For, if BD be again joined,
since, as CA is to AD, so is EA to AB, while,
as CA is to AD, so is the triangle ABC to the triangle BAD,
and, as EA is to AB, so is the triangle EAD to the triangle BAD, [VI. 1]
therefore, as the triangle ABC is to the triangle BAD, so is the triangle EAD to the triangle BAD. [V. 11]
Therefore each of the triangles ABC, EAD has the same ratio to BAD.
Therefore the triangle ABC is equal to the triangle EAD. [V. 9]