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First Principles: Gabriele Stornaloco and Milan Cathedral

  • Giulia Ceriani Sebregondi and Richard Schofield

The construction from 1386 of Milan Cathedral, the largest Gothic church ever constructed in Italy, was one of the most important episodes in the history of Italian and European architecture. The documentation of the late Trecento and early Quattrocento discussions over how to build the Cathedral is extraordinarily rich and extensive, and permits a consideration of the project from many points of view including the relationship between medieval architectural theory and an actual project. At the same time, any enquiry has to contend with the copious modern literature and the conclusions that have been reached hitherto – often erroneously in our view – about many of the most salient points. We thus re-examine published and unpublished documentation and the existing literature, analysing especially the format of the building's elevation, the proposals by Gabriele Stornaloco and Jean Mignot, and the drawings attributed to Antonio di Vincenzo. We also reconsider the notions of ars and scientia which have previously been misinterpreted in discussions of the cathedral documentation.

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1 For a survey of the history of the cathedral in the European context, see Wilson, Christopher, The Gothic Cathedral; the Architecture of the Great Church 1130–1530 (London, 1990), pp. 268–76, a view generally accepted by scholars and based essentially on Ackerman, James S., ‘“Ars sine scientia nihil est”; Gothic Theory of Architecture at the Cathedral of Milan’, The Art Bulletin, 31, 2 (1949), pp. 84111 (reprinted in idem, Distance Points; Essays in Theory and Renaissance Art and Architecture (Cambridge, 1991), pp. 211–68), and on Romanini, Angiola Maria, ‘Architettura’, in Il Duomo di Milano, ed. da Passano, Carlo Ferrari, Romanini, Angiola Maria and Brivio, Ernesto, 2 vols (Milan, 1973), I, pp. 97232 . For the chronology, similarly based on Romanini, see Frankl, Paul, Gothic Architecture [1962], ed. Crossley, Paul (New Haven–London, 2000), pp. 351–52, which reviews the most recent bibliography, including Ascani, Valerio, ‘Le dessin d'architecture medieval en Italie’, in Les Bâtisseurs des cathédrales gothiques, ed. Recht, Roland (Strasbourg, 1989), pp. 255–78; Cadei, Antonio, ‘Cultura artistica delle cattedrali: due esempi a Milano’, Arte medievale, 5 (1991), pp. 83104 ; White, John, Art and Architecture in Italy, 1250–1400 (New Haven–London, 1993), pp. 517–31; Welch, Evelyn, Art and Authority in Renaissance Milan (New Haven–London, 1995), pp. 49114 ; Kidson, Peter, ‘Three Footnotes to the Milan Debates’, in Arte d'Occidente; temi e metodi. Studi in onore di Angiola Maria Romanini, ed. Cadei, Antonio, 3 vols (Rome, 1999), I, pp. 269–78.

2 This complex of problems has been considered repeatedly by scholars from Luca Beltrami onwards. Recently, Trachtenberg has cited the case of Milan Cathedral, wondering ‘how the architecture culture of the period avoided – if it did – turning its long-lived building projects into a cadavre exquis, the earlier Dadaist adoption of the child's game in which the head is drawn at the top of a sheet of paper, which is folded, then a body drawn, the paper refolded, legs drawn, and so on, then finally unfolded to produce a grotesque hybrid figure that in the Dada interpretation was a monster released from the subconscious. One wonders whether traditional historical criticism is correct when suggesting, in effect, that building procedures in the period often resembled the Dadaist game – as in, for example, James Ackerman's celebrated analysis of the planning of Milan Cathedral’; see Trachtenberg, Marvin, Building-in-Time from Giotto to Alberti and Modern Oblivion (New Haven–London, 2010), p. 67 .

3 Booz, Paul, Der Baumeister der Gotik (Munich, 1956), pp. 5152 , following Cesariano's edition of Vitruvius (Cesare Cesariano, Di Lucio Vitruvio Pollione de architectura libri dece traducti de latino in vulgare, Como, 1521, fol. XIVr; see our Fig. 14), tries to lay a system of equilateral triangles over the plan, but without much success.

4 13 October 1391: Nava, Ambrogio, Memorie e documenti storici intorno all'origine, alle vicende ed ai riti del Duomo di Milano (Milan, 1854), p. 27 ; Annali della fabbrica del Duomo di Milano dall'origine fino al presente pubblicati a cura della sua amministrazione, 9 vols (Milan, 1877–85), I, p. 55 . The Deputati of the Cathedral had already called a meeting in August to discuss ‘longitudinem pillonorum et altitudinem ecclesiae’ (24 August 1391: Annali, I, p. 53) and on 24 September they decided to write to Stornaloco. For Stornaloco's name, see Fiori, Giorgio, ‘Stornaloco o Scovaloca? La famiglia di un matematico piacentino del Trecento’, Bollettino storico piacentino, 18 (1986), pp. 253–54.

5 Between 1386, the traditional date of the beginning of work on the cathedral, and 1391, the piers in the apse and those next to them were constructed with the foundations and parts of the perimeter walls.

6 According to Franchetti, the breadth of the aisles and nave taken together is 96 br., 11 on., 3 punti (equivalent to 57.67 m); see Franchetti, Gaetano, Storia e descrizione del Duomo di Milano esposte da Gaetano Franchetti e corredate di xxx tavole incise (Milano, 1821).

7 Here one can agree with Cohen who, when paraphrasing Crosby, Alfred W. (Measure of Reality: Quantification and Western Society, 1250–1600 (Cambridge, 1996), pp. 121–22), focuses on the approximation established by Stornaloco for the height of the equilateral triangle from 83.138 to 84, and underlines how ‘for Stornaloco the message, equilateral triangle, is more important than the vehicle, a significantly compromised equilateral triangle’, which ‘could for all practical purposes be considered identical, with the advantage of being divisible into modules of 14 units’; see Cohen, Matthew A., Beyond Beauty: Re-examining Architectural Proportion Through the Basilica of San Lorenzo and Santo Spirito in Florence (Venice, 2011), pp. 250–51.

8 Frankl, Paul, ‘The Secret of the Mediaeval Masons’, The Art Bulletin, 27, 1 (1945), pp. 4660 ; idem, The Gothic. Literary Sources and Interpretations Through Eight Centuries (Princeton NJ, 1960), pp. 6383 .

9 Frankl, ‘The Secret’, p. 53, followed by Ackerman, ‘Ars sine scientia’, p. 90.

10 Frankl, ‘The Secret’, p. 59.

11 Panofsky, Erwin, ‘An Explanation of Stornaloco's Formula’, The Art Bulletin, 27, 1 (1945), pp. 6164 (p. 61). At the beginning of this article Panofsky maintained that the 96 quantitates equalled 12 unitates and he insisted throughout his article on the difference between unitates and quantitates, making it particularly difficult to follow his explanation. But it does not seem that Stornaloco used two systems or modules in his text, although such a distinction helped to corroborate Frankl's hypothesis about the ‘Great Unit’ (see our Section 2).

12 Panofsky, ‘An eExplanation’, p. 62.

13 Kidson, ‘Three Footnotes’.

14 Ibid. , p. 270.

15 Ibid. , p. 271: ‘the vagueness of the final stages of the deduction may have been deliberate’.

16 Ibid. , p. 269.

17 Ibid. , p. 273.

18 Beaujouan, Guy, ‘Calcul d'expert, en 1391, sur le chantier du Dôme de Milan’, Le Moyen âge: bulletin mensuel d'histoire et de philologie, 69 (1963), pp. 555–63; briefly re-discussed in idem, ‘Réflexions sur les rapports entre theorie et pratique au Moyen Age’, in The Cultural Context of Medieval Learning. Proceedings of the First International Colloquium on Philosophy, Science, and Theology in the Middle Ages, September 1973 ( Boston Studies in the Philosophy of Science, vol. 26), ed. Murdoch, J.E. and Sylla, E.D. (Dordrecht–Boston, 1975), pp. 449–63 (p. 445).

