A Line Is Breadthless Length

Definition 2 from Euclid's Elements (c. 300 BC) defines a line as having length but no breadth — that is, one dimension only. Together with Definition 1 (a point has no parts) and Definition 3 (the ends of a line are points), these opening definitions build a geometric world of pure abstraction. The Elements was used as the standard textbook in mathematics education in Europe and the Arab world for over two thousand years.