E256 -- Specimen de usu observationum in mathesi pura

(Example of the use of observation in pure mathematics)


Euler attempts to explain his thinking process by working out problems in quadratic forms in great detail. Euler notes that numbers of the form 2aa + bb are closed under multiplication. He develops more properites of such numbers and proves some of them. Then he uses the properties to show that 67579 = 2(87)2 + 2292 is prime, and that 40081 isnít.

According to C. G. J. Jacobi, a treatise with this title was read to the Berlin Academy on November 22, 1753.

According to the records, it was presented to the St. Petersburg Academy on September 30, 1754.

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