Synopsis
Unlike some other reproductions of classic texts (1) We have not used OCR(Optical Character Recognition), as this leads to bad quality books with introduced typos. (2) In books where there are images such as portraits, maps, sketches etc We have endeavoured to keep the quality of these images, so they represent accurately the original artefact. Although occasionally there may be certain imperfections with these old texts, we feel they deserve to be made available for future generations to enjoy.
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Présentation de l'éditeur
The matter contained is in no sense new, but a suitable connected treatment in theE nglish language has not been available. As a result, a number of interesting misconceptions are current in English text books. It is sufficient to mention two somewhat striking examples, (a) According to the ordinary definition of an envelope, as the locus of the limits of points of intersection of neighbouring curves, a curve is not the envelope of its circles of curvature, for neighbouring circles of curvature do not intersect, (b) The definitions of an asymptote (1) a straight line, the distance from which of a point on the curve tends to zero as the point tends to infinity; (2) the limit of a tangent to the curve, whose point of contact tends to infinity are not equivalent. The curve may have an asymptote according to the former definition, and the tangent may exist at every point, but have no limit as its point of contact tends to infinity. The subjects dealt with, and the general method of treatment, are similar to those of the usual chapters on geometry in any Cours dA nalyse, except that in general plane curves alone are considered. At the same time extensions to three dimensions are made in a somewhat arbitrary selection of places, where the extension is immediate, and forms a natural commentary on the two dimensional work, or presents special points of interest (F renet sformulae). To make such extensions systematically would make the tract too long. The subject matter being wholly classical, no attempt has been made to give full references to sources of information ;the reader however is referred at most stages to the analogous treatment of the subject in the Cours or Traite dA nalyse of de laV aline Poussin, Goursat, Jordan or Picard, works to which the author is much indebted.
(Typographical errors above are due to OCR software and don't occur in the book.)
About the Publisher
Forgotten Books is a publish
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