem <emph type="italics"/>(Et diameter commen&longs;urabilis est co&longs;t&aelig;, &longs;i b&aelig;c)<emph.end type="italics"/> vide primo Priorum, <lb/>&longs;ecto 3. cap. </s> <s>Ibidem <emph type="italics"/>(Et diameter commen&longs;urabilis est co&longs;t&aelig;, &longs;i b&aelig;c)<emph.end type="italics"/> vide primo Priorum, <lb/>&longs;ecto 3. cap.
  
 <s>23. hoc &longs;olum nunc addendum <emph type="italics"/>(Si h&aelig;c)<emph.end type="italics"/> v. </s> 23. hoc &longs;olum nunc addendum <emph type="italics"/>(Si h&aelig;c)<emph.end type="italics"/> v. </s>
  
 <s>g. </s> <s>g. </s>
  
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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>
  
 <s>circulus non erit figura)<emph.end type="italics"/> In ordine figurarum conueniens e&longs;t, inquit, primam <lb/>facere circulum propter &longs;implici&longs;simam ip&longs;ius naturam, cum vnica, ac per&shy;<lb/>fecta circulari linea comprehendatur: <expan abbr="Triangul&utilde;">Triangulum</expan> ver&ograve; &longs;ecundam, quoniam <lb/>duo anguli recti, ide&longs;t, quia triangulum habet tres angulos &aelig;quales duobus <lb/>rectis angulis; quod fus&egrave; explicatnm e&longs;t lib. </s> <s>circulus non erit figura)<emph.end type="italics"/> In ordine figurarum conueniens e&longs;t, inquit, primam <lb/>facere circulum propter &longs;implici&longs;simam ip&longs;ius naturam, cum vnica, ac per&shy;<lb/>fecta circulari linea comprehendatur: <expan abbr="Triangul&utilde;">Triangulum</expan> ver&ograve; &longs;ecundam, quoniam <lb/>duo anguli recti, ide&longs;t, quia triangulum habet tres angulos &aelig;quales duobus <lb/>rectis angulis; quod fus&egrave; explicatnm e&longs;t lib.
  
 <s>1. Priorum, &longs;ecto 3. cap. </s> 1. Priorum, &longs;ecto 3. cap.
  
 <s>1. De&shy;<lb/>mum &longs;i primum locum dederimus triangulo, nullus alius remanet pro cir&shy;<lb/>culo, quod e&longs;t inconueniens, ergo circulus prima figura erit.</s></p><p type="main"> 1. De&shy;<lb/>mum &longs;i primum locum dederimus triangulo, nullus alius remanet pro cir&shy;<lb/>culo, quod e&longs;t inconueniens, ergo circulus prima figura erit.</s></p><p type="main">
  
 <s><arrow.to.target n="marg107"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg107"></arrow.to.target></s></p><p type="margin">
  
 <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>cuius demon&longs;trationem perfectam videre pote&shy;<lb/>ris in fine commentarij P. </s> <s>cuius demon&longs;trationem perfectam videre pote&shy;<lb/>ris in fine commentarij P. </s>
  
 <s>Clauij &longs;uper 4. Elem. </s> <s>Clauij &longs;uper 4. Elem.
  
 <s>nos <lb/>ea tantum attingimus, qu&aelig; percipi po&longs;&longs;int ab homi&shy;<lb/>ne vix mathematicis tincto: &longs;ed tamen, qu&aelig; &longs;en&longs;um <lb/>Ari&longs;totelis patefaciunt. </s> nos <lb/>ea tantum attingimus, qu&aelig; percipi po&longs;&longs;int ab homi&shy;<lb/>ne vix mathematicis tincto: &longs;ed tamen, qu&aelig; &longs;en&longs;um <lb/>Ari&longs;totelis patefaciunt. </s>
  
 <s>Ali&aelig; porr&ograve; figur&aelig; replen&shy;<lb/>tes locum planum, quibus aliquando Architectores <lb/>vtuntur, vel &longs;unt irregulares, vel ad pr&aelig;dictas redu&shy;<lb/>ci po&longs;&longs;unt. </s> <s>Ali&aelig; porr&ograve; figur&aelig; replen&shy;<lb/>tes locum planum, quibus aliquando Architectores <lb/>vtuntur, vel &longs;unt irregulares, vel ad pr&aelig;dictas redu&shy;<lb/>ci po&longs;&longs;unt. </s>
  
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 <s>Verum enim ver&ograve; plures pyramides <lb/>regulares, &longs;iue plura Tetraedra non po&longs;&longs;e replere vacuum, <expan abbr="&longs;olidum&qacute;">&longs;olidumque</expan>; con&shy;<lb/>&longs;tituere, ex eo patet, quia &longs;i id pr&aelig;&longs;tarent, conflarent nece&longs;&longs;ari&ograve;, vel vnum <lb/>ex <expan abbr="quinq;">quinque</expan> corporibus regularibus, de quibus in 13. Elemen. </s> <s>Verum enim ver&ograve; plures pyramides <lb/>regulares, &longs;iue plura Tetraedra non po&longs;&longs;e replere vacuum, <expan abbr="&longs;olidum&qacute;">&longs;olidumque</expan>; con&shy;<lb/>&longs;tituere, ex eo patet, quia &longs;i id pr&aelig;&longs;tarent, conflarent nece&longs;&longs;ari&ograve;, vel vnum <lb/>ex <expan abbr="quinq;">quinque</expan> corporibus regularibus, de quibus in 13. Elemen. </s>
  
 <s>vel aliud quod&shy;<lb/>piam; non aliud, nam, vt patet ex &longs;cholio 13. Elem. </s> <s>vel aliud quod&shy;<lb/>piam; non aliud, nam, vt patet ex &longs;cholio 13. Elem.
  
 <s>non dantur, ni&longs;i illa. <lb/></s> non dantur, ni&longs;i illa. <lb/></s>
  
 <s>quinque; <expan abbr="neq;">neque</expan> vllum ex illis, quia diameter huiu&longs;modi corporis, quod com&shy;<lb/>poneretur ex illis pyramidibus, e&longs;&longs;et dupla lateris eiu&longs;dem, vt patet, quia <lb/>pyramides ill&aelig; omnes concurrerent ad centrum &longs;ph&aelig;r&aelig; illas omnes com&shy;<lb/>plectentis, quare latus vnius pyramidis &agrave; &longs;uperficie &longs;ph&aelig;r&aelig; incipiens de&longs;i&shy;<lb/>neret in centrum, ergo latus i&longs;tud e&longs;&longs;et &longs;emidiameter, quapropter tota dia&shy;<lb/>meter illius &longs;ph&ecedil;r&aelig;, &amp; con&longs;equenter huius corporis in illa in&longs;cripti, e&longs;&longs;et du&shy;<lb/>pla lateris eiu&longs;dem figur&aelig; &longs;olid&aelig; in&longs;cript&aelig;, &longs;ed nullo talis proportio diame&shy;<lb/>tri alicuius ex illis <expan abbr="quinq;">quinque</expan> &longs;olidis regularibus ad latus eiu&longs;dem reperitur, <lb/>qu&aelig; &longs;it nimirum dupla, vt patet ex vltimis demon&longs;trationibus 13. Elem. </s> <s>quinque; <expan abbr="neq;">neque</expan> vllum ex illis, quia diameter huiu&longs;modi corporis, quod com&shy;<lb/>poneretur ex illis pyramidibus, e&longs;&longs;et dupla lateris eiu&longs;dem, vt patet, quia <lb/>pyramides ill&aelig; omnes concurrerent ad centrum &longs;ph&aelig;r&aelig; illas omnes com&shy;<lb/>plectentis, quare latus vnius pyramidis &agrave; &longs;uperficie &longs;ph&aelig;r&aelig; incipiens de&longs;i&shy;<lb/>neret in centrum, ergo latus i&longs;tud e&longs;&longs;et &longs;emidiameter, quapropter tota dia&shy;<lb/>meter illius &longs;ph&ecedil;r&aelig;, &amp; con&longs;equenter huius corporis in illa in&longs;cripti, e&longs;&longs;et du&shy;<lb/>pla lateris eiu&longs;dem figur&aelig; &longs;olid&aelig; in&longs;cript&aelig;, &longs;ed nullo talis proportio diame&shy;<lb/>tri alicuius ex illis <expan abbr="quinq;">quinque</expan> &longs;olidis regularibus ad latus eiu&longs;dem reperitur, <lb/>qu&aelig; &longs;it nimirum dupla, vt patet ex vltimis demon&longs;trationibus 13. Elem.
  
 <s>ini&shy;<lb/>tio facto &agrave; 13. demon&longs;tratione, in quibus nulla reperitur proportio dupla <lb/>inter diametrum, &amp; latus eiu&longs;dem alicuius ex illis &longs;olidis; ex quibus mani&shy;<lb/>fe&longs;tum e&longs;t, plures regulares pyramides quouis pacto &longs;imul vnitas nullo mo&shy;<lb/>do replere locum &longs;olidum. </s> ini&shy;<lb/>tio facto &agrave; 13. demon&longs;tratione, in quibus nulla reperitur proportio dupla <lb/>inter diametrum, &amp; latus eiu&longs;dem alicuius ex illis &longs;olidis; ex quibus mani&shy;<lb/>fe&longs;tum e&longs;t, plures regulares pyramides quouis pacto &longs;imul vnitas nullo mo&shy;<lb/>do replere locum &longs;olidum. </s>
  
 <s>cum igitur animaduerterem, &longs;en&longs;um Ari&longs;t.  <s>cum igitur animaduerterem, &longs;en&longs;um Ari&longs;t.
  
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 <s>tu ver&ograve;, &longs;i <lb/>adeo es mathematicis imbutus, con&longs;ule po&longs;tremas demon&longs;tra. </s> <s>tu ver&ograve;, &longs;i <lb/>adeo es mathematicis imbutus, con&longs;ule po&longs;tremas demon&longs;tra. </s>
  
 <s>13. Elem. </s> <s>13. Elem.
  
 <s>&amp; <lb/>pr&aelig;cipu&egrave; &longs;cholium vltimum, vbi plura de his corporibus &longs;citu digni&longs;&longs;ima, <lb/><expan abbr="atq;">atque</expan> huc &longs;pectantia reperies ex his omnibus Mathematica, qu&aelig; no&longs;tr&aelig; &longs;unt <lb/>partes, per&longs;picu&egrave; &longs;atis expo&longs;uimus.</s></p><p type="main"> &amp; <lb/>pr&aelig;cipu&egrave; &longs;cholium vltimum, vbi plura de his corporibus &longs;citu digni&longs;&longs;ima, <lb/><expan abbr="atq;">atque</expan> huc &longs;pectantia reperies ex his omnibus Mathematica, qu&aelig; no&longs;tr&aelig; &longs;unt <lb/>partes, per&longs;picu&egrave; &longs;atis expo&longs;uimus.</s></p><p type="main">
  
 <s>Multo po&longs;t tempore, qu&agrave;m h&aelig;c &longs;crip&longs;eram incidi fort&egrave; in cap. </s> <s>Multo po&longs;t tempore, qu&agrave;m h&aelig;c &longs;crip&longs;eram incidi fort&egrave; in cap.
  
 <s>38. &longs;pecu&shy;<lb/>lationem 10. Benedicti de placitis Ari&longs;t. </s> 38. &longs;pecu&shy;<lb/>lationem 10. Benedicti de placitis Ari&longs;t. </s>
  
 <s><expan abbr="reperi&qacute;">reperique</expan>; ab eo vno Ari&longs;t.  <s><expan abbr="reperi&qacute;">reperique</expan>; ab eo vno Ari&longs;t.
  
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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. </s> 
  
 <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> 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>
  
 <s>Simpl. </s> <s>Simpl. </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>&longs;it terra in &longs;igu&shy;<lb/>ra pr&aelig;&longs;enti circulus E C D, cuius medium, &longs;ine c<gap/>&shy;<pb pagenum="88"/>trum A. via, qua a&longs;cendit ignis &longs;it in linea A C B, qu&aelig; facit angulos in &longs;u&shy;<lb/>perficie terr&aelig; &aelig;quales, nimirum angulos B C D, B C E. &longs;imiliter terra per <lb/>candem lineam <expan abbr="faci&etilde;s">faciens</expan> eo&longs;dem angulos &aelig;quales de&longs;cendit. </s> <s>&longs;it terra in &longs;igu&shy;<lb/>ra pr&aelig;&longs;enti circulus E C D, cuius medium, &longs;ine c<gap/>&shy;<pb pagenum="88"/>trum A. via, qua a&longs;cendit ignis &longs;it in linea A C B, qu&aelig; facit angulos in &longs;u&shy;<lb/>perficie terr&aelig; &aelig;quales, nimirum angulos B C D, B C E. &longs;imiliter terra per <lb/>candem lineam <expan abbr="faci&etilde;s">faciens</expan> eo&longs;dem angulos &aelig;quales de&longs;cendit. </s>
  
 <s>linea autem, qu&aelig; <lb/>facit tales angulos tendit ad centrum &longs;ph&aelig;r&aelig; A, vt patet ad &longs;en&longs;um in figu&shy;<lb/>ra, &amp; probari pote&longs;t geometric&egrave; ex primis tertij Elem. </s> <s>linea autem, qu&aelig; <lb/>facit tales angulos tendit ad centrum &longs;ph&aelig;r&aelig; A, vt patet ad &longs;en&longs;um in figu&shy;<lb/>ra, &amp; probari pote&longs;t geometric&egrave; ex primis tertij Elem.
  
