Abstract
In the two editions of his Underweysung der Messung of 1525 and 1538, Albrecht Dürer published designs for four devices to help artists with drawing. The present author has reconstructed all four tools and made experiments, in each case drawing a lute. The paper reports on the problems encountered and the times taken. For comparison, a perspective view of the lute is constructed geometrically, and other drawings are made freehand. The two more complex machines proved to be inaccurate, time-consuming, and almost unworkable. The gridded frame is faster and more accurate. Best of all in terms of speed and precision is tracing on glass, which in the experiments took less than a tenth of the time needed to set up and draw a perspective of the lute’s difficult curved form. The paper follows the historical legacy of Dürer’s devices. The complex machines are republished repeatedly in Renaissance texts on perspective but were arguably little used in practice. By contrast, the gridded frame and tracing on glass were recommended in many teaching texts and used widely by artists right up to the twentieth century.
1 Introduction
In 1525 Albrecht Dürer published his Underweysung der Messung (“Manual of Measurement”).1 The book is an introduction to geometry, with instructions for making drawings of geometrical figures and solid bodies including the basics of linear perspective. Dürer includes engravings of two designs for devices to help artists to draw. A second edition of the Manual was published in 1538 after the artist’s death. Dürer had worked on new material, and this edition contains designs for two further drawing machines. The four devices were extremely influential on later writers of perspective treatises, and the designs, or variants, have been repeatedly republished. I have reconstructed all four and have tried drawing with them. The results are reported in this paper.
One of the illustrations from 1525 shows an artist making a portrait of a gentleman by tracing on a sheet of glass in a frame (Figure 1). The artist looks with one eye, and his eye position is fixed with a peephole in a mask on an adjustable stand. The distance between the picture plane and the artist is strictly limited by his arm’s reach: it cannot be much more than 40 centimetres. The head of the sitter is perhaps twice this distance beyond the glass, so his portrait will come out at about one-third life-size. Dürer says: “This is very suitable for portraiture – especially for those [painters] who are not sure of themselves.”2
An artist painting a portrait on glass. From Dürer, Underweysung der Messung (Nuremberg, 1525), n.p.
Citation: Early Science and Medicine 29, 5-6 (2024) ; 10.1163/15733823-20241334
The reason that the artist must look with one eye is that the perspective views obtained by the two eyes differ slightly. A tracing on the glass made with the left eye would be slightly displaced relative to one made with the right eye. The artist must keep his head fixed in place so that his open eye stays in position. The idea had been anticipated by Leonardo in a thumbnail sketch of an artist studying a scientific instrument – an armillary sphere – through a sheet of glass (Figure 2). Here the artist fixes his eye by looking through a hole in a board. He traces what he sees. Leonardo writes that the plane of a conventional picture can be thought of as resembling a sheet of glass, through which the artist sees the subject, and on which he draws.3
Sketch by Leonardo of an artist drawing an armillary sphere on glass. Codice Atlantico, Biblioteca Ambrosiana Milan, 5r
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Leonardo has specific instructions for working with a similar set-up to Dürer’s. He details these as follows:
Have a piece of glass as large as a half sheet of royal folio paper [30 × 44 centimetres] and set thus firmly in front of your eyes that is, between your eye and the thing you want to draw; then place yourself at a distance of 2/3 of a braccia [40 centimetres] from the glass fixing your head with a machine in such a way that you cannot move it at all. Then shut or entirely cover one eye and with a brush or red chalk draw upon the glass that which you see beyond it; then trace it on paper from the glass, afterwards transfer it onto good paper, and paint if you like, carefully attending to the arial perspective.4
For my recreation of the tool, I used a standard mass-manufactured wooden window measuring 80 centimetres square. I made estimates from Dürer’s illustration – taking my scale from the human figures – of the distances of artist and subject from the frame. I decided not to attempt a portrait, but to draw the same subject with all four devices, so that there could be some comparison on a common basis of the ease or difficulty of the methods and the time taken in each case. I chose a lute; the subject being drawn in another of Dürer’s illustrations. Lutes are difficult to draw because of their complex curved shapes. They have for this reason featured in demonstrations of advanced technique in perspective manuals – as, for example, Pietro Accolti’s Lo inganno de gl’occhi (“Deception of the Eyes”) of 1625.5 Accolti has constructed perspective views of a lute from three different angles, using measurements taken from orthographic plan and side views (Figure 3).
Perspective and orthographic views of a lute. From Pietro Accolti, Lo inganno de gl’occhi (Florence, 1625), 90
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The obvious limitation of my experiments is that they are made by just one draftsman with a specific set of skills. I have much experience in making working drawings and setting up perspectives, and some practice in drawing by eye – although I had never before tried tracing on glass. Even so, I think that the kinds of difficulties that I found, and the broad differences in time taken, would have been experienced by many users of these tools.
2 Drawing on Glass
Tracing on glass proved to be a simple and effective method. In the first place, I drew with a felt pen; later I used media that would have been available to Leonardo and Dürer. Figure 4a shows the experimental set-up. The photo of Figure 4b is taken from a position away from the eyepoint to show the drawing and lute separately. The tracing process took about thirty minutes. A second tracing of a different view of the instrument again took half an hour.
Author’s version of Dürer’s set-up of Figure 1, and a photograph taken from an angle away from the eyepoint to show tracing and lute separately
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It is absolutely essential to keep one’s head fixed in place and shut one eye while tracing. Like Dürer’s artists I used a wooden post to position my drawing eye. I covered the other with an eye patch. A second way of staying in position is to keep checking with what is already drawn, getting the lines back into register if one’s head has moved. I found it difficult to draw for long periods without my arm shaking, since – working on a vertical surface – it was unsupported. On subsequent attempts I used a mahlstick, which helped. It was not so easy to trace smooth long curves. When drafting on paper it is natural to draw these from inside the curve, which one can do by turning the sheet on a drawing table; but of course, this is not possible on the glass.
