The existing fragments of an architectural booklet by the 16th-century Spanish architect Rodrigo Gil de Hontañón reveal an ingenious attempt to systematize the design process by creating a sequence of formulaic procedures to be followed in ecclesiastical projects. The formulae are addressed to two more or less separate issues. The first is to synthesize Gothic and Classic proportioning methods, and demonstrate their fundamental identity. The second is to establish an independent "science" of structural design. Aside from the more theoretical writings of Leonardo da Vinci, the work of Rodrigo Gil is the principal evidence extant for the development of structural thinking among 16th-century master masons. Seven formulae discussed here are concerned with the correct depth of a buttress to support an arch or a rib vault. The formulae do not seem to have been derived through theoretical analysis, using the medieval Scientia de Ponderibus. Rather they are the result of new experimentation and traditional Gothic geometric thinking applied to classical arches, and of new arithmetic procedures applied to Gothic rib vaults.

[Footnotes]

[Footnotes]
1
William Barclay Parsons, Engineers and Engineering in the Renais- sance, 1939, 67-73, 481-492
Parsons
67
Engineers and Engineering in the Renaissance
1939
Gille, Les ingenieurs de la renaissance, Paris, 1964
Gille
Les ingenieurs de la renaissance
1964
Rowland Main- stone, "Structural Theory and Design Before 1742," The Architectural Review, April 1968, 303-3 10
Mainstone
April
303
The Architectural Review
1968
2
Robert Mark, "Structural Experimentation in Gothic Architec- ture," American Scientist, 6, 548-549.
548
6
American Scientist
3
Guy Beaujouan, L'interdipendance entre la science scolastique et les techniques utilitaires, Paris, 1957
Beaujouan
L'interdipendance entre la science scolastique et les techniques utilitaires
1957
Guy Beaujouan, Manuscrits scientifiques medidvaux de l'universite de Salamanque et de ses "Cole- gios Mayores," Bordeaux, 1962
Beaujouan
Colegios Mayores
Manuscrits scientifiques medidvaux de l'universite de Salamanque et de ses
1962
Marshall Clagett, The Science of Me- chanics in the Middle Ages, Madison, Wisconsin, 1959
Clagett
The Science of Mechanics in the Middle Ages
1959
Joseph Brown, "The Scientia de Ponderibus in the Later Middle Ages," dissertation, University of Wisconsin, 1967
Marshall Clagett, Archimedes in the Middle Ages, 3 vols., Philadelphia, 1978
Clagett
3
Archimedes in the Middle Ages
1978
4
Rodrigo Gil is John Hoag, "Rodrigo Gil de Hontafiön, His Work and Writings," dissertation, Yale University, 1958
Later works on Rodrigo's architecture are Marques de Lozoya, Rodrigo Gil de Hontahiin en Segovia, Santander, 1962
Lozoya
Rodrigo Gil de Hontahiin en Segovia
1962
Pedro Navascues Palacio, "Rodrigo Gil y los entalladores de la fachada de la Universidad de Alcali," Archivo Espahol de Arte, XLV, 1972, 103-117
Palacio
Rodrigo Gil y los entalladores de la fachada de la Universidad de Alcali
103
XLV
Archivo Espahol de Arte
1972
A. C. Casa- seca, "Trazas para la Catedral de Segovia," Archivo Espahol de Arte, LI, 1978, 29-51
Casaseca
29
LI
Archivo Espahol de Arte
1978
J. Garcia-Murga, "La intervenciön de Rodrigo Gil de Hontafiön en la iglesia de Santa Maria de Guarefia," Goya, 144, 1978, 314-323
Garcia-Murga
314
144
Goya
1978
5
Eduardo Mariaitegui in El Arte en Espaha, vii, 1868, 113-127, 154-184, 193-215
Mariaitegui
113
vii
El Arte en Espaha
1868
Jose Camén Aznar was published in Salamanca in 1941
Carlos Chanfén Olmos, Mexico, 1980
6
Jose Camén Aznar, "La intervenciön de Rod- rigo Gil de Hontafiön en el manuscrito de Simén Garcia," Archivo Espahol de Arte, xiv, 1941, 300-305
Aznar
300
xiv
Archivo Espahol de Arte
1941
