ON ALGEBRAIC QUANTITIES. 

 /. r' + •{- qc . y^n =m + n V^^, 







.-. r' =z m, and 6 -{- q c — n, 



a 



••• ' = (?)"' 



345 



Biitf = r /1\T = r /1\ 



c 



(?)"•(!)■ 



•■•(?)"""■ = (?)"■(!) 



23. Cor.) Hence /^E^^"' = a\T. 



m-^-n 



^*' (?)™ ■ i^T ~ (?)"'^"' where m and » are any quantities whatever, 

 and E the base of the hyperbolic logarithms. 



For let w = /) + g ^ _ 1 ) 



n — gif /ITT (^'^^^^ P' 9' *' ^ ^"^6 possible quantities. 



then /E 



j + 'aZ-i 



? + < 



= (by Treatise, Art. 88.) /Ey^' . (l)^ 

 = /E\^ + ''^^+^-'*^-^ 



. /a\ . /a\ = ray ", where a, to, n are any quantities whatever. 



25 



MDCCCXXIX. 



2 Y 



