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The intercept theorem, also known as Thales's theorem, basic proportionality theorem or side splitter theorem, is an important theorem in elementary geometry about the ratios of various line segments that are created if two rays with a common starting point are intercepted by a pair of parallels.
Figure 1: Schematic of an electrical circuit illustrating current division. Notation R T refers to the total resistance of the circuit to the right of resistor R X.. In electronics, a current divider is a simple linear circuit that produces an output current (I X) that is a fraction of its input current (I T).
Ax–Grothendieck theorem (model theory) Barwise compactness theorem (mathematical logic) Borel determinacy theorem ; Büchi-Elgot-Trakhtenbrot theorem (mathematical logic) Cantor–Bernstein–Schröder theorem (set theory, cardinal numbers) Cantor's theorem (set theory, Cantor's diagonal argument) Church–Rosser theorem (lambda calculus)
When modelling relations between two different classes of objects, bipartite graphs very often arise naturally. For instance, a graph of football players and clubs, with an edge between a player and a club if the player has played for that club, is a natural example of an affiliation network, a type of bipartite graph used in social network analysis.
The proof was later simplified by Jost Eschenburg and Ernst Heintze. In 1936, Stefan Cohn-Vossen had originally formulated and proved the theorem in the case of two-dimensional manifolds, and Victor Toponogov had extended Cohn-Vossen's work to higher dimensions, under the special condition of nonnegative sectional curvature. [2]
For example, a particularly tricky example of this is the analytic cut rule, used widely in the tableau method, which is a special case of the cut rule where the cut formula is a subformula of side formulae of the cut rule: a proof that contains an analytic cut is by virtue of that rule not analytic.
For example, Elliott didn't put forth board members, as it did in its campaign against airline Southwest . JPMorgan industrials analyst Stephen Tusa estimates Honeywell could be worth $330 a share ...
The midpoint theorem generalizes to the intercept theorem, where rather than using midpoints, both sides are partitioned in the same ratio. [1] [2] The converse of the theorem is true as well. That is if a line is drawn through the midpoint of triangle side parallel to another triangle side then the line will bisect the third side of the triangle.