Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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<
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">Inſuper, ſit alia adſcripta Ellipſis AHCI, cuius ſegmenta diametri HG,
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GI ſint adhuc magis inæqualia, quàm ſegmenta EG, GF: </
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rcm eſſe Ellipſi AHCI. </
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">Oſtendetur enim, vt ſupra, rectangulum EGF ma-
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ius eſſe rectangulo HGI, & </
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AHCI, ſiue Ellipſim AECF inſcribi poſſe AHCI, hoc eſt ipſa minorem eſſe.
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<
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">MAXIMA ſemi-diametrorum, à centro Ellipſeos eductarum,
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eſt ſemi-axis maior, MINIMA verò ſemi-axis minor: </
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<
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">aliarum
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autem, quæ cum MAXIMA minorem conſtituit angulum maior
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eſt: </
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<
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<
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">quatuor ſunt in Ellipſi æquales ſemi-diametri, quarum vna
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tantùm cadit in vnoquoque Ellipſis quadrante, genito ex axium
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interſectione.</
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primùm maiorem ſemi-axim EB eſſe omnium ſemi-diametrorum _MA-_
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_XIMAM_, & </
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">Cum centro enim E, & </
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deſcripto circulo BHD, ipſæ cadit totus
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extra Ellipſim, cum eiſit
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vnde ſemi-diameter EB erit _MAXIMA_;
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<
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">facto cétro E, cum radio EA deſcripto
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circulo EOC, ipſæ totus cadet intra Elli-
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pſim, cum ei ſit inſcriptus, ex quo, E
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erit _MINIMA_. </
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<
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">Ampliùs in quadrãte Ellipſeos AFCE
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ductæ ſint quotcunque ſemi-diametri EF,
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EG, & </
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EF maiorem eſſe EG.</
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">Applicentur enim per F, G, ad maio-
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rem axim BE rectæ KF, LG, quæ produ-
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ctæ, circuli peripheriæ BIH occurrant in I,
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M, & </
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<
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">Erit in ſemi-circulo BHD, quadratum ML ad IK, vt rectangulum DLB
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ad DKB; </
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">in ſemi-Ellipſi BCD, quadratum GL ad FK, vt idem
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gulum DLB ad idem DKB, ergo quadratum ML ad IK, erit vt quadratum
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GL ad FK, ſiue linea ML ad IK, vt pars GL ad partem FK, & </
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ad reliquam IF, ſed eſt GL maior FK: </
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<
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rectangulum MGL ſub maioribus lateribus contentum, maius erit rectan-
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gulo IFK ſub minoribus, & </
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<
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">Iam cum triangula EKI, ELM ſint rectangula ad K, L, erunt triangula
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EFI, EGM obtuſiangula ad F, G, eſtque linea E I æqualis EM, ergo qua-
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dradratum E I, hoc eſt duo ſimul quadrata EF, F I, cum duplo rectanguli
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KEI, maiora erunt quadrato EM, ſiue duobus ſimul quadratis EG, </
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