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 vii
... Four Forms . ..250 Discussion of Problems ... .252 Interpretation of Imaginary Results . .253 Problem of the Lights ..... .254 Problems producing Quadratic Equations .. ..258 SECTION VI . PROPORTION , PERMUTATIONS AND COMBINATIONS ...
... Four Forms . ..250 Discussion of Problems ... .252 Interpretation of Imaginary Results . .253 Problem of the Lights ..... .254 Problems producing Quadratic Equations .. ..258 SECTION VI . PROPORTION , PERMUTATIONS AND COMBINATIONS ...
Σελίδα 32
... four cases which involve all the variations of signs . It will be observed that according to the above interpretation , the multiplicand is to be repeated with its proper sign when the multiplier is positive , but with its sign changed ...
... four cases which involve all the variations of signs . It will be observed that according to the above interpretation , the multiplicand is to be repeated with its proper sign when the multiplier is positive , but with its sign changed ...
Σελίδα 39
... four cases , with results as follows : 1 . 2 . 3 . 4 . + ab ÷ ( + a ) = + b + ab ÷ ( -a ) = - b —ab ÷ ( a ) —b —ab ÷ ( —a ) = + b Hence , 3. - If the dividend and divisor have like signs , the quotient will be positive ; but if the ...
... four cases , with results as follows : 1 . 2 . 3 . 4 . + ab ÷ ( + a ) = + b + ab ÷ ( -a ) = - b —ab ÷ ( a ) —b —ab ÷ ( —a ) = + b Hence , 3. - If the dividend and divisor have like signs , the quotient will be positive ; but if the ...
Σελίδα 46
... four general problems , as follows : 1. - Divide am + bm by a + b . Commencing the division , we have am + Zm am + am - 1b Ja + b am - 1_ m- a 1st rem . -am - 1b + bm -b ( am — 1 ——_ bm — 1 ) -a 2 . m - 2 2d rem . + am - 22 + bm = + b2 ...
... four general problems , as follows : 1. - Divide am + bm by a + b . Commencing the division , we have am + Zm am + am - 1b Ja + b am - 1_ m- a 1st rem . -am - 1b + bm -b ( am — 1 ——_ bm — 1 ) -a 2 . m - 2 2d rem . + am - 22 + bm = + b2 ...
Σελίδα 98
... Four men take stock in a railroad company , amounting in the aggregate to $ 73,500 . A takes a certain sum , B takes three times as much as A , C takes three times as much as A and B togeth- er , and D takes one third as much as B and C ...
... Four men take stock in a railroad company , amounting in the aggregate to $ 73,500 . A takes a certain sum , B takes three times as much as A , C takes three times as much as A and B togeth- er , and D takes one third as much as B and C ...
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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.