Biancani, Giuseppe
,
Aristotelis loca mathematica
,
1615
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77
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non potuerunt tamen deſcribi, niſi finitæ; appoſitæ idcircò ſunt ad partes
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illas, ad quas deberent eſſe infinitæ lineolæ quædam infinitatem indicantes.
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</
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<
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id
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">debemus poſtea, vt mentem Ariſt. percipiamus concipere lineam A G E,
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moueri circulariter facto centro in G. quæ quia infinita ſupponitur ad par
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tem E, ſecabit neceſſariò alteram
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vtrinq;
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infinitam
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grc
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B,
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illamq́
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; neceſſariò
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finito tempore percurret, finito enim tempore tota mundi circulatio per
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agitur, ſpatio videlicet viginti quatuor horarum. </
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<
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id
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">ex quo Ariſt. infert mun
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dum non poſſe eſſe infinitæ magnitudinis; quia ſi mundus eſſet infinitus; &.
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</
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<
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">duæ lineæ infinitæ, quales ſunt prædictæ in ipſo,
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atq;
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cum ipſo moueri alte
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ra earum A E, intelligatur, alteram
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B, manentem in tempore finito, ideſt,
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in diurna conuerſione pertranſibit: fieri autem nequit, vt infinita magni
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tudo finito tempore percurratur; quare dicendum eſt, mundum eſſe finita
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magnitudine præditum.</
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102</
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<
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">Tex. 48.
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(Nihil autem refert grauitates, commenſurabiles ſint, an incommen
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ſurabiles)
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quidnam ſit commenſurabilitas, & incommenſurabilitas, expli
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catum eſt lib. 1. Priorum, ſecto 1. cap. 23.</
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103</
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<
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">Tex. 119.
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(Est autem impoſſibile, & poſſibile; falſum, & verum, ex ſuppoſitio
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ne quidem, dico autem, vt triangulum impoſſibile eſt duos rectos habere, ſi hæc)
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ideſt, ſi ſupponantur falſa quædam, quæ ſupponi poſſunt, ſequetur impoſſi
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bile eſſe triangulum habere tres angulos æquales duobus rectis angulis, vi
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de, quæ ſcripſi lib. 1. Priorum, ſecto 3. cap. 1. de hoc, quod eſt, habere tres
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angulos æquales duobus rectis. </
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<
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">v. g. ſi in triangulo pag. </
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<
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">73. producto late
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re A C, in D. ſi ſupponatur externus angulus B C D, non eſſe æqualis duobus
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internis, & oppoſitis A, & B, nunquam poterimus eo modo, quo Euclides,
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demonſtrare paſſionem prædictam de triangulo A B C. huiuſmodi impoſſi
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bile, cuius oppoſitum non ſolum poſſibile, ſed etiam neceſſarium eſt, vocat
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Ariſt. impoſſibile ex ſuppoſitione, quia ſcilicet impoſſibile euadit ex quo
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dam falſo ſuo ſuppoſito, vt in allato exemplo, triangulum habere tres an
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gulos æquales duobus rectis, quamuis neceſſarium ſit, tamen ex falſa ſup
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poſitione, impoſſibile euaſit.</
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104</
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<
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">Ibidem
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(Et diameter commenſurabilis est coſtæ, ſi hæc)
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vide primo Priorum,
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ſecto 3. cap. 23. hoc ſolum nunc addendum
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(Si hæc)
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v. g. ſi ſupponamus li
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neas eſſe compoſitas ex indiuiſibilibus, conſectarium erit diametrum eſſe
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commenſurabilem coſtæ, quia indiuiſibile illud, ex quo vtraque linea con
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ſtat, erit
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vtriuſq;
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menſura communis.</
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Ex Secundo de Cælo.
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105</
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<
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">Tex. 24.
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(Amplius qui ſolida diuidunt in plana,
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ex planis corpora
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generant, his teſtes fuiſſe videntur: ſolam enim figurarum ſolidarum
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ſphæram non diuidunt, vt non plures ſuperficies. </
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<
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.
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<
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diuidẽs
">diuidens</
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>
in par
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tes diuidat totum, ſed vt in ſpecie diuerſa: patet igitur ſphæram eſſe ſolidarum
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primam)
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qui ſolida diuidunt in plana, ea diuidunt
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ſecũdum
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>
numerum ſuper
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ficierum, quibus ambiuntur, v. g. diuidunt cubum in ſex ſuperficies, quia
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cubus ſex quadratis planis ſuperficiebus continetur: qua ratione nequeunt </
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