Book:Euclid/The Elements/Book VIII

Contents
Book $\text{VIII}$: Theory of Proportions as applied to Number Theory

Comment
Once the more-or-less profound results about the structure of a geometric progression of integers has been comprehended, the rest of the book consists of simple examples.

Once the initial few results have been established in contemporary language (and to as high a power as is desired), the Euclidean proofs of these results, and indeed the results themselves, become all but irrelevant.