Re: [HM] Heron's definitions

Julio Gonzalez Cabillon (jgc@chasque.apc.org)
Fri, 04 Dec 1998 00:24:14 -0200

At 05:18 PM 01/12/1998 U, Mohamed Abattouy wrote:
|
| I would like to know in which article did the late W. R. Knorr say
| that the list of geometrical definitions edited by Heiberg in vol. IV
| of "Herons Opera" is spurious, and can definitely not be ascribed to him ??

Dear Mohamed,

The paper sought is Knorr's "Arithmetike stoicheiosis: On Diophantus and
Hero of Alexandria", _Historia Mathematica_, vol 20, no 2, pp 180-192, 1993.

Incidentally, in this respect, I wouldn't miss Lucio Russo's latest (and
provocative!) article "The Definitions of Fundamental Geometric Entities
Contained in Book I of Euclid's Elements" [AHES 52 (1998) 3, 195-219].

The thesis is sustained that the definitions of fundamental
geometric entities which open Euclid's Elements actually are
excerpts from the Definitions by Heron of Alexandria, interpolated
in late antiquity into Euclid's treatise. As a consequence, one
of the main bases of the traditional Platonist interpretation of
Euclid is refuted. Arguments about the constructivist nature of
Euclid's mathematical philosophy are given.

Best wishes,
Julio