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Volume 2 - Issue 33 - May 1902

Contents

Research Article

  • The Teaching of Euclid

  • B. Russell
  • Published online by Cambridge University Press:
    03 November 2016, pp. 165-167

  • It has been customary when Euclid, considered as a text-book, is attacked for his verbosity or his obscurity or his pedantry, to defend him on the ground that his logical excellence is transcendent, and affords an invaluable training to the youthful powers of reasoning. This claim, however, vanishes on a close inspection. His definitions do not always define, his axioms are not always indemonstrable, his demonstrations require many axioms of which he is quite unconscious. A valid proof retains its demonstrative force when no figure is drawn, but very many of Euclid’s earlier proofs fail before this test.

Other

Meeting Report

Research Article

  • Some Applications of the Theory of Assemblages

  • Arnold Emch
  • Published online by Cambridge University Press:
    03 November 2016, pp. 173-175

  • In order to be able to apply the theory of real numbers to measurable quantities, in particular to linear magnitudes, it is convenient to make use of the theory of groups (displacements). Thus, if B, C, D, …, Y are successive points on a continuous line between the extremities A and Z,

    AB+BC+CD+…+YZ=AZ,

    where AB, BC, … are arcs or consecutive displacements on the given line.

Other

Letter

  • Correspondence

  • Mary Everest Boole
  • Published online by Cambridge University Press:
    03 November 2016, p. 180
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Front Matter

Back Matter