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version 1.43, 2002/08/14 23:03:02 version 1.44, 2002/08/14 23:18:17
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 <s>Item ad primam primi, vide tex. </s> <s>Item ad primam primi, vide tex. </s>
  
 <s>7. &longs;ecundi Po&longs;ter. </s> <s>7. &longs;ecundi Po&longs;ter. loco 2.</s></p><p type="main">
  
 <s>loco 2.</s></p><p type="main"> 
  
 <s>Ad 5. primi, vide cap.  <s>Ad 5. primi, vide cap.
  
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 26. &longs;ecundi <expan abbr="Prior&utilde;">Priorum</expan>, &amp; tex. </s> 26. &longs;ecundi <expan abbr="Prior&utilde;">Priorum</expan>, &amp; tex. </s>
  
 <s>2. <lb/>primi Po&longs;ter. </s> <s>2. <lb/>primi Po&longs;ter. loco 4. &amp; tex. </s>
  
 <s>loco 4. &amp; tex. </s> 
  
 <s>23. primi Po&longs;ter. </s> <s>23. primi Po&longs;ter. </s>
  
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 <s>&amp; tex. </s> <s>&amp; tex. </s>
  
 <s>37. primi Po&longs;ter. </s> <s>37. primi Po&longs;ter. &amp; tex. </s>
  
 <s>&amp; tex. </s> 
  
 <s>39. primi Po&longs;ter. </s> <s>39. primi Po&longs;ter. </s>
  
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 <s>Ad &longs;cholion pr&aelig;cedentis 32. primi, vide tex. </s> <s>Ad &longs;cholion pr&aelig;cedentis 32. primi, vide tex. </s>
  
 <s>39. primi Po&longs;ter. </s> <s>39. primi Po&longs;ter. loco 3. Item <lb/>tex. </s>
  
 <s>loco 3. Item <lb/>tex. </s> 
  
 <s>25. &longs;ecundi Po&longs;ter. </s> <s>25. &longs;ecundi Po&longs;ter. </s>
  
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 31. &longs;ecundi Priorum, &amp; <lb/>tex. </s> 31. &longs;ecundi Priorum, &amp; <lb/>tex. </s>
  
 <s>23. primi Po&longs;ter. </s> <s>23. primi Po&longs;ter. &amp; finem 1. cap. primi Elenchorum. </s>
  
 <s>&amp; finem 1. cap. primi Elenchorum. </s> 
  
 <s>lege primam Ar&shy;<lb/>chimedis de dimen&longs;ione circuli.</s></p><p type="head"> <s>lege primam Ar&shy;<lb/>chimedis de dimen&longs;ione circuli.</s></p><p type="head">
  
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 <s>Ad 31. tertij, vide tex. </s> <s>Ad 31. tertij, vide tex. </s>
  
 <s>11. &longs;ecundi Po&longs;ter. </s> <s>11. &longs;ecundi Po&longs;ter. &amp; tex. </s>
  
 <s>&amp; tex. </s> 
  
 <s>20. &longs;exti Methaph. </s> <s>20. &longs;exti Methaph. </s>
  
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 <s>Ad 10. definitionem 5. vide tex. </s> <s>Ad 10. definitionem 5. vide tex. </s>
  
 <s>29. primi Po&longs;ter. </s> <s>29. primi Po&longs;ter. loco 2.</s></p><p type="main">
  
 <s>loco 2.</s></p><p type="main"> 
  
 <s>Ad 12. definitionem 5. vide tex. </s> <s>Ad 12. definitionem 5. vide tex. </s>
  
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 <s>5. vide tex. </s> <s>5. vide tex. </s>
  
 <s>25. &longs;ecundi Po&longs;ter. </s> <s>25. &longs;ecundi Po&longs;ter. loco 2. ex hac Euclidis demon&shy;<lb/>&longs;tratione patet, vitio&longs;am e&longs;&longs;e illam Auerrois argumentationem, 8. Phy&longs;. <lb/></s>
  
 <s>loco 2. ex hac Euclidis demon&shy;<lb/>&longs;tratione patet, vitio&longs;am e&longs;&longs;e illam Auerrois argumentationem, 8. Phy&longs;. <lb/></s> 
  
 <s>comm. </s> <s>comm. </s>
  
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 <s>9. vide tex. </s> <s>9. vide tex. </s>
  
 <s>20. primi Po&longs;ter. </s> <s>20. primi Po&longs;ter. loco 2.</s></p><p type="main">
  
 <s>loco 2.</s></p><p type="main"> 
  
 <s>Ad 8. propo&longs;. </s> <s>Ad 8. propo&longs;. </s>
  
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 <s>&amp; tex. </s> <s>&amp; tex. </s>
  
 <s>5. primi Po&longs;ter. </s> <s>5. primi Po&longs;ter. &amp; tex. </s>
  
 <s>&amp; tex. </s> 
  
 <s>44. <lb/>primi Po&longs;ter. </s> <s>44. <lb/>primi Po&longs;ter. </s>
  
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 <s>&amp; c.<emph.end type="italics"/>) quod quan&shy;<lb/>titates, qu&aelig; &longs;unt proportionales, &longs;int etiam alternatim, &longs;eu permutatim <lb/>proportionales explicatum e&longs;t ad tex. </s> <s>&amp; c.<emph.end type="italics"/>) quod quan&shy;<lb/>titates, qu&aelig; &longs;unt proportionales, &longs;int etiam alternatim, &longs;eu permutatim <lb/>proportionales explicatum e&longs;t ad tex. </s>
  
