Concept and Reality: Different Technical Variations in the
Geometrical Construction of Maulnes Castle
Jan Pieper and Bruno Schindler
Far far away from the constructive tasks of the historical building sites, architectural reconstructions
- graphical or digital - are developed in the research institutions of the architectural historians and
represent therefore a rather abstract image of the building. Reconstructions communicate a virtual
view of the architecture, and a definite requirement for the restoration of the building fabric only
when the building experience – the tradition of the technical building skills of the times is taken
into account appropriately.
Figure 1. Aerial view of the Maulnes castle (left) with reconstruction of the excavation/plot (right).
Precisely this aspect spurred Prof. Jan Pieper and Dr Susanne Traber on during the course of their
research of the Maulnes Castle to reconstruct the traces (peg outs) of the lost garden complex in
Burgundy, France, in actual size, in situ (fig.1). The construction of the pentagon-shaped hunting
lodge was begun in 1566 by the Clermont-Tonnerre Family who had built a famous castle in the
nearby, Ancy-Le-Franc, 20 years earlier with the prominent architect Sebastanio Serlio (14751554). Maulnes lies in the middle of a thick forest with its pentagon ground plan displaying a
mystery that poses a real challenge to the architectural history of the French Renaissance. Thanks to
the duly justified constructional survey (Pieper 1999) of some archaeological excavations in the
area of the garden (Allimant 1999), many historical queries about the buildings can be cleared. With
these sources and, in particular, the published plans of the Castle in Plus Excellents Bastiments de
France (1551-1584) (Du Cerceau 1576, figs. 264-265) (fig.2), the pre-conditions for a practical
experiment appeared to be conducive. The actual measurements, which had been taken from the site
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and which were absolutely necessary for the experiment, did not however comply with the
historical source. The relative location of the basic elements of the now lost spatial sequence of the
castle complex (the entrance with cour d’honneur, the farm buildings formed like a crescent, with
enclosing galleries, the pentagon-based building with its winding staircase around a central wellspring, the big hall above the nymphaeum, along the southward sloping garden and the final Exedra
surrounded by a fortress type wall) proved to be different from the source and their contradictory
proportions did not support any full-scale reconstruction.
Figure 2. Plan and axonometrical elevation of Maulnes Castle. From, Plus Excellents
Bastiments de France (Du Cerceau, 1576, plates 264-5)
Only a systematic analysis of the geometrical construction, which appears to be the basis of a
copperplate engraving by Du Cerceau, allowed this drawing to be covered with reticules of 10
“pieds de Roy” (1 foot = 32,5 cm), thus establishing the scale line measurement of “T” displayed in
the Exedra of the garden with 50 ft. (fig.3).
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Fig. 3. Plan from Plus Excellents Bastiments de France, with the reconstructed graticule
scale of the land surveyors (Unit = 10 ft).
Figure 4. Aerial view of the measuring experiment in Maulnes. Photo from a hot-air baloon.
September 2000
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Eventually a practical surveying method was developed for the surveying instruments of the 16th
century so that the traces (peg outs) could, not only project a mere enlarged image of the drawing of
Du Cerceau on the fields of Maulnes castle, but also enable one to react flexibly to the practical
requirements of the surveyor, the bricklayers, and the stonecutters. According to this theory, the
specifications of Du Cerceau tallied with the findings on the site. Because the presentation of Du
Cerceau was not interpreted as a reduced image with a homogenous norm, but rather perceived as
an rule for controlled construction conforming to the garden complex, the reconstruction of the
entire castle complex, as a tracing/pegging out of the historically standard figure (Fig.4) could be
realised in September 2000 (Schindler 2005, p.73). The surveying experiment revealed that most of
the confirmed irregularities do not arise out of carelessness of the craftsman, but originated in the
measurement techniques of the times. Beyond that, the evaluation of the results show that the
measuring apparatus reconstructed for Maulnes castle, and the corresponding measuring techniques,
conform only to the exterior complexes (garden, enclosing walls), pegged out by the land
surveyors. Whereas the pentagon-based building – built by the masons/bricklayers and stonecutters
– was built and constructed geometrically with standard norms common to these crafts. As a result,
the various trades of the land surveyor, the mason / bricklayer, the stonecutter can be distinguished
from each other through the measuring techniques reconstructed on the relevant buildings, bringing
a new insight into the various building methods.
