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A SIXTH MEMOIR UPON QUANTICS. 
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229. In ordinary plane geometry, the Absolute degenerates into a pair of points, 
viz. the points of intersection of the line infinity with any evanescent circle, or what 
is the same thing, the Absolute is the two circular points at infinity. The general 
theory is consequently modified, viz. there is not, as regards points, a distance such as 
the quadrant, and the distance of two lines cannot be in any way compared with the 
distance of two points; the distance of a point from a line can be only represented 
as a distance of two points. 
230. I remark in conclusion, that, in my own point of view, the more systematic 
course in the present introductory memoir on the geometrical part of the subject of 
quantics, would have been to ignore altogether the notions of distance and metrical 
geometry; for the theory in effect is, that the metrical properties of a figure are not 
the properties of the figure considered per se apart from everything else, but its 
properties when considered in connexion with another figure, viz. the conic termed the 
Absolute. The original figure might comprise a conic; for instance, we might consider 
the properties of the figure formed by two or more conics, and we are then in the region 
of pure descriptive geometry: we pass out of it into metrical geometry by fixing 
upon a conic of the figure as a standard of reference and calling it the Absolute. 
Metrical geometry is thus a part of descriptive geometry, and descriptive geometry is 
all geometry, and reciprocally; and if this be admitted, there is no ground for the 
consideration, in an introductory memoir, of the special subject of metrical geometry; 
but as the notions of distance and of metrical geometry could not, without explanation, 
be thus ignored, it was necessary to refer to them in order to show that they are 
thus included in descriptive geometry.