Vasari’s Lives of the Artists (1550) marked a significant change. He looked for the origins of perspective in painting practice of the thirteenth century. In his view, perspective arose as part of a general quest for naturalistic representation in art: "They sought to reproduce what they saw in Nature and no more, and thus they came to consider more closely and understand more fully. This encouraged them to make rules for perspective and get their foreshortening in the exact form of natural relief."

    Vasari noted the contributions of Giotto (1266-1377) with respect to foreshortening, while Giotto’s pupil, Stefano (1301-1350), "drew an edifice in perspective perfectly, in a style then little known, displaying improved form and more science." Vasari cited the work of Domenico Bartoli and Jacopo della Quercia. He claimed that Paolo Uccello’s Annunciation was the first painting to use perspective, rather than Masaccio’s Trinity as is often claimed in the twentieth century. Vasari explicitly suggested links between the use of ground-plans and elevations in architecture and early methods of perspective developed by both Uccello and Brunelleschi. In addition, he noted connections with the measurement of ancient ruins, as well as with marquetry, scenography and implicitly with goldsmithing. A complete survey of Vasari’s comments on the early history of perspective is found in Appendix 5.

    In the latter half of the fifteenth century, the origins of perspective became increasingly linked with mathematics. Piero della Francesca, in his Perspective of Painting, cited Euclid’s Elements and in his other two treatises, On the Five Regular Solids and Book of the Abacus, focussed on the construction of the regular solids, thus linking one of the major themes of the western mathematical tradition with perspective. His townsman (from Sansepolcro) and colleague, Luca Pacioli, developed this trend publishing the first treatise on perspective in his Summa of Arithmetic, Geometry, Proportion and Proportionality (1494) and by linking perspective explicitly with mathematical proportion in his Divine Proportion (1509). Dürer’s treatment of perspective in his Instruction in Measurement (1525) also took for granted this mathematical context.

    In the second half of the sixteenth century, a small circle of scholars at Urbino explored the mathematical principles of perspective in greater detail. For instance, Commandino (1559), linked perspective with Euclidean geometry and related it directly to Ptolemy’s work on the planisphere in the context of astronomy. His student, Guidobaldo del Monte (1600) pursued this approach. In the Netherlands, Stevin (1604), reported how the Prince of Orange was dissatisfied by the haphazard ways in which painters arrived at their foreshortenings and wished instead "to design exactly the perspective of any given figure, with knowledge of the causes and its mathematical proof." Paris and later London became the centres for this mathematical approach.

    Meanwhile, authors of perspective treatises were becoming interested in the question. Although, Serlio (c.1540) specifically stated that he chose not to discuss the origins of perspective since Euclid had done so, he emphasized the reciprocal importance of perspective for architecture since: "no perspective workman can make any work without architecture, nor architecture without perspective." Serlio also claimed that perspective was synonmous with what Vitruvius called scenography, "that is the upright part and sides of any building or of any superficies or bodies". Barbaro (1568) began his introduction noting that scenography was an important part of perspective; that Agatharchus had produced a tragic scene and written a first commentary on the topic; that perspective had been important among Roman scene painters and had become so again in the early Renaissance.

    A combination of these artistic and mathematical traditions was carried out by Danti (1583) in his commentary on Vignola. Like Barbaro, Danti also referred to the ancient tradition of scene painting as a source of perspective, but added a more compelling incentive for its origins: "if the marvellous operations of nature and art drew men so much to admiration that they began to philosophize and investigate the causes thereof, they rightly exerted themselves greatly in searching the reasons for the effects which happen at the eye through the variety of the visual rays."

    Hence, claimed Danti, artificers had sought to find rules and instruments with which they could imitate visual effects and appearances and he was concerned: "with the most scientific who are not content in simply knowing how to operate well and knowing that a thing is thus, but in addition to know its causes. Hence I have endeavoured to demonstrate all the principal parts of this geometrically." Danti aimed at reaching a larger group of readers than his contemporaries at Urbino but nonetheless cited various ancient sources: Aristotle, Euclid’s Optics as well as his Elements (in the editions by Peletarius and Clavius), Apollonius’ Conics, Archimedes, and Ptolemy’s Almagest. As a geographer, Danti drew on Ptolemy’s Geography. In optics his chief medieaval source was Witelo’s treatise. Danti also referred to most Renaissance authors on perspective from Alberti through to Stevin.

    In a footnote to this passage, Cassirer was content to cite Panofsky as evidence that perspective in the plastic arts was another manifestation of this phenomenon. For philosophers in the neo-Kantian tradition it was the origins of different kinds of space that was of central interest. In their view perspective was merely one of the practical consequences of this theoretical breakthrough.

    Meanwhile there had been developments on the philosophical front. Although Kant did not specifically discuss perspective he had emphasized space and time as a priori concepts. Hegel, Herder and Alexander von Humboldt pursued these ideas. Building on this tradition neo-Kantians in the late nineteenth century (e.g. Cohen 1889, 1912) claimed that there were direct connections between artistic work (künstlerische Arbeit) and scientific logic (wissenschaftliche Logik) and therefore viewed artists as researchers (Künstler als Forscher), as individuals who prepared the way for science. Cohen specifically cited the case of perspective: artists intuitively understood and drew spatial concepts before they were formalized. As we have just mentioned mathematicians held a similar view. Hence art now became a prefiguration of developments in both mathematics and science.

    The art historian, Panofsky (1914), took up these themes when he began his studies of Dürer. Renaissance art theory, he claimed, involved two major problems: accuracy (Richtigkeit) and beauty. Accuracy entailed a "geometrical-perspectival and empirical-scientific knowledge". He considered the problem of accuracy in greater detail in Dürers Theory of Art (1915). Accuracy, he explained, required representing objects "as they are", which varied according to the medium. In sculpture it entailed congruence of measured size. In painting it meant representing something equivalent to what is seen and this was precisely the problem of linear perspective. At this stage in his career Panofsky believed that one’s theory of representation depended on one’s theory of vision, and hence he searched for the origins of perspective in Euclid’s Optics.

    When Panofsky entered the Warburg circle in Hamburg (1924) he also came into the neo-Kantian sphere of Ernst Cassirer. According to this view there were two fundamentally different approaches to science: one emphasizing substance (and definition) which dominated Antiquity; a second emphasizing function (and relation) which evolved during the Renaissance. In Antiquity the focus on substance was linked with concepts of sensuous space: i.e. unhomogeneous and anisotropic (see below p. 63*). In the Renaissance the concern with function entailed mathematical space: i.e. homogeneous and isotropic. Other historians of science (Cohn,1896; Duhem,1909; Olschki,1924) referred to developments from Antiquity to the Renaissance in terms of a shift from a finite to an infinite world view. Art historians such as Riegl had postulated a parallel shift from depiction of isolated objects in Antiquity to objects in relation during the Renaissance. Panofsky produced a synthesis of these views. Hence he claimed that the Ancients had a finite world view which implied a notion of aggregate space (finite, unhomogeneous and anisotropic). By contrast, the Renaissance transformed this into an infinite world view with a concept of system space (infinite, homogeneous and isotropic). Corresponding to these were different methods of representation. Aggregate space led to a method of (visual-) angle perspective (Winkelperspektive). System space led to linear perspective. Now Panofsky claimed that one’s philosophical world view determined one’s concept of space, theory of vision and method of representation.

    There were problems with this seductive explanation. For instance, Panofsky claimed that in Antiquity a type of curvilinear perspective which he termed angle perspective produced fish-bone perspective. Veltman (1986) demonstrated that this was not so; that Panofsky had misunderstood the projection system he was using. Moreover, if ancient concepts of a finite world were responsible for Euclid’s Optics and angle perspective, then Euclid’s Optics could not be the source of linear perspective as Panofsky had claimed earlier. Panofsky was aware that Renaissance authors of perspective treatises cited Euclid’s Optics; assumed that Euclid’s fundamental premises must have been revised and cited the 1557 edition by Pena as evidence thereof. Panofsky did not explain why the concept of infinity which arose in the thirteenth century, produced a change in the theory of representation by the 1420’s yet supposedly only changed the theory of vision in 1557. If changes in the abstract world of ideas governed innovations in vision and representation why was it that empirical examples of perspectival practice were in evidence a century before the advent of perspectival theory?

    There were other difficulties. Panofsky implied that one world view caused one corresponding theory of vision and one theory of representation. The artistic evidence suggests that there were at least four methods of representation in Antiquity which supposedly emerged from their one world view and one theory of vision: 1) optical adjustments methods which represented things higher up as larger in order that they would appear the same size; 2) so-called fish-bone or axial perspective; 3) inverted perspective and 4) those Pompeian examples which approximate effects of and some have associated with linear perspective. In the case of the Renaissance this proliferation of methods was even more dramatic. For, rather than being replaced, the methods used in Antiquity were continued and in addition there emerged new methods of linear, cylindrical, spherical, conical and pyramidal perspective. The proponents of linear perspective so often projected images onto curved vaults and ceilings that it even becomes difficult to claim that linear perspective was the dominant mode during this period.

    Subsequent champions of Panofsky’s ideas did not remove these difficulties. For example, White (1949-1951, 1957) claimed that he accepted Panofsky, yet insisted that Pompeii showed evidence of linear perspective. If a given world view governs a particular method of representation then why should both a finite world view in Antiquity and an infinite world view in the Renaissance have produced linear perspective? White also claimed that the implications of Euclid’s Optics of Antiquity were the basis for Leonardo’s "synthetic perspective" during the Renaissance. Yet since this synthetic perspective was closely related to Panofsky’s angle perspective, why should a method associated with a finite world view in Antiquity have been developed in the context of an infinite world view during the Renaissance?

    There were further problems with this approach to the origins of perspective. Panofsky relied on Cassirer’s framework which assumed a basic dichotomy between finite and infinite and provided an elegant contrast between Antiquity and Renaissance. The dichotomy was questionable to begin with, for it could be argued that notions of vision and representation in Antiquity were too nebulous to identify a single theory, whereas in the Renaissance there were clearly alternative methods of representation, namely linear, cylindrical and spherical perspective and anamorphosis, such that one could not claim that one world view evoked one theory of vision and representation. Was one to assume, moreover, that there had been no developments since the fifteenth century? If this still seemed feasible in the 1920’s, it was no longer possible in the 1990’s with advanced quantum physics, fractals and catastrophe theory.

    Panofsky’s attempt to find the origins of perspective in philosophy and metaphysics may excite more general attention than precise reflection, but it has helped more than any other text to make questions of origins of perspective important in the twentieth century. The answers offered have ranged from incidental remarks to complex theses. Since many are repetitive it will suffice to mention only some of the key examples. Kallab (1900) argued that Christian symbols as they developed in the later mediaeval period required perspective to a certain amount. This idea was taken up by Kern (1912) who searched for the origins of perspective prior to Brunelleschi in the painting practice of Lorenzetti and suggested links with Ptolemy’s Geography. Later Kern (1938) also suggested that the origins of perspective lay in mathematics and optics, both classical (Euclid) and mediaeval (Witelo). Malle (1960) suggested literary, philosophical and mathematical roots.

    Argan (193), in an influential article, explored the idea that perspective had its origins in a new concept of space in architecture with Brunelleschi. Francastel (1951) used this as a starting point for one of the most eloquent interpretations of Renaissance perspective. He claimed that Brunelleschi introduced a "new aesthetic conception of space....space ceased to be the cube of air that a vault covers; it possesses an homogenous quality and is found everywhere. it is at once container and contained; it envelops and is enveloped." Francastel insisted that Renaissance perspective had enormous consequences after noting that it was a:

fundamental discovery, which concerns the particular qualities of light - an invisible substance, but susceptible to let itself be measured and manipulated by the artist, inspired not only the idea of a new architectonic functionalism but also a new system of pictorial space to be elaborated. Brunelleschi is the man who substituted the plastic evidenc eof the Middle Ages founded in stereotomy, the size and assemblege of blocks and the manipulation of enclosed light, the necessity of another compartmentalization of space, in a system which reproduces a sort of imaginary model but which allows all the regions of space to communicate amongst themselves....

It is not only a new architecture and a new [style of] painting that resulted, but a new society and almost, materially speaking, a new world. The integration of concrete and subtle parts of the physical universe, the faith in the magic of number, prepared the discovery of America, and the new jurisprudence founded on the equilibrium of the States.

    Exactly how all this followed was not explained. Instead, Francastel offered his own provocative survey of the history of perspective from the fourteenth to the twentieth centuries (see below p. 52*). In his concluding section he cited the ideas of Levi-Strauss and insisted that "Scientifically there is no doubt that the art of an epoque is greater than the literary expression of a society: it is founded on the most profound mental and physiological structures of man. It is not asuperstructure, but a language". Francastel developed this analogy of language and art in his Figure and place. (1967) and suggested that seeing was deciphering.

    Boskovits (1962), claimed that the origins of perspective lay neither in vision nor in geometry, but rather in the auxiliary sciences of mediaeval architecture, in workshop traditions; in problems concerning the correct representation of architectural proportions; that perspective involved the geometrical representation of proportions which link one object with another. Hence Ghiberti had insisted that measures were inherent in nature and hence symmetry, proportion, proportionality and commensuration were all linked with the early development of perspective in the Renaissance.

    Garin (1954), turned to the scientific and cultural atmosphere in his search for origins and argued that Leonardo’s interests in optics were more important than his interests in geometry. In the next decade it became the fashion to see optics as a key to the origins of perspective. Parronchi (1964), focussed attention on mediaeval authors, notably Alhazen, Witelo, Bacon, Peckham and Blasius of Parma. Edgerton (1967), also claimed that mediaeval optics was the main source for Renaissance perspective. Dalai (1968), cited both Sanpaolesi’s attention to physiological optics and Parronchi’s twin focus on mediaeval optics and mathematics (e.g. Leonardo Pisano). Dalai also suggested that there were two lines of development: one which had come via Brunelleschi, was based on concerns with reflection and which, though it involved architectural practice and Ptolemaic geography, was concerned primarily with laws of mirrors. A second line of development, based largely on mediaeval sources advanced via Ghiberti and Uccello. Battisti (1971), stressed that Florence was not the only centre to be considered; the Flemish school of Van Eyck had played an important early role, as had other Italian cities including Milan, Padua and Rome. Edgerton (1978), offered an important summary of alternative explanations for origins, suggesting that there were no less than four traditions to be considered: optics, geometry, geography and metaphysical theology. Veltman (1980) noted that in terms of perspective, Ptolemy’s work in astronomy, namely his treatise on the Planisphere, was probably more important than his work on geography, an idea which has been pursued by Aiken (1986) and Sinisgalli (1993).

    Fernande Saint-Martin, in The Topological Foundations of Painting (1980), devoted a chapter to Euclidean space. She claimed that perspective was very much an occidental phenomenon which had (119): "established an essential break in human sensibility such as it was expressed in the pre-history of nearly all other cultures". She acknowledged that many saw it as the ultimate product of sensibility and rationality and that it was an attempt to deal with problems of depth, of foreground and background. She cited the ideas of Gleizes and Metzinger that the space of painters would preferably be Riemannian rather than Euclidean and called for a wider definition of the term (124): "By the term perspective, rather, one should understand every global system which defines the modes of interrelations among the collections of elements, in accordance with certain a-priori co-ordinates." The term Euclidean perspective, claimed Saint Martin, was misleading because it was not based directly on Euclid. Rather, perspective as it developed in the Renaissance, had only been possible as (127): "a result of a sort of transubstantiation of the sensible intuitions subjected to the elements furnished by Euclid, stripping them of their finite and concrete character to permit them to integrate themselves in much more abstract systems of interrelations."

    Saint-Martin cited Doesschate (1964) to note that there was no clear evidence that Alberti or Piero were familiar with Euclid's geometry and followed Edgerton's (1975) claim that it was spatial co-ordinates of Ptolemy's cartography that provided (128) " the fundamental elements in the spatial infra-structure of the Renaissance". The resulting space corresponded neither to the experience of the senses nor to the findings of science concerning the nature of reality. Hence (129) "homogeneous space is never a given; it is a space engendered by a construction". According to Saint-Martin (132), it was Alberti who introduced the vanishing point although, she claimed, it was not until Leonardo that a majority of fifteenth century artists began adopting perspective. In contrast to some historians who have seen the rise of perspective mainly in positive terms, Saint-Martin was convinced that perspective imposed new limitations on western culture (134):

Euclidean perspective imposes a particular hierarchy of emotive experience where the projection of the me in the foreground, the mass, the vivid colouring is at once negated by its insertion into an abstract system where the distant imposes itself as the limit, the end, the point where the co-ordinates of particular experiences join. This forced equilibration always remains an artificial model of the experience of the me and the non-me, because it tends to deny the expressive validity of the near which will inevitably only constitute a stage in a passage towards the far. It also denies the distant itself, by the impossiblity of affirming it by pictorial means themselves, which shrink it to render it nearly imperceptible, which hide it in zones of shade or confused atmospheric pockets, or alternatively bathe it in a diffuse luminosity. Inside this fixed schema, with irremovable boundaries our civilization would like to confine the representations that a person can give of their experience -of me -in the world. It is certain that the survival of artistic activity is linked since the last century with a continuous battle more or less overt but definitive nonetheless, not just against the primacy of the figurative image but in a more essential way in favour of a resourcing, a peremptory reaffirmation of pre-Euclidean spatial experiences at the level of primary forms and topological relations.

    Johannsen and Marcussen (1981), in an important article, explored the role of several disciplines in explaining the origins of perspective: optics, measuring (including surveying) and statics, geography and astronomy as well as the cultural background of early fifteenth century Florence. Five conditions necessary for the construction of perspective were identified: 1) use of a visual pyramid as a geometrical model of the visual process; 2) a plane corresponding to the picture plane; 3) proportionality between the size of an object and its dimensions on the picture plane; 4) a graphic representation; 5) projection methods. Veltman (1986) focussed on the third of these problems, the question of plane thinking, and suggested at least five traditions which helped in this development: geometry, astronomy, architecture, surveying and optics and has since claimed (1992) that all of the above mentioned traditions played some role. Meanwhile Andrews (1988) and Veltman (1992) have emphasized the importance of narrative for the development of pictorial perspective.

    Simon (French, 1988; German, 1991), in a book that focussed on the optical theories of Euclid and Ptolemy, examined the possible consequences thereof for representation. Following the view of Panofsky, Simon (1991, 79) suggested that the fourth postulate of Euclid’s Optics entailed curvilinear rather than linear perspective. Consequently, he claimed, Renaissance theoreticians were torn between two conceptions of perspective, an artificial (künstlichen), plane one for painterly representation and a natural, angle based one for optics. He went on to suggest that (79-80): "the still limited character of their trigonometry" might help account for "the lack of rigour in the perspectival drawing of the Ancients." According to Simon (84): "The analysis of visual perception was doubtless not yet sufficiently advanced in order to be able to distinguish clearly between the description of natural vision and the experiences of perspectival representation."

    Salvemini (1990) offered new criticisms of Panofsky, claiming (60) that his method was a transposition of ideas of pure visibility of the late nineteenth and early twentieth centuries to the past, that was not supported by historical evidence. His method of iconographical analysis was wrong because it (62): "constantly reduces to a schema all that which is not demonstrable extensively through the lack of concrete sources." Salvemini claimed that the inverse size/distance rule was known to Levi ben Gerson,and used this as a starting point for another attack on Panofsky's method (73):

Propositions are demonstrative, they assume the form of a question (quaestio), which is the literary form of the mathematical theorem in which the concepts are not logistic as in contemporary theories of physics....This measure of distance will therefore be neither fixed, nor arbitrary, nor casual nor objective, nor subjective but rather an independent variable.To recognize this general rule in itself does not mathematicize empirical space any more than the perpendicularity of the optical axis geometricizes the visual image.

    Elsewhere Salvemini lamented (97) "the material impossibility of establishing a typological model for perspective studies."

    Kemp (1990), offered three principal reasons for the origins of perspective: a) that the systematic recording of visual phenomena should be seen as a worthwhile goal; b) that the invention should be attainable in terms of the necessary levels of understanding and skill and c) historical factors ranging from the most general aspects of what may be called the world view to the specific circumstances (intellectual and social) of the individual or individuals involved. Kemp noted his intuition (335):

to emphasise the striving for ‘domestic’ naturalism in religious art in response to new kinds of devotion as a necessary background condition for the notion that an illusion of how things appear was desireable. A key stimulus in determining that a precisely proportional system was used, rather than the highly effective but essentially non-mathematical method of Jan van Eyck in the Netherlands, was the annexing of classical aesthetic values, particularly the proportional system of architectural design and town planning. By contrast, mediaeval surveying and optics can be seen to provide available resources, but these resources only became relevant to the painter within a framework of new assumptions about the functions of what we call art.

    Edgerton (1991), returned to these questions of the origins of perspective in The heritage of Giotto’s geometry. Edgerton drew attention to a series of unpublished lectures by F. Cranz (1984) in which he had characterized the re-orientation of the twelfth century as a shift from conjunctive to disjunctive thought: i.e. from an assumption that one was a part of everything that one considered to an awareness that what one sees in one’s mind differs from things in the external world. According to Cranz, Anselm and Abelard had played an important role in leading philosophers to understand themselves (40): "as detached from nature, as outside observers limited by the inadequacy of their mental formae and describing phenomena only metaphorically". Edgerton suggested that the recovery of ancient texts of geometry would have (41) "complemented this increasing twelfth century predilection for disjoining the forms in the mind from the forms in the external world". Edgerton focussed on the importance of Bacon’s views citing in particular a passage from his Optics that stressed the importance of visualization using figures (88):

For without doubt the whole truth of things in the world lies in the literal sense, and especially of things relating to geometry, because we can understand nothing fully unless it is presented before our eyes in figures, and therefore in the scripture of God the whole knowledge of things to be made more certain by geometric figuring is contained and far better than mere philosophy could understand it.

