Glossary
- Geometrical
- Gothic Design
- Aesthetics
- aesthetic qualities
- Gothic architecture
- social meaning and reception
- medieval design process
- Gothic buildings
- geometrical figures
- visual expression
- medieval architectural imagination
- formal order
- classical design tradition
- Greco-Roman antiquity
- Greek builders
- arch
- post-and-lintel system
- series of vertical columns
- series of horizontal beams
- temples
- Parthenon
- Athens
- structural system
- demarcation between supporting and supported elements
- timeless
- stable order
- Greek builders
- human bodies
- canons of proportion
- orders
- plain columns
- Doric order
- Parthenon
- proportions of a male warrior
- Ionic columns
- scrolled capitals
- proportions of a woman
- Corinthian columns
- leafy capitals
- young maiden
- Roman architect
- Vitruvius
- Caesar Augustus
- De Architectura
- ancient world
- variance of proportion
- numerical guidelines
- height–to-width ratio
- 10:1
- human analogy
- classical architectural theory
- leafy form
- Corinthian capital
- metaphor
- growing plant
- Greco-Roman architecture
- Gothic era
- capital type
- Greek architect
- Callimachus
- acanthus plant
- votive basket
- leafy basket
- classical architectural practice
- leafy articulation
- Corinthian capitals
- Gothic design
- Roman architects
- Roman builders
- arches
- vaults
- uninterrupted interior spaces
- Pantheon
- baths of Diocletian
- Santa Maria degli Angeli
- vaults
- volumes
- complex
- organic
- Greek architecture
- traditional classical orders
- visual rhythms of Roman vaulted buildings
- measured
- slow
- large elements
- Gothic design
- spatial outlines
- audience halls
- lightweight timber roofs
- Christian churches
- Emperor Constantine
- Christianity
- architectural history
- Western Europe
- Constantine
- advent of the Gothic era
- twelfth century
- building practice
- Roman practice
- addition of tower complexes to churches
- Carolingian era
- drama
- Early Christian times
- stone vaulting
- small spatial cells
- bays
- Roman Empire
- Romanesque
- Roman design elements
- Romanesque churches
- masonry piers
- bundles of shafts
- Vitruvian convention
- leafy capitals
- Corinthian inspiration
- proportions of the shafts
- human analogy of classical column
- early Middle Ages
- geometrically-based design tradition
- architectural development
- Gothic era
- conventions of classical design: govern the shape of the final object.
- conventions of medieval design: often involved instead the sets of procedural operations used in generating that object. They defined, metaphorically speaking, the rules of the game rather than the final score.
- early medieval designers
- compass
- straightedge
- geometrical operations
- complexity
- manuscripts
- Book of Kells
- dynamic form generation
- manuscripts
- jewelry
- swords
- stone sculpture
- architectural forms
- early Middle Ages
- Romanesque Architecture
- Coherent Geometry
- eleventh century
- Anglo-Norman
- Gothic era
- European architecture
- Saint-Denis Abbey
- large windows
- pointed arches
- lightweight structural system
- ceiling made of vaults with diagonal ribs
- Gothic designers
- new vocabulary
- structural and decorative forms
- spires
- miniature pinnacles
- flying buttresses
- upper walls
- thrust of vaults
- medieval
- modern style
- Renaissance
- slurs
- non-classical design mode
- Gothic style
- twelfth century
- fashionable
- Gothic building projects
- interior of the choir
- scale
- narrow overall proportions
- skeletal structure
- slender shaft bundles
- small capitals
- base of the main vault
- transcendence
- vast windows
- geometrical tracery
- trefoils
- chapels
- first story
- rosettes
- clerestory
- geometrical design principles
- choir
- compasses
- straightedges
- drafting tables
- rib vaults
- interior space
- art historian
- aesthetics of partiality
- complexity of the interior
- changing vistas of related but distinct parts
- screens of columns and shafts
- cosmos
- exterior view
- working structure
- skeletal appearance
- ground level
- slim but solid buttresses
- flank the windows
- window heads
- horizontal cornice wraps the building
- belt
- undulating but facetted outline
- articulated buttresses
- flying buttresses
- bracing the walls
- upper choir
- flyer
- lacy row of openwork tracery
- Gothic
- Italian ‘Gothic’
- Society of Architectural Historians
- roundels
- interpenetration of solid and void
- flying buttress motif
- vertical buttresses
- spiky pinnacles
- crockets
