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 Perspective and Flemish Perspective, again showing reconstructions based on Kern, adding little in terms of new material. Myers (1978), in a speculative dissertation surveyed the origins of perspective with Brunelleschi and Masaccio and claimed that Petrus Christus probably learned about focussing the parallels of several planes in perspective from Antonella da Messina in 1456 and did not know the rules of correct perspective until 1457. Egner (1979), surveyed changes in painted architectural space in the work of Van Eyck, Bouts, Memling and Van Orley.

Baroque (1600-1700)

    Nielsen (1899), examined the work of Poussin, the school of Versailles (Eustache Le Sueur, Charles Le Brun, and Pierre Mignard), the Royal Academy (Bosse and Dubreuil) and later painters (including Watteau and David). Nielsen (1901), explored famous practitioners of perspective in the Netherlands (Rubens, Rembrandt, de Hooch). Daniëls (1978-1979), noted that the seventeenth century brought a shift from a use of architectural interiors as backgrounds for biblical scenes to their being represented for their own sake, and claimed that an analogous shift occured with respect to trees. Govaerts’ Diana spied by Abraham was used as an example.

Neo-Classicism (1700-1800)

    In his Art of wash drawing, Le Sieur de Gautier (1708), noted in connection with scenographic drawings that:

Perspective being the foundation of these sorts of works one sees very few persons who apply themselves and who believe that they possess it perfectly because they are ignorant of perspective.... Cavalier perspective is so little to the taste of persons who are delicate in this regard that they do not even wish to deign to caste their eyes on it. I agree that it is a study that is fairly difficult to understand at first, and even if one possesses it in practice if one does not know how to reason about what one one is doing one falls into the most nasty accidents.

    Nielsen (1899), outlined contributions of the English school (Hogarth, Reynolds, Gainsborough, Brook Taylor).

Romanticism (1800-1900)

    Remarkably little detailed work has been done on the use of perspective in the nineteenth century. Nielsen (1901), included a chapter on Danish contributions (Nicolai Abildgaard, Gustav Frederik Hetsch and Cristoffer Vilhelm Eckersberg). Marcussen (1980), wrote a useful article on the evolution of perspective in France citing the work of Valenciennes (1800), Cloquet (1823), Thibault (1827), Adhémar (1836, 1870), Sutter (1859), and De La Gournerie (1859). Marcussen (1983), pursued this topic of nineteenth century perspective in the context of Eckersberg’s art and his treatise on perspective, using this and the work of contemporaries to raise questions concerning the meaning of neo-classiicism.

Modern Period (1900-1990)

    El Lissitzky (1925), in an article on "Art and pangeometry" challenged the view that linear perspective was objective because it corresponded to the space produced by a camera, claiming that Western art assumed a convex lens whereas Chinese art assumed a concave lens and produced inverted rather than linear perspective. According to El Lissitzky linear perspective bounded space, made it finite and closed it in. This rigid Euclidean space had, he claimed, been destroyed by Lobachewski, Gauss and Riemann. The Impressionists had first begun to explode the inherited perspectival space (105-107):

More important was the the experience of the cubists. They took the space enclosing horizon into the foreground and identified it with the painted surface. They developed what had been a solid surface with psychic characteristics (wallpaper covered walls etc.) and with elementary destructions of form. They built from the picture surface outwards into space. The final consequences of which are the reliefs of Picasso and counter-reliefs of Tatlin.

The Italian Futurists used another method. They took the apex of the visual pyramid out of the eye. They did not want to stand in front of an object but rather in it. They took the unique perspectival centre, spintered it into perspectival schards and spread it over the entire surface of the painting....

Suprematism placed the point of the finite visual pyramid of perspective at infinity. It broke through the blue lampshade of the heavens. For the colour of space it did not take the single blue ray of the spectrum, but rather the entire entity, namely white. Suprematist space allows itself to be extended forwards from the surface as well as backwards into depth. If we take the surface of the picture as 0 then we can name the direction of depth as - (negative) and the forward direction as + (positive), or conversely. We see that Suprematism sweeps away the illusions of planimetric, two dimensional space, the illusions of three dimensional perspectival space from their surface and has created the ultimate illusion of irrational space through endless extendibility, depth, and foreground.

    Among twentieth century artists, it is well known that the the Cubists and other groups were critical of and sometimes directly opposed to traditional linear perspective. Novotny (1939), in an important book on Cezanne and the end of scientific perspective claimed that perspective had died after Cezanne.

    The Swiss monthly magazine, Du, devoted a special issue (November 1949) to the problem of perspective. An opening essay by Meyer surveyed examples by Gaddi, Pinturrichio, Mantegna, Asam, Galli-Bibbiena, Hodler and Cézanne. Meyer claimed that there was a deeper reason for the demise of perspective (22):

a lack of trust in the transparency of reality. Interest in reality as such has not diminished. Knowledge of the appearances of the external world is greater than ever, but man no longer feels himself at the centre of this external world. Its perspectival arrangement in terms of a viewer standing firm at a given place has become questionable. That is both the standpoint and the arrangement....Doing without the perspectival order of objects in pictorial space signifies a dropping of the claim that one wants to master the surrounding world conceptually or even to maintain the dignity of the observer with respect to the surrounding world. The personal observer, as eyepoint and horizon of the field of vision, is surrendered in favour of an impersonal, anonymous objectivity. The painter no longer believes in a binding structure of the world whereby external objects and observer are simultaneously connected in the way that perspectival space encompassed both.

    Unlike the Middle Ages when there was at least a belief in God who held everything together, there was no longer any ordering principle. Hence the chaos of modern paintings which were often reduced to blobs of paint and lines. An article by Du Bois Reymond in the same magazine linked perspective with orientation. Another by Marvil was as its title suggested, a "Rhapsody" on perspective. Eichenberger’s "Notes without perspective" considered paintings by Kandinsky, Gris and Miro and Dali. An article by Pfister described a series of stereoscopic photographs.

    Brion Guerry (1950), pursued this problem of the death of linear perspective in her monograph on Cezanne, arguing that there was not one but rather there were a hundred perspectives insomuch that there were a hundred ways of resolving the questions of three dimensional space on a two dimensional surface. In her introduction she referred to the allegorical perspective of the Greeks, mystical perspective of the Chinese, symbolic perspective of the Middle Ages, rationalist perspective of the Renaissance, and a sentimental perspective of the Baroque. Hence each age had its expressions of space and perspective. (Brion-) Guerry identified clear steps in the development of Cezanne’s approach (9):

At first his visual field is a restrained space where the illusion of the third dimension is suggested by the curve. The point of view, which is not the point of conjunction of the vanishing lines is mobile. This is quite close...to the subjective spatial conception of the Greeks. Through a fairly artificial game of constructive combinations, Cezanne tries to stabilize an essentially moving composition, but he does not reach the point of homogenizing the spatial content, that is to say, the object and its container: the atmospheric envelope.

    This, claimed (Brion-) Guerry, was Cezanne’s goal in his early paintings when he was staying with Pisarro at Auvers in 1872. He then reached a first equilibrium whereby the restrained, unstable visual field of the Modern Olympia became the enlarged, more peaceful space of the House of the Hanged Person (Maison du Pendu). His spatial research using colours brought an impressionist period, then a constructivist period (1878-1892). This brought with it a formal simplification which stiffened and denaturalized the original model such that the image moved away from its concrete base and tended towards pure abstraction thus foreshadowing the activities of the Cubists who took these same principles a degree further. In his late period Cezanne returned to impressionism of a more pacified and stable type, finding a new equilibrium between the rigour of form and the fluctuations of light. (Brion-) Guerry concluded that in the late paintings of Cezanne (179):

the visual field is thus expanded by all that which is evoked without being said. The horizon does not close at the visible limit of a perspective construction such as would occur if, with this construction the figured representation expressed itself in its fullness. The spatial building to the extent that one prolongs it within the bounds of a pre-established constructive schema, does not contain the totality of expression of the image. This is only achieved through the extensions imposed by the imagination of the viewer who dare not refuse it at the risk of ruining at the same time the evocation of the object. Thus the spatial field is rendered limitless: more precisely, one would have to say that it has no limits other than the bounds of creative freedom.

    According to this interpretation Cezanne’s spatial experiments led him to recognize the importance of what Gombrich subsequently termed the beholder’s share in the viewing of pictures.In the second part of his Painting and society, Francastel (1951), described the "Destruction of a cubic space". He too suggested that Cezanne played an important role in this process: Gauguin took it a crucial step further:

A new system of visualization elaborates itself. The qualities of space now concretize themselves. this time in a compartmentaliztion that no longer based on the differential scales of the veduta- combining the two well tempered grids of linear perspective and the single corridor of light- but on a new spatial ambiguity of support -the canvas- opposed to the autonomous values of pure colour. through colour and through the theme, the decorative surface enlarges into three dimension, and still more in the imaginary dimensions.

    The view that Cezanne heralded a rejection of linear perspective became very widespread through authors such as Arnason, who wrote a standard History of modern art (1967 etc.) which began from this premiss (9):

Perspective, although known in antiquity, became for the Renaissance a means of creating paintings that were imitations of nature, visual illusions that made the spectator think he was looking at a man, a still life or a landscape rather than at a canvas covered with paint. Perhaps the greatest revolution of early modern art lay in the abandonment of this attitude and the perspective technique that made it possible. As a consequence, the painting - and the sculpture became a reality in itself, not an imitation of anything else.

