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.

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