353 
HERON OF ALEXANDRIA 
do great weights fall to the ground in a shorter time than 
lighter ones ? ‘ Why does a stick break sooner when one 
puts one’s knee against it in the middle 1 ?’, ‘Why do people 
use pincers rather than the hand to draw a tooth ? ‘ Why 
is it easy to move weights which are suspended ? and 
‘ Why is it the more difficult to move such weights the farther 
the hand is away from them, right up to the point of suspension 
or a point near it ? ‘ Why are great ships turned by a rudder 
although it is so small 1 ‘ Why do arrows penetrate armour 
or metal plates but fail to penetrate cloth spread out ? ’ 
Problems on the centre of gravity, &c. 
II. 35, 36, 37 show how to find the centre of gravity of 
a triangle, a quadrilateral and a pentagon respectively. Then, 
assuming that a triangle of uniform thickness is supported by 
a prop at each angle, Heron finds what weight is supported 
by each prop, (a) when the props support the triangle only, 
(b) when they support the triangle plus a given weight placed 
at any point on it (chaps. 38, 39). Lastly, if known weights 
are put on the triangle at each angle, he finds the centre of 
gravity of the system (chap. 40); the problem is then extended 
to the case of any polygon (chap. 41). 
Book III deals with the practical construction of engines 
for all sorts of purposes, machines employing pulleys with 
one, two, or more supports for lifting weights, oil-presses, &c. 
The Catoptnca. 
This work need not detain us long. Several of the theoretical 
propositions which it contains are the same as propositions 
in the so-called Catoptrica of Euclid, which, as we have 
seen, was in all probability the work of Theon of Alexandria 
and therefore much later in date. In addition to theoretical 
propositions, it contains problems the purpose of which is to 
construct mirrors or combinations of mirrors of such shape 
as will reflect objects in a particular way, e.g. to make the 
right side appear as the right in the picture (instead of the 
reverse), to enable a person to see his back or to appear in 
• the mirror head downwards, with face distorted, with three 
eyes or two noses, and so forth. Concave and convex