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Application of the Multiplication of Matrices to prove a Theorem in Spherical Geometry

Published online by Cambridge University Press:  20 January 2009

Chrystal
Chrystal
Affiliation:
University of Edinburgh
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Extract

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The theorem in question is that if two of the diagonals of a spherical quadrilateral be quadrantal arcs, the third diagonal is also a quadrantal arc. (Fig. 31.)

Denote the direction cosines of the radius to the point 1 by l1, m1, n1, & c., and l1l2 + m1m2 + n1n2 by 12.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 2 , February 1883 , pp. 45 - 47
Copyright
Copyright © Edinburgh Mathematical Society 1883