    Arnason insisted that the visual evidence of the actual works was much more important than verbal evidence even if this came from the artists themselves. Accordingly he included 1549 illustrations in the revised edition (1983). If one looks at these closely one is struck by the number of illustrations which continue to use perspective (cf. Sources, pp. 194-201*) and one is led to ask oneself whether a cultural tradition which is basically iconoclastic might not be affecting the historiography of modern art. Indeed is it a coincidence that the protagonists of claims for a shift from perceptual to conceptual art (e.g. Gablik, Blatt) are also members of the same tradition? Veltman (1993, 1994) has offered further evidence of a revival of interest in perspective.

    An exhibition at the Centraal Museum (Utrecht, 1978) on What is reality? raised some questions concerning spatial illusions and perspective. Another exhibition at the same museum by Blotkamp (1980) on Space and perspective (Ruimte en perspectief), which grew out of a school project (1975), explored both modern and traditional examples in terms of overlapping, light and shade, colour differences, mixing of colours, perspectival diminution and viewpoints. Henderson (1983) in a stimulating thesis on the rise of the fourth dimension in twentieth century art offered evidence that the situation might be considerably more complex.

China, and the Far East

    Practical interest in Chinese perspective began in the second half of the eighteenth century in the context of landscape gardening and has been discussed elsewhere (Sources, II.3). Interest in the history of perspective in the Far East has emerged only in the twentieth century. Parmentier (1907) in a detailed study of the architectural bas-reliefs of Java drew attention to their spatial features. Concern with Chinese methods independent of the West has not yet received systematic study in the West. A major exhibition organized by Ledderose and Butz in connection with the Berliner Festspiele (1985) offers one of the few serious glimpses into the enormous riches to be studied in this context. It is striking that the Chinese had a version of parallel perspective by the sixteenth century (pl. 17.1), which was developed in the context of their chronicles (pl.18-20).What set these apart from Western versions is that their narrative was not compartmentalized into isolated episodes but integrated into a series of scrolls in a continuous fashion (pl. 19) for which modern film techniques would be the only Western "equivalent", a problem upon which Hockney (19**) has reflected in a film on the subject.

    The earliest use of Western perspective in China goes back to the Jesuits in the latter sixteenth century. Secondary literature on this topic began in the twentieth century. Laufer (1910), who was one of the first to explore this, made some mention of perspective. Pelliot (1921) pursued this theme in the context of engravings at the time of the Jesuit Father Ricci. Ferguson (1934) focussed specifically on painters among Catholic missionaries in Peking. Schüller (1936) cited other examples inspired by Father Ricci, a theme taken up by Hart Burling (1941). An important article by Loehr (1963) focussed on the role played by a seventeenth century Florentine Jesuit, Ferdinando Bonaventura Moggi, and demonstrated that western models affected architecture and landscape gardening as well as painting. The Jesuit theme was taken up anew by Palewski (1976). Liu Ruli (1979) wrote an article about the first Chinese editions of Pozzo (1729,1735), which were mentioned again in a discussion of Christian influences on Chinese art by Kao (1987).

    March (1927) was one of the first who specifically included perspective in the title of an article on Chinese art. His extreme view that art had nothing to do with science was challenged almost immediately by Jacot (1927). Auboyer (1935) explored Chinese influence on oriental landscapes and sculpture, drawing attention to links between China and Java and noting some spatial features. Wells (1935) made an extensive study of proto-perspectival forms in art of the Han dynasty of the second century A.D. This theme was taken up anew by Fairbank (1942) in terms of Han mural art and pursued by Bulling (1962) in terms of a landscape of the western Han period.

    In his monumental Science and Civilization in Ancient China, Needham (1971) drew attention to technical and scientific uses of perspective in the context of civil engineering and building. This theme was taken further in an important article by Edgerton (1980) which related divergent approaches to art in terms of different concepts of science in the west and east, a topic to which he returned in his book on Giotto (1990). This problem was touched upon also in the Berlin catalogue (1985) cited earlier, where it was demonstrated how some Christian motifs were mistranslated (pl. 21.1-21.2), in other cases traditional Chinese motifs were presented in Western fashion (pl. 21.3) while sometimes Western motifs were appropriated in an Eastern context, both as buildings and images (pl. 22).

Japan

    During the Muromachi period in the sixteenth century Japan developed a version of parallel perspective which was applied to detailed townscapes and landscapes (fig. 23-24). Aside from one standard study (19**) and a significant catalogue (1989), both in Japanese, the importance of this tradition has not yet been seriously studied by western scholars. Fundamental to the Japanese approach has been a particular attention to recording significant places, which had its roots in Chinese traditions. In the West, significant places on pilgrimages routes were marked with churches. Witness the growth of Romanesque architecture along the Vézalay- San Juan Compostella route linking France and Spain. In Japan, significant places were recorded in diaries and later became the subjects of woodcuts, of which Hiroshige’s series on the high road and coastal low road linking Tokyo and Kyoto are perhaps the most famous. As Hoff (198*) has suggested the particular Japanese notion of (significant, often sacred) place helps to explain why they do not make the same oppositions between interior-exterior as are found in the West; why there is not the same subject-object tension and why there is not the same opposition between man-made and natural world in Japan. Hence while they have adopted Western techniques, they have applied them in very different ways.

    According to Asano (1985), Western rules of painting were introduced by Christian missionaries in the sixteenth century but had effectively no immediate impact on Japanese artists because Christianity was outlawed. Chinese and Western pictorial art were re-introduced to Japan through Nagasaki after the eighth shogun, Yoshimune, lifted the import ban on books other than Chinese literature in 1720. It is generally accepted that Chinese woodblock prints which incorporated western perspective led to the development of uki-e in Japan.The word uki-e, which means "floating picture", is etymologically connected with ukiyo-e, the so-called floating world, said to describe the court that travelled between residences in Edo (Tokyo) and Kyoto and which was defined as follows by Ryoi (1661):

Living only for the moment, turning our full attention to the pleasures of the moon, the snow, the cherry blossoms and the maple leaves; singing songs, drinking wine diverting ourselves in just floating, floating; caring not a whit for the pauperism staring us in the face, refusing to be disenheartened, like a guard floating with the river current: this is what we call the floating world.

    Others have explained that the term derived from the fact that "the scene being represented in them seems to float outward, giving the work a three-dimensional quality" or "in acknowledgement of their illusory effect". Could it also be related to their typically being viewed through a zograscope (fig. 84.2)?

    Masonobu Okumura (1686-1764), signed his work as "uki-e originator" and it said that the earliest known example of Western style perspective during this second period is his All star cast of a Kyogen stage (1740, pl. 25.1). He also represented the outside of a theatre (pl. 26.1) and The evening cool by Ryogoku bridge (late 1740’s). From a technical point of view the perspective in these works is not completely accurate. More interesting is the different approach to space which these works convey. The interior of the theatre does not show the audience separated from the stage, but rather a theatrical space in and through which players and audience interact directly. Similarly sharp distinctions between interior and exterior are handled differently than in the west. Interiors are often shown which interact with exteriors (e.g. pl. 26.2). Inner and outer, subject and object are not opposed: they complement one-another.

    Masonobu’s print showing the interior of Nakamura-za in Kampo during the Kaomise performance (1740) was the basis of his student Torii Kiyotada’s print of a kabuki theatre performance of Mitsugi Taiheki at Nakamura-za in December 1743. The same artist did a Party at Yoshiwara (early 1760’s). Lee (1977) claimed that perspective was introduced to Japan via the Chinese translation of Pozzo (1737) and that it was Kiyotada who produced the first Japanese illustrations.in perspective.

    In the following generation, from the late Gembun to the Horeki period (1752-1764), uki-e became popular through other artists such as Moromasa Furuyama, Shigenaga Nishimura, Kiyotada Torii, Kiyohisa Torii, Jogetsudo and Kogetsudo. Kokan or Suzuki Harushige (1748-1818) produced a striking perspectival print of a Courtesan on a Veranda (c. 1771).

    Toyoharu Okumura (1735-1814) brought a further qualitative change in this technique (e.g. pl. 26.2). He is said to have copied a work of Visentini based on Canaletto (pl. 28). Nor was he alone in this (pl. 27). Hence the greater accuracy in perspectival construction partially reflects greater access to western exemplars. Toyoharu specialized in both "historical or group genre scenes and landscapes in perspective, often combining the two types", often developing earlier themes. For example, Masonobu had drawn The evening cool at Ryogoku bridge. Toyoharu produced Fireworks at Ryogoku Bridge (late 1770’s). Kiyotadu had done a Party at Yoshiwara. Toyoharu did a Party at Shinagawa (late 1770’s). His predecessors had depicted the interiors of theatres. Toyoharu did a Theatre district at night (early 1780’s). Certain scenes were privileged, such as Mimeguri (pl. 29.1-3), which shows a river with dikes strongly reminscent of those along the Rhine and in an atmosphere strongly reminiscent of Netherlandish paintings of the time. Through Toyoharu, uki-e now:

became an integrated form of Japanese art. By the age of the great landscapes of Hokusai and Hiroshige in the following century the perspective style had become so thoroughly assimilated that western students first seeing Japanese prints almost invariably chose these two masters as representatives of the pinnacle of Japanese art, little realizing that part of what they admire is the hidden kniship they feel with their own western tradition. (Ironically enough it was this work of Hokusai and Hiroshige that helped revitalize western painting toward the end of the mnineteenth century, through the admiration of the Impressionists and Post-Impressionists.

