Philosophy of science and nature

Can you measure a pyramid without climbing it?

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Thales of Miletus

Measuring a pyramid with a shadow

According to an ancient account preserved by Diogenes Laertius, Thales measured the height of the pyramids from their shadow; Pamphila also credits him with inscribing a right triangle in a circle, though others tell the same of Pythagoras.

ancient testimony · Diógenes Laercio, Lives of Eminent Philosophers 1.27

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Philosophy of science and nature · geometry

What is claimed and why

  1. Diogenes Laertius, citing Hieronymus of Rhodes, says Thales measured the height of the pyramids by their shadow, at the hour when our shadow is as long as we are tall. ancient testimony
    Diógenes Laercio, Lives of Eminent Philosophers (tr. R. D. Hicks) — 1.27
    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.
    Diógenes Laercio, Lives of Eminent Philosophers (tr. José Ortiz y Sanz) — §5
    Geronimo dice que midio las pirámides por medio de la sombra, proporcionandola con la nuestra quando es igual al cuerpo.
    John Burnet, Early Greek Philosophy — §6
    the height of the pyramids, which is also ascribed to him
  2. According to Pamphila (cited by Diogenes Laertius), Thales was the first to inscribe a right-angled triangle in a circle; others, among them Apollodorus the arithmetician, tell the same of Pythagoras. Burnet warns that Eudemus credited Thales with geometric propositions he merely inferred from the measurements tradition ascribed to him. ancient testimony
    Diógenes Laercio, Lives of Eminent Philosophers (tr. R. D. Hicks) — 1.24; 1.25
    Pamphila states that, having learnt geometry from the Egyptians, he was the first to inscribe a right-angled triangle in a circle, whereupon he sacrificed an ox.
    Others tell this tale of Pythagoras, amongst them Apollodorus the arithmetician.
    John Burnet, Early Greek Philosophy — §6
    Certain feats in the way of measurement were traditionally ascribed to Thales, and Eudemos assumed that he must have known all the propositions these imply.
    Patricia O'Grady, Thales of Miletus (Internet Encyclopedia of Philosophy) — §9a · consulted; copyrighted text, not reproduced

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