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As the simplest possible curve-bounded figure is the circle, its projections claim first attention. We have defined such a figure as the path described by a moving point that is always at the same distance from a fixed point, around which it moves. When such a figure is cut out of any material substance, such as a piece of metal plate, or card, it is called a disc. Looked at in various directions, it assumes different forms. The exact form taken is obtained by projection. Our first problem in connection with it is Problem 47. Given the plan of a circular plate, to find its front and side elevation. Let the straight line AB, Fig. 141, No. 1, be the given plan. Now as the edge view of a disc, looked at from above, is a straight line, we see that if AB is such a view, the plate must be perpendicular to the plane of its projection, or the HP, and being parallel to the IL every part of its surface must be parallel to the YP ; therefore its elevation will be a circle and have its bounding-curved line everywhere equi- distant from its centre. To find this bisect AB in C, and through C draw a projector into the upper plane at right angles to the IL. Take any convenient point in this projector at a greater distance from the IL than half AB say a and through a' draw a line parallel to the IL. With a' as a centre and AC, No. 1, as a radius, describe the circle acbd, No. 2, which will be the front elevation of the circular plate. If correctly drawn, vertical projectors through A and B in the plan should cut the diametral line drawn through the centre a' of the circle in the points a and b in that line. Then as the surface of the plate is parallel MECHANICAL AND ENGINEERING DRAWING 93