By W. W. Rouse Ball

This article continues to be one of many clearest, such a lot authoritative and such a lot actual works within the box. the traditional background treats thousands of figures and colleges instrumental within the improvement of arithmetic, from the Phoenicians to such 19th-century giants as Grassman, Galois, and Riemann.

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Plato left Athens, and being possessed of considerable wealth he spent some years in travelling; it was during this time that he studied mathematics. He visited Egypt with Eudoxus, and Strabo says that in his time the apartments they occupied at Heliopolis were still shewn. Thence Plato went to Cyrene, where he studied under Theodorus. Next he moved to Italy, where he became intimate with Archytas the then head of the Pythagorean school, Eurytas of Metapontum, and Timaeus of Locri. c. Plato, like Pythagoras, was primarily a philosopher, and perhaps his philosophy should be regarded as founded on the Pythagorean rather than on the Socratic teaching.

Hankel in his posthumous Geschichte der Mathematik, Leipzig, 1874. CH. II] IONIAN AND PYTHAGOREAN SCHOOLS 11 The Ionian School. c. c. The materials for an account of his life consist of little more than a few anecdotes which have been handed down by tradition. During the early part of his life Thales was engaged partly in commerce and partly in public affairs; and to judge by two stories that have been preserved, he was then as distinguished for shrewdness in business and readiness in resource as he was subsequently celebrated in science.

We need not here concern ourselves further with the successors of Thales. , but, as time went on, its members occupied themselves more and more with philosophy and less with mathematics. We know very little of the mathematicians comprised in it, but they would seem to have devoted most of their attention to astronomy. They exercised but slight influence on the further advance of Greek mathematics, which was made almost entirely under the influence of the Pythagoreans, who not only immensely developed the science of geometry, but created a science of numbers.