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

278. THEOR. XXIV. PROP. XXXXIII.

In congruentibus Parabolis per diuerſos vertices ſimul adſcri-
ptis, intercepta communium diametrorum ſegmenta inter ſe ſunt
æqualia, & huiuſmodi Parabolæ dicantur ęquidiſtantes. Contin-
gentes verò vtranq; ſectionem ad terminos eiuſdem diametri inter
ſe æquidiſtant.

SInt duæ congruentes Parabolæ A B C, D E F per diuerſos vertices B, E
ſimul adſcriptæ circa communem diametrum B E H, & inter ipſas du-
cta ſit quæcunque alia A D ipſi B E parallela, (quæ vtrique Parabolæ con-
ueniet in A, D eritque earum communis diameter) atque ex terminis A, D, agantur A I, D L Parabolas contingentes in A, D, & communi diame-
tro B E occurrentes in I, L. Dico diametrorum intercepta ſegmenta B E, A D æqualia eſſe, & contingentes A I, D L inter ſe æquidiſtare.

278.1.

26. primi
conic.
46. ibid.
24. ibid.

Nam primum patet ex primo Coroll. 42. primi huius: cumq; omnes interceptæ B E,
A D, & c. ſint æquales vocentur, huiuſmodi
Parabolæ inter ſe ęquidiſtantes. Secundum
verò, ita oſtenditur.

278.1.

0240-01

Applicentur ex A, D ad diametrum B H
rectæ A G, D H; erit A H parallelogram-
mum, ex quo G H æqualis erit A D, ſiue
ipſi B E, quare dempta, vel addita, vti opus
fuerit, communi G E, proueniet B G ęqua-
lis H E, & dupla I G duplæ L H æqualis erit, & eſt G A æqualis H D, & angulus
I G A angulo L H D æqualis, ergo angu-
lus quoque G I A angulo H L D æqualis erit. Quare contingentes A I, D
L inter ſe æquidiſtant. Quod, & c.

278.1.

35. ibid.

279. THEOR. XXV. PROP. XXXXIV.

In Hyperbolis, aut Ellipſibus ſimilibus, & concentricis, per
diuerſos vertices ſimul adſcriptis, intercepta communium dia-
metrorum ſegmenta ad proprias ſemi-diametros vnam eandem-
que habent rationem, & quæ ſectiones contingunt ad terminos
eiuſdem diametri inter ſe æquidiſtant.

SInt duæ Hyperbolæ ſimiles in prima figura, vel duæ ſimiles Ellipſes in ſe-
cunda, quarum commune centrum ſit G, & communis ſemi- diameter
G B E, ſitque ducta quæcumque alia G A D, (quæ tamen in Ellipſi cadat in-
ter coniugatas ſemi-diametros G E, G N) eritque G A D, item commu- nis ſectionum ſemi-diameter, ducãturque A L, D M ad terminos A, D ſe-

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