Principles of Geometry, Volume 5

A₁ adjoint curves aggregate algebraic arbitrary arise assume boundary branch branch place C₁ C₂ called canonical curve circuit coefficients coincident columns common complete intersection conic consider constants contain coordinates corresponding cubic curve cubic surface curve of order defined definite denote determined dimensions double points drawn equal equation exists expression fact follows formula freedom fundamental further genus give given hence homogeneous independent infinite infinity integral linear series linearly lying meets multiple points namely obtained ordinary original osculating plane parameter particular pass places plane curve poles polynomial positive possible primals prime projection proof proved quadric surface quintic curve rational function regard remaining remarked represented respectively result rows shewn simple single space suppose surfaces of order taken tangent line theorem theory values vanishes variable zero