His constructions are based on the idea that the imaginaries d - 1 represent a unit line, and its reverse, perpendicular to the line on which the real units 1 are measured.
And it is quite certain that they cannot be represented by ordinary imaginaries.
The theorem is here referred to partly on account of its bearing on the theory of imaginaries in geometry.
Poncelet throughout his work makes continual use of the foregoing theories of imaginaries and infinity, and also of the before-mentioned theory of reciprocal polars.
And, assuming the above theory of geometrical imaginaries, a curve such that m of its points are situate in an arbitrary line is said to be of the order m; a curve such that n of its tangents pass through an arbitrary point is said to be of the class n; as already appearing, this notion of the order and class of a curve is, however, due to Gergonne.
