Dr. Kim H. Veltman
V Instrumentation and Science
1. Introduction
2. Astronomy
3. Optics
4. Perspective
5. Mathematics
6. Mechanics and Physics
7. Centres
8. Modern Developments
The development of perspective had fundamental consequences for science, art, the environment and the imagination. Each of these domains will be considered in turn in the chapters that follow.
In terms of science, perspective stimulated the use of instruments particularly in astronomy, optics and surveying and introduced a number of mechanical aids including the mirror, window, pantograph, camera obscura and camera lucida. The practical consequences of such instruments for the development of technical drawing have already been noted (see above p. ). Their theoretical consequences lay in focussing attention on the problem of scale and fostering quantification in science. This occurred partly through links between perspective and proportion and partly through the nature of perspectival representation which permitted various scales and views of an object to be related systematically (cf. above p. ). In the case of machines, individual parts could be segmented, and at the same time related back to the whole. Functions could be isolated and catalogued. Thinkers such as Leonardo da Vinci saw in these functions of machines a possibility of cataloguing the powers of nature. Perspective thus became involved with the development of the mechanistic world-view, with its new emphasis on observation, experiment and measurement. We shall show that centres such as Nürnberg, Antwerp, Paris, and London were important in this context and shall also consider more recent developments. By way of introduction, however, it will be useful to return to the traditions of astronomy, optics and surveying.
Ever since the Babylonians, there had been observation of the heavens and, already in Antiquity, there were instruments to observe the apparent motions of the planets and stars. Yet the focus of attention was on finding a pattern for phenomena such as eclipses of the sun and moon. Since the heavens were assumed to be unchanging, astronomy became primarily a conceptual problem of accounting for a set of recurring events. Indeed, once a basic catalogue of stars visible to the naked eye had been made, there was little incentive to look more closely. Hence, paradoxically, although ancient astronomy produced various instruments for observation of the heavens, it remained in many ways unvisual: a question of deceptive appearances1 rather than of visual truth.
The development of the planisphere and astrolabe2 imposed a deductive grid on the heavens, not unlike that of Ptolemy's projection in his Geography. Implicitly Ptolemy's planisphere introduced a new assumption: that the same projection principles apply on earth as in the heavens. Yet this had little impact on cosmology until the Renaissance. The astrolabe shared these assumptions and had the added feature that its scale for angular measurements could be applied equally to terrestrial surveying and celestial observation. The optical commentaries of Biagio Pelacani (c. 1390), and the perspectival studies of Commandino (1558), made explicit the universal mathematical principles involved in these instruments, a theme pursued by Commandino's student, Guidobaldo del Monte (1581, 1600) and popularized by Barbaro, who took Commandino's text as the starting point for part six of his Practice of perspective (1568). Contemporaries such as Egnatio Danti, who wrote a perspective (1583), also designed more practical astrolabes.
The same Egnatio Danti was involved in the design of sundials for the facade of Santa Maria Novella in Florence and elsewhere. He was working in a long tradition. Gnomonic devices had been associated with astronomy at least since Babylonian times. Yet, Renaissance perspectival theorists had a basic impact on this tradition. They developed sundials into highly complex polygonal devices, which used shadows to demonstrate anamorphic effects (figs. 48.1-49.4). Meanwhile, thinkers such as Desargues (1643) and Maignan (1648), showed that these instruments too were based on universal mathematical principles. In so doing, the perspectival authors of the sixteenth and seventeenth centuries prepared the way for Monge's famous insight of the eighteenth century that various practical applications in sundials, stonecutting and surveying all had a common theoretical basis in (descriptive) geometry. Perspective focussed attention on the theoretical, mathematical aspects of instruments and thus helped make them an integral part of the scientific revolution.
The optical tradition also played its role in these developments. Euclid's Optics, although concerned primarily with psychological aspects of vision, dealt with surveying problems in four propositions. This introduced important links between what one sees and measures. Among the Arabs (e.g. Al-Farabi),3 and later in the Latin West (e.g. Gundissalinus),4 these evolved into links between what one sees and what one measures with instruments. By the latter thirteenth century Witelo, in his optical thesaurus, could describe how it is "possible for a plane mirror to be positioned in a room such that in it are seen those things which recur in another house or places or streets" and explain that this could be done "using an astrolabe, or quadrant or some other instrument for the certification of sight."5
Criteria for the certification of sight to guard against the potential deceptivenes of vision, had been a concern among the Stoics.6 Witelo's claim that one could use instruments in this process of certification marked an important advance. It meant that optical theorists were developing criteria for testing the veracity of visual images at about the same time that artists began painting images which could be tested in terms of optical veracity. Hence Witelo's concerns went hand in hand with a new interest in naturalism introduced by the Franciscans, and which Duccio and Giotto developed a generation later, creating what we would term visual metaphor (see below p. ). Indeed, Witelo's use of a mirror to record what was happening outside an enclosed space, presaged in an uncanny way essential elements of Brunelleschi's demonstration of perspective nearly a century and a half later.
