La méthode illustrée d’Archimède : utilisation de la loi du levier pour calculer les aires, les volumes et les centres de gravité

Description

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. Archimedes presented a heuristic method to calculate areas, volumes and centers of gravity of geometric figures utilizing the law of the lever. Normally scientists use mathematics to deduce physical properties. Archimedes reversed this procedure or paradigm with his method, utilizing physics to derive mathematical results. In particular, he utilized the law of the lever to deduce mathematical theorems like the area and volume of a sphere. For this reason his Method has been considered by some authors as a Copernican revolution.

This book presents the essence of Archimedes' method, concentrating upon 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. We present the definition of the center of gravity of rigid bodies, together with its experimental and theoretical determinations. The law of the lever is discussed in detail. The main results obtained by Archimedes related to the circle and sphere are also discussed. Then comes the main portion of the book, presenting 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). We discuss the importance of these three theorems. There is a bibliography at the end of this book.