I was looking through Playford’s Dancing Master (1707, I think) for some tunes, and I noticed that some of the cut-time signatures are backwards. It’s not something I’ve noticed before, so I wondered: is it a thing? On a web search I couldn’t find a mention of it having a specific meaning.
As your handy SMuFL guide will tell you, reversed time signatures represent ‘diminution’ – a reduction in the duration of the notes. (“Faster”, you could say.)
Playford’s Dancing Master was first published in 1651, so 1707 will be a reprint. By that time, the notation would be a bit old-fashioned.