Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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bebit rationem
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quàm idem qua-
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dratum E A ad
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rectangulum A E
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B, & </
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drata E A, ſiue
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vnicum quadra-
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tum A D, ad qua-
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tuor quadrata A
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H, ſiue ad vnicum
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quadratum A B
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minorem habebit
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rationem quàm
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quadratum E A
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ad rectangulum
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A E B, ſed quadratum A D ad A B eſt vt quadratum C D ad F B, & </
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dratum E A ad rectangulum A E B eſt vt quadratum E D ad rectangu-
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lum B E D, cum ſit A E æqualis E D, vel vt recta E D ad rectam E B,
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vel vt quadratum C D ad quadratum G B, quare quadratum C D
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mi conic.</
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F B minorem habebit rationem quàm idem quadratum C D ad quadra-
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tum G B, ergo quadratum F B maius eſt quadrato G B, vnde punctum F
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cadit extra Parabolen, & </
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">ſic de quolibet alio puncto rectæ A C F, præ-
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ter C. </
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contingens. </
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">Sumatur enim poſt D A, A B tertia proportionalis A H, erit ag-
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gregatum extremarum
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A D, A H maius quàm
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duplum mediæ A B,
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ſiue maius quàm du-
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plum A E cum E B,
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ſed eſt A D dupla ad
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A E, ergo A H erit
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maior quàm dupla E
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B, ſed eſt A D dupla
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D E, ergo A D ad D
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E minorem habet ra-
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tionem quàm A H ad
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E B, & </
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A ad A H minorem
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habet rationem quàm D E ad E B, ſed D A ad A H, eſt vt quadratum
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D A ad quadratum A B, vel vt quadratum D C ad quadratum B F, & </
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D E ad E B, eſt vt quadratum D C ad quadratum B G, ergo
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tum D C ad quadratum B F minorem habet rationem quàm idem </
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