    Technically speaking, Hiroshige often deliberately gets the perspective wrong. For instance, in his view of Suruga-cho the "horizon line implied by the buildings on either side of the street is far below that implied by the mountain looming over them".

    Some perspective pictures, known as Megane-e, literally "eye glass pictures", were used with both peep-shows (nozoki karakari, e.g. pl.83) and zograscopes (pl. 84). These pictures often included landscapes with distant vistas (pl.30).

    Most of the secondary literature has been in terms of influences of western perspective on Japanese art. One of the standard works in Japanese (with a partial translation in English) is a catalogue from the National Museum of Modern art in Tokyo (1985). In English one of the earliest studies was Toyama’s (1936) The Western-style colour prints in Japan. French (1974) published a monograph on Shiba Kokan-- Artist, Innovator and Pioneer in the Westernization of Japan and three years later French (1977) produced an exhibition catalogue Through closed doors: western influence on Japanese art 1639-1853. Narazaki (1980) studied Western influence and the revival of tradition in Ukiyoe-e, a subject that was pursued by Sakamoto (1980) with respect to the Tokugawa period. A more general survey was provided by Sullivan (1989) in The meeting of Eastern and Western art. Screech (1991) in a penetrating dissertation on The western scientific gaze and popular culture in late Edo Japan made one of the most detailed English language studies of differences between Western and Eastern methods of representation. The standard Japanese book on the subject remains by Yokoyama (1977) entitled: Eye of Perspective. Space of Renaissance Italy and Japan.

    One of the few scholars concerned with the reciprocal influence of Japanese perspective on Western art has been Inaga (1978) who devoted a thesis in Japanese to this topic. Inaga (198*), summarized these findings in a significant article, in which he demonstrated how spatial themes in Hokusai are reflected in Cezanne (pl. 31.1-2 and 32.1-2). Bicknell (1994) drew attention to other parallels such as the bridges of Hiroshige and those of Whistler (pl. 31.3 and 32.3).

    There has also been some work on cross-cultural spatial methods. A Russian article by Ikonnikov (1973) explored the spatial language of Japanese art. Etymologically the Japanese term for perspective is linked with the term for peep-hole, which was possibly as a result of having seen a Western style show-box. This might explain why some of the earliest Japanese prints using Western perspective are of theatre scenery. These problems are the subject of an article by Kishi (1990) A view through a peep-hole: a semiotic consideration of Uki-e.

    In the past decades there have been a series of reprints of classic works of perspective in Japan. Hosono (1978) pubished Nagasaki prints and early copperplates. An exhibition catalogue reproduced images of Okyo and the Maruyama-Shijo school of Japanese painting (1980). Smith (1986) edited Hiroshige's One Hundred famous Views of Edo and two years later the same Smith (1988) edited Kuwagata Keisai's Panoramic Vision of Japan.

    A short chapter in Ganz (1994) on the social history of lanterns and show boxes (74-85) mentioned connections with the Far East, particularly Japan. One of the Japanese images (84) from a manuscript of the late eighteenth century, was based, as was kindly noted by my friend Corboz (personal communication), on Zocchi’s (1744) View on the river Arno of a part of Florence taken outside the gate at the cross (fig. 27). This is important because it confirms that Renaissance Italian perspective played a role in the development of the subject in Japan. Ganz’s extraordinary collection includes a Japanese manuscript of the 1760’s showing drawings of Dutch clothes and objects , e.g. a Leiden jar. Hence, Japanese fascination with Western technology began in the mid-eighteenth century, a century earlier than is generally assumed.

Russia

    Russian historiography on perspective has emerged in the twentieth century. The mathematician Rynin, in his Descriptive Geometry. Methods of Representation (1916) considered the importance of both Ptolemy’s Geography and Planisphere for the history of perspective and listed a vast literature on links between the history of perspective and the evolution of descriptive geometry. Rynin’s work was one of the sources for a seminal article by Florenskij on Inverted Perspective, written in October 1919; read on 29 October 1920 at the Byzantine section of the Moscow Art-Historical and Museological Research Institute and published in 1922. A footnote to that article gave insight into Florenskij’s motivations. He recalled the vivacity of the discussions after his lecture which he claimed (73):

confirmed for me once more that the problem of space is one of the most fundamental in art, nay I would say in a concept of the world in general. But this problem: space in the figurative arts is not examined in the present article and constitutes the object of my readings on the analysis of perspective held in the years 1921-1923 which are being prepared for publication.

    Florenskij noted that he was interested mainly in outlining an historical approach for the comprehension of an organic world view. He also cited Ernst Mach’s experience concerning the limitations of linear perspective and concluded (117): "Hence perspective in representation is not absolutely a property of objects as vulgar naturalism maintains, but simply a means of symbolic expression, one among the possible symbolic styles". This was written five years before Panofsky gave his lectures on Perspective as a Symbolic Form (1924-1925, published 1927). Florenskij’s article offered a synoptic view of the history of spatial techniques from the Pompeian wall paintings in Antiquity to Giotto’s frescoes in the Mediaeval period to the works of Castagno, Leonardo and Raphael during the Renaissance. These he contrasted with methods of inverted perspective in Russian art to raise the question why artists should deliberately make paintings with deformed or even false perspective.

    At the instigation of the graphic artist Favorskij, Florenskij was given a chair for the analysis of space in works of art at the Moscow Higher Artistic-Technical Workshops from 1921 to 1924 where he developed his ideas on both Russian inverted and Renaissance linear perspective. A group emerged which included the mathematician N. N. Lusin and the artists M. F. Larionow, W. N. Tschekrygin and L. W. Shegin. Florenskij had raised the question whether the seeming näiveté of Russian could be taken at face value, noting that the rules of regular perspective were broken so often that it could hardly be coincidence. His colleague, Shegin made a lifelong study of these problems resulting in an article (1964) and a book (1970). Shegin argued that Russian icons were very systematic in their use of space; that they involved complex combinations of mirror images, cylindrical and spherical projections (pl. 15.3 -16).

    Shegin did not discuss comparisons of painting and language although his book was entitled Language of a Pictorial Work (1970). These analogies were developed in an introductory essay by B. A. Uspensky who, having mentioned that some persons had assumed an ignorance of perspective among old Russian masters, observed that (7):

an opposite approach is possible which could readily be compared with the method of decipherment. In this second approach the challenge arises of reconstructing the specific system of representation in old painting, i.e., to decipher the particular language, which the old master commanded and which was obviously understandable to an observer at the time. And from this system which needs to be deciphered one then must explain in detail all the deformations and shifts in form which have just been mentioned.

    Uspensky added that (12):

If one pursues the analogy with language then it is appropriate to compare the limitations of a given perspectival system with the conventional character of a given language which is used for the communication of a given content. Indeed it gives grounds for the claim that the system of linear perspective cannot a priori be seen as more natural than other systems.

    The title of Uspensky’s essay, "On the Study of the Language of Old Painting", becomes all the more interesting when compared with the titles of a) Kepes’ Language of vision (1944), b) Goodman’s Languages of Art (1969), which has as a starting point the analogy of "learning to read pictures in reversed perspective" (see below p. 88* ), c) Mitchell’s Language of images (1974) and it is realized d) that Uspensky, along with Florenskij and Bakhtin, played an important role in developing analogies between point of view in literature and art (see below pp. 112-113*).

    Nekrasov (1936) offered a brief survey of foreshortening in old Russian art from the fifth through the fifteenth century. Although he did not enter into the details of Shegin’s anaylsis, Rauschenbakh (1975) discussed the problem of inverted perspective at great length in the context of linear perspective and other drawing methods.

3. Histories of Mathematics, Astronomy and Science

    In the sixteenth century encyclopedias such as those of Gregor Reisch (1509 etc.) and Fortius Ringelbergius (1531) surveyed mathematical practice but without historical consciousness. During the seventeenth century these encyclopaedic works gradually included historical references: e.g. Bettini (1642), Kircher (1646). Even so it was not until the second half of the eighteenth century that there was a sudden rise in formal historical treatments of mathematics. This began in Paris with a Universal dictionary of mathematics and physics (1753) for which Saverien wrote an entry on perspective and the Encyclopaedia of Diderot and D’Alembert (1765) for which the entry on perspective was written by Jaucourt.

