Elements of Algebra: Including Sturms' Theorem |
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Page 12
... factors . Thus , in the product ab , there are two factors , a and b ; in the product acd , there are three , a , c , and d . 9. There are three signs used to denote division . Thus , b denotes that a is to be divided by b . a α Ъ alb ...
... factors . Thus , in the product ab , there are two factors , a and b ; in the product acd , there are three , a , c , and d . 9. There are three signs used to denote division . Thus , b denotes that a is to be divided by b . a α Ъ alb ...
Page 13
... factor . Hence , the exponent of a quantity shows how many times the quantity is a factor . It also indicates the number of times , plus one , that the quantity is to be multiplied by itself . When no ex- ponent is written , the ...
... factor . Hence , the exponent of a quantity shows how many times the quantity is a factor . It also indicates the number of times , plus one , that the quantity is to be multiplied by itself . When no ex- ponent is written , the ...
Page 15
... signs of all the terms remain unchanged . For example , the polynomial 4a3 · 3a2b5ac2 = 5ac2 - 3a2 + 4a3 — — 3a2b5ac2 + 4a3 . 25. Each of the literal factors which compose a term CHAP . I. ] 15 DEFINITIONS AND REMARKS .
... signs of all the terms remain unchanged . For example , the polynomial 4a3 · 3a2b5ac2 = 5ac2 - 3a2 + 4a3 — — 3a2b5ac2 + 4a3 . 25. Each of the literal factors which compose a term CHAP . I. ] 15 DEFINITIONS AND REMARKS .
Page 16
Including Sturms' Theorem Charles Davies. 25. Each of the literal factors which compose a term , is called a dimension of the term ; and the degree of a term is the number of these factors or dimensions . Thus , 3a is a term of one ...
Including Sturms' Theorem Charles Davies. 25. Each of the literal factors which compose a term , is called a dimension of the term ; and the degree of a term is the number of these factors or dimensions . Thus , 3a is a term of one ...
Page 27
... factors . It is proved in Arithmetic ( see Davies ' Arithmetic , § 22 ) , that the value of a product is not affected by changing the order of its factors that is , 12ab ab x 12 = ba x 12 = a × 12 × b . For convenience , however , the ...
... factors . It is proved in Arithmetic ( see Davies ' Arithmetic , § 22 ) , that the value of a product is not affected by changing the order of its factors that is , 12ab ab x 12 = ba x 12 = a × 12 × b . For convenience , however , the ...
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Common terms and phrases
affected algebraic quantities arithmetical arrangements becomes binomial called co-efficient common difference consequently contain continued fraction contrary signs cube root decimal deduced denominator divide dividend division entire number enunciation equa equal equation involving example exponent factors figure formula fourth given equation given number gives greater greatest common divisor hence inequality last term least common multiple less logarithm method monomial multiply nth root number of terms obtain operation ounces perfect square positive roots preceding problem progression proposed equation quan quotient real roots Reduce remainder resolved result rule second degree second member second term simplest form square root substituted subtract superior limit suppose take the equation taken third tion tities transformed transposing unity unknown quantity whence whole number
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.