Page "learned" Paragraph 327

We consider now the graph of the function f{t} on Af.

We will refer to the plane of C and Af as the C-plane and to the plane of the graph as the Aj.

The graph, as a set, may have a finite number of components.

We will denote the values of f{t} on different components by Af.

Each point with abscissa T on the graph represents an intersection between C and Af.

There are two types of such intersections, depending essentially on whether the curves cross at the point of intersection.

An ordinary point will be any point of intersection A such that in every neighborhood of A in the C-plane, Af meets both the interior and the exterior of C.

Any other point of intersection between C and Af will be called a tangent point.

This terminology will also be applied to the corresponding points in the Aj.

We can now prove several lemmas.