drawing circles and curves using straight lines asconstruction lines. First, draw two straight linescrossing each other at right angles, as in figure5-63, view A. The point at which they cross willserve as the center of the circle. The four linesradiating from this center will serve as the radiiof the circle. You can use a piece of marked scrappaper to measure an equal distance on each radiusfrom the center. Sketch a square, with the centerof each side passing through the mark defininga radius. (See fig. 5-63, view B.) Now sketch inyour circle, using the angles of the square as aguide for each arc. When larger circles arerequired, you can add 45-degree angles to thesquare to form an octagon. This will provide fouradditional points of tangency for the inscribedcircle.In figure 5-63, view C and view D, four lines,instead of two, are sketched crossing each other.The radii are measured as in constructing the othercircle, but a square is not drawn. For this method,you will find it helpful to rotate the paper andsketch the circle in one direction.For drawing large circles, you can make asubstitute for a compass with a pencil, a piece ofstring, and a thumbtack. Tie one end of the stringto your pencil near the tip. Measure the radiusof the circle you are drawing on the string, andinsert your tack at this point. Now swing yourpencil in a circle, taking care to keep it verticalto the paper.Another technique for drawing circles isshown in figure 5-64. In view A of figure 5-64,observe how the pencil is held beneath the fourfingers with the thumb. This grip tends toproduce a soft or easy motion for sketching largecircles or curves and also makes it possible tosketch small circles, as shown in figure 5-64, viewsB and C. You notice in figure 5-64, view B, thatthe second finger rests at the center of the circleFigure 5-65.-Steps in sketching a circle.and forms the pivot about which the pencil leadcan swing. The distance from the fingertip to thepencil lead determines the radius of the circle. Todraw smaller circles, you need to assume asomewhat different grip on the pencil, as shownin view C of figure 5-64, but the principle is thesame.Figure 5-64.-Proper pencil grip in sketching circles andarcs.As shown in view A of figure 5-65, the firststep in sketching either large or small circles withthe grips shown in the previous figure is placingthe second finger on the paper at the center ofthe proposed circle. Then, with the pencil lightlytouching the paper, use the other hand to rotatethe paper to give you a circle that may look likethe one in figure 5-65, view B. To correct the slighterror of closure shown in view C, erase a sub-stantial section of the circle and correct it by eye,as shown at the right. You now have a completeand round circle, but with only a very light line,5-32