Elements of Algebra: On the Basis of M. Bourdon, Embracing Sturm's and Horner's Theorems : and Practical ExamplesA.S. Barnes & Burr, 1860 - 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
... = 69 ; 2 2 2 and these are the true numbers ; for , 16869237 which is the given sum , aud ― 168 69 = 99 which is the given difference CHAPTER IL ADDITION , SUBTRACTION , MULTIPLICATION , AND DIVISION CHAP . I. ] 25 SOLUTION OF PROBLEMS .
... = 69 ; 2 2 2 and these are the true numbers ; for , 16869237 which is the given sum , aud ― 168 69 = 99 which is the given difference CHAPTER IL ADDITION , SUBTRACTION , MULTIPLICATION , AND DIVISION CHAP . I. ] 25 SOLUTION OF PROBLEMS .
Σελίδα 29
... true difference is expressed by 7a3b 4a3b3a3b . - 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 writing ...
... true difference is expressed by 7a3b 4a3b3a3b . - 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 writing ...
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 Here the true sign of although its algebraic α — ( - b ) = a + b . the second term of the binomial is plus , 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 Here the true sign of although its algebraic α — ( - b ) = a + b . the second term of the binomial is plus , sign is ...
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algebraic expression algebraic quantities approximating fraction arithmetical arithmetical progression becomes binomial 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 99 - A person has two horses, and a saddle worth £50 ; now, if the saddle be put on the back of the first horse, it will make his value double that of the second ; but if it be put on the back of the second, it will make his value triple that of the first ; what is the value of each horse ? Ans.
Σελίδα 364 - 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.
Σελίδα 118 - X 6 62 + 3 x 3; and taken 3 tens times, 32 + 2 (3 X 6) + 6s gives 3 x 6 + 32 ; and their sum is, 33 + 2 (3 x 6) + 63 : that is, Rule. — The square of a number is equal to the square of the tens, plus twice the product of the tens by the units, plus the square of the units.
Σελίδα 174 - Find the value of one of the unknown quantities, in terms of the other and known quantities...
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 200 - Subtract the cube of this number from the first period, and to the remainder bring down the first figure of the next period for a, dividend.
Σελίδα 242 - Four quantities are in proportion when the ratio of the first to the second is equal to the ratio of the third to the fourth.
Σελίδα 215 - Resolve the quantity under the radical sign into two factors, one of which is the highest perfect power of the same degree as the radical. Extract the required root of this factor, and prefix the result to the indicated root of the other.
Σελίδα 41 - Divide the coefficient of the dividend by the coefficient of the divisor.
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.