A course of pure geometry

Askwith E. H. (Edward Harrison) 1864-

Sujets

• Geometry

Informations

• Publié par: les_archives_du_savoir
• Nombre de lectures: 46
• Langue: English
• Poids de l'ouvrage: 9 Mo

Extrait

yC-NRLFLIBRARY
OF THE
University of California.
ClassDigitized by tine Internet Arciiive
in 2008 witii funding from
IVIicrosoft Corporation
http://www.arcliive.org/details/courseofpuregeomOOaskwricliCOURSEA
OF
GEOMETRYPUREHouHou: C. J. CLAY and SONS,
CAMBRIDGE UNIVERSITY PRESS WAREHOUSE,
AVE MARIA LANE.
©laggoto: 50, WELLINGTON STREET.
ILetpjifi: F. A. BROCKHAUS.
i^eto Horfe: THE MACMILLAN COMPANY.
JSombag mtj Calcutta: AND CO., Ltd.
[All Rights reserved]A COURSE
OF
PURE GEOMETRY
BY
E. H. ASKWITH, D.D.
Trinity College, CambridgeChaplain of
CAMBRIDGE
at the University Press
1903:
2^hi
lZ^ZK;^l
CamfariUge
PRINTED BY J. AND F. CliAY,C.
AT THE UNIVERSITY PRESS.PEEFACE.
ri^HIS book, as is obvious from its size, is not intended
to be an exhaustive treatise on Pure Geometry. It
consists of a course of lessons which areon the subject,
adapted to the requirements of students who, after laying
the foundations of Geometry in Euclid or his equivalent,
have studied the properties of the Conic Sections as
derived from their focus and directrix definition.
theIt is assumed that the reader has had practice in
working of examples, and that he is in a position to go on
ofto some of the more modern developments Geometry.
The methods of Coordinate Geometry are excluded
isfrom this work, but not so its ideas, with which it
supposed that the reader is already acquainted.
The writer of this book has been led to put together
these which is the result of somechapters by the feeling,
no book atexperience in teaching the subject, that
thewhich exactly meets the needs ofpresent exists
has in mind. He hopesparticular class of students he
serve to preparehowever that the present course may
Geometry towish to specialise in Purestudents who
a 3
217203VI PREFACE.
books on it already in existence.study some of the
Students of mathematics who do not seek to be specialists
in particular .branch of the science will, it is hoped,this
needed for their purpose. Nofind in this course what is
student of mathematics, however analytical his bent may
can afford to be ignorant of the modern methods ofbe,
Pure Geometry.
It is impossible to draw a hard and fast line between
Geometry. The distinctionPure and Analytical
the two has become one of method rather than of idea,
'when the principle of continuity,' whereby we pass from
real to imaginary points and lines, is admitted into Pure
Geometry. The notion of imaginary points and lines
would never have been arrived at at all but for the
methods of Coordinate Geometry. We take over this
notion into the field of Pure Geometry and thereby
greatly enlarge our view.
Detailed reference to other writers in regard to the
proofs given here of the various propositions is not
attempted. The present course of lessons is the result
of some years' experience on the part of the writer in
teaching the subject. In the course of this experience
he has adopted different ideas and methods from different
writers, with the result that he hardly knows what he
owes to each. But he is sure that he is specially indebted
to Casey, Lachlan and J. W. Russell, all of whose text-
books he has had occasion to use with his pupils. It will
however be seen by those who have knowledge of text-
books at present existing that the course here offered for