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 11
... denote multiplication ; as 3xy , which signifies the same as 3 xxxy . The multiplication of quantities which are represented by letters , is generally indicated by writing the factors one after another with- out any intervening sign ...
... denote multiplication ; as 3xy , which signifies the same as 3 xxxy . The multiplication of quantities which are represented by letters , is generally indicated by writing the factors one after another with- out any intervening sign ...
Página 12
... denotes the cube root of a ; Va denotes the 4th root of a ; and so on . When no index is written over the sign , the index ... denote both involution and evolution in the same expression , the numerator indicating the power to which the ...
... denotes the cube root of a ; Va denotes the 4th root of a ; and so on . When no index is written over the sign , the index ... denote both involution and evolution in the same expression , the numerator indicating the power to which the ...
Página 14
... denote how many times the latter is taken . Thus , in 3x , the number 3 is the coefficient of x , and indicates that x is taken 3 times ; hence , the expression 3x is equivalent to x + x + x . In 4ax , 4 may be regarded as the ...
... denote how many times the latter is taken . Thus , in 3x , the number 3 is the coefficient of x , and indicates that x is taken 3 times ; hence , the expression 3x is equivalent to x + x + x . In 4ax , 4 may be regarded as the ...
Página 19
... unlike signs , are together equal to zero . Thus if a denote the absolute value of any quantity , then + a - a = 0 + 2a - 2a = 0 + 3a - 3a = 0 , etc. ADDITION . 44. Addition , in Algebra , is the DEFINITIONS AND NOTATION . 19.
... unlike signs , are together equal to zero . Thus if a denote the absolute value of any quantity , then + a - a = 0 + 2a - 2a = 0 + 3a - 3a = 0 , etc. ADDITION . 44. Addition , in Algebra , is the DEFINITIONS AND NOTATION . 19.
Página 21
... denotes the sum of the three terms , a , b , and -C . 49. From these principles and illustrations we deduce the following RULE . To add similar terms : I. When the signs are alike , add the coefficients , and prefix the sum , with the ...
... denotes the sum of the three terms , a , b , and -C . 49. From these principles and illustrations we deduce the following RULE . To add similar terms : I. When the signs are alike , add the coefficients , and prefix the sum , with the ...
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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.