Pagina 1 di 3
The Ancient Origins of Modern Perspective
Rocco Sinisgalli (*)
The Optics of Ptolemy was first published in Latin by Gilberto Govi in 1885, but it remained unknown to historians of art and perspective until 1957, when Decio Gioseffi mentioned it for the first time. However this scholar limited his analysis to just a few lines of paragraph 4 of the Third Book, a paragraph which will also be analysed below. From that point on Ptolemy’s Optics has not, as far as I know, been taken into consideration by historians of art and perspective.
The principal cause for this abstention from the study of Ptolemy’s Optics is due above all to the difficulty of the Latin language in which the work has come down to us. The Admiral Eugene of Sicily, who lived in the second half of the Twelfth century at the court of the Norman kings in Palermo, translated Ptolemy’s Optics from Arabic into Latin; Arabic which was in its turn, a translation from the Greek, the language in which Ptolemy, living in the first half of the second century A.D., had written the work. Govi was the first to rightly underscore that the Latin is quite often obscure because it was a literal translation from Arabic and that the geometrical concepts are often improper as a result of the translator’s ignorance of the correct expressions needed to be able to translate them from Arabic into Latin. There is no known documentation regarding the existence of the Arabic text from which the Latin is derived, nor is there any information regarding the original Greek text from which the Arabic is derived.
These same difficulties of interpretation were expressed by Albert Lejeune, who spoke of a translation of a translation, such that could discourage any reader in good faith, and by A. Mark Smith, who spoke of a text difficult to penetrate, being so tortuous and confused that it is often incomprehensible.
Before turning to the analysis of the Ptolemaic passages, it is necessary to underscore what Govi, in his Introduction writes: “Ptolemy like Empedocles, like Plato, like Euclid, maintains that sight occurs by means of rays which exit from the eye and go forward to touch the points of objects, in this way establishing a relationship between the brain and the objects touched by the rays generated by the visual faculty. A relationship that could almost be called tactile, if these tentacle-like visual rays were not more spiritual than corporeal. From this hypothesis derives the form, a bit strange for us, of the demonstrations used by Ptolemy, in which the direction of the rays is reversed in respect to that followed by the Moderns. Vitelo and John Peckham abandoned the hypothesis of ‘Ocular Emission’, and considered light as a virtue, or effective emanations of luminous bodies which, penetrating the eye, can provoke visual sensation. After these, no one has ever again seriously attempted to renew this singular hypothesis of the Ancients. However, one should not believe that Euclid, Ptolemy and the other followers of the same doctrine excluded the emanation of light from certain bodies, for example the Sun. In fact Heliodorus Larisseus states that sight (that is to say the ocular rays) is similar to the Sun, because the rays of sight are reflecting and refracting as are reflected and refracted the rays of the Sun. Thus, for them the rays parting from a luminous body could meet with those of the eye and mingle with them, from this being born, if not all sight, at least a stronger impression of light on the observer”. By citing the thoughts of Govi I have synthesized the common opinion of scholars regarding the Ancient’s ‘Extromissive Theory of Light’.
Nonetheless, regarding the passages and their relative operations which we will now discuss, we are induced to consider the rays which part through sight not as luminous rays but exclusively as visual rays, that is to say as lines which must be traced in order to unite the eye to the things or to the objects which we see or are invited to see in the mirror. Thus is born the necessity to distinguish the ‘Theory of Light’ from the ‘Theory of Vision’: in the latter, in fact, the rays are conducted in the direction which leads from the eyes to the objects and not vice versa. Furthermore, as far as I have been able to see, I have not found in Ptolemy’s work any reference which could lead in particular or specifically to the ‘Extromissive Theory of Light’ by Euclid. Rather, we see that the reasoning followed by Ptolemy appears natural and that still today, without surprising anyone, we use the same terms and the same concepts: that the ‘visual rays’ exit from the eyes corresponds thus to a natural need, above all, if we consider, once we are placed in front of the mirror, that we are invited, so to speak, to retrace as we will see, the single points of the images which appear in the mirror.
