The Early Modern Renaissance of Digital Images: Alberti, Ptolemy, and a Map of Rome
“The Early Modern Renaissance of Digital Images: Alberti, Ptolemy, and a Map of Rome,” in Ptolemy’s Geography in the Renaissance, Transactions of the Conference, London, The Warburg Institute, 27-28 June 2003, edited by Zur Shalev and Charles Burnett, 81-90. London: The Warburg Institute, 2011
The text posted here is an earlier draft and it is different from the published version. Please only cite from copy in print
Around the end of the fifth decade of the fifteenth century Leon Battista Alberti had surveyed and drawn a plan of Rome. He then wrote a brief Latin text, titled Descriptio urbis Romae, where he explains that after drawing a plan of Rome, he had concocted (’excogitatus’) an original method whereby every scholar, even of indifferent talent (’mediocri ingenio praeditus’), would be able to redraw an exact copy of his original drawing. The method is the following: one should make or draw a circle, of which the circumference is divided into a given number of degrees. In the centre of the circle must be fixed a rotating ruler or radius, built in bronze or wood, also divided into a given number of fractions or units of length. In Alberti’s map of Rome, the central point of the device coincides with the top of the Capitoline Hill. Alberti then lists a number of places or points, each one identified by two measurements: an angle, to be read on the circle, and a distance from the centre, to be read on the radius. Following the measurements in the list, and using the circle and radius, the points must be plotted on a board. The result is a new map of Rome, a copy that will be identical (or proportionally identical) to Alberti’s original, as the whole process is purely mathematical and does not allow for visual approximation, nor for personal interpretation, with the exception of one variable that is deliberately left open: the scale of the drawing. Alberti explains that each user of the machine is expected to redraw a new map at a scale of choice, bigger or smaller, according to needs.
This is what Alberti says. What happens in reality is that at the end of the game, if one follows the instructions, what one gets is not a map of Rome, but a surface dotted by some 175 or 176 points—the points of which Alberti lists the coordinates. The drawing must be completed by joining some of the dots with straight lines and curves, as in a children’s game that was popular before the age of Nintendo. After the perimeters of the walls and the banks of the river are traced that way, one is left with a diagram showing the relative positions of some prominent places within a scaled map of the area of the city. In order to generate a real map of Rome Alberti should have added the coordinates of some millions of other points. Perhaps he deemed that unpractical, and gave up. Most likely the Descriptio was meant to offer a demonstration of method, and Alberti thought that others would follow suit and add the coordinates of more places. This however never happened.
To summarize: here we have a work by Alberti entitled A Description of the City of Rome. The text is about a plan of Rome that Alberti claims he has himself surveyed and drawn with the utmost precision and mathematical methods. Then we open the book and we find neither map nor drawings, other than the elementary diagrams of a circle and of its radius, both divided into degrees. Instead of the drawing of a map of Rome, the book contains a list of names of places and numbers. This is the listing of the polar coordinates of 175 locations in the city. Alberti explains how, on that basis, each reader is expected to redraw a new map.
Most scholars who have studied this singular work have concluded that the original map is lost. This is indeed the case if we refer to the map that Alberti had drawn for himself—and kept for himself. What he published and communicated to the public was not his own drawing as such, but a method plus a list of data whereby each user would produce a new map, each one identical, or proportionally identical, to the original. Alberti’s text was not a caption or footnote to a map now lost. This text was the map; indeed, it replaced the original drawing, because it contained all that was necessary in order to draw that original drawing again, anew, and identical.
This begs the question: if Alberti’s aim was to publish his map, why did he not do just that—why did he not publish his map? Instead, as we have seen, Alberti published a sequence of alphabetical letters and numbers (Hindu-Arabic numerals, not the Roman notation that he favoured elsewhere). What Alberti published was a sequence of digital data. A digital file. Together with this, Alberti provided the instructions whereby each user could open, or ‘unzip’ that file, hence recreate the original picture.
Computers did not exist in the 15th century—at least not the electrically powered calculating machines we now call by that name—and not surprisingly Alberti’s high-tech software for digital imaging did not perform well on parchment and quill hardware. As I have suggested elsewhere, Alberti’s digital mapmaking device may be seen as a deliberate, although unstated, revival of Ptolemy’s cartographic methods, as outlined in the first book of Ptolemy’s Geography, or Cosmography. This is the issue that I would like to bring up for discussion today. This is the issue I would like to address in this paper.
