Our knowledge of the history of perspective derives from at least five kinds of sources, notably, histories of art and general histories; histories of mathematics; the treatises themselves; encyclopaedias and bibliographies. Since most of the material is found in the first category, for the sake of convenience separate headings are provided for different chronological periods. The other categories, which vary enormously in terms of both the quantity and quality of information, and are mainly of interest with respect to earlier centuries, will also be treated separately.

2. Histories of Art and General Histories

    Effectively nothing has been written on the possible spatial methods of prehistoric cultures, it being generally assumed that systematic spatial methods first emerged in Egypt. These writings will be considered very briefly. The great majority of those who have written on the early history of perspective fall into two main schools: one assumes that perspective began in Antiquity and was rediscovered during the Renaissance; a second claims that perspective did not begin until the late Middle Ages or the Renaissance.

Prehistory (4000-1000 B.C.)

    Schäfer's (1919) classic Principles of Egyptian Art in fact offered a survey of all pre-Greek art. Schäfer was very (337): "clear that the expressive imprint which a work of art bears is not based on the use of frontal images or perspective". By way of context he explored essential characteristics of Egyptian art and the concept of art and creativity that it entailed. Having described their treatment of isolated objects he examined their methods of rendering spatial distribution: including loose assembly without indication of depth, maps, association of ideas, the use of base lines and ground lines as registers, objects depicted on or above one another without overlapping, figures juxtaposed without overlapping and with overlapping; rising forms which indicate distance without recourse to overlapping. Schäfer noted that there were parallels between the rise of the optical field with distance in art and new terms for this in language. He examined various techniques they used in the rendering of nature such as apparent passing next to and action beside an object, turns, looking and moving out of and into the picture, splitting of groups, the image in correspondence with the position of the viewer and the depiction of trees around open spaces. In all this he made comparisons between ancient Egyptian drawings and modern children's drawings.

    With respect to perspective Schäfer began with perspective-like exceptions to the fundamental rule of depiction based on frontal images, namely, bird flight and related motifs, sunshades, bees, arm-rings, fish-traps, scaling ladders on wheels, back views of serving girls and shields. This led to a discussion of how the human body was rendered in two dimensions to which he claimed the basic principles of rendering nature in three dimensions were related. By way of explanation Lange (1899) had developed what he believed was a "law of frontality". This Schäfer revised with a rule of directional straightness (316):

Three-dimensional representations of human beings, animals and other objects that are symmetrical round an axis, which are produced by all peoples and individuals who have not been influenced directly or indirectly by Greek fifth-century art, conform to the rule of directional straightness. This rule results from the opposition between the method of representation based on frontal images and the structure of the objects serving as originals: a plane is imagined as a starting point and the other principal planes of the torso and limbs adapt to it to form an intersection of planes at right angles.

    Schäfer then turned to technical procedures of Egyptian art. He noted how lines and dots were used in the composition of two-dimensional works in the Old Kingdom and that, in the New Kingdom, these were replaced by squared grids which, like the frameworks, fixed the proportions of the body.

    In a new edition of Schäfer’s work, Brunner-Traut (1974), added an epilogue entitled "Aspective" in which she reconsidered the proto-perspectival methods of pre-Greek art. Meanwhile, Groenewegen-Frankfort (1951), was conscious that pre-Greek art did not have perspective in the modern sense and explicitly pointed out that it was misleading even to use terms such as cavalier perspective (119, 135) in this context. Her concern was however to understand the background that led to objects being represented as they appear to be seen, which involves a relation to an observer and as she noted had two basic implications (3):

Firstly, all rendering which aims at illusionary corporeality- and we shall in future refer to it as functional rendering- implies on the one hand, a wilful act in the choice of viewpoint and, on the other, a resignation in that it accepts the autocracy of the solid form, its inner coherence: no mere viewpoint can tamper with the co-ordination of its parts; foreshortening, overlapping must be registered. And secondly, an object thus rendered is conceived as existing in space, the familiar three-dimensional space which comprises both it and its observer; in fact, corporeality and space are concepts which mutually require each other. Consequently the surface on which the image appears is no longer self sufficient. As substitute for the transparent screen it loses as it were, its solidity, becomes the isolated image of a figure rendered as observed, by a conceptual, three-dimensional void, appears to exist in space.

    Groenewegen-Frankfort relates these problems of space to those of time and narrative in an attempt to explain both the Arrest and movement in the title of her book. Although focussed on art of the ancient near east, this work, like that of Schäfer raises fundamental questions concerning the nature of representation and provides an important context for understanding later periods.

Antiquity (1000 B.C.-321 A.D.).

    During the Renaissance, the first authors on perspective denied that it had existed in Antiquity. Alberti (1434) remarked: "Since this work seems impossible of execution in our times, if I judge rightly, it was probably unknown and unthought of among the Ancients." Filarete was more assertive: "It was not used by the ancients, for even though their intellects were very sublte and sharp, they still never used or understood perspective."

    The first important source for the assumption that perspective originated in Antiquity was a passage in Vitruvius’ Ten books of architecture which referred to scenography and claimed that at the time of Aeschylus, Agatharcus had painted a scene and had written a treatise on the subject as had Democritus and Anaxagoras:

showing how, given a centre in a definite place, the lines should naturally correspond with due regard to the point of sight and the divergence of the visual rays, so that by this deception a faithful representation of the appearance of buildings might be given in painted scenery, and so that, though all is drawn on a vertical flat facade, some parts may seem to be withdrawing into the background, and others to be standing out in front.

    Cesariano, in his famous edition of Vitruvius (Como, 1521), Caporali (1536), Ryff (1547), and subsequent commentators accepted this passage at face value and assumed that scenography was synonymous with perspective. Philologists such as Ermolao Barbaro raised doubts whether Vitruvius intended sciographia rather than scaenographia, but this did not reverse the basic interpretation, and even today the passage remains an important ingredient in debates.

    Philostratus, in his Images, referred to deceiving the eyes in terms of symmetria. The early Renaissance editions translated this Greek term as proportion (proportio), but in 1578 a French edition translated this term as perspective. Further evidence based on texts was collected by Ioannes Schefferus in his book on Graphics, that is, on the art of painting (1669), in which he described proportion as a third part of painting and related this to Cicero’s convenience of parts (convenientia partium); symmetry in Pliny the Elder; congruence in Pliny, competence in Aulus Gellius; the terms commensus and commodulatio in Vitruvius and the Greek term for harmonics. Citing Pliny, Schefferus claimed that the first to practice this method in Antiquity was Euphranor, who taught the rules to Parrhasius. Among modern practitioners Schefferus mentioned authors of perspective texts such as Dürer, Gauricus, Serlio, Ryff, and Lautensack.

    Doubts concerning ancient perspective grew in the seventeenth century. Rubens in a letter to Pieresc written on the sixteenth of March, 1636 commented on a Nymphaeum found in the gardens of Cardinal Barberini in Rome:

This appears to be the work of a good painter but the optics has not been carefully observed, for the lines of the buildings do not intersect the horizon at an equal height, and to put it in a word, the whole perspective is lacking. One finds similar errors in certain buildings represented on the backs of medals...This leads me to conjecture that in spite of the excellent optical precepts given by Euclid and others, this science (perspective) was not nearly as commonly known by all as it is today.

    The grounds for a serious debate on the question whether or not the Ancients had known perspective were prepared when the French architect, Claude Perrault, offered evidence that the Greeks had been ignorant of perspective in his Parallel of the ancients and moderns (1692). Perrault cited the example of the Column of Trajan, noting how the figures further back were not diminished in size. He also claimed that Zeuxis and Apelles never knew the part of painting which involved the composition of a panel following the rules of diminution. Perrault’s arguments provoked the Abbé Sallier (1728) to claim that the Ancients must have had some knowledge of perspective. While careful to acknowledge that their level of theory may have been less extensive than during the Renaissance, Sallier based his claims on three sources, beginning with Plato’s discussion of appearance (phantastike) in the Sophist. Plato had noted that whereas sculptors maintained the true proportions of objects, painters did not, and had described the principle of optical adjustments methods (235e-236a):

objects which are seen at a certain elevation will appear too small and those which are positioned lower will appear too large, the ones being viewed from nearby, the others from afar. That is why workers these days abandon the true and give to their figures not the real measure of the model but that which should produce to the eye the impression of beauty of those figures.

    In Sallier’s interpretation this description of optical adjustments was evidence of perspective. Next he considered the passage from Vitruvius cited above, before turning to passages in Pliny’s Natural history. That the painter Pamphilus was described as being very learned in all the arts and especially in geometry convinced Sallier that he must have had some idea of perspective. Pliny had also described how Apelles ceded to Amphion in disposition, to Asclepiodorus in measures, the degree to which one thing should stand distant from another. This again Sallier interpreted to mean perspective. Franciscus Junius (1638) shared similar views claiming that the paintings of Apelles and Protogenes were proper courses in painting in which one could not doubt that perspective was dealt with thoroughly.

    Sallier’s article stimulated the learned antiquarian, M. le comte de Caylus, to pursue the theme Of perspective of the Ancients (1741) defining perspective as "the change and diminution that air brings to the colour and distance brings to line in objects seen by the eye". Caylus mentioned second-hand reports of recently excavated paintings from Herculaneum, but remained suspicious of what for him was hearsay. He cited Euclid’s Optics as evidence that the Greeks had a sufficient optical knowledge to achieve perspective. He referred to Junius (1638) and examples of Roman painting, the Aldobrandine Marriage, which Rubens had criticized for lack of perspective in his letter of 1636 cited above (cf. Sulzberger 1941, 1956); sculptures, such as the Feast of Trimalcion; marble bas-reliefs; medals and engraved stones.

    Meanwhile, in England, interest in this debate had also been growing. Alexander Pope, in his edition of the Iliad (1721), claimed that perspective had already been fully known at the time of Homer. Turnbull (1753), more cautious, was nonetheless persuaded by Sallier’s claims (70): "that whatever reason there may be to doubt whether perspective was well understood by the Ancients or whether the ancient painters had rules of perspective.... there is none at all to doubt, but they were able at least by the judgement of the eye, to represent and counterfeit any visible appearances". Turnbull supported these claims by citing passages from Plato, Vitruvius and Philostratus. His contemporary, Webb (1760), cited the same passages without acknowledgment to reach a more dramatic conclusion (115-116): "By this it will appear that the Greek painters, not only knew the rules and studied the effects of perspective, but that their greatest philosophers and mathematicians, thought it worthy of their attention, to reduce these effects to sure and determined laws".

    These debates were also taken up in Germany. Lippert (1767-1776), denied that the Greeks had known perspective. Klopstock (1767) rejected both the extreme views of Perrault and Pope and agreed instead with Sallier that there had been some knowledge of its principles among the Greeks and Romans. In addition to the usual passages from Plato, Philostratus, Pliny and Vitruvius, he cited additional evidence of paintings from Herculaneum and ancient coins. Klotz (1768) was even more certain that the Ancients had known perspective and cited as new evidence a cut stone in his collection and a passage from Lucian. Lessing had denied that the Greeks knew perspective in his Laokoon (1766) and took up the matter anew in his Ninth Letter of Antiquarian Contents (1768) as a reply to Klotz. According to Lessing, Klotz had used the term perspective too loosely to refer to diminution of figures in general. Similarly Klotz had used the term military perspective vaguely and had pretended that perspective was a question of genius when it was in fact a matter of mastering basic technical rules which, once established, could be carried out by anyone. Casanova (1770), took a similar tack and claimed that the passage of Philostratus upon which Webb had focussed merely proved that there was a general sense of foreshortening, which was a long way from laws of perspective.

    If we look back over these debates in the forty year period from 1728 to 1768, some significant changes become evident. At the outset Sallier was simply citing ancient texts uncritically. Le comte de Caylus shifted discussion from textual evidence to include works of art. Both were writing in French commenting on the views of other Frenchmen. In the next decades this debate became international and involved English and German as well as French scholars. Moreover, Lessing and his German contemporaries, introduced an element of interpretation. It was not just a question of citing texts, but rather of analysing critically their meaning. There was also a challenge of reconciling opposing interpretations. Fiorillo (1803) is an excellent summary of these new methods. He noted that perspective had a whole range of connotations to different commentators including scenography, composition, the shape of every foreshortened object, diminution of figures, gradual disappearance of chiaroscuro and diminution of colours etc. He cited the passages in question from Vitruvius, Philostratus, new passages from Pliny and reported the opinions of various scholars from Perrault onwards, carefully weighing the pros and cons of Lessing’s debate with Pope and Klotz. His conclusions were less original: that the ancient artists had known and practiced perspective but had sometimes made errors in execution. But then, he added, so too had Guido Reni and no one would accuse a student of Carracci of ignorance of perspective.

