These real projective spaces can be constructed in a slightly more rigorous way as follows. Here, let R"n"+1 denote the real coordinate space of "n"+1 dimensions, and regard the landscape to be painted as a hyperplane in this space. Suppose that the eye of the artist is the origin in R"n"+1. Then along each line through his eye, there is a point of the landscape or a point on its horizon. Thus the real projective space is the space of lines through the origin in R"n"+1. Without reference to coordinates, this is the space of lines through the origin in an ("n"+1)-dimensional real vector space.