E214 -- Principes de la trigonometrie spherique tires de la methode des plus grands et plus petits
(Principles of spherical trigonometry taken from the method of the maxima and minima)
Euler uses a simple result from his earlier work on the "Method of Maxima and Minima" (renamed, a few years later, "Calculus of Variations") to re-derive, without classical geometry, all the formulae to resolve a spherical triangle; that is, knowing any three measures from the set of three angles and three sides, to compute the other three.
He begins with the case of a right spherical triangle, and then considers general triangles. Special attention is called to those formulae which are suited to the use of logarithms.
According to C. G. J. Jacobi, a treatise with this title was presented to the Berlin Academy on January 18, 1753.
Originally published in Memoires de l'academie des sciences de Berlin 9, 1755, pp. 223-257
Opera Omnia: Series 1, Volume 27, pp. 277 - 308
- Original publication: E214
- E214 can be viewed or downloaded from Digitalisierte Akademieschriften und Schriften zur Geschichte der Königlich Preußischen Akademie der Wissenschaften, which includes serial publications of the Prussian Academy of Science in the 18th and 19th Centuries.
- A German translation of E214 was included in the the 1896 book Zwei Abhandlungen uber spharische Trigonometrie, and is now available via Google books. Link to Google books version. (Note: The google Books version includes figures currently missing from the orignal scan above.)
- English translation (George Heine): E214
- The Euler Archive attempts to monitor current scholarship for articles and books that may be of interest to Euler Scholars. Selected references we have found that discuss or cite E214 include:
- McCleary J., “Trigonometries.” American Mathematical Monthly, 109 (7), pp. 623-638 (Aug-Sep 2002).
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