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 the non-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. the intrinsic 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. To the portion dealing
with the differential geometry of curves on quadrics, I have added
Staudes thread-construction for ellipsoids 4210, which is the
three-dimensional analogue of Gravess theorem and his definitions
of confocal quadrics 421ft by means ofbroken distances these are
the analogues of the ordinary definitions of conies by means of
focal radii. In the Golden Age of Euclidean geometry, analogues of
these types were of great interest to men like Jacobi, MacCullagh,
Chasles and M. Roberts, but Staudes constructions have virtually
brought the subject to a conclusion. Staudes treatment is also an
excellent illustration of the elementary and visible meaning of
elliptic and hyper-elliptic in tegrals. New matter is also
contained in Arts. 8Qa, 80, 880, 1590, 172, 173, 1760, 261, 304,
384, and in various paragraphs throughout the book. Most of these
additions are of the nature of commentaries. About 100 examples are
added many of them being solved in order to illustrate the
principles of the articles to which they are appended. The
numbering of the chapters and of the articles is the same as in the
fourth edition, except in Chapter III., where the order has been
somewhat changed, and in Arts. 172, 173. The present edition has
been published by the EDITOBS PBEFACE TO FIFTH EDITION. vii
direction of the Board of Trinity College, who appointed me as
Editor in November, 1910. REGINALD A. P. ROGERS. TRINITY COLLEGE,
DUBLIN, November, 1911. The Sixth Edition 1914 of Vol. I. is
reprinted from the Fifth, with a few corrections, of which the most
important are in Arts 88, 338 Ex., 344, 357 PREFACE TO THE THIRD
EDITION. IN the preface to the second edition of my Higher Plane
Cnrres, I have explained the circumstances under which I obtained
Professor Cayleys valuable help in the preparation of that volume.
I have now very gratefully to acknowledge that the same assistance
has been continued to me in the re-editing of the present work.
Thechanges from the preceding edition are not so numerous here as
in the case of the Higher Plane Curves, partly because the book not
having been so long out of print required less alteration, partly
because the size to which the volume had already swelled made it
necessary to be sparing in the addition of new matter. Prof...
General
Is the information for this product incomplete, wrong or inappropriate?
Let us know about it.
Does this product have an incorrect or missing image?
Send us a new image.
Is this product missing categories?
Add more categories.
Review This Product
No reviews yet - be the first to create one!
Welcome to Loot.co.za!
Sign in / Register |Wishlists & Gift Vouchers |Help | Advanced search
