ALEX TZONIS / LIANE LEFAIVRE

Lines of Vision Lines of Fire

The Role of Analogy and Image Cognition in Designing the Renaissance Bastion

 

Visual thinking, alliance between painting and architecture, design history and psychology of architectural invention, interdependence of building and urban scales are at the heart of Eduard Sekler's œuvre. They are also leitmotifs in the present essay, a small token of appreciation for his great contribution.

The case at hand is the conception of the angular bastion, an important revolutionary event, about which one cannot but agree with J. R. Hale (1965) that it was the most original of all architectural forms invented in the Renaissance. Vasari wrote about it in Le Vite, crediting Michele Sanmicheli with having introduced it in his project for the Cornaro and S. Croce sections of the fortification in Padua. As opposed to the round configuration, Vasari remarks, the angular configuration of the bastion is efficient as well as effective. Most historians since, agreeing with Vasari's attribution to Michele or not, have continued to discuss the development of fortifications in the same terms, as a transition from the round to the angular bastion, limiting their search to the problem of who conceived it first and when. Fewer historians have tried to justify Hale's claim and explain the significance of this invention. Even fewer have tried to explain how this new important conception came about, and those who have usually invoked technological reasons, in particular the appearance of the cannon, for the emergence of he angular bastion.

This paper differs from most previous studies in its focus on the cognitive factors which contributed to the creation of the angular bastion. Shifting our attention away from military "hardware" has two results. It shows that the significance of the emergence of the modern bastion lies not in the new looks of the product so much as in the 'evolutionary aspects of the very design thinking that brought it about and the new programmatic imperative motivating the thinking mechanism.

Our investigation will demonstrate the function of image representation, and the use of precedent and analogy in creative design. We will look at how cognitive factors, hat is to say design thinking "software" -the conventions through which the problem If fortification was represented -, rather than military "hardware", contributed in the creation of the angular bastion and what the catalytic function of image representation, is in the use of precedents and analogy in creative design. We will finally suggest that this new fortification design had repercussions in architecture and urbanism which go well beyond the world of defense.

In order to study the angular bastion as design invention, as a cognitive phenomenon, we have to turn to the documents, to the drawing and texts employed in solving fortification design problems rather than to the material reality of the bastions themselves.

The Roots of the Problems

The first discussion of the angular bastion goes back to Vitruvius. His De Architectura contains a passage (Bk I. Ch. V) devoted to the fortifications of cities which will serve as a point of reference for centuries. Vitruvius sees fortifications as made out of two basic components, towers (turres) and walls (muri). He states that towers should be round or polygonal (rotundae aut polygonae) and not square (quadrata) (Fig. 1). The reasons for his rejection of the square shape is the fragility of its sharp angles when attacked by

military machines (machinae) as opposed to the firmness of the round surfaces (rotundationibus) under the same circumstances. As for city walls, they can be either round or polygonal, although he has a marked preference for the round ones for reasons which are no longer are structural but related to use. Round walls make the attacker vulnerable, while angles obstruct the defender and protect the enemy ("anguli pro current, difficiliter defenditur, quoud angulus magis hostem tuetur quam ivem"). In addition he believes that the round walls make the enemy visible from several sides ("Uti hostis ex pluribus locis conspiciatur"), that they have what we might call a panoptic potential.

From this sample analysis of the parts of fortification and their good or bad performance, Vitruvius goes on to discuss the relation between the parts. Towers have to project outside the line of the wall in order to protect it. The wall between these projections should not be more than a bowshot long, in case one of the towers is occupied. This will allow its neighbouring, unoccupied towers to attack it by means of scorpions and other ballistic engines.

Reversing the Vitruvian choice, a later Roman author, Vegetius, in his De Re militarii, prefers angular to circular walls. They are much better at defending against military engines. Several centuries later, Christine de Pisan, a poetess, philosopher, champion of the cause of women and theoretician of fortifications, taking the side of Vegetius in her Le Livre des Faicts d' Armes et de Chevalerie (written around 1408 [Book II, Ch. XIII]), recommends "crooked", angular walls.

