Dr. Kim H. Veltman
III Treatises
1. Introduction
2.
Early
Treatises
3. Optics
4.
Geometry
5.
Architecture
6.
Themes
7.
Categories
8.
Conclusions
The contents of the early treatises varied enormously because they remained in manuscript form and because perspective was not an independent subject for classification (see below 1.4). Accordingly, as a repertoire of themes emerged in the latter sixteenth century, these dovetailed with at least four traditional disciplines: optics, surveying (particularly in terms of instruments, see below 2.1), geometry (two main methods, polyhedra, letters, human forms) and architecture (e.g. scenography, columns, ruins, idealized buildings, interiors and quadrature). A number of these themes evolved into independent topics, while others remained minor themes in the perspective treatises for the next centuries.
Various branches of perspective also evolved. During the fifteenth century, treatises dealt exclusively with one-point perspective. Pélerin (1505) introduced two-point perspective to the literature. (Three point perspective only became current in the latter nineteenth century.) Meanwhile, Piero della Francesca had introduced another branch: anamorphosis. The seventeenth, eighteenth and nineteenth centuries brought further branches of perspective including cavalier, axonometric, isometric, cylindrical, conic, spherical, aerial, colour, chiaroscuro as well as shades and shadows. Each of these will be considered in turn.
2. Early Treatises (1434-1568)
The early treatises focussed on practical demonstrations. Alberti, in his On painting (1434), the first extant treatise on perspective, began with basic definitions, general remarks about optics, and a description how to make a perspectivally foreshortened plane. In book two, he described the use of a perspectival window (velo). In Elements of painting (1435-1440), Alberti gave examples of perspective involving geometrical diminution, using combinations of squares (fig. 28.1), pentagons and circles. Filarete (1464?), gave an even more elementary treatment in a brief section on perspective in his Treatise on architecture (fol. 173v-178v): basic definitions, a first diagram of the legitimate construction, and a few simplified examples of perspectival diminution.
Piero della Francesca's On perpective of painting (c. 1470-1480), was the first treatise devoted specifically to perspective. It opened with basic definitions and a demonstration of the window principle. Book one contained examples in ground-plan involving geometrical diminution, including a square, octagon, sixteen sided figure, oblique triangle, hexagon, pentagon and octagon. In book two, the same principles were applied to three-dimensional objects: a cube, pentagon, octagon, hexagon, columns, a hexagonal well on stairs, a four sided and an eight sided building and a vault. Book three opened with a description of a second method, involving a combined ground plan and elevation,1 which was then applied to a mazzochio shape, a tilted cube, bases of columns, human heads and an apse. At the end Piero provided three examples of anamorphosis including an egg which became a sphere--an idea he used in his Brera Altar (pl.7.1).
By contrast, the section on perspective in Francesco di Giorgio Martini's treatise on architecture, engineering and military arts, Codex Saluzziano 148 in Turin, was only two pages (fol. 33r-33v) but, nonetheless, important because it demonstrated principles of perspectival diminution in terms of surveying practice. His contemporary, Leonardo da Vinci, gave a more systematic treatment in Manuscript A (1492), beginning with basic definitions (point, line, surface), followed by quantitative demonstrations, connections between surveying and perspective and examples involving polygonal shapes.2 Luca Pacioli's discussion, in his Summa (1494), was limited to four pages, with examples drawn from surveying experience. While Pomponius Gauricus devoted ten pages to perspective in his On sculpture (1504), he emphasized etymological and literary references, mentioned classification (see below p. ) and merely included one paragraph of technical description. With the advent of Northern treatises in the sixteenth century, there was a greater emphasis on illustration. For instance, P,lerin's On artificial perspective (1505), introduced a first series of architectural exteriors (fig. 29.1-2) and interiors (fig. 66.1) of both sacred and secular buildings. These themes were developed in A beautiful useful booklet (1531), edited by Hieronymus Rodler, and in Serlio's works on architecture (1544 etc.). In the next decades, specialized treatises on architectural perspective emerged with the works of Androuet Du Cerceau and Vredeman de Vries (see below 2.4).
Parallel with these developments towards specialization, there was another trend in the direction of compendia. Albrecht Drer's Instruction in measurement (1525) was an early example. It dealt with geometry, regular solids, letters, shadows, methods of perspective and instruments. Daniele Barbaro, building on the work of both Piero della Francesca and Drer, took this approach further in his Practice of perspective (1568) with sections on optics, geometry, the methods of perspective, regular and semi-regular solids, irregular objects, columns, architecture, scenography, anamorphosis, planispheres, shadows, human form and instruments. Since later treatises usually contained most, and occasionally all of these subjects, it will be useful to consider the history of each in turn.
Optics and perspective shared a common etymological root in the Latin perspectiva, and fifteenth century authors no doubt tended to see in optics a theoretical basis for linear perspective. Hence, Ghiberti, active in proto-perspectival demonstrations, also discussed optics at length in his Third commentary.3 Alberti, in his On painting, referred briefly to concepts such as visual angles and central ray, but carefully avoided details of optical debates.4 So too did Piero della Francesca, Leonardo da Vinci, P,lerin and Drer. Indeed, none of these authors mentioned any specific sources on optics. One of the first to do so was Serlio (1540), and then more as a disclaimer: "In this work I will not trouble myself to dispute philosophically what perspective is, or from whence it hath the original, for learned Euclides writeth darkly on the speculation thereof."5 Barbaro (1568) referred to Apollonius' Conics and Euclid's Elements with respect to visual angles, but did not mention Euclid's Optics explicitly, although he cited introductory assumptions from that treatise. Egnazio Danti, who produced an Italian translation of Euclid's Optics (1573), did cite the work specifically in his edition of Vignola's The two rules (1583). No one at the time pointed out basic discrepancies between theories of visual angles and principles of perspectival planes noted above (see p. ). Hence, while most fifteenth and sixteenth century treatises paid lip service to optics, there was no serious consideration of its principles. In the seventeenth century the situation became more complex. For instance, Accolti (1625) cited not only Euclid's Optics, but also Heliodorus of Larissa, Theon of Alexandria, Aristotle, Galen, Hippocrates and Witelo with respect to theory. Nor did he cite blindly. For while acknowledging Witelo's great authority as "the sole and principal head of the school of perspectivists,"6 Accolti noted his mistaken claims with respect to the oblique passage of lights.7 On the other hand, Accolti continued to claim that "perspective is nothing other in effect than a representative section of the visual pyramid,"8 a view which remained popular (see below 1.4), in spite of efforts by Desargues and Bosse to establish that the laws of perspective had their basis not in Euclidean optics, but Euclidean geometry.
The links between geometry and perspective had been implicit from the outset in Alberti's Elements of painting. For authors such as Piero della Francesca, Leonardo, Barbaro and Danti, Euclid was considerably more than a source of geometry: Euclid provided basic definitions (e.g. point, line, surface), principles of proportional diminution and a model for the treatment of the regular solids. Beginning with Piero della Francesca, there was increasing interplay between the goals of mathematics and perspective, which helps explain why Piero's treatises on the abacus, on the five regular solids and on linear perspective were all considered works on perspective by Danti9 (1583). Leonardo da Vinci's quantatitive, experimental demonstrations of perspective contributed to these links.
In Germany, this interplay between mathematics and perspective acquired new connotations. Etymologically the Greek term for geometry, ge metron, meant measurement of the earth. Hence, Drer called his introductory book on geometry Instruction in measurement and devoted a chapter thereof to perspective. The author of A beautiful useful booklet (1531), in turn, equated perspective with measurement. Hirschvogel (1543) went further by entitling his book: Geometry. The book geometry is my name. All liberal arts at first from me came. Architecture and perspective together I bring. Barbaro (1568), included a short section on proportional principles of geometry. Danti (1583), added a larger section and described the goals of perspective in terms of transformational geometry:
In the decades that followed, mathematical aspects of perspective came increasingly to the fore thanks to Commandino and his student Guidobaldo del Monte (1600), who claimed that the nobility of architecture and painting were to be attributed "to mathematical principles and especially to perspective."11 In the Netherlands, Simon Stevin wrote a treatise because his patron, Prince Maurits, wished "to design exactly the perspective of any mathematical figure with knowledge of the causes and its mathematical proof."12 Through Leonardo, Lencker (fig. 32.1), Commandino and Stevin formal mathematical problems such as conic sections also found their way into treatises on perspective (see below pp. ). As a result, by the early seventeenth century perspective had become an area of study for geometers and mathematicians generally, including Aleaume, Migon and more powerful minds such as Desargues and Pascal. It was notuntil the nineteenth century that further developments in mathematics threatened entirely to subsume perspective (see below 1.4).
The intimate links between architecture and perspective were due largely to the Vitruvian tradition. Renaissance thinkers tended to translate Vitruvius' three categories of ichnographia, orthographia and scenographia as ground-plan, elevation and perspective with the result that perspective was seen as part of the architect's profession. Indeed, the authors of fifteenth century treatises were frequently architects, namely, Alberti, Filarete, Francesco di Giorgio Martini and Leonardo da Vinci, a trend which continued in the sixteenth century with Peruzzi, Serlio, Cousin, Androuet Du Cerceau, Barozzi, Danti and Vredeman de Vries.
In Bellini's Sketchbooks (fig. 83.1-2), these connections between architecture and perspective were evident from the outset. Elsewhere they emerged slowly. Filarete's treatise contained only three schematic perspectival diagrams showing the exteriors of an hexagonal, spherical and occtangular building. Piero della Francesca's On perspective of painting, contained two perspectival views of a square and an octangular building, plus a vaulted archway. Francesco di Giorgio Martini's treatise contained various rough perspectival sketches of Roman buildings, including both interiors and exteriors in section (fig. 84.2), using a method associated with Brunelleschi (fig. 84.3) which, as already noted, was also known in Northern practice (fig. 10.1-2) and was published by P,lerin who used it in seven secular and three sacred buildings (fig. 10.3-4). Ringelbergius (1531) provided five simplified versions of such interiors. Rodler (1531) was the first to explore such architectural exteriors and interiors in detail, pointing the way to a new category of books by Androuet Du Cerceau and Vredeman de Vries in the next generation (see below 2.4). The treatises frequently contained architectural sections and cutaways. Francesco di Giorgio Martini employed these in a rough way. Leonardo da Vinci, applying his experience of anatomical sections, improved upon them. Serlio published them often in conjuction with a ground plan. Cousin (1560), employed a geometrical and perspectival ground-plan combined with a perspectival view in section for various idealized architectural buildings, which Androuet Du Cerceau (1576) developed further. In Italy, Barbaro (1568) and Danti (1583) illustrated an alternative using a combined ground-plan, elevation and profile, which became standard in treatises on both perspective and architecture. Vasari, Jr. (1595) and Sirigatti (1596), provided various architectural motifs in their treatises. Meanwhile, Serlio (1545), had argued that the two subjects were not only interdependent, but that perspective was a prerequisite for architecture:
And no perspective workman can make any work without architecture, nor architecture without perspective.
