337 
Arithmetic  of  impojfible  Quantities. 
orrl  y5  - °rd-  iX~5  Ord  3X+  IQ  0rd.  y 
1 6 j and  univerfally, 
if  n be  any  number;  a the  co-efficient  of  the  fecond 
tom  of  a binomial  raifed  to  the  power  n,  b the  co- 
efficient of  the  third,  &c.  and p the  greateft  co-efficient.- 
when  n is  an  even  number, 
xn  - a_  abf.  xx+l  abf.  ^=T4  x 
2n—**  • ~~  — r*~  il 
but  when  n is  an  odd  number, 
oid.  71  =.  -d'  nAni ord-  ^ x «+*  ord.  
2* 
If  now  a-  denote  an  arch  of  a circle,  by  fubftituting  and 
changing  the  %ns  as  oft  as  ord.  x occurs  in  any  of  the 
preceding  expreffions,  we  get 
" I — cof.  2x 
• p ord.  x 
iin.  x = 
.3 
fin  r3-  „ 
4 
fin.  a;  = 3—4  cof.  aa+cof.  4* 
8 
fin  v - j°  fin-  *—.5  ^n.  3^-f  fin.  . 
1 6 • umverfally,  it 
« be  any  number,/  the  greateft  co-effident  of  a binomial 
raifed  to  the  power  n,  a the  co-efficient  next  left  than  A 
B the  co-efficient  next  lefts  than  a,  and  fo  on;  when  n 
is  an  even  number, 
iin.  x ~~  co**  co f.  4* — &c, 
2*—*  l ' 
but  when  n is  an  odd  number, 
iin.  X ZZ  ^ fin«  * 'A  cof,  cof.  £x &C. ^ 
%n — >x 
Thefe 
V* 
