notes at the foot of the page, and has tried instead, in the last chapter,
to give a consecutive account of the history of pure geometry, or, at
least, of as much of it as the student will be able to appreciate who has
mastered the course as given in the preceding chapters. One is not apt to
get a very wide view of the history of a subject by reading a hundred
biographical footnotes, arranged in no sort of sequence. The writer,
moreover, feels that the proper time to learn the history of a subject is
after the student has some general ideas of the subject itself.

The course is not intended to furnish an illustration of how a subject may
be developed, from the smallest possible number of fundamental
assumptions. The author is aware of the importance of work of this sort,
but he does not believe it is possible at the present time to write a book
along such lines which shall be of much use for elementary students. For
the purposes of this course the student should have a thorough grounding
in ordinary elementary geometry so far as to include the study of the
circle and of similar triangles. No solid geometry is needed beyond the
little used in the proof of Desargues’ theorem (25), and, except in
certain metrical developments of the general theory, there will be no call
for a knowledge of trigonometry or analytical geometry. Naturally the
student who is equipped with these subjects as well as with the calculus
will be a little more mature, and may be expected to follow the course all
the more easily. The author has had no difficulty, however, in presenting
it to students in the freshman class at the University of California.

The subject of synthetic projective geometry is, in the opinion of the
writer, destined shortly to force its way down into the secondary schools;
and if this little book helps to accelerate the movement, he will feel
amply repaid for the task of working the materials into a form available
for such schools as well as for the lower classes in the university.