The felt pen was ideal for tracing (one could also use a whiteboard marker pen) but obviously anachronistic. Leonardo specifies chalk or oil paint. Chalk would need the addition of wax to make it adhere to the glass. I have tested modern Chinagraph pencils which are sold for writing on glass or plastic. These did not work well. Wax crayons on the other hand were very effective, although it is difficult to sharpen them sufficiently to make thin lines. Soap is another option mentioned occasionally.6 I have found it difficult to obtain a white soap hard enough for the purpose.
The historian of drawing Joseph Meder mentions the use of charcoal soaked in oil for drawing on glass.7 I have tried leaving sticks of charcoal for several days in linseed oil; but again, the marks made were unsatisfactory. I obtained much better results using black paint thinned with oil, and a very fine brush. One general problem when tracing with one eye closed is that it is difficult to judge precisely where the surface of the glass is in depth. The consequence when painting is that one is liable to crash the brush into the glass and make blobs.
Figure 5 shows a picture of a human skull made with black paint, which took twenty minutes. One virtue of working in paint is that one can then easily transfer the image onto paper by ‘offsetting’. The window is laid flat, and a sheet of paper is placed over the glass while the paint is still tacky. The back of the sheet must be burnished with a hard instrument such as a spoon. This produces a mirrored image (Figure 6). Another simple method of transfer is to put a sheet of paper up against the glass, light the glass from behind, and retrace. This is workable even with medium-weight semi-opaque cartridge paper. Unlike the offset, this second tracing is not reversed relative to the original tracing on the glass.
Author’s painting of a human skull on glass, with the picture and the skull aligned
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Offset onto paper of the painting in Figure 5. The image is mirrored
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Victoria Button, an English conservator of works on paper, wrote a doctoral thesis on Hans Holbein’s portrait drawings in which she discusses the question of whether he traced these on glass.8 Button commissioned a reconstruction of Dürer’s frame and tested it out herself (Figure 7).9 She found the same problem as I did in judging the depth at which the tip of the drawing implement would meet the surface of the glass. She invited trained artists to try the device, but interestingly, “they found it difficult to trace the contours of the sitter’s face on the glass without imposing their own style of drawing. In other words, rather than tracing features they were drawing the portrait on glass.” Dürer, as we have seen, thought that the glass could be useful for beginners “who are not sure of themselves.” Button’s experience suggests that, for this kind of tracing work, careful beginners or technical draftsmen might make a better job than professional artists.
Dürer’s device for drawing on glass. As reconstructed by Victoria Button, in use for making a portrait. Photo by kind permission of Victoria Button
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3 The Gridded Frame
Dürer has a device in the 1538 edition of the Underweysung der Messung, consisting of a grid of strings in a frame. This is his version of the famous ‘veil’ invented by Leon Battista Alberti and described (but not illustrated) in Alberti’s Della pittura (“On Painting”) of 1435.10 Alberti recommends stretching a sheet of transparent cloth, worked with a grid of heavier dark threads, in front of the subject. He specifies cloth, presumably because flat clear glass would not have been available in sufficiently large sheets at this early date. The artist has a piece of paper with a similar grid ruled on it, and uses the two grids to determine the positions of points and lines in his drawing. For a painting, the second grid could in principle be drawn directly on a canvas or other support.
Dürer had access to a copy of Alberti’s book. He was determined to find out more about perspective from Italian painters and mathematicians.11 He made a short visit to Italy in the autumn of 1494, and then went to Venice for a longer stay in 1506. He wrote to his friend Willibald Pirckheimer back in Nuremberg that he was planning to go to Bologna for eight or ten days “for the sake of ‘art’ in secret perspective which someone wants to teach me.”12 However, we do not know who this was, or whether Dürer did in fact go.
Figure 8 is a slightly earlier preparatory sketch by Dürer that he tucked into his own copy of the Underweysung. This shows a solemn-looking artist using a grid of strings to draw a male nude. There are two mistakes here. First, the little pylon that should serve to fix the artist’s eyepoint is some distance in front of him. This means that he can move his head sideways and up or down and still keep looking past the top of the pylon. It should be just in front of his face to fix his view, as with the method of drawing on glass. Secondly, there are fewer grid squares on the paper than in the frame. Both these faults are corrected – and the male replaced with a female model – in the published version (Figure 9). Dürer says that the grid should be made of “strong black thread,” spaced at intervals of “about two fingers wide” (i.e., 4 centimetres).13 The spacing of the threads in the engraving looks to be closer to 10 centimetres. Obviously the finer the grid, the more accurately positions on the subject can be determined.
Dürer, conceptual sketch for a gridded frame being used by an artist. Bayerische Staatsbibliothek, 89bv, L. impr. c. n. mss.199
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An artist using a gridded frame to make a drawing of a woman. From Underweysung der Messung (Nuremberg, 1538), n.p
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Leonardo had previously suggested a version of the gridded frame, but much larger than Dürer’s – roughly 2 metres square – and placed close to the subject. The draughtsman works from a distance, which means that what he sees through the grid is less sensitive to his precise position, and he can look with both eyes. Leonardo recommends that the user place a pellet of wax on the grid to cover some chosen point on the model’s body, say the pit of the throat, or one of the vertebrae in a back view. Then he can get into and stay in position by lining the wax up with the target on the body.
For drawing the lute with the grid, I used another standard wooden window 80 centimetres square, which I threaded with heavy dark string at 4-centimetre spacing. The drawing process proved harder than I anticipated. Figure 10 shows my set-up, with a gridded sheet of paper set between the sighting post and the frame. The difficulty is that the paper and the view to be drawn are in different places, so that one must keep looking back and forth, trying to find and re-find reference positions on the grid. This makes it tricky to draw long smooth curves in the correct positions. I ended up using a combination of working from grid points and drawing by eye. Even a 4-centimetre spacing of the grid is not fine enough to define small features like the tuning pegs. The result is shown in Figure 11. The process took 55 minutes, nearly twice as long as tracing on glass. Compared with tracing on glass, this method has the merit however of producing a drawing on paper directly.
