# Higher Algebra

Fisher and Schwatt, 1901 - 615 páginas

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### Contenido

 CHAPTER I 1 ALGEBRAIC POSITIVE AND NEGATIVE NUMBERS 13 CHAPTER II 19 MultipliCATION OF ALGEBRAIC NUMBERS 30 Division of ALGEBRAIC NUMBERS 38 Positive INTEGRAL Powers 45 1 45 ADDITION AND SUBTRACTION 51 Division 68
 Special Devices 333 SIMULTANEOUS HIGHER EQUATIONS 348 CHAPTER XXV 354 VARIATION 362 DOCTRINE OF EXPONENTS 366 CHAPTER XXVII 379 GEOMETRICAL PROGRESSION 389 HARMONICAL PROGRESSION 398

 CHAPTER IV 80 LINEAR EQUATIONS IN ONE UNKNOWN NUMBER 86 PROBLEMS 89 CHAPTER VI 100 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 LINEAR EQUATIONS 207 Systems OF FRACTIONAL EQUATIONS 218 CHAPTER XIV 225 PROBLEMS WHICH TO SIMULTANEOUS LINEAR EQUATIONS 233 CHAPTER XVI 239 SQUARE Roots OF MULTINOMIALS 246 Roots Of ARITHMETICAL NUMBERS 252 INEQUALITIES 258 Problems 264 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
 CHAPTER XXIX 408 Principles of Logarithms 415 To find the Logarithm of a Given Number 422 Cologarithms 429 Logarithmic Equations 436 PERMUTATIONS AND COMBINATIONS 440 Two IMPORTANT PRINCIPLES 448 CHAPTER XXXII 456 CHAPTER XXXIII 464 The General Term of a Series 472 CHAPTER XXXIV 481 34 486 Roots of Arithmetical Numbers 487 UNDETERMINED COEFFICIENTS 488 CHAPTER XXXVI 501 Properties of Convergents 507 To reduce a Periodic Continued Fraction to an Irrational 513 Convergency of a Recurring Series 523 Interpolation 531 Computation of Logarithms 537 DETERMINANTS 540 Solution of Linear Simultaneous Equations 551 Synthetic Division 557 Symmetrical Functions 5633 563 To transform an Equation into Another whose Roots are 569 Newtons Method 575 575 Greatest and Least Terms in f x 587 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 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 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 64 - In the multiplication of whole numbers, place the multiplier under the multiplicand, and multiply each term of the multiplicand by each term of the multiplier, writing the right-hand figure of each product obtained under the term of the multiplier which produces it.
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.
Página 456 - 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 364 - The volume of a gas varies inversely as the pressure when the temperature is constant. When the pressure is 15, the volume is 20; what is the volume when the pressure is 20 ? Let v stand for the volume and p for the pressure. Then from pv = k we obtain k = 300. Therefore pv = 300. Consequently, when p = 20, 20 v = 300 ; whence v = 15. EXERCISES III. If zee y, what is the expression for x in terms of y, 1.
Página 379 - Progression (AP), is a series in which each term, after the first, is formed by adding a constant number to the preceding term.
Página 204 - A system of linear equations has a definite number of solutions. (i.) When the number of equations is the same as the number of unknown numbers. (ii.) When the equations are independent and consistent.
Página 100 - The square of the sum of two numbers is equal to the square \ (¿ of the first, plus twice the product of the first and second, plus the J square of the second.