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In solido, i.e. as a section of a cone or cylinder, it may be defined, after Menaechmus, as the perpendicular section of an “acute-angled” cone; or, after Apollonius of Perga, as the section of any cone by a plane at a less inclination to the base than a generator; or as an oblique section of a right cylinder.

Although Euclid knew that an ellipse could be otherwise produced, e. g. as an oblique section of a right cylinder, there is no doubt that he produced all three conics from right cones like his predecessors.

We must also remember that the ellipse is an oblique projection of a circle, or an oblique section of a cone.