    Montucla’s (1758) History of mathematics from its origins to our days and Saverien’s (1766; 1776-1778) History of progress of the human spirit were among the first books specifically devoted to the history of mathematics. Modesty was not Savérien’s specialty as we learn from the opening sentence of his preface: "I do not believe that one could find in one book more truths than are found in this history". His treatment of the history of perspective was limited to four pages (253-256). With respect to Antiquity Vitruvius’ discussion of Democritus, Anaxagoras and Aristarchus was cited. The invention of renaissance perspective was attributed to Pietro del Borgo (Piero della Francesca) whose treatise, he claimed, was now lost but had been studied in the sixteenth century by Dürer, who "constructed a machine with which he found the trace of rays of light", and Peruzzi who worked at rendering Piero’s ideas clear and precise. Savérien claimed that Peruzzi also found:

the points of distance on which a line falls which makes an angle of 45 degrees with the painting such that their length on the horizontal line drawn on the panel is equal to the distance of the eye from the panel. Thereby he discovered that all horizontal lines making an angle of 45 degrees with the panel have as images lines that pass through the points of distance.

    Savérien next considered Guido Ubaldi (Guidobaldo del Monte) who discovered "that all lines parallel to themselves and to the horizon even if they be inclined with respect to the axis of the panel, converge or tend to unite towards a point of the horizontal line and it is by this point that the line drawn from the eye parallel to the others passes". Savérien ended with a brief discussion of anamorphosis, citing the contributions of Stevin, Schott, Dubreuil and Leupold.

    Copies of both Montucla and Savérien were owned by Lambert and it is noteworthy that he cited them explicitly as containing the first real attempts at a history of perspective, when he published his own historical introduction in the second part of his Free perspective (1774). In England, Priestley only referred in passing to historical aspects in his Theory and practice of perspective (1770) but pursued them in his History and present state of discoveries relating to vision, light and colours (1772). In Germany, Kästner’s (1797), History of mathematics offered a brief survey of perspective (1-8) and reviewed basic literature (9-34). Meanwhile the bibliographical work of Scheibel (1778) with 207 titles and Murhard (1797-1805) with 246 titles set a standard that was not surpassed until Vagnetti (1979).

    In the first half of the nineteenth century, Piper wrote an article on perspective in the General encyclopaedia of sciences and art (Leipzig, 1834), but it was again in Paris that the key publications occured. Chasles (1837) published a Historical survey on the origin and development of methods in geometry, with various comments on perspective such as Barbaro’s (1569) use of stellated polyhedra and a note (XVIII) "On the identity of homological figures with those which one finds in perspective practice. Remark on the perspective of Stevin." Chales focussed attention on the importance of Desargues and Pascal and related their work on conic sections to their study of perspective. Chales noted that this mathematical work was taken up in the treatises of the artist, Abraham Bosse, and the engraver, Grégoire Huret, in the seventeenth century, later to be taken up anew by mathematicians (Servois, Brianchon, Poncelet, Sturm and Gergonne) in the context of homology. He also touched on the work of Guidobaldo del Monte, Mydorge and De la Hire in this context. Libri (1838-1841, 39-42) in his History of mathematical sciences in Italy mentioned the work of Danti (1583) and listed other authors: Alberti, Leonardo, Serlio, Barbaro, Vignola, Sirigatti and Guidobaldo del Monte. In an appendix (315-320) he published for the first time the opening section from Piero della Francesca’s On perspective of painting.

    In the second half of the nineteenth century, Paris remained important chiefly through the monumental two volume History of ancient and modern perspective containing an exposition of all the known methods of perspective and an analysis of the works on this science by Poudra (finished 1854 published 1864, cf. review 1854). His study dealt with 132 texts. A first section focussed on the optical tradition, notably Euclid, Heliodorus of Larissa, Ptolemy, Witelo, Roger Bacon, Ramus and Risner, Reisch and Finé, Peckham, Aguilonius, Dechales and Lacaille. The second section began with remarks on drawing and painting among the ancients, and considered Vitruvius before turning to Piero della Francesca, Bramante, Baldassare [Peruzzi] of Siena, Leonardo da Vinci, Gauricus, Alberti, Pacioli, Pélerin, Dürer, Reisch etc. Most of the texts after 1600 were by French authors.

    In retrospect there were clear limitations to Poudra’s work. His descriptions of contents were frequently cursory. Sometimes he was misleading. For instance he discussed the work of a J. Pisanus edited by Pachasius Hamellius (1556) and of a Joannis archiepiscopi Cantauriensis (1592) without recognizing that these were merely two editions of the same work Common optics (Perspectivae communis) by John Peckham. On the other hand, it is important to note his genuine contributions. It had generally been assumed that Desargues was the first to recognize that a system of parallel lines in perspective becomes a bundle converging to a point. Poudra noted that this was first demonstrated by Guidobaldo del Monte (1600) and focussed attention on his list of 23 different methods of perspective. Poudra was, moreover, the first to emphasize the interdependence of optics and perspective historically and until Vagnetti (1979) remained the only attempt at a comprehensive survey of the field. Poudra (1861) also published a brief article on the fundamental theorem of Desargues. Marie (1884) referred briefly to perspective in his History of mathematical and physical sciences.

    In Britain, De Morgan (1861-1863) wrote a series of nine witty anecdotal notes on the history of the perspective claiming that he had found nothing on the subject that deserved the name and beginning with Aeschylus as cited by Vitruvius, Hipparchus’ stereographic projection and Ptolemy’s planisphere projection. Notes two and three surveyed Renaissance authors. Note four focussed on Guidobaldo del Monte; note five on Desargues; six on Brook Taylor. Note seven reviewed Montaiglon’s edition of Pélerin; note eight added comments; note nine reflected on problems of distance and vanishing points. Cunningham (1868) produced Notes on the history, method and technological importance of descriptive geometry (cf. Sources,p. 134), which touched on the history of perspective. In Italy, Uglieni (i.e. Cremona, 1865, 1915) wrote on the principles of perspective according to Brook Taylor. Cremona (1865, 1921) also made a lengthy review of Poudra’s (1864) History. Significant bibliographical lists were provided in Riccardi’s (1870-1880) Italian mathematical library (cf. fig.3).

    It was primarily in Germany, however, that a more critical approach to the history of mathematics emerged in the last three decades of the nineteenth century and first decades of the twentieth. Gerhardt (1877,25), in his History of the sciences in Germany, credited Dürer as being the first to introduce the principles of descriptive geometry. Dürer’s significance continued to receive special emphasis by mathematicians which helps explain the great rise of literature generally as well as a series of dissertations on Dürer (q.v. in Appendix 4). In his History of mathematics, Zeuthen (1877) included a section on "Geometry, Application of central projection", noting the importance of Apollonius for Viète, Fermat, Pascal and ultimately De la Hire. The significance of Dürer, Werner, Kepler and Guidobaldo del Monte was acknowledged. Particular attention was focussed on the interdependence of Apollonius’ ideas and the contribution of Desargues. Zeuthen (1886) went on to write a history of conic sections. Wiener’s (1884-1887) Textbook of descriptive geometry included a section on the history of descriptive geometry. As would be expected he mentioned the mathematical contributions of Hipparchus and Ptolemy, Guidobaldo del Monte and Desargues. Striking, however, was his acknowledgment of artists including Masaccio, Donatello and Ghiberti, as well as numerous authors of treatises written primarily for artists: e.g. Alberti, Piero della Francesca, Pélerin, Rodler, Lautensack, Cousin, indeed providing an important survey. The role of Dürer was emphasized. Desargues was given due credit. This survey extended through the eighteenth century with s’Gravesande (1707), Taylor (1715), Lacaille (1750), Lambert (1759, 1774), Zanotti (1766) and into the nineteenth century. There were further sections on the evolution of ground-plan and elevation methods in relation to the development of descriptive geometry in France; relations between descriptive geometry and perspective in Germany; nineteenth century developments in oblique and axonometric perspective by Meyer and Meyer (1852), Pohlke (1860), Staudigl (1875) and even Hauck (1875) and Tessari (1882); relief perspective, photogrammetry, light and shade.

    As part of Cantor’s (1894, 1908, 1913) Lectures on the history of mathematics, the Italian scholar, Loria, wrote a section on "Perspective and descriptive geometry" in four sections: from the middle ages to the seventeenth century (577-594); the so-called golden age of perspective theory (594-617); the precursors of Monge (618-622) and the role of Monge as the founder of descriptive geometry (623-637). Obenrauch (1897), in his History of descriptive and projective geometry (1897) also began with a short history of perspective that included Vitruvius, Peckham, Dürer, Leonardo da Vinci, Desargues, Lambert and Frézier. The main body of Obenrauch’s book focussed on developments in France (Monge) and in Austria. Obenrauch (1903), devoted an article to "The first space curve of the Pythagorean school and its orthogonal and imaginary projection". Papperitz (1901) published On the scientific significance of descriptive geometry and its development until its systematic establishment by Monge, where he gave a summary treatment of the history of descriptive geometry, themes which he developed (1907-1910) in the section on descriptive geometry in the Encyclopaedia of the mathematical sciences. Here the contributions of Renaissance perspective were reduced to a single page (16), while other pages were devoted to Dürer (17), Desargues (18), and Stevin, Gravesande, Taylor and Lambert combined (19). Burmester (1906) offered a brief history of perspective in relation to geometry in a festive address which traced its development from proto-perspectival efforts in Antiquity through the work of Brunelleschi, Alberti, Piero, Pélerin, Guidobaldo del Monte, Desargues, to Breysig, Möbius, Steiner and Von Staudt. The eleventh edition of the Enciclopedia Britannica (1911), in addition to a brief article on perspective which focussed on its mathematical aspects, related it to developments in projective geometry and conic sections in an article on geometrical continuity. Appell (1912) claimed that Cousin’s Book of portraiture (1612) had been a precursor to Monge’s descriptive geometry. Uglieni (i.e. Cremona, 1915) examined Brook Taylor’s principles of perspective. Cassina (1921) examined perspective in relation to the development of the idea of points to infinity.

