Biancani, Giuseppe
,
Aristotelis loca mathematica
,
1615
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propoſitionis, quæ falſa eſt, nimirum ſuppoſito prædictas lineas eſſe comm.
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deducit ad impoſſibile, ſiue, vt ait hic Ariſt. falſum ratiocinatur, quod ſci
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licet idem numerus eſſet par, & impar, quod Ariſt. ſignificat, quando ait,
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imparia æqualia paribus fiunt. </
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<
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">ex quo abſurdo deducitur falſam eſſe prædi
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ctam ſuppoſitionem, quæ aſtruebat eſſe comm. & proinde altera pars con
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tradictionis, quæ eſt, eſſe incomm. vera aſtruitur. </
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<
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">ex quibus ſatis videtur ex
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plicari hic locus. </
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<
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">videas igitur, quàm leuiter nonnulli noſtræ tempeſtatis
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ageometreti iſtud exponant, dicentes diametrum eſſe incomm. coſtæ, nihil
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aliud ſignificare, quam diametrum eſſe longiorem coſta, qua expoſitione
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nihil ineptius. </
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<
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">Aduerte tandem figuram vulgatæ editionis eſſe ineptam,
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cum habeat duo quadrata alterum ſuper diametro alterius, quorum maius
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ſuperuacaneum eſt.</
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6</
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<
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">Et cap. 24. ſecti primi libri primi
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(Sed magis efficitur manifeſtum in deſcri
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ptionibus, vt quod æquicruris, qui ad baſim æquales ſint, ad centrum ductæ A B,
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A C, ſi igitur æqualem accipiat A G, angulum ipſi A B D, non omnino exiſtimans
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æquales, qui ſemicirculorum, & rurſus G, ipſi D, non omnem aſſumens eum, qui ſe
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cti. </
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<
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id
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">amplius ab æqualibus existentibus totis angulis, & ablatorum æquales eſſe re
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liquos E, F, quod ex principio petet, niſi acceperit ab æqualibus demptis æqualia
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derelinqui.)
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Primum ſcias characteres vulgatæ editionis, vna cum figura ip
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ſis reſpondente, eſſe mendoſos; propterea ex textu græco vtrunque corri
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gendum putaui in hunc, quem vidiſti modum. </
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">Secundo, per deſcriptiones
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Ariſt. intelligere
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demõſtrationes
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Geometricas ſupra diximus, quod ex hoc
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loco euidenter confirmatur, vbi manifeſtè loco deſcriptionis ſupponit li
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nearem demonſtrationem. </
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<
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">In hoc
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itaq;
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exemplo vult Ariſt. illud demon
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ſtrare, quod Euclides in 5. primi oſtendit, alio tamen modo, ſcilicet Iſoſce
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lium triangulorum, qui ad baſim ſunt anguli, inter ſe ſunt æquales. </
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<
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">eſt au
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tem figura in omnibus textibus deprauata, quam ſic puto
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rèſtītuendam
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eſſe
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ex quodam græco codice, qui characteres hoc modo appoſuerat. </
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<
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les C A B, cuius baſis C B, Dico angulos ſupra baſim,
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in quibus literæ E F, eſſe inuicem æquales. </
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<
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in A, deſcribatur circulus A B C, tranſiens per puncta
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C B, iam ſic. </
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<
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">omnes anguli ſemicirculi ſunt æquales in
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ter ſe, ergo anguli A C G, A B D, ſunt æquales. </
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<
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rea cùm anguli eiuſdem ſectionis ſint æquales ad inui
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cem, erunt anguli ſectionis C B D G, nimirum anguli,
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in quibus ſunt G, & D, inter ſe æquales:
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cumq́
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; hi duo
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anguli ſectionis ſint partes
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angulorũ
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ſemicirculi A C G,
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A B D, ſi illi ab his auferantur, auferuntur æquales anguli ab æqualibus an
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gulis, ergo anguli, qui remanent, ſcilicet E, & F, erunt æquales, quod erat
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demonſtrandum. </
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<
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">hinc Ariſt. infert manifeſtum eſſe oportere in omni ſyllo
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giſmo, reperiri vniuerſales, & affirmatiuas propoſitiones, vt Factum eſt in
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præcedenti aliter eſſet petitio principij. </
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<
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Geometræ conſiderant, infra cap. 1. ſecti 3. explicabitur.</
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<
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(Secundum veritatem quidem ex ijs, quæ ſecundum
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veritatem deſcribuntur ineſſe, ad dialecticos autem ſyllogiſmos ex propoſitionibus
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ſecundum opinionem)
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verba illa; ex ijs, quæ
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veritatem deſcribuntur </
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