C 573 ] 
in n n in 
becomes a-\-w — 2x^-fw — &> + a ' — « = 4 
x 2 - 4 - 2q x 2 4 - ir. &c. u z x &> z 4 - 2 x &> 2 + 1 — ^ *z 2 ’, 
2 i-j-y i-j-r 
I p 
&c. p being = 1 [Art. II.) and ci 2 (= l 2 ) s=s o.. 
1 + P 
Moreover, one of the other cofines q , r, r, &c. being 
= — 1 [Art. II.), fome one of the factors 2 4- 2 q t 
2-I-2 r, 2 + 25 , &c. will vanifh : Which fadlor 
being expung’d from the product 4 x 2 + 2 q x 2 -{- 2 r, 
&c.. and reftor’d to the divifor w 2 + - — r—? £ s , or 
i+? 
j— 
co 2 -j — a 2 , &c. from which it was taken, that di- 
i-f-r 
vifor will become 4 a 2 \ and the product 4x2 + 2^ 
x 2 + 2r, &c. will then (by Art. V.) be = n 2 . 
» ” 2 « 
Confequently^-f-o) — 2xa-j~oo xa — w *-j- a — 00 r 
will be = n 2 x o z x 4 x w 2 -f t 2 ' x w 1 -j- d 2 , &c. 
where the factor 4^ 2 takes place inftead of oo z + fq. 
of the tang, of po°. 
If y be = 1, and n an odd number, p will be = r, 
and b — o ; but no one of the cofines y, r, r, &c. 
will be = — 1, as when n is an even number. There- 
zn « 
fore, in this cafe, the equation a-j-a> — 2 y x a w 
» zn ______ — — 
x cl — 00 “f* cl — 00 =24 2 y X oo 2 “h* b z ~t~ c z , &c. 
2K " ” 
becomes a-j-w — 2 x a-Yu> x a — w + ^ — ; 
4 x w 2 x co 2 + c 2 x &) 2 + &c. 
