Principles of Geometry, Volume 1Henry 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 first volume, describes the foundations of projective geometry. |
Contents
INTRODUCTORY | 1 |
Remarks in regard to Desargues theorem 810 | 8 |
An important construction determining a sixth point from five | 14 |
General proof of the theorem 2125 | 21 |
Propositions of Incidence in space not limited to three dimensions 3336 | 33 |
On the Principle of Duality in general 42 | 42 |
Pappus theorem The conditions follow if Pappus theorem | 48 |
Related ranges on the same line 53 | 53 |
Extension to fourfold and higher space | 106 |
Postulated Points 114116 | 114 |
The impossibility of Desargues theorem from plane Propositions | 120 |
The abstract notion of order 121 | 121 |
Application of the theory of an abstract order Pappus theorem 128130 | 128 |
Consequences of the equable distribution of points of the harmonic net 136 | 136 |
Theory of two related plane systems 148150 | 148 |
A geometrical existence theorem for the solution of an algebraic | 155 |
Introduction of algebraic symbols | 62 |
Preliminary remarks in regard to the use of the symbols in geometry 69 | 69 |
Representation of the algebraic effect of Pappus theorem in three | 81 |
REAL GEOMETRY | 94 |
Points of a plane system 100103 | 100 |
Statement of the further Axiom henceforth assumed in the Abstract | 164 |
The preceding aggregates in the general Abstract Geometry 172175 | 172 |
| 183 | |
Other editions - View all
Common terms and phrases
abstract actual advance aggregate applicable arbitrary point arising assumed assumption belonging called centre Chapter coincide combination common condition consider construction contains contains a point conversely corresponding corresponding points couple define definite denote Desargues determined draw drawn elements entities equally equivalent example existence fact figure follows former four four points further geometry give given lines harmonic conjugate Hence independent intersection involves joining laws lies lying meet the line namely obtained pairs Pappus particular passing pencil perspective plane plane series point series position possible postulated point preceding proof Propositions of Incidence prove reference regard related ranges remarked represented respectively result seen segment shew shewn similar similarly space statement suppose symbols syzygy taken theorem theory three lines three points threefold space transversal triads true