The following study is an abridged version of a doctoral thesis entitled “By Crafft of Ewclyde: The Sacramental Geometry of Peterborough Cathedral”.  Between about 1000 and 1500 AD, the subject of the present study was known simply as ‘geometrie’.  Why then, one might ask, should it have been felt necessary to call it ‘sacramental geometry’?

     For one thing, the word ‘geometry’ today has connotations very different from those it held a thousand or even five hundred years ago.  Today it is defined as ‘The branch of mathematics that deals with points, lines, planes and solids, and examines their properties, measurement and mutual relations in space’.  In the Middle Ages it meant no more than the creation of geometrical designs by the use of compass and rule.  Discussion, argument and proof had no part in it.   It was an art, and it was wordless.  Like music, it was held to be of divine origin, and it was used primarily for the design of religious items, be they buildings, works of art or artefacts.

      In the nineteenth century, after centuries of disuse, the historical existence of this medieval form of geometry was rediscovered, though not its true character.  In order to differentiate it from the geometry of Euclidian theorems, it was referred to as ‘Sacred Geometry’, and it retained that appellation until about 1960.  By that time, however, the subject of Sacred Geometry had achieved the status of anathema in the world of serious scholarship. The publication of numerous often wildly imaginative and illogical attempts at the discovery of the Sacred Geometry of various famous buildings, often accompanied by incomprehensible explanations, had led the world of scholarship to become wholly alienated from the proponents of Sacred Geometry.  The term was left to be appropriated by the adherents of New Age mysticism, wherein it became involved with such matters as the geometries of plant life and crystals, and the siting of ancient churches and monuments along imaginary ‘ley-lines’ of geographic proportions.

Architectural historians needed a new terminology. One distinguished American professor, Lon. R. Shelby, perhaps the most dedicated investigative student of medieval geometry, coined the term ‘constructive geometry’ (1977, 62), which is accurate enough as far as it goes, for the medieval geometry consisted of constructions created with compass and rule. But the term is perhaps too broad, for many geometric constructions are unconnected with architecture or with religion. Furthermore, the term ‘constructive’ can be misunderstood as being concerned with the practical construction of buildings.  John Bailey (1991, 23) does in fact refer to it as ‘constructional geometry.  But this can lead to a complete misunderstanding of its character and purpose, which was totally unrelated to the construction of buildings, and related solely to the religious nature of the sacred buildings to which it was applied.

      Another American scholar, Bucher, refers to medieval geometry mostly in terms of ‘turned squares’, (1972, 39 & 40), which are found in a great many examples of the art, but this gives no indication of its religious function nor of the great range of geometrical constructional devices that were used in the process of architectural design.   

      The process of geometrical drawing was not inherently sacred although it was used for the sanctification of buildings and artefacts.  Its function was to make them sacred. Thus ‘Sanctifying Geometry’ might be perhaps a sufficiently accurate designation.  But for this writer the term ‘sacramental’ conveys more fundamentally the reverential attitude that I believe characterised the medieval architect’s approach to the application of his geometric skills to his monumental task of designing a House of God.   This does not mean, however, that it was related in any way to the sacrament of the Eucharist, except in the sense that just as bread and wine are not in themselves sacred, even in the vestry cupboard, they become sacred through the proper performance of a special liturgy, so the unsacred stone of a building became sanctified through being carved and arranged in conformity with a special geometry.  That geometry also will be shown to have its origins and character deeply rooted in medieval theology.

     The task that faces the intrepid explorer in the disaster-ridden jungle of the geometric analysis of cathedrals of such great size and complexity is not only monumental, but also perilous, for there cannot be more than a very few architectural historians who could refrain from a sigh of despair at the thought of yet another mass of incoherent geometricalities and algebraic complexities.  One may quote Bucher: ‘Unfortunately the literature on medieval design theory is still permeated by exalted drawings whose lack of common sense and utility is mitigated only by the inherent beauty of geometric exercises’. (1971, 42). Also Morgan B.G. ‘Clearly, there is nothing to be gained in attempting, yet again to apply geometrical figures to the plans and sections of medieval buildings in the hope that some hidden secret will at last be revealed’. (1961, 19).

       The question of relevance to contemporary architecture may present itself.   Religious beliefs of today are very different from those of the twelfth century, and architecture is now a very different occupation.  Architects then were selected from the stone-mason sculptors, and there are not many sculptor architects today.  More importantly the medieval architect was born and bred into a devoutly Christian culture, a culture that was all embracing, and in which he played a very important role.   His profession, even though at certain times involved secular projects such as castles, was deeply rooted in the religious ethos of his time, to a degree that is not easy to envisage today.    

     Thus the search for an ancient geometry imbedded in the masonry of Peterborough cathedral, although very interesting, would appear to be rather purposeless.  But that may be no bad thing.  The world is well supplied with purposeful calamities, and the search for sacramental geometry would seem to be a harmless pursuit that could perhaps lead to a deeper appreciation of the genius of those medieval architects who created the world’s great churches.

      The text of the following study falls into two main sections.  The first half consists mainly of the written word, and is concerned to present the origins, purpose and history of sacramental geometry, supported by illustrative material wherever it might be required to clarify or exemplify.   

       The second half of the thesis is very different in character, for it is essentially geometric and diagrammatic rather than verbal, and requires looking more than reading.  The text includes a brief architectural history of the cathedral, reduced from Professor Lisa A. Reilly’s recent study (1997), which varies in several respects with traditional understandings of that history.  It also includes a description of the methodology of the investigation and of the analytical processes that were undertaken. Many parts of the building are separately analysed in both plan and elevation. The architectural history of each part is discussed and its geometry demonstrated. 

