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Scholars who have studied the tomb slab of Hugues Libergier have taken great pains to describe measure and, indeed, to trace the represented instruments. Yet, curiously, few have considered it worthwhile to give equal attention to the miniature building -- presumably a model of Saint-Nicaise -- cradled in Hugues's right arm. The different treatment given to the instruments and the building, it seems, is dictated by the scale of the objects: the instruments are tantalizingly close to life-size, while the building is unmistakably symbolic. This fact is surely the explanation for the present tendency by some scholars to consider the instruments to be literal representations of thirteenth-century tools. The problems attending such an interpretation are the concern of this paper. I will review the various strategies and applications adopted by scholars in this regard during the last few decades, and examine the dimensions of these engraved images in relation to those of actual architectural elements. The result of these considerations suggests that the engraved images might not have been intended as a literal "to-the-scale" documentation of medieval tools. Rather, they are iconic attributes proclaiming the profession of the person for whom the tomb was created. The square can be documented as far back as the ancient world, with a small number of surviving examples.[6] The various functions it served in the medieval building trade can be glimpsed from representations demonstrating practical methods or depicting construction scenes. The square, for example, appears at least four times in the drawings of Villard de Honnecourt, which show it used for the cutting of stone blocks and as an aid to obtain the diameter of a column.[7] The square's practical usage demonstrated by Villard is affirmed in numerous construction scenes in which it is employed for checking the angle of stone blocks or for creating templates.[8] These visual depictions strongly indicate that the prevalent use of the square was for the workmen to trace angles or outlines in preparation for stone cutting. The construction of the square was of two major types (each
with its variants): the straight-arm square, or the square with
tapering arms. The length of the arms varied, as did the angles
the arms enclosed. While it is easy to ascertain the function
of straight-arm squares for angle-checking, the function(s) of
squares with tapering arms is much more uncertain and has become
the subject of intense debate. A diagram produced by Marie-Therese
Sarrade, for example, shows a reconstructed square traced from
a twelfth-century tomb slab at Ligne-des- Bois in Charente ( The popularity of the Ö2 is well-known, and is found not only in the design of many medieval structures such as Reims, Amiens, Saint-Quentin, and Saint-Urbain in Troyes,[10] but recorded in treatises on geometry and algebra as well.[11] We are aware that this ancient ratio, geometrically expressed by the ratio of the side of a square to its diagonal, belonged to a set of approximations known since late antiquity.[12] It would seem natural for medieval masons to design "customized" squares that would facilitate stone-cutting at the required angles and ratios. However, the reconstruction suggested by Sarrade does not provide a faster. more convenient way for the masons to obtain the ratios. This is because, according to her demonstration, one of the two rectangles must be constructed first, followed by the juggling of the instrument to locate the other rectangle. Since the construction of both the 1½ and Ö2 rectangles is quite easy, the supposition that the slanting arms of the square would help expedite the process is open to question. Already in 1961 a similar, but not identical, purpose for the instrument was proposed by B. G. Morgan.[13] Having studied the dimensions of almost thirty buildings constructed from the thirteenth through the sixteenth centuries in England, Morgan noted that a high percentage of those constructed after the thirteenth century for or associated with royalty have bay widths based on a module of 23½ feet. Believing that the dimensions were arrived at geometrically, he suggests that a number of right-angled triangles may be constructed using two of the bay- width dimensions for the length of the sides enclosing the right angle.[14] Two types of triangles are of particular importance to his thesis: the "general triangle" which encloses the three angles 90°, 60°, 30°, and the "canonical triangle" (for its royal association), which encloses the three angles of 90°, 58° 17 ' and 31° 43 '.[15] The angles enclosed by the so-called "canonical triangle" are in fact almost identical to a "Golden Number triangle".[16] In order to construct these triangular units for the buildings, Morgan alleges that squares enclosing the required angles would have been needed. He first proposes that the ratio of any square's two arms would have been a universal 1: Ö3 [17], a ratio he happily finds in the square on the tomb slab of Hugues Libergier. [18] Furthermore, Morgan calculates that the straight outer edges of Hugues's square enclose the three angles 90°, 60°, 30° of the so-called "general triangle", while their tapering inner edges enclose the three angles of 90°, 58° 29' 50", and 31° 30' 10", which are almost identical to the angles of his so-called "canonical triangle". Because Morgan is able to relate the angles enclosed by Hugues's square with angles he finds relevant in the design of buildings, he asserts that this square was "a full-scale representation of a 13th-century instrument" traced from an actual mason's square, one that was possibly Hugh Libergier's own instrument.[19] With statements like these, the function of the square is no longer limited to the task of cutting stones. The square, we are told, is a sophisticated instrument employed by the master mason for designing buildings on a monumental scale. Another attempt to associate the instrument with the design of actual buildings was made in l982 by Legendre and Veillerot. In their analysis of the ground plan of Reims Cathedral the authors propose to have identified two proportional systems imbedded in the design: a triangle consisting of 90°, 36° and 54° (the "decagonal triangle", a segment of an evenly divided decagon measuring exactly 36°), and a triangle consisting of the Golden Ratio.[20] Of medieval squares with slanting arms studied by the authors, only those depicted in the album of Villard de Honnecourt could produce both triangles simultaneously.[21] Legendre and Veillerot proceed to demonstrate the design sequence of Reims Cathedral in twenty-two steps, beginning with the overall envelope (by means of the decagonal triangle) encompassing the entire area of the cathedral, followed by the placement of the west façade (using the Golden Ratio triangle), the division of nave bay units (using both triangles), the transept (both triangles), the choir straight hays (the Golden Ratio triangle) and finally the five-bay east end (the decagonal triangle).[22] The employment of either triangle in the design of the ground plan does not seem to conform to a particular order, nor have the authors justified the west-east progression of their sequence which, albeit a hypothetical reconstruction, would have been highly unusual in the case of Reims.[23] The suggestion that 36° angles are imbedded in the Reims design, particularly in the east end, is quite understandable since any building with a five-sided east end could easily be interpreted to have been conceived as half of a decagon with five 36° wedges. It is of course tempting to want to relate squares represented
in a group of early thirteenth-century drawings to a major contemporary
building, especially if the artist who executed the drawings
was known to have visited the edifice. However, such hypothetical
connections must be treated with extreme caution, particularly
if the dimensions of the building do not support the theory.
