HERON OF ALEXANDRIA, Greek geometer and writer on mechanical and physical subjects. Heron's date is still a mat ter of controversy. The possible limits are 150 B.C. (for he was later than Apollonius of Perga and Hipparchus) and 25o A.D. (since he preceded Pappus). The latest discussions by scholars have tended to place him as late as the 3rd century A.D. (after Ptolemy), but there are those who still adhere to 150—roo B.c. as the probable date of his activity.
Of Heron's mechanical works, the Pneumatica, Automatopoie tice, Belopoeica and Cheiroballistra survive in Greek. The Pneu matica, in two books, describes many interesting contrivances such as siphons, "Heron's fountain," "penny-in-the-slot" machines, a fire-engine, a water-organ and arrangements employing the force of steam.. The Belopoeica (on engines of war) purports by its title ('"Hpowos Kri rtf3Lov (3EXo7rociKa) to be based on a work by Ctesibius, who was most probably the Ctesibius who lived under Ptolemy II. Philadelphus (285-247 B.e.). Heron's Mechanics, in three books, is extant in Arabic, though not in its original form. This work is cited by Pappus, as is also the Barulcus, "weight lifter," probably the same treatise under a different name. Book II. of the Mechanics deals with the five mechanical powers and mechanical problems of daily life, and Book III. with the con struction of engines of all sorts. Both the Belopoeica and the Mechanics contain Heron's solution of the problem of the two mean proportionals.
The geometrical works attributed to Heron which survive in Greek bear the titles Metrica, Definitiones, Geometria, Geodaesia, Stereometrica (i., ii.), Mensurae and Liber Geeponicus. The Metrica was discovered as recently as 1896 by R. Schone in a ms. at Constantinople. It is by far the most important, as it is the most genuine, of the geometrical works of Heron, and proves him to have been an accomplished mathematician. The other works containing, like the Metrica, problems of mensuration are not Heron's in their present form. A remarkable feature is the statement of a variety of close approximations to the square roots of numbers which are not complete squares; the Metrica describes a general method of finding successive approximations to the val ues of such surds, as well as a method of approximating to the cube root of a non-cube number; the former throws light on sim ilar approximations to surds stated in Archimedes and elsewhere. Book I. of the Metrica includes the mensuration of triangles, quad rilaterals, regular polygons from the equilateral triangle to the reg ular dodecagon, circles and segments thereof, an ellipse, a para bolic segment, and of the surfaces of cylinders, right cones, spheres and segments thereof. Book II. shows how to measure the content of solid figures, including cones, pyramids, frusta of such solids, a sphere and a segment thereof, the five regular solids, besides the two remarkable solid figures measured by Archimedes in his Method (a solid like a hoof cut off by a plane from the end of a cylinder, and a solid made up of eight such "hoofs") . Book III. gives some problems of the same type as those in Euclid's trea tise On Divisions (of figures). Akin to the geometrical works is that On the Dioptra, a remarkable book on land-surveying, so called from the instrument described in it, which was used for the same purposes as the modern theodolite ; this treatise contains (as does the Metrica) a remarkable geometrical proof of the expression for the area of a triangle in terms of its sides, Heron also wrote Catoptrica (on reflecting surfaces) ; and it seems certain that we possess this in a Latin translation by William of Moerbeke of a work which was formerly thought to be a f rag ment of Ptolemy's Optics. Of other treatises by Heron only fragments remain. One on Water-Clocks in four books is referred to by Pappus and Proclus. Another was a commentary on Euclid's Elements, quotations from which are found in the extant Arabian commentary by an-Nairizi.
BIBLIOGRAPHY.—The Pneumatica, Automatopoietice, Belopoeica and Bibliography.—The Pneumatica, Automatopoietice, Belopoeica and Cheiroballistra of Heron were edited in Greek and Latin by Thevenot, (Veterum mathematicorum opera, Paris, 1693). The "geometrical" works (other than the Metrica), in Greek only, were edited by F. Hultsch (Heronis Alexandrini geometricorum et stereometricorum reliquiae, 1864) . Except for the treatises on Engines of War (also edited by C. Wescher, Polyorcetique des Grecs, Paris, 1867), the authoritative edition is now Heronis Alexandrini opera quae supersunt omnia, included in Teubner's series; vol. i. and Supplement (by W. Schmidt) contains the Pneumatica and Automata, the fragment on Water-Clocks, etc.; vol. ii. pt. i. (L. Nix and W. Schmidt) , the Mechanics, Catoptrica, etc.; vol. iii. (H. Schone), the Metrica and Dioptra; vols. iv. and v. (J. L. Heiberg), the geometrical works.
For fuller accounts of Heron's works see G. Loria, Le scienze esatte nell' antica Grecia, 1914; Sir T. L. Heath, History of Greek Mathe matics, vol. ii., pp. ; Pauly-Wissowa's Real-Encyklopddie s.v.
(T. L. H.)