Elements of Algebra: Including Sturms' Theorem |
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Page 6
... Denominator . To Add Fractions To Subtract Fractions . ARTICLES 72 .. .... 73 74 75 76 77 78 To Multiply Fractions . To Divide Fractions . Results from adding to both Terms of a Fraction . CHAPTER IV . EQUATIONS OF THE FIRST DEGREE ...
... Denominator . To Add Fractions To Subtract Fractions . ARTICLES 72 .. .... 73 74 75 76 77 78 To Multiply Fractions . To Divide Fractions . Results from adding to both Terms of a Fraction . CHAPTER IV . EQUATIONS OF THE FIRST DEGREE ...
Page 36
... denominator by the factors 4 , a2 , b , and c , which are common to both the terms of the fraction . In general , to reduce a monomial fraction , we 36 [ CHAP . II . ELEMENTS OF ALGEBRA . Subtraction-Rule-Remark 36-40.
... denominator by the factors 4 , a2 , b , and c , which are common to both the terms of the fraction . In general , to reduce a monomial fraction , we 36 [ CHAP . II . ELEMENTS OF ALGEBRA . Subtraction-Rule-Remark 36-40.
Page 38
... denominator are equal : am am hence , ao = 1 , since each is equal to am We observe again , that the symbol ao is only employed con- ventionally , to preserve in the calculation the trace of a letter which entered in the enunciation of ...
... denominator are equal : am am hence , ao = 1 , since each is equal to am We observe again , that the symbol ao is only employed con- ventionally , to preserve in the calculation the trace of a letter which entered in the enunciation of ...
Page 47
... denominator , and one of these parts is supposed to be taken as many times as there are units in the numerator . Thus , in the fractional expression a + b c + d ' a given unit is supposed to be divided into as many equal parts as there ...
... denominator , and one of these parts is supposed to be taken as many times as there are units in the numerator . Thus , in the fractional expression a + b c + d ' a given unit is supposed to be divided into as many equal parts as there ...
Page 48
... denominator are cancelled . Practice teaches the manner of performing these decompositions , when they are possible . But the two terms of the fraction may be complicated poly- nomials , and then , their decomposition into factors not ...
... denominator are cancelled . Practice teaches the manner of performing these decompositions , when they are possible . But the two terms of the fraction may be complicated poly- nomials , and then , their decomposition into factors not ...
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Common terms and phrases
affected algebraic quantities arithmetical means arithmetical progression binomial called co-efficient common difference consequently contain contrary signs cube root Cx² decimal deduced denominator denote divide dividend division entire number enunciation equa equal equation involving example exponent expression extract the square factors figure find the values formula fourth fraction given equation given number gives greater greatest common divisor hence inequality last term least common multiple less logarithm monomial multiplicand multiplied negative nth root number of terms obtain operation ounces perfect square permutations problem proportion proposed equation quan quotient radical sign Reduce remainder result rule satisfy second degree second member second term simplest form square root substituted subtract suppose supposition take the equation third tion tities total number transposing unity unknown quantity whence whole number ах
Popular passages
Page 30 - 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 275 - 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 27 - 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 179 - 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 180 - 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 90 - 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 346 - 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 34 - I. Divide the coefficient of the dividend by the coefficient of the divisor.
Page 108 - 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 202 - 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.