Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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<
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uerſalius
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quàm in
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4. prop.
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exerc. 6.
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Caual.</
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vtraque parte ſectioni occurrens cum diametro, vel intra, vel extra
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ſectionem conueniat, atque ex ipſius terminis cum ſectione, ad diametrum
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ducantur ordinatæ, erunt ab his abſciſſa diametri ſegmenta ex vertice ſum-
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pta, extremæ, & </
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<
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">abſciſſum ab applicata, erit media trium continuè propor-
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tionalium. </
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">Demonſtratum eſt enim in figuris Theorematis quando AH dia-
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metrum ſecat in M, & </
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<
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">ſectionem in A, H, quod ordinatim applicatis AF,
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HI, eſt FB ad BM, vt BM ad BI.</
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<
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">EX quo etiam elicitur, quod ſi in Parabola ABC ducta AH diametrum
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ſecans in M producatur vſque ad occurſum cum contingente ex verti-
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ce B in S, ſemper rectangulum ſub ſegmentis AS, & </
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contingentem interceptis æqua†@ quadrato ſegmenti SM inter contingẽtem,
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ac diametrum intercepti. </
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">Nam cum ſit vt FB ad BM, ita BM ad BI erit quo-
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que ob parallelas, AS ad SM, vt SM ad SH, quare rectangulum ASH æqua-
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bitur quadrato SM.</
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interior Parabole ADG habuerit ver-
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0049-01
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ticẽ in D puncto medio rectæ AB, ipſa quo-
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que tranſibit per F medium punctum baſis
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AC, & </
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">quæcunque educta ex contactu A,
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qualis eſt AH, bifariam ſecabitur in O ab in-
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terna ſectione; </
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">quare ſi ex O ducatur OLM
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diametro BF æquidiſtans, ipſa erit diameter
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portionis ALH, & </
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AO verò ſemi-applicata. </
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contingens ABC in A, erit OL in trilineo
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mixto ADFB, æqualis LM in trilineo mixto
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ALBP, & </
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ceptis in ijſdem trilineis.</
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<
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tur diſpoſitæ inter eaſdem parallelas BE, AF: </
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vnius, ad baſim DF alterius, ita Parabole ABC ad Parabolen DEF.</
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