    Fascination with the background to Monge culminated in Loria’s (1921, cf. above 1894), History of descriptive geometry, which remains a standard treatment of the subject over seventy years later, although it focussed very narrowly on strictly mathematical aspects and minimized the role of the artistic perspective. These themes were taken up again briefly in Günter and Wieleitner’s (1922-1923) History of mathematics and in an article by Amodeo (1932), who traced the contributions of Piero della Francesca, Dürer, Serlio, Commandino, Barbaro, Danti and his edition of Barozzi, il Vignola, Cousin and Guidobaldo del Monte. A second article by Amodeo (1933), examined the development of perspective in France, focussing on Vaulezard, Desargues and Aleaume, with mention of Aleaume, Bosse and Huret. General articles by Amodeo (1932, 1934, 1935) added little. Kaderavek (1935) considered perspective in the context of geometry and architecture. Enriques (1938) briefly discussed key developments of perspective in a section on the origins of projective geometry.

    Coolidge (1945), in his History of conic sections and quadric surfaces, returned to themes covered by Zeuthen. Enriques and De Santillana (1946) examined the role of perspective in their Compendium of the history of thought. Jones (1951), in a brief summary of an important unpublished thesis, examined the mathematical theory of linear perspective in Brook Taylor. Kline (1953) in a general book on Mathematics in western culture devoted a chapter on "Painting and perspective" and a further chapter on "A science born of art: projective geometry". Wolff’s (1956) "History of perspective up to the year 1600" in five pages offered nothing new. Daumas (1957) in his five volume History of science touched on various aspects of the history of perspective. Taton, famous in the field for his important edition of Desargues (1951), wrote on various mathematical aspects of perspective: a general article on the background to modern geometry (1949); a History of descriptive geometry (1954); and in collaboration with Flocon, a History of artistic perspective (1963), which remains one of the best short histories of the subject.

    Danielowski (1960) in a technical dissertation (Dresden), presented a succinct history of the subject beginning with a section on aspective (Agatharcus, Democritus, Democritus, Euclid, Hipparchus, Vitruvius, Ptolemy, Proclus) and pre-perspective (Alhazen, Bacon, Witelo, Peckham, Bradwardine) followed by an outline of fifteenth century (Brunelleschi, Alberti, Piero della Francesca, Leonardo) and sixteenth century (Dürer, Serlio, Barbaro, Vignola), seventeenth (Guidobaldo, De Caus, Desargues, Bosse, Niceron) and eighteenth century (Frézier, Lambert, Monge) figures.

    Bense (1965) drew attention to mathematics in ornament. Havelka’s (1966) "Historical development of mathematical perspectival constructions" offered a technical outline of developments and also pertained to the related field of mathematical drawing instruments (see below p. 102ff.*). Morozzo della Rocca (1966-1967) examined mathematical harmony in architecture with particular reference to perspective. Vinaty (1985) examined the rise of projective geometry in the context of the figurative arts in the seventeenth century, focussing on the contributions of Kepler, and Desargues, with a section on anamorphosis which touched on Niceron, Kircher, Schott and Le Brun. This led to conclusions which related the work of Kepler, Galileo, Descartes and Kant.

    Coxeter’s Introduction to Geometry (1961, 1969) as well as Coxeter and Greitzer’s Geometry revisited (1964) remain standard texts with numerous historical comments. May’s (196*) bibliography offered further titles as do lists in specialized fields such as Sperry’s (1931) Bibliography of projective differential geometry.

Planispheres and Astrolabes

    In addition to these general works on the history of the mathematics there have been specialized studies on the history of planispheres, astrolabes and their projections. Serious interest in this field began with Delambre’s History of ancient astronomy (1817) and with editions of the treatises of Philoponus by Hase (1839) and of Sabokht by Nau (1899). Favaro (1890) related an anonymous treatise on the astrolabe to Prosdocimo de’Beldomandi (now Florence, Biblioteca Laurenziana). Wittstein (1894) discussed the construction of the astrolabe of Arzachel. Frank (1920) offered a brief history of the astrolabe basing his comments on Al-Biruni’s Thorough treatise of all possible methods for the composition of the astrolabe and Frank (1922) went on to publish a detailed account of Al-Chwarizmi’s use of the astrolabe. As part of the same series Nolte (1922) outlined the history of the armillary sphere.

    Drecker (1927), basing himself on Heiberg’s collation of six extant manuscripts, published a first German translation of Ptolemy’s Planisphere. A first attempt to catalogue all extant astrolabes along with versions of the major texts was made in a fundamental work by Gunther (1936) which contains an important bibliography. Michel’s Treatise on the astrolabe (1947), remains the most lucid study of basic principles and history. Neugebauer (1949), reviewed the early history of the astrolabe.

Map Projections

    Technical discussions of the history of map projections comprise another area of study that relates to the history of perspective. In terms of ancient cartography, Reinganum (1839) provided one of the first serious surveys. Honigmann’s (1929) book on the Seven climates provided important source materials concerning links between astrology and history in the Middle Ages. In terms of Ptolemy’s methods the fundamental studies remain those by Mollweide (1805, 1817), Arnold (1909), who focussed on Ptolemy’s use of a grid system, Schnabel (1930) and von Mzik (1933, 1938). In English the standard articles remain Cooley (1854), Tudeer (1917) and Bagrow (1945), who reviewed theories concerning the origins of Ptolemy’s Geography. Cebrian (19**), who attributed to Thales the use of central perspective, claimed that in addition to his two basic projections Ptolemy had developed a third improved conic projection. Neugebauer (1959) translated the passages from Ptolemy’s Geography, Book VII, chapters 6 and 7), offering a careful commentary noting, for instance that (28): "The meridians are drawn -probably as circle arcs- through three points which are determined on the northern and southern limit of the oikoumene and on the parallel PSX. Thus the representation is again a mapping preserving distances on three parallels and not a perspective picture". Notwithstanding this clear statement scholars such as Edgerton (e.g. 1975, 1991) have cited Neugebauer as evidence that Ptolemy had a third method of cartographic projection which employed linear perspective.

    In terms of Renaissance cartography, Toscanelli is a key figure because of his friendship with Brunelleschi. Fundamental in this context remains the monumental work of Uzielli (1894), who also wrote an article (1902) on the relationship of Paolo Toscanelli and Antonio di Tuccio Manetti. Uzielli was considered critically by Wagner (1894) who offered his own reconstruction of the Toscanelli map. A new awareness of the wealth of cartographical sources was provided by a series of studies on materials in German libraries (1904-1916).

    Lemoine studied links between astronomy, surveying and painting in an article "On the oblique horizon and the use of the torquetum by painters" (1960-1961). Links between surveying, cartography and painting were explored by De Smet (1966).

    With respect to general histories of cartographical projection, D’Avezac’s (1862), monograph cited in our first volume (Sources, pp. 28-29*) remains of fundamental importance. Keuning (1955) published an important article on "The history of geographical projections until 1600" which remains the best brief introduction to the problem. Merriman (1947) offers a useful Introduction to map projections. Basic in the field of nomenclature and classification of map projections remains Lee (1944). Also important in this context is Chovitz’ (1952) "Classification of map projections in terms of the metric tensor to the second order". On the question of Russian map projections, Maling (1960) remains basic.

4. Treatises

    As historical records of practice and theory the treatises go through three distinct phases. In the first century (1430-1530) they contain hardly any historical notes. Filarete’s Treatise on Architecture (c.1464), which refers to Brunelleschi’s demonstration and to Alberti’s treatise, is an exception. The other early treatises of perspective: i.e. Alberti’s On Painting (1435); Francesco di Giorgio Martini’s Treatise on Architecture, Engineering and Military Art; Piero della Francesca’s treatises (On the Abacus, On the Perspective of Painting and On the Five Regular Solids); Leonardo da Vinci’s Manuscript A, make no reference to practical spatial achievements of Renaissance artists. Moreover, the titles of these earliest treatises remind us that perspective began in the shadow of other disciplines. Etymologically and historically it was closely linked with optics. Alberti associated it with painting; Filarete linked it with architecture; Francesco di Giorgio Martini with geometry and surveying. Vasari’s Lives of the Artists (1550) associated perspective with a whole range of disciplines including painting, architecture, inlaid woodwork, and goldsmithing.

