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collinearity
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Pappus's projective theoremPappus of Alexandria (fl. ad 320) proved that the three points (x, y, z) formed by intersecting the six lines that connect two sets of three collinear points (A, B, C; and D, E, F) are also collinear. Pascal's projective theoremThe 17th-century French mathematician Blaise Pascal proved that the three points (x, y, z) formed by intersecting the six lines that connect any six distinct points (A, B, C, D, E, F) on a circle are collinear.
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Pappus's projective theoremPappus of Alexandria (fl. ad 320) proved that the three points (x, y, z) formed by intersecting the six lines that connect two sets of three collinear points (A, B, C; and D, E, F) are also collinear.
Pappus's projective theorem

Pappus of Alexandria (fl. ad 320) proved that the three points (x, y, z) formed by intersecting the six lines that connect two sets of three collinear points (A, B, C; and D, E, F) are also collinear.

In geometry, collinear describes points that lie on the same straight line. This is a fundamental concept in understanding geometric relationships.1

In contrast, noncollinear describes points that do not lie on the same straight line.2

The concept of collinearity is also relevant in projective geometry, where it is considered an invariant property under projection mappings. This means that if points are collinear in one plane, their projections will also be collinear.3

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3 Britannica Sources
  1. collinear
  2. projective geometry
  3. noncollinear

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