E324 -- Proprietates triangulorum, quorum anguli certam inter se tenent rationem

(Properties of triangles for which certain angles have a ratio between themselves)

Summary:

Euler derives properties of a triangle based on relationships between the angles of the triangle; these properties are polynomials that the (lengths of the) sides must satisfy.

According to C. G. J. Jacobi, a treatise with this title was read to the Berlin Academy on September 22, 1763.

According to the records, it was presented to the Petersburg Academy on December 21, 1763.

Publication:

Originally published in Novi Commentarii academiae scientiarum Petropolitanae 11, 1767, pp. 67-102
Opera Omnia: Series 1, Volume 26, pp. 109 - 138

Documents Available:

Original publication: E324
E324 is discussed in Ed Sandifer's How Euler Did It April 2004 column published online by the MAA.
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 E324 include:
- Dhombres J., “Some aspects of the history of functional-equations linked to the evolution of the function concept.” Archive for History of Exact Sciences, 36 (2), pp. 91-181 (1986).
- Lutzen J., “Euler vision of a general partial-differential calculus for a generalized kind of functions.” Mathematics Magazine, 56 (5), pp. 299-306 (1983).

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