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2015-05-25 20:57:25
CLAIRAUT, Alexis Claude.
Recherches sur les courbes a double courbure.Paris: Nyon, Didot and Quillau, 1731. First edition.
Fine large-paper copy of this celebrated treatise, "the first treatise on solid analytic geometry" (Boyer), written when the author was only sixteen. In it Clairaut demonstrates a claim made by Newton that all cubic curves in three dimensions are projections of a cubic curve of a special form. This publication led to Clairaut's election to the Académie des Sciences at the age of eighteen, the rules of admission being suspended to accommodate the mathematical prodigy.<br/><br/> "Alexis Claude Clairaut was one of the most precocious of mathematicians, outdoing even Blaise Pascal in this respect. At the age of ten he was reading the textbooks of L'Hospital on conics and the calculus, when he was thirteen he read a paper on geometry to the Académie des Sciences ... In the year of his election Clairaut published a celebrated treatise, <i>Recherches sur les courbes a double courbure</i>, the substance of which had been presented to the Académie two years earlier ... The treatise of Clairaut carried out for space curves the program that Descartes had suggested almost a century before - their study through projections on two coordinate planes. It was, in fact, this method that suggested the name given by Clairaut to gauche or twisted curves inasmuch as their curvature is determined by the curvatures of the two projections. In the <i>Recherches</i> numerous space curves are determined through intersections of various surfaces, distance formulas for two and three dimensions are given, an intercept form of the plane is included, and tangent lines to space curves are found. This book b … [Click Below for Full Description]
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