E590  Theoremata quaedam analytica, quorum demonstratio adhuc desideratur
(Certain theorems in analysis, of which a demonstration is thus far desired)
Summary:
According to Eneström, "The three theorems are:
 Omnes plane quantitates imaginariae, quaecunque in calculo analytico occurrere possunt,
ad hanc formam simplicissimam a + bi ita revocari possunt, ut litterae a et b quantitates reales denotent.
 Praeter circulum nulla datur curva algebraica, cujus singuli arcus per arcus circulares simpliciter exprimi queant.
 Nulla prorsus datur curva algebraica, cujus singuli arcus simpliciter per logarithmos exprimi queant."
According to the records, it was presented to
the St. Petersburg Academy on May 1, 1775.
Publication:

Originally published in Opuscula Analytica 2, 1785, pp. 7690.

Opera Omnia: Series 1, Volume 21, pp. 78  90
Documents Available:
 Original Publication: E590
 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 E590 include:
 Jahnke HN., “Arithmeticization of mathematics in the 1sthalf of the 19thcentury  Cauchy analysis as viewed by the mathematician Ohm, Martin.” Archive for History of Exact Sciences, 37 (2), pp. 101182 (1987).
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