§ 24:

O88
See the proof of the propositions in this section.

O89
See the proof of the propositions in this section.

O90

The projectivity from a tor b that maps S to B, A to S, and C₁ to C₂, with pappus line AB, generates the conic.
Choose X on a and construct the image point X ' with the theorem of Steiner.
Construct a fifth image point Y ' for Y on a.
XX ' and YY ' are new lines of the conic.
Construct the point of contact on c as in O89.

O91

Construction and explanation are dual to those of the previous problem.