Ellsworth M. Longfield

“ Axis of the Cone.—The line about which the generating surface revolves in forming a solid of revolution is called the axis. It is the shortest distance between the apex (point) and the base, and forms a right angle to the plane of the base.
Elevation of the Cone.—The elevation of the cone, Fig. 116, is drawn in the following manner: Draw a horizontal line four inches long; from the center of this line drop a perpendicular seven inches long. Connect the ends of the four-inch line to the end of the seven-inch line by straight lines. The four-inch line is the Base of the Elevation. ”

“ The profiles of both bases, or ends, will be circles. The smaller circle is generally called the upper base, and the larger circle the lower base of the frustum. The lateral area of a frustum of a cone is found by adding together the circumferences of the upper and lower bases, dividing the sum by 2, and then multiplying by the slant height. This is often expressed as a formula for area of a frustum:
A frustum whose lower base has a circumference of 40" and whose upper base has a circumference of 22" will have a surface area of
if the slant height of the frustum is 16". ”

“ With a radius equal to the distance from this point to the apex, and with the apex as a center, a curved extension line intersecting lines 2 and 2 of the stretchout is drawn. In like manner, the remaining intersections of the stretchout may be traced. A curved line passing through these points will give the miter cut of the roof flange at the roof line. The upper miter line, being parallel to the base, is developed like an ordinary right cone. With a radius equal to the slant height, a curved extension line passing through the stretchout is first drawn. ”