E128 -- Methodus facilis computandi angulorum sinus ac tangentes tam naturales quam artificiales
(An easy method for computing the natural and artificial sines and tangents of angles)
Euler considers a kind of "shifted" sum of reciprocals of squares, 1/(1 ± p) ± 1/(4 ± p) ± 1/(9 ± p) ± 1/(16 ± p) ± .... He uses this to evaluate some sines, cosines log sines, log cosines, tangents and cotangents to 20 decimal places.
the records, it was presented to the St. Petersburg Academy on December 15, 1739.
Originally published in Commentarii academiae scientiarum Petropolitanae 11, 1750, pp. 194-230
Opera Omnia: Series 1, Volume 14, pp. 364 - 406
- A handwritten French translation of this treatise can be found in the library of the observatory in
Uccle, near Brussels.
- Original publication: E128 (in the Commentarii)
- 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 E128 include:
- Katz VJ., “The calculus of the trigonometric functions.” Historia Mathematica, 14 (4), pp. 311-324 (Nov 1987).
Return to the Euler Archive