Figure 5. The level with plumb line, the foot rule with historical divisions (32,5 cm; 2,7 cm per inch)
and the “Carré arpentique” with eight sides (Liebhalt, 1579).
The preliminary studies of the measuring techniques of the sixteenth century led to the development
of the required instruments, namely the geometrical square „croix arpentique“ (Stevin 1634, Vol. 2.
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p. 343) made of brass and named after Simon Stevin (1548-1620) and the wooden rod, described as
“perche royale“(Du Cerceau, 1582, p. 3) of 20 “pieds de Roi“ (= 6, 50 m). Many authors of the 16th
century (Finée, 1544; De Merliers, 1573, etc.) describe the new fixing instruments of the land
surveyors that, essentially, illustrated the simplified horizontal version of the Arabian astrolabes.
Both the geometrical squares which were deployed during the measuring experiments, when fixed
at zero, reduced the possible fixing at 90°, or in many cases at 45°, which in turn increased the
precision of the instruments, (Stevin, 1634) (fig. 5). By contrast there were the forerunners of the
modern leveling devices and theodolites, the sophisticated fixing instruments with swiveling zeros,
which not only surveyed horizontally, but also at vertical angles, but their practical deployment in a
survey was not without dispute (Manesson-Mallet, 1689, Vol. I, p.218).
Figure 6. Fixing the direction of the peg outs with the geometrical square (Photographs, Dr.S.Traber)
The complete conformity of the “perche royale”, described by Du Cerceau, with the graticule of the
drawing of the Plus Excellents Bastiments de France, allowed the peg outs to line with the
geometrically determined run through a mere alternate laying of two leveling staffs, one after
another (fig.6.). Once equipped with the authentic tools the measurement procedure just had to
determine the correct sequence of the measurements.
The plan of the (land) surveyor
The sequence of the various measurements (figs.7-9) can be described through 5 working processes
lasting about a day each during the course of the measuring experiments. First of all the principal
axis was pegged out and then the centre of the complex was determined. Across this point, the
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centre of the construction, the fixing instrument was fixed in such a manner that its visor, the
diagonal axis, fixed the base line of the survey. In the respective tracks, which were respectively
marked with pegs of 20 feet of the measuring staff (~6,50 m), a length of 320 feet was measured on
the diagonal axis, i.e. 160 feet (~52,00 m) each towards the left and right of the measuring
instrument. (fig.7, left). The instruments were then fixed on the end-points of the diagonal axis
pegging out and running parallel north/south (fig.7, right). This procedure of pegs (size »H« with
axis) constitutes the basis for the measuring of each further point (De L’Orme 1648, Vol. II, p. 3133). For controlling purposes the center points of the castle and the garden were marked 40 and 80
feet northwards and southwards on the principal axis. From this point (fig.8, left) the exact position
of the Pegs at 200 and 240 feet was fixed with the eight sided instrument at an angle of 45°-. That
of the right corner containing the garden and the farm building could also be determined at 220 and
260 feet. With the same positioning of the instrument the points at 40 and 80 feet at the base line
were determined. After this control each detail described in the plan of the base figure could be
pegged sidewise from the standard figure of the big »H« (figs. 8-9).
Figure 7.Genesis of the standard figure: Measurement of the axis (De L’Orme, 1648, Vol. II, p. 31-33)
The graduated arches of the complex were determined with a chain and a traction scale with the
corresponding center points and the radians, point for point: the concave farm building, the trench
around the pentagon and the great Exedra at the end of the garden (fig. 8.) The trench around the
pentagon, whose embracing round walls are supported by a Crypto- portico intersects as per the
plan of Du Cerceau at an angle of 60° in the square of the garden and refers as such to the 15°(60°/4 = 15°), which varies from the northern direction (fig.8, right). The tangents of both the
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angles 40:70 (for 30°) und 40:150 (for 15°) do not depict the exact values of modern trigonometric
tables, but do represent their additive characteristics with 150/40 = 70/40 + 80/40: cot(15°) =
cot(30°) + 2.
Figure 8. Genesis of the standard figure: measurement of the parts of the standard figure.
