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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1883 edition. Excerpt: ...to that term of the quotient, at which we intend to stop, the remainder at that point of the division, placed as the numerator of a fraction of which the divisor is the denominator. Examples,--lxiii. Carry on each of the following divisions to 5 terms in the quotient. 1. 2byl + a. 7. 1 by 1 + 2x-2x2. 2. mbym+2. 8. 1+xby 1-x+x2. 3. a-6by a + b. 9. l + 6byl-26. 4. a2 + x2 by a2-x2. 10. x3--63 by x + 6. 5. axbya-x. 11. a2byx-6. 6. 6bya+x. 12. a2by(a+x)2. 13. If the divisor be x-a, the quotient x2-2ax, and the remainder 4a3, what is the dividend? 14. If the divisor be m-5, the quotient m3 + 5m2 + 15m + 34, and the remainder 75, what is the dividend 1 201. If we are required to.multiply such an expression as x2 x 1, x 1 "2" + 3 + 4 y 23' we may multiply each term of the former by each term of the latter, and combine the results by the ordinary methods of addition and-subtraction of fractions, thus 1 Or we may first reduce the multiplicand and the multiplier to single fractions and proceed in the following way: This latter process will be found the simpler by a beginner. Examfles.--Ixiv. Multiply 202. If we have to diViáe such an expression as,y д. + 1? we may proceed as in the division of whole numbers, x carefully observing that the order of descending powers of x is, „ 111 Any isolated digits, as 1, 2, 3... win stand between x li. х Thus the expression arranged according to descending powers of х, will stand thus, The reason for this arrangement will be given in the Chapter 0n the Theory of Indices. Or we may proceed in the following луаy, which will be found simpler by the beginner. 204. When any expression 2? is put in a form of which / is factor, then-j is the other factor....