After Pythagoras and the Italic school, Professor Loria takes up the Eleatics, the Atomists, the Sophists. He expounds the arguments of Zeno (born about the beginning of the 5th century B.C.) against multiplicity and motion, and attributes to the Eleatic philosopher—he was not strictly a mathematician—the great merit of having for the first time discussed infinitesimal and infinite quantities as well as infinite numbers.