SECTION IX. 
EQUATIONS, 
N Equation is, when two equal quantities, dif- 
ferently expressed, are compared together, by 
means of the sign zz placed between them. 
Thus, 8 — 2 zz 6 is an equation, expressing the 
equality of the quantities 8 — 2, and 6 : and x — a + b 
is an equation, shewing that the quantity represented 
by x is equal to the sum of the two quantities repre 
sented by a and b. 
Equations are the means whereby we come at such 
conclusions as answer the conditions of a problem ; 
w herein, from the quantities given, the unknown ones 
are determined ; and this is called the resolution, or re 
duction of equations. 
REDUCTION OF SINGLE EQUATIONS. 
Single equations are such as contain only one un 
known quantity ; which, before that quantity can be 
discovered, must be so ordered and transformed, by the 
addition, subtraction, multiplication, or division, &c. 
of equal quantities, that a just equality between the two 
parts thereof may be stilt preserved, and that there may 
result, at last, an equation, wherein the unknown quan 
tity stands alone on one side, and all the known ones 
on the other. But, though this method of ordering an 
equation is grounded upon self-evident principles, yet 
the operations are sometimes a little difficult to ma 
nage in the best manner; for which reason the follow 
ing Rules are subjoined. 
1°. Any Term of an equation, may be transposed to 
the contrary side, if its sign be changed *. 
* The reason of this Rule is extremely evident; since 
transposing of a quantity thus, is nothing more than 
subtracting or adding it on both sides of the equation, 
according as the sign thereof is positive or negative.