25
Architectural Layout: Design, Structure, and Construction in Northern Europe
One of the most creative periods in architecture occurred in Northern Europe in the years 1000–1300. New approaches to layout in monastic churches and urban cathedrals constitute an essential aspect of Romanesque and Gothic originality. 1 The historical challenge of understanding these changes in design and construction is made all the greater, however, due to a relative lack of period documents, of collected bibliography,2 and an in-depth study embracing this entire period.3 A lack of unity exists within the field as well, where Gothic is typically deemed superior to Romanesque; yet Gothic could not have existed without preceding generations of building in ashlar. Understanding of stone structures presents a special challenge today, since techniques of stone building are only taught for restoration work; medieval design techniques and the building culture itself are rapidly disappearing even within the oral tradition. A general lack of appreciation for the experimental process in medieval science, more specifically, for applied mathematics and its use of approximations, presents another hurdle to a reassessment of early knowledge of physical matters. Finally, with current academic trends seeking international relevance within a global society, European medieval architecture fares less well than at its zenith in the mid-twentieth century. Yet the most advanced studies have been produced in the last few years. An embracing overview “connecting the dots” between architectural phases, scholarly approaches, and disciplines may offer new clarity and direction and, ultimately, enhance the discipline’s future growth.
The concept of layout has many interpretations, reflecting the prevailing philosophy and state of the discipline. Historical studies began with the plan’s general form,4 and continued with comparative development of major formal elements,5 typically with stylistic grouping by region or nation.6 Functional typologies of layout have focused on pilgrimage7 and recently again on liturgy.8 Another renewed theme is the psychological effect of space.9 Formal studies led to investigations of symbolic or iconological meaning, whereby a layout “quotes” an earlier edifice (in plan, elevation, orientation, or implicit meaning).10 Archetypal references, such as Solomon’s Temple and Noah’s Ark, merit more attention.11
From the earliest times, layout has also meant design concept, although this presents methodological problems. To name only five: (1) well into the twentieth century, plans of built monuments typically consisted of symmetrically disposed spaces delineated using just a few measurements taken in situ; (2) many from outside (and within) academia have tried their hand at drawing on such plans, by applying a priori concepts of proportion or geometry; (3) since these plans are typically small scale (not to mention potential distortion from any reproduction process), the applied designs cannot comply with rigorous margins of error; (4) knowledge of medieval practical geometry is still insufficient to justify use of any a priori concept; (5) most importantly, such designs do not take into account wall thickness, hence implications for a three-dimensional structure in elevation. In the past two decades, techniques in monumental archaeology,12 and the measured survey, specifically, the computer-aided survey and drawing with AutoCAD,13 make it theoretically possible to integrate detailed studies in design, structure, and construction. In fact, one cannot exist without the other – one point of view is insufficient in analyzing any complex subject. Together, they may lead us back to an understanding of the design concept in a given monument and, perhaps eventually, of medieval design principles, aided by the as yet unwritten history of practical geometry.
The stone monuments remain the first and final record. In addition to textual sources on building,14 five primary sources provide essential background for research on medieval architecture. Spanning the first millennium and then some, these parchment records speak to concepts in measurement, design, layout, mechanics, mathematics, and the quantified sciences: Vitruvius, the Corpus agrimensorum Romanorum (CAR), the Plan of St Gall, the Latin Euclid tradition, and the Portfolio of Villard de Honnecourt.
Vitruvius
Marcus Vitruvius Pollio’s treatise De architectura (c.33/22 BCE)15 requires little introduction, as it is the only extant treatise on Roman building. While it is not yet clear what explicit effect Vitruvius’ text may have had on medieval readers or builders,16 it provides us with a fundamental, contextual basis. Of special relevance are his sections on the general education of the architect, which should include mathematics and astronomy, on proportion and number in particular, 17 on mechanics,18 and on the orientation and selection of ground for a building site.
Corpus agrimensorum Romanorum
The Corpus agrimensorum Romanorum (CAR), a manuscript collection dating from the first to sixth centuries ce, is even more fundamental, as a source for medieval practical geometry, drawing upon an ancient tradition of land surveying with related problems of measurement and geometry, all amply illustrated.19 Vitruvius’ treatise and the CAR may be compared to Roman technical writing, in particular, building manuals20 and other practical treatises, such as Marcus Terentius Varro’s Rerum rusticarum (first-century BCE), as well as Roman scientific writing.
Plan of St Gall
A design for a Benedictine monastery, the complex plan associated with St Gall (Switzerland) is the earliest extant medieval architectural drawing (c.817/19).21 Apart from several other ninth-century plans,22 there is a gap of 400 years before the next explicit illustration of an architectural concept. For this reason alone, it is invaluable.23 The plan may be considered in terms of Vitruvius’ advice on orientation and planning, and the CAR’s graphic representation of structures and land division.
Latin Euclid
Along with the Bible, the Elements is the most printed work in Western culture.24 It summarizes geometric principles known during the time of Euclid of Alexandria (c.325–c.265 BCE). The Latin manuscript tradition was deemed insignificant, and virtually all scholarly attention has been directed to the Greco-Arabic tradition, transmitted to Northern Europe in the second quarter of the twelfth century. Important new work on the dispersed textual transmission has been done to correct this historical blind spot.25 Between the eighth and eleventh centuries, the Latin Euclid manuscript tradition was reconsolidated from mixed practical-scholarly sources, including the CAR and Gerbert,26 principally in Corbie and the Lorraine.27 Connections have since been made between Latin Euclid and medieval architecture.28
Portfolio of Villard de Honnecourt
The portfolio of Villard de Honnecourt (Paris, Bibliothèque nationale, MS Fr 19093, c.1220/35) is a minuscule manuscript of drawings commented in Picard and Latin.29 Yet it has immeasurable value as the earliest known graphic record of concepts in architecture and mechanics – at least for post-Roman Europe. In many ways, it appears to illustrate a medieval “Vitruvius,”30 and the so-called technical folios (added by other hands post-1220/35) appear to derive from Latin Euclid.31 The best analyses to date, albeit unorthodox, address the drawings within the context of the medieval system of apprenticeship, Compagnonnage.32 The portfolio, together with the other four primary sources, constitutes the roots of the practical geometry tradition, which remained in use until at least the twentieth century.
Hereafter. this chapter examines major themes: the technical education of the builder (applied mathematics and associated use of instruments, the practical geometry tradition); moving from design to execution (structure and construction); and, finally, mathematically based design concepts (dimensions, geometry).
Technical Education of the Builder: Introduction
Discussion of medieval building layout is often reduced to debating the existence of a technical secret or theory of architecture. Frankl’s 1945 article played a pivotal role in bringing the question of a builder’s “secret” to the forefront in America.33 His major work in this domain (The Gothic, 1960)34 continued a German tradition of research on the building lodges, or Bauhütten.35 Much has been written within the field to discount this as a Romantic idea, recasting the builders’ knowledge as rote technical know-how.36 In general, historians outside the field of medieval architecture dismiss medieval builders as mindless laborers, lacking any knowledge of physical forces or theory of structure other than through trial and error. One still ongoing debate is the problem of moving from plan to elevation at Milan Cathedral (begun 1386),37 which by all accounts is after the culmination of Gothic technique. A fresh, better-informed look at scientific and technological knowledge, particularly, in view of the Latin Euclid tradition and the importance of geometry to all the quantified sciences,38 when Romanesque and Gothic masterpieces were being built in the North, would be of great value.39
A parallel theme has been the builder’s training and the socio-economic context. Arguably, the culminating study in the Bauhütten tradition was the 1952 dissertation by Booz, published in 1956, and much read by specialists.40 Better-known, general studies on les bâtisseurs appeared contemporaneously in France and England.41 Since the early twentieth century, however, most scholars tended to focus on the “problem” of the architect’s identity (mason or carpenter).42
After identity came education, specifically, the builders’ mathematical knowledge, a subject long dominated by John Harvey and Lon Shelby.43 In spite of his dedication to the subject, Shelby misunderstands the masons’ legend about Euclid and the Bible, in comparing it with theoretical and intellectual works:44 the medieval records do not function within the realm of linear, narrative thought, but rather in terms of symbols, metaphors, and codes.
