# A Complete Course in Algebra for Academies and High Schools

Leach, Shewell & Sanborn, 1885 - Algebra - 349 pages
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Pages � faire: 111, 112, 113, 114, 115, 117, 118, 119, 135, 136, 138, 139, 140, 143, 146, 147 et 148.

### Contents

 Symbols of Quantity 1 Axioms 10 Addition of Similar Terms 16 USE OF PARENTHESES 24 Division of Monomials 37 FRACTIONS 80 SIMPLE EQUATIONS 106 PROBLEMS LEADING TO SIMPLE EQUATIONS CON 119
 RADICALS 190 PAGE 208 Solution of Quadratic Equations by a Formula 222 EQUATIONS IN THE QUADRATIC FORM 228 65 237 THEORY OF QUADRATIC EQUATIONS 247 RATIO AND PROPORTION 255 ARITHMETICAL PROGRESSION 264

### Popular passages

Page 211 - In any trinomial square (Art. 108), the middle term is twice the product of the square roots of the first and third terms...
Page 253 - 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 256 - Hence -,- = -76" dn that is a" : b" = c" : dn THEOREM IX. 23 1 If any number of quantities are proportional, 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...
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 253 - To express that the ratio of A to B is equal to the ratio of C to D, we write the quantities thus : A : B : : C : D; and read, A is to B as C to D.
Page 164 - 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 42 - 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 105 - Any term may be transposed from one side of an equation to the other by changing its sign.
Page 225 - 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.
Page 231 - Equations of this kind may always be solved by finding the value of one of the unknown quantities in terms of the other from the simple equation, and substituting the result in the other equation. 1. Solve the equations j ^ ~ ** = 6^ 0> 1 x + 2y=7.