19 ‘Erit ergo linea AD que est altitudo sumitatis eclexie radix de duc[tione] in xx senaria quia tregesime, quod est aliquid minus de LXXXIIII’, where ductio in means ‘multiplication by’ in contemporary mathematical Latin. Smith, D.E., in History of Mathematics, 2 vols (New York, 1958), 2, pp. 102 , 105, shows how the verb ducere in and the noun ductus in were used for multiplying and multiplication in medieval and Renaissance texts. See Appendix I, for other examples and the discussion of Beaujouan's emendation.

20 Frankl, ‘The Secret’, p. 50.

21 Kossmann, Bernhard, Einstens maßgebende Gesetze bei der Grundrissgestaltung von Kirchenbauten (Strasbourg, 1925).

22 Frankl, ‘The Secret’, pp. 51–52.

23 Ibid. , pp. 52–53.

24 Ibid. , pp. 50, 51.

25 Ibid. , p. 56.

26 Toker, Franklin, ‘Gothic Architecture by Remote Control: an Illustrated Building Contract of 1340’, The Art Bulletin, 67, 1 (1985), pp. 6795 (p. 82). Toker (p. 80) reports that the dimensions indicated in the Sienese text and drawing tell us that the designer came from the culture of ‘constructive geometry’ diffused all over Europe, which used the two most widely available and reliable schemes, those ad triangulum and ad quadratum. The author, however, whilst providing a different, simpler and more acceptable solution to that proposed by Frankl, agrees with him about the reason for the summons of Stornaloco to the cathedral in Milan and suggests that such geometric solutions were for the ‘ordinary builders’ for whom a mathematician was not available (p. 82). Toker amplifies his argument in idem, Il contratto del 1340: un “unicum” nell'architettura europea’, in Palazzo Sansedoni, ed. Gabbrielli, Fabio (Siena, 2004), pp. 193228 (pp. 206–17 for the subjects discussed above).

27 Cesariano, Di Lucio Vitruvio Pollione, f. 98r, fig. KLMN, with the text: ‘hora resta distinguere la tertia figure excipita dal pariquadrato signato KLMN, la cui diagonale linea si è LM, quale, si il centro del circino collocarai in la littera L, tangendo con laltro centro la littera M, una portione circinarai in sino a la recta linea adiecta da N ad P, quale adiecta serà de più undeci vigintiquattresimi: si como te denota manifestamente la quadratura, si la partirai in duodece parte, epso adiecto serà più cinque & media, ivi signarai QR, per il che concluderai la sua superfice ultima da O a P, refferendo una Hipotamissa in sino ad M, per la qual cosa, volendo performare questo peristyliato atrio seu parte anteriore, ivi collocarai la dicta figura (italics and punctuation mine)’; see Toker, ‘Gothic Architecture’, p. 82.

28 Frankl, ‘The Secret’, p. 50.

29 Gerbino came to much the same conclusion, noting that it is crucial to recognise the distance between the educated elites and the traditional craft-culture. The practical apprenticeship given to future masters offered graphic solutions and empirical procedures based on simple arithmetical and geometrical relationships for most of the problems. These methods reflected the manual character of the design-process in which the elements were not treated in terms of abstract numbers and dimensions; see Gerbino, Anthony, ‘Introduction’, in Geometrical Objects: Architecture and the Mathematical Sciences 1400–1800, ed. Gerbino, Anthony (Cham, 2014), pp. 146 , especially pp. 4–5. But as an example of his main argument about the interaction between high and low mathematics and between geometrical design and arithmetic calculation, he cites (pp. 6–12) once again the case of Milan Cathedral, still accepting the interpretations offered by Frankl, Panofsky, and Ackerman. According to Gerbino, Stornaloco's solution to the problem of working out incommensurable heights was truly ‘decoded’ by Frankl and Panofsky, according to whom Stornaloco solved it by translating it into a true four-step algorism – that is, a calculation using Hindu-Arabic numerals – involving the multiplication and division of sums to three and four places. In his view, ‘Stornaloco's solution is characteristic of an academic mathematician, not a practicing builder’, but he too wonders whether the masters were unable to determine such dimensions using their own methods: ‘They were more than enough to achieve very high levels of building precision. This was true not only for equilateral triangles […], is it possible that they could have approximated it with an arithmetic rule-of-thumb, one that could relate the base of the cathedral to its height in terms of a commensurable ratio? Procedures of this kind are believed to have been used widely […]. The workshop would, in any case, have been fully capable of working out an adequate ratio for the cross-section of the church using scaled drawings or cords set out at full scale’. The real reason for summoning Stornaloco was, according to Gerbino, that the ‘clash of sensibilities [between Lombard and Northern consultants] may have led the two parties to see Stornaloco as a useful go-between’, ‘merely as a security measure’, and that Stornaloco enjoyed the ‘manipulation of the numbers themselves’. Cohen (Beyond Beauty, pp. 250–51, 256–57) follows Gerbino in stating that Stornaloco's approach was ‘more strictly mathematical than the constructive approach’ of the Lombard masters, and well beyond the ‘rudimentary, procedural arithmetic that many masons were probably familiar with’, demonstrating ‘a level of theoretical erudition that may be indicative of a university education’ which could ‘have been entirely without architectural consequences’. And that demonstrates, according to him, that the true difference was between simple and complex mathematics and not so much between geometry and mathematics.

30 Shelby, Lon R., Gothic Design Techniques: the 15th-Century Design Booklets of Mathes Roriczer and Hanns Schmuttermayer (Carbondale, 1977); Shelby, Lon R. and Mark, Robert, ‘Late Gothic Structural Design in the “Instructions” of Lorenz Lechler’, Architectura, 9 (1979), pp. 113–31 (reprinted in The Engineering of Medieval Cathedrals, ed. Courtenay, Lynn T. (Ashgate, 1997), pp. 87105 ); Toker, ‘Gothic Architecture’, p. 87.

31 Shelby, Lon R., ‘The Geometrical Knowledge of Mediaeval Master Masons’, Speculum, 47 (1972), pp. 395421 (reprinted in The Engineering of Medieval Cathedrals, pp. 27–61); Shelby and Mark, Late Gothic’, p. 104.

32 Shelby, ‘The Geometrical Knowledge’, p. 27.

33 Ibid. , pp. 30, 41, for the expressions ‘practical geometry’ and ‘constructive geometry’.

34 Ibid. , p. 42.

35 Frankl, ‘The Secret’, pp. 49–51.

36 Mortet, Victor, ‘La maîtrise d’œuvre dans les grandes constructiones du XIIIe siècle et la profession d'appareilleur’, Bulletin monumental, LXX (1906), pp. 263–70 (p. 267).

37 Frankl, ‘The Secret’, p. 49.

38 In his drawings Peruzzi usually used the Sienese braccio, the Roman palmo and the ancient piede; for example, on Florence, Uffizi, 531Ar, a project for Palazzo Massimo alle Colonne in Rome, he used the palmo; on Ibid., 494Ar, a project for the cathedral in Siena, the braccio; on Ibid., 390Ar, a drawing of the Temple of Venus Genitrix in Rome, the piede. With regards to Antonio da Sangallo the Younger, we can cite Ibid., 189Ar, showing the façade of the Zecca at Castro, for the Roman palmo; and Ibid., 931Ar, a project for the Fortezza da Basso, Florence, for the Florentine braccio. Many of the units of measurement used by him depended on the place where he was working: Bolognese piedi (Ibid., 727Ar), braccia of Ravenna (Ibid., 778Ar), braccia of Piacenza (Ibid., 1395Ar), ancient piedi (Ibid., 796Ar), piedi of Foligno (Ibid., 877Ar–v), etc.

39 Toker, ‘Gothic architecture’, p. 85.

40 Ibid. , pp. 69–71, 88; Cadei, ‘Cultura artistica’. Cadei demonstrates that there is abundant evidence that the procedures for geometric modularity were widely used and did not depend in any way on the arithmetic calculation of dimensions, yet he still follows Frankl's hypothesis that there was a first project for the cathedral in Milan based on modules of 16×10 units without ‘geometrical’ characteristics and based on a system of Milanese braccia, as well as the idea that Stornaloco was summoned to Milan to translate the geometrical construction of a new project ad triangulum into numerical values. Cadei concludes that the new elevation based on Pythagorean triangles proposed by Beltrami was intended to create a manageable metric system, or rather a modern system of numerical quantification; and further, that it was in this respect that the operation in Milan was different, since it moved away from constructive geometry to a system of metrical relationships in scale as in modern systems. See our Sections 4 and 7 for further discussion of these arguments.

41 Frankl, ‘The Secret’, pp. 57–60; Ackerman, ‘Ars sine scientia’, p. 90.

42 Frankl, ‘The Secret’, p. 57.

43 See also Cadei, ‘Cultura artistica’; Crosby, Measure of Reality, pp. 49 and 58.

44 Battisti had already pointed out the cosmological significance of the scheme; see Battisti, Eugenio, ‘Avanguardia e conservatorismo nella storia del Duomo di Milano’, in Il Duomo di Milano, atti del congresso internazionale, Milano, Museo della scienza e della tecnica, 8, 12 settembre 1968, ed. Perer, Maria Luisa Gatti, 2 vols (Milano, 1969), II, pp. 4352 (pp. 47, 49, fig. 4). This theme was taken up again by Valentini, who plausibly suggested that the vertices of the triangle, the square and the hexagon represent the positions of the trigon, the quartile and the sextile of the planets on the ecliptic; see Valentini, Giuseppe, ‘Il contributo di Gabriele Stornaloco, matematico piacentino, alla Fabbrica del Duomo di Milano’, Bollettino storico piacentino, 81 (1986), pp. 242–52 (p. 244); and idem, Il Duomo di Milano; una disputa medievale sul modello del tempio (Milano, 1990), p. 40 (concerning the twelve points of the zodiac in the heavenly vault). See also Hiscock, Nigel, The Symbol at Your Door: Number and Geometry in Religious Architecture of the Greek and Latin Middle Ages (Aldershot 2007), pp. 149–80 (on triangles); pp. 369–72 (on Milan).

45 Serlio, Sebastiano, Quinto libro d'architettura (Paris, 1547), in Sebastiano Serlio, l'architettura: i libri I–VII ed extraordinario nelle prime edizioni, ed. Fiore, Francesco Paolo (Milano, 2001), II, p. 11; Cataneo, Pietro, L'architettura (Venezia, 1567), L. VII, prop. VI, in Trattati, con l'aggiunta degli scritti di architettura di Alvise Cornaro, Francesco Giorgi, Claudio Tolomei, Giangiorgio Trissino, Giorgio Vasari, ed. Bassi, Elena and Benedetti, Sandro (Milano, 1985), p. 405 .

46 See also Bellini, Federico, Le cupole di Borromini: la ‘scienza’ costruttiva in età barocca (Milano, 2004), p. 25 .

47 Annali, I, pp. 56 and 65. ‘Symon de Placentia, magister a lignamine’ is also mentioned in the documents for the building of the Certosa of Pavia on 18 March 1402 (see Beltrami, Luca, Storia documentata della Certosa di Pavia, 2 vols (Milano, 1896), I, p. 214 ).

48 Annali, I, pp. 67, 70–71.

49 16 October 1387: dominus Simone da Cavagnera is mentioned among the Deputati in the ‘General Rules for Administration’ (Annali, I, pp. 4–5, 15); 27 February 1401: he is appointed one of the Deputati ‘per Portam’ (Ibid., p. 221); see also Ibid., pp. 90, 119, 121, 128, 174, 206, 245.

50 Sanvito doubts all this on the grounds that the design of the model was made by Simone da Cavagnera, not Stornaloco; but the timing of events plus the fact that the carpenter was from Piacenza and that Cavagnera was not an architect-engineer, make it certain that Cavagnera was only overseeing the model of Stornaloco's scheme; see Sanvito, Paolo, Il tardogotico del Duomo di Milano: architettura e decorazione intorno all'anno 1400 (Münster, 2002), p. 87 . Beltrami also suggested that the model was made according to Stornaloco's indications; see Beltrami, Luca, ‘Per la facciata del Duomo di Milano’ [1887], in Luca Beltrami e il Duomo di Milano, ed. Ramelli, Antonio Cassi (Milano, 1964), pp. 3791 (p. 77). A summary of available information on the models of the cathedral in this period can be found in Benati, Giulia, ‘Il modello ligneo del Duomo; storia documentale’, Nuovi Annali, 1 (2009), pp. 7793 (p. 77, note 1).

51 1 September 1392: ‘ita sic quod non possit videri sed stet occulta, nisi aliud declaretur’ (Annali, I, p. 82).

52 22 November 1394: Giovannino de Grassi and Giacomo de Campiliono make a ‘designamentum mensure traversus exterius et interius fabrice de versus sacrastias et altitudinis ecclesie’; see Rossi, Marco, Giovannino de Grassi: la corte e la cattedrale (Cinisello Balsamo, 1995), p. 157 , doc. 77.

53 Rossi, Giovannino de Grassi, pp. 157–70.

54 20 May 1414 (Annali, II, p. 12). Another elevation drawing of the church – from the foundations up to the top – was begun in 1399 by Giacomo Cova from Bruges, one of Mignot's companions (20 July 1399: Annali, I, p. 197); given the timing – after the arrival of Cova and Mignot together in April 1399 and before the appointment of the latter as capomastro in October – this must have been a representation of Mignot's proposal, which was a return to Stornaloco I (see our Section 4).

55 Viollet-le-Duc, Eugène, Entretiens sur l'architecture, 2 vols (Paris, 1863), I, p. 394 ; idem, Dictionnaire raisonné de l'architecture française du XI au XVI siècle, 9 vols (Paris, 1845–68), VII, pp. 534–35.

56 Beltrami, ‘Per la facciata’, especially p. 76. For equilateral triangles, see Plutarch, , De Iside et Osiride, ed. Griffiths, J.G. (Cambridge, 1970), p. 238 (381D); for Egyptian triangles, ibid., pp. 207–09 (373F–374A).

57 Cesariano, Di Lucio Vitruvio Pollione, f. 104r: ‘arcuatione si como etiam in terzo acuto como quelle de la sacra aede baricephale’.

58 Corrado Verga tested Beltrami's proportional scheme by superimposing the elevation of the cathedral as built on both projects, that ad triangulum and that with double Pythagorean triangles ( Il Duomo di Milano da Bramante–Cesariano a Stornaloco (Crema, 1980), p. 25 , fig. 9). From Verga's drawing it is clear that Beltrami's scheme, though closer to that based on the equilateral triangle, does not coincide with the building as built either, making it essential to look for a more convincing interpretation (see our Fig. 8).

59 Valentini, ‘Il contributo’; idem, Il Duomo di Milano.

60 Valentini, Il Duomo di Milano, p. 70 and fig. 7, affirms that ‘per il cumularsi delle detrazioni degli spessori, si ebbe un abbassamento di quattro braccia nelle volte mediane [which is correct], che da cinquantasei braccia di altezza del progetto scesero a cinquantadue effettive, e di sei nella nave maggiore [which is incorrect] che da ottantaquattro braccia di altezza del progetto avrebbe dovuto scendere a settantotto mentre in realtà è sessantasette e mezzo’. In fact, in line with this hypothesis, with which we broadly agree, the main vaults would have been 24 braccia high with a total height at the intrados of 76 braccia, losing 8, not 6 braccia, as the author writes. However, the cathedral as built arrives in fact at the intrados at 78 braccia, the reason being that the main vaults are slightly raised, that is, to 26 braccia in height instead of 24: see below and doc. 16 September 1410 note 70.

