A Treatise os Algebra. 77therefore the Proportion will stand thus,

. . . . + ar~ % -f- ar~' = x ; which being, equally,multiply’d by r, gives ar 4- ar 1 4" arS 4“ ar+ — ar *4 - ar" = rx, from which the first Equation being sub-tracted, there will remain — a-\-ar —rx—x ; whence x—(ar —a _a r~fy.r — a \ arss*jr—aa a ^v r — i r — x ' ar — *

to be demonstrated.

Having treated of the Manner of preparing and bring-ing a Question to an Equation, and shewn how suchEquations are to be managed, and likewise laid down suchuseful Theorems, relating to Proportions, as will be neces-sary in what follows, it is now time we should come toexplain the Use of what has been hitherto delivered, inthe Solution of Problems; since ’tis an Observation as justas general, that Arts are more easily learn’d by Examplesthan Precepts.

SECT. XI.

Arithmetical 'Problems,

1

PROBLEM I.

To find a Numhr , to which if 7 5 be added , the SumJbaH be quidruple to the required Number,

L ET the Nunber sought be represented by Xj thenit's Quadrujle, or four times that Number, will berepresented by 4, ; which, by the Condition of theQuestion is equal to x added to 75, that is, 4.x =x 4-75. Now from tach of these equal Quantities, let * besubtracted, and ii is manifest there will remain zx —75,from whence, bt dividing both Sides of the Equation bythere comes oit x (= --) — 25 ; which is the Num-ber that was to b found (for it is plain that 25 4* 75 ‘ s= 4 X 25 (— IOi).

P R O B L E M