Can anyone give some historical examples of methods of exhaustion being used to solve problems. One popular example is the method Archimedes used to find the lower and upper bounds of the area of a circle (and therefore Pi) by inscribing circles inside and outside a circle? In particular i'm looking for early precursors to calculus/infinite series and the idea of limits. Most info points towards the Ancient Greeks as a starting points but surely there must be earlier developments in the field? Maybe early Chinese mathematics or Islamic/Arabic mathematics?