# A Treatise on Algebra

D.F. Finch, 1887 - Algebra - 412 pages
0 Reviews
Reviews aren't verified, but Google checks for and removes fake content when it's identified

### What people are saying -Write a review

We haven't found any reviews in the usual places.

### Contents

 Multiplication 11 Division 13 Involution 14 Evolution 15 Expressions 17 Functions 19 Coefficients Like and Unlike Terms 21 Definitions 22 Examples 25 PRIMARY OPERATIONS 1 Logical Terms 26 Combinatory Properties of Operations 29 Axioms 33 4 33 Axioms 34 Addition Commutative and Associative 35 Sign of Product 36 Multiplication Commutative and Associative 37 Multiplication Distributive as to Addition 45 Proportion 49 Process of Addition 10 Process of Subtraction 52 Process of Multiplication 55 Process of Division 61 Operations on Fractions 65 Examples 69 Measures and Multiples 79 Prime and Composite Numbers Factors 87 Process of Finding the Highest Common Measure 90 Process of Finding the Lowest Common Multiple 95 Process of Factoring 97 Examples 105 PERMUTATIONS AND COMBINATIONS 1 Definitions Permutations Combinations 2 3 106 Examples 119 POWERS AND ROOTS OF POLYNOMIALS 1 Product of Binomial Factors 121 The Binomial Theorem 3 The Polynomial Theorem 125 Roots of Polynomials 5 126 Absolute and Relative Error 129 Roots of Numerals 132 Examples 135 CONTINUED FRACTIONS 137 PAGE 79 138 102 142 Conversion of Surds 143 Computation of Convergents 145 SECTION 147 General Properties 149 Secondary Convergents 153 Examples 155 INCOMMENSURABLES LIMITS INFINITESIMALS AND DERIVATIVES 1 Variables and Constants 157
 Continuity of Powers in General 211 Radicals 217 Operations on Radicals 225 IX 233 6 7 9 239 10 240 14 241 Operations with Common Logarithms 247 21 250 Definitions and Graphic Representation 253 Addition and Subtraction 261 Powers and Roots 269 Abridged Representation 278 23 286 Quadratic Equations involving One Unknown 313 26 316 Graphic Representation of Quadratic Equations 310 313 318 27 323 Maxima and Minima 325 32 330 Simultaneous Equations 333 Special Problems involving Quadratics 340 Binomial Equations 341 Logarithmic and Exponential Equations 342 35 344 52 345 60 346 65 347 Examples 353 147 356 Continuity 357 SERIES 361 Arithmetic Progression 363 Geometric Progression 365 Harmonic Progression 367 Convergence and Divergence 371 5 373 Indeterminate Series 375 Imaginary Series 379 Expansion of Functions in Infinite Series 381 Method of Unknown Coefficients 9 383 Binomial Theorem 390 Finite Differences 395 Interpolation 397 Taylors Theorem 401 Computation of Logarithms 403 Examples 407 375

### Popular passages

Page 336 - 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 be increased one yard, it will make only 4 revolutions more than the hind-wheel in the same distance.
Page 47 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.
Page 45 - 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...
Page 356 - Three numbers may be in proportion when the first is to the second as the second is to the third.
Page 49 - 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.
Page 39 - If both terms of a fraction be multiplied by the same number, the value of the fraction will remain unchanged.
Page 179 - In a right triangle the square of the hypotenuse equals the sum of the squares of the other two sides or legs.
Page 159 - Jesus was the author and finisher of the faith; to which nothing can be added, and from which nothing can be taken...
Page 232 - The logarithm of a product is the sum of the logarithms of its factors.
Page 402 - The interior angles of an irregular polygon are in arithmetical progression ; the least angle is 120�, and the common difference 5�. Find the number of sides.