J. Goudeau, Going round in circles. Circumbulate the Vitruvian volute

GOING ROUND IN CIRCLES. CIRCUMAMBULATE THE VITRUVIAN VOLUTE 1 IN EARLY MODERN ARCHITECTURAL THEORY JEROEN GOUDEAU

Introduction As one of the non-literary, non-philosophical and non-scientific texts from Antiquity the architectural handbook De Architectura Libri Decem achieved an almost unrivalled authority2. From the early Renaissance this book by the Roman architect Marcus 1 Dr. Jeroen Goudeau teaches the history of (early) modern architecture and architectural theory at Radboud University Nijmegen (Netherlands) 1 This article is an adapted version of the paper «Umgehende Bewegungen.

Vitruvs Ionische Volute im frühen Neuzeit», delivered on the 1.

Architekturtheoretisches Kolloquium. Vitruv: Text, Kommentar und Bild, held at the Stiftung Bibliothek Werner Oechslin Einsiedeln (CH), and organised in collaboration with the Centro Internazionale di Studi di Architettura Andrea Palladio (Vicenza) on April 26-29 2012. Originally I discussed this theme in relation to Nicolaus Goldmann in GOUDEAU 2005, pp. 101-128.

2 Vitruvius still plays a decisive role in the history of architectural theory, as is shown in KRUFT 1991. An attempt to grasp the whole of his antique theory was made e.g. by KNELL 1991. A new approach was given by MCEWEN 2003.

J. GOUDEAU

Vitruvius Pollio dating from about 25 BC was cherished as the largest complete and systematic Roman text on architecture and engineering. Handed down in at least seventy-eight manuscripts scattered over monastery libraries in Northern Europe, its importance was established by Italian humanists, i.e. architects, engineers, patrons and amateurs alike, who studied the text meticulously3. Vitruvius’ text appeared to be written in a somewhat archaic, particular and sometimes obscure Latin, interlarded with Greek idiom. This was also the case with his architecture that often tended more to Greek-Hellenistic building than to the practice of contemporary Rome. His authority however remained unquestioned and in 1486 Giovanni Sulpicio in Rome provided the first printed edition, the start of a tradition lasting to our times4.

Reading Vitruvius always implied interpreting the text. When closely examined the fairly exact instructions could not always be understood very easily and required elucidation by specialists, preferably by being visualised in drawings.

Understanding Vitruvius thus meant, and still means, approaching the theory by circumventing the difficult passages and other problems raised in the text. An interesting case in this respect is the question of the Vitruvian volute, just a small passage in the large book but one that fascinated many architectural theorists. They came up with a remarkable variety of solutions, all based on the same indications given by Vitruvius.

A short extract with considerable effects One of the main problems with Vitruvius is that his ten books were without illustrations: either they had been lost in the KRINSKY 1967 and SCHULER 1999.

A catalogue of the successive Vitruvius editions was given in EBHARDT 1962. Further literature in KRUFT 1991.

3 4

62

CIRCUMAMBULATE THE VITRUVIAN VOLUTE

course of time or perhaps had never been incorporated5. In his text Vitruvius refers several times to images that would explain his words. While on the one hand the text without images caused problems and limitations, on the other it provided great opportunities for architects and interpreters. Humanistic discourse flourished with it. Every successive generation could and at the same time even felt obliged to make Vitruvius topical. This mechanism was certainly part of the permanent popularity of De Architectura – every era got its own updated Vitruvius that was in line with the latest insights and aesthetics, and even physical requirements.

In the Vitruvian reception there are various obscure extracts.

One of them is the much discussed problem of the scamilli impares, a notion that from the Renaissance onward has usually been interpreted either as the projection or as the curvature of the stylobate6. This became almost a topos in the Vitruvian exegesis7. Another subject that kept many authors busy is the Vitruvian volute. The volute or voluta – the word is derived from the Latin verb «volvere», which means turn round – is the scroll of the capital of the Ionic order. The volute also appears in the composite capital, being a combination of the Ionic and Corinthian capital (fig. 1). The motif of this curl is inspired by nature and can be taken as the stylised and petrified form of scrolled palm leaves, but for the people of the Renaissance, especially those north of the Alps most of whom had never seen a real palm tree, the form resembled more a snail shell. In Germany, e.g. Albrecht Dürer, Walther Ryff and later authors therefore spoke of «die Schnecke». Volutes had survived 5 See e.g. SCAGLIA 1979. Some further remarks on the illustrations are made

by GROS 1988, esp. 57-59, and HASELBERGER 1989.

6 Scamilli impares, or more correctly inpares. See e.g. BALDI 1612. In this treatise Baldi refutes previous interpretations by Guillaume Philandrier, Daniele Barbaro and Giovan Battista Bertani. On Baldi see ZACCAGNINI 1908.

7 Recent interpretations discuss the term in the context of the so called «Greek refinements», as is summarised in HELLMANN 2002, pp. 186-188.

Horti Hesperidum, II, 2012, 2

63

J. GOUDEAU

Antiquity and throughout the Middle Ages columns and small shafts were adorned with Ionic scrolls. In order to obtain a visually attractive spiral the stone masons had developed different geometric methods. The volute could be drawn and sculpted or carved without too complex calculations.

Mathematicians and art theorists also were concerned with (Archimedean) spirals, of which they considered the volute to be a variant.

With the rediscovery of Vitruvius and the new stress on the right application of the column orders, the volute gained a renewed, yet ancient context8. From now on the ambition of the architectural theorists was fourfold. They had to provide a visually satisfying solution that was constructed according to mathematically (i.e. geometrical) valid principles, and at the same time was manageable for craftsmen, but now, and not least, their solutions had to be consistent with what Vitruvius had written about the volute. However to follow Vitruvius was by no means unambiguous. His description was rather elementary and for the exact details he referred to an illustration that no longer survived. As a result architects and artisans followed the text where they could, combining this with geometrical methods of their own invention. Over time different elegant and feasible solutions emerged. Sculpting a volute was considered as a specialist job that required both practical skills and a certain level of theoretical knowledge.

The Ionic order as a whole, among other things, was the order of scholars par excellence. Noblemen and patrons, humanists from the upper middle class as well as scientists provided their houses with the ionica as the main order, thereby expressing that they were informed about decor and decorum. They presented themselves as distinguished yet modest, steering the middle course with this order of the middle, morally associated with the stoic aurea mediocritas. The volute became one of the most There is a vast amount of literature on the theory of the column orders. A recent introduction is given in GOUDEAU 2013.

8

64

CIRCUMAMBULATE THE VITRUVIAN VOLUTE

applied ornaments of the classical idiom, from the early and high Renaissance, through the freer applications of Mannerism to the various, though severe norms, of classicist architecture.

Enigmatic instructions Vitruvius dealt with the Ionic volute in the fifth chapter of his third book, which is dedicated to the temples. The starting point for dimensioning the column orders is a basic unity, the module or modulus, which is embedded in (half of) the base of the column shaft. Every part of the order is defined in multiples and parts of this module (fig. 2). The module fixes the proportions, not the measures; the module’s unit of measurement is arbitrary and can be chosen at random, depending on the specific application. Vitruvius formulated some specific instructions for the Ionic capital as a whole and its various mouldings such as the cushion shaped, covering abacus and the canalis, kymation and astragalus enclosed by the volute (fig. 3). The overall ratio is 1:2; the height is divided in 9.5 parts: 1½ for the abacus and 8 for the volute itself (fig. 4).

At 4½ parts below the abacus is the oculus (small eye) of 1 part, i.e. the heart of the volute and end of the spiral. Horizontally the capital is divided into 18+1 parts. Virtual perpendiculars or cathetoe determine the rest of the construction. With these indications it is possible to draw the volute, states Vitruvius: «Then, in describing the quadrants, let the size of each be successively less, by half the diameter of the eye, than that which begins under the abacus, and proceed from the eye until that same quadrant under the abacus is reached» 9.

9 VITRUVIUS III 5, 6. Here is preferred the 1914 translation by Morris Hicky Morgan (VITRUVIUS-MORGAN 1960, p. 92) above the most recent and authoritative English translation by Ingrid Rowland (VITRUVIUSROWLAND/HOWE 1999, p. 52): «Then, beginning from the top of the axis beneath the abacus and circling around, reduce each successive axis by half the diameter of the oculus, until one finishes at the axis beneath the abacus».

