E5 -- Problematis traiectoriarum reciprocarum solutio

(Solution to the problem of reciprocal trajectories)

Summary:

This article contains Euler's first published use of complex numbers and a many-axis geometric construction. Euler also calls functions f(x) for which f(x) = f(-x) even functions, perhaps the first use of this term.

Publication:

Originally published in Commentarii academiae scientiarum Petropolitanae 2, 1729, pp. 90-111
Opera Omnia: Series 2, Volume 6, pp.
Reprinted in Comment. acad. sc. Petrop. 2, ed. nova, Bononiae 1741, pp. 79-97 + 1 diagram [E5a]

Documents Available:

Original publication: E005 (in the Commentarii), Volume 2
Ian Bruce has made both a translation and transcription of E5 available at his page Mathematical Works of the 17th Century.

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