    In his book Edgerton outlined the geometrization of pictorial space, supernatural space, terrestial space, heavenly and astronomical space, emphasizing the importance of sixteenth century printed books in the spread of these principles. With respect to the actual origins Edgerton claimed that there were two serious interpretations, one claiming (89):

that Brunelleschi’s two lost pictures were but the latest examples in the gradual evolution of Western art toward realism, incremented by some sort of application of traditional architectural or surveyor’s projection....The second opinion - more revolutionary in the sense of a classical revival- holds that Brunelleschi was inspired less by architectural and surveying technique than by the ancient science of optics....Brunelleschi seems to have exploited an optical theory never applied to painting before, that the implied eye level of the artist/observer must determine the centric point on the picture surface and therefore the horizon within its fictive depth.

    Edgerton did not discuss the possibility that Renaissance optics had in fact integrated essential aspects of the surveying tradition (cf. Sources, p. 142-154*). He returned to his earlier (1975) claims that a third method of cartographical projection attributed to Ptolemy had also played an important role in what he claimed to be the re-discovery of perspective. Notwithstanding, these points on which we disagree, Edgerton’s book is an important attack on fashions in critical theory and methodology that reduced perspective and chiaroscuro as (4):

artificial systems within a linguistic-like sign system expressing the peculiar values of western civilization. Radical supporters of this latest relativism ("multiculturalists" as they like to call themselves) argue that during the Renaissance, upper-class patrons championed linear perspective because it affirmed their exclusive politicial power. Single viewpoint perspective after all, encourages the "male gaze", thus voyeurism and the denigration of women, police-state surveillance and imperialist "marginalizing of the other".

    Piaget had identified five stages in the development of a child (see below fig. 57 and p. 139*). Gablik was able to reduce these to three essential stages. First, there was a pre-operational stage (eighteen months to four years in the child), involving topological relations of space, an enactive mode of painting, and corresponding to ancient and mediaeval art in terms of cultural development. Second, there was a concrete-operational stage (six to fourteen years in the child), involving projective and Euclidean relations of space, and an iconic mode of painting, corresponding to the Renaissance in terms of cultural development. In this model, linear perspective was characterized by the static viewpoint of a single observer and separation of observer and the world. Third and finally, there was a formal-operational stage (above fourteen years in a child) involving indeterminate, atmospheric space, a symbolic mode of painting, and corresponding to modern art in terms of cultural development. In Gablik’s view (12,31):

These stages in the development of art correspond to learning processes and to transformations in concepts of self and society (fundamental transformations, that is from one picture of the world to another)....I wish to assert that it is the transformational element in thinking that is actually the source of art’s development. It has led pictorial imagery on the one hand toward greater mobility; on the other, it has brought about a complete independence from figurative or representational elements.

    Gablik served as a point of departure for a more serious treatment of these problems by Blatt and Blatt (1984). According to their view the tradition of Kant and neo-Kantians such as Cassirer had led to structuralism which attempts to (39): "define principles and cognitive structures that underly all human intellectual endeavors....This search for the underlying, unverbalized (unconscious) order in cognitive endeavors is a quest for the identification of the basic constructs through which individuals understand and organize their universe". The Blatts cited evidence from a whole range of disciplines, to claim that such cognitive schemata had been used to understand neurological processes, memory, perception, information processing, linguistics, social order, structural anthropology, psychoanalysis and the development of children. They related this quest for structure to the search in art history for a (39) "vocabulary of form", "a matrix or scale of structured relationships" and a larger quest to discover (40) "basic relationships of form and their processes of transformation", which they termed mental constructions, "cognitive schemata, patterns or gestalts". They claimed that these conceptual explanations had replaced traditional perceptual explanations.

    Gablik had specifically challenged the perceptual views of Arnheim and the Gestalt school. By contrast, the Blatts accepted the Gestalt school as yet another example of a quest for structure which had been making serious strides since the time of Kant. Historically, Kant himself had been very much concerned with the ways in which knowledge acquired through our senses affected our ideas. The Blatts did not mention this. Historically, there had been notable differences in the approaches of Kant and Hegel in this regard. Hegel was not mentioned in the Blatts’ account. Historically, there had been major differences in approaches to knowledge which psychologists have classed as a struggle between nativism and empiricism (see below pp. 60-61* and fig. 10). The Blatts’ account gave the impression that nativism was the only valid school.

Fig. 1. Parallels between concepts of space, object, and scale, periods in art history and cosmological world view from the time of the Greeks to Impressionism according to Blatt and Blatt (1984).

    In terms of art history, the Blatts used Piaget as a starting point. Piaget’s sensorimotor and pre-operational levels were used to cover paleolithic and Egyptian art. Piaget’s intuitive level was renamed an intuitive (perceptual) level, linked with projective-Euclidean concepts of space and used to explain the time span from Greco-Roman art through to the early Renaissance. Piaget’s concrete operational level was linked with further developments in projective-Euclidean concepts of space, with the period from the late Renaissance to Impressionism, with the Copernican and Newtonian world views and with Stevens’ concept of interval scale. Various steps of each stage were carefully identified (e.g. fig. 1).

    Such schemata which appear to explain the key developments of man’s intellectual and cultural development since the beginning of time in four pages of charts are very seductive. Unfortunately they explain less than they seem. If art from the Greco-Roman period, the Middle Ages and the Early Renaissance belong to the same stage of development how does one account for the rather remarkable differences in style between these periods? Are nearly one thousand years of mediaeval art simply to be explained away as equivalent to a slight regression or progression in the growth of a child? If we accept parallels between cultural growth and child development as true, we are accepting that the greatest achievements of Antiquity correspond to the activities of children between the ages of six and nine and similarly that the heights reached by Leonardo, Raphael and Michelangelo in Renaissance art correspond to the development of persons under the age of twelve. Indeed this view reduces the whole of human culture rather dramatically to various stages of puerile (or puellile) activity.

    There are further problems. Piaget’s claims were based on experiments with Swiss children in the 1940’s, and as subsequent critics have pointed out, these were mainly male children. An obvious question arises: would the spatial abilities of Swiss girls at the time have been the same? More fundamental for our purposes is to ask why this particular sample in a particular place and time should be a model for the whole of history? A child living in Egypt in the eighteenth century B.C. before the discovery of perspective would obviously have reached neither projective-Euclidean concepts of space nor a concrete operational level of objects by the age of eleven nor at any point in their lives. Nor would Renaissance children have mastered Riemannian space at the age of twelve or during their lifetimes.

    While some scholars have gone to considerable pains to distinguish clearly between the rules of grammar applicable to verbal language and other rules in visual language (cf. Saint-Martin, Sonesson), there has been a trend in Russian authors to conflate analogies between language and painting (e.g. Uspensky, see below pp. 51-52*). Damisch followed this Russian structuralist tradition, drawing on analogies of Jakobson (386) "between the role of grammar in poetry and the rules of composition founded in the art of painting on a geometrical order either latent or manifest." Damisch discussed painting in terms of reading, not just a process of describing in the sense of Alpers, but rather as something demonstrative which creates a system. Like the neo-Kantians, he suggested that this system did not derive from geometry but rather prefigured its later developments. Like Husserl, he was interested in the metaphysical or at least the meta-logical implications of these spatial developments. Like the structuralists he continually referred to grammar, but ultimately assumed a combination of geometry and language (406):

In the historical context where we are placed, artificial perspective furnished painting with a formal apparatus such as that of enunciation can be, with which it presents numerous common traits. To begin with the distribution which it organizes of points of view, vanishing points and distance points, and (the corollary thereof), that of the here, the there and the over-there, which allows one to speak, not yet in a metaphorical sense, of a geometry of enunciation which would have its analogue in the figurative register....The enunciation cannot be assigned simply to the network of pronouns and indices of position in time and space. The formal apparatus which puts in place the perspectival paradigm is the equivalent to that of enunciation to the extent that it confers a sense to its direction at the same time that it opens the possibility of something like an enunciation in painting. As Wittgenstein writes, the word is nothing other than a point, the proposition is a vector endowed with a sense, that is too say with a direction.

    In itself this phrase is not particularly dramatic, but it is symptomatic of a branch of Marxist rhetoric which uses a scientific phenomenon as its starting point, interprets it metaphorically, usually socially, such that it completely loses its scientific truth, yet by association with the scientific principle from which it departed takes on an air that is more serious than it deserves. In the hands of enthusiastic commentators this particular sentence has become seen as serious evidence for undermining a one-to-one correspondence between original objects and their images, and has come to play a role in a trend towards anti-ocularism (cf. below p. 215*). A physical phenomenon treated metaphorically has become a starting point for claims about social realities. Debord (1967) extended this approach from a particular image to the concept of spectacle, now denying the physical to emphasize the social: "The spectacle ‘is not a collection of images but a social relation among people, mediated by images. It is the material objectification of alienated socioeconomic relations, the "true reflection of the production of things and the false objectification of the producers.’

    Abels (1982), drawing on ideas of Marx and Holzkamp (1976), considered a developmental approach in which perception and representation became functions of class levels and other societal structures. Goldstein (1988) presented a thorough Marxist analysis which offered the most daring explanation thus far for the origins of perspective. Goldstein began with a critique of Panofsky, Cassirer and Edgerton before arguing (25):

that the relationship between linear perspective and the new cosmology of the renaissance is one of parallelity since both are different representations of an emerging social structure, namely, modern capitalism. Further, the various cultural activities, such as music, drama, prosody and the like are representations of the new production relations; they are parallel precisely because they are representations of one and the same social base.

    Goldstein was concerned with three aspects of linear perspective: first, that space is quantifiable and homogeneous. In his view this was a result of divided labour production because it transformed traditional artisan labor (63):

into unskilled, undifferentiated, homogenized labor. When labor becomes homogenized in fact, it becomes homogenized in concept: it becomes labor as such. The cost of such labor can now be calculated and expressed in terms of expenditure of energy and duration of time....Labor thus becomes quantified....The attitude of calculation spreads as an indispensable part of the new mode of production to all areas of culture, science included.

    This was restated more forcefully when he claimed that the source of quantification lay (73): "in the experience of divided-labor production whereby unskilled labor can and indeed must be regarded as labor as such, homogenized and then divided into time units which can then be multiplied by the rate of reproduction of the worker which is set at subsistence level, which is itself a mathematical calculation".

    One problem with this explanation as he himself admitted (73) "is that it places divided-labor production earlier than any empirical evidence would appear to justify". This question of periodization became the more acute when he turned to what are supposedly corresponding developments in other branches of culture, notably (109) polyphony in music (c.900-1050) and in prosody (110) "the development from alliterative form to accentual-syllabic in the period between the ninth and the thirteenth centuries." If there is a unity of cultural expressions as he claimed then why did perspective not emerge in Carolingian times rather than the Renaissance? And what evidence is there of divided-labor production at the time of Charlemagne? None.

    There were further problems. Goldstein assumed that this new phase entailed a loss of artisinal skills and the rise of unskilled labor. Why then was it precisely in the Renaissance that there was a dramatic development of books on specific trades of which the Book of Trades (Ständebuch) of Jost Amman was the most famous? Or why should Vasari, who was the first to document the rise of perspective, take such pains to emphasize the particular professions and trades of those responsible, be they painters, sculptors, architects, or goldmiths? Indeed was there not serious evidence that the Renaissance saw a new self-consciousness in this tradition of skilled artisans and was it not they, rather than their anonymous unskilled counterparts, who were responsible for the great achievements of pictorial and architectonic space? How else are we to explain that so many Renaissance masterpieces were produced by well known, well trained artisans? What happened to the supposedly revolutionary achievements of the anonymous unskilled?

    The second aspect which interested Goldstein was that physical space is continuous, isotropic, material, three-dimensional and infinite. Here he drew on Marx’s concepts of alienation (Entäusserung) and estrangement (Entfremdung) to claim that (35-36):

the objectification of nature takes place not because labor is alienated in the product, but because under conditions of private property the product is estranged from the producer: the product becomes a commodity....Under conditions of estrangement as it occurs in commodity production, the human being regards nature as an object, distanced and opposed to him, so that space is conceived not as a closed system of which nature is a part, such as we find it in organic conceptions of nature, but as a void within which objects move and which extends in all directions without end. It is a three dimensional infinite world; it is at the same time a mechanistic world.

    In developing these ideas Goldstein also drew on the views of Ruben (74):

The concept of infinity develops as part of a process in which the organic community dissolves and the emphasis is placed on the individual. What is lost in this process is the well defined place of the individual in feudal society as against the indefinite place of the active property owner. It is the transition from immovable property in land to the moveable property (i.e. money itself, tools, commodities, etc.) that generates the new conceptions of time and space. With respect to space, since the individual as property owner has greater potential for movement, his sense of his own movement changes. He conceptualizes his activity as the free movement of a body in absolute space (and time).

    Goldstein reformulated this idea in his own terms (147):

Divided labor is labor coordinated around a machine, so that interdependence in the production of goods is visualized as spatiality. The living experience of co-ordinated undifferentiated labor centered around a machine is visualized as geometrized space in the form of a three-dimensional drawing or a new cosmology, geometrized physical space within which bodies move subject to constant universal natural forces, so that their motions and relationships can be expressed mathematically in equations. In perspective drawing objects diminish in size in proportion to their distance from the viewer: the view is that of a quantifying, geometrizing, mechanizing mentality which is specific to capitalism.

    Here again there were problems. Goldstein claimed that the separation or estrangement of worker from the products of his work caused the distance necessary for a new concept of space. Yet the painters who produced the early works of perspective were precisely those who were not estranged from their work. Artists such as Brunelleschi, Ghiberti and Uccello received commissions and were rewarded for their efforts. Ruben’s assumption that community needed to dissolve for individuals to emerge, was equally misleading. Were not many of the key artists in the Renaissance members of guilds and very much members of their local communities? The notion that mobility generated a concept of space is intriguing. It is true that Brunelleschi went from Florence to Rome and that the author of the first printed French book, Jean Pélerin, was called the pilgrim (le Viateur). But why then were the earliest spatial paintings not done by ancient soldiers or mediaeval pilgrims? Money is spoken of as one of the universalizing elements. This is only partly true since each major town in the Renaissance usually had its own currency as well as its own measures. Whence equivalences through money were by no means as universal then as they are today in a world where credit cards offer a standard.

    A third aspect which interested Goldstein was that perspectival pictures depend on vision of a single pair of eyes viewed from a fixed position. Here he claimed that the rise of individualism, particularly the individual entrepreneur of capitalism, was the source of one-point linear perspective. As he put it (83):

The painting rendered in terms of linear perspective is no less an expression of the bourgeois individual. In such a picture the view presented is, as we have seen, that of a particular pair of eyes, in a particular position, and at a particular time, so that nothing is seen but what the viewer can rationally see. It is the high valuation set on the here and the now that finds expression, the practical realism of the bourgeois-rational, ahistorical and hence, static.

    In itself Goldstein’s association of the capitalist’s viewpoint and one-point perspective is attractive, but becomes confusing in the context of his other arguments. For he also claimed that the concept of homogeneous space necessary for perspective was created by the estrangement of unskilled workers. If the victims of capitalism had this new insight why was it not they who produced the consequences rather than their exploiting entrepreneurial capitalist employers? If the employers could get these insights without their employees, why then should one emphasize a move towards unskilled production? Indeed if unskilled production was so important in this context, why then was the development of perspective linked with the rise of artists’ guilds, academies and eventually schools of drawing? Suppose we accept that both sides of Goldstein’s arguments are important, namely, employers and employees. Why then do Brunelleschi’s first two examples reflect neither a capitalist viewpoint nor unskilled workmanship? Moreover, why are most of the early examples of perspective in an ecclesiastical context and linked with sacred narrative rather than reflecting the new modes of production which were presumably the source of their inspiration?

    Notwithstanding the logical and other contradictions in Goldstein’s approach, subsequent commentators such as Jay (1994) have cited his work as if it were authoritative. Jay, whose work is discussed at length below (p. 215*), related these claims (59) to Williams’ (1973) contention that "only the exaggerated capitalist separation of the spaces of production and consumption permitted a radical disjunction between the working the land and merely viewing it from afar as an aesthetically ‘pleasing prospect’, which was the real estate form of perspectival art." The problem with this reasoning is that a separation of landowner and worker was well established in Egyptian times and continued trhoughout the Middle Ages. Witness, for instance, the Duc de Berry and his Very rich hours (Très riches heures), who must have been very conscious of this distinction in the fourteenth century, even before linear perspective in its technical sense had been discovered. Jay went on to surmise that (59): "The placement of objects in a relational visual field, objects with no intrinsic value of their own outside those relations, may be said to have paralleled the fungibility of exchange value under capitalism", without offering any serious evidence by way of proof.

    Ivins served as a starting point for Marshall McLuhan’s more dramatic claims in the Gutenberg Galaxy (1962, 56): "primitive drawing is two dimensional, whereas the drawing and painting of literate man tends towards perspective". McLuhan remained unclear concerning the precise relationship between perspective and printing. On the one hand, he argued that (138): "the sheer increase in the quantity of information movement favoured the visual organization of knowledge and the rise of perspective even before typography". On the other hand, he suggested that typography was actually a prerequisite for perspective (138): "As the literal or the letter became identified with light on rather than light through the text there was also the equivalent stress on point of view on the fixed position of the reader: "from where I am sitting"....This uniformity and repeatability of typography...is the necessary preliminary to unified or pictorial space perspective ".

    These connections became part of a larger set of basic oppositions that guided his work. There was, he claimed, a basic distinction between the tactile and the visual; between acoustic space and visual space; or between the audile/tactile and the visual. Acoustic space was linked with the two dimensional: visual space was linked with the three dimensional. Visual space was linked with the linear, sequential, print oriented space of continuous vistas and perspective. Whereas acoustic space was analogical, visual space was logical. McLuhan related this to changing emphases on parts of the trivium. Acoustic space thus became linked with rhetoric, visual space with dialectic (i.e.logic). By 1976, McLuhan was relating these oppositions to his claims about the right and left hemisphere of the brain. The right side of the brain was acoustic: the left side of the brain was visual. The right side was simultaneous, qualitative and intuitive. The left side was linear, quantitative and logical. These oppositions he subsequently related to his distinction between figure and ground. Figure, he claimed is visual, conceptual and deals with ascribed cause: ground is acoustic, perceptual and deals with perceived effect.

    From these oppositions emerged a particular view of history. McLuhan saw the advent of the phonetic alphabet in Greece as having set the Western mind off on a detour in the direction of the visual and the logical. The rise of printing and perspective had given undue emphasis to this visual, logical bias and were thus negative. Accordingly the left hemisphere became described as the villain. On the other hand, electronic media, which offered a return to the acoustic, intuitive, analogical processes of the right brain emerged as the heroes of his saga of oppositional anatomical sides.

    There were problems with McLuhan's approach. He claimed that electronic media were primarily acoustic. The rise of multi-media computers has expanded the scope of electronic media to include vision as much as sound: witness the enormous rise of Computer Aided Design (CAD) packages, which rely very heavily on both vision and perspective.

    At a more fundamental level, McLuhan assumed that perspective was necessarily connected with literacy. This was misleading. The Chinese were literate, had a knowledge of printing, yet developed no serious interest in perspective until the Jesuits persuaded them to do so in the seventeenth century. Islam, which produced a great literature tends, even today, to be opposed to perspectival representation of space. Nonetheless, it was in the context of literacy that western art made its gradual progress towards mastery of perspectival space. As we have shown (see Sources, pp. 155-169*, cf. below pp. 20-24*), this mastery occurred at the level of painting practice. At an intuitive level this began seriously with Giotto around 1300. Technically, if we accept Brunelleschi's panels (c.1415-1425) as the earliest known and Masaccio's Trinità (c.1425) as the first extant example of linear perspective, it began some 30 years before the advent of printing in the West. Early treatises consolidated this practical knowledge in mathematical terms before the advent of printing. Even during the half century after Gutenberg, printing had effectively no impact on perspectival treatises. McLuhan's assumption that printing and perspective were necessarily linked was, therefore, untenable.

    McLuhan's suggestion of connections between the development of a particular point of view in literature and a specific viewpoint in art was also misleading because it tended to conflate as if they were two, four separate factors: 1) point of view of the narrator in a text; 2) point of view of the reader of the text; 3) viewpoint established by the artist in a painting and; 4) viewpoint of a person observing the painting. Although 1) has become a popular subject of study for historians of literature (cf below pp. 116-128*) and although 2) and 4) presumably fall under the aegis of reception theory, too little work has been done, to permit a clear decision on so large a topic. As for factor 3) our brief analysis has shown that the development of perspective was not simply the fixing of a single viewpoint. Almost from the outset it involved a conscious playing with fixed viewpoints. Giedion (1941), who is said to have been a starting point for McLuhan was, therefore, also misleading in claiming that in perspective (1977, 31): "The whole picture or design is calculated to be valid for one station or observation point only. To the fifteenth century the principle of perspective came as a complete revolution, involving an extreme and violent break with the mediaeval conception of space".

    As we shall show there was no such sudden break: rather, a gradual evolution. The trend towards perspective was well underway in the fourteenth century and continued after Brunelleschi’s demonstration, Alberti’s treatise, and Gutenberg’s press. A generation later Piero della Francesca wrote the first mathematical treatise on perspective. About 1492 Leonardo made the first recorded systematic quantitative experiments concerning perspective. Seventy years passed before Commandino recognized further links between mathematical projections and perspective and another seventy years passed before Desargues expressed these principles in universal mathematical terms.

    McLuhan was not well understood. Eisenstein, in The Printing Press as an Agent of Change (1979,176), saw McLuhan’s claims as an incautious version of Erwin Panofsky’s analogy between the development of perspective in art and the way in which Renaissance thinkers began to look at the past from a fixed distance. Eisenstein challenged the analogy arguing that (186): "the capacity to see the past in this way could not be obtained by new optical effects devised by Renaissance artists. It required a rearrangement of documents and artifacts rather than a rearrangement of pictorial space". According to Panofsky the development of perspective went hand in hand with the rise of modern science. This Eisenstein challenged also (269):"it is an exaggeration to launch modern science with the advent of perspective renderings and to regard pictorial statements as sufficient in themselves. A method of preserving observations as graphics records and a chance to check them against others should not be presumed to lie in an artist’s sketchpad". Aside from these criticisms, passing comments on treatises by Alberti, Piero della Francesca, Dürer, Jamnitzer and a few general references, Eisenstein did not explore connections between perspective and printing.

