MEASUREMENT OF SOLIDS
333
the parallelepiped (1) is on A R as base and has height h ; the
prism (2) is equal to a parallelepiped on KQ as base and with
height h; the prism (3) is equal to a parallelepiped with JSP
as base and height h\ and finally the pyramid (4) is equal to
a parallelepiped of height h and one-third of RC as base.
E H
Therefore the whole solid is equal to one parallelepiped
with height h and base equal to (AR+KQ + NP + RO + ^R0)
or AO + ^RO.
Now, if AB = a, BO = b, EF = c, FG = d,
AV = |(a + c), AT = %(b + d),RQ = \(a — c), RP = ±(b — d).
Therefore volume of solid
= {\(a + c) {b + d)+-^i a — c ) {b — d)} h.
The solid in question is evidently the true (3u>/j.l(tkos (‘little
altar’), for the formula is used to calculate the content of
a PcofjLicrKos in Stereom. II. 40 (68, Heib.) It is also, I think,
the (7(f)T]VL(TK09 (‘ little wedge ’), a measurement of which is
given in Stereom. I. 26 (25, Heib.) It is true that the second
term of the first factor ^ (a — c) (b — d) is there neglected,
perhaps because in the case taken (a — 7, b = 6, c = 5, d = 4)
this term (— -|) is small compared with the other (= 30). A
particular a-cfrrjvLa-Ko?, in which either c — a or d = b, was
called 6w£; the second term in the factor of the content
vanishes in this case, and, if e.g. c = a, the content is \(b + d)ah.
Another f3oo/jLi(TK09 is measured in Stereom. I. 35 (34, Heib.),
where the solid is inaccurately called ‘a pyramid oblong
(trcpofirjKr]s) and truncated (KoXovpos) or half-perfect