{"id":20243,"date":"2025-10-16T10:29:28","date_gmt":"2025-10-16T14:29:28","guid":{"rendered":"https:\/\/notes.math.ca\/article\/robert-simson-in-canada\/"},"modified":"2025-12-02T10:43:01","modified_gmt":"2025-12-02T15:43:01","slug":"robert-simson-in-canada","status":"publish","type":"article","link":"https:\/\/notes.math.ca\/en\/article\/robert-simson-in-canada\/","title":{"rendered":"Robert Simson in Canada"},"content":{"rendered":"

Two threads in early modern mathematics came together in Robert Simson<\/a>\u2019s 1756 The Elements of Euclid<\/em><\/a> [11]: efforts to compile authoritative editions of Euclid\u2019s Elements of Geometry<\/em>, and adoption of Euclid\u2019s Elements<\/em> as a college textbook, which displaced works on practical geometry as well as compendium textbooks that covered all of the standard mathematical subjects. Simson (1687\u20131768, Figure 1) spent his entire career at the University of Glasgow, in part attempting to restore the original versions of ancient Greek works, especially treatises by Apollonius<\/a> (ca 262\u2013190 BCE) and Euclid<\/a> (ca 325\u2013265 BCE). He thought he could reason out what these authors said before their words were corrupted by copying and translation, mainly by using the ancient Greek methods of proof known as analysis and synthesis [2]. The Elements of Euclid<\/em> was simultaneously published in English and Latin<\/a> (Figure 2), which was one of several signals in the text that Simson saw himself as doing serious historical scholarship.<\/p>\n

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Figure 1.<\/strong> Portrait of Robert Simson painted in 1770 by William Cochrane after a 1746 portrait by Peter De Nune. Hunterian Art Gallery, University of Glasgow, GLAHA:44313<\/a>.<\/h6>\n

Later editors of Euclid, such as Thomas Heath<\/a> (1861\u20131940), agreed that Simson\u2019s editorial work was valuable, even if his ultimate goal of accurately recreating these texts was unrealistic since the earliest surviving versions are centuries removed from their authors\u2019 lifetimes. Simson\u2019s readers, though, were much more interested in how The Elements of Euclid<\/em> could make a difference in teaching and learning Euclidean geometry. The English copies immediately sold in significantly higher numbers than the Latin ones, and in 1762 the publisher began selling a smaller, cheaper version that was even more suitable for college and secondary students [4]. The textbook was translated into Portuguese, Spanish, French, and German, and it was reprinted at least 70 times, including 26 printings in Great Britain before 1780 and 12 printings in the United States in the early 19th century. Further, it has been credited with providing the starting point for most other editors of Euclid\u2019s Elements<\/em> until the 20th century [5].<\/p>\n

\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\"Fig2a-Simson
\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\"Fig2b-Simson\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/p>\n

Figure 2.<\/strong> The English and Latin title pages of The Elements of Euclid<\/em> (1756). Internet Archive.<\/h6>\n

It is unclear when Simson\u2019s textbook first arrived in Canada. Jesuit priests were the first to teach mathematics, using French books and manuscripts in Qu\u00e9bec in the 17th and 18th centuries [6]. Thomas Archibald and Louis Charbonneau have reported that most English-language mathematics textbooks were imported from Great Britain and the United States until the 1850s, although a few arithmetics were reprinted in Canada. They also noted that an anonymous 1853 French-language elementary geometry textbook prepared for Coll\u00e8ge nautique du Canada consisted of a partial translation from Book I of The Elements of Euclid <\/em>[3]. Searches of the Voil\u00e1<\/a>, Aurora<\/a>, and University of Toronto<\/a> (UT) catalogs unearthed several 18th-century print copies of Simson\u2019s full volume scattered across Canadian universities, but most records do not indicate whether the books were used for teaching or were acquired later through donation or purchase. Provenance notes on two of UT\u2019s 1781 6th editions\u2014which indicate that one was used by Irish politician Quintin Dick<\/a> (1777\u20131858) when he was a student at Trinity College Dublin and the other was presented to Scottish politician Andrew Bannatyne<\/a> (1798\u20131871) by Edinburgh mathematician Dugald Stewart<\/a> (1753\u20131823) in 1811\u2014suggest most volumes probably arrived at the libraries holding them today through the latter means of acquisition.<\/p>\n

