demonstrated by the method of Indeterminat.es. 75 



bra. It was soon perceptible that any equation put = 0, consisting 

 of an aggregate of different quantities incapable of amalgamation by 

 the opposition of jjIus and minus, must give each of these quantities 

 equal to zero. Reverting to indefinites, it then appeared that their 

 whole theory might be developed on the same principles, and making 

 trial, we have satisfied ourselves most fully of ha\'ing thus hit upon a 

 method of clearing up all the difficulties of what we shall entitle 



THE CALCULUS OF INDEFINITE DIFFERENCES. 



"A constant quantity is such, that from its very nature it cannot be 

 made less or greater. 



" Constants, as such quantities may be briefly called, are denoted 

 generally by the first letters of the alphabet, 



a, b, c, d, he. 



"A definite quantity is a given value of a quantity essentially 

 variable. 



" Definite quantities are denoted by the last letters of the alpha- 

 bet, as 



z, y, X, w, &c. 



"i/3» indefinite quantity is a quantity essentially variable through 

 all degrees of diminution or of augmentation short of absolute noth- 

 ingness or infinitude. 



" Thus the ordinate of a curve, considered generally, is an indefi- 

 nite, being capable of every degree of diminution. But if any par- 

 ticular value, as that which belongs to a given abscissa, for instance, 

 be fixed upon, this value is definite. All abstract numbers, as 

 1, 2, 3, Stc. and quantities absolutely fixed, are constants. 



"The difference between two definite values of the same quantity 

 (y) is a definite quantity, and may be represented by 



Ay 

 adopting the notation of the Calculus of Finite (or definite) Differ- 

 ences. 



"In the same manner the difference between two definite values 

 of A y is a definite quantity, and is denot-ed by 



A (Ay) 

 or more simply by 



A => y 

 and so on to 



A " y. 



