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cessively, and the sum of the particular products will be the preduct required.

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18.—If one of the factors be a fraction, multiply its numerator by the other factor, and place the product over the given denominator.

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19.—If both factors be fractions, multiply their numerators for the numerator of product, and cir denominators for

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the denominator of the product. If the same letters occur in both numerator and denominator, they may be expunged without altering the value.

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20.- Place the dividend in the form of a numerator, and the divisor in that of a denominator ; expunge like quantities from both, and divide the coefficients by the greatest common measure. Like signs give +, unlike give

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21. Powers of the same root are divided by subtracting their exponents.

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22. If the dividend be a compound quantity, all its parts must be arranged according to the dimensions of fome of its letters; the divisor also must be arranged according to the dimensions of the same letters: Then divide the first term of the dividend by the first term of the divisor; if compound, multi

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ply the whole divisor by the quotient ; from the dividend subtract the product, and the remainder shall give a new dividend ; then proceed as before.

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23. It sometimes happens that the operation may be continued without end, in which case the quotient is called an infinite feries.

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