Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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diametro DE deſcribatur Parabole ADG, cuius AE ſit eius ſemi-applicata:
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</
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<
s
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xml:space
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">dico primum Parabolen ADG, etiam ſi in infinitum producatur, totam ca-
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dere intra ABC, & </
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>
<
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xml:space
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">ſi ex A ducatur quæcunque ANMH, ipſam à Parabola
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ADG ſecari in O, in eadem ratione, ac AC ſecatur in G, & </
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<
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xml:space
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">AB in D.</
s
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<
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">Ducta enim ex A recta AP contingente Parabolen ABC, erit FB æqualis
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BP; </
s
>
<
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xml:space
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">ideoque ED æqualis DR, vnde AR continget Parabolen ADG, & </
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<
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xml:space
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">AH
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ſecabit ipſam in O.</
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<
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<
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<
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">Iam ductis ex H, O, ſemi - applicatis HI, OL, erit, ob Parabolen, FB ad
<
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BI, vt quadratum AF ad HI, vel vt quadratum FM ad quadratum MI; </
s
>
<
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xml:space
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">qua-
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re per Lemma præcedens, erit FB ad BM, vt BM ad BI, & </
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<
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<
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">eiuſ-
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dem, in vtraque figura, erit FM ad MI, vt FB ad BM; </
s
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<
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">eadem penitus ratio-
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ne oſtendetur eſſe EN ad NL, vt ED ad DN, ſed eſt FB ad BM, vt ED ad
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/>
DN, quare & </
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>
<
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">FM ad MI erit vt EN ad NL, ſed FM ad MI, eſt vt AM ad MH,
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& </
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>
<
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xml:space
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">EN ad NL, vt AN ad NO, quare AM ad MH erit vt AN ad NO, & </
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>
<
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">in pri-
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ma figura conuertendo, componendo, & </
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>
<
s
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">permutando, HA ad AO, vt MA
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ad AN; </
s
>
<
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xml:space
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">in ſecunda verò per conuerſionem rationis, conuertendo, & </
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>
<
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">per-
<
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mutando HA ad AO erit vt MA ad AN. </
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<
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xml:space
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">Eſt igitur in vtraque figura HA ad
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AO, vt MA ad AN, vel vt BA ad AD, ſed eſt BA maior AD ex conſtru-
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ctione, quare & </
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<
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">HA erit maior AO, ſed HA tota eſt intra Parabolen ABC,
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vnde punctum O, quod eſt in Parabola ADG erit intra Parabolen ABC, & </
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ſic de quocunque alio puncto Parabolæ ADG, etiam ſi ducta AH cadat in-
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fra AC; </
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<
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">quare ipſa cadit tota intra ABC: </
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">& </
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">cum ſit HA ad AO, vt BA ad
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AD, vel vt FA ad AE, vel ſumptis duplis, vt CA ad AG, erit diuidendo
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HO ad OA, vt CG ad GA. </
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<
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