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Published online by Cambridge University Press: 23 December 2013
In Vol. LXXV (1955) of the JHS I suggested that the determination of the angular diameters of the sun and the moon ascribed to Thales (Diog. Laertius I. 24) may have been obtained by angular measurement, not as is generally supposed by time-measurement. However, the question of the precise technical method that may have been employed was left open. To measure a very small angle with any degree of accuracy is obviously not easy; and a combination of actual measurement with calculation is probably necessary. In what follows I describe a method of measuring very small angles: whether this was the method employed in obtaining the result ascribed to Thales I do not know; all I can claim is that it presupposes neither mathematical knowledge nor mathematical techniques which could not have been at the disposal of an early Greek philosopher-mathematician.
1 See M. Cantor, Vorlesungen über Geschichte der Mathematik, I, 91 (see also p. 93). He argues that the Babylonians used the value Π = 3. This was probably only a rough and ready measure useful for practical purposes; and as such it was probably in use all over the Middle East. Thus, Π = 3 is implied in the measurements given in the Bible, viz. I. Kings, 7. 23 and II. Chronicles, 4. 2. The same value is again implied in the much later Bablyonian Talmud, for which see Cantor, , Zeitschrift Math. Phys. XXGoogle Scholar histor. literar. Abteil. 164.
2 This argument could, of course, be adapted to the supposiion of any other value for Π.
