Dr. Kim H. Veltman

II    Centres

1. Introduction
2. Europe
3. Greater Europe
4. Britain
5. America
6. Far East and Elsewhere
7. Conclusions

    The importance of centres in the development and diffusion of Renaissance culture, assumed by Vasari (1550),1 and discussed by Burckhardt (1860),2 became the topic of an important book by Chastel (1965),3 who acknowledged that there were problems with the approach. For while Florence, Lombardy, Rome, Naples, Venice and Padua were of enormous significance, smaller cities such as Lodi and Prato were also important. In a subsequent book on Italy's workshops (1969)4 Chastel gave greater emphasis to these smaller cities surrounding the larger ones, as, for example, Bergamo, Brescia, Como, Vigevano and Pavia in the case of Milan. Since then there has been increasing attention in the relation between centre and periphery. Ginzburg and Castelnuovo,5 in a fundamental study, have challenged the very notion of a centre.

    A detailed study would need to confront these problems of method, and might draw parallels between criticism of great centres and the fashion to criticize great individuals. Our concern is more modest: to outline the development of the major centres of publication regarding perspective and to trace how these shift with time. Centres in cities were usually due to the presence of a court, university and/or a workshop. They could be centres in at least three different senses: as places of production, as places which attracted painters to meet, or as places of transit. Nor was it just a question of painters. As Settis has shown, humanist counselors played an important part in these developments.

    We shall concentrate on the published treatises, aware that there is a further story to be told in terms of printed engravings and the spread of images through loose drawings, which were occasionally collected in sketchbooks. For our purposes the world as a whole may conveniently be divided into five areas: Europe, greater Europe, Britain, America and the Far East (including India and Australia). The publication of texts on perspective began in Italy in the late fifteenth century. In the sixteenth century it spread to France, Belgium, the Netherlands, Germany and Switzerland. These core European countries are responsible for about 37% of all publications.

    Directly adjacent to these core countries are a number of others, which may be termed greater Europe. These include Spain, Portugal, Denmark, Sweden, Finland, Norway, Austria, Czechoslovakia, Poland, Roumania and the U.S.S.R. Publication in these usually began sporadically in the sixteenth, seventeenth or eighteenth century, with actual centres emerging only in the nineteenth and twentieth centuries. A third area in Britain, in which England, responsible for nearly 15% of all publications, plays a dominant role. In the late sixteenth and throughout the seventeenth centuries it remained very much in the shadow of Europe, relying largely on translations of continental texts. But by the eighteenth century London emerged as the leading centre in the world.

    A fourth area, America, did not emerge until the nineteenth century, when the United States, and New York in particular, became a major centre. Canada, by contrast, has developed no centres. As for South America, Rio di Janeiro has been the only city with more than a few publications. Finally, in the case of the Far East, although perspective was introduced to China by the Jesuits in the early eighteenth century, centres of publication have only emerged in the twentieth century. In Japan, it did not begin until the 1960's, and in Taiwan, not until the 1970's. Publications in India go back to the nineteenth century, but they have remained too sporadic to speak of centres. In Australia the same has been true in the twentieth century. In the Middle East and throughout the whole of Africa no centres of publication have emerged.

    From the above it is clear that although perspective is an international phenomenon the extent of its impact varies enormously. Of the 48 countries involved, three published over eleven hundred treatises each: Germany (1480), England (1187) and France (1185). Three others produced between 400 and 1000, namely, Italy (851), the United States (828) and the Netherlands (425). Five countries produced betwen 100 and 200 texts (Austria, Belgium, Spain, Switzerland and the U.S.S.R.); seven produced between 25 and 100 (China, Czechoslovakia, Denmark, Japan, Poland, Scotland and Sweden), while 31 countries produced less than 25 texts each. In terms of continents, this means that approximately 85% of all publications occurred in Europe, 13% in North America, and 2% in the rest of the world. To understand better how these patterns emerged it will be useful to consider developments in each of the major areas in turn, beginning with Europe, and specifically Italy where it all began.

    We have already suggested (above p. ), that the perspectival principles which Brunelleschi and Alberti applied to paintings, may well have been inspired by Biagio Pelacani's lectures on optics in Padua in which he used Ptolemy's Planisphere as a point of departure in comparing theoretical and practical projection methods. In any case, Padua certainly played a role in the early history of perspective. Here Giotto produced his famous examples of proto-perspectival space in the Scrovegni Chapel (1305-1307), and here, in the fifteenth century, Alberti worked, while Squarcione and Mantegna painted famous early examples of perspective. In the seventeenth century there were also a few publications, including instruments connected with perspective: Galileo's proportional compass (1606) and Scheiner's pantograph (1637) and a treatise by Viola-Zanini (1629, 1677, 1678, 1698). The eighteenth century brought work on conic sections by Rocchius (1756) and a general text on linear perspective by Stellini (1778-1782). The nineteenth century brought a reprint of Barozzi (1808) and two moderately interesting texts by Tabacchi (1844) and Bellavitis (1851). Our century has seen two further such texts by Severi (1918, 1919) and Martinetti (1926) plus one popular work by Campedelli (1945, 1948, 1950, 1960, 1970).

                                                                                        PADUA

                                                                            Biagio Pelacani da Parma

                                                                            |                                      |

                                                                            |                                      |

                                           Paolo Nicolotto d'Udine                                 Prosdocimo da Beldomandi

                                                (Paul of Venice)                                                 |                                |

                                             |                                 |                                           |                                |

                                             |                                 |                                           |                                |

                            Giovanni Fontana               Nicholas of Cusa         Paolo dal Pozzo Toscanelli        L. B. Alberti

Fig. 12. Theoreticians in Padua (1390-1420). In this and the following charts, underlined names indicate authors of texts on perspective and related topics. Names underscored with a broken line indicate authors to whom texts on perspective are attributed. Those not underlined are practitioners.

    But to return to the fifteenth century: from Padua the ideas spread north to Venice and south to Florence (fig. 12). Giovanni Fontana returned to Venice and wrote what may have been the first treatise on perspective--no longer extant--which he dedicated to Jacopo Bellini, author of the famous Sketchbooks (pl. 6.1-2; 9.3-4, 11.2) who, in turn probably influenced Domenico Veneziano. Meanwhile Paolo dal Pozzo Toscanelli and Leon Battista Alberti returned to Florence where both were friends with Filippo Brunelleschi, reputed to have made the first demonstration of perspective sometime between 1415 and 1425. Toscanelli's interest in projection methods is shown by the sundial he constructed by means of an aperture in the cupola of the cathedral at Florence. He may also have been the author of an anonymous treatise on optics entitled On perspective 6 (Florence, Riccardiana ms. 2110). Alberti wrote the first extant treatise on perspective, the Italian version of which he dedicated to Brunelleschi, and also discussed perspective in the context of transformational geometry in his Elements of painting.

    Soon there were direct connections between Florence and Venice. Paolo Uccello, who studied with Donatello in the workshop of Ghiberti (1404), and knew Alberti, worked in Venice on the perspectival mosaics at San Marco (c. 1425-1430) and later also in Urbino (1465). In 1439, Domenico Veneziano moved from Venice to Florence, where he became a teacher of Piero della Francesca, who later also went to Urbino. There, in the atmosphere of the court, Piero became involved in the traditions of classical mathematics, which led to his writing treatises on the subject. Piero's insights became a starting point for two other individuals active in Urbino: the architect-engineer, Francesco di Giorgio Martini and the mathematician, Luca Pacioli. In the early 1490's, Francesco di Giorgio Martini was together with Leonardo da Vinci at Pavia, and from 1496 to 1499 Pacioli and Leonardo worked together at the court of Ludovico il Moro in Milan. Leonardo drafted a treatise on perspective7 in the Manuscript A (36v-42v, 1492), and also wrote a famous treatise which is no longer extant. What emerges therefore is a fascinating network of individuals spreading ideas from Padua to centres such as Venice, Florence, Urbino and Milan. The complexity of this network will emerge more clearly as we examine these centres in turn.

Venice

    There were important links between Florence and Venice. In 1424 Paolo Uccello went from Florence to Venice. He returned to Florence in 1431. In 1423 Jacopo Bellini travelled from Venice to Florence, became a student of Gentile da Fabriano, and came under the influence of Ghiberti, Donatello, Brunelleschi and later perhaps of Masaccio. This has led a modern author, Joost Gaugier, to speak of the tuscanization of Bellini's art.8 Bellini's Sketchbooks, produced mainly in the 1430's and 40's, were, however, much more than simple reflections of Florentine conventions. They emphasized the visual aspects of perspectival space, and introduced a new monumentality that was pioneering at the time. Bellini's two manuscripts, now in the Louvre and British Library, included no discussion of theory and contained instead brilliant examples of imaginary architectural views in perspective (pl. 9.3-4). In so doing, he initiated in tradition, which continued in Rome (see p. ), and which Androuet du Cerceau and Vredeman de Vries popularized in the North during the latter sixteenth century. Bellini's Sketchbooks had a more profound impact on Venetian culture than is usually appreciated. As Corboz (1986)9 has astutely shown, Bellini's visionary drawings functioned in an extraordinary way as an architect's conception of what in the next generation became the Doge's Palace and St. Mark's Square as we know them today.

    In the realm of painting, Vasari tells us10 of Jacopo Bellini's influence on Domenico Veneziano,(figs. 13 and 17), who subsequently went to Florence. Not mentioned by Vasari is Bellini's influence on Carlo Crivelli, which

VENICE I

Giovanni Fontana

Jacopo Bellini

Squarcione

Vivarini Domenico Veneziano

Nicolosia Bellini

+

Mantegna Antonello da Messina Gentile Bellini Giovanni Bellini

Carlo Crivelli Vittore Carpaccio Montagna Cima da Conigliano

Fig. 13. Venetian theoreticians and practitioners (1400-1500).

becomes obvious on comparison of two of Bellini's preparatory sketches for an Annunciation (pl. 83.1-2) with Crivelli's famous version of the same subject now in the National Gallery, London (pl. 83.3). Jacopo Bellini's influence is, of course, most directly evident through his children. His eldest son, Gentile, taught Vittore Carpaccio. Vasari tells us11 that Jacopo Bellini's second son, Giovanni (cf. pl. 7.2), taught both Montagna and Cima da Conegliano. The elder Bellini's daughter, Nicolosia, in turn, married Andrea Mantegna, and thus drew him into the inner circle of Venetian perspectivists, Mantegna influencing them, as much as they did him.

    In the last two decades of the fifteenth century the monk, Luca Pacioli, became fascinated with the theological dimensions of perspective. During one of his many stays in Venice he even gave a sermon on the subject of proportion and perspective12 in the church of of San Bartolomeo on 11 August 1506, which he later published in the 1509 edition of Euclid's Elements. But Pacioli's tendencies as a publicist went well beyond sermons. With the appearance of his Compendium in 1494, Venice became the first city in Italy to publish a work on perspective (fig. 14). The next decades saw the publication there of his Divine proportion (1509), and a second edition of the Summa (1523). By the 1540's, Venice had become the most important publishing centre in Italy for texts on perspective, with 64 titles prior to 1600. Some were classical texts considered important for perspective such as Euclid (1505, 1510), Ptolemy (1511, 1548, 1561, 1562, 1564, 1574) and Vitruvius (1511). Some were architectural treatises: e.g. Cataneo (1554, 1567), Palladio (1570, 1581) and Scamozzi (1582, 1583).

    In some cases, as with Cristoforo Sorte (1580), who had worked with Giulio Romano, only passing comments on perspective were involved. Others, such as Giovanni Battista Benedetti (1586), were highly technical. More important was Daniele Barbaro who, as Patriarch of Aquileia, played an important role as a go-between for new ideas, especially among instrument makers with interests in perspective, such as Baldassare Lanci, Cosimo Bartoli, Silvio Belli and Fabrizio Mordente (fig. 39, see below 2.1). Barbaro alluded to a number of these innovations in his Practice of perspective (1568, 1569), in which he consciously set out to popularize the subject, drawing on both Piero della Francesca and Albrecht Dürer, thus bringing together ideas from both central Italy and Nürnberg. Also important was Sirigatti's treatise (1596), which was based largely on Giorgio Vasari Jr.'s unpublished manuscript, and introduced a number of semi-regular solids (e.g. pl. 37.2) into the printed repertory.

VENICE II

Piero della

Francesca Luca Pacioli Bramiantino Bramante

...........

Giovanni Zamberti Baldassare Peruzzi

..................

Giulio Romano

Christoforo Sorte

Albrecht Dürer Sebastiano Serlio - Pieter Coecke

Jacopo Sansovino Jacopo Meleghino Hieronymus Cock

Daniele Barbaro Giacomo Barozzi G.B. Pittoni

Andrea Palladio Egnazio Danti

Vincenzo Scamozzi

Fig. 14. Venetian theoreticians and practitioners (1500-1600).

    Indeed, Venice itself increasingly functioned as a clearing-house in exporting ideas North of the Alps, as witnessed by the most popular of all sixteenth century publications on perspective by Serlio. While still in Rome, Serlio had inherited the writings and work of Baldassare Peruzzi on the subject. This he collected as a treatise which he published separately (1542) and subsequently as book two of his works on architecture (1544-1568). By 1545, a French translation by Jean Martin appeared in Paris. Two years later, a German (partial) translation by Walther Ryff appeared in Nürnberg, and it is claimed that a Dutch translation by Pieter Coecke van Aelst followed in 1549.

