Leonardo illustrated the problem and solution as follows:
OF EQUAL OBJECTS THE MOST REMOTE LOOK THE SMALLEST.
The practice of perspective may be divided into ... parts [Footnote 4: in ... parte. The space for the number is left blank in the original.], of which the first treats of objects seen by the eye at any distance; and it shows all these objects just as the eye sees them diminished, without obliging a man to stand in one place rather than another so long as the plane does not produce a second foreshortening.
But the second practice is a combination of perspective derived partly from art and partly from nature and the work done by its rules is in every portion of it, influenced by natural perspective and artificial perspective. By natural perspective I mean that the plane on which this perspective is represented is a flat surface, and this plane, although it is parallel both in length and height, is forced to diminish in its remoter parts more than in its nearer ones. And this is proved by the first of what has been said above, and its diminution is natural. But artificial perspective, that is that which is devised by art, does the contrary; for objects equal in size increase on the plane where it is foreshortened in proportion as the eye is more natural and nearer to the plane, and as the part of the plane on which it is figured is farther from the eye. 
And let this plane be d.e. on which are seen 3 equal circles which are beyond this plane d. e, that is the circles a. b. c. Now you see that the eye h sees on the vertical plane the sections of the images, largest of those that are farthest and smallest of the nearest.
Here follows what is wanting in the margin at the foot on the other side of this page.
Natural perspective acts in a contrary way; for, at greater distances the object seen appears smaller, and at a smaller distance the object appears larger. But this said invention requires the spectator to stand with his eye at a small hole and then, at that small hole, it will be very plain. But since many (men’s) eyes endeavour at the same time to see one and the same picture produced by this artifice only one can see clearly the effect of this perspective and all the others will see confusion. It is well therefore to avoid such complex perspective and hold to simple perspective which does not regard planes as foreshortened, but as much as possible in their proper form. This simple perspective, in which the plane intersects the pyramids by which the images are conveyed to the eye at an equal distance from the eye is our constant experience, from the curved form of the pupil of the eye on which the pyramids are intersected at an equal distance from the visual virtue. Pedretti states: “
this is not true” “ that Leonardo had eventually recognised the necessity of representing object foreshortened laterally and as proof, one should consider the note that explains the diagram in MS E 16V: “
let the plan be d.e. above which are represented three equal circles that are placed behind it, that is circles a. b. and c., you now see that the eye at h. will perceive the images of the distant objects on the plane as being larger than those that are nearer”. Thus the diagram clarifies what Leonardo meant in speaking of simple and complex perspective (This is incorrect the diagram in total shows the difference between artificial and simple perspective. This intersecting plane d. e. is the first part of Leonardo’s description demonstrating the problem of Alberti artificial perspective. That the more distant objects become larger than the nearer objects on this intersecting plane). Pedretti continues:
Simple perspective is that which is produced by the intersecting plane furthest from the eye (No this line is not referred to by Leonardo and that is the reason it is not allocated letters: it is not an intersected plane but a demarcation line on which these circles are placed). Pedretti:
and complex perspective is that which is produced by the intersecting plane closest to the eye (No this is the actual plane d. e. describing artificial perspective of the Alberti method). Pedretti:
we can see therefore that complex perspective is actually composed, as Leonardo explains, of natural and artificial perspective. That is why in his diagram Leonardo added a curved line only in the case of the intersecting plane closest to the eye. (A word on the lines referred to by Pedretti as being closest and furthest from the eye. First there is absolutely no difference between these two lines they would both intersect the pyramid in the same way. Secondly, to repeat myself, the line furthest away is not a line of intersection it only a demarcation line on which the circles are placed that is why it is not allocated letters. All relevant points: circles, intersecting plane, and eye are allocated letters).
