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 vii
... Arithmetical Progression ... .285 Application of the Formulas ..287 The Ten Cases Problems .. ..290 .291 Geometrical Progression .293 Application of the Formulas .294 Problems ..298 Identical Equations . .301 Decomposition of Rational ...
... Arithmetical Progression ... .285 Application of the Formulas ..287 The Ten Cases Problems .. ..290 .291 Geometrical Progression .293 Application of the Formulas .294 Problems ..298 Identical Equations . .301 Decomposition of Rational ...
Página 9
... arithmetical computations , letters and other characters used in general analysis , and graphic representations or drawings used in geometrical investigations . 2d . Symbols of Operation , consisting of the signs or characters employed ...
... arithmetical computations , letters and other characters used in general analysis , and graphic representations or drawings used in geometrical investigations . 2d . Symbols of Operation , consisting of the signs or characters employed ...
Página 11
... arithmetical difference is to be taken , when it is not known which is the greater . 10. The Double Sign ,, is written before a quantity to indi- cate that it is to be both added and subtracted ; it serves to unite in a single ...
... arithmetical difference is to be taken , when it is not known which is the greater . 10. The Double Sign ,, is written before a quantity to indi- cate that it is to be both added and subtracted ; it serves to unite in a single ...
Página 20
... Arithmetical Sum of two or more quantities is the sum of their absolute values , and has reference simply to the num- ber of units in the quantities added . 47. The Algebraic Sum of two or more quantities is a quantity , which , taken ...
... Arithmetical Sum of two or more quantities is the sum of their absolute values , and has reference simply to the num- ber of units in the quantities added . 47. The Algebraic Sum of two or more quantities is a quantity , which , taken ...
Página 52
... arithmetical value . Thus , if x - 3 and x + 4x + 2 are the prime factors common to two or more quantities , then according to the above definition , ( x + 4x + 2 ) ( x - 3 ) = x3 + x2 - 10x - 6 , is the greatest common divisor . But ...
... arithmetical value . Thus , if x - 3 and x + 4x + 2 are the prime factors common to two or more quantities , then according to the above definition , ( x + 4x + 2 ) ( x - 3 ) = x3 + x2 - 10x - 6 , is the greatest common divisor . But ...
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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.