Biancani, Giuseppe
,
Aristotelis loca mathematica
,
1615
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tum procedatur, numeri ſemper quadrati progignentur. </
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<
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ratione Gnomonum, ſiue imparium additione fiat ſemper eadem ſpecies,
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ſcilicet quadratus numerus, quod ſignum eſt, inquiunt, imparem numerum
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non infinitatis, ſed finitatis eſſe auctorem. </
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<
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">Poſt prædictam 26. propoſitio
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nem Iordani, ſunt aliquot propoſitiones, quarum ſumma hæc eſt: ſi pares
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numeri ab vnitate coaceruentur; coaceruati erunt ſemper variæ formæ nu
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merorum. </
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<
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">quæ ſic explicantur: ſint ab vnitate pares diſpoſiti ordinatim
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hoc modo, 1. 2. 4. 6. &c. </
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<
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">ſi igitur vnitati binarius coaceruetur, fit numerus
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triangularis, vt in prima figura. </
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<
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coaceruetur ſequens par, fiet altera ſpecies, ni
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mirum hexagonus numerus, vt in ſecunda figu
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ra. </
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<
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">cui ſi ſequens addatur par, ſcilicet ſenarius,
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fiet iterum noua numeri forma, v. g. </
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nus, vt in tertia figura. </
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">& ſic ſemper in infinitum nouæ ac variæ numerorum
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formæ ex hac additione parium prouenient, quod argumento eſt numerum
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parem infiniti naturam ſapere. </
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<
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">Porrò reperiri numeros triangulares, pen
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tagonos, & ſimiles, conſtat ex Arithmetica Nicomachi, Boetij, & Iordani,
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citati in definitionibus 7. ſuæ Arithmeticæ, atque ex tractatu Diophantis
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Alex. de numeris rectangulis. </
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<
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atq;
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ex his locus hic ſatis clarus redditur.</
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94</
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<
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(Vtuntur etiam Mathematici infinito)
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aliquãdo
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Mathematici du
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cunt lineas quantumuis longas, ſeu indefinitæ longitudinis, quas etiam in
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finitas appellant: & hoc modo vtuntur infinito, vt infra tex. 71. ipſe Ariſt.
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exponit. </
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<
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">alio præterea modo vtuntur infinito, vt quando ſupponunt data
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quauis quantitate poſſe ſumi maiorem, vel etiam minorem in infinitum, vt
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patet ex 6. poſtulato primi Elem. editionis Clauianæ. </
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<
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au
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geri poſſe in infinitum, eſt ſecundum poſtulatum libri 7. Elem. vel demum
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quando probant quamlibet lineam poſſe diuidi bifariam, quia hinc ſequitur
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poſſe ſub diuidi in
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infinitũ
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; his igitur modis Mathematicis
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infinitũ
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in vſu eſt.</
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95</
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">Tex. 68. & 69. plura de magnitudine, & numero continent; ſed quæ non
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indigeant opera noſtra.</
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96</
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<
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(Non remouet autem ratio Mathematicos à contemplatione auferens
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ſic eſſe infinitum, vt actu ſit verſus augmentum, vt intranſibile,
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ncq;
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enim nunc in
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digent infinito,
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neq;
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vtuntur, ſed ſolum eſſe
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quantumcunqu;
">quantumcunque</
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velint finitam)
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ratio
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phyſica tollens infinitum actu, non eſt Mathematicis impedimento, quia ipſi
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non vtuntur infinito actu; quam enim ipſi ducunt lineam infinitam, non eſt
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verè infinita, ſed indefinita, eam enim quantumlibet magnam producunt, vt
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poſſit ad demonſtrandum ſufficere.</
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Ex Quarto Phyſicorum.
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97</
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<
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ſurabilitatis, quæ eſt diametri ad coſtam: cuius explicationem vide
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primo Priorum, ſecto primo, cap. 23.</
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