Having looked the other day at some scratched graffiti on a molding plane; https://pfollansbee.wordpress.com/2009/06/29/sketched-on-a-napkin/
I was reminded of an English box I’ve seen with some geometry scribed on the inside face of the box front. This particular example survives in a corrupted configuration; it was once a box with a drawer, and is now just a very deep box.
On the inside face of the bottom section carved with the arcading is a series of attempted spirals, laid out with “a pair of compasses.” The original layout called for three spirals, and only one is complete. The center one is poorly-thought-out, and the one on the proper left end of the box is barely begun. Here are the two better examples:
And a detail of the one on the left above:
This spiral is marked out with two center points; with some help today, it was not too much trouble to figure out the layout.
But my next question – what happened? This face of the board is laid out with a vertical center line, (which is not centered on the present length of the board) and two equidistant lines marked out from that. These all serve as centers for the spirals. One spiral got nowhere fast, two partial arcs. The center one is not a consistent spiral, there are mistakes in its layout. The one on the proper right-hand end is fully-formed, and “correct” in that it follows a system to produce a continuing spiral. Here’s a sketch showing the layout with two center points:
So I wonder, was it was practice? Did the joiner/carver start out wanting a “three-spiral” motif on his drawer front, get frustrated with the geometry, give up & flip the board over to carve the simpler arcading? Maybe it was just a bad day for geometry c. 1605.
The carving, in walnut, is excellent, first-rate work. This box dates from about 1600-1610. A nearly identical example, dated 1605, is at the Metropolitan Museum of Art in New York. Another is in a private collection.
(I can’t think of a carved pattern with spirals that continue outwards so much, most are just one or two turns around…I’ll be on the lookout.)
PETER FOLLANSBEE: JOINER’S NOTES 
Peter,
I can’t comment on the design on the plane, but I’d guess that the spirals were an example of the maker doing his working out on the material available to hand.
In 1605, that most folk were illiterate in the modern sense, numeracy amongst artisans would have been basic, geometry even more so and paper was exceptionally expensive, available only for special purposes for the rich. Sketching out would most likely have been done on the back of the piece, which could well have been used as a rod for the rest of the work, or a slate.
As an example of this, some years ago, back in the ‘70s, I found a part of a very old table in a junk-auction; it was beyond redemption as a useful piece of furniture, but one of the sides was scratched with regular marks and Roman numerals. Obviously the thrifty maker had used his rod in the piece itself – a practice that I personally continue but I make it a feature on the back, or out of sight. Part of the provenance of the piece, you may say.
Best regards
Howard