nMesolabeAn instrument of the ancients for finding two mean proportionals between two given lines, required in solving the problem of the duplication of the cube.
Century Dictionary and Cyclopedia
nmesolabeA mechanical contrivance for geometrically extracting the roots of quantities. It consists of a number of equal rectangles, each having a diagonal marked, and all capable of sliding along a line common to the bases of all, so that they partially overlap one another. The marked diagonals are all parallel. To use the instrument, all the intersections, each formed of the diagonal of one rectangle and the overlapping edge of the next one, are brought, by the sliding along of the rectangles, into one straight line with one extremity of the diagonal of the uppermost rectangle and a point on the exposed edge of the lowermost whose distance from the extremity of the diagonal on the same edge measures the quantity whose root is to be extracted. Then the corresponding distance on the uppermost rectangle is the root multiplied by that of the common altitude of the rectangles, which last is supposed to be known. The exponent of the root is equal to the number of rectangles employed. The mesolabe was invented bv Eratosthenes, about 200 to 250 years before Christ.