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He also wrote an extremely important text on geometry showing the power of synthetic geometry. In his text Traité de géométrie in 1852 Chasles discusses cross ratio, pencils and involutions, all notions which he introduced. In fact Möbius independently introduced the cross ratio. A second text, Traité des sections coniques (1865), applied these techniques to conic sections. The principle of duality occurs throughout his work which was carried on by Steiner.
Chasles was the victim of a celebrated fraud paying the equivalent of 20,000 pounds for various letters from famous men of science and others which turned out to be forged.
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Tell me about Chasles's work on abstract linear spaces
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