The importance of proper proportioning appears in the Netherlandish discourse on the arts from the early decades of the sixteenth century. Its main conduit is Vitruvius: at the time the humanist élite, who read Vitruvius as they would any other Latin text, helped to introduce craftsmen to this notoriously obscure source, which described an architecture and building technology entirely disconnected from contemporary practice. The Vitruvian text had, of course, never been forgotten, but throughout the Middle Ages its impact on the stonemason’s trade, as Joseph Rykwert has argued, was much less significant than that of Euclidian geometry (Rykwert 1982: 76–79).6 In the same milieu, Alberti’s De re aedificatoria was read as shown, for instance, in the work of the aforementioned Cornelis Grapheus. In 1528 Cornelis published Pomponius Gauricus’ 1504 treatise De sculptura (Gaurico 1528) at his brother Joannes (Jan) Grapheus’ printing house in Antwerp (Prims 1938: 172–190).7 In the introduction he quotes Vitruvius and Alberti, and expresses the hope that the passages on symmetria or proportioning will be useful to sculptors, painters, and architects alike, since symmetria feeds all the arts (‘symmetriam … omnium deniq[ue] artificiorum nutricem’; Gaurico 1528: fol. a2 verso–a3 recto).8

A contemporary source, Albrecht Dürer’s Vier Bücher von Menschlicher Proportion (On Human Proportion), which appeared in Nuremberg in the year of his death (Dürer 1528), was certainly known in Antwerp, where the painter had known a resounding success at his visit in 1520–1521 (Albrecht Dürer in de Nederlanden 1977; Plard 1990). The German artist had been working on the manuscript for at least seven years before it was published. The treatise should of course be taken together with its preceding manual on geometry, the Underweysung der messung, mit dem zirckel unn richtscheyt in Linien ebnen unnd gantzen corporen (Dürer 1525). Dürer had quickly published the latter book because he realized that his work on human proportion otherwise could not be understood properly (‘nit gruentlich verstanden mag werdenn’). In both works he incorporated Vitruvius, Alberti and of course Gauricus, but also the teachings received from Luca Pacioli in Venice together with empirical research. Thus he developed original methods of representation and became one of the pioneers of descriptive geometry north of the Alps; the well-known humanist Konrad Celtis lauded his mastery of symmetria in a learned epigram (Haffner 2006: 153; for an overview with older literature, see Hemfort 1988; see also Wuttke 1967: 321, 324). The term Proportion in the title of the treatise may be seen as a significant, and conscious, mark of modernism, contrasting with the homegrown word Messung (measurement) in the manual. It should also be noted that his well-known schemes on the proportions of the human figure presuppose a fairly high level of numeracy, as they show difficult fractions in Arabic numerals.9 On this point Dürer in fact connected with a centuries-old tradition of ‘arithmetical geometry’. As Peter Kidson has stressed, all through the Middle Ages, in continuation of antiquity, mathematicians discussed geometrical proportions in arithmetical terms, using fairly accurate approximations of surds such as √2 and √3 (Kidson 2008: 19–20).10 This mode of expression cannot have remained entirely unknown to building masters either, even before Rodrigo Gil de Hontañón wrote down his precepts for the proportioning of the buttress in mid-sixteenth century Spain, using the square root as a novelty.11

There are correct principles and erroneous ones, Coecke stresses in his publications, first and foremost in the first antique-inspired treatise to appear in the Flemish language, Die Inventie der colommen, published in Antwerp in 1539 (‘On the invention, or design, of columns’; Schéle 1962).12 Here a neologism for the term symmetria, or ‘simmetrie’, is introduced for the first time in the Netherlandish language (Coecke van Aelst 1539a: fol. a 3 verso).13 Die Inventie excerpts Vitruvius almost exclusively on this point, but the theme returns in Coecke’s translation of Serlio’s Book I on Geometry, published posthumously in 1553 by his wife Mayken Verhulst in Antwerp (Coecke van Aelst 1553). While such a book might be deemed superfluous, Coecke says to the reader, it is sorely needed:

This address has Dürerian overtones: In his Underweysung der messung, Dürer had similarly written that the art of geometry constituted the true basis of painting; many painters which had not learnt this art made errors out of ignorance.15 Is this normative mindset a sign of the times? It is worth noting here that in his Unterweisung for his son Moritz (1516), Lorenz Lechler of Heidelberg emphasizes a similar difference between the mason who does not master the art (‘der der kunst nicht erfahren ist’) and those artists who know and understand (‘khunstler, die es verstehn und wissen’), who constitute the true audience of his treatise, which is known through several manuscript copies (Seeliger-Zeiss 1967; Seeliger-Zeiss 1982; Egidy 1988). Even if its vocabulary of forms reflects the southern German Gothic of the late fifteenth century, Lechler’s Unterweisung, it could thus be argued, is part of the same new literary category as Dürer’s and Coecke’s treatises, which are considered as belonging to the Renaissance. At the time, Lechler was architect to the Palatine court in Heidelberg, a flourishing center for the study of (Gallo-)Roman antiquity since the 1480s. Indeed, amongst its connections we find the then owner of the famous Carolingian Vitruvius manuscript now in Sélestat/Schlettstadt, Johann von Dalberg, bishop of Worms.16 We are similarly reminded of the fact that the well-known booklet on Gothic finials published by Mathes Roriczer in Regensburg in 1486 (Büchlein von der Fialen Gerechtigkeit 1486) at the instigation of Wilhelm von Reichenau, the learned bishop of Eichstatt and ‘lover of geometry’ (in Roriczer’s words), was actually produced by the same extended intellectual network (Günther 1988a; Günther 1988b; Günther 2003: 61–65).17 Forty years later, Dürer dedicated his treatise on geometry to Reichenau’s godson, the humanist Willibald Pirckheimer, who was also his friend.

The proportioning system for columns that Coecke presents in his 1539 Inventie is primarily based on a critical but faithful reading of Vitruvius in the Cesariano edition (he in fact contrasts the principles declared in the Cesariano text and those underlying the images), and to a lesser degree of Pliny. Its two-fold way of presenting the column proportions, however, may be called innovative. Coecke adopts a very simple way of showing the basic proportions of the column, which has no exact counterpart in the Cesariano Vitruvius edition, nor in Serlio’s Book IV, which he translated into Flemish in the same year (Coecke van Aelst 1539a: fol. b 5 recto: on the proportioning of the Doric and Ionic column; fol. c 2 recto: on the entasis of the column; fol. c 6 recto: on the proportioning of the Tuscan column, see Figure 1).

It must indeed be stressed that the Inventie shows no sign of Serlio whatsoever.18 Horizontal dividing lines and notches scale each column shaft in the plate, which compares the squat Doric column and the Ionic, and likewise in the figure showing both Tuscan variants. Small relative scales consisting of notched verticals accompanied by numerals indicating the number of subdivisions accompany the Doric and Ionic bases, and a similar device is used for explaining the main proportions of the Corinthian capital (Coecke van Aelst 1539a: fol. c 5 recto; see Figure 2).

Coecke has obviously been inspired by Dürer, who systematically used numbered notches in his 1525 Underweysung to illustrate graphically the subdivision of the antique pedestal, column base and different types of pedestals (Dürer 1525, Book III; see, for instance, fol. g v recto and verso, g vi verso, and h i recto). But Coecke’s horizontal subdivisions of the column shaft are not numbered; they rather resemble the horizontal dividing lines of the human figures in Dürer’s 1528 On Human Proportion. On this point a parallel may also be drawn with Cesariano’s illustration of atria and peristylia with various proportions, where notches and numerals are used to render proportional relationships immediately visible to the eye; and with the unnecessarily complicated, and unworkable, horizontal subdivisions and grid lines with which Cesariano renders his Doric and Ionic capitals and bases (Cesariano 1521: Book VI, fol. 98 recto, and Book V, fol. 47 verso, respectively).19

In the same Vitruvian booklet of 1539, the image showing the construction of the (Doric) pedestal mixes a linear scale with a demonstration of the art of the compasses (Coecke van Aelst 1539a: fol. b 7 recto, see Figure 3, with text on fol. b 6 verso, see below).

If we take the text into account, the result seems ambiguous. On the one hand, while the general structure can be taken from the image, the proportioning of certain details can be guessed at, but only understood completely through reading the accompanying description on the facing page (b and c each equal a divided by 4, as does d, while e is one third of a, and f one sixth). Instead of Dürer’s numbered segments, Coecke uses letters but without indicating the relationship between different quantities, much like Cesariano.20 The image is more autonomous than Serlio’s illustrations in Book IV, for instance, but not completely (Carpo 2003: 452–453; see also Rosenfeld 1989, and Hart 1998). Still, even without the text the image is still much clearer than the Cesariano gloss this passage is generally based on (Cesariano 1521: Book IV, fol. 66; image on fol. 65 verso).