Horti Hesperidum, II, 2012, 2

65

J. GOUDEAU

The outline of the volute is drawn in quarter-circles. Each following segment of the circle diminishes with half the diameter of the oculus. This is only possible when the centre point of the circle is transposed. For the first full turn this causes no difficulties, but with regard to the second and succeeding rotations it is not clear how Vitruvius meant these to be constructed. To repeat the reduction of the segments with half the oculus and still have an elegant construction is not easy.

Vitruvius must have been aware of this difficulty; nevertheless the only thing he writes is: «As for drawing the volutes so that they are properly coiled with the use of a compass, and the way they are drawn, the form and the principle for these will be set down at the end of the book»10. The illustration is lost and the calculations remained a matter for conjecture. The core of the problem was the determination of the centre points and, connected to that, the opening of the pair of compasses. It is very important to avoid twisting the spiral. The tangent lines of two successive segments have to coincide at the point where they meet each other. To achieve this, the new centre point has to be on the line between the previous centre point and the end of the previous quarter-circle. Even then small variations in the centre point in the oculus can lead to very different results. The speed by which the spiral turns, or more exactly, the number of rotations, depends on it. Hellenistic capitals had 2½ turns and sometimes 3, whereas Vitruvius seems to imply a spiral of two

In Rowland’s version the term «quadrants», which is essential here, is left out. The Latin original reads: «Tunc ab summo sub abaco inceptum <schema uolutae>, in singulis tetrantorum actionibus dimidiatum oculi spatium minuatur, doneque in eundem tetrantem qui est sub abaco ueniat»; VITRUVIUS-GROS 2003, p. 27. Note that Morgan translates the word tetrans with the term quadrant, instead of speaking of a quarter-circle. On this subtle but decisive difference: VITRUVIUS-GROS 2003, p. 162.

10 Vitruvius III 5, 8. Translation: VITRUVIUS-ROWLAND/HOWE 1999, p. 52.

In Latin: «De uolutarum descriptionibus, uti ad circinum sint recte inuolutae, quemadmodum describantur, in extremo libro forma et ratio earum erit subscripta»; VITRUVIUS-GROS 2003, p. 28.

66

CIRCUMAMBULATE THE VITRUVIAN VOLUTE

turns11. In the architecture of the Renaissance and classicism volutes of three full rotations were common, but practice shows a much wider range12. In built architecture volutes of 1½ or even 4 rotations can also be found. It is hard to tell which version exactly Vitruvius himself must have had in mind, because while the Ionic order originated in Greece he navigated between Greek and Roman architecture. It is generally assumed that he based his solution on Hellenistic examples from Asia Minor and might even have used Greek written sources for his description of the Ionic capital and the volute13.

The solution is in the oculus After Vitruvius the question of tracing the Ionic volute according to his rules kept architects, mathematicians and publishers alike busy. They published their solutions as commentary in new scholarly editions of De Architectura, as part of larger architectural treatises or as separate – carefully 11 The Ionic order in Antiquity has fascinated many scholars, not in the least because of its variously shaped capital. Early studies are by PUCHSTEIN 1887 and VON LUSCHAN 1912; further KOCH 1956; recent more general summaries are by RYKWERT 1996, pp. 239-249, esp. 242-245; and HELLMANN 2002, pp. 146-168, esp. 162-164.

12 A pure mathematical approach to the Renaissance volute, however with too little notice of the historical context, is given in ANDREY AND GALLI 2004. Probably the first who dealt with Renaissance drawings of the volute in more detail was Hubertus Günther. GÜNTHER 1988, esp. pp. 220-225.

13 The problem of the Vitruvian capital and volute in relation to ancient Greek and Roman architecture from an archaeological point of view is also discussed by various authors. More recent evaluations: Thomas Noble Howe in VITRUVIUS-ROWLAND/HOWE 1999, p. 202 and figs. 49-50; Pierre Gros in VITRUVIUS-GROS 1997, vol. 1, pp. 335-338; and VITRUVIUS-GROS 2003, pp. 158-162 and figs. 30-32. Gros refers to earlier detailed research on the classical Ionic capital executed by R. Carpenter (1926), R. Martin (1946), W. Höpfner (1968), BINGÖL 1980, LEHNHOFF 1984, WESENBERG 1983, H. Büsing and B. Lehnhoff (1985), UEBLACKER 1985, H. Büsing (1987), L. Frey (1990) and O. Bingöl (1993).

Horti Hesperidum, II, 2012, 2

67

J. GOUDEAU

illustrated – texts. From Leon Battista Alberti up to the most recent translations of Vitruvius the solutions have developed and each time the author and editor have been convinced that the problem had now definitively been solved. One of the early and most elaborate overviews of different volute constructions was provided in the first quarter of the nineteenth century by Simone Stratico (1733-1824)14. Between 1825 and 1830 Stratico gave a new impulse to the tradition of editing Vitruvius, which by that time was already four centuries old, with a comprehensive annotated edition consisting of eight parts in four substantial volumes: M. Vitruvii Pollionis Architectura. Textu Ex Recensione Codicum Emandato Cum Exercitationibus Notisque Novissimis Johannes Poleni, Et Commentariis Variorum Additis [...]

(Fratelli Mattiuzzi, Udine). After the death of the mathematician and engineer Giovanni Poleni (1685-1761) Stratico was appointed as the successor of his former teacher at the University of Padua. As indicated in the Stratico’s title, Poleni had previously worked on Vitruvius and had published his no less thorough commentaries as Exercitationes Vitruvianae (Padua 1739-1741). Between Poleni and Stratico another, bilingual edition by Bernardo Galiani had appeared in Italy in Naples 1758. In his version Stratico compiled everything about Vitruvius he could lay his hands on15. With respect to the Ionic volute, in the first part of the third volume Stratico compiled and discussed fourteen different prior versions, ranging from the solution in Cesare Cesariano’s 1521 Vitruvius edition, via trattatisti as Serlio, Philibert de l’Orme, Andrea Palladio and 14 On Stratico and other Italian Vitruvianists of this era, see the contribution

by Elena Granuzzo in this issue.

15 Of course special attention was given to the obscure passages and the explanations of the most important authors: «Loca Vitruvii difficiliora ea sunt, ubi loquitur de Scamilli imparibus, de ratione volutae capituli Ionici construendae, de vasis theatralibus […] Cum igitur de ipsis hisce rebus et Baldius, et Goldmannus, et Bertanus, Salviatus, Cavalierius, Kircherus singillatim disputassent, aequam fuit tantorum ingeniorum inquisitiones plurimi facere»; VITRUVIUS-STRATICO 1825-1830, Vol. I, Pars 1, 1825, «Praefatio Editorum».

68

CIRCUMAMBULATE THE VITRUVIAN VOLUTE

Claude Perrault, up to his contemporary, an Italian marquis, Luigi Marini16. All the variants were explained, critically evaluated and shown comparatively in three compiled engravings (fig. 5 a-c). The visual variety of solutions is what strikes the reader first. The overview proves how the small divergences in the choice of the points in the oculus have great consequences. Secondly, it is remarkable how even the visually convincing examples do not meet the mathematical requirement of the tangential convergence of two fitting arc segments, at least not completely. Moreover, in the end the solutions sacrifice certain points of Vitruvius’ description to the geometrical construction methods. In summary, despite all the visual variation, the number of oculus systems turns out to be limited.

Although Stratico’s survey offers probably the most complete ‘parallel’ comparison in architectural history, at least two important examples have been omitted – those of Alberti and Giacopo Barozzi da Vignola. Furthermore Stratico was not concerned with any chronological representation, but primarily presented a suitable formal arrangement. A systematic and chronological list of twenty two of the most important constructions – the list can easily be extended – with a specification of the oculus division is given in the scheme of figure 6. The oldest solution in print is by Alberti in his De Re Aedificatoria (Florence 1485). Strangely enough he describes (not draws) a construction of semicircles with only 2 rotations.

Cesariano’s Vitruvius edition of 1521 comes up with points on an orthogonal coordinate system in the oculus. With his 3½ rotations this volute had the most windings of all. Another early volute can be found in Albrecht Dürer’s Underweysung der messung [...] (Nurnberg 1525). In his work he presents two construction methods: one is for the Ionic capital proper and consists of semicircles, and one set of different interrelated spirals that are Simone Stratico, «Exercitatio Vitruviana II», in VITRUVIUS-STRATICO 1825-1830, Vol. III, Pars 1, 1828, pp. 1-53.