In the generation that followed, architects began to articulate clearly the need for perspective. For instance, Pietro Cataneo, in his book on architecture, noted that "what is of greater need to the architect and of so much importance is that he be a good perspectivist,"14 adding by way of warning:
But if the architect is not a perspectivist he will never be able to honour himself as well, nor show his concept
Cataneo was so intent to impress upon his readers the need for perspective that he included the phrase "its elevation by means of perspective"16 in no less than eleven chapter headings, although some of the illustrations were simply elevations, others sections, and then rough perspectival views. Meanwhile, the Vitruvian commentaries of Cesariano (1521), Caporali (1536) and Ryff (1548) included perspectival woodcuts as if these were literally a rebirth of Vitruvian methods, an idea which Scamozzi took up explicitly in his Idea of architecture (1617):
As Vitruvius also says, perspective serves to represent all things by means of artificial lines, [when one is]
Scamozzi also emphasized the remarkable qualities of perspective: And it is certainly a marvelous thing to behold such that the planes of panels or pictures, with [the aid of] colours are so well placed and drawn by art that to those who look at them they appear to be in relief, both higher and deeper [than they actually are].18 Scamozzi added that he had written six books on perspective in his youth--alas now lost--which he hoped to publish after finishing his work on architecture.19
By the eighteenth century, it was common for general treaties on perspective tocontain a section dealing specifically with architecture. For instance, Courtonne's (1725) Treatise of practical perspective contained detailed ground-plans and perspectival elevations. This tradition continued throughout the nineteenth century. For example, Edwards (1803) Practical treatise on perspective on the principles of Brook Taylor, gave ground-plans and perspectival views of isolated buildings, buildings in context, and from different viewpoints. Guiot (1845), offered views of interiors and exteriors. Schreiber (1854), gave elevations, multiple views and detailed drawings of historical buildings. Gennerich (1865), gave ground-plans and elevations, not only for buildings, but also for canals.
Meanwhile, architecture increasingly found its way into the titles of perspectival treatises: e.g. Hirschvogel (1543), Bassi (1572). Hence, the 1619 edition of Serlio was headed All the works of architecture and perspective. Later examples included Huret (1678), Oakley (1730), Galli da Bibiena (1740), Piranesi (1800), and Fabris (1860). In the sixteenth century, titles frequently mentioned that the work was dedicated to a number of professions of which architecture was but one of many.20 This continued into the seventeenth century, as in Dubreuil's Practical perspective (1642- 1649), which was addressed to "painters, engravers, sculptors, architects, goldsmiths, embroiderers, tapestry makers and others using drawing."21 By the end of the seventeenth century, this began to change. Pozzo's (1693-1700) treatise, for example, was entitled Perspective of painters and architects. The eighteenth century saw a continuation of this trend towards works on perspective dedicated specifically, or mainly to architects, e.g. Bretez (1706), Costa (1747), Kirby (1761) and Cobin (1794). In the meantime, the interplay between architecture and perspective had become much more complex. On the one hand there were now a number of architectural themes which were regularly included in treatises on perspective (see below pp. ). On the other hand there were new categories of architectural literature which incorporated perspectival principles (see below pp. ).
In addition to these traditional disciplines which served as major topics, there evolved a number of subordinate themes. Some were closely connected with geometry, namely, the two main methods, polyhedra, irregular objects, letters and the human form. We shall consider each of them briefly.
Two Chief Methods
Although we know from Danti (1583) and Guidobaldo del Monte (1600), that there were many competing methods during the sixteenth century, including a number of erroneous ones, there were two methods which gained ascendancy. The chief of these which history has remembered as the legitimate construction, deriving from Benedetti's (1585) phrase: this sole legitimate one (hunc solum legittimam),22 was linked with the perspectival window, and began simply as a verbal description in Alberti (1434). Filarete (1464?), added a scale diagram, such that relative sizes and distances could be deduced. Piero della Francesca (c. 1480), added actual measurements, as did Luca Pacioli (1494). But these involved only isolated cases. Leonardo (1490-1500) described systematic measurements of the diminutions involved. In Piero's treatise the legitimate construction became linked with the ground plan/elevation method. Leonardo evolved new combinations thereof, variations of which were subsequently printed by Barbaro (1568), Danti (1583) and Benedetti (1585).23
Alberti, in his Elements of painting (c 1435-1440), described an alternative geometrical method involving proportional diminution. Piero della Francesca, developed this in books one and two of On perspective of painting (c. 1480). Francesco di Giorgio Martini made this a practical demonstration. With P,lerin (1505), this method emerged as the distance point construction. Ringelbergius (1531) gave quantitative examples of this method, demonstrating what happened to squares positioned 10, 20 or 40 feet from the eye. Beginning with Serlio (1545), it became customary to acknowledge that there were two methods. Danti (1583), set out to demonstrate that they were actually equivalent. Meanwhile the earlier geometrical version of this method in terms of proportional diminution continued. Piero della Francesca's example using a cube was adapted by Barbaro (fig. 28.4). His examples of foreshortened columns were adapted in a rough version by Serlio. The architectural applications of the method, explored by P,lerin (fig. 29.1-2), were developed dramatically by Androuet Du Cerceau (fig. 29.3) and later by Bibiena (fig. 29.4). Discussion of both methods remained a standard topic of perspective treatises until well into the eighteenth century.
Polyhedra
The regular and semi-regular solids became one of the most popular geometrical themes in the perspective treatises. Plato had described the five regular solids in the Timaeus24 and Euclid had outlined their geometrical construction at the end of his Elements. Regiomontanus' lost work25 and Piero della Francesca's treatise on the five regular solids, as well as his work on the abacus, continued this tradition. Leonardo da Vinci's illustrations for Pacioli's Divine proportion (1496-1499), made the regular and semi-regular solids a stock topic for treatises on perspective. Drer, in his Instruction in measurement (1525), published nets (i.e., ground plans) of the regular solids, without giving their three dimensional equivalents. Hirschvogel (1543), was the first to publish nets and perspectival views of the solids together. This subsequently became a fairly standard practice, as witnessed by Cousin (1560), Lautensack (1564), Barbaro (1568) and Danti (1583).
In Antiquity, Archimedes also considered thirteen semi-regular solids, according to an account by Pappus. Leonardo illustrated these for Pacioli's Divine proportion (1496-1499, e.g. figs. 36.1-2). A fascination for such forms and their variants developed soon thereafter. Drer (1525), provided nets or ground-plans for nine of these. Stoer (1567), integrated regular and semi-regular solids into imaginary scenes of architectural ruins in woodcuts intended as models for marquetry. Lencker (1571), also produced a number of semi-regular solids. His contemporary, the goldsmith, Wenzel Jamnitzer, created an extraordinary collection of both regular and semi-regular bodies in his Perspective of regular solids (1568) which, as he explained in his title, was based on Plato's Timaeus and Euclid's Elements. Accordingly, he associated the tetrahedron with fire, octahedron with air, hexahedron with earth, icosahedron with water and dodecahedron with heaven respectively. Using a "particular new adroit method never before in use"26 he provided six regular, six truncated, six stellated and six double stellated variants for each of the regular solids to create a total of 120 versions which, as he pointed out in his long title, was but an "introduction how, out of these five bodies, many other bodies of various kinds and shapes may be made and found without end."27
Meanwhile, in Venice, Barbaro also explored these problems. His Practice of perspective (1568), contained nets and perspectival versions of the five regular solids and five truncated versions. In addition, he provided nets for 16 further semi-regular solids and four stellated versions. His younger contemporary, Danti (1583), was content simply to refer to the work of Piero della Francesca, Luca Pacioli, Lencker, Jamnitzer and Barbaro with respect to polyhedra. Giorgio Vasari, Jr., by contrast, in his manuscript treatise (1595), adapted a number of the forms explored by Jamnitzer, and used them in new combinations (figs. 36.4, 37.4). These, in turn, were adapted by Sirigatti (1596), in his published treatise (fig. 37.2). Hence, if Nrnberg artists such as Drer, Jamnitzer and Lencker, at first profited from their Italian colleagues, Italians such as Barbaro, Vasari, Jr., and Sirigatti in turn learned from their Nrnberg colleagues.
The conscious cumulative dimension which had entered these developments by the end of the sixteenth century was nowhere more evident than in a treatise published by a Nrnberg practitioner, Pfintzing (1598), for his friends (cf. above pp. ). While citing the contributions of predecessors, Pfintzing specifically discussed the use of instruments in drawing the regular solids perspectivally (e.g. figs. 52.2, 4-5). These themes remained popular throughout the seventeenth century. Marolois (1614) continued the tradition of instruments. Halt (1625) in a book devoted entirely to regular and semi-regular solids, provided over 170 illustrations of such shapes often in unlikely combinations. Nic,ron (1638, 1646, etc.), was at pains to give abstract and concrete versions of the solids, an idea which Dubreuil (1647) adopted in his popular work (figs. 35.1-2). Eighteenth century authors such as Courtonne (fig. 35.3, 1725) and Highmore (fig. 35.4,1763) developed this approach, relating several mathematical versions of a given object. The nineteenth century added nothing fundamentally new. Indeed, authors such as Bennett (1837), Catalan (1865), Pillet (1887) or Barbiani (1897), were more concerned with standard examples, than with all the variants which had fascinated sixteenth and seventeenth century artists. The main contribution of the twentieth century has been in developing a systematic framework for explaining these forms, e.g. Cundy and Rollett (1951 etc.)
Irregular Objects
Closely related to the regular and semi-regular solids, was a class of less regular and irregular objects. Sometimes, this was a real object, such as a lute, another form mastered in marquetry and painting practice (figs. 41.1-2) prior to appearing in treatises on perspective. Drer used a lute to illustrate the use of a variant type of perspectival window at the end of his Instruction in measurement (1525), an image later adapted by Barbaro (1568). Other versions of lutes occurred in Jamnitzer's manuscript (fig. 41.3), Vasari, Jr.'s (1595) manuscript and Sirigatti's (1596) treatise (fig. 41.4).
