Thales of Miletus by PATRICIA F. O’GRADY

Author:PATRICIA F. O’GRADY
Language: eng
Format: epub
Publisher: Routledge

Thales’s Determination of the Diameters of the Sun and the Moon

From three ancient writers there are extant reports which are relevant to this topic. The earliest report is that of Apuleius who was born about 123 A.D.

Thales in his declining years devised a marvellous calculation about the sun, which I have not only learnt but verified by experiment, showing how often the sun measures by its own size the circle which it describes. Thales is said to have communicated this discovery soon after it was made to Mandrolytus of Priene,119 who was greatly delighted by this new and unexpected information and asked Thales how much by way of a fee he required to be paid to him for so important a piece of knowledge. ‘I shall be sufficiently paid’, replied the sage, ‘if, when you set to work to tell people what you have learnt from me, you will not take credit for it yourself but will name me, rather than another, as the discoverer’ (Apul. Flor. 18).120

Following soon after Apuleius was Cleomedes (ca. A.D. 150–200) who described a method by which such a calculation could be made:

The absurdity (121) of the rumour that the sun’s diameter is a foot long may be tested by the water-clocks, because it is shown through them that if the sun is one foot in diameter then its greatest orbit of the sky will be seven hundred and fifty feet. This is because, when the sun is measured by water-clocks it is found that its size is one seven-hundred-and-fiftieth of its own orbit. The reason is that while the sun is rising, from its first appearance in the horizon to its complete rising, the water from the water-clock fills one cup, then if the water is left flowing all day and night, it fills seven hundred and fifty cups. It is said that this method was first conceived by the Egyptians.122

The third report is from Diogenes Laertius (ca. first half of the third century A.D.) who recorded only that:

According to some [Thales was] the first to declare the size of the sun to be one seven hundred and twentieth part of the solar circle, and the size of the moon to be the same fraction of the lunar circle (D.L. 1.24).

There are several details of importance in the report from Apuleius. The first point is that Thales made this discovery in his declining years. This indicates that much of his astronomical work was behind him, and that he perhaps had as a basis the accumulated data of years of observation of heavenly phenomena, of records and theories.123 The second point is in the response of Mandrolytus to Thales’s teaching. He was ‘greatly delighted with this new and unexpected information’, which he valued as ‘important … knowledge’. The third detail of interest is that the passage states that, after Thales had explained to Mandrolytus how he arrived at his ‘marvellous calculation’, Apuleius had verified Thales’s calculation by experiment. The fragment fails to give us two

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