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Unformatted text preview: Brianchon ( 1810) A student of Monge. His theorem: If 6 tangents to conic form a circumscribing hexagon, the 3 lines connect- ing opposite vertices are concurrent. Dual of Pascals Theorem. Poncelet A student of Monge. First to view projective geometry as a new branch of mathematics. Captured in Russia in Napoleonic wars. Did work in prison. Principle of Duality Proposed and used by (but not really proved by) Desargues. Content: The words line and point can be interchanged in the plane. The words plane and point can be interchanged in 3-dimensional space. The language needs to be smoothed out. E.g., interchange lie on and pass through. Principle of Continuity More ambiguous and controversial than the Principle of Duality. Poncelet: Let us consider an arbitrary figure in a general position and indeterminate in some way, taken from all those that one can consider without breaking the laws, the conditions, the relationships which exist between the diverse parts of the sys-...
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This note was uploaded on 12/29/2011 for the course MATH 378 taught by Professor Wen during the Fall '10 term at SUNY Stony Brook.
- Fall '10