E231 -- Demonstratio nonnullarum insignium proprietatum, quibus solida hedris planis inclusa sunt praedita
(Proof of some of the properties of solid bodies enclosed by planes)
This paper is a continuation of E230. Here, Euler proves the main theorem (of E230) by showing that the formula is invariant if vertices are removed and their adjacent faces are replaced with a single face. He also gives a formula to determine the volume of a triangular pyramid given the lengths of six sides/edges of the pyramid in question.
According to C. G. J. Jacobi, it might have been read to the Berlin Academy on
September 9, 1751.
According to the records, it was presented to the St. Petersburg Academy on
April 6, 1752.
Originally published in Novi Commentarii academiae scientiarum Petropolitanae 4, 1758, pp. 140-160
Opera Omnia: Series 1, Volume 26, pp. 94 - 108
- According to Jacobi, the manuscript of the printed treatise can be found in the archive of the Berlin
- A handwritten French translation of this treatise can be found in the library of the observatory in
Uccle, near Brussels.
- Original publication: E231
- Christopher Francese and Dave Richeson of Dickinson college have made available their
translation of E231.
- A translation of E231 into German has been done by Dr. Ralf Krömer of Universität Siegen.
- E231 is discussed in Ed Sandifer's How Euler Did It June and July
2004 column published online by the MAA.
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