Author’s reconstruction of Dürer’s gridded frame
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Author’s drawing made with the frame of Figure 10
Citation: Early Science and Medicine 29, 5-6 (2024) ; 10.1163/15733823-20241334
4 Changing the Distance of the Viewpoint from the Frame
One problem with Dürer’s technique for drawing on glass is that the artist’s distance from the frame is limited by the length of his arm. As he writes: “Flat [two-dimensional] things are suitable for tracing on a glass pane from the near point of sight. But other solids become distorted if the eye is too close to them during the process of drawing them.”14 However, if the objects are placed further away, their images become small. What is needed is for the hand to be close to the glass and the eye at a distance. This seems impossible.
In the 1538 edition of his book, Dürer introduces a new set-up for drawing on glass that supposedly solves this difficulty. This, he says, was invented by his ingenious friend Jacob Keser. Figure 12 reproduces Dürer’s illustration. The subject is a large vase. The artist has a sighting tube attached to a string that is tied to a ring on the wall. The artist holds the tube to his eye, looks through it, lines it up with some point on the vase, and marks the corresponding point on the glass. The important operational point is that the drawing’s theoretical perspective ‘viewpoint’ is no longer in the human artist’s eye but is in the ring on the wall. This ‘eye’ can therefore be at some distance behind the artist, while he can still reach the glass with his hand. Different positions of the string can be imagined as theoretical rays of light converging to the theoretical eyepoint. The ring could in principle be moved yet further back to give an even shallower perspective.
Dürer’s device for drawing a vase with a sighting tube, following a design by Jacob Keser. From Underweysung der Messung (Nuremberg, 1538), n.p.
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The idea seems plausible, but I had extreme difficulties making it work and did not in the end embark on any drawing. The tube must be narrow in order that it may be focused on some point in the subject. It must be straight. The artist must look through the tube. But the tube must also be aligned with the cord that runs back to the ring on the wall. In principle this could only work perfectly if the cord ran through the artist’s eye socket and head.
I tried holding the tube tightly – with my left hand – to the right side of my head but could only see through it if the string was diverted around my head. By holding the tube some distance in front of my head I could see the subject through it and keep the string taut, but it was difficult to keep string and tube aligned, which they must be if the method is to succeed. I did not attempt to trace but could tell that it would not be easy, seeing only a small part of the subject at a time. It would be like trying to draw a landscape through a telescope. Also, the artist’s head and body are not fixed in place: he must keep moving, stretching up to draw the highest parts and crouching down to draw the lower sections.
Dürer himself recognised these problems. In a separate diagram in the Underweysung he illustrates not a sighting tube, but a bar attached to the cord, with a little pylon to fix the eyepoint and a hole in a plate to act as a gunsight (Figure 13, bottom).15 This could be held to the side of the head. As Noam Andrews writes in a paper on the Underweysung,
Dürer is extremely careful to note that […] the tip of the device lines up with the eyepiece, and that there is a discrepancy that needs to be accounted for between the line traced by the cord through the base of the device and the imaginary line of sight.16
Drawing by Dürer showing (below) an alternative to the sighting tube in Keser’s drawing instrument and (in the triangle above) how the sightline now differs from the alignment of the cord. From Underweysung der Messung (Nuremberg, 1538), n.p.
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Dürer draws an elongated triangle to show this difference in angle between the cord and the true sightline (Figure 13, top).17 This variant would resolve some of the problems with using a sighting tube. I have not tried out the device; but I suspect that difficulties would remain.
I have begun to wonder whether Dürer himself, or even Keser, ever actually tried this method. Maybe he did not have the opportunity to make practical trials. I have had similar doubts about the second machine illustrated in the 1525 edition of the Underweysung (Figure 14). This too is a response to the intrinsic limit on the distance of the artist to the drawing, imposed by the length of his arm. Once again, the ‘eyepoint’ is moved further back so that the perspective is not so steep. A cord, stretched tight with a weight, again represents ‘rays of light’. This time the subject of the drawing – like mine – is a lute.
Dürer’s device for drawing a lute using a stretched cord. From Underweysung der Messung (Nuremberg, 1525), n.p.
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The machine requires two operatives. The first stands by the lute and moves one end of the weighted cord to different points on the instrument. The cord passes through the open frame and then runs through a ring on the wall at the right. The second stands by the frame and, for every point on the lute, measures the distances of the cord from the top and side of the frame. It looks as though this is done using two moveable rods or wires, one horizontal and the other vertical. There is a white board on which the drawing is being made. The second operative uses the measurements made with the wires to plot each point in turn. The dots are then joined up to make the picture.
I built a set-up like that in the engraving (Figure 15). The distances between lute, frame, and notional ‘eyepoint’ on the wall are broadly as in the illustration. It was not however entirely clear to me how the operator working at the frame proceeds when measuring the positions of the cord. He is making the drawing on the board that looks to be hinged like a casement window in the frame. But does he swing this into the frame to mark points? This would mean moving the cord out of the way. I decided instead to note down the coordinates of the positions of the cord and make a drawing separately. I glued tape measures to the top and side of the frame and used an architect’s T-square sliding on the frame to find the vertical and horizontal positions (the x, y coordinates) of each point. I then plotted these points on to a separate piece of squared paper.
Author’s reconstruction of the device of Figure 14
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It was immediately clear that the measurements were not nearly accurate enough. I found it difficult to measure any more precisely than to the nearest 5 millimetres. This was because there was a certain amount of ‘play’ in the whole system, and the cord vibrated and shifted when touched. The top of the lute is seen at a shallow angle in this position, and slight differences in the recorded positions of the cord can make big differences for the drawing. My assistant and I plotted twenty points, but these were not adequate to draft the outline of the top face of the body of the instrument.
We persevered and plotted another ten points. We measured the four corners of the peg box, the position where the neck meets the body of the lute, and a few other key features. Figure 16 shows all our points plotted on the gridded paper, with a rough freehand attempt to connect them into an outline. In the drawing in Dürer’s engraving there are over 200 points, although some of these are redundant: Dürer shows rows of points along straight lines, where two points at each end of the line would have sufficed. Our work rate was one point per minute, so plotting 200 points would in theory have taken more than three hours. (And if one was summing up the person-hours involved, that total would have to be doubled.) Even this number of points, if accurate, would not produce a very detailed drawing. The pegs in the pegbox are missing from Dürer’s drawing for example.
