Proposition XXIII. Problem.
|(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, 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: