Mathematical Treasure: Robert Simson's The Elements of Euclid

Author(s): 
Cynthia J. Huffman (Pittsburg State University)

The image below is the title page of The Elements of Euclid : viz. the first six books, together with the eleventh and twelfth, by the Scottish mathematician Robert Simson (1687–1768). A Latin version, also by Simson, was published on the same day in 1756. Although Simson attended the University of Glasgow with the intention of entering the ministry, he found his initial studies in theology unsatisfying, and after reading on his own, he developed a fascination with mathematics. In 1711, three days after graduating with his Master of Arts, he was appointed to the chair of mathematics at Glasgow, a position he would hold for 50 years. From the beginning, Simson’s mathematical interests focused on ancient Greek texts, especially in geometry, with the goal of perfecting the existing editions of works of ancient Greek geometers.

Title page of Robert Simson's 1756 The Elements of Euclid.

Thus, in the last page of the Preface, Simson stated, “Upon these Accounts it appeared necessary, and I hope will prove acceptable to all Lovers of Accurate Reasoning and of Mathematical Learning, to remove such blemishes, and restore the principal Books of the Elements to their original Accuracy.” Simson’s restoration of Euclid’s Elements would later appear in over 70 different editions or translations, a record held by very few mathematics books. In fact, even into the 20th century, modern geometry textbooks were greatly influenced by Simson’s version of Euclid. Images from an 1834 American edition of Simson’s The Elements of Euclid are also available on Convergence.

Part of the preface of Robert Simson's 1756 The Elements of Euclid.

The next image shows the first page and begins with definitions. Notice that instead of “plane” Simson used the Latin term “superficies.”

Page 1 of Robert Simson's 1756 The Elements of Euclid.

Interestingly, Simson only has 3 postulates listed on page 6, instead of the usual 5.

Page 6 of Robert Simson's 1756 The Elements of Euclid.

The famous 5th postulate, also known as the Parallel Postulate, appears as Axiom 12.

Page 7 of Robert Simson's 1756 The Elements of Euclid.

In the Notes section at the back of the book, Simson does mention that his Axiom 12 is usually known as the 5th Postulate.

Page 360 of Robert Simson's 1756 The Elements of Euclid.

Below is an image of the Pythagorean Theorem from Book 1, Proposition 47.

Page 51 of Robert Simson's 1756 The Elements of Euclid.

A complete digital scan of The Elements of Euclid is available in the Linda Hall Library Digital Collections. The call number is QA31 .E88 1756.

Images in this article are courtesy of the Linda Hall Library of Science, Engineering & Technology and used with permission. The images may be downloaded and used for the purposes of research, teaching, and private study, provided the Linda Hall Library of Science, Engineering & Technology is credited as the source. For other uses, check out the LHL Image Rights and Reproductions policy.

References

Ackerberg-Hastings, Amy. "Mathematics is a Gentleman's Art: Analysis and Synthesis in American College Geometry Teaching, 1790–1840." PhD diss., Iowa State University, 2000. DOI:10.31274/rtd-180813-13933.

Burnett, John. “Robert Simson’s Euclid and the Foulis Press.” Bibliotheck 11 (1983): 136–148.

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