# The New International Encyclopædia/Hero of Alexandria

**HERO**, or **HERON, OF ALEXANDRIA**.
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 writers, 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
concerning 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
mathematics, his chief work on this subject being the
extension of the ancient mathematics so as to
allow the consideration of the fourth power of
lines. Thus, in his geodesy, γεωδαισία, contained
in his Μετρικά, upon which subject he was the
only Greek writer, he gives the well-known
formula for finding the area of a triangle with sides,
, and semiperimeter ,
,
a formula known by his name. (The proof is given,
possibly an interpolation, in his Ηερὶ διόπτρας.) 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 represents the area of a regular -gon of
side , and if be the numerical coefficient by
which must be multiplied to produce , i.e. so
that then must . He
proceeds to compute for the values ,
with considerable accuracy, but his method is
unknown. He could also solve the complete
quadratic equation , where , are
positive, but not the general form. Hero is credited
with a number of mechanical inventions,
including a contrivance for utilizing the force
of steam and a fountain which bears his name.
Consult: Martin, “Recherches sur la vie et les
ouvrages d'Héron d'Alexandrie,” in vol. iv. of
*Mémoires présentées par divers savants à*
*l'Académie d'Inscriptions* (Série I., Paris, 1854);
Hultsch, *Heronis Alexandrini Geometricorum*
*et Stereometricorum Reliquiæ* (Berlin, 1864);
Schmidt, *Heronis Alexandrini Opera quæ Supersunt*
*Omnia* (Leipzig, 1899—).