Grind it down into point-like particles, hand it to Euclid, and ask “where are your axioms now?”

While he’s examining the particles, measure the change in his weight.

Mass and volume are distinct, so a lack of euclidean geometry is not a big deal as long as your scale is bisecting the physical plane and 100% of the objects mass is acting perpendicular to it.

Probably the metric system

A carnival weight guesser (IDK what they are called).