 

Alberti's Contribution

The question of circular versus angular bastions is dealt with once more in a treatise written forty years after Christine de Pisan's, a text which has been very much underestimated in terms of its contribution to the new military architecture. This is Alberti's De Re Aedificatoria. It contains three chapters (Bk. IV Ch. IV, Bk. IV Ch. V, Bk. V Ch. IV) on fortification. These have been correctly criticised as disregarding the potential of fire arms (Horst de la Croix 1960, p. 34, J. R. Hale 1965, p. 477). The references to canons are indeed limited to the mention of "loop-holes almost at the very bottom of the wall" from "which the enemy is attacked by a weapon". On the other hand, De Re Aedificatoria has been unfairly criticised (De la Croix, 1960) as relying too much on classical writers. In fact Alberti attacks the authors of antiquity who "condemned all Angles for fear of weakness against military engines and of helping the enemy to hide" (Bk. IV, Ch. III) and, if he uses traditional Vitruvian concepts, it is in a new way. The difference is that he no longer sees curved and angular walls and towers as isolated objects to be examined and evaluated separately, but rather as hierarchical components of an integrated system, each part related to another and contributing interactively to an overall objective.1 This means that Alberti combines the Vitruvian imperative of panoptism with Vegetius' contention that the enemy is repelled more effectively if trapped between two angles (Bk. IV Ch. 111)2 (Fig. 2). To satisfy both points of view – the Vitruvian and Vegetian –Alberti proposes a new composite configuration: he gives to the round Vitruvian fortification an angular Vegetian outline. The overall fortification is thus inscribed in a convex shape, while its outline consists of a sequence of embedded concave "angle" units that Alberti likens to a "Star with Rays running out to the circumference" (Bk. V. Ch. IV) extending "like the Fingers of a Man's Hand". Thus, while the global convex shape helps the defendant survey every point of the region that surrounds him, the local concave parts force the enemy to be trapped "between two (projected) angles" (Bk. V Ch. IV).

In its higher systematic organisation, Alberti's heuristic scheme integrates fortification elements in a hierarchy of surveillance and defense: "the wall (is) defended by ...the towers....the towers mutually by one another," (Bk. IV Ch. IV) and all towers together by "one principal tower within the fortress built in the stoutest manner, fortified as strongly as possible, higher than any other part. .." (Bk. V, Ch. IV). Most innovatively the design is conceived not only as purposeful system but also – as much as it is possible to analyse it by relying on Hellenistic mathematics – optimal.3 This means that resources are allocated efficiently to minimize a negative state while maximizing a positive one. More specifically, Alberti chooses to inscribe his star-like fortification in a circle because it offers a pattern which is both "the most capacious of all, and the least expensive to enclose either with wall or rampart" (Fig. 3).

 

Alberti uses words to describe this new system. Design goals and means are explicitly stated. But the product is hard to visualise. For a visual description of this new formal pattern we have to turn to Filarete's Trattato (written c. 1460) and to Giuliano da Sangallo's Taccuino Senese, which show a multi-level hierarchy introducing concentric circles of defence, all panoptically controlled by a centrally located omnipotent tower. Of course what is gained in these drawings in terms of concreteness of the description is lost in expliciteness. The drawings tell us how to shape fortifications but not what for or why.

