chapter iv syntheticprojective geometry the purpose of this chapter is to begin the study of projective spaces mainly from the synthetic point of view but with considerable attention to coordinate ...
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...Chapter iv syntheticprojective geometry the purpose of this is to begin study projective spaces mainly from synthetic point view but with considerable attention coordinate axioms for basic incidence properties are expressible as follows denition a geometrical space s d if following hold p every line contains at least three points and q subspaces then in particular strong version regularity condition g introduced section ii above were established fpn n theorems iii respectively it useful assume several reasons example lines euclidean have innitely many implies high degree on structure that not present general compare exercise below theorem connection note satises exactly two elementary simple consequence denitions subspace respect called or one also says plane l m distinct consists single planes these follow examples weconclude another important result property equivalent provided subset four no which collinear proof suppose holds let be x y z noncollinear xy xz yz contained w third v f...