Book Description

This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1912 edition. Excerpt: ... BOOK III On The Four Mathematical Sciences ON ARITHMETIC INTRODUCTION In examining Isidore's De Arithmetica two peculiarities of the development of the subject should be borne in mind. In the first place, the predominant position among the mathematical sciences which Isidore claims for arithmetic was one acquired by it comparatively late. Owing perhaps to the awkwardness of the Greek notation of number' geometry had been developed first, and historically arithmetic was an off-shoot from geometry and borrowed its terminology largely from it.2 It was not given an independent form until the time of Nicomachus (fl. ioo A. D.) whose Introductio Arithmetica was "the first exhaustive work in which arithmetic was treated quite independently of geometry." * Once it become independent, arithmetic, instead of geometry, came to be regarded as the fundamental mathemetical science. The old tradition is reflected in Martianus Capella's order of subjects, in which geom 1 " The cumulative evidence is surely very strong that the alphabetic numerals were first employed in Alexandria early in the third century II. C." J. Gow, A Short History of Greek Mathematics (Cambridge, 1884), p. 48. * We have in Isidore, for example, the terms Humerus trigonus, numerus quadratus, Humerus quinquangulus, and linealis, superHeialis, and eircutaris Humerus. Cajori, Hist, of Math., p. 72. 123] 3 etry is placed first and arithmetic second, while the newer tradition is seen in the order of Cassiodorus and Isidore, who both have passages also emphasizing the fundamental character of arithmetic. The second peculiarity is one which will surprise the modern reader who is familiar with arithmetic as a utilitarian study. The ancient arithmetica had nothing to do with...