When the metric system was put in place, not without difficulty, in 1793, under the First Republic, then corrected in 1799, the idea was to unify a multitude of distance measurements that were used everywhere in France and in abroad. Each large city had its own standard measures, which the different craftsmen used to carry out their works and to trade, this resulted in immense complexity, which was to prove to be a source of problems when craftsmen from different regions were brought to work together.
Thanks to the use of the preparatory outline of its geometric composition, again visible in places today due to the wear of the pictorial layer, the painter from Châtel has left us clues that allow us to find the stallion that he used to draw the basis of his decor.
Thus, we see that the spacing of his compass was always the same when he was drawing a medallion or a quatrefoil and that this spacing corresponds to a dimension known to be that of a span, that is to say, the width of a hand. This span is sometimes called a pan or palm. There were several kinds of spans, but the one that measures approximately 24.8 cm has been well known and widespread in the building trades since late antiquity.
Contrary to popular belief, the craftsmen of the Middle Ages did not randomly divide the space with each new work to arrive at an empirical and non-reusable unit of measurement, but on the contrary, they used very precise standards whose use corresponded to well-established standards. This is why the 24.8 cm span (this is a span calculated on an 18-finger foot) was the norm for workers working in construction and required a standard of measurement not too large for their work, as in the case of carpenters, glassmakers, painters, etc.
The painter from Theys, therefore, used his standard of measurement with a span and used it to measure the side of a large square. There again, he used a technique well known in the construction trades which consists in drawing a square and checking that its angles are right, in choosing a side of 7 units. Thus, the craftsman knows that the diagonal will have to measure approximately 10 units, and in our case that the half-diagonal will measure 5 units. This is an empirical application of the Pythagorean theorem: 72 + 72 = 98, so the diagonal measures √98 ≈ 9.89 which is a good approximation of 10. In our case, the diagonal of the large square would measure 24, 5 cm instead of 24.8 cm, or 3 mm difference.
I would like to thank Olivier Reguin, associate researcher in the history department of the University of Quebec at Montreal, a specialist in metrology, for his help and his guidance on this complex subject.