Second Cafe of the Cuhick Equation x % -qx~r. 935 
prefixed to them as they had before when ss flood for 
- — — ; and thofe terms of the faid fyftem which are re-' 
prefented by the terms of the faid feries which involve 
the odd powers of ss, to wit, ~ and d 0 A_, &c„ will have 
contrary figns to thofe they had before. Confequently, 
if we change the figns of thofe terms in the feries 2 — 
— - dhf.-- p?— - gee. which involve the odd powers of 
ye' 2436 05.016 A 
ss. to wit, the terms — and &c. the new feries- 
J ' ye 6$6ie 
thereby produced, to wit, 2 - d 2 L + JS^L. _ & c . will 
reprefent, or be equal to, a fyftem of terms which will 
not only be the very fame in point of compofition (or 
will be the fame powers, products, and multiples of the 
two original quantities C. and A), as thofe which were re- 
prefented by the feries 2 — — — dfh. - -~s - See. in the 
former cafe, but will alfo be connected with each other 
in exadllv the fame manner by the figns + and -- : that 
is, by Art. 3 1 . the faid new feries will reprefent, or be 
equal to, the following fyftem of terms, to wit, 2—— +- 
of e ^ fy® 3 yf_ j yf_ 
2*jrr 16 4x2777* 27 x 274* 64 16x274?* 4.X27X27?' 4 27x27x2 7^ 
&c. 
But' 
