Biancani, Giuseppe
,
Aristotelis loca mathematica
,
1615
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171
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culus à ſeipſo ſecundum diametrum mouetur, ideſt circa ſuum centrum re
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trahit continuò extrema diametri; ne recta ſecundum naturalem lationem
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ferantur, ſed in orbem circulariter circa centrum gyrentur. </
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<
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">hæc Ariſt. </
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<
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ſtat vt ſatisfaciam promiſſis.</
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<
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">Dictum eſt ab Ariſt. in textu
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(Sicut diameter ad diametrum, ita maior circu
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lus ad maiorem)
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quæ verba intelligenda eſſe non de circulis, ſed de periphæ
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rijs, vti expoſui, manifeſtum eſt ex 11. propoſit. </
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<
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id
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">5. Pappi Alexandrini, quæ
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talis eſt: Circulorum circunferentiæ inter ſe ſunt vt diametri. </
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<
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">quam etiam
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Pater Clauius demonſtrat propoſ. </
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<
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">2. lib. 8. & propoſ. </
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<
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id
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">1. lib. 4. Geom. pract.
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ſi autem de ipſis circulis intelligerentur falſa eſſent, non enim eſt circulus
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ad circulum, vt diameter ad diametrum; ſed circuli ſunt inter ſe, quemad
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modum à diametris ipſorum quadrata per ſecundam 12. Elem. quadrata
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autem ſunt inter ſe in duplicata ratione laterum per 20. 6.
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eiusq;
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corolla
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rium; hoc eſt ſi fiat, vt latus maioris quadrati ad latus minoris, ita latus mi
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noris ad aliam tertiam lineam, erit quadratum maius ad minus, vt latus
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ipſius ad tertiam illam lineam; non autem vt ad latus minoris. </
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<
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id
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">cum ergo
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circulus ſit ad circulum, vt quadratum diametri ad quadratum diametri,
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& quadrata non
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abbr
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habeãt
">habeant</
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rationem laterum, ſeu diametrorum prædictorum,
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ſed illorum duplicatam,
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neq;
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circuli inuicem illam habere poterunt.</
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<
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">Illud demum non ignorandum, quod Guidus Vbaldus propoſit. </
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<
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">1. de Tro
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chlea, demonſtrat, quod nimirum potentia ſuſtinens pondus per rotulam,
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cui funis ſupernæ fuerit circumductus, qualis ea eſt, qua ad hauriendam ex
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puteis aquam vtimur, talis inquam potentia eſt æqualis ponderi; cuius ra
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tio eſt, quia tunc trochlea fit vectis, cuius fulcimentum eſt in medio vectis,
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pondus verò, & potentia in extremitatibus ſunt, & æquidiſtant ab hypomo
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clio, & propterea cum ſit eadem proportio ponderis ad potentiam, quæ di
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ſtantiæ ad diſtantiam, vt ſupra quęſt. </
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<
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id
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">3. probatum eſt ex Archimede, & Gui
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do Vbaldo, diſtantiæ autem ſint æquales, erunt etiam pondus, & potentia
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æqualia, ideſt, ſi pondus eſſet vnius libræ, ſuſtineretur à tanta vi,
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quãta
">quanta</
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opus
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eſt ad libram vnam ſuſtinendam, & non amplius. </
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<
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id
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">vt autem clarè appareat
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vectis in trochlea, & hypomoclion, & æquales diſtantiæ, ſit figura, in qua
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pondus D, ductario funi D C B E, alligatum. </
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<
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tia
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ſuſtinẽs
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E. axis autem erit diameter rotulæ B A C,
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nam potentia premit rotulam in B, & pondus in C, &
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cum rotula ſuſtineatur in A, à ſuſpenſorio F A. erit
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punctum A, hypomoclion, quia in motu vectis eua
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dit centrum,
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eſtq́
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; punctum manens. </
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<
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id
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">æquales autem
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diſtantiæ
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vtrinq;
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ab hypomoclio ſunt B A, A C, ſunt
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enim ex centro eodem. </
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<
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id
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">ex quibus manifeſtum eſt hu
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iuſmodi rotulam nullam vim mouenti addere, ſed ſo
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lum illud præſtat, vt omne tollat impedimentum,
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quemadmodum ait Ariſt. manifeſtum etiam eſt ma
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iorem vim quamlibet, quam ſit ea, quæ ſuſtinet, poſſe
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idem pondus ſurſum mouere. </
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<
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">hæc & præſenti loco, &
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ſequentibus lucem afferre poſſunt.</
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