Abstract
In general terms the principal problem in astronomical navigation is the solving of a spherical triangle - the PZX-triangle. The fundamental formula of spherical trigonometry for finding an angle given the three sides of a spherical triangle is the cosine formula. By transposition this formula can be used for finding a side given the opposite angle and the other two sides. Because the cosine formula is not suitable for use with logarithms numerous formulae have been derived from it with the aim of simplifying logarithmic computation. The term ‘direct method’ applies to a method the basis of which is generally the cosine formula or any of its derivatives although some direct methods are based on Napier's Rules for right-angled spherical triangles.
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