Notes 48-52 (Book One)

Although there are numerous studies of Alberti's perspective construction, the source of this construction has not been satisfactorily explained. Panofsky [Codex Huygens, London, 1940, pp. 93 ff., and 'Die Perspektive als "Symbolische Form"' Vorträge der Bibliothek Warburg [1924-5], pp. 259-61] relates the construction of orthogonals to shop practice known from the time of Ambrogio Lorenzetti's Presentation in the Temple. The construction of transversals he relates to Brunelleschi. This does not seem wholly acceptable. Ivins [On the Rationalization of Sight, New York, 1938, pp. 14-27] has a clearer understanding of Alberti's construction and advances a more credible hypothesis. According to him, the construction was built up empirically by means of a small box with peep-hole and strings from the hole to a checker-board sort of plane. Although Ivins' hypothesis is ingenious, such an empiric approach is more typical of Brunelleschi than it is of Alberti.

Whether Alberti and Brunelleschi influenced each other in their perspective constructions or whether they arrived at them separately is not of the greatest importance. Fundamentally the results are the same although the means are radically different. Manetti's Life of Brunelleschi [Elena Toesca, ed., Florence, 1927, pp. 9-13] supplies the source for Brunelleschi's reputation as a perspectivist. The approach as described here is basically empirical. In constructing his painting of the Baptistry Brunelleschi stood three braccia inside the door of Santa Maria del Fiore. It would have been possible for this doorway to serve as the frame of his picture similar to Alberti's 'window'. On [p. 112] the frame of the door he could obtain sightings of the various points and angles of the building he wished to draw. His result would be a building drawn in one point perspective, but his method would differ essentially from Alberti's in that he ends with a point rather than beginning with one. Geometry does not enter into Brunelleschi's construction, for it relies solely on sightings.

Perhaps the clue to Alberti's construction can be found in his own words. At the close of Book One he states, "I usually explain these things to my friends with certain prolix geometric demonstrations . . ." [p. 59]. This phrase, taken with Alberti's insistence on the mathematics of vision, implies more geometry than experiment in his construction. Two concepts stressed in Book One may indicate the means by which he arrived at his solution. The similarity of triangles is basic to his construction; his insistence on the importance of a proper viewing point [pp. 48, 51, 56] suggests the application of the first theorem.

Between 1431 and 1434 Alberti composed in Rome a small work entitled Descriptio urbis Romae. It is noteworthy that this is the period when Donatello and perhaps Brunelleschi were in the city and Alberti was performing his 'miracles of painting'. In this slender volume Alberti sets forth a method for surveying and a table of sightings obtained in applying this method to the monuments of Rome. These operations have as their end what he calls a 'picture' of Rome. The instrument which he invented for this purpose is described as a bronze disc mounted parallel to the surface of the earth and divided on the circumference into 48 degrees. At the centre a metal or wooden ruler, divided into 50 degrees, is pivoted. This can be used parallel to the line of sight to obtain the bearing of the monument, and at right angles to the sight to obtain the proportionate width. When the ruler is placed at right angles to the line of sight, it becomes possible to compute the distance of the object--given its width--or its actual width--given the distance--by [p. 113] means of the similarity of triangles. With such an instrument the proportionate quantities vary according to the distance of the object, a statement which frequently occurs in Della pittura. If one were to survey a piazza or some other rectangular planar object with this instrument [diagram 4], the proportionate of the nearer side, A'B', would appear larger than the proportionate of the farther side D'C'. If the square should be further subdivided, a greater number of readings would result in a diagram much like that used in Book Two [p. 71] to put a circle into perspective. Without the diagram one is left with a series of quantities proportionate to an object in nature. The proportionate of the nearer side must certainly be the basis for any further operation. Alberti is perhaps referring to this in his statement, 'To me this base line of the quadrangle is proportional to the nearest transverse and equidistant quantity seen on the pavement' [p. 56]. From the point of view of the surveyor it would be necessary to devise a means to determine the proportionate distance between any two quantities. [p. 114]

There can be no doubt that Alberti understood such a method. In his Ludi mathematici composed for Borso d'Este about 1450 he demonstrates the well known operation of determining the width of a stream by means of a staff and the similarity of triangles. If this area should be the same piazza [diagram 5], the depth of the piazza PQ would appear proportionately on the staff as P'G'. This latter quantity varies as the distance from the object and the height of the observer's eye--in Alberti's terms the 'distance and position of the central ray' or line of sight. The apparent recession of the other transverse quantities can be read from the staff and applied to the preceding diagram.

