Euclid's Proposition 3: To cut off from the greater of two given unequal straight lines a straight line equal to the less.

Construction

1. Let A be the longer line and CD be the shorter line.
2. Construct a line segment equal to CD with an endpoint on A. Mark the other endpoint D'. Proposition 2
3. Construct a circle with center A and radius AD'.
4. Place point E at the intersection of the circle and the line AB.
5. The line segment AE is the same length as CD.