Re-evaluation of the builder’s education would be useful, taking into account new work on literacy, the quadrivium, and mechanical arts.45 Work on the art of memory, oral transmission of knowledge, and professional guilds merits attention. 46 Although monopoly of apprenticeship was suppressed in France in 1919,47 at least one traditional form of Compagnonnage survives today, with its esoteric rituals, rhymes, and songs serving collective identity, but also as mnemonic devices and passwords for guarding trade secrets.48 Traditionally, art historical inquiry dismisses popular sources in favor of theological or literary explanations; one example is the continued, iconographic misidentification of two embracing figures that appear to serve as a Compagnonnique signature on one of the most accomplished Northern Romanesque façades (fig. 25-1).49 It is time for the discipline to embrace the socio-anthropological and cultural history of the medieval builders50 and their self-avowed non-European aspects.51
Technical Education of the Builder: Applied Mathematics and Instruments
Architectural history, in general, would benefit from greater access to the history of medieval mathematics, quantified sciences, and related instruments: arithmetic, finger calculus, abacus; calendar and computus; geometry, field- and earth-measurement (Erdmessung); orientation of churches vis-à-vis cardinal directions, winds, astronomy,52 and the astrolabe. More specifically for building practice: the duodecimal system, carpenters’ runes, masons’ marks,53 and instruments for design (compass, dividers, straightedge, square),54 layout (measuring sticks, sighting instruments, rope),55 and construction (level, plumb rule, templates, the art of stereotomy).56
Another instrument merits attention: Villard’s portfolio shows use of an isosceles right triangle (built of wood?) for measuring the height of a distant tower (fig. 25-2). Similarly, one could use an astrolabe with the alidade set at 45°; this instrument and knowledge of triangle theory were available in Northern Europe prior to 983 CE; use of precisely the same dimensions in both the plan and vault heights of a Burgundian church, St Etienne in Nevers (c.1068/74–c.1090), offers evidence for their rapid spread to the building arts well before Abbot Suger oversaw the new apse at St Denis (c.1140/1).57
FIGURE 25-1 Two men embracing, relief sculpture, west façade, Notre-Dame-la-Grande, Poitiers, c.1100/30. Photo: Marie-Thérèse Zenner.
FIGURE 25-2 Man sighting height of tower, c.1220/35. Paris: Bibliothèque nationale de France, MS Fr 19093, fol. 20v, detail. From Lassus, Album de Villard, 1858, reprint. Éditions Leonce Laget, 1976.
Technical Education of the Builder: Practical Geometry
It would appear that medieval science functioned according to the principle: Geometry is a means of relating three-dimensional objects in terms of a physical law that translates into a two-dimensional plane. The practical geometry tradition, consolidated from the five primary sources in the eighth to eleventh centuries, continued to serve well into the twentieth century for the same type of applications since antiquity (land surveying, mechanics, technical drawing, navigation).58 The elegance of geometry stems from its ability to function independently of arithmetic for the purposes of drawing and layout.59 For example, the technical problem of measuring a column was handed down through the centuries (fig. 25-3).60 A medieval contribution was the geometric determination of appropriate wall thickness for a barrel vault or rib vault;61 wall thickness is one of the most important and least recognized aspects of practical geometry prior to the Late Gothic or Renaissance periods.62
FIGURE 25-3 Technical drawing on how to measure a column, addition to portfolio of Villard de Honnecourt, post-1220/35. Paris: Bibliothèque nationale de France, MS Fr 19093, fol. 20r, detail. From Lassus, Album de Villard, 1858, reprint. Éditions Leonce Laget, 1976.
Much more study is required to produce a history of practical geometry from late antiquity,63 including the Gothic philosophical/theological/theoretical texts,64 and numerous drawings on parchment, plaster, or stone, sketchbooks, and instruction booklets principally from the later Gothic period.65 After Branner, Bucher, and Shelby, German studies of the drawings concentrated on modes of representation, largely under the direction of Roland Recht.66 Future studies should take into account the larger context of technical drawing.67 While the medieval tradition essentially culminated with Dürer’s Underweysung der Messung,68 studies of sixteenth-century technical texts by Rodrigo Gil de Hontañón, and others, offer valuable insight into the medieval graphic tradition of l’art du trait (the art of tracing): stereotomy, drawings of tracery, plans, or elevations.69
Design to Execution: Structure and Construction
Apprenticeship under Compagnonnage focused on l’art du trait, for it would appear that medieval builders conceived of and aimed to guarantee the structural stability of a three-dimensional solid through geometry.70 A great deal of scholarly attention has been given to the argument of structure-as-function and the anti-rationalist response.71 Whether conceived as moving upwards from plan to elevation – or downward from vaults to buttressing into the foundations – structural stability originates in, and is encoded by, the plan. A plan can describe a three-dimensional structure simply by delineating relative proportions of spaces, preferably including the buttressing and wall thickness. As structure implies construction, so the development of the elevation may vary in function of the period, the builders’ knowledge, and financial resources.
For example, one of the most striking elevations is found in the aforementioned Romanesque church at Nevers. A pilgrimage-type church, Nevers is distinguished as the earliest known example of a triple elevation (i.e., with clerestory) under a barrel vault. Yet, the design dispensed with heavy exterior buttressing through the use of (a) exceptionally fine ashlar set under compression; (b) axial distribution within a dynamic wall structure (i.e., transverse bonding stones and blind wall arcades); working in conjunction with perpendicular counterthrust from (c) the earliest known, functional interior flying buttresses.72 Archaeological evidence shows that this proto-Gothic elevation and structural system were known when the plan was established. A measured survey showed that both plan and elevation are related through three principal measures. In this experimental building, it would appear that geometry determined structural stability.73 The geometric relation of plan and elevation needs to be investigated for other buildings, but any study of layout should begin with the monumental archaeology.
Two mathematical approaches to layout are number or geometry.74 Number (or rather dimensions) can imply measure, hence metrology.75 Site-specific use of measure may be rediscovered through a measured survey, which in turn raises questions of interpretation of precision and accuracy.76 Recent topics in metrology include continuity of foot measures,77 application of scale,78 investigation of monuments,79 or general metrological theory.80 Number can be proportion (the relation of two or more measures). Proportion continues to be one of the most studied aspects of architectural design, in particular for medieval layouts.81 Number can also be symbolic number (e.g., as a plan module), a current topic in the third quarter of the twentieth century.82
Studies in geometric architectural design have three aspects, with some overlap: Ad quadratum/Ad triangulum, other geometric forms, and Euclidian. A legacy of Bauhütten studies, the Ad triangulum method as propagated by Georg Dehio83 influenced generations of German scholars.84 Quadrature seems to have held even longer interest. While many works have gone unnoticed,85 that of Maria Velte (1951) received critical attention in Germany and abroad.86 Decades later, design analysis through quadrature is once again drawing significant scholarly interest.87
FIGURE 25-4 Mnemonic devices for principal geometric rules, c.1220/35. Paris: Bibliothèque nationale de France, MS Fr 19093, fol. 18v. From Lassus, Album de Villard, 1858, reprint. Éditions Leonce Laget, 1976.