 

Francesco di Giorgio's thirty-eight Esempli in Disegno

Like Alberti's De Re Aedificatoria, Francesco di Giorgi's summa on architecture half a century later is a series of small treatises. One of these is devoted exclusively to military architecture (Fig. 4). The problem of designing a perfect fortification is seen here a subproblem of the general category of problems to develop an design system capable of minimising costs (simplicita, brevissima spesa, piccolo tempo, facilmente applicare) and maximising benefits (comodita, figura utile, più offesa fortezza, torrone perfettamenta quadrata). In other words, it is seen as part of the search for optimization. The systematic search for optimization comes out even more clearly than in Alberti's writings.4 Di Giorgio cites extensively, although not always accurately Aristotle's Metaphysics, Physics, Posterior Analytics and On the Soul. In addition his book is profusely illustrated, complementing and amplifying rather that simply commenting on the text. Consistent with what one might call laying bare the device of his own thinking, Franceso devotes part of the text to justifying the use of drawings and their indespensability in solving the problem of perfect fortification. The search for the appropriate representation to solve this problem also comes closer to completion than at any other time before.5

While up to that moment writings on military architecture had been loosely put together, Francesco's Quinto Trattato has a carefully articulated argumentation structure and it even contains an explicit discussion about the argumentation's own logical organisation (Di Giorgio 1976, p. 414). Stressing the limitations of abstract contemplation in dealing with complex problems that lead to an "infinity" of possibilities, Francesco brings in no less than thirty-eight concrete, extreme cases of alternative solutions, "examples in design" as Francesco calls them, described through words as well as through drawings.6

Far from being "doodles," as they have been occasionally referred to (Hale, 1965), these drawings are instances of problem solving. They are a series of systematically generated alternatives carried out with the help not of words or numbers but of figures. And in them, that is in the visual thinking they represent, Francesco comes close to designing the angled bastion. Close but not completely. He produces many solutions but no explicit procedure towards them.

What kept Francesco di Giorgio from inventing the bastion? What kept his predecessors from inventing it? The answer might be found in a drawing made by a famous friend of Francesco's and a great admirer of his writings on fortifications: Leonardo da Vinci.

Leonardo's Piramide Balastiche

Here, in one of Leonardo's sketches for the fortifications of Piombino (c. 1504), one observes the outline of a bastion covered by nervous strokes describing trajectories of cannon balls. These strokes, far from obscuring, enlighten. They disclose what made possible the invention of the angled bastion and, indirectly, what kept it from coming about.

We have already remarked how important Francesco thought visual representation was as a means of architectural thinking, as a way of grasping phenomena which otherwise would have remained unrepresented, thus incomprehensible. "Una lineae e una quantita visible" (Ibid., p. 445) he said. But lines in Francesco's esempli in disegno only describe built form.7 Leonardo's sketch, on the other hand, maps process, movement, operation in addition to built form. We see therefore two things represented in the drawing simultaneously: the outline of the bastion and overlayed upon it, the routes of missiles hurled from of shooting points. It is a composite representation, the likes of which are not to be found before. As such, it is a new way dealing with the fortification problem and a new design solution to the problem.

The development of this new representation, capable of simultaneously describing objects moving in space together with objects occupying space and of superimposing the first onto the second, is a "necessary" condition for the solution the fortification problem. Through this representation lines of fire express constraints beyond which the outline of a fortification cannot expand. Through this device the designer can search systematically now for a configuration which minimises costs of defense – number of weapons and defenders and cost of construction – while maximising surveillance. This method of visual representation makes it easy to "see" that if the wall deviates from the outline of the trajectories it will result either in blind spots, undefendable areas, or redundant defence turning the abstract problem to a concrete procedure. Hence the impression that one has, looking at the Da Vinci drawing, that the lines of fire running on the side of the walls actually shape the profile of the fortification. They "streamline" its outline as James Ackerman (1961) remarked about the drawings of Michelangelo carried out later for the fortifications for the Prato d'Ognissanti, or they "scrape" it down, as even later texts refer to this new concept.

How did Leonardo think of using this method to design fortifications? How did he conceive this complex representation system? Where did it come from? Why was it Leonardo who thought of it?

The obvious place to search for an answer to these questions is in Leonardo's drawings more specifically in the analogy between fortification and perspective drawing (Fig. 5). Just as in a perspective drawing there are visual rays ("razzi luminosi"), so in Leonardo's bastion drawing there are lines of fire. Just as in a perspective drawing the lineae occultae shoot out from the eyes, so in Leonardo's sketch lines of fire shoot out from the walls. Finally, as in a perspective drawing, the lineae occultae help trace the picture of the object on the paper, so in Leonardo's bastion drawing the lines of fire form the profile of the bastion.

