A history of Greek mathematics - Wilbourhall.org

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Supports '.
ON THE CENTRE OF GRAVITY 351
As, however, the principles are the same whether
the body is supported or hung up, it does not follow that
this was a different work from that known as wept {vy&v.
Chaps. 32-3, which are on the principles of the lever or of
weighing, end with an explanation amounting to the fact
that ' greater circles overpower smaller when their movement
is about the same centre', a proposition which Pappus says
that Archimedes proved in his work ire pi {vyoov. 1 In chap. 32,
too, Heron gives as his authority a proof given by Archimedes
in the same work. With I. 33 may be compared II. 7,
where Heron returns to the same subject of the greater and
lesser circles moving about the same centre and states the
fact
that weights reciprocally proportional to their radii are
in equilibrium when suspended from opposite ends of the
horizontal diameters, observing that Archimedes proved the
'
proposition in his work On the equalization of inclination
(presumably la-oppoiviai).
Book II. The five mechanical powers.
Heron deals with the wheel and axle, the lever, the pulley,
the wedge and the screw, and with combinations of these
powers. The description of the powers comes first, chaps. 1-6,
and then, after II. 7, the proposition above referred to, and the
theory of the several powers based upon it (chaps. 8-20).
Applications to specific cases follow. Thus it is shown how
to move a weight of 1000 talents by means of a force of
5 talents, first by the system of wheels described in the
BapovXKo?, next by a system of pulleys, and thirdly by a
combination of levers (chaps. 21-5). It is possible to combine
the different powers (other than the wedge) to produce the
same result (chap. 29). The wedge and screw are discussed
with reference to their angles (chaps. 30-1). and chap. 32 refers
to the effect of friction.
Mechanics in daily life;
queries and answers.
After a prefatory chapter (33), a number of queries resembling
the Aristotelian problems are stated and answered
(chap. 34), e.g. 'Why do waggons with two wheels carry
a weight more easily than those with four wheels?', 'Why
1
Pappus, viii, p. 1068. 20-3.