Course description
After the early works of Florentine painters, Venice became the place of privilege for practical experimentation and the theoretical diffusion of linear perspective. The passing of the baton from Florence to Venice occurred when Luca Pacioli published the Summa (1494) and the De divina proportione (1509), which disseminated the contents of the works of Piero della Francesca, in particular the De prospectiva pingendi. Indeed, it is precisely at the turn of the new century that interest in the theory of perspective and Platonic and Archimedean polyhedra began to grow in the lagoon; it is therefore not surprising that, among the painters’ tutors there were also mathematicians such as Girolamo Malatini, who was master of perspective of Giovanni and Gentile Bellini as well as of Vittore Carpaccio.
In works such as Venetie MD by Jacopo de’ Barbari, the Procession in St. Mark’s Square by Gentile Bellini, and the Legend of Saint Ursula by Carpaccio, the city, represented in perspective, coincides with the painted scene while architecture plays the role of co-protagonist together with man. Over time, the illusory architecture conquered the private palaces (Paolo Veronese, villa Barbaro in Maser), the public and religious spaces (Cristoforo and Stefano Rosa, vestibule of the Biblioteca Nazionale Marciana and ceiling of the church of Santa Maria dell’Orto) and the first permanent theaters (Andrea Palladio and Vincenzo Scamozzi, the Olimpico in Vicenza). In this context, Venetian publishing houses were complicit in the freeing of architecture as a new ‘subject’ of artistic representation, printing the treatises dedicated to perspective. Although brief and confused, a first examination of the perspective theory and its application in theatrical scenes appeared in Venice with the Secondo Libro dell’Archittura by Sebastiano Serlio (1545), but the first complete and geometrically correct work was La pratica della perspettiva by Daniele Barbaro (1568). The Venetian nobleman, author of the most important Italian translation of Vitruvius’s De Architectura, was also a patron of Palladio, Alessandro Vittoria and Veronese. Indeed, he addressed his treatise on perspective to painters, sculptors and architects, providing descriptions of machinery to facilitate perspective drawing and organizing the discussion around a series of exercises dedicated to Platonic and Archimedean polyhedra. For the drafting of his treatise Barbaro confessed to having studied with Giovanni Zamberti, another Venetian mathematician influenced by Luca Pacioli. The circle thus closes.
This course offers an unusual reading of Venetian art, linking perspective, mathematics, publishing, painting and architecture. Its purpose is to examine in depth all the possible cultural nuances that are hidden behind a work of art. For this reason, the course investigates Venetian culture, transversally embracing science and art but also philosophy, theatrical scenes and literature. Renaissance Venice can be considered the cultural engine of Europe since its publishing houses reached every part of the known world. Hinging on the history of representation, this course aims to develop a critical method for interpreting the history of art and architecture more widely, contextualizing Venice in the Italian and European cultural landscape.

Learning outcomes of the course
This course will stimulate student’s curiosity and ability to observe, read and think critically about artistic pieces of art. This will be made possible through the conscious use of historiographical and iconographic sources, web resources, a bibliography, and contemporary criticism. In particular:

1. Students will develop their awareness and understanding of the Renaissance Venice cultural world through an in-depth study of original documents, critical essays and direct observation of the art and architectural works. They will enhance their skills of visual analysis and foster their visual literacy.

2. By strengthening their knowledge of Renaissance Venice’s cultural contest (analysis of scientific treatises, the idea that the world was mathematically organized, the problem of proportion in architecture and vision, the social repercussion of the use of perspective for painters, the rebirth of ancient theatrical literature and scenes), students will be better able to critically understand the representation of architecture in works of art. This course instills the principle that the ‘meaning’ of a work of art depends as much on the knowledge of the viewer as the intentions of an artist or a patron. Students come to understand that a works of art offer information not necessarily communicated by other types of historical evidence.

3. Students will be introduced to a wide array of materials and methods. These will include traditional and historical practices as well as digital analysis of the works of art. They will discover that painted architecture is only apparently visually correct because painters deform and scale architectures like the backdrops of a theatrical set, to make it plausible to the eye of the observer. These operations are necessary because vision does not coincide with geometric perspective, but it is also a matter of mental correction.

