Thesalinon (meaning 'salt-cellar' in Greek) is ageometrical figure that consists of foursemicircles. It was first introduced in theBook of Lemmas, a work attributed toArchimedes.^[1]

LetA,D,E, andB be four points on a line in the plane, in that order, withAD =EB. LetO be the bisector of segmentAB (and ofDE). Draw semicircles above lineAB withdiametersAB,AD, andEB, and another semicircle below with diameterDE. A salinon is the figure bounded by these four semicircles.^[2]

Archimedes introduced the salinon in hisBook of Lemmas by applying Book II, Proposition 10 ofEuclid'sElements. Archimedes noted that "the area of the figure bounded by the circumferences of all the semicircles [is] equal to the area of the circle on CF as diameter."^[3]

Namely, if${\displaystyle r_1}$ is the radius of large enclosing semicircle, and${\displaystyle r_2}$ is the radius of the small central semicircle, then the area of the salinon is:^[4]$${\displaystyle A=\frac{1}{4}\pi {\left(r_1+r_2\right)}^2.}$$

Should pointsD andE converge withO, it would form anarbelos, another one of Archimedes' creations, withsymmetry along they-axis.^[3]

• Lune of Hippocrates

• L’arbelos. Partie II by Hamza Khelif atwww.images.math.cnrs.fr ofCNRS

• Piecewise-circular curves
• Archimedes

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• Short description matches Wikidata