16

Horti Hesperidum, II, 2012, 2

69

J. GOUDEAU

in fact applications of the Archimedean spiral. Whereas the geometrical problem is more or less the same, the antique literary sources are different – Vitruvius, Archimedes – as is the purpose – architecture, the goldsmith’s trade. One of the earliest architects who was concerned with the volute construction of whom drawings have survived, is probably Antonio da Sangallo in about 1518-151917. In his writings of about 1540, Sebastiano Serlio too preferred the semicircle with the points of the compass on the perpendicular bisector, in defiance to Vitruvius’ text and the convincing illustration of the volute by Cesariano a few years before.

Salviati sets the standard The solution of Serlio is all the more surprising because he was acquainted with Giuseppe Salviati (1520-1575)18. This painter and architect, interested in mathematical problems, was the first to publish a separate text on the reconstruction of the Ionic volute, Regola di far perfettamente col compasso la voluta et del capitello ionico et d’ogn’altra sorte (Venice 1552)19. By discussing the problem with architects and with a copy of Euclid on his table, Salviati stated he had been able to interpret Vitruvius properly.

He further mentioned that his solution had met with the approval of Serlio. This must have been about 1541. Serlio, who had worked earlier on the subject, had chosen to leave Salviati his own discovery20. Furthermore a case in point is that GÜNTHER 1988, pp. 223-224.

On Salviati see MACTAVISH 1981.

19 SALVIATI 1552. This small treatise was also included in VITRUVIUSSTRATICO 1825-1830, on which occasion was produced a Latin translation: Giuseppe Salviati, Ratio Accvrate Deformandi Tvm Volvtam Tvm Capitvlvm Ionicvm Secvndvm Vitrvvii Praecepta [...]; VITRUVIUS-STRATICO 1825-1830, Vol. I, Pars 1, 1825, pp. 269-273.

20 VITRUVIUS-STRATICO 1825-1830, Vol. I, Pars 1, 1825, pp. 269-270.

Salviati tells how he had met Serlio through Francesco Marcolino.

Afterwards his idea had been stolen, but not by the ‘extraordinary modest’ 17 18

70

CIRCUMAMBULATE THE VITRUVIAN VOLUTE

despite the fact that Serlio went to the royal court of Francis I in France, the most influential contemporary architect of the country, Philibert de L’Orme, disregarded the volute of his close competitor and chose the «winning» oculus with the division of Salviati21. The fact was that Salviati had taken a decisive step that would influence the volute solutions of the following centuries. He arranged the points of the compass in the oculus on the two diagonals being the centre lines of a quarter turned square that is circumscribed by the oculus. He does not explain how he arrived at this solution. It is at least remarkable that this method perfectly accords with the small holes of the chisel that can be traced in the oculi of some antique capitals22. It is tempting to assume that Salviati actually knew antique capitals, from his own observation or through the architects and stone masons to whom he had spoken. So it was in this special case Salviati and not Alberti who may have studied and carefully measured antique examples of capitals.

Serlio, though he could easily have done so,: «Haud multo post id temporis, cum rediissem Venetias, de hoc invento meo certiorem fecit Sebastianum Serlium, virum Architecturae laude clarissimum, Franciscus Marcolinus, quo ego utebar familiarissime. Quare quodam die cum Marcolino domum meam venit ipse Serlius, ut rem praesens inspiceret; modum describendae Volutae et placere sibi magnoper significavit, et commendavit tamquam optimum omnium, quotquot hactenus excogitasset Artificum industria. regulamque universam edoctus spopondit illam se nomine meo publicaturum, siquando contigisset eam ad opus transferre. Post annos aliquot intellexi, totius artificii formam a Discipulo quodam meo fuisse mihi surreptam: quae res in causa esse facile poterat, ut quispiam alienae partum industriae vindicaret sibi, et quasi sui fructum ingenii in publicum esseret: quod Serlium quidem, vir modestiae singularis, nunquam facturus erat». On this early period, see GÜNTHER 1988, pp. 220-225.

21 DE L’ORME 1567, l. V, ch. XXVII-XXIX, pp. 162r-166v.

22 The points in the oculus are sometimes still visible, mostly in unfinished capitals. UEBLACKER 1985, pp. 38-39, studied this Vitruvian scheme in the Maritime Theatre of Hadrian’s Villa at Tivoli. A capital on Delos also shows the four points. Over the last years the research on the Ionic capital has expanded to laser scans, as by RICHENS, HERDT 2009.

Horti Hesperidum, II, 2012, 2

71

J. GOUDEAU

Hereby the fourth and most imitated variant of the volute was introduced, replacing the construction by semicircles, in quadrants on the orthogonal axes, and the Archimedean spiral.

Not only his solution was elegant, geometrically consistent and Vitruvian, Salviati was also in good company. He dedicated his original treatise to the translator of De Architectura Daniele Barbaro, whose very influential Italian edition of 1556 produced in Venice was illustrated by none other than Andrea Palladio. It comes as no surprise then that Palladio’s volute in I Qvattro Libri dell’Architettvra (Venice 1570) clearly resembles the one Salviati had proposed. This line would continue to become the standard. At the end of the sixteenth century the case seemed to be settled and during the next century Palladio, Scamozzi and Vignola endorsed the diagonal construction of Salviati, as did Claude Perrault, François Blondel and a series of contemporaries and others after them (fig. 7)23.

Bertani and after In 1558, six years after Salviati’s, another discourse exclusively dedicated to Vitruvius’ Ionic order was published in Mantua by Giovan Battista Bertani (1516-1576)24. Bertani succeeded Giulio Romano as court architect for the Gonzaga family. In this treatise, Gli Oscvri Et Dificili Passi Dell’Opera Ionica Di Vitrvvio, Bertani in fact combined the orthogonal division of Cesariano and the diagonal structure of Salviati by placing only four points in the four quadrants of the oculus that were formed by the

23 As mentioned, Salviati did not bother about chronology or authorship.

Thus he could write: «Salviati methodus cum Palladiana omnino consentit».

Simone Stratico, «Exercitatio Vitruviana II», in VITRUVIUS-STRATICO 18251830, Vol. III, Pars 1, 1828, p. 21.

24 On Bertani see CARPEGGIANI 1992; and REBECCHINI 2000.

72

CIRCUMAMBULATE THE VITRUVIAN VOLUTE

horizontal and vertical axes25. With this solution he followed Vitruvius in diminishing the arcs consequentially by half the diameter of the oculus, but as a result the spiral went round only twice instead of the more common three turns. Bertani explained that he had come to his results by studying actual antique volutes in Rome, in particular of a ruin in the garden of the cloister of San Bartolomeo all’Isola26. The Ionic capitals found there contained four points in the oculus. Bertani had adopted this division. He was so proud of rediscovering the true Vitruvian Ionic order that he placed two of these Ionic pilasters at the entrance of his own house in Mantua27.

Together with Bertani Salviati had provided the best volute, graphically elegant, accurately Vitruvian in construction and now also founded on archaeological evidence. The majority of later authors made use of these two solutions, above all Salviati’s, although the names of their inventors are only mentioned in passing, if they are referred to as sources at all.

During the eighteenth and nineteenth century different editions of Vitruvius’ theory instituted some new attempts for alternative reconstructions. In the building process they would have played only a minor role. Amateurish and unbalanced was the solution that Bernardo Galiani showed in his Vitruvius

25 BERTANI 1558; also as a Latin translation included in VITRUVIUSSTRATICO 1825-1830, Vol. I, Pars 1, pp. 277-297: Bertanus, «De Opere Jonico Vitruviano».

26 This tenth century building is located on the Tiber Island. The complex itself contains architectural fragments (including capitals) of different ages. A strange coincidence is that in 1557, a year before the publication of Salviati’s text, the site was flooded by the Tiber causing severe damage. What had Salviati seen? Had the water flushed away his material or had it on the contrary brought interesting fragments in sight? VITRUVIUS-STRATICO 18251830, Vol. I, Pars 1, 1825, p. 290, and Simone Stratico, «Exercitatio Vitruviana II», in VITRUVIUS-STRATICO 1825-1830, Vol. III, Pars 1, 1828, p.

