The Teaching of Geometry

by David Eugene Smith

Adding, we have

(s₁ - 2)180° + (s₁ - 2)180° + (v - s₁)360° = ((s₁ - 2) + (v - s₁))360°

= (v - 2)360°.

Equating the two sums already found, we have

(e - f)360° = (v - 2)360°,

or e - f = v - 2,

or e + 2 = v + f.

This proof is too abstract for most pupils in the high school, but it is more scientific than those found in any of the elementary textbooks, and teachers will find it of service in relieving their own minds of any question as to the legitimacy of the theorem.