61 Franchetti, Storia e descrizione, pp. 26–27; Artaria, Ferdinando, Il Duomo di Milano ossia descrizione storico-critica di questo insigne tempio e degli oggetti d'arte che li adornano corredata di 65 tavole (Milano, 1823), p. 43 ; Zuccari, Fermo and de Castro, Giovanni, Il Duomo di Milano (Milano, 1863, reprint Roma, 1992); Beltrami, ‘Per la facciata’, p. 91; Siebenhüner, Herbert, Deutsche Künstler am Mailänder Dom (München, 1944); da Passano, Carlo Ferrari, ‘Storia della veneranda fabbrica: il Duomo di Milano’, in da Passano, Carlo Ferrari, Romanini, Angiola Maria and Brivio, Ernesto, Il Duomo di Milano, 2 vols (Milano, 1973), I, pp. 1196 (pp. 77–80, dis. 3–6); survey made in 2010 by Geometra Regis of the Veneranda Fabbrica del Duomo di Milano, to whom we are grateful for the information he provided on the dimensions of the cathedral. See our Tables 1 and 2.

62 11 br., 96 on. (7.11 m) according to Franchetti, Storia e descrizione.

63 4 br., 3 on. (2.53 m) according to Franchetti, Storia e descrizione.

64 Frankl (‘The Secret’, p. 56) says that all the heights of the cathedral were built half a braccio lower than those in Stornaloco I: i.e. if the height of the equilateral triangle with a base 32 is 27.7 braccia and Stornaloco rounded that up to 28, the master-builders arrived instead at 27.5 (this being followed by Ackerman, ‘Ars sine scientia’, p. 93). Frankl does not give the source for these dimensions, but it seems likely that they were based on those in Beltrami (‘Per la facciata’, p. 91). As one can see from our Table 2, the heights of the cathedral reported by various authors differ slightly, so the information provided by Frankl is not confirmed. And the explanation he proposes, that the Lombard masters rounded down by half a braccio to stay within the system of equilateral triangles, is not convincing, particularly since Frankl himself agrees with Beltrami's hypothesis about the Pythagorean triangles, and that, according to him, the masters had abandoned the heights required by the equilateral triangles and instead used lower triangles.

65 11 December 1391: ‘promisit et contentus fuit quod ipse attendat et cottidie laboret in designando et laborando in operibus fabrice ecclesie Mediolani hinc ad tres menses prossimos (Nava, Memorie e documenti, p. 30; Annali, I, p. 57); 16 May 1392: he was paid for five months work from 12 December 1391 to 12 May 1392 (Annali, Appendix I, p. 229); 7 July 1392: fired because ‘male servierit’ and ‘dedit magnum damnum et detrimentum ipsi fabricae pro suis malegestis’ (Annali, I, p. 71). For a recent discussion of the identity of Parler, see Sanvito, Il tardogotico, pp. 95–96.

66 Cf. ‘volturas sive arcus’ (Q. 5); ‘mediari sive intramezari’ (Q. 7); ‘una sala sive uno corrator’ (Q. 8); ‘pilloni minores sive pilloni cappellarum’ (Q. 11). Frankl, ‘The Secret’, p. 56.

67 Frankl, ‘The Secret’, p. 52; Ackerman, ‘Ars sine scientia’, pp. 93–94. Before them, Nava, Memorie e documenti, p. 33, who is followed by Romanini, Angiola Maria, L'architettura gotica in Lombardia, 2 vols (Milano, 1964), I, pp. 382–83, 387–88; Marco Rossi, ‘Spazio e significato nell'umanesimo milanese: il dibattito per la costruzione del tiburio del Duomo’ (tesi di laurea, Università cattolica del Sacro cuore di Milano, 1980), I, p. 44.

68 Ackerman noticed this contradiction and tried to save his argument by saying that Parler had changed his mind (‘Ars sine scientia’, p. 93, note 37). As regards Annes of Freiburg, 4 and 18 February 1391: nominated engineer (Annali, Appendix I, pp. 159, 161); 12 March 1391: request for a written version of his criticisms of the building (Nava, Memorie e documenti, p. 21; Annali, I, p. 45); 19 June 1391: removed from position of engineer, but allowed to continue as a stone-mason (Annali, I, p. 48). A certain Annex Marchestem is documented at the Fabbrica as a stone-mason between November 1393 and June 1404 – when he died – and this may also be the same person (11 November 1393: Annali, I, p. 104; 16 November 1393: Annali, I, p. 105; 18 and 19 April 1404: Annali, Appendix I, p. 268; 3 and 4 June 1404: Annali, Appendix I, p. 269).

69 For Guidolo Della Croce as Deputato, see Annali, I, pp. 28, 40, 89, 125–126, 128, 158, 201, 206 in a note on pp, 217, 240, 242, 246.

70 1410, 16 September: Infrascripti sunt ordines facti et deliberati per venerabilem virum dominum fratrem Johannem de Gluxiano et magistros Filippinum de Mutina, Christoforum de Giona, Johannem Magattum et Nicorinum Buzardum, inzignerios fabricae, videlicet: in primis deliberaverunt et ordinaverunt quod archus et croxerie et cornixete medii archus magni debeant principiari et incipere, videlicet a capitellis qui sunt facti in nave magna supra, excepto tamen suprascripto magistro Christoforo, qui dixit quod principiari debeat altius per brach. 4. Item quod dicti archus et cornixete medii archus habeant totum spigutum [but see note 71], et quod croxerie habeant illud spigutum quod eis dari comode potest, et quod etiam dicti archus sint alti a linea capitelorum in medio dicti archus, videlicet subtus clavem dicti archus, brach. 24, et quod croserie predicte vadant alte a linea capitellorum supra, subtus clavem dicte croxerie, brach. 26, et quod cornixete medii archus sint altae a linea capitelorum supra, videlicet subtus clavem, brachia 12 et unzias 2 ½ (Annali, I, pp. 302–03).

71 In the Annali the word is printed as ‘spigulum’, but it seems instead to be ‘spigutum’ to judge by the original document in the Archivio della Veneranda Fabbrica del Duomo di Milano (hereafter AFDMi), Ordinazioni capitolari, 1, fol. 440r. The adjective ‘spigutus’ means ‘pointed’, as in: super dictis capitellis deliberaverunt […] fieri facere archus spigutos […] inde dicunt quod archi spiguti non dant impulzam contrafortibus (Annali, I, p. 203); the noun should mean the same.

72 See note 71.

73 See note 70. Eventually the masters decided that the ‘cornixete medii archus sint altae a linea capitelorum supra, videlicet subtus clavem, brachia 12 et unzias 2 ½’. The ‘cornixete’, which had to start above the capitals and were pointed, are the pointed arches or cornices on the lateral walls of the nave between the main arches, within which the windows were placed (which are dealt with later on in the document), and which have a height that seems to match that indicated in the documents.

74 The Milanese architects were, according to Ackerman (‘Ars sine scientia’, p. 85), bogged down by continuous changes of architects, constant indecision and constructional mistakes due to their provincialism and lamentable theoretical and technical knowledge, which resulted, in fact, in the building proceeding ‘haphazardly, without an ultimate aim’ (p. 89). The author also speaks of the ‘provincial character’ of Lombard architecture, of architects who are ‘poorly prepared’ (p. 86); that there was ‘little evidence of technical growth’; of the fact that the ‘French and German masters who were hired to aid the architects of Milan Cathedral were bitterly received and poorly treated’; of the ‘inadequacy of the provincial tradition’ (p. 87); of the ‘difficulties encountered by the Milanese’; of their ‘great uncertainty’ (p. 88), of ‘difficulties in forming a definitive and consistent program’, of the ‘illogical order in which the problems are submitted’ (p. 92), of the ‘capricious shift in mid-air’ (p. 93) for the alleged change to the system of Pythagorean triangles proposed by Beltrami, and so on.

