Some Original Sources for Modern Tales of Thales - The Tale of the Pyramids

Many of the surviving ancient sources mention that Thales traveled to Egypt at some point in his life.  While it is certainly possible for him to have done so, historians have suggested that it is possible that Thales is linked to Egypt simply to strengthen the tradition of tracing Greek mathematics back to Egypt.  In any case, one of the earliest tales regarding Thales and Egypt is that while there, he used shadows to measure the heights of the pyramids.

The earliest reported source for the tale of the pyramids is the philosopher Hieronymus of Rhodes (3rd century BCE).  Unfortunately, none of the works of Hieronymus survive, and we know what he wrote only through brief quotations and summaries that appear in later sources.  The connection to Hieronymus is made in Lives of Eminent Philosophers by Diogenes Laertius.  (This work is something of an enigma: we know nothing of the author other than his name, and it isn’t even known with much precision when the work was written, although many date it to approximately 3rd century CE.)

Figure 3: The first page of the biography of Thales in an edition of Lives of Eminent Philosophers published in France in 1761 (Wikimedia Commons, public domain)

Diogenes Laertius includes a substantial biography of Thales, and he credits the work Scattered Notes by Hieronymus for many of the details, including the following [7, p. 29]:

He had no instructor, except that he went to Egypt and spent some time with the priests there. Hieronymus informs us that he measured the height of the pyramids by the shadow they cast, taking the observation at the hour when our shadow is of the same length as ourselves.

There are some other surviving sources that predate Lives of Eminent Philosophers, but come after Hieronymus, that include the same story.  One example is the Roman author Gaius Plinius Secundus (c. 23 – 79 CE), also known as Pliny the Elder.  In Book 37, Chapter 17 of his work Natural History, Pliny states essentially the same version of the story (although he makes no mention of Hieronymus, and explicitly makes the much bolder claim that Thales was the first to ever measure heights in such a fashion) [3, p. 338]:

The method of ascertaining the height of the Pyramids and all similar edifices was discovered by Thales of Miletus; he measuring the shadow at the hour of the day at which it is equal in length to the body projecting it.

This tale is also told in the Moralia, written by the Greek historian and biographer Plutarch (c. 45 – 120 CE). The second book of the Moralia includes the Dinner of the Seven Sages, a work of historical fiction depicting a dinner for seven wise men of antiquity, including Thales.  Before the dinner begins, the character Neiloxenus, one of the additional characters over and above the seven wise men, says the following to Thales [1, p. 353]:

In your case, for instance, the king finds much to admire in you, and in particular he was immensely pleased with your method of measuring the pyramid, because, without making any ado or asking for any instrument, you simply set your walking-stick upright at the edge of the shadow which the pyramid cast, and, two triangles being formed by the intercepting of the sun's rays, you demonstrated that the height of the pyramid bore the same relation to the length of the stick as the one shadow to the other.

Unlike the other two versions above, Plutarch does not specifically limit Thales’ method to shadows that exactly match the given heights to be measured, but allows that the heights could be computed with shadows of any length. You may also have noted that while all three ancient sources give a basic description, the lack of detail somewhat glosses over practical issues, such as how to measure the entire length of the pyramid’s shadow from tip to the center of the pyramid (see [10] for a recent article that considers these missing details).

Figure 4. A method for measuring the height of a pyramid attributed to Thales