A Treatise on AlgebraHarper & Brothers, 1868 - 384 páginas |
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Página vi
... Roots of Monomials ..... Square Root of Polynomials ... Square Root of Numbers ... 133 136 139 Cube Root of Polynomials ......... .. Cube Root of Numbers ...... 143 146 CHAPTER XIII . RADICAL QUANTITIES . Transformation of Radical ...
... Roots of Monomials ..... Square Root of Polynomials ... Square Root of Numbers ... 133 136 139 Cube Root of Polynomials ......... .. Cube Root of Numbers ...... 143 146 CHAPTER XIII . RADICAL QUANTITIES . Transformation of Radical ...
Página 13
... cube of 2 . 2 × 2 × 2 × 2 = 16 , the fourth power of 2 , etc. So , also , 3 × 3 = 9 , the second power of 3 . Also ... root of a quantity is a factor which , multiplied by itself a certain number of times , will produce the given quantity .
... cube of 2 . 2 × 2 × 2 × 2 = 16 , the fourth power of 2 , etc. So , also , 3 × 3 = 9 , the second power of 3 . Also ... root of a quantity is a factor which , multiplied by itself a certain number of times , will produce the given quantity .
Página 14
... root of that quantity is to be extracted . The name or index of the required root is the number written above the radical sign . Thus , V9 , or simply V9 , denotes the square root of 9 , which is 3 . 64 denotes the cube root of 64 ...
... root of that quantity is to be extracted . The name or index of the required root is the number written above the radical sign . Thus , V9 , or simply V9 , denotes the square root of 9 , which is 3 . 64 denotes the cube root of 64 ...
Página 133
... cube root . If a quantity be resolved into four equal factors , one of them is called the fourth root , and so on . 191. Evolution is the process of extracting any root of a given quantity . Evolution is indicated by the radical sign ...
... cube root . If a quantity be resolved into four equal factors , one of them is called the fourth root , and so on . 191. Evolution is the process of extracting any root of a given quantity . Evolution is indicated by the radical sign ...
Página 134
... root of a monomial , we extract the root of the nu- merical coefficient , and divide the exponent of each letter by the index of the required root . Thus the cube root of 64a6b3 is 4a2b . 195. Sign of the Root . - We have seen , Art ...
... root of a monomial , we extract the root of the nu- merical coefficient , and divide the exponent of each letter by the index of the required root . Thus the cube root of 64a6b3 is 4a2b . 195. Sign of the Root . - We have seen , Art ...
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Términos y frases comunes
algebraic arithmetical progression binomial binomial theorem cent coefficient common denominator common difference compound interest continued fraction cube root decimal denote digits Divide the number dividend divisible dollars equa equal equation whose roots EXAMPLES exponent expression Extract the square factors figure Find the cube Find the fifth Find the fourth Find the number Find the square Find the sum find the values following RULE fourth power geometrical progression Given greatest common divisor Hence indicates infinite series last term least common multiple less logarithm miles monomial Multiply negative nth root number of terms obtain polynomial positive preceding Prob problem quotient radical sign ratio real roots Reduce remainder represent Resolve result second degree second term Solve the equation square root Sturm's Theorem subtract suppose surd third tion unity unknown quantity whence whole number zero
Pasajes populares
Página 72 - Now .} of f- is a compound fraction, whose value is found by multiplying the numerators together for a new numerator, and the denominators for a new denominator.
Página 141 - 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.
Página 39 - ... the square of the second. In the second case, (ab)2 = a?-2ab + bi. (2) That is, the square of the difference of two numbers is equal to the square of the first, minus twice the product of the first by the second, plus the square of the second.
Página 54 - Divide the less number by the remainder, the last divisor by the last remainder, and so on, till nothing remains. The last divisor will be the greatest common divisor sought.
Página 46 - 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.
Página 181 - A vintner draws a certain quantity of wine out of a full vessel that holds 256 gallons ; and then filling the vessel with water, draws off the same quantity of liquor as before, and so on for four draughts, when there were only 81 gallons of pure wine left. How much wine did he draw each time ? 50.
Página 227 - In arithmetical progression there are five parts to be considered, viz : the first term, the last term, the number of terms, the common difference, and the sum of all the terms.
Página 204 - ... 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.
Página 220 - In a series of equal ratios, any antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Let a: 6 = c: d = e :/. Then, by Art.
Página 202 - A , where m=c 9. Find two numbers such that their sum, their product, and the difference of their squares may be all equal to one another.