An interesting discussion of Ackerman's article is presented by Trachtenberg, Building-in-Time, (pp. 240–43, 266), in which the author points out Ackerman's favouritism of the Northern architects and locates his article in the context of the ‘Modernist’ historiography of the twentieth century. But although Trachtenberg states that ‘the Milanese evidently shared with the Northerners the practice of Building-in-Time and its presuppositions regarding procedure, as well as a good measure of common design language and building techniques’ – otherwise the Northerners would not have been summoned to collaborate and work on the same project – he still agrees with Ackerman when he asserts that ‘a great disparity existed in the theoretical presuppositions and cognitive and professional habits’ (p. 243), and concludes that ‘at a deep level there is a certain validity to Ackerman's take on this scene’ (p. 244).

75 Ackerman, ‘Ars sine scientia’, p. 87.

76 15 May 1389: paid as engineer from 7 May (Annali, Appendix I, pp. 82–83); 6 July 1389: taken on as general engineer (Annali, I, p. 25); 16 March 1390: designs for the windows of the apse (Nava, Memorie e documenti, p. 17; Annali, I, pp. 31–32); 22 July 1390: reduction of salary (Annali, I, p. 36); 31 July 1390: fired (Annali, I, p. 36). See Ackerman, ‘Ars sine scientia’, p. 88.

77 See note 65.

78 13 April 1399: Nava, Memorie e documenti, pp. 79–81; Annali, I, pp. 194, 197; Ferrari da Passano, ‘Storia della veneranda fabbrica’, p. 29. In fact, the Deputati decided to summon three people, Jacques Coene (with a salary of 24 fiorini), Johannes Campaniosus and his associate Mignot (salary of 20 fiorini): Mignot thus arrived with two other experts, was named last in the document and received a lower salary.

79 7 July 1398: Giovannino de Grassi (Annali, I, p. 187); 31 October 1398: Giacomo da Campione (Ferrari da Passano, ‘Storia della veneranda fabbrica’, p. 29). Mignot was eventually fired at the end of 1401 for having ‘damaged’ the building in that he had made various elements (some capitals, various blocks of stone, the roofs of the sacristies) without authorization from the Deputati (Nava, Memorie e documenti, pp. 125–26; Annali, I, pp. 237–38).

80 For the exchanges between the cathedral and other European building-sites, see Rossi, Marco, ‘Architettura e scultura tardogotica tra Milano e l'Europa; il cantiere del Duomo alla fine del Trecento’, Arte lombarda, 126 (1999), pp. 529 .

81 Even though we should not forget that the Cathedral was a civil institution and that its construction was not a direct ducal or archiepiscopal commission. See also Romanini, L'architettura gotica, pp. 354–57; Romanini, ‘Architettura’, p. 108.

82 Giorgi, Andrea, Costruire una cattedrale: l'Opera di Santa Maria di Siena tra XII e XIV secolo (Munich, 2005), pp. 73 , 75, 134.

83 Grote, Andreas, L'opera del Duomo di Firenze 1285–1370: traduzione dell'edizione originale del 1959 (Firenze, 2009), pp. 85151 . I thank Ludovica Sebregondi for calling my attention to this and other sources on the subject.

84 Examples in Patetta, Luciano, ‘Appunti sui principali concorsi di architettura del Rinascimento’, in La fabbrica, la critica, la storia: scritti in onore di Carlo Perogalli, ed. Zanella, Graziella Colmuto (Milano, 1993), pp. 5974 , although these are more concerned with the presentation of various projects rather than with the direction of building projects by Deputati. One can also think of the committees used for the great urban projects in Venice in the latter half of the sixteenth century, particularly those for the construction of the Palazzo Ducale after the fires and of the new bridge at Rialto, which involved many architects, engineers and proti (see most recently Howard, Deborah, Venice Disputed: Marc'Antonio Barbaro and Venetian Architecture, 1550–1600 (New Haven and London, 2011), pp. 136–44, 151–69).

85 Pernoud, Régine, ‘Villard, témoin de son temps’, in Carnet de Villard de Honnecourt: d'après le ms. conservé à la Bibliothèque nationale de Paris (no 19093) présenté et commenté par Alain Erlande-Brandenburg (Paris, 1986), pp. 1112 : ‘La disputatio, en leurs temps, c'est une méthode de travail; on dispute entre maître et élève, enseignants ou enseignés; […] la disputatio est un exercice d’école; on l'emploie lorsqu'on étudie la dialectique, mais aussi durant tout le cours des études, puis dans la pratique même de l'art. Et c'est ainsi qu'on trouve, en ‘disputant’. […] Villard nous apprend que l'homme de métier, de terrain qu'il est, use tout naturellement de la disputatio lui aussi’. For instance, the fact that in the reunion of 1 May 1401 Simone da Cavagnera is ‘on one side’ (‘pro parte una’) – that of Mignot – and Antonio da Paderno is ‘on the other’ (‘pro altera’) reinforces the view that ‘disputes’ are part of the decision-making process (AFDMi, Ordinazioni capitolari, I, f. 263).

86 10 July 1390: Simone da Orsenigo was nominated ‘maestro delle opere della fabbrica’ and the Deputati wrote at the same time to Monza and Venice in search of other engineers (Annali, I, p. 36); 14 luglio 1390: Nava, Memorie e documenti, p. 19 (suggesting that it was Matteo da Campione who proposed the enlargement of the piers), followed by Mongeri, Giuseppe, ‘Per la facciata del Duomo di Milano’, Il politecnico, 19, 1–2 (1887), pp. 87 and 101; Annali, I, p. 36. In any case, both architects were Italian and not Northerners.

87 Ackerman, ‘Ars sine scientia’, p. 85.

88 Ibid. , p. 87.

89 Ibid. , p. 89.

90 Ibid. , p. 94.

91 Ibid. , pp. 96, 98 in a note.

92 Ibid. , pp. 100, 101, 105, 107.

93 11 January 1400: ‘Et super dictis capitellis deliberaverunt prout deliberatum est fieri facere archus spigutos secundum ordinem datum per multos alios inzignerios bonos et expertos, inde dicunt quod archi spiguti non dant impulzam contrafortibus, et rationibus praedictis concludunt omnes contrafortes esse fortes et sufficientes ad majus onus, quapropter non indigent facere contrafortes ecclesiae in nulla parte’ (Nava, Memorie e documenti, p. 87; Annali, I, p. 203).

94 Ackerman, ‘Ars sine scientia’, p. 97 (‘It would indeed be a shock to the modern historian if this view were found to be a general currency among Gothic builders, and it is with some relief that we discover in a later discussion that it is as surprising to Mignot as it is to us’), and pp. 99 and 104.

95 22 and 30 January 1400: Nava, Memorie e documenti, p. 85.

96 11 January 1400: ‘Si provvide da’ deputati, il giorno 11, affinché il notajo Nicholino de Lovato, e que’ notaj, che scrissero le osservazioni del Mingoto, fossero compensati “de eo quod habere debent, et debeant”’ (Nava, Memorie e documenti, p. 83); ‘Deliberarono pagarsi i notaj, che scivono i difetti e rimedii necessarii per la fabbrica dietro la requisizione dell'ingegnero Giovanni Mignoto’ (Annali, I, p. 202).

