E83 -- Sur quelques proprietes des Sections coniques qui conviennent a un infinite d'autres lignes courbes

(On some properties shared between conic sections and infinitely many other curves)

Summary:

Euler presents analytical solutions for geometric problems. The first is: “Trouver la courbe AMF rapportée à l’axe AD, qui à la distance DE donnée de l’axe ait le diamètre FEG parallèle à l’axe AD, qui coupe en deux toutes les ordonnées Mm tirées avec l’axe à l’angle donné T.”

According to C. G. J. Jacobi, a treatise with this title (in Latin) was presented to the Berlin Academy on September 6, 1742.

Publication:

Originally published in Memoires de l'academie des sciences de Berlin 1, 1746, pp. 71-98
Opera Omnia: Series 1, Volume 27, pp. 51 - 73

Documents Available:

Original publication: E083
E83 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.
A translation of E83 has been prepared by Thomas Osler and Edward Greve.
Osler and Greve have also prepared a section-by-section Synopsis of E83. This is a good document to read for those looking for just the main ideas this work.

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