The original classification of compact connected surfaces

Question

Who first proved the original classification of compact connected surfaces?

There are many different proofs, for example Seifert and Threlfall's proof (1934) or Conway's proof (1992). However, I suspect there are many more, for example in this article it states the theorem was known as early as the 1860s.

Answer 1

From https://www.seas.upenn.edu/~jean/surfclass-talk2.pdf (the 13th slide):

This result was first proved rigorously by Brahana in 1921, but it had been stated in various forms as early as 1861 by Möbius, by Jordan in 1866, by von Dyck in 1888 and by Dehn and Heegaard in 1907

Thus it should be Brahana who first proved the classification of compact connected surfaces rigorously.

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Möbius' original publication: A. F. Möbius. Theorie der elementaren Verwandschaften. Abhandlung Sächsische Gesellschaft der Wissenschaften , 1863

Jordan's original publication: C. Jordan. Sur la déformation des surfaces. Journal de Mathématique 11:105–109, 1866.