TREATISE ON THE ANALYTIC GEOMETRY OF THREE DIMENSIONS - VOL. 1

A TREATISE ON THE ANALYTIC GEOMETRY OF THREE DIMENSIONS EDITORS PREFACE TO FIFTH EDITION. VOLUME I. IN order to avoid delay it has been thought advisable to publish this edition in two volumes. While pre serving the substance of the fourth edition, I have added some new matter generally enclosed in square brackets and in different type giving brief accounts of methods or points of view which appear to me to be of interest and to fit in with the rest of the work. The additions include illustrations of models of most of the different species of quadrics, with gener ators or lines of curvature Chapter V. articles or paragraphs on the analytical classification of real quadrics 880, on projection and Fiedlers projective coordinates 144e, on thenon-Eucliclean theory of distance and angle 144, and on the expression of twisted cubics and quartics by rational or eUigtic parameters 3330, 3470, 348, 349.-In differential geometry my aim has been to form a closer connecting-link between Salmons book and the more extensive and more purely analytical methods used by Bianchi, Darboux and others. I have there fore added articles on the now well-known Frenet-Serret formulae, with some applications 3680, on vi EDITOES PEEPACE TO FIFTH EDITION. theintrinsic equations of a twisted curve 368J, on Bertrand curves 368c, and on the application of Gausss parametric method to conformal represent ation, geodesic curvature and geodesic torsion 3960, 3965.