I am studying Fermat's procedure for finding tangent lines to curves. In this example he writes:
"Let us consider, for example, the parabola BDN [Fig. 70.2] with vertex D and diameter DC; B is a point on it at which the line BE is to be drawn tangent to the parabola and intersecting the diameter at E. We choose on the segment BE a point O at which we drwa the ordinate OI; also we construct the ordinate BC of the point B.
We have then: CD/DI > BC^2/OI^2, since the point O is exterior to the parabola."
Using that inequality he manages to show a way to express the tangent based on BC and CD. However, I fail to see where that inequality comes from or why we know it applies.
Can anyone explain the inequality to me?
