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 iv
... true educator . Great care has been taken everywhere to set forth in distinct form the principles of the science , their exact log- ical relations being noted by proper references ; while due prominence has been given to those numerous ...
... true educator . Great care has been taken everywhere to set forth in distinct form the principles of the science , their exact log- ical relations being noted by proper references ; while due prominence has been given to those numerous ...
Σελίδα 25
... true subtrahend is not b , but b - c ; and , as we have subtracted a quantity too great by c , the remainder thus obtained must be too small by c ; we therefore add c to the first result , and obtain the true remainder , a - b + c . But ...
... true subtrahend is not b , but b - c ; and , as we have subtracted a quantity too great by c , the remainder thus obtained must be too small by c ; we therefore add c to the first result , and obtain the true remainder , a - b + c . But ...
Σελίδα 83
... true . And such value or values are said to satisfy the equation . An equation may contain two or more unknown quantities . 140. A Root of an equation is any value which , being substi- tuted for the unknown quantity , will satisfy the ...
... true . And such value or values are said to satisfy the equation . An equation may contain two or more unknown quantities . 140. A Root of an equation is any value which , being substi- tuted for the unknown quantity , will satisfy the ...
Σελίδα 84
... true . Thus , the two equations , x + c = 5a xca can not both be true at the same time , unless c = 2a That is , the last equation expresses the condition which will render the other two equations true ; it is therefore called an ...
... true . Thus , the two equations , x + c = 5a xca can not both be true at the same time , unless c = 2a That is , the last equation expresses the condition which will render the other two equations true ; it is therefore called an ...
Σελίδα 107
... true , whatever be the value of m . We may therefore assume m to be of such a value that the co- efficient of one of the unknown quantities shall become zero ; this will eliminate that unknown quantity , by causing the term contain- ing ...
... true , whatever be the value of m . We may therefore assume m to be of such a value that the co- efficient of one of the unknown quantities shall become zero ; this will eliminate that unknown quantity , by causing the term contain- ing ...
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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.