English Title

A universal spherical trigonometry, derived briefly and from first principles

Authors

Leonhard Euler

Enestrom Number

524

Fuss Index

333

Original Language

Latin

Published as

Journal article

Published Date

1782

Written Date

1781

Content Summary

This is an introduction to spherical trigonometry. Euler derives the formulas for a triangle ABC on a unit sphere, where the sides of the triangle are a, b, c: sin C/sin c = sin A/sin a, cos A sin c = cos a sin b – sin a cos b cos C, and cos c = cos a cos b + sin a sin b cos C. Then, he gives a duality theorem: given a spherical triangle with angles A, B, C and sides a, b, c, it is always possible to exhibit an analogous triangle whose angles are complementary to the sides of the first triangle, and the sides are the complements of the angles.

Original Source Citation

Acta Academiae Scientiarum Imperialis Petropolitanae, Volume 1779: I, pp. 72-86.

Opera Omnia Citation

Series 1, Volume 26, pp.224-236.

Record Created

2018-09-25

Included in

Mathematics Commons

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