Biancani, Giuseppe
,
Aristotelis loca mathematica
,
1615
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vt in figura, vbi linea A B, inſiſtens alteri D C, perpendiculariter, ideſt ita
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vt faciat angulos hinc inde æqualis A B D, A B C, prædictos inquam duos
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angulos conſiderat e. </
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<
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">contemplatur præterea Geometra omnes
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angulos rectos eſſe inter ſe æquales, vt in 12. axiomate primi Elem. ponitur,
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& ſimilia plura alia, quorum conſiderationem Faber omninò negligit.</
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302</
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<
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">Libro 2. capite 6.
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(Id quod ſecundum Arithmeticam rationem medium eſt)
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Arithmetica ratio, fiue proportio ea eſt, cuius termini creſcunt per æqua
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les exceſſus, vt 2. 6. 10. 14. horum enim terminorum exceſſus æquales ſunt,
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cum ſint omnes quaternarij. </
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metica analogia, cùm omnes ternario numero ſuperent præcedentes, & à
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ſequentibus ſuperentur. </
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<
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">Porrò apud Mathematicos tria ſunt genera pro
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portionum, ſiue medietatum, Arithmetica quam modo ſuppoſui; Geome
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trica, & Harmonica, quas inferius oblata occaſione opportunius explicabo.</
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303</
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">Lib. 2. cap. 9.
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(Vt circuli medium deprehendere non
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cuiuſlibet, ſed
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ſciẽtis
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ſolummodo eſt)
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Reperire medium,
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ſiue centrum dati circuli docet Euclides propoſitio
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ne prima 3. hoc modo. </
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<
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">in dato circulo ducatur vt
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cunque recta B C, quæ per 10. primi diuidatur bifa
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riam in F, & per F, ducatur
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perpẽdicularis
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A E F D,
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quæ ſecetur bifariam in E,
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; punctum E, non ſo
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lum ipſius lineæ medium; ſed etiam totius circuli
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centrum, quemadmodum ibi demonſtrat Euclides.</
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304</
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">Lib. 3. cap. 3.
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(De æternis autem nemo conſultat, vt
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de mundo, aut diametro, & latere, quod nulla inter ſe
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æquabilitate conueniant)
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Qua ratione diameter, & latus eiuſdem quadrati
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nulla æquabilitate, ideſt nulla communi menſura inter ſe conueniant, fusè
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explicatum eſt libro Priorum, ſecto 1. cap. 23.</
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305</
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">Eodem cap.
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(Qui enim conſultat quærere videtur, & reſoluere prædicto modo,
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quemadmodum deſignationes)
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Per deſignationes Ariſt. intelligere geometri
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cas demonſtrationes ſæpius dictum eſt in logicis textibus, quod pariter ex
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hoc loco confirmatur. </
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<
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">quando autem ait
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(Reſoluere prædicto modo, quemad
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modum deſignationes)
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innuit reſolutionem geometricam, de qua abundè di
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ctum eſt in explicatione tituli librorum Reſolutoriorum; quam expoſui, ni
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hil aliud eſſe, quam medij inquiſitionem ad id, quod propoſitum fuerit de</
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monſtrandum. </
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<
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atq;
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germanam fuiſſe huiuſmodi explicatio
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nem, hoc loco Ariſt. ipſe confirmat, cum hanc reſolutionem dicat eſſe ſimi
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lem conſultationi, ſiue inquiſitioni mediorum ad finem in rebus practicis
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conſequendum; ipſa verò eſt inquiſitio mediorum ad id, quod in rebus ſpe
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culatiuis propoſitum eſt, demonſtrandum. </
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<
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practicis, quod in ſpeculatiuis eſt reſolutio.
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306</
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307</
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<
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">Lib. 5. cap. 3.
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(Quod enim proportione conſtat, id non tam vnitario numero,
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quàm numero in vniuerſum proprium eſt)
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Per vnitarium numerum intelligitur
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numerus ex vnitatibus abſtractis conφlatus, ideſt, cuius vnitates non ſint res
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phyſicæ, ſed à naturalibus abſtractæ, qualis conſiderat Arithmeticus: omni
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tamen numero ſiue abſtracto, ſiue non, conuenit proportiones ſuſcipere,
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id eſt & numero, & rebus numeratis.</
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