On the other hand, the text takes the reader step by step through its construction, or its Simmetria, as Coecke explicitly says, and can indeed be understood without the accompanying image, if we know what a pedestal looks like.

In modular terms, the total width of the pedestal at its base is two times the column diameter (2a), to be subdivided into eight parts. Vertical plumb lines starting from the points at one eighth and at seven eighths of this base line give us the width of the die of the pedestal, the height of which is three times the column width (3a). At the base, the plinth of the pedestal thus projects one eighth of its width or one fourth of a at each side; its height is also one eighth of the base line. The curved transition between plinth and die is also one eighth in height and width. A similar height and projection is given to the pedestal’s crowning cornice, etc. If only Coecke had expressed the values of b, c, d, etc., in multiples of his module a — which he could easily have done without having need of advanced mathematical knowledge, because the relations can all be expressed very simply — this image could have been considered a direct precursor of Vignola’s numerical representation of the proportions of the column (Carpo 2003: 455–456). As it is, in this case the letters refer to different steps in the procedure and not to an algebraic value. Completely numbered presentations of the column elements were available on the market (and, it can be surmised, also in Antwerp libraries),22 but they do not seem to have been taken into account by Coecke. Print series such as the ones produced by G.A., the Master with the Caltrop, c. 1535 and by Jacques Prévost (?), Master P.S., in 1537 indeed show antique bases, capitals, and entablatures with measurements expressed in oncie (inches) and Roman palmi (Zerner 1988; see also Waters 2012).

The necessary step of abstraction, however, is still a few decades away (Fig. 4).

The inspiration for this procedure might have been found in Alberti’s description of the Attic base, which is in fact an algorithm.23 Alberti was known and read by Coecke’s mentor Grapheus, as we have seen. But more than that, it is indeed suggestive that Coecke pioneered the first correct graphical illustration ever published of Alberti’s iterative construction of the Attic base (see Figure 5).

This plate mixes numbers and letters in a much clearer way than the image of the pedestal. Numbered segments show the proportioning, and the significance of the letters can be deduced from the accompanying caption. As in the image of the pedestal (Fig. 3) they denote the different parts of the base, albeit not in the order of proportioning set out in the text.

Dürer might be considered an intermediary phase. In his 1525 Underweysung he demonstrated the construction of a vaguely antique column base in a drawing that shows the general subdivision of the height of the base with a notched and numbered line on the right (Dürer 1525: fol. h iij verso) (Fig. 6). However, all the details explaining the positions of the defining horizontals and verticals must be taken from the text:

Thus Coecke can in fact be credited with the first successful, almost perfectly parallel combination of text and graphics to explain the construction procedure of a column element. Similarly, Coecke’s illustration of the Corinthian capital is much more complete, in the sense of independent from the accompanying text, than Dürer’s (compare Coecke van Aelst 1539a: fol. c 5 recto [Fig. 2] with Dürer 1525: fol. h iiij verso). As Carpo has remarked, this way of working is reminiscent of the oral transmission of knowledge proper to the workshop and the world of the guilds (Carpo 2003).27 On the surface, the circle segments illustrating the general proportions of the Doric pedestal in Coecke’s drawing (3:2) might refer to late mediaeval proportioning techniques with the compass, familiar to many in his audience. But they are not essential. The compass lines might even be said to be redundant since the same information is available through the scales. The Inventie cannot be reduced to a crafts manual only, even if the ‘lovers of architecture’ addressed in the title also include practitioners of the building trades, and even if the large print run (of over 650 copies), the pocket size, and the low price of a single stiver (stuiver) all suggest that particular format (Schéle 1962). Both the opening (I–II) and closing chapters (VIII–X), which bookend the central section on the orders, are uncompromisingly Vitruvian in terminology and tone, defining ‘architecture’ as an intellectual activity based on scientific principles, and discoursing on antique temples and on proportion. Moreover, like the first translation of Sebastiano Serlio’s Quarto libro (1539), the Inventie was printed in a Roman font, not at all easy to read by the common artisan.28

