  This family of arguments has received considerable attention due to a number of its complexities. These involve attempts to answer questions including the following: As we have seen, through his science of perspectival shapes of objects Reid argues that they are geometrically equivalent to shapes projected onto surfaces of spheres. What is Reid's formal proof for this, and is it valid (Yaffe 2002)? Does Reid offer the first recorded non-Euclidean geometry in the history of mathematics (Daniels 1972)? What is the bearing of Reid's repeated attempts to derive Euclid's parallel postulate from the axioms of incidence on an interpretation of the geometry of visible space as non-Euclidean (Grandi 2005)? Where does Reid's theory of perception and geometry of visibles leave the ontology of visible figure (Nichols 2007, ch. 4)? In what ways is visible figure the object of visual perception, and in what ways not (Yaffe 2003; Falkenstein and Grandi 2003)? Does Reid's geometry of visible space jeopardize his theory's ability to avoid a representational theory of visual perception (Van Cleve 2002)? Does visible figure and awareness of it preclude non-inferential perceptual knowledge from vision, or rather, what is the relationship between original and acquired perceptions and visible figure (Nichols 2007, ch. 8)?