Design analysis using other geometric forms has included the circle, oval, and pentagon, sometimes in relation to quadrature.88 A major recent study proposes use of the Platonic solids, but the analysis employs isolated angles from solids (an anti-Platonic idea in itself), which, as with most studies, do not address wall thickness.89 Quite simply, plans which do not integrate structure would never stand up. Our experience with Compagnonnage suggests that whole forms, specifically, the combination of circle, square, and triangle, were used for their simplicity, beauty, and meaning, while a five-pointed star on the entire plan validates its integrity.90 Quite interestingly, a computer-generated analysis of an early Gothic monastic church arrived at just such a combination.91
Finally, the question of Euclidian geometry and medieval design. Traditionally, both architectural and mathematical literature categorically rule out knowledge of Euclid during the Romanesque and early Gothic periods, as well as its applicability to practical geometry during all periods.92 Yet, structure and design were integrated in the case of the eleventh-century church at Nevers, apparently through Euclid. Specifically, the maximum and minimum measures of vault heights were initially used as radii in the plan to determine wall thicknesses;93 these circles were set out according to Euclid proposition 1.1 (vesica piscis), as recalled by an animal device in the thirteenth-century portfolio of Villard (two flamingoes, bottom left, in fig. 25-4).94 The same proposition can be used to generate a square and equilateral triangle, creating a pattern that we propose served as a means to determine the three proportional measures, used to guarantee structural stability of this experimental three-dimensional solid, the elevation of St Etienne in Nevers.95
We have seen that that medieval architectural layout has multiple facets and that its study can take many paths. A comprehensive overview of what is known and awareness of what is not yet known will allow the insightful student to pose the most appropriate questions. For we only find answers to those questions posed. Finding the most relevant and innovative questions to pose is key to advancing historical research.
| AB | Art Bulletin |
| AJA | American Journal of Archaeology |
| BM | Bulletin monumental |
| BurlM | Burlington Magazine |
| GBA | Gazette des Beaux-Arts |
| JSAH | Journal of the Society of Architectural Historians |
| ZfK | Zeitschrift für Kunstgeschichte |
1 This chapter focuses on ecclesiastical layout, since relatively little has been done on layout of military or civil buildings from this period. [On Romanesque and Gothic architecture in general, see chapters 14 and 18 by Fernie and Murray, respectively, in this volume (ed.).]
2 Surprisingly, there is no bibliography or historiography of Gothic architectural studies; for the Romanesque, Davies, Romanesque Architecture, presents a limited list of books, without critical assessment. Two works provide key sources as of the 1980s: von Naredi-Rainer, Architektur und Harmonie, bibliography, pp. 232–86, treats the five primary sources named in this chapter, as well as building construction, in addition to all things Number; Binding et al., “Bibliographie,” covers many works on medieval building by thematic division. References hereafter are designated by “NR-year” or “BI-item number.” Additional sources will be signaled throughout; abbreviated citations refer to items in our bibliographies.
3 The most complete study of Gothic design, emphasizing mathematics: Müller, Grundlagen gotischer, pp. 14–120; appendices 3, 6, and 7, pp. 289–96. Cf. Binding et al., Baubetrieb im Mittelalter: “Planung,” pp. 171–234, and “Vermessung,” pp. 339–54. Both manuals treat structure and construction. An alternate approach, with a short section on design in spite of its subtitle, is Conrad, Kirchenbau im Mittelalter, pp. 73–84, 126–32. Among textbooks, the best illustrated and accessible work is Coldstream, “Structure and Design,” in Medieval Architecture, pp. 55–81. One work of collected studies embraces the period in question: Courtenay, ed., Engineering of Medieval Cathedrals. Another work with valuable technical insight, although sometimes lacking in understanding of things medieval, is by an historian of applied mathematics: Sakarovitch, Epures d’architecture.
4 For example: Weise, Studien zur…; Lehmann, Der frühe deutsche Kirchenbau; Götz, Zentralbau.
5 Bandmann, Die Bauformen, exemplifies a traditional presentation organized according to formal elements; see especially Frankl, with Crossley, Gothic Architecture.
6 For example: Deshoulières, Eléments datés; Ottaway, “Traditions”; and is characteristic of textbooks: Calkins, Medieval Architecture, chs. 10–15.
7 Stalley, Early Medieval Architecture, ch. 7. [On the pilgrimage, see chapter 28 by Gerson in this volume (ed.).]
8 Kohlschein et al., eds., Heiliger Raum; Faupel-Drevs, Vom rechten Gebrauch, discusses sources, including Durandus von Mende (1230/1–1296), after Sauer (see n.10 below).
9 Breysig (NR-1915); Murray et al., “Plan and Space.”
10 On the historiography, see Crossley, “Medieval Architecture,” with reference to Sauer (1902, 2nd rev. edn., NR-1924); Krautheimer (1942); Bandmann (NR-1951a,b [review by Robert Branner, AB 35 (1953), pp. 307–10]). [On formalism in general, see chapter 5 by Seidel in this volume (ed.)]
11 See the excellent study, von Naredi-Rainer, Salomos Tempel, with other works by Bandmann (passim); reviewed by Hartmann-Virnich, BM 155:2 (1997), pp. 169–71. Among recent textbooks, see Stalley, Early Medieval Architecture, ch. 3; Coldstream, Medieval Architecture, ch. 5. On the Mystic Ark, see Conrad Rudolph (forthcoming).
12 A comprehensive approach optimizes historical insight, as shown in Zenner, Methods and Meaning. The dissertation (1989–94) involved: a measured survey (see p. 18 n.35), dimensional analysis (appendices 2–4, pp. 357–69), standard structural study (under guidance of Robert Mark, appendix 5, pp. 370–93), historiographies of measuring bond (pp. 112–21), and dating by tooling marks (pp. 190–7), followed by a survey of coursing heights (pp. 122–47; table 2, pp. 394–405, appendix 6, pp. 406–47), as well as stone-by-stone dating of building and restoration phases (pp. 147–83; chs. 5–6; conclusion, pp. 335–9). Zenner was the first to apply the latter technique to a medieval monument, based on Jean-Claude Bessac’s typo-chronology of stoneworking tools (1986, BI-14.2); cf. BI-14.1 to BI-14.34; cf. Doperé, “Etude de l’évolution,” with reference to 1996 article. For the state of the discipline of monumental archaeology (i.e., full documentation and scientific analysis of standing fabric), see Baud, Cluny; for its historiography and scope, see Zenner, Methods and Meaning, pp. 11–19; and Grossmann, Einführung, esp. pp. 26–35. On material science, see Archaeometry. AVISTA sponsors international conferences on use of materials in medieval architecture: wood and stone (1999), metal (2002), brick (2005); the third volume in the AVISTA series is Bork, ed., De Re Metallica; cf. BI, sections 13–16 on materials. Recent research has focused on technical aspects such as scaffolding: Tardieu and Reveyron, L’Echafaudage; cf. BI-17.1 to BI-17.12; and Huerta, ed., Proceedings.
13 Electronic surveys came late to medieval architectural studies: Davis et al., “Mechanics and Meaning,” continues Neagley’s work begun in 1988 (cf. Wiemer, n.91 below). On the advantages and dangers of CAD, see Zenner, “AutoCAD as an Exploratory Device.” Refer to CSA subject index for related topics such as retrieving dimensions from CAD drawings and models; and n.76 below on the subjective aspect of modern technology.
