# Elements of Algebra with Exercises

Macmillan Company, 1902 - 478 páginas

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### Contenido

 INTRODUCTION 1 ALGEBRAIC POSITIVE AND NEGATIVE NUMBERS 12 CHAPTER II 19 ONE SET OF SIGNS FOR QUALITY AND OPERATION 43 CHAPTER III 49 MULTIPLICATION 56 DivisioN 68 CHAPTER IV 80
 The Fundamental Operations with Irrational Numbers 271 Addition and Subtraction of Surds 278 Surd Factors 284 Evolution of Surd Expressions 290 Complex Numbers 298 QUADRATIC EQUATIONS 304 CHAPTER XXII 327 Special Devices 333

 LINEAR EQUATIONS IN ONE UNKNOWN NUMBER 86 CHAPTER VI 100 TYPEFORMS in Division 107 CHAPTER VII 113 HIGHEST COMMON FACTORS 136 LOWEST COMMON MULTIPLES 147 FRACTIONS 152 CHAPTER X 180 CHAPTER XI 188 CHAPTER XII 196 CHAPTER XIII 203 SYSTEMS OF FRACTIONAL EQUATIONS 218 CHAPTER XIV 225 PROBLEMS WHICH LEAD TO SIMULTANEOUS LINEAR EQUATIONS 233 CHAPTER XVI 239 SQUARE RootS OF MULTINOMIALS 246 Roots OF ARITHMETICAL NUMBERS 252 INEQUALITIES 258 Problems 264
 PROBLEMS 351 PROPORTION 359 VARIATION 365 DOCTRINE OF EXPONENTS 366 CHAPTER XXVII 379 GEOMETRICAL PROGRESSION 389 HARMONICAL PROGRESSION 398 CHAPTER XXIX 408 Two IMPORTANT PRINCIPLES 414 CHAPTER XXXII 429 CHAPTER XXXIII 435 CHAPTER XXXIV 446 Properties of Convergents 452 To reduce a Periodic Continued Fraction to an Irrational 458 LOGARITHMS 460 Principles of Logarithms 467 Exponential Equations 476 Derechos de autor

### Pasajes populares

Página 209 - Nos. 1 and 2, 3 and 4, 5 and 6, 7 and 8, 9 and 10, 11 and 12.
Página 356 - IF the first be the same multiple of the second, or the same part of it, that the third is of the fourth ; the first is to the second, as the third is to the fourth...
Página 73 - Divide the first term of the dividend by the first term of the divisor, the result will be the first term of the quotient.
Página 414 - C„.r. That is, the number of combinations of n dissimilar .things r at a time is equal to the number of combinations of the n things n — r at a time.
Página 359 - In any proportion the terms are in proportion by Composition and Division; that is, the sum of the first two terms is to their difference, as the sum of the last two terms is to their difference.
Página 326 - The fore wheel of a carriage makes 6 revolutions more than the hind wheel, in going 120 yards; but if the circumference of each wheel...
Página 166 - The product of two fractions is a fraction whose numerator is the product of the numerators of the given fractions, and whose denominator is the product of the given denominators.
Página 472 - We therefore have : (i.) The characteristic of the logarithm of a number greater than unity is positive, and is one less than the number of digits in its integral part.
Página 418 - Thus, 16 x2, ± -^/(a? — ж2), etc., are functions of x; corresponding to any value of x, the first function has one value, the second has two values. Again, the area of a circle is a function of its radius ; the distance a train runs is a function of the time and speed. 4. Much simplicity is introduced into mathematical investigations by employing special symbols for functions. The symbol f(x), read function of x, is very commonly used to denote a function of x.
Página 363 - One quantity is said to vary directly as a second and inversely as a third, when it varies as the second and the reciprocal of the third jointly.