The Quarterly Journal of Pure and Applied Mathematics

analytically coincident axis base points binary birational transformation calculation coefficients common perpendicular congruent convergent corresponding covariants Crelle's Journal cubic curve cusp cyclic d/dx denote double point E₁ equating coefficients Eulerian numbers exist finite formula function fundamental branch G. H. HARDY given gives Hence hexahedron hypertacnode integral intersections involution last two figures linear linearly independent Math modp modulus monotonic solutions multiple point nodes non-oscillatory obtain odd and prime ordinary branch oscillating solutions oscillatory p-ic P₁ P₂ pairs of opposite paper parallelopiped plane protomorphs proved quadratic quadratic transformation quartic rational functions relation residues sides being positive singularity spheroid ß³ steady motion suppose tacnode tangent ternary theorem transformation triple point uneven values whence zero