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Some applications of the Gnomonic Projection to Crystallograhy

Published online by Cambridge University Press:  14 March 2018

Harold Hilton
Harold Hilton*
Affiliation:
Magdalen College, Oxford
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Extract

Let the crystallographic axes OA, OB, OC of a crystal, whose axial ratios are a : b : c, meet a plane p in A, B, C. Let a plane through O, parallel to a crystal-face whose indices are h, k, l, meet p in the line f (fig. 1) ; and let the line OF, perpendicular to the face, meet p at the point F. Let the perpendicular from O on p meet it in V, and let OV = m.

Type
Research Article
Information
Mineralogical magazine and journal of the Mineralogical Society , Volume 14 , Issue 64 , May 1905 , pp. 104 - 108
Copyright
Copyright © The Mineralogical Society of Great Britain and Ireland 1905

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References

Page 105 note 1 Since in a plane triangles reciprocal with respect to a circle are homologous, we have incidentally proved that the ares joining corresponding vertices of a spherical triangle and its polar triangle are concurrent, and that the intersections of corresponding sides of the two triangles lie on a great circle.

Page 107 note 1 Another proof is given by von Fedorow, E., Abhandl. k. bayer. Akad. Wiss. Müuchen, Math.phys. Cl., 1900, vol. xx, p. 496 Google Scholar.