The optical tradition linked what one sees and what one measures with instruments. The advent of perspective linked what one sees, measures with instruments, and what one represents. In the latter fifteenth century, with Francesco di Giorgio Martini, this amounted to little more than physically recording one's measurements on an interposed rod or plane. In the sixteenth century, these links between optics, surveying and perspective increased dramatically. For instance, Gemma Frisius (154 ) explicitly described how an architect or painter could use his surveying instrument in drawing architectural views, townscapes and topographical maps.7 In the latter sixteenth century the use of surveying instruments for drawing views and maps had become common practice. Indeed, Bassentin (1555) could claim that instruments were essential for proper measurement:
Since it is not at all possible that the sense [of sight] and reason can know well the true quantity of acute and variable angles, it would be very difficult to comprehend the true quantity of a thing by the science of optics (perspective) alone. For this reason the ancient geometers and measurers invented certain artificial instruments and by means of these made it possible to know the quantities of things easily with the certitude of these.8
Bassentin mentioned the use of various instruments for these purposes, including the quadrant, geometrical triangle, Jacob's staff, geometrical rod and the astrolabe. With authors such as Bartoli (1564), the quest emerged to measure everything, lines, areas and volumes and to represent these systematically. The quest emerged also for a single instrument which could achieve this. Besson's (1567) cosmolabe was an early attempt. It was designed to record all dimensions of planes and heights geometrically, as well as descriptions made by perspective and surveying, to describe the stars of the heavens on a globe and to transform regular paintings into anamorphic ones.9 By the end of the sixteenth century, the military advantages of these surveying instruments with perspectival applications had been clearly recognized by Specklin (pl.58.4,1589) and Romano (1595), an approach which Hulsius (1605, pl. 58.1) and Faulhaber (1610) pursued.
Mirror
Meanwhile a number of perspectival instruments had emerged, which played an important role in making vision and representation into quantitative activities. The simplest of these perspectival aids was the mirror which had interested Witelo, and which Brunelleschi used in his original perspectival construction as suggested by Manetti10 and according to accounts by Filarete:
look at a pavement of square blocks of wood that is stretched out in front of you.... All the sides are equidistant from one another and [yet] looking at them it will seem that they are greater and less, such that those which are closer to you will appear more equal and to the extent that they are more distant, the more they appear attached together in such a way that they all appear to be one. And if you wish to consider the matter better, take a mirror and look into it. You will see clearly that it is thus. And if they were directly in front of the eyes they would all appear equal. And thus I believe that Pippi di ser Brunellescho, the Florentine, found the way to make this plane, which was truly a subtle and beautiful thing, which finds by demonstration that which shows itself to you in a mirror.11
Whether or not the mirror actually led Brunelleschi to arrive at his rule has been sufficiently discussed in the secondary literature.12 For our purposes it is of interest to note that Leonardo may have used plane mirrors in his painting practice which may account for paintings such as the Woman at her Toilet (fig. 53.1) by a member of the school of Fontainebleau, which shows a face reflected in a mirror. In any event, the idea remained, and at the turn of the seventeenth century the mirror recurred as a perspectival aid in Stevin's treatise (1605):
The description of the image (which induced us herebefore to define a glass) appeared so suitable to his Princely Grace, that he wanted not only to imagine such an image in a glass, but also actually to draw it therein, and to this end, he had a glass made in the way shown in the annexed figure, where A denotes the glass (which was the glass of a large crystal mirror), pivoting about the hinge B, so that it may be put as straight or inclined as desired and fixed by means of the small screw C. The hole through which one may look is D, which can be pushed nearer to or further away from the glass and be fixed with the small screw E. The glass may also be set higher or lower and then be fixed with the small screw F. It seems it may be said in truth that postures of men cannot possibly be drawn so perfectly at sight, without a glass.13
According to Stevin, all this was the idea of his prince (fig. 53.3). Was this actually his invention or might not this reflect Brunelleschi's original instrument? Mirrors continued to hold their fascination. Salomon de Caus (1612) entitled his treatise, On perspective with the reason of shadows and mirrors. Hamilton (1738), in his title, referred specifically to: reflections by polished planes. Philips Jacobszoon (1775) entitled one work Introduction to the perspective of mirrors and wrote another (1780), in order that, using the laws of perspective, one can represent all objects in flat mirrors. At the end of the eighteenth century, Martius (fig. 55.4) produced another descendent of Brunelleschi's device. Reflection remained a theme in the titles of Dennis (1876, etc.), Heyn (1885), and Fuchs (1902).
It is important to recall that not only plane mirrors were used. A fourteenth century Boccaccio manuscript (fig. 52.1) showed a woman using a convex mirror in painting her portrait. It is likely that the image depicted on a convex mirror by Petrus Christus (fig. 53.2) was achieved by similar means. Indeed, it may well be the case that the "curvilinear" perspective in Fouquet (fig. 53.30 and Witz (fig. 53.4) was also achieved with the help of convex mirrors. Rodler (1531, 1546) is one of the few authors who specifically discussed the use of convex mirrors with respect to perspective.
Window
The perspectival window (velo, rete, pariete), was by far the most popular of perspectival instruments. Alberti (1434) claimed that it was indispensable for perspectival construction.14 Piero della Francesca (c. 1480) described it, Leonardo drew it (c. 1490), Dürer (1525) published it, and via Barbaro (1568), it subsequently became known as Dürer's window in Italy. Dürer's student, Rodler (1531) used the window for landscapes, an idea which found both military15 and practical applications (fig. 58.1-2).
The window became much more than a simple mechanical aid. According to Danti (1583), Tommaso Laureti produced a model window specifically to demonstrate the principles of perspective, an idea subsequently taken up by the French Academy of Sciences. As early as the 1490's Leonardo da Vinci devised games which used the window principles to improve one's judgment of distance.16 Later authors such as Accolti (1625) and Bosse (1648) used the window to reveal reciprocal relationships of size and distance and as a tool for imposing a geometrical framework on nature. This made possible the equations between optics, geometry and perspective, which were taken for granted until the nineteenth century and have continued to the present (cf. above p. ).
