Addition and Subtraction. 1:

F they be Homogenal, add or fubtract the ra

tional Part, and to their Sum or Difference join the Surd.

A D D I I IO N.

Ι Τ Ι 7V xy 7xV@c

xVaa+cc 24V xy

3*V ac 4xV aa+cc

SU B T R A CT I ON.
14V xy

12xV CC 5yv aa+cc
7Vxy
7*VCC

3yv aa+cc

2d. If the Surds be Heterogeneal, add or subtract according to the Signs.

1 + 213iv xy+v nx 4*Vaa+387**

SUBTRACTION.

MULTIPLICATION.

F the Surds be Homogenal, take away the Sign

and it is done ; so the V XyXV xy=xy and V xx+ aax V xx+aa = xx+aa.

If rational Quantities be joined to the Surds, then multiply the rational into the rational, and the Surd into the Surd, and join the Products together.

Divison of Surd Quantities. F the Quantities are pure Surds of the same

Kind, and can be divided off, without leaving a Remainder, divide thein, and to their Quotient prefix their radical Sign.

V xy

EX A M P L E.
V xynn-i-nybb

V ****

-уууу Vуп

V xx YY

If Rational Quantities are joined to Surd Quancities of the same Kind, divide the Rational by the Raci nal, if it can be done, and to the Quotient join the Quocient of the Surd, divided by the Surd, with its first radical Sign.

E X A M P L E S. 3dx/xyn

202 yılı

ynxxt-dcxx 3dvy

43V xx

9900cQlo9oksoo!oco

2000!c@occo

20000 Involution of Surd Quantities.

HEN the Surds are not joined to raticWA

nal Quantities, they are involved to the faine Height as their Index denotes, by taking away their radical Sign.

When Surds are joined to rational Quantities, involve the rational Quantitie: to the fame Height as the lodex of the Surd denotes; then multiply the involved Quantities into the Surd Quantities, after the radical Sign is taken away, as before.

EQUATIONS.
Lgebra solves Problems by Equations.
Equations we make use of five Processes.

Ini

A

The fint brings each side of the Equation to an entre Piaction.

Tie fecond, brings Equations into Integers, by notipiying al:ernately the Numerator of each Side into the Denominator of the other.

The third, brings by Transposition the several M.mbers of the unknown Quantities to the fame Side of the Equation, (viz.) to that Side, which after Tranfpofition, will render them Afirmative.

The

The fourth, transposes all loose Quantities from the side of the unknown, to the other side of the Equation.

The fifth, finds the unknown Quantity, by dividing the whole Equation by iis Coeficient.

E X A M P L E.

1

2.*

4%
+ 12 = +6
3

5
22x-+36 4x+32
3

5 2 X 3

12x + go 2x + 36 =

5 3 X 5 14 10x + 180 = 12x + go 4 10x 5 130 = 2x + go

5 - 90 6

90 = 2x

ܐ ܀ 6

17 45= *

3x

+ 5 = * + 2

3*+-20

4

+ 4

6

5x+12 4

6 2 X 4 3

20% + 48 3* + 20 =

6 4

18x + 120 = ?Ox + 48 4

5 120 = 2* + 43 5-4 8 16

72. 2x 71 36 = x

3X6

18.

ان 6

N. B. The three Dots in the Margin fignify Consequently.

EXAMPLE.

X2