# Greek Mathematics

# XXII. Mensuration: Heron Of Alexandria

## (a) Definitions

## Heron, Deff., ed. Heiberg (Heron iv.) 14. 1–24

Καὶ τὰ μὲν πρὸ τῆς γεωμετρικῆς στοιχειώσεως τεχνολογούμενα ὑπογράφων σοι καὶ ὑποτυπούμενος, ὡς ἔχει μάλιστα συντόμως, Διονύσιε λαμπρότατε, τήν τε ἀρχὴν καὶ τὴν ὅλην σύνταξιν ποιήσομαι κατὰ τὴν τοῦ Εὐκλείδου τοῦ Στοιχειωτοῦ τῆς ἐν γεωμετρίᾳ θεωρίας διδασκαλίαν· οἶμαι γὰρ οὕτως οὐ μόνον τὰς ἐκείνου πραγματείας

# Mensuration: Heron of Alexandria

# XXII. Mensuration: Heron of Alexandria^{a}

## (a) Definitions

## Heron, Definitions, ed. Heiberg (Heron iv.) 14. 1–24

In setting out for you as briefly as possible, O most excellent Dionysius, a sketch of the technical terms premised in the elements of geometry, I shall take as my starting point, and shall base my whole arrangement upon, the teaching of Euclid, the writer of the elements of theoretical geometry; for in this way I think I shall give you a good general understanding,

- The problem of Heron’s date used to be one of the most disputed questions in the history of Greek mathematics. All that could certainly be said was that he came after Apollonius, whom he quotes, and before Pappus, who cites him, say between 150 b.c. and a.d. 250. But in 1938 0. Neugebauer showed that the eclipse of the moon described in Heron, Dioptra 35 (ed. H. Schöne, 302.3–306.21) as taking place on the tenth day before the spring equinox and beginning at Alexandria at the fifth (seasonal) hour of the night and at Rome at the third (seasonal) hour must have been the eclipse of 13th March a.d. 62. (“Uber eine Methode zur Distanzbestimmung Alexandria – Rom bei Heron”, in Kongelige Danske Videnskabernes Selskabs Skrifter, vol. 26, no. 2, 1938, pp. 21–24, also A History of Ancient Mathematical Astronomy, Part II, 1975, p. 846). Though strictly this establishes only an upper limit, Neugebauer’s argument that Heron was referring to something in the recent memory of his readers has been generally accepted. how to use the force of compressed air, water or steam; they are of great interest in the history of physics, and have led some to describe Heron as “the father of the turbine,” but as they have no mathematical interest they cannot be noticed here. Heron also wrote a Belopoeïca on the construction of engines of war, and a Mechanics, which has survived in Arabic and in a few fragments of the Greek.

DOI: 10.4159/DLCL.heron_alexandria-mensuration.1941