The Euclidean algorithm is one of the oldest algorithms in common use. It appears in Euclid's "Elements" (c. 300 BC), specifically in Book 7 (Propositions 1–2) and Book 10 (Propositions 2–3). In Book 7, the algorithm is formulated for integers, whereas in Book 10, it is formulated for lengths of line segments. (In modern usage, one would say it was formulated there for real numbers. But lengths, areas, and volumes, represented as real numbers in modern usage, are not measured in the same units and there is no natural unit of length, area, or volume; the concept of real numbers was unknown at that time.) The latter algorithm is geometrical. The GCD of two lengths "a" and "b" corresponds to the greatest length "g" that measures "a" and "b" evenly; in other words, the lengths "a" and "b" are both integer multiples of the length "g".