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Colored diff for /texts/archimedes/xml/Attic/carda_propo_01_la_1570.xml between version 1.12 and 1.41

version 1.12, 2002/08/08 23:25:28 version 1.41, 2002/08/18 17:08:53
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         <lang>la</lang>         <lang>la</lang>
         <cvs_file>carda_propo_01_la_1570</cvs_file>         <cvs_file>carda_propo_01_la_1570</cvs_file>
         <cvs_version></cvs_version>         <cvs_version></cvs_version>
         <locator></locator>         <locator>0000000015.xml</locator>
 </info>      <text>          <front>          </front>          <body>            <chap>        <pb/><pb/><pb/><p type="head"> </info>      <text>          <front>          </front>          <body>            <chap>        <pb/><pb/><pb/><p type="head">
  
 <s>HIERONYMI <lb/>CARDANI MEDIO <lb/>LANENSIS, CIVISQV'E BONO&shy;<lb/>NIENSIS, PHILOSOPHI, MEDICI ET <lb/>Mathematici clari&longs;simi,</s></p><p type="head"> <s>HIERONYMI <lb/>CARDANI MEDIO <lb/>LANENSIS, CIVISQV'E BONO&shy;<lb/>NIENSIS, PHILOSOPHI, MEDICI ET <lb/>Mathematici clari&longs;simi,</s></p><p type="head">
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 <s><margin.target id="marg122"></margin.target>C<emph type="italics"/>o<emph.end type="italics"/>^{m}.</s></p><p type="main"> <s><margin.target id="marg122"></margin.target>C<emph type="italics"/>o<emph.end type="italics"/>^{m}.</s></p><p type="main">
  
 <s>Sint duo mobilia a &amp; b in eodem pun&shy;<lb/><figure id="fig28"></figure><lb/>cto, qu&aelig; &aelig;qualiter uer&longs;us candem partem <lb/>moueantur &aelig;qualibus in temporibus, inui <lb/>cem tamen in &aelig;qualiter, ita quod a in f &amp; b <lb/>in g temporibus ab&longs;oluant circulum, &amp; ho <lb/>rum differentia &longs;it h. </s> <s>Sint duo mobilia a &amp; b in eodem pun&shy;<lb/><figure id="fig28"></figure><lb/>cto, qu&aelig; &aelig;qualiter uer&longs;us eandem partem <lb/>moueantur &aelig;qualibus in temporibus, inui <lb/>cem tamen in &aelig;qualiter, ita quod a in f &amp; b <lb/>in g temporibus ab&longs;oluant circulum, &amp; ho <lb/>rum differentia &longs;it h. </s>
  
 <s>Dum ita que a perficit <lb/>circulum b perueniat in c, igitur c d b e&longs;t dif <lb/>ferentia, qu&aelig; &longs;uperanda e&longs;t, &amp; proportio <lb/>circuli ad b c ut g ad f, quare reliqui ad reli&shy;<lb/>quum, ut re&longs;idui ad re&longs;iduum, &longs;cilicet circu&shy;<lb/>li ad c d b, ut g ad h, &amp; b c ad c d b ut f ad h, coniungantur igitur in k <lb/>tempore, eruntque k f g h omiologa, ut productum ex circulo in b c <lb/>diui&longs;o per certam quantitatem &amp; cum circulo &amp; b c &amp; c d b diffe&shy;<lb/>rentia, &amp; &longs;it &longs;productum exfin g, dico quod diui&longs;a &longs; per h exibit k <lb/>tempus coniunctionis prim&aelig;, &longs;it itaque d locus coniunctionis, dico <lb/>igitur quod differentia &longs;patij pertran&longs;iti a b, a &amp; a, b in reditu ex con <lb/>iunctione prima ad d e&longs;t unus circulus completus, non enim po&longs;&shy;<lb/>&longs;unt e&longs;&longs;e plures, nam &longs;equeretur, qu&ograve;d a aliquando pertran&longs;i&longs;&longs;et b, <lb/>et &longs;ic non e&longs;&longs;et prima coniunctio, nec pote&longs;t e&longs;&longs;e minus, nam &longs;ic cum <lb/>a &amp; b &longs;int in d ultra perfectas circulationes uterque eorum pertran <lb/>&longs;iuit arcum b c, igitur nullo modo differentia pote&longs;t e&longs;&longs;e minor cir&shy;<lb/>culo, neque maior, ut declaratum e&longs;t, igitur e&longs;t unus circulus ad un&shy;<pb pagenum="37"/>guem. </s> <s>Dum ita que a perficit <lb/>circulum b perueniat in c, igitur c d b e&longs;t dif <lb/>ferentia, qu&aelig; &longs;uperanda e&longs;t, &amp; proportio <lb/>circuli ad b c ut g ad f, quare reliqui ad reli&shy;<lb/>quum, ut re&longs;idui ad re&longs;iduum, &longs;cilicet circu&shy;<lb/>li ad c d b, ut g ad h, &amp; b c ad c d b ut f ad h, coniungantur igitur in k <lb/>tempore, eruntque k f g h omiologa, ut productum ex circulo in b c <lb/>diui&longs;o per certam quantitatem &amp; cum circulo &amp; b c &amp; c d b diffe&shy;<lb/>rentia, &amp; &longs;it &longs;productum exfin g, dico quod diui&longs;a &longs; per h exibit k <lb/>tempus coniunctionis prim&aelig;, &longs;it itaque d locus coniunctionis, dico <lb/>igitur quod differentia &longs;patij pertran&longs;iti a b, a &amp; a, b in reditu ex con <lb/>iunctione prima ad d e&longs;t unus circulus completus, non enim po&longs;&shy;<lb/>&longs;unt e&longs;&longs;e plures, nam &longs;equeretur, qu&ograve;d a aliquando pertran&longs;i&longs;&longs;et b, <lb/>et &longs;ic non e&longs;&longs;et prima coniunctio, nec pote&longs;t e&longs;&longs;e minus, nam &longs;ic cum <lb/>a &amp; b &longs;int in d ultra perfectas circulationes uterque eorum pertran <lb/>&longs;iuit arcum b c, igitur nullo modo differentia pote&longs;t e&longs;&longs;e minor cir&shy;<lb/>culo, neque maior, ut declaratum e&longs;t, igitur e&longs;t unus circulus ad un&shy;<pb pagenum="37"/>guem. </s>
  
