the denominator of the product. If the fame letters occur in both numerator and denominator, they may be expunged without altering the value. DIVISION. RULE. 26.-Place the dividend in the form of a numerator, and the divifor in that of a denominator; expunge like quantities from both, and divide the coefficients by the greatest common meafure. Like figns give +, unlike give – - 21. Powers of the fame root are divided by subtracting their exponents. 22. If the dividend be a compound quantity, all its parts must be arranged according to the dimenfions of fome of its letters; the divifor alfo must be arranged according to the dimensions of the fame letters: Then divide the first term of the dividend by the firft term of the divifor; if compound, multi ply the whole divifor by the quotient; from the dividend fubtract the product, and the remainder fhall give a new dividend; then proceed as before. 23. It fometimes happens that the operation may be continued without end, in which cafe the quotient is called an infinite feries. 24. Here, in the two foregoing examples, the quotients observe a certain law, which, if attended to, will enable us, after obtaining a few terms, to extend the quotient to any length without dividing further. Thus the firft quotient is 1+a+a2 +a3 ta*, &c. Now, if we obferve, that in each term the power of a encreases by unity, we may continue to add to the former quotient +as+a+a1+a3+ao; and fo on to infinity. The quotient, in the fecond example, may also be extended, by obferving that the powers of the numerators encrease in the feries of the odd numbers, and thofe of the denominators in the series of the eyen numbers. 25. To divide fractions, multiply the numerator of the diyifor by the denominator of the dividend for the denominator of the quotient, and multiply the denominator of the divifor by the numerator of the dividend for the numerator of the quotient. If one of them be a whole quantity, it may be brought into the form of a fraction by placing 1 for its denominator. |