Not only are these points factually incorrect there is an underlined lack of comprehension of the main thrust of the thesis. Carlo Pedretti comes across as someone who is not only unable to follow the reasoning of Leonardo he is clearly blind to both the problem and the very elegant description of the solution. The problem should strike anyone who investigates the translation of the 3D into 2D. That is, they should realise the dilemma between painting an anamorphic
representation which replaces the object if seen from a certain position or paint using lateral perspective i.e. how we see the world. The greater the length of this window: the wider the angle of view, the greater the distortion if we think of our angle of view as 180 degrees the window would be infinitely long but with Alberti perspective we do not need to go down that route, Alberti perspective presents problems at any angle of view. Take for example a drawing of buildings the buildings will not converge as they reach for the skies, If there are two buildings one each side of the canvas they will present the disconcerting appearance of falling outward. This effect can also be seen in works where the Euston Road School has been followed to the letter as in these examples by Coldstream. Although Coldstream was knighted for his contribution to the arts (could this be another oversight by the A.I.S. another example of a gatekeeper not doing their job) Did he not realise that as the plumb line is following the vertical lines of the buildings which perspective is making converge i.e. as the plumb line is in the same 3D world as the buildings on which perspective is acting that the plumb line will be acted upon in exactly the same way. Thinking that the plumb line means parallel to the side of the canvas is a common beginner’s mistake or as it seems in this case also a more long-standing practitioners mistake. When using the Euston Road plumbing of points it is necessary to use horizontal measurements to determine any convergence of such mapping. If we return to the window the similarity with the plumb line will be apparent. However, to make matters worse the same effect operates in all directions laterally on the window. Carlo Pedretti’s ignorance of this gives serious cause for concern. At any level this would be worrying, but at what maybe considered the top end were technical aspects are being explained this is quite unacceptable. This is the equivalent of a top professor at psychics explaining Einstein’s theory of relativity and getting it wrong. Making it very clear that he does not grasp the relevance and then being given a special honour in return for his lack of comprehension. Yes that would be ridiculous in any other field, but why should it be any different in the art world. Although this new classification of visual literacy seems to present problems in other disciplines professor Richard Gregory, professor of perception in his book ‘Eye and Brain the psychology of seeing’ when discussing Young’s experiments with the spectrum writes ‘it is not possible to produce any colour that can be seen. For example, brown can not produced, and neither can the metallic colours, such as silver and gold’. I am sure the reader will not need me to point out that gold and silver are not colours.
It is obviously disappointing that we have someone in Pedretti that is unable to follow Leonardo’s elegant description of this phenomena. But it is of more concern to find, yet again, someone who very clearly suffers from a visual illiteracy, to whom all this is a closed book, operating within the art world and at such a level. The high expectations demanded of the concert pianist or mathematical genius, are obviously not applicable to the visual arts. Again we discover that in the visual arts, operating at such a low level is part of the course and that visual illiterates not only go undetected but are the gatekeepers. The important part of this diagram is not understood by Pedretti that being the curved line indicating that near and far objects need to be measured at the same distance from the eye to avoid the Alberti anamorphism, In practice an artist may be seen holding a pencil vertically at arms length to measure a near object and swinging around with the pencil still at arms length thereby maintaining the same eye to pencil distance to measure the far object.
Pedretti states: “
this curved line represents the lateral foreshortening of the panel. Leonardo never states that the size of the object, as they appear on the curved line of the intersection, should be translated on to the intersecting plane of artificial perspective”
First, the plane of artificial perspective is Alberti perspective why would he propose translating on to this. Yes this curved line will indicate that the panel along with everything else will as Leonardo says, “diminish in its remoter parts”. Leonardo: “By natural perspective” “The plane on which this perspective is represented is forced to diminish the remoter parts”. (Causing the regretted anamorphism). But Leonardo differentiates between natural perspective which will do this and the measuring of objects at equal distance from the eye by the curved intersecting plane of simple perspective with the phrase “and hold to simple perspective” I suggest that “hold to” does mean use this method.
I suggest that “hold to” does mean use this method Leonardo goes on to say: which does not regard planes as foreshortened, which I feel Pedretti should take as self explanatory. It is also very clear by the phrase before this that straight line intersecting plane should be avoided “only one can see clearly the effect of this perspective and all others will see confusion”(anamorphism or complex perspective),“it is well therefore to avoid such complex perspective and hold to simple perspective in which the plane intersects the pyramids by which images are conveyed to the eye at equal distance from the eye, we are given constant experience thanks to the curved form”. Put simply this is how we see, distance and size are inversely proportional that is if the same object at the side of our vision is twice as far as the object in front it will be half its size. On a straight plane intersection the greater the angle of view the greater the distortion, this distortion will be familiar to anyone who has looked into a convex mirror if we consider we have an angle of view of 180 degrees. Fortunately we have a computer which de-scrambles this convex mirror effect. This mechanism of perception is so effective that until it is spelled out by this inverse law, we are not aware of this lens effect. However, although we see the equivalent of a convex mirror to put this down to 2d would not give a fair representation of what we are used to. This is not only due to our perception computer, but because our main area of focus is a much smaller angle of view. Cameras and TV aim at a very small angle of view for the very reason of keeping the distortion to within acceptable limits.