Filarete described a variant of the window method involving a string, which Dürer published, and which Danti (1583) again popularized in Italy (fig. 55.1). Pfintzing (1598) took up this method and reported on improvements introduced by Hans Haiden (c. 1590, figs. 54.5-6). This version of the window principle was adapted by Marolois (1614, fig. 55.2), and remained popular throughout the eighteenth century, as witnessed by Martius (1789, fig. 55.3-4). Drer also published a third version of the window principle (fig. 54.1), the military implications of which were explored by Faulhaber (fig. 54.3). Such versions of the window principle allowed one to take a foreshortened view of a fort and work backwards in determining the layout of its ground-plan, thus illustrating practically the principle of reversibility. The effects of geometrical transformations of images could now be followed.
The window had other functions. It became a standard means of demonstrating the principles of the legitimate construction to such an extent that Benedetti (1585) could equate the two. Nor did this popularily diminish in the seventeenth century. The window now served to demonstrate the complexities of intersecting planes: not only the interplay between patterns on the floor and window, but also between patterns on the ceiling and window, or what happens when the floor is tilted upwards and downwards. Aleaume (1643) was among the first to study these conditions systematically (figs. 30.1-4). The way had been prepared by Marolois (figs. 31.1). Desargues (1636, etc.) explored the consequences, for the implication was that all these practical instances were concrete examples of some more universal principle of interesting planes. This realization did not make the window obsolete. It continued to be a standard item in the introductions to treatises on perspective. Eighteenth century thinkers such as Hamilton (1764) produced ever more elegant illustrations of practical examples of intersections (fig. 31.2). Monge's breakthrough was, in a sense, a new way of relating the practical window to the abstract principles underlying it (fig. 31.3). The window, then, was much more than a simple tool for perspective. It was a means of visualizing mathematical principles of planes and, it could be claimed, made possible a whole school of visual geometry (anschauliche Geometrie) as later developed by Hilbert.17 As such, the window proved as much a tool for abstraction, as it was an aid in concrete representation.
Pantograph
The window also served for systematic alterations in scale. But for this purpose another instrument was developed. Lencker (1571) designed a prototype which involved rulers and compasses (fig. 56.1). Marolois (1604) designed a second prototype (fig. 56.2), which was subsequently made famous by Scheiner (1631) and appeared in ever more elegant versions in the eighteenth (fig. 56.3) and nineteenth centuries (fig. 56.4).
Camera obscura
During the middle ages, the camera obscura was used to demonstrate optical principles by Alkindi and Alhazen.18 In 1285 Guillaume de Saint Cloud used it in observing a solar eclipse.19 In 1342 Levi ben Gerson, at the court of Avignon, used a camera obscura in combination with a Jacob's staff in studying a solar eclipse.20 By the end of the fifteenth century, the camera obscura was being used for a variety of optical demonstrations. Leonardo da Vinci devoted over 270 diagrams to it.21 Cesariano, in his edition of Vitruvius, reported a device found out and verified by the Benedictine monk and architect, Don Papnutio, which:
if it be properly fixed in a leaf of a door or in front of a window shut, so that no light may enter, and if you have a piece of white paper or other material upon which everything passing through the aperture may be represented, you will see everything contained in the earth or sky according to the pyramid found through the aperture and with their colour and forms.22
Beginning with Porta (1558, etc.), the camera obscura began to be recommended specifically as an aid to representation.23 In the seventeenth century, this idea was taken up by the Jesuits such as Leurechon (1626), Bettini (1642, fig. 57.2), Kircher (1646, fig. 57.1), and Zahn (1665), and also attracted the attention of important scientists such as Robert Hooke (1669) and Robert Boyle (1669). This continued in the eighteenth century, when Brander (1764, 1767, 1769) developed camera obscuras in combination with microscopes and telescopes, and Häseler (1779) developed a version in keeping with the theories of Euler. The artistic applications of the camera obscura also became ever more widespread. Gravesande (1711) described a complex portable version in his treatise in perspective. Nollet (1735) described another portable versions. The Encyclop‚die listed a number of versions. How widespread its use had become is suggested by a textbook in landscape painting in 1796:
A good number of persons apparently believe that one can reproduce aplace most correctly using a camera obscura and it is no doubt true that I achieve a proper representation of a place by this means. Even so, it is much more beautiful and better when I draw from Nature directly and without the help of a camera obscura....The camera obscura is primarily a good tool for amateurs and those who cannot draw from Nature directly or do not wish to learn how to do so.24
Camera Lucida
In the nineteenth century the camera obscura continued to be used but artists turned increasingly to a new invention, the camera lucida invented by Wollaston (1807) and developed by Amici (1823), Dollond (1830) and Chevalier (1830).
