Pythagorean Hinduism?

I was reading in Ovid's Metamorphoses tonight -- An interesting section on the Roman monarchy. Romulus has just been deified (Quirinus is his new god name) and Numa has been selected as his predecessor. Suddenly, out of nowhere, Pythagoras (yes, the Pythagorean Theorem math guy) speils for 17 pages about the nature of the universe. He begins by saying that we should basically become vegetarians - eat only vegetables, fruits, grains, etc. Our carnivorous activities are atrocious, imitative of the Cyclopes. After all, only savage animals kill to eat. We may kill ferocious, threatening animals, but we should not consume their flesh once we have done so. Pythagoras then goes on to say (quoted this whole time by Ovid, I might add) that life is an ever changing cycle. Why do you fear the Shades, a fabricated story, he asks. Don't you know that the body may experience death, but the soul will be tranferred to another body? He then claims that during the Trojan was he was Euphorbus, son of Panthous. After many, many pages of the fluid state of life and earth's living energy, he concludes by saying that the reason we should not eat animals is because we must respect the bodies where the souls of our ancestors may have found new homes. Could it be that our Greek friend here believes not in the Greek pantheon, but in the Hindu oneness and transformation of all matter? A quote to stir your thoughts:

"...the heavens and all things beneath the heavens change their forms -- the earth and all that is upon the earth; and since we are parts of the world, we, too, are changeable. For we're not only bodies, but winged souls; and we can dwell in bodies of wild beasts and hide within the shapes of cows and sheep. And so, let us respect --leave whole, intact-- all bodies where our parents' souls or those of brothers or of others dear to us may well have found a home; let us not stuff our bellies banqueting, as did Thyestes. Whover cuts a calf's throat wtih a knife and listens, without pity, to its cries; whoever kills a kid that, like a child, wails loud; whoever feeds upon a bird that he himself has fed --profanely sheds the blood of humans: such a man abets a habit that is evil --little less than murder." (Ovid's Metamorphoses translated by Allen Mandelbaum)