... condition, known as the triangle in-equality, generalizes the principle of plane ge-ometry that the length of any side of a triangleis not longer than the sum of the lengths of the other two sides.divisionalgorithm ... by the radius of the sphere in a direction normal to(x,y,z)] to the area of the region on the sur-face around (x,y,z), as these two areas shrinkto their respective points. Riemann’s concep-tion ... meets the half-line OP. Let OPbe the half-line with direction opposite to that ofOP, and l the supporting line l(P). Then the distance between the parallel lines l and l is the breadth...