Algebra: An Elementary Text-book for the Higher Classes of Secondary Schools and for Colleges, Volume 1A. & C. Black, 1893 - Algebra |
Contents
| 1 | |
| 8 | |
| 14 | |
| 20 | |
| 22 | |
| 30 | |
| 36 | |
| 42 | |
| 48 | |
| 49 | |
| 55 | |
| 78 | |
| 79 | |
| 85 | |
| 93 | |
| 99 | |
| 113 | |
| 119 | |
| 126 | |
| 134 | |
| 142 | |
| 151 | |
| 163 | |
| 176 | |
| 177 | |
| 185 | |
| 194 | |
| 197 | |
| 203 | |
| 210 | |
| 217 | |
| 221 | |
| 228 | |
| 234 | |
| 240 | |
| 248 | |
| 310 | |
| 323 | |
| 330 | |
| 338 | |
| 346 | |
| 364 | |
| 372 | |
| 385 | |
| 391 | |
| 397 | |
| 406 | |
| 413 | |
| 427 | |
| 431 | |
| 438 | |
| 445 | |
| 453 | |
| 461 | |
| 468 | |
| 476 | |
| 482 | |
| 489 | |
| 496 | |
| 502 | |
| 509 | |
| 524 | |
| 531 | |
| 538 | |
Common terms and phrases
1st degree 2nd degree a+b+c a₁ algebraical quantity arithmetical ax² binomial binomial coefficients bracket CHAP chapter coefficients common divisor complex numbers constant definition denote digits divide dividend divisor equal equation exactly divisible Example EXERCISES expressed factorisation finding the G.C.M. given Hence highest term homogeneous function identity imaginary improper fraction integral quotient irrationals law of commutation laws of algebra modulus monomial multiplication negative nth degree nth root obtained operations P₁ partial fractions positive integral powers prime proper fraction proposition prove quadratic quadratic irrationals r(cos radicand radix fraction rational fraction rational integral rationalising factor real quantity remainder result scale Simplify square root student subtraction surd number symmetrical theorem theory values vanish variables vulgar fraction whence x²+1 Y₂i zero СНАР
Popular passages
Page 470 - A horse is sold for £24, and the number expressing the profit per cent expresses also the cost price.
Page 454 - Article ; for the product of the squares ot the differences of all the roots is made up of the product of the squares of the differences of the roots of...
Page 13 - The view which he takes of these laws is expressed by the phrase "canons of the science," as is evidenced by the following passage : ' ' As we have now completed the establishment of the fundamental laws of ordinary algebra, it may be well to insist once more upon the exact position which they hold in the science. To speak, as is sometimes done, of the proof of these laws in all their generality, is an abuse of terms. They are simply laid down as the canons of the science.
Page 471 - D; it can be demonstrated indirectly with the aid of 32. 34. It is required to find a point in a given straight line, such that the rectangle contained by its distances from two given points in the straight line may be equal to the rectangle contained by its distances from two other given points in the straight line.
Page 232 - Hence the product of two complex numbers is a complex number whose modulus is the product of the moduli and whose amplitude is the sum of the amplitudes of the two complex numbers.
Page 12 - CHAP. laws are concerned there is virtually no distinction between addition and subtraction on the one hand and multiplication and division on the other...
Page 511 - ... that the mantissa is independent of the position of the decimal point.
Page 233 - Moivre's theorem, (a + ib) (a' + ib') = /u/u' (cos (a + a') + » sin (a + a') } , which proves that the product of two complex] numbers is a complex number, whose modulus is the product of the two moduli, and whose amplitude is the sum of the two amplitudes.
Page 138 - An improper fraction is one in which the degree of the numerator is greater than or equal to the degree of the denominator.
Page 340 - Considering the remarkable elegance, generality, and simplicity of the method, it is not a little surprising that it has not taken a more prominent place in current mathematical text-books. Although it has been well expounded by several English writers, ... it has scarcely as yet f< und a place in English curricula.