## Elements of Algebra: For Colleges, Schools, and Private Students, Book 2 |

### Contents

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### Common terms and phrases

2d Bk algebraic ALGEBRAIC QUANTITIES arithmetical progression binomial Binomial Theorem coefficient common divisor Completing the square Corollary cube root decimal degree denominator derived polynomial Divide dividend division equa equal roots equation containing equation whose roots evident example exponent Extract the square factors Find the cube find the number Find the square Find the sum find the value geometrical progression given equation given number gives greater greatest common divisor Hence imaginary inequality less letters logarithms method minus monomial Multiply negative roots nth root number of balls number of terms perfect square positive root preceding Proposition quadratic equation quotient ratio real roots reduced remainder Required the number required to find result second term solved square root Sturm's theorem substituted subtracted taken Theorem third tion transform transposing trinomial unity unknown quantity Whence whole number X₁

### Popular passages

Page 136 - Multiply the divisor, thus increased, by the last figure of the root; subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.

Page 289 - Take the first term from the second, the second from the third, the third from the fourth, &c. and the remainders will form a new series, called the first order of

Page 35 - Obtain the exponent of each literal factor in the quotient by subtracting the exponent of each letter in the divisor from the exponent of the same letter in the dividend; Determine the sign of the result by the rule that like signs give plus, and unlike signs give minus.

Page 39 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.

Page 148 - ... by the last figure of the root, and subtract the product from the dividend ; to the remainder bring down the next period for a new dividend.

Page 187 - CD, and, on meeting, it appeared that A had traveled 18 miles more than B ; and that A could have gone B's journey in 15 £ days, but B would have been 28 days in performing A's journey.

Page 68 - Reduce the fractions to a common denominator ; then subtract the numerator of the subtrahend from the numerator of the minuend, and write the result over the common denominator. EXAMPLES. H ,_, Zx . ^ 3x 1. From -^- subtract — . oo . Eeducing to a common denominator, the fractions become Wx 9x "15...

Page 37 - Since, in multiplying a polynomial by a monomial, we multiply each term of the multiplicand by the multiplier ; therefore, we have the following RULE, FOR DIVIDING A POLYNOMIAL BY A MONOMIAL. Divide each term of the dividend, by the divisor, according to the rule for the division of monomials.

Page 236 - In any proportion the product of the means is equal to the product of the extremes.

Page 43 - The square of the difference of two quantities is equal to the square of the first minus twice the product of the first by the second, plus the square of the second.