Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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17532DE CENTRO GRAVIT. SOLID.
SIT fruſtũ pyramidis, uel coni, uel coni portionis a d,
cuius maior baſis a b, minor c d.
& ſecetur altero plano
baſi æquidiſtante, ita utſectio e f ſit proportionalis inter
baſes a b, c d.
conſtituatur autẽ pyramis, uel conus, uel co-
ni portio a g b, cuius baſis ſit eadem, quæ baſis maior fru-
ſti, &
altitudo æqualis. Di-
co fruſtum a d ad pyrami-
dem, uel conum, uel coni
portionem a g b eandem
proportionẽ habere, quã
utræque baſes, a b, c d unà
cum e f ad baſim a b.
eſt
enim fruſtum a d æquale
pyramidi, uel cono, uel co-
ni portioni, cuius baſis ex
tribus baſibus a b, e f, c d
conſtat;
& altitudo ipſius
altitudini eſt æqualis:
quod mox oſtendemus. Sed pyrami
des, coni, uel coni portiões,
quæ ſunt æquali altitudine,
eãdem inter ſe, quam baſes,
proportionem habent, ſicu-
ti demonſtratum eſt, partim
ab Euclide in duodecimo li-
116. 11. duo
decimi
bro elementorum, partim à
nobis in cõmentariis in un-
decimam propoſitionẽ Ar-
chimedis de conoidibus, &

ſphæroidibus.
quare pyra-
mis, uel conus, uel coni por-
tio, cuius baſis eſt tribus illis
baſibus æqualis ad a g b eam
habet proportionem, quam
baſes a b, e f, c d ad ab bafim.
Fruſtum igitur a d ad a g