97 Nava (Memorie e documenti, p. 86) had acutely warned readers about this: ‘Le censure presentate in iscritto dal Mignoto, con le risposte giustificative de’ nostri ingegneri, vennero registrate in forma notarile […], si incontreranno parole e frasi oggidì fatte inintellegibili, sia per la barbarie del latino, in cui furono dettati, sia per l'incuria degli amanuensi che li trascrissero, sia per i processi ora perduti dell'arte edificatoria, sia finalmente, nel caso attuale, per simultaneo concorso di architetti e di operaj, diversi per nazione o per lingua, i quali portando ognuno nella discussione il proprio contingente, hanno dato luogo ad un mosaico di parole’. The error of mentioning three instead of four piers as well as the use of ‘sed’ and not ‘et’ in Appendix II, doc. II, for instance, is hardly attributable to the masters and is clearly a mistake of the transcriber; in Appendix II, doc. III, the only one that answers in Italian is Simone da Cavagnera, probably because he himself is writing, while the rest of the answers were transcribed in Latin by appointed scribe-notaries.

98 Annali, I, p. 208. 21 of the 54 problems raised by Mignot concern structural technicalities and the stability of the building, and about the same number concern small discrepancies detected in the dimensions of the parts built so far; seven concern questions of style or ornament and five the architectural composition or correspondence between architectural elements.

99 Ackerman, ‘Ars sine scientia’, p. 101.

100 One wonders whether ‘fundamentum’ could be interpreted theoretically, as a principle, recalling the ‘correct’ geometrical project of Stornaloco I supported by Mignot.

101 ‘Habent maximum onus et pondus’ means, pleonastically, ‘they produce the greatest load and weight on the supports below’, since the word ‘onus’ is used in this sense in the declaration that ‘voltae acutae sunt plus fortes et cum minori onere quam voltae retondae’; ‘onus et pondus’ looks like a stock phrase. Nava (Memorie e documenti, p. 10 in a note, although not referring specifically to this passage) identifies the properties of the pointed arch precisely. Niebaum, Jens, ‘Filarete's Designs for Centrally Planned Churches in Milan and Sforzinda’, Arte lombarda, N.S., 155, 1 (2009), pp. 125–26, presents the extraordinarily unlikely hypothesis that the four ‘towers’ or piers supporting the tiburio should instead be understood as four giant towers of square plan built over the two sacristies and the first two bays of the aisles.

102 See note 93.

103 That is, ‘archi spiguti non dant lateralem impulzam contrafortibus’.

104 Ackerman, ‘Ars sine scientia’, p. 101.

106 See, for example, what the Lombards say about laying blocks of stone in alternate courses, on the difficulties of cutting blocks big enough to place them with their grains horizontal to ensure greater resistance, on the construction-methods for foundations and piers using metals dowels, or on the strength of local marble compared with Parisian sandstones (11 January 1400: Annali, I, pp. 202–05; 25 January 1400: Appendix II, doc. II). See also Bellini, Le cupole, p. 25. Romanini, L'architettura gotica, pp. 353, 412 notes 167, 170–72; Romanini, ‘Architettura’, p. 180, on the dispute between Mignot and the ‘weak cobbled-together science’ (‘debole “scientia” d'accatto’) of the Lombards, follows, as in many other matters, Frankl, Panofsky and Ackerman.

107 Romanini, L'architettura gotica, pp. 358, 361–76, 378, 380, 383–84, 385, fig. 89; Romanini, ‘Architettura’, pp. 103, 114, 164–68, 172–179, 181, 204 note 10.

108 Bologna, Archivio della fabbriceria di San Petronio, cart. 389, n. 1, 470x330 mm; L'Archivio della fabbriceria di San Petronio in Bologna. Inventario, ed. Fanti, Mario (Bologna, 2008), p. 272 . Summary in Ghisalberti, Carla, ‘cat. 6’, in The Renaissance From Brunelleschi to Michelangelo; the Representation of Architecture, ed. Millon, Henry A. and Lampugnani, Vittorio Magnago (London, 1994), pp. 429–30.

109 Beltrami, Luca, ‘Per la storia della costruzione del Duomo’, in Luca Beltrami e il Duomo di Milano, ed. Ramelli, Antonio Cassi (Milano, 1964), pp. 127–32 (p. 130).

110 Beltrami, ‘Per la storia della costruzione’, followed by Romanini, L'architettura gotica, p. 358; Romanini, ‘Architettura’, pp. 161 and 164–67. Beltrami did not specifically discuss the modularity of the elevation, but, since he dismissed Stornaloco's first project of 1391 as of no importance for the planning of the cathedral, it seems that he thought the drawing, which he dated to 1390, likewise showed a triangular project, thus anticipating and undermining Stornaloco's project.

111 Boito, Camillo, Il Duomo di Milano e i disegni per la sua facciata (Milano, 1889), p. 115 ; see also Siebenhüner, Deutsche Künstler, p. 19.

112 Frankl, ‘The Secret’, pp. 51–52.

113 Ackerman, ‘Ars sine scientia’, p. 89.

114 Romanini (L'architettura gotica, pp. 365–66 and 378) talks of a ‘libero e irregolare schema triangolato’ in which ‘non mancava però unità di misura, ad ordinare, anche se in modo approssimativo, la scansione dell'edificio in altezza. Tale unità di misura era stata fissata infatti nella misura di dieci braccia “milanesi”’. In her view the lack of regulation was the principal objection raised at the time against the engineers of the cathedral, who had begun with an ‘artigianale’ project with the height of the vaults left to trial-and-error (pp. 379 fig. 86; 404 note 63; 405note 72; Romanini, ‘Architettura’, pp. 166–67).

115 Cadei, ‘Cultura artistica’. Cadei previously took this hypothesis as read, and proposed that ‘al livello delle volte tale unità sembra passare a nove braccia col risultato che, postulando per le volte maggiori un'altezza di 27 braccia pari a tre unità, si ottiene la razionalizzazione in interi più vicina all'altezza di un triangolo equilatero di 32 braccia di base, che è appunto la larghezza della navata maggiore del Duomo’; see Antonio Cadei, Induzioni sulla determinazione delle strutture in Bramante’, in Studi bramanteschi, atti del congresso internazionale Milano, Urbino, Roma 1970 (Roma, 1974), pp. 157–70 (p. 162). It is not clear how Cadei arrived at units of 9 braccia and a height of 27 braccia for the vaults of the nave, given that, according to this hypothesis the total height of the nave would be 87 braccia (60+27) and not 76 (as is suggested on the verso of the drawing: see below); nor why 27 could be a whole-number approximation of the height of the equilateral triangle with a base of 32 braccia, since this is 27.7 braccia and should be approximated to 28.

116 Ascani, ‘Le dessin’, pp. 255–60; idem, I disegni architettonici attribuiti ad Antonio di Vincenzo: caratteristiche tecniche e ruolo degli “appunti grafici” nella prassi progettuale tardogotica’, Arte medievale, 5, 1 (1991), pp. 105–15; idem, Il Trecento disegnato: le basi progettuali dell'architettura gotica in Italia (Roma, 1997), pp. 115–17. Ascani is the scholar who first discussed the possibility that these drawings are copies.