4. This course offers a broad understanding of the interactions among mathematics, art and architecture across Renaissance Venice culture, through real examples of art and architectural works. In showing how a work of art reflects the cultural values of the society from which it arose, this course is intended not only for art and architectural history students but it is also addressed to all the students interested in knowing the cultural and artistic Renaissance heritage left to the world by Venice, the city they have chosen for studying.

5. This course transfers instruments for a more scientific approach, observation and reading of the work of art and architecture, which facilitate students’ learning by promoting critical thinking and observing. Abandoning a traditional didactic model, essentially notional, we can identify paths that allow students to become more effective in learning lessons related to art and architecture. This course can serve as a point of departure for research and to some extent can provide a scheme to follow.

Teaching methods
This is a course that surveys the historical factors which made Venice such a receptive setting for the patronage and cultivation of intellectual and artistic ideas during the Renaissance. A constellation of mathematicians (Luca Pacioli, Bartolomeo and Giovanni Zamberti, Girolamo Malatini), humanists and patrons (Pietro Bembo, Ermolao and Daniele Barbaro, Pietro Aretino, Andrea Gritti), artists (Jacopo de Barbari, Giovanni and Gentile Bellini, Vittore Carpaccio, Paolo Veronese, Jacopo Tintoretto, Cristoforo and Stefano Rosa, Albrecht Dürer, Giorgio Vasari), and architects (Andrea Palladio, Jacopo Sansovino, Sebastiano Serlio) prepared the ground for making architecture and its perspectival representation powerful means of communication.

The topics that will be covered in the course comprise four large areas:

- Overview of the cultural background in Renaissance Venice;
- From the theory of perspective to the representation of architecture;
- Architecture, painting and theatrical scenes;
- Analysis of Renaissance Venice works of art.

During lessons, slides will be shown to introduce the students to the areas of the course listed above. Lectures will be complemented by visits to Venice, museums, art galleries, churches and palaces. Moreover, international experts and scholars will be invited to present specific topics of the course. The traditional approach of lecture is intended to be implemented by students by collaborative interaction. The goal is not only to impart information but also to develop cognitive skills and to enhance research attitudes of students, following a simple motto: “the one who does the work does the learning”. So, during lessons questioning techniques will be applied to encourage higher-order thinking skills. Part of each lesson will be dedicated to the presentation of the didactic materials assigned for personal study. The students will be invited to comment in class on the contents of the didactic material. To keep student’s curiosity high, the last part of each lesson will introduce the topic of the next one, discussing about what they expect to hear. Since from the beginning of the course the students will be divided in work groups to mix nationalities and individual acquaintances, every week one group must investigate a topic independently for preparing a brief introductory presentation of it. This group presentation will be performed before the official lecture. This activity will be used to verify, along the way, how students’ aptitudes for research improve and the students can compare their work with the expert’s in-depth themes in order to verify coincidences or gaps with their works.

Evaluation methods
The students’ learning status will be evaluated with two short individual exercises during the course, in the form of seminars, each counting for 20% of the final grade (20%+20%=40%). One group presentation of one topic will count for 20% (20%+20%+20%=60%), remaining 40% will be given according to the results of the final exam, which will consist of a discussion about the themes developed during the course.

Evaluation methods:
20% group presentation
20% 1st individual exercise
20% 2nd individual exercise
40% Final discussion

Bibliography

Main readings
-J. Berzal de Dios, Visual Experiences in Cinquecento Theatrical Spaces, Toronto, University of Toronto Press, 2019.
-M. D’Evelyn, Venice and Vitruvius: reading Venice with Daniele Barbaro and Andrea Palladio, New Haven et London, Yale University Press, 2012.
-J. V. Field, The Invention of Infinity. Mathematics and Art in the Renaissance, Oxford, Oxford University Press, 1977.
-C. Monteleone, K. Williams, Daniele Barbaro’s Perspective of 1568, Cham (CH), Birkhauser, 2021.
-P. L. Rose, The Italian Renaissance of Mathematics. Studies on humanists and mathematicians from Petrarch to Galileo, Ginevra, Droz, 1975.
-M. Tafuri, Venice and the Renaissance, Cambridge (Mass.), The MIT Press, 1995.