     Originally it was intended that the analyses would be presented in the historical order of architectural construction, but as this study records an investigation it would seem to be more fitting to present it in the order in which the investigatory analyses were undertaken.

      The first work to be performed was the detailed measurement of the early thirteenth century western façade and the late fourteenth century porch.  Based on the measurements taken a sufficiently accurate drawing of the elevation of the façade was made, and upon this portrayal the geometric analysis of its design was achieved. 

     The completion of the study of the façade was followed by the geometrical analysis of the plan of the Anglo-Norman church, and then of its elevations, interior and exterior, in nave, choir and transepts, followed by an analysis in elevation of the fourteenth century tower.

       Attention was then directed at the plan development of the western end of the nave, which had undergone several changes of design over a period of about fifty years.  This exercise was completed with an analysis of the plan of the small Perpendicular Porch, followed by the analysis of the Porch’s western elevation.  

     Finally geometrical analyses were made of the plan of the fan-vaulted development of the c.1500 eastern end of the cathedral, and of its central eastern window.  

     The geometrical analyses are then presented as a comparison of the geometries of all the various parts of the cathedral that had been analysed, with the result that a completely integrated geometry covering the whole building over four centuries of development was identified and demonstrated.

     The first chapter of the study is drawn mostly from literary sources, with my own comments and deductions, while the geometric second half, apart from any historical details, is entirely my own.

     Although one accurate plan of the present cathedral, prepared by the architect Sir Charles Peers (1905), was necessarily used, essential measurements were made personally by the writer on site.  In addition, new photographs provided the basis for many of the elevations, but always supported by measurements taken at the same time to provide an accurate scale for each photograph. In addition, wherever necessary, photographs were emended or electronically enhanced in order to eliminate perspective distortion before any analyses were undertaken.  It may be noted that there is no lens or camera that can eliminate perspective in a three-dimensional structure.

      One problem that arises when one has undertaken a geometrical study is the question of how it can be presented to the reader in a form that is readable and interesting, and also in a manner that can reasonably regarded as proving the truth of one’s findings.. 

.  Commentators demand that analyses need to be performed on a large scale (Branner, 1958, 17).  Thus in printing most of the original geometrical drawings have had to be photographically reduced in area to no more than forty-five per cent of the originals.

      In pursuit of comprehendability and persuasive proof, separate drawings for each and every stage of geometric construction are provided in several important areas, all of which were carried out strictly in conformity with the Euclidian rules explained in the text.   Furthermore every effort has been made to avoid the use of arithmetical and algebraic expressions. 

       One other matter requires explanation.   The measurements at Peterborough were recorded in Imperial Feet and Inches.   Metric scales are however provided where they appear desirable.  This does not mean that inches were used by the stone-masons.  They appear to have been used only by carpenters, and even then, to judge by the many documents assembled by Salzman, only late in the Middle Ages when the first mention of an inch appears, and then only in French (Salzman, 1992, 441).  The foot and half a foot appear to have been the mason’s units, although in practice there would seem to have been little need for the hands-on stone-mason to measure anything in such terms.  His master-mason’s templates left little to be measured.  He would not have owned a folding rule or tape-measure, for they did not exist, and for most of the Middle Ages he was almost certainly almost innumerate as well as illiterate (Shelby, 1917b, 238) (Coulton 1961, 7-16).  No expensive mistakes could arise if he was never required to deal with numbers of feet misheard or misunderstood as they passed down the line in various local, even foreign, accents, in a team of masons drawn from far and wide.

     For the architect, however, the English foot was the measure, and here it must be emphasised that the English foot of today is exactly the same as the English foot as decreed by King William 1 in about 1070, which was and is 304.8 millimetres (Zupko, 1977). However, in actuality, William’s ‘English’ foot did not become standardised throughout the realm until the reign of Henry 1, (1100 – 1135).  Before that the ‘Norman’ foot of 297.77 mm or 11¾ inches was widely used, (Harvey 1972 108), and this fact is taken account of in this investigation.

      One other term requires explanation.  The word ‘architect’ is used throughout this study to mean the person who designed the building.  He would be given other titles at various times and in various places, and he may have been burdened with many other responsibilities, but if he designed the building then he was the architect.  

The findings at Peterborough lead one to believe that a similar approach to the design of other buildings of the period would achieve comparable results.  They also raise certain related questions concerning such matters as the method of measurement and scaling used on site by the architects.  These matters are discussed in a later chapter. 1 

    Why was Peterborough Cathedral chosen as the subject for prolonged investigation?  One could say that it was because the beauty of its geometricality has been remarked upon by many in the past, and that its architectural history was spread over the whole medieval period in clearly defined constructional and stylistic areas of the fabric. Or it could have been because Reilly’s Architectural History of Peterborough Cathedral was about to be published.  But the fact is that the cathedral chose itself, for the writer happened by chance to be living in its shadow.  It was a happy choice.



1 The question of masons use of ‘yard-sticks’ may be mentioned here.  In Milan the mathematician Stornaloco recommended yardsticks measuring seven braccia to be use in measuring elevations so that they could be used in whole numbers in proportions of the 84 braccia total height (Frankl  1944, 55) ie. in multiples of seven braccia.  Subdivision into braccia would not be needed.   The ‘Yardstick’ is and was the basic unit.  It varied from building to building, and was not subdivided.