Full Idea
Defining an ellipse in terms of the oblique intersection of a cone and a plane (rather than in terms of the sum of the distance between the foci) gives us a necessary property, but not the essence, because the terms are extrinsic to its nature.
Gist of Idea
Defining an ellipse by conic sections reveals necessities, but not the essence of an ellipse
Source
E.J. Lowe (What is the Source of Knowledge of Modal Truths? [2013], 6)
Book Reference
-: 'Mind' [-], p.18
A Reaction
[compressed wording] Helpful and illuminating. If you say some figure is what results when one thing intersects another, that doesn't tell you what the result actually is. Geometrical essences may be a bit vague, but they are quite meaningful.
Related Idea
Idea 16539 A definition of a circle will show what it is, and show its generating principle [Lowe]