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Symbols, impossible numbers, and geometric entanglements: British algebra through the commentaries on Newton’s Universal arithmetick. (English) Zbl 0876.01002

Cambridge: Cambridge University Press. xi, 328 p. (1997).
This book traces the progress of algebra in England and Scotland, as reflected in publications of the period 1631-1740. The author emphasizes three issues, alluded to in the title, that mathematicians of the time contended with and debated over: symbolic approaches to mathematics, the meaning and nature of negative and complex numbers, and the relationship between and relative merits of algebra and geometry. Providing a backdrop for all this, the first chapter treats the work of Cardano and Viète. The following nine chapters then discuss, respectively, the contributions of Oughtred and Harriot, Collins, Pell and Kersey, Wallis, Hobbes and Barrow, Newton, Berkeley, Simson and MacLaurin, and Saunderson. A short epilogue touches on Maseres, Waring, and others.

MSC:

01-02 Research exposition (monographs, survey articles) pertaining to history and biography

Biographic References:

Newton, I.
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