Let the line A B (fig. 1, [plate X.]) represent the height of the figure to be constructed. At the point A, make the angles of C A D (¹⁄₃), F A G (¹⁄₄), H A I (¹⁄₅), K A L (¹⁄₆), and M A N (¹⁄₇). At the point B, make the angles K B L (¹⁄₈), U B A (¹⁄₁₂), and O B A (¹⁄₁₄).
Through the point K, in which the lines A K and B K intersect one another, draw P K O parallel to A B, and through C F H and M, where this line meets A C, A F, A H, and A M, draw C D, F G, H I, and M N, perpendicular to A B; draw also K L perpendicular to A B; join B F and B H, and through C draw C E, making with A B the angle (¹⁄₂), which completes the arrangement of the eleven angles upon A B; for F B G is very nearly (¹⁄₁₀), and H B I very nearly (¹⁄₉).
At the point f, where A C intersects O B, draw f a perpendicular to A B; and through the point i, where B O intersects M N, draw S i T parallel to A C.
Through m, where S i T intersects F B, draw m n; through β, where S i T intersects K B, draw β w; through T draw T g, making an angle of (¹⁄₃) with O P. Join N P, M B, and g P, and where N P intersects K B, draw Q R perpendicular to A B.
On A E as a diameter, describe a circle cutting A C in r, and draw r o perpendicular to A B.
With A o and o r as semi-axes, describe the ellipse A r e, cutting A H in t; and draw t u perpendicular to A B. With A u and t u, as semi-axes describe the ellipse A t d. On a L, as major axis, describe the ellipse of (¹⁄₃).
For the side aspect or profile of the figure the diagram is thus constructed—
On one side of a line A B (fig. 2, [Plate X.]) construct the rectilinear portion of a diagram the same as fig. 1. Through i draw W Y parallel to A B, and draw A z perpendicular to A B. Make W a equal to A a (fig. 1), and on a l, as major axis, describe the ellipse of (¹⁄₄). Through a draw a p parallel to A F, and through p draw p t perpendicular to W Y. Through a draw f a u perpendicular to W Y.
Upon a diameter equal to A E describe a circle whose circumference shall touch A B and A z. With semi-axes equal to A o and o r (fig. 1), describe an ellipse with its major axis parallel to A B, and its circumference touching O P and z A.