Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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<
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<
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">PAtet etiam quomodo datæ coni-ſectioni, vel circulo ABC per ipſius
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verticem inſcribi poſſit Ellipſis, que ſit _MAXIMA_ circa idem tranſuer-
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ſum, & </
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<
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quamcumque teneat rationem; </
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">& </
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<
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">in Ellipſi, vel circulo data ratio non ſit
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minor ratione recti BE, ad tranſuerſum BD.</
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<
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<
s
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">Nam ſi exempli gratia Parabolæ, vel Hyperbolæ primæ, ac ſecundæ figu-
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ræ inſcribenda ſit _MAXIMA_ Ellipſis circa idem tranſuerſum latus, & </
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<
s
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rectum ad verſum datam habeat rationem, R nempe ad S: </
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<
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">fiat vt R ad S, ita
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rectum EB datæ ſectionis ad BG, nam ſi cum eodem recto EB, ac tranſuerſo
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BG adſcribatur per B Ellipſis GHB, ipſa erit _MAXIMA_ circa idem tranſ-
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uerſum BG, per ea, quæ ſuperius demonſtrata fuerunt. </
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<
s
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">Siverò data ratio R
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ad S non ſit minor ratione recti EB ad tranſuerſum BD; </
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<
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">in tertia, quarta, & </
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quinta figura, fiat vt R ad S, ita EB ad BG, quod erit tranſuerſum quæſitæ
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inſcriptæ Ellipſis, quæ erit _MAXIMA_, &</
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<
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inſcribere, & </
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<
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<
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<
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">Per verticem datæ Parabolæ, cum dato tranſuerſo latere MINI-
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MAM Hyperbolen circumſcribere.</
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<
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">SIt data Hyperbole ABC, cuius vertex B, diameter BD, tranſuerſum la-
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tus BE, rectum BF, & </
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">regula EFO oportet primùm per eius verticem B
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_MAXIMAM_ Parabolen inſcribere.</
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<
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huius.</
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0068-01
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per verticem B, & </
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rabole GBH. </
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<
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_MAM_ quæſitam.</
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<
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">Ducta enim ex F Parabolæ regula
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FI, cum hæc infra contingentem BF,
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regulę EFO, nunquam occurat, (cum
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ſimul conueniãt in F) ſitque regula FI
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propinquior diametro BD quam pro-
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ducta regula FO, erit Parabole
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roll. prop.
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19. huius.</
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datę Hyperbolę ABC inſcripta, eritq;
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</
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Parabole ipſi ABC per verticem B
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adſcripta cum recto BL, quod minus
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ſit recto BF datę Hyperbolæ,
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roll. prop.
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19. huius.</
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eſt Parabola GBH, quælibet verò ad-
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ſcripta cum recto BM, quod excedat
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rectum BF datę Hyperbolæ ipſa </
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