    Had Eisenstein understood the larger context, she could not have claimed that printing caused so sudden a revolution, or that it offered a key to problems of periodization. She would almost certainly not have insisted that it is "an exaggeration to launch modern science with the advent of perspective". She would probably not have dismissed perspective as a lay innovation. After all most of the major examples were in the context of the church and a surprising number of them linked with a few orders (Franciscans, Dominicans, Augustinians and Carmelites). Eisenstein might well have explored the extent to which perspective offers insights into the vexed questions of continuity between middle ages and renaissance, using a periodization such as that outlined below.

    As will be suggested (see below pp. 42*), this story could readily be expanded to include links between perspective and instruments: Piero’s first mathematical treatise of perspective also contained the first description of a perspectival instrument (1434). Leonardo’s notebooks which first described the inverse size distance law also contained a first illustration of a perspectival instrument (c. 1490). The period 1500-1525 brought the first printed treatises in France and Germany and a first printed illustration of a perspectival window. The period 1525-1600 saw the spread of printed treatises to the Netherlands, England, Spain, Austria and Poland. With respect to instruments it saw early attempts at a universal measuring device. The period 1600-1800 brought treatises at different levels some concerned with high mathematics (e.g., Desargues, Brook Taylor, Lambert); some with high practice (e.g., Accolti, Troili); while others were encyclopaedic (e.g., Leupold, Kästner) or simply popularizing (e.g., Dubreuil). This period also saw the development of the Galileian sector and Bürgi type proportional compass which were successful universal measuring devices. The new confidence and universality this brought to the realms of science, was reflected in the confidence with which perspective was gradually applied to the entire environment and reflected in turn in the new confidence of politicians making absolutist claims for power.

    Meanwhile, other connections between perspective, texts and printing culture were suggested. Sir Ernst Gombrich, in Art and Illusion (1960, 129), emphasized the connection between narrative and the development of perspectival representation (mimesis, illusionism). In Means and Ends (1976, 32) he drew attention to: "the increasing demand for what I have called dramatic evocation, the return to the desire not to be told only what happened according to the Scriptures but how it happened, what events must have looked like to an eyewitness". Gombrich also acknowledged that (35): "the conquest of perspective and of anatomy play their part in this story". By implication there was a direct relationship between the re-interpretation of biblical texts and the development of perspective.

    De Kerckhove (1995, 31), made the extra-ordinary claim that: "By showing the proportionate reduction of size and distance on paper as a decreasing vista from the viewpoint, the draughtsman is putting time into space." Pictures in perspective are not per se linked with time. Often they are of timeless scenes. In the Renaissance, as will be noted presently (p. 26*), perspective introduced unexpected tensions in both temporal and spatial frames.

    He also argued that "People only developed a taste for perspective during times of great pushes of alphabetization, that is, when they first learned to read the alphabet during the Golden Age of Ancient Greece and then again around the time when print was invented by Johannes Gutenberg." According to de Kerckhove perspective (32): "could be one of the best examples of how the alphabet re-framed the mind". This unfortunately raised more questions than it answered. Why, for instance, did writing in Greece at the time of Homer begin a few centuries before pseudo-perspective at the time of Aeschylus? Why did perspective in the Renaissance begin prior to Gutenberg, and in Italy rather than Germany? How are we to explain that the Greeks produced pseudo-perspective, whereas the Renaissance produced perspective? Why did all the other cultures that developed alphabets, not develop perspective?

    Giesecke (1991), in a fundamental study concerning the complexities of fifteenth century printing, explained the origins of perspective in terms of the surveying tradition and the optical interests of mediaeval artists. His work provided the most penetrating study to date of the implications of print culture, arguing that the development of linear perspective provided a new model for describing the world systematically which led to a new concept of truth. Giesecke was particularly concerned with the ways in which the advent of printing introduced new knowledge and a redefinition of what constitutes knowledge. In earlier cultures, (both oral and manuscript), technical knowledge had been exchanged primarily through face-to-face situations. The advent of printing introduced a quest to convey knowledge directly in book form without the intermediary of an expert, master or teacher. This posed problems because the objects to be described were no longer present as in a face-to-face situation and thus required the development of a new type of artificial sight (künstliches Sehen) that became basic to scientific description.

    The early texts in the field of technical literature (Fachprosa) had a new emphasis on true (wahren) and correct (rechten) description. This, claimed Giesecke, was no co-incidence. Printing introduced a new distinction betwen inner and outer vision, focussed attention on objects seen by the outer eye, (dismissing everything else as invisible), and systematized new methods that came through the discovery of linear perspective. Others had made general claims about the links between printing and perspective usually with respect to the appearance of perspectival illustrations in printed books (McLuhan, Edgerton). Giesecke was concerned, rather, with the way in which perspective made persons aware that they were viewing an object from a given point of view and that complex objects needed to be viewed and represented from a series of viewpoints to be seen accurately. This led to the creation of multi-dimensional models which were then linked with geometry through Dürer's publications and in turn inspired a new type of verbalisation based on pictures which correlated a series of views. Hence perspective did much more than add a sense of space to illustrations: it introduced a systematic methodology for describing verbally the visual world which Renaissance scientists identified as true description because of its reversibility. While Leonardo da Vinci was the first to articulate this methodology, Giesecke claims that it required the standardizing effects of printing to become established. In this way printing introduced a theory of knowledge (Erkenntnistheorie) that has dominated the West since the Renaissance. Giesecke explored the consequences of these developments for a shift in emphasis within the trivium away from logic and rhetoric in favour of dialectic (630-635). In the final part of section six, Giesecke explored how this inspired trends towards accumulation of information; new emphasis on comparison and contrast; new knowledge and even a realistic extension of fiction.

    Giesecke traced how these developments led to a redefinition of knowledge (Wissenschaft). In the mediaeval tradition knowledge of nature was very much linked with physical ability (cf. the Greek techne which as Panofsky pointed out explains the close connection in German between Kunst and können). This tradition, which led to artist-engineers, assumed that knowledge involved sensori-motor and muscular skill and dexterity, whence the mediaeval emphasis on experts, experience (Erfahrnis), practical wisdom (Weisheit), and a tendency towards secrecy (Geheimnis, Arcanum). By contrast, the new approach defined knowledge as: 1) won through regulated (normierte) processes of visual perception and description or representation by an external observer; 2) stored in print form and 3) spread through a free market, which secured a commitment to dissemination or even revelation (Offenbarung) as they termed it. This led (669) to a new distinction between use (Brauch) and understanding (Verstand) and a gradual supremacy of theory over practice. Giesecke shows (672-678) that these new ideals of knowledge applied even to traditional topics as in Libavius' Alchemy.

    The rise of early modern science is frequently described as a new emphasis on observation. Giesecke's analysis showed that this is too simplistic; that it was rather a question of developing a systematic method of communicating results of observation indirectly, using descriptions that reflected the objective aspects of linear perspective. Giesecke showed that this led to new links between experimenting and idealising (620-623), noting that this redefinition of (scientific) knowledge also entailed new emphasis on instruments (673). This closely argued and carefully documented work led to dramatic conclusions that "knowledge" (Wissen) in its modern sense did not exist (677) and indeed was unthinkable (655) prior to the development of print culture as it evolved in Europe. Giesecke was very sensitive to the price that was paid to achieve this (650):

Authors of technical literature (Fachprosa) and particularly their most radical representatives, "scientists" (Wissenschaftler), are forced to uniocular perception, concentration on visible characteristics (Gestaltmerkmale) and thereby to suppress more complex organs of sense and perceptions.

    This monosensual focus (653) of early modern science destroyed earlier notions of unity of the senses, and required an isolation of the sense of sight which, Giesecke suggested, needed to be transcended in light of the ecological crisis that this one-sense approach to knowledge has produced. New age concerns with body language, feelings, and new relations to nature could be seen as a contemporary expression of this quest to redefine the visual bias of our culture (653). By implication the origins of perspective and printing were intimately connected with a new approach to knowledge.

    Giesecke was very conscious that his telling of the story from a modern point of view meant emphasizing the new aspects of the process and that if one wished to compensate for this shortcoming one would ultimately need to retell the whole story using a mediaeval viewpoint (703). He repeatedly emphasized the gradual evolution of these developments and explicitly acknowledged their roots in mediaeval manuscript culture. He noted, for instance (668), the presence of striking morphological descriptions in the work of Albertus Magnus and Hildegard of Bingen. He accepted that there were numerous mediaeval examples of visual experience and even commitments to dissemination (677). In the case of Ortolf von Bayerland's medical book (Arzneibuch) he described (554-55) a fourteenth century treatise with over 100 manuscripts which explicitly set out to disseminate knowledge in clear tables. In analysing the nexus of perspective, geometry, model-making and systematic representation of knowledge, he repeatedly cited Leonardo da Vinci (e.g. 617, 624, 636, 658, 663). Giesecke did not pretend that printing started the process: he claimed, rather, that printing set in motion a technological system of communication that standardized and spread the process through Germany, made it a European, and ultimately a world-wide phenomenon.

    In terms of stages, distinctions need to be made between (proto-) perspective in a loose sense of some spatial effect as in Giotto; (proto-) perspective with an approximate central vanishing point as in Lorenzetti’s Annunciation (Siena); perspective with a technical vanishing point as in Brunelleschi’s panels or Masaccio’s Trinity (Florence, Santa Maria Novella); general mathematical demonstrations as in Piero della Francesca, or precise ones as in Guidobaldo del Monte or Desargues. Hence the question of origins changes in the course of over three centuries from c. 1300 to 1636.

    If we are concerned with the origins of Giotto’s breakthrough into a general spatial setting witnessed in his cycles at Assisi, Padua and Florence in the first quarter of the fourteenth century, then it is important to recall a new emphasis on narrative painting, inspired by a new attention to nature through the Franciscan Order, which became combined, largely through the English Franciscans (Robert Grosseteste, Roger Bacon and John Peckham), with a new metaphysical theology focussing on geometry and optics as a means of understanding God. The views of optics in this programme came via Witelo (c.1270) from the Arabic tradition of Alhazen (Ibn al-Haytham) who had focussed attention on the criteria for certification of sight and had brought problems of representation within the scope of optical studies.

Fig. 2. Key events in the history of perspective with corresponding origins.

    The tendency in Romanesque and Gothic churches to provide spatial doorways and to a lesser extent windows was common throughout Europe. Some windows, as in the Andreas Kirche (Braunschweig), were actually shaped in the form of pyramidal cones of vision. This provided a common framework for spatial interests within which there were national and regional differences that varied in accordance with different functions and media. Initially there had been a focus on key events in the life of Christ often balancing Old Testament prefigurations with New Testament happenings. Those countries such as France (e.g. Chartres) which used stained glass in their great rose windows to depict these events were severely limited in their spatial explorations.

    This is not to say that perspective was impossible in this medium. The first stained glass window to use pseudo-perspectival effects was by an artist in the workshop of Cimabue, who produced a Coronation of the Virgin in Siena Cathedral (1287-1288), which has been called the (78): "first occasion on which the laws of perspective were used in stained glass." These techniques were developed in a Life of Saint Anthony of Padua at Assisi by the workshop of Giovanni di Bonino (1320). From there the idea went North to the the Cistercian abbey at Königsfelden (1325-1330). It was used again at Stassengel near Graz (c.1350) where "the scenes are each enclosed within a three dimensional niche, like a sort of tower seen in perspective. At Evreux Cathedral (1395-1400), figures were placed on pedestals portrayed in perspective. and in the choir of Tewkesbury Abbey in Gloucestershire, the baldachins were arranged in accordance with....[pseudo-]perspective .

    In the fifteenth century a number of the early pioneers in perspective were also active in stained glass, notably, Lorenzo Ghiberti, Paolo Uccello, Andrea del Castagno and Donatello. Later examples include episodes from the Life of Saint John the Baptist such as the Meeting with Craton (1478) by Cristoforo de Mottis; from the Story of Saint Eligius such as the Investiture of the Saint as a Bishop (1480) by Niccolo da Varallo 127 or the Expulsion of the Merchant from the Temple by Guillaume de Marcillat in Arezzo Cathedral (1519-1525).

    These spatial explorations remained limited when the medium was mosaic as at Monreale. In Italy, where the medium became fresco as at Assisi, Padua or San Gimignano the spatial potentials increased considerably and even more so when the function changed from depicting key events in the life of Christ to narratives of saints’ lives. This quest occured mainly on the walls of chapels in fresco, to a lesser extent in the predellas of altars and occasionally in sculptural reliefs.

    In the Netherlands the scenes were almost always on altars painted in oil. The emphasis remained on the life of Christ and the Virgin, particularly key moments such as the Annunciation, the Adoration of the Shepherds or the Virgin and Child alone or surrounded by saints and/or donors. The spatial setting for all these scenes almost invariably involved a church. Sometimes the portal of the Church served as a window to the interior; sometimes it served more as a gate to a scene beyond; at other times the whole front facade of the church was cut away and served as a window to a scene inside the church. Occasionally the entire scene occured inside the church. In these arrangements the portal often contained painted sculptures which continued the tradition of Old Testament prefigurations and parallels to the New Testament scene. This contrast between the old and the new law in terms of painted sculpture versus painted nature meant that the Netherlandish tradition had a quite different approach to the paragone tradition which in Italy contrasted the effects of sculpture and painting. At the same time the great emphasis this gave to the portal and church interior in Netherlandish art meant an early focus on sacred interior spaces that was to culminate two centuries later in the great interiors of Neefs, De Witte and Saenredam.

    In Switzerland this concern with church interiors emerged with Konrad Witz in the first half of the fifteenth century. In Germany this fascination with church interiors became important in the second half of the fifteenth century with the Master of the Life of Mary (Meister des Marienlebens). In the first decades of the sixteenth century, Altdorfer and Huber developed this theme in important new ways in the context of drawings and engravings, recording actual synagogues as well as churches. In Italy, by contrast, it occured primarily in the context of intarsia work and spread to other media such as painting in the eighteenth century (e.g. Pannini). In Italy, a trend towards secular art, showing everyday events in a sacred context, emerged largely on the walls of the public palaces of the city states, their equivalents of city halls. At the Burgundian court this emphasis on secular events in a sacred context developed in the illustrations to Books of Hours.

    In both sacred and secular art the chief media used included stone, paint, paper, wood, earth and plants (fig. 3). Often these media were used together either in the production of proto-perspectival or technically perspectival spaces. For instance, Giotto used a combination of architecture and paint to produce his proto-perspectival, fictive coreto (Cappella degli Scrovegni, Padua, 1305). This continued in the later work of Bramante (Santa Maria Presso San Satiro, Milan) and Michelangelo (Sistine Chapel, Vatican). Medium specific examples evolved in tandem. For example, in the late twelfth century, a purely architectural sculpture showing a fictive doorway was constructed in the Baptistery of the Palace of Kings of Majorca (Perpignan). By the early fifteenth century, Donatello, was applying proto-perspectival techniques to sculpture in stone while his contemporary, Ghiberti, applied these techniques to sculpture in bronze on the doors of the Baptistery in Florence.

    Paint constituted one of the most complex media. In terms of fresco it was applied to panels, walls and ceilings or quadratura. Here combinations of painting and architecture were often involved. Following early exceptions such as Mantegna’s oculus (Camera degli sposi, Palazzo del Te, Mantua), these became the fashion in the 1560’s in Bologna with Laureti, emerging in the published literature in 1583 (Has, Danti) although it was over a century later that the most famous examples appeared with Pozzo, a trend that continued especially in southern Germany and Austria throughout the eighteenth century. Oil paintings were more specialized.

    Paper was one of the most important media of perspective. Sometimes these were individual sheets. In terms of manuscripts and books, in addition to those devoted to sacred themes, there were texts devoted specifically to regular and semi-regular solids. In Italy the fashion began with Piero della Francesca and Pacioli around 1489 and culminated in the years 1496-1499 when Pacioli and Leonardo worked together to produce the Divine Proportion (published 1509) which was the basis for later work in the period 1568-1596 (Barbaro, Danti, Vasari, Jr. and Sirigatti). In Germany this activity began seriously with Dürer (c.1514) and effectively ended with Halt (c.1625). Another major theme was Roman ruins which, as Vasari reported, began in Italy with Brunelleschi and Donatello (c.1401). The inclusion of a map of Rome with ruins by the Limbourg brothers in the Very rich hours of the Duke of Berry (c. 1415-1416) attests that this interest spread quickly. Even so, systematic study appears not to have occured until the time of Peruzzi (c.1520-1535) whose notes were inherited and published by Serlio from 1537 onwards. The period 1540-1560 saw a high point in this genre with the publications of Androuet Du Cerceau and Cock. Piranesi (1740) brought a revival. As we have shown elsewhere (cf. Sources, pp. 89-98*), the perspectival treatises gradually evolved a whole series of themes.

    Wood also became an important medium. From the fourteenth century onwards, there were proto-perspectival uses of inlaid wood or marquetry in a sacred context, specifically choir stalls, in Italy, with the most famous perspectival examples in the period 1470-1530. In Germany and the Netherlands, where the emphasis in marquetry was rather on secular cabinets often showing combinations of ruins with semi-regular objects, the most important period was from c.1550-1625. Wood also played an important part in stage scenery and scenography, although this typically entailed a series of media including painting and machines. From the outset pioneers in perspective such as Brunelleschi and Masaccio were also engaged in theatre decorations, although these were more by way of machines than stage scenery. Serious stage scenes emerged in the latter half of the sixteenth century (1567, 1589); did not become a regular feature until the early seventeenth century and reached their heights in the first half of the eighteenth century (e.g. 1710, 1740) with families such as the Juvarra, the Bibbiena and others.

Medium Early Examples First Published Famous Examples

Stone:

Architecture c. 1478 1521 1521-

Fictive " " c. 1478 1568 1500-1900

Sculpture c. 1400 1504 1400-1900

Paint:

Fresco c. 1425-1427 -- 1430-1510

Oil c. 1457 -- 1484

Ceilings c. 1480 1568 1500-1700

Paper (Drawings):

Roman Ruins c. 1400 c. 1550 1550-1580,1740-1760

Regular Solids c. 1489 1509 1489-1625

Manuscripts c. 1434 1540 1434-1515

Books 1494 1494 1494-

Wood:

Marquetry c. 1470 1567 1480-1625

Stage Scenery c. 1567 1568 1600-1800

Earth, Plants:

Gardens c. 1550 1600 1550-1800

Fig. 3 Examples of different media that used perspective and related dates.

    In Italy, perspective was applied to gardens from the first half of the sixteenth century onwards. As a topic it entered the literature with Vredeman de Vries and Androuet du Cerceau in the 1560’s. But it was not until the sevententh century that perspective was applied to gardens on a grand scale and not until the eighteenth century that it reached its heights. It continued to be an important theme in the nineteenth century. When we examine these combinations more closely we find that some were particularly favoured in Italy (fig. 4), whereas others were favoured in the North. For example, altars were particularly developed in the Netherlands and Germany; manuscripts, particularly books of hours and histories were favoured in Burgundy and France; while the use of perspective in printed books was favoured first in Germany and subsequently in the Netherlands and France.

Place Medium Italy Burgundy France Netherlands Germany

Walls Mosaic, Fresco *

Chapels Fresco *

Ceilings Fresco *

Choirs Inlaid Wood *

Altars Oil on Canvas * * *

Predellas Fresco, Tempura *

Paintings Oil on Canvas *

Reliefs Sculpture *

Manuscripts Painting * * * * *

Books Woodcut * * * * *

Engravings Ink on Paper * * * *

Gardens Earth, Plants * * * *

Fig 4. Some of the different media and functions of perspective favoured in Italy, Burgundy, France, Netherlands, and Germany.

    Some themes such as gardens were explored throughout Europe but with regional variations (cf. Sources, pp. 170-182). Striking also from this overview is how the uses of perspective were initially much more diverse in the Italian context, which may be one of the central clues why perspective took nearly a century to spread to the major centres of Europe (fig. 5).

Country Italy France Netherlands Germany

Date 1415-1425 c.1450 c.1457 c.1505

Fig. 5. Dates when perspective was first introduced into major European countries.

    Panofsky noted that one of the key sources for Suger's approach lay in the writings of Dionysius, the Pseudo-Areopagite, who used the study of visible things as a means of studying the invisible:

Every creature, visible or invisible, is a light brought into being by the Father of the lights...This stone or that piece of wood is a light to me....For I perceive ...that it exists according to proper rules of proportion; that it differs in kind and species from other kinds and species; that it is defined by its number....As I perceive such and similar things in this stone they become lights to me, that is to say, they enlighten me.

    Read narrowly, this passage would lead one simply to use examples from the material world as a starting point for mystical contemplation of the spiritual world. This, it could be argued, was essentially the path taken by Abbot Suger. Read more broadly, it could lead one to a scientific study of the physical world as a means of gaining understanding of the invisible world of God. This, as will be suggested below, was effectively the path taken by his colleague, Peter the Venerable, Abbot of Cluny, when he instigated a new search for basic texts on scientific knowledge in 1143, one year before Abbot Suger consecrated his new church at Saint-Denis.

    There was more to Saint-Denis than simply a place where the visible beauty of precious stones and objects were a point of departure for invisible truths of religion. In the Latin, Saint-Denis, was Sanctus Dionysius and thus etymologically linked with Dionysius, the Pseudo-Areopagite. Saint-Denis had been the royal abbey for many centuries. It housed the tombs of Charles the Bald and Hugh Capet, founder of the ruling dynasty. Its sculptures and art reflected this historical context. At the same time it brought new emphasis to contemporary figures within this sacred and secular tradition. Hence, an Annunciation scene (c. 1140-1144), in the stained glass windows of the church, showed Abbot Suger, as a donor at the Virgin's feet. Saint-Denis also housed the Chronicle of Saint-Dénis, which was begun in the early twelfth century, with a second version up to the time of Louis VIII in the thirteenth, and a third version after 1286, which included the lives of Saint Louis and Philippe III. In other words, one of the centres that helped to inspire the new realism of Gothic art, also inspired a tendency to record past and contemporary history. All this becomes the more striking when one recalls that Jean Fouquet's version of this same Chronicle of Saint Dénis (1458, now Paris, Bibliothèque Nationale), was one of the first examples of (nearly correct) perspectival art in a French manuscript.

