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The discoveries of Herculaneum and Pompeii and the broadened scope of geography in the eighteenth century, and developments in mathematics and physics that began in the nineteenth and continued into the twentieth, renewed studies of ancient works of art led to the creation of opposing factions regarding the “question of perspective”: those who maintained the existence of a single possible perspective, and those who upheld the existence of multiple perspective constructions. To shed light on the debate, this present paper examines some of the factors behind the two positions.

The cartographic representation of Rome is as varied as its history; however there are several qualitatively significant discontinuities within an evolutionary process we can consider as linear. The research presented here focuses on a specific selection of fourteenth- and fifteenth-century maps of the city of Rome as a way to discuss not only one of these glaring discontinuities, but also several aspects linked to the perception and communication of the image of the city in the period preceding the more meticulous representations executed after the scientific revolution in the field of urban and territorial surveying. An analysis and comparison of these representations was performed using criteria that evolved during the research. It concentrated on three objectives: to produce observations about the perception of the city during that period; to draw attention to select contents in the maps; to discuss related communication strategies.

In 1729 the Dutch cartographer Nicolaas Cruquius engraved a map that became a benchmark for every future illustration of a territory. The map, showing the bed of the river Merwede and its surroundings, was made to control an area subject to inundation and flooding, understand the territory, and plan projects to solve the thorny problem of water management. In this superb map, divided into two tables, Cruquius adopts contour lines of equal value. This was a first. What Cruquius did was reinterpret and reuse the isogones employed roughly thirty years earlier by another scientist to represent a physical phenomenon, and then use them in a different context. In fact, in 1701 Edmund Halley had employed isogones in a map he drew to describe magnetic declination over the ocean. Halley and Cruquius use lines of equal value to describe two very different models (one is a physical phenomenon; the other is an orographic model). However, they both helped to legitimise the use of contour lines to represent geographically-based phenomena. In 1712 Cruquius had made an accurate map of Delfland. This extremely precise map reveals contamination between zenithal projection and perspective view, both of which sometimes appear in the same table in a seamless shift from one projective mode to another. The simultaneous presence of different projective methods was inspired by sixteenth- and seventeenth-century maps. The method creates images that are accurate, measurable, and captivating at the same time, but they are a far cry from the projective integrity that cartography was to acquire during the eighteenth century. Cruquius adopts isobaths to maintain the plastic effect in a zenithal projection, but abandons them in the secondary tributaries where he uses more conventional graphics which were inspired by earlier examples and were to become quite common to portray water flowing along rivers. A similar graphic depiction of water is present in the zenithal plan of Rome by Giovanni Battista Nolli engraved just nineteen years after the Merwede map. The way in which natural elements are represented in Nolli’s map, the accurate measurements, and deliberate rejection of central or pseudo-axonometric projection, warrant a comparison between Curquius’ impressive map and the one made by Nolli.

This contribution focuses on studies concerning the art of defilement (defilade) of fortifications, that is, the art of using uneven terrain to provide protection from the enemy; in particular it will analyse the issues and events which made this military technique one of the first chapters of descriptive geometry, and the important role played by Nicolas-Francois-Antoine de Chastillon, the first commandant of the School of Mezieres. As firearms became more powerful new studies were required about how to defend military fortifications from enemy fire. To solve these, Chastillon first highlighted the flaws of Vauban’s empirical approach and then radically overhauled the study of defilement by tackling it theoretically using graphic analyses carried out ‘on the drawing board’. This new approach concentrated on the depiction of space in two dimensions the need to graphically manage the territory around the fortification. Thus it is Chastillon who, well before Gaspard Monge, identified a method which was to rapidly lead to the definition of the basic operations of descriptive geometry. Together with the study of wood and stone stereotomy, it also paved the way for the new science of scientific representation, the invention of cartography and the geometric control of topographical surfaces.

