The top view is drawn and the circumference of the circle divided into eight equal parts. Straight lines are then drawn connecting point 2 with points A, B, C, and D. These are known as base lines, since they are equal in length to similarly drawn lines on the model; that is, they are true lengths.
Four horizontal lines, Fig. 266, are now drawn equal in length to lines A–2, B–2, C–2, and D–2 of Fig. 264. Corresponding letters and numbers are placed at the extremities of these lines. Perpendicular lines are erected at point 2 of each line, equal in length to line 2–3 of Fig. 265. Points A–3, B–3, C–3, and D–3 may now be connected by straight lines, thereby forming four right triangles. The hypotenuses of these triangles are elements of the surface of the cone; that is, they are equal in length to lines similarly drawn on the surface of the model. That branch of pattern drafting known as triangulation takes its name from the fact that the surfaces are developed from a series of triangles whose hypotenuses are equal to certain elements—straight lines drawn on the surface of the cone.
A vertical line, Fig. 267, is now drawn equal in length to the altitude, line 2–3, of Fig. 265. With point 3 as a center and radii equal to hypotenuse 3–D,3–C, 3–B, and 3–A, arcs are drawn to the left of line 2–3. Point D is located by an arc drawn from point 2 whose radius is equal to distance 2–D of Fig. 266. In like manner points C, B, and A are located by arcs drawn from points D, C, and B respectively. All of these intersecting arcs have the same radii, since the base of the cone was equally divided. A straight line 3–A and a curved line A, B, C, D, 2 completes the half pattern, which may now be copied on the other side of line 2–3 to obtain the full pattern.
It is advisable to make a model by cutting out the triangles of Fig. 266, attaching them to the base lines of Fig. 264, and slipping the envelope, Fig. 267, over this framework.
