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If ABB^' and AC^'C are straight lines with BC and B^'C^' intersecting at D and AB+BD=AC^'+C^'D, then AB^'+B^'D=AC+CD. The origin and some history of this theorem are ...

Mann's theorem is a theorem widely circulated as the "alpha-beta conjecture" that was subsequently proven by Mann (1942). It states that if A and B are sets of integers each ...

The hinge theorem says that if two triangles DeltaABC and DeltaA^'B^'C^' have congruent sides AB=A^'B^' and AC=A^'C^' and ∠A>∠A^', then BC>B^'C^'.

Any motion of a rigid body in space at every instant is a screw motion. This theorem was proved by Mozzi and Cauchy.

Draw three circles in the plane, none of which lies completely inside another, and the common external tangent lines for each pair. Then points of intersection of the three ...

Any triangle that has two equal angle bisectors (each measured from a polygon vertex to the opposite sides) is an isosceles triangle. This theorem is also called the ...

If a continuous function defined on an interval is sometimes positive and sometimes negative, it must be 0 at some point. Bolzano (1817) proved the theorem (which effectively ...

A geometric theorem related to the pentagram and also called the Pratt-kasapi theorem. It states ...

A theorem, also called a unicity theorem, stating the uniqueness of a mathematical object, which usually means that there is only one object fulfilling given properties, or ...

A theorem which asserts that if a sequence or function behaves regularly, then some average of it behaves regularly. For example, A(x)∼x implies A_1(x)=int_0^xA(t)dt∼1/2x^2 ...