Apollonius was born at Perga in Pamphylia, in the south of Asia Minor. The date usually assigned to him is 240 B.C., so that he was about seventy years later than Euclid and about thirty years later than Archimedes. He tells us that it was at the suggestion of the geometer Naucrates that he wrote his treatise on Conics, consisting of eight books, and that he composed them somewhat hurriedly, and submitted them to him without revision, simply putting down the different properties as they occurred to him, intending to go over them again afterwards, the reason for his haste being the approaching departure of his friend and guest. He afterwards found time to revise and publish each book separately, and it is in this revised condition that they have come down to us.

This short paper is supplementary to that read to the Association by Mr. Langley (Jan. 1892); that also being supplementary to one read by Mr. Hayward (Jan. 1889).

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.