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A triangulated polygon, from Les Amusemens Mathématiques by André-Joseph Mancoucke, 1749. This is the earliest appearance I know of the theorem (stated without proof) that every simple polygon can be triangulated by diagonals. In particular, Mancoucke predates both Meister's (1770) and Poinsot's (1809) seminal treatises on polygons.
...Following a rabbit hole inspired by the Numberphile's recent video on Dehn invariants: https://www.youtube.com/watch?v=eYfpSAxGakI
The earliest PROOF of the polygon triangulation theorem that I'm aware of is an unpublished 1899 manuscript of Dehn! See https://www.maths.ed.ac.uk/~v1ranick/papers/guggenheim.pdf
Sorry, that's Panckoucke with a P. (I have no idea where that M came from.)
Here's his actual theorem statement: "Every rectilinear polygon can be split into as many triangles as it has sides, minus two."
@jeffgerickson well, now I know what I'm doing next Shrove Tuesday
@christianp Don't forget to tip your harried waiter! https://en.wikipedia.org/wiki/Pancake_sorting