I: The mathematics of gears -- The geometers -- The translators -- The scientific mechanics -- II: The clock and instrument makers -- The first gear-cutting machines -- Reid, Hindley and Rehe´ -- The instrument makers -- III: Production gear-cutting machines -- Types of gear-cutting machines -- The first production machines, 1800-1850 -- Evolution of the production machine, 1850-1910 -- Formed-cutter types -- Templet types -- Describing-generating types -- Molding-generating types -- Hobbing types -- Impression types -- Automatic gear-cutting machines, 1875-1910 -- Precision-gear grinding, gear shaving, and gear measurement.