Page "learned" Paragraph 354

A final class of exceptional lines is identifiable from the following considerations: Since no two generators of Af can intersect, it follows that their image curves can have no free intersections.

In other words, these curves have only fixed intersections common to them all.

Now the only way in which all curves of the image family of Af can pass through a fixed point is to have a generator of Af which is not a secant but a tangent of **zg, for then any point on such a generator will be transformed into the point of tangency.

Since two curves of symbol Af on Q intersect in Af points, it follows that there are Af lines of Af which are tangent to Aj.

Clearly, any line, l, of any bundle having one of these points of tangency, T, as vertex will be transformed into the entire pencil having the image of the second intersection of L and Q as vertex and lying in the plane determined by the image point and the generator of Af which is tangent to **zg at T.

A line through two of these points, Af and Af, will be transformed into the entire bilinear congruence having the tangents to **zg at Af and Af as directrices.