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

## 289.THEOR. XXXI. PROP. L.

MAXIMA portionum eiuſdem anguli rectilinei, vel cuiuſcunq; coni-ſectionis, quarum baſes ſint æquales, eſt ea, cuius diameter
ſit ſegmentum axis, vel maioris ſemi- axis (reſpectiuè ad Ellipſim)
datæ ſectionis. MINIMA verò in Ellipſi eſt, cuius diameter ſit ſe-
gmentum minoris ſemi- axis.

ESto A B C angulus rectilineus, vt in prima figura; vel Parabole, aut
Hyperbole, vt in ſecunda; vel Ellipſis, vt in tertia, quarum axes ſint B
D, & in Ellipſi axis maior ſit B D N, minor L K M, centrum E, atque ma-
iori axi in quauis figura applicata ſit quęcunque A D C. Dico primùm por-
tionem A B C, quæ tamen in tertia figura ſit minor ſemi-Ellipſi L B M, eſſe
_MAXIMAM_ omnium portionum eiuſdem anguli, vel coni-ſectionis, qua-
rum baſes æquales ſint baſi A C.

Nam, in prima figura, deſcribatur per D in angulo aſymptotali A B C
Hyperbole F D G, in ſecunda verò, ſi A B C fuerit Parabole, deſcribatur per
D congruens Parabole F D G, vel ſi fuerit Hyperbole, deſcribatur item per
D, vti etiam in tertia, eiuſdem nominis ſectio F D G ſimilis, & concentri-
ca ipſi A B C, & tunc recta A D C continget omnino ſectionem F D G in
D; ſumptoque in interiori ſectione F D G quolibet puncto F, per ipſum
ducatur ſectionem contingens H F I exteriori occurrens in H I, deque ipſa
abſcindens portionem H O I, cuius diameter ſit O F.

Iam, in ſingulis ſiguris, baſis A C minor eſt baſi H I, cum ſit _MINIMA_ contingentium ſectionem F D G, quare, & dimidium D C dimidio F I mi-
nus erit. Fiat ergo F P æqualis D C, & ex P agatur P R diametro F O
æquidiſtans, cui ex R applicetur R Q S: patet ipſam R Q S ęquari baſi A C,

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