A history of Greek mathematics - Wilbourhall.org

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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 ' centre of gravity
or ' centre of inclination ' is given, namely ' 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.
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" Bodies", said
Archimedes, " may rest (without inclining one way or another)
with either a line, or only one point, in the body fixed ".' The
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centre of inclination ', says Heron, ' is one single point in any
particular body to which all the vertical lines through the
points of suspension converge.' Comparing Simplicius's quotation
of a definition by Archimedes in his KevrpofiapiKa, 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 ' 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 Book on
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1
Simplicius on Be caelo, p. 543. 31-4, Heib.
2
Pappus, viii, p. 1032. 5-24.