14 Most recently, Parsons, Books and Buildings; Weyer-Davis, Early Medieval Art; Frisch, Gothic Art; Frankl (NR-1960, BI-17.4); Mortet, Recueil de textes; and per Kruft (as in n.16 below), p. 452 n.42, to name the most current printed sources. Each building has its own potential archives held in libraries, architect’s offices, or the local presbytery.
15 Rowland et al. eds. Vitruvius; earlier editions (p. xiv).
16 Kruft, History of Architectural Theory [BI-10.18], pp. 30–40, concludes there was no theory and little influence from Vitruvius during the period in question. On medieval theory, see Germann, Vitruve; on transmission: Reynolds and Weiskittel, “Vitruvius”; the most comprehensive study is Schuler, Vitruv im Mittelalter, with discussion of Ars mechanica and bibliography.
17 With regard to architecture: Conant (NR-1968b; BI-6.12); Heitz, “Vitruve et l’architecture”; Tcherikover, “A Carolingian Lesson,”; Hausmann, “Inque pares numeros omnia convenient”; and to mathematics: Pottage, “Vitruvian Value of Pi”; Frey, “Médiétés.”
18 Fleury, La Mécanique de Vitruve, includes basic bibliography on ancient civil and military engineering.
19 The best introduction is Dilke, Les Arpenteurs; on illustrations, Carder, Art Historical Problems (1978); and Bouma, Marcus Iunius Nypsus, for editions and on surveying instruments, to which we add Folkerts, “Visierkunst,” and Mortet and Tannery, “Un Nouveau Texte” (1896).
20 Plommer, Vitruvius.
21 On earlier plans, see Horn and Born (NR-1979, BI-9.1), 1:53–65, 66–7; and especially Kleinbauer, “Pre-Carolingian Concepts”; along with Badawy, “Ancient Constructional Diagrams”; Haselberger, “Architectural Likenesses”; cf. Sakarovitch, Epures d’architecture, pp. 17–35; Müller, Grundlagen gotischer, pp. 21–9; appendix 5, pp. 292–3.
22 Binding et al., Baubetrieb im Mittelalter, pp. 173–9.
23 The extensive bibliography and debates may be summarized by citing the fundamental study by Horn and Born (NR-1979, BI-9.1 [with review]), and the dissertation (1981, BI-9.9), published in 1992 by Jacobsen, with conclusions on modularity, proportion, and number (pp. 33, 321–332). For an overview of the planning, see Sanderson (1985, BI-9.13). Among recent works, see Kendall, “Plan of St Gall”; cf. BI-9.1 to BI-9.18.
24 In addition to editions by Heath, after Heiberg, see the dynamic modern illustrations online at <http://aleph0.clarku.edu/~djoyce/java/elements/elements.xhtml>.
25 Folkerts, Euclid in Medieval Europe; Stevens, “Euclidian Geometry,” including on the medieval tradition of illustrations.
26 Bubnov, ed., Gerberti; Lindgren, Gerbert von Aurillac.
27 For a concise summary, see Zenner, “Imaging a Building,” esp. 223–7, 224 n.20 (on Corbie, particularly Ullman, 1964), n.21 (on the Lorraine); and Folkerts’ collected studies, Essays (2003).
28 Zenner, “Imaging a Building.” pp. 231–6.
29 The definitive critical edition is Hahnloser (NR-1972 [with reviews], BI-11.5); the critical bibliography by Barnes (1982, BI-11.1) has continuous updates at <www.villardman.net>; cf. BI-11.1 to BI-11.8. Barnes’s new critical edition and color facsimile should be forthcoming with Ashgate in 2006.
30 Suggested in Frankl (see n.14 above), p. 37; Kruft, History of Architectural Theory, p. 37 and n.83, quibbles with it; Sakarovitch, Epures d’architecture, p. 37, categorically dismisses it. Greater knowledge on the history and transmission of civil and military engineering, and the interrelations with architecture, are required.
31 Zenner, “Imaging a Building,” p. 234.
32 Bechmann, Villard, aided by Renaud Beffeyte, a Compagnon initiated in the same tradition as Villard (see n.46 below). Cf. Sakarovitch, Epures d’architecture, pp. 35–51, 127–30.
33 Frankl (NR-1945, BI-6.16), p. 47, pointed to the late Gothic booklets as evidence for a “secret.”
34 Frankl (NR-1960, BI-17.4), esp. 110–58.
35 For instance, Frankl (NR-1945, BI-6.16), p. 46 n.1, cites Janner (NR-1876, BI-2.12). Other notable works: von Heideloff (NR-1844, BI-2.10, also: -10.12); Durach (NR-1928; 1930, BI-2.3); an architect and member of the “Wiener Bauhütte,” Discher (NR-1932, BI-3.11); and on the state of the question in the first issue of Architectura, Habicht (1933, BI-2.9). Influential works by Dehio and Velte will be discussed under triangulation.
36 In a review of Briggs (see n.42 below), Pevsner had already dismissed this idea (1930/31, BI-5.32 [cited here after Habicht, p. 81 n.1]). In an otherwise exemplary analysis of design principles, Bucher (NR-1968, BI-8.10), pp. 50, 71, propagates the error that Euclidian knowledge was only available in the mid-thirteenth century, and dismisses the idea of a secret; followed by Shelby (NR-1976), who argued at length against a “secret”; cf. Recht (1980, BI-5.35).
37 See Ackerman (NR-1949, BI-6.3), following Frankl (NR-1945, BI-6.16); cf. Beaujouan, “Calcul d’expert.” Müller, Grundlagen gotischer, passim, plus appendix 16, pp. 304–5; ch. 14 in Courtenay, ed., Engineering of Medieval Cathedrals; Sakarovitch, Epures d’architecture, pp. 50–1, concludes the medieval masons’ “secret” would consist in the knowledge how to move from plan to elevation (p. 51).
38 On the lack of distinction between sciences and the overarching place of geometry, see Zaitsev, “The Meaning.” Ackerman’s conclusions on the necessary juncture of ars and scientia, versus the Milanese confusion between physical sciences, should be reviewed in this light: (NR-1949, BI-6.3), pp. 102–8, esp. 102, 107.
39 The beginnings of such a reappraisal come from disperse sources: Turnbull, “Ad Hoc Collective Work” offers a reassessment of theory versus practice, as well as modern prejudices and medieval knowledge; Huerta, “Medieval ‘Scientia’,” affirms a masterly body of knowledge, albeit without explicit written record, for the earlier medieval periods.
40 Booz (NR-1956, BI-1.13), with reviews by Busch (NR-1957), Branner (NR-1958b), and others.
41 Du Colombier (NR-1953 [with review by Branner]; 1973 edn., in BI-1.16, also: -8.16); and Gimpel (1958; 1980, BI-1.23), with numerous editions and translations up to the present; in a second wave, Coldstream, Masons and Sculptors. From at least 1933, the more elusive work of Knoop and Jones on the guilds paralleled the German historiographic tradition in the search for Masonic origins (NR-1933; 1967, BI-5.26); on lodge rules, idem et al. (NR-1938, BI-10.17).
42 Mortet, La Maîtrise d’œuvre; Lefèvre-Pontalis (1911, BI-5.28a); Briggs (1927; 1974 ed., BI-5.9); in the Journal of the RIBA: Knoop and Jones, “The Rise of the Mason Contractor,” and “The Decline of the Mason-Architect”; and Harvey, “The Mediaeval Carpenter”; Pevsner (NR-1942a, BI-5.33); Anfray, “Les Architectes des cathédrales”; Lefrançois-Pillion, Maîtres d’œuvre. In Germany, Kletzl (1935, BI-5.25); and recently again, Binding, Der früh- und hochmittelalterliche Bauherr, with review by Schuler, Scriptorium; idem, “Architectus; cf. BI-5.1–BI-5.45.
