Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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caret rectam G I, vt in L, tunc G L æquaretur ipſi H B, ideoque G
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conic.</
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G L inter ſe æquales eſſent, totum, & </
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">Cum ergo puncta I, A cadant in oppoſitas ſectiones, iunctaque ſit I
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A ſecans rectas C O, C D continentes angulum O C D, qui deinceps eſt
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angulo D C E ſectionem A B continenti erunt ex ipſa abſciſſæ lineæ
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I, N A inter aſymptotos, & </
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ducantur F A, F B vſque ad aſymptotos in D, E, agaturque ex I recta
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I O æquidiſtans ad C D. </
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">Cumque triangulorum I O M, N D A, baſes I
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M, N A ſint in directum conſtitutæ ſintque latera I O, N D; </
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inter ſe parallela, ſingula ſingulis, erunt quoque anguli ad I, & </
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etiam ad M, & </
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æquales, vt ſuperiùs demonſtratum fuit, quare, & </
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A D æqualia erunt.</
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">Præterea cum ſit linea B G æqualis H I, erunt quoque E G, C O inter
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ſe æquales (ob æ quidiſtantiam linearum I O, H C, B E,) quibus addita
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communi G C in prima, ſecunda, & </
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ta, proueniet E C, æqualis ipſi G O, ſed F D, E C ſunt æquales (nam
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ſunt latera oppoſita in parallelogrammo C F,) quare F D ipſi G O ęqua-
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lis erit; </
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æquales erunt, at ſunt quoque parallelæ, vnde G F, I A inter ſe ęquidi
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ſtabunt. </
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inæqualitatis, & </
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ad F.</
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G erit quæſitum. </
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erit componendo A G ad G C,
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vt D E ad E H, velad F. </
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faciendum erat.</
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dat infra B, patet. </
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poteſi, A B ad B C habet mi-
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norem rationem quàm D E ad
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F, vel ad E H, quare diuiden-
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do A C ad C B habebit mino-
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rem rationem, quàm D H ad H
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E, vel quàm eadem A C ad C
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G; </
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punctum G cadit infra B. </
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