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

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


Summary:

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.

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