Taken in isolation any one of these perspectival instruments might readily have been dismissed as mere mechanical aids, simple technical shortcuts with no relevance for high level theory and science. By the end of the fifteenth century, however, a larger context was emerging. Luca Pacioli (1494) saw perspective as intimately connected with matematical proportion, and saw instruments such as the ruler and compass as a means of achieving this. With respect to proportion be claimed:
Perspective, if one regards it properly would certainly be nothing if this did not accompany it. Which is amply demonstrated by the monarch of painting of our time, Master Piero della Francesca...Bellini, Malatini, Botticelli, Luca and Pietro da Cortona and Melozzo da Forli who, always proportioning with ruler and compasses bring their work to admirable perfection in such a way that they represent themselves as divine rather than human in our eye.25
He went on to claim that number, measure and proportion were basic to all the arts and sciences. These ideas he pursued on 11 August 1508 when, in the church of Saint Bartholomew in Venice he gave a sermon on proportion claiming that it applied to philosophy, physics, natural philosophy, medicine, astronomy, geography, painting, music, rhetoric, law, ethics and religion as well as perspective. In his mind, proportion was a key to all human knowledge.26
Already in 1494 Pacioli had taken a further step in claiming that the eye on its own was unreliable and that one needed instruments to achieve correct proportion and perspective:
With the mechanical arts, considering all the exercises and trades, one does not see faithfully by the eye alone. If you take from their hands the square and compass with their proportion, they do not know what they are doing.27
Nor was he alone in this view. Leonardo made similar claims.28 Caporali (1536),in his edition of Vitruvius, also assumed a necessary link between instruments, measurement and perspective. The compass, he claimed:
is more necessary for the measurements of geometry and perspective than any other instrument because, with this, all lineal demonstrations are measured and the angular things to which one extends the terminations of lines and divisions...as is well known to the expert line makers who are especially perspectivists.29
In this context we see in a new light Dürer's treatment of perspective in his Instruction in measurement...using the ruler and compass (1525), and similar works by Rodler (1531) and Lautensack (1567). Instrumentation and perspective were now twin keys to universal measurement.
The compass and ruler remained important. In 1560, Tartaglia published the fifth part of his General treatise of numbers and measures...in which is shown the way to execute with the compass and ruler all the geometrical problems of Euclid and other philosophers. The latter sixteenth century also saw the development of at least three new kinds of compasses to deal with this bold task of universal measurement.30 One of these was developed by Fabrizio Mordente in the 1550's, while on a great journey which took him to India, Spain, Portugal, England, Belgium, France, Germany, Czechoslovakia and Austria. It had four moveable points along a two-pronged compass. In 1572, he presented a version of this compass to the Emperor Maximilian. In 1575, with the accession to the throne of the new emperor, Rudolph II, he presented a new version of the compass.31 In 1584, Mordente dedicated a book on this compass to the emperor, explaining that it dealt with all the problems of Euclid.32 The book contained chapters on lines, surfaces, bodies and distances and showed how the compass was intended to be used in conjunction with a ruler on which were inscribed lines of various proportions.
The fascination with proportion33 had led in the meantime to the discovery of various kinds: arithmetical for the simple division of lines, geometrical (based on square roots) for determining areas; stereometrical (based on cube roots) for determining volumes,34 and still other types for determining relations between different sizes of polygons or specific gravities of metals. In the first half of the sixteenth century, these lines were usually discussed in isolation in specialized treatises. In the latter sixteenth century, the growing quest for universal measurement led to these various lines being combined on a single ruler, which could then be used in conjunction with Mordente's compass or other instruments.
A second type of compass consisted of two adjustable rods which intersected to form an X shape. Leonardo da Vinci termed this a proportional compass although it was also known as a reduction compass because of its use in reducing circles to different scales. By 1566, the Augsburg instrument maker, Christoph Schissler, had designed a more complex version which served for the division of lines and circles, as well as inscription of regular polygons.35 The various lines of proportion were now being applied directly to the compass. The evidence of Coignet, the town accountant and gauging master of Antwerp, attests that this was not an isolated case; that there was widespread knowledge of a reduction compass with as many as six basic functions.36 A manuscript attributed to Lencker, and bound with a copy of that author's work on perspective, lends weight to this view.37 An elegant version of this compass was developed by Jobst Bürgi in the 1590's,38 and became associated with his name following a publication by Hulsius (1604).
Perspective continued to play a role in these developments. Besson (1571) outlined an early version of a third type of compass, which consisted of two rulers joined by a pivot in his Description and use of the Euclidean compass including most operations made in geometry, perspective, astronomy and geometry. Danti (1583), in his treatises on perspective described another early version for the inscription of regular polygons and described the systematic transformation of geometrical forms and solids as part of the perspectivists' task (see above p. ). The manuscript on perspective, attributed to Lencker, described a more complex compass with six functions.39 By 1597, Galileo had begun to develop his own version of such a compass which he published in 1606.40 Coignet described a compass with as many as twelve functions41 which may or may not have antedated Galileo's. Of interest for our purposes is that Faulhaber (1610) illustrated the Galileo type and Bürgi type compass along with a perspectival window on the title page of his New geometrical and perspectival inventions. In France, the proportional compass was described in treatises on perspective by Vaulezard (1630, etc.), H‚rigone (1634), Bosse (1648), Huret (1670, etc.), Chales (1674). Elsewhere there were further works by Leupold (1713), Lambert (1752), Taylor (edited by Kirby 1761) and Phélippeaux (1819).
All three versions of the proportional compass were logical developments of attempts at universal measuring instruments mentioned earlier, and hence integrated the measurement of lines, areas and volumes. From the battlefield they included a line of metals, which could be used to compute equivalences among metals of different densities. Meanwhile, the early renaissance had seen the development of geometrical play (de ludo geometrico), whereby regular shapes were transformed. Alberti and Piero della Francesca explored these transformations in two dimensional terms. Leonardo made this into a more serious game of three-dimensional transformations involving both diagrams and models. These became part of the perspective tradition and these too were incorporated into the functions of the proportional compasses. These instruments thus served in bridging abstract and concrete problems of mathematics as well as offering solutions to problems in accounting, gauging, gunnery and surveying all of which combined to create a sense of universal mastery, to which scientific theory subsequently laid claim in the seventeenth century. Indeed, we would maintain that this universality of practice made possible the very conception of a universally applicable theory, and formed the basis of the mathematical sciences which emerged in the seventeenth century (cf. p. ).
