Let be an affine plane. Let be the set of all parallel classes of . We define a new incidence structure by

Then is a projective plane called the projective closure of . The new line is the so called line at infinity of . Obviously, the affine derivative on the line at infinity equals the original affine plane .

**Lemma.** Each
isomorphism
extends to a unique isomorphism
.

**Lemma.** If (o,e,U,V) is a
coordinate frame of
,
then (o,e,U,V) is a quadrangle in
and the corresponding ternary fields of
and
,
respectivly, are equal.

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