103 



h + &c. 



2 



+ a 



n-l O 



Art. 29. I was not aware till a few weeks since that this notation 

 is not original. It is just hinted at by Lacroix, Traite du Cat. Diff. et 

 Int. Tom. II. p. 527. 



Art. 31. This notation will be improved by writing d . u instead 

 oi du; and on the same principle {<p{x)} = <p{a). Thus 



{^} ={!"} 



Art. 32. The necessity of adopting a significant notation to denote 

 the limits of integration has been long felt. Fourier, who has been 

 followed by Cauchy {Memoire sur la Theorie des ondes), proposed to 



adopt J'udx. 



a 



Art. 33. Ex. 9. The very elegant principle on which the demon- 

 stration is founded, was demonstrated independently by Professor Schweins, 

 and Mr. Coddington ; the former in " Theorie der Differenzen und 

 Differentiale," Heidelberg, 1825, and the latter in "An Introduction to 

 the Differential Calculus on Algebraic Principles," Cambridge, 1825. 



