Invention of the catapult --Gastraphetes -- Advanced bow-machines (Plate A) -- Early artillery fortifications? -- Arrow-Firing Catapult of the Greeks 8 -- 4th-century developments -- Arrow-firer in the 3rd century (Plate B) -- Design of the arrow-firer: the spring-frame -- Design of the arrow-firer: the stock and stand -- Design of the arrow-firer: the washers -- Stone-Projecting Catapult of the Greeks 15 -- Early developments -- Design of the stone-projector: the spring-frame and stock -- Design of the stone-projector: the washers -- Stone-projector from Alexander to Demetrius (Plate C) -- Calibres of stone missiles -- Roman Artillery: The Republic and Early Empire 22 -- Legacy of the Greeks -- Artillery in the Republic -- Vitruvius's arrow-firer -- Vitruvius's stone-projector -- Artillery in the early Empire (Plate D) -- Roman artillery missiles -- Roman Artillery Revolution 37 -- Iron-framed arrow-firer (Plate E) -- Heron's cheiroballistra -- Design of the arrow-firing ballista: the field-frames -- Design of the arrow-firing ballista: the spring-frame -- Stone-projecting ballista (Plate F) -- Stone-projecting onager (Plate G).