    Among the individuals directly influenced by Coecke's translation of Serlio, was Hieronymus Cock who went on the produce a work on roman ruins with perspectival views (Antwerp, 1550). This was republished a decade later in Venice, in a pirate edition by Giovanni Battista Pittoni (1560, 1575), which then became the basis for a treatise by Scamozzi (1582). Paolo Gallucci also published his Italian translations of Dürer (1591, 1954), and Pélerin (1599), in Venice. Hence, in addition to exporting local ideas, Venice served as one of the only Italian centres, which publicized work done North of the Alps.

    In the seventeenth century, the significance of Venice as a centre for publishing texts on perspective dwindled considerably with 13 titles in the first three decades and only 5 in the seventy years that followed. The majority of these were reprints. Among the new authors, the best known were Contino (1645, 1660), followed by Diano da Diano (1628) and Raverta (1603) whose work on surveying and perspective also appeared in a German translation in Nürnberg (1726). The eighteenth century brought thirteen further titles, of which only Visentini's (1742) book of Venetian views bears mention. The nineteenth century added only three titles.

Florence

    Florence was never a particularly important place for the publishing of texts on perspective. In the fifteenth century there were none. Its significance for the early history of perspective (cf. fig. XVI) was nonetheless enormous. Here Brunelleschi, who was being referred to as a perspectivist (prospettivo), as early as 1410, performed his historic demonstrations involving the Baptistry and the Piazza Signoria (1415-1425) and even before this, according to Vasari, Lorenzo Ghiberti was exploring proto-perspectival methods which influenced Maso di Christofano, Paolo Uccello,13 Donatello and Antonio Pollaiuolo. In addition, although modern criticism doubts the heritage, Vasari also reports on14 Donatello's significance for both Masolino and Squarcione who in turn taught Mantegna the rudiments of perspective in Padua and influenced the Ferrara school through Cosme Tura and his pupil, Ercole de Roberti (fig.15).

    The perspectival treatises of Alberti and the optical manuscript ascribed to Toscanelli written in Florence have already been mentioned. It is noteworthy that the painter Vasari omits mention of their possible debt to Biagio Pelacani and the Paduan tradition of optics and astronomy, emphasizing instead their association with Brunelleschi and that painter's influence on Masaccio and Filarete.15

    In the second generation (1440-1470), with the exception of a few pages on the subject by Filarete,--who, although Florentine by birth, was much more influenced by the Roman and Milanese tradition--, the field was dominated by practitioners (fig. 16). From the North, Domenico Veneziano brought with him a Venetian sense of space which inspired Fra Angelico and, as Vasari tells us,16 the lineage of painters including Andrea del Castagno, Piero Pollaiuolo, Filippo Lippi and Sandro Botticelli, as well as Andrea del Verrocchio, whose workshops included Sandro Botticelli, Botticini, Fiorenzo di Lorenzo, Leonardo da Vinci, and Perugino. Piero della Francesca was another key figure, who also had a large number of followers, including, as Vasari reports, the maker of intarsia, Cristoforo da Lendinara; the painter Melozzo da Forli,17 the architect-engineer Francesco di Giorgio Martini and the mathematician, Luca Pacioli.

    In the period 1470-1500 (cf. fig. XVIII), four individuals with Florentine connections wrote on perspective, namely, Piero della Francesca, Francesco di Giorgio Martini, Luca Pacioli and Leonardo da Vinci. But of these, Piero and Francesco di Giorgio had Urbino as the chief base for their theoretical work, Leonardo da Vinci did his most significant writing in Milan, while Pacioli's writing occurred in Milan, Venice and Rome.

    Nor did the situation change drastically in the sixteenth century which saw the publication of one important work by Gauricus (1504), a work by Dosio inspired by Roman ruins (1589) and three classical authors believed relevant to perspective, namely, Lucretius (1512), Euclid (1573) and Heliodorus of Larissa (1573). There was also Giorgio Vasari, Jr.'s manuscript of 1595 (pl. 36.3), which served as a basis for Sirigatti's treatise (1596, cf. p. 37.2). If Florence was never really a major centre in terms of theory, it was nonetheless of crucial importance in terms of paintings, gardens (see below II.3), object (e.g. what the Italians call bicchierographia), and architecture.

FLORENCE I

Paolo dal Pozzo Toscanelli Leon Battista Alberti Lorenzo Ghiberti

Taccola - Filippo Brunelleschi Paolo Uccello Donatello Antonio Pollaiuolo

Maso di Christoforo

Masaccio Masolino

Antonio di Tuccio Manetti Filarete Squarcione

Cosme Tura Mantegna Cosme Tura

Ercole di Roberti

Fig. 15. Florentine practitioners and theoreticians (1400-1440).

FLORENCE II

Domenico Veneziano Filarete -- Jean Fouquet

Andrea del Castagno Fra Angelico Piero della Francesca

Piero Pollaiuolo Alesso Baldovinetti

Filippo Lippi Andrea del Verrocchio

Sandro Botticelli Ghirlandaio Botticini Fiorenzo di Lorenzo Perugino

Fig. 16. Florentine practitioners and theoreticians (1440-1470).

FLORENCE III

Francesco di Lauranna Piero della Francesca

C. da Lendinara Melozzo da Forli F. di Giorgio Martini Luca Pacioli Andrea del Verrocchio

Luca Signorelli

Fra Giovanni da Verona Leonardo da Vinci

Perugino

Cennino Cennini Baccio Bandinelli Raphael G.B. Caporali G. Genga

Benedetto da Maiano

Sebastiano Serlio Diaceto Bugiardino Francesco de Salviati

Fra Bartolommeo

Benedetto Salviati della Porta

Giulio Romano Baldassare Lanci

Martino Bassi B.Genga

Ammanati Giorgio Vasari

Giorgio Vasari Jr.

Fig. 17. Florentine practitioners and theoreticians (1470-1600).

    Curiously enough it played the same role with respect to universal measuring instruments and the sector which came to be intimately connected with perspective (cf.pp. ). This story involves a complex heritage of techniques and ideas which can be traced (fig. 41) from Nürnberg in the latter fifteenth and early sixteenth centuries (Peurbach, Regiomontanus, Apian), via Antwerp in the 1530's and 40's (Gemma Frisius, Mercator), and Paris in the 1540's - 1560's (Orone Finé, Pierre de la Ramée and Abel Foullon), south (fig. 39) to Venice in the 1560's (Silvio Belli, Daniele Barbaro, Fabrizio Mordente, Latino Orsini), and finally to Florence (Cosimo Bartoli, Egnazio Danti, Francesco Pifferi) where in 1594, the same Giorgio Vasari, Jr. who wrote on perspective, prepared a compendium of all universal measuring instruments in the grand duke of Tuscany's collection. In terms of practical examples, this manuscript was undoubtedly of interest to Galileo Galilei who, by 1596, was developing his sector in Padua.

    The seventeenth century saw no basic change in this Florentine pattern. There was a book on Roman ruins by Maggi (1600), and on views of Jerusalem by Amico (1620); a manuscript by Galileo's friend Lodovico Cardi (il Cigoli, c. 1612), which was never published; one important textbook by Accolti (1526, cf. 1627, 1628); a significant treatise by Malombra (1630) and a mathematical one by Torricelli (1644). The eighteenth century saw one classical text by Apollonius (1722) and two modern works by Lorenzini (1721) and Grandi (1744, 1750, 1764) on conic sections, plus a significant edition of Leonardo's Treatise of painting (1792). The nineteenth century brought a half dozen new authors: Rossi Melocchi (1805), Benvenuti (1817), Castagnoli (1830), Sanquirico (1840), Cucchi (1862) and Bellotti (1892) plus a new interest in Renaissance authors particularly Ghiberti (1839), Alberti (1843, 1849, 1890) and Barozzi da Vignola (1831). The twentieth century has seen a development of this trend with editions of Toscanelli (1964), Alberti (1950, 1972), Bellini (1908), Francesco di Giorgio Martini (1970), Piero della Francesca (1942, 1974, 1984), Leonardo (1973) and Lomazzo (1975) plus at least ten modern authors, notably Saccardi (1961, 1970, 1975), Monticolo (1965, 1975) and more recently Aterini (1978, 1980). The interest in reprints is a reflection of a larger pattern, for Florence has become one of the leading centres in terms of secondary literature about the history of perspective.

Urbino

    At Urbino interest in perspective was more closely connected with mathematics. As Rose (1975),18 has so elegantly shown, by the 1470's Urbino had become a major centre for the collection of mathematical texts, largely due to duke Guidobaldo da Montefeltro's personal interests. The duke had his own copies of Piero della Francesca's Book of the abacus, Booklet of the five regular solids, and On the perspective of painting, all three of which--as Egnazio Danti (1583) noted--were considered as texts on perspective and served, as Daly Davis (1977)19 has demonstrated, as sources for Luca Pacioli's Summa (1494) and Divine proportion (written 1496-1499) and published 1509). In the latter decades of the fifteenth century, Francesco di Giorgio Martini, who20 was one of the chief architects of the ducal palace, and responsible for the striking perspectival intarsia in the library (pl. 79.1), also wrote on perspective there.

    In the mid-sixteenth century, the collection of mathematical manuscripts was given new impetus by Federico Commandino who launched a programme to edit and publish major Greek and Latin classics. His initiatives attracted a wide circle of scholars and scientists (fig. 38), which included Nicolo Tartaglia, John Dee and Giovanni Battista Benedetti.Of particular interest for our purposes, is Commandino's edition of Ptolemy's Planisphere (1558), in which he related the projections of planispheres with those of linear perspective. This recognition, that perspective involved a special case of projections that occured also in planispheres and astrolabes, brought to light a need for a more general theory of projections, which Commandino's student, Guidobaldo del Monte, attempted to fulfill in his classic text (1600), in which he demonstrated that a single universal principle underlay 23 practical methods then in use.

    In the revival of the Greek mathematical tradition, the texts of Apollonius and Pappus played a special role because they focussed on the theme of conic sections. Already in the 1540's, Nicolo Tartaglia in Venice had drawn attention to them. Francesco Maurolyco had gone further. But again it was Commandino who set about editing them. Both Maurolyco and Commandino were in touch with Christopher Clavius who was, in turn, a mentor of both Paul Guldin and Gregorius Saint Vincent. In the next generation Galileo, a direct descendent of the Urbino tradition, became the teacher of Bonaventura Cavalieri, Italy's foremost expert on conic sections in the early seventeenth century. These same individuals were involved with projection problems in astrolabes (Commandino, Clavius), sundials (Maurolyco, Clavius) and perspective (Commandino, Guidobaldo del Monte), and became aware that such practical interests were related to the projections involved in conic sections.

    The study of conic sections also brought a philosophical problem into focus. A cone at its base is a continuous surface bounded by lines. At its apex it is a discrete point. Ancient philosophers had treated continuous and discrete quantitities, (geometry and arithmetic) as independent worlds. Renaissance thinkers began to explore how the two related to one another: whence Galileo's long introduction in his Dialogue concerning the two chief world systems, devoted to line and point, involving cones as examples, or Cavalieri and Saint-Vincent's preoccupation with indivisibles, or Fermat's concerns with maxima and minima. But in a sense, Urbino merely prepared the way. As will be shown below (pp. ), it was in Paris that these new connections between conic sections and perspective came to fruition.

    In Urbino, this same small circle of Commandino and Guidobaldo del Monte, in touch with Clavius, Mordente and Galileo, were equally involved with the development of universal measuring devices and principles of statics and dynamics. Hence, the search for general principles of perspective in Urbino, was part of a larger trend towards quantification, which made possible the universal claims of early modern science (cf. below 2.1). However after the collapse of Urbino's political power at the end of the sixteenth century, its significance quickly vanished and did not return. Paris soon took its place as the chief centre for mathematics. Meanwhile Rome remained the chief city in Italy.

Rome

    In terms of perspectival practice, Rome was important from the outset, as witnessed by the Annunciation in San Clemente by Masolino and his pupil Masaccio in the late 1420's, and Fra Angelico's work in the Vatican Stanze (c. 1455). With the return of the papal court from Avignon back to Rome, there was renewed papal patronage. Beginning with Sixtus IV in 1482 and continuing until 1527 there emerged in Rome a vision of Italian national art. Sixtus IV saw Rome as a twin capital: through the church it was the capital of Italy, but it was also the capital of the Roman empire.

    The rebuilding of the Vatican complex provided a major incentive for perspectival practice beginning with isolated paintings such as Melozzo da Forli's Inauguration of the Vatican Library (c. 1475), Mantegna's decorations in the chapel of Innocent VIII (1490), and the friezes in the map room of the Palazzo Venezia attributed to him (c. 1490); series by Botticelli, Ghirlandaio and Perugino on the walls of the Sistine Chapel, Michelangelo's trompe l'oeil effects on the ceiling of this same chapel (1506-1508), and finally Raphael's monumental cycles in the Stanze, with the School of Athens (pl. 11.5), which remains one of the most famous perspectival interiors, although the details of its construction may be inaccurate.

ROME I

Foppa Mantegna Melozzo da Forli Leonardo da Vinci

Perugino

Bramante Raphael

Antonio da Sangallo Giulio Romano

Baldassare Peruzzi Antonio da Sangallo, Jr. Cristoforo Sorte

Sebastiano Serlio

Fig. 20. Practitioners and theoreticians in Rome (1450-1550).

