To cut off from the greater of two given unequal straight lines a straight line equal to the less.
Let AB and CD be the two given unequal straight lines, with AB greater.
We want to cut off from AB a segment equal to the shorter line CD.
Using Proposition 2, place AE equal to CD at point A.
With center A and radius AE, describe circle EFC.
Circel EFC intersects AB at F. Since AE equals CD, and AE equals AF (radii), AF equals CD.