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BISECTION OF A LINE
BISECTION  OF  AN  ANGLE

Engineering Aid 3 - Beginning Structural engineering guide book
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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







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