ROME II

Antonio da Sangallo Martin Heemskerck

Hieronymus Cock

Antonio Labacco

Giovanni Battista Pittoni

Etienne du Perac Antoine Lafreri - Antonio Salamanca Vincenzo Scamozzi

Mario Kartarus

J. Sadeler Pieter II. Stevens

Hendrik II Hondius

Samuel Marolois

Fig. 21. Artists and publishers of perspective and Roman ruins (1550-1620).

    The numerous artists' conceptions for the new St. Peter's, by Raphael, Bramante, Antonio da Sangallo, Baldassare Peruzzi (cf. pl. 84.5) and Michelangelo, were a further incentive to perspectival drawings21 (fig.20). In some cases, as with the Farnesina, a commission from within papal circles, led to a remarkable trompe l'oeil interior by Baldassare Peruzzi.

    Meanwhile, there were also the ruins of the ancient city, which made Rome a centre for those concerned with surveying and perspectival representation. This had begun in the early fifteenth century as a type of artistic pilgrimage with architects and painters such as Brunelleschi and Donatello. Alberti's Description of the city of Rome, was part of that tradition, as were Filarete's sketches of isolated buildings--which influenced Fouquet when he visited Rome. Lotz (1967),22 has outlined some of the more important steps in these developments, which continued through the sixteenth century with Agostino Veneziano, Sebastiano Serlio and others producing individual engravings, which were later collected in albums such as the Wolfenbüttel book of engravings (c. 1540).

    From the 1460's onwards, however, others such as Francesco di Giorgio Martini had begun gathering their sketches together in manuscript treatises on architecture and geometry. Bramantino's Antiquity of Rome (c.1500) marked a next step. Meanwhile, another tradition was coming into play. Pope Julius II took particular interest in Rome's antiquity, to study which he brought in Bramante (1501) and Raphael (1508), whom he subsequently (1510) appointed as director of antiquities. Raphael introduced both a new scale in construction and an archaeological dimension. He had his own manuscript translation of Vitruvius, was concerned with how the principles of perspective related to architectural representation (involving ground plan and elevation). As a result, the Roman monuments came to be seen increasingly in the context of contemporary architectural theory and practice. The illustrated editions of Vitruvius, by Fra Giocondo (1511) and Cesariano (1521), heralded this new interest and led to new architectual treatises by Palladio (1570) and Scamozzi (1582).

    At a more practical level, Francesco di Giorgio Martini's student, Baldassare Peruzzi, developed the ordinary rule, a short cut method of finding diagonals, later discussed by Danti in his edition of Vignola's Two rules of practical perspective (1583). Peruzzi also developed a new kind of illustrated architectural book, which included both roman ruins and modern edifices. Serlio systematized this, and began publishing his work in the 1540's. Northerners, such as Francisco de Hollanda, Martin van Heemskerck, Hieronymus Cock and Jacques Androuet du Cerceau developed their own type of sketchbook, specializing in idealized perspectival ruins, which were sometimes a conscious combination of real and phantastic elements. By 1550, Androuet du Cerceau (pl. 86.3-5) in Orl‚ans (and later in Paris), and Hieronymus Cock in Antwerp began publishing these.

    In the 1560's, Antonio Labacco, a student of Antonio da Sangallo, began publishing his own versions of the ruins in Rome (fig. 21). This was followed, in 1575, by Etienne du Pérac's treatise. His acquaintance, Antoine Lafréry, who was both cartographer and publisher, collected together a number of isolated engravings by Antonio Salamanca and others in producing his great Topography of the city of Rome (1575-1602). Cartaro (1578), produced his own collection on a smaller scale. In the seventeenth century, ruins, sometimes in combination with modern buildings, dominated publications in Rome, including Lauro (1612, 1625, 1637, 1641), Orlandi (1612), Maggi (1618, 1649), Montano (1624, 1638, 1691), Bramante (1647), Rossi (1647), Falda (1655, 1663, 1665, 1666, 1667, 1670, 1675, 1680, 1683) and Ferrario (1655, 1665). There were several editions of Barozzi (1602, 1642, 1644, 1684), while the scientific side was dominated by Jesuits, beginning with Scheiner's work on the pantograph (1631), Kircher's encyclopaedia of light and shade (1646), Maignan's great treatise on sundials and perspective (1648, 1698), and at the end of the century, Pozzo's Perspective of painters and architects (1693, 1694). In the eighteenth century, two authors dominated the scene: Pozzo (1700, 1702, 1707, 1717, 1723, 1737, 1741, 1758, 1764, 1793) and Piranesi (1740, 1743, 1748, 1750, 1752, 1761, 1770, 1781, 1797, 1798). There were a number of reprints of earlier works by Maignan (1725), Le Clerc (1746), Barozzi (1770), Du Perac (1773), Falda (1773), Labacco (1773). There was an Italian translation of Taylor's fundamental work (1755, 1756) and there were at least three new treatises by Campiglia (1739), Antonini (1770) and Orsini (1771).

    The nineteenth century added only 25 new titles, as compared to 52 in the eighteenth. There were again reprints such as Leonardo (1817, 1890), and Pozzo (1810, 1828, 1840), plus at least seven new authors including Sereni (1826), Lanciani (1849), Gilli (1887), Fiorini (1889), Garneri (1895), Borgogelli (1897) and Bechetti (1899). Of these Borgogelli remained popular in the twentieth century with at least seven new editions (1905, 1908, 1909, 1915, 1919, 1920, 1937). There have also been at thirty-six other books, notably Fausto Vagnetti's classic textbook (1947), and works by Lazzaroni (1908), Nico (1920, 1923), Simoni (1973, 1976), and Sinisgalli (1978). Rome, which was the world centre of perspective at the turn of the sixteenth century, has thus retained a significant role to this day.

Milan

    The role of Milan in the development of perspective is frequently underestimated. The marriage of Francesco I Sforza with ** Gonzaga (1451), issued in a new era. Vincenzo Foppa went to Mantua, where Mantegna served as an exemplar. By 1468, he was back in Milan working in Sant Eustorgio. In the decades that followed, Bramante produced his great illusionistic Choir in Santa Maria presso San Sepolcro (pl. 5.4) and Leonardo painted the Last Supper (1495-1497). In terms of perspectival practice, these two works could be seen as the greatest examples of the entire Renaissance.

    Milan was also of some importance in terms of theory (fig.18). Vasari reports23 that Filarete taught Vincenzo Foppa, who in turn taught the painter Butinone, Zenale and Bergognone. If credence can be given to the testimony of Lomazzo,24 Foppa, Butinone, Bramante, Zenale and Leonardo da Vinci all wrote treatises. Unfortunately no trace of the originals survives. Even so the scattered evidence in Leonardo's notebooks provides some impression of what was happening in the 1480's and 1490's. Leonardo recognized that perspective involved more than copying the physical world, that it applied equally to different levels of abstraction and served as a bridge between the concreteness of nature and abstractions of mathematics. In addition, while his elder contemporary Piero della Francesca was content to rely on Euclid for theory, Leonardo insisted on systematic experimental demonstrations of the principles of perspective. He also became convinced that these principles could be applied equally to the physics of heat and light, indeed to the whole of nature25 (cf. below 2.1).

MILAN

Fouquet Filarete Jacopo Bellini Pisanello Mantegna

Bramante Leonardo da Vinci

Vincenzo Foppa

Zenale Butinone Luca Pacioli Bergognone

Bramiantino

...........

Lomazzo Jacopo Sansovino Luca Signorelli

Fig. 18. Milanese theoreticians and practitioners (1450-1500).

    In terms of published works during the fifteenth century there was only Fazio Cardan's edition of Peckham's optical textbook, Common perspective (1482). The French invasion of 1499, and the dispersal of the Sforza court temporarily obliterated Milan's importance as a centre.

    And yet it continued to have some importance as is witnessed by the work of Carlo Urbino. Martino Bassi's diatribe against Pellegrino Tebaldi, concerning the relief of the Annunication for the choir of Milan cathedral, remained primarily of academic interest. (This work published in Brescia in 1571, 1572 was reprinted in Milan in 1771.) In the latter sixteenth century, in nearby Cremona, Carlo Urbino is believed26 to have composed the Codex Huygens, based on Leonardo da Vinci's studies of proportion and foreshortening applied to the human body (pl. 68.5). Lomazzo's treatise, published in Milan (1584, 1585), was largely a review of earlier glory. The seventeenth century brought only two new works: Raverta's treatise on surveying and perspective (1602), and Barca (1620), as well as a possible edition of Bramantino (1612). The eighteenth century brought nothing. The nineteenth century, by contrast, brought 52 books published in Milan. A dozen of these were reprints of Renaissance texts, notably Alberti (1803, 1804, 1840), Barozzi (1814, 1819, 1830, 1832, 1840, 1850, 1869) and Leonardo (1804, 1859, 1894). There were at least four original authors: Zanotti (1804, 1825), Taccani (1813, 1825), Bordoni (1816) and Landriani (1815, 1818, 1824, 1827, 1833), plus others such as Sella (1861), Suini (1880, 1896), Aschieri (1883, 1888, 1895) and Vegetti (1894, 1895).

    The twentieth century brought 78 further books, including reprints of five Renaissance authors, Ghiberti (1965), Filarete (1972), Martini (1967), Pacioli (1956, 1973) and Dürer (1973) and one baroque author, Guarini (1968). Thanks to firms such as Hoepli, Milan has become the chief Italian centre for primary texts on perspective in the twentieth century. It has published the two authors who have dominated the scene: Claudi (1896, 1897, 1903, 1910, 1915, 1920, 1924, 1929, 1935, 1938, 1940, 1942, 1951) and Chiesa (1931, 1938, 1943, 1944, 1947, 1951, 1956, 1961, 1967, 1969, 1975, 1980). It has also published three other popular authors: Seller (1942, 1944, 1946, 1949, 1960); Roversi (1945, 1948, 1949, 1952) and Bonfigli (1960, 1962, 1968, 1975, 1976, 1979). Smaller companies such as Bertolini have published Elias (1973) on spherical perspective.

Bologna

    Bologna with its university, the Bentivoglio family, who created a court-like atmosphere, and--after 1500-its connections with the papacy, was another important centre, the history of which sadly needs study. We are told that Albrecht Dürer learned the secret of perspective there. In Bologna, Bramante was responsible for the cloisters of the catholic university. During the sixteenth century, the works of Apollonius and Serenus were published there (1566) as was Ptolemy's study of the planisphere (1572). In the seventeenth century, other than two editions of Vignola (1662, 1682), the main works were by Jesuits: Mario Bettini's monumental Beehive of the universe of philosophy (1642, 1645, 1654, 1660), and Scheiner's work on the pantograph (1653). Giulio Troili also published his important textbook in Bologna (1672, 1683). The eighteenth century saw 26 publications which included two new editions of Scheiner (1726, 1749), a series of editions of Galli da Bibiena (1703, 1725, 1731, 1732, 1745, 1749, 1753, 1764, 1777) and some original work by Quadri (1744), Tesi (1787) and Zanotti (1755, 1766, 1767, 1782). The nineteenth century saw a reprint of Troili (1863), plus a half dozen new authors: Basoli (1810, 1812), Marconi (1811), Magistrini (1816), Fagnoli (1840), Cocchi (1851, 1855), and Fiorini (1892). This pattern remained unchanged in the twentieth century, with one reprint of Barozzi (il Vignola) (1974), and seven new authors: Tagliavini (1904), Severi (1906), Chisini (1960), Boccaleone (1963), Speranza 91963), Lorgna (1971) and Nannoni (1978) none of whom has changed the field.

Naples

    Naples is another centre, which deserves more attention. Under the patronage of Alfonse of Aragon, it was here that Pisanello produced his proto-perspectival frescoes. The city's historical connections with Anjou brought important visitors from the North such as Jean Fouquet and Ren‚ d'Anjou. In Naples, Fra Giocondo worked on his famous edition of Vitruvius (Rome 1511). Publications did not begin until the latter half of the sixteenth century, with Porta's work on natural magic, which discussed the use of camera obscuras in painting (1558, 1569, 1593) and Romano's treatise on military uses of perspective (1595). The seventeenth century brought new editions of Porta (1611, 1726) and Maurolico's (1611) work on optics. The eighteenth century saw reprints of two Renaissance authors, Alberti and Leonardo (1733), plus three new ones: Januariis (1714), Martino (1727, 1734), Grandi (1737). The nineteenth century brought one popular author, Flauti (1815, 1820, 1827, 1841, 1842, 1846) and five further authors of whom Capobianco (1960, 1966), Fusco (1968) and Tenta (1968) may be mentioned in passing.

Other Italian Cities

    There were a number of Italian cities, which published only one title on perspective in the period 1500-1700. Frequently these were in the orbit of a nearby court. Connected with Milan for example were Como, where Cesariano published his edition of Vitruvius (1521); Brescia where Bassi's Various matters (1571) appeared, Vigevano, as well as the court at Mantua, where both Alberti and Mantegna were active. Linked with Urbino, was Pesaro, which saw the first edition of Guidobaldo del Monte's landmark Six books of perspective (1600). Linked with the court of Ferrara was Ravenna.

    Siena offers an interesting case of a city, which began with an independent tradition. Ambrogio Lorenzetti's Annunciation (Siena, Gallery, 1348), is reported to have been the first painting in which all the lines of the floor tiles converge to a single vanishing point.27 But by the fifteenth century, as the Florentines developed demonstrations of perspective, Donatello and Ghiberti influenced the Sienese Il Vecchietta (fig. 19). He, along with another Florentine, Verrocchio, became the teacher of Francesco di Giorgio Martini, who went on to do his main work in Urbino and Rome.

