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

ctiones contingentes, quæ productæ, communi diametro G B E occurent in L, M. Dico primùm G A ad A D eſſe vt G B ad B E, & contingentes
A L, D L inter ſe æquidiſtare.

279.1.

47. ibid.
24. 25.
primi co-
nic.

Applicentur ex A, D ad diametrum communem G B M rectę A I, D H. Erit iam in ſectione D E F, rectangulum G H M ad quadratum H D, vt tranſuerſum ad rectum, vel, ob ſectionum ſimilitudinem, vt tranſuerſum ſe-
ctionis A B C ad eius rectum, vel vt rectangulum G I L ad quadratum I A,
& quadratum D H ad H G, eſt vt quadratum A I ad I G, ergo ex æquo
rectangulum G H M ad quadratum G H, erit vt rectangulum G I L ad qua-
dratum I G, & conuertendo quadratum G H ad rectangulum G H M, vt
quadratum I G ad rectangulum G I L, & per conuerſionem rationis in pri-
ma figura, & componendo in ſecunda, quadratum G H ad rectangulum. H G M, vt quadratum I G ad rectangulum I G L, & permutando quadra-
tum H G ad G I, vel quadratum D G ad G A, erit vt rectangulum H G M
ad rectangulum I G L, vel permutatis æqualibus, vt quadratum E G ad quadratum G B, ſeulinea D G ad G A, vt linea E G ad G B, & diuiden-
do, & conuertendo G A ad A D, vt G B ad B E. Quod primò erat, & c.

279.1.

37. ibid.
0241-01
ibidem.

Præterea, cum ſuperiùs demonſtratum ſit eſſe rectangulum G H M ad
quadratum H D, vt rectangulum G I L ad quadratum I A, erit permutan-
do rectangulum G H M ad G I L, vt quadratum H D ad I A; ſed propor-
tio quadrati H D ad I A componitur ex du@bus rationibus H D ad I A,
vel ex duobus rationibus H G ad G I, & proportio rectanguli G H M ad
G I L componitur ex duobus rationibus, nempe ex G H ad G I, & ex H M
ad I L; ergo proportio G H ad G I, hoc eſt H D ad I A, æqualis eſt pro-
portioni H M ad I I. , & permutando D H ad H M, erit vt A I ad I L, &

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