Se si considera la componente fisica del sistema città come espressione materiale dell’insieme dei fenomeni evolutivi dei luoghi, appare evidente come la sua rappresentazione possa essere considerata come sistema di conoscenza generale in grado di manifestare una convergenza di informazioni di natura altamente eterogenea. Le vaste trasformazioni che hanno interessato le città nella storia hanno determinato una evoluzione non solo nelle modifiche morfologiche degli assetti territoriali e nella stratificazione architettonica delle strutture urbane, ma anche nella percezione e fruizione degli spazi urbani. Se si considera l’organizzazione dello spazio urbano come ambito di relazione tra gli uomini, i contributi che provengono dalle fonti bibliografiche, iconografiche e cartografiche in particolare possono consentire la ricostruzione diacronica dei tessuti urbani. Questa ricostruzione è resa possibile dalla lettura delle diverse rappresentazioni che della città sono state date nel tempo, come rappresentazioni iconografiche o pittoriche, talvolta simboliche se non addirittura metaforiche, che consentono di acquisire conoscenze dei luoghi, anche quando presentano uno scarso grado di attendibilità. L’introduzione dell’informatica nel rilevamento e nella rappresentazione cartografica e la realizzazione dei sistemi informativi territoriali hanno aperto nuove possibilità non solo nella realizzazione di database collegati e georeferenziati, che possono contenere una notevole quantità di informazioni di diversa natura progressivamente incrementabili, ma soprattutto rendendo agevoli sia le molteplici interrogazioni sia le successive elaborazioni. Lo sviluppo della cartografia digitale dalla quale si possono derivare direttamente modelli tridimensionali, si pone quindi come punto di partenza per una corretta rappresentazione della complessità del fenomeno urbano e per un ripensamento dello spazio non più sulla base di esplorazioni planimetriche, ma tramite la creazione di modelli virtuali generati in maniera più o meno automatica a partire dalla cartografia stessa. In questo senso, il modello di derivazione cartografica costituisce l’aspetto metrico-quantitativo della rappresentazione della città, aspetto che risulta tanto più esatto, obiettivo e verificabile in quanto ottenuto con strumenti che rendono le misurazioni sufficientemente attendibili. Si tratta dunque di esplorare la cartografia tridimensionale cogliendone le peculiarità e la ricchezza nella restituzione dello spazio urbano, caratteristiche, queste, che suggeriscono immediatamente di tentare di ricostruire con la stessa vivacità rappresentativa anche tutti i trascorsi storici della città o, quanto meno, di alcuni dei suoi momenti topici, con particolare attenzione alle trasformazioni di natura orografica ed edilizia. In questo quadro emergono due distinti aspetti di natura metodologica, l’uno concernente la generazione del modello urbano e le implicazioni tecniche che questo comporta (implementazione di dati, automatismi, studi tipo-morfologici, scala del modello, …), l’altro relativo all’evoluzione della città attraverso il confronto tra modelli cartografici diversi (bi e tridimensionali). La realizzazione di un modello virtuale basato sulla cartografia digitale 3D, che fotografa lo stato attuale della struttura urbana, può rappresentare la griglia tridimensionale di riferimento per una visualizzazione delle trasformazioni spaziali attuata con una procedura che ripercorre a ritroso il cammino della storia. Si tratta di riferire a questa griglia orientata sulla base di capisaldi topografici certi i dati cartografici e iconografici provenienti dalla ricerca storico-documentaria, sulla base della individuazione di elementi invarianti della struttura urbana, come assetti orografici, vuoti urbani o edifici esistenti, etc., che non hanno mutato la loro localizzazione e le loro caratteristiche morfologiche. Così concepito, il modello tridimensionale di derivazione cartografica si caratterizza per la capacità di recepire e valorizzare documenti molto diversi e non necessariamente “scientifici” ai fini di una visualizzazione interattiva della storia del singolo brano di città o del singolo edificio per valutarne le trasformazioni sul piano morfologico e dimensionale, ma anche percettivo.

This essay intends to enhance the little known figure of Matteo Zaccolini and his unpublished Treatise on Optics which emerges, due to its range and variety of discussion, as an important opportunity to rediscover the knowledge available to the educated painters in the first quarter of the seventeenth century. In this paper some of zaccolini’s propositions concerning different themes are analysed: foreshortening of apparent dimensions, cast shadows tracing, shadows as conical sections and the aerial perspective. Thus far, the Treatise on Optics by Matteo Zaccolini has never been printed, nor it was the subject of a deep and complete critical study regarding its geometric content.

