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

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148124 cioppoſitas, ſit infinitæ extenſionis, ſecaret omnino Parabolen AGC, vt
per ſe patet: quapropter Hyperbole ABC erit _MINIMA_ circumſcripta quę-
ſita. Quod ſecundò faciendum, ac demonſtrandum erat.

MONITVM.

HAEC de MAXIMARVM, & MINIMARVM coni- ſe-
ctionum, circuli, & anguli reciproca inſcriptione, ac circumſcri-
ptione, per punctum in ipſis, vel intra, vel extra datum, iuxta
ſæpius memoratam definitionem, hactenus pertractaſſe ſuffi-
iat, quæ ſi grata vobis fuiſſe perceperimus, multa his ſimilia, & alia
quàm plurima ad aliud tempus proferemus. Cæterum, in proximè ſequenti-
bus, quæ ad vberiorem doctrinam, & alteri præſertim huius operis parti ma-
xime conducunt, hac omiſſa definitione, inſcriptio, & circumſcriptio aliter fiet,
prout in ipſis propoſitionibus exponetur.

LEMMA XI. PROP. LXXIX.

Si recta AB ſecta fuerit in C, & in D, ita vt AB ad BC, ſit vt
AD ad DC: Dico ſi BD bifariam ſecetur in E, punctum E cadere
inter B, & C, & rectangulum AEC, æquari quadrato ED.

CVm ſit enim AB ad BC, vt AD ad DC, erit permu-

114[Figure 114] tando BA ad AD, vt BC ad CD, ſed eſt BA ma-
ior AD, quare BC erit maior CD: ex quo punctum E
bifariam ſecans BD cadit inter B, & C.

Ampliùs producatur BA ad F, & ſecetur AF æqualis
AD.

Iam cum demonſtratum ſit eſſe BA ad AD, vt BC ad
CD, erit BA ad AF, vt BC ad CD; & componendo BF
ad FA, vt BD ad DC; & ſumptis antecedentium dimi-
dijs, EA ad AF, ſiue ad AD, vt ED ad DC, & per con-
uerſionem rationis, AE ad ED, vt DE ad EC, vnde re-
ctãgulum AEC ęquabitur quadrato ED. Quod erat, & c.

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