Biancani, Giuseppe, Aristotelis loca mathematica, 1615

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              <s id="s.002892">
                <pb pagenum="171" xlink:href="009/01/171.jpg"/>
              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. </s>
              <s id="s.002893">hæc Ariſt. </s>
              <s id="s.002894">Re­
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              ſtat vt ſatisfaciam promiſſis.</s>
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              <s id="s.002895">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. </s>
              <s id="s.002896">5. Pappi Alexandrini, quæ
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              talis eſt: Circulorum circunferentiæ inter ſe ſunt vt diametri. </s>
              <s id="s.002897">quam etiam
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              Pater Clauius demonſtrat propoſ. </s>
              <s id="s.002898">2. lib. 8. & propoſ. </s>
              <s id="s.002899">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.
                <expan abbr="eiusq;">eiusque</expan>
              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. </s>
              <s id="s.002900">cum ergo
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              circulus ſit ad circulum, vt quadratum diametri ad quadratum diametri,
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              & quadrata non
                <expan abbr="habeãt">habeant</expan>
              rationem laterum, ſeu diametrorum prædictorum,
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              ſed illorum duplicatam,
                <expan abbr="neq;">neque</expan>
              circuli inuicem illam habere poterunt.</s>
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              <s id="s.002901">Illud demum non ignorandum, quod Guidus Vbaldus propoſit. </s>
              <s id="s.002902">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. </s>
              <s id="s.002903">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,
                <expan abbr="quãta">quanta</expan>
              opus
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              eſt ad libram vnam ſuſtinendam, & non amplius. </s>
              <s id="s.002904">vt autem clarè appareat
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              vectis in trochlea, & hypomoclion, & æquales diſtantiæ, ſit figura, in qua
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                <figure id="id.009.01.171.1.jpg" place="text" xlink:href="009/01/171/1.jpg" number="98"/>
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              pondus D, ductario funi D C B E, alligatum. </s>
              <s id="s.002905">poten­
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              tia
                <expan abbr="ſuſtinẽs">ſuſtinens</expan>
              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,
                <expan abbr="eſtq́">eſtque</expan>
              ; punctum manens. </s>
              <s id="s.002906">æquales autem
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              diſtantiæ
                <expan abbr="vtrinq;">vtrinque</expan>
              ab hypomoclio ſunt B A, A C, ſunt
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              enim ex centro eodem. </s>
              <s id="s.002907">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. </s>
              <s id="s.002908">hæc & præſenti loco, &
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              ſequentibus lucem afferre poſſunt.</s>
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