 <s>13. primi Po&longs;ter. </s> <s>13. primi Po&longs;ter. qu&aelig; etiam nece&longs;&longs;a&shy;<lb/>ria &longs;unt ad hunc locum ben&egrave; intelligendum. </s>
  
 <s>qu&aelig; etiam nece&longs;&longs;a&shy;<lb/>ria &longs;unt ad hunc locum ben&egrave; intelligendum. </s> 
  
 <s>Illud autem commune propter <lb/>quod ea, qu&aelig; &longs;unt proportionalia, &longs;int etiam permutatim proportionalia, <lb/>e&longs;t quoddam innominatum, de quo ibi dictum e&longs;t, quod cum conueniat li&shy;<lb/>neis, &amp; numeris, &amp; tamen &longs;eparatim de vtri&longs;que illa pa&longs;&longs;io demon&longs;tretur, <lb/>qu&aelig;rit cuinam prim&ograve;, &amp; per &longs;e conueniat h&aelig;c pa&longs;&longs;io, e&longs;&longs;e permutatim pro&shy;<lb/>portionale; &longs;cilicet quidnam &longs;it illud innominatum; in quo deinde commu&shy;<lb/>nicent line&aelig;, &amp; numeri, vt inde habeant e&longs;&longs;e etiam permutatim propor&shy;<lb/>tionalia.</s></p><p type="main"> <s>Illud autem commune propter <lb/>quod ea, qu&aelig; &longs;unt proportionalia, &longs;int etiam permutatim proportionalia, <lb/>e&longs;t quoddam innominatum, de quo ibi dictum e&longs;t, quod cum conueniat li&shy;<lb/>neis, &amp; numeris, &amp; tamen &longs;eparatim de vtri&longs;que illa pa&longs;&longs;io demon&longs;tretur, <lb/>qu&aelig;rit cuinam prim&ograve;, &amp; per &longs;e conueniat h&aelig;c pa&longs;&longs;io, e&longs;&longs;e permutatim pro&shy;<lb/>portionale; &longs;cilicet quidnam &longs;it illud innominatum; in quo deinde commu&shy;<lb/>nicent line&aelig;, &amp; numeri, vt inde habeant e&longs;&longs;e etiam permutatim propor&shy;<lb/>tionalia.</s></p><p type="main">
  
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 <s>Ibidem (<emph type="italics"/>Vt extrin&longs;ecos &aelig;quales e&longs;&longs;e<emph.end type="italics"/>) ide&longs;t extrin&longs;ecos angulos cuiu&longs;uis fi&shy;<lb/>gur&aelig; rectiline&aelig; &aelig;quales e&longs;&longs;e quatuor rectis angulis: vide qu&aelig; &longs;crip&longs;imus de <lb/>hac re ad tex. </s> <s>Ibidem (<emph type="italics"/>Vt extrin&longs;ecos &aelig;quales e&longs;&longs;e<emph.end type="italics"/>) ide&longs;t extrin&longs;ecos angulos cuiu&longs;uis fi&shy;<lb/>gur&aelig; rectiline&aelig; &aelig;quales e&longs;&longs;e quatuor rectis angulis: vide qu&aelig; &longs;crip&longs;imus de <lb/>hac re ad tex. </s>
  
 <s>39. &longs;ecundi Po&longs;ter. </s> <s>39. &longs;ecundi Po&longs;ter. qu&aelig; huic pariter loco &longs;atisfaciunt.</s></p><p type="head">
  
 <s>qu&aelig; huic pariter loco &longs;atisfaciunt.</s></p><p type="head"> 
  
 <s><emph type="italics"/>EX TOPICIS.<emph.end type="italics"/></s></p><p type="head"> <s><emph type="italics"/>EX TOPICIS.<emph.end type="italics"/></s></p><p type="head">
  
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 31. <lb/>&amp; quo itidem modo Bry&longs;&longs;o lib.  31. <lb/>&amp; quo itidem modo Bry&longs;&longs;o lib.
  
