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Part I The symbolism of conditions
S1 The number of constants of a structure
S2 The description of the conditions
S3 The dimension of a condition and the level of a system
S4 The principle of conservation of numbers
S5 The representation of the numbers of con\discretionary- ditions by the symbols of conditions, and computations with these symbols
S6 The equations between the elementary conditions of each of the three principal elements
Part II The incidence formulae
S7 The incidence formulae for points and lines
S8 Applications of incidence formulae (I), (II) and (III) to the incidence of a tangent with its point of contact
S9 Further examples for the incidence formulae (I), (II), (III)
S10 The remaining incidence formulae
S11 Examples for the incidence formulae (IV) to (XIV)
S12 Application of the incidence formulae to systems of principal elements incident with principal elements
Part III The coincidence formulae
S13 The coincidence formulae of a pair of points and Bezout's theorems
S14 Application of the coincidence formulae of \S13 to determine the numbers concerning contacts of planar curves and surfaces
S15 The pair of lines and its coincidence conditions
S16 Application of the coincidence formulae for pairs of lines to the two ruled families lying on a surface of degree two [23]
S17 The pairs of distinct principal elements and the coincidence conditions
S18 Derivation of the Cayley-Brill correspondence formula from the general coincidence formulae for pairs of points
Part IV The computations of numbers via degeneracies
S19 Numbers for structures consisting of finitely many principal elements
S20 Numbers for conic sections [30]
S21 The reduction of Chasles and Zeuthen [32]
S22 Numbers for surfaces of degree two [33]
S23 Numbers for cubic planar curves with cusp [34]
S24 Numbers for cubic planar curves with double point [34]
S25 Numbers for cubic space curves [35]
S26 Numbers for planar curves of order four in a fixed plane
S27 Numbers for the linear congruence [40]
S28 Numbers for structures consisting of two lines whose points and planes are projective [41]
S29 Numbers for structures consisting of a pencil of planes and a pencil of lines projective to it [41]
S30 Numbers for the structure consisting of two projective pencils of lines [41]
S31 Numbers for structure consisting of two collinear bundles [42]
S32 Numbers for structures consisting of two correlative bundles [42]
Part V The multiple coincidences
S33 Coincidence of intersection points of a line and a surface [43]
S34 The coincidence of multiple points on a line [48]
S35 The coincidence of multiple lines of a pencil of lines [48]
S36 Singularities of the generic line complex [49]
Part VI The theory of characteristics
S37 The problem of characteristics for an arbitrary structure Gamma
S38 The problem of characteristics for the conic section [51]
S39 Derivation and application of the characteristic formulae for the structure consisting of a line and a point on it [52]
S40 Derivation and application of the characteristic formula for the pencil of lines [52]
S41 Derivation and application of the characteristic formula for the structure consisting of a line, a point on that line, and a plane through that line [52]
S42 The theory of characteristics of the structure consisting of a line and n points on it [53]
S43 Computation of the numbers for multiple secants of the intersection curve of two surfaces
S44 Theory of characteristics of the structure consisting of a pencil of lines and n lines in it. Application to congruences common to two complexes
Remarks on the literature
Index
Author index
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