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 <s>Velut &lt;02&gt; 7/100 quater &longs;um&shy;<lb/>pta efficit &lt;02&gt; 112/100. Et hoc e&longs;t potentia rhete, &longs;ed &longs;i quis auferat mona&shy;<lb/>dem fiet &lt;02&gt; 112/100 m: 1, &amp; hoc e&longs;t reci&longs;um 1, &longs;cilicet 1 p: &lt;02&gt; v: 23/25 m: &lt;02&gt; 28/25, &longs;ed ta <lb/>men uer&egrave; e&longs;t linea media.</s></p><p type="main"> <s>Velut &lt;02&gt; 7/100 quater &longs;um&shy;<lb/>pta efficit &lt;02&gt; 112/100. Et hoc e&longs;t potentia rhete, &longs;ed &longs;i quis auferat mona&shy;<lb/>dem fiet &lt;02&gt; 112/100 m: 1, &amp; hoc e&longs;t reci&longs;um 1, &longs;cilicet 1 p: &lt;02&gt; v: 23/25 m: &lt;02&gt; 28/25, &longs;ed ta <lb/>men uer&egrave; e&longs;t linea media.</s></p><p type="main">
  
 <s>Quod uer&ograve; non contingat coniungi in alio loco, neque tem&shy;<lb/>pore &longs;it, ut a b iungantur in c, &amp; &longs;it reuolutio a triplex integra, &amp; b <pb pagenum="42"/>&longs;excuplex, &amp; tempus totum decem annorum: ita ut a c &longs;it tertia <lb/>pars circuitus, &amp; a circuitus tres anni, &amp; quia circuitus b funt fex <lb/>cum tertia, diuidemus decem per 6 1/3 exit <lb/>1 11/29, dico quod non prius, neque in alio <lb/><figure id="fig31"></figure><lb/>puncto. </s> <s>Quod uer&ograve; non contingat coniungi in alio loco, neque tem&shy;<lb/>pore &longs;it, ut a b iungantur in c, &amp; &longs;it reuolutio a triplex integra, &amp; b <pb pagenum="42"/>&longs;excuplex, &amp; tempus totum decem annorum: ita ut a c &longs;it tertia <lb/>pars circuitus, &amp; a circuitus tres anni, &amp; quia circuitus b &longs;unt fex <lb/>cum tertia, diuidemus decem per 6 1/3 exit <lb/>1 11/29, dico quod non prius, neque in alio <lb/><figure id="fig31"></figure><lb/>puncto. </s>
  
