Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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quoniam harum quoque habemus demonſtrationes breuiores, & </
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uas, non indirectas, quales ab Apollonio exhibentur in prima, ſecunda, ac
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decima tertia, nè noſtri libelli molem aliundè tranſcriptis demonſtratiombus
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augere velle videamur, apponemus hic proprias, ita procedendo.</
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vertice ad vtramque partem diametri ſumatur æqualis ei, quæ po-
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xml:space
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">Prop. 1. 2
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ſecundi
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con ic.</
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teſt quartam figuræ partem, quæ à ſectionis centro ad ſumptos ter-
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minos contingentis ducuntur cum ſectione non conuenient; </
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<
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xml:space
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">(quæ
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in poſterum cum Apollonio vocentur ASYMPTOTI) nec erit al-
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tera aſymptoton, quæ diuidat angulum ab ipſis factum.</
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rectum figuræ latus B F, linea verò D E ſectionem contingat in B, & </
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0040-01
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quartæ parti figuræ, quæ à lateribus
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AB, BF continetur æquale ſit quadra-
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tum vtriuſque ipſarum BD, BE, & </
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ctæ CD, CE producantur. </
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mum eas cum ſectione numquam con-
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uenire.</
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<
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">Nam in altera ipſarum, vt in CD,
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infra contingentem, ſumpto quolibet
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puncto G, ab eo ordinatim applicetur
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GIH ſectionem, ac diametrum ſecans
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in I, H, quæ ipſi D B æquidiſtabit. </
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quoniam eſt vt latus AB ad BF, ita
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quadratum AB ad rectangulum ABF,
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vel ſumptis horum ſub-quadruplis, ita
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quadratum CB ad quadratum BD, vel quadratum CH ad quadratum HG,
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& </
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">vt idem latus AB ad BF ita eſt rectangulum AHB ad quadratum HI,
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mi conic.</
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quadratum CH ad HG, vt rectangulum AHB ad quadratum HI, & </
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tando quadratum CH ad rectangulum AHB, vt quadratum GH, ad HI,
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ſed quadratum CH maius eſt rectangulo AHB (cum eius exceſſus ſit qua-
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dratum CB, nam eſt AB ſecta bifariam in C, & </
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quare & </
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">quadratum GH quadrato IH maius erit, hoc eſt punctum G cadet
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extra Hy perbolen, & </
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<
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">hoc ſemper de omnibus punctis rectarum CDG, CEL
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quamuis in infinitum productarum. </
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quam occurrentes. </
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">Quod erat primò demonſtrandum, taleſque lineæ vo-
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centur ASYMPTOTI.</
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<
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">Amplius, ijſdem manentibus, dico quamlibet aliam CM, quæ diuidat
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angulum DCE, neceſſariò Hyperbolen ſecare. </
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">Ducta enim BM, ex vertice
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B, parallcla ad CD, conueniet cum CM; </
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diſtantium CD conuenit in C: </
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