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  2. Line (geometry) - Wikipedia

    en.wikipedia.org/wiki/Line_(geometry)

    Euclid's Elements defines a straight line as a "breadthless length" that "lies evenly with respect to the points on itself", and introduced several postulates as basic unprovable properties on which the rest of geometry was established. Euclidean line and Euclidean geometry are terms introduced to avoid confusion with generalizations introduced ...

  3. Arrangement of lines - Wikipedia

    en.wikipedia.org/wiki/Arrangement_of_lines

    A simplicial line arrangement (left) and a simple line arrangement (right). In geometry, an arrangement of lines is the subdivision of the Euclidean plane formed by a finite set of lines. An arrangement consists of bounded and unbounded convex polygons , the cells of the arrangement, line segments and rays , the edges of the arrangement, and ...

  4. Secant line - Wikipedia

    en.wikipedia.org/wiki/Secant_line

    Common lines and line segments on a circle, including a secant. A straight line can intersect a circle at zero, one, or two points. A line with intersections at two points is called a secant line, at one point a tangent line and at no points an exterior line. A chord is the line segment that joins two distinct points of a circle. A chord is ...

  5. Foundations of geometry - Wikipedia

    en.wikipedia.org/wiki/Foundations_of_geometry

    Thus, a line segment AB defined as the points A and B and all the points between A and B in absolute geometry, needs to be reformulated. A line segment in this new geometry is determined by three collinear points A, B and C and consists of those three points and all the points not separated from B by A and C. There are further consequences.

  6. Parallel (geometry) - Wikipedia

    en.wikipedia.org/wiki/Parallel_(geometry)

    Line a is a great circle, the equivalent of a straight line in spherical geometry. Line c is equidistant to line a but is not a great circle. It is a parallel of latitude. Line b is another geodesic which intersects a in two antipodal points. They share two common perpendiculars (one shown in blue).

  7. Glossary of classical algebraic geometry - Wikipedia

    en.wikipedia.org/wiki/Glossary_of_classical...

    The terminology of algebraic geometry changed drastically during the twentieth century, with the introduction of the general methods, initiated by David Hilbert and the Italian school of algebraic geometry in the beginning of the century, and later formalized by André Weil, Jean-Pierre Serre and Alexander Grothendieck.

  8. Incidence geometry - Wikipedia

    en.wikipedia.org/wiki/Incidence_geometry

    Intuitively, a point and line are in this relation if and only if the point is on the line. Given a point B and a line m which do not form a flag, that is, the point is not on the line, the pair (B, m) is called an anti-flag.

  9. Aristotle's axiom - Wikipedia

    en.wikipedia.org/wiki/Aristotle's_axiom

    Aristotle's axiom asserts that a line PQ exists which is parallel to AB but greater in length. Note that: 1) the line AB does not need to intersect OY or OX; 2) P and Q do not need to lie on the lines OY and OX, but their rays (i.e. the infinite continuation of these lines).

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