(related to Proposition: 1.10: Bisecting a Segment)

- Let the equilateral triangle $ABC$ have been constructed upon ($AB$) [Prop. 1.1], and let the angle $ACB$ have been cut in half by the straight line $CD$ [Prop. 1.9].
- I say that the straight line $AB$ has been cut in half at point $D$.
- For since $AC$ is equal to $CB$, and $CD$ (is) common, the two (straight lines) $AC$, $CD$ are equal to the two (straight lines) $BC$, $CD$, respectively.
- And the angle $ACD$ is equal to the angle $BCD$.
- Thus, the base $AD$ is equal to the base $BD$ [Prop. 1.4].
- Thus, the given finite straight line $AB$ has been cut in half at (point) $D$.
- (Which is) the very thing it was required to do.∎

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