In the course of some research on old magic books I came across "Deliciae physico-mathematicae oder mathematische und philosophische Erquickstunden" (1653) by Daniel Schwenter and Georg Philipp Harsdörffer. Harsdörffer was of course the author of the "Vollständiges und von neuem vermehrtes Trincir-Buch" (1657), but he was also responsible for a revised and expanded edition of the above book originally written by Daniel Schwenter in 1636. One of his additions was a short chapter on tablecloth folding. The illustrations are the same as in the Trincir-Buch, which he also refers his readers to, but the dates are a bit puzzling because "Deliciae" seems to have been published first.
I've managed to extract the relevant part from the original German and also to do a translation into English - see the attached document. For some reason the German file is larger and is too big to attach, so here is a link to the Google Books version:
http://books.google.ch/books?id=SmM_AAA ... &q&f=false
Starting on page 189
The history of serviette and napkin folding
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- Deliciae physico-mathematicae _On tablecloth folding.pdf
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