Category Archives: Exercise 2 – L. B. Alberti’s map of Rome

Guillaume’s map of Rome

Leon Batista Alberti introduces his work on the delineation of the city of Rome. The main subject is the innovative and mathematical yet easy method he created to complete his attempt.
Therefore, it is said that we firstly need to decide the size of a circle, the “horizon”, where will be depicted the city. Then, we must divide it into 48 equal “degrees”. The 12th is the east on the left, the 24th is the south at the top, the 36th is the west on the right and the 48th is the north at the bottom. Each degree is divided into four “minutes”.
The second part of the instrument, the “spoke”, is a rod which is as long as the radius of the circle. It is divided into fifty “degrees” and each degree is divided into four “minutes”. The end, which marks the fiftieth degree, touches the “horizon” and the opposite end is set at the centre of the circle.
Those two parts help to place strategic coordinates of the city indicated in tables. The “Corners” are the intersections of two lines or a line and a curve. The “Apex” are the points which defines a curve. Each wall has a corresponding table.
For each point, a number indicates where to place the rode on the horizon and another one says where to trace the point according to the rode.
Once the points are correctly set in the card, we just draw the lines and the curves they define.

I decided to draw a circle with a diameter of approximately 17 inches.

Leon Batista Alberti présente son travail de relevé de la villa de Rome. Le sujet principal du texte est la méthode mathématique, innovante et facile qu’il a créée pour mener à bien son entreprise.
Ainsi, il est dit que l’on doit d’abord décider de la taille d’un circle, l’ “horizon”, où sera tracée la villa. Puis, on le divise en 48 “degrés”, tous égaux. Le 12ème est l’Est à gauche, le 24ème est le sud en haut , le 36ème est l’ouest à droite et le 48ème est le nord en bas. Chaque degré est divisé en quatre “minutes”.
La second partie de l’instrument, le “rayon”, set use règle de la taille du rayon du cercle. Elle set divisée en cinquante “degré” et chaque degré set divisé en quatre “minutes”. L’extrémité où est marqué le cinquantième degré se place sur l’ “horizon” et l’extrémité opposée est au centre du cercle.
Ces deux éléments aident à placer des points stratégiques du dessin de la villa relevés en tables. Les “Coins” désignent les intersections entre deux lignes ou une ligne et une courbe. Les “Sommets” sont les points qui définissent les courbes. À chaque table correspond une enceinte. Pour chaque point, une donnée indique où placer la règle sur l’ “horizon” et une autre indique ou tracer le point selon la règle.
Une fois ces points correctement placés sur la carte, il n’y a plus qu’à tracer les lignes et les courbes qu’ils définissent.

J’ai décidé de tracer un cercle de 43 centimètres de diamètre environ.Image

The Horizon: Alberti’s Delineation of Rome

Alberti’s survey of Rome records the passage and lineamenta (outline) of certain features in the city of Rome including: walls, rivers, streets, hills, and buildings, as well as the locations of temples, public works, gates, and monuments.
The device is made up of two main components: the Horizon and the Spoke.
The Horizon is the circle within which the depiction of the city is enclosed. The Horizon is divided into equal degrees (up to 48) and then subdivided into four parts called minutes. The north will be marked at degree 0, the eastern equinox will be at 12, south at 24, and the west equinox at 36.
The Spoke is a straight rod much like an hour hand that is set at the centre of the horizon and extends to its outer circumference. The spoke is divided into 50 equal parts, similarly called degrees.
Once the device is made, the process of tracing the map involves identifying the degrees and minutes in the accompanying table that correspond with a title. These numbers will be used to guide the horizon and the spoke simultaneously to find the titles coordinates.
For example, if we start in the table labeled “Walls of Litium”, under “Horizon” we read: “43 degrees, 2 minutes”. Therefore we position the spoke at this number on the horizon. Next, under “Spoke” we read: “31 degrees, ½ minute”. Therefore, we locate this number on the spoke and we draw a dot at this coordinate. At the end we connect all the coordinates with a straight line, giving us the passage or lineamenta of the wall of Litium.

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Map of Rome: Alberti’s computed reality

This study examines Leon Battista Alberti’s topographical survey of the city of Rome recorded in his book Descriptio vrbis Romæ, published around 1450.

An early form of computer aided drawing where technology in its rational framework maps out a comprehensible grid (by the movement and coordination of the “horizon” and “spoke”) over a rather complex reality. It then synthesizes with a pre-constructed logic (embedded in the instructions and charts from the Descriptio vrbis Romæ) to facilitate the realization of a dynamic visual structure— a structure that the even the drafter himself/herself could be unaware of its is outcome in detail.

Mark L.

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Descriptio urbis Romae

«La théorie d’Alberti est presque entièrement basée sur le système de notation entre le design et le bâtiment, impliquant que les dessins peuvent et doivent, être identiquement transmis à l’objet tridimensionnel.  Dans sa théorie, le design du bâtiment est l’original, et le bâtiment lui-même est une copie.»  Alberti était véritablement obsédé par la division entre le travail de l’auteur et la reproduction.  Il a inventé plusieurs dispositifs pour faciliter la connexion entre le projet et le bâtiment construit.  En fait, les copistes faisaient souvent des erreurs, parfois ils inventaient, interprétaient ou interpolaient ce qu’ils avaient à copier.  Alberti pensait que des mots et des chiffres pouvaient voyager mieux dans le temps et dans l’espace, plus rapidement et avec moins de risques.  La fidélité d’une copie à la main était inversement proportionnelle à la complexité du dessin, et de sa ressemblance à un archétype (comme une forme géométrique).

