Elements of Algebra: Including Sturms' Theorem |
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Page 3
... as a standard or model . The order of arrangement , in many parts , has been changed ; new rules and new methods have been introduced ; and all the modifications which have been suggested by teaching and a careful comparison with other.
... as a standard or model . The order of arrangement , in many parts , has been changed ; new rules and new methods have been introduced ; and all the modifications which have been suggested by teaching and a careful comparison with other.
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... Rule . 33-36 Subtraction - Rule - Remark 36-40 Multiplication - Rule for Monomials 40-42 Rule for Polynomials and Signs 42-45 Remarks - Theorems Proved .... 45-48 Of Factoring Polynomials . 48-49 Division of Monomials - Rule . 49-52 ...
... Rule . 33-36 Subtraction - Rule - Remark 36-40 Multiplication - Rule for Monomials 40-42 Rule for Polynomials and Signs 42-45 Remarks - Theorems Proved .... 45-48 Of Factoring Polynomials . 48-49 Division of Monomials - Rule . 49-52 ...
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... Rule . Questions involving Equations of the First Degree ........ 92-94 94-95 Equations with two or more Unknown Quantities 95-96 Elimination - By Addition - By Subtraction By Comparison ...... 96-103 Indeterminate Problems - Questions ...
... Rule . Questions involving Equations of the First Degree ........ 92-94 94-95 Equations with two or more Unknown Quantities 95-96 Elimination - By Addition - By Subtraction By Comparison ...... 96-103 Indeterminate Problems - Questions ...
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... Rules for Radicals 232 Theory of Exponents ...... 233 Multiplication of Quantities with any Exponent 234 Division 235 Formation of Powers . .... 236 Extraction of Roots ... 237 Method of Indeterminate Co - efficients 238-243 Recurring ...
... Rules for Radicals 232 Theory of Exponents ...... 233 Multiplication of Quantities with any Exponent 234 Division 235 Formation of Powers . .... 236 Extraction of Roots ... 237 Method of Indeterminate Co - efficients 238-243 Recurring ...
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... Rule ... Commensurable Roots of Numerical Equations . Sturms ' Theorem ... Young's Method of resolving Cubic Equations ...... .. Method of Resolving Higher Equations .. ARTICLES 318 319 320-327 327-330 330-333 333-341 342-345 345 ...
... Rule ... Commensurable Roots of Numerical Equations . Sturms ' Theorem ... Young's Method of resolving Cubic Equations ...... .. Method of Resolving Higher Equations .. ARTICLES 318 319 320-327 327-330 330-333 333-341 342-345 345 ...
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Common terms and phrases
affected algebraic quantities arithmetical means arithmetical progression binomial called co-efficient common difference consequently contain contrary signs cube root Cx² decimal deduced denominator denote divide dividend division entire number enunciation equa equal equation involving example exponent expression extract the square factors figure find the values formula fourth fraction given equation given number gives greater greatest common divisor hence inequality last term least common multiple less logarithm monomial multiplicand multiplied negative nth root number of terms obtain operation ounces perfect square permutations problem proportion proposed equation quan quotient radical sign Reduce remainder result rule satisfy second degree second member second term simplest form square root substituted subtract suppose supposition take the equation third tion tities total number transposing unity unknown quantity whence whole number ах
Popular passages
Page 30 - That is, the square of the sum of two quantities is equal to the square of the first, plus twice the product of the first by the second, plus the square of the second.
Page 275 - The characteristic of a number less than 1 is found by subtracting from 9 the number of ciphers between the decimal point and the first significant digit, and writing — 10 after the result.
Page 27 - Hence, for the multiplication of polynomials we have the following RULE. Multiply all the terms of the multiplicand by each term of the multiplier, observing that like signs give plus in the product, and unlike signs minus.
Page 179 - To express that the ratio of A to B is equal to the ratio of C to D, we write the quantities thus : A : B : : C : D; and read, A is to B as C to D.
Page 180 - If the product of two quantities is equal to the product of two other quantities, two of them may be made the extremes, and the other two the means of a proportion.
Page 90 - If A and B together can perform a piece of work in 8 days, A and C together in 9 days, and B and C in 10 days : how many days would it take each person to perform the same work alone ? Ans.
Page 346 - VARIATIONS of signs, nor the number of negative roots greater than the number of PERMANENCES. Consequence. 328. When the roots of an equation are all real, the number of positive roots is equal to the number of variations, and the number of negative roots to , the number of permanences.
Page 34 - I. Divide the coefficient of the dividend by the coefficient of the divisor.
Page 108 - Which proves that the square of a number composed of tens and units, contains the square of the tens plus twice the product of the tens by the units, plus the square of the units.
Page 202 - In each succeeding term the coefficient is found by multiplying the coefficient of the preceding term by the exponent of a in that term, and dividing by the number of the preceding term.