To describe a regular Hexagon.

—With a radius equal to the length of one side of the required hexagon, describe a circle ([Fig. 21]), and set off the same radius round the circumference of the circle, which will be thus divided into six equal parts. Join the points thus found, and the required hexagon will be completed as A B C D E F.

Fig. 22.

To draw a Parabola, the base and height being given.

—Let C A ([Fig. 22]) equal half the base, and C D the height. From the point D draw D E parallel and equal to A C, and from the point A draw A E parallel and equal to C D. Divide D E and A E similarly, making the end E of A E correspond to the end D of E D. Through 1, 2, &c., in DE draw 1, 1; 2, 2, &c., parallel to D C. Join D to the several points 1′, 2′, &c., in A E. The parabola will pass through the points of intersections of these lines with the verticals drawn from D E to C A.

Fig. 23.

Fig. 24.