While, as noted above, The Elements of Euclid<\/em> remained an important source for scholarly analysis of Euclid\u2019s Elements<\/em> until the turn of the 20th century, it was gradually supplanted in British and US geometry classrooms by John Playfair\u2019s 1795 Elements of Geometry<\/em>, translations of Adrien-Marie Legendre\u2019s 1794 \u00c9l\u00e9ments de g\u00e9om\u00e9trie<\/em>, and various descendants of those textbooks. By the middle of the 19th century, it would have been rare to find Simson\u2019s book in a secondary school or college. It is thus notable that, not long after Confederation, two Toronto publishers extended Simson\u2019s influence in Canada by reprinting two geometry texts from earlier in the 19th century that were based on The Elements of Euclid<\/em> [9; 13; Figure 3].<\/p>\n

\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\"Fig3a-Young1871\"
\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\"Fig3b-Potts1876a\"\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/p>\n

Figure 3.<\/strong> Title pages of the Canadian printings of Young\u2019s and Potts\u2019s Euclid\u2019s Elements of Geometry<\/em> (1871 and 1876). Internet Archive.<\/p>\n

Little is known of Francis Young beyond that he was a teacher at St. Edmund’s School in Kingsbridge, Devon, England, who produced at least two textbook series for Routledge in the mid-19th century: Routledge\u2019s Educational Manuals<\/em> and The Class and Home-Lesson Books<\/em> [12]. These seem to have been short volumes of 65\u201380 pages. The first book to appear in the mathematics section of Routledge\u2019s Educational Manuals<\/em> was Euclid\u2019s Elements of Geometry, Book I, Based on Simson\u2019s Text with Explanatory Remarks<\/em> (1858). The 1871 reprint by James Campbell & Son opens with a brief history of geometry, misstates the publication date for The Elements of Euclid<\/em> as 1758\u20131759, and describes it as superseded by Robert Potts\u2019s \u201cvaluable annotated edition,\u201d which will reappear below [13, pp. iii\u2013iv]. The text devoted several pages to definitions and provided Simson\u2019s three postulates and 12 axioms. Similarly, all 48 propositions of Book I are presented, but the proofs are reorganized into numbered steps (Figure 4).<\/p>\n

\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\"Fig4a-Young1871p1\"
\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\"Fig4b-Young1871p27\"\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/p>\n

Figure 4.<\/strong> Young apparently added this division of Simson\u2019s definitions into sections (p. 1) as well as the numbering of steps for the proofs, as in I.9 (p. 27), which were given as prose paragraphs<\/a> in The Elements of Euclid<\/em> and many other geometry textbooks. Internet Archive.<\/p>\n

Robert Potts<\/a> (1805\u20131885) became a private tutor at the University of Cambridge after graduating BA (25th wrangler) in 1832 and MA in 1835 from Trinity College. He edited The Elements of Euclid<\/em> for academies in 1845 and made the book suitable for schools the next year by aiming it at \u201cthe junior classes in public and private schools.\u201d Euclid\u2019s Elements of Geometry: The First Six Books, Chiefly from the Text of Dr. Simson<\/em> was reprinted at least five more times in London [7]; US publishers started to issue the book in 1871 [8]; and Adam Miller & Company in Toronto took it up in 1876, printing both a full version of the text (based upon Potts\u2019s 1850 third and 1863 fifth editions) and a short version containing only Book I [9; 10]. The definitions, axioms, postulates, and propositions appear to come directly from Simson\u2019s work, but Potts added extensive notes at the end of each book (e.g., four pages on the definitions in Book I). He also provided numerous questions for deepening students\u2019 understanding; wrote an essay, \u201cOn the Ancient Geometrical Analysis\u201d (at this point, I confess I began to wonder what sort of teenaged reader would still be with Potts); and included analytical problems, additional propositions, and geometrical exercises for students to prove (Figure 5). For example, Book I alone featured 38 pages of further material, while 20 pages were appended to Book II. Books XI and XII also appeared in the text, although they were never mentioned on Potts\u2019s title pages. Next came hints and explanations for the geometrical exercises. The publisher, presumably, then inserted examination questions from the University of Toronto\u2014these are not found in the versions printed in London and New York. Finally, there was an index of which geometrical exercises had been used on examinations in the colleges of the University of Cambridge.<\/p>\n

\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\"Fig5a-Potts1876ap68\"
\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\"Fig5b-Potts1876aAppendixp1\"\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/p>\n

