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according added Algebra amount arithmetical assume base Binomial called cent changed characteristic coefficient combinations complete containing continued convergent corresponding cube root decimal denominator denote derive difference digits divided dividend division divisor dollars equal equation evident EXAMPLES Expand exponent expression factors figures Find Find the value formula four fourth fraction geometrical given given equation gives greater Hence hold increased indicates integral last term laws less letters limit logarithm lowest mantissa means method miles Multiplying negative Note obtain operation partial permutations positive powers progression proportion prove Putting quadratic quantity quotient radical ratio Reduce remainder result second term Separate Solve the equation square root Substituting Subtracting Theorem third transformed twice unknown quantity variations Whence write written zero
Side 166 - Arts. 200 and 201 we derive the following rule : Extract the required root of the numerical coefficient, and divide the exponent of each letter by the index of the root.
Side 269 - In any proportion the terms are in proportion by Composition; that is, the sum of the first two terms is to the first term as the sum of the last two terms is to the third term.
Side 129 - A person has a hours at his disposal. How far may he ride in a coach which travels b miles an hour, so as to return home in time, walking back at the rate of с miles an hour ? 43.
Side 267 - 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.
Side 5 - If equal quantities be divided by the same quantity, or equal quantities, the quotients will be equal. 5. If the same quantity be both added to and subtracted from another, the value of the latter will not be changed.
Side 227 - A courier proceeds from P to Q in 14 hours. A second courier starts at the same time from a place 10 miles behind P, and arrives at Q at the same time as the first courier. The second courier finds that he takes half an hour less than the first to accomplish 20 miles. Find the distance from P to Q.
Side 44 - The square of the sum of two quantities is equal to the SQuare of the first, plus twice the product of the first by the second, plus the square of the second.
Side 107 - Any term may be transposed from one side of an equation to the other by changing its sign. For, consider the equation x + a = b.