Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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& </
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<
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xml:space
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omnino incedere intra angulum L F I, & </
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<
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poſſit, cumque in ſecunda figura ſpatium F I B ſit occluſum ad I, & </
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rectam L B nunquam poſſit prouenire, eò quod ipſa L B ponatur Hyper-
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bole G F H aſymptotos: </
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<
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">in tertia verò cum ſpatium F I N ſit vndique oc-
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cluſum, neceſſariò, in vtraque figura, deſcripta Hyperbole G F H in ali-
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quo puncto datam ſectionem ſecabit. </
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<
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xml:space
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">Sit ergo harum mutua interſectio
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punctum M, per quod ductis, vt factum fuit in prima figura, rectis lineis
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quæ aſymptotis E D, E C æquidiſtent, ijſdem penitus argumentis, ac in
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primo caſu, demonſtrabitur ipſam Hyperbolen in nullo alio puncto quàm
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M cum data ſectione A B conuenire. </
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</
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<
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bus ductæ ſint aſymptotis æquidiſtantes, eiſque occurrentes: </
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cta linea iungens occurſus; </
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">lineæ, data puncta iungenti, æqui-
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diſtabit.</
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">ESto Hyperbole A B, cuius aſymptoti C D, C E, ſumptaque ſint in
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ſectione duo quælibet puncta A, B, à quibus ductæ ſint A F, B G,
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aſymptotis æquidiſtantes. </
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las.</
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ad aſymptotos in D, & </
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conic.</
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ma figura, B D æqualis A E: </
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da verò, cum ſit A D æqualis B E, ad-
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dita communi A B, erit item D B æ-
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qualis ipſi A E. </
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G, E A F, anguli ad D, B, æquantur
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angulis ad A, & </
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ob paralellas D G, A F, & </
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">quare triangula D B G, A E F ſunt ſimi-
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lia inter ſe, ac propterea vt D B ad B
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G, ita A E ad E F, ſed antecedentes
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D B, A E ſunt ęquales, vt modò oſten-
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dimus, ergo, & </
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æquales erunt, at ſunt quoque inter ſe
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parallelæ, quare, & </
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