Coarse focus is via Rack & Pinion. The rack is embedded in the main support pillar and moves the sliding pillar and microscope body. Note the cutouts (Arrows) allowing the sliding pillar to freely pass the main gear. Ivory handle (A) actuates the pinion gear.
Fine focus is a variation of the Hevelius screw mechanism. During coarse focusing the half-threaded rod (B) slides freely through a hole in the horizontal shaft (arrow). To fine focus, thumbscrew C is a jam screw that fixes the half-threaded rod in place. Turning the ivory thumbscrew (D) then causes the sliding support pillar, and the microscope body, to move up or down in fine increments.

Comparison of the two images shows how the threaded shaft has moved during focusing.