The nature of perspectival representation played its own role in the development of a universal concept in science. In the thirty years between 1485-1515, Leonardo da Vinci discovered that perspective was much more than a means for producing three dimensional effects. It enabled representation of complex organic forms such as the human body in methodical terms: from different viewpoints, as a whole, and in relation to its parts, with a result that the functions thereof could be made manifest. It offered the same possibilities with respect to machines, which led to a catalogue of different mechanical functions. As Reti has shown, Leonardo explored 21 of the 22 elements of machines later listed by Reuleaux: including screws, keys, bearings, pins, axles, couplings, friction wheels, toothed wheels, flywheels, ratchets, brakes, pipes, valves, cams and pulleys.42 These elements provided him with a means of explaining different kinds of motion such as hoisting, dragging and rolling. Not content to stop here, he wished to find the principles underlying these elements, which led him to develop a concept of four basic powers of nature: weight, force, percussion and motion.43 Convinced that these same principles underlay human movement, he decided to preface his treatise on human anatomy with a work on mechanics and the elements of mechanics.44
Proportion and perspective combined to make these insights of fundamental importance. Leonardo believed that proportion underlay everything and therefore set out on a quest to measure not only lines, areas and solids but all the forces of nature in these terms: "Proportion is not only found in numbers and measures but also in sound, weights, times and sites and whatever powers there be."45 He became convinced that these powers of nature obeyed a proportion that was pyramidal and perspectival.
At the same time, his studies of perspective led him to recognize that only the visual was measureable, which forced him to redefine his goals. Traditionally concepts such as motion had been ambiguous in that they included both mental and physical change: i.e., growth and decay, disturbances of the mind and dreams, as well as motions of balls and projectiles. Leonardo was aware of these, but recognized that they could reasonably be reduced to two kinds: visible and invisible.46 And he decided to limit his studies to visible motion, indeed, to make the visible his standard, which explains why he rejected alchemists, astrologers and others who based their claims on invisible things.
The decisions had basic implications for cosmology, which traditionally had emphasized the four elements and used their tactile qualities of hot, cold, dry, wet as basic characteristics of a world defined by substance which, although described by organic metaphors of growth and decay was ultimately static, qualitative and hierarchical. Thinkers such as Aristotle had discussed weight, force, percussion and motion, but their function had remained incidental in a world view dominated by the four elements.
Leonardo focussed his interest in the four elements on their visual rather than their tactile qualities. He added tracers to air in order to make visible flow patterns therein. He also added tracers to water and assumed that the flow patterns therein were slow motion versions of what happened in air.47 He studied falling water and found pyramidal, perspectival effects of percussion which paralleled the pyramidal perspectival percussion of sand on a board.48 This attention to visible rather than tactile qualities shifted concern away from their substance as elements, to their function in terms of the four powers. The traditional quest for qualitative descriptions, which were hierarchical was thereby replaced with a search for quantitative dimensions which were a hierarchical. Leonardo insisted that the universe was not at the centre of the universe, but at the centre of its elements. Thereby he was able to argue that the moon was also at the centre of its elements and that this principle, applied to all the planets and stars.49 Conceptually, this breaking of the chain of being was of greatest importance although it would take the writings of his contemporary, Copernicus, and subsequently, Galileo, to explore the larger consequences thereof.
Leonardo introduced another change that was equally fundamental. For, while he continued to discuss the four elements, he focussed attention in the four powers. Hence, while he continued to pay lip service to organic metaphors, mechanical metaphors now dominated his concerns.50 As Dijksterhuis51 has shown, such metaphors were not new. They had been used since Antiquity. What was different in Leonardo's case was a direct link with the visible world achieved through proportion, perspective and instruments. This served to bridge theory and practice and transformed what had traditionally been loose metaphors into visual hypotheses about the nature of matter and motion which were open to quantatative testing. Which set mechanics, physics, astronomy and cosmology on a new course culminating in early modern science. The scientific revolution is often described as if it occurred primarily in the realm of astronomy. It owed as much to disciplines such as surveying and geography which, combined with perspective, established a vision of universal measurability, which could be applied in the heavens as it is on earth.
In an earlier chapter we have already emphasized the role of centres such as Urbino, Nürnberg, Antwerp, Paris and London, in the development of perspective and have mentioned some connections with science. It is useful to return to these centres at this point, to note that they were also centres in the development of instruments, for these combined activities help us to understand why these centres played a special role in the emergence of early modern science.
At Urbino, (fig.38) already in the latter fifteenth century, Piero della Francesca, was emphasizing not just an abstract mathematical approach to perspective, but one which could be demonstrated using surveying methods and perspectival windows. He also relied on compasses, as we know from the passage in Pacioli, cited earlier. Francesco di Giorgio Martini also used both surveying instruments and compasses in his perspectival demonstrations. In the sixteenth century these connections became more significant. The same Commandino, who was active in perspectival theory (1558), was
URBINO
Euclid
Apollonius
Archimedes Francesco Lauranna
Ptolemy
Piero della Francesca
Diophantus Luca Pacioli
Nicolo Tartaglia
Pappus Francesco di Giorgio Martini
Francesco Maurolyco
John Dee Federico Comandino
Christopher Clavius
Giovanni Battista Benedetti Guidobaldo del Monte
Paolo Gallucci
Paul Guldin Gregorius Saint Vincent
Galileo Galilei
Bonaventura Cavalieri
Fig. 38. Theoreticians on perspective, mathematicians and instrument makers in Urbino (1450-1600).
