[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.
[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.
[239] Cantor believes that the use of the abacus had been forgotten before Isidore’s time, cf. “calculator a calculis, id est a lapillis minutis quos antiqui in manu tenentes numeros componebant.” Etym., 10, 43. See Cantor, Vorlesungen über Geschichte der Mathematik (Leipzig, 1894–1900), vol. i, p. 774.
[240] Isidore adds to the account as found in Cassiodorus a few remarks about numbers in the Scriptures, some derivations of numbers, and the sections on the means and on infinity.
[241] Du Breul has magnitudinis et formarum; Arevalo, magnitudinis formarum.
[242] This derivation points to a soft c in decem.
[243] Six was regarded as a perfect number, because it is equal to the sum of all its factors.
[244] Pariter par, et pariter impar, et impariter par et impariter impar. Since these all profess to be divisions of even number, the word odd is not used in the translation.