 1. Po&longs;ter. </s> 1. Po&longs;ter. tex. </s>
  
 <s>tex. </s> 
  
 <s>23. <expan abbr="&longs;ol&utilde;modo">&longs;olummodo</expan> id hoc loco no&shy;<lb/>tandum per p&longs;eudographiam intelligere, vt apert&egrave; etiam inferius explicat, <lb/>Geometricam demon&longs;trationem fallacem, e&ograve; quod demon&longs;trationes geo&shy;<lb/>metric&aelig; fiant adhibitis de&longs;criptionibus, &longs;eu figurationibus: p&longs;endographia <lb/>autem latin&egrave; idem e&longs;t, ac fal&longs;a de&longs;criptio; quemadmodum &egrave; contrari&ograve;, &longs;i&shy;<lb/>cuti &longs;upra in Topicis, &amp; alibi ob&longs;eruaui, per de&longs;cribere intelligit geometri&shy;<lb/>c&egrave; demon&longs;trare, &amp; per de&longs;criptiones intelligit demon&longs;trationes geometri&shy;<lb/>cas. </s> <s>23. <expan abbr="&longs;ol&utilde;modo">&longs;olummodo</expan> id hoc loco no&shy;<lb/>tandum per p&longs;eudographiam intelligere, vt apert&egrave; etiam inferius explicat, <lb/>Geometricam demon&longs;trationem fallacem, e&ograve; quod demon&longs;trationes geo&shy;<lb/>metric&aelig; fiant adhibitis de&longs;criptionibus, &longs;eu figurationibus: p&longs;endographia <lb/>autem latin&egrave; idem e&longs;t, ac fal&longs;a de&longs;criptio; quemadmodum &egrave; contrari&ograve;, &longs;i&shy;<lb/>cuti &longs;upra in Topicis, &amp; alibi ob&longs;eruaui, per de&longs;cribere intelligit geometri&shy;<lb/>c&egrave; demon&longs;trare, &amp; per de&longs;criptiones intelligit demon&longs;trationes geometri&shy;<lb/>cas. </s>
  
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 <s>po&longs;&longs;umus addere tertiam rat<gap/> <gap/>cet <lb/>Hippocrates non procedebat per communia alijs &longs;ci<gap/>ad <lb/>tex. </s> <s>po&longs;&longs;umus addere tertiam rat<gap/> <gap/>cet <lb/>Hippocrates non procedebat per communia alijs &longs;ci<gap/>ad <lb/>tex. </s>
  
 <s>23. primi Po&longs;ter. </s> <s>23. primi Po&longs;ter. cap.
  
 <s>cap.  
  
 8. vbi ip&longs;ius p&longs;endographi<gap/>d&shy;<lb/>modum igitur Geometra di&longs;&longs;oluit fal&longs;as tantum<gap/>r&shy;<lb/>uatis Geometricis principijs procedunt; non au<gap/> <gap/>ri&aelig; <lb/>principia conuellunt: ita Phy&longs;ico non incumbit <expan abbr="c&otilde;tra">contra</expan> P<gap/> Me&shy;<lb/>li&longs;&longs;um natur&aelig; principia de&longs;truentes di&longs;ceptare, aut falla<gap/> rationes <lb/>coarguere. </s> 8. vbi ip&longs;ius p&longs;endographi<gap/>d&shy;<lb/>modum igitur Geometra di&longs;&longs;oluit fal&longs;as tantum<gap/>r&shy;<lb/>uatis Geometricis principijs procedunt; non au<gap/> <gap/>ri&aelig; <lb/>principia conuellunt: ita Phy&longs;ico non incumbit <expan abbr="c&otilde;tra">contra</expan> P<gap/> Me&shy;<lb/>li&longs;&longs;um natur&aelig; principia de&longs;truentes di&longs;ceptare, aut falla<gap/> rationes <lb/>coarguere. </s>
  
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 <s><margin.target id="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>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>Tex. </s> <s>Tex. </s>
  
 <s>32. <emph type="italics"/>(Sit igitur vt A, quidem album, ad B, quod nigrum; &longs;ic C, ad D; qua&shy;<lb/>re &amp; p<gap/>rmutatim)<emph.end type="italics"/> ide&longs;t, quare &amp; permutando (vt aiunt Geometr&aelig;) erit vt <lb/>A, ad C, ita B, ad D, hunc argumentandi modum &agrave; permutata proportio&shy;<lb/>ne explicaui in primo Po&longs;ter. </s> <s>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>cap.  
  
 5. tex. </s> 5. tex. </s>
  
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 <s><margin.target id="marg182"></margin.target>191</s></p><p type="main"> <s><margin.target id="marg182"></margin.target>191</s></p><p type="main">
  
 <s>Cap, 6. <emph type="italics"/>(Et qui in Die&longs;i &longs;onus latet, quamuis contin<gap/>um exi&longs;tentem audit <lb/>omnem cantum, di&longs;t antia enim eius ad extremos &longs;onos latet)<emph.end type="italics"/> quid &longs;it <lb/>Die&longs;is apud Mu&longs;icos explicatum e&longs;t primo Po&longs;ter. </s> <s>Cap, 6. <emph type="italics"/>(Et qui in Die&longs;i &longs;onus latet, quamuis contin<gap/>um exi&longs;tentem audit <lb/>omnem cantum, di&longs;t antia enim eius ad extremos &longs;onos latet)<emph.end type="italics"/> quid &longs;it <lb/>Die&longs;is apud Mu&longs;icos explicatum e&longs;t primo Po&longs;ter. tex. </s>
  