43 Multiple works on education by Harvey (1945–86) and Shelby (1964–87) are cited in the thematic bibliography, in addition to numerous others by Shelby under Instruments, and Practical Geometry.
44 Shelby (1975, BI-6.40), pp. 133, 135, 136, 137, 143.
45 In general, Murdoch et al., eds., The Cultural Context.
46 On memory, the classic work is Yates, The Art of Memory; cf. Carruthers, Book of Memory. On oral tradition and ritual, see Beffeyte, “The Oral Tradition”; cf. Terrenoire, “Villard de Honnecourt.” On trade secrets, see Long, Openness.
47 Lecotté, Essai bibliographique; followed by Bayard, Le Compagnonnage.
48 The author has been privileged to witness rites in France and Switzerland in the presence of leading European figures of the Enfants de Salomon, a group which identifies with Villard de Honnecourt. Compagnonnage existed or moved to other countries in Europe, then to the New World; the Carpenters’ Company of Philadelphia is one such, albeit publicly unacknowledged, offshoot. See Peterson, ed., Rules of Work, whose introduction begins with the topic of trade secrets (p. ix).
49 Proust, “Des Images à lire,” pp. 266–8, “Les Deux Personnages enlacés,” and ill. 337.
50 Recent research on oral transmission includes Schottner, Die ‘Ordnungen’.
51 Ethnomathematics may serve to show potential differences with mainstream Western culture: Ascher, Mathematics Elsewhere, and earlier work; Selin, ed., Mathematics Across Cultures.
52 McCluskey, Astronomies and Cultures; Haselberger, “Geometrie der Winde”; Obrist, “Wind Diagrams and Medieval Cosmology.”
53 Heinzmann et al., eds., Runica. For signs in masonry work, see Kraack et al., eds., Bibliographie zu historischen Graffiti; and the CIRG: <http://users.skynet.be/sky98372/cirg.xhtml>; cf. BI-3.1 to BI-3.59; and Alexander, “Villard de Honnecourt.”
54 Instruments for design: Mortet, “Note historique”; Funck-Hellet, De la proportion; Shelby, “Medieval Masons’ Tools, II”; Sené, “Les Equerres”; idem, “Un Instrument de précision” (1970b); idem, “Quelques instruments” (1972); Meckseper (NR-1983, BI-11.8); Wu, “Hugues Libergier”.
55 Instruments for layout: measuring tools: Binding (1985, BI-6.7); early medieval sighting instruments: Würschmidt, “Geodätische Messinstrumente”; on staking out: Paquet, “Les Tracés directeurs,” esp. pp. 61–3.
56 Instruments for construction: Shelby, “Medieval Masons’ Tools, I”; on templates: Booz (NR-1956, BI-1.13), pp. 96-104; Shelby (NR-1971, BI-1.52); Adams, “The Use of Templates”; Binding et al., Baubetrieb im Mittelalter, pp. 229–34 (cf. 1986, BI-14.3). Use of templates implies the art of stereotomy: Shelby (1969, BI-6.38); Lalbat et al., “De la stéréotomie”; Müller, Grundlagen gotischer, pp. 121–83; and Sakarovitch, Epures d’architecture, esp. pp. 35–51; bibliography, pp. 400–20; cf. Sanabria, “From Gothic to Renaissance Stereotomy”; cf. BI-14.1 to BI-14.34 on stoneworking.
57 Zenner, “Imaging a Building,” pp. 230–1, 232–3, 238–9.
58 On geometry in post-medieval experimental science, see Bennett, “Practical Geometry”; and Janich, “Was heißt eine Geometrie operativ begründen?”
59 Shelby (1975, BI-6.40), p. 137, implies Euclid’s arithmetic formula for a circumference is inherently superior to the geometrical solution given by Roriczer. But if working within a proportional plan, without dimensions, the latter is more useful.
60 Mortet, “La Mesure des colonnes”; Wirth, “Bermerkungen”; cf. Müller, Grundlagen gotischer, p. 127, ill. 103.
61 Explanation of the diagram in Villard’s portfolio (fol. 21r) is found in Beffeyte, “The Oral Tradition,” pp. 113–15, ills. 5.16–5.18.
62 Shelby (1975, BI-6.40), p. 141, discusses it in Roriczer’s text (cf. Shelby NR-1977, BI-8.88); Zenner, “Imaging a Building,” p. 244 n.95, on Francesco di Giorgio’s factor for calculating wall thickness; Huerta, “The Medieval ‘Scientia’,” pp. 568–73, is not aware of the evidence in Villard, but treats Late Gothic and post-medieval rules in Germany, England, and Spain. The question of wall thickness and laying the ground stone should be examined together (cf. BI-7.1 to BI-7.5).
63 On Latin Euclid and Villard’s portfolio: Martines, “Gromatici veteres”; one of the first studies to treat Gerbert and architecture was Sarrade, Sur les connaissances mathématiques. Scattered studies include: Mortet et al., “Un Formulaire du 8e siècle”; Halleux, “Les Géomètres mosans”; idem et al., “Formules d’architectes.”
64 See, foremost, the short study by Homann, ed., Practical Geometry; with appendix on De arca Noe morali, and bibliography of principal editions of other medieval practical geometry texts: Hahn (1982), Victor (1979), Busard (1965), Curtze (1897). An important analysis of all sources may be found in Presas i Puig, Praktische Geometrie.
65 Connections between practical geometry and the design principals of Gothic architectural drawings were made, particularly by Branner and Bucher in the 1960s and 1970s; Shelby focused on the geometrical knowledge in Villard and the Late Gothic booklets in the 1970s (references in bibliography).
66 A dissertation by Pause (NR-1973, BI-8.77), followed by Recht, “Sur le dessin,” and multiple articles in Recht, ed., Les Bâtisseurs, along with Schöller on tracings (1989b, BI-8.84a; cf. BI-8.84), provides complete bibliography. Cf. Binding, “Architekturdarstellung”; Binding et al., Baubetrieb im Mittelalter; cf. BI-8.1 to BI-8.99. Other documentation of tracings includes: Bessac, “Tracés et épures gravés”; Davis, “On the Drawing Board.” More recent work on drawings: Recht, Le dessin d’architecture; idem, “La Circulation des artistes”; and Neagley, “Late Gothic Architectural Drawing,” with introduction by Thelma K. Thomas, pp. 88–9.
67 See Müller, Grundlagen gotischer; idem, “Le Dessin technique;” Knobloch, “Technische Zeichnungen,” illus. on pp. 67–9. Cf. Sanfaçon, “Le rôle des techniques,” in (1982, BI-1.1), pp. 93–130.
68 Dürer, Géométrie, and facsimile of the 1525 edition (NR-1971); idem, De symmetria, 1532/Underweysung der Messung, Nuremberg, 1538 [electronic resource], comm. by David Price (Oakland, California, 2003), with searchable text.
69 Sanabria, Evolution and Late Transformations; Sakarovitch, Epures d’architecture, up to the nineteenth century; Huerta, “The Medieval ‘Scientia’,” up to the sixteenth century. Cf. technically oriented studies of Gothic in Müller, Grundlagen gotischer.
70 Refer to an experimental study of structural forces broaching the gulf between civil and military engineering, expressed in terms of medieval geometry: Zenner, “Structural Stability,” with abstract and addendum online at <www.nexusjournal.com/conferences/N2002-Zenner.xhtml>. In general, on techniques and geometry of construction, see Müller, Grundlagen gotischer, pp. 121–68; cf. BI-1.1 to BI-1.62, esp. BI-1.32 (Kimpel, 1983).
