many years of assiduous study by dedicated scholars, attempts at geometrical
analysis on the basis of a multitude of meticulous measurements have achieved
results that are disappointingly incommensurate with the monumental efforts
that have been devoted to the task. Even the analyses by computers of masses of
measurements (Wiener & Wetzel 1994) has achieved little more than a few
geometrical forms that are fairly obvious to the unaided eye or brain. Fernie’s Ö2 findings at
On the other hand, the intuitive approach of those like Lesser (1957), described by Branner (1958) as ‘spiritual’ and by Fernie (1990) as ‘romantic’, has led to attempts at analysis that are so visually unconvincing, and so mathematically incomprehensible as to have brought the search for architectural geometry in the great churches into disheartening disrepute. Kenneth Clark (1969, 2), with the best will in the world, complains, ‘Ingenious scholars have produced a system of proportions based on measurements; it’s so complex that I find it very hard to credit’. Fernie (1990) also:
“So much of what has been written in the subject is nonsense (a nonsense which unfortunately lends itself to the computer), consisting of webs of unbelievable complexity and corresponding intellectual nullity which are clearly not worth the effort required to unravel them”(Fernie 1990, 9).
Those, such as Lawlor and Pennick, who are concerned with ‘sacred geometry’ in a larger perspective have broadened out so far into the field of the geometry in nature, even into crystallography and animal life and the imaginary ley-lines of geomatria, as to lose touch with the problem of medieval architecture.
Keith Critchlow has been seriously and actively involved in the subject of ‘sacred geometry’ but in the arena of published works his valuable work on Islamic patterns (1976) is only indirectly concerned with Medieval architecture, while his fascinating and important study of solid geometrical forms (1969) lies beyond the bounds of medieval geometry, as does also his philosophical writing (1994).
In the light of this situation I determined on an approach that would combine the rigour of the mensureist approach with the scholarship of the historians and the exploratory insight of the creative geometer, while avoiding at all costs the extremes of futility and fantasy that they offer.
My first proviso is that the investigation should be limited to one important monument, and that accurate plans and elevations should be acquired. The second is that a sound understanding of the basic history of the building should be acquired.
The third essential is that any necessary measurements should be made on site in order to check the accuracy of other sources and to provide scales on which photographic evidence can be reliably made use of.
Photographs should be made intelligently and must be corrected for perspective distortion. The most modern and professionally made measured drawings and plans should be acquired wherever they are available. All published scales should be checked by measurements made on site. The works of Sir Charles Peers (1906) and George Pace were found to be impeccable. My own measurements made on site were taken to the nearest half-inch or one centimetre, and they were limited to those dimensions that were essential to the process, but not for any kind of mathematical calculation of geometrical forms. On the western façade exhaustive measurements were taken for the express purpose of constructing an accurate ground-plan, and then, in combination with purposefully made photographs, to arrive at an adequately accurate elevation.
The geometrical analysis of the data thus accumulated was to be achieved by a method that might be described by as ‘romantic’ or ‘spiritual, ” consisting of sitting down with a sheet of drafting film over a plan, measured drawing or corrected photograph, on the largest practicable scale, with nothing more than an unmarked straight-edge and a pair of compasses; - no protractors, no set-squares, no calculators, no parallel ruler, but with a head cleared of all thoughts of arithmetic, theorems, algebraic proportions and formulae. Then, in what one hopes was the mind-set of a twelfth century master-mason, well aware of the skills of geometric construction that were possible, but also of the limitations of formal education possessed by such a person, to look at the building and at the geometry that it clearly displays and consider what it is saying. Then to set to work strictly within the rules of Euclidian construction. It has to be said, however, that set-squares were sometimes used for preliminary exploratory constructions, but they were found to be totally inadequate for accurate work even if one had been tempted to make use of them, which I was not.
Medieval life, especially within the monastic world, was a life of Rule and of Order. The monks belonged to an Order and lived by a Rule, but a rule that allowed for individuality and creativity, and that is what must guide our understanding of the geometry that they demanded of the architects who created the building in which they hoped to create a life of Perfection as near as possible to life in Heaven. Such a building would be designed to replicate the conjectured appearance of Heaven, and, like Heaven, to be full of God’s geometry.
