The life of _Leucippus_ is almost unknown. He was probably born in Miletus, visited Elea, and settled in Abdera. _The Later Pythagoreans._ After the Pythagoreans as a religious and political body had been defeated at Crotona, they lost their prestige and were scattered to the four winds. They were beaten in the battle of Crotona (510 B. C.) and dispersed about 450 B. C. Pythagoras died 504 B. C. His scattered followers, these later Pythagoreans, formed a school of philosophy which had its centre at Thebes. Destroyed as a religious body the members lost their superstitions and turned their attention to philosophy, astronomy, mathematics, medicine, and physics. As mathematicians and as astronomers they are the most notable among the ancients. Philolaus is the probable originator of their philosophy of numbers. This school disappeared about 350 B. C. Pythagoreanism reappeared later under the name of neo-Pythagoreanism. =The Philosophy of Empedocles.= Empedocles conceived the number of elements to be four,――earth, air, fire, and water,――an arbitrary enumeration, which nevertheless persisted in the popular imagination throughout the Middle Ages. He chose this number of elements because they included all the elements in his predecessors’ theories. By the transposition and new arrangement of these elements he could account for the variety of the world. The efficient causes that make these different separations and mixtures are Love and Hate, two mythical and sensuous entities. Love is the cause of the union of things, Hate of their separation. This is the general metaphysical theory that Empedocles uses to explain the physical world and especially physiological phenomena; and he is probably best known as the author of the aphorism, “Like attracts Like.” For example, he conceives the physical world as continuously repeating itself through four cosmic stages, each centuries long. The world moves therefore in cyclical evolution, in which Love is bringing like elements together only to be followed by stages of the separation of the like elements by Hate,――an endless cosmic procession.