Euclid, Elements of Geometry, Book I, Proposition 23
(Edited by Dionysius Lardner, 1855)

Proposition XXIII. Problem.
[Euclid, ed. Lardner, 1855, on Google Books]

(102) At a given point (B) in a given right line (B E) to make an angle equal to a given angle (C).


In the sides of the given angle take any points D and F; join D F, and construct a triangle E B A which shall be equilateral with the triangle D C F, A B E F C D and whose sides A B and E B meeting at the given point B shall be equal to F C and D C of the given angle C (XXII). The angle E B A is equal to the given angle D C F.


For as the triangles D C F and E B A have all their sides respectively equal, the angles F C D and A B E opposite the equal sides D F and E A are equal (VIII).

It is evident that the eleventh proposition is a particular case of this

Book I: Euclid, Book I (ed. Dionysius Lardner, 11th Edition, 1855)

Next: Proposition 24

Previous: Proposition 22

This proposition in other editions: