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A crescent-shaped figure formed on a sphere or plane by two arcs intersecting at two points.
‘To illustrate with one example, the work of Hippocrates on the quadrature of lunes is only known to us through Eudemus's History of Geometry.’
‘Hippocrates was able to find the areas of lunes, certain crescent-shaped figures, using his theorem that the ratio of the areas of two circles is the same as the ratio of the squares of their radii.’
‘In particular Simplicius quotes the writing on Eudemus on Antiphon's attempts to square the circle and also the attempts of Hippocrates when he squared certain lunes.’
‘He squared certain lunes, and also the sum of a lune and a circle.’
‘The squaring of the circle by means of lunes is not eristic, but the quadrature of Bryson is eristic.’
‘In case the reader is wondering what Aristotle refers to with his phrase ‘quadrature by means of segments' then it is almost certain that he means the method of lunes of Hippocrates.’
Origin
Early 18th century: from French, from Latin luna ‘moon’.