E275 -- Annotationes in locum quendam Cartesii ad circuli quadraturam spectantem

(Annotations to a certain passage of Descartes for finding the quadrature of the circle)


Euler shows that 4p = tan(p/4) + tan(p/8) + tan(p/16) + 1/8 tan(p /32) + . Combining this with the integral of arctan, he gets an expression for p/4 that converges rapidly. For n = 5, it gives 12 decimal accuracy.

According to C. G. J. Jacobi, a treatise with this title was read to the Berlin Academy on July 20, 1758.

According to the records, it was presented to the St. Petersburg Academy on October 15, 1759.

Publication: Documents Available:

Return to the Euler Archive