Use of "Characteristic" in 19th Cent. Math

  I tried googling "characteristic" in Google Books and found a number of relevant 19th Cent. references that involve its use. One of the books also included expressions for the distances of a point from a line and a plane. One must realize that the use of vectors came later than much of this work. Gibbs and Heaviside were among the chief promoters of the use of vectors by themselves. They were originally introduced as a part of Hamilton's quaternions.

1830 Hymers, Analytical Geometry
     Example: characteristic property of a surface:
     differential equation valid for every pt on surface

1838 Young, Analytical Geometry
     analytical expression must characterize the position of every point in the curve
     characteristic equation

1904 Scott, Determinants (1st ed. 1880)
     characteristic function & equation for a matrix

Also,

1830 Hymers, Analytical Geometry
     distances of a point from a line and a plane