Content of type 'excursus'

Excursus I: Pythagoras and the Pythagoreans

The problem of determining how much of the Pythagorean discoveries in mathematics can be attributed to Pythagoras himself is not only difficult; it may be said to be insoluble. Tradition on the subject is very meagre and uncertain, and further doubt is thrown upon it by the well-known tendency of the later Pythagoreans to ascribe everything to the Master himself (αὐτὸς ἔφα, Ipse dixit). Pythagoras himself left no written exposition of his doctrines, nor did any of his immediate successors, not even Hippasus, about whom the different stories ran (1) that he was expelled from the school because he published doctrines of Pythagoras, and (2) that he was drowned at sea for revealing the construction of the dodecahedron in the sphere and claiming it as his own, or (as others have it) for making known the discovery of the irrational or incommensurable. Nor is the absence of any written record of Pythagorean doctrines down to the time of Philolaus to be put down to a pledge of secrecy binding the school; at all events this did not apply to their mathematics or their physics; and it may be that the supposed secrecy was invented to account for the absence of documents. The fact seems to be that oral communication was the tradition of the school, while their doctrines would in the main be too abstruse to be understood by the generality of people outside. Even Aristotle felt the difficulty; he evidently knew nothing for certain about any ethical or physical doctrines going back to Pythagoras himself; when he speaks of the Pythagorean system, he always refers it to “the Pythagoreans,” sometimes even to “the so-called Pythagoreans.”

Excursus II: Popular Names for Euclidean Propositions

Although some of these time-honoured names are familiar to most educated people, it seems to be impossible to trace them to their original sources, or to say who applied them for the first time respectively. It may be that they were handed down by oral tradition for long periods in each case before they found their way into written documents.