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  2. Newton's theorem (quadrilateral) - Wikipedia

    en.wikipedia.org/wiki/Newton's_theorem...

    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 ...

  3. Complete quadrangle - Wikipedia

    en.wikipedia.org/wiki/Complete_quadrangle

    A complete quadrangle (at left) and a complete quadrilateral (at right).. In mathematics, specifically in incidence geometry and especially in projective geometry, a complete quadrangle is a system of geometric objects consisting of any four points in a plane, no three of which are on a common line, and of the six lines connecting the six pairs of points.

  4. Newton–Gauss line - Wikipedia

    en.wikipedia.org/wiki/Newton–Gauss_line

    The two complete quadrilaterals have a shared diagonal, EF. N lies on the Newton–Gauss line of both quadrilaterals. N is equidistant from G and H, since it is the circumcenter of the cyclic quadrilateral EGFH. If triangles GMP, HMQ are congruent, and it will follow that M lies on the perpendicular bisector of the line HG.

  5. Brahmagupta theorem - Wikipedia

    en.wikipedia.org/wiki/Brahmagupta_theorem

    In geometry, Brahmagupta's theorem states that if a cyclic quadrilateral is orthodiagonal (that is, has perpendicular diagonals), then the perpendicular to a side from the point of intersection of the diagonals always bisects the opposite side. [1] It is named after the Indian mathematician Brahmagupta (598-668). [2]

  6. Mathematics - Wikipedia

    en.wikipedia.org/wiki/Mathematics

    The basic statements are not subject to proof because they are self-evident , or are part of the definition of the subject of study . This principle, foundational for all mathematics, was first elaborated for geometry, and was systematized by Euclid around 300 BC in his book Elements. [21] [22]

  7. Lattice multiplication - Wikipedia

    en.wikipedia.org/wiki/Lattice_multiplication

    A grid is drawn up, and each cell is split diagonally. The two multiplicands of the product to be calculated are written along the top and right side of the lattice, respectively, with one digit per column across the top for the first multiplicand (the number written left to right), and one digit per row down the right side for the second multiplicand (the number written top-down).

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