I have recently shown that any two straight lines that are isotomically conjugate with reference to a triangle are the asymptotes of a conic circumscribed about the triangle; and that, conversely, any circumscribed conic has for its asymptotes two such lines. Now there is a one-fold infinity of conies having a given pair of straight lines for asymptotes; and, as there is a two-fold infinity of pairs of isotomic lines in the plane (with reference to a given triangle), it follows that two conditions must subsist among the coefficients in the equation of a conic, in order that its asymptotes may be isotomic lines.