Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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xml:space
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">ESto Parabole A B C, cuius axis B D, rectum B E. </
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reliquorum rectorum eſſe _MINIMVM_. </
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<
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A F, quæ axi B D æquidiſtabit, ſitque ad A contingens A G, & </
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<
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pr. conic.</
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ipſi A G æquidiſtans, quæ diametro A F erit ordinatim applicata; </
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dem axi applicetur A H, ſumaturque A I æqualis recto diametri A F.</
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<
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">Iam, ob contingentem A G, cum ſit
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H B æqualis B G, & </
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0217-01
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qualis, erit H B ęqualis F A: </
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gulum ergo H B E ad F A I, vel qua-
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dratum H A, ad quadratum B
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primæ 1.
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huius.</
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vel ad quadratum G A, erit vt B E
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ad A I, ſed eſt quadratum A H minus
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quadrato A G, ſiue recta A H minor
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recta A G, cum acutus angulus A G B
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minor ſit recto A H G, quare B E
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rectum, minus erit recto A I: </
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">eadem-
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que ratione demonſtrabitur B E quo-
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cunque alio recto minus eſſe: </
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B E rectum axis, eſt _MINIMVM._
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inter eius rectum, rectumque axis, hanc ipſam reperiri inter qua-
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dratum contingentis interceptæ, à vertice datæ diametri vſque ad axim,
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& </
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veluti ipſorum quandam propagationem ante oculos ponere expetemus, id
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à proximo Theoremate addiſcere liceat.</
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ne linearum ex puncto axis remoto à vertice per quadrantem
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ſui recti, ad ipſarum diametrorum vertices eductarum.</
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<
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ſit B D, & </
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tices iungantur rectis D B, D A, D F, &</
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ctorum diametrorum latera eſſe inter ſe, vt ſunt ipſæ eductæ D B, D A,
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D F, &</
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