SIENA

Il Sassetta Ghiberti Donatello Verrocchio

Il Vecchietta

Francesco di Giorgio Martini Leonardo da Vinci

Agostino Chigi Pintoricchio Sodoma

Baldassare Peruzzi

Fig. 19. Sienese practitioners and theoreticians (1400-1550).

    Some smaller cities, which published treaties on perspective, maintained their independence, notably Cesena, Livorno, Monte Regale, Perugia and Pisa. In the case of Palermo, there were no publications until the eighteenth century, which brought four interesting authors: Spuccez-Lanza (1701-1711), Aidoni (1706), Amato (1714, 1733, 1736) and Amico (1750). Then for almost 150 years there was nothing until Basile (1898), with seven further authors in the twentieth century of which Filosto (1964, 1979) and Santapa (1968) may be mentioned.

    It is important to note, however, that these patterns of publication do not tell the whole story. Some cities had no publications yet owed their significance to an artist who left his mark there. Piero della Francesca in Arezzo is the classic case. Masolino in Castiglione Olona or Filippo Lippi, with his great Annunciation in the cathedral at Spoleto, are other examples. Moreover, as Vasari reminds us, oral communication played a much greater role than is sometimes imagined. This took place at three distinct levels. In rare cases, a thinker would communicate with an author as in the case of Malatini when he advised Daniele Barbaro. Sometimes, a practitioner would counsel a theoretician, as Giulio Romano did with Cristoforo Sorte. More often, the master of a workshop would simply instruct his apprentices directly. This is almost certainly how Masaccio, Fra Angelico, Botticelli, Ghirlandaio, Michelangelo and a number of their contemporaries learned perspective. There was yet another factor. Even after the invention of printing, manuscripts continued to have precedence over books in some humanist libraries which helps explain why none of the major fifteenth century authors on perspective was published at the time (fig. --).

    In the North, the relative emphasis on oral, manuscript and printed communication was different. From the prefaces of Pélerin (1505) in France, and Vredeman de Vries (1604) in the low countries, we know that this oral tradition existed also in the North, but to a lesser degree, and in Germany, Pfintzing (1598) reports only one individual, Hans Haiden, who communicated his ideas by word of mouth. As for manuscripts, we know of isolated instances such as the copy of Alberti made in 1476, but no cases where an author on perspective relied on manuscripts for the spread of his ideas. There was much more emphasis on printing. Indeed authors were sometimes publishers of their own works as with Jacques Androuet Du Cerceau. Others such as Hieronymous Cock, Philippe Galle, Melchior Tavernier and Francois Langlois published their own and other writings. This is also true of Theodore Galle who, in addition, had close contacts with another publisher through his marriage to Christoph Plantin's sister. It is not surprising therefore, that already in the sixteenth century approximately 56% of titles on perspective were published in the North. By the seventeenth century this had risen to 77%. Paris played a special role in this trend. Indeed between 1500 and 1700, 150 books were published there, as many as in the whole of Italy combined. It will be useful therefore to consider this city in some detail before turning to other northern centres.

FRANCE    Paris

    It is generally agreed that Fouquet was the first in France to practice linear perspective, as is evidenced by his rendering of Notre Dame in Paris, in his Hours of Etienne Chevalier (pl. 11.1). He is thought to have learned the principles from Filarete in Rome, sometime between 1445 and 1450 (fig. 22). Around 1476, a French canon, Jean P‚lerin, Le Viator, is also believed to have made a visit to Italy, where he too learned perspective.28 This became the basis for his treatise (Toul, 1505), which was based partly on Parisian scenes (pl. 11.3) and must have been known in the city as it formed the basis of Ringelbergius' treatise (Paris 1521).

    Francis I provided an important catalyst for perspective in France by inviting Italian artists to his courts at Amboise, Romorantin and Fontainebleau, first Leonardo de Vinci (1515-1519), then Rosso Fiorentino, whose students included Jean Cousin, author of a Book of perspective (1560), and Sebastiano Serlio, from 1541 until his death in 1551, who worked on plans for reconstruction of the Louvre, and whose writings were translated by Jean Martin and published in Paris (1545-1547, 1587, 1590).

    Also engaged in these plans for the new Louvre, was Jacques Androuet du Cerceau, a native of Orléans, who published a posthumous treatise of Leonard Thiry from Antwerp, as well as his own writings about architecture and perspective. When religious wars forced Androuet du Cerceau to leave Paris, his architectural projects were inherited by Etienne Du Pérac, of roman ruins fame, who taught Claude Mollet about perspective in gardening and whose son, André Mollet, in turn became a teacher of Andr‚ Le Nôtre, who constructed the great illusionistic gardens at Vaux le Vicomte and Versailles (see below 2.3).

    During the sixteenth century, seventeen books on perspective were published in Paris: approximately 14% of the total in Europe. Even so, only four authors were involved: Androuet Du Cerceau, Cousin, Dürer and Serlio: two French, one German, one Italian. Hence, as late as 1600 Paris was surprisingly limited in its horizon. In the next century this changed radically: a third of all books on the subject were published there. Indeed with 133 books in the seventeenth century Paris became the world's leading centre. This did not involve a complete break with the past. There were reprints of foreign Renaissance authors: Alberti (1651), Barozzi (1620), Leonardo (1651) and Cardi (1663), as well as earlier French authors, particularly Androuet Du Cerceau (1607, 1611, 1615, 1648, 1676) and Cousin, le jeune (1600, 1603, 1612, 1618, 1625, 1635, 1642, 1647, 1656, 1671, 1676). There was a continued interest in both military architecture (e.g. Perret 1601, Bourdin 1655, and Bourgoing 1661) and civil architecture (e.g. Blondel 1675, 1698, Bullet 1675, Rohault, 1682, Deis 1698 and Aviler 1691). But there was a shift in the context of discussions. What had been a topic for painters in the fifteenth, and architects in the sixteenth centuries, now also became a concern for mathematicians.

    The reasons were several. One involved conic sections. As in Urbino (cf. pp. ), the Parisian thinkers were stimulated by problems arising out of the classical texts of Apollonius and Pappus, the difference being that in Paris, the connections between conic sections and perspective were explored much more intensely. Here Jean, le Sieur de Vaulezard (1631) played a role. But it was mainly due to an extraordinary circle of the 1630's known as the Académie Parisienne which included Roberval, Etienne Pascal, Marin Mersenne, Blaise Pascal, Claude Mydorge and Girard Desargues, the latter three of which were at the centre of studies concerning both conic sections and perspective. The questions they raised later directly influenced Philippe de la Hire, Leibniz and Newton.

    In Urbino, thinkers had recognized that this nexus of problems raised philosophical questions concerning the relation of geometry (continuous quantities or lines) to arithmetic (discrete quantities or points). In Paris, these questions became much more acute. In 1600, Henri de Monantheuil, a student of Pierre de la Ramée had written a treatise on the relationship between point and line. His claims were challenged

PARIS I

Filarete

Jean Fouquet

Leonardo da Vinci

Jean P‚lerin

Rosso Fiorentino

Jean Cousin

Leonard Thiry Sebastiano Serlio

Hieronymus Cock

Jacques Androuet du Cerceau

Daniele Barbaro Hans Lencker

Etienne Du P‚rac

Jean Cousin le jeune (?)

Jacques Boyceau Claude Mollet

Andr‚ Mollet Olivier de Serres

Andr‚ le Nostre

Fig 22. The emergence of Paris as a centre for perspectival theory (1450-1600).

by the mathematician, Jacques Aléaume, also the author of a treatise on perspective, edited by Etienne Migon, which influenced both Claude Mydorge and Girard Desargues.

    There were other developments, which gave an unexpected urgency to these debates concerning points, lines, perspective and conic sections. During the sixteenth century, the leading German experts on cossist algebra, notably Michael Stifel, Peter Rothe and Johann Faulhaber, had concentrated on numerical problems and their symbols. French thinkers such as Pierre de La Ramée‚ had suggested that cossist algebra was a vulgar form of the analytical method of Greek mathematics. François Viète developed this idea. He distinguished clearly between a purely numerical approach (logistique numérique), and his more general method (logistique spécieuse or calcul des symbols), whereby he resolved geometrical questions by means of algebraic analysis. Pierre de Fermat further developed Viète's idea of symbolic algebra as a tool by means

PARIS II

Philippe Danfrie Pierre de la Ram‚e Franc ois ViŠte

Salomon de Caus Henry de Suberville Henri de Monantheuil

Johann Faulhaber Jacques Al‚aume

Denis Henrion Etienne Migon Jean,le Sieur Vaulezard

Pierre H‚rigone

Descartes Mersenne Pascal Desargues Mydorge E. Pascal Roberval P. de Fermat

Jean Francois Nic‚ron

Nicolas Poussin Abraham Bosse Jean Curabelle Melchior Tavernier

Laurent de la Hire Philippe de Champaigne Jean Dubreuil

Jean le Bicheur

Gr‚goire Huret

Philippe de la Hire

Leibniz Isaac Newton

Fig. 23. Paris as the world centre for mathematics and perspective.(1600-1700).

of which one could unite the realms of arithmetic and geometry. Fermat's study of Apollonius' Conics, led him to perceive in the cone and its sections, a standard geometrical framework through which he could establish correspondences between equations and curves. The result was an analytic geometry, which concentrated on the geometrical construction of curves.

    His contemporary, René Descartes, another of the founders of analytic geometry, slighted Fermat's manner of construction, and focussed his own energies on a new and more advanced theory of equations. As he explained in a letter to Beeckman on 26 March 1619, Descartes was consciously searching for a new science "by which all questions can be reduced that can be proposed for any sort of quantity either continuous or discrete."29 In arriving at this new science, whereby geometry and arithmetic were reconciled, and numbers could be plotted as lines on coordinates, Descartes also relied on the construction theorems of Apollonius' Conics. This helps to explain both the tremendous fascination with conic sections from the 1630's onwards, and the preoccupation with perspective, which offered a scientific means of visualizing the complex intersections involved (fig.23).

    Yet another factor went hand in hand with these developments. As in other European centres (cf. 2.1), Paris witnessed a great interest in universal measuring instruments in the latter sixteenth century: Abel Foullon's holomètre, Jacques Besson's cosmolabe, Philippe Danfrie's graphomètre and Henry de Suberville's henrymètre. By about 1609, Jacques Aléaume, who also wrote on perspective, had developed his own version of a sector. Denis Henrion improved upon it. Pierre H‚rigone further developed it, and mentioned its application to perspective, a topic which Jean, le Sieur de Vaulezard took further, showing the sector's uses in determining various anamorphic projections in conic mirrors. In his letter to Beeckman about his new science, Descartes had specifically referred to the need for "new kinds of compasses"30 to demonstrate the new method. Was this what H‚rigone and Vaulezard were doing? In any case we find thereafter, especially in the French tradition, an ongoing link between sectors and perspective (e.g. Bosse, Huret, Chales, Lambert).

    There was also a religious and magical context to these studies. As early as the 1450's, Giovanni Fontana, a student of optics and author of what may have been the first treatise on perspective, had used his knowledge in these fields to project images of devils onto the walls of buildings presumably to demonstrate that effects claimed to be supernatural by followers of black magic could be accounted for by purely natural causes. In the sixteenth century, Giovanni Battista della Porta, working in the tradition of artist-engineers, pursued this approach to natural magic.

    Meanwhile, Fontana's contemporary, Taccola had explored other aspects of these natural wonders, particularly those involving hydraulics. Francesco di Giorgio Martini and Leonardo developed these demonstrations and the latter's sojourn in France probably explains the particular attention given this topic in the second half of the sixteenth century by Abel Foullon, Jacques Besson and Agostino Ramelli.

    In the seventeenth century, Salomon de Caus, developing techniques introduced by the Florentine, Buontalenti, effectively combined these two traditions of natural magic and hydraulics in creating his remarkable mechanical automats in grottoes with fountains and optical effects (pl. 98.1). If we, in retrospect, are tempted to dismiss such projects as superficial examples of baroque playfulness, it is instructive to recall that when Descartes, in his Treatise on man, was trying to establish the credibility of his mechanistic model of the nervous system he appealed to "those hydraulically controlled puppets and mechanical statues found in the grottoes and fountains in the gardens of our kings".31 In this context, Baltrusaitis (1956) concerns with both automats and perspective,32 take on greater importance, as does his quote from Jean François Niçéron, where he cites both automats and perspective as instances of natural magic, adding "the true magic or perfection of the sciences consists of perspective which makes us understand and discern more perfectly the beautiful works of nature and art."33

    The small circle of thinkers in the 1630's, who were concerned with automats and used mechanical sectors to demonstrate principles of perspective by means of conic sections, were therefore more than the forerunners of Popular Mechanics. They were stimulating Descartes to articulate a new mechanistic model of reality (cf. below 2.1). Of course, other mechanical devices such as clocks,34 were also important in this context.

    Not all the reactions were so profound. Melchior Tavernier, in a book now lost (1639), sought to popularize these ideas, an aim that was taken up in an anonymous three volume work by Jean Dubreuil entitled, Practical perspective (1642-1649), which emphasized the recreational value of these anamorphic demonstrations, and at the same time misrepresented Girard Desargues' original ideas. Desargues and Dubreuil exchanged pamphlets filled with diatribe. Others followed between Desargues and Curabelle.

