Whitworth's three plates method

The Whitworth Three-Plate Method is a technique for creating precise flat surfaces, invented by Henry Maudslay and popularized by Sir Joseph Whitworth in the 19th century. Crucially, this method does not rely other flat reference surfaces or other precision instruments, and thus solves the bootstrapping problem of how to create the first precise flat surface.

Method

When any two surfaces (call them A and B) are lapped together, the protrusions of the two surfaces will abrade each other off, eventually resulting in two surfaces which will closely agree each other, but which can still be concave or convex (and thus, not flat).

The key insight is to then lap them against a third surface, C, with rotation. The various pairs of surfaces are lapped together in succession, until all 3 agree with each other. It is impossible for any one surface to be concave (or convex), while still agree with 2 other mutually-agreeing surfaces.

With enough iteration, the 3 surfaces will converge on being precisely flat, where successive iterations of the technique will further improve the flatness.