A Treatise on AlgebraHarper & brothers, 1846 - 346 páginas |
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Página 24
... consider negative as well as positive quan- tities ; and by the sum of two quantities , we mean their aggre- gate , regard being paid to their signs . Thus , the sum of +7 and 5 is + 2 , which is numerically less than either 7 or 5 . So ...
... consider negative as well as positive quan- tities ; and by the sum of two quantities , we mean their aggre- gate , regard being paid to their signs . Thus , the sum of +7 and 5 is + 2 , which is numerically less than either 7 or 5 . So ...
Página 29
... consider easterly motion + , westerly motion must be regarded as , and vice versa . And generally , when quantities which are estimated in different direc- tions enter into the same algebraic expression , those which are measured in one ...
... consider easterly motion + , westerly motion must be regarded as , and vice versa . And generally , when quantities which are estimated in different direc- tions enter into the same algebraic expression , those which are measured in one ...
Página 31
... consider the subject of multiplication under several cases . CASE I. ( 49. ) When the factors are both monomials . From Article 14 it appears that in order to represent the multi- plication of two monomials , such as 3abc and 5def , we ...
... consider the subject of multiplication under several cases . CASE I. ( 49. ) When the factors are both monomials . From Article 14 it appears that in order to represent the multi- plication of two monomials , such as 3abc and 5def , we ...
Página 42
... consider the properties of coefficients by themselves , and as preparatory to some investigations which are to follow . The beginner , however , in attempting to apply the method , will need to be particularly cautious not to unite ...
... consider the properties of coefficients by themselves , and as preparatory to some investigations which are to follow . The beginner , however , in attempting to apply the method , will need to be particularly cautious not to unite ...
Página 73
... consider these different cases in succession . I. The unknown quantity may be combined with known quan- tities , by addition . Let it be required to solve the equation x + 6 - 24 . If from the two equal quantities , x +6 and 24 , we ...
... consider these different cases in succession . I. The unknown quantity may be combined with known quan- tities , by addition . Let it be required to solve the equation x + 6 - 24 . If from the two equal quantities , x +6 and 24 , we ...
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Términos y frases comunes
according to Art algebraic arithmetical arithmetical progression binomial cents Charles Anthon coefficients Completing the square contrary sign cube root denotes derived polynomial Divide the number dividend divisible equal roots equation whose roots equation x³ example exponent expression Extract the square factors find the square find the values following RULE fourth power fourth root fraction geometrical geometrical progression given equation greater greatest common divisor Hence infinite series irreducible fraction last term less letters taken method miles monomial mth degree multiplied negative nth root number of permutations number of terms obtain order of differences preceding Prob problem proportion PROPOSITION quadratic equations quotient ratio real roots Reduce remainder represent Required the square Required the sum result second degree second term Sheep extra square root subtract suppose surd theorem unity unknown quantity variation whence whole number
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Página 189 - ... 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.
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Página 43 - 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.