    Subsequently Abraham Bosse, first professor of the Royal Academy and a friend of both Poussin and Desargues, continued the debates on Desargues' behalf, and as mentioned earlier (pp. ) brought into focus the dichotomy between projection planes of linear perspective, based on geometry, and the visual angles principles of Euclid's optics. This inspired the further opposition of Jean Le Brun and more writings against him by Jean Le Bicheur and Grégoire Huret, leading eventually to Bosse's expulsion as the academy's professor of perspective. And ironically, Dubreuil's text, with its various faults, went on to become one of the most popular texts with nine issues by the end of the century and another dozen in the eighteenth century, including translations into English and German. Dubreuil was a Jesuit. So too were Leurechon (1630), Nicéron (1638, 1646, 1651, 1652, 1663, 1669, 1673) and Derand (1643). Their wish to popularize perspective was guided by a desire to stress its moral and didactic potentials. Others were more concerned with popularization for its own sake. Le Clerc's work, for instance, went through five editions in the seventeenth (1679, 1682, 1690, 1691, 1694) and at least seven in the eighteenth century (1712, 1716, 1719, 1744, 1754, 1764, 1774). Even more popular was Ozanam with seven editions before 1700 (1684, 1689, 1693, 1694, 1696, 1697, 1699) and fourteen more in the century that followed (1711, 1720, 1734, 1724, 1725, 1735, 1741, 1749, 1750, 1769, 1770, 1778, 1781, 1790).

    The eighteenth century again brought a few reprints of Renaissance classics, notably Leonardo (1716), Serlio (1745), Barozzi (1786) and Cousin, le jeune (1750) and a number of new works relating to architecture. Chief among these were Bretez (1706, 1746, 1751), Courtonne (1725), Jeaurat (1750) and Roy (1756, 1757). New books specifically devoted to perspective were few: e.g. Lamy (1701), Saurin (1720), Lanselles (1767), Saint Morien (1779, 1788) and Sabro (1790). There were also three new trends. One was the publication in Paris of contemporary foreign works including Wolff (1747), Galli da Bibiena (174 ), Palomino (1749), Gravesande (1755), Muller (1760), Piranesi (1762), Mengs (1788) and Lairesse (1787). A second trend was an increasing emphasis on conic sections with authors such as La Hire (1701, 1757, 1776), L'H"pital (1707, 1720, 1776), Chapelle (1750), Gallimard (1752), Mauduit (1757, 1761), Rivard (1757), Mazens (1758, 1761, 1765, 1768, 1774, 1775, 1777) and Muller (1760). A third trend linked mathematics, engineering and perspective through Bouchotte (1721, 1722, 1743, 1754, 1755), Dupain de Montesson (1750, 1760, 1763, 1774, 1775, 1786, 1789, 1792) and Monge (1785, 1795, 1798, 1799).

    During the eighteenth century Paris, with 144 books, had fallen behind London as the leading centre of publication. In the nineteenth century, with 528 publications, Paris once more took the lead as chief centre. In some respects the patterns of the eighteenth century were maintained. There was no dramatic change in the reprints of Renaissance authors: Alberti, Androuet, Barozzi, Leonardo and Pélerin. The number of editions of contemporary foreign authors remained almost constant although most of the names changed: Piranesi (1804), Smith (1824, 1843), Amici (1823), Burnet (1835), Hughes (1864), Helmholtz (1870), Brucke (1878, 1881, 1885) and Salmon (1870). With respect to architecture and perspective, four authors dominated the scene, each of whom went through a number of editions: Lagardette, Normand, Robinet and Etex. In terms of mechanical drawing and perspective, there were a series of works on new instruments, among them, Ph‚lippeaux, Burnier, Jump, Mauduit, Le Blanc and Petit.

    Other factors led Paris to be the most prolific centre of publication in this field during the nineteenth century. Chief amongst these was the link with descriptive geometry, forged by Monge in the latter eighteenth century, which was spread by further editions of his work (1811, 1820, 1827, 1838, 1847), and a series of followers notably Hachette (1815, 1817, 1818, 1822, 1828), Olivier (1831, 1837, 1839, 1840, etc.), Lefebure (1834, 1837, 1842, 1847, 1864, 1870), Leroy (1834, 1837, 1842, 1846, 1850, 1851, 1855, 1859, 1862, 35c.), and Dufailly (1869, 1873, 1875, 1878, 1880, 1882, 1884, 1886, 1892, 1894). Some individuals, such as La Gournerie, wrote important works on both descriptive geometry (1851, 1853, 1855, 1860) and perspective (1859, 1884, 1898). Pillet was another, who wrote on both descriptive geometry (1876, 1887, 19291), and perspective (1885, 1886, 1888, 1901, 1921, 1953). Meanwhile, another strand, through Poncelet (1822, 1863) and his followers explored an alternative using projective geometry.

    In terms of artistic perspective, there were a number of popular authors including Adhémar, Bouillon, Delaistre, Jaunez-Spauville, Cassagne and Henriet. But the most significant single development in nineteenth century Paris was a new link between drawing (dessin) and perspective which included authors such as Boniface (1823, 1832, 1847), Choquet (1823, 1832, 1847), Francoeur (1827), Paillot de Montabert (1832), Thibault (1837), Trélis (1840), Daix (1842), Lahure (1847), Rouillet (1857, 1863), Grimblot (1869, 1877), Bracquemond (1885), Valtron (1888), Watelet (1893) and Forel (1893). Among the most popular authors were Henry des Vosges, who went through twelve editions and Lamotte, who went through fourteen editions. Underlying this development were basic issues concerning the role of perspective in education, inspired by philosophers such as Locke and Rousseau (see below 1.4).

    The combined result of these developments was to convince thinkers that descriptive geometry, and the principles of perspective, must (somehow) correspond to both objective reality and the laws of vision. Vallée played a considerable role in establishing these suppositions, and accordingly, the second half of the century saw a series of works relating perspective to sight (e.g. Malaval), or to observation (e.g., Babinet, Devinat, Watelet), a theme which continued into the twentieth century (e.g. Bocquillon, Legrand), although new evidence concerning discrepancies between vision and representation had arisen in the meantime (see pp. ).

    In addition, there were a number of works devoted to specialized topics including carpentry (Biston), colour (Roux de Valdonne), landscape (Robert, Demarquet-Crauk), photography (Colson) and even war (Philebert) and many works by minor authors.

    Although the twentieth century has seen 160 further publications, few of these have been innovative. Indeed, in the first decade, many were simply reprints of nineteenth century authors including Breithof, Cassagne, Delaistre, Demarquet-Crauk, Laurent, Lebon, Olagnon, Pillet, Planat, Robert and Tubeuf. Cloquet was one of the few new works to go through several editions (1905, 1912, 1913, 1919, 1927). The period 1910-1960 marked a definite slump, with only a handful of authors rising to prominence, namely: Grosclaude (1919, 1946, 1947), Boll (1921, 1932, 1934), Boucher (1921, 1931, 1934), Gromort (1932, 1945, 1944, 1953) and Olmer (1932, 1943). In the period since 1960, three popularizing authors have dominated the scene: Parrens, Raynaud and Bonbon, their work being almost simplistic when compared to nineteenth century classics such as La Gournerie. The period since 1960, has also seen a revival of interest in Renaissance texts, with reprints of Androuet du Cerceau, Bracelli, Dürer, Jamnitzer and Vredeman de Vries. New trends in recent literature include attention to spherical perspective (Barre et Flocon, cf. pp. ), and the use of models and photography in architectural design (Jantzen).

    In the context of France as a whole, it is striking to note how completely Paris has dominated the scene. Indeed, there are only four other cities worthy of mention: Orléans, Lyon, Rouen and Strasbourg. Orl‚ans had a brief period of importance in the sixteenth century through publications by Androuet Du Cerceau, before he moved to Paris. Lyon, in the sixteenth century produced no original works of its own, but saw the publication of Ringelbergius (1556) and Porta (1571, 1579, 1591), with its description of the camera obscura in respect to painting. The seventeenth century brought three French authors (Binet, Cousin and Chales), and three foreign ones (Caramuel de Lobkowicz, Fabri, Porta). The next century brought one important work in instruments by Grollier de ServiŠre (1719), and a French edition of Brook Taylor (1758). The nineteenth century saw only minor works by Girardon (1850, 1859) and Fournet (1859). In Rouen, by contrast, almost all the activity was limited to the seventeenth century with ten editions of Binet, and seven of Porta, with only one minor work by Tr‚nard (1913) in our century. The fourth city, Strasbourg, has felt the influence of Germany more than France. During the sixteenth century there were pirate editions of Pélerin (1508, 512, 1515) and treatises by Specklin (1589) and Dietterlin (1593). A reprint of Specklin (1608) was the only contribution of the next century. The eighteenth century brought Herttenstein (1736, 1737), Frézier's classic work on stereotomy (1737) and a treatise by Curel (1766). The nineteenth century added a technical work by Rätz (1879, 1883, 1894) and a reprint of Piero (1899). The twentieth century brought a reprint of Dürer (1905), and treatises by Adam-Leonard (1905) and Opitz (1907). Of all these publications outside of Paris, only Frézier's was of fundamental importance, and its conclusions were soon integrated within the Parisian mainstream by thinkers such as Monge. So, in a very real sense, there was only one centre in France. In countries such as the Lowlands and Germany the situation was very different.

BELGIUM

    We have already noted that a fascination with pseudo-perspectival space developed in Flanders in the early fifteenth century at the same time that Brunelleschi and Alberti were exploring the principles of perspective in Florence (pl. 8-11). No evidence has been found to confirm a claim (Fielding 1835), that Jan van Eyck also wrote a treatise on the subject. Instead, it is now generally accepted35 that Petrus Christus brought the principles of perspective to the Lowlands around 1457, probably after a journey to Italy, where he may well have learned them from Antonello da Messina. Over seventy years passed before there were publications in Antwerp. By the early seventeenth century some works also appeared in Brussels, but by then activities had shifted northward with Amsterdam as a new centre, and with Arnhem, the Hague and Leiden as satellites. Each of these will be considered in turn.

Antwerp

    The first publications were foreign books: Gauricus (1528) and Pieter Coecke van Aelst's translations of Serlio (1539, 1542, 1545, 1549, 1550, 1553). Coecke, who was also a translator of Vitruvius, became the teacher of both the painter, Pieter Breughel, the Elder and Hieronymus Cock, who became an artist, engraver and publisher. By the 1550's, Cock's publishing house, At the four winds, played an important role in the spread of perspectival texts: his own Roman views, those of Gerard de Jode and, a decade later, those of Jan Vredeman de Vries--a series of picture books, usually with about twenty perspectival views each of fountains, gardens, tombs, ruins and idealized architectural scenes. When Philippe Galle took over Cock's press there were reissues, frequently with new plates of the perspectival views, of Cock, Jan Vredeman de Vries and his son Paul. Philippe Galle's son, Theodore, continued in his footsteps for another

ANTWERP

Martin Heemskerck Serlio Vitruvius

Peter Fl"tner

Hans Blum

Pieter Coecke van Aelst

G. Ghisi Pieter Breughel the Elder

Hieronymus Cock Gerard de Jode

Hendrick III Cleve

Philippe Galle Jan Vredeman de Vries

Theodore Galle

Paul Vredeman de Vries

Hendrik Hondius, II

Samuel Marolois

Joseph Moxon

Fig. 24. Authors and publishers on perspective in Antwerp (1450-1600).

generation (fig. 24). In all some 30 publications of Vredeman de Vries appeared before Janson began publishing his works in Arnhem and Amsterdam.

    In the seventeenth century this flurry of activity ended as suddenly as it had begun. Aside from reissues of Vredeman de Vries (1606,1673), Blum (1640), and Serlio (1653), there were only a handful of new publications: a collection of ruins and views by Nieulandt (1610, 1628), an optical treatise by Aguilonius (1613), a work on conic sections by Saint Vincent (1647) and a technical treatment of perspective by Tacquet (1669). The eighteenth century saw a reissue of Tacquet (1707), the nineteenth, a new work by Neetsonne (1883) and the twentieth, one by Farcy (1943). Meanwhile Brussels had acquired some significance.

Brussels

    Hondius, one of the students of Vredeman de Vries, is said to have published the first edition of his work on perspective in Brussels (1617, cf. Amsterdam 1623). The latter seventeen century saw a work on military perspective in Spanish by Lepeda (1661). The eighteenth century brought only an edition of Pozzo (1708). The nineteenth century brought sixteen publications: a popular textbook by Smachtens (1820, 1825, 1827); treatises by Brisson (1827), the editor of Monge, and three other mathematicians: Leroy (1837), Charles (1839, 1870) and Schmidt (1869), as well as minor works by Bossuet, Gratry, Mols, Morena and Pierre. Since nineteen hundred there have been six publications of which perhaps only Barre's (1904) discussion of alternative methods of perspective bears mention.

THE NETHERLANDS    Amsterdam

    Aside from ancient texts such as Euclid and Ptolemy, the first perspectival treatise published in Amsterdam was a translation of Blum (1598, 1612, 1619, 1623, 1647). Italian authors published in the first half of the seventeenth century included Serlio (1606, 1616), Alberti (1649) and Gauricus (1649). Of German authors, there was only Jamnitzer (1608, 1618, 1626), who appeared in three anonymous pirate editions. In the latter seventeenth century there were editions of three French authors, Desargues (1686), Ozanam (1683, 1693, 1698) and Le Clerc (1692), as well as one English author, Wren (1671).

