A 16th Century Math Book With Pop-Up Models

Elements of Geometrie of the Most Ancient Philosopher Euclide of Megara

Euclid’s Elements, first published in 300 BC, was one of the most important and influential textbooks ever written in the history of science and it laid the foundations of mathematics. It was one of the earliest mathematical works to be printed after the invention of the printing press, and by some estimates, it is second only to the Bible in the number of editions published since the first printing in 1482. By Queen Victoria’s time, The Elements had became a standard textbook in schools, and even today, Euclid’s mathematics is universally taught to all high school students.

Elements was first translated into English from Greek in 1570, by Sir Henry Billingsley, an English merchant who later became the mayor of London. Billingsley was a mathematics graduate of Cambridge University and well versed in Greek. Instead of translating from the well-known Latin translation, Billingsley chose the Greek edition of Theon of Alexandria (ca. 390).

Billingsley’s translation was a magnum opus. He translated all the thirteen books of Euclid and added three additional books attributed to Euclid, along with notes from various ancient and modern commentators. The finished work was over a thousand pages. A unique feature of Billingsley’s translation was the unique “pop up” models—three-dimensional fold-up diagrams—that he included throughout the book to illustrate geometric solids and different mathematical theorems. It was one of the first books to include such a feature.

Elements of Geometrie of the Most Ancient Philosopher Euclide of Megara

These pop-up models occur throughout Book XI on solid geometry and were hand-glued into each copy of the work. Photo: Special Collections: University of Aberdeen

Elements of Geometrie of the Most Ancient Philosopher Euclide of Megara

Flaps used to represent three-dimensional shapes. Photo: Special Collections: University of Aberdeen

Although Billingsley’s work was renowned for its clarity and accuracy, the author made the embarrassing mistake of confusing Euclide of Megara with Euclid of Alexandria. Thus his book is erroneously titled “The Elements of Geometrie of the Most Ancient Philosopher Euclide of Megara.”

For many years a controversy raged as to who was the real author of this work. The 19th century British mathematician Augustus De Morgan suggested that the translation was solely the work of the Anglo-Welsh mathematician John Dee. The English antiquarian Anthony Wood asserted that the translation was largely the work of the priest David Whytehead, who spent his final years at Billingsley's house. It was only towards the end of the 19th century, when the original copy of Euclid used by Billingsley in his translation found its way to Princeton College, the numerous marginal notes and comments left no doubt who the major contributor to the disputed work was.

Elements of Geometrie of the Most Ancient Philosopher Euclide of Megara