Book III

is on the division of figures. The plane portion is much on the lines of Euclid's _Divisions_ (of figures). The solids divided in given ratios are the sphere, the pyramid, the cone and a frustum thereof. Incidentally Heron shows how he obtained an approximation to the cube root of a non-cube number (100). Quadratic equations are solved by Heron by a regular rule not unlike our method, and the _Geometrica_ contains two interesting indeterminate problems.

Heron also wrote _Pneumatica_ (where the reader will find such things as siphons, Heron's Fountain, penny-in-the-slot machines, a fire-engine, a water-organ, and many arrangements employing the force of steam), _Automaton-making_, _Belopoeïca_ (on engines of war), _Catoptrica_, and _Mechanics_. The _Mechanics_ has been edited from the Arabic; it is (except for considerable fragments) lost in Greek. It deals with the puzzle of 'Aristotle's Wheel', the parallelogram of velocities, definitions of, and problems on, the centre of gravity, the distribution of weights between several supports, the five mechanical powers, mechanics in daily life (queries and answers). Pappus covers much the same ground in