34©  Mr.  playfair  on  the 
the  circumference  being  negative);  and,  for  the  fame 
reafon,  cho.  a+mx-x^-cho.  a-x—+  cho.  x-a.  Hence 
, _ rr*  n cbo.  a4- cho.  x — a 
the  general  expreffion  becomes  — C-Ql-  — = fa  + fb  + 
fc+  ....  ini).  If  therefore  gk  be  drawn  from  the 
center,  bifedting  the  chord  ab  in  h,  and  meeting  the 
circumference  in  k,  the  fum  of  the  chords,  that  is, 
af4-  F B 
FA4-FB  + FC  + FD  + FE  = — — x GK. 
I is. 
2.  Let  n be  an  even  number,  the  reft  remaining  as 
above,  and  let  it  be  required  to  find  the  fum  of  the  ji 
powers  of  the  chords,  that  is,  the  fum  of  fa  +fb  +fc 
(m).  By  reafoning,  as  in  the  cafe  of  the  fines, 
it  will  appear  that,  if  p be  the  greateft  co-efficient  of  a 
binomial  raifed  to  the  power  n ; a the  co-efficient  next 
lefs  than p;  b the  co-efficient  next  lefs  a.  and  fo  on,  then, 
n 
cho.  a zip — 2 A cof.  a-\- 2B  cof.  za+o.'D  cof.  3*4-  &c. 
cho.  a + x ZZ p ■ — 2 A cof.  2 B cof.  2X«+^+2D  cof.  + &C. 
cho.  a+2x  —p — 2 A cof.  a+x+zB  cof.  2X«+2x+  2 D cof.  3X«+2x,  See. 
8cc. 
Each  of  thefe  vertical  columns  is  to  be  continued  down- 
ward, till  the  number  of  terms  be  equal  to  m,  and  there- 
fore the  fum  of  the  fecond  is  mp.  The  fum  of  the  third, 
or  of  -2Axcof.  ^+cof.  ^z+:v+cof.  a+  2X (m\  by 
3Tt  8 is  •—  2 A X co^  g~~"c°f»  a-\-mx — cof.  a — Jf-j-cof.  a-\~mx — .v  
2X  I — col*  x 
(becaufe  mx-fixt  circumference) 
-A,. 