    Nineteenth century contributions to these debates were less dramatic than those of the eighteenth century. Nonetheless, some clear developments deserve mention. In mathematics, Poncelet (1821, xxxvii) drew attention to the importance of the porisms of Euclid. This was one of the starting points for Chales (1837) in his History of geometry who raised the question whether the Ancients knew perspective and concluded that (74): "in spite of all the respect that we have for this great geometer [i.e. Poncelet], we must confess that in reading the Ancients we have not found any trace, any indication which would authorize us to share his opinion in this matter". Indeed, Chales (cf. below p. 69*), believed that Desargues and Pascal had been the first to apply perspective to the theory of conics.

    In archaeology, ever more detailed measurement of ancient architecture led to a new awareness of optical adjustments made by the ancients. Hoffer (1838) made a preliminary report on new measurements of the Parthenon. Pennethorne (1844) offered a larger framework for understanding these adjustments. His ideas were taken up by Penrose (1846) and in an unpublished work of Paccard in the same period. Not everyone was convinced that these curvatures in the Parthenon had been intentional. The possibility that they might have come about through a sagging of the foundations was considered by Bötticher (1862) and Ziller (1865). Further studies of Durm (1871) and Burnouf (1875) gradually established that these curvatures had indeed been intentional. Hauck (1879), in an important study related these curvatures to Greek optical theories and in so doing prepared the way for Goodyear’s (1912) studies and Panofsky’s (1927) claims.

    Nineteenth century developments in philology also brought new precision. For instance, Mullach’s (1843) list of works by Democritus gave a Greek title Ekretasmata for his work on scenography and provided learned notes. A French edition of Philostratus (1881) considered the supposed reference to perspective in a commentary. An article by Sartorius (1897) assessed the question of perspective in the context of Plato’s views on painting with detailed references to the original Greek. Meanwhile a number of scholars continued the general textual approach of the previous century. Some, such as Thibaut (1827), merely summarized what had already been said. Others such as Randoni (1825) offered a more sceptical assessment of the ancient contribution. While accepting that there had obviously been optical adjustments methods, he insisted that a distinction was needed between the general drawings of stage scenery which were known to the Ancients and drawings using linear perspective which were not. Randoni based this claim on a close reading of the passage from Vitruvius, arguing that the Latin term circini centrum had nothing to do with the centre of the eye and referred simply to an opening of the compass. Wieland (1840), also of interest for perspective in literature (see below p.119*), found a passage in Cicero’s Orator which he thought offered further proof of perspective in Antiquity.

    Already in the eighteenth century scholars had recognized Pausanias as one of the richest classical sources for descriptions of Greek art. His detailed description of the murals painted by Polygnotus in the hall of the Knidians at Delphi was particularly problematic because no physical evidence remained of these once great murals. The Comte de Caylus had outlined an imaginative reconstruction of this narrative cycle as being complete with illusionism, spatial effects and perspective. Klotz had taken up this interpretation only to be challenged by Lessing. Schreiber (1897) reviewed the history of these debates and introduced a new approach by noting that the concept of symmetry applied to the disposition of groups of individuals as well as to individual figures. This he demonstrated using well known examples such as the Aldobrandine Wedding in the Vatican and images on a series of amphora. Schreiber concluded that ancient art, to the extent that it involved distinct episodes of narrative and architectural features, was dominated by a principle of concentric arrangements of one to three figures around a central individual in the foreground. These symmetrical arrangements were sometimes shifted slightly to produce variation in the eurythmic effects. Schreiber pointed out that these principles continued into the Renaissance in Masaccio’s frescoes in the Brancacci Chapel and those of Ghirlandaio in Santa Trinità.

    Meanwhile, Blondel (1878), who marked one of the most subtle nineteenth century contributions to the tradition of interpreting ancient sources, heralded a new approach by adding some careful line drawings and photographs of the works in question. From the time of Caylus (1741) scholars had mentioned and cited visual evidence from Herculaneum and other sites. Thibaut (1827) had referred to Pompeii. But this had been prior to the invention of photography and even when photographs became possible, the limitations of printing meant that good reproductions were still not practical in learned books and journals. This changed dramatically in the early twentieth century just as new archaeological digs were uncovering the Villa Boscoreale in Pompeii. For instance, Petersen (1903), included three photographs of this villa in an attack on Mau, to which Mau (1903) responded in the same issue with seven photographs, some of fragments of paintings which he completed and reconstructed using line drawings. This new use of photographic documentation went hand in hand with a shift in the debates to consider functions of the original paintings. Mau claimed that they were more by way of ornamental decorations, hence the tendency of these frescoes to occlude space beyond the room. This idea was pursued by Krieger (1919) using new evidence from the Villa Negroni, Hadrian’s Villa and the walls of the tomb of the Nasoni. On the other hand, Petersen argued that the Pompeian frescoes were prospects and thus effectively like windows into the landscapes. Kern (1912, cf. below p. 50*) and Goldschmidt (1916) subsequently argued that this ancient tradition was the source of mediaeval and fourteenth century examples.

    Rodenwaldt’s (1909) publication of the composition of the Pompeian wall paintings, prompted Pfuhl (1910) to reconsider references to Apollodorus as a shadow painter (o skiagraphos) as possible allusions to his work on perspective. Pfuhl (1911) also drew attention to the importance of vases as another indirect source for the lost paintings of the Greeks, including eleven illustrations. This led to his classic Painting and Drawing of the Greeks (1923). Pfuhl’s work was one of the starting points for a dissertation in Latin by Hoogeveen (1925) on questions of depth and perspective in ancient art, which included no illustrations because these were supposedly sufficiently wide-spread. Kaphingst (1924) avoided illustrations in his thesis for another reason. The paintings were lost and the evidence of vases was too meagre. Consequently he focussed instead on philosophical, astronomical and scientific fragments by Plato, Aristotle, and Theophrastus, citing scattered references in Greek (without translation), to the work of Anaxagoras and Democritus in order to understand the background for ancient writings in optics and perspective, notably Euclid. Meanwhile, Panofsky was formulating his theory of ancient fish-bone perspective (see above p. 4) in lectures at the Warburg Library (1924-1925) which he published in 1927. Curtius (1929) devoted some ten pages (86,117,157,176,184,310, 314,341,392,394) to perspective in his study of the wall paintings of Pompeii (pl. 1.1-2; 33-34).

    Little (1937) basically accepted Panofsky’s explanation but claimed that they had also had a knowledge of two-point perspective. Kern (1938) analysed the mosaic of the Four Seasons (Munich, Glyptothek) to demonstrate that it had (a fish-bone) perspective and used the scenae frons from the Domus Aurea to reconsider the passage in Vitruvius. Beyen (1938), in his massive publication on the Pompeian decorations, provided much new visual evidence and noted a contradiction between references to systematic perspective in ancient texts and lack of perspective in the extant wall paintings. The following year Beyen (1939) published two articles claiming that the visual evidence of the wall paintings in fact confirmed knowledge of a systematic method of central perspective. The 1940’s saw at least four contributions. Bunim (1940) reassessed various interpretations of the passages from Vitruvius. Levy (1943) wrote a general article in which he claimed Greek perspective had influenced both Renaissance and modern art. Richter (1946) provided important material on Attic red-figured vases. Lepik (1949) examined the mathematical planning of ancient theatres. Eith (1947) returned to the question of curvatures in Greek temples examining images in the eye from a medical, ophthalmological point of view.

    Since 1950 there have been a number of contributions. New attention was given to the importance of vase painting. Robertson (1951) offered a brief survey of its development. Beyen (1952) considered a Loutrophoros to reassess the famous passage in Vitruvius. Schweizer (1953) drew on examples of vase painting in a study which explored the roots of perspective in Plato’s philosophy and aesthetics. White (1956) confronted evidence from written sources with visual evidence from Pompeian wall paintings and vases, drawing attention in particular to foreshortened chairs depicted therein. He re-examined carefully the Vitruvian passages and concluded that the ancients must have known linear perspective. The following year he published an abbreviated version of this as a chapter in his Birth and Rebirth of Pictorial Space (1957). That same year MacNair (1957) reviewed the tradition of optical adjustments methods in architecture under the title of spherical perspective. Andreae (1958) examined the spatial characteristics of the Amphora of the Giants from Melos at the Louvre and noted that these were more effective on the original vase than in copies which had been unrolled onto a flat surface.

    Also that same year Gioseffi (1957) produced both a significant article which became the basis for an important book both of which took John White’s Birth and rebirth as a point of departure. In the initial section of his article Gioseffi focussed on the Massacre of the Niobes (Strage dei Niobidi, Museo Nazionale, Naples) as evidence of linear perspective in Antiquity and claimed that Apollodorus of Athens, the so called shadow-painter (skiagraphos), was the first of the Greeks who reproduced visible appearances. In the early section (1-47) of his book on Artificial perspective, Gioseffi (1957) re-considered the classical sources that discussed perspective, namely, Vitruvius, Ptolemy, Daminaus and Proclus. Gioseffi reviewed and dismissed the theories of Borissavlievich and Panofsky, noting that a concept of potential infinity had been admitted by Aristotle. According to Gioseffi there were clear examples of mathematical perspective to be found at Pompeii. He cited as evidence cubicle 16 in the Villa of the Mysteries (pl. 2.1-2.2), cited the use of diagonals in cubicle 14 and the converging lines in both oecus 6 and right side of the wall in alcove b of cubicle 8 in the same villa.

    Since then the most important evidence in favour of Ancient methods approximating those of linear perspective have been provided by the excavations at Oplontis (1975). Here we find receding rows of columns (pl. 3.1-2), which appear at first glance to recede towards a single vanishing point.

Figs. 7-8. Line drawings of Cryptoporticus, Pompeii, with reconstructions according to Little, (1971). The same with extensions by the author of some of the other converging lines to confirm that this is an other example of axial (fishbone) perspective.

    We discover, however, that different parts of the picture converge to different points aong the axis: i.e. that this is another case of fish-bone or axial (pseudo-) perspective, and that this motif is a recurrent one even in the context of this single villa (pl. 4.1-2). Even so this effect is reminiscent of Lucretius’ description in The Nature of Things (see Appendix 1).

    Much important evidence against the existence of linear perspective in Antiquity was provided by the work on vases by Beazley (1956, 1963) and Richter (1946, 1966). The role of vase painting in the development of realism in Greek painting was examined in detail by Moreno (1964-1965). Additional examples of architectural representations on Greek vases were provided in dissertations by Gigante (1980) and Adamopoulos (1986). Further evidence from the walls of Pompeii and Herculaneum was made accessible by Schefold (1962), by Kraus and Von Matt (1973) and through an excellent exhibition catalogue sponsored by the Ecole des beaux arts (Paris), the Institut Français (Naples) and the Getty Trust.

    A series of articles dealt with specialized topics. For instance, new attention was given to the problem of optical adjustments. Stucchi (1952-1954) examined the decorations of the temple of Zeus at Olympia and wrote on optical corrections in Greek art (1955). Stucchi (1970) also proposed that the Charioteer at Delphi was intended to be seen from a given point of view. Purchiaroni (1959-1960) considered the problem of optical corrections in the Hephaesteion of Athene. Stewart (1977) proposed that the sculptures from the cave at Sperlonga were programmatically arranged to be seen from a special position: the emperor’s dinner table. Bertocchi (1961) drew attention to landscape scenes in the Ambrosian Iliad. Andreae (1962) re-examined the spatial effects of the Odyssey Landscapes (Vatican). Adorno (1965) considered perspectival problems in his re-assessment of Plato and Aristotle’s views on art. An important article by Wataghin Cantino (1969) studied the development of bird’s eye views in ancient painting. Keuls (1975) reconsidered the meaning of skiagraphia to conclude that it "was an impressionistic technique, using divisions of bright colours and relying on the phenomenon of optical colour fusion", only to be challenged by Pemberton (1976). A conference at the Swiss Institute in Rome included essays by Lasserre (1985) on Agatharchus, Gioseffi (1985) on Democritus and Krause (1985) who related the problem of Ancient scenography to the architectural tradition which intended that temples be seen from given viewpoints.

    Most of these specialized studies have had little impact on two camps which have have been emerging. One insists that the Greeks had a technical knowledge of perspective. White (1957 etc.) and Little (1971) have become the best known exponents of this view. Little’s diagrams are persuasive (e.g. fig. 7) until one recognizes that he has "omitted" extensions to some of the converging lines. If these are added, one obtains another example of the by now familiar axial perspective (fig. 8).

    The other camp claims that the the Greeks had no technical knowledge of perspective. For instance, Lepik-Kopaczynska (1956), argued that the pervasive evidence of false perspective in Greek art could not be a co-incidence and suggested that one should distinguish between three kinds of pseudo-perspectival techniques, relating to frontal, lateral and oblique views respectively. Richter (1937) also suggested that the Greeks had no technical knowledge of perspective, a view reinforced by her detailed studies of vases (1946, 1966) and which led her to make (1970) what remains the best statement against ancient perspective.

