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Hero of Alexandria

Born: c. 10 AD
Died: c. 70 AD
Cause of death: unspecified

Gender: Male
Religion: Pagan
Race or Ethnicity: White
Occupation: Mathematician

Nationality: Ancient Rome
Executive summary: Metrica

Hero of Alexandria (sometimes Heron), Greek geometer and writer on mechanical and physical subjects, probably flourished in the second half of the 1st century. This is the more modern view, in contrast to the earlier theory most generally accepted, according to which he flourished about 100 BC. The earlier theory started from the superscription of one of his works from which it was inferred that Hero was a pupil of Ctesibius. Martin, Hultsch and Cantor took this Ctesibius to be a barber of that name who lived in the reign of Ptolemy Euergetes II (died in 117 BC) and is credited with having invented an improved water-organ. But this identification is far from certain, as a Ctesibius mechanicus is mentioned by Athenaeus as having lived under Ptolemy II Philadelphus (285-247 BC). Nor can the relation of master and pupil be certainly inferred from the superscription quoted (observe the omission of any article), which really asserts no more than that Hero re-edited an earlier treatise by Ctesibius, and implies nothing about his being an immediate predecessor. Further, it is certain that Hero used physical and mathematical writings by Posidonius, the Stoic, of Apamea, Cicero's teacher, who lived until about the middle of the 1st century BC. The positive arguments for the more modern view of Hero's date are (1) the use by him of Latinisms from which Diels concluded that the 1st century AD was the earliest possible date, (2) the description in Hero's Mechanics III of a small olive-press with one screw which is alluded to by Pliny as having been introduced since AD 55, (3) an allusion by Plutarch (who died AD 120) to the proposition that light is reflected from a surface at an angle equal to the angle of incidence, which Hero proved in his Catopirica, the words used by Plutarch fitting well with the corresponding passage of that work. Thus we arrive at the latter half of the 1st century AD as the approximate date of Hero's activity.

The geometrical treatises which have survived (though not interpolated) in Greek are entitled respectively Definitiones, Geometria, Geodaesia, Stereometrica (I and II), Mensurae, Liber Geoponicus, to which must now be added the Metrica recently discovered by Schöne in a manuscript at Constantinople. These books, except the Definitiones, mostly consist of directions for obtaining, from given parts, the areas or volumes, and other parts, of plane or solid figures. A remarkable feature is the bare statement of a number of very close approximations to the square roots of numbers which are not complete squares. Others occur in the Metrica where also a method of finding such approximate square, and even approximate cube, roots is shown. Hero's expressions for the areas of regular polygons of from 5 to 12 sides in terms of the squares of the sides show interesting approximations to the values of trigonometrical ratios. 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. It is in this book that Hero proves the expression for the area of a triangle in terms of its sides. The Pneumatica in two books is also extant in Greek as is also the Automatopoietca. In the former will be found such things as siphons, "Hero's fountain", "penny-in-the-slot" machines, a fire-engine, a water-organ, and arrangements employing the force of steam. Pappus quotes from three books of Mechanics and from a work called Barulcus, both by Hero. The three books on Mechanics survive in an Arabic translation which, however, bears a title "On the lifting of heavy objects." This corresponds exactly to Barulcus, and it is probable that Barulcus and Mechanics were only alternative titles for one and the same work. It is indeed not credible that Hero wrote two separate treatises on the subject of the mechanical powers, which are fully discussed in the Mechanics II and III. The Belopoiica (on engines of war) is extant in Greek, and both this and the Mechanics contain Hero's solution of the problem of the two mean proportionals. Hero also wrote Catoptrica (on reflecting surfaces), and it seems certain that we possess this in a Lati work, probably translated fro the Greek by Wilhelm van Moerbeek, which was long thought to be a fragment of Ptolemy's Optics, because it bore the title Ptolemaei de speculis in the manuscript. But the attribution to Ptolemy was shown to be wrong as soon as it was made clear (especially by Martin) that another translation by Admrial Eugenius Siculus (12th century) of an optical work from the Arabic was Ptolemy's Optics. Of other treatises by Hero only fragments remain, for instance one of the four books on Water Clocks, of which Proclus has preserved a fragment, and to which Pappus also refers. Another work was a commentary on Euclid (referred to by the Arabs as "the book of the resolution of doubts in Euclid") from which quotations have survived in an-Nairizi's commentary.

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