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 σελίδες |
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Αποτελέσματα 1 - 5 από τα 53.
Σελίδα 31
... suppose it were required to multiply any quantity , as a , by c - d . Now it is evident that a taken c minus d times , is the same as a taken c times , diminished by a taken d times ; or ax ( c - d ) = ac - ad . In the first term of ...
... suppose it were required to multiply any quantity , as a , by c - d . Now it is evident that a taken c minus d times , is the same as a taken c times , diminished by a taken d times ; or ax ( c - d ) = ac - ad . In the first term of ...
Σελίδα 41
... Suppose both dividend and divisor to be arranged according to the descending powers of some letter . Then it follows , from ( 75 , 1 ) , that the first term of the dividend must be the product of the first term of the divisor by the ...
... Suppose both dividend and divisor to be arranged according to the descending powers of some letter . Then it follows , from ( 75 , 1 ) , that the first term of the dividend must be the product of the first term of the divisor by the ...
Σελίδα 54
... suppose A to be a quantity which is exactly divisible by another quantity , D , and let q represent the quotient . Then , A 9 D If we now multiply the dividend by m , we shall have , from ( 84 I ) , in which qm is entire . it will also ...
... suppose A to be a quantity which is exactly divisible by another quantity , D , and let q represent the quotient . Then , A 9 D If we now multiply the dividend by m , we shall have , from ( 84 I ) , in which qm is entire . it will also ...
Σελίδα 55
... Suppose two polynomials to be arranged according to the powers of the same letter , and let A represent the greater and B the less . Then let us divide the greater by the less , the last divisor by the last remainder , and so on , till ...
... Suppose two polynomials to be arranged according to the powers of the same letter , and let A represent the greater and B the less . Then let us divide the greater by the less , the last divisor by the last remainder , and so on , till ...
Σελίδα 89
... one unknown quantity , can not have more than one root . For , whatever the equation may be , suppose it to be cleared of fractions , and the unknown terms transposed to 8 * REDUCTION . 89 Reduction of Simple Equations.
... one unknown quantity , can not have more than one root . For , whatever the equation may be , suppose it to be cleared of fractions , and the unknown terms transposed to 8 * REDUCTION . 89 Reduction of Simple Equations.
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Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 86 - Any term may be transposed from one member of an equation to the other by changing its sign (1, 2).
Σελίδα 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.
Σελίδα 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...
Σελίδα 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...
Σελίδα 31 - That the exponent of any letter in the product is equal to the sum of its exponents in the two factors.
Σελίδα 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.
Σελίδα 52 - Measure, of two or more quantities, is the greatest quantity that will exactly divide each of them.
Σελίδα 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.
Σελίδα 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.