Page:American Journal of Mathematics Vol. 2 (1879).pdf/11

Rh

By the notation here given it is immediately evident what points are on every line and what lines pass through every point, without referring to tables, as Veronese is obliged to do. I shall make use of this notation, so far as any notation is necessary, in describing Veronese's additions to the subject.

Pascal discovered the theorem which bears his name in 1640. The reciprocal theorem of Brianchon remained unknown until 1806. From the time, 1828, when Steiner showed that by taking the six points on the conic in different orders, sixty Pascal lines may be obtained, the development of the figure has been more rapid. Steiner himself showed that the $$60$$ Pascal lines meet in threes in the $$20$$ Steiner points, and he believed that these points were situated in fours on five lines, three through each point. Hesse observed that the $$20$$ Steiner points consist of ten pairs of points harmonically conjugate with respect to the conic, and that the figure of the Steiner points and the Steiner-Plücker lines is identical with that formed by three triangles in perspective. Kirkman showed that the Pascal lines pass by threes through the sixty points called by his name, and that these points are Rh