 <s>ex quibus patet tam <lb/>l&aelig;uia, quam grauia, qu&aelig; per talem lineam ferantur, re&longs;picere centrum A, <lb/>&longs;ph&aelig;r&aelig;. </s> ex quibus patet tam <lb/>l&aelig;uia, quam grauia, qu&aelig; per talem lineam ferantur, re&longs;picere centrum A, <lb/>&longs;ph&aelig;r&aelig;. </s>
  
 <s>Vtrum autem i&longs;tud centrum &longs;it idem cum <expan abbr="c&etilde;tro">centro</expan> totius mundi, alius, <lb/>inquit, e&longs;t &longs;ermo, hoc e&longs;t, ad a&longs;tronomum pertinet. </s> <s>Vtrum autem i&longs;tud centrum &longs;it idem cum <expan abbr="c&etilde;tro">centro</expan> totius mundi, alius, <lb/>inquit, e&longs;t &longs;ermo, hoc e&longs;t, ad a&longs;tronomum pertinet. </s>
  
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 <s><margin.target id="marg124"></margin.target>124</s></p><p type="main"> <s><margin.target id="marg124"></margin.target>124</s></p><p type="main">
  
 <s><emph type="italics"/>Hoc loco de&longs;ideratur commentarius in cap. </s> <s><emph type="italics"/>Hoc loco de&longs;ideratur commentarius in cap.
  
 <s>vlt. </s> vlt. </s>
  
 <s>de C&oelig;lo. </s> <s>de C&oelig;lo. </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><margin.target id="marg131"></margin.target>131</s></p><p type="main"> <s><margin.target id="marg131"></margin.target>131</s></p><p type="main">
  
 <s>Svmma 1. cap. </s> <s>Svmma 1. cap.
  
 <s>3. <emph type="italics"/>(Moles autem terr&aelig; quanta &longs;it ad ambientes magnitudi&shy;<lb/>nes, non immamfestum, iam enim vi&longs;um est per a&longs;trologica theoremata, <lb/>quod mult&ograve; etiam quibu&longs;dam a&longs;tris est minor)<emph.end type="italics"/> Quantitas terr&aelig; non &longs;o&shy;<lb/>lum ab&longs;olut&egrave; con&longs;iderata, ab A&longs;tronomis explorata habetur, vt vi&shy;<lb/>dere e&longs;t in &longs;ph&aelig;ra Clauij; &longs;ed etiam re&longs;pectiu&egrave; con&longs;iderata, ide&longs;t re&longs;pectu <lb/>aliorum elementorum, &amp; ip&longs;orum etiam a&longs;trorum; cuius demon&longs;trationes <lb/>&longs;unt partim in libello Ari&longs;tarchi Samij, de magnitudine, &amp; di&longs;tantia Solis, <lb/>&amp; Lun&aelig;, partim apud Ptol&aelig;meum in magna Syntaxi, &longs;iue Almage&longs;to: par&shy;<lb/>tim apud Albategnium de &longs;cientia &longs;tellarum: partim demum apud Ticho&shy;<lb/>nem Brahe. </s> 3. <emph type="italics"/>(Moles autem terr&aelig; quanta &longs;it ad ambientes magnitudi&shy;<lb/>nes, non immamfestum, iam enim vi&longs;um est per a&longs;trologica theoremata, <lb/>quod mult&ograve; etiam quibu&longs;dam a&longs;tris est minor)<emph.end type="italics"/> Quantitas terr&aelig; non &longs;o&shy;<lb/>lum ab&longs;olut&egrave; con&longs;iderata, ab A&longs;tronomis explorata habetur, vt vi&shy;<lb/>dere e&longs;t in &longs;ph&aelig;ra Clauij; &longs;ed etiam re&longs;pectiu&egrave; con&longs;iderata, ide&longs;t re&longs;pectu <lb/>aliorum elementorum, &amp; ip&longs;orum etiam a&longs;trorum; cuius demon&longs;trationes <lb/>&longs;unt partim in libello Ari&longs;tarchi Samij, de magnitudine, &amp; di&longs;tantia Solis, <lb/>&amp; Lun&aelig;, partim apud Ptol&aelig;meum in magna Syntaxi, &longs;iue Almage&longs;to: par&shy;<lb/>tim apud Albategnium de &longs;cientia &longs;tellarum: partim demum apud Ticho&shy;<lb/>nem Brahe. </s>
  
 <s>Porr&ograve; facile e&longs;t demon&longs;trare Solem e&longs;&longs;e terra mult&ograve; maiorem, <lb/>terram ver&ograve; maiorem Luna, <expan abbr="id&qacute;">idque</expan>; ex eclyp&longs;i lunari, cuius imaginem habes <lb/>in figura &longs;equenti; vbi vmbra terr&aelig; e&longs;t D B E, in quam Luna nigricans im&shy;<lb/>mergitur, ac lumine deficit, reliqua cognitu &longs;unt facilia: quia igitur A&longs;tro&shy;<lb/>nomi ob&longs;eruarunt vmbram terr&aelig; paul&ograve; &longs;upra Lunam pertingere, cum &longs;upe&shy;<lb/>riora a&longs;tra non adeat, hinc collegerunt eam nece&longs;&longs;ari&ograve; e&longs;&longs;e acuminatam, &longs;eu <lb/>conicam, vt figura refert. </s> <s>Porr&ograve; facile e&longs;t demon&longs;trare Solem e&longs;&longs;e terra mult&ograve; maiorem, <lb/>terram ver&ograve; maiorem Luna, <expan abbr="id&qacute;">idque</expan>; ex eclyp&longs;i lunari, cuius imaginem habes <lb/>in figura &longs;equenti; vbi vmbra terr&aelig; e&longs;t D B E, in quam Luna nigricans im&shy;<lb/>mergitur, ac lumine deficit, reliqua cognitu &longs;unt facilia: quia igitur A&longs;tro&shy;<lb/>nomi ob&longs;eruarunt vmbram terr&aelig; paul&ograve; &longs;upra Lunam pertingere, cum &longs;upe&shy;<lb/>riora a&longs;tra non adeat, hinc collegerunt eam nece&longs;&longs;ari&ograve; e&longs;&longs;e acuminatam, &longs;eu <lb/>conicam, vt figura refert. </s>
  
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 <s><margin.target id="marg133"></margin.target>133</s></p><p type="main"> <s><margin.target id="marg133"></margin.target>133</s></p><p type="main">
  
 <s>Summa 1. cap. </s> <s>Summa 1. cap.
  
 <s>4. <emph type="italics"/>(Qu&aelig; igitur astrorum e&longs;t, velox quidem; long&egrave; autem: qu&aelig; <lb/>ver&ograve; Lun&aelig; deor&longs;um quidem, tarda autem: qu&aelig;autem Solis ambo h&aelig;c babet &longs;uffi&shy;<lb/>cienter)<emph.end type="italics"/> qu&aelig; igitur a&longs;trorum, ide&longs;t latio a&longs;trorum e&longs;t velox, &longs;ed procul &agrave; ter&shy;<lb/>ra; Lun&aelig; ver&ograve; latio terr&aelig; quidem proxima, tarda tamen: at ver&ograve; Solis la&shy;<lb/>tio medio modo &longs;e habet inter vtrumque, ide&longs;t, quia <expan abbr="neq;">neque</expan> nimis vt a&longs;tra di&shy;<lb/>&longs;tat, <expan abbr="neq;">neque</expan> tard&egrave; &longs;icut Luna circunfertur. </s> 4. <emph type="italics"/>(Qu&aelig; igitur astrorum e&longs;t, velox quidem; long&egrave; autem: qu&aelig; <lb/>ver&ograve; Lun&aelig; deor&longs;um quidem, tarda autem: qu&aelig;autem Solis ambo h&aelig;c babet &longs;uffi&shy;<lb/>cienter)<emph.end type="italics"/> qu&aelig; igitur a&longs;trorum, ide&longs;t latio a&longs;trorum e&longs;t velox, &longs;ed procul &agrave; ter&shy;<lb/>ra; Lun&aelig; ver&ograve; latio terr&aelig; quidem proxima, tarda tamen: at ver&ograve; Solis la&shy;<lb/>tio medio modo &longs;e habet inter vtrumque, ide&longs;t, quia <expan abbr="neq;">neque</expan> nimis vt a&longs;tra di&shy;<lb/>&longs;tat, <expan abbr="neq;">neque</expan> tard&egrave; &longs;icut Luna circunfertur. </s>
  
 <s>exi&longs;timo Ari&longs;t.  <s>exi&longs;timo Ari&longs;t.
  
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 <s><margin.target id="marg134"></margin.target>134</s></p><p type="main"> <s><margin.target id="marg134"></margin.target>134</s></p><p type="main">
  
 <s>Summa 2. cap. </s> <s>Summa 2. cap.
  
 <s>3. <emph type="italics"/>(Quod accidit circa Mercurij stellam, quia enim modicum <lb/><expan abbr="&longs;upera&longs;c&etilde;dis">&longs;upera&longs;cendis</expan>, &longs;&aelig;p&egrave; non apparet, it a vt po&longs;t tempus multum appareat)<emph.end type="italics"/> quod Mer&shy;<lb/>curius non ni&longs;i rar&ograve; con&longs;pici po&longs;&longs;it, cau&longs;a e&longs;t, quia parum &agrave; Sole elongatur, <lb/>&longs;iue ip&longs;um antecedat, &longs;iue &longs;ub&longs;equatur. </s> 3. <emph type="italics"/>(Quod accidit circa Mercurij stellam, quia enim modicum <lb/><expan abbr="&longs;upera&longs;c&etilde;dis">&longs;upera&longs;cendis</expan>, &longs;&aelig;p&egrave; non apparet, it a vt po&longs;t tempus multum appareat)<emph.end type="italics"/> quod Mer&shy;<lb/>curius non ni&longs;i rar&ograve; con&longs;pici po&longs;&longs;it, cau&longs;a e&longs;t, quia parum &agrave; Sole elongatur, <lb/>&longs;iue ip&longs;um antecedat, &longs;iue &longs;ub&longs;equatur. </s>
  
 <s>ex quo fit, vt diu fer&egrave; &longs;imul cum So&shy;<lb/>le cit cumferatur, &amp; propterea &longs;iue oriatur, &longs;iue occidat, parum &longs;upra ho&shy;<lb/>rizontem eleuatus apparere pote&longs;t, quod Ari&longs;t.  <s>ex quo fit, vt diu fer&egrave; &longs;imul cum So&shy;<lb/>le cit cumferatur, &amp; propterea &longs;iue oriatur, &longs;iue occidat, parum &longs;upra ho&shy;<lb/>rizontem eleuatus apparere pote&longs;t, quod Ari&longs;t.
  
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 <s>optim&egrave; expli&shy;<lb/>cant, quos tu con&longs;ule, ne actum agatur.</s></p><p type="head"> <s>optim&egrave; expli&shy;<lb/>cant, quos tu con&longs;ule, ne actum agatur.</s></p><p type="head">
  
 <s><emph type="italics"/>In cap. </s> <s><emph type="italics"/>In cap.
  
 <s>4. &longs;umm&aelig; 2. lib. </s> 4. &longs;umm&aelig; 2. lib.
  
 <s>1. Meteor. </s> 1. Meteor. </s>
  
 <s>de Cometis.<emph.end type="italics"/></s></p><p type="main"> <s>de Cometis.<emph.end type="italics"/></s></p><p type="main">
  
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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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 <s><margin.target id="marg137"></margin.target>137</s></p><p type="main"> <s><margin.target id="marg137"></margin.target>137</s></p><p type="main">
  
 <s>Summ&aelig; 2. cap. </s> <s>Summ&aelig; 2. cap.
  
 <s>5. <emph type="italics"/>(Ad h&aelig;c autem &longs;i quemadmodum o&longs;tenditur in ijs, qu&aelig; cir&shy;<lb/>ca Astrologiam &longs;peculationibus, Solis magnitudo maior e&longs;t qu&agrave;m terr&aelig;; &amp; diftax&shy;<lb/>tia mult&ograve; maior a&longs;trorum ad terram qu&agrave;m So is; &longs;icut Solis ad terram qu&agrave;m Lu&shy;<lb/>n&aelig;; non <expan abbr="vtiq;">vtique</expan> long&egrave; alicubi &agrave; terra conus, qui &agrave; Sole, corijciet radios, <expan abbr="neq;">neque</expan> vtique <lb/>vmbraterr&aelig;, qu&aelig; vocatur nox, erit apud astra; &longs;ed ne<gap/>&longs;&longs;e Solem omnia a&longs;tra cir&shy;<lb/>cun&longs;picere, &amp; nulli <gap/>p&longs;orum terram ob&longs;istere)<emph.end type="italics"/> ex dictis &longs;umma 1. cap. </s> 5. <emph type="italics"/>(Ad h&aelig;c autem &longs;i quemadmodum o&longs;tenditur in ijs, qu&aelig; cir&shy;<lb/>ca Astrologiam &longs;peculationibus, Solis magnitudo maior e&longs;t qu&agrave;m terr&aelig;; &amp; diftax&shy;<lb/>tia mult&ograve; maior a&longs;trorum ad terram qu&agrave;m So is; &longs;icut Solis ad terram qu&agrave;m Lu&shy;<lb/>n&aelig;; non <expan abbr="vtiq;">vtique</expan> long&egrave; alicubi &agrave; terra conus, qui &agrave; Sole, corijciet radios, <expan abbr="neq;">neque</expan> vtique <lb/>vmbraterr&aelig;, qu&aelig; vocatur nox, erit apud astra; &longs;ed ne<gap/>&longs;&longs;e Solem omnia a&longs;tra cir&shy;<lb/>cun&longs;picere, &amp; nulli <gap/>p&longs;orum terram ob&longs;istere)<emph.end type="italics"/> ex dictis &longs;umma 1. cap.
  
