Geometric Construction with the Compass Alone

A segment AB is given by its end points A and B. Construct segments 2, 3, 4, etc. times larger than AB.

Solution

Swing an arc with the center B of radius AB. With the same radius swing first an arc with the center A until it intersects the first arc at a point C. With C as the center draw and arc to obtained the point D. With D as the center draw and arc to obtained the point E. The segment AE is twice as big as the segment AB. In a similar fashion segment BE can be extended to EF, twice as big a segment as BE. Then AF is three times as long as AB. Etc.