On the Relation Between Real Euclidean and Complex Projective Geometry

Extract

We discuss the deduction of real euclidean theorems from complex projective theorems, and the reverse process: when is it permissible, in proving a complex projective theorem, to project two given points into the circular points at infinity and use real euclidean methods? We emphasise the difference between the real and the complex, and the consequences of using real numbers to define euclidean geometry, and complex numbers to define projective geometry.