New University Algebra
Ivison, Blakeman, Taylor & Company, 1875 - Algebra - 412 pages
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according added algebraic arithmetical Assume becomes binomial called changed coefficients combinations common complete consists contain continued correct cube root decimal denominator denote difference distance Divide dividend division divisor dollars entire equal equation evident EXAMPLES exponent expression factors figure find the values formula four fourth fraction geometrical give given given equation greater greatest Hence indicated inequality involving least less letters logarithm means method miles Multiply negative observe obtain OPERATION period polynomial positive PRACTICE problem progression proportion quadratic quotient radical Raise rational Reduce relation remainder represent respect result rule solution square root Substituting subtracted suppose surd taken third tion transformed trial units unknown quantity whence whole write zero
Page 167 - 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 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 176 - ... 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 167 - 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 141 - But the relations of these quantities will not be changed, if we suppose the path of motion to be a curve, instead of a straight line. The above formula will therefore apply to the hands of a clock moving around the dial-plate, or to the planets moving in the circle of the heavens. It will thus afford a direct solution to the following problems : 1. The hour and minute hands of a clock are together at 12 o'clock ; when are they next together ? The circumference of the dial-plate is divided into 12...
Page 36 - The square of the sum of two quantities is equal to the square of the first, plus twice the product of the first multiplied by the second, plus the square of the second.
Page 31 - That the exponent of any letter in the product is equal to the sum of its exponents in the two factors.
Page 36 - 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.
Page 264 - 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 266 - Conversely, if the product of two quantities is equal to the product of two other quantities, the first two may be made the extremes, and the other two the means of a proportion.