    Among historians of mathematics and science there was some discussion of the role of Euclid’s Optics in the rise of perspective. Veltman (1975, 1980, 1986) accepted Panofsky’s conclusions and offered further reasons for maintaining this position. Brownson (1981) challenged Panofsky’s (1927) claim that Euclid’s theory of vision precluded principles of linear perspective, arguing that five propositions (10, 18-21) employed linear projection albeit he admitted that only one of these (10) involved a visual cone. Andersen (1987) acknowledged proposition 10 as the "one procedure resembling a projection", but concluded that Euclid did not use proposition ten for these purposes. Knorr (1991) went further, arguing that the crucial passage in proposition 10 was not part of the original text and represented a later gloss. He thus rejected links between Euclid’s Optics and linear perspective.

    One reason why there remains so much debate concerning these questions is because classicists and especially classical archaeologists frequently use perspective in a broad sense to include all effects of foreshortening and diminution with distance. This the Greeks and Romans undoubtedly had. They also undoubtedly had some techniques of optical adjustments and corrections. The combined literary evidence suggests that they had some systematic method to produce pseudo-perspectival effects. There is no convincing evidence however that they knew linear perpective as developed in the Renaissance. Indeed, as Panofksy (1927 etc. cf. Veltman 1975, 1986, 1992) claimed, there are serious reasons to insist that the ancients could not develop perspective in the modern sense. If Euclid’s Elements potentially made perspective possible, Euclid’s Optics, which appears to have guided methods of representation, precluded the inverse size/distance principles on which perspective is based. Hence, while many have spoken eloquently about the re-discovery or re-invention of perspective in the Renaissance, the weight of the evidence to date suggests that linear perspective, in a technical sense, was discovered for the first time in the early decades of the fifteenth century.

Mediaeval Period (321-1300)

    The medieaval period as a whole has received remarkably little attention. Those who claim that perspective was discovered in Antiquity usually assume that it was forgotten with the fall of Rome and not recovered until the Renaissance. On the other hand, those who believe that perspective was discovered by Brunelleschi in the Renaissance frequently search for proto-perspectival examples in Cavallini (Santa Maria in Trastevere), Lorenzetti (Siena, Assisi) or Giotto’s cycles (Assisi, Padua, Florence) and in so doing they treat these late thirteenth and fourteenth century examples as if they were part of the early Renaissance. Both schools focus on beginnings rather than continuities, and hence the period in between is usually ignored.

    One of the rare exceptions was Kallab (1900), who argued that the importance of symbolic elements such as tower, arch, crenellated wall and throne during the mediaeval period required the development of some spatial mastery. Another was Panofsky (1927) who made several important points in his landmark article. He noted the existence of inverted perspective in mosaics of the sixth century, and a serious interest in spatial motifs in the Vienna Genesis (c.500 A.D.). He demonstrated that a type of round temple represented in a villa near Boscoreale (now New York, Metropolitan Museum), recurred in Syrian (c. 500 A.D.), and Latin manuscripts (c. 781-783; c.827; c.870). Panofsky showed that the axial (or fishbone) perspective of Roman art, recurred in the Alcuin Bible (London) in the second quarter of the ninth century, and in Duccio’s Maestà (c.1301-1308). He observed that subjects such as the Last Supper were being treated in spatial terms by the twelfth century at Monreale and that a mosaic depicting Christ healing the Lame in that great monastery had a set of tiles converging to a single point. Panofsky established also that while Italian artists such as Lorenzetti played an important role in the evolution of these converging tiles in the fourteenth century (pl. 7.3-4), one needed to take into account northern examples such as Meister Bertram (1379) or the anonymous Missal of Luçon (c.1388). Similarly the spatial interiors of Jan Van Eyck had parallels in the Master of Heiligenthal (Konrad von Vechta?). Implicit in Panofsky’s study was the claim that the development of spatial motifs in the Renaissance was a European rather an Italian phenomenon, although it was in Italy that mathematical perspective emerged. Pinder (1934) suggested that the rise of perspective had undermined the higher ideals of form in mediaeval art, and basic values of belief and community that were above form.

    Panosfky’s essay was one of the starting points for Horb (1938), who examined in more detail the continuity between Pompeian frescoes, early Christian churches such as San Lorenzo fuori le mure and the work of Duccio and Giotto in the Trecento. He argued specifically that the view of an interior as a section which simultaneously gave one a view of the exterior had its roots in Pompeian art, that it could be traced via a fourth century Vergil manuscript (Rome, Vatican 3225) and later examples such as the Vienna Genesis manuscripts. Panofsky also inspired Bunim (1940), which remains the most systematic study of mediaeval space thus far. Bunim identified two basic spatial forms in Roman art. One was a "stage space" which included prospect scenes. While maintaining a vestige of its original stage space structure, this involved a solidifying of the surface to achieve concrete tridimensional forms. A second tradition "derived from the impressionist form of the backgrounds found in the Odyssey Landscapes" and by "substantializing the surface of an illusionistic, representative picture plane", arrived at stage space by a series of modifications. Bunim contrasted developments in Byzantine and Italian art, which were dominated by the tradition of stage space, with developments in Germany, France, and England which were dominated by illusionistic space until the thirteenth century when Germany, and the fourteenth century when France and England introduced a stage space. Bunim’s book was reprinted (1970). No subsequent study has explored questions of continuity and development of space during the entire mediaeval period in greater detail.

    For the period from 1250-1500, White (1957), remains the standard work. Following the example of Vasari he began his account of the rebirth of pictorial space in the Upper Church of San Francesco at Assisi with Cimabue; the master of the Legend of Saint Francis, the Saint Cecilia Master and the painter of bays seven and eight. To explain the context of these developments in Assisi, White turned to Rome, noting the role of Cavallini and that (51-52): "the entire decorative framework of the Saint Francis cycle derives from Roman prototypes, San Paolo amongst them, whilst Cimabue’s frescoes of the Lives of Saints Peter and Paul depend, in all probability, on the lost series in the portico of Old Saint Peter’s....It was in Rome that Italian painters first rediscovered nature through the art of late antiquity".

    White then turned to Giotto’s role in the Arena chapel in Padua and in the Bardi and Peruzzi Chapels of Santa Croce in Florence, before considering the contributions of two early Sienese masters: Duccio di Buoninsegna and Simone Martini. He suggested that Giotto’s Wedding Feast at Cana in the Arena Chapel marked a starting point for the later evolution of Giottesque perspective and that its treatment of oblique perspective could be traced via the master of the Saint Nicholas Chapel in the Lower Church of San Francesco at Assisi and Maso di Banco’s frescoes in the Bardi di Vernio chapel of Santa Croce. White observed that Taddeo Gaddi’s use of an extreme oblique design in his Presentation of the Virgin in Santa Croce recurred in the Très Riches heures du Duc De Berry by Pol de Limbourg; he noted how the conquest of the barriers between reality and art was achieved by a play of painted architectural frames in Assisi, Padua and at Santa Croce in Florence. White focussed on three artists active in Padua in the last quarter of the fourteenth century (Altichiero, Avanzo and Giusto de’Menabuoi) in terms of their compositional content, and developments in spatial design. Following a chapter on Brunelleschi’s perspective demonstrations, White traced the contributions of Masolino, Donatello, Ghiberti and Filippo Lippi. He explored briefly the problem of illusionism in painting and outlined the development of what he termed synthetic perspective in Uccello and Leonardo da Vinci. He explored parallels in French manuscript illustration via Jean de Pucelle, the Limbourg brothers and particularly Jean Fouquet. A final chapter was devoted to re-assessing the question of the discovery of perspective in Antiquity (cf. above p.44*).

    Gioseffi (1957), in the second section (48-73) of his book on Artificial perspective, challenged the explanations of Grabar (1945) and Stefanini (1956) concerning inverted perspective (see below p. 95-96*) and argued that there existed no coherent method of inverted perspective, only episodes that go inversely and that the phenomenon was rather to be understood as a fragmentation of perspectival space. By way of illustration, Gioseffi cited the Sacrifice of Abel and Melchisedech (Ravenna, San Vitale, pl. 15) which he claimed showed two separate perspectival spaces. Gioseffi also reconsidered Giotto’s contribution, making three claims, first, that Giotto had known the basic principles of linear perspective: citing the fictive alcoves (Padua, Arena Chapel) as an example. Second, he claimed that Giotto’s work at Padua and Assisi contained the first applications of a single vanishing point for a whole space: Giotto’s Sermon in the presence of the pope (Predica davanti al papa) was cited as an example. Third, he claimed that some works included a vanishing point and diagonals: for this he cited the Prayer for the miracle of the rods (La Preghiera dei pretendenti,pl. 7.1-7.2). According to Gioseffi these examples confirmed that Giotto had depended on examples of ancient art which would have come into his ken through Roman intermediaries such as the Isaac Master (Maestro di Isacco) and the Master of Saint Cecilia.

    That same year, Parronchi (1957), in a highly imaginative and no less speculative article on "The Sources of Paolo Uccello", raised new questions in terms of the late mediaeval contribution. He suggested, for instance, two strands of development from the time of Giotto. The optical writer Witelo had claimed that parallel lines do not converge with distance. One strand, which included Maso, Stefano, Giottino, Brunelleschi and Masaccio, deliberately went against this prevailing optical theory and insisted on making parallel lines converge to a point. Meanwhile, claimed Parronchi, there had been another strand, more peripheral, which included Taddeo Gaddi, Orcagna and Uccello, and followed more closely the precepts of Witelo’s optics. Parronchi found that Uccello’s compositions lent themselves to be circumscribed by geometrical circles. He believed that there were parallels in Witelo’s optics. More significantly, he thought, Uccello’s sinopia in Santa Maria alla Scala evidenced two diverging vanishing points which, he believed, corresponded to a diagram in Witelo’s optics (Bk. III,45) dealing with binocular vision. In the second part of his article Parronchi suggested parallels linking Uccello’s work with the anonymous On Perspective which he ascribed to Toscanelli; with Aristotelian ideas supposedly acquired second hand through the summa literature; with the Secret of Secrets, and with a treatise On the Moral Eye. From all this Uccello emerged as "a painter with a basis in philosophy who through the lens of optics tried to reflect the Aristotelian cosmos in his paintings".

    The following year Parronchi continued his exploration of mediaeval optics and its role in the "Two Perspectival Panels of Brunelleschi" (1958), examining the influence of Alhazen, Witelo, Bacon, Peckham, Blasius of Parma, the anonymous author of On Perspective and Ghiberti’s Third Commentary. In Witelo’s Optics he found a diagram (V.23) which, he believed, could have inspired Brunelleschi to make his original experiment. He cited once again the concept of binocular vision to which he returned in "The Measures of the Eye According to Ghiberti" (1961), where he argued that the spatial arrangement of the vanishing points in Ghiberti’s scenes from the Stories of Jacob and Joseph on the doors of the Baptistery at Florence (the Gates of Paradise), was in accordance with binocular principles of mediaeval optics. Parronchi argued that the eye which guided fourteenth century architects was based on a concept of deception of the eye as found in optical treatises of the time and that this could account for their lack of clear quantitative measurement. In his view Brunelleschi transformed this approach first in Santa Trinità and then in Santa Maria del Fiore.

    Meanwhile, Parronchi had written another important article on perspective at the time of Dante (1960). Here he examined the impact of mediaeval optics on Dante’s ideas, confronting paragraphs from Roger Bacon and Thomas Aquinas with passages from Dante’s Convivio and exploring parallels between ideas in Alhazen and Witelo with those in Dante. Parronchi (1960-1961), in his "Visualized architecture" suggested that treatises on optics (perspectiva) had been a source of geometrical knowledge to mediaeval architects. To demonstrate these links between architecture and optics Parronchi cited examples of portals in Florence (S. Stefano in Ponte) and Prato (Duomo) the framing bricks of which converged towards

Fig. 9. Map of major developments in perspective in the period 1200-1700 by Harnest (1971).

a central vanishing point and examined the play of light through windows into churches such as Santa Trinità in Florence. These and other articles were reprinted in Parronchi’s book (1964) which, though challenged in many points of detail by Edgerton and others, remains one of the classics in the field.

