affine geometry
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Encyclopedic overview
In affine geometry, one uses Playfair's axiom to find the line through C1 and parallel to B1B2, and to find the line through B2 and parallel to B1C1: their intersection C2 is the result of the indicated translation.
Three-dimensional
Excerpted from Wikipedia’s “affine geometry” article, available under the CC BY-SA 4.0 licence.