Heron of Alexandria (date uncertain; he may have lived as late as the third century A. D.) was an almost encyclopaedic writer on mathematical and physical subjects. He aimed at practical utility rather than theoretical completeness; hence, apart from the interesting collection of _Definitions_ which has come down under his name, and his commentary on Euclid which is represented only by extracts in Proclus and an-Nairīzī, his geometry is mostly mensuration in the shape of numerical examples worked out. As these could be indefinitely multiplied, there was a temptation to add to them and to use Heron's name. However much of the separate works edited by Hultsch (the _Geometrica_, _Geodaesia_, _Stereometrica_, _Mensurae_, _Liber geëponicus_) is genuine, we must now regard as more authoritative the genuine _Metrica_ discovered at Constantinople in 1896 and edited by H. Schöne in 1903 (Teubner). Book I on the measurement of areas is specially interesting for (1) its statement of the formula used by Heron for finding approximations to surds, (2) the elegant geometrical proof of the formula for the area of a triangle Δ {D} = √{_s (s-a) (s-b) (s-c)}, a formula now known to be due to Archimedes, (3) an allusion to limits to the value of π {p} found by Archimedes and more exact than the 3-1/7 and 3-10/71 obtained in the _Measurement of a Circle_. Book I of the _Metrica_ calculates the areas of triangles, quadrilaterals, the regular polygons up to the dodecagon (the areas even of the heptagon, enneagon, and hendecagon are approximately evaluated), the circle and a segment of it, the ellipse, a parabolic segment, and the surfaces of a cylinder, a right cone, a sphere and a segment thereof. Book II deals with the measurement of solids, the cylinder, prisms, pyramids and cones and frusta thereof, the sphere and a segment of it, the anchor-ring or tore, the five regular solids, and finally the two special solids of Archimedes's _Method_; full use is made of all Archimedes's results. 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.