Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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">In Parabolis quibuslibet, vel in ſimilibus Hyperbolis, aut ſimi-
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libus Ellipſbus, ſegmenta diametrorum ſectionum lateribus pro-
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portionalia, ſuſcipiunt applicatasijſdem lateribus proportionales.</
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<
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">SInt, vt in prima figura, duæquælibet Parabolæ, velvt in ſecunda, duæ
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ſimiles Hyperbolæ, vel vt in tertia, duæ ſimiles Ellipſes ABC, DEF,
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quarum diametrorum ſegmenta BG, EH, rectis earum lateribus BI, EL, vel
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tranſuerſis BM, EN ſint proportionalia, dico & </
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<
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">applicatas GA, HD ipſis la-
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teribus eſſe proportionales.</
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mùm, cum ſit rectum BI
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ad rectum EL, vt ſegmẽ-
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tum BG ad EH, erit per-
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mutando IB ad BG, vt
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LE ad EH, vnde rectan-
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gulum I B G ſimile erit
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rectangulo LEH, quare
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rectangulum IBG ad LE
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H, erit vt quadratum la-
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teris I B ad quadratum
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homologilateris LE, ſed
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rectãgulum IBG
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tur quadrato GA, & </
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ctãgulum LEH quadra-
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to HD, vnde quadratum
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GA ad HD, erit vt qua-
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dratum IB ad LE, vel
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applicata GA ad HD, vt
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rectum IB ad rectum LE.
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</
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<
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">In Hyperbolis autem, & </
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Ellipſibus cum ſit vt BI
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ad EL, vel ob ſectionum ſimilitudinem, vt MB ad NE, ita BG ad EH, erit
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permutando MB ad BG, vt NE ad EH, & </
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<
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">in Hyperbolis, componendo, in
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Ellipſibus autem diuidendo, MG ád GB, vt NH ad HE, quare rectangulum
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MGB ſimile erit rectangulo NHE, ſed rectangulum MGB ad quadratum
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GA eſt, vt MB ad BI, vel vt NE ad EL, vel vtrectangulum NHE ad
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mi conic.</
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dratum HD, quare permutando rectangulum MGB ad rectangulum NHE,
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vel (ob ipſorum rectangulorum ſimilitudinem) quadratum BG ad quadra-
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tum EH, vel quadratum BI ad quadratum EL, erit vt quadratum GA ad
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quadratum HD, hoc eſt rectum BI ad rectum EL, vt applicata GA ad appli-
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catam HD. </
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