(Measuring unit = 40 feet)
The division of the garden with 10 feet broad paths yields 30 feet beets and a graticule of 40 and 10
feet in the Plus Excellents Bastiments de France (figs. 3, 9), respectively. The totally free-standing
pentagon surrounded by the Crypto-portico is connected formally with this sectioned beet, because
the water theater in the south is a part of the garden as well as part of the garden and the
Nymphaeum façade; the balconies, the corner towers and the Nymphaeum in the basement of the
castle unfolds as a coherent composition. Consequently, the copperplate engraving in Plus
Excellents Bastiments de France shows 2 x 30 = 60 feet as the measurement of the central square in
the garden. From the position of the centre point of the pentagon on the principal axis at 40 feet and
the 30 feet on the half side of the base line emerges a right angled triangle measuring 30:40:50,
which are characteristic of the pentagon, with similar radius of the circumference of the pentagon,
i.e. 50 ft (fig.9, right).
The Pythagorean triangle 3:4:5 now shows a very blunt approximation for the pentagon and the
accuracy of the drawing of Du Cerceau has to be questioned as a suitable source. Basically, the
corner points of regular polygons are not situated on triangles with whole numbers, but have to be
measured with squares and roots. Even if authors of the mathematical tracts of the sixteenth century
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state the approximation 3:4:5: as a suitable combination of numbers for the pentagon (Bartoli 1564,
p.65), one could still not build so inaccurately. As a matter of fact, the pentagon in the Plus
Excellents Bastiments de France - in contrast to Maulnes castle – is not at all regular; it shows, in a
simple measuring system of the land surveyor, the complex measuring rule realized by the masons
and the stonecutters in the middle of the castle complex. While the tracing of the land surveyor,
even in reduced scale, represented the image of Du Cerceau, the embedded pentagon could be
reproduced only with approximate sectioning. It is not possible that the land surveyors pegged the
pentagon so and then entrusted the masons with the measurements conducted by them around the
principal axis and the base line. Moreover, the bricklayers were familiar with the geometrical
coherences of the building. The occupational title master mason (“Maître Maçon”), and its specific
responsibility at the building site at Maulnes, had been documented in the contract of the builders,
Antoine de Crussol and Louise de Clermont, with the mason, Jehan Verdot, from 7 May 1566
(Auxerre, Archives départementales de l’Yonne, E. 657). The masons were responsible for the
construction of the pentagon as per contract and signature.
Figure 9. Genesis of the standard figure: Measurement of the details of the standard figure
(Measurement unit = 40 ft and 10 ft).
From the plan of the Land Surveyor to the plan of the Masons
The geometrically exact implementation of the masonry of the pentagon at the principal axis of the
system of the land surveyor, with the centre at 40 feet north of the base line (in the middle of the
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arched Crypto-portico), yielding a side for the pentagon of exactly 58 feet, is confirmed by the
actual measurement (fig. 9, right). The characteristic triangle of the polygon – in the measuring
systems of the land surveyors measuring 30:40:50 feet – was implemented by the masons with a
measurement of 29:40:49.1/2 feet. Thus the respective sides of the corner towers now measure 2
feet less (58 instead of 60 feet. Consequently, the garden had to be divided in 4×4 compartments,
measuring 29 + 10 = 39, instead of 30 + 10 = 40 feet so as to guarantee the coherence of the ranks
and the towers in the water theater. Moreover, this harmonization of the module of the garden with
the characteristic geometry of the pentagon had an impact on the circumstance of the
implementation of the castle complex as a whole, and explains the contradictions in Plus Excellents
Bastiments de France and the evidence of the construction itself. Variations from the final
measurements – not from the actual pegging procedure – confirm the conformity of the plan and the
implementation of the measuring procedure caused by the modules that had been adhered to. The
garden yielded 156 instead of 160 feet and breadth wise, for the entire complex the double comes to
312 instead of 320 feet. The masonry added on the exterior boundary walls measured 4 feet and
yielded therefore the parallel run measured by the land surveyors at 160 feet to the left and right of
the principal axis. This specific measure could be confirmed in situ at the remains of the garden
complex, and be supplemented by the archeological findings. They confirm that all building lines
that were formally dependent on the castle were implemented as per the modified modules, whereas
the non-dependent building parts were built as per the described measurement of the land surveyors.
