An introduction to the history of science -- Babylonian planetary astronomy -- Plato and saving the phenomena -- Eudoxus and concentric spheres -- Eccentrics and epicycles -- Equivalence -- Astronomy and physics -- Saving the phenomena quantitatively -- Ptolemy's exposition of mathematical astronomy -- Reality or mathematical fiction? -- The greatest astronomer of antiquity or the greatest fraud in the history of science? -- Islamic planetary astronomy -- Revival in the west -- Copernicus and planetary motions -- The Copernican revolution -- Breaking the circle -- Isaac Newton and gravity -- The Newtonian revolution.