! Approximating the Roots of Numerical 1819 By MARTIN ANDREW NORDGAARD, Ph.D. ACKNOWLEDGMENT The author is deeply appreciative of the services of Professor David Eugene Smith, of Teachers College, Columbia University, whose inspiration and guidance have been a great help in carrying on this research. CHAPTER 1. Egyptian and Babylonian Work in Finding Roots I. The Rise of Numerical Higher Equations among the Arabs 2. A Solution by an Unknown Arab Scholar VII. NEWTON'S METHOD OF APPROXIMATION 1. Advance in Theory of Equations 1. The General Nature of these Methods 2. Chuquet's Rule of Mean Numbers . 5. The Methods of Bürgi and Pitiscus VI. VIETA'S EXTENSION OF THE HINDU METHOD OF APPROXIMATION TO 1. Vieta's Method of Approximation 2. The Modifications of Vieta's Method by Harriot . |