...t (Brianchon's point). This theorem is dual to the [[Pascal theorem|Pascal theorem]], and was demonstrated by Ch.J. Brianchon in 1806.
445 bytes (68 words) - 17:29, 7 February 2011
..._1$. This is sometimes called Pappus' theorem; it is a special case of the theorem of Pascal in the theory of conic sections (namely, when the conic degenerat
...constructing a non-Pascalean geometry follows from the fact that Pascal's theorem is not a consequence of the axioms of incidence, order and parallelism when
2 KB (344 words) - 17:16, 31 March 2018
...ame time Pappus' axiom is a degenerate case of the [[Pascal theorem|Pascal theorem]]. The axiom was proposed by Pappus (3rd century).
1,003 bytes (158 words) - 12:52, 10 August 2014
...continuity, and that without the axiom of continuity in this case Pascal's theorem cannot be proved.
...mption]] with the use of spatial axioms. However, in the proof of Pascal's theorem the particular role of Archimedes' axiom of continuity in infinite planes m
5 KB (796 words) - 21:08, 11 April 2014
...is the [[Brianchon theorem|Brianchon theorem]]. B. Pascal established his theorem in 1639. The special case of a conic degenerating to a pair of lines was kn
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his time. Pascal's father, Étienne, had moved to Paris in 1631 to
Blaise Pascal's prime concern was the equitable division of stakes, the
7 KB (1,004 words) - 19:40, 8 March 2024
enunciating Pascal's Theorem, that the opposite sides of a hexagon inscribed
itself which was published in 1679, is the basis of Pascal's reputation in
15 KB (2,384 words) - 06:52, 6 March 2024
The duality principle in mathematical logic is a theorem on the acceptability of mutual substitution (in a certain sense) of logical
The following theorem is closely connected with the duality principle: If $ F ^ { * } ( A _ {1}
10 KB (1,506 words) - 19:36, 5 June 2020
...dual (see [[Brianchon theorem|Brianchon theorem]]; [[Pascal theorem|Pascal theorem]]). The two other realizations of a configuration $ ( 9 _ {3} ) $,
do not express any general geometrical theorem, and only eight of them can be realized in the real projective plane, but f
27 KB (3,830 words) - 09:57, 26 March 2023
theorem of algebra, an essential contribution to the equations for
11 KB (1,657 words) - 20:48, 21 December 2023
Criticality Theorem of his friend [[Bienaymé, Irenée-Jules|Bienaymé]] in the theory of
13 KB (1,947 words) - 18:43, 4 March 2024
...e foundation of a whole series of results along these lines is the P. Hall theorem on the existence of a system of distinct representatives (a transversal) of
A corollary of Hall's theorem is the theorem on the existence of Latin squares, stating that any Latin rectangle of orde
28 KB (4,167 words) - 17:45, 4 June 2020