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 32
... involve all the variations of signs . It will be observed that according to the above interpretation , the multiplicand is to be repeated with its proper sign when the multiplier is positive , but with its sign changed when the ...
... involve all the variations of signs . It will be observed that according to the above interpretation , the multiplicand is to be repeated with its proper sign when the multiplier is positive , but with its sign changed when the ...
Página 84
... involves but one unknown quantity , its degree is denoted by the highest exponent of this quantity in any term . 2. - If an equation involves more than one unknown quantity , its degree is denoted by the greatest sum which the exponents ...
... involves but one unknown quantity , its degree is denoted by the highest exponent of this quantity in any term . 2. - If an equation involves more than one unknown quantity , its degree is denoted by the greatest sum which the exponents ...
Página 114
... involves ; substitute this value in an equation con- taining two unknown quantities , and thus find the value of a second ; substitute these values in an equation containing three unknown quan- tities , and find the value of a third ...
... involves ; substitute this value in an equation con- taining two unknown quantities , and thus find the value of a second ; substitute these values in an equation containing three unknown quan- tities , and find the value of a third ...
Página 129
... 66 " ( 6 ) , y = 66 པ ( 3 ) , & = - b 1 • ( l — 1 ) ( a − 1 ) mb — q ( a — 1 ) ( m — 1 ) ( a — 1 ) nb - r ( a - 1 ) ( n - 1 ) ( a — 1 ) DISCUSSION OF PROBLEMS INVOLVING SIMPLE EQUATIONS 180. The Discussion of GENERAL PROBLEMS . 129.
... 66 " ( 6 ) , y = 66 པ ( 3 ) , & = - b 1 • ( l — 1 ) ( a − 1 ) mb — q ( a — 1 ) ( m — 1 ) ( a — 1 ) nb - r ( a - 1 ) ( n - 1 ) ( a — 1 ) DISCUSSION OF PROBLEMS INVOLVING SIMPLE EQUATIONS 180. The Discussion of GENERAL PROBLEMS . 129.
Página 130
... INVOLVING SIMPLE EQUATIONS 180. The Discussion of a problem consists in attributing certain values and relations to the arbitrary quantities which enter the equa- tion , and in interpreting the results . 181. When a problem has been ...
... INVOLVING SIMPLE EQUATIONS 180. The Discussion of a problem consists in attributing certain values and relations to the arbitrary quantities which enter the equa- tion , and in interpreting the results . 181. When a problem has been ...
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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.