Poncelet, Chasles, and the Early Years of Projective Geometry
To hear Poncelet tell it, what he invented was a uniform method of tackling problems in geometry, brought about by the use of ideal and imaginary elements, that reduced calculation to a minimum (and thereby made geometry easier to understand). To hear Cauchy tell it, Poncelet’s methods were at best heuristic, and liable to mislead, and insofar as they led to correct conclusions it would be safer to use algebra (in particular, complex numbers) at least to validate the use of ideal methods if not to replace them entirely.
KeywordsProjective Space Projective Plane Projective Geometry Projective Line Projective Transformation
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