A Medieval and an Elizabethan Maths Book

Love it or loathe it maths is a useful skill. This week I thought I’d seek out what the Cathedral library has in terms of historic maths books and found two gems. The first treasure is Anianus’ Computus cum commento (Computus with commentary), a late fifteenth-century arithmetic manual with instructions and demonstrative woodcuts. This short guide was printed in Paris by Guy Marchant in 1497, and the Worcester Cathedral library copy is the only one surviving in the UK.

Anianus, the author of the commentary, is a figure whom we know little about, but some believe he was a French Benedictine monk. He wrote his computus guide at the end of the fourteenth-century and numerous manuscript copies survive. It was so popular in the century that followed that the commentary was printed in Paris, Rouen, Lyon and Basel. The title page of Marchant’s 1497 edition opens with this splendid woodcut:

Photograph, Compotus cum commento. Reproduced by the permission of the Dean and Chapter of Worcester Cathedral (U.K.)

This is just one of six woodcuts which link books to Marchant’s workshop. It depicts two shoe makers working and includes a central shield containing two hands holding open a book. At the top you can see an abbreviated form of his motto “Sola fides suficit” ,“faith alone suffices”.

Computus, for those wondering, was the major form of mathematical learning in the middle Ages. Put simply, it is the mathematical working out of the dates of Lent and Easter for any given year. In Western Christianity, Easter is the first Sunday after the first full moon after the spring equinox. Once this date has been calculated, the rest of the church’s moveable festivals and celebrations can be worked out in relation to this date. Historians of mathematics have stressed the overwhelming complexity of early computus manuals. Anianus’ compoutus manual was likely popular because it followed a much simpler format than others on the subject, such as those written by Bede and Arnold of Villanova. The commentary is written in prose, and explains how to use the hand as a mnemonic device on which to calculate. Here are some of the woodcuts from Marchant’s edition showing how to use the left hand:

Photograph, Compotus cum commento. Reproduced by the permission of the Dean and Chapter of Worcester Cathedral (U.K.)

Fast forward around a hundred and fifty years and we find the second of the Cathedral library’s interesting maths books: A geometrical treatise named pantometria. This Elizabethan geometry book, written by Thomas Digges c. 1570 presents an array of technologies and tools developed in the Elizabethan era for the study of mathematics and topographical work. Pictured below is one such tool, called a Theodelitus, which is described as a “circle divided into 360 grades”, the diameter of which was 2 feet, meaning that the sizeable instrument had to be held down by some type of clamp.

                               Reproduced by the permission of the Dean and Chapter of Worcester Cathedral (U.K.)

The tool is thought to have been invented by Digges’ father, Leonard. Leonard Digges’ died when his son was aged thirteen and left a partially completed manuscript copy of Pantometria to his son. Thomas Digges completed his father's work. As a child Thomas Digges became a ward of the renowned Elizabethan astronomer and mathematician, John Dee, who you can find out about by clicking here.

What’s most interesting about Pantometria is the consistent application of geometry to solving military problems and war-related scenarios. Though composed centuries apart, Pantometria is reminiscent of the military-style textbooks produced for young school children in Nazi Germany, which superimpose basic maths problems with militaristic images. If you look at the woodcut below you can see how one problem is put in the context of an observer trying to estimate how far two rather threatening looking, incoming ships are away.

Reproduced by the permission of the Dean and Chapter of Worcester Cathedral (U.K.)

The woodcuts on folio 30 and 32 take on an even more militaristic framework, as you can see two warring parties firing canons at one another.

Photograph reproduced by the permission of the Dean and Chapter of Worcester Cathedral (U.K.)

We might read this textbook, therefore, as more than simply an instructive manual, it’s constant references to spying, even in the more innocent peeping Tom scenario, conjures to mind the network of spies at home and abroad employed by Queen Elizabeth I during her reign. Many of the geometry problems, particularly in the first part of the book, are aimed at either seeing things you are usually unable to see, or visually penetrating fortified areas. There is even this excellent woodcut of a man using the reflection of a pond to spy on  his wife situated several stories above.

Photograph reproduced by the permission of the Dean and Chapter of Worcester Cathedral (U.K.)

More broadly, the consistent references to sea faring and sea voyages mean the book is clearly a product of the age of exploration. This maths book then, might also be a useful source for military historians or Elizabethan enthusiasts as it clearly reflects national concerns in this period.