    The following year saw the appearance of another classic, Federici Vescovini’s (1965), Studies on mediaeval perspective, which has not received the attention that it deserves. Vecovini focussed on the philosphical context of mediaeval optics in the period 1200-1400, beginning with Grosseteste’s quest to make optics (perspectiva) a demonstrative science. She then examined three texts in the neo-Platonic tradition, the Book of causes by Pseudo-Avicenna, On light by Bartolommeo da Bologna and On intelligences by Pseudo-Witelo. She traced the influence of the Stoic tradition via Alkindi, explored roger Bacon’s efforts to make optics an experimental science, the role of Avicenna, Arabic medical sources, and the gnoseological-optical approach of Ibn al Haytham. The latter part of the book focussed on the contributions of the major fourteenth century authors on optics: Buridan, Henry of Langenstein, Domenicus of Chivasso, a commentator on Euclid, and Blasius of Parma. Vescovini’s importance lies in showing clearly that mediaeval optics was much more than theories about the eye. Indeed optics was central to the major philosphical discussions of the time. She concluded that with the work of Blasius of Parma, the neo-Platonic theoretical approach to vision (267): "is transformed...into a privileging of an empirical, experimental and quantitative understanstanding of nature, on the basis of a different use of geometrical notions of optics from Antiquity".

    Since then other contributions have been made. Ineichen (1975) explored the etymological links of optics and perspective in the Arabic term al-manazir, particularly as used by Alhazen.Veltman (1986) drew attention to Villard de Honnecourt’s (c.1230) use of a strings and nails to make voussoirs which bears an unexpected similarity to the so called workshop method of arriving at vanishing points described by Klein (pl. 5.1). Sabra (1992), published the first two volumes of his monumental edition of Alhazen’s Book on vision (see above p. 26*), making available for the first time to English readers the riches of the Arabic optical tradition, thus clarifying the context whereby the study of vision became intertwined with concerns for representation.

Renaissance (1300-1599)

    The history of Renaissance perspective involves both practice and theory. Most literature on these subjects has been devoted to individual practitioners and theorists and, for the sake of convenience, has been listed separately in alphabetical order in Appendices 3 and 4. Our concern in this section will be focussed on accounts which deal with the period as a whole.

    Among the earliest records of Renaissance perspective practice was Cristoforo Landino’s Apologia of Dante (1481, 1564; cf. Morisani, 1953), who specifically used the term perspective in his descriptions of Uccello, Brunelleschi and Donatello. In his Apologia of the Florentines (cf. Bonucci, 1847,91) Landino also described Leon Battista Alberti as being "more famous in perspective than anyone in many centuries". Massaino (1499) noted Alberti’s accomplishments in perspective theory (cf. Bonucci, 1843, p.CCXXXV). Volaterannus (1506) in his discussion of optics and catoptrics referred to the treatises of Petrus e Burgo Sancti Sepulchri (i.e. Piero della Francesca) adding that: "the use of this discipline is clearly manifest in many things: in measuring buildings, in the principles of architecture and painting, in the positioning of the shadows of objects...and finally in discovering the truth and variety of heavenly and other bodies both in terms of their reflections and refractions". Volaterannus’ statement is important because it makes explicit links between perspective, optics and astronomy which helps explain Leonardo’s and Kepler’s activities in this context (cf. Veltman 1994). It also provides a further context for Edgerton’s (1991) claims concerning links between astronomy and perspective.

    Vasari (1550) began his story of perspectival practice with Cimabue, Giotto and Stefano; mentioned Paolo Uccello, Filippo Brunelleschi, Lorenzo Ghiberti, Masolino and Masaccio among the early masters of perspective and specifically referred to Andrea Verrocchio and Piero della Francesca as perspectivists. Indeed his description of perspectival practice was so detailed that it was not until the twentieth century that scholars compared the details of that story with extant painting in arriving at a more accurate history. In terms of theory Vasari mentioned Brunelleschi’s demonstration and also referred to treatises on perspective, although not to specific titles. A survey of Vasari’s statements on perspective is provided in appendix 5.

    The same trends in nineteenth century scholarship which led to a new study of source materials and prompted new attention to the sources of perspective (cf. above p. 3*) led also to new studies of Renaissance perspective. The long articles and monographs by Nielsen (1895-1901) heralded a more systematic approach. In the earliest of these, Nielsen (1895), focussed on the work of Albrecht Dürer. Nielsen (1896), began with the proto-perspectival efforts of Cimabue and Giotto and explored the foundations of perspective theory in Brunelleschi and his contemporaries Uccello, Ghiberti, and Masaccio and went on to outline the contributions of Alberti, Piero and Pacioli. The latter part of the book examined painting practice in the Netherlandish school; Mantegna, and perspectival practice in Florence (Filippo Lippi, Benozzo Gozzoli, Melozzo da Forli, Luca Signorelli, Domenico Ghirlandaio and Botticelli). Nielsen (1897) turned to the work of Leonardo da Vinci, the contributions of the Umbrian school (Bramante, Perugino, Pinturicchio and Santi), Raphael, Peruzzi, Giulio Romano and Michelangelo.

    Nielsen (1898), began with a chapter on the Venetian school including the Bellini family, Carpaccio, Giorgione, Titian and Veronese (cf. pl. 35). This was followed by chapters on Serlio and Barbaro. A fourth chapter considered Corregggio and Benevenuto Cellini. A fifth chapter examined the work of Giacomo Barozzi, il Vignola and the commentary by Egnazio Danti. Chapter six considered the contribution of Guidobaldo del Monte. Chapter seven turned to the Bolognese school, namely, Guido Reni, Domenichino and Francesco Albani and a final chapter explored connections with scenography with Andrea Palladio, the Galli-Bibbiena family and Andrea Pozzo. Nielsen (1899) examined French contributions beginning with the school of Fontainebleau and Jean Cousin, with chapters on Androuet Du Cerceau and later painters (see below). Nielsen (1901), although focussed on later developments (see below), included a chapter on perspective in the sixteenth century German tradition (Dürer, Holbein). Nielsen was important because he explored perspective practice and theory in tandem as related problems. Prior to Nielsen, discussions had been limited mainly to the Florentine context. Nielsen revealed that perspective affected the whole of Europe including France, Germany, the Netherlands, Denmark and England. Nielsen was among the first to introduce reconstructions of perspectival vanishing points. Since these used simple engravings based on the originals as their starting points, their scholarly value was limited. Even so they prepared the way for the more technical analyses of Kern and a later level of precision which began with Carter (1953).

    More general articles about the development of Renaissance perspective, which began to appear in the first decade of the twentieth century, emphasized perspectival practice. For example, Reymond (1905) focussed on architecture in paintings from the time of Giotto through to Filippo Lippi. In these discussions. Doehlemann and Kern, famous for their debates about Northern perspective (see below p. 59), played a role. Doehlemann (1907-1908) demonstrated that the theme of the Annunciation was particularly significant for the development of spatial effects in illuminated manuscripts as well as frescoes and paintings. Kern (1912) explored the painting practice that made possible Brunelleschi’s so-called first use of perspective. Kern examined a series of paintings with fish-bone perspective applied to ceilings by Simone Martini, the school of Giotto, Ugolino and Barna of Siena, Lorenzo di Bicci, an anonymous master of the Sienese schools, and Spinello Aretino, before considering Giotto’s Apparition to Fra Agostino and the Bishop (Florence, Santa Croce, 1325) which he claimed had all its lines on the ceiling converging to a central point. Since there were obvious differences between the treatment of ceilings and floors, Kern deduced that these paintings could not have been guided by a single theoretical concept of space: rather they must have been the product of painting practice which he claimed went back ultimately to the the Pompeian frescoes of the late Roman period. In this view, the evolution of perspectival forms in the fourteenth century began with a revival of Ancient methods.

    Kern also drew attention to a painting by Francesco Traini which tended towards a vanishing point and two examples by Lorenzetti, his Madonna with Child, Angels and Saints, the so called Little Maestà (Siena, c. 1340), and the Annunciation (Siena, 1344, pl. 7.3), the first known examples of a central vanishing point. Why then did the concept of a vanishing point not triumph sooner? Kern argued that there had been a mediaeval debate concerning the vanishing point and that Witelo, the leading mediaeval author on optics, had argued vehemently against it (cf. Kern 1904). He suggested moreover that this debate again went back to Antiquity when Lucretius had insisted on a single vanishing point while Vitruvius had argued against convergence to a point.

    Grüneisen (1911) argued that the comparative study of techniques was to the history of art what philology was to the history of literature. He examined several characteristics of archaic art: the base plan reduced to an horizontal line, inverted perspective, plans with a vanishing point and bird’s eye perspective. These techniques, he claimed, were taken up in Byzantine art. Citing the work of Russian scholars such as Kondakoff and Likhatscheff, he claimed that these strands of Byzantine art had a seminal influence on the art of Cimabue, Duccio, Giotto and the Italian Renaissance in general. According to Grüneisen, Giotto knew both linear and aerial perspective! Müller (1913) gave his inaugural address as rector of the Technical University at Darmstadt On the beginnings and nature of painterly perspective in which he surveyed its history from proto-perspectival examples in Antiquity to the Renaissance, where he focussed on the contributions of Alberti, Piero della Francesca and Dürer, emphasizing links between mathematics and art which he believed to be of enduring importance to education.

    Pittarelli (1918), provoked by a curious usage of the term perspective in the laws of 20 June, 1909 and 23 June 1913, reviewed the history of the term during the Renaissance, citing Alberti and Galileo and claiming that there were three principle meanings: the art or science of representing objects onto a plane or curved surface using central projection; the same things drawn or painted; natural views of objects which present themselves to the view of a landscape or the like.

    Richter (1936), in an article which focussed on controversies concerning perspective in Antiquity (see above) cited Cennino Cennini’s description of a    proto-perspectival method and mentioned in passing the contributions of Brunelleschi, Alberti, Uccello, Leonardo and Piero della Francesca, noting that Serlio believed Renaissance perspective to be in accordance with the doctrines of Vitruvius.

    Nicco Fasola (1942), in a polemical article argued that perspective was not a discovery but rather an invention of fifteenth century Florence, that it had a basis neither in experiment nor in ocular experience, rather, that it was a product of a cosmological world view in which art, mathematics and science were seen as keys to certainty, while nature was conceived geometrically: hence the identification of the regular solids with the elements. Nicco Fasola noted that the academies had perpetuated the rules of perspective while failing to convey the historical context that had inspired it. That same year Nicco Fasola (1942) wrote an article on the "Development of perspectival thought in treatises from Euclid to Piero della Francesca" summarizing developments in the mediaeval optical tradition (Ptolemy, Alhazen, Witelo, Biagio Pelacani da Parma), focussing on Alberti’s contributions in his On Painting and Elements of Painting as a prelude to the work of Piero della Francesca. A more thorough examination of Piero’s own contributions and a study of how this fitted into the aesthetics and cosmological views of the Renaissance, (particularly Nicholas of Cusa), followed in Nicco Fasola’s (1942) introduction to her edition of Piero’s On perspective of painting.

    Fiocco (1944), in an article entitled "The significance of perspective", offered a brief outline of the history of perspective, claiming that it was "always quite other than systematic and an inseparable companion of intuition," mentioning Brunelleschi, Uccello and Piero della Francesca, emphasizing Mantegna, the illusionism of Veronese and Tiepolo, the negative contributions of the academy and finally Cezanne, who brought about the end of scientific perspective according to Novotny (1939). This Fiocco challenged, claiming that there had never been a scientific perspective in the sense that, from the outset artists had paid attention to intuition, and from the time of Giorgione onwards had given such attention to (subjective) atmospheric perspective that it could undermine the rigour of any linear rules.

    Guerry (1951) summarized the evolution of the notion of space in a page noting that: "To express, three dimensional space using a surface of two dimensions: that is the problem of the painter and which he must resolve by means of a compromise. The history of this compromise, its hesitations, its affirmations, reprisals, omissions and negations, this is the history of perspective itself". These ideas summarized those of her detailed study of Cezanne (see below). Sulzberger (1956) mentioned the historical contributions of Brunelleschi, Alberti, Piero della Francesca and Pélerin, but was more concerned with polemical claims about perspective being an indispensable element for the creation of a work of art and that the rules of perspective did not remove from the artist the possibility of choice since pictorial perspective was partly intuition and feeling.