An analogy also can be found to hold between the representation system used by Leonardo to shape fortification walls and the art of representing shadows. As in fortification design there is a point from which the ballistic lines originate, and as in perspective the visual lines are drawn from the place of the eye, so in "sciagraphia" the shadows of objects are projected from a luminous point. Sciagraphy has a "piramide ombrosa" the way perspective has a "piramide visiva", which in turn corresponds to the ballistic triangle defined by the two extreme fine lines in the Da Vinci drawing.

Through analogy, the representation system developed for perspective and sciagraphy is transfered to fortification, mapping familiar problems of vision into unfamiliar ones of ballistics, connecting objects and relations of explored domains of art and the terra incognita of the new war. Out of these connections it is possible to make explicit the constraints that implicitely underlie the fortification problem and to exploit them in a way that leads to an optimal solution.

 

As the "piramide ombrosa" identifies what is in the dark and what is in the light, and the "piramide visiva" what is visible and what is obscured, so the triangle formed by lines of fire indicates what is within the range of fire arms and what is outside of it, what is defendable and what is unprotected (Fig. 6). With this new method one is able to plot the outline of defense polygon which combines a minimum set of lines of fire without leaving any un- covered points outside the enclosing wall.

The solution to the optimal fortification problem was possible through the establishment of an analogy between the knowledge of perspective and sciagraphy on one hand and fortification design on the other which in turn depended on a more basic pre-existing analogy between lines of vision and lines of fire at the heart of the so called "ballistic" model of vision. This analogy was an old one. Lucretius (ca 55 B.C.) used it when he wrote that objects' "thrown off bodies" which then enter the eye and Hero of Alexandria (first century) believed that "just as a stone is violently hurled against a compact body. ..so the rays (from objects) ...are emitted". Alhazen (11th century) uses the same kind of analogy in the seventh book of De aspectibus between light and catapulted "iron balls," "thrown swords" or a "sphere fixed to the tip of an arrow".

Juring the early Renaissance the malogy becomes widespread and plays an important role in the development of the science of perspective and "sciagraphy". The drawing was perceived as resulting from the visual lines shooting from each point of the objects and: striking the eye after having pierced an imaginary plane on the way (Fig. 7). As Da Vinci says, echoing Alhazen, "the objects which are over against the eyes act with the rays like many archers" (Kubovi, 1986, p. 252) and, to quote Dürer's Unterweysung (1525), "eind durchsichtiger planus oder eben feld der all streymlinien durchschneidet" (Ivins, 1938) (Fig. 8).

The analogy was almost there, but it had to be thought of in a new way, reinvented, overturned. Rather than lines of vision being seen as lines of fire, lines of fire had to be seen as lines of vision (Fig. 9, 10, 11). And this was not easy. That Leonardo was the one to do it and in the process solve the problem of optimal fortification design is not surprising since he new representation emerged by analogy to perspective and sciagraphy and he was an expert of both.

 

From Invention to Routine

The bastion system invented by Leonardo is clearly illustrated for the first time in I quattro primi libri di architettura (1554) by Pietro Cataneo. It is the first book which prints the lines representing lines of cannon fire as determining the shape of the baluardi, the angular bastions. The first diagram (p. 11) shows a simple square plan. The side wall (cortina) is flanked by two walls which form the baluardi which in an angle defend the cortina by shooting the enemy from two sides. At the same time these two walls, the faces of the baluardi, are defended by fire shot out of the two ends of the cortina. As we can easily see, all the parts are now interlinked functionally, dimension- ally, morphologically, in a hierarchical pattern of optimal defense. In the new polygonal pattern emerging each point defends another in a such as manner as to eliminate undefended spots and redundant defences. In Cataneo's diagram the representation system, is clear and easy to apply. In addition the diagram is printed and mass reproduced. The bastion revolution is grounded solidly.