 <s>3. huius, <lb/>&amp; ex figura ibi de&longs;cripta, facil&egrave; e&longs;t intelligere pr&aelig;&longs;entem locum; nam cum <lb/>Sol &longs;it mult&ograve; maior terra, vt ibi probatur, ac minus di&longs;ter &agrave; terra qu&agrave;m fix&aelig; <lb/>&longs;tell&aelig;, magis tamen qu&agrave;m Luna, vt patet ex &longs;olari eclyp&longs;i, &longs;equitur nece&longs;&longs;a&shy;<lb/>ri&ograve; vmbram terr&aelig;, qu&aelig; nox e&longs;t ip&longs;a, effici turbinatam, &amp; vald&egrave; procul &agrave; ter&shy;<lb/>ra acumen coni vmbr&aelig; a&longs;cendet, &longs;ed paul&ograve; &longs;upra Lunam conus hic vmbr&aelig; <lb/>permittet radios Solis &longs;e ip&longs;um ambientes iterum &longs;imul committi, quod il&shy;<lb/>lis verbis <emph type="italics"/>(Conijciet radios)<emph.end type="italics"/> ide&longs;t committet radios expre&longs;&longs;it Ari&longs;t.  3. huius, <lb/>&amp; ex figura ibi de&longs;cripta, facil&egrave; e&longs;t intelligere pr&aelig;&longs;entem locum; nam cum <lb/>Sol &longs;it mult&ograve; maior terra, vt ibi probatur, ac minus di&longs;ter &agrave; terra qu&agrave;m fix&aelig; <lb/>&longs;tell&aelig;, magis tamen qu&agrave;m Luna, vt patet ex &longs;olari eclyp&longs;i, &longs;equitur nece&longs;&longs;a&shy;<lb/>ri&ograve; vmbram terr&aelig;, qu&aelig; nox e&longs;t ip&longs;a, effici turbinatam, &amp; vald&egrave; procul &agrave; ter&shy;<lb/>ra acumen coni vmbr&aelig; a&longs;cendet, &longs;ed paul&ograve; &longs;upra Lunam conus hic vmbr&aelig; <lb/>permittet radios Solis &longs;e ip&longs;um ambientes iterum &longs;imul committi, quod il&shy;<lb/>lis verbis <emph type="italics"/>(Conijciet radios)<emph.end type="italics"/> ide&longs;t committet radios expre&longs;&longs;it Ari&longs;t.
  
 cum igi&shy;<lb/>tur vmbra apud Lunam &longs;it &longs;atis gracilis, breui &longs;upra Lunam de&longs;inet, neque <lb/>vllo pacto ad affixa &longs;ydera protendetur, <expan abbr="neq;">neque</expan> illis renebras offundet. </s> cum igi&shy;<lb/>tur vmbra apud Lunam &longs;it &longs;atis gracilis, breui &longs;upra Lunam de&longs;inet, neque <lb/>vllo pacto ad affixa &longs;ydera protendetur, <expan abbr="neq;">neque</expan> illis renebras offundet. </s>
  
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 <s><margin.target id="marg141"></margin.target>141</s></p><p type="main"> <s><margin.target id="marg141"></margin.target>141</s></p><p type="main">
  
 <s>Summ&aelig; 2. cap. </s> <s>Summ&aelig; 2. cap.
  
 <s>6. Sunt qui velint Ari&longs;t. </s> 6. Sunt qui velint Ari&longs;t. </s>
  
 <s>Galaxiam nihil aliud e&longs;&longs;e, qu&agrave;m <lb/>quandam refractionem lucis &longs;tellarum illarum, qu&aelig; &longs;unt in &aelig;therea Gala&shy;<lb/>xia, qu&aelig; inquam refractio fiat circa &longs;upremam aeris regionem ex occur&longs;u <lb/>exhalationum, qu&aelig; ibi perpetu&ograve; con&longs;eruantur, &amp; vi earumdem &longs;tellarum <lb/>&longs;ur&longs;um &longs;emper attrahuntur, qu&aelig; refractio fiat ad eum modum, quo halo cir&shy;<lb/>ca Solem, &amp; Lunam. </s> <s>Galaxiam nihil aliud e&longs;&longs;e, qu&agrave;m <lb/>quandam refractionem lucis &longs;tellarum illarum, qu&aelig; &longs;unt in &aelig;therea Gala&shy;<lb/>xia, qu&aelig; inquam refractio fiat circa &longs;upremam aeris regionem ex occur&longs;u <lb/>exhalationum, qu&aelig; ibi perpetu&ograve; con&longs;eruantur, &amp; vi earumdem &longs;tellarum <lb/>&longs;ur&longs;um &longs;emper attrahuntur, qu&aelig; refractio fiat ad eum modum, quo halo cir&shy;<lb/>ca Solem, &amp; Lunam. </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><margin.target id="marg145"></margin.target>145</s></p><p type="main"> <s><margin.target id="marg145"></margin.target>145</s></p><p type="main">
  
 <s>Summa 4. cap. </s> <s>Summa 4. cap.
  
 <s>1. <emph type="italics"/>(In A&longs;ia igitur plurimi ex Parna&longs;&longs;o vocato monte videntur <lb/>&longs;tuentes)<emph.end type="italics"/> rect&egrave; dubitat Alexander, qua ratione mons Parna&longs;&longs;us ab Ari&longs;t.  1. <emph type="italics"/>(In A&longs;ia igitur plurimi ex Parna&longs;&longs;o vocato monte videntur <lb/>&longs;tuentes)<emph.end type="italics"/> rect&egrave; dubitat Alexander, qua ratione mons Parna&longs;&longs;us ab Ari&longs;t.
  
 po&shy;<lb/>natur in A&longs;ia, cum cert&ograve; certius con&longs;tet, ip&longs;um in Gr&aelig;cia Europ&aelig; regione <lb/>&longs;itum e&longs;&longs;e. </s> po&shy;<lb/>natur in A&longs;ia, cum cert&ograve; certius con&longs;tet, ip&longs;um in Gr&aelig;cia Europ&aelig; regione <lb/>&longs;itum e&longs;&longs;e. </s>
  
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 <s>vide The&longs;aurum geographicum Abrahami Ortelij. </s> <s>vide The&longs;aurum geographicum Abrahami Ortelij. </s>
  
 <s>Strabo lib. </s> <s>Strabo lib.
  
 <s>15. <lb/>&longs;ic: Indiam &agrave; &longs;eptentrione Tauri extrema terminant, ab Ariana v&longs;que in <lb/>orientale mare, qu&aelig; extrema indigen&aelig; particulatim nominant Poropami&longs;<gap/><pb pagenum="98"/>&longs;um, Emodum, Imauum, &amp; alijs nominibus: Macedones ver&ograve; Cauca&longs;um <lb/>vocant.</s></p><p type="main"> 15. <lb/>&longs;ic: Indiam &agrave; &longs;eptentrione Tauri extrema terminant, ab Ariana v&longs;que in <lb/>orientale mare, qu&aelig; extrema indigen&aelig; particulatim nominant Poropami&longs;<gap/><pb pagenum="98"/>&longs;um, Emodum, Imauum, &amp; alijs nominibus: Macedones ver&ograve; Cauca&longs;um <lb/>vocant.</s></p><p type="main">
  
 <s><arrow.to.target n="marg146"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg146"></arrow.to.target></s></p><p type="margin">
  
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 <s>Is igitur &longs;ect. </s> <s>Is igitur &longs;ect. </s>
  
 <s>3. cap. </s> <s>3. cap.
  
 <s>5. de hoc Ari&longs;t.  5. de hoc Ari&longs;t.
  
 loco &longs;ie loquitur: <lb/>hic locus diligenter expendendus videtur tum quia difficillimus e&longs;t, <expan abbr="t&utilde;">tum</expan> quia <lb/>multis an&longs;am dedit reprehendendi Ari&longs;t.  loco &longs;ie loquitur: <lb/>hic locus diligenter expendendus videtur tum quia difficillimus e&longs;t, <expan abbr="t&utilde;">tum</expan> quia <lb/>multis an&longs;am dedit reprehendendi Ari&longs;t.
  
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 <s>vbi animaduertendum expo&shy;<lb/>&longs;itionem <expan abbr="h&atilde;c">hanc</expan> par&ugrave;m differre &agrave; no&longs;tra mod&ograve; allata, c&ugrave;m <expan abbr="vtraq;">vtraque</expan> in idem tem&shy;<lb/>pus recidat; nam &longs;i dixerimus initio Crepu&longs;culi matutini illuminari ter&shy;<lb/>tiam partem Cauca&longs;i, tempus hoc coincidit cum initio terti&aelig; partis noctis, <lb/>quantitas enim Crepu&longs;culi in poli eleuatione 47. grad. </s> <s>vbi animaduertendum expo&shy;<lb/>&longs;itionem <expan abbr="h&atilde;c">hanc</expan> par&ugrave;m differre &agrave; no&longs;tra mod&ograve; allata, c&ugrave;m <expan abbr="vtraq;">vtraque</expan> in idem tem&shy;<lb/>pus recidat; nam &longs;i dixerimus initio Crepu&longs;culi matutini illuminari ter&shy;<lb/>tiam partem Cauca&longs;i, tempus hoc coincidit cum initio terti&aelig; partis noctis, <lb/>quantitas enim Crepu&longs;culi in poli eleuatione 47. grad. </s>
  
 <s>qualem habet Cau&shy;<lb/>ca&longs;us, per totam &aelig;&longs;tatem tres horas plus minus continet, vt patet ex tabu&shy;<lb/>la quantitatis Crepu&longs;culi, qu&aelig; e&longs;t apud Nonium, &amp; apud Clauium in &longs;ph&aelig;&shy;<lb/>ra vltim&aelig; editionis; qu&aelig; quantitas reperiri geometrico calculo pote&longs;t, vt <lb/>docent Nonius, Clauius, &amp; Maginus lib. </s> <s>qualem habet Cau&shy;<lb/>ca&longs;us, per totam &aelig;&longs;tatem tres horas plus minus continet, vt patet ex tabu&shy;<lb/>la quantitatis Crepu&longs;culi, qu&aelig; e&longs;t apud Nonium, &amp; apud Clauium in &longs;ph&aelig;&shy;<lb/>ra vltim&aelig; editionis; qu&aelig; quantitas reperiri geometrico calculo pote&longs;t, vt <lb/>docent Nonius, Clauius, &amp; Maginus lib.
  
 <s>10. primi mob. </s> 10. primi mob. </s>
  
 <s>quod quidem trium <lb/>circiter horarum tempus e&longs;t tertia fer&egrave; noctis pars in ijs regionibus, quibus <lb/>polus eleuatur 47. grad. </s> <s>quod quidem trium <lb/>circiter horarum tempus e&longs;t tertia fer&egrave; noctis pars in ijs regionibus, quibus <lb/>polus eleuatur 47. grad. </s>
  
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 <s><margin.target id="marg151"></margin.target>151</s></p><p type="main"> <s><margin.target id="marg151"></margin.target>151</s></p><p type="main">
  
 <s>Svmma 4. cap. </s> <s>Svmma 4. cap.
  
 <s>2. quod e&longs;t de permutatione, &amp; vici&longs;&longs;itudine aquarum, <lb/>&amp; continentis. </s> 2. quod e&longs;t de permutatione, &amp; vici&longs;&longs;itudine aquarum, <lb/>&amp; continentis. </s>
  
 <s>Pergratum Lectori fore exi&longs;timaui, nec alienum ab <lb/>in&longs;tituto, &longs;i occa&longs;ione huius permutationis maris, ac terr&aelig;, rem ex&shy;<lb/>po&longs;uero &longs;citu digniffimam, quam pridem ob&longs;eruare c&oelig;pi, ac in dies <lb/>ob&longs;eruo, pr&aelig;&longs;ertim cum nullus pr&aelig;teritorum &longs;criptorum, quod &longs;ciam, eam <lb/>literis mandauerit: Terr&aelig; &longs;cilicet totius molem paulatim reduci ad perfe&shy;<lb/>ctam &longs;ph&aelig;ricitatem, ita vt aliquando nece&longs;&longs;e &longs;it futurum ip&longs;am &agrave; mari inun&shy;<lb/>dari, <expan abbr="atq;">atque</expan> omnin&ograve; inhabitabilem reddi. </s> <s>Pergratum Lectori fore exi&longs;timaui, nec alienum ab <lb/>in&longs;tituto, &longs;i occa&longs;ione huius permutationis maris, ac terr&aelig;, rem ex&shy;<lb/>po&longs;uero &longs;citu digniffimam, quam pridem ob&longs;eruare c&oelig;pi, ac in dies <lb/>ob&longs;eruo, pr&aelig;&longs;ertim cum nullus pr&aelig;teritorum &longs;criptorum, quod &longs;ciam, eam <lb/>literis mandauerit: Terr&aelig; &longs;cilicet totius molem paulatim reduci ad perfe&shy;<lb/>ctam &longs;ph&aelig;ricitatem, ita vt aliquando nece&longs;&longs;e &longs;it futurum ip&longs;am &agrave; mari inun&shy;<lb/>dari, <expan abbr="atq;">atque</expan> omnin&ograve; inhabitabilem reddi. </s>
  
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 <s>cau&longs;am au&shy;<lb/>tem re&longs;tauratri<gap/> huius terren&aelig; <expan abbr="rot&utilde;ditatis">rotunditatis</expan> e&longs;&longs;e aquas tum pluuiales, tum <lb/>fluuiales iamdi&ugrave; ob&longs;eruauimus, vt ex &longs;equentibus ob&longs;eruationibus patebit.</s></p><p type="main"> <s>cau&longs;am au&shy;<lb/>tem re&longs;tauratri<gap/> huius terren&aelig; <expan abbr="rot&utilde;ditatis">rotunditatis</expan> e&longs;&longs;e aquas tum pluuiales, tum <lb/>fluuiales iamdi&ugrave; ob&longs;eruauimus, vt ex &longs;equentibus ob&longs;eruationibus patebit.</s></p><p type="main">
  
 <s>Prim&ograve;, videmus flumina quotidie montium radices corrodere, ac qua&longs;i <lb/>&longs;uffodere, ita vt pa&longs;&longs;im ex hoc, vel illo monte magnas faciant ruinas, ac pr&ecedil;&shy;<lb/>cipitia, <expan abbr="atq;">atque</expan> hiac inde pr&aelig;rupti appareant montes, vt merit&ograve; legamus apud <lb/>Iob cap. </s> <s>Prim&ograve;, videmus flumina quotidie montium radices corrodere, ac qua&longs;i <lb/>&longs;uffodere, ita vt pa&longs;&longs;im ex hoc, vel illo monte magnas faciant ruinas, ac pr&ecedil;&shy;<lb/>cipitia, <expan abbr="atq;">atque</expan> hiac inde pr&aelig;rupti appareant montes, vt merit&ograve; legamus apud <lb/>Iob cap.
  
