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 σελίδες |
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Σελίδα 9
... respect to their relative magnitudes , and certain abbreviations employed in the process of reasoning . 3. Algebra is that branch of mathematics in which quantities are represented by letters , and the operations and relations are ...
... respect to their relative magnitudes , and certain abbreviations employed in the process of reasoning . 3. Algebra is that branch of mathematics in which quantities are represented by letters , and the operations and relations are ...
Σελίδα 28
... respecting the use of the parenthesis should be thoroughly considered by the learner , if he would acquire facility in algebraic transformations . 59. From the definition of the signs of aggregation , ( 17 ) , we understand that if the ...
... respecting the use of the parenthesis should be thoroughly considered by the learner , if he would acquire facility in algebraic transformations . 59. From the definition of the signs of aggregation , ( 17 ) , we understand that if the ...
Σελίδα 44
... respect to absolute value ; and second , the law of change with respect to algebraic signs . 1st . Change of value . 84. In any case of exact division , the quotient is composed of those factors of the dividend which are not included ...
... respect to absolute value ; and second , the law of change with respect to algebraic signs . 1st . Change of value . 84. In any case of exact division , the quotient is composed of those factors of the dividend which are not included ...
Σελίδα 141
... respecting the value of an expression reducible to the form of indetermination . 1. - Let us take the equation , 6x + 7 x + 2 6x - 12 = દ ( 1 ) x - 2 6x + 7 Reducing second member , = : 6 , ( 2 ) x + 2 clearing of fractions , 6x + 7 ...
... respecting the value of an expression reducible to the form of indetermination . 1. - Let us take the equation , 6x + 7 x + 2 6x - 12 = દ ( 1 ) x - 2 6x + 7 Reducing second member , = : 6 , ( 2 ) x + 2 clearing of fractions , 6x + 7 ...
Σελίδα 142
... respecting the values of quantities reducible to the form of indetermination , the result will be an algebraic absurdity . Thus , take the identical equation , 8 + 20 = 8 + 20 . ( 1 ) By transposition , 8-820-20 , ( 2 ) 8-8 20-20 ...
... respecting the values of quantities reducible to the form of indetermination , the result will be an algebraic absurdity . Thus , take the identical equation , 8 + 20 = 8 + 20 . ( 1 ) By transposition , 8-820-20 , ( 2 ) 8-8 20-20 ...
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Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 86 - Any term may be transposed from one member of an equation to the other by changing its sign (1, 2).
Σελίδα 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.
Σελίδα 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...
Σελίδα 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...
Σελίδα 31 - That the exponent of any letter in the product is equal to the sum of its exponents in the two factors.
Σελίδα 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.
Σελίδα 52 - Measure, of two or more quantities, is the greatest quantity that will exactly divide each of them.
Σελίδα 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.
Σελίδα 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.