In this paper, we study the extraction of roots as presented by Al-Kashi in his 1427 book “Key to Arithmetic” and Stevin in his 1585 book “Arithmetic”. In analyzing their methods, we note that Stevin’s technique contains some flaws that we amend to present a coherent algorithm. We then show that the underlying algorithm for the methods of both Al-Kashi and Stevin is the same.

Philosophy, Modern; philosophy and sociology.

Contents: John A. HALL and Ian JARVIE: Preface. John A. HALL and Ian JARVIE: The Life and Times of Ernest Gellner. PART 1 INTELLECTUAL BACKGROUND. Ji_i MUSIL: The Prague Roots of Ernest Gellner's Thinking. Chris HANN: Gellner on Malinowski: Words and Things in Central Europe. Tamara DRAGADZE: Ernest Gellner in the Soviet East. PART 2 NATIONS AND NATIONALISM. Brendan O'LEARY: On the Nature of Nationalism: An Appraisal of Ernest Gellner's Writings on Nationalism. Kenneth MINOGUE: Ernest Gellner and the Dangers of (...) Theorising Nationalism. Anthony D. SMITH: History and Modernity: Reflection on the Theory of Nationalism. Michael MANN: The Emergence of Modern European Nationalism. Nicholas STARGARDT: Gellner's Nationalism: The Spirit of Modernisation? PART 3 PATTERNS OF DEVELOPMENT. Peter BURKE: Reflections on the History of Encyclopaedias. Alan MACFARLANE: Ernest Gellner and the Escape to Modernity. Ronald DORE: Sovereign Individuals. Shmuel EISENSTADT: Japan: Non-Axial Modernity. Marc FERRO: l'Indépendance Telescopée: De la Décolonisation a l'Impérialisme Multinational. PART 4 ISLAM. Abdellah HAMMOUDI: Segmentarity, Social Stratification, Political Power and Sainthood: Reflections on Gellner's Theses. Henry MUNSON, Jr.: Rethinking Gellner's Segmentary Analysis of Morocco's Ait cAtta. Jean BAECHLER: Sur le charisme. Charles LINDHOLM: Despotism and Democracy: State and Society in the Premodern Middle East. Henry MUNSON, Jr.: Muslim and Jew in Morocco: Reflections on the Distinction between Belief and Behavior. Talal ASAD: The Idea of an Anthropology of Islam. PART 5 SCIENCE AND DISENCHANTMENT. Perry ANDERSON: Science, Politics, Enchantment. Ralph SCHROEDER: From the Big Divide to the Rubber Cage: Gellner's Conception of Science and Technology. John DAVIS: Irrationality in Social Life. PART 6 RELATIVISM AND UNIVERSALS. John SKORUPSKI: The Post-Modern Hume: Ernest Gellner's 'Enlightenment Fundamentalism'. John WETTERSTEN: Ernest Gellner: A Wittgensteinian Rationalist. Ian JARVIE: Gellner's Positivism. Raymond BOUDON: Relativising Relativism: When Sociology Refutes the Sociology of Science. Rod AYA: The Devil in Social Anthropology; or, the Empiricist Exorcist; or, the Case Against Cultural Relativism. PART 7 PHILOSOPHY OF HISTORY. William MCNEILL: A Swan Song for British Liberalism? Andrus PARK: Gellner and the Long Trends of History. Eero LOONE: Marx, Gellner, Power. Rosaire LANGLOIS: Coercion, Cognition and Production: Gellner's Challenge to Historical Materialism and Postmodernism. Ernest GELLNER: Reply to Critics. Ian JARVIE: Complete Bibliography of Gellner's Work. Name index. Subject index. (shrink)