22.

27 Actual adress: 8 Via Trieste, Mantua.

Horti Hesperidum, II, 2012, 2

73

J. GOUDEAU

edition at the Napolitan Accademia Ercolanense in 175828. His four points for the compass were on the circumference of the oculus and produced a volute with only 1¾ turn with disturbing kinks as well. In the compilation of Stratico some more deviant constructions are presented, such as the one with one diagonal in the oculus taken from William Newton’s English Vitruvius of 1771. In the volute of the Spanish priest Joseph Ortiz y Sanz the spiral and the groove of the canalis are equally wide. Just as Salviati had done before, he claimed to have studied as many as 130 ancient volutes in Rome and elsewhere29. In 1795 Giovanni Piacenza from Milan suggested a volute that had extra construction lines outside the oculus. In this motley collection of solutions Stratico himself could not lag behind. Seemingly determined to come up with something radically different, his method is purely geometrical30. The construction lines are independent of the oculus and show a strange asymmetry, but in fact the principle is rather elementary. He retains the reduction of the radius of the arcs with half the oculus, which explains the mere 1¾ turn. From the original intention to really grasp what Vitruvius had meant, the problem of the Ionic volute had entered the realm of geometrical sophistication for personal profit, aiming at the increase in professional status of the author.

By way of an appendix at the end of his overview Stratico presented a fully new construction by marchese cavaliere Luigi Marini, who just as many others claimed to have found once again the correct volute method. However he did not divulge where he had found this – not in Antiquity but in the work of

28 Simone Stratico, «Exercitatio Vitruviana II», in VITRUVIUS-STRATICO 1825-1830, Vol. III, Pars 1, 1828, p. 23.

29 Simone Stratico, «Exercitatio Vitruviana II», in VITRUVIUS-STRATICO 1825-1830, Vol. III, Pars 1, 1828, p. 23: «Josephus Ortiz [...] pluribus et usque ad 130 capitulis Jonicis antiquis Romae et alibi observatis, methodum sequentem cum venustioribus congruere docet».

30 VITRUVIUS-STRATICO 1825-1830, Vol. I, Pars 1, 1825, pp. 267-273.

74

CIRCUMAMBULATE THE VITRUVIAN VOLUTE

the seventeenth century architectural theorist Nicolaus Goldmann.

A novel way out The boom in Vitruvius editions that the sixteenth century had seen still had its effect in the next century31. The many reprints that appeared meant that at first there was no market for such costly new seventeenth century enterprises. That changed with the edition of the Leiden scholar Joannes de Laet in 1649, which anticipated by 24 years the second important edition of the age by Claude Perrault32. This folio of 578 pages consisted of the meticulously annotated Latin text of De Architectura, supplemented with a series of commentaries, related treatises, indices and many high-quality engravings. This edition was in a way a worthy alternative for the scholarly milestone of the Vitruvius edition by Daniele Barbaro from1556. As well as presenting e.g. Henry Wotton’s Elements of Architecture (London 1624), the biography of Vitruvius by Philandrier, an adapted version of Bernardino Baldi’s De verborum Vitruvianorum significatione and Baldi’s treatise on the scamilli impares, De Laet had used comments by his colleagues Claude Saumaise and Gerard Vossius in the preparation of the volume33. Two texts had never been published before. The first was Notae in Vitruvium, a treatise on musical harmony in Antiquity by the Dane Marcus Meibom who stayed in Leiden for many years34.

31 On the influence of Vitruvius in the north see e.g. BODAR 1984 for the Netherlands and OECHSLIN 1984 for Germany.

32 VITRUVIUS-DE LAET 1649; VITRUVIUS-PERRAULT 1673.

33 The volume contained also well known texts by Alberti, Gauricus, Demontiosius, Saumaise, and Agricola, which had a connection to Vitruvian theory. On the De Laet see LIAS 1998, esp. the contribution by Koen A. Ottenheym, «The Vitruvius Edition, 1649 of Johannes De Laet (15811649)», pp. 217-229. Further GOUDEAU 2005, pp. 102-103.

34 On Meibom see e.g. FABRICIUS 1945.

Horti Hesperidum, II, 2012, 2

75

J. GOUDEAU

The other was a remarkable contribution on the Ionic volute Vitrvvii Volvta Ionica, Hactenvs Amissa, Restitvta a Nicolao Goldmanno35. Nicolaus Goldmann (1611-1665) was a mathematician from Breslau in Silesia (now Wroclaw in Poland) who worked in Leiden as a private teacher, especially of civil and military architecture, from 1632 until his death36. De Laetâ&#x20AC;&#x2122;s enterprise thus bore a strong Leiden signature. In this centre of scholarship and printing Goldmann wrote several books on fortification, the use of the proportional compass, the invention of a tool for drawing the column orders and a comprehensive work on civil architecture. Because of an untimely death this last book was only published in 1696 in Germany by the architect Leonhard Christoph Sturm (1669-1719)37. Students from various countries came to Leiden to attend Goldmannâ&#x20AC;&#x2122;s courses on architecture. He developed an architectural theory that covered the whole range of civil architecture. Though firmly embedded in Vitruvian theory and with expert knowledge on many other (Italian) authors and architectural problems, Goldmann was able to convert all this into an independent and astonishingly coherent theory that matched perfectly the mathematical demands of contemporary science.

He combined an axiomatic argumentation and arrangement of his material, integrating the theory of Vitruvius, the most important architectural theories of the sixteenth and seventeenth century and the Old Testament. Essentially his whole theory went back to the Temple of Solomon in the reconstruction Goldmann derived from Juan Battista Villalpando38.

35 GOLDMANN 1649. Also in VITRUVIUS-STRATICO 1825-1839, Vol. I, Pars 1, 1825, pp. 259-266.

36 On Goldmann see: GOUDEAU 2005 and GOUDEAU 2007.

37 GOLDMANN 1696.

38 GOUDEAU 2005, pp. 327-342.

76

CIRCUMAMBULATE THE VITRUVIAN VOLUTE

With the text on the Ionic volute of only eight pages in length Goldmann proves to be an independent theorist too39. The crux of his solution is that Goldmann concentrates on half the oculus (fig. 8). An enlarged version of the oculus with its division is shown in the upper corner of the illustration. Instead of introducing new construction lines as other versions did, here a square is drawn in the oculus between the two perpendiculars (cathetoe) that Vitruvius already had defined when discussing the capital as a whole (in III 5, 5-8). The square is subdivided into two inner squares, providing the points for the second and third turn (fig. 9). The corners of the squares are numbered 1-4, 5-8, 9-1240. In the first rotation using the points 1-4, the radius of the arcs diminishes with half the oculus as is immediate clear. The sides of the other squares are in relation to the first one in the proportion of 3:2:141. The point of the compass for every next arc of 90° lies on the radius where the previous ends so their tangents coincide. After every full turn the radius coincides with the basic perpendicular, i.e. the diameter of the oculus. After three times the spiral of the volute merges into the oculus. Geometrically this is a surprisingly elegant construction. Goldmann did not stop there. He did not just show his solution, he also wanted to prove the construction 39 In fact the text is only three pages long, consisting of an introduction (Architectvrae Artificiosae Cvltvribus), the original text (Verba Vitrvvii), the actual argumentation (Demonstratio) and the elaboration of the proof for the duplicated spiral line of the volute (De Duplicatione Volvtae). The other pages are reserved for the title page and three times the same engraving facing the text to make it easier to follow the reasoning. Note that Goldmann refers to the extract as Liber III, caput III, instead of caput V. 40 The numbers 13-16, 17-20, and 21-24 indicate the points of the inner spiral of the duplicated volute.

41 Goldmann here refers to an instruction by Scamozzi, which went back to Antiquity: «Hinc stabilitur Regula Scamozziana, Centra Volutae inter se distare, in prima circumactione ex semisse oculi Volutae; in secunda circumactione ex tertia parte, et in ultima circumactione ex sexta praedictae Diametri oculi Volutae, quae distantiae Antiquitatum auctoritate corrobarantur […]». GOLDMANN 1649, «Demonstratio».