Figure 5.<\/strong> Potts\u2019s analytical problems for Book I (p. 68) and the first page of the University of Toronto examination questions (Appendix, p. 1). Internet Archive.<\/h6>\n

To fully describe and explain the use of Simson\u2019s text in Canada would require considerable legwork in religious and educational archives: What do school and departmental records say about when and where The Elements of Euclid<\/em> was a required text? Which teachers or professors talked about their teaching of geometry in their correspondence and papers? Did former students mention their classroom experiences to family members or colleagues? What changes in content and teaching philosophies are revealed through line-by-line comparisons of texts? How do handwritten annotations on surviving copies indicate what topics were covered and how quickly? Questions such as these about Robert Simson in the US helped lead to my dissertation [1] and a career of trying to understand the history of mathematics education that now stretches over thirty years . . . and has included the analysis of dozens of geometry textbooks that have been quirky at least as often as they have been intellectual.<\/p>\n

References<\/strong><\/p>\n

[1] Ackerberg-Hastings, Amy. (2000) Mathematics is a Gentleman\u2019s Art: Analysis and Synthesis in American College Geometry Teaching, 1790\u20131840<\/a>. Ph.D. diss., Iowa State University.<\/p>\n

[2] Ackerberg-Hastings, Amy. (2023) Analysis and Synthesis in Robert Simson\u2019s The Elements of Euclid<\/em><\/a>. In Research in History and Philosophy of Mathematics: The CSHPM 2021 Volume<\/em>, edited by Maria Zack and David Waszek, 133\u2013147. Annals of the Canadian Society for History and Philosophy of Mathematics. Birkh\u00e4user.<\/p>\n

[3] Archibald, Thomas, and Louis Charbonneau. (1995) Mathematics in Canada before 1945: A preliminary survey. In Mathematics in Canada<\/em><\/a>, edited by Peter Fillmore, vol. 1, 1\u201390. Ottawa: Canadian Mathematical Society. Reprinted (2005) in Mathematics and the Historian\u2019s Craft: The Kenneth O. May Lecture<\/em><\/a>s<\/em>, edited by Glen Van Brummelen and Michael Kinyon, 141\u2013182. CMS Books in Mathematics.<\/em> New York: Springer.<\/p>\n

[4] Burnett, John. (1983) Robert Simson\u2019s Euclid and the Foulis Press<\/a>. Bibliotheck<\/em> 11, 136\u2013148.<\/p>\n

[5] Gibson, G. A. (1927\u20131929) Sketch of the History of Mathematics in Scotland to the end of the 18th Century<\/a>. Proceedings of the Edinburgh Mathematical Society<\/em> 2nd ser., 1, 1\u201318, 71\u201393.<\/p>\n

[6] Orenstein, David. (2007) The Archival Record of Mathematical Sciences in Nouvell-France and Bas-Canada. Proceedings of the Canadian Society for History and Philosophy of Mathematics<\/em><\/a> 20, 200\u2013204.<\/p>\n

[7] Potts, Robert (1859) Euclid\u2019s Elements of Geometry: The First Six Books, Chiefly from the Text of Dr. Simson: The School Edition<\/em><\/a>.<\/em> 5th ed. London: John W. Parker and Son.<\/p>\n

[8] Potts, Robert (1871) Euclid\u2019s Elements of Geometry: The First Six Books, Chiefly from the Text of Dr. Simson<\/em><\/a>.<\/em> Reprint of 1859 5th edition. New York: John F. Trow.<\/p>\n

[9] Potts, Robert. (1876a) Euclid\u2019s Elements of Geometry: The First Six Books, Chiefly from the Text of Dr. Simson<\/em><\/a>. <\/em>Reprint of the 1863 printing of the 5th edition. Toronto: Adam Miller & Co.<\/p>\n

[10] Potts, Robert. (1876b) Euclid\u2019s Elements of Geometry: Book I<\/em><\/a>.<\/em> Toronto: Adam Miller & Co.<\/p>\n

[11] Simson, Robert. (1756) The Elements of Euclid, viz. The First Six Books, Together with the Eleventh and Twelfth<\/em><\/a>.<\/em> Glasgow: Robert and Andrew Foulis.<\/em> Simultaneously published in Latin as Euclidis Elementorum, Libri Priores Sex, Item Undecimus et Duodecimis<\/em><\/a>.<\/em> Glasgow: Robert and Andrew Foulis.<\/p>\n

