The Project Gutenberg EBook of An Elementary Course in Synthetic
Projective Geometry by Lehmer, Derrick Norman

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Title: An Elementary Course in Synthetic Projective Geometry

Author: Lehmer, Derrick Norman

Release Date: November 4, 2005 [Ebook #17001]

Language: English

Character set encoding: US-ASCII

***START OF THE PROJECT GUTENBERG EBOOK AN ELEMENTARY COURSE IN SYNTHETIC PROJECTIVE GEOMETRY***

An Elementary Course in Synthetic Projective Geometry

by Lehmer, Derrick Norman

Edition 1, (November 4, 2005)

PREFACE

The following course is intended to give, in as simple a way as possible,
the essentials of synthetic projective geometry. While, in the main, the
theory is developed along the well-beaten track laid out by the great
masters of the subject, it is believed that there has been a slight
smoothing of the road in some places. Especially will this be observed in
the chapter on Involution. The author has never felt satisfied with the
usual treatment of that subject by means of circles and anharmonic ratios.
A purely projective notion ought not to be based on metrical foundations.
Metrical developments should be made there, as elsewhere in the theory, by
the introduction of infinitely distant elements.

The author has departed from the century-old custom of writing in parallel
columns each theorem and its dual. He has not found that it conduces to
sharpness of vision to try to focus his eyes on two things at once. Those
who prefer the usual method of procedure can, of course, develop the two
sets of theorems side by side; the author has not found this the better
plan in actual teaching.

As regards nomenclature, the author has followed the lead of the earlier
writers in English, and has called the system of lines in a plane which
all pass through a point a _pencil of rays_ instead of a _bundle of rays_,
as later writers seem inclined to do. For a point considered as made up of
all the lines and planes through it he has ventured to use the term _point
system_, as being the natural dualization of the usual term _plane
system_. He has also rejected the term _foci of an involution_, and has
not used the cu