Meredith Houlton

In 2021 Meredith was awarded an M.Sc. by Research from the School of Mathematics and Statistics at the University of St Andrews in St. Andrews, Scotland.  Her research focused on a mathematics textbook, Elementa Geometriae, written in Latin and published in 1686.  The textbook was written by William Sanders, the Regius Chair of Mathematics at the University of St Andrews in the late 17th century, and little was known about him and his textbook prior to her research.  Prior to her research, Elementa Geometriae had not been previously studied in detail nor translated before.  Her 2021 thesis was the first time any of it had been examined and translated by a modern scholar. 

Meredith's research at St Andrews focused on the mathematical specifics of Sanders' Elementa Geometriae.  She focused on instances in which Sanders changed the logic of Euclid, changing Euclidean theorems (which require proofs) into axioms (which are taken as fact and do not require proofs) and changing Euclidean axioms into theorems.  She evaluated these conversions and determined they fell into two categories: conversions pertaining to ratios and conversions pertaining to lines.  This involved translation of the Latin text and comparison to Euclid's Elements.  

Many avenues of research were pursued in tandem with this research, including archival research, research into Scottish History, History of Scottish Science, the Scottish Enlightenment, and Early Modern History.  Additional study was undertaken pertaining to the life and work of James Gregory, who was the first Regius Chair of Mathematics at St Andrews, preceding Sanders.   As a result of her archival work, it is evident that Sanders and Gregory worked together as colleagues at St Andrews.  Their collaborative work The Great and New Art of Weighing Vanity is evidence that Gregory and Sanders worked together in some capacity.  Other Special Collections documents provide evidence of additional collaborations between the two St Andrews mathematicians.  

This research on Sanders involved extensive work with St Andrews Special Collections and archival documents at St Andrews, the University of Edinburgh, the University of Aberdeen, the University of Glasgow, and Oxford.   Online resources including The Hathi Trust and Early English Books Online were also utilized for accessing and viewing sources which have been digitized.  A large part of this research involved translating the text from Latin to English.  Once the text was translated, the text and its mathematical concepts were analyzed.  Sanders’ text and Euclid’s Elements were compared, and axioms and theorems which Sanders changed from the Euclidean format were examined.  

This research at St Andrews led to invitations to present at several conferences, including a conference hosted by the British Society for the History of Mathematics and held at The Queen’s College at the University of Oxford. 

Supervisors: Prof. Isobel Falconer MBE, Prof. Edmund Robertson, and Prof. Peter Maxwell-Stuart

Additional Acknowledgments: Prof. Philip Beeley and Prof. Benjamin Wardhaugh with The Reading Euclid Project (Oxford), and the Special Collections Libraries at: University of St Andrews, University of Edinburgh, University of Aberdeen, University of Glasgow, Cambridge, Eton, and Oxford.  Note: British spelling and American spelling are different (acknowledgment/acknowledgement).