Author’s drawing of a lute made with the device of Figure 15. The plotted points are marked by crosses. The linear outline is a rough attempt to join up the points
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The University of Melbourne Print Collection held a “Dürer Drawing Day” in 2017 at which they too reconstructed this machine and tried drawing a lute. They experienced the same difficulties. The process was “incredibly time-consuming” and quite imprecise. “It required such meticulous positioning of the frame, object, paper and threads, that the slightest movement of any part of the device could undo the accuracy of the drawing.”18
It might in principle be possible to engineer a more accurate method of taking off the coordinates of points, perhaps with a metal frame and rulers running in grooves. But much of the inaccuracy comes from the movement of the cord. Again, I wonder whether Dürer tried the method in practice. In his La pratica della perspettiva (“The Practice of Perspective”) of 1568, Daniele Barbaro writes that he built a version and demonstrated it to his acquaintance Cardinal Turnone, who was delighted.19 Maybe Barbaro took objects of very simple geometry and worked very precisely. He says that he
set up the door [the hinged board in the window] carefully so that when it was closed the points of crossing of the threads touched it precisely, and things came out more certainly, especially if the threads were pulled tight and the cord fixed firmly, because all such measures serve for the cleanness and correctness of the work.20
One feature of Dürer’s illustration that does not inspire confidence is the fact that the picture composed of plotted points on the board is too large. For the relative positions of instrument, frame and eyepoint, it should be about half this size.
5 A Measured Perspective, and Drawing by Eye
Finally, to set against the products of the various Dürer devices, I made two further experiments. I constructed a perspective of the lute geometrically working from plan and side views, as in Accolti’s illustration (Figure 3). I chose a viewpoint and a picture plane and projected an image onto the plane following the general method first set out by Piero della Francesca in his De prospectiva pingendi (“On the Perspective of Painting”), written in the 1470s.21 I also made drawings by eye without any aid.
The process of drawing an accurate plan and side view of the lute is laborious, since it involves taking precise measurements at intervals – from the outside – along the curved body of the instrument (Figure 17). This took nearly three hours. Setting up and drawing the perspective view took another three and a half hours. I made a clean version in pencil and ink (Figure 18) in half an hour, meaning that the whole process took seven hours.
Author’s measured plan and side views of the lute
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Author’s constructed perspective view of a lute
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Even so, the drawing is quite rudimentary and lacks the details of the pegbox and pegs, which would require much more time and effort, if constructed, though one might also add these details by eye. As mentioned, I have experience in setting up perspectives geometrically, and did not waste too much time. A second drawing from a different angle would use the same measurements. But based on my experience, that could still take four hours.
My last exercise was to make several drawings of the lute by eye, without any aid. Figure 19 shows one of my attempts, which took about an hour. The drawing is compared with a photograph of the instrument from the same viewpoint. The main fault is that the body of the lute has ballooned out. It has the wrong silhouette and is out of scale with the pegbox and neck. I do not think there are any very useful general lessons here: but for me at least, tracing on glass made it possible to produce a more accurate drawing of this difficult subject in half the time that it took to draw by eye.
Author’s freehand drawing of a lute compared with a photograph taken from the same viewpoint
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6 Discussion: Tracing on Glass, and the Gridded Frame
Tracing the lute on glass took half an hour, while constructing the measured perspective took seven hours. The tracing was more detailed, and just as accurate. This only confirms what Alberti said about the merits of a method for the direct transcription of appearance – in his case, using the ‘veil’ – over perspective construction, for objects of complex shape. The drawings of lutes that appear in treatises on perspective like Accolti’s are more demonstrations of virtuoso skill than useful methods for practitioners. If a drawing of a lute was wanted for a still life or a painting of a lutenist – and there are many, by Holbein, Caravaggio, Gentileschi, Hals, Vermeer and Steen among others – then tracing on glass from a real instrument would be a rapid and effective way of producing one.
We know that Dürer constructed perspectives geometrically for some of his engravings of buildings and interiors, as, for example, his pictures of “St Jerome in his Cell” of 1511 and “St Jerome in his Study” of 1514. But did he ever draw on glass or use the gridded frame? The question is difficult to answer. I have tried to find out, but with limited success. I am not aware of any published studies. For the gridded frame, the evidence would be in the presence of ruled grids under paintings or drawings. One must be careful, because grids are also a standard means of transferring drawings to canvas, and perhaps for changing their scales in the process. However, a grid deriving from the use of a drawing frame would be beneath other lines in a drawing, while a grid used for transfer would be drawn on top of other lines. There is one landscape in watercolour by Dürer – “Willow Mill,” painted in the 1490s–that has irregularly spaced vertical lines in the sky; but their cause or function is uncertain.22
Tracing on glass would leave little physical evidence, especially if a drawing on paper was retraced from the glass, instead of being offset. There is a certain amount of equivocal evidence from the work of German artists of the generation following that of Dürer. Melchior Lorck (or Lorich) (b. 1526 or 1527, d. after 1583) was a draftsman and printmaker who worked for a time in Nuremberg. Lorck was an admirer of Dürer, made a portrait of his famous predecessor, and adopted a Dürer-type monogram. In 1555 he joined a diplomatic mission to Constantinople, where he drew a greatly elongated panorama of the city, some 11.5 metres in length, on 21 sheets of paper.23 Three historians – Nigel Westbrook, Kenneth Dark, and Rene van Meeuwen – have tested the accuracy of the drawings against the real topography of Istanbul and surviving landmarks, using a digital model of the terrain.24 Their conclusion is that “[t]he relative accuracy of the drawing is confirmed by its close congruence with digital modelling of the city.”25 The authors suggest that to achieve this precision, Lorck used either a gridded frame or traced on glass.
