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
... respect , possesses all the properties of numbers . Proposi tions , therefore , concerning numbers , have this remarkable pecu liarity , that they are propositions concerning all quantities whatever . Algebra extends the generalization ...
... respect , possesses all the properties of numbers . Proposi tions , therefore , concerning numbers , have this remarkable pecu liarity , that they are propositions concerning all quantities whatever . Algebra extends the generalization ...
Σελίδα 49
... respect to polynomials that we can often discover by mere inspection that they are not divisible . When the polynomials contain two or more letters , observe the two terms of the dividend and divisor , which contain the highest powers ...
... respect to polynomials that we can often discover by mere inspection that they are not divisible . When the polynomials contain two or more letters , observe the two terms of the dividend and divisor , which contain the highest powers ...
Σελίδα 156
... respect to the unknown quantity , having the unknown quantity for a first term and the two roots , with their signs changed , for second terms . For example , the equation x2 + 3x - 28 = 0 being solved , gives x = 4 and x = ; We also ...
... respect to the unknown quantity , having the unknown quantity for a first term and the two roots , with their signs changed , for second terms . For example , the equation x2 + 3x - 28 = 0 being solved , gives x = 4 and x = ; We also ...
Σελίδα 175
... respect to these quantities . For , we can substitute for one of the unknown quantities , an auxiliary unknown quantity multiplied into the second un- known quantity , and by combining the two resulting equations we can find an equation ...
... respect to these quantities . For , we can substitute for one of the unknown quantities , an auxiliary unknown quantity multiplied into the second un- known quantity , and by combining the two resulting equations we can find an equation ...
Σελίδα 192
... respect to the exponents , we observe that the ex- ponent of x , in the first term , is equal . to the number of bino- mial factors employed . In each of the following terms to the right , this exponent is diminished by 1 to the last ...
... respect to the exponents , we observe that the ex- ponent of x , in the first term , is equal . to the number of bino- mial factors employed . In each of the following terms to the right , this exponent is diminished by 1 to the last ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
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.