Alternatively it involved a real object such as the mazzocchio, a Florentine hat, which subsequently became transformed into an imaginary shape. Once again, this form was found in painting practice prior to its appearing in treatises on perspective. Paolo Uccello used it in his Battle of San Romano, particularly in the Uffizi version, and in the Flood in the Chiostre Verde of Santa Maria Novella, in Florence, as well as in drawings now in the Uffizi. Piero della Francesca illustrated a simplified mazzocchio in his On perspective of painting. Leonardo (1400-1515) drew several versions in his notebooks. Serlio (1545) adapted the form for architectural purposes in his treatise on perspective. Lencker (1571) produced new variants. Jamnitzer (1568) produced two, interlocking, partial mazzocchio forms, while Barbaro (1568) devoted 16 variant figures to this shape making it a leitmotif of his treatise. Several of these recurred in Vasari, Jr. (1595), and Sirigatti (1596), and indeed the basic shape recurred in treatises over the next centuries, to become one of the forms with which Escher played in his work
To be sure, not every irregular shape was equally popular. In Nrnberg, Jamnitzer produced stellar shapes (cf. fig. 37.3), including piles thereof, combinations of pyramids, hexagonal towers, interlocking quadrangles, crosses, and even a sea shell. Some of these recurred in Lautensack (1564), Vasari Jr. (e.g., fig. 37.4, 1595), Sirigatti (1596) and Pfintzing (1599), while others were not taken up by later authors. One extraordinary polygonal shape, by the PP Master of Ferrara in the 1470's (fig. 40.1), which looks like a prototype for one of Leonardo da Vinci's tanks, was taken up by Barbaro in the manuscript version of his treatise, but not published until the twentieth century.28
One of the most popular of these shapes was a four dimensional cross, which Leonardo da Vinci sketched in his Codex Arundel (fol.223v, 1508). It recurred in Drer's Dresden Sketchbook, in a manuscript by Jamnitzer (fig. 38.1) and a drawing by Stoer (fig. 39.4). In the seventeenth century, it was found in authors such as Marolois (1614), Halt (fig. 38.2, 1625) and Dubreuil (1642- 1649). It remained a familiar theme in eighteenth century treatises, sometimes occurring in unfamiliar contexts as in Kirby (fig. 38.3, 1755). Nineteenth century examples included Gennerich (1853). In the twentieth century the form was adapted by Dali (fig. 38.4) while becoming a symbol for both the international Red Cross and the fourth dimension in art.29
The four dimensional cross was itself a variant of the ordinary cross, which was equally popular (e.g. figs. 37.3-4, fig. 39.3) and, in turn, a variant of the more universal theme of beams and columns, which had its own rich pictorial tradition, as witnessed, for instance, by two examples from Dubreuil's popular text (figs. 40.1-3). Such examples are the more interesting because they illustrate the interplay between geometrical and architectural themes. Indeed there were a number of irregular objects which might conveniently be classed under either or both headings. One was chairs. Giorgio Vasari, Jr., was perhaps to first to consider the perspectival problems of chairs from different points of view in his manuscript treatise (fig. 42.1, 1595). In the seventeenth century, Dubreuil popularized this theme of chairs, (fig. 42.2, 1642-1649), while Nic,ron (fig. 42.3, 1646) explored its anamorphic possibilities. This prospect has continued to fascinate artists into the twentieth century including Ames (fig. 42.4), and more recently, Berset (fig. 42.5, 1985). Stairs constituted another such theme, and here a few examples will serve to indicate another popular topic which persisted through the centuries. Circular stairs, for instance, became a common theme in treatises on perspective and were illustrated by Rodler (1531), Cousin (1560), Lautensack (1564), Jamnitzer (1568), Androuet Du Cerceau (1576), in double form by Danti (fig. 43.1, 1583), Vredeman de Vries (1604), Heinecke (fig. 43.2, 1727) and Fr,zier (1739) among others. The same motif also occurred in painting practice as in Peale's Staircase Group (fig. 43.3, 1795). Regular stairs were no less popular. Here there was a fascination with presenting them from unexpected angles, which often introduced ambiguities as to what was up and what was down: a theme that intrigued Vredeman de Vries (fig. 43.4, 1604) and has continued to intrigue artists in our century such as Escher who applied it not only to stairs but to waterways (fig. 43.5, 1961).
Human Form
The quest to impose geometrical regularity onto irregular forms extended to the human form. It was found that, while simple geometrical shapes required information from only two viewpoints, above and in front (i.e., ground plan and elevation), complex organic objects required at least four viewpoints (above, below, frontal and lateral), in order to arrive at a correct perspectival view. Piero della Francesca illustrated this principle with respect to a human head in On perspective of painting (c. 1480), showing the complications that arose when a head tilted upwards was viewed from below.30 According to Lomazzo, these problems must have been popular in Milan in the last decades of the fifteenth century, for we are told that both Foppa and Bramante wrote on the quadrature of the body--human and horse.31 We know that Leonardo devoted considerable attention to the use of perspective in his anatomical studies.32 He was also concerned with the geometry of movement in the human body as witnessed by the Codex Huygens (fig. 68.5), and a later treatise by Thomas Coke (figs. 68.6-7). In his manuscripts, Leonardo also outlined a simplified approach, which may have been the source of Drer's diagrams in his Four books on human proportion (fig. 68.1, 1528). The same Drer, also offered a more pragmatic solution to the problem: use of a perspectival window.
With Beham (1528) and Sch"n (fig. 18.3, 1538) human and animal proportions and their geometrical forms became an independent theme, leading to treatises such as Bracelli (fig. 68.4, 1625). Nonetheless, the connection with treatises on perspective continued in Germany with Lautensack (1564) and in Italy with Barbaro (1568) who devoted the eighth chapter of his treatise to measures of the human body beginning with the proportions of a young man taken from Vitruvius. Barbaro also integrated the foreshortened figures of hands from Piero's and Drer's works for his own purposes (fig. 68.2).
Meanwhile, the perspectival foreshortening of the entire human body was a problem again solved in painting practice long before it became a topic in the treatises. Paolo Uccello dealt with it in the slain soldiers in all three versions of his Battle of San Romano (London, National Gallery; Paris, Louvre; Florence, Uffizi, 1456), as did Mantegna with the putti in the oculus of the Camera degli Sposi, at Mantua (fig. 70.2, 1473) and the Dead Christ (Milan, Brera, 1480, fig. 70.1). In the treatises the problem was taken up in the Codex Huygens (fig. 70.4), which served as the source of an extraordinary sheet33 by Carlo Urbino (fig. 70.5), variants of which were popularized by Dubreuil (1649) and Houten (1705). Jean Cousin, le jeune's Book of portraiture (1595), the first published treatise which dealt systematically with perspective and human proportions (e.g. fig. 70.3), enjoyed at least a dozen editions in the seventeenth, and five further issues in the eighteenth century.
Perspective and anatomy, a combination which fascinated Leonardo, inspired little interest in his successors. Indeed anatomy books tended to steer an independent course. There were exceptions of course, as, for instance, Cheselden, who regularly used perspectival windows in preparing his anatomical illustrations and recently there have been at least two authors who have dealt specifically with anatomy and perspective: Oliver (1972) and Smith (1984).
Letters
Letters of the alphabet were yet another irregular geometrical form which became a theme in treatises on perspective. Some early authors notably, Pacioli (1509), Drer (1525), Tory (1529), and Serlio (1545) dealt with both perspective and calligraphy without discussing possible links between them. Lencker, by contrast, devoted an entire book to the subject, Perspective of letters (1567, 1695) which, as he explained in his title involved a clear instruction how one can render perspectivally in a plane all the letters of the entire alphabet, in antique or Roman letters in many a kind and position. In the seventeenth century Halt (1625) continued this theme. De Bry (fig. 39.1) produced more ornamental variants combining letters and human forms. Haesel (fig. 39.3) combined letters and regular solids in a striking title page. But these were exceptions. By 1700, letters were no longer a significant theme in treatises on perspective.
Scenography
Among architectural themes in treatises on perspective, scenography was amongst the most complex because its meaning was unclear. One interpretation, obviously based on the passage in Vitruvius cited earlier (p. ), equated scenography with perspectival stage design, whence the discussions of perspectival scenes for theatres by Serlio (1544), Barbaro (1568), Danti (1583) and Guidobaldo del Monte (1600). During the sixteenth century, scenography in this sense was discussed only in Italian treatises and even here there were ambiguities. For, when Serlio considered perspectival foreshortening in this context, he referred to "sciographies," thus perpetuating a Renaissance confusion between sciographia and scenographia.34 Serlio (1544), who was the first to include a chapter on scenography in a treatise on perspective, provided a cross-section and view of a typical stage and auditorium, several illustrations of stairs, plus examples of comic, tragic (fig. 81.3) and satiric stage sets. Barbaro (1568), reprinted Serlio's woodcuts of these three kinds of stage sets, and reported briefly on the methods of Pompeo P(i)edemonte to make painted scenes appear as if they were real buildings. Danti (1583), criticized Serlio's approach, mentioned that the three kinds of sets had been dealt with sufficiently elsewhere, offered his own technical advice, and alluded to examples of Florentine stage practice such as the comedy presented at the ducal palace in 1569, on the occasion of the visit of Archduke Charles of Austria. Guidobaldo del Monte (1600), devoted the last book of his great treatise to a more detailed technical account of perspectival stage design.
The seventeenth century saw the development of more specialized treatises on stage scenery including Sabbatini (1637) and Chiaramonti (1675), some of which remained in manuscript form, e.g. Gallacini (1641) and Aleotti (16__). Architects, such as Furttenbach (1604), helped spread these ideas to the North. The Jesuits also played a significant role in this process. Their efforts at politics through education involved the use of theatre. Accordingly, Dubreuil's well known treatise (1642- 1649), contained a section on perspectival scenery. Even more famous in this regard was the Jesuit, Pozzo's treatise (1693-1700) with editions in Latin, Italian, English, German, French and even Chinese (1729, 1735) and Russian (1737). From the outset, these perspectival scenes had been connected with court life and as such were designed to reflect princely grandeur and magnificence. As the courts of Europe evolved in the direction of absolutist states, the magnificence and splendour of the performances blossomed accordingly and reached its heights in the eighteenth century through the stage settings of individuals such as Juvarra (1710) and families such as the Bibiena, particularly Ferdinando (1703, 1711, 1725) and Giuseppe (fig. 79.2, 1740).
The latter eighteenth and the nineteenth centuries brought a spread of these ideas to more public theatres and treatises on perspective, such as Petitot (1758) or La Gournerie (1884), frequently had a chapter devoted to these problems. There were also specialized treatises on perspectival stage design, including Landriani (1815, 1818, 1827), Taccani (1825), Cocchi (1851, 1855) and Burmester (1884), as well as collections of stage scenery such as Sanquirico (1832, etc.) The twentieth century has brought a few more specialist treatises on perspective in scenography including Arola y Sala (1920, 1922), Sonrel (1943) and Morgan (1979).
Meanwhile, scenography sometimes had other meanings. Vitruvius, in another passage mentioned earlier, referred to three types of architectural drawings, ichnographia, orthographia and scenographia, which were commonly interpreted to mean ground-plan, elevation and perspectival view respectively. Scenography, thus became associated with architecture and had wider connotations to mean perspective generally. Hence P,lerin's treatise, originally entitled, On artificial perspective (1505), appeared subsequently as Treatise on artificial perspective or scenographic architecture (1535, 1583) and On artificial perspective or scenography (1599). Vredeman de Vries also assumed these connotations, when he entitled his work Scenography, or perspective, as the ordinary painter calls buildings which have been drawn optically. Occasionally, this wider context was not acknowledged, but nonetheless assumed. For instance, Barbaro (1568), headed part four of his book on the practice of perspective: "In which one deals with scenography, that is the description of scenes,"35 but dealt therein, not only with stage design but also with the five orders of columns and perspectival problems relating to architecture in general.
Interiors
We have already shown that the mastery of perspective with respect to interiors evolved in painting practice largely independent of the textbooks. Even so, it is useful to recall that interiors constituted a minor theme in the treatises on perspective. With respect to sacred interiors, P,lerin, (1505) was the first (fig. 10.3-4). In the generation that followed, Rodler (1531) offered another example (fig. 16.4). It is noteworthy that during the sixteenth century no Italian treatises included sacred interiors among their illustrations. Vredeman de Vries (1604), provided one of the first detailed engravings of a church interior (fig. 17.1). In the eighteenth century, an important treatise in this regard was Heinecke (1727), which gave general views of church interiors (fig. 19.1) and detailed views of confessionals, etc. (fig. 19.2). Isolated drawings of church interiors remained not uncommon in treatises on perspective until the end of the nineteenth century as witnessed, for example, by Guiot (fig. 19.3, 1845), or La Gournerie (fig. 19.4, 1884).
