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but not coinciding with it, then the section is a hyperbola. If a cone be cut by a plane parallel to its slant side, then the section is a parabola. From its definition it will be readily understood that the elevation of a cone when standing with its axis vertical is a triangle, and its plan a circle. Before attempting the projection of any of its sections, it must first be known how to find the plan, or elevation either being given of a point on its surface, as this will materially assist in finding its sections. In Fig. 151 : If No. 1 be the plan of a cone, No. 2 its elevation, and x in No. 1 a given point on its surface, it will be seen from its assumed mode of generation that this point must lie somewhere in the slant side of its triangular generator a'Ab, No. 2. Now every point in this line it may be assumed to be made up of points in its revolution about the axis a a of the cone describes a circle, and the circle in which x must lie will have a radius equal to the distance between it and a ; therefore in No. 1, with a as a centre and a x as radius, describe a circle cutting the diametral line AB in x. Again, through the given points x and a in No. 1, draw the line axe, cutting the base AB of the cone in c. Find in No. 2 the elevation c of c 106 MECHANICAL AND ENGINEERING DRAWING 107 No, 1, and from it draw the line c'a No. 2 ; then this line will be the elevation of ca, No. 1, on the surface of the cone, and it is in it that the given point x lies. To ascertain where, get the elevation of the circle drawn through x in No. 1 by a projector from x', cutting the slant side a A of No. 2 in point x', then the point #, where a line