Alberti seems to have followed Ptolemy’s definition of geography almost verbatim, but he applied Ptolemy’s geographic method, conceived for the large scale of the surface of the earth, to the small scale of a city: contrary to Ptolemy’s distinction between geography and chorography, Alberti’s map of a city is mathematical, not pictorial; it is based on precise measurements drawn to scale, and it is represented in what we would call parallel, or orthogonal projections. If Alberti had wanted to represent a city ‘chorographically’, as a painter, he might have chosen central projections, or perspective—a technique that, after all, he knew well.
Likewise, Alberti’s idea of listing the numerical coordinates of a series of points in the map may appear Ptolemaic, although Alberti used a system of polar coordinates instead of longitude and latitude. In fact, Alberti’s mechanism is closer to Ptolemy’s first cartographic method, based on a conic diagram, which was constructed using a similar combination of a pivoting ruler or radius and of a graduated horizon. Circular cosmographies were not unknown in the early fifteenth century, sometimes accompanied by lists of polar coordinates—but again, Alberti’s adaption of this method to the scale of a city was original. Additionally, recent philological work has convincingly argued that Alberti knew Ptolemy’s Geography in the Latin translation of Jacopo d’Angiolo, or Angeli: some of Angiolo’s technical terms are used by Alberti, in the same context and with the same meaning; other linguistic correspondences, in particular some recurrent syntactical constructions have also been pointed out.
The key issue where Ptolemy’s example might have been determinant for Alberti bears on the relationship between text and image, or between the drawing of the maps and the digital file where Ptolemy and Alberti recorded the coordinates of some locations in their maps. Unlike Alberti, Ptolemy tried to explain why his maps were translated into numbers, or, as we would say, digitized. As Ptolemy asserts (in Stevenson’s translation, which was based on d’Angiolo Latin and, we may surmise, may have been close to Alberti’s own understanding of this crucial passage) there are two ways of making maps, and
… both have this common purpose, that is, they are constructed for use, to show (in the absence of any picture) how from commentaries alone the student may be able, with the utmost facility, to construct a new map. Recently the making of new copies from earlier copies has had the result of increasing some of the faults that were originally small into great discrepancies. If then there are not enough data for the method of constructing maps from commentaries (without any traditional pictures) it will be impossible for us to reach our desired end.
This, Ptolemy goes on, is precisely what happened with Marinos, as the data that he includes are insufficient and his cartographic method is wrong. As a remedy, Ptolemy then provides two new methods of his own invention, and goes on to list the coordinates of more than 8,000 locations.
Ptolemy’s passage reads more or less similarly in the first Latin version of Jacopo d’Angiolo (about 1409, first printed in 1475), in the first Italian version by Mattioli and Gastaldi (1548, probably from Angiolo’s Latin) and in the second Italian version by Girolamo Ruscelli (1561, purportedly retranslated from the Greek). Things became less straightforward in more recent times, as some reversed the meaning of that passage, particularly of the last phrase, implying that both cartographic methods are useless unless they are accompanied by independent copies of the maps. In 1932 the Jesuit Joseph Fischer tried to systematize what was at that point a growingly acrimonious Ptolemaic Bilderfrage, and he itemized three possible solutions: according to some, the commentaries were meant to generate the maps; according to others, the opposite: the maps were used to rewrite the commentaries; third option (which Fischer endorsed): maps and commentaries were intended to be copied and transmitted independently. More recently, Berggren and Jones have argued that the entire apparatus of Ptolemy’s Geography should be considered as a ‘map-making kit’, and they have accordingly translated the title of Ptolemy’s Geographike Hyphegesis as ‘Guide to Drawing a Map of the World’. The history of the manuscript tradition of Ptolemy’s Geography proves that the maps were often copied regardless of the commentaries; sometimes the opposite; and it also appears that occasionally the maps actually fed back onto the commentaries, which were edited or altered based on independently transmitted drawings. Moreover, several authors including Berggren and Jones have concluded that at some points in time the iconographic transmission of the maps must have been interrupted, and the drawings remade on the basis of the sole commentaries—at least in these cases following the directions that Ptolemy might have mandated right from the start.
