On Nicomachus's Introduction to Arithmetic

IAMBLICHUS OF CHALCIS

IN COELE-SYRIA

ON THE INTRODUCTION TO NICOMACHUS'S ARITHMETIC

Beginning our own discourse regarding the subjects defined in their parts, we start from arithmetic. For this study holds a priority by nature because it deals with simpler and more primary things, which is why the discourse regarding it takes precedence over other mathematical subjects. Now, this discourse itself is not simple, but manifold; for as many as the kinds of existing things are, the subject is divided along with them all and admits of the same divisions. But it is necessary to consider number itself by itself, before the things observed in others, from which we shall be able to examine number also as it exists in nature, in customs, in forms, or in all existing things whatsoever. For this reason, it is necessary to take up the mathematical science of numbers. For it must be set forth as a premise; since, when it is presupposed, it is possible for other sciences to come into being, but without this, even those do not come into being. And for the sake of learning, from this point we begin...

1—p. 4, 11 cf. Nicomachus, Arithmetical Introduction I 1, pp. 1—3, 8 Hoche
4 "Discourse" added in the margin by a recent hand F || 6 sq. "we begin" (as a question)? || 16 sq. "anticipate/take beforehand" (as a suggestion)?