An Elementary Course in Synthetic Projective Geometry

An Elementary Course in Synthetic Projective Geometry

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 [pg iv] 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 customary terms for classifying involutionshyperbolic involution, elliptic involution and parabolic involution. He has found that all these terms are very confusing to the student, who inevitably tries to connect them in some way with the conic sections. ......Buy Now (To Read More)

Product details

Ebook Number: 17001
Author: Lehmer, Derrick Norman
Release Date: Nov 4, 2005
Format: eBook
Language: English