Marco JaffDipartimento di Progettazione dell'Architettura Università degli Studi di Firenze Viale Gramsci, 42 -- 50132 Firenze ITALY Translation by David Vila Domini
Figure
1). As Eugenio Battisti has
noted,
Almost twenty-five years later, Filippo projects for his friend
Masaccio the architecture of the The hypothesis I will seek to prove, and which was not explored
in much depth by the recent exhibition at the Uffizi,
It should be observed on the other hand that the Middle Ages
did not constitute a complete break with the culture of antiquity;
rather, the essence of Humanism consists more of a new attitude
of critical understanding with respect to antiquity, than the
rediscovery of the classical texts (cfr. [Garin 1964: 18]. Brunelleschi
himself turns to classical antiquity not so much "to bring
back to light the ancient charm of the lost and extinguished
style", as Leonardo Bruni said of Petrarch,[5] but above all because from that study
he could draw inspiration to stimulate and nourish a new conception
of architecture and figurative art. Testimony to that, if nothing
else, are his trips to Rome to draw the ancient ruins.[6] And even the discovery of perspective
can be attributed in part to this attitude, and more precisely
to the critical reflection on Ptolemaic theory and methods handed
down from antiquity regarding the observation of the stars, and
consequently also the use of the astrolabe, their main instrument
( As to whether Brunelleschi knew the astrolabe and its theory,
rather than proof, there are clues which, taken all together
give a very convincing A second clue is the friendship between Brunelleschi and the astronomer Paolo Dal Pozzo Toscanelli, who from 1425 helped him in the task of vaulting the dome of S. Maria del Fiore and who, later, built its great sundial.[9] Certainly Toscanelli would have made regular use of the astrolabe and, since this was his only instrument of observation, it seems entirely credible that he would have discussed it with Filippo. The third clue is a figure in the The last conjecture is found in Vasari's In any case, the spread of this instrument from 1300 throughout
the West is well documented. Nevertheless the whole of Western culture remained anchored
in the geocentric system developed by the Greeks, amongst others
by Hipparchus who in the second century B.C., as we have noted,
was also the probable inventor of the astrolabe and of stereographic
projections, as indicated by Vitruvius [10] and above all Ptolemy.[11] Though during the Middle Ages this
whole system of knowledge became weaker, it was not lost altogether
and in the West was newly disseminated by Scholasticism and St.
Thomas Aquinas (1226-1274), and in the Arab world by Averrhoës
(1126-1198) (
Given a sphere, a point All the processes involved in drawing it are eased by an interesting property: the circles on the sphere (and the movement of the stars in the Ptolemaic model) are transformed into further circles on the projection plane. Also, a reference system consisting of celestial parallels and meridians based on the vertical of the observer, given that it is made up of circles, is easily represented on the plane as a grid of as many circles.[13] At this point it is convenient to have a better understanding of the astrolabe: how it is made and what it is for. In essence, the astrolabe is a model of the celestial vault primarily for the measuring of sidereal time. It is composed of many disks superimposed on a "mother" disk which rotate independently over each other: on the back there is normally a scale in degrees, a sight, and often at later dates, a geometric quadrant to measure the angles, altitudes and distances. On the front, on top of the "mother" is found the so-called "tympanum" disc. On this is incised both the azimuth-altitude reference system of the celestial meridians and parallels, as well as the main lines of the celestial vault: the celestial equator, the tropics, the ecliptic (there is obviously a separate tympanum drawn for every point of equal latitude). All these lines, which in the model of the cosmos are circular, as we have noted, are transformed in the stereographic projection on the "tympanum" into a corresponding number of circles. On the "tympanum" is placed the transparent disk of the "grid", also obtained by means of stereographic projection, which represents the position of the principle stars. Rotating around the north-south axis of the universe, every twenty four hours the stars return to occupy their initial positions, and it is clear that at any given time they occupy a specific position within the oriented reference system. And vice versa: from the position they occupy within the oriented reference system can be found the astronomical hour. To observe the stars, the astrolabe is used both in a vertical
position (in order to read the altitude) as well as a horizontal
one (to read the azimuth, the angle the stars form with the direction
north). Vertically the astrolabe is also used as a "quadrant
of the circle" or as "geometric quadrant" depending
on the markings on its reverse ( To represent the position of a star at a given time on the plane of the astrolabe it suffices to know the star's coordinates: the azimuth (the angle with respect to north, given by the meridian) and the altitude (the angle with the horizon represented by the parallel). One has only to imagine that from the centre of projection, the South Pole, there springs a pyramidal arrangement of rays that meet the stars, intersecting the equatorial plane (that, at an infinitely smaller scale, is represented by the plane of the astrolabe): once the coordinates of a star have been obtained, its image on the astrolabe is drawn as a crossing of its co-ordinates which are represented by the network of meridians and parallels already marked on the astrolabe. Therefore, it can be readily seen that if its working principles are known, the astrolabe naturally suggests both the concept of projection and the construction of the perspective device (the astrolabe itself is a perspective device) and makes natural and intuitive the identification of the "point of view" and the "vanishing points", particularly the "centric point".
