Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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da B D erit æqualis radio B C, ſiue C D, vnde in triangulo æquilatero C
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D B anguli ad C, B, æquales erunt, & </
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anguli ad C, B, ſint æquales, atque etiam æquales ad F, cum ſint recti,
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& </
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<
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">latus D F commune, erit reliquum latus C F, reliquo F B æquale, eſtq;
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<
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gulis in Ellipſi applicatis, &</
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">Ad diametrum datæ ſemi - Ellipſis rectam applicare, cuius
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rectangulum in alterum diametri ſegmentum ſit MAXIMVM.</
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<
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applicare oporteat D E, ita vt rectangulum A E D ſit _MAXIMVM._
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">Nam deſcripto ſuper A B ſemi - circulo A F B, erigatur ex E ipſi A B
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perpendicularis E F. </
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eſſe _MAXIMVM_ in ſemi - circulo, &</
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<
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punctum G, præter E, applicenturq;
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tum in ſemi - circulo, tum in ſemi - El-
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lipſi rectæ G H, G I. </
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dratum E F ad G H vt rectangulum
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A E B ad A G B, vel vt
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mi conic.</
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E D ad G I, erit & </
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vt E D ad G I, ſed ratio rectanguli A
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E F ad rectangulum A G H compo-
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nitur ex ratione E F, ad G H, ſiue ex
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ratione E D ad G I, & </
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A ad A G, atque rectangulum A E D
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ad A G I ex ijſdem componitur ratio-
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nibus, vnde rectangulum A E F ad A
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G H erit vt rectangulum A E D ad A G I, & </
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lum A E F _MAXIMVM_ in ſemi - circulo, ergo, & </
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in ſemi - Ellipſi. </
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rectangulis A L M, A G I id, quod _MAXIMO_ propius eſt maius ſit
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remotiori, eadem penitus arte nuper adhibita oſtendetur, ſi ex L
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in ſemi - circulo applicetur L N. </
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rectangulum A L M ad A G I, eſſe vt A L N ad A G H, ſed A L N maius
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eſt A G H, prout in præcedenti ad num. </
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gulum A L M maius erit rectangulo A G I, & </
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