Books about synthetic projective geometry

Question

Are there books in English about synthetic projective geometry? More specifically, results of Karl von Staudt (imaginary elements theory through elliptical involutions, imaginary circle, infinity's imaginary circle)

Answer 1

There is this book by Robin Hartshorne, based on a course he taught at Harvard:

https://www.amazon.com/Foundations-Projective-Geometry-Robin-Hartshorne/dp/4871878376

Answer 2

Derrick Norman Lehmar's book named An Elementary Course Synthetic Projective Geometry is a great book on Synthetic Projective Geometry. I have read it myself and i think it is very informative. Apart from this, can someone tell me where can i get Detailed Information of Government Exams as I want to crack UPSC exam.

Answer 3

There's lots to learn from "modern" texts such as Richter-Gebert, Coxeter, et al. But the heyday of synthetic projective geometry appears to have been in the 19th and early 20th centuries. After that, both research and pedagogy moved to other topics in math.

For the older texts archive.org is your friend, going back to Poncelet's groundbreaking Traité des propriétés projectives des figures which introduces the principle of continuity, an early view of imaginary elements.

Some examples: Milne's Cross-Ratio Geometry (which makes reference to imaginary elements), and Pickford's Elementary Projective Geometry.

Dialing in on your interest in imaginary elements, Chapter XXVII of Russel's Pure Geometry discusses imaginary points and lines and gives some practical constructions.

Also check out Coolidge's Geometry of the Complex Domain (the final chapter is on Von Staudt Theory) and Hatton's Theory of the Imaginary in Geometry.