[12] Young, Francis. (1858) Scripture History: The Pentateuch<\/em><\/a>.<\/em> Routledge\u2019s Educational Manuals. London: Routledge & Co.<\/p>\n

[13] Young, Francis. (1871) Euclid\u2019s Elements of Geometry, Book I, Based on Simson\u2019s Text with Explanatory Remarks<\/em><\/a>. Toronto: James Campbell & Son.<\/p>\n

\u00a0<\/p>\n

Amy Ackerberg-Hastings is co-editor of <\/em>CSHPM Notes<\/em><\/a>, Content Editor of the <\/em>CSHPM <\/em>Bulletin<\/a>, and co-editor of <\/em>MAA Convergence<\/a>. She has written numerous articles on Robert Simson, John Playfair, and the use of their geometry textbooks in Scotland and the United States.<\/em><\/p>\n","protected":false},"author":11,"template":"","section":[58],"keyword":[260,200,258],"class_list":["post-20243","article","type-article","status-publish","hentry","section-cshpm-notes","keyword-history-of-canadian-mathematics-2","keyword-mathematics-education","keyword-primary-sources-2"],"toolset-meta":{"author-4-info":{"author-4-surname":{"type":"textfield","raw":""},"author-4-given-names":{"type":"textfield","raw":""},"author-4-honorific":{"type":"textfield","raw":""},"author-4-institution":{"type":"textfield","raw":""},"author-4-email":{"type":"email","raw":""},"author-4-cms-role":{"type":"textfield","raw":""}},"author-3-info":{"author-3-surname":{"type":"textfield","raw":""},"author-3-given-names":{"type":"textfield","raw":""},"author-3-honorific":{"type":"textfield","raw":""},"author-3-institution":{"type":"textfield","raw":""},"author-3-email":{"type":"email","raw":""},"author-3-cms-role":{"type":"textfield","raw":""}},"author-2-info":{"author-2-surname":{"type":"textfield","raw":""},"author-2-given-names":{"type":"textfield","raw":""},"author-2-honorific":{"type":"textfield","raw":""},"author-2-institution":{"type":"textfield","raw":""},"author-2-email":{"type":"email","raw":""},"author-2-cms-role":{"type":"textfield","raw":""}},"author-info":{"author-surname":{"type":"textfield","raw":"Ackerberg-Hastings"},"author-given-names":{"type":"textfield","raw":"Amy"},"author-honorific":{"type":"textfield","raw":""},"author-email":{"type":"email","raw":"aackerbe@verizon.net"},"author-institution":{"type":"textfield","raw":"MAA Convergence"},"author-cms-role":{"type":"textfield","raw":"Co-editor of CSHPM Notes"}},"unknown":{"downloadable-pdf":{"type":"file","raw":"https:\/\/notes.math.ca\/wp-content\/uploads\/2025\/10\/Robert-Simson-in-Canada-\u2013-CMS-Notes_compressed.pdf","attachment_id":20501},"article-toc-weight":{"type":"numeric","raw":"5"},"author-surname":{"type":"textfield","raw":"Ackerberg-Hastings"},"author-given-names":{"type":"textfield","raw":"Amy"}}},"_links":{"self":[{"href":"https:\/\/notes.math.ca\/en\/wp-json\/wp\/v2\/article\/20243","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/notes.math.ca\/en\/wp-json\/wp\/v2\/article"}],"about":[{"href":"https:\/\/notes.math.ca\/en\/wp-json\/wp\/v2\/types\/article"}],"author":[{"embeddable":true,"href":"https:\/\/notes.math.ca\/en\/wp-json\/wp\/v2\/users\/11"}],"version-history":[{"count":4,"href":"https:\/\/notes.math.ca\/en\/wp-json\/wp\/v2\/article\/20243\/revisions"}],"predecessor-version":[{"id":20500,"href":"https:\/\/notes.math.ca\/en\/wp-json\/wp\/v2\/article\/20243\/revisions\/20500"}],"wp:attachment":[{"href":"https:\/\/notes.math.ca\/en\/wp-json\/wp\/v2\/media?parent=20243"}],"wp:term":[{"taxonomy":"section","embeddable":true,"href":"https:\/\/notes.math.ca\/en\/wp-json\/wp\/v2\/section?post=20243"},{"taxonomy":"keyword","embeddable":true,"href":"https:\/\/notes.math.ca\/en\/wp-json\/wp\/v2\/keyword?post=20243"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}