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CASE II.
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When one of the factors is a compound quantity,

RULE,

Multiply every term of the compound factor, considered as a multiplicand, separately, by the multiplier, as in the forqabcase ; then these progo.placed one after another, with their proper fighs, .# e whole product

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o &c.; though it is usual, in this ease, as well as in addition and subtraction, to put them according to their rank in the alphabet. It may here also be observed, in conformity to the rule given above

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CASE III.

When both the factors are compound quantities.

RULE,

... Multiply every term of the multiplicand separately, by

each term of the multiplier, setting down the products one after another, with their proper signs ; then add the several lines of products together, and theirssum will be the whole product required. -

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o: is the converse of multiplication, and is performed like that of numbers; the e being usually divided into three cases; in each of which like signs give + in the quotient, and unlike signs —, as in findiny. their pigslucts (e). . -

It it e also to be observed, that powers and roots of the same quantity, are divided by subtracting the index ef the divisor from that of the dividend.

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(e) According to the rule here given for the signs, it follows that +ah

+6 as will readily appear by multiplying the quotient by the divisor;

the signs of the products being then the same as would take plaçe in the former rule.

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CASE I.

When the divisor and dividend are both simple
quantities.

RULE.
Set the dividend over the divisor, in the manner of a .

fraction, and reduce it to its simplest form, by cancelling
the letters and figures that are common to each term.

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When the divisor is a simple quantity, and the dividend a
compound one.

RULE,

Divide each term of the dividend by the divisor, as in the former case; setting down such as will not divide in the simplest form they will admit of

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o When the divisor and dividend are both compound or. quantities.

RULE.

* Set them down in the same manner as in division of numbers, ranging the terms of each of them so, that the higher powers of one of the letters may stand before the lower. Then divide the first term of the dividend by the first term of the divisor, and set the result in the quotient, with its proper sign, or simply by itself, if it be affirmative. This being done, multiply the whole divisor by the term thus found; and, having subtracted the result from the dividend, bring down as many terms to the remainder as are requisite for the next operation, which perform as before ; and so on, till the work is finished, as in com: mon arithmetic. - "

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