For two given unequal straight-lines, to cut off from the greater a straight-line equal to the lesser. Let $AB$ and $C$ be the two given unequal straight-lines, of which let the greater be $AB$.  <prf> So $AE$ is also equal to $C$ [C.N.~1]. Thus, for two given unequal straight-lines, $AB$ and $C$, the (straight-line) $AE$, equal to the lesser $C$, has been cut off from the greater $AB$.