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 <WSD>trope</WSD>. The complete section of the surface by a <WSD>trope</WSD> is a conic counted twice; since this passes through six nodes, the <WSD>trope</WSD> must touch the six quadric tangent cones along generators which are tangents to the singular conic. 
Meaning of the word marked with <WSD> tags:  A tangent space meeting a quartic surface in a conic.