# ANTIPARALLELS

, in *Geometry,* are those lines
which make equal angles with two other lines, but contrary
ways; that is, calling the former pair the first and
2d lines, and the latter pair the 3d and 4th lines, if the
angle made by the 1st and 3d liues be equal to the
angle made by the 2d and 4th, and contrariwise the
angle made by the 1st and 4th equal to the angle made
by the 2d and 3d; then each pair of lines are antiparallels
with respect to each other, viz, the first and
2d, and the 3d and 4th. So, if AB and AC be any
two lines, and FC and FE be two others, cutting themso,
that the angle B is equal to the angle E,
and the angle C is equal to the angle D;
then BC and DE are antiparallels with respect to AB
and AC; also these latter are antiparallels with regard
to the two former.—See also Subcontrary.

It is a property of these lines, that each pair cuts the other into proportional segments, taking them alternately, viz AB : AC :: AE : AD :: DB : EC, and FE : FC :: FB : FD :: DE : BC.