(related to Lemma: Lem. 10.016: Incommensurability of Sum of Incommensurable Magnitudes)

- For let the parallelogram $AD$, falling short by the square figure $DB$, have been applied to the straight line $AB$.
- I say that $AD$ is equal to the (rectangle contained) by $AC$ and $CB$.

- And it is immediately obvious.
- For since $DB$ is a square, $DC$ is equal to $CB$.
- And $AD$ is the (rectangle contained) by $AC$ and $CD$ - that is to say, by $AC$ and $CB$.
- Thus, if ... to some straight line, and so on ....∎

**Fitzpatrick, Richard**: Euclid's "Elements of Geometry"