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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Resultados 1-5 de 74
Página 13
... less than . Thus , ab signifies that a is greater than b ; x + y < z signifies that a plus y is less than z . 17. The Signs of Aggregation are the parenthesis , ( ) , brackets , [ ] , brace , { } , vinculum , and bar , . They indicate ...
... less than . Thus , ab signifies that a is greater than b ; x + y < z signifies that a plus y is less than z . 17. The Signs of Aggregation are the parenthesis , ( ) , brackets , [ ] , brace , { } , vinculum , and bar , . They indicate ...
Página 30
... less than the given quantity . 3d . If from any given quantity a positive quantity be subtracted , the result will be less than the given quantity ; but if a negative quantity be subtracted , the result will be greater than the given ...
... less than the given quantity . 3d . If from any given quantity a positive quantity be subtracted , the result will be less than the given quantity ; but if a negative quantity be subtracted , the result will be greater than the given ...
Página 55
... less . Then let us divide the greater by the less , the last divisor by the last remainder , and so on , till nothing remains . If we represent the several quotients by q , q ' , q ' , etc .; and the remainders by R , R ' , R " , etc ...
... less . Then let us divide the greater by the less , the last divisor by the last remainder , and so on , till nothing remains . If we represent the several quotients by q , q ' , q ' , etc .; and the remainders by R , R ' , R " , etc ...
Página 59
... less , and continue the division till the first term of the remainder is of a lower degree than the first term of the divisor ; observing to suppress the monomial factors in every remainder , and to introduce into any dividend , if ...
... less , and continue the division till the first term of the remainder is of a lower degree than the first term of the divisor ; observing to suppress the monomial factors in every remainder , and to introduce into any dividend , if ...
Página 96
... less be added to of the greater , the sum will be equal to greater diminished by of the less . Required the two numbers . Let x = the less ; then x + 6 By the conditions of the problem , х 5 = the greater . x + 6x + 6 3 + = 5 3 6x = 12 ...
... less be added to of the greater , the sum will be equal to greater diminished by of the less . Required the two numbers . Let x = the less ; then x + 6 By the conditions of the problem , х 5 = the greater . x + 6x + 6 3 + = 5 3 6x = 12 ...
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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.