structural:scholar_edition, information:highlighting
The extended Euclidean plane

To turn the ordinary Euclidean plane into a projective plane, proceed as follows:

The extended structure is a projective plane and is called the extended Euclidean plane or the real projective plane. The process outlined above, used to obtain it, is called "projective completion" or projectivization. This plane can also be constructed by starting from R viewed as a vector space, see § Vector space construction below.