On Alberti’s surveying instruments

Xavier Proulx

Preliminary research and starting point

The starting point of our project is the history of cartography in the Renaissance, or more precisely, surveying instruments. As a first exercise for this class, we have already investigated the Mariner’s Astrolabe, an ancient surveying instrument (see the previous post on the blog). The logical step forward in our research has taken place in the second exercise, where we have produced Alberti’s map of Rome. That said, this exercise is linked to our area of interest for the final project.


The way Alberti’s map is constructed is pretty interesting because of the fact that he mistrusted the manuscript copyists and thus provided only a set of polar coordinates in order for the reader to redraw the map. In that spirit, Alberti has been the first computational geometry practitioner in history, suggesting the construction of a city plan on a mathematical basis. By interpreting a set of points in an array, the reader becomes the equivalent of a modern plotter. Alberti’s work is not turned toward drawings – actually there are few drawings in his treaties – he instead relies on words to describe most of his instruments and findings:

 “He simply chose not to use illustrations that would not have be reproducible, replacing them with textual descriptions. In his map of Rome, he instead replaced pictures with computational instructions designed to transform the image in a digital file and then recreate a copy of the original picture when needed.” [3, p.54].

On the other hand, the spirit of a place has been traditionally linked with the sense of vision. You know a place because you see it. With the introduction of surveying instruments, we are beginning to witness a “progressive shift away from the individual human body as a reliable agent for recording spatial information, towards dependence upon instrumentation as the guarantor of accuracy and objectivity in survey data”. [4, p.159]

We shall put maps at the center of attention for this project. At the most basic level, a map, or chorography, is “a mode of description in which truth to the individuality, personality and uniqueness of a place or region was the goal.” [4, p.7] Simply put, mapping was seen as much an art as a science. Alberti’s work is only the beginning of the science of cartography, which later evolved into the art of orthographic projections and picturing machines (cf. Mariano Taccola, Albrecht Dürer, and Gerardus Mercator). However, “Alberti’s images were meant to be carriers of precise quantitative information, and to record measurable data – data that could be used and acted upon.” [3, p.68]


Our preliminary research about surveying, cartography, and data collection throughout history attracted our curiosity about the way Alberti conducted his survey of Rome, as reproduced in the second exercise. In particular, we are interested in the way Alberti used mathematics to “order spatial relationships”, a quality that can be shared by both mapmaking and painting during the Renaissance. [7, p.177] Consequently, as a project goal, we want to keep our focus on the genesis of surveying instruments that were used to render these maps.

In particular, the starting point of our project is a desire to explore the instrumentation that lead to Alberti’s map of Rome and the process in which he transformed his survey data into the basics of a digital file. Alberti certainly took great care to keep a sense of mystery on these in his survey of Rome treatise. However he later explained the surveying instruments he used in his Mathematical Games (Ex Ludis rerum mathematicarum) manuscript. Reading this small treatise let us understand Alberti’s interest in mathematics. Several “games” are depicted and many surveying instruments are drawn. We shall therefore narrow down our interest to the surveying instruments developed by Alberti, as seen in this manuscript. Several examples are pictured here such as the equilibra for leveling surfaces and regulating the course of water, weighing objects or aiming a bombard (a true multipurpose instrument!). He also constructed a device for measuring lengths of distances along a road, and addressed the construction of an instrument for measuring the speed of a ship using wind. Finally, he described the instrument he used for his survey of Rome: a circular disc used to measure angles and estimate distances. These instruments will be the starting point of our investigation.

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We believe that the choice of Alberti’s work as a starting point is relevant in the process of conducting this project. His unique work sits right between the humanism of the Renaissance, and the influence of medieval craftsmanship: he mastered all the traditional arts of a medieval courtier and all new ones of the Renaissance intellectual [7]. He lived at a time right at the beginning of the Renaissance, when the influences of the Middle Ages – notably in craftsmanship – were still present. But at the same time he retained the influence of engineers whose knowledge had started to spread, notably in the science of war: “The engineers were augurs as well as mathematicians and artists.”[5] These explain Alberti’s choice for celebrating these disciplines. In his way, he connected the liberal arts of geometry and astrology with the crafts of painting and sculpture [5]. As we began to discover in our preliminary research, Alberti’s time was a period when engineers’ work blended with the architectural practice in the art of building – but also perhaps in the art of surveying?

In order to nourish this project, we are aiming to pursue research on the historical context that pushed Alberti to undertake his surveys and his work on instruments in his Mathematical Games. At the same time, we will soon choose a precise surveying instrument among the ones identified above and begin the project by replicating it, in the hope that it contributes to further innovation for the final step.

Alberti used instruments to translate the vision of a place on paper. However he added an extra step, which was to transform the measurement into a mathematical array of points. Maybe can we replicate and use one of his instruments taken from his Mathematical Games and then apply the same computational data structure on the resulting measurements? Maybe this instrument’s usage can be actualized or modified in regards to modern architecture practice? As such, we believe nowadays architecture projects could benefit from this basic surveying language, especially in the matter of feeling the sense of a place by surveying it first on a more organic approach basis, rather than the purely computerized methods of today.

Preliminary research bibliography

[1] Alberti, Leon Battista. Ex ludis rerum mathematicarum

[2] Brown, Llyod A., The Story Of Maps, Bonaza Books, New-York, 1949, 393p.

[3] Carpo, Mario, The Alphabet And The Algorithm, MIT Press, Cambridge, 2011, 169p.

[4] Cosgrove, Denis. Geography and Vision: Seeing, Imagining and Representing the World. : I.B. Tauris, London, 2008, 256p.

[5] Grafton, Anthony, Leon Battista Alberti Master Builder Of The Renaissance, Hill and Wang, New-York, 2000, 417p.

[6] Lefevre, Wolfgang, ed., Picturing Machines 1400-1700, MA: The MIT Press, Cambridge, 2004.

[7] Miller, Naomi, Mapping the City, Continuum, London, 2003, 270p.

[8] Woodward, David, Cartography in the European Renaissance, The University of Chicago Press, Chicago , 2007, 2272p.

[9] Williams, Kim, The Mathematical Works of Leon Battista Alberti, Birkhäuser, Berlin, 2010.

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