The world of construction is to a large extent still a closed book to us where it comes to the actual use of geometrical rules of thumb and the tradition of proportioning systems. Contrary to the German lands where some of this knowledge was translated into print at the instigation of enlightened patrons already at the end of the fifteenth century, as we have seen, for the Low Countries only a few sources survive. One particular case may be compared to the German finial booklets, even if it lacks text. It is related to the practice of Alart Duhamel, a respected master who worked on the building sites of the main churches at ’s-Hertogenbosch (1478–1494), Antwerp (1478–1494) and Leuven (1495–1502) (Verreyt and Lehrs 1894; Peeters 1985: 39–40). Duhamel’s designs for a monstrance in the form of a sacrament tower and for a complicated canopy were published in the form of large, signed prints, composed of several leaves.29 These prints were obviously not destined for the lower end of the market; like the German manuals, they might have been of interest to the learned collector. They include, in a kind of geometrical shorthand which is perfectly clear to those who have mastered the art of the compasses, the essence of Duhamel’s design. The key is given by the notation ‘1/8’, indicating that the diagram must be multiplied by eight (Figs. 7a and 7b).

By flipping (achieving one quarter of the plan) and rotating it, the basic plan of his concept and even its proportional scheme may be known. The result is the kind of ‘compressed’ plan (in which several levels are projected upon a single plane at the base) familiar from Gothic architectural drawing.30 This form of geometrical notation may be found in other Netherlandish drawings, too.31 A painter such as Coecke, trained in the rendering of architecture, must have been as familiar with this projective geometry as was Dürer.32 His presentation of the Corinthian capital in a combined plan and vertical profile at least seems to suggest as much (Fig. 2).33

A late sixteenth-century source offers an inkling of what the accompanying oral explanation, transmitted in the workshop, could have been like. The imposing, 578-folio manuscript Architectura. Dat is constelicke bouwijnghen huijt die Antijcken ende Modernen (Artful Buildings from the Antique and the Modern) of 1596–1600 was compiled by the Bruges master mason Charles De Beste at the end of his life (Van den Heuvel 1994; Van den Heuvel 1995). In his Second Book on Geometry he not only drew upon current manuals such as those of Serlio and Dürer but also on older lore (De Beste 1595–1600: Book II, Chap. XVI, fol. 80 recto–fol. 92 recto; new foliation). In ninety–nine examples he demonstrates the ‘art of using the compasses’ by drawing complicated tracery patterns for semi-circular arches (boghen ofte verwelffsels), followed by fifteen rectangular fields which may be used for parapets (bostweeren) or below the windows in the façade (onder die veijnsteren in viercante percken) (Fig. 8).

He finds the need, however, to write a detailed explanation for the procedure in each example, using a technical vocabulary familiar to us from early sixteenth-century contracts and accounts (see Philipp 1989 for samples; for a more extended discussion, see De Jonge 2011a). The similarity with Coecke’s procedure for the construction of the pedestal is striking; here also the design is generated from the base line upwards with the compass. For instance:

Coecke’s image of the pedestal may have profited not from similar Gothic designs35 but from the schemes added by the anonymous French translator of the Medidas del romano (De Sagredo 1526), which show the complete column order (Fig. 9).36 This Vitruvian dialogue was published in Spanish in 1526 by Diego de Sagredo in Toledo, and appeared as Raison darchitecture antique some time in the early 1530s at Simon de Colines’ shop in Paris (Raison darchitecture antique; Lemerle 2000).37 The original illustrations, being rough woodcuts, could not be used in any way for the correct proportioning of the pedestal, or of the column base. The anonymous translator brought the profile of each base nearer to the circle showing the lower horizontal section of the column, and added a regularly subdivided diameter, thus greatly increasing the functionality of each illustration (Raison darchitecture antique: fol. 25 recto–fol. 27 verso; cf. De Sagredo 1526: fol. C iij verso–fol. C vi verso). Still, here also the pedestal was shown in a painterly perspective view without construction lines (Raison darchitecture antique: fol. 28 recto; cf. De Sagredo 1526: fol. C vij recto). For the proper dimensioning of each part one still had to read the accompanying text very carefully. The illustrations of the orders added by the translator, on the other hand, can be understood independently from their accompanying text (Raison darchitecture antique: fol. 44 recto–fol. 45 verso) (Fig. 9). Each order now has a pedestal with specific proportions, indicated by circles in another demonstration of the art of the compasses. This is indeed the first systematic inclusion of the pedestal in the system of the orders, predating Serlio’s Book IV. Serlio on the contrary chose Latin formulae in the tradition of Boethius to express the proportional relationship (proportione quadrata, diagonea, sesquialtera, superbipartiens tertius, and dupla). The author of the Sagredo translation is unknown, but the numerous errors and confusions in the text of the Raison are clear evidence of his unfamiliarity with the Spanish language on the one hand and with this new architectural vocabulary on the other.

