Recherches sur les courbes a double courbure

CLAIRAUT, Alexis Claude

Published by Nyon, Didot and Quillau, Paris, 1731
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"THE FIRST TREATISE ON SOLID ANALYTIC GEOMETRY" (BOYER). First edition, very rare, of Clairaut s first publication, the first extended treatment of the geometry of curves in three dimensions, written when he 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. "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, Recherches sur les courbesà double courbure, 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 Recherches 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 by the teenage Clairaut constitutes the first treatise on solid analytic geometry" (Boyer, History of mathematics, p. 494). "Although the expression double-curvature curve (gauche curve) is attributed to Henri Pitot (1724), Clairaut s treatise on this type of figure is no less original, representing the first serious analytical study of it. The curve is determined by two equations among the three orthogonal coordinates of its point courant (locus). Assimilation of the infinitesimal arc to a segment of a straight line permits determination of the tangent and the perpendiculars. It also permits rectification of the curve. This work also includes quadratures and the generation of some special gauche curves" (DSB). "In his 1731 work Recherches sur les courbes à double courbure, Clairaut studied tangents to curves of double curvature. He saw that a space curve can have an infinity of normals located in a plane perpendicular to the tangent. The expressions for the arc length of a space curve and the quadrature of certain areas on surfaces are also due to him" (Kline, Mathematical Thought from Ancient to Modern Times, p. 557). Provenance: The Earls of Macclesfield (South Library bookplate on front paste-down, small pressure stamp to title). Analytic geometry in two dimensions, i.e., the study of curves in the plane, dates from the work of Descartes, Fermat, Ghetaldi and others in the first half of the seventeenth century. Phillipe de la Hire understood, later in the century, that an equation in three unknowns represents a surface, but he did not study surfaces by means of their equations. John Wallis and Christopher Wren discussed the lines on the single-sheeted hyperboloid in the 1660s, but they did not use coordinates. Indeed, curves and surfaces in three dimensions were not studied in any detail until the eighteenth century. The first explicit analytic treatment of a curved surface was given by Antoine Parent in 1700, "an awkward treatment of the surface of a sphere, but it shows a full knowledge of space coordinates" (Boyer, History of Analytic Geometry, pp. 156-157). However, this work seems to have made little impression upon his contemporaries. Jean Bernoulli, in correspondence with Leibniz in 1715, also showed familiarity with space coordinates, but this too long went unpublished and unnoticed. It was Euler, Seller Inventory # 5797

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Title: Recherches sur les courbes a double courbure
Publisher: Nyon, Didot and Quillau, Paris
Publication Date: 1731
Edition: First edition.

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LeatherBound. Condition: New. LeatherBound edition. Condition: New. Reprinted from 1731 edition. Leather Binding on Spine and Corners with Golden leaf printing on spine. Bound in genuine leather with Satin ribbon page markers and Spine with raised gilt bands. A perfect gift for your loved ones. Pages: 151 NO changes have been made to the original text. This is NOT a retyped or an ocr'd reprint. Illustrations, Index, if any, are included in black and white. Each page is checked manually before printing. As this print on demand book is reprinted from a very old book, there could be some missing or flawed pages, but we always try to make the book as complete as possible. Fold-outs, if any, are not part of the book. If the original book was published in multiple volumes then this reprint is of only one volume, not the whole set. Sewing binding for longer life, where the book block is actually sewn (smythe sewn/section sewn) with thread before binding which results in a more durable type of binding. Pages: 151. Seller Inventory # LB990006183006

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Leather Bound. Condition: New. Language: French. Presenting an Exquisite Leather-Bound Edition, expertly crafted by the prestigious organization "Rare Biblio" with Original Natural Leather that gracefully adorns the spine and corners. The allure continues with Golden Leaf Printing that adds a touch of elegance, while Hand Embossing on the rounded spine lends an artistic flair. This masterpiece has been meticulously reprinted in 2024, utilizing the invaluable guidance of the original edition published many years ago in 1731. The contents of this book are presented in classic black and white. Its durability is ensured through a meticulous sewing binding technique, enhancing its longevity. Imprinted on top-tier quality paper. A team of professionals has expertly processed each page, delicately preserving its content without alteration. Due to the vintage nature of these books, every page has been manually restored for legibility. However, in certain instances, occasional blurriness, missing segments, or faint black spots might persist. We sincerely hope for your understanding of the challenges we faced with these books. Recognizing their significance for readers seeking insight into our historical treasure, we've diligently restored and reissued them. Our intention is to offer this valuable resource once again. We eagerly await your feedback, hoping that you'll find it appealing and will generously share your thoughts and recommendations. Lang: - French, Pages: : - 137, Print on Demand. If it is a multi-volume set, then it is only a single volume. We are specialised in Customisation of books, if you wish to opt different color leather binding, you may contact us. This service is chargeable. Product Disclaimer: Kindly be informed that, owing to the inherent nature of leather as a natural material, minor discolorations or textural variations may be perceptible. Explore the FOLIO EDITION (12x19 Inches): Available Upon Request. 137. Seller Inventory # LB1111004041762

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