Let there be given, in a plane π, six (fundamental) points 1, 2, 3, 4, 5, 6, of which neither any three lie in a right line, nor all in a conic; and consider the six conics [1] ≡ 23456, [2] ≡ 13456, [3] ≡ 12456, [4] ≡ 12356, [5] ≡ 12346, [6] ≡ 12345, and the fifteen right lines 12, 13,…, 16, 23,…, 56.

There is a pencil of cubics 1223456 (curves of the third order, having a node at 1 and passing through the other fundamental points); their tangents at the common node form an involution, viz., they are harmonically conjugate with regard to two fixed rays. Five pairs of conjugate rays of this involution are already known; for instance, the line 12 and the conic [2] have conjugate directions at the point 1, for, they make up a cubic 1223456.