 <s>tex. </s> 
  
 <s>38. cum <lb/>autem Die&longs;is &longs;it minima di&longs;tantia, &longs;eu vt loquuntur Mu&longs;ici, mini&shy;<lb/>mum <expan abbr="interuall&utilde;">interuallum</expan> inter duas voces, hinc fit vt h&aelig;c minima di&longs;tantia inter ex&shy;<lb/>tremos &longs;onos non exaudiatur, quemadmodum nec minima particula alicu&shy;<lb/>ius magni corporis &agrave; long&egrave; vi&longs;i <expan abbr="n&otilde;">non</expan> percipitur, &longs;ed latetinter extrema illius.</s></p><p type="main"> <s>38. cum <lb/>autem Die&longs;is &longs;it minima di&longs;tantia, &longs;eu vt loquuntur Mu&longs;ici, mini&shy;<lb/>mum <expan abbr="interuall&utilde;">interuallum</expan> inter duas voces, hinc fit vt h&aelig;c minima di&longs;tantia inter ex&shy;<lb/>tremos &longs;onos non exaudiatur, quemadmodum nec minima particula alicu&shy;<lb/>ius magni corporis &agrave; long&egrave; vi&longs;i <expan abbr="n&otilde;">non</expan> percipitur, &longs;ed latetinter extrema illius.</s></p><p type="main">
  
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 <s><margin.target id="marg184"></margin.target>193</s></p><p type="main"> <s><margin.target id="marg184"></margin.target>193</s></p><p type="main">
  
 <s>Eodem cap. <emph type="italics"/>(Velut Diapa&longs;on, &amp; Diapente)<emph.end type="italics"/> quid &longs;it con&longs;onantia Diapa&shy;<lb/>&longs;on, explicaui in primo Po&longs;ter. </s> <s>Eodem cap. <emph type="italics"/>(Velut Diapa&longs;on, &amp; Diapente)<emph.end type="italics"/> quid &longs;it con&longs;onantia Diapa&shy;<lb/>&longs;on, explicaui in primo Po&longs;ter. tex. </s>
  
 <s>tex. </s> 
  
 <s>1. Diapente ver&ograve; e&longs;t con&longs;onantia ex duo&shy;<lb/><figure id="fig67"></figure><lb/>bus &longs;onis coale&longs;cens, quorum proportio &longs;it vt <lb/>3. ad 2. qu&aelig; dicitur &longs;e&longs;quialtera. </s> <s>1. Diapente ver&ograve; e&longs;t con&longs;onantia ex duo&shy;<lb/><figure id="fig67"></figure><lb/>bus &longs;onis coale&longs;cens, quorum proportio &longs;it vt <lb/>3. ad 2. qu&aelig; dicitur &longs;e&longs;quialtera. </s>
  
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 <s>Cap. 1. <emph type="italics"/>(Sic meminit eos, qui trianguli, quod duobus rectis &aelig;quales)<emph.end type="italics"/> ide&longs;t <lb/>&longs;ic meminit tres angulos cuiu&longs;uis trianguli &longs;imul &longs;umptos &aelig;qua&shy;<lb/>les e&longs;&longs;e duobus angulis rectis &longs;imul &longs;umptis. </s> <s>Cap. 1. <emph type="italics"/>(Sic meminit eos, qui trianguli, quod duobus rectis &aelig;quales)<emph.end type="italics"/> ide&longs;t <lb/>&longs;ic meminit tres angulos cuiu&longs;uis trianguli &longs;imul &longs;umptos &aelig;qua&shy;<lb/>les e&longs;&longs;e duobus angulis rectis &longs;imul &longs;umptis. </s>
  
  
 <s>lege annotata primo <lb/>Po&longs;ter. </s> <s>lege annotata primo <lb/>Po&longs;ter. &longs;ecto 3. cap.
  
 <s>&longs;ecto 3. cap.  
  
 1.</s></p><p type="main"> 1.</s></p><p type="main">
  
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 <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>2. (<emph type="italics"/>Alia ver&ograve; cau&longs;a e&longs;t forma, &amp; exemplar: h&aelig;c autem e&longs;t ratio ip&shy;<lb/>&longs;ius quid erat e&longs;&longs;e, &amp; borum genera, vt ip&longs;ius Diapa&longs;on duo ad vnum, <lb/>&amp; &longs;impliciter numerus, &amp; partes, qu&aelig; in ra ione &longs;unt<emph.end type="italics"/>) affert exem&shy;<lb/>plum cau&longs;&aelig; formalis ex Mu&longs;ica petitum; <expan abbr="ait&qacute;">aitque</expan>; cau&longs;am formalem <lb/>illius con&longs;onanti&aelig;, qu&aelig; Diapa&longs;on dicitur, <expan abbr="e&longs;t&qacute;">e&longs;tque</expan>; omnium perfecti&longs;&longs;ima, e&longs;&longs;e <lb/>duplam proportionem, ide&longs;t, qu&aelig; e&longs;t inter duo, &amp; vnum, id, quod omnes <lb/>Mu&longs;ici <expan abbr="fat&etilde;tur">fatentur</expan>. </s>
  
 <s>quod vtinelius intelligas, repete, qu&aelig; in 2. Po&longs;ter. </s> <s>quod vtinelius intelligas, repete, qu&aelig; in 2. Po&longs;ter. ad tex. </s>
  
 <s>ad tex. </s> 
  
 <s>1. <lb/>&longs;cripta &longs;unt: necnon qu&aelig; in libro de Sen&longs;u in cap.  <s>1. <lb/>&longs;cripta &longs;unt: necnon qu&aelig; in libro de Sen&longs;u in cap.
  
