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

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127103

THEOR. XXX. PROP. LIX.

Si coni-ſectionem, vel circuli circumferentiam recta linea con-
tingat conueniens cum diametro, cui à tactu ſit ordinatim applica-
ta vſque ad ſectionem, recta linea iungens alterum terminum ap-
plicatæ, & occurſum tangentis cum diametro, erit eidem ſectioni
ad alteram diametri partem contingens.

SIt coni-ſectio quæcunque, vel circuli circumferentia ABC, cuius diame-
ter ſit DE, & ſit quæpiam AD ſectionem contingens in A, diametro oc-
currens in D, & ex contactu A ducta ſit in ſectione diametro DE ordinatim
applicata AC, dico iunctam DC ſectionem quoque contingere.

Si enim poſſibile eſt, quæ ex C ducitur

92[Figure 92] contingens, non ſit CD, ſed alia CF, quæ
1158. h. cum tangente AD conueniet, ſed in alio puncto quàm D, vt in F.

Iam cum FA, FC ſectionem contingant,
& per contactus ducta ſit AC, quæ bifariam
ſecta eſt à diametro D E in E, ſi iungatur
2229. ſe-
cundi co-
nic. FEG ipſa erit ſectionis diameter, hoc eſt bifariam ſecabit quamlibet aliã HI ipſi AC
æquidiſtanter ductam, vt in G, ſed D E L
quoque bifariam ſecat eandem HI in L, cum
DEL ſit diameter, per hypoteſim; ergo ea-
dem recta HI in duobus diuerſis punctis G,
& L bifariam diuiditur: quod eſt abſurdum. Non eſt ergo ex C alia contin-
gens linea quàm CD. Quod erat,

Cum Propoſitionum 13. ac 14. ſept. Pappi, in hac noſtra tractatione fre-
quens ſit vſus, liceat hac eas transferre, vtranque ſimul ſequenti Theo-
remate demonſtrare.

THEOR. XXXI. PROP. LX.

Rectangulorum ſub partibus datæ rectę terminatæ MAXIMVM
eſt id, quod ab æqualibus ſegmentis producitur; reliquorum verò
id, quod fit à partibus minus inæqualibus, maius eſt eo, quod ab
inæqualioribus continetur.

SIt data recta linea AB terminata bifariam ſecta in C, & non bifariam
vtcunque in D, E, & c. Dico, & c.

Cum enim recta AB ſecta ſit bifariam in C, & non bifariam in D, erit
quadratum AC, ſiue rectangulum ACB, æquale rectangulo ADB,

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