 <s>14. allunione paulatim terra con&longs;umitur. </s> 14. allunione paulatim terra con&longs;umitur. </s>
  
 <s>humum porr&ograve; illam ex <lb/>montibus delap&longs;am &longs;emper ad loca humiliora fluuij &longs;ecum detrahunt. </s> <s>humum porr&ograve; illam ex <lb/>montibus delap&longs;am &longs;emper ad loca humiliora fluuij &longs;ecum detrahunt. </s>
  
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 <s>Ad h&aelig;c; antiqua in montium verticibus con&shy;<lb/>&longs;tituta &aelig;deficia, propterea intercidunt, quia terra hinc, &amp; inde ab aquis <lb/>paulatim confumpta, <expan abbr="deor&longs;um&qacute;">deor&longs;umque</expan>; delap&longs;a, fundamenta ip&longs;orum nuda prim&ograve; <lb/>relinquit; deind&eacute; terra etiam ip&longs;a, qua fundamenta innitebatur &longs;en&longs;im de&shy;<lb/>lap&longs;a, ip&longs;a <expan abbr="quoq;">quoque</expan> fundamenta vn&agrave; cum toto &aelig;deficio nece&longs;&longs;e e&longs;t collabi, hu&shy;<lb/>ius &longs;igna infinita propemodum videri po&longs;&longs;unt; vnum tamen, quod toti orbi <lb/>confpicuum e&longs;t, non ommittam; Capitolium videlicet Romanum, cuius <lb/>modo fundamenta tota extant, qu&aelig; olim alt&egrave; &longs;ub terram de&longs;cendebant. </s> <s>Ad h&aelig;c; antiqua in montium verticibus con&shy;<lb/>&longs;tituta &aelig;deficia, propterea intercidunt, quia terra hinc, &amp; inde ab aquis <lb/>paulatim confumpta, <expan abbr="deor&longs;um&qacute;">deor&longs;umque</expan>; delap&longs;a, fundamenta ip&longs;orum nuda prim&ograve; <lb/>relinquit; deind&eacute; terra etiam ip&longs;a, qua fundamenta innitebatur &longs;en&longs;im de&shy;<lb/>lap&longs;a, ip&longs;a <expan abbr="quoq;">quoque</expan> fundamenta vn&agrave; cum toto &aelig;deficio nece&longs;&longs;e e&longs;t collabi, hu&shy;<lb/>ius &longs;igna infinita propemodum videri po&longs;&longs;unt; vnum tamen, quod toti orbi <lb/>confpicuum e&longs;t, non ommittam; Capitolium videlicet Romanum, cuius <lb/>modo fundamenta tota extant, qu&aelig; olim alt&egrave; &longs;ub terram de&longs;cendebant. </s>
  
 <s>vi&shy;<lb/>de pulcherrimam hac de re tractationem apud Georgium Agricolam lib. </s> <s>vi&shy;<lb/>de pulcherrimam hac de re tractationem apud Georgium Agricolam lib.
  
 <s>3. <lb/>cap. </s> 3. <lb/>cap.
  
 <s>1. qui amplius addit illud, quod &amp; mihi maxim&egrave; probatur; flumina ni&shy;<lb/>mirum producere montes, <expan abbr="colles&qacute;">collesque</expan>; hoc modo; vult enim initio mundi non <lb/>extiti&longs;&longs;e tot particulares montes ab inuicem di&longs;cretos, &longs;ed fui&longs;&longs;e perpetua <lb/>qu&aelig;dam terr&aelig; iuga eminentia quidem, &longs;ed non tot vallibus di&longs;&longs;ecta: v. </s> 1. qui amplius addit illud, quod &amp; mihi maxim&egrave; probatur; flumina ni&shy;<lb/>mirum producere montes, <expan abbr="colles&qacute;">collesque</expan>; hoc modo; vult enim initio mundi non <lb/>extiti&longs;&longs;e tot particulares montes ab inuicem di&longs;cretos, &longs;ed fui&longs;&longs;e perpetua <lb/>qu&aelig;dam terr&aelig; iuga eminentia quidem, &longs;ed non tot vallibus di&longs;&longs;ecta: v. </s>
  
 <s>g. <lb/></s> <s>g. <lb/></s>
  
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 <s>quod prim&ograve; Ari&longs;t.  <s>quod prim&ograve; Ari&longs;t.
  
 te&longs;timonio in hoc cap. </s> te&longs;timonio in hoc cap.
  
 <s>comprobatur, <lb/>cum quo pariter &longs;entiunt veteres Geographi, &amp; Hi&longs;torici omnes. </s> comprobatur, <lb/>cum quo pariter &longs;entiunt veteres Geographi, &amp; Hi&longs;torici omnes. </s>
  
 <s>Ari&longs;t.  <s>Ari&longs;t.
  
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 <s>Accedit &amp; Plinij te&shy;<lb/>&longs;timonium, qui tradit multas terras na&longs;ci, non &longs;olum fluminum inuectu, &longs;<gap/>d <pb pagenum="106"/>etiam marium rece&longs;&longs;u; &longs;ic mare ab Ambraci&aelig; portu 10. millia pa&longs;&longs;uum; ab <lb/>Athenarum ver&ograve; <expan abbr="quinq;">quinque</expan> millia, &amp; alijs in locis plus minu&longs;u&egrave; rece&longs;&longs;i&longs;&longs;e &longs;cri&shy;<lb/>bit. </s> <s>Accedit &amp; Plinij te&shy;<lb/>&longs;timonium, qui tradit multas terras na&longs;ci, non &longs;olum fluminum inuectu, &longs;<gap/>d <pb pagenum="106"/>etiam marium rece&longs;&longs;u; &longs;ic mare ab Ambraci&aelig; portu 10. millia pa&longs;&longs;uum; ab <lb/>Athenarum ver&ograve; <expan abbr="quinq;">quinque</expan> millia, &amp; alijs in locis plus minu&longs;u&egrave; rece&longs;&longs;i&longs;&longs;e &longs;cri&shy;<lb/>bit. </s>
  
 <s>Huc facit locus quidam Strabonis ex lib. </s> <s>Huc facit locus quidam Strabonis ex lib.
  
 <s>12. de Pyramo Cilici&aelig; fluuio: <lb/>&longs;ic; montes ver&ograve; egre&longs;&longs;us tantum limum in mare deducit, partim ex Ca&shy;<lb/>taonia, partim ex Cilici&aelig; campis, vt huiu&longs;modi de co oraculum feratur;</s></p><p type="main"> 12. de Pyramo Cilici&aelig; fluuio: <lb/>&longs;ic; montes ver&ograve; egre&longs;&longs;us tantum limum in mare deducit, partim ex Ca&shy;<lb/>taonia, partim ex Cilici&aelig; campis, vt huiu&longs;modi de co oraculum feratur;</s></p><p type="main">
  
 <s><emph type="italics"/>Tempus erit rapidis olim cum Pyramus vndis <lb/>In &longs;acram veniet conge&longs;io litore, Cyprum:<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Tempus erit rapidis olim cum Pyramus vndis <lb/>In &longs;acram veniet conge&longs;io litore, Cyprum:<emph.end type="italics"/></s></p><p type="main">
  
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 <s><margin.target id="marg153"></margin.target>153</s></p><p type="main"> <s><margin.target id="marg153"></margin.target>153</s></p><p type="main">
  
 <s>Summ&aelig; 2. cap. </s> <s>Summ&aelig; 2. cap.
  
 <s>2. <emph type="italics"/>(Quapropter &amp; circa Orionis orturm maxim&egrave; fit tranquilli&shy;<lb/>tas)<emph.end type="italics"/> quando Medici, Philo&longs;ophi, Poet&aelig;, ac reliqui auctores loquuntur de <lb/>ortu a&longs;trorum fixorum, aut con&longs;tellationum, qu&aelig; &longs;unt in firmamento, vti <lb/>e&longs;t Orion (&amp; Canis, de quo po&longs;tea) intelligunt &longs;emper de ortu ip&longs;orum, qui <lb/>fit matutino tempore, quando &longs;cilicet vel &longs;imul cum Sole, vel paul&ograve; ante <lb/>Solem emergunt, ita vt videantur &agrave; nobis; qui ortus dicitur Co&longs;micus, tunc <lb/>propri&egrave;, quando &longs;imul a&longs;trum cum Sole oritur; quando autem incipit appa&shy;<lb/>rere manc ante Solem, dicitur ortus Heliacus. </s> 2. <emph type="italics"/>(Quapropter &amp; circa Orionis orturm maxim&egrave; fit tranquilli&shy;<lb/>tas)<emph.end type="italics"/> quando Medici, Philo&longs;ophi, Poet&aelig;, ac reliqui auctores loquuntur de <lb/>ortu a&longs;trorum fixorum, aut con&longs;tellationum, qu&aelig; &longs;unt in firmamento, vti <lb/>e&longs;t Orion (&amp; Canis, de quo po&longs;tea) intelligunt &longs;emper de ortu ip&longs;orum, qui <lb/>fit matutino tempore, quando &longs;cilicet vel &longs;imul cum Sole, vel paul&ograve; ante <lb/>Solem emergunt, ita vt videantur &agrave; nobis; qui ortus dicitur Co&longs;micus, tunc <lb/>propri&egrave;, quando &longs;imul a&longs;trum cum Sole oritur; quando autem incipit appa&shy;<lb/>rere manc ante Solem, dicitur ortus Heliacus. </s>
  
 <s>i. </s> <s>i. </s>
  
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 <s><margin.target id="marg160"></margin.target>160.a</s></p><p type="main"> <s><margin.target id="marg160"></margin.target>160.a</s></p><p type="main">
  
 <s>Summ&aelig; 2. cap. </s> <s>Summ&aelig; 2. cap.
  
 <s>3. de <expan abbr="v&etilde;tis">ventis</expan> <emph type="italics"/>(Oportet autem de &longs;itu &longs;imul rationes ex de&longs;criptio <lb/>ne con&longs;iderare)<emph.end type="italics"/> ide&longs;t rationes ventorum ex de&longs;criptione, ide&longs;t in figura ali&shy;<lb/>qua, vt in &longs;equenti con&longs;iderare; &longs;olet enim Ari&longs;t.  3. de <expan abbr="v&etilde;tis">ventis</expan> <emph type="italics"/>(Oportet autem de &longs;itu &longs;imul rationes ex de&longs;criptio <lb/>ne con&longs;iderare)<emph.end type="italics"/> ide&longs;t rationes ventorum ex de&longs;criptione, ide&longs;t in figura ali&shy;<lb/>qua, vt in &longs;equenti con&longs;iderare; &longs;olet enim Ari&longs;t.
  
 figuras, im&ograve; demon&longs;tratio&shy;<lb/>nes ip&longs;as Mathematicorum, de&longs;criptiones appellare, vt &longs;&aelig;pius in Logicis <lb/>monuimus.</s></p><p type="main"> figuras, im&ograve; demon&longs;tratio&shy;<lb/>nes ip&longs;as Mathematicorum, de&longs;criptiones appellare, vt &longs;&aelig;pius in Logicis <lb/>monuimus.</s></p><p type="main">
  
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 <s><margin.target id="marg162"></margin.target>161</s></p><p type="main"> <s><margin.target id="marg162"></margin.target>161</s></p><p type="main">
  
 <s>Summ&aelig; 2. cap. </s> <s>Summ&aelig; 2. cap.
  
 <s>2. De Are&aelig; figura <emph type="italics"/>(Refrangitur autem &agrave; con&longs;i&longs;tente caligine <lb/>circa Solem, aut Lunam vi&longs;us; quapropter non ex oppo&longs;ito &longs;icut iris, apparet. </s> 2. De Are&aelig; figura <emph type="italics"/>(Refrangitur autem &agrave; con&longs;i&longs;tente caligine <lb/>circa Solem, aut Lunam vi&longs;us; quapropter non ex oppo&longs;ito &longs;icut iris, apparet. </s>
  
 <s><expan abbr="Vn-diq;">Vn&shy;<lb/>dique</expan> autem &longs;imiliter refracto, nece&longs;&longs;e e&longs;t circulum e&longs;&longs;e, aut circuli partem. </s> <s><expan abbr="Vn-diq;">Vn&shy;<lb/>dique</expan> autem &longs;imiliter refracto, nece&longs;&longs;e e&longs;t circulum e&longs;&longs;e, aut circuli partem. </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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 <s><expan abbr="Atq;">Atque</expan> h&aelig;c cur Halonis figura orbicularis videatur, rationem <lb/>reddunt, <expan abbr="vna&qacute;">vnaque</expan>; textui lucem afferunt.</s></p><p type="head"> <s><expan abbr="Atq;">Atque</expan> h&aelig;c cur Halonis figura orbicularis videatur, rationem <lb/>reddunt, <expan abbr="vna&qacute;">vnaque</expan>; textui lucem afferunt.</s></p><p type="head">
  
 <s><emph type="italics"/>Summ&aelig; 2. cap. </s> <s><emph type="italics"/>Summ&aelig; 2. cap.
  
