"D'ALEMBERT, JEAN LE ROND. - D'ALEMBERT'S THEOREM - THE FUNDAMENTAL THEOREM OF ALGEBRA.

Reference : 46603

(1848)

Berlin, Haude et Spener, 1848-52. 4to. No wrappers as extracted from ""MÃmoires de l'Academie Royale des Sciences et Belles-Lettres"", tome II (1846), tome IV, tome VI a. tome VI. Pp. 182-224, pp. 249-291, pp. (361-) 378, pp. 413-416 and 1 folded engraved plate.

First apperance of d'Alembert's 3 importent papers on the Calculus of Integration, a branch of mathematical science which is greatly indepted to him. He here gives the proof of THE FUNDAMENTAL THEOREM OF ALGEBRA, called d'Alembert's theorem, and later corrected by Gauss (1799).The theorem is based on these three assumptions:Every polynomial with real coefficients which is of odd order has a real root. (This is a corollary of the intermediate value theorem. Every second order polynomial with complex coefficients has two complex roots. For every polynomial p with real coefficients, there exists a field E in which the polynomial may be factored into linear terms.Also with an importent paper by Leonhard Euler ""MÃmoire sur l'Effet de la Propagation successive de la Lumiere dans l'Apparition tant des Planetes que des Cometes"" (Memoir on the effect of the successive propogation of light in the appeareance of both comets and planets). Pp. 141-181 and 2 folded engraved plates. - The paper is founded on Euler's theory of light as waves and not as particles. It is from the same year as his fundamental work on light as waves: ""Nova Theoria"" - Enestroem E 104.

London, Roayl Society, 1926. Royal 8vo. Full cloth. Gilt lettering to spine. In: ""Proceedings of the Royal Society"". Series A, Vol. 111. V,753,LIII pp., textillustr. and plates. (Entire volume offered).

First appearance of these papers constituting Dirac's own theory of quantum mechanics.""Dirac wanted to establish an algebra for quantum variables, or, as he now termed them, q-numbers... He wanted his q-number algebra to be a general and purely mathematical theory that could then be applied to problem of physics. Although it soon turned out that q-number algebra was equivalent to matrix mechanics, in 1926 Dirac's theory was developed as an original alternative to both wave mechanics and matric mechanics. It was very much Dirac's own theory, and he stuck to it without paying much attention to what went on inmatrix mechanics... In the summer of 1926, Dirac published a new and very general version of q-number algebra, this timepresented as a purely mathematical theory. In this paper (offered here) he did not refer to physics at all... The work had little impact on the physics community but seems to have been appreciated by those who cultivated the mathematical aspects of quantum physics. Most of the results obtained by Dirac in his paper ""The Elimination of the Nodes in Quantum Mechanics"" had been found earlier by the German theorists using a method of matric mechanics, but Dirac was able to improve on some of the results and deduce them from his own system of quantum mechanics.""(Helge Kragh).

(Berlin, Haude et Spener, 1770). 4to. No wrappers, as issued in ""MÃmoires de l'Academie Royale des Sciences et Belles-Lettres"", Tome V, pp. 203-221, 1 plate and pp. 222-288, 1 engraved plate.

Both papers first edition. The first paper is Euler's discussion of ""Cramers Paradox"" and it contains his inventions of 2 kinds of curves, ""Cusps of first kind"" or keratoid cusp and ""Cups of second kind"" or ramphoid cusp. - Enestroem E 169.The second paper contains Euler's famous proof of ""The fundamental Theorem of Algebra"". - Enestroem E 170.