Definition: 1.18: Semicircle

And a semicircle is the plane figure contained by the diameter and the circumference cut off by it. And the center of the semicircle is the same (point) as (the center of) the circle.

Modern Definition

Euclid's definition corresponds to today's formulation.

Example

A semicircle is the colored plane figure enclosed by the diameter \(\overline{CB}\) with the center at the point \(A\).

semicircle

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


Thank you to the contributors under CC BY-SA 4.0!

Github:
bookofproofs
non-Github:
@Fitzpatrick


References

Adapted from (subject to copyright, with kind permission)

  1. Fitzpatrick, Richard: Euclid's "Elements of Geometry"