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Through any point in the plane, there is at most one straight line parallel to a given straight line. This axiom is equivalent to the parallel postulate.

If a line intersects one of two parallel lines, both of which are coplanar with the original line, then it must intersect the other also. This axiom is equivalent to the ...

The locus of a point which is derived from a fixed point Q by continuous parallel displacement.

A projection of a figure by parallel rays. In such a projection, tangencies are preserved. Parallel lines project to parallel lines. The ratio of lengths of parallel segments ...

Two vectors u and v are parallel if their cross product is zero, i.e., uxv=0.

A parallel of a surface of revolution is the intersection of the surface with a plane orthogonal to the axis of revolution.

The sum of the angles of a triangle is two right angles. This postulate is equivalent to the parallel postulate.

The point or points to which the extensions of parallel lines appear to converge in a perspective drawing.

Geometry which depends only on the first four of Euclid's postulates and not on the parallel postulate. Euclid himself used only the first four postulates for the first 28 ...

A finite geometry is a geometry with a finite number of points. When confined to a plane, all finite geometries are either projective plane geometries (with no parallel ...