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** July 10-He discovers that every positive integer is representable as a sum of at most three triangular numbers, noting in his diary " Heureka!
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** and July
** See also Salmond on " Citizenship and Allegiance ," in the Law Quarterly Review ( July 1901, January 1902 ).
** In the former doge-state Venice, and while it was a republic resisting annexation by either the kingdom of Piedmont-Sardinia or the Austrian empire, a former Chief Executive ( president, 23 March 18485 July 1848 ), Daniele Manin ( b. 1804-d. 1857 ), was styled Dictator 11 – 13 August 1848 before joining the 13 August 1848-7 March 1849 Triumvirate.
** and discovers
** In the Star Trek: Voyager episode " One Small Step ", USS Voyager discovers the fate of Ares IV, one of the first manned expeditions to Mars in 2032.
** Jigme Lingpa discovers the Longchen Nyingtig ter through a meditative vision which brought him to the Boudhanath Stupa.
** William Rowan Hamilton discovers the calculus of quaternions and deduces that they are non-commutative.
** A U. S. Navy PV-1 Ventura patrol plane discovers survivors of the heavy cruiser, the first indication that Indianapolis is even missing, 84 hours after she had been sunk by the Japanese submarine I-58 in the Philippine Sea.
** The 3rd Soviet Antarctic Expedition discovers the subglacial Gamburtsev Mountain Range in Antarctica ; also becoming the first to reach the Southern Pole of Inaccessibility ( December 14 ).
** and every
** Tarski's theorem: For every infinite set A, there is a bijective map between the sets A and A × A.
** Zorn's lemma: Every non-empty partially ordered set in which every chain ( i. e. totally ordered subset ) has an upper bound contains at least one maximal element.
** Hausdorff maximal principle: In any partially ordered set, every totally ordered subset is contained in a maximal totally ordered subset.
** Gödel's completeness theorem for first-order logic: every consistent set of first-order sentences has a completion.
** The microcode can employ both pipelines to enable auto-repeating instructions such as rep movsw perform one iteration every clock cycle, while the 80486 needed three clocks per iteration ( and the earliest x86-chips significantly more than the 486 ).
** United Kingdom Census held, the first to record names and approximate ages of every household member and to be administered nationally.
** Circuit analysis, the process of finding the voltages across, and the currents through, every component in an electrical circuit
** Unique factorization domain, an integral domain in which every non-zero element can be written as a product of irreducible elements in essentially a unique way
** Atomic domain, an integral domain in which every non-zero non-unit is a finite product of irreducible elements
** Dedekind domain, an integral domain in which every nonzero proper ideal factors into a product of prime ideals
** GCD domain, an integral domain in which every two non-zero elements have a greatest common divisor
1.567 seconds.