For the practical implementation of the pegging out in Maulnes it was only consequent to study
constructively the model of Plus Excellents Bastiments de France, in which the measurements of
the land surveyor had been implemented, rather than copy a descriptive image. Du Cerceau (1576)
particularly defines the ground plan of Maulnes as “dessein du plan comme je vous l’ai figure” and,
as a result, differentiates the procedure of construction implicitly from the plan. Even if these
etymological references (Rey, 1992, [Richelet, 1664]) vary from the Italian “disegno”, and are
contested in research papers, the extreme meaning of “dessein” (horticulture) without “dessin” –
with many instructions but without any visual illustration – of the Protestant Bernard Palissy (1563)
document the contrast between the active construction and the passive picture. Although “plants,
portaicts et montées” are mentioned in the contract of 1566 (Auxerre, Archives départementales de
l’Yonne, E. 657), the French use of the expression “dessein” as opposed to, “dessin”, with the
meaning “intention, goal” instead of “drawing”, is more geometrically apt as the goal for the
implementation of changing architectonic constructional contemplations. This process, a procedure
for different planning of different building phases, will be illustrated in the intersecting works of
land surveyors, masons and stonecutters and will explain the frequently contradicting but not
coincidental facts of the findings.
Read as a “dessein” the plan of Du Cerceau, makes it possible to discern the fundamental module in
its coherence (10 + 30 = 40 ft) and in consideration of the pentagon to reduce (10 + 29 + = 39 ft).
The reduction of measuring units of historical plans permits a very limited discreet gradual
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reduction and does not remain without impact on the form and measurement of the diagram. During
the study of old plans this consequently means the dispensing with the homogeneous reduction of
modern Cartesian scale units and to the crossing over to the discreet construction steps of historical
builders. One can speculate about their identities in Maulnes due to the lack of direct sources. The
project of Du Cerceau or the drawings of the Gdansk Manuscript of Jean Chéreau (16th century)
contain many characteristics of the architecture of Maulnes.
The plan of the Masons
The following analysis of the pentagon actually implemented by maîtres-maçons goes beyond the
practical method of the measuring experiment of September 2000. With its description of the
characteristics of the ground plan, as it unfolded in the interior, we are able to understand the tasks
of the bricklayers better. For this purpose it necessary to study the chronology of the
implementation. After having derived at the actual foundation, the disintegration of the five paged
ground plan on the right angle of the hall and the apartments around the triangular staircase can be
derived at better leading to the ultimate determination of the affiliating outline.
The unconventional division (2 × 29 = 58 feet) of the sides of the pentagon results from a
geometrical simplified triangulation of 72°- and 36°- (fig.10, left), resulting in an isosceles triangle,
the special purpose of which becomes apparent in the bisection of one of either 72°- angles: It
retains in itself a reduced copy as shown in Euclid IV, 10 (Bovelles 1551, p. 21; Benedetti 1553, pp.
23-4). Furthermore, this simplification of the isosceles triangles creates in applied geometry for
similar triangles the pentagonal angle (108° = 3 × 36°) on the side of the bisection of the long side
of the triangle in the so called golden section (Bovelles 1551, p.21): The shorter side of the triangle
(36 ft in Maulnes) has to bear against the larger side of the smaller triangle which is also the shorter
side of the larger triangle (side of the pentagon = 58 ft in Maulnes). And, again, the latter towards
the larger side of the larger triangle (36 + 58 = 94 ft in Maulnes) (fig.10, left). As a matter of fact,
the side of the pentagon – bar a small difference – is the approximated mean proportionate of the
other two measures, i.e. 36 × 94 = 582 + (20).
This triangulation helped preserve the exact position and the angle of the pentagon on the periphery
during the difficult construction of the foundation in the ground water, and above where the
foundation is moistened by the spring water. The remains of the excavated Crypto-portico confirm
also the planned base at the beginning of the construction around the castle at the level of the
garden (Allimant 1999), offering sufficient space for the triangulation (fig.9, right). In contrast to
the mathematically exact measurements of the pentagon (variations of > 5 cm) the triangulation
shows the measurement of 36:58:94 feet (fig.10, left) a sound conformity with the findings. In
particular the decisive position of both the sides of the pentagon at (±46,90; 55,15) feet – very close
to (±47; 55) with (variations > 5 cm) – conforms to the findings at the site of the building.
