[A] view... Aristotle sometimes attributes to the Pythagoreans... thin — Pythagoreanism

"We are told that the other book which passed under the name of Pythagoras was really by Lysis."

"Aristotle... was... out of sympathy with Pythagorean ways of thinking, but took... great... pains to understand them. This was... because they played so great a part in the philosophy of Plato and his successors, and he had to make the relation of the two doctrines as clear as he could to... his disciples."

"[T]he religious revival... suggested the view that philosophy was above all a "way of life." Science too was a "purification," a means of escape from the "wheel." This is the view expressed so strongly in Plato’s Phaedo, which was written under the influence of Pythagorean ideas."

"None of Pythagoras own work has survived, but the ideas fathered on him by his followers would be the most potent in modern history. Pure knowledge, the Pythagoreans argued, was the purification (catharsis) of the soul... rising above the data of the human senses. The pure essential reality... was found only in the realm of numbers. The simple, wonderful proportion if numbers would explain the harmonies of music... [T]hey introduced the musical terminology of the octave, the fifth, the fourth, expressed as 2:1, 3:1, and 4:3. ..."

"This sufficiently justifies... regarding the "fragments of Philolaos" with... more than suspicion."

"It has been no easy task to revise this volume in such a way as to make it more worthy of the favour with which it has been received. Most of it has had to be rewritten in the light of certain discoveries made since the publication of the first edition, above all, that of the extracts from Menon’s Iατρικά, which have furnished, as I believe, a clue to the history of Pythagoreanism."