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 <s>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">
  
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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>ad tex. </s> <s>ad tex. </s>
  
 <s>38. primi Po&longs;ter. </s> <s>38. primi Po&longs;ter. &longs;atis dictum e&longs;t de Die&longs;i, qu&aelig; videas.</s></p><p type="main">
  
 <s>&longs;atis dictum e&longs;t de Die&longs;i, qu&aelig; videas.</s></p><p type="main"> 
  
 <s><arrow.to.target n="marg218"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg218"></arrow.to.target></s></p><p type="margin">
  
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 <s>quid die&longs;is <lb/>dictum &longs;it ad tex. </s> <s>quid die&longs;is <lb/>dictum &longs;it ad tex. </s>
  
 <s>38. primi Po&longs;ter. </s> <s>38. primi Po&longs;ter. quando autem ait <emph type="italics"/>(Vt puta du&aelig; die&longs;es)<emph.end type="italics"/><lb/>ide&longs;t du&aelig; die&longs;es &longs;unt men&longs;ura vnius interualli mu&longs;ici, qui tonus appellatur: <lb/>qu&aelig; quidem du&aelig; die&longs;es non &longs;unt men&longs;ura &longs;en&longs;ibilis, qu&aelig; &longs;cilicet auribus per&shy;<lb/>cipiatur, &longs;ed tantummod&ograve; exi&longs;tunt in numerorum proportionibus, ibi per <lb/>intellectum excogitatis, quando ait <emph type="italics"/>(Et voces plures quibus men&longs;uramus)<emph.end type="italics"/><lb/>quando vtimur eodem interuallo, &longs;iue eadem voce ad cantus men&longs;uram, <lb/>tunc &longs;unt plures men&longs;ur&aelig; numero, quamuis vna tantam &longs;pe<gap/> Ait <emph type="italics"/>(Et dia&shy;<lb/>meter duobus men&longs;uratur)<emph.end type="italics"/> v. </s>
  
 <s>quando autem ait <emph type="italics"/>(Vt puta du&aelig; die&longs;es)<emph.end type="italics"/><lb/>ide&longs;t du&aelig; die&longs;es &longs;unt men&longs;ura vnius interualli mu&longs;ici, qui tonus appellatur: <lb/>qu&aelig; quidem du&aelig; die&longs;es non &longs;unt men&longs;ura &longs;en&longs;ibilis, qu&aelig; &longs;cilicet auribus per&shy;<lb/>cipiatur, &longs;ed tantummod&ograve; exi&longs;tunt in numerorum proportionibus, ibi per <lb/>intellectum excogitatis, quando ait <emph type="italics"/>(Et voces plures quibus men&longs;uramus)<emph.end type="italics"/><lb/>quando vtimur eodem interuallo, &longs;iue eadem voce ad cantus men&longs;uram, <lb/>tunc &longs;unt plures men&longs;ur&aelig; numero, quamuis vna tantam &longs;pe<gap/> Ait <emph type="italics"/>(Et dia&shy;<lb/>meter duobus men&longs;uratur)<emph.end type="italics"/> v. </s> 
  
 <s>g. </s> <s>g. </s>
  
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 <s>hoc &longs;olum addendum ad illorum verborum (<emph type="italics"/>Ex de&shy;<lb/>terminato &longs;ibi principio propter quid a&longs;&longs;ump&longs;erunt<emph.end type="italics"/>) intelligentiam, ide&longs;t ex vna <lb/>conclu&longs;ione demon&longs;trata, tanquam principio alia demon&longs;trant; quod rect&egrave; <lb/>fieri Ari&longs;t.  <s>hoc &longs;olum addendum ad illorum verborum (<emph type="italics"/>Ex de&shy;<lb/>terminato &longs;ibi principio propter quid a&longs;&longs;ump&longs;erunt<emph.end type="italics"/>) intelligentiam, ide&longs;t ex vna <lb/>conclu&longs;ione demon&longs;trata, tanquam principio alia demon&longs;trant; quod rect&egrave; <lb/>fieri Ari&longs;t.
  
 in primo Po&longs;ter. </s> in primo Po&longs;ter. docet.</s></p><p type="main">
  
 <s>docet.</s></p><p type="main"> 
  
 <s><arrow.to.target n="marg312"></arrow.to.target></s></p><p type="margin"> <s><arrow.to.target n="marg312"></arrow.to.target></s></p><p type="margin">
  
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 <s>omnem quamuis optimam, in deterius prolpp&longs;u&shy;<pb pagenum="226"/>ram, c&ugrave;m enim ad &longs;ummam perfectionem peruenerit, qu&aelig; in numero &longs;oli&shy;<lb/>do, &amp; cubico &longs;ignificatur, &longs;i vlterius progre&longs;sura &longs;it, nece&longs;&longs;ari&ograve; &longs;ummam <lb/>perfectionem pr&aelig;teribit, ac derelinquet. </s> <s>omnem quamuis optimam, in deterius prolpp&longs;u&shy;<pb pagenum="226"/>ram, c&ugrave;m enim ad &longs;ummam perfectionem peruenerit, qu&aelig; in numero &longs;oli&shy;<lb/>do, &amp; cubico &longs;ignificatur, &longs;i vlterius progre&longs;sura &longs;it, nece&longs;&longs;ari&ograve; &longs;ummam <lb/>perfectionem pr&aelig;teribit, ac derelinquet. </s>
  
