E230 -- Elementa doctrinae solidorum
(Elements of the doctrine of solids)
Euler presents several results relating the number of plane angles of a solid to the number of faces, edges, and solid angles. The main theorem is that in all solid bodies confined by planes, the sum of the number of solid angles and the number of faces is two less than the number of edges. Euler also classifies polyhedra by the number of solid angles they have.
According to C. G. J. Jacobi, a treatise with this title was read to the Berlin Academy on
November 26, 1750.
Originally published in Novi Commentarii academiae scientiarum Petropolitanae 4, 1758, pp. 109-140
Opera Omnia: Series 1, Volume 26, pp. 71 - 93
- A handwritten French translation of this treatise can be found in the library of the observatory in
Uccle, near Brussels.
- Original publication: E230
- A translation of E230 into German has been done by Dr. Ralf Krömer of Universität Siegen.
- E230 is discussed in Ed Sandifer's How Euler Did It June and July
2004 columns published online by the MAA.
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