Elements of Algebra: Including Sturms' Theorem
A. S. Barnes & Company, 1845 - Algebra - 368 pages
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added affected algebraic apply approximating arithmetical arrangements becomes binomial called changing co-efficient consequently considered contain contrary corresponding cube root decimal denominator denote determine difference divide dividend division entire enunciation equal equation example exponent expression extract factors figure formula four fourth fraction given gives greater greatest common divisor hence indicated involving known least less letters limit logarithm manner method monomial multiply necessary negative observe obtain operation performed polynomial positive preceding principle problem progression proportion proposed question quotient radical raise ratio Reduce reference remainder represent resolved respect result rule satisfy second degree second term similar square root substituted subtract suppose taken tens term third tion transformed true units unity unknown quantity whence whole number write
Page 32 - That is, 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.
Page 277 - The characteristic of a number less than 1 is found by subtracting from 9 the number of ciphers between the decimal point and the first significant digit, and writing — 10 after the result.
Page 29 - Hence, for the multiplication of polynomials we have the following RULE. Multiply all the terms of the multiplicand by each term of the multiplier, observing that like signs give plus in the product, and unlike signs minus.
Page 181 - 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 182 - If the product of two quantities is equal to the product of two other quantities, two of them may be made the extremes, and the other two the means of a proportion.
Page 92 - If A and B together can perform a piece of work in 8 days, A and C together in 9 days, and B and C in 10 days : how many days would it take each person to perform the same work alone ? Ans.
Page 348 - VARIATIONS of signs, nor the number of negative roots greater than the number of PERMANENCES. Consequence. 328. When the roots of an equation are all real, the number of positive roots is equal to the number of variations, and the number of negative roots to , the number of permanences.
Page 36 - I. Divide the coefficient of the dividend by the coefficient of the divisor.
Page 110 - Which proves that the square of a number composed of tens and units, contains the square of the tens plus twice the product of the tens by the units, plus the square of the units.
Page 204 - In each succeeding term the coefficient is found by multiplying the coefficient of the preceding term by the exponent of a in that term, and dividing by the number of the preceding term.