Algebra for Colleges and SchoolsMacmillan, 1897 - 516 páginas |
Dentro del libro
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Página ix
... Rule of Signs 28 Note on Arithmetical and Symbolical Algebra 29 Distributing the Product 31 Products written by Inspection 35 Multiplication by Detached Coefficients 37 V. Division 38 Index Law for Division 39 Division of Compound ...
... Rule of Signs 28 Note on Arithmetical and Symbolical Algebra 29 Distributing the Product 31 Products written by Inspection 35 Multiplication by Detached Coefficients 37 V. Division 38 Index Law for Division 39 Division of Compound ...
Página xiv
... Rule of Signs 469 Derived Functions 472 Equal Roots 472 Location of the Roots 474 Sturm's Theorem and Method 476 Graphical Representation of Functions 480 Solution of Higher Numerical Equations 483 Newton's Method 483 The Cube Roots of ...
... Rule of Signs 469 Derived Functions 472 Equal Roots 472 Location of the Roots 474 Sturm's Theorem and Method 476 Graphical Representation of Functions 480 Solution of Higher Numerical Equations 483 Newton's Method 483 The Cube Roots of ...
Página 12
... rule , for the terms may be added or subtracted in the order we find most convenient . This process is called ... signs is zero . The sum of 5 a and -5 a is 0 . Find the sum of EXAMPLES II . 1. 5a , 7 a , 11 a , a , 23 a . 9 . - - - 11b ...
... rule , for the terms may be added or subtracted in the order we find most convenient . This process is called ... signs is zero . The sum of 5 a and -5 a is 0 . Find the sum of EXAMPLES II . 1. 5a , 7 a , 11 a , a , 23 a . 9 . - - - 11b ...
Página 20
... signs of all the terms in the lower line being changed . by addition 4a - 3b + 5c -3a + 2b + с α -- b + 6 c Rule . Change the sign of every term in the expression to be subtracted , and add it to the other expression . NOTE . It is not ...
... signs of all the terms in the lower line being changed . by addition 4a - 3b + 5c -3a + 2b + с α -- b + 6 c Rule . Change the sign of every term in the expression to be subtracted , and add it to the other expression . NOTE . It is not ...
Página 28
... Rule of Signs in multiplication . Rule of Signs . The product of two terms with like signs is positive ; the product of two terms with unlike signs is neg- ative . 43. The rule of signs , and especially the use of the nega- tive ...
... Rule of Signs in multiplication . Rule of Signs . The product of two terms with like signs is positive ; the product of two terms with unlike signs is neg- ative . 43. The rule of signs , and especially the use of the nega- tive ...
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Términos y frases comunes
a²b a²b² a²x a²x² a³b ab² ab³ algebraic arithmetic means arithmetical ascending powers ax² ax³ b₁ binomial Binomial Theorem bx² cents CHAPTER coefficient column compound expressions continued fraction convergent cube denote digits dimes Divide dividend divisible divisor equal equation EXAMPLES Find the highest find the number Find the square Find the sum find the value fraction harmonic means Hence highest common factor integer letters logarithm lowest common multiple miles an hour Multiply negative number of terms numerator and denominator obtain positive quadratic quadratic equation quotient ratio remainder Resolve into factors result rule of signs Simplify Solve square root Subtract surd symbols unknown quantity whence whole number x²y x²y² x³y xy² xy³ yards zero
Pasajes populares
Página 167 - It is evident from the Rule of Signs that (1) no even power of any quantity can be negative; (2) any odd power of a quantity will have the same sign as the quantity itself. NOTE. It is especially worthy of notice that the square of every expression, whether positive or negative, is positive.
Página 264 - That is, if a quadratic equation be reduced to the form x?+px = q, the algebraic sum of the roots is equal to the coefficient of x with its sign changed, and the product of the roots is equal to the second member, with its sign changed.
Página 351 - The logarithm of a product is the sum of the logarithms of its factors.
Página 352 - The Integral Part of a logarithm is called the Characteristic, and the decimal part the Mantissa.
Página 183 - The sixth root of an expression is found by taking the cube root of the square root, or the square root of the cube root.
Página 102 - ... remainder. The lowest common multiple of two or more algebraic expressions is the expression of lowest degree which will contain them all without a remainder.
Página 289 - Four quantities are in proportion when the ratio of the first to the second is equal to the ratio of the third to the fourth.
Página 328 - A telegraph has 5 arms, and each arm has 4 distinct positions, including the position of rest: find the total number of signals that can be made.
Página 322 - From 7 Englishmen and 4 Americans a committee of 6 Is to be formed: in how many ways can this be done, (1) when the committee contains exactly 2 Americans, (2) at least 2 Americans...
Página 290 - Hence if any three terms of a proportion are given, the fourth may be found. Thus if a...