Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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L, & </
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ipſi E A, & </
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<
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D, G M ad E A, & </
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erit triangulum A D E ſimile triã-
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gulo M F G, & </
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">triangulum E D B
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ſimile triangulo G F N, quare vt
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A D ad D E, ita M F ad F G, & </
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vt E D ad D B, ita G F ad F N;
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">ſuntque A D, D E, D B continuę
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proportionales, vnde M F, F G,
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F N, erunt quoque proportiona-
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les, ſiue rectangulum M F N ęqua-
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bitur quadrato F G.</
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contingat, & </
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gulus D E B æqualis angulo B A
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E, ſed (cum triangula B E C, B A
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E in ſemicirculo ſint ſimilia) eſt
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quoque angulus B E C, æqualis
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lis angulo B A E, ergo angulus
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D E B, ſiue alternus E I G æqua-
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lis erit angulo B E C, ergo linea
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G I ipſi G E æqualis. </
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lus O E A æquatur angulo A B E in alterna portione, ſiue angulo A E C,
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eſtque angulus O E A alterno G L E æqualis, vnde anguli A E C, G L E
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æquales erunt, quare linea G L æqualis eidem G E; </
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<
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">erunt ergo L G, G I
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inter ſe æquales, ſed eſt G F maior I F, habebit ergo L G ad G F mino-
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rem rationem quàm G I ad I F, & </
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ad F M minorem rationem quàm G F ad F I, vel quàm N F ad F B, qua-
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re rectangnlum ſub extremis A F, F B, minus erit rectangulo ſub
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Pappi.</
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dijs M F, F N, ſiue minus quadrato F G. </
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occurrat vltra D; </
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rallelarum, item demonſtrabirur _I G_ ipſi _G L_ æqualem eſſe, & </
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fimili conſtructione, demonſtratio, & </
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ſupra.</
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primi co-
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nic.</
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contingentem lineam ducere.</
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datum in ſectione punctum ſit A, extra verticem B: </
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datæ ſectioni contingentem lineam ducere.</
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