Practical science was composed of personal morality, domestic morality and politics, to which Ibn Sina also appended prophetology. In the 'Prolegomena', Ibn Khaldun, the celebrated historian and sociologist of the eighth/fourteenth century, has given a clear account of the whole field of the sciences as they appeared in his time. Muslim arithmeticians practised exponentiation, and the extraction of square and cube roots, sometimes using the formulae of root approximation borrowed from the Byzantines. The general Ptolemaic theory, accepted by nearly all Muslim astronomers, met with opposition only in Spain, where Ibn Bajja, Ibn Tufayl and Ibn Rushd rejected, in the name of Aristotle, the Ptolemaic account of the movements of the heavenly bodies. In the field of pharmacology, Muslim physicians enriched the materia medica inherited from Greece. In the Middle Ages, Muslim scientists were indisputably at the peak of their progress, scientific curiosity and research.