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First edition, journal issue in original unopened never-bound sheets, of Maxwell's first paper written at Cambridge, presented to the Cambridge Philosophical Society shortly after he graduated as second wrangler at Trinity College. "This is one of the few purely mathematical papers he published, and it exhibited at once to experts the full genius of its author" (Encyclopaedia Britannica 17 (1911), p. 929). Maxwell's paper is a development and geometrical interpretation of work by several continental mathematicians, especially Gauss. In his epochal work Disquisitiones generalis circa superficies curvas (1825), Gauss had introduced the concept of the curvature of a surface and had proved his 'Remarkable Theorem' (Theorema Egregium), that the curvature is unchanged by isometric transformations of the surface (transformations which preserve distance). Maxwell calls such a transformation a 'bending' of the surface: "The operation of bending is a continuous change of the form of a surface, without extension or contraction of any part of it" (p. 446). While Gauss's proof makes extensive use of the calculus, Maxwell opts for a more geometrical approach which involves approximating the surface by an inscribed polygonal surface made up of plane triangles. The curvature can be interpreted in terms of the solid angles at each vertex of the polygonal surface. Maxwell is particularly interested in the question of which surfaces admit a continuous isometric deformation (for example, this is true of a plane as it can be rolled into a cylinder). A complete answer to this question is still unknown. Maxwell is, of course, best known for his contributions to theoretical physics. In the very next part of the Transactions (Vol. X, Part I) appeared his first paper on electromagnetism, 'On Faraday's lines of force'. "From a long view of the history of mankind seen from, say, ten thousand years from now there can be little doubt that the most significant event of the 19th century will be judged as Maxwell's discovery of the laws of electrodynamics" (R. P. Feynman, in The Feynman Lectures on Physics II (1964), p. 1-6). "[Maxwell] may well be judged the greatest theoretical physicist of the 19th century . . . Einstein's work on relativity was founded directly upon Maxwell's electromagnetic theory; it was this that led him to equate Faraday with Galileo and Maxwell with Newton" (PMM). "In 1931, on the 100th anniversary of Maxwell's birth, Einstein described the change in the conception of reality in physics that resulted from Maxwell's work as the most profound and the most fruitful that physics has experienced since the time of Newton" (Britannica). 4to, pp. [xii], [1]-678 (last 4 leaves a little browned). Original never bound sheets. A virtually mint copy.
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