    In a second phase (1540-1758), the treatises frequently contain brief paragraphs on the history of the subject, which provide useful insights into who was considered important at the time. Pélerin (1505) prepared the way for this approach with a list of surnames. Serlio (1540 etc.) went further: he cited the work of Dürer and mentioned some of his contemporaries. Having made the point that architecture, painting and perpective are closely interrelated, Serlio asked in his proem:

For, was not Bramante an excellent Architect, and was he not first a painter who had great skill in perspective art, before he applied himself to the art of architecture? And Raphael D’Urbino, was not he a most cunning painter and an excellent perspective artist before he became an architect? And Baldassare Peruzzi of Siena, was also a painter, and so well seen in perspective art that he, seeking to place certain pillars and other antique works perspectively, took such a pleasure in the proportions and measures thereof, that he also became an architect, wherein he so excelled, that his like was almost not to be found. Was not the learned Geronimo Genga also an excellent painter and most cunning in perspective art as the fair works which he made for the pleasure of his Lord Francesco Maria, Duke of Urbino, can testify, under whom he became a most excellent architect? Giulio Romano, a student of Raphael D’Urbino who by perspective art and painting, became an excellent architect witnesses the same.

    It is noteworthy that Serlio cited only contemporaries and made no reference either to fifteenth century practitioners or authors. By contrast Barbaro (1568), who wrote the next Italian treatise, included a sketchy history of perspective theory:

But in what way and with what precepts they were arranged, no-one (as far as I know) has left any memory in their writings. Unless we wish to call precepts and rules some light practices established without order and foundation and explained roughly, since of these there are some by Pietro dal Borgo S. Stefano [i.e. Piero della Francesca?] and by others which will serve for idiots. Dürer left few things, although they were ingenious and subtle. Serlio dealt with the matter in a rougher way. But both of these authors (I would say) stopped too soon. The painters of our time, otherwise famous and with a great name, let themselves be guided by a simple practice....Federico Commandino in the Planisphere of Ptolemy has made some learned demonstrations as is his wont, pertinent to perspective as principles of this, not unuseful to excite the minds of the studious; but useless as far as practice is concerned and introducing new persons to work in obscure and difficult ways.

    Egnazio Danti in his commentary on Giacomo Barozzi (il Vignola’s) Two Rules of Practical Perspective (1583) marked a major step forward in historical consciousness, but he too made no mention of fifteenth century authors other than Piero della Francesca. Danti noted that Piero wrote three books relating to perspective; that Piero was an important source for Barbaro, as was Baldassare Peruzzi for Serlio. He cited the French authors Jacques Androuet Du Cerceau and Jean Cousin and his Italian contemporary, Pietro Cataneo. With respect to the ordinary rules he referred to books by Leon Battista Alberti, Leonardo da Vinci, Albrecht Dürer, Fortius Ringelbergius, Lencker, Viator and Commandino. On the topic of regular solids Danti cited the works of Jamnitzer, Piero della Francesca and Luca Pacioli. In the course of his commentary Danti referred to various other practitioners and theorists, including Tommaso Laureti, Baldassare Lanci and even Simon Stevin (over 20 years before this author published on perspective). Danti did not however provide either titles or dates of publication for the texts. Nor did he attempt to trace the history of perspectival practice.

    Pfintzing (1598) marked a first serious attempt to chronicle developments in perspective in Nürnberg from the time of Dürer to the 1590’s, citing both published and unpublished contributions. Pfintzing was exceptional in including dates and titles and in giving a detailed description of each work. The tendency was towards lists usually without titles and dates. These lists became a regular feature in the introductions of perspective treatises, but they were seldom accurate. For instance, the Jesuit Father Dubreuil, author of the famous, anonymous Practical Perspective (1642-1649), which went through over 30 editions, claimed that Gregor Reich was the earliest treatise on perspective that he had encountered, followed by the text of Viator. (In fact editions of Gregor Reisch contained a pirate edition of Viator). The German edition of Dubreuil (1710) went on to mention Dürer, Jean Cousin, followed by: "Daniel Barbaro, Vignola, Serlio, du Cerceao [i.e.Androuet du Cerceau], Sirigaty [Sirigatti], Salomon de Caus, Mar[o]lois, Vredement, Vriese [Vredeman De Vries], Guidus, Ubaldus [Guidobaldo del Monte], Pietra Acolty [Accolti], Sieur De Vaulezard and M. Desargues".

    In a third phase, the perspective treatises typically contain a specific chapter on the history of the subject. Lambert (1759) was probably the first to do so seriously. He cited Montucla’s claim that Pietro del Borgo San Stephano [i.e. Piero della Francesca of Borgo San Sepolcro?] was the first to use perspective, followed by Baldassare Peruzzi, who was credited with the invention of the distance point. Lambert’s list of early authors included Leonardo da Vinci, the work edited by Rodler (1530, 1546), Daniele Barbaro (1569), Lencker (1571), Egnazio Danti and Guidobaldo del Monte (1600). Once again fifteenth century theorists as well as the early practitioners were largely ignored.

    This approach continued into the twentieth century. Cole (1921) listed Bartolomeo Bramiantino 1464), Pacioli (1494), Dürer (1525), Cousin (1560), and Guidobaldo del Monte (1600). One of the standard books of the past generation, Abbott (1950) has an historical survey which mentions Uccello, Masaccio and the Van Eycks in terms of practice. Alberti (which he claimed was published in 1434, the year it was written, rather than 1540, the year of the first edition), Jean Pélerin (1505) and Dürer (1525), Vignola (1583) and Guidobaldo del Monte (1600). Hence treatises even in the modern period have remained remarkably primitive in their mention of historical practice and theory.

5. Encyclopaedias

    Voleterrannus (1506), appears to have been the first encyclopaedia to deal with perspective as a secondary source, mentioning in passing only a few authors (see p. 43*). Most of the encyclopaedia in the sixteenth, seventeeth and even eighteenth centuries contained random notes in the form of secondary literature and focussed on re-printing either full texts or handy summaries. For instance, Gregor Reisch’s Philosophical pearl (Margarita philosophica, 1509) included Pélerin’s On artificial perspective. Rivius (1547) included texts by Alberti, Serlio and Gauricus. In the third decade of the seventeenth century the Jesuits introduced a new type of mathematical encyclopaedia. This began with the brief descriptions of problems in optics, perspective etc.: Ens (1636). In the next decades the scope of these expanded enormously through the works of Bettini (1642), Kircher (1646), Schott (166*), Millliet de Chales (167*). Meanwhile many treatments remained summary at best such as the entry under perspective in Baldinucci’s (**), Tuscan vocabulary of the art of drawing, which mentioned in passing the works of Barbaro, Accolti, Leonardo, and Danti’s commentary on Vignola. Similarly, the author of the General theory of fine arts (1779) focussed attention on technical principles leaving only one column at the end to mention his conviction that although the ancients had some knowledge of a science of perspective it remained in a primitive state. He mentioned in passing the work of Leonardo and Dürer and referred those readers interested in the history of the subject to the introduction of part two of Lambert’s Free perspective.

    Interest in historical aspects of perspective grew through mathematical encyclopaedias in the 1850’s and 1870’s (cf. above p. 57*). Some nineteenth century authors such as Piper, in Ersch and Gruber’s (1843), Encyclopaedie der Wissenschaften und Künste continued to focus on technical aspects of perspective, relegating historical considerations to a page and a half of significant titles from the time of Gauricus (1504) to ninteteenth century examples such as Eytelwein (1806) and Schmid (1826). By contrast, Bosc (1879) in his Dictionnaire raisonnée de l’architecture, began with a short definition (twelve lines) followed by nearly five columns on the history of perspective. Bosc cited passages from Vitruvius and Pliny to counter the claims of those who denied the existence of perspective in Antiquity. Three further columns dealt with basic concepts of perspectival practice, and were followed by a bibliography of sources (one and a third columns). Julien (1885) in his article on perspective in Planat‘s Encycopaedia of architecture and construction focussed mainly on technical aspects, relegating historical comments to a note with references to Leonardo, Burnet, Vallée, Chevreul, Bruecke and Helmholtz. The author, O. H. (1911), in the eleventh edition of the Encyclopaedia Britannica, also focussed on technical aspects of perspective, referring only to Stanley’s Descriptive treatise on mathematical drawing instruments

    The anonymous author of the article on perspective in the Enciclopedia universal illustrada (1921) began with a detailed technical description (eight columns), followed by a section on perspectival instruments which entailed several references not usually found in the literature: e.g. diagrafo of Charles Gavard; paralelo universal of Verzy (1810) the quarregrafo of Ancracher (1820), the secater perspective of Lalanne and the stereografo of Fevret de Saint-Misme. A long bibliography (nearly six columns) was notable for its emphasis on eighteenth and nineteenth century authors on perspective, many of them seldom cited before. A section on perspective in painting relied heavily on Nielsen and referred to the work of Leonardo.

    The Encyclopaedia of world art contains an extensive, important article on perspective by Gioseffi (Italian 1958, English 1965), which is misleading in that it presents the author’s personal interpretation of the history of the subject, essentially unchanged from that in his main book (1957), without indicating the existence of alternative views. For instance he claims that there was clear knowledge of linear perspective in Antiquity and that Giotto re-introduced the principles of one-point perspective at the turn of the fourteenth century. This bias is reflected also in the seemingly rich bibliography which omits reference to the most important literature contrary to his viewpoint. A second entry by Gioseffi in the same work, on optical concepts contains useful references to debates concerning links between curvilinear theories of vision and representation with some reference to camera obscuras and anamorphosis, but once again his presentation is one-sided with little indication either of the historical richness or complexity of the debates (cf. below pp. 78 ff.). By contrast, an excellent third article in this work by De’Maffei (Italian 1958, English 1965) on perspectivists, which focussed on illusionist ceiling painting (quadratura), offered the most thorough English language outline of this subject, although the author did not cite Kellermann’s fundamental contribution.

