is perpendicular to the line generated by 
,
the major axis of the ellipse. If we let 
be an arbitrary point of the 
plane, there is a unique
number 
and point 
such that Clearly,
is perpendicular to the line generated by ,
the major axis of the ellipse. If we let
be an arbitrary point of the
plane, there is a unique
number
and point
such that
|
|
The number 
is the distance from
to the line 
.
Now we saw in the Euclidean
context that, if 
is the dihedral angle between the planes
and the graph of 
(that is, the angle formed by intersecting these planes with a plane perpendicular
to ),
then for each 
,
|
|
I noted that 
.
For a point
in the ellipse,
is, by the interpretation of the experiment above, 
, the time of arrival as measured by 
of a light ray emitted by 
.
This number in turn is the length of the segment as measured by
connecting the focus at
the origin to the point
on the ellipse. Therefore the ratio of {the length of the segment connecting
the focus to the point
in the ellipse} to {the distance from
to the line }
is the constant 
.
We usually call 
the eccentricity of the ellipse.
The
calculation in Planes Intersecting Cones actually gave a value for .
The intersection of the directrix
with the extension of the major axis is the point
= 
.
And the value of the eccentricity
is the speed of
as measured by ,
= 
.
.
.