# 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

 Definitions 1 I PRIMARY DEFINITIONS AND SIGNS Number 2 Representation of Numbers 2 Positive and Negative Numbers 3 Special Signs 6 Copulas and Statements 7 Addition 9 Subtraction 10 Multiplication 11
 IX 233 222 6 7 9 239 10 240 19 241 21 250 Addition and Subtraction 259 Multiplication and Division 265 Abridged Representation 278

 Division 13 Involution 14 Evolution 15 Expressions Coefficients Like and Unlike Terms 17 Functions 19 Degree 21 Examples 25 PRIMARY OPERATIONS 1 Logical Terms 26 Combinatory Properties of Operations 3 29 Axioms 4 32 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 89 Process of Finding the Lowest Common Multiple 95 Examples 105 Examples 119 The Binomial Theorem 125 6 132 2 138 Computation of Convergents 144 SECTION 147 General Properties 151 INCOMMENSURABLES LIMITS INFINITESIMALS 157 6 165 General Properties of Limits 171 10 177 Examples 191 Combinations of Commensurable Powers 197 5 207 8 213 Operations on Radicals 225
 EQUATIONS SECTION PAGE 1 Statements 281 Solution of Equations Unknowns 282 Degree of Equation 283 General Properties 284 23 286 Simple Equations involving One Unknown 291 Elimination 293 Simple Equations Two or More Unknowns 298 Graphic Representation of Simple Equations involving Two Unknowns 307 Bezouts Method Unknown Multipliers 308 Special Problems of the First Degree 310 Quadratic Equations involving One Unknown 313 26 316 Graphic Representation of Quadratic Equations 318 27 323 Maxima and Minima 324 32 330 Special Problems involving Quadratics 340 Binomial Equations 341 Logarithmic and Exponential Equations 342 Examples 343 35 344 52 345 60 346 65 347 Examples 353 SERIES 1 Arithmetic Progression 361 Geometric Progression 364 Harmonic Progression 367 Convergence and Divergence 369 369 Indeterminate Series 375 Imaginary Series 378 Expansion of Functions in Infinite Series 381 Method of Unknown Coefficients 383 Binomial Theorem 390 Finite Differences 393 Interpolation 396 Taylors Theorem 400 Computation of Logarithms 403 Examples 405

### Popular passages

Page 342 - 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 51 - 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 49 - 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 53 - 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 43 - If both terms of a fraction be multiplied by the same number, the value of the fraction will remain unchanged.
Page 162 - The circumference of a circle is the limit which the perimeters of regular inscribed and circumscribed polygons approach when the number of their sides is increased indefinitely ; and the area of the circle is the limit of the areas of these polygons.
Page 183 - In a right triangle the square of the hypotenuse equals the sum of the squares of the other two sides or legs.
Page 163 - Jesus was the author and finisher of the faith; to which nothing can be added, and from which nothing can be taken...
Page 61 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.
Page 236 - The logarithm of a product is the sum of the logarithms of its factors.