Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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<
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xml:space
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">Ex dato puncto A ordinatim applicetur A D, occurrens diametro in
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D, & </
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E A ſectionem contingere.</
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<
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">Etenim ſumpto in ea quocunque puncto F, vel ſupra, vel infra A,
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ordinatim agatur F H G, ſectionem ſecans in H, diametrum in G, & </
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<
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per tranſuerſo B C deſcribatur ſemicirculus B L C, cuius diametto B C
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in Ellipſi ex puncto D erigatur perpendicularis D L, iungaturque E L,
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quæ, per Lemma antecedens, erit ipſi circulo contingens in L. </
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Hyperbola ex E puncto ducta ſit diametro C B perpendicularis E L, iun-
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gaturque D L, quæ item, ob præmiſſum Lemma, ſemi-circulum B L C
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continget in L, & </
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<
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">ex G ipſi D L æquidiſtans ducatur G I ſemi-circulum
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primæ figuræ ſecans in M, in qua cum ſit E L I contingens in L, erit ap-
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plicata G I maior G M, ſiue quadratum G I maius quadrato G M, vel
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maius rectangulo C G B, ſed eſt quoque, per idem Lemma, quadratum
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G I (in ſecunda figura) maius rectangulo C G B, quare in vtraque figu-
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ra quadratum G I ad quadratum D L, vel quadratum G E ad quadratum
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E D, vel quadratnm G F ad quadratum D A, maiorem habebit rationem
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quàm rectangulum C G B ad idem quadratum D L, vel ad rectangulum
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C D B, ſed vt rectangulum C G B ad rectangulum C D B, ita
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mi conic.</
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tum G H ad quadratum D A, ergo quadratum G F ad quadratum D A
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maiorem habet rationem quàm quadratum G H ad idem quadratum D
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A; </
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dit extra ſectionem, & </
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ter A. </
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ciendum.</
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