﻿572 
  Mr. 
  A. 
  B. 
  Kempe 
  on 
  the 
  production 
  of 
  [June 
  17, 
  

  

  then 
  

  

  RP 
  O 
  is 
  parallel 
  to 
  FD', 
  

   EFO' 
  „ 
  „ 
  PB. 
  

  

  Thus, 
  if 
  O 
  L, 
  0' 
  L' 
  be 
  drawn 
  perpendicular 
  to 
  A 
  B, 
  

  

  N'L'=B 
  N. 
  

   Therefore 
  BL=B'L'=NN', 
  a 
  constant. 
  

  

  Fig. 
  8. 
  

  

  Thus 
  the 
  loci 
  of 
  O 
  and 
  O' 
  are 
  two 
  parallel 
  straight 
  lines 
  perpendicular 
  

   toAB. 
  

  

  The 
  two 
  added 
  bars 
  may 
  clearly 
  be 
  replaced 
  by 
  the 
  bars 
  f 
  Ceo, 
  gC'w 
  

   parallel 
  to 
  them 
  ; 
  and 
  the 
  points 
  w, 
  w', 
  where 
  these 
  bars 
  cut 
  the 
  line 
  

   O'BO, 
  will 
  move 
  in 
  straight 
  lines 
  cv\, 
  cu'k 
  perpendicular 
  to 
  AB. 
  

  

  III. 
  § 
  9. 
  Fix 
  AB. 
  

  

  Make 
  h=-,k=b. 
  

   a 
  

  

  Then 
  P 
  coincides 
  with 
  C, 
  

  

  D 
  „ 
  „ 
  B'. 
  

  

  Replace 
  C 
  D', 
  C 
  B' 
  by 
  the 
  new 
  bars 
  

  

  B'K=C'D', 
  D'K=C'B' 
  5 
  

  

  so 
  that 
  B' 
  K 
  is 
  parallel 
  to 
  C 
  D. 
  

   Add 
  the 
  two 
  bars 
  

  

  C 
  = 
  B 
  K, 
  KO 
  = 
  B'C 
  ? 
  

   so 
  that 
  P 
  O 
  is 
  parallel 
  and 
  equal 
  to 
  D 
  K, 
  and 
  therefore 
  to 
  C 
  D'< 
  

  

  