- curling leaves
- buttresses
- gables
- pinnacles
- budlike finials
- pinnacle tips
- vegetal forms
- cathedral itself is a living organism
- expression of the growth metaphor
- classical architecture
- Corinthian capitals
- social context
- scholarly reception
- archbishops
- political figures
- Holy Roman Empire
- Petrarch
- intellectual culture
- ancient Rome
- Italian Renaissance
- classical architectural conventions
- nave aisles
- sixteenth century
- fifteenth century
- tastemakers
- Gothic architectural mode
- classicism
- modern style
- barbarians
- Gothic architecture
- De Re Aedificatoria
- De Architectura
- Gothic tradition
- German architect
- booklet
- Gothic technique of pinnacle design
- craft handbooks
- art of geometry
- extruding stonework: extrapolation of a three-dimensional building component out of its ground plan in accord with its elevation, the process that German authors call Auszug, or “pulling out.”
- compass
- pinnacle’s ground plan
- quadrature: inscribing of rotated squares within the framing square. Having established the basic square abcd in step one, for example, he explains the next step as follows: “Divide the distance from a to b into two equal parts, and mark an e at the midpoint. Do the same from b to d and mark an h; from d to c and mark an f; from c to a and mark a g. Then draw lines from e to h, h to f, f to g, and g to e, as in the example of the figure drawn hereafter.
- compass
- rule
- elevation
- stacking a series of modules
- three-dimensional shape of the pinnacle
- extrusion of the plan according to the elevation
- Gothic building elements
- entire churches
- two-plus-two dimensional
- Renaissance design
- three-dimensional volumes
- spheres
- cubes
- Gothic design
- geometrical logic
- scholars
- commentators
- Renaissance
- design process
- Gothic design elements
- Gothic design tradition
- correctness
- convention
- Gothic design
- classical design
- Gothic–to–Renaissance transition
- illustrated treatises
- classical design
- fifteenth-century design booklets
- Sebastiano Serlio
- typical columns
- five major orders
- Tuscan order
- Doric
- Ionic
- Corinthian
- composite: a variant of the Corinthian that incorporates quasi-Ionic scrolls in its capitals.
- column and its corresponding base
- canonical ratio of its height to its width
- correct column forms
- European audience
- Gothic design
- condemnation of Gothic design practice
- Florentine artist
- art–historical writing
- Vite
- Lives of the Artists
- critique of the Gothic design mode
- Gothic mode
- portals
- thin columns twisted in corkscrew fashion
- vine tendrils
- tabernacle
- pyramids
- paper
- stone
- marble
- projections
- openings
- consoles
- twining vines
- out of proportion
- Goths
- ancient buildings
- architects
- northern European building practices
- ancient Goths
- origin myth
- Italian Renaissance
- tastemakers
- historical memory
- Gothic mode
- Gothic architecture
- Myth of the Medieval’
- Gothic Architecture
- Gothic designers
- classicism
- Gothic design
- classical design
- good taste
- political power
- Renaissance mode
- glory of the Roman Empire
- eighteenth century
- Sublime
- aesthetic theory
- Gothic elements
- remodeling
- residence
- German national genius
- eighteenth century
- Gothic revivalism
- Gothic design practice
- Gothic design and aesthetics
- slender piers
- trees of a primeval forest
- immeasurability of the universe
- finite space
- upward soaring of piers and walls
- ceaseless energy
- towers
- turrets
- crystallized nature
- organic and crystalline growth
- good models
- dynamic geometrical practice
- Napoleonic Wars
- cross–section of the choir
- engraver
- western façade
- twin spires
- medieval design drawing
- building campaign
- Prussia
- archaeological precision
- Gothic Revival movement
- medieval design techniques
- handbook of pinnacle design
- geometrical explanations
- Gothic building designs
- Gothic architects
- simple modules and numerical ratios
- dynamic geometry
- building plans
- Gothic builders
- numerical ratios
- arithmetical approximations to quantities originally conceived geometrically
- 7:5
- 12:7
- √2 ratio
- diagonal of a square and its side
- geometry in the Gothic design process
- Gothic builders
- design of whole churches
- design of pinnacles: by defining the ground plan first, and then projecting its elements into the third dimension, while using dynamic geometry to set the proportions of figures in both the horizontal and vertical planes.