Moreover, the building creates further collateral triangulations so as to control the peg outs.
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The unambiguousness of the whole numbers of the bricklayers results from an important procedure
that is of further assistance to the building process, an approximate construction of the pentagon in
accordance with Albrecht Dürer’s “Unterweisung der Messung” (Measuring instructions) (1525).
On the top of the figure of a semi hexagonal emerges the pentagon with similar length sides
elongating the sides of a semi square across the corner intersected by two circulars (fig.10, right).
The centre point of the hexagonal with a radius and sides measuring 58 feet lies accordingly 50 ft
southwards from the base line exactly in compliance with the decimal measuring units of the plan
of the bricklayers. The basic approaches of the different constructions as per Euclid and Dürer
resulted in the approximate conformity of whole numbers, because the side of the pentagon
measures 58 feet, therefore, in this case, the square sides under 45° (Dürer) have to intersect with
the larger triangulation of 72°-triangle of Euclid with the coordinates 47 feet (eastwards and
westwards of the principal axis) and 55 feet northwards of the base line. However, the findings at
the building site show – statistically (±46,9 and 55,15) feet – for the practice of the bricklayers
singularly the measurement and angles of the triangulation as per Euclid with 36:58:94 ft (Bovelles,
1551, pp. 21).
Figure 10. Triangulation of the pentagon as per Euclid (left) and intersected foundation plan with
construction as per Dürer (right)
A “belle invention” (a pretty invention) (Ronsard 1950 (1565), Vol. II, p. 999) allows the
arrangement of the interior of the foundation plan with the rectangular hall at 2:1 and the
rectangular rooms of the apartments of the apartments at 1:1. The principal rooms of the
arrangement at Maulnes, measuring 42 × 21 feet and 21 × 21 feet, corresponds to a space typology
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appropriate to the tasks of construction (Pieper 2005, pp. 37). The over-lapping of the rectangular
rooms with the pentagon created a spatial problem that occurs in the construction of French castles
when two apartments are located in the large hall, and there is no space left for the staircase in the
compact structural parts. With the opening up of a compact rectangular ground plan for the castle,
the same points are formed in the middle and on the sides measuring at a basic type 18°- triangle
around the pentagon (De L’Orme, 1648, Vol. I, p.19), (fig.10, right). The pentagon was the result
of the subsequent implementation of the “pretty invention” and creates in its centre a winding
staircase, which is accessible from the outside via the vestibule on the northern corner. The
illumination is effected through an opaion included above the staircase, which reflects on the water
in the central spring and across the pointed angles of the central triangle, functioning like an
illumination box with large embrasures. Both the collateral triangular walls contain small spaces in
their fabric, the fantastic shape of which is dwarfed by the enormous size of the wall, as seen often
in the manifold projections in the manuscripts of Serlio’s Book VI (Serlio, 1996). They expand as
cabinets in the four apartments located in the upper floors. The bathrooms were built in the lower
floors with hypocaust heating which is still preserved today. (Traber 2005, pp. 36). This bathroom
complex surrounds the Nymphaeum in the plinth of the castle located deep down directly by the
water theater of the gardens. The dimensions of the castle, ensuing from the 40 feet height of the
characteristic triangle of the pentagon, measured from the middle of the stairs up to the water
theater, were determined by the land surveyors at the beginning of their task. The 40 feet divide into
8-3-21-3-5 feet on the stairs, the walls, the hall and in the risalit of the towers (fig.10, right).
Figure 11. South facade of the castle. The plinth contains the rustic mouth of the Nymphaeum.
The much deformed facade has been restored in the upper parts.
