Marks' first lessons in geometry / In two parts. Objectively presented, and designed for the use of primary classes in grammar schools, academies, etc.

by Bernhard Marks

For from the point c draw c e parallel to a b.

Then, because the straight line a d intersects the two parallels a b, c e, in the points a and c,

The opposite exterior and interior angles a and e c d are equal to each other.

And because the straight line b c intersects the same parallels in the points b and c,

The interior alternate angles b and b c e are equal.

Then the angles a and b of the triangle are equal to the angles b c e and e c d.

But the new angle b c d is equal to the angles b c e, e c d.

Then because the new angle b c d, and the angles a and b are separately equal to the angles b c e, e c d, they are equal to each other.

PROPOSITION XI. THEOREM.