Cambridge University Press, 1999, pp: 285, ISBN 0-521-64066-0 (hc); Price: $80.00 (hc).

Isaac Newton’s Principia is justly regarded as one most important works in the history of science. Its central role in presenting Newton’s theory of gravitation and applying that theory to the orbits of the moon and planets is well known to almost all of today’s science students. However, the mathematical presentation of these theories in the Principia would no doubt baffle most undergraduates. Instead of using the newly discovered calculus, Newton largely relied on a geometrical presentation of his theories, a choice which came back to haunt him when he later tried to prove that he had developed the calculus before Leibniz.

In Reading the Principia, Niccolò Guicciardini attempts to uncover the reasons and implications of Newton’s decision to focus on geometrical rather than algebraic proofs by investigating how contemporary readers responded to the book. He focuses on three scientists: Christian Huygens, the leading geometer of his time, Gottfried Wilhelm Leibniz, Newton’s opponent in the priority dispute for the discovery of calculus, and Newton himself. Guiccardini’s careful study reveals many interesting and surprising facets to the story of the Principia and its reception, and on the ensuing dispute between Leibniz and Newton. Particularly interesting is the discovery that Newton’s decision to adopt a geometrical approach in his book was largely due to his desire to adhere to the mathematical styles of the ancients for he believed that all knowledge had been known in ancient times. He went so far are to claim that in formulating his universal law of gravitation he was only re-discovering lost knowledge that had been known to the ancient Chaldeans, the Pythagoreans and other unnamed ancients.

After setting out the purpose of his book, Guiccardini begins by providing a clear presentation of Newton’s mathematical methods, both those used in the Principia and his methods of fluxions. Part two comprises the meat and bones of the study: a close analysis of the response of the three readers to the Principia. Finally, in part three, the author studies the aftermath of the Principia in Britain and in continental Europe. Guiccardini shows that there are more subtleties in the differences in the Principia’s reception between Britain and the continent than are usually acknowledged in the traditional story of Britain accepting Newton and his fluxions and a Europe rejecting Newton and attracted to Leibniz’s calculus. Eventually, of course, the more clearly versatile language of Leibniz’s calculus (dx/dt) rather than Newton’s fluxions (x?) won the day.

This book, though not easy going for those not versed in the language of mathematics, will prove a fascinating read for anyone interested Newton and his work, scientific practice and dispute in the seventeenth century, or indeed in the foundations of today’s mathematical physics.

J.M. Steele,

University of Toronto