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Maligned for mathematics: Sir Thomas Urquhart and his Trissotetras. (English) Zbl 07744051

Author’s summary: “Thomas Urquhart (1611–1660), celebrated for his English translation of Rabelais’ Gargantua et Pantagruel, has earned some notoriety for his eccentric, putatively incomprehensible early book on trigonometry The Trissotetras (1645). The Trissotetras was too impractical to succeed in its own day as a textbook, since it lacked both trigonometric tables and sample calculations. But its current bad reputation is based on literary authors’ amplifications of the verdict prefaced to its 19th century reprinting by one mathematician, William Wallace, who lacked the background to appreciate the book’s historical context. Considering that context (including seventeenth century ‘copious’ prose, and medieval logic and ‘art of memory’), the bad reputation is undeserved: the book is mathematically clear, clever (e.g. in superimposing 16 problems into one diagram), and complete. The Trissotetras may thus be viewed as simply one more of Urquhart’s polymathic projects and involvements – which included education, rise of the middle class, religious and class conflicts, development of science and mathematics, search for patronage, universal language construction, and development of English prose – which serve to make him a lively and instructive intellectual Everyman for his time.”
Reviewer’s remarks: The author did research extensively the Life, Works and Political Influence regarding Sir Thomas Urquhart (1611–1660). Here his excentric (my word) contribution to mathematics, named Trissotetras, is analysed. The author did so, at least by looking at various sources, (seventy-nine footnotes), and each footnote includes several personalities, written sources; the text itself does contain much relevant referential sources, too.
The author has delved himself fully in this material, and he has to be praised for it in doing so. The paper is long, with notably very interesting facts. It is very worthwhile to take knowledge of the paper.
There is at the end a Conclusion, spreaded out over four printed pages. It is argued on the whole, that the Trissotetras is certainly not nonsensical, but that Urquhart’s aims to introduce a coding devise in order to remember the considerable amount of facts regarding trigonometrical formulas and like problems, is correct in itself. In the other hand, in doing so by Urquhart, eventual readers are discouraged off in studying the text of the Trissotetras, in the past and up to our days also.
By the way, the author of the paper is mentioned as “independent researcher” without any comment. It concerns, however, the same person who wrote his dissertation on topology under the guidance of Peter Hilton. As to further information, on the mathematics of the author, one might consult the Zentralblatt für Mathematik.
As to Sir Thomas Urquhart himself, Wikipedia presents a detailed overview about his where-abouts.

MSC:

01A45 History of mathematics in the 17th century
01-11 Research data for problems pertaining to history and biography
51-11 Research data for problems pertaining to geometry
97G60 Plane and spherical trigonometry (educational aspects)
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