    Bishop Geoffrey of Chartres was a personal friend of Abbot Suger. Geoffrey visited Suger at Saint-Denis in 1130, 1137, 1140 and assisted him at the consecration of the new cathedral of Saint-Denis on 11 June 1144. So, from the outset, there were close links between Saint-Denis and Chartres, which became the two key centres of early Gothic architecture and art.

    Most descriptions of the Gothic focus on a new interest in light, a fascination with stained glass windows and a new emphasis on realistic sculpture. Mâle has suggested that the reasons for this new realism could be related to the crusades which led some French noblemen to settle in Greece. We know from Abbot Suger himself that he was personally well acquainted with the cultural heritage afforded by Rome. Speaking of columns, for instance, he noted: "we might obtain them from Rome (for in Rome we had often seen wonderful ones in the Palace of Diocletian and other Baths)". Hence the new realism would mainly be due to a re-discovery of Ancient Greek and Roman examples which, in the French context, became integrated within elaborate typological parallels between the Old and the New Testaments focussing on the Life of Christ.

    More was involved, however. The Gothic period introduced a new approach to story-telling. In terms of stained-glass windows, for example, Brisac noted that the Childhood of Christ on the interior of the west front at Chartres (1150) was:

the earliest surviving example of a composition made up of three illustrated compartments at each level, and it contains a very comprehensive treatment of this period of Christ's life and also of two later events: his Baptism and the Entry into Jerusalem. Some episodes are dealt with in a sequence of several compartments. There are six, for example, in the case of the Adoration of the Magi.

    These themes were continued when Chartres was rebuilt between 1194 and 1240. By the time of the Sainte-Chapelle (1243-1248), a single Story of Esther and Ahaseurus was "told in one hundred and twenty-nine scenes" which, Brisac claimed, made it lose "its narrative precision." In the next century this apparently changed again:

Legendary windows, for example, with multiple medallions, allowed stories to be told with extraordinary narrative diffuseness, whereas in the fourteenth century only the most salient events of their subject's life were portrayed; in the case of saints, for example, it would be their meeting with Christ or their conversion to Christianity, one of their miracles and finally their glorious death. All the subsidiary episodes are dispensed with and the "reading" of the window becomes much easier.

    All this becomes the more intriguing because Gombrich has suggested that the pictorial revolution which led to linear perspective had its roots in a new approach to narrative. We would suggest that this change in narrative first occured in France rather than Italy and began seriously in the century from 1150 to 1250, which is usually associated with Gothic art and architecture. In other words, paradoxically, in the French Gothic emerged basic ingredients essential for the Italian Renaissance: not just a new commitment to realism but a whole new approach to narrative. To understand this we need to look briefly at the new subject matter of stories in the stained-glass windows and relate this to new themes in literature of the time. Then we shall stand back to look more globally at changes in the six centuries from 1000 to 1600.

New Subjects in Windows and Walls

    A closer look at the the interior stained glass windows and the exterior sculptures of the great cathedrals, reveals other aspects of their novelty. Besides introducing new realism into representations of the Life of Christ, their subject matter was increasingly about the lives of the saints, donors, recent champions of the faith and early founders of Christianity in the North. For example, when Canterbury cathedral burned in 1174, the new church had a series illustrating the lives of archbishops of Canterbury, such as Saint Dunstan and Saint Alphège, who lived around 1000. The Trinity and the Corona Chapels contained scenes from the Life of Thomas à Becket, who was murdered in the cathedral in 1170. When Chartres burned in 1194, one of the most impressive windows was dedicated to the life of Charlemagne. When the cathedral at Rouen was burned by a fire in 1200, the sculptures on the doors recorded the lives of Saint Romain, who had been bishop of Rouen from 626 to 638, and Saint Ouen, who was pope from 641 to 684. The great cathedral at Reims, had stained glass windows (c.1160's or after) dedicated to the Life of Saint Nicaise, martyred by the Vandals in 407 and the Life of Saint Remi, who first baptized Clovis and his Franks in 498. When the cathedral was rebuilt after the great fire in 1210, these stories were integrated into the sculptures over the doorways of the North facade of the transept. The Sainte Chapelle (1243-1248), ostensibly about Old and New Testament parallels, emphasized a continuity between Biblical royalty and the Capetian dynasty, as embodied by Saint Louis, founder of the chapel. One set of windows was dedicated specifically to the history of relics of the passion of Christ and traced their lineage right through the Middle Ages. The images of the stained glass windows dovetailed with those in the illuminated manuscripts and hence it is not surprising to find that one of the most impressive proto-perspectival scenes is subsequently found in the Lives and Miracles of Saint-Louis from the collection of Jeanne de France (Paris, BN, ms. fr. 2829, fol 11v.).

    For the pre-history of perspective, this seemingly simple shift in subject matter was of the greatest importance. As long as the Old or New Testament, and particularly the Life of Christ remained the chief topics, artists were challenged to represent places they had never visited and persons they had never seen. To represent Christ very realistically could be seen as too personal or even blasphemous. To represent the space in which he moved in terms of local geography could equally be seen as blasphemous. When the subject matter shifted to the life of a saint, particularly a local saint, these restrictions diminished greatly. It is no-coincidence therefore that most examples of proto- and early perspective involve cycles from the lives of saints rather than the Life of Christ (notwithstanding, as we have discussed elsewhere, that particular scenes from his life such as the Annunciation were very important). Some examples of such cycles are Giotto's Life of Saint Francis (Assisi), Massacio and Masolino's Life of Saint Catherine (Rome, San Clemente), Masolino's Life of Saint John the Baptist (Castiglione D'Olona) and Ghirlandaio's Life of Saint Francis (Florence, Santa Trinità).

    Donor portraits played a special role in this shift of subject matter that prepared the way for perspective narrative. Here again, Gothic art set the stage for that which the Renaissance developed. In early examples, such as Canterbury (1180), donors were typically guilds such as the furriers or goldsmiths and identified generically as such. In the course of the thirteenth and fourteenth centuries, the role of the donor became increasingly personalized to the point that they represented individual portraits. Initially donors were represented in separate spaces or peripheral to scenes in the Life of Christ or the life of a saint. Increasingly they became part of the same scene. By the time of the Renaissance, this had become a commonplace. In Ghirlandaio's Life of Saint Francis (Florence, Santa Trinità, Sassetti Chapel, c.1480), for instance, the scene showing the Pope conferring the rights of the Franciscan order on Saint Francis, was depicted with members of the Sassetti family, the Medici and famous poets such as Poliziano in attendance. This increasing specificity of the donors' portraits went hand in hand with a more precise depiction of their spatial surroundings. In the case of Ghirlandaio's fresco, for example, this entailed the Piazza della Signoria and the Palazzo Vecchio in Florence. As attention shifted to actual spaces and real, physical locations, perspective became ever more important. It is no-coincidence, therefore, that the rise of perspective was so closely linked with the history of surveying, topography and cartography.

    These developments in the treatment of space had implications for concepts of time and meaning (hermeneutics). As paintings became more realistic and tended toward perspectival representation they increasingly represented contempoaray scenes and events. Yet the story depicted was often in the past. So there were temporal discrepancies between the time of the painting and the time of the event depicted. To continue with the example cited above, Ghirlandaio was depicting when the pope gave the Confirmation of the rule of Saint Francis, an event that took place in 1223. Yet Ghirlandaio showed this in the context of his own contemporaries, the Medici and the Sassetti families, when he painted the picture in 1480.

    Sometimes even the treatment of space was implicitly metaphorical. For instance, a detail from a manuscript of Boccaccio's Decameron (Oxford, Bodleian Library, Ms. Holkham Hall misc. 49, fol. 5r, c. 1450-1475) illustrates a group of young men and women taking shelter from the plague oin the church of Santa Maria Novella in Florence. The picture shows an interior in perspective which appears accurate but bears no relation to the actual space of Santa Maria Novella. So although the picture appears to be perfectly realistic, the viewer is expected not to look at it literally: they need to distinguish this picture from the actual building. Hence once again perspective provokes a metaphorical 'reading of the image.

    These discrepancies of temporal and spatial frames had consequences for the meaning of the picture. The viewer had to become conscious of a temporal discrepancy, to distinguish the contemporary figures (of 1480) from the historical ones (of 1223): i.e. to see the scene metaphorically and not literally. Paradoxically, the more realistically and literally painters recorded their surroundings, the more metaphorically and not literally viewers had to see these paintings. So the growth of perspectival realism and the rise of new levels of interpretation go hand in hand. As we have discussed at greater length elsewhere (Sources, p. 185), it is probably no co-incidence that Dante introduced new his distinction between four levels of interpretation (literal, allegorical, moral and anagogical) in the same decade (1300-1310) that Giotto painted the Arena Chapel in Padua and his students were finishing the great fresco cycles in the upper church of San Francesco in Assisi.

    As a result of these shifts in subject matter, and new treatments of space and time, pictorial cycles integrated historical and contemporary secular themes within the Christian context, or rather, they placed Christian themes within a larger historical framework, which established a continuity between Antiquity, Middle Ages and the present. There was, therefore, not just a re-discovery of Ancient examples, but rather a discovery that pagan Antiquity and Christian Middle Ages were part of a single historical tradition. As these connections with everyday life became the more manifest, the need for perspectival narrative became ever more necessary.

New Literature

    Gothic art in the form of stained-glass windows and sculpted walls involved much more than a simple shift in subject matter. It entailed fundamental changes in narrative: what kinds of stories were chosen, how they were told and how they were presented. These changes affected literature as much as art. A variety of influences help to explain why these changes occured. For instance, the Arabic tradition of story-telling, which came to Europe via Mozarabic Spain, probably had a direct influence on the troubadours in Provence. The troubadours developed themes of courtly love, a secular version, so to speak, of the cult of the Virgin.

    These Provençal troubadours influenced the trouvères in Northern France, who also drew on the so-called Brittany corpus (matière de Bretagne), that was linked with English story-telling. The trouvères, in turn, influenced the German Minnesänger tradition. We are told that the realism of the northern trouvères gradually led them away from the quintessential love themes of the south. Arras became a centre for some 180 poets of whom the most famous were Jean Bodel, Adam le Bossu and Baude Fastoul in the thirteenth, with Christine de Pisan, Alain Chartier and Charles d'Orléans in the fourteenth century. Aside from the obvious literary qualities in Christine de Pisan's writings, it is noteworthy that this author, who helped bridge the French and Italian traditions, also inspired some of the most dramatic proto-perspectival illustrations in the illuminated manuscript tradition.

    As in the case of art and architecture, the subject matter of Gothic literature continued to emphasize religious themes, particularly typologies linking the Old and New Testaments. At the same time there was increased attention to secular themes. These secular themes differed from traditional examples in three important ways. First, they introduced a new emphasis on illumination which, besides its purely metaphysical connotations, had a very practical purpose. The beginnings of chapters were illustrated to make the manuscripts much easier to use and thus helped with the classification and ordering of knowledge. Second, they introduced the concept of first person narrative (see below p. 153*), bringing to story-telling an aspect of individual viewpoint which prepared the way and in a sense made necessary the development of linear perspective.

    Third, they focussed on externalizing and rendering visual, internal, psychological aspects. The roots of this approach lay in Antiquity. The Greeks and Romans had represented basic concepts such as war (Mars), human virtues such as wisdom (Pallas Athene) and human emotions such as love (Eros) in terms of beings which could then be sculpted and painted. As Auerbach has convincingly shown this Greco-Roman pantheon remained very impersonal, with no real exploration of character. According to him the roots of a more personal approach came strictly from the Judaeo-Christian tradition with its roots in the Old Testament.

    The story is more complex. The Provençal poets, aside from probable Arabic influences, lived in a part of France known for its heretical tendencies, largely inherited from the Bogomils, which became infamous through the Albigensians against whom Saint Dominic waged war through the Dominican order. On the surface Saint Dominic won the day. Ironically, however, many aspects of the Provençal approach to story-telling, lived on in the Christian conquerors. Whence, the Christians, in fighting the heretics, became the enemy, insomuch as they partially acquired their methods.

    In all there were over 400 troubadours in the twelfth and thirteenth centuries, some thirty of whom were Italian provencalists. These included Sordello di Mantova, Cielo d'Alcamo, Rinaldo d'Aquino, and Odo delle Colonne. The troubadours' story-telling methods lent themselves to visual renditions.The songs of the troubadors had an influence on Dante and were an important source for the stories of Boccaccio (1313-1375), particularly his Decameron (cf. pl. ***). The troubadours' heritage had an even greater impact on the songs (canzone) of Petrarch (1304-1374) who, it bears remembering lived in Avignon and visited Paris, Lyons, Liège, as well as Ghent and Cologne. It is surely no co-incidence, therefore, that it was particularly the verses of Dante (cf. fig 6), stories of Boccaccio and the triumphs of Petrarch (as witnessed particularly in Mantegna), that tended to be illustrated in manuscripts and rendered in pictorial form. The troubadours favoured vernacular, literal treatments of the Bible, an approach that Saint Francis of Assisi followed and which found itself expressed visually on the walls of the church of San Francesco in Assisi through the art of Cimabue, Giotto, Lorenzetti and others. Italy thus made famous French innovations: or rather put into frescoes and paintings what the French had painted in words and illustrated in manuscripts.

    So the roots of the new approaches to story-telling that led to perspective lie not simply in the Old Testament as Auerbach would have claimed, nor just in a re-discovery of Antiquity as is often asserted, but rather in the discovery of a historical continuity linking the middle ages with both the past and present. And some role was played by pagan strands via the heretical troubaours, which were assimilated by the Christian crusaders. This becomes the more evident if attention is turned to the five basic topics in literature of the time: classical stories; mediaeval knights engaged in courtly love; historical stories relating to Charlemagne; histories of the crusades and psychological allegories.

    In terms of classical stories one of the earliest (end of 11th - beginning of 12th century) was the Romance of Alexander the Great . Thereafter, the three most famous examples were all written within a twenty year period in the second half of the twelfth century, namely, the Romance of Thebes (1150-1155), the Romance of Troy (1165) by Benoit de Saint-Maure and the Romance of Aeneas (1160-1170). These classical themes remained important. An anonymous Ancient History until the Time of Caesar (1206-1230) led to some forty illustrated manuscripts. Guido delle Colonne's History of the Destruction of Troy (finished 1287) was translated into almost every vernacular language. A fourteenth century Entry of Theseus into Athens (Vienna, ONB, Cod. 2617, fol. 39) contains another of the outstanding examples of proto-perspectival space in the illuminated manuscript tradition, which again has links to the narrative tradition in stained glass. It is noteworthy that actual historical accounts such as the travels of Marco Polo were frequently referred to as the Romance of the Great Khan and were sometimes even bound with the Alexander Romance (Bodleian Library, Ms. Bodley 264). So legend, story and history dovetailed. It is equally noteworthy that the first printed book in England was William Caxton's Recuyell of the Histories of Troy (1473-1474) and the first English printed book with illustrations was Caxton's Mirror of the World (1481), based on Vincent of Beauvais' Historical Mirror. These historical themes were seen as a top priority by one of the fathers of printing.

    A second important theme focussed on mediaeval knights. Famous in this respect was Chrestien de Troyes (c.1130-c.1227), best noted for Lancelot and the cavalier of the wagon (1179), Yvain and Parsifal . Lancelot was the first French literary work to be illustrated and later books followed the methods developed therein. These books by Chrestien drew heavily on Arthurian legends. It comes as no surprise, therefore, to learn that Chrestien de Troyes is said to have visited England. Chrestien de Troyes was emulated by Thomas d'Angleterre (c.1170), Béroul le Jongleur (c.1190) and by the authors of Tristan and Isolde. By the early twelfth century, depictions of the life of King Arthur were found in the Italian cathedrals of Modena and Otranto. In the thirteenth century, the Arthurian themes were developed in Mallory's famous Death of Arthur (Mort d'Arthur).

    It is striking that this shift in new themes came at a time when both the producers and patrons of manuscripts were changing. During the Middle Ages monks had been the prime producers and the patrons had generally been monks, missionaries and emperors. From the mid-twelfth century onwards, as the universities emerged, the production of manuscripts shifted increasingly to lay persons. Apparently it was particularly minor nobles who commisssioned and enjoyed reading romances of King Arthur and his knights. So the new themes involved both new secular producers and patrons.

    Connected with this Arthurian tradition, but with a firmer basis in history, was a third theme focussing on events in the eighth and ninth centuries. This had its roots in the chronicle literature. As early as the eighth century, the Chronicle of Frédégaire had recounted events in the period 584-642. A second, the Chronicle of Turpin, also known as the History of Charlemagne and Roland was written in Santiago da Compostella (one of the four main pilgrimage sites of Europe) at the end of the eleventh century and served as a sort of guide-book for pilgrims. It is well known that the pilgrim routes to Spain played an important role in the spread of Romanesque and subsequently of Gothic art. It also appears to have affected awareness of historical roots and story-telling. Thus Chaucer's tales told by pilgrims on the way to Canterbury were part of a larger pattern.

    In terms of twelfth century literature, the earliest treatment of the theme of Charlemagne was the famous Song of Roland (1100-1125), which dealt with events on the fifteenth of August, 778. It was said to have been inspired by pilhgrims who found the tomb of Roland on their pilgrimage to Santiago da Compostella, and was a topic taken up explicitly in the window of Charlemagne at Chartres. The same two decades that brought the three classical Romances of Thebes, Troy and Aeneas, brought the Romance of Brut (1155) and its sequel, the Romance of Rou or Deeds of the Normans (1155-1170) both by Wace. About three decades later (c. 1200) there followed the Song of the Saxons by Jean Bodel, which told the story of Charlemagne's expedition against Widekind.

    A fourth theme dealt with the crusades. Here, one of the earliest examples was the Song of William (end of 11th -beginning of 12th) by Garin de Monglane, which told of the exploits of William of Orange against the Saracins in the region of Arles. There followed the Song of Antioch (c.1180), by Graindor de Douai, which recounted events of the first crusade until the taking of Antioch (1098) and the Song of the Crusade against the Albigensians (1207-1218). The Song of Aspremont (c.1240-1250) told the story of the knights of Philip Augustus and Richard the Lion Heart in Sicily during the winter of 1190-1191 during the third crusade against Saladin. The same workshop that produced this work probably illustrated a romance on the chivalric adventures of Alexander the Great, the Romance of all Chivalry (1240-1250).

    A fifth theme was essentially psychological. One aspect thereof had its roots in Aesop's Fables, yet the mediaeval fable (fabliau) literature, linked with bestiaries, imbued this tradition with a much deeper personal dimension. One of the earliest of these was Richeut (before 1170). The most famous of these psychological portraits of virtues and vices was the Romance of the Rose begun by Guillaume de Lorris (1236) and finished by Jean De Meung (1275-1280). The visualization of psychological aspects which this implied, was taken further in the Lower Church of San Francesco in Assisi where obedience, ignorance along with other virtues and vices were carefully represented. In the Renaissance, Mantegna would take this theme one step further.

    On its own any one of this themes amounts to little more than a passing chapter in the history of literature. Cumulatively, the thrust of these classical stories, tales of mediaeval knights and courtly love; Arthurian legends, chronicles of the crusades and fable literature, introduced important worldly themes into a predominantly religious context. A framework which initially focussed on symbolic and typological meaning thus gradually shifted to include more everyday events. Depictions of eternity gave way to narratives involving changes in physical space or time. Typological parallels between Old and New Testaments originally sought to find Old Testament precursors for the Life of Christ. The shift to secular narrative meant that there could now be parallels between the Life of Chist and the Life of Saint Francis as occured at Assisi. Or there could be lives of saints as an independent theme. Abstract symbols gave way to real life donors and other depictions of human activity.

    An important characteristic of these new themes in literature was that they went far beyond verbal expression. The new stories were often illuminated, i.e. they had accompanying visual versions of the stories. These images in manuscripts were, moreover, frequently copied or adapted in stained-glass windows, painted frescoes, sculpted stones and elsewhere. Literature and art thus became increasingly interdependent.

History, Mirrors and Visual Knowledge

    To put it differently: stories gave way to histories and history became inherently visual. This may sound as if it were merely a clever turn of phrase, but it actually reflects profound changes. As early as the sixth century A.D., the Latin term historia was used to refer to a pictorial representation of an event. This meaning became particularly significant in France. In addition to an obvious meaning of "telling of memorable and true events", histoire meant the "representation of a scene with several persons, the illustration of a history book" and was sometimes synonymous with "painting, drawing or representation". The verb historier came to mean, "to represent events", or more precisely "to represent through a painting or a miniature (an historical scene)."

    Another connotation linked history with truth. Hence the adjective, "historical", was synonymous with "veridical". Which helps us to understand the term "natural history", in which history was linked with science, knowledge and understanding of the various productions of nature. In Italy, the oldest pharmacopia as we now know it, the Florentine Recipe Book, mentions that "nearly all the plants and other natural objects have been clarified by the history with the eye itself and with irrefrangible testimonies." Whence, the term, "history", acquired a more powerful meaning as "systematic description (of a plant, of an animal)".

    We have encountered a variant of this concept earlier. Giesecke, it will be recalled, claimed that this kind of systematic description was first introduced by the printing process and therefore argued that printing played a crucial role in the establishment of a new sense of veracity in the sense of scientific truth. We can now assert that it began long before the printing press in the West, while continuing to accept that printing helped enormously in establishing this on a more universal basis.

    When precisely did this new approach to history as a systematic scientific approach begin? Illustrations in literature began, as we have seen, with Lancelot, and spread through texts such as the Romance of the Rose, the Canterbury Tales and the Divine Comedy (fig. 6).

Author Title Manuscripts

Anonymous Lancelot 50

Guillaume de Lorris and Jean de Meun Romance of the Rose 200

Geoffrey Chaucer Canterbury Tales 85

Dante Alighieri Divine Comedy 1200

Fig.6. Examples of some of the great mediaeval illustrated literary texts and approximate numbers of manuscripts.