Again it is worth noting that Albert Lejeune as well as A. Mark Smith, in providing their first translations in French and in English, took upon themselves an onerous task, like that of paleographers, when these attempt to decipher deep layers of a palimpsest. For this reason they were forced to adhere scrupulously to an exegetic reconstruction of a very difficult text. My task, however, has been first of all to take a look at the entire reconstructed work of the Ptolemaic text by Lejeune and Smith and successively to go beyond it in the attempt to specifically illustrate some passages of the Optics with drawings and to compare them in modern terms with the geometric theories of representation. Thus it has been a project of directly re-reading the original Latin, of re-translating and of reconstructing, in light of ‘Descriptive Geometry’, a number of paragraphs of Ptolemy’s work, which every scholar of art history and painting from Panofsky onwards, has not had the possibility to know. I have only begun to bring order to some concepts which have not yet been studied and understood –I repeat – in geometrical terms; something that I have done with pleasure because in this way I was able to clearly describe “The Ancient Origins of Modern Perspective ”.
Let us begin with ‘Sermo Tertius De Opticis Tholomei’, that is to say ‘The Third Speech on the Optics of Ptolemy’, also known as ‘The Third Book’ or ‘Sermon’ on the ‘Optics’ of Ptolemy, according to how we prefer to translate the Latin word ‘Sermo’, naturally limiting ourselves to the analysis of only flat mirrors, upon which we will concentrate our attention. Therefore I intentionally omit any reference to concave or convex mirrors, which Ptolemy discusses amply, also because it consists of a text which is difficult to penetrate: something that would require, at the moment, an unquantifiable amount of thought and study.
I will limit myself to only the paragraphs which I have considered to be the most significant regarding the pre-established scope of this essay. The reader is invited to follow the interpretation of these paragraphs according to a logic which I have attempted to illuminate not only with words but above all with graphics. A number of paragraphs have been reported in full, others only partially, others have been summarized. Finally, each of the paragraphs, portions of the same or summaries will be headed by a title, to indicate each time the argument to be discussed.
The three principles relative to the science of mirrors
“Since, therefore, in every field in which one turns to science there is the necessity of a number of general principles, that is to say, how the objects place themselves, in an unfailing and indisputable manner, in front of us, effectively as well as correctly, from the demonstrations of which one can make deductions, we must say that the principles which one requires for the science of mirrors are specifically three, and that these are primary elements of knowledge that are possible to learn by one-self.
The first [principle] is that by which one recognizes that the objects, which can be seen in mirrors, appear in conformity with the direction of the visual ray, which falls upon the objects by means of its own reflection. This (reflection) is verified in conformity with the position of the pupil with respect to the mirror.
The second (principle), without a doubt, is that by which one recognizes that the single (points) that one sees in the mirrors appear on the perpendicular line which falls from the object that is seen, onto the surface of the mirror and penetrates it.
The third (principle) instead, is that by which one recognizes that the position of the bent ray, which is found between the pupil and the mirror and between the mirror and the thing that is to be seen, is such that each of these two (segments) arrives at the point in respect to which the break occurs, while they contain, parting from the mirror, angles equal with the perpendicular line which exits from the very same point. [...]”
Here are described the general principles relative to the science of flat mirrors and it is specified that they are primary notions which are possible to verify by oneself. The first thing that stands out as evident is that the mirrors constitute a field in which one may turn to science. This is an authentic invitation to experimental verification as to how objects are distributed in front of us in an unfailing and indisputable manner.
In order to better illustrate and render visible what we have to say, we will begin by assigning: (Fig.1)
a) a vertical flat mirror;
b) the position O of our pupil, or of our eye, which orthogonally fixes the mirror at point Oo (the principal point);
c) the real or objective cube;
d) the reflected image of the objective cube.
These elements are indispensable to the best visual understanding of the operation, which will be discussed and demonstrated shortly.
