Translation of "Transmigrar" in English

Pitágoras decía que había recibido como regalo de Mercurio la transmigración perpetua de su alma, para que ella pudiera transmigrar constantemente por toda clase de plantas y animales.

Pythagoras used to say that he had received as a gift from Mercury the perpetual transmigration of his soul, so that it was constantly transmigrating and passing into all sorts of plants or animals.