## New University Algebra: A Theoretical and Practical Treatise, Containing Many New and Original Methods and Applications, for Colleges and High Schools |

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### Common terms and phrases

according added addition algebraic arithmetical arranged Assume becomes binomial called changed coefficients combinations common complete contain continued cube root decimal denominator denote derived difference distance Divide dividend division divisor dollars entire equal equation evident EXAMPLES FOR PRACTICE Expand exponent expression factors figure find the values formula four fourth fraction give given given equation greater greatest common divisor Hence imaginary indicated involving less letters logarithm means method miles Multiply negative observe obtain OPERATION polynomial positive principles problem progression proportion quadratic quotient radical Raise rational Reduce relation remainder represent respect result RULE second member solution square root Substituting subtracted successive suppose surd taken third tion transformed trial true units unknown quantity whence whole write zero

### Popular passages

Page 209 - ... the product of the two, plus the square of the second. In the third case, we have (a + b) (a — 6) = a2 — b2. (3) That is, the product of the sum and difference of two quantities is equal to the difference of their squares.

Page 86 - Any term may be transposed from one member of an equation to the other by changing its sign (1, 2).

Page 66 - To reduce a fraction to its lowest terms. A Fraction is in its lowest terms when the numerator and denominator are prime to each other. 1. Reduce - to its lowest terms.

Page 178 - ... and to the remainder bring down the next period for a dividend. 3. Place the double of the root already found, on the left hand of the dividend for a divisor. 4. Seek how often the divisor is contained...

Page 169 - Subtract the square number from the left hand period, and to the remainder bring down the next period for a dividend. III. Double the root already found for a divisor ; seek how many times the divisor is contained...

Page 31 - That the exponent of any letter in the product is equal to the sum of its exponents in the two factors.

Page 77 - Reduce compound fractions to simple ones, and mixt numbers to improper fractions ; then multiply the numerators together for a new numerator, and the denominators for. a new denominator.

Page 52 - Measure, of two or more quantities, is the greatest quantity that will exactly divide each of them.

Page 266 - To express that the ratio of A to B is equal to the ratio of C to D, we write the quantities thus : A : B : : C : D; and read, A is to B as C to D.

Page 169 - 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.