Secular interiors were a more popular theme in the treatises. Again, P,lerin (1505), was the first to include a view of a room (fig. 66.1). The work edited by Rodler (1531), contained a number of rooms, including artists' workrooms, a study (fig. 67.1), a bedroom and a small assembly hall. Lautensack (1564) included a larger meeting place. Vredeman de Vries (1604) provided a rather luxurious vision of a contemporary bed-sitter (fig. 66.3). Dubreuil (1642-1649) preferred to strip rooms down to their essential lines (fig. 66.2). By the eighteenth century, it was common for perspective treatises to include an interior and these increasingly reflected the taste of the time, for example, in Bischoff's (1741) living room (fig. 67.2). By the early nineteenth century, such interiors had become veritable period pieces, as shown by Wood (fig. 67.3, 1809). A recent example by B,rtschi (fig. 67.4, 1976) confirms that rooms in perspective texts continue to reflect the taste of the day.
Quadratura
There were particular problems involved with paintings on ceilings seen from below (di sotto in su). Again, artists, such as Mantegna (fig. 70.2), had mastered the difficulties in painting practice, long before they were discussed in treatises on perspective. Indeed, the first discussion occurred in Danti (1583), who distinguished between flat and concave ceilings, and cited a number of examples, such as Vignola at Caprarola (fig. 72.2, cf. 72.1), Giovanni Alberti dal Borgo in the Palazzo de Mattei, and Tomaso Laureti in the Bolognese palace of Signore Tasonne and Signor Pompeo Vizani.36 The same year as Danti, there appeared in Vienna an extraordinary collection of 75 examples of such ceilings by Has (fig. 73.3, 1583). Vredeman de Vries (1604), offered examples both of scenes seen from below and scenes seen from above (di su in sotto, fig. 72.1), again without explanation. The Jesuit, Dubreuil (1642-1649), was among the first who set out to clarify the principles involved. Another member of the order, Pozzo, used his practical experience in painting the ceiling of Il Ges_, in Rome, as a starting point for explanations, in his famous Perspective of artists and architects (figs. 73.1-2, 1693-1700). In the course of the eighteenth century, such explanations became a common theme, particularly in perspective treatises associated with architecture such as Decker (1711), Bretez (1751) and Kirby (1755). The continued fascination of such problems in our century is witnessed by Escher (fig. 73.4 cf. 73.3).
Columns
The five orders of columns were probably the most popular architectural theme in the perspective treatises. It evolved in the early fifteenth century as part of a growing interest in the measurement of Roman antiquities. Manetti, for instance, recorded how Brunelleschi and Donatello together:
made rough drawings of almost all the buildings in Rome and in many places beyond the walls, with measurements
According to Manetti, Brunelleschi and Donatello were the only individuals interested in these problems at the time.38 But this soon changed. Starting with Piero della Francesca (c. 1484), columns also became a topic in treatises on perspective. Following the rules of Vitruvius and Alberti, Piero was concerned specifically with a Roman Corinthian column, which he illustrated with four diagrams of bases and three of capitals. Francesco di Giorgio Martini, in his Codex Saluzziano, which also dealt with perspective, included a number of drawings of columns and bases.
Meanwhile, Vitruvius offered a framework for a more systematic study of columns, as witnessed by the editions of Fra Giocondo (1511), Cesariano (1521), Caporali (1536) and Ryff (1547). By the 1530's, artists such as Peter Fl"tner, Jacques Prevost, Sebastiano Serlio and Agostino Veneziano were producing engravings of ancient bases, columns, capitals and architraves. These were sometimes bound together in haphazard fashion, as in a Wolfenbttel volume entitled 93 engravings with studies of columns (1540): cf. a Washington volume by Androuet Du Cerceau (1580?). Inspired by Vitruvius, Serlio organized his material in a treatise specifically devoted to the five orders of columns entitled General rules (1537). This was soon translated into Dutch by Pieter Coecke van Aelst (1539), and was integrated as book four of Serlio's works of architecture.
In Switzerland, this idea of a specialized treatise devoted to the five orders of columns was pursued by Blum (1550), whose work went through various editions (e.g. 1596, 1627, 1635, 1674) and served as the basis for later treatises by Kaessmann (1630) and Erasmus (1667). Blum's illustrations combined geometrical ground-plans and perspectival elevations (e.g. 44.1). The most popular of all works on columns was Giacomo Barozzi, il Vignola's Rules of the five orders of architecture (1563), later versions of which stressed the use of perspective in the form of shades and shadows, with editions in Italian (1808, 1814, 1818, 1831, 1832, 1850); French (1786, 1823, 1827, 1828, 1857, 1865, 1897), and English (1902, 1905, 1910, 1912, 1923, 1931, 1940). This aspect was also stressed in a treatise by Hondius, where the columns were rendered in perspective by Vredeman de Fries (1617, 1620, 1628, 1638).
In addition to these specialized treatises, columns featured regularly as a theme in perspective treatises. For instance, Jean Cousin (1560) provided full page illustrations with a geometrical and a perspectival ground plan as well as combined perspectival views for each of the five orders. Barbaro (1568), who preferred to illustrate elements such as bases, capitals and architraves individually, devoted 21 diagrams to the subject. A shorter treatment occurred in treatises by Danti (e.g. fig. 82.5, 1563), Vasari, Jr. (1595) and Sirigatti (1596). Fascination with the perspectival effects of columns continued throughout the seventeenth and eighteenth centuries. Sometimes, as in the case of Nic,ron (fig. 44.2, 1646), this occurred as a chapter in a more general treatise on perspective. Alternatively, as in the case of Viola-Zanini (1629), Bosse (1664, 1684) or Bosboom (1686), a specialized treatise on the architectural orders was involved.
Illustrations varied considerably. Bosse (1664) produced geometrical ground- plans and elevations, which he combined with their perspectival equivalents (fig. 44.3). His opponent in the French academy, Gr,goire Huret (1678) preferred a more abstract approach with multiple views of a given object (fig. 45.4). Pozzo (1693-1700) was considerably more systematic. He related geometrical ground-plan and elevation, perspectival ground-plan and elevation along with a perspectival view of the appropriate part of a column or architrave (figs. 45.1-2). The clarity and elegance of Pozzo's approach made his text one of the most influential works of the eighteenth century (e.g. 1702, 1708, 1711, 1717, 1737, 1758, 1764, 1800, 1810). Also popular was Schubler (1719, 1732, 1735, 1749, 1758). Authors such as Bretez (fig. 44.4, 1751) provided illustrations from unexpected points of view, but added little in terms of method. Eighteenth century treatises characteristically gave both abstract and realistic versions of various parts of columns, as in Jeaurat (1750, 1760, 1770) or Kirby (fig. 45.3, 1755-1761). By contrast, early nineteenth century authorsn, such as Edwards (1803-1805) preferred to emphasize only abstract essentials. Specialized treatises on columns continued until about the middle of the nineteenth century, e.g. Lagardette (1797, 1823, 1833, 1835, 1851, 1853), Nicholson (1834, 1839) and Rebout (1845), but it continued in reprints of Vignola, in general treatises, and other genres of architectural treatise.
Ruins
As noted above, the study of columns was but one manifestation of a larger concern with ancient monuments which began with Brunelleschi and Donatello and, for which, Alberti's Description of the city of Rome (1430-1440) offered a methodical approach. Even so, systematic treatises were not immediately forthcoming. Francesco di Giorgio Martini's Codex Saluzziano included a number of monuments in no particular order as was also the case with Bramante (c. 1495-1500), Maarten Heemskerck (1532-1536), Francesco de Hollanda (c.1538-1539), and even Serlio (1545-1547), the first published treatise to include ruins, which also dealt with perspective. In exceptional cases, an author such as Cousin (1560), would include examples of ruins in a treatise on perspective. But unlike other themes which became part of the ordinary repertoire of these treatises, ruins effectively became an independent genre from the outset.
Androuet Du Cerceau (1545 etc.), was among the first to publish books which specialized in perspectival ruins. These works in Orl,ans and Paris were soon complemented by De Jode (1550), Cock (1551) and Vredeman de Vries (1560) in Antwerp; Pittoni (1551) and Palladio (1554) in Venice and Labacco (1550) in Rome. In the next generations, with Lafr,ry (1575), Du Perac (1575), Cartaro (1578), Stevens (1600) and Maggi (1601), Rome became and remained the centre for this genre of views (vedute). The illustrations in these books went in two different directions. One was archaeological in spirit, increasingly treated the ruins as objects to be recorded for their own sake, and led via Heemskerck, Francesco de Hollanda and Cock, to Du Perac (fig. 59.1, 1575), Stevens (fig. 85.1, 1600), and eventually to Piranesi (fig. 59.2, 1750), whose work has rightly been compared with actual photographs of the scenes (fig. 59.3). Another strand had little interest in the ruins for their own sake, but used them as a springboard for the imagination (fig. 89.1-4), which led not only to idealized ruins (see below 2.4), but also dovetailed with a more general theme of idealized buildings.
Idealized Buildings
There was a natural link between perspective and idealized buildings for the simple reason that such buildings conformed more readily to the systematic geometrical grids imposed by perspective. As we have shown (see above p. ) such buildings were there from the outset. They dominated Bellini's Sketchbooks (figs. 6.1-2, 9.3-4, 11.2, 82.1), and in painting practice, as characterized by the Baltimore, Berlin and Urbino (fig. 96.3) panels. But these were exceptions in the early period. Even in the sixteenth century interest in the theme varied enormously. In Germany, for instance, where the emphasis was on individual objects, particularly regular solids, such idealized buildings were rare, although authors such as Lencker sometimes included an architectural example, as if it were a variant of the semi- regular solids.
In the course of the sixteenth century, throughout Europe, and particularly in Italy and the Low Countries, the Vitruvian tradition played a significant role in the development of this theme, commentators providing their often phantastic reconstructions of ancient and contemporary buildings, notably Cesariano (fig. 80.2, 82.1, 1521), who directly influenced Caporali (1536) and Ryff (1547). Even more seminal was the work of four individuals: Serlio, Palladio, Androuet Du Cerceau and Vredeman de Vries. Some of Serlio's examples were almost certainly connected with his interest in scenography, and included idealized buildings with colonnaded archways (fig. 82.3), as well as rows of buildings. Others served as instances of his architectural drawing methods (fig. 84.1). However, the majority of examples occurred in his other books in architecture, rather than in his second book devoted specifically to perspective. These included idealized ancient and contemporary buildings, both churches, such as Bramante's Tempietto (cf. fig. 96.4-5), and contemporary Venetian palaces and villas. Palladio took these themes considerably further, particularly in terms of existing and planned country villas. His systematic approach relating ground-plans, elevations and perspectival views made his work a classic which became all the more influential because it was subsequently adapted and transformed to suit English, French and other national tastes.
Androuet Du Cerceau's collections of engravings provided a new repertoire of both idealized Roman ruins (fig. 9.1, 11.1, 86.2-5, 97.1) and contemporary buildings, some real, such as Bramante's Tempietto (fig. 46.5), some purely imaginary (fig. 29.3). His work on the most excellent buildings of France (1576-1579), gave versions of the great chateaux such as Annecy, Chenonceaux and Fontainebleau, which were a curious mixture of fact and fancy. The collections of Vredeman de Vries were also in this tradition, but with a greater emphasis on the imagination, visions of possible architectural environments, rather than careful records of existing ones (figs. 15.4-5, 87.1-2).
