According to Gerhardt, the process of substitution consisted of the union of two residues to fo- m a unitary whole; these residues, previously termed " compound radicals," are atomic complexes which remain over from the interaction of two compounds.
Under the general heading "Geometry" occur the subheadings "Foundations," with the topics principles of geometry, non-Euclidean geometries, hyperspace, methods of analytical geometry; "Elementary Geometry," with the topics planimetry, stereometry, trigonometry, descriptive geometry; "Geometry of Conics and Quadrics," with the implied topics; "Algebraic Curves and Surfaces of Degree higher than the Second," with the implied topics; "Transformations and General Methods for Algebraic Configurations," with the topics collineation, duality, transformations, correspondence, groups of points on algebraic curves and surfaces, genus of curves and surfaces, enumerative geometry, connexes, complexes, congruences, higher elements in space, algebraic configurations in hyperspace; "Infinitesimal Geometry: applications of Differential and Integral Calculus to Geometry," with the topics kinematic geometry, curvature, rectification and quadrature, special transcendental curves and surfaces; "Differential Geometry: applications of Differential Equations to Geometry," with the topics curves on surfaces, minimal surfaces, surfaces determined by differential properties, conformal and other representation of surfaces on others, deformation of surfaces, orthogonal and isothermic surfaces.
The majority of alloys, when examined thus, prove to be complexes of two or more materials, and the patterns showing the distribution of these materials throughout the alloy are of a most varied character.
He holds, like Hume, that nothing is real except our sensations and complexes of sensory elements; that the ego is not a definite, unalterable, sharply bounded unity, but its continuity alone is important; and that we know no real causes at all, much less real causes of our sensations; or, as he expresses it, bodies do not produce sensations, but complexes of sensations form bodies.
In short, sensations are elements and bodies complexes of these elements.
As with Kant against Hume, so with Wundt against Mach and Avenarius, the world we know will contain something more than mere complexes of sensations, more than pure experience: with Wundt it will be a world of real causes and some substances, constituted partly by experience and partly by logical thinking, or active inner will.
Here you would expect him to stop, as the German Neo-Kantism of Lange stops, with the consistent conclusion that all we know of Nature from such data is these complexes of sensation-elements, or phenomena in the Kantian meaning.
Lines and complexes thereof are sufficiently treated as rotors and motors, but points and planes cannot be so treated.
Plucker himself worked out the theory of complexes of the first and second order, introducing in his investigation of the latter the famous complex surfaces of which he caused those models to be constructed which are now so well known to the student of the higher mathematics.
His philosophy, therefore, is that all known things are sensations and complexes of sensory elements, supplemented by an economy of thinking which cannot carry us beyond ideas to real things, or beyond relations of dependency to real causes.
They express the main complexes of land with their dependencies in well-chosen terms; for instance the " Neotropical region " stands short for South and Central America with the Antilles.