Thales and the Diameter of the Sun and Moon

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.