# Algebra for Colleges and Schools

Macmillan Company, 1897 - Algebra - 516 pages
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### Contents

 OHAPTER PAGE 1 Negative Quantities Addition of Like Terms 9 Multiplication 24 72 29 Division 38 78 44 Removal and Insertion of Brackets 48 Simple Equations 55
 Surds Radicals 203 Imaginary Quantities 222 Equations in Quadratic Form 245 Problems 258 Theory of Quadratic Equations 264 Indeterminate Equations of the First Degree 276 Ratio 286 Arithmetical Progression 301

 83 60 Problems Leading to Simple Equations 65 87 70 98 78 Highest Common Factor 92 Lowest Common Multiple 102 Complex Fractions Mixed Expressions 126 Fractional and Literal Equations 136 Simultaneous Equations 147 Problems 160 Involution 169 Evolution 176 141 184 The Theory of Indices 191
 Permutations and Combinations 319 Probability Chance 331 Proof for Positive Integral 338 Logarithms 352 CHAPTER PAGE 355 Interest and Annuities 307 367 Convergency and Divergency of Series 377 Undetermined Coefficients 386 Continued Fractions 400 Summation of Series 413 Proof for Any Index 426 CHAPTER PAGE 435 Theory of Equations 450

### Popular passages

Page 292 - Given that the area of a circle varies as the square of its radius...
Page 161 - 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.
Page 166 - The coefficient of any term may be found by multiplying the coefficient of the preceding term by the exponent of a in that term, and dividing this product by the number of the term.
Page 177 - 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.
Page 283 - In any proportion the product of the extremes is equal to the product of the means. Let the proportion be a : b = с : d.
Page 283 - 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.
Page 316 - 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...
Page 386 - ... continued through the season of 1900 and a few more facts were established which add to our knowledge of the disease. EFFECTS OF THE DISEASE AND APPEARANCE OF AFFECTED PARTS. >A brief discussion of the work of the fungus and the appearance of cankered limbs will not be out of place at this time; but for a fuller discussion of the subject the reader is referred to the former bulletin.
Page 315 - From 12 books in how many ways can a selection of 5 be made, (1) when one specified book is always included, (2) when one specified book is always excluded ? (1) Since the specified book is to be included in every selection, we have only to choose 4 out of the remaining 11. Hence the number of ways...
Page 254 - At what price per dozen did she sell them at first ? 20. Two rectangles contain the same area, 480 square yards. The difference of their lengths is 10 yards, and of their breadths 4 yards ; find their sides. 21. There is a number between 10 and 100 ; when multiplied by the digit on the left the product is 280 ; if the sum of the digits be multiplied by the same digit the product is 55 : required the number.