# A Short Course in Higher Algebra: For Academies, High Schools, and Colleges

Leach, Shewell, and Sanborn, 1889 - Algebra - 426 pages
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### Contents

 Symbols of Quantity 1 Axioms 10 Addition of Similar Terms 16 USE OF PARENTHESES 24 FORMULĘ 37 FACTORING 51 XVI 75 Elimination by Addition or Subtraction 133
 The Problem of the Couriers 263 ARITHMETICAL PROGRESSION 280 GEOMETRICAL PROGRESSION 289 HARMONICAL PROGRESSION 298 THE THEOREM OF Undetermined COEFFICIENTS 308 NEGATIVE EXPONENTS 323 LOGARITHMS 330 COMPOUND INTEREST AND ANNUITIES 354

 SIMPLE EQUATIONS CONTAINING MORE THAN 144 PROBLEMS LEADING TO SIMPLE EQUATIONS CON 158 THE THEORY OF EXPONENTS 180 RADICALS 190 Affected Quadratic Equations 212 Solution of Quadratic Equations by a Formula 222 RATICS 233 INEQUALITIES 256
 PERMUTATIONS AND COMBINATIONS 361 ANSWERS 369 101 369 106 10 136 16 148 51 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 269 - In any proportion the terms are in proportion by Composition; that is, the sum of the first two terms is to the first term as the sum of the last two terms is to the third term.
Page 129 - A person has a hours at his disposal. How far may he ride in a coach which travels b miles an hour, so as to return home in time, walking back at the rate of с miles an hour ? 43.
Page 267 - 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 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 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.
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 136 - Find the value of one of the unknown quantities, in terms of the other and known quantities...