    A section on space and time in the Enciclopedia universale dell’arte began with headings Francastel (1964) on temporal expedients in traditional figurative arts, the time of vision in an image; time and memory; time and space and a "Brief history of figurative systems in space-time", which drew heavily on his earlier books (cf. above p.56*). A further heading by Battisti (1964), addressed the "Possibility of relations in space-time" and considered the contributions of individuals ranging from Giovanni Fontana, Piero della Francesca and Giulio Romano to Paul Klee and Marcel Duchamp.

    An entry on perspective by Carter (1970) in the Encyclopaedia of world art is the best concise introduction to basic principles and the history of the subject. Carter noted the scientific basis of perspective, the psycho-physical basis of the perspective illusion, cues for the perception of depth, basic definitions, measuring in perspective, and marginal distortions. Carter gave a lucid summary of the theory of vanishing points and Desargues’ theorem; the distance-point or three-point construction before offering an outline history of perspective: Antiquity, the role of Euclid, Byzantine, Post-clasiscal, Mediaeval periods, the Renaissance and modern times. Carter, one of the greatest modern practitioners is exemplary in his precision.

    Volume eleven of Artistic techniques contained an appendix by Franchini Guelphi (1973) on "The organization of the image in plane figuration: perspective techniques". Guelphi claimed that perspective was neither an objective instrument of reality nor a system of immutable laws rigourously based on the natural laws of vision." Under the heading of optics and scenography in Antiquity, Guelphi rejected Panofsky’s interpretation as "approximate and arbitrary" and instead accepted Gioseffi’s (1957) claim that the Vitruvian passage indicated the use of linear perspective in Antiquity. The views of White were also reported. With respect to the Middle Ages, Guelphi mistakenly claimed that Alhazen was the first author to describe the camera obscura (cf. below p.103* ), and reviewed the empirical contributions of Giotto, Lorenzetti, Jean de Pucelle’s Belleville Breviary (Bréviaire de Belleville, before 1343) and the Hours (Heures, c. 1395) of the Duc de Berry.

    With respect to the Renaissance Guelphi cited Argan’s (1955) views of Brunelleschi as "the first to think of architecture as space"; cited Parronchi’s analysis; and Edgerton’s interpretation of Alberti; outlined the contributions of Piero della Francesca, mentioned a lost treatise by Foppa and the treatises by Filarete and Gauricus. There followed sections on empirical methods and the systematization of Nordic artists, notably, Pélerin; the crisis of linear perspective in the late fifteenth and sixteenth centuries, i.e. the use of curvilinear methods and anamorphosis; scientific systematization in the seventeenth century; the rise of quadratura; Canaletto and the illumined view of the eighteenth century and the role of photography. A brief entry on perspective by Dalai-Emiliani (1985) in the Encyclopaedia universalis provided a concise summary of the field and added some new material in a section on twentieth century debates.

    In retrospect it can be seen that there has been a gradual shift in the encyclopaedic literature from primary to secondary literature, from technical accounts of perspectival principles to summary accounts of its history and notwithstanding notable exceptions such as Carter (1970) there has been a tendency for these accounts to be secondary in another sense. The most penetrating historical studies remain in the form of specialized monographs and articles.

6. Bibliographies

    Thus far there have been at least thirty six bibliographies with sections devoted specifically to perspective. These are listed below (fig. 13) chronologically by author with the number of titles on perspective cited by each. Vasari is not included because, although he refers to writings, he does not refer to specific titles or editions.

1590 Lomazzo 7 1821 Cicognara 156

1605 Hulsius 14 1830 Rogg 57

1610 Draudius 18 1836 Fielding 9

1651 Leonardo 7 1861 Beelitz 27

1682 Lipenius 38 1864 Poudra 132

1704 Pellegrino 32 1873 Löffelholz 138

1706 Sturm 8 1876 Anonymous 102

1711 Fullenius 31 1888 Soden-Smith 320

1717 Anonymous 36 1889 Riccardi 17

1730 Doppelmayr 29 1893 Riccardi 101

1750 Wolff 28 1921 Loria 128

1770 Murr 101 1934 Amsterdam 70

1772 Tiraboschi 20 1934 Schmid 16

1773 Haym 49 1939 Berlin 66

1778 Scheibel 207 1961 Fowler 121

1783 Malton 25 1973 Schüling 127

1791 Comolli 78 1979 Vagnetti 1283

1805 Murhard 246 1986 Schasfoort 104

Fig. 13. Dates, authors of bibliographies and number of books listed.

    Strictly speaking Lomazzo’s Idea of the Temple of Painting (1590) is also not a bibliography. It is included here because it contains some of the earliest clear references to perspective treatises. It made little mention of fifteenth century sources other than Leonardo, and while mentioning sixteenth century authors such as Peruzzi and Serlio, focussed attention on the Milanese school: Foppa, Butinone and Zenale. Hulsius (1605) listed fourteen works in the midst of treatises on geometry and surveying. Hulsius (1604) was also important for being one of the first to publish on the proportional compass, a universal measuring instrument which included perspective in its scope. Draud(ius) (1610) listed only four authors under the heading of perspective: Crameri [Krammer] (1600); Lautensack (1564), Lencker, and Vredeman de Vries, although further authors were included under other headings such as architects and geometers (Androuet Du Cerceau 1576, Vredeman de Vries 1612); architecture (Vredeman de Vries 1609, Krammer 1600, Ryff 1582, Serlio 1608); fortifications (Faulhaber 1610, Perret 1602, Specklin 1599); the art of writing (Lencker 1595) and geometric instruments (Hulsius 1592, 1594).

    Subsequent bibliographies gradually included more of these titles under the heading of perspective. The 1651 edition of Leonardo still included seven books on perspective in a list of books on art. Lipenius (1682), by contrast, marked a first significant number of books (38) specifically listed under the title of perspective. This had the expected German works (Durer, Lautensack, Lencker, Pfintzing, Faulhaber), but was noteworthy for adding an international selection including Italian authors (Barbaro, Barozzi il Vignola, Guidobaldo del Monte, Accolti), French (Aleaume, Desargues, Bourdin, Dubreuil), Dutch (Vredeman De Vries, Hondius, Marolois), and even English authors (Moxon, Prick as translator and editor of Dubreuil). Pellegrino’s (1704) list of books on architecture and perspective explicitly cited the year of publication and the city where the work was published. He linked architecture and perspective and focussed on Italian works although French works by Desargues, Felibien, Josse, De Lorme, and Niceron and the German work of Jamnitzer were cited.

    Doppelmayr (1730), in a fundamental study of the Nürnberg mathematicians, was among the first to develop a careful biographical approach with detailed bibliogaphical information, prefiguring the modern bio-bibliographical approach. In so doing, Doppelmayr provided important insights into the social and intellectual context of perspectival activities. He drew attention, for example, to a debate concerning the structure of the cosmos arising out of the Aristotelian tradition via Averroes, which was one of the incentives for Regiomontanus to write his treatise on the regular solids. Doppelmayr was remarkable for his detailed references which cited his sources.

    Murr (1770) produced a quantum leap forwards with a list more than three times the length (101 titles) of Lipenius mainly with examples from art history. Murr marked a watershed in other respects also. His titles were more accurate and when in doubt he gave the source of his reference. That same decade Scheibel (1778) more than doubled the known number of texts (from 101 to 207).

    The last decade of the eighteenth century brought two more pioneering works. Comolli (78) treated a relatively small number of texts but discussed their history with a new level of critical acumen carefully weighing conficting evidence from different sources. In the case of Leonardo, for example, he provided a context for historical study of the manuscripts. Murhard (1797-1805) produced what was to remain the largest bibliography on perspective (246) until the late nineteenth century as part of a massive five volume bibliography on all aspects of the history of mathematics. What made Murhard’s work a remarkable contribution is that he painstakingly recorded every book he had actually had in his hands and carefully documented his references in the case of books he had not seen at first hand. This introduced standards of accuracy to his bibliography which have not been uniformally evident even in subsequent contributions.

    The early nineteenth century brought one serious bibliography (with 156 titles on perspective) based on the private collection of Count Cicognara (1821), now in the Vatican Library. In the second half of the century, Poudra (1864) made the first attempt to write a history of perspective from a mathematical viewpoint (see above), using a list of (132) titles as a point of departure. The rise of the National Art Library at South Kensington led Soden Smith (1888) to produce the largest bibliography (320) prior to Vagnetti (1283). This and the catalogue at Neuwied (1876, cf. Sources, fig.46-47), placed perspective in a larger context of drawing books. Meanwhile authors such as Rogg (1830) and Beelitz (1861) were drawing attention to further connections between perspective and mathematics particularly in the realm of conic sections. Riccardi (1889, 1893) furthered this trend by consciously searching for titles not listed by Poudra and by making perspective but one part of a larger bibliography including various branches of the mathematical sciences.