Suggested readings on artists and specific topics

-J. Ackerman, Palladio, Harmondsworth: Penguin books, 1966
-J. Ackerman, Leonardo’s Eye, in “Journal of the Warburg and Courtauld Institutes”, 41, 1978, pp. 108-146.
-K. Andersen, The Geometry of an Art. The History of the Mathematical Theory of Perspective from Alberti to Monge, New York, Springer, 2007.
-L. Armstrong, Studies of Renaissance miniaturists in Venice, Londra, Pindar 2003.
-R. Baldasso, The Portrait of Luca Pacioli and Disciple: a New Mathematical Look, in “Art Bulletin”, XCII, 1-2, 2010, pp. 83-102.
-O. Benesch, A New Contribution to the Problem of the Portrait of Luca Pacioli, in “Gazette des Beaux-Arts”, VI Pér., XLIV, 1954, pp. 203- 206.
- M. Carpo, F. Lemerle, Perspective, Projections and Design: Technologies of Architectural Representation, Routledge, New York, 2007.
-L. Cellauro, Daniele Barbaro and his Venetian editions of Vitruvius of 1556 and 1567, in “Studi Veneziani”, 40, 2000, pp. 87-134.
-L. Cellauro, The Causa Grimani and its Political Overtones, in “Journal of Religious History”, 4, 3, 1967, pp. 184-205.
-R. Cocke, Veronese and Daniele Barbaro: The Decoration of Villa Maser, in “Journal of the Warburg and Courtauld Institutes”, 35, 1972, pp. 226-246.
-A.C. Crombie, Science, Art and Nature in Medieval and Modern Thought, Londra, Hambledon Press, 1996.
-M. Daly Davis, Carpaccio and the Perspective of Regular Bodies, in La prospettiva rinascimentale. Codificazioni e trasgressioni, ed. by M. Dalai Emiliani, Florence, Centro Di, 1980.
-M. Daly Davis, Piero della Francesca’s Mathematical Treatises. The «Trattato d’abaco» and «Libellus de quinque corporibus regularibus”, Ravenna, Longo Editore, 1977.
-J. D’Amico, Drama and the Court in “La Calandria”, in “Theatre Journal”, 43, 1, 1991, pp. 93-106.
-S. Y. Edgerton, Alberti’s Perspective: A New Discovery and e New Evaluation, in “The Art Bulletin”, 48, 1966, pp. 367- 378.
-S. Y. Edgerton, The Renaissance Rediscovery of Linear Perspective, New York, Harper and Row, 1976.
-J. Elkins, The poetics of perspective, Ithaca, Cornell University Press, 1994.
-P. Fane-Saunders, Pliny the Elder and the Emergence of Renaissance Architecture, Cambridge University Press, Cambridge (UK), 2016.
-J. V. Field, Piero della Francesca’s Treatment of the Edge Distortion, in “Journal of Warburg and Courtauld Institutes”, 49, 1986, pp. 66-90.
-J. V. Field, Rediscovering the Archimedean Polyhedra: Piero della Francesca, Luca Pacioli, Leonardo da Vinci, Albrecht Dürer, Daniele Barbaro, and Johannes Kepler, in “Archive for History of Exact Sciences”, 50, 1997, pp. 241- 289.
-P. Fortini Brown, Venetian narrative Painting in the Age of Carpaccio, New Haven and London: Yale University Press, 1988.
-P. F. Grendler, The Universities of the Italian Renaissance, Johns Hopkins University Press, 2004.
-M. Grosso, G. Guidarelli, Tintoretto and Architecture, Venice, Marsilio, 2019.
-M. Y. Hara, Capturing eyes and moving souls: Peruzzi’s perspective set for La Calandra and the performative agency of architectural bodies, in “Renaissance Studies”, 31, 2017, pp. 586-607.