Viviani, Vincenzo - De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei

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126102 plicentur. Dico ipſam eſſe quæſitam. Cum enim ſit CB media proportio
11Coroll.
prop. 1. h. nalis inter altitudinem BA, & latitudinem BE, erit BC, itemque ei æqua- lis BD, deſcriptæ ſectionis ſemi-applicata, nempe ſectio per C, & D omni-
no tranſibit; eſtque A vertex, AB diameter, & AF tranſuerſum Hyperbole,
aut Ellipſis, ex conſtructione: quare factum eſt quod erat propoſitum.

COROLL.

EX hac conſtat quomodo, magnitudine, & poſitione datis tranſuerſo la-
tere, aut diametro AF, & vna applicatarum CD, per terminos, A, C,
F, D, Ellipſis deſcribi poſſit.

THEOR. XXIX. PROP. LIIX.

Si coni-ſectionem, vel circuli circumferentiam duæ rectæ lineæ
contingant, ipſæ productæ conuenient ſimul extra ſectionem; ſed
in Parabola, vel Hyperbola ſibiipſis occurrent ad partes periphe-
riæ à contactibus terminatę: In Ellipſi verò ad partes ſui ipſius por-
tionis à linea tactus iungente abſciſſæ, in qua centrum nõ reperitur.

ESto Parabole, vel Hyperbole ABC (nam de circulo, & Ellipſi id ab
Apollonio oſtenſum fuit in vigeſima ſeptima ſecũdi conicorum) quàm
in punctis A, C tangant rectæ AD, CE.

91[Figure 91] Dico, ſi producantur ad partes ſectionis
ABC à contactibus A, C terminatæ ipſas
inter ſe conuenire.

Si enim per alterum contactuum, vt per
C, intelligatur fectro ris diameter H C G,
2224. 25.
pr. conic. certum eſt contingentem A D, ſi produ- catur, cum diametro HG extra ſectionem
conuenire, hoc eſt ad partes G; ſiergo AD
ſecat CG, neceſſariò ſecabit priùs tangen-
tem CE, quæ cadit inter ſectionis periphe-
riam ABC, & diametrum HC: quare tan-
gentes AD, CE ſibi ipſis occurrunt. Quod
erat, & c.

ALITER.

CVm recta CE ſectioni occurrat, & producta ex vtraque parte extra ſe-
ctionem cadat, ſi ex puncto A, quod eſt in ſectione, ducta ſit AF, ipſi
EC æquidiſtans, producta ex vtraque parte ſectioni occurret; ſed AD 3318. pri-
mi conic. cadit extra ſectionem, cum ſit contingens; quare AD non congruit cum AF,
ſed ipſę ſe mutuò ſecant. Cum ergo DA ſecet alteram æquidiſtantium AF, ſi
producatur, ſecabit, & reliquam CE ad partes peripheriæ ABC à contacti-
bus A, C, terminatæ. Quod demonſtrandum erat.

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