90 
ME. A. CAYLEY’S SIXTH :MEM0IE HPOX QrAXTICS. 
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 qua- 
drant, 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 fine 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 metncal geometi-y ; 
for the theory in effect is, that the metrical properties of a figure are not the properties 
of the figure considered se apart from everything else, but its properties when con- 
sidered 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 descrip- 
tive 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 geometrj is thus 
a part of descriptive geometry, and descriptive geometry is all geometry and recipro- 
cally; and if this be admitted, there is no ground for the consideration, in an introduc- 
tory 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 neces- 
sary to refer to them in order to show that they are thus included in descriptive 
geometry. 