    To understand these developments it is important to trace the changing role of the eye in the acquisition of knowledge. The notion that the eye played a central role in learning had been acknowledged by Plato in the Timaeus. Subsequently, philosophers such as Philo of Alexandria, Augustine and Alcher of Clairvaux distinguished between three kinds of knowledge, corporeal, spiritual and intellectual, which they associated with the eye of the body, reason and contemplation respectively. These three paths were in a hierarchy such that the carnal eye was frequently associated with illusion and limitation whereas the eye of contemplation was that to which one aspired. By the twelfth century Saint Bernhard of Clairvaux maintained this distinction but acknowledged that one could see God in all creatures, i.e. even the physical eye could lead one to God. Hugh of Saint Victor (1118-1140) went further to claim that "if we wish to raise the eye of the spirit to the invisible, we need to comtemplate the similarities of visible things as traces of understanding."

    In the New Testament (Corinthians 13,12), Paul used the metaphor of looking into a glass darkly (i.e.a mirror) to describe how we know God. Medieaval thinkers typically compared the eye to a mirror. Metaphorically the eye became the mirror of the heart. Moreover, the Holy Scripture was also described as like a mirror of the mind, such that things inside us are seen. This image can be traced back to John Chrysostomus (344-407) and Augustine (354-407), and was used by Hugh of Saint Victor (118-1140) and Saint Bonaventure (1221-1274). Mystics such as Meister Eckhart (1260-1328) claimed that one needed a mirror to see God. The Virgin Mary, Christ and the saints were to be seen as mirrors. Some authors deliberately referred to both figurative and literal mirrors. Albrecht von Scharfenberg, for instance, described the knights Akuleis and Mecka who were metaphorically mirrors but at the same time carried real mirrors in fighting basilisks.

    This visualization of interior qualities (cf. theme five above ) was closely linked with the use of metaphors of vision in the moral domain. Chrestien de Troyes, for instance, explored the theme of the eyes as a mirror of the soul in his Cligès. Around 1230, Petrus de Limoges, wrote an anonymous Treatise on the moral eye, which was variously attributed to John Peckham, Robert Grosseteste, Duns Scotus Johannes Gualensis, Hugh of Saint Victor and Thomas Bradwardine. Schleusener-Eichholz (1978) has drawn attention to the interplay between the development of this visual allegory and scientific concepts such as experiment.

    The metaphorical use of mirrors to reflect inner virtues gradually shifted to refer to external objects. Nicolaus von Strassburg claimed that all creatures were as a mirror in which God was reflected. Meister Eckhart and Saint Bonaventure claimed that the whole of creation was a mirror. A next step was taken by the Dominican encyclopaedist, Vincent of Beauvais (c. 1190-1264), who wrote a Natural, Historical and a Doctrinal Mirror, which were combined under the title Greatest Mirror (c. 1244-1260). His Natural Mirror was a record of natural history in the sense explained above. His Historical Mirror began with the creation of the world and ended with the crusade of Louis IX in 1254. His Doctrinal Mirror added another 17 chapters. An anonymous author subequently added a Moral Mirror (c. 1310-1325). The initial Latin manuscripts were not illustrated, but once translated into Middle Dutch (1330) and especially into French (1332) many illustrations were added. Gradually these figurative images of mirrors reflected physical reality, discussions of mirrors, were reflected so to speak in illustrations. Later the quest emerged of using physical mirrors to record that physical world. So verbal descriptions as if they were visual emerged in the period around 1250 even though the visualization this implied was not explored until some eighty years later and not fully exploited until 150 years later at the time of Brunelleschi's demonstrations.

    As a result the image of the mirror as a reflection of Nature, God, truth and history, in the sense of representation of true events, became intertwined: true depictions, visual illustrations, history and mirrors became ever more synonymous. Besides Vincent of Beauvais' Mirror of History, there was an anonymous Historical Bible (1291-1295), the very years that Giotto began work at Assisi), based on the Scholastic History of Petrus Comestor, which linked these themes of historical and scientific truth with theological truth, and inspired some seventy illustrated manuscripts.

    If we look to Italy, it is striking that the breakthroughs in visual narrative came in the context of French narratives as in the town hall at San Gimignano in the period 1280-1300 in the so-called Room of Dante. It is all the more striking then to discover that the definition of history as a "representation, painted or sculpted of a subject or contents taken from a sacred or profane [his]story, from mythology etc. In a concrete sense: painting or sculpture which represent such a fact or such events" was introduced into the Italian language by Dante. Hence, where the French had interpreted history to be a visualization usually in terms of miniatures in manuscripts, Dante interpreted history to include paintings and sculptures on walls. His heightened approach to visualization thus helps explain not only the vast increase in illustrated manuscripts (cf. fig. 6), but also why the themes of the Divine Comedy soon began to populate the walls of monasteries, churches, and even secular buildings. This led to Leonardo's definition as "decorating a surface (a panel, wall etc.) with a representation in painting or sculpture with historical, sacred or legendary facts, linked together by a narrative nexus." Hence, by the late fifteenth century history, sacred accounts and legends were being distinguished anew, but narrative remained a key.

    To return to the thirteenth century, this new approach to narrative meant that the same impulses which brought realism, and a sense of individuality to the statues of cathedrals; brought new attention to the importance of saints and contemporary donors and brought a personal viewpoint to story-telling and a new richness in artistic expressions of story-telling. The same Gothic influences which changed the nature of story-telling in literature, transformed the sculptures of Naumburg (c. 1213-1242), and led to the first stained glass windows on the Life of Saint Francis at Erfurt (c.1220-1230). Paradoxically, while we have traditionally thought of the Gothic as somehow opposed to the Renaissance, the new realism of the Gothic helped to provide the essential narrative impulses that made possible Renaissance perspective.

    We would suggest that the answer may well lie in new interplay between the traditions of Northern Europe and those of Italy, a theme which Castelnuovo (1966) and Ragghianti (1977) have explored with respect to the fifteenth century. The various orders had a network of monasteries which connected the whole of Europe. These connections were stronger when a northern cleric gained a high position in the Church. Gerbert, who became Pope Sylvester II, was an early example. Urban IV of Troyes was another example, and all the more interesting in this context. Besides being the birthplace of Chrestien of Troyes, whose stories introduced new aspects of narrative, and a place the cathedral windows of which were one of the first great expressions of Gothic narrative art (1170), it was the town, less than a century later, where a new mood in painting was introduced:

at Saint Urbain in Troyes, a church built by Urban IV on the site of his birthplace and on which work began in 1262....On the upper story the figures of the prophets, which accompany a crucified Christ surrounded by the Virgin and Saint John, are placed beneath architectural baldachins... Portrayed either in full or three quarter profile, with a strongly expressive feeling of action, these figures seem to be endowed with a strongly expressive feeling of action.

    The pope, at the time, was based in Viterbo and would have been fully informed of these developments. For a person in Italy to learn about the latest trends in Northern realism was nothing new. Different and, possibly seminal, was a particular constellation of events at the time. The date was 1262. Three years later in 1265, Urban IV's successor, Pope Clement IV in Viterbo, commissioned Roger Bacon to write the Greatest Work (Opus Maius), which gave an epistemological (see below p. 41*), as well as a theological basis for a new emphasis on visual veracity through visual representation. Whereas Bacon's predecessors had seen the visible as merely a stepping stone towards the invisible, Bacon claimed that the visible played a crucial role in this understanding. Indeed, he claimed, that an exact knowledge of scientific phenomena was pre-requisite for an understanding of the spiritual sense that lay buried within.

    Edgerton (see above p. 8) and Bergdolt have already drawn attention to a key passage in Bacon's Greatest Work, but it is necessary to cite it again at some length in the context of our discussion. Bacon was considering the uses of geometry. After mentioning the obvious applications to 1) astronomy, 2) geography, 3-4) chronology (in different aspects), he turned to its use 5) in Biblical interpretation or hermeneutics. Here, he linked geometry with picture-making. Geometry combined with art in the form of picture-making thus became a key to unravelling the secrets of the Scriptures. In Bacon's own words:

it is impossible for the spiritual sense to be known without a knowledge of the literal sense. But the literal sense cannot be known unless a man knows the significations of the terms and the properties of the things signified....it is not possible for the literal sense to be known unless a man have these works depicted to his sense, but more so when they are pictured in their physical forms; and thus have the sacred writers and sages of old employed pictures and various figures, that the literal truth might be evident to the eye, and as a consequence the spiritual truth also....But no one would be able to plan and arrange a representation of bodies of this kind, unless he were well acquainted with the books of the Elements of Euclid and Theodosius and Milleius and of other mathematicians.

    This was written in 1265. As will be noted below, four years later in 1269, William of Moerbecke in Viterbo was translating these works, and almost immediately afterwards Witelo, also in Viterbo, used this translation as the basis for Book one of his great work on Optics (Perspectiva) which he dedicated to Moerbecke. In the Opus maius, Bacon went on to express what he hoped would happen: his version of a wish-list:

Oh, how the ineffable beauty of divine wisdom would shine and infinite benifit would overflow, if these matters relating to geometry, which are contained in Scripture, should be placed before our eyes in their physical forms! For thus the evil of the world would be destroyed by a deluge of grace, and we should be lifted on high with Noah and his sons and all animate creatures collected in their places and orders.... Surely the mere vision perceptible to our senses would be beautiful, but more beautiful since we should see in our presence the form of our truth, but most beautiful since aroused by the visible instruments we should rejoice in contemplating the spiritual and literal meaning of the Scripture, because of our knowledge that all things are now complete in the Church of God, which the bodies themselves sensible to our eyes would exhibit. Therefore I count nothing more fitting for a man diligent in the study of God's wisdom than the exhibition of geometrical forms of this kind before his eyes. Oh, that the Lord may command that these things may be done! There are three or four men who would be equal to the task, but they are the most expert of the Latins.

    The passage would seem to be a plea to do a full scale mural version of an illustrated Bible as a key to hermenutics and a deeper understanding of the spiritual truths of the Old and New Testaments. Yet how could Roger Bacon, an Englishman living in Paris at the time, express this wish when he would have seen the Sainte Chapelle and very likely have been aware of Chartres? Was it just a question of wanting a narrative in painted fresco than in stained glass? Perhaps it is significant that he specifically referred to Latins, by which he presumably meant Italians.

    A typical Italian of the time would have used some geometry in doing their painting but would have continued the focus on traditional symbolism thus putting severe limits on the potential naturalism of their work and precluding a proto-perspectival treatment. Roger Bacon was, however, a Franscican. Living in France, he would have been fully aware of the tradition of the troubadours emphasizing vernacular versions of scripture, which Saint Francis had adopted. He would have been equally aware of a Fransciscan tradition, again borrowed from the troubadours, of acting out their stories. In this context the Birth of Christ became transformed into scenes with a real manger and live, local shepherds. The Life of Christ was not just a story to be read. It was something to be re-lived by Saint Francis and indeed by all his followers. If we are right then Bacon's wish-list was not just for another Life of Christ using some geometry, but rather a Life of Christ which would be paralleled with a Life of Saint Francis, in order that obscure meanings of the scriptures could be exemplified in terms of everyday events in the life of the founder of his order.

    All of this becomes the more fascinating if we remind ourselves of the chronology of events surrounding the famous frescoes at Assisi. If we accept Poeschke's dating then the Saint Francis Master had begun working in the lower church of San Francesco around 1260. At the time Bacon was writing the Gothic Master had arrived on the scene (1265-1270), to be followed by the Roman Master (1270-1280). By 1280, Cimabue was beginning a more systematic approach which was then carried out successively by Giotto (1290-1300, 1320), the Giotto School (1300-1305, 1315-1320), Lorenzetti (1315-1320,1325-1330) and Martini (1320-1325). If we are right then Bacon was calling for a systematic decoration of Assisi which began almost immediately and took some sixty years to complete. The result was something that may be remembered as uniquely Italian, yet would not have been possible without a French connection, and for that matter, an English connection. This interplay of North and South continued in the early fourteenth century. Simone Martini from Siena, for example, who contributed to Assisi, also spent time at the papal court in Avignon.

    As we shall see presently, the pope, who commissioned Roger Bacon to write his Greatest Work (Opus maius), had done so with quite another purpose: to put learning on a new track that would avoid the excesses of Aristotelian logic of the Dominicans and the tendencies towards Platonic mysticism of the Franciscans. Bacon set out to find a new goal for knowledge in experiment based on mathematical truth. We shall show that it was ultimately the combination of this scientific and larger, epistemological goal, that transformed the proto-perspectival exercises of Assisi into the mathematical perspective of the Renaissance.

    However, before turning to the scientific origins of perspective, it will be useful to make two brief excurses. First, we shall stand back and summarize some of the major shifts in spatial representation from the eleventh through to the seventeenth century in order to get a big picture. Second, we shall look at three characteristics of perspective, namely, its capacity for relating, emphasizing and varying scenes. This is essential if we are to understand how, and why the tool that began as an aid to narrative, simultaneously undermined many of narrative's premises.

Romanesque (c. 1000- c. 1200) and Gothic Periods (1140- c.1399)

    One strand of the classical heritage that particularly fascinated the middle ages was a neo-Platonic tradition that focussed on the concept of light. Through Plotinus, Augustine, Dionysius the Pseudo-Aeropagite and John Scot, light became a key to understanding the visible world and the visible world a basis for comprehending the invisible world beyond. Hence it was that the chain of being which in the Manichean tradition served as a rationale for rejecting the physical world, became in the Christian tradition the reason for accepting, studying and depicting the visible world of God's creation. As we shall see presently, the English Franciscans, notably Grosseteste and Bacon, found in light an explanation not just for the multiplication of species, but for the origins of the physical world: their version, as it were, of atomic theory. This generated both new interest in the metaphysics of light through authors such as Pseudo-Witelo and new studies of the physics of light, through optical writers such as Bacon, Witelo, Peckham, and their followers. The shift from Romanesque to Gothic began partly as an exploration of how visible light could have metaphysical effects and led to the magic of Chartres. This focus on the forms of light subordinated and tended to obscure the contents of the windows through which the light passed. From the mid-twelfth century onwards however, the contents of the windows increasingly competed with the forms of light that made them visible, as narrative became ever more important.

    In terms of fresco painting, narrative had always played some role. With the Carolingian revival famous monasteries such as the Reichenau had introduced some narrative cycles, but these remained the exception. After the year 1000, as the barbarian invasions receded, Europe entered into a new stability. As Christians realized that they had entered safely into a new millenium, they built new churches by way of thanksgiving. They also gave new attention to biblical stories and their pictorial representation. This began in terms of specific parts of churches such as doors (Verona, Hildesheim), ceilings (Hildesheim), and later rose windows (Reims, Chartres, Paris, York). Symbolic harmony determined the arrangement of individual elements into a coherent whole. Story-telling was gradually extended throughout the entire space of the church as in Monreale and Wienhausen. These masterpieces of later mediaeval art were effectively symbolic Summa which parallelled the philosophical efforts of Hugh of St. Victor, Albertus Magnus and Thomas of Aquinas. In terms of contents, faith was dominant, i.e. Christian values. In order to relate these images more systematically, proto-perspectival elements were introduced in subsequent examples, beginning with individual, often isolated, architectural elements and other objects. This development of isolated spatial forms was one strand in the rise of perspective.

    A second strand entailed the development of spatial context through interior rooms and exterior landscapes. This owed much to the secular literature ranging from the Provençal, courtly love poems and Arthurian legends to chronicles which linked historical events with contemporary happenings such as the crusades. This second strand emerged partly in France, but predominantly through the Burgundian Court, which brought the rise of Netherlandish art. Elsewhere, in Siena, Simone Martini also introduced a new emphasis on spatial context in his famous frescoes in the Palazzo Pubblico. Connections through the papal court of Avignon, brought interplay between the French and Burgundian traditions and these Sienese developments, partly through the direct sojourn in Avignon of Simone Martini himself. In the next generation, the Sienese tradition evolved through painters such as the Lorenzetti brothers and Giovanni di Paolo.

    These two strands of spatial mastery, namely, spatial forms (isolated objects) and spatial contexts (interiors, landscapes) evolved in parallel. Their integration came slowly. Assisi can be seen as one of the first attempts at synthesis. Giotto's Saint Francis cycle (c. 1290-1300) dealt with both spatial objects (such as a niche, a chapel or an interior) and spatial contexts (a landscape with figures). Giotto's subsequent cycles in the Arena Chapel at Padua (1304-1308) and the Peruzzi Chapel in Santa Croce (Florence, c. 1327) pursued this quest as did Lorenzetti's work in Siena and Assisi during the 1330's and 1340's. Further experience led Lorenzetti (1344) to master these proto-perspectival elements and discover practical solutions in terms of vanishing points.

Renaissance (1400-1500)

    The better part of a century passed before these practical solutions led to practical demonstrations by Brunelleschi (c.1415-1425) and almost as much time again before these practical demonstrations had been transformed into quantitative experimental demonstrations by Leonardo (1492). In the course of the fifteenth century artists also discovered that perspectival elements which emphasized scenes offered new possibilities in creating variations thereof. Spatial harmony now outweighed symbolic harmony. The key developments in these new explorations took place in Florence in chapels such as the Brancacci in the Chiesa del Carmine, in Santa Croce; in Santa Maria della Novella and Santa Trinità. With respect to contents, (sacred) faith and (secular) reason were treated increasingly on equal terms.

High Renaissance (1500-1527)

    These principles were then applied to an entire space such as the Sistine Chapel or the Stanze in the Vatican. By now spatial harmony of the individual elements determined symbolic harmony and gave the whole a dramatically new effect. In order to appreciate the element of continuity, it is instructive to compare the ceiling at St. Michael’s, Hildesheim, with the Sistine Chapel in the Vatican. Their basic elements are surprisingly similar: both have central panels with episodes from the Old and New Testaments. Both are flanked by religious prophets and pagan sibyls. But Michelangelo’s version has a number of additional elements: further Old Testament scenes in the roundels, Christ’s forebears, the children of Israel, etc. We are back at Panofsky’s theme of Renaissance and Renascences. There is a continuity between St. Michael’s in Hildesheim and the Sistine Chapel in the Vatican. What sets them apart is that organization in Saint Michael’s is a principle of harmony based mainly on symbolic elements, usually in simple parallels or oppositions as in Old versus New Testament; whereas organization in the Sistine Chapel is dominated by spatial harmonies, allowing a much more complex interplay of related themes with greater emphasis and variation. Raphael developed these potentials in the Stanze, maintaining the assumption that the frame was the key to spatial harmony. But in terms of contents, Christian and pagan elements now vied with one another: faith was being challenged by reason.

Mannerism (1527-1600)

    Mannerism questioned this assumption that a frame was the key to this spatial harmony as in Fontainebleau’s Galerie François Ier or the Villa Maser. Balanced spatial elements as a principle of organization were thus abandoned as, for instance, in Giulio Romano’s Room of the Giants in the Palazzo del Te at Mantua. In terms of contents, faith and reason were now often in conflict. Meanwhile, the spread of printed picture books with perspectival examples created new ambiguities between ancient and modern, ideal and real buildings, provoking new combinations which radically expanded the horizons of the imagination. By this time the combination of perspective and print culture ushered in a revolution.

Baroque (1600-1750)

    These mannerist experiments revealed increasing ambiguities between the spaces of 1) pictures inside the frames; 2) the frame itself; 3) areas beyond the frames. This led to such a conscious play with the boundaries between painted and architectural surfaces and spaces that it became impossible to distinguish them. The manipulation of depicted space thus became combined in a larger programme involving the manipulation of architectural and ultimately environmental space. This again transformed the whole nature of pictorial story-telling. The high mediaeval period began to reduce a basically linear sequence of incidents into a number of key episodes symbolically arranged. During the proto- and early Renaissance these incidents were further reduced, interpreted hierarchically, with some given much more emphasis than others, varied more and increasingly organized in spatial terms. In the high Renaissance these elements were for a brief period combined in a coherent spatial harmony. When this harmony was subsequently challenged by the mannerists and ultimately rejected by baroque artists, the actual content of the stories gradually lost significance. A method which had promised to give new form to narrative content, now increasingly replaced content by new spatial forms. Thus Tiepolo's ceilings of indistinct figures on fluffy clouds prepared the way for the airy ceilings of the enlightenment.

    To understand this paradox of how perspective which, was meant to improve story-telling also helped to destroy it, we need to focus briefly on three of its distinguishing characteristics: its power in relating, emphasizing and varying scenes.

Relating Scenes

    Painters committed to representing a story with many episodes were faced with a problem of individuating the scenes. Framing them was an obvious step. However, frames could not give many clues concerning the order in which the scenes were to be read. Here proto-perspectival elements served to relate scenes while, at the same time, separating them. Duccio’s Maestà (Siena, Museo del Duomo, 1288) offers an excellent case in point. On the back of the altar (Sources, fig. 2), the story begins in the bottom left hand side with Christ’s entry into Jerusalem, moves to the right in an up-down sequence, then returns to the upper left hand side again criss-crossing its way to the far right. Three scenes with Christ and his Apostles (Washing of the Feet, Last Supper and Meeting with Apostles) all share one type of spatial interior with beams of the ceiling converging towards a central axis. Three scenes with Caiphas and the priests occur in an interior with a type of oblique parallel projection. A similar parallel oblique method applied to an awning supported by columns connects scenes with Pontius Pilate in the bottom right and top left. In the Maestà, proto-perspectival elements thus relate separate scenes and help us to follow their sequence.

    Giotto used the same technique in the Scrovegni Chapel in Padua (1304-1308), where an oblique view of an open fronted house served for both the Annunciation to St. Anne and the Birth of the Virgin, and where a temple with a niche served as a continuation between three scenes: Ceremony of the Rods, Prayer for the Miracle of the Rods (pl. 7.1) and Marriage of the Virgin. This function of relating separate scenes in a complex narrative helps to explain why a few proto-perspectival elements became stock images which improved empirically, while other architectural elements remained spatially awkward and unconvincing. Piero della Francesca took up these stock images in his On perspective of painting (De prospectiva pingendi, c.1480). Barbaro published them in his Practice of perspective (Pratica della perspettiva, 1568) and thereafter they became familiar elements in the printed texts. Hence the early manuscripts and printed texts (1450-1550) on perspective consolidated and presented in mathematical terms images that the tradition of painting practice had mastered empirically in the two previous centuries. Their initial role was to standardize rather than to innovate. Meanwhile artists explored the practical potentials of perspective. Paolo Uccello in his Profanation of the Host used two vanishing points going in different directions in order both to separate and to relate the two scenes. The same principle is evident in the Munich manuscript of Boccaccio (Hss. Abt. Cod. gall. 6, 53v.) and in the organization of the Teatro Olimpico at Vincenza (cf. Sources, plate 78.1-3).

