Affine geometry 


in
as the notion of
affine geometry can be developed in two ways that are essentially equivalent.^{[3]}
in
affine geometry can also be developed on the basis of
in more concrete terms, this amounts to having an operation that associates to any ordered pair of points a vector and another operation that allows translation of a point by a vector to give another point; these operations are required to satisfy a number of axioms (notably that two successive translations have the effect of translation by the sum vector). by choosing any point as "origin", the points are in
although this article only discusses


 
by name


by period


In
As the notion of
Affine geometry can be developed in two ways that are essentially equivalent.^{[3]}
In
Affine geometry can also be developed on the basis of
In more concrete terms, this amounts to having an operation that associates to any ordered pair of points a vector and another operation that allows translation of a point by a vector to give another point; these operations are required to satisfy a number of axioms (notably that two successive translations have the effect of translation by the sum vector). By choosing any point as "origin", the points are in
Although this article only discusses