 

The book by Cataneo was the last to include both military and civil architecture on equal terms. Most writings on military architecture that followed leave out the latter.8

Specialised military writings contain a multitude of new fortification devices, the tenaille, ravelins, rondel orman, moyenau, lunette, ouvrage a comes, ouvrage couronne, contregarde. They also include explicit, detailed step by step procedures of "how to do it". These patterns and routines make military architecture increasingly more effective and more efficient keeping up with improving offensive weapons and changing general conditions of war. They originate from the angular bastion not as a form, but as a system of representation and design method.

 

The Imperative of Efficiency

But were the new system of representation of the fortification problem and the bastion born just of the exploitation of pre-existing knowledge? Could cognitive aspects have ignited the fortification revolution on their own? Or was it the improvement of fire arms and the growing power of siege artillery which started the process, a claim which has been stressed since the time of Diderot's article on fortifications in the Encyclopedie.

 

Of course the introduction of the cannon demonstrated that traditional fortifications created blind spots, undefendable areas. But such troubles had existed before the cannon. Military architects had tried to find ways to eradicate them. The cannon did not so much pose the problem as intensify it. We can repeat about the new fortifications what Weber said about the new systematisation of the army. The cannon was "the result and not the cause".

Can one say, then, that the angular bastion, like the systematisation of the army, as Max Weber claimed, was the result of the march of rationalization and the advance of bureaucracy, of the introduction of discipline and mental drilling? After all, there are many parallels between the two reorganisations. The systematisation of modern fortifications resembles, from the structural and organisational point of view, the manner in which the army, soldiers and weapons were arranged within a systematic goal directed framework. Hierarchical principles had been the backbone of Alberti's and di Giorgio's writings on fortification, but also of those of two major protagonists of the army's organisational revolution, Machiavelli's Arte della guerra (1552) and Justus Lipsius' half a century later Politicorum Libri Sex.

However the documentary evidence we have does not appear strong enough to support Max Weber's claim. There is no strong evidence that the systematization of fortifications were associated with the rationalization of the army beyond a few generalities. The abstract ideals of bureaucracy, hierarchy, subordination, articulation and order, although they increasingly dominate the design of fortifications, are not the overriding norms of the sys- tem. They are themselves subordinated to a higher one, efficiency.

Efficiency climbs to the top of the goal system of military architecture only at the time of Alberti, Francesco and Leonardo. And if we are to associate it to any major events external to the problem this is the rise of money economy which destroys old habits of life in peace or war – perhaps it is no accident that while di Giorgio is finishing his treatise, the Summa de Arithmetica by Luca Pacioli, containing the first published exposition of double-entry book-keeping, is being released (1494) – and the mounting cost of war. Being a soldier becomes a way of making money, a job requiring skill and specialization, both scarce resources. And as the mercenary soldiers comes to contemplate his payment with greater interest, his employer in turn becomes increasingly preoccupied with cost cutting schemes for this new war industry. The introduction of gunpowder in Renaissance warfare also raises the cost of war. The cannon introduces new costs, those of its own production, maintainance and operation. The Ordine del l'Esercito Ducale Sforzesco (Paret, 1986, p. 15) refers to these costs as disproportionately high in relation to the rest of war making. The cannon, like any other technological advancement in fighting, never becomes a cost saving device. In fact it raises the cost of war and occupies increasingly a more important position in the world economy. And by the middle of the 16th century the manufacturing of cannons becomes the most profitable proposition in the iron trade (Cipolla, 1965, p. 40).

Macroscopic social, economic or political changes, important as they may be, are not sufficient to make the mind create. They pose new problems but do not help to solve them. Any act of creation, including design, is the result of a dual cognitive process. On one hand there is the perception of the emergence of new imperatives – such as the imperative of economic efficiency – and of new constraints – such as the new constraints imposed by the technology of the cannon – which set up new problems and put into motion the search for their solution. On the other, there is the conception of new representation systems capable of exploiting these constraints and solving these new problems. And this was the case with the new representation system derived by analogy from precedent problems in perspective and sciagraphy which found the solution in the design of the angular bastion.

