A Treatise on AlgebraHarper & brothers, 1846 - 346 páginas |
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Página 25
... perform the operation on the numbers as they were given , we first subtract 8 from 15 and obtain 7. This result is too small by 3 , because the number 8 is larger by 3 than the number which was required to be sub- tracted . Therefore ...
... perform the operation on the numbers as they were given , we first subtract 8 from 15 and obtain 7. This result is too small by 3 , because the number 8 is larger by 3 than the number which was required to be sub- tracted . Therefore ...
Página 27
... performing the ope- ration . This is done by enclosing the polynomial in a paren- thesis , and prefixing the sign ... perform the operation , the expression becomes 5a 36 + 4c 3a +26 8c - or 2a ― b -4c . - - ( 46. ) According to the ...
... performing the ope- ration . This is done by enclosing the polynomial in a paren- thesis , and prefixing the sign ... perform the operation , the expression becomes 5a 36 + 4c 3a +26 8c - or 2a ― b -4c . - - ( 46. ) According to the ...
Página 31
... performed . Thus 2 × 3 × 4 is equal to 2 × 4 × 3 or 4 × 3 × 2 or 3 × 4 × 2 , the product in each case being 24. So also , if a , b and c represent any three numbers , we shall have abc equal to bca or cab . It is convenient to consider ...
... performed . Thus 2 × 3 × 4 is equal to 2 × 4 × 3 or 4 × 3 × 2 or 3 × 4 × 2 , the product in each case being 24. So also , if a , b and c represent any three numbers , we shall have abc equal to bca or cab . It is convenient to consider ...
Página 35
... performed by changing the signs of the subtrahend ; hence we have 483016 + 10 which is equal to 12. This result is obviously correct , for 8-5 is equal to 3 , and 6-2 is equal to 4 ; that is , it was required to multiply 3 by 4 , the ...
... performed by changing the signs of the subtrahend ; hence we have 483016 + 10 which is equal to 12. This result is obviously correct , for 8-5 is equal to 3 , and 6-2 is equal to 4 ; that is , it was required to multiply 3 by 4 , the ...
Página 37
... performing the operation . This is effected by enclosing the quantities in parentheses , and writing them in ... performed , the expression is said to be expanded . ( 60. ) The following Theorems are of such extensive applica- tion that ...
... performing the operation . This is effected by enclosing the quantities in parentheses , and writing them in ... performed , the expression is said to be expanded . ( 60. ) The following Theorems are of such extensive applica- tion that ...
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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.