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Thus, 3a added to 5a, makes Sa.
And - 2ab added 10—7ab, makes-9ab.
And 50 + 76 added to 7a + 3b, makes 12a + 106.

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CASE II.

IVhen the Quantities are Like, but have Unlike Signs :

Add the affirmative co-efficients into one sun, and all the negative ones into another, when there are several of a kind. Then subtract the less sum, or the less co-efficient, from the greater and to the remainder prefix the sign of the greater, and subjoin the common quantity or letters.

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CASE ILI.

When the Quantities are Unlike,

HAVING collected together all the like quantities, as in the two foregoing cases, set down those that are unlike, one after another, with their proper signs.

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Add a + b and 3a – 56 together.
Add 50-8x and 32 - 4x together.
Add 6x-56 +2+8 10-50- 4x + 46-3.
Add a +26-30-10 to 36-40 + 50 + 10 and 56-6.
Add a +b and 2-6 together.
Add 3a + 6-10 to c-d-a and - 4c + 2a-36—7.

-c to 2ab-3a2 + bc-b. Add Q3 +62c-62 to ab2-abc + 62. Add 9a-86 + 10x--64-70 + 50 to 2c - Sa~50 +46 +

6d-10.

Add 3a? +68

SUBTRAC

SUBTRACTION

Set down in one line the first quantities from which the subtraction is to be made ; and underneath them place all the other quantities composing the subtrabend : ranging the like quantities under each other as in Addition.

Then change all the signs ( + and — ) of the lower line, or conceive them to be changed ; after which, collect all the terms together as in the cases of Addition*

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1

From 8.x2y— 6 5V xy + 2x V xy 2V 3-18 + 36
Take-- 2x y +2 7 V xy + - 2xy 9x2-12 + 56+ x

x 3

Rem.

This rule is founded on the consideration, that addition and subtraction are opposite to each other in their nature and operation, as are the signs + and -, by which they are expressed and represent. ed. So that, since to unite a negative quantity with a positive one of the same kind, has the effect of diminishing it, or subducting an equal positive one from it, therefore to subtract a positive (which is the opposite of uniting or adding) is to add the equal negative quantity. In like manner, to subtract a negative quantity, is the same in effect as to add or unite an equal positive one.

So that, by cbanging the sign of a quantity from + to, or from

to t., changes its nature from a subductive quantity to an additive one; and any quantity is in effect subtracted, by barely changing its sign.

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5xy

30 50

773 – 2 (a + b)
2r3 4 (a + b)

7xy

3xy3 + 20 av (xy + 10) 4x,y? + 12 av (ry + 10)

From a + b, take a - b.
From 4a + 4b, lake b + a.
From 4a 46, take 3a + 56.
From 8a 12x, take 4a 3.x,
From 2x 40-26 + 5 take 8 56 + a + 6x.
From 3a + b + c

-d 10, take c + 2a d.
From 3a + btc d-10, take 6 19 + 3a.
From 2ab + 62 40 tbc b, take 3a? -C+ 62.
From a3 + 362c + ab? abc, take 62 + ab? abc.
From 12x + 6a 46 + 40, take 46 - 3a + 4x + 6d- 10.
From 2x - 3a + 4b + 60 -50, take 9a + x + 66-66 -40.
From 6a-46-120 + 12x, take 2x - 80 + 46 - 50.

MULTIPLICATION.

This consists of several cases, according as the factors are

simple or compound quantities.

CASE 1. When both the Factors are Simple Quantities :

First multiply the co-efficients of the two terms together, then to the product' annex all the letters in those terms, which will give the whole product required.

Note* Like signs, in the factors, produce + and unlike signs -, in the products.

EXAMPLES

* That this rule for the signs is true, may be thus shown.

1. When ta is to be multiplied by + c; the meaning is, that to a is to be taken as many times as there are units in c; and since the sum of any number of positive terms is positive, it follows that ta Xtcmakes + ac.

2. When

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