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The present essay stems from a history of polyhedra from 1750 to 1866 written several years ago (as part of a more general work, not published). So many contradictory statements regarding a Descartes manuscript and Euler, by various mathematicians and historians of mathematics, were encountered that it was decided to write a separate study of the relevant part of the Descartes manuscript on polyhedra. The contemplated short paper grew in size, as only a detailed treatment could be of any value. After it was completed it became evident that the entire manuscript should be treated and the work grew some more. The result presented here is, I hope, a complete, accurate, and fair treatment of the entire manuscript. While some views and conclusions are expressed, this is only done with the facts before the reader, who may draw his or her own conclusions. I would like to express my appreciation to Professors H. S. M. Coxeter, Branko Griinbaum, Morris Kline, and Dr. Heinz-Jiirgen Hess for reading the manuscript and for their encouragement and suggestions. I am especially indebted to Dr. Hess, of the Leibniz-Archiv, for his assistance in connection with the manuscript. I have been greatly helped in preparing the translation ofthe manuscript by the collaboration of a Latin scholar, Mr. Alfredo DeBarbieri. The aid of librarians is indispensable, and I am indebted to a number of them, in this country and abroad, for locating material and supplying copies.
List of contents
One: The Manuscript.- 1. Introduction.- 2. History of the Manuscript.- 3. Description of the Leibniz Copy.- 4. Date of the Original Descartes Manuscript.- Two: Solid Geometry: The Elements of Solids.- 5. Some Geometric Background.- 6. Translation and Commentary, Part I.- 7. General Comments.- 8. Note on the Euler Papers of 1750 and 1751.- 9. Descartes and Euler.- Three: Number Theory: Polyhedral Numbers.- 10. The Figurate Numbers of the Greeks.- 11. Translation and Commentary, Part II.- 12. General Comments.- Notes.- Index of Persons.