As in the case of ruins, this repertoire of images of idealized buildings went in two quite different directions during the seventeenth and eighteenth centuries. On the one hand, it led to ever more realistic chateaux and buildings, such as P,relle (1660), and eventually to photographs of famous monuments. On the other hand, it led in a utopian direction with authors such Perret (1601 etc.) who produced extra- ordinary edifices and towns in a roughly parallel perspective, or later designers such as Decker (fig. 93.2, 1711), who gave artists' conceptions of possible buildings appropriate for potentates and the like. Idealized buildings also remained on theme in treatises on perspective such as Dubreuil (1642-1649), a tradition which continued into the nineteenth century (fig. 62.1), although the interplay between ideal and real elements became ever more subtle (figs. 62.2-3, see below 2.4).
Towns As mentioned earlier (p. ), views of towns became a regular feature in the backgrounds of fifteenth century paintings. By the sixteenth century, these came into the foreground, as with the views of Innsbruck attributed to Drer (figs. 60.1-2). The treatise attributed to Rodler (1531), was one of the first to include such townscapes in a work on perspective (fig. 60.3-4). Military interests also played a role, spies being sent out to sketch a town about to be attacked (fig. 58.1, cf. 58.4), as did documentary concerns: artist's sitting in church towers to make views of battles serving as the sixteenth century version of reporter's cameras. These concerns aside, in Italy, with the exception of views of Rome such as Ferrario (166_), there was little interest in this theme. In France, P,relle (1666_) published a collection of views of Paris, chateaux of France and views of Rome.
In Britain, during the eighteenth century, this theme became more important. Buck (1736) published proposals for six perspective views of Canterbury, Rochester and Chicester and in the next decade (1745?) of York and the towns of Leeds and Wakefield. Smith (1750) published perspective views of the chief towns in County Cork. Anonymous views of Oxford (1753) and Shrewsbury (1756) also appeared. In the nineteenth century, views of towns became a regular feature of treatises on perspective. Sometimes, as in the case of Edwards (1805), this involved more than one view of some city (fig. 64.1) or of buildings encroaching into a landscape (fig. 65.2). Sometimes, as with Wood (1809), fashionable views of London were involved, including Portland Place and Hill Street, (fig. 65.1, 3). Authors such as Tilscher (1865) provided a series of views of a given park (fig. 65.4-5). In the twentieth century there has been at least one book, Vlaardigen (1967) devoted specifically to the problem of drawing townscapes.
Landscapes
In many treatises there was no clear separation between townscapes and landscapes, as is vividly illustrated in the treatise by Edwards (1805). His engraving of houses on a hill (fig. 65.2), with its division down the middle, could be seen as a townscape on the left and a landscape on the right side. Indeed, most of Edward's illustrations involved architectural features positioned with varying degrees of prominence within a landscape (figs. 62.1-3, 63.1-3, 64.1), such that clear boundaries between townscape and landscape disappeared. This ambiguity had, in a sense, been present from the outset. Already in the sixteenth century, when authors put their buildings into context (fig. 61.3), or when Du Cerceau did so with his chateaux, the same ambiguity occurred. It arose also in connection with themes such as reflection, as in Dubreuil (fig. 50.1-2), or Robert (fig. 51.3-4), where town and country frequently appeared together.
In the latter eighteenth century, landscape gradually emerged as an independent theme through individuals such as Werner, who extended the application of perspective to various aspects of the organic world: flowers (1765), four footed animals (1768) and humans (1768), as well as landscapes (1768) and views (1781). In the nineteenth century, Basoli (1810, 1830) made a collection of landscape views (paessaggio). In England, landscape often entered into the titles of treatises such as Orme's (1801) Rudiments of landscape drawing, or Noble's (1805) Practical perspective exemplified on landscapes. Subsequent examples included Wood (1814), Varley (1815), Nicholson (1820, 1823), Fielding (1839, 1852), Robert (fig. 51.3-4, 1895) and more recently, Vanderveken (1950).
Gardens
The theme of gardens was closely related to landscapes and in the sixteenth century overlapped also with other themes, such as ruins and idealized buildings. Androuet Du Cerceau, for instance, sometimes included reconstructions of ancient gardens in his views of Roman ruins (fig. 92.1) and, in like manner, included contemporary gardens in his views of modern chateaux and palaces. Vredeman de Vries was the first to publish collections of perspectival views of gardens (fig. 92.2), some of which involved adaptations of the five orders of columns (fig. 92.3). These prepared the way for an approach to nature as pure artifice, which authors such as Salomon de Caus completed, with the aid of automata, and other feats of engineering (fig. 98.1). Books on gardening from the seventeenth century onward frequently contained brief instructions concerning perspectival effects (see below 2.3).
It was not until the eighteenth century that books concerned with perspectival views of specific gardens emerged in England, as for example, Serle's (1745) plan of Mr. Pope's garden, Chatelain's (1753) views of the buildings and gardens at Stowe or Chambers' (1763) views of Kew Gardens. The nineteenth century added books specifically devoted to creating perspectival gardens such as Vergnaud (1835) or Glindemann (1900).
Nature
Landscapes and gardens were in turn related to the theme of nature, which became a regular feature of treatises during the nineteenth century. Sometimes, as in the case of Nicholson (1820, 1923), the title referred explicitly to drawing and painting landscapes from nature. Frequently the reference was to nature in general, as in Th,not (1826, 1829), Krane-Matena (1840), Locock (1852) or Nicholls (1858). The influence of drawing academies and conflicting philosophies with respect to drawing instruction in schools, gave new connotations to nature (see below 1.4). For instance, some thinkers held that model drawing was a first step to drawing from nature. Others acted, as if nature involved drawing from artificial models of nature, more than actually drawing from life. Still others, such as Rosenbeck (1895), saw drawing from nature as a simple alternative to memory drawing.
In addition to the above themes there were different categories or branches of perspective which served as topics in the treatises, many of which subsequently evolved into independent genres of literature. These involved three sub-categories:alternative picture planes, technical applications and special effects, each of which will be considered in turn.
Alternative picture planes: Anamorphosis
In linear perspective the picture plane is usually parallel with the plane in which objects are situated. In cases when objects are at right angles to the picture plane distortions occur. When done deliberately, as with the skull in Holbein's Ambassadors, the effect is termed anamorphosis. Seventeenth century authors used this term in a more general sense to include deliberate perspectival distortions produced by alternative picture planes, particularly cylindrical, conic and spherical ones.
In the early treatises, anamorphosis was a topic specific to Italian texts. Piero della Francesca introduced it (c. 1480), with his famous example of an egg which became a sphere when viewed from below, as in his Brera altar. Leonardo da Vinci took up this theme in both the Manuscript A and Treatise of Painting. Even so, a clear knowledge of the principles cannot have spread quickly, for Barbaro (1680) continued to discuss it in a veiled manner in a chapter entitled: "a beautiful and secret part of perspective."39 Danti (1583), by contrast, gave clear descriptions of two basic anamorphic tricks.40 One, which may have been invented by Leonardo, involved the parts of a portrait being spread out on one surface of a series of triangular slats tilted such that the portrait could only be recognized when viewed in a correctly positioned mirror.41 The second case considered by Danti (1583), involved the face of a man which was greatly extended horizontally along the side wall of a peep show, and required that one viewed it from the side in order that it again appear normal. Anamorphic effects produced by a reclining human body have already been mentioend earlier under the theme of the human form, and were explored by the author of the Codex Huygens (fig. 70.4, 1560-1580), Cousin, le jeune (fig. 70.3, 1595, etc.), Carlo Urbino (fig. 70.5), Dubreuil (1642-1679) and Houten (1701).
In the seventeenth century, Marolois (1614-1617) explored the effects of alternative picture planes, notably cylinders, V shapes and inverted V shapes. Vaulezard (1630) began a more systematic study of anamorphic effects produced in cylinders and cones. The Jesuits were fascinated by these problems as a manifestation of God's subtle laws of nature and for didactic reasons. Accordingly, Nic,ron (1638), wrote a first treatise devoted specifically to anamorphosis. His contemporary, Father Dubreuil, (1642-1649), popularized these findings in his textbook, as did the later Jesuit, Father Pozzo (1693-1700).
Aside from new gadgets to produce some of these effects mechanically by Leupold (1713) and summaries in encyclopaedias, such as Martius (1797), the eighteenth century added nothing to the topic. Indeed the principles involved were increasingly discussed in separate publications devoted to conic, cylindrical and spherical perspective.
Conic Perspective
Ptolemy used conic projections in his Geography (fig. ), a theme which Schubert (1784) pursued and which has continued to interest twentieth century thinkers such as Arden- Close (1925). Vaulezard (1630), the first author to devote a treatise to the subject, began a tradition of discussing conic and cylindrical projection in tandem, which continued with Le Poivre (1704), Morton (1830), in the context of descriptive geometry with Leroy (1834, 1837, 1846, etc.) and more recently with Ridderhof (1925) and Giovanardi (1934). The topic was implicit in more specialized treatises on conic sections by Pascal (1640), La Hire (1673) and others.
Since the late nineteenth century, there have been several French authors who have written specifically on conic perspective, namely, Lebon (1887), Aubert (1895), Raull (1921), Faling (1955) and Fradin (1966, 1980). But the topic has held most fascination in Spain with works by Robira y Rabassa (1910), Adroer (1953), Perez Asensio (1964), Carreras Soto (1960, 1975), Sandoval Guerra (1967), Bonet Minguet (1968, 1979), Martinez La Madrid (1968), Corbella Barrios (1968), Fuentes Alonso (1973), Grajales Carbonnel (1977), Lopez Gonzalez (1962) and Martin Morejon (1983). Meanwhile Adams (1976) has explored a method of tetraconic perspective to approximate visual perception.
Cylindrical Perspective
In cartography, Mercator initiated a serious interest in cylindrical projection (fig. ). However, for many authors on perspective, optics provided the first incentive to studying this alternative, namely, concern with producing a picture plane equidistant from the plane of vision. Leonardo explored this problem in Manuscript A and elsewhere in his notebooks, which subsequently inspired the author of the Codex Huygens (1560-1580) and Cardi (1612). In seventeenth century France, Vaulezard (1630, etc.), explored the anamorphic potentials of cylindrical perspective, a theme which Dubreuil (1642-1649), pursued. Bosse (1643, 1653, 1660, etc.), on the other hand, was more concerned with distinguishing between cylindrical projections, which he associated with vision, and the plane projections of linear perspective.
In the eighteenth century, Pozzo's influential treatise focussed interest back to anamorphic aspects of the problem. The nineteenth century saw examination of geometrical aspects, in the context of descriptive geometry, by authors such as Leroy (1834, etc.) and Bailby (1976), as well as a renewed interest in optical connections through authors such as Herdman (1853) and Ware (1882, 1883, 1894, 1895, 1900, etc.). The twentieth century has seen continued interest in cylindrical perspective by Garnier (1934) and Hammerschmidt (1940), with short sections in treatises on perspective of Abbott (1950) and Vero (1978).
Spherical Perspective
Sixteenth and seventeenth century treatises on perspective almost always avoided questions of spherical perspective, except in connection with astrolabes (see below p. ), but by the eighteenth century this theme emerged with respect to projection problems in astronomy and geography with contributions by Karsten (1768, 1773), Wright (1772), Kautsch (1784) and Schubert (1784, 1788, 1789, 1790) and later by Germain (1866). In the nineteenth century, spherical projections were subsumed as a branch of descriptive geometry by Davies (1826, 1832, etc.), Lacroix (1840), Leroy (1850) and Church (1868, etc.).
