i86 RECTIFICATION of the ELLIPSIS, &c. 

 ■whence -- ^\'''^^ ,, = -^^^^"''^- + 2 <^ cof <!'. Again. 



3 fin ->!'=: I — cof24', and . ' . , , = \l^ . t . » c' 



being r= _ -f : thefe fubftitutions being made, we get 



V'l + f* — 2ccolp v' 1 + ^' + 2c' col 24. v'T'+'^M-'iFcori^ 



+ 2 vj/ cof J*. 



Suppose now, ^7=y^t~^^ = A'— B'cof2'J'+<^'cof4^|/— &c. 



it is evident, from what goes before, that, taking the fluents of 

 die above fluxions, when <p and "^ — w, we ihall have B X ar 



= cX{i + c')X (A' + f ) X ^, and fo B = c X (i + c') X 



(A'+?). 



The values of A' and B', in feries according to the method 

 of M. DE LA Grange, are 



.^B'=(i.' + i-^;.-+iJ-if|4.- + &c.) 



which feries converge very fail, on account of the fmallnefs of 

 c' in rt fped of c 



If, however, it be required to find the value of B by feries 

 ft'l more converging, we may eafily do fo : For it is manifefl 

 that B and B' are fimilar fundions of c and c' : and that if w« 



1— v'l -f * j/y _ l — ^i—c'"^ 



^ake c^^=: Y^^^, ^"' = TT^S^' ^"^ ""^ ^' ^^ ^'^ 



9 A", 



