(μεσολάβιον; mesolábion). A mechanical device invented by Eratosthenes  to establish graphically the two geometric means x and y between two given lines a and b (as in the relationship a:x = x:y = y:b). The mesolabium enabled the mechanical solution of the problem of the duplication of the cube (‘Delian problem’): if b = 2a, then x is the desired solution of the equation for the duplication of the cube (x3 = 2a3 ).
Hippocrates  of Chios
T. L. Heath, A History of Greek Mathematics, Vol. 2, 1921, 258-260.
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Folkerts, Menso (Munich),
Brill’s New Pauly
, Antiquity volumes edited by: Hubert Cancik and , Helmuth Schneider, English Edition by: Christine F. Salazar, Classical Tradition volumes edited by: Manfred Landfester, English Edition by: Francis G. Gentry.
Consulted online on 15 August 2022 <http://dx.doi.org/10.1163/1574-9347_bnp_e800660>
First published online: 2006
First print edition: 9789004122598, 20110510