E147 -- Sur un contradiction apparente dans la doctrine des lignes courbes

(On an apparent contradiction in the doctrine of curved lines)

Summary:

Euler discusses the question of whether nine points determine a unique cubic curve. He also considers the same question for 14 points and quartic curves, 20 points and quintic curves, and so on. Euler solves the problem using a system of equations.

According to C. G. J. Jacobi, a treatise with this title was presented to the Berlin Academy on October 12, 1747.

Publication:

Originally published in Memoires de l'academie des sciences de Berlin 4, 1750, pp. 219-233
Opera Omnia: Series 1, Volume 26, pp. 33 - 45
According to Jacobi, the manuscript of the printed treatise can be found in the archive of the Berlin Academy.

Documents Available:

Original publication: E147
E147 can be viewed or downloaded from Digitalisierte Akademieschriften und Schriften zur Geschichte der Königlich Preußischen Akademie der Wissenschaften, which includes serial publications of the Prussian Academy of Science in the 18th and 19th Centuries.
Winifred Marshall at Adelphi University has an English translation of E147 available in pdf format on Rob Bradley's Home Page.
E147 is discussed in Ed Sandifer's How Euler Did It column from August 2004.
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 E147 include:
- Dorier JL., “A general outline of the genesis of vector-space theory.” Historia Mathematica, 22 (3), pp. 227-261 (Aug 1995).

Return to the Euler Archive