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2. Intercept theorem - Wikipedia

   en.wikipedia.org/wiki/Intercept_theorem

   In particular it is important to assure that for two given line segments, a new line segment can be constructed, such that its length equals the product of lengths of the other two. Similarly one needs to be able to construct, for a line segment of length , a new line segment of length . The intercept theorem can be used to show that for both ...

3. Ceva's theorem - Wikipedia

   en.wikipedia.org/wiki/Ceva's_theorem

   Ceva's theorem, case 1: the three lines are concurrent at a point O inside ABC Ceva's theorem, case 2: the three lines are concurrent at a point O outside ABC. In Euclidean geometry, Ceva's theorem is a theorem about triangles.

4. Line segment - Wikipedia

   en.wikipedia.org/wiki/Line_segment

   A closed line segment includes both endpoints, while an open line segment excludes both endpoints; a half-open line segment includes exactly one of the endpoints. In geometry , a line segment is often denoted using an overline ( vinculum ) above the symbols for the two endpoints, such as in AB .

5. List of mathematical proofs - Wikipedia

   en.wikipedia.org/wiki/List_of_mathematical_proofs

   Fermat's little theorem and some proofs; Gödel's completeness theorem and its original proof; Mathematical induction and a proof; Proof that 0.999... equals 1; Proof that 22/7 exceeds π; Proof that e is irrational; Proof that π is irrational; Proof that the sum of the reciprocals of the primes diverges

6. Quadrature of the Parabola - Wikipedia

   en.wikipedia.org/wiki/Quadrature_of_the_Parabola

   A parabolic segment is the region bounded by a parabola and line. To find the area of a parabolic segment, Archimedes considers a certain inscribed triangle. The base of this triangle is the given chord of the parabola, and the third vertex is the point on the parabola such that the tangent to the parabola at that point is parallel to the chord.

7. Spherical segment - Wikipedia

   en.wikipedia.org/wiki/Spherical_segment

   In geometry, a spherical segment is the solid defined by cutting a sphere or a ball with a pair of parallel planes. It can be thought of as a spherical cap with the top truncated, and so it corresponds to a spherical frustum. The surface of the spherical segment (excluding the bases) is called spherical zone. Geometric parameters for spherical ...