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

The difference of the angles, or F A B, must be measured by half the difference of the arcs, or half of F B.

PROPOSITION XXI. THEOREM.

DEMONSTRATION.

We wish to prove that

Parallel chords intercept equal arcs of the circumference.

Let the chords A B, C D, be parallel; then will the intercepted arcs A C and B D be equal.

For draw the straight line B C.

Because the lines A B and C D are parallel, the interior alternate angles A B C, B C D, are equal.

But the angle A B C is measured by half the arc A C;