71 A useful summary of the literature up to 1949 is in Ackerman (NR-1949, BI-6.3), esp. pp. 84–5; more recently, see Courtenay, ed., Engineering of Medieval Cathedrals, chs. 1–2; cf. Müller Grundlagen gotischer, pp. 184–246, appendices 8–14, pp. 296–303. See also Courtenay: introduction, chs. 8–9 on walling and foundations. Further studies on structure may be found in Courtenay’s bibliography, and in Armi, Design and Construction; cf. BI-12.1 to BI-12.38 (statics). Other recent work includes Fitchen, Building Construction (cf. BI-1.19, also: -12.14); Mainstone, “Structural Analysis”; Theodossopoulos and Sinha, “Structural Masonry.”
72 As demonstrated by Zenner, Methods and Meaning, esp. pp. 338–9, 390–3; cf. idem, Saint-Étienne de Nevers, pp. 30–3.
73 See Zenner, “A Proposal,” in Wu, ed., Ad Quadratum, pp. 25–55.
74 See Sbacchi, “Euclidism and Theory of Architecture,” online at <www.nexusjournal.com/Sbacchi.xhtml>; cf. Gelernter, Sources of Architectural Form, esp. ch. 3; and BI-6.1 to BI-6.48.
75 Metrology is a vast historical sub-discipline; for basic bibliography to 1978, see “Historical Metrology,” repr. in Fernie, Romanesque Architecture; cf. Arens (NR-1938, BI-6.4), Hecht (NR-1965 to 1979d; BI-6.22 to BI-6.25, and BI-9.3); Überwasser (NR-1928 to 1953, esp. NR-1935, BI-6.44); also the series of acts, Ordo et Mensura (St Katharinen, 1991–).
76 Eiteljorg, II, “How Should We Measure?” online at <www.nexusjournal.com/Eiteljorg.xhtml>.
77 Rottländer, “Zum Weiterleben antiker Masseinheiten.”
78 Hiscock, “Design and Dimensioning.”
79 Witthöft, ed., Die historische Metrologie.
80 Fernie, “A Beginner’s Guide,” repr. in idem, Romanesque Architecture; Kidson, “A Metrological Investigation.”
81 For a mathematical history of proportion in architecture, see Presas i Puig, Praktische Geometrie; a useful reference is Herz-Fischler, A Mathematical History; cf. Graf (NR-1958, BI-6.1, a bibliography on proportion), and von Naredi-Rainer, Architektur und Harmonie.
82 For example, Beaujouan (NR-1961), Conant (NR-1960/61), Heitz (NR-1973, NR-1976), Meyer (NR-1975), Sunderland (NR-1959/73), and later, Zimmerman, ed., Mensura. Mass, Zahl (1984).
83 Dehio (NR-1894 [with review]; NR-1895a; NR-1895b).
84 For example, dissertations by Hoeber (NR-1906) and Thomae (NR-1933 [with review]).
85 Lund (NR-1921), Rosenau (1934, BI-8.82), Roosval (NR-1944); and von Rothkirch, Die Bedeutung.
86 Velte (NR-1951 [with multiple reviews], BI-8.96), notably by Ackerman, AB 35 (1953), pp. 155–7, who had recently contributed to the debate on Milan Cathedral (NR-1949, BI-6.3).
87 Witness the first volume in the AVISTA series: Wu, ed., Ad Quadratum; also Lyman, “Opus ad triangulum.”
88 The circle: Mössel (NR-1926 [with multiple reviews]); Paquet, “Les Tracés directeurs”; Zenner, “A Proposal.” The oval: Chappuis, “Utilisation du tracé ovale”. The pentagon: Shortell, “Plan of St Quentin.”
89 Unfortunately, although an expensive production, Hiscock, The Wise Master Builder, suffers from the methodological problems that plague medieval design studies (discussed in our definition of layout). In contrast, the older discipline of classical archaeology has produced a model work based on personal measured surveys: Jones, Principles of Roman Architecture.
90 These forms appear on the title page of Discher (NR-1932, BI-3.11); cf. Bilheust, L’Art des bâtisseurs romans; and Bilheust et al., Les Tracés des maîtres d’oeuvre.
91 Wiemer and Wetzel, “A Report on Data Analysis,” p. 458, ill. 11; cf. Wiemer, “Die computergetützte Proportionsanalyse.”
92 See response in Zenner, “Imaging a Building,” pp. 220–2, 231–6.
93 Zenner, “A Proposal,” p. 49, ill. 2.6; p. 50, ill. 2.11; this is the first known (geometric) calculation of wall thicknesses prior to the Late Gothic (refer to n.62 above).
94 See Zenner, “Villard de Honnecourt”, as well as the expanded English version.
95 Ibid.: in Pour la Science, p. 109, ill. 2b; in Nexus Network Journal, ills. 8–9.
Thematic
Vitruvius
Georg Germann, Vitruve et le Vitruvianisme, (NR-1980 [with reviews], BI-10.9), 2nd edn. (Darmstadt, 1987; trans. Lausanne, 1991).
Leighton D. Reynolds and S. F. Weiskittel, “Vitruvius,” in Reynolds, ed., Texts and Transmission (Oxford, 1983), pp. 440–5.
Stefan Schuler, Vitruv im Mittelalter (Cologne, 1999).
Corpus agrimensorum romanorum
Jelle Bouma, Marcus Iunius Nypsus (Frankfurt am Main, 1993), with editions: Blume et al. (1848–52); Thulin (1911a, 1913); Butzmann (1970); studies: Cantor (NR-1875); esp. Thulin (1911c); drawings, Carder (1978).
James Nelson Carder, Art Historical Problems of a Roman Land Surveying Manuscript (New York, 1978).
Oswald A. W. Dilke, Les Arpenteurs de la Rome antique (1971; rev. edn., François Favory, Sophia Antipolis, 1995).
Victor Mortet and Paul Tannery, “Un Nouveau Texte des traités d’arpentage et de géométrie d’Epaphroditus et de Vitruvius Rufus,” 1896, repr. in Paul Tannery, Mémoires scientifiques, vol. 5, 1922 (repr., Paris, 1996), pp. 29–[81]; cf. Bubnov, Gerberti (1899), pp. 518–51.
Plan of St Gall
Walter Horn and Ernst Born (NR-1979, BI-9.1).
Werner Jacobsen (BI-9.9; published: Berlin, 1992).
W. Eugene Kleinbauer, “Pre-Carolingian Concepts of Architectural Planning,” in Marilyn J. Chiat et al., eds., The Medieval Mediterranean (St Cloud, Minnesota, 1988), pp. 67–79.
Latin Euclid
Menso Folkerts, Euclid in Medieval Europe, ed. Wesley M. Stevens (Winnipeg, 1989); online at <www.math.ubc.ca/people/faculty/cass/Euclid/folkerts/folkerts.xhtml>; and Essays in Early Medieval Mathematics (Aldershot, 2003), including CAR.
Wesley M. Stevens, “Euclidian Geometry in the Early Middle Ages,” in Marie-Thérèse Zenner, ed., Villard’s Legacy (Aldershot, 2004), pp. 229–63.
Marie-Thérèse Zenner, “Imaging a Building: Latin Euclid and Practical Geometry,” in John J. Contreni et al., Word, Image, Number (Florence, 2002), pp. 219–46, 7 ills.
Portfolio of Villard de Honnecourt
Carl F. Barnes, Jr., (1982, BI–11.1), a critical bibliography now online with continuous updates at <www.villardman.net>.
