An instrument used for finding lines that are mean proportionals.
Several different instruments went by this name. The mesolabe of Eratosthenes was used to solve the problem of duplicating the cube, and consisted of three equal adjacent squares, with diagonals marked, which could be slid over one another on a common base. The squares were positioned so that the straight line joining the top left-hand corner of the first square to the midpoint of the right-hand side of the third square also passed through the points at which the diagonals of the second and third squares emerged from their covering squares. The vertical distances from these points to the base had two properties: (a) they were mean proportionals between the length of the sides of the squares and half this length; (b) they were the sides of two cubes, one of which had double the volume of the other.
Late 16th century; earliest use found in Thomas North (1535–?1603), translator. From Middle French mesolabe from classical Latin mesolabus (Vitruvius) or its etymon Hellenistic Greek μεσολάβος from μεσο- + -λάβος.