FLORENCE
Oronce Fin‚ Bartolommeo Genga
Jacques Besson Pierre de la Ram‚e
Baldassare Lanci Cosimo Bartoli Silvio Belli Giorgio Vasari
Fabrizio Mordente Daniello Barbaro
Latino Orsini
Michel Coignet
Egnazio Danti
Agostino Ramelli Giorgio Vasari, Jr.
Ostilio Ricci
Francesco Pifferi Lorenzo Sirigatti
Galileo Galilei Lodovico Cardi
Fig. 39. Links between Florentine theoreticians of perspective and makers of instruments for universal measurement leading to the proportional compass and sector (1550-1610).
NÜRNBERG
Leonardo da Vinci
Bolognese or Venetian Source Jean P‚lerin
Gregor Reisch Joachim Fortius
Albrecht Dürer
Hans Beham Erhard Schön Hieronymus Rodler
Augustin Hirschvogel John Dee
Heinrich Lautensack
Frederic Risner
Pierre de la Ram‚e
Wenzel Jamnitzer Hans Lencker
Hans Haiden
Michael Maestlin
Paul Pfintzing
Jobst Brgi Tycho Brahe
Galileo Galilei Levinus Hulsius
[Michel Coignet]
Benjamin Bramer Johann Faulhaber
Fig. 40. Theoreticians in Nrnberg (1500-1625).
also involved in the development of a new instrument, which was a forerunner of the Galilean sector, while at the same time being at the centre of editing texts basic for the mathematical foundations of science.52 Commandino's student, Guidobaldo del Monte, was deeply involved with perspective, instruments and science. So too was his student, Galileo, and his contemporary, Giovanni Battista Benedetti.
There links are even more striking in the Florentine circles (fig.39), which drew their inspiration partly from Parisian developments by Oronce Fin‚, Jacques Besson and Pierre de la Ram‚e. Cosimo Bartoli (1564) used their work as a starting point for his book on universal measurement, which influenced Silvio Belli (1565). Meanwhile, Baldassare Lanci, an engineer, important for his perspectival decorations for the theatre, also devised his own instruments intended to serve both for surveying and perspective. Daniele Barbaro, active also in Venice, drew directly on the work of these three contemporaries, was in contact with Fabrizio Mordente concerning new universal instruments,53 and reported on the use of instruments in his own treatise on perspective (1568). Latino Orsini, inventor of another universal surveying device,
NÜRNBERG, ANTWERP, PARIS, LONDON
Georg Peurbach
Johannes Müller (Regiomontanus)
Martin Behaim
Martin Waldseemller Peter Apian Sebastian Mnster
Gemma Frisius
John Dee
Mercator
Leonard Digges
Walter Arsenius Oronce Fin‚
Abraham Ortelius
Thomas Hood Michel Coignet Pierre de la Ram‚e
Jodocus I Hondius Frederic Risner
Jodocus II Hondius Abel Foullon
Fig. 41. Links between instrument makers, cartographers and geographers and authors on perspective (1450-1600).
the latin staff (radio latino), cited the influence of Barbaro and, in turn, influenced Egnatio Danti, important not only for his treatise on perspective (1583), but also for his scientific instruments including a large astrolabe (now in the Museum for the History of Science at Florence) and the sundial on Santa Maria Novella in the same city. Danti was also important for Ostilio Ricci,54 author of treatises on practical geometry and surveying, and teacher of Galileo. Among the most interesting figures in this context was Giorgio Vasari Jr., nephew of the famous author of Lives of the Artists, who wrote a manuscript recording all the scientific surveying instruments in the collection of the Grand Duke of Tuscany55 and was also author of a treatise on perspective, upon which Sirigatti based his work, ideas of which were taken up a turn by Cigoli, the author on perspective who was friends with Galileo. For artists, practitioners, and scientists in Nürnberg, instruments were at least as important as we have shown earlier (see above p. and fig.40).
