Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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15924DE CENTRO GRAVIT. SOLID. los contineant. Dico ſolidum a b ad ſolidum a c eãdem ha
bere proportionem, quam axis d e ad axem e f.
Sienim
axes in eadem recta linea fuerint conſtituti, hæc duo ſoli-
da, in unum, atque i @m ſolidum conuenient.
quare ex
iis, quæ proxime tradita ſunt, habebit ſolidum a b ad ſo-
lidum a c eandem proportionem, quam axis d e ad e f
axem.
Siuero axes non ſint in eadem recta linea, demittan
tur a punctis d, f perpendiculares ad baſis planum, d g, fh:
& iungantur e g, e h. Quoniam igitur axes cum baſibus
æquales angulos eontinent, erit d e g angulus æqualis an-
gulo f e h:
& ſunt
114[Figure 114] anguli ad g h re-
cti, quare &
re-
liquus e d g æqua
lis erit reliquo
e fh:
& triangu-
lum d e g triãgu-
lo f e h ſimile.
er-
go g d ad d e eſt,
ut h f ad f e:
& per
mutando g d ad
h f, ut d e ad e f.
Sed ſolidum a b
ad ſolidum a c
eandem propor-
tionem habet,
quam d g altitu-
do ad altitudinẽ
f h.
ergo & ean-
dẽ habebit, quã
axis d e a l e f axẽ
Poſtremo ſint
ſolida parallelepi
peda a b, c d

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