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**The Principia: mathematical principles of natural philosophy. Newly translated from the 3rd edition (1726) by I. Bernard Cohen and Anne Whitman, assisted by Julia Budenz. Preceded by ‘A guide to Newton’s Principia’ by I. Bernard Cohen.**
*(English)*
Zbl 0961.01034

Berkeley, CA: University of California Press. xvii, 974 p. (1999).

This English translation from the Latin of the third edition of Principia Mathematica (1726) is intended to make Newton’s magnum opus more accessible than before to the modern reader of English while largely retaining Newton’s original mathematical notation. It is also the definitive introduction in English to Principia: over one-third of the volume is devoted to commentary and introduction. It is an edition for the twenty-first century and beyond.

The translators have a basic respect for the Motte translation of 1729 and have avoided over-modernizing while at the same time trying to make the text clearer to today’s reader. They have considerably less respect, however, for the Florian Cajori 1934 revision of Motte. They describe a number of errors in the Motte-Cajori version, characterizing them as “astonishing”, “gross”, and “ridiculous”.

The translators have taken pains to put the reader as directly in touch with Newton as possible. The text itself is laid out in a pleasing way with generous margins and line spacing. It is unencumbered by textual apparatus (not needed thanks to the detailed editorial introduction) with the very rare exception of brief footnotes explaining a word or phrase (for example, that “orb” is used by Newton for what we might call a spherical shell) or giving an important alternate reading from another edition. For those wishing to consult the original Latin there is Cohen’s 1972 variorum edition. The translators recommend the Russian translation by A. N. Krylov [Philosophiae Naturalis Principia Mathematica (Klassiki Nauki, Nauka, Moscow) (1989; Zbl 0732.01044)] for its commentary.

The book-by-book guide to Principia brings into play the latest literature on major issues of debate; for example, did Newton indeed prove that an inverse-square law implies a conic orbit? Among the many useful introductory essays is “How to read the Principia” which gives expanded proofs for some of the more important ones that are only hinted at or entirely missing in Newton. An interesting subsection is “Newton’s Numbers: The ‘Fudge Factor’ ”– the latter term coming from Richard Westfall – concerning numbers, such as the velocity of sound and the precession of the equinoxes, which were altered from edition to edition. Another of the smaller subsections is devoted to Newton’s use of English and French units of measure. The analytical table of contents and overall logical design help to make up for the lack of any index except for the two-pages devoted to names mentioned by Newton.

The translators have a basic respect for the Motte translation of 1729 and have avoided over-modernizing while at the same time trying to make the text clearer to today’s reader. They have considerably less respect, however, for the Florian Cajori 1934 revision of Motte. They describe a number of errors in the Motte-Cajori version, characterizing them as “astonishing”, “gross”, and “ridiculous”.

The translators have taken pains to put the reader as directly in touch with Newton as possible. The text itself is laid out in a pleasing way with generous margins and line spacing. It is unencumbered by textual apparatus (not needed thanks to the detailed editorial introduction) with the very rare exception of brief footnotes explaining a word or phrase (for example, that “orb” is used by Newton for what we might call a spherical shell) or giving an important alternate reading from another edition. For those wishing to consult the original Latin there is Cohen’s 1972 variorum edition. The translators recommend the Russian translation by A. N. Krylov [Philosophiae Naturalis Principia Mathematica (Klassiki Nauki, Nauka, Moscow) (1989; Zbl 0732.01044)] for its commentary.

The book-by-book guide to Principia brings into play the latest literature on major issues of debate; for example, did Newton indeed prove that an inverse-square law implies a conic orbit? Among the many useful introductory essays is “How to read the Principia” which gives expanded proofs for some of the more important ones that are only hinted at or entirely missing in Newton. An interesting subsection is “Newton’s Numbers: The ‘Fudge Factor’ ”– the latter term coming from Richard Westfall – concerning numbers, such as the velocity of sound and the precession of the equinoxes, which were altered from edition to edition. Another of the smaller subsections is devoted to Newton’s use of English and French units of measure. The analytical table of contents and overall logical design help to make up for the lack of any index except for the two-pages devoted to names mentioned by Newton.

Reviewer: Albert C.Lewis (Indianapolis)

### MSC:

01A75 | Collected or selected works; reprintings or translations of classics |

01A45 | History of mathematics in the 17th century |

### Citations:

Zbl 0732.01044
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\textit{I. Newton}, The \textit{Principia}: mathematical principles of natural philosophy. Newly translated from the 3rd edition (1726) by I. Bernard Cohen and Anne Whitman, assisted by Julia Budenz. Preceded by `A guide to Newton's Principia' by I. Bernard Cohen. Berkeley, CA: University of California Press (1999; Zbl 0961.01034)