Impossibility of Squaring the Circle in the 17th Century

“This is a highly commendable book about a neglected aspect of a popular story. … Crippa’s book deepens our understanding of the 17th-century discussions about the impossibility (and possibility) of the quadrature of the circle. … Crippa gives an important novel view of Descartes’ problem-solving paradigm and its subsequent extension as well as of the beginning of infinitesimal calcu-lus. Everyone interested in these matters should read Crippa’s well-written book.” (Jesper Lützen, Historia Mathematica, Vol. 52, 2020)“This is an important contribution to the literature that will be of interest to anyone who studies the development of mathematical methods and concepts. ... this is a valuable guide to a fascinating part of 17th-century mathematics.” (Douglas Jesseph, Centaurus, December 3, 2020)“This book, we are told, is an “abridged and improved” version of the author’s doctoral dissertation, and, in fact, it does read something like a doctoral dissertation: very scholarly and thorough, replete with copious and often lengthy footnotes … . people with a serious interest in the history of science or mathematics will want a copy of this book on their shelves. Any good university library will as well.” (Mark Hunacek, MAA Reviews, June 03, 2019)

• FM.-Introduction.- James Gregory and the Impossibility of Squaring the Central Conic Sections.- Leibniz's Arithmetical Quadrature of the Circle.- Conclusion.-BM.