ON THE CENTRE OF GRAVITY 
351 
Supports ’. 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 rrepî Çvymv. 
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 7re pi Çuyœv. 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 laopponiai). 
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 
BapovXKos, 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 resem 
bling 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,