# Elementary Algebra

Macmillan and Company, 1895 - Algebra - 478 pages

### Contents

 CHAPTER 1 Negative Quantities Addition of Like Terms 9 IV 19 Division 34 VII 42 Simple Equations 51 Resolution into Factors 63 XII 77
 Indeterminate Equations of the First Degree 213 Elementary Surds 229 Imaginary Quantities 249 CHAPTER PAGE 254 Ratio 266 Permutations and Combinations 300 Probability Chance 310 Logarithms 325

 Lowest Common Multiple 86 Fractions 95 Addition and Subtraction 102 Rules for Change of Sign 109 Fractional and Literal Equations 126 XXI 152 XXIII 160 Problems 174 Inequalities 180 Equations in Quadratic Form 193 Problems 207
 Interest and Annuities 342 Continued Fractions 369 CHAPTER PAGE 371 Summation of Series 381 Piles of Shot and Shells 390 Exponential and Logarithmic Series 398 Sturms Theorem and Method 441 Solution of Higher Numerical Equations 447 Miscellaneous Examples 456 Copyright

### 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....