There has been a long and vigorous debate about whether Hans Holbein traced his miraculous drawn portraits of members of the court of Henry VIII on glass26 – a debate to which Victoria Button, cited earlier, is the most recent contributor. Holbein would have known the Underweysung der Messung. The qualities that have led critics to believe that Holbein traced on glass are the drawings’ extraordinary likeness to their sitters, remarked on at the time; their simplified and heavily emphasised outlines of facial features; their apparent flattening and lack of roundness or modelling; and the sizes of the heads in the pictures. Holbein, if he traced, must have been at arm’s length from the glass. The sitters would have been close to the glass on the opposite side. These relative distances determine the sizes of the drawn heads, whose dimensions are indeed compatible with such a set-up. (Button does not, in the end, believe Holbein drew on glass.)
My own intuition is that some of the characteristics of Holbein’s drawings do indeed indicate a tracing method.27 It would have been possible for him to trace just the outlines of the face, features and clothing on the glass. He could then have transferred these to paper by retracing and completed the detail by eye. This would explain the sharp difference between the heavy outlines, emphasised in ink, and the more sensitive and subtle treatment in metal point of hair, beards and eyebrows. Joseph Meder in a discussion of the Holbein portraits suggested that Dürer may also have traced portraits on glass occasionally, as, for example, in a 1518 drawing of Philipp von Solms-Lich (Figure 20).28 This has some of the same qualities as the Holbein portraits.
Albrecht Dürer’s portrait drawing of Philipp von Solms-Lich, 1518. Musée Bonnat Helleu, Bayonne: Wikimedia Commons. Notice the flat, traced quality of the hat
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Illustrations of the gridded frame appear in the later perspective literature, some to demonstrate the concept of Alberti’s veil, others recommending this method of drawing. In a manual published in 1531, Johann von Simmern shows an artist using the bars of an actual window as a frame for drawing the landscape beyond (Figure 21).29 In the early seventeenth century, Robert Fludd and John Bate illustrate grids for drawing in books on natural philosophy and mathematical recreations respectively.30 In Differentes manières de dessiner et peindre published around 1667, Abraham Bosse shows an artist using a grid to paint a portrait.31
Illustration by Johann von Simmern of an artist using the bars of a window as a grid with which to draw a landscape. From von Simmern, Eyn schön nützlich Büchlin (Frankfurt?, 1531), fol. Hiiv
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The device, and variants, were still regarded as useful by artists – including some famous names – in the nineteenth and early twentieth centuries. There are grids ruled beneath landscape drawings made by John Constable in the English Lake District in 1806. It has been suggested that Constable was using a type of drawing frame illustrated by Edward Noble in his book The Elements of Linear Perspective of 1771.32 In this device, the lines in the grid are unequally spaced.
The most extraordinary and inventive use of the grid for portraiture was by the Italian artist Antonio Mancini (1852–1930), whose method loosely followed Leonardo.33 Mancini, however, had two large frames of equal size. One was set directly in front of the sitter. The other covered the picture itself so that the strings touched the canvas. He looked carefully at the subject from a distance through the first grid and carried the details across in memory to the corresponding squares in the grid over the canvas. Figure 22 shows his set-up for making a portrait of Mrs Shine in Ireland in 1908. Mancini’s purpose was not just to obtain correct outlines and proportions, but to match hue and tone.
Antonio Mancini’s use of two large, gridded frames for painting Mrs Shine in 1908. The frame on the right is in front of the sitter; the frame at the left is in front of and touching the canvas. Mancini (standing, right) added more diagonal strings as he worked. Photo courtesy of the National Library of Ireland
Citation: Early Science and Medicine 29, 5-6 (2024) ; 10.1163/15733823-20241334
Vincent van Gogh struggled with perspective and built himself a portable frame device that he used outdoors, following a design in an elementary drawing manual by Armande Cassagne, Guide to the Alphabet of Drawing, published in 1880.34 This did not have a regular grid of strings or wires: it had just one vertical, one horizontal, and two diagonals, like a Union Jack flag (Figure 23). Van Gogh used this right up to his final years in Arles. It helped him to judge the angles of receding lines in frontal perspective views.
(Top) Vincent van Gogh’s sketch of his perspective frame with pointed rods for supports, and (bottom) a self-portrait of the artist using the frame on the beach at Scheveningen. From letters to Vincent’s brother Theo van Gogh, 5 and 6 August 1882, <https://vangoghletters.org/orig/let253> and <https://vangoghletters.org/orig/let254>, Van Gogh Museum, Amsterdam, published under a Creative Commons License
Citation: Early Science and Medicine 29, 5-6 (2024) ; 10.1163/15733823-20241334
7 Discussion: The Two More Complex Devices
As for the more complex of Dürer’s machines from the two editions of the Underweysung, the device with the sighting tube (Figure 12) appears to me to be unworkable. And the device with the cord running through the window (Figure 14) is – from the evidence of our experiment and the trial by the University of Melbourne – extremely time-consuming and quite inaccurate. What is strange is that versions of this second machine are illustrated repeatedly in the later perspective literature. I mentioned that Daniele Barbaro reproduced Dürer’s engraving in his Practice of Perspective of 1568 and demonstrated a version of the device in use.35
Gian Paolo Lomazzo describes his own experience with Dürer’s graticola or grid in his immensely longwinded and disorganised Treatise on the Arts of Painting, Sculpture and Architecture of 1584.36 He does not recommend it. In his Sixth Book on ‘Practice’, however, he has a tortuous and meandering description of a drawing device with measuring scales on a rectangular frame, and a string kept taut by a weight. There is no illustration, and Lomazzo says it is his own invention: but he must have taken the idea direct from Dürer’s lute-drawing machine.
The great Mannerist architect Giacomo Barozzi da Vignola wrote a manuscript on perspective, titled The two rules of practical perspective, and not published until 1583, after the author’s death.37 The mathematician and astronomer Ignazio Danti edited the work and added notes and much extra material of his own. He describes a series of variants of Dürer’s windows. One of these again follows closely the method for drawing the lute (Figure 24). The subject of the picture here is an octagonal slab.
