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 11
... evident that this notation cannot be employed when the several factors are represented by figures . We cannot represent 3 times 4 by simply writing the factors together , thus , 34 ; for the product thus indicated could not be ...
... evident that this notation cannot be employed when the several factors are represented by figures . We cannot represent 3 times 4 by simply writing the factors together , thus , 34 ; for the product thus indicated could not be ...
Σελίδα 15
... evident truth . The following axioms underlie the principles of all algebraic operations : 1. If the same quantity or equal quantities be added to equal quantities , the sums will be equal . 2. If the same quantity or equal quantities ...
... evident truth . The following axioms underlie the principles of all algebraic operations : 1. If the same quantity or equal quantities be added to equal quantities , the sums will be equal . 2. If the same quantity or equal quantities ...
Σελίδα 25
... evident that 5 units of any kind or quality subtracted from 8 units of the same kind or quality , must leave 3 units of the same kind or quality . That is , Also , + 8a ( + 5a ) = + 3a —8a — ( .— 5a ) —-3a But these remainders are the ...
... evident that 5 units of any kind or quality subtracted from 8 units of the same kind or quality , must leave 3 units of the same kind or quality . That is , Also , + 8a ( + 5a ) = + 3a —8a — ( .— 5a ) —-3a But these remainders are the ...
Σελίδα 31
... evident that a taken c minus d times , is the same as a taken c times , diminished by a taken d times ; or ax ( c - d ) = ac - ad . In the first term of this result , a is taken c times additively , or a + a + a + a etc. , to c ...
... evident that a taken c minus d times , is the same as a taken c times , diminished by a taken d times ; or ax ( c - d ) = ac - ad . In the first term of this result , a is taken c times additively , or a + a + a + a etc. , to c ...
Σελίδα 43
... evident , from ( 79 ) , that the exact division of one polynomial by another will be impossible , 1. When the first term of the divisor arranged with reference to any one of its letters , is not exactly contained in the first term of ...
... evident , from ( 79 ) , that the exact division of one polynomial by another will be impossible , 1. When the first term of the divisor arranged with reference to any one of its letters , is not exactly contained in the first term of ...
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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.