    As of 1550, Jan Vredeman de Vries had published a series of perspectival views in Antwerp. In 1604, together with his student, Hendrik II Hondius, he issued a more ambitious work with some mention of theoretical principles. This appeared in Leiden. In the next decade, Marolois, another student of Vredeman de Vries, developed a lengthy theoretical section to which he added engravings by Jan and Paul Vredeman de Vries, Hendrik II Hondius, and Pieter Stevens. This work in turn formed part of a massive tome in four sections dealing with geometry, perspective, architecture and fortification respectively, which had its first edition in Leiden (1614) and subsequent editions mainly in Amsterdam. For a generation this remained a standard work appearing in Latin, French, Dutch and German, sometimes complete, frequently in combinations or abridged versions.

    In the mathematical realm, van Schooten's (1659, 1660) treatise on conic sections was the only noteworthy publication in Amsterdam during the seventeenth century. In terms of artistic perspective there were texts by Bosboom (1686) and Hartsoeker (1699), and more general treatises by van de Passe (1643, 1644, 1664), de Graaf (1662, 1679) and de Bisschop (1670). Towards the end of the century there appeared also Lairesse (1694, 1695) who became popular in the next century (1701, 1706, 1707, 1712, 1713, 1719, 1727, 1729, 1766). Foreign publications in Amsterdam during the eighteenth century were limited to Ozanam, Lamy, Le Clerc and a translation of Brook Taylor. There were further editions of Bosboom, Graaf and Hondius. New works ranged from minor texts by Schenk (1705) and Ypey (1764), to significant contributions by Houten (1705), Vlaming (1773) and Gravesande (1774). By far the most influential eighteenth century author was Philips Jacobszoon, with a series of publications (1765, 1767, 1775, 1780, 1781, 1785, 1786, 1788, 1803, 1823, 1827), notable for his use of mirrors and other instruments in connection with perspective.

    In the seventeenth century, 114 books were published in Amsterdam. In the eighteenth, there were 38, and in the nineteenth this dropped to 26, of which only two were translations of foreign works: Lagardette (1833) and Thénot (1859). Most were single publications of local interest including Apol, Bes, Bilderdijk, Bing, Campen, Ferrers, Groenevelt Meerwaldt, Rinkes and Schoone. The one dramatic exception was Versluys, whose textbooks for schools went through a series of editions (1881, 1884, 1887, 1889, 1890, 1891, 1896). The twentieth century has seen at least 35 further publications, the majority of which were again of local interest only, including Albert, Hana, Kumminga, Muyak, Mayens and Ozinga. Only two authors have enjoyed more than one edition, namely, Mialaret (1910, 1922) and Arendzen (1934, 1942, 1950). There was also one translation from the German, Stark (1930).

Arnhem and the Hague

    Intimately connected with publications in Amsterdam in the early seventeenth century, were two other cities: Arnhem and the Hague, due to Jan Jansson's publishing firm. In Arnhem, he published Dürer (1603, 1605, 1613, 1614, 1617), Ptolemy (1617) and Marolois (1621). Since that time, Arnhem has seen only one further treatise by Graaf Hermanszoon (1870). Meanwhile, as mentioned above, Jansson had published a first edition of Marolois (1614) in the Hague. He also published Hondius, but in the 1620's the firm's activities were centred increasingly in Amsterdam. Thereafter, the Hague saw only sporadic publications. In the latter seventeenth century, Rohault (1690) and Ozanam (1691) were published there. The eighteenth century brought an important work by Gravesande (1711, 1771), a treatise by Eckhardt (1778), and an edition of Pascal's Conics (1779). The nineteenth century brought a translation of Lagardette (1821), an anonymous text (1846), and one by a local author, Aken (1891). The twentieth century has added works by three new authors, Sakkers, Schmidt and Woude, but little innovation.

Leiden

    During the sixteenth century, the only work connected with perspective published in Leiden was Porta (1561, 1569), further editions of which appeared in the next century (1644, 1651, 1657). At the turn of the seventeenth century, the Hondius family published Vredeman de Vries (1604-1605, cf. 1664) in Leiden, thus involving that city in a nexus of relations with Amsterdam, Arnhem and the Hague. On the mathematical side, Leiden saw an edition of Stevin's (1634) important work, editions of Van Schooten (1646, 1656, 1657) on conic sections and Huygen's (1690) Treatise on light. Foreign publications included the Jesuit, Milliet de Chales' (1674) compendium. The eighteenth century brought only new editions of Gauricus (1701, 1732), while the nineteenth century added a half dozen authors of books on artistic perspective: Brag, Bregmann, Campen, Fokke-Simonszoon, Richard and Schaap, and a manuscript by Humbert de Superville (1830). The twentieth century has seen a new edition of Ptolemy (1932).

Other Netherlandish Cities

    Three other cities in the Netherlands, which have emerged in the nineteenth and twentieth centuries deserve brief mention: Groningen, Tiel and Deventer. In Groningen, the earliest text on perspective dates back to Frederik (1853, 1935). The decades that followed saw four authors of local interest: Berghuis, Gravelaar, Groneman and Soeren. The two popular authors, Versluys (1877, 1887, 1924) and Bes (1890, 1893, 1900, 1901, 1903) were also published in Amsterdam. The twentieth century has added ten further authors including Alders, Gestel, Jansen, Luinge, Nuyens, Steenderen and Wijdens, who have added nothing fundamental.

    In the nineteenth century, Tiel produced one textbook for schools by Berghuis, which went through at least six editions (1887, 1891, 1894, 1898, 1902, 1907). The twentieth century has brought Jansma's introduction to conic sections which went through eight editions and textbooks by de Vries de Hecklingen (1908), who published other works in Zwolle, Goslinski (1911, 1930) and Scholten (1915). Deventer is of interest mainly due to one individual active in the early twentieth century, namely, Ridderhof, whose textbook on perspective went through eight editions (e.g. 1906, 1949) and who also wrote on parallel perspective and perspective sketching for schools. Texts by Wijdens (1904), Reynders (1945, 1951) and Twijnstra (1948) were also published there.

GERMANY

    Dürer's famous comment, in his letter to Pirckheimer in 1504, that he was hoping to learn the secret of perspective,36 reminds us that perspective reached Germany later than either France or the Lowlands. And unlike France, where everything was centralized, developments in Germany were scattered throughout a number of cities. The earliest of these was Nürnberg, which had a seminal influence on Augsburg and Frankfurt. Cologne developed separately. The seventeenth century saw publications in a few more cities: Hamburg, Stuttgart, Hanover, Freiburg and Munich. The eighteenth century added Berlin, Göttingen and Karlsruhe, followed by Braunschweig, Darmstadt and Wiesbaden in the nineteenth century. Meanwhile, in East Germany, only one real centre emerged at Leipzig, although some works were published at Weimar. Each of these will be considered in turn.

Nürnberg

    Nürnberg was an important trade centre already in mediaeval times. Because it was the leading European city for the production of mathematical instruments (cf. fig. 41), Regiomontanus moved there in the 1470's to pursue his own scientific interests, and to become the world's first publisher specializing in scientific texts. Martin Behaim produced one of the first globes there in 1492. This context accounts for both the fascination with perspectival instruments, which developed later in the century, and the appearance of scientific and mathematical texts, including Ptolemy's Geography (1514), Werner's work on conic sections (1522), Witelo's great optical treatise edited by Apianus (1535), and Peckham's Common perspective (1542).

    On his second Italian journey, Dürer may have obtained a manuscript copy of Alberti's On painting, (possibly the one now in the Bavarian state library?), which could have served as the basis for the alledged 1511 edition (mentioned in earlier bibliographies). But all this is conjecture. The first published text was Dürer's Instruction in measurement (1525) with fourteen pages devoted to the topic.

    In 1531, the author of A beautiful, useful booklet, set out to write a more popular book with numerous perspectival illustrations, including church interiors (pl. 16.4), building construction scenes (pl. 60.3-4) and even demonstrated the use of the perspective window in drawing landscapes (cf. pl. 58.1-2). In the full title of the treatise we read that it is about "the art of measurement called perspectiva in Latin".37 Here the link between perspective and measurement was unequivocal. This treatise, edited by Dürer's student, Hieronymus Rodler, combined serious theoretical discussion and picture-book type practical example in a new way. John Dee made a partial manuscript copy of the work (now British Library Cotton Vitellius VII). Augustin Hirschvogel pursued this approach, explicitly setting out to relate theoretical geometry with practical perspective in a work fittingly entitled: Geometry. The book geometry is my name. Originally all liberal art from me came. I bring architecture and perspective together. Hirschvogel also wrote an unpublished treatise on surveying (now Vienna, Stadtmuseum).

    Dürer had entitled his book Instruction in measurement...with the compass and ruler (1525), and had emphasized the general problem of practical geogetry. Heinrich Lautensack's text (1564) echoed Dürer's title, adding also of perspective. Following a brief introduction on geometry, Lautensack focussed on theoretical and practical aspects of perspective, including anatomical proportion and symmetry, themes which had been explored independently by two of Durer's other students: Hans Beham and Erhard Schön.

    Meanwhile, Hans Lencker and Wenzel Jamnitzer had developed a great interest in the perspectival representation of regular and semi-regular solids (pl. 36.3-37.1). Did they perhaps see therein shapes into which to cut their jewels? They also improved upon the mechanical aids for perspective, which Dürer had developed. When Pierre de La Ramée and Frederick Risner from Paris, visited them in 1568, they were so impressed by their work that they persuaded Jamnitzer and Lencker to publish.38

    The next significant publication was a little known treatise by Paul Pfintzing (1599), originally intended for private distribution among friends. Conscious of the continuity within the Nürnberg tradition (fig.40), Pfintzing traced the development of mechanical devices from Dürer and the anonymous author of A beautiful useful booklet, through Lautensack, Lencker (pl. 54.2), Jamnitzer (pl. 54.4), and the otherwise obscure Hans Haiden (1590), (pl. 54.5). Pfintzing was also aware of both traditional authorities in optics: Euclid, Alhazen and Witelo, as well as foreign authors on perspective, including, Luca Pacioli, Androuet du Cerceau and Lorenzo Sirigatti.

    This awareness of the cumulative nature of knowledge was even more manifest in Levinus Hulsius' four treatises on mathematical instruments (1603-1605), which included mechanical aids for perspective, a description of Jost Bürgi's proportional compass and a similar device (by Michel Coignet) from Belgium. By way of introduction, he provided one of the earliest bibliographies containing dates of publication of the books consulted. The list included works from Germany, France, Italy and the Netherlands (fig.42). The same Hulsius also studied with Galileo in Padua, and subsequently published a first Latin translation (1612) of Galileo's Geometrical and military compass (1606). Hulsius also worked with Jobst Bürgi's brother in law, Benjamin Bramer, active in the construction of the compass, sector and perspectival aids.

    An unexpected pattern thus emerges. The key centres for scientific instruments were also important in the development of perspective: Padua, Florence, Nürnberg, Antwerp and later Paris and London. Moreover, the key figures were often directly in touch with one another or at least indirectly influenced by one another. A more systematic approach to studying the world scientifically brought with it a more systematic network of contacts and a greater awareness of the cumulative effect of knowledge (see below 2.1).

    Meanwhile there had also been publications of foreign authors of perspective in Nürnberg beginning with Gauricus (1542). Of considerable importance was a compendium by Walther Ryff which provided partial translations of Alberti, Gauricus and Serlio (1547, 1558)--a third edition of which later appeared in Basel (1582). The seventeenth century saw new editions of Pfintzing, Dietterlin and Porta; treatises by Krammer (16--) and Brunn (1614), Schwenter's work on perspectival instruments (1616) and his compendium of basic principles (1651). Most popular were two treatises by Albrecht, which may have gone through as many as nine issues (e.g. 1620, 1671, 1677). Erasmus (1667, 1672, 1687), not the humanist, edited an updated version of Blum's work on the five columns, while the famous antiquarian, Sandrart, reported briefly on Italian developments in perspective in his German Academy (1675). In terms of foreign literature published in Nürnberg in the seventeenth century, Daniel Schwenter edited a German translation of Raverta's treatise on surveying and perspective (1627, cf. 1602). There were two editions of Falda (1685, 1695) and a translation of Desargues (1692).

    The eighteenth century saw translations of two Dutch authors, Witgeest (1702) and Lairesse (1727, 1728, 1780) and two French ones, Dupain de Montesson (1759, 1762, 1790) and Bosse (1767). Among the German authors, there were Zahn (1702), of interest concerning camera obscuras and other instruments, Sturm (1704, 1714), who wrote a handy compendium; Pressler (1774), important for his theories of drawing and Mayer (1785). The one major new author was Schubler (1719, 1732, 1734, 1735, 1749, 1758, 1763).

    The nineteenth century saw only one translation from the French: an important book on drawing theory by Thibault (1833, 1834, 1841). German authors included Heidelhoff (e.g. 1827, 1892), whose work on shadow construction for architects went through five editions; Eberlein (1859, 1876, 1878), Gugler, Klingenfeld and Wenz. The twentieth century has brought only two textbooks by Fürst (1908) and Pechwitz (1950).