    Francastel (1951), in Painting and society. Birth and destruction of a plastic space. From the renaissance to cubism, described Brunelleschi as the originator of perspective in the context of architecture; suggesting that his panels were more to "permit a practical study of the plays of light than to realize an exemplary work," claiming that these principles were then applied to sculpture by Donatello, whose David was "conceived not as a massive block, but as a place of intersection of geometrical plans which correspond to the axes of movements." Francastel insisted that Masaccio was not the equal of Brunelleschi ; that his work in the Brancacci chapel was closer to the ancient and mediaeval comic scene in theatre than it was to Florentine streets (cf. the conclusions of on p.** below); and that his colleague Masolino and his contemporary Angelico deserved more credit than they were generally given. The invention of Brunelleschi, claimed Francastel, "at first only appeared as a revolution in the domain of reconstruction..... The first artist who had the revelation of the miracle which passed to the hands of artists is Uccello." Francastel reviewed the paintings of Pietro d’Arezzo, Andrea del Castagno, Bicci di Lorenzo, Sassetta, Domenico di Bartolo and Starnina to claim that linear perspective was but one more method along with other alternatives such as cavalier perspective. Indeed he claimed:

This discovery, this system, to the extent that it only consists in the reduction of the point of view to monocular vision and in the choice of a unique vanishing point situated at the back of the picture, to the extent that the person who uses it does not suspect (knowing) whether the discovery of a new technique does not [pre-] suppose the existence of certain laws of that spirit, revealing a new ideal, is of an application more limited than many others which had appeared towards the end of the fourteenth century in an epoque which one very wrongfully regards as ensconced in academicism.... Ergo linear perspective was not at all the most widespread nor doubtless that which seemed most to take account of the current aspects of the universe."

    Francastel claimed that the first generation of perspective artists had died by 1450; that the second generation spanned from 1450-1480 and that the third included Ghirlandaio, Signorelli, Perugino, Verrocchio, Pollaiuolo and Carpaccio. Theoretically perspective implied an adoption of a true representation of things by uniting their size and scale. He noted, however, that this did not apply to Gozzoli’s Journey of the Magi (Florence, Palazzo Riccardi), or the Mystic Marriage of the Virgin and the Transfiguration by Raphael or a number of other major paintings. Leonardo, he claimed had two meanings of perspective whence, "one will readily conclude", wrote Francastel, "that even for contemporaries, the new system never had the appearance that one now lends it of being a plastic representation of the external world on a plastic screen in two dimensions". Thus perspective was not a constant law of the human spirit but rather "a moment in the history of ideas of space." Perspectival space was in conflict with one of the major subjects of research at the time: "extension. It is through an extraordinary distortion that one has come to say and believe that the linear projection of space on a plane surface departing from a system of geometrical coordinates brought to a single point led to the representation of open space." There was, insisted, Francastel something inherently contradictory in perspective. On the one hand it was theoretically about open space: practically it was about the construction of closed boxes. In the second part of his book he described the steps leading to the rejection of this approach (see below p.67* ).

    Francastel (1967), returned to these themes in his influential Figure and place. The visual order of the Fifteenth century, in which he greatly developed his notion of visual images as a kind of language. He claimed that perspective (255):

generates, among other processes, a differential organization of spaces, a certain implantation of the figures takes them form the interior space of the picture and places them at the intersection between the figurative space and the space of the spectator....The genius of Masaccio’s invention is not in having used form-colour to clothe a human figure in a space not identifiable with the figurative plane of the fresco, but rather in having used a technique that was already universally known to render manifest certain representative ideas of his time....

    He insisted that perspective did not entail the discovery of immutable laws of nature. Rather, it was (255): "the consequence of a transformation of the mental sets of a given milieu." At the same time Francastel suggested that there were three degrees of comprehension, signs, structures and orders and concluded that (345):

Linear perspective constituted only one of these imaginary frameworks, one of the justificatory structures of the new order of significations. It is not perspective that rendered concrete the true invention, the key to the renewal of painting and of the culture of the time. It certainly played a role but it only constitutes one of the means to which artists wishing to take part in the speculations of all the moderns had recourse.

    Siebenhüner (1954), in a published lecture, claimed that to understand the development of the theory of perspective in the Renaissance, mediaeval optics was meaningless and insisted instead that five other factors were crucial (129): the use of the visual pyramid as a means of perception; the parallel axiom of euclid’s Elements for the drawing of orthogonals; the corollary similarity proposition for the drawing of transversals, the introduction of the projection plane and the distance pont construction as construction regulator for the foreshortening factor. A subsequent discussion suggested that perspective was no guarantee for great art and therefore concluded that it had a relative value.

    Gallet, in an important thesis (1956), reported as an article (1959), examined the historical origins of linear perspective, noting the role of mediaeval optics, the role of the University of Padua, with which Alberti, Toscanelli, Nicholas of Cusa, Biagio Pelacani da Parma and Giovanni Fontana were connected and the nexus of Florentines which included Manetti, Toscanelli, Alberti and Brunelleschi. This led to an outline of major fifteenth and sixteenth century theorists. Part two focussed on artistic practice beginning with the Tuscan context, Piero della Francesca’s influence, the art of the great decorators and scenographers, (Pintoricchio, Raphael, Serlio, Palladio and Scamozzi) ending with a chapter on perspective North of the Alps. That which set this study apart from others was Gallet’s painstaking attempt to understand the intellectual circles, the social climate one would say today, that made possible the rise of perspective.

    Gioseffi (1957), in a significant article that also considered questions of perspective in Antiquity (mentioned above p. 39*), reviewed the use of space from Cimabue, through the Northern Italian painters, Avanzo and Giusto de Menabuoi in order to challenge the spatial schemata proposed by White (1957). Where White saw a radical break between the work of Giotto and Brunelleschi, Gioseffi saw a clear continuity. Gioseffi challenged White’s interpretation of Brunelleschi’s experiment, suggested that White’s claims concerning synthetic (i.e. spherical) perspective, could be accounted for more easily by the use of curved mirrors. In the latter part of his article, Gioseffi analysed Paolo Uccello’s use of perspective in the sinopia for and the finished Nativity (Florence, San Martino alla Scala); in predellas showing the Profanation of the host (Urbino, Galleria nazionale delle Marche); in the fresco of John Hawkwood (Florence, Santa Maria Novella) and in the Stories of Noah (Florence, Santa Maria Novella, Chiostre Verde).

    Gioseffi (1957), further developed these ideas in his book entitled Artificial perspective which, (as already seen above) covered the whole history of the subject from Antiquity, through the Middle Ages to the Renaissance. In Gioseffi’s interpretation there were two independent strands of development, one based on spatial intuition, the other on scientific interest, which were first integrated by Brunelleschi. Gioseffi acknowledged the importance of Sanpaolesi’s (1951) attempt to reconstruct the historical context of Brunelleschi’s work, which drew attention to the role of mediaeval optics (e.g. from Alhazen to Biagio Pelacani da Parma) and suggested that this tradition might have provided the impetus for his use of the perspectival window (velo). Gioseffi rejected this interpretation. He suggested instead that Brunelleschi painted directly onto the mirror and that his decision to do so might have been inspired by a study of Ptolemy’s work on mirrors.

    Panofsky had claimed that Alberti did not have knowledge of the distance point. This Gioseffi challenged. He claimed that the distance point was neither Nordic in origin, nor discovered by either Piero della Francesca or Giotto. It derived, claimed Gioseffi, from Brunelleschi’s stereometric method. Gioseffi re-examined the perspectival method found in Gauricus (1504) and went on to challenge the claims of Brockhaus (1886) that Gauricus’ methods were similar to those used by Mantegna in the Eremitani Chapel at Padua. An attack on White’s (1957) claims concerning curvilinear perspective followed. According to Gioseffi there was no similarity between a convex mirror and the curvilinearity of the retina. Moreover, he insisted, we do not see things as they are seen in a convex mirror. Even so Gioseffi was convinced that curved mirrors had been popular in the Renaissance. Gioseffi also re-examined Leonardo da Vinci’s distinctions between simple and natural perspective, concluding that Leonardo had been the (119) "first to have an exact notion of the spherical optical image and of the non-identity between perspectival and ocular image". Gioseffi touched briefly on the origins of Galli-Bibbiena’s angular perspective and concluded his book by voicing diffidence concerning the concept of social space as developed by Francastel. Gioseffi (1958) summarized these findings in an article and subsequently in two entries on "Optical concepts" and "Perspective" in the Italian version (1958) of the Encylopaedia of world art, an English version of which appeared later (1965).

    Wolff (1958), offered a five page history of perspective from the stone age through to the seventeenth century. Wolff criticized Poudra (1864) for having limited himself only to perspectival texts, claiming that it was important to include the evidence of paintings and drawings as well. Wolff’s history focussed on Giotto, Brunelleschi, Alberti, Viator and Dürer, mentioning the later contributions of Guidobaldo del Monte, Stevin and Desargues. Gioseffi (1961), in a polemical article, offered a summary history of perspective in terms of calculation and science. He challenged the ideas of Hauck and Panofsky, claiming that there was a confusion between perspectival representation and retinal image.Gioseffi was particularly critical of Francastel in his Painting and society (195**) and his Style of Florence (196*), who had claimed that the origins of Italian perspective mght be found in Ghent or along the Paris-Padua axis. Gioseffi argued that a clear distinction was needed between the empirical naturalism of the Flemish and the scientific realism of the Florentines. He insisted on the seminal role of Brunelleschi in this context; claimed, on the basis of Uccello's sinopia, that the distance point was also an Italian contribution and suggested that Piero della Francesca was not an innovator, but rather one who carried the Florentine approach to its logical conclusions. Leonardo he claimed had been the most important theorist of perspective. From the mid-sixteenth century onwards perspective had passed from into the hands of mathematicians, and the Renaissance links between art and science came to an end.

    Sanpaolesi (1962), in a basic book about Brunelleschi (see Appendix 3), published a tracing of the sinopia of the Trinity by Masaccio (pl. 8.2), which was important because it drew attention to the role of preparatory drawings in early perspectival works, and re-opened the question of the fresco’s perspectival reconstruction (pl. 8.3). Guerrisi (1962), a professor at the Academy of Fine Arts, (Rome), reacting to the work of Cassirer, Panofsky and Francastel argued that artistic space was independent from the geometrical and symbolic space of philosophers, that the power of Piero della Francesca’s heads lay not in their geometry, but rather in his power of representation.

    Danielowski (1962), offered a brief outline of the history of perspective which he characterized in five steps which were preceded by aspective representation in which no clear determination of boundaries or rules were evident (Early Egyptian art). A first step towards perspective introduced horizontal lines which bounded the picture above and below but left open the sides (Egyptian art). A second step introduced boundaries to the right and left (Pompeian art). In a third step this bounded space was more narrowly defined and tended towards an axial perspective (Late Roman art). In a fourth step this led to a vanishing point with respect to one plane, usually the floor as in Lorenzetti’s Annunciation (Siena, 1344). An interim step led to this principle being applied to each of the sides independently as in Jan van Eyck’s Arnolfini Portrait (London, National Gallery, 1434). In a fifth step this principle was applied to all four sides and co-ordinate to produce a single vanishing point as in Petrus Christus’ Madonna with Saints Jerome and Francis (Frankfurt, Städlisches, 1457).

    Flocon (1963) wrote an article giving a "Succinct history of perspective" in which he linked perspective with the problem of projection, noting that the psychological projections of "primitive" persons on the walls of caves such as Altamira marked a first step. The development of frontal perspective, scenography in Antiquity, mystical and Gothic perspective in the Middle Ages, which led to imitation of Nature in the Renaissance, the development of anamorphosis, perspectival machines and methods of spherical perspective. These themes were developed in book form with René Taton in the What do I know? (Que sais-je? 1050) series which offers one the most accessible histories of perspective to date. While focussing on Renaissance examples it included both predecessors, mathematical connections with projective geometry and modern developments in curvilinear perspective.

    Doesschate (1964), an ophthalmologist, produced one of the most succinct surveys of technical aspects of perspective, including marginal distortions, anamorphosis, visual size constancy; with significant comments on the history of perspective: Antiquity, early Christian and Medieaval, and Renaissance, with sections on Alberti, Uccello, and Piero della Francesca. While he introduced practically no new material, his masterful summary and synthesis makes this perhaps the best short introduction to serious debates in the field.

    Parronchi (1964) re-published a series of earlier articles, (which have been considered above, p. 51*) in his seminal book Studies on sweet perspective (Studi su la dolce prospettiva), which included a re-construction of Brunelleschi’s first perspectival demonstration (pl.10.1), and remains one of the basic works in the field.

    Chastel (1965) published two important books which, from our point of view, are most notable for the way in which they make light of the role of perspective. A first of these, The great atelier of Italy, focussed on the importance of the artistic workshops (botteghe) and concluded with a section on the power of style. An index referred to illusionism, sfumato and chiaroscuro, but not perspective, as aspects of style. Indeed perspective was mentioned only briefly as a technique which after the time of Masaccio, allowed one to: "organize space, distribute figures, and stabilize heirarchies between them. A slight lowering of the horizon exalted the figure. The progressive diminution of meeting points permitted the methodical insertion of useful details in the intervals of the anterior planes." A second book, which was later retitled The centres of the Renaissance, had the same subtitle as its companion volume: Italian art 1460-1500 and was an important contribution because it drew attention to other centres. The renaissance was not just about Florence: it was equally about Padua, Parma, Ferrara, Modena, Mantua, Pavia, Urbino and Milan. This work included a chapter on "Intarsia, geometry and perspective", in which he argued that before before it was taken up by painters, perspective was used by artisans who produced marquetry to create both pure geometric ornament and mathematical space through a use of illusionistic articulation of volumes and lines. Chastel cited examples from Parma, Padua, Genoa and Monteoliveto Maggiore. Chastel’s illustrations included but did not discuss other important examples of perspective such as Donatello’s Martyrdom of Saint Lawrence (Florence, San Lorenzo, pp. 96-97), Bramante’s illusionistic altar in Santa Maria presso San Satiro (135), the Last Supper in the versions of Ghirlandaio and Leonardo (224-225) and the Mystic Marriage of the Virgin by Perugino and Raphael (298-299). In Chastel’s approach perspective remained mainly an instrument of ornament. Paolucci (1966) gave a significant survey of the dissemination of perspective in a popular series (I maestri del colore 257).

