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 |
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Página 14
... 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 - cx , there are three terms , of which 5a is the first , + 262 the second , and -cx the third . 24 ...
... 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 - cx , there are three terms , of which 5a is the first , + 262 the second , and -cx the third . 24 ...
Página 30
... Hence , 1. If the difference of two numbers be added to their sum , the result will be twice the greater number . 2. If the difference of two numbers be subtracted from their sum , the result will be twice the less number ...
... Hence , 1. If the difference of two numbers be added to their sum , the result will be twice the greater number . 2. If the difference of two numbers be subtracted from their sum , the result will be twice the less number ...
Página 31
... Hence , The coefficient of the product is equal to the product of the coeffi cients of the multiplicand and multiplier . 2d . The law of exponents . Let it be required to multiply ab3 by a3b ' . Since a * b * = aaaa bbb , and a3b ...
... Hence , The coefficient of the product is equal to the product of the coeffi cients of the multiplicand and multiplier . 2d . The law of exponents . Let it be required to multiply ab3 by a3b ' . Since a * b * = aaaa bbb , and a3b ...
Página 32
... Hence we conclude that the signs , + and - , when prefixed to a multiplier , must be interpreted as follows : The plus sign before a multiplier shows that the multiplicand is to be successively added ; and the minus sign before a ...
... Hence we conclude that the signs , + and - , when prefixed to a multiplier , must be interpreted as follows : The plus sign before a multiplier shows that the multiplicand is to be successively added ; and the minus sign before a ...
Página 37
... hence by the second formula , ( 2x - 5 ) = 4x - 20x2 + 25 , Ans . 3. What is the product of 5 + y ' and 5.x - y ' ? The square of 5x is 25x , and the square of y ' is y ' ; hence by the third formula , ( 5x + y ) ( 5x - y ' ) = 25x - y ...
... hence by the second formula , ( 2x - 5 ) = 4x - 20x2 + 25 , Ans . 3. What is the product of 5 + y ' and 5.x - y ' ? The square of 5x is 25x , and the square of y ' is y ' ; hence by the third formula , ( 5x + y ) ( 5x - y ' ) = 25x - y ...
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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.