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projection of curved lines that if the position of points in the curve can be determined the problem is virtually solved. In the case of the circle in Fig. 141, it would have been quite possible to have first found any number of points in the bounding line and then to have joined them by a line passed through them, and thus have produced the circle, but the use of the compass obviated the necessity. In the problem before us, the necessity exists for finding exactly several points in the required elevation of the object in the readiest possible way. The original object being a circle, a regular figure as distinguished from an irregular one whose surface is readily divisible into parts, it is apparent that by turning down one half of that surface on the line AB in No. 1 as a diameter, and drawing lines upon it at right angles to AB, through any points in the semi-circle, we can at once find the actual length of those lines and transfer them to their vertical projections in No. 2. The solution of this problem may also be reasoned out in another way. The original line AB, No. 1, is in fact as was shown in the previous problem a curved line, although presented to the eye as a straight one, every point in it, on either side of that at C, being farther from the eye the farther it is to the right or left of C. As the actual length of a line drawn across the circle at C, through its centre to the opposite edge, is known to be equal to AB, or twice Cc, so can the distance across the circle through any other point in AB be ascertained in the same way. For, as the ordinate Cc is measured at right angles to AB, so any other, as 2, 2', is equal to half the distance from the point 2' across the circle to the corresponding opposite point in its edge. With this explanation the following problem should present no difficulty in its solution.