Last Updated：2025/12/29
Sentence
Hence
the
section
must
be
a
conic
passing
through
six
nodes,
that
is,
the
plane
touches
the
surface
all
along
a
conic,
and
is
therefore
a
trope.
The
complete
section
of
the
surface
by
a
trope
is
a
conic
counted
twice;
since
this
passes
through
six
nodes,
the
trope
must
touch
the
six
quadric
tangent
cones
along
generators
which
are
tangents
to
the
singular
conic.
Quizzes for review
Hence the section must be a conic passing through six nodes, that is, the plane touches the surface all along a conic, and is therefore a trope. The complete section of the surface by a trope is a conic counted twice; since this passes through six nodes, the trope must touch the six quadric tangent cones along generators which are tangents to the singular conic.
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