Updated: Oct 24, 2022
Here’s an interesting little “paper recreation” which I’ve come across in two old books – an anonymous manuscript called La Magie du Pont Neuf, which is thought to have been written between 1643 and 1654, and Mechanemata oder der Tausendkünstler (1831) by Dr Heinrich Rockstroh (see my June blog post Artful letter closures from 1831 for details).
La Magie du Pont Neuf was discovered by Daniel Margócsy (Professor of Science, Technology and Medicine at the University of Cambridge) in the Houghton Library of Harvard University in 2004. It was photographed and digitised in 2014 and made available online, and has since been published with a transcription and notes by the French magic historian Philippe Saint-Laurent (Editions Georges Proust, 2015).
The Paper Buckle in La Magie du Pont Neuf (left) and Mechanemata (right)
The Paper Buckle is cut from a single sheet of fairly thick paper in the form shown above, with the prong or bar extending over the frame and being detached from it at the crossover point. This is achieved by carefully separating the top and bottom layers of paper. If it's done neatly the layer separation is not noticed, and it looks like an impossible object.
Here's the text from La Magie du Pont Neuf with a translation by me (though I must admit I'm not quite sure what the author is trying to say about the papermakers' frame towards the end):
To make, from a single piece of paper, a spur buckle whose prong passes over
the buckle, without either of them being cut or glued
Having seen one of these in the hands of an Italian, and no one was ever able to understand how it was made. Here is a drawing of the buckle, said Filidam, where the prong AB must be intact, and the bar CD also intact, so that the prong can be lifted above the bar, and the whole thing is made from a single piece of paper. This can be done by taking a slightly thick piece of paper and carefully peeling it, which is easy with paper that is thicker to slit it in two, as long as you have removed some thickness. After that you can cut your buckle and make sure that the prong extends beyond the bar CD, but at the point where the buckle rests against the bar the paper will seem thinner than the remainder because its thickness will be separated into two. For this reason it would be better to have a frame made like those used by papermakers to make sheets of paper, which would have another one perpendicular in the middle, and onto this draw a sheet that would have the same effect without it seeming that you have glued a half sheet of paper in the middle of another sheet. In this way one could cut the buckle as you have asked.
And from Mechanemata (again with my translation):
A paper buckle with a detached prong
but made from a single piece of paper
This paper buckle with a detached prong, and the way it is cut from a single piece of paper, is an interesting trick, and is shown in the illustration on Plate 4 between 1 and 2. The inner rectangles are cut out, as will be easily understood. However, the prong should be detached at point O so that it can be cut or peeled off the paper and yet leave the paper intact.
Take a piece of thick paper which is large enough – slightly more than 1 inch long and wide – to allow, as shown in the illustration, the buckle and prong to be cut out of it, before doing this – for this is what makes the feat possible – and place it on a hard flat surface, and using a sharp knife try to cut off or peel off a piece of the paper without detaching it completely. Then cut the shape of the buckle with prong out of the paper, so that the cut off or peeled off piece comes away where the prong is supposed to be detached. Anyone else trying to do it will never manage, however hard they try.
Robert Neale's Belt Buckle from his Trapdoor Card manuscript, published by Karl Fulves in 1983, is strikingly similar in appearance to the version is Mechanemata but unrelated in terms of effect, method and overall intention.
Belt Buckle from Robert Neale's Trapdoor Card (1983)
The principle of splitting layers has also been used to make paper chains from a single piece of card (usually a playing card), with each link apparently solid and unbroken. Rockstroh also describes this in Mechanemata, not once but twice - the first time using a playing card and the second time using a piece of paper. Which is strange, because the result is basically the same both times.
The playing card chain comes up again with much clearer drawings in a contribution by Arthur Good to the French magazine La Nature in 1888, and also in the second volume of the German book Kolumbus-Eier (ca. 1902), which was a collection of articles from the children's magazine Der Gute Kamarad.
The Playing Card Chain in La Nature (left) and Kolumbus-Eier (right)
And here's the same thing from Amusements in Mathematics (1917) by the great British puzzle expert Henry Dudeney.