Algebra: An Elementary Text Book for the Higher Classes of Secondary Schools and for Colleges, Part 1 |
Contents
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Common terms and phrases
a+b+c a₁ arithmetic arithmetic mean ax² becomes infinitely small binomial coefficients calculation chap chapter coefficients common complex numbers constant corresponding deduce definition denote derive determine digits divide divisor equal equivalent exactly divisible Example EXERCISES expressed finite geometric given gives graph Hence homogeneous homogeneous function identity imaginary integers integral equation integral function laws of algebra linear logarithm means method multiply negative nth root nth term obtained operations P₁ positive prime proper fraction proposition prove quadratic quadratic function quotient radix rational function rationalising factor reduces remainder result solution solve square root student subtraction suppose surd symmetric function theorem tion turning values vanish variables whence zero
Popular passages
Page 136 - An improper fraction is one in which the degree of the numerator is greater than or equal to the degree of the denominator.
Page 442 - 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 459 - 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 247 - Also a and d are called the extremes and b and c the means. The proportion - = — is sometimes written a : b = c : d, ba and in either case may be read a is to b as c is to d.
Page 248 - If the product of two quantities be equal to the product of two others, two of them may be made the extremes and the other two the means of a proportion.
Page 16 - 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 221 - The former denotes a family of straight lines whose distance from the origin is equal to a, the latter a circle whose centre is at the origin, and whose radius is equal to a. And here, as was noted generally by Lagrange, the singular solution seems to be, in relation to geometry, the more important of the two. 3. A more general class of problems is that in which it is required to determine the curves in which some one of the foregoing elements, Art. 1, is equal...
Page 230 - 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 499 - ... that the mantissa is independent of the position of the decimal point.
Page 277 - ... when substituted therein. No matter how elaborate or ingenious the process by which the solution has been obtained, if it do not stand this test, it is no solution ; and, on the other hand, no matter how simply obtained, provided it do stand this test, it is a solution...