A Treatise on AlgebraHarper & Brothers, 1868 - 384 páginas |
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Página vii
... . Definitions - Method of Differences . Interpolation ..... 248 251 255 257 Development of Algebraic Expressions into Series 259 263 265 PAGE Method of Undetermined Coefficients ........ 267 To resolve a CONTENTS . vii.
... . Definitions - Method of Differences . Interpolation ..... 248 251 255 257 Development of Algebraic Expressions into Series 259 263 265 PAGE Method of Undetermined Coefficients ........ 267 To resolve a CONTENTS . vii.
Página 11
... difference or di- ameter ; r , radius or ratio ; c , circumference ; h , height , etc. All these letters may be used with accents . Thus , in a problem relating to two circles , d may represent the diameter of one cir- cle , and d ' the ...
... difference or di- ameter ; r , radius or ratio ; c , circumference ; h , height , etc. All these letters may be used with accents . Thus , in a problem relating to two circles , d may represent the diameter of one cir- cle , and d ' the ...
Página 12
... difference of these two quantities . 12. The sign of multiplication is an inclined cross , × . When placed between two quantities , it indicates that the first is to be multiplied by the second . Thus , 3 × 5 indicates that 3 is to be ...
... difference of these two quantities . 12. The sign of multiplication is an inclined cross , × . When placed between two quantities , it indicates that the first is to be multiplied by the second . Thus , 3 × 5 indicates that 3 is to be ...
Página 14
... d denotes that the sum of the num- bers designated by a and b , is equal to the difference of the numbers designated by c and d . 19. The sign of inequality is the angle > or 14 ALGEBRA . Symbols which indicate Relation.
... d denotes that the sum of the num- bers designated by a and b , is equal to the difference of the numbers designated by c and d . 19. The sign of inequality is the angle > or 14 ALGEBRA . Symbols which indicate Relation.
Página 18
... difference between six times x and four , is equal to the quotient of five divided by the sum of a and b . Ex . 4. Three quarters of x increased by five , is equal to three sevenths of b diminished by seventeen . Ex . 5. One ninth of ...
... difference between six times x and four , is equal to the quotient of five divided by the sum of a and b . Ex . 4. Three quarters of x increased by five , is equal to three sevenths of b diminished by seventeen . Ex . 5. One ninth of ...
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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.