 <s>Si enim prim&ugrave;m in eodem pun&shy;<lb/>cto, &amp;, gratia exempli, in quatuor annis <lb/>congruit enim, &amp; b dicamus quod per&shy;<lb/>egerit duas reuolutiones cum tertia, hoc <lb/>enim e&longs;t nece&longs;&longs;arium, &longs;i debet perueni&shy;<lb/>re ad c, &amp; erunt anni tres, &amp; 23/19, non ergo <lb/>anni quatuor. </s> <s>Si enim prim&ugrave;m in eodem pun&shy;<lb/>cto, &amp;, gratia exempli, in quatuor annis <lb/>congruit enim, &amp; b dicamus quod per&shy;<lb/>egerit duas reuolutiones cum tertia, hoc <lb/>enim e&longs;t nece&longs;&longs;arium, &longs;i debet perueni&shy;<lb/>re ad c, &amp; erunt anni tres, &amp; 23/19, non ergo <lb/>anni quatuor. </s>
  
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 <s>Dictum e&longs;t &longs;uperius de proportione de&longs;cenfus ad grauitatem: </s></p><p type="main"> <s>Dictum e&longs;t &longs;uperius de proportione de&longs;cen&longs;us ad grauitatem: </s></p><p type="main">
  
 <s><arrow.to.target n="marg165"></arrow.to.target><lb/>&amp; qu&ograve;d &longs;i graue de&longs;cendat ex alto impeditur &agrave; motu a&euml;ris: &amp; qu&ograve;d <lb/><arrow.to.target n="marg166"></arrow.to.target><lb/>res, qu&aelig; mouetur duobus motibus non ad idem tendentibus tar&shy;<lb/><arrow.to.target n="marg167"></arrow.to.target><lb/>dius mouetur, quam motus &longs;it unu&longs;qui&longs;que. </s> <s><arrow.to.target n="marg165"></arrow.to.target><lb/>&amp; qu&ograve;d &longs;i graue de&longs;cendat ex alto impeditur &agrave; motu a&euml;ris: &amp; qu&ograve;d <lb/><arrow.to.target n="marg166"></arrow.to.target><lb/>res, qu&aelig; mouetur duobus motibus non ad idem tendentibus tar&shy;<lb/><arrow.to.target n="marg167"></arrow.to.target><lb/>dius mouetur, quam motus &longs;it unu&longs;qui&longs;que. </s>
  
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 <s><margin.target id="marg649"></margin.target>C<emph type="italics"/>o<emph.end type="italics"/>^{m}.</s></p><p type="main"> <s><margin.target id="marg649"></margin.target>C<emph type="italics"/>o<emph.end type="italics"/>^{m}.</s></p><p type="main">
  
 <s>Sit a b proportio ad partes c d qu&aelig; &longs;int c e, &amp; c d componens f, <lb/>dic<gap/> quod non poterit c d ali&agrave;s diuidi, ut proportio a b ad illas <lb/>componat candem proportionem f. </s> <s>Sit a b proportio ad partes c d qu&aelig; &longs;int c e, &amp; c d componens f, <lb/>dic<gap/> quod non poterit c d ali&agrave;s diuidi, ut proportio a b ad illas <lb/>componat eandem proportionem f. </s>
  
 <s>Aliter &longs;it diui&longs;a in g, &amp; erit mi&shy;<pb pagenum="203"/>nor c g, minor aut maior c d minore, capiam ergo c d minorem, erit <lb/>igitur proportio a b ad c d maioris exce&longs;&longs;us ad proportionem a b <lb/>ad c g, qu&agrave;m &longs;it proportio a b ad g d, ma&shy;<lb/><figure id="fig161"></figure><lb/>ior proportione a b ad c e, propterea quod <lb/>g e communis differentia maiorem habet <lb/>proportionem ad e d quam g c, igitur ma&shy;<lb/>ius e&longs;t aggregatum proportionum a b ad <lb/>c e, &amp; e d, <expan abbr="qu&atilde;">quam</expan> eiu&longs;dem a b ad c g &amp; g d, quod erat demon&longs;trandum.</s></p><p type="main"> <s>Aliter &longs;it diui&longs;a in g, &amp; erit mi&shy;<pb pagenum="203"/>nor c g, minor aut maior c d minore, capiam ergo c d minorem, erit <lb/>igitur proportio a b ad c d maioris exce&longs;&longs;us ad proportionem a b <lb/>ad c g, qu&agrave;m &longs;it proportio a b ad g d, ma&shy;<lb/><figure id="fig161"></figure><lb/>ior proportione a b ad c e, propterea quod <lb/>g e communis differentia maiorem habet <lb/>proportionem ad e d quam g c, igitur ma&shy;<lb/>ius e&longs;t aggregatum proportionum a b ad <lb/>c e, &amp; e d, <expan abbr="qu&atilde;">quam</expan> eiu&longs;dem a b ad c g &amp; g d, quod erat demon&longs;trandum.</s></p><p type="main">
  

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