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How to demonstrate AB + AC = AD With physics !

Physics is driving the convergence between geometry and algebra.\r\nPrototypes of a first "dynamic pedagogical machine", simulating an original physical experiment imagined by the professor who experimentally demonstrates the RELATION DE CHASLES and the LAW OF ADDITION OF VECTORS, systematically posed, usually but abusively, as an artificial Axiom ad hoc. Very arbitrarily parachuted by the textbooks of mathematics, this Axiom meduses generations of students, understandably intimidated.