 <s>4. De Iridis figura.<emph.end type="italics"/></s></p><p type="main"> 4. De Iridis figura.<emph.end type="italics"/></s></p><p type="main">
  
 <s><arrow.to.target n="marg163"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg163"></arrow.to.target></s></p><p type="margin">
  
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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>Hactenus de Iri&shy;<lb/>dis figura &longs;it &longs;atis.</s></p><p type="head"> <s>Hactenus de Iri&shy;<lb/>dis figura &longs;it &longs;atis.</s></p><p type="head">
  
 <s><emph type="italics"/>Summa 2. cap. </s> <s><emph type="italics"/>Summa 2. cap.
  
 <s>5. De Parelio.<emph.end type="italics"/></s></p><p type="main"> 5. De Parelio.<emph.end type="italics"/></s></p><p type="main">
  
 <s><arrow.to.target n="marg173"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg173"></arrow.to.target></s></p><p type="margin">
  
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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. </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>
  
 <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> <s>vide qu&aelig; de hac &aelig;qualitate &longs;crip&longs;i lib, primo <lb/>Priorum, &longs;ecto 3. cap.
  
 <s>vide qu&aelig; de hac &aelig;qualitate &longs;crip&longs;i lib, primo <lb/>Priorum, &longs;ecto 3. cap. </s> 1.</s></p><p type="main">
  
 <s>1.</s></p><p type="main"> 
  
 <s><arrow.to.target n="marg175"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg175"></arrow.to.target></s></p><p type="margin">
  
 <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> <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>&pacute;robat li&shy;<lb/><figure id="fig62"></figure><lb/>neam rectam, duo qu&aelig;libet puncta <expan abbr="qu&atilde;tumuis">quantumuis</expan> pro&shy;<lb/>pinqua in circuli ambitu a&longs;&longs;umpta coniungentem <lb/>cadere intra circulum. </s> &pacute;robat li&shy;<lb/><figure id="fig62"></figure><lb/>neam rectam, duo qu&aelig;libet puncta <expan abbr="qu&atilde;tumuis">quantumuis</expan> pro&shy;<lb/>pinqua in circuli ambitu a&longs;&longs;umpta coniungentem <lb/>cadere intra circulum. </s>
  
 <s>v. </s> <s>v. </s>
  
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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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 anim&aelig; definitionem pr&aelig;&shy;<lb/>mittit duplicem e&longs;&longs;e definitionem, alteram &longs;cilicet, qu&aelig; explicat &longs;olum rei <lb/>e&longs;&longs;entiam, quam dicunt formalem definitionem; alteram ver&ograve;, qu&aelig; pr&aelig;te&shy;<lb/>rea explicat etiam rei cau&longs;am, quam dicunt cau&longs;alem definitionem: vtram&shy;<lb/>que autem exemplo Geometrico explicat.</s></p><p type="main"> anim&aelig; definitionem pr&aelig;&shy;<lb/>mittit duplicem e&longs;&longs;e definitionem, alteram &longs;cilicet, qu&aelig; explicat &longs;olum rei <lb/>e&longs;&longs;entiam, quam dicunt formalem definitionem; alteram ver&ograve;, qu&aelig; pr&aelig;te&shy;<lb/>rea explicat etiam rei cau&longs;am, quam dicunt cau&longs;alem definitionem: vtram&shy;<lb/>que autem exemplo Geometrico explicat.</s></p><p type="main">
  
 <s>In cap. </s> <s>In cap.
  
 <s>igitur de relatione plura &longs;crip&longs;i de tetragoni&longs;mo, &longs;eu qua dratio&shy;<lb/>ne circuli, qu&aelig; huc &longs;pectant. </s> igitur de relatione plura &longs;crip&longs;i de tetragoni&longs;mo, &longs;eu qua dratio&shy;<lb/>ne circuli, qu&aelig; huc &longs;pectant. </s>
  
 <s>propterea nunc tantum propria huius loci <expan abbr="de-clar&atilde;da">de&shy;<lb/>claranda</expan> re&longs;tant. </s> <s>propterea nunc tantum propria huius loci <expan abbr="de-clar&atilde;da">de&shy;<lb/>claranda</expan> re&longs;tant. </s>
  
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 <s>&longs;i quis ver&ograve; dicat tetragoni&longs;mum hunc quadri&shy;<lb/>lateri dati e&longs;&longs;e medi&aelig; pr&aelig;dict&aelig; inuentionem cau&longs;alem afferet definitionem, <lb/>cum rei cau&longs;am dicat. </s> <s>&longs;i quis ver&ograve; dicat tetragoni&longs;mum hunc quadri&shy;<lb/>lateri dati e&longs;&longs;e medi&aelig; pr&aelig;dict&aelig; inuentionem cau&longs;alem afferet definitionem, <lb/>cum rei cau&longs;am dicat. </s>
  
 <s>Aduerte 10. Grammaticum immerit&ograve; accu&longs;are Ale&shy;<lb/>xandrum, quod dicat quadrationem hanc per inuentionem medi&aelig; propor&shy;<lb/>tionalis tradi in 2. Elem. </s> <s>Aduerte 10. Grammaticum immerit&ograve; accu&longs;are Ale&shy;<lb/>xandrum, quod dicat quadrationem hanc per inuentionem medi&aelig; propor&shy;<lb/>tionalis tradi in 2. Elem.
  
 <s>nam ver&egrave; in 14. 2. traditur talis inuentio, quam&shy;<lb/>uis enim ibi nulla fiat expre&longs;&longs;a mentio huiu&longs;modi medi&aelig;, in ip&longs;a tamen e<gap/><lb/>reperitur, ac per eam figur&aelig; rectiline&aelig; quadrantur: quod patet ex figura <lb/>14. pr&aelig;dict&aelig;, qu&aelig; eadem e&longs;t cum figura 13. 6. qua docemur pr&aelig;dictam in&shy;<lb/>uentionem.</s></p><p type="main"> nam ver&egrave; in 14. 2. traditur talis inuentio, quam&shy;<lb/>uis enim ibi nulla fiat expre&longs;&longs;a mentio huiu&longs;modi medi&aelig;, in ip&longs;a tamen e<gap/><lb/>reperitur, ac per eam figur&aelig; rectiline&aelig; quadrantur: quod patet ex figura <lb/>14. pr&aelig;dict&aelig;, qu&aelig; eadem e&longs;t cum figura 13. 6. qua docemur pr&aelig;dictam in&shy;<lb/>uentionem.</s></p><p type="main">
  
 <s><arrow.to.target n="marg177"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg177"></arrow.to.target></s></p><p type="margin">
  
 <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. </s> 13. dicta &longs;unt, illa enim omnia in hunc lo&shy;<lb/>cum quadrant. </s>
  
 <s>13. dicta &longs;unt, illa enim omnia in hunc lo&shy;<lb/>cum quadrant. </s> 
  
 <s>Verum occurrit illa dubitatio; quod cum Ari&longs;t.  <s>Verum occurrit illa dubitatio; quod cum Ari&longs;t.
  
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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> <s>Vide, qu&aelig; cap.
  
 <s>3. &longs;umm&aelig; 1. primi Meteor. <lb/></s> 3. &longs;umm&aelig; 1. primi Meteor. <lb/></s>
  
 <s>Item capite 5. &longs;umm&aelig; 2. de Solis magnitudine &longs;crip&longs;i, ea enim huic loco <lb/>abund&egrave; &longs;atisfaciunt.</s></p><p type="head"> <s>Item capite 5. &longs;umm&aelig; 2. de Solis magnitudine &longs;crip&longs;i, ea enim huic loco <lb/>abund&egrave; &longs;atisfaciunt.</s></p><p type="head">
  
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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. </s> 
  
 <s>1. Priorum, cap. <lb/></s> 
  
 <s>23. vnde &longs;atis huic loco fieri pote&longs;t.</s></p><p type="main"> 1. Priorum, cap. <lb/>23. vnde &longs;atis huic loco fieri pote&longs;t.</s></p><p type="main">
  
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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> 5. tex. </s>
  
 <s>cap. </s> 
  
 <s>5. tex. </s> 
  
 <s>13. dicitur etiam alterna ratio; <lb/>&amp; definitur ab Euclide definitione 12, 5.</s></p><p type="head"> <s>13. dicitur etiam alterna ratio; <lb/>&amp; definitur ab Euclide definitione 12, 5.</s></p><p type="head">
  
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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. </s> 1.</s></p><p type="main">
  
 <s>1.</s></p><p type="main"> 
  
 <s><arrow.to.target n="marg186"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg186"></arrow.to.target></s></p><p type="margin">
  
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 <s>atque h&aelig;c <lb/>ip&longs;a cau&longs;a e&longs;t, cur illud, quod vnum tantum e&longs;t, duo tamen <lb/>emoto oculorum altero, videatur. </s> <s>atque h&aelig;c <lb/>ip&longs;a cau&longs;a e&longs;t, cur illud, quod vnum tantum e&longs;t, duo tamen <lb/>emoto oculorum altero, videatur. </s>
  
 <s>Vide Alhaze&shy;<lb/>num lib. </s> <s>Vide Alhaze&shy;<lb/>num lib.
  
 <s>3. propo&longs;it. </s> 
  
 <s>11. &amp; 12. &amp; infra <lb/>Problem. </s> 3. propo&longs;it. </s>
  
 <s>7. &longs;ectionis 31.</s></p><figure></figure><pb pagenum="137"/><p type="head"> <s>11. &amp; 12. &amp; infra <lb/>Problem. 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="marg192"></margin.target>201</s></p><p type="main"> <s><margin.target id="marg192"></margin.target>201</s></p><p type="main">
  
 <s>Ibidem (<emph type="italics"/>Aut de diametri incommen&longs;ur abilitate, admirabile enim omnibus vi&shy;<lb/>detur, &longs;i quid, cum non &longs;it minimum non men&longs;uretur, decet autem in contrarium, <lb/>&amp; in melius &longs;ecundum prouerbium con&longs;umare, quemadmod&ubreve; in his fit, cum di&longs;cant, <lb/>nihil enim magis vir Geometricus admiraretur, qu&agrave;m &longs;i diamcter commen&longs;urabi&shy;<lb/>lis &longs;ieret<emph.end type="italics"/>) vide qu&aelig; de hac commen&longs;urabilitate &longs;crip&longs;i lib. </s> <s>Ibidem (<emph type="italics"/>Aut de diametri incommen&longs;ur abilitate, admirabile enim omnibus vi&shy;<lb/>detur, &longs;i quid, cum non &longs;it minimum non men&longs;uretur, decet autem in contrarium, <lb/>&amp; in melius &longs;ecundum prouerbium con&longs;umare, quemadmod&ubreve; in his fit, cum di&longs;cant, <lb/>nihil enim magis vir Geometricus admiraretur, qu&agrave;m &longs;i diamcter commen&longs;urabi&shy;<lb/>lis &longs;ieret<emph.end type="italics"/>) vide qu&aelig; de hac commen&longs;urabilitate &longs;crip&longs;i lib.
  
 <s>1. Priorum, &longs;ect. </s> 1. Priorum, &longs;ect. </s>
  
 <s>1. <lb/>cap. </s> <s>1. <lb/>cap.
  
 <s>1. Videtur inquit mirum &agrave; principio Geometriam aggredienti diame&shy;<lb/>trum, &amp; latus eiu&longs;dem quadrati non commen&longs;urari, cum in neutro eorum <lb/>detur minimum, &longs;eu indiui&longs;ibile, videtur enim omne diui&longs;ibile po&longs;&longs;e men&longs;u&shy;<pb pagenum="138"/>rari. </s> 1. Videtur inquit mirum &agrave; principio Geometriam aggredienti diame&shy;<lb/>trum, &amp; latus eiu&longs;dem quadrati non commen&longs;urari, cum in neutro eorum <lb/>detur minimum, &longs;eu indiui&longs;ibile, videtur enim omne diui&longs;ibile po&longs;&longs;e men&longs;u&shy;<pb pagenum="138"/>rari. </s>
  
 <s>po&longs;tea tamen cum in Geometria ver&longs;atus fuerit, maxim&egrave; admirare&shy;<lb/>tur, &longs;i audiret diametrum e&longs;&longs;e lateri commen&longs;urabilem.</s></p><p type="main"> <s>po&longs;tea tamen cum in Geometria ver&longs;atus fuerit, maxim&egrave; admirare&shy;<lb/>tur, &longs;i audiret diametrum e&longs;&longs;e lateri commen&longs;urabilem.</s></p><p type="main">
  
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 <s><margin.target id="marg193"></margin.target>202</s></p><p type="main"> <s><margin.target id="marg193"></margin.target>202</s></p><p type="main">
  
 <s>Summa 2. cap. </s> <s>Summa 2. cap.
  
