What's a good book on geometry to read after Kiselev?

Question

I have finished reading both books on geometry by Kiselev and now look to move on but can't find any book to let me do so. Which book would you suggest that one may read after finishing Kiselev?

Answer 1

Have you tried reading "A sequel to the first six books of Euclid" by Casey? There are other books by Casey on Plane Trigonometry and Spherical Trigonometry. There is also a book on geometric conic sections by William Wallace and another smaller one on geometric conic sections by by W.H. Besant with problems and solutions. Then there is "Constructive Geometry" by Thomas Eagles. Also there are the works in analytic geometry (not synthetic) by George Salmon on "3Dimensional Geometry" and "Conics and quadrics". These are all nineteeth century books available on the internet archive which go into far more detail than any other in their respective fields. For more recent texts, look at the books by Coxeter, like "Geometry Revisited" and "Introduction to Geometry". Also Johnson's "Modern Geometry", or Altschiller-Court's "College Geometry", or Prasolov's "Geometry" (an approach in analytic geometry in the spirit of Klein), or Hilbert's "Geometry and the Imagination", or Andreescu's "Geometric Problems on Maxima and Minima", or Honsberger's "Episodes in 19th ans 20th century Geometry". The first chapter in Porter's "Further Mathematics" contains a brief exposition of some geometric gems. Don't Forget Thomas Heath's works on Archimedes, Apollonius and Euclid's Elements either. Yaglom has 3 books on Geometric Transformations too.