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  "body": "\n## Summary\n\nA partial linear space is an [[incidence structure|FGKNAFNHA3]] of points and lines with two rules.\nTwo distinct points lie on at most one line, and every line has at least two points.\nIt is the common ground of most point-line geometries: projective and affine planes, [[generalized polygons|PCT2HY9AAZ]] and [[polar spaces|Z7T0V2VAWJ]] are all partial linear spaces.\nWhen any two points lie on exactly one line, it is called a linear space.\n\n## Explanations\n\n### L1 human\n\nIn ordinary geometry, two points determine a line.\nA partial linear space keeps only half of this rule: two points determine at most one line, and some pairs of points may lie on no common line.\nFor example, take the nine points of a $3 \\times 3$ grid and use only the three rows and three columns as lines.\nTwo points in the same row or column share exactly one line, and two points in different rows and columns share none.\n",
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