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Hyperbolic Quaternions

  • Alexander Macfarlane (a1)

It is well known that quaternions are intimately connected with spherical trigonometry, and in fact they reduce that subject to a branch of algebra. The question is suggested whether there is not a system of quaternions complementary to that of Hamilton, which is capable of expressing trigonometry on the surface of the equilateral hyperboloids. The rules of vector-analysts are approximately complementary to those of quaternions. In this paper I propose to show how they can be made completely complementary, and that, when so rectified, they yield the hyperbolic counterpart of the spherical quaternions.

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Proceedings of the Royal Society of Edinburgh
  • ISSN: 0370-1646
  • EISSN: 2059-9153
  • URL: /core/journals/proceedings-of-the-royal-society-of-edinburgh
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