Principles of Geometry

Front Cover
Cambridge University Press, Oct 31, 2010 - Mathematics - 272 pages
0 Reviews
Henry Frederick Baker (1866-1956) was a renowned British mathematician specialising in algebraic geometry. He was elected a Fellow of the Royal Society in 1898 and appointed the Lowndean Professor of Astronomy and Geometry in the University of Cambridge in 1914. First published between 1922 and 1925, the six-volume Principles of Geometry was a synthesis of Baker's lecture series on geometry and was the first British work on geometry to use axiomatic methods without the use of co-ordinates. The first four volumes describe the projective geometry of space of between two and five dimensions, with the last two volumes reflecting Baker's later research interests in the birational theory of surfaces. The work as a whole provides a detailed insight into the geometry which was developing at the time of publication. This, the fourth volume, describes the principal configurations of space of four and five dimensions.
  

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

INTRODUCTORY RELATIONS OF
1
The generalised Miquel theorem 810
8
Wallaces theorem for four circles and Moebiuss figure of
18
Theorems for circumscribed circles for any number of lines in
29
Spheres as determined from sections of a quadric in fourfold space 3638
36
Planes lying entirely on the quadric fourfold in the space of five
44
Number of lines common to two congruences in threefold space 50
50
The section of Veroneses surface by a fourold space
54
The bipolar character of the figure obtained 76
76
Eight sections divided into four pairs
77
Relations with metrical geometry
78
The same Hart section arises in different ways
80
Four circles arising from the intersections of three circles
82
A particular form of the equation of the quadric 8586
85
THE PLANE QUARTIC CURVE WITH
89
Inversion of the curve into itself 96
96

Lies correspondence between lines and spheres in space of three dimensions 55
55
Algebraic formulation of the correspondence 56
56
Comparison with deduction of sphere from fourfold space
57
The eight spheres touching four planes
58
Exx 15 Proofs of the theorems 6064
60
Note Another proof of Wallaces theorem and extensions
64
HARTS THEOREM FOR CIRCLES IN A PLANE OR FOR SECTIONS OF A QUADRIC The sections of a quadric which touch three given sections 65
65
A pair of variable sections of a quadric touching one another and two fixed sections
66
Circles cutting three given circles at equal angles
67
Solution of generalised Malfattis problem 68
68
Equations of sections touching three sections of a quadric 69
69
Exx 1015 Various algebraic results 70
70
The Hart circles of three circles when the four have a common orthogonal circle 71
71
The Hart circles of three circles in general 7275
72
The various cases
75
A PARTICULAR FIGURE IN SPACE
104
A FIGURE OF FIFTEEN LINES
113
The six systems of planes 123
123
The equations of the singular solids 129
129
The dual of the figure which has been considered The cubic locus S 151158
151
A QUARTIC SURFACE IN SPACE
161
The selfpolar pentad for the quartic surface 168170
168
Confocal Cyclides Three through arbitrary point with given focal
180
RELATIONS IN SPACE OF FIVE
203
Relation of the transformation to the theory of Rummers surface 211
211
Kummers surface in the geometry of space of five dimensions 218221
218
The common singular points and planes of the six congruences 225227
225
The rationality of the Quadratic Complex and of the Quadratic
234
The singular points and planes of a Quadratic Congruence
240
Copyright

Common terms and phrases

Bibliographic information