Author Archives: rodrigoloaiza

Is a point a part of a line? The question touches on the fundations of geometry. To be able to answer it, one should probably first clarify the notions that are involved in the question. According to the present day understanding, the notions of point and line are left undefined in geometry. We just get used to them by making derivations from the axioms, and then derivations from the derivations, and so on. Lines, if intersect, define a point, while two points define a line. It often helps to have a visual representation of either, but, such a visualization may prove treacherous. For example, in projective geometry, due to the Principle of Duality, the notions of point and line are entirely intercheangiable. Desargues’ Theorem supplies a clearest example of that duality.