ABSTRACT
Descriptive Geometry is not, as a rule, sharply distinguished from projective Geometry. This chapter introduces the elementary sense of between, which is in general not unaltered by projection. Descriptive Geometry applies equally to Euclidean and to hyperbolic space: none of the axioms mentioned discriminate between these two. The chapter shows that descriptive space is not a species of projective space, but a radically distinct entity. In ordinary metrical language, the projective space is finite, while the part of it which is descriptive is infinite. All projective Geometry becomes available; and wherever the ideal points, lines and planes correspond to actual ones, a corresponding projective proposition is obatined. In ordinary metrical language, the projective space is finite, while the part of it which is descriptive is infinite. This illustrates the comparatively superficial nature of metrical notions.
