A Treatise on AlgebraHarper & brothers, 1846 - 346 páginas |
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Página 10
... cent . the question may be solved by Arithmetic , and we obtain an answer , which is applicable only to this problem . But in the solution of an Algebraic problem , we employ letters to which any value may be attributed at pleasure ...
... cent . the question may be solved by Arithmetic , and we obtain an answer , which is applicable only to this problem . But in the solution of an Algebraic problem , we employ letters to which any value may be attributed at pleasure ...
Página 14
... cents , is read one dollar equals one hundred cents . In like manner ab , signifies that a is equal to b ; and a + b = c - d , signifies that the sum of the numbers designated by a and b is equal to the difference of the numbers ...
... cents , is read one dollar equals one hundred cents . In like manner ab , signifies that a is equal to b ; and a + b = c - d , signifies that the sum of the numbers designated by a and b is equal to the difference of the numbers ...
Página 83
... cents amongst them ; to the second he gave twice , and to the third , three times as much as to the first . What did he give to each ? Let x = the sum given to the first . Then 2x = the sum given to the second . and 3x = the sum given ...
... cents amongst them ; to the second he gave twice , and to the third , three times as much as to the first . What did he give to each ? Let x = the sum given to the first . Then 2x = the sum given to the second . and 3x = the sum given ...
Página 84
Elias Loomis. Therefore he gave 10 , 20 and 30 cents to them respectively . The learner should verify this , and all the subsequent results . The same Problem generalised . Prob . 8. Divide the number a into three such parts , that the ...
Elias Loomis. Therefore he gave 10 , 20 and 30 cents to them respectively . The learner should verify this , and all the subsequent results . The same Problem generalised . Prob . 8. Divide the number a into three such parts , that the ...
Página 88
... cents each , and to the rest 7 cents . How many were there of each class ? Ans . Prob . 30. Divide the number a into two such parts , that if the first is multiplied by m , and the second by n , the sum of the products shall be b . b na ...
... cents each , and to the rest 7 cents . How many were there of each class ? Ans . Prob . 30. Divide the number a into two such parts , that if the first is multiplied by m , and the second by n , the sum of the products shall be b . b na ...
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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.