Covering a sphere of four braccia with parallel plates
Why the plates must not overlap, and a platform for stamping the great impression.
Leonardo works out how to clothe a large convex/concave surface with curved metal plates. In a crossed-out rectangle he insists the plates be parallel and never overlap, like the annular circles drawn upon a sphere; an adjacent scheme divided a b c d e is marked 'false' because overlapping parts lose their true curvature. A valid method instead cuts and rejoins the plate so it takes the stamp of the convex stone, allowing a single sheet of four braccia to be assembled. Each plate needs its own guide to give it varied concavity, and the whole platform may be built ten or twelve braccia to a side, taller than wide, so the impression stays square. A quarter-sphere sheathed in ribbed plates is drawn at the foot.
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Parallel plates like annular circles on a sphere
The plates must be parallel and must not overlap in any part, just as the annular circles that are drawn upon a sphere do not cross one another. A scheme in which parts overlap is judged false, because the overlapping regions lose the curvature required at their place on the surface.
A valid way to cut and rejoin a curved plate
The composition of strips a b c d e serves for cutting the plate and rejoining it with a curvature apt to take the stamp of the convex stone, or to join so great a plate of four braccia. Each plate must be given varied concavity by its own guide, formed for its particular situation.
A platform of ten to twelve braccia for the impression
Because the plates lie in the concavity of the framework that supports them, their overlapping widths are pared away so their edges stay in continuous contact and can be soldered. The platform may be built ten or twelve braccia to a side, and should be taller than wide so that the impression comes out square.