Coecke does not stand alone in the Northern artistic milieu of the 1530s. There may indeed be counterparts to his combined geometrical and arithmetical presentation of the proportions of the column. A significant step along similar lines may be found in the work of a Netherlandish anonymous artist active in the 1530s, whose repertory of forms is extremely close to that of the very influential sculptor Jean Mone, ‘artiste de l’empereur’ to Charles V from 1521/1522 (De Jonge 2010a; on Mone, see also De Jonge 2010b, with older literature). In a model book on vellum (Model Book of the Five Orders), now conserved in Madrid in mutilated form,38 this artist gives a demonstration of the proportioning of each of the five orders (with the Plinian proportions used in Serlio’s Book IV for the height of the columns) with the compasses (De Jonge 2011b).

The examples that follow each proportional scheme showcase the column shaft and its decoration in many inventive (and fundamentally un-Roman) ways, reminiscent of the work of Mone and his many Netherlandish followers but also of the Spanish context of his earlier career (he worked with the sculptor Bartholomé Ordóñez in Barcelona from 1517). Unfortunately, only the schemes showing the Grecian orders have survived (Fig. 10).

The Model Book includes not only the pedestal but also the entablature of the order in demonstrations with circles for a column, baluster and pilaster. Smaller circles, the diameters of which correspond to the radius of the column in the thickest part of its shaft (at the entasis), are superimposed on the column base and capital in the Doric and Ionic schemes, showing that they are of the same height. Larger circles are used to show the proportions of the die of the pedestal, which, as in Coecke’s Inventie, is as wide as the plinth of the column base. Their relationship to the smaller circle is not immediately obvious in the Doric and Ionic schemes, but in the Corinthian one, the die and plinth are subdivided into sixths by smaller half-circles, the column diameter at the entasis (highlighted by four small circles) corresponding to four sixths of the former. For every order, the height of the entablature is indicated by three vertically stacked circles of intermediate size; according to a numbered scale in the Doric and Ionic schemes, the architrave takes up three fourths of the diameter, while the cornice equals one circle and the frieze one circle and a fourth part. For the Ionic and Corinthian Orders, the intermediate circle corresponds with the upper diameter of the column shaft; its relation to the larger column diameter is not shown in the Ionic case. According to the Corinthian scheme, however, it equals three fourths (indicated by three small half-circles) of the larger diameter. In the case of the more hefty Doric column, the three intermediate or entablature circles equal two times the upper column diameter, also drawn in. Thus, since the pilasters of the three orders do not have an entasis or taper in any way, the entablature of the pilaster order is systematically taller than that of the variants with columns.

This manuscript, or another copy, was known in the Antwerp milieu, as may be deduced from its Nachleben in the work of Hans Vredeman de Vries, amongst others in the latter’s first essays on the orders and their ornament of 1565 and in his 1577 treatise Architectura oder Bauung der Antiquen auss dem Vitruvius.39 The anonymous author of Model Book indeed had many of his designs published, which were used widely and for a long time: Charles De Beste, for instance, inserted several of them into his Fifth Book on Architecture to illustrate tombs, church furniture, façades of palaces, etc. (De Beste 1596–1600: fol. 363 recto (tomb), fol. 364 recto (stalls), fol. 364 verso (tabernacle), fol. 365 verso (small tabernacle), fol. 366 recto (altar dated 1534), fol. 366 verso (reliquary), fol. 374 recto (five-bay façade). Prints (or proofs) which seem to have been based on the Madrid model book, were recently discovered by Peter Fuhring (Print Proofs).40 However, these combine the demonstration with circles with a notched scale on the side, and thus come one step closer to the Inventie.41 As in Coecke’s representation of the pedestal, two different methods are combined here. These prints, or their preparatory drawings, were certainly known to De Beste, who carefully copied all of them (Fig. 11).42