Version of Dürer’s stretched cord device illustrated by Ignazio Danti in Le due regole della prospettiva prattica (Rome, 1583), 56
Citation: Early Science and Medicine 29, 5-6 (2024) ; 10.1163/15733823-20241334
On the face of it, it is strange that Barbaro, Lomazzo, Vignola and Danti choose to concentrate on the machine for drawing with the cord and frame, given this is the most unwieldy and tedious of Dürer’s techniques. Could it be that they were attracted more by the ingenuity than the utility of the device? I suggest that there is a self-perpetuating scholarly tradition here, relatively independent of actual drawing practice. In The Science of Art, Martin Kemp writes of the machine that
we are still left with the impression that its main use was in the set-piece and pedagogical demonstrations of the solid bodies which were favoured by the perspectivists and that it was not intended for universal application.38
In The Geometry of an Art, Kirsti Andersen expresses similar doubts:
would two men really go through the long arduous process portrayed in Dürer’s illustration? Or did his drawing mainly serve a didactic purpose? I cannot decide, but I am fairly certain that Dürer’s proposed method was not followed […].39
The set-up nevertheless has the virtue for the teacher of perspective theory, that it demonstrates most clearly the relationship of object, eyepoint, picture plane, and light rays – since the rays are embodied in visible material form in the different positions of the cord.
8 Distortions in Close-up Views
The problem that is addressed in principle by the two complex tools is nevertheless a real one. An artist drawing on glass must be within arm’s reach of the frame. This produces a wide-angle view which can result in distortions at the edges of the picture. The purpose behind these more elaborate devices was to move the effective viewpoint back, and to moderate or avoid such distortions. I have drawn two diagrammatic perspectives to illustrate the effect (Figure 25). Imagine that the table extends beyond the frame, and the surface of the table is covered with a square grid. There is a cube standing on this surface. In the first perspective the viewpoint is 40 centimetres (an arm’s length) from the frame. The squares at the near edge of the grid begin to look extremely elongated – as is the cube – because they are seen so obliquely. The perspective geometry is correct: this is what always happens in close-up views, whether drawn or photographed with a normal lens. In the second perspective, constructed with the viewpoint 100 centimetres further back from the frame, the distortions have disappeared.
Perspective drawings of the surface of the table beyond the drawing frame covered with a square grid, as seen from viewpoints 40 centimetres (left) and 140 centimetres (right) in front of the frame. A cube sits on the grid
Citation: Early Science and Medicine 29, 5-6 (2024) ; 10.1163/15733823-20241334
A close viewpoint is fine for a still life or a portrait, as Dürer says. These subjects are shallow, and their shapes are complex. Distortions become more noticeable in scenes with greater depth, or which contain simple forms like cubes, spheres, or grids of tiles, whose true shapes we know. In his illustration of an artist drawing a reclining nude with the grid (Figure 9), Dürer goes against his own advice. The woman’s knees are almost touching the strings, and her body extends back a metre or so. The model’s feet and calves in the drawing would be huge, and her head tiny by comparison. Some Renaissance painters ran into similar difficulties when putting reclining bodies into steep perspective, seen from viewpoints near the underside of the feet; notably Uccello’s fallen soldier in “The Battle of San Romano” and Mantegna’s “Dead Christ.”
9 Conclusion: The Success of Tracing on Glass
The enduring success story has been Dürer’s simplest, fastest, and arguably most accurate method: tracing on glass. Transferring the resulting drawing to paper is not too difficult, as we have seen. A tracing in paint can be offset. A drawing in any medium can be re-traced onto opaque paper with the glass illuminated from behind. This increases the time involved but still takes no longer than drawing with a grid, going by my own experiments.
There are strong indications that amateur and perhaps also professional painters in the eighteenth century traced on glass. In 1776 a German artist Friedrich Christian Müller published Gebrauch der Transparente zum Zeichnen der Natur (“The Use of a Transparency to Draw from Nature”), the first and, I suspect, the only entire book ever written on the subject.40 Figure 26 shows his apparatus. Another instructional text of 1796 covers both the gridded frame and drawing on glass: Johann Heinrich Meynier and Heinrich Jan-Penningh, Theoretisch-practische Anleitung zum Zeichnen und Tuschen der Landschaften (“Theoretical-practical Instructions for Drawing and Inking Landscapes”).41
Apparatus for tracing on glass designed by Friedrich Christian Müller and presented in Gebrauch der Transparente (Frankfurt and Leipzig, 1776), 253, fig. 1
Citation: Early Science and Medicine 29, 5-6 (2024) ; 10.1163/15733823-20241334
According to Joseph Meder, these German writers say that contemporary professional painters of portraits in pastel also traced on glass.42 There is a full-size drawing by the leading Swiss pastel portraitist Jean-Étienne Liotard for one of his most celebrated works, “The Chocolate Girl” of ca. 1744. This was described in the catalogue of an exhibition in 2024 as a “tracing”: but it is on opaque paper.43 If it was indeed traced, this could only have been from a drawing on glass.
Teachers of drawing in the nineteenth century continued to recommend the technique for beginners. In France the painter Aramanthe Rouillet taught his pupils to trace with charcoal, not on glass but on transparent gauze stretched on a frame.44 The technique was taken up by Marie-Elisabeth Cavé, a portrait painter and friend of Delacroix and Ingres. Mme Cavé’s book Le dessin sans maître (“Drawing without a master”) of 1850 was highly influential, and in the 1860s her methods were adopted in schools across France.45 Figure 27 shows Mme Cavé with a tracing on the easel behind her. She is making a copy by eye, to train her visual memory.