The theory outlined here as a source of Alberti's construction does not make use of trigonometry which had not yet been invented in his time. Since he uses the simple geometry of surveying, two steps are required to arrive at his solution. The centric ray assumes a double importance. First, as Alberti says, 'the distance and the position of the central ray are of greatest importance to the certainty of sight' [p. 48]. In practice it is the point of reference; the extrinsic rays measure the quantities on the plane seen in relation to the location of the central ray or line of sight. At the same time it indicates the vanishing point in the perspective construction. If Alberti's construction derives from surveying, the apparently arbitrary location of the perpendicular cutting the height-distance lines becomes clear. For Alberti it would have been a staff held at arm's length or the [p. 115] surface of the panel--in any case, the same predetermined intersection of the visual pyramid in both steps. His silence on the distance from the eye to the object becomes clear from surveying; he knew that the distance had to be the same in both parts of his construction. Hence his insistence on the location of the point of the pyramid. It is not surprising that such a system based on the height of man, the length of his arm, and the distance from eye to arm is expressed in terms of braccia and the height of man.

Alberti is clearly presenting here an abbreviated description of his method. Both the artists of the time and his successors in perspective studies undoubtedly received fuller oral instructions. Some of this oral tradition reappears in Piero della Francesca, Leonardo and Vasari in a way which further illuminates Alberti's innovation. After describing a perspective method essentially the same as Alberti's, Piero introduces a second which he assures us is the same as the first [De prospectiva pingendi, Giusta Nicco Fasola ed., Florence, 1942, pp. 129 ff.]. This system is based on plan and elevation drawings connected by lines from a point of sight and cut by a perpendicular. Essentially it is Alberti's surveying method moved indoors to the drawing board. In all probability Vasari was best acquainted with PieroÍs second method. As an architect he readily attributed what was for him an architectural procedure to the architect Brunelleschi [Vite, II, 332]. Alberti's vagueness on the location of the eye in this construction is clarified by Leonardo. He states, 'The eye f and the eye t are one and the same thing; but the eye f marks the distance, that is to say, how far you are standing from the object; and the eye t shows you the direction of it' [The Literary Works of Leonardo da Vinci, J. P. and I. A. Richter [eds.], 2nd ed., London, 1939. Ï55. Hereafter cited as R.]. The accompanying diagram to this note leaves little doubt that Leonardo was schematically combining the two steps of Alberti's construction into one. In these constructions which all rely on the practice of surveying, the height [p. 116] and distance of the eye from the object and the location of the intersection all remain constant. See also: M. Boskovits, 'Quello ch'e dipintori oggi dicono prospettiva,' Acta Historiae Artium, Academiae Scientiarum Hugaricae, 241-60, VIII [1962] and 139-62, IX [1963]; Decio Gioseffi, Perspectiva artificialis, [Trieste, 1957]; Cecil Grayson, 'L. B. Alberti's "construzione legittima"', Italian Studies, XIX [1964], pp. 14-28; Richard Krautheimer, Lorenzo Ghiberti [Princeton, 1956], especially pp. 234-48; John White, The Birth and Rebirth of Pictorial Space [New York, 1958], and my review of this book in Art Bulletin, XLII, 225-8. See also the forthcoming Samuel Edgerton, Alberti's Optics.

49. This and the following sentence have been transposed from Alberti's order for reasons of clarity. The meaning has not been altered.

50. The Latin continues: For you rarely meet with an aptly composed antique istoria whether painted, cast or carved [O, 9v.].

51. Cicero, De oratore, III, xxiii, 80. Cicero's text is very close to Alberti's Latin.