American Book Company, 1918 - Algebra - 342 pages
This text is arranged to follow a first year course, and meets the requirements in algebra for both college of liberal arts, technical schools, and high schools with advanced courses. The text begins with a review of the first year course, which aims to unify arithmetic, algebra, and plane geometry as effectively as possible. The second part of the text advances to treat the remaining topics belonging to elementary algebra, and finishes with the topics belonging to advanced algebra. The aim of the entire volume is to address all topics with simplicity, clearness, and conciseness without sacrificing rigor.

### Contents

 I The Four Fundamental Operations 1 Formulas and Theorems II III 16 Factoring 20 IV 21 Fractions 25 INVOLUTION AND EVOLUTION 52 I Fractional Exponent Expressions 60 Radical Expressions 69
 32 164 52 166 60 167 LOGARITHMS 170 81 171 87 176 95 177 102 180

 Imaginaries 81 Equations containing Radicals 87 Fundamental Principles in Algebra V I II 89 PART I 90 1 Incomplete Quadratics 93 Complete Quadratics 94 III 95 IV 104 Higher Equations and Quadratics Simultaneous Quadratics 105 Difficult Quadratics 107 PART II 127 Proportion Proper 151 Variation 156 Ratios of Sides in Right Triangles 159 1 161
 104 181 ARITHMETICAL AND GEOMETRICAL PROGRESSIONS 190 XI 206 REASONING IN EQUATIONSDISCUSSION OF QUADRATIC 215 PART III 230 I 257 The Finite Difference Method 308 Undetermined Coefficients 316 COMPLEX NUMBERS 325 XXI GRAPHS OF HIGHER EQUATIONS APPLICATIONS 332 246 339 156 340 160 341 Copyright

### Popular passages

Page 16 - That is, 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 72 - Multiply both numerator and denominator of the fraction by such a quantity as will make the denominator a perfect power of the same degree as the radical; Proceed as in Art.
Page 67 - Multiply the index of the quantity by the index of the power to which it is to be raised, and the result will be -the power required.
Page 188 - My lord, I have undertaken this long journey purposely to see your person, and to know by what engine of wit or ingenuity you came first to think of this most excellent help into astronomy, viz. the logarithms ; but, my lord, being by you found out, I wonder nobody else found it out before, when now known it is so easy.
Page 151 - The first term of a ratio is called the antecedent, and the second term the consequent. Thus, in the ratio a : b, a is the antecedent, and b is the consequent. The first and fourth terms of a proportion are called the extremes, and the second and third terms the means.
Page 53 - ... is found by multiplying the coefficient of the preceding term by the exponent of the leading letter of the same term, and dividing the product by the number which marks its place.
Page 160 - ... is equal to the ratio of the corresponding sides of the other triangle.
Page 113 - The angles opposite the equal sides of an isosceles triangle are equal.
Page 151 - In any proportion, the product of the extremes equals the product of the means.
Page 171 - Exponents. lu 32 = 9, we can say 2 is the logarithm of 9 to base 3. Similarly, since 34 = 81, 4 is the logarithm of 81 to base 3. In logarithms three different numbers are always involved: (1) A number. (2) Its logarithm. (3) The base used. The logarithm of a given number is the exponent of the power to which a base must be raised to produce this number. A system of logarithms is a set of numbers with their logarithms all taken to the same base. Notice that the logarithm of 1 in any system is 0,...