Madame Cavé with a portrait traced on gauze on the easel behind her. She is making a copy by eye. Marie Elisabeth Cavé, Le dessin sans maître (Paris, 1850), frontispiece
Citation: Early Science and Medicine 29, 5-6 (2024) ; 10.1163/15733823-20241334
Meanwhile in England, John Ruskin published an instructional book on perspective for schools in 1859, in whose Introduction he invites the reader to sit by a window with a “pretty view” outside.46 “Every part of your window may be considered, if you choose, as a glass picture; and what you see through it, as painted on its surface. And if, holding your head still, you extend your hand to the glass, you may, with a brush full of colour, trace, roughly, the lines of the landscape on the glass.” Maybe students took him at his word, although Ruskin’s purpose here is to explain the idea of perspective through the window metaphor, and the remainder of his book is devoted to geometrical construction. On the other hand, Ruskin was an early enthusiast for photography – the ultimate descendant of Alberti’s veil and Dürer’s machines – and made drawings and watercolours himself, copied directly from daguerreotypes.
Today there are books, websites and online videos that still teach the use of Dürer’s simpler methods, illustrated with figures reproduced from the Underweysung der Messung.47 Whatever the utility of his more complex designs for actual drawing practice, these simpler methods endure in an ongoing practical tradition.
Albrecht Dürer, Underweysung der Messung (Nuremberg 1525: 2nd edn. Nuremberg 1538); transl. and ed. Walter L. Strauss, The Painter’s Manual (New York 1977). The pages of the originals are not numbered: the engravings of the drawing devices appear at the very ends of both editions.
Dürer, Painter’s Manual, ed. Strauss, 389. In the 1525 Underweysung (n.p.), the page preceding the engraving shown in Figure 1 has the inscription: “Sölichs ist gut all dennen die yemand wöllen ab Conterfeten / und die jrer sach nit gewiß sind […].”
Leonardo da Vinci, Manuscript A (Institut de France, Paris), 10v; see Martin Kemp and Margaret Walker, eds., Leonardo on Painting (New Haven, CT – London, 1989), 57.
Jean Paul Richter ed., The Literary Works of Leonardo da Vinci (London, 1883), vol. 1, 260, quotation 523 (Codex Ashburnham 1, 12b): “Abbi uno uetro grade come uno mezzo foglio regale e quello ferma bene dinazi ali occhi tua, cioè tra l’ochio e la cosa che tu vuoi ritrare, e dipoi ti poni lontano col ochio al detto vetro 2/3 di braccio, e ferma la testa con vno strumeto i modo no possi mouere puto la testa; dipoi serra o ti copri uno ochio, e col penello o co lapis a matita macinata segnia i sul vetro ciò che di là appare, e poi lucida co la carta dal uetro e spoluerizzala sopra bona carta e dipigila, se ti piace, vsando bene poi la prospettiva aerea.”.
Pietro Accolti, Lo inganno de gl’occhi, prospettiva pratica (Florence, 1625).
As a young man the Edwardian architect Edwin Lutyens traced drawings of traditional buildings in Surrey on a piece of glass with a sharpened sliver of soap: see Mary Lutyens, Edwin Lutyens by his Daughter (London, 1980), 17–18.
Joseph Meder, The Mastery of Drawing, transl. Winslow Ames, 2 vols. (New York, 1978), vol. 1, 339.
Victoria Button, “The Portrait Drawings of Hans Holbein the Younger: Function and Use Explored through Materials and Techniques” (PhD thesis, Royal College of Art, London, 2013).
Ibid., Appendix 3, 236–239.
See Leon Battista Alberti, Della pittura (manuscript version, 1435); transl. Cecil Grayson, On Painting (London, 1972); reprinted, ed. Martin Kemp (London, 1991), 65–67.
For Dürer’s biography, see Erwin Panofsky, The Life and Art of Albrecht Dürer, 2 vols. (Princeton, NJ, 1943; 4th edn. Princeton, NJ, 1955).
Ibid. (1955 edn.), 248.
Dürer, Painter’s Manual, ed. Strauss, 435. In the 1538 edition of the Underweysung (n.p.) on the page with the engraving of Figure 9, Dürer writes: “Darzu soll man haben ein ram mit einem gitter von starckem schwartzen zwirn gemacht / die lucken oder fierungen eine ungeferlich zweyer finger breyt.”
Dürer, Painter’s Manual, 431. In the 1538 Underweysung (n.p.), these lines occur two pages before the engraving shown in Figure 12; in the original: “Flache ding leiden sich / das man sie mit einem nahetten aug durchzeychen auf ein glas. Aber andere Corpora gewinnen ein ungestalt / so man d[a]z aug im conterfeten nahent hinzustelt /von der gehen abstehung wegen / dann die nehern ding bey dem aug scheynen gegen den ferreren zu gros.”
Albrecht Dürer, Skizzenbuch, Sächsische Landesbibliothek, Dresden, 89av, L.impr.c.n. mss 199.
Noam Andrews, “Albrecht Dürer’s Personal Underweysung der Messung,” Word and Image, 32 (2016), 409–429, at 421.
Dürer, Underweysung der Messung, 1538 ed., n.p., on the page before the engraving shown as Figure 12.
K. J. Stone, “Finding Dürer’s Perspective,” University of Melbourne Archives and Special Collections blog (13 August 2017), at <https://blogs.unimelb.edu.au/librarycollections/2017/08/13/finding-durers-perspective>, accessed 21 November 2024.
Daniele Barbaro, La pratica della perspettiva (Venice, 1568); in English as Daniele Barbaro’s Perspective of 1568, transl. Kim Williams and Cosimo Monteleone (Cham, 2021).
Barbaro, Daniele Barbaro’s Perspective, 374. The original in La pratica della perspettiva, 191, reads: “Io accommodai anche la portella si bene, che quando era serrata, i punti de gli incrocciamenti de i fili la toccauano a punto, & le cose ueniuano piu certe, especialmente se i fili erano bene tirati, & lo spago fermo, perche tutto serue alla politeZza, & giusteZza del lauroro.”
Piero della Francesca, De prospectiva pingendi. Ms in Biblioteca Ambrosiana, Milan; first printed edn., ed. Giusta Nicco Fasola (Florence, 1974).
Albrecht Dürer, “Willow Mill,” watercolour, ca. 1497, Bibliotèque Nationale, Paris.
Now in the collection of the University of Leiden, <https://digitalcollections.universiteitleiden.nl/view/item/2026523>, accessed 21 November 2024.