    Klein (1970), in Form and the intelligible, included four essays on perspective (republished). A first of these offered a critical review of secondary literature in the years 1956-1963, notably Brion-Guerry, Gioseffi, Maltese, Parronchi, Pedretti, Sanpaolesi and White. A second, written with Henri Zerner, entitled Vitruvius and the theatre of the italian Renaissance, suggested that this period introduced two new languages for the theatre: perspective and archaeological reconstruction which humanists attempted to reconcile. Here he drew attention to Sangallo’s sketches in Verulanus’ edition of Vitruvius. aand outlined some of the key moments in the development of Renaissance stage scenery (cf. below p.*). A third explored the interplay of urbanism and utopianism from the time of Filarete to Valentin Andreae. A fourth on Humanists and science examined critically the claims of Zilsel about early modern science being caused by a combination of humanist and technical strands at the turn of the seventeenth century.

    Harnest (1971) in a work mainly concerned with reconstructions of Renaissance art (see below p. **), offered a synoptic view of key developments in map form (fig. 8). Franchini-Guelfi (1973) contributed a significant appendix on "Organizaton of the image in the drawing of a plane: perspective techniques". Da Costa Kaufmann (1975) presented a useful brief history of the perspective of shadows, exploring the contributions of Alberti, Leonardo and Dürer with brief mentions of later works, the Codex Huygens, De Caus, Marolois, Aguilon(ius), Accolti, Dubreuil, Bosse, Desargues, Hoogstraten and Grimaldi.

    A useful textbook with Danish translations by Johanssen and Marcussen (1978) on Space perception and space construction contained excerpts from basic texts from Antiquity to the Renaissance. These included passages from Plato’s Politics, Theaitetos, Parmenides, and the Nomoi; Aristotle’s De memoria et reminiscentia, Euclid’s Optics, Vitruvius, Ptolemy, Damianus, Proclus, Alhazen, Bacon and Witelo in the early period. Fifteenth century individuals included Ceninni, Manetti, Vasari, Alberti, Ghiberti, Filarete, Piero della Francesca, Francesco di Giorgio Martini and Leonardo da Vinci. Sixteenth century theorists included Gauricus, Pélerin, Dürer, Johann II von Pfalz Simmeren, Serlio, Commandino, Barbaro, Jamnitzer, Vignola and Lomazzo.

    Sinisgalli (1978) produced a significant Italian edition of Stevin’s which began with useful reconstructions of the chief construction methods in the fifteenth and sixteenth centuries, notably, Brunelleschi, Alberti, Piero della Francesca, Leonardo da Vinci, Gauricus, Pélerin, Durer, Serlio, Vignola (cf. pl. 45-46), Commandino, Guidobaldo del Monte and Kepler. Sinisgalli (1981) went on to do an analysis of Borromini’s perspectival alley in the Palazzo Spada, the technical brilliance of which, some would claim, exceeds the evidence of the problem. Since then he has become the leading Italian editor of major treatises on perspective, including Guidobaldo del Monte (1984), Ptolemy’s Planisphere (1992), Commandino’s Planisphere (1992) and his Perspective (1993). These works do an immense service of making accessible important sources in translation (into Italian).

    For the field of perspective studies undoubtedly the most important single event thus far was the first world congress: Renaissance perspective. Codification and transgressions (1977, published 1980). Originating as an idea of the late Eugenio Battisti, but painstakingly organized and edited by Marisa Dalai Emiliani (1980) this brought together for the first—and to date only—time most of the leading scholars in the field. Volume one of the conference proceedings had three sections: 1) a preliminary section raising questions concerning the boundaries of the field; 2) perspectival practice; 3) treatises and questions of theory and method. Section one began with a stimulating speculative essay by Gioseffi on the relation of perspective to semiology. Becchi and Riva reported on their work in spatial analysis of population and raised questions how new approaches to geography, demography and territorial analysis were affecting our traditional notions of perspectival space. Severi raised questions on the use of human figures in perspectival systems: namely, the problem of how perspective emphasizes spatial contexts which dwarf the size and visual significance of human figures.

    Section two began with a significant article by Chastel on the contradictions (apories) of perspective in which he probed into the discrepancies between some of the high ideals initially associated with perspective and the way in which later commentators such as Vasari tended to dismiss it as merely a playful accessory. In a opening section on theory and practice Chastel noted that Alberti’s On painting was not written for practitioners, implying that the development of perspectival practice continued largely independent of theoretical treatises. Chastel raised questions about the function of perspective. Its purpose seemed to be to produce an objective image.Yet did it not accomodate itself to accredited compositional schemes? Was it not transformed by the painted scene? He drew attention to a curious paradox. While perspectival theory spoke of a spectator looking through a window into the picture, perspectival practice demonstrated the opposite, namely structures in which painted inhabitants regard the viewer. Hence the so-called spectator was less a viewer than a person viewed. The important thing in perspective, claimed Chastel, was not the lines going towards the horizon, but rather the buildings that acted as receptacles and the faces that they framed.

    Albertian theory, he went on, had ignored the practical importance of categories or genres of painting. In sacred art, where the goal was an image of piety, space was reduced to nothing or nearly nothing. In narratives of miracles and historic episodes one found the same episodes in monumental cycles as in predellas. He claimed that both those who worked in marquetry and those painted scenes on marriage trunks (cassoni) treated scenes in the same way as social space. He questioned any necessary connection between the urban spaces of these marriage trunks and scenic illusion In the final part of his paper, Chastel urged that it was simplistic to make equations such that perspective = logic = end of transcendence and the reduction of art to purely secular themes. He pointed out that the introduction of perspective which should have reduced paintings to a simple horizon line, often brought, especially in Ferrara, complex painted altars with their own internal scenes. He concluded that perspective, while clearly linking art and science in new ways was at the same time intimately connected with the ornamental and the intuitive thus producing new effects of the marvellous.

    A second essay in the Congress proceedings turned to the question of origins: Lang suggested that Brunelleschi's panels were related to the tradition of Vitruvian theatre. Angeli and Zini returned to the debate whether perspective was an invention or a discovery. A number of contributions examined unknown or largely unfamiliar material. Bora explored the role of foreshortened human figures in ceiling painting (quadratura). This was important because he demonstrated, (in a sense for the first time although Panofsky had published the Codex Huygens in 1940), that there was a considerable corpus of theoretical writings and drawings on the specific problem of foreshortened human forms and that these could in some cases be related directly to the extant evidence of painting practice. Equally significant was a paper by Shearman which compared two illusionistic ceilings by Corregggio namely those in San Giovanni Evangelista and the Duomo in Parma and suggested their links with sacred dramas (sacre rappresentazione). Pochat focussed attention on a Northern Italian manuscript of architectural drawings with scenogaphic motifs (c. 1500-1520) now in the Louvre. Daly Davis drew attention to details of Carpaccio's work on regular solids and related them to figures in manuscripts and published treatises. Mullazani was able to relate the spatial construction of Mantegna's Room of the Married Couple (Camera degli sposi, Mantua) to a newly found literary source. Joost Gaugier discussed the role of Tuscan connections in Jacopo Bellini's Sketchbooks.

    With respect to post-Renaissance perspective, Marinelli examined Tintoretto's use of space, while Zanini explored Klee's deliberate transgressions of space in his avantgarde paintings. Battisti in a brilliant closing address drew on a whole range of sources ranging from Giovanni Fontana in the fifteenth to Oscar Schlemmer in the twentieth century.

    A series of papers included reconstructions: four focussed on this. Robbiani proposed a reading of the fictive choir in Santa Maria presso San Satiro; both Polzer and a group of young scholars (Arese, Bonomi, Cavalieri, Fronza) analysed the space of Leonardo's Last Supper; while Ciati offered reconstructions of a number of intarsia by the Lendinara brothers. Other papers used reconstructions to make further points. For instance, Sindona used reconstructions of Uccello's frescoes to argue for links between perspective and a crisis in humanism. Arasse included reconstructions in his analysis of Masolino's paintings, with a view to showing that some of his seeming errors in perspective were deliberate and had religious motivations. Similarly, Wakayama used reconstructions of Masolino's works to discuss problems in the visualization of narrative (istoria). In section three, a proposed methodology for reconstructions, alas a-historical, was offered by Degl'Innocenti and Bandini (pl. 41-42).

    Section three on the theoretical literature of perspective contained explorations concerning the theoretical origins of perspective. Reacting to Edgerton's claims that Ptolemy's geography was an important source for the (re-)discovery of perspective, Veltman suggested that Ptolemy's work in astronomy was more significant, notably through his writings on the planisphere; a theme which Sinisgalli explored also in his discussion of Commandino's (1558) edition thereof. Saccaro Battisti focussed attention on uses of the camera obscura in an Italian manuscript of Alhazen (Vatican, Vat. Lat. 4595). This was all the more important because Battisti suggested the role of mathematico-geometrical and logical-ontological structures in mediaeval philosophy as premises for the discovery of perspective. This larger philosophical context was also examined in a penetrating paper by Kaori Kitao which examined the role of perspective in relation to optics and the camera obscura in order to explain the origins of Kepler's distinction between images which can be physically projected and measured (pictura) and those which cannot (imago). Pedretti touched upon the symbolic organization of space in Leonardo's drawings of knots.

    In section two, the theme of anamorphosis was touched upon by Battisti, who demonstrated the results of Masters' computer program for reconstructing cylindrical, conic and spherical projection methods. In section three, Maltese took up the theme of curvilinear perspective in Leonardo da Vinci and related this to a surveying instrument by Baldassare Lanci-- a topic to which Maltese (1978) returned when he challenged Pedretti's (1963) claims about Lanci's instrument and his interpretations of Leonardo da Vinci's approach to spherical perspective. Naitza's discussion of anamorphosis, while adding no new material, nonetheless raised larger questions.

    Martinelli and Pino provided a survey of sources in Milanese libraries, a task which Olivato performed for libraries in the Veneto. An unpublished paper by Veltman, originally commissioned, but not published by Daedalus, re-assessing Panofsky's contribution a half centruy after the publication of Perspective as a Symbolic Form (1927), was the final paper in the book. Garriga (1978) published a survey of the conference in Spanish. The bibliography, originally planned as volume two of the congress has grown into the present four volume version.

    At the world congress Vagnetti (1977), offered a magisterial survey of sixteenth century sources that served as a prelude to his subsequent (1979) critical (ragionata) bibliography. This bibliography was was much more than a list of books. Vagnetti provided comments concerning most of the works and was, as his title indicated, a "contribution to the formation of a rational idea, in its development from Euclid to Gaspard Monge." In his introduction, Vagnetti emphasized the universality of problems of spatial representation and suggested (25) that perspective in its technical sense should be considered both a discovery and an invention. A first section of his work considered elements of the phenomenology of vision (35-44) with texts on the principles of physical, percceptual, physiological, psychological and geometrical optics (45-95). A second chapter dealt with anomalous perspectival theories: the methods of Egypt and Mesopotamia, oriental pseudo-prspectival methods in Persia, India and the far East (95-108). A third chapter (108-154) turned to the contributions of classical Antiquity, with a brief discussion of vase painting, Plato’s position, Euclid’s contribution, the accounts of Lucretius and Vitruvius, the evidence of Roman wall paintings, the contribution of Ptolemy and subsequent authors: Galen, Theon’s Commentaries on Euclid’s Optics, Heliodorus of Larissa (Damianus), Proclus and Boethius. Chapter four focussed on the mediaeval period (155-194), noting the importance of Alhazen, Leonard of Pisa (Fibonacci); the Franciscans, Robert Grosseteste and Roger Bacon and John Peckham; Witelo, Henry of Langenstein, Nicholas Oresme, Blasius of Parma, Cennino Cennini.

