The life of Archimedes? -- The law of the lever -- Center of gravity -- Big literary find in Constantinople -- The mechanical method -- Two sums -- The parabola -- Floating bodies -- The spiral -- The sphere -- Archimedes traps [pi] -- Appendix A, Affine mappings and the parabola, Appendix B, The floating paraboloid: special case -- Appendix C, Notation -- Appendix D, References.