# 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.

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Entry taken from A Mathematical and Philosophical Dictionary, by Charles Hutton, 1796.

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