Horti Hesperidum, II, 2012, 2

77

J. GOUDEAU

by calculation (fig. 10)42. Vitruvius had defined the oculus as 1 part, or 1/18 module (M) of the width of the capital. Half the oculus therefore is 1/36 M. The three squares with six corner points on the perpendicular are at equal distance, thus 1/216 M. In order to prove that the end of the last arc exactly corresponds with the oculus (i.e. with the same radius and tangent), Goldmann figures: Total height of the volute (in modules) = 8/18 Distance from the centre to the beginning of = 4½/18 the volute Distance from point 1 to the beginning of = 54/216–3/216 the volute

= 96/216 = 54/216

Reduction in the first rotation = (3x6)/216 Reduction in the second rotation = (3x4)/216 Reduction in the third rotation = (3x2)/216 Transition from the first to the second square Transition from the first to the second square Transition from the first to the second square Total reduction of the radius

= 18/216 = 12/216 = 6/216 = 5/216

= 51/216

= 3/216 = 1/216 = 45/216

The difference between the original distance of the centre of the oculus and the beginning of the spiral of the volute is 51/216 M minus 45/216 M, which is 1/36 M, or half the diameter of the oculus. After that Goldmann executes the same operation for the duplicated volute, i.e. the straps on the side, working with 1944 as the denominator, i.e. 9:8 in relation to the first spiral (fig. 11). He closes his proof triumphantly with: «Quod ostendendum erat».

Shortly after 1649 Goldmann’s volute was already adopted in architectural handbooks, often next to the canonical solution «Cum numeri sensibus sint subjecti, placuit a calculo Demonstrationem mutuari»; GOLDMANN 1649, «Demonstratio».

42

78

CIRCUMAMBULATE THE VITRUVIAN VOLUTE

that went back on Salviati (via Palladio). One of the first to mention Goldmann was Juan Caramuel de Lobkowitz in 167843.

Did Stratico give an overview of historical volute constructions, Caramuel gave in the first place all sorts of possible solutions, based on earlier authors. His overview including volutes of semicircles (two and six points in the oculus), with orthogonal and diagonal divisions, a volute of 4¾ turns, a polygonal volute, and an oval one, and the solutions of Carlos Cesar Osio and Nicolaus Goldmann. This was by far the most original and elaborate contribution to the debate up to his time (fig. 12).

Being published in Spanish, the influence of his compilation on other authors, however, is not clear.

In France Claude Perrault showed Goldmann’s method in his Vitruvius edition of 1673, as did François Blondel in his Cours d’Architecture from 1675, and Augustin Charles d’Aviler in 169144. The mathematician and military engineer Bernard Forest de Bélidor treated Goldmann’s volute in 1729 next to those by Vignola and Scamozzi45. In Germany the method spread via

43 CARAMUEL 1678, (vol. 2) V 7, pp. 58-69, there p. 65. The table of contents states: «Nicolas Goldmanno [...] nos quiere persuadir que sea la misma que tenia Vitruvio, y lo pretende probar muy y larga».

44 VITRUVIUS-PERRAULT 1673, p. 90. BLONDEL 1675, l. IV, ch. II, pp. 75102, there p. 81: «Pour corriger les défauts de Volutes dont nous venons de parler, nous raporterons une excellente methode qui a esté produite depuis peu par un Geometre, appelé Mr. Goldman [...]». AVILER 1691, p. 54: «Qvoyque les deux manieres, dont Vignole se sert pour tracer la Volute Ionique, soient bonnes & faciles [...] neanmoins celle que Goldman à inventé [...] étant absolument la plus parfaite, tant parce qu’elle est Geometrique, que parce que le Listel de la Volute y est tracé avec la mesme justesse que le premier contour [...]».

45 Here used is the annotated edition BÉLIDOR 1813, p. 452: «Le plus sur moyen d’instruire un lecteur à peu de frais, étant de lui mettre d’ abord sous les yeux ce qu’il y a de meilleur, je me contenterai de rapporter seulement la volute de Goldmann, qui est la plus estimée de toutes celles qu’on a imaginées jusqu’ici, parce qu’elle se décrit géometriquement aussi bien le listel ou la volute intérieure».

Horti Hesperidum, II, 2012, 2

79

J. GOUDEAU

Leonhard Christoph Sturm, starting in 169646. The rapid dissemination caused authors to soon forget who was originally behind this variant of the volute. In England for instance, Goldmann’s volute became known as the volute of the eighteenth-century architect James Gibbs47. Although trained in practice by Carlo Fontana in Rome, when working on a systematisation of the column orders Gibbs chose the geometrically fascinating volute of this Dutch architectural theorist.

Where the infinite meets the miniscule: Cleomedes Goldmann’s introduction ended with a statement that alluded to something special - «ac brevem Epilogum subjecimus». This epilogue turned out to be very short indeed and consists of only one mysterious sentence: «Porrò secretum Regulae Cleomedis, de incremento & decremento dierum, in Volutâ hâc latet, cujus secreti involutio Vanitatem osorum obtundet»48. What could Goldmann have meant by this deep secret of Cleomedic rules concerning the growing and shortening of the days? What Vitruvius was to architecture, the Greek Stoic scientist Cleomedes was to Stoic physics. His De motu circulari corporum caelestium dating from the fourth century was the only surviving text of the Stoa on this subject, which moreover compiled the astronomical knowledge

46 STURM 1716, Tab. 7: «Weil Vitruvii Zeichnung von seiner voluta oder Schnecke verlohren gegangen, hat man bis auf Goldmanns Zeit die beschreibung Vitruvii nicht recht verstehen können, bis dieser accurate Mann sie also heraus gebracht, welche Vitruvii text nunmehr deutlich machet». See OECHSLIN 1984, p. 57, and p. 72.

47 GIBBS 1732 Tab. XV. In CHITHAM 1985, pl. 18-19 is Goldmann’s volute the standard. Referring to Gibbs and William Chambers the author seems no longer aware of its origin.

48 GOLDMANN 1649, p. 272.

80

CIRCUMAMBULATE THE VITRUVIAN VOLUTE

of his time and predecessors49. The comprehensive and also remarkably accurate information on the movement of the heavenly bodies made the book an important source for Renaissance scholars. After an editio princeps, the Latin translation by Carolo Valgulio as early as 1497, the most important edition would become the bilingual version by Robert Balfour: Cleomedis Meteora, Graece et Latine (Bordeaux 1605). In various respects the ancient stoic view on the cosmos corresponded with the ideas of humanism. The cosmos was in perfect harmony. The guiding principles were reason and its resulting laws of nature. In stoicism there was no room for mere coincidence and the fate of the world was predestined.

Events contrary to the laws of nature were mere appearances and had to be understood as manifestations of the divine. The work of Cleomedes deals with the laws of the greatest elements of the universe – the motions of the celestial bodies and their interrelations. Soon after appearing the Balfour edition had found its way to Leiden, so it is not surprising that Nicolaus Goldmann knew about this theory50.

Most likely Goldmann referred to one passage in Cleomedes’ theory in particular, viz. a mechanism explained in the sixth chapter of the first book. Here Cleomedes explains how the days lengthen through the year, not by daylight extending every day at the same rate but in a curve. The difference between the shortest and longest day is six hours, he says. The first month the days lengthen by 30’, the second month by 60’, the third by 90’51. In the following three months it goes the other way Gr.: Kleomēdous kuklikēs theōrias meteōrōn. Richard Goulet, «Introduction générale», in the modern French edition: CLEOMEDES-GOULET 1980, pp. 350.

50 In 1609 the copy of Joseph Scaliger had already passed into the hands of the Leiden mathematician Rudolph Snellius. It is now kept in Leiden University Library. GOUDEAU 2005, p. 581.

51 These indications more or less match for the Hellespont in Turkey. This is why has been suggested that Cleomedes wrote his work in that region. It is more likely that in his calculations he chose for a regular example.

CLEOMEDES-GOULET 1980, pp. 194-195.

49

Horti Hesperidum, II, 2012, 2

81

J. GOUDEAU

round; one hour and a half in the fourth month, one hour and half an hour in the fifth and sixth respectively. Schematically: month I II III IV V VI

growth 30’ 60’ 90’ 90’ 60’ 30’

ratio 1/12 2/12 = 1/6 3/12 = 1/4 3/12 = 1/4 2/12 = 1/6 1/12

In fact the interrelation of the points on this curve is nothing but the ratio 1:2:3:3:2:1. Now this ratio corresponds with the reduction of the radius in the three successive turns in Goldmann’s volute. With every turn the square in the oculus is diminished with a fraction 6/216: from 18/216 to 12/216 and to 6/216. The reduction of 18:12:6 equals 3:2:152.

