As in § 1, we show that, if one factor of c x 2 + 2c x xy + c 2 y 2 is
a factor of d x s + Sd l x 2 y + 3d z xy 2 + d 3 y 3 , the corresponding
tangent is an inflexional tangent. The origin is called a
fiecnode in this case (Fig. 8) ;

If both tangents are inflexional tangents, so that the terms
of the second degree in the equation of the curve are a factor



* Other nomenclatures are ' node ' for crunode,. ' isolated point ' or ' con-
jugate point' for acnode. The term ' spinode ' for cusp is obsolete.
113



MULTIPLE POINTS



23



of the terms of the third degree, the origin is called a biflec-
node (Fig. 9).
Similarly if one of the factors (or both) of the terms of the
second degree is a factor of the terms of the third, fourth, . ..
degrees.
Fig. 9.
§ 3. Multiple Points.
If c , c 1; c 2 are all zero, so that the terms of the lowest
degree are the terms of the third degree, the origin is called a
triple point Any line through the origin meets the curve in
three points coinciding with the origin, except the three
tangents at the origin obtained by equating to zero the terms
of lowest degree. These tangents meet the curve at four
points (at least) coinciding with the origin.
