The Illustrated Method of Archimedes : Utilizing the Law of the Lever to Calculate Areas, Volumes, and Centers of Gravity

In 1906 Johan Ludwig Heiberg (1854-1928), a Danish philologist and historian of science, discovered a previously unknown text of Archimedes (287-212 B.C.). It was a letter addressed to Eratosthenes (285-194 B.C.), the famous Greek scholar and head librarian of the Great Library of Alexandria. In it, Archimedes presented a heuristic method for calculating areas, volumes and centers of gravity of geometric figures utilizing the law of the lever. This book presents the essence of Archimedes’s method, concentrating on the physical aspects of his calculations. Figures illustrate all levers in equilibrium, and the postulates he utilized are emphasized. The mathematics is kept to the minimum necessary for the proofs. The definition of the center of gravity of rigid bodies is presented, together with its experimental and theoretical determinations. The law of the lever is discussed in detail. The main results obtained by Archimedes concerning the circle and sphere are also discussed. The book describes the lemmas utilized by Archimedes. The main portion of the book sets out the physical demonstrations of theorems I (area of a parabolic segment), II (volume of a sphere) and V (center of gravity of a segment of a paraboloid of revolution). The importance of these three theorems is discussed. There is a bibliography at the end of this book. The goal of this work is to present the essence of Archimedes's method. The analysis included here will concentrate upon the physical aspects of these calculations. Figures will illustrate all levers in equilibrium. The postulates utilized by Archimedes will be emphasized. The mathematics will be kept to the minimum necessary for the proofs. Front Cover 1 Title Page 1 Bibliographic Information 2 Contents 4 Acknowledgments 5 Chapter 1 - Introduction 7 Chapter 2 - The Physical Principles of Archimedes's Method 10 Chapter 3 - Archimedes, the Circle and the Sphere 14 Chapter 4 - The Illustrated Method of Archimedes 21 Chapter 5 - Conclusion 43 Bibliography 45 Back Cover 48