Elements of Algebra: On the Basis of M. Bourdon, Embracing Sturm's and Horner's Theorems, and Practical ExamplesA. S. Barnes & Company, 1857 - 400 σελίδες |
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Σελίδα 12
... true of all things what- ever , and not like those of number and Geometry , true only for particular classes of things . The symbols of Algebra , there- fore , should not excite in our minds ideas of particular things . The written ...
... true of all things what- ever , and not like those of number and Geometry , true only for particular classes of things . The symbols of Algebra , there- fore , should not excite in our minds ideas of particular things . The written ...
Σελίδα 25
... 2 2 69 ; 2 2 and these are the true numbers ; for , 16869 : = 237 which is the given sum , and 168-69 = 99 which is the given difference . CHAPTER IL . ADDITION , SUBTRACTION , MULTIPLICATION , AND CHAP . I. ] 25 SOLUTION OF PROBLEMS .
... 2 2 69 ; 2 2 and these are the true numbers ; for , 16869 : = 237 which is the given sum , and 168-69 = 99 which is the given difference . CHAPTER IL . ADDITION , SUBTRACTION , MULTIPLICATION , AND CHAP . I. ] 25 SOLUTION OF PROBLEMS .
Σελίδα 29
... true difference is expressed by 7a3b 4a3b - = 3a3b . 37. Generally , if from one polynomial we wish to subtract another , the operation may be indicated by enclosing the second in a parenthesis , prefixing the minus sign , and then ...
... true difference is expressed by 7a3b 4a3b - = 3a3b . 37. Generally , if from one polynomial we wish to subtract another , the operation may be indicated by enclosing the second in a parenthesis , prefixing the minus sign , and then ...
Σελίδα 30
... true remainder , we must increase the first result by d , which gives the expression a - c + d , and this is the true remainder . By comparing this remainder with the given polynomials , we see that we have changed the signs of all the ...
... true remainder , we must increase the first result by d , which gives the expression a - c + d , and this is the true remainder . By comparing this remainder with the given polynomials , we see that we have changed the signs of all the ...
Σελίδα 33
... true sign of the term before which it is placed . Thus , if it were required to subtract -b from a , we should write a ( b ) = a + b . Here the true sign of the second term of the binomial is plus , although its algebraic sign is ...
... true sign of the term before which it is placed . Thus , if it were required to subtract -b from a , we should write a ( b ) = a + b . Here the true sign of the second term of the binomial is plus , although its algebraic sign is ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
algebraic expression algebraic quantities approximating fraction arithmetical arithmetical progression becomes called co-efficient common difference contrary signs cube root deduce denote the number derived polynomial Divide dividend entire number equal exactly divisible example exponent extract the square figures Find the factors find the values following RULE formula fractional unit given equation given number gives greater number greatest common divisor hence indicated inequality irreducible fraction last term leading letter least common multiple logarithm mixed quantity monomial multiplicand and multiplier nth power nth root number of terms obtain operation perfect square positive roots preceding problem proposed equation quotient radical sign real roots Reduce the polynomial remainder required to find result second degree second member second term simplest form square root substituted subtract suppose taken third transformed equation unknown quantity whence whole number X₁
Δημοφιλή αποσπάσματα
Σελίδα 121 - Multiply the divisor, thus augmented, by the last figure of the root, and subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.
Σελίδα 174 - For, we can find the value of one of the unknown quantities in terms of the other and known quantities...
Σελίδα 286 - The logarithm of a number is the exponent of the power to which it is necessary to raise a fixed number, in order to produce the first number.
Σελίδα 39 - 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.
Σελίδα 10 - Logic is a portion of the art of thinking; language is evidently, and by the admission of all philosophers, one of the principal instruments or helps of thought; and any imperfection in the instrument or in the mode of employing it is confessedly liable, still more than in almost any other art, to confuse and impede the process and destroy all ground of confidence in the result.
Σελίδα 200 - RULE. I. Separate the given number into periods of three figures each, beginning at the right hand ; the left hand period will often contain less than three places of figures.
Σελίδα 100 - 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 will it take each person to perform the same work alone.
Σελίδα 35 - We have, then, for the multiplication of polynomials, the following RULE. Multiply all the terms of the multiplicand by each term of the multiplier in succession, aff'ccting the product of any two terms with the sign plus, when tlieir signs are alike, and with the sign minus, when their signs
Σελίδα 41 - Divide the coefficient of the dividend by the coefficient of the divisor.
Σελίδα 200 - The cube of a number is equal to the cube of the tens, plus three times the product of the square of the tens by the units, plus three times the product of the tens by the square of the units, plus the cube of the units.