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

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150126 ABC, erit DB æqualis BF; cumque AH contingat AGC erit DG 1135. pri.
conic. GH, ſed eſt DB maior DG ex conſtructione, quare, & BF erit maior GH, &
GF eò maior GH: quod memento.

22ibidem.

Præterea, in ſecunda figura, cum ſit LB, æqualis MG, & BD maior GD,
ex conſtructione, habebit LB ad BD minorem rationem, quàm MG ad GD,
& componendo LD ad DB, ſiue LF ad FB minorem quàm MD ad 3336. pri-
mi conic. ſiue quàm MH ad HG, & iterum componendo LB ad BF, minorem 44ibidem. MG ad GH, ſed eſt LB æqualis MG, quare BF erit maior GH, & eò magis
GF maior GH.

117[Figure 117]

Intertia denique, cum ſit LB æqualis MG, & DB maior DG, ex conſtru-
ctione, habebit LB ad BD minorem rationem, quàm MG ad GD, & diui-
dendo LD ad DB ſiue LF ad FB, minorem quàm MD ad DG, vel 5536. pri-
mi conic. MH ad HG, & diuidendo iterum, LB ad BF minorem rationem, quàm MG
66ibidem. ad GH, ſed eſt LB æqualis MG, ergo BF maior erit GH, & eò magis GF
maior GH.

Itaque cum demonſtratum ſit in qualibet figura eſſe GF maiorem GH,
punctum H incidet infra F; ſed HAI contingit ſectionem AGC in A, qua-
re FA, quæ contingit ABC, ſi producatur ad partes E, ſecabit ipſam ſectio-
nem ABC, cum inter ſectionem, & contingentem, ex puncto contactus al-
tera recta linea non cadat: quare, & c. Quod erat, & c.

7732. pri-
mi conic.

PROBL. XXXII. PROP. LXXXII.

Dato angulo rectilineo, vel coni-ſectione, vel circulo, perter-
minos, cuiuſcunque in ipſo applicatæ, MAXIMAM Ellipſim in-
ſcribere, cuius tranſuerſum latus æquale ſit dato.

Oportet autem, ſi data ſectio ſuerit Ellipſis, datum tranſuerſum
minus eſſe diametro datæ Ellipſis, ad quam data applicata ordi-
natim ducitur.

ESto ABC datus angulus, vt in prima figura, vel Parabole, vt in ſecunda;
vel Hyperbole, vt in tertia; vel tandem Ellipſis, aut circulus, vt

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