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 second lines, and the latter pair the third and fourth lines, if the angle made by the first and third lines be equal to the angle made by the second and fourth, and contrariwise the angle made by the first and fourth equal to the angle made by the second and third; then each pair of lines are antiparallels with respect to each other, viz. the first and second, and the third and fourth. So, if AB and AC be any two lines, and FC and FE be two others, cutting them so,
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. It is a property of these lines, that each pair cuts the other into proportional segments, taking them alternately,
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