Redefining Geometrical Exactness - (Sources and Studies in the History of Mathematics and Physic) by Henk J M Bos (Paperback)

Book Synopsis

Until the 17th century, rigor and exactness in mathematics meant geometry and Euclid. Other means of confirming results, such as computation, were considered inferior to the traditional constructions using ruler and compass. In 1637 Descartes introduced what is now called analytical geometry, which made algebraic methods equal to geometry in the methods of mathematics. In this detailed study, Bos explores the origins of what is meant by "rigor" in mathematics, and how that definition evolved to include the use of new geometric and algebraic methods.

Review Quotes

"This is a brilliant book and the most satisfactory account of Descartes' mathematical career that I have come across. Although the author does not claim to provide an exhaustive study of Descartes' geometry, he illuminates it in an original way by focusing on the conception and practice of construction. The book covers essentially the period from 1588, when Commandino's Latin translation of the surviving books of Pappus' Collections appeared, to 1650 when Descartes met his untimely death in Sweden. Bos discusses the opinions of five mathematicians who stated their position on construction explicitly, namely Clavius, Viète, Kepler, Molther and Fermat. He then sketches out the background to Descartes' program for restructuring the art of geometrical problem solving that led to the Geometry of 1637, a work that he analyses in detail. The concluding two chapters summarise the dynamics of Descartes' geometrical thinking and sketch the development that followed upon Descartes' achievement."--MATHEMATICAL REVIEWS