Roland Bechmann, Villard de Honnecourt (1991; 2nd rev. edn. Paris, 1993).
Hans R. Hahnloser (NR-1972 [with multiple reviews], BI-11.5).
Technical education of the builder: introduction
Ackerman (NR-1949, BI-6.3).
Renaud Beffeyte, “The Oral Tradition and Villard de Honnecourt,” in Marie-Thérèse Zenner, ed., Villard’s Legacy (Aldershot, 2004), pp. 93–120.
Paul Booz (NR-1956 [with multiple reviews], BI-1.13, also: -6.10, -8.5, -10.1).
Paul Frankl (NR-1945, BI-6.16), (NR-1960, BI-17.4).
John Harvey, “Geometry and Gothic Design,” Transactions of the Ancient Monuments Society 30 (1986), pp. 43–56; (NR-1972, BI-5.20, also: -8.33), with bibliography of his earlier work.
Douglas Knoop and Gwilyn Peredur Jones (NR-1933; repr. 1967, BI-5.26); idem, and Douglas Hamer (NR-1938, BI-10.17).
Lon R. Shelby (1964, BI-5.39), (NR-1970, BI-5.40), (1975, BI-6.40), (NR-1976); “Geometry,” in David L. Wagner, ed., The Seven Liberal Arts (Bloomington, 1983), pp. 196–217; “Masons and Builders,” in Dictionary of the Middle Ages (New York, 1987) 8:172–80.
David Turnbull, “The Ad Hoc Collective Work of Building Gothic Cathedrals with Templates, String, and Geometry,” Science, Technology, and Human Values 18:3 (1993), pp. 315–40.
Technical education of the builder: applied mathematics and instruments
Günther Binding (1985, BI-6.7).
Charles Funck-Hellet, De la proportion – L’équerre des maîtres d’œuvre (Paris, 1951).
Claude Lalbat et al., (1987, BI-11.7, also: -14.14a), and “De la stéréotomie médiévale, pt. 2, BM 147:1 (1989), pp. 11–34.
Cord Meckseper (NR-1983, BI-11.8).
Victor Mortet, “Note historique sur l’emploi de procédés matériels et d’instruments usités dans la géométrie pratique au moyen-âge (10e–13e siècle),” in IIe Congrès international de philosophie, 1904 (Geneva, 1905), pp. 925–42.
Alain Sené, “Les Equerres au moyen-âge,” 95e Congrès national des Sociétés savantes, Archéologie (Reims, 1970), pp. 525–48; [1970b, 1972: see Wu].
Lon R. Shelby “Medieval Masons’ Tools, I, The Level and the Plumb Rule,” Technology and Culture 2 (1961), pp. 127–30; (1969, BI-6.38, also: -8.87a, -12.32), (NR-1971, BI-1.52, also: -10.28, -14.27); [1965: see Wu].
Nancy Wu, “Hugues Libergier and his Instruments,” AVISTA Forum Journal 11.2 (1998/9), pp. 7–13; repr. in Nexus Network Journal 2.4 (2000), pp. 93–102, online at <www.nexusjournal.com/Wu.xhtml>, sites: Sené (1970b, 1972), Shelby (1965), among others.
Technical education of the builder: practical geometry
Günther Binding, Baubetrieb im Mittelalter (1993; 2nd edn. Darmstadt, 1997): pp. 171–234, 339–54.
Robert Branner (NR-1963, repr. in Courtenay [cited under Structure]).
François Bucher (NR-1968, BI-8.10, also: -10.2), (NR-1972, BI-8.12, also: -10.4), (NR-1979, BI-10.5).
Robert Halleux, “Les Géomètres mosans des 10e et 11e siècles et leurs modèles antiques,” Fédération des cercles d’archéologie et d’histoire de Belgique. Annales du 44e congrès (Huy, 1976), pp. 565–70; idem et al., “Formules d’architectes dans les receptaires et les manuscrits d’arpentage de l’Antiquité et du haut moyen-âge,” in Patricia Radelet-de Grave et al., Entre mécanique et architecture (Basel, 1995), pp. [48]–66.
Santiago Huerta, “The Medieval ‘Scientia’ of Structures: The Rules of Rodrigo de Hontañón,” in Antonio Becchi et al., Towards a History of Construction (Basel, 2002), pp. 567–85.
Victor Mortet, “La Mesure des colonnes à la fin de l’époque romaine d’après un très ancien formulaire,” Bibliothèque de l’Ecole des Chartes 57 (1896), pp. 277–324; idem et al., “Un formulaire du 8e siècle pour les fondations d’édifices et de ponts d’après des sources d’origine antique,” BM (1907), pp. 442–65.
Werner Müller, Grundlagen gotischer Bautechnik (Munich, 1990), pp. 14–120; appendices 3, 6, and 7 (pp. 289–96).
Peter Pause (NR-1973, BI-8.77).
Roland Recht, ed., Les Bâtisseurs des cathédrales (Strasburg, 1989), esp. articles by Müller, Recht, and Schöller; and Recht, “Sur le dessin d’architecture gothique,” in Sumner McKnight Crosby et al., eds., Etudes d’art médiéval offertes à Louis Grodecki (Paris, 1981), pp. 233–50.
Joël Sakarovitch, Epures d’architecture. De la coupe des pierres à la géométrie descriptive 16e–19e siècles (Basel, 1998).
Sergio Sanabria, The Evolution and Late Transformations of the Gothic Mensuration System, Ph.D. thesis, 3 vols., Princeton, 1984 (Ann Arbor, 1984).
Wolfgang Schöller (1989, BI-8.84a).
Lon R. Shelby (NR-1972, BI-6.39, repr. in Courtenay [cited under Structure]), (NR-1977 [with review], BI-8.88, also: -10.29); idem, and Robert Mark (NR-1979, BI-8.87, repr. in Courtenay [cited under Structure]).
Karl-August Wirth, “Bermerkungen zum Nachleben Vitruvs…,” Kunstchronik 20:9 (1967), pp. 281–91.
Design to execution: structure and construction
Lynn Courtenay, ed. The Engineering of Medieval Cathedrals (Aldershot, 1997).
Werner Müller, Grundlagen gotischer Bautechnik (Munich, 1990).
Marie-Thérèse Zenner, Methods and Meaning of Physical Analysis in Romanesque Architecture: A Case Study, Saint-Etienne in Nevers, Ph.D. thesis, 3 vols., Bryn Mawr College, 1994 (Ann Arbor, 1994), vols. 1–2; illustrated summary in Saint-Etienne de Nevers. Un ancien prieuré de Cluny dans le Nivernais, CAMOSINE, no. 80 (Nevers, 1995).
Design concepts: dimensions
Eric Fernie, Romanesque Architecture: Design, Meaning and Metrology (London, 1995).
Peter Kidson, “A Metrological Investigation,” Journal of the Warburg and Courtauld Institutes 53 (1990), pp. 71–97.
Paul von Naredi-Rainer, Architektur und Harmonie: Zahl, Mass und Proportion in der abendlandischen Baukunst (Cologne, 1982).
Albert Presas i Puig, Praktische Geometrie und Kosmologie am Beispiel der Architektur, Algorismus, vol. 27, ed. Menso Folkerts (Munich, 1998).
Rolf C. A. Rottländer, “Zum Weiterleben antiker Masseinheiten und Methoden der Bauplanung im Mittelalter,” in Peter Dilg et al., Rhythmus und Saisonalität (Sigmaringen, 1995), pp. 433–46.
Harald Witthöft, ed., Die historische Metrologie in den Wissenschaften (St Katharinen, 1986).