Firstly we shall consider how the representation on a plane
(on a painting) of "earthly things" is not very different
from the representation of the stars on the plane of the astrolabe.
In fact, the method used to represent the constellations (by
joining the stars together with imaginary lines) is very similar
to the method of drawing "earthly things". The difference
consists in the fact that these thing or objects, unless they
are on the picture plane, will appear distorted, that is, smaller
if they are further from the observer, and larger if they are
closer to him. This is precisely because they are arranged differently
on the plane of the earth, as opposed to the stars which instead
are all at the same distance on the celestial sphere (but even
the constellations are deformed when projected on the astrolabe's
plane due to the changing altitude on the horizon). To know the
image of these "things" it is enough to know the image
of their profile which is formed by many points joined by lines
(like the stars and constellations), that is, to find, point
by point, the intersections of the rays of the visual pyramid
with the picture plane and join them together. In that case for
each point we must again, as for the stars, know two co-ordinates:
the azimuth, which in this case is its position in plan, and
the altitude, which is its position in section. In other words
we must draw the things point by point "with the plan and
section and by means of the intersection" [15], which is exactly the method described
by Brunelleschi's biographers, thereafter called the Filippo, therefore, on the wall of the left aisle at the height
of the third arch, probably with the aid of a cartoon, stretches
a cord with a plumbline [cfr. Sampaolesi 1962: 51ff], as if he
were drawing the north-south axis of the world ( It remains to comment on the method, probably of a different
sort, that Filippo had devised earlier to paint the panels of
the Baptistery and of Piazza della Signoria (in order to be brief
I will refer only to the first of the two, which is more complex
because it is a specular image, though the reasoning regarding
the second panel differs little).[17] It is quite clear that in the case
of the Baptistery it was not a question of drawing an imaginary
scene, but of portraying a real one, for which Filippo thought
of creating a Another possible hypothesis is the suggestion by Fondelli [1977-b] , that Brunelleschi constructed a fully working camera obscura by making a hole in the main door of S. Maria del Fiore, and had therefore painted an image which was both in reverse and up-side-down. In any case, Fondelli always points out, the perspective machine as interpreted by Parronchi evidences: the diminution of the image, its straightening, the reinstatement of the main distance, adjustment for clear image,, the relationship of scale, and more, identifies the relationship between point of view, or centre of projection, and principal point: the former over the "hole", the latter in the centre of the image. It must be pointed out that these ideas correspond well with modern photogrammetric principles and above all with the principle of restitution by optical projection. Each one of the hypotheses mentioned above, however, is founded not only on the principles of optics and the abacus,[21] but also on the projective principles that are the basis of the workings of the astrolabe; this, therefore, can be considered as a further clue to support the idea that Filippo derived the origins of linear perspective from this instrument.
[2]
Even in the absence of reliable documentation critics are almost
unanimous in attributing to Brunelleschi the authorship of the
scheme for the chapel of the Trinità. [3]A
reference to the subject addressed here is found in D. Woodward
[Camerota 2001: note 3, p. 261, chap. X.2], where it is claimed
that "The conceptual affinities between this construction
[Ptolemy's third projection] and linear perspective are compelling
but the historical connections must now be shown" ("Le
affinità concettuali tra questa costruzione [quello della
terza proiezione di Tolomeo] e la prospettiva lineare sono stringenti,
ma i legami storici devono ancora essere dimostrati"). The
definition of "stereographic projection" is due to
Aquilonio (1613). [4]
The debate on whether classical antiquity possessed a 'theory'
of perspective,or at least knew of a rigorous rule by which to
represent the three dimensions of space in paintings, murals
or vases has gone on tenacioulsy for at least five centuries.