    If scenes with different vanishing points were implicitly related by means of perspective, scenes physically separated from one another were also explicitly related by means of a single vanishing point as in Giotto’s Annunciation in the Scrovegni Chapel in Padua (1304-1306). Masaccio—and Masolino—developed this idea in their Annnunciation in San Clemente, and Foppa used it dramatically in his Annunciation in S. Eustorgio. This applied equally to other themes. Parronchi (1964) suggested that Ghiberti used it on the doors of the Baptistery in Florence and has convincingly shown that Masaccio used it to relate The Distribution of the Goods with Saint Peter Curing the Sick in the Brancacci Chapel (Florence, Chiesa del Carmine, 1426-1427). More subtle variants were also possible: spatially analogous scenes could be related without necessarily sharing a single vanishing point as, for example, Piero della Francesca’s Annunciation and Dream of Constantine in the chapel at Arezzo or Raphael’s juxtapositions of sacred and profane scenes in the Stanze of the Vatican.

    Aronberg Lavin’s (1990) research into the history of narrative painting brought to light an unusual feature in their arrangement: the narratives did not follow any single, simple sequence from left to right analogous to the sequence of letters on a page. Instead they criss-crossed, zig-zagged and followed other unexpected patterns. Nor did this always improve with time. A comparison of narratives at Monreale (1182), the Lower Church at Assisi, the Scrovegni Chapel in Padua (1304-1306), Arezzo and the Stanze in the Vatican reveals that the sequences became increasingly non-linear.

    Three reasons for this may be suggested. First, whereas art frequently functions as a substitute for literacy in the early middle ages, this changed as literacy became more widespread in the thirteenth and fourteenth centuries and even more so after the advent of printing in the 1450’s, with the spread of vernacular bibles (of which there were 22 in Germany alone before Luther). Artists were increasingly able to take for granted that their viewers had read the biblical stories or at least had heard them read or discussed. This applies even in famous cases such as Assisi. Each of Giotto's frescoes has a Latin inscription as a caption. (Interestingly enough many modern photographs typically cut off these captions so that we learn to see them as pictures in isolation).

    Secondly, the situation was complicated through an increased concern with systematic typological and symbolic presentation. In the great rose windows of the thirteenth century (e.g., Chartres, Paris, York), the emphasis was on parallels between the Old and New Testaments with minor references to relevant pagan figures such as the sibyls. In the next centuries this pagan element gained in significance to the point that Raphael’s task in the Stanze became one of finding parallels between Christian and Antique themes: the Church Fathers vs. the School of Athens. In the great cycles it was no longer a question of telling complete stories, but rather one of choosing key episodes in stories which could be balanced by others. Because perspective provided a framework for the organization and comprehension of such scenes, their narrative order often became less significant.

    There was yet a third complicating factor. Early proto-perspectival elements functioned partly as frames separating one scene from another. In the Scrovegni Chapel in Padua, Giotto explored how this framing function could be manipulated in order to create ambiguities between real and fictive spaces. Sandström (1963) made a perceptive study of these developments. They are of interest for our purposes because the resulting ambiguities increased the potential for polyvalent readings of the scenes theoretically linked and systematically related: for this reason the Sistine Chapel was more complex than the Scrovegni Chapel.

    In the 1470’s artists began to play with relating different viewpoints within a single painting. Piero della Francesca’s Brera Altarpiece (Milan, Brera, 1472-1474) was a case in point. One viewed it frontally to see the context generally and then looked at it from the bottom left in order to recognize that what appeared to be an egg was actually a sphere. Holbein used the same principle in his Ambassadors (London, National Gallery) and Maignan developed it dramatically in his Saint Francis de Paul in S. Trinità in Monte. The development of such anamorphic games (see below pp. 89-90*) further subverted the linear sequence of stories. Sometimes, perspective which developed in the context of narrative, transformed its sequence, and reduced what had been a flowing story into balanced oppositions of key scenes.

Emphasizing Scenes

    This was partly because perspective not only related scenes but also emphasized them in particular ways: exaggerating the geometry of the man-made environment, drawing the viewer’s eye into a spatial scene, while reducing the size of individual figures within that scene to a diminuitive size. This proved inconvenient for a Christian tradition that focussed on Christ, Mary and various saints. A compromise thus ensued. Individual figures continued to dominate the main panels, while scenes relating to their lives were relegated to the predellas where key scenes were emphasized through perspectival effects. In the Life of the Virgin these included the Presentation in the Ternple and Death of the Virgin. In the Life of Christ these were usually the Annunciation, Flagellation and Last Supper. It may be no co-incidence that most of these themes co-incided with those typically found in a Book of Hours, the most popular illustrated text of the time.

    Manetti’s biography indicates that when Brunelleschi made his first perspectival demonstration, he clearly believed that the viewpoint had to be precisely in line with the central vanishing point of his picture. Elementary textbooks ever since have perpetuated this belief. But it is not quite true. Just as in portraits, where eyes facing the viewer continue to follow one as one moves to the side, so too in perspectival pictures do alleys, corridors and other regular spatial features follow one even when seen from the side. For this reason we can look at perspectival settings and movies from more than one seat (see below pp.**). If Renaissance artists did not discuss the problem, they were clearly aware of it. Kubovy (1986) termed this phenomenon robustness of perspective, and noted how Leonardo realized that his Last Supper would work even though he made its vanishing point at a height where no ordinary observer would view it.

    In the Last Supper, perspective emphasized the painting precisely because it could be viewed without undue distortion from anywhere within the refectory of Santa Maria delle Grazie. The same held true for Bramante’s fictive arch in Santa Maria presso San Satiro also in Milan; Tullio Lombardo’s scenes from the Life of St. Mark in the Scuola Grande di San Marco in Venice, and indeed for all Renaissance perspectival pictures with regular receding columns, arches, alleyways etc. The fictive depth involved could be large as in Masolino’s version of Herod’s palace at Castiglione d’Olona or small as in Piero della Francesca’s Brera Altar, but the effects were the same. And like the relating function, the emphasizing function of perspective undermined the continuity of the story, focussing attention on key episodes of a narrative.

Varying Scenes

    Professor Brian Stock, in his important book, The Implications of Literacy (1983) noted that: "With shared assumptions the members were free to discuss, to debate or to disagree on other matters, to engage in personal interpretations of the Bible or to some degree in individual meditation and worship". For art, the implications of literacy were equally important. In pre-literate societies a statue of a given god, insomuch it was often the central object that the members of a tribe had in common, defined the communality of a group. Variation was very limited because deviation from the norm could result in lack of recognition. This changed with the advent of literacy. Characteristics of a given god, or the Diety, were known from texts, and because texts now defined what persons knew and had in common, it was no longer necessary for the work of art to establish a sense of communality. Indeed the challenge arose of creating variants on already well known themes. If this was true for the Bible in general, it was particularly so for key scenes such as the Annunciation. Proto-perspectival features augmented this process of variation even before perspective was formally established, as evidenced by Pietro Cavallini’s Annunciation (Rome, Santa Maria in Trastevere) or Ambrogio Lorenzetti’s Annunciation (Siena, Accademia, 1344), generally accepted to be the first painting in which all the lines of the tiles converge to a single vanishing point.

    After Alberti’s first treatise (1434), and particularly after the advent of printing in the 1450’s, the process of variation increased in intensity. Some examples, such as the unknown fifteenth century painter in Santa Maria Novella continued to produce rough empirical versions. Fra Angelico made several variants using an open colonnaded space (e.g. Madrid, Prado), thus developing a form used earlier by Nicolo di Pietro Gerini (New Haven, Yale University Collection, 1375); or another with a portico opening into a garden (Florence, San Marco), a theme which Domenico Veneziano (Cambridge, Fitzwilliam) also explored. Sometimes the scene was inside on a regular pavement as in the anonymous Annunciation, (New Haven,Gardner Collection); outside on such a pavement, as in the version by Francesco di Giorgio and Naroccio di Landini (New Haven, Yale Collection), or outside in a green garden as in a version by Filippo Lippi (London, National Gallery), and Leonardo da Vinci’s Annunciation (Florence, Uffizi).

    Crivelli, by contrast, developed a spatial example from Bellini’s Sketchbook in his Annunciation (London, National Gallery), which was at once symbolic of Christ’s coming and at the same time a record of a papal grant by Innocent III to the citizens of Ascoli Piceno concerning certain rights of self government which reached the town on the feast of the Annunciation, 25 March 1482. Crivelli thus combined information from a biblical text, a sketchbook and an historical event in his painting. More complex textual sources called for a more complex picture with a spatial arrangement such as that provided by perspective.

    A full classification of varying stylistic elements in Renaissance Annunciations would be a large book in itself. Even so, it is instructive to note how every region developed recognizable variants of the same subject. Flemish versions were normally in living rooms (e.g. Robert Campin’s version in the Metropolitan), bedrooms (e.g. Gerard David in the Städlesches in Frankfurt) or in apses of churches as in Van Eyck’s version (Berlin, Staatliche Museen), which was adapted by the Master of Bruges (Antwerp, Koninklijk Museum voor Schone Kunsten, 1499). In Germany, Annunciations were also frequently in bedrooms as in Dürer’s woodcut (e.g. San Marino, Huntington Library, 1502) and churches as in Grünewald’s Isenheim Altar (Colmar, Musée d’Unterlinden, 1510-1515), but with very different uses of space. Meanwhile, other Flemish versions combined elements of the living room, bedroom and church interior in a single, rather unlikely space as, for instance, the Annunciation attributed to Henri met de Bles (Cambridge, Fitzwilliam Museum). Variants of this composite spatial arrangement became popular in Spain, as witnessed by Alejo Fernandez’ version (Seville, Museo de Bellas Artes) or in Berreguete’s Annunciation (Burgos, Cartuja de Miraflores).

    This practical tradition of using perspective to produce unexpected variants of an already familiar theme continued into the seventeenth century. For instance, nine of Saenredam’s eighteen surviving construction drawings for his famous interiors involved a single church, St. Bavo, in Haarlem, the exterior of which contemporaries such as Berckheyde also depicted from different points of view (cf. Sources, plates 22-23).

    Examples such as the Bayeux Tapestry remind us that already in the eleventh century there were extensive narratives with many scenes. One might have expected that the new links between literacy, biblical texts and proto-perspectival methods would have led directly to a systematic visualization of the story-telling process. Andrews (1988), in an important dissertation, convincingly showed that this was sometimes the case. However, as we have seen, perspective also led particular scenes to be related, emphasized and varied to unexpected degrees. The so-called conquest of reality thus occured through gradual mastery of a surprisingly small number of basic forms in the context of a few stock scenes. As Veltman (1992) has shown, certain orders of the church were particularly active in the development of this repertoire of stories and scenes. Perspectival effects thus began long before the advent of printing. Nor were these effects necessarily linear. As we have shown they often undermined the strict sequence of the storytelling. Spatial harmony thus began to vie with symbolic harmony, spatial form vied with spatial content,  leading to a renewed fascination with light, this time in a secular sense.

    A new attitude to optics as a mathematical science was required. In a sense Brunelleschi, Alberti, Piero della Francesca, Leonardo da Vinci, Guidobaldo del Monte and Desargues (and his popularizer, Bosse) all made mathematical demonstrations of perspective. Yet we need to understand the profundity of changes in the concept of demonstration if we are to appreciate why more than two centuries lay between Brunelleschi’s panels and Desargues’ treatise. For Brunelleschi it sufficed that his representation produced the same effect as the original object. His demonstration lay in showing a physical correspondence. Alberti took a twofold approach. In his On painting he mentioned basic precepts of optics and claimed that these applied. He alluded to mathematical demonstrations which he subsequently recorded in his Elements of painting. These were in fact but a few, simple, isolated examples. Hence Alberti had an optical (visual) and a geometrical demonstration but did not relate the two.

    For Piero della Francesca, geometry served as a basis for truth and hence geometry helped to make perspective a tool for certifying vision as well as representation. Piero’s three treatises, On perspective of painting, On the abacus and Booklet on the five regular solids set about the task of relating perspective to a corpus of mathematical texts that included Euclid’s Optics and Elements, as well as Archimedes. His demonstrations remained predominantly mathematical, yet it is significant that in his On perspective of painting, Piero began with visual demonstrations based on surveying experience, suggesting that this was becoming the more valid mode of demonstration. Leonardo da Vinci went one step further. He was not content until he had demonstrated a systematic series both visually and geometrically. As we have shown elsewhere (1986), this led Leonardo to discover the regularity of the inverse size/distance law that Piero had denied. Leonardo effectively demonstrated that a series of experiences related to surveying, coincided with optical experience and could be reproduced with the mathematical projection methods of perspective.

    It remained to be shown that the projection methods of surveying and perspective were identical to those of planisphere and astrolabe projection. As will be suggested below, the context for this was several centuries in the making, yet it was not until Commandino (1558) that this was actually demonstrated. The principles of geometry in the context of astronomy were now associated with the origins of perspective. Commandino’s student, Guidobaldo (1600), assumed that geometry was the basis of perspective in painting, architecture and scenography and set out to demonstrate this. For Desargues (1636), the origins of perspective lay partly in his practice of architecture and sundials, partly in geometry. As a result, his demonstration could no longer be in some particular example: it focussed on a general principle that made possible and generated such particular examples. Hence from its earliest proto-perspectival beginnings in the fourteenth century to its codification in the seventeenth century, a basic shift took place in the meaning of perspective.

    Scholars have emphasized the interdependence of optics and perspective in these developments. Yet ancient optics clearly did not produce perspective. What changed? As noted elsewhere (Sources, p. 142) one answer lay in the scope of optics itself. In Antiquity optics was included in four domains of study: geometry, physics, philosophy and medicine. Euclid’s geometrical Optics contained but four propositions on objective questions of measurement in a surveying context and devoted the rest of its fifty-five propositions to subjective, psychological questions of how the eye was deceived. The Middle Ages, particularly in the context of the Arabic tradition, integrated these separate domains to create a coherent field of study and focussed attention on the conditions under which the eye would not be deceived. Optics thus became increasingly a preventative study of conditions in which objective sight was possible. This shift in the definition of optics went hand in hand with a gradual recovery of ancient knowledge, a redefinition of knowledge and a new emphasis on instrumentation all of which played their role in preparing the way for perspective.

    In his monumental edition of The Optics of Ibn Al-Haytham (known to the West as Alhazen), Sabra (1989), discussed the importance of the Greek tradition (e.g.vol.II, lxi) and showed that he used Ptolemy's Optics as a point of departure (II, lx ff.); noting basic differences that more superficial readers continue to overlook. He acknowledged, for example, that Ptolemy used the term experimentum eight times and experiri one time in his Optics (II, 17), and expanding on a previous article, suggested that the astronomical tradition was a likely source of his emphasis on experiment (II,14-19). An emphasis on experiment became one of the most striking features of the work. Time and again Ibn Al-Haytham spoke unequivocally of an experimenter and experiments (e.g. I, 8, 19, 22, 36, 37, 38, 39, 40, 153) or of the use of specific instruments (e.g. I, 18, 23, 43, 85, 238) and Sabra rightly related this to one of the most distinctive and important features of Ibn al Haytham’s book (II, lxxxvi): "namely, its adherence to definite forms of argumentation that mainly consist of empirical observations frequently followed by experimental verifications in which geometrical proofs are sometimes employed". Another crucial feature of his approach was an emphasis on psychology. He (II, liv-lv):

maintained that a theory based on the intromission hypothesis could not qualify as a viable explanation of vision unless it was supplemented and supported by a psychological theory setting out the modes of inference that were necessarily involved in the perception of visible properties other than light and colour....The Optics not only introduced a new doctrine but a new methodology for the study of visual perception.

    Sabra explored some aspects of the transmission of this text, which Marshall Clagett is said to have described as the most influential single work of the Middle Ages; how it was apparently unknown to most Arab thinkers until the commentary of Kamal al-Din; how the Latin tradition lost Book I of Ptolemy's Optics and also omitted the opening three chapters of Book I of Ibn al Haytham's Optics; which left Western authors (II, lxxvi-lxxvii): "without a doctrine of light and colour which serves as a basis for the theory of vision in the subsequent chapters of Book I", and which prompted the development of a metaphysical doctrine of multiplication of species as a basis for later mediaeval optical theory in the Latin West. Ancient optics had limited its concerns mainly to the perception of the physical world. Ibn al Haytham specifically discussed errors in vision that frequently occur when looking at paintings (I. 295):

For painters make their pictures and paintings look like the visible bodies to which they correspond, and by means of flat pictures they represent particular animals, individuals, plants, utensils and other solid objects and their features. For this purpose they make skilful use of colours and drawings, paying particular attention to the points of resemblance. For example, when they make pictures of hairy animals, fuzzy plants, rough surfaced leaves or visibly coarse bodies, they make them look like the visible roughness of the surfaces of those animals or plants or inanimate bodies by means of drawings, outlines and different colours, though the pictures they make are flat and smooth or even polished. They also make pictures of individual people, imitating what is visible in their forms of the outlines of their faces and bodies, their hair, the pores and wrinkles in their skin, and the creases in their clothes; thus they represent the roughness visible in their skin on account of the hair and the pores and the roughness in their clothes due to their creases. Painted pictures will be perceived to be like the forms they represent if those who made them were skilled in the art of painting. Therefore looking [for example] at a picture of a hairy animal painted on a wall or a piece of wood or paper, sight will perceive the [painted] hair as if it were real.

    This passage is rather amazing for a culture usually dismissed as iconoclastic in the West as it makes Ibn al Haytham sound like a trompe l'oeil artist, a theme he pursued in the following chapter (I, 309-310), and subsequently when he referred to other illusions of drawn lines in carpentry (I, 318) and to designs which led Sabra to note (II, 20):

The Arabic nuqush (sing. naqsh) is often used in the book to refer to decorative designs, patterns or figures, without specifying whether these are drawn, painted or sculptured- a usage which is widely attested in Arabic literature before and after I. H.'s time. The word may thus be translated as drawings, paintings, mouldings, sculptures or engravings. Reflecting this ambiguity, the Latin translation of the Optics employs two terms picturae and sculpturae.

    In other words, while Ibn al-Haytham expanded the scope of visual perception to include designs in general, and only some references to painting, the Mediaeval Latin West focussed attention specifically on painting and sculpture and thus shifted concern to interplay between optics and representation which resulted in the discovery of linear perspective. In discussing the accurate perception of distance, Ibn al Haytham repeatedly referred to ordered and continuous bodies (e.g. I, 153,157,190). He compared frontal and inclined planes (I, 190) and even described lines drawn on the surface of a transparent body (I, 333), all of which again make a Renaissance historian think of Alberti's transparent veil or window, and new links between optics and surveying which led to linear perspective.

    Panofsky (1927 etc.) claimed that Euclid's angle axiom, which made apparent size a function of the visual angle, was not challenged until the sixteenth century after the principles of linear perspective had demonstrated the contrary. Ibn al Haytham, in the second or third decade of the eleventh century, specifically stated that (I.178): "It is clear from this experiment that sight perceives the size of an object by means of the magnitude of its distance as well as by estimation by means of the angle, and not by estimation of the angle alone". Such passages challenge us to rethink many claims made about mediaeval and renaissance optics and representation, even those by major scholars such as Panofsky (cf. II, 100 re: proportion).

    It is important to recall that Ibn al-Haytham was much more than an optical commentator. He wrote extensively on mathematics, astronomy and even on cosmology. For example, he wrote a Book on the world or the quadrant, which served as a compendium of theories of celestial motion taken from astrology. This work was noteworthy because it linked optics, astronomy and astrology, combined with instruments in trying to reach "true order and absolute demonstrations". A version of this manuscript, translated from the Hebrew into Latin by Abraham of Balines in 1510, which used diagrams as "descriptions", explained that it could serve in resolving a controversy between Giorgio of Cremona and Regiomontanus concerning the distances of things. As will be suggested presently, these links between optics, astronomy, astrology and cosmology became crucial to later developments.

Optics and the Recovery of Ancient Knowledge

    Ibn al-Haytham’s work can be seen as but one part of a much larger project to recover ancient knowledge. Some awareness of classical sources continued after the fall of Rome throughout the so-called dark part of the middle ages. The Carolingian revival brought new attention to this heritage which increased through Benedictine scholars such as Gerbert, who later became Pope Sylvester II. The eleventh century reform movement that spread from Cluny transformed this process into an active campaign. In 1141, Peter the Venerable, the Abbot of Cluny, hired Robert Retinensis and Hermann of Dalmatia to translate Arabic works into Latin. Peter wanted to use two of these works, a Chronicle of the Saracens and the Koran, in his diatribe against infidels. Two other works, Ptolemy’s Planisphere (c. 1143) and Alkindi’s On the judgment of the stars, were intended to serve the translator in composing a treatise on mathematical astronomy and astrology that was to "include in itself the sum of all knowledge." Through the tradition of calculating Christian feasts (computus), the Christian West had of course been well aware of the practical importance of mathematics, but the idea that the mathematical sciences could offer a sum of all knowledge was new. There are some references to this translation having been made by Robert’s friend, Hermann of Carinthia (1143) and other references to a Robert of Chester (Robert Cestiensis) translating Ptolemy’s On the composition of the astrolabe in London (1147). It will be recalled that Abbot Suger's breakthroughs in terms of art and architecture were happening in this same decade of 1140-1150.