Albert Zimmerman, ed., Mensura. Mass, Zahl, Zahlensymbolik im Mittelalter (Berlin, 1984).
Design concepts: geometry
Georg Dehio (NR-1894), (NR-1895a), (NR-1895b).
Nigel Hiscock, The Wise Master Builder (Aldershot, 2000).
Maria Velte (NR-1951 [with multiple reviews], BI-8.96).
Wofgang Wiemer and Gerhard Wetzel, “A Report on Data Analysis of Building Geometry by Computer,” JSAH 53:4 (1994), pp. 448–60.
Nancy Y. Wu, ed., Ad Quadratum (Aldershot, 2002).
Marie-Thérèse Zenner, “Villard de Honnecourt et la géométrie euclidienne,” Pour la Science, Dossier no. 37, Les sciences au moyen-âge (October 2002/January 2003), pp. 108–9; expanded version, “Villard de Honnecourt and Euclidean Geometry,” Nexus Network Journal 4:4 (2002), pp. 65–78, online at <www.nexusjournal.com/Zenner.xhtml>.
General
Janet Adams, “The Use of Templates in Gothic Architecture,” Bulletin of Research in the Humanities 83:2 (1980), pp. 280–91.
Jennifer S. Alexander, “Villard de Honnecourt and Masons’ Marks,” in Marie-Thérèse Zenner, ed., Villard’s Legacy (Aldershot, 2004), pp. 53–69.
Marcel Anfray, “Les Architectes des cathédrales,” Les Cahiers techniques de l’art 1 (Paris, 1947).
C. Edson Armi, Design and Construction in Romanesque Architecture (Cambridge, 2004).
Marcia Ascher, Mathematics Elsewhere (Princeton, 2002).
Alexander Badawy, “Ancient Constructional Diagrams in Egyptian Architecture,” GBA 107 (1986), pp. 51–6.
Günter Bandmann, Die Bauformen des Mittelalters (Bonn, 1949).
Anne Baud, Cluny (Paris, 2003).
Jean-Pierre Bayard, Le Compagnonnage en France (Rennes, 1977; 2nd edn. Paris, 1990).
Guy Beaujouan, “Calcul d’expert” (1963), in Par raison des nombres (Aldershot, 1991).
Jim Bennett, “Practical Geometry and Operative Knowledge,” Configurations 6 (1998), pp. 195–222.
Jean-Claude Bessac, “Tracés et épures gravés dans l’ancienne cathédrale Saint-Just de Narbonne (Aude),” in Actes du Colloque international de glyptographie de Cambrai (Braine-le-Château, 1985), pp. 35–55.
Henri Bilheust, L’Art des bâtisseurs romans, Cahiers de Boscodon 4, 5th rev. edn. (Boscodon, 1990).
Henri Bilheust et al., Les Tracés des maîtres d’oeuvre, Livret no. 4, 2nd edn. (Boscodon, 1997).
Günther Binding, “Architekturdarstellung,” in Lexikon des Mittelalters, vol. 1 (Munich, 1980).
——, Der früh- und hochmittelalterliche Bauherr (1996; 3rd edn. Darmstadt, 1999).
Günther Binding et al., Baubetrieb im Mittelalter (1993; 2nd edn. Darmstadt, 1997).
——, “Bibliographie zum mittelalterlichen Baubetrieb Westeuropas,” Zeitschrift für Archäologie des Mittelalters 16/17 (1988/99), pp. 185–98.
Robert Bork, ed., De Re Metallica (Aldershot, 2005).
Nicolaus Bubnov, ed., Gerberti… Opera mathematica (1899; repr. Berlin, 1963).
Robert G. Calkins, Medieval Architecture (New York, 1998).
Mary Carruthers, The Book of Memory (Cambridge, 1990).
René Chappuis, “Utilisation du tracé ovale,” BM 134 (1976), pp. 7–36.
Nicola Coldstream, Masons and Sculptors (Toronto, 1991).
——, Medieval Architecture (Oxford, 2002).
Dietrich Conrad, Kirchenbau im Mittelalter, Bauplanung und Bauausführung (1990; 3rd edn. Leipzig, 1998).
Lynn Courtenay, ed., The Engineering of Medieval Cathedrals (Aldershot, 1997).
Paul Crossley, “Medieval Architecture and Meaning,” BurlM 130 (1988), pp. 116–21.
Martin Davies, Romanesque Architecture: A Bibliography (New York, 1993).
Michael T. Davis, “On the Drawing Board: Plans of the Clermont Cathedral Terrace,” in Nancy Y. Wu, ed., Ad Quadratum (Aldershot, 2002), pp. 183–204.
Michael T. Davis et al., “Mechanics and Meaning,” Gesta 39 (2000), pp. 159–80.
François Deshoulières, Eléments datés de l’art roman en France (Paris, 1936).
Frans Doperé, “Etude de l’évolution des techniques de taille… pendant le 15e siècle,” in Patrice Beck, ed., L’Innovation technique (Paris, 1998), pp. 234–6.
Albrecht Dürer, Géométrie, ed. Jeanne Peiffer (Paris, 1995).
Harrison Eiteljorg, II, “How Should We Measure an Ancient Structure?,” Nexus Network Journal 4:4 (2002), pp. 14–20.
Kirstin Faupel-Drevs, Vom rechten Gebrauch der Bilder im liturgischen Raum (Leiden, 2000).
John Fitchen, Building Construction Before Mechanization (Cambridge, Mass., 1986).
Phillipe Fleury, La Mécanique de Vitruve (Caen, 1993).
Menso Folkerts, “Visierkunst,” in Lexikon des Mittelalters (Munich, 1997), vol. 8, pp. 1727–30.
Paul Frankl, with Paul Crossley, Gothic Architecture (1962; rev. edn. New Haven, 2000).
Louis Frey, “Médiétés et approximations chez Vitruve,” Revue archéologique 2 (1990), pp. 285–330.
Teresa Grace Frisch, Gothic Art, 1140–c.1450 (Englewood Cliffs, NJ, 1971).
Mark Gelernter, Sources of Architectural Form (Manchester, 1995).
Wolfgang Götz, Zentralbau… in der gotischen Architektur (Berlin, 1968).
G. Ulrich Grossmann, Einführung in die historische Bauforschung (Darmstadt, 1993).
John Harvey, “The Mediaeval Carpenter and his Work as an Architect,” Journal of the RIBA 45 (1938), pp. 733–43.
Lothar Haselberger, “Architectural Likenesses,” Journal of Roman Archaeology 10 (1997), pp. 77–94.
——, “Geometrie der Winde,” in Stadt und Umland… Archäologischen Bauforschung 7 (Mainz, 1999), pp. 90–100.
Axel Hausmann, “Inque pares numeros omnia convenient: Der Bauplan der Aachener Palastkapelle,” in Paul L. Butzer et al., eds., Karl der Grosse und sein Nachwirken, 2 vols. (Turnhout, 1997), vol. 1, pp. 321–66.
Wilhelm Heinzmann et al., eds., Runica, Germanica, Mediaevalia (Berlin, 2003).
Carol Heitz, “Vitruve et l’architecture du haut moyen-âge,” in La Cultura antica…, 2 vols. (Spoleto, 1975), vol. 2, pp. 725–57.
Roger Herz-Fischler, A Mathematical History of the Golden Number (New York, 1998).
Nigel Hiscock, “Design and Dimensioning in Medieval Architecture,” in Rainer S. Elkar et al., eds., Vom rechten Mass der Dinge (St Katharinen, 1996).
Frederick A. Homann, S. J., ed., Practical Geometry [Practica Geometriae] Attributed to Hugh of St Victor (Milwaukee, 1991).
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