[24]
For example, Robert Branner already pointed out that the hemicycle
of Reims encompasses an area larger than 184°.[25] In fact,
fresh measurements confirm that four of the five hemicycle bays
are larger than 36° [26] By superimposing a theoretical decagon
on a schematic ground plan, the complexity of the design is masked.
its intricacies obscured. My own analysis of the design suggests
that the genesis of the Reims hemicycle derived from one circle,
not a decagon, since four of the six hemicycle piers stand on
the circumference of one theoretical circle. However, due to
factors such as possibly the desire to create a rhythmical progression
towards the east by flanking the wide axial bay with narrower
outer bays and/or errors which may have occurred during the staking
process, the not-so-perfect five-sided hemicycle came into being.
The suggestion that the area encompassing the choir straight
bays and the transept is produced by means of the two triangles
respectively is also problematic. Again I refer to the dimensions
of the building itself which strongly suggest that it was most
probably conceived by means of two overlapping Ö2
rectangles, a much simpler procedure for such an immense space
( The potential consequences of a literal, metrological reading of such engraved images compel us to reexamine any assumption that we are dealing with full-scale representations of actual tools, rather than emblematic references. If the assumption is made that the dimensions of the instruments are represented to scale, what about the image of Hugues himself? Might we be looking at the exact height of the architect? Here the numbers become quite intriguing. The overall dimension of the effigy of Hugues, as it turns out, measures 2.1 meters from the tip of his hat to his toes.[28] Even if the 23 centimeter distance from ankle to toe were subtracted, he still would have been an impressive man of 1.87 meters (or slightly over 6 feet 1 inch). This seems unusual for a thirteenth-century person, as male adults over 6 feet in today's general population are still regarded as tall. Of course it is possible that Hugues was tall, but alas this could never be confirmed. However, a quick look at extant medieval effigies indicates that their height tends to be exaggerated. In a survey of more than 200 thirteenth-century English effigies,
H. A. Tummers provides the body length of l66 examples.[29] Among them,
forty-two effigies measure more than two meters (6 feet 6 inches),
twenty-six are between l.9 (almost 6 feet 3 inches) and 2 meters,
and fifteen between 1.8 (5 feet l 1 inches) and 1.9 meters. In
sum, eighty-three effigies are taller than 5 feet 11 inches,
which represent exactly half of the effigies listed. However,
these numbers are not supported by dimensions of eleventh- and
twelfth-century human skeletons recently excavated from a medieval
cemetery, the so-called Saint Nicholas Shambles in London.[30]
We learn from the 234 skeletons buried near the parish church
that adult men ranged from a little over 5 feet 2 inches to about
6 feet 2 inches, while adult women were anywhere between 4 feet
9 inches and 5 feet 8 inches.[31] It is important
to note that the average height of males is about 5 feet 8 inches,
and that of females, 5 feet 2 inches. The average male and female
statures extracted from the Saint Nicholas Shambles are quite
consistent with measurements obtained from at least fourteen
other medieval burial sites in England. The height of male skeletons
from the Saxon period through the sixteenth century, from Kent
to Durham, ranged between 5 feet 5 inches and 5 feet 10 inches.
Female skeletons from these grave sites ranged from 5 feet 1
inch to 5 feet 5 inches.[32] Clearly the vast majority of medieval
English men were shorter than 5 feet 11 inches, or l. 8 meters.
On the other hand, the survey by Tummers lists only forty-three
effigies (26% of total effigies measured) which measure between
l.6 (5 feet 2½ inches) and 1.8 meters (5 feet 11 inches),
the average height of the medieval English population. Moreover,
the number of "average-sized" effigies is the same
as that of effigies over two meters alone! French examples from
the same period yield comparable results. The thirteenth-century
effigy of Jean d'Alluye at the Cloisters Museum (25.120.210),
for example, measures about 6 feet l inch from cranium to heel
( Thus, Hugues's effigy most probably does not represent the
actual height of the architect. In addition, another look at
the measuring rod he holds provides intriguing observations.