Augsburg

    In Augsburg, the first publication was a collection of examples for use in marquetry by Stoer (1567, cf. 1617), of particular interest because the motifs therein appear to have inspired some of the woodwork at the Escorial done that very year.39 Like Nürnberg, Augsburg was famous for its instrument makers,40--notably Christoph Schissler and his son41--, which helps to explain a trend in Augsburg during the early seventeenth century to reprint Nürnberg authors who emphasized the use of instruments in perspective, namely, Lencker (1615, 1617), Lautensack (1616), and Pfintzing (1617). The two new works published in Augsburg at the time also mentioned the use of instruments, although Halt (1625) was mainly concerned with polyhedra, while Furttenbach (1640) focussed on perspective as applied to scenography.

    The eighteenth century saw a small number of significant publications. Three were translation of foreign authors: Dubreuil (1710), Le Clerc (1756) and Pozzo (e.g. 1706, 1800), who went through seven issues. With respect to artistic perspective, Heinecken produced an influential textbook with examples showing church interiors, landscapes and other complex perspectival scenes (1727, 1732, 1743, 1753). On the mathematical and technical side, there were important publications by Lambert (1760, 1768, 1770, 1772) and Brander (1764, 1767, 1769, 1771), which contained new combinations of camera obscuras with surveying instruments, telescopes and microscopes. Augsburg's only contributions to the field since have been two treatises by Voch (1780, 1817).

Frankfurt

    As an important publishing centre, Frankfurt served mainly to make known work done elsewhere. The first treatise on perspective published there, attributed to Rodler (1546), had appeared earlier in Simmeren. The next works were by Nrnberg artists: Beham (1552), 1557, 1587, 1594) and Lautensack (1564, 1565, 1567). There followed Italian authors, Serlio and Porta, and the Frenchman, Boissard (1597, 1603). The seventeenth century saw further works by foreign authors: two French, Perret (1602) and De Caus (1516); two English, Roger Bacon's work on optics entitled, Perspective (1614), and Fludd (1624), and later the Italian, Serlio (1672). German works included an alledged edition of Krammer (1600), editions by the Nürnberg artists Beham (1605) and Lautensack (1618); technical treatises on perspectival instruments by Hulsius (1603, 1605, 1615) and Faulhaber (1610); an encyclopaedic treatment by Schott (1677) and a further discussion of instruments, particularly camera obscuras by Zahn (1686).

    The eighteenth century brought compendia by Sturm (1710) and Wolff (1725, 1750, 1775) and a French treatise by Curel (1768). As in Nürnberg, the nineteenth century brought translations of Thibault's theories of drawing (1800, 1835, 1840). It also brought an anonymous work in drawing and perspective translated by Becker (1815, 1817, 1818) and a text by Ritter (1884). The twentieth century added reprints of Bacon, Jamnitzer, Lencker and Sch"n as well as two new authors: Eith (1940) and Meyers (1951).

Cologne

    Not unlike Frankfurt, but on a smaller scale, Cologne was mainly important for what it published from elsewhere, rather than for its original contributions. Indeed in the sixteenth century it produced only foreign works relating to perspective including Porta (1562, 1563), Peckham's (1580, 1592) optical textbook, Guidobaldo del Monte's (1581) work on the planisphere and Ptolemy's Geography (1584, 1597). This pattern continued in the seventeenth century, with new editions of Ptolemy and Peckham, the Swiss, Blum (1600), the Dutch, Vredeman de Vries (1615, 1655) and the Italian, Bettini (1642). German authors included Krammer (1611) and Kaessmann (1630), based on Blum. Since then there have only been two minor works by Janke (1900) and Boehmler (1969) and a reprint of Ens (1951).

    A different pattern prevailed in the cities which began publishing works on perspective in the seventeenth century (Hamburg, Stuttgart, Hanover, Freiburg and Munich). Although they frequently began with foreign works, they soon relied almost entirely on local authors.

Hamburg

    In the seventeenth century, Hamburg saw only an edition of the optical treatise by Heliodorus of Larissa (1610). The eighteenth century brought works on perspectival instruments by Norberg (1762) and Steinholz (1775) and the nineteenth century brought another by Stuhlmann (1869, 1974, 1876, cf. 1914) as well as a text on descriptive geometry by Schlotke (1867) and optical treatises by the famous physiologist Helmholtz. Apart from one further treatise on perspectival aids, Peter (1911), the twentieth century has brought only textbooks of local interest by Beimföhr, Heinsohn, Kröger, Reichelt, Schaub and Vorwerk.

Stuttgart

    In Stuttgart there has been a consistent emphasis on the mathematical and technical side of perspective. The earliest publication was a new edition of Hirschvogel (1611 cf. 1543). Over two hundred years passed before publication resumed with a translation of Lamotte (1835), on linear drawing. There followed translations of Leroy's influential texts on stereotomy (1846, 1850, 1861, 1876, 1883) and descriptive geometry (1853, 1873), as well as Green's (1892) textbook, which had gone through fourteen editions in England. In terms of German authors, there were mathematical works on conic sections by Riecke (1842) and Zech (1857); on descriptive geometry by Gugler (1844, 1851, 1874, 1875) and Riess (1871); geometrical drawing by Vogel (1874) and Müller (1891); projective drawing by Kleiber (1888) and Vonderlinn (1888, 1889, 1892, 1893) as well as Böckler's popular treatise on construction drawing (1866, 1876, 1878, 1886). With respect to textbooks on artistic perspective there were Vollweider (1862), Niemann (1882, 1902, 1907), Steindorff (1884), Conz (1882, 1902, 1909, 1920) and Söllner (1891).

    There were at least 52 books published on the subject in the nineteenth century, and 41 in the twentieth including Bernhard's popular text on descriptive geometry (1901, 1904, 1909, 1920, 1923). In 1934 there was a debate concerning the role of perspective in art education between Gahlbeck and Klauss. The most significant development has, however, been with respect to architecture. Reile (1922, 1923, 1941, 1949, 1951) developed a new device for architectural perspective, and more recently there have been several books on architectural drawing by Coulin (1966, with later English editions), Jacoby (1971, with later English and Japanese translations), Thomae (1976) and Prenzel (1978).

Hanover

    The seventeenth century saw two editions of Porta (1619, 1644). The next publications in the second half of the nineteenth century were on mathematical perspective, Koutny (1868, 1869) and descriptive geometry, Gerke (1881, 1889), as well as one treatise on artistic perspective, Jantzen (1872). The twentieth century has seen a continued emphasis on the technical and mathematical side of perspective with works on isometrical drawing by Grimshaw (1902) and Vogel (1912); a text on descriptive geometry by Pohl (1951) and a popular work on architectural perspective by Dahmlos (1966, 1970, 1977). There have also been texts on perspective drawing by Zehnder (1907), on perspective and shadow by Heubach (1908) and a reprint of the German translation of Dubreuil (1977 cf. 1710).

Freiburg

    Publications in Freiburg followed a similar pattern. In the seventeenth century there was an edition of Scheiner (1621), of interest regarding camera obscuras, then nothing until the nineteenth century which was dominated by mathematical and technical texts including Ladomus (1812) on geometrical construction drawing, Weisbach (1857) on axonometrical perspective, and Flinch on geometrical perspective. More important was Delabar with no less than ten publications (from 1866 through 1893) relating to linear drawing, descriptive geometry, shades and shadows and parallel perspective. The twentieth century has seen only a work on perspectival instruments by Routschek (1963).

Munich

    As might be expected, there was somewhat more variety in Munich, although the seventeenth century again saw only one technical work on telescopes by Hercynianus (1625)--included under perspective in some in some early bibliographies,--while the eighteenth century saw three further mathematical works: Karsten (1768, 1773) on spherical projections in astronomy, as well as Danzer (1780) and Rauch (1790) on conic sections. The nineteenth century brought Quaglio (1811, 1822, 1823) and Adamo (1899) on architectural perspective; Schrank (1812) on blue shadows, and three authors on linear drawing: Haindl (1835, 1843), Weishaupt, whose influential work went through at least nine issues between 1856 and 1882, and Edelmann (1871). In terms of textbooks on artistic perspective, there were Gottgetreu (1851), Seeberger, whose principles of perspective went through at least ten issues between 1860 and 1904, Kleiber (1885) and Lübenau (1898). The twentieth century has brought at least 29 further publications of which the most original is Klee's (1925) discussion of perspective with respect to modern art. Also worthy of mention are practical textbooks by Pabst (1918, 1921, 1922), Fürstweger (1928) and Fischer (1937, 1943) plus a more recent work on technical drawing by Fäustle (1969, 1971).

Berlin

    In Berlin, the first publication was near the middle of the eighteenth century with Jügel (1744), who wrote on architectural perspective, followed by a general textbook, Segner (1799). However, mathematical texts predominated, including Lambert's (1776) article on aerial perspective, Lagrange (1781) on cartographical perspective, Hildebrandt (1783) on conic sections, Mönnich (1794) and Burja's (1795) textbook addressed specifically to the mathematical painter. The nineteenth century saw 101 further publications. Some ten authors wrote on artistic perspective, namely, Benteli, Berger, Eytelwein, Frangenheim, Gennerich, Kolbenheyer, Lobedan, Rätz, Schmid and Schreiber. There was some work on architectural drawing, Burg, Schmidt; perspective drawing, Francke, Schwedler and drawing generally, Meyer. But the emphasis continued to be on mathematical aspects of perspective, with seven authors on conic sections; Bauer, Grüson, Hamilton, Martus, Pofelger, Schellbach and Schneider. There were works on descriptive geometry by Busch, Flohr, Ohm and Wolff (1835, 1840, 1847, 1861); on more general mathematical topics by Arndt, Caspary, Peschka, Ravoth, Rosanes and Steiner, on instruments by Brauer and Hauck,--also famous for his work on subjective curvatures and curvilinear perspective,--as well as on geometrical drawing by Burg, Heimpl, Hertzsprung and Hoffmann.

    In the twentieth century, there have again been works on artistic perspective by Doehlemann (1912, 1918, 1922), Freyberger (1913, 1918, 1923), Kurth and Tuckermann; reprints of classics including Chippendale, Ghiberti and Lambert; architectural perspective, Danielowski (1968, 1969, 1976, 1982) and gardening perspective, Wilczek (1929, 1941). But the earlier pattern continues and mathematical treatises dominate with writings on descriptive geometry, e.g. Fischer, Kramer, Ludwig (1919, 1922, 1924); Rehbock (1957, 1964, 1969), Scheffers (1919, 1920, 1922, 1927) and Schmid (1912, 1919, 1922); projective geometry, Doehlemann (1924); instruments including Brauer, Edler, Griesinger, Haeder, Traenkle, and geometrical perspective, e.g. Rehbock (1978, 1979, 1980).

    In addition to linear perspective there has been work on cartographic perspective, Greef (1922), Sievke (1934); axonometric perspective, Papperitz (1916); parallel perspective, Vonderlinn (1914, 1920, 1925) and Meyer Sidd (1970), as well as spherical perspective, Birken (1923) and Barre (1963).

Other West German Cities Since 1700

    In the eighteenth century, there were two further cities with publications on perspective, Göttingen and Karlsruhe, and since the nineteenth century three further cities have emerged, namely, Braunschweig, Darmstadt and Wiesbaden. Here too mathematical and technical aspects of perspective were predominant, as will become clear as each is considered in turn.

Göttingen

    In the eighteenth century, publications at Göttingen included a work on scenography, Meister (1753), a treatise on conic sections, Hube (1759), and a reprint of Werner's important work on drawing with geometry and perspective (1796). The chief author at the time, however, was Kästner whose interests ranged from conic sections to mathematical perspective in general (1758, 1759, 1764, 1771, 1774, 1786, 1790, 1792, 1796, 1800). Since the eighteenth century there has only been a German translation of Fuller's Perspective to scale (1955, 1956, 1958, cf. 1952).

Karlsruhe

    In the eighteenth century, there was an important work on conic sections by de la Chapelle (1770, 1771, 1791) followed by two others in the early nineteenth century, by Hofmann (1815) and Ladomus (1817). These were followed by publications by Schreiber on descriptive geometry, technical drawing and perspective (1822, 1828, 1833, 1839, 1854); by Doll (1867) on drawing and geometrical plans, and Riess (1872) on geometrical perspective. The twentieth century has seen a further textbook on descriptive geometry by Reutter (1948, 1958).

Braunschweig

    In Braunschweig, during the nineteenth century, there were works on conic sections by de la Chapelle (1801) and Beyssel (1862); construction drawing using   parallel perspective, Müller (1865, 1874), freehand drawing, Fürstenberg (1854, 1863); perspectival drawing, Klette (1867, 1869, 1870, 1873, 1887) and free perspective, Balmer-Rinck (1887). In addition there were at least two works specifically intended for artists by Frangenheim (1880) and Ehrhardt (1885, 1895). The twentieth century saw a new edition of Haeder's instrument (1949, cf. 1914) and a general textbook by Bärtschi (1982).

Darmstadt

    In the nineteenth century, Darmstadt saw a series on publications on descriptive geometry, geometrical drawing and technical drawing by Rössler (1839, 1845, 1847, 1852, 1853, 1861). The twentieth century added Getrost (1913) on free perspective for schools, and a dissertation by Stoll (1971) on projective geometry, as well as new editions of Vitruvius (1964, 1976).

