Mathematical Treasure: William Oughtred’s Elementi Decimi Euclidis Declaratio

The above image is the title page of Elementi Decimi Euclidis Declaratio (A Clarification of the Tenth Book of Euclid’s Elements, 1662) by William Oughtred (1574–1660). Oughtred, an English clergyman and mathematician, is best known for inventing a slide rule and for his influential work Clavis Mathematicae. Images of a 1631 Latin edition, a 1667 Latin edition, and a 1647 English translation of Oughtred’s Clavis Mathematicae are available on Convergence.

The next two images show the notation used in Oughtred’s work on Euclid, starting off with symbols for equal, greater than, and less than.

The image below is page 5, containing a section of lemmas. With the help of the notation guide (the last two lines of the first page and the first two lines of the second page), one can see that the second lemma shows the expansion of binomials, \(A^2 + E^2 – 2AE = (A-E)^2\) and \(A^2 + E^2 + 2AE = (A+E)^2\).

There is also a section on the five regular solids which includes nets for all but the icosahedron.

A complete digital scan of Oughtred’s 1662 Elementi Decimi Euclidis Declaratio can be found in the Linda Hall Library Digital Collections. It is bound together with a 1667 edition of Oughtred’s Clavis Mathematicae, call number QA33 .O73 1667, and two of Oughtred’s other works, Theorematum in Libris Archimedis de Sphaera & Cylindro Declaratio (1663) and Horologiorum Sciotericorum in Plano (1663).

Images in this article are courtesy of the Linda Hall Library of Science, Engineering & Technology and used with permission. The Linda Hall Library makes available all existing digital images from its collection that are in the public domain to be used for any purpose under the terms of a Creative Commons License CC by 4.0. The Library’s preferred credit line for all use is: “Courtesy of The Linda Hall Library of Science, Engineering & Technology.”

Index to Mathematical Treasures