Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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plicentur. </
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<
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<
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xml:space
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prop. 1. h.</
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nalis inter altitudinem BA, & </
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<
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xml:space
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">latitudinem BE, erit BC, itemque ei æqua- lis BD, deſcriptæ ſectionis ſemi-applicata, nempe ſectio per C, & </
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<
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no tranſibit; </
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<
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aut Ellipſis, ex conſtructione: </
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tere, aut diametro AF, & </
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<
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F, D, Ellipſis deſcribi poſſit.</
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contingant, ipſæ productæ conuenient ſimul extra ſectionem; </
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<
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in Parabola, vel Hyperbola ſibiipſis occurrent ad partes periphe-
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riæ à contactibus terminatę: </
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">In Ellipſi verò ad partes ſui ipſius por-
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tionis à linea tactus iungente abſciſſæ, in qua centrum nõ reperitur.</
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Apollonio oſtenſum fuit in vigeſima ſeptima ſecũdi conicorum) quàm
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in punctis A, C tangant rectæ AD, CE.
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Dico, ſi producantur ad partes ſectionis
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ABC à contactibus A, C terminatæ ipſas
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inter ſe conuenire.</
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<
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<
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C, intelligatur fectro ris diameter H C G,
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pr. conic.</
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certum eſt contingentem A D, ſi produ- catur, cum diametro HG extra ſectionem
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conuenire, hoc eſt ad partes G; </
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ſecat CG, neceſſariò ſecabit priùs tangen-
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tem CE, quæ cadit inter ſectionis periphe-
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riam ABC, & </
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gentes AD, CE ſibi ipſis occurrunt. </
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erat, &</
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ctionem cadat, ſi ex puncto A, quod eſt in ſectione, ducta ſit AF, ipſi
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EC æquidiſtans, producta ex vtraque parte ſectioni occurret; </
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<
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mi conic.</
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cadit extra ſectionem, cum ſit contingens; </
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ſed ipſę ſe mutuò ſecant. </
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<
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producatur, ſecabit, & </
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<
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bus A, C, terminatæ. </
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