350 HERON OF ALEXANDRIA 
between the two portions into which the vertical plane cuts it 
(chap. 23). 
On the centre of gravity. 
This brings Heron to the centre of gravity (chap. 24). Here 
a definition by Posidonius, a Stoic, of the 4 centre of gravity ’ 
or 4 centre of inclination ’ is given, namely 4 a point such that, 
if the body is hung up at it, the body is divided into two 
equal parts’ (he should obviously have said ‘divided by any 
vertical 'plane through the point of suspension into two equal 
parts’). But, Heron says, Archimedes distinguished between 
the ‘centre of gravity’ and the ‘point of suspension’, defining 
the latter as a point on the body such that, if the body is 
hung up at it, all the parts of the body remain in equilibrium 
and do not oscillate or incline in any direction. 4 “Bodies”, said 
Archimedes, 44 may rest (without inclining one way or another) 
with either a line, or only one point, in the body fixed The 
4 centre of inclination ’, says Heron, 4 is one single point in any 
particular body to which all the vertical lines through the 
points of suspension converge.’ Comparing Simplicius’s quo 
tation of a definition by Archimedes in his KevrpofiapLKd, to 
the effect that the centre of gravity is a certain point in the 
body such that, if the body is hung up by a string attached to 
that point, it will remain in its position without inclining in 
any direction, 1 we see that Heron directly used a certain 
treatise of Archimedes. So evidently did Pappus, who has 
a similar definition. Pappus also speaks of a body supported 
at a point by a vertical stick: if, he says, the body is in 
equilibrium, the line of the stick produced upwards must pass 
through the centre of gravity. 2 Similarly Heron says that 
the same principles apply when the body is supported as when 
it is suspended. Taking up next (chaps. 25-31) the question 
of 4 supports ’, he considers cases of a heavy beam or a wall 
supported on a number of pillars, equidistant or not, even 
or not even in number, and projecting or not projecting 
beyond one or both of the extreme pillars, and finds how 
much of the weight is supported on each pillar. He says 
that Archimedes laid down the principles in his 4 Book on 
1 Simplicius on De caelo, p. 543. 31-4, Heib. 
2 Pappus, viii, p. 1032. 5-24.