The Metaphysics of the Pythagorean Theorem by Robert Hahn

Author:Robert Hahn
Language: eng
Format: epub
Publisher: State University of New York Press
Published: 2017-04-14T04:00:00+00:00

Chapter 3

Pythagoras and the Famous Theorems

A

The Problems of Connecting Pythagoras with the Famous Theorem

In the last fifty years, the scholarly consensus on Pythagoras has largely discredited his association with the famous theorem that bears his name, and indeed with any contribution to what we might today call “mathematics.” While this consensus was built throughout the twentieth century, the avalanche of scholarly sentiment came finally with the publication of Walter Burkert’s Lore and Wisdom in Ancient Pythagoreanism (1962, 1972), which subsequently became the foundation of modern Pythagorean studies. The core of Burkert’s thesis was that there was no reliable, secure testimony datable to the fifth and fourth centuries BCE connecting Pythagoras with the famous theorem, or indeed with mathematics in general. And with that verdict, the connection between Pythagoras and the theorem was disengaged. All the reports that connected Pythagoras to the theorem and mathematics were judged too late to be trustworthy. But this is not to deny that the Greeks were aware of the hypotenuse theorem, or even members of Pythagoras’s school, though the usual dating is placed in the fifth century.

Recently, Leonid Zhmud published Pythagoras and the Pythagoreans (2012), a major revision of his 1997 work Wissenschaft, Philosophie und Religion im frühen Pythagoreismus. These works developed the thesis that Zhmud had announced already in 1989, arguing that perhaps Burkert had been too hasty in discrediting “Pythagoras the mathematician.” Zhmud’s most recent version of the argument has two threads, one on securing testimony dating to the fifth and fourth centuries BCE, and the other making a plausible case based on the very internal development of geometry. Diogenes Laertius reports the words of a certain “Apollodorus the arithmetician” that Pythagoras proved that1 in a right-angled triangle the square on the hypotenuse was equal to the sum of the squares on the sides adjacent to the right angle,2 and Zhmud argues that this is the same writer known as Apollodorus Cyzicus, dating to the second half of the fourth century BCE, a follower of Democritus.3 Zhmud argues that writers from Cicero to Proclus refer to this testimony of Apollodorus Logistikos—the very same Apollodorus—and thus these late reports echo testimony from the fourth century BCE.

Ἡνίκα Πυθαγόρης τὸ περικλεὲς εὕρετο γράμμα

κεῖν᾽, ἐφ᾽ὅτῳ κλεινὴν ἤγαγε βουθυσίην

When Pythagoras discovered the famous figure (γράμμα),

He made a splendid sacrifice of oxen.

While it is true that the earliest explicit mention of Pythagoras and the hypotenuse theorem dates to Vitruvius of the first century BCE,4 Zhmud traces the source to Callimachus of the first half of the third century BCE, who mentions Thales’s drawing a geometrical figure in the sand by the temple of Apollo at Didyma but claiming he learned it from Euphorbus, an earlier (re)incarnation of Pythagoras.5 In any case, once again we have an early mention connecting Pythagoras with geometrical figures, and, Zhmud thinks, with the famous theorem itself. Moreover Zhmud’s claim is this: If, in the fourth century, some ten authors mention Pythagoras and mathematics, in the third only Callimachus does so, making use of the

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.