are, of course, the edges of sections of the cone, of which the circles in Fig. 15 are the respective plans. Next, from points as b, c, h, where the circles are cut by the line of section, raise perpendiculars to intersect the horizontals in elevation, and draw the curve through these intersections as shown.
To obtain the Coveting of a Cone.—Let Fig. 17 represent the plan and the elevation of a right cone. If we divide one-half the circumference of base into a number of equal parts, as points 1 to 9, and project these to the base line in elevation, then draw straight lines from the points to the apex of the cone a, we shall have the elevations of a series of lines drawn at equal distances apart upon the surface of the cone, and by their aid we can locate a point or number of points on that surface.
To obtain the Development of the Semi-Cone (tf-i'-g).—With point a as centre and a~ 1' (the length of side) as radius, describe an arc. Upon this set out an equal number of spaces as shown in the plan; and from the last, point 9', draw a line to a.
Then the space bounded by the lines a-1', 9'-a will exactly cover half the cone, and if the other halt is completed similarly, the whole surface will be obtained.
To obtain the Development of Frustum of a Cone as shown by the elevation, C-I), 1 '-9, proceed as described to obtain the covering of the entire cone, and from the apex a describe an arc from I), the top of the frustum. The portion enclosed between the two arcs, and the sides D-1 and €'-<)', is the covering of one half of the frustum.
If the whole cone is not given, all that is necessary to locate point a is to produce the sides of the frustum until they meet. In a subsequent example (page 189) a further use for the radial lines is shown.
The Coverings of Domes.—A dome is a vaulted roof having a circular, elliptic or polygonal plan. The first kind are termed spherical domes or vaults; the second, ellipsoidal domes; the third are specified by terms indicating i6o
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