Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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tranſuerſum latus ad rectum, per conſtructionem, vel vt
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conic.</
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H P Q ad quadratum P A; </
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">ſed eadem H P ad P R (ſumpta communi al-
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titudine P Q) eſt vt idem rectangulum H P Q ad rectangulum R P Q,
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quare quadratum P A æquabitur rectangulo R P Q, eſtque A P ipſi R Q
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perpendicularis, vnde angulus R A Q, & </
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ei deinceps Q A F rectus erit, ſed A Q ſectionem contingit, quare
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pt. Pappi.</
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pendicularis F A erit _MINIMA_ quæſita.</
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huius ad
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num. 1.</
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coniugatum H S, vt in octaua, & </
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bolæ ad datum punctum F ducatur H F, quæ ita ſecetur in I, ita vt H I
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ad I F, ſit vt tranſuerſum latus G B ad rectum B E, ſumptaque H L ęqua-
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li ipſi I F, per I agatur I O N ordinatim ductis æquidiſtans, & </
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<
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cta L O M axi H B D parallela, & </
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H (quod eſt centrum Hyperbolæ) deſcribatur alia Hyperbole H A,
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diconic.</
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alteram A B C in vno tantùm puncto A ſecabit. </
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_MINIMAM_ quæſitam.</
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axemque ſecans in Q, iungaturque IP. </
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conic.</
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aſymptoti O N, O M, ſumptum eſt punctum P, à quo ductæ ſunt P A,
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P H aſymptotis æquidiſtantes, & </
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eorum altero H ducta eſt H L I vtranque aſymptoton ſecans in I, L, eſt-
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que I F in directum, & </
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<
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">æqualis poſita ipſi H L, rectaque F A coniungit
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extremum F cum altero datorum A; </
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<
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P; </
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rum F A, ſi hæc vltra F A producatur. </
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in triangulo F H R recta H P ad P R, vt H I ad I F, vel vt latus tranſuer-
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ſum ad rectum, ex conſtructione, vel vt rectangulum H P Q ad
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conic.</
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tum P A, ſed eadem H P ad P R (ſumpta communi altitudine P Q) eſt
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vt idem rectangulum H P Q ad rectangulum R P Q: </
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