110. By which figures qualitatively indistinguishable from a given figure are obtained 122 111. Anharmonic ratio may and must be descriptively defined 122 112. The quadrilateral construction is essential to the projective definition of points, 123 113. And can be projectively defined, 124 114. By the general principle of projective transformation 126 115. The principle of duality is the mathematical form of a philosophical circle, 127 116. Which is an inevitable consequence of the relativity of space, and makes any definition of the point contradictory 128 117. We define the point as that which is spatial, but contains no space, whence other definitions follow 128 118. What is meant by qualitative equivalence in Geometry? 129 119. Two pairs of points on one straight line, or two pairs of straight lines through one point, are qualitatively equivalent 129 120. This explains why _four_ collinear points are needed, to give an intrinsic relation by which the fourth can be descriptively defined when the first three are given 130 121. Any two projectively related figures are qualitatively equivalent, i.e. differ in no non-quantitative conceptual property 131 122. Three axioms are used by projective Geometry, 132 123. And are required for qualitative spatial comparison, 132 124. Which involves the homogeneity, relativity and passivity of space 133 125. The conception of a form of externality, 134 126. Being a creature of the intellect, can be dealt with by pure mathematics 134 127. The resulting doctrine of extension will be, for the moment, hypothetical 135 128. But is rendered assertorical by the necessity, for experience, of some form of externality 136 129. Any such form must be relational 136 130. And homogeneous 137 131. And the relations constituting it must appear infinitely divisible 137 132. It must have a finite integral number of dimensions, 139 133. Owing to its passivity and homogeneity 140 134. And to the systematic unity of the world 140 135. A one-dimensional form alone would not suffice for experience 141