Hoag, "Rodrigo Gil," 405- 409
Hoag
405
Rodrigo Gil
Hoag, "Rodrigo Gil," 381-387
Hoag
381
Rodrigo Gil
José Camén Aznar, "Sobre la torre de la Catedral Nueva de Salamanca," Archivo Espahiol de Arte, xIv, 1940-194 1
Aznar
1
xIv
Archivo Espahiol de Arte
1940
7
Philibert de L'Orme, who in his Le premier tome de l'architecture, ed. 1568, III, 6, 62r
L'Orme
6
III
Le premier tome de l'architecture
1568
8
Carlo Borromeo in Chapter I of his Instructiones Fabricae et Supellectilis Ecclesiasticae of 1577
Borromeo
Instructiones Fabricae et Supellectilis Ecclesiasticae of 1577
9
Vitruvius, The Ten Books on Architecture, trans. M. H. Morgan, ed. New York, 1914, I, ii, 4-5; III, i; Iv, i, 6-8
Vitruvius
4
I
The Ten Books on Architecture
1914
Richard Betts, "The Architectural Theories of Francesco di Giorgio," dissertation, Princeton University, 1971
Pedro Navascues Palacio, El libro de arqui- tectura de Herndn Ruiz, el Joven, Madrid, 1974, 4ff
Palacio
4
El libro de arquitectura de Herndn Ruiz
1974
10
Villa- fafie, De varia commensuraciön para la escultura y arquitectura, Seville, 1585, Book z
Villafafie
De varia commensuraciön para la escultura y arquitectura
1585
11
"Metrics and Geometry of Romanesque and Gothic St. Benigne, Dijon," The Art Bulletin, LXII, 1980, 510-532
510
LXII
The Art Bulletin
1980
12
Derand in 1643
Conclusion and footnote 32 below
13
George Kubler, "A Late Gothic Computation of Rib Vault Thrusts," Gazette des Beaux- Arts, s.6, z5, 1944, 135-148
Kubler
135
s.6
Gazette des BeauxArts
1944
Hoag, "Rodrigo Gil," 426-435, 441
Hoag
426
Rodrigo Gil
14
Rodrigo's comments in Sr and 181
15
Lon Shelby and Robert Mark, "Late Gothic Structural Design in the 'Instructions' of Lorenz Lechler," Architectura, 9, 2, 1979, 113- 132.
Shelby
113
9
Architectura
1979
16
plans in Fer- nando Chueca, Historia de la arquitectura espaniola. Edad antiqua. Edad media, Madrid, 1965, 579, 634-5
579
Historia de la arquitectura espaniola. Edad antiqua. Edad media
1965
Castor de Uriarte, Las iglesias "salon" Vascas del ultimo periodo del gético, La- bastida, Alava, 1978, 19
Uriarte
19
Las iglesias "salon" Vascas del ultimo periodo del gético
1978
17
Kubler's discussion of this formula, "Late Gothic Computa- tion," 141-142
Kubler
141
Late Gothic Computation
18
Kubler, "Late Gothic Computation," 14Z-143, read the term circumferencia as radius, so he incorrectly believed the formula to be IV radius + height.
Kubler
14Z
Late Gothic Computation
19
Kubler, "Late Gothic Computation," 142, believes the first geo- metric formula is for a barrel vault.
Kubler
142
Late Gothic Computation
Hoag,"Rodrigo Gil," 430-435
Hoag
430
Rodrigo Gil
20
Kubler, "Late Gothic Computation," 14z, states the opposite, claiming that the I:4 formula has a higher safety factor.
Kubler
14z
Late Gothic Computation
23
Although Rodrigo does not mention it, angles EAD, DAC, and CAB are equal, each subtending 1/24 Of a circle, or I degrees.
24
If the diameter of the arch is z radii, distance AF is I + fV, or 2.414 radii, and distance AH is 1/2 + + V2+3, or 2.432 radii.
25
Distance KH is .632 radii and KF is .626.
27
Kubler, "Late Gothic Computation," footnote 19
Kubler
Late Gothic Computation
Hoag, "Rodrigo Gil," 433.
Hoag
433
Rodrigo Gil
31
Lon Shelby, "The Geometric Knowledge of the Medieval Master Masons," Speculum, XLVII, 1972, 395-42-1
Shelby
395
XLVII
Speculum
1972
32
R. P. François Derand, S.I., L'architecture des voutes ou l'art des traits et coupe des voûtes Paris, 1643, 16-17
Derand
16
L'architecture des voutes ou l'art des traits et coupe des voûtes
1643
Hoag, "Rodrigo Gil," 433-434
Hoag
433
Rodrigo Gil
Mainstone, "Structural Theory and Design," 305-306, and fn. 39
Mainstone
305
Structural Theory and Design
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