E256 -- Specimen de usu observationum in mathesi pura

(Example of the use of observation in pure mathematics)


Summary:

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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