Hence, there were close links between authors of treatises on perspective, those connected with new instruments and those at the frontiers of science. A list of titles in a Treatise of mechanical instruments by Levinus Hulsius (fig. 42, 1603-1605) is particularly interesting in this regard. Hulsius mentions Danti, Guidobaldo del Monte and Simon Stevin, each of whom was active on all three fronts. Among the German names we find individuals important for the rise of science such as Peurbach, Apian, Ursus56 and Brahe, also notable for the development of scientific instruments, alongside authors on perspective such as Dürer, Rodler, Lautensack, Jamnitzer, Lencker, Specklin and Pfintzing. Jamnitzer, besides his work on perspective, was responsible for new instruments for gauging and surveying, and is recorded as having designed a whole chest of scientific instruments.57
In this context, it is instructive to recall that a chief incentive for Regiomontanus' move to Nürnberg in the 1470's was precisely because this city was the
Netherlands Italy France Germany
Johannes Werner 1514
Georg Peurbach 1516
Jakob Köbel 1522
Albrecht Dürer 1525
Peter Apian 1533
Hieronymus Rodler 1546
Sebastian Münster 1551
Johann Schöner 1551
Jacques Bassentin 1555
Jacques Androuet du Cerceau 1559
Abel Foullon 1564 Heinrich Lautensack 1565
Wenzel Jamnitzer 1568
Silvio Belli 1570 Oronce Fin‚ 1570 Hans Lencker 1571
Egnazio Danti 1579 Elie Vinet 1574
Michel Coignet 1581 Guidobaldo del Monte 1581 Agostino Ramelli 1580
Latino Orsini 1583 Zacharias Lochner 1583
Girolamo Cataneo 1584
Simon Stevin 1586
Cosimo Bartoli 1589 Daniel Specklin 1589
Giovanni Paolo Gallucci 1592 Andreas Helmreich 1591
Gabriel Busca 1594 Errard de Bar le Duc 1594
Iodocus Hondius 1597 Philippe Danfrie 1597 Nicolaus Ursus 1597
Adrianus Romanus 1597
Henry de Suberville 1598 Tycho Brahe 1598
Paul Pfintzing 1598
Johan Sems/Jan Dou 1600 Fabrizio Padoani 1601
Andrea Palladio 1601 Jacques Perret 1601
Levinus Hulsius
Fig.42. List of titles cited by Levinus Hulsius in his Treatise of Mechanical Instruments (1603-1605). The heading Netherlands includes Flanders, and Germany includes Prague.
leading European centre for the construction of scientific instruments. In the generations that followed, scientific instruments served to secure the cumulative dimensions of scientific knowledge. Regiomontanus' work on science and instruments had a direct impact on Waldseemüller, famous in cartography, Martin Behaim, renowned for producing one of the first globes, Sebastian Münster, and Peter Apian, whose compendium of surveying instruments and fascination with astronomical instruments was a direct inspiration for his Antwerp collaborator, Gemma Frisius, who proved a seminal figure on at least three fronts: at home, through his students, Mercator and Arsenius, which led to the workshops of the Coignet, Ortelius and Hondius families; secondly in England, via John Dee, Digges, father and son and Thomas Hood, and thirdly in France, through Oronce Fin‚, Pierre de la Ram‚e and Abel Foullon, individuals who, as we have noted already, again had their impact on circles in Nürnberg and Florence.
The sixteenth century thus saw the emergence of networks between Florence, Nürnberg, Antwerp, London and Paris (fig.41). These were due as much to the development of standards in instrument making which transcended local workshops, as to the spread of printing. Politics played its inevitable role. When Rudolph II became the Holy Roman Emperor, Prague functioned as a catalyst in this process. Hence Fabrizio Mordente, an Italian active in Venice, published in Antwerp his treatise on a universal compass (1584), which he dedicated to the experor at Prague. To Prague came famous instrument makers such as Schissler, the scientist Kepler, and the astronomer Brahe. Prague drew on the developments at Kassel, where the Landgrave of Hesse established Europe's first astronomical observatory, where Brahe's assistant Bürgi, developed instruments for perspective, surveying, geography and astronomy, activities which were taken up by Hulsius (1603-1605), Faulhaber (1610) and pursued by Bürgi's brother in law, Bramer (1617, 1730). Albrecht (1673) developed this theme describing an instrument with which "a building, landscape on some other object standing before the eyes can be taken perspectivally and drawn in isolation," noting that the same instrument could be used to "diminish or increase all geometrical and perspectival figures in any size you wish as long as you change the foreshortened scale as desired."58
One of the subtle consequences of these developments was that geography and astronomy became visual problems in a way that they had never been in Antiquity. Ptolemy, for instance, in producing his map of the world relied on reports of longitude and latitude for a number of cities. But these were based on shadow projections, which left geography a branch of astronomy and ultimately the determining factor was a conceptual grid, which remained unrelated to the visual evidence of landscapes. The twin developments of surveying and perspective in the fifteenth and sixteenth centuries changed this by making it clear that recording a building, town, landscape, region, province or country were all extensions of a single principle involving changes in scale. What might be termed an inductive approach to map making thus emerged, which began with local sites and led to more generalized patterns with the result that geography now had its starting point in the visual evidence of surveying and perspective. In this context Egnazio Danti's position as cosmographer to the Medici Dukes (pl. 24.5) or the perspectival author, Cristoforo Sorte's, role as a cartographer acquire greater significance.
The incentive to look more closely at the heavens arose from discrepancies between Ptolemy's claims, which needed updating, and the actual evidence. It is noteworthy that the individuals concerned with this task of reconciliation, Peurbach, Regiomontanus, Werner, Apian, Copernicus, Bürgi, Brahe and Kepler, were concerned with both terrestrial and celestial instruments. If a junction between terrestrial and celestial measurement had been implicit ever since Ptolemy wrote his Geography and Almagest as two facets of a single scheme, it now became explicit, partly through the use of common instruments, and partly from the recognition that the same perspectival principles applied to map and planisphere projection. As the sixteenth century progressed, the tandem production of terrestrial and celestial globes became common practice. Cosmological considerations provided another incentive to consider the heavens as a visual problem. Leonardo's speculations about the nature of the moon, mentioned earlier, prompted him to "make glasses to see the moon large"59 and we have several hints concerning his attempts.60 We know, moreover, that his chief writings on vision were intended to serve as an introduction to his great work on cosmology and astronomy. Whether Leonardo's early efforts in the direction of a telescope directly influenced the subsequent attempts of Fracastoro and Digges remains uncertain.61 But such evidence confirms that the stimulus for Galileo's breakthrough in 1609 was at least a century in the making. And underlying this breakthrough was a shift from a deductive to an inductive approach to astronomy.
