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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Σελίδα iii
... of Algebra . The General Theory of Equations is treated in two sections , the one embracing the general properties of equations , and the other the solution of numerical equations of all degrees . The whole subject ( iii )
... of Algebra . The General Theory of Equations is treated in two sections , the one embracing the general properties of equations , and the other the solution of numerical equations of all degrees . The whole subject ( iii )
Σελίδα vi
... Solution of Problems . .124 Discussion of Problems .. ..130 Nothing and Infinity .... .135 Interpretation of Anomalous Forms .. ..136 Problem of the Couriers .. ..138 Inequalities . ..145 SECTION III . POWERS AND ROOTS . Involution ...
... Solution of Problems . .124 Discussion of Problems .. ..130 Nothing and Infinity .... .135 Interpretation of Anomalous Forms .. ..136 Problem of the Couriers .. ..138 Inequalities . ..145 SECTION III . POWERS AND ROOTS . Involution ...
Σελίδα viii
... SOLUTION OF NUMERICAL EQUATIONS OF HIGHER DEGREES . Limits of Roots Limiting Equation Sturm's Theorem .. Horner's Method of Approximation . ... 405 .408 .410 .416 A TREATISE ON ALGEBRA . SECTION I. DEFINITIONS AND NOTATION viii CONTENTS .
... SOLUTION OF NUMERICAL EQUATIONS OF HIGHER DEGREES . Limits of Roots Limiting Equation Sturm's Theorem .. Horner's Method of Approximation . ... 405 .408 .410 .416 A TREATISE ON ALGEBRA . SECTION I. DEFINITIONS AND NOTATION viii CONTENTS .
Σελίδα 94
... Solution of a problem is the process of finding the values of the unknown quantities . 159. Every problem in Algebra contains a statement of the rela- tions between certain known and certain unknown quantities . When these relations are ...
... Solution of a problem is the process of finding the values of the unknown quantities . 159. Every problem in Algebra contains a statement of the rela- tions between certain known and certain unknown quantities . When these relations are ...
Σελίδα 96
... solution of any problem requiring but one equation ; and we may derive from them the following GENERAL RULE . I. Represent one of the unknown quantities by some letter or symbol , and then from the given relations find an algebraic ...
... solution of any problem requiring but one equation ; and we may derive from them the following GENERAL RULE . I. Represent one of the unknown quantities by some letter or symbol , and then from the given relations find an algebraic ...
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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.