A Treatise of Algebra.

57

SECT. IX.

Of E QJJ ATIONS,

And how a Question is brought to an Equation.

A N Equation is when two equal Quantities, diffe-rently expressed, are compared together, or wrotedown with the Sign — between them, which equalQuantities are call’d the Sides or Parts of the Equation.

Thus 10+5 — 24. — g, is an Equation expressing theEquality of the Quantities 10+5 and 24—9, on eachSide thereof. And x = b -f- 2 c—d is an Equation, shew-ing that the simple Quantity *, on one Side, is equal to-the compound Quantity b -f- 2 c — d on the other : TheQuantities *, b, 2c and d are call’d the Terms or Mem-bers of the Equation.

Equations are the Means whereby we come at suchConclusions as answer the Conditions of a Problem.

When a Problem is proposed to be solved algebraically,great Care ought to be taken that it’s true Design andSignification be perfectly understood, so that (if need be)it may be first abstracted from all ambiguous and unne-cessary Phrases, and the Conditions thereof expressed inthe clearest and most simple Manner possible. This be-ing done, and the several Quantities therein concerned,whether known or unknown, being denoted by properSymbols, let the true Sense and Meaning of the Questionbe translated from the verbal, to a symbolical Form ofExpression, and the Conditions of the Question, thusexpressed in algebraic Terms, will (if it be properly li-mited) give as many Equations as are necestary to it’sSolution ; Or, if this can’t be done without some previ-ous Operations (as in many Cafes it cannot,) let theLearner observe this Rule ; let him consider what Me-thod or Process he would take to prove, or satisfy him-self in the Truth of the Solution, if the Numbers thatanswer theConditions of the Question were actually given,

or