Elementary Algebra |
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Page viii
... Solution by Formula . 188 Solution by Factoring 190 XXVII . Equations in Quadratic Form 193 XXVIII . Simultaneous Quadratic Equations 198 Homogeneous Equations of the Same Degree 202 Symmetrical Equations . 203 XXIX . Problems . 207 XXX ...
... Solution by Formula . 188 Solution by Factoring 190 XXVII . Equations in Quadratic Form 193 XXVIII . Simultaneous Quadratic Equations 198 Homogeneous Equations of the Same Degree 202 Symmetrical Equations . 203 XXIX . Problems . 207 XXX ...
Page x
... 441 Graphical Representation of Functions Solution of Higher Numerical Equations Horner's Method of Approximation 444 447 452 Miscellaneous Examples 456 • ALGEBRA . CHAPTER I. DEFINITIONS . SUBSTITUTIONS . 1. Algebra X CONTENTS .
... 441 Graphical Representation of Functions Solution of Higher Numerical Equations Horner's Method of Approximation 444 447 452 Miscellaneous Examples 456 • ALGEBRA . CHAPTER I. DEFINITIONS . SUBSTITUTIONS . 1. Algebra X CONTENTS .
Page 48
... solution of the equation . 67. The solution of equations , and the operations subsidiary to it , form an extremely important part of Mathematics . All sorts of mathematical problems consist in the indirect determi- nation of some ...
... solution of the equation . 67. The solution of equations , and the operations subsidiary to it , form an extremely important part of Mathematics . All sorts of mathematical problems consist in the indirect determi- nation of some ...
Page 49
... SOLUTION OF SIMPLE EQUATIONS . 69. The process of solving a simple equation depends only upon the following axioms : 1 . 2 . If to equals we add equals the sums are equal . If from equals we take equals the remainders are equal . 3. If ...
... SOLUTION OF SIMPLE EQUATIONS . 69. The process of solving a simple equation depends only upon the following axioms : 1 . 2 . If to equals we add equals the sums are equal . If from equals we take equals the remainders are equal . 3. If ...
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... solution by proving that it satisfies the conditions of the question . Example 2. Divide 60 into two parts , so that three times the greater may exceed 100 by as much as 8 times the less falls short of 200 . and Let x be the greater ...
... solution by proving that it satisfies the conditions of the question . Example 2. Divide 60 into two parts , so that three times the greater may exceed 100 by as much as 8 times the less falls short of 200 . and Let x be the greater ...
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Common terms and phrases
a+3b a+b+c a₁ aČ+bČ arithmetic means arithmetical arranged ascending powers b₁ beginner Binomial Theorem cents CHAPTER coefficients column compound expression continued fraction convergent cube root decimal denote digits dimes Divide dividend division divisor equal EXAMPLES XI Find the highest find the number Find the square Find the sum find the value following expressions given expressions greater harmonic mean Hence highest common factor integer less letters logarithm lowest common multiple method miles an hour Multiply number of terms numerator and denominator obtain partial fractions prefixed prove quadratic quadratic equation quotient ratio remainder Resolve into factors result rule of signs second term Simplify SIMULTANEOUS EQUATIONS solution square root subtraction Suppose surds symbols Transposing unknown quantity walk whence write yards zero
Popular passages
Page 331 - The logarithm of a product is equal to the sum of the logarithms of its factors.
Page 256 - In a quadratic equation wJiere the coefficient of the first term is unity, (i) the sum of the roots is equal to the coefficient of x with its sign changed ; (ii) the product of the roots is equal to the third term.
Page 168 - Thus the 4th root (2x2) = the square root of the square root ; the sixth root (3x2) = the cube root of the square root, or the square root of the cube root.
Page 178 - A basket of oranges is emptied by one person taking half of them and one more, a second person taking half of the remainder and one more, and a third person taking half of the remainder and six more. How many did the basket contain at first ? 17.
Page 179 - Two vessels contain mixtures of wine and water ; in one there is three times as much wine as water, in the other five times as much water as wine. Find how much must be drawn off from each to fill a third vessel which holds seven gallons, in order that its contents may be half wine and half water.
Page 280 - The pressure of wind on a plane surface varies jointly as the area of the surface, and the square of the wind's velocity. The pressure on a square foot is 1...
Page 213 - Art. 167 we saw that if the number of unknown quantities is greater than the number of independent equations, there will be an unlimited number of solutions, and the equations will be indeterminate. By introducing conditions, however, we can limit the number of solutions. When positive integral values of the unknown quantities are required, the equations are called simple indeterminate equations. The introduction of this restriction enables us to express the solutions in a very simple form. Ex. 1....