Euclid introduced the subject by the proposition that, if alternate angles are equal, the lines are parallel.
And “if the lines are parallel, are alternate angles necessarily equal?”
The sides of the octagon are equal, and the alternate angles coincident.
We may now state Prop. 16 thus:—If two straight lines which meet are cut by a transversal, their alternate angles are unequal.
That is to say, “If alternate angles are unequal, do the lines meet?”
Frustules oblong or quadrate, adnate in filaments, attached by alternate angles and finally separating.
alternate angles Two angles formed on opposite sides of a line that crosses two other lines. The angles are both exterior or both interior, but not adjacent. |