‎"CLEBSCH, A.‎
‎Ueber symbolische Darstellung algebraischer Formen. - [SEMINAL CONTRIBUTION TO THE SYMBOLIC METHOD IN INVARIANT THEORY]‎

‎Berlin, G. Reimer, 1861. 4to. As extracted from ""Journal für die reine und angewandte Mathematik, 59. Band, 1861"". Without backstrip. Fine and clean. [Clebsch:] Pp. 1-62.‎

Reference : 48050

‎First printing of Clebsch's early and founding paper on the symbolic method in invariant theory. The Symbolic method is based on treating the form as if it were a power of a degree one form, which corresponds to embedding a symmetric power of a vector space into the symmetric elements of a tensor product of copies of it.""Clebsch completed the symbolic calculus for forms and invariants created by Aronhold, and henceforth one spoke of the Clebsch-Aronhold symbolic notation. Clebsch’s own contributions in this field of algebraic geometry include the following. With the help of suitable eliminations he determined a surface of order 11n - 24 intersecting a given surface of order n in points where there is a tangent that touches the surface at more than three coinciding points. For a given cubic surface he calculated the tenth-degree equation on the resolution of which the determination of the Sylvester pentahedron of that surface depends. For a plane quartic curve Clebsch found a remarkable invariant that, when it vanishes, makes it possible to write the curve equation as a sum of five fourth-degree powers. At the end of his life Clebsch inaugurated the notion of a ""connex,"" a geometrical object in the plane obtained by setting a form containing both point and line coordinates equal to zero."" (DSB)‎