N. J. Wildberger
Euclid does not deal directly with distance. The ancient Greeks understood the meaning of saying two segments in the same direction were in the ratio `three to two’, but they did not have a direct notion of distance, because that would have entailed an understanding of real numbers, which they did not have. Similarly, Euclid does not measure angle. To him, an angle was just the geometrical configuration consisting of two intersecting lines. In fact the modern notion of `radian measure’ is only a little more than a hundred years old.
