# 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 $$\overline{AB}$$.

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

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### References

#### Adapted from CC BY-SA 3.0 Sources:

1. Callahan, Daniel: "Euclidâ€™s 'Elements' Redux" 2014