Full text: Viviani, Vincenzio: De maximis et minimis, geometrica divinatio

176. THEOR. XXXIX. PROP. LXXXIII.

Si binarum Ellipſium ſimul adſcriptarum altera alteri fuerit in-
ſcripta, & per terminos communis applicatæ ſe mutuò contingant; quælibet alia Ellipſis datis adſcripta, cum eadem applicata, & cum æquali tranſuerſo latere, inſcriptam Ellipſim omnino ſecabit.

SInt duæ Ellipſes ABCD, AECF ſimul adſcriptæ, circa communem ap-
plicatam AC, ſitque ipſarum altera, nempe AECF, alteri inſcripta, ita
vt in extremis tantùm A, C, ſe mutuò contingant: dico, ſi his alia adſcriba-
tur Ellipſis ALCI, circa eandem applicatam AC, & cum tranſuerſo LI,
quod æquale ſit ipſo BD tranſuerſo circumſcriptæ, ipſam ALCI omnino ſe-
care inſcriptam AECF.

Nam ſi alterum extremum tranſuerſæ
diametri LI, quale eſt punctum L, cadat
intra inſcriptam, vt inter E, & O, tunc aliud
extremum I neceſſariò cadet extra, infra F,
cum ſit LI, ſiue BD maior EF, ex quo ma-
nifeſtè patet, Ellipſim ALCI ſecare inſcri-
ptam AECF.

176.1.

0153-01

Si verò vtrunque extremum L, I, cadit
extra inſcriptam, vti exhibetur ab hac figu-
ra; tunc ducta AG, quæ circumſcriptam
ABCD contingat in A, ipſa, vtrinque pro-
ducta, ad alteram partium ſecabit omni- no ALCI; vnde, quæ ex A cõtingit ALCI,
diuerſa erit ab AG, & ſit ipſa AM.

176.1.

81. h.

Iam ſi ALCI non ſecat inſcriptã AECF; contingat in A, C, ſi poſſibile eſt. Cum ergo recta AM contingat Ellipſim
ALCI, atque hæc contingat inſcriptam Ellipſim AECF, eadem recta AM,
in A quoque continget AECF, ſed etiam AG eandem AECF contingit in
A: quare ex eodem puncto A ductæ erunt binæ rectę lineę eandem Ellipſim
contingentes; quod eſt impoſſibile. Non igitur Ellipſis ALCI contingit inſcriptam AECF, quapropter in occurſibus A, C neceſſariò eam ſecabit,
Quod oſtendere propoſitum fuit. Sed hoc idem

176.1.

ex 32.
pr. conic.

177. ALITER affirmatiuè.

CVm recta AG contingat ad A circumſcriptam Ellipſim ABCD, atque
hæc ad idem A contingat inſcriptam AECF, ipſa AG omninò con-
tinget ad A inſcriptam AECF; ſed MA (quę vt ſupra oſtendimus, diuerſa eſt
à GA) hanc ſecat in A; quare MA producta, ad alteram partium omninò
ſecabit inſcriptam AECF, & eò magis Ellipſis ALCI, quam contingit ad A
recta MA, ad eandem partem ſecabit inſcriptam AECF. Quod erat, & c.

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