117 For Antonio's numerous travels, see Angelo Gatti, ‘Maestro Antonio di Vincenzo, architetto bolognese’; and idem, Documenti riguardanti maestro Antonio di Vincenzo architetto bolognese’, both in Archivio storico dell'arte, 4 (1891), pp. 172–79, 194–201. The essential bolognese documents are these: 27 March 1393: ‘Magistro Antonio muratori, caputmagistro tocius laborerii supradicti, misso ex parte officialium et superstitum dicti laborerii die XVII mensis presentis ad civitatem Mediolani pro negociis dicti laborerii cum uno famulo et duobus equis in qua andata stetit decem diebus, pro expensis per eum factis dicto tempore, libras decem et septem bononinorum’ (Bologna, Archivio della fabbriceria di S. Petronio, Liber expensarum del 1393, c. CXXIIv); 5 April 1393: ‘Magistro Antonio Vicencii muratori caputmagistro tocius laborerii […] misso Florenciam die XXX marcii […] cum uno famulo et duobus equis ad perquirendum de magistris lapidum marmorearum necessariis pro laborerio predicto, pro expensis per eum factis in eundo, redeundo pro se, famulo et equis et pro Paulo Finochi de Florencia magistro dictorum lapidum, in qua andata stetit sex diebus, in summa libras undecim et soldos decem’ (Ibid., c. CCXXIII r), cited in Budriesi, Anna Laura Trombetti, ‘I primi anni del cantiere di San Petronio (1390–1397)’, in Una basilica per una città: sei secoli in San Petronio, atti del convegno di studi per il 6° centenario di fondazione della basilica di San Petronio, 1390–1990, ed. Fanti, Mario (Bologna, 1994), pp. 5175 , (pp. 61, 73 note 69); Cavazzini, Laura, Il crepuscolo della scultura medievale in Lombardia (Firenze, 2004), p. 20 .

118 Ascani (‘I disegni architettonici’, p. 113 note 12) mistakenly transcribes the number LXXVI in reference to the heights of the Pantheon and of San Lorenzo in Milan as LXXXVI.

119 The difference of one braccio, or rather the length of a ruler in Roman numerals, could be simply a slip of the pen. In the debate of 1 May 1392, the architects specifically omit the tiburio from their computations (‘non computando in mensura tiborium fiendum’, see Appendix II, doc. I), and Stornaloco makes no mention of it, although obviously its height could have been established by simply extrapolating broader, taller triangles from Stornaloco I. It had, of course, been discussed, as is proved by the mention of Annechino de Alamania's model of 1387 (‘tiborium unum pombli’: Annali, I, p. 14), by the thickening of the four great piers of the crossing (14 July 1390), and by the representations of it with a cross-vault in Cesariano's plan and in our Bolognese drawing.

120 An explanation of the number 112 by the present authors is available in Disegni per il Duomo di Milano di Antonio di Vincenzo on the site of the Corpus of Drawings of Milan Cathedral ( or in the authors’ web-sites on

121 Romanini, L'architettura gotica, p. 383, when indicating that the height of the piers at 40 braccia was one of the characteristics that remained in place from the first to the second project, seems to contradict herself by also following Frankl's reconstruction of a first project based on units of 10 in which the total height of the columns becomes 50 braccia (see the drawing reproduced on p. 379, fig. 86).

122 The captions with the dimensions are contradictory. The draughtsman says that the height of the outer aisle piers is 30 braccia (‘braza XXX milanese piiando el capitelo’), presumably meaning ‘including the capital’. He uses the word ‘pigliare’ in the same sense at the top of the page: ‘Nota che li quatro pilastri grosi che sono in mezo la croxiera zoe di la truna sono grose piedi sette onze otto [92 onc. bol. = 2.96 m = 5 br] zoe piliando tuti li botazi’. By ‘capital’, then, he seems to mean the impost moulding at the top of the shafts of the outer-aisle piers and is not referring to great tabernacle capitals, since there are no such capitals in the outer aisles. He then says that the inner-aisle piers are ‘40 braccia up to below the capital’ (‘braza XXXX perfino soto el capitelo’), and he placed the great capitals 10 braccia high on top of the 40 braccia pier shafts, arriving at 50 braccia. So the word ‘capitello’ means ‘impost moulding’ in the case of the outer aisles, but ‘great capitals’ in the case of the inner aisles and nave, which is absurd. It seems pretty clear, however, that the captions place the great capitals on top of the piers of the inner aisle and nave at the wrong height, at 40 instead of 28 braccia.

123 Briquet, Charles-Moïse, Les filigranes. Dictionnaire historique des marques du papier des leur apparition vers 1282 jusqu'en 1600, 4 vols (Leipzig, 1923, reprint New York, 1985), II, no. 6392 (Milan 1420; Bergamo 1423); 6393 (Milan 1422); Piccard, Gerhard, Wasserzeichen. Blatt. Blume. Baum (Stuttgart, 1982), pp. 2223 , nos. 618–61.

124 Quintavalle, Augusta Ghidiglia, ‘Antonio di Vincenzo’, in Dizionario biografico degli Italiani (Roma, 1961), III, pp. 581–83.

125 Beltrami (‘Per la storia della costruzione’, p. 132 note 5) suggested that the architect took the measurements from the actual building and so used Bolognese dimensions.

126 Boito, Il Duomo di Milano, p. 105. Bizarrely the same mistake occurs on the much later plan of the cathedral now in Strasburg; see Repishti, Francesco, ‘cat. II, 41’, in Arte lombarda dai Visconti agli Sforza, ed. Natale, Mauro, Romano, Serena (Milano, 2015), p. 171 .

127 Annali, Appendix I, p. 129; Cavazzini, Il crepuscolo, p. 10; the architraves are probably to be attributed to Giacomo da Campione.

128 The work on these doors continued for a number of years: the door of the south sacristy was almost completed in August 1393 (5 August 1393: modifications to the design of the decorations of Giovanni da Fernach; Nava, Memorie e documenti, p. 41; Annali, I, p. 101); by 3 October 1395 Giovannino de Grassi had completed the figures of the North sacristy door (Nava, Memorie e documenti, p. 61; Annali, I, p. 150).

129 Presumably this refers to a drawing which included the door as well as all the rest of the façade of the transept. Leonardo da Vinci also drew a plan of the cathedral between 1493 and 1497 (Codex Forster, III, f. 55v) with only one door, that ‘verso Compedo’ at the North; while Bramante, in another drawing that includes projects for Saint Peter's (Florence, Uffizi, 8Av), drew a plan of Milan Cathedral with doors at both ends of the transepts. The fact that these apertures are represented in both drawings without central pilasters is hardly significant given their very small scale.

130 11 January 1400 (Annali, I, p. 203, nos. 8–9).

131 18 January 1394: a meeting was called to decide on the form-work for the sacristy vaults (Annali, I, p. 108); 5 June 1394: it is decided to construct the form-work (Annali, I, p. 115).

132 2 February 1392 (Annali, I, p. 64).

133 8 June 1393 (Annali, I, p. 99); 14 December 1393 (Annali, I, p. 105); 20 May 1395 (Annali, I, p. 142); 3 October 1395 (Annali, I, p. 150); 9 January 1396 (Annali, I, p. 156); 2 February 1396 (Annali, I, p. 158).

134 16 April 1396: meeting to discuss the final shape of the capitals (Nava, Memorie e documenti, p. 66; Annali, I, p. 162). On these sculptural elements see Antonio Cadei, ‘I capitelli più antichi del Duomo di Milano’, in Il Duomo di Milano, atti del congresso, I, pp. 77–88. Cadei, however, followed Romanini (L'architettura gotica, p. 360) in dating the Antonio da Vincenzo drawing to the middle of 1390, and this was also accepted by Ascani (‘I disegni architettonici’, p. 113 note 25).

135 Annali, I, p. 64.

136 Romanini, ‘Architettura’, p. 171; Rossi, Giovannino de Grassi, pp. 90–91.

137 For the alleged copies of Antonio's drawings made by Severino Tattini, now lost, see Rubbiani, Alfonso, La Chiesa di San Francesco in Bologna (Bologna, 1886), pp. 47ff; Zucchini, Guido, ‘Disegni di Antonio di Vincenzo per il campanile di San Francesco a Bologna’, Architettura ed arti decorative, 1, 6 (1922), pp. 526–35. The three designs for campaniles are in strict orthogonal projection with a ground-plan below two of them. Rubbiani says they are inscribed with dates (15 November 1396, 25 February 1397, 11 December 1400), but these are not visible on his photograph. The campaniles look like pastiches based on the campanile in Florence and that of San Francesco itself with an admixture of decorative elements taken from local buildings such as the Loggia della Mercanzia, S. Petronio and the campanile di S. Domenico: see Armandi, Anna Maria Matteucci, ‘Il gotico cittadino di Antonio di Vincenzo’, in Il tramonto del Medioevo a Bologna; il cantiere di San Petronio, ed. D'Amico, Rosalba and Grandi, Renzo (Bologna, 1987), pp. 2754 (p. 52 note 18).

