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and was accepted by Tycho Brahe; and was
                                         as true a representation of the relative mo-
                                         tions in the solar system as when we sup-
                                         pose the sun to be fixed and the earth to
                                         revolve.
                                            The cumbrous system advocated by Ptolemy
                                         answered its purpose, enabling him to pre-
                                         dict astronomical events approximately. He
                                         improved the lunar theory considerably, and
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