Herakleides, though some critics do not believe him to have strictly adhered to Plato’s primal philosophy,[26] taught the same ethics. Zeller presents him to us imparting, like Hicetas and Ecphantus, the Pythagorean doctrine of the diurnal rotation of the earth and the immobility of the fixed stars, but adds that he was ignorant of the {xxi} annual revolution of the earth around the sun, and of the heliocentric system.[27] But we have good evidence that the latter system was taught in the Mysteries, and that Socrates died for _atheism_, _i. e._, for divulging this sacred knowledge. Herakleides adopted fully the Pythagorean and Platonic views of the human soul, its faculties and its capabilities. He describes it as a luminous, highly ethereal essence. He affirms that souls inhabit the milky way before descending “into generation” or sublunary existence. His dæmons or spirits are airy and vaporous bodies. In the _Epinomis_ is fully stated the doctrine of the Pythagorean numbers in relation to created things. As a true Platonist, its author maintains that wisdom can only be attained by a thorough inquiry into the occult nature of the creation; it alone assures us an existence of bliss after death. The immortality of the soul is greatly speculated upon in this treatise; but its author adds that we can attain to this knowledge only through a complete comprehension of the numbers; for the man, unable to distinguish the straight line from a curved one will never have wisdom enough to secure a mathematical demonstration of the _invisible_, _i. e._, we must assure ourselves of the objective existence of our soul (astral body) before we learn that we are in possession of a divine and immortal spirit. Iamblichus says the same thing; adding, moreover, that it is a secret belonging to the highest initiation. The Divine Power, he says, always felt indignant with those “who rendered manifest the composition of the _icostagonus_,” viz., who delivered the method of inscribing in a sphere the dodecahedron.[28]