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Euler's quadrilateral theorem or Euler's law on quadrilaterals, named after Leonhard Euler (1707–1783), describes a relation between the sides of a convex quadrilateral and its diagonals. It is a generalisation of the parallelogram law which in turn can be seen as generalisation of the Pythagorean theorem .
Pitot's theorem states that, for these quadrilaterals, the two sums of lengths of opposite sides are the same. Both sums of lengths equal the semiperimeter of the quadrilateral. [2] The converse implication is also true: whenever a convex quadrilateral has pairs of opposite sides with the same sums of lengths, it has an inscribed circle ...
Theorems about quadrilaterals and circles (6 P) Pages in category "Theorems about quadrilaterals" The following 11 pages are in this category, out of 11 total.
The theorem is named after the Greek astronomer and mathematician Ptolemy (Claudius Ptolemaeus). [1] Ptolemy used the theorem as an aid to creating his table of chords, a trigonometric table that he applied to astronomy. If the vertices of the cyclic quadrilateral are A, B, C, and D in order, then the theorem states that:
Pages in category "Theorems about quadrilaterals and circles" The following 6 pages are in this category, out of 6 total. This list may not reflect recent changes .
Theorems about quadrilaterals (1 C, 11 P) ... Pages in category "Quadrilaterals" The following 9 pages are in this category, out of 9 total. ... additional terms may ...
Newton's theorem can easily be derived from Anne's theorem considering that in tangential quadrilaterals the combined lengths of opposite sides are equal (Pitot theorem: a + c = b + d). According to Anne's theorem, showing that the combined areas of opposite triangles PAD and PBC and the combined areas of triangles PAB and PCD are equal is ...
Moreover, the area identity of the theorem holds in this case for any inner point of the quadrilateral. The converse of Anne's theorem is true as well, that is for any point on the Newton line which is an inner point of the quadrilateral, the area identity holds.