To Pythagoras and his disciples there are, moreover, many scientific conclusions and discoveries ascribed, which, however, do not concern us at all. Thus, according to Diogenes Laertius (VIII. 14, 27), he is said to have known that the morning and evening star is the same, and that the moon derives her light from the sun. We have already mentioned what he says of music. But what is best known is the Pythagorean Theorem; it really is the main proposition in geometry, and cannot be regarded like any other theorem. According to Diogenes, (VIII. 12), Pythagoras, on discovering the theorem, sacrificed a hecatomb, so important did he think it; and it may indeed seem remarkable that his joy should have gone so far as to ordain a great feast to which rich men and all the people were invited. It was worth the trouble; it was a rejoicing, a feast of spiritual cognition—at the cost of the oxen. Other ideas which are brought forward by the Pythagoreans casually and without any connection, have no philosophic interest, and need only be mentioned. Aristotle, for instance, says (Phys. IV. 6) that “the Pythagoreans believed in an empty space which the heavens inspire, and an empty space which separates natural things and brings about the distinction between continuous and discrete; it first exists in numbers and makes them to be different.” Diogenes Laertius (VIII. 26-28) says much more, all of which is dull; this is like the later writers, who, generally speaking, take up what is external and devoid of any intellectual meaning. “The air which encircles the earth is immovable” (_ἄσειστον_, at least through itself) “and diseased, and all that is in it is mortal; but what is highest is in continual movement, pure and healthy, and in it everything is immortal—divine. Sun, moon and the other stars are gods, for in them warmth has predominance and is the cause of life. Man is related to the gods because he participates in warmth, and hence God cares for us. A ray penetrates from the sun through the thick and cold ether and gives life to everything; they call air, cold ether, the sea and moisture, thick ether. The soul is a detached portion of ether.” C. THE ELEATIC SCHOOL.