 <s>Qu&ograve;d autem numerus 1728. &longs;it <lb/>numerus &longs;olidus, &amp; cubus ip&longs;ius Duodenarij &longs;ic pal<gap/>m fiet, &longs;i tamen prius, <lb/>ea repetiueris, qu&aelig; &longs;upra in primo Po&longs;ter. </s> <s>Qu&ograve;d autem numerus 1728. &longs;it <lb/>numerus &longs;olidus, &amp; cubus ip&longs;ius Duodenarij &longs;ic pal<gap/>m fiet, &longs;i tamen prius, <lb/>ea repetiueris, qu&aelig; &longs;upra in primo Po&longs;ter. num. </s>
  
 <s>num. </s> 
  
 <s>33. marginali, de numero <lb/>Quadrato, &amp; Cubo dicta &longs;unt: e&longs;t autem cubus numerus is, qui ex gemina&shy;<lb/>to ductu alicuius numeri in &longs;e ip&longs;um, producitur. </s> <s>33. marginali, de numero <lb/>Quadrato, &amp; Cubo dicta &longs;unt: e&longs;t autem cubus numerus is, qui ex gemina&shy;<lb/>to ductu alicuius numeri in &longs;e ip&longs;um, producitur. </s>
  
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 <s>re&longs;pondet inde prouenire, quia h&aelig;c vox <lb/>cantandi principium e&longs;t. </s> <s>re&longs;pondet inde prouenire, quia h&aelig;c vox <lb/>cantandi principium e&longs;t. </s>
  
 <s>vbi per cantandi principium puto ip&longs;um intellige&shy;<lb/>re &longs;emitonium, &longs;iue die&longs;im, nam, vtip&longs;e ait primo <lb/><figure id="fig147"></figure><lb/>re &longs;emitonium, &longs;iue die&longs;im, nam, vt ip&longs;e ait primo <lb/>Po&longs;ter. </s> <s>vbi per cantandi principium puto ip&longs;um intellige&shy;<lb/>re &longs;emitonium, &longs;iue die&longs;im, nam, vtip&longs;e ait primo <lb/><figure id="fig147"></figure><lb/>re &longs;emitonium, &longs;iue die&longs;im, nam, vt ip&longs;e ait primo <lb/>Po&longs;ter. cap.
  
 <s>cap.  
  
 38. die&longs;is h&ecedil;c, &longs;iue &longs;emitonium dicitur <lb/>principium cantus, quia minimum e&longs;t omnium in&shy;<lb/>teruallorum, qu&aelig; voce po&longs;&longs;int exprimi: <expan abbr="atq;">atque</expan> ex eo <lb/>alia interualla con&longs;tant, <expan abbr="e&longs;t&qacute;">e&longs;tque</expan>; veluti illorum ele&shy;<lb/>mentum. </s> 38. die&longs;is h&ecedil;c, &longs;iue &longs;emitonium dicitur <lb/>principium cantus, quia minimum e&longs;t omnium in&shy;<lb/>teruallorum, qu&aelig; voce po&longs;&longs;int exprimi: <expan abbr="atq;">atque</expan> ex eo <lb/>alia interualla con&longs;tant, <expan abbr="e&longs;t&qacute;">e&longs;tque</expan>; veluti illorum ele&shy;<lb/>mentum. </s>
  
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 <s>ver&ograve; 31. <emph type="italics"/>(Figurarum autem maxim&egrave; &longs;cientialis <lb/>est prima, mathematic&aelig; <expan abbr="namq;">namque</expan> <expan abbr="&longs;ci&etilde;ti&aelig;">&longs;cienti&aelig;</expan> per hanc demon&longs;trationes ferunt, vt Arith&shy;<lb/>metica, &amp; Geometria, &amp; Per&longs;pectiua, &amp; fer&egrave; dixerim qu&aelig;cunque ip&longs;ius Propter <lb/>quid con&longs;iderationem faciunt)<emph.end type="italics"/> po&longs;tea tex. </s> <s>ver&ograve; 31. <emph type="italics"/>(Figurarum autem maxim&egrave; &longs;cientialis <lb/>est prima, mathematic&aelig; <expan abbr="namq;">namque</expan> <expan abbr="&longs;ci&etilde;ti&aelig;">&longs;cienti&aelig;</expan> per hanc demon&longs;trationes ferunt, vt Arith&shy;<lb/>metica, &amp; Geometria, &amp; Per&longs;pectiua, &amp; fer&egrave; dixerim qu&aelig;cunque ip&longs;ius Propter <lb/>quid con&longs;iderationem faciunt)<emph.end type="italics"/> po&longs;tea tex. </s>
  
