Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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C E ipſi B A parallela, vel ad eaſdem, vel ad oppoſitas partes, & </
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ducatur quælibet A D E vtranque B C, C E ſecans in D, & </
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">dico aggregatum triangulorum A D B, D C E ad triangulum A
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C B eſſe vt aggregatum extremarum poſt B D, D C, ad B C.</
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<
s
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">Iam triangulum D C E ad A D C eſt vt E D ad D A, vel vt C D ad
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D B, vel vt D F ad D C; </
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triangulum A D C ad trian-
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gulum A B C, eſt vt D C
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ad C B, ergo ex æquali triã-
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gulum D C E ad A B C, erit
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vt D F ad C B; </
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<
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lum A D B ad idem A B C
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eſt vt B D ad B C, quare
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duo ſimul triangula D C E,
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A D B, ad triangulum A C
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B, erunt vt duæ ſimul lineæ
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D F, D B, hoc eſt tota B F,
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aggregatum extremarum poſt B D, D C, ad B C. </
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conſtitutis, & </
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æquidiſtanter ducta, ad contrarias tamen partes, & </
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producta: </
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re ęquidiſtanti occurrentem, ita vt, cum ipſa bina ſimilia triangula
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ad verticem conſtituat, horũ aggregatum ſit MINIMA quantitas.</
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<
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">SInt A B, B C rectæ lineæ terminatæ ad quemcunque angulum A B C
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compoſitæ, ſitque C D in infinitum producta ipſi B A parallela, ſed ad
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oppoſit as partes rectæ C B: </
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<
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ita vt aggregatum ſimilium triangulorum A E B, C E D ad verticem E
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ſit _MINIMVM_.</
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exceſſum diametri ſuper latus: </
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tremarum proportionalium poſt B E, E C ſit _MINIMVM_ (per </
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