Elements of Algebra: For Colleges, Schools, and Private Students, Βιβλίο 2Wilson, Hinkle & Company, 1866 - 406 σελίδες |
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Σελίδα 13
... preceding it is to be divided by that following it . Division is also expressed by placing the dividend as the numerator , and the divisor as the denominator of a frac- tion . Thus , ab , or α ō ' signifies that a is to be divided by b ...
... preceding it is to be divided by that following it . Division is also expressed by placing the dividend as the numerator , and the divisor as the denominator of a frac- tion . Thus , ab , or α ō ' signifies that a is to be divided by b ...
Σελίδα 20
... preceding , we derive the following GENERAL RULE FOR ADDITION OF ALGEBRAIC QUANTITIES . 1. Write the quantities to be added , placing those that are similar under each other . 2. Add the similar quantities by the rules already given 20 ...
... preceding , we derive the following GENERAL RULE FOR ADDITION OF ALGEBRAIC QUANTITIES . 1. Write the quantities to be added , placing those that are similar under each other . 2. Add the similar quantities by the rules already given 20 ...
Σελίδα 22
... preceding , we derive the following RULE FOR SUBTRACTION OF ALGEBRAIC QUANTITIES . 1. Write the quantities , placing similar terms under each other . 2. Conceive the signs of all the terms of the 22 RAY'S ALGEBRA , SECOND BOOK .
... preceding , we derive the following RULE FOR SUBTRACTION OF ALGEBRAIC QUANTITIES . 1. Write the quantities , placing similar terms under each other . 2. Conceive the signs of all the terms of the 22 RAY'S ALGEBRA , SECOND BOOK .
Σελίδα 24
... the signs of all the inclosed terms be changed . This is evident from the preceding principle . Thus , ab + c = a— ( b — c ) —c— ( b — a ) . This principle often enables us to express the same quan- 24 RAY'S ALGEBRA , SECOND BOOK .
... the signs of all the inclosed terms be changed . This is evident from the preceding principle . Thus , ab + c = a— ( b — c ) —c— ( b — a ) . This principle often enables us to express the same quan- 24 RAY'S ALGEBRA , SECOND BOOK .
Σελίδα 28
... cn — 1— c2n 4. a3x2z axz2- a * x3 3 7. xm + pXxn - P xm + n . 57. From the two preceding articles , we derive the fol- lowing GENERAL RULE FOR MULTIPLYING ONE POSITIVE MONOMIAL BY ANOTHER . 28 RAY'S ALGEBRA , SECOND BOOK .
... cn — 1— c2n 4. a3x2z axz2- a * x3 3 7. xm + pXxn - P xm + n . 57. From the two preceding articles , we derive the fol- lowing GENERAL RULE FOR MULTIPLYING ONE POSITIVE MONOMIAL BY ANOTHER . 28 RAY'S ALGEBRA , SECOND BOOK .
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Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
2d Bk algebraic ALGEBRAIC QUANTITIES arithmetical progression binomial Binomial Theorem coefficient common divisor Completing the square Corollary cube root decimal degree denominator derived polynomial Divide dividend division equa equal roots equation containing equation whose roots evident example exponent Extract the square factors Find the cube find the number Find the square Find the sum find the value geometrical progression given equation given number gives greater greatest common divisor Hence imaginary inequality less letters logarithms method minus monomial Multiply negative roots nth root number of balls number of terms perfect square positive root preceding Proposition quadratic equation quotient ratio real roots reduced remainder Required the number required to find result second term solved square root Sturm's theorem substituted subtracted taken Theorem third tion transform transposing trinomial unity unknown quantity Whence whole number X₁
Δημοφιλή αποσπάσματα
Σελίδα 136 - 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.
Σελίδα 289 - Take the first term from the second, the second from the third, the third from the fourth, &c. and the remainders will form a new series, called the first order of
Σελίδα 35 - Obtain the exponent of each literal factor in the quotient by subtracting the exponent of each letter in the divisor from the exponent of the same letter in the dividend; Determine the sign of the result by the rule that like signs give plus, and unlike signs give minus.
Σελίδα 39 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.
Σελίδα 148 - ... by the last figure of the root, and subtract the product from the dividend ; to the remainder bring down the next period for a new dividend.
Σελίδα 187 - CD, and, on meeting, it appeared that A had traveled 18 miles more than B ; and that A could have gone B's journey in 15 £ days, but B would have been 28 days in performing A's journey.
Σελίδα 68 - Reduce the fractions to a common denominator ; then subtract the numerator of the subtrahend from the numerator of the minuend, and write the result over the common denominator. EXAMPLES. H ,_, Zx . ^ 3x 1. From -^- subtract — . oo . Eeducing to a common denominator, the fractions become Wx 9x "15...
Σελίδα 37 - Since, in multiplying a polynomial by a monomial, we multiply each term of the multiplicand by the multiplier ; therefore, we have the following RULE, FOR DIVIDING A POLYNOMIAL BY A MONOMIAL. Divide each term of the dividend, by the divisor, according to the rule for the division of monomials.
Σελίδα 236 - In any proportion the product of the means is equal to the product of the extremes.
Σελίδα 43 - The square of the difference of two quantities is equal to the square of the first minus twice the product of the first by the second, plus the square of the second.