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Some Original Sources for Modern Tales of Thales - A 'Quotation' from Thales

Michael Molinsky (University of Maine at Farmington)

Many modern works provide quotations that are attributed to Thales.  For example, in his book In Mathematical Circles, Howard Eves gives many such quotations, including the following: “I will be sufficiently rewarded if, when telling it to others, you will not claim the discovery as your own, but will say it was mine. [5, p. 24]” As mentioned earlier, we have no existing works written by Thales, and unfortunately Eves provides no citation or source, so the question remains: where exactly does this “quotation” come from? 

It can actually be traced back to the Florida, a collection of speeches by the author Apuleius (2nd century CE).  In the eighteenth speech of the collection, Apuleius addresses the residents of Carthage and offers anecdotes of the achievements of both Thales and the Greek philosopher Protagoras (c. 490 – c. 420 BCE).  After listing a wide range of other achievements attributed to Thales, Apuleius concludes [12, p. 159]:

He also, when far advanced in old age, devised a divine theory about the sun, which I have not only learned but confirmed by experience, namely, by what multiple of its size the sun measures its own orbit.  Thales is reported to have explained this when he had just discovered it to Mandraytus of Priene, who was delighted by the new and unexpected knowledge, and asked him to name whatever amount of money he wanted to receive as a reward for so wonderful a proof.  ‘It will be enough of a reward,’ said Thales the Sage, ‘if, when you begin to make known to others what you have learned from me, you do not attribute it to yourself, but declare that I, and no one else, is responsible for the discovery.’  A handsome reward indeed, worthy of such a man, and everlasting!

In this context, the discovery for which Thales expects acknowledgement appears to be measuring the angular diameter of the sun as it appears from the Earth.  It is interesting to note that no other existing source before Apuleius credits Thales with this discovery; in fact, the only other ancient author who credits Thales with this computation is Diogenes Laertius, who states in Lives of Eminent Philosophers 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 …" [7, p. 25], which is indeed a relatively accurate approximation of the Sun’s apparent angular diameter.

Figure 6: Angular diameter of the Sun (or other distant object)

Unfortunately, neither Apuleius nor Diogenes give any indication of any older authorities from which they might be drawing this information.  Also, there are other ancient authors who credit the discovery differently.  For example, in The Sand Reckoner, Archimedes (c. 287 – 212 BCE) attributes the calculation to Aristarchus of Samos (c. 310 – c. 230 BCE), saying “… Aristarchus discovered that the sun appeared to be about one seven hundred and twentieth part of the circle of the zodiac …" [6, p. 223].  On the other hand, the Greek astronomer Cleomedes (who lived sometime in the 2nd - 4th centuries CE) makes no mention of Thales or Aristarchus and instead credits the Egyptians, claiming that they used a water clock to approximate the Sun’s angular diameter to one seven hundred and fiftieth part of a complete orbit (see [11] for an evaluation of this claim). 

Given that it is open to question whether or not Thales really did measure the sun’s apparently angular diameter, it seems fair to also express doubt about the quotation Apuleius attributes to Thales.  Of course it is possible that Apuleius had access to sources no longer available to us today, including ones that might contain the exact words of Thales; however, it seems more reasonable to posit that Apuleius wanted to make a speech about giving credit where credit was due, and the wide fame of Thales made him a natural choice for the protagonist of the story.

Michael Molinsky (University of Maine at Farmington), "Some Original Sources for Modern Tales of Thales - A 'Quotation' from Thales," Convergence (November 2015)