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

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211

DE MAXIMIS, ET MINIMIS

Geometrica diuinatio in V. conic.
Apoll. Pergæi.

LIBER PRIMVS.

MONITVM.

_A_NTEQV AM inſtitutum opus aggrediamur, ſiquidem in
ipſo frequenter accider vti, proferreque affectiones propoſi-
tionum 11. 12. ac 13. primi conic. non erit fortaſſe omninò
incongruum meas earundem demonſtrationes hic exhibere,
quales olim, cum primùm ad elementa conica me conuerte-
rem, aliter ac breuius vnico tantùm Theoremate concludi poſſe animaduer-
ti, eaſque proponi enunciationibus, vtirebar genuinis, ac proximis ad trium
coni-ſectionum, Parabolæ, nempe, Hyperbolæ, & Ellipſis laterum inuen-
tionem. Verùm antea mihi detur, vt quibuſdam morem gerens, qui tres
prædictas Apollonĳ propoſitiones difſiciles admodum exiſtimant, ob nimium
in ea vſum 23. ſexti Elementorum; earundem demonſtr ationes ſingillatim
afferre poſsim eodem penitus modo, quo aliquibus, voce, & ſcriptis expli-
care ſolitus fui, hoc eſt ſine compoſita proportione, quam, neſcio quaratione
faſtidiant.

Stantibus igitur ĳſdem hypoteſibus, expoſitionibus, ac conſtructionibus
prædictarum Apoll. propoſitionum, adhibitiſque figuris, quæ ibi in Comman-
dini verſione.

_QVo ad 11. primi conic. poſt ea verba_ Rectangulum igitur MLN æquale eſt
quadrato K L ſequatur ſic.

Itaque, quoniam quadratum BC ad rectangulum BAC eſt vt HF
ad FA ex conſtructione, & rectangulum BAC ad rectangulum ACB vt AB
ad BC, vel vt ablata BF ad ablatam BG, hoc eſt vt reliqua FA ad reliquam
GC, ſiue ad LN, ergo ex æquo quadratum BC ad rectangulum ACB, vel
recta BC ad CA, vel BG ad GF, vel ML ad LF, erit vt HF ad LN, ideoque
rectangulum ſub extremis ML, LN, ſiue quadratum KL æquatur rectangu-
lo HFL. _Vocetur autem huiuſmodi ſectio & c._ vt ibi vſque ad finem.

Quo ad 12. primi poſt ea verba, _ergo rectangulum RNS æquale eſt MN qua-_
_drato_, ſic dicatur.

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