Why would Goldmann take all this effort to explain such elementary ratios? The answer is that with this connection he could provide the Vitruvian volute with a new, profound meaning. A corner of the veil of the enigmatic formulation in the text of 1649 was lifted in another treatise by Goldmann from 1661. Here he put several notions together into a meaningful whole. Goldmann connected the volute with the architecture of the Temple of Solomon. The capitals of the Temple columns were ornamented with volutes. This building given by God himself contained ineffable secrets, he stated. So the Demiurge not only had built the heavens but also had given architecture to man. The length of the days was determined by universal divine laws. Cleomedes had described these laws for the longitude of the Holy Land, being the location of the 52 There is something remarkable with this ratio 1:2:3. It is also connected to both the classical and the Vitruvian Ionic capital in another way. The Vitruvian proportions of the capital reveal the ratio 8:16:24 for its height, the distance of the centres of the two oculi and its overall width. LEHNHOFF 1948 called this type the 1-2-3 capital. See also VITRUVIUS-GROS 1997, pp.

335-338; VITRUVIUS-GROS 2003, pp. 164-165.

82

CIRCUMAMBULATE THE VITRUVIAN VOLUTE

Temple53. By implication the capitals of the Temple of the Lord therefore must have been decorated with volutes that corresponded to the rotation of the celestial divinely ordained bodies, more precisely the sun. As a consequence the Ionic volute from Antiquity must have stemmed from the orbit of the sun54. In order to act in harmony with the universe man, himself created in God’s image, had taken the Temple as the example for his architecture. Since Vitruvius had known this ancient architecture best, his description of the volute was the most reliable source and came closest to the architecture of God. Man and the work of man was incidental; the laws of divine nature were universal. By this Goldmann once again strengthened the indissoluble bond between God, Nature and man55. He fused the largest elements of the universe, the planets, with one of the particles of man-made architecture the oculus of the Ionic volute.

53 Cleomedes did not give any geographical locations. According to modern insight Cleomedes’ observations can be situated between the Thracian Lysimachia (Turkey), Rhodos, Alexandria and Syene (Aswan). CLEOMEDESGOULET 1980, pp. 3-5, 252.

54 Note that here the implication of the ancient geocentric world view has not been considered. Goldmann writes: «diese Schneckken [wurden] sein ebener gestald aus dehr heyligen Baukunst hergenommen, und bedeuten unaußsprechliche Geheymnüsse: inn dehr Natur zwar, nehmlich inn dehr grossen Weld, das abnehmen und zuenehmen der Tagelängen nach der Regel Cleomedis, vors Gelobte Land: also werden auch darinne, dehr kleinen weld des menschen Geheymnüsse begriffen. Denn die Götliche Weysheyt ist allegemein, da die menschliche nur stückwerck ist, und des inn vielen trift.» GOLDMANN 1661, p. iv.

55 «Die Gottliche Weissheit ist freylich allgemein, und begreifft allezeit in einem Bilde die dreyfache Weissheit, die Gottliche, Naturliche und Menschliche, welcher Mensch in solche Insicht die kleine Welt genennet wird». GOLDMANN 1696, II 2, p. 79.

Horti Hesperidum, II, 2012, 2

83

J. GOUDEAU

Final observations Goldmannâ&#x20AC;&#x2122;s volute had beauty and was in a way even practical.

Moreover, he achieved different things. He confirmed the authority of Vitruvius by showing how all his indications made sense. He deployed mathematics in a text-critical examination of an ancient source. His argumentation was an arithmetic proof of what in fact was a geometrical approach that served philological aims. In accordance with the spirit of his era Goldmann relied on mathematics as the only secure way to reach certainty â&#x20AC;&#x201C; the ideal of the mos geometricus. In addition he expanded the iconography of the Ionic order with a radically new concept by linking the volute to cosmology. The absurdity of his small fractions, as criticised by several authors, is to a certain extent exaggerated. The calculations only served the argumentation, not the application.

In general, the history of reconstruction of the Vitruvian volute shows a gradual development. Starting in humanist circles with predominantly philological interests, the attention of the architects made it a problem that should be solved primarily geometrically. Vitruvian theorists detached the problem from practical applicability. A basically practical issue was reduced to theoretical discussions. During the eighteenth century another shift took place from Roman to Greek examples, nourishing a new archaeological interest in the volute. Then there were the more complex solutions by engineers and mathematicians, methods that required external construction lines.

What about actually sculpting the Ionic capital? As a matter of fact the whole Vitruvian discussion was beyond the practice of the stone masons, although they certainly were consulted in this matter. When the real Ionic capitals are looked at, the variety in forms and proportions is remarkable56. The sculpting of volutes was not affected too much by these discussions. The quality of For an examination of a series of volutes on buildings in Leiden at the time of Nicolaus Goldmann, see GOUDEAU 2005, pp. 127-128.

56

84

CIRCUMAMBULATE THE VITRUVIAN VOLUTE

a capital was in the first place determined by the skills of the craftsman, who was frequently the stone supplier and stone trader as well, and could therefore act as designer, as executor, or both. The choice of the division method, as has been discussed above, came second. Only then was the architect or designer of influence on the appearance of the volute57. In relation to built architecture it is useful to be aware of the somewhat vague position of the theoretical debate. Another thing to keep in mind is that the volute is not interchangeable with the Ionic order as a whole, not with the column, nor even with the capital. The debate on the volute must therefore not be evaluated as a design issue, but above all as a topos, or as Pierre Gros formulated it, a vexata quaestio of Vitruvianism58. The goal was a proper reconstruction; the immediate cause was an interest in the debates of oneâ&#x20AC;&#x2122;s own time; the personal motivation was status. Reading Vitruvius is interpreting and also reading between the lines, both of the original text and of the texts of its interpreters. Goldmann for instance came to his solution within the theoretical context of a mathematical universe still mixed with mystic-cosmological concepts. In the end historical motivated projects such as the reconstruction of the volute reveal much about the ideals and prevailing standards of their own age.

57 In Goldmannâ&#x20AC;&#x2122;s time the volutes were still constructed in the classical way.

The four points for the compass and construction lines are for instance found in the Ionic volutes of the capitals in the Amsterdam Burgerweeshuis, in the wing built by the Dutch architect Jacob van Campen in 1634. In this case Van Campen will have worked most likely after the method of Scamozzi.

58 VITRUVIUS-GROS 1997, vol. 1, p. 335 n. 177.

Horti Hesperidum, II, 2012, 2

85

J. GOUDEAU

Bibliography Primary sources AVILER 1691 = AUGUSTIN CHARLES D’AVILER, Cours D’Architecture qui comprend Les Ordres De Vignole, Avec des Commentaires […], Paris 1691.

BALDI 1612 = BERNARDINO BALDI, Scamilli Impares Vitrvviani [...]

Nova Ratione Explicati, Augsburg 1612.

BÉLIDOR 1813 = BERNARD FOREST DE BÉLIDOR, La science des ingénieurs, dans la conduite des travaux de Fortification et d’Architecture civile (1729), ed. M. Navier, Paris 1813.

BERTANI 1558 = GIOVAN BATTISTA BERTANI, Gli Oscvri Et Dificili Passi Dell’Opera Ionica Di Vitrvvio, Di Latino in Volgare Et Alla Chiara Intelligentia Tradotti [...], Mantua 1558.

BLONDEL 1675 = FRANÇOIS BLONDEL, Cours D’Architecture Enseigné Dans L’Académie Royale D’Architecture, 5 vols. (1675-1683), Premiere Partie, Paris 1675.

CARAMUEL 1678 = JUAN CARAMUEL DE LOBKOWITZ, Architectvra Civil Recta Y Obliqua; Considerada Y Dibvxada En El Templo De Ierusalen, Vigevano 1678.

CLEOMEDES-BALFOUR 1605 = Cleomedis Meteora, Graece et Latine, ed.

ROBERT BALFOUR, Bordeaux 1605.

CLEOMEDES-GOULET 1980 = CLÉOMÈDES, Théorie élémentaire (‘De motu circulari corporum caelestium’), ed. and transl. RICHARD GOULET, Paris 1980.

DE L’ORME 1567 = PHILIBERT DE L’ORME, Le Premier Tome De L’Architectvre, Paris 1567.

