◀ ▲ ▶Branches / Geometry / Elements-euclid / Book--1-plane-geometry / Definition: 1.17: Diameter of the Circle

Definition: 1.17: Diameter of the Circle

And a diameter of the circle is any straight line, being drawn through the center, and terminated in each direction by the circumference of the circle. (And) any such (straight line) also cuts the circle in half.

Modern Definition

A diameter of a circle is any segment \(\overline{AB}\) drawn in its interior, connecting two points of its circumference and containing its center.

Notes

• Euclid does not differentiate between straight lines and segments.
• Moreover, Euclid's definition uses "cutting the circle in half" as a defining property of a diameter, but it should really be counted as a postulate, rather than as part of a definition. Since it is not necessary to define a diameter

Example

A circle with the diameter \(\overline{AB}\).

Mentioned in:

Corollaries: 1 2
Definitions: 3 4 5 6 7
Problems: 8
Proofs: 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41
Propositions: 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57
Solutions: 58

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

Github:

non-Github:

@Calahan

@Fitzpatrick

References

Adapted from CC BY-SA 3.0 Sources:

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

Adapted from (subject to copyright, with kind permission)

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