The aim of this research has been the digital reconstruction of an unrealized project for a scientific villa designed by Francesco Borromini around 1644. We refer to the actual Villa Dorja Pamphilj, that was indeed built but following a totally different project made by Alessandro Algardi (1598-1654) and Francesco Grimaldi (1543-1613). The documents about this topic are conserved in the Vatican Library and in the National Archive of Rome. These sources are both graphical and written: the graphical are the blueprint by Francesco Borromini, a plan and a symmetrical façade in two solutions and a sketch attributed to Virgilio Spada that shows some variation compared to Borromini plan. The literary documents consist in Latin language munuscripts by the monk Emmanuel Maignan, where the author describes 21 scientific games conceived to decorate the villa and a letter written by Borromini and addressed to Cardinal Camillo Pamphilj. To realize the digital clone of the villa I followed the information given by graphics documents, respecting the real functioning of Emmanuel Maignan scientific games listed in his manuscripts.

In the middle of the XVIIth century the architect Francesco Borromini and the monk Emmanuel Maignan collaborated together in a project for a villa commissioned by Cardinal Camillo Pamphilj. Borromini realized the blueprints and Maignan wrote a list of scientific devices conceived as decoration of the dwelling and its gardens around. Some points of the Munuscript describe anamorphical projections similar to optic experiments and generally connected to perspective laws. Deeply inside, the monk suggests to create a direct anamorphosis in the main hall of the villa, designed to be observed from the northern loggia; a catoptric anamorphosis, provided with some conical mirrors, on the cross vaults of the same portico; a dioptric anamorphosis, arranged to be seen through a monocle equipped with a prismatic lens, in the southern loggia. These three types of anamorphic images respect the ones explained by father Jean François Niceron in his treatise La Perspective Curieuse, that probably influenced the scientific manuscript by Maignan for Villa Pamphilj.

The goal of this research is the identification of the tools available to achieve a convincing effect of perspective illusionism in artworks between the XVth and XVIIth century. We need to understand the psychological and physiological mechanisms that oversee the human visual perception; then we will identify the geometric tools that can reproduce and control these mechanisms in artwork. In particular we will study three different aspects: foreshortening of apparent dimensions, linear perspective and aerial perspective. Once we identified these instruments we will propose a set of experimental tests to evaluate the illusory perspective effect and, finally, we will apply this methodology to the case study of the Saint Ignazio’s Glory painted by Andrea Pozzo. The results of these tests showed that the Pozzo’s artwork is characterized by a high consistency of all the visual cues provided to the viewer.

Il modello marmoreo rinvenuto in frammenti presso gli ambienti contigui le così dette Grandi Terme della Villa Adriana a Tivoli costituisce un vero e proprio unicum, data la scarsità di reperti ascrivibili all’ambito delle progettazione architettonica pervenutici dal mondo antico. Sebbene il reperto sia stato oggetto di numerosi studi a partire dalla fine degli anni ’60, cioè dopo il suo ritrovamento, si è ritenuto opportuno approfondirne alcuni aspetti a partire da una nuova campagna di rilievo con sensori attivi che ha permesso di realizzare un assemblaggio virtuale dei frammenti al fine di studiarne la forma all’interno di programmi di modellazione 3D. Grazie al confronto tipologico e ad una approfondita analisi metrologica si è riusciti a chiarire la funzione del manufatto e a decodificarne l’”algoritmo” alla base del suo proporzionamento grazie al confronto con le regole geometrico - matematiche presenti nei due trattati dei Erone di Alessandria “Stereometrica” e “De Mensuris”.

No theory, practice, education, criticism and history of Design can exist without being continuously and directly compared to the various components involved: both Leonardo and Plato (although in different manners) can help us understand how important it is to be able to create a connection amongst these components and especially between “practice” and “science”. Although they are quite opposite, these should not be separated or used as the endpoints of a cognitive process because they represent knowledge and its concrete expression. Life revolves around opposites that only appear to be irreconcilable since they are a necessary part of it. The relationship that exists between opposites creates energy to allow them to flow from one pole to another in unison.

This contribution moves from the careful choice to reflect on the role of architecture’s representation, in all its aspects and through the centuries, as “warranter” for the correspondence between theory and practice of the built work. This characteristic should be caught as something enriching the definition of the discipline’s identity, as it contains the basic elements of its existence as well as the capacity to bring achieved knowledge into theoretic foundations. This contribution wants to outline the way in which the consolidation of new theories typical of the representation will need to be based on the principle of a continuous renewal of ideas, fed by scientific and technological research along with a common idea of the future.