geometry is that of imaginary magnitude in analysis and of
imaginary space (or space as a locus in quo of imaginary points
and figures) in geometry. In the case of two given curves
there are two equations satisfied by the coordinates (x, y) of the
several points of intersection, and these give rise to an equation
of a certain order for the coordinate x or y of a point of inter-
section. In the case of a straight line and a circle this is a
quadratic equation; it has two roots real or imaginary. There
are thus two values, say of x, and to each of these corresponds
a single value of y. There are therefore two points of inter-
section, viz., a straight line and a circle intersect always in
two points, real or imaginary. It is in this way we are led
analytically to the notion of imaginary points in geometry.
He asks, What is an imaginary point? Is there in a plane a
point the coordinates of which have given imaginary values?
He seems to say No, and to fall back on the notion of an imagi-
nary space as the locus in quo of the imaginary point.

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