GIBBS 1732 = JAMES GIBBS, Rules for Drawing the Several Parts of Architecture, London 1732.

GOLDMANN 1649 = NICOLAUS GOLDMANN, «Vitrvvii Volvta Ionica», in: Vitruvius-De Laet 1649, pp. 265-272.

GOLDMANN 1661 = NICOLAUS GOLDMANN, Tractatvs De Stylometris [...], Leiden 1661.

GOLDMANN 1696 = NICOLAUS GOLDMANN, Vollständige Anweisung zu der Civil Bau=Kunst [...], ed. Leonhard Christoph Sturm, Wolfenbüttel 1696.

POLENI 1739-1741 = GIOVANNI POLENI, Exercitationes Vitruvianae, Padua 1739-1741.

SALVIATI 1552 = GIUSEPPE SALVIATI, Regola di far perfettamente col compasso la voluta et del capitello ionico et d’ogn’altra sorte, Venice 1552.

86

CIRCUMAMBULATE THE VITRUVIAN VOLUTE

STURM 1716 = LEONHARD CHRISTOPH STURM, Vollständige Anweisung, Alle Arten von regularen Pracht=Gebäuden nach gewissen Reguln zu erfinden, Augsburg 1716.

VITRUVIUS-DE LAET 1649 = M. Vitrvvii Pollionis De Architectvra Libri Decem; Cum Notis, Castigationibus & Observationibus […] Cum variis Indicibvs copiosissimis; Omnia in unum collecta, digesta & illustrata A IOANNE DE LAET, Leiden 1649.

VITRUVIUS-GROS 1997 = VITRUVIO, De Architectura, ed. PIERRE GROS, transl. Antonio Corso and Elisa Romano, 2 vols., Turin 1997.

VITRUVIUS-GROS 2003 = VITRUVE, De l’architecture, Livre III, ed., transl., and comm. PIERRE GROS, Paris 2003.

VITRUVIUS-MORGAN 1960 = VITRUVIUS, The Ten Books on Architecture, transl. MORRIS HICKY MORGAN (1914), New York 1960.

VITRUVIUS-PERRAULT 1673 = Les Dix Livres D’ Architecture De Vitruve Corrigez et Tradvits nouvellement en François, avec des Notes & des Figures […], ed. CLAUDE PERRAULT, Paris 1673.

VITRUVIUS-ROWLAND/HOWE 1999 = VITRUVIUS, Ten Books on Architecture, ed., transl., comm., and ills. INGRID D. ROWLAND AND THOMAS NOBLE HOWE, Cambridge 1999.

VITRUVIUS-STRATICO 1825-1830 = M. Vitruvii Pollionis Architectura; Textu Ex Recensione Codicum Emendato Cum Exercitationibus Notisque Novissimis Joannes Poleni, Et Commentariis Variorum Additis Nunc Primum Studiis SIMONIS STRATICO, Vol.I-III, Pars I-VIII, Udine 1825/ 1827/ 1828/ 1829/ 1830.

Secondary literature ANDREY AND GALLI 2004 = DENISE ANDREY AND MIRKO GALLI, «Geometric Methods of the 1500s for laying out the Ionic Volute», Nexus Network Journal 6 (Autumn 2004) 2. Online source: http://www.nexusjournal.com/AndGal.html (Stand: September 2012) BINGÖL 1980 = ORHAN BINGÖL, Das ionische Normalkapitell in hellenistischer und römischer Zeit in Kleinasien, Istanbuler Mitteilungen Beiheft 20, Tübingen 1980.

BODAR 1984 = ANTOINE BODAR, «Vitruvius in de Nederlanden», in: Ed de Heer et al., eds., Bouwen in Nederland; Vijfentwintig opstellen over Nederlandse architectuur opgedragen aan prof.ir J.J. Terwen, Leids Kunsthistorisch Jaarboek 3, Delft 1985, pp. 55-104.

Horti Hesperidum, II, 2012, 2

87

J. GOUDEAU

CARPEGGIANI 1992 = PAOLO CARPEGGIANI, Il libro di pietra; Giovan Battista Bertani architetto del Cinquecento, Milan 1992.

CHITHAM 1985 = ROBERT CHITHAM, The Classical Orders of Architecture, London 1985.

EBHARDT 1962 = BODO EBHARD, Vitruvius; Die Zehn Bücher der Architektur des Vitruv und ihre Herausgeber […] (1918), Ossining and New York 1962.

FABRICIUS 1945 = K. FABRICIUS, L.L. HAMMERICH AND VILH. LORENZEN, Holland-Danmark, 2 vols., Copenhagen 1945, vol. 2, pp. 277 ff., p. 363.

GOUDEAU 2005 = JEROEN GOUDEAU, Nicolaus Goldmann (16111665) en de wiskundige architectuurwetenschap, Groningen 2005.

GOUDEAU 2007 = JEROEN GOUDEAU, «A Northern Scamozzi; Nicolaus Goldmann and the Universal Theory of Architecture», Annali di Architettura; Rivista del CISA Andrea Palladio 18-19 (20062007), pp. 235-248.

GOUDEAU 2013 = JEROEN GOUDEAU, «Die Sprache der Säulen», in: Uwe Albrecht and Regina Becker, eds., Architectura; Werke zur Architektur aus den Sammlungen der Christian-Albrechts-Universität zu Kiel, Regensburg 2013.

GROS 1988 = PIERRE GROS, «Vitruve et les ordres», in: Jean Guillaume, ed., Les traités d’architecture de la Renaissance, Actes du colloque tenu à Tours du 1er au 11 juillet 1981, De Architectura, Paris 1988, pp. 49-59.

GÜNTHER 1988 = HUBERTUS GÜNTHER, Das Studium der antiken Architektur in den Zeichnungen der Hochrenaissance, Tübingen 1988.

HASELBERGER 1989 = LOTHAR HASELBERGER, «Die Zeichnungen in Vitruvs De Architectura; Zur Illustration antiker Schriften über das Konstruktionswesen», in: H. Geertman and J.J. de Jong, eds., Munus non ingratum; Proceedings of the International Symposium on Vitruvius’ De Architectura and the Hellenistic and Republican Architecture, Babesch, supplement 2, Leiden 1989, pp. 69-70.

HELLMANN 2002 = MARIE-CHRISTINE HELLMANN, L’Architecture Grecque; 1. Les principes de la construction, Paris 2002.

KNELL 1991 = HEINER KNELL, Vitruvs Architekturtheorie; Versuch einer Interpretation (1985), Darmstadt 1991².

KOCH 1956 = HERBERT KOCH, Von Ionischer Baukunst, Die Gestalt; Abhandlungen zu einer allgemeinen Morphologie 26, Cologne and Graz 1956.

88

CIRCUMAMBULATE THE VITRUVIAN VOLUTE

KRINSKY 1967 = CAROL HERSELLE KRINSKY, «Seventy-eight Vitruvius Manuscripts», Journal of the Warburg and Courtauld Institutes 30 (1967), pp. 36-70.

KRUFT 1991 = HANNO-WALTER KRUFT, Geschichte der Architekturtheorie; Von der Antike bis zur Gegenwart (1985), München 1991³.

LEHNHOFF 1984 = BERND LEHNHOFF, «Das ionische Normalkapitell vom Typus 1:2:3 und die Angaben Vitruvs zum ionischen Kapitell», in Vitruv-Kolloquium des Deutschen ArchäologenVerbandes e.V. durchgefürt an der Technischen Hochschule Darmstadt, 17. bis 18. Juni 1982, Darmstadt 1984, pp. 97-122.

LIAS 1998 = P.G. HOFTIJZER AND R.H. BREMMER, eds., «Johannes de Laet», special issue LIAS 25 (1998) 2.

MACTAVISH 1981 = DAVID MACTAVISH, Giuseppe Porta, called Giuseppe Salviati, New York 1981.

McEwen 2003 = Indra Kagis McEwen, Writing the Body of Architecture, Cambridge Mass. 2003.

OECHSLIN 1984 = WERNER OECHSLIN, «Vitruvianismus» in Deutschland’, in: Ulrich Schütte, ed., Architekt und Ingenieur; Baumeister in Krieg und Frieden, Ausstellungskataloge der Herzog August Bibliothek 42, Wolffenbüttel 1984, pp. 53-76.