    Chapter five on the fifteenth century (195-280) marked the beginning of Part two on the modern age. Vagnetti began with a graphic reconstruction of Brunelleschi’s first (pl. 10.2) and second panels: assuming that he had used a ground-plan and elevation method and Alberti’s "abbreviated" method. Vagnetti linked Brunelleschi’s invention with his profession as an architect, and traced his influence on Donatello and Masaccio. Vagnetti drew attention to those who spread the principles of perspective: Ghiberti, Filarete, Francesco di Giorgio Martini; Piero della Francesca, the first codifier; Bramante, Leonardo da Vinci. Most earlier authors had focussed on one of these figures and attributed to them the glory of having invented perspective, such that there were camps in favour of Brunelleschi versus those in favour of Piero della Francesca. One of Vagnetti’s great contributions was to treat all these theoreticians as part of a cumulative tradition, thus making it clear that perspective was not some sudden event but rather a gradual development.

    This approach continued in his sixth chapter on the sixteenth century (281-348) where he turned to how perspective spread throughout Europe, noting the role of Pélerin, of German authors (Dürer Ryff, Lautensack, Stoer, Lencker, Jamnitzer), and French authors (including the Italian Serlio who worked in France, Cousin, Du Cerceau). Vagnetti drew attention to the importance of Commandino for the scientific maturation of perspective; the rise of manuals (Vredeman de Vries, Cataneo, Vasari Jr. and Cigoli); the role of particular theorists (Bassi, the author of the Codex Huyghens, Lomazzo) and the rise of perspective as a science (Benedetti, and Guidobaldo del Monte).

    Vagnetti’s next chapter on the seventeenth century (349-424) traced the contribution of the Low Countries (Aguilonius, Marolois and Hondius), the role of manuals (Sirigatti, De Caus and Ferdinado di Diano) and the emerging predominance of the French (Migon, Aleaume, Vaulezard, Desargues, Bosse); polemical debates (Desargues and Bosse versus Le Brun and Le Bicheur); optical-perspectival pastimes, i.e. anamorphosis (Niceron, Maignan, Dubreuil, Bettini, Kircher, Schott, Tacquet); the revival of scientific theories and empirical practices (Battaz, Contino, Gaultier de Maignannes, van Schooten, Guarini, Milliet Dechales, Ozanam, Le Clerc, Troili, Scheiner, Moxon and Hartnaccius), with a special section on Pozzo and the revival of experimentalism. Chapter eight focussed on eighteenth century developments (425-463), on the emerging scientific context (Lamy, Galli Bibiena, s’Gravesande, Amato, Taylor, his commentators, Hamilton, Kirby, Jacquier, Fournier, Highmore, Michel, Malton; special attention to Lambert; Karsten and Burja); the limits of illuminist experimentalism and the background to Monge. Part three included two brief sections without an introduction on the nineteenth (465-477) and twentieth (478-492) centuries.

    There are some clear limitations to Vagnetti’s monumental work. The sections on the nineteenth and twentieth centuries are by no means comprehensive, but then, as the title indicates, they were not intended to be so. There are many spelling mistakes. But all these are minor shortcomings compared to the great contribution that he made. Vagnetti was the first scholar to view the entire history of perspective as a single complex whole, integrating a series of disciplines beyond his own specialty of architecture, namely: art history, optics, psychology, mathematics and science. He created a framework for understanding perspective not as a simple event that happened one day when Brunelleschi did his demonstration, but rather as a series of methods that developed slowly in the course of several centuries. While future scholars may decide that a number of details in this plan need correction, the grand scheme he outlined assures for Vagnetti an enduring place in the history of perspective.

    Salvemini (1984) studied the etymological history of vernacular Italian usage of the term perspective (prospettiva) during the twelfth and thirteenth centuries, which was reprinted in her book (1990). She drew attention (10) to a legal use in the late twelfth century, (although this became the late thirteenth century (22) in the next chapter), where perspectiva meant "view of a prospect". The use of this concept was traced through the writings of Alhazen, Grosseteste, Bacon, Peckham and Witelo, before concluding that (15): "Perspective does not reproduce in this way, as it expresses aesthetically, merely a visual phenomenon. It establishes and determines the cognition of the view of a prospect".

    A second chapter explored the contributions of Levi ben Gerson, particularly with respect to his staff (baculus). Its transmission through a number of individuals was suggested, namely, Jacob ben David Yamtab, Simone di Covino, Emmanuel ben Iacob di Tarascon, Abraham Zacuto, Regiomontanus, Ser Filippo di Ugolino Peruzzi and Paolo dal Pozzo Toscanelli. Following a description of the instrument, it was claimed that (50): "Constructed in this way an instrument similar to that used by Levi ben Gerson could apply to the visual pyramid defined by it, the formula of proportionality inverse to the distance and establish the relation of scales between the two aligned surfaces". A chapter entitled "Natural artifice of artists" explored differences (97) between Alberti who was concerned with a visual attitude and Gauricus who described a visual ideal.

    A final chapter explored the background to Lorenzetti’s Annunciation in terms of architectural enclosures as painted space. Giotto's Sermon to Onorio III (Assisi) and Simone Martini's Death of Saint Martin (Assisi) were cited as early examples. Martini's connections with the court of Avignon were noted and attention was focussed on one of his followers there, Matteo Giovannetti, whose Stories of Saint John the Baptist (Palace of the Popes, Avignon) was claimed to play a key role in changing the function of this motif from a purely ornamental one such that "the fresco regains in its proper drawing the architectonic wall, reducing it visibly to an inarticulated support". Subsequent examples by Giusto de Menabuoi (1370) and Fra Angelico (1427) were given. An appendix reconstructed the steps used in Alberti's method (132-155).

    Thuillier (1984), summarizing the ideas of Panofsky, Gadol, Edgerton and Baxandall, was concerned with links between perspective and space, arguing that art was a preparation for science and citing Galileo: "The most artistic ‘imitation is that which represents three dimensionality in its opposite which is a plane surface". Thuillier emphasized the need to see perspective as "a new way of seeing the world, of sensing its organization, of imagining its structures." He argued that "research into a homogeneous and unified space corresponded to a general preoccupation of advanced societies at the time." He claimed that the development of practical mathematics helped one to understand "why and how the view taken of things transformed itself, geometricized itself in some way. To discover proportions, identify triangles, cones and cylinders was from now on a kind of cultural habit." He went on to suggest that " topography, cartography, and perspective appeared as branches of a general science of spatial representation." Thuillier concluded that "classic linear perspective, in spite of its interest, cannot be considered as a system endowed with an absolute value. It is convenient, it gives a certain satisfaction to the intellect but other systems are possible such as the so-called curved or curvilinear perspective the principles of which have been known a long time." Veltman (1986), in a basic book on Leonardo, showed that perspective evolvd gradually in the course of the Renaissance, and that Leonardo’s contribution lay in the introduction of a systematic experimental approach (cf. pl. 11-12).

    A major book by Kemp (1990), The science of art. Optical themes in western art from Brunelleschi to the present, provides the best generally accessible survey on the history of perspective in recent years, with three main sections on perspectival principles, machines and colour respectively. One of the very attractive features of the work is that Kemp provides reconstructions of a number of key frecoes and paintings by the two key practitioners of proto-perspective Giotto, and Lorenzetti, and many of the principal artists in the fifteenth century including Brunelleschi, Masaccio, Alberti, Ghiberti, Piero, Uccello, Gauricus, Mantegna and Leonardo. These reconstructions are so elegantly presented that only the most attentive of readers will be aware that there are considerable controversies as to how such lines are to be drawn. For instance, there is no mention of three contending theories (Panofsky, Grayson and ParronchI) concerning Alberti’s method in his treatise On painting.

    With respect to the sixteenth century Kemp begins with Dürer and Cousin before examining links between illusion and mathematics in Italian quadratura: e.g. Raphael, Forbito, the Rosa brothers, Laureti, Mascherino, Sabbatini, Vanosino, Bassi and to Carlo Urbino, the presumed author of the Codex Huygens, Vignola and Lomazzo as well those who established new links between mathematics and science, notably, Commandino, Benedetti, Guidobaldo, Galileo and Cigoli. Seventeenth and eighteenth century authors include examples from Belgium (Rubens, Aguilonius), Spain (Velazquez), Netherlands (Saenredam, Houckgeest, Hooch, Hoogstraten), France (Desargues, Bosse, Dubreuil, Poussin, De la Hire, Le Sueur); Italy (Colonna, Mitelli, Zanini, Pozzo, Galli da Bibbiena, Canaletto) and Britain (Ditton, Taylor, Hamilton, Kirby, Malton, Turner). Non-experts might assume that this list is both the result of the author’s personal research and exhaustive. Some may note that problems such as quadratura (Sjöström) and theorists who have been studied in detail by others such as Commandino (Sinisgalli), Cigoli (Camerota), Saenredam (Ruurs) are given more detailed treatment. Indeed experts in the field will recognize that Kemp has provided a remarkable survey of secondary literature of the past decades in particular and the past century in general.

    This applies also to the second section of Kemp’s book which is devoted to a series of specialized perspectival instruments and machines (De Keyser, Amman), as well as the perspective window, camera obscura and camera lucida. A further chapter examines devices connected with what he terms artificial magic, namely, peep show, zograscope, panorama, stereoscope, stroboscopic disc, zoetrope and photography. A chapter on seeing, knowing and creating considers the work of eighteenth century theorists such as Lambert, Monge, Valenciennes, Adhémar and Choisy and examines some of the precursors of curvilinear perspective: Parsey, Herdman, Hauck, Ruskin. Section three on colour falls outside the scope of the present study. Two appendices deal with the basis of the perspective construction and Brunelleschi’s demonstration panels. A revised version (1992), which corrected minor typographical errors, assures that Kemp will remain an important reference work.

    Elkins (1995) in the Poetics of Perspective claimed (xi) that perspective was "more a collection of rational methods than a 'rationalization of sight'". His interest lay in tracing how "the recession of perspective as a method was paralleled by the growth of perspective as a metaphor, a powerful concept for ordering our perception and accounting for our subjectivity". While tracing the history of perspective as a metaphor he added little in terms of new sources. Useful, however, was his use of this evolution as a means of relating traditional (positivistic) historical analyses (e.g. M. Kemp) and more recent fashions in scholarship (e.g. Damish, Bryson, Lacan), thus showing connections between what some have assumed were mutually exclusive approaches .

1. Workshop constructions Unwritten late medieval practice:

Principal point, diagonal, bifocal, monofocal constructions

2. Distance-point Pélerin, Vignola

3. The costruzione legittima Alberti

4. Reformed workshop methods Inaccurate mixtures of classes 2 and 3:

Filarete, Gauricus, Ringelbergius; also in Serlio and Leonardo

5. Visual-ray Method Plans and elevations, with lines drawn to a center of projection

Vignola, Piero, Cataneo, Sirigatti, Cousin, Barbaro,

Commandino, Benedetti, Guidobaldo del Monte

6. Circumscribed rectangle method Rectangle with triangular foreshortened version on top:

Alberti, Piero, Cousin, Barbaro, Benedetti, Serlio,

Guidobaldo del Monte

7. Direct method A plan below a ground line, without the use of a surrounding rectangle:

Vignola, Du Cerceau, Ringelbergius

8. Vanishing point method Based on the generalized law of the vanishing point:

Guidobaldo del Monte

9. Inverse method Reconstructing plans from perspectives:

Leonardo, Guidobaldo del Monte

10. Mechanical methods Alberti, Leonardo, Dürer, Laureti, Lanci, Jamnitzer, Cigoli.

Fig. 10. Ten classes of renaissance perspective according to Elkins (1995), p. 87.

    A first chapter outlined the scope of modern perspective including a metaphor for vision, pluralism, states of mind and epochs of art. Elkins began by tracing the early history of perspective in the Renaissance, noting that it was used in parts of paintings and not entire paintings or ways of making paintings. Elkins therefore preferred to speak of Renaissance perspectives and claimed that there were at least ten classes thereof (fig. 10 ). All of these, he claimed sought to establish a ground for perspective that was independent of mediaeval optics, was more generally valid and more logical. While Elkins is right in reminding us that the notion of a single method of Renaissance perspective is an invention of later historiography, his proposed classification is not quite as unproblematic as it may at first appear. Itis true that Renaissance authors were very much aware of alternative methods. Guidobaldo del Monte listed no less than 26. On the other hand, throughout the fifteenth and sixteenth century authors consciously spoke of two main methods. Veltman (1996) has therefore offered a rather different outline of these two methods, suggesting that as they evolvedtheir relative importance shifted (fig 11).

Method based on optics, surveying Method based on geometry

(vision) (mathematics)

window and thread proportion theory

(legitimate construction) (distance point construction)

Brunelleschi?