A comparison between Ptolemy’s and Alberti’s digital maps may help to untangle this notorious interpretive and philological conundrum. A few centuries apart, but in similar technological environments, Ptolemy and Alberti found themselves in the same predicament, as they faced the same problem—the reliable transmission of quantitative information in a visual format. As it appears, confronted with the same challenge, they came to similar conclusions, which Alberti might have found regardless of Ptolemy’s example or, more likely, aware of it.
The manual copying of a drawing is always a risky venture, particularly when the drawing is proportional, and there is a need that proportions be identical in the original and in all copies. This is obviously the case for geographical maps accurately surveyed with mathematical instruments and methods, precisely measured, and drawn to scale. From one manual copy to the next, as Ptolemy pointed out, errors accumulate, distances are distorted, and the maps become unusable. To avoid this unpredictable drift Ptolemy listed several thousand locations, and of each place he indicated the geographic coordinates. Then, depending on how we read those crucial passages, Ptolemy seems to suggest that each reader should redraw one or more maps on the basis of the numerical data exclusively, whereas no map, once drawn, should ever be copied again. If this is the case, then each map should be generated each time anew from Ptolemy’s lists of coordinates, in the absence of any other transmitted picture or image.
One possible reason for Ptolemy’s stance is that Ptolemy might have concluded, with some reason, that alphabetical letters and numbers could be transmitted in space and time better, more safely, and more precisely than hand-made drawings. Consequently, Ptolemy’s maps of the world, like Alberti’s map of Rome, were encrypted in alpha-numerical sequences right from the start. This alpha-numerical file alone was meant to be copied and transmitted; maps were to be drawn based on the data and instructions contained in this file but, once drawn, they were not meant to be copied again. Every map was a one-off, intended and licensed, as Microsoft would require today, for private and personal use only: copies of copies were forbidden. Ptolemy’s and Alberti’s texts, on the contrary, were designed as map-generating programmes. Whenever a new image was needed, the programme had to be rerun. Each map, or each image, was the occasional and ephemeral epiphany of the text that contained its encryption. Alberti’s maps, as well as Ptolemy’s, were intended for visual apprehension, but were excluded from visual transmission. These images were designed and conceived to travel in space and time encapsulated in a digital file.
The unreliability of manually reproduced images was well known to the technical and scientific writers of Antiquity, of the Middle Ages, and of the early Renaissance—who in many cases had to devise strategies, rhetorical or otherwise, in order to transmit visual information while avoiding the manual copy of drawings. Witness the case, which is capital for the history of architecture, of Vitruvius’s illustrations: their loss was deeply lamented by Renaissance architects and scholars—and in some cases it still is to this day. But these images that were presumed lost, stolen, or hidden, in fact never existed, with the misleading exception of the nine to eleven geometrical diagrams that Vitruvius mentions and must have accompanied his text. All of these geometrical diagrams, however, were simple intersections of lines and elementary figures, as triangles and circles. Vitruvius never mentioned nor promised a picture of a Corinthian capital, and chances are that his treatise never included such a picture. Vitruvius certainly knew, as everyone knew at the time, that the fidelity of a manual copy of a drawing is in reverse proportion to its complexity, and he acted accordingly—he avoided a complex iconography that would not have been transmissible.
Likewise, none of Alberti’s treatises were illustrated, nor ever meant to be—including his works on perspective, architecture, and sculpture. This was by choice and not by chance. Alberti’s obsession with the fidelity of the copy of his manuscripts is well known, as in some cases his recommendations to copyists remained in later editions in print; equally well known are other curious ecphrastic stratagems that Alberti invented in order to record images while avoiding hand-made drawings. Alberti’s preeminent preoccupation with the fidelity of the copy was one reason why he abstained from images that could not be copied as precisely or as predictably as letters and numbers. Indeed, the whole Descriptio urbis Romae can be seen as a stratagem to record images without transmitting drawings. In this case Alberti’s stratagem, as we have seen, was based on an algorithmic encryption.
Alberti was not unfamiliar with the notion of encryption. In the De componendis cifris, one of his last writings, he describes an actual coding machine (which has earned him a place in the history of espionage). This was based on a device similar to the wheel and the radius that he had already used in the Descriptio urbis Romae, and on a secret code, the key of the machine, which Alberti called the ‘cipher’. Additionally, in spite of its title, Alberti’s De statua is not really a treatise on sculpture. Most of the treatise is devoted to the invention of another digital machine, this time Alberti’s more ambitious aim being the scanning and algorithmical reproduction of a three-dimensional object (in fact, a statue or a human body). Alberti suggests that by using an appropriate instrument, a three-dimensional archetype can be translated into a sequence of numbers, and recorded as a digital file. This list of numbers, once taken down, will enable the original body to be copied and reproduced ad infinitum, in distant places and future times, at the same scale, or proportionally enlarged or diminished. Alberti also suggests that, using the same technique, parts of a single statue can be manufactured simultaneously in different workshops—for example, one in Tuscany and another in Greece; when assembled on site, the different parts will all fit together.
