What is Geometry? The Formal Side
We have seen a number of types of argument used in geometry: algebraic, differential geometric, projective and, especially, axiomatic arguments. An interesting paper published by the American historian and philosopher of mathematics Ernest Nagel, in 1939, made the provocative suggestion that the principle of duality in plane projective geometry was an important stimulus to thinking of geometry in a purely logical way, independent of any appeal to intuition .
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