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The prismatic volume of the building is divided horizontally on the façade by various cornices into
a plinth, piano nobile and the mezzanine. The corresponding heights comply with the foundation
plans for the contours of the pentagonal plinth, resulting in cubic proportions for the pentagonal
structure: 58 feet (= one side of the pentagon) for the height from the threshold of the Nymphaeum
up to the cornice, 49. 1/2 feet (= Radius of the circumference) from the base of the trench up to the
cornice, 36 feet (ratios 36:58:94) from plinth till just below the cornice. The implementation
technique is determined by the standard coursing of the one-foot deep layers of stone, which are
regulated by the 1 to 2 inch variations in the next layer. The corner towers divide the facades of the
pentagon – comparable with the balance between the side and the diagonal of the polygon – into
golden sections, so that these proportions have a strong impact looking towards the castle over the
trees of the forest.
Figure 12. The reconstructed South Facade. To the right, the on-site findings revealing two mezzanine
floors between the Nymphaeum and the hall. To the left, the reconstruction with a single mezzanine
floor (Unit of measure =1 foot).
The cited mathematical sources do not document the building skills of the 16th century craftsmen.
Those published before the middle of the century were not addressed at a popular audience. They
were written in Latin and the statements of the antique authors were often printed in the original
language, also the Arabic translations. Didactic texts, intended for the common public and
craftsmen, were produced only in the second half of the century - more as an explanation and less as
a commentary. The aristocracy, to whom the builders of Maulnes belonged, was instructed directly
by mathematicians like Ramus (1515-1572), or, Vieta (1540-1603), as the case may be. By means
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of the new books craftsman like Jean Chérau (Ms2280, Gdanks Library) could begin to implement
the geometrical documentations of the ancient authors in their constructions, but in daily use their
craft remained true to the tradition of the middle Ages.
The plan of the stonecutters
The understanding between the stonecutters and the bricklayers at Maulnes must have been rather
weak at the beginning. The probably difficult drainage of the trench did not affect the pegging out
of the bricklayers, because this could take place within the planned and leveled trench around the
moat (fig.9, right). The stonecutters however required precise measurements to be taken right at
the bottom of the muddy centre. Instead of assuming it to be 40 feet away from the South Façade –
which would have conformed to the centre of the pentagon, as per the corresponding system of the
land surveyor and the bricklayers – they joined the angles of the already built plinth of the southern
towers to the left and right of the Nymphaeum façade, with the center of the pentagonal sides of the
apartments lying on the opposite side. The outcome of the measurements in the trench was a fixed
point 6 inches southwards, that is, at 39. ½ feet instead of 40 feet north of the base line, because the
approximate construction of the outlines of the building had been accomplished irrespective of the
centre. From this it can be concluded that the staircase was built later, with some delay, when the
exteriors walls had attained a certain height and the measuring unit of the bricklayers around the
building had become inaccessible on the inside. The delay could have ensued from the reworking of
the originally planned staircase, when it became evident that the water level in the Nymphaeum and
the well could not be brought to the level of the garden, but instead lay 8. ½ feet (2.76 m) deeper,
in the newly constructed water theater (fig. 12). According to this hypothesis the winding stairs
would have had to be built later, after the construction of the walls had already progressed and had
covered the peg outs lying much higher in the trench.
The actual work of the stonecutters, took place around the new center of the castle as shown, 39. ½
feet north of the run of the southern towers, i.e. the core of the winding staircase (fig.13). The
outlines emerging from the decagon complement the pentagon with the lateral surface of the pillars.
The decagon lies around a circle with a radius of 3. ¼ ft = 39 in. (fig.13, left). The corresponding
lateral surface of the decagon measuring 2 feet, that is as much the mouth of the spring. The
side/surface enabled the circumference to be divided by 10, by deducting the 15-inch deep pillar
from the 39-inch radius. The circumference of the decagon would have affected the small
pentagram contained in the plans of the bricklayers, had the stonecutters built it along with the
bricklayers from the same central point. The runs and the connexions of the pillars and the openings
of the ground plan of the decagon can be proven very easily in situ, with the historical measuring
unit of “Pieds de Roi” and “Pouces” (1 inch = 1/12 feet) (fig.14). Around the pentagon at the core
of the stairs stood the pedestals and the reorganized flights of the stair on a square ground plan (fig.
13). This ground plan could be archaeologically excavated, partly as a model for the flooring in the
basement.
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Figure 13. Left, geometrical plan of the core of the winding staircase (Measuring unit = 32. ½ feet).
