This rings a bell with me. If memory serves me correctly, I recall seeing some Renaissance mathematical instruments like sectors or folding squares that had hour scales on them. These were scales not for laying out sundials (dialling scales were not uncommon on these instruments), but were scales to be used for telling time. They worked as altitude dials. When the two arms of the instrument were opened to form a right angle, and a gnomon pin was placed in a hole on one arm, its shadow would fall on the other arm's scale.
A carpenter's square, suitably inscribed, could be used in a similar manner. Cheers, Sara Schechner 39:00 N 77:01 W
