New University Algebra: A Theoretical and Practical Treatise, Containing Many New and Original Methods and Applications, for Colleges and High SchoolsIvison, Phinney & Company, 1863 - 420 páginas |
Dentro del libro
Resultados 1-5 de 32
Página viii
... Derived Polynomials .374 Composition of Derived Polynomials Equal Roots ..375 ... 376 Transformations .. Detached Coefficients Synthetic Division .. Surd and Imaginary Roots .380 .388 ..392 ..398 Rule of Des Cartes .... Cardan's Rule ...
... Derived Polynomials .374 Composition of Derived Polynomials Equal Roots ..375 ... 376 Transformations .. Detached Coefficients Synthetic Division .. Surd and Imaginary Roots .380 .388 ..392 ..398 Rule of Des Cartes .... Cardan's Rule ...
Página 32
... the principles already established we derive the following RULE . I. Multiply the coefficients of the two terms together for the coefficient of the product . II . Write all the letters of both terms for " ENTIRE QUANTITIES . 32.
... the principles already established we derive the following RULE . I. Multiply the coefficients of the two terms together for the coefficient of the product . II . Write all the letters of both terms for " ENTIRE QUANTITIES . 32.
Página 79
... derive a general rule for the division of frac- tions , from the following example : α 1. Divide by b с OPERATION . α C ab - 1 ÷ cd - 1- = b d . ab - 1 ad cd - 1 = bc By inspecting this result , we find that the new numerator may be ...
... derive a general rule for the division of frac- tions , from the following example : α 1. Divide by b с OPERATION . α C ab - 1 ÷ cd - 1- = b d . ab - 1 ad cd - 1 = bc By inspecting this result , we find that the new numerator may be ...
Página 81
... derived from the following observations : 1. — If a fraction be multiplied by its own denominator , the product will be the numerator . 2. — If a fraction be multiplied by any multiple of its denomina- tor , the product must be entire ...
... derived from the following observations : 1. — If a fraction be multiplied by its own denominator , the product will be the numerator . 2. — If a fraction be multiplied by any multiple of its denomina- tor , the product must be entire ...
Página 88
... derived from its numera- tor must be changed . NOTES . 1. The pupil should observe that in multiplying any fraction it will be most convenient to divide the multiplier by the denominator and multiply the numerator by the quotient . 2 ...
... derived from its numera- tor must be changed . NOTES . 1. The pupil should observe that in multiplying any fraction it will be most convenient to divide the multiplier by the denominator and multiply the numerator by the quotient . 2 ...
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Términos y frases comunes
added algebraic quantity arithmetical progression binomial factors clearing of fractions coefficients cube root degree denote derived polynomial dividend division dollars EXAMPLES FOR PRACTICE exponent expression figure Find the cube Find the logarithm Find the sum find the values following RULE formula fourth geometrical progression geometrical series given equation given number given quantities greater greatest common divisor identical equation imaginary indicated inequality irreducible fraction last term least common multiple less letters minus sign monomial Multiply negative quantity nth root number of terms obtain OPERATION partial fractions permutations positive roots problem proportion quadratic quadratic equation quotient radical sign rational Reduce remainder represent required root result second member second term square root Sturm's Theorem subtracted suppose surd taken third three numbers tion transformed equation transposing trial divisor unknown quantity whence whole number X₁ zero
Pasajes populares
Página 209 - ... the product of the two, plus the square of the second. In the third case, we have (a + b) (a — 6) = a2 — b2. (3) That is, the product of the sum and difference of two quantities is equal to the difference of their squares.
Página 86 - Any term may be transposed from one member of an equation to the other by changing its sign (1, 2).
Página 66 - To reduce a fraction to its lowest terms. A Fraction is in its lowest terms when the numerator and denominator are prime to each other. 1. Reduce - to its lowest terms.
Página 178 - ... and to the remainder bring down the next period for a dividend. 3. Place the double of the root already found, on the left hand of the dividend for a divisor. 4. Seek how often the divisor is contained...
Página 169 - Subtract the square number from the left hand period, and to the remainder bring down the next period for a dividend. III. Double the root already found for a divisor ; seek how many times the divisor is contained...
Página 31 - That the exponent of any letter in the product is equal to the sum of its exponents in the two factors.
Página 77 - Reduce compound fractions to simple ones, and mixt numbers to improper fractions ; then multiply the numerators together for a new numerator, and the denominators for. a new denominator.
Página 52 - Measure, of two or more quantities, is the greatest quantity that will exactly divide each of them.
Página 266 - 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.
Página 169 - Multiply the divisor, thus increased, by the last figure of the root; subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.