The idea that a statue may be made through the assembly of digitally prefabricated parts evokes for us an uneasy feeling of a technological déjà-vu. Alberti’s notion that the perpetuity of a monument can be better guaranteed by a sequence of letters and numbers than by the original monument itself may also sound odd. Daily experience suggests that stone and marble may be stronger and more resistant in time than parchment and papyrus. In fact, Alberti’s issue here was not the life span or duration of the original: his digital technology was aimed at the recording, at the transmission, and at the reproduction of identical copies. Hence the same centuries-old barrier: the limited reliability of hand-made copies of drawings. Admittedly, one drawing may be faithful to the original. But what if the next copyist is less gifted than the first artist? In the chain of manuscript transmission, as in all chains, the strength of the system is that of its weakest link. When copying letters and numbers, mistakes may be edited out; on the contrary, a bad copy of a good drawing cannot be so easily restored. Drawings cannot be copied verbatim, for the simple but determinant reason that they cannot be broken down into verba—words, and exactly repeatable, standardized alphabetical letters. The alphabet (supplemented, in Alberti’s case, by the Hindu-Arabic or even by the Latin notation for numerals) is a technology that makes the transmission of words easy. Alberti must have concluded that at his time no similar technology existed for images. Images cannot be dictated.
Hence Alberti’s predicament, and Alberti’s solution. As Ptolemy had done long before, Alberti translated analog images into digital, alpha-numerical files. Alberti may in fact have generalized Ptolemy’s method, but in doing so he also extended its scope well beyond the limits of practical use. None of Alberti’s image-making technologies could have worked at his time. Alberti wanted pixel-rich pictures. His machinery and digital software could not deliver that, because no one at his time could have manipulated the huge amount of data that his machines would have generated or required.
In short, this is the story of a high-tech flop. Alberti’s ambitions were obviously ahead of the computing skills of his time. But another reason why Alberti’s digital technology would soon fall out of sight is, of course, that while Alberti was trying to develop an algorithmic, number-based method to record and transmit precise visual information, a new and much more practical technology was being invented that would soon deliver just that. Technically speaking, all that would have been necessary to print Alberti’s map of Rome was available and existed at the time when Alberti wrote his Description of the City of Rome—everything, that is, except the idea that a map of a city could be printed.
In hindsight, no one should blame Alberti for having failed to realize that the right technical solution to his intellectual requirements was to be found, and would soon be found, in another and, at his time, highly improbable technology: a marginal production of printed images already existed in the first half of the fifteenth century, but no scientist and no humanist would have known or cared. Evidently, Alberti never thought that printed images could serve scholarly purposes, and as a result most of his image-making digital gadgetry was useless fifty years after he had conceived it. And in fact, very little of it was used, witness the oblivion of his Descriptio urbis Romae, forgotten soon after Alberti wrote it and only recently brought back to light. Printed images liquidated Alberti’s digital prototypes. At the same time, Alberti’s premature experiments with digital technologies are a reminder of the urgency of the quest for the precise transmission of visual information that characterizes Alberti’s time as well as most of Alberti’s work. Alberti could already produce modern images—but he could not yet reproduce them. His ill-timed and ill-fated digital machines signal the cultural inevitability of the invention of print.
 The Descriptio was first partially published in Operette di Iacopo Morelli bibliotecario di S. Marco ora insieme raccolte con opuscoli di antichi scrittori, II, 5, Venice, Tip. di Alvisopoli, 1820, pp. 268-70; then first published in full in Piante icnografiche e prospettiche di Roma anteriori al secolo XVI, ed. Giovanni Battista De Rossi, Rome, Salviucci, 1879, pp. 131-8. The two most recent editions are based on six extant witnesses: see Leon Battista Alberti, Descriptio Urbis Romae, transl. and eds Martine Furno and Mario Carpo, Geneva, Droz, 2000; and ‘Leonis Baptistae Alberti Descriptio urbis Romae’, eds Jean-Yves Boriaud and Francesco Furlan, French transl. Jean-Yves Boriaud, Italian transl. Carmela Colombo, English transl. Peter Hicks, postface by Mario Carpo, Albertiana, 6, 2003, pp. 125-215.
