Problem 654: Archimedes' Book of Lemmas: Proposition 14 - Semicircles, Diameter, Salinon

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Let AEB be a semicircle on AB as diameter, and let AC, BD be equal lengths measured along AB from A, B respectively. On AC, BD as diameters describe semicircles on the side towards E, and on CD as diameter a semicircle on the opposite side. The figure included between the circumferences of the four semicircles is "what Archimedes called salinon". Let the perpendicular to AB through O, the center of the first semicircle, meet the opposite semicircles in E, F respectively. Then shall the area of the salinon be equal to the area of the circle on EF as diameter.

"Salinon" means salt - cellar in Greek.

  

Archimedes' Book of Lemmas: Proposition 14: Salinon, Semicircles
 
 

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