On the quartic surface

Abstract

Summary1. The projective transformations of F into itself … 1212. The flecnodal curve, and the lines of F … 1223. A geometric characterization of F, and the six different types of F in the real domain … 1234. The τ-points and τ-planes, and a notation for the lines of F … 1245. The incidence conditions for the lines of F … 1256. The tetrads of the first kind … 1267. The tetrads of the second kind … 1268. The pairs of lines of F … 1279. The tetrads of the third kind … 12910. The 16-tangent quadrics of F … 13011. The conics of the first kind … 13112. The conics of the second kind … 13213. No other irreducible conics lie on F … 13314. The tangent planes of F of multiplicity greater than 3 … 13615. On twisted curves, especially cubics and quartics, lying on F … 13816. The T-transformations … 13917. Construction of an infinite discontinuous group of birational transformations of F into itself … 14218. Deduction of an infinity of unicursal curves lying on F … 143