 The existence of a 176th point, which would identify the church of San Giacomo al Gianicolo (‘Iacobi sub Iano’) is controversial, as that location is listed in the Furno edition of the Descriptio (n. 1 above), but contested by Boriaud and Furlan (Descriptio, n. 1 above).
 Alberti explains how he actually carried out his survey of Rome in another work, the Ludi rerum mathematicarum: see Leon Battista Alberti, Ludi rerum mathematicarum, in Id., Opere volgari, III, ed. Cecil Grayson, Bari, Laterza, 1973, pp. 131-73 (163).
 Both diagrams are included, with small variances, in all six extant MSS: see Descriptio, eds Boriaud and Furlan (n. 1 above), pp. 135-7.
 Following the pioneering study by Samuel Y. Edgerton, ‘Florentine Interest in Ptolemaic Cartography as Background for Renaissance Painting, Architecture, and the Discovery of America’, Journal of the Society of Architectural Historians, 33 no. 4, December 1974, pp. 275-92. See in particular p. 288: ‘The original map is lost […]’. Edgerton describes Alberti’s circle and radius as a ‘mechanical measuring device’ to be set up on the Capitoline Hill, in the location coinciding with the centre of the circular map, and concludes: ‘Thus [Alberti] had devised a very simple system for fixing a set of coordinates to every landmark in Rome. He then provided a table listing all the sites and coordinates so they could be found on the map.’ A persistent tradition, established by Constantin Winterberg in 1886, claims that a drawing of the map was actually attached to one extant MS of the Descriptio, the Codex Marciano Ital.[Zen.] XI67 (7351). As Winterberg discusses errors in the heights of buildings represented in this drawing, and Alberti’s Descriptio is a plan, in 1972 Luigi Vagnetti first suspected that this drawing might not have been the one that according to Vagnetti should have accompanied Alberti’s original text (‘il grafico che era verosimilmente allegato al testo originale albertiano’). This suspicion could not be validated as no one after Winterberg seems to have seen that drawing. Vagnetti could not find it when he looked for it in 1968, and declared it mislaid or lost. Recently Francesco Furlan further investigated the matter and excluded the possibility that that Codex may ever have included a drawing. See [C.?] Winterberg, ‘Leon Baptist Alberti’s technische Schriften’, Repertorium für Kunstwissenschaft, VI, 1886, pp. 326-56 (335-44); Luigi Vagnetti, ‘Lo studio di Roma negli scritti Albertiani’, in Atti del Convegno Internazionale Indetto nel V Centenario di Leon Battista Alberti, Rome-Mantua-Florence, 25-29 April 1972, Rome, Accademia Nazionale dei Lincei, 1974, pp. 73-110 (84, 92, and n. 87); Francesco Furlan, ‘In margine all’edizione degli Ex Ludis rerum mathematicarum’, in Atti del Convegno internazionale di studi ‘Francesco Maurolico e le matematiche del Rinascimento’, Messina, 16-19 October 2002, eds. Veronica Gavagna and Rosario Moscheo, Messina, Università degli Studi di Messina, [forthcoming], nn. 15-16.
 See my ‘Ecphrasis géographique et culture visuelle à l’aube de la révolution typographique’, in Alberti, Descriptio, eds M. Furno and M. Carpo (n. 1 above), pp. 65-96; and Architecture in the Age of Printing: Orality, Writing, Typography, and Printed Images in the History of Architectural Theory, Cambridge, MA and London, The MIT Press, 2001, pp. 119-24.
 Ptolemy, Geography, I, 1. See Geography of Claudius Ptolemy. Translated into English and Edited by Edward Luther Stevenson […] with an Introduction by […] Joseph Fischer, S.J., New York: New York Public Library, 1932, pp. 25-6; J. Lennart Berggren and Alexander Jones, Ptolemy’s Geography: An Annotated Translation of the Theoretical Chapters, Princeton and Oxford, Princeton University Press, 2000, pp. 57-8, where ‘geography’ and ’chorography’ are translated as ‘world cartography’ and ‘regional cartography’, respectively.
