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The product of a multiplied by c*,

dxc or do=36.

d disor-=2

The quotient of d divided by s,

The square root of ac,

ac-6.. 6. Plus and minus are always opposed to each other. Thus, if + signifies gain, fignifies loss; if + fignifies stock, fignifies debt; if + signifies a positive quantity, signifies a negative one.

And so on. 7.—When letters are placed together without any sign between them, they denote the rectangle or product of the quantities they represent. Thus, the product of a into b is ab=24.

A number prefixed to any quantity is understood to multiply the quantity, and is called its co-efficient. Thus, on=18..

8.—Division is often represented by placing the dividend in the form of a numerator, and the divisor in that of a denomis.

b 8 nator. Thus, b divided by a is - = = 2..

3 9.–The continual multiplication of quantities, by others of the like kind and dimension, is called powers of that quantity, and are commonly expressed by small numbers placed at the corners of the letters, called indices, or exponents. Thus, the square of a is a2, the cube a3, the fourth power a*, &c. The exponent of the original quantity, or root, is unity, and is 'cla dom or never expreflcd.

10.-Quantities of the like dimenfions, which, by their fucceilive multiplication, produce any given quantity, are called roots of the given quantity. Thus, a is the iquare root al.

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When no sign is market between two or more quantities, it denotes their product.

Exercises for practice.

3.

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1. 2atb=2X3+8=14.
2. bc+d=8X12+10=106.
bc 8812

-=32

3 4. cd-am+c=12*10^3*6+144=246.

c2= ad

30 5 - +62462=2+144-64586.

5 5 6.

5 P

a2+ 32 +8 17 7.

17 42-06 328

5.

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ADDITION.

RULE I.

U. When the quantities are alike, and their signs the fame, add the co-esficients, and to the sum prefix the sign, and annex the common letter or letters

RULE II. When the quantities are alike, but their signs difftrent, subtract the lefser co-efficient from the greater ; to their difference prefix the sign of the greater, and annex the comn, on letter or letters.

RULE III. When the quantities are unlike, write them one after another, with their proper signs and coefficients.

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By Rule II.

Ex. 5th,

6th,

7th, 8th. 40 -50+46

5ab

-5ab4c4 de --50 2c +86

-ab + 2ab-3de + c -30+1 26

4ab -3a6—2de---30 In example 8th, the articles are to be arranged, so that like may stand under like.

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SUBTRACTION.

RULE.

12.

Change the signs of the subtrahend, or suppose them changed, then proceed as in addition.

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The reason of the foregoing rule is obvious ; for if from any quantity a decrement be subtracted, it is the same as adding ani equal increment. For example, If a man owe 100l. more than his stock, the state of his affairs may be represented - 100l. or he is rool. worse than nothing. But if another add 100l. to his ftock, it is the same thing as taking away his debt, for in either of these cafes he will be worth nothing.

MULTIPLICATION.

RULE.

14.-Multiply the coefficients, and to their product annex the letters of both factors together. If the signs of the factors be like, the fign of their product is +; but if the signs of the factors be unlike, the sign of the product is

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15.-Powers of the fame root are multiplied by adding their exponents.

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16.-Radical quantities, under the like fign, are multiplied like others, and the product is placed under the same fign.

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17.--If one or both factors be compound, multiply each term of the multiplicand by all the terms of the multiplier fuc

cellively

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