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  2. Casey's theorem - Wikipedia

    en.wikipedia.org/wiki/Casey's_theorem

    Casey's theorem and its converse can be used to prove a variety of statements in Euclidean geometry. For example, the shortest known proof [ 1 ] : 411 of Feuerbach's theorem uses the converse theorem.

  3. On the Fourfold Root of the Principle of Sufficient Reason

    en.wikipedia.org/wiki/On_the_Fourfold_Root_of...

    The first makes arithmetic possible, and is presupposed for all other forms of the principle of sufficient reason; the other makes geometry possible. Time is one dimensional and purely successive; each moment determines the following moment; in space, any position is determined only in its relations to all other positions [fixed baselines] in a ...

  4. List of theorems - Wikipedia

    en.wikipedia.org/wiki/List_of_theorems

    Full employment theorem (theoretical computer science) Fulton–Hansen connectedness theorem (algebraic geometry) Fundamental theorem of algebra (complex analysis) Fundamental theorem of arbitrage-free pricing (financial mathematics) Fundamental theorem of arithmetic (number theory) Fundamental theorem of calculus

  5. Foundations of geometry - Wikipedia

    en.wikipedia.org/wiki/Foundations_of_geometry

    Based on ancient Greek methods, an axiomatic system is a formal description of a way to establish the mathematical truth that flows from a fixed set of assumptions. Although applicable to any area of mathematics, geometry is the branch of elementary mathematics in which this method has most extensively been successfully applied.

  6. Hilbert's program - Wikipedia

    en.wikipedia.org/wiki/Hilbert's_program

    The main goal of Hilbert's program was to provide secure foundations for all mathematics. In particular, this should include: A formulation of all mathematics; in other words all mathematical statements should be written in a precise formal language, and manipulated according to well defined rules.

  7. Menelaus's theorem - Wikipedia

    en.wikipedia.org/wiki/Menelaus's_theorem

    In Euclidean geometry, Menelaus's theorem, named for Menelaus of Alexandria, is a proposition about triangles in plane geometry. Suppose we have a triangle ABC, and a transversal line that crosses BC, AC, AB at points D, E, F respectively, with D, E, F distinct from A, B, C. A weak version of the theorem states that

  8. Hilbert's axioms - Wikipedia

    en.wikipedia.org/wiki/Hilbert's_axioms

    To a system of points, straight lines, and planes, it is impossible to add other elements in such a manner that the system thus generalized shall form a new geometry obeying all of the five groups of axioms. In other words, the elements of geometry form a system which is not susceptible of extension, if we regard the five groups of axioms as valid.

  9. Pappus's hexagon theorem - Wikipedia

    en.wikipedia.org/wiki/Pappus's_hexagon_theorem

    If the affine form of the statement can be proven, then the projective form of Pappus's theorem is proven, as the extension of a pappian plane to a projective plane is unique. Because of the parallelity in an affine plane one has to distinct two cases: g ∦ h {\displaystyle g\not \parallel h} and g ∥ h {\displaystyle g\parallel h} .