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 vii
... Combinations ..278 Examples of Permutations and Combinations . ..283 SECTION VII . OF SERIES . Arithmetical Progression ... .285 Application of the Formulas ..287 The Ten Cases Problems .. ..290 .291 Geometrical Progression .293 ...
... Combinations ..278 Examples of Permutations and Combinations . ..283 SECTION VII . OF SERIES . Arithmetical Progression ... .285 Application of the Formulas ..287 The Ten Cases Problems .. ..290 .291 Geometrical Progression .293 ...
Σελίδα 11
... combinations of the same quantities . Thus , ab is equivalent to a + b and a - b , and is read a plus or minus b . 11. The Sign of Multiplication is the oblique cross , X. It in- dicates that the quantity before it is to be multiplied ...
... combinations of the same quantities . Thus , ab is equivalent to a + b and a - b , and is read a plus or minus b . 11. The Sign of Multiplication is the oblique cross , X. It in- dicates that the quantity before it is to be multiplied ...
Σελίδα 13
... combination of the sign of ratio and the sign of equality , : = : ; or a combination of points only , :::: . Thus , a b c d , signifies that the ratio of a to b is equal to the ratio of c to d ; and the expression ab :: c : d signifies ...
... combination of the sign of ratio and the sign of equality , : = : ; or a combination of points only , :::: . Thus , a b c d , signifies that the ratio of a to b is equal to the ratio of c to d ; and the expression ab :: c : d signifies ...
Σελίδα 14
... combination of symbols as factors , or several combina- tions or parts . The parts are called terms ; hence , - 23. The Terms of an algebraic quantity are the parts or divis- ions made by the signs and Thus , in the quantity 5a + 262 ...
... combination of symbols as factors , or several combina- tions or parts . The parts are called terms ; hence , - 23. The Terms of an algebraic quantity are the parts or divis- ions made by the signs and Thus , in the quantity 5a + 262 ...
Σελίδα 113
... combination , we shall have n - 1 derived equations containing all of the unknown quantities except the one eliminated . 2. — If then we combine one of these derived equations with each of the others , eliminating another letter , we ...
... combination , we shall have n - 1 derived equations containing all of the unknown quantities except the one eliminated . 2. — If then we combine one of these derived equations with each of the others , eliminating another letter , we ...
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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.