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 41.
Σελίδα 11
... writing the factors one after another with- out any intervening sign . Thus , 3abc signifies the same as 3 × a × bxc , or 3.abc . It is evident that this notation cannot be employed when the several factors are represented by figures ...
... writing the factors one after another with- out any intervening sign . Thus , 3abc signifies the same as 3 × a × bxc , or 3.abc . It is evident that this notation cannot be employed when the several factors are represented by figures ...
Σελίδα 21
... sum of the positive and of the negative coefficients separately , and prefix the difference of the two sums , with the sign of the greater , to the common literal part . To add polynomials : I. Write the quantities to be ADDITION . 21.
... sum of the positive and of the negative coefficients separately , and prefix the difference of the two sums , with the sign of the greater , to the common literal part . To add polynomials : I. Write the quantities to be ADDITION . 21.
Σελίδα 22
... Write the quantities to be added , placing the similar terms together in separate columns .. II . Add each column , and connect the several results by their respective signs . — EXAMPLES FOR PRACTICE . ( 1. ) ( 2. ) ( 3. ) 3xy -6a2b + a ...
... Write the quantities to be added , placing the similar terms together in separate columns .. II . Add each column , and connect the several results by their respective signs . — EXAMPLES FOR PRACTICE . ( 1. ) ( 2. ) ( 3. ) 3xy -6a2b + a ...
Σελίδα 26
... Write the subtrahend underneath the minuend , placing the similar terms together in the same column . II . Conceive the signs of the subtrahend to be changed , unite the similar terms as in addition , and bring down all the remaining ...
... Write the subtrahend underneath the minuend , placing the similar terms together in the same column . II . Conceive the signs of the subtrahend to be changed , unite the similar terms as in addition , and bring down all the remaining ...
Σελίδα 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.
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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.