- ground plan
- elevation
- semicircular plinth
- radius at ground level
- radius equals the diagonal of a square
- fan-shaped array
- faceted outline
- center point
- Geometry of Creation
- geometrically derived quantities
- precise geometrical relationships
- Vectorworks
- CAD system
- baseline
- one sixth of a semicircle
- one twelfth of a full circle
- geometrical constructions
- choir
- twelve-sided dodecagon
- inscribes a circle within a square
- smaller square within that circle
- original framing square
- cosine of the 45-degree angle
- equator of the original square
- medieval builders
- compasses
- straightedges
- interlocking figures
- scaling by .707 a quadrature factor
- shaded arcs
- original framing square
- geometry of the dodecagon
- dodecagon inscribed within a circle within a framing dodecagon
- dodecature factor of .966
- cosine of the 15-degree wedge between its equator and its corner
- plan
- elevation
- basic plinth forms
- radius of the circle
- engaged piers
- one factor quadrature factor and two dodecature factors
- third dodecature factor
- outer corners
- outboard surfaces of the large buttresses between the chapels
- pier centers
- main choir vessel
- building centerline
- main pier axes of the choir
- unit
- choir plan
- main vessel width
- ground plan
- choir elevation
- rotated square framing this octagon
- main vault keystones
- height–to-width ratio
- crystalline figure
- lateral corners of the rotated square
- vertical axes
- buttress superstructure
- articulation style
- geometrical scheme
- ground plan
- height of the roofs over the side aisles
- upper lateral corners
- rays through the chapel buttresses intersect the semicircular outline of the plinth
- baseline of the composition
- outer buttress faces
- diameter of a large half-dodecagon
- midpoint of the choir floor
- horizontal molding
- outboard buttresses
- interior story
- outer buttresses
- buttress superstructure
- ground plan
- vertical lines
- semicircle of the plinth
- outer wall surfaces of the choir aisles
- diagonal lines
- stained glass windows
- width of the chapel
- axial piers framing its entrance
- outline of a regular octagon
- interior
- exterior
- two equilateral triangles
- axes of the main piers
- groundline
- main arcade capitals
- story division
- high capitals
- main vaults spring
- shape of the exterior superstructure
- dodecagon
- lower facet
- floor of the main choir vessel
- pinnacles
- main vault
- circle framing a dodecagon
- timber roof truss
- geometrical system
- static order
- Greco-Roman buildings
- triforium falls
- geometrical growth processes
- growing systems in nature
- mineral crystals
- Gothic design process
- methods used by Gothic designers
- medieval craft traditions
Figure 1
Figure 2
Figure 3
Figure 4
Figure 7
Source Citation
Bork, Robert. “The Geometrical Roots of Gothic Design and Aesthetics: The Case of the Cologne Cathedral Choir,” Excerpted from The Edinburgh Companion to Gothic and the Arts, edited by David Punter (Edinburgh: Edinburgh University Press, 2019), pp. 52-68.