## A treatise on the line complex |

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belong bitangent centre coefficients coincide complex cone complex surface conic conjugate consecutive contains coordinates corresponding lines corresponding points cosingular complexes degree denoted determined directrix double curve double line double points double ratio double ray double tangents dXi dXi Fm+n focal surface follows four points given line hence hyperplane hypersphere Integral surface involution Kummer surface last equation line geometry line joining linear congruences lines of curvature lines which meet null-plane obtain partial differential equation pass pencil of planes plane at infinity plane pencil point of intersection points S2 polar lines pole principal tangent curves quadratic complex quadric quantities quartic surface regulus ruled cubic ruled quartic ruled surface seen similarly singular lines singular points singular surface special complex sphere surface elements tangent linear complexes tetrahedral complex tetrahedron of reference touches twisted cubic vertex zero