To some extent, the book justifies Arthur Cayley (the inventor of matrix algebra)'s adage that "Projective geometry is all geometry". Towards the end of the book, models of non-Euclidean geometries are built within CP^2. I've written up an overview in this Wikipedia sandbox: https://en.wikipedia.org/wiki/User:Svennik/sandbox
To some extent, the book justifies Arthur Cayley (the inventor of matrix algebra)'s adage that "Projective geometry is all geometry". Towards the end of the book, models of non-Euclidean geometries are built within CP^2. I've written up an overview in this Wikipedia sandbox: https://en.wikipedia.org/wiki/User:Svennik/sandbox