Alberti, On Painting, Bk.1 Alberti, On Painting, Bk.II, Elements of Painting

Filarete, On Architecture (method two) Filarete, On Architecture (method one)

Piero, On Perspective... (method two) Piero, On Perspective... (method one)

F. Di Giorgio Martini, Treatises (method two) F. Di Giorgio Martini, Treatises (method one)

Leonardo da Vinci, Manuscript A (method one) Leonardo da Vinci, Manuscript A (method two)

Dürer, Instruction Dürer, Instruction

Serlio, Architecture Bk. II (method one) Serlio, Architecture Bk. II (method two)

Danti, Vignola, Two Rules (method one ) Danti, Vignola, Two Rules (method two)

Figure 11. Summary of the two chief methods of perspective in the Renaissance.

    If one accepts this model then Elkin's classes can be greatly reduced. Since, in the absence of written documents, we cannot know precisely what the much vaunted "workshop-methods" were, it is even open to question whether his categories 1 and 4 should be termed methods (fig. 12). Whichever way we read the evidence Elkin's point that Renaissance perspective was monolithic neither in theory or practice is important.

1. Distance-point Vanishing point method

Direct method

Circumscribed rectangle method

2. The costruzione legittima Mechanical methods

. Inverse method

Visual-ray method

3. Workshop constructions Unwritten late medieval and renaissance practices

Fig. 12. Another way of looking at Elkin's classes.

    A chapter on the practice of perspective turned to demonstrations of skill, examples of play, notably eccentric vanishing points as in Uccello's Profanation of the Host (Sources, pl. )or Tintoretto's Removal of the Body of Saint Mark and what he terms anti perspective in Northern intarsia. A third part of the chapter examined arcane versions: Dürer's use of perspective in Melancolia, Holbein's anamorphic skull in the Ambassadors and tendencies toward indecorum in facade painting as in Holbein's Design for the Dance House (Haus zum Tanz, formerly Basel). While one of Elkins basic points was that perspective never clearly fit within any set of disciplines, his chapter on such attempts focussed mainly on curvilinear variants. A final chapter dealt with the fossilization of painting practice. An appendix on mathematics and perspective dealt briefly with Desargues' theorem, rabatments, cross-ratio, harmonic-ratio, projective and descriptive geometry.

Northern Art

    Nineteenth century studies of Northern art remained sporadic. Von Berlepsch (1875) drew attention to the sketchbook, which had belonged to H. E. v. Berlepsch, of a sixteenth century architect with drawings mainly of fountains, tomb monuments and other architectural features dated 1573. The first decades of the twentieth century saw the emergence of a literature specifically devoted to perspective in Northern art. A context for this work was provided in a major article by Schmarsow (1904) on painting in the upper Rhineland and neighbouring territories in the period 1430-1460. He focussed on the work of three individuals, Konrad Witz, Hans Multscher from Ulm, and Lucas Moser from Weil, noting links with the Van Eyck brothers in the Netherlands, Master Broederlam and the Limbourg brothers in Burgundy as well as links with Italian art. Among the examples he cited was an Annunciation by Justus de Allemagna in the convent of Santa Maria di Castello in Genoa which was clearly based on the Ghent Altarpiece: northern space in an Italian context.

    Kern (1904), in a fundamental and very controversial article argued that the Van Eyck brothers (q.v. in appendix 3, cf. pl. 36.1) must have known the principles of linear perspective although he claimed that Petrus Christus’ Staedel Madonna and Child with Saints Francis and Jerome (1457) was the first to use perspective for an entire scene. This was challenged by Doehlemann (1904-1905, pl. 36.2; 1906). Doehlemann (1911) re-examined the history of spatial methods in early Netherlandish art. The Van Eyck brothers, he claimed, had used purely empirical methods; Rogier van der Weyden, by contrast had been more old fashioned, with no real interest in spatial effects. The Master of Flémalle, while still empirical had come very close to achieving such real spatial effects. Use of perspective had begun with Dirk Bouts’ Last Supper (1464-1467). Petrus Christus and Ouwater had not had theoretical knowledge of perspective, nor in all probability either Memling or Geertgen van Haarlem. Gerhard David had been the first to draw correctly a foreshortened pavement. Exact constructions were also to be found in Lucas van Leyden and Jan Gossart, less so in Van Orley. It was however not until Vredeman de Vries (1560) that the principles of Italian perspective were fully understood in netherlandish art. Kern (1912) concluded that the discovery of one point perspective by either Jan van Eyck or Petrus Christus lay between 1436 and 1453. Doehlemann (1912) returned to the question of the brothers Van Eyck to which Kern again replied. Kern’s views were accepted by Panofsky in his classic Perspective as Symbolic Form (1927).

    Bombe (1911), examined in detail Justus van Ghent’s role in the studiolo and library of Duke Federigo da Montefeltre. This provided valuable material concerning interplay of north and south although it contained nothing on linear perspective in a technical sense. Jantzen (1912), in his book on Seventeenth century Dutch Painting, included a significant chapter on "The interior". Mesnil (1912) examined northern resistance to concepts of regular space found in perspective, claiming that this stemmed from the realm of sculpture, particularly in connection with sculpted altarpieces, the discontinuity of space of which derived from medieaval mystery plays, specifically those connnected with the holy sepulchre. This made all the more interesting Kern’s (1912) findings that Van Eyck’s paintings had a particular connection with the holy sepulchre. Mesnil (1932) returned to the debates of Doehlemann and Kern arguing that there they had more in common than at first appeared: that an essential characteristic of early netherlandish art was a convergence towards a vanishing area rather than to a single point and that this characteristic was already clearly evidenced in the Master of Flémalle’s Donor with Saint John the Baptist and Saint Barbara seated, two wings of an altar executed for Heinrich van der Werl (Madrid, Prado, 1438). He argued that Northern art had developed independently of Italy, that its interests in space prepared it for Italy’s solutions in terms of linear perspective, but that there was no evidence of direct Italian contact in the first half of the fifteenth century.

    Kern (1937), in a synthetic article, returned to his earlier themes but also added some new suggestions. Having noted that Ambrogio Lorenzetti’s Annunciation, (Pinacoteca, Siena, 1344), introduced the first known vanishing point for a pavement in a painting, Kern pointed out that this proto-perspectival method recurred in Dijon in the the work of the Burgundian Master, Broederlam, and since Jan Van Eyck was in the employ of the Burgundian court, Burgundian artists from the circle of Broederlam would have acquainted him with this method. Kern surmised that Avignon would have been an obvious intermediary in the transmission from Siena to Dijon. This suggestion becomes the more interesting when it is recalled that from 1340 to 1344, i.e. the same time that Lorenzetti was doing his painting, Simone Martini was at Avignon establishing an Italian-French connection (see below p.117*).

    Oertel (1940), in an important article on the origins of preparatory drawings in relation to monumental fresco painting in Italy, inadvertently drew attention to the importance of such drawings for the spread of Italian motifs to the North. In the Baroncelli chapel of Santa Croce, Taddeo Gaddi had depicted a Presentation of the Virgin with a particularly impressive proto-perspectival temple. This theme was taken up by the Master of the Rinuccini Chapel in Santa Croce. A preparatory drawing ascribed to the same Master now in the Louvre, may explain why a very similar treatment of the same subject should occur in the Très Riches Heures Du Duc De Berry (c.1420, f.5v). Pinder (1941) reconsidered the question of interior spaces. Pächt (1937 published 1952) examined German concepts of painting in the late Gothic and Renaissance, to explain why they did not focus on visual, perspectival aspects, why they maintained an abstract, ideographic conception and why there was a chasm between art and life in German art. Bouchery (1957-1958) returned to the question of development of the interiors in Dutch art, claiming that in this branch of Dutch art it was particularly difficult to trace a continuity from the fifteenth to the seventeenth centuries; that after Aertsen and Beuckelaar in the mid-sixteenth century there was an hiatus in this theme, which began anew in the period 1615-1640, which laid the foundation of a new approach to interiors.

    Danielowski (1960), analysed a series of Northern paintings in terms of their perspectival constructions including Jan Van Eyck’s Arnolfini Wedding (1434) and Madonna with the Chancellor Rolin (1435-1436); the Master of Flemalle’s Saint Barbara (1438); Konrad Witz’s Annunciation (c. 1440); claiming that the Madonna with Two Saints (1457) by Petrus Christus and Dirk Bouts’ Last Supper (1464-1467) were the first Northern paintings accurately constructed in terms of linear perspective.

    Phillipot (1959), outlined basic differences between Flemish and Italian art. This was the starting point for a significant article (1962) in which he examined a crisis in South netherlandish art around 1480. According to Phillipot, there was an intellectualization of aesthetic consciousness which led to a new awareness of the painting as a painting as seen in the work of Vranck Van der Stock. There was a new emphasis on dynamic continuity between interior and exterior space which led to a return to narrative features. There was also a new interest in copies. Phillipot cited the work of a Follower of Rogier van der Weyden; the Master of the Legend of Saint Barbara; the Master of the View of Sainte-Gudule; the Master of the Abbey of Afflighem; the Master of the Legend of Saint Lucy, the Master of the Sibyl of Tibur, the Master of the Virgo inter Virgines ending with Geertgen tot Sint Jans and Hieronymus Bosch.

    Levenson (1965), in a thesis on Petrus Christus and the Rational Use of Space, began with a history of scholarship listing the conclusions of Kern and Doehlemann and noting distinctions made by Bunim (1940) in order to suggest that Petrus Christus probably had "an awareness of a single vanishing point without an understanding of its mathematical basis". This led to a chapter on the spatial solutions of Christus’ predecessors Jan Van Eyck, the Master of Flemalle and Rogier van der Weyden, and a further chapter on three spatial solutions of Christus himself in terms of the exterior scene, the portrait and the interior-exterior scene. This led to a rejection from the corpus of Petrus Christus of five problem paintings, namely: the Madonna and Child with Saints Barbara and Elisabeth of Hungary, and a Carthusian (New York, Frick Collection); Saint Jerome in his Study (Detroit, Institute of Fine Arts); the Friedsam Annunciation (New York, Metropolitan); Portrait of a Man (Los Angeles, County Museum); Madonna and Child (Turin, Galleria Sabauda). Levenson also claimed that the late paintings could be dated as follows: Staedel Madonna (1457), the Donor Panels (1457-1460) and the Dormition of the Virgin (1460’s). Castelnuovo (1966) provided an important brief survey of interplay between Italian perspective and Flemish microcosm in a popular series (I maestri del colore 259), drawing attention to the role of René d’Anjou in early contacts and to a Master of Aix (Maestro di Aix) whose Annunciation (c.1440) marked the use of Northern space in southern France.

    An important dissertation on Trompe l’oeil in Dutch seventeenth century painting by Burda (1969) identified a typology of principle themes namely, walls of letters, wall cabinets, music instruments, reproductions of artworks, hunting weapons and representations of hunting bounty, raising basic questions concerning their function, their relation to other represented objects etc. Harnest (1971), offered a survey of early perspective (fig. 9), analysed a number of Northern paintings, particularly German ones in terms of their perspectival constructions. His enthusiasm for their posited precision sometimes imposed regularity not evident to other scholars. This approach was pursued in his Habilitation (197*).

    Collier (1975), returned to questions of perspective in the art of Petrus Christus and Dirk Bouts. He began with a survey of the work of Kern and Doehlemann. He noted that Schöne’s (1938), monograph on Bouts had "pointed out that Bouts learned to handle perspective with some competence and used two examples...to illustrate the point". Brand Philips (1967), had emphasized symbolic aspects of Van Eyck’s use of space. Upton (1972), had attributed Christus’ use of a unified perspective to an empirical development. Like Upton, Schabacker (1974), was interested in the aesthetic effects of perspective without explaining how it arose or what methods were used. Bazin (1952), had suggested that Christus might have travelled to Italy and learned the theory. Collier (1975,97) claimed that Christus:

seems to have been the first Northern artist to display both the correct use of the vanishing point for a single surface and for a unified perspective of several planes. Both of these discoveries probably occured in the decade of the 1450’s. It is perhaps of some conseuqence that this occured precisely during the years that the artist’s name vanished from the documents of Northern Europe, and that when it reappeared, the technique emerged in the work of Dirk Bouts. Bouts handled perspective in the same manner as Christus, but added the discovery of transversal spacing to art. His knowledge of perspective seems to have been passed on only to his son Albrecht and probably to Hugo van der Goes. Later in the century, even artists of the stature of Hans Memlinc and Gerard David showed ignorance of this knowledge, although David did display the first accurate oblique perspective even before the publications of Jean Pélerin. At this point, perspective became common knowledge, and Gossaert, van Orley and other painters displayed a mastery of its use.

    The final chapter of Collier’s thesis focussed specifically on the work of Christus and Bouts. Ragghianti (1977), in his book on Brunelleschi returned to these themes in a chapter entitled: Tuscany and Burgundy: Italian Perspectiv