E125 -- Consideratio progressionis cuiusdam ad circuli quadraturam inveniendam idoneae
(Consideration of a progression suitable for finding the quadrature of a circle)
Summary:
Euler presents an elementary derivation of a semi-convergent series for arctan, which is a special case of the Euler Summation
Formula.
According to
the records, it was presented to the St. Petersburg Academy on March 23, 1739.
Publication:
-
Originally published in Commentarii academiae scientiarum Petropolitanae 11, 1750, pp. 116-127
-
Opera Omnia: Series 1, Volume 14, pp. 350 - 363
- A handwritten French translation of this treatise can be found in the library of the observatory in
Uccle, near Brussels.
Documents Available:
- Original publication: E125
(in the Commentarii, Volume 11)
- 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 E125 include:
- Ferraro G., “Convergence and formal manipulation of series from the origins of calculus to about 1730.” Annals of Science, 59 (2), pp. 179-199 (Apr 2002).
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