    Ptolemy was becoming of particular interest. Eugene, the emir of Sicily, translated Ptolemy’s Optics (1141) from Arabic into Latin. Hermann of Carinthia also translated Ptolemy’s Optics (1143) from Arabic into Latin. Eugene, the emir, subsequently helped with an anonymous translation of Ptolemy’s Almagest (c.1160) from Greek into Latin. A desire to find an Arabic version of the Almagest for purposes of translation is said to have been Gerard of Cremona’s (d.1187) chief reason for going to Toledo. While there, as part of a corpus of over fifty works, he also translated Tideus’ On the mirror and Al-Kindi’s On vision. By the end of the twelfth century Euclid’s Optics, Hero’s On mirrors attributed to Euclid and the great treatise on Optics by Alhazen had also been translated into Latin (cf. pl. 9.1).

    Around 1261, the Franciscan, Roger Bacon, wrote a preliminary version of his work, On optics (De perspectiva), which cited extensively both classical and arabic authors. In 1265, when Guido Folcodi, became Pope Clement IV, he commissioned his friend, Bacon, to write his major work (Opus Maius) of which the treatise On optics became section five. The incentives for studying optics were increasing rapidly. Peter of Spain (Petrus Hispanus or Hispalensis), having taught at Paris and Siena, wrote a treatise On diseases of the eye and moved to Viterbo. In 1268 or 1269 Witelo, who had studied in Paris, also came to Viterbo. In 1269 or 1270 Siger of Brabant raised the question: "Whether music, perspective and astrology are natural" and decided that they were, noting that "in those things which are tried by abstract principles in geometry, the student of optics (perspectivus) applies to sensible matter." This physical aspect of optical studies had been implicit in Aristotle, but in this context it gained new importance, for the study of physical optics was now linked to its legitimation as a "natural" science.

    In 1269, around the same time that Witelo moved to Viterbo, William of Moerbeke also at Viterbo, translated a series of important mathematical and scientific texts including Alhazen’s On burning mirrors, Jordanus of Nemore’s Booklet on the measurement of weights, Archimedes’ On volutes which the Greeks call helices, On centres of gravity, On quadrature of the parabola, On the sphere and cylinder along with Eutocius’ commentary, Archimedes’ On cones and spheres, Ptolemy’s Analemma and (Pseudo-) Ptolemy’s On mirrors (i.e. Hero’s Catoptrics). In 1269 a new manuscript of Alhazen’s Optics was also produced. Almost immediately afterwards Witelo used William of Moerbeke’s manuscript of translations (now Vat. Ottob. Lat 1850), when he wrote his great compendium of Optics, dedicated to Moerbeke. Shortly thereafter, Peckham also wrote his two treatises on optics: De perspectiva (1269-1275) and Perspectiva communis (c.1277-1279). It is noteworthy that Moerbeke’s original manuscript (Vat. Ottob. Lat.1850) has appended to it a copy of Pecham’s Optics.

Quadrant

    In the Arabic tradition, the concerns of astronomy became intertwined with those of surveying such that the backs of astronomical astrolabes typically had shadow scales for surveying purposes. The back of Al -Zarqali’s universal astrolabe contained an orthogonal projection of the sphere and a fourth quadrant with a representation of sines that Millas Vallacrosa called the oldest quadrant (quadrans vetustissimus). Hermann the Lame introduced a quadrant with a cursor into the West. In the period 1260-1270 Campanus wrote a treatise on the quadrant. Around 1276, William the Englishman, produced a revised instrument that is remembered as the old quadrant (quadrans vetus) to distinguish it from the new quadrant (quadrans novus), namely, the Quadrant of Israel (Roba’Yisrael) written in Hebrew by Ibn Tibbon or (Profatius Judaeus), which used as a starting point a treatise of Ibn al-Saffar. This inspired a Treatise of the new quadrant (1293) by Peter Philemon of Dacia and a Latin translation attributed to Armengaud, the son of Blaise (1299). An expansion of the work (1301) was in turn translated into Latin by Peter of Saint Olmer (1309) and subsequently led to a revision of the new quadrant by John of Gmunden (1424-1425) who also produced two other versions of quadrants (1425, 1439).

Rod or Jacob’s Staff

    According to legend, this instrument had been invented by the Old Testament figure, Jacob. In the 1340’s, Levi ben Gerson, at the court of Avignon, systematically explored the uses of this instrument for astronomy and surveying, both in isolation and in combination with other instruments such as the camera obscura. In the first half of the sixteenth century, Apianus and Gemma Frisius greatly developed this instrument for purposes of measuring and representation. The latter sixteenth century saw further refinements in the rod of Orsino Latino (radio orsino), which was subsequently edited by Egnazio Danti.

Planisphere

    In astronomy, the most basic instrument was the planisphere. As mentioned above, Ptolemy’s treatise thereon was translated by Robert the Englishman (c.1143, possibly identical with references to Robert Cestensis, i.e. Robert of Chester in 1147). Around 1220, Jordanus of Nemore, one of the greatest mechanicians of the Middle Ages, wrote a commentary on this work. Ptolemy had demonstrated that circles are projected as circles only in special cases. Jordanus provided a first general demonstration of this fundamental property of stereographic projection. William of Moerbecke’s translation of Ptolemy’s Analemma (c.1269) pointed to connections with sundial projection. These connections continued yet it was not until 1558 that Commandino published his editions of both Ptolemy’s Planisphere and Analemma and his commentary thereon, making clear their links with perspectival projection, which have recently been republished in the useful editions of Sinisgalli (1992, 1992, 1993). This tradition continued into the next centuries. In 1688 Edmond Halley, of comet fame, dedicated a planisphere of the southern heavens to king Charles II. Nicholas Bion (1652-1733), constructed a celestial planisphere that reflected the most recent observations made by members of the Academy of Sciences.

Astrolabe

    The astrolabe which was a direct development of the principles of the planisphere was perhaps the most widespread instrument at the time and inspired treatises by many of the key individuals concerned with the revival of ancient learning. In addition to Gerbert and Herman the Lame mentioned above, there were Hugh of Saint Victor (d.1141); Plato of Tivoli (fl. c.1100-1150), Adelard of Bath (c.1142-1146) and Raymond of Marseilles (c.1140-1150), whose description became a standard one in university instruction during the next two centuries.

    Around the middle of the thirteenth century, Peter of Spain, one of those active at Viterbo, translated the treatise of Mesahalla (Masha’allah). Later treatises by Bredon (1300-1372) and Chaucer (1391) were also based on this version. Peter of Maricourt (Petrus Peregrinus), praised by Roger Bacon as the greatest instrument maker of his time, wrote a treatise on the astrolabe. So too did Campanus of Novara. Hagin, who worked in a shop for scientific instruments with Henry Bate of Malines (i.e. Mechelen), made a translation of Ibn Ezra’s work on the astrolabe. Moerbeke, working in Viterbo, personally asked Henry Bate of Malines to write his Magisterial construction of the astrolabe (1274), designed specifically for the rapid acquisition of astrological data. In the fourteenth and fifteenth centuries this tradition continued with further treatises by the anatomist, Guy De Chauliac (1290-1370); the mathematician, John of Gmunden (c.1380-1442); the astronomer, Peurbach (1423-1461), and his student, Regiomontanus. This tradition continued through the sixteenth century with Werner (1516), Nunez (c.1540), Geminus (1552-1555), Danti (1569,1578), Clavius (1593,1604) and into the seventeenth century with Vernier (1631).

Universal Astrolabe or Saphea

    A regular astrolabe involved projection principles with respect to a given latitude and required a new face or dial with each significant change in latitude. In the Arabic tradition, Al-Khujandi (d.1000), produced a universal instrument the projections of which could be adjusted for new latitudes. Sometime before 1078, Al-Zarqali had produced two accounts of the instrument, a major one of 100 chapters, which was known at the courts of Alfonso X but seems to have had little impact on the West, and a minor one with 61 chapters, of which William the Englishman (1200-1300) apparently had indirect knowledge, and which was subsequently transmitted to the West through the translation of Ibn-Tibbon (c.1263) and Moshe Galino before being published in the sixteenth and seventeenth centuries by Schöner (1526), Gemma Frisius, Juan de Rojas and Philippe de la Hire. Variants on this instrument included the meteoroscope by Werner (1468-1522) designed to solve problems of spherical astronomy. Like the saphea, its first and third quadrants contained stereographic projections of the circles of latitude and longitude while the second and fourth had two different types of sine divisions.

Equatorium

    Campanus of Novara, in addition to his writings on the astrolabe and quadrant, described in his Theory of the planets an equatorium: an instrument which provided a model of the motions of the planets. His contemporary, Henry Bate of Malines also wrote a treatise on the equatorium. John of Lignères (active in Paris 1320-1335), produced an adaptation of Campanus’ instrument as well as an independent treatise on the equatorium. A related instrument was described by Richard of Wallingford in his Treatise of the Albion (1326-1327). The albion was an equatorium to assist in calculating planetary positions together with ancillary instruments concerned with eclipse calculation, ordinary astrolabe practice and a saphea or universal astrolabe in the tradition of al-Zarchel. But in contrast to his predecessors, Wallingford set out to construct this instrument in the form of a complex clock complete with planetary trains and tidal dials. Simon Tunsted produced a new version. In Italy, Wallingford’s younger contemporary, Giovanni De Dondi, inspired by the description of Campanus, also wrote on and then constructed a related equatorium in the form of a great planetary clock (1348-1364). This tradition continued through Chaucer (1392), Jean Fusoris (1365-1436), John of Gmunden (1415-1432) and through the sixteenth century in the writings of Oronce Finé at Paris and the models of Jobst Bürgi at Kassel.

Instruments and New Links Between Observation and Representation

    Studied in isolation any one of these instruments are of interest only to experts in the history of technology. Considered as a whole these instruments offer important insights for historians of science, culture and philosophy. First, it is evident that the same individuals concerned with the recovery of ancient learning were also those engaged in the rise of scientific instrumentation. Typically one individual wrote on and/or produced more than one instrument. Herman the Lame (1013-1054) considered three: astrolabe, cylindrical sundial and quadrant. John of Gmunden (1380-1442) considered six: astrolabe, quadrant (in three versions), albion, equatorium, torquetum and cylindrical sundial. Regiomontanus and Apianus produced treatises on different instruments, preparing the way for the more specialized catalogues of Besson, Ramelli, Vasari Jr., Gallucci and Brahe. As a result instruments were no longer limited to an isolated problem in astronomy, optics or physics. They became essential tools of science.

    Second, these individuals gradually recognized the universality of the principles involved. Ptolemy’s description of the planisphere focussed on the perspectival projection of a few key points in order to arrive at the circles that represented the tropics of Cancer and Capricorn. Jordanus of Nemore’s commentary established that the projection principles involved were of a more general nature; a fact confirmed by the use of these projections in a whole range of instruments, notably planispheres, astrolabes, universal astrolabes, quadrants, and equatoria. Projection methods became basic to instrument construction as a whole.

    Third, the links between theoretical description and practical construction became interdependent. Early manuscripts often contained only verbal descriptions. By the thirteenth century there were frequently very careful diagrams sufficiently detailed to permit a reconstruction based on visual evidence alone. To cite an example from the artistic tradition: Taddeo Gaddi’s representation of a Virtue (Baroncelli Chapel, Santa Croce, Florence, c. 1336-1338), showed an angel holding a spatially rendered armillary sphere. By the sixteenth century the books sometimes contained actual cardboard models of the instruments, the Astronomicon Cesareum of Apianus (1540) being an example par excellence. Hand in hand with this trend towards a visual illustration of the instruments was a trend to represent the projection methods that they entailed.

    When William of Moerbeke made his translations of Archimedes, Eutocius, Hero and Ptolemy in 1269, these short works were bound together in a single manuscript. There were practical reasons for this. The treatises and/or fragments were often short and thus were conveniently bound together. This applied equally to the optical texts. In rare cases a compendium of treatises would be almost entirely limited to optics as for example: Ptolemy’s Optics, Bacon’s Optics, Albertus Magnus’ Question on the form resulting in a mirror, Tideus’ On mirrors, Alkindi’s Optics, Malfegyr’s On twilight and Pseudo-Euclid’s On mirrors (Paris, Bibliothèque Nationale, Ms. Lat. 10260). In most cases, however, compendia contained optical treatises along with other subjects such as mechanics and water. For instance, one manuscript (Vatican, Ms. Lat. 2975), contains the above works by Ptolemy, Bacon, Albertus Magnus, Tideus, Malfegyr and two versions of a work On weights and balances attributed to Euclid, Thebit Ibn Qurra’s On weights and measures and Philon’s Pneumatics. There were many combinations of themes. Sometimes it was optics and geometry (e.g. Vatican, Lat. 3102), or optics and astronomy (e.g. Vatican, Lat. 4082) or optics and instruments (e.g. Vatican, Pal. Lat. 1377).

    Our concern here is not with the details of these combinations, but rather with the underlying trend that they reveal, whereby optics, which had traditionally been a topic of philosophical debate, became increasingly linked with using mechanical measuring instruments and geometrical demonstrations. Indeed, as the passage cited below (p. 47) from Witelo’s dedication to Moerbeke confirms, the conviction that the heavens were the source of all change on earth introduced new incentives to study astronomy and astrology using optics, or rather optics aided with "instruments for the certification of sight", to use Witelo’s phrase for astrolabes, quadrants and the like. Hence the development of optics especially from the tenth century onwards goes hand in hand with a rise in the development of scientific instruments, and the resulting knowledge is increasingly made available in a new kind of compendium that links rather than separates various disciplines.

    This shift in how knowledge was presented played its role in a more fundamental shift in the definition of knowledge itself. In Mediaeval versions of the Platonic tradition, truth and knowledge had been linked mainly with logic and the other branches of the trivium, namely dialectic and rhetoric. As late as the twelfth century, monks such as Alcher of Clairvaux had distinguished three functions of reason: logic (truth and falsity), ethics (virtues and vices) and physics (experiments which investigate the nature of things). Truth was in a different cubbyhole than experiment and experience.

    Meanwhile, a change was underway. It had begun with the revival of learning in the early ninth century, gained momentum in the late tenth century with Gerbert of Aurillac (Pope Sylvester II), and particularly from the second half of the thirteenth century onwards, when these tendencies and isolated initiatives acquired a programmatic character. As part of this change, experimentation and verification became linked in the quest for truth. In turn, concepts of truth and knowledge became increasingly linked with the mathematical sciences, and with the rise of scientific instruments outlined above, which served to certify observation and experience. As we have noted, Robert Retensis’ desire to use astronomy and astrology as a means of achieving the sum of all knowledge (c.1143) marked a first formal step in this process. The decision to make the subjects of the quadrivium (arithmetic, geometry, astronomy and music) formally a subdivision of mathematics in the Guide to the candidate (c.1230-1240) at the University of Paris marked another step. Increasing references to truth and instruments, often in combination, with respect to astronomy and optics marked another step.

    During this period, while the two new orders of the Church, the Franciscans and the Dominicans, were establishing themselves within the framework of the University of Paris, two major approaches to knowledge emerged. One, championed by the Franciscan, Saint Bonaventure, focussed on inner spiritualism, claiming that knowledge was faith and prepared the way for the Augustinian revival after 1270 that included Plotinian and neo-Platonic strands. The second, championed by the Dominican, Albertus Magnus, and subsequently by his even more famous student, Thomas Aquinas, emphasized Aristotelianism particularly in the sense of relying on logic and claimed that knowledge was reason. As will be suggested below, the heads of the church were not unaware of the dangers of both extremes and almost certainly saw the study of mathematical sciences, particularly optics, astrology and astronomy as providing a middle ground between these extremes. It may be no co-incidence that in 1268, three years after Bacon was commissioned to write the Greatest work (Opus maius), and one year before Gerard of Cremona did his translation, the church organized a debate on the problem of the organization of knowledge (scientia), with a special session devoted to the gift of science.

    The Franciscan, Robert Grosseteste, had claimed that there were four basic themes worthy of study: preliminary science; experimental science, metaphysics and morals. His student, Roger Bacon, the protégé of Clement IV at Viterbo, claimed that there were three kinds of knowledge, namely, authority, reason, experience and that attention should be focussed on this third kind of knowledge Hence Bacon emphasized the importance of the greatest scientific instrument maker of his time, Pierre de Maricourt (Petrus Peregrinus), whom he termed a master of experiments (dominus experimentorum). While these were physical experiments, it is important to note that they were not usually systematic as in modern experiments. Peckham, for instance, studied the properties of a light source passing through a triangular aperture. He observed that in some cases the resulting form on a wall beyond the aperture was triangular, whereas at other times it was spherical. It does not seem to have occured to him to change systematically the distance between aperture and wall or the distance of a light source, as Leonardo da Vinci later did.

    It is significant that Peter of Spain at Viterbo, when he became Pope John XXI, was the individual who ordered the investigation into the use of Aristotelianism at Paris which, thanks to a perhaps overzealous bishop, led to the famous condemnation of Aristotelianism in 1277. In short, the new emphasis on mathematical optics in the second half of the thirteenth century marked an effort by the leaders of the Church to redefine the scope of knowledge by shifting attention to the quadrivium in its new mathematical sense in order to avoid the verbal squabbles of the trivium, thus preparing the way for a view that the trivium was trivial.

    These trends are all the more striking in light of parallels with the Arabic tradition where students of mathematics began with Euclid’s Elements and were then given a series of intermediate works (mutawaisitat) such as Autolycus, Aristarchus, Euclid, Apollonius, Archimedes, Hypsicles, Theodosius and Menelaus prior to studying Ptolemy’s Almagest. Towards the mid-thirteenth century, Nasir al-Din (1201-1274), wrote a series of these recensions (tahrir) on these authors while one of his colleagues, Al-Maghribi (fl.1260-1265), produced new versions of the Greek classics including Euclid’s Elements, Apollonius’ Conics, Theodosius’ Spherics and Menelaus’ Spherics. These, especially the recensions, became standard texts in the teaching of mathematics in the very decades that there was an extraordinary surge in mathematical, scientific and optical treatises in the Latin west.

    The neo-Platonic tradition, particularly via Pseudo-Dionysius, had developed a metaphysics of light to account for the origins of the universe. Working within this tradition, Robert Grosseteste (1175-1253), wrote On light or the beginning of forms, in which he explained that light was "the first corporeal form which some call corporeity," and used a concept of multiplication of form (species) to account for the propagation of the many from the one. So light was both a universal form and a bearer of all particular form and matter. The same Grosseteste made geometry and optics basic elements for an understanding of nature, and made science an essential ingredient for knowledge, claiming that "The usefulness of considering lines, angles and figures is the greatest because it is impossible to understand natural philosophy without these....All the causes of natural effects should be reached by lines, angles and figures; otherwise it is impossible to know their cause". These geometrical forms were also discussed in his treatise On light. Hence, according to Grosseteste, optics (light) and geometry (lines, angles, figures) were essential to understand the relation of universals and particulars.

    It seems that the next generation added another ingredient to this discussion. Ptolemy, in addition to his great works on astronomy, optics, and geography, had written a fundamental work on astrology. The Arabic tradition emphasized the importance of astrology and treated it as a science. When Gerard of Cremona went on his translating campaign, he included works such as Al-Farghani’s Book on the influences of the science of stars. In Witelo’s dedication to Moerbeke in his great compendium On optics, we learn that there were deeper reasons for these concerns. Astrology and astronomy were now being combined with the metaphysics of light in the optical tradition, in order to explain the shift from the original universal to the particular:

Now you well understand, sedulous as you are in the study of the being of all things, that the influence of divine powers is, in a wonderful manner, brought to bear upon inferior corporeal things through superior corporeal powers; as you show where you unite in thought the intelligible, derived from its own first principles, to sensible individual things in the manner of a cause and pursue for particular things, particular causes....

Now verily, of corporeal influences, perceptible light is the mediator, wonderfully assimilating and connecting inferior bodies, which change both form and place, to superior bodies, which are unchanging in substance and only changeable as to their place.

For light is a diffusion of the higher corporeal forms, moulding, as is the nature of corporeal form, the matter of inferior bodies, and imprinting upon perishable bodies, many in number the forms it brings with it of the divine and indivisible artificers, in themselves unique and indivisible and producing by their union with them ever new specific and individual forms in which results, through the activity of light, the divine contrivance both of the movement of the spheres and of the powers which produce change.

    This passage is remarkable because it helps to explain why concerns of optics became inextricably linked with those of astrology and astronomy; why these three sciences played a key role in the continuing debates over universals and particulars which had dominated discussions of the late twelfth and early thirteenth centuries and why writings and later publications on astrology continued to increase in the next centuries. Astrology was much more than a source of horoscopes. Along with optics, geometry and astronomy, it was one of the keys for understanding the mystery of creation: a basis for cosmology. Since astrology was seen as a basis of health, this combination of disciplines therefore became crucial for medicine as well as being fundamental to philosophy, science and theology. In the short term, a ‘negative’ consequence was an ongoing interdependence between metaphysical and physical optics such that there was no immediate separation between inner subjective and outer objective optics. In the long term, a positive consequence was that it prepared the way for Kepler’s Commentary on Witelo concerning the astronomical part of optics where precisely this distinction was brought into focus.

    It is no co-incidence, therefore, that the four greatest names in fourteenth century optics were also involved with geometry, astronomy, astrology as well as cosmology, namely, Dominicus da Chivasso, Nicolas Oresme, Henry of Langenstein and Blasius of Parma. Dominicus da Chivasso (Clavasio or Clivaxo), a student of Buridan at Paris, was active in the second half of the century as a medical doctor, astronomer, physicist, geometer and perspectivist (perspectivus). In addition to his Questions on optics, he wrote a treatise on geometry and a commentary on Aristotle’s On the heavens (De coelo). This work, entitled Questions on the heavens and the world, became linked with other treatises on physics by Bradwardine, Burley, Swineshead, Jordanus of Nemore and Oresme (e.g. Vatican, Vat. Lat. 2185). Oresme wrote on many aspects of optics, astronomy and cosmology including a Treatise on the incommensurability of celestial motions (Vat Lat 4082). His student, Henry of Langenstein, besides his Questions on perspective, wrote on geometry and various aspects of astrology: On the characteristics of causes, On the reduction of effects and a Treatise against the conjunctive astrologers. Blasius of Parma, besides writing on optics, was active in natural philosophy, mathematics, astronomy, and astrology. He explicity claimed that "astrology can do nothing without optics (perspectiva)," and wrote, for instance, Geometrical demonstrations concerning the theory of the planets (Vat. Lat. 3379). Vescovini (1965) has been prophetic in emphasizing the importance of these nexes, except that where she emphasized philosophy, we would insist more on the interdependence of theology, science and philosophy.

