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[235] geometry had been developed first, and historically arithmetic was an off-shoot from geometry and borrowed its terminology largely from it.[236] It was not given an independent form until the time of Nicomachus (fl. 100 A.D.) whose _Introductio Arithmetica_ was “the first exhaustive work in which arithmetic was treated quite independently of geometry.”[237] Once it become independent, arithmetic, instead of geometry, came to be regarded as the fundamental mathematical science. The old tradition is reflected in Martianus Capella’s order of subjects, in which geometry 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. [235] “The cumulative evidence is surely very strong that the alphabetic numerals were first employed in Alexandria early in the third century B.C.” J. Gow, _A Short History of Greek Mathematics_ (Cambridge, 1884), p. 48. [236] We have in Isidore, for example, the terms _numerus trigonus_, _numerus quadratus_, _numerus quinquangulus_, and _linealis_, _superficialis_, and _circularis numerus_. [237] Cajori, _Hist. of Math._, p. 72. 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 the art of reckoning, which was called _logistica_.[238] The science and the art of numbers were completely divorced and the latter was excluded from the higher education as we have it in the seven liberal arts. Consequently we can expect nothing practical in Isidore’s _De Arithmetica_. Nothing is said of methods of calculation, elementary or advanced, and, as a matter of course, nothing is to be found here on such topics as the use of the abacus[239] or the method of computing Easter, though the latter was the greatest mathematical problem of the time. [238] Gow, speaking of the Greek ἀριθμητική, says: “Its aim was entirely different from that of the ordinary calculator, and it was natural that the philosopher who sought in numbers to find the plan on which the creator worked, should begin to regard with contempt the merchant who wanted only to know how many sardines at ten for an obol he could buy for a talent.” Gow, _op. cit._, p. 72.