 <s>3. (<emph type="italics"/>Pythagorici primi Mathematicis operam dedere, h&aelig;c pr&aelig;po&shy;<lb/>nebant, &amp; in cis enutriti, eorum principia, entium <expan abbr="quoq;">quoque</expan> cunctorum putant e&longs;&longs;e <lb/>principia<emph.end type="italics"/>) vtinam no&longs;trates Philo&longs;ophi Pythagoricos imitarentur; enimue&shy;<lb/>r&ograve; mult&ograve; melius &amp; &longs;ibi, &amp; Philo&longs;ophi&aelig; con&longs;ulerent. </s> 3. (<emph type="italics"/>Pythagorici primi Mathematicis operam dedere, h&aelig;c pr&aelig;po&shy;<lb/>nebant, &amp; in cis enutriti, eorum principia, entium <expan abbr="quoq;">quoque</expan> cunctorum putant e&longs;&longs;e <lb/>principia<emph.end type="italics"/>) vtinam no&longs;trates Philo&longs;ophi Pythagoricos imitarentur; enimue&shy;<lb/>r&ograve; mult&ograve; melius &amp; &longs;ibi, &amp; Philo&longs;ophi&aelig; con&longs;ulerent. </s>
  
 <s>At ver&ograve; non &longs;ine ma&shy;<lb/>gno artium, <expan abbr="atq;">atque</expan> di&longs;ciplinarum omnium di&longs;pendio &agrave; plurimis hac tempe&shy;<lb/>&longs;tate de&longs;pectui habentur; &longs;ed quid mirum cum quas &longs;cientiarum omnium <lb/>alumni Pythagorei omnibus &longs;cientijs anteferebant; eas no&longs;tri &longs;eculi quam&shy;<lb/>plures omnibus alijs facultatibus po&longs;thabeant.</s></p><p type="main"> <s>At ver&ograve; non &longs;ine ma&shy;<lb/>gno artium, <expan abbr="atq;">atque</expan> di&longs;ciplinarum omnium di&longs;pendio &agrave; plurimis hac tempe&shy;<lb/>&longs;tate de&longs;pectui habentur; &longs;ed quid mirum cum quas &longs;cientiarum omnium <lb/>alumni Pythagorei omnibus &longs;cientijs anteferebant; eas no&longs;tri &longs;eculi quam&shy;<lb/>plures omnibus alijs facultatibus po&longs;thabeant.</s></p><p type="main">
  
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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. </s> 
  
 <s>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">
  
 <s><emph type="italics"/>Ex Quinto Metaphy&longs;ic&aelig;.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Ex Quinto Metaphy&longs;ic&aelig;.<emph.end type="italics"/></s></p><p type="main">
  
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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. </s> 
  
 <s>8. Amplius inquit can&longs;am <lb/>formalem genericam eiu&longs;dem Diapa&longs;on e&longs;&longs;e numerum, &amp; partes numeri, <lb/>&longs;ub numero enim continentur &amp; duo, &amp; vnum. </s> 8. Amplius inquit can&longs;am <lb/>formalem genericam eiu&longs;dem Diapa&longs;on e&longs;&longs;e numerum, &amp; partes numeri, <lb/>&longs;ub numero enim continentur &amp; duo, &amp; vnum. </s>
  
 <s>Occurrit hoc loco vnum <lb/>magnopere notandum, videlicet tam con&longs;onantias, quam di&longs;&longs;onantias ha&shy;<lb/>bere proportiones numerorum, hoc tamen di&longs;crimine, quod con&longs;onanti&aelig; <lb/>habent &longs;ol&ugrave;m proportiones numerorum eorum, qui quaternario continen&shy;<lb/>tur, ex veterum pr&aelig;&longs;ertim Pythagoreorum &longs;ententia, qui propterea vltra <lb/>quaternarium progredi vetabant. </s> <s>Occurrit hoc loco vnum <lb/>magnopere notandum, videlicet tam con&longs;onantias, quam di&longs;&longs;onantias ha&shy;<lb/>bere proportiones numerorum, hoc tamen di&longs;crimine, quod con&longs;onanti&aelig; <lb/>habent &longs;ol&ugrave;m proportiones numerorum eorum, qui quaternario continen&shy;<lb/>tur, ex veterum pr&aelig;&longs;ertim Pythagoreorum &longs;ententia, qui propterea vltra <lb/>quaternarium progredi vetabant. </s>
  
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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. &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>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>&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> <s>2. huius cap.
  
 <s>explicatum e&longs;t.</s></p><pb pagenum="141"/><p type="main"> explicatum e&longs;t.</s></p><pb pagenum="141"/><p type="main">
  
 <s><arrow.to.target n="marg204"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg204"></arrow.to.target></s></p><p type="margin">
  
 <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. </s> 
  
 <s>23.</s></p><figure></figure><p type="main"> 23.</s></p><figure></figure><p type="main">
  
 <s><arrow.to.target n="marg207"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg207"></arrow.to.target></s></p><p type="margin">
  
 <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. </s> 
  
 <s>23.</s></p><p type="main"> 23.</s></p><p type="main">
  
 <s><arrow.to.target n="marg209"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg209"></arrow.to.target></s></p><p type="margin">
  
 <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> <s>Vide declarationem huius <lb/>lib.
  
 <s>primo Priornm, &longs;ecto 3. cap. </s> primo Priornm, &longs;ecto 3. cap.
  
 <s>1.</s></p><p type="head"> 1.</s></p><p type="head">
  
 <s><emph type="italics"/>Ex Sexto Metaphy&longs;ic&aelig;.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Ex Sexto Metaphy&longs;ic&aelig;.<emph.end type="italics"/></s></p><p type="main">
  
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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><emph type="italics"/>Vt &longs;i quis dicat diametrum po&longs;&longs;e commen&longs;arari, non tamen commen&longs;u&shy;<lb/>rabitur<emph.end type="italics"/>) &amp; paul&ograve; infra (<emph type="italics"/>Commen&longs;urari enim impo&longs;&longs;ibile e&longs;t<emph.end type="italics"/>) expo&longs;i&shy;<lb/>tionem horum reperies 1. Priorum, &longs;ecto 1. cap. </s> <s><emph type="italics"/>Vt &longs;i quis dicat diametrum po&longs;&longs;e commen&longs;arari, non tamen commen&longs;u&shy;<lb/>rabitur<emph.end type="italics"/>) &amp; paul&ograve; infra (<emph type="italics"/>Commen&longs;urari enim impo&longs;&longs;ibile e&longs;t<emph.end type="italics"/>) expo&longs;i&shy;<lb/>tionem horum reperies 1. Priorum, &longs;ecto 1. cap.
  
 <s>23.</s></p><p type="main"> 23.</s></p><p type="main">
  
 <s><arrow.to.target n="marg212"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg212"></arrow.to.target></s></p><p type="margin">
  
 <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>
  
 <s>Dicit igitur, quod demon&longs;trationes &longs;uas Geometr&aelig; inueniunt, <lb/>reducendo ad actum ea, qu&aelig; erant in potentia, diuidentes enim educunt in <lb/>actum, figuras, angulos, lineas, &amp; c&aelig;tera huiu&longs;inodi, qu&aelig; prius &longs;ol&ugrave;m erat <lb/>in potentia, ex quibus po&longs;tea &longs;uas demon&longs;trationes perficiunt (<emph type="italics"/>Cur triangu&shy;<lb/>lus duo recti<emph.end type="italics"/>) affert exemplum eius, quod proxim&egrave; dixerat, &longs;cilicet Geome&shy;<lb/>tras demon&longs;trare producendo ad actum entia qu&aelig;dam Mathematica, quod <lb/>exemplum, vt intelligas ijs opus habes, qu&aelig; primo Priorum, &longs;ecto 3. cap. </s> <s>Dicit igitur, quod demon&longs;trationes &longs;uas Geometr&aelig; inueniunt, <lb/>reducendo ad actum ea, qu&aelig; erant in potentia, diuidentes enim educunt in <lb/>actum, figuras, angulos, lineas, &amp; c&aelig;tera huiu&longs;inodi, qu&aelig; prius &longs;ol&ugrave;m erat <lb/>in potentia, ex quibus po&longs;tea &longs;uas demon&longs;trationes perficiunt (<emph type="italics"/>Cur triangu&shy;<lb/>lus duo recti<emph.end type="italics"/>) affert exemplum eius, quod proxim&egrave; dixerat, &longs;cilicet Geome&shy;<lb/>tras demon&longs;trare producendo ad actum entia qu&aelig;dam Mathematica, quod <lb/>exemplum, vt intelligas ijs opus habes, qu&aelig; primo Priorum, &longs;ecto 3. cap.
  
 <s>1. <lb/>con&longs;cripta &longs;unt (<emph type="italics"/>Cur triangulus duo recti?<emph.end type="italics"/>) ide&longs;t, cur triangulus habet tres <lb/>angulos &aelig;quales duobus rectis angulis (<emph type="italics"/>Quia qui circa vnum punctum anguli <lb/>duobus rectis angulis &aelig;quales &longs;unt<emph.end type="italics"/>) ni&longs;i hoc dictum ad bonum trahatur &longs;en&longs;um, <lb/><figure id="fig68"></figure><lb/>fal&longs;um e&longs;t, nam omnes anguli, qui circa vnum <lb/>punctum, v. </s> 1. <lb/>con&longs;cripta &longs;unt (<emph type="italics"/>Cur triangulus duo recti?<emph.end type="italics"/>) ide&longs;t, cur triangulus habet tres <lb/>angulos &aelig;quales duobus rectis angulis (<emph type="italics"/>Quia qui circa vnum punctum anguli <lb/>duobus rectis angulis &aelig;quales &longs;unt<emph.end type="italics"/>) ni&longs;i hoc dictum ad bonum trahatur &longs;en&longs;um, <lb/><figure id="fig68"></figure><lb/>fal&longs;um e&longs;t, nam omnes anguli, qui circa vnum <lb/>punctum, v. </s>
  
 <s>g. </s> <s>g. </s>
  
 <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> <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>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> 
  
 <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> 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>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> <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>1.</s></p><p type="main"> 1.</s></p><p type="main">
  
 <s><arrow.to.target n="marg215"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg215"></arrow.to.target></s></p><p type="margin">
  
 <s><margin.target id="marg215"></margin.target>224</s></p><p type="main"> <s><margin.target id="marg215"></margin.target>224</s></p><p type="main">
  
 <s>Ibidem (<emph type="italics"/>Verum aliquid quidem, aliquid ver&ograve; non, vt puta parem numerum <lb/>primum nullum e&longs;&longs;e; aut quo&longs;dam quidem, quo&longs;dam ver&ograve; non<emph.end type="italics"/>) definitione 11. <lb/>7. Elem. </s> <s>Ibidem (<emph type="italics"/>Verum aliquid quidem, aliquid ver&ograve; non, vt puta parem numerum <lb/>primum nullum e&longs;&longs;e; aut quo&longs;dam quidem, quo&longs;dam ver&ograve; non<emph.end type="italics"/>) definitione 11. <lb/>7. Elem.
  
 <s>&longs;ic numerus ille, qui &agrave; Mathematicis dicitur primus, definitur, pri&shy;<lb/>mus numerus e&longs;t, quem vnitas &longs;ola metitur, vnde patet inter numeros pa&shy;<lb/>res &longs;olum binarium e&longs;&longs;e primum, cum ip&longs;um &longs;ola vnitas bis replicata men&shy;<lb/>&longs;uraret. </s> &longs;ic numerus ille, qui &agrave; Mathematicis dicitur primus, definitur, pri&shy;<lb/>mus numerus e&longs;t, quem vnitas &longs;ola metitur, vnde patet inter numeros pa&shy;<lb/>res &longs;olum binarium e&longs;&longs;e primum, cum ip&longs;um &longs;ola vnitas bis replicata men&shy;<lb/>&longs;uraret. </s>
  
 <s>quaternarium autem, &longs;enarium, &amp;c. </s> <s>quaternarium autem, &longs;enarium, &amp;c. </s>
  
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 <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>Eodem tex. </s> <s>Eodem tex. </s>
  
 <s>&longs;ed cap. </s> <s>&longs;ed cap.
  
 <s>3. <emph type="italics"/>(Nox &longs;emper autem men&longs;ura numero vnum e&longs;t, verum <lb/>aliquando plura, vt puta die&longs;es du&aelig;, non quidem &longs;ecundum cuditum, &longs;ed in ratio&shy;<lb/>nibus, &amp; voces plures, quibus men&longs;uramus, &amp; diameter duobus men&longs;uratur, &amp; la&shy;<lb/>tus, &amp; omnes magnitudines)<emph.end type="italics"/> ita corrigenda e&longs;t antiqua tran&longs;latio. </s> 3. <emph type="italics"/>(Nox &longs;emper autem men&longs;ura numero vnum e&longs;t, verum <lb/>aliquando plura, vt puta die&longs;es du&aelig;, non quidem &longs;ecundum cuditum, &longs;ed in ratio&shy;<lb/>nibus, &amp; voces plures, quibus men&longs;uramus, &amp; diameter duobus men&longs;uratur, &amp; la&shy;<lb/>tus, &amp; omnes magnitudines)<emph.end type="italics"/> ita corrigenda e&longs;t antiqua tran&longs;latio. </s>
  
 <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>Svmma r. </s> <s>Svmma r. </s>
  
 <s>cap. </s> <s>cap.
  
 <s>2. <emph type="italics"/>(Si quis ver&ograve; lineas, aut qu&aelig; has &longs;equuntur, dico autem <lb/>primas &longs;uperficies principia e&longs;&longs;e ponat. </s> 2. <emph type="italics"/>(Si quis ver&ograve; lineas, aut qu&aelig; has &longs;equuntur, dico autem <lb/>primas &longs;uperficies principia e&longs;&longs;e ponat. </s>
  
 <s>b&aelig;c non &longs;unt &longs;ub&longs;tanti&aelig; &longs;eparabiles, <lb/>ver&ugrave;m &longs;ectiones, &amp; diui&longs;iones, ill&aelig; quidem in &longs;uperficierum, h&aelig;c ver&ograve; cor&shy;<lb/>porum, puncta ver&ograve; linearum &longs;unt, &amp; etiam ip&longs;arum earumdem termini; <lb/>h&aelig;c autem omnia in alijs &longs;unt, &amp; nihil &longs;eparabile e&longs;t)<emph.end type="italics"/> ait puncta oriri ex &longs;ectio&shy;<lb/>ne line&aelig;, quamuis &longs;int etiam termini illius; lineas ver&ograve; oriri ex diui&longs;ione <lb/>&longs;uperficierum, quamuis &longs;int etiam termini illarum. </s> <s>b&aelig;c non &longs;unt &longs;ub&longs;tanti&aelig; &longs;eparabiles, <lb/>ver&ugrave;m &longs;ectiones, &amp; diui&longs;iones, ill&aelig; quidem in &longs;uperficierum, h&aelig;c ver&ograve; cor&shy;<lb/>porum, puncta ver&ograve; linearum &longs;unt, &amp; etiam ip&longs;arum earumdem termini; <lb/>h&aelig;c autem omnia in alijs &longs;unt, &amp; nihil &longs;eparabile e&longs;t)<emph.end type="italics"/> ait puncta oriri ex &longs;ectio&shy;<lb/>ne line&aelig;, quamuis &longs;int etiam termini illius; lineas ver&ograve; oriri ex diui&longs;ione <lb/>&longs;uperficierum, quamuis &longs;int etiam termini illarum. </s>
  
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 <s><margin.target id="marg223"></margin.target>232</s></p><p type="main"> <s><margin.target id="marg223"></margin.target>232</s></p><p type="main">
  
 <s>Summa 3. cap. </s> <s>Summa 3. cap.
  
