Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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178FED. COMMANDINI producantur. Quoniam igitur pyramis ſecatur planis bafi
æquidiſtantibus, ſectiones ſimiles erunt:
atque erunt qua-
119. huius drata, uel rectangula circa circulos, uel ellipſes deſcripta,
in ipſa baſi. Sed cum circuli inter ſe eã
222. duode-
cimi.
itemq;
ellipſes eam quam rectangula ex ipſarum diametris
conſtantia:
& ſit circulus, uel ellipſis circa diametrum e f
337. de co-
noidibus
& ſphæ-
roidibus
proportionalis inter circulos, uel ellipſes a b, c d;
erit re-
ctangulum e f etiam inter rectangula a b, c d proportio-
nale:
per rectangulum enim nunc breuitatis cauſa etiã ip-
quare ex iis, quæ proxime
dicta ſunt, pyramis baſim habens æqualem dictis rectangu
lis, &
altitudinem eandem, quam fruſtum a d, ipſi fruſto à
pyramide abſciſſo æqualis probabitur.
ut autem rectangu
lum c d ad rectangulũ e f, ita circulus, uel ellipſis c d a d e f
circulum, uel ellipſim:
componendoq; ut rectangula c d,
e f, ad e f rectangulum, ita circuli, uel ellipſes e d, e f, ad e f:
& ut rectangulum e f ad rectangulum a b, ita cir culus, uel
cllipſis e f ad a b circulum, uel ellipſim.
ergo ex æquali, &
componendo, utrectãgula c d, e f, a b ad ipſum a b, ita