Definition: Def. 11.18: Cone

(Definition 18 from Book 11 of Euclid's “Elements”)

A cone is the (solid) figure enclosed when, one of the sides of a right-angled triangle about the right angle remaining (fixed), the triangle is carried around, and again established at the same (position) from which it began to be moved. And if the fixed straight line is equal to the remaining (straight line) about the right angle, (which is) carried around, then the cone will be right-angled, and if less, obtuse-angled, and if greater, acute-angled.

Modern Formulation

(not yet contributed)

Definitions: 1
Proofs: 2 3 4 5 6
Propositions: 7 8 9 10 11

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



Adapted from (subject to copyright, with kind permission)

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

Adapted from CC BY-SA 3.0 Sources:

  1. Prime.mover and others: "Pr∞fWiki",, 2016