"A Jew, Nicomachus, of Gerasa, published an Arithmetic, which, or rather a Latin translation of it) remained for a thousand years a standard authority on the subject. Geometrical demonstrations are here abandoned, and the work is a mere classification of the results then known, with numerical illustrations: the evidence of the truth of the propositions enunciated, for I cannot call them proofs, being in general an induction from numerical instances. The object of the book is the study of the properties of numbers, and particularly of their ratios. Nicomachus commences with the usual distinctions between even, odd, prime, and perfect numbers; he next discusses fractions in a somewhat clumsy manner; he then turns to polygonal and to solid numbers; and finally treats of ratio, proportion, and progressions. Arithmetic of this kind is usually termed Boethian, and the work of Boethius on it was a recognised text-book in the middle ages."