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explained) is divided into 360, one-sixth of the circle must contain 60, or the angle which the two lines in the problem have to make with each other. Knowing this specific relation subsisting between the radius and the chord of an arc of 60 of a circle, we are enabled to lay down any angle with the assistance of a " scale of chords," which will be found on one of the set of drawing-scales previously recommended. To show its use, let us take, for example Problem 9 (Fig. 52). To draw a line, making an angle of, say, 70, with a given line at a given point in it. Let AB be the given line, and a the given point in it. From the zero point, on the extreme left of the scale of chords, and with a radius in the compasses equal to the distance from that point to the one marked 60 with the arrow over it on the scale, draw with a, on the line AB as a centre, the arc be, cutting AB in c, and from c as a centre, with a radius equal to 70 on the scale of chords, cut the arc be in . A line, drawn through b and a will make, with the given line AB, an angle of 70; and so with any other angle, always remembering that from zero to 60 on the scale of chords is the radius with which the first arc in the construction is to be drawn. CHAPTER Y PLANE GEOMETRICAL FIGURES 13. IT may be noted, before passing on to the construction of the plane geometrical figures which form the surfaces of the plane solids whose projections we shall next show how to obtain, that as the angles most generally chosen for the surfaces of mechanical details are those which contain some multiple of 5, it is not necessary to use even a scale of chords in laying them down on paper or other material, as most