For the first principle, (Fig. 2) the objects, that are seen a mirror, appear in conformity with the direction of the visual ray, which falls upon a mirror through a reflection, that is verified in conformity with the position of the pupil in respect to the mirror.
It is certainly natural to conduct the visual ray from the eye which ends at point A’: this is the image reflected in the mirror of the real point A.
For the second principle, (Fig. 3) the single points that are seen in a mirror appear to be found on the other side of the mirror, on the perpendicular line, which parts from the real object towards the surface of the mirror and penetrates the mirror itself. The image point A’, therefore, appears as if it were to be found on the other side of the mirror, precisely at the virtual point A”, on the perpendicular line r conducted from A to the mirror.
For the third principle (Fig.4) one recognizes that the position of the fractured ray, which is found between the pupil and the mirror and between the mirror and the real object, is such that each of the two segments arrives at the point where the fracture occurs, forming, between the mirror and the perpendicular line p to the mirror at point A’, two equal angles, on one side and on the other of the perpendicular line p. The reason why we have added the dashed lines OoO ”and O”A’ to the figure will be made clear shortly.
For the moment let one consider the plane formed by the perpendicular line r and the visual ray passing through the pupil and through A’. This plane is orthogonal to the mirror and contains: the pupil, the visual ray OA’ and the refracted ray AA’, the objective point A, the image A’ of the objective point, the perpendicular line p, the virtual point A” and the point T where the perpendicular from A intersects the plane of the mirror. This same orthogonal plane intersects the mirror in the line that passes through O°, through the reflected image A’ of point A and through the point T. Let one also observe that the visual ray and the reflected ray (to this latter we assign the direction which goes from the objective point A to the image A’), form, parting from the line O°A’T (which is found on the mirror), on one side and on the other of the perpendicular line p to the mirror in A’, two angles equal among themselves. That is to say that angle ß, on one side is equal to angle ß on the other and that angle g on one side is equal to the angle g on the other. That this is true is easily demonstrated by the dashed lines O°O”A’-A’A”T which complete the drawing seen as a spatial vision. If we now free such an orthogonal plane from the spatial vision of the preceding illustration and represent it as it effectively exists on the plane, (Fig.5) we may observe that the two angles b and the two angles g are equal among themselves because of two elementary laws of geometry: that of the similarity of the triangles OO”A’-A’AA”; and that of the equality of the triangles A’O°O-A’O°O” and of the triangles A’TA”-A’TA.
The fundamental operations of experimentation: the tracing and the observationin conformity to the origin of the rayand to the distance
“The topics relative to the principles set forth will now be made manifest through the objects which appear, as we will show.
In effect, for all mirrors, we have discovered that if on the surface of each of these we will have marked the points in the places in which the objects to be observed appear, and we will have con-nected them, certainly the form of the object to be seen will not then appear.
Certainly after, when we will have composed one object after another and we will have turned our gaze towards the places investigated, the marked points and the form of the thing to be observed will appear together, in conformity with the alignment of the origin of the visual ray.
And when we will have raised upon the surfaces of the mirrors at right angles, some long objects in a straight line and the distance will be established, the images of those objects will appear in a
straight line: these same ones in truth and in addition the objects that are observed.”
In this paragraph can be found two invitations. The first consists of marking, or better yet tracing, the points that appear on the mirror and then to opportunely interweave them. The second consists of the observing of the traced images in a way that makes them coincide with the reflected images, because after having completed the operation of tracing, it will no longer be possible to have the marked points and the reflected images coincide, without conforming oneself to the alignment of the origin of the visual ray and to the distance of this origin from the mirror.
Therefore once the tracing of the points has been realized, one cannot choose (Fig. 6) another pupil O*, or another eye, in order to observe the traced image. Only from point O, in fact, will one see the traced images coincide with those reflected and the conditions as described in the previously analyzed ‘Third Principle’ will be respected. The point A’, in fact, observed from O*, would not be seen in A”, but would distance itself beyond measure on the same perpendicular line that is traced from A to the mirror and furthermore the original orthogonal plane would also be changed: this original plane passes through the principal ray OO° and through the perpendicular line from A to the mirror.
