A Treatise on Algebra

D. F. Finch, 1887 - Algebra - 412 pages
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Contents

 Definitions 20 Degree 21 SECTION 24 Examples Coefficients 25 PRIMARY OPERATIONS 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 71 Measures and Multiples 79 Prime and Composite Numbers 89 Process of Finding the Lowest Common Multiple 95 PERMUTATIONS AND COMBINATIONS 106 4 115 POWERS AND ROOTS OF POLYNOMIALS 121 6 132 2 138 Computation of Convergents 145 General Properties 151 INCOMMENSURABLES LIMITS INFINITESIMALS 157 SECTION PAGE 3 Limits 161 Infinitesimals and Infinites 163 Derivatives 165 First Principles 167 Primary Operations on Incommensurables 168 General Properties of Limits 169 General Properties of Derivatives 173 Indeterminate Forms 178
 Continuity of Powers in General 209 Derivatives of Powers 213 Radicals 215 Operations on Radicals 223 Examples 227 LOGARITHMS 1 General Properties 233 Special Properties Base 10 236 Computation of Logarithms 237 2 3 6 7 9 239 10 240 19 241 21 250 IMAGINARIES 1 Definitions and Graphic Representation 251 Addition and Subtraction 259 Multiplication and Division 264 Powers and Roots 268 Abridged Representation 278 Examples 279 23 286 Simple Equations involving One Unknown 291 Simple Equations Two or More Unknowns 298 Graphic Representation of Simple Equations involving 307 Quadratic Equations involving One Unknown 313 26 316 27 323 Simultaneous Equations 333 Special Problems involving Quadratics 340 35 344 37 345 60 346 65 347 Arithmetic Progression 363 Convergence and Divergence 371 Imaginary Series 379 10 393 Taylors Theorem 401 Examples 407

Popular passages

Page 334 - 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 354 - 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 158 - 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 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 57 - 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.