Biancani, Giuseppe, Aristotelis loca mathematica, 1615

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              308</s>
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              <s id="s.003653">Ibidem
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              (N im proportio æqualitas eſt rationum)
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              Per proportionem hoc lo­
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              co intelligenda eſt illa, quam nunc appellant proportionalitatem, quæ eſt
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              duarum rationum, ſeu proportionum ſimilitudo, ſiue æqualitas, vt manife­
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              ſtum eſt ex 4. definit. </s>
              <s id="s.003654">5. Elem. v. g. cum ſit eadem ratio 9. ad 6. quæ eſt 6. ad
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              4. propterea hæc rationum ſimilitudo, vel æqualitas dicitur ipſa proportio,
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              ſeu diſtinctionis gratia Proportionalitas.</s>
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              309</s>
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              <s id="s.003657">Ibidem
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              (In quatuorqué minimis reperitur, diſiunctam ſanè in quatuor conſistere
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              perſpicuum eſt: ſed & continentem nihilominus, vno enim hæc perinde, aψ duobus
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              vtitur, biſque id accipit in hunc modum, qualis primi reſpectus eſt ad ſecundum,
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              talis ſecundi ad tertium; bis enim hic, ſecundum dictum eſt, quare ſi ſecundum bis
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              poſitum ſit, quatuor erunt ea, quæ conſtant proportione)
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              Quæ hic ab Ariſtot. di­
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              cuntur deſumpta ſunt, partim ex definit. </s>
              <s id="s.003658">6. 5. partim ex 9. definit. </s>
              <s id="s.003659">eiuſdem.
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              </s>
              <s id="s.003660">breuiter autem ſic ſe habent. </s>
              <s id="s.003661">Ad conſtituendam proportionalitatem ne­
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              ceſſarij ſunt omninò quatuor termini, quod quidem primum perſpicuum
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              eſt in ea proportionalitate, quam Diſiunctam vocant, quæ eſt huiuſmodi,
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              vt 9. ad 6. ita 3. ad 2. deinde
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              eſt etiam in ea, quam continuam dicunt,
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              quæ talis eſt, vt 9. ad 6. ita 6. ad 4. quæ in tribus quidem terminis 9. 6. 4.
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              conſiſtit, ſed tamen, quia medius 6.
                <expan abbr="vtrumq;">vtrumque</expan>
              reſpicit extremum, ideò vices
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              duorum gerit, ac proinde eſt, ac ſi hoc modo termini diſponantur 9. 6. 6. 4.
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              vbi 6. bis ponitur,
                <expan abbr="ſuntq́">ſuntque</expan>
              ; quatuor huius etiam proportionalitatis termini.
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              </s>
              <s id="s.003662">hinc Ariſt. textum ſatis intelligere poteris.</s>
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              310</s>
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              <s id="s.003665">Eodem cap.
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              (Sicut igitur primus terminus ſe habebit ad ſecundum, ita tertius
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              ad quartum; igitur etiam alterna vice, ſicut primus ad tertium, ita ſecundus ad
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              quartum. </s>
              <s id="s.003666">quare etiam totum ad totum, quod diſtributio binatim copulat. </s>
              <s id="s.003667">quæ ſi
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              etiam ita compoſita fuerint, iustè copulat)
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              Accipit Ariſt. illum argumentandi
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              modum, quem Geometræ alternam rationem vocant,
                <expan abbr="quàmq́">quàmque</expan>
              ; definit. </s>
              <s id="s.003668">12.
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              5. exponunt, vt eam rebus ipſis accommodet,
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              in praxim deducat; eſt
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              autem huiuſmodi, ſint primum quatuor termini proportionales, ideſt, vt
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              primus ad ſecundum, ita tertius ad quartum. </s>
              <s id="s.003669">v. g. vt 9. ad 6. ita 3. ad 2.
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              valet conſequentia hæc, ergò etiam alternatim erit, vt primus ad tertium,
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              ita ſecundus ad quartum, v. g. in allato exemplo, ita erit 9. ad 3. vt 6. ad 2.
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              quam ſequelam eſſe validam probat deinde Euclides propoſit. </s>
              <s id="s.003670">16. 5. hinc
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              aliam deducit conſequentiam, quam Euclides propoſit. </s>
              <s id="s.003671">12. 5. demonſtrat,
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              dum ait, quare etiam totum ad totum erit. </s>
              <s id="s.003672">v. g. quia concluſum eſt ita eſſe
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              9. ad 3. quemadmodum 6. ad 2. ita etiam erit totum ad totum, ideſt ita
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              etiam erunt antecedentes termini ſimul ad conſequentes ſimul, v. g. ita erit
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              etiam totum 15. quod eſt totum ex antecedentibus terminis 9. & 6. ad to­
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              tum 5. conflatum ex conſequentibus terminis 3. & 2. In ſumma igitur ſi fue­
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              rit vt 9. ad 3. ita 6. ad 2. ita etiam erit 15. ad 5. quod verum eſſe apparet in
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              his numeris, cum tam 9. ad 3. quà 6. ad 2. & 15. ad 5. habeant triplam
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              proportionem.</s>
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              <s id="s.003673">Horum exemplum in rebus practicis ſit hoc: ſit vt Plato ad Proclum, ita
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              mille aurei ad quingentos aureos, ergò alternatim ita erit Plato ad 1000.
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              aureos, ſicuti Proclus ad 500. quare ita etiam totum erit ad totum, ſcilicet
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              Plato, & Proclus ſimul ad 1000. & 500. ſimul, quæ duo tota, diſtributio mo­
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              ralis, ac practica diuidit, & binatim copulat, hoc modo dicens, vt Plato ad </s>
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