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Volume 9 - December 1918

Contents

Page 5 of 14

Mathematical Notes

Reviews

Mathematical Notes

Front Matter

Other

Mathematical Notes

Research Article

  • Euclid’s Definition of Parallel Straight Lines Considered in Reference to the ‘Line at Infinity.’

  • J. L. S. Hatton
  • Published online by Cambridge University Press:
    03 November 2016, pp. 43-45

  • Euclid’s definition of two parallel straight lines seems to be the correct one for the absolute ideal of a plane and of a straight line. The conception of a line at infinity, it would seem, should be stated if used in some such words as these. Points may be supposed to exist at such a distance from the points generally considered in a plane that their distances from all such points in the plane may be regarded as equal, i.e. the differences of these distances may in general be regarded as negligible. These points, as a first approximation, may, under certain circumstances, be regarded, when considered in relationship to points at a finite distance, as lying on a straight line. Parallel straight lines may be regarded—for most practical purposes—as far as points at a finite distance are concerned, as intersecting at one of these points.

Reviews

Mathematical Notes

Other

General Section

  • Nomography

  • S. Brodetsky
  • Published online by Cambridge University Press:
    15 September 2017, pp. 213-224

  • The algebraic solution of any problem formulated in mathematical symbols takes one of two forms: it is either given in the explicit form x=f(a, b, c,...), where → is some functional form of a, b, c, ... , which are supposed known in any particular case, or the solution required is to be found from an equation F(x, a, b, c, ...)=0, where F is a known functional form of the unknown x and of the quantities a, b, c, ... . The mathematician is generally concerned on the one hand with reducing f(a, b, c, ...) into its simplest, often its “prettiest” form, and on the other hand with investigating what method, if any, exists for “solving” the equation F(x, a, b, c, ...) = 0, i.e. finding x in terms of a, b, c, ... . The course included in any text-book of algebra consists principally of the former, since the latter is distinctly more difficult.

Front Matter

Mathematical Notes

Back Matter

Mathematical Notes

Reviews

Mathematical Notes

Reviews

Page 5 of 14