Two are the main positions in this debate: that which argues
that western antiquity developed a specific body of knowledge
(see amongst these the many works by Decio Gioseffi); and the
other, for which perspective is an artistic expression bound
to the specific culture at a certain time, and not an objective
representational method (see, for example, [Panofsky 1927]. [5] "[R]ivocare in luce l'antica leggiadria dello
stilo perduto e spento" [Bruni 1847: 53]. [6] Thus according to Antonio di Tuccio Manetti in the
[7] Cfr. [Vagnetti 1979: 196]. Vagnetti and several
English-speaking academics have put forward the hypothesis that
Brunelleschi may have known the works of Ptolemy. [8] For the classification of the various types of projection
see for example [Traversi 1968]. [9] For the relationship between Brunelleschi and Dal
Pozzo Toscanelli see for example the Introduction to [Galluzzi
1996]. [10] Vitruvius speaks very obscurely of this in book
IX from chap. 4 to chap.
8 [1999: 113-118]. [11] On this point see the recent anthology of classical
and historical texts on perspective edited by Rocco Sinisgalli
[1994]. [12] "[Ptolemy's Planisphaerium] is an explanation
of the system of projection know as stereographic, by which points
on the heavenly sphere are represented on the plane of the equator
by projection from one point, the pole" [Heath 1981, 2:
292]. [13] We see how this property can be proved by means
of Euclidean geometry, which Brunelleschi certainly knew and
used. Given the sphere SAxSA'=SBxSB' and hence SA:SB=SB':SA';
therefore the triangles SA'B' and SAB are similar:
consequently, since AB is the image form of a circle,
A'B' is also. This is even more evident if we exchange
the positions of the segments SA and SB, and we
replace A in A'' and B in B";
it is as if we made a 180° rotation of the cone of vertex
S, and therefore A''B'' still represents a circle
belonging to the cone. But A''B'' is parallel to A'B'
given the similarity between SA'B' and SB''A''
and therefore A'B' represents a circle as well. It is
therefore very simple to construct the projection of circles
on the surface of the sphere. And it becomes very easy to represent
on the plane the reference system of meridians and parallels
arranged on the sphere. return to
text[14] The 'geometric quadrant' and the 'quadrant of a
circle' are two simple, slightly different instruments; one is
square, the other the shape of a quarter of a circle. Relying
on the use of the vertical and the alignment with an alidad,
or revolving index for reading the graduation, they allow the
measurement of angles formed between two directions. The distances
to distant points are then determined through the use of proportion.
The front of the astrolabe was incised in such a way that it
could be used as one of these instruments when held vertically. [15] "con la pianta e proffilo e per via della intersegazione"
[Vasari 1985: 329]. [16] In the re-construction by Sanpaolesi [1962] the
distance from the viewpoint is drawn equal to about 10 braccia
(the text however indicates a distance of about ml 10); in that
by E. Battisti [1976], ml 8.942; in that by J. V. Field [Camerota
2001], ml 6.85; in that by Maria Teresa Bartoli [1997], ml 4.45.
These differences depend, above all, on the different hypothesis
adopted with regard to the structure of the chapel. The author
is currently undertaking further re-constructions of the chapel.
[17] On this point see, amongst others, E. Battisti [1976:
102]. [18] "Abbi uno specchio (...) e guarda in esso (...) e veramente da questo modo credo che Pippo (...) trovasse questa prospettiva" [Filarete 1973: 651 ff]. return to text [19] It has recently been suggested that the use of mirrors
may not have been unusual amongst so called Flemish Primitives.
But there are no signs of this in the texts, other than in Filarete's
[20] In Alberti's theory, put forward in his [21] It is known that Brunelleschi as a young man attended
the Florentine "scuola di abbaco" where, amongst other
things, optics was taught.
Le ragioni geometriche
del segno architettonico. Florence.Battisti, Eugenio. 1976. Bruni, Leonardo. 1847. Camerota, F. 2001. Edgerton, S.Y. 1974. Florentine interest in
Ptolemaic Cartography as Background for Renaissance Painting,
Architecture and Discovery of America. Filarete (Antonio Averlino). 1973. Fondelli, M. 1977-a. Le tecniche mensorie del XV secolo. Florence. Fondelli, M. 1977-b. I fondamenti della fotogrammetria
nella prima esperienza prospettica di F. Brunelleschi. Gioseffi, D. 1957-a. Gioseffi, D. 1957-b. Complementi
di Prospettiva. Heath, Thomas1981. Galluzzi, Paolo. 1996. Garin, E. 1964. L Jaff, Marco. 1999. L'astrolabio
del Brunelleschi. Panofsky, Erwin. 1927. Sampaolesi, P. 1962. Sinisgalli, Rocco. 1994-. Domus perspectivae. Florence. Traversi, C. 1968. Vagnetti, L. 1979. Vasari, Giorgio. 1985. Vitruvius. 1999.
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