 <s>11. 2. Po&longs;ter. </s> <s>11. 2. Po&longs;ter. a&longs;&longs;erit demon&longs;tratio&shy;<lb/>nemillam, qua Geometra probat, angulum in &longs;emicirculo e&longs;&longs;e rectum, e&longs;&longs;e <lb/>&agrave; cau&longs;a materiali, im&ograve; eam tanquam optimum huiu&longs;modi demon&longs;trationis <lb/>exemplum affert. </s>
  
 <s>a&longs;&longs;erit demon&longs;tratio&shy;<lb/>nemillam, qua Geometra probat, angulum in &longs;emicirculo e&longs;&longs;e rectum, e&longs;&longs;e <lb/>&agrave; cau&longs;a materiali, im&ograve; eam tanquam optimum huiu&longs;modi demon&longs;trationis <lb/>exemplum affert. </s> 
  
 <s>&longs;ed de hac eadem demon&longs;tratione infra iterum dicendum <lb/>erit; vide interim pr&aelig;dicti loci explicationem &longs;upra in locis Mathemat. </s> <s>&longs;ed de hac eadem demon&longs;tratione infra iterum dicendum <lb/>erit; vide interim pr&aelig;dicti loci explicationem &longs;upra in locis Mathemat. </s>
  
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 <s>2. Ex Themi&longs;tio cap, 2. &longs;u&aelig; paraphr. </s> <s>2. Ex Themi&longs;tio cap, 2. &longs;u&aelig; paraphr. </s>
  
 <s>2. Po&longs;ter. </s> <s>2. Po&longs;ter. Demon&longs;tratio poti&longs;&longs;ima <lb/>debet o&longs;tendere, &amp; quod, &amp; Propter quid. </s>
  
 <s>Demon&longs;tratio poti&longs;&longs;ima <lb/>debet o&longs;tendere, &amp; quod, &amp; Propter quid. </s> 
  
 <s>quod profect&ograve; c&aelig;teris demon&shy;<lb/>&longs;trationibus melius pr&aelig;&longs;tant Geometric&aelig;, &amp; Arithmetic&aelig;. </s> <s>quod profect&ograve; c&aelig;teris demon&shy;<lb/>&longs;trationibus melius pr&aelig;&longs;tant Geometric&aelig;, &amp; Arithmetic&aelig;. </s>
  
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 <s>&amp; quoniam &longs;upra tex. </s> <s>&amp; quoniam &longs;upra tex. </s>
  
 <s>23. 1. Po&longs;ter. </s> <s>23. 1. Po&longs;ter. nos eam per cau&longs;am ma&shy;<lb/>terralem procedere o&longs;tendimus, ide&ograve; ne actum agamus, <expan abbr="explication&etilde;">explicationem</expan> illam <lb/>nunc opus e&longs;t relegere. </s>
  
 <s>nos eam per cau&longs;am ma&shy;<lb/>terralem procedere o&longs;tendimus, ide&ograve; ne actum agamus, <expan abbr="explication&etilde;">explicationem</expan> illam <lb/>nunc opus e&longs;t relegere. </s> 
  
 <s>Hoc tamen loco partem ip&longs;ius primam, angulum, <lb/>videlicet externum cuiu&longs;uis trianguli, &aelig;qualem e&longs;&longs;e duobus internis, &amp; op&shy;<lb/>po&longs;itis, examin<gap/> bo; cuius medium, &longs;i ad rigorem demon&longs;trationis rediga&shy;<lb/>tur, e&longs;t hoc; externus angulus e&longs;t diui&longs;ibilis in duos angulos, quorum &longs;ingu&shy;<lb/>li &longs;ingulis internis &longs;unt &aelig; quales, ergo <expan abbr="eti&atilde;">etiam</expan> totalis anguius erit &aelig;qualis am&shy;<lb/>bobus internis &longs;imul &longs;umptis. </s> <s>Hoc tamen loco partem ip&longs;ius primam, angulum, <lb/>videlicet externum cuiu&longs;uis trianguli, &aelig;qualem e&longs;&longs;e duobus internis, &amp; op&shy;<lb/>po&longs;itis, examin<gap/> bo; cuius medium, &longs;i ad rigorem demon&longs;trationis rediga&shy;<lb/>tur, e&longs;t hoc; externus angulus e&longs;t diui&longs;ibilis in duos angulos, quorum &longs;ingu&shy;<lb/>li &longs;ingulis internis &longs;unt &aelig; quales, ergo <expan abbr="eti&atilde;">etiam</expan> totalis anguius erit &aelig;qualis am&shy;<lb/>bobus internis &longs;imul &longs;umptis. </s>
  
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 <s>&amp; tex. </s> <s>&amp; tex. </s>
  
 <s>11. 2. Po&longs;ter. </s> <s>11. 2. Po&longs;ter. vtitur &longs;imili <expan abbr="ex&etilde;-plo">exen&shy;<lb/>plo</expan> ad <expan abbr="material&etilde;">materialem</expan> cau&longs;am explicandam. </s>
  
 <s>vtitur &longs;imili <expan abbr="ex&etilde;-plo">exen&shy;<lb/>plo</expan> ad <expan abbr="material&etilde;">materialem</expan> cau&longs;am explicandam. </s> 
  
