i86 RECTIFICATION of the ELLIPSIS, &c. 



-whence ^y^lb£L==— - ^^c'^^n^^. _^ ^ ^ ^^^ 



2 fin ^'l' =: I — cof 24^, and ' -^ = ^^+"'^ ^' 



being zr j-— -==-: thefe fubftitutions being made, we get 



2 <p Cof ^ 



Vi + f* — 2CC01P \/ I + (/* + 2c'coiz-^ v^ 1 -j- t' » + 2<:' coi 24. 



+ 2 t^ Cof 'J'. 



Suppose now, ^=~— ^ = A'-B'cof2v;'+^^cof4,f,— &c. 



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

 the above fluxions, when (p and 4^ := ar, we fliall have B X ar 



=z c X (i + c') X (A' + f ) X z^, and fo B = <7 X (i -f c) X 



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

 of M. DE LA Grange, are 



A-=l+^c"+ '^C' +^r:^. c" + &c. 



a \2 ' 2 3. 4 ' 2. 4 2. 4. 6 ' ' 



which feries converge very fall, on account of the fmallnefs of* 

 c' in rtfpedl of c. 



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

 ft"; I more converging, we may eafily do fo : For it is manifeft 

 that B and B' are fimilar fundions of c and c' : and that if wc 



«^ake ^"= i+^^x-I^-^ ''" = i'7!/r^7^ ^ ^"""^ ^"^ ^""^ ^^^ P'"'' 



9 A", 



