Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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le, & </
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">quarum diametri ſint æquales, eſt ea, cuius diameter ſit axis
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dati anguli, vel Hyperbolæ.</
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">ESto primùm, in prima figura, A B C angulus rectilineus, circa axim B
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D, cui applicata ſit perpendiculariter quæcunque A E C, eum ſecans
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in E. </
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quorum diametri ſint æquales ipſi B E, _MAXIMVM_ eſſe A B C.</
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s
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laris ad A C, facto centro B in-
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teruallo B D, ac circulo deſcri-
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pto, eius peripheria continget re-
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ctam A C in D, anguli latera ſe-
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cans in F, K; </
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quales abſciſſorum triangulorum
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ad peripheriam F E K pertingẽt:
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</
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">ſumpto igitur in ipſa quocunque
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puncto G, iungatur B G, & </
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catur per G recta L G M ipſi A C
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æquidiſtans, axim ſecans in N,
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& </
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">erit L N æqualis N M, vnde
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L G minor G M; </
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O ipſi L G ęqualis, & </
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<
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parallela ad B A, iungaturque
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I G, & </
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ſecet in I, alteram quoque paral-
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lelam B A ſecabit in H, eritque I G æqualis G H, ſed anguli ad verticem
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I G O, H G L ſunt æquales, ergo, & </
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<
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">triangulum I G O triangulo H G L æ-
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quale erit, & </
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æquale triangulo H B I, ſed triangulum A B C maius eſt quadrilatero B L
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O I, totum ſua parte, quare triangulum A B C erit quoque maius triangulo
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H B I, cuius diameter B G æqualis eſt axi B E trianguli A B C, & </
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per de quolibet alio triangulo circa diametrum ipſi B E ęqualem; </
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triangulum A B C eſt _MAXIMVM_. </
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<
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">Sit præterea, in ſecunda figura, Hyperbole A B C, cuius centrum D,
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axis D B E, ex quo dempta ſit B E, eique per E applicata A E C, & </
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quælibet alia diameter D F G, ex qua ſumatur F G ipſi B E æqualis, appli-
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ceturque H G I. </
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<
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">Nam cum ſit ſemi-axis D B ſemi-diametrorum _MINIMA_, hæc erit
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ior D F, eſtque B E æqualis F G, quare D B ad B E minorem habebit ra-
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tionem quàm D F ad F G: </
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<
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bit D F ad F L minorem rationem quàm D F ad F G, ideoque F L maior
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erit F G, ſi ergo per L applicetur M L N, quæ ipſi H G I æquidiſtet, </
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