They may also be compared to the representation of the orders in a French manuscript treatise on geometry which belonged to Henry VIII of England (Geometria; Thurley 1993: 89 and 94, fig. 123).43 Schemes for pedestals drawn with circles taken from the Raison darchitecture antique are combined here with a half section along the axis, subdivided into numbered parts; the Ionic entablature shows the three circles characteristic of the Anonymus Model Book of the Five Orders, while the Tuscan column has obviously been borrowed from Serlio’s Book IV. Jacques Androuet du Cerceau the Elder, who liberally borrowed from the Model Book throughout his career (especially column shaft ornaments and designs for goldsmith’s work), uses horizontal, numbered subdivisions and circles in the album on vellum which he created for Governor Peter Ernst von Mansfeld in the mid-1550s (Androuet du Cerceau c. 1555: especially fol. 132 recto–fol. 140 recto; for dating of the binding, see Le Bars 2007: 166–167).

Without doubt, Hans Blum’s singular way of representing the orders, both in his Quinque columnarum exacta descriptio atque delineatio cum symetrica earum distributione (Zürich, 1550) and in the Ein kunstreych Buoch von allerley antiquiteten (Zürich, c.1560), is also based upon these precedents. The 1550 Latin book on the orders had been published in German in the same year (as Von den fünff Sülen Grundtlicher bericht) and published in French by Hans Lieferinck in Antwerp in 1551 (with the title Les cincq coulomnes de l’architecture, ascavoir, la Tuscane, Doricque, Ionicque, Corinthie, & Composite, avec la vraye symmetrie & proportion dicelles), followed by many other editions (Schildt-Specker 1988; Hänsli 2004; Hänsli 2006). The double-size (or ‘imperial size’, as Lieferinck calls it), fold-out leaves show a combination of numbered scales (both horizontal and vertical) and diagrams with circles (for pedestal and entablature), combined with Serlio’s particular way of indicating the diminution of the column above the entasis. The Kunstreych Buoch has similar foldouts and comes even closer to the Model Book’s proportional schemes, as circles are also used here across the thickness of the column shaft (Fig. 12). Blum’s considerable influence in France, Germany, the Netherlands and England until the seventeenth century, including in such well-known treatises as Jean Bullant’s, is thus also indebted to these earlier experiments in representing the proportional relationships of the column order (Pauwels e.a. 2004; Pauwels 2008; Pauwels 2010).

In the Low Countries of the early modern period (De Jonge 2012) the Vitruvian column orders offered a new field for experimentation to artists trained in the Gothic culture of proportion. The result of such experimentation cannot be qualified simply as ‘traditional’, as Carpo did in his 2003 essay; nor can an overt ‘battle’ between geometry — standing pars pro toto for the Gothic — and numeracy — seen as characteristic for Renaissance architectural theory and practice — be observed in the surviving sources.44 In the stylistically pluralistic Netherlandish context, textual description of geometrical procedure could be combined with graphical demonstration of the art of the compasses and with numerical notation, as shown both by Dürer’s Underweysung and Coecke’s Inventie. In spite of its erudite Vitruvian literary format, the Inventie presented a notation system understandable by all, from the erudite amateur of geometry and architecture to the members of the construction guilds. This is entirely in keeping with Coecke’s intention to establish a new, universally understood terminology of architecture. In his Serlio editions he consciously did not translate the Italian volgare terms, preferring to use the Latin ones given by Vitruvius, as he explains in the preface to the second Flemish edition of Book IV:

The drawings in Die Inventie could also be understood both by the craftsman and the scholar, even one only moderately familiar with compasses and with Euclidian basics46: There was no secret knowledge involved in it, contrary to, for instance, Alart Duhamel’s prints. The booklet’s low price of only one stiver — one-fourteenth the cost of the Serlio translations, which were priced at one guilder — made it affordable. Conversely, expensive manuscripts on vellum, such as the Madrid model book, and folio-sized printed books with copperplate fold-out illustrations, such as the Lieferinck edition of Blum’s treatise, must have addressed chiefly the upper end of the market — the well-heeled collectors and learned dilettantes ‘who take pleasure in the buildings of antiquity’ and socially aspiring artists.47 Paradoxically, their notation system was more hermetical, necessitating experience with tools of the trade such as the compass, to be fully understood.