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A quadrantal spherical triangle together with Napier's circle for use in his mnemonics. A quadrantal spherical triangle is defined to be a spherical triangle in which one of the sides subtends an angle of π /2 radians at the centre of the sphere: on the unit sphere the side has length π /2.
Given a unit sphere, a "spherical triangle" on the surface of the sphere is defined by the great circles connecting three points u, v, and w on the sphere (shown at right). If the lengths of these three sides are a (from u to v ), b (from u to w ), and c (from v to w ), and the angle of the corner opposite c is C , then the (first) spherical ...
The volume has a preface by Robert and several appendices, including a section on John Napier's methods for more easily solving spherical triangles, and a section by Henry Biggs on “another and better kind of logarithms,” namely base 10 or common logarithms. An English translation by William Rae Macdonald was published, with annotations, in ...
A quadrantal spherical triangle together with Napier's circle for use in his mnemonics. A quadrantal spherical triangle is defined to be a spherical triangle in which one of the sides subtends an angle of π /2 radians at the centre of the sphere: on the unit sphere the side has length π /2.
This shape was described by John Napier in his 1614 book Mirifici Logarithmorum Canonis Descriptio (Description of the Admirable Table of Logarithms) along with rules that link the values of trigonometric functions of five parts of a right spherical triangle (two angles and three sides).
For the spherical case, one can first compute the length of side from the point at α to the ship (i.e. the side opposite to β) via the ASA formula = (+) + (), and insert this into the AAS formula for the right subtriangle that contains the angle α and the sides b and d: = = + . (The planar ...
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Spherical triangle solved by the law of cosines. Versions similar to the law of cosines for the Euclidean plane also hold on a unit sphere and in a hyperbolic plane. In spherical geometry, a triangle is defined by three points u, v, and w on the unit sphere, and the arcs of great circles connecting those points.