ON ALGEBRAIC QUANTITIES. 
r' + 0 + 9 c . */ — 1 — m + n ^ — 1, 
0 
r' = m, and 6 + q c = n, 
345 
(?p 
But § = r 
■\g = r 
c — r 
m + n a/ — 1 
(0 
•or 
(?rcr 
( E ror- 
(!) 
4 + 
••• ( E ) 
23. Cor.) Hence /E ^ V_1 - 
( E ) =cr- 
24. ^Ey i . (Ej = (Ey +n , where m and n are any quantities whatever, 
and E the base of the hyperbolic logarithms. 
For let m = p + q — 1 1 
n = s t J — \) 
then . (Yy = ^'Ey + ?v ~ 1 
where p, q , 5, t are possible quantities, 
* + 1 V — 1 
(?) 
= /E 
(?) • (!) 7 • (?) • (!)’ 
= (by Treatise, Art. 88.) ^E^ + 1 . ^1^ 
= (?) 
(?y 
i +t 
c 
^P + s -jjy + t. V ~ 1 
— • / t ?\ ^ ^ 
25 
■ crc)"=c) \ where a, m, n are any quantities whatever. 
2 v 
MDCCCXXIX. 
