Dearest Dancing Friends, what you in the 21st Century would call a square dance was once called a quadrille or a cotillion. It is a beautiful thing to watch, as this group from the Grand Napoleonic Ball in Florence demonstrates in HD:
Getting people to "slip" in a circle together, in time and in rhythm, is quite an accomplishment in itself.
You might scoff at the French, but they have some intricate and beautiful contredanses, like this one, also from Florence in HD:
And from Vienna comes the waltz, which was just catching on in the early 1800's. The proximity of the dancers and the way they held each other caused quite a stir. Gasp! What are they doing! Yet our group from Florence has avoided these issues:
This doesn't really look like a waltz at all, but more like a contredanse. Oh who cares... My Lady, may I honour you with this dance...