The silence of Filippo is the main cause of the discussions that followed on the argument. This seems to be common to all the Middle Ages constructions. Fitchen speaks of "... the total lack of written documentation on both the engineering structure and the erectional procedures..." (Fitchen 1961).
Many authors have related the dome and his master: among many others let's remember Giovanni di Gherardo da Prato (1421), Manetti (1480?), Vasari (1550), Opera del Duomo (1691) (The Opera del Duomo was charged by the Duke of Tuscany to write down an essay on the stability of the Dome, threatened by cracks), Guasti (1887), and recently Sanpaolesi (1962), Fondelli (2004), Rocchi (1994). Sgrilli and Ximenes have rendered the dome accurately in the XVIII century.
Nevertheless as a result of this information neither thorough study on the geometry of the dome, nor on its statics is carried out.
Beyond these arguments, the topics which interest many researchers, e.g. Di Pasquale (1977), Bartoli (1994), are the methods of construction and erection of the dome and of the masonry, particularly the special one called "a spina pesce".
The survey of Fondelli, based upon photogramme-try, must be remembered for its accuracy. It started in 1968 and was carried on for many years. Fondelli's target was to render both the outside and the inside of the great cathedral and at the same time to link the survey to the Italian geodetic net.
The task of this paper is to give a contribution to the knowledge of Filippo's work on the following four topics:
- based on Brunelleschi's specifications, the above papers and our observations the geometrical shape of the internal surface of the dome is proposed;
- the proposed shape is compared to the results of the survey of the dome;
- the differential geometry of the surface is exposed;
- the statics of a Brunelleschi-like dome is defined and analyzed.
Further researches will discuss the masonry, the engineering structure, the details and the erectional procedures.
Figure 2. Plan of the cathedral of S. Maria del Fiore (Ximenes).
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