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

SOLUTION.

Let a b be the given line.

With the point a as a centre, and a b as a radius, draw the circumference of the circle, or a part of one.

With the point b as a centre, and the same radius a b, draw another circumference, or a part of one.

From the point c, in which the circumferences or arcs intersect, draw the straight lines a c and b c.

Now, because the lines a b and a c are radii of the same circle, they are equal.

And, because the lines a b and b c are radii of the same circle, they are also equal.

Then, because the two lines a c, b c, are separately equal to the line a b, they are equal to each other, and the triangle is equilateral.