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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 Quotient of the Surd, divided by the Surd, with its first radical Sign.

E X A M P L E S.

204 yiv

ynxx+dcxx 12/ 3dry

43V xx

3dxv xуп

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THEN the Surds are not joined to ratio

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

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When Surds are joined to rational Quantities, involve the rational Quantities to the same Height as the Index of the Surd denotes; then multiply the involved Quantities into the Surd Quantities, after the radical Sgn is taken away, as before.

E X A M P L E S. 11! *yy.

5*v **yy I Q 214 xmyy 25****+25**yy

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EQUATIONS. Lgebra solves Problems by Equations. A

Equations we make use of five Processes.

In

The first brings each side of the Equation to an entire Piaction.

The second, brings Equations into Integers, by met iying alternately the Numerator of each side into the Denominator of the other.

The third, brings by Transposition the several Members of the unkoown Quantities to the same Side of the Equation, (viz.) to that Side, which after Transposition, will render them Affirmative,

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*

+ 12 +6
3

5
2 2x+36 4*+39
3

5
2 X 3
131

12x +90 2x + 36

5 3 X 5 14 10x + 180 = 12x to go 1Ω

5

180 = 2x + go 5 - 90 6

90 = 2x 6 = 2

17

45 =*

4

2 X 4

3x

=

+
4

6
2 3*+-20 5x+12
4

6
3

20* + 48 3* + 20 =

6 3 x 6

41

18x + 120 = 20x + 48 4 18.

15 120 = 2x + 43 5 -4

8
161

72 - 2x 6

2

71 36

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

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11! 5%

1 2

888-7x

12

7x
8 = 74 —

9
І ..25%-72

9
2 X913)

7992-703x 5x — 72 = 3 х 12 14 бох

864 = 7992

- 63х 4 + 634 512 3* - 864 = 7992 5 + 8646123x = 8856 6 : 123171 х = 72

1 2

* Гоо

-24

6
4 = 24

8
2*2

192-X 6

8 1ҳ6 13

52—6x
24 =

8
141
18х -

192 = 152 — бя
4+6x 514x- 192 = 1152
5+192 614* = 1344
6-14 [7lx = 96

3х8

EXAMPLE.

5*-6

E X A M P L E S.
W 128 216

34-4
1X3.42 648x4864

54-6 2X57-63640x — 768 = 648* - 864 3+864 4640x + 96 = 6483 4-640* 1596 = 8x 5 8 1612 = *

128

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Il 45

57 2x+3 4*-5 IX2x+32

114x+171 45

4+5 2X4*-513180x 225 = 114* + 171 3+225 4180* = 114x + 396 4–1142566x = 396 5-66 16* = 6

1

EXAMPLE

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