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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 Find four fourth fraction geometrical given given equation greater happen Hence hold hour imaginary increased interest involving last term laws less letters limit logarithm manner means method miles Multiplying negative Note obtained permutations positive positive integer present probability progression proportion prove Putting quadratic quotient rational reduced remainder represented respect result root rule satisfied Solve the equation square square root Substituting Subtracting successive surd taken taking term Theorem third transformed unity unknown quantities variations varies Whence written zero
Página 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.
Página 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.
Página 269 - If the product of two quantities is equal to the product of two others, one pair may be made the extremes, and the other pair the means, of a proportion. Let ad = ос.
Página 268 - The terms of a ratio are the two numbers to be compared; thus, in the above ratio, 20 and 4 are the terms. When both terms are considered together, they are called a couplet ; when considered separately, the first term is called the antecedent, and the second term the consequent. Thus, in the ratio 20 : 4, 20 and 4 form a couplet, and 20 is the antecedent, and 4 the consequent.
Página 140 - ... from the given expression. Divide the first term of the remainder by twice the first term of the root, and add the quotient to the root and also to the divisor.
Página 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.
Página 38 - Divide the first term of the dividend by the first term of the divisor, giving the first term of the quotient. Multiply the whole divisor by this term, and subtract the product from the dividend, arranging the remainder in the same order of powers as the dividend and divisor.
Página 79 - Multiply the numerators together for the numerator of the product, and the denominators together for the denominator of the product.