The ray at S' which corresponds to the common ray SS' is tangent to the locus at S'.
In the same manner the tangent at S may be constructed.
62. Determination of the locus. We now show that it is possible to assign arbitrarily the position of three points, A, B, and C, on the locus (besides the points S and S'); but, these three points being chosen, the locus is completely determined.
63. This statement is equivalent to the following:
Given three pairs of corresponding rays in two projective pencils, it is possible to find a ray of one which corresponds to any ray of the other.
64. We proceed, then, to the solution of the fundamental
Problem: Given three pairs of rays, aa', bb', and cc', of two protective pencils, S and S', to find the ray d' of S' which corresponds to any ray d of S.