In connection with optics, there has been some confusion between spherical and cylindrical perspective, the sphere of vision frequently being represented simply as a circle equidistant from the eye. This confusion led Drer (1525), for instance, to adopt his method of negative perspective, whereby objects further from the eye were represented as larger in order that their apparent size remain constant. Serlio (1545) took up this principle, as did Barbaro (1568) and thereafter it became a commonplace in both treatises on perspective and architecture (cf. fig. 2.1). In the nineteenth century, Hauck (1879), believed that the subjective curvatures of Greek architecture corresponded to spherical theories of vision. These possible links between architecture and optics were also touched upon by Maertens (1884) and taken up seriously by Borissavlievich (1921, etc.), who gradually evolved a personal theory of spherical perspective with respect to architecture.
Connections between spherical projections and optics also arose from unexpected quarters such as landscape gardening. Seventeenth century authors, such as Tacquet (1668, etc.) had suggested that trees should be planted in rows of half hyperbolas in order to appear parallel. This problem was taken up by an anonymous author (1719) and Varignon (1720), only to be challenged by Bouguer (1755). Debates concerning curvature of parallel rows continued in the twentieth century with experiments by Hillebrand (1902), Blumenfeld (1913) and Luneberg (1947). In the nineteenth century, Helmholtz (1866, 1896), developed a new demonstration involving a curved checkerboard to illustrate subjective curvatures. Two other important demonstrations evolved: one using the vault of the heavens, e.g. Reimann (1890-1891) and Zoth (1899), the other using the apparent bending of light from lighthouses on the horizon, e.g. Bernstein (1904).
The twentieth century has seen an increasing interest in relating spherical projections of optical theories with painting practice. Deininger, in a lecture to the central organization of Austrian architects on 15 August 1914, outlined what he believed was a new theory of artistic painters' perspective, and its practical results, in which he claimed that:
only (on such) a spherical surface is it possible to represent graphically all those lengths, i.e., all the
In New Hampshire, an artist and a physicist, Ames and Proctor (1921) did experiments together:
for the purpose of determining the exact nature of the image received by the human eye in the belief
Birker (1923), took out two patents for a mechanical means of producing spherical perspective. Stark (1928) and Hegenwald (1932), wished to use the spherical surface of the retina as the basis for their theories of spherical perspective, but were hesitant in their application thereof. An important book, in Canada, by Jobin (1932), argued that with the development of skyscrapers one needed to apply perspective to the vertical as well as the horizontal axis. In part two Jobin set out:
to show that the curved line, determined by the principles of the optical sphere, today constitutes a theory
He illustrated his theories with an impressive series of illustrations using a four point, spherical perspective. Similar ideas were explored two years later by Garnier (1934) and Serrano (1934, 1952). These works were virtually ignored, however, and it was over a decade before a next wave of interest was initiated, this time largely by architects, i.e. La Grassa (1947), Giorgi (1947), Mohrle (1949) and Zanetti (1951) and an opthalomologist, Graf (1949). These again had no sustained impact. Another decade passed before the matter was taken up afresh by Barre and Flocon (1962, 1964, 1968). This work excited more attention and was eventually translated into German (1983), Spanish (1985) and English (1988).
During the 1970's problems of spherical perspective inspired the imagination of American artists. Hansen (1973), who has since translated Barre and Flocon into English, developed a five point spherical perspective, which he termed hyperbolic linear perspective. Independently, Termes developed 4, 5 and 6 point spherical perspective methods (fig. ). Turner (1976) and Casas (1983) developed alternative methods to accommodate the complexities of visual perception. A recent exhibition by Marcia Clark (1988) attests that a number of artists, notably Jacqueline Lima, have been developing their own empirical methods. At the same time there have been developments elsewhere. In Buenos Aires, Reggini (e.g.1973) has written a number of articles on the problem. In London, Shaw (1977) has devoted an important thesis to spherical perspective. In Paris, Blotti (1986, 1987) has created a series of demonstrations including spherical and other alternative projection methods for the Mus,e des sciences et de l'industrie de la Villette. There have also been books by Elias (1973), Fuentes Alonso (1975), and Bonbon (1983). Indeed, these interests are leading to new links between objective and subjective elements (see below pp. ).
TECHNICAL APPLICATIONS
Various methods of parallel perspective were developed for military purposes and different types of technical drawing (e.g. geometrical, linear, machine, etc., cf. 1.4 below). These methods included cavalier and military perspective, orthogonal or parallel perspective, cabinet perspective, axonometric perspective with its three branches, isometric, dimetric and trimetric, and multiview perspective. Because a number of these distinctions only emerged in the twentieth century, historical discussion thereof must be approximate.
Cavalier and Military Perspective
Today, cavalier perspective is defined as a dimetric projection and distinguished from military perspective which can be either dimetric or trimetric (cf. above, p. and fig. ). In the sixteenth century, these distinctions were not made. Military perspective was an ambiguous term. On the one hand, it could refer loosely to presentation drawings designed to impress patrons by artist engineers such as Francesco di Giorgio Martini and Leonardo da Vinci. This led to commemorative paintings of battles such as those of Giorgio Vasari in the Palazzo Vecchio, books with elaborate military drawings, such as Perret (1601, 1602) and a tradition of military examples in regular treatises on perspective such as Androuet Du Cerceau (1576), Marolois (1614) and Dubreuil (1642-1649). On the other hand, it also referred to simplified methods adapted for military purposes, as outlined by Cataneo (1567), or Specklin (fig. 58.4, 1589). At the turn of the seventeenth century, Romano (1595), Hulsius (fig. 58.1, 1605), and Faulhaber (1610) adapted the perspectival window for these purposes. But in the heat of a battle there was frequently not time for even these methods. As a result, practitioners developed rough and ready methods of parallel perspective, technically inaccurate, yet sufficient to convey essential information concerning a site.45
It was particularly in France that these new methods evolved, heralded by practical theorists such as H,rigone (1634, 1642). Bourdin (1635), was the first to devote a published treatise to this new kind of military perspective and the Jesuit, Dubreuil soon incorporated it as an appendix to the second edition of his influential Practical perspective (1663). The following year analogous methods were outlined by Luders (1664). In the mid eighteenth century, Dupain de Montesson, wrote a basic treatise which related military perspective directly to professional surveying and drawing techniques (1750, 1760, 1712, 1790, 1799, etc.), followed by The art of drawing up plans (1763, 1792, 1804, 1811) and a text for officers (1774). Other treatises were by Dupuis (1773), Keller (1856) and Philibert (1898).
The nineteenth century brought a number of works which related cavalier perspective to axonometric and isometric perspective, including Adh,mar (1852, 1866, 1875), an anonymous author (1867), which have continued in our century with Corsanego Wauters-Horcasitas (1926), Labalette (1927), Bonet Minguet (1944), Gomes de los Reyes and Cano de la Torre (1966) and Alonso Misol (19__). Breithof (1881, 1905), in his treatise on cavalier perspective, compared the advantages of linear perspective to those of orthogonal projection methods. Authors who wrote specifically on cavalier perspective included Ciani (1900, 1903), Darcheville (1914), Carreras Soto (1943), Breton (1970) and Garcia Gutierrez (1970).
Orthographic Perspective
The evidence of the early treatises suggests that orthographic or parallel perspective began less as an alternative, and more as a complementary method to linear perspective, particularly in the case of complex organic objects for which a simple ground plan and elevation did not suffice. Piero della Francesca (c. 1480) and Leonardo da Vinci (e.g.W 12605r, c.1490-1492) used it in their representations of human heads. Gauricus (1504) used a variant. These principles were adapted by Drer (fig. 68.1, 1525) and further standardized by Barbaro, (fig. 68.2, 1568). These principles were then extended to the entire human body by Cousin, le jeune (fig. 70.3, 1595, etc.) and Carlo Urbino (fig. 70.5,c.1580).
However, it was not until the mid-eighteenth century that thinkers in London began to describe orthographic perspective as an independent method. Emerson (1749, 1769), for instance, consciously compared orthographic, stereographic and gnomonic projections. Walker (1777) wrote one of the earliest treatises devoted specifically to this method. In the mid-nineteenth century, Binns (1857, 1961, 1863, etc.), produced a standard textbook on orthogonal perspective which went through thirteen editions by 1899. Other authors included Bradley (1861, 1862), Davidson (1868, 1873), Plunkett (1885) and Carroll (1888). In Germany, there were some works on orthographic perspective, e.g. Gerke (1881), Kr"ger (1911), cf. Fliesen (1877, 1880), Reutter (1948); as was later the case in Italy, with authors such as Monti (1900), Magri Tilli (1967), Mondino (1968) and Bartoli (1975). In France these problems were usually classified under descriptive geometry (cf. fig. ) and drawing (dessin). In the United States, works entitled orthographic perspective were also the exception, e.g. Church (1911) or Ashley (1975), the topic usually being dealt with in various types of drawing books: geometrical, industrial, linear, machine, mechanical, etc.
Parallel Perspective
Raverta (1627), was probably the first to refer to parallel lines in connection with perspective in the title of a treatise. Even so, it was not until the mid-nineteenth century that German publications in Czechoslovakia referred specifically to parallel-perspective, e.g. Schnedar (1856, 1864) and Skuhersky (1958). The term soon spread to Austria with Klamminger (1865) and Barzala (1882) and Germany, where it was used by a number of authors including Mller (1865), Koutny (1867), Delabar (1870, 1888, 1893, 1907), Hauck (1888), Freyberger (1897, 1899, 1903), Hertzer (1902), Papperitz (1906), Vonderlinn (1920), Brunschwiler (1939), Mayer-Sidd (1940) and Schumacher (1951). In the United States, there were some publications under this title by Noble (1886), Cooper (1900), Adler (1912) and Koller (1940). Elsewhere there were works by Werner (1904, 1908, 1915, 1923, 1930, 1935) and Lagerquist (1963) in Sweden; Ridderhof (1913, 1918, 1925) and Keulen (1957) in the Netherlands, andKirchmayr (1935) in Italy.
Axonometric Perspective
Awareness that parallel perspective might be further divided began in the eighteenth century with preliminary distinctions between parallel, and military or cavalier perspective. The nineteenth century gradually brought formal distinctions. For instance, the term axonometric perspective made one of its earliest appearances in a bilingual title of a work by Engel (1854) in Berlin. Other German authors soon took up the term including Meyer (1855-1863), Weisbach (1857), Largiader (1858), Schmidt (1859), Hertel (1862), Weishaupt (1863), Sellar (1865), Butz (1870), Pelz (1870) and Beyel (1887). This trend has continued in our century with Vonderlinn (1905, 1920) who distinguished between right-angled (i.e. isometric) and oblique (dimetric, trimetric) axonometry; Schssler (1905), Papperitz (1906, 1916), Haase (1907), Meyer (1922), Pechwitz (1950), Berns (1962, 1968) and Thomae (1976).