Nigel Westbrook, Kenneth Rainsbury Dark and Rene van Meeuwen, “Constructing Melchior Lorich’s Panorama of Constantinople,” Journal of the Society of Architectural Historians (March 2010), 62–87. I am grateful to Nigel Westbrook for clarifying some technical points about the drawings.
Ibid., 82.
See Karl Theodore Parker, The Drawings of Hans Holbein in the Collection of His Majesty the King at Windsor Castle (Oxford – London, 1945), 30–33; Meder, Mastery of Drawing, 339; Susan Foister, Drawings by Holbein from the Royal Library (Windsor, 1983), 14–15; Maryan Ainsworth, “‘Paternes for phisioneamyes’: Holbein’s Portraiture Reconsidered,” The Burlington Magazine, 132 (1990), 173–186; and Jim Murrell, “Observations on Holbein’s Portrait Drawings,” The Paper Conservator, 20 (1996), 1–7.
Holbein’s painting “The Ambassadors” of 1533 in the National Gallery in London features both a lute, and the famous anamorphic skull in the foreground. The skull could have been drawn from life (death?) either using a grid which was then distorted, or else by tracing on a very oblique sheet of glass. I have tried the latter method, and it is workable.
Meder, Mastery of Drawing, 339.
Johann van Simmern, Eyn schön nützlich Büchlin und Underweisung der Kunst des Messens (Frankfurt?, 1531), fol. Hiiv. For the identification of the author of this work, see Kirsti Andersen, The Geometry of an Art: The History of Mathematical Theory of Perspective from Alberti to Monge (New York, 2007), 213–215.
Robert Fludd, Utriusque cosmi maioris scilicet et minoris metaphysica (Oppenheim, 1617), 307; John Bate, The Mysteries of Nature and Art (London, 1635), 110.
Abraham Bosse, Differentes manières de dessiner et peindre (Paris, 1667[?]), unnumbered plate.
Edward Noble, The Elements of Linear Perspective, Demonstrated by Geometrical Principles (London, 1771); see Iris Wien, “Constable and the Dynamics of Vision,” Tate Papers, 33 (2020), <www.tate.org.uk/research/tate-papers/33/constable-dynamics-vision>, accessed 21 November 2024. Constable also traced landscapes on glass; see Arthur Parsey, The Science of Vision; Or Natural Perspective! (London, 1840), 134.
See Ulrich W. Hiesinger, Antonio Mancini: Nineteenth-Century Italian Master (Philadelphia, PA, 2007).
Armand Cassagne, Guide de l’alphabet du dessin (Paris, 1880); see also Vincent van Gogh, letters to Theo van Gogh, The Hague, 5 and 6 August 1882; nos. 253 and 254 in Vincent van Gogh, The Letters (Van Gogh Museum, Amsterdam), <https://vangoghletters.org/orig/let253> and <https://vangoghletters.org/orig/let254>, accessed 21 November 2024.
The French garden designer Salomon de Caus also reproduces Dürer’s engraving in La perspective avec la raison des ombres et miroirs (London, 1612), “theoresme dixiesme,” n.p. The two men are drawing a cube. Such a simple task hardly justifies such an elaborate method. J. M. W. Turner, in turn, copied De Caus’s plate for the lectures on perspective that he gave at the Royal Academy in London from 1811; see Maurice Davies, Turner as Professor: The Artist and Linear Perspective (London, 1992), 17, fig. 5
Gian Paolo Lomazzo, Trattato dell’arte della pittura, scoltura et architettura (Milan, 1584), 319–320.
Giacomo Barozzi da Vignola and Egnazio Danti, Le due regole della prospettiva prattica (Rome, 1583).
Martin Kemp, The Science of Art: Optical Themes in Western Art from Brunelleschi to Seurat (New Haven, CT, 1990), 173.
Andersen, Geometry of an Art, 208.
Friedrich Christian Müller, Gebrauch der Transparente zum Zeichnen nach der Natur (Frankfurt and Leipzig, 1776).
Johann Heinrich Meynier and Heinrich Jan-Penningh, Theoretisch-practische Anleitung zum Zeichnen und Tuschen der Landschaften (Hof, 1796).
Meder, Mastery of Drawing, 339.
Francesca Whitlum Cooper, ed., Liotard and the Lavergne Family Breakfast, catalogue of an exhibition held at the National Gallery London (London, 2024), 75 and fig. 53. The drawing is made on four sheets joined together and is pricked for transfer. The historian of photography Heinrich Schwarz hinted that Liotard may have used some sort of optical drawing aid, quoting Horace Walpole as saying that the portraits were “too like to please”: see Art and Photography: Forerunners and Influences: Selected Essays by Heinrich Schwarz (Rochester, NY, 1985), 102.
“Nouvelles inventions: le procédé Rouillet,” L’Illustration (8 April 1843), 90. The history of Rouillet’s method is described by Camilla Murgia in “The Rouillet Process and Drawing Education in Mid-Nineteenth-Century France,” Nineteenth-Century Art Worldwide, 2 /1 (2003), <https://19thc-artworldwide.org/winter03> accessed 21 November 2024.
Marie Elisabeth Cavé, Le dessin sans maître: méthode pour apprendre à dessiner de mémoire (Paris, 1850). For accounts of Cavé’s life and work, see Frank Anderson Trapp, “A Mistress and a Master: Madame Cavé and Delacroix,” Art Journal, 27 (1967), 40–60, at 40–47 and 59–60; and Delanie Linden, “‘The Future of Women in the Future of the Nation’: Marie-Élisabeth Cavé’s Drawing Manuals and Education in Nineteenth-century France,” Getty Research Journal, 15 (2022), 87–112. The head of Mme Cavé in Figure 27 closely resembles a portrait in profile by Ingres.
John Ruskin, The Elements of Perspective, Arranged for the Use of Schools (London, 1859), 1.
See, for example, <https://thehelpfulartteacher.blogspot.com>, and <www.youtube.com/watch?v=XEC2KdXM3CY>, both accessed 21 November 2024.
