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Using Clebsch-Aronhold notation, an algebraic curve satisfies xi_1^na_y^n+xi_1^(n-1)xi_2a_y^(n-1)a_x+1/2n(n-1)xi_1^(n-2)xi_2^2a_y^(n-2)a_x^2+... ...

A transformation of an algebraic curve which is of the same type as its inverse. A Jonquière's transformation is always factorable.

If a real algebraic curve has no singularities except nodes and cusps, bitangents, and inflection points, then n+2tau_2^'+iota^'=m+2delta_2^'+kappa^', where n is the order, ...

The Maclaurin-Bézout theorem says that two curves of degree n intersect in n^2 points, so two cubics intersect in nine points. This means that n(n+3)/2 points do not always ...

If each of two nonparallel transversals with nonminimal directions meets a given curve in finite points only, then the ratio of products of the distances from the two sets of ...

Any cubic curve that passes through eight of the nine intersections of two given cubic curves automatically passes through the ninth.

Any irreducible curve may be carried by a factorable Cremona transformation into one with none but ordinary singular points.

An adjoint curve which bears a special relation to the base curve.

A surface constructed by placing a family of figure-eight curves into R^3 such that the first and last curves reduce to points. The surface has parametric equations x(u,v) = ...

The whole neighborhood of any point y_i of an algebraic curve may be uniformly represented by a certain finite number of convergent developments in power series, ...