Mathematics begin with the tremendous but obscure career of Euclid. Nothing is known about Euclid: indeed one thinks of him to-day more as a branch of knowledge than as a man. But Euclid was once alive, landing here in the reign of Ptolemy Philadelphus, and informing that superficial monarch that there is “no royal road to geometry.” Here he composed, among other works, his “Elements” in which he incorporated all previous knowledge, and which have remained the world’s text book for Geometry almost down to the present day. Here he founded a mathematical school that lasted 700 years, and acknowledged his leadership to the last. Apollonius of Perga, who inaugurated the study of Conic Sections, was his immediate pupil: Hyspicles added to the thirteen books of his “Elements” two books more: and Theon—father to the martyred Hypatia—edited the “Elements” and gave them their present form, so that from first to last the mathematicians of Alexandria were preoccupied with him. An insignificant man, according to tradition, and very shy; his snub to Philadelphus seems to have been exceptional. (ii). GEOGRAPHY. In Geography there are two leading figures—Eratosthenes and Claudius Ptolemy. Eratosthenes is the greater. He seems to have been an all round genius, eminent in literature as well as science. He was born at Cyrene in B.C. 276 and, on the death of Callimachus, was invited to Alexandria to become librarian. It was in the Mouseion observatory that he measured the Earth—perhaps not the greatest achievement of Alexandrian science, but certainly the most thrilling. His method was as follows. He knew that the earth is round, and he was told that the midsummer sun at Assouan in Upper Egypt cast no shadow at midday. At Alexandria, at the same moment, it did cast a shadow, Alexandria being further to the north on the same longitude. On measuring the Alexandria shadow he found that it was 7⅕ degrees—_i.e._ 1/50th of a complete circle—so that the distance from Alexandria to Assouan must be 1/50th the circumference of the Earth. He estimated the distance at 500 miles, and consequently arrived at 250,000 miles for the complete circumference, and 7,850 for the diameter; in the latter calculation he is only 50 miles out. It is strange that when science had once gained such triumphs mankind should ever have slipped back again into fairy tales and barbarism. [Illustration: The World according to Eratosthenes B.C. 250] [Illustration: The World according To Claudius Ptolemy A.D. 100]