# A Complete Course in Algebra

Leach, Shewell, and Sanborn, 1885
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### Contents

 Symbols of Quantity 1 Axioms 10 SUBTRACTION 20 DIVISION 27 FORMULĘ 37 FACTORING 51 FRACTIONS 80 SIMPLE EQUATIONS 106
 Involution and Evolution of Radicals 199 Affected Quadratic Equations 212 Solution of Quadratic Equations by a Formula 222 EQUATIONS IN THE QUADRATIC FORM 228 THEORY OF QUADRATIC EQUATIONS 247 RATIO AND PROPORTION 255 ARITHMETICAL PROGRESSION 264 GEOMETRICAL PROGRESSION 273

 PROBLEMS LEADING TO SIMPLE EQUATIONS CON 119 SIMPLE EQUATIONS CONTAINING Two UNKNOWN 132 SIMPLE EQUATIONS CONTAINING MORE THAN 144 PROBLEMS LEADING TO SIMPLE EQUATIONS CON 158 Evolution of Monomials 165 Cube Root of Polynomials 173 THE THEORY OF EXPONENTS 180 RADICALS 190
 LOGARITHMS 287 888 294 PAGE 307 88 314 119 321 144 327 Copyright

### Popular passages

Page 166 - Arts. 200 and 201 we derive the following rule : Extract the required root of the numerical coefficient, and divide the exponent of each letter by the index of the root.
Page 213 - In any trinomial square (Art. 108), the middle term is twice the product of the square roots of the first and third terms...
Page 44 - ... the product of the two, plus the square of the second. In the third case, we have (a + b) (a — 6) = a2 — b2. (3) That is, the product of the sum and difference of two quantities is equal to the difference of their squares.
Page 49 - The exponent of b in the second term is 1, and increases by 1 in each succeeding term.
Page 255 - The first and fourth terms of a proportion are called the extremes; and the second and third terms the means. Thus, in the proportion a : b = с : d, a and d are the extremes, and b and с the means.
Page 258 - In a series of equal ratios, any antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Let a: b = c: d = e:f.
Page 5 - If equal quantities be divided by the same quantity, or equal quantities, the quotients will be equal. 5. If the same quantity be both added to and subtracted from another, the value of the latter will not be changed.
Page 44 - 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 107 - Any term may be transposed from one side of an equation to the other by changing its sign. For, consider the equation x + a = b.
Page 227 - A' courier proceeds from P to Q in 14 hours. A second courier starts at the same time from a place 10 miles behind P, and arrives at Q at the same time as the first courier. The second courier finds that he takes half an hour less than the first to accomplish 20 miles. Find the distance from P to Q.