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.

(1) Generation of the concept through **imaginaries** and development into a method applicable to Euclidean geometry.

The theorem is here referred to partly on account of its bearing on the theory of **imaginaries** in geometry.

Bearing in a somewhat similar manner also on the theory of **imaginaries** in geometry (but the notion presents itself in a more explicit form), there is the memoir by L.

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.