TRANSFER OF AN ANGLE

Figure 4-8.-Dividing a line into proportional parts. Figure 4-7.-Using a scale to lay off equal intervals on a random line. to A, and project the other points of intersection from CB to AB by lines parallel to the first one. The projected points of intersection divide AB into 10 equal parts. Figure 4-7 shows how you can use a scale to lay off equal intervals on the ray line. DIVISION INTO PROPORTIONAL PARTS Figure 4-8 show’s a method of dividing a line into given proportional parts. The problem here is to divide the line AB into parts that are proportional as 2:3:4. Lay off ray line CB from B at a convenient acute angle to AB. Set a compass to a convenient spread, and lay off this interval from B on CB the number of times that is equal to the sum of the figures in the proportion (2 + 3 + 4 = 9). Draw a line from the point of intersection of the last interval to A, and use a straightedge and triangle to project the second and fifth intercepts on CB to AB by lines parallel to the first one. The projected intercepts divide AB into segments that are proportional as 2:3:4. Here again, you could use a scale to lay off nine equal intervals on CB. Figure 4-9.-Dividing a line into parts according to a given ratio. of doing this is shown in figure 4-9. Here, it is required that AB be divided so that the ratio between AB and a part of AB is the same as the ratio between CD and EF. From A, draw a ray line AG at a convenient acute angle from AB. On AG, lay off AH equal to EF and AI equal to CD. Draw a line from I to B, and use a straightedge and triangle to project H to J on a line parallel to IB. The ratio of AB to AJ is the same as that of CD to EF. ANGLES You already know how to lay off an angle of given size with a protractor, or trigonometrically by the use of the tangent or the chord method. DIVISION ACCORDING TO A GIVEN RATIO TRANSFER OF AN ANGLE You may be required to divide a line into parts so that the ratio between the whole line and one of the parts is the same as that between two other lines. A method There is a geometric construction for laying off, on another part of the same drawing or on a different drawing, an angle 4-3