HERO, or HERON, OF AL'EXAN'DRIA. The leading Greek mathematician and physicist of his time. Not only are the dates of his birth and death unknown. but there is great uncertainty as to the century in which he lived. The most recent investigation of the evidence, by Schmidt (1899, work cited below, Bd. 1, p. ix.), leads to the conclusion that he may have lived in the first century A.D., but other writer:, who, it must be said, have not considered the question so fully, have usually placed him in the first or even the second century B.C, There is much confusion con cerning the works of Hero of Alexandria. there having been no less than eighteen Greek writers of this name. It is. however, fairly certain that he wrote at least thirteen books on mathematics and physics. He seems to have been an Egyptian, and it is certain that his style is not that of a Greek. He contributed little to pure mathe matics, his chief work on this subject being the extension of the ancient mathematics so as to allow the eonsidoration of the fourth power of lines. Thus, in his geodesy, -,e(atatcia, contained in his Merpool, upon which subject be was the only Greek writer, he gives the well-known for mula for finding the area of a triangle with sides. a, b, c, and serniperimeter s. ca-a, f (s-e), a formula known by his name. (The proof is given,
possibly an interpolation, in his llepi cfni7rpac.) He seems also to have had some idea of trigonometry, and in his geometry is to be found the first definite use of a trigonometric formula. He asserts in substance, using modern symbols, that if A represents the area of a regular n-gnn of side s, and if e he the numerical coefficient by which must he multiplied to produce A. i.e. so ° that A = es' then must cot 180 4 . He pro ceeds to compute c for the values a=3, 4, ... 12, with considerable accuracy. but his method is un known. He could also solve the complete quad ratic equation b.r = c, where a, b, c. are positive, hut not the general form. Hero is cred ited with a number of mechanical inventions. including a contrivance for utilizing the force of steam and a fountain which hears his name. Consult: Martin, "Becherehes cur hi vie et lee onvrages d'Heron d'Alexandrie." in vol. iv. of .11Fmoirec prt'vrmWcg par dirrrs sarantg a I.tea Wmie dingeriptions (S•rie I., Paris, 1854) ; Ilultseh. Heron is .4 lexandrini Geometricorum et gtereomet Henn's)? ilelianim (Berlin. 1864) : Schmidt, Heronis ilexandrini Opera afar Super sunt Omnia (Leipzig. 1899-1.