 Its basic concepts were the points, lines, and planes of a space that was \(\mathbb{R}^3\) enriched with what was often called a plane at infinity, so that any two coplanar lines meet. Prior to axiomatisations of the theory at the end of the 19th century, point, line, and plane were basic concepts with an intuitive interpretation that allowed for a ready passage between projective and Euclidean geometry. The allowed transformations of the geometry map points to points, lines to lines, and planes to planes and preserve cross-ratio. They act transitively on the space, so no point, line, or plane is special, and therefore lines that are parallel in any finite part of the space may be mapped to intersecting lines and vice versa.