- Let $ABC$ be the given circle.
- So it is required to find the center of circle $ABC$.
- Let some straight line $AB$ have been drawn through ($ABC$), at random, and let ($AB$) have been cut in half at point $D$ [Prop. 1.9].
- And let $DC$ have been drawn from $D$, at right angles to $AB$ [Prop. 1.11].
- And let ($CD$) have been drawn through to $E$.
- And let $CE$ have been cut in half at $F$ [Prop. 1.9].
- I say that (point) $F$ is the center of the [circle] $ABC$.

It is possible to locate the center of a circle.

Proofs: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

Propositions: 29 30 31

Sections: 32

**Callahan, Daniel**: "Euclid’s 'Elements' Redux" 2014

**Casey, John**: "The First Six Books of the Elements of Euclid"

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