conversed much with the philosophers of the east; but if he invented the XLVIIth proposition in the first book of Euclid, which is unanimously ascribed to him by all antiquity, one can hardly have a profound esteem for the mathematical skill of his masters. It is indeed a very noble proposition, the foundation of trigonometry, of universal and various use in those curious speculations about incommensurable numbers, which his disciples from him, and from them, the Platonists, so exceedingly admired. But this shows the infancy of geometry, in his days, in that very country which claims the glory of inventing it, to herself. It is probable, indeed, that the Egyptians might find it out, but then we ought also to take notice, that it is the only very considerable instance of the real learning of Pythagoras that is preserved; which is the more observable because the Pythagoreans paid the greatest respect to their master of any sect whatsoever, and so we may be sure that we should have heard much more of his learning, if much more could have been said, and though the books of Hermippus and Aristoxenus are lost, yet Laertius who had read them, and Porphyry, and Jamblichus,
