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according adding arithmetical Assume balls base called changed coefficient column common complete Consider contains continued convergent corresponding cube decimal denominator denote derivative determinant Dividing divisible divisor drawn equal equation event evident EXAMPLES Expand exponent expression factors figures four fourth fraction geometrical given given equation greater happen Hence hold imaginary increased infinite series interest involving last term laws less letters limit logarithm manner means method Multiplying negative Note obtained permutations positive positive integer present probability progression proportion prove Putting quotient rational reduced remainder represented respect result root rule square root Substituting Subtracting successive surd taken taking term Theorem third transformed unity unknown quantities variations varies Whence written zero
Page 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.
Page 38 - 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.
Page 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.
Page 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.
Page 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.
Page 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.
Page 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.
Page 150 - Multiply the complete divisor by the figure of the root last obtained, and subtract the product from the remainder. If other...
Page 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.
Page 279 - One quantity is said to vary inversely as another when the first varies directly as the reciprocal of the second. Thus, the...