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

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19513 bita tamen ratione proportionis inter minorem axim, & maiorem, quæ
proportio, quò minor fuerit, eò magis E, terminus ſemi - recti lateris,
remouebitur à centro H, vt vel modicè introſpicienti ſatit conſtat.

THEOR. VI. PROP. X.

Si quamcunque coni - fectionem recta linea contingat, cui à
tactu extra ſectionem perpendicularis erigatur, in qua ſumptum
ſit quodlibet punctum. Linea intercepta inter aſſumptum pun-
ctum, & contactum, erit MINIMA ducibilium ab eodem pun-
cto, ad conuexam coni-ſectionis peripheriam.

ESto coni-ſectio A B C, quam contingat recta D E in B, à quo ipſi
erecta ſit perpendicularis B F ad partes conuexæ peripheriæ ABC,
ſitque in ea aſſumptum quodlibet punctum F. Dico rectam F B eſſe _MI-_
_NIMAM_ rectarum ducibilium ab F ad conuexam peripheriam A B C.

Hoc enim per ſe ſatis patet: nam cum

155[Figure 155] F B ſit perpendicularis rectæ D E, erit
quoque _MINIMA_ ducibilium ad 11ex ele-
mentis. D E, quare F B eò magis erit _MINIMA_
ducibilium ad conuexam A B C, quę ca-
dit infra D E. Quod erat, & c.

Quod autem de coni - ſectione hoc
loco oſtenditur, de quacunque etiam
curua linea verificari ex ipſa figura ſatis
patet, dummodo curua A B C ſit tota ad
alteram partem contingentis D E, per-
pendicularis verò B F ad aliam.

THEOR. VII. PROP. XI.

Si quamcunq, coni-ſectionem recta linea, pręter ad axis ver-
ticem contingat, cui à tactu intra ſectionem erigatur perpendi-
cularis, in qua ſumptum ſit punctum quodlibet, non tamen, quò
ad Ellipſim, vltra maiorem axim; linea intercepta inter aſſum-
ptum punctum, & contactum erit MINIMA ducibilium ex eo-
dem puncto, ad coni- ſectionis peripheriam.

Si verò in Ellipſi aſſumptum punctum in perpendiculari fue-
rit, vel in ipſo minori axe, vel vltra: linea inter punctum, &
contactum intercepta erit MAXIMA ducibilium ex ipſomet pun-
cto ad Ellipſis peripheriam.

ESto A B C Parabole, vel Hyperbole, vt in prima figura, vel Ellipſis,
vt in ſecunda, circa maiorem axim B D, quas in puncto A

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