Both the artwork and the math for Propositions 18 through 22 form a group. Math-wise these propositions are about how the sides of triangles and the angles they subtend relate. Triangles math-wise led to bridges, structures, and machines art-wise.
Since Propositions 18 and 19 are two sides of the same statement, the artwork for both uses a vintage drawing from a patent for…not sure what…. but the structure for this machine is, of course, a triangle, a stable and rigid building structure. The artwork for proposition 20 uses the triangular structures for a bridge, at various scales. The artwork for Proposition 21 uses yet another vintage machine drawing. And in the artwork for Proposition 22, I’ve used appropriately scaled circles from a lightbulb and a gear to draw the proof itself.
Although Euclid was writing about abstractions, the geometrical relationships are used all the time in some very real, down-to-earth stuff.