Since its publication by the Royal Society in 1687, Newton's * Principia * has been recognised as a scientific masterpiece. Even Newton's adversary Leibniz recognised the work's profound mathematical accomplishment; in conversation he was reported to declare that taking mathematics from the beginning of the world to the time of Newton, what Newton "had done was much the better half". In this foundational work of the modern science of physics, Newton set out in mathematical form the principles of dynamics, stating the laws of motion and the theory of universal gravitation, concepts that have shaped subsequent science.

Newton's arguments continue to exercise interest; mathematicians, physicists and historians still debate the veracity of his proofs. Bernard Cohen's translation and guide to Newton's * Philosophiae Naturalis Principia * Mathematica will be of interest to a wide scientific and scholarly audience.

The publication of Cohen's volume is the culmination of a lifetime's commitment to Newtonian themes. It is the first translation of the * Principia * since Andrew Motte's of 1729 (revised in Florian Cajori's modernisation, published in 1934), and it complements Cohen's 1972 variorum edition of * Principia * , which embraces the 1687, 1713 and 1726 editions of Newton's text and incorporates manuscript variants. Cohen's preliminary guide to Newton's work complements his earlier * Introduction to Newton's Principia * (1971).

Cohen and Anne Whitman's translation offers a much needed replacement for Motte-Cajori, the text long familiar to scholars and students. Where Motte-Cajori creaks and puffs, its curious combination of Motte's archaic language and Cajori's modernisation amplifying the difficulties of comprehending Newton's argument, the new translation flows smoothly and elegantly. Having recently worked closely on two passages in the Latin text of Principia, I appreciate this new translation's virtues, clearing the impediments to intelligibility of this classic scientific text. The translation is based on the third Latin edition of 1726, with variants from the earlier editions recorded in footnotes, and it is apparent that the greatest effort has been expended in paying minute attention to the original text to repair the faults of the Motte-Cajori edition.

Cohen and Whitman strive to grasp Newton's meaning, to remain faithful to his conceptualisations yet to communicate the text most immediately to the modern reader. Cajori removed the word force from the expression "force of inertia ( * vis inertiae * )" in Newton's text; while making good sense to a modern reader, this rendition violates Newton's concept. Cohen and Whitman restore Newton's expression, and expose an important issue of interpretation in understanding Newton's concept of "force". They do not, however, retain cumbersome archaic language, for example in expressing ratios - after all, the purist can refer to the Latin original.

The attention paid to Newton's diagrams illustrates their sensitivity to advances in Newtonian scholarship. The diagrams reproduced here are drawn from the Motte-Cajori version, but alerted by the work of J. A. Lohne and especially Bruce Brackenridge, some corrections have been introduced, notably to the diagram accompanying the Keplerian proposition on elliptical orbits, which posterity has considered to be the mathematical highlight of Principia.

The work is written in a scientific, mathematical and philosophical idiom that is far removed from the modern style. To take the most obvious point, it appears to be written in the style of Greek geometry, but it becomes apparent that this is superficial. Newton's claim that the arguments in * Principia * are essentially analyses in his fluxional calculus clothed in the guise of traditional geometry is likewise misleading. As D. T. Whiteside, to whom this volume is dedicated, has shown, the mathematical argument of * Principia * is based on an infinitesimal method, Newton's deployment of the geometrical limit-increment of a variable line-segment. Attention to the core of the mathematical argument highlights the need to approach the text with recognition of every historical nuance. In his preliminary guide, Cohen elucidated its major features, confronting the many difficulties faced by the prospective reader. Here Cohen works through the main argument of the Principia's three books, clarifying their structure and detail, and offers commentary on the definitions, the laws of motion and the concluding General Scholium topics of paramount important to the student.

Cohen also attends to a variety of special topics. One issue likely to interest the modern physicist is the claim of the 19th-century physicist P. G. Tait that Newton had stated the law of the conservation of energy, a concept that became fundamental to the science of energy and to the science of physics only after 1850. Noting Tait's "radical rephrasing" of Newton, and insisting on a contemporary reading of Newton's text, Cohen considers the issue of unravelling the mathematical argument of Book I, Proposition 40, where Newton's construction can be translated into a relation between work and kinetic energy. Cohen's chapter offering advice on how to read the * Principia * is a typical example of his scholarly openness.

The * Principia * is not an easy task to grapple with and this guide will be of value to scholars in the field, as Cohen draws on and integrates the rich accomplishments of contemporary Newtonian scholarship, in elucidating Newton's path to composition and publication and in clarifying the subtleties of Newton's argument.

Peter Harman is professor of the history of science, University of Lancaster.

## The Principia:

Mathematical Principles of Natural Philosophy

Author - Isaac Newton

ISBN - 0 520 08816 6 and 08817 4

Publisher - University of California Press

Price - £47.00 and £22.00

Pages - 974

Translator - I. Bernard Cohen and Anne Whitman

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