EVOLL'TIO FUNCTIOMS PEBIXRBATRICIS ETC. 265 



+00 /f/A('}\ . . . , „ , -*-M A/A(0\ 



£ lal — — \simjsw(y-*-ix—a — o')= — S tal Icos j C<-»-1 )r-t-2x — o — o' > : 



-</) \ (/a f ■" "^ -00 \ f/a / ^ ^ -^ > ' 



+00 /</A(0\ . . , , +M /fM(')\ 



+00 ,/(/A(0\ ^ +00 /</A(')\ 



- E ia I — — lsinjjsinQ-H2j: — o — o )=S /«'! — _ lcosU«-t-1)7'-*-2a: — o — o' j ; 



^+co ,(dhi')\ . . . , , _+oo /f/A(')\ 



^ V (l?? jsin./s.nCr-HO-«') =-2 _^,a ^ -;^ )cos ( (/^1 )j-^«_«' j ■ 



posito igitur «=(« — 1 ), quod per num. 15, salva magni- 

 ludine, fieri potest, et terniiiiis duclis per cos(/^-)-2x — ai- — a,') 

 ab lis secretis , quos per cos(/j-(-a — a') niuliiplicanlur; fa- 

 ctor product! ee' evadet 



'./A('-i) 



Xcos(ij-+-2x — « — i)') 



Notandum est, alteram hujus factoris partem, mutato i iu 

 — ^^, ct loco A^~'^ substituto A^'\(2), (num. 5) eamdem ma- 

 gnitudinem retinere, ideoque converti posse in 



+001 



-00/ 





Quo patet, nos uti posse utraque forni;i modo utriusque di- 

 midium sumamus . Ergo si ponatur 



