An introduction to mathematics, by A. N. Whitehead.

CONIC SECTIONS 141
will be seen how far in the course of ages of
study we have drifted away from the old
original idea of the sections of a circular cone.
We know now that the Greeks had got hold
of a minor property of comparatively slight
importance; though by some divine good
fortune the curves themselves deserved all
the attention which was paid to them. This
unimportance of the "section" idea is now
marked in ordinary mathematical phraseology by dropping the word from their
names. As often as not, they are now
named merely "conics" instead of "conic
sections."
Finally, we come back to the point at
which we left coordinate geometry in the last
chapter. We had asked what was the type
of loci corresponding to the general algebraic
form ax+by =c, and had found that it was
the class of straight lines in the plane. We
had seen that every straight line possesses an
equation of this form, and that every equation
of this form corresponds to a straight line.
We now wish to go on to the next general
type of algebraic forms. This is evidently
to be obtained by introducing terms involving x2 and xy and y2. Thus the new general
form must be writtenax2 +2hxy +by2 +2gx +2fy +c = 0
What does this represent? The answer is