 <s>2. <emph type="italics"/>(Vt puta &longs;ub Cane fiat frigus)<emph.end type="italics"/> ideft &longs;ub ortum Canis c&oelig;&shy;<lb/>l&aelig;&longs;tis, &longs;eu Canicul&aelig;. </s> 2. <emph type="italics"/>(Vt puta &longs;ub Cane fiat frigus)<emph.end type="italics"/> ideft &longs;ub ortum Canis c&oelig;&shy;<lb/>l&aelig;&longs;tis, &longs;eu Canicul&aelig;. </s>
  
 <s>Vide qu&aelig; libro &longs;ecundo Meteororum, &longs;umma 2. cap. </s> <s>Vide qu&aelig; libro &longs;ecundo Meteororum, &longs;umma 2. cap.
  
 <s>2. <lb/>de hac &longs;tella &longs;crip&longs;imus.</s></p><p type="head"> 2. <lb/>de hac &longs;tella &longs;crip&longs;imus.</s></p><p type="head">
  
 <s><emph type="italics"/>Ex Duodecimo Metaphy&longs;ic&aelig;.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Ex Duodecimo Metaphy&longs;ic&aelig;.<emph.end type="italics"/></s></p><p type="main">
  
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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. </s> 
  
 <s>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. 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><margin.target id="marg228"></margin.target>237</s></p><p type="main"> <s><margin.target id="marg228"></margin.target>237</s></p><p type="main">
  
 <s>Svmma 1. cap. </s> <s>Svmma 1. cap.
  
 <s>3. <emph type="italics"/>(Qui dicunt Mathematicas &longs;cientias nihil de bono, vel <lb/>pulchro dicere, fal&longs;um dicunt. </s> 3. <emph type="italics"/>(Qui dicunt Mathematicas &longs;cientias nihil de bono, vel <lb/>pulchro dicere, fal&longs;um dicunt. </s>
  
 <s>dicunt. </s> <s>dicunt. </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>quam etiam <lb/>Pater Clauius demon&longs;trat propo&longs;. </s> <s>quam etiam <lb/>Pater Clauius demon&longs;trat propo&longs;. </s>
  
 <s>2. lib. </s> <s>2. lib.
  
 <s>8. &amp; propo&longs;. </s> 8. &amp; propo&longs;. </s>
  
 <s>1. lib. </s> <s>1. lib.
  
 <s>4. Geom. </s> 4. Geom. </s>
  
 <s>pract. <lb/></s> <s>pract. <lb/></s>
  
 <s>&longs;i autem de ip&longs;is circulis intelligerentur fal&longs;a e&longs;&longs;ent, non enim e&longs;t circulus <lb/>ad circulum, vt diameter ad diametrum; &longs;ed circuli &longs;unt inter &longs;e, quemad&shy;<lb/>modum &agrave; diametris ip&longs;orum quadrata per &longs;ecundam 12. Elem. </s> <s>&longs;i autem de ip&longs;is circulis intelligerentur fal&longs;a e&longs;&longs;ent, non enim e&longs;t circulus <lb/>ad circulum, vt diameter ad diametrum; &longs;ed circuli &longs;unt inter &longs;e, quemad&shy;<lb/>modum &agrave; diametris ip&longs;orum quadrata per &longs;ecundam 12. Elem.
  
 <s>quadrata <lb/>autem &longs;unt inter &longs;e in duplicata ratione laterum per 20. 6. <expan abbr="eiusq;">eiusque</expan> corolla&shy;<lb/>rium; hoc e&longs;t &longs;i fiat, vt latus maioris quadrati ad latus minoris, ita latus mi&shy;<lb/>noris ad aliam tertiam lineam, erit quadratum maius ad minus, vt latus <lb/>ip&longs;ius ad tertiam illam lineam; non autem vt ad latus minoris. </s> quadrata <lb/>autem &longs;unt inter &longs;e in duplicata ratione laterum per 20. 6. <expan abbr="eiusq;">eiusque</expan> corolla&shy;<lb/>rium; hoc e&longs;t &longs;i fiat, vt latus maioris quadrati ad latus minoris, ita latus mi&shy;<lb/>noris ad aliam tertiam lineam, erit quadratum maius ad minus, vt latus <lb/>ip&longs;ius ad tertiam illam lineam; non autem vt ad latus minoris. </s>
  
 <s>cum ergo <lb/>circulus &longs;it ad circulum, vt quadratum diametri ad quadratum diametri, <lb/>&amp; quadrata non <expan abbr="habe&atilde;t">habeant</expan> rationem laterum, &longs;eu diametrorum pr&aelig;dictorum, <lb/>&longs;ed illorum duplicatam, <expan abbr="neq;">neque</expan> circuli inuicem illam habere poterunt.</s></p><p type="main"> <s>cum ergo <lb/>circulus &longs;it ad circulum, vt quadratum diametri ad quadratum diametri, <lb/>&amp; quadrata non <expan abbr="habe&atilde;t">habeant</expan> rationem laterum, &longs;eu diametrorum pr&aelig;dictorum, <lb/>&longs;ed illorum duplicatam, <expan abbr="neq;">neque</expan> circuli inuicem illam habere poterunt.</s></p><p type="main">
  
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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><margin.target id="marg252"></margin.target>262</s></p><p type="main"> <s><margin.target id="marg252"></margin.target>262</s></p><p type="main">
  
 <s>Rhombus ex definitione 23. primi Elem. </s> <s>Rhombus ex definitione 23. primi Elem.
  
 <s>e&longs;t figura &aelig;quilatera qui&shy;<lb/><figure id="fig103"></figure><lb/>dem, &longs;ed non &aelig;quiangula, habet enim <lb/>binos oppo&longs;itos angulos acutos, &amp; alies <lb/>binos oppo&longs;itos obtu&longs;os, talis e&longs;t pr&aelig;&shy;<lb/>&longs;ens figura A B D C. </s> e&longs;t figura &aelig;quilatera qui&shy;<lb/><figure id="fig103"></figure><lb/>dem, &longs;ed non &aelig;quiangula, habet enim <lb/>binos oppo&longs;itos angulos acutos, &amp; alies <lb/>binos oppo&longs;itos obtu&longs;os, talis e&longs;t pr&aelig;&shy;<lb/>&longs;ens figura A B D C. </s>
  
 <s>In pr&aelig;&longs;enti porr&ograve; qu&aelig;&longs;tione <lb/>&longs;upponitur punctum A, quod e&longs;t vnum extremum <lb/>in rhombo moueri &longs;uper latus A B, ver&longs;us B, &amp; &longs;i&shy;<lb/>militer interim &aelig;qua velocitate moueri alterum <lb/>extremum B, &longs;uper idem latus A B_{2} ver&longs;us A, &amp; in&shy;<lb/>terim dum h&aelig;c duo puncta hoc modo &longs;ibi obuiam <lb/>procedunt, moueri latus totum A B, eadem ve&shy;<lb/>locitate, ver&longs;us latus C D, ita vt &longs;emper ip&longs;i C D, <lb/>&aelig;quidi&longs;ter, <expan abbr="de&longs;cendat&qacute;">de&longs;cendatque</expan>; per latera A C, B D, quo&shy;<lb/>u&longs;que ip&longs;i C D, congruat.</s></p><p type="main"> <s>In pr&aelig;&longs;enti porr&ograve; qu&aelig;&longs;tione <lb/>&longs;upponitur punctum A, quod e&longs;t vnum extremum <lb/>in rhombo moueri &longs;uper latus A B, ver&longs;us B, &amp; &longs;i&shy;<lb/>militer interim &aelig;qua velocitate moueri alterum <lb/>extremum B, &longs;uper idem latus A B_{2} ver&longs;us A, &amp; in&shy;<lb/>terim dum h&aelig;c duo puncta hoc modo &longs;ibi obuiam <lb/>procedunt, moueri latus totum A B, eadem ve&shy;<lb/>locitate, ver&longs;us latus C D, ita vt &longs;emper ip&longs;i C D, <lb/>&aelig;quidi&longs;ter, <expan abbr="de&longs;cendat&qacute;">de&longs;cendatque</expan>; per latera A C, B D, quo&shy;<lb/>u&longs;que ip&longs;i C D, congruat.</s></p><p type="main">
  
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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><margin.target id="marg261"></margin.target>271</s></p><p type="main"> <s><margin.target id="marg261"></margin.target>271</s></p><p type="main">
  
 <s>In 2. cap. </s> <s>In 2. cap.
  
 <s>recen&longs;et Planetarum ordinem, iuxta antiqui&longs;&longs;imorum <lb/>A&longs;tronomorum traditiones, qui ob paucas, <expan abbr="eas&qacute;">easque</expan>; imperfectas ob&shy;<lb/>&longs;eruationes muita ignorarunt, <expan abbr="atq;">atque</expan> in multis, &amp; pr&aelig;cipu&egrave; in ordine Plane&shy;<lb/>tarum &longs;tatuendo, fal&longs;i &longs;unt: A&longs;tronomi enim po&longs;teriores, &amp; maxim&egrave; Ptol&aelig;&shy;<lb/>meus, vn&agrave; cum recentioribus no&longs;tri &longs;eculi alium ordinem exactioribus ob&shy;<lb/>&longs;eruationibus, <expan abbr="atq;">atque</expan> demon&longs;trationibus a&longs;trucntes vetu&longs;ti&longs;&longs;imorum illorum <lb/>errores patefecerunt. </s> recen&longs;et Planetarum ordinem, iuxta antiqui&longs;&longs;imorum <lb/>A&longs;tronomorum traditiones, qui ob paucas, <expan abbr="eas&qacute;">easque</expan>; imperfectas ob&shy;<lb/>&longs;eruationes muita ignorarunt, <expan abbr="atq;">atque</expan> in multis, &amp; pr&aelig;cipu&egrave; in ordine Plane&shy;<lb/>tarum &longs;tatuendo, fal&longs;i &longs;unt: A&longs;tronomi enim po&longs;teriores, &amp; maxim&egrave; Ptol&aelig;&shy;<lb/>meus, vn&agrave; cum recentioribus no&longs;tri &longs;eculi alium ordinem exactioribus ob&shy;<lb/>&longs;eruationibus, <expan abbr="atq;">atque</expan> demon&longs;trationibus a&longs;trucntes vetu&longs;ti&longs;&longs;imorum illorum <lb/>errores patefecerunt. </s>
  
 <s>E&longs;t autem verus ordo, vt Luna &longs;it omnium terris pro&shy;<lb/>xima, deinde Mercurius, t&ugrave;m Venus, po&longs;tea Sol, Mars, Iupiter, <expan abbr="Saturnus&qacute;">Saturnusque</expan>; <lb/>&agrave; terris alti&longs;&longs;imus, quos omnes &longs;tellarum affixarum &longs;ph&aelig;ra, qu&aelig; etiam fir&shy;<lb/>mamentum dicitur, complectitur. </s> <s>E&longs;t autem verus ordo, vt Luna &longs;it omnium terris pro&shy;<lb/>xima, deinde Mercurius, t&ugrave;m Venus, po&longs;tea Sol, Mars, Iupiter, <expan abbr="Saturnus&qacute;">Saturnusque</expan>; <lb/>&agrave; terris alti&longs;&longs;imus, quos omnes &longs;tellarum affixarum &longs;ph&aelig;ra, qu&aelig; etiam fir&shy;<lb/>mamentum dicitur, complectitur. </s>
  
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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>quod adhuc ma&shy;<lb/>nife&longs;tius erit, &longs;i con&longs;ideremus, quod quanto tardius quotidie Luna oritur, <lb/>tanto etiam maris &aelig;&longs;tus tardius incipit. </s> <s>quod adhuc ma&shy;<lb/>nife&longs;tius erit, &longs;i con&longs;ideremus, quod quanto tardius quotidie Luna oritur, <lb/>tanto etiam maris &aelig;&longs;tus tardius incipit. </s>
  
 <s>Porr&ograve; vt appareat hanc e&longs;&longs;e vete&shy;<lb/>rum &longs;ententiam libet hic attexere qu&aelig;dam ex lib. </s> <s>Porr&ograve; vt appareat hanc e&longs;&longs;e vete&shy;<lb/>rum &longs;ententiam libet hic attexere qu&aelig;dam ex lib.
  
 <s>3. Strabonis, qu&aelig; ip&longs;e ex <lb/>Po&longs;&longs;idonio acceperat. </s> 3. Strabonis, qu&aelig; ip&longs;e ex <lb/>Po&longs;&longs;idonio acceperat. </s>
  
 <s>&longs;ic. </s> <s>&longs;ic. </s>
  
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 <s>de creatione mundi tantummodo &longs;ine vlla expo&longs;itione, <expan abbr="atq;">atque</expan> con&shy;<lb/>firmatione proponit. </s> <s>de creatione mundi tantummodo &longs;ine vlla expo&longs;itione, <expan abbr="atq;">atque</expan> con&shy;<lb/>firmatione proponit. </s>
  
 <s>in eadem pror&longs;us &longs;ententia e&longs;t Rogerius Bachon inter <lb/>Opticos probati&longs;&longs;imus, cap. </s> <s>in eadem pror&longs;us &longs;ententia e&longs;t Rogerius Bachon inter <lb/>Opticos probati&longs;&longs;imus, cap.
  