 In the case of Ptolemy, the ruler was fixed at the North Pole and slid along an arc of the equatorial line divided into 180 degrees or twelve hours: Ptolemy, Geography, I, 24. See Geography, ed. Stevenson (n. 7 above), pp. 42-3; Berggren and Jones, Geography (n. 7 above), pp. 86-8.
 Carpo, ‘Ecphrasis’ (n. 6 above); in particular p. 82 and n. 41.
 Martine Furno, ‘La Descriptio Urbis Romae dans l’histoire du latin et de la culture humaniste’, in Alberti, Descriptio, eds M. Furno and M. Carpo (n. 1 above), pp. 97-123 (100-102).
 Ptolemy, Geography, I, 18. See Geography, ed. Stevenson (n. 7 above), p. 38. Berggren and Jones construct the second part of the passage differently but the meaning does not change: ‘We must still investigate the method of drawing the map. This undertaking can take two forms: the first sets out the oikoumene on a part of a spherical surface, and the second on a plane. The object in both is the same, namely convenience; that is, to show how, without having a model already at hand, but merely by having the texts beside us, we can most conveniently make the map. After all, continually transferring [a map] from earlier exemplars to subsequent ones tends to bring about grave distortions in the transcriptions through gradual changes. If this method based on a text did not suffice to show how to set [the map] out, then it would be impossible for people without access to the picture to accomplish their object properly. And in fact this is what happens to most people [who try to draw] a map based on Marinos, since they do not possess a model based on his final compilation; instead they draw on his writings and err in most respects from the consensus of opinion, because his guide is so hard to use and so poorly arranged, as anyone who tries it can see.’ Berggren and Jones, Ptolemy’s Geography (n. 7 above), pp. 80-81.
 Cf. Claudii Ptolemæi Cosmographiæ, Vicenza, Hermanus Levilapis [i.e. Liechtenstein] Coloniensis, 1475, caput xviii, f. s.n°: ‘Reliquum est ut quæ ad descript<i>onis ipsius rem pertinent animaduertamus: duplex ergo cum forma sit huius operis. nam cum primo ea fit: quæ superficiei nostræ habitabilis in sphærico ponit: Deinde ea quæ in plano notatur / unum ambobus commune est facilitas scilicet operis hoc est quomodo etiam absque exemplari pictura ex solis com<m>entariis quæ maxime fieri possit descriptio commoda habilisque in tabula fiat. Sedulo enim a prioribus exemplaribus noua condere per uicium paulatim conceptum ad dissimilitudinem maximam duci solitum est. siquidem modus qui per commentaria captatur forte non sufficit ad condendam tabulam: his quibus exemplar imaginis deest omnino inpossibile fiet optato quodammodo potiri’ (I owe this transcription of Angiolo’s princeps to Francesco Furlan). See also Claudii Ptolemaei Cosmographiae, Bologna, Dominicus de Lapis, 1462 [but 1477], and La Geografia di Claudio Ptolemeo alessandrino […], ridotta in volgare italiano da Pietro Andrea Mattiolo senese […], Venice, Giovanni Battista Pedrazzano, 1548, p. 26: ‘Resta ora, che consideriamo gli andamenti [i.e. methods], che si ricercano intorno alla descrittione. Essendo adunque la via di far questo in due modi, il primo che disegna la dispositione del mondo in la parte della superficie spherica, e il secondo nel piano, questo si conviene ad amenduni, che si proponga una certa facilità d’operare, cioè che si dimostri in che modo, ancora che non sia in ciò proposto alcuno essemplare [i.e. drawing]. Che possiamo fare la descrittione, quanto far si può comodissimamente, con quella dottrina sola, la quale si tratta nelli commentarii. Veramente le continue tradottioni, che si fanno da i primi essemplari a gli ultimi, sogliono indurre in questa cosa egregia, per ogni picciola variatione, mutationi grandemente dissimili. Così parimenti anchora per quel modo, il quale si tratta solamente per i commentarii, sarà impossibile a coloro di posser giustamente conseguire il suo proposito, se non accaderà, che sia quel modo sufficiente per dimostrare l’espositione’. See also La Geografia di Claudio Tolomeo alessandrino, nuovamente tradotta di Greco in Italiano, da Girolamo Ruscelli […], Venice, Valgrisi, 1561.