Wiesbaden

    Wiesbaden, also had some mathematical publications during the nineteenth century including Hildenbrand (1867) on conic sections; Gut (1888), and Bouffier (1893) with respect to perspectival shadows. There were also works on artistic perspective, namely, Eberhard (1824) and Bouffier (1892, 1905). In the twentieth century there was a greater emphasis on the technical side with works on perspectival instruments, Haeder (1914), Ranke (1955); engineering perspective, Ranke and Niebler (1956, 1957, 1960); parallel perspective, Schumacher (1951) and architectural perspective, Bonbon (1977), König (1978, 1979). There was also one popular textbook on artistic perspective, Schmidt (1972, 1976, 1978).

EAST GERMANY   Leipzig

    In East Germany, Leipzig was slow in becoming a major publishing centre for perspective. During the sixteenth century, there was only an edition of Peckham's optical textbook (1504), and an alledged edition of Brunn (1595). The seventeenth century was almost as sparse, with optical treatises by Euclid (1607) and Kohlhans (1663, 1777). The eighteenth century brought fifteen books of which only two dealt with artistic perspective, namely, Lairesse (1745) and Horstig (1979). All the rest dealt with mathematical aspects including general principles, Kästner (1752), Schönberg (1770, 1771, 1773); map projection, Hasius (1717, 1719), Lambert (1763); instruments, Wilke (1772), Leupold (1774), Adams (1795) and encyclopaedic summaries, Adelung (1781), Karsten (1782).

    But it was only in the nineteenth century that Leipzig emerged as a major centre, with some 170 books in the field, of which no less than 43 were due to the emergence of Teubner, which published classics such as Euclid, Hero of Alexandria, Ptolemy, Proclus and Serenus as well as books in mathematics and science. These subjects dominated the field in Leipzig. There were some general works, including those of Beck, Bünau, Holzmüller and Schubert. On conic sections there was little in the first half of the century other than Grunert (1824) and Jahn (1836), whose work had the remarkable title, Introduction to more than 50 million primarily new geometrical projections as a result of conic sections. But when Salmon's work was translated into German it went thorugh at least ten issues from 1860 to 1918, cf. 1848. Dietzel, a younger contemporary went through five editions from 1864 to 1902; Fiedler, went through four, while Erler went through eleven from 1877 to 1911. Other publications on conic sections appeared by Drach, Eckhardt, Meyer, Schröter and Zeuthen.

    With respect to descriptive geometry there were important texts by Stoevesandt (1869), Wiener (1884), Disteli (1888) and a new edition of Monge (1900). In terms of projective geometry there were contributions by Bünau, Hänkel, Hoch and Sturm. Cartographical projections were treated by Reusch (19881) and Wangerin (1884). Drawing books ranged from general works such as Ehrenberg (1868) to various kinds, including axonometric drawing, Mayer (1855), Schmidt (1859); cavalier drawing, Neigebaur (1836); construction drawing, Steiner (1861); geometrical drawing, Schmidt (1859) and technical drawing, Schmidt (1886). Versatile individuals such as Schreiber wrote on linear, projective and technical drawing as well as perspective, descriptive geometry and shadow projection.

    In terms of artistic perspective, three individuals dominated the field: Berger, who went through twelve editions from 1855 to 1898, Kleiber with six editions and Freyberger whose works went through six and four issues respectively. Fliesen's three textbooks went through two editions each. Other authors included Burmester, Gehler, Hetsch, Heyn, Krause and Morstadt. The twentieth century has brought two significant textbooks by Doehlemann (1916, 1928) and Baier (1955, 1957, 1957) and a half dozen more general works by Albert, Beuhne, Meise, Riegel, Schulze and Weiner.

    The most important contributions have again been in terms of mathematical and technical aspects. With respect to general theory, Von Öttingen (1901, 1905, 1906, 1907), has made important contributions. In descriptive geometry the chief authors have been Mller, with five editions, and Papperitz, with three editions. Other authors included Geyger, Gercken, Hessenberg, Opitz, Salkowski, Schlotke and Timerding. In projective geometry there was Doehlemann (1898, 1901, 1905). With respect to shadow projection there was Vonderlinn (1904, 1904) who also wrote on parallel perspective (1905, 1910, 1914, 1920). With respect to drawing there were general works such as Ebner (1924), and specific studies in axonometric drawing, Papperitz (1906), Haase (1907); perspective drawing, with three significant authors, Gründling, Severin; Weishaupt, and projective drawing, Geissler (1911).

Other East German Cities

    Four other East German cities deserve brief mention. Weimar, with 21 publications, was dominated by the works of four authors concerned mainly with perspective in relation to drawing: Hertel, Steiner, Thon, Weishaupt. Greifswald was essentially a one author town, responsible for the encyclopaedic works of Karsten. Halle played a similar role with respect to Wolff's compendia, while Dresden published mainly the works of Schlotke on descriptive geometry and perspective.

SWITZERLAND   Basel

    In Switzerland, there were three centres in Basel, Zürich and Geneva. In the sixteenth century, Basel's role lay in the dissemination of texts, rather than in original contributions. At the outset, there were classical texts, which the Renaissance associated with perspective, namely, Galen (1533), Ptolemy, in six editions, and Euclid (1537, 1546, 1558). Later, the chief mediaeval authors on optics, Alhazen and Witelo (1572), appeared there. In terms of artistic perspective, there were editions of P‚lerin (1535, 1583), the acknowledged first edition of Alberti (1540 cf. 1582, although there was alledged to have been an earlier 1511 edition in Nürnberg), Ringelbergius (1541), Serlio (1582) and Gauricus (1582). The seventeenth century brought only editions of Serlio (1608, 1609) and Meyer (1676); the eighteenth century, nothing, and the nineteenth century general textbooks, Merian (1832) and Balmer-Rinck (1884). The twentieth century has brought two new textbooks by Billeter (1904) and Artaria (1947).

Zürich

    In the sixteenth century, Zürich had one significant author, Blum,--the so called Swiss Serlio--, whose works on ruins and the five orders of columns went through numerous editions. The eighteenth century brought a more original author, Lambert (1759, 1774, 1789), concerned mainly with the mathematical and technical side of perspective. Interest in this dimension dominated nineteenth century publications by Largiader (1858), Kronauer (1861), Geiser (1866), Graberg (1868), Ott (1868) and Möllinger (1882). The twentieth century brought a new interest in artistic perspective, with textbooks by Gull (1839, 1941), Brunschwiler (1941, 1958, cf. 1939), Artaria (1945), Meier (1945) and Schedegger (1963).

Geneva

    Geneva's role was more restricted. In the eighteenth century publications were limited to a compendium by Wolff (1732, 1740, 1741, 1743, 1773, 1783). The nineteenth century brought a textbook by Prader (1897) and a new perspectival instrument, Ziegler (1889). The twentieth century has seen another instrument, Odier (1934); a textbook, Leone (1962) and reprints of earlier works: Gauricus (1969), Bosse (1973) and Valenciennes (1973).

3. Greater Europe

    Adjacent to the half dozen core European countries discussed above, were a series of other countries: Spain, Portugal, Denmark, Sweden, Norway, Finland, Austria, Czechoslovakia, Poland, Roumania and Russia. Almost all of these were in some way directly affected by the Renaissance. Some even played a significant role in its development. In rare cases isolated books on perspective were published in the sixteenth or seventeenth centuries. And yet it was not until the eighteenth and usually only in the nineteenth or twentieth centuries that centres of publication emerged in these countries, as will become apparent as each is considered in turn.

SPAIN   Madrid

    Spain has had three centres: Madrid, Barcelona and Valencia. During the sixteenth century Madrid saw only a translation of Euclid's Optics (1585) and in the seventeenth century, a general textbook, Hidalgo (1693). The eighteenth century saw editions of Renaissance treatises by Alberti (1784, cf. 1827) and Barozzi (1792) and texts on artistic perspective by Palomino de Castro y Velasco (1715, 1724, 1795, 1947), Tosca (1721) and Casanova (1794). This genre developed in the nineteenth century with authors such as Brambila (1817), Rodriguez (1834), Herñaez de Perea (1875), Aranaz y Izaguirre (1891), Muñoz Morillejo (1893) and Salvador y Rodrianez (1897, 1898). On the mathematical and technical side, there was a Spanish translation of Vallée's (1838) Manual of the science of drawing; a work on descriptive geometry by Lavina Blasco (1859); on shades and shadows by Pereda y Lopez (1866) and on axonometry by Torroja y Caball‚ (1879).

    The twentieth century brought further works on artistic perspective, a compendium by Muñoz Morrilejo (1914, 1923), and texts by Arola y Sala (1920, 1921), Marin Magallon (1924), Martines Sanz (1936) and Iniguez (1962). But the mathematical and technical side has continued also, with texts on cavalier and axonometric perspective by Alonso Misol (1911), shades and shadows by Fernandez Casanova (1917) and Arola y Sala (1921). Since 1950 this dimension has dominated the scene, with texts on descriptive geometry, Soto Hidalgo (1960, 1967); cavalier and axonometric perspective, Cano de la Torre (1966, 1970) and Garcia Gutierrez (1978, 1979).

    There has also been a surprising amount of attention to alternative forms, namely, spherical perspective, Flocon (1966) and conic perspective, Adroer (1953), Sandoval Guerra (1967), Corbella Barrios (1968), Martinez la Madrid (1968) and Fuentes Alonso (1973, 1975).

Barcelona

    In Barcelona, publications began much later, with only four textbooks on artistic perspective during the nineteenth century: Planella y Corominas (1840), Alsamora (1842) and Castelucho (1892, 1896) as well as one text on descriptive geometry, Cardona y Escarrabil (1896). Nevertheless, in the twentieth century, Barcelona became the leading centre in Spain, with 65 publications. Of these 15 were translations of Italian, German and English texts, namely, Claudi (1914, 1965, 1971), Raneletti (1921), Reile (1928, 1972), Gull (1948, 1965), Schaarw„chter (1970, 1974), Norden (1954), Morehead (1956), Lawson (1959, 1975) and Brown (1982).

    There has been some attention to mathematical and technical aspects, namely, descriptive geometry, Ranelletti (1921); shades and shadows, Arola y Sala (1923) and Rovira y Rabassa (1956); and conic perspective, Robira y Rabassa (1910), and Perez Asensio (1964). Even so the major emphasis has been on artistic perspective including authors such as Calvo y Verdonces (1912, 1924), Salat y Ferrando (1919), Vidal y Vidal (1935), Anasagasti y Algan (1945), Daming (1954), Basilio Gomez (1961, 1964) and Mestres Cabanez (1964). Four authors have stood out in terms of popularity: an individual known only by his initials F. T. D. (1933, 1942, 1958, 1964, 1969, 1973); Freixas Arangaren (1944, 1960, 1968, 1978); Parramon Vilasalo (1966, 1972, 1974, 1977) and particularly Rovira Sumalla, whose text went through 12 editions between 1966 and 1977.

Valencia

    In the sixteenth century, there was an early edition of Peckham's optical treatise, Common perspective (1504), in Valencia. The eighteenth century saw editions of Tosca's compendium (1707, 1712, 1757). The nineteenth century brought texts on descriptive geometry, Alix (1767) and artistic perspective, Salva (1880). The twentieth century has added works by Bonuet Minguet on different branches of perspective: axonometric (1944), conic (1968, 1979) as well as linear (1969). Conic perspective has also been treated by Grajales Carbonell (1977).

DENMARK   Copenhagen

    In Scandinavia, publication has been centred in the capitals, quantity varying considerably with 38 books in Copenhagen, 61 in Stockholm, 2 in Oslo and 16 in Helsinki. In Copenhagen publications began near the mid-eighteenth century with Horrebow's (1748) text on conic sections. There followed a textbook on artistic perspective by Jardin (1758), a compendium by Kästner (1788) and a mathematical treatise by Krebs (1799). In the nineteenth century, the field was dominated by three individuals: Hetsch, who wrote textbooks on both geometrical drawing (1822, 1828, 1840, 1844), and perspective (1839, 1851, 1868, 1881); Eckersberg (1833, 1841, 1978) and Nielsen (1869, 1878, 1884, 1894, 1899, 1907), also famous as a pioneer in the history of perspective. Less prolific authors included Fabris (1860), Klein (1879), Kranys-Hansen (1879, 1880) and Blom (1899). On the mathematical and technical side there were Schjödte (1864), Seidelin (1890), Janniche (1891, 1897) and Christensen (1896) on stereometric drawing and Petersen (1897) on descriptive geometry. The twentieth century brought further works on this subject by Hjelmslev (1943) and Pihl (1955) as well as texts on artistic perspective by Riberholt (1956), Schiellerup (1964) and Baro (1979).

SWEDEN   Stockholm

    Publications in Stockholm began just over a century later than in Copenhagen, with isolated works on geometrical drawing by Mandelgren (1849) and Hetsch (1852). Since the latter nineteenth century, the field has been dominated by a handful of individuals, the most influential of which was Henriques. His textbook on geometrical and projection drawing went through 24 editions between 1896 and 1953, while his textbook on perspective for technical schools went through six editions. Indeed, technical works have been predominant, notably, Segerborg, with six editions, Werner, with five and more recently, Lagerquist, with five. In terms of artistic perspective, the major author has been Johansson, whose textbook has enjoyed seven issues.

NORWAY   Oslo

    Oslo's publications have been limited to a text on artistic perspective by Guldberg (1880), and a technical treatment by Bergh (1872), with an appendix on axonometric perspective.

FINLAND   Helsinki

    During the nin