Hero of Alexandria

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Hero of Alexandria


Dates of birth and death unknown; probably in the first century A.D. Ancient Greek scientist who worked in Alexandria.

Hero’s works systematically set forth the basic achievements of the ancient world in the field of applied mechanics. In Pneumatics he described the various mechanisms that make use of the movement of heated or compressed air or steam: the so-called aeolipile (a globe that revolves under the action of steam), an automatic device for opening doors, a fire pump, various siphons, a water organ, a mechanical marionette theater, and so forth. In Mechanics, Hero described five simple machines: the lever, the windlass, the wedge, the screw, and the pulley. He was also familiar with the parallelogram of forces. Using a tooth gearing, Hero built a device for measuring the length of roads, founded on the same principle as that used in present-day taxi meters. Hero’s automatic machine for the sale of “holy” water was a prototype of our automatic machines that dispense liquids. Hero’s mechanisms and automatic machines did not find any wide practical application. They were mainly used in construction of mechanical toys. The only exceptions were his hydraulic machines; ancient water engines were perfected with their help. In his work On the Dioptera, Hero set forth rules of land surveying, actually based on the use of right-angle coordinates. He also provides a description of the dioptera, a device for measuring corners that is a prototype of the present-day theodolite. Hero wrote about the bases of ancient artillery in the treatise On the Manufacture of Missile Machines.

Hero’s mathematical works are an encyclopedia of ancient applied mathematics. In Metrics he provides rules and formulas for both the exact and approximate calculation of various geometric figures. Examples include Hero’s formula for determining the area of a triangle, the rules for the numerical solution of quadratic equations, and the rules for the approximate extraction of square roots and cubic roots. On the whole, the exposition in Hero’s mathematical works is dogmatic. The rules are often not deduced, but are only explained by examples.


Diels, H. Antichnaia tekhnika. Moscow-Leningrad, 1934. (Translated from German.)
Vygodskii, M. Ia. Arifmetika i algebra v drevnem mire, 2nd ed. Moscow, 1967.