Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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<
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xml:space
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nor A C, centrum E, & </
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<
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<
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ctas in ſectione applicare quales inuenire propoſuimus.</
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<
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<
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xml:space
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<
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xml:space
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">Dico rectangulum G F H eſſe _MINIMVM, MAXIMVM_ verò I F L.</
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<
s
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plicata M F N, & </
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<
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M O N ſit vertex O, atque ex
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axium verticibus A, B, vti e-
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tiam ex O agantur contingen-
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tes A P, B Q, P O Q, quæ ſi-
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mul occurrent in R, P, Q.</
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mih.</
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Erit ergo rectangulum G F H
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ad I F L, vt quadratum B
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conic.</
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ad quadratum A R, ſed eſt
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contingens B R, minor A
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huius.</
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ſiue quadratum B R minus quadrato A R, ergo, & </
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<
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minus erit rectangulo I F L.</
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</
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<
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xml:space
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">Præterea rectangulum G F H ad M F N eſt vt quadratum B Q ad qua-
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dratum O Q, ſed eſt contingens B Q minor contingente O Q, ſiue
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dratum B Q minus quadrato O Q, ergo rectangulum G F H minus eſt re-
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ctangulo M F N, & </
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<
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re rectangulum G F H eſt _MINIMVM_ quæſitum.</
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<
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xml:space
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huius.</
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quadratum QP, ſitque contingens A P maior contingente Q P erit
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huius.</
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dratum A P maius quadrato Q P, ergo rectangulum quoque I F L maius
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erit rectangulo N F M, & </
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<
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applicatas I F L, G F H quare rectangulum I F L eſt _MAXIMVM_ quæſi-
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tum. </
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tantùm voco omnem figuram planam, circa diametrum, in alteram par-
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tem deficientem, & </
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<
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in qua omnes rectæ lineæ A
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C, E F, G H, &</
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<
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rimetro terminatæ, ac inter ſe
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æquidiſtantes, à quadam re-
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cta B D bifariam ſecentur, & </
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in alteram partem, vt puta ad
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B, continuò decreſcant, do-
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nec abeant in punctum B, ſit-
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que earum perimeter A G B H C ad eaſdem partes cauus vocetur </
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