Use of the term was by no means restricted to Germany. It soon spread to Italy with Sella (1861), where there have been works since by Capelli (1905), Tomasinni (1943), Roversi (1945, 1948, 1949, 1952, 1954), Calloni (1948), and Aterini (1980). It reached England through an article in the Athenaeum (1865). In the next decades it spread to Sweden with Bergh (1872), the Netherlands with Versluys (188 ) and later Thiel (1913) and Reynders (1951), as well as Denmark with Seidelin (1890) and Gjerding (1967), and Spain with an anonymous author (1867), Valenzuela (1896), Corsanego Wauters-Horcasitas (1926), Bonet Minguet (1944) and Garcia Gutierrez (1979). In the twentieth century, there have been further authors in Poland, Plamitzer (1925), Piotrowski (1956), Lange (1962) and Lewandowski (1973); the United States, e.g. Roever (1941) and Bartholemew (1944); Finland, Nystrom (1943) and Kivela (1979) and Portugal, e.g. Aires de Silva (1945).
In addition to these texts where axonometric perspective was specifically mentioned in the title, there were numerous other works on drawing, architecture and mathematics which dealt with these problems. Axonometric perspective was, in turn, subdivided into three branches: isometric, dimetric and trimetric perspective (cf. above p. and fig. ). In Britain, during the second world war special templates were used to produce these variants. While all three branches were discussed in books, only the first of these, namely, isometrical perspective inspired an independent literature.
Isometrical Perspective
The term isometrical perspective emerged some three decades before axonometric perspective which was subsequently to become the more universal term. Isometrical perspective was developed as a formal method by Farish (1821, 1923) as a means of best conveying information about models of the more important machines used by British manufacturers at the time.46 In the decade that followed his ideas were spread by Bradley (1831), Jopling (1833, 1834, 1835, 1839, 1842) and Sopwith (1834, 1836, 1838), and were subsequently taken up by other English authors, including Heather (1851), who related isometrical perspective to Monge's descriptive geometry, Burn (1853, 1855), Atkinson (1860), Binns (1864), Davidson (1868, 1873), Spriggs (1871), Spanton (1895), Middleton (1919), who applied it to architecture and Parkinson (1953). Through the Oxford press, there was also a work by Dean (1933) in Australia. In Europe, isometrical perspective made no dramatic impact as an independent topic. Nonetheless, there were authors such as M"llinger (1840) in Switzerland; Adh,mar (1852, 1866, 1875), Car,nou (1880) and Labalette (1927) in France; an anonymous author (1867) in Spain; Versluys (188_) in the Netherlands, as well as Schmidt (1888), Grimshaw (1902) and Vogel (1902) in Germany.
In the United States, by contrast, isometrical perspective inspired more interest than anywhere else. At the outset this was sparked by authors concerned with drawing, notably, Minifie (1849, 1851, 1855, 1857, 1868, 1873, 1875, 1877, 1882, 1890), Appleton (1857, 1862, 1864, 1866, 1869), Beard (1858) and subsequently Klein (1869), Palmer (1894), Jamison (1911), Jameson (1932) and Locke (1981). But as early as 1860 Warren sought to put this discussion in a wider mathematical context as suggested by his title: General problems from the orthographic projections of geometry with their applications to oblique - including isometrical - projections, graphical constructions in spherical trigonometry, topographical projection and graphic transformation. The relationship between descriptive geometry and isometrical perspective was next considered in an influential work by Church (1864, 1865, 1867, 1868, 1870, 1875, 1877,1892, 1911), and later by Randall (1905) and Bartlett (1911). Others, such as Comfort (1874), were content to discuss its connections with projections generally, while Richards (1903), was concerned merely with showing that this branch was the only practical perspective.
Multiview Projection
Axonometric perspective, and its branches (isometric, dimetric and trimetric), assumed that the objects considered were in some way oblique or tilted in relation to the picture plane. In multiview projection it was assumed that the face(s) of the objects were parallel to the picture plane. In Britain, these methods were typically discussed in works on practical geometry or machine drawing, such as Abbott (1930). In the United States, by contrast, these problems were usually considered in works on machine drawing, solid geometry or more general works on drawing or architectural drafting such as Weidhaas (1981). The solutions reached also differed widely. In Britain a preference evolved for first angle projection (fig. ), which could be seen as almost a direct development of the picture plane tradition (figs. 30-31), or Pozzo's methods in architecture (fig. 45.1-2), i.e., a looking out at projections on planes beyond the object. This method of first angle projection was accepted as a standard by the British Standards Institution in 1927 (Report No. 308). Meanwhile, American texts favoured third-angle-projection, i.e., a method of looking in at the projections of an object as if encased in a transparent plane (fig.** ). Although this so called glass box method was in common use by the First World War, it was not accepted as a standard until 1935.
Special Effects
Already in the fifteenth century, thinkers recognized that linear perspective alone could not achieve all the spatial effects of three-dimensional objects. Hence, Leonardo da Vinci, explored the role of colour perspective, aerial perspective and what he termed disappearance of form perspective. He also noted the importance of shading in creating contours and saw these effects of chiaroscuro or relief (relievo) as an extension of perspective. This later emerged as an independent topic of shades and shadows. In addition, Leonardo recognized that motion perspective was also important. Since most of these categories have developed an independent literature, each will be considered in turn.
Colour Perspective
In his Optics, Ptolemy (c. 150) referred briefly to an empirical use of colour by Roman artists in representing effects of distance.47 During the Renaissance, Fontana was the first to explore these principles in his now lost treatise, of which we have only a description by Pompilius Azalus:
From this natural experience, pictorial art took its optical rules as was described clearly in a book dedicated to Jacopo Bellini, the famous Venetian painter, and by which means he knew how to oppose dark and bright colours such that, by means of ratios, not only the raised parts of an image were seen depicted on a plane, but actually seemed to be seen extending beyond the hand or foot. And those things which were in the same plane of men, animals or mountains, by these means appeared to be distant by miles and so on. Indeed, the art of painting teaches that nearby objects should be tinged with bright colours, remote ones with dark colours, and medium range distances with mixed colours.48
In the period 1480-1518, Leonardo da Vinci explored the principles of colour perspective in his notebooks. Curiously enough, this theme was not taken up in published treatises during the sixteenth century. Zaccolini (c. 1600), who may have drawn on now lost works of Leonardo, devoted two manuscripts to problems of colour perspective.49 Accolti (1625), was one of the first to mention colour perspective in a published treatise. Even so, it was not until the turn of the nineteenth century that colour emerged as an independent category as indicated, for instance, in the title John Wood's (1799, 1801) treatise Elements of perspective, containing the nature and light of colours, or simply found in a chapter of Cloquet (1823).
Awareness of colour perspective went hand in hand with a growing attention to shades and shadows (cf. below p. ), as witnessed by Schrank (1812), Hummel (1830, 1842) and Delabar (1875), as well as colour itself by authors, such as Le Blon (172_, 1756, 1916), Schreiber (1868) and Bracquemond (1885), which led to a gradual distinction between coloured lights of optics and coloured pigments of painting. Since then Scharf (1949) has written on tensions between colour stereoscopy in vision and effects of drawing in linear perspective.
Authors who have written specifically on colour perspective include Roux de Valdonne (1898), Adam Leonard (1905) and Cloquet (1913). The last decades have also seen at least one important work in Russia, namely, Aksenov (1976), and increasing interest in the Far East as witnessed by Ota (1968), Yamasiro (1975) and Takahasi (1977) in Tokyo, as well as Wang (1977) in Hong Kong.
Aerial Perspective
Leonardo da Vinci (fl. 1480-1519), was one of the first to discuss aerial perspective at length. Even so, it was not until the latter eighteenth century, that this topic emerged as an independent category through the publications of Lambert (1776), Saint Morien (1779, 1788) and Casanova (1794). In the first half of the nineteenth century authors frequently referred to linear and aerial perspective in tandem in their titles, as with Valenciennes (1803), Clinchamp (1820, 1840), Vallée (1821, 1838), Isabeau (1827, 1832), Kercado-Molac (1932), Fielding (1836-1843), Laurent (1840) or Howard (1840, 1876) who reversed their order. Bayliss (1855) wrote more specifically on The elements of aerial perspective or light, shade and colour. Sutter (1858, 1870) wrote on the Philosophy of the fine arts applied to painting containing the aesthetics of aerial perspective. An author known only by the initials R.B. (1916) wrote on aerial perspective in relation to photography. Cole (1920) devoted a section of his textbook to the subject, while Baier (1955) wrote an entire book on it. Meanwhile the precise meaning of the term varied considerably as becomes clear when one compares various definitions given by authors of treatises. Brunel de Varennes (1830), for instance, claimed tersely:
We divide perspective into two principal sections. The first is linear perspective, the second
Vergnaud (1835), in his Manual of perspective, provided a more detailed and poetic distinction between linear and aerial perspective:
Perspective has as its goal to represent on one and the same surface the whole and details of
Brisson (1838) in his Theory of shadows and perspective which served as an appendix to Monge's Descriptive geometry saw this distinction in more clear cut ways:
As in the theory of shadows, one has to admit two distinct parts. The one is
purely geometrical
and its object is to determine in a precise manner on the canvas the position of
each point
that
is represented. The other has as its object a study of the tint of the shadow
and light which
one
needs to give to each part of the canvas, and it is by means of physical
considerations that
one
can deal with it in general. This latter part, which one designates under the
name of
aerial
perspective, enters wholly into the circle of studies, which we shall attempt to
expose later
to
complete the theory of shadows. Hence we shall occupy ourselves here only with
the first
part,
called, linear perspective.52
Jules de la Gournerie (1859), by contrast, associated aerial perspective with colour, and as something dispensable:
Perspective is the art of representing objects on a canvas while maintaining their appearance.
Just over a decade later, the Larousse encyclopaedia, in an article on drawing, cited the views of Delacroix on the subject (see below p. ), which attributed to aerial perspective a more fundamental importance. Brücke (1878) was of a similar view, but for different reasons, when he devoted a chapter of his Scientific principles of the fine arts to "Aerial perspective and the apparent size of objects,"54 his main concern being to relate it to problems of steroscopic vision. The Dictionary of pedagogy (1883) was, nonetheless, able to provide a simple distinction:
Linear perspective studies the reproduction of contours of objects. Aerial perspective is
Delaistre (1897), writing at the end of the century, was closer to La Gournerie's view that the distinction was between line and colour, although he decided that both should be dealt with:
Perspective, considered as a whole is the science, art of representing objects
onto a
surface
in accordance with their optical effects, that is, in accordance with the laws
of vision and
of
light, which means that one divides it into two classes. The one is what one
calls linear,
the
other is what one calls aerial. Linear perspective is made by lines alone.
Aerial perspective
is
made by the degradation of colours resulting from the greater distance of the
light, as well
as
from the greater distance of the objects, as well as the greater or lesser
intensity of the
vapours
which interpose themselves between the eye of the spectator and these same
objects.56
Chiaroscuro
Alberti mentioned colour perspective in his treatise, On painting, but concluded that the highest goal of art lies in knowing how to use black and white, because light and shade make things appear in relief.57 Piero della Francesca's definition of colour also referred to effects of chiaroscuro: "By colour we mean giving colours as they are shown in things, bright (chiari) and dark (uscuri) as the lights make them vary."58 Leonardo da Vinci pursued problems of chiaroscuro and relief, which he saw as an extension of perspective.59
Again, it was not until the end of the eighteenth century that this emerged as an independent category with Breysig's (1798) attempt to explain relief perspective. In the nineteenth century, the term, relief perspective, was more popular than chiaroscuro, and works were often addressed to a specific discipline: Amati (1840) and Berti (1841) to architecture, Burnet (1827, 1828, 1830) to painting; Noelli (1917) to sculpture, Poudra (1862) to theatre. More frequently, they were addressed to mathematics as with Anger (1834, 1836, 1840), Morstadt (1867), Tessari (1880, 1883), Vecchi (1891), Becchetti (1894, 1900) and Loria (1924). There were also a number of more general works, frequently with a mathematical slant, by Poudra (1860, 1866), Staudigl (1868), Burmester (1883), Cloquet (1913, 1934), Stuhlmann (1914), Berger (1944) and Steen de Jehay (1964, 1965, 1966).
