Figure 4-8.-Dividing a line into proportional parts.Figure 4-7.-Using a scale to lay off equal intervals on arandom line.to A, and project the other points of intersectionfrom CB to AB by lines parallel to the first one.The projected points of intersection divide ABinto 10 equal parts.Figure 4-7 shows how you can use a scale tolay off equal intervals on the ray line.DIVISION INTOPROPORTIONAL PARTSFigure 4-8 show’s a method of dividinga line into given proportional parts. Theproblem here is to divide the line AB intoparts that are proportional as 2:3:4. Layoff ray line CB from B at a convenientacute angle to AB. Set a compass to aconvenient spread, and lay off this intervalfrom B on CB the number of times thatis equal to the sum of the figures in theproportion (2 + 3 + 4 = 9). Draw a line fromthe point of intersection of the last intervalto A, and use a straightedge and triangle toproject the second and fifth intercepts on CBto AB by lines parallel to the first one. Theprojected intercepts divide AB into segmentsthat are proportional as 2:3:4.Here again, you could use a scale to lay offnine equal intervals on CB.Figure 4-9.-Dividing a line into parts according to a givenratio.of doing this is shown in figure 4-9. Here,it is required that AB be divided so thatthe ratio between AB and a part of ABis the same as the ratio between CD andEF. From A, draw a ray line AG at a convenientacute angle from AB. On AG, lay off AHequal to EF and AI equal to CD. Drawa line from I to B, and use a straightedgeand triangle to project H to J on a lineparallel to IB. The ratio of AB to AJ is the sameas that of CD to EF.ANGLESYou already know how to lay off anangle of given size with a protractor, ortrigonometrically by the use of the tangent or thechord method.DIVISION ACCORDINGTO A GIVEN RATIOTRANSFER OF AN ANGLEYou may be required to divide a line intoparts so that the ratio between the wholeline and one of the parts is the same asthat between two other lines. A methodThere is a geometric construction forlaying off, on another part of the samedrawing or on a different drawing, an angle4-3
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