Macmillian Company, 1900 - Algebra - 442 pages
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added algebraic arithmetical arranged assumed balls base binomial called coefficient combinations common complete condition Consequently contains convergent correction corresponding cube decimal definition denominator Determine difference digits divergent divided division divisor dollars equal equation equivalent evidently example EXERCISES expansion exponent expressions factors feet figure Find Find the value finite following expressions four fraction give given given series greater Hence illustrate increases infinite integer less letters limit logarithm mantissa means method miles multiplied negative obtained permutations positive preceding principle probability problem progression proportion proved quotient ratio receive remainder result root Simplify solution Solve square square root stand Substituting subtracted surd taken term things third units unknown number variable whence Write yards
Page 316 - In any proportion the terms are in proportion by Composition and Division; that is, the sum of the first two terms is to their difference, as the sum of the last two terms is to their difference.
Page 74 - Divide the first term of the dividend by the first term of the divisor, the result will be the first term of the quotient.
Page 354 - That is, the number of combinations of n dissimilar things r at a time is equal to the number of combinations of the n things n — r at a time.
Page 351 - We will now derive a formula for the number of permutations of n things, taken all at a time, when some of them are alike.
Page 216 - ... term by the exponent of a in that term, and dividing the product by a number greater by 1 than the exponent of b in that term.
Page 313 - IF the first be the same multiple of the second, or the same part of it, that the third is of the fourth ; the first is to the second, as the third is to the fourth...
Page 317 - 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 179 - If necessary, multiply the given equations by such numbers as will make the coefficients of one of the unknown numbers in the resulting equations of equal absolute value.
Page 95 - That is, the difference of the squares of two numbers is exactly divisible by the sum of the numbers, and also by the difference of the numbers, taken in the same order...
Page 334 - Evidently the sum can be made to differ from 2 by as little as we please, by taking a sufficient number of terms.