Right, plan and section of the stairs on the main floor of the hall (measuring unit = 32½ / 29 feet)
The geometrical run of the winding staircase required a precise unitized measurement and a
precision that did not normally appear in the building. That is why one can see through this example
how the stonecutters worked with apparent independence and freedom from the rigid feet
measurement regulations of the bricklayers. In order to determine the measuring unit of the steps of
the staircase the height of the floor of 16.¼ feet was divided in 29 steps. In part they refer to the
cuboids of the pillar and vary significently from the accomplishment of the external “Pied de Roi”
employed by the bricklayer (fig.13, right). The Tuscan Doric pillars at the entrance of the stairs to
the hall do not only represent the standing and the military rank of the builder, but documents also
their determination to create an interior on the principles of the rigid geometrical harmony of the
exterior. In fact, the height of 7. ¼ feet gained from the 13 ascents of the pillars on an axis of the
exterior façade (i.e. the 58 ft of the pentagon side), conforms exactly to the diagonal of the center of
the pentagonal core of the winding staircase.
Conclusion and method of study
The practical application of the measuring procedure of the land surveyor of the 16th century, using
authentic measuring instruments, enabled us for the first time ever to do a full-scale reconstruction
of an existing documented building from the French Renaissance, set in the middle of a large
garden complex. This practical experiment demonstrated that the instruments of the period could be
put to use fairly accurately - geometrical square measuring indirectly, and the measuring rods
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directly. The inaccuracy of the fixed direction was under 1/600 of the measured length, constituting
about 10 cm over 60 meters. The tolerances of the lengthwise dimensions resulted from inertia and
the displacement of the surveyor’s staff at the time of pegging, and were under 1/1000.
Figure 14. View of the central, pentagonal core of the winding staircase. The extensions of the left
embrasures run exactly across the opposite corner of the pillar. Each of these corners lies on a decagon.
Much more significant is the experience of seeing how the specifications of a drawing from the
sixteenth century enabled the step by step reconstruction of an entire hierarchal castle complex.
However, this became possible only after the drawn specifications of Du Cerceau, which had served
as source, were revealed not as a scaled down plan, but as a structured construction in real terms.
Certain differences between plan and building can indeed be measured today, but occurred in the
sixteenth century mainly because the drawing and the plan required varying measuring units during
the course of construction. This varying of measuring units encompasses the entire corpus of
historical architecture, so that it is not surprising that one comes across such inaccuracies in
measuring units, even in the illustrated architecture. These inaccuracies are to be found mostly in
the transition of the constructional tasks between the various building trades involved in the
process. Therefore, through their use of independent but “tolerant” measuring methods, groups of
craftsmen active at historical building sites can be separated from one another, but this observation
ought to be evaluated socio-historically on other buildings as well.
The complex interaction of the interdependent measuring systems of historical architecture which,
in the relation of the abstract design to the built reality is seldom decipherable, can be understood
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and defined in Maulnes Castle due to the free association of different modules. The sectioning of
the garden plan of Maulnes in a path module constituting 10 feet with a rebate module constituting
30 feet, as in the plan of Du Cerceau (fig. 3) does not, in itself, facilitate the implementation of the
„dessein“. Only with a reinterpretation of the pair (10 and 30) against the pair (10 and 29) is the
arrangement of the pentagon successful. Such a sectioning of the construction dimensions in
manifold modules of varying sizes facilitates a theoretical procedure to be matched against a
concrete model. Mathematically speaking (Lang 1987) the module pair denotes the constructional
dimensions of the base of the vector space: each constructional dimension is printed with the
appropriate linear-combination of the ground module as a dimensioning chain and the dimension of
the ground module as per the dimensions matched against each other arbitrarily (30 constitutes e.g.
29). Through the linear dependency the elements of the base (here it is 3 X 10 = 30) can, however,
create mathematically speaking many user-defined, conforming measuring chains, which then
explain the possible existence of numerous meaningless proportional studies of historical
architecture.
Maulnes Castle proved to be exceptionally suitable for the application of mathematical analysis,
which is rather unusual in architectural history. In particular the alternative of the pentagonal
geometry proved itself to be a useful practical guideline. With this mathematical instrument the
complex dimensional interaction can sometimes be regulated and allocated to the typical
dimensions used by the various group of crafts.
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