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.