LIE, Marius Sophus (1842–1899). Repräsentation der Imaginären der Plangeometrie. – Repräsentation der Imaginären der Plangeometrie (Forsetzung). Christiania [Oslo], Verhandlungen der Gesellschaft der Wissenschaften in Christiania, 1869.

First edition of Lie’s first printed work, the beginnings of his contributions to geometry. Aged 27, Lie published the present paper on presenting imaginary points and curves as three-dimensional line-geometry objects—representing his earliest engagement in print with ideas behind what would become his first original discovery in mathematics, contact transformations. Lie received a travel scholarship to Berlin on the basis of this paper, where he first met his friend and collaborator Felix Klein. Not in Sommerville, Bibliography of Non-Euclidean Geometry (1911).

Octavo (206 × 127mm). Title-page and “Forzetzung” title-page, in-text diagrams (lightly toned, final leaf trimmed close to fore-edge with partial loss to some letters). Later quarter brown cloth over paper boards.

Sale, Dreweatts, London, 17 September 2015, lot 324.