usbidcheck download

found by drawing lines through the points in the semi-circle (cut by the assumed section planes) parallel to the axis of the cylinder. For the corresponding triangular sections of the cone, describe on its base B C as a diameter the semi-circle B X C. On its axis, A A' produced, set off from A' the several distances that the points 5, 6, 7, 8 in the base of the triangle a a b are from the point a in it. Through the points 5', 6', 7', 8, thus found, draw lines parallel to B A' C, and from where they cut the semi-circle find by projection the elevation of the triangular sections of the cone, as shown in No. 2 ; then the points where the corresponding sections of the two solids intersect are points in their lines of penetration. The two points, x y in those lines or where the plane drawn through a 8 in the side elevation is tangent to the surface of the cylinder are found by drawing a line through as, where the plane a 8 touches, and intersecting it with the triangular section A x" y of the cone made by the same plane. The plans of the lines of intersection 1x2 and 3 y 4 in No. 2 are most easily determined by finding horizontal sections of the cone which will all be circles at several points in those lines in elevation, and letting fall projectors from them on to the circular sections so found ; then the points where the projectors cut these sections will be those through which the required lines of penetration are to be drawn. As the solids are directly at right angles to each other, their lines of intersection are consequently symmetrical on either side of the cone, both in plan and elevation. 76. As the procedure in finding the lines of intersection of a cone and cylinder having their axes in the same plane, but not at right angles, would be the same as in the last example, as any plane passing