Principles of Geometry, Volume 5

adjoint curve aggregate algebraic arbitrary arbitrary points arises assumed boundary branch called circuit closed coefficients coincident columns common complete complete intersection conic consider constants contain Conversely coordinates corresponding cubic curve curve of order defined definite denote depends determined dimensions double points equal equation exists expression fact follows formula freedom fundamental further genus give given Hence homogeneous independent infinite infinities integral intersections involve linear series linearly lying meet multiple points namely neighbourhood obtained original parameter particular pass places plane curve poles polynomial positive possible power series prime projection proved quadric surface quartic quintic curve rational function reduced regarded remaining remarked represented respectively result rows satisfying shewn simple single space suppose surface surfaces of order symbols taken tangent line theorem theory transformation values vanishes variable zero