Elements of Algebra: On the Basis of M. Bourdon, Embracing Sturm's and Horner's Theorems, and Practical ExamplesA. S. Barnes & Company, 1857 - 400 páginas |
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Página 3
... ar- rangement , in many parts , has been changed ; new rules and new methods have been introduced : the modifica- tions indicated by its use , for twenty years , as a text book in the Military Academy have been freely made , for.
... ar- rangement , in many parts , has been changed ; new rules and new methods have been introduced : the modifica- tions indicated by its use , for twenty years , as a text book in the Military Academy have been freely made , for.
Página 20
... changed . For example , make a 7 and b = 4 : there results a - b 3 . Now , make a = 7+ 5 = 12 , and b = 4 + 5 = 9 , and there results , as before , a b = 12 9 = 3 . - ― = The 23. Of the different terms which compose a polynomial , some ...
... changed . For example , make a 7 and b = 4 : there results a - b 3 . Now , make a = 7+ 5 = 12 , and b = 4 + 5 = 9 , and there results , as before , a b = 12 9 = 3 . - ― = The 23. Of the different terms which compose a polynomial , some ...
Página 30
... changed , and then add the result to the other quantity . EXAMPLES . ( 1 ) . From - 6ac 5ab + c2 Take 7c 3ac + 3ab Remainder Зас - - 8ab + c2 + 7c . ( 2 ) . 5bc + 7ac The same with the signs of the lower line changed . From 16a2 - 19abc ...
... changed , and then add the result to the other quantity . EXAMPLES . ( 1 ) . From - 6ac 5ab + c2 Take 7c 3ac + 3ab Remainder Зас - - 8ab + c2 + 7c . ( 2 ) . 5bc + 7ac The same with the signs of the lower line changed . From 16a2 - 19abc ...
Página 32
... changed when the term is placed within the parenthesis . Hence , if we have ` one or more terms included within a parenthesis having the minus sign before it , the signs of all the terms must be changed when the parenthesis is omitted ...
... changed when the term is placed within the parenthesis . Hence , if we have ` one or more terms included within a parenthesis having the minus sign before it , the signs of all the terms must be changed when the parenthesis is omitted ...
Página 33
... changed by changing the order of its factors ; hence , we may write the product as follows : 7 × 4aaaaabbb , which is equivalent to 28a5b3 . Comparing this result with the given factors , we see that the co - efficient in the product is ...
... changed by changing the order of its factors ; hence , we may write the product as follows : 7 × 4aaaaabbb , which is equivalent to 28a5b3 . Comparing this result with the given factors , we see that the co - efficient in the product is ...
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Términos y frases comunes
algebraic expression algebraic quantities approximating fraction arithmetical arithmetical progression becomes called co-efficient common difference contrary signs cube root deduce denote the number derived polynomial Divide dividend entire number equal exactly divisible example exponent extract the square figures Find the factors find the values following RULE formula fractional unit given equation given number gives greater number greatest common divisor hence indicated inequality irreducible fraction last term leading letter least common multiple logarithm mixed quantity monomial multiplicand and multiplier nth power nth root number of terms obtain operation perfect square positive roots preceding problem proposed equation quotient radical sign real roots Reduce the polynomial remainder required to find result second degree second member second term simplest form square root substituted subtract suppose taken third transformed equation unknown quantity whence whole number X₁
Pasajes populares
Página 121 - Multiply the divisor, thus augmented, by the last figure of the root, and subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.
Página 174 - For, we can find the value of one of the unknown quantities in terms of the other and known quantities...
Página 286 - The logarithm of a number is the exponent of the power to which it is necessary to raise a fixed number, in order to produce the first number.
Página 39 - That is, the square of the sum of two quantities is equal to the square of the first, plus twice the product of the first by the second, plus the square of the second.
Página 10 - Logic is a portion of the art of thinking; language is evidently, and by the admission of all philosophers, one of the principal instruments or helps of thought; and any imperfection in the instrument or in the mode of employing it is confessedly liable, still more than in almost any other art, to confuse and impede the process and destroy all ground of confidence in the result.
Página 200 - RULE. I. Separate the given number into periods of three figures each, beginning at the right hand ; the left hand period will often contain less than three places of figures.
Página 100 - If A and B together can perform a piece of work in 8 days, A and c together in 9 days, and B and c in 10 days, how many days will it take each person to perform the same work alone.
Página 35 - We have, then, for the multiplication of polynomials, the following RULE. Multiply all the terms of the multiplicand by each term of the multiplier in succession, aff'ccting the product of any two terms with the sign plus, when tlieir signs are alike, and with the sign minus, when their signs
Página 41 - Divide the coefficient of the dividend by the coefficient of the divisor.
Página 200 - The cube of a number is equal to the cube of the tens, plus three times the product of the square of the tens by the units, plus three times the product of the tens by the square of the units, plus the cube of the units.