Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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ſuntque in triangulis D F A, D F L anguli ad F æquales, cum ſint recti,
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& </
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">latus F D commune, atque angulus A D F minor eſt angulo L D F,
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quare & </
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bit ergo H F ad F L minorem rationem, quàm eadem F H ad H A, & </
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componendo H L ad L F, ſiue G H ad D F, minorem quàm F A ad A
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H, vnde rectangulum G H A ſub extremis minus erit rectangulo D F
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Pappi.</
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ſub medijs, & </
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ter D, & </
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<
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">K, vel in ipſo K, nempe rectangulum ad G, vel K, pertin-
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gens, minus eſſe rectangulo D F A, ſiue D F A maius eſſe quocunque
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prædictorum rectangulorum G H A, vel K C A, &</
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<
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">Si autem punctum ſumatur in quadrante A K, vt in O; </
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pendiculari O P. </
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ctangulum K C A maius rectangulo O P C, ſed rectangulum D F A oſtẽ-
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ſum eſt maius rectangulo K C A, ergo rectangulum D F A eò amplius
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maius erit rectangulo O P A.</
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<
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">Si denique punctum ſumatur in peripheriæ ſextante D B, veluti in Q,
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demiſſa perpendiculari Q R, & </
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">iuncta D Q, & </
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o mnino cum diametro A B ad partes B, vt in S, quoniam angulus E D
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Q eſt in portione E A Q ſemi - circulo maiori, ac propterea acutus, & </
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angulus D F S rectus eſt, &</
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">Et cum arcus A I E æqualis ſit arcui D B
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E, vterque enim eſt triens peripheriæ, erit arcus A I E maior arcu Q B
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E, ac ideo angulus A D E, vel A D F maior angulo Q D E, vel S D F,
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ſed in triangulis A F D, S F D latus F D eſt commune, & </
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ſunt æquales, eò quod ſint recti, & </
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<
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D F, vnde latus A F maius eſt latere F S, & </
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<
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habebit ergo F R ad R S maiorem rationem quàm eadem R F ad F A, & </
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componendo F S ad S R, vel D F ad Q R, maiorem quàm R A ad A F;
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<
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Pappi.</
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ſub medijs, & </
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tante D B. </
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">Quare cum rectangulum A F D demonſtratum ſit maius om-
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nium applicatosum, tum in triente A D, tum in ſextante D B, ipſum A
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F D erit _MAXIMV M_, & </
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">ſumptis duplis, rectangulum ſub ſagitta A F in
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chordam D E, erit _MAXIMV M_ rectangulum ſub qualibet alia ſagitta in
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ſuam chordam. </
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<
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nentibus poſitione ijſdem punctis K, D, E, dico talium rectang lo-
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rum id, quod puncto D propinquius eſt, ſemper maius eſſe remotiori.</
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<
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">Nam de ijs, quæ ad arcum quadrantis A K pertingunt, vtputa de re-
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ctangulis A C K, A F R, A H G, &</
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maius eſſe rectangulo A F R, quod ab ipſo D magis remouetur, & </
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R maius eſſe A H G, &</
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ſes C A, F A, H A continuè decreſcant.</
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<
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L, ita ratiocinabimur. </
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lares I M N, L O P, & </
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L cum diametro in Q (nam arcus N A L maior eſt ſemi-peripheria, </
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