Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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ptoti coniugatis diametris æquidiſtent; </
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punctis Ellipſis peripheriam ſecabit.</
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">ESto Ellipſis A B C D, cuius centrum E, & </
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A C, B D quibus ductæ ſint F G, H C ipſis diametris altera alteri ę-
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quidiſtantes, & </
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">cum aſymptotis G F, G H, per
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centrum E, deſcripta ſit Hyperbole I E L. </
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">Dico hanc, Ellipſis periphe-
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riam in duobus tantùm punctis ſecare.</
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<
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ſumptum ſit punctum E, per
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quod ductæ ſunt A E C, D E B
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aſymptotis æquidiſtantes, ipſæ
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in puncto tantùm E ſectioni oc-
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current, & </
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lo B E A, inter E A, & </
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ſemper incedet, pariterque in
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angulo C E D, inter E D, & </
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G H; </
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">ſed anguli B E A, C E D
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terminantur à peripherijs B A,
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C D, quare Hyperbole ex vtra-
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que parte producta ipſas peri-
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pherias omninò ſecabit, vt in
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I, L. </
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">Si ergo ex I ducantur M
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I N, O I F diametris æquidiſtã-
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tes, ob eandem rationem ſupe-
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riùs allatam ſectio E I P, in nullo alio puncto, quàm I cum rectis N I M,
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F I O conueniet, ſed ipſæ N I M, F I O nil aliud commune habent
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cum peripheria quadrantis A B, quàm idem punctum I, quare
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Hyperbole E I P in vno tantùm puncto I Ellipſis periphe-
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riam ſecabit in quadrante A B. </
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& </
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">argumento, oſtendetur ſectionem E L Q in
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alio puncto quàm L peripheriam D C non
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ſecare: </
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<
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">quare huiuſmodi Hyperbole in
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duobus tantùm punctis ſecat El-
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lipſis peripheriam. </
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erat demonſtrandum.</
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