 See for example the Latin translation by Karl Müller (1883): ’Duplex igitur quum rei tractandae sit modus […] commune in utroque hoc propositum est, ut ad usum accomodatus sit, sive ut demonstretur, quomodo, etiamsi nulla subiecta sit imago, ex iis solis quae commentarii suppeditant, facilitate quam maxima delineare tabulam possis. Quodsi enim priora exemplaria ad posteriora perpetuo transferuntur, invalescente paullatim mutatione translationes in insignem exire solent dissimilitudinem; sin illa ratio, qua sola commentariorum ope tabula describitur, ad expositionis demonstrationem non suffecerit, fieri nequit ut imagine carentes propositum, ut par est, assequantur’ [emphasis mine]. Claudii Ptolemæi Geographia, E codicibus recognovit, prolegomenis, annotatione, indicibus, tabulis instruxit Carolus Müllerus [Karl Müller], Paris, Firmin Didot, 1883-1901, I, part 1, 1883, pp. 48-9.
 Joseph Fischer, ‘De Cl. Ptolemaei vita operibus geographia praesertim eiusque fatis’, in Claudii Ptolemaei Geographiae Codex Urbinas Graecus 82, phototypice depictus […], I, Leiden and Lepzig, E. J. Brill and Otto Harrassowitz, 1932, pp. 136-58.
 Berggren and Jones, Geography (n. 7 above), pp. 4-5.
 Fischer, ‘De Cl. Ptolemaei vita’ (n. 14 above), pp. 136-58; Alexander Jones, ‘Ptolemy’s Geography: A User’s Guide’, paper presented at the Conference Ptolemy’s Geography in the Renaissance, London, The Warburg Institute, 27-28 June 2003; see this volume pp. 000-000.
 The iconographic transmission of the maps would have been interrupted, and the maps would have been redrawn from the coordinates in the commentaries at least twice, first by the Alexandrian engineer Agathos Daimon in the 5th century, then by the Byzantine monk Maximos Planudes about AD 1300. See Berggren and Jones, Geography (n. 7 above), pp. 46-9. On the ’legend of Agathos Daimon’, see Fischer, ‘De Cl. Ptolemaei vita’ (n. 14 above), pp. 109-20; and Carpo, ‘Ecphrasis’ (n. 6 above), p. 78 and n. 34.
 See Carpo, ‘Ecphrasis’ (n. 6 above), pp. 65-96.
 See Carpo, Architecture in the Age of Printing (n. 6 above), pp. 119-24; and ‘How do You Imitate a Building That You Have Never Seen? Printed Images, Ancient Models, and Handmade Drawings in Renaissance Architectural Theory’, Zeitschrift für Kunstgeschichte 64 no. 2 (2001), pp. 223-34.
 Carpo, Architecture in the Age of Printing (n. 6 above), pp. 16-23.
 With the exception, again, of some elementary geometrical diagrams and, more significantly, of the Ludi rerum mathematicarum, where the text refers to 29 drawings. The Ludi, however, first drafted in the form of a letter to Meliaduso d’Este, were originally not meant for publication, hence those images were not destined to be copied. See Carpo, ‘Ecphrasis’ (n. 6 above), p. 92 and n. 60.
 Carpo, Architecture in the Age of Printing (n. 6 above), pp. 119-24 (120).
 Ironically, Alberti’s work on criptography opens with Alberti’s only known reference to the invention of printing with moveable type. Alberti does not mention printed images. Carpo, Architecture in the Age of Printing (n. 6 above), p. 119.
 Carpo, ‘Ecphrasis’ (n. 6 above), pp. 89-96.
 Or, to be precise, of proportionally identical (scaled, or homothetical) copies. The list of the proportions of the human body that Alberti appended at the end of the De Statua has been often read and seen out of context (not surprisingly, it was used as the source for drawn illustrations), and as such it may have been more influential that Alberti’s mechanisms and measuring methods, which it was meant to exemplify. In fact, as Alberti explains, the proportions he lists are not ideal, but mathematically averaged, and he assessed them using the exempeda, the more general instrument, not the finitorium with the wheel and moveable radius, designed to record the special measurements of individual bodies.
 Carpo, Architecture in the Age of Printing (n. 6 above), pp. 121-2.
“The Early Modern Renaissance of Digital Images: Alberti, Ptolemy, and a Map of Rome,” in Ptolemy’s Geography in the Renaissance, Transactions of the Conference, London, The Warburg Institute, 27-28 June 2003, edited by Zur Shalev and Charles Burnett, 81-90. London: The Warburg Institute, 2011