A curve of order 
is generally determined by 
points. So a conic section
is determined by five points and a cubic curve should
require nine. But the Maclaurin-Bézout
theorem says that two curves of degree 
intersect in 
points, so two cubics intersect in nine points. This means that 
points do not always uniquely determine a single curve
of order 
.
The paradox was publicized by Stirling, and explained by Plücker.
Cramér-Euler Paradox
See also
Cubic Curve, Maclaurin-Bézout TheoremExplore with Wolfram|Alpha
References
Euler, L. "Sur une contradiction apparente dans la doctrine des lignes courbes." Mémoires de l'Academie des Sciences de Berlin 4, 219-233, 1750 Reprinted in Opera Omnia, Series Prima, Vol. 26. Boston: Birkhäuser, pp. 33-45, 1992.Sandifer, E. "How Euler Did It: CramerÕs Paradox." Aug. 2004. http://www.maa.org/editorial/euler/How%20Euler%20Did%20It%2010%20Cramers%20Paradox.pdf.Referenced on Wolfram|Alpha
Cramér-Euler ParadoxCite this as:
Weisstein, Eric W. "Cramér-Euler Paradox." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Cramer-EulerParadox.html