- Wilbur R. Knorr
ExtractStatics (in the phrase of *Pappus), is the branch of *mechanics dealing with the relations of weights in static equilibrium. The classic formulation of the principles is from *Archimedes (Plane Equilibria, bk. 1) in which he proves that the centre of gravity of two weights is the point dividing the line between their respective centres of gravity into segments inversely proportional to the weights (props. 6–7). This is apparently a reformulation in statical terms of the analogous principle of the lever, conceived dynamically in the Peripatetic Mechanica. Archimedes' definition of centre of gravity is not transmitted in his extant mechanical writings, but can be inferred from accounts by *Heron, Pappus, and Eutocius. In a lost work On balances (Peri zygön) Archimedes appears to have applied a version of the equilibrium principle toward the analysis of uneven-armed balances of the bismar type. In the Plane Equilibria he determines the barycentres of the parallelogram, triangle, trapezium, and parabolic segment.
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