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The doctrine of triangles : a history of modern trigonometry / Glen Van Brummelen.

by Van Brummelen, Glen, author.

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Princeton : Princeton University Press, [2021]

Trigonometry -- History.

9780691179414 (hardback)

0691179417 (hardback)

xvi, 372 pages : illustrations ; 25 cm

European trigonometry comes of age -- What's in a name? -- Trigonometric tables evolving -- Algebraic gems by Viète -- New theorems, plane and spherical -- Consolidating the solutions of triangles -- Widening applications -- Logarithms -- Napier, Briggs, and the birth of logarithms -- Interlude: Joost Bürgi's surprising method of calculating a sine table -- The explosion of tables of logarithms -- Computing tables effectively: logarithms -- Computing tables effectively: interpolation -- Napier on spherical trigonometry -- Further theoretical developments -- Developments in notation -- Practical and scientific applications -- Calculus -- Quadratures in trigonometry before Newton and Leibniz -- Tangents in Trigonometry before Newton and Leibniz -- Infinite sequences and series in trigonometry -- Transforming the construction of trigonometric tables with series -- Geometric derivatives and integrals of trigonometric functions -- A transition to analytical conceptions -- Euler on the analysis of trigonometric functions -- Euler on spherical trigonometry -- China -- Indian and Islamic trigonometry in China -- Indigenous Chinese geometry -- Indigenous Chinese trigonometry -- The Jesuits arrive -- Trigonometry in the Chongzhen lishu -- Logarithms in China -- The Kangxi Period and Mei Wending --Dai Zhen: philology encounters mathematics -- Infinite series -- Europe after Euler -- Normal science: gap filling in spherical trigonometry -- Symmetry and unity -- The return of stereographic projection -- Surveying and Legendre's theorem -- Trigonometry in navigation -- Tables -- Fourier series -- Concerns about negativity -- Education.

"An interdisciplinary history of trigonometry from the mid-sixteenth century through to the early twentieth century The Doctrine of Triangles offers an interdisciplinary history of trigonometry that spans four centuries, starting in 1550 and concluding in the 1900s. Glen Van Brummelen tells the story of trigonometry as it evolved from an instrument for understanding the heavens to a practical tool, used in fields such as surveying and navigation. In Europe, China, and America, trigonometry aided and was itself transformed by concurrent mathematical revolutions, as well as the rise of science and technology. Following its uses in mid-sixteenth-century Europe as the "foot of the ladder to the stars" and the mathematical helpmate of astronomy, trigonometry became a ubiquitous tool for modeling various phenomena, including animal populations and sound waves. In the late sixteenth century, trigonometry increasingly entered the physical world through the practical disciplines, and its societal reach expanded with the invention of logarithms. Calculus shifted mathematical reasoning from geometric to algebraic patterns of thought, and trigonometry's participation in this new mathematical analysis grew, encouraging such innovations as complex numbers and non-Euclidean geometry. Meanwhile in China, trigonometry was evolving rapidly too, sometimes merging with indigenous forms of knowledge, and with Western discoveries. In the nineteenth century, trigonometry became even more integral to science and industry as a fundamental part of the science and engineering toolbox, and a staple subject in high school classrooms"--

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