Alberti utilisait rarement des illustrations complexes dans ses livres, choisissant simplement de ne pas montrer ce qui était difficilement reproductible.  Il les remplaçait par des descriptions, avec parfois des systèmes composés de lettres et de chiffres.  On pourrait affirmer que déjà, entre 1430 et 1440, dans sa Descriptio urbis Romae, Alberti a créé la toute première image digitalisée, dans un système de coordonnées polaires.  Le lecteur est amené à dessiner lui-même sa carte de Rome, tel un traceur ou une imprimante.  Alberti a utilisé cette idée pour annoter plusieurs bâtiments, objets, peintures, et même des sculptures.  Il a d’ailleurs suggéré l’idée que si des parties d’une sculpture sont produites dans tes ateliers différents, ces parties pourraient s’emboîter parfaitement, comme dans un système préindustriel Tayloriste.  Bien entendu, les inventions d’Alberti ne sont pas parfaites, dû notamment à la technologie elle-même, l’erreur humaine étant toujours possible.

Selon Mario Carpo, dans notre culture Occidentale moderne nous assistons à l’inversion du paradigme Albertien.  L’ère digitale a fortement déterminé les bases et les standards en architecture.  Il est maintenant possible de reproduire des copies parfaitement identiques, mécaniquement, et cela a un impact sur notre environnement construit.  Cela affecte indéniablement notre culture visuelle et nos fonctions et valeurs de signes.

Source : The Alphabet and the Algorithm, Mario Carpo

La carte réalisée fait un diamètre de 400 mm et a été entièrement dessinée à la main à la plume fontaine et au crayon à la mine sur du carton.  La règle est en bois (tilleul).

«Alberti’s entire architectural theory is predicated on the notational sameness between design and building, implying that drawings can, and must, be identically translated into three-dimensional objects.  In Alberti’s theory, the design of a building is the original, and the building is a copy.»  He was obsessed by the division between the work of the author and the reproduction.  Alberti made a lot of inventions to facilitate the translation between the project to the constructed building.  In fact, the copyists often make mistakes, sometimes they can invent, interpretate or interpolate what they have to copy.  Alberti thought that texts and numbers could better travel in time and space, faster and more safely than images.  The fidelity of a handmade copy drawing was an inverse proportion to the complexity of the drawing, and of its distance from the archetype (like simple geometries).

Alberti rarely used complex illustrations in his books, he simply chose to not show what is hardly reproductible.  He replaced them by descriptions, with numerical or letter-based strategies.  We could say that even around 1430-1440, In the Descriptio urbis Romae, Alberti has created the first digitalised image using a system of polar coordinates.  Then, the reader is involved in a DIY process, where he is the «plotter» of the image.  Alberti used the same idea to notate buildings, objects, paintings and sculptures, he even suggested that the parts could be produced in different workshops and they would fit perfectly, like in a pre-industrial, taylorist system.  Of course, that system is not perfect because of the technology itself, in those inventions the human mistake is still possible in the process.

According to Mario Carpo, in our modern Western culture, we assist at the reversal of the Albertian Paradigm.  The digital time have determined a lot of the basics and the standards in architecture.  It can produce exactly repeatable, mechanical imprints and it has an impact on our visual envrionnement.  It indeniably affects our visual culture, our functions and values of signs.

Source : The Alphabet and the Algorithm, Mario Carpo

The map realized is all drawn by hand with fountain pen and pencil on thick paper, the map has a diameter of 400 mm.  The rule is in wood.

Émélie DT

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Martina’s Map of Rome Part 1

In the 15th century, Alberti was commissioned to carry out a topographical survey of the city of Rome. He invented a mathematical instrument to do so accurately, a technical drawing instrument, which would essentially locate the given sites. The instrument consisted of a circular disk he named, the ‘horizon.’ The circumference of this circle would be equally divided into 48 parts or ‘degrees.’ The distance between these degrees was further divided into 4 parts deemed ‘minutes.’ The completion of the first part of the instrument is now complete. 

The ‘spoke’ will act as the rule of this circle and will rotate around it’s centre. Its length is equal to the radius of the circle. It is divided into 50 equal segments (degrees) and then further divided into 4 minutes. Once the spoke is in place, we are able to start depicting points and measurements from Alberti’s tables. For instance, if given ‘coordinates’ for the Porta Portuense (Horizon: 27degrees, 3minutes and Spoke:26degrees, 2minutes) then we locate them on the horizon and spoke appropriately. Finally, he differentiates the technique between apexes and corners. Points of an apex should be curved and not simply connected in a direct straight path.

Brian’s Horizon Tool – Drawing a Map of Rome

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Above are two versions of the Horizon tool invented and described by Leon Battista Alberti to allow a man of average intellect to accurately draw the map of Rome.

The tools have been cut to a 15″ diameter to allow for a decently scaled map. A second Spokeless version of the toll was created for more accurate plotting (as opposed to the previous version being interrupted with spokes).

Synopsis: 

After having read Alberti’s description of the construction the “Horizon” tool it becomes clear that this tool is made only to replicate his initial surveying studies. There is some complexity when he begins to differentiated a corner from an apex, consequentially suggesting different drawing rules when constructing the lines through the co-ordinates.

I would imagine that because the grid used to initially survey City Walls was a radial one as opposed to an orthogonal grid, that it would have been quite difficult to locate the co-ordinates (possibly having to return to the Capitol to count the number of steps for every important corner, apex or gate).