138 See Maria Lodynska-Kosinska, ‘Quelques remarques au sujet du dessins d'Antonio di Vincenzo’, in Il Duomo di Milano, atti del congresso, I, pp. 129–31. Lodynska-Kosinska dates the design – as usual – to about 1390, and notes (p. 129) how ‘le tracé géométrique, visible sur son dessin, est caracteristique pour les méthodes employeés aux dessins architectoniques par les bâtisseurs gothiques d'au déla des Alpes [French and German]’, and she proposes that Antonio was copying a design by Nicolas de Bonaventure, who would then have been responsible for establishing the definitive plan of the cathedral.

139 In particular, see the replies to the seventh question by Serina, Donato, Alcherio, Della Croce, and Scrosato in Appendix II, doc. III.

140 Booz, Der Baumeister der Gotik, p. 62, fig. 9, appears to have been the only scholar to agree with what is proposed here – i.e. that the proportional schemes presented by Stornaloco, Parler and Mignot coincided. This adds weight to the proposal, often ignored, by Verga, Il Duomo di Milano, that the ad quadratum system was used only for the plan, while the ad triangulum format was used for the elevation. The element that ties the two systems together was the side of the square that matches the base of the triangle, from which the height of the equilateral triangle was generated by means of a pair of compasses: a very simple system which resolved more-or-less automatically all problems of height and stability.

141 ‘Sono certo che non si potrebbe farlo né più bello né più lodevole, e che il detto Mignoto è un vero maestro di geometria, giacché trovo che i suoi progetti sono consimili a quelli di quell'eccellentissimo maestro Enrico, che altre volte abbiamo avuto qui, come se ci fosse stato mandato da Dio, e che avremmo ancora se non lo avessimo espulso’ (Nava, Memorie e documenti, p. 109; Annali, I, p. 224). The fact that these three participants supported Mignot's position reinforces our hypothesis that the model overseen by Simone da Cavagnera embodied Stornaloco I (see our Section 3).

142 Annali I, pp. xvi–xvii. Parler is characterised as a man of the greatest honesty and an absolute expert in geometry (‘probissimus vir geometrieque expertissimus’) and Mignot as a man of exceptional vigour and wisdom and a truly expert geometrician (‘vir quidem tante industrie et sagacitatis […] in dicta sua geometrie arte verus et expertus’). In the end, however, the duke declined the invitation and the cathedral today stands as a monument to Stornaloco II and the competence of the much-maligned Milanese masters, described as ‘falsi testes, ignari, rudes et penitus dicte artis ydioti’.

143 9 February 1387: order to pay ‘Anechino de Alamania qui fecit tiborium unum plombi’ (Annali, Appendix I, p. 14); Siebenhüner, Deutsche Künstler, p. 10; Rossi, Marco, ‘La correlazione di problemi statici, proporzionali e simbolici nelle prime proposte per la costruzione del tiburio del Duomo di Milano’, Arte lombarda, 58/59 (1981), pp. 2128 (p. 21). See also Sanvito (Il tardogotico, pp. 126–27) for the types of models used at the cathedral.

144 Cesariano, Di Lucio Vitruvio Pollione, may be another useful witness: he describes the plan and elevation of the cathedral as being of German origin (f. 14r: ‘Ichnographia fundamenti sacrae aedis baricephalae germanico more a trigono e pariquadrato perstructa’; f. 15r: ‘Orthographiae ab ichnographia exorta perfiguratio […] secundum germanicam symmetriam’). See also Lodynska-Kosinska, ‘Quelques remarques,’ p. 130. One must bear in mind, however, that during the Cinquecento the term ‘German’ acquired the generic meaning of ‘Gothic’ without a particular reference to the geographic origin of the style; see, for example, Vasari, Giorgio, Le vite de’ più eccellenti pittori, scultori e architettori nelle redazioni del 1550 e 1568, ed. Bettarini, Rosanna and Barocchi, Paola, 6 vols (Florence, 1966–87), III, p. 23 : ‘egli [Jacopo della Quercia] se n'andò a Bologna, dove col favore di Giovanni Bentivogli gli fu dato a fare di marmo dagl'Operai di San Petronio la porta principale di quella chiesa, la quale egli seguitò di lavorare d'ordine tedesco per non alterare il modo che già era stato cominciato’; Ibid., IV, p. 321: ‘essendo condotto a Bologna dagl'Operai di San Petronio perché facesse il modello della facciata di quel tempio, [Baldassarre Peruzzi] ne fece due piante grandi e due proffili, uno alla moderna et un altro alla tedesca’.

145 See also Valentini, Il Duomo di Milano, pp. 31 and 61.

146 See Schofield, Richard, ‘A Humanist Description of the Architecture for the Wedding of G.G. Sforza and Isabella D'Aragona’, Papers of the British School at Rome, 56 (1988), pp. 213–40; idem, Amadeo, Bramante, and Leonardo and the Tiburio of Milan Cathedral’, Achademia Leonardi Vinci, 2 (1989), pp. 68100 (pp. 82–84).

147 Gritti has demonstrated that the famous drawing in the Raccolta Bianconi, which illustrates Stornaloco's project, was probably made by Cesariano himself in preparation for his edition of Vitruvius; see Gritti, Jessica, ‘Cesare Cesariano, il Duomo di Milano e le tavole dell'edizione di Vitruvio del 1521’, Arte lombarda, N.S., 167, 1 (2013), pp. 8195 . A drawing by Peruzzi (Florence, Uffizi 629Av) showing the construction ad triangulum of a church with a nave and four aisles and pointed vaults is interesting in this context since it testifies to the persisting appeal of such a scheme.

148 Nava, Ambrogio, Relazione dei ristauri intrapresi alla gran guglia del Duomo di Milano nell'anno 1844 ed ultimati nela primavera del corrente 1845 secondo il progetto, e colla direzione del Conte Ambrogio Nava (Milano, 1845), p. 14 note 9: ‘La dimostrazione recata dal Gallio [Cesariano] all'oggetto di far conoscere la ragione geometrica nelle proporzioni assegnate al nostro Duomo in tutte le sue parti, coincide con quella stabilita dal matematico piacentino Gabriele Scornaloco [sic] nell'anno 1390, quattro anni, cioè, dopo incominciato il Duomo’. See Nava (Memorie e documenti, pp. 9, 28–29, 132) on the hypothesis of a single project continued without uninterruption from the beginning; and also Mongeri, ‘Per la facciata’, p. 102: ‘E’ lui [Stornaloco] che, inconscio indubbiamente dell'opera sua, lascia le maggiori impronte al monumento, quelle del sistema lineare delle sue elevazioni’; pp. 104–05 for the adoption of Stornaloco's project which was then followed continuously; and p. 109: ‘Lo Stornaloco era scomparso ma lo Stornaloco era rimasto’. See also Valentini, ‘Il contributo’, p. 248.

149 Beltrami, ‘Per la facciata’, pp. 70–71, 73, 78–79; repeated by Romanini, ‘Architettura’, p. 174: ’Il perfetto alzato gotico “ad triangulum” previsto dallo Stornaloco fu accettato solo come suggerimento teorico, ma non fornì la soluzione definitiva alla “crisi” del 1391’; and Ascani, Il Trecento disegnato, p. 122 (‘sostanziale accantonamento delle idee del matematico piacentino’).

150 For the tiburio, see Schofield, ‘Amadeo, Bramante, and Leonardo’.

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Architectural History
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