The rod has often been referred to as a vergette, or marker,
which is a rather general term used to describe such a measuring
or marking instrument. However in several descriptions published
in the nineteenth century it was also referred to as a In pursuit of an answer, I compared modern readings of the
slab's overall dimensions against those given by Tarbé.
The height of the slab, according to Tarbé, measures 8
The square's function as a mason's tool and as a design instrument cannot be ignored. And if a square -- or any image for that matter -- is engraved on a thirteenth-century tomb slab, it ought to be studied, traced, and scrutinized in every way possible. The challenge, though, is to be able to distinguish between representational and emblematic images. Even if a correlation is established between the dimensions of the tools and the building, the assumption that they are causally related must remain hypothetical.
[2]
Bideault and Lautier, [3]
H. Jadart, "Les inscriptions lapidaires de Notre-Dame de
Reims", [4]
P. du Colombier, [5]
L. Legendre and J.-M. Veillerot, "L'architecte, l'équerre
et la géometrie instrumentale au Moyen Age: analyse du
plan de la Cathédrale de Reims", [6]
J. Murdoch, [7]
L. Shelby, "Setting out the Keystones of Pointed Arches:
A Note on Medieval 'Baugeometrie'", [8]
The representations of building the Tower of Babel, a popular
Old Testament subject, constitute a substantial body of medieval
construction scenes. Numerous examples are illustrated in du
Colombier and Recht. See note 4. [9]
M.-Th. Sarrade, [10] The popularity of Ö2 is in no way limited to the continent. For English
buildings, see E. Fernie, [11] Recht, [12] Kidson, [13] B.G. Morgan, [14] [15]. Ibid., p. 55. [16] The three angles of an exact Golden number triangle
are: 90°, 31°43', and 58° 16'. Morgan, Canonic Design,
p. 52. [17] "The thesis that the several bay-width dimensions
of 'royal' work are geometrically related stems from an examination
of the form of the mediaeval mason's square, and, in particular,
from the observation that the arms of the square appear to have
a length relationship of 1: Ö3." Morgan, [18] Ibid., pp. 55-61. [19] In fact, he remarked amusingly that "the carver
of the tomb could hardly have anticipated that this ancillary
symbol would bccome the subject of critical interest seven hundred
years after his death." Morgan, [20] Legendre and Veillerot, "L'architecte, l'équerre
et la géometrie au Moyen Age" (as in note 5), p.
67. [21] Ibid., pp. 68-71. When discussing the Libergier
square in their survey, the authors adopted Morgan's analysis
wholeheartedly. Cf. pp. 64-65. [22] Ibid., pp. 73-76. [23] Though suggestions have been made that the nave
of Reims might have preceded the east end, the majority of scholars
agree that the east end must have been begun before the nave
and the west facade. This has been confirmed by the recent excavation
of the cathedral's foundation in which fragments from earlier
structures thrown into the foundation are found primarily east
of the nave proper. [24]. The study of Legendre and Veillerot includes diagrams
that are perfect examples of over-reading into a ground plan
design, tilling it with a maze of lines that do not necessarily
indicate any actual members or spatial units of the building.
See also G. Lesser, [25] R. Branner, "Jean d'Orbais and the Cathedral
of Reims", Art Bulletin, 43 (1961), pp. 131-133. Another
famous example of such an hémicycle outrepassé
is at Bourges. [26] The angles of the five radiating bays are (from
north to south): 36.215°, 37.770°, 38.698°, 37.628°,
and 38.090°. For an analysis of the Reims hemicycle, see
N. Wu, [27] J. Poterlet, [28] Some of the measurements provided here were obtained
by Marie-Therise Zenner, to whom I am grateful. [29] H. A. Tummers, [30] W. White, [31] Of all the skeletons complete enough for calculating
body height, only five are over 180 centimeters (or just under
6 feet). Only one is over 6 feet. [32] White, [33] Information on the body height of medieval French
men and women is scarce, and so are precise dimensions of effigies. [34] I. Taylor, [35] l [36] Tarbé, [37] The shortest foot I have come across is the so-called
[38] A. E. Berriman, [39] See Shelby, "Masons' Tools" (as in note
5), pp. 247-248. Umberto Eco. Lesser, Thomas Maude. B.G. Morgan, H. Michel, Roger Stalley. Percy Watson. **Nixnet Medieval Architecture****Photographs of Reims Cathedral****The WWW Virtual Library History Index Medieval Europe****AVISTA & Villard de Honnecourt****Association Villard de Honnecourt for the Interdisciplinary Study of Medieval Study of Science, Technology and Art (AVISTA) home page**
well as contributing an article to Ad Quadratum, a volume
dedicated to the art of practical geometry and medieval architecture,
sponsored by Avista and to be published by Ashgate Publishing.
She also serves on theProgramming Committee of the International Medieval Congress at Leeds, UK, and is responsible for programming all art history and architectural sessions of the conference.
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