OF ALGEBRAIC QUANTITIES. 359 



61. With respect to quantities such as sin {a-{- b^ — l),cos(a + 6^/ — 1), 



&c., quantities strictly speaking not algebraic, it may be observed, that if it be 



found useful to introduce these quantities into algebra, they may without im 



propriety be introduced, by giving to sines, cosines, &c., algebraic definitions ; 



thus sin A may be defined to signify 



A - A 



A V- 1 /E\~ A V— 1 



('■)' -(!) • „_ (f) -gy 



2 -/ - I 



„ , or ■ , and we shall have 



sin (a -f 6 



2^-1 2 \/ - 1 



therefore, considering sines, cosines, &c., merely as algebraic quantities, we 

 may make use of the expressions sin {a -\- b ^ — l), cos {a -\- b .J — l), &c., 

 if such expressions be found convenient in algebraic operations. 



Jesu-s College, Cambridge, J. W. 



April 22, 1829. 