 <s>quamuis autem Geometr&aelig; non di&shy;<lb/>cant talem angulum, vel talem figuram e&longs;&longs;e <expan abbr="diui&longs;ibil&etilde;">diui&longs;ibilem</expan> in partes &aelig;quales alijs <lb/>quibu&longs;dam, &longs;ed &longs;tatim diuidant, id faciunt breuitatis cau&longs;a; vtuntur enim <lb/>actu pro potentia, quia actus potentiam &longs;upponit, qu&ograve;d optim&egrave; Ari&longs;tot. </s> <s>quamuis autem Geometr&aelig; non di&shy;<lb/>cant talem angulum, vel talem figuram e&longs;&longs;e <expan abbr="diui&longs;ibil&etilde;">diui&longs;ibilem</expan> in partes &aelig;quales alijs <lb/>quibu&longs;dam, &longs;ed &longs;tatim diuidant, id faciunt breuitatis cau&longs;a; vtuntur enim <lb/>actu pro potentia, quia actus potentiam &longs;upponit, qu&ograve;d optim&egrave; Ari&longs;tot. </s>
  
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 <s>Vide huius explicationem tex. </s> <s>Vide huius explicationem tex. </s>
  
 <s>23. <lb/>1. Po&longs;ter. </s> <s>23. <lb/>1. Po&longs;ter. vbi etiam videbis eam po&longs;&longs;e demon&longs;trari modo Pythagoreorum, <lb/>ab&longs;que vlla diui&longs;ione, &longs;ed per partes actu exi&longs;tentes. </s>
  
 <s>vbi etiam videbis eam po&longs;&longs;e demon&longs;trari modo Pythagoreorum, <lb/>ab&longs;que vlla diui&longs;ione, &longs;ed per partes actu exi&longs;tentes. </s> 
  
 <s>hoc dico propter eos, <lb/>qui per ha&longs;ce diui&longs;iones timent, ne non inueniatur medium &aacute; priori. </s> <s>hoc dico propter eos, <lb/>qui per ha&longs;ce diui&longs;iones timent, ne non inueniatur medium &aacute; priori. </s>
  
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 <s>Pr&aelig;terea fal&longs;um e&longs;t, Geometram ex communibus pluribus &longs;cientijs pro&shy;<lb/>cedere, quod vetat Ari&longs;t. </s> <s>Pr&aelig;terea fal&longs;um e&longs;t, Geometram ex communibus pluribus &longs;cientijs pro&shy;<lb/>cedere, quod vetat Ari&longs;t. </s>
  
 <s>1. Po&longs;ter. </s> <s>1. Po&longs;ter. procedit enim ex principijs communi&shy;<lb/>bus quantitatibus terminatis, ide&longs;t figuris, &amp; numeris; quod non &longs;olum li&shy;<lb/>cet, &longs;ed etiam debet fieri ex 1. Po&longs;ter. tex. </s>
  
 <s>procedit enim ex principijs communi&shy;<lb/>bus quantitatibus terminatis, ide&longs;t figuris, &amp; numeris; quod non &longs;olum li&shy;<lb/>cet, &longs;ed etiam debet fieri ex 1. Po&longs;ter. </s> 
  
 <s>tex. </s> 
  
 <s>20. &amp; 25. <expan abbr="neq;">neque</expan> vnquam idem prin&shy;<lb/>cipium repetit, ni&longs;i vbi e&longs;t effectus formalis ip&longs;ius, &amp; non ni&longs;i contrahendo <lb/>ad illud particulare.</s></p><p type="head"> <s>20. &amp; 25. <expan abbr="neq;">neque</expan> vnquam idem prin&shy;<lb/>cipium repetit, ni&longs;i vbi e&longs;t effectus formalis ip&longs;ius, &amp; non ni&longs;i contrahendo <lb/>ad illud particulare.</s></p><p type="head">
  
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 <s>non dee&longs;t tamen Ari&longs;t.  <s>non dee&longs;t tamen Ari&longs;t.
  
 authoritas 1. Po&longs;ter. </s> authoritas 1. Po&longs;ter. tex. </s>
  
 <s>tex. </s> 
  
 <s>30. a&longs;&longs;erentis eas <lb/>habere cau&longs;as demon&longs;trationum, &longs;ic. </s> <s>30. a&longs;&longs;erentis eas <lb/>habere cau&longs;as demon&longs;trationum, &longs;ic. </s>
  
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 <s>qu&agrave;m fu&longs;i&longs;&longs;im&egrave; explicaui &longs;upra ad tex. </s> <s>qu&agrave;m fu&longs;i&longs;&longs;im&egrave; explicaui &longs;upra ad tex. </s>
  
 <s>23. primi <lb/>Po&longs;ter. </s> <s>23. primi <lb/>Po&longs;ter. vbi Ari&longs;t.
  
 <s>vbi Ari&longs;t.  
  
 eam in exemplum perfecti&longs;&longs;im&aelig; demon&longs;trationis adducit.</s></p><p type="main"> eam in exemplum perfecti&longs;&longs;im&aelig; demon&longs;trationis adducit.</s></p><p type="main">
  

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