    In the twentieth century, Loria (1921), continued this mathematical theme in the context of descriptive geometry. There were three further catalogues of important collections, Amsterdam (1934), Berlin (1939) and the Fowler Architectural Collection (1961), the last of which introduced a new standard in bibliographical detail and accuracy. Schüling (1973), the chief librarian at Giessen, also produced a model bibliography which attempted, for the first time, to give some idea of extant copies of perspective treatises written before 1601. Vagnetti (1979) in a pioneering work combined for the first time titles from the realm of optics, art, architecture and mathematics to arrive at a list four times longer than any earlier bibliography (1283). Vagnetti patiently collected titles for over thirty years and provided useful descriptions both for major periods and individual authors.

    Vagnetti was convinced that there was much more to be found and it was specifically at his suggestion that the present author undertook to write some 65 libraries. This number has since expanded to over 180 (see Sources, V.2) and has brought to light over 8,000 titles of primary and 7000 titles of secondary literature. Ironically, five hundred years after the introduction of perspective we are only beginning to become aware of the enormous corpus of material that awaits study.

7. Conclusions

    Our survey of the historiography of perspective has focussed on work by historians of art, and mathematics as well as authors of treatises, encyclopaedias and bibliographies. Historians of art have tended to focus on a given period, treatments of which have varied considerably. In the case of pre-history it is notable that there was little serious study prior to the work of Lange (1899), followed by the fundamental work of Schäfer (1919) since which time there has only been a new edition of Schäfer (1974) and one major contribution by Groenewegen-Frankfort (1951).

    With respect to perspective in Antiquity the debate is much older with one side claiming that they did have perspective: e.g. Vitruvius (1521) and Philostratus (1578); while another side has argued that they did not or even could not have had perspective: e.g. Rubens (1636) and Perrault (1692). While these debates have continued for the past three centuries, it is striking to note how the evidence cited in these debates has shifted enormously. In the sixteenth century the presence of a related word such as proportion or analogy in an Ancient text was frequently considered sufficient as evidence. In the seventeenth century the concept of evidence expanded to include relevant passages from Ancient sources and general allusions to examples. In the eighteenth century European scholars, particularly in Paris and London, sometimes relied on second hand reports of those who had travelled to Rome, Pompeii and Herculaneum. For examples of perspective they also turned to a wider range of objects, including ancient coins and cut stones as well as paintings. In the nineteenth century this list expanded further to include architecture, largely through the rise of archaeology which saw a new interest in actually measuring the ruins and studying details of their entasis and other possible optical adjustments. With respect to sources there was new interest in citing sources in the original Greek and Latin, collecting these systematically and analysing them with the new tools of the emerging discipline of philology. The last quarter of the nineteenth century added the visual evidence of drawings and photography to the repertoire, a trend which has continued through the twentieth century although there is still no readily available corpus with colour photographs of all the visual materials. As Bergmann (1994), has noted, digital reconstruction and computer generated reconstructions linked with virtual reality are emerging as new tools in the case of sites such as Pompeii. Similarly, although there have been some attempts to analyze (pseudo-) perspectival lines, a systematic study of their possible underlying lines has yet to be made. Perhaps the only area where there has been some approximation of systematic treatment is in the context of textual sources, where scholars have paid increasing attention to comparing and integrating evidence from literary (Plato, Vitruvius) and mathematical sources (Euclid, Hero of Alexandria, Ptolemy, Proclus).

    Historiography of the Mediaeval period (321-1300) has generated three basic interpretations. A first, introduced by Vasari, ignored the early Middle Ages and saw Cimabue and Giotto in the late thirteenth century as the pioneers of new methods that led directly to the Renaissance. A second view has focussed on the same timeframe but has suggested that this birth was in fact a rebirth of methods which had been introduced in Antiquity. The most famous exponents of this approach have been White (1957) and Parronchi (1957,...,1964), the latter of whom has expanded the context of dicussion to include mediaeval optics (Witelo) and literature (Dante). A third interpretation has argued for a continuity throughout the Middle Ages of certain spatial motifs that were initiated in Antiquity. This view, established by Kallab (1900), Kern (1912) and Goldschmidt (1916), found its most famous exponents in Panofsky (1927) and his follower Bunim (1940) .

    With respect to the Renaissance, from the time of Alberti’s On Painting (1434), the first treatise on perspective, there have been debates about whether it was something entirely new or merely a re-birth of Ancient methods. All have agreed that something important happened. Thoughts about wherein that contribution lay, who the key figures were and the scope of their activities have, however, changed greatly in the past centuries. The fifteenth century offered only isolated comments about the rise of perspectival methods. The sixteenth century, most notably in Vasari, saw first attempts at documenting the phenomenon, with a marked emphasis on the role of Florence and both a conscious and unconscious downplaying of the importance of other centres. The seventeenth and eighteenth centuries added mainly general comments and shifted attention to perspective in the sixteenth century. The latter nineteenth century saw a first attempt to reproduce basic sources (Alberti, Filarete etc.) a process that has continued into the twentieth century. This also led to analysis of the actual methods used and first attempts to determine how these methods worked in the actual paintings by reconstructing their vanishing points, an approach that has continued to gain ground. In the last decade of the nineteenth century, Nielsen introduced the idea of studying specific centres, notably, Florence, Umbria, Rome, Siena, Milan, Urbino, Padua and Venice. The twentieth century has developed aspects of this approach through champions such as Chastel who have taught us to look at Italy as a whole series of centres. A number of scholars, most notably, Parronchi and Edgerton, have continued to emphasize the central importance of Florence. Some, particularly Battisti and Dalai Emiliani, have drawn attention to the importance of Milan and Northern Italy as a whole in the early history of perspective. White and Gallet have focussed new attention on the particular role of Padua.

    In all there have been hundreds of articles on Renaissance perspective If we stand back, however, to look at the big picture, it is striking to note what has not yet been done. Linear perspective evolved in two contexts: one narrative, as in the lives of the saints mainly in fresco; the other, emblematic, mainly in inlaid wood (intarsia), dominated by scenes of idealized towns, and instruments. In the case of narrative, notwithstanding a monumental contribution by Kaftal, which is being continued by the important work of Bisogni, we still do not even have a catalogue of all the narratives involved. In the case of emblems, there have only been discussions and plans for a comprehensive catalogue. In short no one has access to the primary materials either in terms of practice or theory. While all the major texts of the fifteenth century are now available in some form, no compendium of extant manuscripts of the early period has even been attempted.

    Meanwhile our knowledge of individual centres is far from complete. While the importance of Florence continues to be emphasized, it is often forgotten that the most striking examples of proto-perspective are South of Florence along an axis which starts from Assisi and runs northwest via Perugia and Cortona to Arezzo and then west to Siena; with another axis that runs almost directly North from Assisi through Gubbio, Citta di Castello (cf. Raphael) to Sansepolcro (cf. Piero della Francesca) whence it branches both west to Anghiari and Arezzo and east to Urbino. It is generally known, that the connections between these centres were largely through the travels of artists such as a Giotto who worked in Assisi, Padua and Florence; or a Masolino who worked in Florence, then San Clemente in Rome, before going to Castiglione D’Olona on his way to Budapest. With computers it is possible to make dynamic maps which trace these peregrinations systematically and allow us at the same time to trace the spread of specific themes. Approached in this way, studies of Renaissance perspective have scarcely begun in spite of claims by some that the field has been exhausted.

    In the case of perspective since the Renaissance, the immensity of what has not yet been studied is even more striking. While there have been significant studies on individual applications such as ceiling painting or theatre, as well as of individual artists, the interplay between techniques and the details of influence have remained largely unexamined. Pioneering work on the institutionalization of artistic techniques, largely through the academies, (e.g. Pevsner) have provided an initial framework for understanding how teaching shifted gradually from the context of masters in workshops to courses in schools How perspective was in the process reduced to a dry, academic subject, devoid of creativity has yet to be studied. So too has the whole resurgence of perspective in the second half of the twentieth century.

    In the history of mathematics, it was only in the second half of the eighteenth century that a serious interest in the history of perspective emerged in Paris. This remained the chief centre for over a century until the 1870’s when Berlin and Leipzig became the leading centres in Germany. For a period of nearly fifty years there was a concerted effort to understand major patterns in the history of mathematics, culminating in the studies of Cantor. One of the major motivations for studying perspective was a belief that Dürer had been the founder of descriptive geometry. When a series of dissertations demonstrated that this was not the case, German interest ebbed. While the period since the early 1920’s has produced a series of isolated studies, attempts to understand the big picture have been absent, mainly because of trends in specialization.

    The earliest treatises (1435-c.1539) contained hardly any historical notes. In a next phase that lasted just over two centuries (1540-1758) they typically contained brief paragraphs on the history of perspective. Beginning with Lambert (1859) some treatises have contained short sections on the history of the subject but these have seldom been very accurate and never approached any measure of comprehensive treatment. Encyclopaedias have proved useful both for reprints of primary sources and general surveys of secondary sources but these too have never approached a comprehensive treatment of the subject.