PUCHSTEIN 1887 = OTTO PUCHSTEIN, Das Ionische Capitell, 47.

Programm zum Winckelmannsfeste der Archaeologischen Gesellschaft zu Berlin, Berlin 1887.

REBECCHINI 2000 = GUIDO REBECCHINI, «Giovan Battista Bertani; L’inventario dei beni di un architetto e imprenditore mantovano», Annali di Architettura; Rivista del CISA Andrea Palladio 12 (2000), pp.

69-73.

RICHENS AND HERDT 2009 = PAUL RICHENS AND GEORG HERDT, «Modelling the Ionic Capital», in: Computation: The New Realm of Architectural Design, 27 ed. Conference on Education and Research in Computer Aided Architectural Design in Europe, eCAADe, Istanbul 2009, pp. 809-816. Online source: http://www.ecaade.org (Stand: September 2012) RYKWERT 1996 = JOSEPH RYKWERT, The Dancing Column; On Order in Architecture, Cambridge Mass. and London 1996.

SCAGLIA 1979 = GUSTINA SCAGLIA, «A Translation of Vitruvius and Copies of Late Antique Drawings in Buonaccorso Ghiberti’s Zibaldone», Transactions of the American Philosophical Society, 69 (1979) 1, pp. 3-30.

Horti Hesperidum, II, 2012, 2

89

J. GOUDEAU

SCHULER 1999 = STEPHAN SCHULER, Vitruv im Mittelalter; Die Rezeption von «De Architectura» von der Antike bis in die frühe Neuzeit, Cologne, Weimar and Vienna 1999.

UEBLACKER 1985 = MATHIAS UEBLACKER, Das Teatro Marittimo in der Villa Hadriana, w. contrib. Catia Caprino, Mainz 1985.

VON LUSCHAN 1912 = FELIX VON LUSCHAN, Entstehung und Herkunft der Ionischen Säule, Der Alte Orient, Gemeinverständliche Darstellungen 13-4, Leipzig 1912.

WESENBERG 1983 = BURKHARDT WESENBERG, Beiträge zur Rekonstruktion Griechischer Architektur nach literarischen Quellen, Mitteilungen des Deutschen Archäologischen Instituts Athenischen Abteilung, 9. Beiheft, Berlin 1983.

ZACCAGNINI 1908 = GUIDO ZACCAGNINI, Bernardino Baldi nella vita e nelle opere, Pistoia 1908.

90

CIRCUMAMBULATE THE VITRUVIAN VOLUTE

Captions 1. The volute in a Roman composite capital. Baths of Caracalla, Rome ca. 216 AD. (Photo by the author) 2. The proportioning of the base and capital of the Ionic column expressed in parts of the module after Cesariano’s 1521 Vitruvius edition. Walther Ryff, Vitruuius Teutsch [...], Nurnberg 1548, pl. IV. (Herzog August Bibliothek, Wolfenbüttel) 3. The Vitruvian capital with its mouldings. Giovanni Battista Bertani, Gli Oscuri Et Difficili Passi [...], Mantua 1558, [34] (Private collection) 4. The vertical division of the Vitruvian volute. The numerals are added. Giovanni Battista Bertani, Gli Oscuri Et Difficili Passi [...], Mantua 1558, [31] (Private collection) 5. a-c. The volute of Vitruvius reconstructed fourteen times: Cesariano, Serlio, De L’Orme, Goldmann, Palladio/ Scamozzi, Salviati, Bertani, Perrault, Galiani, Newton, Ortiz y Sanz, Placentia, Marini, Stratico. M. Vitruvii Pollionis Architectura [...],ed.

Simone Stratico, Vol. III, Pars 1, Udine 1828, Tab. I-III. (Leiden University Library) 6. Diagram of the main volute constructions as presented in architectural treatises in chronological order. They were published in Vitruvius editions (V) as part of a larger treatise (T) or as separate text (S). Indicated are the method of dividing the oculus, the number of rotations from abacus to oculus and the basic form of the volute with a single or double spiral (s/ d).

7. The Ionic capital with entablature, the tracing of the volute, and the division of the oculus according to Scamozzi. Vincenzo Scamozzi, L’Idea Della Architettvra Vniversale [...] in X. Libri, Venice 1615, p. 101. (Herzog August Bibliothek, Wolfenbüttel) 8. Nicolaus Goldmann, «Vitrvvii Volvta Ionica», in: M. Vitrvvii Pollionis De Architectvra Libri Decem, ed. Johannes De Laet, Amsterdam 1649, p. 268. (Leiden University Library) 9. Division and proportions of Goldmann’s oculus. (Drawing Joh. P.M. Goudeau) 10. Sketch in ink and calculations of the volute by Goldmann. Note that the drawing is a mirror image of the printed illustration.

Nicolaus Goldmann, [ Architektonische Zeichnungen und Kupferstiche – 2], p. 114. (Staatsbibliothek, Berlin, sign. Ms.germ.fol.239) 11. Four variants of the volute with single, doubled or tripled bands.

Sketches in ink. Nicolaus Goldmann, Entwerffung dehr Baukunst, Horti Hesperidum, II, 2012, 2

91

J. GOUDEAU

1663, ill. 7-10. (Herzog August Bibliothek, Wolfenb端ttel, sign.

1.7.11.Aug.fol.)

12. The Ionic volute by Carlos Cesar Osio. Juan Caramuel de Lobkowitz, Architectvra Civil Recta Y Obliqua [...], Vigevano 1678, vol.3, Lamina XXXV. (Online source http://www.archive.org/stream/architecturacivi00cara#page/n78 6/mode/1up (Stand: September 2012).

92

CIRCUMAMBULATE THE VITRUVIAN VOLUTE

on 1

Illustration 2 1

2

Horti Hesperidum, II, 2012, 2

93

J. GOUDEAU

n3

3

94

CIRCUMAMBULATE THE VITRUVIAN VOLUTE

4

4

Horti Hesperidum, II, 2012, 2

95

Illustration 5

J. GOUDEAU

5

96

CIRCUMAMBULATE THE VITRUVIAN VOLUTE

Theorist

Char. of publ.

Stratico

Partition of the oculus

Rotations

T

-

Semicircles

2x; s

Cesariano Sagredo Dürer Serlio Philander

Year ofpublicati on Ca. 1450 Publ. 1485 1521 1526 1525 1528 1552

V T T T V

01 02 -

3½ x; d 2x; s 2+; s 3x; s 3½ x; d

Salviati

1552

S

06

Barbaro Bertani

1665 1558

V S

07

De l’Orme 1567 Palladio 1570

T T

03 05

Vignola

T

-

Scamozzi 1615 Goldmann 1649 Perrault 1673/ 1684

T S T/ V

05 04 08

Caramuel de Lobkowitz

T

-

Orthogonal axes Semicircles Variant of Archimedes’ spiral Semicircles Orthogonal axes (sc.

Cesariano) Quarter turned quadrant with diagonals (Illustration by Palladio) Orthogonal and diagonal construction; one centre per quadrant Diagonal axes Quarter turned quadrant with diagonals Eighth circles (orthogonal + diagonal) As Palladio Quadrant on the centre line Quadrant and diagonal; separate from the oculus/ quarter turned quadrant with diagonals 17 different solutions, including Osio, Goldmann, older and fantastic ones.

Orthogonal axes Only one diagonal Quarter turned quadrant Quadrant with diagonals outside the oculus Quadrant on the centre circle Arc of the circle independent from oculus

Alberti

1572

Galiani Newton Ortiz Piacenza

1758 1771 1787 1795

V V V S

09 10 11 12

Marini Stratico

1825 S 1825-1830 V

13 14

3x; d 3x; d 2x; d 3x; s 3x; d 3x. d 3x; d 3x; d 3x; d

Max. 4¾x 1¾x; d 3x; d 2x; d 3x; d 2x; s 1¾x; d

6

Horti Hesperidum, II, 2012, 2

97

J. GOUDEAU

on 7

7

98

CIRCUMAMBULATE THE VITRUVIAN VOLUTE

Illustration 8

n9

8

9 Horti Hesperidum, II, 2012, 2

99

J. GOUDEAU

10

100

CIRCUMAMBULATE THE VITRUVIAN VOLUTE

1

11 Horti Hesperidum, II, 2012, 2

101

J. GOUDEAU

12

102