 <s>5. de Speculis Mathematicis.</s></p><p type="main"> 5. de Speculis Mathematicis.</s></p><p type="main">
  
 <s>Aliorum demum opinationes, &longs;iue Angelo cuidam, &longs;iue virtuti totam <lb/>terram peruadenti hunc &aelig;&longs;tum a&longs;cribentium, non e&longs;t meum refellere, cum <lb/>non phy&longs;icum, &longs;ed mathematicum agere in&longs;tituerim.</s></p><p type="main"> <s>Aliorum demum opinationes, &longs;iue Angelo cuidam, &longs;iue virtuti totam <lb/>terram peruadenti hunc &aelig;&longs;tum a&longs;cribentium, non e&longs;t meum refellere, cum <lb/>non phy&longs;icum, &longs;ed mathematicum agere in&longs;tituerim.</s></p><p type="main">
  
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 <s>A lint<gap/>igentiam igitur huius operis nece&longs;&longs;arium e&longs;t noui&longs;&longs;e, qu&aelig; nam <lb/>&longs;int quantitates commen&longs;urabiles, &amp; qu&aelig; in commen&longs;urabiles. </s> <s>A lint<gap/>igentiam igitur huius operis nece&longs;&longs;arium e&longs;t noui&longs;&longs;e, qu&aelig; nam <lb/>&longs;int quantitates commen&longs;urabiles, &amp; qu&aelig; in commen&longs;urabiles. </s>
  
 <s>qu&aelig; prima, <lb/>&amp; &longs;ecunda definitione 10. Elem. </s> <s>qu&aelig; prima, <lb/>&amp; &longs;ecunda definitione 10. Elem.
  
 <s>explicantur; <expan abbr="ego&qacute;">egoque</expan>; eas primo Priorum oc&shy;<lb/>ca&longs;ione a&longs;ymetri&aelig; diametri cum co&longs;ta &longs;atis expo&longs;ui: vtrumuis locum vide&shy;<lb/>ris pr&aelig;&longs;enti nece&longs;&longs;itati con&longs;ultum erit.</s></p><p type="main"> explicantur; <expan abbr="ego&qacute;">egoque</expan>; eas primo Priorum oc&shy;<lb/>ca&longs;ione a&longs;ymetri&aelig; diametri cum co&longs;ta &longs;atis expo&longs;ui: vtrumuis locum vide&shy;<lb/>ris pr&aelig;&longs;enti nece&longs;&longs;itati con&longs;ultum erit.</s></p><p type="main">
  
 <s><arrow.to.target n="marg267"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg267"></arrow.to.target></s></p><p type="margin">
  
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 <s>Ve&shy;<lb/>r&ugrave;m neque &longs;ecundum &longs;e aliquam definitam naturam habebunt, &longs;ed collat&aelig; &longs;ibi ip&longs;is <lb/>tam rationales, qu&agrave;m irrationales erunt omnes.<emph.end type="italics"/></s></p><p type="main"> <s>Ve&shy;<lb/>r&ugrave;m neque &longs;ecundum &longs;e aliquam definitam naturam habebunt, &longs;ed collat&aelig; &longs;ibi ip&longs;is <lb/>tam rationales, qu&agrave;m irrationales erunt omnes.<emph.end type="italics"/></s></p><p type="main">
  
 <s>H&aelig;c e&longs;t alia eorumdem ratio ad idem comprobandum: quam, vt ben&egrave; <lb/>percipiamus, nonnulla prius ex definitionibus 10. Elem. </s> <s>H&aelig;c e&longs;t alia eorumdem ratio ad idem comprobandum: quam, vt ben&egrave; <lb/>percipiamus, nonnulla prius ex definitionibus 10. Elem.
  
 <s>&longs;unt explicanda: <lb/>vt qu&aelig; nam &longs;int line&aelig; rationales, qu&aelig; irrationales, qu&aelig; ex binis nomini&shy;<lb/>bus, qu&aelig; Apotom&aelig;.</s></p><p type="main"> &longs;unt explicanda: <lb/>vt qu&aelig; nam &longs;int line&aelig; rationales, qu&aelig; irrationales, qu&aelig; ex binis nomini&shy;<lb/>bus, qu&aelig; Apotom&aelig;.</s></p><p type="main">
  
 <s>Propo&longs;ita igitur linea quapiam, v. </s> <s>Propo&longs;ita igitur linea quapiam, v. </s>
  
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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>indiu du&aelig; autem line&aelig; &longs;ibi ip&longs;is co<gap/>men&longs;urabiles &longs;unt longitudine, cuminter &longs;e <lb/>&longs;iat &aelig;quales; quare po<gap/>emia quoque, quod &longs;i hoc e&longs;t, diuiduum erit quadratum.<emph.end type="italics"/></s></p><pb pagenum="207"/><p type="main"> <s>indiu du&aelig; autem line&aelig; &longs;ibi ip&longs;is co<gap/>men&longs;urabiles &longs;unt longitudine, cuminter &longs;e <lb/>&longs;iat &aelig;quales; quare po<gap/>emia quoque, quod &longs;i hoc e&longs;t, diuiduum erit quadratum.<emph.end type="italics"/></s></p><pb pagenum="207"/><p type="main">
  
 <s>Pergit adhuc nouis rationibus aduer&longs;arios refellere, dicens, &longs;i extarent <lb/>huiu&longs;modi indiuidu&aelig; line&aelig;, &longs;equeretur omnes omnin&ograve; lineas e&longs;&longs;e commen&shy;<lb/>&longs;urabiles, quod e&longs;t contra demon&longs;trata in 10. Elem. </s> <s>Pergit adhuc nouis rationibus aduer&longs;arios refellere, dicens, &longs;i extarent <lb/>huiu&longs;modi indiuidu&aelig; line&aelig;, &longs;equeretur omnes omnin&ograve; lineas e&longs;&longs;e commen&shy;<lb/>&longs;urabiles, quod e&longs;t contra demon&longs;trata in 10. Elem.
  
 <s>quia cum omnes line&aelig; <lb/><expan abbr="con&longs;t&etilde;t">con&longs;tent</expan> per ip&longs;os ex lineis atomis, i&longs;t&aelig; atom&aelig; e&longs;&longs;ent omnium linearum com&shy;<lb/>munes men&longs;ur&aelig;, vnde &amp; ill&aelig;, qu&aelig; dicuntur potentia tantum commen&longs;ura&shy;<lb/>biles, vt &longs;upra explicaui, erunt etiam commen&longs;urabiles longitudine. </s> quia cum omnes line&aelig; <lb/><expan abbr="con&longs;t&etilde;t">con&longs;tent</expan> per ip&longs;os ex lineis atomis, i&longs;t&aelig; atom&aelig; e&longs;&longs;ent omnium linearum com&shy;<lb/>munes men&longs;ur&aelig;, vnde &amp; ill&aelig;, qu&aelig; dicuntur potentia tantum commen&longs;ura&shy;<lb/>biles, vt &longs;upra explicaui, erunt etiam commen&longs;urabiles longitudine. </s>
  
 <s>indiui&shy;<lb/>du&aelig; ver&ograve; ip&longs;&aelig;, cum &longs;int inuicem &aelig;quales, erunt ip&longs;&aelig; <expan abbr="quoq;">quoque</expan> commen&longs;urabi&shy;<lb/>les longitudine, quare &amp; potentia, omnes enim longitudine commen&longs;ura&shy;<lb/>biles, &longs;unt etiam potentia commen&longs;urabiles, ex 9. 10. vnde &longs;equitur qua&shy;<lb/>drata earum omnia e&longs;&longs;e <expan abbr="quoq;">quoque</expan> commen&longs;urabilia: <expan abbr="atq;">atque</expan> hinc con&longs;equitur, in&shy;<lb/>quit, ea e&longs;&longs;e <expan abbr="quoq;">quoque</expan> diuidua (quam con&longs;ecutionem probat infra num. </s> <s>indiui&shy;<lb/>du&aelig; ver&ograve; ip&longs;&aelig;, cum &longs;int inuicem &aelig;quales, erunt ip&longs;&aelig; <expan abbr="quoq;">quoque</expan> commen&longs;urabi&shy;<lb/>les longitudine, quare &amp; potentia, omnes enim longitudine commen&longs;ura&shy;<lb/>biles, &longs;unt etiam potentia commen&longs;urabiles, ex 9. 10. vnde &longs;equitur qua&shy;<lb/>drata earum omnia e&longs;&longs;e <expan abbr="quoq;">quoque</expan> commen&longs;urabilia: <expan abbr="atq;">atque</expan> hinc con&longs;equitur, in&shy;<lb/>quit, ea e&longs;&longs;e <expan abbr="quoq;">quoque</expan> diuidua (quam con&longs;ecutionem probat infra num. </s>
  
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 <s>in omni autem &aelig;quilatero perpendicularis <lb/>in mediam ba&longs;im mcidit, quare, &amp; in medium indiuidu&aelig;.<emph.end type="italics"/></s></p><p type="main"> <s>in omni autem &aelig;quilatero perpendicularis <lb/>in mediam ba&longs;im mcidit, quare, &amp; in medium indiuidu&aelig;.<emph.end type="italics"/></s></p><p type="main">
  
 <s>Ex 22. primi Elem. </s> <s>Ex 22. primi Elem.
  
 <s>ex tribus datis lineis, quarum qu&aelig;libet du&aelig; &longs;int, re&shy;<lb/>liqua maiores pote&longs;t con&longs;titui triangulum: poterit igitur ex tribus indiui&shy;<lb/><figure id="fig122"></figure><lb/>duis con&longs;titui <expan abbr="tri&atilde;gulum">triangulum</expan>, <expan abbr="illud&qacute;">illudque</expan>; &aelig;quilaterum, cum omnes in&shy;<lb/>diuidu&aelig; line&aelig; &longs;int &aelig;quales. </s> ex tribus datis lineis, quarum qu&aelig;libet du&aelig; &longs;int, re&shy;<lb/>liqua maiores pote&longs;t con&longs;titui triangulum: poterit igitur ex tribus indiui&shy;<lb/><figure id="fig122"></figure><lb/>duis con&longs;titui <expan abbr="tri&atilde;gulum">triangulum</expan>, <expan abbr="illud&qacute;">illudque</expan>; &aelig;quilaterum, cum omnes in&shy;<lb/>diuidu&aelig; line&aelig; &longs;int &aelig;quales. </s>
  
 <s>&longs;it igitur ex eis triangulum A B C, <lb/>&longs;i igitur ab angulo A, ducatur perpendicularis A D, ad ba&longs;im <lb/>B C, eam bif<gap/>riam &longs;ecabit ex &longs;cholio 26. primi, erit igitur li&shy;<lb/>nea B C, &longs;ecabilis, contra quam aduer&longs;arij opinantur.</s></p><p type="main"> <s>&longs;it igitur ex eis triangulum A B C, <lb/>&longs;i igitur ab angulo A, ducatur perpendicularis A D, ad ba&longs;im <lb/>B C, eam bif<gap/>riam &longs;ecabit ex &longs;cholio 26. primi, erit igitur li&shy;<lb/>nea B C, &longs;ecabilis, contra quam aduer&longs;arij opinantur.</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. </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>
  
 <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> 
  
 <s>Automata hodie &longs;unt Horologia, qu&aelig; ex <lb/>multis dentatis rotis Germani con&longs;truunt.</s></p><p type="main"> <s>Automata hodie &longs;unt Horologia, qu&aelig; ex <lb/>multis dentatis rotis Germani con&longs;truunt.</s></p><p type="main">
  
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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. </s> 
  
 <s>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. </s> 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.
  
 <s>1. Priorum, &longs;ecto 3. cap. </s> 1. Priorum, &longs;ecto 3. cap.
  
 <s>1.</s></p><p type="main"> 1.</s></p><p type="main">
  
 <s><arrow.to.target n="marg291"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg291"></arrow.to.target></s></p><p type="margin">
  
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 <s>Ibidem <emph type="italics"/>(Et diametrum incommen&longs;urabilem e&longs;&longs;e cum co&longs;t a &longs;empiternum e&longs;t: at&shy;<lb/>tamen cau&longs;a eorum aliqua &amp; demon&longs;tratio e&longs;t.<emph.end type="italics"/></s></p><p type="main"> <s>Ibidem <emph type="italics"/>(Et diametrum incommen&longs;urabilem e&longs;&longs;e cum co&longs;t a &longs;empiternum e&longs;t: at&shy;<lb/>tamen cau&longs;a eorum aliqua &amp; demon&longs;tratio e&longs;t.<emph.end type="italics"/></s></p><p type="main">
  
 <s>Qu&aelig;libro 1. Priorum, &longs;ecto 1. cap. </s> <s>Qu&aelig;libro 1. Priorum, &longs;ecto 1. cap.
  
 <s>23. de hac re annotata &longs;unt, abund&egrave; <lb/>huic etiam loco &longs;atisfaciunt.</s></p><p type="head"> 23. de hac re annotata &longs;unt, abund&egrave; <lb/>huic etiam loco &longs;atisfaciunt.</s></p><p type="head">
  
 <s><emph type="italics"/>In Ethica, &longs;eu Moralia ad Nicomachum.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>In Ethica, &longs;eu Moralia ad Nicomachum.<emph.end type="italics"/></s></p><p type="main">
  
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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. </s> 
  
 <s>7. <emph type="italics"/>(Faber enim, &amp; Geometra diuer&longs;o modo rectum angulum <lb/><expan abbr=&q