11. Although, associated ruled surfaces were classical objects. 12. The hyperbolic paraboloid is a doubly ruled surface : it contains two families of mutually skew lines. 13. Edge made a " systematic classification of the quintic and sextic ruled surfaces of three-dimensional projective space ." 14. Edge s dissertation extended Luigi Cremona s 1868 delineation of the quadric ruled surfaces in projective 3-space "'RP "'3. 15. When the idea of introducing vineyards out where Spanish daggers and cactus rule surfaced , there were plenty of doubters. 16. A Clifford surface is thus a ruled surface since every point is on two lines, each contained in the surface. 17. Out of this work came another of Wren's important mathematical results, namely that the hyperboloid of revolution is a ruled surface . 18. In his later designs, ruled surfaces are prominent in the nave's vaults and windows and the surfaces of the Passion fa�ade. 19. Rational surfaces and more generally ruled surfaces ( these include quadrics and cubic surfaces in projective 3-space ) have the simplest geometry. 20. In the exceptional cases the intersection of the quadrics through the canonical curve is respectively a ruled surface and a Veronese surface.
