General investigations of curved surfaces

INTRODUCTION
In 1827 Gauss presented to the Royal Society of Göttingen his important paper on the theory of surfaces, which seventy-three years afterward the eminent French geometer, who has done more than any one else to propagate these principles, characterizes as one of Gauss's chief titles to fame, and as still the most finished andusefulintroductiontothestudyofinfinitesimalgeometry.∗ Thismemoirmay be called: General Investigations of Curved Surfaces, or the Paper of 1827, to distinguish it from the original draft written out in 1825, but not published until 1900. A list of the editions and translations of the Paper of 1827 follows. There are three editions in Latin, two translations into French, and two into German. The paper was originally published in Latin under the title:
Ia. Disquisitiones generales circa superficies curvas auctore Carolo Friderico Gauss.
Societati regiæ oblatæ D. 8. Octob. 1827,
and was printed in: Commentationes societatis regiæ scientiarum Gottingensis recentiores, Commentationes classis mathematicæ. Tom. VI. (ad a. 1823-1827). Gottingæ, 1828, pages 99-146. This sixth volume is rare; so much so, indeed, that the British Museum Catalogue indicates that it is missing in that collection. With the signatures changed, and the paging changed to pages 1-50, Ia also appears with the title page added:
Ib. Disquisitiones generales circa superficies curvas auctore Carolo Friderico Gauss.
Gottingæ. Typis Dieterichianis. 1828.
II. In Monge's Application de l'analyse à la géométrie, fifth edition, edited
by Liouville, Paris, 1850, on pages 505-546, is a reprint, added by the Editor, in Latin under the title: Recherches sur la théorie générale des surfaces courbes; Par M. C.-F. Gauss.
IIIa. A third Latin edition of this paper stands in: Gauss, Werke, Her- ausgegeben von der Königlichen Gesellschaft der Wissenschaften zu Göttingen, Vol. 4, Göttingen, 1873, pages 217-258, without change of the title of the original paper (Ia).
IIIb. The same, without change, in Vol. 4 of Gauss, Werke, Zweiter Abdruck, Göttingen, 1880.
IV. A French translation was made from Liouville's edition, II, by Captain Tiburce Abadie, ancien élève de l'École Polytechnique, and appears in Nouvelles Annales de Mathématique, Vol. 11, Paris, 1852, pages 195-252, under the title: Recherches générales sur les surfaces courbes; Par M. Gauss. This latter also appears under its own title.
Va. Another French translation is: Recherches Générales sur les Surfaces Courbes. Par M. C.-F. Gauss, traduites en français, suivies de notes et d'études sur divers points de la Théorie des Surfaces et sur certaines classes de Courbes, par M. E. Roger, Paris, 1855.