Geocentro Magazine - numero 6 - novembre/dicembre 2009

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66 ANNO I | n. 6 | NOVEMBRE - DICEMBRE <strong>2009</strong> territorio dei tanti agrimensori e periti del suo tempo, anche se il suo avvicinamento alla rappresentazione cartografica non deriva certo da intenti di tipo professionale. Leonardo non è un cartografo in senso stretto, ma si occupa di cartografia per specifiche necessità di studio e per esigenze di analisi, finalizzate alla progettazione territoriale o alla pianificazione di attività belliche. Per entrare più direttamente nel merito delle sue opere cartografiche bisogna preliminarmente spostare l’attenzione dal mondo delle mappe a quello della rappresentazione in generale, cioè del disegno e della pittura, che per Leonardo non sono semplicemente un linguaggio per ripetere visivamente cose già note, ma, come ha osservato Giulio Carlo Argan, “sono la chiave con cui si penetra nel mondo dei fenomeni”. È infatti dai precetti derivanti dal Libro di pittura che si recuperano i fondamenti innovativi della sua produzione cartografica. La formula adotta da Leonardo nel rilevamento e nella rappresentazione cartografica è sintetizzata nel precetto che egli stesso ferma nei suoi appunti del Manoscritto L dell’Istituto di Francia, dove egli annota: “scorta sulle sommità e in su’ lati dei colli le figure di terreni e le sue divisioni e nelle cose volte a te, fale in propria forma” (Ms. L dell’Istituto di Francia, f. 21 are solved through the use of the fi rst principle of similitude between right-angled triangles and through the so called “rule of three”. However, the most relevant contribution of this work consist in a new method of topographical surveying that is meant to solve the question of the mutual position on the urban scale through a triangulation work. Such a work had already been anticipated by Giovanni Fontana in his Tractatus de trigono balistario abbreviatus […] in 1440. Th is essay was recovered and completed by diff erent Renaissance scholars, and was furthermore ameliorated for other fi ve centuries, until nowadays. For this triangulation, they used a goniometer divided in 48 parts, still without an alidade and a compass pointing to the magnetic North, and still with the help of a plumb line. Alberti fully describes his method, explaining how to manufacture the adequate instrument and, step by step, how operate in order to obtain a correct survey. Moreover, he explains all the rules to follow in the observation of the angular directions among the diff erent sites and in their registrations. Nevertheless, there are no instructions about the representation of the dimensions and the orientation of the various polygons surveyed. Th e second essay, Descriptio urbis Romae, is a much more original step forward. It shows how an urban plan could be sketched on a map, according to polar coordinates collected and organised within standard tables. Th e instrument that enables the technicians to draw such tables is a protractor, called Orizon. It is provided with a graduated radius that is hinged in the middle of the instrument itself, exactly as it happens in the modern, graduated circular protractor having a pivoted arm, used for measuring or marking off angles. When it has represented on a sheet of paper the plan of a town measured through the triangulation method explained in the Ludi, a surveyor establish in this representation the basis of a cartographic system of reference: starting from a central point, he can measure with the Orizon the polar coordinates of every single place on the graphic. We are talking about distances and angles from a starting point that can give way to the setting down of a table with the name and the position of every represented topographical detail, a sort of encrypted map. Such a table, obtained through a graphical representation and not by a practical survey on the fi eld, represents a revolutionary step forward: the cartographer willing to obtain another map, identical to the original one, could certainly be able to make a copy perfectly matching the fi rst sample. Considered from this point of view, the whole method suggested by the Descriptio could appear like a mere academic exercise: the advantages of taking polar coordinates as a reference are obvious at fi rst sight, as such a process allows the creation of a faithful reproduction from an original map. However, this method is by far more productive than a simple technique for a geometrical copy of a topographical map (a copy that http://it.wikipedia.org/wiki/File:Leonardo_self.jpg
http://commons.wikimedia.org/wiki/File:Mona_Lisa-restored.jpg Leonardo da Vinci, Monna Lisa dopo il restauro (particolare) Leonardo da Vinci, Mona Lisa restored (detail) could be realised by an easy tracing from fi rst model). Its real innovation consists in the introduction of the concept of “scalability” starting from the real measurements. In such a way, the cartographer can draw from the same positional data a n number of maps, identical as for their proportions, but all diff erent in their scale if compared with the model, according to the decrease factor chosen in the defi nition of the distances from the origin (scale of the map). 67
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FONDAZIONE GEOMETRI ITALIANI AVVENI
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40 OSSERVATORIO Urban Best Practice
Page 5 and 6: photo©shutterstock.com/Lee Morris
Page 7 and 8: photo©shutterstock.com/Dmitriy Shi
Page 9 and 10: photo©shutterstock.com/Mariusz S.
Page 11 and 12: www.shutterstock.com/izoom “Quand
Page 13 and 14: Justine Lee (grande), Ishida Shunji
Page 15 and 16: 20 SOCIETÀ E COSTUME Quelle luci l
Page 17 and 18: 22 ANNO I | n. 6 | NOVEMBRE - DICEM
Page 19 and 20: per promuovere questi obiettivi e,
Page 21 and 22: e alla costituzione della società
Page 23 and 24: photo©shutterstock.com/Sailorr str
Page 25 and 26: Coloretrend, Urban city e accenti.
Page 27 and 28: Il teatro di Fantiano L’area dell
Page 29 and 30: viene ricavata la cavea per gli spe
Page 31 and 32: 38 COSTRUIRE “átika”, tradizio
Page 33 and 34: 40 OSSERVATORIO Urban Best Practice
Page 35 and 36: ANNO I | n. 6 | NOVEMBRE - DICEMBRE
Page 37 and 38: UN Photo/Marco Castro Trovare un ac
Page 39 and 40: 48 VERDE PENSILE Un tetto a giardin
Page 43 and 44: http://commons.wikimedia.org/wiki/C
Page 45 and 46: http://en.wikipedia.org/wiki/Ecumen
Page 47 and 48: http://commons.wikimedia.org/wiki/L
Page 49: Vagnetti L., Lo studio di Roma negl
Page 53: http://commons.wikimedia.org/wiki/L
Page 62 and 63: 72 IL PUNTO DI VISTA Sicurezza nei
Page 70 and 71: 80 APPROFONDIMENTI Palermo, stima d
Page 74 and 75: 84 FORMAZIONE La qualifi cazione en
Page 80 and 81: 90 REDAZIONALE Topcon IP-S2 Sistema
Page 82 and 83: 92 REDAZIONALE South NTS962R & pfCA
Page 84 and 85: 94 REDAZIONALE Interventi sulle cop
Page 86: Nel prossimo numero CITTÀ Rigenera
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Geocentro Magazine - numero 6 - novembre/dicembre 2009

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