 

From Solution to Precedent

As with most human artifacts, a moment arrives when angle bastions become obsolete. The change in context within which war is carried out takes its toll. Soon after the end of the Ancien Regime, angularly bastioned fortifications ceased to be constructed. In many cases they even started to be demolished, giving way to public buildings and parks, playgrounds and highways. And those few which did survive become the object of tourist visits or, often, the hiding place of shelterless lovers.

This was the dawn of a new world, where fortifications were no longer needed. Here the money economy became even more widely spread and deeply rooted than during the Renaissance and the Ancien regime. The norm of economic efficiency spread across most aspects of civic life. Control and surveillance became priorities in a large number of cases of civic architecture, for buildings and urban complexes. Once more designers were compelled to provide the solution to a new problem. And once more the rules of intelligent thinking, the "ars inveniendi," heuristics, whispered to them: "Have you seen a similar problem? How does it relate to yours? Can you use precedent solutions? Think by analogy."

The time had come for the bastion itself to take the role of a precedent to help master the unfamiliar. And seems it was the bastion and not the Menagerie of Versailles, the anatomical theater, or the various therapeutic institutions, as has been claimed, which provided the precedent for the modern workplace, the productive building and the productive city. But unlike the case of the conception of the bastion in the Renaissance, where analogical had to transfer knowledge from two district distant domains, from vision to ballistics, the gap was shorter now. Innovation involved transferring structured information between two artifacts only, the bastion and the work place, architectural or urban.

As in the bastioned complexes, where the military engineers had started from the analysis of the parts of the fortress, linking each part to the other in a hierarchical way for the purpose of "continua vigilanzia," of omnipresent defence control, so in the new workplace, foremen and directors organised each department of production into networks of increasing inspection and super- vision, the flow of information between groups playing the same morphogenetic role the lines of fire had for fortification. But now the topology of panoptism was turned inside out. The workplace, the productive building and the city became objects of a surveillance that was "intramural" rather than extra muros. And, while the bastion was vanishing as an artifact in the landscape, it emerged a universal building metaphor on the horizon of the mind. But this is an altogether different story (Fig. 12).

 

Coda

The invention of the angle bastion in Italy around 1500 is indeed one of the most fascinating moments in the history of design thinking and one of the most intriguing examples of creative thinking on general. Its study helps us better understand key cognitive mechanisms, the significance of representation in problem solving and of the role of analogy in the conception of new artifacts. It also reveals the very unique of mental imagery and of the drawing. In addition, the study of the angle bastion in the mind demonstrates the cooperative links between the knowledge domain of the single building and the urban complex, each providing a harvest of design precedents bases for the solution of new target problems as needed. Finally investigating the design of the angle bastion sheds light into the darkness of the mind, offering a momentary glimpse of an unexpected complex figure, two bodies clasped tightly, inseparably, not in struggle but in a strange communion, that of Eros – Creator, and that of Thanatos – Warrior.

 

NOTES

 

1 Much before becoming preoccupations of military architecture associated with the fortification, the ideas of the systemic, the optimal, the hierarchical organisation of control and defence, the effective and efficient distribution of resources can be found in the phalanx and in the Tactics by Polybius shaping a formless (atakton) crowd into divisions of appropriate numbers (arithmon epitedion).

2 The angular shape suggested is probably transfered from the koilembolon, hollow-wedge formation of the phalanax (fig. 1c). (Asclepiodotus XI, 5).

3 The identification of the circle as the shape which combines the maximum surface for the minimum periphery goes back to hellenistic thinking to the formulation of the so called "isoperimetral" problems by Zenodorus and Pappus. It is contained in Pappus's Collection written down probably about A.D. 320. Pappus implies the economic application of his investigation in the eloquent preface of his proof. There he pays homage to the sagacity of bees and their talent to store honey in hexagonal hives "which would contain more honey for the same expenditure of material" and then proceeds to the "wider problem," and arrives at the optimality of the circle, a problem worthy of people who "claim they have a greater wisdom than bees".

