demonstrated by the method of Indeterminates. 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 plus 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 having 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 menated 
generally by the first letters of the alphabet, 
a, b, c,d, Sc. 
“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 
“An INDEFINITE quantity is a quantity essentially variable through 
all degrees of diminution or of augmentation short of absolute Noru- 
INGNESS 07 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, &c. 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 
“f 
adopting the notation of the Calculus of Finite (or definite) Differ- 
ences. 
“In the same manner the difference taewens two definite values 
of A y isa definite quantity, and is denoted by 
A (Ay) 
or more simply by 
are f 
and so on to 
Ay: 