This is the paragraph that Decio Gioseffi translated and published in 1957: he maintained that these passages justly inspired Filippo Brunelleschi (Florence 1377-1446) in the construction of the famous panel of the Baptistery. But Gioseffi just made reference to only the few lines of this paragraph, regarding tracing, and then proceeded to transcribe the drawing, which we will analyze in paragraphs 79, 80, 81 and 82 maintaining it to be in conformity both with the position assumed by Brunelleschi regarding the Baptistery in the creation of the panel, as well as the construction of the intersegatione of the Visual Pyramid of Leon Battista Alberti (Genoa 1404 –Rome 1472). The exposition did not confirm the expectations that the scholar had imagined. That which Gioseffi maintained was soon forgotten: the few lines that he analyzed, though important for the theory of tracing, were still too generic in order to remove the doubts that his affirmations provoked regarding the origins of perspective of the Ancients. What’s more the scientific and geometrical context in which Ptolemy had presented such experiments had been completely neglected: a context which was much more ample, embracing, as we will now see, the very concept of the vanishing point of orthogonal lines.
It was necessary to translate, read and illustrate Paragraph 3 that we have analyzed as well as not a few of the paragraphs following Paragraph 4. The tracing, the observation of the images, to be realized under the conditions described, and the rectilinear corrispondence, are fundamental observations which required verifications and deductions which Ptolemy himself prepares to illustrate in all their wide-ranging, problematic nature.
The five geometric deductions
“From both of these things [is derived]: that the object to be seen must appear in the mirror at the place of the point in which are connected the visual ray and the perpendicular line which falls from the object to be observed onto the mirror; that also the site of these two aforementioned lines is found on the same surface because the one [of the two] meets the other; and that the surface itself, in which they find themselves, is orthogonal to the surface of the mirror at right angles, because one of these two (lines) is perpendicular to the surface of the mirror; and that the visual ray, when it will have fractured in the direction of the object to be observed, finds itself on the same surface of which we have spoken; and that the perpendicular line, exiting from the point of reflection on the surface of the mirror, is the common distinction of all the different surfaces which form themselves around the reflection of the visual rays.”
After having analyzed, in the preceding paragraph, the two fundamental operations of tracing and of observation according to the origin of the ray and according to the distance, Ptolemy sets forth the five deductions which are obtained from these operations. (Fig.7) Such deductions, which have already been anticipated in part by us in order to better introduce the drawings examined, are the following:
1) the object to be seen A (‘res videnda’) appears in the mirror in the point where point A” appears, in which the visual ray OA’ and the perpendicular r conducted from point A to the mirror are joined: the object to be seen, therefore, is as if it were positioned in A”;
2) the two aforementioned lines, that is to say the visual ray OA’ and the perpendicular r, conducted from point A to the mirror, form, as we have already anticipated, a surface since one meets the other, connecting in A”;
3) this surface is orthogonal to that of the mirror at right angles because the line AA”, which goes from the point to be observed to the mirror, is perpendicular to the mirror;
4) the segment of the refracted ray AA’ is found on the same surface which is orthogonal to that of the mirror;
5) the perpendicular p, exiting from the point of reflection A’ on the surface of the mirror, constitutes a distinction common to all the diverse surfaces which form themselves around the reflection of the rays.
It is necessary to fix well in one’s mind that the five geometric deductions now described conduct us to construction in space:
1) of the vertical plane OA”O1, which contains the ray OA” and serves to find the virtual point A”;
2) of the plane that projects through the eye the line r, orthogonal to the surface of the mirror: this plane intersects the surface of the mirror according to the line O°T, which is the perspective or the image of the line r orthogonal to the plane of the mirror; the line O°T must pass thus through O°.