E252 -- Observationes de comparatione arcuum curvarum irrectificibilium

(Observations on the comparison of arcs of irrectifiable curves)

Summary:

Euler presents theorems on elliptic, hyperbolic, and lemniscate arcs whose coordinates are the sum or difference of an algebraic function, or of arcs that are multiples of each other.

According to C. G. J. Jacobi, a treatise with this title was presented to the Berlin Academy on January 27, 1752.

Publication:

Originally published in Novi Commentarii academiae scientiarum Petropolitanae 6, 1761, pp. 58-84
Opera Omnia: Series 1, Volume 20, pp. 80 - 107
An English translation of the first of selections of E252, along with some brief commenatary, is published in D. J. Struik's A Source Book in Mathematics, 1200-1800 (1969, Harvard University Press), pp. 379-383.
According to Jacobi, the manuscript of the printed treatise can be found in the archive of the Berlin Academy.

Documents Available:

Original publication: E252
German translation (Artur Diener and Alexander Aycock): E252
E252 is discussed in Ed Sandifer's How Euler Did It May 2005 column published online by the MAA.
The Euler Archive attempts to monitor current scholarship for articles and books that may be of interest to Euler Scholars. Selected references we have found that discuss or cite E252 include:
- Dhombres J., “Some aspects of the history of functional-equations linked to the evolution of the function concept.” Archive for History of Exact Sciences, 36 (2), pp. 91-181 (1986).

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