ASPECTS OF ITS ARCHITECTURAL GEOMETRY
Colin Joseph Dudley
The nature of medieval architectural geometry has been fully dealt with in the first three chapters of the preceding work on Peterborough Cathedral. Readers unacquainted with them are advised to peruse them before entering into the following investigation into the geometry discovered at Canterbury Cathedral.
Suffice it to say that the ‘high art’ of medieval geometry required no mathematical knowledge of any kind, except, as has been shown in the Appendix above, by the master mason transferring his drawings to scale to his building site. It demands not even the ability to count, to measure, to read, to write or even to speak. Its constructions, which are performed with no more than an unmarked straight-edge and a compass, are within the ability of a nine-year old child, following the very simple rules known as Euclid’s Postulates, with the greatest care and accuracy. It needs only sharp eyesight, and a steady hand.
For the reader today an understanding of the term ‘geometrical progression’ is needed, while it should be pointed out that although three terms are required to identify a numerical geometrical progression, only two are needed to identify a progression in geometry.
All the drawings and geometries presented here, both in the Peterborough work above and in the following work on Canterbury, are the unaided original work of this author, except where otherwise attributed. They were all drawn on drafting film using only a compass, an unmarked straight-edge and a drafting pen. The medieval architect, the Master Mason, would have used silverpoint on prepared parchment, so difficult to obtain today. His small drawing compasses, which are now known as “dividers”, were equipped with needle sharp points of silver. Computers have been used in the present work only to record and to make copies and to enlarge or reduce illustrations. They have not been used to create geometry.
No attempt had been made to achieve a complete geometry of Canterbury Cathedral, but only to investigate a few particularly interesting aspects.
The Postulates of Euclid
Only an unmarked straight-edge and a compass may be used. Any straight line must past from a one point to another point, but may be extended. Any circle must be centred on a point and pass through another point. The crossing of any two lines constitutes a point.
In practice every construction must begin with a straight line and a circle. A tangent is a point. Symmetry must be maintained.
The following study could never have been brought to a conclusion without the unremitting patience and encouragement of my wife, Joy Elaine, and the practical skills and technological assistance of our daughter Celia. My heartfelt gratitude to you both.
C.J.D. March 2009