4 "Membrification", hierarchisation means and ends, systematic interrelation of parts which play an important role in the book, are obviously a continuation of what Panofsky called (1957, p. 68) scholastic "mental habit' put into a new use. Di Giorgio in the highly Aristotelian methodological passage of his treatise refers to the philosopher as the "calculatore". This is most probably to acknowledge his debt to the medieval scholastic philosopher Richard Swineshead known also as "The Calculator," whose famous Calculations were published for the first time in Padua (1477) while Francesco was working on his treatise. One may safely assert that Scholasticism and medieval ideas of theology contributed to the erection not only of awesome cathedrals but also of formidable new fortifications. It is easy to demonstrate that Alberti's and di Giorgio's panoptic or periscopic fortifi- cation configurations, offering "continua vigilanzia," exploited a repertory of forms originating in worlds of divination and ritual such as the spatial schema of the omnipresent pantocrator radiating from his seat in the middle of the sacred rotunda, surrounded by hierarchies of archangels, apostels and saints.

5 Francesco di Giorgio's writings were not to be published until 1841 when Carlo Promis edited them in a incomplete form, and 1976 when Maltese published it in toto. In his short biography of Francesco di Giorgio, Vasari has noted that the Duke of Cosimo de Medici had a copy of the book which he considered among his choicest posessions and Leonardo da Vinci, who met Francesco di Giorgio in Milan and in Padua in 1490, probably owned the manuscript at that period, now in the Laurentian Library (Asburnham, MS. 361), and which Leonardo annoted in the margin (Pedretti, 1981). Leonardo also incorporated several passages extensively in his own manuscript treatise on fortifications which is included in the Codex Madrid II manuscript (1974, pp. 164, 198). Although unpublished, it is not exaggerated therefore to say that Francesco di Giorgio's writings were not unknown and to claim that he was the father of the modem fortification (Promis, 1841; Ackerman, 1970).

6 It is not by chance that one of the most important contributions to the fortification revolutions, di Giorgio's treatise, was written with the collaboration of Federigo de Montefeltro, the famous, most well-read condottiere.

7 In fact the closest Francesco came to designing the bastion is in another drawing – attributed to him – in the Gabinetto delle Stampe of the Uffizi Galleries in Florence. The drawing lies outside the corpus of the Trattati and although as a design product it "leaves little to be added by later military architects" (Horst de la Croix, 1960) it is too much of a fragment to be taken as evidence that Francesco found a physical design solution to the problem he had verbally so well stated.

8 See Daniel Speckle in Architectura van Vestungen (1589) (fig. 7a, b, c, d), Simon Stevin in De Stercktenbouwing (1954), written in Delft. Stevin's text is not very original but it is remarkably acute in its argumentation and its general observations. He had also a special interest in terminology. "As it is always for new arts" Stevin writes, "that one gives to new things new names", he proposed the word strijcken for aligning fortifications with five lines from the German Streichen (Speckle, 1589) or Italian strisciare, although Stevin retranslates the word in Italian as scopare next to the French nettoyer, in the border of his text.

In the same text Stevin explicity acknowledges the role of perspective in the genesis of the bastion. He identifies "fortresses of the present time" ("de sterckten deses tijts") as those which are "drawn most advantageously by mathematical methods through visual rays" ("wisconstich beleyt, met

 

sichtstraler opt meeste vooderelle gheteychkent worden", Stevin himself calls them on the border of his text "radi visualius"). He praises modern bastions (bolwercken) through which "one could destroy many soldiers without yet breaking one's head" based upon the perspective ("Doorsichtighen, ende met de wisconsten groote gemeenschap hebbende"). Strijcken oder strisciare of flanking as it was also called, could not shape a bastion on its own.

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