Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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<
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">Iam applicata quacunque OPQR, tùm in Parabola AED, tùm in ſemi-
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Parabola DHC; </
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<
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">cum ſit quadratum AD ad OP vt linca GF ad FS, vel vt DH
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ad HQ, vel vt quadratum DC ad QR, ſintque antecedentia AD, DC ęqua-
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lia, erunt & </
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<
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">conſequentia OP, QR æqualia, nempè applicata OP æqualis ap-
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plicatæ QR, & </
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<
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<
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<
s
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xml:space
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">quare integra Parabole AED æquatur
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ſemi-Parabolæ DHC.</
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<
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">Amplius ducta quacunque TVX
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parallela ad BD, erit BD ad TX, vt
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rectangulum ADC ad AXC, vel vt
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HD ad VX, & </
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<
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BD dupla DH, & </
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<
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">TX erit dupla XV,
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& </
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">ſic de omnibus interceptis, & </
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<
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quidiſtantibus in ſemi-Parabola DB
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C, & </
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<
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xml:space
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">in ſemi-Parabola DHC, vnde
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tota ſemi-Parabole DBC dupla eſt
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totius ſemi-Parabolæ DHC, & </
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<
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xml:space
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ptis æqualibus; </
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<
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">ſemi-Parabole ABD
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dupla Parabolæ AFD, ſiue trilineum
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ANBDFA, æquale erit Parabolæ
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AFD.</
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<
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">Tandé, ſi ſit AE contingens ABC
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in A, erit EB æqualis BD, & </
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<
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">ducta
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in trilineo AEBDFA quacunque IKZ parallela ad ED, erit IK æqualis
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roll. 13. h.</
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& </
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<
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">ANBDFA quare
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totum trilineum AEBNA æquabitur toto trilineo ANBDFA, ſed hoc, modò
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oſtenſum fuit æquale Parabolæ AFD, quapropter totum triangulum AED
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erit ſeſquialterum ſemi-Parabolæ ABD, vel erit vt 6 ad 4, ſed ad triangulum
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ABD eſt vt 6 ad 3; </
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<
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">quare ſemi - Parabole ABD ad inſcriptum triangulum
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ABD erit vt 4 ad 3, & </
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<
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xml:space
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">duplum ad duplum, hoc eſt Parabole ABC ad trian-
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gulum ABC, ſuper eadem baſi AC, & </
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<
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xml:space
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">eiuſdem altitudinis cum Parabola,
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erit vt 4, ad 3, nempe ſeſquitertium. </
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<
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">Sed iam tempus eſt vt ſuſceptum opus aggrediamur, initio facto à defini-
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tionibus.</
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I.</
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">CONI SECTIONES ÆQVALITER INCLINAT Æ
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vocentur illę, quarum ordinatim ductæ æquales inuicem
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angulos cum earum diametris efficiunt.</
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<
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">Videlicet coni - ſectio ABC vocabitur æqualiter incli-
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nata, vel eiuſdem inclinationis, ac ſectio conica DEF, cum
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vtriuſque ordinatim ductæ AGC, DHF, earum diametros
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BG, EH, ad æquales diuidunt angulos, hoc eſt cum an-
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gulus AGB, angulo DHE, & </
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<
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">qui ei deinceps CGB reli-
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quo FHE æqualis fuerit.</
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<
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<
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