508 DR. A. N. WHITEHEAD ON 



*20'233. Definition. A point, which is a member of a figure, will be said to lie in 



that figure. 



*20'234. Definition. A point, which lies in the punctual associate of a class of 

 objective reals, will be said to be on, or upon, that class. 



*20'235. Definition. A punctual line is said to join two points if both the points 

 lie in it. 



*20'236. Definition. -Two punctual lines, which possess a common point, will be 

 said to meet at that point. Similarly, any two classes of points will be said to meet in 

 their common subclass, and this subclass will be called their meeting. 



*20'24. Definition. A class of points is called collinear if there exist a punctual 

 line in which they all lie. The symbol coll Rt !w will denote that u is a class of collinear 

 points at the instant t. The symbolic definition is 



. melin R( . wecls'm Df 



*20'31. Definition. Two figures are in perspective if (i) they have a one-one 

 correspondence to each other, (ii) the joint figure formed by the two figures combined 

 is not collinear, and (iii) there exists a point (the centre of perspective) which lies in 

 every punctual line joining two distinct corresponding points. The statement that 

 u and v are in perspective with each other at the instant t, and that S is the requisite 

 one-one correspondence, will be denoted by u (S persp) R( v. The symbolic definition is 



w(Spersp) u , v . = : u, vecls'pnt R( . co\\ m l(u u v) . S e 1 * 1 . u S'(;-) . v = S ; (-;) : 



(gV) : melinR, . S ; (AA') . A ^ A'. A, A'em . D,,,, A , A ,. V em Df 



*20'32. Definition. The symbol [AB] persp, [A'B'] denotes that A, B, A', B' are 

 points, and that the figure formed by A and B is in perspective with the figure 

 formed by A' and B', and that the one-one correspondence of the perspective is of 

 A to A' and of B to B'. Also [ABC] persp R( [A'B'C'] has a similar meaning, and so 

 on. In symbols, 



[AB] P ersp K( [A'B'] . = . (gS) . (I'A u I'B) (S persp) Ht (i'A' u i'B') . S ; (AA') . S ; (BB') Df 



[ABC] perepH, [A'B'C'] . = . (gS) . (i'A u i'B u i'C) (S persp) H( (i'A' u i'B' u i'C') . 



S ; (AA').S ; (BB').S : (CC') Df 



*20'33. Definition. The symbol Mpersp R( v denotes that there exists a one-one 

 relation S such that, at the instant t, u is in perspective with v and S is the requisite 

 one-one correspondence. In symbols, 



u persp Rt v . = . (gS) . u (S persp) H( v Df 



*20'41. Definition. Two objective reals, a and c, are called cogredient at an 

 instant t when (1) if u, v, iv are three interpoints on a, and u', v', it/ are three 

 interpoints on c, and the dominant points u st , v w , w Rt are a trio of points in 