When Galileo published his Assayer ( 16**), he included an engraved portrait flanked by his two chief instruments the sector and the telescope. These are usually discussed in isolation as if they represented unrelated aspects of his work. We would argue otherwise and claim that their appearance together confirmed how surveying, geography and astronomy had emerged as elements in a single challenge of mapping the universe, a challenge to which perspective offered a key.
We have returned to the problem of scale considered earlier in chapter two. There we were concerned with its importance in the so-called conquest of reality, in leading artists to recognize that the representation of interiors, exteriors, birds' eye views, landscapes, maps of the earth and the heavens (cf. figs. 20-27) were all the same problem in different scales. Here we are concerned with its role in the emergence of early modern science, and would suggest that scale might be seen as the problem of proportion with a visual dimension added through perspective and instruments. We would go further to suggest that a theory of perspective, and practice of instruments, combined in introducing a visual approach to surveying, geography and astronomy which led inevitably to a visual standard of truth.
Traditionally the shift from a deductive to an inductive method, and the shift from a mental to an experimental approach have been described as abstract philosophical problems. If we are right there were more concrete reasons for these shifts, which depended on a more systematic, quantitative approach to concepts of scale, brought into focus through perspective and instruments; concrete reasons which also throw light on the shift from substance to function which Cassirer sought to explain abstractly.62 For scale is seeing relations, functions.
It would be wrong to imagine, however, that the problem of scale was one of these insights that came suddenly only then to be taken for granted. Leonardo could be said to have introduced the problem and Galileo to have begun its serious study. But the concept was so seminal that in a sense the whole of western science since the sixteenth century could be seen as a continuing exploration of its dimensions. The seventeenth century explored how one could increase the scales of visible things in both the macrocosm and the microcosm through telescopes and microscopes. The eighteenth and the nineteenth centuries extended these principles.
A whole as yet unwritten chapter would, for example, need to be written concerning the implications of photographic perspective on concepts of scale. For what are lenses but systematic tools for changing scale? Such a chapter would need include the role of photography in surveying and cartography as developed say, by Deville (1895), and relate how World War I, which saw the first use of cameras in airplanes, brought new questions of relating perspectival photographs to scale maps on which accurate distances could be measured. Theoretically, these problems had been broached by Brook Taylor (1715). Even so J. W. Gordon's solution in Generalized linear perspective (1922) marked a breakthrough in using perspective to simulate nature, and led to a new science of photogrammetry. This made it possible to map unexplored country, lay out highways, locate bridges, even provide contour surveys without the expenses of traditional surveying. Deneux (1930) and Hildenbrandt (1759) introduced new photographic methods , since superceded anew with the advent of satellites.
Twentieth century architects have played a significant role in these continuing explorations of scale. For example, Holmes (1937) showed that one could use a photograph of a building, draw in its perspectival lines, and work backwards to establish the measured ground plan of the original. These principles have proved very important in the area of town planning. Danielowski (1968), for instance, used a photograph of a street where a building had been torn down, drew in perspectival lines and added a drawing of a proposed new building to show how it would fit into the existing context. M"ller (1979) invented an "endoscope", which permitted one to photograph an architect's model from a viewpoint simulating a model-pedestrian. In France, the Ministry of the environment (1980) developed similar methods, using photo montage to demonstrate effects of a proposed housing estate on a landscape. Jantzen (1963), developed a complex interplay between architectural plans, models, photographs and perspectival views, which permit one to simulate effects of replacing buildings in any given context. Hiss (1985) explicitly related scales in photographic lenses with different scales in architecture.
Meanwhile these questions of relating different scales have increasingly become the domain of computers. In the early 1970's the Sutherland company, then at the frontiers of computer graphics, simulated, in three point perspective, architect's conceptions of buildings in various scales. A Cornell project (1974) extended this principle to simulation of a whole context of buildings, within which a proposed new building could be moved at will.63 It also simulated different viewpoints of an imaginary viewer within a planned context. Since then there has been much attention to creating simulations at different levels of abstraction and relating them to one another. The French Ministry of the environment, which also worked with photo montages, created elaborate wire line simulations of sites which could be viewed from various prints (1980). Reynolds (1987), demonstrated how one could relate wire line, hidden line and hidden surface versions of a same building. This method of providing perspectival views of different layers of a proposed building, for which models and photographs exist, has also been used in designing the new Museum of Man in Ottawa.64 A new method called radiosity developed at Cornell, enables one to take a room with complex spatial elements and to recreate it from different viewpoints under various lighting conditions.65 The latest methods of computer aided design (CAD), explore combinations of real buildings and imaginary conceptions of possible buildings. In future this could be given an historical dimension such that computerized repertoires of ruins and monuments of the past could inspire new representations and constructions, a systematic approach as it were to the tendencies of post-modernism.
A full survey of twentieth century innovations with respect to perspective and instruments would readily be a book in itself. Morgan (1950) was still able to limit his list to nine significant methods: office, measuring points, direct projection, Reile, perspectigraph, charts, calibron machine and photography.66 Since then extraordinary developments in satellite photography, lasers and holography have opened further horizons, marking new steps in systematic treatment of scale and the automation of perspectival principles. Indeed these momentous developments with cameras and computers may help explain renewed interest in perspectival effects and the history thereof. And yet science is but one part of the story. As will be seen in the chapters that follow, the impact of perspective on art, the environment and imagination has been equally profound.
Last Update: August 4, 1998