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according adding approximate arithmetical arranged Assume balls called changed coefficient complete Consider containing continued convergent corresponding cube root decimal denominator denote derivative determinant Dividing divisible divisor equal equivalent evident EXAMPLES exponent expression Extracting the square figures Find four fourth fraction give given given equation greater happen Hence hold hour increased indefinitely involved last term laws less letters limit logarithm manner means method miles Multiplying negative Note obtained operation polynomial positive integer probability problem progression proportion prove pure imaginary Putting quotient radical sign Raising rational rational numbers real number reduced remainder represented respect result satisfied Solve the equation square root Substituting Subtracting surd taken taking term Theorem third tion unity unknown quantities Whence write written zero
Side 41 - The square of the sum of two numbers 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 268 - 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 268 - The first and fourth terms of a proportion are called the extremes, and the second and third terms, the means. Thus, in the foregoing proportion, 8 and 3 are the extremes and 4 and 6 are the means.
Side 271 - In a series of equal ratios, any antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Let a: 6 = c: d = e :/. Then, by Art.
Side 270 - 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 269 - If the product of two quantities is equal to thé product of two others, one pair may be made the extremes, and the other pair the means, of a proportion. Let ad = be.
Side 150 - Multiply the complete divisor by the figure of the root last obtained, and subtract the product from the remainder. If other...
Side 137 - 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.