Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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xml:space
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s
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alterius ſimilis, & </
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40. huius.</
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ptoti, & </
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G ſit G 2, regulis HI, LM parallela, recta latera ſecans in 2, & </
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æqualis GL, & </
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">GB æqualis GH, erit E 3 æqualis 3 M, & </
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ſiue 3 4, quare E 4 eſt aggregatum E 3 cum B 2. </
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<
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GE 3 ſit quarta pars rectanguli LEM, & </
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<
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li ſubquadruplum, ergo quadratum EY ęquatur rectangulo GE 3: </
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que ratione eſt quadratum BX æquale rectangulo GB 2, ſed rectangulum
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GE 3 excedit rectangulum GB 2 rectangulo BE 4, ſiue quadrato KE,
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1. huius.</
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re quadratum EY ſuperat quadratum BX quadrato EK: </
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plicatis AN, QS vſque ad communes aſymptotos, ipſas, ac ſectiones ſecan-
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tibus in 5 ADFC 6, & </
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lo 5 D 6, & </
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exceſſus æquatur exceſſui rectãgulorum, ſed exceſſus quadratorum eſt qua-
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dratum EK, & </
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pt. Pappi.</
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ADC; </
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">eademque ratione
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oſtendetur idem quadratum EK æquale rectangulo QR 8, quare rectangu-
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la ADC, QR 8 inter ſe ſunt æqualia, ideoque R 8 ad DC, vt DA ad QR,
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ſed eſt R 8 maior DC (cum ſit RS maior DN, & </
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erit maior QR, & </
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dum.</
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ctas ad interuallum peruenire minus quolibet dato interuallo R
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. </
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eadem penitus conſtructione, ac in vltima parte 42. </
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nitur, non abſimili eiuſdem argumento demonſtrabitur. </
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ſos vertices ſimul adſcriptarum, Aſymptotos communes eſſe.</
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gula ſegmentorum applicatarum vtranque Hyperbolen ſecantium,
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qualia ſunt rectangula ADC, QR8, omnia inter ſe æqualia eſſe.</
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rollarijs oſtendimus, vniuerſaliùs ſequenti Theoremate demonſtrabitur.</
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