Shades and Shadows
Although shades and shadows is listed as one of the offical subjects in the Library of Congress classification, its precise meaning is elusive indeed. One reason was etymological. Renaissance thinkers sometimes thought sciographia was synonymous with scaenographia with the result that shadows and perspective were sometimes treated as if they were interchangeable as in Piranesi's (178_) Sciographia of four old temples, or Puckett's (1808) Sciography or radial projection of shadows. Notwithstanding this tradition, systematic treatment of shadow in treatises on perspective evolved only gradually. Alberti (1434) mentioned shadows,60 but did not explore them. Leonardo da Vinci explored them in his Manuscript C (c. 1490), in a lost treatise on light and shade, and elsewhere. Dürer (1525) was the first to publish rough principles of shadow projection (fig. 46.1), which were taken up by Barbaro (1568) and Danti (1583) and thereafter became a stock theme in treatises on perspective.61 By the mid-seventeenth century the study of perspectival shadow included attention to objects in a room, as for example, in Dubreuil (fig. 46.3 1642-1649). These examples became increasingly subtle as seen in Huret (fig. 46.4, 1670), and by the early nineteenth century included veritable tour de force cases, as in Cloquet (fig. 47.3-4), which uncannily prefigures pointilist techniques by half a century. Meanwhile, corresponding attention was being given to complex arrangements of individual objects as seen in Highmore (fig. 46.2, 1764), or Cloquet (fig. 47.1, 1983), who was at pains to correlate the geometry of individual objects with views showing context. In the next generation, Gennerich (fig. 47.2, 1865), included penumbral effects.
While almost every treatise on perspective from the latter sixteenth century onwards included a brief chapter or section on shadows, more detailed studies emerged on at least three fronts. First, there were a number of treatises which made direct reference to the importance of shadows in their titles. Second, there were some books dedicated specifically to this theme. Third, there were a series of other books on shades and shadows which arose in the contexts of architecture, drawing and geometry. Each of these will be considered briefly.
Salomon de Caus' (1612), Perspective with an explanation of shadows and mirrors, was among the first treatises to mention shadows and mirrors in its title. In the eighteenth century, Hamilton (1738) pursued these themes in his Compleat body of perspective together with their projections on shadows and the reflections by polished surfaces, and it was developed in Clinchamp's (1826) New theory of perspective of shadows and theory of reflections for the use of artists. Thereafter, the twin themes of perspectival shadows and reflections were taken up by a series of authors, including Berg (1854), Smith (1857), Heyn (1885), Charles (188 ), Kleiber (1892), Crosskey (1901), Petty (1901), Fuchs (1902), Beuhne (1907), Swinstead (1907), Tagliavini (1910), Masriera (1912), Arjona Lechuga (1918) and Bonbon (1986).
More frequently, authors referred only to linear perspective and shadows in their titles, as in Ozanam's (1686) Theoretical and practical perspective and how to represent the shadows caused by the sun or a small light or Curel (1768). The nineteenth century saw a dramatic rise in such works including Richard (1828), Davies (1832) Treatise on shades, shadows and linear perspective, Francke (1836), Barnes (1842), Hummel (1842), Kempees (1846), Menzel (1849), Leve (1858), Warren (1863), Fliesen (1877) and Neel (1879). The 1880's brought at least seven new authors on this topic including Nielsen (1884), Böklen (1886), Chizzoni (1886), Lebon (1887), Hauck (1888), Gut (1888) and Kajetan (1888). The 1890's brought four new authors, Hill (1894), Freyberger (1897), Sparton (1898) and Willson (1898). In the first decade of the twentieth century, interest in this topic reached a peak with no less than eight further authors including Hertzer (1902), Johnson (1902), Lafarga (1902), Fernandez Casanova (1907), Haase (1907), Heubach (1908), Hauck (1910) and Spink et al. (1910). Thereafter interest faded temporarily, but since the 1930's there have been a series of further works by Giombini (1934), Erremes (1934), Brunschwiler (1939), Kirchmayr (1945), Pasman (1947), Pinheiro (1948), Holmes (1950), Nordlindh (1950), Parrens (1961), Boccaleone (1963), Geiger (1965), Fradin (1966, etc.), Carreras Soto (1967), Folina (1975) and Mondino (1976). While most authors have emphasized the relation of perspective to shades and shadows, some have discussed the problem in terms of lighting as, for instance, Schwedler (1852) in Practical introduction to making a perspective drawing and lighting of same; Rohn and Papperitz (1906) in Axonometry, perspective, lighting or Vries de Hecklingen (1907) in Teaching of projection and lighting.
The earliest manuscripts specifically on light and shade in connection with perspective were probably Leonardo da Vinci's (1490) Manuscript C and his now lost treatise. Theriaci's (1551) Discourse and explanation of shadows, may well have been the first published work on the subject. The seventeenth century brought several more works including a manuscript by Zaccolini (c.1600) On the description of shadows produced by rectilinear opaque bodies; an optical text by Maurolico (1612), often classed as perspective; Albrecht (1622) etc. who devoted the second of his two treatises on perspective specifically to shadows; Kircher's (1646, etc.), Great art of light and shade, an encyclopaedic tome which dealt with gnomonics, surveying and optics as well as perspective and shadows. The eighteenth century added at least one interesting title: Philip Jacobszoon's (1785) Scientific, mathematical and perspectival introduction to the placing of the sun and moon in a picture in order to determine their cast shadows.
The nineteenth century saw more than a dozen works devoted specifically to perspective and shadows including Marconi (1812) On the theory of shading, Schrank (1812), Muhlert (1821), who set out to determine shadows following optical principles; Similien (1842), Hinckley (1851), Fournet (1859) with Researches into coloured shadows which manifest themselves at different seasons and on the application of the phenomenon, Rätz (1864), Schreiber (1868), Delabar (1871), Seeberger (1876), Landriani (1879), Steindorff (1884) and Cabuzel (1887).
Such works have continued in the twentieth century with Weishaupt (1901), Vonderlinn (1904), Jaulin (1909), Luckiesh (1916), Arola y Sala (1921), Opitz (1926), Gromort (1932) and Grondona (1932) with a Treatise on the theory of shadows and more recently Bärtschi (1978). This interest has also spread to the Far East with Jin's (1959) Research on shadows in perspective and a work by the association, Tong-ji-da-xue-gong-cheng-h (1961), on Shadows and perspective.
Shades and shadows have played an important role in architecture from the outset as, for instance, in the method of representing cross-sections of buildings attributed to Brunelleschi (fig. 84.3), and particularly in connection with the five orders of columns (figs. 44-45) as evidenced by an early compilation of engravings by Veneziano, Serlio, Prevost and Flötner (c. 1540), or the classic treatises by Blum (1550 etc.), Barozzi, il Vignola (1583, etc.) and Hondius (1617, 1620, etc.) On the five orders of architecture with some fine architectural designs rendered in perspective invented by Jan Vredeman de Vries and his son Paul.
The latter seventeenth century saw new examples of shades and shadows in Bosse's (1664), On the orders of columns in architecture, and Huret's (1678) New treatise on architecture, as well as adaptations of earlier works, such as Erasmus' (1682) version of Blum and Bosboom's (1686) edition of Scamozzi. The latter eighteenth century brought treatises on shades and shadows intended as a direct complement to Vignola, including Spampani and Antonini (1770), Lagardette (1797, etc.), Heidelhoff (1834, c. 1851, 1859, 1888, 1812), Bourgeois (1838) and Rebout (1845). It also brought direct additions to Vignola's work such as Elementary lessons of shadows in architecture demonstrated by principles taken from nature. (e.g. 1786, cf. 1792, 1823, 1902, 1905, 1910, 1912, 1923, 1940).
Meanwhile, Nicholson, who also wrote a new work on the five orders of columns (1795, 1804, 184_), published a more general work (1795, etc.) on Principle of architecture containing...the true method of drawing the ichnography and orthography of objects; geometrical rules for shadows. In the nineteenth century such books, which applied perspective and shadows to architecture generally emerged as an independent genre, with authors such as Rossi Melocchi (1805), Heidelhoff (1888), Watelet (1896) and Planat (1899). Some books were addressed specifically to students at schools of architecture, e.g. L'Eveille (1812), Ribbans (1843), Pillet (1888) and Lawrence (1893).
The nineteenth and twentieth centuries saw a development in two opposite directions. On the one hand, there were ever more specialized works (cf. fig. ), such as Beuhne's (1907) Textbook of linear perspective with construction of shadows and reflections and application to drawing of furniture and interiors or Gründling, who wrote on descriptive geometry, projection and the perspective of shadows specifically for masons (1912), and a similar work specifically for carpenters (1912). On the other hand there was a trend towards more universal books such as Burg (1830) or Robinet (1855), which combined architectural and machine drawing. Tessari (1880) took this approach further, when he made his theory of shadows and chiaroscuro volume one of his applications of descriptive geometry "for the use of engineers, architects and designers."62 In the twentieth century works on shades and shadows officially addressed to architects, have frequently assumed applications to engineering and other disciplines, as in McGoodwin (1904), Ware (1912), Holmes (1929), Buck (1930), Shelton (1931) Vriend and Arendzen (1934), Morgan (1950), Turner (1952), Doria (1958), Mandino (1962), Parrens (1962), Fradin (1966), Carter (1967), Klimukhin (1967), Hasegawa (1977), and Vroman (1978, 1983).
One of the earliest drawing books which dealt with perspective and shadows, was produced for the military: Bouchotte's (1721, 1743, 1754, 1755) Rules of drawing and wash drawing. This connection with water-colours, or wash drawing, continued in the nineteenth century with Tripon (1848), Armengaud (1849), Delaistre (1855), and Pillet (1875), who produced a Theory of shadows and wash drawings. From the mid-eighteenth century onwards, there was increasing emphasis on the scientific dimensions of drawing. Seminal in this respect were Dupain de Montesson's (1750, etc.) Science of shadows with respect to drawing and Vallée's (1821) Treatise of the science of drawing, containing a general theory of shadows, linear and aerial perspective.
As in the case of architectural books, drawing books on shades and shadows also went in two directions. On the one hand, there was greater specialization as shades and shadows became associated with different kinds of drawing, such as construction drawing, e.g. Arbesser (1824), Muller (1865); linear drawing, Laurent (1827), Burg (1845), Edelmann (1871), Anonymous (1875), Segerborg (1896, etc.); machine drawing, Astolfi (1824) and technical drawing, Dietzel (1864), Bretagne (1967). On the other hand, there was a growing conviction that the laws of drawing were universally applicable as with Ryan (1860), Pereda y Lopez (1866), Davidson (1868, etc..), Ryan (1869), Krüsi (1876, etc.), Spanton (1896), or Curtis (1909), who entit