Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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<
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">Si in angulo A B C applicatæ fuerint quotcunque rectæ lineæ
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A C, D E, &</
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">quæ a quacunque alia recta F
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G vtrique lateri dati anguli occurrente in F, G, ſecentur in
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H, I, &</
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gulum FIG, ad AIC.</
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">ETenim ratio rectanguli F
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H G ad D H E, com-
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ponitur ex ratione F H ad H
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D, ſiue ex F I ad I A; </
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ratione G H ad H E, ſiue ex
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G I ad I C; </
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ctanguli F I G ad A I C ex
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ijſdem rationibus componi-
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tur, quapropter rectangulum
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F H G ad D H E, eſt vt re-
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ctangulum F I G ad A I C.
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</
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do, rectangulum F H G ad FIG, vt rectangulum D H E ad AIC.</
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<
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">Si fuerint duæ æquales portiones de eodem angulo, vel de
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eadem coni - ſectione, vel circulo, & </
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vnius portionis applicata ſit in angulo, vel ſectione quædam
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recta linea baſi alterius portionis æquidiſtans: </
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ſegmentis huius applicatæ æquabitur quadrato ſemi - baſis eiuſ-
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dem portionis, cui hæc ipſa applicata æquidiſtanter ducta fuit.</
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<
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">SInt de eodem angulo, vt in præſenti figura, vel de quacunque coni-ſe-
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ctione, vt in figuris tertij Schematiſmi, abſciſſæ duæ æquales portio-
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nes A B C, H E I (vti docuimus in præcedenti, atque ex quadrageſima
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huius abſolui poſſe elicitur) quarum diametri ſint B F, E G baſes verò
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ſint A C, H I ab ipſis diametris bifariam ſectæ in F, G. </
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<
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75. h. &
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per 1. Co-
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roll. 40. h.</
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baſes omninò ſe mutuò ſecare, atque inter portionum diametros vt in
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M, ſiue, punctum earum occurſus M differre à punctis medijs F, G.
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<
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plicetur in angulo, vel ſectione recta S G T parallela alteri baſi A C, hæc
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omnino ad vtranque partem cum anguli lateribus, vel cum ſectione conue-
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niet, cumipſa ſit vna applicatarum ad diametrum B F. </
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<
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T: </
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<
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C æquale eſſe.</
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