On Mathematical Concepts of the Material World

4-concurrence 4-maximal 4-point 4-prime A. N. WHITEHEAD axioms cardinal number class of objective class of points classical concept cm'u cm'v cogredient point collinear common 4-subregion common member Concept IV Concept IVA concurrent lines contained coplanar copunctual corpuscle defined definition in symbols Definition.-A class denotes the class Df cf Df Df Df Df Note dimu distinct points dominant points entities essential relation Euclidean geometry exist extraneous relations Hence cf homaloty hypothesis identical II.-XIII II.-XIV instant intersecting intpnt Hp linear objective reals logical sum material world monistic non-cogredient point nonsecant null class p-axial p-dimension p-equivalent p-plane particles persPRt plane point of Type possesses projective geometry Proof Proof.-Cf Proposition.-Assuming II.-VI Proposition.-If propositions punctual associate punctual line R(abc R(abcdt Rin BCDt self-p-concurrence statement straight lines subclass symbolic definition theory of dimensions theory of interpoints three interpoints triadic relation unit class XII Hp