6 o A Treatise os Algebra.

Value of 7* -f- 8y -f- jz will from thence be given — 2 c

— b. Hence it is manifest that giving the Value of 7*+ 8y + 9z, in the third Equation, contributes nothingtowards limiting the Problem ; and that the Problem it-self is not only unlimited, but also impossible, unless d isgiven equal to 2c — b.

Of the Reduction of Jingle Equations.

After a Question, by the Methods explained in thelast Section, is brought to an Equation, involving oneunknown Quantity with others that are known, thatEquation before the Value which answers the Conditionsof the Question can be known, is to be so order’d andtransform’d by the Addition, Subtraction, Multiplication,or Division, &c. of equal Quantities, on each Side thereof,as to preserve a just Equality between it’s Parts, and sothat an Equation may, at last, result, wherein (if possi-ble) the unknown Quantity may stand alone on one'Side, and all the known ones, by themselves, on theother : And this is call’d the Reduction of an Equation.But though this Method of ordering an Equation ifgrounded upon self-evident Principles; yet the Opera-tions are sometimes a little difficult to manage in the bestManner; for which Reason the following Rules aresubjoined.

1°. If in an Equation there are two or more Terms ofthe fame kind, or which differ only in their numeral Coeffi-cients, (or prefix'd Figures) let those Terms (when they donot defiroy one another) be reduced into one, by Addition, orSubtraflion , and the Equation will be contracted thereby.

Thus, if there be given the Equation 30 -f- x — 2 a~c — -s- ; then, 3 a — 2a being reduced to a,

and — 2b -f- 3^ to b, the Equation will become a-\- x

c -j- b : Also, if the given Equation be 3*— 20 = 2x-f- 10, by subtracting 2x from each Side thereof, weshall have at— 20= to, and,,by increasing the equalQuantities, on each Side, by 20, there will come outx — 10 -(- 20 =: 30. Moreover if you have qx -f- 3 b

— 2* — <7—3* -j- aar, then, by adding 3*, to each Side,

you will have 6* -j- 3 b — a-f ax. Un-