E749 -- Geometrica et sphaerica quaedam
(About geometry and spheres)
This paper is about certain geometry and spheres, the main theorem being
"In whatever triangle ABC, straight lines Aa, Bb, Cc are drawn from the angles to the opposite sides
so that they all meet at some point O, then they will always have the following property
AO/Oa * BO/Ob * CO/Oc = AO/Oa + BO/Ob + CO/Oc + 2."
Originally published in Memoires de l'academie des sciences de St.-Petersbourg 5, 1815, pp. 96-114
Opera Omnia: Series 1, Volume 26, pp. 344 - 358
- Original publication: E749
- Homer White of Georgetown College has provided a translation
of E749 to the Euler Archive.
- E749 is discussed in Ed Sandifer's How Euler Did It May 2006 column published online by the MAA.
- Other works that cite this paper include:
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