I took it as axiomatic that the vertical geometry of any column will lie in the axis of the column and not in its edges. Horizontal geometry will lie along the level of the imposts at the top of capitals, as will the centres of all arcs of arches, unless, as a few are, they are stepped. The essential arc of any arch moulding will be expected to be found arising from the central axis of its supporting column. All these assumptions were found to be correct, although it was also found unexpectedly, that the geometry of stringcourses lay along their underside, i.e., elevational sections did not end with a stringcourse, they began with a stringcourse.
The analyses were to be made on the largest practicable scale and with the highest possible degree of accuracy. This latter principle was to mean the production of many constructions that had to be discarded, corrected, improved, altered and simplified. Thus the constructions presented in the following pages represent no more than the “tip of the iceberg” that needed to be amassed and discarded before totally convincing results were achieved. It also meant that a line drawn in two seconds that was half a millimetre out of place could take half-an-hour to correct, and could mean repeating a whole series of constructions. There was to be no fudging.
With regard to the policy of working to the largest practicable scale, it needs to be recorded that in order to present it in A4 format nearly all the geometry presented in this study has been reduced in linear scale of less than 70% of that of the original drawings, which comes down to less than 50% in area. In the light of this situation a large-scale plan of the cathedral with its geometrical analysis superimposed is provided inside the back cover, although even here the original analysis was made at more than twice the presented scale. (Fig.267).
There was one more self-imposed rule. As far as was practicable each arc was to be completed as a circle. The reasons for this were, first: that it would be in the tradition of the belief in the circle as a sacred form, not to be defaced or deformed, and second: that this process provided the full range of predetermined points available for development. It was in fact found in practice that every square, octagram and hexagram needs to be preceded by an inscribing circle in order to preserve the highest degree of accuracy. Drawing a true square requires considerable care. However, in the presented designs the constructional circles have been omitted in many cases for the sake of clarity.
Not only were the rules on Euclidian construction to be rigorously adhered to, but, most importantly, no preconceived geometrical devices were to be postulated. Every analysis would be required to conform exactly with the geometric forms clearly displayed on the fabric. Any construction that did not do so was to be discarded.
Finally, if and when all the available architectural elements had been analysed, a comparison should be made in order to seek for any unifying factor that might exist between all the geometries of the various parts of the building and over the whole history of its construction. This is what the rule of geometric continuity would lead one to expect. In the event far more than this would be discovered.
An important problem that needed to be addressed concerned the manner of presentation of the results. It was felt necessary that they should be presented in a clear and comprehendable manner that would allow the reader to maintain interest in the developments and to make an intelligent assessment of the correctness of the findings. In order to achieve this it was found desirable in certain key instances, to present each and every geometrical development of a complex construction, in order to make the process plain.
For similar reasons of clarity it was decided from the very beginning that there would be no explanatory material in the form of arithmetical explanations; no formulae, no abstruse mathematical expressions, no equations. Nor would there be a multitude of measurements. The measurements taken would be solely for the purpose of providing accurate plans and elevations, and the only calculations would be for the purpose of providing reliable scales.
The essential character of my method of research analysis may be described as putting oneself into the mind-set, as far as one was able, of a medieval architect equipped with no more than his compass and unmarked rule, working in an ancient tradition of a high art, according to strict rules of procedure, without books or sine or square root tables or theories, but inspired only by his love of making geometry to a degree of perfection, and by an awareness that he was involved in an art of divine origin shared with all the church architects of the past. As Sir Kenneth Clark observes: “One must remember that to medieval man geometry was a divine activity. God was the great geometer, and this concept inspired the architect.”(1969, p. 52). More recently we have the heartfelt words of the twentieth century English church architect George Pace already quoted: “the Church architect must desire to build a church as an act of worship” (Pace P. 1990).
One thing more needs to be explained. This analysis of the geometry of Peterborough cathedral began, in the event, with the analysis of the western façade, c.1220, and the reason for doing so was firstly, that it looked so full of geometry, and secondly, that the measuring was so easily available at any time. When the analysis of the façade had been achieved, the geometry of the rest of the building was tackled, as far as possible, in historical order, but beginning with the plan before moving on to the elevations. Finally, it was decided that the many geometries from the various parts of the cathedral should be displayed together in order to examine them for evidence of a continuity of the geometry across the four centuries of the cathedral’s construction.