### Definition of Hypersurface

1. Noun. (mathematics) A (n)-dimensional surface in a space (often a Euclidean space) of dimension (n)+1 ¹

¹ Source: wiktionary.com

1. [n -S]

### Literary usage of Hypersurface

Below you will find example usage of this term as found in modern and/or classical literature:

1. Higher Geometry: An Introduction to Advanced Methods in Analytic Geometry by Frederick Shenstone Woods (1922)
"Similarly, any plane intersects the hypersurface (1) in a conic or lies entirely on it. ... If in equation (2) the point yi is taken on the hypersurface, ..."

2. Geometry of Four Dimensions by Henry Parker Manning (1914)
"Any directing-curve of a plano-cylindrical hypersurface of revolution is a directing-curve of a circular cylindrical surface* PROOF. ..."

3. Geometry of Riemannian Spaces by Elie Cartan (1983)
"This hypersurface is called the focal hypersurface of the point 0 and the first point where a ... Conversely, let us assume that there exists a hypersurface ..."