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Volume 18 - Issue 230 - October 1934

Contents

Page 1 of 3

Other

Research Article

  • Introductory Theorems in Geometrical Conics

  • B. E. Lawrence
  • Published online by Cambridge University Press:
    03 November 2016, pp. 223-227

  • 1. Nowadays the beginning of conics is a blend of pure and coordinate geometry, but the starting point is generally the focus-directrix definition. From this the standard equations and properties are deduced, but a good deal of time is taken before some of the more powerful methods can be applied.

    The object here is to indicate compact proofs of some well-known results, and to obtain, at an early stage, such results as Newton’s Theorem and the cross-ratio property from the focus-directrix definition.

Meeting Report

Other

Obituary

  • Sir Thomas Muir

  • E. H. N.
  • Published online by Cambridge University Press:
    03 November 2016, p. 257
    • Article
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Research Article

  • The Tracing of Cubic Curves

  • E. H. Neville
  • Published online by Cambridge University Press:
    03 November 2016, pp. 258-266

  • 1. We all know that if we wish to sketch a cubic curve such as

    xy (x + 2y − 1 ) = 2x − 3y + 4,

    the first thing to do is to draw the three asymptotes and the satellite. These divide the plane into eleven compartments, and the simple consideration that there can be no points of the curve in a compartment throughout which xy (x + 2y − 1 ) and 2x − 3y + 4 have different signs enables us at once to rule out six of the compartments, and so to see how the curve goes to infinity.

Mathematical Notes

Page 1 of 3