    Other factors contributed to this growing interdependence of disciplines. In the twelfth century, Averroes (1126-1198), active at Cordoba and Seville, had criticized Aristotle, claiming that "The model that has been developed in the times in which we live accords with the computations not with existence" and that Ptolemy’s explanation was "mathematical and not physical". In his quest to create an explanation that corresponded with physical experience, Averroes wrote a now lost treatise on the regular solids and which of them do or do not fill spaces completely. This began a serious controversy which provoked commentary by Bacon, and prompted Regiomontanus to write his now lost treatise on the regular solids. A few decades later Piero della Francesca produced his booklet On the five regular solids. Maurolycus, one of the greatest mathematicians of the sixteenth century, knew of, but had not seen Regiomontanus' manuscript when he wrote his treatise On the five solids, which are popularly called regular, namely which of them fill a space and which do not, against Averroes, the commentator of Aristotle, in 1529 (with emendations in 1535). Renaissance authors considered Piero's treatise on the solids to be a perspective treatise, and hence it is not surprising that the regular solids became an important theme in perspective treatises (cf. Sources, pp. 90-91) . Seen in this larger context whereby astronomy, astrology, and optics (perspectiva) were linked with cosmology, one of the major incentives that led to the spatial initiatives of scientific perspective becomes clear: a quest not just to measure and represent but also to explain the structure of the universe. Hence, it is no co-incidence that a number of the early individuals concerned with perspective were among the leading figures of early modern science and mathematics: Piero della Francesca, Leonardo da Vinci, Pacioli, Commandino, Benedetti, Guidobaldo del Monte, Galileo, Descartes, Leibniz and Newton.

    Meanwhile, the fourteenth century also brought a gradual shift that emanated from the University of Oxford through Bradwardine (1290-1349), who set out to destroy the union between faith and reason, which led to mathematics, astronomy and optics being freed from theological suppositions. At the University of Paris, Buridan (1300-1352), developed a new theory which relied on calculations and promised to save the phenomena using a universal formula. This he applied to so-called natural movements including the accelerated fall of weights and the trajectories of celestial bodies. His younger contemporary, Nicole Oresme (1325-1382), argued that space and time are divisible to infinity and that their continuity extends to all the forms of change such that it is possible to measure geometrically the variations in intensity in same way that we measure spatial change. In order to facilitate this measurement, Oresme conceived of two coordinate axes corresponding to intension and extension, a graphic equivalent, as it were, to the hypothesis of impetus (impétuosité or vertu motive). Oresme also discussed the image of the cosmos as a clock. Marsilius of Padua (d. 1336/1343) defended Oresme’s theory of intension of forms and represented graphically the heating of a body using a series of diagonals that parted from a right angle. Albert of Saxony (1325-1352) pursued the interests of Bradwardine, Buridan and Oresme in astronomy, optics and physics. Albert studied quadrature of the circle which, it has been argued, prepared the way for analysis of the continuous and of incommensurability. He also distinguished the geometric centre of the earth from the mechanical centre of the celestial motions.

    These developments attest to a gradual shift in the thirteenth and fourteenth centuries whereby problems of astronomy, optics and physics were being analysed geometrically as well as mechanically and both methods were being compared with one another. Optics was no longer simply a trivial matter of philosophical debate. Its principles were studied physically and recorded instrumentally. Geometrical rays were no longer just abstract mathematical principles to be discussed verbally. They were practical phenomena to be recorded and represented visually and instrumentally. In Roger Bacon’s terms, knowledge as authority and reason, was being replaced by knowledge as experience. Is it mere co-incidence that this shift took place in the generation before Dante changed the course of literature and Giotto changed the course of art? These new trends were more than new ways of looking at the world. They reflected a re-definition of what it means to know.

    By today’s stadards, this shift in the definition of knowledge was very slow. For if the 1260’s marked a first conscious articulation of that goal, the first serious repercussions in curriculum could be seen to begin with John of Gmunden’s chair of astronomy at Vienna in the early 1400’s which combined the use of practical instruments and theoretical texts.

    Meanwhile, Florence, which became the artistic centre of the Renaissance in the early fifteenth century and saw the first technical demonstrations of perspective did not have the appropriate combinations of theory and practice with respect to scientific perspective found in other centres such as Padua and Vienna. From Ghiberti's Commentary it is clear that the Florentines were aware of the mediaeval optical tradition. They knew Alhazen in translation and studied Bacon, Witelo and Peckham. So they were well aware of experiments with camera obscuras. But Brunelleschi, as an architect, was concerned primarily with practice and there is no evidence of his trying to deal with or write about perspectival theory. His panels made some time between 1415 and 1425 remained strictly practical demonstrations.

    Leon Battista Alberti's On Painting, the first treatise to discuss perspective did so in terms of grammar, dialectic and rhetoric rather than geometry, arithmetic, music and astronomy, i.e. focussing on the trivium rather than the quadrivium and thus emphasizing the concept of (hi-)story (istoria), which helps to explain the absence of technical diagrams in the early manuscripts. Nonetheless, as a universal man of the Renaissance, Alberti was aware of two methods or rather two ways of demonstrating the principles of perspective. In On Painting he described a demonstration based on surveying practice, which he may well have learned in Padua (see Sources, p.43-44). In his Elements of Painting, by contrast, Alberti linked perspective with Euclid's Elements, i.e. with geometry and more precisely with geometrical proportion. In the next generation Filarete alluded to both of these methods but as a pragmatic architect he added nothing substantial to the discussions.

    Piero della Francesca made two major contributions. First, he set out to establish that both of these methods had their foundations in Euclidean geometry. Having discussed durveying principles in the introduction to his On Perspective of Painting, he devoted books one and two to the method of geometrical proportion which Alberti had discussed in his Elements of Painting. In book three of On Perspective of Painting, Piero turned to the alternative method entailing a perspectival window and strings, which history has remembered as the legitimate construction.

    Piero second contribution was to expand the Florentine and Tuscan context of painter's perspective to the larger context of mediaeval optics (perspectiva). As noted earlier (Sources, p. 90), Piero's two other treatises included a Book of the Abacus and a Booklet of the Five Regular Solids. Both of these dealt with the construction and representation as well as the measurement of the five regular solids. Both of these books were viewed by sixteenth century authors as perspective texts. Now as we have noted, ever since the time of Averroes, the regular solids had become of central importance in debates concerning the structure of the heavens. So perspective was no longer just about painting practice. It extended to questions of astronomy and cosmology. Perspective was no longer merely a theme for how to do it books. It was concerned with questions of why: with causes. All of which helps to explain why Piero's student, Luca Pacioli linked perspective with both astronomy and cosmology in his treatise on Divine Proportion (1496-1499, printed 1509) or why perspective became a gateway to Leonardo's scientific method.

    The links with measurement made explicit by Piero, were broached in more practical terms by Francesco di Giorgio Martini and developed by Leonardo da Vinci. Dürer included this approach to perspective in his Instruction in Measurement (1525). Rodler (1531), went further and made perspective synonymous with measurement. Even so it was not until the 1550’s until the scientific dimensions of perspective became a programmatic part of teaching through the efforts of the Jesuits. By 1556 the Jesuits had established themselves in twenty Italian cities, including Rome, Naples, Florence, Siena, Bologna, Padua and Venice. By 1557, preliminary attempts at a Jesuit curriculum had begun, although the first formal plan (ratio studiorum) was not established until 1586.

    Jesuit interest in compendia of optical texts, mentioned above, is, for instance, found in a fifteenth century manuscript that was owned by the Jesuits in the sixteenth century (Rome, Biblioteca Nazionale, Mss. Gesuitici 2546 419), which contains Ptolemy’s Optics, Euclid’s On Mirrors, and Albertus Magnus’ On the forms that appear in mirrors. A closely related Vatican manuscript of 1554 (Vat. Lat. 2975) also contains Ptolemy’s Optics, Bacon’s Optics, Euclid’s On Mirrors, Tideus’ On the quality of that which is seen in mirrors and their deceptions and Albertus Magnus’ On the forms that appear in mirrors. Such compendia reflected a renewed interest in ancient and mediaeval treatises in optics and instruments in the 1550’s. For example, another manuscript in the same library (Vat. Barb Lat. 304), contains a fragment of Ptolemy’s Analemma (fol. 160-162r); lists of Greek manuscipts in the library at Carpi including On optical hypotheses and Heliodorus of Larissa’s Optics (f. 163r); mention that one needs good instruments and good compasses if one is to draw properly (202r); a list of scientific and mathematical books including the Planisphere of Federico [Commandino]; a section On practical perspective (211-212v), explaining that it is derived from both geometry and optics, referring to an instrument for perspective produced by Witelo; mention of Barozzi il Vignola’s work on sundials (204r); drafts of a first lecture on sundials, dated 1558 (205r); a third, fourth and fifth lecture on the analemma and sundials (213v-221v) and various lists of books. We are told that M. Federico [Commandino] has a large Ptolemy and the Planisphere of Ptolemy and the sphere...and the astrolabe (254v). Reference is made to the Optics of Peckham, Euclid, Bacon and Ptolemy (264r). There is a mention of a First lecture on optics (perspectiva) (264r); to treatises on perspective by Piero della Francesca (270r) and Master Federico [Commandino] (271r); to Maurolycus being in touch with Master Jeronymo [Cardan?] concerning Master Federico’s problem of proportional division of lines on 8 October 1557, evidently one of the contexts for the development of the proportional compass or sector.

    Towards the end of the manuscript there is a reading list for optics (perspectiva), namely: Ptolemy, Euclid, Alhazen, Witelo, the commentary on the Common perspective of Butius, the canons of the instrument of Witelo and Federico [Commandino’s] Practical perspective. Hence, Commandino’s interest in perspective and its relation to Ptolemy’s Planisphere and Analemma was part of a larger trend to understand the theory and practice of optics and perspective. Indeed there is evidence that it was connected directly with a new curriculum for the mathematical sciences that was being developed by the Jesuits in these very years.

    We know that one of the earliest study lists of the Jesuits included the sphere, geography, theory of the planets, the astrolabe and optics (perspectiva). In the earliest cases Peckham and Witelo were used. In later outlines this became part of a more comprehensive plan:

And starting at the beginning, dialectics, three months before the first year, it will be well that they hear practical arithmetic for the months of August, September and October; and at the beginning of logic they hear the first three books of Euclid, which they will read in less than four months; and they will also hear the sphere which will last another four months and geography, which will last another three or four months and thus the second year will be completed. In the third year [they will hear] the theory of the planets for a space of four months and the astrolabe for another four [months], and optics (perspectiva) for the other four [months]. And in this manner they will always hear two lectures, one in the morning in the first hour and the other after eating...and that each person has a compass and ruler with which they can exercise on some figures, and that four or five months after they have begun the course they can have the fourth, fifth and eleventh book of Euclid and go on to the theories and to introduce the tables and if they have time that they hear something about sundials, either the ring, or the quadrant or the radius or the ecclesiastical computus or the solid sphere.

    This became one of a series of new programmes which formalized the interplay between theoretical study of texts and practical use of instruments for observing, recording and representing the physical world that had been emerging since the eleventh century and was given a new impetus at Viterbo in the 1260’s. A manuscript probably written in the 1570’s or 1580’s by Clavius, who subsequently became head of the Jesuits, outlined:

A way in which the mathematical disciplines can be promoted in the schools of the Society of Jesus.

Now since among the experts it is held that in physics nothing can be perceived without these [mathematical sciences], especially with respect to that which pertains to that domain, where one deals with the number and motion of the heavenly bodies, with the number of the intelligences, with the effects of the stars, which depend on the various conjunctions, oppositions and the rest of the distances amongst them; with the infinite division of continuous quantity; with the ebb and flow of the ocean; with comets, rainbows, haloes, and other meteorological matters; with the proportion of motions, qualities, actions, passions and reactions etc. of which the calculators speak.

    As we have noted France was one of the first centres of systematic attempts at the recuperation of classical mathematical and scientific knowledge. Spain followed soon after. Through the efforts of the Franciscan, Grosseteste, and others, the work of the Toledan translators became known at Oxford and elsewhere in England. The Anjou-Plantagenet connection brought further co-ordination of French and English efforts in the recuperation of ancient knowledge. In the period 1220-1250, the Emperor Frederick II’s alternating co-operation with the pope meant that initiatives in Germany, Northern Italy and the Kingdom of Sicily (which included Southern Italy) became integrated in the recuperation of ancient knowledge. After 1265, when the pope gave Southern Italy and Sicily to Charles of Anjou these French, English, Spanish, and German initiatives became further linked with Sicilian efforts in the translation of ancient sources of knowledge.

    Indeed there are striking ways in which the new developments in Italy can be seen in terms of new Guelph-Anjou power and new links with France. In the latter twelfth century, Saint Francis, is said to have received his name because he was born on one of his father’s business trips to France. The Franciscans, particularly through their English branch (Grosseteste, Bacon, Peckham), devoted new attention to study of the natural world using the mathematical sciences. The period 1254-1268, which saw a decline of the Hohenstaufens, brought a dramatic rise in influence of the Guelphs through new links between the pope and Charles of Anjou (1265). With the death of Manfred at the Battle of Benevento (1266) and the defeat of Conradin at the battle of Tagliacozzo (1268), Guelph influence spread to other cultural centres such as Siena. The same decade brought new links between Viterbo and Paris and the first examples of persons such as Brunetto Latini, who travelled from Italy to France, came under the influence of the Provençale troubadour poets and then returned to Italy where they became major literary figures. Hence it is no-coincidence that Assisi, Siena, Florence, which were under Guelph rule and had French connections, became the key cities in the development of proto- and linear- perspective.

    The expansion of the Papal Estates particularly in the second half of the thirteenth century, meant that there was a strip of land linking Rome, Viterbo, Orvieto, and Ancona; and closely bordering on cities such as Perugia and Assisi. As White (1957), has noted (see below p. 58*), it was precisely in this period that knowledge of the great Roman narrative fresco cycles travelled North to these cities, In the next generation individuals such as Cimabue worked in both Guelph (Florence) and Ghibelline (Arezzo) territories thus eroding the significance of these political factions with respect to cultural development.

    In the twentieth century, discipline centred approaches came to dominate explanations. Some art historians such as Panofsky continued an awareness of the philosophical tradition: most returned to explanations involving specific disciplines, notably optics, geography and astronomy. In the nineteenth century, art historians had been fascinated by possible connections between phylogenetic and ontogenetic development (cf. below pp. 142-144*). Ironically, when they abandoned this approach in the twentieth century, it was adopted by psychologists, who used it for their version of historical treatment. Marxists offered a fascinating social explanation which as we have shown bore little correspondence with historical evidence. It is noteworthy that historians of mathematics, who remained very interested in perspective as a key to understanding the origins of descriptive geometry, devoted minimal attention to the origins of perspective as a topic in its own right. Similarly historians of science continued to show some interest in the history of optics but tended to dismiss perspective as merely artistic.

    In reassessing these explanations we distinguished clearly between different stages of development. The conditions for Giotto to produce a proto-perspectival representation of space in Assisi or Padua were different from those involving partial or systematic mathematical demonstrations. Because these developments involved a whole range of media they necessarily entailed a whole range of professions. Hence, the trend of scholarship in the past century which identified a single individual as if perspective were a simple event was misleading. This led us to look at a series of factors including the development of narrative on the artistic side. Here we found that Renaissance Italian developments owed much to innovations in Gothic art and literature in France. In trying to outline key shifts in the representation of space from Gothic, through Renaissance, to Baroque art, we discovered that perspective, which initially set out to enhance the effects of pictorial narrative also undermined it. To understand this paradox, there was an excursus on three distinguishing characteristics of perspective: how perspective helps in relating, emphasizing and varying scenes.

    To understand the mathematical and scientific origins of perspective, we explored how developments in optics related to shifts in the meaning of knowledge during the thirteenth and fourteenth centuries. We suggested that the history of instruments, which historians of technology had typically treated in terms of particular objects, offered a more universal context for the spread of planispheric projection techniques with a whole series of applications. In these developments astronomy and surveying played a seminal role.

    Scholars such as Crombie (1953) claimed that a fundamental quest for truth, which was originally developed in Greece, was recovered by Grosseteste and his followers in the thirteenth century. According to Crombie, it was Grosseteste who introduced terms such as experiment and observation, which were to prove crucial for the later development of Renaissance science. He claimed that the use of these terms remained constant for the next centuries and that there was therefore a continuity via texts and print culture linking Fibonacci and Grosseteste in the thirteenth with Galileo in the seventeenth century. There is certainly some truth to this. Persons kept quoting Aristotle and Plato, kept depending on Euclidean geometry and made similar philosophical claims rhetorically. A number of the Oxford Franciscan physicists of the thirteenth century and their successors in the fourteenth century, the calculators (e.g. Swineshead), were published in the late fifteenth century and became part of the Jesuit curriculum in the latter sixteenth century.

    Even so, as we have shown, there were also basic factors that changed such as a new mathematical approach to optics, fresh links between mathematics and knowledge, the development of scientific instruments to record nature and the rise of perspective both to record and to reproduce records of nature. These developments created bridges between abstract mathematics, concrete instruments and objects, thus changing science from an intellectual exercise to a process involving physical practice as well as mental theory. This process was slow, cumulative and incontrovertible, leading from Fibonacci (in the thirteenth century) through Regiomontanus (in the fifteenth) to Leonardo da Vinci (in the sixteenth) and Galileo (in the seventeenth century), such that Galileo’s world also seems fundamentally different from that of the middle ages. We suggested that to understand this process requires attention to basic shifts in knowledge both inside and outside the universities, as well as to the changing political context.

    This suggests a picture that is considerably richer than that offered by earlier scholars (Ivins, McLuhan, Panofsky, Eisenstein, Gombrich, Crombie). We have shown that the so-called conquest of reality depended largely on painting practice. The contents of perspectival treatises introduced various independent themes: regular solids, semi-regular bodies; other objects such as lutes, chairs and stairs as well as buildings and gardens. The combination of these themes created a new interplay of printed images, painted and actual objects, resulting in new horizons of the imagination and plays between real and fictive space. Thus by the latter sixteenth century the traditions of perspectival practice in painting and perspectival theory in printed texts had begun to interact in revolutionary ways that affected not only spatial representations of images but transformed the very layout of the environment, first on a small scale with piazzas such as the Capitoline, ultimately on an enormous scale as at Vaux le Vicomte, where villages were razed to raise a view, and Versailles, where an horizon was altered to suit a sun king.

    Eisenstein’s book argued for a sudden revolution in printing, making the 1480’s a turning point, in explaining the rise of perspective and in settling fluid boundaries between Mediaeval and Renaissance culture.We have shown that the processes of innovation that we remember as the Renaissance were both slower and more cumulative than generally assumed; that the fundamental implications of printing emerged only gradually in the course of three centuries and that printing in isolation was ill suited to settle boundary disputes in the wars of periodization. We suggested that perspective offered a better framework for understanding key aspects of this transition period and that perspective involved the history of art, science and mathematics, entailing the rise of new orders in the church as well as more general changes in politics. It was part of a fundamental shift not just in the presentation of knowledge but in its re-definition, which owed much to a combination of a Franciscan emphasis on nature with both Cluniac and later Dominican concerns to recover a corpus of Ancient knowledge and to arrive at a new level of encyclopaedic insight. It entailed contributions by Benedictines such as Gerbert and Maurolyco; propagation by Jesuits such as Clavius, and explanation by learned Dominicans such as Danti.

    Giesecke (1991) argued that the rise of printing led to a new visual and ultimately perspectival approach to description that was intimately connected with a shift in the concept of knowledge and the emergence of a new sense of truth. While fully accepting the general thrust of these findings, we are now, in retrospect, able to assert that the origins of this shift can be traced clearly to at least the year thousand although it was not until the mid thirteenth century that the Dominican recuperation of ancient knowledge and the new Franciscan approaches to science, history and experience/experiment introduced the final ingredients for this new approach.

    In the fields of economic and political history, Braudel and other members of the Annales school have argued that we need to understand change in terms of long term movements (la longue durée). Our study would suggest that this phenomenon applies equally in the history of art, of science and culture as a whole. Where others would have us believe that the origins of perspective lie in some spontaneous, sudden discovery made by a Brunelleschi, an Alberti or the like, we would stress the need to understand a complex shift that was centuries in the making, the consequences of which have taken centuries to understand and indeed the complexities of which are even today not yet adequately appreciated.

    Hence, perspective is much more than a painting technique made possible through combinations of surveying and optics that made it practical on a terrestrial plane. As we have shown, its origins were as much in the heavens as on earth, in new combinations of instruments being applied to optics, astronomy, and astrology. While the planisphere became a symbol for these connections, it was actually only one member of a complex family of instruments that established projection methods as a universal principle. All the ingredients had classical precedents. Some Ancients had sought for truth and to understand causes. Some had used instruments. What was different about the developments in the latter Middle Ages was that these initiatives became increasingly programmatic. The accumulation of knowledge changed from the individual efforts of a brilliant Greek or Roman philosopher, to the combined concerns of orders of the Church with teams of scholars in thousands of monasteries across Europe.This made their efforts much more than a passing fashion of making realistic images.

    The re-definition of knowledge in the period 1000-1600 entailed a new commitment to instrumental observation, recording and representation, to establish new standards of certification and truth, and for this reason it became so integrally connected with philosophy, science and theology. When Panofsky emphasized that the rise of linear perspective was linked with changes in a world view, he was both wrong and right. He was wrong to assume that perspective was merely a physical consequence and manifestation of a new abstract concept of infinity. He was right, in senses he did not suspect, because perspective was not just a means of recording the effects of philosophy. It provided philosophy and ultimately both science and theology new methods for understanding causes. To repeat the words of Danti cited earlier (p. 2) the concern was:

with the most scientific who are not content in simply knowing how to operate well and knowing that a thing is thus, but in addition to know its causes. Hence I have endeavoured to demonstrate all the principal parts of this geometrically.